LMFDB - Embedded newform 585.2.bt.b.376.24

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [585,2,Mod(376,585)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(585, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0, 3]))

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

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

chi := DirichletCharacter("585.376");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 585 = 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	585.bt (of order $6$, degree $2$, 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:	$4.67124851824$
Analytic rank:	$0$
Dimension:	$108$
Relative dimension:	$54$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			376.24
Character	$\chi$	$=$	585.376
Dual form			585.2.bt.b.571.24

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.355151 - 0.205047i) q^{2} +(0.841866 - 1.51369i) q^{3} +(-0.915912 - 1.58641i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(-0.609367 + 0.364968i) q^{6} +(-0.661508 - 0.381922i) q^{7} +1.57141i q^{8} +(-1.58252 - 2.54865i) q^{9} +O(q^{10})$	\(q+(-0.355151 - 0.205047i) q^{2} +(0.841866 - 1.51369i) q^{3} +(-0.915912 - 1.58641i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(-0.609367 + 0.364968i) q^{6} +(-0.661508 - 0.381922i) q^{7} +1.57141i q^{8} +(-1.58252 - 2.54865i) q^{9} +0.410093 q^{10} +(0.384678 + 0.222094i) q^{11} +(-3.17240 + 0.0508663i) q^{12} +(-3.48567 - 0.921994i) q^{13} +(0.156624 + 0.271280i) q^{14} +(0.0277681 + 1.73183i) q^{15} +(-1.50961 + 2.61472i) q^{16} -1.99449 q^{17} +(0.0394425 + 1.22965i) q^{18} -3.58544i q^{19} +(1.58641 + 0.915912i) q^{20} +(-1.13501 + 0.679791i) q^{21} +(-0.0910792 - 0.157754i) q^{22} +(0.803282 + 1.39133i) q^{23} +(2.37862 + 1.32291i) q^{24} +(0.500000 - 0.866025i) q^{25} +(1.04889 + 1.04217i) q^{26} +(-5.19014 + 0.249828i) q^{27} +1.39923i q^{28} +(0.298185 - 0.516472i) q^{29} +(0.345244 - 0.620755i) q^{30} +(-6.94569 + 4.01010i) q^{31} +(3.79404 - 2.19049i) q^{32} +(0.660028 - 0.395310i) q^{33} +(0.708345 + 0.408963i) q^{34} +0.763843 q^{35} +(-2.59374 + 4.84486i) q^{36} +0.218284i q^{37} +(-0.735183 + 1.27338i) q^{38} +(-4.33009 + 4.50004i) q^{39} +(-0.785703 - 1.36088i) q^{40} +(-0.971758 + 0.561045i) q^{41} +(0.542490 - 0.00869829i) q^{42} +(-0.412762 + 0.714925i) q^{43} -0.813673i q^{44} +(2.64483 + 1.41594i) q^{45} -0.658842i q^{46} +(3.55589 + 2.05299i) q^{47} +(2.68699 + 4.48633i) q^{48} +(-3.20827 - 5.55689i) q^{49} +(-0.355151 + 0.205047i) q^{50} +(-1.67909 + 3.01904i) q^{51} +(1.72991 + 6.37416i) q^{52} +5.08548 q^{53} +(1.89451 + 0.975495i) q^{54} -0.444187 q^{55} +(0.600154 - 1.03950i) q^{56} +(-5.42725 - 3.01846i) q^{57} +(-0.211802 + 0.122284i) q^{58} +(3.52561 - 2.03551i) q^{59} +(2.72195 - 1.63025i) q^{60} +(1.88333 - 3.26202i) q^{61} +3.28903 q^{62} +(0.0734659 + 2.29035i) q^{63} +4.24184 q^{64} +(3.47968 - 0.944367i) q^{65} +(-0.315467 + 0.00505820i) q^{66} +(-12.0106 + 6.93435i) q^{67} +(1.82677 + 3.16406i) q^{68} +(2.78229 - 0.0446113i) q^{69} +(-0.271280 - 0.156624i) q^{70} -12.1545i q^{71} +(4.00497 - 2.48679i) q^{72} -3.80995i q^{73} +(0.0447585 - 0.0775240i) q^{74} +(-0.889962 - 1.48592i) q^{75} +(-5.68797 + 3.28395i) q^{76} +(-0.169645 - 0.293833i) q^{77} +(2.46055 - 0.710326i) q^{78} +(4.87017 - 8.43538i) q^{79} -3.01922i q^{80} +(-3.99124 + 8.06660i) q^{81} +0.460162 q^{82} +(-13.4267 - 7.75194i) q^{83} +(2.11800 + 1.17796i) q^{84} +(1.72728 - 0.997243i) q^{85} +(0.293186 - 0.169271i) q^{86} +(-0.530747 - 0.886160i) q^{87} +(-0.348999 + 0.604485i) q^{88} -12.2951i q^{89} +(-0.648982 - 1.04519i) q^{90} +(1.95367 + 1.94116i) q^{91} +(1.47147 - 2.54866i) q^{92} +(0.222706 + 13.8896i) q^{93} +(-0.841918 - 1.45825i) q^{94} +(1.79272 + 3.10508i) q^{95} +(-0.121652 - 7.58710i) q^{96} +(-12.3546 - 7.13294i) q^{97} +2.63138i q^{98} +(-0.0427216 - 1.33188i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q - 6 q^{3} + 52 q^{4} - 14 q^{9}+O(q^{10}) $ 108 * q - 6 * q^3 + 52 * q^4 - 14 * q^9	$ 108 q - 6 q^{3} + 52 q^{4} - 14 q^{9} - 8 q^{10} - 36 q^{12} - 4 q^{13} - 8 q^{14} - 64 q^{16} + 36 q^{17} + 24 q^{22} - 22 q^{23} + 54 q^{25} + 40 q^{26} + 48 q^{27} - 16 q^{29} + 20 q^{30} - 40 q^{35} - 76 q^{36} - 12 q^{38} + 26 q^{39} - 52 q^{42} - 6 q^{43} - 68 q^{48} + 58 q^{49} + 34 q^{51} + 22 q^{52} - 116 q^{53} + 24 q^{55} + 40 q^{56} + 18 q^{61} + 152 q^{62} - 216 q^{64} + 2 q^{65} - 72 q^{66} - 134 q^{69} + 32 q^{74} + 40 q^{77} - 34 q^{78} + 18 q^{79} + 34 q^{81} + 88 q^{82} + 60 q^{87} + 8 q^{90} + 16 q^{91} + 176 q^{92} - 76 q^{94} - 56 q^{95}+O(q^{100}) $ 108 * q - 6 * q^3 + 52 * q^4 - 14 * q^9 - 8 * q^10 - 36 * q^12 - 4 * q^13 - 8 * q^14 - 64 * q^16 + 36 * q^17 + 24 * q^22 - 22 * q^23 + 54 * q^25 + 40 * q^26 + 48 * q^27 - 16 * q^29 + 20 * q^30 - 40 * q^35 - 76 * q^36 - 12 * q^38 + 26 * q^39 - 52 * q^42 - 6 * q^43 - 68 * q^48 + 58 * q^49 + 34 * q^51 + 22 * q^52 - 116 * q^53 + 24 * q^55 + 40 * q^56 + 18 * q^61 + 152 * q^62 - 216 * q^64 + 2 * q^65 - 72 * q^66 - 134 * q^69 + 32 * q^74 + 40 * q^77 - 34 * q^78 + 18 * q^79 + 34 * q^81 + 88 * q^82 + 60 * q^87 + 8 * q^90 + 16 * q^91 + 176 * q^92 - 76 * q^94 - 56 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/585\mathbb{Z}\right)^\times$.

$n$	$326$	$352$	$496$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$-1$

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 $

$2$	−0.355151	−	0.205047i	−0.251130	−	0.144990i	0.369152	−	0.929369i	$-0.379648\pi$
$2$	−0.355151	−	0.205047i	−0.251130	−	0.144990i	−0.620282	+	0.784379i	$0.712982\pi$
$3$	0.841866	−	1.51369i	0.486052	−	0.873930i
$3$	0.841866	−	1.51369i	0.486052	−	0.873930i
$4$	−0.915912	−	1.58641i	−0.457956	−	0.793203i
$5$	−0.866025	+	0.500000i	−0.387298	+	0.223607i
$5$	−0.866025	+	0.500000i	−0.387298	+	0.223607i
$6$	−0.609367	+	0.364968i	−0.248773	+	0.148997i
$7$	−0.661508	−	0.381922i	−0.250026	−	0.144353i	0.369750	−	0.929131i	$-0.379443\pi$
$7$	−0.661508	−	0.381922i	−0.250026	−	0.144353i	−0.619776	+	0.784779i	$0.712777\pi$
$8$			1.57141i			0.555576i
$9$	−1.58252	−	2.54865i	−0.527508	−	0.849550i
$10$	0.410093			0.129683
$11$	0.384678	+	0.222094i	0.115985	+	0.0669638i	0.556870	−	0.830600i	$-0.312002\pi$
$11$	0.384678	+	0.222094i	0.115985	+	0.0669638i	−0.440885	+	0.897563i	$0.645335\pi$
$12$	−3.17240	+	0.0508663i	−0.915794	+	0.0146838i
$13$	−3.48567	−	0.921994i	−0.966752	−	0.255715i
$13$	−3.48567	−	0.921994i	−0.966752	−	0.255715i
$14$	0.156624	+	0.271280i	0.0418594	+	0.0725026i
$15$	0.0277681	+	1.73183i	0.00716970	+	0.447156i
$16$	−1.50961	+	2.61472i	−0.377403	+	0.653681i
$17$	−1.99449			−0.483734			−0.241867	−	0.970309i	$-0.577760\pi$
$17$	−1.99449			−0.483734			−0.241867	+	0.970309i	$0.577760\pi$
$18$	0.0394425	+	1.22965i	0.00929669	+	0.289831i
$19$		−	3.58544i		−	0.822557i	−0.911510	−	0.411279i	$-0.865082\pi$
$19$		−	3.58544i		−	0.822557i	0.911510	−	0.411279i	$-0.134918\pi$
$20$	1.58641	+	0.915912i	0.354731	+	0.204804i
$21$	−1.13501	+	0.679791i	−0.247680	+	0.148343i
$22$	−0.0910792	−	0.157754i	−0.0194181	−	0.0336332i
$23$	0.803282	+	1.39133i	0.167496	+	0.290112i	0.937539	−	0.347881i	$-0.113099\pi$
$23$	0.803282	+	1.39133i	0.167496	+	0.290112i	−0.770043	+	0.637992i	$0.779765\pi$
$24$	2.37862	+	1.32291i	0.485534	+	0.270039i
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$	1.04889	+	1.04217i	0.205704	+	0.204387i
$27$	−5.19014	+	0.249828i	−0.998844	+	0.0480793i
$28$			1.39923i			0.264429i
$29$	0.298185	−	0.516472i	0.0553716	−	0.0959064i	−0.837011	−	0.547186i	$-0.815699\pi$
$29$	0.298185	−	0.516472i	0.0553716	−	0.0959064i	0.892383	+	0.451280i	$0.149032\pi$
$30$	0.345244	−	0.620755i	0.0630326	−	0.113334i
$31$	−6.94569	+	4.01010i	−1.24748	+	0.720235i	−0.970607	−	0.240671i	$-0.922633\pi$
$31$	−6.94569	+	4.01010i	−1.24748	+	0.720235i	−0.276876	+	0.960906i	$0.589299\pi$
$32$	3.79404	−	2.19049i	0.670697	−	0.387227i
$33$	0.660028	−	0.395310i	0.114896	−	0.0688146i
$34$	0.708345	+	0.408963i	0.121480	+	0.0701366i
$35$	0.763843			0.129113
$36$	−2.59374	+	4.84486i	−0.432291	+	0.807477i
$37$			0.218284i			0.0358857i	0.999839	+	0.0179429i	$0.00571170\pi$
$37$			0.218284i			0.0358857i	−0.999839	+	0.0179429i	$0.994288\pi$
$38$	−0.735183	+	1.27338i	−0.119263	+	0.206569i
$39$	−4.33009	+	4.50004i	−0.693369	+	0.720583i
$40$	−0.785703	−	1.36088i	−0.124231	−	0.215174i
$41$	−0.971758	+	0.561045i	−0.151763	+	0.0876205i	−0.573959	−	0.818884i	$-0.694593\pi$
$41$	−0.971758	+	0.561045i	−0.151763	+	0.0876205i	0.422195	+	0.906505i	$0.361260\pi$
$42$	0.542490	−	0.00869829i	0.0837081	−	0.00134218i
$43$	−0.412762	+	0.714925i	−0.0629456	+	0.109025i	−0.895781	−	0.444496i	$-0.853383\pi$
$43$	−0.412762	+	0.714925i	−0.0629456	+	0.109025i	0.832835	+	0.553521i	$0.186716\pi$
$44$		−	0.813673i		−	0.122666i
$45$	2.64483	+	1.41594i	0.394268	+	0.211075i
$46$		−	0.658842i		−	0.0971409i
$47$	3.55589	+	2.05299i	0.518679	+	0.299460i	0.736394	−	0.676553i	$-0.236527\pi$
$47$	3.55589	+	2.05299i	0.518679	+	0.299460i	−0.217715	+	0.976012i	$0.569860\pi$
$48$	2.68699	+	4.48633i	0.387834	+	0.647547i
$49$	−3.20827	−	5.55689i	−0.458325	−	0.793841i
$50$	−0.355151	+	0.205047i	−0.0502260	+	0.0289980i
$51$	−1.67909	+	3.01904i	−0.235120	+	0.422750i
$52$	1.72991	+	6.37416i	0.239896	+	0.883937i
$53$	5.08548			0.698544			0.349272	−	0.937021i	$-0.386429\pi$
$53$	5.08548			0.698544			0.349272	+	0.937021i	$0.386429\pi$
$54$	1.89451	+	0.975495i	0.257811	+	0.132748i
$55$	−0.444187			−0.0598942
$56$	0.600154	−	1.03950i	0.0801989	−	0.138909i
$57$	−5.42725	−	3.01846i	−0.718857	−	0.399805i
$58$	−0.211802	+	0.122284i	−0.0278109	+	0.0160566i
$59$	3.52561	−	2.03551i	0.458996	−	0.265001i	−0.252626	−	0.967564i	$-0.581294\pi$
$59$	3.52561	−	2.03551i	0.458996	−	0.265001i	0.711622	+	0.702563i	$0.247961\pi$
$60$	2.72195	−	1.63025i	0.351402	−	0.210465i
$61$	1.88333	−	3.26202i	0.241136	−	0.417659i	−0.719902	−	0.694075i	$-0.755814\pi$
$61$	1.88333	−	3.26202i	0.241136	−	0.417659i	0.961038	+	0.276416i	$0.0891468\pi$
$62$	3.28903			0.417707
$63$	0.0734659	+	2.29035i	0.00925583	+	0.288557i
$64$	4.24184			0.530230
$65$	3.47968	−	0.944367i	0.431601	−	0.117134i
$66$	−0.315467	+	0.00505820i	−0.0388313	+	0.000622621i
$67$	−12.0106	+	6.93435i	−1.46733	+	0.847165i	−0.999331	−	0.0365620i	$-0.988359\pi$
$67$	−12.0106	+	6.93435i	−1.46733	+	0.847165i	−0.468002	+	0.883727i	$0.655026\pi$
$68$	1.82677	+	3.16406i	0.221529	+	0.383699i
$69$	2.78229	−	0.0446113i	0.334949	−	0.00537057i
$70$	−0.271280	−	0.156624i	−0.0324242	−	0.0187201i
$71$		−	12.1545i		−	1.44248i	−0.692687	−	0.721238i	$-0.743573\pi$
$71$		−	12.1545i		−	1.44248i	0.692687	−	0.721238i	$-0.256427\pi$
$72$	4.00497	−	2.48679i	0.471990	−	0.293070i
$73$		−	3.80995i		−	0.445921i	−0.974827	−	0.222961i	$-0.928428\pi$
$73$		−	3.80995i		−	0.445921i	0.974827	−	0.222961i	$-0.0715721\pi$
$74$	0.0447585	−	0.0775240i	0.00520307	−	0.00901198i
$75$	−0.889962	−	1.48592i	−0.102764	−	0.171580i
$76$	−5.68797	+	3.28395i	−0.652455	+	0.376695i
$77$	−0.169645	−	0.293833i	−0.0193328	−	0.0334854i
$78$	2.46055	−	0.710326i	0.278603	−	0.0804285i
$79$	4.87017	−	8.43538i	0.547937	−	0.949055i	−0.450479	−	0.892787i	$-0.648747\pi$
$79$	4.87017	−	8.43538i	0.547937	−	0.949055i	0.998416	−	0.0562674i	$-0.0179199\pi$
$80$		−	3.01922i		−	0.337559i
$81$	−3.99124	+	8.06660i	−0.443472	+	0.896288i
$82$	0.460162			0.0508164
$83$	−13.4267	−	7.75194i	−1.47378	−	0.850885i	−0.474213	−	0.880410i	$-0.657267\pi$
$83$	−13.4267	−	7.75194i	−1.47378	−	0.850885i	−0.999564	+	0.0295248i	$0.990601\pi$
$84$	2.11800	+	1.17796i	0.231092	+	0.128526i
$85$	1.72728	−	0.997243i	0.187349	−	0.108166i
$86$	0.293186	−	0.169271i	0.0316151	−	0.0182530i
$87$	−0.530747	−	0.886160i	−0.0569020	−	0.0950064i
$88$	−0.348999	+	0.604485i	−0.0372035	+	0.0644383i
$89$		−	12.2951i		−	1.30328i	−0.758527	−	0.651641i	$-0.774081\pi$
$89$		−	12.2951i		−	1.30328i	0.758527	−	0.651641i	$-0.225919\pi$
$90$	−0.648982	−	1.04519i	−0.0684087	−	0.110172i
$91$	1.95367	+	1.94116i	0.204800	+	0.203489i
$92$	1.47147	−	2.54866i	0.153412	−	0.265717i
$93$	0.222706	+	13.8896i	0.0230935	+	1.44028i
$94$	−0.841918	−	1.45825i	−0.0868372	−	0.150407i
$95$	1.79272	+	3.10508i	0.183929	+	0.318575i
$96$	−0.121652	−	7.58710i	−0.0124160	−	0.774355i
$97$	−12.3546	−	7.13294i	−1.25442	−	0.724241i	−0.282437	−	0.959286i	$-0.591143\pi$
$97$	−12.3546	−	7.13294i	−1.25442	−	0.724241i	−0.971984	+	0.235045i	$0.924476\pi$
$98$			2.63138i			0.265810i
$99$	−0.0427216	−	1.33188i	−0.00429369	−	0.133859i
$100$	−1.83182			−0.183182
$101$	2.17351	−	3.76463i	0.216272	−	0.374594i	−0.737393	−	0.675464i	$-0.763944\pi$
$101$	2.17351	−	3.76463i	0.216272	−	0.374594i	0.953665	+	0.300869i	$0.0972768\pi$
$102$	1.21537	−	0.727923i	0.120340	−	0.0720751i
$103$	−3.41027	−	5.90676i	−0.336024	−	0.582010i	0.647657	−	0.761932i	$-0.275749\pi$
$103$	−3.41027	−	5.90676i	−0.336024	−	0.582010i	−0.983681	+	0.179922i	$0.942416\pi$
$104$	1.44883	−	5.47741i	0.142069	−	0.537104i
$105$	0.643054	−	1.15622i	0.0627556	−	0.112836i
$106$	−1.80611	−	1.04276i	−0.175425	−	0.101282i
$107$	13.2610			1.28199			0.640994	−	0.767546i	$-0.278522\pi$
$107$	13.2610			1.28199			0.640994	+	0.767546i	$0.278522\pi$
$108$	5.15004	+	8.00485i	0.495563	+	0.770267i
$109$		−	5.04666i		−	0.483382i	−0.970353	−	0.241691i	$-0.922298\pi$
$109$		−	5.04666i		−	0.483382i	0.970353	−	0.241691i	$-0.0777020\pi$
$110$	0.157754	+	0.0910792i	0.0150412	+	0.00868406i
$111$	0.330415	+	0.183766i	0.0313616	+	0.0174423i
$112$	1.99724	−	1.15311i	0.188721	−	0.108958i
$113$	5.92692	+	10.2657i	0.557557	+	0.965718i	0.997700	+	0.0677897i	$0.0215947\pi$
$113$	5.92692	+	10.2657i	0.557557	+	0.965718i	−0.440142	+	0.897928i	$0.645072\pi$
$114$	1.30857	+	2.18485i	0.122559	+	0.204630i
$115$	−1.39133	−	0.803282i	−0.129742	−	0.0749065i
$116$	−1.09244			−0.101431
$117$	3.16632	+	10.3428i	0.292726	+	0.956196i
$118$	−1.66950			−0.153690
$119$	1.31937	+	0.761737i	0.120946	+	0.0698283i
$120$	−2.72140	+	0.0436350i	−0.248429	+	0.00398331i
$121$	−5.40135	−	9.35541i	−0.491032	−	0.850492i
$122$	−1.33773	+	0.772341i	−0.121113	+	0.0699245i
$123$	0.0311583	+	1.94327i	0.00280945	+	0.175218i
$124$	12.7233	+	7.34579i	1.14258	+	0.659671i
$125$			1.00000i			0.0894427i
$126$	0.443538	−	0.828485i	0.0395135	−	0.0738074i
$127$	7.14987			0.634449			0.317224	−	0.948351i	$-0.397249\pi$
$127$	7.14987			0.634449			0.317224	+	0.948351i	$0.397249\pi$
$128$	−9.09457	−	5.25075i	−0.803854	−	0.464105i
$129$	0.734685	+	1.22667i	0.0646854	+	0.108002i
$130$	−1.42945	−	0.378104i	−0.125371	−	0.0331619i
$131$	2.96349	+	5.13292i	0.258921	+	0.448465i	0.965953	−	0.258717i	$-0.0832996\pi$
$131$	2.96349	+	5.13292i	0.258921	+	0.448465i	−0.707032	+	0.707182i	$0.749966\pi$
$132$	−1.23165	−	0.685004i	−0.107201	−	0.0596219i
$133$	−1.36936	+	2.37180i	−0.118738	+	0.205661i
$134$	5.68746			0.491322
$135$	4.36988	−	2.81143i	0.376100	−	0.241969i
$136$		−	3.13415i		−	0.268751i
$137$	7.89240	+	4.55668i	0.674293	+	0.389303i	0.797701	−	0.603053i	$-0.206049\pi$
$137$	7.89240	+	4.55668i	0.674293	+	0.389303i	−0.123408	+	0.992356i	$0.539382\pi$
$138$	−0.997283	−	0.554657i	−0.0848944	−	0.0472155i
$139$	−9.30433	−	16.1156i	−0.789183	−	1.36690i	−0.926468	−	0.376373i	$-0.877171\pi$
$139$	−9.30433	−	16.1156i	−0.789183	−	1.36690i	0.137285	−	0.990532i	$-0.456162\pi$
$140$	−0.699613	−	1.21177i	−0.0591281	−	0.102413i
$141$	6.10117	−	3.65417i	0.513812	−	0.307737i
$142$	−2.49225	+	4.31670i	−0.209145	+	0.362249i
$143$	−1.13609	−	1.12882i	−0.0950048	−	0.0943964i
$144$	9.05301	−	0.290387i	0.754418	−	0.0241989i
$145$			0.596370i			0.0495259i
$146$	−0.781218	+	1.35311i	−0.0646541	+	0.111984i
$147$	−11.1124	+	0.178175i	−0.916531	+	0.0146957i
$148$	0.346288	−	0.199929i	0.0284647	−	0.0164341i
$149$	13.2410	−	7.64470i	1.08475	−	0.626279i	0.152574	−	0.988292i	$-0.451244\pi$
$149$	13.2410	−	7.64470i	1.08475	−	0.626279i	0.932173	+	0.362014i	$0.117911\pi$
$150$	0.0113875	+	0.710211i	0.000929788	+	0.0579885i
$151$	6.89403	+	3.98027i	0.561029	+	0.323910i	0.753558	−	0.657381i	$-0.228336\pi$
$151$	6.89403	+	3.98027i	0.561029	+	0.323910i	−0.192530	+	0.981291i	$0.561669\pi$
$152$	5.63419			0.456993
$153$	3.15632	+	5.08325i	0.255173	+	0.410956i
$154$			0.139140i			0.0112123i
$155$	4.01010	−	6.94569i	0.322099	−	0.557891i
$156$	11.1049	+	2.74763i	0.889101	+	0.219987i
$157$	6.94705	+	12.0326i	0.554435	+	0.960310i	0.997947	+	0.0640415i	$0.0203990\pi$
$157$	6.94705	+	12.0326i	0.554435	+	0.960310i	−0.443512	+	0.896268i	$0.646268\pi$
$158$	−3.45930	+	1.99722i	−0.275207	+	0.158891i
$159$	4.28129	−	7.69784i	0.339528	−	0.610478i
$160$	−2.19049	+	3.79404i	−0.173173	+	0.299945i
$161$		−	1.22716i		−	0.0967140i
$162$	3.07153	−	2.04647i	0.241322	−	0.160786i
$163$		−	12.4121i		−	0.972194i	−0.873905	−	0.486097i	$-0.838420\pi$
$163$		−	12.4121i		−	0.972194i	0.873905	−	0.486097i	$-0.161580\pi$
$164$	1.78009	+	1.02774i	0.139002	+	0.0802526i
$165$	−0.373946	+	0.672363i	−0.0291117	+	0.0523434i
$166$	3.17902	+	5.50622i	0.246740	+	0.427366i
$167$	0.855330	−	0.493825i	0.0661874	−	0.0382133i	−0.466541	−	0.884500i	$-0.654500\pi$
$167$	0.855330	−	0.493825i	0.0661874	−	0.0382133i	0.532728	+	0.846286i	$0.321167\pi$
$168$	−1.06823	−	1.78356i	−0.0824156	−	0.137605i
$169$	11.2999	+	6.42754i	0.869220	+	0.494426i
$170$	−0.817926			−0.0627321
$171$	−9.13804	+	5.67404i	−0.698804	+	0.433905i
$172$	1.51221			0.115305
$173$	−11.8687	+	20.5572i	−0.902362	+	1.56294i	−0.0779430	+	0.996958i	$0.524835\pi$
$173$	−11.8687	+	20.5572i	−0.902362	+	1.56294i	−0.824419	+	0.565979i	$0.808498\pi$
$174$	0.00679119	+	0.423549i	0.000514839	+	0.0321092i
$175$	−0.661508	+	0.381922i	−0.0500053	+	0.0288706i
$176$	−1.16143	+	0.670551i	−0.0875459	+	0.0505446i
$177$	−0.113045	−	7.05032i	−0.00849698	−	0.529935i
$178$	−2.52108	+	4.36664i	−0.188963	+	0.327293i
$179$	−14.4659			−1.08123			−0.540616	−	0.841270i	$-0.681809\pi$
$179$	−14.4659			−1.08123			−0.540616	+	0.841270i	$0.681809\pi$
$180$	−0.176183	−	5.49265i	−0.0131319	−	0.409398i
$181$	12.7677			0.949018			0.474509	−	0.880251i	$-0.342626\pi$
$181$	12.7677			0.949018			0.474509	+	0.880251i	$0.342626\pi$
$182$	−0.295820	−	1.09000i	−0.0219277	−	0.0807961i
$183$	−3.35218	−	5.59696i	−0.247800	−	0.413739i
$184$	−2.18634	+	1.26228i	−0.161179	+	0.0930567i
$185$	−0.109142	−	0.189040i	−0.00802430	−	0.0138985i
$186$	2.76892	−	4.97858i	0.203027	−	0.365047i
$187$	−0.767234	−	0.442963i	−0.0561057	−	0.0323927i
$188$		−	7.52143i		−	0.548557i
$189$	3.52873	+	1.81696i	0.256678	+	0.132165i
$190$		−	1.47037i		−	0.106672i
$191$	3.92931	−	6.80577i	0.284315	−	0.492448i	−0.688128	−	0.725590i	$-0.741567\pi$
$191$	3.92931	−	6.80577i	0.284315	−	0.492448i	0.972443	+	0.233141i	$0.0749004\pi$
$192$	3.57106	−	6.42083i	0.257719	−	0.463384i
$193$	−1.16373	+	0.671881i	−0.0837672	+	0.0483630i	−0.541299	−	0.840830i	$-0.682067\pi$
$193$	−1.16373	+	0.671881i	−0.0837672	+	0.0483630i	0.457531	+	0.889194i	$0.348734\pi$
$194$	2.92517	+	5.06655i	0.210015	+	0.363757i
$195$	1.49994	−	6.06219i	0.107413	−	0.434123i
$196$	−5.87699	+	10.1792i	−0.419785	+	0.727089i
$197$			13.7449i			0.979283i	0.871924	+	0.489642i	$0.162872\pi$
$197$			13.7449i			0.979283i	−0.871924	+	0.489642i	$0.837128\pi$
$198$	−0.257924	+	0.481778i	−0.0183299	+	0.0342385i
$199$	14.2438			1.00972			0.504858	−	0.863202i	$-0.331545\pi$
$199$	14.2438			1.00972			0.504858	+	0.863202i	$0.331545\pi$
$200$	1.36088	+	0.785703i	0.0962286	+	0.0555576i
$201$	0.385108	+	24.0182i	0.0271634	+	1.69411i
$202$	−1.54385	+	0.891341i	−0.108625	+	0.0627146i
$203$	−0.394503	+	0.227767i	−0.0276887	+	0.0159861i
$204$	6.32731	−	0.101452i	0.443001	−	0.00710307i
$205$	0.561045	−	0.971758i	0.0391851	−	0.0678705i
$206$			2.79706i			0.194880i
$207$	2.27479	−	4.24909i	0.158109	−	0.295332i
$208$	7.67277	−	7.72223i	0.532011	−	0.535440i
$209$	0.796304	−	1.37924i	0.0550815	−	0.0954040i
$210$	−0.465461	+	0.278778i	−0.0321199	+	0.0192375i
$211$	−2.36532	−	4.09686i	−0.162836	−	0.282040i	0.773049	−	0.634346i	$-0.218731\pi$
$211$	−2.36532	−	4.09686i	−0.162836	−	0.282040i	−0.935885	+	0.352307i	$0.885397\pi$
$212$	−4.65785	−	8.06763i	−0.319902	−	0.554087i
$213$	−18.3982	−	10.2325i	−1.26062	−	0.701118i
$214$	−4.70966	−	2.71912i	−0.321946	−	0.185875i
$215$		−	0.825524i		−	0.0563003i
$216$	−0.392581	−	8.15582i	−0.0267117	−	0.554933i
$217$	6.12617			0.415872
$218$	−1.03480	+	1.79233i	−0.0700855	+	0.121392i
$219$	−5.76709	−	3.20747i	−0.389704	−	0.216741i
$220$	0.406836	+	0.704661i	0.0274289	+	0.0475083i
$221$	6.95213	+	1.83890i	0.467651	+	0.123698i
$222$	−0.0796668	−	0.133015i	−0.00534688	−	0.00892741i
$223$	−19.1394	−	11.0502i	−1.28167	−	0.739973i	−0.304517	−	0.952507i	$-0.598495\pi$
$223$	−19.1394	−	11.0502i	−1.28167	−	0.739973i	−0.977154	+	0.212534i	$0.931828\pi$
$224$	−3.34638			−0.223589
$225$	−2.99846	+	0.0961793i	−0.199897	+	0.00641195i
$226$		−	4.86118i		−	0.323361i
$227$	15.6911	+	9.05927i	1.04146	+	0.601285i	0.920245	−	0.391342i	$-0.127989\pi$
$227$	15.6911	+	9.05927i	1.04146	+	0.601285i	0.121211	+	0.992627i	$0.461322\pi$
$228$	0.182378	+	11.3745i	0.0120783	+	0.753293i
$229$	23.5892	−	13.6192i	1.55882	−	0.899985i	0.561449	−	0.827511i	$-0.310244\pi$
$229$	23.5892	−	13.6192i	1.55882	−	0.899985i	0.997370	−	0.0724733i	$-0.0230892\pi$
$230$	0.329421	+	0.570574i	0.0217214	+	0.0376225i
$231$	−0.587591	+	0.00942144i	−0.0386607	+	0.000619885i
$232$	0.811587	+	0.468570i	0.0532833	+	0.0307631i
$233$	−7.19231			−0.471184			−0.235592	−	0.971852i	$-0.575703\pi$
$233$	−7.19231			−0.471184			−0.235592	+	0.971852i	$0.575703\pi$
$234$	0.996244	−	4.32252i	0.0651265	−	0.282572i
$235$	−4.10598			−0.267845
$236$	−6.45830	−	3.72870i	−0.420400	−	0.242718i
$237$	−8.66853	−	14.4734i	−0.563082	−	0.940148i
$238$	−0.312384	−	0.541064i	−0.0202488	−	0.0350720i
$239$	−20.5740	+	11.8784i	−1.33082	+	0.768352i	−0.985426	−	0.170104i	$-0.945590\pi$
$239$	−20.5740	+	11.8784i	−1.33082	+	0.768352i	−0.345398	+	0.938456i	$0.612256\pi$
$240$	−4.57017	−	2.54178i	−0.295003	−	0.164071i
$241$	7.56313	+	4.36658i	0.487184	+	0.281276i	0.723406	−	0.690423i	$-0.242576\pi$
$241$	7.56313	+	4.36658i	0.487184	+	0.281276i	−0.236221	+	0.971699i	$0.575909\pi$
$242$			4.43012i			0.284779i
$243$	8.85024	+	12.8325i	0.567743	+	0.823206i
$244$	−6.89985			−0.441718
$245$	5.55689	+	3.20827i	0.355017	+	0.204969i
$246$	0.387395	−	0.696543i	0.0246994	−	0.0444099i
$247$	−3.30576	+	12.4977i	−0.210340	+	0.795209i
$248$	−6.30149	−	10.9145i	−0.400145	−	0.693072i
$249$	−23.0376	+	13.7979i	−1.45995	+	0.874404i
$250$	0.205047	−	0.355151i	0.0129683	−	0.0224617i
$251$	−2.37245			−0.149748			−0.0748739	−	0.997193i	$-0.523855\pi$
$251$	−2.37245			−0.149748			−0.0748739	+	0.997193i	$0.523855\pi$
$252$	3.56614	−	2.21431i	0.224646	−	0.139488i
$253$			0.713616i			0.0448646i
$254$	−2.53929	−	1.46606i	−0.159329	−	0.0919887i
$255$	−0.0553832	−	3.45411i	−0.00346823	−	0.216305i
$256$	−2.08854	−	3.61745i	−0.130534	−	0.226091i
$257$	0.973773	+	1.68662i	0.0607423	+	0.105209i	0.894797	−	0.446472i	$-0.147320\pi$
$257$	0.973773	+	1.68662i	0.0607423	+	0.105209i	−0.834055	+	0.551681i	$0.813987\pi$
$258$	−0.00940068	−	0.586297i	−0.000585261	−	0.0365012i
$259$	0.0833675	−	0.144397i	0.00518021	−	0.00897238i
$260$	−4.68523	−	4.65523i	−0.290566	−	0.288705i
$261$	−1.78819	+	0.0573585i	−0.110686	+	0.00355040i
$262$		−	2.43062i		−	0.150164i
$263$	−5.16187	+	8.94061i	−0.318294	+	0.551302i	−0.980132	−	0.198345i	$-0.936443\pi$
$263$	−5.16187	+	8.94061i	−0.318294	+	0.551302i	0.661838	+	0.749647i	$0.269777\pi$
$264$	0.621192	+	1.03717i	0.0382317	+	0.0638336i
$265$	−4.40415	+	2.54274i	−0.270545	+	0.156199i
$266$	0.972659	−	0.561565i	0.0596375	−	0.0344317i
$267$	−18.6110	−	10.3509i	−1.13898	−	0.633463i
$268$	22.0014	+	12.7025i	1.34395	+	0.775929i
$269$	−29.9938			−1.82875			−0.914377	−	0.404864i	$-0.867319\pi$
$269$	−29.9938			−1.82875			−0.914377	+	0.404864i	$0.867319\pi$
$270$	−2.12844	+	0.102453i	−0.129533	+	0.00623507i
$271$			9.71520i			0.590156i	0.955473	+	0.295078i	$0.0953457\pi$
$271$			9.71520i			0.590156i	−0.955473	+	0.295078i	$0.904654\pi$
$272$	3.01090	−	5.21503i	0.182563	−	0.316208i
$273$	4.58305	−	1.32306i	0.277379	−	0.0800751i
$274$	−1.86866	−	3.23662i	−0.112890	−	0.195531i
$275$	0.384678	−	0.222094i	0.0231969	−	0.0133928i
$276$	−2.61911	−	4.37299i	−0.157652	−	0.263223i
$277$	−1.76433	+	3.05592i	−0.106009	+	0.183612i	−0.914150	−	0.405376i	$-0.867140\pi$
$277$	−1.76433	+	3.05592i	−0.106009	+	0.183612i	0.808141	+	0.588989i	$0.200474\pi$
$278$			7.63129i			0.457694i
$279$	21.2121	+	11.3561i	1.26993	+	0.679871i
$280$			1.20031i			0.0717321i
$281$	10.2662	+	5.92722i	0.612433	+	0.353588i	0.773917	−	0.633287i	$-0.218295\pi$
$281$	10.2662	+	5.92722i	0.612433	+	0.353588i	−0.161484	+	0.986875i	$0.551628\pi$
$282$	−2.91612	+	0.0467570i	−0.173652	+	0.00278434i
$283$	−2.73202	−	4.73201i	−0.162402	−	0.281289i	0.773328	−	0.634007i	$-0.218591\pi$
$283$	−2.73202	−	4.73201i	−0.162402	−	0.281289i	−0.935730	+	0.352718i	$0.885257\pi$
$284$	−19.2820	+	11.1325i	−1.14418	+	0.660591i
$285$	6.20937	−	0.0995611i	0.367811	−	0.00589749i
$286$	0.172024	+	0.633853i	0.0101720	+	0.0374805i
$287$	0.857101			0.0505930
$288$	−11.5869	−	6.20318i	−0.682767	−	0.365526i
$289$	−13.0220			−0.766001
$290$	0.122284	−	0.211802i	0.00718075	−	0.0124374i
$291$	−21.1980	+	12.6961i	−1.24265	+	0.744258i
$292$	−6.04413	+	3.48958i	−0.353706	+	0.204212i
$293$	−9.54928	+	5.51328i	−0.557875	+	0.322089i	−0.752292	−	0.658830i	$-0.771052\pi$
$293$	−9.54928	+	5.51328i	−0.557875	+	0.322089i	0.194417	+	0.980919i	$0.437718\pi$
$294$	3.98310	+	2.21527i	0.232299	+	0.129197i
$295$	−2.03551	+	3.52561i	−0.118512	+	0.205269i
$296$	−0.343013			−0.0199373
$297$	−2.05202	−	1.05660i	−0.119070	−	0.0613099i
$298$	−6.27009			−0.363216
$299$	−1.51719	−	5.59033i	−0.0877412	−	0.323297i
$300$	−1.54215	+	2.77282i	−0.0890361	+	0.160089i
$301$	0.546090	−	0.315285i	0.0314761	−	0.0181728i
$302$	−1.63228	−	2.82720i	−0.0939274	−	0.162687i
$303$	−3.86868	−	6.45933i	−0.222250	−	0.371079i
$304$	9.37494	+	5.41263i	0.537690	+	0.310435i
$305$			3.76666i			0.215678i
$306$	−0.0786675	−	2.45252i	−0.00449712	−	0.140201i
$307$			5.83757i			0.333168i	0.986027	+	0.166584i	$0.0532736\pi$
$307$			5.83757i			0.333168i	−0.986027	+	0.166584i	$0.946726\pi$
$308$	−0.310759	+	0.538251i	−0.0177072	+	0.0306697i
$309$	−11.8120	+	0.189394i	−0.671961	+	0.0107742i
$310$	−2.84838	+	1.64451i	−0.161777	+	0.0934022i
$311$	−6.41979	−	11.1194i	−0.364033	−	0.630523i	0.624588	−	0.780955i	$-0.285267\pi$
$311$	−6.41979	−	11.1194i	−0.364033	−	0.630523i	−0.988620	+	0.150432i	$0.951934\pi$
$312$	−7.07139	−	6.80432i	−0.400339	−	0.385219i
$313$	0.0950885	−	0.164698i	0.00537472	−	0.00930929i	−0.863326	−	0.504647i	$-0.831622\pi$
$313$	0.0950885	−	0.164698i	0.00537472	−	0.00930929i	0.868700	+	0.495338i	$0.164956\pi$
$314$		−	5.69788i		−	0.321550i
$315$	−1.20880	−	1.94677i	−0.0681081	−	0.109688i
$316$	−17.8426			−1.00372
$317$	−7.66153	−	4.42339i	−0.430314	−	0.248442i	0.269166	−	0.963094i	$-0.413252\pi$
$317$	−7.66153	−	4.42339i	−0.430314	−	0.248442i	−0.699481	+	0.714652i	$0.746585\pi$
$318$	−3.09892	+	1.85603i	−0.173779	+	0.104081i
$319$	0.229410	−	0.132450i	0.0128445	−	0.00741578i
$320$	−3.67354	+	2.12092i	−0.205357	+	0.118563i
$321$	11.1640	−	20.0731i	0.623113	−	1.12037i
$322$	−0.251626	+	0.435829i	−0.0140226	+	0.0242878i
$323$			7.15112i			0.397899i
$324$	16.4525	−	1.05656i	0.914029	−	0.0586976i
$325$	−2.54131	+	2.55769i	−0.140966	+	0.141875i
$326$	−2.54507	+	4.40819i	−0.140958	+	0.244147i
$327$	−7.63908	−	4.24861i	−0.422442	−	0.234949i
$328$	−0.881629	−	1.52703i	−0.0486798	−	0.0843159i
$329$	−1.56816	−	2.71614i	−0.0864556	−	0.149746i
$330$	0.270673	−	0.162114i	0.0149001	−	0.00892408i
$331$	−5.81280	−	3.35602i	−0.319500	−	0.184464i	0.331669	−	0.943396i	$-0.392388\pi$
$331$	−5.81280	−	3.35602i	−0.319500	−	0.184464i	−0.651170	+	0.758932i	$0.725721\pi$
$332$			28.4004i			1.55867i
$333$	0.556331	−	0.345440i	0.0304867	−	0.0189300i
$334$	−0.405029			−0.0221622
$335$	6.93435	−	12.0106i	0.378864	−	0.656211i
$336$	−0.0640393	−	3.99396i	−0.00349363	−	0.217889i
$337$	3.79578	+	6.57448i	0.206769	+	0.358135i	0.950695	−	0.310128i	$-0.100372\pi$
$337$	3.79578	+	6.57448i	0.206769	+	0.358135i	−0.743926	+	0.668262i	$0.767038\pi$
$338$	−2.69521	−	4.59975i	−0.146600	−	0.250193i
$339$	20.5288	−	0.329159i	1.11497	−	0.0178775i
$340$	−3.16406	−	1.82677i	−0.171595	−	0.0990707i
$341$	−3.56247			−0.192919
$342$	4.40883	−	0.141419i	0.238402	−	0.00764706i
$343$			10.2481i			0.553347i
$344$	−1.12344	−	0.648617i	−0.0605717	−	0.0349711i
$345$	−2.38723	+	1.42978i	−0.128524	+	0.0769769i
$346$	8.43039	−	4.86729i	0.453220	−	0.261667i
$347$	−8.64183	−	14.9681i	−0.463918	−	0.803529i	0.535234	−	0.844704i	$-0.320223\pi$
$347$	−8.64183	−	14.9681i	−0.463918	−	0.803529i	−0.999152	+	0.0411747i	$0.986890\pi$
$348$	−0.919692	+	1.65362i	−0.0493007	+	0.0886436i
$349$	10.4484	+	6.03237i	0.559289	+	0.322905i	0.752860	−	0.658181i	$-0.228674\pi$
$349$	10.4484	+	6.03237i	0.559289	+	0.322905i	−0.193571	+	0.981086i	$0.562007\pi$
$350$	0.313247			0.0167438
$351$	18.3215	+	3.91446i	0.977929	+	0.208938i
$352$	1.94597			0.103721
$353$	10.5227	+	6.07527i	0.560066	+	0.323354i	0.753172	−	0.657824i	$-0.228523\pi$
$353$	10.5227	+	6.07527i	0.560066	+	0.323354i	−0.193106	+	0.981178i	$0.561856\pi$
$354$	−1.40550	+	2.52711i	−0.0747014	+	0.134314i
$355$	6.07726	+	10.5261i	0.322548	+	0.558669i
$356$	−19.5051	+	11.2613i	−1.03377	+	0.596846i
$357$	2.26377	−	1.35583i	0.119811	−	0.0717584i
$358$	5.13758	+	2.96618i	0.271530	+	0.156768i
$359$			0.257324i			0.0135810i	0.999977	+	0.00679052i	$0.00216151\pi$
$359$			0.257324i			0.0135810i	−0.999977	+	0.00679052i	$0.997838\pi$
$360$	−2.22501	+	4.15610i	−0.117268	+	0.219046i
$361$	6.14460			0.323400
$362$	−4.53448	−	2.61798i	−0.238327	−	0.137598i
$363$	−18.7084	+	0.299971i	−0.981937	+	0.0157444i
$364$	1.29008	−	4.87725i	0.0676184	−	0.255637i
$365$	1.90498	+	3.29952i	0.0997110	+	0.172705i
$366$	0.0428929	+	2.67512i	0.00224205	+	0.139831i
$367$	−7.37634	+	12.7762i	−0.385042	+	0.666912i	−0.991775	−	0.127993i	$-0.959146\pi$
$367$	−7.37634	+	12.7762i	−0.385042	+	0.666912i	0.606733	+	0.794906i	$0.292480\pi$
$368$	−4.85058			−0.252854
$369$	2.96774	+	1.58881i	0.154494	+	0.0827100i
$370$			0.0895170i			0.00465377i
$371$	−3.36408	−	1.94225i	−0.174654	−	0.100837i
$372$	21.8306	−	13.0749i	1.13186	−	0.677905i
$373$	13.1782	+	22.8252i	0.682339	+	1.18185i	0.974265	+	0.225405i	$0.0723705\pi$
$373$	13.1782	+	22.8252i	0.682339	+	1.18185i	−0.291926	+	0.956441i	$0.594296\pi$
$374$	0.181656	+	0.314638i	0.00939322	+	0.0162695i
$375$	1.51369	+	0.841866i	0.0781667	+	0.0434738i
$376$	−3.22608	+	5.58774i	−0.166372	+	0.288166i
$377$	−1.51556	+	1.52533i	−0.0780553	+	0.0785584i
$378$	−0.880672	−	1.36885i	−0.0452969	−	0.0704062i
$379$		−	20.4293i		−	1.04938i	−0.851293	−	0.524691i	$-0.824181\pi$
$379$		−	20.4293i		−	1.04938i	0.851293	−	0.524691i	$-0.175819\pi$
$380$	3.28395	−	5.68797i	0.168463	−	0.291787i
$381$	6.01924	−	10.8227i	0.308375	−	0.554464i
$382$	−2.79100	+	1.61139i	−0.142800	+	0.0824457i
$383$	32.6742	−	18.8644i	1.66957	−	0.963928i	0.701704	−	0.712469i	$-0.252423\pi$
$383$	32.6742	−	18.8644i	1.66957	−	0.963928i	0.967868	−	0.251459i	$-0.0809104\pi$
$384$	−15.6044	+	9.34594i	−0.796310	+	0.476933i
$385$	0.293833	+	0.169645i	0.0149751	+	0.00864590i
$386$	0.551068			0.0280486
$387$	2.47530	−	0.0793983i	0.125827	−	0.00403604i
$388$			26.1326i			1.32668i
$389$	−16.3053	+	28.2416i	−0.826712	+	1.43191i	0.0738923	+	0.997266i	$0.476458\pi$
$389$	−16.3053	+	28.2416i	−0.826712	+	1.43191i	−0.900604	+	0.434640i	$0.856875\pi$
$390$	−1.77574	+	1.84544i	−0.0899181	+	0.0934473i
$391$	−1.60214	−	2.77498i	−0.0810235	−	0.140337i
$392$	8.73213	−	5.04150i	0.441039	−	0.254634i
$393$	10.2645	−	0.164581i	0.517776	−	0.00830203i
$394$	2.81835	−	4.88152i	0.141986	−	0.245927i
$395$			9.74034i			0.490090i
$396$	−2.07377	+	1.28766i	−0.104211	+	0.0647071i
$397$		−	19.0703i		−	0.957113i	−0.878057	−	0.478556i	$-0.841160\pi$
$397$		−	19.0703i		−	0.957113i	0.878057	−	0.478556i	$-0.158840\pi$
$398$	−5.05870	−	2.92064i	−0.253570	−	0.146399i
$399$	2.43735	+	4.06952i	0.122020	+	0.203731i
$400$	1.50961	+	2.61472i	0.0754806	+	0.130736i
$401$	−21.4147	+	12.3638i	−1.06940	+	0.617417i	−0.928017	−	0.372539i	$-0.878487\pi$
$401$	−21.4147	+	12.3638i	−1.06940	+	0.617417i	−0.141380	+	0.989955i	$0.545154\pi$
$402$	4.78808	−	8.60906i	0.238808	−	0.429381i
$403$	27.9077	−	7.57401i	1.39018	−	0.377288i
$404$	−7.96296			−0.396172
$405$	−0.576779	−	8.98150i	−0.0286604	−	0.446294i
$406$	0.186811			0.00927129
$407$	−0.0484796	+	0.0839691i	−0.00240304	+	0.00416220i
$408$	−4.74413	−	2.63853i	−0.234870	−	0.130627i
$409$	4.97619	−	2.87301i	0.246057	−	0.142061i	−0.371900	−	0.928273i	$-0.621294\pi$
$409$	4.97619	−	2.87301i	0.246057	−	0.142061i	0.617957	+	0.786212i	$0.287960\pi$
$410$	−0.398512	+	0.230081i	−0.0196811	+	0.0113629i
$411$	13.5417	−	8.11054i	0.667965	−	0.400064i
$412$	−6.24701	+	10.8201i	−0.307768	+	0.533070i
$413$	−3.10963			−0.153015
$414$	−1.67916	+	1.04263i	−0.0825261	+	0.0512426i
$415$	15.5039			0.761055
$416$	−15.2444	+	4.13725i	−0.747418	+	0.202845i
$417$	−32.2270	+	0.516728i	−1.57816	+	0.0253043i
$418$	−0.565617	+	0.326559i	−0.0276652	+	0.0159725i
$419$	3.75989	+	6.51233i	0.183683	+	0.318148i	0.943132	−	0.332419i	$-0.107865\pi$
$419$	3.75989	+	6.51233i	0.183683	+	0.318148i	−0.759449	+	0.650567i	$0.774531\pi$
$420$	−2.42322	+	0.0388539i	−0.118241	+	0.00189588i
$421$	16.3791	+	9.45649i	0.798270	+	0.460881i	0.842866	−	0.538124i	$-0.180867\pi$
$421$	16.3791	+	9.45649i	0.798270	+	0.460881i	−0.0445961	+	0.999005i	$0.514200\pi$
$422$			1.94001i			0.0944381i
$423$	−0.394911	−	12.3116i	−0.0192012	−	0.598611i
$424$			7.99135i			0.388094i
$425$	−0.997243	+	1.72728i	−0.0483734	+	0.0837852i
$426$	4.43601	+	7.40657i	0.214925	+	0.358850i
$427$	−2.49167	+	1.43857i	−0.120580	+	0.0696172i
$428$	−12.1459	−	21.0373i	−0.587094	−	1.01688i
$429$	−2.66512	+	0.769380i	−0.128673	+	0.0371460i
$430$	−0.169271	+	0.293186i	−0.00816297	+	0.0141387i
$431$		−	7.12386i		−	0.343144i	−0.985172	−	0.171572i	$-0.945115\pi$
$431$		−	7.12386i		−	0.343144i	0.985172	−	0.171572i	$-0.0548847\pi$
$432$	7.18187	−	13.9479i	0.345538	−	0.671070i
$433$	−5.14134			−0.247077			−0.123538	−	0.992340i	$-0.539424\pi$
$433$	−5.14134			−0.247077			−0.123538	+	0.992340i	$0.539424\pi$
$434$	−2.17572	−	1.25615i	−0.104438	−	0.0602972i
$435$	0.902720	+	0.502064i	0.0432821	+	0.0240721i
$436$	−8.00604	+	4.62229i	−0.383420	+	0.221368i
$437$	4.98852	−	2.88012i	0.238633	−	0.137775i
$438$	1.39051	+	2.32166i	0.0664411	+	0.110933i
$439$	−6.34688	+	10.9931i	−0.302920	+	0.524673i	−0.976796	−	0.214172i	$-0.931295\pi$
$439$	−6.34688	+	10.9931i	−0.302920	+	0.524673i	0.673876	+	0.738844i	$0.264628\pi$
$440$		−	0.697999i		−	0.0332758i
$441$	−9.08541	+	16.9707i	−0.432639	+	0.808127i
$442$	−2.09200	−	2.07860i	−0.0995062	−	0.0988690i
$443$	15.7797	−	27.3312i	0.749715	−	1.29854i	−0.198244	−	0.980153i	$-0.563524\pi$
$443$	15.7797	−	27.3312i	0.749715	−	1.29854i	0.947959	−	0.318392i	$-0.103143\pi$
$444$	−0.0111033	−	0.692486i	−0.000526941	−	0.0328639i
$445$	6.14757	+	10.6479i	0.291423	+	0.504759i
$446$	4.53160	+	7.84896i	0.214577	+	0.371659i
$447$	−0.424558	−	26.4786i	−0.0200809	−	1.25240i
$448$	−2.80601	−	1.62005i	−0.132571	−	0.0765401i
$449$		−	9.40266i		−	0.443739i	−0.975076	−	0.221869i	$-0.928784\pi$
$449$		−	9.40266i		−	0.443739i	0.975076	−	0.221869i	$-0.0712159\pi$
$450$	1.08463	+	0.580666i	0.0511298	+	0.0273728i
$451$	−0.498418			−0.0234696
$452$	10.8571	−	18.8050i	0.510673	−	0.884512i
$453$	11.8288	−	7.08458i	0.555763	−	0.332863i
$454$	−3.71515	−	6.43483i	−0.174361	−	0.302001i
$455$	−2.66251	−	0.704258i	−0.124820	−	0.0330161i
$456$	4.74323	−	8.52842i	0.222122	−	0.399380i
$457$	−20.8562	−	12.0413i	−0.975612	−	0.563270i	−0.0746694	−	0.997208i	$-0.523790\pi$
$457$	−20.8562	−	12.0413i	−0.975612	−	0.563270i	−0.900942	+	0.433939i	$0.857123\pi$
$458$	−11.1703			−0.521955
$459$	10.3517	−	0.498278i	0.483175	−	0.0232576i
$460$			2.94294i			0.137215i
$461$	29.3557	+	16.9485i	1.36723	+	0.789370i	0.990573	−	0.136983i	$-0.0437405\pi$
$461$	29.3557	+	16.9485i	1.36723	+	0.789370i	0.376656	+	0.926353i	$0.377074\pi$
$462$	0.210616	+	0.117138i	0.00979873	+	0.00544974i
$463$	27.8998	−	16.1079i	1.29661	−	0.748599i	0.316795	−	0.948494i	$-0.397393\pi$
$463$	27.8998	−	16.1079i	1.29661	−	0.748599i	0.979817	+	0.199895i	$0.0640600\pi$
$464$	0.900287	+	1.55934i	0.0417948	+	0.0723907i
$465$	−7.13767	−	11.9174i	−0.331001	−	0.552656i
$466$	2.55436	+	1.47476i	0.118328	+	0.0683169i
$467$	22.9157			1.06041			0.530206	−	0.847869i	$-0.322115\pi$
$467$	22.9157			1.06041			0.530206	+	0.847869i	$0.322115\pi$
$468$	13.5079	−	14.4962i	0.624402	−	0.670087i
$469$	10.5935			0.489163
$470$	1.45825	+	0.841918i	0.0672638	+	0.0388348i
$471$	24.0622	−	0.385813i	1.10873	−	0.0177773i
$472$	3.19862	+	5.54017i	0.147228	+	0.255007i
$473$	−0.317561	+	0.183344i	−0.0146015	+	0.00843015i
$474$	0.110918	+	6.91770i	0.00509465	+	0.317741i
$475$	−3.10508	−	1.79272i	−0.142471	−	0.0822557i
$476$		−	2.79074i		−	0.127913i
$477$	−8.04788	−	12.9611i	−0.368487	−	0.593448i
$478$	9.74254			0.445613
$479$	−24.2251	−	13.9864i	−1.10687	−	0.639053i	−0.168855	−	0.985641i	$-0.554007\pi$
$479$	−24.2251	−	13.9864i	−1.10687	−	0.639053i	−0.938018	+	0.346587i	$0.887340\pi$
$480$	3.89890	+	6.50979i	0.177960	+	0.297130i
$481$	0.201257	−	0.760869i	0.00917652	−	0.0346926i
$482$	−1.79070	−	3.10159i	−0.0815644	−	0.141274i
$483$	−1.85755	−	1.03311i	−0.0845213	−	0.0470080i
$484$	−9.89432	+	17.1375i	−0.449742	+	0.778975i
$485$	14.2659			0.647781
$486$	−0.511912	−	6.37220i	−0.0232208	−	0.289049i
$487$		−	17.7388i		−	0.803820i	−0.915679	−	0.401910i	$-0.868347\pi$
$487$		−	17.7388i		−	0.803820i	0.915679	−	0.401910i	$-0.131653\pi$
$488$	5.12596	+	2.95947i	0.232041	+	0.133969i
$489$	−18.7882	−	10.4494i	−0.849630	−	0.472537i
$490$	−1.31569	−	2.27884i	−0.0594369	−	0.102948i
$491$	11.1026	+	19.2302i	0.501052	+	0.867847i	0.999999	+	0.00121505i	$0.000386762\pi$
$491$	11.1026	+	19.2302i	0.501052	+	0.867847i	−0.498947	+	0.866632i	$0.666280\pi$
$492$	3.05427	−	1.82929i	0.137697	−	0.0824708i
$493$	−0.594726	+	1.03010i	−0.0267851	+	0.0463932i
$494$	3.73665	−	3.76074i	0.168120	−	0.169204i
$495$	0.702937	+	1.13208i	0.0315947	+	0.0508832i
$496$		−	24.2148i		−	1.08727i
$497$	−4.64208	+	8.04031i	−0.208226	+	0.360657i
$498$	11.0110	−	0.176551i	0.493416	−	0.00791143i
$499$	−1.82679	+	1.05470i	−0.0817782	+	0.0472147i	−0.540331	−	0.841452i	$-0.681701\pi$
$499$	−1.82679	+	1.05470i	−0.0817782	+	0.0472147i	0.458553	+	0.888667i	$0.348368\pi$
$500$	1.58641	−	0.915912i	0.0709462	−	0.0409608i
$501$	−0.0274252	−	1.71044i	−0.00122527	−	0.0764168i
$502$	0.842579	+	0.486463i	0.0376062	+	0.0217119i
$503$	27.2835			1.21651			0.608256	−	0.793741i	$-0.291869\pi$
$503$	27.2835			1.21651			0.608256	+	0.793741i	$0.291869\pi$
$504$	−3.59907	+	0.115445i	−0.160315	+	0.00514232i
$505$			4.34702i			0.193440i
$506$	0.146325	−	0.253442i	0.00650492	−	0.0112669i
$507$	19.2423	−	11.6934i	0.854580	−	0.519321i
$508$	−6.54865	−	11.3426i	−0.290550	−	0.503247i
$509$	1.10835	−	0.639905i	0.0491267	−	0.0283633i	−0.475236	−	0.879859i	$-0.657637\pi$
$509$	1.10835	−	0.639905i	0.0491267	−	0.0283633i	0.524362	+	0.851495i	$0.324304\pi$
$510$	−0.688584	+	1.23809i	−0.0304910	+	0.0548234i
$511$	−1.45510	+	2.52031i	−0.0643700	+	0.111492i
$512$			22.7160i			1.00391i
$513$	0.895743	+	18.6090i	0.0395480	+	0.821606i
$514$		−	0.798676i		−	0.0352281i
$515$	5.90676	+	3.41027i	0.260283	+	0.150274i
$516$	1.27308	−	2.28903i	0.0560443	−	0.100769i
$517$	0.911913	+	1.57948i	0.0401059	+	0.0694654i
$518$	−0.0592162	+	0.0341885i	−0.00260181	+	0.00150216i
$519$	21.1254	+	35.2720i	0.927303	+	1.54827i
$520$	1.48398	+	5.46799i	0.0650770	+	0.239787i
$521$	−8.57816			−0.375816			−0.187908	−	0.982187i	$-0.560171\pi$
$521$	−8.57816			−0.375816			−0.187908	+	0.982187i	$0.560171\pi$
$522$	0.646840	+	0.346292i	0.0283114	+	0.0151568i
$523$	−3.25874			−0.142495			−0.0712473	−	0.997459i	$-0.522698\pi$
$523$	−3.25874			−0.142495			−0.0712473	+	0.997459i	$0.522698\pi$
$524$	5.42859	−	9.40260i	0.237149	−	0.410754i
$525$	0.0212105	+	1.32285i	0.000925702	+	0.0577337i
$526$	3.66649	−	2.11685i	0.159866	−	0.0922989i
$527$	13.8531	−	7.99808i	0.603450	−	0.348402i
$528$	0.0372399	+	2.32256i	0.00162066	+	0.101076i
$529$	10.2095	−	17.6833i	0.443890	−	0.768840i
$530$	2.08552			0.0905892
$531$	−10.7672	−	5.76431i	−0.467256	−	0.250150i
$532$	5.01684			0.217508
$533$	3.90451	−	1.05967i	0.169123	−	0.0458992i
$534$	4.48733	+	7.49226i	0.194186	+	0.324222i
$535$	−11.4844	+	6.63050i	−0.496512	+	0.286661i
$536$	−10.8967	−	18.8736i	−0.470665	−	0.815215i
$537$	−12.1783	+	21.8969i	−0.525534	+	0.944921i
$538$	10.6523	+	6.15013i	0.459255	+	0.265151i
$539$		−	2.85015i		−	0.122765i
$540$	−8.46249	−	4.35738i	−0.364168	−	0.187512i
$541$			4.56408i			0.196225i	0.995175	+	0.0981126i	$0.0312805\pi$
$541$			4.56408i			0.196225i	−0.995175	+	0.0981126i	$0.968719\pi$
$542$	1.99207	−	3.45037i	0.0855667	−	0.148206i
$543$	10.7487	−	19.3264i	0.461272	−	0.829376i
$544$	−7.56715	+	4.36890i	−0.324439	+	0.187315i
$545$	2.52333	+	4.37053i	0.108088	+	0.187213i
$546$	−1.89896	−	0.469853i	−0.0812682	−	0.0201079i
$547$	−19.2674	+	33.3721i	−0.823814	+	1.42689i	0.0790092	+	0.996874i	$0.474824\pi$
$547$	−19.2674	+	33.3721i	−0.823814	+	1.42689i	−0.902823	+	0.430013i	$0.858509\pi$
$548$		−	16.6941i		−	0.713135i
$549$	−11.2942	+	0.362274i	−0.482023	+	0.0154615i
$550$	−0.182158			−0.00776726
$551$	−1.85178	−	1.06913i	−0.0788885	−	0.0455463i
$552$	0.0701025	+	4.37211i	0.00298376	+	0.186090i
$553$	−6.44331	+	3.72005i	−0.273997	+	0.158192i
$554$	1.25321	−	0.723542i	0.0532439	−	0.0307404i
$555$	−0.378031	+	0.00606135i	−0.0160465	+	0.000257290i
$556$	−17.0439	+	29.5209i	−0.722822	+	1.25196i
$557$			30.0258i			1.27223i	0.771593	+	0.636117i	$0.219460\pi$
$557$			30.0258i			1.27223i	−0.771593	+	0.636117i	$0.780540\pi$
$558$	−5.20496	−	8.38259i	−0.220344	−	0.354863i
$559$	2.09791	−	2.11143i	0.0887322	−	0.0893040i
$560$	−1.15311	+	1.99724i	−0.0487276	+	0.0843988i
$561$	−1.31642	+	0.788440i	−0.0555792	+	0.0332880i
$562$	−2.43071	−	4.21012i	−0.102534	−	0.177593i
$563$	−18.2775	−	31.6575i	−0.770303	−	1.33420i	−0.937397	−	0.348263i	$-0.886772\pi$
$563$	−18.2775	−	31.6575i	−0.770303	−	1.33420i	0.167094	−	0.985941i	$-0.446562\pi$
$564$	−11.3851	−	6.33204i	−0.479400	−	0.266627i
$565$	−10.2657	−	5.92692i	−0.431882	−	0.249347i
$566$			2.24077i			0.0941866i
$567$	5.72105	−	3.81177i	0.240261	−	0.160079i
$568$	19.0997			0.801405
$569$	−17.1303	+	29.6706i	−0.718141	+	1.24386i	0.243594	+	0.969877i	$0.421673\pi$
$569$	−17.1303	+	29.6706i	−0.718141	+	1.24386i	−0.961736	+	0.273980i	$0.911660\pi$
$570$	−2.22568	−	1.23785i	−0.0932235	−	0.0518479i
$571$	−6.12399	−	10.6071i	−0.256281	−	0.443892i	0.708962	−	0.705247i	$-0.249164\pi$
$571$	−6.12399	−	10.6071i	−0.256281	−	0.443892i	−0.965243	+	0.261355i	$0.915831\pi$
$572$	−0.750201	+	2.83620i	−0.0313675	+	0.118587i
$573$	−6.99388	−	11.6773i	−0.292174	−	0.487827i
$574$	−0.304400	−	0.175746i	−0.0127054	−	0.00733548i
$575$	1.60656			0.0669984
$576$	−6.71280	−	10.8110i	−0.279700	−	0.450457i
$577$			15.7757i			0.656752i	0.944547	+	0.328376i	$0.106501\pi$
$577$			15.7757i			0.656752i	−0.944547	+	0.328376i	$0.893499\pi$
$578$	4.62479	+	2.67012i	0.192366	+	0.111063i
$579$	0.0373138	+	2.32716i	0.00155071	+	0.0967136i
$580$	0.946085	−	0.546222i	0.0392840	−	0.0226807i
$581$	5.92126	+	10.2559i	0.245655	+	0.425488i
$582$	10.1318	−	0.162453i	0.419976	−	0.00673390i
$583$	1.95627	+	1.12945i	0.0810204	+	0.0467771i
$584$	5.98698			0.247743
$585$	−7.91353	−	7.37401i	−0.327184	−	0.304878i
$586$	4.52192			0.186799
$587$	−22.9033	−	13.2232i	−0.945319	−	0.545780i	−0.0536950	−	0.998557i	$-0.517100\pi$
$587$	−22.9033	−	13.2232i	−0.945319	−	0.545780i	−0.891624	+	0.452777i	$0.850433\pi$
$588$	10.4606	+	17.4655i	0.431387	+	0.720265i
$589$	14.3780	+	24.9034i	0.592434	+	1.02613i
$590$	1.44583	−	0.834751i	0.0595240	−	0.0343662i
$591$	20.8055	+	11.5714i	0.855825	+	0.475982i
$592$	−0.570754	−	0.329525i	−0.0234578	−	0.0135434i
$593$			25.5965i			1.05112i	0.850755	+	0.525562i	$0.176145\pi$
$593$			25.5965i			1.05112i	−0.850755	+	0.525562i	$0.823855\pi$
$594$	0.512125	+	0.796011i	0.0210128	+	0.0326607i
$595$	−1.52347			−0.0624564
$596$	−24.2552	−	14.0037i	−0.993532	−	0.573616i
$597$	11.9914	−	21.5607i	0.490774	−	0.882421i
$598$	−0.607448	+	2.29651i	−0.0248404	+	0.0939112i
$599$	11.9132	+	20.6343i	0.486760	+	0.843094i	0.999884	−	0.0152210i	$-0.00484518\pi$
$599$	11.9132	+	20.6343i	0.486760	+	0.843094i	−0.513124	+	0.858315i	$0.671512\pi$
$600$	2.33499	−	1.39849i	0.0953255	−	0.0570932i
$601$	17.8735	−	30.9578i	0.729075	−	1.26279i	−0.228200	−	0.973614i	$-0.573284\pi$
$601$	17.8735	−	30.9578i	0.729075	−	1.26279i	0.957275	−	0.289180i	$-0.0933827\pi$
$602$	−0.258593			−0.0105395
$603$	36.6803	+	19.6372i	1.49374	+	0.799687i
$604$		−	14.5823i		−	0.593346i
$605$	9.35541	+	5.40135i	0.380352	+	0.219596i
$606$	0.0495018	+	3.08730i	0.00201087	+	0.125413i
$607$	−0.271769	−	0.470717i	−0.0110307	−	0.0191058i	0.860457	−	0.509522i	$-0.170178\pi$
$607$	−0.271769	−	0.470717i	−0.0110307	−	0.0191058i	−0.871488	+	0.490417i	$0.836845\pi$
$608$	−7.85387	−	13.6033i	−0.318516	−	0.551687i
$609$	0.0126493	+	0.788905i	0.000512576	+	0.0319681i
$610$	0.772341	−	1.33773i	0.0312712	−	0.0541632i
$611$	−10.5018	−	10.4346i	−0.424858	−	0.422137i
$612$	5.17319	−	9.66301i	0.209114	−	0.390604i
$613$		−	13.0014i		−	0.525121i	−0.964915	−	0.262561i	$-0.915433\pi$
$613$		−	13.0014i		−	0.525121i	0.964915	−	0.262561i	$-0.0845670\pi$
$614$	1.19697	−	2.07322i	0.0483059	−	0.0836683i
$615$	−0.998617	−	1.66734i	−0.0402681	−	0.0672336i
$616$	0.461731	−	0.266581i	0.0186037	−	0.0107408i
$617$	26.3363	−	15.2053i	1.06026	−	0.612140i	0.134755	−	0.990879i	$-0.456975\pi$
$617$	26.3363	−	15.2053i	1.06026	−	0.612140i	0.925504	+	0.378739i	$0.123642\pi$
$618$	4.23388	+	2.35475i	0.170312	+	0.0947219i
$619$	−12.0117	−	6.93494i	−0.482790	−	0.278739i	0.238789	−	0.971072i	$-0.423250\pi$
$619$	−12.0117	−	6.93494i	−0.482790	−	0.278739i	−0.721578	+	0.692333i	$0.756583\pi$
$620$	−14.6916			−0.590028
$621$	−4.51674	−	7.02050i	−0.181251	−	0.281723i
$622$			5.26543i			0.211124i
$623$	−4.69578	+	8.13333i	−0.188132	+	0.325855i
$624$	−5.22962	−	18.1153i	−0.209352	−	0.725192i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−0.0675416	+	0.0389952i	−0.00269951	+	0.00155856i
$627$	−1.41736	−	2.36649i	−0.0566040	−	0.0945087i
$628$	12.7258	−	22.0417i	0.507814	−	0.879559i
$629$		−	0.435365i		−	0.0173592i
$630$	0.0301279	+	0.939258i	0.00120032	+	0.0374209i
$631$		−	39.4067i		−	1.56875i	−0.620284	−	0.784377i	$-0.712983\pi$
$631$		−	39.4067i		−	1.56875i	0.620284	−	0.784377i	$-0.287017\pi$
$632$	13.2554	+	7.65301i	0.527272	+	0.304421i
$633$	−8.19267	+	0.131361i	−0.325629	+	0.00522114i
$634$	1.81400	+	3.14194i	0.0720432	+	0.124782i
$635$	−6.19197	+	3.57494i	−0.245721	+	0.141867i
$636$	−16.1332	+	0.258679i	−0.639722	+	0.0102573i
$637$	6.05958	+	22.3275i	0.240089	+	0.884648i
$638$	−0.108634			−0.00430085
$639$	−30.9776	+	19.2348i	−1.22546	+	0.760917i
$640$	10.5015			0.415108
$641$	7.56874	−	13.1094i	0.298947	−	0.517792i	−0.676948	−	0.736031i	$-0.736698\pi$
$641$	7.56874	−	13.1094i	0.298947	−	0.517792i	0.975895	+	0.218239i	$0.0700312\pi$
$642$	−8.08082	+	4.83983i	−0.318924	+	0.191013i
$643$	10.8835	−	6.28358i	0.429203	−	0.247800i	−0.269804	−	0.962915i	$-0.586959\pi$
$643$	10.8835	−	6.28358i	0.429203	−	0.247800i	0.699007	+	0.715115i	$0.253626\pi$
$644$	−1.94678	+	1.12397i	−0.0767138	+	0.0442908i
$645$	−1.24959	−	0.694981i	−0.0492025	−	0.0273648i
$646$	1.46631	−	2.53973i	0.0576913	−	0.0999243i
$647$	23.0846			0.907549			0.453774	−	0.891117i	$-0.350077\pi$
$647$	23.0846			0.907549			0.453774	+	0.891117i	$0.350077\pi$
$648$	−12.6759	−	6.27186i	−0.497956	−	0.246382i
$649$	1.80830			0.0709820
$650$	1.42699	−	0.387279i	0.0559713	−	0.0151903i
$651$	5.15742	−	9.27313i	0.202135	−	0.363443i
$652$	−19.6907	+	11.3684i	−0.771147	+	0.445222i
$653$	14.0585	+	24.3500i	0.550151	+	0.952889i	0.998263	+	0.0589116i	$0.0187630\pi$
$653$	14.0585	+	24.3500i	0.550151	+	0.952889i	−0.448113	+	0.893977i	$0.647904\pi$
$654$	1.84187	+	3.07527i	0.0720227	+	0.120252i
$655$	−5.13292	−	2.96349i	−0.200560	−	0.115793i
$656$		−	3.38784i		−	0.132273i
$657$	−9.71024	+	6.02934i	−0.378833	+	0.235227i
$658$			1.28619i			0.0501408i
$659$	−16.0785	+	27.8487i	−0.626328	+	1.08483i	0.361954	+	0.932196i	$0.382110\pi$
$659$	−16.0785	+	27.8487i	−0.626328	+	1.08483i	−0.988282	+	0.152637i	$0.951224\pi$
$660$	1.40914	−	0.0225942i	0.0548508	−	0.000879477i
$661$	37.1818	−	21.4669i	1.44621	−	0.834967i	0.447953	−	0.894057i	$-0.352153\pi$
$661$	37.1818	−	21.4669i	1.44621	−	0.834967i	0.998253	+	0.0590895i	$0.0188197\pi$
$662$	1.37628	+	2.38379i	0.0534908	+	0.0926487i
$663$	8.63630	−	8.97527i	0.335406	−	0.348571i
$664$	12.1814	−	21.0989i	0.472731	−	0.818795i
$665$		−	2.73872i		−	0.106203i
$666$	−0.268413	+	0.00860969i	−0.0104008	+	0.000333619i
$667$	0.958107			0.0370981
$668$	−1.56681	−	0.904600i	−0.0606218	−	0.0350000i
$669$	−32.8394	+	19.6684i	−1.26964	+	0.760426i
$670$	−4.92549	+	2.84373i	−0.190288	+	0.109863i
$671$	1.44895	−	0.836551i	0.0559360	−	0.0322947i
$672$	−2.81720	+	5.06538i	−0.108676	+	0.195401i
$673$	3.65511	−	6.33084i	0.140894	−	0.244036i	−0.786939	−	0.617030i	$-0.788336\pi$
$673$	3.65511	−	6.33084i	0.140894	−	0.244036i	0.927834	+	0.372994i	$0.121669\pi$
$674$		−	3.11325i		−	0.119918i
$675$	−2.37871	+	4.61971i	−0.0915568	+	0.177813i
$676$	−0.152986	−	23.8132i	−0.00588406	−	0.915893i
$677$	−17.2093	+	29.8074i	−0.661407	+	1.14559i	0.318839	+	0.947809i	$0.396707\pi$
$677$	−17.2093	+	29.8074i	−0.661407	+	1.14559i	−0.980246	+	0.197782i	$0.936626\pi$
$678$	−7.35833	−	4.09246i	−0.282595	−	0.157170i
$679$	5.44845	+	9.43699i	0.209092	+	0.362159i
$680$	1.56707	+	2.71425i	0.0600945	+	0.104087i
$681$	26.9228	−	16.1248i	1.03168	−	0.617904i
$682$	1.26522	+	0.730473i	0.0484476	+	0.0279713i
$683$		−	29.3368i		−	1.12254i	−0.827632	−	0.561272i	$-0.810312\pi$
$683$		−	29.3368i		−	1.12254i	0.827632	−	0.561272i	$-0.189688\pi$
$684$	17.3710	+	9.29972i	0.664196	+	0.355584i
$685$	−9.11336			−0.348204
$686$	2.10135	−	3.63964i	0.0802298	−	0.138962i
$687$	−0.756362	−	47.1724i	−0.0288570	−	1.79974i
$688$	−1.24622	−	2.15852i	−0.0475117	−	0.0822927i
$689$	−17.7263	−	4.68878i	−0.675319	−	0.178628i
$690$	1.14100	−	0.0182948i	0.0434372	−	0.000696472i
$691$	−19.4151	−	11.2093i	−0.738585	−	0.426422i	0.0829697	−	0.996552i	$-0.473560\pi$
$691$	−19.4151	−	11.2093i	−0.738585	−	0.426422i	−0.821555	+	0.570130i	$0.806893\pi$
$692$	43.4828			1.65297
$693$	−0.480412	+	0.897363i	−0.0182493	+	0.0340880i
$694$			7.08791i			0.269054i
$695$	16.1156	+	9.30433i	0.611298	+	0.352933i
$696$	1.39252	−	0.834019i	0.0527832	−	0.0316134i
$697$	1.93816	−	1.11900i	0.0734130	−	0.0423850i
$698$	−2.47384	−	4.28481i	−0.0936361	−	0.162182i
$699$	−6.05496	+	10.8869i	−0.229020	+	0.411782i
$700$	1.21177	+	0.699613i	0.0458004	+	0.0264429i
$701$	−44.3730			−1.67595			−0.837973	−	0.545711i	$-0.816260\pi$
$701$	−44.3730			−1.67595			−0.837973	+	0.545711i	$0.816260\pi$
$702$	−5.70426	−	5.14699i	−0.215293	−	0.194261i
$703$	0.782646			0.0295181
$704$	1.63174	+	0.942085i	0.0614985	+	0.0355062i
$705$	−3.45669	+	6.21519i	−0.130186	+	0.234078i
$706$	−2.49143	−	4.31528i	−0.0937662	−	0.162408i
$707$	−2.87558	+	1.66022i	−0.108147	+	0.0624390i
$708$	−11.0811	+	6.63681i	−0.416454	+	0.249427i
$709$	−12.0856	−	6.97761i	−0.453883	−	0.262050i	0.255585	−	0.966786i	$-0.417732\pi$
$709$	−12.0856	−	6.97761i	−0.453883	−	0.262050i	−0.709469	+	0.704737i	$0.751065\pi$
$710$		−	4.98449i		−	0.187065i
$711$	−29.2060	+	0.936819i	−1.09531	+	0.0351335i
$712$	19.3207			0.724072
$713$	−11.1587	−	6.44248i	−0.417897	−	0.241273i
$714$	−1.08199	+	0.0173486i	−0.0404924	+	0.000649256i
$715$	1.54829	+	0.409538i	0.0579029	+	0.0153159i
$716$	13.2495	+	22.9488i	0.495156	+	0.857636i
$717$	0.659684	+	41.1428i	0.0246363	+	1.53651i
$718$	0.0527634	−	0.0913890i	0.00196911	−	0.00341061i
$719$	37.5186			1.39921			0.699604	−	0.714530i	$-0.253360\pi$
$719$	37.5186			1.39921			0.699604	+	0.714530i	$0.253360\pi$
$720$	−7.69495	+	4.77799i	−0.286774	+	0.178065i
$721$			5.20982i			0.194024i
$722$	−2.18226	−	1.25993i	−0.0812154	−	0.0468897i
$723$	12.9768	−	7.77218i	0.482612	−	0.289050i
$724$	−11.6941	−	20.2548i	−0.434608	−	0.752764i
$725$	−0.298185	−	0.516472i	−0.0110743	−	0.0191813i
$726$	6.70583	+	3.72956i	0.248877	+	0.138417i
$727$	13.2056	−	22.8728i	0.489768	−	0.848303i	−0.510162	−	0.860078i	$-0.670415\pi$
$727$	13.2056	−	22.8728i	0.489768	−	0.848303i	0.999931	+	0.0117747i	$0.00374808\pi$
$728$	−3.05035	+	3.07001i	−0.113054	+	0.113782i
$729$	26.8752	−	2.59328i	0.995377	−	0.0960475i
$730$		−	1.56244i		−	0.0578284i
$731$	0.823248	−	1.42591i	0.0304489	−	0.0527391i
$732$	−5.80875	+	10.4442i	−0.214698	+	0.386030i
$733$	2.11871	−	1.22324i	0.0782565	−	0.0451814i	−0.460361	−	0.887732i	$-0.652280\pi$
$733$	2.11871	−	1.22324i	0.0782565	−	0.0451814i	0.538618	+	0.842550i	$0.318947\pi$
$734$	5.23944	−	3.02499i	0.193391	−	0.111654i
$735$	9.53449	−	5.71048i	0.351685	−	0.210634i
$736$	6.09537	+	3.51916i	0.224678	+	0.129718i
$737$	−6.16030			−0.226918
$738$	−0.728216	−	1.17279i	−0.0268060	−	0.0431711i
$739$			43.2972i			1.59271i	0.604828	+	0.796356i	$0.293242\pi$
$739$			43.2972i			1.59271i	−0.604828	+	0.796356i	$0.706758\pi$
$740$	−0.199929	+	0.346288i	−0.00734955	+	0.0127298i
$741$	16.1346	+	15.5253i	0.592721	+	0.570335i
$742$	0.796505	+	1.37959i	0.0292406	+	0.0506463i
$743$	8.86986	−	5.12101i	0.325403	−	0.187872i	−0.328395	−	0.944540i	$-0.606508\pi$
$743$	8.86986	−	5.12101i	0.325403	−	0.187872i	0.653799	+	0.756669i	$0.273174\pi$
$744$	−21.8262	+	0.349961i	−0.800187	+	0.0128302i
$745$	−7.64470	+	13.2410i	−0.280080	+	0.485113i
$746$		−	10.8085i		−	0.395729i
$747$	1.49115	+	46.4877i	0.0545584	+	1.70090i
$748$			1.62286i			0.0593376i
$749$	−8.77225	−	5.06466i	−0.320531	−	0.185059i
$750$	−0.364968	−	0.609367i	−0.0133267	−	0.0222510i
$751$	−0.679184	−	1.17638i	−0.0247838	−	0.0429267i	0.853368	−	0.521310i	$-0.174556\pi$
$751$	−0.679184	−	1.17638i	−0.0247838	−	0.0429267i	−0.878151	+	0.478383i	$0.841223\pi$
$752$	−10.7360	+	6.19844i	−0.391502	+	0.226034i
$753$	−1.99729	+	3.59116i	−0.0727852	+	0.130869i
$754$	0.851017	−	0.230962i	0.0309922	−	0.00841113i
$755$	−7.96054			−0.289714
$756$	−0.349565	−	7.26218i	−0.0127136	−	0.264123i
$757$	−7.30237			−0.265409			−0.132705	−	0.991156i	$-0.542366\pi$
$757$	−7.30237			−0.265409			−0.132705	+	0.991156i	$0.542366\pi$
$758$	−4.18896	+	7.25549i	−0.152150	+	0.263531i
$759$	1.08019	+	0.600769i	0.0392086	+	0.0218065i
$760$	−4.87935	+	2.81709i	−0.176993	+	0.102187i
$761$	27.6772	−	15.9794i	1.00330	−	0.579254i	0.0940752	−	0.995565i	$-0.470011\pi$
$761$	27.6772	−	15.9794i	1.00330	−	0.579254i	0.909222	+	0.416311i	$0.136677\pi$
$762$	−4.35690	+	2.60947i	−0.157834	+	0.0945312i
$763$	−1.92743	+	3.33840i	−0.0697775	+	0.120858i
$764$	−14.3956			−0.520815
$765$	−5.27508	−	2.82406i	−0.190721	−	0.102104i
$766$	−15.4724			−0.559039
$767$	−14.1659	+	3.84455i	−0.511500	+	0.138819i
$768$	−7.23398	+	0.115990i	−0.261034	+	0.00418542i
$769$	−10.1273	+	5.84703i	−0.365202	+	0.210849i	−0.671360	−	0.741131i	$-0.734290\pi$
$769$	−10.1273	+	5.84703i	−0.365202	+	0.210849i	0.306159	+	0.951981i	$0.400956\pi$
$770$	−0.0695702	−	0.120499i	−0.00250714	−	0.00434249i
$771$	3.37282	−	0.0540797i	0.121469	−	0.00194763i
$772$	2.13175	+	1.23077i	0.0767234	+	0.0442963i
$773$			30.4439i			1.09499i	0.836809	+	0.547495i	$0.184418\pi$
$773$			30.4439i			1.09499i	−0.836809	+	0.547495i	$0.815582\pi$
$774$	−0.895386	−	0.479354i	−0.0321840	−	0.0172300i
$775$			8.02020i			0.288094i
$776$	11.2087	−	19.4141i	0.402371	−	0.696926i
$777$	−0.148388	−	0.247756i	−0.00532339	−	0.00888818i
$778$	11.5817	−	6.68670i	0.415224	−	0.239730i
$779$	2.01159	+	3.48418i	0.0720728	+	0.124834i
$780$	−10.9909	+	3.17291i	−0.393538	+	0.113609i
$781$	2.69944	−	4.67557i	0.0965937	−	0.167305i
$782$			1.31405i			0.0469904i
$783$	−1.41859	+	2.75506i	−0.0506964	+	0.0984577i
$784$	19.3730			0.691892
$785$	−12.0326	−	6.94705i	−0.429464	−	0.247951i
$786$	−3.67920	−	2.04625i	−0.131233	−	0.0729875i
$787$	−23.0594	+	13.3134i	−0.821979	+	0.474570i	−0.851099	−	0.525006i	$-0.824063\pi$
$787$	−23.0594	+	13.3134i	−0.821979	+	0.474570i	0.0291191	+	0.999576i	$0.490730\pi$
$788$	21.8050	−	12.5891i	0.776770	−	0.448468i
$789$	9.18773	+	15.3403i	0.327092	+	0.546128i
$790$	1.99722	−	3.45930i	0.0710581	−	0.123076i
$791$		−	9.05447i		−	0.321940i
$792$	2.09292	−	0.0671330i	0.0743687	−	0.00238547i
$793$	−9.57223	+	9.63393i	−0.339920	+	0.342111i
$794$	−3.91031	+	6.77286i	−0.138772	+	0.240360i
$795$	0.141214	+	8.80717i	0.00500835	+	0.312358i
$796$	−13.0461	−	22.5964i	−0.462405	−	0.800909i
$797$	−12.0971	−	20.9528i	−0.428501	−	0.742186i	0.568239	−	0.822864i	$-0.307625\pi$
$797$	−12.0971	−	20.9528i	−0.428501	−	0.742186i	−0.996740	+	0.0806776i	$0.974292\pi$
$798$	−0.0311872	−	1.94507i	−0.00110402	−	0.0688546i
$799$	−7.09216	−	4.09466i	−0.250903	−	0.144859i
$800$		−	4.38098i		−	0.154891i
$801$	−31.3360	+	19.4573i	−1.10720	+	0.687491i
$802$	10.1406			0.358077
$803$	0.846167	−	1.46560i	0.0298606	−	0.0517200i
$804$	37.7499	−	22.6095i	1.33134	−	0.797375i
$805$	0.613582	+	1.06275i	0.0216259	+	0.0374572i
$806$	−11.4645	−	3.03246i	−0.403819	−	0.106814i
$807$	−25.2508	+	45.4013i	−0.888869	+	1.59820i
$808$	5.91575	+	3.41546i	0.208116	+	0.120156i
$809$	19.8529			0.697990			0.348995	−	0.937125i	$-0.386523\pi$
$809$	19.8529			0.697990			0.348995	+	0.937125i	$0.386523\pi$
$810$	−1.63678	+	3.30806i	−0.0575107	+	0.116233i
$811$			54.3008i			1.90676i	0.301772	+	0.953380i	$0.402422\pi$
$811$			54.3008i			1.90676i	−0.301772	+	0.953380i	$0.597578\pi$
$812$	0.722661	+	0.417228i	0.0253604	+	0.0146418i
$813$	14.7058	+	8.17890i	0.515755	+	0.286846i
$814$	0.0344352	−	0.0198812i	0.00120695	−	0.000696835i
$815$	6.20607	+	10.7492i	0.217389	+	0.376529i
$816$	−5.35917	−	8.94793i	−0.187609	−	0.313240i
$817$	2.56332	+	1.47993i	0.0896793	+	0.0517764i
$818$	−2.35640			−0.0823897
$819$	1.85561	−	8.05116i	0.0648403	−	0.281330i
$820$	−2.05547			−0.0717801
$821$	46.2258	+	26.6885i	1.61329	+	0.931433i	0.988601	+	0.150560i	$0.0481076\pi$
$821$	46.2258	+	26.6885i	1.61329	+	0.931433i	0.624689	+	0.780874i	$0.285226\pi$
$822$	−6.47241	+	0.103779i	−0.225751	+	0.00361970i
$823$	−22.5541	−	39.0649i	−0.786187	−	1.36172i	−0.928287	−	0.371864i	$-0.878719\pi$
$823$	−22.5541	−	39.0649i	−0.786187	−	1.36172i	0.142100	−	0.989852i	$-0.454615\pi$
$824$	9.28192	−	5.35892i	0.323351	−	0.186687i
$825$	−0.0123343	−	0.769256i	−0.000429424	−	0.0267821i
$826$	1.10439	+	0.637619i	0.0384266	+	0.0221856i
$827$		−	18.3981i		−	0.639763i	−0.947458	−	0.319882i	$-0.896357\pi$
$827$		−	18.3981i		−	0.639763i	0.947458	−	0.319882i	$-0.103643\pi$
$828$	−8.82429	+	0.283050i	−0.306665	+	0.00983667i
$829$	−36.6699			−1.27360			−0.636799	−	0.771030i	$-0.719742\pi$
$829$	−36.6699			−1.27360			−0.636799	+	0.771030i	$0.719742\pi$
$830$	−5.50622	−	3.17902i	−0.191124	−	0.110345i
$831$	3.14038	+	5.24333i	0.108939	+	0.181889i
$832$	−14.7857	−	3.91095i	−0.512601	−	0.135588i
$833$	6.39885	+	11.0831i	0.221707	+	0.384008i
$834$	11.5514	+	6.42452i	0.399993	+	0.222463i
$835$	−0.493825	+	0.855330i	−0.0170895	+	0.0295999i
$836$	−2.91738			−0.100900
$837$	35.0473	−	22.5482i	1.21141	−	0.779380i
$838$		−	3.08382i		−	0.106529i
$839$	−25.5676	−	14.7615i	−0.882692	−	0.509622i	−0.0111469	−	0.999938i	$-0.503548\pi$
$839$	−25.5676	−	14.7615i	−0.882692	−	0.509622i	−0.871545	+	0.490315i	$0.836882\pi$
$840$	1.81690	+	1.01050i	0.0626888	+	0.0348655i
$841$	14.3222	+	24.8067i	0.493868	+	0.855404i
$842$	−3.87805	−	6.71697i	−0.133646	−	0.231482i
$843$	17.6148	−	10.5500i	0.606686	−	0.363361i
$844$	−4.33286	+	7.50473i	−0.149143	+	0.258323i
$845$	−12.9997	+	0.0835155i	−0.447204	+	0.00287302i
$846$	−2.38420	+	4.45346i	−0.0819706	+	0.153113i
$847$			8.25157i			0.283527i
$848$	−7.67709	+	13.2971i	−0.263632	+	0.456625i
$849$	−9.46279	+	0.151726i	−0.324762	+	0.00520724i
$850$	0.708345	−	0.408963i	0.0242960	−	0.0140273i
$851$	−0.303705	+	0.175344i	−0.0104109	+	0.00601072i
$852$	0.618256	+	38.5591i	0.0211811	+	1.32101i
$853$	−41.1747	−	23.7722i	−1.40979	−	0.813945i	−0.414425	−	0.910083i	$-0.636017\pi$
$853$	−41.1747	−	23.7722i	−1.40979	−	0.813945i	−0.995368	+	0.0961386i	$0.969351\pi$
$854$	1.17989			0.0403752
$855$	5.07675	−	9.48289i	0.173621	−	0.324308i
$856$			20.8384i			0.712242i
$857$	19.5794	−	33.9125i	0.668820	−	1.15843i	−0.309415	−	0.950927i	$-0.600133\pi$
$857$	19.5794	−	33.9125i	0.668820	−	1.15843i	0.978234	−	0.207503i	$-0.0665336\pi$
$858$	1.10428	+	0.273227i	0.0376995	+	0.00932783i
$859$	−10.9226	−	18.9185i	−0.372675	−	0.645492i	0.617301	−	0.786727i	$-0.288226\pi$
$859$	−10.9226	−	18.9185i	−0.372675	−	0.645492i	−0.989976	+	0.141235i	$0.954893\pi$
$860$	−1.30962	+	0.756107i	−0.0446575	+	0.0257830i
$861$	0.721564	−	1.29739i	0.0245908	−	0.0442148i
$862$	−1.46072	+	2.53005i	−0.0497525	+	0.0861738i
$863$		−	23.4531i		−	0.798354i	−0.916874	−	0.399177i	$-0.869296\pi$
$863$		−	23.4531i		−	0.798354i	0.916874	−	0.399177i	$-0.130704\pi$
$864$	−19.1443	+	12.3168i	−0.651304	+	0.419026i
$865$		−	23.7374i		−	0.807097i
$866$	1.82595	+	1.05421i	0.0620484	+	0.0358237i
$867$	−10.9628	+	19.7113i	−0.372316	+	0.669432i
$868$	−5.61103	−	9.71859i	−0.190451	−	0.329871i
$869$	3.74689	−	2.16327i	0.127105	−	0.0733838i
$870$	−0.217656	−	0.363409i	−0.00737922	−	0.0123207i
$871$	48.2586	−	13.0971i	1.63518	−	0.443780i
$872$	7.93034			0.268555
$873$	1.37208	+	42.7757i	0.0464380	+	1.44774i
$874$	−2.36224			−0.0799040
$875$	0.381922	−	0.661508i	0.0129113	−	0.0223630i
$876$	0.193798	+	12.0867i	0.00654784	+	0.408372i
$877$	12.7378	−	7.35420i	0.430126	−	0.248334i	−0.269274	−	0.963064i	$-0.586784\pi$
$877$	12.7378	−	7.35420i	0.430126	−	0.248334i	0.699401	+	0.714730i	$0.253450\pi$
$878$	4.50821	−	2.60281i	0.152145	−	0.0878407i
$879$	0.306187	+	19.0961i	0.0103274	+	0.644095i
$880$	0.670551	−	1.16143i	0.0226043	−	0.0391517i
$881$	4.05323			0.136557			0.0682784	−	0.997666i	$-0.478249\pi$
$881$	4.05323			0.136557			0.0682784	+	0.997666i	$0.478249\pi$
$882$	6.70648	−	4.16422i	0.225819	−	0.140217i
$883$	−44.5006			−1.49756			−0.748782	−	0.662816i	$-0.769361\pi$
$883$	−44.5006			−1.49756			−0.748782	+	0.662816i	$0.769361\pi$
$884$	−3.45029	−	12.7132i	−0.116046	−	0.427590i
$885$	3.62306	+	6.04924i	0.121788	+	0.203343i
$886$	−11.2083	+	6.47114i	−0.376552	+	0.217402i
$887$	−16.2864	−	28.2089i	−0.546844	−	0.947162i	−0.998488	−	0.0549638i	$-0.982496\pi$
$887$	−16.2864	−	28.2089i	−0.546844	−	0.947162i	0.451644	−	0.892198i	$-0.350838\pi$
$888$	−0.288771	+	0.519216i	−0.00969053	+	0.0174238i
$889$	−4.72970	−	2.73069i	−0.158629	−	0.0915844i
$890$		−	5.04216i		−	0.169013i
$891$	−3.32688	+	2.21661i	−0.111455	+	0.0742592i
$892$			40.4839i			1.35550i
$893$	7.36088	−	12.7494i	0.246323	−	0.426643i
$894$	−5.27857	+	9.49098i	−0.176542	+	0.317426i
$895$	12.5278	−	7.23295i	0.418759	−	0.241771i
$896$	4.01075	+	6.94682i	0.133990	+	0.232077i
$897$	−9.73930	−	2.40976i	−0.325186	−	0.0804594i
$898$	−1.92798	+	3.33937i	−0.0643377	+	0.111436i
$899$			4.78301i			0.159522i
$900$	2.89890	+	4.66868i	0.0966301	+	0.155623i
$901$	−10.1429			−0.337909
$902$	0.177014	+	0.102199i	0.00589392	+	0.00340286i
$903$	−0.0175098	−	1.09204i	−0.000582689	−	0.0363408i
$904$	−16.1316	+	9.31359i	−0.536530	+	0.309765i
$905$	−11.0572	+	6.38387i	−0.367553	+	0.212207i
$906$	−5.65367	+	0.0906510i	−0.187831	+	0.00301168i
$907$	24.1319	−	41.7976i	0.801285	−	1.38787i	−0.117485	−	0.993075i	$-0.537483\pi$
$907$	24.1319	−	41.7976i	0.801285	−	1.38787i	0.918770	−	0.394792i	$-0.129183\pi$
$908$		−	33.1900i		−	1.10145i
$909$	−13.0343	+	0.418093i	−0.432322	+	0.0138673i
$910$	0.801188	+	0.796057i	0.0265591	+	0.0263890i
$911$	27.5211	−	47.6679i	0.911814	−	1.57931i	0.100313	−	0.994956i	$-0.468016\pi$
$911$	27.5211	−	47.6679i	0.911814	−	1.57931i	0.811501	−	0.584351i	$-0.198651\pi$
$912$	16.0855	−	9.63406i	0.532644	−	0.319016i
$913$	−3.44331	−	5.96399i	−0.113957	−	0.197379i
$914$	4.93807	+	8.55299i	0.163337	+	0.282908i
$915$	5.70156	+	3.17102i	0.188488	+	0.104831i
$916$	−43.2113	−	24.9480i	−1.42774	−	0.824306i
$917$		−	4.52729i		−	0.149504i
$918$	−3.77858	−	1.94561i	−0.124712	−	0.0642148i
$919$	−22.7248			−0.749623			−0.374811	−	0.927101i	$-0.622293\pi$
$919$	−22.7248			−0.749623			−0.374811	+	0.927101i	$0.622293\pi$
$920$	1.26228	−	2.18634i	0.0416162	−	0.0720814i
$921$	8.83627	+	4.91445i	0.291165	+	0.161937i
$922$	−6.95047	−	12.0386i	−0.228902	−	0.396469i
$923$	−11.2064	+	42.3667i	−0.368863	+	1.39452i
$924$	0.553128	+	0.923529i	0.0181966	+	0.0303819i
$925$	0.189040	+	0.109142i	0.00621559	+	0.00358857i
$926$	−13.2115			−0.434158
$927$	−9.65744	+	18.0392i	−0.317192	+	0.592484i
$928$		−	2.61268i		−	0.0857655i
$929$	5.89962	+	3.40614i	0.193560	+	0.111752i	0.593648	−	0.804725i	$-0.297687\pi$
$929$	5.89962	+	3.40614i	0.193560	+	0.111752i	−0.400088	+	0.916477i	$0.631020\pi$
$930$	0.0913302	+	5.69603i	0.00299484	+	0.186780i
$931$	−19.9239	+	11.5031i	−0.652980	+	0.376998i
$932$	6.58752	+	11.4099i	0.215781	+	0.373744i
$933$	−22.2359	+	0.356531i	−0.727972	+	0.0116723i
$934$	−8.13854	−	4.69879i	−0.266301	−	0.153749i
$935$	0.885926			0.0289729
$936$	−16.2528	+	4.97557i	−0.531240	+	0.162632i
$937$	−57.0664			−1.86428			−0.932140	−	0.362099i	$-0.882060\pi$
$937$	−57.0664			−1.86428			−0.932140	+	0.362099i	$0.882060\pi$
$938$	−3.76230	−	2.17216i	−0.122843	−	0.0709237i
$939$	−0.169250	−	0.282588i	−0.00552328	−	0.00922192i
$940$	3.76072	+	6.51375i	0.122661	+	0.212455i
$941$	−36.0727	+	20.8266i	−1.17594	+	0.678928i	−0.955071	−	0.296376i	$-0.904222\pi$
$941$	−36.0727	+	20.8266i	−1.17594	+	0.678928i	−0.220866	+	0.975304i	$0.570888\pi$
$942$	−8.62484	−	4.79685i	−0.281012	−	0.156290i
$943$	−1.56119	−	0.901355i	−0.0508394	−	0.0293522i
$944$			12.2913i			0.400049i
$945$	−3.96446	+	0.190829i	−0.128964	+	0.00620767i
$946$	0.150376			0.00488915
$947$	0.504502	+	0.291274i	0.0163941	+	0.00946515i	0.508175	−	0.861254i	$-0.330320\pi$
$947$	0.504502	+	0.291274i	0.0163941	+	0.00946515i	−0.491781	+	0.870719i	$0.663654\pi$
$948$	−15.0211	+	27.0082i	−0.487862	+	0.877184i
$949$	−3.51275	+	13.2803i	−0.114029	+	0.431095i
$950$	0.735183	+	1.27338i	0.0238525	+	0.0413137i
$951$	−13.1456	+	7.87329i	−0.426276	+	0.255309i
$952$	−1.19700	+	2.07326i	−0.0387949	+	0.0671948i
$953$	8.69087			0.281525			0.140763	−	0.990043i	$-0.455045\pi$
$953$	8.69087			0.281525			0.140763	+	0.990043i	$0.455045\pi$
$954$	0.200584	+	6.25335i	0.00649414	+	0.202460i
$955$			7.85863i			0.254299i
$956$	37.6880	+	21.7592i	1.21892	+	0.703742i
$957$	−0.00735579	−	0.458762i	−0.000237779	−	0.0148297i
$958$	5.73572	+	9.93456i	0.185313	+	0.320971i
$959$	−3.48059	−	6.02856i	−0.112394	−	0.194672i
$960$	0.117788	+	7.34613i	0.00380159	+	0.237095i
$961$	16.6618	−	28.8590i	0.537476	−	0.930936i
$962$	−0.227490	+	0.228956i	−0.00733458	+	0.00738185i
$963$	−20.9858	−	33.7976i	−0.676259	−	1.08911i
$964$		−	15.9976i		−	0.515248i
$965$	0.671881	−	1.16373i	0.0216286	−	0.0374618i
$966$	0.447875	+	0.747794i	0.0144101	+	0.0240599i
$967$	2.60064	−	1.50148i	0.0836311	−	0.0482844i	−0.457601	−	0.889158i	$-0.651291\pi$
$967$	2.60064	−	1.50148i	0.0836311	−	0.0482844i	0.541232	+	0.840873i	$0.317958\pi$
$968$	14.7011	−	8.48771i	0.472513	−	0.272805i
$969$	10.8246	+	6.02028i	0.347736	+	0.193399i
$970$	−5.06655	−	2.92517i	−0.162677	−	0.0939217i
$971$	−4.32102			−0.138668			−0.0693341	−	0.997593i	$-0.522087\pi$
$971$	−4.32102			−0.138668			−0.0693341	+	0.997593i	$0.522087\pi$
$972$	12.2515	−	25.7935i	0.392968	−	0.827327i
$973$			14.2141i			0.455683i
$974$	−3.63727	+	6.29994i	−0.116546	+	0.201863i
$975$	1.73211	+	5.99998i	0.0554718	+	0.192153i
$976$	5.68619	+	9.84877i	0.182010	+	0.315251i
$977$	34.0847	−	19.6788i	1.09046	−	0.629580i	0.156765	−	0.987636i	$-0.449894\pi$
$977$	34.0847	−	19.6788i	1.09046	−	0.629580i	0.933700	+	0.358056i	$0.116560\pi$
$978$	4.53003	+	7.56356i	0.144854	+	0.241856i
$979$	2.73067	−	4.72967i	0.0872727	−	0.151161i
$980$		−	11.7540i		−	0.375467i
$981$	−12.8622	+	7.98645i	−0.410657	+	0.254988i
$982$		−	9.10618i		−	0.290590i
$983$	−14.9197	−	8.61391i	−0.475866	−	0.274741i	0.242826	−	0.970070i	$-0.421926\pi$
$983$	−14.9197	−	8.61391i	−0.475866	−	0.274741i	−0.718692	+	0.695329i	$0.755259\pi$
$984$	−3.05366	+	0.0489624i	−0.0973471	+	0.00156086i
$985$	−6.87245	−	11.9034i	−0.218974	−	0.379275i
$986$	0.422436	−	0.243893i	0.0134531	−	0.00776715i
$987$	−5.43158	+	0.0870900i	−0.172889	+	0.00277210i
$988$	22.8542	−	6.20251i	0.727088	−	0.197328i
$989$	−1.32626			−0.0421726
$990$	−0.0175199	−	0.546194i	−0.000556818	−	0.0173592i
$991$	39.3598			1.25030			0.625152	−	0.780503i	$-0.285037\pi$
$991$	39.3598			1.25030			0.625152	+	0.780503i	$0.285037\pi$
$992$	−17.5681	+	30.4289i	−0.557789	+	0.966119i
$993$	−9.97358	+	5.97346i	−0.316502	+	0.189562i
$994$	3.29728	−	1.90368i	0.104583	−	0.0603812i
$995$	−12.3355	+	7.12190i	−0.391061	+	0.225779i
$996$	42.9894	+	23.9093i	1.36217	+	0.757595i
$997$	14.3605	−	24.8731i	0.454802	−	0.787740i	−0.543875	−	0.839166i	$-0.683043\pi$
$997$	14.3605	−	24.8731i	0.454802	−	0.787740i	0.998677	+	0.0514265i	$0.0163768\pi$
$998$	0.865048			0.0273826
$999$	−0.0545335	−	1.13293i	−0.00172536	−	0.0358442i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.bt.b.376.24	✓	108
9.4	even	3	inner	585.2.bt.b.571.31	yes	108
13.12	even	2	inner	585.2.bt.b.376.31	yes	108
117.103	even	6	inner	585.2.bt.b.571.24	yes	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
585.2.bt.b.376.24	✓	108	1.1	even	1	trivial
585.2.bt.b.376.31	yes	108	13.12	even	2	inner
585.2.bt.b.571.24	yes	108	117.103	even	6	inner
585.2.bt.b.571.31	yes	108	9.4	even	3	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:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	585.bt (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.355151 - 0.205047i) q^{2} +(0.841866 - 1.51369i) q^{3} +(-0.915912 - 1.58641i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(-0.609367 + 0.364968i) q^{6} +(-0.661508 - 0.381922i) q^{7} +1.57141i q^{8} +(-1.58252 - 2.54865i) q^{9} +O(q^{10})\)	\(q+(-0.355151 - 0.205047i) q^{2} +(0.841866 - 1.51369i) q^{3} +(-0.915912 - 1.58641i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(-0.609367 + 0.364968i) q^{6} +(-0.661508 - 0.381922i) q^{7} +1.57141i q^{8} +(-1.58252 - 2.54865i) q^{9} +0.410093 q^{10} +(0.384678 + 0.222094i) q^{11} +(-3.17240 + 0.0508663i) q^{12} +(-3.48567 - 0.921994i) q^{13} +(0.156624 + 0.271280i) q^{14} +(0.0277681 + 1.73183i) q^{15} +(-1.50961 + 2.61472i) q^{16} -1.99449 q^{17} +(0.0394425 + 1.22965i) q^{18} -3.58544i q^{19} +(1.58641 + 0.915912i) q^{20} +(-1.13501 + 0.679791i) q^{21} +(-0.0910792 - 0.157754i) q^{22} +(0.803282 + 1.39133i) q^{23} +(2.37862 + 1.32291i) q^{24} +(0.500000 - 0.866025i) q^{25} +(1.04889 + 1.04217i) q^{26} +(-5.19014 + 0.249828i) q^{27} +1.39923i q^{28} +(0.298185 - 0.516472i) q^{29} +(0.345244 - 0.620755i) q^{30} +(-6.94569 + 4.01010i) q^{31} +(3.79404 - 2.19049i) q^{32} +(0.660028 - 0.395310i) q^{33} +(0.708345 + 0.408963i) q^{34} +0.763843 q^{35} +(-2.59374 + 4.84486i) q^{36} +0.218284i q^{37} +(-0.735183 + 1.27338i) q^{38} +(-4.33009 + 4.50004i) q^{39} +(-0.785703 - 1.36088i) q^{40} +(-0.971758 + 0.561045i) q^{41} +(0.542490 - 0.00869829i) q^{42} +(-0.412762 + 0.714925i) q^{43} -0.813673i q^{44} +(2.64483 + 1.41594i) q^{45} -0.658842i q^{46} +(3.55589 + 2.05299i) q^{47} +(2.68699 + 4.48633i) q^{48} +(-3.20827 - 5.55689i) q^{49} +(-0.355151 + 0.205047i) q^{50} +(-1.67909 + 3.01904i) q^{51} +(1.72991 + 6.37416i) q^{52} +5.08548 q^{53} +(1.89451 + 0.975495i) q^{54} -0.444187 q^{55} +(0.600154 - 1.03950i) q^{56} +(-5.42725 - 3.01846i) q^{57} +(-0.211802 + 0.122284i) q^{58} +(3.52561 - 2.03551i) q^{59} +(2.72195 - 1.63025i) q^{60} +(1.88333 - 3.26202i) q^{61} +3.28903 q^{62} +(0.0734659 + 2.29035i) q^{63} +4.24184 q^{64} +(3.47968 - 0.944367i) q^{65} +(-0.315467 + 0.00505820i) q^{66} +(-12.0106 + 6.93435i) q^{67} +(1.82677 + 3.16406i) q^{68} +(2.78229 - 0.0446113i) q^{69} +(-0.271280 - 0.156624i) q^{70} -12.1545i q^{71} +(4.00497 - 2.48679i) q^{72} -3.80995i q^{73} +(0.0447585 - 0.0775240i) q^{74} +(-0.889962 - 1.48592i) q^{75} +(-5.68797 + 3.28395i) q^{76} +(-0.169645 - 0.293833i) q^{77} +(2.46055 - 0.710326i) q^{78} +(4.87017 - 8.43538i) q^{79} -3.01922i q^{80} +(-3.99124 + 8.06660i) q^{81} +0.460162 q^{82} +(-13.4267 - 7.75194i) q^{83} +(2.11800 + 1.17796i) q^{84} +(1.72728 - 0.997243i) q^{85} +(0.293186 - 0.169271i) q^{86} +(-0.530747 - 0.886160i) q^{87} +(-0.348999 + 0.604485i) q^{88} -12.2951i q^{89} +(-0.648982 - 1.04519i) q^{90} +(1.95367 + 1.94116i) q^{91} +(1.47147 - 2.54866i) q^{92} +(0.222706 + 13.8896i) q^{93} +(-0.841918 - 1.45825i) q^{94} +(1.79272 + 3.10508i) q^{95} +(-0.121652 - 7.58710i) q^{96} +(-12.3546 - 7.13294i) q^{97} +2.63138i q^{98} +(-0.0427216 - 1.33188i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q - 6 q^{3} + 52 q^{4} - 14 q^{9}+O(q^{10}) \) 108 * q - 6 * q^3 + 52 * q^4 - 14 * q^9	\( 108 q - 6 q^{3} + 52 q^{4} - 14 q^{9} - 8 q^{10} - 36 q^{12} - 4 q^{13} - 8 q^{14} - 64 q^{16} + 36 q^{17} + 24 q^{22} - 22 q^{23} + 54 q^{25} + 40 q^{26} + 48 q^{27} - 16 q^{29} + 20 q^{30} - 40 q^{35} - 76 q^{36} - 12 q^{38} + 26 q^{39} - 52 q^{42} - 6 q^{43} - 68 q^{48} + 58 q^{49} + 34 q^{51} + 22 q^{52} - 116 q^{53} + 24 q^{55} + 40 q^{56} + 18 q^{61} + 152 q^{62} - 216 q^{64} + 2 q^{65} - 72 q^{66} - 134 q^{69} + 32 q^{74} + 40 q^{77} - 34 q^{78} + 18 q^{79} + 34 q^{81} + 88 q^{82} + 60 q^{87} + 8 q^{90} + 16 q^{91} + 176 q^{92} - 76 q^{94} - 56 q^{95}+O(q^{100}) \) 108 * q - 6 * q^3 + 52 * q^4 - 14 * q^9 - 8 * q^10 - 36 * q^12 - 4 * q^13 - 8 * q^14 - 64 * q^16 + 36 * q^17 + 24 * q^22 - 22 * q^23 + 54 * q^25 + 40 * q^26 + 48 * q^27 - 16 * q^29 + 20 * q^30 - 40 * q^35 - 76 * q^36 - 12 * q^38 + 26 * q^39 - 52 * q^42 - 6 * q^43 - 68 * q^48 + 58 * q^49 + 34 * q^51 + 22 * q^52 - 116 * q^53 + 24 * q^55 + 40 * q^56 + 18 * q^61 + 152 * q^62 - 216 * q^64 + 2 * q^65 - 72 * q^66 - 134 * q^69 + 32 * q^74 + 40 * q^77 - 34 * q^78 + 18 * q^79 + 34 * q^81 + 88 * q^82 + 60 * q^87 + 8 * q^90 + 16 * q^91 + 176 * q^92 - 76 * q^94 - 56 * q^95

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