LMFDB - Embedded newform 31.2.d.a.4.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [31,2,Mod(2,31)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(31, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([8]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("31.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	31.d (of order $5$, degree $4$, 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:	$0.247536246266$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			4.1
Root			$-0.309017 - 0.951057i$ of defining polynomial
Character	$\chi$	$=$	31.4
Dual form			31.2.d.a.8.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.190983 - 0.587785i) q^{2} +(-0.309017 + 0.951057i) q^{3} +(1.30902 - 0.951057i) q^{4} -2.61803 q^{5} +0.618034 q^{6} +(-2.42705 + 1.76336i) q^{7} +(-1.80902 - 1.31433i) q^{8} +(1.61803 + 1.17557i) q^{9} +(0.500000 + 1.53884i) q^{10} +(0.618034 - 0.449028i) q^{11} +(0.500000 + 1.53884i) q^{12} +(1.50000 - 4.61653i) q^{13} +(1.50000 + 1.08981i) q^{14} +(0.809017 - 2.48990i) q^{15} +(0.572949 - 1.76336i) q^{16} +(-0.190983 - 0.138757i) q^{17} +(0.381966 - 1.17557i) q^{18} +(1.54508 + 4.75528i) q^{19} +(-3.42705 + 2.48990i) q^{20} +(-0.927051 - 2.85317i) q^{21} +(-0.381966 - 0.277515i) q^{22} +(4.42705 + 3.21644i) q^{23} +(1.80902 - 1.31433i) q^{24} +1.85410 q^{25} -3.00000 q^{26} +(-4.04508 + 2.93893i) q^{27} +(-1.50000 + 4.61653i) q^{28} +(-2.66312 - 8.19624i) q^{29} -1.61803 q^{30} +(-5.54508 + 0.502029i) q^{31} -5.61803 q^{32} +(0.236068 + 0.726543i) q^{33} +(-0.0450850 + 0.138757i) q^{34} +(6.35410 - 4.61653i) q^{35} +3.23607 q^{36} +0.236068 q^{37} +(2.50000 - 1.81636i) q^{38} +(3.92705 + 2.85317i) q^{39} +(4.73607 + 3.44095i) q^{40} +(2.00000 + 6.15537i) q^{41} +(-1.50000 + 1.08981i) q^{42} +(-1.42705 - 4.39201i) q^{43} +(0.381966 - 1.17557i) q^{44} +(-4.23607 - 3.07768i) q^{45} +(1.04508 - 3.21644i) q^{46} +(-1.04508 + 3.21644i) q^{47} +(1.50000 + 1.08981i) q^{48} +(0.618034 - 1.90211i) q^{49} +(-0.354102 - 1.08981i) q^{50} +(0.190983 - 0.138757i) q^{51} +(-2.42705 - 7.46969i) q^{52} +(10.2812 + 7.46969i) q^{53} +(2.50000 + 1.81636i) q^{54} +(-1.61803 + 1.17557i) q^{55} +6.70820 q^{56} -5.00000 q^{57} +(-4.30902 + 3.13068i) q^{58} +(2.92705 - 9.00854i) q^{59} +(-1.30902 - 4.02874i) q^{60} -6.94427 q^{61} +(1.35410 + 3.16344i) q^{62} -6.00000 q^{63} +(-0.0729490 - 0.224514i) q^{64} +(-3.92705 + 12.0862i) q^{65} +(0.381966 - 0.277515i) q^{66} -4.23607 q^{67} -0.381966 q^{68} +(-4.42705 + 3.21644i) q^{69} +(-3.92705 - 2.85317i) q^{70} +(-0.0729490 - 0.0530006i) q^{71} +(-1.38197 - 4.25325i) q^{72} +(6.92705 - 5.03280i) q^{73} +(-0.0450850 - 0.138757i) q^{74} +(-0.572949 + 1.76336i) q^{75} +(6.54508 + 4.75528i) q^{76} +(-0.708204 + 2.17963i) q^{77} +(0.927051 - 2.85317i) q^{78} +(-1.50000 + 4.61653i) q^{80} +(0.309017 + 0.951057i) q^{81} +(3.23607 - 2.35114i) q^{82} +(-1.26393 - 3.88998i) q^{83} +(-3.92705 - 2.85317i) q^{84} +(0.500000 + 0.363271i) q^{85} +(-2.30902 + 1.67760i) q^{86} +8.61803 q^{87} -1.70820 q^{88} +(5.16312 - 3.75123i) q^{89} +(-1.00000 + 3.07768i) q^{90} +(4.50000 + 13.8496i) q^{91} +8.85410 q^{92} +(1.23607 - 5.42882i) q^{93} +2.09017 q^{94} +(-4.04508 - 12.4495i) q^{95} +(1.73607 - 5.34307i) q^{96} +(4.28115 - 3.11044i) q^{97} -1.23607 q^{98} +1.52786 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 3 q^{2} + q^{3} + 3 q^{4} - 6 q^{5} - 2 q^{6} - 3 q^{7} - 5 q^{8} + 2 q^{9} + 2 q^{10} - 2 q^{11} + 2 q^{12} + 6 q^{13} + 6 q^{14} + q^{15} + 9 q^{16} - 3 q^{17} + 6 q^{18} - 5 q^{19} - 7 q^{20}+ \cdots + 24 q^{99}+O(q^{100}) $ 4 * q - 3 * q^2 + q^3 + 3 * q^4 - 6 * q^5 - 2 * q^6 - 3 * q^7 - 5 * q^8 + 2 * q^9 + 2 * q^10 - 2 * q^11 + 2 * q^12 + 6 * q^13 + 6 * q^14 + q^15 + 9 * q^16 - 3 * q^17 + 6 * q^18 - 5 * q^19 - 7 * q^20 + 3 * q^21 - 6 * q^22 + 11 * q^23 + 5 * q^24 - 6 * q^25 - 12 * q^26 - 5 * q^27 - 6 * q^28 + 5 * q^29 - 2 * q^30 - 11 * q^31 - 18 * q^32 - 8 * q^33 + 11 * q^34 + 12 * q^35 + 4 * q^36 - 8 * q^37 + 10 * q^38 + 9 * q^39 + 10 * q^40 + 8 * q^41 - 6 * q^42 + q^43 + 6 * q^44 - 8 * q^45 - 7 * q^46 + 7 * q^47 + 6 * q^48 - 2 * q^49 + 12 * q^50 + 3 * q^51 - 3 * q^52 + 21 * q^53 + 10 * q^54 - 2 * q^55 - 20 * q^57 - 15 * q^58 + 5 * q^59 - 3 * q^60 + 8 * q^61 - 8 * q^62 - 24 * q^63 - 7 * q^64 - 9 * q^65 + 6 * q^66 - 8 * q^67 - 6 * q^68 - 11 * q^69 - 9 * q^70 - 7 * q^71 - 10 * q^72 + 21 * q^73 + 11 * q^74 - 9 * q^75 + 15 * q^76 + 24 * q^77 - 3 * q^78 - 6 * q^80 - q^81 + 4 * q^82 - 14 * q^83 - 9 * q^84 + 2 * q^85 - 7 * q^86 + 30 * q^87 + 20 * q^88 + 5 * q^89 - 4 * q^90 + 18 * q^91 + 22 * q^92 - 4 * q^93 - 14 * q^94 - 5 * q^95 - 2 * q^96 - 3 * q^97 + 4 * q^98 + 24 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/31\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{3}{5}\right)$

Coefficient data

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

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

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

$2$	−0.190983	−	0.587785i	−0.135045	−	0.415627i	0.860552	−	0.509363i	$-0.170119\pi$
$2$	−0.190983	−	0.587785i	−0.135045	−	0.415627i	−0.995597	+	0.0937362i	$0.970119\pi$
$3$	−0.309017	+	0.951057i	−0.178411	+	0.549093i	−0.999773	−	0.0213149i	$-0.993215\pi$
$3$	−0.309017	+	0.951057i	−0.178411	+	0.549093i	0.821362	+	0.570408i	$0.193215\pi$
$4$	1.30902	−	0.951057i	0.654508	−	0.475528i
$5$	−2.61803			−1.17082			−0.585410	−	0.810737i	$-0.699067\pi$
$5$	−2.61803			−1.17082			−0.585410	+	0.810737i	$0.699067\pi$
$6$	0.618034			0.252311
$7$	−2.42705	+	1.76336i	−0.917339	+	0.666486i	−0.942860	−	0.333188i	$-0.891875\pi$
$7$	−2.42705	+	1.76336i	−0.917339	+	0.666486i	0.0255212	+	0.999674i	$0.491875\pi$
$8$	−1.80902	−	1.31433i	−0.639584	−	0.464685i
$9$	1.61803	+	1.17557i	0.539345	+	0.391857i
$10$	0.500000	+	1.53884i	0.158114	+	0.486624i
$11$	0.618034	−	0.449028i	0.186344	−	0.135387i	−0.490702	−	0.871327i	$-0.663260\pi$
$11$	0.618034	−	0.449028i	0.186344	−	0.135387i	0.677046	+	0.735940i	$0.263260\pi$
$12$	0.500000	+	1.53884i	0.144338	+	0.444225i
$13$	1.50000	−	4.61653i	0.416025	−	1.28039i	−0.495306	−	0.868719i	$-0.664944\pi$
$13$	1.50000	−	4.61653i	0.416025	−	1.28039i	0.911331	−	0.411675i	$-0.135056\pi$
$14$	1.50000	+	1.08981i	0.400892	+	0.291265i
$15$	0.809017	−	2.48990i	0.208887	−	0.642889i
$16$	0.572949	−	1.76336i	0.143237	−	0.440839i
$17$	−0.190983	−	0.138757i	−0.0463202	−	0.0336536i	0.564384	−	0.825512i	$-0.309114\pi$
$17$	−0.190983	−	0.138757i	−0.0463202	−	0.0336536i	−0.610704	+	0.791859i	$0.709114\pi$
$18$	0.381966	−	1.17557i	0.0900303	−	0.277085i
$19$	1.54508	+	4.75528i	0.354467	+	1.09094i	0.956318	+	0.292328i	$0.0944300\pi$
$19$	1.54508	+	4.75528i	0.354467	+	1.09094i	−0.601851	+	0.798608i	$0.705570\pi$
$20$	−3.42705	+	2.48990i	−0.766312	+	0.556758i
$21$	−0.927051	−	2.85317i	−0.202299	−	0.622613i
$22$	−0.381966	−	0.277515i	−0.0814354	−	0.0591663i
$23$	4.42705	+	3.21644i	0.923104	+	0.670674i	0.944295	−	0.329101i	$-0.106746\pi$
$23$	4.42705	+	3.21644i	0.923104	+	0.670674i	−0.0211907	+	0.999775i	$0.506746\pi$
$24$	1.80902	−	1.31433i	0.369264	−	0.268286i
$25$	1.85410			0.370820
$26$	−3.00000			−0.588348
$27$	−4.04508	+	2.93893i	−0.778477	+	0.565597i
$28$	−1.50000	+	4.61653i	−0.283473	+	0.872441i
$29$	−2.66312	−	8.19624i	−0.494529	−	1.52200i	−0.817690	−	0.575659i	$-0.804746\pi$
$29$	−2.66312	−	8.19624i	−0.494529	−	1.52200i	0.323161	−	0.946344i	$-0.395254\pi$
$30$	−1.61803			−0.295411
$31$	−5.54508	+	0.502029i	−0.995927	+	0.0901670i
$31$	−5.54508	+	0.502029i	−0.995927	+	0.0901670i
$32$	−5.61803			−0.993137
$33$	0.236068	+	0.726543i	0.0410942	+	0.126475i
$34$	−0.0450850	+	0.138757i	−0.00773201	+	0.0237967i
$35$	6.35410	−	4.61653i	1.07404	−	0.780335i
$36$	3.23607			0.539345
$37$	0.236068			0.0388093			0.0194047	−	0.999812i	$-0.493823\pi$
$37$	0.236068			0.0388093			0.0194047	+	0.999812i	$0.493823\pi$
$38$	2.50000	−	1.81636i	0.405554	−	0.294652i
$39$	3.92705	+	2.85317i	0.628831	+	0.456873i
$40$	4.73607	+	3.44095i	0.748838	+	0.544063i
$41$	2.00000	+	6.15537i	0.312348	+	0.961307i	0.976833	+	0.214005i	$0.0686510\pi$
$41$	2.00000	+	6.15537i	0.312348	+	0.961307i	−0.664485	+	0.747302i	$0.731349\pi$
$42$	−1.50000	+	1.08981i	−0.231455	+	0.168162i
$43$	−1.42705	−	4.39201i	−0.217623	−	0.669775i	−0.998957	−	0.0456620i	$-0.985460\pi$
$43$	−1.42705	−	4.39201i	−0.217623	−	0.669775i	0.781334	−	0.624113i	$-0.214540\pi$
$44$	0.381966	−	1.17557i	0.0575835	−	0.177224i
$45$	−4.23607	−	3.07768i	−0.631476	−	0.458794i
$46$	1.04508	−	3.21644i	0.154089	−	0.474238i
$47$	−1.04508	+	3.21644i	−0.152441	+	0.469166i	−0.997893	−	0.0648863i	$-0.979332\pi$
$47$	−1.04508	+	3.21644i	−0.152441	+	0.469166i	0.845451	+	0.534052i	$0.179332\pi$
$48$	1.50000	+	1.08981i	0.216506	+	0.157301i
$49$	0.618034	−	1.90211i	0.0882906	−	0.271730i
$50$	−0.354102	−	1.08981i	−0.0500776	−	0.154123i
$51$	0.190983	−	0.138757i	0.0267430	−	0.0194299i
$52$	−2.42705	−	7.46969i	−0.336571	−	1.03586i
$53$	10.2812	+	7.46969i	1.41222	+	1.02604i	0.992994	+	0.118162i	$0.0377001\pi$
$53$	10.2812	+	7.46969i	1.41222	+	1.02604i	0.419231	+	0.907880i	$0.362300\pi$
$54$	2.50000	+	1.81636i	0.340207	+	0.247175i
$55$	−1.61803	+	1.17557i	−0.218176	+	0.158514i
$56$	6.70820			0.896421
$57$	−5.00000			−0.662266
$58$	−4.30902	+	3.13068i	−0.565802	+	0.411079i
$59$	2.92705	−	9.00854i	0.381070	−	1.17281i	−0.558222	−	0.829692i	$-0.688516\pi$
$59$	2.92705	−	9.00854i	0.381070	−	1.17281i	0.939292	−	0.343120i	$-0.111484\pi$
$60$	−1.30902	−	4.02874i	−0.168993	−	0.520108i
$61$	−6.94427			−0.889123			−0.444561	−	0.895748i	$-0.646640\pi$
$61$	−6.94427			−0.889123			−0.444561	+	0.895748i	$0.646640\pi$
$62$	1.35410	+	3.16344i	0.171971	+	0.401757i
$63$	−6.00000			−0.755929
$64$	−0.0729490	−	0.224514i	−0.00911863	−	0.0280642i
$65$	−3.92705	+	12.0862i	−0.487091	+	1.49911i
$66$	0.381966	−	0.277515i	0.0470168	−	0.0341597i
$67$	−4.23607			−0.517518			−0.258759	−	0.965942i	$-0.583314\pi$
$67$	−4.23607			−0.517518			−0.258759	+	0.965942i	$0.583314\pi$
$68$	−0.381966			−0.0463202
$69$	−4.42705	+	3.21644i	−0.532954	+	0.387214i
$70$	−3.92705	−	2.85317i	−0.469372	−	0.341019i
$71$	−0.0729490	−	0.0530006i	−0.00865746	−	0.00629001i	0.583448	−	0.812150i	$-0.301703\pi$
$71$	−0.0729490	−	0.0530006i	−0.00865746	−	0.00629001i	−0.592106	+	0.805860i	$0.701703\pi$
$72$	−1.38197	−	4.25325i	−0.162866	−	0.501251i
$73$	6.92705	−	5.03280i	0.810750	−	0.589044i	−0.103298	−	0.994650i	$-0.532940\pi$
$73$	6.92705	−	5.03280i	0.810750	−	0.589044i	0.914048	+	0.405606i	$0.132940\pi$
$74$	−0.0450850	−	0.138757i	−0.00524102	−	0.0161302i
$75$	−0.572949	+	1.76336i	−0.0661585	+	0.203615i
$76$	6.54508	+	4.75528i	0.750773	+	0.545468i
$77$	−0.708204	+	2.17963i	−0.0807073	+	0.248392i
$78$	0.927051	−	2.85317i	0.104968	−	0.323058i
$79$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$79$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$80$	−1.50000	+	4.61653i	−0.167705	+	0.516143i
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$	3.23607	−	2.35114i	0.357364	−	0.259640i
$83$	−1.26393	−	3.88998i	−0.138735	−	0.426981i	0.857418	−	0.514621i	$-0.172067\pi$
$83$	−1.26393	−	3.88998i	−0.138735	−	0.426981i	−0.996152	+	0.0876401i	$0.972067\pi$
$84$	−3.92705	−	2.85317i	−0.428476	−	0.311306i
$85$	0.500000	+	0.363271i	0.0542326	+	0.0394023i
$86$	−2.30902	+	1.67760i	−0.248988	+	0.180900i
$87$	8.61803			0.923950
$88$	−1.70820			−0.182095
$89$	5.16312	−	3.75123i	0.547290	−	0.397629i	−0.279496	−	0.960147i	$-0.590167\pi$
$89$	5.16312	−	3.75123i	0.547290	−	0.397629i	0.826785	+	0.562518i	$0.190167\pi$
$90$	−1.00000	+	3.07768i	−0.105409	+	0.324416i
$91$	4.50000	+	13.8496i	0.471728	+	1.45183i
$92$	8.85410			0.923104
$93$	1.23607	−	5.42882i	0.128174	−	0.562943i
$94$	2.09017			0.215585
$95$	−4.04508	−	12.4495i	−0.415017	−	1.27729i
$96$	1.73607	−	5.34307i	0.177187	−	0.545325i
$97$	4.28115	−	3.11044i	0.434685	−	0.315817i	−0.348834	−	0.937184i	$-0.613422\pi$
$97$	4.28115	−	3.11044i	0.434685	−	0.315817i	0.783520	+	0.621367i	$0.213422\pi$
$98$	−1.23607			−0.124862
$99$	1.52786			0.153556
$100$	2.42705	−	1.76336i	0.242705	−	0.176336i
$101$	−3.85410	−	2.80017i	−0.383497	−	0.278627i	0.379288	−	0.925279i	$-0.376169\pi$
$101$	−3.85410	−	2.80017i	−0.383497	−	0.278627i	−0.762786	+	0.646651i	$0.776169\pi$
$102$	−0.118034	−	0.0857567i	−0.0116871	−	0.00849118i
$103$	−0.0450850	−	0.138757i	−0.00444235	−	0.0136722i	0.948811	−	0.315845i	$-0.102288\pi$
$103$	−0.0450850	−	0.138757i	−0.00444235	−	0.0136722i	−0.953253	+	0.302173i	$0.902288\pi$
$104$	−8.78115	+	6.37988i	−0.861063	+	0.625599i
$105$	2.42705	+	7.46969i	0.236856	+	0.728968i
$106$	2.42705	−	7.46969i	0.235736	−	0.725521i
$107$	−0.881966	−	0.640786i	−0.0852629	−	0.0619471i	0.544337	−	0.838867i	$-0.316781\pi$
$107$	−0.881966	−	0.640786i	−0.0852629	−	0.0619471i	−0.629600	+	0.776919i	$0.716781\pi$
$108$	−2.50000	+	7.69421i	−0.240563	+	0.740376i
$109$	−2.60081	+	8.00448i	−0.249113	+	0.766690i	0.745820	+	0.666147i	$0.232058\pi$
$109$	−2.60081	+	8.00448i	−0.249113	+	0.766690i	−0.994933	+	0.100543i	$0.967942\pi$
$110$	1.00000	+	0.726543i	0.0953463	+	0.0692731i
$111$	−0.0729490	+	0.224514i	−0.00692401	+	0.0213099i
$112$	1.71885	+	5.29007i	0.162416	+	0.499864i
$113$	1.50000	−	1.08981i	0.141108	−	0.102521i	−0.514992	−	0.857195i	$-0.672205\pi$
$113$	1.50000	−	1.08981i	0.141108	−	0.102521i	0.656100	+	0.754674i	$0.272205\pi$
$114$	0.954915	+	2.93893i	0.0894360	+	0.275256i
$115$	−11.5902	−	8.42075i	−1.08079	−	0.785239i
$116$	−11.2812	−	8.19624i	−1.04743	−	0.761002i
$117$	7.85410	−	5.70634i	0.726112	−	0.527551i
$118$	−5.85410			−0.538914
$119$	0.708204			0.0649209
$120$	−4.73607	+	3.44095i	−0.432342	+	0.314115i
$121$	−3.21885	+	9.90659i	−0.292622	+	0.900599i
$122$	1.32624	+	4.08174i	0.120072	+	0.369543i
$123$	−6.47214			−0.583573
$124$	−6.78115	+	5.93085i	−0.608966	+	0.532606i
$125$	8.23607			0.736656
$126$	1.14590	+	3.52671i	0.102085	+	0.314184i
$127$	3.16312	−	9.73508i	0.280681	−	0.863849i	−0.706979	−	0.707235i	$-0.749942\pi$
$127$	3.16312	−	9.73508i	0.280681	−	0.863849i	0.987660	−	0.156614i	$-0.0500577\pi$
$128$	−9.20820	+	6.69015i	−0.813898	+	0.591331i
$129$	4.61803			0.406595
$130$	7.85410			0.688850
$131$	−0.0729490	+	0.0530006i	−0.00637359	+	0.00463068i	−0.590967	−	0.806695i	$-0.701254\pi$
$131$	−0.0729490	+	0.0530006i	−0.00637359	+	0.00463068i	0.584594	+	0.811326i	$0.301254\pi$
$132$	1.00000	+	0.726543i	0.0870388	+	0.0632374i
$133$	−12.1353	−	8.81678i	−1.05226	−	0.764512i
$134$	0.809017	+	2.48990i	0.0698884	+	0.215094i
$135$	10.5902	−	7.69421i	0.911457	−	0.662212i
$136$	0.163119	+	0.502029i	0.0139873	+	0.0430486i
$137$	−2.00000	+	6.15537i	−0.170872	+	0.525888i	−0.999421	−	0.0340275i	$-0.989167\pi$
$137$	−2.00000	+	6.15537i	−0.170872	+	0.525888i	0.828549	+	0.559916i	$0.189167\pi$
$138$	2.73607	+	1.98787i	0.232910	+	0.169219i
$139$	1.80902	−	5.56758i	0.153439	−	0.472236i	−0.844561	−	0.535460i	$-0.820138\pi$
$139$	1.80902	−	5.56758i	0.153439	−	0.472236i	0.997999	+	0.0632239i	$0.0201382\pi$
$140$	3.92705	−	12.0862i	0.331896	−	1.02147i
$141$	−2.73607	−	1.98787i	−0.230418	−	0.167409i
$142$	−0.0172209	+	0.0530006i	−0.00144515	+	0.00444771i
$143$	−1.14590	−	3.52671i	−0.0958248	−	0.294918i
$144$	3.00000	−	2.17963i	0.250000	−	0.181636i
$145$	6.97214	+	21.4580i	0.579004	+	1.78199i
$146$	−4.28115	−	3.11044i	−0.354311	−	0.257422i
$147$	1.61803	+	1.17557i	0.133453	+	0.0969594i
$148$	0.309017	−	0.224514i	0.0254010	−	0.0184549i
$149$	−17.0344			−1.39552			−0.697758	−	0.716334i	$-0.745819\pi$
$149$	−17.0344			−1.39552			−0.697758	+	0.716334i	$0.745819\pi$
$150$	1.14590			0.0935622
$151$	15.7812	−	11.4657i	1.28425	−	0.933064i	0.284579	−	0.958652i	$-0.408146\pi$
$151$	15.7812	−	11.4657i	1.28425	−	0.933064i	0.999673	+	0.0255888i	$0.00814604\pi$
$152$	3.45492	−	10.6331i	0.280231	−	0.862461i
$153$	−0.145898	−	0.449028i	−0.0117952	−	0.0363018i
$154$	1.41641			0.114137
$155$	14.5172	−	1.31433i	1.16605	−	0.105569i
$156$	7.85410			0.628831
$157$	3.00000	+	9.23305i	0.239426	+	0.736878i	0.996503	+	0.0835524i	$0.0266266\pi$
$157$	3.00000	+	9.23305i	0.239426	+	0.736878i	−0.757077	+	0.653325i	$0.773373\pi$
$158$		0			0
$159$	−10.2812	+	7.46969i	−0.815348	+	0.592385i
$160$	14.7082			1.16279
$161$	−16.4164			−1.29379
$162$	0.500000	−	0.363271i	0.0392837	−	0.0285413i
$163$	10.2812	+	7.46969i	0.805282	+	0.585072i	0.912459	−	0.409168i	$-0.134181\pi$
$163$	10.2812	+	7.46969i	0.805282	+	0.585072i	−0.107177	+	0.994240i	$0.534181\pi$
$164$	8.47214	+	6.15537i	0.661563	+	0.480653i
$165$	−0.618034	−	1.90211i	−0.0481139	−	0.148079i
$166$	−2.04508	+	1.48584i	−0.158729	+	0.115324i
$167$	−2.85410	−	8.78402i	−0.220857	−	0.679728i	−0.998686	−	0.0512518i	$-0.983679\pi$
$167$	−2.85410	−	8.78402i	−0.220857	−	0.679728i	0.777829	−	0.628476i	$-0.216321\pi$
$168$	−2.07295	+	6.37988i	−0.159931	+	0.492219i
$169$	−8.54508	−	6.20837i	−0.657314	−	0.477567i
$170$	0.118034	−	0.363271i	0.00905279	−	0.0278616i
$171$	−3.09017	+	9.51057i	−0.236311	+	0.727291i
$172$	−6.04508	−	4.39201i	−0.460933	−	0.334888i
$173$	0.281153	−	0.865300i	0.0213757	−	0.0657875i	−0.939800	−	0.341726i	$-0.888989\pi$
$173$	0.281153	−	0.865300i	0.0213757	−	0.0657875i	0.961175	+	0.275938i	$0.0889886\pi$
$174$	−1.64590	−	5.06555i	−0.124775	−	0.384019i
$175$	−4.50000	+	3.26944i	−0.340168	+	0.247147i
$176$	−0.437694	−	1.34708i	−0.0329924	−	0.101540i
$177$	7.66312	+	5.56758i	0.575995	+	0.418485i
$178$	−3.19098	−	2.31838i	−0.239174	−	0.173770i
$179$	−16.0172	+	11.6372i	−1.19718	+	0.869805i	−0.994005	−	0.109337i	$-0.965127\pi$
$179$	−16.0172	+	11.6372i	−1.19718	+	0.869805i	−0.203179	+	0.979142i	$0.565127\pi$
$180$	−8.47214			−0.631476
$181$	17.0000			1.26360			0.631800	−	0.775131i	$-0.282316\pi$
$181$	17.0000			1.26360			0.631800	+	0.775131i	$0.282316\pi$
$182$	7.28115	−	5.29007i	0.539715	−	0.392126i
$183$	2.14590	−	6.60440i	0.158629	−	0.488211i
$184$	−3.78115	−	11.6372i	−0.278750	−	0.857905i
$185$	−0.618034			−0.0454388
$186$	−3.42705	+	0.310271i	−0.251284	+	0.0227502i
$187$	−0.180340			−0.0131878
$188$	1.69098	+	5.20431i	0.123328	+	0.379563i
$189$	4.63525	−	14.2658i	0.337165	−	1.03769i
$190$	−6.54508	+	4.75528i	−0.474830	+	0.344984i
$191$	−16.0902			−1.16424			−0.582122	−	0.813102i	$-0.697777\pi$
$191$	−16.0902			−1.16424			−0.582122	+	0.813102i	$0.697777\pi$
$192$	0.236068			0.0170367
$193$	1.92705	−	1.40008i	0.138712	−	0.100780i	−0.516265	−	0.856429i	$-0.672678\pi$
$193$	1.92705	−	1.40008i	0.138712	−	0.100780i	0.654977	+	0.755648i	$0.272678\pi$
$194$	−2.64590	−	1.92236i	−0.189964	−	0.138017i
$195$	−10.2812	−	7.46969i	−0.736249	−	0.534916i
$196$	−1.00000	−	3.07768i	−0.0714286	−	0.219835i
$197$	−13.2812	+	9.64932i	−0.946243	+	0.687486i	−0.949915	−	0.312507i	$-0.898831\pi$
$197$	−13.2812	+	9.64932i	−0.946243	+	0.687486i	0.00367232	+	0.999993i	$0.498831\pi$
$198$	−0.291796	−	0.898056i	−0.0207370	−	0.0638221i
$199$	−8.25329	+	25.4010i	−0.585060	+	1.80063i	0.0139686	+	0.999902i	$0.495554\pi$
$199$	−8.25329	+	25.4010i	−0.585060	+	1.80063i	−0.599029	+	0.800728i	$0.704446\pi$
$200$	−3.35410	−	2.43690i	−0.237171	−	0.172315i
$201$	1.30902	−	4.02874i	0.0923309	−	0.284165i
$202$	−0.909830	+	2.80017i	−0.0640154	+	0.197019i
$203$	20.9164	+	15.1967i	1.46804	+	1.06660i
$204$	0.118034	−	0.363271i	0.00826403	−	0.0254341i
$205$	−5.23607	−	16.1150i	−0.365703	−	1.12552i
$206$	−0.0729490	+	0.0530006i	−0.00508260	+	0.00369272i
$207$	3.38197	+	10.4086i	0.235063	+	0.723449i
$208$	−7.28115	−	5.29007i	−0.504857	−	0.366800i
$209$	3.09017	+	2.24514i	0.213752	+	0.155300i
$210$	3.92705	−	2.85317i	0.270992	−	0.196887i
$211$	−8.00000			−0.550743			−0.275371	−	0.961338i	$-0.588801\pi$
$211$	−8.00000			−0.550743			−0.275371	+	0.961338i	$0.588801\pi$
$212$	20.5623			1.41222
$213$	0.0729490	−	0.0530006i	0.00499838	−	0.00363154i
$214$	−0.208204	+	0.640786i	−0.0142325	+	0.0438032i
$215$	3.73607	+	11.4984i	0.254798	+	0.784187i
$216$	11.1803			0.760726
$217$	12.5729	−	10.9964i	0.853507	−	0.746485i
$218$	5.20163			0.352299
$219$	2.64590	+	8.14324i	0.178793	+	0.550269i
$220$	−1.00000	+	3.07768i	−0.0674200	+	0.207497i
$221$	−0.927051	+	0.673542i	−0.0623602	+	0.0453073i
$222$	0.145898			0.00979203
$223$	0.708204			0.0474248			0.0237124	−	0.999719i	$-0.492451\pi$
$223$	0.708204			0.0474248			0.0237124	+	0.999719i	$0.492451\pi$
$224$	13.6353	−	9.90659i	0.911044	−	0.661912i
$225$	3.00000	+	2.17963i	0.200000	+	0.145309i
$226$	−0.927051	−	0.673542i	−0.0616665	−	0.0448033i
$227$	−6.40983	−	19.7274i	−0.425435	−	1.30936i	−0.902577	−	0.430529i	$-0.858327\pi$
$227$	−6.40983	−	19.7274i	−0.425435	−	1.30936i	0.477141	−	0.878827i	$-0.341673\pi$
$228$	−6.54508	+	4.75528i	−0.433459	+	0.314926i
$229$	−2.23607	−	6.88191i	−0.147764	−	0.454769i	0.849592	−	0.527440i	$-0.176848\pi$
$229$	−2.23607	−	6.88191i	−0.147764	−	0.454769i	−0.997356	+	0.0726703i	$0.976848\pi$
$230$	−2.73607	+	8.42075i	−0.180411	+	0.555248i
$231$	−1.85410	−	1.34708i	−0.121991	−	0.0886316i
$232$	−5.95492	+	18.3273i	−0.390959	+	1.20325i
$233$	5.80902	−	17.8783i	0.380561	−	1.17125i	−0.559088	−	0.829108i	$-0.688849\pi$
$233$	5.80902	−	17.8783i	0.380561	−	1.17125i	0.939649	−	0.342139i	$-0.111151\pi$
$234$	−4.85410	−	3.52671i	−0.317323	−	0.230548i
$235$	2.73607	−	8.42075i	0.178481	−	0.549309i
$236$	−4.73607	−	14.5761i	−0.308292	−	0.948824i
$237$		0			0
$238$	−0.135255	−	0.416272i	−0.00876727	−	0.0269829i
$239$	10.8541	+	7.88597i	0.702093	+	0.510101i	0.880613	−	0.473836i	$-0.157131\pi$
$239$	10.8541	+	7.88597i	0.702093	+	0.510101i	−0.178520	+	0.983936i	$0.557131\pi$
$240$	−3.92705	−	2.85317i	−0.253490	−	0.184171i
$241$	6.89919	−	5.01255i	0.444416	−	0.322887i	−0.342971	−	0.939346i	$-0.611433\pi$
$241$	6.89919	−	5.01255i	0.444416	−	0.322887i	0.787387	+	0.616459i	$0.211433\pi$
$242$	6.43769			0.413831
$243$	−16.0000			−1.02640
$244$	−9.09017	+	6.60440i	−0.581938	+	0.422803i
$245$	−1.61803	+	4.97980i	−0.103372	+	0.318148i
$246$	1.23607	+	3.80423i	0.0788088	+	0.242549i
$247$	24.2705			1.54430
$248$	10.6910	+	6.37988i	0.678878	+	0.405123i
$249$	4.09017			0.259204
$250$	−1.57295	−	4.84104i	−0.0994820	−	0.306174i
$251$	0.291796	−	0.898056i	0.0184180	−	0.0566848i	−0.941425	−	0.337222i	$-0.890513\pi$
$251$	0.291796	−	0.898056i	0.0184180	−	0.0566848i	0.959843	+	0.280537i	$0.0905127\pi$
$252$	−7.85410	+	5.70634i	−0.494762	+	0.359466i
$253$	4.18034			0.262816
$254$	−6.32624			−0.396943
$255$	−0.500000	+	0.363271i	−0.0313112	+	0.0227489i
$256$	5.30902	+	3.85723i	0.331814	+	0.241077i
$257$	−1.14590	−	0.832544i	−0.0714792	−	0.0519326i	0.551472	−	0.834194i	$-0.314066\pi$
$257$	−1.14590	−	0.832544i	−0.0714792	−	0.0519326i	−0.622951	+	0.782261i	$0.714066\pi$
$258$	−0.881966	−	2.71441i	−0.0549088	−	0.168992i
$259$	−0.572949	+	0.416272i	−0.0356013	+	0.0258659i
$260$	6.35410	+	19.5559i	0.394065	+	1.21281i
$261$	5.32624	−	16.3925i	0.329686	−	1.01467i
$262$	0.0450850	+	0.0327561i	0.00278536	+	0.00202368i
$263$	−3.33688	+	10.2699i	−0.205761	+	0.633267i	0.793920	+	0.608022i	$0.208037\pi$
$263$	−3.33688	+	10.2699i	−0.205761	+	0.633267i	−0.999681	+	0.0252452i	$0.991963\pi$
$264$	0.527864	−	1.62460i	0.0324878	−	0.0999871i
$265$	−26.9164	−	19.5559i	−1.65346	−	1.20131i
$266$	−2.86475	+	8.81678i	−0.175649	+	0.540591i
$267$	1.97214	+	6.06961i	0.120693	+	0.371454i
$268$	−5.54508	+	4.02874i	−0.338720	+	0.246094i
$269$	−0.427051	−	1.31433i	−0.0260378	−	0.0801360i	0.937193	−	0.348811i	$-0.113414\pi$
$269$	−0.427051	−	1.31433i	−0.0260378	−	0.0801360i	−0.963231	+	0.268675i	$0.913414\pi$
$270$	−6.54508	−	4.75528i	−0.398321	−	0.289397i
$271$	−7.73607	−	5.62058i	−0.469933	−	0.341426i	0.327482	−	0.944857i	$-0.393800\pi$
$271$	−7.73607	−	5.62058i	−0.469933	−	0.341426i	−0.797415	+	0.603431i	$0.793800\pi$
$272$	−0.354102	+	0.257270i	−0.0214706	+	0.0155993i
$273$	−14.5623			−0.881351
$274$	4.00000			0.241649
$275$	1.14590	−	0.832544i	0.0691003	−	0.0502043i
$276$	−2.73607	+	8.42075i	−0.164692	+	0.506870i
$277$	4.11803	+	12.6740i	0.247429	+	0.761507i	0.995228	+	0.0975818i	$0.0311108\pi$
$277$	4.11803	+	12.6740i	0.247429	+	0.761507i	−0.747799	+	0.663925i	$0.768889\pi$
$278$	−3.61803			−0.216995
$279$	−9.56231	−	5.70634i	−0.572480	−	0.341630i
$280$	−17.5623			−1.04955
$281$	5.88197	+	18.1028i	0.350889	+	1.07992i	0.958355	+	0.285579i	$0.0921859\pi$
$281$	5.88197	+	18.1028i	0.350889	+	1.07992i	−0.607466	+	0.794345i	$0.707814\pi$
$282$	−0.645898	+	1.98787i	−0.0384627	+	0.118376i
$283$	−5.30902	+	3.85723i	−0.315588	+	0.229288i	−0.734291	−	0.678835i	$-0.762485\pi$
$283$	−5.30902	+	3.85723i	−0.315588	+	0.229288i	0.418702	+	0.908124i	$0.362485\pi$
$284$	−0.145898			−0.00865746
$285$	13.0902			0.775395
$286$	−1.85410	+	1.34708i	−0.109635	+	0.0796547i
$287$	−15.7082	−	11.4127i	−0.927226	−	0.673669i
$288$	−9.09017	−	6.60440i	−0.535643	−	0.389168i
$289$	−5.23607	−	16.1150i	−0.308004	−	0.947939i
$290$	11.2812	−	8.19624i	0.662452	−	0.481300i
$291$	1.63525	+	5.03280i	0.0958603	+	0.295028i
$292$	4.28115	−	13.1760i	0.250536	−	0.771069i
$293$	6.66312	+	4.84104i	0.389264	+	0.282817i	0.765154	−	0.643848i	$-0.222663\pi$
$293$	6.66312	+	4.84104i	0.389264	+	0.282817i	−0.375890	+	0.926664i	$0.622663\pi$
$294$	0.381966	−	1.17557i	0.0222767	−	0.0685607i
$295$	−7.66312	+	23.5847i	−0.446164	+	1.37315i
$296$	−0.427051	−	0.310271i	−0.0248218	−	0.0180341i
$297$	−1.18034	+	3.63271i	−0.0684903	+	0.210791i
$298$	3.25329	+	10.0126i	0.188458	+	0.580014i
$299$	21.4894	−	15.6129i	1.24276	−	0.902919i
$300$	0.927051	+	2.85317i	0.0535233	+	0.164728i
$301$	11.2082	+	8.14324i	0.646030	+	0.469368i
$302$	−9.75329	−	7.08618i	−0.561239	−	0.407764i
$303$	3.85410	−	2.80017i	0.221412	−	0.160866i
$304$	9.27051			0.531700
$305$	18.1803			1.04100
$306$	−0.236068	+	0.171513i	−0.0134951	+	0.00980477i
$307$	1.88197	−	5.79210i	0.107409	−	0.330572i	−0.882879	−	0.469601i	$-0.844398\pi$
$307$	1.88197	−	5.79210i	0.107409	−	0.330572i	0.990288	+	0.139028i	$0.0443979\pi$
$308$	1.14590	+	3.52671i	0.0652936	+	0.200953i
$309$	0.145898			0.00829985
$310$	−3.54508	−	8.28199i	−0.201347	−	0.470386i
$311$	16.4721			0.934049			0.467025	−	0.884244i	$-0.345326\pi$
$311$	16.4721			0.934049			0.467025	+	0.884244i	$0.345326\pi$
$312$	−3.35410	−	10.3229i	−0.189889	−	0.584417i
$313$	0.381966	−	1.17557i	0.0215900	−	0.0664472i	−0.939681	−	0.342052i	$-0.888878\pi$
$313$	0.381966	−	1.17557i	0.0215900	−	0.0664472i	0.961271	+	0.275605i	$0.0888781\pi$
$314$	4.85410	−	3.52671i	0.273933	−	0.199024i
$315$	15.7082			0.885057
$316$		0			0
$317$	−20.9443	+	15.2169i	−1.17635	+	0.854666i	−0.991755	−	0.128149i	$-0.959097\pi$
$317$	−20.9443	+	15.2169i	−1.17635	+	0.854666i	−0.184593	+	0.982815i	$0.559097\pi$
$318$	6.35410	+	4.61653i	0.356320	+	0.258882i
$319$	−5.32624	−	3.86974i	−0.298212	−	0.216664i
$320$	0.190983	+	0.587785i	0.0106763	+	0.0328582i
$321$	0.881966	−	0.640786i	0.0492265	−	0.0357652i
$322$	3.13525	+	9.64932i	0.174721	+	0.537736i
$323$	0.364745	−	1.12257i	0.0202950	−	0.0624615i
$324$	1.30902	+	0.951057i	0.0727232	+	0.0528365i
$325$	2.78115	−	8.55951i	0.154271	−	0.474796i
$326$	2.42705	−	7.46969i	0.134422	−	0.413708i
$327$	−6.80902	−	4.94704i	−0.376540	−	0.273572i
$328$	4.47214	−	13.7638i	0.246932	−	0.759980i
$329$	−3.13525	−	9.64932i	−0.172852	−	0.531984i
$330$	−1.00000	+	0.726543i	−0.0550482	+	0.0399948i
$331$	3.48278	+	10.7189i	0.191431	+	0.589164i	1.00000		0.000762014i	$0.000242557\pi$
$331$	3.48278	+	10.7189i	0.191431	+	0.589164i	−0.808569	+	0.588402i	$0.799757\pi$
$332$	−5.35410	−	3.88998i	−0.293845	−	0.213491i
$333$	0.381966	+	0.277515i	0.0209316	+	0.0152077i
$334$	−4.61803	+	3.35520i	−0.252688	+	0.183588i
$335$	11.0902			0.605921
$336$	−5.56231			−0.303449
$337$	−15.3541	+	11.1554i	−0.836391	+	0.607674i	−0.921360	−	0.388710i	$-0.872921\pi$
$337$	−15.3541	+	11.1554i	−0.836391	+	0.607674i	0.0849690	+	0.996384i	$0.472921\pi$
$338$	−2.01722	+	6.20837i	−0.109722	+	0.337691i
$339$	0.572949	+	1.76336i	0.0311183	+	0.0957723i
$340$	1.00000			0.0542326
$341$	−3.20163	+	2.80017i	−0.173378	+	0.151638i
$342$	6.18034			0.334195
$343$	−4.63525	−	14.2658i	−0.250280	−	0.770283i
$344$	−3.19098	+	9.82084i	−0.172046	+	0.529504i
$345$	11.5902	−	8.42075i	0.623994	−	0.453358i
$346$	−0.562306			−0.0302298
$347$	8.12461			0.436152			0.218076	−	0.975932i	$-0.430022\pi$
$347$	8.12461			0.436152			0.218076	+	0.975932i	$0.430022\pi$
$348$	11.2812	−	8.19624i	0.604733	−	0.439364i
$349$	13.5172	+	9.82084i	0.723560	+	0.525697i	0.887520	−	0.460770i	$-0.152427\pi$
$349$	13.5172	+	9.82084i	0.723560	+	0.525697i	−0.163959	+	0.986467i	$0.552427\pi$
$350$	2.78115	+	2.02063i	0.148659	+	0.108007i
$351$	7.50000	+	23.0826i	0.400320	+	1.23206i
$352$	−3.47214	+	2.52265i	−0.185065	+	0.134458i
$353$	−10.0066	−	30.7971i	−0.532596	−	1.63916i	−0.748786	−	0.662812i	$-0.769363\pi$
$353$	−10.0066	−	30.7971i	−0.532596	−	1.63916i	0.216190	−	0.976351i	$-0.430637\pi$
$354$	1.80902	−	5.56758i	0.0961482	−	0.295914i
$355$	0.190983	+	0.138757i	0.0101363	+	0.00736447i
$356$	3.19098	−	9.82084i	0.169122	−	0.520503i
$357$	−0.218847	+	0.673542i	−0.0115826	+	0.0356476i
$358$	9.89919	+	7.19218i	0.523188	+	0.380119i
$359$	−7.82624	+	24.0867i	−0.413053	+	1.27125i	0.500928	+	0.865489i	$0.332992\pi$
$359$	−7.82624	+	24.0867i	−0.413053	+	1.27125i	−0.913981	+	0.405757i	$0.867008\pi$
$360$	3.61803	+	11.1352i	0.190687	+	0.586875i
$361$	−4.85410	+	3.52671i	−0.255479	+	0.185616i
$362$	−3.24671	−	9.99235i	−0.170643	−	0.525186i
$363$	−8.42705	−	6.12261i	−0.442305	−	0.321354i
$364$	19.0623	+	13.8496i	0.999136	+	0.725915i
$365$	−18.1353	+	13.1760i	−0.949243	+	0.689665i
$366$	−4.29180			−0.224336
$367$	−36.2705			−1.89331			−0.946653	−	0.322256i	$-0.895559\pi$
$367$	−36.2705			−1.89331			−0.946653	+	0.322256i	$0.895559\pi$
$368$	8.20820	−	5.96361i	0.427882	−	0.310875i
$369$	−4.00000	+	12.3107i	−0.208232	+	0.640871i
$370$	0.118034	+	0.363271i	0.00613629	+	0.0188856i
$371$	−38.1246			−1.97933
$372$	−3.54508	−	8.28199i	−0.183804	−	0.429401i
$373$	−0.347524			−0.0179941			−0.00899706	−	0.999960i	$-0.502864\pi$
$373$	−0.347524			−0.0179941			−0.00899706	+	0.999960i	$0.502864\pi$
$374$	0.0344419	+	0.106001i	0.00178095	+	0.00548119i
$375$	−2.54508	+	7.83297i	−0.131428	+	0.404493i
$376$	6.11803	−	4.44501i	0.315514	−	0.229234i
$377$	−41.8328			−2.15450
$378$	−9.27051			−0.476824
$379$	14.8992	−	10.8249i	0.765320	−	0.556037i	−0.135218	−	0.990816i	$-0.543173\pi$
$379$	14.8992	−	10.8249i	0.765320	−	0.556037i	0.900537	+	0.434779i	$0.143173\pi$
$380$	−17.1353	−	12.4495i	−0.879020	−	0.638645i
$381$	8.28115	+	6.01661i	0.424256	+	0.308240i
$382$	3.07295	+	9.45756i	0.157226	+	0.483891i
$383$	13.6353	−	9.90659i	0.696729	−	0.506203i	−0.182136	−	0.983273i	$-0.558301\pi$
$383$	13.6353	−	9.90659i	0.696729	−	0.506203i	0.878865	+	0.477070i	$0.158301\pi$
$384$	−3.51722	−	10.8249i	−0.179487	−	0.552406i
$385$	1.85410	−	5.70634i	0.0944938	−	0.290822i
$386$	−1.19098	−	0.865300i	−0.0606194	−	0.0440426i
$387$	2.85410	−	8.78402i	0.145082	−	0.446517i
$388$	2.64590	−	8.14324i	0.134325	−	0.413410i
$389$	23.5172	+	17.0863i	1.19237	+	0.866308i	0.993513	−	0.113721i	$-0.0362769\pi$
$389$	23.5172	+	17.0863i	1.19237	+	0.866308i	0.198858	+	0.980028i	$0.436277\pi$
$390$	−2.42705	+	7.46969i	−0.122899	+	0.378243i
$391$	−0.399187	−	1.22857i	−0.0201878	−	0.0621315i
$392$	−3.61803	+	2.62866i	−0.182738	+	0.132767i
$393$	−0.0278640	−	0.0857567i	−0.00140556	−	0.00432585i
$394$	8.20820	+	5.96361i	0.413523	+	0.300442i
$395$		0			0
$396$	2.00000	−	1.45309i	0.100504	−	0.0730203i
$397$	16.2918			0.817662			0.408831	−	0.912610i	$-0.365937\pi$
$397$	16.2918			0.817662			0.408831	+	0.912610i	$0.365937\pi$
$398$	16.5066			0.827400
$399$	12.1353	−	8.81678i	0.607523	−	0.441391i
$400$	1.06231	−	3.26944i	0.0531153	−	0.163472i
$401$	−9.21885	−	28.3727i	−0.460367	−	1.41686i	−0.864717	−	0.502260i	$-0.832502\pi$
$401$	−9.21885	−	28.3727i	−0.460367	−	1.41686i	0.404349	−	0.914605i	$-0.367498\pi$
$402$	−2.61803			−0.130576
$403$	−6.00000	+	26.3521i	−0.298881	+	1.31269i
$404$	−7.70820			−0.383497
$405$	−0.809017	−	2.48990i	−0.0402004	−	0.123724i
$406$	4.93769	−	15.1967i	0.245054	−	0.754198i
$407$	0.145898	−	0.106001i	0.00723190	−	0.00525428i
$408$	−0.527864			−0.0261332
$409$	−6.18034			−0.305598			−0.152799	−	0.988257i	$-0.548829\pi$
$409$	−6.18034			−0.305598			−0.152799	+	0.988257i	$0.548829\pi$
$410$	−8.47214	+	6.15537i	−0.418409	+	0.303992i
$411$	−5.23607	−	3.80423i	−0.258276	−	0.187649i
$412$	−0.190983	−	0.138757i	−0.00940906	−	0.00683608i
$413$	8.78115	+	27.0256i	0.432092	+	1.32984i
$414$	5.47214	−	3.97574i	0.268941	−	0.195397i
$415$	3.30902	+	10.1841i	0.162433	+	0.499918i
$416$	−8.42705	+	25.9358i	−0.413170	+	1.27161i
$417$	4.73607	+	3.44095i	0.231926	+	0.168504i
$418$	0.729490	−	2.24514i	0.0356805	−	0.109813i
$419$	1.38197	−	4.25325i	0.0675135	−	0.207785i	−0.911608	−	0.411060i	$-0.865159\pi$
$419$	1.38197	−	4.25325i	0.0675135	−	0.207785i	0.979122	+	0.203275i	$0.0651586\pi$
$420$	10.2812	+	7.46969i	0.501669	+	0.364484i
$421$	4.56231	−	14.0413i	0.222353	−	0.684333i	−0.776196	−	0.630491i	$-0.782853\pi$
$421$	4.56231	−	14.0413i	0.222353	−	0.684333i	0.998549	−	0.0538414i	$-0.0171466\pi$
$422$	1.52786	+	4.70228i	0.0743753	+	0.228904i
$423$	−5.47214	+	3.97574i	−0.266064	+	0.193307i
$424$	−8.78115	−	27.0256i	−0.426450	−	1.31248i
$425$	−0.354102	−	0.257270i	−0.0171765	−	0.0124794i
$426$	−0.0450850	−	0.0327561i	−0.00218437	−	0.00158704i
$427$	16.8541	−	12.2452i	0.815627	−	0.592588i
$428$	−1.76393			−0.0852629
$429$	3.70820			0.179034
$430$	6.04508	−	4.39201i	0.291520	−	0.211802i
$431$	9.03444	−	27.8052i	0.435174	−	1.33933i	−0.457735	−	0.889089i	$-0.651339\pi$
$431$	9.03444	−	27.8052i	0.435174	−	1.33933i	0.892908	−	0.450238i	$-0.148661\pi$
$432$	2.86475	+	8.81678i	0.137830	+	0.424197i
$433$	0.583592			0.0280456			0.0140228	−	0.999902i	$-0.495536\pi$
$433$	0.583592			0.0280456			0.0140228	+	0.999902i	$0.495536\pi$
$434$	−8.86475	−	5.29007i	−0.425521	−	0.253931i
$435$	−22.5623			−1.08178
$436$	4.20820	+	12.9515i	0.201536	+	0.620265i
$437$	−8.45492	+	26.0216i	−0.404453	+	1.24478i
$438$	4.28115	−	3.11044i	0.204561	−	0.148623i
$439$	41.8328			1.99657			0.998286	−	0.0585295i	$-0.0186412\pi$
$439$	41.8328			1.99657			0.998286	+	0.0585295i	$0.0186412\pi$
$440$	4.47214			0.213201
$441$	3.23607	−	2.35114i	0.154098	−	0.111959i
$442$	0.572949	+	0.416272i	0.0272524	+	0.0198000i
$443$	33.2705	+	24.1724i	1.58073	+	1.14847i	0.915853	+	0.401514i	$0.131516\pi$
$443$	33.2705	+	24.1724i	1.58073	+	1.14847i	0.664877	+	0.746953i	$0.268484\pi$
$444$	0.118034	+	0.363271i	0.00560165	+	0.0172401i
$445$	−13.5172	+	9.82084i	−0.640778	+	0.465552i
$446$	−0.135255	−	0.416272i	−0.00640451	−	0.0197110i
$447$	5.26393	−	16.2007i	0.248975	−	0.766268i
$448$	0.572949	+	0.416272i	0.0270693	+	0.0196670i
$449$	7.43769	−	22.8909i	0.351006	−	1.08029i	−0.607283	−	0.794486i	$-0.707740\pi$
$449$	7.43769	−	22.8909i	0.351006	−	1.08029i	0.958289	−	0.285801i	$-0.0922596\pi$
$450$	0.708204	−	2.17963i	0.0333851	−	0.102749i
$451$	4.00000	+	2.90617i	0.188353	+	0.136846i
$452$	0.927051	−	2.85317i	0.0436048	−	0.134202i
$453$	6.02786	+	18.5519i	0.283214	+	0.871642i
$454$	−10.3713	+	7.53521i	−0.486750	+	0.353645i
$455$	−11.7812	−	36.2587i	−0.552309	−	1.69983i
$456$	9.04508	+	6.57164i	0.423575	+	0.307745i
$457$	12.7361	+	9.25330i	0.595768	+	0.432851i	0.844374	−	0.535754i	$-0.179972\pi$
$457$	12.7361	+	9.25330i	0.595768	+	0.432851i	−0.248606	+	0.968605i	$0.579972\pi$
$458$	−3.61803	+	2.62866i	−0.169060	+	0.122829i
$459$	1.18034			0.0550935
$460$	−23.1803			−1.08079
$461$	−8.69098	+	6.31437i	−0.404779	+	0.294089i	−0.771485	−	0.636248i	$-0.780486\pi$
$461$	−8.69098	+	6.31437i	−0.404779	+	0.294089i	0.366705	+	0.930337i	$0.380486\pi$
$462$	−0.437694	+	1.34708i	−0.0203634	+	0.0626720i
$463$	−9.61803	−	29.6013i	−0.446988	−	1.37569i	−0.880289	−	0.474438i	$-0.842651\pi$
$463$	−9.61803	−	29.6013i	−0.446988	−	1.37569i	0.433301	−	0.901249i	$-0.357349\pi$
$464$	−15.9787			−0.741793
$465$	−3.23607	+	14.2128i	−0.150069	+	0.659105i
$466$	−11.6180			−0.538195
$467$	−10.1287	−	31.1729i	−0.468699	−	1.44251i	−0.854270	−	0.519830i	$-0.825995\pi$
$467$	−10.1287	−	31.1729i	−0.468699	−	1.44251i	0.385571	−	0.922678i	$-0.374005\pi$
$468$	4.85410	−	14.9394i	0.224381	−	0.690574i
$469$	10.2812	−	7.46969i	0.474740	−	0.344918i
$470$	−5.47214			−0.252411
$471$	−9.70820			−0.447330
$472$	−17.1353	+	12.4495i	−0.788714	+	0.573034i
$473$	−2.85410	−	2.07363i	−0.131232	−	0.0953454i
$474$		0			0
$475$	2.86475	+	8.81678i	0.131444	+	0.404542i
$476$	0.927051	−	0.673542i	0.0424913	−	0.0308717i
$477$	7.85410	+	24.1724i	0.359615	+	1.10678i
$478$	2.56231	−	7.88597i	0.117197	−	0.360696i
$479$	7.23607	+	5.25731i	0.330624	+	0.240213i	0.740696	−	0.671841i	$-0.234496\pi$
$479$	7.23607	+	5.25731i	0.330624	+	0.240213i	−0.410071	+	0.912054i	$0.634496\pi$
$480$	−4.54508	+	13.9883i	−0.207454	+	0.638477i
$481$	0.354102	−	1.08981i	0.0161457	−	0.0496912i
$482$	−4.26393	−	3.09793i	−0.194217	−	0.141107i
$483$	5.07295	−	15.6129i	0.230827	−	0.710413i
$484$	5.20820	+	16.0292i	0.236737	+	0.728600i
$485$	−11.2082	+	8.14324i	−0.508938	+	0.369765i
$486$	3.05573	+	9.40456i	0.138611	+	0.426600i
$487$	−18.5451	−	13.4738i	−0.840358	−	0.610556i	0.0821126	−	0.996623i	$-0.473833\pi$
$487$	−18.5451	−	13.4738i	−0.840358	−	0.610556i	−0.922471	+	0.386067i	$0.873833\pi$
$488$	12.5623	+	9.12705i	0.568669	+	0.413162i
$489$	−10.2812	+	7.46969i	−0.464930	+	0.337791i
$490$	3.23607			0.146191
$491$	−27.5967			−1.24542			−0.622712	−	0.782451i	$-0.713969\pi$
$491$	−27.5967			−1.24542			−0.622712	+	0.782451i	$0.713969\pi$
$492$	−8.47214	+	6.15537i	−0.381953	+	0.277505i
$493$	−0.628677	+	1.93487i	−0.0283142	+	0.0871421i
$494$	−4.63525	−	14.2658i	−0.208550	−	0.641851i
$495$	−4.00000			−0.179787
$496$	−2.29180	+	10.0656i	−0.102905	+	0.451959i
$497$	0.270510			0.0121340
$498$	−0.781153	−	2.40414i	−0.0350043	−	0.107732i
$499$	1.28115	−	3.94298i	0.0573523	−	0.176512i	−0.918277	−	0.395940i	$-0.870419\pi$
$499$	1.28115	−	3.94298i	0.0573523	−	0.176512i	0.975629	+	0.219427i	$0.0704189\pi$
$500$	10.7812	−	7.83297i	0.482148	−	0.350301i
$501$	9.23607			0.412637
$502$	−0.583592			−0.0260470
$503$	−10.6353	+	7.72696i	−0.474203	+	0.344528i	−0.799077	−	0.601229i	$-0.794678\pi$
$503$	−10.6353	+	7.72696i	−0.474203	+	0.344528i	0.324874	+	0.945757i	$0.394678\pi$
$504$	10.8541	+	7.88597i	0.483480	+	0.351269i
$505$	10.0902	+	7.33094i	0.449007	+	0.326222i
$506$	−0.798374	−	2.45714i	−0.0354920	−	0.109233i
$507$	8.54508	−	6.20837i	0.379501	−	0.275723i
$508$	−5.11803	−	15.7517i	−0.227076	−	0.698868i
$509$	−0.590170	+	1.81636i	−0.0261588	+	0.0805086i	−0.963284	−	0.268486i	$-0.913477\pi$
$509$	−0.590170	+	1.81636i	−0.0261588	+	0.0805086i	0.937125	+	0.348994i	$0.113477\pi$
$510$	0.309017	+	0.224514i	0.0136835	+	0.00994165i
$511$	−7.93769	+	24.4297i	−0.351143	+	1.08071i
$512$	−5.78115	+	17.7926i	−0.255493	+	0.786327i
$513$	−20.2254	−	14.6946i	−0.892974	−	0.648784i
$514$	−0.270510	+	0.832544i	−0.0119317	+	0.0367219i
$515$	0.118034	+	0.363271i	0.00520120	+	0.0160076i
$516$	6.04508	−	4.39201i	0.266120	−	0.193348i
$517$	0.798374	+	2.45714i	0.0351124	+	0.108065i
$518$	0.354102	+	0.257270i	0.0155583	+	0.0113038i
$519$	0.736068	+	0.534785i	0.0323098	+	0.0234744i
$520$	22.9894	−	16.7027i	1.00815	−	0.732464i
$521$	31.0689			1.36115			0.680576	−	0.732677i	$-0.261729\pi$
$521$	31.0689			1.36115			0.680576	+	0.732677i	$0.261729\pi$
$522$	−10.6525			−0.466246
$523$	−27.6074	+	20.0579i	−1.20719	+	0.877073i	−0.994972	−	0.100150i	$-0.968068\pi$
$523$	−27.6074	+	20.0579i	−1.20719	+	0.877073i	−0.212215	+	0.977223i	$0.568068\pi$
$524$	−0.0450850	+	0.138757i	−0.00196955	+	0.00606164i
$525$	−1.71885	−	5.29007i	−0.0750166	−	0.230877i
$526$	6.67376			0.290990
$527$	1.12868	+	0.673542i	0.0491659	+	0.0293399i
$528$	1.41641			0.0616412
$529$	2.14590	+	6.60440i	0.0932999	+	0.287148i
$530$	−6.35410	+	19.5559i	−0.276005	+	0.849455i
$531$	15.3262	−	11.1352i	0.665102	−	0.483225i
$532$	−24.2705			−1.05226
$533$	31.4164			1.36080
$534$	3.19098	−	2.31838i	0.138087	−	0.100326i
$535$	2.30902	+	1.67760i	0.0998275	+	0.0725289i
$536$	7.66312	+	5.56758i	0.330996	+	0.240483i
$537$	−6.11803	−	18.8294i	−0.264013	−	0.812547i
$538$	−0.690983	+	0.502029i	−0.0297904	+	0.0216440i
$539$	−0.472136	−	1.45309i	−0.0203363	−	0.0625888i
$540$	6.54508	−	20.1437i	0.281656	−	0.866847i
$541$	−17.7984	−	12.9313i	−0.765212	−	0.555959i	0.135293	−	0.990806i	$-0.456803\pi$
$541$	−17.7984	−	12.9313i	−0.765212	−	0.555959i	−0.900504	+	0.434847i	$0.856803\pi$
$542$	−1.82624	+	5.62058i	−0.0784436	+	0.241425i
$543$	−5.25329	+	16.1680i	−0.225440	+	0.693834i
$544$	1.07295	+	0.779543i	0.0460023	+	0.0334226i
$545$	6.80902	−	20.9560i	0.291666	−	0.897656i
$546$	2.78115	+	8.55951i	0.119022	+	0.366313i
$547$	19.1803	−	13.9353i	0.820092	−	0.595832i	−0.0966468	−	0.995319i	$-0.530812\pi$
$547$	19.1803	−	13.9353i	0.820092	−	0.595832i	0.916739	+	0.399487i	$0.130812\pi$
$548$	3.23607	+	9.95959i	0.138238	+	0.425453i
$549$	−11.2361	−	8.16348i	−0.479544	−	0.348409i
$550$	−0.708204	−	0.514540i	−0.0301979	−	0.0219401i
$551$	34.8607	−	25.3278i	1.48511	−	1.07900i
$552$	12.2361			0.520802
$553$		0			0
$554$	6.66312	−	4.84104i	0.283089	−	0.205676i
$555$	0.190983	−	0.587785i	0.00810678	−	0.0249501i
$556$	−2.92705	−	9.00854i	−0.124135	−	0.382047i
$557$	35.8885			1.52065			0.760323	−	0.649545i	$-0.225041\pi$
$557$	35.8885			1.52065			0.760323	+	0.649545i	$0.225041\pi$
$558$	−1.52786	+	6.71040i	−0.0646796	+	0.284074i
$559$	−22.4164			−0.948113
$560$	−4.50000	−	13.8496i	−0.190160	−	0.585251i
$561$	0.0557281	−	0.171513i	0.00235284	−	0.00724130i
$562$	9.51722	−	6.91467i	0.401460	−	0.291678i
$563$	−8.56231			−0.360858			−0.180429	−	0.983588i	$-0.557749\pi$
$563$	−8.56231			−0.360858			−0.180429	+	0.983588i	$0.557749\pi$
$564$	−5.47214			−0.230418
$565$	−3.92705	+	2.85317i	−0.165212	+	0.120034i
$566$	3.28115	+	2.38390i	0.137917	+	0.100203i
$567$	−2.42705	−	1.76336i	−0.101927	−	0.0740540i
$568$	0.0623059	+	0.191758i	0.00261430	+	0.00804598i
$569$	−12.5623	+	9.12705i	−0.526639	+	0.382626i	−0.819099	−	0.573652i	$-0.805526\pi$
$569$	−12.5623	+	9.12705i	−0.526639	+	0.382626i	0.292460	+	0.956278i	$0.405526\pi$
$570$	−2.50000	−	7.69421i	−0.104713	−	0.322275i
$571$	2.16312	−	6.65740i	0.0905237	−	0.278603i	−0.895538	−	0.444986i	$-0.853209\pi$
$571$	2.16312	−	6.65740i	0.0905237	−	0.278603i	0.986061	+	0.166383i	$0.0532087\pi$
$572$	−4.85410	−	3.52671i	−0.202960	−	0.147459i
$573$	4.97214	−	15.3027i	0.207714	−	0.639278i
$574$	−3.70820	+	11.4127i	−0.154777	+	0.476356i
$575$	8.20820	+	5.96361i	0.342306	+	0.248700i
$576$	0.145898	−	0.449028i	0.00607908	−	0.0187095i
$577$	12.0451	+	37.0710i	0.501443	+	1.54328i	0.806669	+	0.591004i	$0.201268\pi$
$577$	12.0451	+	37.0710i	0.501443	+	1.54328i	−0.305225	+	0.952280i	$0.598732\pi$
$578$	−8.47214	+	6.15537i	−0.352394	+	0.256030i
$579$	0.736068	+	2.26538i	0.0305899	+	0.0941462i
$580$	29.5344	+	21.4580i	1.22635	+	0.890996i
$581$	9.92705	+	7.21242i	0.411843	+	0.299222i
$582$	2.64590	−	1.92236i	0.109676	−	0.0796843i
$583$	9.70820			0.402073
$584$	−19.1459			−0.792263
$585$	−20.5623	+	14.9394i	−0.850147	+	0.617668i
$586$	1.57295	−	4.84104i	0.0649779	−	0.199981i
$587$	11.1287	+	34.2505i	0.459330	+	1.41367i	0.865976	+	0.500086i	$0.166698\pi$
$587$	11.1287	+	34.2505i	0.459330	+	1.41367i	−0.406646	+	0.913586i	$0.633302\pi$
$588$	3.23607			0.133453
$589$	−10.9549	−	25.5928i	−0.451389	−	1.05453i
$590$	15.3262			0.630971
$591$	−5.07295	−	15.6129i	−0.208673	−	0.642230i
$592$	0.135255	−	0.416272i	0.00555894	−	0.0171087i
$593$	−4.94427	+	3.59222i	−0.203037	+	0.147515i	−0.684658	−	0.728865i	$-0.740048\pi$
$593$	−4.94427	+	3.59222i	−0.203037	+	0.147515i	0.481621	+	0.876380i	$0.340048\pi$
$594$	2.36068			0.0968599
$595$	−1.85410			−0.0760108
$596$	−22.2984	+	16.2007i	−0.913377	+	0.663607i
$597$	−21.6074	−	15.6987i	−0.884332	−	0.642505i
$598$	−13.2812	−	9.64932i	−0.543107	−	0.394590i
$599$	9.20820	+	28.3399i	0.376237	+	1.15794i	0.942640	+	0.333810i	$0.108334\pi$
$599$	9.20820	+	28.3399i	0.376237	+	1.15794i	−0.566403	+	0.824128i	$0.691666\pi$
$600$	3.35410	−	2.43690i	0.136931	−	0.0994859i
$601$	6.79837	+	20.9232i	0.277311	+	0.853477i	0.988599	+	0.150575i	$0.0481126\pi$
$601$	6.79837	+	20.9232i	0.277311	+	0.853477i	−0.711287	+	0.702902i	$0.751887\pi$
$602$	2.64590	−	8.14324i	0.107839	−	0.331894i
$603$	−6.85410	−	4.97980i	−0.279121	−	0.202793i
$604$	9.75329	−	30.0175i	0.396856	−	1.22140i
$605$	8.42705	−	25.9358i	0.342608	−	1.05444i
$606$	−2.38197	−	1.73060i	−0.0967608	−	0.0703008i
$607$	−7.85410	+	24.1724i	−0.318788	+	0.981129i	0.655379	+	0.755300i	$0.272509\pi$
$607$	−7.85410	+	24.1724i	−0.318788	+	0.981129i	−0.974167	+	0.225829i	$0.927491\pi$
$608$	−8.68034	−	26.7153i	−0.352034	−	1.08345i
$609$	−20.9164	+	15.1967i	−0.847576	+	0.615800i
$610$	−3.47214	−	10.6861i	−0.140583	−	0.432669i
$611$	13.2812	+	9.64932i	0.537298	+	0.390370i
$612$	−0.618034	−	0.449028i	−0.0249825	−	0.0181509i
$613$	−20.2705	+	14.7274i	−0.818718	+	0.594834i	−0.916345	−	0.400390i	$-0.868875\pi$
$613$	−20.2705	+	14.7274i	−0.818718	+	0.594834i	0.0976269	+	0.995223i	$0.468875\pi$
$614$	−3.76393			−0.151900
$615$	16.9443			0.683259
$616$	4.14590	−	3.01217i	0.167043	−	0.121364i
$617$	−4.39919	+	13.5393i	−0.177105	+	0.545072i	−0.999723	−	0.0235215i	$-0.992512\pi$
$617$	−4.39919	+	13.5393i	−0.177105	+	0.545072i	0.822619	+	0.568593i	$0.192512\pi$
$618$	−0.0278640	−	0.0857567i	−0.00112086	−	0.00344964i
$619$	−40.0000			−1.60774			−0.803868	−	0.594808i	$-0.797228\pi$
$619$	−40.0000			−1.60774			−0.803868	+	0.594808i	$0.797228\pi$
$620$	17.7533	−	15.5272i	0.712989	−	0.623586i
$621$	−27.3607			−1.09795
$622$	−3.14590	−	9.68208i	−0.126139	−	0.388216i
$623$	−5.91641	+	18.2088i	−0.237036	+	0.729521i
$624$	7.28115	−	5.29007i	0.291479	−	0.211772i
$625$	−30.8328			−1.23331
$626$	−0.763932			−0.0305329
$627$	−3.09017	+	2.24514i	−0.123410	+	0.0896623i
$628$	12.7082	+	9.23305i	0.507113	+	0.368439i
$629$	−0.0450850	−	0.0327561i	−0.00179766	−	0.00130607i
$630$	−3.00000	−	9.23305i	−0.119523	−	0.367854i
$631$	7.06231	−	5.13107i	0.281146	−	0.204264i	−0.438271	−	0.898843i	$-0.644409\pi$
$631$	7.06231	−	5.13107i	0.281146	−	0.204264i	0.719417	+	0.694578i	$0.244409\pi$
$632$		0			0
$633$	2.47214	−	7.60845i	0.0982586	−	0.302409i
$634$	12.9443	+	9.40456i	0.514083	+	0.373503i
$635$	−8.28115	+	25.4868i	−0.328628	+	1.01141i
$636$	−6.35410	+	19.5559i	−0.251957	+	0.775442i
$637$	−7.85410	−	5.70634i	−0.311191	−	0.226093i
$638$	−1.25735	+	3.86974i	−0.0497791	+	0.153204i
$639$	−0.0557281	−	0.171513i	−0.00220457	−	0.00678497i
$640$	24.1074	−	17.5150i	0.952928	−	0.692343i
$641$	−12.6976	−	39.0791i	−0.501523	−	1.54353i	−0.806538	−	0.591183i	$-0.798661\pi$
$641$	−12.6976	−	39.0791i	−0.501523	−	1.54353i	0.305014	−	0.952348i	$-0.401339\pi$
$642$	−0.545085	−	0.396027i	−0.0215128	−	0.0156300i
$643$	−6.59017	−	4.78804i	−0.259891	−	0.188822i	0.450208	−	0.892924i	$-0.351350\pi$
$643$	−6.59017	−	4.78804i	−0.259891	−	0.188822i	−0.710099	+	0.704102i	$0.751350\pi$
$644$	−21.4894	+	15.6129i	−0.846799	+	0.615236i
$645$	−12.0902			−0.476050
$646$	−0.729490			−0.0287014
$647$	24.1803	−	17.5680i	0.950627	−	0.690671i	−0.000327889	−	1.00000i	$-0.500104\pi$
$647$	24.1803	−	17.5680i	0.950627	−	0.690671i	0.950955	+	0.309329i	$0.100104\pi$
$648$	0.690983	−	2.12663i	0.0271444	−	0.0835418i
$649$	−2.23607	−	6.88191i	−0.0877733	−	0.270139i
$650$	−5.56231			−0.218172
$651$	6.57295	+	15.3557i	0.257614	+	0.601836i
$652$	20.5623			0.805282
$653$	12.2533	+	37.7117i	0.479508	+	1.47577i	0.839780	+	0.542927i	$0.182684\pi$
$653$	12.2533	+	37.7117i	0.479508	+	1.47577i	−0.360272	+	0.932847i	$0.617316\pi$
$654$	−1.60739	+	4.94704i	−0.0628540	+	0.193445i
$655$	0.190983	−	0.138757i	0.00746232	−	0.00542170i
$656$	12.0000			0.468521
$657$	17.1246			0.668095
$658$	−5.07295	+	3.68571i	−0.197764	+	0.143684i
$659$	−18.3541	−	13.3350i	−0.714974	−	0.519459i	0.169800	−	0.985478i	$-0.445688\pi$
$659$	−18.3541	−	13.3350i	−0.714974	−	0.519459i	−0.884775	+	0.466019i	$0.845688\pi$
$660$	−2.61803	−	1.90211i	−0.101907	−	0.0740396i
$661$	−5.13525	−	15.8047i	−0.199738	−	0.614731i	−0.999889	−	0.0149316i	$-0.995247\pi$
$661$	−5.13525	−	15.8047i	−0.199738	−	0.614731i	0.800150	−	0.599800i	$-0.204753\pi$
$662$	5.63525	−	4.09425i	0.219020	−	0.159128i
$663$	−0.354102	−	1.08981i	−0.0137522	−	0.0423249i
$664$	−2.82624	+	8.69827i	−0.109679	+	0.337558i
$665$	31.7705	+	23.0826i	1.23201	+	0.895106i
$666$	0.0901699	−	0.277515i	0.00349401	−	0.0107535i
$667$	14.5729	−	44.8509i	0.564267	−	1.73663i
$668$	−12.0902	−	8.78402i	−0.467783	−	0.339864i
$669$	−0.218847	+	0.673542i	−0.00846112	+	0.0260406i
$670$	−2.11803	−	6.51864i	−0.0818268	−	0.251837i
$671$	−4.29180	+	3.11817i	−0.165683	+	0.120376i
$672$	5.20820	+	16.0292i	0.200911	+	0.618340i
$673$	3.57295	+	2.59590i	0.137727	+	0.100065i	0.654516	−	0.756049i	$-0.272873\pi$
$673$	3.57295	+	2.59590i	0.137727	+	0.100065i	−0.516788	+	0.856113i	$0.672873\pi$
$674$	9.48936	+	6.89442i	0.365516	+	0.265563i
$675$	−7.50000	+	5.44907i	−0.288675	+	0.209735i
$676$	−17.0902			−0.657314
$677$	28.6525			1.10120			0.550602	−	0.834768i	$-0.314398\pi$
$677$	28.6525			1.10120			0.550602	+	0.834768i	$0.314398\pi$
$678$	0.927051	−	0.673542i	0.0356032	−	0.0258672i
$679$	−4.90576	+	15.0984i	−0.188266	+	0.579423i
$680$	−0.427051	−	1.31433i	−0.0163767	−	0.0504022i
$681$	20.7426			0.794860
$682$	2.25735	+	1.34708i	0.0864386	+	0.0515825i
$683$	10.0557			0.384772			0.192386	−	0.981319i	$-0.438377\pi$
$683$	10.0557			0.384772			0.192386	+	0.981319i	$0.438377\pi$
$684$	5.00000	+	15.3884i	0.191180	+	0.588391i
$685$	5.23607	−	16.1150i	0.200060	−	0.615721i
$686$	−7.50000	+	5.44907i	−0.286351	+	0.208046i
$687$	7.23607			0.276073
$688$	−8.56231			−0.326435
$689$	49.9058	−	36.2587i	1.90126	−	1.38134i
$690$	−7.16312	−	5.20431i	−0.272695	−	0.198125i
$691$	−3.10081	−	2.25287i	−0.117960	−	0.0857033i	0.527241	−	0.849716i	$-0.323227\pi$
$691$	−3.10081	−	2.25287i	−0.117960	−	0.0857033i	−0.645201	+	0.764013i	$0.723227\pi$
$692$	−0.454915	−	1.40008i	−0.0172933	−	0.0532232i
$693$	−3.70820	+	2.69417i	−0.140863	+	0.102343i
$694$	−1.55166	−	4.77553i	−0.0589003	−	0.181277i
$695$	−4.73607	+	14.5761i	−0.179649	+	0.552904i
$696$	−15.5902	−	11.3269i	−0.590944	−	0.429346i
$697$	0.472136	−	1.45309i	0.0178834	−	0.0550395i
$698$	3.19098	−	9.82084i	0.120780	−	0.371724i
$699$	15.2082	+	11.0494i	0.575227	+	0.417927i
$700$	−2.78115	+	8.55951i	−0.105118	+	0.323519i
$701$	−9.28115	−	28.5645i	−0.350544	−	1.07886i	−0.958548	−	0.284930i	$-0.908030\pi$
$701$	−9.28115	−	28.5645i	−0.350544	−	1.07886i	0.608004	−	0.793934i	$-0.291970\pi$
$702$	12.1353	−	8.81678i	0.458016	−	0.332768i
$703$	0.364745	+	1.12257i	0.0137566	+	0.0423385i
$704$	−0.145898	−	0.106001i	−0.00549874	−	0.00399507i
$705$	7.16312	+	5.20431i	0.269779	+	0.196006i
$706$	−16.1910	+	11.7634i	−0.609356	+	0.442723i
$707$	14.2918			0.537498
$708$	15.3262			0.575995
$709$	−3.35410	+	2.43690i	−0.125966	+	0.0915196i	−0.648984	−	0.760802i	$-0.724806\pi$
$709$	−3.35410	+	2.43690i	−0.125966	+	0.0915196i	0.523018	+	0.852321i	$0.324806\pi$
$710$	0.0450850	−	0.138757i	0.00169201	−	0.00520747i
$711$		0			0
$712$	−14.2705			−0.534810
$713$	−26.1631	−	15.6129i	−0.979817	−	0.584709i
$714$	0.437694			0.0163803
$715$	3.00000	+	9.23305i	0.112194	+	0.345297i
$716$	−9.89919	+	30.4666i	−0.369950	+	1.13859i
$717$	−10.8541	+	7.88597i	−0.405354	+	0.294507i
$718$	15.6525			0.584145
$719$	−41.3820			−1.54329			−0.771643	−	0.636055i	$-0.780565\pi$
$719$	−41.3820			−1.54329			−0.771643	+	0.636055i	$0.780565\pi$
$720$	−7.85410	+	5.70634i	−0.292705	+	0.212663i
$721$	0.354102	+	0.257270i	0.0131874	+	0.00958124i
$722$	3.00000	+	2.17963i	0.111648	+	0.0811173i
$723$	2.63525	+	8.11048i	0.0980062	+	0.301632i
$724$	22.2533	−	16.1680i	0.827037	−	0.600878i
$725$	−4.93769	−	15.1967i	−0.183381	−	0.564390i
$726$	−1.98936	+	6.12261i	−0.0738320	+	0.227231i
$727$	19.2812	+	14.0086i	0.715098	+	0.519549i	0.884814	−	0.465944i	$-0.154285\pi$
$727$	19.2812	+	14.0086i	0.715098	+	0.519549i	−0.169716	+	0.985493i	$0.554285\pi$
$728$	10.0623	−	30.9686i	0.372934	−	1.14777i
$729$	4.01722	−	12.3637i	0.148786	−	0.457916i
$730$	11.2082	+	8.14324i	0.414834	+	0.301395i
$731$	−0.336881	+	1.03681i	−0.0124600	+	0.0383479i
$732$	−3.47214	−	10.6861i	−0.128334	−	0.394971i
$733$	−22.6074	+	16.4252i	−0.835023	+	0.606680i	−0.920976	−	0.389619i	$-0.872607\pi$
$733$	−22.6074	+	16.4252i	−0.835023	+	0.606680i	0.0859529	+	0.996299i	$0.472607\pi$
$734$	6.92705	+	21.3193i	0.255682	+	0.786909i
$735$	−4.23607	−	3.07768i	−0.156250	−	0.113522i
$736$	−24.8713	−	18.0701i	−0.916769	−	0.666072i
$737$	−2.61803	+	1.90211i	−0.0964365	+	0.0700652i
$738$	8.00000			0.294484
$739$	21.7082			0.798549			0.399275	−	0.916831i	$-0.369262\pi$
$739$	21.7082			0.798549			0.399275	+	0.916831i	$0.369262\pi$
$740$	−0.809017	+	0.587785i	−0.0297401	+	0.0216074i
$741$	−7.50000	+	23.0826i	−0.275519	+	0.847961i
$742$	7.28115	+	22.4091i	0.267300	+	0.822663i
$743$	−3.43769			−0.126117			−0.0630584	−	0.998010i	$-0.520085\pi$
$743$	−3.43769			−0.126117			−0.0630584	+	0.998010i	$0.520085\pi$
$744$	−9.37132	+	8.19624i	−0.343569	+	0.300489i
$745$	44.5967			1.63390
$746$	0.0663712	+	0.204270i	0.00243002	+	0.00747884i
$747$	2.52786	−	7.77997i	0.0924897	−	0.284654i
$748$	−0.236068	+	0.171513i	−0.00863150	+	0.00627115i
$749$	3.27051			0.119502
$750$	5.09017			0.185867
$751$	32.2254	−	23.4131i	1.17592	−	0.854358i	0.184217	−	0.982886i	$-0.441025\pi$
$751$	32.2254	−	23.4131i	1.17592	−	0.854358i	0.991706	+	0.128528i	$0.0410252\pi$
$752$	5.07295	+	3.68571i	0.184991	+	0.134404i
$753$	0.763932	+	0.555029i	0.0278392	+	0.0202264i
$754$	7.98936	+	24.5887i	0.290955	+	0.895468i
$755$	−41.3156	+	30.0175i	−1.50363	+	1.09245i
$756$	−7.50000	−	23.0826i	−0.272772	−	0.839507i
$757$	13.3262	−	41.0139i	0.484350	−	1.49068i	−0.348569	−	0.937283i	$-0.613332\pi$
$757$	13.3262	−	41.0139i	0.484350	−	1.49068i	0.832920	−	0.553394i	$-0.186668\pi$
$758$	−9.20820	−	6.69015i	−0.334457	−	0.242997i
$759$	−1.29180	+	3.97574i	−0.0468892	+	0.144310i
$760$	−9.04508	+	27.8379i	−0.328100	+	1.00979i
$761$	−2.83688	−	2.06111i	−0.102837	−	0.0747154i	0.535178	−	0.844739i	$-0.320244\pi$
$761$	−2.83688	−	2.06111i	−0.102837	−	0.0747154i	−0.638015	+	0.770024i	$0.720244\pi$
$762$	1.95492	−	6.01661i	0.0708191	−	0.217959i
$763$	−7.80244	−	24.0134i	−0.282467	−	0.869345i
$764$	−21.0623	+	15.3027i	−0.762007	+	0.553631i
$765$	0.381966	+	1.17557i	0.0138100	+	0.0425028i
$766$	−8.42705	−	6.12261i	−0.304482	−	0.221219i
$767$	−37.1976	−	27.0256i	−1.34313	−	0.975838i
$768$	−5.30902	+	3.85723i	−0.191573	+	0.139186i
$769$	−53.7426			−1.93801			−0.969005	−

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:	\( N \)	\(=\)	\( 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	31.d (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.190983 - 0.587785i) q^{2} +(-0.309017 + 0.951057i) q^{3} +(1.30902 - 0.951057i) q^{4} -2.61803 q^{5} +0.618034 q^{6} +(-2.42705 + 1.76336i) q^{7} +(-1.80902 - 1.31433i) q^{8} +(1.61803 + 1.17557i) q^{9} +(0.500000 + 1.53884i) q^{10} +(0.618034 - 0.449028i) q^{11} +(0.500000 + 1.53884i) q^{12} +(1.50000 - 4.61653i) q^{13} +(1.50000 + 1.08981i) q^{14} +(0.809017 - 2.48990i) q^{15} +(0.572949 - 1.76336i) q^{16} +(-0.190983 - 0.138757i) q^{17} +(0.381966 - 1.17557i) q^{18} +(1.54508 + 4.75528i) q^{19} +(-3.42705 + 2.48990i) q^{20} +(-0.927051 - 2.85317i) q^{21} +(-0.381966 - 0.277515i) q^{22} +(4.42705 + 3.21644i) q^{23} +(1.80902 - 1.31433i) q^{24} +1.85410 q^{25} -3.00000 q^{26} +(-4.04508 + 2.93893i) q^{27} +(-1.50000 + 4.61653i) q^{28} +(-2.66312 - 8.19624i) q^{29} -1.61803 q^{30} +(-5.54508 + 0.502029i) q^{31} -5.61803 q^{32} +(0.236068 + 0.726543i) q^{33} +(-0.0450850 + 0.138757i) q^{34} +(6.35410 - 4.61653i) q^{35} +3.23607 q^{36} +0.236068 q^{37} +(2.50000 - 1.81636i) q^{38} +(3.92705 + 2.85317i) q^{39} +(4.73607 + 3.44095i) q^{40} +(2.00000 + 6.15537i) q^{41} +(-1.50000 + 1.08981i) q^{42} +(-1.42705 - 4.39201i) q^{43} +(0.381966 - 1.17557i) q^{44} +(-4.23607 - 3.07768i) q^{45} +(1.04508 - 3.21644i) q^{46} +(-1.04508 + 3.21644i) q^{47} +(1.50000 + 1.08981i) q^{48} +(0.618034 - 1.90211i) q^{49} +(-0.354102 - 1.08981i) q^{50} +(0.190983 - 0.138757i) q^{51} +(-2.42705 - 7.46969i) q^{52} +(10.2812 + 7.46969i) q^{53} +(2.50000 + 1.81636i) q^{54} +(-1.61803 + 1.17557i) q^{55} +6.70820 q^{56} -5.00000 q^{57} +(-4.30902 + 3.13068i) q^{58} +(2.92705 - 9.00854i) q^{59} +(-1.30902 - 4.02874i) q^{60} -6.94427 q^{61} +(1.35410 + 3.16344i) q^{62} -6.00000 q^{63} +(-0.0729490 - 0.224514i) q^{64} +(-3.92705 + 12.0862i) q^{65} +(0.381966 - 0.277515i) q^{66} -4.23607 q^{67} -0.381966 q^{68} +(-4.42705 + 3.21644i) q^{69} +(-3.92705 - 2.85317i) q^{70} +(-0.0729490 - 0.0530006i) q^{71} +(-1.38197 - 4.25325i) q^{72} +(6.92705 - 5.03280i) q^{73} +(-0.0450850 - 0.138757i) q^{74} +(-0.572949 + 1.76336i) q^{75} +(6.54508 + 4.75528i) q^{76} +(-0.708204 + 2.17963i) q^{77} +(0.927051 - 2.85317i) q^{78} +(-1.50000 + 4.61653i) q^{80} +(0.309017 + 0.951057i) q^{81} +(3.23607 - 2.35114i) q^{82} +(-1.26393 - 3.88998i) q^{83} +(-3.92705 - 2.85317i) q^{84} +(0.500000 + 0.363271i) q^{85} +(-2.30902 + 1.67760i) q^{86} +8.61803 q^{87} -1.70820 q^{88} +(5.16312 - 3.75123i) q^{89} +(-1.00000 + 3.07768i) q^{90} +(4.50000 + 13.8496i) q^{91} +8.85410 q^{92} +(1.23607 - 5.42882i) q^{93} +2.09017 q^{94} +(-4.04508 - 12.4495i) q^{95} +(1.73607 - 5.34307i) q^{96} +(4.28115 - 3.11044i) q^{97} -1.23607 q^{98} +1.52786 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 3 q^{2} + q^{3} + 3 q^{4} - 6 q^{5} - 2 q^{6} - 3 q^{7} - 5 q^{8} + 2 q^{9} + 2 q^{10} - 2 q^{11} + 2 q^{12} + 6 q^{13} + 6 q^{14} + q^{15} + 9 q^{16} - 3 q^{17} + 6 q^{18} - 5 q^{19} - 7 q^{20}+ \cdots + 24 q^{99}+O(q^{100}) \) 4 * q - 3 * q^2 + q^3 + 3 * q^4 - 6 * q^5 - 2 * q^6 - 3 * q^7 - 5 * q^8 + 2 * q^9 + 2 * q^10 - 2 * q^11 + 2 * q^12 + 6 * q^13 + 6 * q^14 + q^15 + 9 * q^16 - 3 * q^17 + 6 * q^18 - 5 * q^19 - 7 * q^20 + 3 * q^21 - 6 * q^22 + 11 * q^23 + 5 * q^24 - 6 * q^25 - 12 * q^26 - 5 * q^27 - 6 * q^28 + 5 * q^29 - 2 * q^30 - 11 * q^31 - 18 * q^32 - 8 * q^33 + 11 * q^34 + 12 * q^35 + 4 * q^36 - 8 * q^37 + 10 * q^38 + 9 * q^39 + 10 * q^40 + 8 * q^41 - 6 * q^42 + q^43 + 6 * q^44 - 8 * q^45 - 7 * q^46 + 7 * q^47 + 6 * q^48 - 2 * q^49 + 12 * q^50 + 3 * q^51 - 3 * q^52 + 21 * q^53 + 10 * q^54 - 2 * q^55 - 20 * q^57 - 15 * q^58 + 5 * q^59 - 3 * q^60 + 8 * q^61 - 8 * q^62 - 24 * q^63 - 7 * q^64 - 9 * q^65 + 6 * q^66 - 8 * q^67 - 6 * q^68 - 11 * q^69 - 9 * q^70 - 7 * q^71 - 10 * q^72 + 21 * q^73 + 11 * q^74 - 9 * q^75 + 15 * q^76 + 24 * q^77 - 3 * q^78 - 6 * q^80 - q^81 + 4 * q^82 - 14 * q^83 - 9 * q^84 + 2 * q^85 - 7 * q^86 + 30 * q^87 + 20 * q^88 + 5 * q^89 - 4 * q^90 + 18 * q^91 + 22 * q^92 - 4 * q^93 - 14 * q^94 - 5 * q^95 - 2 * q^96 - 3 * q^97 + 4 * q^98 + 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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