LMFDB - Embedded newform 18.26.c.b.13.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [18,26,Mod(7,18)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("18.7"); S:= CuspForms(chi, 26); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(18, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4])) N = Newforms(chi, 26, names="a")

Level:	$ N $	$=$	$ 18 = 2 \cdot 3^{2} $
Weight:	$ k $	$=$	$ 26 $
Character orbit:	$[\chi]$	$=$	18.c (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [26] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$71.2794203914$
Analytic rank:	$0$
Dimension:	$26$
Relative dimension:	$13$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			13.2
Character	$\chi$	$=$	18.13
Dual form			18.26.c.b.7.2

$q$-expansion

comment:q-expansion

sage:f.q_expansion() # note that sage often uses an isomorphic number field

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2048.00 - 3547.24i) q^{2} +(-912391. + 121783. i) q^{3} +(-8.38861e6 + 1.45295e7i) q^{4} +(-2.67172e8 + 4.62756e8i) q^{5} +(2.30057e9 + 2.98706e9i) q^{6} +(-2.63260e10 - 4.55979e10i) q^{7} +6.87195e10 q^{8} +(8.17626e11 - 2.22227e11i) q^{9} +2.18867e12 q^{10} +(-1.14644e12 - 1.98570e12i) q^{11} +(5.88425e12 - 1.42782e13i) q^{12} +(-5.91540e13 + 1.02458e14i) q^{13} +(-1.07831e14 + 1.86769e14i) q^{14} +(1.87410e14 - 4.54751e14i) q^{15} +(-1.40737e14 - 2.43764e14i) q^{16} -3.24582e15 q^{17} +(-2.46279e15 - 2.44520e15i) q^{18} -9.89108e15 q^{19} +(-4.48240e15 - 7.76375e15i) q^{20} +(2.95726e16 + 3.83971e16i) q^{21} +(-4.69583e15 + 8.13342e15i) q^{22} +(-6.83368e16 + 1.18363e17i) q^{23} +(-6.26990e16 + 8.36886e15i) q^{24} +(6.24973e15 + 1.08249e16i) q^{25} +4.84589e17 q^{26} +(-7.18932e17 + 3.02331e17i) q^{27} +8.83353e17 q^{28} +(-5.60187e17 - 9.70272e17i) q^{29} +(-1.99693e18 + 2.66543e17i) q^{30} +(-3.54604e18 + 6.14192e18i) q^{31} +(-5.76461e17 + 9.98459e17i) q^{32} +(1.28783e18 + 1.67212e18i) q^{33} +(6.64744e18 + 1.15137e19i) q^{34} +2.81342e19 q^{35} +(-3.62990e18 + 1.37439e19i) q^{36} -5.21691e19 q^{37} +(2.02569e19 + 3.50860e19i) q^{38} +(4.14940e19 - 1.00685e20i) q^{39} +(-1.83599e19 + 3.18003e19i) q^{40} +(5.13284e19 - 8.89035e19i) q^{41} +(7.56389e19 - 1.83538e20i) q^{42} +(1.54059e20 + 2.66839e20i) q^{43} +3.84682e19 q^{44} +(-1.15610e20 + 4.37734e20i) q^{45} +5.59815e20 q^{46} +(-8.79358e19 - 1.52309e20i) q^{47} +(1.58094e20 + 2.05269e20i) q^{48} +(-7.15578e20 + 1.23942e21i) q^{49} +(2.55989e19 - 4.43386e19i) q^{50} +(2.96146e21 - 3.95286e20i) q^{51} +(-9.92439e20 - 1.71895e21i) q^{52} -6.17278e21 q^{53} +(2.54481e21 + 1.93105e21i) q^{54} +1.22519e21 q^{55} +(-1.80911e21 - 3.13346e21i) q^{56} +(9.02453e21 - 1.20456e21i) q^{57} +(-2.29453e21 + 3.97424e21i) q^{58} +(-8.12913e21 + 1.40801e22i) q^{59} +(5.03520e21 + 6.53770e21i) q^{60} +(-1.48254e22 - 2.56784e22i) q^{61} +2.90492e22 q^{62} +(-3.16579e22 - 3.14317e22i) q^{63} +4.72237e21 q^{64} +(-3.16086e22 - 5.47477e22i) q^{65} +(3.29392e21 - 7.99273e21i) q^{66} +(-5.60505e21 + 9.70822e21i) q^{67} +(2.72279e22 - 4.71601e22i) q^{68} +(4.79353e22 - 1.16315e23i) q^{69} +(-5.76189e22 - 9.97989e22i) q^{70} +9.20095e22 q^{71} +(5.61869e22 - 1.52713e22i) q^{72} +2.36565e23 q^{73} +(1.06842e23 + 1.85056e23i) q^{74} +(-7.02048e21 - 9.11539e21i) q^{75} +(8.29724e22 - 1.43712e23i) q^{76} +(-6.03624e22 + 1.04551e23i) q^{77} +(-4.42135e23 + 5.90147e22i) q^{78} +(-1.18959e23 - 2.06044e23i) q^{79} +1.50405e23 q^{80} +(6.19128e23 - 3.63398e23i) q^{81} -4.20483e23 q^{82} +(6.88013e22 + 1.19167e23i) q^{83} +(-8.05963e23 + 1.07577e23i) q^{84} +(8.67193e23 - 1.50202e24i) q^{85} +(6.31027e23 - 1.09297e24i) q^{86} +(6.29272e23 + 8.17047e23i) q^{87} +(-7.87829e22 - 1.36456e23i) q^{88} -1.02686e24 q^{89} +(1.78952e24 - 4.86383e23i) q^{90} +6.22914e24 q^{91} +(-1.14650e24 - 1.98580e24i) q^{92} +(2.48739e24 - 6.03568e24i) q^{93} +(-3.60185e23 + 6.23859e23i) q^{94} +(2.64262e24 - 4.57715e24i) q^{95} +(4.04362e23 - 9.81188e23i) q^{96} +(-4.55407e24 - 7.88787e24i) q^{97} +5.86201e24 q^{98} +(-1.37864e24 - 1.36879e24i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 26 q - 53248 q^{2} + 151593 q^{3} - 218103808 q^{4} + 49854096 q^{5} + 768700416 q^{6} - 35213963498 q^{7} + 1786706395136 q^{8} - 906685440585 q^{9} - 408404754432 q^{10} - 1998346177329 q^{11} - 5691905409024 q^{12}+ \cdots + 19\!\cdots\!26 q^{99}+O(q^{100}) $ 26 * q - 53248 * q^2 + 151593 * q^3 - 218103808 * q^4 + 49854096 * q^5 + 768700416 * q^6 - 35213963498 * q^7 + 1786706395136 * q^8 - 906685440585 * q^9 - 408404754432 * q^10 - 1998346177329 * q^11 - 5691905409024 * q^12 - 158355783504242 * q^13 - 144236394487808 * q^14 + 757025799267528 * q^15 - 3659174697238528 * q^16 + 3616705586624034 * q^17 - 4642789512634368 * q^18 - 5058456299228762 * q^19 + 836412937076736 * q^20 - 29294425090653330 * q^21 - 8185225942339584 * q^22 - 155570710082203362 * q^23 + 10417391636840448 * q^24 - 888197302847183911 * q^25 + 1297250578466750464 * q^26 - 128834992514474784 * q^27 + 1181584543644123136 * q^28 - 3925320594794185038 * q^29 + 1179164452501389312 * q^30 - 6592704741949460996 * q^31 - 14987979559889010688 * q^32 - 32016980184606395901 * q^33 - 7407013041406021632 * q^34 - 49533545961137501568 * q^35 + 34228523324500082688 * q^36 + 78961008772462984600 * q^37 + 10359718500820504576 * q^38 + 95123937845402314992 * q^39 + 3425947390266310656 * q^40 - 13758002834178626109 * q^41 - 84162935852722520064 * q^42 - 191473700412044564123 * q^43 + 67053370919645872128 * q^44 - 785051209702697530104 * q^45 + 1274435256993409941504 * q^46 + 154470707996501871078 * q^47 + 52824690354265522176 * q^48 - 1713680737743395735817 * q^49 - 3638056152462065299456 * q^50 - 6870371606317236873627 * q^51 - 2656769184699904950272 * q^52 - 1171350014833338971736 * q^53 + 6559921495334108123136 * q^54 + 23890981280754645933408 * q^55 - 2419885145383164182528 * q^56 + 10363602109274891230719 * q^57 - 16078113156276981915648 * q^58 + 545848631253825283329 * q^59 - 17530642949329649664000 * q^60 - 10067352509024211048296 * q^61 + 54007437246049984479232 * q^62 - 73084560995643274477092 * q^63 + 122781528554610775556096 * q^64 + 12640794081283966054032 * q^65 + 110029145383180853084160 * q^66 + 79389140801664567200479 * q^67 - 30339125417599064604672 * q^68 + 374832866262531575458800 * q^69 + 101444702128409603211264 * q^70 + 415430508733527088013160 * q^71 - 62306949041150817730560 * q^72 - 539343970915021400375282 * q^73 - 161712145966004192460800 * q^74 + 441981606129534342907005 * q^75 + 42433406979360786743296 * q^76 - 327594537754607633577834 * q^77 - 746813223797009911111680 * q^78 + 611076271613290617275908 * q^79 - 28065361021061616893952 * q^80 + 2402122114376356742905779 * q^81 + 112705559217591305084928 * q^82 - 400615093454630506593780 * q^83 + 836210282594461940711424 * q^84 - 1703025287061576739254000 * q^85 - 784276276887734534647808 * q^86 - 11524978140836672774065086 * q^87 - 137325303643434746118144 * q^88 + 18509149037385930189952524 * q^89 + 4759337318576276074954752 * q^90 + 10266453492659369810870360 * q^91 - 2610043406322503560200192 * q^92 + 21848889054937494966552000 * q^93 + 632712019953671663935488 * q^94 - 16882199861176698021554184 * q^95 - 391144761338937332465664 * q^96 + 3205637813401802510221951 * q^97 + 14038472603593897867812864 * q^98 + 19880662798402511958071226 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/18\mathbb{Z}\right)^\times$.

$n$	$11$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−2048.00	−	3547.24i	−0.353553	−	0.612372i
$2$	−2048.00	−	3547.24i	−0.353553	−	0.612372i
$3$	−912391.	+	121783.i	−0.991209	+	0.132303i
$3$	−912391.	+	121783.i	−0.991209	+	0.132303i
$4$	−8.38861e6	+	1.45295e7i	−0.250000	+	0.433013i
$5$	−2.67172e8	+	4.62756e8i	−0.489402	+	0.847670i	−0.999926	−	0.0121942i	$-0.996118\pi$
$5$	−2.67172e8	+	4.62756e8i	−0.489402	+	0.847670i	0.510523	+	0.859864i	$0.329452\pi$
$6$	2.30057e9	+	2.98706e9i	0.431464	+	0.560213i
$7$	−2.63260e10	−	4.55979e10i	−0.718884	−	1.24514i	−0.961442	−	0.275006i	$-0.911320\pi$
$7$	−2.63260e10	−	4.55979e10i	−0.718884	−	1.24514i	0.242559	−	0.970137i	$-0.422013\pi$
$8$	6.87195e10			0.353553
$9$	8.17626e11	−	2.22227e11i	0.964992	−	0.262280i
$10$	2.18867e12			0.692119
$11$	−1.14644e12	−	1.98570e12i	−0.110140	−	0.190768i	0.805687	−	0.592342i	$-0.201796\pi$
$11$	−1.14644e12	−	1.98570e12i	−0.110140	−	0.190768i	−0.915826	+	0.401574i	$0.868463\pi$
$12$	5.88425e12	−	1.42782e13i	0.190513	−	0.462282i
$13$	−5.91540e13	+	1.02458e14i	−0.704193	+	1.21970i	0.262789	+	0.964853i	$0.415358\pi$
$13$	−5.91540e13	+	1.02458e14i	−0.704193	+	1.21970i	−0.966982	+	0.254845i	$0.917975\pi$
$14$	−1.07831e14	+	1.86769e14i	−0.508328	+	0.880449i
$15$	1.87410e14	−	4.54751e14i	0.372951	−	0.904968i
$16$	−1.40737e14	−	2.43764e14i	−0.125000	−	0.216506i
$17$	−3.24582e15			−1.35118			−0.675590	−	0.737278i	$-0.736111\pi$
$17$	−3.24582e15			−1.35118			−0.675590	+	0.737278i	$0.736111\pi$
$18$	−2.46279e15	−	2.44520e15i	−0.501789	−	0.498204i
$19$	−9.89108e15			−1.02524			−0.512618	−	0.858617i	$-0.671324\pi$
$19$	−9.89108e15			−1.02524			−0.512618	+	0.858617i	$0.671324\pi$
$20$	−4.48240e15	−	7.76375e15i	−0.244701	−	0.423835i
$21$	2.95726e16	+	3.83971e16i	0.877301	+	1.13909i
$22$	−4.69583e15	+	8.13342e15i	−0.0778805	+	0.134893i
$23$	−6.83368e16	+	1.18363e17i	−0.650215	+	1.12620i	0.332856	+	0.942978i	$0.391988\pi$
$23$	−6.83368e16	+	1.18363e17i	−0.650215	+	1.12620i	−0.983071	+	0.183227i	$0.941346\pi$
$24$	−6.26990e16	+	8.36886e15i	−0.350445	+	0.0467763i
$25$	6.24973e15	+	1.08249e16i	0.0209706	+	0.0363222i
$26$	4.84589e17			0.995880
$27$	−7.18932e17	+	3.02331e17i	−0.921808	+	0.387646i
$28$	8.83353e17			0.718884
$29$	−5.60187e17	−	9.70272e17i	−0.294007	−	0.509235i	0.680746	−	0.732519i	$-0.261656\pi$
$29$	−5.60187e17	−	9.70272e17i	−0.294007	−	0.509235i	−0.974753	+	0.223284i	$0.928322\pi$
$30$	−1.99693e18	+	2.66543e17i	−0.686035	+	0.0915697i
$31$	−3.54604e18	+	6.14192e18i	−0.808579	+	1.40050i	0.105269	+	0.994444i	$0.466430\pi$
$31$	−3.54604e18	+	6.14192e18i	−0.808579	+	1.40050i	−0.913848	+	0.406056i	$0.866904\pi$
$32$	−5.76461e17	+	9.98459e17i	−0.0883883	+	0.153093i
$33$	1.28783e18	+	1.67212e18i	0.134411	+	0.174519i
$34$	6.64744e18	+	1.15137e19i	0.477714	+	0.827425i
$35$	2.81342e19			1.40729
$36$	−3.62990e18	+	1.37439e19i	−0.127677	+	0.483424i
$37$	−5.21691e19			−1.30284			−0.651421	−	0.758717i	$-0.725827\pi$
$37$	−5.21691e19			−1.30284			−0.651421	+	0.758717i	$0.725827\pi$
$38$	2.02569e19	+	3.50860e19i	0.362475	+	0.627826i
$39$	4.14940e19	−	1.00685e20i	0.536633	−	1.30214i
$40$	−1.83599e19	+	3.18003e19i	−0.173030	+	0.299697i
$41$	5.13284e19	−	8.89035e19i	0.355271	−	0.615347i	−0.631893	−	0.775055i	$-0.717722\pi$
$41$	5.13284e19	−	8.89035e19i	0.355271	−	0.615347i	0.987164	+	0.159708i	$0.0510552\pi$
$42$	7.56389e19	−	1.83538e20i	0.387373	−	0.939963i
$43$	1.54059e20	+	2.66839e20i	0.587939	+	1.01834i	0.994502	+	0.104718i	$0.0333940\pi$
$43$	1.54059e20	+	2.66839e20i	0.587939	+	1.01834i	−0.406563	+	0.913623i	$0.633273\pi$
$44$	3.84682e19			0.110140
$45$	−1.15610e20	+	4.37734e20i	−0.249942	+	0.946355i
$46$	5.59815e20			0.919542
$47$	−8.79358e19	−	1.52309e20i	−0.110393	−	0.191207i	0.805536	−	0.592547i	$-0.201878\pi$
$47$	−8.79358e19	−	1.52309e20i	−0.110393	−	0.191207i	−0.915929	+	0.401341i	$0.868544\pi$
$48$	1.58094e20	+	2.05269e20i	0.152546	+	0.198065i
$49$	−7.15578e20	+	1.23942e21i	−0.533588	+	0.924201i
$50$	2.55989e19	−	4.43386e19i	0.0148285	−	0.0256837i
$51$	2.96146e21	−	3.95286e20i	1.33930	−	0.178766i
$52$	−9.92439e20	−	1.71895e21i	−0.352097	−	0.609849i
$53$	−6.17278e21			−1.72597			−0.862983	−	0.505233i	$-0.831406\pi$
$53$	−6.17278e21			−1.72597			−0.862983	+	0.505233i	$0.831406\pi$
$54$	2.54481e21	+	1.93105e21i	0.563292	+	0.427436i
$55$	1.22519e21			0.215610
$56$	−1.80911e21	−	3.13346e21i	−0.254164	−	0.440225i
$57$	9.02453e21	−	1.20456e21i	1.01622	−	0.135642i
$58$	−2.29453e21	+	3.97424e21i	−0.207895	+	0.360084i
$59$	−8.12913e21	+	1.40801e22i	−0.594831	+	1.03028i	0.398739	+	0.917064i	$0.369448\pi$
$59$	−8.12913e21	+	1.40801e22i	−0.594831	+	1.03028i	−0.993571	+	0.113214i	$0.963886\pi$
$60$	5.03520e21	+	6.53770e21i	0.298625	+	0.387734i
$61$	−1.48254e22	−	2.56784e22i	−0.715129	−	1.23864i	−0.962910	−	0.269824i	$-0.913034\pi$
$61$	−1.48254e22	−	2.56784e22i	−0.715129	−	1.23864i	0.247780	−	0.968816i	$-0.420299\pi$
$62$	2.90492e22			1.14350
$63$	−3.16579e22	−	3.14317e22i	−1.02029	−	1.01300i
$64$	4.72237e21			0.125000
$65$	−3.16086e22	−	5.47477e22i	−0.689268	−	1.19385i
$66$	3.29392e21	−	7.99273e21i	0.0593491	−	0.144011i
$67$	−5.60505e21	+	9.70822e21i	−0.0836843	+	0.144946i	−0.904830	−	0.425773i	$-0.860002\pi$
$67$	−5.60505e21	+	9.70822e21i	−0.0836843	+	0.144946i	0.821145	+	0.570719i	$0.193335\pi$
$68$	2.72279e22	−	4.71601e22i	0.337795	−	0.585078i
$69$	4.79353e22	−	1.16315e23i	0.495498	−	1.20233i
$70$	−5.76189e22	−	9.97989e22i	−0.497553	−	0.861788i
$71$	9.20095e22			0.665431			0.332716	−	0.943027i	$-0.392035\pi$
$71$	9.20095e22			0.665431			0.332716	+	0.943027i	$0.392035\pi$
$72$	5.61869e22	−	1.52713e22i	0.341176	−	0.0927302i
$73$	2.36565e23			1.20897			0.604485	−	0.796617i	$-0.293379\pi$
$73$	2.36565e23			1.20897			0.604485	+	0.796617i	$0.293379\pi$
$74$	1.06842e23	+	1.85056e23i	0.460624	+	0.797824i
$75$	−7.02048e21	−	9.11539e21i	−0.0255918	−	0.0332284i
$76$	8.29724e22	−	1.43712e23i	0.256309	−	0.443940i
$77$	−6.03624e22	+	1.04551e23i	−0.158355	+	0.274279i
$78$	−4.42135e23	+	5.90147e22i	−0.987125	+	0.131758i
$79$	−1.18959e23	−	2.06044e23i	−0.226496	−	0.392302i	0.730271	−	0.683157i	$-0.239394\pi$
$79$	−1.18959e23	−	2.06044e23i	−0.226496	−	0.392302i	−0.956767	+	0.290855i	$0.906060\pi$
$80$	1.50405e23			0.244701
$81$	6.19128e23	−	3.63398e23i	0.862418	−	0.506197i
$82$	−4.20483e23			−0.502429
$83$	6.88013e22	+	1.19167e23i	0.0706514	+	0.122372i	0.899187	−	0.437565i	$-0.144159\pi$
$83$	6.88013e22	+	1.19167e23i	0.0706514	+	0.122372i	−0.828536	+	0.559936i	$0.810826\pi$
$84$	−8.05963e23	+	1.07577e23i	−0.712564	+	0.0951107i
$85$	8.67193e23	−	1.50202e24i	0.661271	−	1.14535i
$86$	6.31027e23	−	1.09297e24i	0.415736	−	0.720076i
$87$	6.29272e23	+	8.17047e23i	0.358796	+	0.465861i
$88$	−7.87829e22	−	1.36456e23i	−0.0389403	−	0.0674465i
$89$	−1.02686e24			−0.440691			−0.220346	−	0.975422i	$-0.570718\pi$
$89$	−1.02686e24			−0.440691			−0.220346	+	0.975422i	$0.570718\pi$
$90$	1.78952e24	−	4.86383e23i	0.667890	−	0.181529i
$91$	6.22914e24			2.02493
$92$	−1.14650e24	−	1.98580e24i	−0.325107	−	0.563102i
$93$	2.48739e24	−	6.03568e24i	0.616180	−	1.49517i
$94$	−3.60185e23	+	6.23859e23i	−0.0780598	+	0.135204i
$95$	2.64262e24	−	4.57715e24i	0.501753	−	0.869061i
$96$	4.04362e23	−	9.81188e23i	0.0673566	−	0.163441i
$97$	−4.55407e24	−	7.88787e24i	−0.666427	−	1.15429i	−0.978896	−	0.204357i	$-0.934490\pi$
$97$	−4.55407e24	−	7.88787e24i	−0.666427	−	1.15429i	0.312469	−	0.949928i	$-0.398844\pi$
$98$	5.86201e24			0.754607
$99$	−1.37864e24	−	1.36879e24i	−0.156318	−	0.155202i
$100$	−2.09706e23			−0.0209706
$101$	−7.28126e24	−	1.26115e25i	−0.642968	−	1.11365i	−0.984767	−	0.173880i	$-0.944369\pi$
$101$	−7.28126e24	−	1.26115e25i	−0.642968	−	1.11365i	0.341799	−	0.939773i	$-0.388964\pi$
$102$	−7.46724e24	−	9.69546e24i	−0.582986	−	0.756948i
$103$	−5.81135e24	+	1.00655e25i	−0.401616	+	0.695620i	−0.993921	−	0.110094i	$-0.964885\pi$
$103$	−5.81135e24	+	1.00655e25i	−0.401616	+	0.695620i	0.592305	+	0.805714i	$0.298218\pi$
$104$	−4.06503e24	+	7.04084e24i	−0.248970	+	0.431229i
$105$	−2.56694e25	+	3.42627e24i	−1.39492	+	0.186190i
$106$	1.26418e25	+	2.18963e25i	0.610221	+	1.05693i
$107$	5.40947e24			0.232197			0.116099	−	0.993238i	$-0.462961\pi$
$107$	5.40947e24			0.232197			0.116099	+	0.993238i	$0.462961\pi$
$108$	1.63812e24	−	1.29819e25i	0.0625962	−	0.496066i
$109$	2.52516e25			0.859921			0.429960	−	0.902848i	$-0.358527\pi$
$109$	2.52516e25			0.859921			0.429960	+	0.902848i	$0.358527\pi$
$110$	−2.50919e24	−	4.34604e24i	−0.0762298	−	0.132034i
$111$	4.75986e25	−	6.35330e24i	1.29139	−	0.172370i
$112$	−7.41010e24	+	1.28347e25i	−0.179721	+	0.311286i
$113$	−3.27463e25	+	5.67182e25i	−0.710692	+	1.23096i	0.253905	+	0.967229i	$0.418285\pi$
$113$	−3.27463e25	+	5.67182e25i	−0.710692	+	1.23096i	−0.964598	+	0.263726i	$0.915049\pi$
$114$	−2.27551e25	−	2.95452e25i	−0.442352	−	0.574350i
$115$	−3.65154e25	−	6.32465e25i	−0.636433	−	1.10233i
$116$	1.87968e25			0.294007
$117$	−2.55970e25	+	9.69177e25i	−0.359638	+	1.36170i
$118$	6.65938e25			0.841218
$119$	8.54493e25	+	1.48003e26i	0.971341	+	1.68241i
$120$	1.28787e25	−	3.12503e25i	0.131858	−	0.319954i
$121$	5.15449e25	−	8.92783e25i	0.475739	−	0.824003i
$122$	−6.07250e25	+	1.05179e26i	−0.505673	+	0.875851i
$123$	−3.60047e25	+	8.73656e25i	−0.270735	+	0.656942i
$124$	−5.94927e25	−	1.03044e26i	−0.404289	−	0.700250i
$125$	−1.65926e26			−1.01986
$126$	−4.66604e25	+	1.76670e26i	−0.259607	+	0.982951i
$127$	1.97673e26			0.996324			0.498162	−	0.867084i	$-0.334009\pi$
$127$	1.97673e26			0.996324			0.498162	+	0.867084i	$0.334009\pi$
$128$	−9.67141e24	−	1.67514e25i	−0.0441942	−	0.0765466i
$129$	−1.73059e26	−	2.24699e26i	−0.717501	−	0.931603i
$130$	−1.29469e26	+	2.24246e26i	−0.487386	+	0.844177i
$131$	−1.22618e26	+	2.12381e26i	−0.419435	+	0.726483i	−0.995883	−	0.0906514i	$-0.971105\pi$
$131$	−1.22618e26	+	2.12381e26i	−0.419435	+	0.726483i	0.576448	+	0.817134i	$0.304438\pi$
$132$	−3.50981e25	+	4.68477e24i	−0.109171	+	0.0145718i
$133$	2.60392e26	+	4.51012e26i	0.737025	+	1.27656i
$134$	4.59165e25			0.118348
$135$	5.21730e25	−	4.13464e26i	0.122539	−	0.971104i
$136$	−2.23051e26			−0.477714
$137$	1.65780e26	+	2.87139e26i	0.323984	+	0.561157i	0.981306	−	0.192453i	$-0.0616442\pi$
$137$	1.65780e26	+	2.87139e26i	0.323984	+	0.561157i	−0.657322	+	0.753610i	$0.728311\pi$
$138$	−5.10770e26	+	6.81759e25i	−0.911459	+	0.121658i
$139$	−2.22092e26	+	3.84674e26i	−0.362116	+	0.627203i	−0.988309	−	0.152465i	$-0.951279\pi$
$139$	−2.22092e26	+	3.84674e26i	−0.362116	+	0.627203i	0.626193	+	0.779668i	$0.284612\pi$
$140$	−2.36007e26	+	4.08776e26i	−0.351823	+	0.609376i
$141$	9.87805e25	+	1.28257e26i	0.134720	+	0.174920i
$142$	−1.88435e26	−	3.26380e26i	−0.235266	−	0.407492i
$143$	2.71267e26			0.310239
$144$	−1.69242e26	−	1.68033e26i	−0.177409	−	0.176142i
$145$	5.98665e26			0.575551
$146$	−4.84486e26	−	8.39154e26i	−0.427435	−	0.740340i
$147$	5.01947e26	−	1.21798e27i	0.406622	−	0.986672i
$148$	4.37626e26	−	7.57990e26i	0.325710	−	0.564147i
$149$	−1.23942e26	+	2.14674e26i	−0.0847990	+	0.146876i	−0.905306	−	0.424761i	$-0.860358\pi$
$149$	−1.23942e26	+	2.14674e26i	−0.0847990	+	0.146876i	0.820507	+	0.571637i	$0.193691\pi$
$150$	−1.79565e25	+	4.35717e25i	−0.0113001	+	0.0274197i
$151$	7.69621e26	+	1.33302e27i	0.445723	+	0.772015i	0.998102	−	0.0615779i	$-0.0196133\pi$
$151$	7.69621e26	+	1.33302e27i	0.445723	+	0.772015i	−0.552379	+	0.833593i	$0.686280\pi$
$152$	−6.79710e26			−0.362475
$153$	−2.65387e27	+	7.21310e26i	−1.30388	+	0.354388i
$154$	4.94489e26			0.223948
$155$	−1.89481e27	−	3.28190e27i	−0.791441	−	1.37082i
$156$	1.11483e27	+	1.44750e27i	0.429687	+	0.557905i
$157$	2.04672e27	−	3.54503e27i	0.728305	−	1.26146i	−0.229295	−	0.973357i	$-0.573642\pi$
$157$	2.04672e27	−	3.54503e27i	0.728305	−	1.26146i	0.957599	−	0.288103i	$-0.0930247\pi$
$158$	−4.87258e26	+	8.43956e26i	−0.160157	+	0.277400i
$159$	5.63199e27	−	7.51739e26i	1.71079	−	0.228351i
$160$	−3.08028e26	−	5.33521e26i	−0.0865149	−	0.149848i
$161$	7.19613e27			1.86971
$162$	−2.55703e27	−	1.45196e27i	−0.614892	−	0.349153i
$163$	4.23059e27			0.942011			0.471006	−	0.882130i	$-0.343891\pi$
$163$	4.23059e27			0.942011			0.471006	+	0.882130i	$0.343891\pi$
$164$	8.61148e26	+	1.49155e27i	0.177636	+	0.307674i
$165$	−1.11785e27	+	1.49207e26i	−0.213715	+	0.0285260i
$166$	2.81810e26	−	4.88109e26i	0.0499581	−	0.0865299i
$167$	8.67352e26	−	1.50230e27i	0.142639	−	0.247059i	−0.785850	−	0.618417i	$-0.787774\pi$
$167$	8.67352e26	−	1.50230e27i	0.142639	−	0.247059i	0.928490	+	0.371358i	$0.121108\pi$
$168$	2.03221e27	+	2.63863e27i	0.310173	+	0.402728i
$169$	−3.47018e27	−	6.01052e27i	−0.491777	−	0.851782i
$170$	−7.10404e27			−0.935178
$171$	−8.08721e27	+	2.19807e27i	−0.989343	+	0.268899i
$172$	−5.16938e27			−0.587939
$173$	3.31360e27	+	5.73933e27i	0.350529	+	0.607134i	0.986342	−	0.164709i	$-0.0526685\pi$
$173$	3.31360e27	+	5.73933e27i	0.350529	+	0.607134i	−0.635813	+	0.771843i	$0.719335\pi$
$174$	1.60951e27	−	3.90549e27i	0.158427	−	0.384424i
$175$	3.29060e26	−	5.69949e26i	0.0301509	−	0.0522229i
$176$	−3.22695e26	+	5.58924e26i	−0.0275349	+	0.0476919i
$177$	5.70223e27	−	1.38365e28i	0.453293	−	1.09992i
$178$	2.10300e27	+	3.64250e27i	0.155808	+	0.269867i
$179$	9.59382e27			0.662718			0.331359	−	0.943505i	$-0.392493\pi$
$179$	9.59382e27			0.662718			0.331359	+	0.943505i	$0.392493\pi$
$180$	−5.39025e27	−	5.35174e27i	−0.347298	−	0.344817i
$181$	−9.66845e26			−0.0581265			−0.0290633	−	0.999578i	$-0.509252\pi$
$181$	−9.66845e26			−0.0581265			−0.0290633	+	0.999578i	$0.509252\pi$
$182$	−1.27573e28	−	2.20962e28i	−0.715922	−	1.24001i
$183$	1.66538e28	+	2.16233e28i	0.872719	+	1.13314i
$184$	−4.69607e27	+	8.13383e27i	−0.229886	+	0.398173i
$185$	1.39381e28	−	2.41415e28i	0.637614	−	1.10438i
$186$	−2.65042e28	+	3.53769e27i	−1.13345	+	0.151289i
$187$	3.72115e27	+	6.44522e27i	0.148818	+	0.257761i
$188$	2.95064e27			0.110393
$189$	3.27122e28	+	2.48226e28i	1.14535	+	0.869110i
$190$	−2.16483e28			−0.709585
$191$	−2.39797e28	−	4.15340e28i	−0.736082	−	1.27493i	−0.954247	−	0.299019i	$-0.903341\pi$
$191$	−2.39797e28	−	4.15340e28i	−0.736082	−	1.27493i	0.218165	−	0.975912i	$-0.429993\pi$
$192$	−4.30865e27	+	5.75103e26i	−0.123901	+	0.0165379i
$193$	7.86286e27	−	1.36189e28i	0.211892	−	0.367007i	−0.740415	−	0.672150i	$-0.765371\pi$
$193$	7.86286e27	−	1.36189e28i	0.211892	−	0.367007i	0.952307	+	0.305143i	$0.0987042\pi$
$194$	−1.86535e28	+	3.23087e28i	−0.471235	+	0.816203i
$195$	3.55067e28	+	4.61019e28i	0.841158	+	1.09216i
$196$	−1.20054e28	−	2.07940e28i	−0.266794	−	0.462100i
$197$	−5.06048e28			−1.05527			−0.527636	−	0.849471i	$-0.676921\pi$
$197$	−5.06048e28			−1.05527			−0.527636	+	0.849471i	$0.676921\pi$
$198$	−2.03197e27	+	7.69364e27i	−0.0397742	+	0.150597i
$199$	2.23009e28			0.409882			0.204941	−	0.978774i	$-0.434300\pi$
$199$	2.23009e28			0.409882			0.204941	+	0.978774i	$0.434300\pi$
$200$	4.29478e26	+	7.43878e26i	0.00741424	+	0.0128418i
$201$	3.93170e27	−	9.54030e27i	0.0637719	−	0.154743i
$202$	−2.98241e28	+	5.16568e28i	−0.454647	+	0.787472i
$203$	−2.94949e28	+	5.10867e28i	−0.422714	+	0.732162i
$204$	−1.90992e28	+	4.63444e28i	−0.257418	+	0.624626i
$205$	2.74271e28	+	4.75050e28i	0.347741	+	0.602305i
$206$	4.76065e28			0.567971
$207$	−2.95705e28	+	1.11963e29i	−0.332070	+	1.25732i
$208$	3.33007e28			0.352097
$209$	1.13396e28	+	1.96407e28i	0.112919	+	0.195582i
$210$	6.47248e28	+	8.40386e28i	0.607197	+	0.788384i
$211$	−8.01727e28	+	1.38863e29i	−0.708754	+	1.22760i	0.256565	+	0.966527i	$0.417409\pi$
$211$	−8.01727e28	+	1.38863e29i	−0.708754	+	1.22760i	−0.965320	+	0.261071i	$0.915924\pi$
$212$	5.17810e28	−	8.96873e28i	0.431491	−	0.747365i
$213$	−8.39487e28	+	1.12052e28i	−0.659582	+	0.0880388i
$214$	−1.10786e28	−	1.91887e28i	−0.0820942	−	0.142191i
$215$	−1.64642e29			−1.15096
$216$	−4.94046e28	+	2.07760e28i	−0.325908	+	0.137054i
$217$	3.73411e29			2.32510
$218$	−5.17154e28	−	8.95737e28i	−0.304028	−	0.526592i
$219$	−2.15840e29	+	2.88096e28i	−1.19834	+	0.159951i
$220$	−1.02776e28	+	1.78014e28i	−0.0539026	+	0.0933621i
$221$	1.92003e29	−	3.32559e29i	0.951492	−	1.64803i
$222$	−1.20019e29	−	1.55832e29i	−0.562130	−	0.729869i
$223$	−1.65131e29	−	2.86016e29i	−0.731171	−	1.26642i	−0.956383	−	0.292115i	$-0.905641\pi$
$223$	−1.65131e29	−	2.86016e29i	−0.731171	−	1.26642i	0.225212	−	0.974310i	$-0.427692\pi$
$224$	6.07035e28			0.254164
$225$	7.51553e27	+	7.46183e27i	0.0297631	+	0.0295504i
$226$	2.68258e29			1.00507
$227$	9.70258e28	+	1.68054e29i	0.344004	+	0.595833i	0.985172	−	0.171567i	$-0.0548832\pi$
$227$	9.70258e28	+	1.68054e29i	0.344004	+	0.595833i	−0.641168	+	0.767401i	$0.721550\pi$
$228$	−5.82015e28	+	1.41226e29i	−0.195321	+	0.473948i
$229$	1.86490e29	−	3.23009e29i	0.592531	−	1.02629i	−0.401359	−	0.915921i	$-0.631462\pi$
$229$	1.86490e29	−	3.23009e29i	0.592531	−	1.02629i	0.993890	−	0.110373i	$-0.0352045\pi$
$230$	−1.49567e29	+	2.59058e29i	−0.450026	+	0.779468i
$231$	4.23416e28	−	1.02742e29i	0.120675	−	0.292819i
$232$	−3.84958e28	−	6.66766e28i	−0.103947	−	0.180042i
$233$	−5.51565e29			−1.41139			−0.705696	−	0.708515i	$-0.749365\pi$
$233$	−5.51565e29			−1.41139			−0.705696	+	0.708515i	$0.749365\pi$
$234$	3.96213e29	−	1.07689e29i	0.961016	−	0.261200i
$235$	9.39760e28			0.216107
$236$	−1.36384e29	−	2.36224e29i	−0.297416	−	0.515139i
$237$	1.33630e29	+	1.73505e29i	0.276408	+	0.358888i
$238$	3.50001e29	−	6.06219e29i	0.686842	−	1.18964i
$239$	3.63713e29	−	6.29969e29i	0.677306	−	1.17313i	−0.298483	−	0.954415i	$-0.596481\pi$
$239$	3.63713e29	−	6.29969e29i	0.677306	−	1.17313i	0.975789	−	0.218714i	$-0.0701860\pi$
$240$	−1.37228e29	+	1.83167e28i	−0.242550	+	0.0323748i
$241$	1.83625e29	+	3.18049e29i	0.308120	+	0.533679i	0.977951	−	0.208834i	$-0.0669669\pi$
$241$	1.83625e29	+	3.18049e29i	0.308120	+	0.533679i	−0.669831	+	0.742513i	$0.733634\pi$
$242$	−4.22256e29			−0.672796
$243$	−5.20631e29	+	4.06960e29i	−0.787865	+	0.615848i
$244$	4.97459e29			0.715129
$245$	−3.82365e29	−	6.62275e29i	−0.522278	−	0.904612i
$246$	3.83645e29	−	5.12076e28i	0.498012	−	0.0664730i
$247$	5.85096e29	−	1.01342e30i	0.721964	−	1.25048i
$248$	−2.43682e29	+	4.22070e29i	−0.285876	+	0.495151i
$249$	−7.72862e28	−	1.00348e29i	−0.0862205	−	0.111949i
$250$	3.39816e29	+	5.88579e29i	0.360574	+	0.624532i
$251$	−1.05096e30			−1.06087			−0.530436	−	0.847725i	$-0.677972\pi$
$251$	−1.05096e30			−1.06087			−0.530436	+	0.847725i	$0.677972\pi$
$252$	7.22252e29	−	1.96305e29i	0.693717	−	0.188549i
$253$	3.13377e29			0.286458
$254$	−4.04834e29	−	7.01193e29i	−0.352254	−	0.610121i
$255$	−6.08298e29	+	1.47604e30i	−0.503923	+	1.22277i
$256$	−3.96141e28	+	6.86136e28i	−0.0312500	+	0.0541266i
$257$	−6.32849e29	+	1.09613e30i	−0.475484	+	0.823563i	−0.999606	−	0.0280808i	$-0.991060\pi$
$257$	−6.32849e29	+	1.09613e30i	−0.475484	+	0.823563i	0.524122	+	0.851643i	$0.324394\pi$
$258$	−4.42638e29	+	1.07407e30i	−0.316813	+	0.768749i
$259$	1.37340e30	+	2.37880e30i	0.936592	+	1.62222i
$260$	1.06061e30			0.689268
$261$	−6.73645e29	−	6.68831e29i	−0.417277	−	0.414296i
$262$	1.00449e30			0.593171
$263$	−5.63686e29	−	9.76332e29i	−0.317388	−	0.549732i	0.662554	−	0.749014i	$-0.269472\pi$
$263$	−5.63686e29	−	9.76332e29i	−0.317388	−	0.549732i	−0.979942	+	0.199282i	$0.936139\pi$
$264$	8.84989e28	+	1.14907e29i	0.0475213	+	0.0617017i
$265$	1.64919e30	−	2.85649e30i	0.844692	−	1.46305i
$266$	1.06657e30	−	1.84735e30i	0.521155	−	0.902668i
$267$	9.36894e29	−	1.25053e29i	0.436817	−	0.0583049i
$268$	−9.40371e28	−	1.62877e29i	−0.0418422	−	0.0724728i
$269$	−1.24272e30			−0.527799			−0.263900	−	0.964550i	$-0.585009\pi$
$269$	−1.24272e30			−0.527799			−0.263900	+	0.964550i	$0.585009\pi$
$270$	−1.57351e30	+	6.61704e29i	−0.638001	+	0.268298i
$271$	2.14231e29			0.0829406			0.0414703	−	0.999140i	$-0.486796\pi$
$271$	2.14231e29			0.0829406			0.0414703	+	0.999140i	$0.486796\pi$
$272$	4.56809e29	+	7.91216e29i	0.168897	+	0.292539i
$273$	−5.68341e30	+	7.58603e29i	−2.00713	+	0.267905i
$274$	6.79033e29	−	1.17612e30i	0.229091	−	0.396798i
$275$	1.43299e28	−	2.48202e28i	0.00461940	−	0.00800103i
$276$	1.28789e30	+	1.67220e30i	0.396750	+	0.515139i
$277$	9.45371e29	+	1.63743e30i	0.278359	+	0.482132i	0.970977	−	0.239173i	$-0.0768762\pi$
$277$	9.45371e29	+	1.63743e30i	0.278359	+	0.482132i	−0.692618	+	0.721304i	$0.743543\pi$
$278$	1.81938e30			0.512109
$279$	−1.53443e30	+	5.80982e30i	−0.412948	+	1.56354i
$280$	1.93337e30			0.497553
$281$	−3.38822e30	−	5.86857e30i	−0.833954	−	1.44445i	−0.894879	−	0.446309i	$-0.852738\pi$
$281$	−3.38822e30	−	5.86857e30i	−0.833954	−	1.44445i	0.0609245	−	0.998142i	$-0.480595\pi$
$282$	2.52654e29	−	6.13068e29i	0.0594857	−	0.144343i
$283$	−2.19382e30	+	3.79981e30i	−0.494163	+	0.855916i	−0.999977	−	0.00672645i	$-0.997859\pi$
$283$	−2.19382e30	+	3.79981e30i	−0.494163	+	0.855916i	0.505814	+	0.862643i	$0.331192\pi$
$284$	−7.71832e29	+	1.33685e30i	−0.166358	+	0.288140i
$285$	−1.85368e30	+	4.49798e30i	−0.382362	+	0.927805i
$286$	−5.55554e29	−	9.62247e29i	−0.109686	−	0.189982i
$287$	−5.40508e30			−1.02159
$288$	−2.49445e29	+	9.44472e29i	−0.0451407	+	0.170916i
$289$	4.76473e30			0.825686
$290$	−1.22607e30	−	2.12361e30i	−0.203488	−	0.352452i
$291$	5.11570e30	+	6.64222e30i	0.813284	+	1.05597i
$292$	−1.98445e30	+	3.43718e30i	−0.302242	+	0.523499i
$293$	−5.27144e30	+	9.13040e30i	−0.769279	+	1.33243i	0.168675	+	0.985672i	$0.446051\pi$
$293$	−5.27144e30	+	9.13040e30i	−0.769279	+	1.33243i	−0.937954	+	0.346759i	$0.887282\pi$
$294$	−5.34845e30	+	7.13893e29i	−0.747973	+	0.0998370i
$295$	−4.34375e30	−	7.52360e30i	−0.582224	−	1.00844i
$296$	−3.58503e30			−0.460624
$297$	1.42455e30	+	1.08098e30i	0.175478	+	0.133156i
$298$	1.01533e30			0.119924
$299$	−8.08478e30	−	1.40033e31i	−0.915753	−	1.58613i
$300$	1.91334e29	−	2.55386e28i	0.0207863	−	0.00277448i
$301$	8.11152e30	−	1.40496e31i	0.845320	−	1.46414i
$302$	3.15237e30	−	5.46006e30i	0.315174	−	0.545897i
$303$	8.17923e30	+	1.06199e31i	0.784656	+	1.01880i
$304$	1.39205e30	+	2.41109e30i	0.128154	+	0.221970i
$305$	1.58438e31			1.39994
$306$	7.99378e30	+	7.93667e30i	0.678008	+	0.673163i
$307$	−2.89881e30			−0.236043			−0.118021	−	0.993011i	$-0.537655\pi$
$307$	−2.89881e30			−0.236043			−0.118021	+	0.993011i	$0.537655\pi$
$308$	−1.01271e30	−	1.75407e30i	−0.0791776	−	0.137140i
$309$	4.07641e30	−	9.89144e30i	0.306053	−	0.742640i
$310$	−7.76112e30	+	1.34427e31i	−0.559633	+	0.969313i
$311$	1.21109e31	−	2.09766e31i	0.838823	−	1.45288i	−0.0520564	−	0.998644i	$-0.516578\pi$
$311$	1.21109e31	−	2.09766e31i	0.838823	−	1.45288i	0.890879	−	0.454240i	$-0.150089\pi$
$312$	2.85144e30	−	6.91905e30i	0.189728	−	0.460377i
$313$	1.43964e31	+	2.49352e31i	0.920340	+	1.59408i	0.798889	+	0.601478i	$0.205421\pi$
$313$	1.43964e31	+	2.49352e31i	0.920340	+	1.59408i	0.121451	+	0.992597i	$0.461245\pi$
$314$	−1.67667e31			−1.02998
$315$	2.30033e31	−	6.25220e30i	1.35803	−	0.369106i
$316$	3.99162e30			0.226496
$317$	1.35301e30	+	2.34347e30i	0.0738004	+	0.127826i	0.900564	−	0.434724i	$-0.143154\pi$
$317$	1.35301e30	+	2.34347e30i	0.0738004	+	0.127826i	−0.826764	+	0.562550i	$0.809821\pi$
$318$	−1.42009e31	−	1.84384e31i	−0.744693	−	0.966908i
$319$	−1.28444e30	+	2.22472e30i	−0.0647637	+	0.112174i
$320$	−1.26168e30	+	2.18530e30i	−0.0611753	+	0.105959i
$321$	−4.93555e30	+	6.58781e29i	−0.230156	+	0.0307205i
$322$	−1.47377e31	−	2.55264e31i	−0.661044	−	1.14496i
$323$	3.21047e31			1.38528
$324$	8.63639e28	+	1.20440e31i	0.00358525	+	0.499987i
$325$	−1.47879e30			−0.0590695
$326$	−8.66425e30	−	1.50069e31i	−0.333051	−	0.576862i
$327$	−2.30394e31	+	3.07522e30i	−0.852362	+	0.113770i
$328$	3.52726e30	−	6.10940e30i	0.125607	−	0.217558i
$329$	−4.62999e30	+	8.01937e30i	−0.158720	+	0.274911i
$330$	2.81864e30	+	3.65972e30i	0.0930282	+	0.120788i
$331$	−2.09369e31	−	3.62637e31i	−0.665367	−	1.15245i	−0.979186	−	0.202967i	$-0.934942\pi$
$331$	−2.09369e31	−	3.62637e31i	−0.665367	−	1.15245i	0.313818	−	0.949483i	$-0.398392\pi$
$332$	−2.30859e30			−0.0706514
$333$	−4.26548e31	+	1.15934e31i	−1.25723	+	0.341710i
$334$	−7.10535e30			−0.201723
$335$	−2.99502e30	−	5.18753e30i	−0.0819106	−	0.141873i
$336$	5.19786e30	−	1.26127e31i	0.136957	−	0.332327i
$337$	2.33964e31	−	4.05238e31i	0.593985	−	1.02881i	−0.399704	−	0.916644i	$-0.630887\pi$
$337$	2.33964e31	−	4.05238e31i	0.593985	−	1.02881i	0.993689	−	0.112168i	$-0.0357794\pi$
$338$	−1.42138e31	+	2.46191e31i	−0.347739	+	0.602301i
$339$	2.29701e31	−	5.57372e31i	0.541585	−	1.31416i
$340$	1.45491e31	+	2.51998e31i	0.330635	+	0.572677i
$341$	1.62613e31			0.356226
$342$	2.43597e31	+	2.41856e31i	0.514452	+	0.510776i
$343$	4.74323e30			0.0965824
$344$	1.05869e31	+	1.83370e31i	0.207868	+	0.360038i
$345$	4.10186e31	+	5.32586e31i	0.776681	+	1.00844i
$346$	1.35725e31	−	2.35083e31i	0.247861	−	0.429309i
$347$	−1.91284e31	+	3.31313e31i	−0.336945	+	0.583606i	−0.983857	−	0.178959i	$-0.942727\pi$
$347$	−1.91284e31	+	3.31313e31i	−0.336945	+	0.583606i	0.646911	+	0.762565i	$0.276060\pi$
$348$	−1.71500e31	+	2.28912e30i	−0.291423	+	0.0388981i
$349$	2.74851e31	+	4.76057e31i	0.450589	+	0.780442i	0.998423	−	0.0561447i	$-0.0178808\pi$
$349$	2.74851e31	+	4.76057e31i	0.450589	+	0.780442i	−0.547834	+	0.836587i	$0.684547\pi$
$350$	−2.69566e30			−0.0426398
$351$	1.15515e31	−	9.15441e31i	0.176319	−	1.39731i
$352$	2.64352e30			0.0389403
$353$	1.26114e31	+	2.18436e31i	0.179299	+	0.310556i	0.941641	−	0.336619i	$-0.109284\pi$
$353$	1.26114e31	+	2.18436e31i	0.179299	+	0.310556i	−0.762341	+	0.647175i	$0.775950\pi$
$354$	−6.07596e31	+	8.10999e30i	−0.833823	+	0.111296i
$355$	−2.45824e31	+	4.25779e31i	−0.325664	+	0.564066i
$356$	8.61389e30	−	1.49197e31i	0.110173	−	0.190825i
$357$	−9.59874e31	−	1.24630e32i	−1.18539	−	1.53911i
$358$	−1.96481e31	−	3.40316e31i	−0.234306	−	0.405830i
$359$	8.67229e30			0.0998742			0.0499371	−	0.998752i	$-0.484098\pi$
$359$	8.67229e30			0.0998742			0.0499371	+	0.998752i	$0.484098\pi$
$360$	−7.94466e30	+	3.00809e31i	−0.0883678	+	0.334587i
$361$	4.75689e30			0.0511073
$362$	1.98010e30	+	3.42963e30i	0.0205508	+	0.0355951i
$363$	−3.61565e31	+	8.77340e31i	−0.362538	+	0.879701i
$364$	−5.22538e31	+	9.05062e31i	−0.506233	+	0.876821i
$365$	−6.32037e31	+	1.09472e32i	−0.591673	+	1.02481i
$366$	4.25960e31	−	1.03359e32i	0.385350	−	0.935054i
$367$	1.58949e31	+	2.75308e31i	0.138974	+	0.240710i	0.927108	−	0.374793i	$-0.122286\pi$
$367$	1.58949e31	+	2.75308e31i	0.138974	+	0.240710i	−0.788135	+	0.615503i	$0.788953\pi$
$368$	3.84702e31			0.325107
$369$	2.22107e31	−	8.40964e31i	0.181440	−	0.686986i
$370$	−1.14181e32			−0.901722
$371$	1.62504e32	+	2.81466e32i	1.24077	+	2.14907i
$372$	6.68296e31	+	8.67715e31i	0.493381	+	0.640605i
$373$	−1.17829e32	+	2.04085e32i	−0.841184	+	1.45697i	0.0477112	+	0.998861i	$0.484807\pi$
$373$	−1.17829e32	+	2.04085e32i	−0.841184	+	1.45697i	−0.888895	+	0.458111i	$0.848526\pi$
$374$	1.52418e31	−	2.63996e31i	0.105231	−	0.182265i
$375$	1.51389e32	−	2.02070e31i	1.01089	−	0.134930i
$376$	−6.04290e30	−	1.04666e31i	−0.0390299	−	0.0676018i
$377$	1.32549e32			0.828152
$378$	2.10571e31	−	1.66875e32i	0.127278	−	1.00866i
$379$	−1.64115e32			−0.959749			−0.479874	−	0.877337i	$-0.659318\pi$
$379$	−1.64115e32			−0.959749			−0.479874	+	0.877337i	$0.659318\pi$
$380$	4.43358e31	+	7.67919e31i	0.250876	+	0.434530i
$381$	−1.80355e32	+	2.40732e31i	−0.987565	+	0.131817i
$382$	−9.82207e31	+	1.70123e32i	−0.520488	+	0.901512i
$383$	−1.23171e32	+	2.13338e32i	−0.631716	+	1.09416i	0.355484	+	0.934682i	$0.384316\pi$
$383$	−1.23171e32	+	2.13338e32i	−0.631716	+	1.09416i	−0.987201	+	0.159483i	$0.949017\pi$
$384$	1.08641e31	+	1.41060e31i	0.0539330	+	0.0700266i
$385$	−3.22543e31	−	5.58661e31i	−0.154999	−	0.268466i
$386$	−6.44125e31			−0.299660
$387$	1.85262e32	+	1.83938e32i	0.834448	+	0.828485i
$388$	1.52809e32			0.666427
$389$	−1.32576e32	−	2.29629e32i	−0.559880	−	0.969741i	−0.997506	−	0.0705837i	$-0.977514\pi$
$389$	−1.32576e32	−	2.29629e32i	−0.559880	−	0.969741i	0.437626	−	0.899157i	$-0.355820\pi$
$390$	9.08167e31	−	2.20368e32i	0.371414	−	0.901239i
$391$	2.21809e32	−	3.84185e32i	0.878557	−	1.52170i
$392$	−4.91741e31	+	8.51721e31i	−0.188652	+	0.326754i
$393$	8.60116e31	−	2.08708e32i	0.319632	−	0.775589i
$394$	1.03639e32	+	1.79508e32i	0.373095	+	0.646219i
$395$	1.27131e32			0.443391
$396$	3.14526e31	−	8.54869e30i	0.106284	−	0.0288875i
$397$	−5.54754e32			−1.81643			−0.908217	−	0.418501i	$-0.862556\pi$
$397$	−5.54754e32			−1.81643			−0.908217	+	0.418501i	$0.862556\pi$
$398$	−4.56722e31	−	7.91066e31i	−0.144915	−	0.251000i
$399$	−2.92505e32	−	3.79788e32i	−0.899440	−	1.16783i
$400$	1.75914e30	−	3.04693e30i	0.00524266	−	0.00908055i
$401$	−9.55165e29	+	1.65439e30i	−0.00275914	+	0.00477897i	−0.867402	−	0.497609i	$-0.834212\pi$
$401$	−9.55165e29	+	1.65439e30i	−0.00275914	+	0.00477897i	0.864643	+	0.502388i	$0.167545\pi$
$402$	−4.18938e31	+	5.59185e30i	−0.117307	+	0.0156578i
$403$	−4.19525e32	−	7.26638e32i	−1.13879	−	1.97245i
$404$	2.44319e32			0.642968
$405$	2.75064e30	+	3.83595e32i	0.00701853	+	0.978780i
$406$	2.41622e32			0.597808
$407$	5.98089e31	+	1.03592e32i	0.143495	+	0.248540i
$408$	2.03510e32	−	2.71638e31i	0.473515	−	0.0632031i
$409$	−4.94043e31	+	8.55707e31i	−0.111487	+	0.193101i	−0.916370	−	0.400333i	$-0.868895\pi$
$409$	−4.94043e31	+	8.55707e31i	−0.111487	+	0.193101i	0.804883	+	0.593433i	$0.202228\pi$
$410$	1.12341e32	−	1.94581e32i	0.245890	−	0.425894i
$411$	−1.86224e32	−	2.41794e32i	−0.395379	−	0.513360i
$412$	−9.74982e31	−	1.68872e32i	−0.200808	−	0.347810i
$413$	8.56028e32			1.71046
$414$	4.57720e32	−	1.24406e32i	0.887351	−	0.241178i
$415$	−7.35272e31			−0.138308
$416$	−6.81999e31	−	1.18126e32i	−0.124485	−	0.215614i
$417$	1.55788e32	−	3.78020e32i	0.275952	−	0.669598i
$418$	4.64468e31	−	8.04482e31i	0.0798459	−	0.138297i
$419$	−6.66279e31	+	1.15403e32i	−0.111168	+	0.192549i	−0.916242	−	0.400626i	$-0.868793\pi$
$419$	−6.66279e31	+	1.15403e32i	−0.111168	+	0.192549i	0.805073	+	0.593175i	$0.202126\pi$
$420$	1.65549e32	−	4.01706e32i	0.268108	−	0.650567i
$421$	−1.18831e32	−	2.05822e32i	−0.186812	−	0.323568i	0.757374	−	0.652982i	$-0.226482\pi$
$421$	−1.18831e32	−	2.05822e32i	−0.186812	−	0.323568i	−0.944186	+	0.329414i	$0.893149\pi$
$422$	6.56774e32			1.00233
$423$	−1.05746e32	−	1.04990e32i	−0.156678	−	0.155559i
$424$	−4.24190e32			−0.610221
$425$	−2.02855e31	−	3.51355e31i	−0.0283351	−	0.0490778i
$426$	2.11674e32	+	2.74838e32i	0.287110	+	0.372783i
$427$	−7.80588e32	+	1.35202e33i	−1.02819	+	1.78088i
$428$	−4.53779e31	+	7.85968e31i	−0.0580493	+	0.100544i
$429$	−2.47501e32	+	3.30356e31i	−0.307511	+	0.0410456i
$430$	3.37186e32	+	5.84023e32i	0.406924	+	0.704814i
$431$	−3.21537e32			−0.376933			−0.188467	−	0.982080i	$-0.560352\pi$
$431$	−3.21537e32			−0.376933			−0.188467	+	0.982080i	$0.560352\pi$
$432$	1.74878e32	+	1.32701e32i	0.199154	+	0.151122i
$433$	1.39301e33			1.54118			0.770591	−	0.637330i	$-0.219961\pi$
$433$	1.39301e33			1.54118			0.770591	+	0.637330i	$0.219961\pi$
$434$	−7.64747e32	−	1.32458e33i	−0.822046	−	1.42383i
$435$	−5.46217e32	+	7.29072e31i	−0.570492	+	0.0761473i
$436$	−2.11826e32	+	3.66894e32i	−0.214980	+	0.372357i
$437$	6.75924e32	−	1.17074e33i	0.666623	−	1.15462i
$438$	5.44235e32	+	7.06635e32i	0.521627	+	0.677281i
$439$	3.60483e32	+	6.24375e32i	0.335798	+	0.581619i	0.983638	−	0.180157i	$-0.0576607\pi$
$439$	3.60483e32	+	6.24375e32i	0.335798	+	0.581619i	−0.647840	+	0.761777i	$0.724327\pi$
$440$	8.41944e31			0.0762298
$441$	−3.09643e32	+	1.17240e33i	−0.272508	+	1.03180i
$442$	−1.57289e33			−1.34561
$443$	3.58390e32	+	6.20749e32i	0.298063	+	0.516261i	0.975693	−	0.219143i	$-0.0703260\pi$
$443$	3.58390e32	+	6.20749e32i	0.298063	+	0.516261i	−0.677629	+	0.735404i	$0.736993\pi$
$444$	−3.06976e32	+	7.44879e32i	−0.248209	+	0.602280i
$445$	2.74347e32	−	4.75183e32i	0.215675	−	0.373561i
$446$	−6.76378e32	+	1.17152e33i	−0.517016	+	0.895498i
$447$	8.69401e31	−	2.10961e32i	0.0646213	−	0.156804i
$448$	−1.24321e32	−	2.15330e32i	−0.0898605	−	0.155643i
$449$	7.57627e32			0.532569			0.266285	−	0.963894i	$-0.414204\pi$
$449$	7.57627e32			0.532569			0.266285	+	0.963894i	$0.414204\pi$
$450$	1.10771e31	−	4.19412e31i	0.00757303	−	0.0286737i
$451$	−2.35380e32			−0.156518
$452$	−5.49392e32	−	9.51574e32i	−0.355346	−	0.615478i
$453$	−8.64535e32	−	1.12251e33i	−0.543945	−	0.706258i
$454$	3.97418e32	−	6.88348e32i	0.243248	−	0.421318i
$455$	−1.66425e33	+	2.88257e33i	−0.991007	+	1.71647i
$456$	6.20161e32	−	8.27770e31i	0.359289	−	0.0479567i
$457$	−3.47702e32	−	6.02238e32i	−0.195999	−	0.339481i	0.751228	−	0.660042i	$-0.229462\pi$
$457$	−3.47702e32	−	6.02238e32i	−0.195999	−	0.339481i	−0.947228	+	0.320562i	$0.896128\pi$
$458$	−1.52772e33			−0.837965
$459$	2.33352e33	−	9.81313e32i	1.24553	−	0.523780i
$460$	1.22525e33			0.636433
$461$	−8.96494e32	−	1.55277e33i	−0.453196	−	0.784958i	0.545387	−	0.838185i	$-0.316383\pi$
$461$	−8.96494e32	−	1.55277e33i	−0.453196	−	0.784958i	−0.998582	+	0.0532264i	$0.983049\pi$
$462$	−4.51167e32	+	6.02203e31i	−0.221979	+	0.0296291i
$463$	1.43327e33	−	2.48250e33i	0.686384	−	1.18885i	−0.286616	−	0.958046i	$-0.592530\pi$
$463$	1.43327e33	−	2.48250e33i	0.686384	−	1.18885i	0.973000	−	0.230806i	$-0.0741363\pi$
$464$	−1.57679e32	+	2.73107e32i	−0.0735018	+	0.127309i
$465$	2.12848e33	+	2.76362e33i	0.965847	+	1.25406i
$466$	1.12960e33	+	1.95653e33i	0.499002	+	0.864297i
$467$	−1.57286e33			−0.676442			−0.338221	−	0.941067i	$-0.609825\pi$
$467$	−1.57286e33			−0.676442			−0.338221	+	0.941067i	$0.609825\pi$
$468$	−1.19344e33	−	1.18492e33i	−0.499722	−	0.496151i
$469$	5.90233e32			0.240637
$470$	−1.92463e32	−	3.33355e32i	−0.0764053	−	0.132338i
$471$	−1.43569e33	+	3.48371e33i	−0.555007	+	1.34673i
$472$	−5.58629e32	+	9.67574e32i	−0.210305	+	0.364258i
$473$	3.53241e32	−	6.11831e32i	0.129511	−	0.224319i
$474$	3.41791e32	−	8.29357e32i	0.122048	−	0.296150i
$475$	−6.18166e31	−	1.07069e32i	−0.0214998	−	0.0372388i
$476$	−2.86720e33			−0.971341
$477$	−5.04702e33	+	1.37176e33i	−1.66554	+	0.452687i
$478$	−2.97954e33			−0.957855
$479$	2.69749e33	+	4.67219e33i	0.844824	+	1.46328i	0.885774	+	0.464117i	$0.153628\pi$
$479$	2.69749e33	+	4.67219e33i	0.844824	+	1.46328i	−0.0409494	+	0.999161i	$0.513038\pi$
$480$	3.46016e32	+	4.49267e32i	0.105580	+	0.137085i
$481$	3.08601e33	−	5.34512e33i	0.917452	−	1.58907i
$482$	7.52130e32	−	1.30273e33i	0.217874	−	0.377368i
$483$	−6.56568e33	+	8.76365e32i	−1.85328	+	0.247369i
$484$	8.64779e32	+	1.49784e33i	0.237869	+	0.412002i
$485$	4.86688e33			1.30460
$486$	2.50984e33	+	1.01335e33i	0.655681	+	0.264732i
$487$	6.61224e33			1.68359			0.841795	−	0.539797i	$-0.181499\pi$
$487$	6.61224e33			1.68359			0.841795	+	0.539797i	$0.181499\pi$
$488$	−1.01880e33	−	1.76461e33i	−0.252836	−	0.437926i
$489$	−3.85996e33	+	5.15214e32i	−0.933731	+	0.124631i
$490$	−1.56617e33	+	2.71268e33i	−0.369306	+	0.639657i
$491$	−6.28060e32	+	1.08783e33i	−0.144372	+	0.250059i	−0.929138	−	0.369732i	$-0.879449\pi$
$491$	−6.28060e32	+	1.08783e33i	−0.144372	+	0.250059i	0.784767	+	0.619791i	$0.212783\pi$
$492$	−9.67350e32	−	1.25601e33i	−0.216780	−	0.281467i
$493$	1.81827e33	+	3.14933e33i	0.397257	+	0.688069i
$494$	−4.79311e33			−1.02101
$495$	1.00175e33	−	2.72271e32i	0.208062	−	0.0565504i
$496$	1.99624e33			0.404289
$497$	−2.42224e33	−	4.19544e33i	−0.478368	−	0.828557i
$498$	−1.97678e32	+	4.79666e32i	−0.0380707	+	0.0923788i
$499$	3.38024e33	−	5.85476e33i	0.634879	−	1.09964i	−0.351661	−	0.936127i	$-0.614383\pi$
$499$	3.38024e33	−	5.85476e33i	0.634879	−	1.09964i	0.986541	−	0.163516i	$-0.0522836\pi$
$500$	1.39189e33	−	2.41082e33i	0.254964	−	0.441611i
$501$	−6.08410e32	+	1.47631e33i	−0.108699	+	0.263759i
$502$	2.15236e33	+	3.72799e33i	0.375075	+	0.649649i
$503$	1.11786e33			0.190015			0.0950074	−	0.995477i	$-0.469713\pi$
$503$	1.11786e33			0.190015			0.0950074	+	0.995477i	$0.469713\pi$
$504$	−2.17551e33	−	2.15997e33i	−0.360728	−	0.358151i
$505$	7.78140e33			1.25868
$506$	−6.41796e32	−	1.11162e33i	−0.101278	−	0.175419i
$507$	3.89814e33	+	5.06134e33i	0.600147	+	0.779230i
$508$	−1.65820e33	+	2.87209e33i	−0.249081	+	0.431421i
$509$	−8.63537e32	+	1.49569e33i	−0.126564	+	0.219215i	−0.922343	−	0.386372i	$-0.873728\pi$
$509$	−8.63537e32	+	1.49569e33i	−0.126564	+	0.219215i	0.795779	+	0.605587i	$0.207061\pi$
$510$	6.48167e33	−	8.65151e32i	0.926957	−	0.123727i
$511$	−6.22781e33	−	1.07869e34i	−0.869109	−	1.50534i
$512$	3.24519e32			0.0441942
$513$	7.11101e33	−	2.99038e33i	0.945070	−	0.397429i
$514$	5.18430e33			0.672436
$515$	−3.10526e33	−	5.37847e33i	−0.393104	−	0.680876i
$516$	4.71649e33	−	6.29542e32i	0.582771	−	0.0777863i
$517$	−2.01627e32	+	3.49228e32i	−0.0243174	+	0.0421189i
$518$	5.62545e33	−	9.74356e33i	0.662270	−	1.14709i
$519$	−3.72225e33	−	4.83297e33i	−0.427773	−	0.555421i
$520$	−2.17212e33	−	3.76223e33i	−0.243693	−	0.422089i
$521$	−1.56282e34			−1.71174			−0.855872	−	0.517188i	$-0.826979\pi$
$521$	−1.56282e34			−1.71174			−0.855872	+	0.517188i	$0.826979\pi$
$522$	−9.92882e32	+	3.75935e33i	−0.106174	+	0.402005i
$523$	1.33112e34			1.38978			0.694892	−	0.719114i	$-0.255452\pi$
$523$	1.33112e34			1.38978			0.694892	+	0.719114i	$0.255452\pi$
$524$	−2.05720e33	−	3.56317e33i	−0.209717	−	0.363241i
$525$	−2.30822e32	+	5.60091e32i	−0.0229766	+	0.0557528i
$526$	−2.30886e33	+	3.99906e33i	−0.224427	+	0.388719i
$527$	1.15098e34	−	1.99356e34i	1.09254	−	1.89233i
$528$	2.26357e32	−	5.49256e32i	0.0209831	−	0.0509156i
$529$	−3.81695e33	−	6.61115e33i	−0.345558	−	0.598524i
$530$	−1.35102e34			−1.19457
$531$	−3.51762e33	+	1.33187e34i	−0.303785	+	1.15022i
$532$	−8.73731e33			−0.737025
$533$	6.07256e33	+	1.05180e34i	0.500359	+	0.866647i
$534$	−2.36235e33	−	3.06728e33i	−0.190142	−	0.246881i
$535$	−1.44526e33	+	2.50326e33i	−0.113638	+	0.196827i
$536$	−3.85176e32	+	6.67144e32i	−0.0295869	+	0.0512460i
$537$	−8.75332e33	+	1.16836e33i	−0.656892	+	0.0876797i
$538$	2.54508e33	+	4.40821e33i	0.186605	+	0.323210i
$539$	3.28148e33			0.235077
$540$	5.56977e33	+	4.22644e33i	0.389866	+	0.295837i
$541$	2.50096e32			0.0171057			0.00855286	−	0.999963i	$-0.497278\pi$
$541$	2.50096e32			0.0171057			0.00855286	+	0.999963i	$0.497278\pi$
$542$	−4.38746e32	−	7.59930e32i	−0.0293239	−	0.0507905i
$543$	8.82140e32	−	1.17745e32i	0.0576156	−	0.00769033i
$544$	1.87109e33	−	3.24082e33i	0.119429	−	0.206856i
$545$	−6.74654e33	+	1.16853e34i	−0.420847	+	0.728929i
$546$	1.43306e34	+	1.86068e34i	0.873686	+	1.13439i
$547$	1.31322e31	+	2.27457e31i	0.000782522	+	0.00135537i	0.866416	−	0.499322i	$-0.166418\pi$
$547$	1.31322e31	+	2.27457e31i	0.000782522	+	0.00135537i	−0.865634	+	0.500678i	$0.833084\pi$
$548$	−5.56264e33			−0.323984
$549$	−1.78281e34	−	1.77007e34i	−1.01497	−	1.00771i
$550$	−1.17391e32			−0.00653281
$551$	5.54085e33	+	9.59704e33i	0.301427	+	0.522086i
$552$	3.29409e33	−	7.99314e33i	0.175185	−	0.425088i
$553$	−6.26344e33	+	1.08486e34i	−0.325649	+	0.564040i
$554$	3.87224e33	−	6.70692e33i	0.196829	−	0.340919i
$555$	−9.77699e33	+	2.37239e34i	−0.485896	+	1.17903i
$556$	−3.72608e33	−	6.45376e33i	−0.181058	−	0.313601i
$557$	3.71442e34			1.76482			0.882412	−	0.470477i	$-0.155918\pi$
$557$	3.71442e34			1.76482			0.882412	+	0.470477i	$0.155918\pi$
$558$	2.37514e34	−	6.45551e33i	1.10347	−	0.299919i
$559$	−3.64529e34			−1.65609
$560$	−3.95954e33	−	6.85813e33i	−0.175912	−	0.304688i
$561$	−4.18006e33	−	5.42739e33i	−0.181613	−	0.235806i
$562$	−1.38781e34	+	2.40376e34i	−0.589695	+	1.02138i
$563$	−1.64703e34	+	2.85274e34i	−0.684458	+	1.18552i	0.289149	+	0.957284i	$0.406628\pi$
$563$	−1.64703e34	+	2.85274e34i	−0.684458	+	1.18552i	−0.973607	+	0.228231i	$0.926706\pi$
$564$	−2.69213e33	+	3.59337e32i	−0.109423	+	0.0146054i
$565$	−1.74978e34	−	3.03071e34i	−0.695629	−	1.20486i
$566$	1.79718e34			0.698853
$567$	−3.28693e34	−	1.86641e34i	−1.25027	−	0.709937i
$568$	6.32284e33			0.235266
$569$	1.35740e34	+	2.35108e34i	0.494088	+	0.855785i	0.999977	−	0.00681352i	$-0.00216883\pi$
$569$	1.35740e34	+	2.35108e34i	0.494088	+	0.855785i	−0.505889	+	0.862599i	$0.668835\pi$
$570$	1.97518e34	−	2.63640e33i	0.703348	−	0.0938805i
$571$	−1.73272e34	+	3.00117e34i	−0.603640	+	1.04553i	0.388625	+	0.921396i	$0.372950\pi$
$571$	−1.73272e34	+	3.00117e34i	−0.603640	+	1.04553i	−0.992265	+	0.124139i	$0.960383\pi$
$572$	−2.27555e33	+	3.94137e33i	−0.0775596	+	0.134337i
$573$	2.69370e34	+	3.49749e34i	0.898289	+	1.16634i
$574$	1.10696e34	+	1.91731e34i	0.361188	+	0.625596i
$575$	−1.70835e33			−0.0545416
$576$	3.86113e33	−	1.04944e33i	0.120624	−	0.0327851i
$577$	1.02989e34			0.314843			0.157422	−	0.987531i	$-0.449682\pi$
$577$	1.02989e34			0.314843			0.157422	+	0.987531i	$0.449682\pi$
$578$	−9.75816e33	−	1.69016e34i	−0.291924	−	0.505628i
$579$	−5.51546e33	+	1.33833e34i	−0.161473	+	0.391815i
$580$	−5.02197e33	+	8.69831e33i	−0.143888	+	0.249221i
$581$	3.62252e33	−	6.27439e33i	0.101580	−	0.175942i
$582$	1.30846e34	−	3.17499e34i	0.359106	−	0.871374i
$583$	7.07673e33	+	1.22573e34i	0.190097	+	0.329258i
$584$	1.62566e34			0.427435
$585$	−3.80104e34	−	3.77388e34i	−0.978260	−	0.971271i
$586$	4.31836e34			1.08792
$587$	2.21175e34	+	3.83086e34i	0.545456	+	0.944757i	0.998578	+	0.0533087i	$0.0169767\pi$
$587$	2.21175e34	+	3.83086e34i	0.545456	+	0.944757i	−0.453122	+	0.891448i	$0.649690\pi$
$588$	1.34860e34	+	1.75102e34i	0.325586	+	0.422741i
$589$	3.50741e34	−	6.07502e34i	0.828984	−	1.43584i
$590$	−1.77920e34	+	3.08167e34i	−0.411694	+	0.713075i
$591$	4.61714e34	−	6.16280e33i	1.04600	−	0.139616i
$592$	7.34214e33	+	1.27170e34i	0.162855	+	0.282073i
$593$	−4.45127e34			−0.966719			−0.483360	−	0.875422i	$-0.660584\pi$
$593$	−4.45127e34			−0.966719			−0.483360	+	0.875422i	$0.660584\pi$
$594$	9.16996e32	−	7.26706e33i	0.0195001	−	0.154536i
$595$	−9.13187e34			−1.90151
$596$	−2.07940e33	−	3.60163e33i	−0.0423995	−	0.0734381i
$597$	−2.03471e34	+	2.71587e33i	−0.406279	+	0.0542287i
$598$	−3.31153e34	+	5.73573e34i	−0.647535	+	1.12156i
$599$	2.98093e34	−	5.16312e34i	0.570843	−	0.988729i	−0.425637	−	0.904894i	$-0.639950\pi$
$599$	2.98093e34	−	5.16312e34i	0.570843	−	0.988729i	0.996480	−	0.0838348i	$-0.0267168\pi$
$600$	−4.82444e32	−	6.26405e32i	−0.00904808	−	0.0117480i
$601$	−2.12684e34	−	3.68380e34i	−0.390665	−	0.676651i	0.601873	−	0.798592i	$-0.294421\pi$
$601$	−2.12684e34	−	3.68380e34i	−0.390665	−	0.676651i	−0.992537	+	0.121941i	$0.961088\pi$
$602$	−6.64496e34			−1.19546
$603$	−2.42540e33	+	9.18330e33i	−0.0427383	+	0.161820i
$604$	−2.58242e34			−0.445723
$605$	2.75427e34	+	4.77054e34i	0.465655	+	0.806538i
$606$	2.09203e34	−	5.07632e34i	0.346465	−	0.840701i
$607$	−8.96624e33	+	1.55300e34i	−0.145463	+	0.251949i	−0.929545	−	0.368707i	$-0.879800\pi$
$607$	−8.96624e33	+	1.55300e34i	−0.145463	+	0.251949i	0.784083	+	0.620656i	$0.213134\pi$
$608$	5.70182e33	−	9.87584e33i	0.0906189	−	0.156956i
$609$	2.06894e34	−	5.02030e34i	0.322131	−	0.781652i
$610$	−3.24481e34	−	5.62017e34i	−0.494955	−	0.857287i
$611$	2.08070e34			0.310953
$612$	1.17820e34	−	4.46102e34i	0.172515	−	0.653192i
$613$	2.87121e34			0.411916			0.205958	−	0.978561i	$-0.433969\pi$
$613$	2.87121e34			0.411916			0.205958	+	0.978561i	$0.433969\pi$
$614$	5.93677e33	+	1.02828e34i	0.0834537	+	0.144546i
$615$	−3.08095e34	−	4.00030e34i	−0.424371	−	0.551003i
$616$	−4.14807e33	+	7.18467e33i	−0.0559870	+	0.0969724i
$617$	−9.06267e33	+	1.56970e34i	−0.119865	+	0.207612i	−0.919714	−	0.392589i	$-0.871579\pi$
$617$	−9.06267e33	+	1.56970e34i	−0.119865	+	0.207612i	0.799849	+	0.600201i	$0.204913\pi$
$618$	−4.34358e34	+	5.79766e33i	−0.562978	+	0.0751445i
$619$	4.79033e34	+	8.29710e34i	0.608461	+	1.05388i	0.991494	+	0.130150i	$0.0415460\pi$
$619$	4.79033e34	+	8.29710e34i	0.608461	+	1.05388i	−0.383034	+	0.923734i	$0.625121\pi$
$620$	6.35791e34			0.791441
$621$	1.33447e34	−	1.05755e35i	0.162804	−	1.29020i
$622$	−9.92122e34			−1.18627
$623$	2.70330e34	+	4.68225e34i	0.316806	+	0.548724i
$624$	−3.03833e34	+	4.05546e33i	−0.349001	+	0.0465835i
$625$	4.24682e34	−	7.35571e34i	0.478150	−	0.828180i
$626$	5.89675e34	−	1.02135e35i	0.650779	−	1.12718i
$627$	−1.27380e34	−	1.65390e34i	−0.137803	−	0.178923i
$628$	3.43383e34	+	5.94757e34i	0.364152	+	0.630730i
$629$	1.69331e35			1.76037
$630$	−6.92888e34	−	6.87937e34i	−0.706165	−	0.701120i
$631$	1.58378e35			1.58244			0.791222	−	0.611530i	$-0.209445\pi$
$631$	1.58378e35			1.58244			0.791222	+	0.611530i	$0.209445\pi$
$632$	−8.17483e33	−	1.41592e34i	−0.0800784	−	0.138700i
$633$	5.62377e34	−	1.36461e35i	0.540108	−	1.31058i
$634$	5.54191e33	−	9.59887e33i	0.0521848	−	0.0903866i
$635$	−5.28127e34	+	9.14742e34i	−0.487603	+	0.844553i
$636$	−3.63221e34	+	8.81359e34i	−0.328819	+	0.797883i
$637$	−8.46585e34	−	1.46633e35i	−0.751498	−	1.30163i
$638$	1.05222e34			0.0915897
$639$	7.52294e34	−	2.04470e34i	0.642136	−	0.174530i
$640$	1.03357e34			0.0865149
$641$	7.22487e34	+	1.25138e35i	0.593068	+	1.02722i	0.993816	+	0.111036i	$0.0354168\pi$
$641$	7.22487e34	+	1.25138e35i	0.593068	+	1.02722i	−0.400749	+	0.916188i	$0.631250\pi$
$642$	1.24449e34	+	1.61584e34i	0.100185	+	0.130080i
$643$	−2.08866e34	+	3.61766e34i	−0.164903	+	0.285621i	−0.936621	−	0.350344i	$-0.886065\pi$
$643$	−2.08866e34	+	3.61766e34i	−0.164903	+	0.285621i	0.771718	+	0.635965i	$0.219398\pi$
$644$	−6.03655e34	+	1.04556e35i	−0.467429	+	0.809610i
$645$	1.50217e35	−	2.00505e34i	1.14084	−	0.152275i
$646$	−6.57504e34	−	1.13883e35i	−0.489769	−	0.848305i
$647$	−1.10759e35			−0.809235			−0.404617	−	0.914486i	$-0.632595\pi$
$647$	−1.10759e35			−0.809235			−0.404617	+	0.914486i	$0.632595\pi$
$648$	4.25462e34	−	2.49725e34i	0.304911	−	0.178968i
$649$	3.72783e34			0.262058
$650$	3.02855e33	+	5.24561e33i	0.0208842	+	0.0361725i
$651$	−3.40697e35	+	4.54751e34i	−2.30466	+	0.307618i
$652$	−3.54888e34	+	6.14684e34i	−0.235503	+	0.407903i
$653$	6.33473e34	−	1.09721e35i	0.412395	−	0.714289i	−0.582756	−	0.812647i	$-0.698026\pi$
$653$	6.33473e34	−	1.09721e35i	0.412395	−	0.714289i	0.995151	+	0.0983583i	$0.0313591\pi$
$654$	5.80932e34	+	7.54282e34i	0.371025	+	0.481739i
$655$	−6.55205e34	−	1.13485e35i	−0.410545	−	0.711085i
$656$	−2.88953e34			−0.177636
$657$	1.93422e35	−	5.25713e34i	1.16665	−	0.317089i
$658$	3.79289e34			0.224464
$659$	4.99095e34	+	8.64459e34i	0.289812	+	0.501969i	0.973765	−	0.227558i	$-0.0730740\pi$
$659$	4.99095e34	+	8.64459e34i	0.289812	+	0.501969i	−0.683953	+	0.729526i	$0.739741\pi$
$660$	7.20932e33	−	1.74935e34i	0.0410767	−	0.0996729i
$661$	−8.56160e34	+	1.48291e35i	−0.478671	+	0.829082i	−0.999701	−	0.0244562i	$-0.992215\pi$
$661$	−8.56160e34	+	1.48291e35i	−0.478671	+	0.829082i	0.521030	+	0.853538i	$0.325548\pi$
$662$	−8.57574e34	+	1.48536e35i	−0.470486	+	0.814905i
$663$	−1.34682e35	+	3.26807e35i	−0.725087	+	1.75943i
$664$	4.72799e33	+	8.18912e33i	0.0249790	+	0.0432649i
$665$	−2.78278e35			−1.44281
$666$	1.28482e35	+	1.27564e35i	0.653752	+	0.649081i
$667$	1.53126e35			0.764671
$668$	1.45518e34	+	2.52044e34i	0.0713197	+	0.123529i
$669$	1.85496e35	+	2.40848e35i	0.892295	+	1.15856i
$670$	−1.22676e34	+	2.12481e34i	−0.0579196	+	0.100320i
$671$	−3.39930e34	+	5.88777e34i	−0.157528	+	0.272847i
$672$	−5.53854e34	+	7.39265e33i	−0.251929	+	0.0336267i
$673$	6.87961e33	+	1.19158e34i	0.0307168	+	0.0532030i	0.880975	−	0.473163i	$-0.156888\pi$
$673$	6.87961e33	+	1.19158e34i	0.0307168	+	0.0532030i	−0.850258	+	0.526366i	$0.823554\pi$
$674$	−1.91663e35			−0.840021
$675$	−7.76582e33	−	5.89284e33i	−0.0334111	−	0.0253529i
$676$	1.16440e35			0.491777
$677$	−1.58719e35	−	2.74909e35i	−0.658066	−	1.13980i	−0.981116	−	0.193422i	$-0.938041\pi$
$677$	−1.58719e35	−	2.74909e35i	−0.658066	−	1.13980i	0.323050	−	0.946382i	$-0.395292\pi$
$678$	−2.44756e35	+	3.26692e34i	−0.996235	+	0.132974i
$679$	−2.39780e35	+	4.15312e35i	−0.958167	+	1.65959i
$680$	5.95930e34	−	1.03218e35i	0.233794	−	0.404944i
$681$	−1.08992e35	−	1.41515e35i	−0.419811	−	0.545082i
$682$	−3.33032e34	−	5.76828e34i	−0.125945	−	0.218143i
$683$	2.98631e35			1.10886			0.554429	−	0.832231i	$-0.312937\pi$
$683$	2.98631e35			1.10886			0.554429	+	0.832231i	$0.312937\pi$
$684$	3.59036e34	−	1.35942e35i	0.130899	−	0.495623i
$685$	−1.77167e35			−0.634235
$686$	−9.71414e33	−	1.68254e34i	−0.0341470	−	0.0591444i
$687$	−1.30814e35	+	3.17422e35i	−0.451540	+	1.09567i
$688$	4.33639e34	−	7.51084e34i	0.146985	−	0.254585i
$689$	3.65144e35	−	6.32448e35i	1.21541	−	2.10516i
$690$	1.04915e35	−	2.54577e35i	0.342944	−	0.832156i
$691$	−1.45840e34	−	2.52603e34i	−0.0468169	−	0.0810892i	0.841667	−	0.539996i	$-0.181574\pi$
$691$	−1.45840e34	−	2.52603e34i	−0.0468169	−	0.0810892i	−0.888484	+	0.458907i	$0.848241\pi$
$692$	−1.11186e35			−0.350529
$693$	−2.61199e34	+	9.88976e34i	−0.0808734	+	0.306211i
$694$	1.56700e35			0.476512
$695$	−1.18673e35	−	2.05548e35i	−0.354441	−	0.613909i
$696$	4.32433e34	+	5.61470e34i	0.126854	+	0.164707i
$697$	−1.66603e35	+	2.88565e35i	−0.480035	+	0.831445i
$698$	1.12579e35	−	1.94993e35i	0.318614	−	0.551856i
$699$	5.03243e35	−	6.71711e34i	1.39898	−	0.186732i
$700$	5.52072e33	+	9.56216e33i	0.0150754	+	0.0261114i
$701$	3.55864e34			0.0954571			0.0477286	−	0.998860i	$-0.484802\pi$
$701$	3.55864e34			0.0954571			0.0477286	+	0.998860i	$0.484802\pi$
$702$	−3.48387e35	+	1.46506e35i	−0.918010	+	0.386049i
$703$	5.16008e35			1.33572
$704$	−5.41392e33	−	9.37719e33i	−0.0137675	−	0.0238459i
$705$	−8.57428e34	+	1.14447e34i	−0.214207	+	0.0285916i
$706$	5.16562e34	−	8.94712e34i	0.126784	−	0.219596i
$707$	−3.83372e35	+	6.64020e35i	−0.924439	+	1.60117i
$708$	1.53204e35	+	1.98920e35i	0.362956	+	0.471261i
$709$	−8.26584e34	−	1.43169e35i	−0.192402	−	0.333250i	0.753644	−	0.657283i	$-0.228294\pi$
$709$	−8.26584e34	−	1.43169e35i	−0.192402	−	0.333250i	−0.946046	+	0.324033i	$0.894961\pi$
$710$	2.01379e35			0.460558
$711$	−1.43053e35	−	1.42031e35i	−0.321460	−	0.319163i
$712$	−7.05650e34			−0.155808
$713$	−4.84650e35	−	8.39438e35i	−1.05150	−	1.82125i
$714$	−2.45510e35	+	5.95733e35i	−0.523410	+	1.27006i
$715$	−7.24748e34	+	1.25530e35i	−0.151831	+	0.262980i
$716$	−8.04788e34	+	1.39393e35i	−0.165679	+	0.286965i
$717$	−2.55129e35	+	6.19072e35i	−0.516143	+	1.25243i
$718$	−1.77609e34	−	3.07627e34i	−0.0353109	−	0.0611602i
$719$	−2.44699e35			−0.478103			−0.239052	−	0.971007i	$-0.576837\pi$
$719$	−2.44699e35			−0.478103			−0.239052	+	0.971007i	$0.576837\pi$
$720$	1.22975e35	−	3.34240e34i	0.236135	−	0.0641803i
$721$	6.11957e35			1.15486
$722$	−9.74211e33	−	1.68738e34i	−0.0180692	−	0.0312967i
$723$	−2.06271e35	−	2.67822e35i	−0.376019	−	0.488223i
$724$	8.11048e33	−	1.40478e34i	0.0145316	−	0.0251695i
$725$	7.00204e33	−	1.21279e34i	0.0123310	−	0.0213580i
$726$	3.85262e35	−	5.14235e34i	0.666881	−	0.0890131i
$727$	−3.60561e34	−	6.24509e34i	−0.0613477	−	0.106257i	0.833720	−	0.552187i	$-0.186207\pi$
$727$	−3.60561e34	−	6.24509e34i	−0.0613477	−	0.106257i	−0.895068	+	0.445930i	$0.852873\pi$
$728$	4.28063e35			0.715922
$729$	4.25459e35	−	4.34711e35i	0.699460	−	0.714671i
$730$	5.17765e35			0.836752
$731$	−5.00049e35	−	8.66111e35i	−0.794412	−	1.37596i
$732$	−4.53877e35	+	6.05820e34i	−0.708843	+	0.0946140i
$733$	6.31230e35	−	1.09332e36i	0.969143	−	1.67860i	0.271096	−	0.962552i	$-0.412614\pi$
$733$	6.31230e35	−	1.09332e36i	0.969143	−	1.67860i	0.698047	−	0.716052i	$-0.254053\pi$
$734$	6.51056e34	−	1.12766e35i	0.0982693	−	0.170207i
$735$	4.29520e35	+	5.57689e35i	0.637370	+	0.827561i
$736$	−7.87870e34	−	1.36463e35i	−0.114943	−	0.199087i
$737$	2.57035e34			0.0368679
$738$	−3.43798e35	+	9.34427e34i	−0.484840	+	0.131777i
$739$	4.34025e35			0.601810			0.300905	−	0.953654i	$-0.402711\pi$
$739$	4.34025e35			0.601810			0.300905	+	0.953654i	$0.402711\pi$
$740$	2.33843e35	+	4.05028e35i	0.318807	+	0.552190i
$741$	−4.10420e35	+	9.95887e35i	−0.550175	+	1.33500i
$742$	6.65617e35	−	1.15288e36i	0.877356	−	1.51962i
$743$	−5.62510e35	+	9.74297e35i	−0.729072	+	1.26279i	0.228204	+	0.973613i	$0.426715\pi$
$743$	−5.62510e35	+	9.74297e35i	−0.729072	+	1.26279i	−0.957276	+	0.289176i	$0.906619\pi$
$744$	1.70932e35	−	4.14769e35i	0.217853	−	0.528621i
$745$	−6.62278e34	−	1.14710e35i	−0.0830016	−	0.143763i
$746$	9.65253e35			1.18961
$747$	8.27360e34	+	8.21449e34i	0.100274	+	0.0995572i
$748$	−1.24861e35			−0.148818
$749$	−1.42409e35	−	2.46660e35i	−0.166923	−	0.289119i
$750$	−3.81724e35	−	4.95631e35i	−0.440032	−	0.571337i
$751$	−6.69580e35	+	1.15975e36i	−0.759107	+	1.31481i	0.184199	+	0.982889i	$0.441031\pi$
$751$	−6.69580e35	+	1.15975e36i	−0.759107	+	1.31481i	−0.943306	+	0.331924i	$0.892302\pi$
$752$	−2.47517e34	+	4.28712e34i	−0.0275983	+	0.0478017i
$753$	9.58883e35	−	1.27988e35i	1.05155	−	0.140357i
$754$	−2.71461e35	−	4.70184e35i	−0.292796	−	0.507137i
$755$	−8.22485e35			−0.872552
$756$	−6.35070e35	+	2.67065e35i	−0.662673	+	0.278673i
$757$	8.86136e35			0.909498			0.454749	−	0.890620i	$-0.349729\pi$
$757$	8.86136e35			0.909498			0.454749	+	0.890620i	$0.349729\pi$
$758$	3.36107e35	+	5.82155e35i	0.339322	+	0.587724i
$759$	−2.85922e35	+	3.81639e34i	−0.283940	+	0.0378993i
$760$	1.81599e35	−	3.14539e35i	0.177396	−	0.307259i
$761$	4.28800e35	−	7.42703e35i	0.412047	−	0.713686i	−0.583067	−	0.812424i	$-0.698147\pi$
$761$	4.28800e35	−	7.42703e35i	0.412047	−	0.713686i	0.995113	+	0.0987386i	$0.0314808\pi$
$762$	4.54760e35	+	5.90460e35i	0.429878	+	0.558153i
$763$	−6.64774e35	−	1.15142e36i	−0.618183	−	1.07072i
$764$	8.04624e35			0.736082
$765$	3.75250e35	−	1.42081e36i	0.337716	−	1.27870i
$766$	1.00901e36			0.893382
$767$	−9.61740e35	−	1.66578e36i	−0.837752	−	1.45103i
$768$	2.77876e34	−	6.74268e34i	0.0238142	−	0.0577853i
$769$	−9.81133e35	+	1.69937e36i	−0.827272	+	1.43288i	0.0728981	+	0.997339i	$0.476775\pi$
$769$	−9.81133e35	+	1.69937e36i	−0.827272	+	1.43288i	−0.900170	+	0.435538i	$0.856558\pi$
$770$	−1.32114e35	+	2.28828e35i	−0.109601	+	0.189834i
$771$	4.43916e35	−	1.07717e36i	0.362344	−	0.879231i
$772$	1.31917e35	+	2.28487e35i	0.105946	+	0.183504i
$773$	−1.80488e36			−1.42628			−0.713140	−	0.701022i	$-0.752728\pi$
$773$	−1.80488e36			−1.42628			−0.713140	+	0.701022i	$0.752728\pi$
$774$	2.73057e35	−	1.03387e36i	0.212320	−	0.803906i
$775$	−8.86472e34			−0.0678256
$776$	−3.12953e35	−	5.42050e35i	−0.235618	−	0.408101i
$777$	−1.54278e36	−	2.00314e36i	−1.14298	−	1.48405i
$778$	−5.43032e35	+	9.40558e35i	−0.395895	+	0.685710i
$779$	−5.07693e35	+	8.79351e35i	−0.364236	+	0.630876i
$780$	−9.67689e35	+	1.29164e35i	−0.683209	+	0.0911924i
$781$	−1.05484e35	−	1.82703e35i	−0.0732904	−	0.126943i
$782$	−1.81706e36			−1.24247
$783$	6.96080e35	+	5.28198e35i	0.468422	+	0.355447i
$784$	4.02834e35			0.266794
$785$	1.09365e36	+	1.89426e36i	0.712868	+	1.23472i
$786$	−9.16488e35	+	1.22330e35i	−0.587956	+	0.0784784i
$787$	−8.38175e35	+	1.45176e36i	−0.529238	+	0.916667i	0.470181	+	0.882570i	$0.344189\pi$
$787$	−8.38175e35	+	1.45176e36i	−0.529238	+	0.916667i	−0.999419	+	0.0340965i	$0.989145\pi$
$788$	4.24504e35	−	7.35263e35i	0.263818	−	0.456946i
$789$	6.33203e35	+	8.22150e35i	0.387329	+	0.502908i
$790$	−2.60364e35	−	4.50963e35i	−0.156762	−	0.271520i
$791$	3.44831e36			2.04362
$792$	−9.47393e34	−	9.40624e34i	−0.0552669	−	0.0548720i
$793$	3.50793e36			2.01436
$794$	1.13614e36	+	1.96785e36i	0.642206	+	1.11233i
$795$	−1.15684e36	+	2.80708e36i	−0.643700	+	1.56194i
$796$	−1.87073e35	+	3.24021e35i	−0.102471	+	0.177484i
$797$	4.01924e35	−	6.96153e35i	0.216728	−	0.375384i	−0.737078	−	0.675808i	$-0.763795\pi$
$797$	4.01924e35	−	6.96153e35i	0.216728	−	0.375384i	0.953806	+	0.300424i	$0.0971282\pi$
$798$	−7.48150e35	+	1.81539e36i	−0.397148	+	0.963683i
$799$	2.85424e35	+	4.94369e35i	0.149161	+	0.258355i
$800$	−1.44109e34			−0.00741424
$801$	−8.39584e35	+	2.28195e35i	−0.425263	+	0.115585i
$802$	7.82471e33			0.00390201
$803$	−2.71209e35	−	4.69747e35i	−0.133156	−	0.230632i
$804$	1.05634e35	+	1.37155e35i	0.0510627	+	0.0662998i
$805$	−1.92260e36	+	3.33005e36i	−0.915043	+	1.58490i
$806$	−1.71837e36	+	2.97631e36i	−0.805247	+	1.39473i
$807$	1.13384e36	−	1.51342e35i	0.523159	−	0.0698296i
$808$	−5.00365e35	−	8.66657e35i	−0.227324	−	0.393736i
$809$	−6.22907e35			−0.278655			−0.139327	−	0.990246i	$-0.544494\pi$
$809$	−6.22907e35			−0.278655			−0.139327	+	0.990246i	$0.544494\pi$
$810$	1.35507e36	−	7.95359e35i	0.596896	−	0.350349i
$811$	−1.68893e36			−0.732571			−0.366286	−	0.930502i	$-0.619371\pi$
$811$	−1.68893e36			−0.732571			−0.366286	+	0.930502i	$0.619371\pi$
$812$	−4.94843e35	−	8.57092e35i	−0.211357	−	0.366081i
$813$	−1.95463e35	+	2.60897e34i	−0.0822115	+	0.0109733i
$814$	2.44977e35	−	4.24313e35i	0.101466	−	0.175744i
$815$	−1.13030e36	+	1.95773e36i	−0.461023	+	0.798515i
$816$	−5.13145e35	−	6.66267e35i	−0.206117	−	0.267622i
$817$	−1.52381e36	−	2.63932e36i	−0.602776	−	1.04404i
$818$	4.04720e35			0.157666
$819$	5.09311e36	−	1.38428e36i	1.95404	−	0.531100i
$820$	−9.20299e35			−0.347741
$821$	1.08245e36	+	1.87486e36i	0.402827	+	0.697716i	0.994066	−	0.108780i	$-0.0346944\pi$
$821$	1.08245e36	+	1.87486e36i	0.402827	+	0.697716i	−0.591239	+	0.806496i	$0.701361\pi$
$822$	−4.76312e35	+	1.15578e36i	−0.174580	+	0.423619i
$823$	−1.30345e36	+	2.25764e36i	−0.470539	+	0.814998i	−0.999432	−	0.0336904i	$-0.989274\pi$
$823$	−1.30345e36	+	2.25764e36i	−0.470539	+	0.814998i	0.528893	+	0.848689i	$0.322607\pi$
$824$	−3.99353e35	+	6.91699e35i	−0.141993	+	0.245939i
$825$	−1.00518e34	+	2.43908e34i	−0.00352023	+	0.00854186i
$826$	−1.75315e36	−	3.03654e36i	−0.604738	−	1.04744i
$827$	1.38043e36			0.469024			0.234512	−	0.972113i	$-0.424651\pi$
$827$	1.38043e36			0.469024			0.234512	+	0.972113i	$0.424651\pi$
$828$	−1.37871e36	−	1.36886e36i	−0.461417	−	0.458120i
$829$	−5.79342e35			−0.190987			−0.0954933	−	0.995430i	$-0.530443\pi$
$829$	−5.79342e35			−0.190987			−0.0954933	+	0.995430i	$0.530443\pi$
$830$	1.50584e35	+	2.60818e35i	0.0488992	+	0.0846959i
$831$	−1.06196e36	−	1.37885e36i	−0.339700	−	0.441066i
$832$	−2.79347e35	+	4.83843e35i	−0.0880242	+	0.152462i
$833$	2.32264e36	−	4.02293e36i	0.720973	−	1.24876i
$834$	−1.65998e36	+	2.21569e35i	−0.507607	+	0.0677537i
$835$	4.63465e35	+	8.02745e35i	0.139616	+	0.241822i
$836$	−3.80492e35			−0.112919
$837$	6.92466e35	−	5.48770e36i	0.202456	−	1.60443i
$838$	5.45816e35			0.157216
$839$	2.77444e36	+	4.80547e36i	0.787319	+	1.36368i	0.927604	+	0.373565i	$0.121865\pi$
$839$	2.77444e36	+	4.80547e36i	0.787319	+	1.36368i	−0.140285	+	0.990111i	$0.544802\pi$
$840$	−1.76399e36	+	2.35451e35i	−0.493180	+	0.0658280i
$841$	1.18756e36	−	2.05692e36i	0.327119	−	0.566588i
$842$	−4.86733e35	+	8.43047e35i	−0.132096	+	0.228797i
$843$	3.80607e36	+	4.94180e36i	1.01773	+	1.32142i
$844$	−1.34507e36	−	2.32974e36i	−0.354377	−	0.613799i
$845$	3.70854e36			0.962706
$846$	−1.55858e35	+	5.90126e35i	−0.0398658	+	0.150944i
$847$	−5.42787e36			−1.36800
$848$	8.68741e35	+	1.50470e36i	0.215746	+	0.373683i
$849$	1.53887e36	−	3.73408e36i	0.376579	−	0.913771i
$850$	−8.30895e34	+	1.43915e35i	−0.0200359	+	0.0347032i
$851$	3.56507e36	−	6.17488e36i	0.847126	−	1.46727i
$852$	5.41407e35	−	1.31373e36i	0.126774	−	0.307617i
$853$	1.41675e36	+	2.45388e36i	0.326911	+	0.566226i	0.981897	−	0.189414i	$-0.0606590\pi$
$853$	1.41675e36	+	2.45388e36i	0.326911	+	0.566226i	−0.654986	+	0.755641i	$0.727326\pi$
$854$	6.39458e36			1.45408
$855$	1.14351e36	−	4.32966e36i	0.256249	−	0.970236i
$856$	3.71736e35			0.0820942
$857$	−2.26133e36	−	3.91674e36i	−0.492157	−	0.852441i	0.507802	−	0.861474i	$-0.330458\pi$
$857$	−2.26133e36	−	3.91674e36i	−0.492157	−	0.852441i	−0.999959	+	0.00903256i	$0.997125\pi$
$858$	6.24068e35	+	8.10289e35i	0.133857	+	0.173800i
$859$	4.66495e35	−	8.07994e35i	0.0986127	−	0.170802i	−0.812498	−	0.582964i	$-0.801893\pi$
$859$	4.66495e35	−	8.07994e35i	0.0986127	−	0.170802i	0.911111	+	0.412162i	$0.135226\pi$
$860$	1.38111e36	−	2.39216e36i	0.287739	−	0.498378i
$861$	4.93155e36	−	6.58246e35i	1.01261	−	0.135160i
$862$	6.58507e35	+	1.14057e36i	0.133266	+	0.230824i
$863$	−9.75467e36			−1.94571			−0.972854	−	0.231421i	$-0.925663\pi$
$863$	−9.75467e36			−1.94571			−0.972854	+	0.231421i	$0.925663\pi$
$864$	1.12571e35	−	8.92106e35i	0.0221311	−	0.175386i
$865$	−3.54121e36			−0.686199
$866$	−2.85287e36	−	4.94132e36i	−0.544890	−	0.943778i
$867$	−4.34730e36	+	5.80262e35i	−0.818428	+	0.109241i
$868$	−3.13240e36	+	5.42548e36i	−0.581274	+	1.00680i
$869$	−2.72760e35	+	4.72435e35i	−0.0498924	+	0.0864161i
$870$	1.37727e36	+	1.78825e36i	0.248330	+	0.322431i
$871$	−6.63121e35	−	1.14856e36i	−0.117860	−	0.204139i
$872$	1.73528e36			0.304028
$873$	−5.47642e36	−	5.43730e36i	−0.945843	−	0.939085i
$874$	−5.53717e36			−0.942747
$875$	4.36816e36	+	7.56588e36i	0.733159	+	1.26987i
$876$	1.39201e36	−	3.37772e36i	0.230325	−	0.558885i
$877$	−2.08866e36	+	3.61766e36i	−0.340700	+	0.590110i	−0.984563	−	0.175031i	$-0.943998\pi$
$877$	−2.08866e36	+	3.61766e36i	−0.340700	+	0.590110i	0.643863	+	0.765141i	$0.277331\pi$
$878$	1.47654e36	−	2.55744e36i	0.237445	−	0.411267i
$879$	3.69769e36	−	8.97247e36i	0.586232	−	1.42250i
$880$	−1.72430e35	−	2.98658e35i	−0.0269513	−	0.0466810i
$881$	−8.59059e36			−1.32381			−0.661903	−	0.749590i	$-0.730251\pi$
$881$	−8.59059e36			−1.32381			−0.661903	+	0.749590i	$0.730251\pi$
$882$	4.79294e36	−	1.30270e36i	0.728189	−	0.197919i
$883$	−1.65189e36			−0.247442			−0.123721	−	0.992317i	$-0.539483\pi$
$883$	−1.65189e36			−0.247442			−0.123721	+	0.992317i	$0.539483\pi$
$884$	3.22128e36	+	5.57942e36i	0.475746	+	0.824016i
$885$	4.87945e36	+	6.33547e36i	0.710526	+	0.922546i
$886$	1.46796e36	−	2.54259e36i	0.210763	−	0.365052i
$887$	−8.79092e35	+	1.52263e36i	−0.124448	+	0.215551i	−0.921517	−	0.388338i	$-0.873049\pi$
$887$	−8.79092e35	+	1.52263e36i	−0.124448	+	0.215551i	0.797069	+	0.603888i	$0.206383\pi$
$888$	3.27095e36	−	4.36596e35i	0.456575	−	0.0609421i
$889$	−5.20393e36	−	9.01346e36i	−0.716241	−	1.24057i
$890$	−2.24745e36			−0.305011
$891$	−1.43139e36	−	8.12786e35i	−0.191552	−	0.108769i
$892$	5.54089e36			0.731171
$893$	8.69780e35	+	1.50650e36i	0.113179	+	0.196032i
$894$	−9.26382e35	+	1.23650e35i	−0.118870	+	0.0158663i
$895$	−2.56320e36	+	4.43959e36i	−0.324336	+	0.561766i
$896$	−5.09218e35	+	8.81992e35i	−0.0635409	+	0.110056i
$897$	9.08184e36	+	1.17919e37i	1.11755	+	1.45103i
$898$	−1.55162e36	−	2.68748e36i	−0.188292	−	0.326131i
$899$	7.94578e36			0.950912
$900$	−1.71461e35	+	4.66025e34i	−0.0202365	+	0.00550019i
$901$	2.00357e37			2.33209
$902$	4.82059e35	+	8.34951e35i	0.0553374	+	0.0958472i
$903$	−5.68988e36	+	1.38065e37i	−0.644179	+	1.56311i
$904$	−2.25031e36	+	3.89765e36i	−0.251268	+	0.435208i
$905$	2.58314e35	−	4.47413e35i	0.0284473	−	0.0492721i
$906$	−2.21125e36	+	5.36562e36i	−0.240179	+	0.582797i
$907$	−4.62387e36	−	8.00879e36i	−0.495353	−	0.857977i	0.504632	−	0.863334i	$-0.331628\pi$
$907$	−4.62387e36	−	8.00879e36i	−0.495353	−	0.857977i	−0.999986	+	0.00535740i	$0.998295\pi$
$908$	−3.25565e36			−0.344004
$909$	−8.75598e36	−	8.69341e36i	−0.912549	−	0.906028i
$910$	1.36336e37			1.40150
$911$	−5.33751e36	−	9.24484e36i	−0.541202	−	0.937389i	−0.998835	−	0.0482479i	$-0.984636\pi$
$911$	−5.33751e36	−	9.24484e36i	−0.541202	−	0.937389i	0.457634	−	0.889141i	$-0.348697\pi$
$912$	−1.56372e36	−	2.03033e36i	−0.156395	−	0.203063i
$913$	1.57754e35	−	2.73237e35i	0.0155630	−	0.0269560i
$914$	−1.42419e36	+	2.46676e36i	−0.138592	+	0.240049i
$915$	−1.44557e37	+	1.92950e36i	−1.38764	+	0.185217i
$916$	3.12878e36	+	5.41920e36i	0.296265	+	0.513147i
$917$	1.29122e37			1.20610
$918$	−8.26001e36	−	6.26784e36i	−0.761109	−	0.577543i
$919$	1.18007e37			1.07266			0.536331	−	0.844008i	$-0.319810\pi$
$919$	1.18007e37			1.07266			0.536331	+	0.844008i	$0.319810\pi$
$920$	−2.50932e36	−	4.34627e36i	−0.225013	−	0.389734i
$921$	2.64485e36	−	3.53026e35i	0.233968	−	0.0312292i
$922$	−3.67204e36	+	6.36016e36i	−0.320458	+	0.555049i
$923$	−5.44273e36	+	9.42708e36i	−0.468592	+	0.811626i
$924$	1.13761e36	+	1.47707e36i	0.0966256	+	0.125459i
$925$	−3.26043e35	−	5.64723e35i	−0.0273214	−	0.0473221i
$926$	−1.17414e37			−0.970693
$927$	−2.51467e36	+	9.52130e36i	−0.205109	+	0.776604i
$928$	1.29170e36			0.103947
$929$	8.60572e36	+	1.49055e37i	0.683267	+	1.18345i	0.973978	+	0.226643i	$0.0727749\pi$
$929$	8.60572e36	+	1.49055e37i	0.683267	+	1.18345i	−0.290711	+	0.956811i	$0.593892\pi$
$930$	5.44409e36	−	1.32101e37i	0.426470	−	1.03483i
$931$	7.07783e36	−	1.22592e37i	0.547053	−	0.947523i
$932$	4.62686e36	−	8.01396e36i	0.352848	−	0.611150i
$933$	−8.49525e36	+	2.06138e37i	−0.639228	+	1.55109i
$934$	3.22123e36	+	5.57933e36i	0.239158	+	0.414234i
$935$	−3.97675e36			−0.291328
$936$	−1.75901e36	+	6.66013e36i	−0.127151	+	0.481432i
$937$	−1.53160e37			−1.09244			−0.546222	−	0.837640i	$-0.683935\pi$
$937$	−1.53160e37			−1.09244			−0.546222	+	0.837640i	$0.683935\pi$
$938$	−1.20880e36	−	2.09370e36i	−0.0850781	−	0.147360i
$939$	−1.61718e37	−	2.09974e37i	−1.12315	−	1.45830i
$940$	−7.88328e35	+	1.36542e36i	−0.0540267	+	0.0935770i
$941$	−1.31053e37	+	2.26990e37i	−0.886289	+	1.53510i	−0.0420604	+	0.999115i	$0.513392\pi$
$941$	−1.31053e37	+	2.26990e37i	−0.886289	+	1.53510i	−0.844229	+	0.535983i	$0.819941\pi$
$942$	1.52978e37	−	2.04190e36i	1.02092	−	0.136270i
$943$	7.01524e36	+	1.21508e37i	0.462005	+	0.800216i
$944$	4.57629e36			0.297416
$945$	−2.02266e37	+	8.50586e36i	−1.29725	+	0.545532i
$946$	−2.89375e36			−0.183156
$947$	−1.09844e37	−	1.90255e37i	−0.686122	−	1.18840i	−0.973083	−	0.230456i	$-0.925978\pi$
$947$	−1.09844e37	−	1.90255e37i	−0.686122	−	1.18840i	0.286960	−	0.957942i	$-0.407355\pi$
$948$	−3.64192e36	+	4.86111e35i	−0.224505	+	0.0299662i
$949$	−1.39938e37	+	2.42379e37i	−0.851348	+	1.47458i
$950$	−2.53201e35	+	4.38557e35i	−0.0152027	+	0.0263318i
$951$	−1.51986e36	−	1.97339e36i	−0.0900634	−	0.116938i
$952$	5.87203e36	+	1.01707e37i	0.343421	+	0.594822i
$953$	−1.45507e37			−0.839889			−0.419945	−	0.907550i	$-0.637951\pi$
$953$	−1.45507e37			−0.839889			−0.419945	+	0.907550i	$0.637951\pi$
$954$	1.52023e37	+	1.50936e37i	0.866071	+	0.859883i
$955$	2.56268e37			1.44096
$956$	6.10209e36	+	1.05691e37i	0.338653	+	0.586564i
$957$	9.00983e35	−	2.18624e36i	0.0493534	−	0.119756i
$958$	1.10489e37	−	1.91373e37i	0.597381	−	1.03469i
$959$	8.72861e36	−	1.51184e37i	0.465814	−	0.806814i
$960$	8.85017e35	−	2.14750e36i	0.0466188	−	0.113121i
$961$	−1.55324e37	−	2.69029e37i	−0.807599	−	1.39880i
$962$	−2.52806e37			−1.29747
$963$	4.42292e36	−	1.20213e36i	0.224068	−	0.0609008i
$964$	−6.16145e36			−0.308120
$965$	4.20147e36	+	7.27716e36i	0.207401	+	0.359228i
$966$	1.65552e37	+	2.14953e37i	0.806715	+	1.04744i
$967$	7.99476e36	−	1.38473e37i	0.384569	−	0.666094i	−0.607140	−	0.794595i	$-0.707683\pi$
$967$	7.99476e36	−	1.38473e37i	0.384569	−	0.666094i	0.991709	+	0.128501i	$0.0410166\pi$
$968$	3.54214e36	−	6.13516e36i	0.168199	−	0.291329i
$969$	−2.92920e37	+	3.90980e36i	−1.37310	+	0.183277i
$970$	−9.96736e36	−	1.72640e37i	−0.461247	−	0.798903i
$971$	6.76726e36			0.309152			0.154576	−	0.987981i	$-0.450599\pi$
$971$	6.76726e36			0.309152			0.154576	+	0.987981i	$0.450599\pi$
$972$	−1.54555e36	−	1.09783e37i	−0.0697037	−	0.495118i
$973$	2.33871e37			1.04128
$974$	−1.35419e37	−	2.34552e37i	−0.595239	−	1.03098i
$975$	1.34923e36	−	1.80091e35i	0.0585502	−	0.00781509i
$976$	−4.17299e36	+	7.22783e36i	−0.178782	+	0.309660i
$977$	7.73075e36	−	1.33900e37i	0.326994	−	0.566370i	−0.654920	−	0.755698i	$-0.727298\pi$
$977$	7.73075e36	−	1.33900e37i	0.326994	−	0.566370i	0.981914	+	0.189328i	$0.0606311\pi$
$978$	9.73278e36	+	1.26370e37i	0.406444	+	0.527727i
$979$	1.17723e36	+	2.03902e36i	0.0485376	+	0.0840696i
$980$	1.28300e37			0.522278
$981$	2.06464e37	−	5.61160e36i	0.829817	−	0.225540i
$982$	5.14507e36			0.204173
$983$	−1.00444e37	−	1.73974e37i	−0.393555	−	0.681657i	0.599361	−	0.800479i	$-0.295421\pi$
$983$	−1.00444e37	−	1.73974e37i	−0.393555	−	0.681657i	−0.992916	+	0.118822i	$0.962088\pi$
$984$	−2.47422e36	+	6.00372e36i	−0.0957194	+	0.232264i
$985$	1.35202e37	−	2.34177e37i	0.516452	−	0.894522i
$986$	7.44762e36	−	1.28997e37i	0.280903	−	0.486538i
$987$	3.24774e36	−	7.88066e36i	0.120953	−	0.293493i
$988$	9.81629e36	+	1.70023e37i	0.360982	+	0.625239i
$989$	−4.21117e37			−1.52915
$990$	−3.01739e36	−	2.99583e36i	−0.108191	−	0.107418i
$991$	3.83890e37			1.35921			0.679604	−	0.733579i	$-0.262152\pi$
$991$	3.83890e37			1.35921			0.679604	+	0.733579i	$0.262152\pi$
$992$	−4.08830e36	−	7.08115e36i	−0.142938	−	0.247576i
$993$	2.35189e37	+	3.05369e37i	0.811991	+	1.05429i
$994$	−9.92149e36	+	1.71845e37i	−0.338257	+	0.585879i
$995$	−5.95818e36	+	1.03199e37i	−0.200597	+	0.347445i
$996$	2.10634e36	−	2.81147e35i	0.0700303	−	0.00934741i
$997$	1.08622e37	+	1.88139e37i	0.356639	+	0.617717i	0.987397	−	0.158263i	$-0.0505893\pi$
$997$	1.08622e37	+	1.88139e37i	0.356639	+	0.617717i	−0.630758	+	0.775979i	$0.717256\pi$
$998$	−2.76910e37			−0.897855
$999$	3.75060e37	−	1.57723e37i	1.20097	−	0.505042i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	18.26.c.b.13.2	yes	26
3.2	odd	2		54.26.c.b.37.10		26
9.2	odd	6		54.26.c.b.19.10		26
9.7	even	3	inner	18.26.c.b.7.2	✓	26

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
18.26.c.b.7.2	✓	26	9.7	even	3	inner
18.26.c.b.13.2	yes	26	1.1	even	1	trivial
54.26.c.b.19.10		26	9.2	odd	6
54.26.c.b.37.10		26	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 18 = 2 \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 26 \)
Character orbit:	\([\chi]\)	\(=\)	18.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2048.00 - 3547.24i) q^{2} +(-912391. + 121783. i) q^{3} +(-8.38861e6 + 1.45295e7i) q^{4} +(-2.67172e8 + 4.62756e8i) q^{5} +(2.30057e9 + 2.98706e9i) q^{6} +(-2.63260e10 - 4.55979e10i) q^{7} +6.87195e10 q^{8} +(8.17626e11 - 2.22227e11i) q^{9} +2.18867e12 q^{10} +(-1.14644e12 - 1.98570e12i) q^{11} +(5.88425e12 - 1.42782e13i) q^{12} +(-5.91540e13 + 1.02458e14i) q^{13} +(-1.07831e14 + 1.86769e14i) q^{14} +(1.87410e14 - 4.54751e14i) q^{15} +(-1.40737e14 - 2.43764e14i) q^{16} -3.24582e15 q^{17} +(-2.46279e15 - 2.44520e15i) q^{18} -9.89108e15 q^{19} +(-4.48240e15 - 7.76375e15i) q^{20} +(2.95726e16 + 3.83971e16i) q^{21} +(-4.69583e15 + 8.13342e15i) q^{22} +(-6.83368e16 + 1.18363e17i) q^{23} +(-6.26990e16 + 8.36886e15i) q^{24} +(6.24973e15 + 1.08249e16i) q^{25} +4.84589e17 q^{26} +(-7.18932e17 + 3.02331e17i) q^{27} +8.83353e17 q^{28} +(-5.60187e17 - 9.70272e17i) q^{29} +(-1.99693e18 + 2.66543e17i) q^{30} +(-3.54604e18 + 6.14192e18i) q^{31} +(-5.76461e17 + 9.98459e17i) q^{32} +(1.28783e18 + 1.67212e18i) q^{33} +(6.64744e18 + 1.15137e19i) q^{34} +2.81342e19 q^{35} +(-3.62990e18 + 1.37439e19i) q^{36} -5.21691e19 q^{37} +(2.02569e19 + 3.50860e19i) q^{38} +(4.14940e19 - 1.00685e20i) q^{39} +(-1.83599e19 + 3.18003e19i) q^{40} +(5.13284e19 - 8.89035e19i) q^{41} +(7.56389e19 - 1.83538e20i) q^{42} +(1.54059e20 + 2.66839e20i) q^{43} +3.84682e19 q^{44} +(-1.15610e20 + 4.37734e20i) q^{45} +5.59815e20 q^{46} +(-8.79358e19 - 1.52309e20i) q^{47} +(1.58094e20 + 2.05269e20i) q^{48} +(-7.15578e20 + 1.23942e21i) q^{49} +(2.55989e19 - 4.43386e19i) q^{50} +(2.96146e21 - 3.95286e20i) q^{51} +(-9.92439e20 - 1.71895e21i) q^{52} -6.17278e21 q^{53} +(2.54481e21 + 1.93105e21i) q^{54} +1.22519e21 q^{55} +(-1.80911e21 - 3.13346e21i) q^{56} +(9.02453e21 - 1.20456e21i) q^{57} +(-2.29453e21 + 3.97424e21i) q^{58} +(-8.12913e21 + 1.40801e22i) q^{59} +(5.03520e21 + 6.53770e21i) q^{60} +(-1.48254e22 - 2.56784e22i) q^{61} +2.90492e22 q^{62} +(-3.16579e22 - 3.14317e22i) q^{63} +4.72237e21 q^{64} +(-3.16086e22 - 5.47477e22i) q^{65} +(3.29392e21 - 7.99273e21i) q^{66} +(-5.60505e21 + 9.70822e21i) q^{67} +(2.72279e22 - 4.71601e22i) q^{68} +(4.79353e22 - 1.16315e23i) q^{69} +(-5.76189e22 - 9.97989e22i) q^{70} +9.20095e22 q^{71} +(5.61869e22 - 1.52713e22i) q^{72} +2.36565e23 q^{73} +(1.06842e23 + 1.85056e23i) q^{74} +(-7.02048e21 - 9.11539e21i) q^{75} +(8.29724e22 - 1.43712e23i) q^{76} +(-6.03624e22 + 1.04551e23i) q^{77} +(-4.42135e23 + 5.90147e22i) q^{78} +(-1.18959e23 - 2.06044e23i) q^{79} +1.50405e23 q^{80} +(6.19128e23 - 3.63398e23i) q^{81} -4.20483e23 q^{82} +(6.88013e22 + 1.19167e23i) q^{83} +(-8.05963e23 + 1.07577e23i) q^{84} +(8.67193e23 - 1.50202e24i) q^{85} +(6.31027e23 - 1.09297e24i) q^{86} +(6.29272e23 + 8.17047e23i) q^{87} +(-7.87829e22 - 1.36456e23i) q^{88} -1.02686e24 q^{89} +(1.78952e24 - 4.86383e23i) q^{90} +6.22914e24 q^{91} +(-1.14650e24 - 1.98580e24i) q^{92} +(2.48739e24 - 6.03568e24i) q^{93} +(-3.60185e23 + 6.23859e23i) q^{94} +(2.64262e24 - 4.57715e24i) q^{95} +(4.04362e23 - 9.81188e23i) q^{96} +(-4.55407e24 - 7.88787e24i) q^{97} +5.86201e24 q^{98} +(-1.37864e24 - 1.36879e24i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 26 q - 53248 q^{2} + 151593 q^{3} - 218103808 q^{4} + 49854096 q^{5} + 768700416 q^{6} - 35213963498 q^{7} + 1786706395136 q^{8} - 906685440585 q^{9} - 408404754432 q^{10} - 1998346177329 q^{11} - 5691905409024 q^{12}+ \cdots + 19\!\cdots\!26 q^{99}+O(q^{100}) \) 26 * q - 53248 * q^2 + 151593 * q^3 - 218103808 * q^4 + 49854096 * q^5 + 768700416 * q^6 - 35213963498 * q^7 + 1786706395136 * q^8 - 906685440585 * q^9 - 408404754432 * q^10 - 1998346177329 * q^11 - 5691905409024 * q^12 - 158355783504242 * q^13 - 144236394487808 * q^14 + 757025799267528 * q^15 - 3659174697238528 * q^16 + 3616705586624034 * q^17 - 4642789512634368 * q^18 - 5058456299228762 * q^19 + 836412937076736 * q^20 - 29294425090653330 * q^21 - 8185225942339584 * q^22 - 155570710082203362 * q^23 + 10417391636840448 * q^24 - 888197302847183911 * q^25 + 1297250578466750464 * q^26 - 128834992514474784 * q^27 + 1181584543644123136 * q^28 - 3925320594794185038 * q^29 + 1179164452501389312 * q^30 - 6592704741949460996 * q^31 - 14987979559889010688 * q^32 - 32016980184606395901 * q^33 - 7407013041406021632 * q^34 - 49533545961137501568 * q^35 + 34228523324500082688 * q^36 + 78961008772462984600 * q^37 + 10359718500820504576 * q^38 + 95123937845402314992 * q^39 + 3425947390266310656 * q^40 - 13758002834178626109 * q^41 - 84162935852722520064 * q^42 - 191473700412044564123 * q^43 + 67053370919645872128 * q^44 - 785051209702697530104 * q^45 + 1274435256993409941504 * q^46 + 154470707996501871078 * q^47 + 52824690354265522176 * q^48 - 1713680737743395735817 * q^49 - 3638056152462065299456 * q^50 - 6870371606317236873627 * q^51 - 2656769184699904950272 * q^52 - 1171350014833338971736 * q^53 + 6559921495334108123136 * q^54 + 23890981280754645933408 * q^55 - 2419885145383164182528 * q^56 + 10363602109274891230719 * q^57 - 16078113156276981915648 * q^58 + 545848631253825283329 * q^59 - 17530642949329649664000 * q^60 - 10067352509024211048296 * q^61 + 54007437246049984479232 * q^62 - 73084560995643274477092 * q^63 + 122781528554610775556096 * q^64 + 12640794081283966054032 * q^65 + 110029145383180853084160 * q^66 + 79389140801664567200479 * q^67 - 30339125417599064604672 * q^68 + 374832866262531575458800 * q^69 + 101444702128409603211264 * q^70 + 415430508733527088013160 * q^71 - 62306949041150817730560 * q^72 - 539343970915021400375282 * q^73 - 161712145966004192460800 * q^74 + 441981606129534342907005 * q^75 + 42433406979360786743296 * q^76 - 327594537754607633577834 * q^77 - 746813223797009911111680 * q^78 + 611076271613290617275908 * q^79 - 28065361021061616893952 * q^80 + 2402122114376356742905779 * q^81 + 112705559217591305084928 * q^82 - 400615093454630506593780 * q^83 + 836210282594461940711424 * q^84 - 1703025287061576739254000 * q^85 - 784276276887734534647808 * q^86 - 11524978140836672774065086 * q^87 - 137325303643434746118144 * q^88 + 18509149037385930189952524 * q^89 + 4759337318576276074954752 * q^90 + 10266453492659369810870360 * q^91 - 2610043406322503560200192 * q^92 + 21848889054937494966552000 * q^93 + 632712019953671663935488 * q^94 - 16882199861176698021554184 * q^95 - 391144761338937332465664 * q^96 + 3205637813401802510221951 * q^97 + 14038472603593897867812864 * q^98 + 19880662798402511958071226 * q^99

Introduction

L-functions

Modular forms

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Database

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