LMFDB - Embedded newform 546.2.ch.a.137.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(137,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 8, 11]))

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

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

chi := DirichletCharacter("546.137");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.ch (of order $12$, degree $4$, 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:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$152$
Relative dimension:	$38$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			137.10
Character	$\chi$	$=$	546.137
Dual form			546.2.ch.a.275.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(0.116244 - 1.72815i) q^{3} -1.00000i q^{4} +(-1.15194 - 0.308662i) q^{5} +(1.13979 + 1.30418i) q^{6} +(1.79371 + 1.94489i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.97297 - 0.401773i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(0.116244 - 1.72815i) q^{3} -1.00000i q^{4} +(-1.15194 - 0.308662i) q^{5} +(1.13979 + 1.30418i) q^{6} +(1.79371 + 1.94489i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.97297 - 0.401773i) q^{9} +(1.03280 - 0.596290i) q^{10} +(-1.47854 + 5.51798i) q^{11} +(-1.72815 - 0.116244i) q^{12} +(1.33942 + 3.34753i) q^{13} +(-2.64359 - 0.106905i) q^{14} +(-0.667320 + 1.95484i) q^{15} -1.00000 q^{16} +0.354208 q^{17} +(2.38631 - 1.81811i) q^{18} +(7.62256 - 2.04246i) q^{19} +(-0.308662 + 1.15194i) q^{20} +(3.56957 - 2.87371i) q^{21} +(-2.85632 - 4.94729i) q^{22} +3.17450 q^{23} +(1.30418 - 1.13979i) q^{24} +(-3.09843 - 1.78888i) q^{25} +(-3.31417 - 1.41995i) q^{26} +(-1.03991 + 5.09103i) q^{27} +(1.94489 - 1.79371i) q^{28} +(1.84232 + 1.06367i) q^{29} +(-0.910418 - 1.85415i) q^{30} +(3.27069 - 0.876378i) q^{31} +(0.707107 - 0.707107i) q^{32} +(9.36401 + 3.19656i) q^{33} +(-0.250463 + 0.250463i) q^{34} +(-1.46593 - 2.79406i) q^{35} +(-0.401773 + 2.97297i) q^{36} +(3.68290 - 3.68290i) q^{37} +(-3.94572 + 6.83420i) q^{38} +(5.94072 - 1.92558i) q^{39} +(-0.596290 - 1.03280i) q^{40} +(0.740026 + 2.76181i) q^{41} +(-0.492050 + 4.55608i) q^{42} +(-2.54122 + 1.46717i) q^{43} +(5.51798 + 1.47854i) q^{44} +(3.30068 + 1.38046i) q^{45} +(-2.24471 + 2.24471i) q^{46} +(-0.977655 + 3.64866i) q^{47} +(-0.116244 + 1.72815i) q^{48} +(-0.565228 + 6.97714i) q^{49} +(3.45585 - 0.925991i) q^{50} +(0.0411745 - 0.612122i) q^{51} +(3.34753 - 1.33942i) q^{52} +(5.89543 + 3.40373i) q^{53} +(-2.86457 - 4.33523i) q^{54} +(3.40639 - 5.90003i) q^{55} +(-0.106905 + 2.64359i) q^{56} +(-2.64359 - 13.4103i) q^{57} +(-2.05484 + 0.550594i) q^{58} +(-6.57515 - 6.57515i) q^{59} +(1.95484 + 0.667320i) q^{60} +(-2.26655 + 3.92578i) q^{61} +(-1.69303 + 2.93242i) q^{62} +(-4.55124 - 6.50279i) q^{63} +1.00000i q^{64} +(-0.509675 - 4.26959i) q^{65} +(-8.88167 + 4.36104i) q^{66} +(-0.454718 + 1.69703i) q^{67} -0.354208i q^{68} +(0.369016 - 5.48599i) q^{69} +(3.01227 + 0.939125i) q^{70} +(-9.64463 - 2.58427i) q^{71} +(-1.81811 - 2.38631i) q^{72} +(2.55089 + 9.52006i) q^{73} +5.20841i q^{74} +(-3.45161 + 5.14659i) q^{75} +(-2.04246 - 7.62256i) q^{76} +(-13.3840 + 7.02205i) q^{77} +(-2.83914 + 5.56231i) q^{78} +(3.83593 + 6.64402i) q^{79} +(1.15194 + 0.308662i) q^{80} +(8.67716 + 2.38892i) q^{81} +(-2.47617 - 1.42962i) q^{82} +(0.796640 - 0.796640i) q^{83} +(-2.87371 - 3.56957i) q^{84} +(-0.408027 - 0.109330i) q^{85} +(0.759464 - 2.83436i) q^{86} +(2.05233 - 3.06016i) q^{87} +(-4.94729 + 2.85632i) q^{88} +(11.9584 + 11.9584i) q^{89} +(-3.31007 + 1.35780i) q^{90} +(-4.10807 + 8.60951i) q^{91} -3.17450i q^{92} +(-1.13431 - 5.75410i) q^{93} +(-1.88868 - 3.27130i) q^{94} -9.41118 q^{95} +(-1.13979 - 1.30418i) q^{96} +(-2.45789 + 9.17298i) q^{97} +(-4.53391 - 5.33326i) q^{98} +(6.61264 - 15.8108i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 152 q + 8 q^{7}+O(q^{10}) $ 152 * q + 8 * q^7	$ 152 q + 8 q^{7} - 152 q^{16} - 8 q^{18} + 36 q^{19} + 8 q^{21} + 24 q^{27} - 12 q^{28} - 24 q^{30} - 36 q^{31} + 12 q^{33} + 24 q^{36} - 12 q^{37} - 8 q^{39} - 36 q^{42} + 84 q^{43} - 40 q^{45} + 8 q^{46} + 4 q^{49} - 20 q^{52} - 12 q^{54} + 16 q^{55} - 8 q^{57} + 8 q^{58} + 24 q^{60} - 32 q^{61} - 28 q^{63} + 16 q^{66} + 92 q^{67} + 84 q^{69} - 8 q^{72} + 84 q^{73} - 48 q^{76} - 8 q^{78} + 32 q^{79} - 24 q^{81} - 48 q^{82} - 8 q^{84} - 152 q^{85} - 96 q^{87} - 88 q^{91} - 48 q^{93} + 32 q^{94} - 100 q^{97} + 16 q^{99}+O(q^{100}) $ 152 * q + 8 * q^7 - 152 * q^16 - 8 * q^18 + 36 * q^19 + 8 * q^21 + 24 * q^27 - 12 * q^28 - 24 * q^30 - 36 * q^31 + 12 * q^33 + 24 * q^36 - 12 * q^37 - 8 * q^39 - 36 * q^42 + 84 * q^43 - 40 * q^45 + 8 * q^46 + 4 * q^49 - 20 * q^52 - 12 * q^54 + 16 * q^55 - 8 * q^57 + 8 * q^58 + 24 * q^60 - 32 * q^61 - 28 * q^63 + 16 * q^66 + 92 * q^67 + 84 * q^69 - 8 * q^72 + 84 * q^73 - 48 * q^76 - 8 * q^78 + 32 * q^79 - 24 * q^81 - 48 * q^82 - 8 * q^84 - 152 * q^85 - 96 * q^87 - 88 * q^91 - 48 * q^93 + 32 * q^94 - 100 * q^97 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{11}{12}\right)$

Coefficient data

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

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

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

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$	0.116244	−	1.72815i	0.0671135	−	0.997745i
$3$	0.116244	−	1.72815i	0.0671135	−	0.997745i
$4$		−	1.00000i		−	0.500000i
$5$	−1.15194	−	0.308662i	−0.515165	−	0.138038i	−0.00813552	−	0.999967i	$-0.502590\pi$
$5$	−1.15194	−	0.308662i	−0.515165	−	0.138038i	−0.507029	+	0.861929i	$0.669256\pi$
$6$	1.13979	+	1.30418i	0.465316	+	0.532429i
$7$	1.79371	+	1.94489i	0.677958	+	0.735101i
$7$	1.79371	+	1.94489i	0.677958	+	0.735101i
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	−2.97297	−	0.401773i	−0.990992	−	0.133924i
$10$	1.03280	−	0.596290i	0.326601	−	0.188563i
$11$	−1.47854	+	5.51798i	−0.445796	+	1.66373i	0.268029	+	0.963411i	$0.413628\pi$
$11$	−1.47854	+	5.51798i	−0.445796	+	1.66373i	−0.713825	+	0.700324i	$0.753039\pi$
$12$	−1.72815	−	0.116244i	−0.498873	−	0.0335568i
$13$	1.33942	+	3.34753i	0.371487	+	0.928438i
$13$	1.33942	+	3.34753i	0.371487	+	0.928438i
$14$	−2.64359	−	0.106905i	−0.706529	−	0.0285716i
$15$	−0.667320	+	1.95484i	−0.172301	+	0.504739i
$16$	−1.00000			−0.250000
$17$	0.354208			0.0859080			0.0429540	−	0.999077i	$-0.486323\pi$
$17$	0.354208			0.0859080			0.0429540	+	0.999077i	$0.486323\pi$
$18$	2.38631	−	1.81811i	0.562458	−	0.428534i
$19$	7.62256	−	2.04246i	1.74873	−	0.468572i	0.764379	−	0.644767i	$-0.223046\pi$
$19$	7.62256	−	2.04246i	1.74873	−	0.468572i	0.984355	+	0.176195i	$0.0563791\pi$
$20$	−0.308662	+	1.15194i	−0.0690190	+	0.257582i
$21$	3.56957	−	2.87371i	0.778944	−	0.627094i
$22$	−2.85632	−	4.94729i	−0.608969	−	1.05477i
$23$	3.17450			0.661928			0.330964	−	0.943643i	$-0.392626\pi$
$23$	3.17450			0.661928			0.330964	+	0.943643i	$0.392626\pi$
$24$	1.30418	−	1.13979i	0.266215	−	0.232658i
$25$	−3.09843	−	1.78888i	−0.619685	−	0.357776i
$26$	−3.31417	−	1.41995i	−0.649963	−	0.278475i
$27$	−1.03991	+	5.09103i	−0.200131	+	0.979769i
$28$	1.94489	−	1.79371i	0.367550	−	0.338979i
$29$	1.84232	+	1.06367i	0.342111	+	0.197518i	0.661205	−	0.750205i	$-0.270045\pi$
$29$	1.84232	+	1.06367i	0.342111	+	0.197518i	−0.319094	+	0.947723i	$0.603379\pi$
$30$	−0.910418	−	1.85415i	−0.166219	−	0.338520i
$31$	3.27069	−	0.876378i	0.587433	−	0.157402i	0.0471532	−	0.998888i	$-0.484985\pi$
$31$	3.27069	−	0.876378i	0.587433	−	0.157402i	0.540280	+	0.841486i	$0.318318\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	9.36401	+	3.19656i	1.63006	+	0.556450i
$34$	−0.250463	+	0.250463i	−0.0429540	+	0.0429540i
$35$	−1.46593	−	2.79406i	−0.247788	−	0.472282i
$36$	−0.401773	+	2.97297i	−0.0669622	+	0.495496i
$37$	3.68290	−	3.68290i	0.605465	−	0.605465i	−0.336292	−	0.941758i	$-0.609173\pi$
$37$	3.68290	−	3.68290i	0.605465	−	0.605465i	0.941758	+	0.336292i	$0.109173\pi$
$38$	−3.94572	+	6.83420i	−0.640081	+	1.10865i
$39$	5.94072	−	1.92558i	0.951277	−	0.308339i
$40$	−0.596290	−	1.03280i	−0.0942817	−	0.163301i
$41$	0.740026	+	2.76181i	0.115573	+	0.431323i	0.999329	−	0.0366242i	$-0.0116605\pi$
$41$	0.740026	+	2.76181i	0.115573	+	0.431323i	−0.883757	+	0.467947i	$0.844994\pi$
$42$	−0.492050	+	4.55608i	−0.0759249	+	0.703019i
$43$	−2.54122	+	1.46717i	−0.387532	+	0.223742i	−0.681090	−	0.732200i	$-0.738494\pi$
$43$	−2.54122	+	1.46717i	−0.387532	+	0.223742i	0.293558	+	0.955941i	$0.405161\pi$
$44$	5.51798	+	1.47854i	0.831867	+	0.222898i
$45$	3.30068	+	1.38046i	0.492037	+	0.205788i
$46$	−2.24471	+	2.24471i	−0.330964	+	0.330964i
$47$	−0.977655	+	3.64866i	−0.142606	+	0.532212i	0.857245	+	0.514909i	$0.172174\pi$
$47$	−0.977655	+	3.64866i	−0.142606	+	0.532212i	−0.999850	+	0.0173023i	$0.994492\pi$
$48$	−0.116244	+	1.72815i	−0.0167784	+	0.249436i
$49$	−0.565228	+	6.97714i	−0.0807468	+	0.996735i
$50$	3.45585	−	0.925991i	0.488730	−	0.130955i
$51$	0.0411745	−	0.612122i	0.00576559	−	0.0857143i
$52$	3.34753	−	1.33942i	0.464219	−	0.185744i
$53$	5.89543	+	3.40373i	0.809800	+	0.467538i	0.846886	−	0.531774i	$-0.178474\pi$
$53$	5.89543	+	3.40373i	0.809800	+	0.467538i	−0.0370865	+	0.999312i	$0.511808\pi$
$54$	−2.86457	−	4.33523i	−0.389819	−	0.589950i
$55$	3.40639	−	5.90003i	0.459317	−	0.795560i
$56$	−0.106905	+	2.64359i	−0.0142858	+	0.353265i
$57$	−2.64359	−	13.4103i	−0.350152	−	1.77624i
$58$	−2.05484	+	0.550594i	−0.269814	+	0.0722965i
$59$	−6.57515	−	6.57515i	−0.856012	−	0.856012i	0.134854	−	0.990865i	$-0.456943\pi$
$59$	−6.57515	−	6.57515i	−0.856012	−	0.856012i	−0.990865	+	0.134854i	$0.956943\pi$
$60$	1.95484	+	0.667320i	0.252369	+	0.0861506i
$61$	−2.26655	+	3.92578i	−0.290202	+	0.502644i	−0.973857	−	0.227161i	$-0.927056\pi$
$61$	−2.26655	+	3.92578i	−0.290202	+	0.502644i	0.683655	+	0.729805i	$0.260389\pi$
$62$	−1.69303	+	2.93242i	−0.215015	+	0.372418i
$63$	−4.55124	−	6.50279i	−0.573402	−	0.819274i
$64$			1.00000i			0.125000i
$65$	−0.509675	−	4.26959i	−0.0632174	−	0.529578i
$66$	−8.88167	+	4.36104i	−1.09326	+	0.536807i
$67$	−0.454718	+	1.69703i	−0.0555527	+	0.207325i	−0.988124	−	0.153662i	$-0.950893\pi$
$67$	−0.454718	+	1.69703i	−0.0555527	+	0.207325i	0.932571	+	0.360987i	$0.117560\pi$
$68$		−	0.354208i		−	0.0429540i
$69$	0.369016	−	5.48599i	0.0444243	−	0.660436i
$70$	3.01227	+	0.939125i	0.360035	+	0.112247i
$71$	−9.64463	−	2.58427i	−1.14461	−	0.306697i	−0.363805	−	0.931475i	$-0.618523\pi$
$71$	−9.64463	−	2.58427i	−1.14461	−	0.306697i	−0.780802	+	0.624778i	$0.785189\pi$
$72$	−1.81811	−	2.38631i	−0.214267	−	0.281229i
$73$	2.55089	+	9.52006i	0.298559	+	1.11424i	0.938349	+	0.345689i	$0.112355\pi$
$73$	2.55089	+	9.52006i	0.298559	+	1.11424i	−0.639790	+	0.768550i	$0.720979\pi$
$74$			5.20841i			0.605465i
$75$	−3.45161	+	5.14659i	−0.398558	+	0.594277i
$76$	−2.04246	−	7.62256i	−0.234286	−	0.874367i
$77$	−13.3840	+	7.02205i	−1.52524	+	0.800236i
$78$	−2.83914	+	5.56231i	−0.321469	+	0.629808i
$79$	3.83593	+	6.64402i	0.431575	+	0.747510i	0.997009	−	0.0772833i	$-0.0246246\pi$
$79$	3.83593	+	6.64402i	0.431575	+	0.747510i	−0.565434	+	0.824794i	$0.691291\pi$
$80$	1.15194	+	0.308662i	0.128791	+	0.0345095i
$81$	8.67716	+	2.38892i	0.964128	+	0.265436i
$82$	−2.47617	−	1.42962i	−0.273448	−	0.157875i
$83$	0.796640	−	0.796640i	0.0874426	−	0.0874426i	−0.662032	−	0.749475i	$-0.730306\pi$
$83$	0.796640	−	0.796640i	0.0874426	−	0.0874426i	0.749475	+	0.662032i	$0.230306\pi$
$84$	−2.87371	−	3.56957i	−0.313547	−	0.389472i
$85$	−0.408027	−	0.109330i	−0.0442567	−	0.0118586i
$86$	0.759464	−	2.83436i	0.0818951	−	0.305637i
$87$	2.05233	−	3.06016i	0.220033	−	0.328083i
$88$	−4.94729	+	2.85632i	−0.527383	+	0.304485i
$89$	11.9584	+	11.9584i	1.26759	+	1.26759i	0.947330	+	0.320260i	$0.103770\pi$
$89$	11.9584	+	11.9584i	1.26759	+	1.26759i	0.320260	+	0.947330i	$0.396230\pi$
$90$	−3.31007	+	1.35780i	−0.348912	+	0.143125i
$91$	−4.10807	+	8.60951i	−0.430643	+	0.902522i
$92$		−	3.17450i		−	0.330964i
$93$	−1.13431	−	5.75410i	−0.117623	−	0.596672i
$94$	−1.88868	−	3.27130i	−0.194803	−	0.337409i
$95$	−9.41118			−0.965566
$96$	−1.13979	−	1.30418i	−0.116329	−	0.133107i
$97$	−2.45789	+	9.17298i	−0.249561	+	0.931375i	0.721475	+	0.692441i	$0.243465\pi$
$97$	−2.45789	+	9.17298i	−0.249561	+	0.931375i	−0.971036	+	0.238934i	$0.923202\pi$
$98$	−4.53391	−	5.33326i	−0.457994	−	0.538741i
$99$	6.61264	−	15.8108i	0.664595	−	1.58904i
$100$	−1.78888	+	3.09843i	−0.178888	+	0.309843i
$101$	−7.03517	−	12.1853i	−0.700026	−	1.21248i	−0.968457	−	0.249181i	$-0.919839\pi$
$101$	−7.03517	−	12.1853i	−0.700026	−	1.21248i	0.268431	−	0.963299i	$-0.413495\pi$
$102$	0.403721	+	0.461951i	0.0399743	+	0.0457399i
$103$	−4.37855	+	2.52796i	−0.431432	+	0.249087i	−0.699956	−	0.714186i	$-0.746797\pi$
$103$	−4.37855	+	2.52796i	−0.431432	+	0.249087i	0.268525	+	0.963273i	$0.413464\pi$
$104$	−1.41995	+	3.31417i	−0.139238	+	0.324981i
$105$	−4.99894	+	2.20855i	−0.487847	+	0.215533i
$106$	−6.57550	+	1.76190i	−0.638669	+	0.171131i
$107$		−	9.35066i		−	0.903962i	−0.892028	−	0.451981i	$-0.850717\pi$
$107$		−	9.35066i		−	0.903962i	0.892028	−	0.451981i	$-0.149283\pi$
$108$	5.09103	+	1.03991i	0.489885	+	0.100066i
$109$	6.30163	−	1.68852i	0.603587	−	0.161731i	0.0559316	−	0.998435i	$-0.482187\pi$
$109$	6.30163	−	1.68852i	0.603587	−	0.161731i	0.547656	+	0.836704i	$0.315520\pi$
$110$	1.76328	+	6.58063i	0.168122	+	0.627439i
$111$	−5.93647	−	6.79271i	−0.563465	−	0.644735i
$112$	−1.79371	−	1.94489i	−0.169489	−	0.183775i
$113$	7.52001	−	4.34168i	0.707423	−	0.408431i	−0.102683	−	0.994714i	$-0.532743\pi$
$113$	7.52001	−	4.34168i	0.707423	−	0.408431i	0.810106	+	0.586283i	$0.199409\pi$
$114$	11.3518	+	7.61322i	1.06320	+	0.713044i
$115$	−3.65684	−	0.979847i	−0.341002	−	0.0913712i
$116$	1.06367	−	1.84232i	0.0987588	−	0.171055i
$117$	−2.63710	−	10.4903i	−0.243800	−	0.969825i
$118$	9.29867			0.856012
$119$	0.635345	+	0.688896i	0.0582420	+	0.0631510i
$120$	−1.85415	+	0.910418i	−0.169260	+	0.0831094i
$121$	−18.7358	−	10.8171i	−1.70325	−	0.983374i
$122$	−1.17325	−	4.37864i	−0.106221	−	0.396423i
$123$	4.85884	−	0.957828i	0.438107	−	0.0863644i
$124$	−0.876378	−	3.27069i	−0.0787011	−	0.293716i
$125$	7.23346	+	7.23346i	0.646980	+	0.646980i
$126$	7.81638	+	1.37995i	0.696338	+	0.122936i
$127$	−14.2090	−	8.20357i	−1.26084	−	0.727949i	−0.287607	−	0.957749i	$-0.592860\pi$
$127$	−14.2090	−	8.20357i	−1.26084	−	0.727949i	−0.973238	+	0.229799i	$0.926193\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	2.24009	+	4.56214i	0.197229	+	0.401674i
$130$	3.37945	+	2.65866i	0.296398	+	0.233180i
$131$	8.79754	−	5.07926i	0.768645	−	0.443777i	−0.0637462	−	0.997966i	$-0.520305\pi$
$131$	8.79754	−	5.07926i	0.768645	−	0.443777i	0.832391	+	0.554189i	$0.186971\pi$
$132$	3.19656	−	9.36401i	0.278225	−	0.815032i
$133$	17.6450	+	11.1615i	1.53002	+	0.967824i
$134$	−0.878448	−	1.52152i	−0.0758864	−	0.131439i
$135$	2.76933	−	5.54359i	0.238346	−	0.477117i
$136$	0.250463	+	0.250463i	0.0214770	+	0.0214770i
$137$	−3.94584	−	3.94584i	−0.337115	−	0.337115i	0.518165	−	0.855281i	$-0.326615\pi$
$137$	−3.94584	−	3.94584i	−0.337115	−	0.337115i	−0.855281	+	0.518165i	$0.826615\pi$
$138$	3.61825	+	4.14011i	0.308006	+	0.352430i
$139$	0.130427	+	0.225906i	0.0110627	+	0.0191611i	0.871504	−	0.490389i	$-0.163145\pi$
$139$	0.130427	+	0.225906i	0.0110627	+	0.0191611i	−0.860441	+	0.509550i	$0.829812\pi$
$140$	−2.79406	+	1.46593i	−0.236141	+	0.123894i
$141$	6.19177	+	2.11367i	0.521441	+	0.178003i
$142$	8.64714	−	4.99243i	0.725652	−	0.418955i
$143$	−20.4520	+	2.44142i	−1.71028	+	0.204162i
$144$	2.97297	+	0.401773i	0.247748	+	0.0334811i
$145$	−1.79394	−	1.79394i	−0.148978	−	0.148978i
$146$	−8.53545	−	4.92795i	−0.706399	−	0.407840i
$147$	11.9918	+	1.78785i	0.989068	+	0.147459i
$148$	−3.68290	−	3.68290i	−0.302733	−	0.302733i
$149$	1.03734	+	3.87141i	0.0849823	+	0.317158i	0.995311	−	0.0967282i	$-0.0308378\pi$
$149$	1.03734	+	3.87141i	0.0849823	+	0.317158i	−0.910329	+	0.413886i	$0.864171\pi$
$150$	−1.19853	−	6.07985i	−0.0978592	−	0.496417i
$151$	−4.52196	−	16.8762i	−0.367992	−	1.37337i	−0.863319	−	0.504659i	$-0.831618\pi$
$151$	−4.52196	−	16.8762i	−0.367992	−	1.37337i	0.495327	−	0.868707i	$-0.335048\pi$
$152$	6.83420	+	3.94572i	0.554326	+	0.320041i
$153$	−1.05305	−	0.142311i	−0.0851341	−	0.0115052i
$154$	4.49855	−	14.4292i	0.362504	−	1.16274i
$155$	−4.03815			−0.324352
$156$	−1.92558	−	5.94072i	−0.154169	−	0.475638i
$157$	−1.41596	+	2.45251i	−0.113006	+	0.195732i	−0.916981	−	0.398931i	$-0.869381\pi$
$157$	−1.41596	+	2.45251i	−0.113006	+	0.195732i	0.803975	+	0.594663i	$0.202715\pi$
$158$	−7.41044	−	1.98562i	−0.589543	−	0.157968i
$159$	6.56745	−	9.79250i	0.520833	−	0.776596i
$160$	−1.03280	+	0.596290i	−0.0816503	+	0.0471408i
$161$	5.69412	+	6.17406i	0.448759	+	0.486584i
$162$	−7.82490	+	4.44645i	−0.614782	+	0.349346i
$163$	−5.85442	−	21.8490i	−0.458553	−	1.71134i	−0.677426	−	0.735591i	$-0.736904\pi$
$163$	−5.85442	−	21.8490i	−0.458553	−	1.71134i	0.218872	−	0.975754i	$-0.429762\pi$
$164$	2.76181	−	0.740026i	0.215661	−	0.0577863i
$165$	−9.80014	−	6.57257i	−0.762940	−	0.511674i
$166$			1.12662i			0.0874426i
$167$	3.14515	−	0.842741i	0.243379	−	0.0652133i	−0.135067	−	0.990836i	$-0.543125\pi$
$167$	3.14515	−	0.842741i	0.243379	−	0.0652133i	0.378446	+	0.925623i	$0.376458\pi$
$168$	4.55608	+	0.492050i	0.351509	+	0.0379625i
$169$	−9.41193	+	8.96747i	−0.723994	+	0.689806i
$170$	0.365827	−	0.211210i	0.0280576	−	0.0161991i
$171$	−23.4823	+	3.00963i	−1.79573	+	0.230153i
$172$	1.46717	+	2.54122i	0.111871	+	0.193766i
$173$	4.98606	−	8.63612i	0.379083	−	0.656592i	−0.611846	−	0.790977i	$-0.709573\pi$
$173$	4.98606	−	8.63612i	0.379083	−	0.656592i	0.990929	+	0.134385i	$0.0429060\pi$
$174$	0.712643	+	3.61507i	0.0540253	+	0.274058i
$175$	−2.07849	−	9.23484i	−0.157119	−	0.698088i
$176$	1.47854	−	5.51798i	0.111449	−	0.415934i
$177$	−12.1271	+	10.5985i	−0.911532	+	0.796632i
$178$	−16.9118			−1.26759
$179$	6.56403	+	11.3692i	0.490619	+	0.849777i	0.999942	−	0.0107988i	$-0.00343742\pi$
$179$	6.56403	+	11.3692i	0.490619	+	0.849777i	−0.509323	+	0.860576i	$0.670104\pi$
$180$	1.38046	−	3.30068i	0.102894	−	0.246019i
$181$			20.7974i			1.54586i	0.634491	+	0.772930i	$0.281210\pi$
$181$			20.7974i			1.54586i	−0.634491	+	0.772930i	$0.718790\pi$
$182$	−3.18300	−	8.99269i	−0.235940	−	0.666583i
$183$	6.52084	+	4.37328i	0.482035	+	0.323282i
$184$	2.24471	+	2.24471i	0.165482	+	0.165482i
$185$	−5.37926	+	3.10572i	−0.395491	+	0.228337i
$186$	4.87084	+	3.26668i	0.357147	+	0.239525i
$187$	−0.523710	+	1.95451i	−0.0382975	+	0.142928i
$188$	3.64866	+	0.977655i	0.266106	+	0.0713028i
$189$	−11.7668	+	7.10930i	−0.855910	+	0.517125i
$190$	6.65471	−	6.65471i	0.482783	−	0.482783i
$191$	8.08187	+	4.66607i	0.584784	+	0.337625i	0.763032	−	0.646360i	$-0.223710\pi$
$191$	8.08187	+	4.66607i	0.584784	+	0.337625i	−0.178248	+	0.983986i	$0.557043\pi$
$192$	1.72815	+	0.116244i	0.124718	+	0.00838919i
$193$	1.23955	+	0.332138i	0.0892251	+	0.0239078i	0.303155	−	0.952941i	$-0.401960\pi$
$193$	1.23955	+	0.332138i	0.0892251	+	0.0239078i	−0.213930	+	0.976849i	$0.568627\pi$
$194$	−4.74828	−	8.22427i	−0.340907	−	0.590468i
$195$	−7.43772	+	0.384478i	−0.532626	+	0.0275330i
$196$	6.97714	+	0.565228i	0.498367	+	0.0403734i
$197$	−6.46249	−	24.1184i	−0.460434	−	1.71836i	−0.671602	−	0.740912i	$-0.734394\pi$
$197$	−6.46249	−	24.1184i	−0.460434	−	1.71836i	0.211169	−	0.977450i	$-0.432273\pi$
$198$	6.50407	+	15.8558i	0.462224	+	1.12682i
$199$		−	23.6263i		−	1.67482i	−0.546574	−	0.837411i	$-0.684068\pi$
$199$		−	23.6263i		−	1.67482i	0.546574	−	0.837411i	$-0.315932\pi$
$200$	−0.925991	−	3.45585i	−0.0654775	−	0.244365i
$201$	2.87986	+	0.983089i	0.203130	+	0.0693418i
$202$	13.5909	+	3.64167i	0.956253	+	0.256227i
$203$	1.23587	+	5.49103i	0.0867411	+	0.385394i
$204$	−0.612122	−	0.0411745i	−0.0428571	−	0.00288279i
$205$		−	3.40987i		−	0.238156i
$206$	1.30857	−	4.88364i	0.0911722	−	0.340259i
$207$	−9.43769	−	1.27543i	−0.655965	−	0.0886483i
$208$	−1.33942	−	3.34753i	−0.0928718	−	0.232110i
$209$			45.0810i			3.11832i
$210$	1.97310	−	5.09647i	0.136157	−	0.351690i
$211$	−4.71972	+	8.17479i	−0.324919	+	0.562776i	−0.981496	−	0.191483i	$-0.938670\pi$
$211$	−4.71972	+	8.17479i	−0.324919	+	0.562776i	0.656577	+	0.754259i	$0.272004\pi$
$212$	3.40373	−	5.89543i	0.233769	−	0.404900i
$213$	−5.58713	+	16.3669i	−0.382824	+	1.12144i
$214$	6.61191	+	6.61191i	0.451981	+	0.451981i
$215$	3.38020	−	0.905721i	0.230528	−	0.0617697i
$216$	−4.33523	+	2.86457i	−0.294975	+	0.194909i
$217$	7.57112	+	4.78918i	0.513961	+	0.325110i
$218$	−3.26197	+	5.64989i	−0.220928	+	0.382659i
$219$	16.7486	−	3.30166i	1.13176	−	0.223106i
$220$	−5.90003	−	3.40639i	−0.397780	−	0.229658i
$221$	0.474431	+	1.18572i	0.0319137	+	0.0797602i
$222$	9.00089	+	0.605447i	0.604100	+	0.0406349i
$223$	1.64939	−	0.441951i	0.110451	−	0.0295953i	−0.203170	−	0.979143i	$-0.565124\pi$
$223$	1.64939	−	0.441951i	0.110451	−	0.0295953i	0.313621	+	0.949548i	$0.398458\pi$
$224$	2.64359	+	0.106905i	0.176632	+	0.00714291i
$225$	8.49282	+	6.56315i	0.566188	+	0.437544i
$226$	−2.24742	+	8.38748i	−0.149496	+	0.557927i
$227$	18.6501	−	18.6501i	1.23785	−	1.23785i	0.276976	−	0.960877i	$-0.410668\pi$
$227$	18.6501	−	18.6501i	1.23785	−	1.23785i	0.960877	−	0.276976i	$-0.0893321\pi$
$228$	−13.4103	+	2.64359i	−0.888119	+	0.175076i
$229$	14.1059	+	3.77967i	0.932145	+	0.249767i	0.692769	−	0.721160i	$-0.256391\pi$
$229$	14.1059	+	3.77967i	0.932145	+	0.249767i	0.239376	+	0.970927i	$0.423057\pi$
$230$	3.27863	−	1.89292i	0.216186	−	0.124815i
$231$	10.5793	+	23.9457i	0.696068	+	1.57551i
$232$	0.550594	+	2.05484i	0.0361482	+	0.134907i
$233$	−8.66736	−	15.0123i	−0.567818	−	0.983489i	−0.996781	−	0.0801674i	$-0.974454\pi$
$233$	−8.66736	−	15.0123i	−0.567818	−	0.983489i	0.428964	−	0.903322i	$-0.358879\pi$
$234$	9.28245	+	5.55303i	0.606813	+	0.363013i
$235$	2.25241	−	3.90128i	0.146931	−	0.254492i
$236$	−6.57515	+	6.57515i	−0.428006	+	0.428006i
$237$	11.9277	−	5.85671i	0.774790	−	0.380434i
$238$	−0.936380	−	0.0378667i	−0.0606965	−	0.00245453i
$239$	−13.3221	+	13.3221i	−0.861737	+	0.861737i	−0.991540	−	0.129803i	$-0.958566\pi$
$239$	−13.3221	+	13.3221i	−0.861737	+	0.861737i	0.129803	+	0.991540i	$0.458566\pi$
$240$	0.667320	−	1.95484i	0.0430753	−	0.126185i
$241$	−11.8279	+	11.8279i	−0.761905	+	0.761905i	−0.976666	−	0.214762i	$-0.931102\pi$
$241$	−11.8279	+	11.8279i	−0.761905	+	0.761905i	0.214762	+	0.976666i	$0.431102\pi$
$242$	20.8971	−	5.59935i	1.34331	−	0.359940i
$243$	5.13708	−	14.7177i	0.329544	−	0.944140i
$244$	3.92578	+	2.26655i	0.251322	+	0.145101i
$245$	2.80469	−	7.86281i	0.179185	−	0.502336i
$246$	−2.75843	+	4.11300i	−0.175871	+	0.262236i
$247$	17.0470	+	22.7810i	1.08467	+	1.44952i
$248$	2.93242	+	1.69303i	0.186209	+	0.107508i
$249$	−1.28411	−	1.46932i	−0.0813769	−	0.0931141i
$250$	−10.2297			−0.646980
$251$	8.46027	+	14.6536i	0.534008	+	0.924928i	0.999211	+	0.0397242i	$0.0126479\pi$
$251$	8.46027	+	14.6536i	0.534008	+	0.924928i	−0.465203	+	0.885204i	$0.654019\pi$
$252$	−6.50279	+	4.55124i	−0.409637	+	0.286701i
$253$	−4.69362	+	17.5168i	−0.295085	+	1.10127i
$254$	15.8481	−	4.24648i	0.994397	−	0.266448i
$255$	−0.236370	+	0.692421i	−0.0148020	+	0.0433611i
$256$	1.00000			0.0625000
$257$	−26.1963			−1.63408			−0.817039	−	0.576583i	$-0.804386\pi$
$257$	−26.1963			−1.63408			−0.817039	+	0.576583i	$0.804386\pi$
$258$	−4.80990	−	1.64194i	−0.299451	−	0.102223i
$259$	13.7689	+	0.556806i	0.855558	+	0.0345983i
$260$	−4.26959	+	0.509675i	−0.264789	+	0.0316087i
$261$	−5.04982	−	3.90245i	−0.312576	−	0.241555i
$262$	−2.62922	+	9.81238i	−0.162434	+	0.606211i
$263$	−3.29203	+	1.90066i	−0.202995	+	0.117199i	−0.598052	−	0.801457i	$-0.704058\pi$
$263$	−3.29203	+	1.90066i	−0.202995	+	0.117199i	0.395056	+	0.918657i	$0.370725\pi$
$264$	4.36104	+	8.88167i	0.268404	+	0.546629i
$265$	−5.74060	−	5.74060i	−0.352642	−	0.352642i
$266$	−20.3693	+	4.58453i	−1.24892	+	0.281096i
$267$	22.0560	−	19.2758i	1.34980	−	1.17966i
$268$	1.69703	+	0.454718i	0.103663	+	0.0277763i
$269$		−	13.3821i		−	0.815920i	−0.913000	−	0.407960i	$-0.866240\pi$
$269$		−	13.3821i		−	0.815920i	0.913000	−	0.407960i	$-0.133760\pi$
$270$	1.96170	+	5.87812i	0.119385	+	0.357731i
$271$	−18.6235	+	18.6235i	−1.13130	+	1.13130i	−0.141337	+	0.989962i	$0.545140\pi$
$271$	−18.6235	+	18.6235i	−1.13130	+	1.13130i	−0.989962	+	0.141337i	$0.954860\pi$
$272$	−0.354208			−0.0214770
$273$	14.4010	+	8.10015i	0.871585	+	0.490244i
$274$	5.58025			0.337115
$275$	14.4521	−	14.4521i	0.871497	−	0.871497i
$276$	−5.48599	−	0.369016i	−0.330218	−	0.0222122i
$277$		−	11.3468i		−	0.681761i	−0.940107	−	0.340881i	$-0.889275\pi$
$277$		−	11.3468i		−	0.681761i	0.940107	−	0.340881i	$-0.110725\pi$
$278$	−0.251966	−	0.0675140i	−0.0151119	−	0.00404922i
$279$	−10.0758	+	1.29137i	−0.603221	+	0.0773126i
$280$	0.939125	−	3.01227i	0.0561235	−	0.180017i
$281$	22.2733	+	22.2733i	1.32871	+	1.32871i	0.906495	+	0.422216i	$0.138748\pi$
$281$	22.2733	+	22.2733i	1.32871	+	1.32871i	0.422216	+	0.906495i	$0.361252\pi$
$282$	−5.87283	+	2.88365i	−0.349722	+	0.171719i
$283$	−7.36826	+	4.25406i	−0.437997	+	0.252878i	−0.702748	−	0.711439i	$-0.748044\pi$
$283$	−7.36826	+	4.25406i	−0.437997	+	0.252878i	0.264750	+	0.964317i	$0.414710\pi$
$284$	−2.58427	+	9.64463i	−0.153348	+	0.572304i
$285$	−1.09399	+	16.2639i	−0.0648026	+	0.963389i
$286$	12.7354	−	16.1881i	0.753060	−	0.957222i
$287$	−4.04405	+	6.39316i	−0.238712	+	0.377376i
$288$	−2.38631	+	1.81811i	−0.140614	+	0.107133i
$289$	−16.8745			−0.992620
$290$	2.53701			0.148978
$291$	15.5665	+	5.31390i	0.912526	+	0.311506i
$292$	9.52006	−	2.55089i	0.557120	−	0.149280i
$293$	4.14076	−	15.4535i	0.241906	−	0.902805i	−0.733008	−	0.680220i	$-0.761884\pi$
$293$	4.14076	−	15.4535i	0.241906	−	0.902805i	0.974913	−	0.222584i	$-0.0714493\pi$
$294$	−9.74369	+	7.21529i	−0.568264	+	0.420805i
$295$	5.54470	+	9.60370i	0.322825	+	0.559149i
$296$	5.20841			0.302733
$297$	−26.5547	−	13.2655i	−1.54086	−	0.769743i
$298$	−3.47101	−	2.00399i	−0.201070	−	0.116088i
$299$	4.25197	+	10.6267i	0.245898	+	0.614559i
$300$	5.14659	+	3.45161i	0.297138	+	0.199279i
$301$	−7.41169	−	2.31072i	−0.427203	−	0.133188i
$302$	15.1308	+	8.73576i	0.870679	+	0.502687i
$303$	−21.8757	+	10.7413i	−1.25673	+	0.617073i
$304$	−7.62256	+	2.04246i	−0.437184	+	0.117143i
$305$	3.82267	−	3.82267i	0.218886	−	0.218886i
$306$	0.845248	−	0.643990i	0.0483196	−	0.0368144i
$307$	6.63650	−	6.63650i	0.378765	−	0.378765i	−0.491891	−	0.870657i	$-0.663694\pi$
$307$	6.63650	−	6.63650i	0.378765	−	0.378765i	0.870657	+	0.491891i	$0.163694\pi$
$308$	7.02205	+	13.3840i	0.400118	+	0.762622i
$309$	3.85970	+	7.86064i	0.219571	+	0.447176i
$310$	2.85540	−	2.85540i	0.162176	−	0.162176i
$311$	−2.61000	+	4.52065i	−0.148000	+	0.256343i	−0.930488	−	0.366322i	$-0.880617\pi$
$311$	−2.61000	+	4.52065i	−0.148000	+	0.256343i	0.782488	+	0.622665i	$0.213950\pi$
$312$	5.56231	+	2.83914i	0.314904	+	0.160734i
$313$	−7.22572	−	12.5153i	−0.408422	−	0.707407i	0.586291	−	0.810100i	$-0.300587\pi$
$313$	−7.22572	−	12.5153i	−0.408422	−	0.707407i	−0.994713	+	0.102693i	$0.967254\pi$
$314$	−0.732954	−	2.73542i	−0.0413630	−	0.154369i
$315$	3.23560	+	8.89563i	0.182306	+	0.501212i
$316$	6.64402	−	3.83593i	0.373755	−	0.215788i
$317$	−16.3525	−	4.38163i	−0.918447	−	0.246097i	−0.231525	−	0.972829i	$-0.574372\pi$
$317$	−16.3525	−	4.38163i	−0.918447	−	0.246097i	−0.686921	+	0.726732i	$0.741038\pi$
$318$	2.28046	+	11.5682i	0.127882	+	0.648714i
$319$	−8.59323	+	8.59323i	−0.481129	+	0.481129i
$320$	0.308662	−	1.15194i	0.0172547	−	0.0643956i
$321$	−16.1593	−	1.08696i	−0.901924	−	0.0606681i
$322$	−8.39207	−	0.339370i	−0.467672	−	0.0189124i
$323$	2.69997	−	0.723454i	0.150230	−	0.0402541i
$324$	2.38892	−	8.67716i	0.132718	−	0.482064i
$325$	1.83824	−	12.7681i	0.101967	−	0.708249i
$326$	19.5893	+	11.3099i	1.08495	+	0.626396i
$327$	−2.18548	−	11.0864i	−0.120857	−	0.613081i
$328$	−1.42962	+	2.47617i	−0.0789375	+	0.136724i
$329$	−8.84988	+	4.64319i	−0.487910	+	0.255987i
$330$	11.5773	−	2.28224i	0.637307	−	0.125633i
$331$	12.4023	−	3.32319i	0.681692	−	0.182659i	0.0986762	−	0.995120i	$-0.468539\pi$
$331$	12.4023	−	3.32319i	0.681692	−	0.182659i	0.583016	+	0.812461i	$0.301873\pi$
$332$	−0.796640	−	0.796640i	−0.0437213	−	0.0437213i
$333$	−12.4289	+	9.46948i	−0.681098	+	0.518924i
$334$	−1.62805	+	2.81987i	−0.0890830	+	0.154296i
$335$	1.04762	−	1.81453i	0.0572375	−	0.0991383i
$336$	−3.56957	+	2.87371i	−0.194736	+	0.156773i
$337$			11.2966i			0.615366i	0.951489	+	0.307683i	$0.0995537\pi$
$337$			11.2966i			0.615366i	−0.951489	+	0.307683i	$0.900446\pi$
$338$	0.314276	−	12.9962i	0.0170944	−	0.706900i
$339$	−6.62890	−	13.5004i	−0.360032	−	0.733239i
$340$	−0.109330	+	0.408027i	−0.00592928	+	0.0221284i
$341$			19.3434i			1.04750i
$342$	14.4763	−	18.7326i	0.782791	−	1.01294i
$343$	−14.5837	+	11.4156i	−0.787443	+	0.616387i
$344$	−2.83436	−	0.759464i	−0.152818	−	0.0409476i
$345$	−2.11840	+	6.20565i	−0.114051	+	0.334101i
$346$	2.58098	+	9.63234i	0.138754	+	0.517838i
$347$		−	23.8503i		−	1.28035i	−0.768228	−	0.640177i	$-0.778861\pi$
$347$		−	23.8503i		−	1.28035i	0.768228	−	0.640177i	$-0.221139\pi$
$348$	−3.06016	−	2.05233i	−0.164042	−	0.110016i
$349$	−7.34912	−	27.4273i	−0.393389	−	1.46815i	−0.824506	−	0.565853i	$-0.808547\pi$
$349$	−7.34912	−	27.4273i	−0.393389	−	1.46815i	0.431117	−	0.902296i	$-0.358120\pi$
$350$	7.99973	+	5.06030i	0.427604	+	0.270484i
$351$	−18.4353	+	3.33786i	−0.984001	+	0.178162i
$352$	2.85632	+	4.94729i	0.152242	+	0.263691i
$353$	31.0370	+	8.31634i	1.65193	+	0.442634i	0.960153	−	0.279474i	$-0.0901601\pi$
$353$	31.0370	+	8.31634i	1.65193	+	0.442634i	0.691780	+	0.722108i	$0.256827\pi$
$354$	1.08091	−	16.0694i	0.0574500	−	0.854082i
$355$	10.3124	+	5.95387i	0.547325	+	0.315998i
$356$	11.9584	−	11.9584i	0.633795	−	0.633795i
$357$	1.26437	−	1.01789i	0.0669175	−	0.0538724i
$358$	−12.6807	−	3.39779i	−0.670198	−	0.179579i
$359$	6.42391	−	23.9744i	0.339041	−	1.26532i	−0.560380	−	0.828235i	$-0.689345\pi$
$359$	6.42391	−	23.9744i	0.339041	−	1.26532i	0.899421	−	0.437083i	$-0.143988\pi$
$360$	1.35780	+	3.31007i	0.0715624	+	0.174456i
$361$	37.4772	−	21.6375i	1.97249	−	1.13882i
$362$	−14.7060	−	14.7060i	−0.772930	−	0.772930i
$363$	−20.8715	+	31.1207i	−1.09547	+	1.63342i
$364$	8.60951	+	4.10807i	0.451261	+	0.215322i
$365$		−	11.7539i		−	0.615229i
$366$	−7.70331	+	1.51856i	−0.402658	+	0.0793764i
$367$	−5.26269	−	9.11525i	−0.274710	−	0.475812i	0.695352	−	0.718670i	$-0.255249\pi$
$367$	−5.26269	−	9.11525i	−0.274710	−	0.475812i	−0.970062	+	0.242858i	$0.921915\pi$
$368$	−3.17450			−0.165482
$369$	−1.09045	−	8.50812i	−0.0567668	−	0.442915i
$370$	1.60764	−	5.99979i	0.0835772	−	0.311914i
$371$	3.95479	+	17.5713i	0.205322	+	0.912256i
$372$	−5.75410	+	1.13431i	−0.298336	+	0.0588113i
$373$	15.6167	−	27.0489i	0.808602	−	1.40054i	−0.105230	−	0.994448i	$-0.533558\pi$
$373$	15.6167	−	27.0489i	0.808602	−	1.40054i	0.913832	−	0.406092i	$-0.133109\pi$
$374$	−1.01173	−	1.75237i	−0.0523153	−	0.0906128i
$375$	13.3413	−	11.6596i	0.688942	−	0.602100i
$376$	−3.27130	+	1.88868i	−0.168704	+	0.0974015i
$377$	−1.09302	+	7.59192i	−0.0562932	+	0.391004i
$378$	3.29336	−	13.3474i	0.169392	−	0.686517i
$379$	13.9432	−	3.73606i	0.716212	−	0.191908i	0.117731	−	0.993046i	$-0.462438\pi$
$379$	13.9432	−	3.73606i	0.716212	−	0.191908i	0.598481	+	0.801137i	$0.295771\pi$
$380$			9.41118i			0.482783i
$381$	−15.8287	+	23.6016i	−0.810928	+	1.20915i
$382$	−9.01416	+	2.41534i	−0.461205	+	0.123579i
$383$	−4.85640	−	18.1243i	−0.248150	−	0.926110i	−0.971774	−	0.235915i	$-0.924191\pi$
$383$	−4.85640	−	18.1243i	−0.248150	−	0.926110i	0.723623	−	0.690195i	$-0.242475\pi$
$384$	−1.30418	+	1.13979i	−0.0665537	+	0.0581645i
$385$	17.5850	−	3.95787i	0.896215	−	0.201712i
$386$	−1.11135	+	0.641641i	−0.0565665	+	0.0326587i
$387$	8.14444	−	3.34087i	0.414005	−	0.169826i
$388$	9.17298	+	2.45789i	0.465687	+	0.124781i
$389$	−15.2716	+	26.4512i	−0.774302	+	1.34113i	0.160884	+	0.986973i	$0.448566\pi$
$389$	−15.2716	+	26.4512i	−0.774302	+	1.34113i	−0.935186	+	0.354157i	$0.884768\pi$
$390$	4.98740	−	5.53113i	0.252547	−	0.280080i
$391$	1.12443			0.0568649
$392$	−5.33326	+	4.53391i	−0.269370	+	0.228997i
$393$	−7.75504	−	15.7939i	−0.391190	−	0.796695i
$394$	21.6239	+	12.4846i	1.08940	+	0.628964i
$395$	−2.36801	−	8.83753i	−0.119148	−	0.444665i
$396$	−15.8108	−	6.61264i	−0.794522	−	0.332298i
$397$	−5.39334	−	20.1282i	−0.270684	−	1.01021i	−0.958679	−	0.284491i	$-0.908175\pi$
$397$	−5.39334	−	20.1282i	−0.270684	−	1.01021i	0.687995	−	0.725716i	$-0.258491\pi$
$398$	16.7063	+	16.7063i	0.837411	+	0.837411i
$399$	21.3398	−	29.1957i	1.06833	−	1.46161i
$400$	3.09843	+	1.78888i	0.154921	+	0.0894439i
$401$	8.66659	+	8.66659i	0.432789	+	0.432789i	0.889576	−	0.456787i	$-0.151000\pi$
$401$	8.66659	+	8.66659i	0.432789	+	0.432789i	−0.456787	+	0.889576i	$0.651000\pi$
$402$	−2.73152	+	1.34122i	−0.136236	+	0.0668939i
$403$	7.31452	+	9.77489i	0.364362	+	0.486922i
$404$	−12.1853	+	7.03517i	−0.606240	+	0.350013i
$405$	−9.25822	−	5.43021i	−0.460045	−	0.269829i
$406$	−4.75663	−	3.00885i	−0.236068	−	0.149327i
$407$	14.8769	+	25.7675i	0.737419	+	1.27725i
$408$	0.461951	−	0.403721i	0.0228700	−	0.0199872i
$409$	22.1902	+	22.1902i	1.09723	+	1.09723i	0.994733	+	0.102499i	$0.0326840\pi$
$409$	22.1902	+	22.1902i	1.09723	+	1.09723i	0.102499	+	0.994733i	$0.467316\pi$
$410$	2.41114	+	2.41114i	0.119078	+	0.119078i
$411$	−7.27766	+	6.36030i	−0.358980	+	0.313730i
$412$	2.52796	+	4.37855i	0.124544	+	0.215716i
$413$	0.994077	−	24.5819i	0.0489153	−	1.20959i
$414$	7.57532	−	5.77159i	0.372307	−	0.283658i
$415$	−1.16358	+	0.671792i	−0.0571178	+	0.0329769i
$416$	3.31417	+	1.41995i	0.162491	+	0.0696189i
$417$	0.405560	−	0.199137i	0.0198604	−	0.00975176i
$418$	−31.8771	−	31.8771i	−1.55916	−	1.55916i
$419$	3.67573	+	2.12218i	0.179571	+	0.103675i	0.587091	−	0.809521i	$-0.300273\pi$
$419$	3.67573	+	2.12218i	0.179571	+	0.103675i	−0.407520	+	0.913196i	$0.633606\pi$
$420$	2.20855	+	4.99894i	0.107766	+	0.243923i
$421$	11.4058	+	11.4058i	0.555885	+	0.555885i	0.928133	−	0.372248i	$-0.121413\pi$
$421$	11.4058	+	11.4058i	0.555885	+	0.555885i	−0.372248	+	0.928133i	$0.621413\pi$
$422$	−2.44311	−	9.11779i	−0.118929	−	0.443847i
$423$	4.37248	−	10.4546i	0.212597	−	0.508319i
$424$	1.76190	+	6.57550i	0.0855654	+	0.319335i
$425$	−1.09749	−	0.633634i	−0.0532359	−	0.0307358i
$426$	−7.62247	−	15.5239i	−0.369310	−	0.752133i
$427$	−11.7008	+	2.63350i	−0.566239	+	0.127444i
$428$	−9.35066			−0.451981
$429$	1.84171	+	35.6278i	0.0889185	+	1.72013i
$430$	−1.74972	+	3.03060i	−0.0843789	+	0.146149i
$431$	−38.4395	−	10.2998i	−1.85157	−	0.496126i	−0.851945	−	0.523631i	$-0.824577\pi$
$431$	−38.4395	−	10.2998i	−1.85157	−	0.496126i	−0.999622	+	0.0275053i	$0.991244\pi$
$432$	1.03991	−	5.09103i	0.0500329	−	0.244942i
$433$	−6.81696	+	3.93577i	−0.327602	+	0.189141i	−0.654776	−	0.755823i	$-0.727237\pi$
$433$	−6.81696	+	3.93577i	−0.327602	+	0.189141i	0.327174	+	0.944964i	$0.393904\pi$
$434$	−8.74005	+	1.96713i	−0.419536	+	0.0944253i
$435$	−3.30872	+	2.89165i	−0.158641	+	0.138644i
$436$	−1.68852	−	6.30163i	−0.0808653	−	0.301794i
$437$	24.1978	−	6.48377i	1.15754	−	0.310161i
$438$	−9.50841	+	14.1777i	−0.454329	+	0.677435i
$439$		−	6.46351i		−	0.308487i	−0.988033	−	0.154243i	$-0.950706\pi$
$439$		−	6.46351i		−	0.308487i	0.988033	−	0.154243i	$-0.0492940\pi$
$440$	6.58063	−	1.76328i	0.313719	−	0.0840608i
$441$	4.48364	−	20.5158i	0.213507	−	0.976942i
$442$	−1.17391	−	0.502958i	−0.0558370	−	0.0239233i
$443$	12.6734	−	7.31696i	0.602129	−	0.347639i	−0.167750	−	0.985830i	$-0.553650\pi$
$443$	12.6734	−	7.31696i	0.602129	−	0.347639i	0.769879	+	0.638190i	$0.220317\pi$
$444$	−6.79271	+	5.93647i	−0.322368	+	0.281733i
$445$	−10.0843	−	17.4665i	−0.478042	−	0.827993i
$446$	−0.853785	+	1.47880i	−0.0404279	+	0.0700231i
$447$	6.81094	−	1.34265i	0.322147	−	0.0635051i
$448$	−1.94489	+	1.79371i	−0.0918876	+	0.0847447i
$449$	7.90982	−	29.5198i	0.373287	−	1.39313i	−0.482544	−	0.875872i	$-0.660287\pi$
$449$	7.90982	−	29.5198i	0.373287	−	1.39313i	0.855831	−	0.517255i	$-0.173046\pi$
$450$	−10.6462	+	1.36448i	−0.501866	+	0.0643223i
$451$	−16.3338			−0.769129
$452$	−4.34168	−	7.52001i	−0.204215	−	0.353712i
$453$	−29.6902	+	5.85285i	−1.39497	+	0.274991i
$454$			26.3753i			1.23785i
$455$	7.38970	−	8.64966i	0.346434	−	0.405502i
$456$	7.61322	−	11.3518i	0.356522	−	0.531598i
$457$	26.1800	+	26.1800i	1.22465	+	1.22465i	0.965961	+	0.258689i	$0.0832905\pi$
$457$	26.1800	+	26.1800i	1.22465	+	1.22465i	0.258689	+	0.965961i	$0.416710\pi$
$458$	−12.6470	+	7.30176i	−0.590956	+	0.341189i
$459$	−0.368345	+	1.80328i	−0.0171929	+	0.0841700i
$460$	−0.979847	+	3.65684i	−0.0456856	+	0.170501i
$461$	4.81513	+	1.29021i	0.224263	+	0.0600911i	0.369201	−	0.929350i	$-0.379632\pi$
$461$	4.81513	+	1.29021i	0.224263	+	0.0600911i	−0.144938	+	0.989441i	$0.546298\pi$
$462$	−24.4129	−	9.45147i	−1.13579	−	0.439722i
$463$	24.2773	−	24.2773i	1.12826	−	1.12826i	0.137804	−	0.990460i	$-0.455996\pi$
$463$	24.2773	−	24.2773i	1.12826	−	1.12826i	0.990460	−	0.137804i	$-0.0440044\pi$
$464$	−1.84232	−	1.06367i	−0.0855277	−	0.0493794i
$465$	−0.469411	+	6.97851i	−0.0217684	+	0.323621i
$466$	16.7441	+	4.48656i	0.775653	+	0.207836i
$467$	−9.10311	−	15.7671i	−0.421242	−	0.729612i	0.574819	−	0.818280i	$-0.305072\pi$
$467$	−9.10311	−	15.7671i	−0.421242	−	0.729612i	−0.996061	+	0.0886680i	$0.971739\pi$
$468$	−10.4903	+	2.63710i	−0.484913	+	0.121900i
$469$	−4.11618	+	2.15960i	−0.190068	+	0.0997210i
$470$	1.16593	+	4.35131i	0.0537804	+	0.200711i
$471$	4.07370	+	2.73207i	0.187706	+	0.125887i
$472$		−	9.29867i		−	0.428006i
$473$	−4.33854	−	16.1917i	−0.199486	−	0.744494i
$474$	−4.29286	+	12.5755i	−0.197178	+	0.577612i
$475$	−27.2716	−	7.30741i	−1.25131	−	0.335287i
$476$	0.688896	−	0.635345i	0.0315755	−	0.0291210i
$477$	−16.1594	−	12.4878i	−0.739890	−	0.571778i
$478$		−	18.8403i		−	0.861737i
$479$	−4.43302	+	16.5443i	−0.202550	+	0.755926i	0.787633	+	0.616145i	$0.211307\pi$
$479$	−4.43302	+	16.5443i	−0.202550	+	0.755926i	−0.990182	+	0.139781i	$0.955360\pi$
$480$	0.910418	+	1.85415i	0.0415547	+	0.0846300i
$481$	17.2616	+	7.39569i	0.787060	+	0.337214i
$482$		−	16.7272i		−	0.761905i
$483$	11.3316	−	9.12256i	0.515605	−	0.415091i
$484$	−10.8171	+	18.7358i	−0.491687	+	0.851627i
$485$	5.66270	−	9.80809i	0.257130	−	0.445362i
$486$	6.77452	+	14.0394i	0.307298	+	0.636842i
$487$	−21.2104	−	21.2104i	−0.961134	−	0.961134i	0.0381382	−	0.999272i	$-0.487857\pi$
$487$	−21.2104	−	21.2104i	−0.961134	−	0.961134i	−0.999272	+	0.0381382i	$0.987857\pi$
$488$	−4.37864	+	1.17325i	−0.198212	+	0.0531106i
$489$	−38.4388	+	7.57747i	−1.73826	+	0.342665i
$490$	3.57663	+	7.54306i	0.161576	+	0.340761i
$491$	19.1661	−	33.1966i	0.864952	−	1.49814i	−0.00214208	−	0.999998i	$-0.500682\pi$
$491$	19.1661	−	33.1966i	0.864952	−	1.49814i	0.867094	−	0.498144i	$-0.165985\pi$
$492$	−0.957828	−	4.85884i	−0.0431822	−	0.219053i
$493$	0.652565	+	0.376758i	0.0293900	+	0.0169683i
$494$	−28.1627	−	4.05460i	−1.26710	−	0.182425i
$495$	−12.4976	+	16.1721i	−0.561724	+	0.726880i
$496$	−3.27069	+	0.876378i	−0.146858	+	0.0393505i
$497$	−12.2735	−	23.3932i	−0.550542	−	1.04933i
$498$	1.94696	+	0.130963i	0.0872455	+	0.00586859i
$499$	−1.94052	+	7.24212i	−0.0868696	+	0.324202i	−0.995662	−	0.0930475i	$-0.970339\pi$
$499$	−1.94052	+	7.24212i	−0.0868696	+	0.324202i	0.908792	+	0.417249i	$0.137006\pi$
$500$	7.23346	−	7.23346i	0.323490	−	0.323490i
$501$	−1.09077	−	5.53324i	−0.0487322	−	0.247207i
$502$	−16.3440	−	4.37936i	−0.729468	−	0.195460i
$503$	15.8920	−	9.17526i	0.708590	−	0.409105i	−0.101949	−	0.994790i	$-0.532508\pi$
$503$	15.8920	−	9.17526i	0.708590	−	0.409105i	0.810539	+	0.585685i	$0.199174\pi$
$504$	1.37995	−	7.81638i	0.0614679	−	0.348169i
$505$	4.34298	+	16.2082i	0.193260	+	0.721257i
$506$	−9.06737	−	15.7051i	−0.403094	−	0.698179i
$507$	14.4030	+	17.3076i	0.639661	+	0.768657i
$508$	−8.20357	+	14.2090i	−0.363975	+	0.630422i
$509$	16.2428	−	16.2428i	0.719950	−	0.719950i	−0.248645	−	0.968595i	$-0.579985\pi$
$509$	16.2428	−	16.2428i	0.719950	−	0.719950i	0.968595	+	0.248645i	$0.0799853\pi$
$510$	−0.322477	−	0.656754i	−0.0142795	−	0.0290816i
$511$	−13.9400	+	22.0374i	−0.616667	+	0.974878i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	2.47141	+	40.9306i	0.109116	+	1.80713i
$514$	18.5235	−	18.5235i	0.817039	−	0.817039i
$515$	5.82413	−	1.56057i	0.256642	−	0.0687669i
$516$	4.56214	−	2.24009i	0.200837	−	0.0986143i
$517$	−18.6877	−	10.7894i	−0.821886	−	0.474516i
$518$	−10.1298	+	9.34236i	−0.445078	+	0.410480i
$519$	−14.3449	−	9.62054i	−0.629670	−	0.422295i
$520$	2.65866	−	3.37945i	0.116590	−	0.148199i
$521$	20.2233	+	11.6759i	0.885999	+	0.511532i	0.872632	−	0.488379i	$-0.162412\pi$
$521$	20.2233	+	11.6759i	0.885999	+	0.511532i	0.0133675	+	0.999911i	$0.495745\pi$
$522$	6.33021	−	0.811320i	0.277066	−	0.0355105i
$523$	37.5961			1.64396			0.821980	−	0.569516i	$-0.192869\pi$
$523$	37.5961			1.64396			0.821980	+	0.569516i	$0.192869\pi$
$524$	−5.07926	−	8.79754i	−0.221889	−	0.384322i
$525$	−16.2008	+	2.51844i	−0.707059	+	0.109914i
$526$	0.983852	−	3.67179i	0.0428980	−	0.160097i
$527$	1.15850	−	0.310420i	0.0504652	−	0.0135221i
$528$	−9.36401	−	3.19656i	−0.407516	−	0.139113i
$529$	−12.9226			−0.561851
$530$	8.11843			0.352642
$531$	16.9060	+	22.1895i	0.733659	+	0.962941i
$532$	11.1615	−	17.6450i	0.483912	−	0.765008i
$533$	−8.25405	+	6.17648i	−0.357523	+	0.267533i
$534$	−1.96589	+	29.2260i	−0.0850724	+	1.26473i
$535$	−2.88619	+	10.7714i	−0.124781	+	0.465689i
$536$	−1.52152	+	0.878448i	−0.0657195	+	0.0379432i
$537$	20.4107	−	10.0220i	0.880788	−	0.432481i
$538$	9.46256	+	9.46256i	0.407960	+	0.407960i
$539$	−37.6640	−	13.4349i	−1.62231	−	0.578682i
$540$	−5.54359	−	2.76933i	−0.238558	−	0.119173i
$541$	1.45261	+	0.389226i	0.0624526	+	0.0167341i	0.289910	−	0.957054i	$-0.406375\pi$
$541$	1.45261	+	0.389226i	0.0624526	+	0.0167341i	−0.227457	+	0.973788i	$0.573041\pi$
$542$		−	26.3376i		−	1.13130i
$543$	35.9410	+	2.41758i	1.54237	+	0.103748i
$544$	0.250463	−	0.250463i	0.0107385	−	0.0107385i
$545$	−7.78030			−0.333272
$546$	−15.9107	+	4.45534i	−0.680915	+	0.190671i
$547$	−31.1734			−1.33288			−0.666439	−	0.745559i	$-0.732183\pi$
$547$	−31.1734			−1.33288			−0.666439	+	0.745559i	$0.732183\pi$
$548$	−3.94584	+	3.94584i	−0.168558	+	0.168558i
$549$	8.31567	−	10.7606i	0.354904	−	0.459251i
$550$			20.4384i			0.871497i
$551$	16.2157	+	4.34498i	0.690812	+	0.185102i
$552$	4.14011	−	3.61825i	0.176215	−	0.154003i
$553$	−6.04138	+	19.3779i	−0.256906	+	0.824032i
$554$	8.02338	+	8.02338i	0.340881	+	0.340881i
$555$	4.74183	+	9.65717i	0.201279	+	0.409924i
$556$	0.225906	−	0.130427i	0.00958056	−	0.00553134i
$557$	−5.34928	+	19.9638i	−0.226656	+	0.845892i	0.755078	+	0.655635i	$0.227599\pi$
$557$	−5.34928	+	19.9638i	−0.226656	+	0.845892i	−0.981734	+	0.190257i	$0.939068\pi$
$558$	6.21151	−	8.03779i	0.262954	−	0.340267i
$559$	−8.31515	−	6.54165i	−0.351693	−	0.276682i
$560$	1.46593	+	2.79406i	0.0619470	+	0.118070i
$561$	3.31680	+	1.13225i	0.140036	+	0.0478035i
$562$	−31.4992			−1.32871
$563$	−3.26523			−0.137613			−0.0688065	−	0.997630i	$-0.521919\pi$
$563$	−3.26523			−0.137613			−0.0688065	+	0.997630i	$0.521919\pi$
$564$	2.11367	−	6.19177i	0.0890014	−	0.260720i
$565$	−10.0027	+	2.68023i	−0.420818	+	0.112758i
$566$	2.20207	−	8.21822i	0.0925597	−	0.345438i
$567$	10.9181	+	21.1612i	0.458516	+	0.888686i
$568$	−4.99243	−	8.64714i	−0.209478	−	0.362826i
$569$	−13.3448			−0.559442			−0.279721	−	0.960081i	$-0.590242\pi$
$569$	−13.3448			−0.559442			−0.279721	+	0.960081i	$0.590242\pi$
$570$	−10.7267	−	12.2739i	−0.449293	−	0.514096i
$571$	−4.66115	−	2.69111i	−0.195063	−	0.112620i	0.399288	−	0.916826i	$-0.369257\pi$
$571$	−4.66115	−	2.69111i	−0.195063	−	0.112620i	−0.594351	+	0.804206i	$0.702591\pi$
$572$	2.44142	+	20.4520i	0.102081	+	0.855141i
$573$	9.00312	−	13.4243i	0.376111	−	0.560806i
$574$	−1.66107	−	7.38022i	−0.0693318	−	0.308044i
$575$	−9.83594	−	5.67878i	−0.410187	−	0.236822i
$576$	0.401773	−	2.97297i	0.0167406	−	0.123874i
$577$	6.78215	−	1.81727i	0.282345	−	0.0756540i	−0.114867	−	0.993381i	$-0.536644\pi$
$577$	6.78215	−	1.81727i	0.282345	−	0.0756540i	0.397212	+	0.917727i	$0.369978\pi$
$578$	11.9321	−	11.9321i	0.496310	−	0.496310i
$579$	0.718073	−	2.10352i	0.0298421	−	0.0874194i
$580$	−1.79394	+	1.79394i	−0.0744892	+	0.0744892i
$581$	2.97832	+	0.120442i	0.123562	+	0.00499676i
$582$	−14.7647	+	7.24970i	−0.612016	+	0.300510i
$583$	−27.4984	+	27.4984i	−1.13887	+	1.13887i
$584$	−4.92795	+	8.53545i	−0.203920	+	0.353200i
$585$	−0.200158	+	12.8982i	−0.00827550	+	0.533273i
$586$	7.99933	+	13.8553i	0.330449	+	0.572355i
$587$	6.01305	+	22.4410i	0.248185	+	0.926240i	0.971756	+	0.235989i	$0.0758330\pi$
$587$	6.01305	+	22.4410i	0.248185	+	0.926240i	−0.723570	+	0.690251i	$0.757500\pi$
$588$	1.78785	−	11.9918i	0.0737296	−	0.494534i
$589$	23.1410	−	13.3605i	0.953510	−	0.550509i
$590$	−10.7115	−	2.87015i	−0.440987	−	0.118162i
$591$	−42.4312	+	8.36451i	−1.74539	+	0.344070i
$592$	−3.68290	+	3.68290i	−0.151366	+	0.151366i
$593$	1.91496	−	7.14673i	0.0786380	−	0.293481i	−0.915396	−	0.402555i	$-0.868122\pi$
$593$	1.91496	−	7.14673i	0.0786380	−	0.293481i	0.994034	+	0.109075i	$0.0347887\pi$
$594$	28.1571	−	9.39685i	1.15530	−	0.385557i
$595$	−0.519245	−	0.989676i	−0.0212870	−	0.0405728i
$596$	3.87141	−	1.03734i	0.158579	−	0.0424911i
$597$	−40.8296	−	2.74641i	−1.67105	−	0.112403i
$598$	−10.5208	−	4.50763i	−0.430228	−	0.184331i
$599$	−16.0265	−	9.25291i	−0.654825	−	0.378064i	0.135477	−	0.990780i	$-0.456743\pi$
$599$	−16.0265	−	9.25291i	−0.654825	−	0.378064i	−0.790303	+	0.612717i	$0.790077\pi$
$600$	−6.07985	+	1.19853i	−0.248209	+	0.0489296i
$601$	15.9794	−	27.6771i	0.651812	−	1.12897i	−0.330871	−	0.943676i	$-0.607342\pi$
$601$	15.9794	−	27.6771i	0.651812	−	1.12897i	0.982683	−	0.185296i	$-0.0593242\pi$
$602$	6.87479	−	3.60693i	0.280195	−	0.147008i
$603$	2.03369	−	4.86254i	0.0828182	−	0.198018i
$604$	−16.8762	+	4.52196i	−0.686683	+	0.183996i
$605$	18.2437	+	18.2437i	0.741713	+	0.741713i
$606$	7.87320	−	23.0637i	0.319827	−	0.936900i
$607$	5.28558	−	9.15490i	0.214535	−	0.371586i	−0.738593	−	0.674151i	$-0.764510\pi$
$607$	5.28558	−	9.15490i	0.214535	−	0.371586i	0.953129	+	0.302565i	$0.0978430\pi$
$608$	3.94572	−	6.83420i	0.160020	−	0.277163i
$609$	9.63295	−	1.49747i	0.390347	−	0.0606803i
$610$			5.40608i			0.218886i
$611$	−13.5235	+	1.61434i	−0.547102	+	0.0653093i
$612$	−0.142311	+	1.05305i	−0.00575259	+	0.0425670i
$613$	−7.84149	+	29.2648i	−0.316715	+	1.18200i	0.605668	+	0.795718i	$0.292906\pi$
$613$	−7.84149	+	29.2648i	−0.316715	+	1.18200i	−0.922382	+	0.386278i	$0.873761\pi$
$614$			9.38543i			0.378765i
$615$	−5.89275	−	0.396377i	−0.237619	−	0.0159835i
$616$	−14.4292	−	4.49855i	−0.581370	−	0.181252i
$617$	7.29810	+	1.95552i	0.293811	+	0.0787263i	0.402714	−	0.915326i	$-0.368067\pi$
$617$	7.29810	+	1.95552i	0.293811	+	0.0787263i	−0.108903	+	0.994052i	$0.534734\pi$
$618$	−8.28753	−	2.82909i	−0.333373	−	0.113803i
$619$	−3.16181	−	11.8000i	−0.127084	−	0.474283i	0.872822	−	0.488039i	$-0.162288\pi$
$619$	−3.16181	−	11.8000i	−0.127084	−	0.474283i	−0.999905	+	0.0137563i	$0.995621\pi$
$620$			4.03815i			0.162176i
$621$	−3.30120	+	16.1614i	−0.132473	+	0.648537i
$622$	−1.35104	−	5.04213i	−0.0541716	−	0.202171i
$623$	−1.80796	+	44.7078i	−0.0724342	+	1.79118i
$624$	−5.94072	+	1.92558i	−0.237819	+	0.0770847i
$625$	2.84455	+	4.92691i	0.113782	+	0.197076i
$626$	13.9590	+	3.74031i	0.557914	+	0.149493i
$627$	77.9065	+	5.24040i	3.11129	+	0.209281i
$628$	2.45251	+	1.41596i	0.0978659	+	0.0565029i
$629$	1.30451	−	1.30451i	0.0520143	−	0.0520143i
$630$	−8.57808	−	4.00224i	−0.341759	−	0.159453i
$631$	−31.5550	−	8.45512i	−1.25618	−	0.336593i	−0.431461	−	0.902132i	$-0.642002\pi$
$631$	−31.5550	−	8.45512i	−1.25618	−	0.336593i	−0.824722	+	0.565538i	$0.808668\pi$
$632$	−1.98562	+	7.41044i	−0.0789838	+	0.294771i
$633$	13.5786	+	9.10663i	0.539700	+	0.361956i
$634$	14.6612	−	8.46467i	0.582272	−	0.336175i
$635$	13.8358	+	13.8358i	0.549058	+	0.549058i
$636$	−9.79250	−	6.56745i	−0.388298	−	0.260416i
$637$	−24.1133	+	7.45318i	−0.955403	+	0.295306i
$638$		−	12.1527i		−	0.481129i
$639$	27.6350	+	11.5579i	1.09322	+	0.457225i
$640$	0.596290	+	1.03280i	0.0235704	+	0.0408252i
$641$	−1.82154			−0.0719466			−0.0359733	−	0.999353i	$-0.511453\pi$
$641$	−1.82154			−0.0719466			−0.0359733	+	0.999353i	$0.511453\pi$
$642$	12.1949	−	10.6578i	0.481296	−	0.420628i
$643$	−2.58523	+	9.64823i	−0.101952	+	0.380489i	−0.997982	−	0.0635049i	$-0.979772\pi$
$643$	−2.58523	+	9.64823i	−0.101952	+	0.380489i	0.896030	+	0.443994i	$0.146439\pi$
$644$	6.17406	−	5.69412i	0.243292	−	0.224380i
$645$	−1.17229	−	5.94676i	−0.0461589	−	0.234153i
$646$	−1.39761	+	2.42072i	−0.0549881	+	0.0952421i
$647$	4.93136	+	8.54136i	0.193872	+	0.335795i	0.946530	−	0.322616i	$-0.104562\pi$
$647$	4.93136	+	8.54136i	0.193872	+	0.335795i	−0.752658	+	0.658411i	$0.771229\pi$
$648$	4.44645	+	7.82490i	0.174673	+	0.307391i
$649$	46.0032	−	26.5600i	1.80578	−	1.04257i
$650$	7.72860	+	10.3283i	0.303141	+	0.405108i
$651$	9.15649	−	12.5273i	0.358871	−	0.490983i
$652$	−21.8490	+	5.85442i	−0.855672	+	0.229277i
$653$			3.06238i			0.119840i	0.998203	+	0.0599200i	$0.0190846\pi$
$653$			3.06238i			0.119840i	−0.998203	+	0.0599200i	$0.980915\pi$
$654$	9.38465	+	6.29392i	0.366969	+	0.246112i
$655$	−11.7020	+	3.13555i	−0.457237	+	0.122516i
$656$	−0.740026	−	2.76181i	−0.0288931	−	0.107831i
$657$	−3.75883	−	29.3278i	−0.146646	−	1.14419i
$658$	2.97458	−	9.54104i	0.115961	−	0.371949i
$659$	−28.9800	+	16.7316i	−1.12890	+	0.651771i	−0.943658	−	0.330921i	$-0.892641\pi$
$659$	−28.9800	+	16.7316i	−1.12890	+	0.651771i	−0.185243	+	0.982693i	$0.559307\pi$
$660$	−6.57257	+	9.80014i	−0.255837	+	0.381470i
$661$	47.6811	+	12.7761i	1.85458	+	0.496933i	0.999758	−	0.0219918i	$-0.00700077\pi$
$661$	47.6811	+	12.7761i	1.85458	+	0.496933i	0.854820	+	0.518925i	$0.173667\pi$
$662$	−6.41990	+	11.1196i	−0.249517	+	0.432176i
$663$	2.10425	−	0.682054i	0.0817222	−	0.0264888i
$664$	1.12662			0.0437213
$665$	−16.8809	−	18.3037i	−0.654613	−	0.709789i
$666$	2.09260	−	15.4845i	0.0810866	−	0.600011i
$667$	5.84844	+	3.37660i	0.226453	+	0.130742i
$668$	−0.842741	−	3.14515i	−0.0326066	−	0.121690i
$669$	−0.572025	−	2.90175i	−0.0221158	−	0.112188i
$670$	0.542288	+	2.02384i	0.0209504	+	0.0781879i
$671$	−18.3112	−	18.3112i	−0.706896	−	0.706896i
$672$	0.492050	−	4.55608i	0.0189812	−	0.175755i
$673$	9.67449	+	5.58557i	0.372924	+	0.215308i	0.674735	−	0.738060i	$-0.264258\pi$
$673$	9.67449	+	5.58557i	0.372924	+	0.215308i	−0.301811	+	0.953368i	$0.597591\pi$
$674$	−7.98792	−	7.98792i	−0.307683	−	0.307683i
$675$	12.3293	−	13.9139i	0.474556	−	0.535546i
$676$	8.96747	+	9.41193i	0.344903	+	0.361997i
$677$	−33.6674	+	19.4379i	−1.29394	+	0.747058i	−0.979351	−	0.202169i	$-0.935201\pi$
$677$	−33.6674	+	19.4379i	−1.29394	+	0.747058i	−0.314592	+	0.949227i	$0.601868\pi$
$678$	14.2335	+	4.85886i	0.546636	+	0.186604i
$679$	−22.2492	+	11.6733i	−0.853846	+	0.447980i
$680$	−0.211210	−	0.365827i	−0.00809955	−	0.0140288i
$681$	−30.0622	−	34.3981i	−1.15198	−	1.31814i
$682$	−13.6778	−	13.6778i	−0.523751	−	0.523751i
$683$	−3.42624	−	3.42624i	−0.131102	−	0.131102i	0.638511	−	0.769613i	$-0.279551\pi$
$683$	−3.42624	−	3.42624i	−0.131102	−	0.131102i	−0.769613	+	0.638511i	$0.779551\pi$
$684$	3.00963	+	23.4823i	0.115076	+	0.897867i
$685$	3.32745	+	5.76331i	0.127135	+	0.220205i
$686$	2.24012	−	18.3843i	0.0855283	−	0.701915i
$687$	8.17154	−	23.9377i	0.311764	−	0.913280i
$688$	2.54122	−	1.46717i	0.0968830	−	0.0559354i
$689$	−3.49765	+	24.2942i	−0.133250	+	0.925534i
$690$	−2.89012	−	5.88599i	−0.110025	−	0.224076i
$691$	−1.68824	−	1.68824i	−0.0642238	−	0.0642238i	0.674265	−	0.738489i	$-0.264460\pi$
$691$	−1.68824	−	1.68824i	−0.0642238	−	0.0642238i	−0.738489	+	0.674265i	$0.764460\pi$
$692$	−8.63612	−	4.98606i	−0.328296	−	0.189542i
$693$	42.6115	−	15.4990i	1.61868	−	0.588760i
$694$	16.8647	+	16.8647i	0.640177	+	0.640177i
$695$	−0.0805158	−	0.300489i	−0.00305414	−	0.0113982i
$696$	3.61507	−	0.712643i	0.137029	−	0.0270126i
$697$	0.262123	+	0.978255i	0.00992861	+	0.0370541i
$698$	24.5906	+	14.1974i	0.930769	+	0.537380i
$699$	−26.9510	+	13.2334i	−1.01938	+	0.500532i
$700$	−9.23484	+	2.07849i	−0.349044	+	0.0785597i
$701$	15.6689			0.591806			0.295903	−	0.955218i	$-0.404380\pi$
$701$	15.6689			0.591806			0.295903	+	0.955218i	$0.404380\pi$
$702$	10.6755	−	15.3959i	0.402920	−	0.581082i
$703$	20.5509	−	35.5953i	0.775094	−	1.34250i
$704$	−5.51798	−	1.47854i	−0.207967	−	0.0557245i
$705$	−6.48015	−	4.34599i	−0.244057	−	0.163679i
$706$	−27.8270	+	16.0659i	−1.04728	+	0.604650i
$707$	11.0800	−	35.5395i	0.416707	−	1.33660i
$708$	10.5985	+	12.1271i	0.398316	+	0.455766i
$709$	−6.23279	−	23.2611i	−0.234077	−	0.873589i	−0.978563	−	0.205950i	$-0.933972\pi$
$709$	−6.23279	−	23.2611i	−0.234077	−	0.873589i	0.744485	−	0.667639i	$-0.232695\pi$
$710$	−11.5020	+	3.08195i	−0.431662	+	0.115663i
$711$	−8.73472	−	21.2937i	−0.327578	−	0.798575i
$712$			16.9118i			0.633795i
$713$	10.3828	−	2.78206i	0.388838	−	0.104189i
$714$	−0.174288	+	1.61380i	−0.00652255	+	0.0603949i
$715$	24.3131	+	3.50038i	0.909259	+	0.130907i
$716$	11.3692	−	6.56403i	0.424888	−	0.245309i
$717$	21.4740	+	24.5712i	0.801960	+	0.917629i
$718$	12.4100	+	21.4948i	0.463139	+	0.802179i
$719$	−6.34863	+	10.9961i	−0.236764	+	0.410087i	−0.959784	−	0.280740i	$-0.909420\pi$
$719$	−6.34863	+	10.9961i	−0.236764	+	0.410087i	0.723020	+	0.690827i	$0.242753\pi$
$720$	−3.30068	−	1.38046i	−0.123009	−	0.0514469i
$721$	−12.7705	−	3.98140i	−0.475597	−	0.148275i
$722$	−11.2004	+	41.8004i	−0.416835	+	1.55565i
$723$	19.0655	+	21.8153i	0.709053	+	0.811321i
$724$	20.7974			0.772930
$725$	−3.80553	−	6.59138i	−0.141334	−	0.244798i
$726$	−7.24733	−	36.7640i	−0.268974	−	1.36444i
$727$			0.382934i			0.0142022i	0.999975	+	0.00710112i	$0.00226038\pi$
$727$			0.382934i			0.0142022i	−0.999975	+	0.00710112i	$0.997740\pi$
$728$	−8.99269	+	3.18300i	−0.333291	+	0.117970i
$729$	−24.8372	−	10.5885i	−0.919895	−	0.392165i
$730$	8.31129	+	8.31129i	0.307614	+	0.307614i
$731$	−0.900118	+	0.519684i	−0.0332921	+	0.0192212i
$732$	4.37328	−	6.52084i	0.161641	−	0.241017i
$733$	−5.72548	+	21.3678i	−0.211475	+	0.789237i	0.775902	+	0.630853i	$0.217295\pi$
$733$	−5.72548	+	21.3678i	−0.211475	+	0.789237i	−0.987378	+	0.158384i	$0.949372\pi$
$734$	10.1667	+	2.72417i	0.375261	+	0.100551i
$735$	−13.2620	−	5.76092i	−0.489178	−	0.212495i
$736$	2.24471	−	2.24471i	0.0827410	−	0.0827410i
$737$	−8.69188	−	5.01826i	−0.320169	−	0.184850i
$738$	6.78722	+	5.24508i	0.249841	+	0.193074i
$739$	−0.0135161	−	0.00362162i	−0.000497196	−	0.000133223i	0.258570	−	0.965992i	$-0.416749\pi$
$739$	−0.0135161	−	0.00362162i	−0.000497196	−	0.000133223i	−0.259068	+	0.965859i	$0.583415\pi$
$740$	3.10572	+	5.37926i	0.114169	+	0.197746i
$741$	41.3506	−	26.8115i	1.51905	−	0.984944i
$742$	−15.2212	−	9.62832i	−0.558789	−	0.353467i
$743$	9.36709	+	34.9585i	0.343645	+	1.28250i	0.894187	+	0.447694i	$0.147755\pi$
$743$	9.36709	+	34.9585i	0.343645	+	1.28250i	−0.550541	+	0.834808i	$0.685579\pi$
$744$	3.26668	−	4.87084i	0.119762	−	0.178574i
$745$		−	4.77983i		−	0.175119i
$746$	8.08380	+	30.1692i	0.295969	+	1.10457i
$747$	−2.68846	+	2.04832i	−0.0983656	+	0.0749442i
$748$	1.95451	+	0.523710i	0.0714640	+	0.0191487i
$749$	18.1860	−	16.7723i	0.664503	−	0.612848i
$750$	−1.18914	+	17.6783i	−0.0434211	+	0.645521i
$751$			23.2161i			0.847168i	0.905857	+	0.423584i	$0.139228\pi$
$751$			23.2161i			0.847168i	−0.905857	+	0.423584i	$0.860772\pi$
$752$	0.977655	−	3.64866i	0.0356514	−	0.133053i
$753$	26.3070	−	12.9172i	0.958682	−	0.470728i
$754$	−4.59542	−	6.14118i	−0.167355	−	0.223649i
$755$			20.8362i			0.758306i
$756$	7.10930	+	11.7668i	0.258563	+	0.427955i
$757$	14.7473	−	25.5431i	0.536000	−	0.928379i	−0.463114	−	0.886298i	$-0.653268\pi$
$757$	14.7473	−	25.5431i	0.536000	−	0.928379i	0.999114	−	0.0420803i	$-0.0133985\pi$
$758$	−7.21751	+	12.5011i	−0.262152	+	0.454060i
$759$	29.7260	+	10.1475i	1.07899	+	0.368330i
$760$	−6.65471	−	6.65471i	−0.241392	−	0.241392i
$761$	41.7333	−	11.1824i	1.51283	−	0.405362i	0.595457	−	0.803387i	$-0.296971\pi$
$761$	41.7333	−	11.1824i	1.51283	−	0.405362i	0.917374	+	0.398025i	$0.130304\pi$
$762$	−5.49629	−	27.8814i	−0.199110	−	1.01004i
$763$	14.5873	+	9.22731i	0.528095	+	0.334051i
$764$	4.66607	−	8.08187i	0.168813	−	0.292392i
$765$	1.16913	+	0.488971i	0.0422699	+	0.0176788i
$766$	16.2498	+	9.38185i	0.587130	+	0.338980i
$767$	13.2037	−	30.8174i	0.476756	−	1.11275i
$768$	0.116244	−	1.72815i	0.00419460	−	0.0623591i
$769$	43.5288	−	11.6635i	1.56969	−	0.420597i	0.633974	−	0.773355i	$-0.281423\pi$
$769$	43.5288	−	11.6635i	1.56969	−	0.420597i	0.935715	+	0.352758i	$0.114756\pi$
$770$	−9.63583	+	15.2331i	−0.347251	+	0.548963i
$771$	−3.04516	+	45.2709i	−0.109669	+	1.63039i
$772$	0.332138	−	1.23955i	0.0119539	−	0.0446126i
$773$	−18.7842	+	18.7842i	−0.675619	+	0.675619i	−0.959006	−	0.283386i	$-0.908542\pi$
$773$	−18.7842	+	18.7842i	−0.675619	+	0.675619i	0.283386	+	0.959006i	$0.408542\pi$
$774$	−3.39664	+	8.12135i	−0.122090	+	0.291916i
$775$	−11.7017	−	3.13547i	−0.420338	−	0.112629i
$776$	−8.22427	+	4.74828i	−0.295234	+	0.170453i
$777$	2.56280	−	23.7299i	0.0919398	−	0.851307i
$778$	−7.90517	−	29.5025i	−0.283414	−	1.05772i
$779$	11.2818	+	19.5406i	0.404211	+	0.700115i
$780$	0.384478	+	7.43772i	0.0137665	+	0.266313i
$781$	28.5199	−	49.3980i	1.02052	−	1.76760i
$782$	−0.795092	+	0.795092i	−0.0284324	+	0.0284324i
$783$	−7.33101	+	8.27320i	−0.261989	+	0.295660i
$784$	0.565228	−	6.97714i	0.0201867	−	0.249184i
$785$	2.38810	−	2.38810i	0.0852350	−	0.0852350i
$786$	16.6516	+	5.68431i	0.593943	+	0.202752i
$787$	4.02821	−	4.02821i	0.143590	−	0.143590i	−0.631657	−	0.775248i	$-0.717625\pi$
$787$	4.02821	−	4.02821i	0.143590	−	0.143590i	0.775248	+	0.631657i	$0.217625\pi$
$788$	−24.1184	+	6.46249i	−0.859181	+	0.230217i
$789$	2.90193	+	5.91005i	0.103311	+	0.210403i
$790$	7.92352	+	4.57464i	0.281906	+	0.162759i
$791$	21.9328	+	6.83792i	0.779841	+	0.243129i
$792$	15.8558	−	6.50407i	0.563410	−	0.231112i
$793$	−16.1775	−	2.32909i	−0.574481	−	0.0827085i
$794$	18.0465	+	10.4191i	0.640445	+	0.369761i
$795$	−10.5879	+	9.25328i	−0.375514	+	0.328180i
$796$	−23.6263			−0.837411
$797$	−13.3058	−	23.0463i	−0.471315	−	0.816342i	0.528146	−	0.849154i	$-0.322887\pi$
$797$	−13.3058	−	23.0463i	−0.471315	−	0.816342i	−0.999462	+	0.0328112i	$0.989554\pi$
$798$	5.55493	+	35.7340i	0.196642	+	1.26497i
$799$	−0.346293	+	1.29238i	−0.0122510	+	0.0457212i
$800$	−3.45585	+	0.925991i	−0.122183	+	0.0327387i
$801$	−30.7475	−	40.3566i	−1.08641	−	1.42593i
$802$	−12.2564			−0.432789
$803$	−56.3031			−1.98689
$804$	0.983089	−	2.87986i	0.0346709	−	0.101565i
$805$	−4.65360	−	8.86972i	−0.164018	−	0.312617i
$806$	−12.0840	−	1.73975i	−0.425642	−	0.0612801i
$807$	−23.1262	−	1.55559i	−0.814080	−	0.0547593i
$808$	3.64167	−	13.5909i	0.128114	−	0.478126i
$809$	−34.0929	+	19.6836i	−1.19864	+	0.692037i	−0.960253	−	0.279132i	$-0.909953\pi$
$809$	−34.0929	+	19.6836i	−1.19864	+	0.692037i	−0.238391	+	0.971169i	$0.576620\pi$
$810$	10.3863	−	2.70681i	0.364937	−	0.0951075i
$811$	9.03151	+	9.03151i	0.317139	+	0.317139i	0.847667	−	0.530528i	$-0.178006\pi$
$811$	9.03151	+	9.03151i	0.317139	+	0.317139i	−0.530528	+	0.847667i	$0.678006\pi$
$812$	5.49103	−	1.23587i	0.192697	−	0.0433706i
$813$	30.0193	+	34.3490i	1.05282	+	1.20467i
$814$	−28.7399	−	7.70084i	−1.00733	−	0.269914i
$815$			26.9758i			0.944922i
$816$	−0.0411745	+	0.612122i	−0.00144140	+	0.0214286i
$817$	−16.3739	+	16.3739i	−0.572851	+	0.572851i
$818$	−31.3816			−1.09723
$819$	15.6723	−	23.9454i	0.547633	−	0.836718i
$820$	−3.40987			−0.119078
$821$	−27.8018	+	27.8018i	−0.970291	+	0.970291i	−0.999571	−	0.0292801i	$-0.990679\pi$
$821$	−27.8018	+	27.8018i	−0.970291	+	0.970291i	0.0292801	+	0.999571i	$0.490679\pi$
$822$	0.648671	−	9.64349i	0.0226250	−	0.336355i
$823$			14.6810i			0.511747i	0.966710	+	0.255874i	$0.0823631\pi$
$823$			14.6810i			0.511747i	−0.966710	+	0.255874i	$0.917637\pi$
$824$	−4.88364	−	1.30857i	−0.170130	−	0.0455861i
$825$	−23.2954	−	26.6554i	−0.811043	−	0.928021i
$826$	16.6791	+	18.0849i	0.580340	+	0.629255i
$827$	13.2579	+	13.2579i	0.461023	+	0.461023i	0.898991	−	0.437967i	$-0.144301\pi$
$827$	13.2579	+	13.2579i	0.461023	+	0.461023i	−0.437967	+	0.898991i	$0.644301\pi$
$828$	−1.27543	+	9.43769i	−0.0443242	+	0.327983i
$829$	−13.8950	+	8.02231i	−0.482595	+	0.278626i	−0.721497	−	0.692417i	$-0.756546\pi$
$829$	−13.8950	+	8.02231i	−0.482595	+	0.278626i	0.238902	+	0.971044i	$0.423212\pi$
$830$	0.347745	−	1.29780i	0.0120704	−	0.0450474i
$831$	−19.6089	−	1.31899i	−0.680224	−	0.0457554i
$832$	−3.34753	+	1.33942i	−0.116055	+	0.0464359i
$833$	−0.200208	+	2.47136i	−0.00693679	+	0.0856275i
$834$	−0.145964	+	0.427585i	−0.00505430	+	0.0148061i
$835$	−3.88316			−0.134382
$836$	45.0810			1.55916
$837$	1.06043	+	17.5625i	0.0366540	+	0.607050i
$838$	−4.09974	+	1.09852i	−0.141623	+	0.0379478i
$839$	−2.78849	+	10.4068i	−0.0962694	+	0.359282i	−0.997209	−	0.0746625i	$-0.976212\pi$
$839$	−2.78849	+	10.4068i	−0.0962694	+	0.359282i	0.900939	+	0.433945i	$0.142879\pi$
$840$	−5.09647	−	1.97310i	−0.175845	−	0.0680785i
$841$	−12.2372	−	21.1955i	−0.421974	−	0.730880i
$842$	−16.1303			−0.555885
$843$	41.0806	−	35.9023i	1.41489	−	1.23654i
$844$	8.17479	+	4.71972i	0.281388	+	0.162459i
$845$	13.6099	−	7.42491i	0.468196	−	0.255425i
$846$	4.30069	+	10.4843i	0.147861	+	0.360458i
$847$	−12.5684	−	55.8419i	−0.431855	−	1.91875i
$848$	−5.89543	−	3.40373i	−0.202450	−	0.116885i
$849$	6.49513	+	13.2279i	0.222912	+	0.453981i
$850$	1.22409	−	0.327993i	0.0419858	−	0.0112501i
$851$	11.6914	−	11.6914i	0.400774	−	0.400774i
$852$	16.3669	+	5.58713i	0.560722	+	0.191412i
$853$	2.41269	−	2.41269i	0.0826091	−	0.0826091i	−0.664595	−	0.747204i	$-0.731396\pi$
$853$	2.41269	−	2.41269i	0.0826091	−	0.0826091i	0.747204	+	0.664595i	$0.231396\pi$
$854$	6.41151	−	10.1358i	0.219398	−	0.346841i
$855$	27.9792	+	3.78116i	0.956868	+	0.129313i
$856$	6.61191	−	6.61191i	0.225991	−	0.225991i
$857$	8.99629	−	15.5820i	0.307308	−	0.532272i	−0.670465	−	0.741941i	$-0.733905\pi$
$857$	8.99629	−	15.5820i	0.307308	−	0.532272i	0.977772	+	0.209669i	$0.0672386\pi$
$858$	−26.4950	−	23.8904i	−0.904523	−	0.815605i
$859$	−2.43440	−	4.21650i	−0.0830605	−	0.143865i	0.821503	−	0.570205i	$-0.193136\pi$
$859$	−2.43440	−	4.21650i	−0.0830605	−	0.143865i	−0.904563	+	0.426340i	$0.859803\pi$
$860$	−0.905721	−	3.38020i	−0.0308848	−	0.115264i
$861$	10.5782	+	7.73187i	0.360504	+	0.263501i
$862$	34.4639	−	19.8978i	1.17385	−	0.677720i
$863$	−33.2645	−	8.91318i	−1.13234	−	0.303408i	−0.356470	−	0.934307i	$-0.616020\pi$
$863$	−33.2645	−	8.91318i	−1.13234	−	0.303408i	−0.775865	+	0.630899i	$0.782686\pi$
$864$	2.86457	+	4.33523i	0.0974547	+	0.147488i
$865$	−8.40930	+	8.40930i	−0.285925	+	0.285925i
$866$	2.03731	−	7.60333i	0.0692305	−	0.258372i
$867$	−1.96156	+	29.1617i	−0.0666182	+	0.990382i
$868$	4.78918	−	7.57112i	0.162555	−	0.256981i
$869$	−42.3331	+	11.3431i	−1.43605	+	0.384789i
$870$	0.294912	−	4.38432i	0.00999846	−	0.148642i
$871$	−6.28992	+	0.750848i	−0.213126	+	0.0254415i
$872$	5.64989	+	3.26197i	0.191329	+	0.110464i
$873$	10.9927	−	26.2835i	0.372047	−	0.889562i
$874$	−12.5257	+	21.6951i	−0.423688	+	0.733848i
$875$	−1.09360	+	27.0430i	−0.0369706	+	0.914221i
$876$	−3.30166	−	16.7486i	−0.111553	−	0.565882i
$877$	21.4092	−	5.73659i	0.722939	−	0.193711i	0.121456	−	0.992597i	$-0.461244\pi$
$877$	21.4092	−	5.73659i	0.722939	−	0.193711i	0.601483	+	0.798886i	$0.294577\pi$
$878$	4.57039	+	4.57039i	0.154243	+	0.154243i
$879$	−26.2246	−	8.95222i	−0.884534	−	0.301951i
$880$	−3.40639	+	5.90003i	−0.114829	+	0.198890i
$881$	−1.23947	+	2.14683i	−0.0417588	+	0.0723284i	−0.886149	−	0.463400i	$-0.846629\pi$
$881$	−1.23947	+	2.14683i	−0.0417588	+	0.0723284i	0.844391	+	0.535728i	$0.179963\pi$
$882$	11.3364	+	17.6773i	0.381718	+	0.595224i
$883$		−	36.1379i		−	1.21614i	−0.793884	−	0.608069i	$-0.791944\pi$
$883$		−	36.1379i		−	1.21614i	0.793884	−	0.608069i	$-0.208056\pi$
$884$	1.18572	−	0.474431i	0.0398801	−	0.0159569i
$885$	17.2411	−	8.46567i	0.579554	−	0.284570i
$886$	−3.78754	+	14.1353i	−0.127245	+	0.474884i
$887$			22.3008i			0.748787i	0.927270	+	0.374393i	$0.122149\pi$
$887$			22.3008i			0.748787i	−0.927270	+	0.374393i	$0.877851\pi$
$888$	0.605447	−	9.00089i	0.0203175	−	0.302050i
$889$	−9.53171	−	42.3498i	−0.319683	−	1.42037i
$890$	19.4814	+	5.22002i	0.653017	+	0.174975i
$891$	−26.0116	+	44.3483i	−0.871420	+	1.48572i
$892$	−0.441951	−	1.64939i	−0.0147976	−	0.0552255i
$893$			29.8089i			0.997518i
$894$	−3.86667	+	5.76546i	−0.129321	+	0.192826i
$895$	−4.05214	−	15.1228i	−0.135448	−	0.505499i
$896$	0.106905	−	2.64359i	0.00357145	−	0.0883162i
$897$	18.8588	−	6.11273i	0.629677	−	0.204098i
$898$	15.2806	+	26.4668i	0.509920	+	0.883207i
$899$	6.95783	+	1.86435i	0.232057	+	0.0621794i
$900$	6.56315	−	8.49282i	0.218772	−	0.283094i
$901$	2.08821	+	1.20563i	0.0695683	+	0.0401653i
$902$	11.5497	−	11.5497i	0.384564	−	0.384564i
$903$	−4.85483	+	12.5399i	−0.161559	+	0.417301i
$904$	8.38748	+	2.24742i	0.278964	+	0.0747481i
$905$	6.41938	−	23.9574i	0.213387	−	0.796372i
$906$	16.8555	−	25.1327i	0.559988	−	0.834979i
$907$	13.4885	−	7.78757i	0.447877	−	0.258582i	−0.259056	−	0.965862i	$-0.583411\pi$
$907$	13.4885	−	7.78757i	0.447877	−	0.258582i	0.706933	+	0.707280i	$0.250078\pi$
$908$	−18.6501	−	18.6501i	−0.618926	−	0.618926i
$909$	16.0197	+	39.0530i	0.531339	+	1.29531i
$910$	0.890930	+	11.3415i	0.0295340	+	0.375968i
$911$			9.61228i			0.318469i	0.987241	+	0.159235i	$0.0509026\pi$
$911$			9.61228i			0.318469i	−0.987241	+	0.159235i	$0.949097\pi$
$912$	2.64359	+	13.4103i	0.0875379	+	0.444060i
$913$	3.21798	+	5.57371i	0.106500	+	0.184463i
$914$	−37.0241			−1.22465
$915$	−6.16178	−	7.05050i	−0.203702	−	0.233082i
$916$	3.77967	−	14.1059i	0.124884	−	0.466072i
$917$	25.6588	+	7.99958i	0.847330	+	0.264169i
$918$	−1.01465	−	1.53557i	−0.0334885	−	0.0506814i
$919$	1.80194	−	3.12105i	0.0594405	−	0.102954i	−0.834774	−	0.550593i	$-0.814402\pi$
$919$	1.80194	−	3.12105i	0.0594405	−	0.102954i	0.894214	+	0.447639i	$0.147735\pi$
$920$	−1.89292	−	3.27863i	−0.0624077	−	0.108093i
$921$	−10.6974	−	12.2403i	−0.352491	−	0.403331i
$922$	−4.31713	+	2.49250i	−0.142177	+	0.0820860i
$923$	−4.26725	−	35.7471i	−0.140458	−	1.17663i
$924$	23.9457	−	10.5793i	0.787756	−	0.348034i
$925$	−17.9995	+	4.82294i	−0.591819	+	0.158577i
$926$			34.3333i			1.12826i
$927$	14.0330	−	5.75637i	0.460904	−	0.189064i
$928$	2.05484	−	0.550594i	0.0674535	−	0.0180741i
$929$	12.3097	+	45.9406i	0.403870	+	1.50726i	0.806131	+	0.591737i	$0.201558\pi$
$929$	12.3097	+	45.9406i	0.403870	+	1.50726i	−0.402261	+	0.915525i	$0.631776\pi$
$930$	−4.60263	−	5.26648i	−0.150926	−	0.172695i
$931$	9.94204	+	54.3381i	0.325837	+	1.78086i
$932$	−15.0123	+	8.66736i	−0.491745	+	0.283909i
$933$	7.50895	+	5.03596i	0.245832	+	0.164870i
$934$	17.5859	+	4.71212i	0.575427	+	0.154185i
$935$	1.20657	−	2.08984i	0.0394590	−	0.0683450i
$936$	5.55303	−	9.28245i	0.181506	−	0.303406i
$937$	26.2935			0.858971			0.429486	−	0.903074i	$-0.358695\pi$
$937$	26.2935			0.858971			0.429486	+	0.903074i	$0.358695\pi$
$938$	1.38351	−	4.43765i	0.0451732	−	0.144894i
$939$	−22.4682	+	11.0323i	−0.733223	+	0.360024i
$940$	−3.90128	−	2.25241i	−0.127246	−	0.0734654i
$941$	−2.13565	−	7.97037i	−0.0696203	−	0.259827i	0.922339	−	0.386381i	$-0.126275\pi$
$941$	−2.13565	−	7.97037i	−0.0696203	−	0.259827i	−0.991960	+	0.126554i	$0.959608\pi$
$942$	−4.81241	+	0.948675i	−0.156797	+	0.0309095i
$943$	2.34921	+	8.76736i	0.0765007	+	0.285505i
$944$	6.57515	+	6.57515i	0.214003	+	0.214003i
$945$	15.7491	−	4.55753i	0.512317	−	0.148257i
$946$	14.5170	+	8.38142i	0.471990	+	0.272504i
$947$	−2.08153	−	2.08153i	−0.0676408	−	0.0676408i	0.672477	−	0.740118i	$-0.265230\pi$
$947$	−2.08153	−	2.08153i	−0.0676408	−	0.0676408i	−0.740118	+	0.672477i	$0.765230\pi$
$948$	−5.85671	−	11.9277i	−0.190217	−	0.387395i
$949$	−28.4520	+	21.2905i	−0.923591	+	0.691120i
$950$	24.4511	−	14.1168i	0.793298	−	0.458011i
$951$	−9.47298	+	27.7501i	−0.307182	+	0.899860i
$952$	−0.0378667	+	0.936380i	−0.00122727	+	0.0303482i
$953$	15.9473	+	27.6215i	0.516584	+	0.894749i	0.999815	+	0.0192560i	$0.00612976\pi$
$953$	15.9473	+	27.6215i	0.516584	+	0.894749i	−0.483231	+	0.875493i	$0.660537\pi$
$954$	20.2567	−	2.59622i	0.655834	−	0.0840558i
$955$	−7.86962	−	7.86962i	−0.254655	−	0.254655i
$956$	13.3221	+	13.3221i	0.430869	+	0.430869i
$957$	13.8514	+	15.8493i	0.447754	+	0.512334i
$958$	−8.56393	−	14.8332i	−0.276688	−	0.479238i
$959$	0.596559	−	14.7519i	0.0192639	−	0.476364i
$960$	−1.95484	−	0.667320i	−0.0630924	−	0.0215377i
$961$	−16.9174	+	9.76728i	−0.545723	+	0.315074i
$962$	−17.4353	+	6.97623i	−0.562137	+	0.224923i
$963$	−3.75684	+	27.7993i	−0.121063	+	0.895819i
$964$	11.8279	+	11.8279i	0.380952	+	0.380952i
$965$	−1.32538	−	0.765207i	−0.0426654	−	0.0246329i
$966$	−1.56201	+	14.4633i	−0.0502568	+	0.465348i
$967$	13.8784	+	13.8784i	0.446300	+	0.446300i	0.894123	−	0.447822i	$-0.147800\pi$
$967$	13.8784	+	13.8784i	0.446300	+	0.446300i	−0.447822	+	0.894123i	$0.647800\pi$
$968$	−5.59935	−	20.8971i	−0.179970	−	0.671657i
$969$	−0.936379	−	4.75003i	−0.0300808	−	0.152593i
$970$	2.93123	+	10.9395i	0.0941161	+	0.351246i
$971$	−25.5554	−	14.7544i	−0.820111	−	0.473491i	0.0303437	−	0.999540i	$-0.490340\pi$
$971$	−25.5554	−	14.7544i	−0.820111	−	0.473491i	−0.850455	+	0.526048i	$0.823673\pi$
$972$	−14.7177	−	5.13708i	−0.472070	−	0.164772i
$973$	−0.205416	+	0.658876i	−0.00658533	+	0.0211226i
$974$	29.9960			0.961134
$975$	−21.8515	−	4.66097i	−0.699808	−	0.149270i
$976$	2.26655	−	3.92578i	0.0725505	−	0.125661i
$977$	−35.9433	−	9.63099i	−1.14993	−	0.308123i	−0.366992	−	0.930224i	$-0.619612\pi$
$977$	−35.9433	−	9.63099i	−1.14993	−	0.308123i	−0.782937	+	0.622101i	$0.786279\pi$
$978$	21.8222	−	32.5384i	0.697798	−	1.04046i
$979$	−83.6673	+	48.3054i	−2.67402	+	1.54385i
$980$	−7.86281	−	2.80469i	−0.251168	−	0.0895925i
$981$	−19.4130	+	2.48809i	−0.619809	+	0.0794387i
$982$	9.92108	+	37.0260i	0.316595	+	1.18155i
$983$	16.6593	−	4.46383i	0.531348	−	0.142374i	0.0168372	−	0.999858i	$-0.494640\pi$
$983$	16.6593	−	4.46383i	0.531348	−	0.142374i	0.514511	+	0.857484i	$0.327974\pi$
$984$	4.11300	+	2.75843i	0.131118	+	0.0879356i
$985$			29.7777i			0.948796i
$986$	−0.727841	+	0.195024i	−0.0231792	+	0.00621084i
$987$	6.99536	+	15.8336i	0.222665	+	0.503990i
$988$	22.7810	−	17.0470i	0.724761	−	0.542336i
$989$	−8.06708	+	4.65753i	−0.256518	+	0.148101i
$990$	−2.59825	−	20.2725i	−0.0825778	−	0.644302i
$991$	−10.3528	−	17.9316i	−0.328868	−	0.569616i	0.653420	−	0.756996i	$-0.273334\pi$
$991$	−10.3528	−	17.9316i	−0.328868	−	0.569616i	−0.982288	+	0.187380i	$0.940000\pi$
$992$	1.69303	−	2.93242i	0.0537538	−	0.0931044i
$993$	−4.30126	−	21.8193i	−0.136496	−	0.692414i
$994$	25.2202	+	7.86282i	0.799936	+	0.249393i
$995$	−7.29253	+	27.2161i	−0.231189	+	0.862809i
$996$	−1.46932	+	1.28411i	−0.0465570	+	0.0406885i
$997$	4.65340			0.147375			0.0736873	−	0.997281i	$-0.476523\pi$
$997$	4.65340			0.147375			0.0736873	+	0.997281i	$0.476523\pi$
$998$	−3.74880	−	6.49311i	−0.118666	−	0.205536i
$999$	14.9199	+	22.5797i	0.472043	+	0.714389i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.ch.a.137.10	yes	152
3.2	odd	2	inner	546.2.ch.a.137.21	yes	152
7.2	even	3		546.2.bw.a.527.34	yes	152
13.2	odd	12		546.2.bw.a.431.15	✓	152
21.2	odd	6		546.2.bw.a.527.15	yes	152
39.2	even	12		546.2.bw.a.431.34	yes	152
91.2	odd	12	inner	546.2.ch.a.275.21	yes	152
273.2	even	12	inner	546.2.ch.a.275.10	yes	152

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bw.a.431.15	✓	152	13.2	odd	12
546.2.bw.a.431.34	yes	152	39.2	even	12
546.2.bw.a.527.15	yes	152	21.2	odd	6
546.2.bw.a.527.34	yes	152	7.2	even	3
546.2.ch.a.137.10	yes	152	1.1	even	1	trivial
546.2.ch.a.137.21	yes	152	3.2	odd	2	inner
546.2.ch.a.275.10	yes	152	273.2	even	12	inner
546.2.ch.a.275.21	yes	152	91.2	odd	12	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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.ch (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(0.116244 - 1.72815i) q^{3} -1.00000i q^{4} +(-1.15194 - 0.308662i) q^{5} +(1.13979 + 1.30418i) q^{6} +(1.79371 + 1.94489i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.97297 - 0.401773i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(0.116244 - 1.72815i) q^{3} -1.00000i q^{4} +(-1.15194 - 0.308662i) q^{5} +(1.13979 + 1.30418i) q^{6} +(1.79371 + 1.94489i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.97297 - 0.401773i) q^{9} +(1.03280 - 0.596290i) q^{10} +(-1.47854 + 5.51798i) q^{11} +(-1.72815 - 0.116244i) q^{12} +(1.33942 + 3.34753i) q^{13} +(-2.64359 - 0.106905i) q^{14} +(-0.667320 + 1.95484i) q^{15} -1.00000 q^{16} +0.354208 q^{17} +(2.38631 - 1.81811i) q^{18} +(7.62256 - 2.04246i) q^{19} +(-0.308662 + 1.15194i) q^{20} +(3.56957 - 2.87371i) q^{21} +(-2.85632 - 4.94729i) q^{22} +3.17450 q^{23} +(1.30418 - 1.13979i) q^{24} +(-3.09843 - 1.78888i) q^{25} +(-3.31417 - 1.41995i) q^{26} +(-1.03991 + 5.09103i) q^{27} +(1.94489 - 1.79371i) q^{28} +(1.84232 + 1.06367i) q^{29} +(-0.910418 - 1.85415i) q^{30} +(3.27069 - 0.876378i) q^{31} +(0.707107 - 0.707107i) q^{32} +(9.36401 + 3.19656i) q^{33} +(-0.250463 + 0.250463i) q^{34} +(-1.46593 - 2.79406i) q^{35} +(-0.401773 + 2.97297i) q^{36} +(3.68290 - 3.68290i) q^{37} +(-3.94572 + 6.83420i) q^{38} +(5.94072 - 1.92558i) q^{39} +(-0.596290 - 1.03280i) q^{40} +(0.740026 + 2.76181i) q^{41} +(-0.492050 + 4.55608i) q^{42} +(-2.54122 + 1.46717i) q^{43} +(5.51798 + 1.47854i) q^{44} +(3.30068 + 1.38046i) q^{45} +(-2.24471 + 2.24471i) q^{46} +(-0.977655 + 3.64866i) q^{47} +(-0.116244 + 1.72815i) q^{48} +(-0.565228 + 6.97714i) q^{49} +(3.45585 - 0.925991i) q^{50} +(0.0411745 - 0.612122i) q^{51} +(3.34753 - 1.33942i) q^{52} +(5.89543 + 3.40373i) q^{53} +(-2.86457 - 4.33523i) q^{54} +(3.40639 - 5.90003i) q^{55} +(-0.106905 + 2.64359i) q^{56} +(-2.64359 - 13.4103i) q^{57} +(-2.05484 + 0.550594i) q^{58} +(-6.57515 - 6.57515i) q^{59} +(1.95484 + 0.667320i) q^{60} +(-2.26655 + 3.92578i) q^{61} +(-1.69303 + 2.93242i) q^{62} +(-4.55124 - 6.50279i) q^{63} +1.00000i q^{64} +(-0.509675 - 4.26959i) q^{65} +(-8.88167 + 4.36104i) q^{66} +(-0.454718 + 1.69703i) q^{67} -0.354208i q^{68} +(0.369016 - 5.48599i) q^{69} +(3.01227 + 0.939125i) q^{70} +(-9.64463 - 2.58427i) q^{71} +(-1.81811 - 2.38631i) q^{72} +(2.55089 + 9.52006i) q^{73} +5.20841i q^{74} +(-3.45161 + 5.14659i) q^{75} +(-2.04246 - 7.62256i) q^{76} +(-13.3840 + 7.02205i) q^{77} +(-2.83914 + 5.56231i) q^{78} +(3.83593 + 6.64402i) q^{79} +(1.15194 + 0.308662i) q^{80} +(8.67716 + 2.38892i) q^{81} +(-2.47617 - 1.42962i) q^{82} +(0.796640 - 0.796640i) q^{83} +(-2.87371 - 3.56957i) q^{84} +(-0.408027 - 0.109330i) q^{85} +(0.759464 - 2.83436i) q^{86} +(2.05233 - 3.06016i) q^{87} +(-4.94729 + 2.85632i) q^{88} +(11.9584 + 11.9584i) q^{89} +(-3.31007 + 1.35780i) q^{90} +(-4.10807 + 8.60951i) q^{91} -3.17450i q^{92} +(-1.13431 - 5.75410i) q^{93} +(-1.88868 - 3.27130i) q^{94} -9.41118 q^{95} +(-1.13979 - 1.30418i) q^{96} +(-2.45789 + 9.17298i) q^{97} +(-4.53391 - 5.33326i) q^{98} +(6.61264 - 15.8108i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 152 q + 8 q^{7}+O(q^{10}) \) 152 * q + 8 * q^7	\( 152 q + 8 q^{7} - 152 q^{16} - 8 q^{18} + 36 q^{19} + 8 q^{21} + 24 q^{27} - 12 q^{28} - 24 q^{30} - 36 q^{31} + 12 q^{33} + 24 q^{36} - 12 q^{37} - 8 q^{39} - 36 q^{42} + 84 q^{43} - 40 q^{45} + 8 q^{46} + 4 q^{49} - 20 q^{52} - 12 q^{54} + 16 q^{55} - 8 q^{57} + 8 q^{58} + 24 q^{60} - 32 q^{61} - 28 q^{63} + 16 q^{66} + 92 q^{67} + 84 q^{69} - 8 q^{72} + 84 q^{73} - 48 q^{76} - 8 q^{78} + 32 q^{79} - 24 q^{81} - 48 q^{82} - 8 q^{84} - 152 q^{85} - 96 q^{87} - 88 q^{91} - 48 q^{93} + 32 q^{94} - 100 q^{97} + 16 q^{99}+O(q^{100}) \) 152 * q + 8 * q^7 - 152 * q^16 - 8 * q^18 + 36 * q^19 + 8 * q^21 + 24 * q^27 - 12 * q^28 - 24 * q^30 - 36 * q^31 + 12 * q^33 + 24 * q^36 - 12 * q^37 - 8 * q^39 - 36 * q^42 + 84 * q^43 - 40 * q^45 + 8 * q^46 + 4 * q^49 - 20 * q^52 - 12 * q^54 + 16 * q^55 - 8 * q^57 + 8 * q^58 + 24 * q^60 - 32 * q^61 - 28 * q^63 + 16 * q^66 + 92 * q^67 + 84 * q^69 - 8 * q^72 + 84 * q^73 - 48 * q^76 - 8 * q^78 + 32 * q^79 - 24 * q^81 - 48 * q^82 - 8 * q^84 - 152 * q^85 - 96 * q^87 - 88 * q^91 - 48 * q^93 + 32 * q^94 - 100 * q^97 + 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more