LMFDB - Embedded newform 460.2.w.a.167.68

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [460,2,Mod(3,460)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(460, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([22, 33, 32]))

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

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

chi := DirichletCharacter("460.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 460 = 2^{2} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	460.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:	$3.67311849298$
Analytic rank:	$0$
Dimension:	$1360$
Relative dimension:	$68$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			167.68
Character	$\chi$	$=$	460.167
Dual form			460.2.w.a.303.68

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.41275 + 0.0643210i) q^{2} +(-0.525955 - 0.963215i) q^{3} +(1.99173 + 0.181739i) q^{4} +(-1.99984 - 1.00031i) q^{5} +(-0.681088 - 1.39461i) q^{6} +(1.66882 + 2.22929i) q^{7} +(2.80212 + 0.384861i) q^{8} +(0.970769 - 1.51055i) q^{9} +O(q^{10})$	\(q+(1.41275 + 0.0643210i) q^{2} +(-0.525955 - 0.963215i) q^{3} +(1.99173 + 0.181739i) q^{4} +(-1.99984 - 1.00031i) q^{5} +(-0.681088 - 1.39461i) q^{6} +(1.66882 + 2.22929i) q^{7} +(2.80212 + 0.384861i) q^{8} +(0.970769 - 1.51055i) q^{9} +(-2.76094 - 1.54183i) q^{10} +(3.27861 - 1.49729i) q^{11} +(-0.872505 - 2.01405i) q^{12} +(-3.80227 - 2.84634i) q^{13} +(2.21424 + 3.25677i) q^{14} +(0.0883099 + 2.45240i) q^{15} +(3.93394 + 0.723948i) q^{16} +(6.92477 - 0.495269i) q^{17} +(1.46861 - 2.07158i) q^{18} +(-3.19458 - 3.68675i) q^{19} +(-3.80134 - 2.35580i) q^{20} +(1.26956 - 2.77994i) q^{21} +(4.72817 - 1.90442i) q^{22} +(-3.46185 + 3.31898i) q^{23} +(-1.10309 - 2.90146i) q^{24} +(2.99874 + 4.00094i) q^{25} +(-5.18857 - 4.26573i) q^{26} +(-5.24954 - 0.375455i) q^{27} +(2.91869 + 4.74342i) q^{28} +(-2.12080 - 1.83768i) q^{29} +(-0.0329808 + 3.47031i) q^{30} +(1.29646 + 4.41535i) q^{31} +(5.51111 + 1.27579i) q^{32} +(-3.16662 - 2.37050i) q^{33} +(9.81482 - 0.254284i) q^{34} +(-1.10740 - 6.12758i) q^{35} +(2.20803 - 2.83217i) q^{36} +(0.419826 + 1.92991i) q^{37} +(-4.27601 - 5.41393i) q^{38} +(-0.741816 + 5.15945i) q^{39} +(-5.21882 - 3.57266i) q^{40} +(-1.99060 + 1.27928i) q^{41} +(1.97238 - 3.84571i) q^{42} +(-0.476441 - 0.872536i) q^{43} +(6.80221 - 2.38634i) q^{44} +(-3.45240 + 2.04978i) q^{45} +(-5.10420 + 4.46622i) q^{46} +(-5.08007 + 5.08007i) q^{47} +(-1.37176 - 4.17000i) q^{48} +(-0.212626 + 0.724136i) q^{49} +(3.97913 + 5.84521i) q^{50} +(-4.11917 - 6.40955i) q^{51} +(-7.05578 - 6.36015i) q^{52} +(8.33446 + 11.1335i) q^{53} +(-7.39214 - 0.868079i) q^{54} +(-8.05447 - 0.285294i) q^{55} +(3.81828 + 6.88900i) q^{56} +(-1.87092 + 5.01613i) q^{57} +(-2.87795 - 2.73260i) q^{58} +(1.69668 + 11.8007i) q^{59} +(-0.269807 + 4.90055i) q^{60} +(-7.24417 + 2.12708i) q^{61} +(1.54758 + 6.32118i) q^{62} +(4.98749 - 0.356712i) q^{63} +(7.70376 + 2.15686i) q^{64} +(4.75670 + 9.49569i) q^{65} +(-4.32117 - 3.55260i) q^{66} +(1.68770 + 4.52489i) q^{67} +(13.8822 + 0.272060i) q^{68} +(5.01767 + 1.58887i) q^{69} +(-1.17034 - 8.72796i) q^{70} +(-6.18592 - 2.82501i) q^{71} +(3.30156 - 3.85912i) q^{72} +(-5.82325 - 0.416487i) q^{73} +(0.468976 + 2.75348i) q^{74} +(2.27656 - 4.99275i) q^{75} +(-5.69271 - 7.92357i) q^{76} +(8.80933 + 4.81026i) q^{77} +(-1.37986 + 7.24129i) q^{78} +(-1.35651 - 9.43474i) q^{79} +(-7.14309 - 5.38296i) q^{80} +(0.161636 + 0.353934i) q^{81} +(-2.89451 + 1.67927i) q^{82} +(1.33661 + 6.14431i) q^{83} +(3.03383 - 5.30616i) q^{84} +(-14.3439 - 5.93648i) q^{85} +(-0.616969 - 1.26332i) q^{86} +(-0.654638 + 3.00932i) q^{87} +(9.76332 - 2.93378i) q^{88} +(1.68044 - 5.72305i) q^{89} +(-5.00923 + 2.67376i) q^{90} -13.2264i q^{91} +(-7.49823 + 5.98134i) q^{92} +(3.57105 - 3.57105i) q^{93} +(-7.50363 + 6.85012i) q^{94} +(2.70076 + 10.5685i) q^{95} +(-1.66973 - 5.97939i) q^{96} +(11.3889 + 2.47750i) q^{97} +(-0.346964 + 1.00935i) q^{98} +(0.921046 - 6.40602i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1360 q - 18 q^{2} - 36 q^{5} - 44 q^{6} - 18 q^{8}+O(q^{10}) $ 1360 * q - 18 * q^2 - 36 * q^5 - 44 * q^6 - 18 * q^8	$ 1360 q - 18 q^{2} - 36 q^{5} - 44 q^{6} - 18 q^{8} - 18 q^{10} - 6 q^{12} - 36 q^{13} - 44 q^{16} - 36 q^{17} - 38 q^{18} - 14 q^{20} - 88 q^{21} - 28 q^{22} - 36 q^{25} - 36 q^{26} - 34 q^{28} + 2 q^{30} + 2 q^{32} - 60 q^{33} - 36 q^{36} - 36 q^{37} - 10 q^{38} + 2 q^{40} - 56 q^{41} - 202 q^{42} - 120 q^{45} - 44 q^{46} - 50 q^{48} - 34 q^{50} - 250 q^{52} - 84 q^{53} - 84 q^{56} - 44 q^{57} - 58 q^{58} - 42 q^{60} - 136 q^{61} - 82 q^{62} - 68 q^{65} - 84 q^{66} - 4 q^{68} + 16 q^{70} - 104 q^{72} - 36 q^{73} + 4 q^{76} - 44 q^{77} - 50 q^{78} + 204 q^{80} + 80 q^{81} - 10 q^{82} - 252 q^{85} + 44 q^{86} - 50 q^{88} + 264 q^{90} - 22 q^{92} - 88 q^{93} + 52 q^{96} - 36 q^{97} + 30 q^{98}+O(q^{100}) $ 1360 * q - 18 * q^2 - 36 * q^5 - 44 * q^6 - 18 * q^8 - 18 * q^10 - 6 * q^12 - 36 * q^13 - 44 * q^16 - 36 * q^17 - 38 * q^18 - 14 * q^20 - 88 * q^21 - 28 * q^22 - 36 * q^25 - 36 * q^26 - 34 * q^28 + 2 * q^30 + 2 * q^32 - 60 * q^33 - 36 * q^36 - 36 * q^37 - 10 * q^38 + 2 * q^40 - 56 * q^41 - 202 * q^42 - 120 * q^45 - 44 * q^46 - 50 * q^48 - 34 * q^50 - 250 * q^52 - 84 * q^53 - 84 * q^56 - 44 * q^57 - 58 * q^58 - 42 * q^60 - 136 * q^61 - 82 * q^62 - 68 * q^65 - 84 * q^66 - 4 * q^68 + 16 * q^70 - 104 * q^72 - 36 * q^73 + 4 * q^76 - 44 * q^77 - 50 * q^78 + 204 * q^80 + 80 * q^81 - 10 * q^82 - 252 * q^85 + 44 * q^86 - 50 * q^88 + 264 * q^90 - 22 * q^92 - 88 * q^93 + 52 * q^96 - 36 * q^97 + 30 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/460\mathbb{Z}\right)^\times$.

$n$	$231$	$277$	$281$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{9}{11}\right)$

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 $

$2$	1.41275	+	0.0643210i	0.998965	+	0.0454818i
$2$	1.41275	+	0.0643210i	0.998965	+	0.0454818i
$3$	−0.525955	−	0.963215i	−0.303660	−	0.556112i	0.680639	−	0.732619i	$-0.261702\pi$
$3$	−0.525955	−	0.963215i	−0.303660	−	0.556112i	−0.984299	+	0.176507i	$0.943520\pi$
$4$	1.99173	+	0.181739i	0.995863	+	0.0908695i
$5$	−1.99984	−	1.00031i	−0.894357	−	0.447354i
$5$	−1.99984	−	1.00031i	−0.894357	−	0.447354i
$6$	−0.681088	−	1.39461i	−0.278053	−	0.569348i
$7$	1.66882	+	2.22929i	0.630757	+	0.842592i	0.996095	−	0.0882825i	$-0.0281378\pi$
$7$	1.66882	+	2.22929i	0.630757	+	0.842592i	−0.365339	+	0.930875i	$0.619047\pi$
$8$	2.80212	+	0.384861i	0.990699	+	0.136069i
$9$	0.970769	−	1.51055i	0.323590	−	0.503515i
$10$	−2.76094	−	1.54183i	−0.873085	−	0.487568i
$11$	3.27861	−	1.49729i	0.988539	−	0.451451i	0.145532	−	0.989354i	$-0.453511\pi$
$11$	3.27861	−	1.49729i	0.988539	−	0.451451i	0.843007	+	0.537903i	$0.180783\pi$
$12$	−0.872505	−	2.01405i	−0.251870	−	0.581405i
$13$	−3.80227	−	2.84634i	−1.05456	−	0.789433i	−0.0763551	−	0.997081i	$-0.524328\pi$
$13$	−3.80227	−	2.84634i	−1.05456	−	0.789433i	−0.978204	+	0.207648i	$0.933419\pi$
$14$	2.21424	+	3.25677i	0.591781	+	0.870408i
$15$	0.0883099	+	2.45240i	0.0228015	+	0.633207i
$16$	3.93394	+	0.723948i	0.983485	+	0.180987i
$17$	6.92477	−	0.495269i	1.67950	−	0.120120i	0.801254	−	0.598324i	$-0.204167\pi$
$17$	6.92477	−	0.495269i	1.67950	−	0.120120i	0.878249	+	0.478204i	$0.158712\pi$
$18$	1.46861	−	2.07158i	0.346155	−	0.488277i
$19$	−3.19458	−	3.68675i	−0.732888	−	0.845798i	0.259906	−	0.965634i	$-0.416308\pi$
$19$	−3.19458	−	3.68675i	−0.732888	−	0.845798i	−0.992794	+	0.119836i	$0.961763\pi$
$20$	−3.80134	−	2.35580i	−0.850006	−	0.526773i
$21$	1.26956	−	2.77994i	0.277040	−	0.606633i
$22$	4.72817	−	1.90442i	1.00805	−	0.406023i
$23$	−3.46185	+	3.31898i	−0.721845	+	0.692055i
$23$	−3.46185	+	3.31898i	−0.721845	+	0.692055i
$24$	−1.10309	−	2.90146i	−0.225166	−	0.592259i
$25$	2.99874	+	4.00094i	0.599749	+	0.800189i
$26$	−5.18857	−	4.26573i	−1.01756	−	0.836579i
$27$	−5.24954	−	0.375455i	−1.01027	−	0.0722563i
$28$	2.91869	+	4.74342i	0.551581	+	0.896423i
$29$	−2.12080	−	1.83768i	−0.393822	−	0.341249i	0.435331	−	0.900271i	$-0.356631\pi$
$29$	−2.12080	−	1.83768i	−0.393822	−	0.341249i	−0.829153	+	0.559022i	$0.811177\pi$
$30$	−0.0329808	+	3.47031i	−0.00602145	+	0.633588i
$31$	1.29646	+	4.41535i	0.232852	+	0.793020i	0.990157	+	0.139959i	$0.0446972\pi$
$31$	1.29646	+	4.41535i	0.232852	+	0.793020i	−0.757305	+	0.653061i	$0.773485\pi$
$32$	5.51111	+	1.27579i	0.974236	+	0.225530i
$33$	−3.16662	−	2.37050i	−0.551237	−	0.412651i
$34$	9.81482	−	0.254284i	1.68323	−	0.0436093i
$35$	−1.10740	−	6.12758i	−0.187184	−	1.03575i
$36$	2.20803	−	2.83217i	0.368005	−	0.472028i
$37$	0.419826	+	1.92991i	0.0690190	+	0.317275i	0.998693	−	0.0511078i	$-0.0162752\pi$
$37$	0.419826	+	1.92991i	0.0690190	+	0.317275i	−0.929674	+	0.368383i	$0.879912\pi$
$38$	−4.27601	−	5.41393i	−0.693661	−	0.878255i
$39$	−0.741816	+	5.15945i	−0.118786	+	0.826172i
$40$	−5.21882	−	3.57266i	−0.825168	−	0.564888i
$41$	−1.99060	+	1.27928i	−0.310880	+	0.199791i	−0.686772	−	0.726873i	$-0.740973\pi$
$41$	−1.99060	+	1.27928i	−0.310880	+	0.199791i	0.375892	+	0.926664i	$0.377336\pi$
$42$	1.97238	−	3.84571i	0.304344	−	0.593405i
$43$	−0.476441	−	0.872536i	−0.0726565	−	0.133060i	0.838826	−	0.544400i	$-0.183243\pi$
$43$	−0.476441	−	0.872536i	−0.0726565	−	0.133060i	−0.911482	+	0.411340i	$0.865061\pi$
$44$	6.80221	−	2.38634i	1.02547	−	0.359755i
$45$	−3.45240	+	2.04978i	−0.514654	+	0.305563i
$46$	−5.10420	+	4.46622i	−0.752574	+	0.658508i
$47$	−5.08007	+	5.08007i	−0.741005	+	0.741005i	−0.972771	−	0.231766i	$-0.925549\pi$
$47$	−5.08007	+	5.08007i	−0.741005	+	0.741005i	0.231766	+	0.972771i	$0.425549\pi$
$48$	−1.37176	−	4.17000i	−0.197996	−	0.601887i
$49$	−0.212626	+	0.724136i	−0.0303751	+	0.103448i
$50$	3.97913	+	5.84521i	0.562734	+	0.826638i
$51$	−4.11917	−	6.40955i	−0.576799	−	0.897516i
$52$	−7.05578	−	6.36015i	−0.978460	−	0.881994i
$53$	8.33446	+	11.1335i	1.14483	+	1.52931i	0.809414	+	0.587238i	$0.199785\pi$
$53$	8.33446	+	11.1335i	1.14483	+	1.52931i	0.335413	+	0.942071i	$0.391124\pi$
$54$	−7.39214	−	0.868079i	−1.00594	−	0.118131i
$55$	−8.05447	−	0.285294i	−1.08606	−	0.0384690i
$56$	3.81828	+	6.88900i	0.510239	+	0.920582i
$57$	−1.87092	+	5.01613i	−0.247810	+	0.664403i
$58$	−2.87795	−	2.73260i	−0.377894	−	0.358807i
$59$	1.69668	+	11.8007i	0.220889	+	1.53632i	0.734688	+	0.678405i	$0.237329\pi$
$59$	1.69668	+	11.8007i	0.220889	+	1.53632i	−0.513799	+	0.857910i	$0.671762\pi$
$60$	−0.269807	+	4.90055i	−0.0348320	+	0.632659i
$61$	−7.24417	+	2.12708i	−0.927521	+	0.272345i	−0.710398	−	0.703800i	$-0.751485\pi$
$61$	−7.24417	+	2.12708i	−0.927521	+	0.272345i	−0.217122	+	0.976144i	$0.569667\pi$
$62$	1.54758	+	6.32118i	0.196543	+	0.802790i
$63$	4.98749	−	0.356712i	0.628364	−	0.0449415i
$64$	7.70376	+	2.15686i	0.962970	+	0.269607i
$65$	4.75670	+	9.49569i	0.589996	+	1.17780i
$66$	−4.32117	−	3.55260i	−0.531899	−	0.437295i
$67$	1.68770	+	4.52489i	0.206185	+	0.552804i	0.998345	−	0.0575101i	$-0.0183161\pi$
$67$	1.68770	+	4.52489i	0.206185	+	0.552804i	−0.792160	+	0.610314i	$0.791043\pi$
$68$	13.8822	+	0.272060i	1.68347	+	0.0329921i
$69$	5.01767	+	1.58887i	0.604056	+	0.191277i
$70$	−1.17034	−	8.72796i	−0.139883	−	1.04319i
$71$	−6.18592	−	2.82501i	−0.734133	−	0.335267i	0.0130235	−	0.999915i	$-0.495854\pi$
$71$	−6.18592	−	2.82501i	−0.734133	−	0.335267i	−0.747157	+	0.664648i	$0.768582\pi$
$72$	3.30156	−	3.85912i	0.389093	−	0.454802i
$73$	−5.82325	−	0.416487i	−0.681560	−	0.0487461i	−0.273734	−	0.961806i	$-0.588259\pi$
$73$	−5.82325	−	0.416487i	−0.681560	−	0.0487461i	−0.407827	+	0.913059i	$0.633713\pi$
$74$	0.468976	+	2.75348i	0.0545173	+	0.320086i
$75$	2.27656	−	4.99275i	0.262875	−	0.576513i
$76$	−5.69271	−	7.92357i	−0.652999	−	0.908896i
$77$	8.80933	+	4.81026i	1.00392	+	0.548180i
$78$	−1.37986	+	7.24129i	−0.156239	+	0.819915i
$79$	−1.35651	−	9.43474i	−0.152619	−	1.06149i	−0.911807	−	0.410619i	$-0.865313\pi$
$79$	−1.35651	−	9.43474i	−0.152619	−	1.06149i	0.759187	−	0.650872i	$-0.225597\pi$
$80$	−7.14309	−	5.38296i	−0.798622	−	0.601833i
$81$	0.161636	+	0.353934i	0.0179596	+	0.0393260i
$82$	−2.89451	+	1.67927i	−0.319645	+	0.185444i
$83$	1.33661	+	6.14431i	0.146712	+	0.674425i	0.990473	+	0.137706i	$0.0439729\pi$
$83$	1.33661	+	6.14431i	0.146712	+	0.674425i	−0.843761	+	0.536719i	$0.819663\pi$
$84$	3.03383	−	5.30616i	0.331018	−	0.578949i
$85$	−14.3439	−	5.93648i	−1.55581	−	0.643902i
$86$	−0.616969	−	1.26332i	−0.0665295	−	0.136227i
$87$	−0.654638	+	3.00932i	−0.0701845	+	0.322633i
$88$	9.76332	−	2.93378i	1.04077	−	0.312742i
$89$	1.68044	−	5.72305i	0.178126	−	0.606642i	−0.821224	−	0.570606i	$-0.806709\pi$
$89$	1.68044	−	5.72305i	0.178126	−	0.606642i	0.999350	−	0.0360365i	$-0.0114733\pi$
$90$	−5.00923	+	2.67376i	−0.528019	+	0.281839i
$91$		−	13.2264i		−	1.38650i
$92$	−7.49823	+	5.98134i	−0.781745	+	0.623598i
$93$	3.57105	−	3.57105i	0.370301	−	0.370301i
$94$	−7.50363	+	6.85012i	−0.773940	+	0.706536i
$95$	2.70076	+	10.5685i	0.277092	+	1.08431i
$96$	−1.66973	−	5.97939i	−0.170417	−	0.610269i
$97$	11.3889	+	2.47750i	1.15636	+	0.251552i	0.749543	−	0.661956i	$-0.230273\pi$
$97$	11.3889	+	2.47750i	1.15636	+	0.251552i	0.406822	+	0.913508i	$0.366637\pi$
$98$	−0.346964	+	1.00935i	−0.0350486	+	0.101959i
$99$	0.921046	−	6.40602i	0.0925686	−	0.643829i
$100$	5.24555	+	8.51377i	0.524555	+	0.851377i
$101$	−5.11760	−	3.28888i	−0.509220	−	0.327256i	0.260675	−	0.965427i	$-0.416055\pi$
$101$	−5.11760	−	3.28888i	−0.509220	−	0.327256i	−0.769895	+	0.638171i	$0.779691\pi$
$102$	−5.40708	−	9.32004i	−0.535381	−	0.922821i
$103$	4.01736	−	10.7710i	0.395842	−	1.06129i	−0.574276	−	0.818662i	$-0.694716\pi$
$103$	4.01736	−	10.7710i	0.395842	−	1.06129i	0.970118	−	0.242632i	$-0.0780108\pi$
$104$	−9.55896	−	9.43913i	−0.937333	−	0.925583i
$105$	−5.31973	+	4.28949i	−0.519153	+	0.418612i
$106$	11.0584	+	16.2650i	1.07409	+	1.57980i
$107$	−3.96147	+	7.25489i	−0.382970	+	0.701356i	−0.996062	−	0.0886545i	$-0.971743\pi$
$107$	−3.96147	+	7.25489i	−0.382970	+	0.701356i	0.613093	+	0.790011i	$0.289925\pi$
$108$	−10.3874	−	1.70185i	−0.999529	−	0.163760i
$109$	−3.79022	−	3.28424i	−0.363037	−	0.314573i	0.454173	−	0.890914i	$-0.349935\pi$
$109$	−3.79022	−	3.28424i	−0.363037	−	0.314573i	−0.817210	+	0.576340i	$0.804480\pi$
$110$	−11.3606	−	0.921121i	−1.08319	−	0.0878254i
$111$	1.63811	−	1.41943i	0.155482	−	0.134726i
$112$	4.95117	+	9.97804i	0.467842	+	0.942836i
$113$	3.55991	+	9.54447i	0.334888	+	0.897869i	0.989838	+	0.142197i	$0.0454167\pi$
$113$	3.55991	+	9.54447i	0.334888	+	0.897869i	−0.654951	+	0.755672i	$0.727311\pi$
$114$	−2.96579	+	6.96620i	−0.277771	+	0.652445i
$115$	10.2432	−	3.17450i	0.955181	−	0.296024i
$116$	−3.89007	−	4.04559i	−0.361184	−	0.375623i
$117$	−7.99065	+	2.98036i	−0.738735	+	0.275534i
$118$	1.63795	+	16.7805i	0.150786	+	1.54477i
$119$	12.6603	+	14.6108i	1.16057	+	1.33937i
$120$	−0.696379	+	6.90590i	−0.0635704	+	0.630420i
$121$	1.30395	−	1.50484i	0.118541	−	0.136803i
$122$	−10.3710	+	2.53908i	−0.938947	+	0.229877i
$123$	2.27919	+	1.24453i	0.205508	+	0.112216i
$124$	1.77976	+	9.02978i	0.159827	+	0.810899i
$125$	−1.99481	−	11.0009i	−0.178422	−	0.983954i
$126$	7.06901	−	0.183145i	0.629758	−	0.0163158i
$127$	−18.4061	−	6.86511i	−1.63327	−	0.609180i	−0.645318	−	0.763914i	$-0.723275\pi$
$127$	−18.4061	−	6.86511i	−1.63327	−	0.609180i	−0.987956	+	0.154735i	$0.950548\pi$
$128$	10.7448	+	3.54261i	0.949712	+	0.313126i
$129$	−0.589853	+	0.917829i	−0.0519337	+	0.0808104i
$130$	6.10925	+	13.7210i	0.535817	+	1.20341i
$131$	−7.54788	−	1.08522i	−0.659462	−	0.0948163i	−0.195544	−	0.980695i	$-0.562647\pi$
$131$	−7.54788	−	1.08522i	−0.659462	−	0.0948163i	−0.463917	+	0.885879i	$0.653556\pi$
$132$	−5.87622	−	5.29688i	−0.511459	−	0.461034i
$133$	2.88762	−	13.2742i	0.250389	−	1.15102i
$134$	2.09325	+	6.50110i	0.180829	+	0.561609i
$135$	10.1227	+	6.00204i	0.871222	+	0.516574i
$136$	19.5946	+	1.27727i	1.68023	+	0.109525i
$137$	−10.9659	−	10.9659i	−0.936879	−	0.936879i	0.0612440	−	0.998123i	$-0.480493\pi$
$137$	−10.9659	−	10.9659i	−0.936879	−	0.936879i	−0.998123	+	0.0612440i	$0.980493\pi$
$138$	6.98651	+	2.56741i	0.594731	+	0.218553i
$139$	−2.27525			−0.192984			−0.0964922	−	0.995334i	$-0.530762\pi$
$139$	−2.27525			−0.192984			−0.0964922	+	0.995334i	$0.530762\pi$
$140$	−1.09201	−	12.4057i	−0.0922920	−	1.04847i
$141$	7.56509	+	2.22131i	0.637096	+	0.187068i
$142$	−8.55745	−	4.38892i	−0.718125	−	0.368310i
$143$	−16.7280	−	3.63894i	−1.39886	−	0.304304i
$144$	4.91250	−	5.23961i	0.409375	−	0.436634i
$145$	2.40300	+	5.79654i	0.199558	+	0.481376i
$146$	−8.20001	−	0.962950i	−0.678638	−	0.0796943i
$147$	0.809330	−	0.176059i	0.0667524	−	0.0145211i
$148$	0.485439	+	3.92015i	0.0399028	+	0.322234i
$149$	9.45107	−	4.31616i	0.774262	−	0.353593i	0.0112151	−	0.999937i	$-0.496430\pi$
$149$	9.45107	−	4.31616i	0.774262	−	0.353593i	0.763046	+	0.646344i	$0.223703\pi$
$150$	3.53735	−	6.90708i	0.288824	−	0.563960i
$151$	7.82257	−	1.12472i	0.636592	−	0.0915281i	0.183540	−	0.983012i	$-0.441244\pi$
$151$	7.82257	−	1.12472i	0.636592	−	0.0915281i	0.453052	+	0.891484i	$0.350335\pi$
$152$	−7.53272	−	11.5602i	−0.610985	−	0.937655i
$153$	5.97422	−	10.9410i	0.482987	−	0.884525i
$154$	12.1360	+	7.36232i	0.977945	+	0.593272i
$155$	1.82401	−	10.1269i	0.146508	−	0.813410i
$156$	−2.41517	+	10.1414i	−0.193368	+	0.811960i
$157$	0.458566	−	6.41159i	0.0365975	−	0.511701i	−0.945782	−	0.324803i	$-0.894702\pi$
$157$	0.458566	−	6.41159i	0.0365975	−	0.511701i	0.982379	−	0.186898i	$-0.0598433\pi$
$158$	−1.30956	−	13.4162i	−0.104183	−	1.06733i
$159$	6.34044	−	13.8836i	0.502829	−	1.10104i
$160$	−9.74516	−	8.06423i	−0.770423	−	0.637533i
$161$	−13.1762	−	2.17866i	−1.03843	−	0.171702i
$162$	0.205586	+	0.510416i	0.0161524	+	0.0401021i
$163$	−22.8263	+	8.51376i	−1.78789	+	0.666849i	−0.789287	+	0.614024i	$0.789550\pi$
$163$	−22.8263	+	8.51376i	−1.78789	+	0.666849i	−0.998604	+	0.0528250i	$0.983177\pi$
$164$	−4.19723	+	2.18621i	−0.327749	+	0.170714i
$165$	3.96149	+	7.90824i	0.308402	+	0.615656i
$166$	1.49309	+	8.76634i	0.115886	+	0.680400i
$167$	1.02144	+	14.2815i	0.0790411	+	1.10514i	0.869929	+	0.493178i	$0.164165\pi$
$167$	1.02144	+	14.2815i	0.0790411	+	1.10514i	−0.790888	+	0.611961i	$0.790381\pi$
$168$	4.62735	−	7.30113i	0.357007	−	0.563295i
$169$	2.69305	+	9.17167i	0.207157	+	0.705513i
$170$	−19.8825	−	9.30938i	−1.52492	−	0.713997i
$171$	−8.67020	+	1.24659i	−0.663027	+	0.0953288i
$172$	−0.790365	−	1.82444i	−0.0602648	−	0.139112i
$173$	22.7819	+	8.49722i	1.73208	+	0.646032i	0.999403	−	0.0345466i	$-0.0109987\pi$
$173$	22.7819	+	8.49722i	1.73208	+	0.646032i	0.732675	+	0.680578i	$0.238271\pi$
$174$	−1.11840	+	4.20931i	−0.0847858	+	0.319107i
$175$	−3.91488	+	13.3619i	−0.295937	+	1.01007i
$176$	13.9818	−	3.51672i	1.05392	−	0.265082i
$177$	10.4742	−	7.84089i	0.787289	−	0.589357i
$178$	2.74215	−	7.97715i	0.205533	−	0.597913i
$179$	4.18298	−	2.68824i	0.312650	−	0.200928i	−0.374899	−	0.927066i	$-0.622323\pi$
$179$	4.18298	−	2.68824i	0.312650	−	0.200928i	0.687550	+	0.726137i	$0.258686\pi$
$180$	−7.24877	+	3.45516i	−0.540291	+	0.257533i
$181$	−5.22397	−	1.53390i	−0.388295	−	0.114014i	0.0817574	−	0.996652i	$-0.473947\pi$
$181$	−5.22397	−	1.53390i	−0.388295	−	0.114014i	−0.470052	+	0.882639i	$0.655765\pi$
$182$	0.850735	−	18.6856i	0.0630606	−	1.38507i
$183$	5.85894	+	5.85894i	0.433105	+	0.433105i
$184$	−10.9779	+	7.96785i	−0.809298	+	0.587398i
$185$	1.09093	−	4.27947i	0.0802067	−	0.314633i
$186$	5.27469	−	4.81531i	0.386759	−	0.353075i
$187$	21.9621	−	11.9922i	1.60603	−	0.876956i
$188$	−11.0414	+	9.19487i	−0.805274	+	0.670605i
$189$	−7.92357	−	12.3293i	−0.576355	−	0.896826i
$190$	3.13572	+	15.1044i	0.227489	+	1.09579i
$191$	10.3853	+	1.49318i	0.751455	+	0.108043i	0.507391	−	0.861716i	$-0.330610\pi$
$191$	10.3853	+	1.49318i	0.751455	+	0.108043i	0.244064	+	0.969759i	$0.421519\pi$
$192$	−1.97432	−	8.55479i	−0.142484	−	0.617389i
$193$	−3.83245	+	0.833699i	−0.275866	+	0.0600110i	−0.348370	−	0.937357i	$-0.613265\pi$
$193$	−3.83245	+	0.833699i	−0.275866	+	0.0600110i	0.0725039	+	0.997368i	$0.476901\pi$
$194$	15.9303	+	4.23263i	1.14373	+	0.303885i
$195$	6.64458	−	9.57603i	0.475828	−	0.685754i
$196$	−0.555095	+	1.40364i	−0.0396497	+	0.100260i
$197$	−3.79516	+	5.06974i	−0.270394	+	0.361204i	−0.915100	−	0.403227i	$-0.867889\pi$
$197$	−3.79516	+	5.06974i	−0.270394	+	0.361204i	0.644707	+	0.764430i	$0.276980\pi$
$198$	1.71325	−	8.99086i	0.121755	−	0.638953i
$199$	18.3544	−	5.38935i	1.30111	−	0.382041i	0.443470	−	0.896289i	$-0.353747\pi$
$199$	18.3544	−	5.38935i	1.30111	−	0.382041i	0.857641	+	0.514249i	$0.171929\pi$
$200$	6.86303	+	12.3652i	0.485290	+	0.874354i
$201$	3.47079	−	4.00551i	0.244811	−	0.282527i
$202$	−7.01835	−	4.97554i	−0.493809	−	0.350078i
$203$	0.557483	−	7.79464i	0.0391277	−	0.547076i
$204$	−7.03939	−	13.5147i	−0.492856	−	0.946217i
$205$	5.26058	−	0.567136i	0.367415	−	0.0396105i
$206$	6.36832	−	14.9583i	0.443702	−	1.04219i
$207$	1.65282	+	8.45124i	0.114879	+	0.587401i
$208$	−12.8973	−	13.9500i	−0.894266	−	0.967257i
$209$	−15.9939	−	7.30419i	−1.10632	−	0.505241i
$210$	−7.79136	+	5.71781i	−0.537655	+	0.394566i
$211$	21.9269	−	18.9997i	1.50951	−	1.30800i	0.721143	−	0.692786i	$-0.243617\pi$
$211$	21.9269	−	18.9997i	1.50951	−	1.30800i	0.788364	−	0.615209i	$-0.210929\pi$
$212$	14.5766	+	23.6897i	1.00112	+	1.62701i
$213$	0.532420	+	7.44420i	0.0364808	+	0.510068i
$214$	−6.06320	+	9.99454i	−0.414472	+	0.683212i
$215$	0.0799963	+	2.22152i	0.00545570	+	0.151507i
$216$	−14.5654	−	3.07242i	−0.991047	−	0.209051i
$217$	−7.67952	+	10.2586i	−0.521320	+	0.696402i
$218$	−5.14338	−	4.88360i	−0.348354	−	0.330759i
$219$	2.66160	+	5.82810i	0.179854	+	0.393826i
$220$	−15.9905	−	2.03204i	−1.07808	−	0.137000i
$221$	−27.7395	−	17.8271i	−1.86596	−	1.19918i
$222$	2.40554	−	1.89993i	0.161449	−	0.127515i
$223$	7.22169	−	5.40609i	0.483600	−	0.362018i	−0.329488	−	0.944160i	$-0.606876\pi$
$223$	7.22169	−	5.40609i	0.483600	−	0.362018i	0.813087	+	0.582142i	$0.197785\pi$
$224$	6.35297	+	14.4149i	0.424476	+	0.963138i
$225$	8.95469	−	0.645747i	0.596979	−	0.0430498i
$226$	4.41535	+	13.7129i	0.293704	+	0.912171i
$227$	12.2492	−	6.68857i	0.813008	−	0.443936i	−0.0182424	−	0.999834i	$-0.505807\pi$
$227$	12.2492	−	6.68857i	0.813008	−	0.443936i	0.831251	+	0.555897i	$0.187625\pi$
$228$	−4.63799	+	9.65074i	−0.307158	+	0.639136i
$229$			4.83648i			0.319603i	0.987149	+	0.159802i	$0.0510855\pi$
$229$			4.83648i			0.319603i	−0.987149	+	0.159802i	$0.948915\pi$
$230$	14.6752	−	3.82593i	0.967656	−	0.252274i
$231$		−	11.0153i		−	0.724751i
$232$	−5.23548	−	5.96562i	−0.343726	−	0.391662i
$233$	−12.5499	+	6.85278i	−0.822173	+	0.448940i	−0.834516	−	0.550983i	$-0.814253\pi$
$233$	−12.5499	+	6.85278i	−0.822173	+	0.448940i	0.0123433	+	0.999924i	$0.496071\pi$
$234$	−11.4805	+	3.69653i	−0.750503	+	0.241650i
$235$	15.2410	−	5.07768i	0.994215	−	0.331231i
$236$	1.23468	+	23.8120i	0.0803708	+	1.55003i
$237$	−8.37422	+	6.26886i	−0.543964	+	0.407206i
$238$	16.9461	+	21.4557i	1.09845	+	1.39077i
$239$	−0.689667	−	0.443222i	−0.0446108	−	0.0286696i	0.518145	−	0.855293i	$-0.326623\pi$
$239$	−0.689667	−	0.443222i	−0.0446108	−	0.0286696i	−0.562756	+	0.826623i	$0.690259\pi$
$240$	−1.42800	+	9.71152i	−0.0921772	+	0.626876i
$241$	4.61197	+	10.0988i	0.297083	+	0.650521i	0.998033	−	0.0626894i	$-0.0199677\pi$
$241$	4.61197	+	10.0988i	0.297083	+	0.650521i	−0.700950	+	0.713210i	$0.747240\pi$
$242$	1.93895	−	2.04209i	0.124640	−	0.131270i
$243$	−9.20601	+	12.2978i	−0.590566	+	0.788903i
$244$	−14.8150	+	2.92001i	−0.948431	+	0.186935i
$245$	1.14958	−	1.23547i	0.0734441	−	0.0789310i
$246$	3.13988	+	1.90481i	0.200191	+	0.121447i
$247$	1.65292	+	23.1109i	0.105173	+	1.47051i
$248$	1.93355	+	12.8713i	0.122781	+	0.817329i
$249$	5.21529	−	4.51907i	0.330505	−	0.286385i
$250$	−2.11058	−	15.6699i	−0.133485	−	0.991051i
$251$	−4.73907	−	2.16426i	−0.299127	−	0.136607i	0.260198	−	0.965555i	$-0.416212\pi$
$251$	−4.73907	−	2.16426i	−0.299127	−	0.136607i	−0.559325	+	0.828949i	$0.688940\pi$
$252$	9.99853	+	0.195948i	0.629848	+	0.0123436i
$253$	−6.38057	+	16.0650i	−0.401143	+	1.01000i
$254$	−25.5616	−	10.8826i	−1.60388	−	0.682833i
$255$	1.82612	+	16.9386i	0.114356	+	1.06073i
$256$	14.9518	+	5.69594i	0.934487	+	0.355996i
$257$	0.578114	−	8.08308i	0.0360617	−	0.504209i	−0.947036	−	0.321127i	$-0.895938\pi$
$257$	0.578114	−	8.08308i	0.0360617	−	0.504209i	0.983098	−	0.183082i	$-0.0586072\pi$
$258$	−0.892351	+	1.25872i	−0.0555553	+	0.0783647i
$259$	−3.60171	+	4.15659i	−0.223799	+	0.258278i
$260$	7.74830	+	19.7773i	0.480529	+	1.22654i
$261$	−4.83470	+	1.41960i	−0.299261	+	0.0878708i
$262$	−10.5935	−	2.01863i	−0.654467	−	0.124712i
$263$	−10.2684	+	13.7170i	−0.633177	+	0.845825i	−0.996302	−	0.0859150i	$-0.972619\pi$
$263$	−10.2684	+	13.7170i	−0.633177	+	0.845825i	0.363126	+	0.931740i	$0.381710\pi$
$264$	−7.96093	−	7.86114i	−0.489961	−	0.483819i
$265$	−5.53058	−	30.6024i	−0.339741	−	1.87989i
$266$	4.93330	−	18.5674i	0.302480	−	1.13844i
$267$	−6.39636	+	1.39144i	−0.391451	+	0.0851549i
$268$	2.53908	+	9.31906i	0.155099	+	0.569252i
$269$	−0.526571	−	0.0757094i	−0.0321056	−	0.00461608i	0.126243	−	0.991999i	$-0.459708\pi$
$269$	−0.526571	−	0.0757094i	−0.0321056	−	0.00461608i	−0.158349	+	0.987383i	$0.550617\pi$
$270$	13.9148	+	9.13049i	0.846826	+	0.555664i
$271$	−9.87294	−	15.3626i	−0.599738	−	0.933211i	−0.999860	−	0.0167489i	$-0.994668\pi$
$271$	−9.87294	−	15.3626i	−0.599738	−	0.933211i	0.400121	−	0.916462i	$-0.368968\pi$
$272$	27.6002	+	3.06481i	1.67351	+	0.185832i
$273$	−12.7399	+	6.95649i	−0.771051	+	0.421026i
$274$	−14.7867	−	16.1974i	−0.893298	−	0.978520i
$275$	15.8223	+	8.62755i	0.954120	+	0.520261i
$276$	9.70505	+	4.07649i	0.584176	+	0.245376i
$277$	5.81826	+	5.81826i	0.349585	+	0.349585i	0.859955	−	0.510370i	$-0.170491\pi$
$277$	5.81826	+	5.81826i	0.349585	+	0.349585i	−0.510370	+	0.859955i	$0.670491\pi$
$278$	−3.21436	−	0.146346i	−0.192785	−	0.00877727i
$279$	7.92815	+	2.32792i	0.474646	+	0.139369i
$280$	−0.744794	−	17.5964i	−0.0445100	−	1.05159i
$281$	18.6748	−	12.0016i	1.11404	−	0.715953i	0.151873	−	0.988400i	$-0.451469\pi$
$281$	18.6748	−	12.0016i	1.11404	−	0.715953i	0.962171	+	0.272447i	$0.0878331\pi$
$282$	10.5447	+	3.62475i	0.627928	+	0.215851i
$283$	10.8335	−	8.10984i	0.643984	−	0.482080i	−0.226673	−	0.973971i	$-0.572785\pi$
$283$	10.8335	−	8.10984i	0.643984	−	0.482080i	0.870657	+	0.491891i	$0.163694\pi$
$284$	−11.8072	−	6.75088i	−0.700631	−	0.400591i
$285$	8.75926	−	8.15997i	0.518854	−	0.483355i
$286$	−23.3984	−	6.21688i	−1.38357	−	0.367612i
$287$	−6.17386	−	2.30273i	−0.364432	−	0.135926i
$288$	7.27716	−	7.08628i	0.428811	−	0.417563i
$289$	30.8801	−	4.43989i	1.81648	−	0.261170i
$290$	3.02200	+	8.34362i	0.177458	+	0.489954i
$291$	−3.60367	−	12.2730i	−0.211251	−	0.719455i
$292$	−11.5226	−	1.88784i	−0.674311	−	0.110477i
$293$	0.369436	+	5.16539i	0.0215827	+	0.301766i	0.996766	+	0.0803645i	$0.0256084\pi$
$293$	0.369436	+	5.16539i	0.0215827	+	0.301766i	−0.975183	+	0.221401i	$0.928937\pi$
$294$	1.15471	−	0.196670i	0.0673438	−	0.0114701i
$295$	8.41128	−	25.2967i	0.489724	−	1.47283i
$296$	0.433656	+	5.56941i	0.0252057	+	0.323716i
$297$	−17.7734	+	6.62913i	−1.03132	+	0.384661i
$298$	13.6296	−	5.48975i	0.789542	−	0.318013i
$299$	22.6098	−	2.76605i	1.30756	−	0.159965i
$300$	5.44167	−	9.53045i	0.314175	−	0.550241i
$301$	1.15004	−	2.51823i	0.0662871	−	0.145149i
$302$	11.1237	−	1.08579i	0.640096	−	0.0624800i
$303$	−0.476272	+	6.65915i	−0.0273611	+	0.382558i
$304$	−9.89829	−	16.8162i	−0.567706	−	0.964473i
$305$	16.6149	+	2.99262i	0.951369	+	0.171357i
$306$	9.14381	−	15.0726i	0.522717	−	0.861642i
$307$	−0.274261	+	0.502272i	−0.0156529	+	0.0286662i	−0.885388	−	0.464852i	$-0.846108\pi$
$307$	−0.274261	+	0.502272i	−0.0156529	+	0.0286662i	0.869735	+	0.493518i	$0.164289\pi$
$308$	16.6716	+	11.1817i	0.949950	+	0.637137i
$309$	−12.4877	+	1.79546i	−0.710400	+	0.102140i
$310$	3.22825	−	14.1894i	0.183352	−	0.805905i
$311$	−5.42761	+	2.47871i	−0.307772	+	0.140555i	−0.563313	−	0.826243i	$-0.690474\pi$
$311$	−5.42761	+	2.47871i	−0.307772	+	0.140555i	0.255541	+	0.966798i	$0.417746\pi$
$312$	−4.06433	+	14.1719i	−0.230097	+	0.802325i
$313$	−16.9994	+	3.69799i	−0.960861	+	0.209022i	−0.665529	−	0.746372i	$-0.731794\pi$
$313$	−16.9994	+	3.69799i	−0.960861	+	0.209022i	−0.295332	+	0.955395i	$0.595430\pi$
$314$	1.06024	−	9.02848i	0.0598327	−	0.509506i
$315$	−10.3310	−	4.27568i	−0.582086	−	0.240908i
$316$	−0.987138	−	19.0379i	−0.0555308	−	1.07097i
$317$	32.4220	+	7.05298i	1.82100	+	0.396135i	0.987659	−	0.156621i	$-0.0500600\pi$
$317$	32.4220	+	7.05298i	1.82100	+	0.396135i	0.833344	+	0.552755i	$0.186424\pi$
$318$	9.85046	−	19.2063i	0.552386	−	1.07703i
$319$	−9.70482	−	2.84959i	−0.543365	−	0.159546i
$320$	−13.2488	−	12.0196i	−0.740629	−	0.671914i
$321$	9.07157			0.506325
$322$	−18.4745	−	3.92541i	−1.02954	−	0.218754i
$323$	−23.9477	−	23.9477i	−1.33248	−	1.33248i
$324$	0.257611	+	0.734314i	0.0143117	+	0.0407952i
$325$	−0.0139708	−	23.7481i	−0.000774963	−	1.31731i
$326$	−32.7954	+	10.5596i	−1.81637	+	0.584842i
$327$	−1.16995	+	5.37816i	−0.0646982	+	0.297413i
$328$	−6.07026	+	2.81860i	−0.335174	+	0.155631i
$329$	−19.8027	−	2.84720i	−1.09176	−	0.156971i
$330$	5.08793	+	11.4272i	0.280081	+	0.629045i
$331$	−0.512569	+	0.797574i	−0.0281734	+	0.0438386i	−0.855055	−	0.518538i	$-0.826476\pi$
$331$	−0.512569	+	0.797574i	−0.0281734	+	0.0438386i	0.826881	+	0.562377i	$0.190113\pi$
$332$	1.54550	+	12.4807i	0.0848206	+	0.684967i
$333$	3.32277	+	1.23933i	0.182087	+	0.0679148i
$334$	0.524431	+	20.2420i	0.0286956	+	1.10759i
$335$	1.15118	−	10.7373i	0.0628959	−	0.586641i
$336$	7.00690	−	10.0170i	0.382258	−	0.546474i
$337$	−8.31641	−	4.54110i	−0.453024	−	0.247370i	0.236502	−	0.971631i	$-0.423999\pi$
$337$	−8.31641	−	4.54110i	−0.453024	−	0.247370i	−0.689525	+	0.724261i	$0.742181\pi$
$338$	3.21467	+	13.1305i	0.174855	+	0.714205i
$339$	7.32103	−	8.44892i	0.397624	−	0.458882i
$340$	−27.4902	−	14.4307i	−1.49086	−	0.782614i
$341$	10.8617	+	12.5350i	0.588193	+	0.678810i
$342$	−12.3290	+	1.20344i	−0.666676	+	0.0650745i
$343$	16.2949	−	6.07768i	0.879842	−	0.328164i
$344$	−0.999239	−	2.62831i	−0.0538753	−	0.141709i
$345$	−8.44517	−	8.19673i	−0.454673	−	0.441297i
$346$	31.6386	+	13.4698i	1.70090	+	0.724141i
$347$	−5.39100	−	14.4538i	−0.289404	−	0.775922i	−0.997557	−	0.0698628i	$-0.977744\pi$
$347$	−5.39100	−	14.4538i	−0.289404	−	0.775922i	0.708153	−	0.706059i	$-0.249529\pi$
$348$	−1.85077	+	5.87477i	−0.0992116	+	0.314921i
$349$	−9.32482	+	8.08001i	−0.499146	+	0.432513i	−0.867696	−	0.497095i	$-0.834400\pi$
$349$	−9.32482	+	8.08001i	−0.499146	+	0.432513i	0.368550	+	0.929608i	$0.379854\pi$
$350$	−6.39020	+	18.6253i	−0.341571	+	0.995563i
$351$	18.8915	+	16.3696i	1.00835	+	0.873742i
$352$	19.9790	−	4.06891i	1.06489	−	0.216874i
$353$	13.9611	−	25.5679i	0.743076	−	1.36084i	−0.182852	−	0.983140i	$-0.558533\pi$
$353$	13.9611	−	25.5679i	0.743076	−	1.36084i	0.925928	−	0.377701i	$-0.123285\pi$
$354$	15.3018	−	10.4035i	0.813279	−	0.552940i
$355$	9.54496	+	11.8374i	0.506594	+	0.628266i
$356$	4.38707	−	11.0933i	0.232514	−	0.587946i
$357$	7.41457	−	19.8792i	0.392421	−	1.05212i
$358$	6.08241	−	3.52875i	0.321465	−	0.186500i
$359$	−20.5568	−	13.2110i	−1.08495	−	0.697252i	−0.129251	−	0.991612i	$-0.541257\pi$
$359$	−20.5568	−	13.2110i	−1.08495	−	0.697252i	−0.955695	+	0.294360i	$0.904894\pi$
$360$	−10.4629	+	4.41503i	−0.551445	+	0.232693i
$361$	−0.682751	+	4.74863i	−0.0359342	+	0.249928i
$362$	−7.28151	−	2.50302i	−0.382707	−	0.131556i
$363$	−2.13530	−	0.464506i	−0.112074	−	0.0243803i
$364$	2.40375	−	26.3433i	0.125991	−	1.38077i
$365$	11.2290	+	6.65799i	0.587751	+	0.348495i
$366$	7.90037	+	8.65407i	0.412959	+	0.452356i
$367$	−21.4967	+	21.4967i	−1.12212	+	1.12212i	−0.130699	+	0.991422i	$0.541722\pi$
$367$	−21.4967	+	21.4967i	−1.12212	+	1.12212i	−0.991422	+	0.130699i	$0.958278\pi$
$368$	−16.0215	+	10.5505i	−0.835177	+	0.549982i
$369$			4.24879i			0.221183i
$370$	1.81647	−	5.97566i	0.0944338	−	0.310660i
$371$	−10.9111	+	37.1599i	−0.566477	+	1.92924i
$372$	7.76155	−	6.46355i	0.402418	−	0.335119i
$373$	4.69995	−	21.6053i	0.243354	−	1.11868i	−0.679543	−	0.733636i	$-0.737822\pi$
$373$	4.69995	−	21.6053i	0.243354	−	1.11868i	0.922897	−	0.385046i	$-0.125814\pi$
$374$	31.7983	−	15.5294i	1.64425	−	0.803004i
$375$	−9.54709	+	7.70743i	−0.493009	+	0.398010i
$376$	−16.1901	+	12.2799i	−0.834941	+	0.633285i
$377$	2.83317	+	13.0239i	0.145916	+	0.670763i
$378$	−10.4010	−	17.9279i	−0.534969	−	0.922111i
$379$	3.54404	+	7.76036i	0.182045	+	0.398623i	0.978550	−	0.206009i	$-0.0660476\pi$
$379$	3.54404	+	7.76036i	0.182045	+	0.398623i	−0.796505	+	0.604632i	$0.793320\pi$
$380$	3.45847	+	21.5404i	0.177416	+	1.10500i
$381$	3.06819	+	21.3397i	0.157188	+	1.09327i
$382$	14.5758	+	2.77749i	0.745763	+	0.142109i
$383$	10.4284	+	5.69435i	0.532867	+	0.290968i	0.723067	−	0.690778i	$-0.242732\pi$
$383$	10.4284	+	5.69435i	0.532867	+	0.290968i	−0.190200	+	0.981745i	$0.560914\pi$
$384$	−2.23896	−	12.2128i	−0.114257	−	0.623230i
$385$	−12.8055	−	18.4319i	−0.652629	−	0.939374i
$386$	−5.46792	+	0.931301i	−0.278310	+	0.0474020i
$387$	−1.78052	−	0.127345i	−0.0905088	−	0.00647332i
$388$	22.2333	+	7.00430i	1.12872	+	0.355589i
$389$	1.21321	+	0.554056i	0.0615124	+	0.0280918i	0.445934	−	0.895066i	$-0.352872\pi$
$389$	1.21321	+	0.554056i	0.0615124	+	0.0280918i	−0.384421	+	0.923158i	$0.625599\pi$
$390$	10.0031	−	13.1012i	0.506525	−	0.663403i
$391$	−22.3287	+	24.6977i	−1.12921	+	1.24902i
$392$	−0.874494	+	1.94729i	−0.0441686	+	0.0983528i
$393$	2.92455	+	7.84101i	0.147524	+	0.395527i
$394$	−5.68770	+	6.91816i	−0.286542	+	0.348532i
$395$	−6.72490	+	20.2249i	−0.338366	+	1.01763i
$396$	2.99869	−	12.5916i	0.150690	−	0.632754i
$397$	−23.6196	+	1.68931i	−1.18544	+	0.0847840i	−0.650096	−	0.759852i	$-0.725271\pi$
$397$	−23.6196	+	1.68931i	−1.18544	+	0.0847840i	−0.535340	+	0.844636i	$0.679817\pi$
$398$	26.2769	−	6.43323i	1.31714	−	0.322468i
$399$	−14.3047	+	4.20022i	−0.716128	+	0.210274i
$400$	8.90040	+	17.9104i	0.445020	+	0.895521i
$401$	4.17013	+	29.0039i	0.208247	+	1.44839i	0.778876	+	0.627178i	$0.215790\pi$
$401$	4.17013	+	29.0039i	0.208247	+	1.44839i	−0.570629	+	0.821208i	$0.693301\pi$
$402$	5.16100	−	5.43553i	0.257407	−	0.271100i
$403$	7.63809	−	20.4785i	0.380480	−	1.02011i
$404$	−9.59514	−	7.48062i	−0.477376	−	0.372175i
$405$	0.0307981	−	0.869498i	0.00153037	−	0.0432057i
$406$	1.28894	−	10.9760i	0.0639692	−	0.544731i
$407$	4.26608	+	5.69882i	0.211462	+	0.282480i
$408$	−9.07562	−	19.5456i	−0.449310	−	0.967653i
$409$	0.529961	+	0.824635i	0.0262049	+	0.0407756i	0.854109	−	0.520094i	$-0.174103\pi$
$409$	0.529961	+	0.824635i	0.0262049	+	0.0407756i	−0.827904	+	0.560870i	$0.810467\pi$
$410$	7.46837	−	0.462856i	0.368836	−	0.0228588i
$411$	−4.79494	+	16.3301i	−0.236517	+	0.805503i
$412$	9.95898	−	20.7227i	0.490644	−	1.02093i
$413$	−23.4756	+	23.4756i	−1.15516	+	1.15516i
$414$	1.79143	+	12.0458i	0.0880438	+	0.592019i
$415$	3.47322	−	13.6247i	0.170494	−	0.668809i
$416$	−17.3234	−	20.5374i	−0.849348	−	1.00693i
$417$	1.19668	+	2.19156i	0.0586017	+	0.107321i
$418$	−22.1256	−	11.3477i	−1.08220	−	0.555036i
$419$	0.419874	−	0.269836i	0.0205122	−	0.0131824i	−0.530345	−	0.847782i	$-0.677937\pi$
$419$	0.419874	−	0.269836i	0.0205122	−	0.0131824i	0.550857	+	0.834600i	$0.314301\pi$
$420$	−11.3750	+	7.57669i	−0.555044	+	0.369705i
$421$	−4.81656	+	33.4999i	−0.234745	+	1.63268i	0.442388	+	0.896824i	$0.354131\pi$
$421$	−4.81656	+	33.4999i	−0.234745	+	1.63268i	−0.677133	+	0.735861i	$0.736778\pi$
$422$	32.1992	−	25.4315i	1.56743	−	1.23799i
$423$	2.74211	+	12.6053i	0.133326	+	0.612889i
$424$	19.0693	+	34.4051i	0.926087	+	1.67086i
$425$	22.7471	+	26.2204i	1.10340	+	1.27188i
$426$	0.273358	+	10.5510i	0.0132442	+	0.511199i
$427$	−16.8311	−	12.5996i	−0.814515	−	0.609738i
$428$	−9.20865	+	13.7298i	−0.445117	+	0.663654i
$429$	5.29307	+	18.0265i	0.255552	+	0.870329i
$430$	−0.0298759	+	3.14360i	−0.00144075	+	0.151598i
$431$	−15.1372	−	13.1165i	−0.729135	−	0.631799i	0.209061	−	0.977903i	$-0.432959\pi$
$431$	−15.1372	−	13.1165i	−0.729135	−	0.631799i	−0.938196	+	0.346103i	$0.887505\pi$
$432$	−20.3796	−	5.27741i	−0.980513	−	0.253910i
$433$	−4.26335	−	0.304921i	−0.204884	−	0.0146536i	−0.0314799	−	0.999504i	$-0.510022\pi$
$433$	−4.26335	−	0.304921i	−0.204884	−	0.0146536i	−0.173404	+	0.984851i	$0.555477\pi$
$434$	−11.5091	+	13.9989i	−0.552454	+	0.671971i
$435$	4.31944	−	5.36332i	0.207101	−	0.257152i
$436$	−6.95220	−	7.23014i	−0.332950	−	0.346261i
$437$	23.2954	+	2.16019i	1.11437	+	0.103336i
$438$	3.38531	+	8.40484i	0.161756	+	0.401599i
$439$	−4.92943	+	10.7939i	−0.235269	+	0.515167i	−0.990034	−	0.140828i	$-0.955023\pi$
$439$	−4.92943	+	10.7939i	−0.235269	+	0.515167i	0.754765	+	0.655995i	$0.227751\pi$
$440$	−22.4598	−	3.89928i	−1.07073	−	0.185891i
$441$	0.887430	+	1.02415i	0.0422586	+	0.0487690i
$442$	−38.0423	−	26.9695i	−1.80949	−	1.28281i
$443$	−22.4169	+	1.60329i	−1.06506	+	0.0761744i	−0.592850	−	0.805313i	$-0.701997\pi$
$443$	−22.4169	+	1.60329i	−1.06506	+	0.0761744i	−0.472208	+	0.881487i	$0.656543\pi$
$444$	3.52063	−	2.52940i	0.167081	−	0.120040i
$445$	−9.08546	+	9.76423i	−0.430692	+	0.462869i
$446$	10.5502	−	7.17294i	0.499565	−	0.339649i
$447$	−9.12822	−	6.83330i	−0.431750	−	0.323204i
$448$	8.04798	+	20.7733i	0.380231	+	0.981448i
$449$	−18.3697	+	8.38914i	−0.866918	+	0.395908i	−0.798676	−	0.601761i	$-0.794466\pi$
$449$	−18.3697	+	8.38914i	−0.866918	+	0.395908i	−0.0682413	+	0.997669i	$0.521739\pi$
$450$	12.6923	−	0.336305i	0.598320	−	0.0158536i
$451$	−4.61096	+	7.17479i	−0.217122	+	0.337848i
$452$	5.35575	+	19.6569i	0.251913	+	0.924585i
$453$	−5.19766	−	6.94326i	−0.244208	−	0.326223i
$454$	17.7353	−	8.66140i	0.832358	−	0.406500i
$455$	−13.2305	+	26.4507i	−0.620258	+	1.24003i
$456$	−7.17306	+	13.3358i	−0.335909	+	0.624504i
$457$	−7.76317	−	14.2172i	−0.363146	−	0.665052i	0.630675	−	0.776047i	$-0.282778\pi$
$457$	−7.76317	−	14.2172i	−0.363146	−	0.665052i	−0.993821	+	0.110995i	$0.964596\pi$
$458$	−0.311087	+	6.83273i	−0.0145361	+	0.319273i
$459$	−36.5378			−1.70544
$460$	20.9785	−	4.46116i	0.978128	−	0.208002i
$461$	22.6998			1.05724			0.528618	−	0.848860i	$-0.322711\pi$
$461$	22.6998			1.05724			0.528618	+	0.848860i	$0.322711\pi$
$462$	0.708512	−	15.5618i	0.0329630	−	0.724001i
$463$	−19.4707	−	35.6578i	−0.904878	−	1.65716i	−0.741878	−	0.670535i	$-0.766065\pi$
$463$	−19.4707	−	35.6578i	−0.904878	−	1.65716i	−0.163000	−	0.986626i	$-0.552117\pi$
$464$	−7.01271	−	8.76468i	−0.325557	−	0.406890i
$465$	−10.7137	+	3.56937i	−0.496836	+	0.165525i
$466$	−18.1707	+	8.87404i	−0.841741	+	0.411082i
$467$	12.0498	+	16.0967i	0.557600	+	0.744866i	0.987432	−	0.158043i	$-0.0505183\pi$
$467$	12.0498	+	16.0967i	0.557600	+	0.744866i	−0.429833	+	0.902909i	$0.641427\pi$
$468$	−16.4568	+	4.48384i	−0.760717	+	0.207266i
$469$	−7.27082	+	11.3136i	−0.335735	+	0.522414i
$470$	21.8584	−	6.19317i	1.00825	−	0.285670i
$471$	−6.41692	+	2.93051i	−0.295676	+	0.135031i
$472$	0.212680	+	33.7199i	0.00978939	+	1.55208i
$473$	−2.86851	−	2.14734i	−0.131894	−	0.0987346i
$474$	−12.2339	+	8.31770i	−0.561922	+	0.382044i
$475$	5.17073	−	23.8370i	0.237249	−	1.09371i
$476$	22.5605	+	31.4016i	1.03406	+	1.43929i
$477$	24.9086	−	1.78150i	1.14048	−	0.0815691i
$478$	−0.945818	−	0.670522i	−0.0432607	−	0.0306689i
$479$	−18.6590	−	21.5336i	−0.852552	−	0.983897i	0.147435	−	0.989072i	$-0.452898\pi$
$479$	−18.6590	−	21.5336i	−0.852552	−	0.983897i	−0.999987	+	0.00517451i	$0.998353\pi$
$480$	−2.64207	+	13.6281i	−0.120593	+	0.622035i
$481$	3.89689	−	8.53299i	0.177683	−	0.389071i
$482$	5.86599	+	14.5637i	0.267189	+	0.663360i
$483$	4.83156	+	13.8374i	0.219844	+	0.629622i
$484$	2.87060	−	2.76025i	0.130482	−	0.125466i
$485$	−20.2977	−	16.3471i	−0.921670	−	0.742282i
$486$	−13.7968	+	16.7816i	−0.625835	+	0.761227i
$487$	12.9661	+	0.927357i	0.587552	+	0.0420226i	0.361951	−	0.932197i	$-0.382111\pi$
$487$	12.9661	+	0.927357i	0.587552	+	0.0420226i	0.225601	+	0.974220i	$0.427565\pi$
$488$	−21.1177	+	3.17233i	−0.955952	+	0.143605i
$489$	20.2062	+	17.5087i	0.913754	+	0.791773i
$490$	1.70354	−	1.67146i	0.0769580	−	0.0755090i
$491$	−4.67527	−	15.9225i	−0.210992	−	0.718572i	−0.995181	−	0.0980509i	$-0.968739\pi$
$491$	−4.67527	−	15.9225i	−0.210992	−	0.718572i	0.784190	−	0.620521i	$-0.213079\pi$
$492$	4.31335	+	2.89299i	0.194461	+	0.130426i
$493$	−15.5962	−	11.6751i	−0.702416	−	0.525822i
$494$	0.848652	+	32.7562i	0.0381826	+	1.47377i
$495$	−8.24998	+	11.8897i	−0.370809	+	0.534402i
$496$	1.90373	+	18.3083i	0.0854799	+	0.822067i
$497$	−4.02544	−	18.5047i	−0.180566	−	0.830047i
$498$	7.65857	−	6.04887i	0.343189	−	0.271056i
$499$	0.806917	−	5.61223i	0.0361225	−	0.251238i	−0.963757	−	0.266783i	$-0.914039\pi$
$499$	0.806917	−	5.61223i	0.0361225	−	0.251238i	0.999879	+	0.0155452i	$0.00494839\pi$
$500$	−1.97382	−	22.2734i	−0.0882720	−	0.996096i
$501$	13.2190	−	8.49531i	0.590580	−	0.379543i
$502$	−6.55591	−	3.36238i	−0.292605	−	0.150070i
$503$	3.88366	+	7.11238i	0.173164	+	0.317126i	0.949819	−	0.312800i	$-0.101267\pi$
$503$	3.88366	+	7.11238i	0.173164	+	0.317126i	−0.776655	+	0.629926i	$0.783085\pi$
$504$	14.1128	+	0.919941i	0.628635	+	0.0409774i
$505$	6.94448	+	11.6965i	0.309025	+	0.520485i
$506$	−10.0475	+	22.2855i	−0.446665	+	0.990711i
$507$	7.41787	−	7.41787i	0.329439	−	0.329439i
$508$	−35.4122	−	17.0185i	−1.57116	−	0.755074i
$509$	−0.997311	+	3.39653i	−0.0442050	+	0.150549i	−0.978638	−	0.205590i	$-0.934089\pi$
$509$	−0.997311	+	3.39653i	−0.0442050	+	0.150549i	0.934433	+	0.356138i	$0.115907\pi$
$510$	1.49035	+	24.0474i	0.0659939	+	1.06484i
$511$	−8.78952	−	13.6768i	−0.388825	−	0.605024i
$512$	20.7568	+	9.00865i	0.917329	+	0.398130i
$513$	15.3859	+	20.5532i	0.679304	+	0.907444i
$514$	1.33664	−	11.3822i	0.0589568	−	0.502047i
$515$	−18.8084	+	17.5216i	−0.828798	+	0.772094i
$516$	−1.34163	+	1.72086i	−0.0590620	+	0.0757568i
$517$	−9.04924	+	24.2620i	−0.397985	+	1.06704i
$518$	−5.35567	+	5.64056i	−0.235315	+	0.247832i
$519$	−3.79762	−	26.4131i	−0.166697	−	1.15940i
$520$	9.67432	+	28.4388i	0.424247	+	1.24712i
$521$	−35.2094	+	10.3384i	−1.54255	+	0.452934i	−0.938864	−	0.344287i	$-0.888121\pi$
$521$	−35.2094	+	10.3384i	−1.54255	+	0.452934i	−0.603688	+	0.797221i	$0.706303\pi$
$522$	−6.92154	+	1.69456i	−0.302947	+	0.0741690i
$523$	−26.6608	+	1.90682i	−1.16579	+	0.0833793i	−0.640787	−	0.767719i	$-0.721392\pi$
$523$	−26.6608	+	1.90682i	−1.16579	+	0.0833793i	−0.525007	+	0.851098i	$0.675937\pi$
$524$	−14.8361	−	3.53321i	−0.648118	−	0.154349i
$525$	14.9295	−	3.25691i	0.651575	−	0.142143i
$526$	−15.3890	+	18.7182i	−0.670991	+	0.816152i
$527$	11.1645	+	29.9332i	0.486333	+	1.30391i
$528$	−10.7412	−	11.6179i	−0.467449	−	0.505603i
$529$	0.968753	−	22.9796i	0.0421197	−	0.999113i
$530$	−5.84495	−	43.5893i	−0.253888	−	1.89340i
$531$	19.4725	+	8.89280i	0.845035	+	0.385915i
$532$	8.16379	−	25.9137i	0.353945	−	1.12350i
$533$	11.2101	+	0.801761i	0.485563	+	0.0347281i
$534$	−9.12596	+	1.55434i	−0.394919	+	0.0672629i
$535$	15.1795	−	10.5459i	0.656266	−	0.455940i
$536$	2.98768	+	13.3288i	0.129048	+	0.575718i
$537$	−4.78941	−	2.61521i	−0.206678	−	0.112855i
$538$	−0.739043	−	0.140828i	−0.0318624	−	0.00607153i
$539$	0.387127	+	2.69252i	0.0166747	+	0.115975i
$540$	19.0708	+	13.7941i	0.820677	+	0.593604i
$541$	−13.7926	−	30.2016i	−0.592991	−	1.29847i	−0.933618	−	0.358270i	$-0.883367\pi$
$541$	−13.7926	−	30.2016i	−0.592991	−	1.29847i	0.340627	−	0.940198i	$-0.389361\pi$
$542$	−12.9599	−	22.3385i	−0.556674	−	0.959523i
$543$	1.27010	+	5.83857i	0.0545053	+	0.250557i
$544$	38.7950	+	6.10509i	1.66332	+	0.261753i
$545$	4.29456	+	10.3594i	0.183959	+	0.443747i
$546$	−18.4457	+	9.00834i	−0.789402	+	0.385521i
$547$	3.48849	−	16.0363i	0.149157	−	0.685664i	−0.840453	−	0.541885i	$-0.817711\pi$
$547$	3.48849	−	16.0363i	0.149157	−	0.685664i	0.989610	−	0.143779i	$-0.0459256\pi$
$548$	−19.8481	−	23.8340i	−0.847869	−	1.01814i
$549$	−3.81936	+	13.0075i	−0.163006	+	0.555148i
$550$	21.7980	+	13.2063i	0.929471	+	0.563117i
$551$			13.6895i			0.583191i
$552$	13.4486	+	6.38330i	0.572411	+	0.271691i
$553$	18.7690	−	18.7690i	0.798139	−	0.798139i
$554$	7.84551	+	8.59398i	0.333324	+	0.365123i
$555$	−4.69583	+	1.20001i	−0.199327	+	0.0509376i
$556$	−4.53168	−	0.413502i	−0.192186	−	0.0175364i
$557$	4.50070	+	0.979067i	0.190701	+	0.0414844i	0.306901	−	0.951741i	$-0.400708\pi$
$557$	4.50070	+	0.979067i	0.190701	+	0.0414844i	−0.116201	+	0.993226i	$0.537072\pi$
$558$	11.0508	+	3.79871i	0.467816	+	0.160812i
$559$	−0.671980	+	4.67372i	−0.0284217	+	0.197677i
$560$	0.0796102	−	24.9072i	0.00336415	−	1.05252i
$561$	−23.1021	−	14.8468i	−0.975372	−	0.626834i
$562$	27.1547	−	15.7540i	1.14545	−	0.664543i
$563$	13.5793	−	36.4074i	0.572298	−	1.53439i	−0.251704	−	0.967804i	$-0.580991\pi$
$563$	13.5793	−	36.4074i	0.572298	−	1.53439i	0.824002	−	0.566587i	$-0.191736\pi$
$564$	14.6639	+	5.79912i	0.617461	+	0.244187i
$565$	2.42822	−	22.6485i	0.102156	−	0.952828i
$566$	15.8266	−	10.7604i	0.665243	−	0.452292i
$567$	−0.519278	+	0.950987i	−0.0218076	+	0.0399377i
$568$	−16.2465	−	10.2968i	−0.681686	−	0.432042i
$569$	21.9844	+	19.0496i	0.921633	+	0.798600i	0.979856	−	0.199704i	$-0.0639981\pi$
$569$	21.9844	+	19.0496i	0.921633	+	0.798600i	−0.0582232	+	0.998304i	$0.518544\pi$
$570$	12.8995	−	10.9646i	0.540301	−	0.459256i
$571$	2.90188	−	2.51450i	0.121440	−	0.105228i	−0.592024	−	0.805921i	$-0.701671\pi$
$571$	2.90188	−	2.51450i	0.121440	−	0.105228i	0.713464	+	0.700692i	$0.247125\pi$
$572$	−32.6562	−	10.2879i	−1.36542	−	0.430159i
$573$	−4.02395	−	10.7886i	−0.168103	−	0.450702i
$574$	−8.57401	−	3.65029i	−0.357872	−	0.152360i
$575$	−23.6602	−	3.89788i	−0.986700	−	0.162553i
$576$	10.7366	−	9.54307i	0.447358	−	0.397628i
$577$	−10.6275	+	3.96387i	−0.442430	+	0.165018i	−0.560799	−	0.827952i	$-0.689506\pi$
$577$	−10.6275	+	3.96387i	−0.442430	+	0.165018i	0.118369	+	0.992970i	$0.462233\pi$
$578$	43.9115	−	4.28622i	1.82648	−	0.178283i
$579$	2.81873	+	3.25299i	0.117142	+	0.135189i
$580$	3.73266	+	11.9818i	0.154990	+	0.497518i
$581$	−11.4669	+	13.2335i	−0.475726	+	0.549017i
$582$	−4.30168	−	17.5704i	−0.178310	−	0.728318i
$583$	43.9956	+	24.0234i	1.82211	+	0.994949i
$584$	−16.1572	−	3.40819i	−0.668588	−	0.141032i
$585$	18.9613	+	2.03291i	0.783954	+	0.0840506i
$586$	0.189678	+	7.32117i	0.00783552	+	0.302435i
$587$	−8.70929	−	3.24840i	−0.359471	−	0.134076i	0.163239	−	0.986587i	$-0.447806\pi$
$587$	−8.70929	−	3.24840i	−0.359471	−	0.134076i	−0.522709	+	0.852511i	$0.675079\pi$
$588$	1.64396	−	0.203574i	0.0677958	−	0.00839527i
$589$	12.1366	−	18.8849i	0.500080	−	0.778140i
$590$	13.5101	−	35.1969i	0.556204	−	1.44903i
$591$	6.87933	+	0.989098i	0.282978	+	0.0406860i
$592$	0.254417	+	7.89608i	0.0104565	+	0.324527i
$593$	4.12795	−	18.9759i	0.169515	−	0.779247i	−0.811351	−	0.584560i	$-0.801267\pi$
$593$	4.12795	−	18.9759i	0.169515	−	0.779247i	0.980865	−	0.194687i	$-0.0623691\pi$
$594$	−25.5357	+	8.22210i	−1.04774	+	0.337357i
$595$	−10.7033	−	41.8836i	−0.438791	−	1.71706i
$596$	19.6083	−	6.87897i	0.803189	−	0.281774i
$597$	−14.8447	−	14.8447i	−0.607553	−	0.607553i
$598$	32.1199	−	2.45345i	1.31348	−	0.100329i
$599$	−7.39642			−0.302210			−0.151105	−	0.988518i	$-0.548283\pi$
$599$	−7.39642			−0.302210			−0.151105	+	0.988518i	$0.548283\pi$
$600$	8.30072	−	13.1141i	0.338876	−	0.535382i
$601$	0.418223	+	0.122801i	0.0170597	+	0.00500917i	0.290251	−	0.956950i	$-0.406261\pi$
$601$	0.418223	+	0.122801i	0.0170597	+	0.00500917i	−0.273192	+	0.961960i	$0.588079\pi$
$602$	1.78669	−	3.48366i	0.0728201	−	0.141983i
$603$	8.47342	+	1.84328i	0.345064	+	0.0750641i
$604$	15.7848	−	0.818460i	0.642275	−	0.0333026i
$605$	−4.11301	+	1.70508i	−0.167217	+	0.0693214i
$606$	−1.10118	+	9.37708i	−0.0447322	+	0.380918i
$607$	−13.0494	+	2.83873i	−0.529660	+	0.115220i	−0.469439	−	0.882965i	$-0.655544\pi$
$607$	−13.0494	+	2.83873i	−0.529660	+	0.115220i	−0.0602203	+	0.998185i	$0.519180\pi$
$608$	−12.9022	−	24.3937i	−0.523253	−	0.989295i
$609$	−7.80112	+	3.56265i	−0.316117	+	0.144366i
$610$	23.2803	+	5.29651i	0.942591	+	0.214450i
$611$	33.7754	−	4.85617i	1.36641	−	0.196460i
$612$	13.8874	−	20.7057i	0.561365	−	0.836976i
$613$	−1.01372	+	1.85649i	−0.0409438	+	0.0749829i	−0.897350	−	0.441320i	$-0.854510\pi$
$613$	−1.01372	+	1.85649i	−0.0409438	+	0.0749829i	0.856406	+	0.516303i	$0.172692\pi$
$614$	−0.419769	+	0.691944i	−0.0169405	+	0.0279246i
$615$	−3.31310	−	4.76878i	−0.133597	−	0.192296i
$616$	22.8335	+	16.8693i	0.919989	+	0.679683i
$617$	−0.381823	+	5.33858i	−0.0153716	+	0.214923i	0.983961	+	0.178386i	$0.0570874\pi$
$617$	−0.381823	+	5.33858i	−0.0153716	+	0.214923i	−0.999332	+	0.0365376i	$0.988367\pi$
$618$	−17.7575	+	1.73331i	−0.714310	+	0.0697241i
$619$	−10.0965	+	22.1084i	−0.405815	+	0.888610i	0.590833	+	0.806794i	$0.298799\pi$
$619$	−10.0965	+	22.1084i	−0.405815	+	0.888610i	−0.996647	+	0.0818160i	$0.973928\pi$
$620$	5.47338	−	19.8385i	0.219816	−	0.796732i
$621$	19.4192	−	16.1234i	0.779267	−	0.647008i
$622$	−7.82730	+	3.15269i	−0.313846	+	0.126411i
$623$	15.5627	−	5.80458i	0.623506	−	0.232556i
$624$	−6.65343	+	19.7599i	−0.266350	+	0.791030i
$625$	−7.01509	+	23.9956i	−0.280603	+	0.959824i
$626$	−24.2537	+	4.13091i	−0.969373	+	0.165104i
$627$	1.37659	+	19.2473i	0.0549758	+	0.768662i
$628$	2.07857	−	12.6868i	0.0829441	−	0.506258i
$629$	3.86302	+	13.1562i	0.154029	+	0.524574i
$630$	−14.3201	−	6.70497i	−0.570527	−	0.267133i
$631$	−14.4458	+	2.07699i	−0.575077	+	0.0826836i	−0.423716	−	0.905795i	$-0.639275\pi$
$631$	−14.4458	+	2.07699i	−0.575077	+	0.0826836i	−0.151361	+	0.988479i	$0.548366\pi$
$632$	−0.170040	−	26.9594i	−0.00676381	−	1.07239i
$633$	−29.8334	−	11.1273i	−1.18577	−	0.442269i
$634$	45.3506	+	12.0495i	1.80110	+	0.478547i
$635$	29.9420	+	32.1410i	1.18821	+	1.27548i
$636$	15.1516	−	26.5001i	0.600800	−	1.05080i
$637$	2.86960	−	2.14815i	0.113698	−	0.0851129i
$638$	−13.5272	−	4.64998i	−0.535547	−	0.184095i
$639$	−10.2724	+	6.60167i	−0.406370	+	0.261158i
$640$	−17.9441	−	17.8328i	−0.709303	−	0.704904i
$641$	39.7557	+	11.6733i	1.57026	+	0.461069i	0.947076	−	0.321010i	$-0.104022\pi$
$641$	39.7557	+	11.6733i	1.57026	+	0.461069i	0.623180	+	0.782079i	$0.285840\pi$
$642$	12.8159	+	0.583492i	0.505802	+	0.0230286i
$643$	−16.1386	−	16.1386i	−0.636443	−	0.636443i	0.313234	−	0.949676i	$-0.398588\pi$
$643$	−16.1386	−	16.1386i	−0.636443	−	0.636443i	−0.949676	+	0.313234i	$0.898588\pi$
$644$	−25.8474	−	6.73392i	−1.01853	−	0.265354i
$645$	2.09773	−	1.24548i	0.0825981	−	0.0490406i
$646$	−32.2918	−	35.3724i	−1.27050	−	1.39171i
$647$	14.3419	−	7.83129i	0.563840	−	0.307880i	−0.171933	−	0.985109i	$-0.555001\pi$
$647$	14.3419	−	7.83129i	0.563840	−	0.307880i	0.735772	+	0.677229i	$0.236819\pi$
$648$	0.316708	+	1.05397i	0.0124415	+	0.0414039i
$649$	23.2318	+	36.1494i	0.911928	+	1.41899i
$650$	1.50776	−	33.5510i	0.0591393	−	1.31598i
$651$	13.9204	+	2.00145i	0.545582	+	0.0784428i
$652$	−47.0109	+	12.8086i	−1.84109	+	0.501625i
$653$	−38.0361	+	8.27424i	−1.48847	+	0.323796i	−0.881976	−	0.471295i	$-0.843787\pi$
$653$	−38.0361	+	8.27424i	−1.48847	+	0.323796i	−0.606490	+	0.795091i	$0.707423\pi$
$654$	−1.99877	+	7.52274i	−0.0781581	+	0.294162i
$655$	14.0090	+	9.72053i	0.547378	+	0.379813i
$656$	−8.75706	+	3.59153i	−0.341906	+	0.140226i
$657$	−6.28215	+	8.39197i	−0.245090	+	0.327402i
$658$	−27.7931	−	5.29611i	−1.08349	−	0.206464i
$659$	5.50403	−	1.61613i	0.214406	−	0.0629554i	−0.172765	−	0.984963i	$-0.555270\pi$
$659$	5.50403	−	1.61613i	0.214406	−	0.0629554i	0.387172	+	0.922008i	$0.373452\pi$
$660$	6.45297	+	16.4710i	0.251181	+	0.641133i
$661$	3.39161	−	3.91412i	0.131918	−	0.152242i	−0.685947	−	0.727651i	$-0.740612\pi$
$661$	3.39161	−	3.91412i	0.131918	−	0.152242i	0.817865	+	0.575410i	$0.195157\pi$
$662$	−0.775433	+	1.09380i	−0.0301381	+	0.0425119i
$663$	−2.58159	+	36.0954i	−0.100261	+	1.40183i
$664$	1.38064	+	17.7315i	0.0535793	+	0.688116i
$665$	−19.0531	+	23.6578i	−0.738849	+	0.917408i
$666$	4.61453	+	1.96459i	0.178809	+	0.0761261i
$667$	13.4411	−	0.677113i	0.520441	−	0.0262179i
$668$	−0.561092	+	28.6305i	−0.0217093	+	1.10775i
$669$	−9.00551	−	4.11268i	−0.348173	−	0.159005i
$670$	2.31697	−	15.0951i	0.0895124	−	0.583174i
$671$	−20.5660	+	17.8205i	−0.793940	+	0.687953i
$672$	10.5433	−	13.7009i	0.406717	−	0.528523i
$673$	−0.471472	−	6.59204i	−0.0181739	−	0.254105i	−0.998414	−	0.0562942i	$-0.982072\pi$
$673$	−0.471472	−	6.59204i	−0.0181739	−	0.254105i	0.980240	−	0.197810i	$-0.0633830\pi$
$674$	−11.4569	−	6.95036i	−0.441304	−	0.267718i
$675$	−14.2399	−	22.1290i	−0.548092	−	0.851746i
$676$	3.69696	+	18.7569i	0.142191	+	0.721419i
$677$	25.1926	−	33.6533i	0.968229	−	1.29340i	0.0122635	−	0.999925i	$-0.496096\pi$
$677$	25.1926	−	33.6533i	0.968229	−	1.29340i	0.955966	−	0.293478i	$-0.0948128\pi$
$678$	10.8862	−	11.4653i	0.418083	−	0.440323i
$679$	13.4830	+	29.5236i	0.517429	+	1.13301i
$680$	−37.9085	−	22.1551i	−1.45373	−	0.849611i
$681$	−12.8851	−	8.28073i	−0.493757	−	0.317318i
$682$	14.5386	+	18.4075i	0.556710	+	0.704860i
$683$	3.99322	−	2.98929i	0.152796	−	0.114382i	−0.520144	−	0.854078i	$-0.674122\pi$
$683$	3.99322	−	2.98929i	0.152796	−	0.114382i	0.672941	+	0.739696i	$0.265031\pi$
$684$	−17.4952	+	0.907145i	−0.668946	+	0.0346856i
$685$	10.9607	+	32.8994i	0.418787	+	1.25702i
$686$	23.4115	−	7.53815i	0.893857	−	0.287808i
$687$	4.65857	−	2.54377i	0.177735	−	0.0970508i
$688$	−1.24262	−	3.77742i	−0.0473744	−	0.144013i
$689$		−	66.0554i		−	2.51651i
$690$	−11.4037	−	12.1231i	−0.434131	−	0.461520i
$691$		−	2.10376i		−	0.0800309i	−0.999199	−	0.0400154i	$-0.987259\pi$
$691$		−	2.10376i		−	0.0800309i	0.999199	−	0.0400154i	$-0.0127407\pi$
$692$	43.8311	+	21.0645i	1.66621	+	0.800752i
$693$	15.8179	−	8.63724i	0.600873	−	0.328102i
$694$	−6.68645	−	20.7664i	−0.253814	−	0.788282i
$695$	4.55015	+	2.27597i	0.172597	+	0.0863323i
$696$	−2.99254	+	8.18053i	−0.113432	+	0.310082i
$697$	−13.1509	+	9.84463i	−0.498125	+	0.372892i
$698$	−13.6934	+	10.8152i	−0.518301	+	0.409363i
$699$	13.2014	+	8.48402i	0.499322	+	0.320895i
$700$	−10.2258	+	25.9018i	−0.386497	+	0.978997i
$701$	−0.781664	−	1.71161i	−0.0295230	−	0.0646464i	0.894296	−	0.447476i	$-0.147677\pi$
$701$	−0.781664	−	1.71161i	−0.0295230	−	0.0646464i	−0.923819	+	0.382829i	$0.874950\pi$
$702$	25.6360	+	24.3412i	0.967570	+	0.918700i
$703$	5.77392	−	7.71305i	0.217767	−	0.290903i
$704$	28.4871	−	4.46329i	1.07365	−	0.168216i
$705$	−12.9070	−	12.0097i	−0.486105	−	0.452313i
$706$	21.3681	−	35.2230i	0.804200	−	1.32564i
$707$	−1.20851	−	16.8972i	−0.0454507	−	0.635484i
$708$	22.2867	−	13.7133i	0.837586	−	0.515378i
$709$	−3.47553	+	3.01156i	−0.130526	+	0.113102i	−0.717678	−	0.696376i	$-0.754795\pi$
$709$	−3.47553	+	3.01156i	−0.130526	+	0.113102i	0.587151	+	0.809477i	$0.300249\pi$
$710$	12.7232	+	17.3373i	0.477495	+	0.650657i
$711$	−15.5685	−	7.10988i	−0.583863	−	0.266641i
$712$	6.91137	−	15.3899i	0.259015	−	0.576762i
$713$	−19.1426	−	10.9823i	−0.716897	−	0.411291i
$714$	11.7536	−	27.6075i	0.439867	−	1.03318i
$715$	29.8132	+	24.0105i	1.11495	+	0.897943i
$716$	8.81990	−	4.59402i	0.329615	−	0.171686i
$717$	−0.0641841	+	0.897412i	−0.00239700	+	0.0335145i
$718$	−28.1919	−	19.9861i	−1.05211	−	0.745876i
$719$	33.4815	−	38.6397i	1.24865	−	1.44102i	0.396239	−	0.918147i	$-0.370315\pi$
$719$	33.4815	−	38.6397i	1.24865	−	1.44102i	0.852411	−	0.522872i	$-0.175139\pi$
$720$	−15.0655	+	5.56435i	−0.561458	+	0.207371i
$721$	30.7158	−	9.01898i	1.14392	−	0.335885i
$722$	−1.26999	+	6.66472i	−0.0472642	+	0.248035i
$723$	7.30163	−	9.75383i	0.271550	−	0.362749i
$724$	−10.1260	−	4.00450i	−0.376328	−	0.148826i
$725$	0.992732	−	13.9959i	0.0368692	−	0.519795i
$726$	−2.98677	−	0.793576i	−0.110849	−	0.0294524i
$727$	−11.3137	+	2.46114i	−0.419600	+	0.0912785i	−0.417408	−	0.908719i	$-0.637061\pi$
$727$	−11.3137	+	2.46114i	−0.419600	+	0.0912785i	−0.00219228	+	0.999998i	$0.500698\pi$
$728$	5.09033	−	37.0620i	0.188660	−	1.37361i
$729$	17.8428	+	2.56540i	0.660843	+	0.0950149i
$730$	15.4355	+	10.1283i	0.571293	+	0.374867i
$731$	−3.73138	−	5.80614i	−0.138010	−	0.214748i
$732$	10.6046	+	12.7342i	0.391957	+	0.470670i
$733$	4.47126	−	2.44149i	0.165150	−	0.0901787i	−0.394548	−	0.918875i	$-0.629099\pi$
$733$	4.47126	−	2.44149i	0.165150	−	0.0901787i	0.559698	+	0.828697i	$0.310917\pi$
$734$	−31.7522	+	28.9868i	−1.17200	+	1.06992i
$735$	−1.79465	−	0.457494i	−0.0661966	−	0.0168749i
$736$	−23.3129	+	13.8747i	−0.859327	+	0.511427i
$737$	12.3084	+	12.3084i	0.453386	+	0.453386i
$738$	−0.273286	+	6.00247i	−0.0100598	+	0.220954i
$739$	−17.9486	−	5.27019i	−0.660251	−	0.193867i	−0.0655934	−	0.997846i	$-0.520894\pi$
$739$	−17.9486	−	5.27019i	−0.660251	−	0.193867i	−0.594657	+	0.803979i	$0.702712\pi$
$740$	2.95058	−	8.32527i	0.108465	−	0.306043i
$741$	21.3914	−	13.7474i	0.785831	−	0.505023i
$742$	−17.8048	+	51.7958i	−0.653636	+	1.90148i
$743$	27.3800	−	20.4964i	1.00448	−	0.751942i	0.0355697	−	0.999367i	$-0.488675\pi$
$743$	27.3800	−	20.4964i	1.00448	−	0.751942i	0.968907	+	0.247425i	$0.0795845\pi$
$744$	11.3809	−	8.63215i	0.417243	−	0.316470i
$745$	−23.2182	−	0.822401i	−0.850648	−	0.0301304i
$746$	8.02954	−	30.2206i	0.293982	−	1.10646i
$747$	10.5788	+	3.94569i	0.387058	+	0.144365i
$748$	45.9219	−	19.8938i	1.67907	−	0.727389i
$749$	−22.7842	+	3.27588i	−0.832518	+	0.119698i
$750$	−13.9834	+	10.2746i	−0.510601	+	0.375175i
$751$	2.78572	+	9.48729i	0.101652	+	0.346196i	0.994576	−	0.104012i	$-0.0331680\pi$
$751$	2.78572	+	9.48729i	0.101652	+	0.346196i	−0.892924	+	0.450208i	$0.851350\pi$
$752$	−23.6624	+	16.3070i	−0.862880	+	0.594655i
$753$	0.407890	+	5.70304i	0.0148643	+	0.207830i
$754$	3.16485	+	18.5817i	0.115257	+	0.676705i
$755$	−16.7690	−	5.57577i	−0.610286	−	0.202923i
$756$	−13.5409	−	25.9966i	−0.492476	−	0.945488i
$757$	21.9853	−	8.20009i	0.799069	−	0.298037i	0.0834351	−	0.996513i	$-0.473411\pi$
$757$	21.9853	−	8.20009i	0.799069	−	0.298037i	0.715633	+	0.698476i	$0.246138\pi$
$758$	4.50769	+	11.1914i	0.163727	+	0.406490i
$759$	18.8300	−	2.30363i	0.683485	−	0.0836165i
$760$	3.50045	+	30.6536i	0.126975	+	1.11192i
$761$	5.34731	−	11.7090i	0.193840	−	0.424450i	−0.787609	−	0.616176i	$-0.788681\pi$
$761$	5.34731	−	11.7090i	0.193840	−	0.424450i	0.981449	+	0.191726i	$0.0614084\pi$
$762$	2.96199	+	30.3450i	0.107302	+	1.09929i
$763$	0.996316	−	13.9303i	0.0360690	−	0.504311i
$764$	20.4133	+	4.86142i	0.738528	+	0.175880i
$765$	−22.8919	+	15.9041i	−0.827659	+	0.575015i
$766$	14.3665	+	8.71546i	0.519082	+	0.314902i
$767$	27.1375	−	49.6986i	0.979878	−	1.79451i
$768$	−2.37756	−	17.3976i	−0.0857928	−	0.627782i
$769$	−8.54368	+	1.22840i	−0.308093	+	0.0442971i	−0.294627	−	0.955612i	$-0.595195\pi$
$769$	−8.54368	+	1.22840i	−0.308093	+	0.0442971i	−0.0134657	+	0.999909i	$0.504286\pi$
$770$	−16.9054	−	26.8633i	−0.609229	−	0.968085i
$771$	−8.08981	+	3.69449i	−0.291347	+	0.133054i
$772$	−7.78471	+	0.963994i	−0.280178	+	0.0346949i
$773$	2.50655	−	0.545266i	0.0901542	−	0.0196118i	−0.167262	−	0.985912i	$-0.553493\pi$
$773$	2.50655	−	0.545266i	0.0901542	−	0.0196118i	0.257416	+	0.966301i	$0.417129\pi$
$774$	−2.50724	−	0.294432i	−0.0901208	−	0.0105831i
$775$	−13.7778	+	18.4276i	−0.494913	+	0.661938i
$776$	30.9595	+	11.3254i	1.11138	+	0.406558i
$777$	5.89803	+	1.28304i	0.211591	+	0.0460287i
$778$	1.67833	+	0.860778i	0.0601711	+	0.0308604i
$779$	11.0755	+	3.25207i	0.396823	+	0.116518i
$780$	14.9745	−	17.8652i	0.536174	−	0.639678i
$781$	−24.5111			−0.877076
$782$	−33.1334	+	33.4555i	−1.18485	+	1.19637i
$783$	10.4432	+	10.4432i	0.373211	+	0.373211i
$784$	−1.36069	+	2.69478i	−0.0485962	+	0.0962421i
$785$	−7.33066	+	12.3635i	−0.261643	+	0.441271i
$786$	3.62731	+	11.2655i	0.129382	+	0.401827i
$787$	11.5949	−	53.3008i	0.413313	−	1.89997i	−0.0221328	−	0.999755i	$-0.507046\pi$
$787$	11.5949	−	53.3008i	0.413313	−	1.89997i	0.435446	−	0.900215i	$-0.356591\pi$
$788$	−8.48028	+	9.40779i	−0.302097	+	0.335139i
$789$	18.6131	+	2.67616i	0.662644	+	0.0952739i
$790$	−10.8015	+	28.1402i	−0.384300	+	1.00118i
$791$	−15.3365	+	23.8641i	−0.545304	+	0.848510i
$792$	5.04631	−	17.5960i	0.179313	−	0.625245i
$793$	33.5986	+	12.5316i	1.19312	+	0.445012i
$794$	−33.4773	+	0.867334i	−1.18807	+	0.0307805i
$795$	−26.5679	+	21.4226i	−0.942265	+	0.759782i
$796$	37.5364	−	7.39839i	1.33044	−	0.262229i
$797$	−28.4711	−	15.5464i	−1.00850	−	0.550681i	−0.111989	−	0.993709i	$-0.535722\pi$
$797$	−28.4711	−	15.5464i	−1.00850	−	0.550681i	−0.896507	+	0.443029i	$0.853904\pi$
$798$	−20.4791	+	5.01378i	−0.724951	+	0.177486i
$799$	−32.6623	+	37.6943i	−1.15551	+	1.33353i
$800$	11.4220	+	25.8754i	0.403830	+	0.914834i
$801$	−7.01361	−	8.09414i	−0.247814	−	0.285992i
$802$	4.02580	+	41.2435i	0.142156	+	1.45636i
$803$	−19.7158	+	7.35361i	−0.695755	+	0.259503i
$804$	7.64082	−	7.34709i	0.269471	−	0.259112i
$805$	24.1709	+	17.5373i	0.851914	+	0.618109i
$806$	12.1079	−	28.4397i	0.426483	−	1.00175i
$807$	0.204028	+	0.547020i	0.00718213	+	0.0192560i
$808$	−13.0744	−	11.1854i	−0.459955	−	0.393501i
$809$	−16.5707	+	14.3586i	−0.582595	+	0.504821i	−0.895558	−	0.444944i	$-0.853224\pi$
$809$	−16.5707	+	14.3586i	−0.582595	+	0.504821i	0.312964	+	0.949765i	$0.398678\pi$
$810$	0.0994371	−	1.22640i	0.00349386	−	0.0430914i
$811$	41.8742	+	36.2842i	1.47040	+	1.27411i	0.886869	+	0.462021i	$0.152876\pi$
$811$	41.8742	+	36.2842i	1.47040	+	1.27411i	0.583533	+	0.812089i	$0.301670\pi$
$812$	2.52694	−	15.4235i	0.0886783	−	0.541257i
$813$	−9.60475	+	17.5898i	−0.336853	+	0.616901i
$814$	5.66036	+	8.32541i	0.198395	+	0.291805i
$815$	54.1654	+	5.80726i	1.89733	+	0.203420i
$816$	−11.5644	−	28.1969i	−0.404834	−	0.987087i
$817$	−1.69479	+	4.54390i	−0.0592932	+	0.158971i
$818$	0.695661	+	1.19909i	0.0243232	+	0.0419252i
$819$	−19.9791	−	12.8398i	−0.698125	−	0.448658i
$820$	10.5807	−	0.173528i	0.369494	−	0.00605984i
$821$	−0.994729	+	6.91849i	−0.0347163	+	0.241457i	−0.999789	−	0.0205238i	$-0.993467\pi$
$821$	−0.994729	+	6.91849i	−0.0347163	+	0.241457i	0.965073	+	0.261981i	$0.0843757\pi$
$822$	−7.82442	+	22.7619i	−0.272908	+	0.793912i
$823$	15.3023	+	3.32881i	0.533405	+	0.116035i	0.471197	−	0.882028i	$-0.343822\pi$
$823$	15.3023	+	3.32881i	0.533405	+	0.116035i	0.0622081	+	0.998063i	$0.480186\pi$
$824$	15.4024	−	28.6354i	0.536570	−	0.997561i
$825$	−0.0116352	−	19.7780i	−0.000405087	−	0.688581i
$826$	−34.6752	+	31.6552i	−1.20650	+	1.10143i
$827$	19.6235	−	19.6235i	0.682375	−	0.682375i	−0.278160	−	0.960535i	$-0.589725\pi$
$827$	19.6235	−	19.6235i	0.682375	−	0.682375i	0.960535	+	0.278160i	$0.0897246\pi$
$828$	1.75604	+	17.1329i	0.0610266	+	0.595410i
$829$		−	46.6687i		−	1.62087i	−0.585827	−	0.810436i	$-0.699230\pi$
$829$		−	46.6687i		−	1.62087i	0.585827	−	0.810436i	$-0.300770\pi$
$830$	5.78315	−	19.0249i	0.200736	−	0.660363i
$831$	2.54409	−	8.66437i	0.0882535	−	0.300564i
$832$	−23.1526	−	30.1285i	−0.802672	−	1.04452i
$833$	−1.11374	+	5.11978i	−0.0385888	+	0.177390i
$834$	1.54965	+	3.17309i	0.0536599	+	0.109875i
$835$	12.2433	−	29.5826i	0.423698	−	1.02375i
$836$	−30.5281	−	17.4547i	−1.05584	−	0.603682i
$837$	−5.14808	−	23.6653i	−0.177944	−	0.817993i
$838$	0.610533	−	0.354205i	0.0210905	−	0.0122358i
$839$	19.2108	+	42.0658i	0.663230	+	1.45227i	0.879481	+	0.475934i	$0.157890\pi$
$839$	19.2108	+	42.0658i	0.663230	+	1.45227i	−0.216251	+	0.976338i	$0.569383\pi$
$840$	−16.5574	+	9.97232i	−0.571284	+	0.344078i
$841$	−3.00642	−	20.9101i	−0.103670	−	0.721039i
$842$	−8.95934	+	47.0172i	−0.308759	+	1.62032i
$843$	−21.3822	−	11.6755i	−0.736441	−	0.402127i
$844$	47.1253	−	33.8573i	1.62212	−	1.16542i
$845$	3.78889	−	21.0358i	0.130342	−	0.723653i
$846$	3.06313	+	17.9845i	0.105313	+	0.618318i
$847$	5.53078	+	0.395569i	0.190040	+	0.0135919i
$848$	24.7272	+	49.8324i	0.849135	+	1.71125i
$849$	−13.5094	−	6.16956i	−0.463643	−	0.211739i
$850$	30.4495	+	38.5060i	1.04441	+	1.32075i
$851$	−7.85870	−	5.28765i	−0.269393	−	0.181258i
$852$	−0.292467	+	14.9236i	−0.0100198	+	0.511273i
$853$	9.40205	+	25.2079i	0.321920	+	0.863102i	0.992608	+	0.121362i	$0.0387262\pi$
$853$	9.40205	+	25.2079i	0.321920	+	0.863102i	−0.670688	+	0.741739i	$0.734001\pi$
$854$	−22.9677	−	18.8827i	−0.785940	−	0.646153i
$855$	18.5860	+	6.17995i	0.635628	+	0.211350i
$856$	−13.8926	+	18.8045i	−0.474841	+	0.642723i
$857$	17.2766	−	1.23565i	0.590157	−	0.0422088i	0.226932	−	0.973911i	$-0.427130\pi$
$857$	17.2766	−	1.23565i	0.590157	−	0.0422088i	0.363224	+	0.931702i	$0.381676\pi$
$858$	6.31830	+	25.8074i	0.215703	+	0.881052i
$859$	−31.1277	+	9.13992i	−1.06206	+	0.311850i	−0.765682	−	0.643219i	$-0.777598\pi$
$859$	−31.1277	+	9.13992i	−1.06206	+	0.311850i	−0.296382	+	0.955069i	$0.595780\pi$
$860$	−0.244407	+	4.43921i	−0.00833421	+	0.151376i
$861$	1.02915	+	7.15789i	0.0350733	+	0.243940i
$862$	−20.5415	−	19.5040i	−0.699645	−	0.664308i
$863$	−6.37939	+	17.1038i	−0.217157	+	0.582221i	−0.999157	−	0.0410582i	$-0.986927\pi$
$863$	−6.37939	+	17.1038i	−0.217157	+	0.582221i	0.782000	+	0.623279i	$0.214200\pi$
$864$	−28.4518	−	8.76650i	−0.967950	−	0.298242i
$865$	−37.0604	−	39.7822i	−1.26009	−	1.35264i
$866$	−6.00344	−	0.705000i	−0.204005	−	0.0239569i
$867$	−20.5181	−	27.4090i	−0.696833	−	0.930859i
$868$	−17.1599	+	19.0367i	−0.582445	+	0.646149i
$869$	−18.5740	−	28.9018i	−0.630081	−	0.980425i
$870$	6.44726	−	7.29921i	0.218583	−	0.247466i
$871$	6.46231	−	22.0086i	0.218967	−	0.745733i
$872$	−9.35667	−	10.6615i	−0.316857	−	0.361046i
$873$	14.7983	−	14.7983i	0.500848	−	0.500848i
$874$	32.7716	+	4.55019i	1.10852	+	0.153912i
$875$	21.1953	−	22.8057i	0.716531	−	0.770972i
$876$	4.24199	+	12.0917i	0.143324	+	0.408540i
$877$	−0.713440	−	1.30657i	−0.0240911	−	0.0441196i	0.865356	−	0.501157i	$-0.167092\pi$
$877$	−0.713440	−	1.30657i	−0.0240911	−	0.0441196i	−0.889447	+	0.457038i	$0.848910\pi$
$878$	−7.65832	+	14.9321i	−0.258456	+	0.503933i
$879$	4.78108	−	3.07261i	0.161262	−	0.103637i
$880$	−31.4793	−	6.95335i	−1.06117	−	0.234397i
$881$	0.957651	−	6.66061i	0.0322641	−	0.224402i	−0.967310	−	0.253598i	$-0.918386\pi$
$881$	0.957651	−	6.66061i	0.0322641	−	0.224402i	0.999574	+	0.0291967i	$0.00929492\pi$
$882$	1.18784	+	1.50395i	0.0399967	+	0.0506405i
$883$	−0.774462	−	3.56015i	−0.0260627	−	0.119808i	0.962278	−	0.272070i	$-0.0877081\pi$
$883$	−0.774462	−	3.56015i	−0.0260627	−	0.119808i	−0.988340	+	0.152261i	$0.951344\pi$
$884$	−52.0096	−	40.5480i	−1.74927	−	1.36378i
$885$	−28.7901	+	5.20305i	−0.967769	+	0.174899i
$886$	−31.7726	+	0.823167i	−1.06742	+	0.0276549i
$887$	28.8218	+	21.5758i	0.967743	+	0.724443i	0.961291	−	0.275536i	$-0.0888554\pi$
$887$	28.8218	+	21.5758i	0.967743	+	0.724443i	0.00645188	+	0.999979i	$0.497946\pi$
$888$	5.13646	−	3.34696i	0.172368	−	0.112317i
$889$	−15.4122	−	52.4891i	−0.516908	−	1.76043i
$890$	−13.4635	+	13.2100i	−0.451299	+	0.442801i
$891$	1.05988	+	0.918395i	0.0355075	+	0.0307674i
$892$	15.3661	−	9.45498i	0.514496	−	0.316576i
$893$	34.9577	+	2.50022i	1.16981	+	0.0836667i
$894$	−12.4564	−	10.2409i	−0.416603	−	0.342506i
$895$	−11.0544	+	1.19176i	−0.369507	+	0.0398361i
$896$	10.0336	+	29.8652i	0.335200	+	0.997726i
$897$	−14.5560	−	20.3233i	−0.486012	−	0.678574i
$898$	−26.4913	+	10.6702i	−0.884027	+	0.356069i
$899$	5.36447	−	11.7465i	0.178915	−	0.391769i
$900$	17.9526	+	0.341265i	0.598421	+	0.0113755i
$901$	63.2283	+	72.9694i	2.10644	+	2.43096i
$902$	−6.97562	+	9.83961i	−0.232263	+	0.327623i
$903$	−3.03047	+	0.216743i	−0.100848	+	0.00721277i
$904$	6.30198	+	28.1148i	0.209601	+	0.935086i
$905$	8.91275	+	8.29317i	0.296270	+	0.275674i
$906$	−6.89640	−	10.1434i	−0.229118	−	0.336992i
$907$	−12.2338	−	9.15814i	−0.406218	−	0.304091i	0.376560	−	0.926392i	$-0.377107\pi$
$907$	−12.2338	−	9.15814i	−0.406218	−	0.304091i	−0.782778	+	0.622301i	$0.786198\pi$
$908$	25.6126	−	11.0956i	0.849985	−	0.368222i
$909$	−9.93601	+	4.53762i	−0.329557	+	0.150503i
$910$	−20.3928	+	36.5172i	−0.676015	+	1.21053i
$911$	21.6465	−	33.6827i	0.717182	−	1.11596i	−0.270987	−	0.962583i	$-0.587350\pi$
$911$	21.6465	−	33.6827i	0.717182	−	1.11596i	0.988168	−	0.153373i	$-0.0490137\pi$
$912$	−10.9915	+	18.3787i	−0.363965	+	0.608580i
$913$	13.5821	+	18.1435i	0.449500	+	0.600462i
$914$	−10.0530	−	20.5847i	−0.332522	−	0.680880i
$915$	−5.85618	−	17.5777i	−0.193599	−	0.581102i
$916$	−0.878976	+	9.63293i	−0.0290422	+	0.318281i
$917$	−10.1768	−	18.6375i	−0.336068	−	0.615463i
$918$	−51.6188	−	2.35015i	−1.70367	−	0.0775664i
$919$	34.7977			1.14787			0.573935	−	0.818901i	$-0.305416\pi$
$919$	34.7977			1.14787			0.573935	+	0.818901i	$0.305416\pi$
$920$	29.9243	−	4.95314i	0.986576	−	0.163300i
$921$	0.628045			0.0206948
$922$	32.0692	+	1.46007i	1.05614	+	0.0480850i
$923$	15.4796	+	28.3487i	0.509516	+	0.933108i
$924$	2.00190	−	21.9394i	0.0658577	−	0.721752i
$925$	−6.46251	+	7.46700i	−0.212486	+	0.245513i
$926$	−25.2136	−	51.6280i	−0.828571	−	1.69660i
$927$	−12.3701	−	16.5245i	−0.406287	−	0.542736i
$928$	−9.34345	−	12.8334i	−0.306714	−	0.421276i
$929$	0.584367	−	0.909293i	0.0191725	−	0.0298330i	−0.831535	−	0.555472i	$-0.812537\pi$
$929$	0.584367	−	0.909293i	0.0191725	−	0.0298330i	0.850708	+	0.525639i	$0.176174\pi$
$930$	−15.3654	+	4.35350i	−0.503851	+	0.142757i
$931$	3.34896	−	1.52942i	0.109758	−	0.0501246i
$932$	−26.2414	+	11.3680i	−0.859566	+	0.372373i
$933$	5.24221	+	3.92427i	0.171622	+	0.128475i
$934$	15.9880	+	23.5157i	0.523145	+	0.769456i
$935$	−55.9167	+	2.01354i	−1.82867	+	0.0658497i
$936$	−23.5378	+	5.27603i	−0.769356	+	0.172452i
$937$	−29.1225	+	2.08289i	−0.951392	+	0.0680449i	−0.538400	−	0.842690i	$-0.680971\pi$
$937$	−29.1225	+	2.08289i	−0.951392	+	0.0680449i	−0.412992	+	0.910734i	$0.635516\pi$
$938$	−10.9996	+	15.5157i	−0.359148	+	0.506604i
$939$	12.5029	+	14.4291i	0.408015	+	0.470875i
$940$	31.2787	−	7.34346i	1.02020	−	0.239517i
$941$	−20.4803	+	44.8457i	−0.667640	+	1.46193i	0.207588	+	0.978216i	$0.433439\pi$
$941$	−20.4803	+	44.8457i	−0.667640	+	1.46193i	−0.875228	+	0.483711i	$0.839288\pi$
$942$	−9.25400	+	3.72734i	−0.301512	+	0.121443i
$943$	2.64525	−	11.0355i	0.0861411	−	0.359364i
$944$	−1.86843	+	47.6514i	−0.0608123	+	1.55092i
$945$	3.51270	+	32.5828i	0.114268	+	1.05992i
$946$	−3.91436	−	3.21815i	−0.127267	−	0.104631i
$947$	−41.2596	−	2.95095i	−1.34076	−	0.0958929i	−0.617554	−	0.786528i	$-0.711876\pi$
$947$	−41.2596	−	2.95095i	−1.34076	−	0.0958929i	−0.723203	+	0.690635i	$0.757331\pi$
$948$	−17.8184	+	10.9639i	−0.578716	+	0.356092i
$949$	20.9561	+	18.1586i	0.680263	+	0.589451i
$950$	8.83816	−	33.3431i	0.286748	−	1.08179i
$951$	−10.2590	−	34.9389i	−0.332671	−	1.13297i
$952$	29.8526	+	45.8137i	0.967529	+	1.48483i
$953$	−10.7013	−	8.01090i	−0.346650	−	0.259499i	0.411738	−	0.911302i	$-0.364922\pi$
$953$	−10.7013	−	8.01090i	−0.346650	−	0.259499i	−0.758388	+	0.651804i	$0.774013\pi$
$954$	35.3042	−	0.914665i	1.14301	−	0.0296134i
$955$	−19.2753	−	13.3747i	−0.623735	−	0.432795i
$956$	−1.29308	−	1.00812i	−0.0418211	−	0.0326048i
$957$	2.35953	+	10.8466i	0.0762727	+	0.350620i
$958$	−24.9755	−	31.6218i	−0.806920	−	1.02165i
$959$	6.14599	−	42.7463i	0.198464	−	1.38035i
$960$	−4.60915	+	19.0832i	−0.148760	+	0.615907i
$961$	8.26436	−	5.31118i	0.266592	−	0.171328i
$962$	6.05418	−	11.8043i	0.195195	−	0.380587i
$963$	7.11317	+	13.0268i	0.229219	+	0.419782i
$964$	7.35043	+	20.9522i	0.236741	+	0.674825i
$965$	8.49826	+	2.16639i	0.273569	+	0.0697386i
$966$	5.93575	+	19.8595i	0.190980	+	0.638969i
$967$	14.9528	−	14.9528i	0.480848	−	0.480848i	−0.424554	−	0.905402i	$-0.639569\pi$
$967$	14.9528	−	14.9528i	0.480848	−	0.480848i	0.905402	+	0.424554i	$0.139569\pi$
$968$	4.23298	−	3.71490i	0.136053	−	0.119401i
$969$	−10.4714	+	35.6622i	−0.336388	+	1.14563i
$970$	−27.6241	−	24.3999i	−0.886956	−	0.783433i
$971$	17.2541	+	26.8479i	0.553709	+	0.861589i	0.999436	−	0.0335805i	$-0.0106910\pi$
$971$	17.2541	+	26.8479i	0.553709	+	0.861589i	−0.445727	+	0.895169i	$0.647055\pi$
$972$	−20.5708	+	22.8207i	−0.659810	+	0.731975i
$973$	−3.79700	−	5.07219i	−0.121726	−	0.162607i
$974$	18.2583	+	2.14412i	0.585033	+	0.0687020i
$975$	−22.8672	+	12.5039i	−0.732335	+	0.400445i
$976$	−30.0380	+	3.12340i	−0.961494	+	0.0999778i
$977$	−1.40952	+	3.77907i	−0.0450946	+	0.120903i	−0.957545	−	0.288284i	$-0.906915\pi$
$977$	−1.40952	+	3.77907i	−0.0450946	+	0.120903i	0.912450	+	0.409188i	$0.134188\pi$
$978$	27.4201	+	26.0352i	0.876798	+	0.832513i
$979$	−3.05957	−	21.2798i	−0.0977843	−	0.680104i
$980$	2.51418	−	2.25179i	0.0803126	−	0.0719306i
$981$	−8.64042	+	2.53706i	−0.275867	+	0.0810019i
$982$	−5.58083	−	22.7952i	−0.178092	−	0.727425i
$983$	−11.8206	+	0.845429i	−0.377020	+	0.0269650i	−0.258564	−	0.965994i	$-0.583249\pi$
$983$	−11.8206	+	0.845429i	−0.377020	+	0.0269650i	−0.118457	+	0.992959i	$0.537795\pi$
$984$	5.90760	+	4.36451i	0.188327	+	0.139135i
$985$	12.6610	−	6.34232i	0.403414	−	0.202083i
$986$	−21.2825	−	17.4972i	−0.677774	−	0.557225i
$987$	7.67287	+	20.5718i	0.244230	+	0.654806i
$988$	−0.907978	+	46.3309i	−0.0288866	+	1.47398i
$989$	4.54529	+	1.43929i	0.144532	+	0.0457667i
$990$	−12.4199	+	16.2665i	−0.394731	+	0.516984i
$991$	−15.0134	−	6.85638i	−0.476915	−	0.217800i	0.162429	−	0.986720i	$-0.448067\pi$
$991$	−15.0134	−	6.85638i	−0.476915	−	0.217800i	−0.639345	+	0.768920i	$0.720794\pi$
$992$	1.51188	+	25.9875i	0.0480024	+	0.825104i
$993$	1.03782	+	0.0742266i	0.0329343	+	0.00235551i
$994$	−4.49670	−	26.4014i	−0.142627	−	0.837401i
$995$	−42.0970	−	7.58235i	−1.33457	−	0.240377i
$996$	11.2087	−	8.05293i	0.355162	−	0.255167i
$997$	13.1531	+	7.18212i	0.416562	+	0.227460i	0.673840	−	0.738877i	$-0.264644\pi$
$997$	13.1531	+	7.18212i	0.416562	+	0.227460i	−0.257278	+	0.966337i	$0.582826\pi$
$998$	1.50096	−	7.87677i	0.0475119	−	0.249335i
$999$	−1.47930	−	10.2888i	−0.0468030	−	0.325522i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	460.2.w.a.167.68	yes	1360
4.3	odd	2	inner	460.2.w.a.167.53	yes	1360
5.3	odd	4	inner	460.2.w.a.443.34	yes	1360
20.3	even	4	inner	460.2.w.a.443.19	yes	1360
23.4	even	11	inner	460.2.w.a.27.19	✓	1360
92.27	odd	22	inner	460.2.w.a.27.34	yes	1360
115.73	odd	44	inner	460.2.w.a.303.53	yes	1360
460.303	even	44	inner	460.2.w.a.303.68	yes	1360

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
460.2.w.a.27.19	✓	1360	23.4	even	11	inner
460.2.w.a.27.34	yes	1360	92.27	odd	22	inner
460.2.w.a.167.53	yes	1360	4.3	odd	2	inner
460.2.w.a.167.68	yes	1360	1.1	even	1	trivial
460.2.w.a.303.53	yes	1360	115.73	odd	44	inner
460.2.w.a.303.68	yes	1360	460.303	even	44	inner
460.2.w.a.443.19	yes	1360	20.3	even	4	inner
460.2.w.a.443.34	yes	1360	5.3	odd	4	inner

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:	\( N \)	\(=\)	\( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	460.w (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(1.41275 + 0.0643210i) q^{2} +(-0.525955 - 0.963215i) q^{3} +(1.99173 + 0.181739i) q^{4} +(-1.99984 - 1.00031i) q^{5} +(-0.681088 - 1.39461i) q^{6} +(1.66882 + 2.22929i) q^{7} +(2.80212 + 0.384861i) q^{8} +(0.970769 - 1.51055i) q^{9} +O(q^{10})\)	\(q+(1.41275 + 0.0643210i) q^{2} +(-0.525955 - 0.963215i) q^{3} +(1.99173 + 0.181739i) q^{4} +(-1.99984 - 1.00031i) q^{5} +(-0.681088 - 1.39461i) q^{6} +(1.66882 + 2.22929i) q^{7} +(2.80212 + 0.384861i) q^{8} +(0.970769 - 1.51055i) q^{9} +(-2.76094 - 1.54183i) q^{10} +(3.27861 - 1.49729i) q^{11} +(-0.872505 - 2.01405i) q^{12} +(-3.80227 - 2.84634i) q^{13} +(2.21424 + 3.25677i) q^{14} +(0.0883099 + 2.45240i) q^{15} +(3.93394 + 0.723948i) q^{16} +(6.92477 - 0.495269i) q^{17} +(1.46861 - 2.07158i) q^{18} +(-3.19458 - 3.68675i) q^{19} +(-3.80134 - 2.35580i) q^{20} +(1.26956 - 2.77994i) q^{21} +(4.72817 - 1.90442i) q^{22} +(-3.46185 + 3.31898i) q^{23} +(-1.10309 - 2.90146i) q^{24} +(2.99874 + 4.00094i) q^{25} +(-5.18857 - 4.26573i) q^{26} +(-5.24954 - 0.375455i) q^{27} +(2.91869 + 4.74342i) q^{28} +(-2.12080 - 1.83768i) q^{29} +(-0.0329808 + 3.47031i) q^{30} +(1.29646 + 4.41535i) q^{31} +(5.51111 + 1.27579i) q^{32} +(-3.16662 - 2.37050i) q^{33} +(9.81482 - 0.254284i) q^{34} +(-1.10740 - 6.12758i) q^{35} +(2.20803 - 2.83217i) q^{36} +(0.419826 + 1.92991i) q^{37} +(-4.27601 - 5.41393i) q^{38} +(-0.741816 + 5.15945i) q^{39} +(-5.21882 - 3.57266i) q^{40} +(-1.99060 + 1.27928i) q^{41} +(1.97238 - 3.84571i) q^{42} +(-0.476441 - 0.872536i) q^{43} +(6.80221 - 2.38634i) q^{44} +(-3.45240 + 2.04978i) q^{45} +(-5.10420 + 4.46622i) q^{46} +(-5.08007 + 5.08007i) q^{47} +(-1.37176 - 4.17000i) q^{48} +(-0.212626 + 0.724136i) q^{49} +(3.97913 + 5.84521i) q^{50} +(-4.11917 - 6.40955i) q^{51} +(-7.05578 - 6.36015i) q^{52} +(8.33446 + 11.1335i) q^{53} +(-7.39214 - 0.868079i) q^{54} +(-8.05447 - 0.285294i) q^{55} +(3.81828 + 6.88900i) q^{56} +(-1.87092 + 5.01613i) q^{57} +(-2.87795 - 2.73260i) q^{58} +(1.69668 + 11.8007i) q^{59} +(-0.269807 + 4.90055i) q^{60} +(-7.24417 + 2.12708i) q^{61} +(1.54758 + 6.32118i) q^{62} +(4.98749 - 0.356712i) q^{63} +(7.70376 + 2.15686i) q^{64} +(4.75670 + 9.49569i) q^{65} +(-4.32117 - 3.55260i) q^{66} +(1.68770 + 4.52489i) q^{67} +(13.8822 + 0.272060i) q^{68} +(5.01767 + 1.58887i) q^{69} +(-1.17034 - 8.72796i) q^{70} +(-6.18592 - 2.82501i) q^{71} +(3.30156 - 3.85912i) q^{72} +(-5.82325 - 0.416487i) q^{73} +(0.468976 + 2.75348i) q^{74} +(2.27656 - 4.99275i) q^{75} +(-5.69271 - 7.92357i) q^{76} +(8.80933 + 4.81026i) q^{77} +(-1.37986 + 7.24129i) q^{78} +(-1.35651 - 9.43474i) q^{79} +(-7.14309 - 5.38296i) q^{80} +(0.161636 + 0.353934i) q^{81} +(-2.89451 + 1.67927i) q^{82} +(1.33661 + 6.14431i) q^{83} +(3.03383 - 5.30616i) q^{84} +(-14.3439 - 5.93648i) q^{85} +(-0.616969 - 1.26332i) q^{86} +(-0.654638 + 3.00932i) q^{87} +(9.76332 - 2.93378i) q^{88} +(1.68044 - 5.72305i) q^{89} +(-5.00923 + 2.67376i) q^{90} -13.2264i q^{91} +(-7.49823 + 5.98134i) q^{92} +(3.57105 - 3.57105i) q^{93} +(-7.50363 + 6.85012i) q^{94} +(2.70076 + 10.5685i) q^{95} +(-1.66973 - 5.97939i) q^{96} +(11.3889 + 2.47750i) q^{97} +(-0.346964 + 1.00935i) q^{98} +(0.921046 - 6.40602i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1360 q - 18 q^{2} - 36 q^{5} - 44 q^{6} - 18 q^{8}+O(q^{10}) \) 1360 * q - 18 * q^2 - 36 * q^5 - 44 * q^6 - 18 * q^8	\( 1360 q - 18 q^{2} - 36 q^{5} - 44 q^{6} - 18 q^{8} - 18 q^{10} - 6 q^{12} - 36 q^{13} - 44 q^{16} - 36 q^{17} - 38 q^{18} - 14 q^{20} - 88 q^{21} - 28 q^{22} - 36 q^{25} - 36 q^{26} - 34 q^{28} + 2 q^{30} + 2 q^{32} - 60 q^{33} - 36 q^{36} - 36 q^{37} - 10 q^{38} + 2 q^{40} - 56 q^{41} - 202 q^{42} - 120 q^{45} - 44 q^{46} - 50 q^{48} - 34 q^{50} - 250 q^{52} - 84 q^{53} - 84 q^{56} - 44 q^{57} - 58 q^{58} - 42 q^{60} - 136 q^{61} - 82 q^{62} - 68 q^{65} - 84 q^{66} - 4 q^{68} + 16 q^{70} - 104 q^{72} - 36 q^{73} + 4 q^{76} - 44 q^{77} - 50 q^{78} + 204 q^{80} + 80 q^{81} - 10 q^{82} - 252 q^{85} + 44 q^{86} - 50 q^{88} + 264 q^{90} - 22 q^{92} - 88 q^{93} + 52 q^{96} - 36 q^{97} + 30 q^{98}+O(q^{100}) \) 1360 * q - 18 * q^2 - 36 * q^5 - 44 * q^6 - 18 * q^8 - 18 * q^10 - 6 * q^12 - 36 * q^13 - 44 * q^16 - 36 * q^17 - 38 * q^18 - 14 * q^20 - 88 * q^21 - 28 * q^22 - 36 * q^25 - 36 * q^26 - 34 * q^28 + 2 * q^30 + 2 * q^32 - 60 * q^33 - 36 * q^36 - 36 * q^37 - 10 * q^38 + 2 * q^40 - 56 * q^41 - 202 * q^42 - 120 * q^45 - 44 * q^46 - 50 * q^48 - 34 * q^50 - 250 * q^52 - 84 * q^53 - 84 * q^56 - 44 * q^57 - 58 * q^58 - 42 * q^60 - 136 * q^61 - 82 * q^62 - 68 * q^65 - 84 * q^66 - 4 * q^68 + 16 * q^70 - 104 * q^72 - 36 * q^73 + 4 * q^76 - 44 * q^77 - 50 * q^78 + 204 * q^80 + 80 * q^81 - 10 * q^82 - 252 * q^85 + 44 * q^86 - 50 * q^88 + 264 * q^90 - 22 * q^92 - 88 * q^93 + 52 * q^96 - 36 * q^97 + 30 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more