LMFDB - Embedded newform 46.2.c.a.31.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [46,2,Mod(3,46)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(46, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([16]))

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

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

chi := DirichletCharacter("46.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 46 = 2 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	46.c (of order $11$, degree $10$, 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:	$0.367311849298$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\Q(\zeta_{22})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + 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:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			31.1
Root			$0.142315 - 0.989821i$ of defining polynomial
Character	$\chi$	$=$	46.31
Dual form			46.2.c.a.3.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.142315 + 0.989821i) q^{2} +(0.580699 + 1.27155i) q^{3} +(-0.959493 - 0.281733i) q^{4} +(-1.66741 - 1.92429i) q^{5} +(-1.34125 + 0.393828i) q^{6} +(1.75667 + 1.12894i) q^{7} +(0.415415 - 0.909632i) q^{8} +(0.684944 - 0.790468i) q^{9} +O(q^{10})$	\(q+(-0.142315 + 0.989821i) q^{2} +(0.580699 + 1.27155i) q^{3} +(-0.959493 - 0.281733i) q^{4} +(-1.66741 - 1.92429i) q^{5} +(-1.34125 + 0.393828i) q^{6} +(1.75667 + 1.12894i) q^{7} +(0.415415 - 0.909632i) q^{8} +(0.684944 - 0.790468i) q^{9} +(2.14200 - 1.37658i) q^{10} +(-0.543474 - 3.77994i) q^{11} +(-0.198939 - 1.38365i) q^{12} +(-5.21228 + 3.34973i) q^{13} +(-1.36745 + 1.57812i) q^{14} +(1.47858 - 3.23763i) q^{15} +(0.841254 + 0.540641i) q^{16} +(-1.24982 + 0.366979i) q^{17} +(0.684944 + 0.790468i) q^{18} +(2.38000 + 0.698830i) q^{19} +(1.05773 + 2.31611i) q^{20} +(-0.415415 + 2.88927i) q^{21} +3.81881 q^{22} +(-1.33380 + 4.60662i) q^{23} +1.39788 q^{24} +(-0.211072 + 1.46804i) q^{25} +(-2.57385 - 5.63594i) q^{26} +(5.42663 + 1.59340i) q^{27} +(-1.36745 - 1.57812i) q^{28} +(-6.87690 + 2.01924i) q^{29} +(2.99425 + 1.92429i) q^{30} +(-1.67062 + 3.65814i) q^{31} +(-0.654861 + 0.755750i) q^{32} +(4.49081 - 2.88607i) q^{33} +(-0.185376 - 1.28932i) q^{34} +(-0.756669 - 5.26275i) q^{35} +(-0.879900 + 0.565477i) q^{36} +(7.48386 - 8.63683i) q^{37} +(-1.03043 + 2.25632i) q^{38} +(-7.28612 - 4.68251i) q^{39} +(-2.44306 + 0.717348i) q^{40} +(2.81130 + 3.24442i) q^{41} +(-2.80075 - 0.822373i) q^{42} +(-1.15394 - 2.52678i) q^{43} +(-0.543474 + 3.77994i) q^{44} -2.66317 q^{45} +(-4.36992 - 1.97581i) q^{46} +9.34150 q^{47} +(-0.198939 + 1.38365i) q^{48} +(-1.09653 - 2.40107i) q^{49} +(-1.42306 - 0.417848i) q^{50} +(-1.19240 - 1.37610i) q^{51} +(5.94487 - 1.74557i) q^{52} +(-1.99027 - 1.27907i) q^{53} +(-2.34947 + 5.14463i) q^{54} +(-6.36752 + 7.34850i) q^{55} +(1.75667 - 1.12894i) q^{56} +(0.493462 + 3.43211i) q^{57} +(-1.02000 - 7.09427i) q^{58} +(0.514407 - 0.330589i) q^{59} +(-2.33083 + 2.68992i) q^{60} +(1.67815 - 3.67464i) q^{61} +(-3.38316 - 2.17422i) q^{62} +(2.09561 - 0.615327i) q^{63} +(-0.654861 - 0.755750i) q^{64} +(15.1368 + 4.44457i) q^{65} +(2.21758 + 4.85583i) q^{66} +(-1.82531 + 12.6953i) q^{67} +1.30258 q^{68} +(-6.63211 + 0.979068i) q^{69} +5.31686 q^{70} +(0.940875 - 6.54393i) q^{71} +(-0.434499 - 0.951419i) q^{72} +(2.80644 + 0.824045i) q^{73} +(7.48386 + 8.63683i) q^{74} +(-1.98926 + 0.584100i) q^{75} +(-2.08671 - 1.34105i) q^{76} +(3.31264 - 7.25366i) q^{77} +(5.67177 - 6.54557i) q^{78} +(-1.58724 + 1.02006i) q^{79} +(-0.362362 - 2.52028i) q^{80} +(0.678585 + 4.71966i) q^{81} +(-3.61148 + 2.32096i) q^{82} +(-6.83698 + 7.89030i) q^{83} +(1.21259 - 2.65520i) q^{84} +(2.79013 + 1.79310i) q^{85} +(2.66528 - 0.782598i) q^{86} +(-6.56099 - 7.57178i) q^{87} +(-3.66412 - 1.07588i) q^{88} +(2.08216 + 4.55930i) q^{89} +(0.379009 - 2.63606i) q^{90} -12.9379 q^{91} +(2.57760 - 4.04425i) q^{92} -5.62165 q^{93} +(-1.32943 + 9.24642i) q^{94} +(-2.62367 - 5.74504i) q^{95} +(-1.34125 - 0.393828i) q^{96} +(-8.21585 - 9.48159i) q^{97} +(2.53268 - 0.743663i) q^{98} +(-3.36017 - 2.15945i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - q^{2} - 4 q^{3} - q^{4} - 6 q^{5} - 4 q^{6} + 3 q^{7} - q^{8} + 9 q^{9}+O(q^{10}) $ 10 * q - q^2 - 4 * q^3 - q^4 - 6 * q^5 - 4 * q^6 + 3 * q^7 - q^8 + 9 * q^9	\( 10 q - q^{2} - 4 q^{3} - q^{4} - 6 q^{5} - 4 q^{6} + 3 q^{7} - q^{8} + 9 q^{9} - 6 q^{10} - 12 q^{11} + 7 q^{12} - 14 q^{13} + 3 q^{14} - 13 q^{15} - q^{16} + 15 q^{17} + 9 q^{18} + 2 q^{19} + 5 q^{20} + q^{21} + 10 q^{22} - q^{23} - 4 q^{24} + 13 q^{25} - 3 q^{26} + 26 q^{27} + 3 q^{28} - 8 q^{29} + 20 q^{30} - 21 q^{31} - q^{32} - 15 q^{33} - 7 q^{34} + 7 q^{35} - 13 q^{36} + 28 q^{37} - 9 q^{38} - 12 q^{39} - 6 q^{40} - 31 q^{41} - 10 q^{42} + 11 q^{43} - 12 q^{44} + 10 q^{45} - 12 q^{46} + 18 q^{47} + 7 q^{48} - 24 q^{49} + 2 q^{50} - 17 q^{51} + 8 q^{52} - 21 q^{53} - 29 q^{54} + 5 q^{55} + 3 q^{56} + 19 q^{57} - 8 q^{58} - 5 q^{59} - 13 q^{60} + 37 q^{61} + q^{62} + 17 q^{63} - q^{64} + 37 q^{65} + 29 q^{66} - 13 q^{67} + 26 q^{68} - 15 q^{69} + 18 q^{70} + 49 q^{71} + 20 q^{72} - 8 q^{73} + 28 q^{74} + 8 q^{75} - 20 q^{76} - 8 q^{77} + 10 q^{78} + 8 q^{79} + 5 q^{80} - 11 q^{81} + 2 q^{82} - 7 q^{83} + q^{84} - 42 q^{85} + 22 q^{86} - 21 q^{87} - q^{88} - 13 q^{89} - 45 q^{90} - 24 q^{91} - 23 q^{92} - 40 q^{93} - 37 q^{94} - 10 q^{95} - 4 q^{96} - 32 q^{97} - 24 q^{98} + 20 q^{99}+O(q^{100}) \) 10 * q - q^2 - 4 * q^3 - q^4 - 6 * q^5 - 4 * q^6 + 3 * q^7 - q^8 + 9 * q^9 - 6 * q^10 - 12 * q^11 + 7 * q^12 - 14 * q^13 + 3 * q^14 - 13 * q^15 - q^16 + 15 * q^17 + 9 * q^18 + 2 * q^19 + 5 * q^20 + q^21 + 10 * q^22 - q^23 - 4 * q^24 + 13 * q^25 - 3 * q^26 + 26 * q^27 + 3 * q^28 - 8 * q^29 + 20 * q^30 - 21 * q^31 - q^32 - 15 * q^33 - 7 * q^34 + 7 * q^35 - 13 * q^36 + 28 * q^37 - 9 * q^38 - 12 * q^39 - 6 * q^40 - 31 * q^41 - 10 * q^42 + 11 * q^43 - 12 * q^44 + 10 * q^45 - 12 * q^46 + 18 * q^47 + 7 * q^48 - 24 * q^49 + 2 * q^50 - 17 * q^51 + 8 * q^52 - 21 * q^53 - 29 * q^54 + 5 * q^55 + 3 * q^56 + 19 * q^57 - 8 * q^58 - 5 * q^59 - 13 * q^60 + 37 * q^61 + q^62 + 17 * q^63 - q^64 + 37 * q^65 + 29 * q^66 - 13 * q^67 + 26 * q^68 - 15 * q^69 + 18 * q^70 + 49 * q^71 + 20 * q^72 - 8 * q^73 + 28 * q^74 + 8 * q^75 - 20 * q^76 - 8 * q^77 + 10 * q^78 + 8 * q^79 + 5 * q^80 - 11 * q^81 + 2 * q^82 - 7 * q^83 + q^84 - 42 * q^85 + 22 * q^86 - 21 * q^87 - q^88 - 13 * q^89 - 45 * q^90 - 24 * q^91 - 23 * q^92 - 40 * q^93 - 37 * q^94 - 10 * q^95 - 4 * q^96 - 32 * q^97 - 24 * q^98 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/46\mathbb{Z}\right)^\times$.

$n$	$5$
$\chi(n)$	$e\left(\frac{3}{11}\right)$

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 $

$2$	−0.142315	+	0.989821i	−0.100632	+	0.699909i
$2$	−0.142315	+	0.989821i	−0.100632	+	0.699909i
$3$	0.580699	+	1.27155i	0.335267	+	0.734132i	0.999915	−	0.0130243i	$-0.00414589\pi$
$3$	0.580699	+	1.27155i	0.335267	+	0.734132i	−0.664648	+	0.747156i	$0.731419\pi$
$4$	−0.959493	−	0.281733i	−0.479746	−	0.140866i
$5$	−1.66741	−	1.92429i	−0.745687	−	0.860569i	0.248456	−	0.968643i	$-0.420077\pi$
$5$	−1.66741	−	1.92429i	−0.745687	−	0.860569i	−0.994143	+	0.108075i	$0.965531\pi$
$6$	−1.34125	+	0.393828i	−0.547564	+	0.160779i
$7$	1.75667	+	1.12894i	0.663958	+	0.426700i	0.828743	−	0.559629i	$-0.189057\pi$
$7$	1.75667	+	1.12894i	0.663958	+	0.426700i	−0.164785	+	0.986330i	$0.552693\pi$
$8$	0.415415	−	0.909632i	0.146871	−	0.321603i
$9$	0.684944	−	0.790468i	0.228315	−	0.263489i
$10$	2.14200	−	1.37658i	0.677360	−	0.435313i
$11$	−0.543474	−	3.77994i	−0.163864	−	1.13970i	−0.891265	−	0.453483i	$-0.850181\pi$
$11$	−0.543474	−	3.77994i	−0.163864	−	1.13970i	0.727401	−	0.686212i	$-0.240728\pi$
$12$	−0.198939	−	1.38365i	−0.0574287	−	0.399425i
$13$	−5.21228	+	3.34973i	−1.44563	+	0.929047i	−0.446207	+	0.894930i	$0.647226\pi$
$13$	−5.21228	+	3.34973i	−1.44563	+	0.929047i	−0.999418	+	0.0341173i	$0.989138\pi$
$14$	−1.36745	+	1.57812i	−0.365467	+	0.421771i
$15$	1.47858	−	3.23763i	0.381767	−	0.835953i
$16$	0.841254	+	0.540641i	0.210313	+	0.135160i
$17$	−1.24982	+	0.366979i	−0.303125	+	0.0890055i	−0.429758	−	0.902944i	$-0.641401\pi$
$17$	−1.24982	+	0.366979i	−0.303125	+	0.0890055i	0.126633	+	0.991950i	$0.459583\pi$
$18$	0.684944	+	0.790468i	0.161443	+	0.186315i
$19$	2.38000	+	0.698830i	0.546009	+	0.160323i	0.543092	−	0.839673i	$-0.317253\pi$
$19$	2.38000	+	0.698830i	0.546009	+	0.160323i	0.00291665	+	0.999996i	$0.499072\pi$
$20$	1.05773	+	2.31611i	0.236516	+	0.517897i
$21$	−0.415415	+	2.88927i	−0.0906510	+	0.630491i
$22$	3.81881			0.814174
$23$	−1.33380	+	4.60662i	−0.278116	+	0.960548i
$23$	−1.33380	+	4.60662i	−0.278116	+	0.960548i
$24$	1.39788			0.285341
$25$	−0.211072	+	1.46804i	−0.0422145	+	0.293608i
$26$	−2.57385	−	5.63594i	−0.504773	−	1.10530i
$27$	5.42663	+	1.59340i	1.04436	+	0.306650i
$28$	−1.36745	−	1.57812i	−0.258424	−	0.298237i
$29$	−6.87690	+	2.01924i	−1.27701	+	0.374964i	−0.848799	−	0.528716i	$-0.822674\pi$
$29$	−6.87690	+	2.01924i	−1.27701	+	0.374964i	−0.428210	+	0.903679i	$0.640856\pi$
$30$	2.99425	+	1.92429i	0.546673	+	0.351326i
$31$	−1.67062	+	3.65814i	−0.300052	+	0.657022i	−0.998266	−	0.0588671i	$-0.981251\pi$
$31$	−1.67062	+	3.65814i	−0.300052	+	0.657022i	0.698214	+	0.715889i	$0.253978\pi$
$32$	−0.654861	+	0.755750i	−0.115764	+	0.133599i
$33$	4.49081	−	2.88607i	0.781749	−	0.502400i
$34$	−0.185376	−	1.28932i	−0.0317918	−	0.221117i
$35$	−0.756669	−	5.26275i	−0.127900	−	0.889566i
$36$	−0.879900	+	0.565477i	−0.146650	+	0.0942462i
$37$	7.48386	−	8.63683i	1.23034	−	1.41989i	0.356059	−	0.934463i	$-0.384120\pi$
$37$	7.48386	−	8.63683i	1.23034	−	1.41989i	0.874279	−	0.485423i	$-0.161334\pi$
$38$	−1.03043	+	2.25632i	−0.167157	+	0.366023i
$39$	−7.28612	−	4.68251i	−1.16671	−	0.749801i
$40$	−2.44306	+	0.717348i	−0.386282	+	0.113423i
$41$	2.81130	+	3.24442i	0.439052	+	0.506693i	0.931546	−	0.363623i	$-0.118460\pi$
$41$	2.81130	+	3.24442i	0.439052	+	0.506693i	−0.492494	+	0.870316i	$0.663915\pi$
$42$	−2.80075	−	0.822373i	−0.432165	−	0.126895i
$43$	−1.15394	−	2.52678i	−0.175974	−	0.385330i	0.801007	−	0.598655i	$-0.204298\pi$
$43$	−1.15394	−	2.52678i	−0.175974	−	0.385330i	−0.976981	+	0.213325i	$0.931571\pi$
$44$	−0.543474	+	3.77994i	−0.0819318	+	0.569848i
$45$	−2.66317			−0.397002
$46$	−4.36992	−	1.97581i	−0.644309	−	0.291318i
$47$	9.34150			1.36260			0.681299	−	0.732005i	$-0.261415\pi$
$47$	9.34150			1.36260			0.681299	+	0.732005i	$0.261415\pi$
$48$	−0.198939	+	1.38365i	−0.0287143	+	0.199713i
$49$	−1.09653	−	2.40107i	−0.156647	−	0.343010i
$50$	−1.42306	−	0.417848i	−0.201251	−	0.0590926i
$51$	−1.19240	−	1.37610i	−0.166970	−	0.192693i
$52$	5.94487	−	1.74557i	0.824405	−	0.242067i
$53$	−1.99027	−	1.27907i	−0.273385	−	0.175694i	0.396764	−	0.917921i	$-0.370133\pi$
$53$	−1.99027	−	1.27907i	−0.273385	−	0.175694i	−0.670148	+	0.742227i	$0.733770\pi$
$54$	−2.34947	+	5.14463i	−0.319723	+	0.700095i
$55$	−6.36752	+	7.34850i	−0.858596	+	0.990872i
$56$	1.75667	−	1.12894i	0.234745	−	0.150861i
$57$	0.493462	+	3.43211i	0.0653607	+	0.454593i
$58$	−1.02000	−	7.09427i	−0.133933	−	0.931524i
$59$	0.514407	−	0.330589i	0.0669701	−	0.0430390i	−0.506727	−	0.862106i	$-0.669145\pi$
$59$	0.514407	−	0.330589i	0.0669701	−	0.0430390i	0.573697	+	0.819067i	$0.305509\pi$
$60$	−2.33083	+	2.68992i	−0.300909	+	0.347267i
$61$	1.67815	−	3.67464i	0.214865	−	0.470489i	−0.771254	−	0.636527i	$-0.780370\pi$
$61$	1.67815	−	3.67464i	0.214865	−	0.470489i	0.986119	+	0.166038i	$0.0530976\pi$
$62$	−3.38316	−	2.17422i	−0.429661	−	0.276127i
$63$	2.09561	−	0.615327i	0.264022	−	0.0775240i
$64$	−0.654861	−	0.755750i	−0.0818576	−	0.0944687i
$65$	15.1368	+	4.44457i	1.87749	+	0.551281i
$66$	2.21758	+	4.85583i	0.272966	+	0.597711i
$67$	−1.82531	+	12.6953i	−0.222997	+	1.55098i	0.503614	+	0.863929i	$0.332003\pi$
$67$	−1.82531	+	12.6953i	−0.222997	+	1.55098i	−0.726611	+	0.687049i	$0.758906\pi$
$68$	1.30258			0.157961
$69$	−6.63211	+	0.979068i	−0.798412	+	0.117866i
$70$	5.31686			0.635487
$71$	0.940875	−	6.54393i	0.111661	−	0.776621i	−0.854642	−	0.519217i	$-0.826224\pi$
$71$	0.940875	−	6.54393i	0.111661	−	0.776621i	0.966304	−	0.257404i	$-0.0828673\pi$
$72$	−0.434499	−	0.951419i	−0.0512062	−	0.112126i
$73$	2.80644	+	0.824045i	0.328469	+	0.0964472i	0.441809	−	0.897109i	$-0.354337\pi$
$73$	2.80644	+	0.824045i	0.328469	+	0.0964472i	−0.113340	+	0.993556i	$0.536155\pi$
$74$	7.48386	+	8.63683i	0.869981	+	1.00401i
$75$	−1.98926	+	0.584100i	−0.229700	+	0.0674461i
$76$	−2.08671	−	1.34105i	−0.239362	−	0.153828i
$77$	3.31264	−	7.25366i	0.377510	−	0.826631i
$78$	5.67177	−	6.54557i	0.642201	−	0.741140i
$79$	−1.58724	+	1.02006i	−0.178578	+	0.114765i	−0.626876	−	0.779119i	$-0.715667\pi$
$79$	−1.58724	+	1.02006i	−0.178578	+	0.114765i	0.448298	+	0.893884i	$0.352030\pi$
$80$	−0.362362	−	2.52028i	−0.0405133	−	0.281776i
$81$	0.678585	+	4.71966i	0.0753983	+	0.524407i
$82$	−3.61148	+	2.32096i	−0.398822	+	0.256307i
$83$	−6.83698	+	7.89030i	−0.750456	+	0.866073i	−0.994612	−	0.103663i	$-0.966944\pi$
$83$	−6.83698	+	7.89030i	−0.750456	+	0.866073i	0.244156	+	0.969736i	$0.421489\pi$
$84$	1.21259	−	2.65520i	0.132304	−	0.289706i
$85$	2.79013	+	1.79310i	0.302632	+	0.194490i
$86$	2.66528	−	0.782598i	0.287405	−	0.0843897i
$87$	−6.56099	−	7.57178i	−0.703412	−	0.811780i
$88$	−3.66412	−	1.07588i	−0.390597	−	0.114690i
$89$	2.08216	+	4.55930i	0.220709	+	0.483285i	0.987303	−	0.158846i	$-0.0507775\pi$
$89$	2.08216	+	4.55930i	0.220709	+	0.483285i	−0.766594	+	0.642132i	$0.778050\pi$
$90$	0.379009	−	2.63606i	0.0399510	−	0.277865i
$91$	−12.9379			−1.35626
$92$	2.57760	−	4.04425i	0.268734	−	0.421642i
$93$	−5.62165			−0.582938
$94$	−1.32943	+	9.24642i	−0.137121	+	0.953696i
$95$	−2.62367	−	5.74504i	−0.269183	−	0.589429i
$96$	−1.34125	−	0.393828i	−0.136891	−	0.0401949i
$97$	−8.21585	−	9.48159i	−0.834193	−	0.962710i	0.165531	−	0.986205i	$-0.447066\pi$
$97$	−8.21585	−	9.48159i	−0.834193	−	0.962710i	−0.999724	+	0.0234947i	$0.992521\pi$
$98$	2.53268	−	0.743663i	0.255840	−	0.0751213i
$99$	−3.36017	−	2.15945i	−0.337710	−	0.217033i
$100$	0.616117	−	1.34911i	0.0616117	−	0.134911i
$101$	−2.30675	+	2.66214i	−0.229531	+	0.264893i	−0.858819	−	0.512280i	$-0.828801\pi$
$101$	−2.30675	+	2.66214i	−0.229531	+	0.264893i	0.629288	+	0.777172i	$0.283347\pi$
$102$	1.53179	−	0.984424i	0.151670	−	0.0974725i
$103$	−0.222897	−	1.55028i	−0.0219627	−	0.152754i	0.975889	−	0.218267i	$-0.0700405\pi$
$103$	−0.222897	−	1.55028i	−0.0219627	−	0.152754i	−0.997852	+	0.0655137i	$0.979131\pi$
$104$	0.881761	+	6.13278i	0.0864637	+	0.601368i
$105$	6.25247	−	4.01822i	0.610178	−	0.392138i
$106$	1.54929	−	1.78798i	0.150481	−	0.173664i
$107$	1.41373	−	3.09564i	0.136671	−	0.299267i	−0.828905	−	0.559389i	$-0.811036\pi$
$107$	1.41373	−	3.09564i	0.136671	−	0.299267i	0.965576	+	0.260122i	$0.0837629\pi$
$108$	−4.75790	−	3.05772i	−0.457829	−	0.294229i
$109$	8.27394	−	2.42945i	0.792499	−	0.232699i	0.139664	−	0.990199i	$-0.455398\pi$
$109$	8.27394	−	2.42945i	0.792499	−	0.232699i	0.652835	+	0.757500i	$0.273579\pi$
$110$	−6.36752	−	7.34850i	−0.607119	−	0.700652i
$111$	15.3281	+	4.50073i	1.45488	+	0.427190i
$112$	0.867451	+	1.89945i	0.0819664	+	0.179481i
$113$	0.507526	−	3.52992i	0.0477441	−	0.332067i	−0.951925	−	0.306332i	$-0.900898\pi$
$113$	0.507526	−	3.52992i	0.0477441	−	0.332067i	0.999669	−	0.0257353i	$-0.00819269\pi$
$114$	−3.46740			−0.324752
$115$	11.0885	−	5.11450i	1.03400	−	0.476930i
$116$	7.16723			0.665460
$117$	−0.922268	+	6.41451i	−0.0852637	+	0.593022i
$118$	0.254017	+	0.556219i	0.0233841	+	0.0512041i
$119$	−2.60981	−	0.766310i	−0.239241	−	0.0702475i
$120$	−2.33083	−	2.68992i	−0.212775	−	0.245555i
$121$	−3.43819	+	1.00954i	−0.312563	+	0.0917767i
$122$	3.39841	+	2.18402i	0.307677	+	0.197732i
$123$	−2.49293	+	5.45876i	−0.224780	+	0.492199i
$124$	2.63357	−	3.03930i	0.236501	−	0.272937i
$125$	−7.53312	+	4.84124i	−0.673783	+	0.433014i
$126$	0.310827	+	2.16185i	0.0276907	+	0.192593i
$127$	0.800045	+	5.56443i	0.0709925	+	0.493764i	0.994035	+	0.109065i	$0.0347856\pi$
$127$	0.800045	+	5.56443i	0.0709925	+	0.493764i	−0.923042	+	0.384699i	$0.874305\pi$
$128$	0.841254	−	0.540641i	0.0743570	−	0.0477863i
$129$	2.54284	−	2.93460i	0.223885	−	0.258377i
$130$	−6.55353	+	14.3502i	−0.574783	+	1.25860i
$131$	6.70728	+	4.31051i	0.586018	+	0.376611i	0.799797	−	0.600271i	$-0.204941\pi$
$131$	6.70728	+	4.31051i	0.586018	+	0.376611i	−0.213778	+	0.976882i	$0.568577\pi$
$132$	−5.12200	+	1.50395i	−0.445813	+	0.130902i
$133$	3.39193	+	3.91449i	0.294117	+	0.339430i
$134$	−12.3063	−	3.61346i	−1.06310	−	0.312155i
$135$	−5.98223	−	13.0993i	−0.514868	−	1.12740i
$136$	−0.185376	+	1.28932i	−0.0158959	+	0.110558i
$137$	2.06934			0.176796			0.0883979	−	0.996085i	$-0.471825\pi$
$137$	2.06934			0.176796			0.0883979	+	0.996085i	$0.471825\pi$
$138$	−0.0252558	−	6.70394i	−0.00214992	−	0.570677i
$139$	−13.0620			−1.10790			−0.553950	−	0.832550i	$-0.686880\pi$
$139$	−13.0620			−1.10790			−0.553950	+	0.832550i	$0.686880\pi$
$140$	−0.756669	+	5.26275i	−0.0639502	+	0.444783i
$141$	5.42460	+	11.8782i	0.456834	+	1.00033i
$142$	6.34342	+	1.86260i	0.532328	+	0.156306i
$143$	15.4945	+	17.8816i	1.29572	+	1.49534i
$144$	1.00357	−	0.294675i	0.0836309	−	0.0245563i
$145$	15.3522	+	9.86626i	1.27493	+	0.819348i
$146$	−1.21506	+	2.66060i	−0.100559	+	0.220193i
$147$	2.41633	−	2.78860i	0.199296	−	0.230000i
$148$	−9.61399	+	6.17853i	−0.790265	+	0.507872i
$149$	−2.11269	−	14.6941i	−0.173079	−	1.20379i	−0.872332	−	0.488914i	$-0.837393\pi$
$149$	−2.11269	−	14.6941i	−0.173079	−	1.20379i	0.699254	−	0.714874i	$-0.253516\pi$
$150$	−0.295053	−	2.05214i	−0.0240910	−	0.167557i
$151$	3.24142	−	2.08313i	0.263783	−	0.169523i	−0.402064	−	0.915612i	$-0.631707\pi$
$151$	3.24142	−	2.08313i	0.263783	−	0.169523i	0.665846	+	0.746089i	$0.268071\pi$
$152$	1.62436	−	1.87462i	0.131753	−	0.152052i
$153$	−0.565969	+	1.23930i	−0.0457559	+	0.100191i
$154$	6.70839	+	4.31122i	0.540577	+	0.347408i
$155$	9.82493	−	2.88486i	0.789157	−	0.231718i
$156$	5.67177	+	6.54557i	0.454105	+	0.524065i
$157$	−21.7336	−	6.38156i	−1.73453	−	0.509304i	−0.746742	−	0.665114i	$-0.768383\pi$
$157$	−21.7336	−	6.38156i	−1.73453	−	0.509304i	−0.987787	+	0.155810i	$0.950201\pi$
$158$	−0.783785	−	1.71625i	−0.0623546	−	0.136538i
$159$	0.470657	−	3.27349i	0.0373255	−	0.259605i
$160$	2.54620			0.201295
$161$	−7.54365	+	6.58653i	−0.594523	+	0.519091i
$162$	−4.76820			−0.374625
$163$	2.69879	−	18.7705i	0.211385	−	1.47022i	−0.557152	−	0.830411i	$-0.688106\pi$
$163$	2.69879	−	18.7705i	0.211385	−	1.47022i	0.768537	−	0.639806i	$-0.220985\pi$
$164$	−1.78337	−	3.90503i	−0.139258	−	0.304932i
$165$	−13.0416	−	3.82937i	−1.01529	−	0.298116i
$166$	−6.83698	−	7.89030i	−0.530653	−	0.612406i
$167$	0.939952	−	0.275995i	0.0727356	−	0.0213571i	−0.245162	−	0.969482i	$-0.578841\pi$
$167$	0.939952	−	0.275995i	0.0727356	−	0.0213571i	0.317898	+	0.948125i	$0.397023\pi$
$168$	2.45561	+	1.57812i	0.189454	+	0.121755i
$169$	10.5468	−	23.0942i	0.811289	−	1.77648i
$170$	−2.17193	+	2.50654i	−0.166579	+	0.192243i
$171$	2.18257	−	1.40265i	0.166905	−	0.107263i
$172$	0.395323	+	2.74953i	0.0301431	+	0.209650i
$173$	1.26974	+	8.83122i	0.0965364	+	0.671425i	0.979420	+	0.201833i	$0.0646899\pi$
$173$	1.26974	+	8.83122i	0.0965364	+	0.671425i	−0.882884	+	0.469592i	$0.844401\pi$
$174$	8.42844	−	5.41663i	0.638958	−	0.410633i
$175$	−2.02812	+	2.34057i	−0.153311	+	0.176931i
$176$	1.58639	−	3.47372i	0.119579	−	0.261841i
$177$	0.719078	+	0.462123i	0.0540492	+	0.0347353i
$178$	−4.80922	+	1.41211i	−0.360466	+	0.105842i
$179$	5.56076	+	6.41746i	0.415631	+	0.479663i	0.924501	−	0.381180i	$-0.124482\pi$
$179$	5.56076	+	6.41746i	0.415631	+	0.479663i	−0.508870	+	0.860843i	$0.669937\pi$
$180$	2.55529	+	0.750302i	0.190460	+	0.0559242i
$181$	−0.223254	−	0.488859i	−0.0165944	−	0.0363366i	0.901153	−	0.433500i	$-0.142722\pi$
$181$	−0.223254	−	0.488859i	−0.0165944	−	0.0363366i	−0.917748	+	0.397164i	$0.869994\pi$
$182$	1.84125	−	12.8062i	0.136483	−	0.949259i
$183$	5.64700			0.417438
$184$	3.63625	+	3.12693i	0.268068	+	0.230520i
$185$	−29.0984			−2.13936
$186$	0.800045	−	5.56443i	0.0586621	−	0.408004i
$187$	2.06640	+	4.52479i	0.151110	+	0.330885i
$188$	−8.96311	−	2.63181i	−0.653702	−	0.191944i
$189$	7.73393	+	8.92543i	0.562561	+	0.649230i
$190$	6.05995	−	1.77936i	0.439635	−	0.129088i
$191$	−22.5725	−	14.5065i	−1.63329	−	1.04965i	−0.946455	−	0.322836i	$-0.895364\pi$
$191$	−22.5725	−	14.5065i	−1.63329	−	1.04965i	−0.686834	−	0.726815i	$-0.741000\pi$
$192$	0.580699	−	1.27155i	0.0419084	−	0.0917665i
$193$	0.919649	−	1.06133i	0.0661978	−	0.0763964i	−0.721685	−	0.692222i	$-0.756632\pi$
$193$	0.919649	−	1.06133i	0.0661978	−	0.0763964i	0.787883	+	0.615826i	$0.211177\pi$
$194$	10.5543	−	6.78285i	0.757756	−	0.486980i
$195$	3.13843	+	21.8283i	0.224748	+	1.56315i
$196$	0.375655	+	2.61274i	0.0268325	+	0.186624i
$197$	−6.93589	+	4.45743i	−0.494162	+	0.317579i	−0.763877	−	0.645361i	$-0.776707\pi$
$197$	−6.93589	+	4.45743i	−0.494162	+	0.317579i	0.269715	+	0.962940i	$0.413070\pi$
$198$	2.61567	−	3.01865i	0.185888	−	0.214526i
$199$	−1.29407	+	2.83361i	−0.0917339	+	0.200869i	−0.949937	−	0.312441i	$-0.898854\pi$
$199$	−1.29407	+	2.83361i	−0.0917339	+	0.200869i	0.858203	+	0.513310i	$0.171581\pi$
$200$	1.24769	+	0.801844i	0.0882253	+	0.0566989i
$201$	−17.2027	+	5.05117i	−1.21339	+	0.356282i
$202$	−2.30675	−	2.66214i	−0.162303	−	0.187307i
$203$	−14.3600	−	4.21649i	−1.00788	−	0.295940i
$204$	0.756407	+	1.65630i	0.0529591	+	0.115964i
$205$	1.55561	−	10.8195i	0.108649	−	0.755669i
$206$	1.56622			0.109124
$207$	2.72781	+	4.20960i	0.189596	+	0.292588i
$208$	−6.19584			−0.429604
$209$	1.34807	−	9.37605i	0.0932481	−	0.648555i
$210$	3.08750	+	6.76068i	0.213058	+	0.466531i
$211$	21.1163	+	6.20030i	1.45370	+	0.426846i	0.910765	−	0.412926i	$-0.135493\pi$
$211$	21.1163	+	6.20030i	1.45370	+	0.426846i	0.542940	+	0.839772i	$0.317311\pi$
$212$	1.54929	+	1.78798i	0.106406	+	0.122799i
$213$	8.86732	−	2.60368i	0.607579	−	0.178401i
$214$	2.86294	+	1.83990i	0.195706	+	0.125773i
$215$	−2.93817	+	6.43369i	−0.200381	+	0.438774i
$216$	3.70371	−	4.27431i	0.252006	−	0.290830i
$217$	−7.06456	+	4.54012i	−0.479573	+	0.308203i
$218$	1.22721	+	8.53547i	0.0831175	+	0.578095i
$219$	0.581880	+	4.04706i	0.0393198	+	0.273475i
$220$	8.17990	−	5.25690i	0.551489	−	0.354420i
$221$	5.28511	−	6.09934i	0.355515	−	0.410286i
$222$	−6.63633	+	14.5315i	−0.445401	+	0.975293i
$223$	10.3556	+	6.65515i	0.693463	+	0.445662i	0.839316	−	0.543645i	$-0.182956\pi$
$223$	10.3556	+	6.65515i	0.693463	+	0.445662i	−0.145852	+	0.989306i	$0.546592\pi$
$224$	−2.00357	+	0.588302i	−0.133869	+	0.0393075i
$225$	1.01587	+	1.17237i	0.0677244	+	0.0781581i
$226$	3.42177	+	1.00472i	0.227612	+	0.0668331i
$227$	2.21520	+	4.85061i	0.147028	+	0.321946i	0.968789	−	0.247885i	$-0.0797357\pi$
$227$	2.21520	+	4.85061i	0.147028	+	0.321946i	−0.821761	+	0.569832i	$0.807008\pi$
$228$	0.493462	−	3.43211i	0.0326803	−	0.227297i
$229$	14.1070			0.932216			0.466108	−	0.884728i	$-0.345656\pi$
$229$	14.1070			0.932216			0.466108	+	0.884728i	$0.345656\pi$
$230$	3.48439	+	11.7035i	0.229754	+	0.771704i
$231$	11.1471			0.733423
$232$	−1.02000	+	7.09427i	−0.0669664	+	0.465762i
$233$	7.13799	+	15.6300i	0.467625	+	1.02396i	0.985683	+	0.168610i	$0.0539279\pi$
$233$	7.13799	+	15.6300i	0.467625	+	1.02396i	−0.518058	+	0.855346i	$0.673345\pi$
$234$	−6.21797	−	1.82576i	−0.406481	−	0.119354i
$235$	−15.5761	−	17.9758i	−1.01607	−	1.17261i
$236$	−0.586707	+	0.172273i	−0.0381914	+	0.0112140i
$237$	−2.21876	−	1.42591i	−0.144124	−	0.0926230i
$238$	1.12992	−	2.47419i	0.0732421	−	0.160378i
$239$	3.69369	−	4.26274i	0.238925	−	0.275734i	−0.623606	−	0.781739i	$-0.714333\pi$
$239$	3.69369	−	4.26274i	0.238925	−	0.275734i	0.862530	+	0.506005i	$0.168878\pi$
$240$	2.99425	−	1.92429i	0.193278	−	0.124212i
$241$	0.716936	+	4.98640i	0.0461819	+	0.321202i	0.999797	+	0.0201721i	$0.00642141\pi$
$241$	0.716936	+	4.98640i	0.0461819	+	0.321202i	−0.953615	+	0.301030i	$0.902669\pi$
$242$	−0.509962	−	3.54687i	−0.0327816	−	0.228001i
$243$	8.66645	−	5.56959i	0.555953	−	0.357289i
$244$	−2.64544	+	3.05300i	−0.169357	+	0.195448i
$245$	−2.79199	+	6.11360i	−0.178374	+	0.390584i
$246$	−5.04841	−	3.24442i	−0.321875	−	0.206857i
$247$	−14.7461	+	4.32984i	−0.938271	+	0.275501i
$248$	2.63357	+	3.03930i	0.167232	+	0.192995i
$249$	−14.0032	−	4.11170i	−0.887415	−	0.260569i
$250$	−3.71989	−	8.14543i	−0.235267	−	0.515162i
$251$	2.51629	−	17.5012i	0.158827	−	1.10466i	−0.741973	−	0.670429i	$-0.766110\pi$
$251$	2.51629	−	17.5012i	0.158827	−	1.10466i	0.900800	−	0.434234i	$-0.142981\pi$
$252$	−2.18408			−0.137584
$253$	18.1377	+	2.53810i	1.14031	+	0.159569i
$254$	−5.62165			−0.352734
$255$	−0.659806	+	4.58905i	−0.0413186	+	0.287377i
$256$	0.415415	+	0.909632i	0.0259634	+	0.0568520i
$257$	−21.1716	−	6.21655i	−1.32065	−	0.387778i	−0.455922	−	0.890020i	$-0.650690\pi$
$257$	−21.1716	−	6.21655i	−1.32065	−	0.387778i	−0.864727	+	0.502242i	$0.832509\pi$
$258$	2.54284	+	2.93460i	0.158311	+	0.182700i
$259$	22.8971	−	6.72321i	1.42276	−	0.417760i
$260$	−13.2715	−	8.52907i	−0.823063	−	0.528951i
$261$	−3.11415	+	6.81904i	−0.192761	+	0.422088i
$262$	−5.22118	+	6.02556i	−0.322566	+	0.372261i
$263$	−6.52680	+	4.19452i	−0.402460	+	0.258645i	−0.726176	−	0.687509i	$-0.758704\pi$
$263$	−6.52680	+	4.19452i	−0.402460	+	0.258645i	0.323716	+	0.946154i	$0.395068\pi$
$264$	−0.759710	−	5.28390i	−0.0467569	−	0.325201i
$265$	0.857290	+	5.96258i	0.0526629	+	0.366279i
$266$	−4.35737	+	2.80031i	−0.267168	+	0.171698i
$267$	−4.58829	+	5.29517i	−0.280799	+	0.324059i
$268$	5.32805	−	11.6668i	0.325462	−	0.712663i
$269$	14.3175	+	9.20132i	0.872955	+	0.561014i	0.898655	−	0.438655i	$-0.144545\pi$
$269$	14.3175	+	9.20132i	0.872955	+	0.561014i	−0.0256999	+	0.999670i	$0.508181\pi$
$270$	13.8173	−	4.05712i	0.840893	−	0.246909i
$271$	−7.62747	−	8.80257i	−0.463336	−	0.534718i	0.475210	−	0.879872i	$-0.342372\pi$
$271$	−7.62747	−	8.80257i	−0.463336	−	0.534718i	−0.938546	+	0.345154i	$0.887827\pi$
$272$	−1.24982	−	0.366979i	−0.0757812	−	0.0222514i
$273$	−7.51302	−	16.4512i	−0.454709	−	0.995673i
$274$	−0.294498	+	2.04828i	−0.0177913	+	0.123741i
$275$	5.66382			0.341541
$276$	6.63929	+	0.929071i	0.399639	+	0.0559235i
$277$	16.8299			1.01121			0.505604	−	0.862766i	$-0.331270\pi$
$277$	16.8299			1.01121			0.505604	+	0.862766i	$0.331270\pi$
$278$	1.85891	−	12.9290i	0.111490	−	0.775430i
$279$	1.74736	+	3.82620i	0.104612	+	0.229068i
$280$	−5.10149	−	1.49793i	−0.304873	−	0.0895186i
$281$	3.46454	+	3.99829i	0.206677	+	0.238518i	0.849619	−	0.527397i	$-0.176832\pi$
$281$	3.46454	+	3.99829i	0.206677	+	0.238518i	−0.642942	+	0.765915i	$0.722286\pi$
$282$	−12.5293	+	3.67894i	−0.746111	+	0.219078i
$283$	−12.9297	−	8.30943i	−0.768592	−	0.493944i	0.0966376	−	0.995320i	$-0.469191\pi$
$283$	−12.9297	−	8.30943i	−0.768592	−	0.493944i	−0.865230	+	0.501375i	$0.832828\pi$
$284$	−2.74640	+	6.01378i	−0.162969	+	0.356852i
$285$	5.78156	−	6.67228i	0.342470	−	0.395232i
$286$	−19.9047	+	12.7920i	−1.17699	+	0.756406i
$287$	1.27577	+	8.87317i	0.0753062	+	0.523766i
$288$	0.148853	+	1.03529i	0.00877122	+	0.0610052i
$289$	−12.8739	+	8.27358i	−0.757291	+	0.486681i
$290$	−11.9507	+	13.7918i	−0.701768	+	0.809884i
$291$	7.28542	−	15.9528i	0.427079	−	0.935172i
$292$	−2.46060	−	1.58133i	−0.143996	−	0.0925404i
$293$	10.3195	−	3.03008i	0.602871	−	0.177019i	0.0339673	−	0.999423i	$-0.489186\pi$
$293$	10.3195	−	3.03008i	0.602871	−	0.177019i	0.568904	+	0.822404i	$0.307368\pi$
$294$	2.41633	+	2.78860i	0.140923	+	0.162634i
$295$	−1.49387	−	0.438641i	−0.0869767	−	0.0255387i
$296$	−4.74743	−	10.3954i	−0.275939	−	0.604222i
$297$	3.07374	−	21.3783i	0.178356	−	1.24050i
$298$	14.8452			0.859959
$299$	−8.47881	−	28.4788i	−0.490342	−	1.64697i
$300$	2.07324			0.119699
$301$	0.825496	−	5.74145i	0.0475808	−	0.330932i
$302$	1.60063	+	3.50489i	0.0921058	+	0.201683i
$303$	−4.72458	−	1.38726i	−0.271420	−	0.0796961i
$304$	1.62436	+	1.87462i	0.0931637	+	0.107517i
$305$	−9.86922	+	2.89786i	−0.565110	+	0.165931i
$306$	−1.14614	−	0.736579i	−0.0655204	−	0.0421074i
$307$	−10.7114	+	23.4548i	−0.611333	+	1.33863i	0.310325	+	0.950631i	$0.399562\pi$
$307$	−10.7114	+	23.4548i	−0.611333	+	1.33863i	−0.921658	+	0.388003i	$0.873165\pi$
$308$	−5.22204	+	6.02656i	−0.297553	+	0.343395i
$309$	1.84183	−	1.18367i	0.104778	−	0.0673368i
$310$	1.45726	+	10.1355i	0.0827670	+	0.575657i
$311$	−2.32213	−	16.1508i	−0.131676	−	0.915827i	−0.943370	−	0.331743i	$-0.892363\pi$
$311$	−2.32213	−	16.1508i	−0.131676	−	0.915827i	0.811694	−	0.584083i	$-0.198546\pi$
$312$	−7.28612	+	4.68251i	−0.412495	+	0.265095i
$313$	−8.18796	+	9.44940i	−0.462811	+	0.534112i	−0.938398	−	0.345557i	$-0.887690\pi$
$313$	−8.18796	+	9.44940i	−0.462811	+	0.534112i	0.475587	+	0.879669i	$0.342236\pi$
$314$	9.40962	−	20.6042i	0.531015	−	1.16276i
$315$	−4.67831	−	3.00657i	−0.263593	−	0.169401i
$316$	1.81033	−	0.531560i	0.101839	−	0.0299026i
$317$	8.86597	+	10.2319i	0.497963	+	0.574680i	0.947976	−	0.318342i	$-0.103126\pi$
$317$	8.86597	+	10.2319i	0.497963	+	0.574680i	−0.450013	+	0.893022i	$0.648581\pi$
$318$	3.17319	+	0.931733i	0.177944	+	0.0522490i
$319$	11.3700	+	24.8969i	0.636600	+	1.39396i
$320$	−0.362362	+	2.52028i	−0.0202567	+	0.140888i
$321$	4.75723			0.265523
$322$	−5.44592	−	8.40423i	−0.303489	−	0.468349i
$323$	−3.23101			−0.179778
$324$	0.678585	−	4.71966i	0.0376992	−	0.262203i
$325$	−3.81737	−	8.35886i	−0.211749	−	0.463666i
$326$	18.1953	+	5.34263i	1.00775	+	0.295901i
$327$	7.89384	+	9.10998i	0.436530	+	0.503783i
$328$	4.11908	−	1.20947i	0.227438	−	0.0667819i
$329$	16.4099	+	10.5460i	0.904709	+	0.581421i
$330$	5.64641	−	12.3639i	0.310825	−	0.680611i
$331$	−18.5543	+	21.4128i	−1.01984	+	1.17696i	−0.0357339	+	0.999361i	$0.511377\pi$
$331$	−18.5543	+	21.4128i	−1.01984	+	1.17696i	−0.984104	+	0.177594i	$0.943169\pi$
$332$	8.78299	−	5.64449i	0.482029	−	0.309781i
$333$	−1.70111	−	11.8315i	−0.0932204	−	0.648362i
$334$	0.139416	+	0.969662i	0.00762853	+	0.0530576i
$335$	27.4730	−	17.6558i	1.50101	−	0.964640i
$336$	−1.91153	+	2.20602i	−0.104282	+	0.120348i
$337$	−6.01754	+	13.1766i	−0.327797	+	0.717774i	−0.999739	−	0.0228287i	$-0.992733\pi$
$337$	−6.01754	+	13.1766i	−0.327797	+	0.717774i	0.671943	+	0.740603i	$0.265460\pi$
$338$	21.3582	+	13.7261i	1.16173	+	0.746599i
$339$	4.78321	−	1.40448i	0.259788	−	0.0762807i
$340$	−2.17193	−	2.50654i	−0.117789	−	0.135936i
$341$	14.7355	+	4.32674i	0.797973	+	0.234306i
$342$	1.07776	+	2.35997i	0.0582787	+	0.127613i
$343$	2.86466	−	19.9241i	0.154677	−	1.07580i
$344$	−2.77780			−0.149769
$345$	12.9424	+	11.1296i	0.696797	+	0.599197i
$346$	−8.92203			−0.479651
$347$	−4.68287	+	32.5701i	−0.251390	+	1.74845i	0.338496	+	0.940968i	$0.390082\pi$
$347$	−4.68287	+	32.5701i	−0.251390	+	1.74845i	−0.589886	+	0.807487i	$0.700827\pi$
$348$	4.16200	+	9.11351i	0.223107	+	0.488536i
$349$	10.8999	+	3.20050i	0.583458	+	0.171319i	0.560124	−	0.828409i	$-0.310754\pi$
$349$	10.8999	+	3.20050i	0.583458	+	0.171319i	0.0233345	+	0.999728i	$0.492572\pi$
$350$	−2.02812	−	2.34057i	−0.108407	−	0.125109i
$351$	−33.6226	+	9.87247i	−1.79464	+	0.526954i
$352$	3.21259	+	2.06461i	0.171232	+	0.110044i
$353$	0.624933	−	1.36841i	0.0332618	−	0.0728332i	−0.892272	−	0.451499i	$-0.850890\pi$
$353$	0.624933	−	1.36841i	0.0332618	−	0.0728332i	0.925534	+	0.378665i	$0.123617\pi$
$354$	−0.559755	+	0.645991i	−0.0297506	+	0.0343341i
$355$	−14.1612	+	9.10087i	−0.751600	+	0.483024i
$356$	−0.713318	−	4.96123i	−0.0378058	−	0.262945i
$357$	−0.541111	−	3.76351i	−0.0286386	−	0.199186i
$358$	−7.14352	+	4.59086i	−0.377547	+	0.242635i
$359$	−13.3293	+	15.3828i	−0.703492	+	0.811873i	−0.989220	−	0.146438i	$-0.953219\pi$
$359$	−13.3293	+	15.3828i	−0.703492	+	0.811873i	0.285728	+	0.958311i	$0.407765\pi$
$360$	−1.10632	+	2.42250i	−0.0583082	+	0.127677i
$361$	−10.8078	−	6.94575i	−0.568831	−	0.365566i
$362$	0.515656	−	0.151410i	0.0271023	−	0.00795794i
$363$	−3.28024	−	3.78560i	−0.172168	−	0.198693i
$364$	12.4138	+	3.64502i	0.650661	+	0.191051i
$365$	−3.09377	−	6.77442i	−0.161936	−	0.354589i
$366$	−0.803651	+	5.58952i	−0.0420075	+	0.292169i
$367$	−12.2425			−0.639051			−0.319525	−	0.947578i	$-0.603523\pi$
$367$	−12.2425			−0.639051			−0.319525	+	0.947578i	$0.603523\pi$
$368$	−3.61259	+	3.15423i	−0.188319	+	0.164426i
$369$	4.49019			0.233750
$370$	4.14113	−	28.8022i	0.215287	−	1.49736i
$371$	−2.05225	−	4.49380i	−0.106548	−	0.233306i
$372$	5.39394	+	1.58380i	0.279663	+	0.0821164i
$373$	−10.7554	−	12.4124i	−0.556892	−	0.642688i	0.405583	−	0.914058i	$-0.367069\pi$
$373$	−10.7554	−	12.4124i	−0.556892	−	0.642688i	−0.962475	+	0.271371i	$0.912523\pi$
$374$	−4.77281	+	1.40142i	−0.246796	+	0.0724659i
$375$	−10.5304	−	6.76747i	−0.543787	−	0.349470i
$376$	3.88060	−	8.49733i	0.200127	−	0.438216i
$377$	29.0804	−	33.5606i	1.49772	−	1.72846i
$378$	−9.93524	+	6.38499i	−0.511013	+	0.328408i
$379$	3.66573	+	25.4957i	0.188296	+	1.30963i	0.836419	+	0.548091i	$0.184645\pi$
$379$	3.66573	+	25.4957i	0.188296	+	1.30963i	−0.648123	+	0.761536i	$0.724446\pi$
$380$	0.898830	+	6.25150i	0.0461090	+	0.320695i
$381$	−6.61089	+	4.24856i	−0.338686	+	0.217660i
$382$	17.5712	−	20.2783i	0.899021	−	1.03753i
$383$	−6.26867	+	13.7265i	−0.320314	+	0.701390i	−0.999468	−	0.0326054i	$-0.989620\pi$
$383$	−6.26867	+	13.7265i	−0.320314	+	0.701390i	0.679154	+	0.733996i	$0.262347\pi$
$384$	1.17597	+	0.755750i	0.0600109	+	0.0385667i
$385$	−19.4817	+	5.72033i	−0.992877	+	0.291535i
$386$	0.919649	+	1.06133i	0.0468089	+	0.0540204i
$387$	−2.78772	−	0.818550i	−0.141708	−	0.0416092i
$388$	5.21177	+	11.4122i	0.264588	+	0.579366i
$389$	−3.27106	+	22.7507i	−0.165849	+	1.15351i	0.721502	+	0.692412i	$0.243452\pi$
$389$	−3.27106	+	22.7507i	−0.165849	+	1.15351i	−0.887351	+	0.461094i	$0.847457\pi$
$390$	−22.0527			−1.11668
$391$	−0.0235341	−	6.24691i	−0.00119017	−	0.315920i
$392$	−2.63960			−0.133320
$393$	−1.58613	+	11.0318i	−0.0800097	+	0.556480i
$394$	−3.42498	−	7.49965i	−0.172548	−	0.377827i
$395$	4.60945	+	1.35346i	0.231927	+	0.0680998i
$396$	2.61567	+	3.01865i	0.131443	+	0.151693i
$397$	28.4653	−	8.35817i	1.42863	−	0.419484i	0.526217	−	0.850350i	$-0.323610\pi$
$397$	28.4653	−	8.35817i	1.42863	−	0.419484i	0.902416	+	0.430866i	$0.141792\pi$
$398$	−2.62060	−	1.68416i	−0.131359	−	0.0844193i
$399$	−3.00780	+	6.58616i	−0.150578	+	0.329720i
$400$	−0.971248	+	1.12088i	−0.0485624	+	0.0560440i
$401$	24.5924	−	15.8045i	1.22808	−	0.789241i	0.244492	−	0.969651i	$-0.421379\pi$
$401$	24.5924	−	15.8045i	1.22808	−	0.789241i	0.983592	+	0.180410i	$0.0577424\pi$
$402$	−2.55156	−	17.7465i	−0.127260	−	0.885114i
$403$	−3.54606	−	24.6634i	−0.176642	−	1.22857i
$404$	2.96333	−	1.90441i	0.147431	−	0.0947481i
$405$	7.95052	−	9.17539i	0.395065	−	0.455929i
$406$	6.21722	−	13.6138i	0.308555	−	0.675642i
$407$	−36.7140	−	23.5947i	−1.81985	−	1.16954i
$408$	−1.74709	+	0.512992i	−0.0864938	+	0.0253969i
$409$	−22.0687	−	25.4686i	−1.09123	−	1.25934i	−0.963550	−	0.267528i	$-0.913793\pi$
$409$	−22.0687	−	25.4686i	−1.09123	−	1.25934i	−0.127677	−	0.991816i	$-0.540752\pi$
$410$	10.4880	+	3.07956i	0.517966	+	0.152089i
$411$	1.20167	+	2.63128i	0.0592738	+	0.129791i
$412$	−0.222897	+	1.55028i	−0.0109813	+	0.0763769i
$413$	1.27686			0.0628301
$414$	−4.55496	+	2.10096i	−0.223864	+	0.103256i
$415$	26.5833			1.30492
$416$	0.881761	−	6.13278i	0.0432319	−	0.300684i
$417$	−7.58507	−	16.6090i	−0.371442	−	0.813345i
$418$	9.08877	+	2.66870i	0.444546	+	0.130531i
$419$	−5.77988	−	6.67033i	−0.282366	−	0.325867i	0.596794	−	0.802394i	$-0.296441\pi$
$419$	−5.77988	−	6.67033i	−0.282366	−	0.325867i	−0.879160	+	0.476527i	$0.841895\pi$
$420$	−7.13126	+	2.09393i	−0.347970	+	0.102173i
$421$	23.0285	+	14.7995i	1.12234	+	0.721283i	0.963947	−	0.266093i	$-0.0857329\pi$
$421$	23.0285	+	14.7995i	1.12234	+	0.721283i	0.158391	+	0.987376i	$0.449369\pi$
$422$	−9.14235	+	20.0189i	−0.445043	+	0.974507i
$423$	6.39841	−	7.38416i	0.311101	−	0.359030i
$424$	−1.99027	+	1.27907i	−0.0966561	+	0.0621171i
$425$	−0.274938	−	1.91224i	−0.0133365	−	0.0927572i
$426$	1.31523	+	9.14761i	0.0637230	+	0.443203i
$427$	7.09640	−	4.56058i	0.343419	−	0.220702i
$428$	−2.22861	+	2.57195i	−0.107724	+	0.124320i
$429$	−13.7398	+	30.0860i	−0.663364	+	1.45256i
$430$	−5.95006	−	3.82387i	−0.286937	−	0.184403i
$431$	28.6589	−	8.41502i	1.38045	−	0.405337i	0.494525	−	0.869163i	$-0.335342\pi$
$431$	28.6589	−	8.41502i	1.38045	−	0.405337i	0.885926	+	0.463826i	$0.153524\pi$
$432$	3.70371	+	4.27431i	0.178195	+	0.205648i
$433$	−26.2406	−	7.70492i	−1.26104	−	0.370275i	−0.418159	−	0.908374i	$-0.637325\pi$
$433$	−26.2406	−	7.70492i	−1.26104	−	0.370275i	−0.842882	+	0.538099i	$0.819143\pi$
$434$	−3.48851	−	7.63878i	−0.167454	−	0.366673i
$435$	−3.63047	+	25.2505i	−0.174068	+	1.21067i
$436$	−8.62324			−0.412978
$437$	−6.39368	+	10.0317i	−0.305851	+	0.479879i
$438$	−4.08868			−0.195365
$439$	1.86711	−	12.9861i	0.0891124	−	0.619791i	−0.895503	−	0.445055i	$-0.853184\pi$
$439$	1.86711	−	12.9861i	0.0891124	−	0.619791i	0.984615	−	0.174735i	$-0.0559069\pi$
$440$	4.03927	+	8.84477i	0.192565	+	0.421658i
$441$	−2.64903	−	0.777826i	−0.126144	−	0.0370393i
$442$	5.28511	+	6.09934i	0.251387	+	0.290116i
$443$	10.3339	−	3.03431i	0.490979	−	0.144164i	−0.0268659	−	0.999639i	$-0.508553\pi$
$443$	10.3339	−	3.03431i	0.490979	−	0.144164i	0.517845	+	0.855475i	$0.326735\pi$
$444$	−13.4392	−	8.63683i	−0.637795	−	0.409886i
$445$	5.30161	−	11.6089i	0.251320	−	0.550315i
$446$	−8.06117	+	9.30308i	−0.381707	+	0.440514i
$447$	17.4575	−	11.2193i	0.825712	−	0.530653i
$448$	−0.297176	−	2.06690i	−0.0140402	−	0.0976519i
$449$	−0.667871	−	4.64515i	−0.0315188	−	0.219218i	0.967974	−	0.251049i	$-0.0807754\pi$
$449$	−0.667871	−	4.64515i	−0.0315188	−	0.219218i	−0.999493	+	0.0318306i	$0.989866\pi$
$450$	−1.30501	+	0.838680i	−0.0615188	+	0.0395357i
$451$	10.7358	−	12.3898i	0.505531	−	0.583414i
$452$	−1.48146	+	3.24395i	−0.0696821	+	0.152583i
$453$	4.53110	+	2.91196i	0.212890	+	0.136816i
$454$	−5.11649	+	1.50234i	−0.240129	+	0.0705082i
$455$	21.5727	+	24.8962i	1.01134	+	1.16715i
$456$	3.32694	+	0.976879i	0.155798	+	0.0457465i
$457$	2.88119	+	6.30892i	0.134776	+	0.295119i	0.964972	−	0.262353i	$-0.0844986\pi$
$457$	2.88119	+	6.30892i	0.134776	+	0.295119i	−0.830196	+	0.557472i	$0.811771\pi$
$458$	−2.00763	+	13.9634i	−0.0938105	+	0.652467i
$459$	−7.36703			−0.343864
$460$	−12.0802	+	1.78335i	−0.563243	+	0.0831491i
$461$	−21.3273			−0.993312			−0.496656	−	0.867947i	$-0.665439\pi$
$461$	−21.3273			−0.993312			−0.496656	+	0.867947i	$0.665439\pi$
$462$	−1.58639	+	11.0336i	−0.0738057	+	0.513330i
$463$	−2.66484	−	5.83519i	−0.123846	−	0.271185i	0.837546	−	0.546366i	$-0.183989\pi$
$463$	−2.66484	−	5.83519i	−0.123846	−	0.271185i	−0.961392	+	0.275182i	$0.911262\pi$
$464$	−6.87690	−	2.01924i	−0.319252	−	0.0937409i
$465$	9.37358	+	10.8177i	0.434690	+	0.501659i
$466$	−16.4868	+	4.84095i	−0.763734	+	0.224253i
$467$	12.1748	+	7.82429i	0.563384	+	0.362065i	0.791123	−	0.611657i	$-0.209497\pi$
$467$	12.1748	+	7.82429i	0.563384	+	0.362065i	−0.227739	+	0.973722i	$0.573133\pi$
$468$	2.69209	−	5.89485i	0.124442	−	0.272489i
$469$	−17.5387	+	20.2408i	−0.809863	+	0.934632i
$470$	20.0095	−	12.8593i	0.922970	−	0.593157i
$471$	−4.50618	−	31.3412i	−0.207634	−	1.44413i
$472$	−0.0870222	−	0.605253i	−0.00400552	−	0.0278590i
$473$	−8.92395	+	5.73507i	−0.410324	+	0.263699i
$474$	1.72716	−	1.99325i	0.0793311	−	0.0915530i
$475$	−1.52826	+	3.34643i	−0.0701215	+	0.153545i
$476$	2.28820	+	1.47054i	0.104880	+	0.0674020i
$477$	−2.37429	+	0.697154i	−0.108711	+	0.0319205i
$478$	3.69369	+	4.26274i	0.168945	+	0.194973i
$479$	5.15751	+	1.51438i	0.235653	+	0.0691938i	0.397427	−	0.917634i	$-0.369903\pi$
$479$	5.15751	+	1.51438i	0.235653	+	0.0691938i	−0.161774	+	0.986828i	$0.551722\pi$
$480$	1.47858	+	3.23763i	0.0674875	+	0.147777i
$481$	−10.0769	+	70.0864i	−0.459467	+	3.19567i
$482$	−5.03768			−0.229460
$483$	−12.7557	−	5.76737i	−0.580406	−	0.262424i
$484$	3.58334			0.162879
$485$	−4.54617	+	31.6193i	−0.206431	+	1.43576i
$486$	4.27953	+	9.37087i	0.194124	+	0.425071i
$487$	−3.08891	−	0.906986i	−0.139972	−	0.0410994i	0.210996	−	0.977487i	$-0.432329\pi$
$487$	−3.08891	−	0.906986i	−0.139972	−	0.0410994i	−0.350968	+	0.936387i	$0.614147\pi$
$488$	−2.64544	−	3.05300i	−0.119753	−	0.138203i
$489$	25.4348	−	7.46834i	1.15020	−	0.337730i
$490$	−5.65403	−	3.63363i	−0.255423	−	0.164151i
$491$	12.4938	−	27.3575i	0.563836	−	1.23463i	−0.386179	−	0.922424i	$-0.626205\pi$
$491$	12.4938	−	27.3575i	0.563836	−	1.23463i	0.950015	−	0.312204i	$-0.101067\pi$
$492$	3.92986	−	4.53530i	0.177172	−	0.204467i
$493$	7.85384	−	5.04736i	0.353719	−	0.227322i
$494$	−2.18718	−	15.2122i	−0.0984061	−	0.684429i
$495$	1.44736	+	10.0666i	0.0650541	+	0.452461i
$496$	−3.38316	+	2.17422i	−0.151908	+	0.0976255i
$497$	9.04052	−	10.4333i	0.405523	−	0.467998i
$498$	6.06271	−	13.2755i	0.271677	−	0.594889i
$499$	14.9310	+	9.59557i	0.668403	+	0.429557i	0.830350	−	0.557243i	$-0.188141\pi$
$499$	14.9310	+	9.59557i	0.668403	+	0.429557i	−0.161946	+	0.986800i	$0.551777\pi$
$500$	8.59191	−	2.52281i	0.384242	−	0.112824i
$501$	0.896771	+	1.03493i	0.0400648	+	0.0462372i
$502$	16.9649	+	4.98135i	0.757182	+	0.222329i
$503$	10.2877	+	22.5269i	0.458705	+	1.00442i	0.987781	+	0.155850i	$0.0498115\pi$
$503$	10.2877	+	22.5269i	0.458705	+	1.00442i	−0.529076	+	0.848575i	$0.677461\pi$
$504$	0.310827	−	2.16185i	0.0138454	−	0.0962966i
$505$	8.96902			0.399116
$506$	−5.09352	+	17.5918i	−0.226435	+	0.782053i
$507$	35.4900			1.57617
$508$	0.800045	−	5.56443i	0.0354963	−	0.246882i
$509$	−12.8953	−	28.2367i	−0.571572	−	1.25157i	−0.945956	−	0.324295i	$-0.894873\pi$
$509$	−12.8953	−	28.2367i	−0.571572	−	1.25157i	0.374384	−	0.927274i	$-0.377854\pi$
$510$	−4.44844	−	1.30618i	−0.196980	−	0.0578386i
$511$	3.99969	+	4.61588i	0.176936	+	0.204195i
$512$	−0.959493	+	0.281733i	−0.0424040	+	0.0124509i
$513$	11.8018	+	7.58459i	0.521064	+	0.334868i
$514$	9.16631	−	20.0714i	0.404308	−	0.885312i
$515$	−2.61153	+	3.01387i	−0.115078	+	0.132807i
$516$	−3.26661	+	2.09932i	−0.143805	+	0.0924176i
$517$	−5.07686	−	35.3104i	−0.223280	−	1.55295i
$518$	3.39617	+	23.6209i	0.149219	+	1.03784i
$519$	−10.4920	+	6.74282i	−0.460549	+	0.295977i
$520$	10.3310	−	11.9226i	0.453044	−	0.522841i
$521$	13.8381	−	30.3013i	0.606259	−	1.32752i	−0.318844	−	0.947807i	$-0.603295\pi$
$521$	13.8381	−	30.3013i	0.606259	−	1.32752i	0.925103	−	0.379715i	$-0.123978\pi$
$522$	−6.30644	−	4.05290i	−0.276025	−	0.177391i
$523$	−29.7832	+	8.74514i	−1.30233	+	0.382398i	−0.858085	−	0.513507i	$-0.828346\pi$
$523$	−29.7832	+	8.74514i	−1.30233	+	0.382398i	−0.444244	+	0.895906i	$0.646528\pi$
$524$	−5.22118	−	6.02556i	−0.228088	−	0.263228i
$525$	−4.15389	−	1.21969i	−0.181291	−	0.0532317i
$526$	−3.22296	−	7.05731i	−0.140528	−	0.307713i
$527$	0.745503	−	5.18509i	0.0324746	−	0.225866i
$528$	5.33823			0.232317
$529$	−19.4420	−	12.2886i	−0.845303	−	0.534287i
$530$	−6.02390			−0.261661
$531$	0.0910199	−	0.633057i	0.00394993	−	0.0274723i
$532$	−2.15169	−	4.71154i	−0.0932876	−	0.204271i
$533$	−25.5212	−	7.49370i	−1.10545	−	0.324588i
$534$	−4.58829	−	5.29517i	−0.198555	−	0.229144i
$535$	−8.31418	+	2.44126i	−0.359453	+	0.105545i
$536$	10.7898	+	6.93418i	0.466048	+	0.299511i
$537$	−4.93102	+	10.7974i	−0.212789	+	0.465943i
$538$	−11.1453	+	12.8623i	−0.480506	+	0.554534i
$539$	−8.47997	+	5.44975i	−0.365258	+	0.234737i
$540$	2.04942	+	14.2540i	0.0881930	+	0.613396i
$541$	0.731645	+	5.08870i	0.0314559	+	0.218780i	0.999486	−	0.0320528i	$-0.0102045\pi$
$541$	0.731645	+	5.08870i	0.0314559	+	0.218780i	−0.968030	+	0.250833i	$0.919295\pi$
$542$	9.79847	−	6.29709i	0.420880	−	0.270483i
$543$	0.491967	−	0.567760i	0.0211123	−	0.0243649i
$544$	0.541111	−	1.18487i	0.0231999	−	0.0508008i
$545$	−18.4710	−	11.8706i	−0.791210	−	0.508480i
$546$	17.3530	−	5.09530i	0.742639	−	0.218059i
$547$	−12.4508	−	14.3689i	−0.532356	−	0.614371i	0.424325	−	0.905510i	$-0.360511\pi$
$547$	−12.4508	−	14.3689i	−0.532356	−	0.614371i	−0.956681	+	0.291139i	$0.905966\pi$
$548$	−1.98552	−	0.583001i	−0.0848172	−	0.0249046i
$549$	−1.75524	−	3.84344i	−0.0749119	−	0.164034i
$550$	−0.806046	+	5.60617i	−0.0343699	+	0.239048i
$551$	−17.7781			−0.757373
$552$	−1.86448	+	6.43950i	−0.0793577	+	0.274083i
$553$	−3.93983			−0.167539
$554$	−2.39514	+	16.6586i	−0.101760	+	0.707754i
$555$	−16.8974	−	37.0002i	−0.717256	−	1.57057i
$556$	12.5329	+	3.67998i	0.531511	+	0.156066i
$557$	−7.90600	−	9.12401i	−0.334988	−	0.386597i	0.563118	−	0.826377i	$-0.309602\pi$
$557$	−7.90600	−	9.12401i	−0.334988	−	0.386597i	−0.898105	+	0.439780i	$0.855056\pi$
$558$	−4.03593	+	1.18505i	−0.170854	+	0.0501674i
$559$	14.4787	+	9.30489i	0.612383	+	0.393555i
$560$	2.20870	−	4.83639i	0.0933348	−	0.204375i
$561$	−4.55356	+	5.25508i	−0.192251	+	0.221870i
$562$	−4.45065	+	2.86026i	−0.187739	+	0.120653i
$563$	3.02219	+	21.0198i	0.127370	+	0.885879i	0.948869	+	0.315669i	$0.102229\pi$
$563$	3.02219	+	21.0198i	0.127370	+	0.885879i	−0.821499	+	0.570210i	$0.806862\pi$
$564$	−1.85839	−	12.9254i	−0.0782522	−	0.544256i
$565$	−7.63885	+	4.90919i	−0.321369	+	0.206531i
$566$	10.0649	−	11.6156i	0.423061	−	0.488238i
$567$	−4.13618	+	9.05697i	−0.173703	+	0.380357i
$568$	−5.56171	−	3.57430i	−0.233364	−	0.149974i
$569$	−11.2469	+	3.30239i	−0.471496	+	0.138444i	−0.508844	−	0.860859i	$-0.669927\pi$
$569$	−11.2469	+	3.30239i	−0.471496	+	0.138444i	0.0373485	+	0.999302i	$0.488109\pi$
$570$	5.78156	+	6.67228i	0.242163	+	0.279471i
$571$	42.5321	+	12.4886i	1.77991	+	0.522630i	0.995255	−	0.0972968i	$-0.0310196\pi$
$571$	42.5321	+	12.4886i	1.77991	+	0.522630i	0.784660	+	0.619927i	$0.212838\pi$
$572$	−9.82904	−	21.5226i	−0.410973	−	0.899905i
$573$	5.33792	−	37.1260i	0.222995	−	1.55096i
$574$	−8.96441			−0.374167
$575$	−6.48118	−	2.93040i	−0.270284	−	0.122206i
$576$	−1.04594			−0.0435808
$577$	−4.25824	+	29.6167i	−0.177273	+	1.23296i	0.685766	+	0.727822i	$0.259467\pi$
$577$	−4.25824	+	29.6167i	−0.177273	+	1.23296i	−0.863039	+	0.505138i	$0.831442\pi$
$578$	−6.35721	−	13.9204i	−0.264425	−	0.579011i
$579$	1.88358	+	0.553069i	0.0782789	+	0.0229848i
$580$	−11.9507	−	13.7918i	−0.496225	−	0.572674i
$581$	−20.9180	+	6.14208i	−0.867825	+	0.254816i
$582$	14.7536	+	9.48159i	0.611558	+	0.393025i
$583$	−3.75315	+	8.21825i	−0.155440	+	0.340365i
$584$	1.91542	−	2.21051i	0.0792604	−	0.0914714i
$585$	13.8812	−	8.92089i	0.573916	−	0.368833i
$586$	1.53062	+	10.6457i	0.0632292	+	0.439769i
$587$	−1.50360	−	10.4578i	−0.0620602	−	0.431638i	−0.997037	−	0.0769284i	$-0.975489\pi$
$587$	−1.50360	−	10.4578i	−0.0620602	−	0.431638i	0.934976	−	0.354710i	$-0.115420\pi$
$588$	−3.10409	+	1.99488i	−0.128011	+	0.0822675i
$589$	−6.53249	+	7.53889i	−0.269167	+	0.310635i
$590$	0.646777	−	1.41624i	0.0266274	−	0.0583058i
$591$	−9.69553	−	6.23094i	−0.398821	−	0.256307i
$592$	10.9652	−	3.21969i	0.450669	−	0.132328i
$593$	−5.66384	−	6.53642i	−0.232586	−	0.268419i	0.627444	−	0.778661i	$-0.284101\pi$
$593$	−5.66384	−	6.53642i	−0.232586	−	0.268419i	−0.860030	+	0.510243i	$0.829556\pi$
$594$	20.7233	+	6.08491i	0.850287	+	0.249667i
$595$	2.87701	+	6.29978i	0.117946	+	0.258266i
$596$	−2.11269	+	14.6941i	−0.0865393	+	0.601894i
$597$	−4.35455			−0.178220
$598$	29.3956	−	4.33955i	1.20208	−	0.177457i
$599$	20.5800			0.840877			0.420439	−	0.907321i	$-0.361876\pi$
$599$	20.5800			0.840877			0.420439	+	0.907321i	$0.361876\pi$
$600$	−0.295053	+	2.05214i	−0.0120455	+	0.0837783i
$601$	7.34180	+	16.0763i	0.299478	+	0.655766i	0.998222	−	0.0596061i	$-0.0189845\pi$
$601$	7.34180	+	16.0763i	0.299478	+	0.655766i	−0.698744	+	0.715372i	$0.746257\pi$
$602$	5.56553	+	1.63419i	0.226834	+	0.0666045i
$603$	8.78499	+	10.1384i	0.357753	+	0.412868i
$604$	−3.69700	+	1.08554i	−0.150429	+	0.0441699i
$605$	7.67551	+	4.93275i	0.312054	+	0.200545i
$606$	2.04552	−	4.47906i	0.0830936	−	0.181950i
$607$	27.4879	−	31.7227i	1.11570	−	1.28758i	0.162010	−	0.986789i	$-0.448202\pi$
$607$	27.4879	−	31.7227i	1.11570	−	1.28758i	0.953689	−	0.300795i	$-0.0972521\pi$
$608$	−2.08671	+	1.34105i	−0.0846272	+	0.0543866i
$609$	−2.97737	−	20.7081i	−0.120649	−	0.839134i
$610$	−1.46383	−	10.1812i	−0.0592688	−	0.412224i
$611$	−48.6905	+	31.2915i	−1.96981	+	1.26592i
$612$	0.892194	−	1.02965i	0.0360648	−	0.0416210i
$613$	7.45006	−	16.3134i	0.300905	−	0.658890i	−0.697425	−	0.716658i	$-0.745671\pi$
$613$	7.45006	−	16.3134i	0.300905	−	0.658890i	0.998330	+	0.0577675i	$0.0183982\pi$
$614$	−21.6916	−	13.9404i	−0.875403	−	0.562587i
$615$	14.6610	−	4.30485i	0.591187	−	0.173588i
$616$	−5.22204	−	6.02656i	−0.210402	−	0.242817i
$617$	−2.83913	−	0.833643i	−0.114299	−	0.0335612i	0.224083	−	0.974570i	$-0.428061\pi$
$617$	−2.83913	−	0.833643i	−0.114299	−	0.0335612i	−0.338382	+	0.941009i	$0.609880\pi$
$618$	0.909504	+	1.99154i	0.0365856	+	0.0801114i
$619$	−3.98738	+	27.7328i	−0.160266	+	1.11468i	0.737865	+	0.674949i	$0.235834\pi$
$619$	−3.98738	+	27.7328i	−0.160266	+	1.11468i	−0.898131	+	0.439728i	$0.855075\pi$
$620$	−10.2397			−0.411237
$621$	−14.5782	+	22.8732i	−0.585004	+	0.917869i
$622$	16.3169			0.654247
$623$	−1.48952	+	10.3598i	−0.0596763	+	0.415058i
$624$	−3.59792	−	7.87835i	−0.144032	−	0.315386i
$625$	28.9920	+	8.51283i	1.15968	+	0.340513i
$626$	−8.18796	−	9.44940i	−0.327257	−	0.377674i
$627$	12.7050	−	3.73052i	0.507388	−	0.148983i
$628$	19.0553	+	12.2461i	0.760391	+	0.488673i
$629$	−6.18391	+	13.5409i	−0.246569	+	0.539910i
$630$	3.64175	−	4.20281i	0.145091	−	0.167444i
$631$	−2.05053	+	1.31779i	−0.0816302	+	0.0524605i	−0.580819	−	0.814033i	$-0.697268\pi$
$631$	−2.05053	+	1.31779i	−0.0816302	+	0.0524605i	0.499189	+	0.866493i	$0.333631\pi$
$632$	0.268513	+	1.86755i	0.0106809	+	0.0742871i
$633$	4.37819	+	30.4510i	0.174018	+	1.21032i
$634$	−11.3895	+	7.31958i	−0.452335	+	0.290698i
$635$	9.37358	−	10.8177i	0.371979	−	0.429287i
$636$	−1.37384	+	3.00829i	−0.0544763	+	0.119287i
$637$	13.7583	+	8.84195i	0.545126	+	0.350331i
$638$	−26.2616	+	7.71110i	−1.03971	+	0.305286i
$639$	−4.52832	−	5.22596i	−0.179137	−	0.206736i
$640$	−2.44306	−	0.717348i	−0.0965705	−	0.0283557i
$641$	1.33060	+	2.91362i	0.0525557	+	0.115081i	0.934088	−	0.357043i	$-0.116215\pi$
$641$	1.33060	+	2.91362i	0.0525557	+	0.115081i	−0.881532	+	0.472124i	$0.843488\pi$
$642$	−0.677024	+	4.70881i	−0.0267200	+	0.185842i
$643$	35.8609			1.41422			0.707108	−	0.707105i	$-0.249999\pi$
$643$	35.8609			1.41422			0.707108	+	0.707105i	$0.249999\pi$
$644$	9.09372	−	4.19444i	0.358343	−	0.165284i
$645$	−9.88697			−0.389299
$646$	0.459821	−	3.19813i	0.0180914	−	0.125829i
$647$	4.09842	+	8.97429i	0.161126	+	0.352816i	0.972925	−	0.231120i	$-0.0742391\pi$
$647$	4.09842	+	8.97429i	0.161126	+	0.352816i	−0.811800	+	0.583936i	$0.801512\pi$
$648$	4.57505	+	1.34336i	0.179725	+	0.0527720i
$649$	−1.52917	−	1.76476i	−0.0600254	−	0.0692730i
$650$	8.81705	−	2.58892i	0.345833	−	0.101546i
$651$	−9.87538	−	6.34652i	−0.387047	−	0.248740i
$652$	−7.87772	+	17.2498i	−0.308515	+	0.675554i
$653$	8.37325	−	9.66324i	0.327671	−	0.378152i	−0.567880	−	0.823111i	$-0.692236\pi$
$653$	8.37325	−	9.66324i	0.327671	−	0.378152i	0.895551	+	0.444959i	$0.146782\pi$
$654$	−10.1407	+	6.51701i	−0.396531	+	0.254835i
$655$	−2.88910	−	20.0941i	−0.112886	−	0.785143i
$656$	0.610955	+	4.24928i	0.0238538	+	0.165907i
$657$	2.57364	−	1.65398i	0.100407	−	0.0645277i
$658$	−12.7741	+	14.7420i	−0.497984	+	0.574705i
$659$	−2.12193	+	4.64638i	−0.0826587	+	0.180997i	−0.946448	−	0.322855i	$-0.895357\pi$
$659$	−2.12193	+	4.64638i	−0.0826587	+	0.180997i	0.863790	+	0.503853i	$0.168085\pi$
$660$	11.4345	+	7.34850i	0.445087	+	0.286040i
$661$	25.8606	−	7.59336i	1.00586	−	0.295348i	0.263002	−	0.964795i	$-0.415287\pi$
$661$	25.8606	−	7.59336i	1.00586	−	0.295348i	0.742859	+	0.669448i	$0.233469\pi$
$662$	−18.5543	−	21.4128i	−0.721134	−	0.832233i
$663$	10.8247	+	3.17842i	0.420396	+	0.123439i
$664$	4.33708	+	9.49689i	0.168311	+	0.368551i
$665$	1.87690	−	13.0541i	0.0727829	−	0.506216i
$666$	11.9532			0.463176
$667$	−0.129492	−	34.3726i	−0.00501396	−	1.33091i
$668$	−0.979634			−0.0379032
$669$	−2.44888	+	17.0324i	−0.0946793	+	0.658509i
$670$	13.5663	+	29.7060i	0.524111	+	1.14764i
$671$	−14.8019	−	4.34624i	−0.571423	−	0.167785i
$672$	−1.91153	−	2.20602i	−0.0737388	−	0.0850992i
$673$	−26.0210	+	7.64046i	−1.00304	+	0.294518i	−0.741702	−	0.670730i	$-0.765981\pi$
$673$	−26.0210	+	7.64046i	−1.00304	+	0.294518i	−0.261335	+	0.965248i	$0.584163\pi$
$674$	−12.1861	−	7.83152i	−0.469390	−	0.301659i
$675$	−3.48459	+	7.63019i	−0.134122	+	0.293686i
$676$	−16.6259	+	19.1873i	−0.639459	+	0.737974i
$677$	23.7332	−	15.2524i	0.912140	−	0.586197i	0.00177304	−	0.999998i	$-0.499436\pi$
$677$	23.7332	−	15.2524i	0.912140	−	0.586197i	0.910367	+	0.413802i	$0.135799\pi$
$678$	0.709460	+	4.93440i	0.0272466	+	0.189505i
$679$	−3.72835	−	25.9312i	−0.143081	−	0.995149i
$680$	2.79013	−	1.79310i	0.106996	−	0.0687624i
$681$	−4.88145	+	5.63349i	−0.187057	+	0.215876i
$682$	−6.37978	+	13.9698i	−0.244294	+	0.534930i
$683$	−1.90711	−	1.22563i	−0.0729736	−	0.0468973i	0.503645	−	0.863911i	$-0.331992\pi$
$683$	−1.90711	−	1.22563i	−0.0729736	−	0.0468973i	−0.576619	+	0.817013i	$0.695628\pi$
$684$	−2.48933	+	0.730934i	−0.0951820	+	0.0279479i
$685$	−3.45043	−	3.98201i	−0.131834	−	0.152145i
$686$	19.3136	+	5.67099i	0.737398	+	0.216520i
$687$	8.19192	+	17.9378i	0.312541	+	0.684370i
$688$	0.395323	−	2.74953i	0.0150715	−	0.104825i
$689$	14.6584			0.558439
$690$	−12.8582	+	11.2268i	−0.489504	+	0.427397i
$691$	2.62969			0.100038			0.0500191	−	0.998748i	$-0.484072\pi$
$691$	2.62969			0.100038			0.0500191	+	0.998748i	$0.484072\pi$
$692$	1.26974	−	8.83122i	0.0482682	−	0.335713i
$693$	−3.46481	−	7.58688i	−0.131617	−	0.288202i
$694$	−31.5721	−	9.27042i	−1.19846	−	0.351900i
$695$	21.7796	+	25.1350i	0.826147	+	0.953424i
$696$	−9.61307	+	2.82265i	−0.364382	+	0.106992i
$697$	−4.70425	−	3.02324i	−0.178186	−	0.114513i
$698$	−4.71914	+	10.3335i	−0.178622	+	0.391128i
$699$	−15.7294	+	18.1527i	−0.594940	+	0.686597i
$700$	2.60538	−	1.67438i	0.0984741	−	0.0632854i
$701$	2.45078	+	17.0456i	0.0925647	+	0.643802i	0.982299	+	0.187322i	$0.0599808\pi$
$701$	2.45078	+	17.0456i	0.0925647	+	0.643802i	−0.889734	+	0.456480i	$0.849110\pi$
$702$	−4.98700	−	34.6853i	−0.188222	−	1.30911i
$703$	23.8472	−	15.3257i	0.899416	−	0.578019i
$704$	−2.50079	+	2.88607i	−0.0942521	+	0.108773i
$705$	13.8121	−	30.2443i	0.520195	−	1.13907i
$706$	1.26555	+	0.813317i	0.0476295	+	0.0306096i
$707$	−7.05760	+	2.07230i	−0.265428	+	0.0779368i
$708$	−0.559755	−	0.645991i	−0.0210369	−	0.0242778i
$709$	−34.6715	−	10.1805i	−1.30212	−	0.382336i	−0.444109	−	0.895973i	$-0.646480\pi$
$709$	−34.6715	−	10.1805i	−1.30212	−	0.382336i	−0.858008	+	0.513637i	$0.828298\pi$
$710$	−6.99289	−	15.3123i	−0.262438	−	0.574660i
$711$	−0.280848	+	1.95334i	−0.0105326	+	0.0732560i
$712$	5.01225			0.187842
$713$	−14.6234	−	12.5751i	−0.547652	−	0.470942i
$714$	3.80221			0.142294
$715$	8.57377	−	59.6319i	0.320641	−	2.23011i
$716$	−3.52750	−	7.72416i	−0.131829	−	0.288665i
$717$	7.56523	+	2.22135i	0.282529	+	0.0829579i
$718$	−13.3293	−	15.3828i	−0.497444	−	0.574081i
$719$	−26.8795	+	7.89253i	−1.00244	+	0.294342i	−0.741455	−	0.671003i	$-0.765864\pi$
$719$	−26.8795	+	7.89253i	−1.00244	+	0.294342i	−0.260980	+	0.965344i	$0.584046\pi$
$720$	−2.24040	−	1.43982i	−0.0834948	−	0.0536589i
$721$	1.35862	−	2.97497i	0.0505977	−	0.110794i
$722$	8.41316	−	9.70930i	0.313105	−	0.361343i
$723$	−5.92415	+	3.80722i	−0.220322	+	0.141592i
$724$	0.0764836	+	0.531955i	0.00284249	+	0.0197699i
$725$	−1.51280	−	10.5218i	−0.0561841	−	0.390769i
$726$	4.21390	−	2.70811i	0.156392	−	0.100507i
$727$	−31.8709	+	36.7809i	−1.18202	+	1.36413i	−0.265520	+	0.964105i	$0.585544\pi$
$727$	−31.8709	+	36.7809i	−1.18202	+	1.36413i	−0.916505	+	0.400024i	$0.869002\pi$
$728$	−5.37459	+	11.7687i	−0.199196	+	0.436178i
$729$	24.1484	+	15.5192i	0.894386	+	0.574787i
$730$	7.14576	−	2.09818i	0.264476	−	0.0776573i
$731$	2.36949	+	2.73454i	0.0876388	+	0.101141i
$732$	−5.41825	−	1.59094i	−0.200264	−	0.0588029i
$733$	−1.42468	−	3.11960i	−0.0526216	−	0.115225i	0.881495	−	0.472194i	$-0.156538\pi$
$733$	−1.42468	−	3.11960i	−0.0526216	−	0.115225i	−0.934116	+	0.356968i	$0.883810\pi$
$734$	1.74228	−	12.1178i	0.0643088	−	0.447278i
$735$	−9.39508			−0.346543
$736$	−2.60800	−	4.02471i	−0.0961323	−	0.148353i
$737$	48.9795			1.80418
$738$	−0.639021	+	4.44449i	−0.0235227	+	0.163604i
$739$	−5.04671	−	11.0508i	−0.185646	−	0.406509i	0.793810	−	0.608166i	$-0.208095\pi$
$739$	−5.04671	−	11.0508i	−0.185646	−	0.406509i	−0.979456	+	0.201657i	$0.935367\pi$
$740$	27.9197	+	8.19797i	1.02635	+	0.301363i
$741$	−14.0687	−	16.2361i	−0.516826	−	0.596449i
$742$	4.74013	−	1.39183i	0.174015	−	0.0510956i
$743$	−37.8162	−	24.3030i	−1.38734	−	0.891590i	−0.387797	−	0.921745i	$-0.626764\pi$
$743$	−37.8162	−	24.3030i	−1.38734	−	0.891590i	−0.999545	+	0.0301545i	$0.990400\pi$
$744$	−2.33532	+	5.11364i	−0.0856170	+	0.187475i
$745$	−24.7530	+	28.5665i	−0.906879	+	1.04659i
$746$	13.8167	−	8.87943i	0.505864	−	0.325099i
$747$	1.55408	+	10.8088i	0.0568606	+	0.395474i
$748$	−0.707918	−	4.92368i	−0.0258840	−	0.180027i
$749$	5.97826	−	3.84200i	0.218441	−	0.140383i
$750$	8.19721	−	9.46009i	0.299320	−	0.345434i
$751$	2.56678	−	5.62046i	0.0936631	−	0.205094i	−0.857002	−	0.515314i	$-0.827675\pi$
$751$	2.56678	−	5.62046i	0.0936631	−	0.205094i	0.950665	+	0.310220i	$0.100403\pi$
$752$	7.85857	+	5.05040i	0.286573	+	0.184169i
$753$	23.7149	−	6.96332i	0.864218	−	0.253757i
$754$	29.0804	+	33.5606i	1.05905	+	1.22220i
$755$	−9.41331	−	2.76400i	−0.342585	−	0.100592i
$756$	−4.90607	−	10.7428i	−0.178432	−	0.390711i
$757$	−1.95623	+	13.6059i	−0.0711003	+	0.494513i	0.922892	+	0.385060i	$0.125819\pi$
$757$	−1.95623	+	13.6059i	−0.0711003	+	0.494513i	−0.993992	+	0.109454i	$0.965090\pi$
$758$	−25.7579			−0.935569
$759$	7.30520	+	24.5369i	0.265162	+	0.890633i
$760$	−6.31578			−0.229098
$761$	7.27388	−	50.5910i	0.263678	−	1.83392i	−0.240894	−	0.970551i	$-0.577441\pi$
$761$	7.27388	−	50.5910i	0.263678	−	1.83392i	0.504572	−	0.863369i	$-0.331650\pi$
$762$	−3.26449	−	7.14824i	−0.118260	−	0.258953i
$763$	17.2773	+	5.07306i	0.625479	+	0.183657i
$764$	17.5712	+	20.2783i	0.635704	+	0.733642i
$765$	3.32847	−	0.977328i	0.120341	−	0.0353354i
$766$	−12.6946	−	8.15835i	−0.458676	−	0.294773i
$767$	−1.57385	+	3.44624i	−0.0568283	+	0.124437i
$768$	−0.915415	+	1.05645i	−0.0330322	+	0.0381212i
$769$	13.1308	−	8.43865i	0.473509	−	0.304306i	−0.282035	−	0.959404i	$-0.591009\pi$
$769$	13.1308	−	8.43865i	0.473509	−	0.304306i	0.755543	+	0.655099i	$0.227373\pi$
$770$	−2.88958	−	20.0974i	−0.104133	−	0.724262i
$771$	−4.38967	−	30.5308i	−0.158090	−	1.09954i
$772$	−1.18141	+	0.759245i	−0.0425198	+	0.0273258i
$773$	1.72841	−	1.99469i	0.0621666	−	0.0717441i	−0.723814	−	0.689995i	$-0.757613\pi$
$773$	1.72841	−	1.99469i	0.0621666	−	0.0717441i	0.785981	+	0.618251i	$0.212158\pi$
$774$	1.20695	−	2.64286i	0.0433830	−	0.0949955i
$775$	−5.01768	−	3.22467i	−0.180240	−	0.115833i
$776$	−12.0377	+	3.53460i	−0.432130	+	0.126885i
$777$	21.8453	+	25.2108i	0.783695	+	0.904432i
$778$	−22.0536	−	6.47552i	−0.790660	−	0.232159i
$779$	4.42360	+	9.68633i	0.158492	+	0.347049i
$780$	3.13843	−	21.8283i	0.112374	−	0.781577i
$781$	−25.2470			−0.903409
$782$	6.18667	+	0.865733i	0.221235	+	0.0309586i
$783$	−40.5359			−1.44863
$784$	0.375655	−	2.61274i	0.0134162	−	0.0933121i
$785$	23.9588	+	52.4624i	0.855125	+	1.87246i
$786$	−10.6938	−	3.13997i	−0.381434	−	0.111999i
$787$	−23.9564	−	27.6471i	−0.853953	−	0.985514i	0.146040	−	0.989279i	$-0.453347\pi$
$787$	−23.9564	−	27.6471i	−0.853953	−	0.985514i	−0.999993	+	0.00376486i	$0.998802\pi$
$788$	7.91074	−	2.32280i	0.281809	−	0.0827465i
$789$	−9.12367	−	5.86342i	−0.324811	−	0.208743i
$790$	−1.99567	+	4.36992i	−0.0710029	+	0.155475i
$791$	4.87664	−	5.62794i	0.173393	−	0.200106i
$792$	−3.36017	+	2.15945i	−0.119399	+	0.0767328i
$793$	3.56204	+	24.7746i	0.126492	+	0.879770i
$794$	4.22206	+	29.3651i	0.149835	+	1.04213i
$795$	−7.08392	+	4.55256i	−0.251241	+	0.161463i
$796$	2.03997	−	2.35425i	0.0723047	−	0.0834441i
$797$	−8.18044	+	17.9127i	−0.289766	+	0.634499i	−0.997399	−	0.0720814i	$-0.977036\pi$
$797$	−8.18044	+	17.9127i	−0.289766	+	0.634499i	0.707633	+	0.706580i	$0.249763\pi$
$798$	−6.09107	−	3.91449i	−0.215622	−	0.138572i
$799$	−11.6752	+	3.42814i	−0.413038	+	0.121279i
$800$	−0.971248	−	1.12088i	−0.0343388	−	0.0396291i
$801$	5.03015	+	1.47699i	0.177732	+	0.0521867i
$802$	12.1438	+	26.5913i	0.428813	+	0.938970i
$803$	1.58962	−	11.0560i	0.0560964	−	0.390159i
$804$	17.9290			0.632306
$805$	25.2527	+	3.53375i	0.890042	+	0.124548i
$806$	24.9170			0.877664
$807$	−3.38579	+	23.5487i	−0.119186	+	0.828954i
$808$	1.46330	+	3.20419i	0.0514789	+	0.112723i
$809$	13.0460	+	3.83066i	0.458674	+	0.134679i	0.502904	−	0.864343i	$-0.332265\pi$
$809$	13.0460	+	3.83066i	0.458674	+	0.134679i	−0.0442295	+	0.999021i	$0.514083\pi$
$810$	7.95052	+	9.17539i	0.279353	+	0.322390i
$811$	21.7495	−	6.38622i	0.763728	−	0.224251i	0.123405	−	0.992356i	$-0.460619\pi$
$811$	21.7495	−	6.38622i	0.763728	−	0.224251i	0.640323	+	0.768106i	$0.278801\pi$
$812$	12.5904	+	8.09138i	0.441838	+	0.283952i
$813$	6.76367	−	14.8104i	0.237212	−	0.519423i
$814$	28.5795	−	32.9825i	1.00171	−	1.15603i
$815$	−40.6198	+	26.1048i	−1.42285	+	0.914410i
$816$	−0.259133	−	1.80231i	−0.00907149	−	0.0630936i
$817$	−0.980588	−	6.82014i	−0.0343064	−	0.238606i
$818$	28.3501	−	18.2195i	0.991239	−	0.637030i
$819$	−8.86173	+	10.2270i	−0.309654	+	0.357360i
$820$	−4.54081	+	9.94299i	−0.158572	+	0.347224i
$821$	−13.8794	−	8.91972i	−0.484393	−	0.311300i	0.275554	−	0.961286i	$-0.411139\pi$
$821$	−13.8794	−	8.91972i	−0.484393	−	0.311300i	−0.759947	+	0.649985i	$0.774775\pi$
$822$	−2.77551	+	0.814964i	−0.0968071	+	0.0284251i
$823$	20.0185	+	23.1025i	0.697800	+	0.805304i	0.988454	−	0.151524i	$-0.0484182\pi$
$823$	20.0185	+	23.1025i	0.697800	+	0.805304i	−0.290654	+	0.956828i	$0.593873\pi$
$824$	−1.50278	−	0.441256i	−0.0523518	−	0.0153719i
$825$	3.28898	+	7.20185i	0.114507	+	0.250736i
$826$	−0.181716	+	1.26386i	−0.00632270	+	0.0439754i
$827$	24.1171			0.838633			0.419316	−	0.907840i	$-0.362270\pi$
$827$	24.1171			0.838633			0.419316	+	0.907840i	$0.362270\pi$
$828$	−1.43133	−	4.80760i	−0.0497423	−	0.167076i
$829$	−11.3407			−0.393879			−0.196939	−	0.980416i	$-0.563100\pi$
$829$	−11.3407			−0.393879			−0.196939	+	0.980416i	$0.563100\pi$
$830$	−3.78319	+	26.3127i	−0.131316	+	0.913326i
$831$	9.77309	+	21.4001i	0.339025	+	0.742360i
$832$	5.94487	+	1.74557i	0.206101	+	0.0605168i
$833$	2.25160	+	2.59849i	0.0780135	+	0.0900324i
$834$	17.5194	−	5.14416i	0.606647	−	0.178128i
$835$	−2.09838	−	1.34854i	−0.0726173	−	0.0466683i
$836$	−3.93501	+	8.61646i	−0.136095	+	0.298006i
$837$	−14.8947	+	17.1894i	−0.514837	+	0.594154i
$838$	7.42500	−	4.77176i	0.256492	−	0.164838i
$839$	2.68009	+	18.6404i	0.0925270	+	0.643540i	0.982325	+	0.187185i	$0.0599362\pi$
$839$	2.68009	+	18.6404i	0.0925270	+	0.643540i	−0.889798	+	0.456355i	$0.849155\pi$
$840$	−1.05773	−	7.35667i	−0.0364951	−	0.253829i
$841$	18.8181	−	12.0937i	0.648900	−	0.417023i
$842$	−17.9262	+	20.6879i	−0.617776	+	0.712951i
$843$	−3.07219	+	6.72715i	−0.105812	+	0.231695i
$844$	−18.5141	−	11.8983i	−0.637281	−	0.409556i
$845$	−62.0256	+	18.2124i	−2.13375	+	0.626524i
$846$	6.39841	+	7.38416i	0.219982	+	0.253873i
$847$	−7.17947	−	2.10808i	−0.246690	−	0.0724346i
$848$	−0.982805	−	2.15204i	−0.0337497	−	0.0739014i
$849$	3.05761	−	21.2661i	0.104937	−	0.729851i
$850$	1.93190			0.0662637
$851$	29.8047	+	45.9951i	1.02169	+	1.57669i
$852$	−9.24168			−0.316615
$853$	−0.350759	+	2.43958i	−0.0120098	+	0.0835297i	−0.994945	−	0.100423i	$-0.967980\pi$
$853$	−0.350759	+	2.43958i	−0.0120098	+	0.0835297i	0.982935	+	0.183953i	$0.0588894\pi$
$854$	3.50424	+	7.67321i	0.119913	+	0.262572i
$855$	−6.33834	−	1.86110i	−0.216767	−	0.0636484i
$856$	−2.22861	−	2.57195i	−0.0761723	−	0.0879075i
$857$	14.6515	−	4.30206i	0.500485	−	0.146956i	−0.0217395	−	0.999764i	$-0.506920\pi$
$857$	14.6515	−	4.30206i	0.500485	−	0.146956i	0.522225	+	0.852808i	$0.325102\pi$
$858$	−27.8243	−	17.8816i	−0.949907	−	0.610468i
$859$	−1.64666	+	3.60568i	−0.0561833	+	0.123024i	−0.935641	−	0.352952i	$-0.885178\pi$
$859$	−1.64666	+	3.60568i	−0.0561833	+	0.123024i	0.879458	+	0.475976i	$0.157905\pi$
$860$	4.63173	−	5.34530i	0.157941	−	0.182273i
$861$	−10.5419	+	6.77485i	−0.359266	+	0.230886i
$862$	4.25077	+	29.5648i	0.144782	+	1.00698i
$863$	−1.02540	−	7.13184i	−0.0349052	−	0.242771i	0.964898	−	0.262626i	$-0.0845886\pi$
$863$	−1.02540	−	7.13184i	−0.0349052	−	0.242771i	−0.999803	+	0.0198553i	$0.993679\pi$
$864$	−4.75790	+	3.05772i	−0.161867	+	0.104026i
$865$	14.8767	−	17.1686i	0.505821	−	0.583749i
$866$	11.3609	−	24.8769i	0.386060	−	0.845353i
$867$	−17.9962	−	11.5655i	−0.611183	−	0.392783i
$868$	8.05749	−	2.36589i	0.273489	−	0.0803036i
$869$	4.71837	+	5.44529i	0.160060	+	0.184719i
$870$	−24.4768	−	7.18704i	−0.829841	−	0.243663i
$871$	−33.0118	−	72.2857i	−1.11856	−	2.44931i
$872$	1.22721	−	8.53547i	0.0415587	−	0.289047i
$873$	−13.1223			−0.444122
$874$	−9.01963	−	7.75626i	−0.305094	−	0.262359i
$875$	−18.6987			−0.632131
$876$	0.581880	−	4.04706i	0.0196599	−	0.136738i
$877$	−19.3665	−	42.4067i	−0.653960	−	1.43197i	−0.888045	−	0.459756i	$-0.847937\pi$
$877$	−19.3665	−	42.4067i	−0.653960	−	1.43197i	0.234086	−	0.972216i	$-0.424790\pi$
$878$	12.5882	+	3.69622i	0.424830	+	0.124741i
$879$	9.84543	+	11.3622i	0.332078	+	0.383239i
$880$	−9.32960	+	2.73942i	−0.314501	+	0.0923457i
$881$	0.943904	+	0.606610i	0.0318009	+	0.0204372i	0.556445	−	0.830885i	$-0.312165\pi$
$881$	0.943904	+	0.606610i	0.0318009	+	0.0204372i	−0.524644	+	0.851322i	$0.675801\pi$
$882$	1.14690	−	2.51137i	0.0386183	−	0.0845623i
$883$	1.38840	−	1.60230i	0.0467235	−	0.0539218i	−0.731907	−	0.681405i	$-0.761369\pi$
$883$	1.38840	−	1.60230i	0.0467235	−	0.0539218i	0.778630	+	0.627483i	$0.215915\pi$
$884$	−6.78940	+	4.36329i	−0.228352	+	0.146753i
$885$	−0.309736	−	2.15426i	−0.0104117	−	0.0724147i
$886$	1.53276	+	10.6605i	0.0514939	+	0.358148i
$887$	13.1254	−	8.43516i	0.440706	−	0.283225i	−0.301412	−	0.953494i	$-0.597458\pi$
$887$	13.1254	−	8.43516i	0.440706	−	0.283225i	0.742118	+	0.670269i	$0.233821\pi$
$888$	10.4615	−	12.0732i	0.351065	−	0.405151i
$889$	−4.87651	+	10.6781i	−0.163553	+	0.358131i
$890$	10.7362	+	6.89976i	0.359880	+	0.231281i
$891$	17.4713	−	5.13003i	0.585309	−	0.171862i
$892$	−8.06117	−	9.30308i	−0.269908	−	0.311490i
$893$	22.2328	+	6.52813i	0.743991	+	0.218455i
$894$	8.62060	+	18.8765i	0.288316	+	0.631324i
$895$	3.07700	−	21.4010i	0.102853	−	0.715358i
$896$	2.08816			0.0697604
$897$	31.2888	−	27.3189i	1.04470	−	0.912152i
$898$	4.69291			0.156605
$899$	4.10201	−	28.5301i	0.136810	−	0.951532i
$900$	−0.644421	−	1.41108i	−0.0214807	−	0.0470362i
$901$	2.95686	+	0.868213i	0.0985074	+	0.0289244i
$902$	10.7358	+	12.3898i	0.357465	+	0.412536i
$903$	7.77993	−	2.28439i	0.258900	−	0.0760198i
$904$	−3.00010	−	1.92805i	−0.0997818	−	0.0641258i
$905$	−0.568451	+	1.24473i	−0.0188959	+	0.0413763i
$906$	−3.52717	+	4.07057i	−0.117182	+	0.135236i
$907$	−25.6515	+	16.4852i	−0.851745	+	0.547383i	−0.892118	−	0.451802i	$-0.850781\pi$
$907$	−25.6515	+	16.4852i	−0.851745	+	0.547383i	0.0403738	+	0.999185i	$0.487145\pi$
$908$	−0.758893	−	5.27822i	−0.0251848	−	0.175164i
$909$	0.524335	+	3.64683i	0.0173911	+	0.120958i
$910$	−27.7130	+	17.8100i	−0.918676	+	0.590397i
$911$	23.4601	−	27.0744i	0.777267	−	0.897014i	−0.219642	−	0.975581i	$-0.570489\pi$
$911$	23.4601	−	27.0744i	0.777267	−	0.897014i	0.996909	+	0.0785669i	$0.0250344\pi$
$912$	−1.44041	+	3.15406i	−0.0476967	+	0.104441i
$913$	33.5406	+	21.5552i	1.11003	+	0.713374i
$914$	−6.65474	+	1.95401i	−0.220119	+	0.0646328i
$915$	−9.41584	−	10.8665i	−0.311278	−	0.359234i
$916$	−13.5356	−	3.97440i	−0.447227	−	0.131318i
$917$	6.91616	+	15.1443i	0.228392	+	0.500108i
$918$	1.04844	−	7.29205i	0.0346036	−	0.240673i
$919$	29.8477			0.984585			0.492292	−	0.870430i	$-0.336159\pi$
$919$	29.8477			0.984585			0.492292	+	0.870430i	$0.336159\pi$
$920$	−0.0460029	−	12.2111i	−0.00151667	−	0.402587i
$921$	−36.0441			−1.18769
$922$	3.03519	−	21.1102i	0.0999588	−	0.695228i
$923$	17.0163	+	37.2604i	0.560097	+	1.22644i
$924$	−10.6955	−	3.14049i	−0.351857	−	0.103315i
$925$	11.0996	+	12.8096i	0.364952	+	0.421177i
$926$	6.15505	−	1.80729i	0.202267	−	0.0593911i
$927$	−1.37812	−	0.885663i	−0.0452634	−	0.0290890i
$928$	2.97737	−	6.51954i	0.0977371	−	0.214014i
$929$	26.0036	−	30.0097i	0.853149	−	0.984586i	−0.146841	−	0.989160i	$-0.546910\pi$
$929$	26.0036	−	30.0097i	0.853149	−	0.984586i	0.999990	+	0.00457391i	$0.00145593\pi$
$930$	−12.0416	+	7.73866i	−0.394859	+	0.253761i
$931$	−0.931802	−	6.48083i	−0.0305386	−	0.212401i
$932$	−2.44536	−	17.0079i	−0.0801006	−	0.557112i
$933$	19.1881	−	12.3315i	0.628191	−	0.403714i
$934$	−9.47731	+	10.9374i	−0.310107	+	0.357883i
$935$	5.26148	−	11.5210i	0.172069	−	0.376778i
$936$	5.45172	+	3.50361i	0.178195	+	0.114519i
$937$	−20.0227	+	5.87920i	−0.654113	+	0.192065i	−0.591917	−	0.805999i	$-0.701629\pi$
$937$	−20.0227	+	5.87920i	−0.654113	+	0.192065i	−0.0621963	+	0.998064i	$0.519810\pi$
$938$	−17.5387	−	20.2408i	−0.572660	−	0.660884i
$939$	−16.7702	−	4.92417i	−0.547274	−	0.160694i
$940$	9.88079	+	21.6359i	0.322276	+	0.705686i
$941$	5.00314	−	34.7976i	0.163098	−	1.13437i	−0.729653	−	0.683818i	$-0.760318\pi$
$941$	5.00314	−	34.7976i	0.163098	−	1.13437i	0.892750	−	0.450551i	$-0.148773\pi$
$942$	31.6635			1.03165
$943$	−18.6955	+	8.62323i	−0.608810	+	0.280811i
$944$	0.611476			0.0199019
$945$	4.27951	−	29.7646i	0.139212	−	0.968244i
$946$	−4.40669	−	9.64930i	−0.143274	−	0.313726i
$947$	−27.4913	−	8.07217i	−0.893347	−	0.262310i	−0.197331	−	0.980337i	$-0.563227\pi$
$947$	−27.4913	−	8.07217i	−0.893347	−	0.262310i	−0.696016	+	0.718027i	$0.745046\pi$
$948$	1.72716	+	1.99325i	0.0560956	+	0.0647378i
$949$	−17.3883	+	5.10565i	−0.564447	+	0.165737i
$950$	−3.09487	−	1.98895i	−0.100411	−	0.0645302i
$951$	−7.86192	+	17.2152i	−0.254940	+	0.558241i
$952$	−1.78121	+	2.05563i	−0.0577295	+	0.0666234i
$953$	−16.4844	+	10.5939i	−0.533982	+	0.343169i	−0.779681	−	0.626177i	$-0.784619\pi$
$953$	−16.4844	+	10.5939i	−0.533982	+	0.343169i	0.245699	+	0.969346i	$0.420982\pi$
$954$	−0.352161	−	2.44934i	−0.0114016	−	0.0793002i
$955$	9.72289	+	67.6242i	0.314625	+	2.18827i
$956$	−4.74502	+	3.04944i	−0.153465	+	0.0986259i
$957$	−25.0552	+	28.9152i	−0.809919	+	0.934696i
$958$	−2.23296	+	4.88949i	−0.0721436	+	0.157972i
$959$	3.63515	+	2.33617i	0.117385	+	0.0754388i
$960$	−3.41510	+	1.00276i	−0.110222	+	0.0323641i
$961$	9.70963	+	11.2055i	0.313214	+	0.361468i
$962$	−67.9390	−	19.9487i	−2.19044	−	0.643171i
$963$	−1.47868	−	3.23785i	−0.0476497	−	0.104338i
$964$	0.716936	−	4.98640i	0.0230910	−	0.160601i
$965$	−3.57574			−0.115107
$966$	7.52399	−	11.8051i	0.242080	−	0.379823i
$967$	−45.4032			−1.46007			−0.730035	−	0.683410i	$-0.760496\pi$
$967$	−45.4032			−1.46007			−0.730035	+	0.683410i	$0.760496\pi$
$968$	−0.509962	+	3.54687i	−0.0163908	+	0.114001i
$969$	−1.87625	−	4.10841i	−0.0602738	−	0.131981i
$970$	−30.6505	−	8.99980i	−0.984129	−	0.288966i
$971$	−25.1610	−	29.0373i	−0.807454	−	0.931852i	0.191311	−	0.981529i	$-0.438726\pi$
$971$	−25.1610	−	29.0373i	−0.807454	−	0.931852i	−0.998765	+	0.0496774i	$0.984181\pi$
$972$	−9.88453	+	2.90236i	−0.317046	+	0.0930932i
$973$	−22.9455	−	14.7462i	−0.735600	−	0.472741i
$974$	1.33735	−	2.92839i	0.0428515	−	0.0938317i
$975$	8.41201	−	9.70797i	0.269400	−	0.310904i
$976$	3.39841	−	2.18402i	0.108780	−	0.0699089i
$977$	0.166188	+	1.15586i	0.00531683	+	0.0369794i	0.992307	−	0.123800i	$-0.0395082\pi$
$977$	0.166188	+	1.15586i	0.00531683	+	0.0369794i	−0.986990	+	0.160780i	$0.948599\pi$
$978$	3.77257	+	26.2388i	0.120634	+	0.839025i
$979$	16.1023	−	10.3483i	0.514632	−	0.330734i
$980$	4.40129	−	5.07936i	0.140594	−	0.162254i
$981$	3.74679	−	8.20432i	0.119626	−	0.261944i
$982$	25.3010	+	16.2600i	0.807388	+	0.518877i
$983$	53.3799	−	15.6738i	1.70255	−	0.499915i	0.721299	−	0.692624i	$-0.243545\pi$
$983$	53.3799	−	15.6738i	1.70255	−	0.499915i	0.981256	+	0.192709i	$0.0617273\pi$
$984$	3.92986	+	4.53530i	0.125279	+	0.144580i
$985$	20.1423	+	5.91432i	0.641788	+	0.188446i
$986$	3.87827	+	8.49222i	0.123509	+	0.270447i
$987$	−3.88060	+	26.9902i	−0.123521	+	0.859107i
$988$	15.3686			0.488941
$989$	13.1791	−	1.94556i	0.419069	−	0.0618654i
$990$	−10.1701			−0.323229
$991$	−4.17451	+	29.0344i	−0.132608	+	0.922307i	0.809529	+	0.587079i	$0.199722\pi$
$991$	−4.17451	+	29.0344i	−0.132608	+	0.922307i	−0.942137	+	0.335228i	$0.891187\pi$
$992$	−1.67062	−	3.65814i	−0.0530422	−	0.116146i
$993$	−38.0020	−	11.1584i	−1.20596	−	0.354101i
$994$	9.04052	+	10.4333i	0.286748	+	0.330925i
$995$	7.61042	−	2.23462i	0.241267	−	0.0708422i
$996$	12.2775	+	7.89030i	0.389029	+	0.250014i
$997$	9.48155	−	20.7617i	0.300284	−	0.657530i	−0.698000	−	0.716098i	$-0.745926\pi$
$997$	9.48155	−	20.7617i	0.300284	−	0.657530i	0.998283	+	0.0585684i	$0.0186536\pi$
$998$	−11.6228	+	13.4134i	−0.367913	+	0.424595i
$999$	54.3741	−	34.9441i	1.72032	−	1.10558i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	46.2.c.a.31.1	yes	10
3.2	odd	2		414.2.i.f.307.1		10
4.3	odd	2		368.2.m.b.353.1		10
23.3	even	11	inner	46.2.c.a.3.1	✓	10
23.7	odd	22		1058.2.a.l.1.5		5
23.16	even	11		1058.2.a.m.1.5		5
69.26	odd	22		414.2.i.f.325.1		10
69.53	even	22		9522.2.a.bu.1.4		5
69.62	odd	22		9522.2.a.bp.1.2		5
92.3	odd	22		368.2.m.b.49.1		10
92.7	even	22		8464.2.a.bw.1.1		5
92.39	odd	22		8464.2.a.bx.1.1		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
46.2.c.a.3.1	✓	10	23.3	even	11	inner
46.2.c.a.31.1	yes	10	1.1	even	1	trivial
368.2.m.b.49.1		10	92.3	odd	22
368.2.m.b.353.1		10	4.3	odd	2
414.2.i.f.307.1		10	3.2	odd	2
414.2.i.f.325.1		10	69.26	odd	22
1058.2.a.l.1.5		5	23.7	odd	22
1058.2.a.m.1.5		5	23.16	even	11
8464.2.a.bw.1.1		5	92.7	even	22
8464.2.a.bx.1.1		5	92.39	odd	22
9522.2.a.bp.1.2		5	69.62	odd	22
9522.2.a.bu.1.4		5	69.53	even	22

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:	\( N \)	\(=\)	\( 46 = 2 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	46.c (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.142315 + 0.989821i) q^{2} +(0.580699 + 1.27155i) q^{3} +(-0.959493 - 0.281733i) q^{4} +(-1.66741 - 1.92429i) q^{5} +(-1.34125 + 0.393828i) q^{6} +(1.75667 + 1.12894i) q^{7} +(0.415415 - 0.909632i) q^{8} +(0.684944 - 0.790468i) q^{9} +O(q^{10})\)	\(q+(-0.142315 + 0.989821i) q^{2} +(0.580699 + 1.27155i) q^{3} +(-0.959493 - 0.281733i) q^{4} +(-1.66741 - 1.92429i) q^{5} +(-1.34125 + 0.393828i) q^{6} +(1.75667 + 1.12894i) q^{7} +(0.415415 - 0.909632i) q^{8} +(0.684944 - 0.790468i) q^{9} +(2.14200 - 1.37658i) q^{10} +(-0.543474 - 3.77994i) q^{11} +(-0.198939 - 1.38365i) q^{12} +(-5.21228 + 3.34973i) q^{13} +(-1.36745 + 1.57812i) q^{14} +(1.47858 - 3.23763i) q^{15} +(0.841254 + 0.540641i) q^{16} +(-1.24982 + 0.366979i) q^{17} +(0.684944 + 0.790468i) q^{18} +(2.38000 + 0.698830i) q^{19} +(1.05773 + 2.31611i) q^{20} +(-0.415415 + 2.88927i) q^{21} +3.81881 q^{22} +(-1.33380 + 4.60662i) q^{23} +1.39788 q^{24} +(-0.211072 + 1.46804i) q^{25} +(-2.57385 - 5.63594i) q^{26} +(5.42663 + 1.59340i) q^{27} +(-1.36745 - 1.57812i) q^{28} +(-6.87690 + 2.01924i) q^{29} +(2.99425 + 1.92429i) q^{30} +(-1.67062 + 3.65814i) q^{31} +(-0.654861 + 0.755750i) q^{32} +(4.49081 - 2.88607i) q^{33} +(-0.185376 - 1.28932i) q^{34} +(-0.756669 - 5.26275i) q^{35} +(-0.879900 + 0.565477i) q^{36} +(7.48386 - 8.63683i) q^{37} +(-1.03043 + 2.25632i) q^{38} +(-7.28612 - 4.68251i) q^{39} +(-2.44306 + 0.717348i) q^{40} +(2.81130 + 3.24442i) q^{41} +(-2.80075 - 0.822373i) q^{42} +(-1.15394 - 2.52678i) q^{43} +(-0.543474 + 3.77994i) q^{44} -2.66317 q^{45} +(-4.36992 - 1.97581i) q^{46} +9.34150 q^{47} +(-0.198939 + 1.38365i) q^{48} +(-1.09653 - 2.40107i) q^{49} +(-1.42306 - 0.417848i) q^{50} +(-1.19240 - 1.37610i) q^{51} +(5.94487 - 1.74557i) q^{52} +(-1.99027 - 1.27907i) q^{53} +(-2.34947 + 5.14463i) q^{54} +(-6.36752 + 7.34850i) q^{55} +(1.75667 - 1.12894i) q^{56} +(0.493462 + 3.43211i) q^{57} +(-1.02000 - 7.09427i) q^{58} +(0.514407 - 0.330589i) q^{59} +(-2.33083 + 2.68992i) q^{60} +(1.67815 - 3.67464i) q^{61} +(-3.38316 - 2.17422i) q^{62} +(2.09561 - 0.615327i) q^{63} +(-0.654861 - 0.755750i) q^{64} +(15.1368 + 4.44457i) q^{65} +(2.21758 + 4.85583i) q^{66} +(-1.82531 + 12.6953i) q^{67} +1.30258 q^{68} +(-6.63211 + 0.979068i) q^{69} +5.31686 q^{70} +(0.940875 - 6.54393i) q^{71} +(-0.434499 - 0.951419i) q^{72} +(2.80644 + 0.824045i) q^{73} +(7.48386 + 8.63683i) q^{74} +(-1.98926 + 0.584100i) q^{75} +(-2.08671 - 1.34105i) q^{76} +(3.31264 - 7.25366i) q^{77} +(5.67177 - 6.54557i) q^{78} +(-1.58724 + 1.02006i) q^{79} +(-0.362362 - 2.52028i) q^{80} +(0.678585 + 4.71966i) q^{81} +(-3.61148 + 2.32096i) q^{82} +(-6.83698 + 7.89030i) q^{83} +(1.21259 - 2.65520i) q^{84} +(2.79013 + 1.79310i) q^{85} +(2.66528 - 0.782598i) q^{86} +(-6.56099 - 7.57178i) q^{87} +(-3.66412 - 1.07588i) q^{88} +(2.08216 + 4.55930i) q^{89} +(0.379009 - 2.63606i) q^{90} -12.9379 q^{91} +(2.57760 - 4.04425i) q^{92} -5.62165 q^{93} +(-1.32943 + 9.24642i) q^{94} +(-2.62367 - 5.74504i) q^{95} +(-1.34125 - 0.393828i) q^{96} +(-8.21585 - 9.48159i) q^{97} +(2.53268 - 0.743663i) q^{98} +(-3.36017 - 2.15945i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - q^{2} - 4 q^{3} - q^{4} - 6 q^{5} - 4 q^{6} + 3 q^{7} - q^{8} + 9 q^{9}+O(q^{10}) \) 10 * q - q^2 - 4 * q^3 - q^4 - 6 * q^5 - 4 * q^6 + 3 * q^7 - q^8 + 9 * q^9	\( 10 q - q^{2} - 4 q^{3} - q^{4} - 6 q^{5} - 4 q^{6} + 3 q^{7} - q^{8} + 9 q^{9} - 6 q^{10} - 12 q^{11} + 7 q^{12} - 14 q^{13} + 3 q^{14} - 13 q^{15} - q^{16} + 15 q^{17} + 9 q^{18} + 2 q^{19} + 5 q^{20} + q^{21} + 10 q^{22} - q^{23} - 4 q^{24} + 13 q^{25} - 3 q^{26} + 26 q^{27} + 3 q^{28} - 8 q^{29} + 20 q^{30} - 21 q^{31} - q^{32} - 15 q^{33} - 7 q^{34} + 7 q^{35} - 13 q^{36} + 28 q^{37} - 9 q^{38} - 12 q^{39} - 6 q^{40} - 31 q^{41} - 10 q^{42} + 11 q^{43} - 12 q^{44} + 10 q^{45} - 12 q^{46} + 18 q^{47} + 7 q^{48} - 24 q^{49} + 2 q^{50} - 17 q^{51} + 8 q^{52} - 21 q^{53} - 29 q^{54} + 5 q^{55} + 3 q^{56} + 19 q^{57} - 8 q^{58} - 5 q^{59} - 13 q^{60} + 37 q^{61} + q^{62} + 17 q^{63} - q^{64} + 37 q^{65} + 29 q^{66} - 13 q^{67} + 26 q^{68} - 15 q^{69} + 18 q^{70} + 49 q^{71} + 20 q^{72} - 8 q^{73} + 28 q^{74} + 8 q^{75} - 20 q^{76} - 8 q^{77} + 10 q^{78} + 8 q^{79} + 5 q^{80} - 11 q^{81} + 2 q^{82} - 7 q^{83} + q^{84} - 42 q^{85} + 22 q^{86} - 21 q^{87} - q^{88} - 13 q^{89} - 45 q^{90} - 24 q^{91} - 23 q^{92} - 40 q^{93} - 37 q^{94} - 10 q^{95} - 4 q^{96} - 32 q^{97} - 24 q^{98} + 20 q^{99}+O(q^{100}) \) 10 * q - q^2 - 4 * q^3 - q^4 - 6 * q^5 - 4 * q^6 + 3 * q^7 - q^8 + 9 * q^9 - 6 * q^10 - 12 * q^11 + 7 * q^12 - 14 * q^13 + 3 * q^14 - 13 * q^15 - q^16 + 15 * q^17 + 9 * q^18 + 2 * q^19 + 5 * q^20 + q^21 + 10 * q^22 - q^23 - 4 * q^24 + 13 * q^25 - 3 * q^26 + 26 * q^27 + 3 * q^28 - 8 * q^29 + 20 * q^30 - 21 * q^31 - q^32 - 15 * q^33 - 7 * q^34 + 7 * q^35 - 13 * q^36 + 28 * q^37 - 9 * q^38 - 12 * q^39 - 6 * q^40 - 31 * q^41 - 10 * q^42 + 11 * q^43 - 12 * q^44 + 10 * q^45 - 12 * q^46 + 18 * q^47 + 7 * q^48 - 24 * q^49 + 2 * q^50 - 17 * q^51 + 8 * q^52 - 21 * q^53 - 29 * q^54 + 5 * q^55 + 3 * q^56 + 19 * q^57 - 8 * q^58 - 5 * q^59 - 13 * q^60 + 37 * q^61 + q^62 + 17 * q^63 - q^64 + 37 * q^65 + 29 * q^66 - 13 * q^67 + 26 * q^68 - 15 * q^69 + 18 * q^70 + 49 * q^71 + 20 * q^72 - 8 * q^73 + 28 * q^74 + 8 * q^75 - 20 * q^76 - 8 * q^77 + 10 * q^78 + 8 * q^79 + 5 * q^80 - 11 * q^81 + 2 * q^82 - 7 * q^83 + q^84 - 42 * q^85 + 22 * q^86 - 21 * q^87 - q^88 - 13 * q^89 - 45 * q^90 - 24 * q^91 - 23 * q^92 - 40 * q^93 - 37 * q^94 - 10 * q^95 - 4 * q^96 - 32 * q^97 - 24 * q^98 + 20 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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