LMFDB - Embedded newform 18.26.c.b.13.4

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			13.4
Character	$\chi$	$=$	18.13
Dual form			18.26.c.b.7.4

$q$-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} +(-539595. - 745739. i) q^{3} +(-8.38861e6 + 1.45295e7i) q^{4} +(1.32723e8 - 2.29884e8i) q^{5} +(-1.54022e9 + 3.44134e9i) q^{6} +(1.71990e10 + 2.97895e10i) q^{7} +6.87195e10 q^{8} +(-2.64964e11 + 8.04793e11i) q^{9} -1.08727e12 q^{10} +(2.36007e12 + 4.08776e12i) q^{11} +(1.53617e13 - 1.58433e12i) q^{12} +(-7.65246e13 + 1.32545e14i) q^{13} +(7.04470e13 - 1.22018e14i) q^{14} +(-2.43050e14 + 2.50670e13i) q^{15} +(-1.40737e14 - 2.43764e14i) q^{16} +3.04534e15 q^{17} +(3.39744e15 - 7.08326e14i) q^{18} -1.34946e16 q^{19} +(2.22673e15 + 3.85681e15i) q^{20} +(1.29347e16 - 2.89002e16i) q^{21} +(9.66685e15 - 1.67435e16i) q^{22} +(-2.18045e16 + 3.77665e16i) q^{23} +(-3.70807e16 - 5.12468e16i) q^{24} +(1.13781e17 + 1.97074e17i) q^{25} +6.26890e17 q^{26} +(7.43139e17 - 2.36668e17i) q^{27} -5.77102e17 q^{28} +(-1.77130e18 - 3.06797e18i) q^{29} +(5.86685e17 + 8.10819e17i) q^{30} +(3.31858e18 - 5.74794e18i) q^{31} +(-5.76461e17 + 9.98459e17i) q^{32} +(1.77492e18 - 3.96573e18i) q^{33} +(-6.23686e18 - 1.08026e19i) q^{34} +9.13082e18 q^{35} +(-9.47056e18 - 1.06009e19i) q^{36} -4.38443e19 q^{37} +(2.76370e19 + 4.78686e19i) q^{38} +(1.40136e20 - 1.44530e19i) q^{39} +(9.12068e18 - 1.57975e19i) q^{40} +(-1.03447e19 + 1.79175e19i) q^{41} +(-1.29006e20 + 1.33051e19i) q^{42} +(-4.98521e19 - 8.63463e19i) q^{43} -7.91908e19 q^{44} +(1.49842e20 + 1.67726e20i) q^{45} +1.78622e20 q^{46} +(-2.23292e20 - 3.86754e20i) q^{47} +(-1.05843e20 + 2.36487e20i) q^{48} +(7.89248e19 - 1.36702e20i) q^{49} +(4.66045e20 - 8.07214e20i) q^{50} +(-1.64325e21 - 2.27103e21i) q^{51} +(-1.28387e21 - 2.22373e21i) q^{52} +4.84464e21 q^{53} +(-2.36147e21 - 2.15139e21i) q^{54} +1.25295e21 q^{55} +(1.18190e21 + 2.04712e21i) q^{56} +(7.28162e21 + 1.00634e22i) q^{57} +(-7.25522e21 + 1.25664e22i) q^{58} +(2.56635e21 - 4.44505e21i) q^{59} +(1.67464e21 - 3.74167e21i) q^{60} +(-8.18264e21 - 1.41727e22i) q^{61} -2.71858e22 q^{62} +(-2.85315e22 + 5.94848e21i) q^{63} +4.72237e21 q^{64} +(2.03132e22 + 3.51835e22i) q^{65} +(-1.77024e22 + 1.82575e21i) q^{66} +(-4.45640e22 + 7.71871e22i) q^{67} +(-2.55462e22 + 4.42473e22i) q^{68} +(3.99295e22 - 4.11814e21i) q^{69} +(-1.86999e22 - 3.23892e22i) q^{70} -1.00409e23 q^{71} +(-1.82082e22 + 5.53050e22i) q^{72} -3.45994e23 q^{73} +(8.97932e22 + 1.55526e23i) q^{74} +(8.55702e22 - 1.91191e23i) q^{75} +(1.13201e23 - 1.96070e23i) q^{76} +(-8.11816e22 + 1.40611e23i) q^{77} +(-3.38266e23 - 4.67496e23i) q^{78} +(1.58647e23 + 2.74785e23i) q^{79} -7.47166e22 q^{80} +(-5.77486e23 - 4.26482e23i) q^{81} +8.47436e22 q^{82} +(-8.67339e23 - 1.50228e24i) q^{83} +(3.11401e23 + 4.30367e23i) q^{84} +(4.04188e23 - 7.00075e23i) q^{85} +(-2.04194e23 + 3.53675e23i) q^{86} +(-1.33212e24 + 2.97639e24i) q^{87} +(1.62183e23 + 2.80909e23i) q^{88} -9.46991e23 q^{89} +(2.88087e23 - 8.75027e23i) q^{90} -5.26458e24 q^{91} +(-3.65819e23 - 6.33617e23i) q^{92} +(-6.07715e24 + 6.26768e23i) q^{93} +(-9.14605e23 + 1.58414e24i) q^{94} +(-1.79105e24 + 3.10219e24i) q^{95} +(1.05564e24 - 1.08874e23i) q^{96} +(7.88434e23 + 1.36561e24i) q^{97} -6.46552e23 q^{98} +(-3.91514e24 + 8.16260e23i) 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
$3$	−539595.	−	745739.i	−0.586208	−	0.810160i
$3$	−539595.	−	745739.i	−0.586208	−	0.810160i
$4$	−8.38861e6	+	1.45295e7i	−0.250000	+	0.433013i
$5$	1.32723e8	−	2.29884e8i	0.243121	−	0.421098i	−0.718481	−	0.695547i	$-0.755162\pi$
$5$	1.32723e8	−	2.29884e8i	0.243121	−	0.421098i	0.961602	+	0.274449i	$0.0884955\pi$
$6$	−1.54022e9	+	3.44134e9i	−0.288864	+	0.645413i
$7$	1.71990e10	+	2.97895e10i	0.469653	+	0.813463i	0.999398	−	0.0346941i	$-0.0110457\pi$
$7$	1.71990e10	+	2.97895e10i	0.469653	+	0.813463i	−0.529745	+	0.848157i	$0.677712\pi$
$8$	6.87195e10			0.353553
$9$	−2.64964e11	+	8.04793e11i	−0.312720	+	0.949845i
$10$	−1.08727e12			−0.343825
$11$	2.36007e12	+	4.08776e12i	0.226734	+	0.392714i	0.956838	−	0.290621i	$-0.0938619\pi$
$11$	2.36007e12	+	4.08776e12i	0.226734	+	0.392714i	−0.730104	+	0.683336i	$0.760529\pi$
$12$	1.53617e13	−	1.58433e12i	0.497362	−	0.0512956i
$13$	−7.65246e13	+	1.32545e14i	−0.910981	+	1.57787i	−0.0982994	+	0.995157i	$0.531340\pi$
$13$	−7.65246e13	+	1.32545e14i	−0.910981	+	1.57787i	−0.812681	+	0.582708i	$0.801993\pi$
$14$	7.04470e13	−	1.22018e14i	0.332095	−	0.575205i
$15$	−2.43050e14	+	2.50670e13i	−0.483676	+	0.0498841i
$16$	−1.40737e14	−	2.43764e14i	−0.125000	−	0.216506i
$17$	3.04534e15			1.26772			0.633862	−	0.773446i	$-0.281469\pi$
$17$	3.04534e15			1.26772			0.633862	+	0.773446i	$0.281469\pi$
$18$	3.39744e15	−	7.08326e14i	0.692222	−	0.144320i
$19$	−1.34946e16			−1.39875			−0.699375	−	0.714755i	$-0.746538\pi$
$19$	−1.34946e16			−1.39875			−0.699375	+	0.714755i	$0.746538\pi$
$20$	2.22673e15	+	3.85681e15i	0.121560	+	0.210549i
$21$	1.29347e16	−	2.89002e16i	0.383721	−	0.857353i
$22$	9.66685e15	−	1.67435e16i	0.160325	−	0.277691i
$23$	−2.18045e16	+	3.77665e16i	−0.207467	+	0.359343i	−0.950916	−	0.309450i	$-0.899855\pi$
$23$	−2.18045e16	+	3.77665e16i	−0.207467	+	0.359343i	0.743449	+	0.668792i	$0.233189\pi$
$24$	−3.70807e16	−	5.12468e16i	−0.207256	−	0.286435i
$25$	1.13781e17	+	1.97074e17i	0.381784	+	0.661270i
$26$	6.26890e17			1.28832
$27$	7.43139e17	−	2.36668e17i	0.952846	−	0.303454i
$28$	−5.77102e17			−0.469653
$29$	−1.77130e18	−	3.06797e18i	−0.929642	−	1.61019i	−0.783920	−	0.620862i	$-0.786783\pi$
$29$	−1.77130e18	−	3.06797e18i	−0.929642	−	1.61019i	−0.145723	−	0.989325i	$-0.546551\pi$
$30$	5.86685e17	+	8.10819e17i	0.201553	+	0.278553i
$31$	3.31858e18	−	5.74794e18i	0.756712	−	1.31066i	−0.187807	−	0.982206i	$-0.560138\pi$
$31$	3.31858e18	−	5.74794e18i	0.756712	−	1.31066i	0.944519	−	0.328457i	$-0.106529\pi$
$32$	−5.76461e17	+	9.98459e17i	−0.0883883	+	0.153093i
$33$	1.77492e18	−	3.96573e18i	0.185248	−	0.413903i
$34$	−6.23686e18	−	1.08026e19i	−0.448208	−	0.776319i
$35$	9.13082e18			0.456730
$36$	−9.47056e18	−	1.06009e19i	−0.333115	−	0.372873i
$37$	−4.38443e19			−1.09494			−0.547472	−	0.836824i	$-0.684410\pi$
$37$	−4.38443e19			−1.09494			−0.547472	+	0.836824i	$0.684410\pi$
$38$	2.76370e19	+	4.78686e19i	0.494533	+	0.856556i
$39$	1.40136e20	−	1.44530e19i	1.81235	−	0.186917i
$40$	9.12068e18	−	1.57975e19i	0.0859562	−	0.148881i
$41$	−1.03447e19	+	1.79175e19i	−0.0716010	+	0.124017i	−0.899603	−	0.436708i	$-0.856144\pi$
$41$	−1.03447e19	+	1.79175e19i	−0.0716010	+	0.124017i	0.828002	+	0.560725i	$0.189477\pi$
$42$	−1.29006e20	+	1.33051e19i	−0.660685	+	0.0681399i
$43$	−4.98521e19	−	8.63463e19i	−0.190251	−	0.329525i	0.755082	−	0.655630i	$-0.227597\pi$
$43$	−4.98521e19	−	8.63463e19i	−0.190251	−	0.329525i	−0.945333	+	0.326105i	$0.894264\pi$
$44$	−7.91908e19			−0.226734
$45$	1.49842e20	+	1.67726e20i	0.323949	+	0.362613i
$46$	1.78622e20			0.293402
$47$	−2.23292e20	−	3.86754e20i	−0.280318	−	0.485524i	0.691145	−	0.722716i	$-0.257106\pi$
$47$	−2.23292e20	−	3.86754e20i	−0.280318	−	0.485524i	−0.971463	+	0.237191i	$0.923773\pi$
$48$	−1.05843e20	+	2.36487e20i	−0.102129	+	0.228188i
$49$	7.89248e19	−	1.36702e20i	0.0588521	−	0.101935i
$50$	4.66045e20	−	8.07214e20i	0.269962	−	0.467589i
$51$	−1.64325e21	−	2.27103e21i	−0.743150	−	1.02706i
$52$	−1.28387e21	−	2.22373e21i	−0.455490	−	0.788933i
$53$	4.84464e21			1.35461			0.677303	−	0.735705i	$-0.263149\pi$
$53$	4.84464e21			1.35461			0.677303	+	0.735705i	$0.263149\pi$
$54$	−2.36147e21	−	2.15139e21i	−0.522709	−	0.476209i
$55$	1.25295e21			0.220495
$56$	1.18190e21	+	2.04712e21i	0.166047	+	0.287603i
$57$	7.28162e21	+	1.00634e22i	0.819959	+	1.13321i
$58$	−7.25522e21	+	1.25664e22i	−0.657356	+	1.13857i
$59$	2.56635e21	−	4.44505e21i	0.187787	−	0.325257i	−0.756725	−	0.653733i	$-0.773202\pi$
$59$	2.56635e21	−	4.44505e21i	0.187787	−	0.325257i	0.944512	+	0.328476i	$0.106535\pi$
$60$	1.67464e21	−	3.74167e21i	0.0993186	−	0.221909i
$61$	−8.18264e21	−	1.41727e22i	−0.394703	−	0.683646i	0.598360	−	0.801227i	$-0.295819\pi$
$61$	−8.18264e21	−	1.41727e22i	−0.394703	−	0.683646i	−0.993063	+	0.117582i	$0.962486\pi$
$62$	−2.71858e22			−1.07015
$63$	−2.85315e22	+	5.94848e21i	−0.919534	+	0.191712i
$64$	4.72237e21			0.125000
$65$	2.03132e22	+	3.51835e22i	0.442957	+	0.767224i
$66$	−1.77024e22	+	1.82575e21i	−0.318958	+	0.0328958i
$67$	−4.45640e22	+	7.71871e22i	−0.665348	+	1.15242i	0.313842	+	0.949475i	$0.398384\pi$
$67$	−4.45640e22	+	7.71871e22i	−0.665348	+	1.15242i	−0.979191	+	0.202942i	$0.934950\pi$
$68$	−2.55462e22	+	4.42473e22i	−0.316931	+	0.548941i
$69$	3.99295e22	−	4.11814e21i	0.412744	−	0.0425685i
$70$	−1.86999e22	−	3.23892e22i	−0.161478	−	0.279689i
$71$	−1.00409e23			−0.726179			−0.363089	−	0.931754i	$-0.618278\pi$
$71$	−1.00409e23			−0.726179			−0.363089	+	0.931754i	$0.618278\pi$
$72$	−1.82082e22	+	5.53050e22i	−0.110563	+	0.335821i
$73$	−3.45994e23			−1.76820			−0.884102	−	0.467294i	$-0.845229\pi$
$73$	−3.45994e23			−1.76820			−0.884102	+	0.467294i	$0.845229\pi$
$74$	8.97932e22	+	1.55526e23i	0.387121	+	0.670514i
$75$	8.55702e22	−	1.91191e23i	0.311930	−	0.696949i
$76$	1.13201e23	−	1.96070e23i	0.349688	−	0.605677i
$77$	−8.11816e22	+	1.40611e23i	−0.212972	+	0.368879i
$78$	−3.38266e23	−	4.67496e23i	−0.755225	−	1.04375i
$79$	1.58647e23	+	2.74785e23i	0.302060	+	0.523184i	0.976602	−	0.215053i	$-0.0689923\pi$
$79$	1.58647e23	+	2.74785e23i	0.302060	+	0.523184i	−0.674542	+	0.738236i	$0.735659\pi$
$80$	−7.47166e22			−0.121560
$81$	−5.77486e23	−	4.26482e23i	−0.804413	−	0.594071i
$82$	8.47436e22			0.101259
$83$	−8.67339e23	−	1.50228e24i	−0.890662	−	1.54267i	−0.839083	−	0.544003i	$-0.816908\pi$
$83$	−8.67339e23	−	1.50228e24i	−0.890662	−	1.54267i	−0.0515784	−	0.998669i	$-0.516425\pi$
$84$	3.11401e23	+	4.30367e23i	0.275314	+	0.380494i
$85$	4.04188e23	−	7.00075e23i	0.308210	−	0.533836i
$86$	−2.04194e23	+	3.53675e23i	−0.134528	+	0.233009i
$87$	−1.33212e24	+	2.97639e24i	−0.759546	+	1.69706i
$88$	1.62183e23	+	2.80909e23i	0.0801625	+	0.138846i
$89$	−9.46991e23			−0.406416			−0.203208	−	0.979136i	$-0.565137\pi$
$89$	−9.46991e23			−0.406416			−0.203208	+	0.979136i	$0.565137\pi$
$90$	2.88087e23	−	8.75027e23i	0.107521	−	0.326581i
$91$	−5.26458e24			−1.71138
$92$	−3.65819e23	−	6.33617e23i	−0.103733	−	0.179671i
$93$	−6.07715e24	+	6.26768e23i	−1.50544	+	0.155264i
$94$	−9.14605e23	+	1.58414e24i	−0.198215	+	0.343318i
$95$	−1.79105e24	+	3.10219e24i	−0.340065	+	0.589011i
$96$	1.05564e24	−	1.08874e23i	0.175844	−	0.0181357i
$97$	7.88434e23	+	1.36561e24i	0.115377	+	0.199839i	0.917930	−	0.396742i	$-0.129859\pi$
$97$	7.88434e23	+	1.36561e24i	0.115377	+	0.199839i	−0.802553	+	0.596580i	$0.796526\pi$
$98$	−6.46552e23			−0.0832295
$99$	−3.91514e24	+	8.16260e23i	−0.443922	+	0.0925525i
$100$	−3.81784e24			−0.381784
$101$	4.23384e24	+	7.33323e24i	0.373867	+	0.647557i	0.990157	−	0.139963i	$-0.0446983\pi$
$101$	4.23384e24	+	7.33323e24i	0.373867	+	0.647557i	−0.616290	+	0.787520i	$0.711365\pi$
$102$	−4.69051e24	+	1.04801e25i	−0.366200	+	0.818205i
$103$	6.13560e24	−	1.06272e25i	0.424025	−	0.734433i	−0.572304	−	0.820042i	$-0.693950\pi$
$103$	6.13560e24	−	1.06272e25i	0.424025	−	0.734433i	0.996329	+	0.0856089i	$0.0272835\pi$
$104$	−5.25873e24	+	9.10839e24i	−0.322080	+	0.557860i
$105$	−4.92694e24	−	6.80921e24i	−0.267739	−	0.370024i
$106$	−9.92181e24	−	1.71851e25i	−0.478925	−	0.829523i
$107$	−9.32764e24			−0.400382			−0.200191	−	0.979757i	$-0.564156\pi$
$107$	−9.32764e24			−0.400382			−0.200191	+	0.979757i	$0.564156\pi$
$108$	−2.79523e24	+	1.27827e25i	−0.106812	+	0.488458i
$109$	1.87852e25			0.639711			0.319856	−	0.947466i	$-0.396366\pi$
$109$	1.87852e25			0.639711			0.319856	+	0.947466i	$0.396366\pi$
$110$	−2.56603e24	−	4.44450e24i	−0.0779567	−	0.135025i
$111$	2.36582e25	+	3.26964e25i	0.641865	+	0.887080i
$112$	4.84108e24	−	8.38500e24i	0.117413	−	0.203366i
$113$	2.40021e25	−	4.15728e25i	0.520917	−	0.902254i	−0.478787	−	0.877931i	$-0.658923\pi$
$113$	2.40021e25	−	4.15728e25i	0.520917	−	0.902254i	0.999704	−	0.0243235i	$-0.00774317\pi$
$114$	2.07847e25	−	4.64396e25i	0.404049	−	0.902771i
$115$	5.78793e24	+	1.00250e25i	0.100879	+	0.174727i
$116$	5.94348e25			0.929642
$117$	−8.63947e25	−	9.67060e25i	−1.21385	−	1.35872i
$118$	−2.10235e25			−0.265571
$119$	5.23768e25	+	9.07193e25i	0.595390	+	1.03125i
$120$	−1.67023e25	+	1.72259e24i	−0.171005	+	0.0176367i
$121$	4.30337e25	−	7.45365e25i	0.397184	−	0.687942i
$122$	−3.35161e25	+	5.80516e25i	−0.279097	+	0.483410i
$123$	1.89437e25	−	1.95377e24i	0.142446	−	0.0146912i
$124$	5.56765e25	+	9.64345e25i	0.378356	+	0.655332i
$125$	1.39515e26			0.857521
$126$	7.95332e25	+	8.90256e25i	0.442503	+	0.495317i
$127$	1.71215e26			0.862970			0.431485	−	0.902120i	$-0.357990\pi$
$127$	1.71215e26			0.862970			0.431485	+	0.902120i	$0.357990\pi$
$128$	−9.67141e24	−	1.67514e25i	−0.0441942	−	0.0765466i
$129$	−3.74919e25	+	8.37686e25i	−0.155441	+	0.347304i
$130$	8.32029e25	−	1.44112e26i	0.313218	−	0.542509i
$131$	6.13452e25	−	1.06253e26i	0.209841	−	0.363454i	−0.741824	−	0.670595i	$-0.766039\pi$
$131$	6.13452e25	−	1.06253e26i	0.209841	−	0.363454i	0.951664	+	0.307141i	$0.0993722\pi$
$132$	4.27309e25	+	5.90556e25i	0.132913	+	0.183691i
$133$	−2.32093e26	−	4.01998e26i	−0.656927	−	1.13783i
$134$	3.65068e26			0.940945
$135$	4.42257e25	−	2.02247e26i	0.103873	−	0.475017i
$136$	2.09274e26			0.448208
$137$	3.33562e26	+	5.77747e26i	0.651883	+	1.12909i	0.982665	+	0.185388i	$0.0593540\pi$
$137$	3.33562e26	+	5.77747e26i	0.651883	+	1.12909i	−0.330782	+	0.943707i	$0.607313\pi$
$138$	−9.63837e25	−	1.33206e26i	−0.171995	−	0.237703i
$139$	2.83147e26	−	4.90426e26i	0.461666	−	0.799628i	−0.537379	−	0.843341i	$-0.680585\pi$
$139$	2.83147e26	−	4.90426e26i	0.461666	−	0.799628i	0.999044	+	0.0437129i	$0.0139187\pi$
$140$	−7.65949e25	+	1.32666e26i	−0.114182	+	0.197770i
$141$	−1.67930e26	+	3.75208e26i	−0.229028	+	0.511721i
$142$	2.05638e26	+	3.56175e26i	0.256743	+	0.444692i
$143$	−7.22414e26			−0.826201
$144$	2.33470e26	−	4.86758e25i	0.244738	−	0.0510249i
$145$	−9.40369e26			−0.904062
$146$	7.08595e26	+	1.22732e27i	0.625154	+	1.08280i
$147$	−1.44531e26	+	1.49063e25i	−0.117083	+	0.0120754i
$148$	3.67793e26	−	6.37036e26i	0.273736	−	0.474125i
$149$	5.55749e26	−	9.62585e26i	0.380233	−	0.658583i	−0.610862	−	0.791737i	$-0.709177\pi$
$149$	5.55749e26	−	9.62585e26i	0.380233	−	0.658583i	0.991095	+	0.133154i	$0.0425104\pi$
$150$	−8.53447e26	+	8.80205e25i	−0.537076	+	0.0553915i
$151$	−3.78651e26	−	6.55843e26i	−0.219294	−	0.379829i	0.735298	−	0.677744i	$-0.237042\pi$
$151$	−3.78651e26	−	6.55843e26i	−0.219294	−	0.379829i	−0.954592	+	0.297915i	$0.903709\pi$
$152$	−9.27342e26			−0.494533
$153$	−8.06906e26	+	2.45087e27i	−0.396442	+	1.20414i
$154$	6.65039e26			0.301188
$155$	−8.80905e26	−	1.52577e27i	−0.367945	−	0.637299i
$156$	−9.65551e26	+	2.15734e27i	−0.372150	+	0.831499i
$157$	−4.05457e26	+	7.02271e26i	−0.144278	+	0.249896i	−0.929103	−	0.369821i	$-0.879419\pi$
$157$	−4.05457e26	+	7.02271e26i	−0.144278	+	0.249896i	0.784826	+	0.619717i	$0.212752\pi$
$158$	6.49819e26	−	1.12552e27i	0.213589	−	0.369947i
$159$	−2.61414e27	−	3.61283e27i	−0.794081	−	1.09745i
$160$	1.53020e26	+	2.65038e26i	0.0429781	+	0.0744403i
$161$	−1.50006e27			−0.389749
$162$	−3.30142e26	+	2.92192e27i	−0.0793896	+	0.702636i
$163$	4.58614e27			1.02118			0.510590	−	0.859824i	$-0.329427\pi$
$163$	4.58614e27			1.02118			0.510590	+	0.859824i	$0.329427\pi$
$164$	−1.73555e26	−	3.00606e26i	−0.0358005	−	0.0620083i
$165$	−6.76083e26	−	9.34370e26i	−0.129256	−	0.178636i
$166$	−3.55262e27	+	6.15332e27i	−0.629793	+	1.09083i
$167$	−3.98366e27	+	6.89990e27i	−0.655129	+	1.13472i	0.326733	+	0.945117i	$0.394052\pi$
$167$	−3.98366e27	+	6.89990e27i	−0.655129	+	1.13472i	−0.981862	+	0.189599i	$0.939281\pi$
$168$	8.88866e26	−	1.98601e27i	0.135666	−	0.303120i
$169$	−8.18383e27	−	1.41748e28i	−1.15977	−	2.00878i
$170$	−3.31111e27			−0.435875
$171$	3.57558e27	−	1.08604e28i	0.437417	−	1.32860i
$172$	1.67276e27			0.190251
$173$	−4.54830e27	−	7.87788e27i	−0.481141	−	0.833361i	0.518625	−	0.855002i	$-0.326444\pi$
$173$	−4.54830e27	−	7.87788e27i	−0.481141	−	0.833361i	−0.999766	+	0.0216410i	$0.993111\pi$
$174$	1.32861e28	−	1.37027e27i	1.30778	−	0.134878i
$175$	−3.91382e27	+	6.77894e27i	−0.358612	+	0.621135i
$176$	6.64301e26	−	1.15060e27i	0.0566834	−	0.0981786i
$177$	−4.69964e27	+	4.84698e26i	−0.373593	+	0.0385306i
$178$	1.93944e27	+	3.35921e27i	0.143690	+	0.248878i
$179$	−1.04876e28			−0.724459			−0.362229	−	0.932089i	$-0.617984\pi$
$179$	−1.04876e28			−0.724459			−0.362229	+	0.932089i	$0.617984\pi$
$180$	−3.69394e27	+	7.70142e26i	−0.238003	+	0.0496209i
$181$	−1.06095e28			−0.637839			−0.318920	−	0.947782i	$-0.603320\pi$
$181$	−1.06095e28			−0.637839			−0.318920	+	0.947782i	$0.603320\pi$
$182$	1.07819e28	+	1.86747e28i	0.605064	+	1.04800i
$183$	−6.15386e27	+	1.37496e28i	−0.322484	+	0.720531i
$184$	−1.49839e27	+	2.59529e27i	−0.0733505	+	0.127047i
$185$	−5.81917e27	+	1.00791e28i	−0.266204	+	0.461079i
$186$	1.46693e28	+	2.02735e28i	0.627332	+	0.866995i
$187$	7.18722e27	+	1.24486e28i	0.287436	+	0.497854i
$188$	7.49245e27			0.280318
$189$	1.98315e28	+	1.80673e28i	0.694356	+	0.632587i
$190$	1.46723e28			0.480925
$191$	−1.98703e28	−	3.44164e28i	−0.609941	−	1.05645i	−0.991250	−	0.132002i	$-0.957860\pi$
$191$	−1.98703e28	−	3.44164e28i	−0.609941	−	1.05645i	0.381308	−	0.924448i	$-0.375474\pi$
$192$	−2.54816e27	−	3.52165e27i	−0.0732760	−	0.101270i
$193$	2.01477e27	−	3.48968e27i	0.0542948	−	0.0940414i	−0.837601	−	0.546283i	$-0.816042\pi$
$193$	2.01477e27	−	3.48968e27i	0.0542948	−	0.0940414i	0.891895	+	0.452242i	$0.149376\pi$
$194$	3.22943e27	−	5.59353e27i	0.0815837	−	0.141307i
$195$	1.52768e28	−	3.41332e28i	0.361909	−	0.808619i
$196$	1.32414e27	+	2.29347e27i	0.0294261	+	0.0509675i
$197$	−1.57433e28			−0.328298			−0.164149	−	0.986436i	$-0.552488\pi$
$197$	−1.57433e28			−0.328298			−0.164149	+	0.986436i	$0.552488\pi$
$198$	1.09137e28	+	1.22162e28i	0.213627	+	0.239123i
$199$	−8.51081e27			−0.156425			−0.0782127	−	0.996937i	$-0.524921\pi$
$199$	−8.51081e27			−0.156425			−0.0782127	+	0.996937i	$0.524921\pi$
$200$	7.81894e27	+	1.35428e28i	0.134981	+	0.233794i
$201$	8.16079e28	−	8.41666e27i	1.32368	−	0.136518i
$202$	1.73418e28	−	3.00369e28i	0.264364	−	0.457892i
$203$	6.09289e28	−	1.05532e29i	0.873219	−	1.51246i
$204$	4.67815e28	−	4.82482e27i	0.630518	−	0.0650286i
$205$	2.74596e27	+	4.75615e27i	0.0348154	+	0.0603020i
$206$	−5.02628e28			−0.599662
$207$	−2.46168e28	−	2.75549e28i	−0.276441	−	0.309435i
$208$	4.30795e28			0.455490
$209$	−3.18482e28	−	5.51627e28i	−0.317144	−	0.549309i
$210$	−1.40635e28	+	3.14223e28i	−0.131933	+	0.294779i
$211$	1.02857e29	−	1.78154e29i	0.909294	−	1.57494i	0.0942462	−	0.995549i	$-0.469956\pi$
$211$	1.02857e29	−	1.78154e29i	0.909294	−	1.57494i	0.815048	−	0.579394i	$-0.196711\pi$
$212$	−4.06397e28	+	7.03901e28i	−0.338651	+	0.586561i
$213$	5.41802e28	+	7.48789e28i	0.425692	+	0.588321i
$214$	1.91030e28	+	3.30874e28i	0.141556	+	0.245183i
$215$	−2.64661e28			−0.185016
$216$	5.10681e28	−	1.62637e28i	0.336882	−	0.107287i
$217$	2.28304e29			1.42157
$218$	−3.84720e28	−	6.66355e28i	−0.226172	−	0.391742i
$219$	1.86696e29	+	2.58021e29i	1.03654	+	1.43253i
$220$	−1.05105e28	+	1.82047e28i	−0.0551237	+	0.0954771i
$221$	−2.33044e29	+	4.03644e29i	−1.15487	+	2.00030i
$222$	6.75301e28	−	1.50883e29i	0.316290	−	0.706691i
$223$	−1.75459e29	−	3.03903e29i	−0.776898	−	1.34563i	−0.933722	−	0.358000i	$-0.883459\pi$
$223$	−1.75459e29	−	3.03903e29i	−0.776898	−	1.34563i	0.156824	−	0.987627i	$-0.449874\pi$
$224$	−3.96581e28			−0.166047
$225$	−1.88751e29	+	3.93525e28i	−0.747496	+	0.155844i
$226$	−1.96625e29			−0.736688
$227$	−7.43757e27	−	1.28823e28i	−0.0263699	−	0.0456740i	0.852539	−	0.522663i	$-0.175061\pi$
$227$	−7.43757e27	−	1.28823e28i	−0.0263699	−	0.0456740i	−0.878909	+	0.476989i	$0.841728\pi$
$228$	−2.07299e29	+	2.13799e28i	−0.695685	+	0.0717497i
$229$	−1.92922e29	+	3.34151e29i	−0.612968	+	1.06169i	0.377769	+	0.925900i	$0.376691\pi$
$229$	−1.92922e29	+	3.34151e29i	−0.612968	+	1.06169i	−0.990737	+	0.135792i	$0.956642\pi$
$230$	2.37074e28	−	4.10624e28i	0.0713322	−	0.123551i
$231$	1.48664e29	−	1.53325e28i	0.423697	−	0.0436981i
$232$	−1.21722e29	−	2.10829e29i	−0.328678	−	0.569287i
$233$	−3.90887e29			−1.00024			−0.500118	−	0.865957i	$-0.666710\pi$
$233$	−3.90887e29			−1.00024			−0.500118	+	0.865957i	$0.666710\pi$
$234$	−1.66103e29	+	5.04517e29i	−0.402883	+	1.22371i
$235$	−1.18544e29			−0.272604
$236$	4.30562e28	+	7.45756e28i	0.0938936	+	0.162628i
$237$	1.19313e29	−	2.66582e29i	0.246792	−	0.551412i
$238$	2.14535e29	−	3.71586e29i	0.421005	−	0.729201i
$239$	−3.63162e29	+	6.29015e29i	−0.676280	+	1.17135i	0.299813	+	0.953998i	$0.403076\pi$
$239$	−3.63162e29	+	6.29015e29i	−0.676280	+	1.17135i	−0.976093	+	0.217354i	$0.930257\pi$
$240$	4.03167e28	+	5.57191e28i	0.0712598	+	0.0984835i
$241$	−1.38816e29	−	2.40436e29i	−0.232930	−	0.403446i	0.725739	−	0.687970i	$-0.241498\pi$
$241$	−1.38816e29	−	2.40436e29i	−0.232930	−	0.403446i	−0.958669	+	0.284524i	$0.908165\pi$
$242$	−3.52532e29			−0.561702
$243$	−6.43567e27	+	6.60781e29i	−0.00973902	+	0.999953i
$244$	2.74564e29			0.394703
$245$	−2.09503e28	−	3.62870e28i	−0.0286164	−	0.0495650i
$246$	−4.57272e28	−	6.31966e28i	−0.0593589	−	0.0820361i
$247$	1.03267e30	−	1.78864e30i	1.27423	−	2.20704i
$248$	2.28051e29	−	3.94996e29i	0.267538	−	0.463389i
$249$	−6.52293e29	+	1.45743e30i	−0.727698	+	1.62591i
$250$	−2.85726e29	−	4.94892e29i	−0.303179	−	0.525122i
$251$	1.12542e29			0.113604			0.0568020	−	0.998385i	$-0.481910\pi$
$251$	1.12542e29			0.113604			0.0568020	+	0.998385i	$0.481910\pi$
$252$	1.52911e29	−	4.64448e29i	0.146870	−	0.446098i
$253$	−2.05841e29			−0.188159
$254$	−3.50649e29	−	6.07341e29i	−0.305106	−	0.528459i
$255$	−7.40170e29	+	7.63377e28i	−0.613168	+	0.0632393i
$256$	−3.96141e28	+	6.86136e28i	−0.0312500	+	0.0541266i
$257$	−6.96320e29	+	1.20606e30i	−0.523173	+	0.906161i	0.476464	+	0.879194i	$0.341918\pi$
$257$	−6.96320e29	+	1.20606e30i	−0.523173	+	0.906161i	−0.999636	+	0.0269673i	$0.991415\pi$
$258$	3.73931e29	−	3.85655e28i	0.267636	−	0.0276027i
$259$	−7.54078e29	−	1.30610e30i	−0.514244	−	0.890696i
$260$	−6.81598e29			−0.442957
$261$	2.93841e30	−	6.12625e29i	1.82015	−	0.379479i
$262$	−5.02540e29			−0.296759
$263$	7.47940e29	+	1.29547e30i	0.421133	+	0.729424i	0.996051	−	0.0887872i	$-0.0282991\pi$
$263$	7.47940e29	+	1.29547e30i	0.421133	+	0.729424i	−0.574917	+	0.818212i	$0.694966\pi$
$264$	1.21972e29	−	2.72523e29i	0.0654952	−	0.146337i
$265$	6.42996e29	−	1.11370e30i	0.329333	−	0.570421i
$266$	−9.50655e29	+	1.64658e30i	−0.464518	+	0.804568i
$267$	5.10992e29	+	7.06208e29i	0.238245	+	0.329262i
$268$	−7.47660e29	−	1.29498e30i	−0.332674	−	0.576209i
$269$	−1.83919e30			−0.781130			−0.390565	−	0.920575i	$-0.627720\pi$
$269$	−1.83919e30			−0.781130			−0.390565	+	0.920575i	$0.627720\pi$
$270$	−8.07992e29	+	2.57322e29i	−0.327612	+	0.104335i
$271$	4.56536e30			1.76750			0.883749	−	0.467961i	$-0.155011\pi$
$271$	4.56536e30			1.76750			0.883749	+	0.467961i	$0.155011\pi$
$272$	−4.28594e29	−	7.42346e29i	−0.158466	−	0.274470i
$273$	2.84074e30	+	3.92600e30i	1.00322	+	1.38649i
$274$	1.36627e30	−	2.36645e30i	0.460951	−	0.798390i
$275$	−5.37060e29	+	9.30216e29i	−0.173127	+	0.299865i
$276$	−2.75119e29	+	6.14702e29i	−0.0847533	+	0.189365i
$277$	−1.50581e28	−	2.60814e28i	−0.00443376	−	0.00767950i	0.863800	−	0.503835i	$-0.168078\pi$
$277$	−1.50581e28	−	2.60814e28i	−0.00443376	−	0.00767950i	−0.868234	+	0.496155i	$0.834745\pi$
$278$	−2.31954e30			−0.652894
$279$	3.74660e30	+	4.19376e30i	1.00829	+	1.12863i
$280$	6.27465e29			0.161478
$281$	−2.79701e30	−	4.84457e30i	−0.688439	−	1.19241i	−0.972343	−	0.233558i	$-0.924963\pi$
$281$	−2.79701e30	−	4.84457e30i	−0.688439	−	1.19241i	0.283904	−	0.958853i	$-0.408370\pi$
$282$	1.67487e30	−	1.72738e29i	0.394337	−	0.0406701i
$283$	3.70023e29	−	6.40898e29i	0.0833485	−	0.144364i	−0.821338	−	0.570442i	$-0.806772\pi$
$283$	3.70023e29	−	6.40898e29i	0.0833485	−	0.144364i	0.904686	+	0.426078i	$0.140105\pi$
$284$	8.42292e29	−	1.45889e30i	0.181545	−	0.314445i
$285$	3.27986e30	−	3.38270e29i	0.676542	−	0.0697754i
$286$	1.47950e30	+	2.56257e30i	0.292106	+	0.505942i
$287$	−7.11672e29			−0.134510
$288$	−6.50812e29	−	7.28487e29i	−0.117774	−	0.131830i
$289$	3.50349e30			0.607124
$290$	1.92588e30	+	3.33571e30i	0.319634	+	0.553623i
$291$	5.92952e29	−	1.32484e30i	0.0942664	−	0.210621i
$292$	2.90240e30	−	5.02711e30i	0.442051	−	0.765655i
$293$	−5.90145e29	+	1.02216e30i	−0.0861219	+	0.149168i	−0.905869	−	0.423559i	$-0.860781\pi$
$293$	−5.90145e29	+	1.02216e30i	−0.0861219	+	0.149168i	0.819747	+	0.572726i	$0.194114\pi$
$294$	3.48876e29	+	4.82159e29i	0.0487898	+	0.0674292i
$295$	−6.81230e29	−	1.17992e30i	−0.0913100	−	0.158154i
$296$	−3.01296e30			−0.387121
$297$	2.72130e30	+	2.47922e30i	0.335213	+	0.305393i
$298$	−4.55269e30			−0.537731
$299$	−3.33716e30	−	5.78013e30i	−0.377996	−	0.654709i
$300$	2.06009e30	+	2.84711e30i	0.223805	+	0.309307i
$301$	1.71481e30	−	2.97014e30i	0.178704	−	0.309525i
$302$	−1.55096e30	+	2.68633e30i	−0.155065	+	0.268580i
$303$	3.18411e30	−	7.11431e30i	0.305461	−	0.682496i
$304$	1.89920e30	+	3.28951e30i	0.174844	+	0.302838i
$305$	−4.34411e30			−0.383842
$306$	1.03464e31	−	2.15710e30i	0.877547	−	0.182958i
$307$	−1.44737e31			−1.17855			−0.589276	−	0.807932i	$-0.700587\pi$
$307$	−1.44737e31			−1.17855			−0.589276	+	0.807932i	$0.700587\pi$
$308$	−1.36200e30	−	2.35905e30i	−0.106486	−	0.184440i
$309$	−1.12358e31	+	1.15881e30i	−0.843575	+	0.0870024i
$310$	−3.60819e30	+	6.24956e30i	−0.260176	+	0.450639i
$311$	−5.85692e30	+	1.01445e31i	−0.405662	+	0.702627i	−0.994398	−	0.105698i	$-0.966292\pi$
$311$	−5.85692e30	+	1.01445e31i	−0.405662	+	0.702627i	0.588736	+	0.808325i	$0.299626\pi$
$312$	9.63006e30	−	9.93199e29i	0.640762	−	0.0660852i
$313$	−3.19904e30	−	5.54090e30i	−0.204511	−	0.354223i	0.745466	−	0.666544i	$-0.232227\pi$
$313$	−3.19904e30	−	5.54090e30i	−0.204511	−	0.354223i	−0.949977	+	0.312321i	$0.898894\pi$
$314$	3.32150e30			0.204039
$315$	−2.41934e30	+	7.34843e30i	−0.142828	+	0.433823i
$316$	−5.32331e30			−0.302060
$317$	−8.22057e29	−	1.42384e30i	−0.0448396	−	0.0776644i	0.842735	−	0.538329i	$-0.180944\pi$
$317$	−8.22057e29	−	1.42384e30i	−0.0448396	−	0.0776644i	−0.887574	+	0.460665i	$0.847611\pi$
$318$	−7.46183e30	+	1.66721e31i	−0.391297	+	0.874279i
$319$	8.36076e30	−	1.44813e31i	0.421563	−	0.730168i
$320$	6.26768e29	−	1.08559e30i	0.0303901	−	0.0526372i
$321$	5.03314e30	+	6.95598e30i	0.234707	+	0.324374i
$322$	3.07212e30	+	5.32107e30i	0.137797	+	0.238672i
$323$	−4.10957e31			−1.77323
$324$	1.10409e31	−	4.81299e30i	0.458343	−	0.199803i
$325$	−3.48281e31			−1.39119
$326$	−9.39242e30	−	1.62682e31i	−0.361042	−	0.625343i
$327$	−1.01364e31	−	1.40088e31i	−0.375004	−	0.518269i
$328$	−7.10881e29	+	1.23128e30i	−0.0253148	+	0.0438465i
$329$	7.68080e30	−	1.33035e31i	0.263304	−	0.456056i
$330$	−1.92982e30	+	4.31182e30i	−0.0636930	+	0.142310i
$331$	−1.48237e30	−	2.56754e30i	−0.0471093	−	0.0815958i	0.841509	−	0.540243i	$-0.181668\pi$
$331$	−1.48237e30	−	2.56754e30i	−0.0471093	−	0.0815958i	−0.888619	+	0.458647i	$0.848334\pi$
$332$	2.91031e31			0.890662
$333$	1.16172e31	−	3.52856e31i	0.342410	−	1.04003i
$334$	3.26342e31			0.926492
$335$	1.18294e31	+	2.04891e31i	0.323520	+	0.560354i
$336$	−8.86524e30	+	9.14319e29i	−0.233587	+	0.0240911i
$337$	−1.64567e31	+	2.85038e31i	−0.417800	+	0.723651i	−0.995718	−	0.0924441i	$-0.970532\pi$
$337$	−1.64567e31	+	2.85038e31i	−0.417800	+	0.723651i	0.577918	+	0.816095i	$0.303865\pi$
$338$	−3.35210e31	+	5.80600e31i	−0.820083	+	1.42043i
$339$	−4.39539e31	+	4.53319e30i	−1.03634	+	0.106883i
$340$	6.78115e30	+	1.17453e31i	0.154105	+	0.266918i
$341$	3.13283e31			0.686289
$342$	−4.58471e31	+	9.55859e30i	−0.968246	+	0.201868i
$343$	5.15597e31			1.04987
$344$	−3.42581e30	−	5.93367e30i	−0.0672640	−	0.116505i
$345$	4.35289e30	−	9.72572e30i	0.0824212	−	0.184155i
$346$	−1.86298e31	+	3.22678e31i	−0.340218	+	0.589275i
$347$	2.48515e31	−	4.30441e31i	0.437759	−	0.758220i	−0.559758	−	0.828656i	$-0.689106\pi$
$347$	2.48515e31	−	4.30441e31i	0.437759	−	0.758220i	0.997516	+	0.0704362i	$0.0224391\pi$
$348$	−3.20707e31	−	4.43228e31i	−0.544964	−	0.753159i
$349$	−1.48658e31	−	2.57483e31i	−0.243709	−	0.422116i	0.718059	−	0.695982i	$-0.245031\pi$
$349$	−1.48658e31	−	2.57483e31i	−0.243709	−	0.422116i	−0.961768	+	0.273866i	$0.911697\pi$
$350$	3.20620e31			0.507154
$351$	−2.54993e31	+	1.16610e32i	−0.389215	+	1.77990i
$352$	−5.44195e30			−0.0801625
$353$	−3.99075e31	−	6.91218e31i	−0.567376	−	0.982724i	−0.996824	−	0.0796324i	$-0.974625\pi$
$353$	−3.99075e31	−	6.91218e31i	−0.567376	−	0.982724i	0.429448	−	0.903091i	$-0.358708\pi$
$354$	1.13442e31	+	1.56781e31i	0.155680	+	0.215155i
$355$	−1.33266e31	+	2.30824e31i	−0.176549	+	0.305792i
$356$	7.94394e30	−	1.37593e31i	0.101604	−	0.175983i
$357$	3.93906e31	−	8.80110e31i	0.486452	−	1.08689i
$358$	2.14786e31	+	3.72021e31i	0.256135	+	0.443639i
$359$	1.48192e32			1.70665			0.853324	−	0.521380i	$-0.174583\pi$
$359$	1.48192e32			1.70665			0.853324	+	0.521380i	$0.174583\pi$
$360$	1.02971e31	+	1.15260e31i	0.114533	+	0.128203i
$361$	8.90279e31			0.956502
$362$	2.17282e31	+	3.76343e31i	0.225510	+	0.390595i
$363$	−7.88055e31	+	8.12763e30i	−0.790176	+	0.0814950i
$364$	4.41625e31	−	7.64917e31i	0.427845	−	0.741049i
$365$	−4.59214e31	+	7.95383e31i	−0.429887	+	0.744587i
$366$	6.13764e31	−	6.33007e30i	0.555249	−	0.0572658i
$367$	−4.12223e31	−	7.13991e31i	−0.360418	−	0.624262i	0.627612	−	0.778526i	$-0.284032\pi$
$367$	−4.12223e31	−	7.13991e31i	−0.360418	−	0.624262i	−0.988030	+	0.154265i	$0.950699\pi$
$368$	1.22748e31			0.103733
$369$	−1.16789e31	−	1.30728e31i	−0.0954055	−	0.106792i
$370$	4.76706e31			0.376469
$371$	8.33228e31	+	1.44319e32i	0.636194	+	1.10192i
$372$	4.18722e31	−	9.35556e31i	0.309128	−	0.690690i
$373$	−5.32861e31	+	9.22942e31i	−0.380411	+	0.658891i	−0.991121	−	0.132963i	$-0.957551\pi$
$373$	−5.32861e31	+	9.22942e31i	−0.380411	+	0.658891i	0.610710	+	0.791854i	$0.290884\pi$
$374$	2.94389e31	−	5.09896e31i	0.203248	−	0.352036i
$375$	−7.52814e31	−	1.04042e32i	−0.502686	−	0.694730i
$376$	−1.53445e31	−	2.65775e31i	−0.0991073	−	0.171659i
$377$	5.42191e32			3.38755
$378$	2.34741e31	−	1.07349e32i	0.141887	−	0.648857i
$379$	−1.49459e32			−0.874044			−0.437022	−	0.899451i	$-0.643967\pi$
$379$	−1.49459e32			−0.874044			−0.437022	+	0.899451i	$0.643967\pi$
$380$	−3.00488e31	−	5.20461e31i	−0.170033	−	0.294505i
$381$	−9.23868e31	−	1.27682e32i	−0.505880	−	0.699144i
$382$	−8.13889e31	+	1.40970e32i	−0.431294	+	0.747023i
$383$	1.00039e32	−	1.73272e32i	0.513078	−	0.888677i	−0.486807	−	0.873510i	$-0.661838\pi$
$383$	1.00039e32	−	1.73272e32i	0.513078	−	0.888677i	0.999885	−	0.0151676i	$-0.00482817\pi$
$384$	−7.27350e30	+	1.62513e31i	−0.0361080	+	0.0806766i
$385$	2.15494e31	+	3.73246e31i	0.103556	+	0.179364i
$386$	−1.65050e31			−0.0767844
$387$	8.26999e31	−	1.72420e31i	0.372493	−	0.0776604i
$388$	−2.64555e31			−0.115377
$389$	−1.28159e32	−	2.21978e32i	−0.541227	−	0.937433i	−0.998834	−	0.0482784i	$-0.984627\pi$
$389$	−1.28159e32	−	2.21978e32i	−0.541227	−	0.937433i	0.457607	−	0.889155i	$-0.348707\pi$
$390$	−1.52365e32	+	1.57143e31i	−0.623131	+	0.0642667i
$391$	−6.64022e31	+	1.15012e32i	−0.263010	+	0.455547i
$392$	5.42367e30	−	9.39407e30i	0.0208074	−	0.0360394i
$393$	−1.12339e32	+	1.15861e31i	−0.417467	+	0.0430555i
$394$	3.22423e31	+	5.58453e31i	0.116071	+	0.201041i
$395$	8.42247e31			0.293749
$396$	2.09827e31	−	6.37322e31i	0.0709041	−	0.215362i
$397$	9.44560e31			0.309277			0.154639	−	0.987971i	$-0.450579\pi$
$397$	9.44560e31			0.309277			0.154639	+	0.987971i	$0.450579\pi$
$398$	1.74301e31	+	3.01899e31i	0.0553047	+	0.0957906i
$399$	−1.74549e32	+	3.89997e32i	−0.536730	+	1.19922i
$400$	3.20264e31	−	5.54713e31i	0.0954461	−	0.165318i
$401$	−2.95530e32	+	5.11873e32i	−0.853683	+	1.47862i	0.0241781	+	0.999708i	$0.492303\pi$
$401$	−2.95530e32	+	5.11873e32i	−0.853683	+	1.47862i	−0.877861	+	0.478915i	$0.841030\pi$
$402$	−1.96989e32	−	2.72246e32i	−0.551590	−	0.762316i
$403$	5.07905e32	+	8.79718e32i	1.37870	+	2.38798i
$404$	−1.42064e32			−0.373867
$405$	−1.74687e32	+	7.61505e31i	−0.445731	+	0.194305i
$406$	−4.99130e32			−1.23492
$407$	−1.03476e32	−	1.79225e32i	−0.248261	−	0.430000i
$408$	−1.12923e32	−	1.56064e32i	−0.262743	−	0.363120i
$409$	−3.51371e32	+	6.08593e32i	−0.792912	+	1.37336i	0.131244	+	0.991350i	$0.458103\pi$
$409$	−3.51371e32	+	6.08593e32i	−0.792912	+	1.37336i	−0.924156	+	0.382014i	$0.875231\pi$
$410$	1.12475e31	−	1.94812e31i	0.0246182	−	0.0426400i
$411$	2.50860e32	−	5.60499e32i	0.532608	−	1.19001i
$412$	1.02938e32	+	1.78294e32i	0.212012	+	0.367216i
$413$	1.76554e32			0.352779
$414$	−4.73285e31	+	1.43754e32i	−0.0917526	+	0.278687i
$415$	−4.60465e32			−0.866154
$416$	−8.82269e31	−	1.52813e32i	−0.161040	−	0.278930i
$417$	−5.18514e32	+	5.34771e31i	−0.918459	+	0.0947256i
$418$	−1.30450e32	+	2.25946e32i	−0.224255	+	0.388420i
$419$	3.54977e32	−	6.14837e32i	0.592276	−	1.02585i	−0.401649	−	0.915794i	$-0.631563\pi$
$419$	3.54977e32	−	6.14837e32i	0.592276	−	1.02585i	0.993925	−	0.110059i	$-0.0351039\pi$
$420$	1.40265e32	−	1.44662e31i	0.227160	−	0.0234282i
$421$	−4.79284e32	−	8.30145e32i	−0.753472	−	1.30505i	−0.946131	−	0.323785i	$-0.895044\pi$
$421$	−4.79284e32	−	8.30145e32i	−0.753472	−	1.30505i	0.192659	−	0.981266i	$-0.438289\pi$
$422$	−8.42607e32			−1.28594
$423$	3.70421e32	−	7.72284e31i	0.548834	−	0.114425i
$424$	3.32921e32			0.478925
$425$	3.46501e32	+	6.00157e32i	0.483997	+	0.838308i
$426$	1.54652e32	−	3.45542e32i	0.209767	−	0.468685i
$427$	2.81466e32	−	4.87513e32i	0.370747	−	0.642152i
$428$	7.82459e31	−	1.35526e32i	0.100095	−	0.173370i
$429$	3.89811e32	+	5.38732e32i	0.484326	+	0.669355i
$430$	5.42027e31	+	9.38818e31i	0.0654131	+	0.113299i
$431$	1.23517e31			0.0144798			0.00723989	−	0.999974i	$-0.497695\pi$
$431$	1.23517e31			0.0144798			0.00723989	+	0.999974i	$0.497695\pi$
$432$	−1.62279e32	−	1.47843e32i	−0.184806	−	0.168365i
$433$	−5.28994e32			−0.585264			−0.292632	−	0.956225i	$-0.594531\pi$
$433$	−5.28994e32			−0.585264			−0.292632	+	0.956225i	$0.594531\pi$
$434$	−4.67567e32	−	8.09851e32i	−0.502600	−	0.870529i
$435$	5.07418e32	+	7.01270e32i	0.529969	+	0.732435i
$436$	−1.57582e32	+	2.72939e32i	−0.159928	+	0.277003i
$437$	2.94243e32	−	5.09644e32i	0.290194	−	0.502631i
$438$	5.32908e32	−	1.19068e33i	0.510770	−	1.14122i
$439$	−2.47060e32	−	4.27921e32i	−0.230142	−	0.398618i	0.727707	−	0.685888i	$-0.240586\pi$
$439$	−2.47060e32	−	4.27921e32i	−0.230142	−	0.398618i	−0.957850	+	0.287269i	$0.907253\pi$
$440$	8.61018e31			0.0779567
$441$	8.91044e31	+	9.97391e31i	0.0784182	+	0.0877775i
$442$	1.90909e33			1.63324
$443$	−8.61201e32	−	1.49164e33i	−0.716239	−	1.24056i	−0.962480	−	0.271354i	$-0.912529\pi$
$443$	−8.61201e32	−	1.49164e33i	−0.716239	−	1.24056i	0.246240	−	0.969209i	$-0.420805\pi$
$444$	−6.73522e32	+	6.94638e31i	−0.544583	+	0.0561658i
$445$	−1.25688e32	+	2.17698e32i	−0.0988083	+	0.171141i
$446$	−7.18678e32	+	1.24479e33i	−0.549350	+	0.951502i
$447$	−1.01772e33	+	1.04962e32i	−0.756454	+	0.0780171i
$448$	8.12199e31	+	1.40677e32i	0.0587066	+	0.101683i
$449$	1.93531e33			1.36042			0.680209	−	0.733019i	$-0.261889\pi$
$449$	1.93531e33			1.36042			0.680209	+	0.733019i	$0.261889\pi$
$450$	5.26156e32	+	5.88953e32i	0.359714	+	0.402647i
$451$	−9.76567e31			−0.0649374
$452$	4.02688e32	+	6.97476e32i	0.260458	+	0.451127i
$453$	−2.84769e32	+	6.36264e32i	−0.179170	+	0.400322i
$454$	−3.04643e31	+	5.27657e31i	−0.0186463	+	0.0322964i
$455$	−6.98733e32	+	1.21024e33i	−0.416072	+	0.720658i
$456$	5.00389e32	+	6.91555e32i	0.289899	+	0.400651i
$457$	3.28123e32	+	5.68326e32i	0.184963	+	0.320365i	0.943564	−	0.331190i	$-0.107450\pi$
$457$	3.28123e32	+	5.68326e32i	0.184963	+	0.320365i	−0.758601	+	0.651555i	$0.774117\pi$
$458$	1.58042e33			0.866868
$459$	2.26311e33	−	7.20736e32i	1.20795	−	0.384696i
$460$	−1.94211e32			−0.100879
$461$	3.64612e32	+	6.31526e32i	0.184319	+	0.319249i	0.943347	−	0.331809i	$-0.107659\pi$
$461$	3.64612e32	+	6.31526e32i	0.184319	+	0.319249i	−0.759028	+	0.651058i	$0.774326\pi$
$462$	−3.58852e32	−	4.95946e32i	−0.176559	−	0.244011i
$463$	1.64393e33	−	2.84736e33i	0.787263	−	1.36358i	−0.140374	−	0.990099i	$-0.544831\pi$
$463$	1.64393e33	−	2.84736e33i	0.787263	−	1.36358i	0.927638	−	0.373482i	$-0.121836\pi$
$464$	−4.98575e32	+	8.63558e32i	−0.232411	+	0.402547i
$465$	−6.62496e32	+	1.48022e33i	−0.300622	+	0.671685i
$466$	8.00537e32	+	1.38657e33i	0.353637	+	0.612517i
$467$	−1.54771e33			−0.665624			−0.332812	−	0.942993i	$-0.607997\pi$
$467$	−1.54771e33			−0.665624			−0.332812	+	0.942993i	$0.607997\pi$
$468$	2.12982e33	−	4.44042e32i	0.891805	−	0.185931i
$469$	−3.06582e33			−1.24993
$470$	2.42779e32	+	4.20506e32i	0.0963802	+	0.166935i
$471$	7.42493e32	−	7.65772e31i	0.287032	−	0.0296032i
$472$	1.76358e32	−	3.05462e32i	0.0663928	−	0.114996i
$473$	2.35309e32	−	4.07567e32i	0.0862728	−	0.149429i
$474$	−1.18998e33	+	1.22729e32i	−0.424924	+	0.0438246i
$475$	−1.53542e33	−	2.65943e33i	−0.534021	−	0.924952i
$476$	−1.75747e33			−0.595390
$477$	−1.28365e33	+	3.89893e33i	−0.423612	+	1.28667i
$478$	2.97502e33			0.956405
$479$	9.88473e32	+	1.71208e33i	0.309578	+	0.536206i	0.978270	−	0.207334i	$-0.0664787\pi$
$479$	9.88473e32	+	1.71208e33i	0.309578	+	0.536206i	−0.668692	+	0.743540i	$0.733145\pi$
$480$	1.15080e32	−	2.57126e32i	0.0351144	−	0.0784567i
$481$	3.35517e33	−	5.81133e33i	0.997473	−	1.72767i
$482$	−5.68589e32	+	9.84824e32i	−0.164706	+	0.285280i
$483$	8.09425e32	+	1.11865e33i	0.228474	+	0.315759i
$484$	7.21985e32	+	1.25052e33i	0.198592	+	0.343971i
$485$	4.18574e32			0.112202
$486$	2.35713e33	−	1.33045e33i	0.615787	−	0.347573i
$487$	4.90778e33			1.24960			0.624802	−	0.780783i	$-0.285180\pi$
$487$	4.90778e33			1.24960			0.624802	+	0.780783i	$0.285180\pi$
$488$	−5.62307e32	−	9.73943e32i	−0.139549	−	0.241705i
$489$	−2.47466e33	−	3.42007e33i	−0.598625	−	0.827320i
$490$	−8.58125e31	+	1.48632e32i	−0.0202348	+	0.0350478i
$491$	1.01574e32	−	1.75931e32i	0.0233488	−	0.0404412i	−0.854115	−	0.520084i	$-0.825901\pi$
$491$	1.01574e32	−	1.75931e32i	0.0233488	−	0.0404412i	0.877464	+	0.479643i	$0.159234\pi$
$492$	−1.30524e32	+	2.91632e32i	−0.0292501	+	0.0653539i
$493$	−5.39420e33	−	9.34303e33i	−1.17853	−	2.04127i
$494$	−8.45963e33			−1.80204
$495$	−3.31985e32	+	1.00836e33i	−0.0689531	+	0.209436i
$496$	−1.86819e33			−0.378356
$497$	−1.72693e33	−	2.99114e33i	−0.341052	−	0.590719i
$498$	6.50575e33	−	6.70972e32i	1.25294	−	0.129222i
$499$	−1.42155e33	+	2.46220e33i	−0.266997	+	0.462452i	−0.968085	−	0.250623i	$-0.919365\pi$
$499$	−1.42155e33	+	2.46220e33i	−0.266997	+	0.462452i	0.701088	+	0.713075i	$0.252698\pi$
$500$	−1.17033e33	+	2.02708e33i	−0.214380	+	0.371317i
$501$	7.29509e33	−	7.52381e32i	1.30334	−	0.134421i
$502$	−2.30486e32	−	3.99214e32i	−0.0401651	−	0.0695680i
$503$	4.97587e33			0.845802			0.422901	−	0.906176i	$-0.361012\pi$
$503$	4.97587e33			0.845802			0.422901	+	0.906176i	$0.361012\pi$
$504$	−1.96067e33	+	4.08776e32i	−0.325104	+	0.0677804i
$505$	2.24772e33			0.363580
$506$	4.21561e32	+	7.30166e32i	0.0665242	+	0.115223i
$507$	−6.15475e33	+	1.37516e34i	−0.947569	+	2.11717i
$508$	−1.43626e33	+	2.48767e33i	−0.215742	+	0.373677i
$509$	−4.63620e33	+	8.03014e33i	−0.679501	+	1.17693i	0.295630	+	0.955303i	$0.404470\pi$
$509$	−4.63620e33	+	8.03014e33i	−0.679501	+	1.17693i	−0.975131	+	0.221628i	$0.928863\pi$
$510$	1.78666e33	+	2.46922e33i	0.255514	+	0.353129i
$511$	−5.95074e33	−	1.03070e34i	−0.830442	−	1.43837i
$512$	3.24519e32			0.0441942
$513$	−1.00284e34	+	3.19375e33i	−1.33279	+	0.424457i
$514$	5.70426e33			0.739878
$515$	−1.62867e33	−	2.82095e33i	−0.206179	−	0.357112i
$516$	−9.02611e32	−	1.24744e33i	−0.111527	−	0.154134i
$517$	1.05397e33	−	1.82553e33i	0.127115	−	0.220170i
$518$	−3.08870e33	+	5.34979e33i	−0.363625	+	0.629817i
$519$	−3.42060e33	+	7.64270e33i	−0.393107	+	0.878325i
$520$	1.39591e33	+	2.41779e33i	0.156609	+	0.271255i
$521$	−1.64259e34			−1.79911			−0.899557	−	0.436804i	$-0.856110\pi$
$521$	−1.64259e34			−1.79911			−0.899557	+	0.436804i	$0.856110\pi$
$522$	−8.19100e33	−	9.16860e33i	−0.875902	−	0.980442i
$523$	−8.40356e33			−0.877389			−0.438695	−	0.898636i	$-0.644559\pi$
$523$	−8.40356e33			−0.877389			−0.438695	+	0.898636i	$0.644559\pi$
$524$	1.02920e33	+	1.78263e33i	0.104920	+	0.181727i
$525$	7.16719e33	−	7.39190e32i	0.713440	−	0.0735809i
$526$	3.06356e33	−	5.30624e33i	0.297786	−	0.515781i
$527$	1.01062e34	−	1.75045e34i	0.959302	−	1.66156i
$528$	−1.21650e33	+	1.25464e32i	−0.112769	+	0.0116304i
$529$	4.57201e33	+	7.91896e33i	0.413915	+	0.716922i
$530$	−5.26743e33			−0.465747
$531$	2.89736e33	+	3.24316e33i	0.250219	+	0.280083i
$532$	7.78776e33			0.656927
$533$	−1.58325e33	−	2.74226e33i	−0.130454	−	0.225953i
$534$	1.45858e33	−	3.25892e33i	0.117399	−	0.262306i
$535$	−1.23800e33	+	2.14427e33i	−0.0973412	+	0.168600i
$536$	−3.06241e33	+	5.30426e33i	−0.235236	+	0.407441i
$537$	5.65906e33	+	7.82102e33i	0.424684	+	0.586928i
$538$	3.76666e33	+	6.52405e33i	0.276171	+	0.478342i
$539$	7.45072e32			0.0533751
$540$	2.56755e33	+	2.33915e33i	0.179720	+	0.163733i
$541$	−2.09754e34			−1.43464			−0.717321	−	0.696742i	$-0.754632\pi$
$541$	−2.09754e34			−1.43464			−0.717321	+	0.696742i	$0.754632\pi$
$542$	−9.34986e33	−	1.61944e34i	−0.624905	−	1.08237i
$543$	5.72481e33	+	7.91189e33i	0.373907	+	0.516752i
$544$	−1.75552e33	+	3.04065e33i	−0.112052	+	0.194080i
$545$	2.49323e33	−	4.31841e33i	0.155527	−	0.269381i
$546$	8.10863e33	−	1.81172e34i	0.494356	−	1.10455i
$547$	−2.29840e33	−	3.98095e33i	−0.136957	−	0.237217i	0.789386	−	0.613897i	$-0.210399\pi$
$547$	−2.29840e33	−	3.98095e33i	−0.136957	−	0.237217i	−0.926343	+	0.376680i	$0.877066\pi$
$548$	−1.11925e34			−0.651883
$549$	1.35742e34	−	2.83007e33i	0.772789	−	0.161117i
$550$	4.39960e33			0.244838
$551$	2.39029e34	+	4.14011e34i	1.30034	+	2.25225i
$552$	2.74394e33	−	2.82997e32i	0.145927	−	0.0150502i
$553$	−5.45714e33	+	9.45204e33i	−0.283727	+	0.491429i
$554$	−6.16779e31	+	1.06829e32i	−0.00313514	+	0.00543023i
$555$	1.06564e34	−	1.09905e33i	0.529598	−	0.0546203i
$556$	4.75042e33	+	8.22798e33i	0.230833	+	0.399814i
$557$	3.15350e34			1.49832			0.749158	−	0.662391i	$-0.230458\pi$
$557$	3.15350e34			1.49832			0.749158	+	0.662391i	$0.230458\pi$
$558$	7.20325e33	−	2.18789e34i	0.334658	−	1.01648i
$559$	1.52596e34			0.693261
$560$	−1.28505e33	−	2.22577e33i	−0.0570912	−	0.0988849i
$561$	5.40524e33	−	1.20770e34i	0.234844	−	0.524715i
$562$	−1.14566e34	+	1.98433e34i	−0.486800	+	0.843162i
$563$	4.91693e33	−	8.51638e33i	0.204333	−	0.353916i	−0.745587	−	0.666409i	$-0.767831\pi$
$563$	4.91693e33	−	8.51638e33i	0.204333	−	0.353916i	0.949920	+	0.312493i	$0.101164\pi$
$564$	−4.04288e33	−	5.58741e33i	−0.164325	−	0.227102i
$565$	−6.37128e33	−	1.10354e34i	−0.253292	−	0.438714i
$566$	−3.03122e33			−0.117873
$567$	2.77252e33	−	2.45381e34i	0.105460	−	0.933367i
$568$	−6.90006e33			−0.256743
$569$	−7.27436e33	−	1.25996e34i	−0.264784	−	0.458619i	0.702723	−	0.711464i	$-0.251967\pi$
$569$	−7.27436e33	−	1.25996e34i	−0.264784	−	0.458619i	−0.967507	+	0.252844i	$0.918634\pi$
$570$	−7.91708e33	−	1.09417e34i	−0.281922	−	0.389627i
$571$	5.50961e33	−	9.54292e33i	0.191942	−	0.332453i	−0.753952	−	0.656930i	$-0.771855\pi$
$571$	5.50961e33	−	9.54292e33i	0.191942	−	0.332453i	0.945894	+	0.324477i	$0.105188\pi$
$572$	6.06005e33	−	1.04963e34i	0.206550	−	0.357755i
$573$	−1.49437e34	+	3.33890e34i	−0.498341	+	1.11345i
$574$	1.45750e33	+	2.52447e33i	0.0475566	+	0.0823705i
$575$	−9.92372e33			−0.316830
$576$	−1.25126e33	+	3.80053e33i	−0.0390900	+	0.118731i
$577$	4.28784e34			1.31081			0.655406	−	0.755277i	$-0.272497\pi$
$577$	4.28784e34			1.31081			0.655406	+	0.755277i	$0.272497\pi$
$578$	−7.17514e33	−	1.24277e34i	−0.214651	−	0.371786i
$579$	−3.68954e33	+	3.80522e32i	−0.108017	+	0.0111403i
$580$	7.88839e33	−	1.36631e34i	0.226016	−	0.391470i
$581$	2.98347e34	−	5.16752e34i	0.836604	−	1.44904i
$582$	−5.91389e33	+	6.09931e32i	−0.162307	+	0.0167395i
$583$	1.14337e34	+	1.98037e34i	0.307135	+	0.531973i
$584$	−2.37765e34			−0.625154
$585$	−3.36977e34	+	7.02558e33i	−0.867266	+	0.180815i
$586$	4.83447e33			0.121795
$587$	3.25757e34	+	5.64228e34i	0.803374	+	1.39148i	0.917383	+	0.398005i	$0.130297\pi$
$587$	3.25757e34	+	5.64228e34i	0.803374	+	1.39148i	−0.114009	+	0.993480i	$0.536369\pi$
$588$	9.95835e32	−	2.22501e33i	0.0240420	−	0.0537174i
$589$	−4.47829e34	+	7.75662e34i	−1.05845	+	1.83329i
$590$	−2.79032e33	+	4.83297e33i	−0.0645659	+	0.111831i
$591$	8.49501e33	+	1.17404e34i	0.192451	+	0.265974i
$592$	6.17054e33	+	1.06877e34i	0.136868	+	0.237062i
$593$	6.49827e34			1.41128			0.705641	−	0.708569i	$-0.250659\pi$
$593$	6.49827e34			1.41128			0.705641	+	0.708569i	$0.250659\pi$
$594$	3.22116e33	−	1.47306e34i	0.0684985	−	0.313248i
$595$	2.78065e34			0.579007
$596$	9.32391e33	+	1.61495e34i	0.190117	+	0.329292i
$597$	4.59239e33	+	6.34684e33i	0.0916979	+	0.126730i
$598$	−1.36690e34	+	2.36754e34i	−0.267284	+	0.462949i
$599$	3.34332e34	−	5.79079e34i	0.640239	−	1.10893i	−0.345140	−	0.938551i	$-0.612169\pi$
$599$	3.34332e34	−	5.79079e34i	0.640239	−	1.10893i	0.985379	−	0.170375i	$-0.0544980\pi$
$600$	5.88034e33	−	1.31385e34i	0.110284	−	0.246409i
$601$	−4.00918e34	−	6.94411e34i	−0.736419	−	1.27552i	−0.954098	−	0.299495i	$-0.903182\pi$
$601$	−4.00918e34	−	6.94411e34i	−0.736419	−	1.27552i	0.217679	−	0.976020i	$-0.430152\pi$
$602$	−1.40477e34			−0.252726
$603$	−5.03118e34	−	5.63166e34i	−0.886551	−	0.992362i
$604$	1.27054e34			0.219294
$605$	−1.14231e34	−	1.97855e34i	−0.193127	−	0.334506i
$606$	−3.17572e34	+	3.27529e33i	−0.525938	+	0.0542428i
$607$	−2.20568e34	+	3.82036e34i	−0.357837	+	0.619791i	−0.987599	−	0.156997i	$-0.949819\pi$
$607$	−2.20568e34	+	3.82036e34i	−0.357837	+	0.619791i	0.629763	+	0.776788i	$0.283152\pi$
$608$	7.77911e33	−	1.34738e34i	0.123633	−	0.214139i
$609$	−1.11576e35	+	1.15074e34i	−1.73722	+	0.179169i
$610$	8.89673e33	+	1.54096e34i	0.135709	+	0.235054i
$611$	6.83494e34			1.02146
$612$	−2.88411e34	−	3.22833e34i	−0.422298	−	0.472700i
$613$	−8.57385e34			−1.23004			−0.615021	−	0.788511i	$-0.710853\pi$
$613$	−8.57385e34			−1.23004			−0.615021	+	0.788511i	$0.710853\pi$
$614$	2.96420e34	+	5.13415e34i	0.416681	+	0.721712i
$615$	2.06514e33	−	4.61416e33i	0.0284452	−	0.0635556i
$616$	−5.57875e33	+	9.66269e33i	−0.0752971	+	0.130418i
$617$	−4.85117e34	+	8.40247e34i	−0.641626	+	1.11133i	0.343444	+	0.939173i	$0.388406\pi$
$617$	−4.85117e34	+	8.40247e34i	−0.641626	+	1.11133i	−0.985070	+	0.172155i	$0.944927\pi$
$618$	2.71215e34	+	3.74829e34i	0.351527	+	0.485822i
$619$	−2.10368e34	−	3.64367e34i	−0.267206	−	0.462814i	0.700933	−	0.713227i	$-0.252767\pi$
$619$	−2.10368e34	−	3.64367e34i	−0.267206	−	0.462814i	−0.968139	+	0.250413i	$0.919434\pi$
$620$	2.95583e34			0.367945
$621$	−7.26563e33	+	3.32262e34i	−0.0886397	+	0.405355i
$622$	4.79799e34			0.573692
$623$	−1.62873e34	−	2.82104e34i	−0.190875	−	0.330604i
$624$	−2.32455e34	−	3.21261e34i	−0.267012	−	0.369020i
$625$	−1.53924e34	+	2.66604e34i	−0.173303	+	0.300170i
$626$	−1.31033e34	+	2.26955e34i	−0.144611	+	0.250473i
$627$	−2.39518e34	+	5.35159e34i	−0.259116	+	0.578947i
$628$	−6.80243e33	−	1.17822e34i	−0.0721388	−	0.124948i
$629$	−1.33521e35			−1.38809
$630$	3.10214e34	−	6.46760e33i	0.316159	−	0.0659154i
$631$	−7.03375e34			−0.702781			−0.351390	−	0.936229i	$-0.614291\pi$
$631$	−7.03375e34			−0.702781			−0.351390	+	0.936229i	$0.614291\pi$
$632$	1.09021e34	+	1.88831e34i	0.106794	+	0.184973i
$633$	−1.88358e35	+	1.94263e34i	−1.80899	+	0.186571i
$634$	−3.36715e33	+	5.83207e33i	−0.0317064	+	0.0549170i
$635$	2.27242e34	−	3.93596e34i	0.209806	−	0.363395i
$636$	7.44216e34	−	7.67549e33i	0.673729	−	0.0694852i
$637$	1.20794e34	+	2.09221e34i	0.107226	+	0.185721i
$638$	−6.84913e34			−0.596180
$639$	2.66048e34	−	8.08085e34i	0.227090	−	0.689757i
$640$	−5.13449e33			−0.0429781
$641$	4.16184e34	+	7.20852e34i	0.341633	+	0.591726i	0.984736	−	0.174053i	$-0.0556865\pi$
$641$	4.16184e34	+	7.20852e34i	0.341633	+	0.591726i	−0.643103	+	0.765780i	$0.722353\pi$
$642$	1.43667e34	−	3.20996e34i	0.115656	−	0.258412i
$643$	4.34702e34	−	7.52926e34i	0.343206	−	0.594450i	−0.641820	−	0.766855i	$-0.721821\pi$
$643$	4.34702e34	−	7.52926e34i	0.343206	−	0.594450i	0.985026	+	0.172405i	$0.0551539\pi$
$644$	1.25834e34	−	2.17951e34i	0.0974373	−	0.168766i
$645$	1.42810e34	+	1.97368e34i	0.108458	+	0.149893i
$646$	8.41640e34	+	1.45776e35i	0.626931	+	1.08588i
$647$	2.39516e35			1.74997			0.874987	−	0.484147i	$-0.160870\pi$
$647$	2.39516e35			1.74997			0.874987	+	0.484147i	$0.160870\pi$
$648$	−3.96846e34	−	2.93076e34i	−0.284403	−	0.210036i
$649$	2.42271e34			0.170311
$650$	7.13279e34	+	1.23544e35i	0.491861	+	0.851928i
$651$	−1.23192e35	−	1.70255e35i	−0.833335	−	1.15170i
$652$	−3.84714e34	+	6.66344e34i	−0.255295	+	0.442184i
$653$	6.00416e34	−	1.03995e35i	0.390875	−	0.677015i	−0.601690	−	0.798729i	$-0.705506\pi$
$653$	6.00416e34	−	1.03995e35i	0.390875	−	0.677015i	0.992565	+	0.121715i	$0.0388393\pi$
$654$	−2.89334e34	+	6.46463e34i	−0.184790	+	0.412878i
$655$	−1.62839e34	−	2.82045e34i	−0.102033	−	0.176727i
$656$	5.82354e33			0.0358005
$657$	9.16758e34	−	2.78453e35i	0.552952	−	1.67952i
$658$	−6.29211e34			−0.372368
$659$	−4.13089e34	−	7.15492e34i	−0.239870	−	0.415467i	0.720807	−	0.693136i	$-0.243772\pi$
$659$	−4.13089e34	−	7.15492e34i	−0.239870	−	0.415467i	−0.960677	+	0.277669i	$0.910438\pi$
$660$	1.92473e34	−	1.98508e33i	0.109666	−	0.0113104i
$661$	−3.31071e34	+	5.73431e34i	−0.185098	+	0.320600i	−0.943610	−	0.331060i	$-0.892594\pi$
$661$	−3.31071e34	+	5.73431e34i	−0.185098	+	0.320600i	0.758511	+	0.651660i	$0.225927\pi$
$662$	−6.07179e33	+	1.05167e34i	−0.0333113	+	0.0576969i
$663$	4.26762e35	−	4.40142e34i	2.29756	−	0.236959i
$664$	−5.96031e34	−	1.03236e35i	−0.314897	−	0.545417i
$665$	−1.23217e35			−0.638851
$666$	−1.48959e35	+	3.10561e34i	−0.757945	+	0.158023i
$667$	1.54489e35			0.771479
$668$	−6.68347e34	−	1.15761e35i	−0.327564	−	0.567358i
$669$	−1.31956e35	+	2.94831e35i	−0.634749	+	1.41823i
$670$	4.84531e34	−	8.39232e34i	0.228763	−	0.396230i
$671$	3.86232e34	−	6.68973e34i	0.178985	−	0.310011i
$672$	2.13993e34	+	2.95746e34i	0.0973384	+	0.134525i
$673$	−3.53069e34	−	6.11533e34i	−0.157642	−	0.273043i	0.776376	−	0.630270i	$-0.217056\pi$
$673$	−3.53069e34	−	6.11533e34i	−0.157642	−	0.273043i	−0.934018	+	0.357227i	$0.883722\pi$
$674$	1.34813e35			0.590858
$675$	1.31196e35	+	1.19525e35i	0.564447	+	0.514234i
$676$	2.74604e35			1.15977
$677$	−1.17229e35	−	2.03047e35i	−0.486046	−	0.841856i	0.513825	−	0.857895i	$-0.328228\pi$
$677$	−1.17229e35	−	2.03047e35i	−0.486046	−	0.841856i	−0.999871	+	0.0160384i	$0.994895\pi$
$678$	1.06098e35	+	1.46631e35i	0.431852	+	0.596835i
$679$	−2.71205e34	+	4.69741e34i	−0.108374	+	0.187710i
$680$	2.77756e34	−	4.81088e34i	0.108969	−	0.188739i
$681$	−5.59352e33	+	1.24977e34i	−0.0215450	+	0.0481383i
$682$	−6.41603e34	−	1.11129e35i	−0.242640	−	0.420264i
$683$	1.42849e35			0.530420			0.265210	−	0.964191i	$-0.414559\pi$
$683$	1.42849e35			0.530420			0.265210	+	0.964191i	$0.414559\pi$
$684$	1.27802e35	+	1.43055e35i	0.465945	+	0.521556i
$685$	1.77086e35			0.633946
$686$	−1.05594e35	−	1.82895e35i	−0.371184	−	0.642909i
$687$	3.53289e35	−	3.64365e34i	1.21947	−	0.125770i
$688$	−1.40321e34	+	2.43043e34i	−0.0475628	+	0.0823812i
$689$	−3.70734e35	+	6.42130e35i	−1.23402	+	2.13738i
$690$	−4.34142e34	+	4.47753e33i	−0.141912	+	0.0146361i
$691$	2.88162e34	+	4.99111e34i	0.0925041	+	0.160222i	0.908564	−	0.417745i	$-0.137180\pi$
$691$	2.88162e34	+	4.99111e34i	0.0925041	+	0.160222i	−0.816060	+	0.577967i	$0.803846\pi$
$692$	1.52616e35			0.481141
$693$	−9.16523e34	−	1.02591e35i	−0.283777	−	0.317647i
$694$	−2.03584e35			−0.619084
$695$	−7.51605e34	−	1.30182e35i	−0.224481	−	0.388813i
$696$	−9.15429e34	+	2.04536e35i	−0.268540	+	0.600003i
$697$	−3.15031e34	+	5.45650e34i	−0.0907703	+	0.157219i
$698$	−6.08904e34	+	1.05465e35i	−0.172328	+	0.298481i
$699$	2.10921e35	+	2.91500e35i	0.586346	+	0.810351i
$700$	−6.56630e34	−	1.13732e35i	−0.179306	−	0.310567i
$701$	−6.28311e35			−1.68539			−0.842693	−	0.538395i	$-0.819031\pi$
$701$	−6.28311e35			−1.68539			−0.842693	+	0.538395i	$0.819031\pi$
$702$	4.65866e35	−	1.48365e35i	1.22757	−	0.390947i
$703$	5.91662e35			1.53155
$704$	1.11451e34	+	1.93039e34i	0.0283417	+	0.0490893i
$705$	6.39659e34	+	8.84032e34i	0.159803	+	0.220853i
$706$	−1.63461e35	+	2.83123e35i	−0.401195	+	0.694891i
$707$	−1.45635e35	+	2.52248e35i	−0.351176	+	0.608254i
$708$	3.23810e34	−	7.23493e34i	0.0767139	−	0.171403i
$709$	−3.60866e35	−	6.25039e35i	−0.839979	−	1.45489i	−0.889911	−	0.456134i	$-0.849234\pi$
$709$	−3.60866e35	−	6.25039e35i	−0.839979	−	1.45489i	0.0499322	−	0.998753i	$-0.484099\pi$
$710$	1.09172e35			0.249678
$711$	−2.63181e35	+	5.48701e34i	−0.591404	+	0.123301i
$712$	−6.50768e34			−0.143690
$713$	1.44720e35	+	2.50662e35i	0.313985	+	0.543838i
$714$	−3.92868e35	+	4.05186e34i	−0.837566	+	0.0863826i
$715$	−9.58812e34	+	1.66071e35i	−0.200867	+	0.347911i
$716$	8.79764e34	−	1.52380e35i	0.181115	−	0.313700i
$717$	6.65041e35	−	6.85892e34i	1.34542	−	0.138761i
$718$	−3.03497e35	−	5.25673e35i	−0.603391	−	1.04510i
$719$	−7.06277e35			−1.37995			−0.689975	−	0.723833i	$-0.742379\pi$
$719$	−7.06277e35			−1.37995			−0.689975	+	0.723833i	$0.742379\pi$
$720$	1.97972e34	−	6.01314e34i	0.0380143	−	0.115464i
$721$	4.22104e35			0.796578
$722$	−1.82329e35	−	3.15803e35i	−0.338175	−	0.585736i
$723$	−1.04398e35	+	2.33258e35i	−0.190311	+	0.425214i
$724$	8.89986e34	−	1.54150e35i	0.159460	−	0.276193i
$725$	4.03078e35	−	6.98152e35i	0.709846	−	1.22949i
$726$	1.90224e35	+	2.62897e35i	0.329275	+	0.455069i
$727$	−1.02681e35	−	1.77849e35i	−0.174707	−	0.302601i	0.765353	−	0.643611i	$-0.222564\pi$
$727$	−1.02681e35	−	1.77849e35i	−0.174707	−	0.302601i	−0.940060	+	0.341010i	$0.889231\pi$
$728$	−3.61779e35			−0.605064
$729$	4.96243e35	−	3.51755e35i	0.815831	−	0.578290i
$730$	3.76188e35			0.607953
$731$	−1.51817e35	−	2.62954e35i	−0.241186	−	0.417747i
$732$	−1.48153e35	−	2.04753e35i	−0.231378	−	0.319773i
$733$	−3.49051e35	+	6.04573e35i	−0.535906	+	0.928216i	0.463213	+	0.886247i	$0.346697\pi$
$733$	−3.49051e35	+	6.04573e35i	−0.535906	+	0.928216i	−0.999119	+	0.0419694i	$0.986637\pi$
$734$	−1.68846e35	+	2.92451e35i	−0.254854	+	0.441420i
$735$	−1.57560e34	+	3.52038e34i	−0.0233805	+	0.0522393i
$736$	−2.51389e34	−	4.35418e34i	−0.0366753	−	0.0635234i
$737$	−4.20697e35			−0.603428
$738$	−2.24540e34	+	6.82011e34i	−0.0316657	+	0.0961805i
$739$	1.04387e36			1.44741			0.723704	−	0.690110i	$-0.242438\pi$
$739$	1.04387e36			1.44741			0.723704	+	0.690110i	$0.242438\pi$
$740$	−9.76294e34	−	1.69099e35i	−0.133102	−	0.230539i
$741$	−1.89108e36	+	1.95037e35i	−2.53502	+	0.261450i
$742$	3.41290e35	−	5.91132e35i	0.449857	−	0.779176i
$743$	−4.89050e35	+	8.47060e35i	−0.633860	+	1.09788i	0.352896	+	0.935663i	$0.385197\pi$
$743$	−4.89050e35	+	8.47060e35i	−0.633860	+	1.09788i	−0.986755	+	0.162215i	$0.948136\pi$
$744$	−4.17618e35	+	4.30712e34i	−0.532253	+	0.0548940i
$745$	−1.47522e35	−	2.55515e35i	−0.184885	−	0.320231i
$746$	4.36519e35			0.537983
$747$	1.43883e36	−	2.99980e35i	1.74383	−	0.363567i
$748$	−2.41163e35			−0.287436
$749$	−1.60426e35	−	2.77866e35i	−0.188041	−	0.325696i
$750$	−2.14884e35	+	4.80118e35i	−0.247707	+	0.553455i
$751$	−1.26972e35	+	2.19922e35i	−0.143949	+	0.249327i	−0.928980	−	0.370129i	$-0.879313\pi$
$751$	−1.26972e35	+	2.19922e35i	−0.143949	+	0.249327i	0.785031	+	0.619456i	$0.212647\pi$
$752$	−6.28512e34	+	1.08861e35i	−0.0700794	+	0.121381i
$753$	−6.07271e34	−	8.39270e34i	−0.0665956	−	0.0920375i
$754$	−1.11041e36	−	1.92328e36i	−1.19768	−	2.07444i
$755$	−2.01023e35			−0.213260
$756$	−4.28867e35	+	1.36582e35i	−0.447507	+	0.142518i
$757$	−7.81917e35			−0.802532			−0.401266	−	0.915962i	$-0.631430\pi$
$757$	−7.81917e35			−0.802532			−0.401266	+	0.915962i	$0.631430\pi$
$758$	3.06093e35	+	5.30169e35i	0.309021	+	0.535241i
$759$	1.11070e35	+	1.53503e35i	0.110300	+	0.152439i
$760$	−1.23080e35	+	2.13181e35i	−0.120231	+	0.208247i
$761$	−8.13655e35	+	1.40929e36i	−0.781865	+	1.35423i	0.148988	+	0.988839i	$0.452398\pi$
$761$	−8.13655e35	+	1.40929e36i	−0.781865	+	1.35423i	−0.930854	+	0.365392i	$0.880935\pi$
$762$	−2.63710e35	+	5.89210e35i	−0.249281	+	0.556972i
$763$	3.23086e35	+	5.59601e35i	0.300442	+	0.520382i
$764$	6.66738e35			0.609941
$765$	4.56320e35	+	5.10782e35i	0.410678	+	0.459693i
$766$	−8.19517e35			−0.725602
$767$	3.92778e35	+	6.80312e35i	0.342141	+	0.592606i
$768$	7.25434e34	−	7.48178e33i	0.0621702	−	0.00641194i
$769$	−1.40603e35	+	2.43531e35i	−0.118553	+	0.205340i	−0.919195	−	0.393804i	$-0.871159\pi$
$769$	−1.40603e35	+	2.43531e35i	−0.118553	+	0.205340i	0.800641	+	0.599144i	$0.204492\pi$
$770$	8.82663e34	−	1.52882e35i	0.0732252	−	0.126830i
$771$	1.27514e36	−	1.31512e35i	1.04082	−	0.107346i
$772$	3.38022e34	+	5.85471e34i	0.0271474	+	0.0470207i
$773$	6.80034e35			0.537387			0.268693	−	0.963226i	$-0.413408\pi$
$773$	6.80034e35			0.537387			0.268693	+	0.963226i	$0.413408\pi$
$774$	−2.30531e35	−	2.58045e35i	−0.179253	−	0.200647i
$775$	1.51036e36			1.15560
$776$	5.41808e34	+	9.38438e34i	0.0407919	+	0.0706536i
$777$	−5.67114e35	+	1.26711e36i	−0.420153	+	0.938753i
$778$	−5.24940e35	+	9.09223e35i	−0.382705	+	0.662865i
$779$	1.39597e35	−	2.41790e35i	0.100152	−	0.173468i
$780$	3.67787e35	+	5.08294e35i	0.259665	+	0.358866i
$781$	−2.36972e35	−	4.10448e35i	−0.164649	−	0.285181i
$782$	5.43967e35			0.371953
$783$	−2.04241e36	−	1.86072e36i	−1.37442	−	1.25216i
$784$	−4.44307e34			−0.0294261
$785$	1.07627e35	+	1.86416e35i	0.0701538	+	0.121510i
$786$	2.71168e35	+	3.74763e35i	0.173963	+	0.240423i
$787$	5.70824e35	−	9.88697e35i	0.360428	−	0.624279i	−0.627603	−	0.778533i	$-0.715964\pi$
$787$	5.70824e35	−	9.88697e35i	0.360428	−	0.624279i	0.988031	+	0.154254i	$0.0492974\pi$
$788$	1.32064e35	−	2.28742e35i	0.0820745	−	0.142157i
$789$	5.62497e35	−	1.25680e36i	0.344079	−	0.768780i
$790$	−1.72492e35	−	2.98765e35i	−0.103856	−	0.179884i
$791$	1.65125e36			0.978601
$792$	−2.69046e35	+	5.60929e34i	−0.156950	+	0.0327223i
$793$	2.50469e36			1.43827
$794$	−1.93446e35	−	3.35058e35i	−0.109346	−	0.189393i
$795$	−1.17749e36	+	1.21441e35i	−0.655190	+	0.0675732i
$796$	7.13938e34	−	1.23658e35i	0.0391064	−	0.0677342i
$797$	−4.10949e35	+	7.11785e35i	−0.221595	+	0.383813i	−0.955292	−	0.295663i	$-0.904460\pi$
$797$	−4.10949e35	+	7.11785e35i	−0.221595	+	0.383813i	0.733698	+	0.679476i	$0.237793\pi$
$798$	1.74089e36	−	1.79547e35i	0.924133	−	0.0953108i
$799$	−6.80002e35	−	1.17780e36i	−0.355365	−	0.615511i
$800$	−2.62360e35			−0.134981
$801$	2.50918e35	−	7.62132e35i	0.127094	−	0.386033i
$802$	2.42098e36			1.20729
$803$	−8.16569e35	−	1.41434e36i	−0.400912	−	0.694399i
$804$	−5.62287e35	+	1.25633e36i	−0.271805	+	0.607298i
$805$	−1.99093e35	+	3.44839e35i	−0.0947562	+	0.164123i
$806$	2.08038e36	−	3.60332e36i	0.974888	−	1.68856i
$807$	9.92417e35	+	1.37156e36i	0.457905	+	0.632840i
$808$	2.90947e35	+	5.03936e35i	0.132182	+	0.228946i
$809$	−5.29083e35			−0.236683			−0.118341	−	0.992973i	$-0.537758\pi$
$809$	−5.29083e35			−0.236683			−0.118341	+	0.992973i	$0.537758\pi$
$810$	6.27884e35	+	4.63701e35i	0.276577	+	0.204256i
$811$	1.68688e36			0.731682			0.365841	−	0.930677i	$-0.380781\pi$
$811$	1.68688e36			0.731682			0.365841	+	0.930677i	$0.380781\pi$
$812$	1.02222e36	+	1.77053e36i	0.436609	+	0.756230i
$813$	−2.46344e36	−	3.40457e36i	−1.03612	−	1.43196i
$814$	−4.23836e35	+	7.34106e35i	−0.175547	+	0.304056i
$815$	6.08689e35	−	1.05428e36i	0.248270	−	0.430017i
$816$	−3.22329e35	+	7.20185e35i	−0.129471	+	0.289279i
$817$	6.72734e35	+	1.16521e36i	0.266114	+	0.460923i
$818$	2.87843e36			1.12135
$819$	1.39492e36	−	4.23690e36i	0.535182	−	1.62555i
$820$	−9.21392e34			−0.0348154
$821$	−1.60023e36	−	2.77169e36i	−0.595517	−	1.03147i	−0.993474	−	0.114061i	$-0.963614\pi$
$821$	−1.60023e36	−	2.77169e36i	−0.595517	−	1.03147i	0.397957	−	0.917404i	$-0.369719\pi$
$822$	−2.50199e36	+	2.58043e35i	−0.917038	+	0.0945789i
$823$	−2.28957e36	+	3.96566e36i	−0.826527	+	1.43159i	0.0742202	+	0.997242i	$0.476353\pi$
$823$	−2.28957e36	+	3.96566e36i	−0.826527	+	1.43159i	−0.900747	+	0.434344i	$0.856980\pi$
$824$	4.21635e35	−	7.30293e35i	0.149915	−	0.259661i
$825$	9.83493e35	−	1.01433e35i	0.344427	−	0.0355226i
$826$	−3.61584e35	−	6.26281e35i	−0.124726	−	0.216032i
$827$	1.41774e36			0.481701			0.240851	−	0.970562i	$-0.422574\pi$
$827$	1.41774e36			0.481701			0.240851	+	0.970562i	$0.422574\pi$
$828$	6.06859e35	−	1.26523e35i	0.203099	−	0.0423438i
$829$	−2.97714e36			−0.981450			−0.490725	−	0.871315i	$-0.663268\pi$
$829$	−2.97714e36			−0.981450			−0.490725	+	0.871315i	$0.663268\pi$
$830$	9.43032e35	+	1.63338e36i	0.306232	+	0.530409i
$831$	−1.13246e34	+	2.53027e34i	−0.00362252	+	0.00809385i
$832$	−3.61377e35	+	6.25924e35i	−0.113873	+	0.197233i
$833$	2.40353e35	−	4.16304e35i	0.0746083	−	0.129225i
$834$	1.25161e36	+	1.72977e36i	0.382732	+	0.528949i
$835$	1.05745e36	+	1.83156e36i	0.318551	+	0.551746i
$836$	1.06865e36			0.317144
$837$	1.10581e36	−	5.05692e36i	0.323304	−	1.47849i
$838$	−2.90797e36			−0.837605
$839$	1.35797e36	+	2.35208e36i	0.385360	+	0.667463i	0.991819	−	0.127652i	$-0.0407440\pi$
$839$	1.35797e36	+	2.35208e36i	0.385360	+	0.667463i	−0.606459	+	0.795115i	$0.707411\pi$
$840$	−3.38577e35	−	4.67925e35i	−0.0946600	−	0.130823i
$841$	−4.45979e36	+	7.72458e36i	−1.22847	+	2.12777i
$842$	−1.96315e36	+	3.40027e36i	−0.532785	+	0.922810i
$843$	−2.10353e36	+	4.69994e36i	−0.562475	+	1.25675i
$844$	1.72566e36	+	2.98893e36i	0.454647	+	0.787472i
$845$	−4.34474e36			−1.12786
$846$	−1.03257e36	−	1.15581e36i	−0.264113	−	0.295635i
$847$	2.96054e36			0.746154
$848$	−6.81822e35	−	1.18095e36i	−0.169326	−	0.293281i
$849$	−6.77605e35	+	6.98849e34i	−0.165817	+	0.0171016i
$850$	1.41927e36	−	2.45824e36i	0.342238	−	0.592773i
$851$	9.56004e35	−	1.65585e36i	0.227164	−	0.393460i
$852$	−1.54245e36	+	1.59081e35i	−0.361174	+	0.0372497i
$853$	−2.52908e34	−	4.38049e34i	−0.00583578	−	0.0101079i	0.863093	−	0.505045i	$-0.168524\pi$
$853$	−2.52908e34	−	4.38049e34i	−0.00583578	−	0.0101079i	−0.868929	+	0.494938i	$0.835191\pi$
$854$	−2.30577e36			−0.524315
$855$	−2.02206e36	−	2.26339e36i	−0.453124	−	0.507205i
$856$	−6.40990e35			−0.141556
$857$	−2.07326e36	−	3.59100e36i	−0.451226	−	0.781546i	0.547237	−	0.836978i	$-0.315680\pi$
$857$	−2.07326e36	−	3.59100e36i	−0.451226	−	0.781546i	−0.998462	+	0.0554317i	$0.982346\pi$
$858$	1.11268e36	−	2.48607e36i	0.238660	−	0.533240i
$859$	−1.38778e36	+	2.40370e36i	−0.293362	+	0.508119i	−0.974603	−	0.223941i	$-0.928108\pi$
$859$	−1.38778e36	+	2.40370e36i	−0.293362	+	0.508119i	0.681240	+	0.732060i	$0.261441\pi$
$860$	2.22014e35	−	3.84540e35i	0.0462541	−	0.0801144i
$861$	3.84014e35	+	5.30721e35i	0.0788511	+	0.108975i
$862$	−2.52963e34	−	4.38145e34i	−0.00511937	−	0.00886702i
$863$	1.35077e36			0.269431			0.134715	−	0.990884i	$-0.456988\pi$
$863$	1.35077e36			0.269431			0.134715	+	0.990884i	$0.456988\pi$
$864$	−1.92086e35	+	8.78424e35i	−0.0377637	+	0.172696i
$865$	−2.41466e36			−0.467902
$866$	1.08338e36	+	1.87647e36i	0.206922	+	0.358399i
$867$	−1.89046e36	−	2.61269e36i	−0.355901	−	0.491868i
$868$	−1.91516e36	+	3.31715e36i	−0.355392	+	0.615557i
$869$	−7.48836e35	+	1.29702e36i	−0.136975	+	0.237247i
$870$	1.44838e36	−	3.23613e36i	0.261151	−	0.583493i
$871$	−6.82049e36	−	1.18134e37i	−1.21224	−	2.09966i
$872$	1.29091e36			0.226172
$873$	−1.30794e36	+	2.72690e35i	−0.225896	+	0.0470967i
$874$	−2.41044e36			−0.410396
$875$	2.39951e36	+	4.15607e36i	0.402737	+	0.697561i
$876$	−5.31503e36	+	5.48168e35i	−0.879437	+	0.0907010i
$877$	−3.29641e36	+	5.70955e36i	−0.537707	+	0.931337i	0.461320	+	0.887234i	$0.347376\pi$
$877$	−3.29641e36	+	5.70955e36i	−0.537707	+	0.931337i	−0.999027	+	0.0441026i	$0.985957\pi$
$878$	−1.01196e36	+	1.75277e36i	−0.162735	+	0.281866i
$879$	1.08070e36	−	1.11459e35i	0.171335	−	0.0176707i
$880$	−1.76336e35	−	3.05424e35i	−0.0275619	−	0.0477386i
$881$	1.19143e37			1.83599			0.917995	−	0.396593i	$-0.129808\pi$
$881$	1.19143e37			1.83599			0.917995	+	0.396593i	$0.129808\pi$
$882$	1.71313e35	−	5.20340e35i	0.0260275	−	0.0790552i
$883$	1.83480e36			0.274841			0.137420	−	0.990513i	$-0.456119\pi$
$883$	1.83480e36			0.274841			0.137420	+	0.990513i	$0.456119\pi$
$884$	−3.90982e36	−	6.77201e36i	−0.577436	−	1.00015i
$885$	−5.12327e35	+	1.14470e36i	−0.0746031	+	0.166687i
$886$	−3.52748e36	+	6.10978e36i	−0.506458	+	0.877210i
$887$	6.33369e36	−	1.09703e37i	0.896626	−	1.55300i	0.0648476	−	0.997895i	$-0.479344\pi$
$887$	6.33369e36	−	1.09703e37i	0.896626	−	1.55300i	0.831779	−	0.555107i	$-0.187323\pi$
$888$	1.62578e36	+	2.24688e36i	0.226934	+	0.313630i
$889$	2.94472e36	+	5.10041e36i	0.405296	+	0.701994i
$890$	1.02964e36			0.139736
$891$	3.80449e35	−	3.36715e36i	0.0509126	−	0.450600i
$892$	5.88741e36			0.776898
$893$	3.01324e36	+	5.21909e36i	0.392094	+	0.679127i
$894$	2.45661e36	+	3.39512e36i	0.315222	+	0.435648i
$895$	−1.39195e36	+	2.41093e36i	−0.176131	+	0.305068i
$896$	3.32677e35	−	5.76213e35i	0.0415119	−	0.0719006i
$897$	−2.50975e36	+	5.60758e36i	−0.308834	+	0.690033i
$898$	−3.96352e36	−	6.86502e36i	−0.480980	−	0.833082i
$899$	−2.35127e37			−2.81389
$900$	1.01159e36	−	3.07258e36i	0.119391	−	0.362636i
$901$	1.47536e37			1.71727
$902$	2.00001e35	+	3.46412e35i	0.0229589	+	0.0397659i
$903$	−3.14025e36	+	3.23870e35i	−0.355522	+	0.0366669i
$904$	1.64941e36	−	2.85686e36i	0.184172	−	0.318995i
$905$	−1.40812e36	+	2.43894e36i	−0.155072	+	0.268593i
$906$	2.84019e36	−	2.92924e35i	0.308493	−	0.0318165i
$907$	−3.20559e35	−	5.55225e35i	−0.0343413	−	0.0594809i	0.848344	−	0.529446i	$-0.177600\pi$
$907$	−3.20559e35	−	5.55225e35i	−0.0343413	−	0.0594809i	−0.882685	+	0.469965i	$0.844267\pi$
$908$	2.49564e35			0.0263699
$909$	−7.02355e36	+	1.46433e36i	−0.731995	+	0.152612i
$910$	5.72402e36			0.588415
$911$	4.43527e36	+	7.68211e36i	0.449718	+	0.778934i	0.998367	−	0.0571183i	$-0.0181912\pi$
$911$	4.43527e36	+	7.68211e36i	0.449718	+	0.778934i	−0.548650	+	0.836052i	$0.684858\pi$
$912$	1.42832e36	−	3.19130e36i	0.142853	−	0.319178i
$913$	4.09396e36	−	7.09095e36i	0.403886	−	0.699552i
$914$	1.34399e36	−	2.32786e36i	0.130789	−	0.226532i
$915$	2.34406e36	+	3.23957e36i	0.225011	+	0.310974i
$916$	−3.23669e36	−	5.60612e36i	−0.306484	−	0.530846i
$917$	4.22030e36			0.394209
$918$	−7.19148e36	−	6.55173e36i	−0.662651	−	0.603702i
$919$	1.08231e37			0.983800			0.491900	−	0.870652i	$-0.336303\pi$
$919$	1.08231e37			0.983800			0.491900	+	0.870652i	$0.336303\pi$
$920$	3.97744e35	+	6.88912e35i	0.0356661	+	0.0617755i
$921$	7.80991e36	+	1.07936e37i	0.690877	+	0.954816i
$922$	1.49345e36	−	2.58673e36i	0.130333	−	0.225743i
$923$	7.68376e36	−	1.33087e37i	0.661535	−	1.14581i
$924$	−1.02431e36	+	2.28863e36i	−0.0870025	+	0.194391i
$925$	−4.98864e36	−	8.64057e36i	−0.418033	−	0.724054i
$926$	−1.34670e37			−1.11336
$927$	6.92696e36	+	7.75370e36i	0.564997	+	0.632430i
$928$	4.08433e36			0.328678
$929$	2.23607e35	+	3.87298e35i	0.0177537	+	0.0307503i	0.874766	−	0.484546i	$-0.161015\pi$
$929$	2.23607e35	+	3.87298e35i	0.0177537	+	0.0307503i	−0.857012	+	0.515296i	$0.827682\pi$
$930$	6.60750e36	−	6.81466e35i	0.517607	−	0.0533836i
$931$	−1.06506e36	+	1.84474e36i	−0.0823195	+	0.142581i
$932$	3.27900e36	−	5.67939e36i	0.250059	−	0.433115i
$933$	1.07255e37	−	1.10618e36i	0.807043	−	0.0832346i
$934$	3.16971e36	+	5.49010e36i	0.235334	+	0.407610i
$935$	3.81565e36			0.279527
$936$	−5.93700e36	−	6.64559e36i	−0.429160	−	0.480380i
$937$	−1.11792e37			−0.797383			−0.398692	−	0.917085i	$-0.630536\pi$
$937$	−1.11792e37			−0.797383			−0.398692	+	0.917085i	$0.630536\pi$
$938$	6.27880e36	+	1.08752e37i	0.441918	+	0.765424i
$939$	−2.40588e36	+	5.37549e36i	−0.167091	+	0.373335i
$940$	9.94423e35	−	1.72239e36i	0.0681511	−	0.118041i
$941$	−9.90013e36	+	1.71475e37i	−0.669531	+	1.15966i	0.308505	+	0.951223i	$0.400171\pi$
$941$	−9.90013e36	+	1.71475e37i	−0.669531	+	1.15966i	−0.978036	+	0.208438i	$0.933162\pi$
$942$	−1.79226e36	−	2.47697e36i	−0.119609	−	0.165304i
$943$	−4.51121e35	−	7.81365e35i	−0.0297096	−	0.0514586i
$944$	−1.44473e36			−0.0938936
$945$	6.78547e36	−	2.16098e36i	0.435193	−	0.138597i
$946$	−1.92765e36			−0.122008
$947$	1.08685e37	+	1.88247e37i	0.678881	+	1.17586i	0.975318	+	0.220804i	$0.0708682\pi$
$947$	1.08685e37	+	1.88247e37i	0.678881	+	1.17586i	−0.296437	+	0.955052i	$0.595799\pi$
$948$	2.87243e36	+	3.96980e36i	0.177070	+	0.244717i
$949$	2.64770e37	−	4.58596e37i	1.61080	−	2.78999i
$950$	−6.28910e36	+	1.08930e37i	−0.377610	+	0.654040i
$951$	−6.18239e35	+	1.38134e36i	−0.0366353	+	0.0818547i
$952$	3.59931e36	+	6.23418e36i	0.210502	+	0.364601i
$953$	2.05005e37			1.18332			0.591661	−	0.806187i	$-0.298472\pi$
$953$	2.05005e37			1.18332			0.591661	+	0.806187i	$0.298472\pi$
$954$	1.64594e37	−	3.43158e36i	0.937688	−	0.195497i
$955$	−1.05490e37			−0.593158
$956$	−6.09285e36	−	1.05531e37i	−0.338140	−	0.585676i
$957$	−1.53107e37	+	1.57907e36i	−0.838677	+	0.0864972i
$958$	4.04878e36	−	7.01270e36i	0.218905	−	0.379155i
$959$	−1.14739e37	+	1.98733e37i	−0.612318	+	1.06057i
$960$	−1.14777e36	+	1.18376e35i	−0.0604595	+	0.00623551i
$961$	−1.24095e37	−	2.14939e37i	−0.645226	−	1.11756i
$962$	−2.74856e37			−1.41064
$963$	2.47149e36	−	7.50682e36i	0.125207	−	0.380301i
$964$	4.65788e36			0.232930
$965$	−5.34813e35	−	9.26323e35i	−0.0264004	−	0.0457268i
$966$	2.31043e36	−	5.16222e36i	0.112585	−	0.251549i
$967$	−1.26084e37	+	2.18383e37i	−0.606495	+	1.05048i	0.385318	+	0.922784i	$0.374092\pi$
$967$	−1.26084e37	+	2.18383e37i	−0.606495	+	1.05048i	−0.991813	+	0.127697i	$0.959242\pi$
$968$	2.95725e36	−	5.12211e36i	0.140426	−	0.243224i
$969$	2.21750e37	+	3.06467e37i	1.03948	+	1.43660i
$970$	−8.57241e35	−	1.48478e36i	−0.0396694	−	0.0687095i
$971$	−1.87523e37			−0.856669			−0.428335	−	0.903620i	$-0.640900\pi$
$971$	−1.87523e37			−0.856669			−0.428335	+	0.903620i	$0.640900\pi$
$972$	−9.54683e36	−	5.63654e36i	−0.430557	−	0.254205i
$973$	1.94794e37			0.867290
$974$	−1.00511e37	−	1.74091e37i	−0.441802	−	0.765224i
$975$	1.87930e37	+	2.59726e37i	0.815529	+	1.12709i
$976$	−2.30321e36	+	3.98927e36i	−0.0986757	+	0.170911i
$977$	1.83554e37	−	3.17925e37i	0.776393	−	1.34475i	−0.157616	−	0.987501i	$-0.550381\pi$
$977$	1.83554e37	−	3.17925e37i	0.776393	−	1.34475i	0.934008	−	0.357251i	$-0.116286\pi$
$978$	−7.06369e36	+	1.57825e37i	−0.294982	+	0.659083i
$979$	−2.23497e36	−	3.87107e36i	−0.0921483	−	0.159605i
$980$	7.02976e35			0.0286164
$981$	−4.97739e36	+	1.51182e37i	−0.200050	+	0.607627i
$982$	−8.32094e35			−0.0330201
$983$	−1.22359e37	−	2.11933e37i	−0.479422	−	0.830383i	0.520299	−	0.853984i	$-0.325820\pi$
$983$	−1.22359e37	−	2.11933e37i	−0.479422	−	0.830383i	−0.999721	+	0.0236005i	$0.992487\pi$
$984$	1.30180e36	−	1.34262e35i	0.0503624	−	0.00519414i
$985$	−2.08951e36	+	3.61913e36i	−0.0798161	+	0.138246i
$986$	−2.20946e37	+	3.82691e37i	−0.833347	+	1.44340i
$987$	−1.40655e37	+	1.45065e36i	−0.523830	+	0.0540253i
$988$	1.73253e37	+	3.00083e37i	0.637117	+	1.10352i
$989$	4.34800e36			0.157883
$990$	4.25681e36	−	8.87494e35i	0.152632	−	0.0318219i
$991$	−5.14810e37			−1.82274			−0.911372	−	0.411583i	$-0.864976\pi$
$991$	−5.14810e37			−1.82274			−0.911372	+	0.411583i	$0.864976\pi$
$992$	3.82606e36	+	6.62693e36i	0.133769	+	0.231695i
$993$	−1.11484e36	+	2.49089e36i	−0.0384898	+	0.0859982i
$994$	−7.07352e36	+	1.22517e37i	−0.241160	+	0.417702i
$995$	−1.12958e36	+	1.95650e36i	−0.0380303	+	0.0658704i
$996$	−1.57039e37	−	2.17033e37i	−0.522113	−	0.721579i
$997$	−2.18392e37	−	3.78266e37i	−0.717047	−	1.24196i	−0.962165	−	0.272468i	$-0.912160\pi$
$997$	−2.18392e37	−	3.78266e37i	−0.717047	−	1.24196i	0.245118	−	0.969493i	$-0.421173\pi$
$998$	1.16454e37			0.377591
$999$	−3.25824e37	+	1.03766e37i	−1.04331	+	0.332265i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	18.26.c.b.13.4	yes	26
3.2	odd	2		54.26.c.b.37.5		26
9.2	odd	6		54.26.c.b.19.5		26
9.7	even	3	inner	18.26.c.b.7.4	✓	26

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
18.26.c.b.7.4	✓	26	9.7	even	3	inner
18.26.c.b.13.4	yes	26	1.1	even	1	trivial
54.26.c.b.19.5		26	9.2	odd	6
54.26.c.b.37.5		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} +(-539595. - 745739. i) q^{3} +(-8.38861e6 + 1.45295e7i) q^{4} +(1.32723e8 - 2.29884e8i) q^{5} +(-1.54022e9 + 3.44134e9i) q^{6} +(1.71990e10 + 2.97895e10i) q^{7} +6.87195e10 q^{8} +(-2.64964e11 + 8.04793e11i) q^{9} -1.08727e12 q^{10} +(2.36007e12 + 4.08776e12i) q^{11} +(1.53617e13 - 1.58433e12i) q^{12} +(-7.65246e13 + 1.32545e14i) q^{13} +(7.04470e13 - 1.22018e14i) q^{14} +(-2.43050e14 + 2.50670e13i) q^{15} +(-1.40737e14 - 2.43764e14i) q^{16} +3.04534e15 q^{17} +(3.39744e15 - 7.08326e14i) q^{18} -1.34946e16 q^{19} +(2.22673e15 + 3.85681e15i) q^{20} +(1.29347e16 - 2.89002e16i) q^{21} +(9.66685e15 - 1.67435e16i) q^{22} +(-2.18045e16 + 3.77665e16i) q^{23} +(-3.70807e16 - 5.12468e16i) q^{24} +(1.13781e17 + 1.97074e17i) q^{25} +6.26890e17 q^{26} +(7.43139e17 - 2.36668e17i) q^{27} -5.77102e17 q^{28} +(-1.77130e18 - 3.06797e18i) q^{29} +(5.86685e17 + 8.10819e17i) q^{30} +(3.31858e18 - 5.74794e18i) q^{31} +(-5.76461e17 + 9.98459e17i) q^{32} +(1.77492e18 - 3.96573e18i) q^{33} +(-6.23686e18 - 1.08026e19i) q^{34} +9.13082e18 q^{35} +(-9.47056e18 - 1.06009e19i) q^{36} -4.38443e19 q^{37} +(2.76370e19 + 4.78686e19i) q^{38} +(1.40136e20 - 1.44530e19i) q^{39} +(9.12068e18 - 1.57975e19i) q^{40} +(-1.03447e19 + 1.79175e19i) q^{41} +(-1.29006e20 + 1.33051e19i) q^{42} +(-4.98521e19 - 8.63463e19i) q^{43} -7.91908e19 q^{44} +(1.49842e20 + 1.67726e20i) q^{45} +1.78622e20 q^{46} +(-2.23292e20 - 3.86754e20i) q^{47} +(-1.05843e20 + 2.36487e20i) q^{48} +(7.89248e19 - 1.36702e20i) q^{49} +(4.66045e20 - 8.07214e20i) q^{50} +(-1.64325e21 - 2.27103e21i) q^{51} +(-1.28387e21 - 2.22373e21i) q^{52} +4.84464e21 q^{53} +(-2.36147e21 - 2.15139e21i) q^{54} +1.25295e21 q^{55} +(1.18190e21 + 2.04712e21i) q^{56} +(7.28162e21 + 1.00634e22i) q^{57} +(-7.25522e21 + 1.25664e22i) q^{58} +(2.56635e21 - 4.44505e21i) q^{59} +(1.67464e21 - 3.74167e21i) q^{60} +(-8.18264e21 - 1.41727e22i) q^{61} -2.71858e22 q^{62} +(-2.85315e22 + 5.94848e21i) q^{63} +4.72237e21 q^{64} +(2.03132e22 + 3.51835e22i) q^{65} +(-1.77024e22 + 1.82575e21i) q^{66} +(-4.45640e22 + 7.71871e22i) q^{67} +(-2.55462e22 + 4.42473e22i) q^{68} +(3.99295e22 - 4.11814e21i) q^{69} +(-1.86999e22 - 3.23892e22i) q^{70} -1.00409e23 q^{71} +(-1.82082e22 + 5.53050e22i) q^{72} -3.45994e23 q^{73} +(8.97932e22 + 1.55526e23i) q^{74} +(8.55702e22 - 1.91191e23i) q^{75} +(1.13201e23 - 1.96070e23i) q^{76} +(-8.11816e22 + 1.40611e23i) q^{77} +(-3.38266e23 - 4.67496e23i) q^{78} +(1.58647e23 + 2.74785e23i) q^{79} -7.47166e22 q^{80} +(-5.77486e23 - 4.26482e23i) q^{81} +8.47436e22 q^{82} +(-8.67339e23 - 1.50228e24i) q^{83} +(3.11401e23 + 4.30367e23i) q^{84} +(4.04188e23 - 7.00075e23i) q^{85} +(-2.04194e23 + 3.53675e23i) q^{86} +(-1.33212e24 + 2.97639e24i) q^{87} +(1.62183e23 + 2.80909e23i) q^{88} -9.46991e23 q^{89} +(2.88087e23 - 8.75027e23i) q^{90} -5.26458e24 q^{91} +(-3.65819e23 - 6.33617e23i) q^{92} +(-6.07715e24 + 6.26768e23i) q^{93} +(-9.14605e23 + 1.58414e24i) q^{94} +(-1.79105e24 + 3.10219e24i) q^{95} +(1.05564e24 - 1.08874e23i) q^{96} +(7.88434e23 + 1.36561e24i) q^{97} -6.46552e23 q^{98} +(-3.91514e24 + 8.16260e23i) 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

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