LMFDB - Embedded newform 6.31.b.a.5.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6,31,Mod(5,6)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 31, names="a")

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

chi := DirichletCharacter("6.5");

S:= CuspForms(chi, 31);

N := Newforms(S);

Level:	$ N $	$=$	$ 6 = 2 \cdot 3 $
Weight:	$ k $	$=$	$ 31 $
Character orbit:	$[\chi]$	$=$	6.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:	$34.2085571416$
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} + \cdots + 17\!\cdots\!00 $ x^10 + 8552062877595970390x^8 + 25392807796994293834069533242559594025x^6 + 31363214047445929775687291161211122208644643150843750000x^4 + 14997479733093492468171154918719535444710088825890735887189931640625000000x^2 + 1779211874045772876005913493072356377360261727229346754892124420427761840820312500000000000
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{104}\cdot 3^{53}\cdot 5^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			5.6
Root			$-4.15807e8i$ of defining polynomial
Character	$\chi$	$=$	6.5
Dual form			6.31.b.a.5.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+23170.5i q^{2} +(-1.23817e7 - 7.25146e6i) q^{3} -5.36871e8 q^{4} -9.97937e9i q^{5} +(1.68020e11 - 2.86891e11i) q^{6} +1.72818e12 q^{7} -1.24396e13i q^{8} +(1.00724e14 + 1.79571e14i) q^{9} +O(q^{10})$	\(q+23170.5i q^{2} +(-1.23817e7 - 7.25146e6i) q^{3} -5.36871e8 q^{4} -9.97937e9i q^{5} +(1.68020e11 - 2.86891e11i) q^{6} +1.72818e12 q^{7} -1.24396e13i q^{8} +(1.00724e14 + 1.79571e14i) q^{9} +2.31227e14 q^{10} +2.24453e15i q^{11} +(6.64740e15 + 3.89310e15i) q^{12} +4.54133e16 q^{13} +4.00427e16i q^{14} +(-7.23650e16 + 1.23562e17i) q^{15} +2.88230e17 q^{16} +6.96449e16i q^{17} +(-4.16075e18 + 2.33382e18i) q^{18} -2.04157e19 q^{19} +5.35763e18i q^{20} +(-2.13979e19 - 1.25318e19i) q^{21} -5.20068e19 q^{22} +8.65857e19i q^{23} +(-9.02049e19 + 1.54023e20i) q^{24} +8.31735e20 q^{25} +1.05225e21i q^{26} +(5.50170e19 - 2.95380e21i) q^{27} -9.27809e20 q^{28} -1.04339e22i q^{29} +(-2.86299e21 - 1.67673e21i) q^{30} -4.83485e21 q^{31} +6.67843e21i q^{32} +(1.62761e22 - 2.77912e22i) q^{33} -1.61371e21 q^{34} -1.72461e22i q^{35} +(-5.40757e22 - 9.64066e22i) q^{36} -5.92612e23 q^{37} -4.73042e23i q^{38} +(-5.62296e23 - 3.29313e23i) q^{39} -1.24139e23 q^{40} -2.69151e24i q^{41} +(2.90368e23 - 4.95799e23i) q^{42} -9.89138e22 q^{43} -1.20502e24i q^{44} +(1.79201e24 - 1.00516e24i) q^{45} -2.00623e24 q^{46} -1.51260e25i q^{47} +(-3.56879e24 - 2.09009e24i) q^{48} -1.95527e25 q^{49} +1.92717e25i q^{50} +(5.05027e23 - 8.62325e23i) q^{51} -2.43811e25 q^{52} +9.28067e25i q^{53} +(6.84410e25 + 1.27477e24i) q^{54} +2.23990e25 q^{55} -2.14978e25i q^{56} +(2.52782e26 + 1.48044e26i) q^{57} +2.41759e26 q^{58} +3.99723e26i q^{59} +(3.88506e25 - 6.63368e25i) q^{60} -3.46628e26 q^{61} -1.12026e26i q^{62} +(1.74069e26 + 3.10331e26i) q^{63} -1.54743e26 q^{64} -4.53196e26i q^{65} +(6.43934e26 + 3.77125e26i) q^{66} -3.03256e27 q^{67} -3.73903e25i q^{68} +(6.27873e26 - 1.07208e27i) q^{69} +3.99601e26 q^{70} -3.43715e27i q^{71} +(2.23379e27 - 1.25296e27i) q^{72} -8.79355e27 q^{73} -1.37311e28i q^{74} +(-1.02983e28 - 6.03129e27i) q^{75} +1.09606e28 q^{76} +3.87895e27i q^{77} +(7.63033e27 - 1.30287e28i) q^{78} -9.05146e27 q^{79} -2.87636e27i q^{80} +(-2.21006e28 + 3.61742e28i) q^{81} +6.23635e28 q^{82} +8.35020e28i q^{83} +(1.14879e28 + 6.72797e27i) q^{84} +6.95012e26 q^{85} -2.29188e27i q^{86} +(-7.56613e28 + 1.29190e29i) q^{87} +2.79209e28 q^{88} -1.10242e29i q^{89} +(2.32900e28 + 4.15217e28i) q^{90} +7.84823e28 q^{91} -4.64854e28i q^{92} +(5.98638e28 + 3.50597e28i) q^{93} +3.50477e29 q^{94} +2.03736e29i q^{95} +(4.84284e28 - 8.26906e28i) q^{96} -1.33091e29 q^{97} -4.53046e29i q^{98} +(-4.03053e29 + 2.26077e29i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 14139762 q^{3} - 5368709120 q^{4} - 145788764160 q^{6} - 1459334601196 q^{7} + 41713120268730 q^{9}+O(q^{10}) $ 10 * q + 14139762 * q^3 - 5368709120 * q^4 - 145788764160 * q^6 - 1459334601196 * q^7 + 41713120268730 * q^9	$ 10 q + 14139762 q^{3} - 5368709120 q^{4} - 145788764160 q^{6} - 1459334601196 q^{7} + 41713120268730 q^{9} - 11\!\cdots\!60 q^{10}+ \cdots + 27\!\cdots\!20 q^{99}+O(q^{100}) $ 10 * q + 14139762 * q^3 - 5368709120 * q^4 - 145788764160 * q^6 - 1459334601196 * q^7 + 41713120268730 * q^9 - 1111538175836160 * q^10 - 7591226920402944 * q^12 + 11241857908456580 * q^13 - 1208370750576105600 * q^15 + 2882303761517117440 * q^16 + 4378961453216956416 * q^18 - 406434941012438620 * q^19 + 189341373476724706020 * q^21 - 175966920878069907456 * q^22 + 78269746773932113920 * q^24 - 538750688835772733030 * q^25 - 509686212259700532126 * q^27 + 783474298257252810752 * q^28 + 3618734882327478927360 * q^30 - 3850790055930904811020 * q^31 + 13877514934601873876352 * q^33 - 21974427701517892976640 * q^34 - 22394560921038760181760 * q^36 + 691786417224189171658916 * q^37 + 264189297409049008449300 * q^39 + 596752514183975581777920 * q^40 + 2551733261187619598893056 * q^42 - 10594373354873893550389372 * q^43 + 21961398854703004532478720 * q^45 - 14905926072892021549301760 * q^46 + 4075508919955679952764928 * q^48 - 14303693611422252234715650 * q^49 + 100757981401326611204590080 * q^51 - 6035426507887496617000960 * q^52 + 186364360915292902942310400 * q^54 - 905529883473273884900970240 * q^55 + 1357830109447011748343825076 * q^57 - 1026862318649343581985177600 * q^58 + 648739106895918338880307200 * q^60 - 2949272535924647913201299260 * q^61 + 5088794127795653673352888692 * q^63 - 1547425049106725343623905280 * q^64 + 3787402697011447732654571520 * q^66 - 10556251754234326335356822044 * q^67 + 15764240424701154050198334720 * q^69 - 8691440888931957213379952640 * q^70 - 2350937029001432724922171392 * q^72 + 12106003505184711607130189300 * q^73 - 7500206691267464218185712830 * q^75 + 218203097450014125263421440 * q^76 - 23839067108381696719249735680 * q^78 + 68719005124237783442983312820 * q^79 - 111620808361643664456575921430 * q^81 + 18283730424263848186657898496 * q^82 - 101651875857781803693889290240 * q^84 + 403836274868708986530058828800 * q^85 - 512433611792960206983797969280 * q^87 + 94471521293641232015658319872 * q^88 - 426164288449255115819581440000 * q^90 + 1222541373056582384854822798600 * q^91 - 983623123086267594817934884284 * q^93 - 80746046881825464175401369600 * q^94 - 42020750332529991826318295040 * q^96 - 1391585232259866867438139103212 * q^97 + 2707446209006624257844338302720 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/6\mathbb{Z}\right)^\times$.

$n$	$5$
$\chi(n)$	$-1$

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 $

$2$			23170.5i			0.707107i
$2$			23170.5i			0.707107i
$3$	−1.23817e7	−	7.25146e6i	−0.862905	−	0.505367i
$3$	−1.23817e7	−	7.25146e6i	−0.862905	−	0.505367i
$4$	−5.36871e8			−0.500000
$5$		−	9.97937e9i		−	0.327004i	−0.986543	−	0.163502i	$-0.947721\pi$
$5$		−	9.97937e9i		−	0.327004i	0.986543	−	0.163502i	$-0.0522790\pi$
$6$	1.68020e11	−	2.86891e11i	0.357348	−	0.610166i
$7$	1.72818e12			0.364014			0.182007	−	0.983297i	$-0.441741\pi$
$7$	1.72818e12			0.364014			0.182007	+	0.983297i	$0.441741\pi$
$8$		−	1.24396e13i		−	0.353553i
$9$	1.00724e14	+	1.79571e14i	0.489209	+	0.872166i
$10$	2.31227e14			0.231227
$11$			2.24453e15i			0.537322i	0.963235	+	0.268661i	$0.0865811\pi$
$11$			2.24453e15i			0.537322i	−0.963235	+	0.268661i	$0.913419\pi$
$12$	6.64740e15	+	3.89310e15i	0.431452	+	0.252683i
$13$	4.54133e16			0.887223			0.443611	−	0.896219i	$-0.353697\pi$
$13$	4.54133e16			0.887223			0.443611	+	0.896219i	$0.353697\pi$
$14$			4.00427e16i			0.257397i
$15$	−7.23650e16	+	1.23562e17i	−0.165257	+	0.282173i
$16$	2.88230e17			0.250000
$17$			6.96449e16i			0.0243308i	0.999926	+	0.0121654i	$0.00387246\pi$
$17$			6.96449e16i			0.0243308i	−0.999926	+	0.0121654i	$0.996128\pi$
$18$	−4.16075e18	+	2.33382e18i	−0.616715	+	0.345923i
$19$	−2.04157e19			−1.34481			−0.672405	−	0.740184i	$-0.734739\pi$
$19$	−2.04157e19			−1.34481			−0.672405	+	0.740184i	$0.734739\pi$
$20$			5.35763e18i			0.163502i
$21$	−2.13979e19	−	1.25318e19i	−0.314109	−	0.183961i
$22$	−5.20068e19			−0.379944
$23$			8.65857e19i			0.324735i	0.986730	+	0.162367i	$0.0519130\pi$
$23$			8.65857e19i			0.324735i	−0.986730	+	0.162367i	$0.948087\pi$
$24$	−9.02049e19	+	1.54023e20i	−0.178674	+	0.305083i
$25$	8.31735e20			0.893068
$26$			1.05225e21i			0.627361i
$27$	5.50170e19	−	2.95380e21i	0.0186226	−	0.999827i
$28$	−9.27809e20			−0.182007
$29$		−	1.04339e22i		−	1.20915i	−0.796550	−	0.604573i	$-0.793344\pi$
$29$		−	1.04339e22i		−	1.20915i	0.796550	−	0.604573i	$-0.206656\pi$
$30$	−2.86299e21	−	1.67673e21i	−0.199527	−	0.116854i
$31$	−4.83485e21			−0.206043			−0.103021	−	0.994679i	$-0.532851\pi$
$31$	−4.83485e21			−0.206043			−0.103021	+	0.994679i	$0.532851\pi$
$32$			6.67843e21i			0.176777i
$33$	1.62761e22	−	2.77912e22i	0.271545	−	0.463658i
$34$	−1.61371e21			−0.0172044
$35$		−	1.72461e22i		−	0.119034i
$36$	−5.40757e22	−	9.64066e22i	−0.244605	−	0.436083i
$37$	−5.92612e23			−1.77723			−0.888617	−	0.458649i	$-0.848333\pi$
$37$	−5.92612e23			−1.77723			−0.888617	+	0.458649i	$0.848333\pi$
$38$		−	4.73042e23i		−	0.950924i
$39$	−5.62296e23	−	3.29313e23i	−0.765589	−	0.448373i
$40$	−1.24139e23			−0.115613
$41$		−	2.69151e24i		−	1.73076i	−0.501113	−	0.865382i	$-0.667076\pi$
$41$		−	2.69151e24i		−	1.73076i	0.501113	−	0.865382i	$-0.332924\pi$
$42$	2.90368e23	−	4.95799e23i	0.130080	−	0.222109i
$43$	−9.89138e22			−0.0311337			−0.0155668	−	0.999879i	$-0.504955\pi$
$43$	−9.89138e22			−0.0311337			−0.0155668	+	0.999879i	$0.504955\pi$
$44$		−	1.20502e24i		−	0.268661i
$45$	1.79201e24	−	1.00516e24i	0.285202	−	0.159973i
$46$	−2.00623e24			−0.229622
$47$		−	1.51260e25i		−	1.25388i	−0.779067	−	0.626941i	$-0.784307\pi$
$47$		−	1.51260e25i		−	1.25388i	0.779067	−	0.626941i	$-0.215693\pi$
$48$	−3.56879e24	−	2.09009e24i	−0.215726	−	0.126342i
$49$	−1.95527e25			−0.867494
$50$			1.92717e25i			0.631495i
$51$	5.05027e23	−	8.62325e23i	0.0122959	−	0.0209951i
$52$	−2.43811e25			−0.443611
$53$			9.28067e25i			1.26894i	0.772947	+	0.634470i	$0.218782\pi$
$53$			9.28067e25i			1.26894i	−0.772947	+	0.634470i	$0.781218\pi$
$54$	6.84410e25	+	1.27477e24i	0.706984	+	0.0131682i
$55$	2.23990e25			0.175706
$56$		−	2.14978e25i		−	0.128698i
$57$	2.52782e26	+	1.48044e26i	1.16044	+	0.679622i
$58$	2.41759e26			0.854995
$59$			3.99723e26i			1.09390i	0.837165	+	0.546951i	$0.184212\pi$
$59$			3.99723e26i			1.09390i	−0.837165	+	0.546951i	$0.815788\pi$
$60$	3.88506e25	−	6.63368e25i	0.0826284	−	0.141087i
$61$	−3.46628e26			−0.575328			−0.287664	−	0.957731i	$-0.592879\pi$
$61$	−3.46628e26			−0.575328			−0.287664	+	0.957731i	$0.592879\pi$
$62$		−	1.12026e26i		−	0.145694i
$63$	1.74069e26	+	3.10331e26i	0.178079	+	0.317481i
$64$	−1.54743e26			−0.125000
$65$		−	4.53196e26i		−	0.290125i
$66$	6.43934e26	+	3.77125e26i	0.327856	+	0.192011i
$67$	−3.03256e27			−1.23222			−0.616109	−	0.787661i	$-0.711292\pi$
$67$	−3.03256e27			−1.23222			−0.616109	+	0.787661i	$0.711292\pi$
$68$		−	3.73903e25i		−	0.0121654i
$69$	6.27873e26	−	1.07208e27i	0.164110	−	0.280215i
$70$	3.99601e26			0.0841698
$71$		−	3.43715e27i		−	0.585226i	−0.956231	−	0.292613i	$-0.905475\pi$
$71$		−	3.43715e27i		−	0.585226i	0.956231	−	0.292613i	$-0.0945248\pi$
$72$	2.23379e27	−	1.25296e27i	0.308357	−	0.172962i
$73$	−8.79355e27			−0.987009			−0.493505	−	0.869743i	$-0.664284\pi$
$73$	−8.79355e27			−0.987009			−0.493505	+	0.869743i	$0.664284\pi$
$74$		−	1.37311e28i		−	1.25669i
$75$	−1.02983e28	−	6.03129e27i	−0.770633	−	0.451327i
$76$	1.09606e28			0.672405
$77$			3.87895e27i			0.195593i
$78$	7.63033e27	−	1.30287e28i	0.317047	−	0.541353i
$79$	−9.05146e27			−0.310679			−0.155340	−	0.987861i	$-0.549647\pi$
$79$	−9.05146e27			−0.310679			−0.155340	+	0.987861i	$0.549647\pi$
$80$		−	2.87636e27i		−	0.0817510i
$81$	−2.21006e28	+	3.61742e28i	−0.521348	+	0.853344i
$82$	6.23635e28			1.22384
$83$			8.35020e28i			1.36624i	0.730308	+	0.683118i	$0.239376\pi$
$83$			8.35020e28i			1.36624i	−0.730308	+	0.683118i	$0.760624\pi$
$84$	1.14879e28	+	6.72797e27i	0.157055	+	0.0919803i
$85$	6.95012e26			0.00795625
$86$		−	2.29188e27i		−	0.0220148i
$87$	−7.56613e28	+	1.29190e29i	−0.611062	+	1.04338i
$88$	2.79209e28			0.189972
$89$		−	1.10242e29i		−	0.633135i	−0.948570	−	0.316568i	$-0.897470\pi$
$89$		−	1.10242e29i		−	0.633135i	0.948570	−	0.316568i	$-0.102530\pi$
$90$	2.32900e28	+	4.15217e28i	0.113118	+	0.201668i
$91$	7.84823e28			0.322962
$92$		−	4.64854e28i		−	0.162367i
$93$	5.98638e28	+	3.50597e28i	0.177795	+	0.104127i
$94$	3.50477e29			0.886629
$95$			2.03736e29i			0.439758i
$96$	4.84284e28	−	8.26906e28i	0.0893370	−	0.152541i
$97$	−1.33091e29			−0.210171			−0.105085	−	0.994463i	$-0.533512\pi$
$97$	−1.33091e29			−0.210171			−0.105085	+	0.994463i	$0.533512\pi$
$98$		−	4.53046e29i		−	0.613411i
$99$	−4.03053e29	+	2.26077e29i	−0.468634	+	0.262863i
$100$	−4.46534e29			−0.446534
$101$		−	1.82032e30i		−	1.56793i	−0.620802	−	0.783967i	$-0.713193\pi$
$101$		−	1.82032e30i		−	1.56793i	0.620802	−	0.783967i	$-0.286807\pi$
$102$	1.99805e28	+	1.17017e28i	0.0148458	+	0.00869455i
$103$	−2.32336e30			−1.49127			−0.745637	−	0.666353i	$-0.767855\pi$
$103$	−2.32336e30			−1.49127			−0.745637	+	0.666353i	$0.767855\pi$
$104$		−	5.64921e29i		−	0.313681i
$105$	−1.25060e29	+	2.13537e29i	−0.0601558	+	0.102715i
$106$	−2.15037e30			−0.897276
$107$		−	1.66207e30i		−	0.602409i	−0.953560	−	0.301205i	$-0.902611\pi$
$107$		−	1.66207e30i		−	0.602409i	0.953560	−	0.301205i	$-0.0973887\pi$
$108$	−2.95370e28	+	1.58581e30i	−0.00931131	+	0.499913i
$109$	4.82225e30			1.32389			0.661946	−	0.749552i	$-0.269731\pi$
$109$	4.82225e30			1.32389			0.661946	+	0.749552i	$0.269731\pi$
$110$			5.18995e29i			0.124243i
$111$	7.33757e30	+	4.29730e30i	1.53358	+	0.898155i
$112$	4.98114e29			0.0910035
$113$		−	9.04984e30i		−	1.44699i	−0.690332	−	0.723493i	$-0.742535\pi$
$113$		−	9.04984e30i		−	1.44699i	0.690332	−	0.723493i	$-0.257465\pi$
$114$	−3.43024e30	+	5.85708e30i	−0.480565	+	0.820557i
$115$	8.64071e29			0.106190
$116$			5.60168e30i			0.604573i
$117$	4.57420e30	+	8.15493e30i	0.434038	+	0.773806i
$118$	−9.26176e30			−0.773506
$119$			1.20359e29i			0.00885674i
$120$	1.53706e30	+	9.00188e29i	0.0997633	+	0.0584271i
$121$	1.24115e31			0.711285
$122$		−	8.03152e30i		−	0.406818i
$123$	−1.95174e31	+	3.33256e31i	−0.874670	+	1.49348i
$124$	2.59569e30			0.103021
$125$		−	1.75942e31i		−	0.619041i
$126$	−7.19053e30	+	4.03326e30i	−0.224493	+	0.125921i
$127$	1.64122e31			0.455105			0.227552	−	0.973766i	$-0.426928\pi$
$127$	1.64122e31			0.455105			0.227552	+	0.973766i	$0.426928\pi$
$128$		−	3.58546e30i		−	0.0883883i
$129$	1.22473e30	+	7.17269e29i	0.0268654	+	0.0157339i
$130$	1.05008e31			0.205150
$131$		−	9.10400e31i		−	1.58549i	−0.609555	−	0.792744i	$-0.708652\pi$
$131$		−	9.10400e31i		−	1.58549i	0.609555	−	0.792744i	$-0.291348\pi$
$132$	−8.73816e30	+	1.49203e31i	−0.135772	+	0.231829i
$133$	−3.52820e31			−0.489530
$134$		−	7.02659e31i		−	0.871309i
$135$	−2.94771e31	−	5.49035e29i	−0.326947	−	0.00608967i
$136$	8.66352e29			0.00860222
$137$		−	1.28442e32i		−	1.14261i	−0.820738	−	0.571305i	$-0.806437\pi$
$137$		−	1.28442e32i		−	1.14261i	0.820738	−	0.571305i	$-0.193563\pi$
$138$	2.48407e31	+	1.45481e31i	0.198142	+	0.116043i
$139$	−5.98257e31			−0.428219			−0.214110	−	0.976810i	$-0.568685\pi$
$139$	−5.98257e31			−0.428219			−0.214110	+	0.976810i	$0.568685\pi$
$140$			9.25895e30i			0.0595170i
$141$	−1.09686e32	+	1.87286e32i	−0.633670	+	1.08198i
$142$	7.96405e31			0.413817
$143$			1.01931e32i			0.476724i
$144$	2.90317e31	+	5.17579e31i	0.122302	+	0.218042i
$145$	−1.04124e32			−0.395395
$146$		−	2.03751e32i		−	0.697921i
$147$	2.42097e32	+	1.41786e32i	0.748565	+	0.438402i
$148$	3.18156e32			0.888617
$149$			6.44525e32i			1.62722i	0.581413	+	0.813609i	$0.302500\pi$
$149$			6.44525e32i			1.62722i	−0.581413	+	0.813609i	$0.697500\pi$
$150$	1.39748e32	−	2.38617e32i	0.319136	−	0.544920i
$151$	−2.56533e32			−0.530260			−0.265130	−	0.964213i	$-0.585415\pi$
$151$	−2.56533e32			−0.530260			−0.265130	+	0.964213i	$0.585415\pi$
$152$			2.53963e32i			0.475462i
$153$	−1.25062e31	+	7.01490e30i	−0.0212205	+	0.0119028i
$154$	−8.98770e31			−0.138305
$155$			4.82487e31i			0.0673768i
$156$	3.01880e32	+	1.76798e32i	0.382794	+	0.224186i
$157$	−3.20265e31			−0.0368990			−0.0184495	−	0.999830i	$-0.505873\pi$
$157$	−3.20265e31			−0.0368990			−0.0184495	+	0.999830i	$0.505873\pi$
$158$		−	2.09727e32i		−	0.219683i
$159$	6.72984e32	−	1.14911e33i	0.641280	−	1.09497i
$160$	6.66466e31			0.0578067
$161$			1.49636e32i			0.118208i
$162$	−8.38174e32	−	5.12081e32i	−0.603405	−	0.368649i
$163$	3.91181e32			0.256782			0.128391	−	0.991724i	$-0.459019\pi$
$163$	3.91181e32			0.256782			0.128391	+	0.991724i	$0.459019\pi$
$164$			1.44499e33i			0.865382i
$165$	−2.77338e32	−	1.62425e32i	−0.151618	−	0.0887961i
$166$	−1.93478e33			−0.966074
$167$		−	1.28350e33i		−	0.585663i	−0.956164	−	0.292831i	$-0.905403\pi$
$167$		−	1.28350e33i		−	0.585663i	0.956164	−	0.292831i	$-0.0945975\pi$
$168$	−1.55890e32	+	2.66180e32i	−0.0650399	+	0.111054i
$169$	−5.57628e32			−0.212836
$170$			1.61038e31i			0.00562592i
$171$	−2.05635e33	−	3.66608e33i	−0.657893	−	1.17290i
$172$	5.31040e31			0.0155668
$173$		−	4.81850e32i		−	0.129485i	−0.997902	−	0.0647426i	$-0.979377\pi$
$173$		−	4.81850e32i		−	0.129485i	0.997902	−	0.0647426i	$-0.0206226\pi$
$174$	−2.99340e33	−	1.75311e33i	−0.737779	−	0.432086i
$175$	1.43739e33			0.325089
$176$			6.46941e32i			0.134331i
$177$	2.89857e33	−	4.94926e33i	0.552821	−	0.943933i
$178$	2.55436e33			0.447694
$179$			1.06649e34i			1.71855i	0.511514	+	0.859275i	$0.329085\pi$
$179$			1.06649e34i			1.71855i	−0.511514	+	0.859275i	$0.670915\pi$
$180$	−9.62077e32	+	5.39641e32i	−0.142601	+	0.0799867i
$181$	8.74279e33			1.19254			0.596268	−	0.802785i	$-0.296650\pi$
$181$	8.74279e33			1.19254			0.596268	+	0.802785i	$0.296650\pi$
$182$			1.81847e33i			0.228368i
$183$	4.29185e33	+	2.51355e33i	0.496453	+	0.290752i
$184$	1.07709e33			0.114811
$185$			5.91390e33i			0.581163i
$186$	−8.12349e32	+	1.38707e33i	−0.0736290	+	0.125720i
$187$	−1.56320e32			−0.0130735
$188$			8.12072e33i			0.626941i
$189$	9.50793e31	−	5.10470e33i	0.00677889	−	0.363951i
$190$	−4.72066e33			−0.310956
$191$			8.19998e33i			0.499243i	0.968343	+	0.249622i	$0.0803063\pi$
$191$			8.19998e33i			0.499243i	−0.968343	+	0.249622i	$0.919694\pi$
$192$	1.91598e33	+	1.12211e33i	0.107863	+	0.0631708i
$193$	−2.27173e34			−1.18304			−0.591518	−	0.806292i	$-0.701471\pi$
$193$	−2.27173e34			−1.18304			−0.591518	+	0.806292i	$0.701471\pi$
$194$		−	3.08378e33i		−	0.148613i
$195$	−3.28633e33	+	5.61136e33i	−0.146620	+	0.250351i
$196$	1.04973e34			0.433747
$197$		−	2.53204e34i		−	0.969343i	−0.874696	−	0.484671i	$-0.838939\pi$
$197$		−	2.53204e34i		−	0.969343i	0.874696	−	0.484671i	$-0.161061\pi$
$198$	−5.23832e33	−	9.33892e33i	−0.185872	−	0.331374i
$199$	−2.42645e34			−0.798316			−0.399158	−	0.916882i	$-0.630698\pi$
$199$	−2.42645e34			−0.798316			−0.399158	+	0.916882i	$0.630698\pi$
$200$		−	1.03464e34i		−	0.315747i
$201$	3.75484e34	+	2.19905e34i	1.06329	+	0.622722i
$202$	4.21777e34			1.10870
$203$		−	1.80317e34i		−	0.440146i
$204$	−2.71134e32	+	4.62957e32i	−0.00614797	+	0.0104976i
$205$	−2.68596e34			−0.565967
$206$		−	5.38333e34i		−	1.05449i
$207$	−1.55483e34	+	8.72125e33i	−0.283223	+	0.158863i
$208$	1.30895e34			0.221806
$209$		−	4.58237e34i		−	0.722596i
$210$	−4.94776e33	−	2.89769e33i	−0.0726305	−	0.0425366i
$211$	−1.07541e35			−1.47007			−0.735036	−	0.678028i	$-0.762835\pi$
$211$	−1.07541e35			−1.47007			−0.735036	+	0.678028i	$0.762835\pi$
$212$		−	4.98252e34i		−	0.634470i
$213$	−2.49244e34	+	4.25579e34i	−0.295754	+	0.504994i
$214$	3.85109e34			0.425968
$215$			9.87098e32i			0.0101808i
$216$	−3.67440e34	−	6.84387e32i	−0.353492	−	0.00658409i
$217$	−8.35548e33			−0.0750024
$218$			1.11734e35i			0.936132i
$219$	1.08879e35	+	6.37660e34i	0.851695	+	0.498801i
$220$	−1.20254e34			−0.0878532
$221$			3.16280e33i			0.0215868i
$222$	−9.95706e34	+	1.70015e35i	−0.635092	+	1.08441i
$223$	1.87300e35			1.11677			0.558387	−	0.829581i	$-0.311421\pi$
$223$	1.87300e35			1.11677			0.558387	+	0.829581i	$0.311421\pi$
$224$			1.15415e34i			0.0643492i
$225$	8.37755e34	+	1.49356e35i	0.436897	+	0.778904i
$226$	2.09689e35			1.02317
$227$		−	9.17418e34i		−	0.418966i	−0.977812	−	0.209483i	$-0.932822\pi$
$227$		−	9.17418e34i		−	0.418966i	0.977812	−	0.209483i	$-0.0671782\pi$
$228$	−1.35711e35	−	7.94804e34i	−0.580221	−	0.339811i
$229$	1.91797e35			0.767910			0.383955	−	0.923352i	$-0.374562\pi$
$229$	1.91797e35			0.767910			0.383955	+	0.923352i	$0.374562\pi$
$230$			2.00209e34i			0.0750874i
$231$	2.81280e34	−	4.80281e34i	0.0988460	−	0.168778i
$232$	−1.29794e35			−0.427498
$233$		−	8.02007e34i		−	0.247651i	−0.992304	−	0.123825i	$-0.960484\pi$
$233$		−	8.02007e34i		−	0.247651i	0.992304	−	0.123825i	$-0.0395163\pi$
$234$	−1.88953e35	+	1.05986e35i	−0.547163	+	0.306911i
$235$	−1.50948e35			−0.410024
$236$		−	2.14599e35i		−	0.546951i
$237$	1.12073e35	+	6.56363e34i	0.268087	+	0.157007i
$238$	−2.78877e33			−0.00626266
$239$		−	3.38486e35i		−	0.713793i	−0.934144	−	0.356897i	$-0.883835\pi$
$239$		−	3.38486e35i		−	0.713793i	0.934144	−	0.356897i	$-0.116165\pi$
$240$	−2.08578e34	+	3.56143e34i	−0.0413142	+	0.0705433i
$241$	−5.57750e35			−1.03797			−0.518984	−	0.854784i	$-0.673690\pi$
$241$	−5.57750e35			−1.03797			−0.518984	+	0.854784i	$0.673690\pi$
$242$			2.87580e35i			0.502954i
$243$	5.35959e35	−	2.87639e35i	0.881125	−	0.472882i
$244$	1.86094e35			0.287664
$245$			1.95124e35i			0.283674i
$246$	−7.72169e35	−	4.52226e35i	−1.05605	−	0.618485i
$247$	−9.27145e35			−1.19315
$248$			6.01433e34i			0.0728471i
$249$	6.05511e35	−	1.03390e36i	0.690450	−	1.17893i
$250$	4.07666e35			0.437728
$251$			5.48333e35i			0.554547i	0.960791	+	0.277273i	$0.0894308\pi$
$251$			5.48333e35i			0.554547i	−0.960791	+	0.277273i	$0.910569\pi$
$252$	−9.34525e34	−	1.66608e35i	−0.0890395	−	0.158740i
$253$	−1.94344e35			−0.174487
$254$			3.80279e35i			0.321808i
$255$	−8.60546e33	−	5.03985e33i	−0.00686549	−	0.00402082i
$256$	8.30767e34			0.0625000
$257$		−	4.72644e35i		−	0.335380i	−0.985840	−	0.167690i	$-0.946369\pi$
$257$		−	4.72644e35i		−	0.335380i	0.985840	−	0.167690i	$-0.0536308\pi$
$258$	−1.66195e34	+	2.83775e34i	−0.0111256	+	0.0189967i
$259$	−1.02414e36			−0.646938
$260$			2.43308e35i			0.145063i
$261$	1.87364e36	−	1.05095e36i	1.05458	−	0.591525i
$262$	2.10944e36			1.12111
$263$			3.46209e36i			1.73781i	0.494980	+	0.868904i	$0.335175\pi$
$263$			3.46209e36i			1.73781i	−0.494980	+	0.868904i	$0.664825\pi$
$264$	−3.45710e35	−	2.02467e35i	−0.163928	−	0.0960055i
$265$	9.26152e35			0.414948
$266$		−	8.17501e35i		−	0.346150i
$267$	−7.99414e35	+	1.36499e36i	−0.319965	+	0.546336i
$268$	1.62809e36			0.616109
$269$			4.06223e36i			1.45372i	0.686787	+	0.726859i	$0.259021\pi$
$269$			4.06223e36i			1.45372i	−0.686787	+	0.726859i	$0.740979\pi$
$270$	1.27214e34	−	6.82998e35i	0.00430605	−	0.231187i
$271$	−3.68452e36			−1.17989			−0.589946	−	0.807443i	$-0.700851\pi$
$271$	−3.68452e36			−1.17989			−0.589946	+	0.807443i	$0.700851\pi$
$272$			2.00738e34i			0.00608269i
$273$	−9.71747e35	−	5.69111e35i	−0.278685	−	0.163214i
$274$	2.97606e36			0.807948
$275$			1.86685e36i			0.479865i
$276$	−3.37087e35	+	5.75570e35i	−0.0820551	+	0.140108i
$277$	1.48383e36			0.342126			0.171063	−	0.985260i	$-0.445280\pi$
$277$	1.48383e36			0.342126			0.171063	+	0.985260i	$0.445280\pi$
$278$		−	1.38619e36i		−	0.302797i
$279$	−4.86984e35	−	8.68200e35i	−0.100798	−	0.179703i
$280$	−2.14534e35			−0.0420849
$281$		−	6.23773e36i		−	1.15993i	−0.814642	−	0.579965i	$-0.803066\pi$
$281$		−	6.23773e36i		−	1.15993i	0.814642	−	0.579965i	$-0.196934\pi$
$282$	−4.33952e36	−	2.54147e36i	−0.765076	−	0.448072i
$283$	−6.72055e36			−1.12359			−0.561796	−	0.827276i	$-0.689889\pi$
$283$	−6.72055e36			−1.12359			−0.561796	+	0.827276i	$0.689889\pi$
$284$			1.84531e36i			0.292613i
$285$	1.47738e36	−	2.52261e36i	0.222239	−	0.379469i
$286$	−2.36180e36			−0.337095
$287$		−	4.65141e36i		−	0.630022i
$288$	−1.19926e36	+	6.72678e35i	−0.154179	+	0.0864808i
$289$	8.18862e36			0.999408
$290$		−	2.41261e36i		−	0.279587i
$291$	1.64790e36	+	9.65103e35i	0.181357	+	0.106213i
$292$	4.72100e36			0.493505
$293$		−	1.69952e37i		−	1.68776i	−0.536529	−	0.843882i	$-0.680265\pi$
$293$		−	1.69952e37i		−	1.68776i	0.536529	−	0.843882i	$-0.319735\pi$
$294$	−3.28525e36	+	5.60950e36i	−0.309997	+	0.529315i
$295$	3.98898e36			0.357710
$296$			7.37183e36i			0.628347i
$297$	6.62989e36	+	1.23487e35i	0.537229	+	0.0100063i
$298$	−1.49339e37			−1.15062
$299$			3.93214e36i			0.288112i
$300$	5.52887e36	+	3.23802e36i	0.385317	+	0.225663i
$301$	−1.70941e35			−0.0113331
$302$		−	5.94398e36i		−	0.374950i
$303$	−1.32000e37	+	2.25388e37i	−0.792381	+	1.35298i
$304$	−5.88443e36			−0.336202
$305$			3.45912e36i			0.188135i
$306$	−1.62539e35	−	2.89775e35i	−0.00841657	−	0.0150051i
$307$	−1.17349e37			−0.578633			−0.289316	−	0.957234i	$-0.593428\pi$
$307$	−1.17349e37			−0.578633			−0.289316	+	0.957234i	$0.593428\pi$
$308$		−	2.08249e36i		−	0.0977964i
$309$	2.87672e37	+	1.68477e37i	1.28683	+	0.753640i
$310$	−1.11795e36			−0.0476426
$311$		−	9.76799e36i		−	0.396642i	−0.980137	−	0.198321i	$-0.936451\pi$
$311$		−	9.76799e36i		−	0.396642i	0.980137	−	0.198321i	$-0.0635489\pi$
$312$	−4.09650e36	+	6.99471e36i	−0.158524	+	0.270677i
$313$	1.71954e37			0.634230			0.317115	−	0.948387i	$-0.397286\pi$
$313$	1.71954e37			0.634230			0.317115	+	0.948387i	$0.397286\pi$
$314$		−	7.42069e35i		−	0.0260915i
$315$	3.09691e36	−	1.73710e36i	0.103817	−	0.0582326i
$316$	4.85947e36			0.155340
$317$		−	3.20717e34i		−	0.000977763i	−1.00000		0.000488881i	$-0.999844\pi$
$317$		−	3.20717e34i		−	0.000977763i	1.00000		0.000488881i	$-0.000155616\pi$
$318$	2.66254e37	+	1.55933e37i	0.774264	+	0.453453i
$319$	2.34193e37			0.649701
$320$			1.54423e36i			0.0408755i
$321$	−1.20524e37	+	2.05793e37i	−0.304437	+	0.519822i
$322$	−3.46713e36			−0.0835857
$323$		−	1.42185e36i		−	0.0327202i
$324$	1.18651e37	−	1.94209e37i	0.260674	−	0.426672i
$325$	3.77718e37			0.792351
$326$			9.06385e36i			0.181572i
$327$	−5.97078e37	−	3.49683e37i	−1.14239	−	0.669050i
$328$	−3.34812e37			−0.611918
$329$		−	2.61405e37i		−	0.456431i
$330$	3.76347e36	−	6.42606e36i	0.0627884	−	0.107210i
$331$	−1.08913e38			−1.73644			−0.868220	−	0.496179i	$-0.834736\pi$
$331$	−1.08913e38			−1.73644			−0.868220	+	0.496179i	$0.834736\pi$
$332$		−	4.48298e37i		−	0.683118i
$333$	−5.96902e37	−	1.06416e38i	−0.869440	−	1.55004i
$334$	2.97392e37			0.414126
$335$			3.02630e37i			0.402940i
$336$	−6.16751e36	−	3.61205e36i	−0.0785274	−	0.0459901i
$337$	5.85023e37			0.712401			0.356200	−	0.934410i	$-0.384072\pi$
$337$	5.85023e37			0.712401			0.356200	+	0.934410i	$0.384072\pi$
$338$		−	1.29205e37i		−	0.150498i
$339$	−6.56245e37	+	1.12053e38i	−0.731258	+	1.24861i
$340$	−3.73132e35			−0.00397813
$341$		−	1.08519e37i		−	0.110711i
$342$	8.49448e37	−	4.76466e37i	0.829364	−	0.465201i
$343$	−7.27426e37			−0.679794
$344$			1.23044e36i			0.0110074i
$345$	−1.06987e37	−	6.26577e36i	−0.0916315	−	0.0536647i
$346$	1.11647e37			0.0915599
$347$			2.45550e38i			1.92840i	0.265173	+	0.964201i	$0.414571\pi$
$347$			2.45550e38i			1.92840i	−0.265173	+	0.964201i	$0.585429\pi$
$348$	4.06204e37	−	6.93586e37i	0.305531	−	0.521689i
$349$	2.61780e38			1.88606			0.943028	−	0.332713i	$-0.107964\pi$
$349$	2.61780e38			1.88606			0.943028	+	0.332713i	$0.107964\pi$
$350$			3.33049e37i			0.229873i
$351$	2.49850e36	−	1.34142e38i	0.0165224	−	0.887069i
$352$	−1.49899e37			−0.0949860
$353$		−	1.13048e38i		−	0.686500i	−0.939244	−	0.343250i	$-0.888472\pi$
$353$		−	1.13048e38i		−	0.686500i	0.939244	−	0.343250i	$-0.111528\pi$
$354$	1.14677e38	+	6.71613e37i	0.667462	+	0.390904i
$355$	−3.43006e37			−0.191371
$356$			5.91857e37i			0.316568i
$357$	8.72777e35	−	1.49025e36i	0.00447590	−	0.00764252i
$358$	−2.47111e38			−1.21520
$359$			2.21010e38i			1.04231i	0.853463	+	0.521153i	$0.174498\pi$
$359$			2.21010e38i			1.04231i	−0.853463	+	0.521153i	$0.825502\pi$
$360$	−1.25037e37	−	2.22918e37i	−0.0565591	−	0.100834i
$361$	1.86335e38			0.808513
$362$			2.02575e38i			0.843250i
$363$	−1.53676e38	−	9.00015e37i	−0.613771	−	0.359460i
$364$	−4.21349e37			−0.161481
$365$			8.77540e37i			0.322756i
$366$	−5.82403e37	+	9.94443e37i	−0.205592	+	0.351046i
$367$	5.97989e37			0.202629			0.101315	−	0.994854i	$-0.467695\pi$
$367$	5.97989e37			0.202629			0.101315	+	0.994854i	$0.467695\pi$
$368$			2.49566e37i			0.0811837i
$369$	4.83318e38	−	2.71099e38i	1.50951	−	0.846706i
$370$	−1.37028e38			−0.410944
$371$			1.60387e38i			0.461912i
$372$	−3.21391e37	−	1.88225e37i	−0.0888976	−	0.0520635i
$373$	−9.93224e37			−0.263885			−0.131943	−	0.991257i	$-0.542121\pi$
$373$	−9.93224e37			−0.263885			−0.131943	+	0.991257i	$0.542121\pi$
$374$		−	3.62201e36i		−	0.00924433i
$375$	−1.27584e38	+	2.17847e38i	−0.312843	+	0.534173i
$376$	−1.88161e38			−0.443314
$377$		−	4.73840e38i		−	1.07278i
$378$	1.18278e38	+	2.20303e36i	0.257352	+	0.00479340i
$379$	−7.72952e37			−0.161646			−0.0808229	−	0.996728i	$-0.525755\pi$
$379$	−7.72952e37			−0.161646			−0.0808229	+	0.996728i	$0.525755\pi$
$380$		−	1.09380e38i		−	0.219879i
$381$	−2.03212e38	−	1.19013e38i	−0.392712	−	0.229995i
$382$	−1.89997e38			−0.353018
$383$		−	9.02831e38i		−	1.61296i	−0.591259	−	0.806482i	$-0.701369\pi$
$383$		−	9.02831e38i		−	1.61296i	0.591259	−	0.806482i	$-0.298631\pi$
$384$	−2.59998e37	+	4.43942e37i	−0.0446685	+	0.0762707i
$385$	3.87094e37			0.0639596
$386$		−	5.26371e38i		−	0.836532i
$387$	−9.96298e36	−	1.77621e37i	−0.0152309	−	0.0271537i
$388$	7.14526e37			0.105085
$389$		−	3.50498e38i		−	0.495955i	−0.968766	−	0.247977i	$-0.920234\pi$
$389$		−	3.50498e38i		−	0.495955i	0.968766	−	0.247977i	$-0.0797658\pi$
$390$	−1.30018e38	−	7.61459e37i	−0.177025	−	0.103676i
$391$	−6.03026e36			−0.00790104
$392$			2.43227e38i			0.306705i
$393$	−6.60173e38	+	1.12723e39i	−0.801253	+	1.36813i
$394$	5.86686e38			0.685429
$395$			9.03279e37i			0.101593i
$396$	2.16387e38	−	1.21374e38i	0.234317	−	0.131431i
$397$	5.52290e38			0.575851			0.287925	−	0.957653i	$-0.407034\pi$
$397$	5.52290e38			0.575851			0.287925	+	0.957653i	$0.407034\pi$
$398$		−	5.62220e38i		−	0.564495i
$399$	4.36853e38	+	2.55846e38i	0.422417	+	0.247392i
$400$	2.39731e38			0.223267
$401$			1.25312e39i			1.12416i	0.827083	+	0.562080i	$0.189999\pi$
$401$			1.25312e39i			1.12416i	−0.827083	+	0.562080i	$0.810001\pi$
$402$	−5.09530e38	+	8.70014e38i	−0.440331	+	0.751857i
$403$	−2.19566e38			−0.182806
$404$			9.77278e38i			0.783967i
$405$	3.60996e38	+	2.20550e38i	0.279047	+	0.170483i
$406$	4.17804e38			0.311230
$407$		−	1.33013e39i		−	0.954947i
$408$	−1.07269e37	−	6.28231e36i	−0.00742290	−	0.00434727i
$409$	−1.21209e39			−0.808509			−0.404255	−	0.914647i	$-0.632469\pi$
$409$	−1.21209e39			−0.808509			−0.404255	+	0.914647i	$0.632469\pi$
$410$		−	6.22349e38i		−	0.400199i
$411$	−9.31391e38	+	1.59033e39i	−0.577437	+	0.985964i
$412$	1.24734e39			0.745637
$413$			6.90792e38i			0.398196i
$414$	−2.02076e38	−	3.60262e38i	−0.112333	−	0.200269i
$415$	8.33297e38			0.446764
$416$			3.03290e38i			0.156840i
$417$	7.40747e38	+	4.33824e38i	0.369512	+	0.216408i
$418$	1.06176e39			0.510952
$419$			6.48973e38i			0.301312i	0.988586	+	0.150656i	$0.0481386\pi$
$419$			6.48973e38i			0.301312i	−0.988586	+	0.150656i	$0.951861\pi$
$420$	6.71409e37	−	1.14642e38i	0.0300779	−	0.0513575i
$421$	−3.40219e39			−1.47071			−0.735355	−	0.677682i	$-0.762985\pi$
$421$	−3.40219e39			−1.47071			−0.735355	+	0.677682i	$0.762985\pi$
$422$		−	2.49178e39i		−	1.03950i
$423$	2.71620e39	−	1.52355e39i	1.09359	−	0.613411i
$424$	1.15447e39			0.448638
$425$			5.79261e37i			0.0217290i
$426$	−9.86088e38	−	5.77509e38i	−0.357085	−	0.209129i
$427$	−5.99034e38			−0.209427
$428$			8.92315e38i			0.301205i
$429$	7.39151e38	−	1.26209e39i	0.240921	−	0.411368i
$430$	−2.28715e37			−0.00719893
$431$		−	1.75593e39i		−	0.533761i	−0.963730	−	0.266881i	$-0.914007\pi$
$431$		−	1.75593e39i		−	0.533761i	0.963730	−	0.266881i	$-0.0859929\pi$
$432$	1.58576e37	−	8.51375e38i	0.00465565	−	0.249957i
$433$	−1.72970e39			−0.490516			−0.245258	−	0.969458i	$-0.578873\pi$
$433$	−1.72970e39			−0.490516			−0.245258	+	0.969458i	$0.578873\pi$
$434$		−	1.93600e38i		−	0.0530347i
$435$	1.28924e39	+	7.55052e38i	0.341189	+	0.199820i
$436$	−2.58893e39			−0.661946
$437$		−	1.76771e39i		−	0.436706i
$438$	−1.47749e39	+	2.52279e39i	−0.352706	+	0.602239i
$439$	−2.57059e39			−0.593014			−0.296507	−	0.955031i	$-0.595822\pi$
$439$	−2.57059e39			−0.593014			−0.296507	+	0.955031i	$0.595822\pi$
$440$		−	2.78633e38i		−	0.0621216i
$441$	−1.96943e39	−	3.51111e39i	−0.424386	−	0.756599i
$442$	−7.32837e37			−0.0152642
$443$			3.06729e39i			0.617588i	0.951129	+	0.308794i	$0.0999253\pi$
$443$			3.06729e39i			0.617588i	−0.951129	+	0.308794i	$0.900075\pi$
$444$	−3.93933e39	−	2.30710e39i	−0.766792	−	0.449078i
$445$	−1.10014e39			−0.207038
$446$			4.33983e39i			0.789678i
$447$	4.67374e39	−	7.98034e39i	0.822341	−	1.40413i
$448$	−2.67423e38			−0.0455018
$449$			1.38459e39i			0.227839i	0.993490	+	0.113919i	$0.0363406\pi$
$449$			1.38459e39i			0.227839i	−0.993490	+	0.113919i	$0.963659\pi$
$450$	−3.46064e39	+	1.94112e39i	−0.550768	+	0.308933i
$451$	6.04116e39			0.929978
$452$			4.85860e39i			0.723493i
$453$	3.17632e39	+	1.86024e39i	0.457564	+	0.267975i
$454$	2.12570e39			0.296254
$455$		−	7.83204e38i		−	0.105610i
$456$	1.84160e39	−	3.14450e39i	0.240283	−	0.410278i
$457$	3.69937e39			0.467073			0.233536	−	0.972348i	$-0.424970\pi$
$457$	3.69937e39			0.467073			0.233536	+	0.972348i	$0.424970\pi$
$458$			4.44404e39i			0.542995i
$459$	2.05717e38	+	3.83166e36i	0.0243265	+	0.000453102i
$460$	−4.63895e38			−0.0530948
$461$			1.22265e40i			1.35452i	0.735742	+	0.677262i	$0.236834\pi$
$461$			1.22265e40i			1.35452i	−0.735742	+	0.677262i	$0.763166\pi$
$462$	1.11283e39	+	6.51739e38i	0.119344	+	0.0698947i
$463$	1.43137e40			1.48606			0.743031	−	0.669257i	$-0.233388\pi$
$463$	1.43137e40			1.48606			0.743031	+	0.669257i	$0.233388\pi$
$464$		−	3.00738e39i		−	0.302286i
$465$	3.49873e38	−	5.97403e38i	0.0340500	−	0.0581397i
$466$	1.85829e39			0.175115
$467$			1.13800e40i			1.03846i	0.854635	+	0.519229i	$0.173781\pi$
$467$			1.13800e40i			1.03846i	−0.854635	+	0.519229i	$0.826219\pi$
$468$	−2.45576e39	−	4.37814e39i	−0.217019	−	0.386903i
$469$	−5.24081e39			−0.448544
$470$		−	3.49754e39i		−	0.289931i
$471$	3.96544e38	+	2.32239e38i	0.0318403	+	0.0186475i
$472$	4.97237e39			0.386753
$473$		−	2.22015e38i		−	0.0167288i
$474$	−1.52082e39	+	2.59678e39i	−0.111021	+	0.189566i
$475$	−1.69805e40			−1.20101
$476$		−	6.46172e37i		−	0.00442837i
$477$	−1.66654e40	+	9.34785e39i	−1.10673	+	0.620777i
$478$	7.84288e39			0.504728
$479$		−	2.53707e40i		−	1.58234i	−0.611596	−	0.791170i	$-0.709472\pi$
$479$		−	2.53707e40i		−	1.58234i	0.611596	−	0.791170i	$-0.290528\pi$
$480$	−8.25200e38	−	4.83285e38i	−0.0498817	−	0.0292136i
$481$	−2.69125e40			−1.57680
$482$		−	1.29233e40i		−	0.733954i
$483$	1.08508e39	−	1.85275e39i	0.0597384	−	0.102002i
$484$	−6.66337e39			−0.355643
$485$			1.32816e39i			0.0687267i
$486$	6.66473e39	+	1.24184e40i	0.334378	+	0.623050i
$487$	2.94896e40			1.43461			0.717305	−	0.696759i	$-0.245375\pi$
$487$	2.94896e40			1.43461			0.717305	+	0.696759i	$0.245375\pi$
$488$			4.31189e39i			0.203409i
$489$	−4.84350e39	−	2.83663e39i	−0.221578	−	0.129769i
$490$	−4.52112e39			−0.200588
$491$		−	1.61090e40i		−	0.693180i	−0.938017	−	0.346590i	$-0.887340\pi$
$491$		−	1.61090e40i		−	0.693180i	0.938017	−	0.346590i	$-0.112660\pi$
$492$	1.04783e40	−	1.78915e40i	0.437335	−	0.746742i
$493$	7.26671e38			0.0294194
$494$		−	2.14824e40i		−	0.843681i
$495$	2.25611e39	+	4.02221e39i	0.0859572	+	0.153245i
$496$	−1.39355e39			−0.0515107
$497$		−	5.94002e39i		−	0.213031i
$498$	2.39560e40	+	1.40300e40i	0.833630	+	0.488222i
$499$	−4.08317e39			−0.137876			−0.0689381	−	0.997621i	$-0.521961\pi$
$499$	−4.08317e39			−0.137876			−0.0689381	+	0.997621i	$0.521961\pi$
$500$			9.44581e39i			0.309520i
$501$	−9.30722e39	+	1.58919e40i	−0.295974	+	0.505371i
$502$	−1.27051e40			−0.392124
$503$		−	1.64420e40i		−	0.492533i	−0.969202	−	0.246267i	$-0.920796\pi$
$503$		−	1.64420e40i		−	0.492533i	0.969202	−	0.246267i	$-0.0792039\pi$
$504$	3.86038e39	−	2.16534e39i	0.112246	−	0.0629605i
$505$	−1.81657e40			−0.512721
$506$		−	4.50304e39i		−	0.123381i
$507$	6.90441e39	+	4.04362e39i	0.183657	+	0.107560i
$508$	−8.81124e39			−0.227552
$509$		−	3.05128e39i		−	0.0765095i	−0.999268	−	0.0382548i	$-0.987820\pi$
$509$		−	3.05128e39i		−	0.0765095i	0.999268	−	0.0382548i	$-0.0121798\pi$
$510$	1.16776e38	−	1.99393e38i	0.00284315	−	0.00485463i
$511$	−1.51968e40			−0.359285
$512$			1.92493e39i			0.0441942i
$513$	−1.12321e39	+	6.03040e40i	−0.0250439	+	1.34458i
$514$	1.09514e40			0.237149
$515$			2.31856e40i			0.487652i
$516$	−6.57519e38	−	3.85081e38i	−0.0134327	−	0.00786695i
$517$	3.39508e40			0.673738
$518$		−	2.37298e40i		−	0.457455i
$519$	−3.49411e39	+	5.96614e39i	−0.0654375	+	0.111733i
$520$	−5.63756e39			−0.102575
$521$			4.61044e40i			0.815035i	0.913197	+	0.407517i	$0.133605\pi$
$521$			4.61044e40i			0.815035i	−0.913197	+	0.407517i	$0.866395\pi$
$522$	2.43509e40	+	4.34131e40i	0.418272	+	0.745698i
$523$	1.09190e41			1.82245			0.911226	−	0.411906i	$-0.135137\pi$
$523$	1.09190e41			1.82245			0.911226	+	0.411906i	$0.135137\pi$
$524$			4.88767e40i			0.792744i
$525$	−1.77973e40	−	1.04231e40i	−0.280521	−	0.164289i
$526$	−8.02183e40			−1.22882
$527$		−	3.36722e38i		−	0.00501317i
$528$	4.69126e39	−	8.01026e39i	0.0678861	−	0.115914i
$529$	6.35973e40			0.894547
$530$			2.14594e40i			0.293413i
$531$	−7.17787e40	+	4.02616e40i	−0.954065	+	0.535147i
$532$	1.89419e40			0.244765
$533$		−	1.22230e41i		−	1.53557i
$534$	−3.16274e40	−	1.85228e40i	−0.386318	−	0.226250i
$535$	−1.65864e40			−0.196990
$536$			3.77237e40i			0.435655i
$537$	7.73362e40	−	1.32050e41i	0.868498	−	1.48294i
$538$	−9.41238e40			−1.02793
$539$		−	4.38867e40i		−	0.466123i
$540$	1.58254e40	+	2.94761e38i	0.163474	+	0.00304483i
$541$	1.07854e41			1.08362			0.541812	−	0.840500i	$-0.317738\pi$
$541$	1.07854e41			1.08362			0.541812	+	0.840500i	$0.317738\pi$
$542$		−	8.53722e40i		−	0.834309i
$543$	−1.08251e41	−	6.33980e40i	−1.02904	−	0.602668i
$544$	−4.65119e38			−0.00430111
$545$		−	4.81230e40i		−	0.432918i
$546$	1.31866e40	−	2.25159e40i	0.115410	−	0.197060i
$547$	−1.04978e41			−0.893896			−0.446948	−	0.894560i	$-0.647489\pi$
$547$	−1.04978e41			−0.893896			−0.446948	+	0.894560i	$0.647489\pi$
$548$			6.89567e40i			0.571305i
$549$	−3.49137e40	−	6.22444e40i	−0.281456	−	0.501782i
$550$	−4.32558e40			−0.339316
$551$			2.13017e41i			1.62607i
$552$	−1.33362e40	−	7.81046e39i	−0.0990710	−	0.0580217i
$553$	−1.56425e40			−0.113092
$554$			3.43809e40i			0.241920i
$555$	4.28844e40	−	7.32243e40i	0.293700	−	0.501488i
$556$	3.21187e40			0.214110
$557$			3.71621e40i			0.241142i	0.992705	+	0.120571i	$0.0384725\pi$
$557$			3.71621e40i			0.241142i	−0.992705	+	0.120571i	$0.961527\pi$
$558$	2.01166e40	−	1.12837e40i	0.127070	−	0.0712749i
$559$	−4.49200e39			−0.0276225
$560$		−	4.97086e39i		−	0.0297585i
$561$	1.93551e39	+	1.13355e39i	0.0112811	+	0.00660688i
$562$	1.44531e41			0.820194
$563$			1.56858e41i			0.866722i	0.901221	+	0.433361i	$0.142672\pi$
$563$			1.56858e41i			0.866722i	−0.901221	+	0.433361i	$0.857328\pi$
$564$	5.88870e40	−	1.00549e41i	0.316835	−	0.540990i
$565$	−9.03117e40			−0.473170
$566$		−	1.55718e41i		−	0.794499i
$567$	−3.81937e40	+	6.25156e40i	−0.189778	+	0.310629i
$568$	−4.27567e40			−0.206909
$569$			1.84297e41i			0.868629i	0.900761	+	0.434315i	$0.143009\pi$
$569$			1.84297e41i			0.868629i	−0.900761	+	0.434315i	$0.856991\pi$
$570$	5.84500e40	+	3.42317e40i	0.268325	+	0.157147i
$571$	−3.56640e41			−1.59473			−0.797367	−	0.603495i	$-0.793774\pi$
$571$	−3.56640e41			−1.59473			−0.797367	+	0.603495i	$0.793774\pi$
$572$		−	5.47240e40i		−	0.238362i
$573$	5.94618e40	−	1.01530e41i	0.252301	−	0.430799i
$574$	1.07775e41			0.445493
$575$			7.20164e40i			0.290010i
$576$	−1.55863e40	−	2.77873e40i	−0.0611512	−	0.109021i
$577$	3.45743e41			1.32165			0.660824	−	0.750540i	$-0.270207\pi$
$577$	3.45743e41			1.32165			0.660824	+	0.750540i	$0.270207\pi$
$578$			1.89734e41i			0.706688i
$579$	2.81280e41	+	1.64734e41i	1.02085	+	0.597867i
$580$	5.59012e40			0.197698
$581$			1.44306e41i			0.497329i
$582$	−2.23619e40	+	3.81826e40i	−0.0751041	+	0.128239i
$583$	−2.08307e41			−0.681829
$584$			1.09388e41i			0.348960i
$585$	8.13810e40	−	4.56477e40i	0.253038	−	0.141932i
$586$	3.93786e41			1.19343
$587$		−	2.74430e41i		−	0.810699i	−0.914162	−	0.405350i	$-0.867150\pi$
$587$		−	2.74430e41i		−	0.810699i	0.914162	−	0.405350i	$-0.132850\pi$
$588$	−1.29975e41	−	7.61207e40i	−0.374282	−	0.219201i
$589$	9.87069e40			0.277088
$590$			9.24265e40i			0.252939i
$591$	−1.83610e41	+	3.13511e41i	−0.489873	+	0.836450i
$592$	−1.70809e41			−0.444309
$593$		−	4.42778e41i		−	1.12296i	−0.827489	−	0.561482i	$-0.810231\pi$
$593$		−	4.42778e41i		−	1.12296i	0.827489	−	0.561482i	$-0.189769\pi$
$594$	−2.86126e39	+	1.53618e41i	−0.00707555	+	0.379878i
$595$	1.20111e39			0.00289619
$596$		−	3.46027e41i		−	0.813609i
$597$	3.00437e41	+	1.75953e41i	0.688871	+	0.403442i
$598$	−9.11096e40			−0.203726
$599$			1.77400e41i			0.386857i	0.981114	+	0.193429i	$0.0619608\pi$
$599$			1.77400e41i			0.386857i	−0.981114	+	0.193429i	$0.938039\pi$
$600$	−7.50265e40	+	1.28107e41i	−0.159568	+	0.272460i
$601$	−6.27569e41			−1.30180			−0.650900	−	0.759163i	$-0.725608\pi$
$601$	−6.27569e41			−1.30180			−0.650900	+	0.759163i	$0.725608\pi$
$602$		−	3.96078e39i		−	0.00801370i
$603$	−3.05451e41	−	5.44561e41i	−0.602812	−	1.07470i
$604$	1.37725e41			0.265130
$605$		−	1.23859e41i		−	0.232593i
$606$	−5.22234e41	−	3.05850e41i	−0.956700	−	0.560298i
$607$	−4.45955e41			−0.797004			−0.398502	−	0.917167i	$-0.630470\pi$
$607$	−4.45955e41			−0.797004			−0.398502	+	0.917167i	$0.630470\pi$
$608$		−	1.36345e41i		−	0.237731i
$609$	−1.30756e41	+	2.23264e41i	−0.222435	+	0.379804i
$610$	−8.01495e40			−0.133031
$611$		−	6.86922e41i		−	1.11247i
$612$	6.71423e39	−	3.76610e39i	0.0106102	−	0.00595142i
$613$	2.70329e41			0.416855			0.208428	−	0.978038i	$-0.433165\pi$
$613$	2.70329e41			0.416855			0.208428	+	0.978038i	$0.433165\pi$
$614$		−	2.71903e41i		−	0.409155i
$615$	3.32568e41	+	1.94771e41i	0.488375	+	0.286021i
$616$	4.82523e40			0.0691525
$617$		−	5.02351e41i		−	0.702635i	−0.936256	−	0.351318i	$-0.885734\pi$
$617$		−	5.02351e41i		−	0.702635i	0.936256	−	0.351318i	$-0.114266\pi$
$618$	−3.90370e41	+	6.66549e41i	−0.532904	+	0.909924i
$619$	1.11746e42			1.48892			0.744460	−	0.667667i	$-0.232707\pi$
$619$	1.11746e42			1.48892			0.744460	+	0.667667i	$0.232707\pi$
$620$		−	2.59033e40i		−	0.0336884i
$621$	2.55757e41	+	4.76369e39i	0.324679	+	0.00604741i
$622$	2.26329e41			0.280469
$623$		−	1.90518e41i		−	0.230470i
$624$	−1.62071e41	−	9.49179e40i	−0.191397	−	0.112093i
$625$	5.99034e41			0.690640
$626$			3.98425e41i			0.448469i
$627$	−3.32288e41	+	5.67377e41i	−0.365176	+	0.623531i
$628$	1.71941e40			0.0184495
$629$		−	4.12724e40i		−	0.0432415i
$630$	4.02494e40	+	7.17569e40i	0.0411766	+	0.0734100i
$631$	−2.79299e41			−0.279016			−0.139508	−	0.990221i	$-0.544552\pi$
$631$	−2.79299e41			−0.279016			−0.139508	+	0.990221i	$0.544552\pi$
$632$			1.12596e41i			0.109842i
$633$	1.33155e42	+	7.79831e41i	1.26853	+	0.742925i
$634$	7.43117e38			0.000691383
$635$		−	1.63784e41i		−	0.148821i
$636$	−3.61305e41	+	6.16923e41i	−0.320640	+	0.547487i
$637$	−8.87954e41			−0.769660
$638$			5.42636e41i			0.459408i
$639$	6.17214e41	−	3.46203e41i	0.510415	−	0.286298i
$640$	−3.57806e40			−0.0289033
$641$		−	2.54654e40i		−	0.0200946i	−0.999950	−	0.0100473i	$-0.996802\pi$
$641$		−	2.54654e40i		−	0.0200946i	0.999950	−	0.0100473i	$-0.00319821\pi$
$642$	−4.76831e41	−	2.79260e41i	−0.367569	−	0.215270i
$643$	−2.57675e41			−0.194047			−0.0970235	−	0.995282i	$-0.530932\pi$
$643$	−2.57675e41			−0.194047			−0.0970235	+	0.995282i	$0.530932\pi$
$644$		−	8.03350e40i		−	0.0591040i
$645$	7.15790e39	−	1.22220e40i	0.00514505	−	0.00878509i
$646$	3.29450e40			0.0231367
$647$			2.31844e42i			1.59086i	0.606047	+	0.795429i	$0.292754\pi$
$647$			2.31844e42i			1.59086i	−0.606047	+	0.795429i	$0.707246\pi$
$648$	4.49991e41	+	2.74921e41i	0.301703	+	0.184325i
$649$	−8.97188e41			−0.587778
$650$			8.75191e41i			0.560277i
$651$	1.03455e41	+	6.05894e40i	0.0647199	+	0.0379037i
$652$	−2.10014e41			−0.128391
$653$		−	9.36746e40i		−	0.0559660i	−0.999608	−	0.0279830i	$-0.991092\pi$
$653$		−	9.36746e40i		−	0.0559660i	0.999608	−	0.0279830i	$-0.00890842\pi$
$654$	8.10233e41	−	1.38346e42i	0.473090	−	0.807793i
$655$	−9.08522e41			−0.518461
$656$		−	7.75774e41i		−	0.432691i
$657$	−8.85720e41	−	1.57907e42i	−0.482854	−	0.860836i
$658$	6.05687e41			0.322745
$659$			1.08424e42i			0.564735i	0.959306	+	0.282367i	$0.0911197\pi$
$659$			1.08424e42i			0.564735i	−0.959306	+	0.282367i	$0.908880\pi$
$660$	1.48895e41	+	8.72013e40i	0.0758090	+	0.0443981i
$661$	8.45392e41			0.420762			0.210381	−	0.977620i	$-0.432530\pi$
$661$	8.45392e41			0.420762			0.210381	+	0.977620i	$0.432530\pi$
$662$		−	2.52357e42i		−	1.22785i
$663$	2.29349e40	−	3.91610e40i	0.0109092	−	0.0186274i
$664$	1.03873e42			0.483037
$665$			3.52092e41i			0.160078i
$666$	2.46571e42	−	1.38305e42i	1.09605	−	0.614787i
$667$	9.03431e41			0.392652
$668$			6.89072e41i			0.292831i
$669$	−2.31910e42	−	1.35820e42i	−0.963669	−	0.564380i
$670$	−7.01209e41			−0.284922
$671$		−	7.78015e41i		−	0.309136i
$672$	8.36929e40	−	1.42904e41i	0.0325199	−	0.0555272i
$673$	−2.65552e42			−1.00908			−0.504538	−	0.863390i	$-0.668337\pi$
$673$	−2.65552e42			−1.00908			−0.504538	+	0.863390i	$0.668337\pi$
$674$			1.35553e42i			0.503744i
$675$	4.57596e40	−	2.45678e42i	0.0166313	−	0.892914i
$676$	2.99374e41			0.106418
$677$			1.46765e42i			0.510260i	0.966907	+	0.255130i	$0.0821182\pi$
$677$			1.46765e42i			0.510260i	−0.966907	+	0.255130i	$0.917882\pi$
$678$	−2.59632e42	−	1.52055e42i	−0.882901	−	0.517078i
$679$	−2.30005e41			−0.0765051
$680$		−	8.64564e39i		−	0.00281296i
$681$	−6.65261e41	+	1.13592e42i	−0.211732	+	0.361528i
$682$	2.51445e41			0.0782847
$683$		−	3.36895e42i		−	1.02609i	−0.858363	−	0.513044i	$-0.828518\pi$
$683$		−	3.36895e42i		−	1.02609i	0.858363	−	0.513044i	$-0.171482\pi$
$684$	1.10399e42	+	1.96821e42i	0.328947	+	0.586449i
$685$	−1.28177e42			−0.373638
$686$		−	1.68548e42i		−	0.480687i
$687$	−2.37479e42	−	1.39081e42i	−0.662633	−	0.388076i
$688$	−2.85100e40			−0.00778341
$689$			4.21466e42i			1.12583i
$690$	1.45181e41	−	2.47894e41i	0.0379466	−	0.0647932i
$691$	5.95928e42			1.52413			0.762067	−	0.647498i	$-0.224185\pi$
$691$	5.95928e42			1.52413			0.762067	+	0.647498i	$0.224185\pi$
$692$			2.58691e41i			0.0647426i
$693$	−6.96547e41	+	3.90702e41i	−0.170589	+	0.0956858i
$694$	−5.68951e42			−1.36359
$695$			5.97023e41i			0.140029i
$696$	1.60707e42	+	9.41193e41i	0.368890	+	0.216043i
$697$	1.87450e41			0.0421108
$698$			6.06556e42i			1.33364i
$699$	−5.81572e41	+	9.93025e41i	−0.125154	+	0.213699i
$700$	−7.71691e41			−0.162545
$701$			5.46222e42i			1.12616i	0.826403	+	0.563079i	$0.190383\pi$
$701$			5.46222e42i			1.12616i	−0.826403	+	0.563079i	$0.809617\pi$
$702$	3.10813e42	+	5.78915e40i	0.627252	+	0.0116831i
$703$	1.20986e43			2.39004
$704$		−	3.47324e41i		−	0.0671653i
$705$	1.86900e42	+	1.09459e42i	0.353812	+	0.207213i
$706$	2.61937e42			0.485429
$707$		−	3.14584e42i		−	0.570750i
$708$	−1.55616e42	+	2.65711e42i	−0.276411	+	0.471967i
$709$	−1.68414e41			−0.0292876			−0.0146438	−	0.999893i	$-0.504661\pi$
$709$	−1.68414e41			−0.0292876			−0.0146438	+	0.999893i	$0.504661\pi$
$710$		−	7.94762e41i		−	0.135320i
$711$	−9.11698e41	−	1.62538e42i	−0.151987	−	0.270964i
$712$	−1.37136e42			−0.223847
$713$		−	4.18629e41i		−	0.0669092i
$714$	3.45299e40	+	2.02227e40i	0.00540408	+	0.00316494i
$715$	1.01721e42			0.155891
$716$		−	5.72568e42i		−	0.859275i
$717$	−2.45452e42	+	4.19105e42i	−0.360727	+	0.615935i
$718$	−5.12090e42			−0.737021
$719$		−	5.05843e42i		−	0.712989i	−0.934297	−	0.356494i	$-0.883972\pi$
$719$		−	5.05843e42i		−	0.712989i	0.934297	−	0.356494i	$-0.116028\pi$
$720$	5.16511e41	−	2.89718e41i	0.0713005	−	0.0399933i
$721$	−4.01517e42			−0.542845
$722$			4.31748e42i			0.571705i
$723$	6.90592e42	+	4.04450e42i	0.895668	+	0.524554i
$724$	−4.69375e42			−0.596268
$725$		−	8.67828e42i		−	1.07985i
$726$	2.08538e42	−	3.56075e42i	0.254176	−	0.434002i
$727$	2.50758e42			0.299391			0.149695	−	0.988732i	$-0.452171\pi$
$727$	2.50758e42			0.299391			0.149695	+	0.988732i	$0.452171\pi$
$728$		−	9.76285e41i		−	0.114184i
$729$	−8.72191e42	−	3.25019e41i	−0.999306	−	0.0372388i
$730$	−2.03330e42			−0.228223
$731$		−	6.88884e39i		−	0.000757505i
$732$	−2.30417e42	−	1.34945e42i	−0.248227	−	0.145376i
$733$	−1.57553e42			−0.166290			−0.0831452	−	0.996537i	$-0.526497\pi$
$733$	−1.57553e42			−0.166290			−0.0831452	+	0.996537i	$0.526497\pi$
$734$			1.38557e42i			0.143281i
$735$	1.41493e42	−	2.41597e42i	0.143359	−	0.244784i
$736$	−5.78257e41			−0.0574055
$737$		−	6.80666e42i		−	0.662098i
$738$	6.28150e42	+	1.11987e43i	0.598712	+	1.06739i
$739$	−1.30331e43			−1.21725			−0.608626	−	0.793457i	$-0.708279\pi$
$739$	−1.30331e43			−1.21725			−0.608626	+	0.793457i	$0.708279\pi$
$740$		−	3.17500e42i		−	0.290581i
$741$	1.14797e43	+	6.72315e42i	1.02957	+	0.602976i
$742$	−3.71623e42			−0.326621
$743$		−	1.39272e43i		−	1.19959i	−0.800156	−	0.599793i	$-0.795250\pi$
$743$		−	1.39272e43i		−	1.19959i	0.800156	−	0.599793i	$-0.204750\pi$
$744$	4.36127e41	−	7.44679e41i	0.0368145	−	0.0628601i
$745$	6.43195e42			0.532107
$746$		−	2.30135e42i		−	0.186595i
$747$	−1.49946e43	+	8.41064e42i	−1.19158	+	0.668375i
$748$	8.39236e40			0.00653673
$749$		−	2.87235e42i		−	0.219285i
$750$	−5.04761e42	−	2.95617e42i	−0.377718	−	0.221213i
$751$	4.41396e42			0.323765			0.161882	−	0.986810i	$-0.448243\pi$
$751$	4.41396e42			0.323765			0.161882	+	0.986810i	$0.448243\pi$
$752$		−	4.35978e42i		−	0.313471i
$753$	3.97621e42	−	6.78931e42i	0.280249	−	0.478521i
$754$	1.09791e43			0.758571
$755$			2.56003e42i			0.173397i
$756$	−5.10453e40	+	2.74056e42i	−0.00338945	+	0.181975i
$757$	−2.71157e43			−1.76516			−0.882578	−	0.470166i	$-0.844194\pi$
$757$	−2.71157e43			−1.76516			−0.882578	+	0.470166i	$0.844194\pi$
$758$		−	1.79097e42i		−	0.114301i
$759$	2.40632e42	+	1.40928e42i	0.150566	+	0.0881800i
$760$	2.53439e42			0.155478
$761$			6.43479e42i			0.387048i	0.981096	+	0.193524i	$0.0619917\pi$
$761$			6.43479e42i			0.387048i	−0.981096	+	0.193524i	$0.938008\pi$
$762$	2.75758e42	−	4.70852e42i	0.162631	−	0.277689i
$763$	8.33371e42			0.481915
$764$		−	4.40233e42i		−	0.249622i
$765$	7.00043e40	+	1.24804e41i	0.00389227	+	0.00693918i
$766$	2.09190e43			1.14054
$767$			1.81527e43i			0.970535i
$768$	−1.02863e42	−	6.02428e41i	−0.0539315	−	0.0315854i
$769$	1.68057e43			0.864094			0.432047	−	0.901851i	$-0.357792\pi$
$769$	1.68057e43			0.864094			0.432047	+	0.901851i	$0.357792\pi$
$770$			8.96916e41i			0.0452263i
$771$	−3.42736e42	+	5.85215e42i	−0.169490	+	0.289401i
$772$	1.21963e43			0.591518
$773$			1.45315e43i			0.691223i	0.938378	+	0.345611i	$0.112328\pi$
$773$			1.45315e43i			0.691223i	−0.938378	+	0.345611i	$0.887672\pi$
$774$	4.11556e41	−	2.30847e41i	0.0192006	−	0.0107699i
$775$	−4.02131e42			−0.184010
$776$			1.65559e42i			0.0743066i
$777$	1.26806e43	+	7.42651e42i	0.558246	+	0.326941i
$778$	8.12121e42			0.350693
$779$			5.49491e43i			2.32755i
$780$	1.76434e42	−	3.01257e42i	0.0733098	−	0.125175i
$781$	7.71478e42			0.314455
$782$		−	1.39724e41i		−	0.00558688i
$783$	−3.08198e43	−	5.74045e41i	−1.20894	−	0.0225174i
$784$	−5.63569e42			−0.216873
$785$			3.19604e41i			0.0120661i
$786$	−2.61186e43	−	1.52965e43i	−0.967411	−	0.566571i
$787$	−2.19228e43			−0.796664			−0.398332	−	0.917241i	$-0.630411\pi$
$787$	−2.19228e43			−0.796664			−0.398332	+	0.917241i	$0.630411\pi$
$788$			1.35938e43i			0.484671i
$789$	2.51052e43	−	4.28667e43i	0.878230	−	1.49956i
$790$	−2.09294e42			−0.0718373
$791$		−	1.56397e43i		−	0.526723i
$792$	2.81230e42	+	5.01380e42i	0.0929361	+	0.165687i
$793$	−1.57415e43			−0.510444
$794$			1.27968e43i			0.407188i
$795$	−1.14674e43	−	6.71595e42i	−0.358061	−	0.209701i
$796$	1.30269e43			0.399158
$797$		−	4.56968e43i		−	1.37408i	−0.726621	−	0.687038i	$-0.758910\pi$
$797$		−	4.56968e43i		−	1.37408i	0.726621	−	0.687038i	$-0.241090\pi$
$798$	−5.92808e42	+	1.01221e43i	−0.174932	+	0.298694i
$799$	1.05345e42			0.0305079
$800$			5.55469e42i			0.157874i
$801$	1.97963e43	−	1.11040e43i	0.552199	−	0.309736i
$802$	−2.90354e43			−0.794901
$803$		−	1.97374e43i		−	0.530342i
$804$	−2.01586e43	−	1.18060e43i	−0.531643	−	0.311361i
$805$	1.49327e42			0.0386545
$806$		−	5.08745e42i		−	0.129263i
$807$	2.94571e43	−	5.02975e43i	0.734660	−	1.25442i
$808$	−2.26440e43			−0.554348
$809$			9.09764e42i			0.218626i	0.994007	+	0.109313i	$0.0348650\pi$
$809$			9.09764e42i			0.218626i	−0.994007	+	0.109313i	$0.965135\pi$
$810$	−5.11024e42	+	8.36445e42i	−0.120550	+	0.197316i
$811$	−2.04935e43			−0.474574			−0.237287	−	0.971440i	$-0.576258\pi$
$811$	−2.04935e43			−0.474574			−0.237287	+	0.971440i	$0.576258\pi$
$812$			9.68071e42i			0.220073i
$813$	4.56208e43	+	2.67182e43i	1.01813	+	0.596278i
$814$	3.08199e43			0.675250
$815$		−	3.90374e42i		−	0.0839686i
$816$	1.45564e41	−	2.48548e41i	0.00307399	−	0.00524878i
$817$	2.01940e42			0.0418688
$818$		−	2.80847e43i		−	0.571702i
$819$	7.90504e42	+	1.40932e43i	0.157996	+	0.281676i
$820$	1.44201e43			0.282983
$821$			1.96574e43i			0.378773i	0.981903	+	0.189386i	$0.0606499\pi$
$821$			1.96574e43i			0.378773i	−0.981903	+	0.189386i	$0.939350\pi$
$822$	−3.68488e43	−	2.15808e43i	−0.697182	−	0.408310i
$823$	7.66818e42			0.142461			0.0712303	−	0.997460i	$-0.477307\pi$
$823$	7.66818e42			0.142461			0.0712303	+	0.997460i	$0.477307\pi$
$824$			2.89015e43i			0.527245i
$825$	1.35374e43	−	2.31149e43i	0.242508	−	0.414078i
$826$	−1.60060e43			−0.281567
$827$		−	1.54095e43i		−	0.266199i	−0.991103	−	0.133100i	$-0.957507\pi$
$827$		−	1.54095e43i		−	0.266199i	0.991103	−	0.133100i	$-0.0424930\pi$
$828$	8.34744e42	−	4.68219e42i	0.141611	−	0.0794317i
$829$	−1.48513e43			−0.247427			−0.123713	−	0.992318i	$-0.539480\pi$
$829$	−1.48513e43			−0.247427			−0.123713	+	0.992318i	$0.539480\pi$
$830$			1.93079e43i			0.315910i
$831$	−1.83723e43	−	1.07599e43i	−0.295222	−	0.172899i
$832$	−7.02737e42			−0.110903
$833$		−	1.36175e42i		−	0.0211068i
$834$	−1.00519e43	+	1.71635e43i	−0.153023	+	0.261285i
$835$	−1.28085e43			−0.191514
$836$			2.46014e43i			0.361298i
$837$	−2.65999e41	+	1.42812e43i	−0.00383705	+	0.206007i
$838$	−1.50370e43			−0.213060
$839$			1.18735e44i			1.65252i	0.563286	+	0.826262i	$0.309537\pi$
$839$			1.18735e44i			1.65252i	−0.563286	+	0.826262i	$0.690463\pi$
$840$	2.65631e42	+	1.55569e42i	0.0363152	+	0.0212683i
$841$	−3.44043e43			−0.462033
$842$		−	7.88303e43i		−	1.03995i
$843$	−4.52326e43	+	7.72339e43i	−0.586189	+	1.00091i
$844$	5.77358e43			0.735036
$845$			5.56478e42i			0.0695981i
$846$	3.53014e43	+	6.29356e43i	0.433747	+	0.773288i
$847$	2.14493e43			0.258918
$848$			2.67497e43i			0.317235i
$849$	8.32121e43	+	4.87338e43i	0.969553	+	0.567826i
$850$	−1.34218e42			−0.0153647
$851$		−	5.13118e43i		−	0.577130i
$852$	1.33812e43	−	2.28481e43i	0.147877	−	0.252497i
$853$	5.75065e43			0.624427			0.312214	−	0.950012i	$-0.398930\pi$
$853$	5.75065e43			0.624427			0.312214	+	0.950012i	$0.398930\pi$
$854$		−	1.38799e43i		−	0.148088i
$855$	−3.65852e43	+	2.05211e43i	−0.383542	+	0.215134i
$856$	−2.06754e43			−0.212984
$857$		−	1.06519e44i		−	1.07824i	−0.842229	−	0.539120i	$-0.818757\pi$
$857$		−	1.06519e44i		−	1.07824i	0.842229	−	0.539120i	$-0.181243\pi$
$858$	2.92432e43	+	1.71265e43i	0.290881	+	0.170357i
$859$	1.59628e44			1.56032			0.780158	−	0.625582i	$-0.215138\pi$
$859$	1.59628e44			1.56032			0.780158	+	0.625582i	$0.215138\pi$
$860$		−	5.29944e41i		−	0.00509041i
$861$	−3.37295e43	+	5.75925e43i	−0.318392	+	0.543649i
$862$	4.06856e43			0.377426
$863$		−	4.70431e43i		−	0.428878i	−0.976737	−	0.214439i	$-0.931208\pi$
$863$		−	4.70431e43i		−	0.428878i	0.976737	−	0.214439i	$-0.0687924\pi$
$864$	1.97268e43	+	3.67428e41i	0.176746	+	0.00329204i
$865$	−4.80856e42			−0.0423422
$866$		−	4.00780e43i		−	0.346847i
$867$	−1.01389e44	−	5.93794e43i	−0.862394	−	0.505067i
$868$	4.48581e42			0.0375012
$869$		−	2.03162e43i		−	0.166935i
$870$	−1.74949e43	+	2.98723e43i	−0.141294	+	0.241257i
$871$	−1.37719e44			−1.09325
$872$		−	5.99866e43i		−	0.468066i
$873$	−1.34054e43	−	2.38993e43i	−0.102818	−	0.183304i
$874$	4.09587e43			0.308798
$875$		−	3.04059e43i		−	0.225340i
$876$	−5.84542e43	−	3.42341e43i	−0.425847	−	0.249401i
$877$	−1.55157e44			−1.11116			−0.555581	−	0.831462i	$-0.687504\pi$
$877$	−1.55157e44			−1.11116			−0.555581	+	0.831462i	$0.687504\pi$
$878$		−	5.95618e43i		−	0.419324i
$879$	−1.23240e44	+	2.10430e44i	−0.852939	+	1.45638i
$880$	6.45606e42			0.0439266
$881$		−	9.93897e43i		−	0.664818i	−0.943135	−	0.332409i	$-0.892139\pi$
$881$		−	9.93897e43i		−	0.664818i	0.943135	−	0.332409i	$-0.107861\pi$
$882$	8.13541e43	−	4.56326e43i	0.534996	−	0.300086i
$883$	−1.59634e43			−0.103208			−0.0516041	−	0.998668i	$-0.516433\pi$
$883$	−1.59634e43			−0.103208			−0.0516041	+	0.998668i	$0.516433\pi$
$884$		−	1.69802e42i		−	0.0107934i
$885$	−4.93905e43	−	2.89259e43i	−0.308670	−	0.180775i
$886$	−7.10705e43			−0.436700
$887$		−	1.92695e44i		−	1.16417i	−0.813129	−	0.582084i	$-0.802238\pi$
$887$		−	1.92695e44i		−	1.16417i	0.813129	−	0.582084i	$-0.197762\pi$
$888$	5.34565e43	−	9.12761e43i	0.317546	−	0.542204i
$889$	2.83633e43			0.165665
$890$		−	2.54909e43i		−	0.146398i
$891$	−8.11941e43	−	4.96053e43i	−0.458520	−	0.280132i
$892$	−1.00556e44			−0.558387
$893$			3.08809e44i			1.68623i
$894$	1.84908e44	+	1.08293e44i	0.992873	+	0.581483i
$895$	1.06429e44			0.561973
$896$		−	6.19631e42i		−	0.0321746i
$897$	2.85138e43	−	4.86868e43i	0.145602	−	0.248613i
$898$	−3.20817e43			−0.161106
$899$			5.04465e43i			0.249136i
$900$	−4.49767e43	−	8.01847e43i	−0.218449	−	0.389452i
$901$	−6.46351e42			−0.0308743
$902$			1.39977e44i			0.657594i
$903$	2.11654e42	+	1.23957e42i	0.00977938	+	0.00572736i
$904$	−1.12576e44			−0.511587
$905$		−	8.72475e43i		−	0.389964i
$906$	−4.31025e43	+	7.35969e43i	−0.189487	+	0.323546i
$907$	3.94802e44			1.70714			0.853572	−	0.520976i	$-0.174432\pi$
$907$	3.94802e44			1.70714			0.853572	+	0.520976i	$0.174432\pi$
$908$			4.92535e43i			0.209483i
$909$	3.26878e44	−	1.83350e44i	1.36750	−	0.767048i
$910$	1.81472e43			0.0746773
$911$			4.31263e44i			1.74569i	0.488001	+	0.872843i	$0.337726\pi$
$911$			4.31263e44i			1.74569i	−0.488001	+	0.872843i	$0.662274\pi$
$912$	7.28595e43	+	4.26707e43i	0.290111	+	0.169905i
$913$	−1.87423e44			−0.734108
$914$			8.57161e43i			0.330270i
$915$	2.50837e43	−	4.28300e43i	0.0950769	−	0.162342i
$916$	−1.02970e44			−0.383955
$917$		−	1.57333e44i		−	0.577140i
$918$	−8.87813e40	+	4.76656e42i	−0.000320392	+	0.0172015i
$919$	5.26461e44			1.86911			0.934553	−	0.355824i	$-0.115800\pi$
$919$	5.26461e44			1.86911			0.934553	+	0.355824i	$0.115800\pi$
$920$		−	1.07487e43i		−	0.0375437i
$921$	1.45298e44	+	8.50950e43i	0.499305	+	0.292422i
$922$	−2.83293e44			−0.957793
$923$		−	1.56092e44i		−	0.519226i
$924$	−1.51011e43	+	2.57849e43i	−0.0494230	+	0.0843890i
$925$	−4.92896e44			−1.58719
$926$			3.31655e44i			1.05080i
$927$	−2.34017e44	−	4.17208e44i	−0.729545	−	1.30064i
$928$	6.96824e43			0.213749
$929$			5.03805e44i			1.52064i	0.649547	+	0.760321i	$0.274958\pi$
$929$			5.03805e44i			1.52064i	−0.649547	+	0.760321i	$0.725042\pi$
$930$	1.38421e43	+	8.10673e42i	0.0411110	+	0.0240770i
$931$	3.99183e44			1.16661
$932$			4.30574e43i			0.123825i
$933$	−7.08321e43	+	1.20945e44i	−0.200450	+	0.342265i
$934$	−2.63680e44			−0.734301
$935$			1.55997e42i			0.00427507i
$936$	1.01444e44	−	5.69010e43i	0.273582	−	0.153456i
$937$	3.04855e43			0.0809095			0.0404547	−	0.999181i	$-0.487119\pi$
$937$	3.04855e43			0.0809095			0.0404547	+	0.999181i	$0.487119\pi$
$938$		−	1.21432e44i		−	0.317169i
$939$	−2.12909e44	−	1.24692e44i	−0.547280	−	0.320519i
$940$	8.10396e43			0.205012
$941$			2.78830e43i			0.0694216i	0.999397	+	0.0347108i	$0.0110510\pi$
$941$			2.78830e43i			0.0694216i	−0.999397	+	0.0347108i	$0.988949\pi$
$942$	−5.38108e42	+	9.18811e42i	−0.0131858	+	0.0225145i
$943$	2.33046e44			0.562039
$944$			1.15212e44i			0.273476i
$945$	−5.09416e43	−	9.48831e41i	−0.119013	−	0.00221672i
$946$	5.14419e42			0.0118290
$947$		−	4.61822e44i		−	1.04526i	−0.852559	−	0.522630i	$-0.824951\pi$
$947$		−	4.61822e44i		−	1.04526i	0.852559	−	0.522630i	$-0.175049\pi$
$948$	−6.01686e43	−	3.52382e43i	−0.134043	−	0.0785034i
$949$	−3.99344e44			−0.875697
$950$		−	3.93446e44i		−	0.849240i
$951$	−2.32567e41	+	3.97104e41i	−0.000494129	+	0.000843716i
$952$	1.49721e42			0.00313133
$953$			4.89172e44i			1.00709i	0.863969	+	0.503545i	$0.167971\pi$
$953$			4.89172e44i			1.00709i	−0.863969	+	0.503545i	$0.832029\pi$
$954$	−2.16594e44	−	3.86146e44i	−0.438956	−	0.782574i
$955$	8.18306e43			0.163255
$956$			1.81723e44i			0.356897i
$957$	−2.89971e44	−	1.69824e44i	−0.560630	−	0.328337i
$958$	5.87851e44			1.11888
$959$		−	2.21971e44i		−	0.415926i
$960$	1.11979e43	−	1.91203e43i	0.0206571	−	0.0352717i
$961$	−5.27243e44			−0.957546
$962$		−	6.23575e44i		−	1.11497i
$963$	2.98459e44	−	1.67410e44i	0.525401	−	0.294704i
$964$	2.99440e44			0.518984
$965$			2.26705e44i			0.386857i
$966$	4.29291e43	+	2.51417e43i	0.0721265	+	0.0422414i
$967$	−2.46172e44			−0.407232			−0.203616	−	0.979051i	$-0.565269\pi$
$967$	−2.46172e44			−0.407232			−0.203616	+	0.979051i	$0.565269\pi$
$968$		−	1.54394e44i		−	0.251477i
$969$	−1.03105e43	+	1.76050e43i	−0.0165357	+	0.0282344i
$970$	−3.07742e43			−0.0485971
$971$		−	6.32191e44i		−	0.983014i	−0.870874	−	0.491507i	$-0.836446\pi$
$971$		−	6.32191e44i		−	0.983014i	0.870874	−	0.491507i	$-0.163554\pi$
$972$	−2.87741e44	+	1.54425e44i	−0.440563	+	0.236441i
$973$	−1.03390e44			−0.155878
$974$			6.83287e44i			1.01442i
$975$	−4.67681e44	−	2.73901e44i	−0.683723	−	0.400428i
$976$	−9.99086e43			−0.143832
$977$		−	8.47613e44i		−	1.20165i	−0.799380	−	0.600826i	$-0.794838\pi$
$977$		−	8.47613e44i		−	1.20165i	0.799380	−	0.600826i	$-0.205162\pi$
$978$	6.57262e43	−	1.12226e44i	0.0917604	−	0.156679i
$979$	2.47441e44			0.340198
$980$		−	1.04756e44i		−	0.141837i
$981$	4.85716e44	+	8.65938e44i	0.647660	+	1.15465i
$982$	3.73253e44			0.490152
$983$			1.33104e45i			1.72143i	0.509087	+	0.860715i	$0.329983\pi$
$983$			1.33104e45i			1.72143i	−0.509087	+	0.860715i	$0.670017\pi$
$984$	4.14555e44	+	2.42787e44i	0.528027	+	0.309243i
$985$	−2.52682e44			−0.316979
$986$			1.68373e43i			0.0208027i
$987$	−1.89556e44	+	3.23664e44i	−0.230665	+	0.393856i
$988$	4.97757e44			0.596573
$989$		−	8.56453e42i		−	0.0101102i
$990$	−9.31966e43	+	5.22752e43i	−0.108361	+	0.0607809i
$991$	7.68887e44			0.880558			0.440279	−	0.897861i	$-0.354880\pi$
$991$	7.68887e44			0.880558			0.440279	+	0.897861i	$0.354880\pi$
$992$		−	3.22892e43i		−	0.0364235i
$993$	1.34853e45	+	7.89778e44i	1.49838	+	0.877539i
$994$	1.37633e44			0.150635
$995$			2.42144e44i			0.261053i
$996$	−3.25081e44	+	5.55071e44i	−0.345225	+	0.589465i
$997$	−1.77067e45			−1.85230			−0.926150	−	0.377156i	$-0.876902\pi$
$997$	−1.77067e45			−1.85230			−0.926150	+	0.377156i	$0.876902\pi$
$998$		−	9.46089e43i		−	0.0974931i
$999$	−3.26038e43	+	1.75046e45i	−0.0330968	+	1.77693i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6.31.b.a.5.6	yes	10
3.2	odd	2	inner	6.31.b.a.5.1	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6.31.b.a.5.1	✓	10	3.2	odd	2	inner
6.31.b.a.5.6	yes	10	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 6 = 2 \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 31 \)
Character orbit:	\([\chi]\)	\(=\)	6.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+23170.5i q^{2} +(-1.23817e7 - 7.25146e6i) q^{3} -5.36871e8 q^{4} -9.97937e9i q^{5} +(1.68020e11 - 2.86891e11i) q^{6} +1.72818e12 q^{7} -1.24396e13i q^{8} +(1.00724e14 + 1.79571e14i) q^{9} +O(q^{10})\)	\(q+23170.5i q^{2} +(-1.23817e7 - 7.25146e6i) q^{3} -5.36871e8 q^{4} -9.97937e9i q^{5} +(1.68020e11 - 2.86891e11i) q^{6} +1.72818e12 q^{7} -1.24396e13i q^{8} +(1.00724e14 + 1.79571e14i) q^{9} +2.31227e14 q^{10} +2.24453e15i q^{11} +(6.64740e15 + 3.89310e15i) q^{12} +4.54133e16 q^{13} +4.00427e16i q^{14} +(-7.23650e16 + 1.23562e17i) q^{15} +2.88230e17 q^{16} +6.96449e16i q^{17} +(-4.16075e18 + 2.33382e18i) q^{18} -2.04157e19 q^{19} +5.35763e18i q^{20} +(-2.13979e19 - 1.25318e19i) q^{21} -5.20068e19 q^{22} +8.65857e19i q^{23} +(-9.02049e19 + 1.54023e20i) q^{24} +8.31735e20 q^{25} +1.05225e21i q^{26} +(5.50170e19 - 2.95380e21i) q^{27} -9.27809e20 q^{28} -1.04339e22i q^{29} +(-2.86299e21 - 1.67673e21i) q^{30} -4.83485e21 q^{31} +6.67843e21i q^{32} +(1.62761e22 - 2.77912e22i) q^{33} -1.61371e21 q^{34} -1.72461e22i q^{35} +(-5.40757e22 - 9.64066e22i) q^{36} -5.92612e23 q^{37} -4.73042e23i q^{38} +(-5.62296e23 - 3.29313e23i) q^{39} -1.24139e23 q^{40} -2.69151e24i q^{41} +(2.90368e23 - 4.95799e23i) q^{42} -9.89138e22 q^{43} -1.20502e24i q^{44} +(1.79201e24 - 1.00516e24i) q^{45} -2.00623e24 q^{46} -1.51260e25i q^{47} +(-3.56879e24 - 2.09009e24i) q^{48} -1.95527e25 q^{49} +1.92717e25i q^{50} +(5.05027e23 - 8.62325e23i) q^{51} -2.43811e25 q^{52} +9.28067e25i q^{53} +(6.84410e25 + 1.27477e24i) q^{54} +2.23990e25 q^{55} -2.14978e25i q^{56} +(2.52782e26 + 1.48044e26i) q^{57} +2.41759e26 q^{58} +3.99723e26i q^{59} +(3.88506e25 - 6.63368e25i) q^{60} -3.46628e26 q^{61} -1.12026e26i q^{62} +(1.74069e26 + 3.10331e26i) q^{63} -1.54743e26 q^{64} -4.53196e26i q^{65} +(6.43934e26 + 3.77125e26i) q^{66} -3.03256e27 q^{67} -3.73903e25i q^{68} +(6.27873e26 - 1.07208e27i) q^{69} +3.99601e26 q^{70} -3.43715e27i q^{71} +(2.23379e27 - 1.25296e27i) q^{72} -8.79355e27 q^{73} -1.37311e28i q^{74} +(-1.02983e28 - 6.03129e27i) q^{75} +1.09606e28 q^{76} +3.87895e27i q^{77} +(7.63033e27 - 1.30287e28i) q^{78} -9.05146e27 q^{79} -2.87636e27i q^{80} +(-2.21006e28 + 3.61742e28i) q^{81} +6.23635e28 q^{82} +8.35020e28i q^{83} +(1.14879e28 + 6.72797e27i) q^{84} +6.95012e26 q^{85} -2.29188e27i q^{86} +(-7.56613e28 + 1.29190e29i) q^{87} +2.79209e28 q^{88} -1.10242e29i q^{89} +(2.32900e28 + 4.15217e28i) q^{90} +7.84823e28 q^{91} -4.64854e28i q^{92} +(5.98638e28 + 3.50597e28i) q^{93} +3.50477e29 q^{94} +2.03736e29i q^{95} +(4.84284e28 - 8.26906e28i) q^{96} -1.33091e29 q^{97} -4.53046e29i q^{98} +(-4.03053e29 + 2.26077e29i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 14139762 q^{3} - 5368709120 q^{4} - 145788764160 q^{6} - 1459334601196 q^{7} + 41713120268730 q^{9}+O(q^{10}) \) 10 * q + 14139762 * q^3 - 5368709120 * q^4 - 145788764160 * q^6 - 1459334601196 * q^7 + 41713120268730 * q^9	\( 10 q + 14139762 q^{3} - 5368709120 q^{4} - 145788764160 q^{6} - 1459334601196 q^{7} + 41713120268730 q^{9} - 11\!\cdots\!60 q^{10}+ \cdots + 27\!\cdots\!20 q^{99}+O(q^{100}) \) 10 * q + 14139762 * q^3 - 5368709120 * q^4 - 145788764160 * q^6 - 1459334601196 * q^7 + 41713120268730 * q^9 - 1111538175836160 * q^10 - 7591226920402944 * q^12 + 11241857908456580 * q^13 - 1208370750576105600 * q^15 + 2882303761517117440 * q^16 + 4378961453216956416 * q^18 - 406434941012438620 * q^19 + 189341373476724706020 * q^21 - 175966920878069907456 * q^22 + 78269746773932113920 * q^24 - 538750688835772733030 * q^25 - 509686212259700532126 * q^27 + 783474298257252810752 * q^28 + 3618734882327478927360 * q^30 - 3850790055930904811020 * q^31 + 13877514934601873876352 * q^33 - 21974427701517892976640 * q^34 - 22394560921038760181760 * q^36 + 691786417224189171658916 * q^37 + 264189297409049008449300 * q^39 + 596752514183975581777920 * q^40 + 2551733261187619598893056 * q^42 - 10594373354873893550389372 * q^43 + 21961398854703004532478720 * q^45 - 14905926072892021549301760 * q^46 + 4075508919955679952764928 * q^48 - 14303693611422252234715650 * q^49 + 100757981401326611204590080 * q^51 - 6035426507887496617000960 * q^52 + 186364360915292902942310400 * q^54 - 905529883473273884900970240 * q^55 + 1357830109447011748343825076 * q^57 - 1026862318649343581985177600 * q^58 + 648739106895918338880307200 * q^60 - 2949272535924647913201299260 * q^61 + 5088794127795653673352888692 * q^63 - 1547425049106725343623905280 * q^64 + 3787402697011447732654571520 * q^66 - 10556251754234326335356822044 * q^67 + 15764240424701154050198334720 * q^69 - 8691440888931957213379952640 * q^70 - 2350937029001432724922171392 * q^72 + 12106003505184711607130189300 * q^73 - 7500206691267464218185712830 * q^75 + 218203097450014125263421440 * q^76 - 23839067108381696719249735680 * q^78 + 68719005124237783442983312820 * q^79 - 111620808361643664456575921430 * q^81 + 18283730424263848186657898496 * q^82 - 101651875857781803693889290240 * q^84 + 403836274868708986530058828800 * q^85 - 512433611792960206983797969280 * q^87 + 94471521293641232015658319872 * q^88 - 426164288449255115819581440000 * q^90 + 1222541373056582384854822798600 * q^91 - 983623123086267594817934884284 * q^93 - 80746046881825464175401369600 * q^94 - 42020750332529991826318295040 * q^96 - 1391585232259866867438139103212 * q^97 + 2707446209006624257844338302720 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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