LMFDB - Embedded newform 6.31.b.a.5.8

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			5.8
Root			$-8.86301e8i$ of defining polynomial
Character	$\chi$	$=$	6.5
Dual form			6.31.b.a.5.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+23170.5i q^{2} +(6.21475e6 + 1.29332e7i) q^{3} -5.36871e8 q^{4} -2.12712e10i q^{5} +(-2.99669e11 + 1.43999e11i) q^{6} -1.34382e12 q^{7} -1.24396e13i q^{8} +(-1.28645e14 + 1.60753e14i) q^{9} +O(q^{10})$	\(q+23170.5i q^{2} +(6.21475e6 + 1.29332e7i) q^{3} -5.36871e8 q^{4} -2.12712e10i q^{5} +(-2.99669e11 + 1.43999e11i) q^{6} -1.34382e12 q^{7} -1.24396e13i q^{8} +(-1.28645e14 + 1.60753e14i) q^{9} +4.92865e14 q^{10} -4.92637e15i q^{11} +(-3.33652e15 - 6.94347e15i) q^{12} +6.88812e16 q^{13} -3.11371e16i q^{14} +(2.75105e17 - 1.32195e17i) q^{15} +2.88230e17 q^{16} -1.65076e18i q^{17} +(-3.72473e18 - 2.98076e18i) q^{18} +1.39359e17 q^{19} +1.14199e19i q^{20} +(-8.35153e18 - 1.73800e19i) q^{21} +1.14146e20 q^{22} -3.70752e20i q^{23} +(1.60883e20 - 7.73087e19i) q^{24} +4.78857e20 q^{25} +1.59601e21i q^{26} +(-2.87855e21 - 6.64752e20i) q^{27} +7.21460e20 q^{28} +9.68870e21i q^{29} +(3.06303e21 + 6.37432e21i) q^{30} -8.03421e20 q^{31} +6.67843e21i q^{32} +(6.37138e22 - 3.06161e22i) q^{33} +3.82488e22 q^{34} +2.85848e22i q^{35} +(6.90657e22 - 8.63038e22i) q^{36} +5.84005e23 q^{37} +3.22901e21i q^{38} +(4.28080e23 + 8.90856e23i) q^{39} -2.64605e23 q^{40} +1.21144e24i q^{41} +(4.02702e23 - 1.93509e23i) q^{42} +4.57437e24 q^{43} +2.64482e24i q^{44} +(3.41942e24 + 2.73644e24i) q^{45} +8.59050e24 q^{46} -4.58851e24i q^{47} +(1.79128e24 + 3.72775e24i) q^{48} -2.07335e25 q^{49} +1.10954e25i q^{50} +(2.13496e25 - 1.02590e25i) q^{51} -3.69803e25 q^{52} -5.51049e25i q^{53} +(1.54026e25 - 6.66974e25i) q^{54} -1.04790e26 q^{55} +1.67166e25i q^{56} +(8.66080e23 + 1.80236e24i) q^{57} -2.24492e26 q^{58} +3.03191e25i q^{59} +(-1.47696e26 + 7.09718e25i) q^{60} -9.38409e26 q^{61} -1.86157e25i q^{62} +(1.72876e26 - 2.16024e26i) q^{63} -1.54743e26 q^{64} -1.46519e27i q^{65} +(7.09390e26 + 1.47628e27i) q^{66} +2.46316e27 q^{67} +8.86243e26i q^{68} +(4.79501e27 - 2.30413e27i) q^{69} -6.62324e26 q^{70} -4.09982e26i q^{71} +(1.99970e27 + 1.60029e27i) q^{72} +7.27398e24 q^{73} +1.35317e28i q^{74} +(2.97598e27 + 6.19316e27i) q^{75} -7.48177e25 q^{76} +6.62018e27i q^{77} +(-2.06416e28 + 9.91881e27i) q^{78} +4.60559e28 q^{79} -6.13101e27i q^{80} +(-9.29211e27 - 4.13602e28i) q^{81} -2.80696e28 q^{82} -1.19904e29i q^{83} +(4.48369e27 + 9.33080e27i) q^{84} -3.51136e28 q^{85} +1.05990e29i q^{86} +(-1.25306e29 + 6.02129e28i) q^{87} -6.12818e28 q^{88} -2.72734e29i q^{89} +(-6.34045e28 + 7.92296e28i) q^{90} -9.25643e28 q^{91} +1.99046e29i q^{92} +(-4.99306e27 - 1.03908e28i) q^{93} +1.06318e29 q^{94} -2.96434e27i q^{95} +(-8.63736e28 + 4.15048e28i) q^{96} +5.73161e29 q^{97} -4.80404e29i q^{98} +(7.91930e29 + 6.33752e29i) 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
$3$	6.21475e6	+	1.29332e7i	0.433116	+	0.901338i
$3$	6.21475e6	+	1.29332e7i	0.433116	+	0.901338i
$4$	−5.36871e8			−0.500000
$5$		−	2.12712e10i		−	0.697016i	−0.937306	−	0.348508i	$-0.886688\pi$
$5$		−	2.12712e10i		−	0.697016i	0.937306	−	0.348508i	$-0.113312\pi$
$6$	−2.99669e11	+	1.43999e11i	−0.637342	+	0.306260i
$7$	−1.34382e12			−0.283056			−0.141528	−	0.989934i	$-0.545201\pi$
$7$	−1.34382e12			−0.283056			−0.141528	+	0.989934i	$0.545201\pi$
$8$		−	1.24396e13i		−	0.353553i
$9$	−1.28645e14	+	1.60753e14i	−0.624820	+	0.780769i
$10$	4.92865e14			0.492865
$11$		−	4.92637e15i		−	1.17933i	−0.807647	−	0.589667i	$-0.799259\pi$
$11$		−	4.92637e15i		−	1.17933i	0.807647	−	0.589667i	$-0.200741\pi$
$12$	−3.33652e15	−	6.94347e15i	−0.216558	−	0.450669i
$13$	6.88812e16			1.34571			0.672854	−	0.739776i	$-0.265068\pi$
$13$	6.88812e16			1.34571			0.672854	+	0.739776i	$0.265068\pi$
$14$		−	3.11371e16i		−	0.200151i
$15$	2.75105e17	−	1.32195e17i	0.628247	−	0.301889i
$16$	2.88230e17			0.250000
$17$		−	1.65076e18i		−	0.576699i	−0.957525	−	0.288349i	$-0.906894\pi$
$17$		−	1.65076e18i		−	0.576699i	0.957525	−	0.288349i	$-0.0931065\pi$
$18$	−3.72473e18	−	2.98076e18i	−0.552087	−	0.441815i
$19$	1.39359e17			0.00917975			0.00458987	−	0.999989i	$-0.498539\pi$
$19$	1.39359e17			0.00917975			0.00458987	+	0.999989i	$0.498539\pi$
$20$			1.14199e19i			0.348508i
$21$	−8.35153e18	−	1.73800e19i	−0.122596	−	0.255129i
$22$	1.14146e20			0.833915
$23$		−	3.70752e20i		−	1.39048i	−0.718776	−	0.695242i	$-0.755297\pi$
$23$		−	3.70752e20i		−	1.39048i	0.718776	−	0.695242i	$-0.244703\pi$
$24$	1.60883e20	−	7.73087e19i	0.318671	−	0.153130i
$25$	4.78857e20			0.514169
$26$			1.59601e21i			0.951559i
$27$	−2.87855e21	−	6.64752e20i	−0.974356	−	0.225011i
$28$	7.21460e20			0.141528
$29$			9.68870e21i			1.12278i	0.827550	+	0.561391i	$0.189734\pi$
$29$			9.68870e21i			1.12278i	−0.827550	+	0.561391i	$0.810266\pi$
$30$	3.06303e21	+	6.37432e21i	0.213468	+	0.444237i
$31$	−8.03421e20			−0.0342388			−0.0171194	−	0.999853i	$-0.505450\pi$
$31$	−8.03421e20			−0.0342388			−0.0171194	+	0.999853i	$0.505450\pi$
$32$			6.67843e21i			0.176777i
$33$	6.37138e22	−	3.06161e22i	1.06298	−	0.510789i
$34$	3.82488e22			0.407788
$35$			2.85848e22i			0.197294i
$36$	6.90657e22	−	8.63038e22i	0.312410	−	0.390384i
$37$	5.84005e23			1.75142			0.875711	−	0.482836i	$-0.160393\pi$
$37$	5.84005e23			1.75142			0.875711	+	0.482836i	$0.160393\pi$
$38$			3.22901e21i			0.00649106i
$39$	4.28080e23	+	8.90856e23i	0.582848	+	1.21294i
$40$	−2.64605e23			−0.246432
$41$			1.21144e24i			0.779012i	0.921024	+	0.389506i	$0.127354\pi$
$41$			1.21144e24i			0.779012i	−0.921024	+	0.389506i	$0.872646\pi$
$42$	4.02702e23	−	1.93509e23i	0.180403	−	0.0866885i
$43$	4.57437e24			1.43981			0.719903	−	0.694075i	$-0.244186\pi$
$43$	4.57437e24			1.43981			0.719903	+	0.694075i	$0.244186\pi$
$44$			2.64482e24i			0.589667i
$45$	3.41942e24	+	2.73644e24i	0.544208	+	0.435510i
$46$	8.59050e24			0.983220
$47$		−	4.58851e24i		−	0.380368i	−0.981748	−	0.190184i	$-0.939092\pi$
$47$		−	4.58851e24i		−	0.380368i	0.981748	−	0.190184i	$-0.0609084\pi$
$48$	1.79128e24	+	3.72775e24i	0.108279	+	0.225334i
$49$	−2.07335e25			−0.919879
$50$			1.10954e25i			0.363572i
$51$	2.13496e25	−	1.02590e25i	0.519801	−	0.249778i
$52$	−3.69803e25			−0.672854
$53$		−	5.51049e25i		−	0.753446i	−0.926326	−	0.376723i	$-0.877051\pi$
$53$		−	5.51049e25i		−	0.753446i	0.926326	−	0.376723i	$-0.122949\pi$
$54$	1.54026e25	−	6.66974e25i	0.159106	−	0.688974i
$55$	−1.04790e26			−0.822014
$56$			1.67166e25i			0.100075i
$57$	8.66080e23	+	1.80236e24i	0.00397590	+	0.00827405i
$58$	−2.24492e26			−0.793927
$59$			3.03191e25i			0.0829729i	0.999139	+	0.0414865i	$0.0132093\pi$
$59$			3.03191e25i			0.0829729i	−0.999139	+	0.0414865i	$0.986791\pi$
$60$	−1.47696e26	+	7.09718e25i	−0.314123	+	0.150944i
$61$	−9.38409e26			−1.55756			−0.778779	−	0.627298i	$-0.784161\pi$
$61$	−9.38409e26			−1.55756			−0.778779	+	0.627298i	$0.784161\pi$
$62$		−	1.86157e25i		−	0.0242105i
$63$	1.72876e26	−	2.16024e26i	0.176859	−	0.221001i
$64$	−1.54743e26			−0.125000
$65$		−	1.46519e27i		−	0.937979i
$66$	7.09390e26	+	1.47628e27i	0.361182	+	0.751639i
$67$	2.46316e27			1.00085			0.500426	−	0.865779i	$-0.333177\pi$
$67$	2.46316e27			1.00085			0.500426	+	0.865779i	$0.333177\pi$
$68$			8.86243e26i			0.288349i
$69$	4.79501e27	−	2.30413e27i	1.25330	−	0.602241i
$70$	−6.62324e26			−0.139508
$71$		−	4.09982e26i		−	0.0698055i	−0.999391	−	0.0349028i	$-0.988888\pi$
$71$		−	4.09982e26i		−	0.0698055i	0.999391	−	0.0349028i	$-0.0111122\pi$
$72$	1.99970e27	+	1.60029e27i	0.276043	+	0.220907i
$73$	7.27398e24			0.000816449			0.000408225	−	1.00000i	$-0.499870\pi$
$73$	7.27398e24			0.000816449			0.000408225		1.00000i	$0.499870\pi$
$74$			1.35317e28i			1.23844i
$75$	2.97598e27	+	6.19316e27i	0.222695	+	0.463440i
$76$	−7.48177e25			−0.00458987
$77$			6.62018e27i			0.333817i
$78$	−2.06416e28	+	9.91881e27i	−0.857676	+	0.412136i
$79$	4.60559e28			1.58081			0.790403	−	0.612587i	$-0.209871\pi$
$79$	4.60559e28			1.58081			0.790403	+	0.612587i	$0.209871\pi$
$80$		−	6.13101e27i		−	0.174254i
$81$	−9.29211e27	−	4.13602e28i	−0.219199	−	0.975680i
$82$	−2.80696e28			−0.550845
$83$		−	1.19904e29i		−	1.96184i	−0.194420	−	0.980918i	$-0.562282\pi$
$83$		−	1.19904e29i		−	1.96184i	0.194420	−	0.980918i	$-0.437718\pi$
$84$	4.48369e27	+	9.33080e27i	0.0612981	+	0.127564i
$85$	−3.51136e28			−0.401968
$86$			1.05990e29i			1.01810i
$87$	−1.25306e29	+	6.02129e28i	−1.01201	+	0.486296i
$88$	−6.12818e28			−0.416957
$89$		−	2.72734e29i		−	1.56635i	−0.621800	−	0.783176i	$-0.713598\pi$
$89$		−	2.72734e29i		−	1.56635i	0.621800	−	0.783176i	$-0.286402\pi$
$90$	−6.34045e28	+	7.92296e28i	−0.307952	+	0.384813i
$91$	−9.25643e28			−0.380910
$92$			1.99046e29i			0.695242i
$93$	−4.99306e27	−	1.03908e28i	−0.0148294	−	0.0308607i
$94$	1.06318e29			0.268961
$95$		−	2.96434e27i		−	0.00639843i
$96$	−8.63736e28	+	4.15048e28i	−0.159336	+	0.0765649i
$97$	5.73161e29			0.905109			0.452554	−	0.891737i	$-0.350513\pi$
$97$	5.73161e29			0.905109			0.452554	+	0.891737i	$0.350513\pi$
$98$		−	4.80404e29i		−	0.650453i
$99$	7.91930e29	+	6.33752e29i	0.920786	+	0.736871i
$100$	−2.57085e29			−0.257085
$101$			1.83357e29i			0.157935i	0.996877	+	0.0789673i	$0.0251623\pi$
$101$			1.83357e29i			0.157935i	−0.996877	+	0.0789673i	$0.974838\pi$
$102$	2.37707e29	+	4.94680e29i	0.176620	+	0.367555i
$103$	1.47645e30			0.947679			0.473840	−	0.880611i	$-0.342868\pi$
$103$	1.47645e30			0.947679			0.473840	+	0.880611i	$0.342868\pi$
$104$		−	8.56852e29i		−	0.475779i
$105$	−3.69693e29	+	1.77647e29i	−0.177829	+	0.0854514i
$106$	1.27681e30			0.532767
$107$			8.26001e29i			0.299381i	0.988733	+	0.149690i	$0.0478277\pi$
$107$			8.26001e29i			0.299381i	−0.988733	+	0.149690i	$0.952172\pi$
$108$	1.54541e30	+	3.56886e29i	0.487178	+	0.112505i
$109$	−5.95352e30			−1.63447			−0.817234	−	0.576306i	$-0.804494\pi$
$109$	−5.95352e30			−1.63447			−0.817234	+	0.576306i	$0.804494\pi$
$110$		−	2.42803e30i		−	0.581252i
$111$	3.62944e30	+	7.55306e30i	0.758570	+	1.57862i
$112$	−3.87331e29			−0.0707639
$113$		−	1.05842e31i		−	1.69231i	−0.532934	−	0.846157i	$-0.678911\pi$
$113$		−	1.05842e31i		−	1.69231i	0.532934	−	0.846157i	$-0.321089\pi$
$114$	−4.17615e28	+	2.00675e28i	−0.00585064	+	0.00281139i
$115$	−7.88635e30			−0.969189
$116$		−	5.20158e30i		−	0.561391i
$117$	−8.86122e30	+	1.10729e31i	−0.840825	+	1.05069i
$118$	−7.02508e29			−0.0586707
$119$			2.21833e30i			0.163238i
$120$	−1.64445e30	−	3.42219e30i	−0.106734	−	0.222119i
$121$	−6.81970e30			−0.390827
$122$		−	2.17434e31i		−	1.10136i
$123$	−1.56678e31	+	7.52879e30i	−0.702153	+	0.337403i
$124$	4.31334e29			0.0171194
$125$		−	2.99963e31i		−	1.05540i
$126$	5.00539e30	+	4.00563e30i	0.156271	+	0.125058i
$127$	5.53338e31			1.53439			0.767194	−	0.641416i	$-0.221653\pi$
$127$	5.53338e31			1.53439			0.767194	+	0.641416i	$0.221653\pi$
$128$		−	3.58546e30i		−	0.0883883i
$129$	2.84285e31	+	5.91612e31i	0.623604	+	1.29775i
$130$	3.39491e31			0.663251
$131$		−	5.82123e30i		−	0.101378i	−0.998714	−	0.0506892i	$-0.983858\pi$
$131$		−	5.82123e30i		−	0.101378i	0.998714	−	0.0506892i	$-0.0161418\pi$
$132$	−3.42061e31	+	1.64369e31i	−0.531489	+	0.255394i
$133$	−1.87274e29			−0.00259838
$134$			5.70725e31i			0.707710i
$135$	−1.41401e31	+	6.12304e31i	−0.156836	+	0.679142i
$136$	−2.05347e31			−0.203894
$137$		−	7.97012e31i		−	0.709016i	−0.935053	−	0.354508i	$-0.884648\pi$
$137$		−	7.97012e31i		−	0.709016i	0.935053	−	0.354508i	$-0.115352\pi$
$138$	5.33878e31	+	1.11103e32i	0.425849	+	0.886214i
$139$	3.08125e31			0.220549			0.110274	−	0.993901i	$-0.464827\pi$
$139$	3.08125e31			0.220549			0.110274	+	0.993901i	$0.464827\pi$
$140$		−	1.53464e31i		−	0.0986472i
$141$	5.93442e31	−	2.85164e31i	0.342840	−	0.164744i
$142$	9.49948e30			0.0493600
$143$		−	3.39334e32i		−	1.58704i
$144$	−3.70794e31	+	4.63340e31i	−0.156205	+	0.195192i
$145$	2.06091e32			0.782597
$146$			1.68542e29i			0.000577317i
$147$	−1.28853e32	−	2.68150e32i	−0.398415	−	0.829122i
$148$	−3.13535e32			−0.875711
$149$			1.33313e32i			0.336573i	0.985738	+	0.168286i	$0.0538233\pi$
$149$			1.33313e32i			0.336573i	−0.985738	+	0.168286i	$0.946177\pi$
$150$	−1.43499e32	+	6.89548e31i	−0.327702	+	0.157469i
$151$	−7.74147e32			−1.60018			−0.800091	−	0.599879i	$-0.795216\pi$
$151$	−7.74147e32			−1.60018			−0.800091	+	0.599879i	$0.795216\pi$
$152$		−	1.73356e30i		−	0.00324553i
$153$	2.65365e32	+	2.12361e32i	0.450268	+	0.360333i
$154$	−1.53393e32			−0.236044
$155$			1.70898e31i			0.0238649i
$156$	−2.29823e32	−	4.78275e32i	−0.291424	−	0.606469i
$157$	−6.57205e32			−0.757193			−0.378596	−	0.925562i	$-0.623593\pi$
$157$	−6.57205e32			−0.757193			−0.378596	+	0.925562i	$0.623593\pi$
$158$			1.06714e33i			1.11780i
$159$	7.12683e32	−	3.42463e32i	0.679109	−	0.326330i
$160$	1.42059e32			0.123216
$161$			4.98226e32i			0.393584i
$162$	9.58336e32	−	2.15303e32i	0.689910	−	0.154997i
$163$	1.09803e33			0.720775			0.360387	−	0.932803i	$-0.382645\pi$
$163$	1.09803e33			0.720775			0.360387	+	0.932803i	$0.382645\pi$
$164$		−	6.50387e32i		−	0.389506i
$165$	−6.51243e32	−	1.35527e33i	−0.356028	−	0.740912i
$166$	2.77824e33			1.38723
$167$			1.41544e33i			0.645867i	0.946422	+	0.322934i	$0.104669\pi$
$167$			1.41544e33i			0.645867i	−0.946422	+	0.322934i	$0.895331\pi$
$168$	−2.16199e32	+	1.03889e32i	−0.0902017	+	0.0433443i
$169$	2.12463e33			0.810929
$170$		−	8.13599e32i		−	0.284234i
$171$	−1.79278e31	+	2.24024e31i	−0.00573569	+	0.00716726i
$172$	−2.45584e33			−0.719903
$173$			6.48308e33i			1.74217i	0.491135	+	0.871084i	$0.336582\pi$
$173$			6.48308e33i			1.74217i	−0.491135	+	0.871084i	$0.663418\pi$
$174$	−1.39516e33	−	2.90340e33i	−0.343863	−	0.715597i
$175$	−6.43500e32			−0.145539
$176$		−	1.41993e33i		−	0.294833i
$177$	−3.92124e32	+	1.88426e32i	−0.0747866	+	0.0359369i
$178$	6.31938e33			1.10758
$179$			1.00599e34i			1.62106i	0.585694	+	0.810532i	$0.300822\pi$
$179$			1.00599e34i			1.62106i	−0.585694	+	0.810532i	$0.699178\pi$
$180$	−1.83579e33	−	1.46911e33i	−0.272104	−	0.217755i
$181$	−3.60276e33			−0.491425			−0.245712	−	0.969343i	$-0.579022\pi$
$181$	−3.60276e33			−0.491425			−0.245712	+	0.969343i	$0.579022\pi$
$182$		−	2.14476e33i		−	0.269344i
$183$	−5.83197e33	−	1.21366e34i	−0.674604	−	1.40389i
$184$	−4.61199e33			−0.491610
$185$		−	1.24225e34i		−	1.22077i
$186$	2.40760e32	−	1.15692e32i	0.0218218	−	0.0104859i
$187$	−8.13223e33			−0.680120
$188$			2.46344e33i			0.190184i
$189$	3.86827e33	+	8.93310e32i	0.275797	+	0.0636905i
$190$	6.86851e31			0.00452437
$191$			1.01338e34i			0.616983i	0.951227	+	0.308492i	$0.0998242\pi$
$191$			1.01338e34i			0.616983i	−0.951227	+	0.308492i	$0.900176\pi$
$192$	−9.61686e32	−	2.00132e33i	−0.0541396	−	0.112667i
$193$	−2.46806e34			−1.28528			−0.642638	−	0.766170i	$-0.722160\pi$
$193$	−2.46806e34			−1.28528			−0.642638	+	0.766170i	$0.722160\pi$
$194$			1.32804e34i			0.640009i
$195$	1.89496e34	−	9.10578e33i	0.845436	−	0.406254i
$196$	1.11312e34			0.459940
$197$		−	3.46118e34i		−	1.32505i	−0.749041	−	0.662523i	$-0.769486\pi$
$197$		−	3.46118e34i		−	1.32505i	0.749041	−	0.662523i	$-0.230514\pi$
$198$	−1.46843e34	+	1.83494e34i	−0.521047	+	0.651094i
$199$	3.29640e34			1.08454			0.542268	−	0.840205i	$-0.317566\pi$
$199$	3.29640e34			1.08454			0.542268	+	0.840205i	$0.317566\pi$
$200$		−	5.95677e33i		−	0.181786i
$201$	1.53079e34	+	3.18565e34i	0.433486	+	0.902107i
$202$	−4.24847e33			−0.111677
$203$		−	1.30199e34i		−	0.317810i
$204$	−1.14620e34	+	5.50778e33i	−0.259900	+	0.124889i
$205$	2.57688e34			0.542984
$206$			3.42101e34i			0.670110i
$207$	5.95996e34	+	4.76954e34i	1.08565	+	0.868802i
$208$	1.98537e34			0.336427
$209$		−	6.86533e32i		−	0.0108260i
$210$	−4.11617e33	−	8.56597e33i	−0.0604233	−	0.125744i
$211$	−5.60105e34			−0.765654			−0.382827	−	0.923820i	$-0.625049\pi$
$211$	−5.60105e34			−0.765654			−0.382827	+	0.923820i	$0.625049\pi$
$212$			2.95842e34i			0.376723i
$213$	5.30239e33	−	2.54794e33i	0.0629184	−	0.0302339i
$214$	−1.91388e34			−0.211694
$215$		−	9.73024e34i		−	1.00357i
$216$	−8.26921e33	+	3.58079e34i	−0.0795532	+	0.344487i
$217$	1.07966e33			0.00969148
$218$		−	1.37946e35i		−	1.15574i
$219$	4.52059e31	+	9.40759e31i	0.000353618	+	0.000735897i
$220$	5.62587e34			0.411007
$221$		−	1.13706e35i		−	0.776068i
$222$	−1.75008e35	+	8.40959e34i	−1.11626	+	0.536390i
$223$	−1.43401e35			−0.855028			−0.427514	−	0.904009i	$-0.640610\pi$
$223$	−1.43401e35			−0.855028			−0.427514	+	0.904009i	$0.640610\pi$
$224$		−	8.97465e33i		−	0.0500377i
$225$	−6.16026e34	+	7.69779e34i	−0.321263	+	0.401447i
$226$	2.45241e35			1.19665
$227$		−	7.50661e34i		−	0.342812i	−0.985200	−	0.171406i	$-0.945169\pi$
$227$		−	7.50661e34i		−	0.342812i	0.985200	−	0.171406i	$-0.0548309\pi$
$228$	−4.64973e32	−	9.67634e32i	−0.00198795	−	0.00413703i
$229$	−2.75820e35			−1.10432			−0.552159	−	0.833739i	$-0.686196\pi$
$229$	−2.75820e35			−1.10432			−0.552159	+	0.833739i	$0.686196\pi$
$230$		−	1.82730e35i		−	0.685320i
$231$	−8.56202e34	+	4.11427e34i	−0.300882	+	0.144582i
$232$	1.20523e35			0.396964
$233$			4.70589e35i			1.45312i	0.687101	+	0.726562i	$0.258883\pi$
$233$			4.70589e35i			1.45312i	−0.687101	+	0.726562i	$0.741117\pi$
$234$	−2.56564e35	−	2.05319e35i	−0.742947	−	0.594553i
$235$	−9.76033e34			−0.265122
$236$		−	1.62774e34i		−	0.0414865i
$237$	2.86226e35	+	5.95650e35i	0.684673	+	1.42484i
$238$	−5.13997e34			−0.115427
$239$		−	2.12065e35i		−	0.447198i	−0.974681	−	0.223599i	$-0.928219\pi$
$239$		−	2.12065e35i		−	0.447198i	0.974681	−	0.223599i	$-0.0717806\pi$
$240$	7.92937e34	−	3.81027e34i	0.157062	−	0.0754722i
$241$	3.25643e35			0.606018			0.303009	−	0.952988i	$-0.402009\pi$
$241$	3.25643e35			0.606018			0.303009	+	0.952988i	$0.402009\pi$
$242$		−	1.58016e35i		−	0.276357i
$243$	4.77172e35	−	3.77220e35i	0.784479	−	0.620156i
$244$	5.03804e35			0.778779
$245$			4.41027e35i			0.641170i
$246$	−1.74446e35	−	3.63031e35i	−0.238580	−	0.496497i
$247$	9.59921e33			0.0123533
$248$			9.99420e33i			0.0121052i
$249$	1.55075e36	−	7.45174e35i	1.76828	−	0.849704i
$250$	6.95028e35			0.746280
$251$			7.31813e35i			0.740107i	0.929010	+	0.370053i	$0.120661\pi$
$251$			7.31813e35i			0.740107i	−0.929010	+	0.370053i	$0.879339\pi$
$252$	−9.28123e34	+	1.15977e35i	−0.0884295	+	0.110501i
$253$	−1.82646e36			−1.63984
$254$			1.28211e36i			1.08498i
$255$	−2.18222e35	−	4.54132e35i	−0.174099	−	0.362309i
$256$	8.30767e34			0.0625000
$257$			3.71986e35i			0.263955i	0.991253	+	0.131978i	$0.0421327\pi$
$257$			3.71986e35i			0.263955i	−0.991253	+	0.131978i	$0.957867\pi$
$258$	−1.37079e36	+	6.58702e35i	−0.917649	+	0.440954i
$259$	−7.84801e35			−0.495750
$260$			7.86617e35i			0.468990i
$261$	−1.55749e36	−	1.24640e36i	−0.876634	−	0.701538i
$262$	1.34881e35			0.0716853
$263$		−	7.46679e35i		−	0.374799i	−0.982284	−	0.187399i	$-0.939994\pi$
$263$		−	7.46679e35i		−	0.374799i	0.982284	−	0.187399i	$-0.0600058\pi$
$264$	−3.80851e35	−	7.92571e35i	−0.180591	−	0.375819i
$265$	−1.17215e36			−0.525163
$266$		−	4.33923e33i		−	0.00183733i
$267$	3.52733e36	−	1.69497e36i	1.41181	−	0.678413i
$268$	−1.32240e36			−0.500426
$269$		−	3.78362e35i		−	0.135401i	−0.997706	−	0.0677007i	$-0.978434\pi$
$269$		−	3.78362e35i		−	0.135401i	0.997706	−	0.0677007i	$-0.0215663\pi$
$270$	−1.41874e36	−	3.27632e35i	−0.480226	−	0.110900i
$271$	2.45440e36			0.785971			0.392985	−	0.919545i	$-0.371442\pi$
$271$	2.45440e36			0.785971			0.392985	+	0.919545i	$0.371442\pi$
$272$		−	4.75798e35i		−	0.144175i
$273$	−5.75264e35	−	1.19715e36i	−0.164979	−	0.343329i
$274$	1.84671e36			0.501350
$275$		−	2.35903e36i		−	0.606377i
$276$	−2.57430e36	+	1.23702e36i	−0.626648	+	0.301121i
$277$	−2.81120e36			−0.648180			−0.324090	−	0.946026i	$-0.605058\pi$
$277$	−2.81120e36			−0.648180			−0.324090	+	0.946026i	$0.605058\pi$
$278$			7.13940e35i			0.155952i
$279$	1.03356e35	−	1.29153e35i	0.0213931	−	0.0267325i
$280$	3.55582e35			0.0697541
$281$			7.18422e36i			1.33593i	0.744191	+	0.667967i	$0.232835\pi$
$281$			7.18422e36i			1.33593i	−0.744191	+	0.667967i	$0.767165\pi$
$282$	6.60739e35	+	1.37503e36i	0.116491	+	0.242425i
$283$	1.68433e36			0.281598			0.140799	−	0.990038i	$-0.455033\pi$
$283$	1.68433e36			0.281598			0.140799	+	0.990038i	$0.455033\pi$
$284$			2.20108e35i			0.0349028i
$285$	3.83384e34	−	1.84226e34i	0.00576715	−	0.00277126i
$286$	7.86254e36			1.12221
$287$		−	1.62796e36i		−	0.220504i
$288$	−1.07358e36	−	8.59147e35i	−0.138022	−	0.110454i
$289$	5.46847e36			0.667418
$290$			4.77522e36i			0.553380i
$291$	3.56205e36	+	7.41282e36i	0.392017	+	0.815809i
$292$	−3.90519e33			−0.000408225
$293$			4.16236e36i			0.413357i	0.978409	+	0.206679i	$0.0662654\pi$
$293$			4.16236e36i			0.413357i	−0.978409	+	0.206679i	$0.933735\pi$
$294$	6.21317e36	−	2.98559e36i	0.586278	−	0.281722i
$295$	6.44925e35			0.0578334
$296$		−	7.26476e36i		−	0.619221i
$297$	−3.27481e36	+	1.41808e37i	−0.265362	+	1.14909i
$298$	−3.08893e36			−0.237993
$299$		−	2.55379e37i		−	1.87118i
$300$	−1.59772e36	−	3.32493e36i	−0.111348	−	0.231720i
$301$	−6.14715e36			−0.407545
$302$		−	1.79374e37i		−	1.13150i
$303$	−2.37140e36	+	1.13952e36i	−0.142352	+	0.0684041i
$304$	4.01675e34			0.00229494
$305$			1.99611e37i			1.08564i
$306$	−4.92052e36	+	6.14862e36i	−0.254794	+	0.318388i
$307$	−2.37583e37			−1.17150			−0.585748	−	0.810494i	$-0.699199\pi$
$307$	−2.37583e37			−1.17150			−0.585748	+	0.810494i	$0.699199\pi$
$308$		−	3.55418e36i		−	0.166909i
$309$	9.17579e36	+	1.90953e37i	0.410455	+	0.854179i
$310$	−3.95978e35			−0.0168751
$311$		−	3.63505e37i		−	1.47606i	−0.674767	−	0.738031i	$-0.735756\pi$
$311$		−	3.63505e37i		−	1.47606i	0.674767	−	0.738031i	$-0.264244\pi$
$312$	1.10818e37	−	5.32512e36i	0.428838	−	0.206068i
$313$	−3.73427e37			−1.37734			−0.688669	−	0.725076i	$-0.741805\pi$
$313$	−3.73427e37			−1.37734			−0.688669	+	0.725076i	$0.741805\pi$
$314$		−	1.52278e37i		−	0.535416i
$315$	−4.59510e36	−	3.67729e36i	−0.154041	−	0.123274i
$316$	−2.47261e37			−0.790403
$317$			1.62114e37i			0.494233i	0.968986	+	0.247116i	$0.0794830\pi$
$317$			1.62114e37i			0.494233i	−0.968986	+	0.247116i	$0.920517\pi$
$318$	7.93503e36	+	1.65132e37i	0.230750	+	0.480203i
$319$	4.77301e37			1.32414
$320$			3.29156e36i			0.0871270i
$321$	−1.06829e37	+	5.13339e36i	−0.269843	+	0.129667i
$322$	−1.15441e37			−0.278306
$323$		−	2.30048e35i		−	0.00529395i
$324$	4.98866e36	+	2.22051e37i	0.109600	+	0.487840i
$325$	3.29843e37			0.691921
$326$			2.54418e37i			0.509665i
$327$	−3.69996e37	−	7.69982e37i	−0.707915	−	1.47321i
$328$	1.50698e37			0.275422
$329$			6.16615e36i			0.107665i
$330$	3.14023e37	−	1.50896e37i	0.523904	−	0.251750i
$331$	9.03289e37			1.44015			0.720073	−	0.693898i	$-0.244108\pi$
$331$	9.03289e37			1.44015			0.720073	+	0.693898i	$0.244108\pi$
$332$			6.43731e37i			0.980918i
$333$	−7.51293e37	+	9.38808e37i	−1.09432	+	1.36746i
$334$	−3.27963e37			−0.456697
$335$		−	5.23944e37i		−	0.697610i
$336$	−2.40717e36	−	5.00944e36i	−0.0306490	−	0.0637822i
$337$	7.23816e37			0.881414			0.440707	−	0.897651i	$-0.354728\pi$
$337$	7.23816e37			0.881414			0.440707	+	0.897651i	$0.354728\pi$
$338$			4.92287e37i			0.573413i
$339$	1.36888e38	−	6.57781e37i	1.52535	−	0.732969i
$340$	1.88515e37			0.200984
$341$			3.95795e36i			0.0403789i
$342$	−5.19074e35	−	4.15396e35i	−0.00506802	−	0.00405575i
$343$	5.81511e37			0.543433
$344$		−	5.69031e37i		−	0.509048i
$345$	−4.90117e37	−	1.01996e38i	−0.419772	−	0.873567i
$346$	−1.50216e38			−1.23190
$347$			7.86327e37i			0.617534i	0.951138	+	0.308767i	$0.0999163\pi$
$347$			7.86327e37i			0.617534i	−0.951138	+	0.308767i	$0.900084\pi$
$348$	6.72732e37	−	3.23265e37i	0.506003	−	0.243148i
$349$	−5.42563e37			−0.390903			−0.195451	−	0.980713i	$-0.562617\pi$
$349$	−5.42563e37			−0.390903			−0.195451	+	0.980713i	$0.562617\pi$
$350$		−	1.49102e37i		−	0.102911i
$351$	−1.98278e38	−	4.57889e37i	−1.31120	−	0.302798i
$352$	3.29004e37			0.208479
$353$			2.27864e38i			1.38374i	0.722022	+	0.691870i	$0.243213\pi$
$353$			2.27864e38i			1.38374i	−0.722022	+	0.691870i	$0.756787\pi$
$354$	−4.36591e36	−	9.08569e36i	−0.0254112	−	0.0528821i
$355$	−8.72083e36			−0.0486555
$356$			1.46423e38i			0.783176i
$357$	−2.86901e37	+	1.37863e37i	−0.147133	+	0.0707010i
$358$	−2.33094e38			−1.14627
$359$		−	1.38456e38i		−	0.652975i	−0.945202	−	0.326487i	$-0.894135\pi$
$359$		−	1.38456e38i		−	0.652975i	0.945202	−	0.326487i	$-0.105865\pi$
$360$	3.40401e37	−	4.25361e37i	0.153976	−	0.192407i
$361$	−2.30447e38			−0.999916
$362$		−	8.34777e37i		−	0.347490i
$363$	−4.23827e37	−	8.82007e37i	−0.169274	−	0.352267i
$364$	4.96951e37			0.190455
$365$		−	1.54727e35i		−	0.000569078i
$366$	2.81212e38	−	1.35130e38i	0.992698	−	0.477017i
$367$	2.31630e37			0.0784882			0.0392441	−	0.999230i	$-0.487505\pi$
$367$	2.31630e37			0.0784882			0.0392441	+	0.999230i	$0.487505\pi$
$368$		−	1.06862e38i		−	0.347621i
$369$	−1.94743e38	−	1.55846e38i	−0.608228	−	0.486743i
$370$	2.87835e38			0.863214
$371$			7.40513e37i			0.213267i
$372$	2.68063e36	+	5.57853e36i	0.00741468	+	0.0154303i
$373$	−1.14320e38			−0.303732			−0.151866	−	0.988401i	$-0.548528\pi$
$373$	−1.14320e38			−0.303732			−0.151866	+	0.988401i	$0.548528\pi$
$374$		−	1.88428e38i		−	0.480918i
$375$	3.87948e38	−	1.86419e38i	0.951272	−	0.457111i
$376$	−5.70790e37			−0.134480
$377$			6.67370e38i			1.51094i
$378$	−2.06984e37	+	8.96297e37i	−0.0450360	+	0.195018i
$379$	7.02964e38			1.47009			0.735046	−	0.678017i	$-0.237160\pi$
$379$	7.02964e38			1.47009			0.735046	+	0.678017i	$0.237160\pi$
$380$			1.59147e36i			0.00319921i
$381$	3.43886e38	+	7.15644e38i	0.664568	+	1.38300i
$382$	−2.34806e38			−0.436273
$383$			8.94855e37i			0.159871i	0.996800	+	0.0799357i	$0.0254715\pi$
$383$			8.94855e37i			0.159871i	−0.996800	+	0.0799357i	$0.974528\pi$
$384$	4.63715e37	−	2.22827e37i	0.0796678	−	0.0382824i
$385$	1.40819e38			0.232676
$386$		−	5.71862e38i		−	0.908828i
$387$	−5.88469e38	+	7.35344e38i	−0.899620	+	1.12416i
$388$	−3.07714e38			−0.452554
$389$		−	2.70836e38i		−	0.383233i	−0.981470	−	0.191617i	$-0.938627\pi$
$389$		−	2.70836e38i		−	0.383233i	0.981470	−	0.191617i	$-0.0613730\pi$
$390$	2.10985e38	+	4.39071e38i	0.287265	+	0.597814i
$391$	−6.12021e38			−0.801890
$392$			2.57915e38i			0.325226i
$393$	7.52872e37	−	3.61775e37i	0.0913761	−	0.0439086i
$394$	8.01973e38			0.936949
$395$		−	9.79665e38i		−	1.10185i
$396$	−4.25164e38	−	3.40243e38i	−0.460393	−	0.368436i
$397$	8.34966e38			0.870585			0.435292	−	0.900289i	$-0.356645\pi$
$397$	8.34966e38			0.870585			0.435292	+	0.900289i	$0.356645\pi$
$398$			7.63792e38i			0.766883i
$399$	−1.16386e36	−	2.42205e36i	−0.00112540	−	0.00234202i
$400$	1.38021e38			0.128542
$401$		−	1.30396e39i		−	1.16977i	−0.811118	−	0.584883i	$-0.801140\pi$
$401$		−	1.30396e39i		−	1.16977i	0.811118	−	0.584883i	$-0.198860\pi$
$402$	−7.38131e38	+	3.54691e38i	−0.637886	+	0.306521i
$403$	−5.53407e37			−0.0460753
$404$		−	9.84391e37i		−	0.0789673i
$405$	−8.79783e38	+	1.97655e38i	−0.680064	+	0.152785i
$406$	3.01678e38			0.224726
$407$		−	2.87702e39i		−	2.06551i
$408$	−1.27618e38	−	2.65579e38i	−0.0883098	−	0.183777i
$409$	−9.09207e38			−0.606476			−0.303238	−	0.952915i	$-0.598068\pi$
$409$	−9.09207e38			−0.606476			−0.303238	+	0.952915i	$0.598068\pi$
$410$			5.97076e38i			0.383947i
$411$	1.03079e39	−	4.95323e38i	0.639063	−	0.307087i
$412$	−7.92665e38			−0.473840
$413$		−	4.07436e37i		−	0.0234860i
$414$	−1.10512e39	+	1.38095e39i	−0.614336	+	0.767668i
$415$	−2.55051e39			−1.36743
$416$			4.60019e38i			0.237890i
$417$	1.91492e38	+	3.98505e38i	0.0955233	+	0.198789i
$418$	1.59073e37			0.00765513
$419$			3.70693e39i			1.72109i	0.509373	+	0.860546i	$0.329877\pi$
$419$			3.70693e39i			1.72109i	−0.509373	+	0.860546i	$0.670123\pi$
$420$	1.98478e38	−	9.53737e37i	0.0889144	−	0.0427257i
$421$	3.68929e38			0.159482			0.0797410	−	0.996816i	$-0.474591\pi$
$421$	3.68929e38			0.159482			0.0797410	+	0.996816i	$0.474591\pi$
$422$		−	1.29779e39i		−	0.541399i
$423$	7.37618e38	+	5.90289e38i	0.296979	+	0.237662i
$424$	−6.85480e38			−0.266383
$425$		−	7.90477e38i		−	0.296521i
$426$	5.90369e37	+	1.22859e38i	0.0213786	+	0.0444900i
$427$	1.26106e39			0.440876
$428$		−	4.43456e38i		−	0.149690i
$429$	4.38868e39	−	2.10888e39i	1.43046	−	0.687372i
$430$	2.25454e39			0.709629
$431$			8.39829e38i			0.255289i	0.991820	+	0.127644i	$0.0407416\pi$
$431$			8.39829e38i			0.255289i	−0.991820	+	0.127644i	$0.959258\pi$
$432$	−8.29686e38	−	1.91602e38i	−0.243589	−	0.0562526i
$433$	2.73840e39			0.776566			0.388283	−	0.921540i	$-0.373068\pi$
$433$	2.73840e39			0.776566			0.388283	+	0.921540i	$0.373068\pi$
$434$			2.50162e37i			0.00685291i
$435$	1.28080e39	+	2.66541e39i	0.338956	+	0.705385i
$436$	3.19627e39			0.817234
$437$		−	5.16676e37i		−	0.0127643i
$438$	−2.17978e36	+	1.04744e36i	−0.000520358	+	0.000250045i
$439$	−5.86875e39			−1.35387			−0.676936	−	0.736042i	$-0.736693\pi$
$439$	−5.86875e39			−1.35387			−0.676936	+	0.736042i	$0.736693\pi$
$440$			1.30354e39i			0.290626i
$441$	2.66726e39	−	3.33298e39i	0.574759	−	0.718213i
$442$	2.63463e39			0.548763
$443$			6.41790e39i			1.29222i	0.763244	+	0.646111i	$0.223606\pi$
$443$			6.41790e39i			1.29222i	−0.763244	+	0.646111i	$0.776394\pi$
$444$	−1.94854e39	−	4.05502e39i	−0.379285	−	0.789312i
$445$	−5.80139e39			−1.09177
$446$		−	3.32268e39i		−	0.604596i
$447$	−1.72417e39	+	8.28507e38i	−0.303366	+	0.145775i
$448$	2.07947e38			0.0353820
$449$			4.56054e39i			0.750449i	0.926934	+	0.375224i	$0.122434\pi$
$449$			4.56054e39i			0.750449i	−0.926934	+	0.375224i	$0.877566\pi$
$450$	−1.78361e39	−	1.42736e39i	−0.283866	−	0.227167i
$451$	5.96800e39			0.918715
$452$			5.68234e39i			0.846157i
$453$	−4.81113e39	−	1.00122e40i	−0.693065	−	1.44230i
$454$	1.73932e39			0.242405
$455$			1.96896e39i			0.265500i
$456$	2.24205e37	−	1.07737e37i	0.00292532	−	0.00140569i
$457$	−7.13698e39			−0.901097			−0.450549	−	0.892752i	$-0.648772\pi$
$457$	−7.13698e39			−0.901097			−0.450549	+	0.892752i	$0.648772\pi$
$458$		−	6.39089e39i		−	0.780870i
$459$	−1.09734e39	+	4.75179e39i	−0.129763	+	0.561910i
$460$	4.23395e39			0.484594
$461$		−	6.32798e39i		−	0.701054i	−0.936553	−	0.350527i	$-0.886002\pi$
$461$		−	6.32798e39i		−	0.701054i	0.936553	−	0.350527i	$-0.113998\pi$
$462$	−9.53296e38	−	1.98386e39i	−0.102235	−	0.212756i
$463$	−4.28953e39			−0.445343			−0.222672	−	0.974894i	$-0.571478\pi$
$463$	−4.28953e39			−0.445343			−0.222672	+	0.974894i	$0.571478\pi$
$464$			2.79258e39i			0.280696i
$465$	−2.21026e38	+	1.06209e38i	−0.0215104	+	0.0103363i
$466$	−1.09038e40			−1.02751
$467$			2.08786e40i			1.90523i	0.304180	+	0.952614i	$0.401617\pi$
$467$			2.08786e40i			1.90523i	−0.304180	+	0.952614i	$0.598383\pi$
$468$	4.75733e39	−	5.94471e39i	0.420413	−	0.525343i
$469$	−3.31005e39			−0.283297
$470$		−	2.26151e39i		−	0.187470i
$471$	−4.08437e39	−	8.49978e39i	−0.327953	−	0.682486i
$472$	3.77156e38			0.0293354
$473$		−	2.25350e40i		−	1.69801i
$474$	−1.38015e40	+	6.63198e39i	−1.00751	+	0.484137i
$475$	6.67330e37			0.00471994
$476$		−	1.19096e39i		−	0.0816190i
$477$	8.85829e39	+	7.08896e39i	0.588267	+	0.470768i
$478$	4.91364e39			0.316217
$479$			1.64568e39i			0.102639i	0.998682	+	0.0513196i	$0.0163427\pi$
$479$			1.64568e39i			0.102639i	−0.998682	+	0.0513196i	$0.983657\pi$
$480$	8.82858e38	+	1.83727e39i	0.0533669	+	0.111059i
$481$	4.02270e40			2.35690
$482$			7.54530e39i			0.428520i
$483$	−6.44366e39	+	3.09635e39i	−0.354753	+	0.170468i
$484$	3.66130e39			0.195414
$485$		−	1.21918e40i		−	0.630875i
$486$	8.74037e39	+	1.10563e40i	0.438516	+	0.554710i
$487$	−1.27695e39			−0.0621213			−0.0310607	−	0.999518i	$-0.509889\pi$
$487$	−1.27695e39			−0.0621213			−0.0310607	+	0.999518i	$0.509889\pi$
$488$			1.16734e40i			0.550680i
$489$	6.82397e39	+	1.42010e40i	0.312179	+	0.649662i
$490$	−1.02188e40			−0.453376
$491$		−	1.69619e40i		−	0.729883i	−0.931031	−	0.364941i	$-0.881089\pi$
$491$		−	1.69619e40i		−	0.729883i	0.931031	−	0.364941i	$-0.118911\pi$
$492$	8.41159e39	−	4.04199e39i	0.351077	−	0.168701i
$493$	1.59937e40			0.647508
$494$			2.22418e38i			0.00873507i
$495$	1.34807e40	−	1.68453e40i	0.513611	−	0.641803i
$496$	−2.31570e38			−0.00855969
$497$			5.50944e38i			0.0197589i
$498$	1.72660e40	+	3.59315e40i	0.600831	+	1.25036i
$499$	−3.65315e40			−1.23356			−0.616779	−	0.787136i	$-0.711563\pi$
$499$	−3.65315e40			−1.23356			−0.616779	+	0.787136i	$0.711563\pi$
$500$			1.61041e40i			0.527700i
$501$	−1.83061e40	+	8.79658e39i	−0.582145	+	0.279736i
$502$	−1.69565e40			−0.523335
$503$		−	4.79985e39i		−	0.143783i	−0.997412	−	0.0718916i	$-0.977096\pi$
$503$		−	4.79985e39i		−	0.143783i	0.997412	−	0.0718916i	$-0.0229036\pi$
$504$	−2.68725e39	−	2.15050e39i	−0.0781357	−	0.0625291i
$505$	3.90023e39			0.110083
$506$		−	4.23200e40i		−	1.15954i
$507$	1.32040e40	+	2.74783e40i	0.351227	+	0.730921i
$508$	−2.97071e40			−0.767194
$509$			3.70503e39i			0.0929020i	0.998921	+	0.0464510i	$0.0147911\pi$
$509$			3.70503e39i			0.0929020i	−0.998921	+	0.0464510i	$0.985209\pi$
$510$	1.05225e40	−	5.05631e39i	0.256191	−	0.123107i
$511$	−9.77495e36			−0.000231101
$512$			1.92493e39i			0.0441942i
$513$	−4.01152e38	−	9.26391e37i	−0.00894434	−	0.00206554i
$514$	−8.61910e39			−0.186644
$515$		−	3.14060e40i		−	0.660547i
$516$	−1.52624e40	−	3.17620e40i	−0.311802	−	0.648876i
$517$	−2.26047e40			−0.448581
$518$		−	1.81842e40i		−	0.350548i
$519$	−8.38471e40	+	4.02907e40i	−1.57028	+	0.754561i
$520$	−1.82263e40			−0.331626
$521$		−	6.39183e40i		−	1.12995i	−0.825108	−	0.564975i	$-0.808886\pi$
$521$		−	6.39183e40i		−	1.12995i	0.825108	−	0.564975i	$-0.191114\pi$
$522$	2.88798e40	−	3.60878e40i	0.496062	−	0.619874i
$523$	9.20196e40			1.53587			0.767936	−	0.640526i	$-0.221284\pi$
$523$	9.20196e40			1.53587			0.767936	+	0.640526i	$0.221284\pi$
$524$			3.12525e39i			0.0506892i
$525$	−3.99919e39	−	8.32253e39i	−0.0630351	−	0.131179i
$526$	1.73009e40			0.265023
$527$			1.32625e39i			0.0197454i
$528$	1.83642e40	−	8.82450e39i	0.265744	−	0.127697i
$529$	−6.63626e40			−0.933444
$530$		−	2.71592e40i		−	0.371347i
$531$	−4.87390e39	−	3.90040e39i	−0.0647826	−	0.0518432i
$532$	1.00542e38			0.00129919
$533$			8.34455e40i			1.04832i
$534$	3.92734e40	+	8.17299e40i	0.479711	+	0.998303i
$535$	1.75701e40			0.208673
$536$		−	3.06406e40i		−	0.353855i
$537$	−1.30107e41	+	6.25200e40i	−1.46113	+	0.702110i
$538$	8.76682e39			0.0957432
$539$			1.02141e41i			1.08484i
$540$	7.59140e39	−	3.28728e40i	0.0784179	−	0.339571i
$541$	1.33893e41			1.34524			0.672619	−	0.739989i	$-0.265169\pi$
$541$	1.33893e41			1.34524			0.672619	+	0.739989i	$0.265169\pi$
$542$			5.68697e40i			0.555765i
$543$	−2.23903e40	−	4.65953e40i	−0.212844	−	0.442940i
$544$	1.10245e40			0.101947
$545$			1.26639e41i			1.13925i
$546$	2.77386e40	−	1.33291e40i	0.242770	−	0.116657i
$547$	−1.31885e39			−0.0112302			−0.00561508	−	0.999984i	$-0.501787\pi$
$547$	−1.31885e39			−0.0112302			−0.00561508	+	0.999984i	$0.501787\pi$
$548$			4.27892e40i			0.354508i
$549$	1.20722e41	−	1.50852e41i	0.973194	−	1.21609i
$550$	5.46598e40			0.428773
$551$			1.35021e39i			0.0103069i
$552$	−2.86623e40	−	5.96478e40i	−0.212924	−	0.443107i
$553$	−6.18910e40			−0.447456
$554$		−	6.51370e40i		−	0.458333i
$555$	1.60663e41	−	7.72027e40i	1.10033	−	0.528735i
$556$	−1.65423e40			−0.110274
$557$			9.73108e40i			0.631442i	0.948852	+	0.315721i	$0.102246\pi$
$557$			9.73108e40i			0.631442i	−0.948852	+	0.315721i	$0.897754\pi$
$558$	2.99253e39	+	2.39481e39i	0.0189028	+	0.0151272i
$559$	3.15088e41			1.93756
$560$			8.23901e39i			0.0493236i
$561$	−5.05398e40	−	1.05176e41i	−0.294571	−	0.613018i
$562$	−1.66462e41			−0.944648
$563$		−	1.53661e41i		−	0.849061i	−0.905414	−	0.424531i	$-0.860439\pi$
$563$		−	1.53661e41i		−	0.849061i	0.905414	−	0.424531i	$-0.139561\pi$
$564$	−3.18602e40	+	1.53096e40i	−0.171420	+	0.0823718i
$565$	−2.25139e41			−1.17957
$566$			3.90267e40i			0.199120i
$567$	1.24870e40	+	5.55809e40i	0.0620456	+	0.276172i
$568$	−5.10000e39			−0.0246800
$569$			8.35023e40i			0.393563i	0.980447	+	0.196782i	$0.0630490\pi$
$569$			8.35023e40i			0.393563i	−0.980447	+	0.196782i	$0.936951\pi$
$570$	4.26860e38	+	8.88319e38i	0.00195958	+	0.00407799i
$571$	−2.85244e41			−1.27549			−0.637743	−	0.770249i	$-0.720132\pi$
$571$	−2.85244e41			−1.27549			−0.637743	+	0.770249i	$0.720132\pi$
$572$			1.82179e41i			0.793519i
$573$	−1.31063e41	+	6.29793e40i	−0.556111	+	0.267226i
$574$	3.77207e40			0.155920
$575$		−	1.77537e41i		−	0.714944i
$576$	1.99068e40	−	2.48754e40i	0.0781025	−	0.0975961i
$577$	2.60269e40			0.0994912			0.0497456	−	0.998762i	$-0.484159\pi$
$577$	2.60269e40			0.0994912			0.0497456	+	0.998762i	$0.484159\pi$
$578$			1.26707e41i			0.471936i
$579$	−1.53384e41	−	3.19200e41i	−0.556674	−	1.15847i
$580$	−1.10644e41			−0.391299
$581$			1.61130e41i			0.555309i
$582$	−1.71758e41	+	8.25344e40i	−0.576864	+	0.277198i
$583$	−2.71467e41			−0.888564
$584$		−	9.04851e37i		−	0.000288658i
$585$	2.35534e41	+	1.88489e41i	0.732345	+	0.586068i
$586$	−9.64439e40			−0.292288
$587$		−	5.77727e41i		−	1.70668i	−0.521358	−	0.853338i	$-0.674574\pi$
$587$		−	5.77727e41i		−	1.70668i	0.521358	−	0.853338i	$-0.325426\pi$
$588$	6.91776e40	+	1.43962e41i	0.199207	+	0.414561i
$589$	−1.11964e38			−0.000314303
$590$			1.49432e40i			0.0408944i
$591$	4.47642e41	−	2.15104e41i	1.19431	−	0.573899i
$592$	1.68328e41			0.437855
$593$		−	1.25451e41i		−	0.318165i	−0.987265	−	0.159083i	$-0.949146\pi$
$593$		−	1.25451e41i		−	0.318165i	0.987265	−	0.159083i	$-0.0508536\pi$
$594$	−3.28576e41	−	7.58789e40i	−0.812530	−	0.187640i
$595$	4.71865e40			0.113779
$596$		−	7.15719e40i		−	0.168286i
$597$	2.04863e41	+	4.26331e41i	0.469731	+	0.977534i
$598$	5.91724e41			1.32313
$599$			2.45816e41i			0.536053i	0.963412	+	0.268026i	$0.0863714\pi$
$599$			2.45816e41i			0.536053i	−0.963412	+	0.268026i	$0.913629\pi$
$600$	7.70402e40	−	3.70198e40i	0.163851	−	0.0787346i
$601$	5.12731e40			0.106359			0.0531793	−	0.998585i	$-0.483065\pi$
$601$	5.12731e40			0.106359			0.0531793	+	0.998585i	$0.483065\pi$
$602$		−	1.42432e41i		−	0.288178i
$603$	−3.16873e41	+	3.95961e41i	−0.625353	+	0.781434i
$604$	4.15617e41			0.800091
$605$			1.45063e41i			0.272413i
$606$	−2.64032e40	−	5.49464e40i	−0.0483690	−	0.100658i
$607$	5.38034e41			0.961567			0.480784	−	0.876839i	$-0.340352\pi$
$607$	5.38034e41			0.961567			0.480784	+	0.876839i	$0.340352\pi$
$608$			9.30699e38i			0.00162277i
$609$	1.68389e41	−	8.09155e40i	0.286454	−	0.137649i
$610$	−4.62508e41			−0.767665
$611$		−	3.16062e41i		−	0.511864i
$612$	−1.42467e41	−	1.14011e41i	−0.225134	−	0.180167i
$613$	−4.75543e41			−0.733301			−0.366651	−	0.930359i	$-0.619496\pi$
$613$	−4.75543e41			−0.733301			−0.366651	+	0.930359i	$0.619496\pi$
$614$		−	5.50492e41i		−	0.828372i
$615$	1.60147e41	+	3.33274e41i	0.235175	+	0.489412i
$616$	8.23520e40			0.118022
$617$			7.84060e41i			1.09666i	0.836262	+	0.548330i	$0.184736\pi$
$617$			7.84060e41i			1.09666i	−0.836262	+	0.548330i	$0.815264\pi$
$618$	−4.42447e41	+	2.12607e41i	−0.603996	+	0.290236i
$619$	3.82475e41			0.509616			0.254808	−	0.966992i	$-0.417988\pi$
$619$	3.82475e41			0.509616			0.254808	+	0.966992i	$0.417988\pi$
$620$		−	9.17499e39i		−	0.0119325i
$621$	−2.46458e41	+	1.06723e42i	−0.312873	+	1.35483i
$622$	8.42258e41			1.04373
$623$			3.66507e41i			0.443365i
$624$	1.23386e41	+	2.56772e41i	0.145712	+	0.303234i
$625$	−1.92087e41			−0.221461
$626$		−	8.65248e41i		−	0.973925i
$627$	8.87908e39	−	4.26663e39i	0.00975787	−	0.00468891i
$628$	3.52834e41			0.378596
$629$		−	9.64050e41i		−	1.01004i
$630$	8.52046e40	−	1.06471e41i	0.0871675	−	0.108924i
$631$	−4.10177e41			−0.409761			−0.204881	−	0.978787i	$-0.565681\pi$
$631$	−4.10177e41			−0.409761			−0.204881	+	0.978787i	$0.565681\pi$
$632$		−	5.72914e41i		−	0.558899i
$633$	−3.48091e41	−	7.24395e41i	−0.331617	−	0.690113i
$634$	−3.75626e41			−0.349475
$635$		−	1.17702e42i		−	1.06949i
$636$	−3.82619e41	+	1.83858e41i	−0.339555	+	0.163165i
$637$	−1.42815e42			−1.23789
$638$			1.10593e42i			0.936305i
$639$	6.59060e40	+	5.27422e40i	0.0545020	+	0.0436159i
$640$	−7.62671e40			−0.0616081
$641$			4.78275e41i			0.377404i	0.982034	+	0.188702i	$0.0604281\pi$
$641$			4.78275e41i			0.377404i	−0.982034	+	0.188702i	$0.939572\pi$
$642$	−1.18943e41	−	2.47527e41i	−0.0916883	−	0.190808i
$643$	−2.12683e42			−1.60165			−0.800825	−	0.598898i	$-0.795605\pi$
$643$	−2.12683e42			−1.60165			−0.800825	+	0.598898i	$0.795605\pi$
$644$		−	2.67483e41i		−	0.196792i
$645$	1.25843e42	−	6.04710e41i	0.904553	−	0.434662i
$646$	5.33031e39			0.00374339
$647$			6.79348e41i			0.466153i	0.972458	+	0.233076i	$0.0748792\pi$
$647$			6.79348e41i			0.466153i	−0.972458	+	0.233076i	$0.925121\pi$
$648$	−5.14503e41	+	1.15590e41i	−0.344955	+	0.0774986i
$649$	1.49363e41			0.0978527
$650$			7.64262e41i			0.489262i
$651$	6.70980e39	+	1.39634e40i	0.00419754	+	0.00873530i
$652$	−5.89499e41			−0.360387
$653$		−	2.80383e42i		−	1.67515i	−0.546322	−	0.837576i	$-0.683972\pi$
$653$		−	2.80383e42i		−	1.67515i	0.546322	−	0.837576i	$-0.316028\pi$
$654$	1.78408e42	−	8.57299e41i	1.04172	−	0.500572i
$655$	−1.23825e41			−0.0706623
$656$			3.49174e41i			0.194753i
$657$	−9.35761e38	+	1.16932e39i	−0.000510134	+	0.000637458i
$658$	−1.42873e41			−0.0761309
$659$			2.53176e42i			1.31869i	0.751842	+	0.659343i	$0.229165\pi$
$659$			2.53176e42i			1.31869i	−0.751842	+	0.659343i	$0.770835\pi$
$660$	3.49633e41	+	7.27605e41i	0.178014	+	0.370456i
$661$	3.34928e42			1.66698			0.833488	−	0.552537i	$-0.186340\pi$
$661$	3.34928e42			1.66698			0.833488	+	0.552537i	$0.186340\pi$
$662$			2.09296e42i			1.01834i
$663$	1.47059e42	−	7.06655e41i	0.699500	−	0.336128i
$664$	−1.49155e42			−0.693614
$665$			3.98355e39i			0.00181111i
$666$	−2.17526e42	−	1.74078e42i	−0.966937	−	0.773804i
$667$	3.59211e42			1.56121
$668$		−	7.59907e41i		−	0.322934i
$669$	−8.91203e41	−	1.85464e42i	−0.370327	−	0.770669i
$670$	1.21400e42			0.493285
$671$			4.62295e42i			1.83688i
$672$	1.16071e41	−	5.57752e40i	0.0451009	−	0.0216721i
$673$	7.11464e41			0.270350			0.135175	−	0.990822i	$-0.456840\pi$
$673$	7.11464e41			0.270350			0.135175	+	0.990822i	$0.456840\pi$
$674$			1.67712e42i			0.623254i
$675$	−1.37842e42	−	3.18321e41i	−0.500984	−	0.115693i
$676$	−1.14065e42			−0.405464
$677$			4.34336e41i			0.151007i	0.997146	+	0.0755033i	$0.0240563\pi$
$677$			4.34336e41i			0.151007i	−0.997146	+	0.0755033i	$0.975944\pi$
$678$	1.52411e42	+	3.17175e42i	0.518287	+	1.07858i
$679$	−7.70228e41			−0.256196
$680$			4.36798e41i			0.142117i
$681$	9.70845e41	−	4.66517e41i	0.308989	−	0.148477i
$682$	−9.17076e40			−0.0285522
$683$		−	7.91005e41i		−	0.240918i	−0.992718	−	0.120459i	$-0.961563\pi$
$683$		−	7.91005e41i		−	0.240918i	0.992718	−	0.120459i	$-0.0384366\pi$
$684$	9.62493e39	−	1.20272e40i	0.00286785	−	0.00358363i
$685$	−1.69534e42			−0.494195
$686$			1.34739e42i			0.384265i
$687$	−1.71415e42	−	3.56724e42i	−0.478298	−	0.995363i
$688$	1.31847e42			0.359952
$689$		−	3.79569e42i		−	1.01392i
$690$	2.36329e42	−	1.13562e42i	0.617705	−	0.296823i
$691$	1.94866e42			0.498387			0.249193	−	0.968454i	$-0.419835\pi$
$691$	1.94866e42			0.498387			0.249193	+	0.968454i	$0.419835\pi$
$692$		−	3.48058e42i		−	0.871084i
$693$	−1.06422e42	−	8.51652e41i	−0.260634	−	0.208576i
$694$	−1.82196e42			−0.436663
$695$		−	6.55420e41i		−	0.153726i
$696$	7.49021e41	+	1.55875e42i	0.171931	+	0.357798i
$697$	1.99979e42			0.449255
$698$		−	1.25714e42i		−	0.276410i
$699$	−6.08622e42	+	2.92459e42i	−1.30976	+	0.629372i
$700$	3.45477e41			0.0727693
$701$			2.60093e42i			0.536239i	0.963386	+	0.268119i	$0.0864022\pi$
$701$			2.60093e42i			0.536239i	−0.963386	+	0.268119i	$0.913598\pi$
$702$	1.06095e42	−	4.59420e42i	0.214111	−	0.927157i
$703$	8.13863e40			0.0160776
$704$			7.62319e41i			0.147417i
$705$	−6.06580e41	−	1.26232e42i	−0.114829	−	0.238965i
$706$	−5.27971e42			−0.978452
$707$		−	2.46400e41i		−	0.0447043i
$708$	2.10520e41	−	1.01160e41i	0.0373933	−	0.0179685i
$709$	−2.10921e41			−0.0366798			−0.0183399	−	0.999832i	$-0.505838\pi$
$709$	−2.10921e41			−0.0366798			−0.0183399	+	0.999832i	$0.505838\pi$
$710$		−	2.02066e41i		−	0.0344047i
$711$	−5.92486e42	+	7.40363e42i	−0.987720	+	1.23424i
$712$	−3.39269e42			−0.553789
$713$			2.97870e41i			0.0476084i
$714$	−3.19436e41	−	6.64763e41i	−0.0499932	−	0.104038i
$715$	−7.21806e42			−1.10619
$716$		−	5.40089e42i		−	0.810532i
$717$	2.74268e42	−	1.31793e42i	0.403076	−	0.193689i
$718$	3.20810e42			0.461723
$719$			6.06364e42i			0.854674i	0.904093	+	0.427337i	$0.140548\pi$
$719$			6.06364e42i			0.854674i	−0.904093	+	0.427337i	$0.859452\pi$
$720$	9.85581e41	+	7.88724e41i	0.136052	+	0.108877i
$721$	−1.98409e42			−0.268246
$722$		−	5.33957e42i		−	0.707047i
$723$	2.02379e42	+	4.21161e42i	0.262476	+	0.546227i
$724$	1.93422e42			0.245712
$725$			4.63951e42i			0.577300i
$726$	2.04365e42	−	9.82028e41i	0.249091	−	0.119695i
$727$	7.82360e42			0.934094			0.467047	−	0.884232i	$-0.345318\pi$
$727$	7.82360e42			0.934094			0.467047	+	0.884232i	$0.345318\pi$
$728$			1.15146e42i			0.134672i
$729$	7.84417e42	+	3.82705e42i	0.898740	+	0.438481i
$730$	3.58509e39			0.000402399
$731$		−	7.55116e42i		−	0.830335i
$732$	3.13102e42	+	6.51581e42i	0.337302	+	0.701943i
$733$	7.57461e42			0.799467			0.399734	−	0.916631i	$-0.369103\pi$
$733$	7.57461e42			0.799467			0.399734	+	0.916631i	$0.369103\pi$
$734$			5.36698e41i			0.0554996i
$735$	−5.70389e42	+	2.74087e42i	−0.577911	+	0.277701i
$736$	2.47604e42			0.245805
$737$		−	1.21344e43i		−	1.18034i
$738$	3.61102e42	−	4.51229e42i	0.344179	−	0.430082i
$739$	−3.80040e41			−0.0354946			−0.0177473	−	0.999843i	$-0.505649\pi$
$739$	−3.80040e41			−0.0354946			−0.0177473	+	0.999843i	$0.505649\pi$
$740$			6.66928e42i			0.610384i
$741$	5.96567e40	+	1.24149e41i	0.00535040	+	0.0111345i
$742$	−1.71580e42			−0.150803
$743$		−	1.94215e43i		−	1.67283i	−0.548097	−	0.836415i	$-0.684648\pi$
$743$		−	1.94215e43i		−	1.67283i	0.548097	−	0.836415i	$-0.315352\pi$
$744$	−1.29257e41	+	6.21114e40i	−0.0109109	+	0.00524297i
$745$	2.83573e42			0.234596
$746$		−	2.64885e42i		−	0.214771i
$747$	1.92750e43	+	1.54251e43i	1.53174	+	1.22580i
$748$	4.36596e42			0.340060
$749$		−	1.11000e42i		−	0.0847415i
$750$	4.31942e42	+	8.98894e42i	0.323226	+	0.672651i
$751$	−2.31437e42			−0.169759			−0.0848796	−	0.996391i	$-0.527051\pi$
$751$	−2.31437e42			−0.169759			−0.0848796	+	0.996391i	$0.527051\pi$
$752$		−	1.32255e42i		−	0.0950920i
$753$	−9.46470e42	+	4.54803e42i	−0.667087	+	0.320552i
$754$	−1.54633e43			−1.06839
$755$			1.64671e43i			1.11535i
$756$	−2.07676e42	−	4.79592e41i	−0.137899	−	0.0318453i
$757$	−9.70553e42			−0.631802			−0.315901	−	0.948792i	$-0.602307\pi$
$757$	−9.70553e42			−0.631802			−0.315901	+	0.948792i	$0.602307\pi$
$758$			1.62880e43i			1.03951i
$759$	−1.13510e43	−	2.36220e43i	−0.710243	−	1.47805i
$760$	−3.68750e40			−0.00226219
$761$			4.53894e42i			0.273014i	0.990639	+	0.136507i	$0.0435876\pi$
$761$			4.53894e42i			0.273014i	−0.990639	+	0.136507i	$0.956412\pi$
$762$	−1.65818e43	+	7.96800e42i	−0.977930	+	0.469921i
$763$	8.00049e42			0.462646
$764$		−	5.44056e42i		−	0.308492i
$765$	4.51719e42	−	5.64463e42i	0.251158	−	0.313844i
$766$	−2.07342e42			−0.113046
$767$			2.08842e42i			0.111657i
$768$	5.16301e41	+	1.07445e42i	0.0270698	+	0.0563336i
$769$	−1.41690e43			−0.728527			−0.364263	−	0.931296i	$-0.618679\pi$
$769$	−1.41690e43			−0.728527			−0.364263	+	0.931296i	$0.618679\pi$
$770$			3.26285e42i			0.164527i
$771$	−4.81098e42	+	2.31180e42i	−0.237913	+	0.114323i
$772$	1.32503e43			0.642638
$773$		−	2.72275e43i		−	1.29514i	−0.762008	−	0.647568i	$-0.775786\pi$
$773$		−	2.72275e43i		−	1.29514i	0.762008	−	0.647568i	$-0.224214\pi$
$774$	−1.70383e43	−	1.36351e43i	−0.794898	−	0.636127i
$775$	−3.84724e41			−0.0176045
$776$		−	7.12987e42i		−	0.320004i
$777$	−4.87734e42	−	1.01500e43i	−0.214718	−	0.446838i
$778$	6.27541e42			0.270987
$779$			1.68825e41i			0.00715113i
$780$	−1.01735e43	+	4.88863e42i	−0.422718	+	0.203127i
$781$	−2.01972e42			−0.0823240
$782$		−	1.41808e43i		−	0.567022i
$783$	6.44058e42	−	2.78895e43i	0.252638	−	1.09399i
$784$	−5.97602e42			−0.229970
$785$			1.39796e43i			0.527775i
$786$	8.38249e41	+	1.74444e42i	0.0310481	+	0.0646127i
$787$	4.67769e43			1.69985			0.849925	−	0.526903i	$-0.176647\pi$
$787$	4.67769e43			1.69985			0.849925	+	0.526903i	$0.176647\pi$
$788$			1.85821e43i			0.662523i
$789$	9.65696e42	−	4.64042e42i	0.337820	−	0.162331i
$790$	2.26993e43			0.779123
$791$			1.42233e43i			0.479019i
$792$	7.88360e42	−	9.85126e42i	0.260523	−	0.325547i
$793$	−6.46387e43			−2.09602
$794$			1.93466e43i			0.615596i
$795$	−7.28461e42	−	1.51596e43i	−0.227457	−	0.473350i
$796$	−1.76974e43			−0.542268
$797$			4.55004e43i			1.36817i	0.729403	+	0.684085i	$0.239798\pi$
$797$			4.55004e43i			1.36817i	−0.729403	+	0.684085i	$0.760202\pi$
$798$	5.61202e40	−	2.69672e40i	0.00165606	−	0.000795779i
$799$	−7.57451e42			−0.219358
$800$			3.19802e42i			0.0908931i
$801$	4.38429e43	+	3.50859e43i	1.22296	+	0.978689i
$802$	3.02134e43			0.827150
$803$		−	3.58343e40i		−	0.000962866i
$804$	−8.21837e42	−	1.71029e43i	−0.216743	−	0.451053i
$805$	1.05979e43			0.274335
$806$		−	1.28227e42i		−	0.0325802i
$807$	4.89343e42	−	2.35142e42i	0.122042	−	0.0586445i
$808$	2.28088e42			0.0558383
$809$			1.53851e43i			0.369719i	0.982765	+	0.184859i	$0.0591830\pi$
$809$			1.53851e43i			0.369719i	−0.982765	+	0.184859i	$0.940817\pi$
$810$	−4.57975e42	−	2.03850e43i	−0.108035	−	0.480878i
$811$	−1.76792e43			−0.409402			−0.204701	−	0.978825i	$-0.565622\pi$
$811$	−1.76792e43			−0.409402			−0.204701	+	0.978825i	$0.565622\pi$
$812$			6.99002e42i			0.158905i
$813$	1.52535e43	+	3.17433e43i	0.340417	+	0.708425i
$814$	6.66620e43			1.46054
$815$		−	2.33564e43i		−	0.502391i
$816$	6.15360e42	−	2.95696e42i	0.129950	−	0.0624444i
$817$	6.37479e41			0.0132171
$818$		−	2.10668e43i		−	0.428843i
$819$	1.19079e43	−	1.48800e43i	0.238000	−	0.297403i
$820$	−1.38345e43			−0.271492
$821$			7.78397e43i			1.49987i	0.661511	+	0.749935i	$0.269915\pi$
$821$			7.78397e43i			1.49987i	−0.661511	+	0.749935i	$0.730085\pi$
$822$	1.14769e43	+	2.38839e43i	0.217143	+	0.451886i
$823$	−3.87235e42			−0.0719411			−0.0359705	−	0.999353i	$-0.511452\pi$
$823$	−3.87235e42			−0.0719411			−0.0359705	+	0.999353i	$0.511452\pi$
$824$		−	1.83664e43i		−	0.335055i
$825$	3.05098e43	−	1.46608e43i	0.546551	−	0.262632i
$826$	9.44048e41			0.0166071
$827$		−	1.09288e43i		−	0.188795i	−0.995535	−	0.0943975i	$-0.969908\pi$
$827$		−	1.09288e43i		−	0.188795i	0.995535	−	0.0943975i	$-0.0300925\pi$
$828$	−3.19973e43	−	2.56063e43i	−0.542823	−	0.434401i
$829$	−6.07876e43			−1.01274			−0.506369	−	0.862317i	$-0.669013\pi$
$829$	−6.07876e43			−1.01274			−0.506369	+	0.862317i	$0.669013\pi$
$830$		−	5.90965e43i		−	0.966920i
$831$	−1.74709e43	−	3.63579e43i	−0.280738	−	0.584230i
$832$	−1.06589e43			−0.168213
$833$			3.42259e43i			0.530493i
$834$	−9.23354e42	+	4.43696e42i	−0.140565	+	0.0675452i
$835$	3.01081e43			0.450180
$836$			3.68580e41i			0.00541299i
$837$	2.31269e42	+	5.34076e41i	0.0333607	+	0.00770408i
$838$	−8.58913e43			−1.21700
$839$		−	3.23195e43i		−	0.449816i	−0.974380	−	0.224908i	$-0.927792\pi$
$839$		−	3.23195e43i		−	0.449816i	0.974380	−	0.224908i	$-0.0722082\pi$
$840$	2.20985e42	+	4.59882e42i	0.0302116	+	0.0628720i
$841$	−1.94081e43			−0.260641
$842$			8.54826e42i			0.112771i
$843$	−9.29151e43	+	4.46481e43i	−1.20413	+	0.578615i
$844$	3.00704e43			0.382827
$845$		−	4.51935e43i		−	0.565230i
$846$	−1.36773e43	+	1.70910e43i	−0.168052	+	0.209996i
$847$	9.16449e42			0.110626
$848$		−	1.58829e43i		−	0.188361i
$849$	1.04677e43	+	2.17838e43i	0.121965	+	0.253815i
$850$	1.83157e43			0.209672
$851$		−	2.16521e44i		−	2.43532i
$852$	−2.84670e42	+	1.36791e42i	−0.0314592	+	0.0151170i
$853$	−1.01699e44			−1.10428			−0.552140	−	0.833751i	$-0.686189\pi$
$853$	−1.01699e44			−1.10428			−0.552140	+	0.833751i	$0.686189\pi$
$854$			2.92193e43i			0.311746i
$855$	4.76527e41	+	3.81347e41i	0.00499569	+	0.00399787i
$856$	1.02751e43			0.105847
$857$			6.47231e43i			0.655159i	0.944824	+	0.327579i	$0.106233\pi$
$857$			6.47231e43i			0.655159i	−0.944824	+	0.327579i	$0.893767\pi$
$858$	4.88637e43	+	1.01688e44i	0.486046	+	1.01149i
$859$	−1.29699e43			−0.126777			−0.0633885	−	0.997989i	$-0.520191\pi$
$859$	−1.29699e43			−0.126777			−0.0633885	+	0.997989i	$0.520191\pi$
$860$			5.22388e43i			0.501784i
$861$	2.10548e43	−	1.01174e43i	0.198749	−	0.0955038i
$862$	−1.94592e43			−0.180516
$863$			3.53421e43i			0.322204i	0.986938	+	0.161102i	$0.0515048\pi$
$863$			3.53421e43i			0.322204i	−0.986938	+	0.161102i	$0.948495\pi$
$864$	4.43950e42	−	1.92242e43i	0.0397766	−	0.172243i
$865$	1.37903e44			1.21432
$866$			6.34500e43i			0.549115i
$867$	3.39852e43	+	7.07249e43i	0.289070	+	0.601570i
$868$	−5.79637e41			−0.00484574
$869$		−	2.26888e44i		−	1.86430i
$870$	−6.17589e43	+	2.96768e43i	−0.498782	+	0.239678i
$871$	1.69665e44			1.34685
$872$			7.40592e43i			0.577872i
$873$	−7.37343e43	+	9.21376e43i	−0.565530	+	0.706680i
$874$	1.19716e42			0.00902571
$875$			4.03097e43i			0.298737i
$876$	−2.42698e40	−	5.05066e40i	−0.000176809	−	0.000367948i
$877$	1.43246e43			0.102586			0.0512931	−	0.998684i	$-0.483666\pi$
$877$	1.43246e43			0.102586			0.0512931	+	0.998684i	$0.483666\pi$
$878$		−	1.35982e44i		−	0.957332i
$879$	−5.38327e43	+	2.58680e43i	−0.372575	+	0.179032i
$880$	−3.02036e43			−0.205503
$881$		−	1.32246e44i		−	0.884597i	−0.896868	−	0.442298i	$-0.854163\pi$
$881$		−	1.32246e44i		−	0.884597i	0.896868	−	0.442298i	$-0.145837\pi$
$882$	7.72266e43	+	6.18016e43i	0.507853	+	0.406416i
$883$	2.69909e44			1.74505			0.872523	−	0.488573i	$-0.162482\pi$
$883$	2.69909e44			1.74505			0.872523	+	0.488573i	$0.162482\pi$
$884$			6.10455e43i			0.388034i
$885$	4.00804e42	+	8.34095e42i	0.0250486	+	0.0521275i
$886$	−1.48706e44			−0.913739
$887$			2.18727e44i			1.32144i	0.750632	+	0.660720i	$0.229749\pi$
$887$			2.18727e44i			1.32144i	−0.750632	+	0.660720i	$0.770251\pi$
$888$	9.39567e43	−	4.51487e43i	0.558128	−	0.268195i
$889$	−7.43590e43			−0.434317
$890$		−	1.34421e44i		−	0.772000i
$891$	−2.03756e44	+	4.57763e43i	−1.15065	+	0.258509i
$892$	7.69880e43			0.427514
$893$		−	6.39450e41i		−	0.00349168i
$894$	−1.91969e43	−	3.99498e43i	−0.103079	−	0.214512i
$895$	2.13987e44			1.12991
$896$			4.81823e42i			0.0250188i
$897$	3.30287e44	−	1.58711e44i	1.68657	−	0.810441i
$898$	−1.05670e44			−0.530647
$899$		−	7.78411e42i		−	0.0384427i
$900$	3.30726e43	−	4.13272e43i	0.160632	−	0.200724i
$901$	−9.09647e43			−0.434511
$902$			1.38281e44i			0.649630i
$903$	−3.82030e43	−	7.95024e43i	−0.176515	−	0.367336i
$904$	−1.31663e44			−0.598323
$905$			7.66352e43i			0.342531i
$906$	2.31988e44	−	1.11476e44i	1.01986	−	0.490071i
$907$	−7.85257e43			−0.339549			−0.169774	−	0.985483i	$-0.554304\pi$
$907$	−7.85257e43			−0.339549			−0.169774	+	0.985483i	$0.554304\pi$
$908$			4.03008e43i			0.171406i
$909$	−2.94753e43	−	2.35880e43i	−0.123310	−	0.0986807i
$910$	−4.56217e43			−0.187737
$911$			1.47451e44i			0.596858i	0.954432	+	0.298429i	$0.0964626\pi$
$911$			1.47451e44i			0.596858i	−0.954432	+	0.298429i	$0.903537\pi$
$912$	2.49631e41	+	5.19495e41i	0.000993975	+	0.00206851i
$913$	−5.90692e44			−2.31366
$914$		−	1.65367e44i		−	0.637172i
$915$	−2.58161e44	+	1.24053e44i	−0.978531	+	0.470210i
$916$	1.48080e44			0.552159
$917$			7.82271e42i			0.0286957i
$918$	−1.10101e44	−	2.54260e43i	−0.397331	−	0.0917565i
$919$	−4.83654e44			−1.71712			−0.858562	−	0.512709i	$-0.828642\pi$
$919$	−4.83654e44			−1.71712			−0.858562	+	0.512709i	$0.828642\pi$
$920$			9.81027e43i			0.342660i
$921$	−1.47652e44	−	3.07272e44i	−0.507394	−	1.05591i
$922$	1.46622e44			0.495720
$923$		−	2.82401e43i		−	0.0939378i
$924$	4.59670e43	−	2.20883e43i	0.150441	−	0.0722908i
$925$	2.79655e44			0.900527
$926$		−	9.93904e43i		−	0.314905i
$927$	−1.89938e44	+	2.37345e44i	−0.592129	+	0.739918i
$928$	−6.47054e43			−0.198482
$929$			5.12269e44i			1.54619i	0.634292	+	0.773093i	$0.281292\pi$
$929$			5.12269e44i			1.54619i	−0.634292	+	0.773093i	$0.718708\pi$
$930$	−2.46090e42	−	5.12127e42i	−0.00730887	−	0.0152101i
$931$	−2.88939e42			−0.00844426
$932$		−	2.52645e44i		−	0.726562i
$933$	4.70129e44	−	2.25909e44i	1.33043	−	0.639306i
$934$	−4.83766e44			−1.34720
$935$			1.72983e44i			0.474054i
$936$	1.37742e44	+	1.10230e44i	0.371474	+	0.297277i
$937$	6.54877e44			1.73806			0.869032	−	0.494756i	$-0.164743\pi$
$937$	6.54877e44			1.73806			0.869032	+	0.494756i	$0.164743\pi$
$938$		−	7.66955e43i		−	0.200321i
$939$	−2.32075e44	−	4.82961e44i	−0.596548	−	1.24145i
$940$	5.24004e43			0.132561
$941$		−	4.18353e44i		−	1.04159i	−0.853680	−	0.520797i	$-0.825635\pi$
$941$		−	4.18353e44i		−	1.04159i	0.853680	−	0.520797i	$-0.174365\pi$
$942$	1.96944e44	−	9.46367e43i	0.482591	−	0.231897i
$943$	4.49144e44			1.08320
$944$			8.73889e42i			0.0207432i
$945$	1.90018e43	−	8.22829e43i	0.0443933	−	0.192235i
$946$	5.22147e44			1.20068
$947$			6.18689e44i			1.40030i	0.713993	+	0.700152i	$0.246885\pi$
$947$			6.18689e44i			1.40030i	−0.713993	+	0.700152i	$0.753115\pi$
$948$	−1.53666e44	−	3.19787e44i	−0.342337	−	0.712420i
$949$	5.01041e41			0.00109870
$950$			1.54624e42i			0.00333750i
$951$	−2.09665e44	+	1.00750e44i	−0.445471	+	0.214060i
$952$	2.75950e43			0.0577133
$953$		−	2.20104e44i		−	0.453142i	−0.973995	−	0.226571i	$-0.927248\pi$
$953$		−	2.20104e44i		−	0.453142i	0.973995	−	0.226571i	$-0.0727515\pi$
$954$	−1.64255e44	+	2.05251e44i	−0.332883	+	0.415967i
$955$	2.15559e44			0.430047
$956$			1.13851e44i			0.223599i
$957$	2.96631e44	+	6.17304e44i	0.573505	+	1.19349i
$958$	−3.81312e43			−0.0725768
$959$			1.07104e44i			0.200691i
$960$	−4.25705e43	+	2.04562e43i	−0.0785308	+	0.0377361i
$961$	−5.49973e44			−0.998828
$962$			9.32079e44i			1.66658i
$963$	−1.32782e44	−	1.06261e44i	−0.233747	−	0.187059i
$964$	−1.74828e44			−0.303009
$965$			5.24987e44i			0.895858i
$966$	−7.17438e43	−	1.49303e44i	−0.120539	−	0.250848i
$967$	1.02714e45			1.69915			0.849577	−	0.527465i	$-0.176857\pi$
$967$	1.02714e45			1.69915			0.849577	+	0.527465i	$0.176857\pi$
$968$			8.48341e43i			0.138178i
$969$	2.97525e42	−	1.42969e42i	0.00477164	−	0.00229290i
$970$	2.82491e44			0.446096
$971$		−	5.43527e44i		−	0.845148i	−0.906328	−	0.422574i	$-0.861127\pi$
$971$		−	5.43527e44i		−	0.845148i	0.906328	−	0.422574i	$-0.138873\pi$
$972$	−2.56180e44	+	2.02518e44i	−0.392239	+	0.310078i
$973$	−4.14066e43			−0.0624276
$974$		−	2.95876e43i		−	0.0439264i
$975$	2.04989e44	+	4.26593e44i	0.299682	+	0.623655i
$976$	−2.70478e44			−0.389390
$977$		−	1.03285e45i		−	1.46426i	−0.681163	−	0.732132i	$-0.738525\pi$
$977$		−	1.03285e45i		−	1.46426i	0.681163	−	0.732132i	$-0.261475\pi$
$978$	−3.29045e44	+	1.58115e44i	−0.459380	+	0.220744i
$979$	−1.34359e45			−1.84725
$980$		−	2.36774e44i		−	0.320585i
$981$	7.65891e44	−	9.57049e44i	1.02125	−	1.27614i
$982$	3.93016e44			0.516105
$983$		−	4.70541e43i		−	0.0608547i	−0.999537	−	0.0304274i	$-0.990313\pi$
$983$		−	4.70541e43i		−	0.0608547i	0.999537	−	0.0304274i	$-0.00968683\pi$
$984$	9.36549e43	+	1.94901e44i	0.119290	+	0.248249i
$985$	−7.36236e44			−0.923578
$986$			3.70581e44i			0.457857i
$987$	−7.97482e43	+	3.83211e43i	−0.0970429	+	0.0466316i
$988$	−5.15354e42			−0.00617663
$989$		−	1.69595e45i		−	2.00203i
$990$	3.90314e44	+	3.12354e44i	0.453823	+	0.363178i
$991$	7.30066e44			0.836098			0.418049	−	0.908425i	$-0.362714\pi$
$991$	7.30066e44			0.836098			0.418049	+	0.908425i	$0.362714\pi$
$992$		−	5.36560e42i		−	0.00605261i
$993$	5.61371e44	+	1.16824e45i	0.623751	+	1.29806i
$994$	−1.27656e43			−0.0139716
$995$		−	7.01185e44i		−	0.755939i
$996$	−8.32551e44	+	4.00062e44i	−0.884139	+	0.424852i
$997$	−6.83357e44			−0.714858			−0.357429	−	0.933940i	$-0.616347\pi$
$997$	−6.83357e44			−0.714858			−0.357429	+	0.933940i	$0.616347\pi$
$998$		−	8.46453e44i		−	0.872257i
$999$	−1.68109e45	−	3.88218e44i	−1.70651	−	0.394088i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6.31.b.a.5.8	yes	10
3.2	odd	2	inner	6.31.b.a.5.3	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6.31.b.a.5.3	✓	10	3.2	odd	2	inner
6.31.b.a.5.8	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)

\(f(q)\)	\(=\)	\(q+23170.5i q^{2} +(6.21475e6 + 1.29332e7i) q^{3} -5.36871e8 q^{4} -2.12712e10i q^{5} +(-2.99669e11 + 1.43999e11i) q^{6} -1.34382e12 q^{7} -1.24396e13i q^{8} +(-1.28645e14 + 1.60753e14i) q^{9} +O(q^{10})\)	\(q+23170.5i q^{2} +(6.21475e6 + 1.29332e7i) q^{3} -5.36871e8 q^{4} -2.12712e10i q^{5} +(-2.99669e11 + 1.43999e11i) q^{6} -1.34382e12 q^{7} -1.24396e13i q^{8} +(-1.28645e14 + 1.60753e14i) q^{9} +4.92865e14 q^{10} -4.92637e15i q^{11} +(-3.33652e15 - 6.94347e15i) q^{12} +6.88812e16 q^{13} -3.11371e16i q^{14} +(2.75105e17 - 1.32195e17i) q^{15} +2.88230e17 q^{16} -1.65076e18i q^{17} +(-3.72473e18 - 2.98076e18i) q^{18} +1.39359e17 q^{19} +1.14199e19i q^{20} +(-8.35153e18 - 1.73800e19i) q^{21} +1.14146e20 q^{22} -3.70752e20i q^{23} +(1.60883e20 - 7.73087e19i) q^{24} +4.78857e20 q^{25} +1.59601e21i q^{26} +(-2.87855e21 - 6.64752e20i) q^{27} +7.21460e20 q^{28} +9.68870e21i q^{29} +(3.06303e21 + 6.37432e21i) q^{30} -8.03421e20 q^{31} +6.67843e21i q^{32} +(6.37138e22 - 3.06161e22i) q^{33} +3.82488e22 q^{34} +2.85848e22i q^{35} +(6.90657e22 - 8.63038e22i) q^{36} +5.84005e23 q^{37} +3.22901e21i q^{38} +(4.28080e23 + 8.90856e23i) q^{39} -2.64605e23 q^{40} +1.21144e24i q^{41} +(4.02702e23 - 1.93509e23i) q^{42} +4.57437e24 q^{43} +2.64482e24i q^{44} +(3.41942e24 + 2.73644e24i) q^{45} +8.59050e24 q^{46} -4.58851e24i q^{47} +(1.79128e24 + 3.72775e24i) q^{48} -2.07335e25 q^{49} +1.10954e25i q^{50} +(2.13496e25 - 1.02590e25i) q^{51} -3.69803e25 q^{52} -5.51049e25i q^{53} +(1.54026e25 - 6.66974e25i) q^{54} -1.04790e26 q^{55} +1.67166e25i q^{56} +(8.66080e23 + 1.80236e24i) q^{57} -2.24492e26 q^{58} +3.03191e25i q^{59} +(-1.47696e26 + 7.09718e25i) q^{60} -9.38409e26 q^{61} -1.86157e25i q^{62} +(1.72876e26 - 2.16024e26i) q^{63} -1.54743e26 q^{64} -1.46519e27i q^{65} +(7.09390e26 + 1.47628e27i) q^{66} +2.46316e27 q^{67} +8.86243e26i q^{68} +(4.79501e27 - 2.30413e27i) q^{69} -6.62324e26 q^{70} -4.09982e26i q^{71} +(1.99970e27 + 1.60029e27i) q^{72} +7.27398e24 q^{73} +1.35317e28i q^{74} +(2.97598e27 + 6.19316e27i) q^{75} -7.48177e25 q^{76} +6.62018e27i q^{77} +(-2.06416e28 + 9.91881e27i) q^{78} +4.60559e28 q^{79} -6.13101e27i q^{80} +(-9.29211e27 - 4.13602e28i) q^{81} -2.80696e28 q^{82} -1.19904e29i q^{83} +(4.48369e27 + 9.33080e27i) q^{84} -3.51136e28 q^{85} +1.05990e29i q^{86} +(-1.25306e29 + 6.02129e28i) q^{87} -6.12818e28 q^{88} -2.72734e29i q^{89} +(-6.34045e28 + 7.92296e28i) q^{90} -9.25643e28 q^{91} +1.99046e29i q^{92} +(-4.99306e27 - 1.03908e28i) q^{93} +1.06318e29 q^{94} -2.96434e27i q^{95} +(-8.63736e28 + 4.15048e28i) q^{96} +5.73161e29 q^{97} -4.80404e29i q^{98} +(7.91930e29 + 6.33752e29i) 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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