LMFDB - Embedded newform 572.2.bn.a.95.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(95,572)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(572, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([15, 21, 5]))

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

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

chi := DirichletCharacter("572.95");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.bn (of order $30$, degree $8$, 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:	$4.56744299562$
Analytic rank:	$0$
Dimension:	$640$
Relative dimension:	$80$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			95.7
Character	$\chi$	$=$	572.95
Dual form			572.2.bn.a.283.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.38137 - 0.302995i) q^{2} +(-0.868428 + 0.781936i) q^{3} +(1.81639 + 0.837098i) q^{4} +(1.42384 + 1.95975i) q^{5} +(1.43655 - 0.817017i) q^{6} +(-2.34374 - 2.11032i) q^{7} +(-2.25548 - 1.70670i) q^{8} +(-0.170842 + 1.62546i) q^{9} +O(q^{10})$	\(q+(-1.38137 - 0.302995i) q^{2} +(-0.868428 + 0.781936i) q^{3} +(1.81639 + 0.837098i) q^{4} +(1.42384 + 1.95975i) q^{5} +(1.43655 - 0.817017i) q^{6} +(-2.34374 - 2.11032i) q^{7} +(-2.25548 - 1.70670i) q^{8} +(-0.170842 + 1.62546i) q^{9} +(-1.37306 - 3.13856i) q^{10} +(3.11466 + 1.13968i) q^{11} +(-2.23196 + 0.693340i) q^{12} +(-1.56279 + 3.24926i) q^{13} +(2.59817 + 3.62528i) q^{14} +(-2.76890 - 0.588548i) q^{15} +(2.59853 + 3.04099i) q^{16} +(1.00824 - 2.26454i) q^{17} +(0.728502 - 2.19360i) q^{18} +(0.884301 + 4.16031i) q^{19} +(0.945745 + 4.75156i) q^{20} +3.68550 q^{21} +(-3.95720 - 2.51805i) q^{22} +(-5.70725 - 3.29508i) q^{23} +(3.29325 - 0.281490i) q^{24} +(-0.268206 + 0.825454i) q^{25} +(3.14331 - 4.01493i) q^{26} +(-3.18327 - 4.38139i) q^{27} +(-2.49061 - 5.79510i) q^{28} +(-1.02798 + 4.83626i) q^{29} +(3.64656 + 1.65197i) q^{30} +(2.36910 + 1.72125i) q^{31} +(-2.66814 - 4.98809i) q^{32} +(-3.59601 + 1.44574i) q^{33} +(-2.07889 + 2.82268i) q^{34} +(0.798571 - 7.59790i) q^{35} +(-1.67098 + 2.80945i) q^{36} +(-2.30543 + 10.8462i) q^{37} +(0.0390015 - 6.01488i) q^{38} +(-1.18354 - 4.04375i) q^{39} +(0.133269 - 6.85023i) q^{40} +(-7.19829 - 7.99451i) q^{41} +(-5.09106 - 1.11669i) q^{42} +(-3.54724 - 6.14400i) q^{43} +(4.70342 + 4.67738i) q^{44} +(-3.42874 + 1.97958i) q^{45} +(6.88546 + 6.28101i) q^{46} +(-2.87748 + 8.85598i) q^{47} +(-4.63450 - 0.608994i) q^{48} +(0.308000 + 2.93042i) q^{49} +(0.620601 - 1.05900i) q^{50} +(0.895141 + 2.75496i) q^{51} +(-5.55858 + 4.59371i) q^{52} +(6.84093 + 4.97022i) q^{53} +(3.06975 + 7.01686i) q^{54} +(2.20130 + 7.72668i) q^{55} +(1.68457 + 8.75984i) q^{56} +(-4.02105 - 2.92146i) q^{57} +(2.88538 - 6.36921i) q^{58} +(-9.13027 + 10.1402i) q^{59} +(-4.53672 - 3.38687i) q^{60} +(-1.69505 + 3.80713i) q^{61} +(-2.75109 - 3.09552i) q^{62} +(3.83064 - 3.44912i) q^{63} +(2.17434 + 7.69885i) q^{64} +(-8.59289 + 1.56375i) q^{65} +(5.40549 - 0.907534i) q^{66} +(-1.20894 + 2.09394i) q^{67} +(3.72699 - 3.26928i) q^{68} +(7.53288 - 1.60116i) q^{69} +(-3.40525 + 10.2536i) q^{70} +(-7.68076 - 3.41970i) q^{71} +(3.15950 - 3.37460i) q^{72} +(1.80501 + 5.55525i) q^{73} +(6.47100 - 14.2841i) q^{74} +(-0.412534 - 0.926567i) q^{75} +(-1.87635 + 8.29699i) q^{76} +(-4.89489 - 9.24404i) q^{77} +(0.409680 + 5.94453i) q^{78} +(1.82433 + 1.32545i) q^{79} +(-2.25968 + 9.42236i) q^{80} +(1.39432 + 0.296372i) q^{81} +(7.52123 + 13.2245i) q^{82} +(3.61003 + 4.96878i) q^{83} +(6.69430 + 3.08513i) q^{84} +(5.87349 - 1.24845i) q^{85} +(3.03847 + 9.56196i) q^{86} +(-2.88892 - 5.00375i) q^{87} +(-5.07996 - 7.88632i) q^{88} +(-10.9834 - 6.34125i) q^{89} +(5.33617 - 1.69565i) q^{90} +(10.5197 - 4.31745i) q^{91} +(-7.60828 - 10.7627i) q^{92} +(-3.40331 + 0.357702i) q^{93} +(6.65819 - 11.3616i) q^{94} +(-6.89406 + 7.65663i) q^{95} +(6.21745 + 2.24548i) q^{96} +(8.70931 + 0.915385i) q^{97} +(0.462440 - 4.14133i) q^{98} +(-2.38461 + 4.86805i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 640 q - 15 q^{2} - 3 q^{4} - 15 q^{6} - 78 q^{9}+O(q^{10}) $ 640 * q - 15 * q^2 - 3 * q^4 - 15 * q^6 - 78 * q^9	$ 640 q - 15 q^{2} - 3 q^{4} - 15 q^{6} - 78 q^{9} - 4 q^{12} - 20 q^{13} - 12 q^{14} - 19 q^{16} - 10 q^{17} - 45 q^{20} - 15 q^{22} - 15 q^{24} + 104 q^{25} - 20 q^{26} - 15 q^{28} - 10 q^{29} + 45 q^{30} - 24 q^{33} + 4 q^{36} - 18 q^{37} - 14 q^{38} - 20 q^{40} - 30 q^{41} - 13 q^{42} - 108 q^{45} - 15 q^{46} + 35 q^{48} - 74 q^{49} - 90 q^{50} + 15 q^{52} - 8 q^{53} + 50 q^{56} + 27 q^{58} - 10 q^{61} - 5 q^{62} - 84 q^{64} - 146 q^{66} - 70 q^{68} - 26 q^{69} - 15 q^{72} - 55 q^{74} + 44 q^{77} + 24 q^{78} - 39 q^{80} + 30 q^{81} - 29 q^{82} + 30 q^{84} - 30 q^{85} - 75 q^{88} - 24 q^{89} + 30 q^{90} + 14 q^{92} + 66 q^{93} - 5 q^{94} - 30 q^{97}+O(q^{100}) $ 640 * q - 15 * q^2 - 3 * q^4 - 15 * q^6 - 78 * q^9 - 4 * q^12 - 20 * q^13 - 12 * q^14 - 19 * q^16 - 10 * q^17 - 45 * q^20 - 15 * q^22 - 15 * q^24 + 104 * q^25 - 20 * q^26 - 15 * q^28 - 10 * q^29 + 45 * q^30 - 24 * q^33 + 4 * q^36 - 18 * q^37 - 14 * q^38 - 20 * q^40 - 30 * q^41 - 13 * q^42 - 108 * q^45 - 15 * q^46 + 35 * q^48 - 74 * q^49 - 90 * q^50 + 15 * q^52 - 8 * q^53 + 50 * q^56 + 27 * q^58 - 10 * q^61 - 5 * q^62 - 84 * q^64 - 146 * q^66 - 70 * q^68 - 26 * q^69 - 15 * q^72 - 55 * q^74 + 44 * q^77 + 24 * q^78 - 39 * q^80 + 30 * q^81 - 29 * q^82 + 30 * q^84 - 30 * q^85 - 75 * q^88 - 24 * q^89 + 30 * q^90 + 14 * q^92 + 66 * q^93 - 5 * q^94 - 30 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/572\mathbb{Z}\right)^\times$.

$n$	$287$	$353$	$365$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{10}\right)$

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 $

$2$	−1.38137	−	0.302995i	−0.976779	−	0.214250i
$2$	−1.38137	−	0.302995i	−0.976779	−	0.214250i
$3$	−0.868428	+	0.781936i	−0.501387	+	0.451451i	−0.880601	−	0.473858i	$-0.842861\pi$
$3$	−0.868428	+	0.781936i	−0.501387	+	0.451451i	0.379214	+	0.925309i	$0.376194\pi$
$4$	1.81639	+	0.837098i	0.908194	+	0.418549i
$5$	1.42384	+	1.95975i	0.636761	+	0.876426i	0.998438	−	0.0558775i	$-0.0177956\pi$
$5$	1.42384	+	1.95975i	0.636761	+	0.876426i	−0.361677	+	0.932304i	$0.617796\pi$
$6$	1.43655	−	0.817017i	0.586467	−	0.333546i
$7$	−2.34374	−	2.11032i	−0.885852	−	0.797624i	0.0943680	−	0.995537i	$-0.469917\pi$
$7$	−2.34374	−	2.11032i	−0.885852	−	0.797624i	−0.980220	+	0.197913i	$0.936584\pi$
$8$	−2.25548	−	1.70670i	−0.797431	−	0.603410i
$9$	−0.170842	+	1.62546i	−0.0569475	+	0.541819i
$10$	−1.37306	−	3.13856i	−0.434201	−	0.992500i
$11$	3.11466	+	1.13968i	0.939107	+	0.343626i
$11$	3.11466	+	1.13968i	0.939107	+	0.343626i
$12$	−2.23196	+	0.693340i	−0.644311	+	0.200150i
$13$	−1.56279	+	3.24926i	−0.433440	+	0.901182i
$13$	−1.56279	+	3.24926i	−0.433440	+	0.901182i
$14$	2.59817	+	3.62528i	0.694390	+	0.968896i
$15$	−2.76890	−	0.588548i	−0.714927	−	0.151962i
$16$	2.59853	+	3.04099i	0.649633	+	0.760248i
$17$	1.00824	−	2.26454i	0.244533	−	0.549231i	−0.749026	−	0.662540i	$-0.769478\pi$
$17$	1.00824	−	2.26454i	0.244533	−	0.549231i	0.993560	+	0.113309i	$0.0361451\pi$
$18$	0.728502	−	2.19360i	0.171710	−	0.517036i
$19$	0.884301	+	4.16031i	0.202873	+	0.954441i	0.955271	+	0.295732i	$0.0955636\pi$
$19$	0.884301	+	4.16031i	0.202873	+	0.954441i	−0.752398	+	0.658708i	$0.771103\pi$
$20$	0.945745	+	4.75156i	0.211475	+	1.06248i
$21$	3.68550			0.804242
$22$	−3.95720	−	2.51805i	−0.843678	−	0.536850i
$23$	−5.70725	−	3.29508i	−1.19004	−	0.687072i	−0.231728	−	0.972781i	$-0.574438\pi$
$23$	−5.70725	−	3.29508i	−1.19004	−	0.687072i	−0.958317	+	0.285708i	$0.907771\pi$
$24$	3.29325	−	0.281490i	0.672231	−	0.0574588i
$25$	−0.268206	+	0.825454i	−0.0536412	+	0.165091i
$26$	3.14331	−	4.01493i	0.616453	−	0.787392i
$27$	−3.18327	−	4.38139i	−0.612620	−	0.843200i
$28$	−2.49061	−	5.79510i	−0.470680	−	1.09517i
$29$	−1.02798	+	4.83626i	−0.190891	+	0.898071i	0.773542	+	0.633744i	$0.218483\pi$
$29$	−1.02798	+	4.83626i	−0.190891	+	0.898071i	−0.964433	+	0.264326i	$0.914850\pi$
$30$	3.64656	+	1.65197i	0.665767	+	0.301606i
$31$	2.36910	+	1.72125i	0.425504	+	0.309146i	0.779848	−	0.625968i	$-0.215296\pi$
$31$	2.36910	+	1.72125i	0.425504	+	0.309146i	−0.354345	+	0.935115i	$0.615296\pi$
$32$	−2.66814	−	4.98809i	−0.471665	−	0.881778i
$33$	−3.59601	+	1.44574i	−0.625986	+	0.251671i
$34$	−2.07889	+	2.82268i	−0.356527	+	0.484086i
$35$	0.798571	−	7.59790i	0.134983	−	1.28428i
$36$	−1.67098	+	2.80945i	−0.278497	+	0.468241i
$37$	−2.30543	+	10.8462i	−0.379010	+	1.78310i	0.212875	+	0.977079i	$0.431717\pi$
$37$	−2.30543	+	10.8462i	−0.379010	+	1.78310i	−0.591885	+	0.806022i	$0.701616\pi$
$38$	0.0390015	−	6.01488i	0.00632688	−	0.975743i
$39$	−1.18354	−	4.04375i	−0.189518	−	0.647518i
$40$	0.133269	−	6.85023i	0.0210717	−	1.08312i
$41$	−7.19829	−	7.99451i	−1.12418	−	1.24853i	−0.965274	−	0.261239i	$-0.915869\pi$
$41$	−7.19829	−	7.99451i	−1.12418	−	1.24853i	−0.158910	−	0.987293i	$-0.550798\pi$
$42$	−5.09106	−	1.11669i	−0.785567	−	0.172309i
$43$	−3.54724	−	6.14400i	−0.540949	−	0.936951i	−0.998850	−	0.0479480i	$-0.984732\pi$
$43$	−3.54724	−	6.14400i	−0.540949	−	0.936951i	0.457901	−	0.889003i	$-0.348602\pi$
$44$	4.70342	+	4.67738i	0.709067	+	0.705141i
$45$	−3.42874	+	1.97958i	−0.511126	+	0.295099i
$46$	6.88546	+	6.28101i	1.01521	+	0.926084i
$47$	−2.87748	+	8.85598i	−0.419724	+	1.29178i	0.488233	+	0.872713i	$0.337642\pi$
$47$	−2.87748	+	8.85598i	−0.419724	+	1.29178i	−0.907957	+	0.419064i	$0.862358\pi$
$48$	−4.63450	−	0.608994i	−0.668932	−	0.0879008i
$49$	0.308000	+	2.93042i	0.0440000	+	0.418632i
$50$	0.620601	−	1.05900i	0.0877663	−	0.149765i
$51$	0.895141	+	2.75496i	0.125345	+	0.385772i
$52$	−5.55858	+	4.59371i	−0.770837	+	0.637033i
$53$	6.84093	+	4.97022i	0.939673	+	0.682713i	0.948342	−	0.317250i	$-0.102759\pi$
$53$	6.84093	+	4.97022i	0.939673	+	0.682713i	−0.00866856	+	0.999962i	$0.502759\pi$
$54$	3.06975	+	7.01686i	0.417739	+	0.954873i
$55$	2.20130	+	7.72668i	0.296824	+	1.04186i
$56$	1.68457	+	8.75984i	0.225111	+	1.17058i
$57$	−4.02105	−	2.92146i	−0.532601	−	0.386957i
$58$	2.88538	−	6.36921i	0.378869	−	0.836318i
$59$	−9.13027	+	10.1402i	−1.18866	+	1.32014i	−0.252905	+	0.967491i	$0.581386\pi$
$59$	−9.13027	+	10.1402i	−1.18866	+	1.32014i	−0.935755	+	0.352650i	$0.885281\pi$
$60$	−4.53672	−	3.38687i	−0.585688	−	0.437243i
$61$	−1.69505	+	3.80713i	−0.217028	+	0.487454i	−0.988947	−	0.148267i	$-0.952630\pi$
$61$	−1.69505	+	3.80713i	−0.217028	+	0.487454i	0.771919	+	0.635721i	$0.219297\pi$
$62$	−2.75109	−	3.09552i	−0.349388	−	0.393132i
$63$	3.83064	−	3.44912i	0.482615	−	0.434548i
$64$	2.17434	+	7.69885i	0.271792	+	0.962356i
$65$	−8.59289	+	1.56375i	−1.06582	+	0.193960i
$66$	5.40549	−	0.907534i	0.665370	−	0.111710i
$67$	−1.20894	+	2.09394i	−0.147695	+	0.255815i	−0.930375	−	0.366609i	$-0.880519\pi$
$67$	−1.20894	+	2.09394i	−0.147695	+	0.255815i	0.782680	+	0.622424i	$0.213852\pi$
$68$	3.72699	−	3.26928i	0.451964	−	0.396459i
$69$	7.53288	−	1.60116i	0.906852	−	0.192757i
$70$	−3.40525	+	10.2536i	−0.407005	+	1.22554i
$71$	−7.68076	−	3.41970i	−0.911539	−	0.405843i	−0.103268	−	0.994654i	$-0.532930\pi$
$71$	−7.68076	−	3.41970i	−0.911539	−	0.405843i	−0.808271	+	0.588810i	$0.799597\pi$
$72$	3.15950	−	3.37460i	0.372351	−	0.397700i
$73$	1.80501	+	5.55525i	0.211260	+	0.650192i	0.999398	+	0.0346934i	$0.0110455\pi$
$73$	1.80501	+	5.55525i	0.211260	+	0.650192i	−0.788138	+	0.615499i	$0.788955\pi$
$74$	6.47100	−	14.2841i	0.752238	−	1.66049i
$75$	−0.412534	−	0.926567i	−0.0476353	−	0.106991i
$76$	−1.87635	+	8.29699i	−0.215233	+	0.951730i
$77$	−4.89489	−	9.24404i	−0.557825	−	1.05346i
$78$	0.409680	+	5.94453i	0.0463871	+	0.673086i
$79$	1.82433	+	1.32545i	0.205253	+	0.149125i	0.685663	−	0.727919i	$-0.259512\pi$
$79$	1.82433	+	1.32545i	0.205253	+	0.149125i	−0.480410	+	0.877044i	$0.659512\pi$
$80$	−2.25968	+	9.42236i	−0.252640	+	1.05345i
$81$	1.39432	+	0.296372i	0.154925	+	0.0329303i
$82$	7.52123	+	13.2245i	0.830581	+	1.46040i
$83$	3.61003	+	4.96878i	0.396252	+	0.545394i	0.959798	−	0.280690i	$-0.0905633\pi$
$83$	3.61003	+	4.96878i	0.396252	+	0.545394i	−0.563546	+	0.826085i	$0.690563\pi$
$84$	6.69430	+	3.08513i	0.730408	+	0.336615i
$85$	5.87349	−	1.24845i	0.637069	−	0.135413i
$86$	3.03847	+	9.56196i	0.327646	+	1.03109i
$87$	−2.88892	−	5.00375i	−0.309725	−	0.536459i
$88$	−5.07996	−	7.88632i	−0.541525	−	0.840684i
$89$	−10.9834	−	6.34125i	−1.16423	−	0.672171i	−0.211920	−	0.977287i	$-0.567972\pi$
$89$	−10.9834	−	6.34125i	−1.16423	−	0.672171i	−0.952315	+	0.305116i	$0.901305\pi$
$90$	5.33617	−	1.69565i	0.562482	−	0.178738i
$91$	10.5197	−	4.31745i	1.10277	−	0.452592i
$92$	−7.60828	−	10.7627i	−0.793218	−	1.12209i
$93$	−3.40331	+	0.357702i	−0.352906	+	0.0370920i
$94$	6.65819	−	11.3616i	0.686740	−	1.17186i
$95$	−6.89406	+	7.65663i	−0.707315	+	0.785553i
$96$	6.21745	+	2.24548i	0.634566	+	0.229178i
$97$	8.70931	+	0.915385i	0.884296	+	0.0929433i	0.535778	−	0.844359i	$-0.320018\pi$
$97$	8.70931	+	0.915385i	0.884296	+	0.0929433i	0.348518	+	0.937302i	$0.386685\pi$
$98$	0.462440	−	4.14133i	0.0467135	−	0.418338i
$99$	−2.38461	+	4.86805i	−0.239663	+	0.489257i
$100$	−1.17815	+	1.27483i	−0.117815	+	0.127483i
$101$	−6.90164	−	15.5013i	−0.686739	−	1.54244i	−0.833047	−	0.553202i	$-0.813406\pi$
$101$	−6.90164	−	15.5013i	−0.686739	−	1.54244i	0.146308	−	0.989239i	$-0.453261\pi$
$102$	−0.401786	−	4.07686i	−0.0397827	−	0.403669i
$103$	7.07887	−	2.30006i	0.697502	−	0.226632i	0.0612601	−	0.998122i	$-0.480488\pi$
$103$	7.07887	−	2.30006i	0.697502	−	0.226632i	0.636242	+	0.771490i	$0.280488\pi$
$104$	9.07035	−	4.66141i	0.889421	−	0.457089i
$105$	5.24757	+	7.22266i	0.512110	+	0.704859i
$106$	−7.94393	−	8.93850i	−0.771582	−	0.868184i
$107$	−4.37101	−	4.85450i	−0.422562	−	0.469303i	0.493845	−	0.869550i	$-0.335591\pi$
$107$	−4.37101	−	4.85450i	−0.422562	−	0.469303i	−0.916407	+	0.400247i	$0.868924\pi$
$108$	−2.11440	−	10.6230i	−0.203458	−	1.02220i
$109$	10.2542			0.982175			0.491088	−	0.871110i	$-0.336599\pi$
$109$	10.2542			0.982175			0.491088	+	0.871110i	$0.336599\pi$
$110$	−0.699682	−	11.3404i	−0.0667121	−	1.08127i
$111$	−6.47892	−	11.2218i	−0.614952	−	1.06513i
$112$	0.327157	−	12.6110i	0.0309134	−	1.19163i
$113$	5.99469	−	1.27421i	0.563933	−	0.119868i	0.0828806	−	0.996559i	$-0.473588\pi$
$113$	5.99469	−	1.27421i	0.563933	−	0.119868i	0.481052	+	0.876692i	$0.340255\pi$
$114$	4.66938	+	5.25399i	0.437328	+	0.492081i
$115$	−1.66868	−	15.8764i	−0.155605	−	1.48049i
$116$	−5.91563	+	7.92400i	−0.549253	+	0.735725i
$117$	−5.01454	−	3.09536i	−0.463594	−	0.286166i
$118$	15.6847	−	11.2410i	1.44390	−	1.03482i
$119$	−7.14193	+	3.17979i	−0.654700	+	0.291491i
$120$	5.24071	+	6.05314i	0.478409	+	0.552574i
$121$	8.40227	+	7.09943i	0.763843	+	0.645402i
$122$	3.49503	−	4.74549i	0.316426	−	0.429636i
$123$	12.5024	+	1.31405i	1.12730	+	0.118484i
$124$	2.86235	+	5.10964i	0.257047	+	0.458859i
$125$	9.51955	−	3.09309i	0.851454	−	0.276654i
$126$	−6.33661	+	3.60386i	−0.564510	+	0.321058i
$127$	1.25913	+	11.9798i	0.111729	+	1.06303i	0.896438	+	0.443169i	$0.146146\pi$
$127$	1.25913	+	11.9798i	0.111729	+	1.06303i	−0.784709	+	0.619865i	$0.787187\pi$
$128$	−0.670862	−	11.2938i	−0.0592964	−	0.998240i
$129$	7.88473	+	2.56191i	0.694212	+	0.225563i
$130$	12.3438	+	0.443476i	1.08262	+	0.0388954i
$131$	10.0494			0.878019			0.439009	−	0.898482i	$-0.355329\pi$
$131$	10.0494			0.878019			0.439009	+	0.898482i	$0.355329\pi$
$132$	−7.74199	−	0.384192i	−0.673853	−	0.0334396i
$133$	6.70699	−	11.6169i	0.581570	−	1.00731i
$134$	2.30444	−	2.52621i	0.199074	−	0.218231i
$135$	4.05396	−	12.4768i	0.348909	−	1.07383i
$136$	−6.13894	+	3.38685i	−0.526410	+	0.290420i
$137$	7.98964	−	17.9450i	0.682601	−	1.53315i	−0.155621	−	0.987817i	$-0.549738\pi$
$137$	7.98964	−	17.9450i	0.682601	−	1.53315i	0.838222	−	0.545330i	$-0.183595\pi$
$138$	−10.8909	−	0.0706182i	−0.927092	−	0.00601142i
$139$	−6.77830	+	7.52807i	−0.574928	+	0.638522i	−0.958535	−	0.284974i	$-0.908015\pi$
$139$	−6.77830	+	7.52807i	−0.574928	+	0.638522i	0.383607	+	0.923496i	$0.374682\pi$
$140$	7.81070	−	13.1323i	0.660125	−	1.10988i
$141$	−4.42592	−	9.94078i	−0.372730	−	0.837165i
$142$	9.57386	+	7.05111i	0.803420	+	0.591716i
$143$	−8.57067	+	8.33928i	−0.716716	+	0.697365i
$144$	−5.38694	+	3.70427i	−0.448912	+	0.308689i
$145$	−10.9415	+	4.87148i	−0.908644	+	0.404554i
$146$	−0.810182	−	8.22078i	−0.0670511	−	0.680357i
$147$	−2.55888	−	2.30402i	−0.211053	−	0.190033i
$148$	−13.2669	+	17.7710i	−1.09053	+	1.46077i
$149$	−3.04980	−	1.35786i	−0.249849	−	0.111240i	0.277991	−	0.960584i	$-0.410331\pi$
$149$	−3.04980	−	1.35786i	−0.249849	−	0.111240i	−0.527840	+	0.849344i	$0.676998\pi$
$150$	0.289119	+	1.40493i	0.0236065	+	0.114712i
$151$	12.6676	+	4.11595i	1.03087	+	0.334951i	0.775135	−	0.631795i	$-0.217682\pi$
$151$	12.6676	+	4.11595i	1.03087	+	0.334951i	0.255738	+	0.966746i	$0.417682\pi$
$152$	5.10589	−	10.8927i	0.414142	−	0.883516i
$153$	3.50866	+	2.02572i	0.283658	+	0.163770i
$154$	3.96078	+	14.2526i	0.319169	+	1.14851i
$155$			7.09364i			0.569775i
$156$	1.23524	−	8.33576i	0.0988985	−	0.667395i
$157$	−2.47344	+	7.61246i	−0.197402	+	0.607540i	0.802538	+	0.596600i	$0.203482\pi$
$157$	−2.47344	+	7.61246i	−0.197402	+	0.607540i	−0.999940	+	0.0109396i	$0.996518\pi$
$158$	−2.11847	−	2.38371i	−0.168537	−	0.189638i
$159$	−9.82724	+	1.03288i	−0.779351	+	0.0819131i
$160$	5.97639	−	12.3311i	0.472475	−	0.974861i
$161$	6.42267	+	19.7669i	0.506177	+	1.55785i
$162$	−1.83628	−	0.831873i	−0.144272	−	0.0653581i
$163$	−0.925172	+	8.80242i	−0.0724650	+	0.689459i	0.896632	+	0.442777i	$0.146007\pi$
$163$	−0.925172	+	8.80242i	−0.0724650	+	0.689459i	−0.969097	+	0.246681i	$0.920660\pi$
$164$	−6.38270	−	20.5468i	−0.498405	−	1.60444i
$165$	−7.95344	−	4.98878i	−0.619174	−	0.388376i
$166$	−3.48129	−	7.95756i	−0.270200	−	0.617627i
$167$	7.58745	+	17.0417i	0.587135	+	1.31873i	0.925869	+	0.377844i	$0.123334\pi$
$167$	7.58745	+	17.0417i	0.587135	+	1.31873i	−0.338735	+	0.940882i	$0.609999\pi$
$168$	−8.31256	−	6.29005i	−0.641328	−	0.485288i
$169$	−8.11537	−	10.1558i	−0.624260	−	0.781217i
$170$	−8.49176	−	0.0550620i	−0.651288	−	0.00422306i
$171$	−6.91348	+	0.726636i	−0.528687	+	0.0555673i
$172$	−1.30003	−	14.1293i	−0.0991267	−	1.07735i
$173$	2.16089	+	10.1662i	0.164290	+	0.772923i	0.980711	+	0.195465i	$0.0626217\pi$
$173$	2.16089	+	10.1662i	0.164290	+	0.772923i	−0.816421	+	0.577457i	$0.804045\pi$
$174$	2.47457	+	7.78738i	0.187596	+	0.590360i
$175$	2.37057	−	1.36865i	0.179199	−	0.103460i
$176$	4.62781	+	12.4332i	0.348834	+	0.937184i
$177$		−	15.9453i		−	1.19852i
$178$	13.2508	+	12.0875i	0.993188	+	0.906000i
$179$	8.69776	−	7.83150i	0.650101	−	0.585354i	−0.276677	−	0.960963i	$-0.589233\pi$
$179$	8.69776	−	7.83150i	0.650101	−	0.585354i	0.926778	+	0.375609i	$0.122567\pi$
$180$	−7.88503	+	0.725501i	−0.587715	+	0.0540756i
$181$	18.6392	−	13.5421i	1.38544	−	1.00658i	0.389090	−	0.921200i	$-0.372789\pi$
$181$	18.6392	−	13.5421i	1.38544	−	1.00658i	0.996348	−	0.0853803i	$-0.0272105\pi$
$182$	−15.8399	+	2.77658i	−1.17413	+	0.205814i
$183$	−1.50491	−	4.63164i	−0.111246	−	0.342380i
$184$	7.24884	+	17.1726i	0.534392	+	1.26598i
$185$	−24.5383	+	10.9252i	−1.80410	+	0.803235i
$186$	4.80962	+	0.537064i	0.352658	+	0.0393794i
$187$	5.72116	−	5.90421i	0.418373	−	0.431758i
$188$	−12.6399	+	13.6772i	−0.921863	+	0.997510i
$189$	−1.78536	+	16.9866i	−0.129866	+	1.23559i
$190$	11.8432	−	8.48780i	0.859195	−	0.615770i
$191$	9.74527	+	8.77468i	0.705143	+	0.634914i	0.941602	−	0.336728i	$-0.109320\pi$
$191$	9.74527	+	8.77468i	0.705143	+	0.634914i	−0.236459	+	0.971641i	$0.575987\pi$
$192$	−7.90826	−	4.98570i	−0.570729	−	0.359812i
$193$	1.16433	+	11.0779i	0.0838106	+	0.797404i	0.953009	+	0.302941i	$0.0979686\pi$
$193$	1.16433	+	11.0779i	0.0838106	+	0.797404i	−0.869199	+	0.494463i	$0.835365\pi$
$194$	−11.7535	−	3.90336i	−0.843849	−	0.280245i
$195$	6.23955	−	8.07709i	0.446824	−	0.578413i
$196$	−1.89360	+	5.58061i	−0.135257	+	0.398615i
$197$	2.13219	−	3.69307i	0.151913	−	0.263120i	−0.780018	−	0.625757i	$-0.784790\pi$
$197$	2.13219	−	3.69307i	0.151913	−	0.263120i	0.931931	+	0.362637i	$0.118123\pi$
$198$	4.76904	−	6.00207i	0.338921	−	0.426548i
$199$	0.118161	−	0.0682202i	0.00837620	−	0.00483600i	−0.495806	−	0.868433i	$-0.665127\pi$
$199$	0.118161	−	0.0682202i	0.00837620	−	0.00483600i	0.504182	+	0.863597i	$0.331794\pi$
$200$	2.01374	−	1.40404i	0.142393	−	0.0992808i
$201$	−0.587452	−	2.76374i	−0.0414357	−	0.194939i
$202$	4.83692	+	23.5043i	0.340325	+	1.65376i
$203$	12.6153	−	9.16559i	0.885424	−	0.643298i
$204$	−0.680249	+	5.75340i	−0.0476270	+	0.402819i
$205$	5.41801	−	25.4897i	0.378410	−	1.78028i
$206$	−10.4755	+	1.03239i	−0.729861	+	0.0719299i
$207$	6.33106	−	8.71395i	0.440039	−	0.605662i
$208$	−13.9419	+	3.69088i	−0.966699	+	0.255916i
$209$	−1.98711	+	13.9658i	−0.137451	+	0.966034i
$210$	−5.06042	−	11.5672i	−0.349202	−	0.798211i
$211$	5.91787	−	2.63480i	0.407403	−	0.181387i	−0.192795	−	0.981239i	$-0.561755\pi$
$211$	5.91787	−	2.63480i	0.407403	−	0.181387i	0.600198	+	0.799852i	$0.295089\pi$
$212$	8.26521	+	14.7544i	0.567657	+	1.01334i
$213$	9.34417	−	3.03610i	0.640252	−	0.208030i
$214$	4.56712	+	8.03028i	0.312202	+	0.548939i
$215$	6.98999	−	15.6998i	0.476713	−	1.07072i
$216$	−0.297949	+	15.3150i	−0.0202728	+	1.04205i
$217$	−1.92018	−	9.03374i	−0.130350	−	0.613250i
$218$	−14.1649	−	3.10697i	−0.959368	−	0.210431i
$219$	−5.91136	−	3.41293i	−0.399453	−	0.230624i
$220$	−2.46956	+	15.8774i	−0.166498	+	1.07045i
$221$	5.78240	+	6.81502i	0.388967	+	0.458428i
$222$	5.54966	+	17.4646i	0.372469	+	1.17215i
$223$	9.46027	+	10.5067i	0.633507	+	0.703580i	0.971358	−	0.237619i	$-0.0763669\pi$
$223$	9.46027	+	10.5067i	0.633507	+	0.703580i	−0.337852	+	0.941199i	$0.609700\pi$
$224$	−4.27300	+	17.3214i	−0.285502	+	1.15734i
$225$	−1.29592	−	0.576980i	−0.0863946	−	0.0384653i
$226$	−8.66699	−	0.0561982i	−0.576520	−	0.00373825i
$227$	−5.55177	−	4.99883i	−0.368484	−	0.331784i	0.463999	−	0.885836i	$-0.346414\pi$
$227$	−5.55177	−	4.99883i	−0.368484	−	0.331784i	−0.832482	+	0.554052i	$0.813081\pi$
$228$	−4.85823	−	8.67252i	−0.321744	−	0.574352i
$229$	0.822680	−	1.13232i	0.0543642	−	0.0748259i	−0.780969	−	0.624569i	$-0.785275\pi$
$229$	0.822680	−	1.13232i	0.0543642	−	0.0748259i	0.835334	+	0.549743i	$0.185275\pi$
$230$	−2.50541	+	22.4369i	−0.165202	+	1.47945i
$231$	11.4791	+	4.20028i	0.755269	+	0.276358i
$232$	10.5726	−	9.15361i	0.694127	−	0.600964i
$233$	14.6931	−	20.2234i	0.962579	−	1.32488i	0.0168718	−	0.999858i	$-0.494629\pi$
$233$	14.6931	−	20.2234i	0.962579	−	1.32488i	0.945707	−	0.325019i	$-0.105371\pi$
$234$	5.98908	+	5.79523i	0.391518	+	0.378846i
$235$	−21.4526	+	6.97036i	−1.39941	+	0.454696i
$236$	−25.0725	+	10.7756i	−1.63208	+	0.701432i
$237$	−2.62072	+	0.275448i	−0.170234	+	0.0178923i
$238$	10.8291	−	2.22852i	0.701949	−	0.144453i
$239$	3.54552	+	1.15201i	0.229341	+	0.0745174i	0.421433	−	0.906860i	$-0.361527\pi$
$239$	3.54552	+	1.15201i	0.229341	+	0.0745174i	−0.192092	+	0.981377i	$0.561527\pi$
$240$	−5.40531	−	9.94956i	−0.348911	−	0.642241i
$241$	−5.96960	−	10.3396i	−0.384535	−	0.666035i	0.607169	−	0.794573i	$-0.292305\pi$
$241$	−5.96960	−	10.3396i	−0.384535	−	0.666035i	−0.991705	+	0.128538i	$0.958972\pi$
$242$	−9.45559	−	12.3528i	−0.607828	−	0.794068i
$243$	12.6278	−	7.29066i	0.810073	−	0.467696i
$244$	−6.26581	+	5.49632i	−0.401127	+	0.351866i
$245$	−5.30435	+	4.77605i	−0.338882	+	0.305131i
$246$	−16.8723	−	5.60336i	−1.07574	−	0.357257i
$247$	−14.8999	−	3.62837i	−0.948058	−	0.230868i
$248$	−2.40579	−	7.92560i	−0.152768	−	0.503276i
$249$	−7.02032	−	1.49221i	−0.444894	−	0.0945652i
$250$	−14.0872	+	1.38834i	−0.890955	+	0.0878062i
$251$	−0.0358383	−	0.00376676i	−0.00226209	−	0.000237756i	0.103397	−	0.994640i	$-0.467029\pi$
$251$	−0.0358383	−	0.00376676i	−0.00226209	−	0.000237756i	−0.105659	+	0.994402i	$0.533695\pi$
$252$	9.84518	−	3.05832i	0.620188	−	0.192656i
$253$	−14.0208	−	16.7675i	−0.881483	−	1.05416i
$254$	1.89049	−	16.9301i	0.118620	−	1.06229i
$255$	−4.12449	+	5.67688i	−0.258286	+	0.355500i
$256$	−2.49525	+	15.8042i	−0.155953	+	0.987764i
$257$	−0.0117429	−	0.00249604i	−0.000732504	−	0.000155698i	0.207545	−	0.978225i	$-0.433453\pi$
$257$	−0.0117429	−	0.00249604i	−0.000732504	−	0.000155698i	−0.208278	+	0.978070i	$0.566786\pi$
$258$	−10.1155	−	5.92798i	−0.629765	−	0.369060i
$259$	28.2922	−	20.5555i	1.75799	−	1.27726i
$260$	−16.9170	−	4.35272i	−1.04915	−	0.269944i
$261$	−7.68551	−	2.49717i	−0.475721	−	0.154571i
$262$	−13.8820	−	3.04491i	−0.857630	−	0.188115i
$263$	3.64242	−	6.30886i	0.224601	−	0.389021i	−0.731598	−	0.681736i	$-0.761225\pi$
$263$	3.64242	−	6.30886i	0.224601	−	0.389021i	0.956200	+	0.292715i	$0.0945587\pi$
$264$	10.5782	+	2.87649i	0.651041	+	0.177036i
$265$			20.4833i			1.25828i
$266$	−12.7847	+	14.0150i	−0.783881	+	0.859317i
$267$	14.4967	−	3.08137i	0.887184	−	0.188577i
$268$	−3.94873	+	2.79141i	−0.241207	+	0.170512i
$269$	18.4130	+	8.19799i	1.12266	+	0.499840i	0.882226	−	0.470826i	$-0.156044\pi$
$269$	18.4130	+	8.19799i	1.12266	+	0.499840i	0.240433	+	0.970666i	$0.422711\pi$
$270$	−9.38044	+	16.0068i	−0.570876	+	0.974143i
$271$	−0.547082	+	2.57382i	−0.0332329	+	0.156348i	−0.991635	−	0.129072i	$-0.958800\pi$
$271$	−0.547082	+	2.57382i	−0.0332329	+	0.156348i	0.958402	+	0.285421i	$0.0921334\pi$
$272$	9.50637	−	2.81843i	0.576408	−	0.170893i
$273$	−5.75967	+	11.9752i	−0.348591	+	0.724769i
$274$	−16.4739	+	22.3680i	−0.995226	+	1.35130i
$275$	−1.77612	+	2.26534i	−0.107104	+	0.136605i
$276$	15.0230	+	3.39743i	0.904276	+	0.204501i
$277$	−6.05410	−	0.636311i	−0.363755	−	0.0382322i	−0.0791121	−	0.996866i	$-0.525209\pi$
$277$	−6.05410	−	0.636311i	−0.363755	−	0.0382322i	−0.284643	+	0.958633i	$0.591875\pi$
$278$	11.6443	−	8.34528i	0.698381	−	0.500517i
$279$	−3.20257	+	3.55681i	−0.191733	+	0.212941i
$280$	−14.7685	+	15.7739i	−0.882587	+	0.942674i
$281$	−11.0329	+	8.01584i	−0.658165	+	0.478185i	−0.866043	−	0.499970i	$-0.833344\pi$
$281$	−11.0329	+	8.01584i	−0.658165	+	0.478185i	0.207878	+	0.978155i	$0.433344\pi$
$282$	3.10185	+	15.0730i	0.184712	+	0.897582i
$283$	−7.65119	−	8.49751i	−0.454816	−	0.505124i	0.471503	−	0.881865i	$-0.343712\pi$
$283$	−7.65119	−	8.49751i	−0.454816	−	0.505124i	−0.926319	+	0.376740i	$0.877045\pi$
$284$	−11.0886	−	12.6411i	−0.657989	−	0.750108i
$285$		−	12.0399i		−	0.713184i
$286$	14.3661	−	8.92279i	0.849483	−	0.527616i
$287$			33.9277i			2.00269i
$288$	8.56375	−	3.48477i	0.504624	−	0.205342i
$289$	7.26364	+	8.06709i	0.427273	+	0.474534i
$290$	16.5904	−	3.41411i	0.974220	−	0.200484i
$291$	−8.27917	+	6.01517i	−0.485334	+	0.352616i
$292$	−1.37169	+	11.6015i	−0.0802721	+	0.678924i
$293$	−13.2634	+	14.7305i	−0.774855	+	0.860564i	−0.993333	−	0.115278i	$-0.963224\pi$
$293$	−13.2634	+	14.7305i	−0.774855	+	0.860564i	0.218478	+	0.975842i	$0.429891\pi$
$294$	2.83666	+	3.95804i	0.165437	+	0.230838i
$295$	−32.8723	−	3.45502i	−1.91390	−	0.201159i
$296$	23.7110	−	20.5286i	1.37818	−	1.19320i
$297$	−4.92144	−	17.2745i	−0.285571	−	1.00237i
$298$	3.80149	+	2.79978i	0.220214	+	0.162187i
$299$	19.6258	−	13.3948i	1.13499	−	0.774642i
$300$	0.0263053	−	2.02834i	0.00151873	−	0.117106i
$301$	−4.65196	+	21.8858i	−0.268135	+	1.26147i
$302$	−16.2516	−	9.52387i	−0.935172	−	0.548037i
$303$	18.1146	+	8.06515i	1.04066	+	0.463331i
$304$	−10.3536	+	13.4999i	−0.593819	+	0.774270i
$305$	−9.87450	+	2.09889i	−0.565412	+	0.120182i
$306$	−4.23298	−	3.86139i	−0.241984	−	0.220741i
$307$			17.3697i			0.991340i	0.868511	+	0.495670i	$0.165077\pi$
$307$			17.3697i			0.991340i	−0.868511	+	0.495670i	$0.834923\pi$
$308$	−1.15286	−	20.8883i	−0.0656904	−	1.19022i
$309$	−4.34898	+	7.53266i	−0.247405	+	0.428518i
$310$	2.14934	−	9.79897i	0.122074	−	0.556544i
$311$	5.95501	+	1.93490i	0.337678	+	0.109718i	0.472947	−	0.881091i	$-0.343190\pi$
$311$	5.95501	+	1.93490i	0.337678	+	0.109718i	−0.135270	+	0.990809i	$0.543190\pi$
$312$	−4.23202	+	11.1405i	−0.239591	+	0.630708i
$313$	−9.01284	+	6.54821i	−0.509436	+	0.370127i	−0.812610	−	0.582808i	$-0.801954\pi$
$313$	−9.01284	+	6.54821i	−0.509436	+	0.370127i	0.303174	+	0.952935i	$0.401954\pi$
$314$	5.72328	−	9.76621i	0.322983	−	0.551139i
$315$	12.2136	+	2.59609i	0.688160	+	0.146273i
$316$	2.20416	+	3.93468i	0.123993	+	0.221343i
$317$	−1.89947	+	2.61440i	−0.106685	+	0.146839i	−0.859021	−	0.511940i	$-0.828927\pi$
$317$	−1.89947	+	2.61440i	−0.106685	+	0.146839i	0.752336	+	0.658779i	$0.228927\pi$
$318$	13.8881	+	1.55080i	0.778804	+	0.0869647i
$319$	−8.71358	+	13.8918i	−0.487867	+	0.777789i
$320$	−11.9919	+	15.2231i	−0.670367	+	0.850996i
$321$	7.59182	+	0.797932i	0.423734	+	0.0445362i
$322$	−2.88283	−	29.2516i	−0.160654	−	1.63013i
$323$	10.3128	+	2.19204i	0.573817	+	0.121969i
$324$	2.28454	+	1.70551i	0.126919	+	0.0947507i
$325$	−2.26296	−	2.16148i	−0.125527	−	0.119897i
$326$	3.94510	−	11.8791i	0.218499	−	0.657923i
$327$	−8.90504	+	8.01813i	−0.492450	+	0.443404i
$328$	2.59132	+	30.3168i	0.143082	+	1.67396i
$329$	25.4330	−	14.6837i	1.40217	−	0.809541i
$330$	9.47510	+	9.30122i	0.521587	+	0.512015i
$331$	−7.93160	−	13.7379i	−0.435960	−	0.755106i	0.561413	−	0.827536i	$-0.310258\pi$
$331$	−7.93160	−	13.7379i	−0.435960	−	0.755106i	−0.997373	+	0.0724302i	$0.976925\pi$
$332$	2.39786	+	12.0472i	0.131600	+	0.661175i
$333$	−17.2361	−	5.60036i	−0.944535	−	0.306898i
$334$	−5.31756	−	25.8399i	−0.290964	−	1.41390i
$335$	−5.82492	+	0.612224i	−0.318249	+	0.0334494i
$336$	9.57690	+	11.2076i	0.522463	+	0.611423i
$337$	−16.7776	+	5.45137i	−0.913934	+	0.296955i	−0.727976	−	0.685603i	$-0.759539\pi$
$337$	−16.7776	+	5.45137i	−0.913934	+	0.296955i	−0.185958	+	0.982558i	$0.559539\pi$
$338$	8.13321	+	16.4879i	0.442388	+	0.896824i
$339$	−4.20960	+	5.79402i	−0.228634	+	0.314688i
$340$	11.7136	+	2.64902i	0.635260	+	0.143663i
$341$	5.41729	+	8.06115i	0.293363	+	0.436535i
$342$	9.77027	+	1.09099i	0.528316	+	0.0589941i
$343$	−7.51413	+	10.3423i	−0.405725	+	0.558432i
$344$	−2.48526	+	19.9117i	−0.133996	+	1.07357i
$345$	13.8635	+	12.4827i	0.746385	+	0.672048i
$346$	0.0953048	−	14.6981i	0.00512362	−	0.790173i
$347$	3.65109	+	1.62557i	0.196001	+	0.0872651i	0.502390	−	0.864641i	$-0.332454\pi$
$347$	3.65109	+	1.62557i	0.196001	+	0.0872651i	−0.306389	+	0.951906i	$0.599121\pi$
$348$	−1.05876	−	11.5071i	−0.0567557	−	0.616844i
$349$	10.5937	+	11.7655i	0.567070	+	0.629795i	0.956665	−	0.291191i	$-0.0940516\pi$
$349$	10.5937	+	11.7655i	0.567070	+	0.629795i	−0.389595	+	0.920986i	$0.627385\pi$
$350$	−3.68934	+	1.17235i	−0.197204	+	0.0626647i
$351$	19.2111	−	3.49607i	1.02541	−	0.186606i
$352$	−2.62556	−	18.5770i	−0.139943	−	0.990160i
$353$	10.8942	+	6.28975i	0.579838	+	0.334770i	0.761069	−	0.648671i	$-0.224675\pi$
$353$	10.8942	+	6.28975i	0.579838	+	0.334770i	−0.181231	+	0.983441i	$0.558008\pi$
$354$	−4.83135	+	22.0264i	−0.256783	+	1.17069i
$355$	−4.23444	−	19.9215i	−0.224741	−	1.05732i
$356$	−14.6418	−	20.7123i	−0.776015	−	1.09775i
$357$	3.71586	−	8.34595i	0.196664	−	0.441715i
$358$	−14.3878	+	8.18285i	−0.760417	+	0.432477i
$359$	−8.81092	+	2.86284i	−0.465022	+	0.151095i	−0.532151	−	0.846649i	$-0.678616\pi$
$359$	−8.81092	+	2.86284i	−0.465022	+	0.151095i	0.0671288	+	0.997744i	$0.478616\pi$
$360$	11.1120	+	1.38693i	0.585653	+	0.0730978i
$361$	0.831169	−	0.370060i	0.0437457	−	0.0194768i
$362$	−29.8509	+	13.0592i	−1.56893	+	0.686376i
$363$	−12.8481	+	0.404699i	−0.674348	+	0.0212412i
$364$	22.7221	+	0.963893i	1.19096	+	0.0505217i
$365$	−8.31684	+	11.4471i	−0.435323	+	0.599171i
$366$	0.675482	+	6.85400i	0.0353080	+	0.358264i
$367$	6.37961	−	30.0137i	0.333013	−	1.56670i	−0.419269	−	0.907862i	$-0.637714\pi$
$367$	6.37961	−	30.0137i	0.333013	−	1.56670i	0.752282	−	0.658841i	$-0.228953\pi$
$368$	−4.81016	−	25.9181i	−0.250747	−	1.35107i
$369$	14.2245	−	10.3347i	0.740498	−	0.538003i
$370$	37.2069	−	7.65676i	1.93430	−	0.398056i
$371$	−5.54463	−	26.0854i	−0.287863	−	1.35429i
$372$	−6.48116	−	2.19918i	−0.336032	−	0.114022i
$373$	−14.0778	+	8.12780i	−0.728919	+	0.420841i	−0.818026	−	0.575181i	$-0.804932\pi$
$373$	−14.0778	+	8.12780i	−0.728919	+	0.420841i	0.0891078	+	0.996022i	$0.471598\pi$
$374$	−9.69201	+	6.42244i	−0.501162	+	0.332096i
$375$	−5.84844	+	10.1298i	−0.302012	+	0.523100i
$376$	21.6046	−	15.0634i	1.11417	−	0.776837i
$377$	−14.1077	−	10.8982i	−0.726586	−	0.561287i
$378$	7.61309	−	22.9238i	0.391575	−	1.17908i
$379$	−0.828124	−	7.87907i	−0.0425379	−	0.404721i	−0.994986	−	0.100019i	$-0.968110\pi$
$379$	−0.828124	−	7.87907i	−0.0425379	−	0.404721i	0.952448	−	0.304702i	$-0.0985569\pi$
$380$	−18.9316	+	8.13640i	−0.971172	+	0.417389i
$381$	−10.4609	−	9.41902i	−0.535927	−	0.482551i
$382$	−10.8032	−	15.0739i	−0.552739	−	0.771247i
$383$	−0.569231	+	5.41587i	−0.0290863	+	0.276738i	0.970306	+	0.241881i	$0.0777643\pi$
$383$	−0.569231	+	5.41587i	−0.0290863	+	0.276738i	−0.999392	+	0.0348572i	$0.988902\pi$
$384$	9.41362	+	9.28328i	0.480387	+	0.473735i
$385$	11.1464	−	22.7548i	0.568075	−	1.15969i
$386$	1.74816	−	15.6555i	0.0889792	−	0.796844i
$387$	10.5928	−	4.71623i	0.538464	−	0.239739i
$388$	15.0532	+	8.95324i	0.764211	+	0.454532i
$389$	−8.77817	−	27.0164i	−0.445071	−	1.36979i	−0.882406	−	0.470489i	$-0.844078\pi$
$389$	−8.77817	−	27.0164i	−0.445071	−	1.36979i	0.437335	−	0.899299i	$-0.355922\pi$
$390$	−11.0665	+	9.26694i	−0.560373	+	0.469250i
$391$	−13.2161	+	9.60206i	−0.668367	+	0.485597i
$392$	4.30667	−	7.13516i	0.217520	−	0.360380i
$393$	−8.72716	+	7.85797i	−0.440227	+	0.396382i
$394$	−4.06434	+	4.45547i	−0.204758	+	0.224463i
$395$			5.46246i			0.274846i
$396$	−8.40642	+	6.84611i	−0.422438	+	0.344030i
$397$	−8.04713	+	4.64601i	−0.403874	+	0.233177i	−0.688154	−	0.725564i	$-0.741579\pi$
$397$	−8.04713	+	4.64601i	−0.403874	+	0.233177i	0.284280	+	0.958741i	$0.408245\pi$
$398$	−0.183895	+	0.0584355i	−0.00921781	+	0.00292911i
$399$	3.25909	+	15.3328i	0.163159	+	0.767602i
$400$	−3.20714	+	1.32936i	−0.160357	+	0.0664678i
$401$	7.39574	−	0.777324i	0.369326	−	0.0388177i	0.0819522	−	0.996636i	$-0.473885\pi$
$401$	7.39574	−	0.777324i	0.369326	−	0.0388177i	0.287374	+	0.957819i	$0.407218\pi$
$402$	−0.0259092	+	3.99576i	−0.00129223	+	0.199290i
$403$	−9.29522	+	5.00787i	−0.463028	+	0.249460i
$404$	0.440084	−	33.9338i	0.0218950	−	1.68827i
$405$	1.40448	+	3.15451i	0.0697890	+	0.156749i
$406$	−20.2036	+	8.83872i	−1.00269	+	0.438658i
$407$	−19.5418	+	31.1548i	−0.968650	+	1.54429i
$408$	2.68293	−	7.74149i	0.132825	−	0.383261i
$409$	−2.84362	+	27.0552i	−0.140608	+	1.33779i	0.665665	+	0.746251i	$0.268148\pi$
$409$	−2.84362	+	27.0552i	−0.140608	+	1.33779i	−0.806273	+	0.591544i	$0.798519\pi$
$410$	−15.2076	+	33.5692i	−0.751048	+	1.65787i
$411$	7.09343	+	21.8313i	0.349893	+	1.07686i
$412$	14.7834	+	1.74790i	0.728324	+	0.0861128i
$413$	42.7980	−	4.49825i	2.10595	−	0.221345i
$414$	−11.3858	+	10.1189i	−0.559583	+	0.497319i
$415$	−4.59745	+	14.1495i	−0.225680	+	0.694572i
$416$	20.3773	−	0.874151i	0.999081	−	0.0428588i
$417$		−	11.8378i		−	0.579698i
$418$	6.97650	−	18.6899i	0.341232	−	0.914153i
$419$	17.4988	+	10.1029i	0.854873	+	0.493561i	0.862292	−	0.506412i	$-0.169028\pi$
$419$	17.4988	+	10.1029i	0.854873	+	0.493561i	−0.00741926	+	0.999972i	$0.502362\pi$
$420$	3.48555	+	17.5119i	0.170077	+	0.854492i
$421$	16.9912	+	5.52077i	0.828099	+	0.269066i	0.692245	−	0.721663i	$-0.256622\pi$
$421$	16.9912	+	5.52077i	0.828099	+	0.269066i	0.135855	+	0.990729i	$0.456622\pi$
$422$	−8.97312	+	1.84657i	−0.436805	+	0.0898895i
$423$	−13.9034	−	6.19020i	−0.676007	−	0.300978i
$424$	−6.94685	−	22.8856i	−0.337369	−	1.11142i
$425$	1.59885	+	1.43962i	0.0775559	+	0.0698316i
$426$	−13.8277	+	1.36276i	−0.669955	+	0.0660260i
$427$	12.0070	−	5.34586i	0.581060	−	0.258704i
$428$	−3.87576	−	12.4766i	−0.187342	−	0.603081i
$429$	0.922232	−	13.9438i	0.0445258	−	0.673212i
$430$	−14.4127	+	19.5693i	−0.695044	+	0.943717i
$431$	−4.00141	−	8.98732i	−0.192741	−	0.432904i	0.791162	−	0.611607i	$-0.209477\pi$
$431$	−4.00141	−	8.98732i	−0.192741	−	0.432904i	−0.983903	+	0.178703i	$0.942810\pi$
$432$	5.05195	−	21.0655i	0.243062	−	1.01351i
$433$	−2.83918	+	3.15323i	−0.136442	+	0.151534i	−0.807493	−	0.589877i	$-0.799176\pi$
$433$	−2.83918	+	3.15323i	−0.136442	+	0.151534i	0.671051	+	0.741411i	$0.265843\pi$
$434$	−0.0846883	+	13.0608i	−0.00406517	+	0.626937i
$435$	5.69274	−	12.7861i	0.272946	−	0.613046i
$436$	18.6256	+	8.58378i	0.892006	+	0.411089i
$437$	8.66164	−	26.6578i	0.414342	−	1.27521i
$438$	7.13171	+	6.50564i	0.340766	+	0.310852i
$439$	−8.75053	+	15.1564i	−0.417640	+	0.723373i	−0.995702	−	0.0926196i	$-0.970476\pi$
$439$	−8.75053	+	15.1564i	−0.417640	+	0.723373i	0.578062	+	0.815993i	$0.303809\pi$
$440$	8.22215	−	21.1843i	0.391975	−	1.00992i
$441$	−4.81589			−0.229328
$442$	−5.92275	−	11.1661i	−0.281716	−	0.531118i
$443$	−31.8990	−	10.3646i	−1.51557	−	0.492438i	−0.571055	−	0.820912i	$-0.693466\pi$
$443$	−31.8990	−	10.3646i	−1.51557	−	0.492438i	−0.944513	+	0.328474i	$0.893466\pi$
$444$	−2.37447	−	25.8067i	−0.112687	−	1.22473i
$445$	−3.21131	−	30.5536i	−0.152231	−	1.44838i
$446$	−9.88470	−	17.3801i	−0.468054	−	0.822971i
$447$	3.71029	−	1.20555i	0.175491	−	0.0570204i
$448$	11.1509	−	22.6327i	0.526831	−	1.06929i
$449$	31.6048	+	3.32180i	1.49152	+	0.156765i	0.814915	−	0.579580i	$-0.196783\pi$
$449$	31.6048	+	3.32180i	1.49152	+	0.156765i	0.676606	+	0.736345i	$0.263450\pi$
$450$	1.61533	+	1.18968i	0.0761472	+	0.0560821i
$451$	−13.3091	−	33.1039i	−0.626701	−	1.55880i
$452$	11.9553	+	2.70368i	0.562331	+	0.127171i
$453$	−14.2193	+	6.33083i	−0.668080	+	0.297448i
$454$	6.15445	+	8.58741i	0.288842	+	0.403027i
$455$	23.4395	+	14.4687i	1.09886	+	0.678302i
$456$	4.08331	+	13.4520i	0.191218	+	0.629948i
$457$	1.70106	+	16.1845i	0.0795724	+	0.757081i	0.959450	+	0.281880i	$0.0909579\pi$
$457$	1.70106	+	16.1845i	0.0795724	+	0.757081i	−0.879877	+	0.475201i	$0.842375\pi$
$458$	−1.47952	+	1.31489i	−0.0691333	+	0.0614409i
$459$	−13.1313	+	2.79115i	−0.612917	+	0.130280i
$460$	10.2592	−	30.2346i	0.478336	−	1.40970i
$461$	−7.54614	−	13.0703i	−0.351459	−	0.608744i	0.635047	−	0.772474i	$-0.280981\pi$
$461$	−7.54614	−	13.0703i	−0.351459	−	0.608744i	−0.986505	+	0.163730i	$0.947648\pi$
$462$	−14.5843	−	9.28027i	−0.678522	−	0.431757i
$463$	23.3231			1.08392			0.541958	−	0.840405i	$-0.317683\pi$
$463$	23.3231			1.08392			0.541958	+	0.840405i	$0.317683\pi$
$464$	−17.3783	+	9.44111i	−0.806765	+	0.438292i
$465$	−5.54677	−	6.16031i	−0.257225	−	0.285678i
$466$	−26.4243	+	23.4841i	−1.22408	+	1.08788i
$467$	−9.87554	−	13.5925i	−0.456985	−	0.628986i	0.516895	−	0.856049i	$-0.327088\pi$
$467$	−9.87554	−	13.5925i	−0.456985	−	0.628986i	−0.973880	+	0.227062i	$0.927088\pi$
$468$	−6.51723	−	9.82004i	−0.301259	−	0.453931i
$469$	7.25230	−	2.35642i	0.334880	−	0.108809i
$470$	31.7460	−	3.12866i	1.46433	−	0.144314i
$471$	−3.80445	−	8.54493i	−0.175300	−	0.393730i
$472$	37.8994	−	7.28830i	1.74446	−	0.335471i
$473$	−4.04629	−	23.1792i	−0.186048	−	1.06578i
$474$	3.70365	+	0.413566i	0.170114	+	0.0189957i
$475$	−3.67132	−	0.385871i	−0.168452	−	0.0177050i
$476$	−15.6343	−	0.202760i	−0.716598	−	0.00929348i
$477$	−9.24760	+	10.2705i	−0.423419	+	0.470254i
$478$	−4.54864	−	2.66563i	−0.208050	−	0.121923i
$479$	8.57328	−	0.901089i	0.391723	−	0.0411718i	0.0933804	−	0.995631i	$-0.470233\pi$
$479$	8.57328	−	0.901089i	0.391723	−	0.0411718i	0.298343	+	0.954459i	$0.403566\pi$
$480$	4.45209	+	15.3818i	0.203209	+	0.702082i
$481$	−31.6392	−	24.4412i	−1.44262	−	1.11442i
$482$	5.11339	+	16.0917i	0.232908	+	0.732956i
$483$	−21.0341	−	12.1440i	−0.957084	−	0.552573i
$484$	9.31887	+	19.9288i	0.423585	+	0.905856i
$485$	10.6067	+	18.3714i	0.481627	+	0.834203i
$486$	−19.6527	+	6.24497i	−0.891466	+	0.283278i
$487$	15.4413	−	3.28215i	0.699711	−	0.148728i	0.155698	−	0.987805i	$-0.450237\pi$
$487$	15.4413	−	3.28215i	0.699711	−	0.148728i	0.544013	+	0.839077i	$0.316904\pi$
$488$	10.3208	−	5.69396i	0.467200	−	0.257753i
$489$	−6.07948	−	8.36769i	−0.274924	−	0.378400i
$490$	8.77440	−	4.99033i	0.396387	−	0.225440i
$491$	21.5584	+	4.58238i	0.972917	+	0.206800i	0.666835	−	0.745205i	$-0.267648\pi$
$491$	21.5584	+	4.58238i	0.972917	+	0.206800i	0.306082	+	0.952005i	$0.400982\pi$
$492$	21.6092	+	12.8526i	0.974218	+	0.579438i
$493$	9.91544	+	7.20399i	0.446569	+	0.324451i
$494$	19.4830	+	9.52673i	0.876580	+	0.428628i
$495$	−12.9355	+	2.25808i	−0.581405	+	0.101493i
$496$	0.921875	+	11.6772i	0.0413934	+	0.524320i
$497$	10.7851	+	24.2237i	0.483778	+	1.08658i
$498$	9.24555	+	4.18842i	0.414303	+	0.187688i
$499$	−4.02351	−	12.3831i	−0.180117	−	0.554343i	0.819713	−	0.572774i	$-0.194133\pi$
$499$	−4.02351	−	12.3831i	−0.180117	−	0.554343i	−0.999830	+	0.0184312i	$0.994133\pi$
$500$	19.8804	+	2.35055i	0.889079	+	0.105120i
$501$	−19.9147	−	8.86658i	−0.889722	−	0.396130i
$502$	0.0483648	+	0.0160621i	0.00215863	+	0.000716888i
$503$	−12.8168	+	2.72429i	−0.571471	+	0.121470i	−0.484578	−	0.874748i	$-0.661027\pi$
$503$	−12.8168	+	2.72429i	−0.571471	+	0.121470i	−0.0868925	+	0.996218i	$0.527694\pi$
$504$	−14.5265	+	1.24165i	−0.647063	+	0.0553076i
$505$	20.5519	−	35.5969i	0.914547	−	1.58404i
$506$	14.2876	+	27.4104i	0.635160	+	1.21854i
$507$	14.9888	+	2.47389i	0.665677	+	0.109869i
$508$	−7.74119	+	22.8140i	−0.343460	+	1.01221i
$509$	−29.5127	+	26.5733i	−1.30813	+	1.17784i	−0.336404	+	0.941718i	$0.609211\pi$
$509$	−29.5127	+	26.5733i	−1.30813	+	1.17784i	−0.971723	+	0.236125i	$0.924123\pi$
$510$	7.41753	−	6.59219i	0.328454	−	0.291907i
$511$	7.49285	−	16.8292i	0.331464	−	0.744480i
$512$	8.23547	−	21.0755i	0.363960	−	0.931415i
$513$	15.4130	−	17.1179i	0.680500	−	0.755772i
$514$	0.0154651	+	0.00700600i	0.000682136	+	0.000309022i
$515$	14.5867	+	10.5979i	0.642768	+	0.466998i
$516$	12.1772	+	11.2537i	0.536070	+	0.495417i
$517$	−19.0554	+	24.3040i	−0.838053	+	1.06889i
$518$	−45.3103	+	19.8224i	−1.99082	+	0.870947i
$519$	−9.82590	−	7.13893i	−0.431309	−	0.313364i
$520$	22.0499	+	11.1385i	0.966953	+	0.488456i
$521$	6.62223	+	20.3811i	0.290125	+	0.892914i	0.984815	+	0.173605i	$0.0555415\pi$
$521$	6.62223	+	20.3811i	0.290125	+	0.892914i	−0.694690	+	0.719309i	$0.744459\pi$
$522$	9.85993	+	5.77820i	0.431557	+	0.252905i
$523$	−0.171765	−	1.63424i	−0.00751078	−	0.0714603i	0.990124	−	0.140191i	$-0.0447717\pi$
$523$	−0.171765	−	1.63424i	−0.00751078	−	0.0714603i	−0.997635	+	0.0687309i	$0.978105\pi$
$524$	18.2536	+	8.41232i	0.797412	+	0.367494i
$525$	−0.988474	+	3.04221i	−0.0431406	+	0.132773i
$526$	−6.94310	+	7.61126i	−0.302734	+	0.331867i
$527$	6.28646	−	3.62949i	0.273843	−	0.158103i
$528$	−13.7408	−	7.17864i	−0.597994	−	0.312410i
$529$	10.2152	+	17.6932i	0.444137	+	0.769268i
$530$	6.20633	−	28.2951i	0.269586	−	1.22906i
$531$	−14.9226	−	16.5732i	−0.647586	−	0.719217i
$532$	21.9070	−	15.4863i	0.949787	−	0.671416i
$533$	37.2256	−	10.8954i	1.61242	−	0.471931i
$534$	−20.9590	−	0.135902i	−0.906986	−	0.00588105i
$535$	3.28998	−	15.4781i	0.142238	−	0.669178i
$536$	6.30045	−	2.65953i	0.272138	−	0.114874i
$537$	−1.42965	+	13.6022i	−0.0616938	+	0.586977i
$538$	−22.9513	−	16.9035i	−0.989499	−	0.728763i
$539$	−2.38042	+	9.47830i	−0.102532	+	0.408259i
$540$	17.8079	−	19.2692i	0.766329	−	0.829213i
$541$	18.8712	+	13.7107i	0.811337	+	0.589471i	0.914218	−	0.405223i	$-0.132806\pi$
$541$	18.8712	+	13.7107i	0.811337	+	0.589471i	−0.102881	+	0.994694i	$0.532806\pi$
$542$	1.53558	−	3.38965i	0.0659588	−	0.145598i
$543$	−5.59768	+	26.3350i	−0.240219	+	1.13014i
$544$	−13.9858	+	1.01293i	−0.599637	+	0.0434291i
$545$	14.6004	+	20.0957i	0.625411	+	0.860804i
$546$	11.5847	−	14.7970i	0.495778	−	0.633254i
$547$	7.64860	−	23.5400i	0.327030	−	1.00650i	−0.643485	−	0.765458i	$-0.722512\pi$
$547$	7.64860	−	23.5400i	0.327030	−	1.00650i	0.970516	−	0.241038i	$-0.0774877\pi$
$548$	29.5340	−	25.9070i	1.26163	−	1.10669i
$549$	−5.89875	−	3.40564i	−0.251752	−	0.145349i
$550$	3.13988	−	2.59113i	0.133885	−	0.110486i
$551$	−21.0294			−0.895882
$552$	−19.7229	−	9.24499i	−0.839464	−	0.393493i
$553$	−1.47863	−	6.95643i	−0.0628779	−	0.295817i
$554$	8.17017	+	2.71334i	0.347117	+	0.115279i
$555$	12.7670	−	28.6751i	0.541929	−	1.21719i
$556$	−18.6138	+	7.99979i	−0.789399	+	0.339267i
$557$	−20.3950	−	4.33510i	−0.864165	−	0.183684i	−0.245556	−	0.969383i	$-0.578970\pi$
$557$	−20.3950	−	4.33510i	−0.864165	−	0.183684i	−0.618610	+	0.785699i	$0.712304\pi$
$558$	5.50164	−	3.94293i	0.232903	−	0.166917i
$559$	25.5070	−	1.92412i	1.07883	−	0.0813817i
$560$	25.1803	−	17.3149i	1.06406	−	0.731690i
$561$	−0.351703	+	9.60095i	−0.0148489	+	0.405353i
$562$	17.6693	−	7.72998i	0.745333	−	0.326069i
$563$	−1.55792	+	14.8226i	−0.0656584	+	0.624698i	0.911370	+	0.411588i	$0.135026\pi$
$563$	−1.55792	+	14.8226i	−0.0656584	+	0.624698i	−0.977028	+	0.213110i	$0.931641\pi$
$564$	0.282219	−	21.7613i	0.0118836	−	0.916314i
$565$	11.0326	+	9.93381i	0.464146	+	0.417919i
$566$	7.99446	+	14.0565i	0.336032	+	0.590839i
$567$	−2.64249	−	3.63708i	−0.110974	−	0.152743i
$568$	11.4874	+	20.8218i	0.481999	+	0.873664i
$569$	12.4579	−	11.2172i	0.522264	−	0.470248i	−0.365328	−	0.930879i	$-0.619043\pi$
$569$	12.4579	−	11.2172i	0.522264	−	0.470248i	0.887592	+	0.460630i	$0.152377\pi$
$570$	−3.64804	+	16.6317i	−0.152799	+	0.696623i
$571$	−41.9626			−1.75608			−0.878040	−	0.478586i	$-0.841149\pi$
$571$	−41.9626			−1.75608			−0.878040	+	0.478586i	$0.841149\pi$
$572$	−22.5485	+	7.97287i	−0.942799	+	0.333362i
$573$	−15.3243			−0.640182
$574$	10.2799	−	46.8669i	0.429076	−	1.95619i
$575$	4.25066	−	3.82731i	0.177265	−	0.159610i
$576$	−12.8856	+	2.21900i	−0.536901	+	0.0924584i
$577$	−14.9731	−	20.6087i	−0.623340	−	0.857953i	0.374251	−	0.927327i	$-0.377900\pi$
$577$	−14.9731	−	20.6087i	−0.623340	−	0.857953i	−0.997591	+	0.0693741i	$0.977900\pi$
$578$	−7.58951	−	13.3445i	−0.315682	−	0.555058i
$579$	−9.67334	−	8.70991i	−0.402010	−	0.361972i
$580$	−23.9520	−	0.310630i	−0.994551	−	0.0128982i
$581$	2.02471	−	19.2638i	0.0839992	−	0.799199i
$582$	13.2592	−	5.80066i	0.549612	−	0.240445i
$583$	15.6427	+	23.2770i	0.647856	+	0.964036i
$584$	5.41000	−	15.6103i	0.223867	−	0.645960i
$585$	−1.07378	−	14.2345i	−0.0443954	−	0.588525i
$586$	22.7850	−	16.3296i	0.941238	−	0.674568i
$587$	16.4328	+	3.49290i	0.678254	+	0.144167i	0.534143	−	0.845394i	$-0.320634\pi$
$587$	16.4328	+	3.49290i	0.678254	+	0.144167i	0.144111	+	0.989561i	$0.453968\pi$
$588$	−2.71922	−	6.32703i	−0.112139	−	0.260922i
$589$	−5.06595	+	11.3783i	−0.208739	+	0.468835i
$590$	44.3621	+	14.7328i	1.82636	+	0.606540i
$591$	1.03609	+	4.87440i	0.0426189	+	0.200506i
$592$	−38.9739	+	21.1734i	−1.60182	+	0.870221i
$593$	−2.50791			−0.102987			−0.0514937	−	0.998673i	$-0.516398\pi$
$593$	−2.50791			−0.102987			−0.0514937	+	0.998673i	$0.516398\pi$
$594$	1.56427	+	25.3537i	0.0641829	+	1.04027i
$595$	−16.4006	−	9.46887i	−0.672358	−	0.388186i
$596$	−4.40296	−	5.01938i	−0.180352	−	0.205602i
$597$	−0.0492703	+	0.151638i	−0.00201650	+	0.00620615i
$598$	−31.1692	+	12.5567i	−1.27460	+	0.513483i
$599$	−19.8608	−	27.3360i	−0.811489	−	1.11692i	−0.991092	−	0.133179i	$-0.957481\pi$
$599$	−19.8608	−	27.3360i	−0.811489	−	1.11692i	0.179603	−	0.983739i	$-0.442519\pi$
$600$	−0.650913	+	2.79392i	−0.0265734	+	0.114061i
$601$	4.21213	−	19.8165i	0.171816	−	0.808332i	−0.804835	−	0.593499i	$-0.797746\pi$
$601$	4.21213	−	19.8165i	0.171816	−	0.808332i	0.976651	−	0.214833i	$-0.0689206\pi$
$602$	13.0574	−	28.8229i	0.532179	−	1.17473i
$603$	−3.19707	−	2.32281i	−0.130195	−	0.0945920i
$604$	19.5638	+	18.0802i	0.796039	+	0.735671i
$605$	−1.94959	+	26.5748i	−0.0792622	+	1.08042i
$606$	−22.5794	−	16.6296i	−0.917224	−	0.675532i
$607$	−1.68315	+	16.0141i	−0.0683169	+	0.649991i	0.905763	+	0.423785i	$0.139299\pi$
$607$	−1.68315	+	16.0141i	−0.0683169	+	0.649991i	−0.974079	+	0.226206i	$0.927368\pi$
$608$	18.3926	−	15.5113i	0.745917	−	0.629065i
$609$	−3.78862	+	17.8240i	−0.153523	+	0.722267i
$610$	14.2763	+	0.0925701i	0.578032	+	0.00374805i
$611$	−24.2785	−	23.1897i	−0.982202	−	0.938156i
$612$	4.67735	+	6.61659i	0.189071	+	0.267460i
$613$	15.1520	+	16.8280i	0.611984	+	0.679677i	0.966881	−	0.255229i	$-0.0821507\pi$
$613$	15.1520	+	16.8280i	0.611984	+	0.679677i	−0.354897	+	0.934905i	$0.615484\pi$
$614$	5.26292	−	23.9940i	0.212394	−	0.968320i
$615$	15.2262	+	26.3725i	0.613979	+	1.06344i
$616$	−4.73650	+	29.2038i	−0.190839	+	1.17666i
$617$	20.8829	−	12.0567i	0.840713	−	0.485386i	−0.0167937	−	0.999859i	$-0.505346\pi$
$617$	20.8829	−	12.0567i	0.840713	−	0.485386i	0.857506	+	0.514473i	$0.172013\pi$
$618$	8.28993	−	9.08770i	0.333470	−	0.365561i
$619$	−8.38064	+	25.7930i	−0.336846	+	1.03671i	0.628959	+	0.777438i	$0.283481\pi$
$619$	−8.38064	+	25.7930i	−0.336846	+	1.03671i	−0.965805	+	0.259268i	$0.916519\pi$
$620$	−5.93807	+	12.8848i	−0.238479	+	0.517466i
$621$	3.73066	+	35.4949i	0.149706	+	1.42436i
$622$	−7.63983	−	4.47716i	−0.306329	−	0.179518i
$623$	12.3602	+	38.0406i	0.495199	+	1.52407i
$624$	9.22153	−	14.1070i	0.369157	−	0.564730i
$625$	23.1269	+	16.8026i	0.925074	+	0.672106i
$626$	14.4342	−	6.31469i	0.576906	−	0.252386i
$627$	−9.19469	−	13.6821i	−0.367200	−	0.546409i
$628$	−10.8651	+	11.7567i	−0.433564	+	0.469142i
$629$	22.2372	+	16.1562i	0.886654	+	0.644192i
$630$	−16.0850	−	7.28683i	−0.640841	−	0.290314i
$631$	20.6278	−	22.9095i	0.821181	−	0.912014i	−0.176199	−	0.984355i	$-0.556380\pi$
$631$	20.6278	−	22.9095i	0.821181	−	0.912014i	0.997380	+	0.0723410i	$0.0230470\pi$
$632$	−1.85258	−	6.10311i	−0.0736915	−	0.242769i
$633$	−3.07899	+	6.91553i	−0.122379	+	0.274868i
$634$	3.41603	−	3.03593i	0.135668	−	0.120572i
$635$	−21.6846	+	19.5249i	−0.860526	+	0.774821i
$636$	−18.7147	−	6.35025i	−0.742087	−	0.251804i
$637$	−10.0030	−	3.57886i	−0.396335	−	0.141800i
$638$	16.2458	−	16.5495i	0.643179	−	0.655203i
$639$	6.87077	−	11.9005i	0.271803	−	0.470777i
$640$	21.1778	−	17.3953i	0.837126	−	0.687609i
$641$	−16.9753	+	3.60822i	−0.670486	+	0.142516i	−0.530562	−	0.847646i	$-0.678019\pi$
$641$	−16.9753	+	3.60822i	−0.670486	+	0.142516i	−0.139924	+	0.990162i	$0.544686\pi$
$642$	−10.2454	−	3.40252i	−0.404353	−	0.134287i
$643$	26.2695	+	11.6959i	1.03597	+	0.461243i	0.853019	−	0.521879i	$-0.174769\pi$
$643$	26.2695	+	11.6959i	1.03597	+	0.461243i	0.182949	+	0.983122i	$0.441436\pi$
$644$	−4.88081	+	41.2808i	−0.192331	+	1.62669i
$645$	6.20591	+	19.0998i	0.244358	+	0.752055i
$646$	−13.5816	−	6.15275i	−0.534361	−	0.242077i
$647$	10.8075	+	24.2740i	0.424885	+	0.954308i	0.991474	+	0.130307i	$0.0415964\pi$
$647$	10.8075	+	24.2740i	0.424885	+	0.954308i	−0.566588	+	0.824001i	$0.691737\pi$
$648$	−2.63904	−	3.04815i	−0.103671	−	0.119743i
$649$	−39.9943	+	21.1777i	−1.56991	+	0.831299i
$650$	2.47108	+	3.67148i	0.0969238	+	0.144007i
$651$	8.73134	+	6.34369i	0.342208	+	0.248629i
$652$	−9.04896	+	15.2142i	−0.354385	+	0.595832i
$653$	−13.3476	−	2.83712i	−0.522332	−	0.111025i	−0.0608021	−	0.998150i	$-0.519366\pi$
$653$	−13.3476	−	2.83712i	−0.522332	−	0.111025i	−0.461530	+	0.887125i	$0.652699\pi$
$654$	14.7306	−	8.37786i	0.576014	−	0.327600i
$655$	14.3087	+	19.6943i	0.559088	+	0.769518i
$656$	5.60624	−	42.6639i	0.218887	−	1.66575i
$657$	−9.33818	+	1.98489i	−0.364317	+	0.0774380i
$658$	−39.5816	+	12.5777i	−1.54305	+	0.490329i
$659$	−1.57490	−	2.72781i	−0.0613494	−	0.106260i	0.833719	−	0.552188i	$-0.186207\pi$
$659$	−1.57490	−	2.72781i	−0.0613494	−	0.106260i	−0.895069	+	0.445928i	$0.852874\pi$
$660$	−10.2704	−	15.7194i	−0.399776	−	0.611876i
$661$	−19.0859	−	11.0192i	−0.742355	−	0.428599i	0.0805701	−	0.996749i	$-0.474326\pi$
$661$	−19.0859	−	11.0192i	−0.742355	−	0.428599i	−0.822925	+	0.568150i	$0.807659\pi$
$662$	6.79399	+	21.3805i	0.264056	+	0.830976i
$663$	−10.3505	−	1.39688i	−0.401980	−	0.0542503i
$664$	0.337893	−	17.3682i	0.0131128	−	0.674017i
$665$	32.3158	−	3.39653i	1.25315	−	0.131712i
$666$	22.1127	+	12.9587i	0.856849	+	0.502138i
$667$	21.8028	−	24.2145i	0.844208	−	0.937588i
$668$	−0.483814	+	37.3058i	−0.0187193	+	1.44340i
$669$	−16.4311	−	1.72698i	−0.635264	−	0.0667689i
$670$	8.23190	+	0.919211i	0.318026	+	0.0355122i
$671$	−9.61840	+	9.92614i	−0.371314	+	0.383194i
$672$	−9.83344	−	18.3836i	−0.379333	−	0.709163i
$673$	−8.29423	−	18.6291i	−0.319719	−	0.718101i	0.680169	−	0.733055i	$-0.261906\pi$
$673$	−8.29423	−	18.6291i	−0.319719	−	0.718101i	−0.999888	+	0.0149544i	$0.995240\pi$
$674$	24.8279	−	2.44686i	0.956334	−	0.0942495i
$675$	4.47041	−	1.45252i	0.172066	−	0.0559077i
$676$	−6.23925	−	25.2403i	−0.239971	−	0.970780i
$677$	19.3833	+	26.6788i	0.744959	+	1.02535i	0.998318	+	0.0579759i	$0.0184646\pi$
$677$	19.3833	+	26.6788i	0.744959	+	1.02535i	−0.253359	+	0.967372i	$0.581535\pi$
$678$	7.57060	−	6.72822i	0.290747	−	0.258396i
$679$	−18.4806	−	20.5248i	−0.709221	−	0.787670i
$680$	−15.3782	−	7.20845i	−0.589729	−	0.276431i
$681$	8.73007			0.334537
$682$	−5.04082	−	12.7769i	−0.193023	−	0.489252i
$683$	18.0251	+	31.2205i	0.689713	+	1.19462i	0.971931	+	0.235268i	$0.0755967\pi$
$683$	18.0251	+	31.2205i	0.689713	+	1.19462i	−0.282218	+	0.959350i	$0.591070\pi$
$684$	−13.1658	−	4.46741i	−0.503408	−	0.170816i
$685$	46.5437	−	9.89317i	1.77834	−	0.377998i
$686$	13.5135	−	12.0099i	0.515947	−	0.458538i
$687$	0.170965	+	1.62662i	0.00652272	+	0.0620595i
$688$	9.46623	−	26.7525i	0.360897	−	1.01993i
$689$	−26.8405	+	14.4605i	−1.02254	+	0.550902i
$690$	−15.3685	−	21.4439i	−0.585067	−	0.816355i
$691$	−3.21491	+	1.43137i	−0.122301	+	0.0544519i	−0.466975	−	0.884271i	$-0.654656\pi$
$691$	−3.21491	+	1.43137i	−0.122301	+	0.0544519i	0.344674	+	0.938722i	$0.387989\pi$
$692$	−4.58509	+	20.2747i	−0.174299	+	0.770727i
$693$	15.8620	−	6.37717i	0.602549	−	0.242248i
$694$	−4.55098	−	3.35178i	−0.172753	−	0.127232i
$695$	−24.4043	−	2.56500i	−0.925709	−	0.0972959i
$696$	−2.02403	+	16.2164i	−0.0767207	+	0.614680i
$697$	−25.3614	+	8.24043i	−0.960633	+	0.312129i
$698$	−11.0690	−	19.4625i	−0.418969	−	0.736665i
$699$	3.05345	+	29.0516i	0.115492	+	1.09883i
$700$	5.45158	−	0.501600i	0.206050	−	0.0189587i
$701$	−18.7744	−	6.10016i	−0.709097	−	0.230400i	−0.0678075	−	0.997698i	$-0.521600\pi$
$701$	−18.7744	−	6.10016i	−0.709097	−	0.230400i	−0.641290	+	0.767299i	$0.721600\pi$
$702$	−27.5970	−	0.991475i	−1.04158	−	0.0374208i
$703$	−47.1622			−1.77876
$704$	−2.00187	+	26.4574i	−0.0754484	+	0.997150i
$705$	13.1796	−	22.8278i	0.496373	−	0.859744i
$706$	−13.1432	−	11.9894i	−0.494649	−	0.451226i
$707$	−16.5370	+	50.8958i	−0.621940	+	1.91413i
$708$	13.3478	−	28.9629i	0.501641	−	1.08849i
$709$	−13.9396	+	31.3090i	−0.523515	+	1.17583i	0.437471	+	0.899233i	$0.355874\pi$
$709$	−13.9396	+	31.3090i	−0.523515	+	1.17583i	−0.960985	+	0.276600i	$0.910792\pi$
$710$	−0.186757	+	28.8020i	−0.00700887	+	1.08092i
$711$	−2.46614	+	2.73892i	−0.0924874	+	0.102718i
$712$	13.9501	+	33.0479i	0.522802	+	1.23852i
$713$	−7.84940	−	17.6300i	−0.293962	−	0.660250i
$714$	−7.66177	+	10.4030i	−0.286735	+	0.389322i
$715$	−28.5462	−	4.92256i	−1.06757	−	0.184093i
$716$	22.3542	−	6.94416i	0.835417	−	0.259516i
$717$	−3.97983	+	1.77193i	−0.148629	+	0.0661741i
$718$	13.0386	−	1.28499i	0.486596	−	0.0479555i
$719$	−13.3035	−	11.9785i	−0.496136	−	0.446723i	0.382682	−	0.923880i	$-0.375001\pi$
$719$	−13.3035	−	11.9785i	−0.496136	−	0.446723i	−0.878818	+	0.477157i	$0.841667\pi$
$720$	−14.9296	−	5.28275i	−0.556393	−	0.196876i
$721$	−21.4449	−	9.54789i	−0.798650	−	0.355582i
$722$	−1.26028	+	0.259352i	−0.0469028	+	0.00965207i
$723$	13.2691	+	4.31139i	0.493483	+	0.160342i
$724$	45.1921	−	8.99499i	1.67955	−	0.334296i
$725$	−3.71640	−	2.14566i	−0.138024	−	0.0796879i
$726$	17.8706	+	3.33385i	0.663240	+	0.123731i
$727$		−	20.8418i		−	0.772979i	−0.922294	−	0.386489i	$-0.873688\pi$
$727$		−	20.8418i		−	0.772979i	0.922294	−	0.386489i	$-0.126312\pi$
$728$	−31.0956	−	8.21616i	−1.15248	−	0.304511i
$729$	−6.58698	+	20.2726i	−0.243962	+	0.750839i
$730$	14.9571	−	13.2928i	0.553587	−	0.491990i
$731$	−17.4898	+	1.83825i	−0.646883	+	0.0679901i
$732$	1.14363	−	9.67261i	0.0422699	−	0.357510i
$733$	−11.7444	−	36.1454i	−0.433788	−	1.33506i	−0.894324	−	0.447421i	$-0.852343\pi$
$733$	−11.7444	−	36.1454i	−0.433788	−	1.33506i	0.460536	−	0.887641i	$-0.347657\pi$
$734$	−17.9066	+	39.5272i	−0.660946	+	1.45897i
$735$	0.871873	−	8.29531i	0.0321595	−	0.305977i
$736$	−1.20841	+	37.2600i	−0.0445425	+	1.37342i
$737$	−6.15184	+	5.14412i	−0.226606	+	0.189486i
$738$	−22.7807	+	9.96614i	−0.838570	+	0.366859i
$739$	2.73563	+	6.14432i	0.100632	+	0.226022i	0.956844	−	0.290601i	$-0.0938553\pi$
$739$	2.73563	+	6.14432i	0.100632	+	0.226022i	−0.856213	+	0.516624i	$0.827189\pi$
$740$	−53.7166	−	0.696645i	−1.97466	−	0.0256092i
$741$	15.7766	−	8.49979i	0.579569	−	0.312248i
$742$	−0.244542	+	37.7137i	−0.00897743	+	1.38452i
$743$	−52.0905	+	5.47493i	−1.91101	+	0.200856i	−0.984498	−	0.175398i	$-0.943879\pi$
$743$	−52.0905	+	5.47493i	−1.91101	+	0.200856i	−0.926517	+	0.376254i	$0.877212\pi$
$744$	8.28656	+	5.00164i	0.303800	+	0.183369i
$745$	−1.68137	−	7.91022i	−0.0616006	−	0.289808i
$746$	21.9093	−	6.96204i	0.802158	−	0.254898i
$747$	−8.69328	+	5.01907i	−0.318071	+	0.183638i
$748$	15.3342	−	5.93516i	0.560676	−	0.217011i
$749$			20.6019i			0.752778i
$750$	11.1482	−	12.2210i	0.407073	−	0.446247i
$751$	−2.00077	+	1.80150i	−0.0730090	+	0.0657376i	−0.704827	−	0.709379i	$-0.748976\pi$
$751$	−2.00077	+	1.80150i	−0.0730090	+	0.0657376i	0.631818	+	0.775117i	$0.282309\pi$
$752$	−34.4082	+	14.2622i	−1.25474	+	0.520087i
$753$	0.0340683	−	0.0247521i	0.00124152	−	0.000902016i
$754$	16.1860	+	19.3291i	0.589458	+	0.703924i
$755$	9.97039	+	30.6857i	0.362860	+	1.11677i
$756$	−17.4623	+	29.3597i	−0.635099	+	1.06780i
$757$	−23.0266	+	10.2521i	−0.836918	+	0.372620i	−0.780016	−	0.625760i	$-0.784789\pi$
$757$	−23.0266	+	10.2521i	−0.836918	+	0.372620i	−0.0569020	+	0.998380i	$0.518122\pi$
$758$	−1.24337	+	11.1349i	−0.0451612	+	0.404436i
$759$	25.2872	+	3.59797i	0.917867	+	0.130598i
$760$	28.6170	−	5.50323i	1.03805	−	0.199623i
$761$	4.06501	−	38.6760i	0.147356	−	1.40200i	−0.631780	−	0.775148i	$-0.717675\pi$
$761$	4.06501	−	38.6760i	0.147356	−	1.40200i	0.779136	−	0.626855i	$-0.215658\pi$
$762$	11.5965	+	16.1808i	0.420096	+	0.586168i
$763$	−24.0332	−	21.6396i	−0.870062	−	0.783407i
$764$	10.3559	+	24.0960i	0.374664	+	0.871762i
$765$	1.02586	+	9.76039i	0.0370900	+	0.352888i
$766$	2.42730	−	7.30887i	0.0877020	−	0.264080i
$767$	−18.6794	−	45.5136i	−0.674475	−	1.64340i
$768$	−10.1909	−	15.6760i	−0.367734	−	0.565657i
$769$	−4.94985	+	8.57339i	−0.178496	+	0.309164i	−0.941366	−	0.337388i	$-0.890457\pi$
$769$	−4.94985	+	8.57339i	−0.178496	+	0.309164i	0.762870	+	0.646552i	$0.223790\pi$
$770$	−22.2920	+	28.0556i	−0.803347	+	1.01105i
$771$	0.0121496	−	0.00701459i	0.000437558	−	0.000252624i
$772$	−7.15840	+	21.0964i	−0.257637	+	0.759277i
$773$	−3.53957	−	16.6524i	−0.127309	−	0.598944i	−0.994831	−	0.101544i	$-0.967622\pi$
$773$	−3.53957	−	16.6524i	−0.127309	−	0.598944i	0.867522	−	0.497399i	$-0.165712\pi$
$774$	−16.0616	+	3.30531i	−0.577324	+	0.118807i
$775$	−2.05622	+	1.49393i	−0.0738618	+	0.0536637i
$776$	−18.0813	−	16.9288i	−0.649082	−	0.607709i
$777$	−8.49666	+	39.9736i	−0.304816	+	1.43405i
$778$	3.94010	+	39.9795i	0.141259	+	1.43334i
$779$	26.8942	−	37.0167i	0.963584	−	1.32626i
$780$	18.0948	−	9.44802i	0.647897	−	0.338293i
$781$	−20.0257	−	19.4048i	−0.716574	−	0.694358i
$782$	21.1657	−	9.25962i	0.756886	−	0.331123i
$783$	24.4619	−	10.8911i	0.874196	−	0.389217i
$784$	−8.11104	+	8.55142i	−0.289680	+	0.305408i
$785$	−18.4403	+	5.99161i	−0.658162	+	0.213850i
$786$	14.4364	−	8.21051i	0.514929	−	0.292859i
$787$	19.1158	−	42.9348i	0.681405	−	1.53046i	−0.158285	−	0.987393i	$-0.550596\pi$
$787$	19.1158	−	42.9348i	0.681405	−	1.53046i	0.839690	−	0.543067i	$-0.182737\pi$
$788$	6.96436	−	4.92319i	0.248095	−	0.175381i
$789$	1.76994	+	8.32693i	0.0630116	+	0.296446i
$790$	1.65510	−	7.54569i	0.0588857	−	0.268464i
$791$	−16.7390	−	9.66427i	−0.595170	−	0.343622i
$792$	13.6867	−	6.90994i	0.486337	−	0.245534i
$793$	−9.72137	−	11.4574i	−0.345216	−	0.406864i
$794$	12.5238	−	3.97964i	0.444454	−	0.141232i
$795$	−16.0166	−	17.7883i	−0.568051	−	0.630885i
$796$	0.271733	−	0.0250021i	0.00963132	−	0.000886177i
$797$	33.7084	+	15.0080i	1.19401	+	0.531609i	0.904875	−	0.425678i	$-0.139964\pi$
$797$	33.7084	+	15.0080i	1.19401	+	0.531609i	0.289139	+	0.957287i	$0.406631\pi$
$798$	0.143740	−	22.1679i	0.00508835	−	0.784734i
$799$	17.1535	+	15.4451i	0.606847	+	0.546408i
$800$	4.83305	−	0.864592i	0.170874	−	0.0305679i
$801$	12.1839	−	16.7696i	0.430495	−	0.592526i
$802$	−10.4518	−	1.16710i	−0.369066	−	0.0412116i
$803$	−0.709191	+	19.3599i	−0.0250268	+	0.683194i
$804$	1.24648	−	5.51179i	0.0439601	−	0.194386i
$805$	−29.5934	+	40.7318i	−1.04303	+	1.43561i
$806$	14.3575	−	4.10134i	0.505722	−	0.144464i
$807$	−22.4006	+	7.27841i	−0.788540	+	0.256212i
$808$	−10.8897	+	46.7419i	−0.383098	+	1.64438i
$809$	39.8178	−	4.18502i	1.39992	−	0.147138i	0.625705	−	0.780060i	$-0.284811\pi$
$809$	39.8178	−	4.18502i	1.39992	−	0.147138i	0.774216	+	0.632922i	$0.218145\pi$
$810$	−0.984309	−	4.78310i	−0.0345851	−	0.168061i
$811$	27.8931	+	9.06301i	0.979458	+	0.318245i	0.754628	−	0.656153i	$-0.227817\pi$
$811$	27.8931	+	9.06301i	0.979458	+	0.318245i	0.224830	+	0.974398i	$0.427817\pi$
$812$	30.5869	−	6.08798i	1.07339	−	0.213646i
$813$	−1.53746	−	2.66296i	−0.0539211	−	0.0933941i
$814$	36.4343	−	37.1153i	1.27702	−	1.30089i
$815$	−18.5678	+	10.7201i	−0.650402	+	0.375510i
$816$	−6.05176	+	9.88098i	−0.211854	+	0.345903i
$817$	22.4241	−	20.1908i	0.784521	−	0.706386i
$818$	12.1257	−	36.5118i	0.423965	−	1.27660i
$819$	5.22061	+	17.8370i	0.182423	+	0.623275i
$820$	31.1786	−	41.7639i	1.08880	−	1.45846i
$821$	5.87945	+	1.24972i	0.205194	+	0.0436154i	0.309362	−	0.950944i	$-0.399885\pi$
$821$	5.87945	+	1.24972i	0.205194	+	0.0436154i	−0.104168	+	0.994560i	$0.533218\pi$
$822$	−3.18390	−	32.3065i	−0.111051	−	1.12682i
$823$	−2.07428	−	0.218015i	−0.0723048	−	0.00759954i	0.0683070	−	0.997664i	$-0.478240\pi$
$823$	−2.07428	−	0.218015i	−0.0723048	−	0.00759954i	−0.140612	+	0.990065i	$0.544907\pi$
$824$	−19.8917	−	6.89378i	−0.692962	−	0.240156i
$825$	−0.228918	−	3.35610i	−0.00796991	−	0.116844i
$826$	−60.4830	−	6.75381i	−2.10447	−	0.234995i
$827$	13.3047	−	18.3124i	0.462651	−	0.636784i	−0.512405	−	0.858744i	$-0.671245\pi$
$827$	13.3047	−	18.3124i	0.462651	−	0.636784i	0.975056	+	0.221960i	$0.0712453\pi$
$828$	18.7941	−	10.5282i	0.653140	−	0.365880i
$829$	16.0265	+	3.40654i	0.556623	+	0.118314i	0.477630	−	0.878561i	$-0.341496\pi$
$829$	16.0265	+	3.40654i	0.556623	+	0.118314i	0.0789934	+	0.996875i	$0.474829\pi$
$830$	10.6380	−	18.1527i	0.369251	−	0.630091i
$831$	5.75510	−	4.18132i	0.199642	−	0.145049i
$832$	−28.4136	−	4.96670i	−0.985064	−	0.172189i
$833$	6.94658	+	2.25708i	0.240685	+	0.0782032i
$834$	−3.58678	+	16.3524i	−0.124200	+	0.566237i
$835$	−22.5941	+	39.1341i	−0.781901	+	1.35429i
$836$	−15.3001	+	23.7039i	−0.529165	+	0.819816i
$837$		−	15.8592i		−	0.548174i
$838$	−21.1113	−	19.2580i	−0.729276	−	0.665256i
$839$	33.5035	−	7.12139i	1.15667	−	0.245858i	0.410657	−	0.911790i	$-0.365299\pi$
$839$	33.5035	−	7.12139i	1.15667	−	0.245858i	0.746012	+	0.665932i	$0.231966\pi$
$840$	0.491164	−	25.2466i	0.0169468	−	0.871089i
$841$	4.16016	+	1.85222i	0.143454	+	0.0638697i
$842$	−21.7984	−	12.7745i	−0.751223	−	0.440238i
$843$	3.31337	−	15.5882i	0.114118	−	0.536885i
$844$	12.9547	+	0.168008i	0.445920	+	0.00578309i
$845$	8.34785	−	30.3644i	0.287175	−	1.04457i
$846$	17.3302	+	12.7636i	0.595825	+	0.438823i
$847$	−4.71073	−	34.3707i	−0.161863	−	1.18099i
$848$	2.66197	+	33.7185i	0.0914124	+	1.15790i
$849$	13.2890	+	1.39673i	0.456078	+	0.0479357i
$850$	−1.77242	−	2.47309i	−0.0607935	−	0.0848264i
$851$	48.8967	−	54.3053i	1.67616	−	1.86156i
$852$	19.5142	+	2.30724i	0.668544	+	0.0790448i
$853$	15.5091	−	11.2680i	0.531022	−	0.385810i	−0.289718	−	0.957112i	$-0.593561\pi$
$853$	15.5091	−	11.2680i	0.531022	−	0.385810i	0.820740	+	0.571302i	$0.193561\pi$
$854$	−18.2059	+	3.74658i	−0.622994	+	0.128205i
$855$	−11.2677	−	12.5141i	−0.385348	−	0.427972i
$856$	1.57352	+	18.4092i	0.0537820	+	0.629215i
$857$			15.2199i			0.519902i	0.965622	+	0.259951i	$0.0837064\pi$
$857$			15.2199i			0.519902i	−0.965622	+	0.259951i	$0.916294\pi$
$858$	−5.49884	+	18.9821i	−0.187727	+	0.648039i
$859$			38.6771i			1.31965i	0.751421	+	0.659823i	$0.229369\pi$
$859$			38.6771i			1.31965i	−0.751421	+	0.659823i	$0.770631\pi$
$860$	25.8388	−	22.6656i	0.881095	−	0.772890i
$861$	−26.5293	−	29.4638i	−0.904116	−	1.00412i
$862$	2.80434	+	13.6273i	0.0955160	+	0.464146i
$863$	−36.4589	+	26.4889i	−1.24108	+	0.901694i	−0.997670	−	0.0682301i	$-0.978265\pi$
$863$	−36.4589	+	26.4889i	−1.24108	+	0.901694i	−0.243406	+	0.969924i	$0.578265\pi$
$864$	−13.3614	+	27.5686i	−0.454563	+	0.937903i
$865$	−16.8464	+	18.7099i	−0.572796	+	0.636155i
$866$	4.87738	−	3.49553i	0.165740	−	0.118783i
$867$	−12.6159	−	1.32598i	−0.428458	−	0.0450327i
$868$	4.07433	−	18.0162i	0.138292	−	0.611508i
$869$	4.17158	+	6.20748i	0.141511	+	0.210574i
$870$	−11.7379	+	15.9375i	−0.397953	+	0.540332i
$871$	−4.91444	−	7.20053i	−0.166519	−	0.243981i
$872$	−23.1281	−	17.5009i	−0.783217	−	0.592655i
$873$	−2.97584	+	14.0002i	−0.100717	+	0.473836i
$874$	−20.0421	+	34.1999i	−0.677935	+	1.15683i
$875$	−28.8388	−	12.8398i	−0.974928	−	0.434066i
$876$	−7.88038	−	11.1476i	−0.266253	−	0.376642i
$877$	−5.65438	+	1.20187i	−0.190935	+	0.0405844i	−0.302386	−	0.953185i	$-0.597783\pi$
$877$	−5.65438	+	1.20187i	−0.190935	+	0.0405844i	0.111452	+	0.993770i	$0.464450\pi$
$878$	16.6800	−	18.2852i	0.562924	−	0.617097i
$879$		−	23.1635i		−	0.781284i
$880$	−17.7766	+	26.7722i	−0.599249	+	0.902490i
$881$	−4.55260	+	7.88533i	−0.153381	+	0.265664i	−0.932468	−	0.361252i	$-0.882349\pi$
$881$	−4.55260	+	7.88533i	−0.153381	+	0.265664i	0.779087	+	0.626915i	$0.215683\pi$
$882$	6.65255	+	1.45919i	0.224003	+	0.0491335i
$883$	−2.25805	−	0.733685i	−0.0759894	−	0.0246905i	0.270776	−	0.962642i	$-0.412720\pi$
$883$	−2.25805	−	0.733685i	−0.0759894	−	0.0246905i	−0.346765	+	0.937952i	$0.612720\pi$
$884$	4.79825	+	17.2192i	0.161383	+	0.579143i
$885$	31.2488	−	22.7036i	1.05042	−	0.763172i
$886$	40.9240	+	23.9826i	1.37487	+	0.805713i
$887$	5.16937	+	1.09878i	0.173570	+	0.0368935i	0.293877	−	0.955843i	$-0.405054\pi$
$887$	5.16937	+	1.09878i	0.173570	+	0.0368935i	−0.120306	+	0.992737i	$0.538388\pi$
$888$	−4.53926	+	36.3681i	−0.152327	+	1.22043i
$889$	22.3301	−	30.7347i	0.748926	−	1.03081i
$890$	−4.82155	+	43.1789i	−0.161619	+	1.44736i
$891$	4.00508	+	2.51218i	0.134175	+	0.0841611i
$892$	8.38839	+	27.0034i	0.280864	+	0.904141i
$893$	−39.3882	−	4.13987i	−1.31808	−	0.138535i
$894$	−5.49057	+	0.541112i	−0.183632	+	0.0180975i
$895$	27.7320	+	5.89462i	0.926978	+	0.197035i
$896$	−22.2612	+	27.8855i	−0.743693	+	0.931589i
$897$	−6.56971	+	26.9786i	−0.219356	+	0.900788i
$898$	−42.6515	−	14.1647i	−1.42330	−	0.472683i
$899$	−10.7598	+	9.68819i	−0.358860	+	0.323119i
$900$	−1.87090	−	2.13283i	−0.0623634	−	0.0710944i
$901$	18.1525	−	10.4804i	0.604748	−	0.349152i
$902$	8.35451	+	49.7615i	0.278175	+	1.65688i
$903$	−13.0734	−	22.6437i	−0.435054	−	0.753536i
$904$	−15.6956	−	7.35720i	−0.522027	−	0.244697i
$905$	53.0784	+	17.2462i	1.76439	+	0.573284i
$906$	21.5603	−	4.43688i	0.716295	−	0.147405i
$907$	38.9929	−	4.09832i	1.29474	−	0.136082i	0.568018	−	0.823016i	$-0.307710\pi$
$907$	38.9929	−	4.09832i	1.29474	−	0.136082i	0.726720	+	0.686934i	$0.241044\pi$
$908$	−5.89965	−	13.7272i	−0.195787	−	0.455553i
$909$	26.3759	−	8.57003i	0.874832	−	0.284250i
$910$	−27.9948	−	27.0887i	−0.928020	−	0.897982i
$911$	7.71305	−	10.6161i	0.255545	−	0.351727i	−0.661899	−	0.749593i	$-0.730249\pi$
$911$	7.71305	−	10.6161i	0.255545	−	0.351727i	0.917443	+	0.397866i	$0.130249\pi$
$912$	−1.56469	−	19.8195i	−0.0518119	−	0.656289i
$913$	5.58123	+	19.5904i	0.184712	+	0.648346i
$914$	2.55402	−	22.8723i	0.0844796	−	0.756549i
$915$	6.93409	−	9.54396i	0.229234	−	0.315513i
$916$	2.44217	−	1.36807i	0.0806916	−	0.0452024i
$917$	−23.5532	−	21.2074i	−0.777794	−	0.700329i
$918$	18.9850	+	0.123102i	0.626597	+	0.00406296i
$919$	38.3360	+	17.0683i	1.26459	+	0.563031i	0.925865	−	0.377855i	$-0.123338\pi$
$919$	38.3360	+	17.0683i	1.26459	+	0.563031i	0.338724	+	0.940886i	$0.390005\pi$
$920$	−23.3327	+	38.6569i	−0.769256	+	1.27448i
$921$	−13.5820	−	15.0843i	−0.447541	−	0.497045i
$922$	6.46381	+	20.3414i	0.212874	+	0.669908i
$923$	23.1149	−	19.6125i	0.760836	−	0.645554i
$924$	17.3345	+	17.2385i	0.570262	+	0.567104i
$925$	−8.33469	−	4.81204i	−0.274043	−	0.158219i
$926$	−32.2179	−	7.06678i	−1.05875	−	0.232229i
$927$	2.52928	+	11.8993i	0.0830726	+	0.390826i
$928$	26.8665	−	7.77618i	0.881935	−	0.255266i
$929$	−0.359060	+	0.806463i	−0.0117804	+	0.0264592i	−0.919340	−	0.393464i	$-0.871276\pi$
$929$	−0.359060	+	0.806463i	−0.0117804	+	0.0264592i	0.907559	+	0.419924i	$0.137943\pi$
$930$	5.79562	+	10.1903i	0.190046	+	0.334154i
$931$	−11.9191	+	3.87275i	−0.390633	+	0.126924i
$932$	43.6174	−	24.4339i	1.42873	−	0.800359i
$933$	−6.68446	+	2.97611i	−0.218839	+	0.0974336i
$934$	9.52335	+	21.7686i	0.311614	+	0.712290i
$935$	19.7168	+	2.80538i	0.644808	+	0.0917459i
$936$	6.02732	+	15.5398i	0.197009	+	0.507935i
$937$	10.7987	−	14.8632i	0.352779	−	0.485558i	−0.595340	−	0.803474i	$-0.702983\pi$
$937$	10.7987	−	14.8632i	0.352779	−	0.485558i	0.948119	+	0.317915i	$0.102983\pi$
$938$	−10.7321	+	1.05768i	−0.350416	+	0.0345346i
$939$	2.70672	−	12.7341i	0.0883305	−	0.415562i
$940$	−44.8011	−	5.29702i	−1.46125	−	0.172770i
$941$	−23.4081	+	17.0070i	−0.763081	+	0.554411i	−0.899854	−	0.436192i	$-0.856327\pi$
$941$	−23.4081	+	17.0070i	−0.763081	+	0.554411i	0.136773	+	0.990602i	$0.456327\pi$
$942$	2.66630	+	12.9565i	0.0868727	+	0.422145i
$943$	14.7399	+	69.3456i	0.479996	+	2.25820i
$944$	−54.5615	−	1.41544i	−1.77583	−	0.0460687i
$945$	−35.8314	+	20.6873i	−1.16560	+	0.672958i
$946$	−1.43375	+	33.2452i	−0.0466151	+	1.08089i
$947$	25.0231	−	43.3414i	0.813143	−	1.40840i	−0.0975107	−	0.995234i	$-0.531088\pi$
$947$	25.0231	−	43.3414i	0.813143	−	1.40840i	0.910654	−	0.413170i	$-0.135579\pi$
$948$	−4.99081	−	1.69348i	−0.162094	−	0.0550015i
$949$	−20.8713	−	2.81674i	−0.677511	−	0.0914353i
$950$	4.95455	+	1.64542i	0.160747	+	0.0533846i
$951$	−0.394738	−	3.75568i	−0.0128002	−	0.121786i
$952$	21.5354	+	5.01721i	0.697967	+	0.162609i
$953$	−13.2404	−	11.9217i	−0.428898	−	0.386182i	0.426216	−	0.904621i	$-0.359846\pi$
$953$	−13.2404	−	11.9217i	−0.428898	−	0.386182i	−0.855114	+	0.518440i	$0.826513\pi$
$954$	15.8863	−	11.3854i	0.514338	−	0.368617i
$955$	−3.32045	+	31.5920i	−0.107447	+	1.02229i
$956$	5.47570	+	5.06045i	0.177097	+	0.163667i
$957$	−3.29535	−	18.8774i	−0.106523	−	0.610221i
$958$	−12.1159	−	1.35292i	−0.391448	−	0.0437109i
$959$	−56.5953	+	25.1979i	−1.82756	+	0.813681i
$960$	−1.48938	−	22.5970i	−0.0480696	−	0.729316i
$961$	−6.92959	−	21.3271i	−0.223535	−	0.687971i
$962$	36.3000	+	43.3490i	1.17036	+	1.39763i
$963$	8.63754	−	6.27554i	0.278341	−	0.202226i
$964$	−2.18781	−	23.7779i	−0.0704645	−	0.765836i
$965$	−20.0521	+	18.0550i	−0.645499	+	0.581209i
$966$	25.3764	+	23.1487i	0.816471	+	0.744796i
$967$		−	28.3218i		−	0.910766i	−0.890296	−	0.455383i	$-0.849502\pi$
$967$		−	28.3218i		−	0.910766i	0.890296	−	0.455383i	$-0.150498\pi$
$968$	−6.83451	−	30.3528i	−0.219670	−	0.975574i
$969$	−10.6699	+	6.16028i	−0.342767	+	0.197897i
$970$	−9.08543	−	28.5916i	−0.291716	−	0.918020i
$971$	11.8504	+	55.7515i	0.380296	+	1.78915i	0.585757	+	0.810487i	$0.300797\pi$
$971$	11.8504	+	55.7515i	0.380296	+	1.78915i	−0.205461	+	0.978665i	$0.565869\pi$
$972$	29.0400	−	2.67197i	0.931457	−	0.0857033i
$973$	31.7732	−	3.33950i	1.01860	−	0.107059i
$974$	−22.3247	−	0.144757i	−0.715328	−	0.00463831i
$975$	3.65536	+	0.107599i	0.117065	+	0.00344593i
$976$	−15.9821	+	4.73835i	−0.511574	+	0.151671i
$977$	−6.80596	−	15.2864i	−0.217742	−	0.489056i	0.771340	−	0.636423i	$-0.219587\pi$
$977$	−6.80596	−	15.2864i	−0.217742	−	0.489056i	−0.989082	+	0.147367i	$0.952920\pi$
$978$	5.86267	+	13.4010i	0.187468	+	0.428515i
$979$	−26.9825	−	32.2684i	−0.862366	−	1.03130i
$980$	−13.6328	+	4.23491i	−0.435483	+	0.135279i
$981$	−1.75185	+	16.6678i	−0.0559324	+	0.532161i
$982$	−28.3918	−	12.8621i	−0.906018	−	0.410445i
$983$	−12.1454	−	37.3797i	−0.387378	−	1.19223i	−0.934740	−	0.355332i	$-0.884368\pi$
$983$	−12.1454	−	37.3797i	−0.387378	−	1.19223i	0.547362	−	0.836896i	$-0.315632\pi$
$984$	−25.9561	−	24.3017i	−0.827451	−	0.774709i
$985$	10.2734	−	1.07978i	0.327337	−	0.0344046i
$986$	−11.5142	−	12.9557i	−0.366686	−	0.412594i
$987$	−10.6050	+	32.6387i	−0.337560	+	1.03890i
$988$	−24.0267	−	19.0632i	−0.764392	−	0.606481i
$989$			46.7538i			1.48668i
$990$	18.5529	+	0.800120i	0.589649	+	0.0254295i
$991$	−11.3307	−	6.54179i	−0.359932	−	0.207807i	0.309119	−	0.951023i	$-0.399966\pi$
$991$	−11.3307	−	6.54179i	−0.359932	−	0.207807i	−0.669051	+	0.743217i	$0.733299\pi$
$992$	2.26466	−	16.4099i	0.0719032	−	0.521013i
$993$	17.6302	+	5.72840i	0.559478	+	0.181785i
$994$	−7.55859	−	36.7299i	−0.239744	−	1.16500i
$995$	0.301937	+	0.134431i	0.00957203	+	0.00426174i
$996$	−11.5025	−	8.58713i	−0.364470	−	0.272094i
$997$	−17.3811	−	15.6500i	−0.550465	−	0.495641i	0.346314	−	0.938119i	$-0.387433\pi$
$997$	−17.3811	−	15.6500i	−0.550465	−	0.495641i	−0.896780	+	0.442477i	$0.854100\pi$
$998$	1.80596	+	18.3248i	0.0571666	+	0.580061i
$999$	54.8602	−	24.4253i	1.73570	−	0.772783i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.bn.a.95.7	✓	640
4.3	odd	2	inner	572.2.bn.a.95.29	yes	640
11.8	odd	10	inner	572.2.bn.a.459.55	yes	640
13.10	even	6	inner	572.2.bn.a.491.22	yes	640
44.19	even	10	inner	572.2.bn.a.459.22	yes	640
52.23	odd	6	inner	572.2.bn.a.491.55	yes	640
143.140	odd	30	inner	572.2.bn.a.283.29	yes	640
572.283	even	30	inner	572.2.bn.a.283.7	yes	640

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.bn.a.95.7	✓	640	1.1	even	1	trivial
572.2.bn.a.95.29	yes	640	4.3	odd	2	inner
572.2.bn.a.283.7	yes	640	572.283	even	30	inner
572.2.bn.a.283.29	yes	640	143.140	odd	30	inner
572.2.bn.a.459.22	yes	640	44.19	even	10	inner
572.2.bn.a.459.55	yes	640	11.8	odd	10	inner
572.2.bn.a.491.22	yes	640	13.10	even	6	inner
572.2.bn.a.491.55	yes	640	52.23	odd	6	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:	\( N \)	\(=\)	\( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	572.bn (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.38137 - 0.302995i) q^{2} +(-0.868428 + 0.781936i) q^{3} +(1.81639 + 0.837098i) q^{4} +(1.42384 + 1.95975i) q^{5} +(1.43655 - 0.817017i) q^{6} +(-2.34374 - 2.11032i) q^{7} +(-2.25548 - 1.70670i) q^{8} +(-0.170842 + 1.62546i) q^{9} +O(q^{10})\)	\(q+(-1.38137 - 0.302995i) q^{2} +(-0.868428 + 0.781936i) q^{3} +(1.81639 + 0.837098i) q^{4} +(1.42384 + 1.95975i) q^{5} +(1.43655 - 0.817017i) q^{6} +(-2.34374 - 2.11032i) q^{7} +(-2.25548 - 1.70670i) q^{8} +(-0.170842 + 1.62546i) q^{9} +(-1.37306 - 3.13856i) q^{10} +(3.11466 + 1.13968i) q^{11} +(-2.23196 + 0.693340i) q^{12} +(-1.56279 + 3.24926i) q^{13} +(2.59817 + 3.62528i) q^{14} +(-2.76890 - 0.588548i) q^{15} +(2.59853 + 3.04099i) q^{16} +(1.00824 - 2.26454i) q^{17} +(0.728502 - 2.19360i) q^{18} +(0.884301 + 4.16031i) q^{19} +(0.945745 + 4.75156i) q^{20} +3.68550 q^{21} +(-3.95720 - 2.51805i) q^{22} +(-5.70725 - 3.29508i) q^{23} +(3.29325 - 0.281490i) q^{24} +(-0.268206 + 0.825454i) q^{25} +(3.14331 - 4.01493i) q^{26} +(-3.18327 - 4.38139i) q^{27} +(-2.49061 - 5.79510i) q^{28} +(-1.02798 + 4.83626i) q^{29} +(3.64656 + 1.65197i) q^{30} +(2.36910 + 1.72125i) q^{31} +(-2.66814 - 4.98809i) q^{32} +(-3.59601 + 1.44574i) q^{33} +(-2.07889 + 2.82268i) q^{34} +(0.798571 - 7.59790i) q^{35} +(-1.67098 + 2.80945i) q^{36} +(-2.30543 + 10.8462i) q^{37} +(0.0390015 - 6.01488i) q^{38} +(-1.18354 - 4.04375i) q^{39} +(0.133269 - 6.85023i) q^{40} +(-7.19829 - 7.99451i) q^{41} +(-5.09106 - 1.11669i) q^{42} +(-3.54724 - 6.14400i) q^{43} +(4.70342 + 4.67738i) q^{44} +(-3.42874 + 1.97958i) q^{45} +(6.88546 + 6.28101i) q^{46} +(-2.87748 + 8.85598i) q^{47} +(-4.63450 - 0.608994i) q^{48} +(0.308000 + 2.93042i) q^{49} +(0.620601 - 1.05900i) q^{50} +(0.895141 + 2.75496i) q^{51} +(-5.55858 + 4.59371i) q^{52} +(6.84093 + 4.97022i) q^{53} +(3.06975 + 7.01686i) q^{54} +(2.20130 + 7.72668i) q^{55} +(1.68457 + 8.75984i) q^{56} +(-4.02105 - 2.92146i) q^{57} +(2.88538 - 6.36921i) q^{58} +(-9.13027 + 10.1402i) q^{59} +(-4.53672 - 3.38687i) q^{60} +(-1.69505 + 3.80713i) q^{61} +(-2.75109 - 3.09552i) q^{62} +(3.83064 - 3.44912i) q^{63} +(2.17434 + 7.69885i) q^{64} +(-8.59289 + 1.56375i) q^{65} +(5.40549 - 0.907534i) q^{66} +(-1.20894 + 2.09394i) q^{67} +(3.72699 - 3.26928i) q^{68} +(7.53288 - 1.60116i) q^{69} +(-3.40525 + 10.2536i) q^{70} +(-7.68076 - 3.41970i) q^{71} +(3.15950 - 3.37460i) q^{72} +(1.80501 + 5.55525i) q^{73} +(6.47100 - 14.2841i) q^{74} +(-0.412534 - 0.926567i) q^{75} +(-1.87635 + 8.29699i) q^{76} +(-4.89489 - 9.24404i) q^{77} +(0.409680 + 5.94453i) q^{78} +(1.82433 + 1.32545i) q^{79} +(-2.25968 + 9.42236i) q^{80} +(1.39432 + 0.296372i) q^{81} +(7.52123 + 13.2245i) q^{82} +(3.61003 + 4.96878i) q^{83} +(6.69430 + 3.08513i) q^{84} +(5.87349 - 1.24845i) q^{85} +(3.03847 + 9.56196i) q^{86} +(-2.88892 - 5.00375i) q^{87} +(-5.07996 - 7.88632i) q^{88} +(-10.9834 - 6.34125i) q^{89} +(5.33617 - 1.69565i) q^{90} +(10.5197 - 4.31745i) q^{91} +(-7.60828 - 10.7627i) q^{92} +(-3.40331 + 0.357702i) q^{93} +(6.65819 - 11.3616i) q^{94} +(-6.89406 + 7.65663i) q^{95} +(6.21745 + 2.24548i) q^{96} +(8.70931 + 0.915385i) q^{97} +(0.462440 - 4.14133i) q^{98} +(-2.38461 + 4.86805i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 640 q - 15 q^{2} - 3 q^{4} - 15 q^{6} - 78 q^{9}+O(q^{10}) \) 640 * q - 15 * q^2 - 3 * q^4 - 15 * q^6 - 78 * q^9	\( 640 q - 15 q^{2} - 3 q^{4} - 15 q^{6} - 78 q^{9} - 4 q^{12} - 20 q^{13} - 12 q^{14} - 19 q^{16} - 10 q^{17} - 45 q^{20} - 15 q^{22} - 15 q^{24} + 104 q^{25} - 20 q^{26} - 15 q^{28} - 10 q^{29} + 45 q^{30} - 24 q^{33} + 4 q^{36} - 18 q^{37} - 14 q^{38} - 20 q^{40} - 30 q^{41} - 13 q^{42} - 108 q^{45} - 15 q^{46} + 35 q^{48} - 74 q^{49} - 90 q^{50} + 15 q^{52} - 8 q^{53} + 50 q^{56} + 27 q^{58} - 10 q^{61} - 5 q^{62} - 84 q^{64} - 146 q^{66} - 70 q^{68} - 26 q^{69} - 15 q^{72} - 55 q^{74} + 44 q^{77} + 24 q^{78} - 39 q^{80} + 30 q^{81} - 29 q^{82} + 30 q^{84} - 30 q^{85} - 75 q^{88} - 24 q^{89} + 30 q^{90} + 14 q^{92} + 66 q^{93} - 5 q^{94} - 30 q^{97}+O(q^{100}) \) 640 * q - 15 * q^2 - 3 * q^4 - 15 * q^6 - 78 * q^9 - 4 * q^12 - 20 * q^13 - 12 * q^14 - 19 * q^16 - 10 * q^17 - 45 * q^20 - 15 * q^22 - 15 * q^24 + 104 * q^25 - 20 * q^26 - 15 * q^28 - 10 * q^29 + 45 * q^30 - 24 * q^33 + 4 * q^36 - 18 * q^37 - 14 * q^38 - 20 * q^40 - 30 * q^41 - 13 * q^42 - 108 * q^45 - 15 * q^46 + 35 * q^48 - 74 * q^49 - 90 * q^50 + 15 * q^52 - 8 * q^53 + 50 * q^56 + 27 * q^58 - 10 * q^61 - 5 * q^62 - 84 * q^64 - 146 * q^66 - 70 * q^68 - 26 * q^69 - 15 * q^72 - 55 * q^74 + 44 * q^77 + 24 * q^78 - 39 * q^80 + 30 * q^81 - 29 * q^82 + 30 * q^84 - 30 * q^85 - 75 * q^88 - 24 * q^89 + 30 * q^90 + 14 * q^92 + 66 * q^93 - 5 * q^94 - 30 * q^97

Introduction

L-functions

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