LMFDB - Embedded newform 546.2.bw.a.431.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(11,546)]

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, 7]))

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

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

chi := DirichletCharacter("546.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bw (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			431.19
Character	$\chi$	$=$	546.431
Dual form			546.2.bw.a.527.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.965926 + 0.258819i) q^{2} +(1.72806 - 0.117493i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-1.12449 + 4.19664i) q^{5} +(-1.63877 + 0.560745i) q^{6} +(-2.63306 - 0.258797i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.97239 - 0.406071i) q^{9} +O(q^{10})$	\(q+(-0.965926 + 0.258819i) q^{2} +(1.72806 - 0.117493i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-1.12449 + 4.19664i) q^{5} +(-1.63877 + 0.560745i) q^{6} +(-2.63306 - 0.258797i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.97239 - 0.406071i) q^{9} -4.34468i q^{10} +(1.35259 - 1.35259i) q^{11} +(1.43780 - 0.965783i) q^{12} +(-0.217387 + 3.59899i) q^{13} +(2.61033 - 0.431508i) q^{14} +(-1.45010 + 7.38416i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-0.351682 - 0.609132i) q^{17} +(-2.76601 + 1.16155i) q^{18} +(-2.51491 + 2.51491i) q^{19} +(1.12449 + 4.19664i) q^{20} +(-4.58050 - 0.137850i) q^{21} +(-0.956425 + 1.65658i) q^{22} +(-0.914210 + 1.58346i) q^{23} +(-1.13884 + 1.30500i) q^{24} +(-12.0172 - 6.93811i) q^{25} +(-0.721508 - 3.53262i) q^{26} +(5.08876 - 1.05095i) q^{27} +(-2.40970 + 1.09241i) q^{28} +(-6.59692 + 3.80874i) q^{29} +(-0.510470 - 7.50787i) q^{30} +(1.94735 + 7.26761i) q^{31} +(-0.258819 + 0.965926i) q^{32} +(2.17844 - 2.49628i) q^{33} +(0.497354 + 0.497354i) q^{34} +(4.04692 - 10.7590i) q^{35} +(2.37113 - 1.83786i) q^{36} +(1.43162 - 0.383602i) q^{37} +(1.77831 - 3.08012i) q^{38} +(0.0471984 + 6.24482i) q^{39} +(-2.17234 - 3.76260i) q^{40} +(0.735223 - 2.74389i) q^{41} +(4.46010 - 1.05237i) q^{42} +(3.30528 + 1.90831i) q^{43} +(0.495082 - 1.84767i) q^{44} +(-1.63828 + 12.9307i) q^{45} +(0.473230 - 1.76612i) q^{46} +(0.438948 + 0.117616i) q^{47} +(0.762278 - 1.55529i) q^{48} +(6.86605 + 1.36286i) q^{49} +(13.4034 + 3.59143i) q^{50} +(-0.679298 - 1.01130i) q^{51} +(1.61123 + 3.22551i) q^{52} +(-6.96361 - 4.02044i) q^{53} +(-4.64336 + 2.33221i) q^{54} +(4.15536 + 7.19729i) q^{55} +(2.04485 - 1.67886i) q^{56} +(-4.05043 + 4.64140i) q^{57} +(5.38637 - 5.38637i) q^{58} +(6.58533 + 1.76453i) q^{59} +(2.43626 + 7.11992i) q^{60} +10.3019 q^{61} +(-3.76199 - 6.51596i) q^{62} +(-7.93158 + 0.299964i) q^{63} -1.00000i q^{64} +(-14.8592 - 4.95931i) q^{65} +(-1.45812 + 2.97504i) q^{66} +(1.89378 - 1.89378i) q^{67} +(-0.609132 - 0.351682i) q^{68} +(-1.39377 + 2.84373i) q^{69} +(-1.12439 + 11.4398i) q^{70} +(12.7586 - 3.41866i) q^{71} +(-1.81466 + 2.38893i) q^{72} +(-13.7090 + 3.67331i) q^{73} +(-1.28356 + 0.741062i) q^{74} +(-21.5816 - 10.5775i) q^{75} +(-0.920521 + 3.43543i) q^{76} +(-3.91150 + 3.21141i) q^{77} +(-1.66187 - 6.01982i) q^{78} +(-0.155398 - 0.269158i) q^{79} +(3.07215 + 3.07215i) q^{80} +(8.67021 - 2.41400i) q^{81} +2.84068i q^{82} +(-0.970732 - 0.970732i) q^{83} +(-4.03576 + 2.17087i) q^{84} +(2.95177 - 0.790923i) q^{85} +(-3.68656 - 0.987812i) q^{86} +(-10.9524 + 7.35682i) q^{87} +1.91285i q^{88} +(3.19161 + 11.9113i) q^{89} +(-1.76425 - 12.9141i) q^{90} +(1.50380 - 9.42012i) q^{91} +1.82842i q^{92} +(4.21904 + 12.3301i) q^{93} -0.454432 q^{94} +(-7.72618 - 13.3821i) q^{95} +(-0.333765 + 1.69959i) q^{96} +(-2.18315 - 8.14762i) q^{97} +(-6.98483 + 0.460643i) q^{98} +(3.47117 - 4.56967i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 152 q + 12 q^{7}+O(q^{10}) $ 152 * q + 12 * q^7	$ 152 q + 12 q^{7} + 76 q^{16} - 8 q^{18} + 12 q^{19} + 8 q^{21} + 24 q^{27} + 16 q^{28} - 12 q^{31} - 48 q^{33} + 24 q^{36} - 36 q^{37} - 8 q^{39} + 84 q^{43} - 40 q^{45} - 16 q^{46} - 28 q^{49} + 4 q^{52} + 24 q^{54} + 16 q^{55} - 8 q^{57} - 16 q^{58} + 64 q^{61} - 100 q^{63} + 16 q^{66} - 112 q^{67} + 84 q^{69} + 16 q^{72} - 120 q^{73} - 48 q^{76} - 8 q^{78} + 32 q^{79} + 48 q^{81} - 8 q^{84} - 152 q^{85} + 48 q^{87} + 16 q^{91} - 12 q^{93} - 64 q^{94} - 100 q^{97} + 16 q^{99}+O(q^{100}) $ 152 * q + 12 * q^7 + 76 * q^16 - 8 * q^18 + 12 * q^19 + 8 * q^21 + 24 * q^27 + 16 * q^28 - 12 * q^31 - 48 * q^33 + 24 * q^36 - 36 * q^37 - 8 * q^39 + 84 * q^43 - 40 * q^45 - 16 * q^46 - 28 * q^49 + 4 * q^52 + 24 * q^54 + 16 * q^55 - 8 * q^57 - 16 * q^58 + 64 * q^61 - 100 * q^63 + 16 * q^66 - 112 * q^67 + 84 * q^69 + 16 * q^72 - 120 * q^73 - 48 * q^76 - 8 * q^78 + 32 * q^79 + 48 * q^81 - 8 * q^84 - 152 * q^85 + 48 * q^87 + 16 * q^91 - 12 * q^93 - 64 * q^94 - 100 * q^97 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−0.965926	+	0.258819i	−0.683013	+	0.183013i
$2$	−0.965926	+	0.258819i	−0.683013	+	0.183013i
$3$	1.72806	−	0.117493i	0.997697	−	0.0678347i
$3$	1.72806	−	0.117493i	0.997697	−	0.0678347i
$4$	0.866025	−	0.500000i	0.433013	−	0.250000i
$5$	−1.12449	+	4.19664i	−0.502885	+	1.87679i	−0.0224773	+	0.999747i	$0.507155\pi$
$5$	−1.12449	+	4.19664i	−0.502885	+	1.87679i	−0.480408	+	0.877045i	$0.659511\pi$
$6$	−1.63877	+	0.560745i	−0.669025	+	0.228923i
$7$	−2.63306	−	0.258797i	−0.995205	−	0.0978162i
$7$	−2.63306	−	0.258797i	−0.995205	−	0.0978162i
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	2.97239	−	0.406071i	0.990797	−	0.135357i
$10$		−	4.34468i		−	1.37391i
$11$	1.35259	−	1.35259i	0.407821	−	0.407821i	−0.473157	−	0.880978i	$-0.656886\pi$
$11$	1.35259	−	1.35259i	0.407821	−	0.407821i	0.880978	+	0.473157i	$0.156886\pi$
$12$	1.43780	−	0.965783i	0.415057	−	0.278797i
$13$	−0.217387	+	3.59899i	−0.0602924	+	0.998181i
$13$	−0.217387	+	3.59899i	−0.0602924	+	0.998181i
$14$	2.61033	−	0.431508i	0.697639	−	0.115325i
$15$	−1.45010	+	7.38416i	−0.374415	+	1.90658i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	−0.351682	−	0.609132i	−0.0852955	−	0.147736i	0.820222	−	0.572046i	$-0.193850\pi$
$17$	−0.351682	−	0.609132i	−0.0852955	−	0.147736i	−0.905517	+	0.424310i	$0.860517\pi$
$18$	−2.76601	+	1.16155i	−0.651955	+	0.273779i
$19$	−2.51491	+	2.51491i	−0.576960	+	0.576960i	−0.934064	−	0.357105i	$-0.883764\pi$
$19$	−2.51491	+	2.51491i	−0.576960	+	0.576960i	0.357105	+	0.934064i	$0.383764\pi$
$20$	1.12449	+	4.19664i	0.251443	+	0.938396i
$21$	−4.58050	−	0.137850i	−0.999547	−	0.0300814i
$22$	−0.956425	+	1.65658i	−0.203910	+	0.353183i
$23$	−0.914210	+	1.58346i	−0.190626	+	0.330174i	−0.945458	−	0.325744i	$-0.894385\pi$
$23$	−0.914210	+	1.58346i	−0.190626	+	0.330174i	0.754832	+	0.655918i	$0.227718\pi$
$24$	−1.13884	+	1.30500i	−0.232465	+	0.266383i
$25$	−12.0172	−	6.93811i	−2.40343	−	1.38762i
$26$	−0.721508	−	3.53262i	−0.141499	−	0.692804i
$27$	5.08876	−	1.05095i	0.979333	−	0.202256i
$28$	−2.40970	+	1.09241i	−0.455390	+	0.206445i
$29$	−6.59692	+	3.80874i	−1.22502	+	0.707265i	−0.965984	−	0.258604i	$-0.916738\pi$
$29$	−6.59692	+	3.80874i	−1.22502	+	0.707265i	−0.259035	+	0.965868i	$0.583404\pi$
$30$	−0.510470	−	7.50787i	−0.0931987	−	1.37074i
$31$	1.94735	+	7.26761i	0.349754	+	1.30530i	0.886959	+	0.461849i	$0.152814\pi$
$31$	1.94735	+	7.26761i	0.349754	+	1.30530i	−0.537204	+	0.843452i	$0.680519\pi$
$32$	−0.258819	+	0.965926i	−0.0457532	+	0.170753i
$33$	2.17844	−	2.49628i	0.379217	−	0.434546i
$34$	0.497354	+	0.497354i	0.0852955	+	0.0852955i
$35$	4.04692	−	10.7590i	0.684054	−	1.81860i
$36$	2.37113	−	1.83786i	0.395188	−	0.306311i
$37$	1.43162	−	0.383602i	0.235357	−	0.0630638i	−0.139212	−	0.990263i	$-0.544457\pi$
$37$	1.43162	−	0.383602i	0.235357	−	0.0630638i	0.374570	+	0.927199i	$0.377790\pi$
$38$	1.77831	−	3.08012i	0.288480	−	0.499662i
$39$	0.0471984	+	6.24482i	0.00755780	+	0.999971i
$40$	−2.17234	−	3.76260i	−0.343477	−	0.594919i
$41$	0.735223	−	2.74389i	0.114822	−	0.428523i	−0.884451	−	0.466633i	$-0.845467\pi$
$41$	0.735223	−	2.74389i	0.114822	−	0.428523i	0.999274	+	0.0381096i	$0.0121336\pi$
$42$	4.46010	−	1.05237i	0.688209	−	0.162384i
$43$	3.30528	+	1.90831i	0.504051	+	0.291014i	0.730385	−	0.683036i	$-0.239341\pi$
$43$	3.30528	+	1.90831i	0.504051	+	0.291014i	−0.226334	+	0.974050i	$0.572674\pi$
$44$	0.495082	−	1.84767i	0.0746364	−	0.278547i
$45$	−1.63828	+	12.9307i	−0.244220	+	1.92759i
$46$	0.473230	−	1.76612i	0.0697740	−	0.260400i
$47$	0.438948	+	0.117616i	0.0640271	+	0.0171560i	0.290690	−	0.956817i	$-0.406115\pi$
$47$	0.438948	+	0.117616i	0.0640271	+	0.0171560i	−0.226663	+	0.973973i	$0.572782\pi$
$48$	0.762278	−	1.55529i	0.110025	−	0.224487i
$49$	6.86605	+	1.36286i	0.980864	+	0.194694i
$50$	13.4034	+	3.59143i	1.89553	+	0.507905i
$51$	−0.679298	−	1.01130i	−0.0951207	−	0.141610i
$52$	1.61123	+	3.22551i	0.223438	+	0.447298i
$53$	−6.96361	−	4.02044i	−0.956526	−	0.552250i	−0.0614236	−	0.998112i	$-0.519564\pi$
$53$	−6.96361	−	4.02044i	−0.956526	−	0.552250i	−0.895102	+	0.445862i	$0.852897\pi$
$54$	−4.64336	+	2.33221i	−0.631881	+	0.317374i
$55$	4.15536	+	7.19729i	0.560308	+	0.970482i
$56$	2.04485	−	1.67886i	0.273255	−	0.224347i
$57$	−4.05043	+	4.64140i	−0.536493	+	0.614769i
$58$	5.38637	−	5.38637i	0.707265	−	0.707265i
$59$	6.58533	+	1.76453i	0.857336	+	0.229723i	0.660604	−	0.750735i	$-0.270300\pi$
$59$	6.58533	+	1.76453i	0.857336	+	0.229723i	0.196732	+	0.980457i	$0.436967\pi$
$60$	2.43626	+	7.11992i	0.314519	+	0.919178i
$61$	10.3019			1.31903			0.659513	−	0.751693i	$-0.270762\pi$
$61$	10.3019			1.31903			0.659513	+	0.751693i	$0.270762\pi$
$62$	−3.76199	−	6.51596i	−0.477773	−	0.827528i
$63$	−7.93158	+	0.299964i	−0.999286	+	0.0377919i
$64$		−	1.00000i		−	0.125000i
$65$	−14.8592	−	4.95931i	−1.84306	−	0.615127i
$66$	−1.45812	+	2.97504i	−0.179483	+	0.366202i
$67$	1.89378	−	1.89378i	0.231362	−	0.231362i	−0.581899	−	0.813261i	$-0.697690\pi$
$67$	1.89378	−	1.89378i	0.231362	−	0.231362i	0.813261	+	0.581899i	$0.197690\pi$
$68$	−0.609132	−	0.351682i	−0.0738681	−	0.0426478i
$69$	−1.39377	+	2.84373i	−0.167790	+	0.342344i
$70$	−1.12439	+	11.4398i	−0.134390	+	1.36732i
$71$	12.7586	−	3.41866i	1.51417	−	0.405720i	0.596351	−	0.802724i	$-0.296617\pi$
$71$	12.7586	−	3.41866i	1.51417	−	0.405720i	0.917817	+	0.397004i	$0.129950\pi$
$72$	−1.81466	+	2.38893i	−0.213860	+	0.281538i
$73$	−13.7090	+	3.67331i	−1.60451	+	0.429928i	−0.946402	−	0.322991i	$-0.895312\pi$
$73$	−13.7090	+	3.67331i	−1.60451	+	0.429928i	−0.658112	+	0.752920i	$0.728645\pi$
$74$	−1.28356	+	0.741062i	−0.149211	+	0.0861468i
$75$	−21.5816	−	10.5775i	−2.49202	−	1.22139i
$76$	−0.920521	+	3.43543i	−0.105591	+	0.394071i
$77$	−3.91150	+	3.21141i	−0.445757	+	0.365974i
$78$	−1.66187	−	6.01982i	−0.188170	−	0.681610i
$79$	−0.155398	−	0.269158i	−0.0174837	−	0.0302826i	0.857151	−	0.515065i	$-0.172232\pi$
$79$	−0.155398	−	0.269158i	−0.0174837	−	0.0302826i	−0.874635	+	0.484782i	$0.838899\pi$
$80$	3.07215	+	3.07215i	0.343477	+	0.343477i
$81$	8.67021	−	2.41400i	0.963357	−	0.268223i
$82$			2.84068i			0.313701i
$83$	−0.970732	−	0.970732i	−0.106552	−	0.106552i	0.651821	−	0.758373i	$-0.274005\pi$
$83$	−0.970732	−	0.970732i	−0.106552	−	0.106552i	−0.758373	+	0.651821i	$0.774005\pi$
$84$	−4.03576	+	2.17087i	−0.440337	+	0.236861i
$85$	2.95177	−	0.790923i	0.320164	−	0.0857877i
$86$	−3.68656	−	0.987812i	−0.397532	−	0.106518i
$87$	−10.9524	+	7.35682i	−1.17422	+	0.788734i
$88$			1.91285i			0.203910i
$89$	3.19161	+	11.9113i	0.338310	+	1.26259i	0.900235	+	0.435403i	$0.143394\pi$
$89$	3.19161	+	11.9113i	0.338310	+	1.26259i	−0.561925	+	0.827188i	$0.689939\pi$
$90$	−1.76425	−	12.9141i	−0.185968	−	1.36126i
$91$	1.50380	−	9.42012i	0.157641	−	0.987496i
$92$			1.82842i			0.190626i
$93$	4.21904	+	12.3301i	0.437494	+	1.27857i
$94$	−0.454432			−0.0468711
$95$	−7.72618	−	13.3821i	−0.792690	−	1.37298i
$96$	−0.333765	+	1.69959i	−0.0340648	+	0.173464i
$97$	−2.18315	−	8.14762i	−0.221665	−	0.827266i	−0.983713	−	0.179745i	$-0.942473\pi$
$97$	−2.18315	−	8.14762i	−0.221665	−	0.827266i	0.762048	−	0.647521i	$-0.224194\pi$
$98$	−6.98483	+	0.460643i	−0.705574	+	0.0465320i
$99$	3.47117	−	4.56967i	0.348866	−	0.459269i
$100$	−13.8762			−1.38762
$101$	16.0093			1.59299			0.796493	−	0.604647i	$-0.206686\pi$
$101$	16.0093			1.59299			0.796493	+	0.604647i	$0.206686\pi$
$102$	0.917894	+	0.801023i	0.0908850	+	0.0793130i
$103$	−0.487403	+	0.281403i	−0.0480253	+	0.0277274i	−0.523820	−	0.851829i	$-0.675494\pi$
$103$	−0.487403	+	0.281403i	−0.0480253	+	0.0277274i	0.475795	+	0.879556i	$0.342160\pi$
$104$	−2.39116	−	2.69859i	−0.234472	−	0.264618i
$105$	5.72921	−	19.0677i	0.559114	−	1.86082i
$106$	7.76690	+	2.08113i	0.754388	+	0.202138i
$107$	9.00024	+	5.19629i	0.870086	+	0.502345i	0.867377	−	0.497652i	$-0.165804\pi$
$107$	9.00024	+	5.19629i	0.870086	+	0.502345i	0.00270934	+	0.999996i	$0.499138\pi$
$108$	3.88152	−	3.45453i	0.373500	−	0.332412i
$109$	−2.17796	−	8.12825i	−0.208611	−	0.778546i	−0.988319	−	0.152402i	$-0.951299\pi$
$109$	−2.17796	−	8.12825i	−0.208611	−	0.778546i	0.779708	−	0.626143i	$-0.215368\pi$
$110$	−5.87656	−	5.87656i	−0.560308	−	0.560308i
$111$	2.42886	−	0.831094i	0.230537	−	0.0788839i
$112$	−1.54066	+	2.15090i	−0.145578	+	0.203241i
$113$	12.1496	+	7.01456i	1.14294	+	0.659874i	0.947156	−	0.320774i	$-0.103943\pi$
$113$	12.1496	+	7.01456i	1.14294	+	0.659874i	0.195780	+	0.980648i	$0.437276\pi$
$114$	2.71113	−	5.53158i	0.253921	−	0.518080i
$115$	−5.61718	−	5.61718i	−0.523805	−	0.523805i
$116$	−3.80874	+	6.59692i	−0.353632	+	0.612509i
$117$	0.815286	+	10.7859i	0.0753732	+	0.997155i
$118$	−6.81763			−0.627614
$119$	0.768361	+	1.69490i	0.0704355	+	0.155371i
$120$	−4.19601	−	6.24677i	−0.383042	−	0.570249i
$121$			7.34101i			0.667364i
$122$	−9.95090	+	2.66633i	−0.900912	+	0.241399i
$123$	0.948121	−	4.82799i	0.0854892	−	0.435325i
$124$	5.32026	+	5.32026i	0.477773	+	0.477773i
$125$	27.2691	−	27.2691i	2.43902	−	2.43902i
$126$	7.58369	−	2.34259i	0.675608	−	0.208694i
$127$	9.30962	−	5.37491i	0.826095	−	0.476946i	−0.0264185	−	0.999651i	$-0.508410\pi$
$127$	9.30962	−	5.37491i	0.826095	−	0.476946i	0.852514	+	0.522705i	$0.175077\pi$
$128$	0.258819	+	0.965926i	0.0228766	+	0.0853766i
$129$	5.93594	+	2.90932i	0.522631	+	0.256151i
$130$	15.6365	+	0.944478i	1.37141	+	0.0828362i
$131$	16.3398	−	9.43381i	1.42762	−	0.824235i	0.430685	−	0.902502i	$-0.358272\pi$
$131$	16.3398	−	9.43381i	1.42762	−	0.824235i	0.996932	+	0.0782669i	$0.0249386\pi$
$132$	0.638443	−	3.25106i	0.0555693	−	0.282968i
$133$	7.27277	−	5.97107i	0.630629	−	0.517757i
$134$	−1.33911	+	2.31940i	−0.115681	+	0.200366i
$135$	−1.31178	+	22.5375i	−0.112900	+	1.93972i
$136$	0.679398	+	0.182044i	0.0582579	+	0.0156102i
$137$	−0.822183	−	0.220303i	−0.0702438	−	0.0188218i	0.223526	−	0.974698i	$-0.428243\pi$
$137$	−0.822183	−	0.220303i	−0.0702438	−	0.0188218i	−0.293770	+	0.955876i	$0.594910\pi$
$138$	0.610263	−	3.10756i	0.0519491	−	0.264533i
$139$	−5.07478	+	8.78979i	−0.430438	+	0.745540i	−0.996911	−	0.0785402i	$-0.974974\pi$
$139$	−5.07478	+	8.78979i	−0.430438	+	0.745540i	0.566473	+	0.824080i	$0.308307\pi$
$140$	−1.87476	−	11.3410i	−0.158446	−	0.958491i
$141$	0.772348	+	0.151674i	0.0650434	+	0.0127732i
$142$	−11.4390	+	6.60434i	−0.959944	+	0.554224i
$143$	4.57392	+	5.16199i	0.382490	+	0.431667i
$144$	1.13453	−	2.77720i	0.0945440	−	0.231433i
$145$	−8.56573	−	31.9678i	−0.711346	−	2.65478i
$146$	12.2911	−	7.09629i	1.01722	−	0.587293i
$147$	12.0251	+	1.54839i	0.991812	+	0.127709i
$148$	1.04802	−	1.04802i	0.0861468	−	0.0861468i
$149$	−14.7603	−	14.7603i	−1.20921	−	1.20921i	−0.971282	−	0.237931i	$-0.923531\pi$
$149$	−14.7603	−	14.7603i	−1.20921	−	1.20921i	−0.237931	−	0.971282i	$-0.576469\pi$
$150$	23.5839	+	4.63140i	1.92561	+	0.378152i
$151$	4.44000	−	1.18969i	0.361322	−	0.0968159i	−0.0735909	−	0.997289i	$-0.523446\pi$
$151$	4.44000	−	1.18969i	0.361322	−	0.0968159i	0.434913	+	0.900473i	$0.356779\pi$
$152$		−	3.55662i		−	0.288480i
$153$	−1.29269	−	1.66777i	−0.104508	−	0.134831i
$154$	2.94704	−	4.11435i	0.237480	−	0.331544i
$155$	−32.6893			−2.62567
$156$	3.16328	+	5.38457i	0.253265	+	0.431111i
$157$	5.46618	−	9.46769i	0.436248	−	0.755604i	−0.561148	−	0.827715i	$-0.689640\pi$
$157$	5.46618	−	9.46769i	0.436248	−	0.755604i	0.997397	+	0.0721111i	$0.0229736\pi$
$158$	0.219766	+	0.219766i	0.0174837	+	0.0174837i
$159$	−12.5059	−	6.12939i	−0.991784	−	0.486093i
$160$	−3.76260	−	2.17234i	−0.297460	−	0.171738i
$161$	2.81697	−	3.93275i	0.222008	−	0.309944i
$162$	−7.74999	+	4.57576i	−0.608897	+	0.359506i
$163$	6.59866	+	6.59866i	0.516847	+	0.516847i	0.916616	−	0.399769i	$-0.130910\pi$
$163$	6.59866	+	6.59866i	0.516847	+	0.516847i	−0.399769	+	0.916616i	$0.630910\pi$
$164$	−0.735223	−	2.74389i	−0.0574112	−	0.214262i
$165$	8.02634	+	11.9491i	0.624850	+	0.930238i
$166$	1.18890	+	0.686411i	0.0922765	+	0.0532759i
$167$	−9.37699	−	2.51256i	−0.725614	−	0.194428i	−0.122939	−	0.992414i	$-0.539232\pi$
$167$	−9.37699	−	2.51256i	−0.725614	−	0.194428i	−0.602675	+	0.797987i	$0.705898\pi$
$168$	3.33638	−	3.14143i	0.257407	−	0.242367i
$169$	−12.9055	−	1.56475i	−0.992730	−	0.120365i
$170$	−2.64648	+	1.52795i	−0.202976	+	0.117188i
$171$	−6.45406	+	8.49653i	−0.493555	+	0.649746i
$172$	3.81661			0.291014
$173$	−5.30084			−0.403015			−0.201508	−	0.979487i	$-0.564584\pi$
$173$	−5.30084			−0.403015			−0.201508	+	0.979487i	$0.564584\pi$
$174$	8.67511	−	9.94083i	0.657658	−	0.753613i
$175$	29.8464	+	21.3785i	2.25617	+	1.61606i
$176$	−0.495082	−	1.84767i	−0.0373182	−	0.139273i
$177$	11.5872	+	2.27549i	0.870945	+	0.171036i
$178$	−6.16573	−	10.6793i	−0.462141	−	0.800451i
$179$	12.2235			0.913630			0.456815	−	0.889562i	$-0.348990\pi$
$179$	12.2235			0.913630			0.456815	+	0.889562i	$0.348990\pi$
$180$	5.04654	+	12.0174i	0.376147	+	0.895726i
$181$		−	0.772809i		−	0.0574424i	−0.999587	−	0.0287212i	$-0.990856\pi$
$181$		−	0.772809i		−	0.0574424i	0.999587	−	0.0287212i	$-0.00914351\pi$
$182$	0.985542	+	9.48835i	0.0730532	+	0.703323i
$183$	17.8024	−	1.21041i	1.31599	−	0.0894758i
$184$	−0.473230	−	1.76612i	−0.0348870	−	0.130200i
$185$			6.43935i			0.473431i
$186$	−7.26653	−	10.8180i	−0.532808	−	0.793212i
$187$	−1.29959	−	0.348223i	−0.0950352	−	0.0254646i
$188$	0.438948	−	0.117616i	0.0320136	−	0.00857801i
$189$	−13.6710	+	1.45026i	−0.994420	+	0.105491i
$190$	10.9265	+	10.9265i	0.792690	+	0.792690i
$191$			12.6770i			0.917274i	0.888624	+	0.458637i	$0.151662\pi$
$191$			12.6770i			0.917274i	−0.888624	+	0.458637i	$0.848338\pi$
$192$	−0.117493	−	1.72806i	−0.00847934	−	0.124712i
$193$	−1.42433	−	1.42433i	−0.102525	−	0.102525i	0.653983	−	0.756509i	$-0.273097\pi$
$193$	−1.42433	−	1.42433i	−0.102525	−	0.102525i	−0.756509	+	0.653983i	$0.773097\pi$
$194$	4.21752	+	7.30496i	0.302800	+	0.524465i
$195$	−26.2603	−	6.82413i	−1.88054	−	0.488686i
$196$	6.62760	−	2.25275i	0.473400	−	0.160911i
$197$	−1.77065	+	6.60816i	−0.126154	+	0.470812i	−0.999878	−	0.0156093i	$-0.995031\pi$
$197$	−1.77065	+	6.60816i	−0.126154	+	0.470812i	0.873725	+	0.486421i	$0.161698\pi$
$198$	−2.17018	+	5.31237i	−0.154228	+	0.377533i
$199$	−17.7513	+	10.2487i	−1.25836	+	0.726513i	−0.972755	−	0.231835i	$-0.925527\pi$
$199$	−17.7513	+	10.2487i	−1.25836	+	0.726513i	−0.285602	+	0.958348i	$0.592194\pi$
$200$	13.4034	−	3.59143i	0.947763	−	0.253952i
$201$	3.05007	−	3.49508i	0.215135	−	0.246524i
$202$	−15.4638	+	4.14352i	−1.08803	+	0.291537i
$203$	18.3558	−	8.32138i	1.28833	−	0.584046i
$204$	−1.09394	−	0.536160i	−0.0765909	−	0.0375387i
$205$	10.6884	+	6.17092i	0.746507	+	0.430996i
$206$	0.397963	−	0.397963i	0.0277274	−	0.0277274i
$207$	−2.07439	+	5.07789i	−0.144180	+	0.352938i
$208$	3.00812	+	1.98776i	0.208576	+	0.137826i
$209$			6.80328i			0.470593i
$210$	−0.598915	+	19.9008i	−0.0413291	+	1.37329i
$211$	−6.47471	−	11.2145i	−0.445737	−	0.772040i	0.552366	−	0.833602i	$-0.313725\pi$
$211$	−6.47471	−	11.2145i	−0.445737	−	0.772040i	−0.998103	+	0.0615620i	$0.980392\pi$
$212$	−8.04089			−0.552250
$213$	21.6460	−	7.40670i	1.48316	−	0.507499i
$214$	−10.0385	−	2.68980i	−0.686215	−	0.183871i
$215$	−11.7252	+	11.7252i	−0.799652	+	0.799652i
$216$	−2.85516	+	4.34143i	−0.194269	+	0.295397i
$217$	−3.24666	−	19.6401i	−0.220398	−	1.33325i
$218$	4.20749	+	7.28759i	0.284967	+	0.493578i
$219$	−23.2584	+	7.95841i	−1.57165	+	0.537780i
$220$	7.19729	+	4.15536i	0.485241	+	0.280154i
$221$	2.26871	−	1.13328i	0.152610	−	0.0762330i
$222$	−2.13100	+	1.43141i	−0.143023	+	0.0960700i
$223$	−11.0922	−	2.97214i	−0.742788	−	0.199029i	−0.132471	−	0.991187i	$-0.542291\pi$
$223$	−11.0922	−	2.97214i	−0.742788	−	0.199029i	−0.610317	+	0.792157i	$0.708958\pi$
$224$	0.931466	−	2.47636i	0.0622362	−	0.165459i
$225$	−38.5371	−	15.7430i	−2.56914	−	1.04953i
$226$	−13.5511	−	3.63100i	−0.901405	−	0.241531i
$227$	1.90921	−	7.12528i	0.126719	−	0.472922i	−0.873176	−	0.487405i	$-0.837944\pi$
$227$	1.90921	−	7.12528i	0.126719	−	0.472922i	0.999895	+	0.0144831i	$0.00461028\pi$
$228$	−1.18708	+	6.04479i	−0.0786161	+	0.400326i
$229$	3.77001	−	14.0699i	0.249129	−	0.929762i	−0.722134	−	0.691753i	$-0.756839\pi$
$229$	3.77001	−	14.0699i	0.249129	−	0.929762i	0.971263	−	0.238009i	$-0.0764948\pi$
$230$	6.87962	+	3.97195i	0.453628	+	0.261903i
$231$	−6.38199	+	6.00908i	−0.419904	+	0.395368i
$232$	1.97155	−	7.35791i	0.129438	−	0.483071i
$233$	−11.3337	−	19.6305i	−0.742493	−	1.28603i	−0.951357	−	0.308090i	$-0.900310\pi$
$233$	−11.3337	−	19.6305i	−0.742493	−	1.28603i	0.208865	−	0.977945i	$-0.433023\pi$
$234$	−3.57910	−	10.2074i	−0.233973	−	0.667276i
$235$	−0.987180	+	1.70985i	−0.0643965	+	0.111538i
$236$	6.58533	−	1.76453i	0.428668	−	0.114861i
$237$	−0.300162	−	0.446863i	−0.0194976	−	0.0290269i
$238$	−1.18085	−	1.43828i	−0.0765432	−	0.0932298i
$239$	−3.33310	−	3.33310i	−0.215600	−	0.215600i	0.591041	−	0.806641i	$-0.298717\pi$
$239$	−3.33310	−	3.33310i	−0.215600	−	0.215600i	−0.806641	+	0.591041i	$0.798717\pi$
$240$	5.66982	+	4.94791i	0.365985	+	0.319386i
$241$	−2.72052	+	10.1531i	−0.175244	+	0.654019i	0.821266	+	0.570546i	$0.193268\pi$
$241$	−2.72052	+	10.1531i	−0.175244	+	0.654019i	−0.996510	+	0.0834739i	$0.973398\pi$
$242$	−1.89999	−	7.09087i	−0.122136	−	0.455818i
$243$	14.6990	−	5.19024i	0.942943	−	0.332954i
$244$	8.92173	−	5.15096i	0.571155	−	0.329757i
$245$	−13.4402	+	27.2818i	−0.858662	+	1.74297i
$246$	0.333761	+	4.90887i	0.0212798	+	0.312978i
$247$	−8.50443	−	9.59785i	−0.541124	−	0.610697i
$248$	−6.51596	−	3.76199i	−0.413764	−	0.238887i
$249$	−1.79154	−	1.56343i	−0.113534	−	0.0990784i
$250$	−19.2822	+	33.3977i	−1.21951	+	2.11225i
$251$	4.52381	−	7.83547i	0.285540	−	0.494570i	−0.687200	−	0.726468i	$-0.741160\pi$
$251$	4.52381	−	7.83547i	0.285540	−	0.494570i	0.972740	+	0.231898i	$0.0744936\pi$
$252$	−6.71897	+	4.22557i	−0.423255	+	0.266186i
$253$	0.905218	+	3.37832i	0.0569105	+	0.212393i
$254$	−7.60127	+	7.60127i	−0.476946	+	0.476946i
$255$	5.00790	−	1.71358i	0.313607	−	0.107308i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−6.86346	+	11.8879i	−0.428131	+	0.741544i	−0.996707	−	0.0810865i	$-0.974161\pi$
$257$	−6.86346	+	11.8879i	−0.428131	+	0.741544i	0.568576	+	0.822630i	$0.307494\pi$
$258$	−6.48667	−	1.27385i	−0.403842	−	0.0793066i
$259$	−3.86883	+	0.639549i	−0.240397	+	0.0397396i
$260$	−15.3481	+	3.13472i	−0.951849	+	0.194407i
$261$	−18.0620	+	13.9999i	−1.11801	+	0.866570i
$262$	−13.3414	+	13.3414i	−0.824235	+	0.824235i
$263$			22.3462i			1.37793i	0.724796	+	0.688963i	$0.241934\pi$
$263$			22.3462i			1.37793i	−0.724796	+	0.688963i	$0.758066\pi$
$264$	0.224747	+	3.30552i	0.0138322	+	0.203441i
$265$	24.7028	−	24.7028i	1.51748	−	1.51748i
$266$	−5.47953	+	7.64994i	−0.335972	+	0.469048i
$267$	6.91480	+	20.2084i	0.423179	+	1.23673i
$268$	0.693173	−	2.58696i	0.0423423	−	0.158023i
$269$	23.1251	−	13.3513i	1.40996	−	0.814041i	0.414576	−	0.910014i	$-0.363930\pi$
$269$	23.1251	−	13.3513i	1.40996	−	0.814041i	0.995384	+	0.0959735i	$0.0305964\pi$
$270$	−4.56604	−	22.1090i	−0.277881	−	1.34551i
$271$	21.5953	−	5.78645i	1.31182	−	0.351502i	0.465914	−	0.884830i	$-0.345725\pi$
$271$	21.5953	−	5.78645i	1.31182	−	0.351502i	0.845909	+	0.533328i	$0.179059\pi$
$272$	−0.703365			−0.0426478
$273$	1.49187	−	16.4552i	0.0902918	−	0.995915i
$274$	0.851187			0.0514221
$275$	−25.6387	+	6.86986i	−1.54607	+	0.414268i
$276$	0.214827	+	3.15962i	0.0129311	+	0.190187i
$277$	−18.1674	+	10.4889i	−1.09157	+	0.630219i	−0.933995	−	0.357287i	$-0.883702\pi$
$277$	−18.1674	+	10.4889i	−1.09157	+	0.630219i	−0.157577	+	0.987507i	$0.550368\pi$
$278$	2.62690	−	9.80373i	0.157551	−	0.587989i
$279$	8.73945	+	20.8114i	0.523217	+	1.24595i
$280$	4.74616	+	10.4694i	0.283637	+	0.625664i
$281$	−7.69733	+	7.69733i	−0.459184	+	0.459184i	−0.898388	−	0.439203i	$-0.855261\pi$
$281$	−7.69733	+	7.69733i	−0.459184	+	0.459184i	0.439203	+	0.898388i	$0.355261\pi$
$282$	−0.785286	+	0.0533927i	−0.0467631	+	0.00317949i
$283$			13.9199i			0.827453i	0.910401	+	0.413726i	$0.135773\pi$
$283$			13.9199i			0.827453i	−0.910401	+	0.413726i	$0.864227\pi$
$284$	9.33994	−	9.33994i	0.554224	−	0.554224i
$285$	−14.9236	−	22.2174i	−0.883999	−	1.31604i
$286$	−5.75409	−	3.80228i	−0.340246	−	0.224834i
$287$	−2.64600	+	7.03456i	−0.156188	+	0.415237i
$288$	−0.377077	+	2.97621i	−0.0222195	+	0.175375i
$289$	8.25264	−	14.2940i	0.485449	−	0.840823i
$290$	16.5477	+	28.6615i	0.971716	+	1.68306i
$291$	−4.72991	−	13.8231i	−0.277272	−	0.810324i
$292$	−10.0357	+	10.0357i	−0.587293	+	0.587293i
$293$	3.30757	+	12.3440i	0.193230	+	0.721145i	0.992718	+	0.120462i	$0.0384377\pi$
$293$	3.30757	+	12.3440i	0.193230	+	0.721145i	−0.799488	+	0.600682i	$0.794896\pi$
$294$	−12.0161	+	1.61669i	−0.700792	+	0.0942872i
$295$	−14.8102	+	25.6520i	−0.862283	+	1.49352i
$296$	−0.741062	+	1.28356i	−0.0430734	+	0.0746053i
$297$	5.46150	−	8.30451i	0.316908	−	0.481876i
$298$	18.0776	+	10.4371i	1.04721	+	0.604606i
$299$	−5.50012	−	3.63446i	−0.318080	−	0.210186i
$300$	−23.9790	+	1.63036i	−1.38443	+	0.0941290i
$301$	−8.20915	−	5.88009i	−0.473168	−	0.338923i
$302$	−3.98079	+	2.29831i	−0.229069	+	0.132253i
$303$	27.6651	−	1.88099i	1.58932	−	0.108060i
$304$	0.920521	+	3.43543i	0.0527955	+	0.197035i
$305$	−11.5844	+	43.2334i	−0.663319	+	2.47554i
$306$	1.68029	+	1.27637i	0.0960559	+	0.0729652i
$307$	14.4885	+	14.4885i	0.826902	+	0.826902i	0.987087	−	0.160185i	$-0.0512092\pi$
$307$	14.4885	+	14.4885i	0.826902	+	0.826902i	−0.160185	+	0.987087i	$0.551209\pi$
$308$	−1.78175	+	4.73691i	−0.101525	+	0.269910i
$309$	−0.809200	+	0.543547i	−0.0460338	+	0.0309213i
$310$	31.5754	−	8.46061i	1.79336	−	0.480530i
$311$	−13.5468	+	23.4638i	−0.768170	+	1.33051i	0.170384	+	0.985378i	$0.445499\pi$
$311$	−13.5468	+	23.4638i	−0.768170	+	1.33051i	−0.938554	+	0.345132i	$0.887834\pi$
$312$	−4.44913	−	4.38238i	−0.251882	−	0.248103i
$313$	0.0972614	+	0.168462i	0.00549754	+	0.00952202i	0.868761	−	0.495231i	$-0.164917\pi$
$313$	0.0972614	+	0.168462i	0.00549754	+	0.00952202i	−0.863264	+	0.504753i	$0.831583\pi$
$314$	−2.82950	+	10.5598i	−0.159678	+	0.595926i
$315$	7.66011	−	33.6233i	0.431598	−	1.89446i
$316$	−0.269158	−	0.155398i	−0.0151413	−	0.00874184i
$317$	−2.25773	+	8.42596i	−0.126807	+	0.473249i	−0.999898	−	0.0143085i	$-0.995445\pi$
$317$	−2.25773	+	8.42596i	−0.126807	+	0.473249i	0.873091	+	0.487557i	$0.162112\pi$
$318$	13.6662	+	2.68377i	0.766362	+	0.150498i
$319$	−3.77127	+	14.0746i	−0.211151	+	0.788025i
$320$	4.19664	+	1.12449i	0.234599	+	0.0628606i
$321$	16.1635	+	7.92204i	0.902158	+	0.442165i
$322$	−1.70311	+	4.52783i	−0.0949107	+	0.252326i
$323$	2.41636	+	0.647462i	0.134450	+	0.0360258i
$324$	6.30162	−	6.42569i	0.350090	−	0.356983i
$325$	27.5826	−	41.7414i	1.53001	−	2.31540i
$326$	−8.08167	−	4.66596i	−0.447602	−	0.258423i
$327$	−4.71866	−	13.7902i	−0.260943	−	0.762601i
$328$	1.42034	+	2.46010i	0.0784252	+	0.135836i
$329$	−1.12534	−	0.423288i	−0.0620419	−	0.0233366i
$330$	−10.8455	−	9.46460i	−0.597026	−	0.521009i
$331$	20.3694	−	20.3694i	1.11961	−	1.11961i	0.127807	−	0.991799i	$-0.459206\pi$
$331$	20.3694	−	20.3694i	1.11961	−	1.11961i	0.991799	−	0.127807i	$-0.0407937\pi$
$332$	−1.32604	−	0.355313i	−0.0727762	−	0.0195003i
$333$	4.09957	−	1.72156i	0.224655	−	0.0943407i
$334$	9.70778			0.531186
$335$	5.81799	+	10.0770i	0.317871	+	0.550568i
$336$	−2.40963	+	3.89791i	−0.131456	+	0.212648i
$337$			1.00336i			0.0546566i	0.999627	+	0.0273283i	$0.00869995\pi$
$337$			1.00336i			0.0546566i	−0.999627	+	0.0273283i	$0.991300\pi$
$338$	12.8707	−	1.82875i	0.700075	−	0.0994710i
$339$	21.8194	+	10.6941i	1.18507	+	0.580823i
$340$	2.16084	−	2.16084i	0.117188	−	0.117188i
$341$	12.4641	+	7.19612i	0.674966	+	0.389692i
$342$	4.03508	−	9.87745i	0.218192	−	0.534111i
$343$	−17.7260	−	5.36541i	−0.957116	−	0.289705i
$344$	−3.68656	+	0.987812i	−0.198766	+	0.0532592i
$345$	−10.3668	−	9.04686i	−0.558131	−	0.487066i
$346$	5.12022	−	1.37196i	0.275265	−	0.0737569i
$347$	−20.9701	+	12.1071i	−1.12574	+	0.649944i	−0.942859	−	0.333192i	$-0.891874\pi$
$347$	−20.9701	+	12.1071i	−1.12574	+	0.649944i	−0.182877	+	0.983136i	$0.558541\pi$
$348$	−5.80663	+	11.8474i	−0.311268	+	0.635087i
$349$	−1.03946	+	3.87933i	−0.0556411	+	0.207656i	−0.988150	−	0.153492i	$-0.950948\pi$
$349$	−1.03946	+	3.87933i	−0.0556411	+	0.207656i	0.932509	+	0.361147i	$0.117615\pi$
$350$	−34.3625	−	12.9252i	−1.83676	−	0.690882i
$351$	2.67613	+	18.5429i	0.142841	+	0.989746i
$352$	0.956425	+	1.65658i	0.0509776	+	0.0882958i
$353$	9.93251	+	9.93251i	0.528654	+	0.528654i	0.920171	−	0.391517i	$-0.128050\pi$
$353$	9.93251	+	9.93251i	0.528654	+	0.528654i	−0.391517	+	0.920171i	$0.628050\pi$
$354$	−11.7813	+	0.801025i	−0.626168	+	0.0425740i
$355$			57.3874i			3.04581i
$356$	8.71965	+	8.71965i	0.462141	+	0.462141i
$357$	1.52691	+	2.83861i	0.0808128	+	0.150235i
$358$	−11.8070	+	3.16368i	−0.624021	+	0.167206i
$359$	−14.7324	−	3.94752i	−0.777544	−	0.208342i	−0.151843	−	0.988405i	$-0.548521\pi$
$359$	−14.7324	−	3.94752i	−0.777544	−	0.208342i	−0.625702	+	0.780062i	$0.715187\pi$
$360$	−7.98492	−	10.3018i	−0.420842	−	0.542952i
$361$			6.35046i			0.334234i
$362$	0.200018	+	0.746476i	0.0105127	+	0.0392339i
$363$	0.862519	+	12.6857i	0.0452705	+	0.665827i
$364$	−3.40773	−	8.90996i	−0.178613	−	0.467009i
$365$		−	61.6622i		−	3.22755i
$366$	−16.8825	+	5.77675i	−0.882461	+	0.301956i
$367$	19.0750			0.995707			0.497853	−	0.867261i	$-0.334122\pi$
$367$	19.0750			0.995707			0.497853	+	0.867261i	$0.334122\pi$
$368$	0.914210	+	1.58346i	0.0476565	+	0.0825435i
$369$	1.07116	−	8.45446i	0.0557621	−	0.440122i
$370$	−1.66663	−	6.21994i	−0.0866438	−	0.323359i
$371$	17.2952	+	12.3882i	0.897920	+	0.643166i
$372$	9.81883	+	8.56864i	0.509083	+	0.444263i
$373$	−20.6207			−1.06770			−0.533851	−	0.845579i	$-0.679256\pi$
$373$	−20.6207			−1.06770			−0.533851	+	0.845579i	$0.679256\pi$
$374$	1.34543			0.0695706
$375$	43.9187	−	50.3266i	2.26795	−	2.59885i
$376$	−0.393550	+	0.227216i	−0.0202958	+	0.0117178i
$377$	−12.2735	−	24.5702i	−0.632119	−	1.26543i
$378$	12.8298	−	4.93917i	0.659895	−	0.254043i
$379$	28.8905	+	7.74120i	1.48401	+	0.397639i	0.907709	−	0.419600i	$-0.137830\pi$
$379$	28.8905	+	7.74120i	1.48401	+	0.397639i	0.576299	+	0.817239i	$0.304496\pi$
$380$	−13.3821	−	7.72618i	−0.686489	−	0.396345i
$381$	15.4561	−	10.3820i	0.791839	−	0.531886i
$382$	−3.28104	−	12.2450i	−0.167873	−	0.626510i
$383$	−19.2054	−	19.2054i	−0.981351	−	0.981351i	0.0184784	−	0.999829i	$-0.494118\pi$
$383$	−19.2054	−	19.2054i	−0.981351	−	0.981351i	−0.999829	+	0.0184784i	$0.994118\pi$
$384$	0.560745	+	1.63877i	0.0286154	+	0.0836281i
$385$	−9.07868	−	20.0263i	−0.462692	−	1.02064i
$386$	1.74444	+	1.00715i	0.0887895	+	0.0512627i
$387$	10.5995	+	4.33005i	0.538803	+	0.220109i
$388$	−5.96447	−	5.96447i	−0.302800	−	0.302800i
$389$	−3.66874	+	6.35444i	−0.186012	+	0.322183i	−0.943917	−	0.330182i	$-0.892890\pi$
$389$	−3.66874	+	6.35444i	−0.186012	+	0.322183i	0.757905	+	0.652365i	$0.226223\pi$
$390$	27.1317	−	0.205062i	1.37387	−	0.0103837i
$391$	1.28605			0.0650382
$392$	−5.81872	+	3.89134i	−0.293890	+	0.196542i
$393$	27.1278	−	18.2220i	1.36842	−	0.919179i
$394$		−	6.84127i		−	0.344658i
$395$	1.30430	−	0.349486i	0.0656264	−	0.0175846i
$396$	0.721291	−	5.69304i	0.0362462	−	0.286086i
$397$	−3.98862	−	3.98862i	−0.200183	−	0.200183i	0.599895	−	0.800078i	$-0.295209\pi$
$397$	−3.98862	−	3.98862i	−0.200183	−	0.200183i	−0.800078	+	0.599895i	$0.795209\pi$
$398$	14.4939	−	14.4939i	0.726513	−	0.726513i
$399$	11.8662	−	11.1729i	0.594055	−	0.559343i
$400$	−12.0172	+	6.93811i	−0.600858	+	0.346905i
$401$	−3.99356	−	14.9042i	−0.199429	−	0.744278i	−0.991076	−	0.133300i	$-0.957443\pi$
$401$	−3.99356	−	14.9042i	−0.199429	−	0.744278i	0.791647	−	0.610979i	$-0.209224\pi$
$402$	−2.04154	+	4.16540i	−0.101823	+	0.207751i
$403$	−26.5794	+	5.42861i	−1.32401	+	0.270418i
$404$	13.8645	−	8.00466i	0.689783	−	0.398247i
$405$	0.381166	+	39.1002i	0.0189403	+	1.94291i
$406$	−15.5766	+	12.7887i	−0.773055	+	0.634691i
$407$	1.41754	−	2.45525i	0.0702649	−	0.121702i
$408$	1.19543	+	0.234759i	0.0591826	+	0.0116223i
$409$	−0.0271377	−	0.00727153i	−0.00134187	−	0.000359554i	0.258148	−	0.966105i	$-0.416888\pi$
$409$	−0.0271377	−	0.00727153i	−0.00134187	−	0.000359554i	−0.259490	+	0.965746i	$0.583554\pi$
$410$	−11.9213	−	3.19430i	−0.588751	−	0.157755i
$411$	−1.44667	−	0.284097i	−0.0713588	−	0.0140135i
$412$	−0.281403	+	0.487403i	−0.0138637	+	0.0240126i
$413$	−16.8829	−	6.35039i	−0.830754	−	0.312482i
$414$	0.689455	−	5.44176i	0.0338849	−	0.267448i
$415$	5.16538	−	2.98224i	0.253559	−	0.146392i
$416$	−3.42010	−	1.14147i	−0.167684	−	0.0559651i
$417$	−7.73680	+	15.7855i	−0.378873	+	0.773021i
$418$	−1.76082	−	6.57146i	−0.0861244	−	0.321421i
$419$	−9.40071	+	5.42750i	−0.459255	+	0.265151i	−0.711731	−	0.702452i	$-0.752088\pi$
$419$	−9.40071	+	5.42750i	−0.459255	+	0.265151i	0.252476	+	0.967603i	$0.418755\pi$
$420$	−4.57220	−	19.3777i	−0.223100	−	0.945535i
$421$	15.2184	−	15.2184i	0.741700	−	0.741700i	−0.231205	−	0.972905i	$-0.574267\pi$
$421$	15.2184	−	15.2184i	0.741700	−	0.741700i	0.972905	+	0.231205i	$0.0742668\pi$
$422$	9.15662	+	9.15662i	0.445737	+	0.445737i
$423$	1.35248	+	0.171356i	0.0657600	+	0.00833161i
$424$	7.76690	−	2.08113i	0.377194	−	0.101069i
$425$			9.76005i			0.473432i
$426$	−18.9914	+	12.7567i	−0.920137	+	0.618065i
$427$	−27.1256	−	2.66611i	−1.31270	−	0.129022i
$428$	10.3926			0.502345
$429$	8.51051	+	8.38283i	0.410891	+	0.404727i
$430$	8.29097	−	14.3604i	0.399826	−	0.692519i
$431$	−17.0428	−	17.0428i	−0.820924	−	0.820924i	0.165316	−	0.986241i	$-0.447136\pi$
$431$	−17.0428	−	17.0428i	−0.820924	−	0.820924i	−0.986241	+	0.165316i	$0.947136\pi$
$432$	1.63423	−	4.93247i	0.0786270	−	0.237314i
$433$	−2.73877	−	1.58123i	−0.131617	−	0.0759891i	0.432746	−	0.901516i	$-0.357545\pi$
$433$	−2.73877	−	1.58123i	−0.131617	−	0.0759891i	−0.564363	+	0.825527i	$0.690878\pi$
$434$	8.21925	+	18.1305i	0.394537	+	0.870294i
$435$	−18.5581	−	54.2358i	−0.889793	−	2.60041i
$436$	−5.95029	−	5.95029i	−0.284967	−	0.284967i
$437$	−1.68310	−	6.28141i	−0.0805136	−	0.300481i
$438$	20.4061	−	13.7069i	0.975039	−	0.654943i
$439$	−14.7347	−	8.50708i	−0.703249	−	0.406021i	0.105307	−	0.994440i	$-0.466417\pi$
$439$	−14.7347	−	8.50708i	−0.703249	−	0.406021i	−0.808556	+	0.588419i	$0.799751\pi$
$440$	−8.02753	−	2.15097i	−0.382698	−	0.102543i
$441$	20.9620	+	1.26285i	0.998190	+	0.0601356i
$442$	−1.89809	+	1.68185i	−0.0902830	+	0.0799977i
$443$	−4.31236	+	2.48974i	−0.204886	+	0.118291i	−0.598933	−	0.800799i	$-0.704408\pi$
$443$	−4.31236	+	2.48974i	−0.204886	+	0.118291i	0.394046	+	0.919091i	$0.371075\pi$
$444$	1.68791	−	1.93418i	0.0801046	−	0.0917921i
$445$	−53.5762			−2.53975
$446$	11.4835			0.543759
$447$	−27.2410	−	23.7725i	−1.28845	−	1.12440i
$448$	−0.258797	+	2.63306i	−0.0122270	+	0.124401i
$449$	8.91938	+	33.2876i	0.420932	+	1.57094i	0.772650	+	0.634832i	$0.218931\pi$
$449$	8.91938	+	33.2876i	0.420932	+	1.57094i	−0.351718	+	0.936106i	$0.614402\pi$
$450$	41.2985	+	5.23240i	1.94683	+	0.246658i
$451$	−2.71690	−	4.70580i	−0.127934	−	0.221588i
$452$	14.0291			0.659874
$453$	7.53280	−	2.57753i	0.353922	−	0.121103i
$454$			7.37664i			0.346203i
$455$	37.8418	+	16.9037i	1.77405	+	0.792458i
$456$	−0.417879	−	6.14606i	−0.0195690	−	0.287815i
$457$	−0.510419	−	1.90491i	−0.0238764	−	0.0891079i	0.952960	−	0.303098i	$-0.0980208\pi$
$457$	−0.510419	−	1.90491i	−0.0238764	−	0.0891079i	−0.976836	+	0.213990i	$0.931354\pi$
$458$			14.5662i			0.680633i
$459$	−2.42980	−	2.73013i	−0.113413	−	0.127431i
$460$	−7.67322	−	2.05603i	−0.357766	−	0.0958630i
$461$	−13.1727	+	3.52962i	−0.613515	+	0.164391i	−0.552178	−	0.833726i	$-0.686203\pi$
$461$	−13.1727	+	3.52962i	−0.613515	+	0.164391i	−0.0613369	+	0.998117i	$0.519536\pi$
$462$	4.60926	−	7.45611i	0.214442	−	0.346889i
$463$	5.51839	+	5.51839i	0.256461	+	0.256461i	0.823613	−	0.567152i	$-0.191955\pi$
$463$	5.51839	+	5.51839i	0.256461	+	0.256461i	−0.567152	+	0.823613i	$0.691955\pi$
$464$			7.61747i			0.353632i
$465$	−56.4891	+	3.84077i	−2.61962	+	0.178111i
$466$	16.0282	+	16.0282i	0.742493	+	0.742493i
$467$	7.36371	+	12.7543i	0.340752	+	0.590200i	0.984573	−	0.174977i	$-0.0559850\pi$
$467$	7.36371	+	12.7543i	0.340752	+	0.590200i	−0.643821	+	0.765177i	$0.722652\pi$
$468$	6.09900	+	8.93321i	0.281926	+	0.412938i
$469$	−5.47656	+	4.49635i	−0.252884	+	0.207622i
$470$	0.511002	−	1.90709i	0.0235708	−	0.0879673i
$471$	8.33350	−	17.0030i	0.383987	−	0.783457i
$472$	−5.90424	+	3.40882i	−0.271765	+	0.156903i
$473$	7.05184	−	1.88953i	0.324244	−	0.0868809i
$474$	0.405591	+	0.353949i	0.0186294	+	0.0162574i
$475$	47.6708	−	12.7734i	2.18729	−	0.586082i
$476$	1.51287	+	1.08364i	0.0693422	+	0.0496687i
$477$	−22.3312	−	9.12261i	−1.02247	−	0.417695i
$478$	4.08220	+	2.35686i	0.186715	+	0.107800i
$479$	12.1470	−	12.1470i	0.555009	−	0.555009i	−0.372874	−	0.927882i	$-0.621627\pi$
$479$	12.1470	−	12.1470i	0.555009	−	0.555009i	0.927882	+	0.372874i	$0.121627\pi$
$480$	−6.75724	−	3.31185i	−0.308424	−	0.151165i
$481$	1.06936	+	5.23579i	0.0487588	+	0.238731i
$482$		−	10.5113i		−	0.478775i
$483$	4.40582	−	7.12701i	0.200472	−	0.324290i
$484$	3.67050	+	6.35750i	0.166841	+	0.288977i
$485$	36.6475			1.66408
$486$	−12.8548	+	8.81777i	−0.583107	+	0.399982i
$487$	12.6766	+	3.39668i	0.574431	+	0.153918i	0.534328	−	0.845277i	$-0.320565\pi$
$487$	12.6766	+	3.39668i	0.574431	+	0.153918i	0.0401029	+	0.999196i	$0.487231\pi$
$488$	−7.28456	+	7.28456i	−0.329757	+	0.329757i
$489$	12.1782	+	10.6276i	0.550716	+	0.480596i
$490$	5.92118	−	29.8308i	0.267492	−	1.34762i
$491$	−3.28493	−	5.68966i	−0.148247	−	0.256771i	0.782333	−	0.622861i	$-0.214030\pi$
$491$	−3.28493	−	5.68966i	−0.148247	−	0.256771i	−0.930579	+	0.366090i	$0.880696\pi$
$492$	−1.59290	−	4.65522i	−0.0718134	−	0.209874i
$493$	4.64004	+	2.67893i	0.208977	+	0.120653i
$494$	10.6988	+	7.06970i	0.481360	+	0.318081i
$495$	15.2740	+	19.7058i	0.686513	+	0.885709i
$496$	7.26761	+	1.94735i	0.326325	+	0.0874386i
$497$	−34.4789	+	5.69965i	−1.54659	+	0.255664i
$498$	2.13514	+	1.04647i	0.0956779	+	0.0468936i
$499$	−33.9764	−	9.10395i	−1.52099	−	0.407549i	−0.600925	−	0.799306i	$-0.705201\pi$
$499$	−33.9764	−	9.10395i	−1.52099	−	0.407549i	−0.920069	+	0.391757i	$0.871867\pi$
$500$	9.98118	−	37.2503i	0.446372	−	1.66588i
$501$	−16.4992	−	3.24012i	−0.737131	−	0.144758i
$502$	−2.34170	+	8.73933i	−0.104515	+	0.390055i
$503$	16.1705	+	9.33603i	0.721006	+	0.416273i	0.815123	−	0.579288i	$-0.196669\pi$
$503$	16.1705	+	9.33603i	0.721006	+	0.416273i	−0.0941167	+	0.995561i	$0.530003\pi$
$504$	5.39637	−	5.82058i	0.240373	−	0.259269i
$505$	−18.0022	+	67.1853i	−0.801089	+	2.98971i
$506$	−1.74875	−	3.02892i	−0.0777413	−	0.134652i
$507$	−22.4853	−	1.18768i	−0.998608	−	0.0527466i
$508$	5.37491	−	9.30962i	0.238473	−	0.413048i
$509$	27.2472	−	7.30085i	1.20771	−	0.323605i	0.401846	−	0.915707i	$-0.368369\pi$
$509$	27.2472	−	7.30085i	1.20771	−	0.323605i	0.805863	+	0.592103i	$0.201702\pi$
$510$	−4.39376	+	2.95133i	−0.194559	+	0.130687i
$511$	37.0472	−	6.12421i	1.63887	−	0.270919i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	−10.1547	+	15.4408i	−0.448342	+	0.681729i
$514$	3.55279	−	13.2592i	0.156707	−	0.584837i
$515$	−0.632866	−	2.36189i	−0.0278874	−	0.104077i
$516$	6.59534	−	0.448426i	0.290344	−	0.0197408i
$517$	0.752801	−	0.434630i	0.0331082	−	0.0191150i
$518$	3.57147	−	1.61908i	0.156922	−	0.0711384i
$519$	−9.16017	+	0.622813i	−0.402087	+	0.0273384i
$520$	14.0138	−	7.00029i	0.614546	−	0.306983i
$521$	−26.7604	−	15.4501i	−1.17239	−	0.676881i	−0.218151	−	0.975915i	$-0.570002\pi$
$521$	−26.7604	−	15.4501i	−1.17239	−	0.676881i	−0.954243	+	0.299034i	$0.903336\pi$
$522$	13.8231	−	18.1976i	0.605022	−	0.796489i
$523$	13.0710	−	22.6396i	0.571553	−	0.989958i	−0.424854	−	0.905262i	$-0.639675\pi$
$523$	13.0710	−	22.6396i	0.571553	−	0.989958i	0.996407	−	0.0846966i	$-0.0269921\pi$
$524$	9.43381	−	16.3398i	0.412118	−	0.713809i
$525$	54.0882	+	33.4366i	2.36060	+	1.45929i
$526$	−5.78363	−	21.5848i	−0.252178	−	0.941141i
$527$	3.74208	−	3.74208i	0.163008	−	0.163008i
$528$	−1.07262	−	3.13472i	−0.0466798	−	0.136421i
$529$	9.82844	+	17.0234i	0.427323	+	0.740146i
$530$	−17.4675	+	30.2546i	−0.758741	+	1.31418i
$531$	20.2907	+	2.57077i	0.880541	+	0.111562i
$532$	3.31287	−	8.80748i	0.143631	−	0.381853i
$533$	9.71540	+	3.24255i	0.420821	+	0.140450i
$534$	−11.9095	−	17.7301i	−0.515375	−	0.767258i
$535$	−31.9276	+	31.9276i	−1.38035	+	1.38035i
$536$			2.67821i			0.115681i
$537$	21.1230	−	1.43618i	0.911526	−	0.0619759i
$538$	−18.8815	+	18.8815i	−0.814041	+	0.814041i
$539$	11.1303	−	7.44355i	0.479417	−	0.320616i
$540$	10.1327	+	20.1739i	0.436042	+	0.868147i
$541$	−2.24375	+	8.37380i	−0.0964665	+	0.360018i	−0.997238	−	0.0742761i	$-0.976335\pi$
$541$	−2.24375	+	8.37380i	−0.0964665	+	0.360018i	0.900771	+	0.434294i	$0.143002\pi$
$542$	−19.3618	+	11.1786i	−0.831663	+	0.480161i
$543$	−0.0907998	−	1.33546i	−0.00389659	−	0.0573101i
$544$	0.679398	−	0.182044i	0.0291290	−	0.00780508i
$545$	36.5604			1.56608
$546$	2.81789	+	16.2806i	0.120595	+	0.696747i
$547$	−34.8587			−1.49045			−0.745225	−	0.666813i	$-0.767658\pi$
$547$	−34.8587			−1.49045			−0.745225	+	0.666813i	$0.767658\pi$
$548$	−0.822183	+	0.220303i	−0.0351219	+	0.00941089i
$549$	30.6213	−	4.18331i	1.30689	−	0.178539i
$550$	22.9870	−	13.2716i	0.980169	−	0.565901i
$551$	7.01204	−	26.1693i	0.298723	−	1.11485i
$552$	−1.02528	−	2.99636i	−0.0436387	−	0.127534i
$553$	0.339516	+	0.748926i	0.0144377	+	0.0318476i
$554$	14.8336	−	14.8336i	0.630219	−	0.630219i
$555$	0.756581	+	11.1276i	0.0321151	+	0.472340i
$556$			10.1496i			0.430438i
$557$	−17.3299	+	17.3299i	−0.734289	+	0.734289i	−0.971466	−	0.237177i	$-0.923778\pi$
$557$	−17.3299	+	17.3299i	−0.734289	+	0.734289i	0.237177	+	0.971466i	$0.423778\pi$
$558$	−13.8281	−	17.8403i	−0.585388	−	0.755242i
$559$	−7.58650	+	11.4808i	−0.320875	+	0.485588i
$560$	−7.29410	−	8.88423i	−0.308232	−	0.375427i
$561$	−2.28668	−	0.449058i	−0.0965436	−	0.0189593i
$562$	5.44284	−	9.42727i	0.229592	−	0.397665i
$563$	−22.5671	−	39.0874i	−0.951090	−	1.64734i	−0.743072	−	0.669212i	$-0.766632\pi$
$563$	−22.5671	−	39.0874i	−0.951090	−	1.64734i	−0.208019	−	0.978125i	$-0.566702\pi$
$564$	0.744709	−	0.254820i	0.0313579	−	0.0107299i
$565$	−43.0996	+	43.0996i	−1.81321	+	1.81321i
$566$	−3.60274	−	13.4456i	−0.151434	−	0.565161i
$567$	−23.4540	+	4.11240i	−0.984974	+	0.172704i
$568$	−6.60434	+	11.4390i	−0.277112	+	0.479972i
$569$	19.2515	−	33.3446i	0.807065	−	1.39788i	−0.107823	−	0.994170i	$-0.534388\pi$
$569$	19.2515	−	33.3446i	0.807065	−	1.39788i	0.914888	−	0.403708i	$-0.132279\pi$
$570$	20.1654	+	17.5978i	0.844636	+	0.737092i
$571$	7.09334	+	4.09534i	0.296847	+	0.171385i	0.641026	−	0.767519i	$-0.278509\pi$
$571$	7.09334	+	4.09534i	0.296847	+	0.171385i	−0.344179	+	0.938904i	$0.611843\pi$
$572$	6.54213	+	2.18346i	0.273540	+	0.0912949i
$573$	1.48946	+	21.9066i	0.0622231	+	0.915161i
$574$	0.735161	−	7.47970i	0.0306850	−	0.312196i
$575$	21.9724	−	12.6858i	0.916313	−	0.529034i
$576$	−0.406071	−	2.97239i	−0.0169196	−	0.123850i
$577$	3.58621	+	13.3839i	0.149296	+	0.557180i	0.999527	+	0.0307697i	$0.00979584\pi$
$577$	3.58621	+	13.3839i	0.149296	+	0.557180i	−0.850231	+	0.526411i	$0.823537\pi$
$578$	−4.27188	+	15.9429i	−0.177687	+	0.663136i
$579$	−2.62867	−	2.29398i	−0.109244	−	0.0953344i
$580$	−23.4020	−	23.4020i	−0.971716	−	0.971716i
$581$	2.30478	+	2.80722i	0.0956183	+	0.116463i
$582$	8.14642	+	12.1279i	0.337680	+	0.502717i
$583$	−14.8569	+	3.98090i	−0.615310	+	0.164872i
$584$	7.09629	−	12.2911i	0.293647	−	0.508611i
$585$	−46.1812	−	8.70711i	−1.90936	−	0.359995i
$586$	−6.38973	−	11.0673i	−0.263957	−	0.457187i
$587$	−3.18558	+	11.8888i	−0.131483	+	0.490701i	−0.999988	−	0.00497976i	$-0.998415\pi$
$587$	−3.18558	+	11.8888i	−0.131483	+	0.490701i	0.868505	+	0.495681i	$0.165082\pi$
$588$	11.1882	−	4.67159i	0.461394	−	0.192653i
$589$	−23.1748	−	13.3800i	−0.954901	−	0.551312i
$590$	7.66632	−	28.6111i	0.315618	−	1.17790i
$591$	−2.28338	+	11.6273i	−0.0939256	+	0.478285i
$592$	0.383602	−	1.43162i	0.0157660	−	0.0588393i
$593$	−12.9309	−	3.46484i	−0.531010	−	0.142284i	−0.0166555	−	0.999861i	$-0.505302\pi$
$593$	−12.9309	−	3.46484i	−0.531010	−	0.142284i	−0.514355	+	0.857578i	$0.671969\pi$
$594$	−3.12604	+	9.43508i	−0.128263	+	0.387126i
$595$	−7.97688	+	1.31864i	−0.327020	+	0.0540591i
$596$	−20.1630	−	5.40265i	−0.825908	−	0.221301i
$597$	−29.4712	+	19.7961i	−1.20618	+	0.810200i
$598$	6.25337	+	2.08708i	0.255719	+	0.0853472i
$599$	0.589433	+	0.340309i	0.0240836	+	0.0139047i	0.511993	−	0.858989i	$-0.328907\pi$
$599$	0.589433	+	0.340309i	0.0240836	+	0.0139047i	−0.487910	+	0.872894i	$0.662241\pi$
$600$	22.7399	−	7.78102i	0.928354	−	0.317659i
$601$	−1.74839	−	3.02830i	−0.0713184	−	0.123527i	0.828161	−	0.560490i	$-0.189387\pi$
$601$	−1.74839	−	3.02830i	−0.0713184	−	0.123527i	−0.899479	+	0.436963i	$0.856054\pi$
$602$	9.45131	+	3.55504i	0.385207	+	0.144893i
$603$	4.86005	−	6.39807i	0.197917	−	0.260550i
$604$	3.25030	−	3.25030i	0.132253	−	0.132253i
$605$	−30.8075	−	8.25486i	−1.25250	−	0.335608i
$606$	−26.2356	+	8.97714i	−1.06575	+	0.364672i
$607$	26.1270			1.06046			0.530231	−	0.847853i	$-0.322105\pi$
$607$	26.1270			1.06046			0.530231	+	0.847853i	$0.322105\pi$
$608$	−1.77831	−	3.08012i	−0.0721200	−	0.124915i
$609$	30.7423	−	16.5365i	1.24574	−	0.670094i
$610$		−	44.7585i		−	1.81222i
$611$	−0.518720	+	1.55420i	−0.0209851	+	0.0628762i
$612$	−1.95339	−	0.797987i	−0.0789609	−	0.0322567i
$613$	28.5138	−	28.5138i	1.15166	−	1.15166i	0.165442	−	0.986219i	$-0.447095\pi$
$613$	28.5138	−	28.5138i	1.15166	−	1.15166i	0.986219	−	0.165442i	$-0.0529052\pi$
$614$	−17.7447	−	10.2449i	−0.716118	−	0.413451i
$615$	19.1952	+	9.40792i	0.774024	+	0.379364i
$616$	0.495040	−	5.03665i	0.0199457	−	0.202933i
$617$	12.8924	−	3.45450i	0.519028	−	0.139073i	0.0102110	−	0.999948i	$-0.496750\pi$
$617$	12.8924	−	3.45450i	0.519028	−	0.139073i	0.508817	+	0.860875i	$0.330083\pi$
$618$	0.640947	−	0.734463i	0.0257827	−	0.0295444i
$619$	−20.6664	+	5.53754i	−0.830651	+	0.222572i	−0.648998	−	0.760790i	$-0.724812\pi$
$619$	−20.6664	+	5.53754i	−0.830651	+	0.222572i	−0.181654	+	0.983363i	$0.558145\pi$
$620$	−28.3097	+	16.3446i	−1.13695	+	0.656417i
$621$	−2.98806	+	9.01863i	−0.119907	+	0.361905i
$622$	7.01235	−	26.1705i	0.281170	−	1.04934i
$623$	−5.32112	−	32.1891i	−0.213186	−	1.28963i
$624$	5.43177	+	3.08153i	0.217445	+	0.123360i
$625$	49.0842	+	85.0163i	1.96337	+	3.40065i
$626$	−0.137548	−	0.137548i	−0.00549754	−	0.00549754i
$627$	0.799339	+	11.7565i	0.0319225	+	0.469509i
$628$		−	10.9324i		−	0.436248i
$629$	−0.737141	−	0.737141i	−0.0293917	−	0.0293917i
$630$	1.30325	+	34.4602i	0.0519226	+	1.37293i
$631$	7.73214	−	2.07182i	0.307812	−	0.0824779i	−0.101607	−	0.994825i	$-0.532398\pi$
$631$	7.73214	−	2.07182i	0.307812	−	0.0824779i	0.409418	+	0.912347i	$0.365732\pi$
$632$	0.300206	+	0.0804401i	0.0119416	+	0.00319973i
$633$	−12.5063	−	18.6187i	−0.497082	−	0.740025i
$634$		−	8.72319i		−	0.346442i
$635$	12.0880	+	45.1131i	0.479698	+	1.79026i
$636$	−13.8951	+	0.944750i	−0.550978	+	0.0374618i
$637$	−6.39751	+	24.4146i	−0.253479	+	0.967341i
$638$		−	14.5711i		−	0.576874i
$639$	36.5353	−	15.3425i	1.44532	−	0.606939i
$640$	−4.34468			−0.171738
$641$	6.45150	+	11.1743i	0.254819	+	0.441360i	0.964846	−	0.262815i	$-0.0846507\pi$
$641$	6.45150	+	11.1743i	0.254819	+	0.441360i	−0.710027	+	0.704174i	$0.751317\pi$
$642$	−17.6631	−	3.46868i	−0.697108	−	0.136898i
$643$	−9.32124	−	34.7873i	−0.367594	−	1.37188i	−0.863870	−	0.503714i	$-0.831966\pi$
$643$	−9.32124	−	34.7873i	−0.367594	−	1.37188i	0.496277	−	0.868164i	$-0.334700\pi$
$644$	0.473190	−	4.81435i	0.0186463	−	0.189712i
$645$	−18.8842	+	21.6395i	−0.743566	+	0.852054i
$646$	−2.50160			−0.0984242
$647$	−2.75300			−0.108231			−0.0541157	−	0.998535i	$-0.517234\pi$
$647$	−2.75300			−0.108231			−0.0541157	+	0.998535i	$0.517234\pi$
$648$	−4.42381	+	7.83772i	−0.173784	+	0.307895i
$649$	11.2939	−	6.52055i	0.443325	−	0.255954i
$650$	−15.8393	+	47.4580i	−0.621267	+	1.86146i
$651$	−7.91800	−	33.5577i	−0.310331	−	1.31523i
$652$	9.01393	+	2.41528i	0.353013	+	0.0945895i
$653$	6.75178	+	3.89814i	0.264218	+	0.152546i	0.626257	−	0.779617i	$-0.284586\pi$
$653$	6.75178	+	3.89814i	0.264218	+	0.152546i	−0.362039	+	0.932163i	$0.617919\pi$
$654$	8.12705	+	12.0991i	0.317793	+	0.473110i
$655$	21.2163	+	79.1805i	0.828991	+	3.09384i
$656$	−2.00867	−	2.00867i	−0.0784252	−	0.0784252i
$657$	−39.2568	+	16.4853i	−1.53155	+	0.643154i
$658$	1.19655	+	0.117606i	0.0466463	+	0.00458475i
$659$	30.1598	+	17.4128i	1.17486	+	0.678306i	0.954820	−	0.297185i	$-0.0960479\pi$
$659$	30.1598	+	17.4128i	1.17486	+	0.678306i	0.220040	+	0.975491i	$0.429381\pi$
$660$	12.9256	+	6.33508i	0.503127	+	0.246593i
$661$	−24.9621	−	24.9621i	−0.970914	−	0.970914i	0.0286743	−	0.999589i	$-0.490871\pi$
$661$	−24.9621	−	24.9621i	−0.970914	−	0.970914i	−0.999589	+	0.0286743i	$0.990871\pi$
$662$	−14.4034	+	24.9474i	−0.559803	+	0.969607i
$663$	3.78732	−	2.22494i	0.147087	−	0.0864096i
$664$	1.37282			0.0532759
$665$	16.8803	+	37.2355i	0.654589	+	1.44393i
$666$	−3.51431	+	2.72394i	−0.136177	+	0.105551i
$667$		−	13.9279i		−	0.539292i
$668$	−9.37699	+	2.51256i	−0.362807	+	0.0972138i
$669$	−19.5172	−	3.83279i	−0.754578	−	0.148184i
$670$	−8.22788	−	8.22788i	−0.317871	−	0.317871i
$671$	13.9343	−	13.9343i	0.537926	−	0.537926i
$672$	1.31867	−	4.38875i	0.0508690	−	0.169300i
$673$	22.7367	−	13.1271i	0.876437	−	0.506011i	0.00695514	−	0.999976i	$-0.497786\pi$
$673$	22.7367	−	13.1271i	0.876437	−	0.506011i	0.869482	+	0.493965i	$0.164453\pi$
$674$	−0.259689	−	0.969173i	−0.0100028	−	0.0373311i
$675$	−68.4441	−	22.6769i	−2.63441	−	0.872836i
$676$	−11.9589	+	5.09763i	−0.459956	+	0.196063i
$677$	−28.1917	+	16.2765i	−1.08349	+	0.625555i	−0.931837	−	0.362878i	$-0.881794\pi$
$677$	−28.1917	+	16.2765i	−1.08349	+	0.625555i	−0.151657	+	0.988433i	$0.548461\pi$
$678$	−23.8437	−	4.68243i	−0.915713	−	0.179828i
$679$	3.63979	+	22.0182i	0.139682	+	0.844981i
$680$	−1.52795	+	2.64648i	−0.0585941	+	0.101488i
$681$	2.46207	−	12.5372i	0.0943466	−	0.480428i
$682$	−13.9018	−	3.72499i	−0.532329	−	0.142637i
$683$	14.9363	+	4.00216i	0.571520	+	0.153138i	0.532994	−	0.846119i	$-0.321067\pi$
$683$	14.9363	+	4.00216i	0.571520	+	0.153138i	0.0385265	+	0.999258i	$0.487734\pi$
$684$	−1.34112	+	10.5852i	−0.0512790	+	0.404737i
$685$	1.84907	−	3.20268i	0.0706492	−	0.122368i
$686$	18.5107	+	0.594751i	0.706742	+	0.0227077i
$687$	4.86169	−	24.7565i	0.185485	−	0.944520i
$688$	3.30528	−	1.90831i	0.126013	−	0.0727535i
$689$	15.9833	−	24.1880i	0.608917	−	0.921489i
$690$	12.3551	+	6.05546i	0.470350	+	0.230527i
$691$	3.08383	+	11.5090i	0.117314	+	0.437824i	0.999450	−	0.0331728i	$-0.0105612\pi$
$691$	3.08383	+	11.5090i	0.117314	+	0.437824i	−0.882135	+	0.470996i	$0.843894\pi$
$692$	−4.59066	+	2.65042i	−0.174511	+	0.100754i
$693$	−10.3224	+	11.1339i	−0.392117	+	0.422942i
$694$	17.1221	−	17.1221i	0.649944	−	0.649944i
$695$	−31.1810	−	31.1810i	−1.18276	−	1.18276i
$696$	2.54245	−	12.9466i	0.0963713	−	0.490738i
$697$	−1.92995	+	0.517130i	−0.0731022	+	0.0195877i
$698$		−	4.01617i		−	0.152014i
$699$	−21.8917	−	32.5910i	−0.828020	−	1.23271i
$700$	36.5370	+	3.59113i	1.38097	+	0.135732i
$701$	−20.9371			−0.790783			−0.395392	−	0.918513i	$-0.629391\pi$
$701$	−20.9371			−0.790783			−0.395392	+	0.918513i	$0.629391\pi$
$702$	−7.38420	−	17.2184i	−0.278698	−	0.649867i
$703$	−2.63568	+	4.56513i	−0.0994065	+	0.172177i
$704$	−1.35259	−	1.35259i	−0.0509776	−	0.0509776i
$705$	−1.50501	+	3.07071i	−0.0566821	+	0.115649i
$706$	−12.1648	−	7.02334i	−0.457828	−	0.264327i
$707$	−42.1536	−	4.14317i	−1.58535	−	0.155820i
$708$	11.1725	−	3.82295i	0.419889	−	0.143675i
$709$	−21.3623	−	21.3623i	−0.802276	−	0.802276i	0.181175	−	0.983451i	$-0.442010\pi$
$709$	−21.3623	−	21.3623i	−0.802276	−	0.802276i	−0.983451	+	0.181175i	$0.942010\pi$
$710$	−14.8530	−	55.4320i	−0.557422	−	2.08033i
$711$	−0.571201	−	0.736939i	−0.0214217	−	0.0276374i
$712$	−10.6793	−	6.16573i	−0.400226	−	0.231070i
$713$	−13.2882	−	3.56058i	−0.497649	−	0.133345i
$714$	−2.20957	−	2.34669i	−0.0826911	−	0.0878227i
$715$	−26.8063	+	13.3905i	−1.00250	+	0.500776i
$716$	10.5859	−	6.11177i	0.395613	−	0.228408i
$717$	−6.15142	−	5.36819i	−0.229729	−	0.200479i
$718$	15.2521			0.569202
$719$	21.9643			0.819131			0.409565	−	0.912281i	$-0.365680\pi$
$719$	21.9643			0.819131			0.409565	+	0.912281i	$0.365680\pi$
$720$	10.3791	+	7.88412i	0.386808	+	0.293824i
$721$	1.35619	−	0.614812i	0.0505072	−	0.0228968i
$722$	−1.64362	−	6.13407i	−0.0611692	−	0.228286i
$723$	−3.50830	+	17.8648i	−0.130475	+	0.664401i
$724$	−0.386405	−	0.669272i	−0.0143606	−	0.0248733i
$725$	105.702			3.92566
$726$	−4.11643	−	12.0302i	−0.152775	−	0.446483i
$727$		−	46.5924i		−	1.72802i	−0.503477	−	0.864009i	$-0.667946\pi$
$727$		−	46.5924i		−	1.72802i	0.503477	−	0.864009i	$-0.332054\pi$
$728$	5.59768	+	7.72438i	0.207464	+	0.286284i
$729$	24.7910	−	10.6961i	0.918185	−	0.396151i
$730$	15.9593	+	59.5611i	0.590682	+	2.20445i
$731$		−	2.68447i		−	0.0992887i
$732$	14.8121	−	9.94942i	0.547471	−	0.367741i
$733$	−8.03756	−	2.15366i	−0.296874	−	0.0795472i	0.107308	−	0.994226i	$-0.465777\pi$
$733$	−8.03756	−	2.15366i	−0.296874	−	0.0795472i	−0.404182	+	0.914679i	$0.632444\pi$
$734$	−18.4250	+	4.93697i	−0.680080	+	0.182227i
$735$	−20.0200	+	48.7237i	−0.738451	+	1.79720i
$736$	−1.29289	−	1.29289i	−0.0476565	−	0.0476565i
$737$		−	5.12302i		−	0.188709i
$738$	1.15352	+	8.44362i	0.0424616	+	0.310814i
$739$	−1.79379	−	1.79379i	−0.0659858	−	0.0659858i	0.673344	−	0.739330i	$-0.264857\pi$
$739$	−1.79379	−	1.79379i	−0.0659858	−	0.0659858i	−0.739330	+	0.673344i	$0.764857\pi$
$740$	3.21968	+	5.57664i	0.118358	+	0.205002i
$741$	−15.8239	−	15.5865i	−0.581304	−	0.572583i
$742$	−19.9121	−	7.48981i	−0.730998	−	0.274960i
$743$	0.458051	−	1.70947i	0.0168043	−	0.0627143i	−0.957015	−	0.290040i	$-0.906331\pi$
$743$	0.458051	−	1.70947i	0.0168043	−	0.0627143i	0.973819	+	0.227325i	$0.0729981\pi$
$744$	−11.7020	−	5.73537i	−0.429016	−	0.210269i
$745$	78.5415	−	45.3459i	2.87754	−	1.66135i
$746$	19.9181	−	5.33704i	0.729254	−	0.195403i
$747$	−3.27958	−	2.49121i	−0.119994	−	0.0911486i
$748$	−1.29959	+	0.348223i	−0.0475176	+	0.0127323i
$749$	−22.3534	−	16.0114i	−0.816776	−	0.585044i
$750$	−29.3967	+	59.9787i	−1.07342	+	2.19011i
$751$	1.63978	+	0.946727i	0.0598364	+	0.0345466i	0.529620	−	0.848235i	$-0.322335\pi$
$751$	1.63978	+	0.946727i	0.0598364	+	0.0345466i	−0.469783	+	0.882782i	$0.655668\pi$
$752$	0.321332	−	0.321332i	0.0117178	−	0.0117178i
$753$	6.89680	−	14.0717i	0.251333	−	0.512801i
$754$	18.2146	+	20.5564i	0.663335	+	0.748621i
$755$			19.9708i			0.726813i
$756$	−11.1143	+	8.09147i	−0.404224	+	0.294284i
$757$	15.1635	+	26.2640i	0.551128	+	0.954581i	0.998194	+	0.0600801i	$0.0191356\pi$
$757$	15.1635	+	26.2640i	0.551128	+	0.954581i	−0.447066	+	0.894501i	$0.647531\pi$
$758$	−29.9097			−1.08637
$759$	1.96120	+	5.73158i	0.0711871	+	0.208043i
$760$	14.9258	+	3.99937i	0.541417	+	0.145072i
$761$	11.8216	−	11.8216i	0.428532	−	0.428532i	−0.459596	−	0.888128i	$-0.652006\pi$
$761$	11.8216	−	11.8216i	0.428532	−	0.428532i	0.888128	+	0.459596i	$0.152006\pi$
$762$	−12.2424	+	14.0286i	−0.443494	+	0.508201i
$763$	3.63114	+	21.9659i	0.131456	+	0.795218i
$764$	6.33849	+	10.9786i	0.229319	+	0.397191i
$765$	8.45263	−	3.54956i	0.305606	−	0.128335i
$766$	23.5217	+	13.5803i	0.849875	+	0.490675i
$767$	−7.78211	+	23.3169i	−0.280996	+	0.841926i
$768$	−0.965783	−	1.43780i	−0.0348497	−	0.0518821i
$769$	6.14055	+	1.64536i	0.221434	+	0.0593331i	0.367830	−	0.929893i	$-0.380101\pi$
$769$	6.14055	+	1.64536i	0.221434	+	0.0593331i	−0.146396	+	0.989226i	$0.546767\pi$
$770$	13.9525	+	16.9942i	0.502814	+	0.612428i
$771$	−10.4637	+	21.3493i	−0.376842	+	0.768878i
$772$	−1.94567	−	0.521340i	−0.0700261	−	0.0187634i
$773$	0.849915	−	3.17193i	0.0305693	−	0.114086i	−0.948955	−	0.315410i	$-0.897858\pi$
$773$	0.849915	−	3.17193i	0.0305693	−	0.114086i	0.979525	+	0.201324i	$0.0645245\pi$
$774$	−11.3590	−	1.43916i	−0.408292	−	0.0517294i
$775$	27.0219	−	100.847i	0.970654	−	3.62253i
$776$	7.30496	+	4.21752i	0.262233	+	0.151400i
$777$	−6.61043	+	1.55974i	−0.237148	+	0.0559554i
$778$	1.89908	−	7.08746i	0.0680853	−	0.254098i
$779$	5.05161	+	8.74965i	0.180993	+	0.313489i
$780$	−26.1542	+	7.22028i	−0.936469	+	0.258528i
$781$	12.6331	−	21.8812i	0.452048	−	0.782970i
$782$	−1.24223	+	0.332853i	−0.0444219	+	0.0119028i
$783$	−29.5674	+	26.3148i	−1.05665	+	0.940414i
$784$	4.61329	−	5.26474i	0.164761	−	0.188027i
$785$	33.5858	+	33.5858i	1.19873	+	1.19873i
$786$	−21.4873	+	24.6223i	−0.766425	+	0.878249i
$787$	4.80131	−	17.9187i	0.171148	−	0.638733i	−0.826028	−	0.563630i	$-0.809405\pi$
$787$	4.80131	−	17.9187i	0.171148	−	0.638733i	0.997176	−	0.0751038i	$-0.0239288\pi$
$788$	1.77065	+	6.60816i	0.0630768	+	0.235406i
$789$	2.62553	+	38.6156i	0.0934713	+	1.37475i
$790$	−1.16940	+	0.675155i	−0.0416055	+	0.0240209i
$791$	−30.1752	−	21.6141i	−1.07291	−	0.768507i
$792$	0.776752	+	5.68573i	0.0276007	+	0.202034i
$793$	−2.23951	+	37.0765i	−0.0795273	+	1.31663i
$794$	4.88504	+	2.82038i	0.173363	+	0.100091i
$795$	39.7856	−	45.5904i	1.41105	−	1.61692i
$796$	−10.2487	+	17.7513i	−0.363257	+	0.629179i
$797$	8.29031	−	14.3592i	0.293658	−	0.508631i	−0.681014	−	0.732271i	$-0.738461\pi$
$797$	8.29031	−	14.3592i	0.293658	−	0.508631i	0.974672	+	0.223640i	$0.0717940\pi$
$798$	−8.57015	+	13.8634i	−0.303380	+	0.490758i
$799$	−0.0827267	−	0.308740i	−0.00292666	−	0.0109225i
$800$	9.81197	−	9.81197i	0.346905	−	0.346905i
$801$	14.3235	+	34.1089i	0.506098	+	1.20518i
$802$	7.71496	+	13.3627i	0.272425	+	0.471854i
$803$	−13.5741	+	23.5111i	−0.479021	+	0.829688i
$804$	0.893895	−	4.55186i	0.0315252	−	0.160532i
$805$	13.3367	+	16.2441i	0.470057	+	0.572530i
$806$	24.2687	−	12.1229i	0.854829	−	0.427011i
$807$	38.3929	−	25.7888i	1.35149	−	0.907810i
$808$	−11.3203	+	11.3203i	−0.398247	+	0.398247i
$809$		−	48.7489i		−	1.71392i	−0.515383	−	0.856960i	$-0.672350\pi$
$809$		−	48.7489i		−	1.71392i	0.515383	−	0.856960i	$-0.327650\pi$
$810$	−10.4881	−	37.6693i	−0.368513	−	1.32356i
$811$	−8.20253	+	8.20253i	−0.288030	+	0.288030i	−0.836301	−	0.548271i	$-0.815286\pi$
$811$	−8.20253	+	8.20253i	−0.288030	+	0.288030i	0.548271	+	0.836301i	$0.315286\pi$
$812$	11.7359	−	16.3844i	0.411850	−	0.574981i
$813$	36.6382	−	12.5366i	1.28496	−	0.439679i
$814$	−0.733773	+	2.73848i	−0.0257187	+	0.0959836i
$815$	−35.1123	+	20.2721i	−1.22993	+	0.710100i
$816$	−1.21546	+	0.0826406i	−0.0425495	+	0.00289300i
$817$	−13.1117	+	3.51327i	−0.458720	+	0.122914i
$818$	0.0280950			0.000982319
$819$	0.644657	−	28.6109i	0.0225262	−	0.999746i
$820$	12.3418			0.430996
$821$	−4.53552	+	1.21529i	−0.158291	+	0.0424139i	−0.337094	−	0.941471i	$-0.609444\pi$
$821$	−4.53552	+	1.21529i	−0.158291	+	0.0424139i	0.178803	+	0.983885i	$0.442777\pi$
$822$	1.47090	−	0.100009i	0.0513036	−	0.00348820i
$823$	−7.77851	+	4.49092i	−0.271142	+	0.156544i	−0.629406	−	0.777076i	$-0.716702\pi$
$823$	−7.77851	+	4.49092i	−0.271142	+	0.156544i	0.358265	+	0.933620i	$0.383369\pi$
$824$	0.145665	−	0.543628i	0.00507447	−	0.0189382i
$825$	−43.4980	+	14.8839i	−1.51441	+	0.518191i
$826$	17.9513	+	1.76438i	0.624604	+	0.0613908i
$827$	−6.72026	+	6.72026i	−0.233686	+	0.233686i	−0.814229	−	0.580543i	$-0.802840\pi$
$827$	−6.72026	+	6.72026i	−0.233686	+	0.233686i	0.580543	+	0.814229i	$0.302840\pi$
$828$	0.742469	+	5.43478i	0.0258026	+	0.188872i
$829$			48.0277i			1.66807i	0.551712	+	0.834035i	$0.313975\pi$
$829$			48.0277i			1.66807i	−0.551712	+	0.834035i	$0.686025\pi$
$830$	−4.21752	+	4.21752i	−0.146392	+	0.146392i
$831$	−30.1620	+	20.2601i	−1.04631	+	0.702814i
$832$	3.59899	+	0.217387i	0.124773	+	0.00753655i
$833$	−1.58451	−	4.66162i	−0.0548999	−	0.161516i
$834$	3.38758	−	17.2501i	0.117302	−	0.597322i
$835$	21.0886	−	36.5265i	0.729800	−	1.26405i
$836$	3.40164	+	5.89181i	0.117648	+	0.203773i
$837$	17.5475	+	34.9366i	0.606531	+	1.20758i
$838$	7.67565	−	7.67565i	0.265151	−	0.265151i
$839$	4.99773	+	18.6518i	0.172541	+	0.643931i	0.996957	+	0.0779477i	$0.0248367\pi$
$839$	4.99773	+	18.6518i	0.172541	+	0.643931i	−0.824417	+	0.565983i	$0.808497\pi$
$840$	9.43173	+	17.5341i	0.325425	+	0.604982i
$841$	14.5129	−	25.1372i	0.500446	−	0.866798i
$842$	−10.7610	+	18.6387i	−0.370850	+	0.642331i
$843$	−12.3971	+	14.2058i	−0.426978	+	0.489275i
$844$	−11.2145	−	6.47471i	−0.386020	−	0.222869i
$845$	21.0787	−	52.4001i	0.725130	−	1.80262i
$846$	−1.35075	+	0.184532i	−0.0464397	+	0.00634433i
$847$	1.89983	−	19.3293i	0.0652790	−	0.664164i
$848$	−6.96361	+	4.02044i	−0.239131	+	0.138063i
$849$	1.63550	+	24.0545i	0.0561300	+	0.825547i
$850$	−2.52609	−	9.42748i	−0.0866440	−	0.323360i
$851$	−0.701386	+	2.61761i	−0.0240432	+	0.0897305i
$852$	15.0426	−	17.2374i	0.515351	−	0.590543i
$853$	9.76140	+	9.76140i	0.334224	+	0.334224i	0.854188	−	0.519964i	$-0.174055\pi$
$853$	9.76140	+	9.76140i	0.334224	+	0.334224i	−0.519964	+	0.854188i	$0.674055\pi$
$854$	26.8914	−	4.44536i	0.920204	−	0.152117i
$855$	−28.3993	−	36.6396i	−0.971237	−	1.25305i
$856$	−10.0385	+	2.68980i	−0.343108	+	0.0919354i
$857$	−16.4315	+	28.4602i	−0.561289	+	0.972182i	0.436095	+	0.899901i	$0.356361\pi$
$857$	−16.4315	+	28.4602i	−0.561289	+	0.972182i	−0.997384	+	0.0722810i	$0.976972\pi$
$858$	−10.3902	−	5.89451i	−0.354714	−	0.201235i
$859$	−6.35388	−	11.0052i	−0.216792	−	0.375494i	0.737034	−	0.675856i	$-0.236226\pi$
$859$	−6.35388	−	11.0052i	−0.216792	−	0.375494i	−0.953825	+	0.300362i	$0.902893\pi$
$860$	−4.29172	+	16.0169i	−0.146347	+	0.546173i
$861$	−3.74593	+	12.4670i	−0.127661	+	0.424875i
$862$	20.8731	+	12.0511i	0.710941	+	0.410462i
$863$	2.29597	−	8.56869i	0.0781559	−	0.291682i	−0.915775	−	0.401693i	$-0.868422\pi$
$863$	2.29597	−	8.56869i	0.0781559	−	0.291682i	0.993930	+	0.110011i	$0.0350886\pi$
$864$	−0.301928	+	5.18737i	−0.0102718	+	0.176478i
$865$	5.96071	−	22.2457i	0.202670	−	0.756376i
$866$	3.05470	+	0.818505i	0.103803	+	0.0278139i
$867$	12.5816	−	25.6705i	0.427294	−	0.871816i
$868$	−12.6317	−	15.3855i	−0.428748	−	0.522216i
$869$	−0.574250	−	0.153870i	−0.0194801	−	0.00521967i
$870$	31.9630	+	47.5846i	1.08365	+	1.61327i
$871$	6.40402	+	7.22739i	0.216992	+	0.244891i
$872$	7.28759	+	4.20749i	0.246789	+	0.142484i
$873$	−9.79768	−	23.3314i	−0.331601	−	0.789648i
$874$	3.25150	+	5.63176i	0.109984	+	0.190497i
$875$	−78.8584	+	64.7441i	−2.66590	+	2.18875i
$876$	−16.1631	+	18.5214i	−0.546101	+	0.625779i
$877$	2.76520	−	2.76520i	0.0933743	−	0.0933743i	−0.658877	−	0.752251i	$-0.728968\pi$
$877$	2.76520	−	2.76520i	0.0933743	−	0.0933743i	0.752251	+	0.658877i	$0.228968\pi$
$878$	16.4344	+	4.40359i	0.554635	+	0.148614i
$879$	7.16602	+	20.9426i	0.241704	+	0.706376i
$880$	8.31071			0.280154
$881$	3.11388	+	5.39339i	0.104909	+	0.181708i	0.913701	−	0.406387i	$-0.133211\pi$
$881$	3.11388	+	5.39339i	0.104909	+	0.181708i	−0.808792	+	0.588095i	$0.799878\pi$
$882$	−20.5746	+	4.20555i	−0.692782	+	0.141608i
$883$		−	21.8076i		−	0.733883i	−0.930244	−	0.366942i	$-0.880405\pi$
$883$		−	21.8076i		−	0.733883i	0.930244	−	0.366942i	$-0.119595\pi$
$884$	1.39812	−	2.11581i	0.0470239	−	0.0711624i
$885$	−22.5790	+	46.0684i	−0.758985	+	1.54857i
$886$	3.52102	−	3.52102i	0.118291	−	0.118291i
$887$	3.25715	+	1.88052i	0.109365	+	0.0631416i	0.553685	−	0.832726i	$-0.313221\pi$
$887$	3.25715	+	1.88052i	0.109365	+	0.0631416i	−0.444320	+	0.895868i	$0.646555\pi$
$888$	−1.12979	+	2.30514i	−0.0379133	+	0.0773553i
$889$	−25.9038	+	11.7432i	−0.868787	+	0.393854i
$890$	51.7506	−	13.8665i	1.73468	−	0.464807i
$891$	8.46208	−	14.9924i	0.283490	−	0.502264i
$892$	−11.0922	+	2.97214i	−0.371394	+	0.0995147i
$893$	−1.39971	+	0.808121i	−0.0468394	+	0.0270427i
$894$	32.4655	+	15.9120i	1.08581	+	0.532177i
$895$	−13.7452	+	51.2977i	−0.459451	+	1.71469i
$896$	−0.431508	−	2.61033i	−0.0144157	−	0.0872049i
$897$	−9.93156	−	5.63434i	−0.331605	−	0.188125i
$898$	−17.2309	−	29.8448i	−0.575003	−	0.995935i
$899$	−40.5269	−	40.5269i	−1.35165	−	1.35165i
$900$	−41.2455	+	5.63473i	−1.37485	+	0.187824i
$901$			5.65568i			0.188418i
$902$	3.84227	+	3.84227i	0.127934	+	0.127934i
$903$	−14.8768	−	9.19663i	−0.495069	−	0.306045i
$904$	−13.5511	+	3.63100i	−0.450702	+	0.120765i
$905$	3.24320	+	0.869012i	0.107808	+	0.0288869i
$906$	−6.60902	+	4.43934i	−0.219570	+	0.147487i
$907$		−	39.7380i		−	1.31948i	−0.751495	−	0.659739i	$-0.770667\pi$
$907$		−	39.7380i		−	1.31948i	0.751495	−	0.659739i	$-0.229333\pi$
$908$	−1.90921	−	7.12528i	−0.0633595	−	0.236461i
$909$	47.5859	−	6.50092i	1.57833	−	0.215622i
$910$	−40.9274	−	6.53354i	−1.35673	−	0.216585i
$911$			32.9753i			1.09252i	0.837616	+	0.546260i	$0.183949\pi$
$911$			32.9753i			1.09252i	−0.837616	+	0.546260i	$0.816051\pi$
$912$	1.99436	+	5.82848i	0.0660397	+	0.193000i
$913$	−2.62600			−0.0869080
$914$	0.986054	+	1.70790i	0.0326158	+	0.0564922i
$915$	−14.9389	+	76.0711i	−0.493863	+	2.51483i
$916$	−3.77001	−	14.0699i	−0.124565	−	0.464881i
$917$	−45.4653	+	20.6111i	−1.50139	+	0.680639i
$918$	3.05361	+	2.00822i	0.100784	+	0.0662812i
$919$	−9.72717			−0.320870			−0.160435	−	0.987046i	$-0.551290\pi$
$919$	−9.72717			−0.320870			−0.160435	+	0.987046i	$0.551290\pi$
$920$	7.94390			0.261903
$921$	26.7393	+	23.3347i	0.881090	+	0.768904i
$922$	11.8103	−	6.81870i	0.388953	−	0.224562i
$923$	9.53016	+	46.6613i	0.313689	+	1.53587i
$924$	−2.52242	+	8.39501i	−0.0829817	+	0.276176i
$925$	−19.8655	−	5.32295i	−0.653174	−	0.175017i
$926$	−6.75861	−	3.90209i	−0.222102	−	0.128231i
$927$	−1.33448	+	1.03436i	−0.0438302	+	0.0339728i
$928$	−1.97155	−	7.35791i	−0.0647192	−	0.241535i
$929$	8.51157	+	8.51157i	0.279255	+	0.279255i	0.832812	−	0.553556i	$-0.186730\pi$
$929$	8.51157	+	8.51157i	0.279255	+	0.279255i	−0.553556	+	0.832812i	$0.686730\pi$
$930$	53.5702	−	18.3303i	1.75664	−	0.601076i
$931$	−20.6950	+	13.8400i	−0.678250	+	0.453589i
$932$	−19.6305	−	11.3337i	−0.643017	−	0.371246i
$933$	−20.6529	+	42.1385i	−0.676146	+	1.37955i
$934$	−10.4139	−	10.4139i	−0.340752	−	0.340752i
$935$	2.92273	−	5.06232i	0.0955835	−	0.165556i
$936$	−8.20327	−	7.05028i	−0.268132	−	0.230446i
$937$	−14.9299			−0.487737			−0.243869	−	0.969808i	$-0.578417\pi$
$937$	−14.9299			−0.487737			−0.243869	+	0.969808i	$0.578417\pi$
$938$	4.12621	−	5.76057i	0.134725	−	0.188089i
$939$	0.187867	+	0.279685i	0.00613080	+	0.00912716i
$940$			1.97436i			0.0643965i
$941$	46.3899	−	12.4301i	1.51227	−	0.405211i	0.595079	−	0.803667i	$-0.297121\pi$
$941$	46.3899	−	12.4301i	1.51227	−	0.405211i	0.917187	+	0.398456i	$0.130454\pi$
$942$	−3.64884	+	18.5805i	−0.118886	+	0.605385i
$943$	3.67268	+	3.67268i	0.119599	+	0.119599i
$944$	4.82079	−	4.82079i	0.156903	−	0.156903i
$945$	9.28663	−	59.0031i	0.302094	−	1.91937i
$946$	−6.32251	+	3.65030i	−0.205562	+	0.118681i
$947$	3.56628	+	13.3095i	0.115888	+	0.432502i	0.999352	−	0.0359985i	$-0.0114612\pi$
$947$	3.56628	+	13.3095i	0.115888	+	0.432502i	−0.883463	+	0.468500i	$0.844794\pi$
$948$	−0.483379	−	0.236913i	−0.0156994	−	0.00769459i
$949$	−10.2401	−	50.1370i	−0.332406	−	1.62752i
$950$	−42.7405	+	24.6762i	−1.38668	+	0.800602i
$951$	−2.91150	+	14.8258i	−0.0944118	+	0.480761i
$952$	−1.74179	−	0.655160i	−0.0564516	−	0.0212339i
$953$	0.835017	−	1.44629i	0.0270489	−	0.0468500i	−0.852184	−	0.523242i	$-0.824722\pi$
$953$	0.835017	−	1.44629i	0.0270489	−	0.0468500i	0.879233	+	0.476392i	$0.158056\pi$
$954$	23.9313	+	3.03203i	0.774806	+	0.0981657i
$955$	−53.2007	−	14.2551i	−1.72153	−	0.461283i
$956$	−4.55310	−	1.22000i	−0.147258	−	0.0394576i
$957$	−4.86332	+	24.7648i	−0.157209	+	0.800533i
$958$	−8.58920	+	14.8769i	−0.277504	+	0.480652i
$959$	2.10785	+	0.792851i	0.0680659	+	0.0256025i
$960$	7.38416	+	1.45010i	0.238323	+	0.0468019i
$961$	−22.1792	+	12.8052i	−0.715458	+	0.413070i
$962$	−2.38805	−	4.78061i	−0.0769938	−	0.154133i
$963$	28.8623	+	11.7907i	0.930075	+	0.379949i
$964$	2.72052	+	10.1531i	0.0876220	+	0.327010i
$965$	7.57902	−	4.37575i	0.243977	−	0.140860i
$966$	−2.41109	+	8.02447i	−0.0775756	+	0.258183i
$967$	17.1848	−	17.1848i	0.552625	−	0.552625i	−0.374573	−	0.927198i	$-0.622211\pi$
$967$	17.1848	−	17.1848i	0.552625	−	0.552625i	0.927198	+	0.374573i	$0.122211\pi$
$968$	−5.19088	−	5.19088i	−0.166841	−	0.166841i
$969$	4.25169	+	0.834948i	0.136584	+	0.0268224i
$970$	−35.3988	+	9.48508i	−1.13659	+	0.304547i
$971$		−	58.4967i		−	1.87725i	−0.344941	−	0.938624i	$-0.612101\pi$
$971$		−	58.4967i		−	1.87725i	0.344941	−	0.938624i	$-0.387899\pi$
$972$	10.1346	−	11.8444i	0.325068	−	0.379909i
$973$	15.6370	−	21.8307i	0.501299	−	0.699861i
$974$	−13.1238			−0.420513
$975$	42.7601	−	75.3725i	1.36942	−	2.41385i
$976$	5.15096	−	8.92173i	0.164878	−	0.285578i
$977$	−26.9776	−	26.9776i	−0.863088	−	0.863088i	0.128607	−	0.991696i	$-0.458949\pi$
$977$	−26.9776	−	26.9776i	−0.863088	−	0.863088i	−0.991696	+	0.128607i	$0.958949\pi$
$978$	−14.5138	−	7.11351i	−0.464101	−	0.227465i
$979$	20.4280	+	11.7941i	0.652881	+	0.376941i
$980$	2.00135	+	30.3468i	0.0639307	+	0.969394i
$981$	−9.77439	−	23.2759i	−0.312072	−	0.743144i
$982$	4.64559	+	4.64559i	0.148247	+	0.148247i
$983$	−5.83696	−	21.7838i	−0.186170	−	0.694796i	−0.994377	−	0.105898i	$-0.966228\pi$
$983$	−5.83696	−	21.7838i	−0.186170	−	0.694796i	0.808207	−	0.588899i	$-0.200438\pi$
$984$	2.74348	+	4.08433i	0.0874590	+	0.130204i
$985$	−25.7410	−	14.8616i	−0.820175	−	0.473528i
$986$	−5.17530	−	1.38672i	−0.164815	−	0.0441621i
$987$	−1.99439	−	0.599248i	−0.0634820	−	0.0190743i
$988$	−12.1640	−	4.05977i	−0.386988	−	0.129158i
$989$	−6.04345	+	3.48918i	−0.192170	+	0.110950i
$990$	−19.8537	−	15.0811i	−0.630993	−	0.479310i
$991$	−20.2315			−0.642675			−0.321338	−	0.946965i	$-0.604132\pi$
$991$	−20.2315			−0.642675			−0.321338	+	0.946965i	$0.604132\pi$
$992$	−7.52398			−0.238887
$993$	32.8064	−	37.5929i	1.04108	−	1.19298i
$994$	31.8289	−	14.4292i	1.00955	−	0.457668i
$995$	−23.0491	−	86.0204i	−0.730705	−	2.72703i
$996$	−2.33323	−	0.458201i	−0.0739313	−	0.0145186i
$997$	21.6297	+	37.4637i	0.685018	+	1.18649i	0.973431	+	0.228980i	$0.0735391\pi$
$997$	21.6297	+	37.4637i	0.685018	+	1.18649i	−0.288413	+	0.957506i	$0.593128\pi$
$998$	35.1750			1.11344
$999$	6.88204	−	3.45663i	0.217738	−	0.109363i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bw.a.431.19	✓	152
3.2	odd	2	inner	546.2.bw.a.431.38	yes	152
7.2	even	3		546.2.ch.a.275.26	yes	152
13.7	odd	12		546.2.ch.a.137.7	yes	152
21.2	odd	6		546.2.ch.a.275.7	yes	152
39.20	even	12		546.2.ch.a.137.26	yes	152
91.72	odd	12	inner	546.2.bw.a.527.38	yes	152
273.254	even	12	inner	546.2.bw.a.527.19	yes	152

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bw.a.431.19	✓	152	1.1	even	1	trivial
546.2.bw.a.431.38	yes	152	3.2	odd	2	inner
546.2.bw.a.527.19	yes	152	273.254	even	12	inner
546.2.bw.a.527.38	yes	152	91.72	odd	12	inner
546.2.ch.a.137.7	yes	152	13.7	odd	12
546.2.ch.a.137.26	yes	152	39.20	even	12
546.2.ch.a.275.7	yes	152	21.2	odd	6
546.2.ch.a.275.26	yes	152	7.2	even	3

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.bw (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.965926 + 0.258819i) q^{2} +(1.72806 - 0.117493i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-1.12449 + 4.19664i) q^{5} +(-1.63877 + 0.560745i) q^{6} +(-2.63306 - 0.258797i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.97239 - 0.406071i) q^{9} +O(q^{10})\)	\(q+(-0.965926 + 0.258819i) q^{2} +(1.72806 - 0.117493i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-1.12449 + 4.19664i) q^{5} +(-1.63877 + 0.560745i) q^{6} +(-2.63306 - 0.258797i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.97239 - 0.406071i) q^{9} -4.34468i q^{10} +(1.35259 - 1.35259i) q^{11} +(1.43780 - 0.965783i) q^{12} +(-0.217387 + 3.59899i) q^{13} +(2.61033 - 0.431508i) q^{14} +(-1.45010 + 7.38416i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-0.351682 - 0.609132i) q^{17} +(-2.76601 + 1.16155i) q^{18} +(-2.51491 + 2.51491i) q^{19} +(1.12449 + 4.19664i) q^{20} +(-4.58050 - 0.137850i) q^{21} +(-0.956425 + 1.65658i) q^{22} +(-0.914210 + 1.58346i) q^{23} +(-1.13884 + 1.30500i) q^{24} +(-12.0172 - 6.93811i) q^{25} +(-0.721508 - 3.53262i) q^{26} +(5.08876 - 1.05095i) q^{27} +(-2.40970 + 1.09241i) q^{28} +(-6.59692 + 3.80874i) q^{29} +(-0.510470 - 7.50787i) q^{30} +(1.94735 + 7.26761i) q^{31} +(-0.258819 + 0.965926i) q^{32} +(2.17844 - 2.49628i) q^{33} +(0.497354 + 0.497354i) q^{34} +(4.04692 - 10.7590i) q^{35} +(2.37113 - 1.83786i) q^{36} +(1.43162 - 0.383602i) q^{37} +(1.77831 - 3.08012i) q^{38} +(0.0471984 + 6.24482i) q^{39} +(-2.17234 - 3.76260i) q^{40} +(0.735223 - 2.74389i) q^{41} +(4.46010 - 1.05237i) q^{42} +(3.30528 + 1.90831i) q^{43} +(0.495082 - 1.84767i) q^{44} +(-1.63828 + 12.9307i) q^{45} +(0.473230 - 1.76612i) q^{46} +(0.438948 + 0.117616i) q^{47} +(0.762278 - 1.55529i) q^{48} +(6.86605 + 1.36286i) q^{49} +(13.4034 + 3.59143i) q^{50} +(-0.679298 - 1.01130i) q^{51} +(1.61123 + 3.22551i) q^{52} +(-6.96361 - 4.02044i) q^{53} +(-4.64336 + 2.33221i) q^{54} +(4.15536 + 7.19729i) q^{55} +(2.04485 - 1.67886i) q^{56} +(-4.05043 + 4.64140i) q^{57} +(5.38637 - 5.38637i) q^{58} +(6.58533 + 1.76453i) q^{59} +(2.43626 + 7.11992i) q^{60} +10.3019 q^{61} +(-3.76199 - 6.51596i) q^{62} +(-7.93158 + 0.299964i) q^{63} -1.00000i q^{64} +(-14.8592 - 4.95931i) q^{65} +(-1.45812 + 2.97504i) q^{66} +(1.89378 - 1.89378i) q^{67} +(-0.609132 - 0.351682i) q^{68} +(-1.39377 + 2.84373i) q^{69} +(-1.12439 + 11.4398i) q^{70} +(12.7586 - 3.41866i) q^{71} +(-1.81466 + 2.38893i) q^{72} +(-13.7090 + 3.67331i) q^{73} +(-1.28356 + 0.741062i) q^{74} +(-21.5816 - 10.5775i) q^{75} +(-0.920521 + 3.43543i) q^{76} +(-3.91150 + 3.21141i) q^{77} +(-1.66187 - 6.01982i) q^{78} +(-0.155398 - 0.269158i) q^{79} +(3.07215 + 3.07215i) q^{80} +(8.67021 - 2.41400i) q^{81} +2.84068i q^{82} +(-0.970732 - 0.970732i) q^{83} +(-4.03576 + 2.17087i) q^{84} +(2.95177 - 0.790923i) q^{85} +(-3.68656 - 0.987812i) q^{86} +(-10.9524 + 7.35682i) q^{87} +1.91285i q^{88} +(3.19161 + 11.9113i) q^{89} +(-1.76425 - 12.9141i) q^{90} +(1.50380 - 9.42012i) q^{91} +1.82842i q^{92} +(4.21904 + 12.3301i) q^{93} -0.454432 q^{94} +(-7.72618 - 13.3821i) q^{95} +(-0.333765 + 1.69959i) q^{96} +(-2.18315 - 8.14762i) q^{97} +(-6.98483 + 0.460643i) q^{98} +(3.47117 - 4.56967i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 152 q + 12 q^{7}+O(q^{10}) \) 152 * q + 12 * q^7	\( 152 q + 12 q^{7} + 76 q^{16} - 8 q^{18} + 12 q^{19} + 8 q^{21} + 24 q^{27} + 16 q^{28} - 12 q^{31} - 48 q^{33} + 24 q^{36} - 36 q^{37} - 8 q^{39} + 84 q^{43} - 40 q^{45} - 16 q^{46} - 28 q^{49} + 4 q^{52} + 24 q^{54} + 16 q^{55} - 8 q^{57} - 16 q^{58} + 64 q^{61} - 100 q^{63} + 16 q^{66} - 112 q^{67} + 84 q^{69} + 16 q^{72} - 120 q^{73} - 48 q^{76} - 8 q^{78} + 32 q^{79} + 48 q^{81} - 8 q^{84} - 152 q^{85} + 48 q^{87} + 16 q^{91} - 12 q^{93} - 64 q^{94} - 100 q^{97} + 16 q^{99}+O(q^{100}) \) 152 * q + 12 * q^7 + 76 * q^16 - 8 * q^18 + 12 * q^19 + 8 * q^21 + 24 * q^27 + 16 * q^28 - 12 * q^31 - 48 * q^33 + 24 * q^36 - 36 * q^37 - 8 * q^39 + 84 * q^43 - 40 * q^45 - 16 * q^46 - 28 * q^49 + 4 * q^52 + 24 * q^54 + 16 * q^55 - 8 * q^57 - 16 * q^58 + 64 * q^61 - 100 * q^63 + 16 * q^66 - 112 * q^67 + 84 * q^69 + 16 * q^72 - 120 * q^73 - 48 * q^76 - 8 * q^78 + 32 * q^79 + 48 * q^81 - 8 * q^84 - 152 * q^85 + 48 * q^87 + 16 * q^91 - 12 * q^93 - 64 * q^94 - 100 * q^97 + 16 * q^99

Introduction

L-functions

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