LMFDB - Embedded newform 76.2.k.a.15.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [76,2,Mod(3,76)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(76, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 13]))

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

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

chi := DirichletCharacter("76.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	76.k (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$0.606863055362$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$8$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			15.4
Character	$\chi$	$=$	76.15
Dual form			76.2.k.a.71.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.312491 + 1.37926i) q^{2} +(-0.547993 - 3.10782i) q^{3} +(-1.80470 - 0.862010i) q^{4} +(1.46633 - 1.23040i) q^{5} +(4.45773 + 0.215343i) q^{6} +(1.58907 + 0.917452i) q^{7} +(1.75289 - 2.21977i) q^{8} +(-6.53918 + 2.38007i) q^{9} +O(q^{10})$	\(q+(-0.312491 + 1.37926i) q^{2} +(-0.547993 - 3.10782i) q^{3} +(-1.80470 - 0.862010i) q^{4} +(1.46633 - 1.23040i) q^{5} +(4.45773 + 0.215343i) q^{6} +(1.58907 + 0.917452i) q^{7} +(1.75289 - 2.21977i) q^{8} +(-6.53918 + 2.38007i) q^{9} +(1.23882 + 2.40694i) q^{10} +(-2.10674 + 1.21633i) q^{11} +(-1.69001 + 6.08106i) q^{12} +(2.49843 + 0.440541i) q^{13} +(-1.76197 + 1.90504i) q^{14} +(-4.62741 - 3.88286i) q^{15} +(2.51388 + 3.11134i) q^{16} +(0.818624 + 0.297955i) q^{17} +(-1.23929 - 9.76296i) q^{18} +(4.35874 + 0.0369281i) q^{19} +(-3.70691 + 0.956507i) q^{20} +(1.98048 - 5.44131i) q^{21} +(-1.01929 - 3.28582i) q^{22} +(-4.69241 + 5.59220i) q^{23} +(-7.85923 - 4.23124i) q^{24} +(-0.231990 + 1.31568i) q^{25} +(-1.38836 + 3.30832i) q^{26} +(6.24660 + 10.8194i) q^{27} +(-2.07695 - 3.02552i) q^{28} +(-0.967934 - 2.65938i) q^{29} +(6.80148 - 5.16903i) q^{30} +(2.07350 - 3.59141i) q^{31} +(-5.07690 + 2.49502i) q^{32} +(4.93460 + 5.88083i) q^{33} +(-0.666769 + 1.03598i) q^{34} +(3.45895 - 0.609906i) q^{35} +(13.8529 + 1.34154i) q^{36} -1.48548i q^{37} +(-1.41300 + 6.00029i) q^{38} -8.00610i q^{39} +(-0.160893 - 5.41168i) q^{40} +(-1.43355 + 0.252774i) q^{41} +(6.88609 + 4.43195i) q^{42} +(5.26751 + 6.27757i) q^{43} +(4.85052 - 0.379072i) q^{44} +(-6.66019 + 11.5358i) q^{45} +(-6.24674 - 8.21955i) q^{46} +(-0.855159 - 2.34953i) q^{47} +(8.29190 - 9.51767i) q^{48} +(-1.81656 - 3.14638i) q^{49} +(-1.74217 - 0.731112i) q^{50} +(0.477390 - 2.70741i) q^{51} +(-4.12917 - 2.94872i) q^{52} +(-1.18928 + 1.41733i) q^{53} +(-16.8748 + 5.23470i) q^{54} +(-1.59262 + 4.37567i) q^{55} +(4.82200 - 1.91919i) q^{56} +(-2.27379 - 13.5664i) q^{57} +(3.97043 - 0.503998i) q^{58} +(-6.43248 - 2.34123i) q^{59} +(5.00401 + 10.9963i) q^{60} +(-8.58916 - 7.20716i) q^{61} +(4.30553 + 3.98217i) q^{62} +(-12.5748 - 2.21728i) q^{63} +(-1.85478 - 7.78202i) q^{64} +(4.20558 - 2.42810i) q^{65} +(-9.65319 + 4.96838i) q^{66} +(-2.59900 + 0.945959i) q^{67} +(-1.22053 - 1.24338i) q^{68} +(19.9510 + 11.5187i) q^{69} +(-0.239673 + 4.96136i) q^{70} +(6.12140 - 5.13647i) q^{71} +(-6.17923 + 18.6875i) q^{72} +(2.02346 + 11.4756i) q^{73} +(2.04886 + 0.464198i) q^{74} +4.21603 q^{75} +(-7.83439 - 3.82393i) q^{76} -4.46368 q^{77} +(11.0425 + 2.50183i) q^{78} +(0.908863 + 5.15442i) q^{79} +(7.51438 + 1.46919i) q^{80} +(14.2094 - 11.9231i) q^{81} +(0.0993319 - 2.05623i) q^{82} +(-8.19927 - 4.73385i) q^{83} +(-8.26463 + 8.11274i) q^{84} +(1.56698 - 0.570334i) q^{85} +(-10.3044 + 5.30356i) q^{86} +(-7.73445 + 4.46548i) q^{87} +(-0.992905 + 6.80856i) q^{88} +(-6.18655 - 1.09085i) q^{89} +(-13.8296 - 12.7909i) q^{90} +(3.56602 + 2.99225i) q^{91} +(13.2889 - 6.04733i) q^{92} +(-12.2977 - 4.47601i) q^{93} +(3.50784 - 0.445277i) q^{94} +(6.43681 - 5.30885i) q^{95} +(10.5362 + 14.4108i) q^{96} +(-2.11617 + 5.81414i) q^{97} +(4.90733 - 1.52229i) q^{98} +(10.8814 - 12.9680i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 6 q^{2} - 12 q^{5} - 12 q^{6} - 9 q^{8} - 18 q^{9}+O(q^{10}) $ 48 * q - 6 * q^2 - 12 * q^5 - 12 * q^6 - 9 * q^8 - 18 * q^9	$ 48 q - 6 q^{2} - 12 q^{5} - 12 q^{6} - 9 q^{8} - 18 q^{9} - 3 q^{10} - 9 q^{12} - 3 q^{14} - 12 q^{17} - 42 q^{20} - 18 q^{21} - 12 q^{22} + 24 q^{24} - 12 q^{25} + 21 q^{26} - 12 q^{29} + 42 q^{30} + 9 q^{32} - 36 q^{33} + 87 q^{36} + 60 q^{38} + 6 q^{40} + 30 q^{41} + 3 q^{42} + 45 q^{44} - 6 q^{45} + 36 q^{46} + 45 q^{48} - 18 q^{49} + 18 q^{50} - 15 q^{52} - 24 q^{53} - 75 q^{54} - 12 q^{57} + 60 q^{58} + 6 q^{60} - 66 q^{62} - 45 q^{64} + 18 q^{65} - 42 q^{66} - 42 q^{68} + 126 q^{69} - 63 q^{70} - 78 q^{72} - 12 q^{73} - 105 q^{74} - 126 q^{76} - 36 q^{77} + 3 q^{78} - 3 q^{80} + 72 q^{81} - 111 q^{82} - 117 q^{84} + 108 q^{85} - 24 q^{86} - 81 q^{88} - 18 q^{90} + 36 q^{92} + 30 q^{93} - 66 q^{96} - 6 q^{97} + 39 q^{98}+O(q^{100}) $ 48 * q - 6 * q^2 - 12 * q^5 - 12 * q^6 - 9 * q^8 - 18 * q^9 - 3 * q^10 - 9 * q^12 - 3 * q^14 - 12 * q^17 - 42 * q^20 - 18 * q^21 - 12 * q^22 + 24 * q^24 - 12 * q^25 + 21 * q^26 - 12 * q^29 + 42 * q^30 + 9 * q^32 - 36 * q^33 + 87 * q^36 + 60 * q^38 + 6 * q^40 + 30 * q^41 + 3 * q^42 + 45 * q^44 - 6 * q^45 + 36 * q^46 + 45 * q^48 - 18 * q^49 + 18 * q^50 - 15 * q^52 - 24 * q^53 - 75 * q^54 - 12 * q^57 + 60 * q^58 + 6 * q^60 - 66 * q^62 - 45 * q^64 + 18 * q^65 - 42 * q^66 - 42 * q^68 + 126 * q^69 - 63 * q^70 - 78 * q^72 - 12 * q^73 - 105 * q^74 - 126 * q^76 - 36 * q^77 + 3 * q^78 - 3 * q^80 + 72 * q^81 - 111 * q^82 - 117 * q^84 + 108 * q^85 - 24 * q^86 - 81 * q^88 - 18 * q^90 + 36 * q^92 + 30 * q^93 - 66 * q^96 - 6 * q^97 + 39 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$e\left(\frac{11}{18}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.312491	+	1.37926i	−0.220964	+	0.975282i
$2$	−0.312491	+	1.37926i	−0.220964	+	0.975282i
$3$	−0.547993	−	3.10782i	−0.316384	−	1.79430i	−0.564353	−	0.825534i	$-0.690874\pi$
$3$	−0.547993	−	3.10782i	−0.316384	−	1.79430i	0.247969	−	0.968768i	$-0.420237\pi$
$4$	−1.80470	−	0.862010i	−0.902349	−	0.431005i
$5$	1.46633	−	1.23040i	0.655765	−	0.550252i	−0.253049	−	0.967453i	$-0.581433\pi$
$5$	1.46633	−	1.23040i	0.655765	−	0.550252i	0.908814	+	0.417201i	$0.136989\pi$
$6$	4.45773	+	0.215343i	1.81986	+	0.0879135i
$7$	1.58907	+	0.917452i	0.600613	+	0.346764i	0.769283	−	0.638909i	$-0.220614\pi$
$7$	1.58907	+	0.917452i	0.600613	+	0.346764i	−0.168670	+	0.985673i	$0.553947\pi$
$8$	1.75289	−	2.21977i	0.619739	−	0.784808i
$9$	−6.53918	+	2.38007i	−2.17973	+	0.793356i
$10$	1.23882	+	2.40694i	0.391750	+	0.761142i
$11$	−2.10674	+	1.21633i	−0.635206	+	0.366736i	−0.782765	−	0.622317i	$-0.786191\pi$
$11$	−2.10674	+	1.21633i	−0.635206	+	0.366736i	0.147560	+	0.989053i	$0.452858\pi$
$12$	−1.69001	+	6.08106i	−0.487865	+	1.75545i
$13$	2.49843	+	0.440541i	0.692941	+	0.122184i	0.509017	−	0.860756i	$-0.330009\pi$
$13$	2.49843	+	0.440541i	0.692941	+	0.122184i	0.183924	+	0.982940i	$0.441120\pi$
$14$	−1.76197	+	1.90504i	−0.470907	+	0.509145i
$15$	−4.62741	−	3.88286i	−1.19479	−	1.00255i
$16$	2.51388	+	3.11134i	0.628469	+	0.777835i
$17$	0.818624	+	0.297955i	0.198545	+	0.0722646i	0.439379	−	0.898302i	$-0.355199\pi$
$17$	0.818624	+	0.297955i	0.198545	+	0.0722646i	−0.240833	+	0.970566i	$0.577421\pi$
$18$	−1.23929	−	9.76296i	−0.292103	−	2.30115i
$19$	4.35874	+	0.0369281i	0.999964	+	0.00847188i
$19$	4.35874	+	0.0369281i	0.999964	+	0.00847188i
$20$	−3.70691	+	0.956507i	−0.828890	+	0.213882i
$21$	1.98048	−	5.44131i	0.432175	−	1.18739i
$22$	−1.01929	−	3.28582i	−0.217313	−	0.700540i
$23$	−4.69241	+	5.59220i	−0.978436	+	1.16605i	0.00767613	+	0.999971i	$0.497557\pi$
$23$	−4.69241	+	5.59220i	−0.978436	+	1.16605i	−0.986112	+	0.166084i	$0.946888\pi$
$24$	−7.85923	−	4.23124i	−1.60426	−	0.863698i
$25$	−0.231990	+	1.31568i	−0.0463980	+	0.263136i
$26$	−1.38836	+	3.30832i	−0.272279	+	0.648815i
$27$	6.24660	+	10.8194i	1.20216	+	2.08220i
$28$	−2.07695	−	3.02552i	−0.392506	−	0.571770i
$29$	−0.967934	−	2.65938i	−0.179741	−	0.493834i	0.816802	−	0.576918i	$-0.195745\pi$
$29$	−0.967934	−	2.65938i	−0.179741	−	0.493834i	−0.996542	+	0.0830848i	$0.973523\pi$
$30$	6.80148	−	5.16903i	1.24177	−	0.943731i
$31$	2.07350	−	3.59141i	0.372412	−	0.645036i	−0.617524	−	0.786552i	$-0.711864\pi$
$31$	2.07350	−	3.59141i	0.372412	−	0.645036i	0.989936	+	0.141516i	$0.0451975\pi$
$32$	−5.07690	+	2.49502i	−0.897477	+	0.441061i
$33$	4.93460	+	5.88083i	0.859004	+	1.02372i
$34$	−0.666769	+	1.03598i	−0.114350	+	0.177670i
$35$	3.45895	−	0.609906i	0.584669	−	0.103093i
$36$	13.8529	+	1.34154i	2.30882	+	0.223590i
$37$		−	1.48548i		−	0.244211i	−0.992517	−	0.122106i	$-0.961035\pi$
$37$		−	1.48548i		−	0.244211i	0.992517	−	0.122106i	$-0.0389646\pi$
$38$	−1.41300	+	6.00029i	−0.229219	+	0.973375i
$39$		−	8.00610i		−	1.28200i
$40$	−0.160893	−	5.41168i	−0.0254394	−	0.855662i
$41$	−1.43355	+	0.252774i	−0.223883	+	0.0394766i	−0.284464	−	0.958687i	$-0.591816\pi$
$41$	−1.43355	+	0.252774i	−0.223883	+	0.0394766i	0.0605811	+	0.998163i	$0.480705\pi$
$42$	6.88609	+	4.43195i	1.06255	+	0.683864i
$43$	5.26751	+	6.27757i	0.803288	+	0.957321i	0.999731	−	0.0231942i	$-0.00738360\pi$
$43$	5.26751	+	6.27757i	0.803288	+	0.957321i	−0.196443	+	0.980515i	$0.562939\pi$
$44$	4.85052	−	0.379072i	0.731243	−	0.0571472i
$45$	−6.66019	+	11.5358i	−0.992843	+	1.71965i
$46$	−6.24674	−	8.21955i	−0.921032	−	1.21191i
$47$	−0.855159	−	2.34953i	−0.124738	−	0.342714i	0.861568	−	0.507643i	$-0.169483\pi$
$47$	−0.855159	−	2.34953i	−0.124738	−	0.342714i	−0.986306	+	0.164928i	$0.947261\pi$
$48$	8.29190	−	9.51767i	1.19683	−	1.37376i
$49$	−1.81656	−	3.14638i	−0.259509	−	0.449483i
$50$	−1.74217	−	0.731112i	−0.246379	−	0.103395i
$51$	0.477390	−	2.70741i	0.0668480	−	0.379114i
$52$	−4.12917	−	2.94872i	−0.572613	−	0.408914i
$53$	−1.18928	+	1.41733i	−0.163360	+	0.194685i	−0.841515	−	0.540234i	$-0.818336\pi$
$53$	−1.18928	+	1.41733i	−0.163360	+	0.194685i	0.678154	+	0.734919i	$0.262780\pi$
$54$	−16.8748	+	5.23470i	−2.29637	+	0.712352i
$55$	−1.59262	+	4.37567i	−0.214748	+	0.590016i
$56$	4.82200	−	1.91919i	0.644367	−	0.256463i
$57$	−2.27379	−	13.5664i	−0.301171	−	1.79692i
$58$	3.97043	−	0.503998i	0.521343	−	0.0661782i
$59$	−6.43248	−	2.34123i	−0.837437	−	0.304802i	−0.112530	−	0.993648i	$-0.535895\pi$
$59$	−6.43248	−	2.34123i	−0.837437	−	0.304802i	−0.724907	+	0.688846i	$0.758118\pi$
$60$	5.00401	+	10.9963i	0.646015	+	1.41961i
$61$	−8.58916	−	7.20716i	−1.09973	−	0.922782i	−0.102322	−	0.994751i	$-0.532627\pi$
$61$	−8.58916	−	7.20716i	−1.09973	−	0.922782i	−0.997407	+	0.0719693i	$0.977072\pi$
$62$	4.30553	+	3.98217i	0.546802	+	0.505737i
$63$	−12.5748	−	2.21728i	−1.58428	−	0.279351i
$64$	−1.85478	−	7.78202i	−0.231848	−	0.972752i
$65$	4.20558	−	2.42810i	0.521639	−	0.301168i
$66$	−9.65319	+	4.96838i	−1.18823	+	0.611565i
$67$	−2.59900	+	0.945959i	−0.317519	+	0.115567i	−0.495863	−	0.868401i	$-0.665148\pi$
$67$	−2.59900	+	0.945959i	−0.317519	+	0.115567i	0.178344	+	0.983968i	$0.442926\pi$
$68$	−1.22053	−	1.24338i	−0.148011	−	0.150782i
$69$	19.9510	+	11.5187i	2.40181	+	1.38669i
$70$	−0.239673	+	4.96136i	−0.0286464	+	0.592997i
$71$	6.12140	−	5.13647i	0.726477	−	0.609587i	−0.202692	−	0.979243i	$-0.564969\pi$
$71$	6.12140	−	5.13647i	0.726477	−	0.609587i	0.929169	+	0.369656i	$0.120524\pi$
$72$	−6.17923	+	18.6875i	−0.728229	+	2.20234i
$73$	2.02346	+	11.4756i	0.236828	+	1.34312i	0.838730	+	0.544547i	$0.183299\pi$
$73$	2.02346	+	11.4756i	0.236828	+	1.34312i	−0.601902	+	0.798570i	$0.705590\pi$
$74$	2.04886	+	0.464198i	0.238175	+	0.0539620i
$75$	4.21603			0.486825
$76$	−7.83439	−	3.82393i	−0.898666	−	0.438634i
$77$	−4.46368			−0.508684
$78$	11.0425	+	2.50183i	1.25031	+	0.283277i
$79$	0.908863	+	5.15442i	0.102255	+	0.579918i	0.992281	+	0.124008i	$0.0395749\pi$
$79$	0.908863	+	5.15442i	0.102255	+	0.579918i	−0.890026	+	0.455910i	$0.849314\pi$
$80$	7.51438	+	1.46919i	0.840133	+	0.164260i
$81$	14.2094	−	11.9231i	1.57882	−	1.32479i
$82$	0.0993319	−	2.05623i	0.0109694	−	0.227072i
$83$	−8.19927	−	4.73385i	−0.899987	−	0.519608i	−0.0227911	−	0.999740i	$-0.507255\pi$
$83$	−8.19927	−	4.73385i	−0.899987	−	0.519608i	−0.877196	+	0.480132i	$0.840589\pi$
$84$	−8.26463	+	8.11274i	−0.901745	+	0.885172i
$85$	1.56698	−	0.570334i	0.169963	−	0.0618614i
$86$	−10.3044	+	5.30356i	−1.11116	+	0.571898i
$87$	−7.73445	+	4.46548i	−0.829220	+	0.478750i
$88$	−0.992905	+	6.80856i	−0.105844	+	0.725795i
$89$	−6.18655	−	1.09085i	−0.655773	−	0.115630i	−0.164145	−	0.986436i	$-0.552487\pi$
$89$	−6.18655	−	1.09085i	−0.655773	−	0.115630i	−0.491627	+	0.870806i	$0.663598\pi$
$90$	−13.8296	−	12.7909i	−1.45776	−	1.34828i
$91$	3.56602	+	2.99225i	0.373820	+	0.313673i
$92$	13.2889	−	6.04733i	1.38547	−	0.630477i
$93$	−12.2977	−	4.47601i	−1.27521	−	0.464140i
$94$	3.50784	−	0.445277i	0.361806	−	0.0459268i
$95$	6.43681	−	5.30885i	0.660403	−	0.544677i
$96$	10.5362	+	14.4108i	1.07534	+	1.47080i
$97$	−2.11617	+	5.81414i	−0.214865	+	0.590337i	−0.999564	−	0.0295408i	$-0.990595\pi$
$97$	−2.11617	+	5.81414i	−0.214865	+	0.590337i	0.784699	+	0.619877i	$0.212818\pi$
$98$	4.90733	−	1.52229i	0.495715	−	0.153775i
$99$	10.8814	−	12.9680i	1.09362	−	1.30333i
$100$	1.55280	−	2.17443i	0.155280	−	0.217443i
$101$	−0.868620	+	4.92619i	−0.0864309	+	0.490174i	0.910608	+	0.413272i	$0.135614\pi$
$101$	−0.868620	+	4.92619i	−0.0864309	+	0.490174i	−0.997039	+	0.0769024i	$0.975497\pi$
$102$	3.58504	+	1.50449i	0.354972	+	0.148966i
$103$	−7.63840	−	13.2301i	−0.752634	−	1.30360i	−0.946542	−	0.322581i	$-0.895449\pi$
$103$	−7.63840	−	13.2301i	−0.752634	−	1.30360i	0.193907	−	0.981020i	$-0.437884\pi$
$104$	5.35737	−	4.77374i	0.525334	−	0.468104i
$105$	−3.79096	−	10.4156i	−0.369959	−	1.01645i
$106$	−1.58322	−	2.08322i	−0.153776	−	0.202341i
$107$	2.60064	−	4.50444i	0.251414	−	0.435461i	−0.712502	−	0.701670i	$-0.752438\pi$
$107$	2.60064	−	4.50444i	0.251414	−	0.435461i	0.963915	+	0.266209i	$0.0857713\pi$
$108$	−1.94677	−	24.9105i	−0.187328	−	2.39701i
$109$	0.530188	+	0.631854i	0.0507828	+	0.0605206i	0.790838	−	0.612026i	$-0.209645\pi$
$109$	0.530188	+	0.631854i	0.0507828	+	0.0605206i	−0.740055	+	0.672546i	$0.765201\pi$
$110$	−5.53750	−	3.56398i	−0.527980	−	0.339813i
$111$	−4.61660	+	0.814031i	−0.438188	+	0.0772644i
$112$	1.14023	+	7.25050i	0.107742	+	0.685108i
$113$			7.40610i			0.696707i	0.937363	+	0.348353i	$0.113259\pi$
$113$			7.40610i			0.696707i	−0.937363	+	0.348353i	$0.886741\pi$
$114$	19.4221	+	1.10324i	1.81905	+	0.103328i
$115$			13.9736i			1.30304i
$116$	−0.545581	+	5.63374i	−0.0506559	+	0.523080i
$117$	−17.3862	+	3.06566i	−1.60736	+	0.283421i
$118$	5.23925	−	8.14042i	0.482312	−	0.749387i
$119$	1.02749	+	1.22452i	0.0941902	+	0.112252i
$120$	−16.7304	+	3.46559i	−1.52727	+	0.316364i
$121$	−2.54110	+	4.40132i	−0.231009	+	0.400120i
$122$	12.6246	−	9.59448i	1.14297	−	0.868644i
$123$	1.57115	+	4.31671i	0.141666	+	0.389224i
$124$	−6.83788	+	4.69403i	−0.614060	+	0.421537i
$125$	6.06405	+	10.5032i	0.542385	+	0.939438i
$126$	6.98772	−	16.6510i	0.622516	−	1.48339i
$127$	−0.543667	+	3.08329i	−0.0482426	+	0.273598i	−0.999381	−	0.0351659i	$-0.988804\pi$
$127$	−0.543667	+	3.08329i	−0.0482426	+	0.273598i	0.951139	+	0.308764i	$0.0999152\pi$
$128$	11.3130	−	0.126411i	0.999938	−	0.0111733i
$129$	16.6230	−	19.8105i	1.46358	−	1.74422i
$130$	2.03476	+	6.55934i	0.178460	+	0.575292i
$131$	−3.36828	+	9.25428i	−0.294288	+	0.808550i	0.701139	+	0.713025i	$0.252675\pi$
$131$	−3.36828	+	9.25428i	−0.294288	+	0.808550i	−0.995427	+	0.0955253i	$0.969547\pi$
$132$	−3.83613	−	14.8668i	−0.333893	−	1.29399i
$133$	6.89248	+	4.05762i	0.597654	+	0.351840i
$134$	−0.492556	−	3.88029i	−0.0425504	−	0.335206i
$135$	22.4719	+	8.17909i	1.93407	+	0.703944i
$136$	2.09635	−	1.29488i	0.179760	−	0.111035i
$137$	13.0208	+	10.9257i	1.11244	+	0.933448i	0.998198	−	0.0600045i	$-0.0191115\pi$
$137$	13.0208	+	10.9257i	1.11244	+	0.933448i	0.114242	+	0.993453i	$0.463556\pi$
$138$	−22.1217	+	23.9180i	−1.88313	+	2.03604i
$139$	9.34767	+	1.64825i	0.792859	+	0.139803i	0.555387	−	0.831592i	$-0.312570\pi$
$139$	9.34767	+	1.64825i	0.792859	+	0.139803i	0.237472	+	0.971394i	$0.423681\pi$
$140$	−6.76810	−	1.88095i	−0.572009	−	0.158969i
$141$	−6.83330	+	3.94521i	−0.575468	+	0.332246i
$142$	5.17163	+	10.0481i	0.433993	+	0.843217i
$143$	−5.79939	+	2.11081i	−0.484970	+	0.176514i
$144$	−23.8439	−	14.3624i	−1.98699	−	1.19687i
$145$	−4.69141	−	2.70859i	−0.389601	−	0.224936i
$146$	−16.4601	−	0.795153i	−1.36225	−	0.0658073i
$147$	−8.78293	+	7.36975i	−0.724404	+	0.607847i
$148$	−1.28050	+	2.68084i	−0.105256	+	0.220364i
$149$	−3.22494	−	18.2896i	−0.264198	−	1.49834i	−0.771310	−	0.636459i	$-0.780398\pi$
$149$	−3.22494	−	18.2896i	−0.264198	−	1.49834i	0.507112	−	0.861880i	$-0.330713\pi$
$150$	−1.31747	+	5.81498i	−0.107571	+	0.474792i
$151$	−5.44123			−0.442801			−0.221400	−	0.975183i	$-0.571063\pi$
$151$	−5.44123			−0.442801			−0.221400	+	0.975183i	$0.571063\pi$
$152$	7.72235	−	9.61069i	0.626365	−	0.779530i
$153$	−6.06228			−0.490107
$154$	1.39486	−	6.15656i	0.112401	−	0.496110i
$155$	−1.37843	−	7.81745i	−0.110718	−	0.627913i
$156$	−6.90135	+	14.4486i	−0.552550	+	1.15681i
$157$	9.83579	−	8.25321i	0.784982	−	0.658678i	−0.159516	−	0.987195i	$-0.550993\pi$
$157$	9.83579	−	8.25321i	0.784982	−	0.658678i	0.944498	+	0.328518i	$0.106549\pi$
$158$	−7.39328	−	0.357154i	−0.588178	−	0.0284136i
$159$	5.05652	+	2.91938i	0.401008	+	0.231522i
$160$	−4.37456	+	9.90515i	−0.345840	+	0.783071i
$161$	−12.5872	+	4.58135i	−0.992007	+	0.361061i
$162$	12.0047	+	23.3243i	0.943180	+	1.83253i
$163$	16.8860	−	9.74913i	1.32261	−	0.763611i	0.338468	−	0.940978i	$-0.390091\pi$
$163$	16.8860	−	9.74913i	1.32261	−	0.763611i	0.984145	+	0.177367i	$0.0567581\pi$
$164$	2.80502	+	0.779556i	0.219036	+	0.0608731i
$165$	14.4716	+	2.55173i	1.12661	+	0.198652i
$166$	9.09140	−	9.82962i	0.705629	−	0.762926i
$167$	17.0859	+	14.3367i	1.32214	+	1.10941i	0.985846	+	0.167655i	$0.0536196\pi$
$167$	17.0859	+	14.3367i	1.32214	+	1.10941i	0.336299	+	0.941755i	$0.390825\pi$
$168$	−8.60693	−	13.9342i	−0.664039	−	1.07505i
$169$	−6.16790	−	2.24493i	−0.474454	−	0.172687i
$170$	0.296970	+	2.33949i	0.0227766	+	0.179431i
$171$	−28.5905	+	10.1326i	−2.18637	+	0.774861i
$172$	−4.09493	−	15.8698i	−0.312236	−	1.21006i
$173$	7.49191	−	20.5839i	0.569600	−	1.56496i	−0.235532	−	0.971867i	$-0.575683\pi$
$173$	7.49191	−	20.5839i	0.569600	−	1.56496i	0.805132	−	0.593096i	$-0.202094\pi$
$174$	−3.74211	−	12.0632i	−0.283688	−	0.914510i
$175$	−1.57572	+	1.87787i	−0.119113	+	0.141954i
$176$	−9.08048	−	3.49708i	−0.684467	−	0.263603i
$177$	−3.75117	+	21.2740i	−0.281955	+	1.59905i
$178$	3.43781	−	8.19195i	0.257675	−	0.614013i
$179$	−4.97474	−	8.61650i	−0.371829	−	0.644027i	0.618018	−	0.786164i	$-0.287936\pi$
$179$	−4.97474	−	8.61650i	−0.371829	−	0.644027i	−0.989847	+	0.142137i	$0.954603\pi$
$180$	21.9636	−	15.0775i	1.63707	−	1.12381i
$181$	−1.36725	−	3.75648i	−0.101627	−	0.279217i	0.878451	−	0.477833i	$-0.158578\pi$
$181$	−1.36725	−	3.75648i	−0.101627	−	0.279217i	−0.980077	+	0.198616i	$0.936355\pi$
$182$	−5.24142	+	3.98341i	−0.388520	+	0.295270i
$183$	−17.6918	+	30.6430i	−1.30781	+	2.26520i
$184$	4.18815	+	20.2186i	0.308754	+	1.49053i
$185$	−1.82773	−	2.17821i	−0.134378	−	0.160145i
$186$	10.0165	−	15.5630i	0.734445	−	1.14114i
$187$	−2.08704	+	0.368001i	−0.152619	+	0.0269109i
$188$	−0.482015	+	4.97735i	−0.0351546	+	0.363011i
$189$			22.9238i			1.66746i
$190$	5.31082	+	10.5370i	0.385288	+	0.764433i
$191$		−	5.39176i		−	0.390134i	−0.980790	−	0.195067i	$-0.937508\pi$
$191$		−	5.39176i		−	0.390134i	0.980790	−	0.195067i	$-0.0624924\pi$
$192$	−23.1687	+	10.0288i	−1.67206	+	0.723768i
$193$	−15.2825	+	2.69472i	−1.10006	+	0.193970i	−0.694070	−	0.719908i	$-0.744184\pi$
$193$	−15.2825	+	2.69472i	−1.10006	+	0.193970i	−0.405990	+	0.913878i	$0.633073\pi$
$194$	−7.35791	−	4.73561i	−0.528267	−	0.339997i
$195$	−9.85072	−	11.7396i	−0.705425	−	0.840692i
$196$	0.566138	+	7.24417i	0.0404384	+	0.517441i
$197$	2.13117	−	3.69129i	0.151839	−	0.262993i	−0.780064	−	0.625699i	$-0.784814\pi$
$197$	2.13117	−	3.69129i	0.151839	−	0.262993i	0.931904	+	0.362706i	$0.118147\pi$
$198$	14.4858	+	19.0606i	1.02946	+	1.35458i
$199$	−2.62112	−	7.20146i	−0.185806	−	0.510498i	0.811459	−	0.584410i	$-0.198674\pi$
$199$	−2.62112	−	7.20146i	−0.185806	−	0.510498i	−0.997265	+	0.0739116i	$0.976452\pi$
$200$	2.51386	+	2.82120i	0.177757	+	0.199489i
$201$	4.36411	+	7.55886i	0.307820	+	0.533161i
$202$	−6.52305	−	2.73744i	−0.458960	−	0.192606i
$203$	0.901732	−	5.11397i	0.0632892	−	0.358931i
$204$	−3.19536	+	4.47455i	−0.223720	+	0.313281i
$205$	−1.79105	+	2.13449i	−0.125093	+	0.149080i
$206$	20.6346	−	6.40103i	1.43768	−	0.445981i
$207$	17.3747	−	47.7367i	1.20763	−	3.31793i
$208$	4.91008	+	8.88094i	0.340453	+	0.615783i
$209$	−9.22765	+	5.22386i	−0.638290	+	0.361342i
$210$	15.5504	−	1.97393i	1.07308	−	0.136214i
$211$	−19.2013	−	6.98869i	−1.32187	−	0.481121i	−0.417812	−	0.908533i	$-0.637203\pi$
$211$	−19.2013	−	6.98869i	−1.32187	−	0.481121i	−0.904057	+	0.427412i	$0.859425\pi$
$212$	3.36804	−	1.53268i	0.231318	−	0.105265i
$213$	−19.3177	−	16.2095i	−1.32363	−	1.11066i
$214$	5.40011	+	4.99455i	0.369144	+	0.341420i
$215$	15.4479	+	2.72388i	1.05354	+	0.185767i
$216$	34.9663	+	5.09919i	2.37915	+	0.346956i
$217$	6.58989	−	3.80468i	0.447351	−	0.258278i
$218$	−1.03717	+	0.533817i	−0.0702459	+	0.0361547i
$219$	34.5553	−	12.5771i	2.33503	−	0.849881i
$220$	6.64607	−	6.52392i	0.448078	−	0.439843i
$221$	1.91402	+	1.10506i	0.128751	+	0.0743343i
$222$	0.319888	−	6.62186i	0.0214695	−	0.444430i
$223$	−7.79705	+	6.54250i	−0.522129	+	0.438118i	−0.865373	−	0.501128i	$-0.832919\pi$
$223$	−7.79705	+	6.54250i	−0.522129	+	0.438118i	0.343244	+	0.939246i	$0.388474\pi$
$224$	−10.3566	−	0.693048i	−0.691981	−	0.0463062i
$225$	−1.61438	−	9.15562i	−0.107626	−	0.610375i
$226$	−10.2149	−	2.31434i	−0.679486	−	0.153947i
$227$	−12.9399			−0.858848			−0.429424	−	0.903103i	$-0.641283\pi$
$227$	−12.9399			−0.858848			−0.429424	+	0.903103i	$0.641283\pi$
$228$	−7.59089	+	26.4434i	−0.502719	+	1.75125i
$229$	14.2432			0.941219			0.470610	−	0.882342i	$-0.344034\pi$
$229$	14.2432			0.941219			0.470610	+	0.882342i	$0.344034\pi$
$230$	−19.2732	−	4.36662i	−1.27083	−	0.287926i
$231$	2.44607	+	13.8723i	0.160939	+	0.912732i
$232$	−7.59989	−	2.51299i	−0.498957	−	0.164986i
$233$	12.3534	−	10.3658i	0.809300	−	0.679083i	−0.141141	−	0.989990i	$-0.545077\pi$
$233$	12.3534	−	10.3658i	0.809300	−	0.679083i	0.950441	+	0.310906i	$0.100633\pi$
$234$	1.20471	−	24.9381i	0.0787540	−	1.63025i
$235$	−4.14481	−	2.39301i	−0.270378	−	0.156103i
$236$	9.59052	+	9.77008i	0.624289	+	0.635978i
$237$	15.5210	−	5.64917i	1.00820	−	0.366953i
$238$	−2.01001	+	1.03453i	−0.130290	+	0.0670584i
$239$	18.4124	−	10.6304i	1.19100	−	0.687625i	0.232468	−	0.972604i	$-0.425320\pi$
$239$	18.4124	−	10.6304i	1.19100	−	0.687625i	0.958534	+	0.284979i	$0.0919867\pi$
$240$	0.448152	−	24.1584i	0.0289281	−	1.55942i
$241$	5.49009	+	0.968052i	0.353648	+	0.0623577i	0.347650	−	0.937624i	$-0.386980\pi$
$241$	5.49009	+	0.968052i	0.353648	+	0.0623577i	0.00599789	+	0.999982i	$0.498091\pi$
$242$	−5.27647	−	4.88020i	−0.339185	−	0.313711i
$243$	−16.1305	−	13.5351i	−1.03477	−	0.868277i
$244$	9.28820	+	20.4107i	0.594616	+	1.30666i
$245$	−6.53500	−	2.37855i	−0.417506	−	0.151960i
$246$	−6.44482	+	0.818091i	−0.410906	+	0.0521596i
$247$	10.8738	+	2.01247i	0.691881	+	0.128050i
$248$	−4.33750	−	10.8980i	−0.275432	−	0.692026i
$249$	−10.2188	+	28.0760i	−0.647592	+	1.77924i
$250$	−16.3816	+	5.08171i	−1.03607	+	0.321396i
$251$	−5.90861	+	7.04161i	−0.372948	+	0.444462i	−0.919575	−	0.392914i	$-0.871467\pi$
$251$	−5.90861	+	7.04161i	−0.372948	+	0.444462i	0.546627	+	0.837376i	$0.315912\pi$
$252$	20.7825	+	14.8412i	1.30917	+	0.934906i
$253$	3.08375	−	17.4888i	0.193874	−	1.09951i
$254$	−4.08276	−	1.71336i	−0.256175	−	0.107506i
$255$	−2.63119	−	4.55736i	−0.164772	−	0.285393i
$256$	−3.36086	+	15.6430i	−0.210054	+	0.977690i
$257$	6.16751	+	16.9451i	0.384719	+	1.05701i	0.969345	+	0.245703i	$0.0790189\pi$
$257$	6.16751	+	16.9451i	0.384719	+	1.05701i	−0.584626	+	0.811303i	$0.698759\pi$
$258$	22.1293	+	29.1180i	1.37771	+	1.81281i
$259$	1.36285	−	2.36053i	0.0846836	−	0.146676i
$260$	−9.68286	+	0.756723i	−0.600505	+	0.0469300i
$261$	12.6590	+	15.0864i	0.783572	+	0.933824i
$262$	−11.7115	−	7.53760i	−0.723537	−	0.465675i
$263$	−10.7849	+	1.90167i	−0.665025	+	0.117262i	−0.495963	−	0.868343i	$-0.665185\pi$
$263$	−10.7849	+	1.90167i	−0.665025	+	0.117262i	−0.169062	+	0.985605i	$0.554074\pi$
$264$	21.7039	−	0.645272i	1.33578	−	0.0397137i
$265$			3.54157i			0.217557i
$266$	−7.75033	+	8.23853i	−0.475203	+	0.505137i
$267$			19.8245i			1.21324i
$268$	5.50584	+	0.533195i	0.336323	+	0.0325701i
$269$	26.9447	−	4.75109i	1.64285	−	0.289679i	0.725638	−	0.688077i	$-0.241545\pi$
$269$	26.9447	−	4.75109i	1.64285	−	0.289679i	0.917213	+	0.398398i	$0.130434\pi$
$270$	−18.3033	+	28.4386i	−1.11390	+	1.73072i
$271$	−15.2661	−	18.1934i	−0.927347	−	1.10517i	−0.994215	−	0.107407i	$-0.965745\pi$
$271$	−15.2661	−	18.1934i	−0.927347	−	1.10517i	0.0668682	−	0.997762i	$-0.478699\pi$
$272$	1.13088	+	3.29604i	0.0685697	+	0.199852i
$273$	7.34521	−	12.7223i	0.444553	−	0.769988i
$274$	−19.1383	+	14.5448i	−1.15619	+	0.878684i
$275$	−1.11155	−	3.05397i	−0.0670292	−	0.184161i
$276$	−26.0762	−	37.9857i	−1.56961	−	2.28647i
$277$	−1.99118	−	3.44882i	−0.119638	−	0.207220i	0.799986	−	0.600019i	$-0.204840\pi$
$277$	−1.99118	−	3.44882i	−0.119638	−	0.207220i	−0.919624	+	0.392799i	$0.871507\pi$
$278$	−5.19442	+	12.3778i	−0.311541	+	0.742370i
$279$	−5.01121	+	28.4200i	−0.300013	+	1.70146i
$280$	4.70929	−	8.74717i	0.281434	−	0.522743i
$281$	−3.21635	+	3.83310i	−0.191871	+	0.228664i	−0.853400	−	0.521256i	$-0.825464\pi$
$281$	−3.21635	+	3.83310i	−0.191871	+	0.228664i	0.661529	+	0.749920i	$0.269908\pi$
$282$	−3.30611	−	10.6577i	−0.196876	−	0.634658i
$283$	−3.20210	+	8.79770i	−0.190345	+	0.522969i	−0.997751	−	0.0670271i	$-0.978649\pi$
$283$	−3.20210	+	8.79770i	−0.190345	+	0.522969i	0.807406	+	0.589996i	$0.200871\pi$
$284$	−15.4750	+	3.99306i	−0.918271	+	0.236945i
$285$	−20.0263	−	17.0953i	−1.18626	−	1.01264i
$286$	−1.09909	−	8.65846i	−0.0649903	−	0.511985i
$287$	−2.50993	−	0.913538i	−0.148156	−	0.0539245i
$288$	27.2605	−	28.3987i	1.60634	−	1.67341i
$289$	−12.4414	−	10.4396i	−0.731846	−	0.614092i
$290$	5.20186	−	5.62425i	0.305464	−	0.330268i
$291$	19.2290	+	3.39059i	1.12722	+	0.198760i
$292$	6.24035	−	22.4542i	0.365189	−	1.31404i
$293$	1.03094	−	0.595211i	0.0602279	−	0.0347726i	−0.469584	−	0.882888i	$-0.655596\pi$
$293$	1.03094	−	0.595211i	0.0602279	−	0.0347726i	0.529812	+	0.848115i	$0.322263\pi$
$294$	−7.42020	−	14.4169i	−0.432755	−	0.840811i
$295$	−12.3128	+	4.48150i	−0.716880	+	0.260923i
$296$	−3.29742	−	2.60387i	−0.191659	−	0.151347i
$297$	−26.3199	−	15.1958i	−1.52724	−	0.881751i
$298$	26.2338	+	1.26730i	1.51968	+	0.0734126i
$299$	−14.1873	+	11.9045i	−0.820472	+	0.688457i
$300$	−7.60866	−	3.63426i	−0.439286	−	0.209824i
$301$	2.61109	+	14.8082i	0.150501	+	0.853531i
$302$	1.70033	−	7.50485i	0.0978433	−	0.431856i
$303$	15.7857			0.906866
$304$	10.8424	+	13.6544i	0.621857	+	0.783131i
$305$	−21.4623			−1.22893
$306$	1.89441	−	8.36145i	0.108296	−	0.477992i
$307$	−3.77412	−	21.4041i	−0.215401	−	1.22160i	−0.880210	−	0.474584i	$-0.842598\pi$
$307$	−3.77412	−	21.4041i	−0.215401	−	1.22160i	0.664810	−	0.747013i	$-0.268513\pi$
$308$	8.05560	+	3.84774i	0.459011	+	0.219245i
$309$	−36.9310	+	30.9888i	−2.10093	+	1.76289i
$310$	11.2130	+	0.541677i	0.636856	+	0.0307652i
$311$	28.7054	+	16.5731i	1.62773	+	0.939773i	0.984767	+	0.173880i	$0.0556303\pi$
$311$	28.7054	+	16.5731i	1.62773	+	0.939773i	0.642968	+	0.765893i	$0.277703\pi$
$312$	−17.7717	−	14.0338i	−1.00613	−	0.794507i
$313$	29.2682	−	10.6528i	1.65434	−	0.602130i	0.664880	−	0.746951i	$-0.268483\pi$
$313$	29.2682	−	10.6528i	1.65434	−	0.602130i	0.989458	+	0.144821i	$0.0462607\pi$
$314$	8.30970	+	16.1451i	0.468943	+	0.911123i
$315$	−21.1671	+	12.2208i	−1.19263	+	0.688565i
$316$	2.80294	−	10.0856i	0.157678	−	0.567361i
$317$	−11.1921	−	1.97346i	−0.628609	−	0.110841i	−0.149738	−	0.988726i	$-0.547843\pi$
$317$	−11.1921	−	1.97346i	−0.628609	−	0.110841i	−0.478872	+	0.877885i	$0.658954\pi$
$318$	−5.60670	+	6.06196i	−0.314408	+	0.339938i
$319$	5.27385	+	4.42529i	0.295279	+	0.247769i
$320$	−12.2947	−	9.12892i	−0.687296	−	0.510322i
$321$	−15.4241	−	5.61393i	−0.860892	−	0.313339i
$322$	−2.38549	−	18.7926i	−0.132938	−	1.04727i
$323$	3.55717	+	1.32894i	0.197926	+	0.0739441i
$324$	−35.9216	+	9.26896i	−1.99564	+	0.514942i
$325$	−1.15922	+	3.18494i	−0.0643021	+	0.176669i
$326$	8.16983	+	26.3366i	0.452485	+	1.45865i
$327$	1.67315	−	1.99398i	0.0925254	−	0.110267i
$328$	−1.95175	+	3.62524i	−0.107767	+	0.200171i
$329$	0.796670	−	4.51814i	0.0439219	−	0.249093i
$330$	−8.04172	+	19.1626i	−0.442682	+	1.05487i
$331$	0.569873	+	0.987049i	0.0313230	+	0.0542531i	0.881262	−	0.472628i	$-0.156695\pi$
$331$	0.569873	+	0.987049i	0.0313230	+	0.0542531i	−0.849939	+	0.526881i	$0.823361\pi$
$332$	10.7166	+	15.6110i	0.588149	+	0.856767i
$333$	3.53554	+	9.71381i	0.193746	+	0.532314i
$334$	−25.1132	+	19.0857i	−1.37414	+	1.04432i
$335$	−2.64710	+	4.58491i	−0.144626	+	0.250500i
$336$	21.9084	−	7.51685i	1.19520	−	0.410078i
$337$	11.8905	+	14.1706i	0.647718	+	0.771920i	0.985568	−	0.169280i	$-0.0541442\pi$
$337$	11.8905	+	14.1706i	0.647718	+	0.771920i	−0.337850	+	0.941200i	$0.609700\pi$
$338$	5.02375	−	7.80560i	0.273256	−	0.424569i
$339$	23.0168	−	4.05849i	1.25010	−	0.220427i
$340$	−3.31956	−	0.321472i	−0.180029	−	0.0174343i
$341$			10.0882i			0.546308i
$342$	−5.04122	−	42.6000i	−0.272598	−	2.30354i
$343$		−	19.5108i		−	1.05348i
$344$	23.1681	−	0.688804i	1.24914	−	0.0371378i
$345$	43.4274	−	7.65742i	2.33805	−	0.412262i
$346$	26.0493	+	16.7655i	1.40042	+	0.901321i
$347$	11.4936	+	13.6975i	0.617008	+	0.735321i	0.980553	−	0.196255i	$-0.0628782\pi$
$347$	11.4936	+	13.6975i	0.617008	+	0.735321i	−0.363545	+	0.931577i	$0.618434\pi$
$348$	17.8076	−	1.39168i	0.954590	−	0.0746019i
$349$	−4.75225	+	8.23114i	−0.254382	+	0.440603i	−0.964727	−	0.263251i	$-0.915205\pi$
$349$	−4.75225	+	8.23114i	−0.254382	+	0.440603i	0.710345	+	0.703853i	$0.248539\pi$
$350$	−2.09767	−	2.76014i	−0.112125	−	0.147536i
$351$	10.8403	+	29.7835i	0.578614	+	1.58973i
$352$	7.66095	−	11.4315i	0.408330	−	0.609302i
$353$	−5.73568	−	9.93449i	−0.305280	−	0.528760i	0.672044	−	0.740511i	$-0.265417\pi$
$353$	−5.73568	−	9.93449i	−0.305280	−	0.528760i	−0.977324	+	0.211751i	$0.932083\pi$
$354$	−28.1701	−	11.8218i	−1.49722	−	0.628319i
$355$	2.65611	−	15.0636i	0.140972	−	0.799491i
$356$	10.2245	+	7.30153i	0.541899	+	0.386980i
$357$	3.24253	−	3.86430i	0.171613	−	0.204520i
$358$	13.4389	−	4.16886i	0.710269	−	0.220331i
$359$	−8.61799	+	23.6777i	−0.454840	+	1.24966i	0.474440	+	0.880288i	$0.342651\pi$
$359$	−8.61799	+	23.6777i	−0.454840	+	1.24966i	−0.929280	+	0.369376i	$0.879572\pi$
$360$	13.9323	+	35.0050i	0.734296	+	1.84493i
$361$	18.9973	+	0.321920i	0.999856	+	0.0169432i
$362$	5.60840	−	0.711918i	0.294771	−	0.0374176i
$363$	15.0710	+	5.48540i	0.791023	+	0.287909i
$364$	−3.85624	−	8.47405i	−0.202122	−	0.444161i
$365$	17.0867	+	14.3374i	0.894356	+	0.750454i
$366$	−36.7361	−	33.9772i	−1.92023	−	1.77601i
$367$	−6.93117	−	1.22215i	−0.361804	−	0.0637958i	−0.0102088	−	0.999948i	$-0.503250\pi$
$367$	−6.93117	−	1.22215i	−0.361804	−	0.0637958i	−0.351595	+	0.936152i	$0.614361\pi$
$368$	−29.1954	−	0.541589i	−1.52191	−	0.0282323i
$369$	8.77264	−	5.06489i	0.456685	−	0.263667i
$370$	3.57546	−	1.84024i	0.185879	−	0.0956697i
$371$	−3.19018	+	1.16113i	−0.165626	+	0.0602829i
$372$	18.3353	+	18.6786i	0.950643	+	0.968441i
$373$	−28.1670	−	16.2622i	−1.45843	−	0.842025i	−0.459496	−	0.888180i	$-0.651970\pi$
$373$	−28.1670	−	16.2622i	−1.45843	−	0.842025i	−0.998934	+	0.0461546i	$0.985303\pi$
$374$	0.144612	−	2.99356i	0.00747772	−	0.154793i
$375$	29.3191	−	24.6017i	1.51403	−	1.27043i
$376$	−6.71442	−	2.22020i	−0.346270	−	0.114498i
$377$	−1.24675	−	7.07069i	−0.0642111	−	0.364159i
$378$	−31.6178	−	7.16349i	−1.62625	−	0.368450i
$379$	−23.4446			−1.20427			−0.602135	−	0.798394i	$-0.705683\pi$
$379$	−23.4446			−1.20427			−0.602135	+	0.798394i	$0.705683\pi$
$380$	−16.1928	+	4.03228i	−0.830673	+	0.206852i
$381$	9.88024			0.506180
$382$	7.43662	+	1.68487i	0.380490	+	0.0862057i
$383$	3.75733	+	21.3089i	0.191990	+	1.08883i	0.916640	+	0.399714i	$0.130891\pi$
$383$	3.75733	+	21.3089i	0.191990	+	1.08883i	−0.724650	+	0.689118i	$0.757998\pi$
$384$	−6.59231	−	35.0895i	−0.336412	−	1.79065i
$385$	−6.54525	+	5.49212i	−0.333577	+	0.279904i
$386$	1.05894	−	21.9206i	0.0538985	−	1.11573i
$387$	−49.3863	−	28.5132i	−2.51044	−	1.44941i
$388$	8.83091	−	8.66861i	0.448321	−	0.440082i
$389$	−21.8603	+	7.95648i	−1.10836	+	0.403410i	−0.830391	−	0.557181i	$-0.811883\pi$
$389$	−21.8603	+	7.95648i	−1.10836	+	0.403410i	−0.277968	+	0.960590i	$0.589661\pi$
$390$	19.2702	−	9.91814i	0.975786	−	0.502225i
$391$	−5.50754	+	3.17978i	−0.278528	+	0.160808i
$392$	−10.1685	−	1.48289i	−0.513586	−	0.0748972i
$393$	30.6064	+	5.39674i	1.54389	+	0.272230i
$394$	4.42527	+	4.09292i	0.222942	+	0.206198i
$395$	7.67470	+	6.43984i	0.386156	+	0.324023i
$396$	−30.8162	+	14.0234i	−1.54857	+	0.704701i
$397$	24.0948	+	8.76979i	1.20928	+	0.440143i	0.866455	−	0.499255i	$-0.166393\pi$
$397$	24.0948	+	8.76979i	1.20928	+	0.440143i	0.342828	+	0.939398i	$0.388615\pi$
$398$	10.7517	−	1.36480i	0.538936	−	0.0684114i
$399$	8.83332	−	23.6441i	0.442219	−	1.18369i
$400$	−4.67672	+	2.58566i	−0.233836	+	0.129283i
$401$	0.905379	−	2.48751i	0.0452125	−	0.124220i	−0.915032	−	0.403382i	$-0.867834\pi$
$401$	0.905379	−	2.48751i	0.0452125	−	0.124220i	0.960244	+	0.279162i	$0.0900567\pi$
$402$	−11.7893	+	3.65715i	−0.587999	+	0.182402i
$403$	6.76267	−	8.05944i	0.336873	−	0.401469i
$404$	5.81403	−	8.14153i	0.289259	−	0.405056i
$405$	6.16554	−	34.9665i	0.306368	−	1.73750i
$406$	6.77170	+	2.84179i	0.336074	+	0.141036i
$407$	1.80683	+	3.12951i	0.0895610	+	0.155124i
$408$	−5.17303	−	5.80549i	−0.256103	−	0.287414i
$409$	−7.31695	−	20.1032i	−0.361800	−	0.994038i	−0.978393	−	0.206755i	$-0.933710\pi$
$409$	−7.31695	−	20.1032i	−0.361800	−	0.994038i	0.616593	−	0.787282i	$-0.288513\pi$
$410$	−2.38433	−	3.13733i	−0.117754	−	0.154942i
$411$	26.8199	−	46.4535i	1.32293	−	2.29138i
$412$	2.38053	+	30.4607i	0.117280	+	1.50069i
$413$	−8.07371	−	9.62187i	−0.397281	−	0.473461i
$414$	60.4117	+	38.8815i	2.96907	+	1.91092i
$415$	−17.8474	+	3.14698i	−0.876095	+	0.154479i
$416$	−13.7835	+	3.99705i	−0.675790	+	0.195971i
$417$		−	29.9541i		−	1.46686i
$418$	−4.32148	−	14.3597i	−0.211371	−	0.702356i
$419$		−	3.96184i		−	0.193549i	−0.995306	−	0.0967744i	$-0.969147\pi$
$419$		−	3.96184i		−	0.193549i	0.995306	−	0.0967744i	$-0.0308525\pi$
$420$	−2.13679	+	22.0648i	−0.104265	+	1.07665i
$421$	−39.1951	+	6.91115i	−1.91025	+	0.336829i	−0.997437	−	0.0715443i	$-0.977207\pi$
$421$	−39.1951	+	6.91115i	−1.91025	+	0.336829i	−0.912815	+	0.408373i	$0.866096\pi$
$422$	15.6394	−	24.2996i	0.761315	−	1.18288i
$423$	11.1841	+	13.3287i	0.543789	+	0.648062i
$424$	1.06148	+	5.12434i	0.0515498	+	0.248860i
$425$	−0.581925	+	1.00792i	−0.0282275	+	0.0488915i
$426$	28.3937	−	21.5788i	1.37568	−	1.04549i
$427$	−7.03658	−	19.3328i	−0.340524	−	0.935582i
$428$	−8.57625	+	5.88738i	−0.414549	+	0.284577i
$429$	9.73803	+	16.8668i	0.470157	+	0.814335i
$430$	−8.58424	+	20.4554i	−0.413969	+	0.986446i
$431$	3.45718	−	19.6067i	0.166527	−	0.944419i	−0.780950	−	0.624594i	$-0.785265\pi$
$431$	3.45718	−	19.6067i	0.166527	−	0.944419i	0.947476	−	0.319826i	$-0.103624\pi$
$432$	−17.9597	+	46.6340i	−0.864088	+	2.24368i
$433$	−19.0331	+	22.6828i	−0.914675	+	1.09007i	0.0809587	+	0.996717i	$0.474202\pi$
$433$	−19.0331	+	22.6828i	−0.914675	+	1.09007i	−0.995633	+	0.0933494i	$0.970243\pi$
$434$	3.18834	+	10.2781i	0.153045	+	0.493364i
$435$	−5.84695	+	16.0644i	−0.280340	+	0.770227i
$436$	−0.412166	−	1.59733i	−0.0197392	−	0.0764984i
$437$	−20.6595	+	24.2017i	−0.988279	+	1.15772i
$438$	6.54883	+	51.5908i	0.312915	+	2.46510i
$439$	−0.0910357	−	0.0331343i	−0.00434490	−	0.00158141i	0.339847	−	0.940481i	$-0.389625\pi$
$439$	−0.0910357	−	0.0331343i	−0.00434490	−	0.00158141i	−0.344192	+	0.938899i	$0.611847\pi$
$440$	6.92133	+	11.2053i	0.329961	+	0.534192i
$441$	19.3675	+	16.2512i	0.922260	+	0.773868i
$442$	−2.12227	+	2.29460i	−0.100946	+	0.109143i
$443$	−21.2279	−	3.74305i	−1.00857	−	0.177838i	−0.355129	−	0.934817i	$-0.615563\pi$
$443$	−21.2279	−	3.74305i	−1.00857	−	0.177838i	−0.653438	+	0.756980i	$0.726674\pi$
$444$	9.03328	+	2.51048i	0.428700	+	0.119142i
$445$	−10.4137	+	6.01237i	−0.493658	+	0.285014i
$446$	−6.58728	−	12.7986i	−0.311917	−	0.606032i
$447$	−55.0735	+	20.0451i	−2.60489	+	0.948101i
$448$	4.19224	−	14.0679i	0.198065	−	0.664644i
$449$	16.9734	+	9.79959i	0.801024	+	0.462471i	0.843829	−	0.536612i	$-0.180296\pi$
$449$	16.9734	+	9.79959i	0.801024	+	0.462471i	−0.0428051	+	0.999083i	$0.513629\pi$
$450$	13.1324	+	0.634400i	0.619069	+	0.0299059i
$451$	2.71266	−	2.27620i	0.127734	−	0.107182i
$452$	6.38413	−	13.3658i	0.300284	−	0.628673i
$453$	2.98175	+	16.9104i	0.140095	+	0.794518i
$454$	4.04359	−	17.8474i	0.189775	−	0.837619i
$455$	8.91064			0.417737
$456$	−34.1001	−	18.7331i	−1.59688	−	0.877258i
$457$	9.26419			0.433360			0.216680	−	0.976243i	$-0.430477\pi$
$457$	9.26419			0.433360			0.216680	+	0.976243i	$0.430477\pi$
$458$	−4.45088	+	19.6451i	−0.207976	+	0.917954i
$459$	1.88992	+	10.7183i	0.0882138	+	0.500285i
$460$	12.0454	−	25.2181i	0.561619	−	1.17580i
$461$	3.95276	−	3.31676i	0.184098	−	0.154477i	−0.546081	−	0.837732i	$-0.683881\pi$
$461$	3.95276	−	3.31676i	0.184098	−	0.154477i	0.730179	+	0.683256i	$0.239437\pi$
$462$	−19.8979	−	0.961224i	−0.925733	−	0.0447202i
$463$	27.6307	+	15.9526i	1.28411	+	0.741379i	0.977596	−	0.210488i	$-0.0675054\pi$
$463$	27.6307	+	15.9526i	1.28411	+	0.741379i	0.306510	+	0.951867i	$0.400839\pi$
$464$	5.84095	−	9.69691i	0.271159	−	0.450168i
$465$	−23.5399	+	8.56781i	−1.09164	+	0.397323i
$466$	10.4367	+	20.2778i	0.483471	+	0.939349i
$467$	−20.9939	+	12.1208i	−0.971481	+	0.560885i	−0.899687	−	0.436535i	$-0.856206\pi$
$467$	−20.9939	+	12.1208i	−0.971481	+	0.560885i	−0.0717935	+	0.997420i	$0.522872\pi$
$468$	34.0196	+	9.45452i	1.57255	+	0.437035i
$469$	−4.99788	−	0.881260i	−0.230780	−	0.0406928i
$470$	4.59579	−	4.96897i	0.211988	−	0.229201i
$471$	−31.0394	−	26.0452i	−1.43022	−	1.20010i
$472$	−16.4724	+	10.1747i	−0.758203	+	0.468330i
$473$	−18.7328	−	6.81820i	−0.861337	−	0.313501i
$474$	2.94150	+	23.1727i	0.135107	+	1.06436i
$475$	−1.05977	+	5.72614i	−0.0486256	+	0.262733i
$476$	−0.798768	−	3.09560i	−0.0366115	−	0.141887i
$477$	4.40358	−	12.0987i	0.201626	−	0.553963i
$478$	8.90837	+	28.7174i	0.407459	+	1.31350i
$479$	1.51494	−	1.80544i	0.0692195	−	0.0824926i	−0.730323	−	0.683101i	$-0.760631\pi$
$479$	1.51494	−	1.80544i	0.0692195	−	0.0824926i	0.799543	+	0.600609i	$0.205075\pi$
$480$	33.1807	+	8.16741i	1.51448	+	0.372790i
$481$	0.654415	−	3.71137i	0.0298387	−	0.169224i
$482$	−3.05080	+	7.26974i	−0.138960	+	0.331128i
$483$	21.1357	+	36.6081i	0.961707	+	1.66573i
$484$	8.37990	−	5.75259i	0.380905	−	0.261482i
$485$	4.05070	+	11.1292i	0.183933	+	0.505352i
$486$	23.7090	−	18.0185i	1.07546	−	0.817336i
$487$	16.3996	−	28.4049i	0.743135	−	1.28715i	−0.207926	−	0.978145i	$-0.566671\pi$
$487$	16.3996	−	28.4049i	0.743135	−	1.28715i	0.951061	−	0.309003i	$-0.0999954\pi$
$488$	−31.0541	+	6.43265i	−1.40575	+	0.291192i
$489$	−39.5520	−	47.1362i	−1.78860	−	2.13157i
$490$	5.32276	−	8.27017i	0.240458	−	0.373608i
$491$	13.1877	−	2.32535i	0.595154	−	0.104942i	0.132046	−	0.991244i	$-0.457845\pi$
$491$	13.1877	−	2.32535i	0.595154	−	0.104942i	0.463108	+	0.886302i	$0.346734\pi$
$492$	0.885589	−	9.14470i	0.0399254	−	0.412275i
$493$		−	2.46543i		−	0.111037i
$494$	−6.17367	+	14.3688i	−0.277766	+	0.646485i
$495$		−	32.4039i		−	1.45645i
$496$	16.3866	−	2.57699i	0.735781	−	0.115710i
$497$	14.4398	−	2.54613i	0.647714	−	0.114210i
$498$	−35.5307	−	22.8679i	−1.59217	−	1.02473i
$499$	21.7580	+	25.9301i	0.974021	+	1.16079i	0.986975	+	0.160876i	$0.0514321\pi$
$499$	21.7580	+	25.9301i	0.974021	+	1.16079i	−0.0129539	+	0.999916i	$0.504123\pi$
$500$	−1.88988	−	24.1825i	−0.0845179	−	1.08147i
$501$	35.1931	−	60.9563i	1.57231	−	2.72333i
$502$	−7.86580	−	10.3499i	−0.351068	−	0.461940i
$503$	−12.7105	−	34.9217i	−0.566731	−	1.55708i	−0.809575	−	0.587016i	$-0.800302\pi$
$503$	−12.7105	−	34.9217i	−0.566731	−	1.55708i	0.242844	−	0.970065i	$-0.421920\pi$
$504$	−26.9641	+	24.0266i	−1.20108	+	1.07023i
$505$	4.78750	+	8.29219i	0.213041	+	0.368998i
$506$	23.1579	+	9.71837i	1.02949	+	0.432034i
$507$	−3.59689	+	20.3990i	−0.159743	+	0.905949i
$508$	3.63898	−	5.09576i	0.161454	−	0.226088i
$509$	6.82338	−	8.13179i	0.302441	−	0.360435i	−0.593323	−	0.804964i	$-0.702184\pi$
$509$	6.82338	−	8.13179i	0.302441	−	0.360435i	0.895764	+	0.444529i	$0.146629\pi$
$510$	7.10799	−	2.20496i	0.314747	−	0.0976371i
$511$	−7.31289	+	20.0920i	−0.323503	+	0.888817i
$512$	−20.5255	−	9.52379i	−0.907109	−	0.420896i
$513$	26.8278	+	47.3898i	1.18448	+	2.09231i
$514$	−25.2989	+	3.21139i	−1.11589	+	0.141648i
$515$	−27.4788	−	10.0015i	−1.21086	−	0.440717i
$516$	−47.0764	+	21.4229i	−2.07243	+	0.943088i
$517$	4.65939	+	3.90969i	0.204920	+	0.171948i
$518$	2.82990	+	2.61737i	0.124339	+	0.115001i
$519$	−68.0765	−	12.0037i	−2.98823	−	0.526905i
$520$	1.98209	−	13.5916i	0.0869204	−	0.596032i
$521$	−12.4939	+	7.21337i	−0.547369	+	0.316024i	−0.748060	−	0.663631i	$-0.769015\pi$
$521$	−12.4939	+	7.21337i	−0.547369	+	0.316024i	0.200691	+	0.979655i	$0.435681\pi$
$522$	−24.7638	+	12.7456i	−1.08388	+	0.557861i
$523$	25.6633	−	9.34069i	1.12218	−	0.408440i	0.286732	−	0.958011i	$-0.407431\pi$
$523$	25.6633	−	9.34069i	1.12218	−	0.408440i	0.835447	+	0.549571i	$0.185209\pi$
$524$	14.0560	−	13.7977i	0.614040	−	0.602755i
$525$	6.69957	+	3.86800i	0.292393	+	0.168813i
$526$	0.747294	−	15.4694i	0.0325836	−	0.674498i
$527$	2.76750	−	2.32220i	0.120554	−	0.101157i
$528$	−5.89228	+	30.1369i	−0.256428	+	1.31154i
$529$	−5.26005	−	29.8312i	−0.228698	−	1.29701i
$530$	−4.88473	−	1.10671i	−0.212179	−	0.0480723i
$531$	47.6354			2.06720
$532$	−8.94114	−	13.2642i	−0.387648	−	0.575075i
$533$	−3.69299			−0.159961
$534$	−27.3430	−	6.19496i	−1.18325	−	0.268082i
$535$	−1.72886	−	9.80485i	−0.0747452	−	0.423901i
$536$	−2.45594	+	7.42735i	−0.106080	+	0.320813i
$537$	−24.0524	+	20.1824i	−1.03794	+	0.870934i
$538$	−1.86702	+	38.6484i	−0.0804930	+	1.66625i
$539$	7.65406	+	4.41907i	0.329684	+	0.190343i
$540$	−33.5045	−	34.1318i	−1.44180	−	1.46880i
$541$	14.6005	−	5.31414i	0.627724	−	0.228473i	−0.00851644	−	0.999964i	$-0.502711\pi$
$541$	14.6005	−	5.31414i	0.627724	−	0.228473i	0.636240	+	0.771491i	$0.280489\pi$
$542$	29.8638	−	15.3705i	1.28276	−	0.660222i
$543$	−10.9252	+	6.30768i	−0.468846	+	0.270688i
$544$	−4.89947	+	0.529793i	−0.210063	+	0.0227147i
$545$	1.55487	+	0.274165i	0.0666032	+	0.0117439i
$546$	15.2520	+	14.1065i	0.652725	+	0.603704i
$547$	22.9739	+	19.2774i	0.982292	+	0.824241i	0.984434	−	0.175757i	$-0.0562373\pi$
$547$	22.9739	+	19.2774i	0.982292	+	0.824241i	−0.00214187	+	0.999998i	$0.500682\pi$
$548$	−14.0805	−	30.9417i	−0.601489	−	1.32176i
$549$	73.3196	+	26.6861i	3.12920	+	1.13894i
$550$	4.55956	−	0.578781i	0.194420	−	0.0246793i
$551$	−4.12077	−	11.6273i	−0.175551	−	0.495339i
$552$	60.5407	−	24.0957i	2.57678	−	1.02558i
$553$	−3.28468	+	9.02459i	−0.139679	+	0.383765i
$554$	5.37904	−	1.66862i	0.228534	−	0.0708929i
$555$	−5.76790	+	6.87391i	−0.244834	+	0.291781i
$556$	−15.4489	−	11.0324i	−0.655181	−	0.467877i
$557$	3.59379	−	20.3814i	0.152274	−	0.863587i	−0.808962	−	0.587861i	$-0.799970\pi$
$557$	3.59379	−	20.3814i	0.152274	−	0.863587i	0.961236	−	0.275727i	$-0.0889185\pi$
$558$	−37.6325	−	15.7927i	−1.59311	−	0.668559i
$559$	10.3950	+	18.0047i	0.439662	+	0.761516i
$560$	10.5930	+	9.22873i	0.447635	+	0.389985i
$561$	2.28736	+	6.28448i	0.0965725	+	0.265331i
$562$	−4.28175	−	5.63398i	−0.180615	−	0.237655i
$563$	4.49016	−	7.77718i	0.189238	−	0.327769i	−0.755759	−	0.654850i	$-0.772732\pi$
$563$	4.49016	−	7.77718i	0.189238	−	0.327769i	0.944996	+	0.327081i	$0.106065\pi$
$564$	15.7329	−	1.22954i	0.662473	−	0.0517728i
$565$	9.11247	+	10.8598i	0.383364	+	0.456876i
$566$	−11.1337	−	7.16572i	−0.467983	−	0.301198i
$567$	33.5187	−	5.91025i	1.40765	−	0.248207i
$568$	−0.671669	−	22.5918i	−0.0281826	−	0.947930i
$569$		−	23.6238i		−	0.990361i	−0.868790	−	0.495181i	$-0.835102\pi$
$569$		−	23.6238i		−	0.990361i	0.868790	−	0.495181i	$-0.164898\pi$
$570$	29.8368	−	22.2793i	1.24972	−	0.933177i
$571$			23.3260i			0.976163i	0.872798	+	0.488082i	$0.162303\pi$
$571$			23.3260i			0.976163i	−0.872798	+	0.488082i	$0.837697\pi$
$572$	12.2857	+	1.18977i	0.513691	+	0.0497467i
$573$	−16.7566	+	2.95464i	−0.700018	+	0.123432i
$574$	2.04433	−	3.17636i	0.0853288	−	0.132579i
$575$	−6.26895	−	7.47105i	−0.261433	−	0.311564i
$576$	30.6505	+	46.4735i	1.27710	+	1.93640i
$577$	−15.3325	+	26.5567i	−0.638302	+	1.10557i	0.347503	+	0.937679i	$0.387030\pi$
$577$	−15.3325	+	26.5567i	−0.638302	+	1.10557i	−0.985805	+	0.167893i	$0.946304\pi$
$578$	18.2867	−	13.8976i	0.760625	−	0.578064i
$579$	16.7494	+	46.0187i	0.696082	+	1.91247i
$580$	6.13176	+	8.93223i	0.254607	+	0.370891i
$581$	−8.68616	−	15.0449i	−0.360363	−	0.624166i
$582$	−10.6854	+	25.4622i	−0.442923	+	1.05544i
$583$	0.781568	−	4.43249i	0.0323692	−	0.183575i
$584$	29.0201	+	15.6238i	1.20086	+	0.646517i
$585$	−21.7221	+	25.8873i	−0.898096	+	1.07031i
$586$	0.498791	+	1.60792i	0.0206049	+	0.0664227i
$587$	5.84762	−	16.0662i	0.241357	−	0.663123i	−0.758576	−	0.651584i	$-0.774105\pi$
$587$	5.84762	−	16.0662i	0.241357	−	0.663123i	0.999933	−	0.0115389i	$-0.00367302\pi$
$588$	22.2034	−	5.72921i	0.915651	−	0.236269i
$589$	9.17048	−	15.5775i	0.377863	−	0.641858i
$590$	−2.33349	−	18.3830i	−0.0960684	−	0.756814i
$591$	−12.6397	−	4.60049i	−0.519929	−	0.189239i
$592$	4.62183	−	3.73431i	0.189956	−	0.153479i
$593$	−4.15251	−	3.48437i	−0.170523	−	0.143086i	0.553532	−	0.832828i	$-0.313280\pi$
$593$	−4.15251	−	3.48437i	−0.170523	−	0.143086i	−0.724055	+	0.689742i	$0.757724\pi$
$594$	29.1837	−	31.5534i	1.19742	−	1.29465i
$595$	3.01330	+	0.531326i	0.123533	+	0.0217822i
$596$	−9.94574	+	35.7871i	−0.407394	+	1.46590i
$597$	−20.9445	+	12.0923i	−0.857202	+	0.494906i
$598$	−11.9860	−	23.2880i	−0.490145	−	0.952316i
$599$	21.5337	−	7.83764i	0.879845	−	0.320237i	0.137698	−	0.990474i	$-0.456030\pi$
$599$	21.5337	−	7.83764i	0.879845	−	0.320237i	0.742147	+	0.670237i	$0.233807\pi$
$600$	7.39021	−	9.35862i	0.301704	−	0.382064i
$601$	−11.7394	−	6.77773i	−0.478859	−	0.276469i	0.241082	−	0.970505i	$-0.422498\pi$
$601$	−11.7394	−	6.77773i	−0.478859	−	0.276469i	−0.719941	+	0.694035i	$0.755831\pi$
$602$	−21.2403	−	1.02607i	−0.865688	−	0.0418196i
$603$	14.7439	−	12.3716i	0.600418	−	0.503810i
$604$	9.81978	+	4.69040i	0.399561	+	0.190850i
$605$	1.68928	+	9.58038i	0.0686789	+	0.389498i
$606$	−4.93289	+	21.7726i	−0.200385	+	0.884450i
$607$	7.35854			0.298674			0.149337	−	0.988786i	$-0.452286\pi$
$607$	7.35854			0.298674			0.149337	+	0.988786i	$0.452286\pi$
$608$	−22.2210	+	10.6876i	−0.901182	+	0.433441i
$609$	−16.3875			−0.664054
$610$	6.70677	−	29.6020i	0.271549	−	1.19855i
$611$	−1.10149	−	6.24688i	−0.0445617	−	0.252722i
$612$	10.9406	+	5.22575i	0.442247	+	0.211238i
$613$	−13.2122	+	11.0863i	−0.533635	+	0.447773i	−0.869354	−	0.494189i	$-0.835465\pi$
$613$	−13.2122	+	11.0863i	−0.533635	+	0.447773i	0.335719	+	0.941962i	$0.391021\pi$
$614$	30.7011	+	1.48311i	1.23900	+	0.0598533i
$615$	7.61511	+	4.39659i	0.307071	+	0.177288i
$616$	−7.82433	+	9.90836i	−0.315251	+	0.399219i
$617$	26.1889	−	9.53198i	1.05433	−	0.383743i	0.244032	−	0.969767i	$-0.421530\pi$
$617$	26.1889	−	9.53198i	1.05433	−	0.383743i	0.810294	+	0.586024i	$0.199308\pi$
$618$	−31.2009	−	60.6211i	−1.25508	−	2.43854i
$619$	−1.02147	+	0.589747i	−0.0410564	+	0.0237039i	−0.520388	−	0.853930i	$-0.674213\pi$
$619$	−1.02147	+	0.589747i	−0.0410564	+	0.0237039i	0.479331	+	0.877634i	$0.340879\pi$
$620$	−4.25108	+	15.2964i	−0.170727	+	0.614317i
$621$	−89.8161	−	15.8370i	−3.60419	−	0.635517i
$622$	−31.8287	+	34.4132i	−1.27621	+	1.37984i
$623$	−8.83007	−	7.40930i	−0.353769	−	0.296848i
$624$	24.9097	−	20.1264i	0.997186	−	0.805699i
$625$	15.5381	+	5.65540i	0.621523	+	0.226216i
$626$	5.54684	+	43.6973i	0.221696	+	1.74649i
$627$	21.2915	+	25.8153i	0.850300	+	1.03096i
$628$	−24.8650	+	6.41600i	−0.992221	+	0.256026i
$629$	0.442605	−	1.21605i	0.0176478	−	0.0484870i
$630$	−10.2411	−	33.0137i	−0.408016	−	1.31530i
$631$	−30.4723	+	36.3155i	−1.21308	+	1.44570i	−0.352941	+	0.935646i	$0.614818\pi$
$631$	−30.4723	+	36.3155i	−1.21308	+	1.44570i	−0.860144	+	0.510052i	$0.829626\pi$
$632$	13.0348	+	7.01764i	0.518496	+	0.279147i
$633$	−11.1974	+	63.5038i	−0.445058	+	2.52405i
$634$	6.21933	−	14.8201i	0.247001	−	0.588579i
$635$	2.99648	+	5.19006i	0.118912	+	0.205961i
$636$	−6.60896	−	9.62738i	−0.262062	−	0.381750i
$637$	−3.15246	−	8.66130i	−0.124905	−	0.343173i
$638$	−7.75164	+	5.89113i	−0.306890	+	0.233232i
$639$	−27.8038	+	48.1577i	−1.09990	+	1.90509i
$640$	16.4331	−	14.1049i	0.649576	−	0.557545i
$641$	7.60426	+	9.06241i	0.300350	+	0.357944i	0.895020	−	0.446027i	$-0.147161\pi$
$641$	7.60426	+	9.06241i	0.300350	+	0.357944i	−0.594669	+	0.803970i	$0.702717\pi$
$642$	12.5630	−	19.5196i	0.495820	−	0.770375i
$643$	−25.5305	+	4.50172i	−1.00683	+	0.177531i	−0.652659	−	0.757652i	$-0.726347\pi$
$643$	−25.5305	+	4.50172i	−1.00683	+	0.177531i	−0.354167	+	0.935182i	$0.615235\pi$
$644$	26.6652	+	2.58230i	1.05076	+	0.101757i
$645$		−	49.5019i		−	1.94913i
$646$	−2.94453	+	4.49097i	−0.115851	+	0.176695i
$647$			16.7243i			0.657501i	0.944417	+	0.328751i	$0.106628\pi$
$647$			16.7243i			0.657501i	−0.944417	+	0.328751i	$0.893372\pi$
$648$	−1.55912	−	52.4415i	−0.0612481	−	2.06010i
$649$	16.3992	−	2.89163i	0.643727	−	0.113506i
$650$	−4.03060	−	2.59413i	−0.158093	−	0.101750i
$651$	−15.4355	−	18.3953i	−0.604964	−	0.720968i
$652$	−38.8780	+	3.03834i	−1.52258	+	0.118991i
$653$	−3.05595	+	5.29306i	−0.119588	+	0.207133i	−0.919605	−	0.392845i	$-0.871491\pi$
$653$	−3.05595	+	5.29306i	−0.119588	+	0.207133i	0.800016	+	0.599978i	$0.204824\pi$
$654$	2.22737	+	2.93081i	0.0870971	+	0.114604i
$655$	6.44744	+	17.7142i	0.251922	+	0.692151i
$656$	−4.39024	−	3.82482i	−0.171410	−	0.149334i
$657$	−40.5445	−	70.2251i	−1.58179	−	2.73974i
$658$	5.98273	+	2.51069i	0.233231	+	0.0978770i
$659$	8.40615	−	47.6737i	0.327457	−	1.85710i	−0.164355	−	0.986401i	$-0.552554\pi$
$659$	8.40615	−	47.6737i	0.327457	−	1.85710i	0.491812	−	0.870701i	$-0.336335\pi$
$660$	−23.9172	−	17.0797i	−0.930975	−	0.664828i
$661$	14.9228	−	17.7843i	0.580430	−	0.691729i	−0.393307	−	0.919407i	$-0.628669\pi$
$661$	14.9228	−	17.7843i	0.580430	−	0.691729i	0.973736	+	0.227678i	$0.0731134\pi$
$662$	−1.53947	+	0.477557i	−0.0598334	+	0.0185608i
$663$	2.38546	−	6.55399i	0.0926435	−	0.254536i
$664$	−24.8805	+	9.90262i	−0.965549	+	0.384296i
$665$	15.0992	−	2.53069i	0.585521	−	0.0981359i
$666$	−14.5027	+	1.84094i	−0.561967	+	0.0713349i
$667$	19.4137	+	7.06601i	0.751702	+	0.273597i
$668$	−18.4764	−	40.6017i	−0.714874	−	1.57093i
$669$	24.6057	+	20.6466i	0.951310	+	0.798244i
$670$	−5.49657	−	5.08377i	−0.212351	−	0.196403i
$671$	26.8614	+	4.73638i	1.03697	+	0.182846i
$672$	3.52148	+	32.5663i	0.135844	+	1.25627i
$673$	22.5139	−	12.9984i	0.867848	−	0.501052i	0.00121569	−	0.999999i	$-0.499613\pi$
$673$	22.5139	−	12.9984i	0.867848	−	0.501052i	0.866633	+	0.498947i	$0.166280\pi$
$674$	−23.2605	+	11.9719i	−0.895962	+	0.461141i
$675$	−15.6841	+	5.70853i	−0.603680	+	0.219721i
$676$	9.19605	+	9.36823i	0.353694	+	0.360316i
$677$	38.3495	+	22.1411i	1.47389	+	0.850952i	0.999568	−	0.0293990i	$-0.00935935\pi$
$677$	38.3495	+	22.1411i	1.47389	+	0.850952i	0.474324	+	0.880351i	$0.342693\pi$
$678$	−1.59485	+	33.0144i	−0.0612499	+	1.26791i
$679$	−8.69695	+	7.29761i	−0.333758	+	0.280056i
$680$	1.48073	−	4.47807i	0.0567832	−	0.171726i
$681$	7.09095	+	40.2148i	0.271726	+	1.54103i
$682$	−13.9142	−	3.15248i	−0.532804	−	0.120715i
$683$	−37.9898			−1.45364			−0.726819	−	0.686829i	$-0.759002\pi$
$683$	−37.9898			−1.45364			−0.726819	+	0.686829i	$0.759002\pi$
$684$	60.3317	+	6.35898i	2.30684	+	0.243142i
$685$	32.5359			1.24313
$686$	26.9104	+	6.09694i	1.02744	+	0.232782i
$687$	−7.80519	−	44.2654i	−0.297787	−	1.68883i
$688$	−6.28979	+	32.1700i	−0.239796	+	1.22647i
$689$	−3.59573	+	3.01717i	−0.136986	+	0.114945i
$690$	−3.00912	+	62.2904i	−0.114555	+	2.37136i
$691$	0.0712585	+	0.0411411i	0.00271080	+	0.00156508i	0.501355	−	0.865242i	$-0.332835\pi$
$691$	0.0712585	+	0.0411411i	0.00271080	+	0.00156508i	−0.498644	+	0.866807i	$0.666168\pi$
$692$	−31.2642	+	30.6896i	−1.18848	+	1.16664i
$693$	29.1888	−	10.6239i	1.10879	−	0.403567i
$694$	−22.4840	+	11.5722i	−0.853482	+	0.439277i
$695$	15.7348	−	9.08450i	0.596856	−	0.344595i
$696$	−3.64524	+	24.9962i	−0.138172	+	0.947478i
$697$	−1.24886	−	0.220207i	−0.0473038	−	0.00834093i
$698$	−9.86782	−	9.12673i	−0.373502	−	0.345452i
$699$	−38.9845	−	32.7119i	−1.47453	−	1.23728i
$700$	4.46245	−	2.03070i	0.168665	−	0.0767534i
$701$	6.42635	+	2.33900i	0.242720	+	0.0883428i	0.460516	−	0.887652i	$-0.347664\pi$
$701$	6.42635	+	2.33900i	0.242720	+	0.0883428i	−0.217796	+	0.975994i	$0.569887\pi$
$702$	−44.4667	+	5.64450i	−1.67829	+	0.213038i
$703$	0.0548558	−	6.47482i	0.00206893	−	0.244202i
$704$	13.3730	+	14.1387i	0.504014	+	0.532871i
$705$	−5.16572	+	14.1927i	−0.194552	+	0.534528i
$706$	15.4946	−	4.80654i	0.583146	−	0.180897i
$707$	−5.89984	+	7.03116i	−0.221886	+	0.264434i
$708$	25.1081	−	35.1595i	0.943621	−	1.32138i
$709$	−3.47480	+	19.7066i	−0.130499	+	0.740096i	0.847390	+	0.530971i	$0.178173\pi$
$709$	−3.47480	+	19.7066i	−0.130499	+	0.740096i	−0.977889	+	0.209125i	$0.932938\pi$
$710$	19.9465	+	8.37069i	0.748579	+	0.314146i
$711$	−18.2111	−	31.5425i	−0.682969	−	1.18294i
$712$	−13.2658	+	11.8206i	−0.497155	+	0.442995i
$713$	10.3542	+	28.4478i	0.387766	+	1.06538i
$714$	4.31660	+	5.67984i	0.161545	+	0.212563i
$715$	−5.90671	+	10.2307i	−0.220898	+	0.382607i
$716$	1.55039	+	19.8385i	0.0579409	+	0.741398i
$717$	−43.1273	−	51.3972i	−1.61062	−	1.91946i
$718$	−29.9646	−	19.2855i	−1.11827	−	0.719729i
$719$	−16.0253	+	2.82569i	−0.597642	+	0.105380i	−0.464282	−	0.885687i	$-0.653688\pi$
$719$	−16.0253	+	2.82569i	−0.597642	+	0.105380i	−0.133360	+	0.991068i	$0.542577\pi$
$720$	−52.6346	+	8.27743i	−1.96158	+	0.308482i
$721$		−	28.0315i		−	1.04395i
$722$	−6.38049	+	26.1015i	−0.237457	+	0.971398i
$723$		−	17.5927i		−	0.654280i
$724$	−0.770656	+	7.95789i	−0.0286412	+	0.295753i
$725$	3.72344	−	0.656543i	0.138285	−	0.0243834i
$726$	−12.2753	+	19.0727i	−0.455580	+	0.707853i
$727$	−1.48698	−	1.77212i	−0.0551491	−	0.0657242i	0.737765	−	0.675058i	$-0.235881\pi$
$727$	−1.48698	−	1.77212i	−0.0551491	−	0.0657242i	−0.792914	+	0.609334i	$0.791437\pi$
$728$	12.8929	−	2.67069i	0.477844	−	0.0989823i
$729$	−5.40168	+	9.35598i	−0.200062	+	0.346518i
$730$	−25.1144	+	19.0866i	−0.929525	+	0.706426i
$731$	2.44168	+	6.70845i	0.0903087	+	0.248121i
$732$	58.3429	−	40.0510i	2.15642	−	1.48033i
$733$	7.32768	+	12.6919i	0.270654	+	0.468786i	0.969029	−	0.246945i	$-0.0794268\pi$
$733$	7.32768	+	12.6919i	0.270654	+	0.468786i	−0.698376	+	0.715732i	$0.746093\pi$
$734$	3.85159	−	9.17795i	0.142165	−	0.338764i
$735$	−3.81096	+	21.6131i	−0.140570	+	0.797210i
$736$	9.87028	−	40.0987i	0.363823	−	1.47806i
$737$	4.32482	−	5.15412i	0.159307	−	0.189855i
$738$	4.24441	+	13.6825i	0.156239	+	0.503658i
$739$	1.64645	−	4.52359i	0.0605657	−	0.166403i	−0.905719	−	0.423878i	$-0.860668\pi$
$739$	1.64645	−	4.52359i	0.0605657	−	0.166403i	0.966285	+	0.257475i	$0.0828906\pi$
$740$	1.42087	+	5.50653i	0.0522322	+	0.202424i
$741$	0.295650	−	34.8965i	0.0108610	−	1.28196i
$742$	−0.604595	−	4.76292i	−0.0221954	−	0.174852i
$743$	39.1760	+	14.2589i	1.43723	+	0.523108i	0.938993	−	0.343935i	$-0.111760\pi$
$743$	39.1760	+	14.2589i	1.43723	+	0.523108i	0.498233	+	0.867043i	$0.333982\pi$
$744$	−31.4922	+	19.4522i	−1.15456	+	0.713153i
$745$	−27.2323	−	22.8506i	−0.997716	−	0.837183i
$746$	31.2317	−	33.7677i	1.14347	−	1.23632i
$747$	64.8834	+	11.4407i	2.37396	+	0.418593i
$748$	4.08369	+	1.13492i	0.149315	+	0.0414967i
$749$	8.26522	−	4.77193i	0.302005	−	0.174362i
$750$	24.7701	+	48.1264i	0.904475	+	1.75733i
$751$	10.4064	−	3.78761i	0.379734	−	0.138212i	−0.145099	−	0.989417i	$-0.546350\pi$
$751$	10.4064	−	3.78761i	0.379734	−	0.138212i	0.524833	+	0.851205i	$0.324128\pi$
$752$	5.16042	−	8.56712i	0.188181	−	0.312411i
$753$	25.1219	+	14.5042i	0.915494	+	0.528561i
$754$	10.1419	+	0.489933i	0.369346	+	0.0178423i
$755$	−7.97866	+	6.69489i	−0.290373	+	0.243652i
$756$	19.7606	−	41.3706i	0.718685	−	1.50463i
$757$	0.827186	+	4.69120i	0.0300646	+	0.170505i	0.996143	−	0.0877439i	$-0.0279657\pi$
$757$	0.827186	+	4.69120i	0.0300646	+	0.170505i	−0.966078	+	0.258249i	$0.916855\pi$
$758$	7.32623	−	32.3362i	0.266101	−	1.17450i
$759$	−56.0420			−2.03419
$760$	−0.501448	−	23.5941i	−0.0181894	−	0.855847i
$761$	−1.17846			−0.0427193			−0.0213597	−	0.999772i	$-0.506800\pi$
$761$	−1.17846			−0.0427193			−0.0213597	+	0.999772i	$0.506800\pi$
$762$	−3.08748	+	13.6274i	−0.111848	+	0.493668i
$763$	0.262813	+	1.49048i	0.00951446	+	0.0539592i
$764$	−4.64775	+	9.73050i	−0.168150	+	0.352037i
$765$	−8.88934	+	7.45904i	−0.321395	+	0.269682i
$766$	−30.5645	−	1.47651i	−1.10434	−	0.0533483i
$767$	−15.0397	−	8.68318i	−0.543053	−	0.313532i
$768$	50.4575	+	1.87267i	1.82073	+	0.0675742i
$769$	−16.7613	+	6.10062i	−0.604429	+	0.219994i	−0.626064	−	0.779772i	$-0.715335\pi$
$769$	−16.7613	+	6.10062i	−0.604429	+	0.219994i	0.0216350	+	0.999766i	$0.493113\pi$
$770$	−5.52971	−	10.7438i	−0.199277	−	0.387180i
$771$	49.2826	−	28.4533i	1.77487	−	1.02472i
$772$	29.9032	+	8.31053i	1.07624	+	0.299103i
$773$	−28.7474	−	5.06894i	−1.03397	−	0.182317i	−0.369190	−	0.929354i	$-0.620365\pi$
$773$	−28.7474	−	5.06894i	−1.03397	−	0.182317i	−0.664783	+	0.747037i	$0.731476\pi$
$774$	54.7597	−	59.2062i	1.96830	−	2.12812i
$775$	4.24412	+	3.56124i	0.152453	+	0.127923i
$776$	9.19666	+	14.8890i	0.330141	+	0.534482i
$777$	−8.08295	−	2.94195i	−0.289974	−	0.105542i
$778$	−4.14290	−	32.6372i	−0.148530	−	1.17010i
$779$	−6.25782	+	1.04884i	−0.224210	+	0.0375785i
$780$	7.65790	+	29.6779i	0.274197	+	1.06264i
$781$	−6.64858	+	18.2668i	−0.237905	+	0.653638i
$782$	−2.66468	−	8.58997i	−0.0952887	−	0.307177i
$783$	22.7266	−	27.0846i	0.812184	−	0.967923i
$784$	5.22284	−	13.5616i	0.186530	−	0.484342i
$785$	4.26781	−	24.2039i	0.152325	−	0.863875i
$786$	−17.0077	+	40.5277i	−0.606646	+	1.44558i
$787$	0.668131	+	1.15724i	0.0238163	+	0.0412510i	0.877688	−	0.479233i	$-0.159085\pi$
$787$	0.668131	+	1.15724i	0.0238163	+	0.0412510i	−0.853872	+	0.520484i	$0.825752\pi$
$788$	−7.02804	+	4.82458i	−0.250364	+	0.171868i
$789$	11.8201	+	32.4754i	0.420807	+	1.15616i
$790$	−11.2805	+	8.57299i	−0.401341	+	0.305013i
$791$	−6.79474	+	11.7688i	−0.241593	+	0.418451i
$792$	−9.71205	−	46.8856i	−0.345103	−	1.66601i
$793$	−18.2844	−	21.7905i	−0.649298	−	0.773803i
$794$	−19.6252	+	30.4924i	−0.696472	+	1.08214i
$795$	11.0066	−	1.94075i	0.390362	−	0.0688314i
$796$	−1.47741	+	15.2559i	−0.0523653	+	0.540731i
$797$			36.9364i			1.30835i	0.756341	+	0.654177i	$0.226985\pi$
$797$			36.9364i			1.30835i	−0.756341	+	0.654177i	$0.773015\pi$
$798$	29.8510	+	19.5720i	1.05671	+	0.692841i
$799$		−	2.17818i		−	0.0770585i
$800$	−2.10485	−	7.25839i	−0.0744178	−	0.256623i
$801$	43.0513	−	7.59110i	1.52114	−	0.268218i
$802$	3.14799	+	2.02607i	0.111159	+	0.0715432i
$803$	−18.2210	−	21.7149i	−0.643004	−	0.766302i
$804$	−1.36009	−	17.4034i	−0.0479666	−	0.613769i
$805$	−12.8201	+	22.2050i	−0.451849	+	0.782625i
$806$	9.00277	+	11.8460i	0.317109	+	0.417256i
$807$	−29.5311	−	81.1359i	−1.03954	−	2.85612i
$808$	9.41243	+	10.5632i	0.331128	+	0.371612i
$809$	−13.2530	−	22.9549i	−0.465951	−	0.807050i	0.533293	−	0.845930i	$-0.320954\pi$
$809$	−13.2530	−	22.9549i	−0.465951	−	0.807050i	−0.999244	+	0.0388803i	$0.987621\pi$
$810$	46.3012	+	19.4306i	1.62686	+	0.682722i
$811$	1.61077	−	9.13515i	0.0565619	−	0.320778i	−0.943378	−	0.331719i	$-0.892371\pi$
$811$	1.61077	−	9.13515i	0.0565619	−	0.320778i	0.999940	+	0.0109405i	$0.00348255\pi$
$812$	−6.03565	+	8.45188i	−0.211810	+	0.296603i
$813$	−48.1761	+	57.4140i	−1.68961	+	2.01360i
$814$	−4.88102	+	1.51413i	−0.171080	+	0.0530703i
$815$	12.7652	−	35.0720i	0.447144	−	1.22852i
$816$	9.62378	−	5.32078i	0.336900	−	0.186265i
$817$	22.7279	+	27.5568i	0.795149	+	0.964092i
$818$	30.0139	−	3.80990i	1.04941	−	0.133210i
$819$	−30.4406	−	11.0795i	−1.06368	−	0.387148i
$820$	5.07227	−	2.30821i	0.177131	−	0.0806063i
$821$	−7.41970	−	6.22587i	−0.258949	−	0.217284i	0.504065	−	0.863666i	$-0.331837\pi$
$821$	−7.41970	−	6.22587i	−0.258949	−	0.217284i	−0.763015	+	0.646381i	$0.776282\pi$
$822$	55.6903	+	51.5079i	1.94242	+	1.79654i
$823$	14.8508	+	2.61860i	0.517666	+	0.0912785i	0.426376	−	0.904546i	$-0.359790\pi$
$823$	14.8508	+	2.61860i	0.517666	+	0.0912785i	0.0912898	+	0.995824i	$0.470901\pi$
$824$	−42.7571	−	6.23534i	−1.48951	−	0.217218i
$825$	−8.88207	+	5.12806i	−0.309234	+	0.178536i
$826$	15.7940	−	8.12897i	0.549543	−	0.282843i
$827$	−9.22703	+	3.35836i	−0.320855	+	0.116782i	−0.497427	−	0.867506i	$-0.665722\pi$
$827$	−9.22703	+	3.35836i	−0.320855	+	0.116782i	0.176571	+	0.984288i	$0.443499\pi$
$828$	−72.5057	+	71.1731i	−2.51975	+	2.47344i
$829$	−42.6296	−	24.6122i	−1.48059	−	0.854817i	−0.480829	−	0.876814i	$-0.659664\pi$
$829$	−42.6296	−	24.6122i	−1.48059	−	0.854817i	−0.999758	+	0.0219971i	$0.992998\pi$
$830$	1.23666	−	25.5996i	0.0429251	−	0.888574i
$831$	−9.62718	+	8.07816i	−0.333963	+	0.280228i
$832$	−1.20575	−	20.2600i	−0.0418019	−	0.702388i
$833$	−0.549604	−	3.11696i	−0.0190426	−	0.107996i
$834$	41.3144	+	9.36039i	1.43060	+	0.324124i
$835$	42.6936			1.47747
$836$	21.1561	−	1.47316i	0.731701	−	0.0509501i
$837$	51.8094			1.79079
$838$	5.46440	+	1.23804i	0.188765	+	0.0427674i
$839$	1.74578	+	9.90080i	0.0602710	+	0.341814i	1.00000		0.000106438i	$-3.38803e-5\pi$
$839$	1.74578	+	9.90080i	0.0602710	+	0.341814i	−0.939729	+	0.341920i	$0.888923\pi$
$840$	−29.7653	−	9.84224i	−1.02700	−	0.339589i
$841$	16.0799	−	13.4926i	0.554479	−	0.465264i
$842$	2.71586	−	56.2198i	0.0935946	−	1.93746i
$843$	13.6751	+	7.89534i	0.470996	+	0.271930i
$844$	28.6282	+	29.1642i	0.985422	+	1.00387i
$845$	−11.8064	+	4.29717i	−0.406152	+	0.147827i
$846$	−21.8786	+	11.2606i	−0.752201	+	0.387149i
$847$	−8.07599	+	4.66267i	−0.277494	+	0.160211i
$848$	−7.39949	−	0.137264i	−0.254099	−	0.00471368i
$849$	29.0964	+	5.13048i	0.998587	+	0.176078i
$850$	−1.20834	−	1.11759i	−0.0414457	−	0.0383331i
$851$	8.30709	+	6.97048i	0.284763	+	0.238945i
$852$	20.8899	+	45.9053i	0.715676	+	1.57269i
$853$	21.0381	+	7.65726i	0.720332	+	0.262180i	0.676067	−	0.736840i	$-0.263683\pi$
$853$	21.0381	+	7.65726i	0.720332	+	0.262180i	0.0442655	+	0.999020i	$0.485905\pi$
$854$	28.8638	−	3.66391i	0.987699	−	0.125376i
$855$	−29.4561	+	50.0356i	−1.00738	+	1.71118i
$856$	−5.44021	−	13.6686i	−0.185943	−	0.467183i
$857$	7.26265	−	19.9540i	0.248087	−	0.681615i	−0.751669	−	0.659541i	$-0.770751\pi$
$857$	7.26265	−	19.9540i	0.248087	−	0.681615i	0.999756	−	0.0220739i	$-0.00702692\pi$
$858$	−26.3067	+	8.16054i	−0.898094	+	0.278596i
$859$	4.83618	−	5.76354i	0.165008	−	0.196649i	−0.677204	−	0.735795i	$-0.736808\pi$
$859$	4.83618	−	5.76354i	0.165008	−	0.196649i	0.842212	+	0.539146i	$0.181253\pi$
$860$	−25.5307	−	18.2320i	−0.870591	−	0.621706i
$861$	−1.46369	+	8.30102i	−0.0498825	+	0.282898i
$862$	25.9623	+	10.8952i	0.884279	+	0.371093i
$863$	−12.1124	−	20.9793i	−0.412311	−	0.714143i	0.582831	−	0.812593i	$-0.301945\pi$
$863$	−12.1124	−	20.9793i	−0.412311	−	0.714143i	−0.995142	+	0.0984500i	$0.968612\pi$
$864$	−58.7080	−	39.3438i	−1.99729	−	1.33850i
$865$	−14.3408	−	39.4009i	−0.487600	−	1.33967i
$866$	−25.3378	−	33.3398i	−0.861012	−	1.13293i
$867$	−25.6265	+	44.3864i	−0.870322	+	1.50744i
$868$	−15.1724	+	1.18574i	−0.514986	+	0.0402466i
$869$	−8.18419	−	9.75354i	−0.277630	−	0.330866i
$870$	−20.3298	−	13.0844i	−0.689243	−	0.443603i
$871$	−6.91017	+	1.21845i	−0.234142	+	0.0412856i
$872$	2.33193	−	0.0693299i	0.0789692	−	0.00234781i
$873$		−	43.0564i		−	1.45724i
$874$	−26.9244	−	36.0576i	−0.910732	−	1.21967i
$875$			22.2539i			0.752319i
$876$	−73.2034	−	7.08915i	−2.47332	−	0.239520i
$877$	−23.2095	+	4.09245i	−0.783728	+	0.138192i	−0.551173	−	0.834391i	$-0.685820\pi$
$877$	−23.2095	+	4.09245i	−0.783728	+	0.138192i	−0.232555	+	0.972583i	$0.574708\pi$
$878$	0.0741485	−	0.115207i	0.00250239	−	0.00388806i
$879$	−2.41476	−	2.87779i	−0.0814477	−	0.0970656i
$880$	−17.6178	+	6.04474i	−0.593897	+	0.203768i
$881$	12.5493	−	21.7361i	0.422797	−	0.732306i	−0.573415	−	0.819265i	$-0.694382\pi$
$881$	12.5493	−	21.7361i	0.422797	−	0.732306i	0.996212	+	0.0869589i	$0.0277149\pi$
$882$	−28.4668	+	21.6343i	−0.958526	+	0.728466i
$883$	16.9886	+	46.6758i	0.571712	+	1.57077i	0.801797	+	0.597596i	$0.203877\pi$
$883$	16.9886	+	46.6758i	0.571712	+	1.57077i	−0.230085	+	0.973171i	$0.573900\pi$
$884$	−2.50165	−	3.64420i	−0.0841397	−	0.122568i
$885$	20.6750	+	35.8102i	0.694983	+	1.20375i
$886$	11.7961	−	28.1090i	0.396299	−	0.944341i
$887$	−5.78998	+	32.8366i	−0.194408	+	1.10255i	0.718850	+	0.695165i	$0.244669\pi$
$887$	−5.78998	+	32.8366i	−0.194408	+	1.10255i	−0.913259	+	0.407380i	$0.866442\pi$
$888$	−6.28541	+	11.6747i	−0.210925	+	0.391778i
$889$	−3.69270	+	4.40078i	−0.123849	+	0.147598i
$890$	−5.03841	−	16.2420i	−0.168888	−	0.544434i
$891$	−15.4331	+	42.4022i	−0.517029	+	1.42053i
$892$	19.7110	−	5.08611i	0.659974	−	0.170295i
$893$	−3.64066	−	10.2726i	−0.121830	−	0.343759i
$894$	−10.4374	−	82.2244i	−0.349078	−	2.74999i
$895$	−17.8964	−	6.51375i	−0.598210	−	0.217731i
$896$	18.0932	+	10.1783i	0.604450	+	0.340032i
$897$	44.7717	+	37.5679i	1.49488	+	1.25436i
$898$	−18.8202	+	20.3484i	−0.628038	+	0.679034i
$899$	−11.5579	−	2.03797i	−0.385478	−	0.0679702i
$900$	−4.97877	+	17.9148i	−0.165959	+	0.597159i
$901$	−1.39587	+	0.805907i	−0.0465032	+	0.0268487i
$902$	2.29178	+	4.45275i	0.0763078	+	0.148260i
$903$	44.5904	−	16.2296i	1.48388	−	0.540087i
$904$	16.4398	+	12.9820i	0.546781	+	0.431776i
$905$	−6.62681	−	3.82599i	−0.220283	−	0.127180i
$906$	−24.2555	−	1.17173i	−0.805835	−	0.0389282i
$907$	17.9605	−	15.0706i	0.596367	−	0.500412i	−0.293908	−	0.955834i	$-0.594956\pi$
$907$	17.9605	−	15.0706i	0.596367	−	0.500412i	0.890276	+	0.455422i	$0.150512\pi$
$908$	23.3525	+	11.1543i	0.774981	+	0.370168i
$909$	−6.04460	−	34.2806i	−0.200487	−	1.13702i
$910$	−2.78449	+	12.2901i	−0.0923051	+	0.407412i
$911$	35.7961			1.18598			0.592989	−	0.805211i	$-0.297948\pi$
$911$	35.7961			1.18598			0.592989	+	0.805211i	$0.297948\pi$
$912$	36.4937	−	41.1789i	1.20843	−	1.36357i
$913$	23.0316			0.762236
$914$	−2.89497	+	12.7777i	−0.0957573	+	0.422649i
$915$	11.7612	+	66.7009i	0.388812	+	2.20506i
$916$	−25.7047	−	12.2778i	−0.849309	−	0.405670i
$917$	−13.8428	+	11.6155i	−0.457130	+	0.383577i
$918$	−15.3738	−	0.742676i	−0.507411	−	0.0245119i
$919$	−24.2681	−	14.0112i	−0.800530	−	0.462186i	0.0431266	−	0.999070i	$-0.486268\pi$
$919$	−24.2681	−	14.0112i	−0.800530	−	0.462186i	−0.843656	+	0.536884i	$0.819601\pi$
$920$	31.0182	+	24.4941i	1.02264	+	0.807546i
$921$	−64.4520	+	23.4586i	−2.12376	+	0.772987i
$922$	3.33946	+	6.48832i	0.109979	+	0.213682i
$923$	17.5568	−	10.1364i	0.577888	−	0.333644i
$924$	7.54368	−	27.1439i	0.248169	−	0.892969i
$925$	1.95441	+	0.344616i	0.0642607	+	0.0113309i
$926$	−30.6370	+	33.1248i	−1.00680	+	1.08855i
$927$	81.4375	+	68.3341i	2.67476	+	2.24439i
$928$	11.5493	+	11.0864i	0.379124	+	0.363928i
$929$	−7.13749	−	2.59784i	−0.234174	−	0.0852322i	0.222268	−	0.974986i	$-0.428654\pi$
$929$	−7.13749	−	2.59784i	−0.234174	−	0.0852322i	−0.456442	+	0.889753i	$0.650876\pi$
$930$	−4.46122	−	35.1449i	−0.146289	−	1.15245i
$931$	−7.80175	−	13.7814i	−0.255692	−	0.451666i
$932$	−31.2296	+	8.05828i	−1.02296	+	0.263958i
$933$	35.7758	−	98.2932i	1.17125	−	3.21798i
$934$	−10.1573	−	32.7436i	−0.332358	−	1.07140i
$935$	−2.60751	+	3.10750i	−0.0852746	+	0.101626i
$936$	−23.6710	+	43.9673i	−0.773711	+	1.43711i
$937$	0.989598	−	5.61229i	0.0323288	−	0.183345i	−0.964367	−	0.264567i	$-0.914771\pi$
$937$	0.989598	−	5.61229i	0.0323288	−	0.183345i	0.996696	+	0.0812214i	$0.0258821\pi$
$938$	2.77727	−	6.61797i	0.0906812	−	0.216084i
$939$	−49.1457	−	85.1228i	−1.60381	−	2.77788i
$940$	5.41734	+	7.89153i	0.176694	+	0.257393i
$941$	11.9414	+	32.8089i	0.389280	+	1.06954i	0.967326	+	0.253534i	$0.0815931\pi$
$941$	11.9414	+	32.8089i	0.389280	+	1.06954i	−0.578046	+	0.816004i	$0.696185\pi$
$942$	45.6225	−	34.6725i	1.48646	−	1.12969i
$943$	5.31325	−	9.20283i	0.173023	−	0.299685i
$944$	−8.88609	−	25.8992i	−0.289217	−	0.842946i
$945$	28.2055	+	33.6140i	0.917525	+	1.09346i
$946$	15.2579	−	23.7068i	0.496077	−	0.770774i
$947$	−57.4378	+	10.1278i	−1.86648	+	0.329110i	−0.988694	−	0.149946i	$-0.952090\pi$
$947$	−57.4378	+	10.1278i	−1.86648	+	0.329110i	−0.877784	+	0.479057i	$0.840979\pi$
$948$	−32.8803	−	3.18419i	−1.06790	−	0.103418i
$949$			29.5625i			0.959638i
$950$	−7.56665	−	3.25106i	−0.245495	−	0.105478i
$951$			35.8644i			1.16298i
$952$	4.51924	−	0.134360i	0.146469	−	0.00435463i
$953$	14.1731	−	2.49911i	0.459113	−	0.0809540i	0.0606917	−	0.998157i	$-0.480669\pi$
$953$	14.1731	−	2.49911i	0.459113	−	0.0809540i	0.398421	+	0.917203i	$0.369558\pi$
$954$	15.3112	+	9.85441i	0.495718	+	0.319048i
$955$	−6.63402	−	7.90612i	−0.214672	−	0.255836i
$956$	−42.3924	+	3.31300i	−1.37107	+	0.107150i
$957$	10.8630	−	18.8152i	0.351150	−	0.608210i
$958$	2.01676	+	2.65368i	0.0651585	+	0.0857364i
$959$	10.6671	+	29.3077i	0.344460	+	0.946396i
$960$	−21.6336	+	43.2124i	−0.698222	+	1.39467i
$961$	6.90118	+	11.9532i	0.222619	+	0.385587i
$962$	4.91443	+	2.06238i	0.158448	+	0.0664937i
$963$	−6.28519	+	35.6451i	−0.202537	+	1.14865i
$964$	−9.07350	−	6.47956i	−0.292238	−	0.208693i
$965$	−19.0937	+	22.7550i	−0.614648	+	0.732509i
$966$	−57.0967	+	17.7119i	−1.83706	+	0.569869i
$967$	9.26769	−	25.4628i	0.298029	−	0.818827i	−0.696800	−	0.717265i	$-0.745394\pi$
$967$	9.26769	−	25.4628i	0.298029	−	0.818827i	0.994829	−	0.101562i	$-0.0323841\pi$
$968$	5.31566	+	13.3557i	0.170852	+	0.429268i
$969$	2.18080	−	11.7833i	0.0700574	−	0.378534i
$970$	−16.6159	+	2.10918i	−0.533503	+	0.0677218i
$971$	25.5203	+	9.28864i	0.818986	+	0.298087i	0.717331	−	0.696733i	$-0.245364\pi$
$971$	25.5203	+	9.28864i	0.818986	+	0.298087i	0.101656	+	0.994820i	$0.467586\pi$
$972$	17.4433	+	38.3314i	0.559494	+	1.22948i
$973$	13.3419	+	11.1952i	0.427723	+	0.358902i
$974$	34.0529	+	31.4955i	1.09113	+	1.00918i
$975$	10.5335	+	1.85733i	0.337341	+	0.0594823i
$976$	0.831837	−	44.8417i	0.0266264	−	1.43535i
$977$	−23.9247	+	13.8130i	−0.765420	+	0.441916i	−0.831238	−	0.555916i	$-0.812368\pi$
$977$	−23.9247	+	13.8130i	−0.765420	+	0.441916i	0.0658183	+	0.997832i	$0.479034\pi$
$978$	77.3725	−	39.8227i	2.47410	−	1.27339i
$979$	14.3603	−	5.22671i	0.458956	−	0.167046i
$980$	9.74338	+	9.92580i	0.311241	+	0.317068i
$981$	−4.97085	−	2.86992i	−0.158707	−	0.0916296i
$982$	−0.913787	+	18.9159i	−0.0291601	+	0.603631i
$983$	−21.7373	+	18.2398i	−0.693313	+	0.581759i	−0.919863	−	0.392241i	$-0.871700\pi$
$983$	−21.7373	+	18.2398i	−0.693313	+	0.581759i	0.226549	+	0.974000i	$0.427255\pi$
$984$	12.3362	+	4.07909i	0.393262	+	0.130037i
$985$	−1.41676	−	8.03485i	−0.0451418	−	0.256012i
$986$	3.40046	+	0.770424i	0.108293	+	0.0245353i
$987$	−14.4782			−0.460845
$988$	−17.8891	−	13.0052i	−0.569128	−	0.413751i
$989$	−59.8228			−1.90225
$990$	44.6933	+	10.1259i	1.42044	+	0.321823i
$991$	5.06926	+	28.7492i	0.161030	+	0.913248i	0.953064	+	0.302770i	$0.0979114\pi$
$991$	5.06926	+	28.7492i	0.161030	+	0.913248i	−0.792033	+	0.610478i	$0.790977\pi$
$992$	−1.56633	+	23.4066i	−0.0497312	+	0.743162i
$993$	2.75529	−	2.31196i	0.0874363	−	0.0733678i
$994$	−1.00055	+	20.7119i	−0.0317354	+	0.656940i
$995$	−12.7041	−	7.33473i	−0.402748	−	0.232527i
$996$	42.6437	−	41.8600i	1.35122	−	1.32638i
$997$	−28.5953	+	10.4078i	−0.905623	+	0.329620i	−0.752504	−	0.658588i	$-0.771154\pi$
$997$	−28.5953	+	10.4078i	−0.905623	+	0.329620i	−0.153119	+	0.988208i	$0.548932\pi$
$998$	−42.5635	+	21.9069i	−1.34732	+	0.693451i
$999$	16.0720	−	9.27919i	0.508497	−	0.293581i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.2.k.a.15.4	yes	48
3.2	odd	2		684.2.cf.a.91.5		48
4.3	odd	2	inner	76.2.k.a.15.3	✓	48
12.11	even	2		684.2.cf.a.91.6		48
19.14	odd	18	inner	76.2.k.a.71.3	yes	48
57.14	even	18		684.2.cf.a.451.6		48
76.71	even	18	inner	76.2.k.a.71.4	yes	48
228.71	odd	18		684.2.cf.a.451.5		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.2.k.a.15.3	✓	48	4.3	odd	2	inner
76.2.k.a.15.4	yes	48	1.1	even	1	trivial
76.2.k.a.71.3	yes	48	19.14	odd	18	inner
76.2.k.a.71.4	yes	48	76.71	even	18	inner
684.2.cf.a.91.5		48	3.2	odd	2
684.2.cf.a.91.6		48	12.11	even	2
684.2.cf.a.451.5		48	228.71	odd	18
684.2.cf.a.451.6		48	57.14	even	18

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:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	76.k (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.312491 + 1.37926i) q^{2} +(-0.547993 - 3.10782i) q^{3} +(-1.80470 - 0.862010i) q^{4} +(1.46633 - 1.23040i) q^{5} +(4.45773 + 0.215343i) q^{6} +(1.58907 + 0.917452i) q^{7} +(1.75289 - 2.21977i) q^{8} +(-6.53918 + 2.38007i) q^{9} +O(q^{10})\)	\(q+(-0.312491 + 1.37926i) q^{2} +(-0.547993 - 3.10782i) q^{3} +(-1.80470 - 0.862010i) q^{4} +(1.46633 - 1.23040i) q^{5} +(4.45773 + 0.215343i) q^{6} +(1.58907 + 0.917452i) q^{7} +(1.75289 - 2.21977i) q^{8} +(-6.53918 + 2.38007i) q^{9} +(1.23882 + 2.40694i) q^{10} +(-2.10674 + 1.21633i) q^{11} +(-1.69001 + 6.08106i) q^{12} +(2.49843 + 0.440541i) q^{13} +(-1.76197 + 1.90504i) q^{14} +(-4.62741 - 3.88286i) q^{15} +(2.51388 + 3.11134i) q^{16} +(0.818624 + 0.297955i) q^{17} +(-1.23929 - 9.76296i) q^{18} +(4.35874 + 0.0369281i) q^{19} +(-3.70691 + 0.956507i) q^{20} +(1.98048 - 5.44131i) q^{21} +(-1.01929 - 3.28582i) q^{22} +(-4.69241 + 5.59220i) q^{23} +(-7.85923 - 4.23124i) q^{24} +(-0.231990 + 1.31568i) q^{25} +(-1.38836 + 3.30832i) q^{26} +(6.24660 + 10.8194i) q^{27} +(-2.07695 - 3.02552i) q^{28} +(-0.967934 - 2.65938i) q^{29} +(6.80148 - 5.16903i) q^{30} +(2.07350 - 3.59141i) q^{31} +(-5.07690 + 2.49502i) q^{32} +(4.93460 + 5.88083i) q^{33} +(-0.666769 + 1.03598i) q^{34} +(3.45895 - 0.609906i) q^{35} +(13.8529 + 1.34154i) q^{36} -1.48548i q^{37} +(-1.41300 + 6.00029i) q^{38} -8.00610i q^{39} +(-0.160893 - 5.41168i) q^{40} +(-1.43355 + 0.252774i) q^{41} +(6.88609 + 4.43195i) q^{42} +(5.26751 + 6.27757i) q^{43} +(4.85052 - 0.379072i) q^{44} +(-6.66019 + 11.5358i) q^{45} +(-6.24674 - 8.21955i) q^{46} +(-0.855159 - 2.34953i) q^{47} +(8.29190 - 9.51767i) q^{48} +(-1.81656 - 3.14638i) q^{49} +(-1.74217 - 0.731112i) q^{50} +(0.477390 - 2.70741i) q^{51} +(-4.12917 - 2.94872i) q^{52} +(-1.18928 + 1.41733i) q^{53} +(-16.8748 + 5.23470i) q^{54} +(-1.59262 + 4.37567i) q^{55} +(4.82200 - 1.91919i) q^{56} +(-2.27379 - 13.5664i) q^{57} +(3.97043 - 0.503998i) q^{58} +(-6.43248 - 2.34123i) q^{59} +(5.00401 + 10.9963i) q^{60} +(-8.58916 - 7.20716i) q^{61} +(4.30553 + 3.98217i) q^{62} +(-12.5748 - 2.21728i) q^{63} +(-1.85478 - 7.78202i) q^{64} +(4.20558 - 2.42810i) q^{65} +(-9.65319 + 4.96838i) q^{66} +(-2.59900 + 0.945959i) q^{67} +(-1.22053 - 1.24338i) q^{68} +(19.9510 + 11.5187i) q^{69} +(-0.239673 + 4.96136i) q^{70} +(6.12140 - 5.13647i) q^{71} +(-6.17923 + 18.6875i) q^{72} +(2.02346 + 11.4756i) q^{73} +(2.04886 + 0.464198i) q^{74} +4.21603 q^{75} +(-7.83439 - 3.82393i) q^{76} -4.46368 q^{77} +(11.0425 + 2.50183i) q^{78} +(0.908863 + 5.15442i) q^{79} +(7.51438 + 1.46919i) q^{80} +(14.2094 - 11.9231i) q^{81} +(0.0993319 - 2.05623i) q^{82} +(-8.19927 - 4.73385i) q^{83} +(-8.26463 + 8.11274i) q^{84} +(1.56698 - 0.570334i) q^{85} +(-10.3044 + 5.30356i) q^{86} +(-7.73445 + 4.46548i) q^{87} +(-0.992905 + 6.80856i) q^{88} +(-6.18655 - 1.09085i) q^{89} +(-13.8296 - 12.7909i) q^{90} +(3.56602 + 2.99225i) q^{91} +(13.2889 - 6.04733i) q^{92} +(-12.2977 - 4.47601i) q^{93} +(3.50784 - 0.445277i) q^{94} +(6.43681 - 5.30885i) q^{95} +(10.5362 + 14.4108i) q^{96} +(-2.11617 + 5.81414i) q^{97} +(4.90733 - 1.52229i) q^{98} +(10.8814 - 12.9680i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 6 q^{2} - 12 q^{5} - 12 q^{6} - 9 q^{8} - 18 q^{9}+O(q^{10}) \) 48 * q - 6 * q^2 - 12 * q^5 - 12 * q^6 - 9 * q^8 - 18 * q^9	\( 48 q - 6 q^{2} - 12 q^{5} - 12 q^{6} - 9 q^{8} - 18 q^{9} - 3 q^{10} - 9 q^{12} - 3 q^{14} - 12 q^{17} - 42 q^{20} - 18 q^{21} - 12 q^{22} + 24 q^{24} - 12 q^{25} + 21 q^{26} - 12 q^{29} + 42 q^{30} + 9 q^{32} - 36 q^{33} + 87 q^{36} + 60 q^{38} + 6 q^{40} + 30 q^{41} + 3 q^{42} + 45 q^{44} - 6 q^{45} + 36 q^{46} + 45 q^{48} - 18 q^{49} + 18 q^{50} - 15 q^{52} - 24 q^{53} - 75 q^{54} - 12 q^{57} + 60 q^{58} + 6 q^{60} - 66 q^{62} - 45 q^{64} + 18 q^{65} - 42 q^{66} - 42 q^{68} + 126 q^{69} - 63 q^{70} - 78 q^{72} - 12 q^{73} - 105 q^{74} - 126 q^{76} - 36 q^{77} + 3 q^{78} - 3 q^{80} + 72 q^{81} - 111 q^{82} - 117 q^{84} + 108 q^{85} - 24 q^{86} - 81 q^{88} - 18 q^{90} + 36 q^{92} + 30 q^{93} - 66 q^{96} - 6 q^{97} + 39 q^{98}+O(q^{100}) \) 48 * q - 6 * q^2 - 12 * q^5 - 12 * q^6 - 9 * q^8 - 18 * q^9 - 3 * q^10 - 9 * q^12 - 3 * q^14 - 12 * q^17 - 42 * q^20 - 18 * q^21 - 12 * q^22 + 24 * q^24 - 12 * q^25 + 21 * q^26 - 12 * q^29 + 42 * q^30 + 9 * q^32 - 36 * q^33 + 87 * q^36 + 60 * q^38 + 6 * q^40 + 30 * q^41 + 3 * q^42 + 45 * q^44 - 6 * q^45 + 36 * q^46 + 45 * q^48 - 18 * q^49 + 18 * q^50 - 15 * q^52 - 24 * q^53 - 75 * q^54 - 12 * q^57 + 60 * q^58 + 6 * q^60 - 66 * q^62 - 45 * q^64 + 18 * q^65 - 42 * q^66 - 42 * q^68 + 126 * q^69 - 63 * q^70 - 78 * q^72 - 12 * q^73 - 105 * q^74 - 126 * q^76 - 36 * q^77 + 3 * q^78 - 3 * q^80 + 72 * q^81 - 111 * q^82 - 117 * q^84 + 108 * q^85 - 24 * q^86 - 81 * q^88 - 18 * q^90 + 36 * q^92 + 30 * q^93 - 66 * q^96 - 6 * q^97 + 39 * q^98

Introduction

L-functions

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