LMFDB - Embedded newform 690.2.w.b.493.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(7,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([0, 11, 38]))

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

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

chi := DirichletCharacter("690.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.w (of order $44$, degree $20$, 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:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$12$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			493.3
Character	$\chi$	$=$	690.493
Dual form			690.2.w.b.7.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.997452 - 0.0713392i) q^{2} +(-0.212565 - 0.977147i) q^{3} +(0.989821 + 0.142315i) q^{4} +(-0.619349 + 2.14858i) q^{5} +(0.142315 + 0.989821i) q^{6} +(-1.99507 - 3.65370i) q^{7} +(-0.977147 - 0.212565i) q^{8} +(-0.909632 + 0.415415i) q^{9} +O(q^{10})$	\(q+(-0.997452 - 0.0713392i) q^{2} +(-0.212565 - 0.977147i) q^{3} +(0.989821 + 0.142315i) q^{4} +(-0.619349 + 2.14858i) q^{5} +(0.142315 + 0.989821i) q^{6} +(-1.99507 - 3.65370i) q^{7} +(-0.977147 - 0.212565i) q^{8} +(-0.909632 + 0.415415i) q^{9} +(0.771049 - 2.09892i) q^{10} +(1.81253 + 1.57056i) q^{11} +(-0.0713392 - 0.997452i) q^{12} +(-2.13024 - 1.16320i) q^{13} +(1.72934 + 3.78672i) q^{14} +(2.23113 + 0.148481i) q^{15} +(0.959493 + 0.281733i) q^{16} +(1.26206 - 1.68592i) q^{17} +(0.936950 - 0.349464i) q^{18} +(-0.707077 + 4.91783i) q^{19} +(-0.918820 + 2.03857i) q^{20} +(-3.14612 + 2.72613i) q^{21} +(-1.69587 - 1.69587i) q^{22} +(-0.560058 + 4.76302i) q^{23} +1.00000i q^{24} +(-4.23281 - 2.66144i) q^{25} +(2.04183 + 1.31221i) q^{26} +(0.599278 + 0.800541i) q^{27} +(-1.45479 - 3.90044i) q^{28} +(-3.75233 + 0.539504i) q^{29} +(-2.21486 - 0.307269i) q^{30} +(-8.69709 + 5.58928i) q^{31} +(-0.936950 - 0.349464i) q^{32} +(1.14939 - 2.10495i) q^{33} +(-1.37912 + 1.59159i) q^{34} +(9.08592 - 2.02366i) q^{35} +(-0.959493 + 0.281733i) q^{36} +(-0.758926 + 2.03476i) q^{37} +(1.05611 - 4.85486i) q^{38} +(-0.683801 + 2.32881i) q^{39} +(1.06191 - 1.96783i) q^{40} +(3.56457 - 7.80531i) q^{41} +(3.33258 - 2.49474i) q^{42} +(0.874892 - 0.190321i) q^{43} +(1.57056 + 1.81253i) q^{44} +(-0.329174 - 2.21171i) q^{45} +(0.898421 - 4.71093i) q^{46} +(-5.40977 + 5.40977i) q^{47} +(0.0713392 - 0.997452i) q^{48} +(-5.58473 + 8.69001i) q^{49} +(4.03216 + 2.95663i) q^{50} +(-1.91566 - 0.874852i) q^{51} +(-1.94302 - 1.45452i) q^{52} +(-8.38229 + 4.57707i) q^{53} +(-0.540641 - 0.841254i) q^{54} +(-4.49707 + 2.92164i) q^{55} +(1.17283 + 3.99428i) q^{56} +(4.95574 - 0.354442i) q^{57} +(3.78126 - 0.270441i) q^{58} +(3.47547 + 11.8364i) q^{59} +(2.18729 + 0.464493i) q^{60} +(-6.51558 - 10.1384i) q^{61} +(9.07367 - 4.95460i) q^{62} +(3.33258 + 2.49474i) q^{63} +(0.909632 + 0.415415i) q^{64} +(3.81859 - 3.85657i) q^{65} +(-1.29663 + 2.01759i) q^{66} +(-0.779972 + 10.9054i) q^{67} +(1.48915 - 1.48915i) q^{68} +(4.77322 - 0.465193i) q^{69} +(-9.20714 + 1.37032i) q^{70} +(3.90649 + 4.50833i) q^{71} +(0.977147 - 0.212565i) q^{72} +(-5.19195 + 3.88665i) q^{73} +(0.902151 - 1.97543i) q^{74} +(-1.70087 + 4.70181i) q^{75} +(-1.39976 + 4.76715i) q^{76} +(2.12225 - 9.75581i) q^{77} +(0.848195 - 2.27410i) q^{78} +(0.848029 - 0.249004i) q^{79} +(-1.19959 + 1.88706i) q^{80} +(0.654861 - 0.755750i) q^{81} +(-4.11231 + 7.53113i) q^{82} +(-2.04613 - 0.763166i) q^{83} +(-3.50206 + 2.25064i) q^{84} +(2.84068 + 3.75582i) q^{85} +(-0.886240 + 0.127422i) q^{86} +(1.32479 + 3.55190i) q^{87} +(-1.43726 - 1.91995i) q^{88} +(-10.1999 - 6.55508i) q^{89} +(0.170554 + 2.22955i) q^{90} +10.1039i q^{91} +(-1.23221 + 4.63483i) q^{92} +(7.31025 + 7.31025i) q^{93} +(5.78191 - 5.01006i) q^{94} +(-10.1284 - 4.56506i) q^{95} +(-0.142315 + 0.989821i) q^{96} +(13.2754 - 4.95146i) q^{97} +(6.19044 - 8.26946i) q^{98} +(-2.30117 - 0.675684i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 24 q^{6}+O(q^{10}) $ 240 * q + 24 * q^6	$ 240 q + 24 q^{6} - 44 q^{10} + 24 q^{16} - 44 q^{21} + 96 q^{23} + 16 q^{25} + 16 q^{26} + 44 q^{28} - 16 q^{31} + 44 q^{33} + 16 q^{35} - 24 q^{36} + 44 q^{37} - 88 q^{43} + 8 q^{46} + 96 q^{47} - 24 q^{50} - 24 q^{55} + 44 q^{57} - 16 q^{58} + 88 q^{61} + 56 q^{62} - 88 q^{65} + 132 q^{67} - 56 q^{70} + 16 q^{71} + 48 q^{73} + 24 q^{81} - 24 q^{82} + 44 q^{85} - 16 q^{87} + 44 q^{88} - 124 q^{92} + 32 q^{93} + 20 q^{95} - 24 q^{96} - 56 q^{98}+O(q^{100}) $ 240 * q + 24 * q^6 - 44 * q^10 + 24 * q^16 - 44 * q^21 + 96 * q^23 + 16 * q^25 + 16 * q^26 + 44 * q^28 - 16 * q^31 + 44 * q^33 + 16 * q^35 - 24 * q^36 + 44 * q^37 - 88 * q^43 + 8 * q^46 + 96 * q^47 - 24 * q^50 - 24 * q^55 + 44 * q^57 - 16 * q^58 + 88 * q^61 + 56 * q^62 - 88 * q^65 + 132 * q^67 - 56 * q^70 + 16 * q^71 + 48 * q^73 + 24 * q^81 - 24 * q^82 + 44 * q^85 - 16 * q^87 + 44 * q^88 - 124 * q^92 + 32 * q^93 + 20 * q^95 - 24 * q^96 - 56 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$e\left(\frac{3}{22}\right)$

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 $

$2$	−0.997452	−	0.0713392i	−0.705305	−	0.0504444i
$2$	−0.997452	−	0.0713392i	−0.705305	−	0.0504444i
$3$	−0.212565	−	0.977147i	−0.122725	−	0.564156i
$3$	−0.212565	−	0.977147i	−0.122725	−	0.564156i
$4$	0.989821	+	0.142315i	0.494911	+	0.0711574i
$5$	−0.619349	+	2.14858i	−0.276981	+	0.960875i
$5$	−0.619349	+	2.14858i	−0.276981	+	0.960875i
$6$	0.142315	+	0.989821i	0.0580998	+	0.404093i
$7$	−1.99507	−	3.65370i	−0.754066	−	1.38097i	−0.918837	−	0.394637i	$-0.870870\pi$
$7$	−1.99507	−	3.65370i	−0.754066	−	1.38097i	0.164771	−	0.986332i	$-0.447311\pi$
$8$	−0.977147	−	0.212565i	−0.345474	−	0.0751532i
$9$	−0.909632	+	0.415415i	−0.303211	+	0.138472i
$10$	0.771049	−	2.09892i	0.243827	−	0.663738i
$11$	1.81253	+	1.57056i	0.546497	+	0.473543i	0.883807	−	0.467851i	$-0.154972\pi$
$11$	1.81253	+	1.57056i	0.546497	+	0.473543i	−0.337310	+	0.941394i	$0.609517\pi$
$12$	−0.0713392	−	0.997452i	−0.0205938	−	0.287940i
$13$	−2.13024	−	1.16320i	−0.590822	−	0.322613i	0.155876	−	0.987777i	$-0.450180\pi$
$13$	−2.13024	−	1.16320i	−0.590822	−	0.322613i	−0.746698	+	0.665163i	$0.768362\pi$
$14$	1.72934	+	3.78672i	0.462185	+	1.01204i
$15$	2.23113	+	0.148481i	0.576076	+	0.0383375i
$16$	0.959493	+	0.281733i	0.239873	+	0.0704331i
$17$	1.26206	−	1.68592i	0.306095	−	0.408895i	−0.620947	−	0.783853i	$-0.713252\pi$
$17$	1.26206	−	1.68592i	0.306095	−	0.408895i	0.927042	+	0.374957i	$0.122343\pi$
$18$	0.936950	−	0.349464i	0.220841	−	0.0823695i
$19$	−0.707077	+	4.91783i	−0.162215	+	1.12823i	0.732233	+	0.681054i	$0.238478\pi$
$19$	−0.707077	+	4.91783i	−0.162215	+	1.12823i	−0.894447	+	0.447173i	$0.852431\pi$
$20$	−0.918820	+	2.03857i	−0.205454	+	0.455838i
$21$	−3.14612	+	2.72613i	−0.686539	+	0.594890i
$22$	−1.69587	−	1.69587i	−0.361560	−	0.361560i
$23$	−0.560058	+	4.76302i	−0.116780	+	0.993158i
$23$	−0.560058	+	4.76302i	−0.116780	+	0.993158i
$24$			1.00000i			0.204124i
$25$	−4.23281	−	2.66144i	−0.846563	−	0.532289i
$26$	2.04183	+	1.31221i	0.400436	+	0.257345i
$27$	0.599278	+	0.800541i	0.115331	+	0.154064i
$28$	−1.45479	−	3.90044i	−0.274929	−	0.737114i
$29$	−3.75233	+	0.539504i	−0.696791	+	0.100183i	−0.481603	−	0.876389i	$-0.659945\pi$
$29$	−3.75233	+	0.539504i	−0.696791	+	0.100183i	−0.215188	+	0.976573i	$0.569036\pi$
$30$	−2.21486	−	0.307269i	−0.404375	−	0.0560995i
$31$	−8.69709	+	5.58928i	−1.56204	+	1.00386i	−0.580133	+	0.814521i	$0.697000\pi$
$31$	−8.69709	+	5.58928i	−1.56204	+	1.00386i	−0.981911	+	0.189344i	$0.939364\pi$
$32$	−0.936950	−	0.349464i	−0.165631	−	0.0617771i
$33$	1.14939	−	2.10495i	0.200083	−	0.366425i
$34$	−1.37912	+	1.59159i	−0.236517	+	0.272955i
$35$	9.08592	−	2.02366i	1.53580	−	0.342061i
$36$	−0.959493	+	0.281733i	−0.159915	+	0.0469554i
$37$	−0.758926	+	2.03476i	−0.124767	+	0.334512i	−0.984284	−	0.176595i	$-0.943492\pi$
$37$	−0.758926	+	2.03476i	−0.124767	+	0.334512i	0.859517	+	0.511107i	$0.170765\pi$
$38$	1.05611	−	4.85486i	0.171324	−	0.787562i
$39$	−0.683801	+	2.32881i	−0.109496	+	0.372909i
$40$	1.06191	−	1.96783i	0.167903	−	0.311141i
$41$	3.56457	−	7.80531i	0.556692	−	1.21899i	−0.396894	−	0.917864i	$-0.629912\pi$
$41$	3.56457	−	7.80531i	0.556692	−	1.21899i	0.953586	−	0.301121i	$-0.0973607\pi$
$42$	3.33258	−	2.49474i	0.514229	−	0.384947i
$43$	0.874892	−	0.190321i	0.133420	−	0.0290237i	−0.145359	−	0.989379i	$-0.546434\pi$
$43$	0.874892	−	0.190321i	0.133420	−	0.0290237i	0.278779	+	0.960355i	$0.410070\pi$
$44$	1.57056	+	1.81253i	0.236771	+	0.273249i
$45$	−0.329174	−	2.21171i	−0.0490704	−	0.329702i
$46$	0.898421	−	4.71093i	0.132465	−	0.694588i
$47$	−5.40977	+	5.40977i	−0.789096	+	0.789096i	−0.981346	−	0.192250i	$-0.938422\pi$
$47$	−5.40977	+	5.40977i	−0.789096	+	0.789096i	0.192250	+	0.981346i	$0.438422\pi$
$48$	0.0713392	−	0.997452i	0.0102969	−	0.143970i
$49$	−5.58473	+	8.69001i	−0.797819	+	1.24143i
$50$	4.03216	+	2.95663i	0.570234	+	0.418130i
$51$	−1.91566	−	0.874852i	−0.268246	−	0.122504i
$52$	−1.94302	−	1.45452i	−0.269448	−	0.201706i
$53$	−8.38229	+	4.57707i	−1.15140	+	0.628709i	−0.937444	−	0.348135i	$-0.886815\pi$
$53$	−8.38229	+	4.57707i	−1.15140	+	0.628709i	−0.213951	+	0.976844i	$0.568633\pi$
$54$	−0.540641	−	0.841254i	−0.0735719	−	0.114480i
$55$	−4.49707	+	2.92164i	−0.606385	+	0.393953i
$56$	1.17283	+	3.99428i	0.156726	+	0.533759i
$57$	4.95574	−	0.354442i	0.656404	−	0.0469469i
$58$	3.78126	−	0.270441i	0.496504	−	0.0355107i
$59$	3.47547	+	11.8364i	0.452468	+	1.54097i	0.798059	+	0.602580i	$0.205861\pi$
$59$	3.47547	+	11.8364i	0.452468	+	1.54097i	−0.345590	+	0.938386i	$0.612321\pi$
$60$	2.18729	+	0.464493i	0.282378	+	0.0599657i
$61$	−6.51558	−	10.1384i	−0.834235	−	1.29810i	−0.952323	−	0.305092i	$-0.901313\pi$
$61$	−6.51558	−	10.1384i	−0.834235	−	1.29810i	0.118088	−	0.993003i	$-0.462324\pi$
$62$	9.07367	−	4.95460i	1.15236	−	0.629235i
$63$	3.33258	+	2.49474i	0.419866	+	0.314308i
$64$	0.909632	+	0.415415i	0.113704	+	0.0519269i
$65$	3.81859	−	3.85657i	0.473638	−	0.478349i
$66$	−1.29663	+	2.01759i	−0.159604	+	0.248348i
$67$	−0.779972	+	10.9054i	−0.0952888	+	1.33231i	0.694749	+	0.719253i	$0.255516\pi$
$67$	−0.779972	+	10.9054i	−0.0952888	+	1.33231i	−0.790037	+	0.613059i	$0.789939\pi$
$68$	1.48915	−	1.48915i	0.180586	−	0.180586i
$69$	4.77322	−	0.465193i	0.574628	−	0.0560027i
$70$	−9.20714	+	1.37032i	−1.10046	+	0.163785i
$71$	3.90649	+	4.50833i	0.463615	+	0.535040i	0.938625	−	0.344940i	$-0.112101\pi$
$71$	3.90649	+	4.50833i	0.463615	+	0.535040i	−0.475010	+	0.879981i	$0.657555\pi$
$72$	0.977147	−	0.212565i	0.115158	−	0.0250511i
$73$	−5.19195	+	3.88665i	−0.607672	+	0.454898i	−0.858273	−	0.513193i	$-0.828463\pi$
$73$	−5.19195	+	3.88665i	−0.607672	+	0.454898i	0.250601	+	0.968090i	$0.419372\pi$
$74$	0.902151	−	1.97543i	0.104873	−	0.229640i
$75$	−1.70087	+	4.70181i	−0.196400	+	0.542918i
$76$	−1.39976	+	4.76715i	−0.160564	+	0.546829i
$77$	2.12225	−	9.75581i	0.241853	−	1.11178i
$78$	0.848195	−	2.27410i	0.0960392	−	0.257491i
$79$	0.848029	−	0.249004i	0.0954107	−	0.0280151i	−0.233679	−	0.972314i	$-0.575076\pi$
$79$	0.848029	−	0.249004i	0.0954107	−	0.0280151i	0.329089	+	0.944299i	$0.393258\pi$
$80$	−1.19959	+	1.88706i	−0.134118	+	0.210980i
$81$	0.654861	−	0.755750i	0.0727623	−	0.0839722i
$82$	−4.11231	+	7.53113i	−0.454129	+	0.831674i
$83$	−2.04613	−	0.763166i	−0.224592	−	0.0837684i	0.234649	−	0.972080i	$-0.424606\pi$
$83$	−2.04613	−	0.763166i	−0.224592	−	0.0837684i	−0.459241	+	0.888312i	$0.651879\pi$
$84$	−3.50206	+	2.25064i	−0.382107	+	0.245565i
$85$	2.84068	+	3.75582i	0.308115	+	0.407375i
$86$	−0.886240	+	0.127422i	−0.0955657	+	0.0137403i
$87$	1.32479	+	3.55190i	0.142032	+	0.380804i
$88$	−1.43726	−	1.91995i	−0.153212	−	0.204667i
$89$	−10.1999	−	6.55508i	−1.08119	−	0.694837i	−0.126356	−	0.991985i	$-0.540328\pi$
$89$	−10.1999	−	6.55508i	−1.08119	−	0.694837i	−0.954831	+	0.297148i	$0.903964\pi$
$90$	0.170554	+	2.22955i	0.0179780	+	0.235016i
$91$			10.1039i			1.05918i
$92$	−1.23221	+	4.63483i	−0.128466	+	0.483215i
$93$	7.31025	+	7.31025i	0.758038	+	0.758038i
$94$	5.78191	−	5.01006i	0.596359	−	0.516748i
$95$	−10.1284	−	4.56506i	−1.03916	−	0.468366i
$96$	−0.142315	+	0.989821i	−0.0145249	+	0.101023i
$97$	13.2754	−	4.95146i	1.34791	−	0.502744i	0.431185	−	0.902264i	$-0.358096\pi$
$97$	13.2754	−	4.95146i	1.34791	−	0.502744i	0.916725	+	0.399519i	$0.130823\pi$
$98$	6.19044	−	8.26946i	0.625329	−	0.835342i
$99$	−2.30117	−	0.675684i	−0.231276	−	0.0679088i
$100$	−3.81097	−	3.23675i	−0.381097	−	0.323675i
$101$	7.35927	+	16.1145i	0.732275	+	1.60346i	0.795860	+	0.605481i	$0.207019\pi$
$101$	7.35927	+	16.1145i	0.732275	+	1.60346i	−0.0635851	+	0.997976i	$0.520253\pi$
$102$	1.84837	+	1.00929i	0.183016	+	0.0999341i
$103$	−0.811754	−	11.3498i	−0.0799845	−	1.11833i	−0.865974	−	0.500090i	$-0.833300\pi$
$103$	−0.811754	−	11.3498i	−0.0799845	−	1.11833i	0.785989	−	0.618240i	$-0.212154\pi$
$104$	1.83430	+	1.58943i	0.179868	+	0.155857i
$105$	−3.90877	−	8.44812i	−0.381456	−	0.824452i
$106$	8.68745	−	3.96743i	0.843800	−	0.385351i
$107$	12.4593	+	2.71036i	1.20449	+	0.262020i	0.769636	−	0.638483i	$-0.220438\pi$
$107$	12.4593	+	2.71036i	1.20449	+	0.262020i	0.434850	+	0.900503i	$0.356801\pi$
$108$	0.479249	+	0.877679i	0.0461158	+	0.0844547i
$109$	−0.155453	−	1.08120i	−0.0148897	−	0.103560i	0.981021	−	0.193900i	$-0.0621138\pi$
$109$	−0.155453	−	1.08120i	−0.0148897	−	0.103560i	−0.995911	+	0.0903398i	$0.971205\pi$
$110$	4.69404	−	2.59338i	0.447559	−	0.247269i
$111$	2.14958	+	0.309063i	0.204029	+	0.0293350i
$112$	−0.884891	−	4.06778i	−0.0836143	−	0.384369i
$113$	−17.9582	−	1.28440i	−1.68936	−	0.120826i	−0.806741	−	0.590905i	$-0.798771\pi$
$113$	−17.9582	−	1.28440i	−1.68936	−	0.120826i	−0.882624	+	0.470080i	$0.844225\pi$
$114$	−4.96840			−0.465333
$115$	−9.88687	−	4.15330i	−0.921955	−	0.387297i
$116$	−3.79092			−0.351978
$117$	2.42095	+	0.173149i	0.223816	+	0.0160077i
$118$	−2.62222	−	12.0542i	−0.241395	−	1.10968i
$119$	−8.67774	−	1.24767i	−0.795487	−	0.114374i
$120$	−2.14858	−	0.619349i	−0.196138	−	0.0565385i
$121$	−0.746880	−	5.19466i	−0.0678982	−	0.472242i
$122$	5.77572	+	10.5774i	0.522909	+	0.957636i
$123$	−8.38464	−	1.82397i	−0.756018	−	0.164462i
$124$	−9.40401	+	4.29467i	−0.844505	+	0.385672i
$125$	8.33992	−	7.44619i	0.745945	−	0.666007i
$126$	−3.14612	−	2.72613i	−0.280279	−	0.242863i
$127$	−0.937327	−	13.1055i	−0.0831743	−	1.16293i	−0.852025	−	0.523501i	$-0.824626\pi$
$127$	−0.937327	−	13.1055i	−0.0831743	−	1.16293i	0.768851	−	0.639428i	$-0.220829\pi$
$128$	−0.877679	−	0.479249i	−0.0775766	−	0.0423600i
$129$	−0.371943	−	0.814442i	−0.0327478	−	0.0717076i
$130$	−4.08399	+	3.57433i	−0.358189	+	0.313490i
$131$	−7.31640	−	2.14829i	−0.639237	−	0.187697i	−0.0539763	−	0.998542i	$-0.517190\pi$
$131$	−7.31640	−	2.14829i	−0.639237	−	0.187697i	−0.585260	+	0.810845i	$0.699008\pi$
$132$	1.43726	−	1.91995i	0.125097	−	0.167110i
$133$	19.3789	−	7.22797i	1.68037	−	0.626745i
$134$	1.55597	−	10.8220i	0.134415	−	0.934879i
$135$	−2.09119	+	0.791783i	−0.179981	+	0.0681459i
$136$	−1.59159	+	1.37912i	−0.136478	+	0.118258i
$137$	−0.0816534	−	0.0816534i	−0.00697612	−	0.00697612i	0.703610	−	0.710586i	$-0.251570\pi$
$137$	−0.0816534	−	0.0816534i	−0.00697612	−	0.00697612i	−0.710586	+	0.703610i	$0.751570\pi$
$138$	−4.79424	+	0.123491i	−0.408113	+	0.0105122i
$139$		−	7.81204i		−	0.662608i	−0.943524	−	0.331304i	$-0.892511\pi$
$139$		−	7.81204i		−	0.662608i	0.943524	−	0.331304i	$-0.107489\pi$
$140$	9.28144	−	0.710002i	0.784425	−	0.0600061i
$141$	6.43607	+	4.13621i	0.542015	+	0.348332i
$142$	−3.57491	−	4.77553i	−0.300000	−	0.400753i
$143$	−2.03424	−	5.45401i	−0.170112	−	0.456087i
$144$	−0.989821	+	0.142315i	−0.0824851	+	0.0118596i
$145$	1.16483	−	8.39634i	0.0967342	−	0.697278i
$146$	5.45600	−	3.50636i	0.451541	−	0.290188i
$147$	9.67854	+	3.60991i	0.798272	+	0.297740i
$148$	−1.04078	+	1.90604i	−0.0855514	+	0.156676i
$149$	−6.50574	+	7.50803i	−0.532971	+	0.615082i	−0.956831	−	0.290647i	$-0.906130\pi$
$149$	−6.50574	+	7.50803i	−0.532971	+	0.615082i	0.423859	+	0.905728i	$0.360675\pi$
$150$	2.03196	−	4.56849i	0.165909	−	0.373016i
$151$	10.7016	−	3.14227i	0.870884	−	0.255715i	0.184393	−	0.982853i	$-0.440968\pi$
$151$	10.7016	−	3.14227i	0.870884	−	0.255715i	0.686491	+	0.727138i	$0.259150\pi$
$152$	1.73628	−	4.65514i	0.140831	−	0.377582i
$153$	−0.447657	+	2.05784i	−0.0361909	+	0.166367i
$154$	−2.81281	+	9.57956i	−0.226663	+	0.771943i
$155$	−6.62250	−	22.1481i	−0.531932	−	1.77898i
$156$	−1.00827	+	2.20779i	−0.0807259	+	0.176765i
$157$	0.763456	−	0.571516i	0.0609304	−	0.0456120i	−0.568378	−	0.822767i	$-0.692429\pi$
$157$	0.763456	−	0.571516i	0.0609304	−	0.0456120i	0.629309	+	0.777155i	$0.283338\pi$
$158$	−0.863632	+	0.187872i	−0.0687069	+	0.0149463i
$159$	6.25426	+	7.21780i	0.495995	+	0.572409i
$160$	1.33115	−	1.79667i	0.105237	−	0.142040i
$161$	18.5200	−	7.45627i	1.45958	−	0.587637i
$162$	−0.707107	+	0.707107i	−0.0555556	+	0.0555556i
$163$	1.51888	−	21.2367i	0.118968	−	1.66338i	−0.491151	−	0.871074i	$-0.663424\pi$
$163$	1.51888	−	21.2367i	0.118968	−	1.66338i	0.610119	−	0.792310i	$-0.291122\pi$
$164$	4.63910	−	7.21858i	0.362253	−	0.563676i
$165$	3.81079	+	3.77326i	0.296670	+	0.293748i
$166$	1.98647	+	0.907191i	0.154180	+	0.0704117i
$167$	2.96458	+	2.21926i	0.229406	+	0.171732i	0.707797	−	0.706415i	$-0.249689\pi$
$167$	2.96458	+	2.21926i	0.229406	+	0.171732i	−0.478391	+	0.878147i	$0.658780\pi$
$168$	3.65370	−	1.99507i	0.281889	−	0.153923i
$169$	−3.84344	−	5.98051i	−0.295649	−	0.460039i
$170$	−2.56550	−	3.94890i	−0.196765	−	0.302867i
$171$	−1.39976	−	4.76715i	−0.107042	−	0.364553i
$172$	0.893072	−	0.0638738i	0.0680961	−	0.00487033i
$173$	2.02328	−	0.144708i	0.153827	−	0.0110020i	0.00578693	−	0.999983i	$-0.498158\pi$
$173$	2.02328	−	0.144708i	0.153827	−	0.0110020i	0.148040	+	0.988981i	$0.452703\pi$
$174$	−1.06803	−	3.63736i	−0.0809668	−	0.275748i
$175$	−1.27935	+	20.7752i	−0.0967098	+	1.57046i
$176$	1.29663	+	2.01759i	0.0977370	+	0.152082i
$177$	10.8271	−	5.91205i	0.813816	−	0.444377i
$178$	9.70628	+	7.26603i	0.727516	+	0.544612i
$179$	17.2600	+	7.88238i	1.29007	+	0.589157i	0.937941	−	0.346794i	$-0.112730\pi$
$179$	17.2600	+	7.88238i	1.29007	+	0.589157i	0.352132	+	0.935950i	$0.385457\pi$
$180$	−0.0110650	−	2.23604i	−0.000824735	−	0.166665i
$181$	6.50319	−	10.1192i	0.483378	−	0.752151i	−0.510823	−	0.859686i	$-0.670659\pi$
$181$	6.50319	−	10.1192i	0.483378	−	0.752151i	0.994201	+	0.107535i	$0.0342957\pi$
$182$	0.720806	−	10.0782i	0.0534297	−	0.747045i
$183$	−8.52177	+	8.52177i	−0.629947	+	0.629947i
$184$	1.55971	−	4.53512i	0.114983	−	0.334333i
$185$	−3.90181	−	2.89084i	−0.286867	−	0.212539i
$186$	−6.77012	−	7.81313i	−0.496409	−	0.572887i
$187$	4.93536	−	1.07362i	0.360909	−	0.0785110i
$188$	−6.12460	+	4.58482i	−0.446682	+	0.334382i
$189$	1.72934	−	3.78672i	0.125791	−	0.275443i
$190$	9.77696	+	5.27599i	0.709295	+	0.382760i
$191$	0.384993	−	1.31116i	0.0278571	−	0.0948725i	−0.944391	−	0.328824i	$-0.893348\pi$
$191$	0.384993	−	1.31116i	0.0278571	−	0.0948725i	0.972248	+	0.233952i	$0.0751658\pi$
$192$	0.212565	−	0.977147i	0.0153406	−	0.0705195i
$193$	−4.94501	+	13.2581i	−0.355950	+	0.954339i	0.628365	+	0.777919i	$0.283724\pi$
$193$	−4.94501	+	13.2581i	−0.355950	+	0.954339i	−0.984315	+	0.176420i	$0.943548\pi$
$194$	−13.5948	+	3.99179i	−0.976048	+	0.286594i
$195$	−4.58014	−	2.91155i	−0.327990	−	0.208501i
$196$	−6.76460	+	7.80677i	−0.483186	+	0.557626i
$197$	0.0462241	−	0.0846530i	0.00329333	−	0.00603128i	−0.876027	−	0.482262i	$-0.839815\pi$
$197$	0.0462241	−	0.0846530i	0.00329333	−	0.00603128i	0.879320	+	0.476231i	$0.157997\pi$
$198$	2.24710	+	0.838126i	0.159695	+	0.0595630i
$199$	−11.4132	+	7.33479i	−0.809057	+	0.519949i	−0.878560	−	0.477632i	$-0.841495\pi$
$199$	−11.4132	+	7.33479i	−0.809057	+	0.519949i	0.0695028	+	0.997582i	$0.477859\pi$
$200$	3.57035	+	3.50037i	0.252462	+	0.247514i
$201$	10.8220	−	1.55597i	0.763326	−	0.109750i
$202$	−6.19092	−	16.5985i	−0.435592	−	1.16787i
$203$	9.45736	+	12.6336i	0.663776	+	0.886702i
$204$	−1.77166	−	1.13857i	−0.124041	−	0.0797162i
$205$	14.5627	+	12.4930i	1.01710	+	0.872547i
$206$			11.3788i			0.792799i
$207$	−1.46918	−	4.56525i	−0.102115	−	0.317307i
$208$	−1.71624	−	1.71624i	−0.119000	−	0.119000i
$209$	−9.00536	+	7.80319i	−0.622914	+	0.539758i
$210$	3.29612	+	8.70544i	0.227454	+	0.600733i
$211$	−0.193391	+	1.34506i	−0.0133136	+	0.0925979i	−0.995395	−	0.0958601i	$-0.969440\pi$
$211$	−0.193391	+	1.34506i	−0.0133136	+	0.0925979i	0.982081	+	0.188458i	$0.0603489\pi$
$212$	−8.94835	+	3.33756i	−0.614575	+	0.229225i
$213$	3.57491	−	4.77553i	0.244949	−	0.327214i
$214$	−12.2342	−	3.59229i	−0.836313	−	0.245564i
$215$	−0.132943	+	1.99765i	−0.00906661	+	0.136239i
$216$	−0.415415	−	0.909632i	−0.0282654	−	0.0618926i
$217$	37.7729	+	20.6256i	2.56419	+	1.40015i
$218$	0.0779253	+	1.08954i	0.00527777	+	0.0737928i
$219$	4.90146	+	4.24714i	0.331210	+	0.286995i
$220$	−4.86709	+	2.25190i	−0.328139	+	0.151823i
$221$	−4.64955	+	2.12338i	−0.312763	+	0.142834i
$222$	−2.12206	−	0.461625i	−0.142423	−	0.0309822i
$223$	−9.49628	−	17.3911i	−0.635918	−	1.16460i	−0.974655	−	0.223715i	$-0.928181\pi$
$223$	−9.49628	−	17.3911i	−0.635918	−	1.16460i	0.338737	−	0.940881i	$-0.390000\pi$
$224$	0.592444	+	4.12054i	0.0395843	+	0.275315i
$225$	4.95591	+	0.662560i	0.330394	+	0.0441706i
$226$	17.8208	+	2.56225i	1.18542	+	0.170438i
$227$	−3.86873	−	17.7842i	−0.256776	−	1.18038i	−0.907163	−	0.420779i	$-0.861757\pi$
$227$	−3.86873	−	17.7842i	−0.256776	−	1.18038i	0.650387	−	0.759603i	$-0.274607\pi$
$228$	4.95574	+	0.354442i	0.328202	+	0.0234735i
$229$	3.78792			0.250313			0.125156	−	0.992137i	$-0.460057\pi$
$229$	3.78792			0.250313			0.125156	+	0.992137i	$0.460057\pi$
$230$	9.56538	+	4.84804i	0.630723	+	0.319670i
$231$	−9.98398			−0.656898
$232$	3.78126	+	0.270441i	0.248252	+	0.0177553i
$233$	1.91845	+	8.81897i	0.125682	+	0.577750i	0.996311	+	0.0858109i	$0.0273481\pi$
$233$	1.91845	+	8.81897i	0.125682	+	0.577750i	−0.870630	+	0.491939i	$0.836288\pi$
$234$	−2.40242	−	0.345417i	−0.157051	−	0.0225806i
$235$	−8.27280	−	14.9739i	−0.539658	−	0.976788i
$236$	1.75561	+	12.2105i	0.114280	+	0.794837i
$237$	−0.423575	−	0.775719i	−0.0275141	−	0.0503884i
$238$	8.56662	+	1.86355i	0.555292	+	0.120796i
$239$	10.4854	−	4.78854i	0.678247	−	0.309745i	−0.0463424	−	0.998926i	$-0.514757\pi$
$239$	10.4854	−	4.78854i	0.678247	−	0.309745i	0.724590	+	0.689180i	$0.242029\pi$
$240$	2.09892	+	0.771049i	0.135485	+	0.0497710i
$241$	3.23799	+	2.80574i	0.208577	+	0.180733i	0.752884	−	0.658153i	$-0.228662\pi$
$241$	3.23799	+	2.80574i	0.208577	+	0.180733i	−0.544307	+	0.838886i	$0.683207\pi$
$242$	0.374394	+	5.23471i	0.0240669	+	0.336500i
$243$	−0.877679	−	0.479249i	−0.0563031	−	0.0307438i
$244$	−5.00641	−	10.9625i	−0.320503	−	0.701803i
$245$	−15.2123	−	17.3814i	−0.971879	−	1.11046i
$246$	8.23316	+	2.41747i	0.524927	+	0.154132i
$247$	7.22666	−	9.65369i	0.459821	−	0.614249i
$248$	9.68643	−	3.61285i	0.615089	−	0.229416i
$249$	−0.310790	+	2.16159i	−0.0196955	+	0.136985i
$250$	−8.84988	+	6.83225i	−0.559715	+	0.432110i
$251$	−6.22965	+	5.39802i	−0.393212	+	0.340720i	−0.828919	−	0.559368i	$-0.811044\pi$
$251$	−6.22965	+	5.39802i	−0.393212	+	0.340720i	0.435707	+	0.900088i	$0.356498\pi$
$252$	2.94362	+	2.94362i	0.185431	+	0.185431i
$253$	−8.49574	+	7.75349i	−0.534123	+	0.487458i
$254$			13.1390i			0.824416i
$255$	3.06615	−	3.57411i	0.192010	−	0.223820i
$256$	0.841254	+	0.540641i	0.0525783	+	0.0337901i
$257$	−5.72627	−	7.64941i	−0.357195	−	0.477157i	0.585566	−	0.810624i	$-0.300872\pi$
$257$	−5.72627	−	7.64941i	−0.357195	−	0.477157i	−0.942762	+	0.333468i	$0.891781\pi$
$258$	0.312894	+	0.838901i	0.0194799	+	0.0522277i
$259$	8.94852	−	1.28660i	0.556034	−	0.0799456i
$260$	4.32857	−	3.27388i	0.268447	−	0.203037i
$261$	3.18912	−	2.04953i	0.197402	−	0.126862i
$262$	7.14450	+	2.66476i	0.441389	+	0.164629i
$263$	−14.0953	+	25.8136i	−0.869153	+	1.59174i	−0.0645561	+	0.997914i	$0.520563\pi$
$263$	−14.0953	+	25.8136i	−0.869153	+	1.59174i	−0.804597	+	0.593821i	$0.797619\pi$
$264$	−1.57056	+	1.81253i	−0.0966615	+	0.111553i
$265$	−4.64266	−	20.8448i	−0.285197	−	1.28049i
$266$	−19.8452	+	5.82708i	−1.21679	+	0.357281i
$267$	−4.23713	+	11.3602i	−0.259308	+	0.695232i
$268$	−2.32404	+	10.6834i	−0.141963	+	0.652595i
$269$	3.97503	−	13.5377i	0.242362	−	0.825408i	−0.745019	−	0.667043i	$-0.767560\pi$
$269$	3.97503	−	13.5377i	0.242362	−	0.825408i	0.987381	−	0.158365i	$-0.0506222\pi$
$270$	2.14235	−	0.640582i	0.130379	−	0.0389846i
$271$	3.69039	−	8.08083i	0.224175	−	0.490876i	−0.763807	−	0.645445i	$-0.776672\pi$
$271$	3.69039	−	8.08083i	0.224175	−	0.490876i	0.987982	+	0.154570i	$0.0493991\pi$
$272$	1.68592	−	1.26206i	0.102224	−	0.0765238i
$273$	9.87302	−	2.14774i	0.597542	−	0.129987i
$274$	0.0756202	+	0.0872704i	0.00456839	+	0.00527220i
$275$	−3.49212	−	11.4718i	−0.210583	−	0.691778i
$276$	4.79084	+	0.218841i	0.288374	+	0.0131727i
$277$	−13.2715	+	13.2715i	−0.797406	+	0.797406i	−0.982686	−	0.185280i	$-0.940681\pi$
$277$	−13.2715	+	13.2715i	−0.797406	+	0.797406i	0.185280	+	0.982686i	$0.440681\pi$
$278$	−0.557304	+	7.79213i	−0.0334249	+	0.467341i
$279$	5.58928	−	8.69709i	0.334622	−	0.520681i
$280$	−9.30844	+	0.0460625i	−0.556286	+	0.00275276i
$281$	−19.0081	−	8.68070i	−1.13393	−	0.517847i	−0.242112	−	0.970248i	$-0.577840\pi$
$281$	−19.0081	−	8.68070i	−1.13393	−	0.517847i	−0.891815	+	0.452401i	$0.850568\pi$
$282$	−6.12460	−	4.58482i	−0.364714	−	0.273022i
$283$	−11.6948	+	6.38585i	−0.695184	+	0.379599i	−0.787655	−	0.616116i	$-0.788705\pi$
$283$	−11.6948	+	6.38585i	−0.695184	+	0.379599i	0.0924712	+	0.995715i	$0.470523\pi$
$284$	3.22512	+	5.01839i	0.191376	+	0.297787i
$285$	−2.30778	+	10.8673i	−0.136701	+	0.643726i
$286$	1.63997	+	5.58523i	0.0969736	+	0.330262i
$287$	−35.6298	+	2.54830i	−2.10316	+	0.150421i
$288$	0.997452	−	0.0713392i	0.0587754	−	0.00420370i
$289$	3.53994	+	12.0559i	0.208232	+	0.709171i
$290$	−1.76085	+	8.29185i	−0.103401	+	0.486914i
$291$	−7.66018	−	11.9195i	−0.449048	−	0.698732i
$292$	−5.69224	+	3.10820i	−0.333113	+	0.181893i
$293$	−13.5050	−	10.1097i	−0.788972	−	0.590617i	0.126980	−	0.991905i	$-0.459472\pi$
$293$	−13.5050	−	10.1097i	−0.788972	−	0.590617i	−0.915952	+	0.401288i	$0.868563\pi$
$294$	−9.39635	−	4.29117i	−0.548006	−	0.250266i
$295$	−27.5840	+	0.136498i	−1.60600	+	0.00794725i
$296$	1.17410	−	1.82694i	0.0682433	−	0.106189i
$297$	−0.171094	+	2.39221i	−0.00992788	+	0.138810i
$298$	7.02478	−	7.02478i	0.406935	−	0.406935i
$299$	6.73340	−	9.49491i	0.389402	−	0.549105i
$300$	−2.35270	+	4.41189i	−0.135833	+	0.254721i
$301$	−2.44085	−	2.81689i	−0.140688	−	0.162363i
$302$	−10.8985	+	2.37082i	−0.627139	+	0.136426i
$303$	14.1820	−	10.6165i	0.814732	−	0.609901i
$304$	−2.06395	+	4.51942i	−0.118376	+	0.259206i
$305$	25.8187	−	7.72004i	1.47838	−	0.442048i
$306$	0.593321	−	2.02067i	0.0339179	−	0.115514i
$307$	−3.14925	+	14.4769i	−0.179737	+	0.826238i	0.795653	+	0.605753i	$0.207128\pi$
$307$	−3.14925	+	14.4769i	−0.179737	+	0.826238i	−0.975390	+	0.220486i	$0.929236\pi$
$308$	3.48904	−	9.35449i	0.198807	−	0.533021i
$309$	−10.9179	+	3.20578i	−0.621096	+	0.182370i
$310$	5.02560	+	22.5642i	0.285435	+	1.28156i
$311$	0.626634	−	0.723174i	0.0355331	−	0.0410074i	−0.737705	−	0.675123i	$-0.764090\pi$
$311$	0.626634	−	0.723174i	0.0355331	−	0.0410074i	0.773238	+	0.634116i	$0.218636\pi$
$312$	1.16320	−	2.13024i	0.0658532	−	0.120601i
$313$	−22.5730	−	8.41928i	−1.27590	−	0.475886i	−0.382004	−	0.924161i	$-0.624766\pi$
$313$	−22.5730	−	8.41928i	−1.27590	−	0.475886i	−0.893896	+	0.448275i	$0.852039\pi$
$314$	−0.802283	+	0.515596i	−0.0452754	+	0.0290967i
$315$	−7.42419	+	5.61522i	−0.418305	+	0.316382i
$316$	0.874834	−	0.125782i	0.0492133	−	0.00707580i
$317$	−5.93440	−	15.9107i	−0.333309	−	0.893637i	−0.990201	−	0.139652i	$-0.955402\pi$
$317$	−5.93440	−	15.9107i	−0.333309	−	0.893637i	0.656891	−	0.753985i	$-0.271871\pi$
$318$	−5.72341	−	7.64558i	−0.320953	−	0.428743i
$319$	−7.64853	−	4.91541i	−0.428235	−	0.275210i
$320$	−1.45593	+	1.69713i	−0.0813891	+	0.0948726i
$321$		−	12.7507i		−	0.711675i
$322$	−19.0047	+	6.11608i	−1.05909	+	0.340836i
$323$	7.39868	+	7.39868i	0.411674	+	0.411674i
$324$	0.755750	−	0.654861i	0.0419861	−	0.0363812i
$325$	5.92112	+	10.5931i	0.328445	+	0.587601i
$326$	−3.03001	+	21.0742i	−0.167817	+	1.16719i
$327$	−1.02345	+	0.381727i	−0.0565969	+	0.0211096i
$328$	−5.14224	+	6.86923i	−0.283933	+	0.379290i
$329$	30.5586	+	8.97280i	1.68475	+	0.494686i
$330$	−3.53190	−	4.03550i	−0.194425	−	0.222147i
$331$	13.7121	+	30.0253i	0.753686	+	1.65034i	0.759626	+	0.650360i	$0.225382\pi$
$331$	13.7121	+	30.0253i	0.753686	+	1.65034i	−0.00594002	+	0.999982i	$0.501891\pi$
$332$	−1.91669	−	1.04659i	−0.105192	−	0.0574392i
$333$	−0.154926	−	2.16615i	−0.00848991	−	0.118704i
$334$	−2.79871	−	2.42510i	−0.153139	−	0.132695i
$335$	−22.9482	−	8.43010i	−1.25379	−	0.460586i
$336$	−3.78672	+	1.72934i	−0.206582	+	0.0943430i
$337$	10.4554	+	2.27444i	0.569543	+	0.123896i	0.488110	−	0.872782i	$-0.337687\pi$
$337$	10.4554	+	2.27444i	0.569543	+	0.123896i	0.0814332	+	0.996679i	$0.474050\pi$
$338$	3.40700	+	6.23946i	0.185316	+	0.339382i
$339$	2.56225	+	17.8208i	0.139162	+	0.967894i
$340$	2.27725	+	4.12186i	0.123501	+	0.223539i
$341$	−24.5420	−	3.52861i	−1.32903	−	0.191085i
$342$	1.05611	+	4.85486i	0.0571079	+	0.262521i
$343$	13.8265	+	0.988890i	0.746560	+	0.0533951i
$344$	−0.895354			−0.0482742
$345$	−1.95678	+	10.5438i	−0.105349	+	0.567657i
$346$	−2.02845			−0.109050
$347$	−4.08084	−	0.291868i	−0.219071	−	0.0156683i	−0.0386279	−	0.999254i	$-0.512299\pi$
$347$	−4.08084	−	0.291868i	−0.219071	−	0.0156683i	−0.180443	+	0.983585i	$0.557753\pi$
$348$	0.805818	+	3.70429i	0.0431964	+	0.198571i
$349$	−4.82009	−	0.693025i	−0.258014	−	0.0370968i	0.0120941	−	0.999927i	$-0.496150\pi$
$349$	−4.82009	−	0.693025i	−0.258014	−	0.0370968i	−0.270108	+	0.962830i	$0.587059\pi$
$350$	2.75818	−	20.6310i	0.147431	−	1.10277i
$351$	−0.345417	−	2.40242i	−0.0184370	−	0.128232i
$352$	−1.14939	−	2.10495i	−0.0612627	−	0.112194i
$353$	14.1962	+	3.08820i	0.755589	+	0.164368i	0.573830	−	0.818975i	$-0.305457\pi$
$353$	14.1962	+	3.08820i	0.755589	+	0.164368i	0.181759	+	0.983343i	$0.441821\pi$
$354$	−11.2213	+	5.12459i	−0.596405	+	0.272369i
$355$	−12.1060	+	5.60119i	−0.642519	+	0.297280i
$356$	−9.16319	−	7.93995i	−0.485648	−	0.420817i
$357$	0.625429	+	8.74464i	0.0331012	+	0.462815i
$358$	−16.6537	−	9.09361i	−0.880176	−	0.480612i
$359$	7.91579	+	17.3332i	0.417779	+	0.914809i	0.995154	+	0.0983295i	$0.0313499\pi$
$359$	7.91579	+	17.3332i	0.417779	+	0.914809i	−0.577375	+	0.816479i	$0.695923\pi$
$360$	−0.148481	+	2.23113i	−0.00782561	+	0.117591i
$361$	−5.45472	−	1.60165i	−0.287091	−	0.0842974i
$362$	−7.20851	+	9.62944i	−0.378871	+	0.506112i
$363$	−4.91719	+	1.83402i	−0.258085	+	0.0962609i
$364$	−1.43794	+	10.0011i	−0.0753685	+	0.524199i
$365$	−5.13516	−	13.5625i	−0.268786	−	0.709895i
$366$	9.10799	−	7.89212i	0.476082	−	0.412528i
$367$	6.60131	+	6.60131i	0.344586	+	0.344586i	0.858088	−	0.513502i	$-0.171652\pi$
$367$	6.60131	+	6.60131i	0.344586	+	0.344586i	−0.513502	+	0.858088i	$0.671652\pi$
$368$	−1.87927	+	4.41230i	−0.0979637	+	0.230007i
$369$			8.58074i			0.446695i
$370$	3.68564	+	3.16183i	0.191607	+	0.164376i
$371$	33.4465	+	21.4948i	1.73646	+	1.11595i
$372$	6.19549	+	8.27620i	0.321221	+	0.429101i
$373$	1.53183	+	4.10700i	0.0793153	+	0.212652i	0.970555	−	0.240880i	$-0.0774362\pi$
$373$	1.53183	+	4.10700i	0.0793153	+	0.212652i	−0.891240	+	0.453533i	$0.850163\pi$
$374$	−4.99938	+	0.718802i	−0.258512	+	0.0371684i
$375$	−9.04880	−	6.56652i	−0.467278	−	0.339094i
$376$	6.43607	−	4.13621i	0.331915	−	0.213309i
$377$	8.62092	+	3.21544i	0.444000	+	0.165604i
$378$	−1.99507	+	3.65370i	−0.102615	+	0.187926i
$379$	11.4462	−	13.2096i	0.587950	−	0.678530i	−0.381345	−	0.924433i	$-0.624539\pi$
$379$	11.4462	−	13.2096i	0.587950	−	0.678530i	0.969295	+	0.245903i	$0.0790843\pi$
$380$	−9.37567	−	5.96003i	−0.480962	−	0.305743i
$381$	−12.6068	+	3.70169i	−0.645866	+	0.189643i
$382$	−0.477549	+	1.28036i	−0.0244335	+	0.0655089i
$383$	−4.44093	+	20.4146i	−0.226921	+	1.04314i	0.712846	+	0.701321i	$0.247406\pi$
$383$	−4.44093	+	20.4146i	−0.226921	+	1.04314i	−0.939766	+	0.341817i	$0.888958\pi$
$384$	−0.281733	+	0.959493i	−0.0143771	+	0.0489639i
$385$	19.6468	+	10.6021i	1.00129	+	0.540332i
$386$	5.87824	−	12.8715i	0.299194	−	0.655144i
$387$	−0.716768	+	0.536565i	−0.0364353	+	0.0272752i
$388$	13.8449	−	3.01178i	0.702869	−	0.152900i
$389$	−8.89356	−	10.2637i	−0.450921	−	0.520391i	0.484085	−	0.875021i	$-0.339152\pi$
$389$	−8.89356	−	10.2637i	−0.450921	−	0.520391i	−0.935007	+	0.354630i	$0.884607\pi$
$390$	4.36076	+	3.23088i	0.220816	+	0.163602i
$391$	7.32323	+	6.95544i	0.370351	+	0.351751i
$392$	7.30430	−	7.30430i	0.368923	−	0.368923i
$393$	−0.543981	+	7.60585i	−0.0274402	+	0.383664i
$394$	−0.0521454	+	0.0811398i	−0.00262705	+	0.00408776i
$395$	0.00977956	+	1.97628i	0.000492063	+	0.0994374i
$396$	−2.18158	−	0.996296i	−0.109629	−	0.0500658i
$397$	24.2049	+	18.1195i	1.21481	+	0.909394i	0.997768	−	0.0667688i	$-0.0212690\pi$
$397$	24.2049	+	18.1195i	1.21481	+	0.909394i	0.217040	+	0.976163i	$0.430360\pi$
$398$	11.9073	−	6.50189i	0.596861	−	0.325911i
$399$	−11.1821	−	17.3997i	−0.559804	−	0.871072i
$400$	−3.31154	−	3.74616i	−0.165577	−	0.187308i
$401$	4.05107	+	13.7967i	0.202301	+	0.688972i	0.996670	+	0.0815378i	$0.0259831\pi$
$401$	4.05107	+	13.7967i	0.202301	+	0.688972i	−0.794370	+	0.607435i	$0.792199\pi$
$402$	−10.9054	+	0.779972i	−0.543914	+	0.0389015i
$403$	25.0284	−	1.79006i	1.24675	−	0.0891694i
$404$	4.99102	+	16.9979i	0.248313	+	0.845675i
$405$	1.21820	+	1.87509i	0.0605330	+	0.0931742i
$406$	−8.53200	−	13.2760i	−0.423436	−	0.658879i
$407$	−4.57129	+	2.49611i	−0.226591	+	0.123728i
$408$	1.68592	+	1.26206i	0.0834654	+	0.0624814i
$409$	−3.18455	−	1.45433i	−0.157466	−	0.0719121i	0.335123	−	0.942174i	$-0.391222\pi$
$409$	−3.18455	−	1.45433i	−0.157466	−	0.0719121i	−0.492589	+	0.870262i	$0.663949\pi$
$410$	−13.6343	−	13.5000i	−0.673350	−	0.666719i
$411$	−0.0624307	+	0.0971440i	−0.00307948	+	0.00479176i
$412$	0.811754	−	11.3498i	0.0399923	−	0.559165i
$413$	36.3128	−	36.3128i	1.78683	−	1.78683i
$414$	1.13976	+	4.65843i	0.0560160	+	0.228949i
$415$	2.90699	−	3.92361i	0.142699	−	0.192602i
$416$	1.58943	+	1.83430i	0.0779283	+	0.0899341i
$417$	−7.63351	+	1.66057i	−0.373815	+	0.0813184i
$418$	9.53908	−	7.14087i	0.466572	−	0.349271i
$419$	3.27598	−	7.17339i	0.160042	−	0.350443i	−0.812575	−	0.582857i	$-0.801935\pi$
$419$	3.27598	−	7.17339i	0.160042	−	0.350443i	0.972617	+	0.232413i	$0.0746622\pi$
$420$	−2.66669	−	8.91841i	−0.130121	−	0.435174i
$421$	4.95922	−	16.8896i	0.241698	−	0.823147i	−0.745889	−	0.666071i	$-0.767975\pi$
$421$	4.95922	−	16.8896i	0.241698	−	0.823147i	0.987586	−	0.157076i	$-0.0502069\pi$
$422$	0.288854	−	1.32784i	0.0140612	−	0.0646382i
$423$	2.67360	−	7.16820i	0.129995	−	0.348530i
$424$	9.16365	−	2.69069i	0.445026	−	0.130671i
$425$	−9.82905	+	3.77727i	−0.476779	+	0.183224i
$426$	−3.90649	+	4.50833i	−0.189270	+	0.218429i
$427$	−24.0438	+	44.0329i	−1.16356	+	2.13090i
$428$	11.9468	+	4.45591i	0.577469	+	0.215385i
$429$	−4.89696	+	3.14708i	−0.236427	+	0.151943i
$430$	0.275115	−	1.98308i	0.0132672	−	0.0956326i
$431$	−19.9566	+	2.86933i	−0.961278	+	0.138211i	−0.605049	−	0.796188i	$-0.706847\pi$
$431$	−19.9566	+	2.86933i	−0.961278	+	0.138211i	−0.356229	+	0.934399i	$0.615938\pi$
$432$	0.349464	+	0.936950i	0.0168136	+	0.0450790i
$433$	10.2283	+	13.6635i	0.491543	+	0.656624i	0.975893	−	0.218250i	$-0.0700349\pi$
$433$	10.2283	+	13.6635i	0.491543	+	0.656624i	−0.484350	+	0.874874i	$0.660944\pi$
$434$	−36.2052	−	23.2677i	−1.73791	−	1.11689i
$435$	−8.45206	+	0.646557i	−0.405245	+	0.0310000i
$436$		−	1.09232i		−	0.0523127i
$437$	−23.0277	−	6.12209i	−1.10156	−	0.292859i
$438$	−4.58598	−	4.58598i	−0.219127	−	0.219127i
$439$	−12.7822	+	11.0758i	−0.610059	+	0.528620i	−0.904182	−	0.427148i	$-0.859518\pi$
$439$	−12.7822	+	11.0758i	−0.610059	+	0.528620i	0.294122	+	0.955768i	$0.404973\pi$
$440$	5.01534	−	1.89895i	0.239097	−	0.0905287i
$441$	1.47009	−	10.2247i	0.0700042	−	0.486890i
$442$	4.78919	−	1.78627i	0.227798	−	0.0849644i
$443$	−16.8866	+	22.5578i	−0.802306	+	1.07176i	0.193575	+	0.981085i	$0.437992\pi$
$443$	−16.8866	+	22.5578i	−0.802306	+	1.07176i	−0.995881	+	0.0906699i	$0.971099\pi$
$444$	2.08372	+	0.611834i	0.0988888	+	0.0290364i
$445$	20.4014	−	17.8554i	0.967120	−	0.846429i
$446$	8.23141	+	18.0243i	0.389769	+	0.853474i
$447$	8.71934	+	4.76112i	0.412411	+	0.225193i
$448$	−0.296979	−	4.15231i	−0.0140309	−	0.196178i
$449$	22.7466	+	19.7100i	1.07348	+	0.930174i	0.997756	−	0.0669553i	$-0.0213285\pi$
$449$	22.7466	+	19.7100i	1.07348	+	0.930174i	0.0757217	+	0.997129i	$0.475874\pi$
$450$	−4.89601	−	1.01442i	−0.230800	−	0.0478203i
$451$	18.7196	−	8.54896i	0.881472	−	0.402555i
$452$	−17.5926	−	3.82704i	−0.827487	−	0.180009i
$453$	−5.34525	−	9.78910i	−0.251142	−	0.459932i
$454$	2.59016	+	18.0149i	0.121562	+	0.845482i
$455$	−21.7091	−	6.25785i	−1.01774	−	0.293373i
$456$	−4.91783	−	0.707077i	−0.230298	−	0.0331119i
$457$	−0.254817	−	1.17137i	−0.0119198	−	0.0547946i	0.970803	−	0.239879i	$-0.0771078\pi$
$457$	−0.254817	−	1.17137i	−0.0119198	−	0.0547946i	−0.982723	+	0.185084i	$0.940744\pi$
$458$	−3.77827	−	0.270227i	−0.176547	−	0.0126269i
$459$	2.10597			0.0982984
$460$	−9.19515	−	5.51807i	−0.428726	−	0.257281i
$461$	−10.7712			−0.501666			−0.250833	−	0.968030i	$-0.580704\pi$
$461$	−10.7712			−0.501666			−0.250833	+	0.968030i	$0.580704\pi$
$462$	9.95854	+	0.712249i	0.463313	+	0.0331368i
$463$	6.25966	+	28.7752i	0.290911	+	1.33730i	0.858004	+	0.513643i	$0.171705\pi$
$463$	6.25966	+	28.7752i	0.290911	+	1.33730i	−0.567093	+	0.823654i	$0.691932\pi$
$464$	−3.75233	−	0.539504i	−0.174198	−	0.0250458i
$465$	−20.2343	+	11.1791i	−0.938342	+	0.518418i
$466$	−1.28442	−	8.93336i	−0.0594998	−	0.413830i
$467$	−8.86559	−	16.2361i	−0.410250	−	0.751318i	0.588097	−	0.808791i	$-0.299877\pi$
$467$	−8.86559	−	16.2361i	−0.410250	−	0.751318i	−0.998347	+	0.0574731i	$0.981696\pi$
$468$	2.37166	+	0.515924i	0.109630	+	0.0238486i
$469$	41.4013	−	18.9073i	1.91173	−	0.873060i
$470$	7.18350	+	15.5259i	0.331350	+	0.716156i
$471$	−0.720740	−	0.624524i	−0.0332099	−	0.0287766i
$472$	−0.880046	−	12.3046i	−0.0405074	−	0.566367i
$473$	1.88468	+	1.02911i	0.0866575	+	0.0473186i
$474$	0.367156	+	0.803960i	0.0168640	+	0.0369271i
$475$	16.0815	−	18.9344i	0.737868	−	0.868770i
$476$	−8.41185	−	2.46994i	−0.385557	−	0.113210i
$477$	5.72341	−	7.64558i	0.262057	−	0.350067i
$478$	−10.8003	+	4.02832i	−0.493996	+	0.184251i
$479$	−3.18838	+	22.1757i	−0.145681	+	1.01323i	0.777504	+	0.628877i	$0.216485\pi$
$479$	−3.18838	+	22.1757i	−0.145681	+	1.01323i	−0.923185	+	0.384355i	$0.874424\pi$
$480$	−2.03857	−	0.918820i	−0.0930476	−	0.0419382i
$481$	3.98353	−	3.45175i	0.181633	−	0.157386i
$482$	−3.02958	−	3.02958i	−0.137994	−	0.137994i
$483$	−11.2226	−	16.5118i	−0.510645	−	0.751313i
$484$		−	5.24808i		−	0.238549i
$485$	2.41653	+	31.5899i	0.109729	+	1.43442i
$486$	0.841254	+	0.540641i	0.0381600	+	0.0245240i
$487$	11.2854	+	15.0755i	0.511390	+	0.683138i	0.979710	−	0.200422i	$-0.0642312\pi$
$487$	11.2854	+	15.0755i	0.511390	+	0.683138i	−0.468319	+	0.883559i	$0.655140\pi$
$488$	4.21160	+	11.2917i	0.190650	+	0.511153i
$489$	−21.0742	+	3.03001i	−0.953008	+	0.137022i
$490$	13.9336	+	18.4223i	0.629455	+	0.832237i
$491$	20.4311	−	13.1303i	0.922045	−	0.592562i	0.00879448	−	0.999961i	$-0.497201\pi$
$491$	20.4311	−	13.1303i	0.922045	−	0.592562i	0.913250	+	0.407399i	$0.133564\pi$
$492$	−8.03972	−	2.99866i	−0.362459	−	0.135190i
$493$	−3.82612	+	7.00701i	−0.172320	+	0.315580i
$494$	−7.89693	+	9.11355i	−0.355300	+	0.410038i
$495$	2.87699	−	4.52576i	0.129311	−	0.203418i
$496$	−9.91948	+	2.91262i	−0.445398	+	0.130781i
$497$	8.67836	−	23.2676i	0.389277	−	1.04369i
$498$	0.464204	−	2.13391i	0.0208015	−	0.0956229i
$499$	11.3858	−	38.7766i	0.509701	−	1.73588i	−0.154181	−	0.988043i	$-0.549274\pi$
$499$	11.3858	−	38.7766i	0.509701	−	1.73588i	0.663881	−	0.747838i	$-0.268908\pi$
$500$	9.31473	−	6.18350i	0.416568	−	0.276535i
$501$	1.53838	−	3.36857i	0.0687295	−	0.150497i
$502$	6.59886	−	4.93985i	0.294522	−	0.220476i
$503$	21.3555	−	4.64561i	0.952196	−	0.207137i	0.290470	−	0.956884i	$-0.406188\pi$
$503$	21.3555	−	4.64561i	0.952196	−	0.207137i	0.661725	+	0.749746i	$0.269825\pi$
$504$	−2.72613	−	3.14612i	−0.121431	−	0.140139i
$505$	−39.1814	+	5.83147i	−1.74355	+	0.259497i
$506$	9.02722	−	7.12765i	0.401309	−	0.316863i
$507$	−5.02685	+	5.02685i	−0.223250	+	0.223250i
$508$	0.937327	−	13.1055i	0.0415872	−	0.581465i
$509$	21.3574	−	33.2328i	0.946652	−	1.47302i	0.0668030	−	0.997766i	$-0.478720\pi$
$509$	21.3574	−	33.2328i	0.946652	−	1.47302i	0.879849	−	0.475253i	$-0.157644\pi$
$510$	−3.31332	+	3.34627i	−0.146716	+	0.148175i
$511$	24.5590	+	11.2157i	1.08642	+	0.496154i
$512$	−0.800541	−	0.599278i	−0.0353793	−	0.0264846i
$513$	−4.36066	+	2.38110i	−0.192528	+	0.105128i
$514$	5.16598	+	8.03842i	0.227862	+	0.354560i
$515$	24.8888	+	5.28537i	1.09673	+	0.232901i
$516$	−0.252250	−	0.859086i	−0.0111047	−	0.0378191i
$517$	−18.3017	+	1.30897i	−0.804909	+	0.0575682i
$518$	−9.01750	+	0.644944i	−0.396206	+	0.0283372i
$519$	−0.571481	−	1.94629i	−0.0250852	−	0.0854325i
$520$	−4.55110	+	2.95674i	−0.199579	+	0.129662i
$521$	−12.3630	−	19.2372i	−0.541631	−	0.842795i	0.457286	−	0.889320i	$-0.348822\pi$
$521$	−12.3630	−	19.2372i	−0.541631	−	0.842795i	−0.998917	+	0.0465248i	$0.985185\pi$
$522$	−3.32721	+	1.81679i	−0.145628	+	0.0795189i
$523$	12.7901	+	9.57453i	0.559271	+	0.418665i	0.841163	−	0.540781i	$-0.181871\pi$
$523$	12.7901	+	9.57453i	0.559271	+	0.418665i	−0.281893	+	0.959446i	$0.590962\pi$
$524$	−6.93620	−	3.16765i	−0.303009	−	0.138380i
$525$	20.5724	−	3.16597i	0.897852	−	0.138174i
$526$	15.9009	−	24.7423i	0.693312	−	1.07882i
$527$	−1.55320	+	21.7166i	−0.0676586	+	0.945990i
$528$	1.69587	−	1.69587i	0.0738031	−	0.0738031i
$529$	−22.3727	−	5.33513i	−0.972725	−	0.231962i
$530$	3.14378	+	21.1229i	0.136557	+	0.917521i
$531$	−8.07841	−	9.32299i	−0.350573	−	0.404583i
$532$	20.2103	−	4.39649i	0.876229	−	0.190612i
$533$	−16.6725	+	12.4809i	−0.722167	+	0.540607i
$534$	5.03676	−	11.0290i	0.217962	−	0.477270i
$535$	−13.5401	+	25.0912i	−0.585389	+	1.08479i
$536$	3.08026	−	10.4904i	0.133047	−	0.453117i
$537$	4.03336	−	18.5411i	0.174053	−	0.800107i
$538$	−4.93067	+	13.2196i	−0.212576	+	0.569939i
$539$	−23.7707	+	6.97970i	−1.02388	+	0.300637i
$540$	−2.18259	+	0.486117i	−0.0939236	+	0.0209191i
$541$	−15.8295	+	18.2682i	−0.680564	+	0.785413i	−0.985990	−	0.166803i	$-0.946656\pi$
$541$	−15.8295	+	18.2682i	−0.680564	+	0.785413i	0.305426	+	0.952216i	$0.401201\pi$
$542$	−4.25747	+	7.79697i	−0.182874	+	0.334909i
$543$	−11.2703	−	4.20359i	−0.483653	−	0.180393i
$544$	−1.77166	+	1.13857i	−0.0759591	+	0.0488160i
$545$	2.41933	+	0.335637i	0.103633	+	0.0143771i
$546$	−10.0011	+	1.43794i	−0.428007	+	0.0615381i
$547$	1.44358	+	3.87039i	0.0617231	+	0.165486i	0.964151	−	0.265356i	$-0.0854894\pi$
$547$	1.44358	+	3.87039i	0.0617231	+	0.165486i	−0.902427	+	0.430842i	$0.858217\pi$
$548$	−0.0692018	−	0.0924427i	−0.00295615	−	0.00394896i
$549$	10.1384	+	6.51558i	0.432698	+	0.278078i
$550$	2.66483	+	11.6917i	0.113629	+	0.498537i
$551$		−	18.8348i		−	0.802390i
$552$	−4.76302	−	0.560058i	−0.202727	−	0.0238377i
$553$	−2.60166	−	2.60166i	−0.110634	−	0.110634i
$554$	14.1844	−	12.2909i	0.602639	−	0.522190i
$555$	−1.99539	+	4.42713i	−0.0846995	+	0.187921i
$556$	1.11177	−	7.73252i	0.0471495	−	0.327932i
$557$	−14.4129	+	5.37572i	−0.610693	+	0.227777i	−0.635732	−	0.771910i	$-0.719302\pi$
$557$	−14.4129	+	5.37572i	−0.610693	+	0.227777i	0.0250393	+	0.999686i	$0.492029\pi$
$558$	−6.19549	+	8.27620i	−0.262276	+	0.350360i
$559$	−2.08511	−	0.612244i	−0.0881908	−	0.0258952i
$560$	9.28801	+	0.618111i	0.392490	+	0.0261200i
$561$	−2.09817	−	4.59436i	−0.0885849	−	0.193974i
$562$	18.3404	+	10.0146i	0.773642	+	0.422441i
$563$	−2.28016	−	31.8808i	−0.0960972	−	1.34361i	−0.785331	−	0.619076i	$-0.787507\pi$
$563$	−2.28016	−	31.8808i	−0.0960972	−	1.34361i	0.689234	−	0.724539i	$-0.257947\pi$
$564$	5.78191	+	5.01006i	0.243463	+	0.210961i
$565$	13.8820	−	37.7892i	0.584021	−	1.58980i
$566$	12.1206	−	5.53528i	0.509466	−	0.232665i
$567$	−4.06778	−	0.884891i	−0.170831	−	0.0371619i
$568$	−2.85890	−	5.23568i	−0.119957	−	0.219684i
$569$	−3.01357	−	20.9598i	−0.126335	−	0.878682i	−0.950144	−	0.311813i	$-0.899064\pi$
$569$	−3.01357	−	20.9598i	−0.126335	−	0.878682i	0.823808	−	0.566869i	$-0.191845\pi$
$570$	3.07717	−	10.6750i	0.128889	−	0.447127i
$571$	−36.5962	−	5.26174i	−1.53150	−	0.220197i	−0.675574	−	0.737292i	$-0.736104\pi$
$571$	−36.5962	−	5.26174i	−1.53150	−	0.220197i	−0.855928	+	0.517095i	$0.827013\pi$
$572$	−1.23735	−	5.68800i	−0.0517361	−	0.237827i
$573$	−1.36304	−	0.0974863i	−0.0569417	−	0.00407255i
$574$	35.7209			1.49096
$575$	15.0471	−	18.6704i	0.627508	−	0.778610i
$576$	−1.00000			−0.0416667
$577$	−2.72780	−	0.195096i	−0.113560	−	0.00812194i	0.0144437	−	0.999896i	$-0.495402\pi$
$577$	−2.72780	−	0.195096i	−0.113560	−	0.00812194i	−0.128003	+	0.991774i	$0.540857\pi$
$578$	−2.67086	−	12.2777i	−0.111093	−	0.510686i
$579$	14.0062	+	2.01379i	0.582080	+	0.0836904i
$580$	2.34790	−	8.14510i	0.0974913	−	0.338207i
$581$	1.29379	+	8.99851i	0.0536755	+	0.373321i
$582$	6.79034	+	12.4356i	0.281469	+	0.515471i
$583$	−22.3817	−	4.86884i	−0.926955	−	0.201647i
$584$	5.89947	−	2.69420i	0.244122	−	0.111487i
$585$	−1.87144	+	5.09436i	−0.0773743	+	0.210626i
$586$	12.7494	+	11.0474i	0.526673	+	0.456364i
$587$	2.30681	+	32.2534i	0.0952120	+	1.33124i	0.790480	+	0.612488i	$0.209831\pi$
$587$	2.30681	+	32.2534i	0.0952120	+	1.33124i	−0.695268	+	0.718751i	$0.744714\pi$
$588$	9.06628	+	4.95056i	0.373887	+	0.204158i
$589$	−21.3376	−	46.7229i	−0.879202	−	1.92518i
$590$	27.5234	+	1.83167i	1.13312	+	0.0754085i
$591$	−0.0925441	−	0.0271734i	−0.00380675	−	0.00111776i
$592$	−1.30144	+	1.73852i	−0.0534890	+	0.0714529i
$593$	−7.21223	+	2.69002i	−0.296171	+	0.110466i	−0.493157	−	0.869940i	$-0.664157\pi$
$593$	−7.21223	+	2.69002i	−0.296171	+	0.110466i	0.196986	+	0.980406i	$0.436884\pi$
$594$	0.341316	−	2.37390i	0.0140044	−	0.0974025i
$595$	8.05527	−	17.8721i	0.330234	−	0.732685i
$596$	−7.50803	+	6.50574i	−0.307541	+	0.266486i
$597$	9.59320	+	9.59320i	0.392624	+	0.392624i
$598$	−7.39360	+	8.99037i	−0.302347	+	0.367643i
$599$		−	26.4177i		−	1.07940i	−0.841857	−	0.539700i	$-0.818538\pi$
$599$		−	26.4177i		−	1.07940i	0.841857	−	0.539700i	$-0.181462\pi$
$600$	2.66144	−	4.23281i	0.108653	−	0.172804i
$601$	39.4156	+	25.3309i	1.60780	+	1.03327i	0.963215	+	0.268733i	$0.0866049\pi$
$601$	39.4156	+	25.3309i	1.60780	+	1.03327i	0.644582	+	0.764535i	$0.277031\pi$
$602$	2.23367	+	2.98384i	0.0910378	+	0.121612i
$603$	−3.82079	−	10.2439i	−0.155595	−	0.417166i
$604$	11.0399	−	1.58729i	0.449206	−	0.0645861i
$605$	11.6237	+	1.61257i	0.472572	+	0.0655605i
$606$	−14.9032	+	9.57770i	−0.605401	+	0.389067i
$607$	−25.9930	−	9.69489i	−1.05502	−	0.393504i	−0.238697	−	0.971094i	$-0.576720\pi$
$607$	−25.9930	−	9.69489i	−1.05502	−	0.393504i	−0.816327	+	0.577590i	$0.803993\pi$
$608$	2.38110	−	4.36066i	0.0965664	−	0.176848i
$609$	10.3345	−	11.9267i	0.418776	−	0.483294i
$610$	−26.3037	+	5.85848i	−1.06500	+	0.237203i
$611$	17.8168	−	5.23147i	0.720789	−	0.211643i
$612$	−0.735962	+	1.97319i	−0.0297495	+	0.0797615i
$613$	7.71286	−	35.4555i	0.311520	−	1.43203i	−0.509174	−	0.860664i	$-0.670049\pi$
$613$	7.71286	−	35.4555i	0.311520	−	1.43203i	0.820693	−	0.571369i	$-0.193587\pi$
$614$	4.17399	−	14.2153i	0.168449	−	0.573683i
$615$	9.11196	−	16.8854i	0.367430	−	0.680886i
$616$	−4.14749	+	9.08175i	−0.167107	+	0.365914i
$617$	−8.30198	+	6.21479i	−0.334225	+	0.250198i	−0.753188	−	0.657806i	$-0.771485\pi$
$617$	−8.30198	+	6.21479i	−0.334225	+	0.250198i	0.418962	+	0.908004i	$0.362394\pi$
$618$	11.1188	−	2.41874i	0.447262	−	0.0972959i
$619$	16.1279	+	18.6126i	0.648237	+	0.748105i	0.980809	−	0.194973i	$-0.0624619\pi$
$619$	16.1279	+	18.6126i	0.648237	+	0.748105i	−0.332572	+	0.943078i	$0.607916\pi$
$620$	−3.40309	−	22.8652i	−0.136671	−	0.918288i
$621$	−4.14862	+	2.40602i	−0.166478	+	0.0965503i
$622$	−0.676628	+	0.676628i	−0.0271303	+	0.0271303i
$623$	−3.60076	+	50.3452i	−0.144261	+	2.01704i
$624$	−1.31221	+	2.04183i	−0.0525303	+	0.0817387i
$625$	10.8334	+	22.5308i	0.433337	+	0.901232i
$626$	21.9148	+	10.0082i	0.875892	+	0.400007i
$627$	9.53908	+	7.14087i	0.380954	+	0.285179i
$628$	0.837021	−	0.457048i	0.0334008	−	0.0182382i
$629$	2.47263	+	3.84748i	0.0985900	+	0.153409i
$630$	7.80585	−	5.07127i	0.310993	−	0.202044i
$631$	8.17723	+	27.8491i	0.325530	+	1.10865i	0.945931	+	0.324369i	$0.105152\pi$
$631$	8.17723	+	27.8491i	0.325530	+	1.10865i	−0.620400	+	0.784285i	$0.713030\pi$
$632$	−0.881578	+	0.0630517i	−0.0350673	+	0.00250806i
$633$	1.35543	−	0.0969424i	0.0538736	−	0.00385311i
$634$	4.78422	+	16.2936i	0.190006	+	0.647100i
$635$	28.7389	+	6.10298i	1.14047	+	0.242189i
$636$	5.16340	+	8.03440i	0.204742	+	0.318585i
$637$	22.0050	−	12.0157i	0.871871	−	0.476078i
$638$	7.27838	+	5.44853i	0.288154	+	0.215709i
$639$	−5.42629	−	2.47811i	−0.214661	−	0.0980323i
$640$	1.57330	−	1.58894i	0.0621900	−	0.0628085i
$641$	−17.2775	+	26.8843i	−0.682420	+	1.06187i	0.311337	+	0.950300i	$0.399223\pi$
$641$	−17.2775	+	26.8843i	−0.682420	+	1.06187i	−0.993757	+	0.111567i	$0.964413\pi$
$642$	−0.909624	+	12.7182i	−0.0359000	+	0.501948i
$643$	26.5965	−	26.5965i	1.04886	−	1.04886i	0.0501201	−	0.998743i	$-0.484040\pi$
$643$	26.5965	−	26.5965i	1.04886	−	1.04886i	0.998743	−	0.0501201i	$-0.0159604\pi$
$644$	19.3926	−	4.74471i	0.764177	−	0.186968i
$645$	1.98026	−	0.294727i	0.0779726	−	0.0116049i
$646$	−6.85201	−	7.90764i	−0.269589	−	0.311122i
$647$	−27.0993	+	5.89509i	−1.06538	+	0.231760i	−0.710893	−	0.703300i	$-0.751709\pi$
$647$	−27.0993	+	5.89509i	−1.06538	+	0.231760i	−0.354490	+	0.935060i	$0.615346\pi$
$648$	−0.800541	+	0.599278i	−0.0314482	+	0.0235419i
$649$	−12.2904	+	26.9122i	−0.482440	+	1.05640i
$650$	−5.15033	−	10.9885i	−0.202013	−	0.431006i
$651$	12.1250	−	41.2939i	0.475216	−	1.61844i
$652$	4.52571	−	20.8044i	0.177240	−	0.814761i
$653$	−11.7827	+	31.5907i	−0.461093	+	1.23624i	0.473586	+	0.880747i	$0.342959\pi$
$653$	−11.7827	+	31.5907i	−0.461093	+	1.23624i	−0.934680	+	0.355491i	$0.884314\pi$
$654$	1.04807	−	0.307742i	0.0409830	−	0.0120337i
$655$	9.14718	−	14.3893i	0.357410	−	0.562238i
$656$	5.61919	−	6.48489i	0.219392	−	0.253192i
$657$	3.10820	−	5.69224i	0.121262	−	0.222075i
$658$	−29.8406	−	11.1300i	−1.16331	−	0.433891i
$659$	−13.9981	+	8.99606i	−0.545290	+	0.350437i	−0.784105	−	0.620628i	$-0.786878\pi$
$659$	−13.9981	+	8.99606i	−0.545290	+	0.350437i	0.238815	+	0.971065i	$0.423241\pi$
$660$	3.23501	+	4.27718i	0.125923	+	0.166489i
$661$	−10.8953	+	1.56651i	−0.423778	+	0.0609301i	−0.350905	−	0.936411i	$-0.614126\pi$
$661$	−10.8953	+	1.56651i	−0.423778	+	0.0609301i	−0.0728733	+	0.997341i	$0.523217\pi$
$662$	−11.5352	−	30.9271i	−0.448328	−	1.20201i
$663$	3.06319	+	4.09194i	0.118964	+	0.158918i
$664$	1.83714	+	1.18066i	0.0712951	+	0.0458185i
$665$	3.52757	+	46.1139i	0.136793	+	1.78822i
$666$			2.17169i			0.0841511i
$667$	−0.468143	−	18.1746i	−0.0181266	−	0.703723i
$668$	2.61858	+	2.61858i	0.101316	+	0.101316i
$669$	−14.9751	+	12.9760i	−0.578971	+	0.501681i
$670$	22.2883	+	10.0457i	0.861072	+	0.388100i
$671$	4.11340	−	28.6093i	0.158796	−	1.10445i
$672$	3.90044	−	1.45479i	0.150463	−	0.0561197i
$673$	−7.66478	+	10.2389i	−0.295456	+	0.394682i	−0.923565	−	0.383443i	$-0.874738\pi$
$673$	−7.66478	+	10.2389i	−0.295456	+	0.394682i	0.628109	+	0.778125i	$0.283829\pi$
$674$	−10.2665	−	3.01452i	−0.395452	−	0.116115i
$675$	−0.406036	−	4.98349i	−0.0156283	−	0.191814i
$676$	−2.95320	−	6.46661i	−0.113585	−	0.248716i
$677$	−9.66573	−	5.27789i	−0.371484	−	0.202846i	0.282652	−	0.959223i	$-0.408786\pi$
$677$	−9.66573	−	5.27789i	−0.371484	−	0.202846i	−0.654136	+	0.756377i	$0.726968\pi$
$678$	−1.28440	−	17.9582i	−0.0493269	−	0.689680i
$679$	−44.5764	−	38.6257i	−1.71069	−	1.48232i
$680$	−1.97740	−	4.27381i	−0.0758299	−	0.163893i
$681$	−16.5555	+	7.56063i	−0.634407	+	0.289724i
$682$	24.2278	+	5.27043i	0.927730	+	0.201815i
$683$	5.01281	+	9.18027i	0.191810	+	0.351273i	0.955831	−	0.293918i	$-0.0949594\pi$
$683$	5.01281	+	9.18027i	0.191810	+	0.351273i	−0.764021	+	0.645192i	$0.776778\pi$
$684$	−0.707077	−	4.91783i	−0.0270358	−	0.188038i
$685$	0.226011	−	0.124867i	0.00863543	−	0.00477093i
$686$	−13.7207	−	1.97274i	−0.523859	−	0.0753196i
$687$	−0.805180	−	3.70135i	−0.0307195	−	0.141215i
$688$	0.893072	+	0.0638738i	0.0340481	+	0.00243517i
$689$	23.1803			0.883100
$690$	2.70398	−	10.3773i	0.102939	−	0.395057i
$691$	−32.6896			−1.24357			−0.621785	−	0.783188i	$-0.713592\pi$
$691$	−32.6896			−1.24357			−0.621785	+	0.783188i	$0.713592\pi$
$692$	2.02328	+	0.144708i	0.0769137	+	0.00550098i
$693$	2.12225	+	9.75581i	0.0806175	+	0.370593i
$694$	4.04963	+	0.582248i	0.153722	+	0.0221018i
$695$	16.7848	+	4.83838i	0.636684	+	0.183530i
$696$	−0.539504	−	3.75233i	−0.0204499	−	0.142232i
$697$	−8.66041	−	15.8604i	−0.328036	−	0.600754i
$698$	4.75837	+	1.03512i	0.180107	+	0.0391799i
$699$	8.20963	−	3.74921i	0.310517	−	0.141808i
$700$	−4.22295	+	20.3817i	−0.159612	+	0.770355i
$701$	21.6976	+	18.8011i	0.819507	+	0.710107i	0.960008	−	0.279973i	$-0.0903257\pi$
$701$	21.6976	+	18.8011i	0.819507	+	0.710107i	−0.140500	+	0.990081i	$0.544871\pi$
$702$	0.173149	+	2.42095i	0.00653510	+	0.0913727i
$703$	−9.46998	−	5.17100i	−0.357167	−	0.195028i
$704$	0.996296	+	2.18158i	0.0375493	+	0.0822216i
$705$	−12.8732	+	11.2667i	−0.484831	+	0.424327i
$706$	−13.9397	−	4.09308i	−0.524629	−	0.154045i
$707$	44.1955	−	59.0382i	1.66214	−	2.22036i
$708$	11.5583	−	4.31102i	0.434387	−	0.162018i
$709$	−3.32846	+	23.1499i	−0.125003	+	0.869414i	0.826755	+	0.562563i	$0.190185\pi$
$709$	−3.32846	+	23.1499i	−0.125003	+	0.869414i	−0.951757	+	0.306851i	$0.900725\pi$
$710$	12.4747	−	4.72328i	0.468168	−	0.177262i
$711$	−0.667954	+	0.578786i	−0.0250502	+	0.0217062i
$712$	8.57342	+	8.57342i	0.321302	+	0.321302i
$713$	−21.7510	−	44.5547i	−0.814580	−	1.66859i
$714$		−	8.76698i		−	0.328096i
$715$	12.9783	−	0.992799i	0.485360	−	0.0371286i
$716$	15.9625	+	10.2585i	0.596548	+	0.383378i
$717$	−6.90795	−	9.22795i	−0.257982	−	0.344624i
$718$	−6.65908	−	17.8537i	−0.248515	−	0.666294i
$719$	16.8280	−	2.41950i	0.627579	−	0.0902323i	0.178815	−	0.983883i	$-0.442774\pi$
$719$	16.8280	−	2.41950i	0.627579	−	0.0902323i	0.448764	+	0.893650i	$0.351864\pi$
$720$	0.307269	−	2.21486i	0.0114513	−	0.0825428i
$721$	−39.8493	+	25.6096i	−1.48407	+	0.953751i
$722$	5.32656	+	1.98670i	0.198234	+	0.0739375i
$723$	2.05333	−	3.76040i	0.0763642	−	0.139851i
$724$	7.87710	−	9.09066i	0.292750	−	0.337852i
$725$	17.3188	+	7.70300i	0.643204	+	0.286082i
$726$	5.03550	−	1.47856i	0.186885	−	0.0548743i
$727$	−6.80999	+	18.2583i	−0.252569	+	0.677163i	0.747350	+	0.664430i	$0.231326\pi$
$727$	−6.80999	+	18.2583i	−0.252569	+	0.677163i	−0.999919	+	0.0127326i	$0.995947\pi$
$728$	2.14774	−	9.87302i	0.0796007	−	0.365918i
$729$	−0.281733	+	0.959493i	−0.0104345	+	0.0355368i
$730$	4.15453	+	13.8943i	0.153766	+	0.514252i
$731$	0.783302	−	1.71519i	0.0289715	−	0.0634387i
$732$	−9.64780	+	7.22225i	−0.356593	+	0.266942i
$733$	4.90971	−	1.06804i	0.181344	−	0.0394490i	−0.120976	−	0.992655i	$-0.538602\pi$
$733$	4.90971	−	1.06804i	0.181344	−	0.0394490i	0.302320	+	0.953206i	$0.402239\pi$
$734$	−6.11356	−	7.05543i	−0.225656	−	0.260421i
$735$	−13.7506	+	18.5593i	−0.507198	+	0.684572i
$736$	2.18925	−	4.26699i	0.0806968	−	0.157283i
$737$	−18.5414	+	18.5414i	−0.682981	+	0.682981i
$738$	0.612143	−	8.55887i	0.0225333	−	0.315057i
$739$	18.2846	−	28.4514i	0.672610	−	1.04660i	−0.322379	−	0.946611i	$-0.604483\pi$
$739$	18.2846	−	28.4514i	0.672610	−	1.04660i	0.994988	−	0.0999901i	$-0.0318811\pi$
$740$	−3.45069	−	3.41670i	−0.126850	−	0.125600i
$741$	−10.9692	−	5.00947i	−0.402964	−	0.184027i
$742$	−31.8279	−	23.8260i	−1.16844	−	0.874682i
$743$	−31.0152	+	16.9356i	−1.13784	+	0.621305i	−0.933849	−	0.357668i	$-0.883572\pi$
$743$	−31.0152	+	16.9356i	−1.13784	+	0.621305i	−0.203987	+	0.978974i	$0.565390\pi$
$744$	−5.58928	−	8.69709i	−0.204913	−	0.318851i
$745$	−12.1023	−	18.6282i	−0.443394	−	0.682485i
$746$	−1.23494	−	4.20582i	−0.0452143	−	0.153986i
$747$	2.17825	−	0.155792i	0.0796982	−	0.00570012i
$748$	5.03792	−	0.360319i	0.184205	−	0.0131746i
$749$	−14.9544	−	50.9299i	−0.546421	−	1.86094i
$750$	8.55729	+	7.19533i	0.312468	+	0.262736i
$751$	−23.9542	−	37.2734i	−0.874100	−	1.36013i	−0.932249	−	0.361819i	$-0.882156\pi$
$751$	−23.9542	−	37.2734i	−0.874100	−	1.36013i	0.0581483	−	0.998308i	$-0.481480\pi$
$752$	−6.71474	+	3.66653i	−0.244862	+	0.133704i
$753$	6.59886	+	4.93985i	0.240476	+	0.180018i
$754$	−8.36957	−	3.82226i	−0.304802	−	0.139198i
$755$	0.123412	+	24.9394i	0.00449143	+	0.907639i
$756$	2.25064	−	3.50206i	0.0818550	−	0.127369i
$757$	2.52829	−	35.3501i	0.0918923	−	1.28482i	−0.717086	−	0.696984i	$-0.754525\pi$
$757$	2.52829	−	35.3501i	0.0918923	−	1.28482i	0.808979	−	0.587838i	$-0.200021\pi$
$758$	−12.3594	+	12.3594i	−0.448912	+	0.448912i
$759$	9.38220	+	6.65346i	0.340552	+	0.241505i
$760$	8.92659	+	6.61369i	0.323802	+	0.239904i
$761$	−9.90609	−	11.4322i	−0.359095	−	0.414418i	0.547241	−	0.836975i	$-0.315678\pi$
$761$	−9.90609	−	11.4322i	−0.359095	−	0.414418i	−0.906336	+	0.422557i	$0.861133\pi$
$762$	12.8388	−	2.79290i	0.465099	−	0.101176i
$763$	−3.64025	+	2.72506i	−0.131786	+	0.0986537i
$764$	0.567672	−	1.24303i	0.0205377	−	0.0449712i
$765$	−4.14419	−	2.23635i	−0.149834	−	0.0808554i
$766$	5.88598	−	20.0458i	0.212669	−	0.724284i
$767$	6.36447	−	29.2570i	0.229808	−	1.05641i
$768$	0.349464	−	0.936950i	0.0126102	−	0.0338093i
$769$	36.5309	−	10.7264i	1.31734	−	0.386806i	0.453807	−	0.891100i	$-0.350066\pi$
$769$	36.5309	−	10.7264i	1.31734	−	0.386806i	0.863532	+	0.504294i	$0.168247\pi$
$770$	−18.8404	−	11.9766i	−0.678959	−	0.431608i
$771$	−6.25739	+	7.22141i	−0.225354	+	0.260073i
$772$	−6.78150	+	12.4194i	−0.244072	+	0.446984i
$773$	−27.7503	−	10.3503i	−0.998107	−	0.372275i	−0.203287	−	0.979119i	$-0.565162\pi$
$773$	−27.7503	−	10.3503i	−0.998107	−	0.372275i	−0.794821	+	0.606845i	$0.792435\pi$
$774$	0.753219	−	0.484065i	0.0270739	−	0.0173993i
$775$	51.6888	−	0.511573i	1.85671	−	0.0183762i
$776$	−14.0245	+	2.01642i	−0.503450	+	0.0723852i
$777$	−3.15934	−	8.47053i	−0.113341	−	0.303878i
$778$	8.13869	+	10.8720i	0.291786	+	0.389781i
$779$	35.8648	+	23.0489i	1.28499	+	0.825812i
$780$	−4.11916	−	3.53374i	−0.147490	−	0.126528i
$781$			14.3068i			0.511939i
$782$	−6.80837	−	7.46015i	−0.243467	−	0.266774i
$783$	−2.68058	−	2.68058i	−0.0957963	−	0.0957963i
$784$	−7.80677	+	6.76460i	−0.278813	+	0.241593i
$785$	0.755104	+	1.99432i	0.0269508	+	0.0711802i
$786$	1.08519	−	7.54766i	0.0387074	−	0.269216i
$787$	−33.9871	+	12.6765i	−1.21151	+	0.451869i	−0.872360	−	0.488864i	$-0.837411\pi$
$787$	−33.9871	+	12.6765i	−1.21151	+	0.451869i	−0.339148	+	0.940733i	$0.610139\pi$
$788$	0.0578009	−	0.0772130i	0.00205907	−	0.00275060i
$789$	28.2199	+	8.28610i	1.00465	+	0.294993i
$790$	0.131232	−	1.97194i	0.00466901	−	0.0701586i
$791$	31.1351	+	68.1763i	1.10704	+	2.42407i
$792$	2.10495	+	1.14939i	0.0747962	+	0.0408418i
$793$	2.08673	+	29.1763i	0.0741019	+	1.03608i
$794$	−22.8506	−	19.8001i	−0.810937	−	0.702681i
$795$	−19.3816	+	8.96745i	−0.687394	+	0.318043i
$796$	−12.3408	+	5.63587i	−0.437409	+	0.199758i
$797$	−31.5093	−	6.85442i	−1.11612	−	0.242796i	−0.383568	−	0.923512i	$-0.625305\pi$
$797$	−31.5093	−	6.85442i	−1.11612	−	0.242796i	−0.732547	+	0.680716i	$0.761669\pi$
$798$	9.91231	+	18.1530i	0.350892	+	0.642611i
$799$	2.29296	+	15.9479i	0.0811191	+	0.564196i
$800$	3.03586	+	3.97286i	0.107334	+	0.140462i
$801$	12.0012	+	1.72552i	0.424043	+	0.0609681i
$802$	−3.05650	−	14.0505i	−0.107929	−	0.496141i
$803$	−15.5148	−	1.10964i	−0.547505	−	0.0391583i
$804$	10.9333			0.385588
$805$	4.55009	+	44.4098i	0.160370	+	1.56524i
$806$	−25.0923			−0.883838
$807$	−14.0733	−	1.00654i	−0.495403	−	0.0354319i
$808$	−3.76569	−	17.3106i	−0.132477	−	0.608985i
$809$	30.5354	+	4.39033i	1.07357	+	0.154356i	0.656355	−	0.754453i	$-0.272098\pi$
$809$	30.5354	+	4.39033i	1.07357	+	0.154356i	0.417214	+	0.908808i	$0.363007\pi$
$810$	−1.08133	−	1.95722i	−0.0379941	−	0.0687698i
$811$	−8.01681	−	55.7582i	−0.281508	−	1.95793i	−0.286939	−	0.957949i	$-0.592638\pi$
$811$	−8.01681	−	55.7582i	−0.281508	−	1.95793i	0.00543063	−	0.999985i	$-0.498271\pi$
$812$	7.56315	+	13.8509i	0.265415	+	0.486071i
$813$	−8.68061	−	1.88835i	−0.304442	−	0.0662274i
$814$	4.73772	−	2.16364i	0.166057	−	0.0758356i
$815$	44.6880	+	16.4163i	1.56535	+	0.575039i
$816$	−1.59159	−	1.37912i	−0.0557167	−	0.0482788i
$817$	0.317351	+	4.43714i	0.0111027	+	0.155236i
$818$	3.07268	+	1.67781i	0.107434	+	0.0586633i
$819$	−4.19732	−	9.19085i	−0.146666	−	0.321154i
$820$	12.6365	+	14.4383i	0.441285	+	0.504207i
$821$	−7.75274	−	2.27641i	−0.270572	−	0.0794472i	0.143632	−	0.989631i	$-0.454122\pi$
$821$	−7.75274	−	2.27641i	−0.270572	−	0.0794472i	−0.414204	+	0.910184i	$0.635940\pi$
$822$	0.0692018	−	0.0924427i	0.00241369	−	0.00322431i
$823$	−2.19463	+	0.818556i	−0.0765001	+	0.0285331i	−0.387423	−	0.921902i	$-0.626635\pi$
$823$	−2.19463	+	0.818556i	−0.0765001	+	0.0285331i	0.310923	+	0.950435i	$0.399362\pi$
$824$	−1.61937	+	11.2630i	−0.0564135	+	0.392365i
$825$	−10.4674	+	5.85083i	−0.364427	+	0.203700i
$826$	−38.8108	+	33.6297i	−1.35040	+	1.17013i
$827$	10.7490	+	10.7490i	0.373779	+	0.373779i	0.868852	−	0.495073i	$-0.164859\pi$
$827$	10.7490	+	10.7490i	0.373779	+	0.373779i	−0.495073	+	0.868852i	$0.664859\pi$
$828$	−0.804525	−	4.72787i	−0.0279592	−	0.164305i
$829$			17.8742i			0.620795i	0.950607	+	0.310398i	$0.100462\pi$
$829$			17.8742i			0.620795i	−0.950607	+	0.310398i	$0.899538\pi$
$830$	−3.17949	+	3.70623i	−0.110362	+	0.128645i
$831$	15.7892	+	10.1471i	0.547723	+	0.352000i
$832$	−1.45452	−	1.94302i	−0.0504266	−	0.0673620i
$833$	7.60236	+	20.3827i	0.263406	+	0.706220i
$834$	7.73252	−	1.11177i	0.267755	−	0.0384974i
$835$	−6.60438	+	4.99516i	−0.228554	+	0.172865i
$836$	−10.0242	+	6.44216i	−0.346694	+	0.222807i
$837$	−9.68643	−	3.61285i	−0.334812	−	0.124878i
$838$	−3.77938	+	6.92141i	−0.130556	+	0.239096i
$839$	−4.39668	+	5.07403i	−0.151790	+	0.175175i	−0.826552	−	0.562860i	$-0.809701\pi$
$839$	−4.39668	+	5.07403i	−0.151790	+	0.175175i	0.674762	+	0.738036i	$0.264246\pi$
$840$	2.02366	+	9.08592i	0.0698229	+	0.313494i
$841$	−14.0364	+	4.12145i	−0.484012	+	0.142119i
$842$	−6.15148	+	16.4927i	−0.211994	+	0.568378i
$843$	−4.44186	+	20.4189i	−0.152986	+	0.703264i
$844$	−0.382845	+	1.30385i	−0.0131781	+	0.0448803i
$845$	15.2300	−	4.55393i	0.523929	−	0.156660i
$846$	−3.17816	+	6.95920i	−0.109267	+	0.239262i
$847$	−17.4897	+	13.0926i	−0.600952	+	0.449867i
$848$	−9.33225	+	2.03011i	−0.320471	+	0.0697142i
$849$	8.72582	+	10.0701i	0.299469	+	0.345606i
$850$	10.0735	−	3.06645i	0.345517	−	0.105178i
$851$	−9.26655	−	4.75436i	−0.317653	−	0.162977i
$852$	4.21816	−	4.21816i	0.144512	−	0.144512i
$853$	−1.48947	+	20.8255i	−0.0509983	+	0.713050i	0.906059	+	0.423151i	$0.139076\pi$
$853$	−1.48947	+	20.8255i	−0.0509983	+	0.713050i	−0.957057	+	0.289899i	$0.906378\pi$
$854$	27.1238	−	42.2055i	0.928157	−	1.44424i
$855$	11.1095	−	0.0549753i	0.379938	−	0.00188011i
$856$	−11.5984	−	5.29683i	−0.396427	−	0.181042i
$857$	7.83024	+	5.86164i	0.267476	+	0.200230i	0.724594	−	0.689176i	$-0.242027\pi$
$857$	7.83024	+	5.86164i	0.267476	+	0.200230i	−0.457118	+	0.889406i	$0.651118\pi$
$858$	5.10899	−	2.78972i	0.174418	−	0.0952395i
$859$	21.1186	+	32.8611i	0.720556	+	1.12121i	0.987519	+	0.157500i	$0.0503435\pi$
$859$	21.1186	+	32.8611i	0.720556	+	1.12121i	−0.266963	+	0.963707i	$0.586020\pi$
$860$	−0.415885	+	1.95840i	−0.0141816	+	0.0667809i
$861$	10.0637	+	34.2739i	0.342971	+	1.16805i
$862$	20.1105	−	1.43833i	0.684966	−	0.0489898i
$863$	−10.2885	+	0.735845i	−0.350223	+	0.0250485i	−0.245343	−	0.969436i	$-0.578901\pi$
$863$	−10.2885	+	0.735845i	−0.350223	+	0.0250485i	−0.104880	+	0.994485i	$0.533446\pi$
$864$	−0.281733	−	0.959493i	−0.00958474	−	0.0326426i
$865$	−0.942201	+	4.43682i	−0.0320358	+	0.150856i
$866$	−9.22754	−	14.3583i	−0.313564	−	0.487916i
$867$	11.0279	−	6.02171i	0.374528	−	0.204508i
$868$	34.4531	+	25.7913i	1.16941	+	0.875413i
$869$	1.92815	+	0.880557i	0.0654080	+	0.0298708i
$870$	8.47665	−	0.0419465i	0.287385	−	0.00142212i
$871$	14.3467	−	22.3239i	0.486120	−	0.756418i
$872$	−0.0779253	+	1.08954i	−0.00263888	+	0.0368964i
$873$	−10.0188	+	10.0188i	−0.339085	+	0.339085i
$874$	22.5323	+	7.74927i	0.762166	+	0.262123i
$875$	−43.8449	−	15.6159i	−1.48223	−	0.527913i
$876$	4.24714	+	4.90146i	0.143497	+	0.165605i
$877$	34.1631	−	7.43173i	1.15361	−	0.250952i	0.405223	−	0.914218i	$-0.367194\pi$
$877$	34.1631	−	7.43173i	1.15361	−	0.250952i	0.748384	+	0.663266i	$0.230830\pi$
$878$	13.5397	−	10.1357i	0.456944	−	0.342064i
$879$	−7.00800	+	15.3454i	−0.236374	+	0.517586i
$880$	−5.13803	+	1.53632i	−0.173203	+	0.0517893i
$881$	−0.420297	+	1.43140i	−0.0141602	+	0.0482251i	−0.966270	−	0.257531i	$-0.917091\pi$
$881$	−0.420297	+	1.43140i	−0.0141602	+	0.0482251i	0.952110	+	0.305756i	$0.0989092\pi$
$882$	−2.19576	+	10.0938i	−0.0739352	+	0.339875i
$883$	−5.56528	+	14.9211i	−0.187287	+	0.502135i	−0.996328	−	0.0856168i	$-0.972714\pi$
$883$	−5.56528	+	14.9211i	−0.187287	+	0.502135i	0.809042	+	0.587751i	$0.199987\pi$
$884$	−4.90442	+	1.44007i	−0.164953	+	0.0484347i
$885$	5.99677	+	26.9246i	0.201579	+	0.905060i
$886$	18.4528	−	21.2957i	0.619935	−	0.715443i
$887$	−0.466448	+	0.854235i	−0.0156618	+	0.0286824i	−0.885393	−	0.464844i	$-0.846110\pi$
$887$	−0.466448	+	0.854235i	−0.0156618	+	0.0286824i	0.869731	+	0.493526i	$0.164292\pi$
$888$	−2.03476	−	0.758926i	−0.0682821	−	0.0254679i
$889$	−46.0137	+	29.5712i	−1.54325	+	0.991787i
$890$	−21.6232	+	16.3545i	−0.724812	+	0.548205i
$891$	2.37390	−	0.341316i	0.0795288	−	0.0114345i
$892$	−6.92460	−	18.5656i	−0.231853	−	0.621621i
$893$	−22.7792	−	30.4294i	−0.762277	−	1.01828i
$894$	−8.35747	−	5.37102i	−0.279516	−	0.179634i
$895$	−27.6259	+	32.2026i	−0.923432	+	1.07641i
$896$			4.16291i			0.139073i
$897$	−10.7092	−	4.56123i	−0.357570	−	0.152295i
$898$	−21.2825	−	21.2825i	−0.710207	−	0.710207i
$899$	29.6190	−	25.6650i	0.987848	−	0.855975i
$900$	4.81117	+	1.36111i	0.160372	+	0.0453705i
$901$	−2.86239	+	19.9084i	−0.0953602	+	0.663245i
$902$	−19.2818	+	7.19174i	−0.642013	+	0.239459i
$903$	−2.23367	+	2.98384i	−0.0743320	+	0.0992960i
$904$	17.2748	+	5.07233i	0.574551	+	0.168703i
$905$	17.7141	+	20.2399i	0.588837	+	0.672798i
$906$	4.63329	+	10.1455i	0.153931	+	0.337061i
$907$	−12.4678	−	6.80791i	−0.413985	−	0.226053i	0.258738	−	0.965948i	$-0.416694\pi$
$907$	−12.4678	−	6.80791i	−0.413985	−	0.226053i	−0.672723	+	0.739895i	$0.734875\pi$
$908$	−1.29839	−	18.1538i	−0.0430884	−	0.602455i
$909$	−13.3885	−	11.6012i	−0.444067	−	0.384786i
$910$	21.2074	+	7.79062i	0.703018	+	0.258257i
$911$	20.5218	−	9.37201i	0.679919	−	0.310509i	−0.0453529	−	0.998971i	$-0.514441\pi$
$911$	20.5218	−	9.37201i	0.679919	−	0.310509i	0.725272	+	0.688462i	$0.241714\pi$
$912$	4.85486	+	1.05611i	0.160760	+	0.0349713i
$913$	−2.51006	−	4.59683i	−0.0830709	−	0.152133i
$914$	0.170603	+	1.18657i	0.00564303	+	0.0392482i
$915$	−13.0318	−	23.5877i	−0.430817	−	0.779784i
$916$	3.74936	+	0.539077i	0.123882	+	0.0178116i
$917$	6.74754	+	31.0179i	0.222823	+	1.02430i
$918$	−2.10061	−	0.150238i	−0.0693303	−	0.00495860i
$919$	−52.2012			−1.72196			−0.860979	−	0.508641i	$-0.830148\pi$
$919$	−52.2012			−1.72196			−0.860979	+	0.508641i	$0.830148\pi$
$920$	8.77807	+	6.15999i	0.289404	+	0.203089i
$921$	14.8154			0.488186
$922$	10.7438	+	0.768410i	0.353827	+	0.0253062i
$923$	−3.07768	−	14.1478i	−0.101303	−	0.465682i
$924$	−9.88236	−	1.42087i	−0.325106	−	0.0467431i
$925$	8.62779	−	6.59292i	0.283680	−	0.216774i
$926$	−4.19091	−	29.1485i	−0.137722	−	0.957878i
$927$	5.45328	+	9.98693i	0.179109	+	0.328014i
$928$	3.70429	+	0.805818i	0.121599	+	0.0264523i
$929$	−32.5449	+	14.8628i	−1.06776	+	0.487631i	−0.870220	−	0.492663i	$-0.836024\pi$
$929$	−32.5449	+	14.8628i	−1.06776	+	0.487631i	−0.197543	+	0.980294i	$0.563296\pi$
$930$	20.9802	−	9.70711i	0.687969	−	0.318309i
$931$	−38.7872	−	33.6093i	−1.27120	−	1.10150i
$932$	0.643852	+	9.00223i	0.0210901	+	0.294878i
$933$	−0.839848	−	0.458591i	−0.0274954	−	0.0150136i
$934$	7.68473	+	16.8272i	0.251452	+	0.550603i
$935$	−0.749943	+	11.2690i	−0.0245258	+	0.368535i
$936$	−2.32881	−	0.683801i	−0.0761197	−	0.0223507i
$937$	0.0258332	−	0.0345091i	0.000843934	−	0.00112736i	−0.800119	−	0.599841i	$-0.795230\pi$
$937$	0.0258332	−	0.0345091i	0.000843934	−	0.00112736i	0.800963	+	0.598714i	$0.204321\pi$
$938$	−42.6446	+	15.9056i	−1.39240	+	0.519337i
$939$	−3.42864	+	23.8467i	−0.111890	+	0.778209i
$940$	−6.05759	−	15.9988i	−0.197577	−	0.521823i
$941$	14.8117	−	12.8344i	0.482849	−	0.418391i	−0.379124	−	0.925346i	$-0.623774\pi$
$941$	14.8117	−	12.8344i	0.482849	−	0.418391i	0.861972	+	0.506955i	$0.169229\pi$
$942$	0.674350	+	0.674350i	0.0219715	+	0.0219715i
$943$	35.1805	+	21.3495i	1.14563	+	0.695236i
$944$			12.3361i			0.401505i
$945$	7.06501	+	6.06092i	0.229825	+	0.197162i
$946$	−1.80646	−	1.16094i	−0.0587330	−	0.0377454i
$947$	20.4267	+	27.2868i	0.663777	+	0.886702i	0.998451	−	0.0556315i	$-0.0177172\pi$
$947$	20.4267	+	27.2868i	0.663777	+	0.886702i	−0.334674	+	0.942334i	$0.608626\pi$
$948$	−0.308867	−	0.828104i	−0.0100315	−	0.0268956i
$949$	15.5811	−	2.24022i	0.505783	−	0.0727206i
$950$	−17.3912	+	17.7389i	−0.564246	+	0.575527i
$951$	−14.2857	+	9.18086i	−0.463245	+	0.297710i
$952$	8.21422	+	3.06374i	0.266224	+	0.0992965i
$953$	15.1469	−	27.7395i	0.490656	−	0.898570i	−0.508637	−	0.860981i	$-0.669851\pi$
$953$	15.1469	−	27.7395i	0.490656	−	0.898570i	0.999293	−	0.0375887i	$-0.0119677\pi$
$954$	−6.25426	+	7.21780i	−0.202489	+	0.233685i
$955$	2.57870	+	1.63926i	0.0834448	+	0.0530451i
$956$	11.0602	−	3.24757i	0.357713	−	0.105034i
$957$	−3.17727	+	8.51858i	−0.102706	+	0.275367i
$958$	4.76225	−	21.8917i	0.153861	−	0.707289i
$959$	−0.135433	+	0.461241i	−0.00437335	+	0.0148943i
$960$	1.96783	+	1.06191i	0.0635114	+	0.0342730i
$961$	31.5215	−	69.0225i	1.01682	−	2.22653i
$962$	−4.21962	+	3.15877i	−0.136046	+	0.101843i
$963$	−12.4593	+	2.71036i	−0.401495	+	0.0873400i
$964$	2.80574	+	3.23799i	0.0903667	+	0.104289i
$965$	−25.4234	−	18.8362i	−0.818409	−	0.606357i
$966$	10.0161	+	17.2703i	0.322261	+	0.555664i
$967$	−6.63281	+	6.63281i	−0.213297	+	0.213297i	−0.805666	−	0.592370i	$-0.798193\pi$
$967$	−6.63281	+	6.63281i	−0.213297	+	0.213297i	0.592370	+	0.805666i	$0.298193\pi$
$968$	−0.374394	+	5.23471i	−0.0120335	+	0.168250i
$969$	5.65689	−	8.80230i	0.181726	−	0.282771i
$970$	−0.156777	−	31.6818i	−0.00503379	−	1.01724i
$971$	11.9808	+	5.47145i	0.384482	+	0.175587i	0.598273	−	0.801292i	$-0.295854\pi$
$971$	11.9808	+	5.47145i	0.384482	+	0.175587i	−0.213791	+	0.976879i	$0.568581\pi$
$972$	−0.800541	−	0.599278i	−0.0256774	−	0.0192218i
$973$	−28.5428	+	15.5856i	−0.915042	+	0.499651i
$974$	−10.1812	−	15.8422i	−0.326226	−	0.507617i
$975$	9.09241	−	8.03754i	0.291190	−	0.257407i
$976$	−3.39533	−	11.5634i	−0.108682	−	0.370136i
$977$	19.8294	−	1.41822i	0.634397	−	0.0453730i	0.249563	−	0.968359i	$-0.419713\pi$
$977$	19.8294	−	1.41822i	0.634397	−	0.0453730i	0.384835	+	0.922986i	$0.374259\pi$
$978$	21.2367	−	1.51888i	0.679074	−	0.0485683i
$979$	−8.19242	−	27.9008i	−0.261831	−	0.891715i
$980$	−12.5838	−	19.3694i	−0.401976	−	0.618733i
$981$	0.590553	+	0.918919i	0.0188549	+	0.0293388i
$982$	−21.3158	+	11.6393i	−0.680214	+	0.371425i
$983$	23.2318	+	17.3911i	0.740978	+	0.554689i	0.901727	−	0.432306i	$-0.142300\pi$
$983$	23.2318	+	17.3911i	0.740978	+	0.554689i	−0.160749	+	0.986995i	$0.551391\pi$
$984$	7.80531	+	3.56457i	0.248824	+	0.113634i
$985$	0.153255	+	0.151746i	0.00488312	+	0.00483503i
$986$	4.31624	−	6.71621i	0.137457	−	0.213888i
$987$	2.27206	−	31.7675i	0.0723203	−	1.01117i
$988$	8.52697	−	8.52697i	0.271279	−	0.271279i
$989$	0.416512	+	4.27372i	0.0132443	+	0.135896i
$990$	−3.19252	+	4.30899i	−0.101465	+	0.136949i
$991$	−7.39400	−	8.53313i	−0.234878	−	0.271064i	0.626058	−	0.779776i	$-0.284667\pi$
$991$	−7.39400	−	8.53313i	−0.234878	−	0.271064i	−0.860937	+	0.508712i	$0.830122\pi$
$992$	10.1020	−	2.19755i	0.320739	−	0.0697724i
$993$	26.4245	−	19.7811i	0.838555	−	0.627734i
$994$	−10.3161	+	22.5892i	−0.327208	+	0.716485i
$995$	−8.69068	−	29.0649i	−0.275513	−	0.921419i
$996$	−0.615253	+	2.09536i	−0.0194950	+	0.0663940i
$997$	5.38424	−	24.7509i	0.170521	−	0.783870i	−0.809839	−	0.586652i	$-0.800446\pi$
$997$	5.38424	−	24.7509i	0.170521	−	0.783870i	0.980360	−	0.197218i	$-0.0631908\pi$
$998$	−14.1231	+	37.8656i	−0.447060	+	1.19861i
$999$	−2.08372	+	0.611834i	−0.0659259	+	0.0193576i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.w.b.493.3	yes	240
5.2	odd	4	inner	690.2.w.b.217.11	yes	240
23.7	odd	22	inner	690.2.w.b.283.11	yes	240
115.7	even	44	inner	690.2.w.b.7.3	✓	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.w.b.7.3	✓	240	115.7	even	44	inner
690.2.w.b.217.11	yes	240	5.2	odd	4	inner
690.2.w.b.283.11	yes	240	23.7	odd	22	inner
690.2.w.b.493.3	yes	240	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:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.w (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.997452 - 0.0713392i) q^{2} +(-0.212565 - 0.977147i) q^{3} +(0.989821 + 0.142315i) q^{4} +(-0.619349 + 2.14858i) q^{5} +(0.142315 + 0.989821i) q^{6} +(-1.99507 - 3.65370i) q^{7} +(-0.977147 - 0.212565i) q^{8} +(-0.909632 + 0.415415i) q^{9} +O(q^{10})\)	\(q+(-0.997452 - 0.0713392i) q^{2} +(-0.212565 - 0.977147i) q^{3} +(0.989821 + 0.142315i) q^{4} +(-0.619349 + 2.14858i) q^{5} +(0.142315 + 0.989821i) q^{6} +(-1.99507 - 3.65370i) q^{7} +(-0.977147 - 0.212565i) q^{8} +(-0.909632 + 0.415415i) q^{9} +(0.771049 - 2.09892i) q^{10} +(1.81253 + 1.57056i) q^{11} +(-0.0713392 - 0.997452i) q^{12} +(-2.13024 - 1.16320i) q^{13} +(1.72934 + 3.78672i) q^{14} +(2.23113 + 0.148481i) q^{15} +(0.959493 + 0.281733i) q^{16} +(1.26206 - 1.68592i) q^{17} +(0.936950 - 0.349464i) q^{18} +(-0.707077 + 4.91783i) q^{19} +(-0.918820 + 2.03857i) q^{20} +(-3.14612 + 2.72613i) q^{21} +(-1.69587 - 1.69587i) q^{22} +(-0.560058 + 4.76302i) q^{23} +1.00000i q^{24} +(-4.23281 - 2.66144i) q^{25} +(2.04183 + 1.31221i) q^{26} +(0.599278 + 0.800541i) q^{27} +(-1.45479 - 3.90044i) q^{28} +(-3.75233 + 0.539504i) q^{29} +(-2.21486 - 0.307269i) q^{30} +(-8.69709 + 5.58928i) q^{31} +(-0.936950 - 0.349464i) q^{32} +(1.14939 - 2.10495i) q^{33} +(-1.37912 + 1.59159i) q^{34} +(9.08592 - 2.02366i) q^{35} +(-0.959493 + 0.281733i) q^{36} +(-0.758926 + 2.03476i) q^{37} +(1.05611 - 4.85486i) q^{38} +(-0.683801 + 2.32881i) q^{39} +(1.06191 - 1.96783i) q^{40} +(3.56457 - 7.80531i) q^{41} +(3.33258 - 2.49474i) q^{42} +(0.874892 - 0.190321i) q^{43} +(1.57056 + 1.81253i) q^{44} +(-0.329174 - 2.21171i) q^{45} +(0.898421 - 4.71093i) q^{46} +(-5.40977 + 5.40977i) q^{47} +(0.0713392 - 0.997452i) q^{48} +(-5.58473 + 8.69001i) q^{49} +(4.03216 + 2.95663i) q^{50} +(-1.91566 - 0.874852i) q^{51} +(-1.94302 - 1.45452i) q^{52} +(-8.38229 + 4.57707i) q^{53} +(-0.540641 - 0.841254i) q^{54} +(-4.49707 + 2.92164i) q^{55} +(1.17283 + 3.99428i) q^{56} +(4.95574 - 0.354442i) q^{57} +(3.78126 - 0.270441i) q^{58} +(3.47547 + 11.8364i) q^{59} +(2.18729 + 0.464493i) q^{60} +(-6.51558 - 10.1384i) q^{61} +(9.07367 - 4.95460i) q^{62} +(3.33258 + 2.49474i) q^{63} +(0.909632 + 0.415415i) q^{64} +(3.81859 - 3.85657i) q^{65} +(-1.29663 + 2.01759i) q^{66} +(-0.779972 + 10.9054i) q^{67} +(1.48915 - 1.48915i) q^{68} +(4.77322 - 0.465193i) q^{69} +(-9.20714 + 1.37032i) q^{70} +(3.90649 + 4.50833i) q^{71} +(0.977147 - 0.212565i) q^{72} +(-5.19195 + 3.88665i) q^{73} +(0.902151 - 1.97543i) q^{74} +(-1.70087 + 4.70181i) q^{75} +(-1.39976 + 4.76715i) q^{76} +(2.12225 - 9.75581i) q^{77} +(0.848195 - 2.27410i) q^{78} +(0.848029 - 0.249004i) q^{79} +(-1.19959 + 1.88706i) q^{80} +(0.654861 - 0.755750i) q^{81} +(-4.11231 + 7.53113i) q^{82} +(-2.04613 - 0.763166i) q^{83} +(-3.50206 + 2.25064i) q^{84} +(2.84068 + 3.75582i) q^{85} +(-0.886240 + 0.127422i) q^{86} +(1.32479 + 3.55190i) q^{87} +(-1.43726 - 1.91995i) q^{88} +(-10.1999 - 6.55508i) q^{89} +(0.170554 + 2.22955i) q^{90} +10.1039i q^{91} +(-1.23221 + 4.63483i) q^{92} +(7.31025 + 7.31025i) q^{93} +(5.78191 - 5.01006i) q^{94} +(-10.1284 - 4.56506i) q^{95} +(-0.142315 + 0.989821i) q^{96} +(13.2754 - 4.95146i) q^{97} +(6.19044 - 8.26946i) q^{98} +(-2.30117 - 0.675684i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 24 q^{6}+O(q^{10}) \) 240 * q + 24 * q^6	\( 240 q + 24 q^{6} - 44 q^{10} + 24 q^{16} - 44 q^{21} + 96 q^{23} + 16 q^{25} + 16 q^{26} + 44 q^{28} - 16 q^{31} + 44 q^{33} + 16 q^{35} - 24 q^{36} + 44 q^{37} - 88 q^{43} + 8 q^{46} + 96 q^{47} - 24 q^{50} - 24 q^{55} + 44 q^{57} - 16 q^{58} + 88 q^{61} + 56 q^{62} - 88 q^{65} + 132 q^{67} - 56 q^{70} + 16 q^{71} + 48 q^{73} + 24 q^{81} - 24 q^{82} + 44 q^{85} - 16 q^{87} + 44 q^{88} - 124 q^{92} + 32 q^{93} + 20 q^{95} - 24 q^{96} - 56 q^{98}+O(q^{100}) \) 240 * q + 24 * q^6 - 44 * q^10 + 24 * q^16 - 44 * q^21 + 96 * q^23 + 16 * q^25 + 16 * q^26 + 44 * q^28 - 16 * q^31 + 44 * q^33 + 16 * q^35 - 24 * q^36 + 44 * q^37 - 88 * q^43 + 8 * q^46 + 96 * q^47 - 24 * q^50 - 24 * q^55 + 44 * q^57 - 16 * q^58 + 88 * q^61 + 56 * q^62 - 88 * q^65 + 132 * q^67 - 56 * q^70 + 16 * q^71 + 48 * q^73 + 24 * q^81 - 24 * q^82 + 44 * q^85 - 16 * q^87 + 44 * q^88 - 124 * q^92 + 32 * q^93 + 20 * q^95 - 24 * q^96 - 56 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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