LMFDB - Embedded newform 5.24.b.a.4.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5,24,Mod(4,5)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 24, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("5.4");

S:= CuspForms(chi, 24);

N := Newforms(S);

Level:	$ N $	$=$	$ 5 $
Weight:	$ k $	$=$	$ 24 $
Character orbit:	$[\chi]$	$=$	5.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$16.7602018673$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 15644845 x^{8} + 79349217360160 x^{6} + \cdots + 34\!\cdots\!24 $ x^10 + 15644845x^8 + 79349217360160x^6 + 150324497245503837440x^4 + 76751558562242644579450880x^2 + 3490504262440921471663078375424
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{32}\cdot 3^{12}\cdot 5^{22} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			4.3
Root			$-1812.37i$ of defining polynomial
Character	$\chi$	$=$	5.4
Dual form			5.24.b.a.4.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3624.75i q^{2} +421266. i q^{3} -4.75020e6 q^{4} +(-7.79198e6 - 1.08905e8i) q^{5} +1.52698e9 q^{6} +4.49913e9i q^{7} -1.31883e10i q^{8} -8.33219e10 q^{9} +O(q^{10})$	\(q-3624.75i q^{2} +421266. i q^{3} -4.75020e6 q^{4} +(-7.79198e6 - 1.08905e8i) q^{5} +1.52698e9 q^{6} +4.49913e9i q^{7} -1.31883e10i q^{8} -8.33219e10 q^{9} +(-3.94752e11 + 2.82440e10i) q^{10} -1.32771e12 q^{11} -2.00110e12i q^{12} +8.78673e12i q^{13} +1.63082e13 q^{14} +(4.58778e13 - 3.28249e12i) q^{15} -8.76519e13 q^{16} +1.40846e14i q^{17} +3.02021e14i q^{18} +8.14305e13 q^{19} +(3.70134e13 + 5.17318e14i) q^{20} -1.89533e15 q^{21} +4.81262e15i q^{22} +1.29455e15i q^{23} +5.55580e15 q^{24} +(-1.17995e16 + 1.69716e15i) q^{25} +3.18497e16 q^{26} +4.55865e15i q^{27} -2.13717e16i q^{28} -2.61170e16 q^{29} +(-1.18982e16 - 1.66296e17i) q^{30} -2.15045e17 q^{31} +2.07084e17i q^{32} -5.59320e17i q^{33} +5.10533e17 q^{34} +(4.89976e17 - 3.50571e16i) q^{35} +3.95795e17 q^{36} +1.82503e18i q^{37} -2.95165e17i q^{38} -3.70155e18 q^{39} +(-1.43627e18 + 1.02763e17i) q^{40} +9.22963e17 q^{41} +6.87010e18i q^{42} -2.81152e18i q^{43} +6.30689e18 q^{44} +(6.49242e17 + 9.07413e18i) q^{45} +4.69242e18 q^{46} -1.85047e19i q^{47} -3.69248e19i q^{48} +7.12657e18 q^{49} +(6.15179e18 + 4.27702e19i) q^{50} -5.93338e19 q^{51} -4.17387e19i q^{52} -1.04927e20i q^{53} +1.65240e19 q^{54} +(1.03455e19 + 1.44594e20i) q^{55} +5.93360e19 q^{56} +3.43039e19i q^{57} +9.46676e19i q^{58} -9.90799e19 q^{59} +(-2.17929e20 + 1.55925e19i) q^{60} +4.58851e20 q^{61} +7.79484e20i q^{62} -3.74876e20i q^{63} +1.53514e19 q^{64} +(9.56915e20 - 6.84660e19i) q^{65} -2.02739e21 q^{66} -5.55952e20i q^{67} -6.69048e20i q^{68} -5.45350e20 q^{69} +(-1.27073e20 - 1.77604e21i) q^{70} +1.12726e21 q^{71} +1.09888e21i q^{72} +1.23821e21i q^{73} +6.61526e21 q^{74} +(-7.14958e20 - 4.97073e21i) q^{75} -3.86811e20 q^{76} -5.97355e21i q^{77} +1.34172e22i q^{78} -1.14793e22 q^{79} +(6.82982e20 + 9.54570e21i) q^{80} -9.76459e21 q^{81} -3.34551e21i q^{82} +4.00901e21i q^{83} +9.00319e21 q^{84} +(1.53388e22 - 1.09747e21i) q^{85} -1.01911e22 q^{86} -1.10022e22i q^{87} +1.75103e22i q^{88} +3.83393e22 q^{89} +(3.28915e22 - 2.35334e21i) q^{90} -3.95326e22 q^{91} -6.14937e21i q^{92} -9.05911e22i q^{93} -6.70749e22 q^{94} +(-6.34505e20 - 8.86816e21i) q^{95} -8.72376e22 q^{96} +4.53282e22i q^{97} -2.58320e22i q^{98} +1.10627e23 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 41272680 q^{4} + 124761750 q^{5} - 2262077880 q^{6} - 189250631370 q^{9}+O(q^{10}) $ 10 * q - 41272680 * q^4 + 124761750 * q^5 - 2262077880 * q^6 - 189250631370 * q^9	$ 10 q - 41272680 q^{4} + 124761750 q^{5} - 2262077880 q^{6} - 189250631370 q^{9} - 992748199000 q^{10} - 1448637536280 q^{11} + 20750531044440 q^{14} - 14566613457000 q^{15} + 307971806876960 q^{16} + 887626815301400 q^{19} - 23\!\cdots\!00 q^{20}+ \cdots + 41\!\cdots\!60 q^{99}+O(q^{100}) $ 10 * q - 41272680 * q^4 + 124761750 * q^5 - 2262077880 * q^6 - 189250631370 * q^9 - 992748199000 * q^10 - 1448637536280 * q^11 + 20750531044440 * q^14 - 14566613457000 * q^15 + 307971806876960 * q^16 + 887626815301400 * q^19 - 2363707755099000 * q^20 - 781158183715080 * q^21 + 58473619965621600 * q^24 - 15436708968968750 * q^25 - 49259739315596880 * q^26 + 68538893585329500 * q^29 - 283259561673249000 * q^30 - 303703652281842880 * q^31 - 288299835336191360 * q^34 + 568057466315481000 * q^35 + 3242003939215214760 * q^36 - 8628905972055907440 * q^39 + 9426000384456940000 * q^40 - 6658832954283527580 * q^41 + 14990828914855427040 * q^44 - 8490880963475889750 * q^45 + 16736621075351903320 * q^46 + 51294362631233173870 * q^49 - 96456356624588250000 * q^50 - 117334349391643270080 * q^51 + 6367892697021344400 * q^54 + 8046234911696751000 * q^55 - 93285217288146540000 * q^56 + 461218638014732785800 * q^59 + 1248088814097510276000 * q^60 + 202894074812420701820 * q^61 - 2597882075263561124480 * q^64 + 404224351485216078000 * q^65 - 2067527591150630859360 * q^66 + 1761142984477245282360 * q^69 + 2651929720118465517000 * q^70 - 6362428274364321596880 * q^71 + 21369976437605310645840 * q^74 - 1268180400269994750000 * q^75 - 28533821601830896716000 * q^76 + 8008906997916696975200 * q^79 + 50390556129429851388000 * q^80 - 63620987817532049079390 * q^81 + 26983560053969205971040 * q^84 + 58719411820058643416000 * q^85 - 73642932902287825779480 * q^86 + 17045340818835962686500 * q^89 + 218378490181286718303000 * q^90 - 261754857315780277067280 * q^91 + 163995755653951693894840 * q^94 + 287254967024630517105000 * q^95 - 1029134712278532215134080 * q^96 + 411070875879864759534360 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/5\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$-1$

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 $

$2$		−	3624.75i		−	1.25151i	−0.780021	−	0.625753i	$-0.784792\pi$
$2$		−	3624.75i		−	1.25151i	0.780021	−	0.625753i	$-0.215208\pi$
$3$			421266.i			1.37297i	0.727143	+	0.686486i	$0.240848\pi$
$3$			421266.i			1.37297i	−0.727143	+	0.686486i	$0.759152\pi$
$4$	−4.75020e6			−0.566267
$5$	−7.79198e6	−	1.08905e8i	−0.0713662	−	0.997450i
$5$	−7.79198e6	−	1.08905e8i	−0.0713662	−	0.997450i
$6$	1.52698e9			1.71828
$7$			4.49913e9i			0.860005i	0.902828	+	0.430003i	$0.141487\pi$
$7$			4.49913e9i			0.860005i	−0.902828	+	0.430003i	$0.858513\pi$
$8$		−	1.31883e10i		−	0.542819i
$9$	−8.33219e10			−0.885055
$10$	−3.94752e11	+	2.82440e10i	−1.24831	+	0.0893152i
$11$	−1.32771e12			−1.40310			−0.701549	−	0.712621i	$-0.747508\pi$
$11$	−1.32771e12			−1.40310			−0.701549	+	0.712621i	$0.747508\pi$
$12$		−	2.00110e12i		−	0.777470i
$13$			8.78673e12i			1.35981i	0.733300	+	0.679905i	$0.237979\pi$
$13$			8.78673e12i			1.35981i	−0.733300	+	0.679905i	$0.762021\pi$
$14$	1.63082e13			1.07630
$15$	4.58778e13	−	3.28249e12i	1.36947	−	0.0979839i
$16$	−8.76519e13			−1.24561
$17$			1.40846e14i			0.996743i	0.866964	+	0.498371i	$0.166068\pi$
$17$			1.40846e14i			0.996743i	−0.866964	+	0.498371i	$0.833932\pi$
$18$			3.02021e14i			1.10765i
$19$	8.14305e13			0.160369			0.0801846	−	0.996780i	$-0.474449\pi$
$19$	8.14305e13			0.160369			0.0801846	+	0.996780i	$0.474449\pi$
$20$	3.70134e13	+	5.17318e14i	0.0404124	+	0.564824i
$21$	−1.89533e15			−1.18076
$22$			4.81262e15i			1.75599i
$23$			1.29455e15i			0.283302i	0.989917	+	0.141651i	$0.0452410\pi$
$23$			1.29455e15i			0.283302i	−0.989917	+	0.141651i	$0.954759\pi$
$24$	5.55580e15			0.745276
$25$	−1.17995e16	+	1.69716e15i	−0.989814	+	0.142368i
$26$	3.18497e16			1.70181
$27$			4.55865e15i			0.157817i
$28$		−	2.13717e16i		−	0.486993i
$29$	−2.61170e16			−0.397509			−0.198754	−	0.980049i	$-0.563690\pi$
$29$	−2.61170e16			−0.397509			−0.198754	+	0.980049i	$0.563690\pi$
$30$	−1.18982e16	−	1.66296e17i	−0.122627	−	1.71390i
$31$	−2.15045e17			−1.52009			−0.760046	−	0.649870i	$-0.774823\pi$
$31$	−2.15045e17			−1.52009			−0.760046	+	0.649870i	$0.774823\pi$
$32$			2.07084e17i			1.01607i
$33$		−	5.59320e17i		−	1.92642i
$34$	5.10533e17			1.24743
$35$	4.89976e17	−	3.50571e16i	0.857812	−	0.0613753i
$36$	3.95795e17			0.501178
$37$			1.82503e18i			1.68636i	0.537634	+	0.843178i	$0.319318\pi$
$37$			1.82503e18i			1.68636i	−0.537634	+	0.843178i	$0.680682\pi$
$38$		−	2.95165e17i		−	0.200703i
$39$	−3.70155e18			−1.86698
$40$	−1.43627e18	+	1.02763e17i	−0.541435	+	0.0387389i
$41$	9.22963e17			0.261921			0.130960	−	0.991388i	$-0.458194\pi$
$41$	9.22963e17			0.261921			0.130960	+	0.991388i	$0.458194\pi$
$42$			6.87010e18i			1.47773i
$43$		−	2.81152e18i		−	0.461375i	−0.973028	−	0.230688i	$-0.925902\pi$
$43$		−	2.81152e18i		−	0.461375i	0.973028	−	0.230688i	$-0.0740975\pi$
$44$	6.30689e18			0.794529
$45$	6.49242e17	+	9.07413e18i	0.0631630	+	0.882798i
$46$	4.69242e18			0.354554
$47$		−	1.85047e19i		−	1.09183i	−0.837839	−	0.545917i	$-0.816181\pi$
$47$		−	1.85047e19i		−	1.09183i	0.837839	−	0.545917i	$-0.183819\pi$
$48$		−	3.69248e19i		−	1.71019i
$49$	7.12657e18			0.260391
$50$	6.15179e18	+	4.27702e19i	0.178175	+	1.23876i
$51$	−5.93338e19			−1.36850
$52$		−	4.17387e19i		−	0.770017i
$53$		−	1.04927e20i		−	1.55495i	−0.628917	−	0.777473i	$-0.716501\pi$
$53$		−	1.04927e20i		−	1.55495i	0.628917	−	0.777473i	$-0.283499\pi$
$54$	1.65240e19			0.197509
$55$	1.03455e19	+	1.44594e20i	0.100134	+	1.39952i
$56$	5.93360e19			0.466827
$57$			3.43039e19i			0.220182i
$58$			9.46676e19i			0.497484i
$59$	−9.90799e19			−0.427747			−0.213874	−	0.976861i	$-0.568608\pi$
$59$	−9.90799e19			−0.427747			−0.213874	+	0.976861i	$0.568608\pi$
$60$	−2.17929e20	+	1.55925e19i	−0.775487	+	0.0554851i
$61$	4.58851e20			1.35014			0.675070	−	0.737753i	$-0.264113\pi$
$61$	4.58851e20			1.35014			0.675070	+	0.737753i	$0.264113\pi$
$62$			7.79484e20i			1.90240i
$63$		−	3.74876e20i		−	0.761152i
$64$	1.53514e19			0.0260063
$65$	9.56915e20	−	6.84660e19i	1.35634	−	0.0970445i
$66$	−2.02739e21			−2.41092
$67$		−	5.55952e20i		−	0.556131i	−0.960562	−	0.278065i	$-0.910307\pi$
$67$		−	5.55952e20i		−	0.556131i	0.960562	−	0.278065i	$-0.0896932\pi$
$68$		−	6.69048e20i		−	0.564423i
$69$	−5.45350e20			−0.388965
$70$	−1.27073e20	−	1.77604e21i	−0.0768116	−	1.07356i
$71$	1.12726e21			0.578834			0.289417	−	0.957203i	$-0.406539\pi$
$71$	1.12726e21			0.578834			0.289417	+	0.957203i	$0.406539\pi$
$72$			1.09888e21i			0.480424i
$73$			1.23821e21i			0.461934i	0.972962	+	0.230967i	$0.0741889\pi$
$73$			1.23821e21i			0.461934i	−0.972962	+	0.230967i	$0.925811\pi$
$74$	6.61526e21			2.11049
$75$	−7.14958e20	−	4.97073e21i	−0.195468	−	1.35899i
$76$	−3.86811e20			−0.0908118
$77$		−	5.97355e21i		−	1.20667i
$78$			1.34172e22i			2.33654i
$79$	−1.14793e22			−1.72664			−0.863322	−	0.504654i	$-0.831620\pi$
$79$	−1.14793e22			−1.72664			−0.863322	+	0.504654i	$0.831620\pi$
$80$	6.82982e20	+	9.54570e21i	0.0888944	+	1.24243i
$81$	−9.76459e21			−1.10173
$82$		−	3.34551e21i		−	0.327795i
$83$			4.00901e21i			0.341695i	0.985297	+	0.170848i	$0.0546506\pi$
$83$			4.00901e21i			0.341695i	−0.985297	+	0.170848i	$0.945349\pi$
$84$	9.00319e21			0.668628
$85$	1.53388e22	−	1.09747e21i	0.994201	−	0.0711338i
$86$	−1.01911e22			−0.577414
$87$		−	1.10022e22i		−	0.545769i
$88$			1.75103e22i			0.761628i
$89$	3.83393e22			1.46440			0.732200	−	0.681090i	$-0.238494\pi$
$89$	3.83393e22			1.46440			0.732200	+	0.681090i	$0.238494\pi$
$90$	3.28915e22	−	2.35334e21i	1.10483	−	0.0790489i
$91$	−3.95326e22			−1.16944
$92$		−	6.14937e21i		−	0.160424i
$93$		−	9.05911e22i		−	2.08704i
$94$	−6.70749e22			−1.36644
$95$	−6.34505e20	−	8.86816e21i	−0.0114449	−	0.159960i
$96$	−8.72376e22			−1.39503
$97$			4.53282e22i			0.643419i	0.946838	+	0.321709i	$0.104257\pi$
$97$			4.53282e22i			0.643419i	−0.946838	+	0.321709i	$0.895743\pi$
$98$		−	2.58320e22i		−	0.325881i
$99$	1.10627e23			1.24182
$100$	5.60499e22	−	8.06186e21i	0.560499	−	0.0806186i
$101$	6.23046e22			0.555679			0.277840	−	0.960627i	$-0.410382\pi$
$101$	6.23046e22			0.555679			0.277840	+	0.960627i	$0.410382\pi$
$102$			2.15070e23i			1.71269i
$103$		−	1.46554e23i		−	1.04320i	−0.853189	−	0.521602i	$-0.825335\pi$
$103$		−	1.46554e23i		−	1.04320i	0.853189	−	0.521602i	$-0.174665\pi$
$104$	1.15882e23			0.738131
$105$	1.47684e22	+	2.06410e23i	0.0842666	+	1.17775i
$106$	−3.80334e23			−1.94602
$107$			1.58884e23i			0.729739i	0.931059	+	0.364870i	$0.118886\pi$
$107$			1.58884e23i			0.729739i	−0.931059	+	0.364870i	$0.881114\pi$
$108$		−	2.16545e22i		−	0.0893665i
$109$	9.52168e22			0.353435			0.176717	−	0.984262i	$-0.443452\pi$
$109$	9.52168e22			0.353435			0.176717	+	0.984262i	$0.443452\pi$
$110$	5.24117e23	−	3.74998e22i	1.75151	−	0.125318i
$111$	−7.68822e23			−2.31532
$112$		−	3.94357e23i		−	1.07123i
$113$			2.39129e23i			0.586450i	0.956043	+	0.293225i	$0.0947285\pi$
$113$			2.39129e23i			0.586450i	−0.956043	+	0.293225i	$0.905271\pi$
$114$	1.24343e23			0.275560
$115$	1.40983e23	−	1.00871e22i	0.282579	−	0.0202182i
$116$	1.24061e23			0.225096
$117$		−	7.32126e23i		−	1.20351i
$118$			3.59140e23i			0.535328i
$119$	−6.33686e23			−0.857204
$120$	−4.32906e22	−	6.05052e23i	−0.0531875	−	0.743375i
$121$	8.67388e23			0.968683
$122$		−	1.66322e24i		−	1.68971i
$123$			3.88813e23i			0.359610i
$124$	1.02151e24			0.860778
$125$	2.76770e23	+	1.27180e24i	0.212645	+	0.977130i
$126$	−1.35883e24			−0.952586
$127$			1.87891e24i			1.20272i	0.798979	+	0.601358i	$0.205374\pi$
$127$			1.87891e24i			1.20272i	−0.798979	+	0.601358i	$0.794626\pi$
$128$			1.68150e24i			0.983521i
$129$	1.18440e24			0.633455
$130$	−2.48172e23	−	3.46858e24i	−0.121452	−	1.69747i
$131$	−2.74374e24			−1.22949			−0.614743	−	0.788727i	$-0.710740\pi$
$131$	−2.74374e24			−1.22949			−0.614743	+	0.788727i	$0.710740\pi$
$132$			2.65688e24i			1.09087i
$133$			3.66367e23i			0.137918i
$134$	−2.01519e24			−0.696001
$135$	4.96458e23	−	3.55209e22i	0.157414	−	0.0112628i
$136$	1.85753e24			0.541051
$137$			2.05252e24i			0.549541i	0.961510	+	0.274770i	$0.0886019\pi$
$137$			2.05252e24i			0.549541i	−0.961510	+	0.274770i	$0.911398\pi$
$138$			1.97676e24i			0.486793i
$139$	−1.37816e24			−0.312340			−0.156170	−	0.987730i	$-0.549915\pi$
$139$	−1.37816e24			−0.312340			−0.156170	+	0.987730i	$0.549915\pi$
$140$	−2.32748e24	+	1.66528e23i	−0.485751	+	0.0347548i
$141$	7.79541e24			1.49906
$142$		−	4.08604e24i		−	0.724414i
$143$		−	1.16662e25i		−	1.90795i
$144$	7.30332e24			1.10243
$145$	2.03503e23	+	2.84426e24i	0.0283687	+	0.396495i
$146$	4.48818e24			0.578113
$147$			3.00218e24i			0.357510i
$148$		−	8.66923e24i		−	0.954929i
$149$	−1.82455e25			−1.86001			−0.930003	−	0.367553i	$-0.880196\pi$
$149$	−1.82455e25			−1.86001			−0.930003	+	0.367553i	$0.880196\pi$
$150$	−1.80176e25	+	2.59154e24i	−1.70078	+	0.244629i
$151$	9.31609e24			0.814702			0.407351	−	0.913272i	$-0.366453\pi$
$151$	9.31609e24			0.814702			0.407351	+	0.913272i	$0.366453\pi$
$152$		−	1.07393e24i		−	0.0870514i
$153$		−	1.17356e25i		−	0.882172i
$154$	−2.16526e25			−1.51016
$155$	1.67562e24	+	2.34194e25i	0.108483	+	1.51622i
$156$	1.75831e25			1.05721
$157$		−	2.33674e25i		−	1.30546i	−0.757590	−	0.652730i	$-0.773623\pi$
$157$		−	2.33674e25i		−	1.30546i	0.757590	−	0.652730i	$-0.226377\pi$
$158$			4.16095e25i			2.16090i
$159$	4.42022e25			2.13490
$160$	2.25524e25	−	1.61360e24i	1.01348	−	0.0725129i
$161$	−5.82435e24			−0.243641
$162$			3.53942e25i			1.37883i
$163$		−	1.86484e25i		−	0.676837i	−0.940996	−	0.338418i	$-0.890108\pi$
$163$		−	1.86484e25i		−	0.676837i	0.940996	−	0.338418i	$-0.109892\pi$
$164$	−4.38425e24			−0.148317
$165$	−6.09125e25	+	4.35821e24i	−1.92150	+	0.137481i
$166$	1.45317e25			0.427634
$167$		−	1.97955e25i		−	0.543660i	−0.962345	−	0.271830i	$-0.912371\pi$
$167$		−	1.97955e25i		−	0.543660i	0.962345	−	0.271830i	$-0.0876288\pi$
$168$			2.49963e25i			0.640941i
$169$	−3.54526e25			−0.849086
$170$	−3.97806e24	−	5.55994e25i	−0.0890243	−	1.24425i
$171$	−6.78494e24			−0.141935
$172$			1.33553e25i			0.261262i
$173$			3.00497e25i			0.549932i	0.961454	+	0.274966i	$0.0886667\pi$
$173$			3.00497e25i			0.549932i	−0.961454	+	0.274966i	$0.911333\pi$
$174$	−3.98802e25			−0.683033
$175$	−7.63576e24	−	5.30875e25i	−0.122438	−	0.851245i
$176$	1.16376e26			1.74771
$177$		−	4.17390e25i		−	0.587286i
$178$		−	1.38970e26i		−	1.83270i
$179$	5.16274e25			0.638367			0.319183	−	0.947693i	$-0.396591\pi$
$179$	5.16274e25			0.638367			0.319183	+	0.947693i	$0.396591\pi$
$180$	−3.08403e24	−	4.31039e25i	−0.0357671	−	0.499900i
$181$	2.33111e25			0.253664			0.126832	−	0.991924i	$-0.459519\pi$
$181$	2.33111e25			0.253664			0.126832	+	0.991924i	$0.459519\pi$
$182$			1.43296e26i			1.46357i
$183$			1.93299e26i			1.85371i
$184$	1.70730e25			0.153781
$185$	1.98754e26	−	1.42206e25i	1.68206	−	0.120349i
$186$	−3.28370e26			−2.61195
$187$		−	1.87003e26i		−	1.39853i
$188$			8.79010e25i			0.618270i
$189$	−2.05100e25			−0.135723
$190$	−3.21448e25	+	2.29992e24i	−0.200191	+	0.0143234i
$191$	−1.47504e26			−0.864807			−0.432403	−	0.901680i	$-0.642334\pi$
$191$	−1.47504e26			−0.864807			−0.432403	+	0.901680i	$0.642334\pi$
$192$			6.46703e24i			0.0357060i
$193$			9.71669e25i			0.505370i	0.967549	+	0.252685i	$0.0813136\pi$
$193$			9.71669e25i			0.505370i	−0.967549	+	0.252685i	$0.918686\pi$
$194$	1.64303e26			0.805243
$195$	2.88424e25	+	4.03116e26i	0.133240	+	1.86222i
$196$	−3.38526e25			−0.147451
$197$			1.44154e26i			0.592195i	0.955158	+	0.296098i	$0.0956854\pi$
$197$			1.44154e26i			0.592195i	−0.955158	+	0.296098i	$0.904315\pi$
$198$		−	4.00997e26i		−	1.55414i
$199$	−6.33541e25			−0.231721			−0.115860	−	0.993266i	$-0.536962\pi$
$199$	−6.33541e25			−0.231721			−0.115860	+	0.993266i	$0.536962\pi$
$200$	2.23828e25	+	1.55616e26i	0.0772803	+	0.537290i
$201$	2.34204e26			0.763553
$202$		−	2.25839e26i		−	0.695436i
$203$		−	1.17504e26i		−	0.341860i
$204$	2.81847e26			0.774937
$205$	−7.19170e24	−	1.00515e26i	−0.0186923	−	0.261253i
$206$	−5.31221e26			−1.30558
$207$		−	1.07864e26i		−	0.250737i
$208$		−	7.70173e26i		−	1.69379i
$209$	−1.08116e26			−0.225014
$210$	7.48185e26	−	5.35316e25i	1.47397	−	0.105460i
$211$	−4.57057e26			−0.852555			−0.426278	−	0.904592i	$-0.640175\pi$
$211$	−4.57057e26			−0.852555			−0.426278	+	0.904592i	$0.640175\pi$
$212$			4.98424e26i			0.880515i
$213$			4.74877e26i			0.794724i
$214$	5.75916e26			0.913273
$215$	−3.06188e26	+	2.19073e25i	−0.460199	+	0.0329266i
$216$	6.01210e25			0.0856660
$217$		−	9.67515e26i		−	1.30729i
$218$		−	3.45137e26i		−	0.442325i
$219$	−5.21614e26			−0.634223
$220$	−4.91431e25	−	6.86849e26i	−0.0567025	−	0.792503i
$221$	−1.23758e27			−1.35538
$222$			2.78679e27i			2.89764i
$223$			1.05226e27i			1.03901i	0.854468	+	0.519504i	$0.173883\pi$
$223$			1.05226e27i			1.03901i	−0.854468	+	0.519504i	$0.826117\pi$
$224$	−9.31700e26			−0.873824
$225$	9.83156e26	−	1.41411e26i	0.876039	−	0.126004i
$226$	8.66784e26			0.733946
$227$		−	2.81634e26i		−	0.226667i	−0.993557	−	0.113333i	$-0.963847\pi$
$227$		−	2.81634e26i		−	0.226667i	0.993557	−	0.113333i	$-0.0361528\pi$
$228$		−	1.62950e26i		−	0.124682i
$229$	1.95381e27			1.42159			0.710794	−	0.703400i	$-0.248336\pi$
$229$	1.95381e27			1.42159			0.710794	+	0.703400i	$0.248336\pi$
$230$	−3.65632e25	−	5.11026e26i	−0.0253031	−	0.353650i
$231$	2.51645e27			1.65673
$232$			3.44440e26i			0.215775i
$233$			2.11096e27i			1.25860i	0.777163	+	0.629299i	$0.216658\pi$
$233$			2.11096e27i			1.25860i	−0.777163	+	0.629299i	$0.783342\pi$
$234$	−2.65377e27			−1.50620
$235$	−2.01525e27	+	1.44188e26i	−1.08905	+	0.0779201i
$236$	4.70649e26			0.242219
$237$		−	4.83583e27i		−	2.37063i
$238$			2.29695e27i			1.07280i
$239$	2.06518e27			0.919142			0.459571	−	0.888141i	$-0.348003\pi$
$239$	2.06518e27			0.919142			0.459571	+	0.888141i	$0.348003\pi$
$240$	−4.02128e27	+	2.87717e26i	−1.70583	+	0.122050i
$241$	2.70918e26			0.109557			0.0547787	−	0.998499i	$-0.482555\pi$
$241$	2.70918e26			0.109557			0.0547787	+	0.998499i	$0.482555\pi$
$242$		−	3.14407e27i		−	1.21231i
$243$		−	3.68432e27i		−	1.35483i
$244$	−2.17963e27			−0.764541
$245$	−5.55301e25	−	7.76116e26i	−0.0185831	−	0.259727i
$246$	1.40935e27			0.450054
$247$			7.15508e26i			0.218072i
$248$			2.83608e27i			0.825134i
$249$	−1.68886e27			−0.469139
$250$	4.60994e27	−	1.00322e27i	1.22288	−	0.266126i
$251$	−1.37358e26			−0.0348021			−0.0174010	−	0.999849i	$-0.505539\pi$
$251$	−1.37358e26			−0.0348021			−0.0174010	+	0.999849i	$0.505539\pi$
$252$			1.78073e27i			0.431015i
$253$		−	1.71879e27i		−	0.397500i
$254$	6.81058e27			1.50521
$255$	4.62328e26	+	6.46172e27i	0.0976647	+	1.36501i
$256$	6.22381e27			1.25689
$257$			1.71094e26i			0.0330372i	0.999864	+	0.0165186i	$0.00525827\pi$
$257$			1.71094e26i			0.0330372i	−0.999864	+	0.0165186i	$0.994742\pi$
$258$		−	4.29315e27i		−	0.792773i
$259$	−8.21103e27			−1.45028
$260$	−4.54553e27	+	3.25227e26i	−0.768053	+	0.0549532i
$261$	2.17612e27			0.351817
$262$			9.94538e27i			1.53871i
$263$		−	5.10195e27i		−	0.755518i	−0.925904	−	0.377759i	$-0.876695\pi$
$263$		−	5.10195e27i		−	0.755518i	0.925904	−	0.377759i	$-0.123305\pi$
$264$	−7.37650e27			−1.04569
$265$	−1.14270e28	+	8.17589e26i	−1.55098	+	0.110971i
$266$	1.32799e27			0.172606
$267$			1.61511e28i			2.01058i
$268$			2.64088e27i			0.314919i
$269$	−1.46374e27			−0.167229			−0.0836145	−	0.996498i	$-0.526646\pi$
$269$	−1.46374e27			−0.167229			−0.0836145	+	0.996498i	$0.526646\pi$
$270$	−1.28754e26	−	1.79954e27i	−0.0140954	−	0.197005i
$271$	3.14244e27			0.329701			0.164851	−	0.986319i	$-0.447286\pi$
$271$	3.14244e27			0.329701			0.164851	+	0.986319i	$0.447286\pi$
$272$		−	1.23455e28i		−	1.24155i
$273$		−	1.66538e28i		−	1.60562i
$274$	7.43985e27			0.687754
$275$	1.56663e28	−	2.25335e27i	1.38881	−	0.199757i
$276$	2.59052e27			0.220258
$277$			4.74756e27i			0.387216i	0.981079	+	0.193608i	$0.0620189\pi$
$277$			4.74756e27i			0.387216i	−0.981079	+	0.193608i	$0.937981\pi$
$278$			4.99547e27i			0.390896i
$279$	1.79179e28			1.34536
$280$	−4.62345e26	−	6.46197e27i	−0.0333157	−	0.465637i
$281$	−5.85197e27			−0.404743			−0.202372	−	0.979309i	$-0.564865\pi$
$281$	−5.85197e27			−0.404743			−0.202372	+	0.979309i	$0.564865\pi$
$282$		−	2.82564e28i		−	1.87608i
$283$			2.14031e28i			1.36437i	0.731180	+	0.682184i	$0.238970\pi$
$283$			2.14031e28i			1.36437i	−0.731180	+	0.682184i	$0.761030\pi$
$284$	−5.35472e27			−0.327775
$285$	3.73585e27	−	2.67295e26i	0.219621	−	0.0157136i
$286$	−4.22872e28			−2.38781
$287$			4.15253e27i			0.225253i
$288$		−	1.72547e28i		−	0.899276i
$289$	1.29862e26			0.00650362
$290$	1.03097e28	−	7.37648e26i	0.496216	−	0.0355036i
$291$	−1.90952e28			−0.883397
$292$		−	5.88172e27i		−	0.261578i
$293$			5.57509e27i			0.238382i	0.992871	+	0.119191i	$0.0380301\pi$
$293$			5.57509e27i			0.238382i	−0.992871	+	0.119191i	$0.961970\pi$
$294$	1.08822e28			0.447425
$295$	7.72028e26	+	1.07903e28i	0.0305267	+	0.426657i
$296$	2.40691e28			0.915386
$297$		−	6.05258e27i		−	0.221432i
$298$			6.61354e28i			2.32781i
$299$	−1.13749e28			−0.385237
$300$	3.39619e27	+	2.36119e28i	0.110687	+	0.769550i
$301$	1.26494e28			0.396785
$302$		−	3.37685e28i		−	1.01960i
$303$			2.62468e28i			0.762933i
$304$	−7.13754e27			−0.199757
$305$	−3.57536e27	−	4.99710e28i	−0.0963544	−	1.34670i
$306$	−4.25385e28			−1.10404
$307$			1.96856e28i			0.492105i	0.969257	+	0.246052i	$0.0791335\pi$
$307$			1.96856e28i			0.492105i	−0.969257	+	0.246052i	$0.920866\pi$
$308$			2.83755e28i			0.683299i
$309$	6.17382e28			1.43229
$310$	8.48894e28	−	6.07372e27i	1.89755	−	0.135767i
$311$	−4.15965e28			−0.896010			−0.448005	−	0.894031i	$-0.647865\pi$
$311$	−4.15965e28			−0.896010			−0.448005	+	0.894031i	$0.647865\pi$
$312$			4.88173e28i			1.01343i
$313$		−	5.77713e28i		−	1.15598i	−0.816042	−	0.577992i	$-0.803836\pi$
$313$		−	5.77713e28i		−	1.15598i	0.816042	−	0.577992i	$-0.196164\pi$
$314$	−8.47009e28			−1.63379
$315$	−4.08257e28	+	2.92102e27i	−0.759211	+	0.0543205i
$316$	5.45288e28			0.977742
$317$			1.05133e28i			0.181785i	0.995861	+	0.0908926i	$0.0289720\pi$
$317$			1.05133e28i			0.181785i	−0.995861	+	0.0908926i	$0.971028\pi$
$318$		−	1.60222e29i		−	2.67184i
$319$	3.46759e28			0.557743
$320$	−1.19618e26	−	1.67184e27i	−0.00185597	−	0.0259400i
$321$	−6.69326e28			−1.00191
$322$			2.11118e28i			0.304918i
$323$			1.14692e28i			0.159847i
$324$	4.63837e28			0.623875
$325$	−1.49125e28	−	1.03679e29i	−0.193594	−	1.34596i
$326$	−6.75957e28			−0.847065
$327$			4.01116e28i			0.485256i
$328$		−	1.21723e28i		−	0.142176i
$329$	8.32551e28			0.938984
$330$	1.57974e28	+	2.20793e29i	0.172058	+	2.40477i
$331$	−3.28043e27			−0.0345071			−0.0172536	−	0.999851i	$-0.505492\pi$
$331$	−3.28043e27			−0.0345071			−0.0172536	+	0.999851i	$0.505492\pi$
$332$		−	1.90436e28i		−	0.193491i
$333$		−	1.52065e29i		−	1.49252i
$334$	−7.17537e28			−0.680393
$335$	−6.05457e28	+	4.33197e27i	−0.554713	+	0.0396890i
$336$	1.66129e29			1.47077
$337$		−	2.19307e28i		−	0.187633i	−0.995590	−	0.0938164i	$-0.970093\pi$
$337$		−	2.19307e28i		−	0.187633i	0.995590	−	0.0938164i	$-0.0299067\pi$
$338$			1.28507e29i			1.06264i
$339$	−1.00737e29			−0.805180
$340$	−7.28624e28	+	5.21321e27i	−0.562984	+	0.0402807i
$341$	2.85518e29			2.13284
$342$			2.45937e28i			0.177633i
$343$			1.55199e29i			1.08394i
$344$	−3.70793e28			−0.250443
$345$	4.24936e27	+	5.93912e28i	0.0277590	+	0.387974i
$346$	1.08922e29			0.688244
$347$			1.00094e29i			0.611815i	0.952061	+	0.305908i	$0.0989598\pi$
$347$			1.00094e29i			0.611815i	−0.952061	+	0.305908i	$0.901040\pi$
$348$			5.22626e28i			0.309051i
$349$	−1.71065e29			−0.978744			−0.489372	−	0.872075i	$-0.662774\pi$
$349$	−1.71065e29			−0.978744			−0.489372	+	0.872075i	$0.662774\pi$
$350$	−1.92429e29	+	2.76777e28i	−1.06534	+	0.153231i
$351$	−4.00556e28			−0.214601
$352$		−	2.74948e29i		−	1.42564i
$353$			5.39751e28i			0.270885i	0.990785	+	0.135442i	$0.0432455\pi$
$353$			5.39751e28i			0.270885i	−0.990785	+	0.135442i	$0.956754\pi$
$354$	−1.51293e29			−0.734991
$355$	−8.78360e27	−	1.22764e29i	−0.0413092	−	0.577358i
$356$	−1.82119e29			−0.829242
$357$		−	2.66951e29i		−	1.17692i
$358$		−	1.87136e29i		−	0.798920i
$359$	3.31606e29			1.37100			0.685498	−	0.728074i	$-0.259584\pi$
$359$	3.31606e29			1.37100			0.685498	+	0.728074i	$0.259584\pi$
$360$	1.19673e29	−	8.56242e27i	0.479199	−	0.0342861i
$361$	−2.51199e29			−0.974282
$362$		−	8.44969e28i		−	0.317463i
$363$			3.65401e29i			1.32998i
$364$	1.87788e29			0.662218
$365$	1.34846e29	−	9.64807e27i	0.460756	−	0.0329665i
$366$	7.00659e29			2.31993
$367$			1.56920e29i			0.503523i	0.967789	+	0.251761i	$0.0810098\pi$
$367$			1.56920e29i			0.503523i	−0.967789	+	0.251761i	$0.918990\pi$
$368$		−	1.13470e29i		−	0.352883i
$369$	−7.69030e28			−0.231814
$370$	−5.15460e28	−	7.20433e29i	−0.150617	−	2.10510i
$371$	4.72081e29			1.33726
$372$			4.30325e29i			1.18182i
$373$		−	1.68528e29i		−	0.448767i	−0.974501	−	0.224383i	$-0.927963\pi$
$373$		−	1.68528e29i		−	0.448767i	0.974501	−	0.224383i	$-0.0720367\pi$
$374$	−6.77840e29			−1.75027
$375$	−5.35764e29	+	1.16594e29i	−1.34157	+	0.291955i
$376$	−2.44046e29			−0.592669
$377$		−	2.29483e29i		−	0.540537i
$378$			7.43435e28i			0.169859i
$379$	6.08625e29			1.34896			0.674480	−	0.738293i	$-0.264368\pi$
$379$	6.08625e29			1.34896			0.674480	+	0.738293i	$0.264368\pi$
$380$	3.01402e27	+	4.21255e28i	0.00648089	+	0.0905803i
$381$	−7.91521e29			−1.65130
$382$			5.34664e29i			1.08231i
$383$			8.86754e29i			1.74188i	0.491392	+	0.870938i	$0.336488\pi$
$383$			8.86754e29i			1.74188i	−0.491392	+	0.870938i	$0.663512\pi$
$384$	−7.08361e29			−1.35035
$385$	−6.50547e29	+	4.65458e28i	−1.20359	+	0.0861156i
$386$	3.52206e29			0.632473
$387$			2.34261e29i			0.408342i
$388$		−	2.15318e29i		−	0.364347i
$389$	8.86629e29			1.45654			0.728268	−	0.685292i	$-0.240326\pi$
$389$	8.86629e29			1.45654			0.728268	+	0.685292i	$0.240326\pi$
$390$	1.46119e30	−	1.04546e29i	2.33058	−	0.166750i
$391$	−1.82333e29			−0.282379
$392$		−	9.39876e28i		−	0.141345i
$393$		−	1.15585e30i		−	1.68805i
$394$	5.22522e29			0.741136
$395$	8.94462e28	+	1.25015e30i	0.123224	+	1.72224i
$396$	−5.25502e29			−0.703201
$397$			6.09688e29i			0.792532i	0.918136	+	0.396266i	$0.129694\pi$
$397$			6.09688e29i			0.792532i	−0.918136	+	0.396266i	$0.870306\pi$
$398$			2.29643e29i			0.290000i
$399$	−1.54338e29			−0.189358
$400$	1.03425e30	−	1.48760e29i	1.23292	−	0.177335i
$401$	−6.73182e29			−0.779781			−0.389890	−	0.920861i	$-0.627487\pi$
$401$	−6.73182e29			−0.779781			−0.389890	+	0.920861i	$0.627487\pi$
$402$		−	8.48929e29i		−	0.955591i
$403$		−	1.88954e30i		−	2.06704i
$404$	−2.95959e29			−0.314663
$405$	7.60855e28	+	1.06341e30i	0.0786265	+	1.09892i
$406$	−4.25922e29			−0.427839
$407$		−	2.42311e30i		−	2.36612i
$408$			7.82514e29i			0.742848i
$409$	−2.08598e29			−0.192527			−0.0962637	−	0.995356i	$-0.530689\pi$
$409$	−2.08598e29			−0.192527			−0.0962637	+	0.995356i	$0.530689\pi$
$410$	−3.64341e29	+	2.60681e28i	−0.326960	+	0.0233935i
$411$	−8.64655e29			−0.754505
$412$			6.96160e29i			0.590733i
$413$		−	4.45773e29i		−	0.367865i
$414$	−3.90981e29			−0.313799
$415$	4.36600e29	−	3.12381e28i	0.340824	−	0.0243855i
$416$	−1.81959e30			−1.38166
$417$		−	5.80570e29i		−	0.428835i
$418$			3.91894e29i			0.281606i
$419$	1.78044e30			1.24470			0.622352	−	0.782738i	$-0.286177\pi$
$419$	1.78044e30			1.24470			0.622352	+	0.782738i	$0.286177\pi$
$420$	−7.01527e28	−	9.80489e29i	−0.0477175	−	0.666923i
$421$	2.49338e30			1.65023			0.825115	−	0.564965i	$-0.191110\pi$
$421$	2.49338e30			1.65023			0.825115	+	0.564965i	$0.191110\pi$
$422$			1.65672e30i			1.06698i
$423$			1.54185e30i			0.966333i
$424$	−1.38381e30			−0.844054
$425$	−2.39039e29	−	1.66192e30i	−0.141905	−	0.986590i
$426$	1.72131e30			0.994601
$427$			2.06443e30i			1.16113i
$428$		−	7.54732e29i		−	0.413228i
$429$	4.91459e30			2.61956
$430$	7.94085e28	+	1.10985e30i	0.0412078	+	0.575941i
$431$	−3.28146e30			−1.65798			−0.828990	−	0.559264i	$-0.811084\pi$
$431$	−3.28146e30			−1.65798			−0.828990	+	0.559264i	$0.811084\pi$
$432$		−	3.99575e29i		−	0.196578i
$433$			1.73262e30i			0.830030i	0.909815	+	0.415015i	$0.136224\pi$
$433$			1.73262e30i			0.830030i	−0.909815	+	0.415015i	$0.863776\pi$
$434$	−3.50700e30			−1.63608
$435$	−1.19819e30	+	8.57290e28i	−0.544377	+	0.0389494i
$436$	−4.52299e29			−0.200138
$437$			1.05416e29i			0.0454328i
$438$			1.89072e30i			0.793734i
$439$	−2.53714e30			−1.03753			−0.518767	−	0.854916i	$-0.673609\pi$
$439$	−2.53714e30			−1.03753			−0.518767	+	0.854916i	$0.673609\pi$
$440$	1.90695e30	−	1.36440e29i	0.759686	−	0.0543545i
$441$	−5.93799e29			−0.230460
$442$			4.48591e30i			1.69627i
$443$		−	8.05773e29i		−	0.296873i	−0.988922	−	0.148436i	$-0.952576\pi$
$443$		−	8.05773e29i		−	0.296873i	0.988922	−	0.148436i	$-0.0474240\pi$
$444$	3.65205e30			1.31109
$445$	−2.98739e29	−	4.17533e30i	−0.104509	−	1.46067i
$446$	3.81420e30			1.30033
$447$		−	7.68622e30i		−	2.55374i
$448$			6.90680e28i			0.0223656i
$449$	−3.64186e30			−1.14945			−0.574725	−	0.818347i	$-0.694891\pi$
$449$	−3.64186e30			−1.14945			−0.574725	+	0.818347i	$0.694891\pi$
$450$	−5.12579e29	−	3.56369e30i	−0.157695	−	1.09637i
$451$	−1.22543e30			−0.367500
$452$		−	1.13591e30i		−	0.332088i
$453$			3.92455e30i			1.11856i
$454$	−1.02085e30			−0.283675
$455$	3.08037e29	+	4.30529e30i	0.0834588	+	1.16646i
$456$	4.52411e29			0.119519
$457$			7.09124e30i			1.82678i	0.407086	+	0.913390i	$0.366545\pi$
$457$			7.09124e30i			1.82678i	−0.407086	+	0.913390i	$0.633455\pi$
$458$		−	7.08206e30i		−	1.77913i
$459$	−6.42070e29			−0.157303
$460$	−6.69695e29	+	4.79157e28i	−0.160015	+	0.0114489i
$461$	4.70455e30			1.09637			0.548186	−	0.836357i	$-0.315319\pi$
$461$	4.70455e30			1.09637			0.548186	+	0.836357i	$0.315319\pi$
$462$		−	9.12151e30i		−	2.07340i
$463$		−	1.09310e30i		−	0.242371i	−0.992630	−	0.121185i	$-0.961330\pi$
$463$		−	1.09310e30i		−	0.242371i	0.992630	−	0.121185i	$-0.0386695\pi$
$464$	2.28921e30			0.495140
$465$	−9.86579e30	+	7.05884e29i	−2.08172	+	0.148944i
$466$	7.65170e30			1.57514
$467$		−	5.29263e30i		−	1.06299i	−0.847063	−	0.531493i	$-0.821631\pi$
$467$		−	5.29263e30i		−	1.06299i	0.847063	−	0.531493i	$-0.178369\pi$
$468$			3.47774e30i			0.681507i
$469$	2.50130e30			0.478276
$470$	5.22646e29	+	7.30477e30i	0.0975175	+	1.36295i
$471$	9.84388e30			1.79236
$472$			1.30670e30i			0.232189i
$473$			3.73289e30i			0.647354i
$474$	−1.75287e31			−2.96686
$475$	−9.60839e29	+	1.38201e29i	−0.158736	+	0.0228315i
$476$	3.01013e30			0.485407
$477$			8.74272e30i			1.37621i
$478$		−	7.48577e30i		−	1.15031i
$479$	1.13138e31			1.69727			0.848637	−	0.528976i	$-0.177424\pi$
$479$	1.13138e31			1.69727			0.848637	+	0.528976i	$0.177424\pi$
$480$	6.79754e29	+	9.50058e30i	0.0995582	+	1.39148i
$481$	−1.60360e31			−2.29313
$482$		−	9.82009e29i		−	0.137112i
$483$		−	2.45360e30i		−	0.334512i
$484$	−4.12026e30			−0.548534
$485$	4.93645e30	−	3.53197e29i	0.641778	−	0.0459184i
$486$	−1.33547e31			−1.69558
$487$			1.15082e31i			1.42700i	0.700655	+	0.713500i	$0.252891\pi$
$487$			1.15082e31i			1.42700i	−0.700655	+	0.713500i	$0.747109\pi$
$488$		−	6.05149e30i		−	0.732882i
$489$	7.85593e30			0.929278
$490$	−2.81323e30	+	2.01283e29i	−0.325050	+	0.0232569i
$491$	−1.38830e29			−0.0156692			−0.00783460	−	0.999969i	$-0.502494\pi$
$491$	−1.38830e29			−0.0156692			−0.00783460	+	0.999969i	$0.502494\pi$
$492$		−	1.84694e30i		−	0.203635i
$493$		−	3.67849e30i		−	0.396214i
$494$	2.59354e30			0.272918
$495$	−8.62006e29	−	1.20478e31i	−0.0886239	−	1.23865i
$496$	1.88491e31			1.89344
$497$			5.07170e30i			0.497800i
$498$			6.12169e30i			0.587130i
$499$	7.39989e30			0.693536			0.346768	−	0.937951i	$-0.387279\pi$
$499$	7.39989e30			0.693536			0.346768	+	0.937951i	$0.387279\pi$
$500$	−1.31471e30	−	6.04128e30i	−0.120414	−	0.553317i
$501$	8.33917e30			0.746430
$502$			4.97887e29i			0.0435550i
$503$			2.05696e30i			0.175871i	0.996126	+	0.0879355i	$0.0280269\pi$
$503$			2.05696e30i			0.175871i	−0.996126	+	0.0879355i	$0.971973\pi$
$504$	−4.94399e30			−0.413168
$505$	−4.85476e29	−	6.78526e30i	−0.0396567	−	0.554263i
$506$	−6.23018e30			−0.497473
$507$		−	1.49350e31i		−	1.16577i
$508$		−	8.92519e30i		−	0.681059i
$509$	−1.58413e31			−1.18178			−0.590889	−	0.806753i	$-0.701223\pi$
$509$	−1.58413e31			−1.18178			−0.590889	+	0.806753i	$0.701223\pi$
$510$	2.34221e31	−	1.67582e30i	1.70832	−	0.122228i
$511$	−5.57085e30			−0.397266
$512$		−	8.45426e30i		−	0.589483i
$513$			3.71214e29i			0.0253089i
$514$	6.20172e29			0.0413462
$515$	−1.59604e31	+	1.14194e30i	−1.04054	+	0.0744495i
$516$	−5.62612e30			−0.358705
$517$			2.45689e31i			1.53195i
$518$			2.97629e31i			1.81503i
$519$	−1.26589e31			−0.755042
$520$	−9.02952e29	−	1.26201e31i	−0.0526776	−	0.736249i
$521$	−2.83462e31			−1.61756			−0.808780	−	0.588111i	$-0.799872\pi$
$521$	−2.83462e31			−1.61756			−0.808780	+	0.588111i	$0.799872\pi$
$522$		−	7.88788e30i		−	0.440301i
$523$		−	2.34054e31i		−	1.27805i	−0.769187	−	0.639023i	$-0.779339\pi$
$523$		−	2.34054e31i		−	1.27805i	0.769187	−	0.639023i	$-0.220661\pi$
$524$	1.30333e31			0.696218
$525$	2.23640e31	−	3.21669e30i	1.16874	−	0.168104i
$526$	−1.84933e31			−0.945536
$527$		−	3.02883e31i		−	1.51514i
$528$			4.90255e31i			2.39956i
$529$	1.92046e31			0.919740
$530$	2.96356e30	+	4.14202e31i	0.138880	+	1.94106i
$531$	8.25552e30			0.378580
$532$		−	1.74031e30i		−	0.0780986i
$533$			8.10982e30i			0.356163i
$534$	5.85435e31			2.51625
$535$	1.73032e31	−	1.23802e30i	0.727879	−	0.0520787i
$536$	−7.33208e30			−0.301878
$537$			2.17489e31i			0.876460i
$538$			5.30567e30i			0.209288i
$539$	−9.46203e30			−0.365354
$540$	−2.35827e30	+	1.68731e29i	−0.0891387	+	0.00637775i
$541$	6.56342e30			0.242863			0.121432	−	0.992600i	$-0.461251\pi$
$541$	6.56342e30			0.242863			0.121432	+	0.992600i	$0.461251\pi$
$542$		−	1.13906e31i		−	0.412623i
$543$			9.82018e30i			0.348274i
$544$	−2.91671e31			−1.01276
$545$	−7.41927e29	−	1.03696e31i	−0.0252233	−	0.352533i
$546$	−6.03657e31			−2.00944
$547$		−	3.35932e31i		−	1.09496i	−0.836820	−	0.547478i	$-0.815588\pi$
$547$		−	3.35932e31i		−	1.09496i	0.836820	−	0.547478i	$-0.184412\pi$
$548$		−	9.74985e30i		−	0.311187i
$549$	−3.82324e31			−1.19495
$550$	−8.16781e30	−	5.67865e31i	−0.249997	−	1.73810i
$551$	−2.12672e30			−0.0637481
$552$			7.19226e30i			0.211138i
$553$		−	5.16467e31i		−	1.48492i
$554$	1.72087e31			0.484603
$555$	5.99064e30	+	8.37282e31i	0.165236	+	2.30942i
$556$	6.54651e30			0.176868
$557$			3.54567e31i			0.938348i	0.883106	+	0.469174i	$0.155448\pi$
$557$			3.54567e31i			0.938348i	−0.883106	+	0.469174i	$0.844552\pi$
$558$		−	6.49480e31i		−	1.68373i
$559$	2.47041e31			0.627383
$560$	−4.29473e31	+	3.07282e30i	−1.06850	+	0.0764496i
$561$	7.87782e31			1.92014
$562$			2.12119e31i			0.506539i
$563$		−	1.08341e31i		−	0.253480i	−0.991936	−	0.126740i	$-0.959549\pi$
$563$		−	1.08341e31i		−	0.253480i	0.991936	−	0.126740i	$-0.0404515\pi$
$564$	−3.70297e31			−0.848869
$565$	2.60423e31	−	1.86329e30i	0.584955	−	0.0418527i
$566$	7.75807e31			1.70752
$567$		−	4.39322e31i		−	0.947496i
$568$		−	1.48667e31i		−	0.314202i
$569$	−3.70914e27			−7.68214e−5			−3.84107e−5	−	1.00000i	$-0.500012\pi$
$569$	−3.70914e27			−7.68214e−5			−3.84107e−5		1.00000i	$0.500012\pi$
$570$	−9.68878e29	−	1.35415e31i	−0.0196657	−	0.274857i
$571$	−3.35260e31			−0.666908			−0.333454	−	0.942766i	$-0.608214\pi$
$571$	−3.35260e31			−0.666908			−0.333454	+	0.942766i	$0.608214\pi$
$572$			5.54169e31i			1.08041i
$573$		−	6.21383e31i		−	1.18736i
$574$	1.50519e31			0.281906
$575$	−2.19707e30	−	1.52751e31i	−0.0403332	−	0.280416i
$576$	−1.27911e30			−0.0230170
$577$			9.77579e31i			1.72437i	0.506595	+	0.862184i	$0.330904\pi$
$577$			9.77579e31i			1.72437i	−0.506595	+	0.862184i	$0.669096\pi$
$578$		−	4.70715e29i		−	0.00813932i
$579$	−4.09331e31			−0.693859
$580$	−9.66680e29	−	1.35108e31i	−0.0160643	−	0.224522i
$581$	−1.80371e31			−0.293860
$582$			6.92155e31i			1.10558i
$583$			1.39313e32i			2.18174i
$584$	1.63299e31			0.250746
$585$	−7.97319e31	+	5.70471e30i	−1.20044	+	0.0858897i
$586$	2.02083e31			0.298337
$587$		−	2.38230e31i		−	0.344872i	−0.985021	−	0.172436i	$-0.944836\pi$
$587$		−	2.38230e31i		−	0.344872i	0.985021	−	0.172436i	$-0.0551639\pi$
$588$		−	1.42610e31i		−	0.202446i
$589$	−1.75112e31			−0.243776
$590$	3.91120e31	−	2.79841e30i	0.533963	−	0.0382044i
$591$	−6.07272e31			−0.813068
$592$		−	1.59967e32i		−	2.10054i
$593$			5.33605e31i			0.687212i	0.939114	+	0.343606i	$0.111649\pi$
$593$			5.33605e31i			0.687212i	−0.939114	+	0.343606i	$0.888351\pi$
$594$	−2.19391e31			−0.277124
$595$	4.93767e30	+	6.90114e31i	0.0611754	+	0.855018i
$596$	8.66698e31			1.05326
$597$		−	2.66889e31i		−	0.318146i
$598$			4.12310e31i			0.482126i
$599$	7.01277e29			0.00804417			0.00402208	−	0.999992i	$-0.498720\pi$
$599$	7.01277e29			0.00804417			0.00402208	+	0.999992i	$0.498720\pi$
$600$	−6.55556e31	+	9.42910e30i	−0.737684	+	0.106104i
$601$	8.82159e31			0.973846			0.486923	−	0.873445i	$-0.338119\pi$
$601$	8.82159e31			0.973846			0.486923	+	0.873445i	$0.338119\pi$
$602$		−	4.58509e31i		−	0.496579i
$603$			4.63230e31i			0.492206i
$604$	−4.42532e31			−0.461339
$605$	−6.75867e30	−	9.44626e31i	−0.0691313	−	0.966213i
$606$	9.51381e31			0.954815
$607$		−	1.43907e32i		−	1.41713i	−0.705644	−	0.708567i	$-0.749342\pi$
$607$		−	1.43907e32i		−	1.41713i	0.705644	−	0.708567i	$-0.250658\pi$
$608$			1.68630e31i			0.162946i
$609$	4.95004e31			0.469364
$610$	−1.81132e32	+	1.29598e31i	−1.68540	+	0.120588i
$611$	1.62596e32			1.48469
$612$			5.57463e31i			0.499545i
$613$			6.04596e31i			0.531704i	0.964014	+	0.265852i	$0.0856533\pi$
$613$			6.04596e31i			0.531704i	−0.964014	+	0.265852i	$0.914347\pi$
$614$	7.13554e31			0.615872
$615$	4.23435e31	−	3.02962e30i	0.358693	−	0.0256640i
$616$	−7.87811e31			−0.655004
$617$		−	1.70563e32i		−	1.39189i	−0.718096	−	0.695944i	$-0.754986\pi$
$617$		−	1.70563e32i		−	1.39189i	0.718096	−	0.695944i	$-0.245014\pi$
$618$		−	2.23785e32i		−	1.79252i
$619$	−2.17441e32			−1.70962			−0.854810	−	0.518940i	$-0.826327\pi$
$619$	−2.17441e32			−1.70962			−0.854810	+	0.518940i	$0.826327\pi$
$620$	−7.95954e30	−	1.11247e32i	−0.0614305	−	0.858583i
$621$	−5.90141e30			−0.0447098
$622$			1.50777e32i			1.12136i
$623$			1.72494e32i			1.25939i
$624$	3.24448e32			2.32553
$625$	1.36348e32	−	4.00514e31i	0.959462	−	0.281837i
$626$	−2.09406e32			−1.44672
$627$		−	4.55457e31i		−	0.308938i
$628$			1.11000e32i			0.739240i
$629$	−2.57048e32			−1.68086
$630$	1.05880e31	+	1.47983e32i	0.0679824	+	0.950157i
$631$	1.45351e31			0.0916389			0.0458195	−	0.998950i	$-0.485410\pi$
$631$	1.45351e31			0.0916389			0.0458195	+	0.998950i	$0.485410\pi$
$632$			1.51392e32i			0.937255i
$633$		−	1.92543e32i		−	1.17054i
$634$	3.81081e31			0.227505
$635$	2.04622e32	−	1.46404e31i	1.19965	−	0.0858333i
$636$	−2.09969e32			−1.20892
$637$			6.26192e31i			0.354082i
$638$		−	1.25691e32i		−	0.698019i
$639$	−9.39256e31			−0.512300
$640$	1.83124e32	−	1.31022e31i	0.981013	−	0.0701901i
$641$	−2.67442e32			−1.40722			−0.703610	−	0.710587i	$-0.748430\pi$
$641$	−2.67442e32			−1.40722			−0.703610	+	0.710587i	$0.748430\pi$
$642$			2.42614e32i			1.25390i
$643$			2.47788e32i			1.25792i	0.777437	+	0.628961i	$0.216520\pi$
$643$			2.47788e32i			1.25792i	−0.777437	+	0.628961i	$0.783480\pi$
$644$	2.76668e31			0.137966
$645$	−9.22880e30	−	1.28986e32i	−0.0452073	−	0.631840i
$646$	4.15730e31			0.200049
$647$			1.64796e32i			0.779020i	0.921022	+	0.389510i	$0.127356\pi$
$647$			1.64796e32i			0.779020i	−0.921022	+	0.389510i	$0.872644\pi$
$648$			1.28779e32i			0.598042i
$649$	1.31550e32			0.600171
$650$	−3.75810e32	+	5.40541e31i	−1.68448	+	0.242284i
$651$	4.07581e32			1.79487
$652$			8.85835e31i			0.383270i
$653$		−	4.24593e32i		−	1.80497i	−0.430717	−	0.902487i	$-0.641739\pi$
$653$		−	4.24593e32i		−	1.80497i	0.430717	−	0.902487i	$-0.358261\pi$
$654$	1.45395e32			0.607301
$655$	2.13792e31	+	2.98806e32i	0.0877437	+	1.22635i
$656$	−8.08995e31			−0.326251
$657$		−	1.03170e32i		−	0.408837i
$658$		−	3.01779e32i		−	1.17514i
$659$	3.99260e32			1.52782			0.763912	−	0.645320i	$-0.223276\pi$
$659$	3.99260e32			1.52782			0.763912	+	0.645320i	$0.223276\pi$
$660$	2.89346e32	−	2.07023e31i	1.08808	−	0.0778510i
$661$	2.44282e31			0.0902766			0.0451383	−	0.998981i	$-0.485627\pi$
$661$	2.44282e31			0.0902766			0.0451383	+	0.998981i	$0.485627\pi$
$662$			1.18907e31i			0.0431858i
$663$		−	5.21350e32i		−	1.86090i
$664$	5.28722e31			0.185479
$665$	3.98990e31	−	2.85472e30i	0.137567	−	0.00984271i
$666$	−5.51196e32			−1.86790
$667$		−	3.38098e31i		−	0.112615i
$668$			9.40325e31i			0.307857i
$669$	−4.43283e32			−1.42653
$670$	1.57023e31	+	2.19463e32i	0.0496710	+	0.694227i
$671$	−6.09223e32			−1.89438
$672$		−	3.92493e32i		−	1.19974i
$673$			2.78910e32i			0.838090i	0.907966	+	0.419045i	$0.137635\pi$
$673$			2.78910e32i			0.838090i	−0.907966	+	0.419045i	$0.862365\pi$
$674$	−7.94933e31			−0.234823
$675$	−7.73678e30	−	5.37898e31i	−0.0224681	−	0.156209i
$676$	1.68407e32			0.480809
$677$		−	1.30709e32i		−	0.366889i	−0.983030	−	0.183444i	$-0.941275\pi$
$677$		−	1.30709e32i		−	0.366889i	0.983030	−	0.183444i	$-0.0587247\pi$
$678$			3.65147e32i			1.00769i
$679$	−2.03938e32			−0.553344
$680$	−1.44738e31	−	2.02293e32i	−0.0386128	−	0.539671i
$681$	1.18643e32			0.311207
$682$		−	1.03493e33i		−	2.66926i
$683$		−	9.55373e31i		−	0.242290i	−0.992635	−	0.121145i	$-0.961343\pi$
$683$		−	9.55373e31i		−	0.242290i	0.992635	−	0.121145i	$-0.0386565\pi$
$684$	3.22298e31			0.0803734
$685$	2.23528e32	−	1.59932e31i	0.548140	−	0.0392186i
$686$	5.62557e32			1.35656
$687$			8.23073e32i			1.95180i
$688$			2.46435e32i			0.574693i
$689$	9.21965e32			2.11443
$690$	2.15278e32	−	1.54028e31i	0.485551	−	0.0347405i
$691$	−4.07892e32			−0.904790			−0.452395	−	0.891818i	$-0.649430\pi$
$691$	−4.07892e32			−0.904790			−0.452395	+	0.891818i	$0.649430\pi$
$692$		−	1.42742e32i		−	0.311409i
$693$			4.97727e32i			1.06797i
$694$	3.62816e32			0.765690
$695$	1.07386e31	+	1.50088e32i	0.0222905	+	0.311544i
$696$	−1.45101e32			−0.296254
$697$			1.29996e32i			0.261068i
$698$			6.20068e32i			1.22490i
$699$	−8.89276e32			−1.72802
$700$	3.62714e31	+	2.52176e32i	0.0693324	+	0.482032i
$701$	−8.86866e30			−0.0166763			−0.00833817	−	0.999965i	$-0.502654\pi$
$701$	−8.86866e30			−0.0166763			−0.00833817	+	0.999965i	$0.502654\pi$
$702$			1.45192e32i			0.268574i
$703$			1.48613e32i			0.270440i
$704$	−2.03823e31			−0.0364894
$705$	−6.07416e31	−	8.48956e32i	−0.106982	−	1.49524i
$706$	1.95646e32			0.339014
$707$			2.80317e32i			0.477887i
$708$			1.98268e32i			0.332561i
$709$	−5.49173e32			−0.906312			−0.453156	−	0.891431i	$-0.649702\pi$
$709$	−5.49173e32			−0.906312			−0.453156	+	0.891431i	$0.649702\pi$
$710$	−4.44989e32	+	3.18384e31i	−0.722567	+	0.0516987i
$711$	9.56474e32			1.52817
$712$		−	5.05632e32i		−	0.794904i
$713$		−	2.78387e32i		−	0.430644i
$714$	−9.67629e32			−1.47292
$715$	−1.27051e33	+	9.09031e31i	−1.90308	+	0.136163i
$716$	−2.45240e32			−0.361486
$717$			8.69991e32i			1.26196i
$718$		−	1.20199e33i		−	1.71581i
$719$	4.17889e32			0.587055			0.293528	−	0.955951i	$-0.405171\pi$
$719$	4.17889e32			0.587055			0.293528	+	0.955951i	$0.405171\pi$
$720$	−5.69073e31	−	7.95365e32i	−0.0786764	−	1.09962i
$721$	6.59365e32			0.897161
$722$			9.10532e32i			1.21932i
$723$			1.14128e32i			0.150419i
$724$	−1.10732e32			−0.143642
$725$	3.08168e32	−	4.43249e31i	0.393459	−	0.0565927i
$726$	1.32449e33			1.66447
$727$		−	4.50949e32i		−	0.557804i	−0.960320	−	0.278902i	$-0.910029\pi$
$727$		−	4.50949e32i		−	0.557804i	0.960320	−	0.278902i	$-0.0899705\pi$
$728$			5.21369e32i			0.634797i
$729$	6.32811e32			0.758416
$730$	−3.49718e31	−	4.88784e32i	−0.0412577	−	0.576639i
$731$	3.95993e32			0.459872
$732$		−	9.18206e32i		−	1.04969i
$733$		−	9.59936e32i		−	1.08031i	−0.841567	−	0.540153i	$-0.818367\pi$
$733$		−	9.59936e32i		−	1.08031i	0.841567	−	0.540153i	$-0.181633\pi$
$734$	5.68796e32			0.630162
$735$	3.26951e32	−	2.33929e31i	0.356598	−	0.0255141i
$736$	−2.68081e32			−0.287854
$737$			7.38144e32i			0.780306i
$738$			2.78754e32i			0.290117i
$739$	9.36109e32			0.959214			0.479607	−	0.877483i	$-0.340779\pi$
$739$	9.36109e32			0.959214			0.479607	+	0.877483i	$0.340779\pi$
$740$	−9.44120e32	+	6.75505e31i	−0.952494	+	0.0681496i
$741$	−3.01419e32			−0.299407
$742$		−	1.71117e33i		−	1.67359i
$743$		−	1.27404e33i		−	1.22691i	−0.789730	−	0.613455i	$-0.789779\pi$
$743$		−	1.27404e33i		−	1.22691i	0.789730	−	0.613455i	$-0.210221\pi$
$744$	−1.19475e33			−1.13289
$745$	1.42169e32	+	1.98702e33i	0.132741	+	1.85526i
$746$	−6.10872e32			−0.561634
$747$		−	3.34038e32i		−	0.302419i
$748$			8.88303e32i			0.791941i
$749$	−7.14842e32			−0.627580
$750$	4.22624e32	+	1.94201e33i	0.365384	+	1.67899i
$751$	−1.43159e33			−1.21888			−0.609439	−	0.792833i	$-0.708605\pi$
$751$	−1.43159e33			−1.21888			−0.609439	+	0.792833i	$0.708605\pi$
$752$			1.62197e33i			1.36000i
$753$		−	5.78641e31i		−	0.0477823i
$754$	−8.31818e32			−0.676485
$755$	−7.25907e31	−	1.01457e33i	−0.0581422	−	0.812625i
$756$	9.74264e31			0.0768557
$757$		−	7.55107e32i		−	0.586686i	−0.956007	−	0.293343i	$-0.905232\pi$
$757$		−	7.55107e32i		−	0.586686i	0.956007	−	0.293343i	$-0.0947678\pi$
$758$		−	2.20611e33i		−	1.68823i
$759$	7.24068e32			0.545757
$760$	−1.16956e32	+	8.36806e30i	−0.0868294	+	0.00621253i
$761$	9.98284e32			0.730013			0.365006	−	0.931005i	$-0.381067\pi$
$761$	9.98284e32			0.730013			0.365006	+	0.931005i	$0.381067\pi$
$762$			2.86907e33i			2.06661i
$763$			4.28393e32i			0.303956i
$764$	7.00671e32			0.489712
$765$	−1.27806e33	+	9.14434e31i	−0.879923	+	0.0629573i
$766$	3.21426e33			2.17997
$767$		−	8.70588e32i		−	0.581655i
$768$			2.62188e33i			1.72567i
$769$	−2.39712e33			−1.55431			−0.777154	−	0.629311i	$-0.783337\pi$
$769$	−2.39712e33			−1.55431			−0.777154	+	0.629311i	$0.783337\pi$
$770$	1.68717e32	+	2.35807e33i	0.107774	+	1.50631i
$771$	−7.20760e31			−0.0453592
$772$		−	4.61562e32i		−	0.286174i
$773$			1.47864e33i			0.903227i	0.892214	+	0.451614i	$0.149151\pi$
$773$			1.47864e33i			0.903227i	−0.892214	+	0.451614i	$0.850849\pi$
$774$	8.49138e32			0.511043
$775$	2.53742e33	−	3.64966e32i	1.50461	−	0.216413i
$776$	5.97804e32			0.349260
$777$		−	3.45903e33i		−	1.99119i
$778$		−	3.21381e33i		−	1.82286i
$779$	7.51573e31			0.0420040
$780$	−1.37007e32	−	1.91488e33i	−0.0754492	−	1.05452i
$781$	−1.49668e33			−0.812161
$782$			6.60911e32i			0.353399i
$783$		−	1.19058e32i		−	0.0627335i
$784$	−6.24658e32			−0.324345
$785$	−2.54481e33	+	1.82078e32i	−1.30213	+	0.0931658i
$786$	−4.18965e33			−2.11261
$787$			1.59314e33i			0.791672i	0.918321	+	0.395836i	$0.129545\pi$
$787$			1.59314e33i			0.791672i	−0.918321	+	0.395836i	$0.870455\pi$
$788$		−	6.84760e32i		−	0.335341i
$789$	2.14928e33			1.03731
$790$	4.53146e33	−	3.24220e32i	2.15539	−	0.154216i
$791$	−1.07587e33			−0.504350
$792$		−	1.45899e33i		−	0.674083i
$793$			4.03180e33i			1.83594i
$794$	2.20996e33			0.991858
$795$	−3.44423e32	−	4.81382e33i	−0.152360	−	2.12945i
$796$	3.00944e32			0.131216
$797$			1.15462e32i			0.0496213i	0.999692	+	0.0248107i	$0.00789829\pi$
$797$			1.15462e32i			0.0496213i	−0.999692	+	0.0248107i	$0.992102\pi$
$798$			5.59436e32i			0.236983i
$799$	2.60632e33			1.08828
$800$	−3.51456e32	−	2.44349e33i	−0.144656	−	1.00572i
$801$	−3.19450e33			−1.29607
$802$			2.44012e33i			0.975900i
$803$		−	1.64398e33i		−	0.648138i
$804$	−1.11251e33			−0.432375
$805$	4.53832e31	+	6.34299e32i	0.0173877	+	0.243020i
$806$	−6.84911e33			−2.58691
$807$		−	6.16622e32i		−	0.229601i
$808$		−	8.21694e32i		−	0.301633i
$809$	3.07292e33			1.11210			0.556049	−	0.831149i	$-0.312317\pi$
$809$	3.07292e33			1.11210			0.556049	+	0.831149i	$0.312317\pi$
$810$	3.85459e33	−	2.75791e32i	1.37531	−	0.0984015i
$811$	1.46735e33			0.516173			0.258086	−	0.966122i	$-0.416908\pi$
$811$	1.46735e33			0.516173			0.258086	+	0.966122i	$0.416908\pi$
$812$			5.58166e32i			0.193584i
$813$			1.32380e33i			0.452671i
$814$	−8.78316e33			−2.96122
$815$	−2.03090e33	+	1.45308e32i	−0.675111	+	0.0483033i
$816$	5.20072e33			1.70462
$817$		−	2.28944e32i		−	0.0739903i
$818$			7.56116e32i			0.240949i
$819$	3.29393e33			1.03502
$820$	3.41620e31	+	4.77465e32i	0.0105848	+	0.147939i
$821$	3.65133e33			1.11559			0.557795	−	0.829979i	$-0.311647\pi$
$821$	3.65133e33			1.11559			0.557795	+	0.829979i	$0.311647\pi$
$822$			3.13416e33i			0.944267i
$823$			3.41236e33i			1.01381i	0.862002	+	0.506906i	$0.169211\pi$
$823$			3.41236e33i			1.01381i	−0.862002	+	0.506906i	$0.830789\pi$
$824$	−1.93280e33			−0.566271
$825$	9.49258e32	+	6.59969e33i	0.274261	+	1.90679i
$826$	−1.61582e33			−0.460385
$827$		−	8.11953e32i		−	0.228149i	−0.993472	−	0.114074i	$-0.963610\pi$
$827$		−	8.11953e32i		−	0.228149i	0.993472	−	0.114074i	$-0.0363902\pi$
$828$			5.12377e32i			0.141984i
$829$	6.99412e33			1.91142			0.955710	−	0.294310i	$-0.0950897\pi$
$829$	6.99412e33			1.91142			0.955710	+	0.294310i	$0.0950897\pi$
$830$	−1.13230e32	−	1.58256e33i	−0.0305186	−	0.426544i
$831$	−1.99998e33			−0.531637
$832$			1.34889e32i			0.0353637i
$833$			1.00375e33i			0.259543i
$834$	−2.10442e33			−0.536690
$835$	−2.15582e33	+	1.54246e32i	−0.542273	+	0.0387989i
$836$	5.13573e32			0.127418
$837$		−	9.80315e32i		−	0.239896i
$838$		−	6.45365e33i		−	1.55775i
$839$	−2.54032e33			−0.604819			−0.302410	−	0.953178i	$-0.597791\pi$
$839$	−2.54032e33			−0.604819			−0.302410	+	0.953178i	$0.597791\pi$
$840$	2.72221e33	−	1.94770e32i	0.639307	−	0.0457415i
$841$	−3.63462e33			−0.841987
$842$		−	9.03788e33i		−	2.06527i
$843$		−	2.46524e33i		−	0.555701i
$844$	2.17111e33			0.482774
$845$	2.76246e32	+	3.86096e33i	0.0605960	+	0.846921i
$846$	5.58881e33			1.20937
$847$			3.90249e33i			0.833073i
$848$			9.19706e33i			1.93685i
$849$	−9.01638e33			−1.87324
$850$	−6.02403e33	+	8.66458e32i	−1.23472	+	0.177595i
$851$	−2.36259e33			−0.477748
$852$		−	2.25576e33i		−	0.450026i
$853$			1.73147e33i			0.340801i	0.985375	+	0.170401i	$0.0545062\pi$
$853$			1.73147e33i			0.340801i	−0.985375	+	0.170401i	$0.945494\pi$
$854$	7.48305e33			1.45316
$855$	5.28681e31	+	7.38912e32i	0.0101294	+	0.141574i
$856$	2.09542e33			0.396116
$857$		−	8.75135e33i		−	1.63228i	−0.577852	−	0.816141i	$-0.696109\pi$
$857$		−	8.75135e33i		−	1.63228i	0.577852	−	0.816141i	$-0.303891\pi$
$858$		−	1.78142e34i		−	3.27840i
$859$	−1.03232e34			−1.87454			−0.937270	−	0.348603i	$-0.886656\pi$
$859$	−1.03232e34			−1.87454			−0.937270	+	0.348603i	$0.886656\pi$
$860$	1.45445e33	−	1.04064e32i	0.260595	−	0.0186452i
$861$	−1.74932e33			−0.309267
$862$			1.18945e34i			2.07497i
$863$		−	1.06820e34i		−	1.83878i	−0.393344	−	0.919391i	$-0.628682\pi$
$863$		−	1.06820e34i		−	1.83878i	0.393344	−	0.919391i	$-0.371318\pi$
$864$	−9.44026e32			−0.160353
$865$	3.27255e33	−	2.34146e32i	0.548530	−	0.0392466i
$866$	6.28033e33			1.03879
$867$			5.47062e31i			0.00892930i
$868$			4.59589e33i			0.740274i
$869$	1.52412e34			2.42265
$870$	3.10746e32	+	4.34314e33i	0.0487454	+	0.681291i
$871$	4.88500e33			0.756233
$872$		−	1.25575e33i		−	0.191851i
$873$		−	3.77683e33i		−	0.569461i
$874$	3.82106e32			0.0568595
$875$	−5.72197e33	+	1.24523e33i	−0.840337	+	0.182876i
$876$	2.47777e33			0.359140
$877$			9.63434e33i			1.37825i	0.724645	+	0.689123i	$0.242004\pi$
$877$			9.63434e33i			1.37825i	−0.724645	+	0.689123i	$0.757996\pi$
$878$			9.19649e33i			1.29848i
$879$	−2.34859e33			−0.327292
$880$	−9.06803e32	−	1.26739e34i	−0.124727	−	1.74325i
$881$	1.26522e33			0.171769			0.0858843	−	0.996305i	$-0.472628\pi$
$881$	1.26522e33			0.171769			0.0858843	+	0.996305i	$0.472628\pi$
$882$			2.15237e33i			0.288422i
$883$		−	2.00898e33i		−	0.265722i	−0.991135	−	0.132861i	$-0.957584\pi$
$883$		−	2.00898e33i		−	0.265722i	0.991135	−	0.132861i	$-0.0424163\pi$
$884$	5.87874e33			0.767509
$885$	−4.54557e33	+	3.25229e32i	−0.585788	+	0.0419123i
$886$	−2.92073e33			−0.371538
$887$			1.01400e34i			1.27326i	0.771169	+	0.636631i	$0.219672\pi$
$887$			1.01400e34i			1.27326i	−0.771169	+	0.636631i	$0.780328\pi$
$888$			1.01395e34i			1.25680i
$889$	−8.45346e33			−1.03434
$890$	−1.51345e34	+	1.08285e33i	−1.82803	+	0.130793i
$891$	1.29646e34			1.54584
$892$		−	4.99846e33i		−	0.588357i
$893$		−	1.50685e33i		−	0.175097i
$894$	−2.78606e34			−3.19602
$895$	−4.02279e32	−	5.62246e33i	−0.0455578	−	0.636739i
$896$	−7.56531e33			−0.845833
$897$		−	4.79184e33i		−	0.528919i
$898$			1.32008e34i			1.43854i
$899$	5.61633e33			0.604249
$900$	−4.67018e33	+	6.71729e32i	−0.496072	+	0.0713519i
$901$	1.47786e34			1.54988
$902$			4.44187e33i			0.459929i
$903$			5.32876e33i			0.544775i
$904$	3.15372e33			0.318336
$905$	−1.81640e32	−	2.53869e33i	−0.0181031	−	0.253018i
$906$	1.42255e34			1.39989
$907$		−	4.66626e33i		−	0.453404i	−0.973964	−	0.226702i	$-0.927206\pi$
$907$		−	4.66626e33i		−	0.453404i	0.973964	−	0.226702i	$-0.0727944\pi$
$908$			1.33782e33i			0.128354i
$909$	−5.19134e33			−0.491807
$910$	1.56056e34	−	1.11656e33i	1.45984	−	0.104449i
$911$	−1.53509e34			−1.41799			−0.708996	−	0.705212i	$-0.750852\pi$
$911$	−1.53509e34			−1.41799			−0.708996	+	0.705212i	$0.750852\pi$
$912$		−	3.00680e33i		−	0.274261i
$913$		−	5.32281e33i		−	0.479432i
$914$	2.57040e34			2.28623
$915$	2.10511e34	−	1.50618e33i	1.84898	−	0.132292i
$916$	−9.28097e33			−0.804999
$917$		−	1.23445e34i		−	1.05736i
$918$			2.32734e33i			0.196865i
$919$	1.30968e34			1.09405			0.547023	−	0.837117i	$-0.315761\pi$
$919$	1.30968e34			1.09405			0.547023	+	0.837117i	$0.315761\pi$
$920$	−1.33032e32	−	1.85932e33i	−0.0109748	−	0.153389i
$921$	−8.29288e33			−0.675647
$922$		−	1.70528e34i		−	1.37212i
$923$			9.90495e33i			0.787105i
$924$	−1.19536e34			−0.938151
$925$	−3.09737e33	−	2.15344e34i	−0.240084	−	1.66918i
$926$	−3.96223e33			−0.303328
$927$			1.22111e34i			0.923293i
$928$		−	5.40843e33i		−	0.403896i
$929$	−1.22763e34			−0.905494			−0.452747	−	0.891639i	$-0.649556\pi$
$929$	−1.22763e34			−0.905494			−0.452747	+	0.891639i	$0.649556\pi$
$930$	2.55865e33	+	3.57610e34i	0.186405	+	2.60529i
$931$	5.80320e32			0.0417587
$932$		−	1.00275e34i		−	0.712703i
$933$		−	1.75232e34i		−	1.23020i
$934$	−1.91845e34			−1.33033
$935$	−2.03655e34	+	1.45713e33i	−1.39496	+	0.0998076i
$936$	−9.65552e33			−0.653286
$937$			1.02902e34i			0.687729i	0.939019	+	0.343864i	$0.111736\pi$
$937$			1.02902e34i			0.687729i	−0.939019	+	0.343864i	$0.888264\pi$
$938$		−	9.06659e33i		−	0.598565i
$939$	2.43371e34			1.58714
$940$	9.57282e33	−	6.84922e32i	0.616694	−	0.0441236i
$941$	−1.68361e34			−1.07142			−0.535712	−	0.844401i	$-0.679957\pi$
$941$	−1.68361e34			−1.07142			−0.535712	+	0.844401i	$0.679957\pi$
$942$		−	3.56816e34i		−	2.24315i
$943$			1.19482e33i			0.0742026i
$944$	8.68454e33			0.532806
$945$	1.59813e32	+	2.23363e33i	0.00968606	+	0.135377i
$946$	1.35308e34			0.810168
$947$			3.88670e33i			0.229909i	0.993371	+	0.114954i	$0.0366722\pi$
$947$			3.88670e33i			0.229909i	−0.993371	+	0.114954i	$0.963328\pi$
$948$			2.29711e34i			1.34241i
$949$	−1.08798e34			−0.628143
$950$	5.00944e32	+	3.48280e33i	0.0285738	+	0.198659i
$951$	−4.42890e33			−0.249586
$952$			8.35727e33i			0.465307i
$953$			2.75869e34i			1.51752i	0.651370	+	0.758760i	$0.274194\pi$
$953$			2.75869e34i			1.51752i	−0.651370	+	0.758760i	$0.725806\pi$
$954$	3.16902e34			1.72234
$955$	1.14934e33	+	1.60638e34i	0.0617180	+	0.862601i
$956$	−9.81002e33			−0.520480
$957$			1.46078e34i			0.765767i
$958$		−	4.10098e34i		−	2.12415i
$959$	−9.23454e33			−0.472608
$960$	7.04289e32	−	5.03910e31i	0.0356149	−	0.00254820i
$961$	2.62310e34			1.31068
$962$			5.81265e34i			2.86986i
$963$		−	1.32385e34i		−	0.645859i
$964$	−1.28691e33			−0.0620387
$965$	1.05819e34	−	7.57122e32i	0.504081	−	0.0360663i
$966$	−8.89369e33			−0.418644
$967$			2.07772e34i			0.966456i	0.875494	+	0.483228i	$0.160536\pi$
$967$			2.07772e34i			0.966456i	−0.875494	+	0.483228i	$0.839464\pi$
$968$		−	1.14394e34i		−	0.525820i
$969$	−4.83158e33			−0.219465
$970$	−1.28025e33	−	1.78934e34i	−0.0574671	−	0.803190i
$971$	−2.50796e34			−1.11250			−0.556249	−	0.831016i	$-0.687760\pi$
$971$	−2.50796e34			−1.11250			−0.556249	+	0.831016i	$0.687760\pi$
$972$			1.75013e34i			0.767198i
$973$		−	6.20050e33i		−	0.268614i
$974$	4.17143e34			1.78590
$975$	4.36764e34	−	6.28214e33i	1.84797	−	0.265800i
$976$	−4.02192e34			−1.68175
$977$		−	4.51790e34i		−	1.86702i	−0.358550	−	0.933511i	$-0.616729\pi$
$977$		−	4.51790e34i		−	1.86702i	0.358550	−	0.933511i	$-0.383271\pi$
$978$		−	2.84758e34i		−	1.16300i
$979$	−5.09036e34			−2.05470
$980$	2.63779e32	+	3.68670e33i	0.0105230	+	0.147075i
$981$	−7.93364e33			−0.312809
$982$			5.03224e32i			0.0196101i
$983$			2.15265e34i			0.829101i	0.910026	+	0.414550i	$0.136061\pi$
$983$			2.15265e34i			0.829101i	−0.910026	+	0.414550i	$0.863939\pi$
$984$	5.12779e33			0.195203
$985$	1.56990e34	−	1.12324e33i	0.590685	−	0.0422627i
$986$	−1.33336e34			−0.495864
$987$			3.50725e34i			1.28920i
$988$		−	3.39880e33i		−	0.123487i
$989$	3.63966e33			0.130708
$990$	−4.36704e34	+	3.12456e33i	−1.55018	+	0.110913i
$991$	−6.42651e32			−0.0225490			−0.0112745	−	0.999936i	$-0.503589\pi$
$991$	−6.42651e32			−0.0225490			−0.0112745	+	0.999936i	$0.503589\pi$
$992$		−	4.45324e34i		−	1.54452i
$993$		−	1.38193e33i		−	0.0473773i
$994$	1.83836e34			0.623000
$995$	4.93654e32	+	6.89956e33i	0.0165370	+	0.231130i
$996$	8.02242e33			0.265658
$997$		−	4.23139e33i		−	0.138513i	−0.997599	−	0.0692563i	$-0.977937\pi$
$997$		−	4.23139e33i		−	0.138513i	0.997599	−	0.0692563i	$-0.0220626\pi$
$998$		−	2.68227e34i		−	0.867964i
$999$	−8.31967e33			−0.266135

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5.24.b.a.4.3	✓	10
3.2	odd	2		45.24.b.b.19.8		10
5.2	odd	4		25.24.a.f.1.8		10
5.3	odd	4		25.24.a.f.1.3		10
5.4	even	2	inner	5.24.b.a.4.8	yes	10
15.14	odd	2		45.24.b.b.19.3		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.24.b.a.4.3	✓	10	1.1	even	1	trivial
5.24.b.a.4.8	yes	10	5.4	even	2	inner
25.24.a.f.1.3		10	5.3	odd	4
25.24.a.f.1.8		10	5.2	odd	4
45.24.b.b.19.3		10	15.14	odd	2
45.24.b.b.19.8		10	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 5 \)
Weight:	\( k \)	\(=\)	\( 24 \)
Character orbit:	\([\chi]\)	\(=\)	5.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-3624.75i q^{2} +421266. i q^{3} -4.75020e6 q^{4} +(-7.79198e6 - 1.08905e8i) q^{5} +1.52698e9 q^{6} +4.49913e9i q^{7} -1.31883e10i q^{8} -8.33219e10 q^{9} +O(q^{10})\)	\(q-3624.75i q^{2} +421266. i q^{3} -4.75020e6 q^{4} +(-7.79198e6 - 1.08905e8i) q^{5} +1.52698e9 q^{6} +4.49913e9i q^{7} -1.31883e10i q^{8} -8.33219e10 q^{9} +(-3.94752e11 + 2.82440e10i) q^{10} -1.32771e12 q^{11} -2.00110e12i q^{12} +8.78673e12i q^{13} +1.63082e13 q^{14} +(4.58778e13 - 3.28249e12i) q^{15} -8.76519e13 q^{16} +1.40846e14i q^{17} +3.02021e14i q^{18} +8.14305e13 q^{19} +(3.70134e13 + 5.17318e14i) q^{20} -1.89533e15 q^{21} +4.81262e15i q^{22} +1.29455e15i q^{23} +5.55580e15 q^{24} +(-1.17995e16 + 1.69716e15i) q^{25} +3.18497e16 q^{26} +4.55865e15i q^{27} -2.13717e16i q^{28} -2.61170e16 q^{29} +(-1.18982e16 - 1.66296e17i) q^{30} -2.15045e17 q^{31} +2.07084e17i q^{32} -5.59320e17i q^{33} +5.10533e17 q^{34} +(4.89976e17 - 3.50571e16i) q^{35} +3.95795e17 q^{36} +1.82503e18i q^{37} -2.95165e17i q^{38} -3.70155e18 q^{39} +(-1.43627e18 + 1.02763e17i) q^{40} +9.22963e17 q^{41} +6.87010e18i q^{42} -2.81152e18i q^{43} +6.30689e18 q^{44} +(6.49242e17 + 9.07413e18i) q^{45} +4.69242e18 q^{46} -1.85047e19i q^{47} -3.69248e19i q^{48} +7.12657e18 q^{49} +(6.15179e18 + 4.27702e19i) q^{50} -5.93338e19 q^{51} -4.17387e19i q^{52} -1.04927e20i q^{53} +1.65240e19 q^{54} +(1.03455e19 + 1.44594e20i) q^{55} +5.93360e19 q^{56} +3.43039e19i q^{57} +9.46676e19i q^{58} -9.90799e19 q^{59} +(-2.17929e20 + 1.55925e19i) q^{60} +4.58851e20 q^{61} +7.79484e20i q^{62} -3.74876e20i q^{63} +1.53514e19 q^{64} +(9.56915e20 - 6.84660e19i) q^{65} -2.02739e21 q^{66} -5.55952e20i q^{67} -6.69048e20i q^{68} -5.45350e20 q^{69} +(-1.27073e20 - 1.77604e21i) q^{70} +1.12726e21 q^{71} +1.09888e21i q^{72} +1.23821e21i q^{73} +6.61526e21 q^{74} +(-7.14958e20 - 4.97073e21i) q^{75} -3.86811e20 q^{76} -5.97355e21i q^{77} +1.34172e22i q^{78} -1.14793e22 q^{79} +(6.82982e20 + 9.54570e21i) q^{80} -9.76459e21 q^{81} -3.34551e21i q^{82} +4.00901e21i q^{83} +9.00319e21 q^{84} +(1.53388e22 - 1.09747e21i) q^{85} -1.01911e22 q^{86} -1.10022e22i q^{87} +1.75103e22i q^{88} +3.83393e22 q^{89} +(3.28915e22 - 2.35334e21i) q^{90} -3.95326e22 q^{91} -6.14937e21i q^{92} -9.05911e22i q^{93} -6.70749e22 q^{94} +(-6.34505e20 - 8.86816e21i) q^{95} -8.72376e22 q^{96} +4.53282e22i q^{97} -2.58320e22i q^{98} +1.10627e23 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 41272680 q^{4} + 124761750 q^{5} - 2262077880 q^{6} - 189250631370 q^{9}+O(q^{10}) \) 10 * q - 41272680 * q^4 + 124761750 * q^5 - 2262077880 * q^6 - 189250631370 * q^9	\( 10 q - 41272680 q^{4} + 124761750 q^{5} - 2262077880 q^{6} - 189250631370 q^{9} - 992748199000 q^{10} - 1448637536280 q^{11} + 20750531044440 q^{14} - 14566613457000 q^{15} + 307971806876960 q^{16} + 887626815301400 q^{19} - 23\!\cdots\!00 q^{20}+ \cdots + 41\!\cdots\!60 q^{99}+O(q^{100}) \) 10 * q - 41272680 * q^4 + 124761750 * q^5 - 2262077880 * q^6 - 189250631370 * q^9 - 992748199000 * q^10 - 1448637536280 * q^11 + 20750531044440 * q^14 - 14566613457000 * q^15 + 307971806876960 * q^16 + 887626815301400 * q^19 - 2363707755099000 * q^20 - 781158183715080 * q^21 + 58473619965621600 * q^24 - 15436708968968750 * q^25 - 49259739315596880 * q^26 + 68538893585329500 * q^29 - 283259561673249000 * q^30 - 303703652281842880 * q^31 - 288299835336191360 * q^34 + 568057466315481000 * q^35 + 3242003939215214760 * q^36 - 8628905972055907440 * q^39 + 9426000384456940000 * q^40 - 6658832954283527580 * q^41 + 14990828914855427040 * q^44 - 8490880963475889750 * q^45 + 16736621075351903320 * q^46 + 51294362631233173870 * q^49 - 96456356624588250000 * q^50 - 117334349391643270080 * q^51 + 6367892697021344400 * q^54 + 8046234911696751000 * q^55 - 93285217288146540000 * q^56 + 461218638014732785800 * q^59 + 1248088814097510276000 * q^60 + 202894074812420701820 * q^61 - 2597882075263561124480 * q^64 + 404224351485216078000 * q^65 - 2067527591150630859360 * q^66 + 1761142984477245282360 * q^69 + 2651929720118465517000 * q^70 - 6362428274364321596880 * q^71 + 21369976437605310645840 * q^74 - 1268180400269994750000 * q^75 - 28533821601830896716000 * q^76 + 8008906997916696975200 * q^79 + 50390556129429851388000 * q^80 - 63620987817532049079390 * q^81 + 26983560053969205971040 * q^84 + 58719411820058643416000 * q^85 - 73642932902287825779480 * q^86 + 17045340818835962686500 * q^89 + 218378490181286718303000 * q^90 - 261754857315780277067280 * q^91 + 163995755653951693894840 * q^94 + 287254967024630517105000 * q^95 - 1029134712278532215134080 * q^96 + 411070875879864759534360 * q^99

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