LMFDB - Embedded newform 672.2.bs.a.155.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [672,2,Mod(155,672)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(672, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 1, 4, 0]))

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

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

chi := DirichletCharacter("672.155");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 672 = 2^{5} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	672.bs (of order $8$, 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:	$5.36594701583$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$48$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			155.5
Character	$\chi$	$=$	672.155
Dual form			672.2.bs.a.659.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.34768 - 0.428658i) q^{2} +(0.151828 + 1.72538i) q^{3} +(1.63251 + 1.15539i) q^{4} +(0.849301 - 2.05039i) q^{5} +(0.534982 - 2.39035i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(-1.70483 - 2.25689i) q^{8} +(-2.95390 + 0.523925i) q^{9} +O(q^{10})$	\(q+(-1.34768 - 0.428658i) q^{2} +(0.151828 + 1.72538i) q^{3} +(1.63251 + 1.15539i) q^{4} +(0.849301 - 2.05039i) q^{5} +(0.534982 - 2.39035i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(-1.70483 - 2.25689i) q^{8} +(-2.95390 + 0.523925i) q^{9} +(-2.02351 + 2.39922i) q^{10} +(-0.0295405 + 0.0713171i) q^{11} +(-1.74563 + 2.99212i) q^{12} +(-1.14967 + 0.476209i) q^{13} +(1.25606 - 0.649850i) q^{14} +(3.66666 + 1.15406i) q^{15} +(1.33015 + 3.77236i) q^{16} +6.97270 q^{17} +(4.20550 + 0.560125i) q^{18} +(2.92490 + 7.06134i) q^{19} +(3.75549 - 2.36600i) q^{20} +(-1.32739 - 1.11267i) q^{21} +(0.0703819 - 0.0834502i) q^{22} +(-1.61455 + 1.61455i) q^{23} +(3.63515 - 3.28415i) q^{24} +(0.0527330 + 0.0527330i) q^{25} +(1.75352 - 0.148964i) q^{26} +(-1.35246 - 5.01706i) q^{27} +(-1.97134 + 0.337371i) q^{28} +(-0.0732676 + 0.0303484i) q^{29} +(-4.44681 - 3.12705i) q^{30} +3.03932i q^{31} +(-0.175567 - 5.65413i) q^{32} +(-0.127534 - 0.0401407i) q^{33} +(-9.39699 - 2.98890i) q^{34} +(0.849301 + 2.05039i) q^{35} +(-5.42759 - 2.55759i) q^{36} +(-2.61795 - 1.08439i) q^{37} +(-0.914948 - 10.7702i) q^{38} +(-0.996195 - 1.91132i) q^{39} +(-6.07542 + 1.57881i) q^{40} +(0.557782 + 0.557782i) q^{41} +(1.31195 + 2.06853i) q^{42} +(11.9085 + 4.93266i) q^{43} +(-0.130624 + 0.0822947i) q^{44} +(-1.43449 + 6.50162i) q^{45} +(2.86800 - 1.48382i) q^{46} +7.68083i q^{47} +(-6.30682 + 2.86777i) q^{48} -1.00000i q^{49} +(-0.0484631 - 0.0936719i) q^{50} +(1.05865 + 12.0306i) q^{51} +(-2.42705 - 0.550904i) q^{52} +(-2.78861 - 1.15508i) q^{53} +(-0.327916 + 7.34115i) q^{54} +(0.121139 + 0.121139i) q^{55} +(2.80136 + 0.390360i) q^{56} +(-11.7394 + 6.11869i) q^{57} +(0.111751 - 0.00949338i) q^{58} +(0.581466 + 0.240851i) q^{59} +(4.65246 + 6.12044i) q^{60} +(0.417378 + 1.00764i) q^{61} +(1.30283 - 4.09604i) q^{62} +(1.71825 - 2.45919i) q^{63} +(-2.18708 + 7.69524i) q^{64} +2.76172i q^{65} +(0.154670 + 0.108766i) q^{66} +(5.88321 - 2.43691i) q^{67} +(11.3830 + 8.05618i) q^{68} +(-3.03086 - 2.54059i) q^{69} +(-0.265672 - 3.12734i) q^{70} +(4.95414 + 4.95414i) q^{71} +(6.21834 + 5.77340i) q^{72} +(0.857420 - 0.857420i) q^{73} +(3.06334 + 2.58362i) q^{74} +(-0.0829783 + 0.0989911i) q^{75} +(-3.38368 + 14.9071i) q^{76} +(-0.0295405 - 0.0713171i) q^{77} +(0.523255 + 3.00288i) q^{78} -13.6667 q^{79} +(8.86452 + 0.476545i) q^{80} +(8.45101 - 3.09524i) q^{81} +(-0.512617 - 0.990812i) q^{82} +(-4.47245 + 1.85255i) q^{83} +(-0.881400 - 3.35009i) q^{84} +(5.92192 - 14.2968i) q^{85} +(-13.9345 - 11.7523i) q^{86} +(-0.0634868 - 0.121807i) q^{87} +(0.211316 - 0.0549143i) q^{88} +(-4.13898 + 4.13898i) q^{89} +(4.72021 - 8.14722i) q^{90} +(0.476209 - 1.14967i) q^{91} +(-4.50120 + 0.770327i) q^{92} +(-5.24399 + 0.461455i) q^{93} +(3.29245 - 10.3513i) q^{94} +16.9626 q^{95} +(9.72888 - 1.16138i) q^{96} +1.21515 q^{97} +(-0.428658 + 1.34768i) q^{98} +(0.0498948 - 0.226140i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q - 16 q^{4}+O(q^{10}) $ 192 * q - 16 * q^4	$ 192 q - 16 q^{4} + 8 q^{10} + 16 q^{16} + 16 q^{22} + 24 q^{27} - 84 q^{30} + 40 q^{36} + 32 q^{37} + 24 q^{39} - 96 q^{46} - 72 q^{48} + 16 q^{52} - 32 q^{55} - 72 q^{58} - 28 q^{60} - 16 q^{61} - 64 q^{64} - 12 q^{66} - 32 q^{67} + 56 q^{69} - 24 q^{70} + 60 q^{72} + 80 q^{75} - 56 q^{76} + 100 q^{78} - 32 q^{79} - 120 q^{82} - 56 q^{87} + 40 q^{88} + 60 q^{90} - 80 q^{93} + 216 q^{94} + 96 q^{96} - 64 q^{99}+O(q^{100}) $ 192 * q - 16 * q^4 + 8 * q^10 + 16 * q^16 + 16 * q^22 + 24 * q^27 - 84 * q^30 + 40 * q^36 + 32 * q^37 + 24 * q^39 - 96 * q^46 - 72 * q^48 + 16 * q^52 - 32 * q^55 - 72 * q^58 - 28 * q^60 - 16 * q^61 - 64 * q^64 - 12 * q^66 - 32 * q^67 + 56 * q^69 - 24 * q^70 + 60 * q^72 + 80 * q^75 - 56 * q^76 + 100 * q^78 - 32 * q^79 - 120 * q^82 - 56 * q^87 + 40 * q^88 + 60 * q^90 - 80 * q^93 + 216 * q^94 + 96 * q^96 - 64 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/672\mathbb{Z}\right)^\times$.

$n$	$127$	$421$	$449$	$577$
$\chi(n)$	$-1$	$e\left(\frac{1}{8}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	−1.34768	−	0.428658i	−0.952957	−	0.303107i
$2$	−1.34768	−	0.428658i	−0.952957	−	0.303107i
$3$	0.151828	+	1.72538i	0.0876582	+	0.996151i
$3$	0.151828	+	1.72538i	0.0876582	+	0.996151i
$4$	1.63251	+	1.15539i	0.816253	+	0.577695i
$5$	0.849301	−	2.05039i	0.379819	−	0.916964i	−0.612180	−	0.790718i	$-0.709707\pi$
$5$	0.849301	−	2.05039i	0.379819	−	0.916964i	0.991999	−	0.126245i	$-0.0402927\pi$
$6$	0.534982	−	2.39035i	0.218405	−	0.975858i
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i
$8$	−1.70483	−	2.25689i	−0.602750	−	0.797930i
$9$	−2.95390	+	0.523925i	−0.984632	+	0.174642i
$10$	−2.02351	+	2.39922i	−0.639889	+	0.758701i
$11$	−0.0295405	+	0.0713171i	−0.00890680	+	0.0215029i	−0.928270	−	0.371906i	$-0.878704\pi$
$11$	−0.0295405	+	0.0713171i	−0.00890680	+	0.0215029i	0.919364	+	0.393409i	$0.128704\pi$
$12$	−1.74563	+	2.99212i	−0.503920	+	0.863750i
$13$	−1.14967	+	0.476209i	−0.318861	+	0.132077i	−0.536373	−	0.843981i	$-0.680206\pi$
$13$	−1.14967	+	0.476209i	−0.318861	+	0.132077i	0.217512	+	0.976058i	$0.430206\pi$
$14$	1.25606	−	0.649850i	0.335697	−	0.173680i
$15$	3.66666	+	1.15406i	0.946728	+	0.297977i
$16$	1.33015	+	3.77236i	0.332537	+	0.943090i
$17$	6.97270			1.69113			0.845564	−	0.533875i	$-0.179265\pi$
$17$	6.97270			1.69113			0.845564	+	0.533875i	$0.179265\pi$
$18$	4.20550	+	0.560125i	0.991247	+	0.132023i
$19$	2.92490	+	7.06134i	0.671019	+	1.61998i	0.779883	+	0.625926i	$0.215279\pi$
$19$	2.92490	+	7.06134i	0.671019	+	1.61998i	−0.108864	+	0.994057i	$0.534721\pi$
$20$	3.75549	−	2.36600i	0.839754	−	0.529055i
$21$	−1.32739	−	1.11267i	−0.289660	−	0.242805i
$22$	0.0703819	−	0.0834502i	0.0150055	−	0.0177916i
$23$	−1.61455	+	1.61455i	−0.336657	+	0.336657i	−0.855108	−	0.518450i	$-0.826509\pi$
$23$	−1.61455	+	1.61455i	−0.336657	+	0.336657i	0.518450	+	0.855108i	$0.326509\pi$
$24$	3.63515	−	3.28415i	0.742022	−	0.670375i
$25$	0.0527330	+	0.0527330i	0.0105466	+	0.0105466i
$26$	1.75352	−	0.148964i	0.343894	−	0.0292143i
$27$	−1.35246	−	5.01706i	−0.260280	−	0.965533i
$28$	−1.97134	+	0.337371i	−0.372548	+	0.0637572i
$29$	−0.0732676	+	0.0303484i	−0.0136054	+	0.00563556i	−0.389476	−	0.921037i	$-0.627344\pi$
$29$	−0.0732676	+	0.0303484i	−0.0136054	+	0.00563556i	0.375870	+	0.926672i	$0.377344\pi$
$30$	−4.44681	−	3.12705i	−0.811872	−	0.570919i
$31$			3.03932i			0.545878i	0.962031	+	0.272939i	$0.0879957\pi$
$31$			3.03932i			0.545878i	−0.962031	+	0.272939i	$0.912004\pi$
$32$	−0.175567	−	5.65413i	−0.0310361	−	0.999518i
$33$	−0.127534	−	0.0401407i	−0.0222009	−	0.00698761i
$34$	−9.39699	−	2.98890i	−1.61157	−	0.512592i
$35$	0.849301	+	2.05039i	0.143558	+	0.346580i
$36$	−5.42759	−	2.55759i	−0.904598	−	0.426265i
$37$	−2.61795	−	1.08439i	−0.430389	−	0.178273i	0.156963	−	0.987604i	$-0.449830\pi$
$37$	−2.61795	−	1.08439i	−0.430389	−	0.178273i	−0.587352	+	0.809332i	$0.699830\pi$
$38$	−0.914948	−	10.7702i	−0.148424	−	1.74716i
$39$	−0.996195	−	1.91132i	−0.159519	−	0.306056i
$40$	−6.07542	+	1.57881i	−0.960609	+	0.249631i
$41$	0.557782	+	0.557782i	0.0871110	+	0.0871110i	0.749320	−	0.662209i	$-0.230381\pi$
$41$	0.557782	+	0.557782i	0.0871110	+	0.0871110i	−0.662209	+	0.749320i	$0.730381\pi$
$42$	1.31195	+	2.06853i	0.202438	+	0.319180i
$43$	11.9085	+	4.93266i	1.81603	+	0.752223i	0.978630	+	0.205630i	$0.0659244\pi$
$43$	11.9085	+	4.93266i	1.81603	+	0.752223i	0.837398	+	0.546593i	$0.184076\pi$
$44$	−0.130624	+	0.0822947i	−0.0196923	+	0.0124064i
$45$	−1.43449	+	6.50162i	−0.213842	+	0.969204i
$46$	2.86800	−	1.48382i	0.422863	−	0.218777i
$47$			7.68083i			1.12036i	0.828369	+	0.560182i	$0.189269\pi$
$47$			7.68083i			1.12036i	−0.828369	+	0.560182i	$0.810731\pi$
$48$	−6.30682	+	2.86777i	−0.910310	+	0.413926i
$49$		−	1.00000i		−	0.142857i
$50$	−0.0484631	−	0.0936719i	−0.00685371	−	0.0132472i
$51$	1.05865	+	12.0306i	0.148241	+	1.68462i
$52$	−2.42705	−	0.550904i	−0.336571	−	0.0763966i
$53$	−2.78861	−	1.15508i	−0.383045	−	0.158662i	0.182848	−	0.983141i	$-0.441468\pi$
$53$	−2.78861	−	1.15508i	−0.383045	−	0.158662i	−0.565893	+	0.824479i	$0.691468\pi$
$54$	−0.327916	+	7.34115i	−0.0446236	+	0.999004i
$55$	0.121139	+	0.121139i	0.0163344	+	0.0163344i
$56$	2.80136	+	0.390360i	0.374348	+	0.0521640i
$57$	−11.7394	+	6.11869i	−1.55493	+	0.810440i
$58$	0.111751	−	0.00949338i	0.0146736	−	0.00124654i
$59$	0.581466	+	0.240851i	0.0757005	+	0.0313562i	0.420212	−	0.907426i	$-0.361956\pi$
$59$	0.581466	+	0.240851i	0.0757005	+	0.0313562i	−0.344512	+	0.938782i	$0.611956\pi$
$60$	4.65246	+	6.12044i	0.600629	+	0.790145i
$61$	0.417378	+	1.00764i	0.0534397	+	0.129015i	0.948345	−	0.317242i	$-0.102757\pi$
$61$	0.417378	+	1.00764i	0.0534397	+	0.129015i	−0.894905	+	0.446257i	$0.852757\pi$
$62$	1.30283	−	4.09604i	0.165459	−	0.520198i
$63$	1.71825	−	2.45919i	0.216479	−	0.309829i
$64$	−2.18708	+	7.69524i	−0.273385	+	0.961905i
$65$			2.76172i			0.342549i
$66$	0.154670	+	0.108766i	0.0190385	+	0.0133881i
$67$	5.88321	−	2.43691i	0.718749	−	0.297716i	0.00682950	−	0.999977i	$-0.497826\pi$
$67$	5.88321	−	2.43691i	0.718749	−	0.297716i	0.711919	+	0.702261i	$0.247826\pi$
$68$	11.3830	+	8.05618i	1.38039	+	0.976956i
$69$	−3.03086	−	2.54059i	−0.364872	−	0.305851i
$70$	−0.265672	−	3.12734i	−0.0317539	−	0.373789i
$71$	4.95414	+	4.95414i	0.587948	+	0.587948i	0.937075	−	0.349127i	$-0.113522\pi$
$71$	4.95414	+	4.95414i	0.587948	+	0.587948i	−0.349127	+	0.937075i	$0.613522\pi$
$72$	6.21834	+	5.77340i	0.732839	+	0.680402i
$73$	0.857420	−	0.857420i	0.100353	−	0.100353i	−0.655148	−	0.755501i	$-0.727394\pi$
$73$	0.857420	−	0.857420i	0.100353	−	0.100353i	0.755501	+	0.655148i	$0.227394\pi$
$74$	3.06334	+	2.58362i	0.356106	+	0.300340i
$75$	−0.0829783	+	0.0989911i	−0.00958151	+	0.0114305i
$76$	−3.38368	+	14.9071i	−0.388135	+	1.70996i
$77$	−0.0295405	−	0.0713171i	−0.00336645	−	0.00812734i
$78$	0.523255	+	3.00288i	0.0592470	+	0.340009i
$79$	−13.6667			−1.53763			−0.768813	−	0.639473i	$-0.779152\pi$
$79$	−13.6667			−1.53763			−0.768813	+	0.639473i	$0.779152\pi$
$80$	8.86452	+	0.476545i	0.991083	+	0.0532793i
$81$	8.45101	−	3.09524i	0.939001	−	0.343915i
$82$	−0.512617	−	0.990812i	−0.0566091	−	0.109417i
$83$	−4.47245	+	1.85255i	−0.490915	+	0.203344i	−0.614388	−	0.789004i	$-0.710597\pi$
$83$	−4.47245	+	1.85255i	−0.490915	+	0.203344i	0.123473	+	0.992348i	$0.460597\pi$
$84$	−0.881400	−	3.35009i	−0.0961687	−	0.365525i
$85$	5.92192	−	14.2968i	0.642322	−	1.55070i
$86$	−13.9345	−	11.7523i	−1.50259	−	1.26729i
$87$	−0.0634868	−	0.121807i	−0.00680649	−	0.0130591i
$88$	0.211316	−	0.0549143i	0.0225264	−	0.00585388i
$89$	−4.13898	+	4.13898i	−0.438731	+	0.438731i	−0.891585	−	0.452854i	$-0.850406\pi$
$89$	−4.13898	+	4.13898i	−0.438731	+	0.438731i	0.452854	+	0.891585i	$0.350406\pi$
$90$	4.72021	−	8.14722i	0.497554	−	0.858793i
$91$	0.476209	−	1.14967i	0.0499202	−	0.120518i
$92$	−4.50120	+	0.770327i	−0.469283	+	0.0803122i
$93$	−5.24399	+	0.461455i	−0.543777	+	0.0478507i
$94$	3.29245	−	10.3513i	0.339590	−	1.06766i
$95$	16.9626			1.74033
$96$	9.72888	−	1.16138i	0.992950	−	0.118533i
$97$	1.21515			0.123380			0.0616899	−	0.998095i	$-0.480351\pi$
$97$	1.21515			0.123380			0.0616899	+	0.998095i	$0.480351\pi$
$98$	−0.428658	+	1.34768i	−0.0433010	+	0.136137i
$99$	0.0498948	−	0.226140i	0.00501462	−	0.0227280i
$100$	0.0251597	+	0.147014i	0.00251597	+	0.0147014i
$101$	−2.77931	+	6.70985i	−0.276552	+	0.667655i	−0.999735	−	0.0230006i	$-0.992678\pi$
$101$	−2.77931	+	6.70985i	−0.276552	+	0.667655i	0.723184	+	0.690656i	$0.242678\pi$
$102$	3.73027	−	16.6672i	0.369351	−	1.65030i
$103$	11.7023	−	11.7023i	1.15306	−	1.15306i	0.167126	−	0.985936i	$-0.446551\pi$
$103$	11.7023	−	11.7023i	1.15306	−	1.15306i	0.985936	−	0.167126i	$-0.0534485\pi$
$104$	3.03475	+	1.78282i	0.297581	+	0.174820i
$105$	−3.40877	+	1.77668i	−0.332662	+	0.173386i
$106$	3.26303	+	2.75204i	0.316933	+	0.267302i
$107$	−0.966854	+	2.33419i	−0.0934693	+	0.225655i	−0.963699	−	0.266992i	$-0.913970\pi$
$107$	−0.966854	+	2.33419i	−0.0934693	+	0.225655i	0.870230	+	0.492646i	$0.163970\pi$
$108$	3.58877	−	9.75299i	0.345329	−	0.938482i
$109$	−9.12325	+	3.77897i	−0.873849	+	0.361960i	−0.774108	−	0.633054i	$-0.781801\pi$
$109$	−9.12325	+	3.77897i	−0.873849	+	0.361960i	−0.0997405	+	0.995013i	$0.531801\pi$
$110$	−0.111330	−	0.215185i	−0.0106149	−	0.0205171i
$111$	1.47351	−	4.68161i	0.139859	−	0.444359i
$112$	−3.60802	−	1.72691i	−0.340926	−	0.163177i
$113$	0.427877			0.0402513			0.0201256	−	0.999797i	$-0.493593\pi$
$113$	0.427877			0.0402513			0.0201256	+	0.999797i	$0.493593\pi$
$114$	18.4439	−	3.21386i	1.72743	−	0.301006i
$115$	1.93923	+	4.68171i	0.180834	+	0.436571i
$116$	−0.154674	−	0.0351087i	−0.0143611	−	0.00325976i
$117$	3.14651	−	2.00901i	0.290895	−	0.185733i
$118$	−0.680390	−	0.573841i	−0.0626350	−	0.0528264i
$119$	−4.93044	+	4.93044i	−0.451973	+	0.451973i
$120$	−3.64647	−	10.2427i	−0.332875	−	0.935029i
$121$	7.77396	+	7.77396i	0.706724	+	0.706724i
$122$	−0.130561	−	1.53689i	−0.0118205	−	0.139144i
$123$	−0.877701	+	1.04708i	−0.0791397	+	0.0944116i
$124$	−3.51160	+	4.96170i	−0.315351	+	0.445574i
$125$	10.4049	−	4.30984i	0.930640	−	0.385484i
$126$	−3.36981	+	2.57767i	−0.300206	+	0.229637i
$127$		−	15.1838i		−	1.34735i	−0.739029	−	0.673674i	$-0.764715\pi$
$127$		−	15.1838i		−	1.34735i	0.739029	−	0.673674i	$-0.235285\pi$
$128$	6.24611	−	9.43324i	0.552084	−	0.833789i
$129$	−6.70268	+	21.2956i	−0.590138	+	1.87498i
$130$	1.18383	−	3.72193i	0.103829	−	0.326434i
$131$	−8.45160	−	20.4040i	−0.738420	−	1.78270i	−0.612204	−	0.790700i	$-0.709717\pi$
$131$	−8.45160	−	20.4040i	−0.738420	−	1.78270i	−0.126215	−	0.992003i	$-0.540283\pi$
$132$	−0.161822	−	0.212882i	−0.0140848	−	0.0185290i
$133$	−7.06134	−	2.92490i	−0.612296	−	0.253621i
$134$	−8.97331	+	0.762296i	−0.775176	+	0.0658524i
$135$	−11.4356	−	1.48792i	−0.984218	−	0.128060i
$136$	−11.8873	−	15.7366i	−1.01933	−	1.34940i
$137$	11.0046	+	11.0046i	0.940190	+	0.940190i	0.998310	−	0.0581193i	$-0.0185104\pi$
$137$	11.0046	+	11.0046i	0.940190	+	0.940190i	−0.0581193	+	0.998310i	$0.518510\pi$
$138$	2.99560	+	4.72311i	0.255002	+	0.402058i
$139$	−12.9248	−	5.35364i	−1.09627	−	0.454090i	−0.240081	−	0.970753i	$-0.577174\pi$
$139$	−12.9248	−	5.35364i	−1.09627	−	0.454090i	−0.856189	+	0.516663i	$0.827174\pi$
$140$	−0.982516	+	4.32855i	−0.0830378	+	0.365829i
$141$	−13.2524	+	1.16617i	−1.11605	+	0.0982091i
$142$	−4.55299	−	8.80025i	−0.382078	−	0.738500i
$143$		−	0.0960585i		−	0.00803282i
$144$	−5.90555	−	10.4463i	−0.492129	−	0.870522i
$145$			0.176002i			0.0146162i
$146$	−1.52307	+	0.787991i	−0.126050	+	0.0652146i
$147$	1.72538	−	0.151828i	0.142307	−	0.0125226i
$148$	−3.02093	−	4.79503i	−0.248319	−	0.394149i
$149$	−13.3393	−	5.52531i	−1.09280	−	0.452651i	−0.237815	−	0.971310i	$-0.576431\pi$
$149$	−13.3393	−	5.52531i	−1.09280	−	0.452651i	−0.854981	+	0.518659i	$0.826431\pi$
$150$	0.154262	−	0.0978394i	0.0125954	−	0.00798856i
$151$	13.8044	+	13.8044i	1.12339	+	1.12339i	0.991228	+	0.132160i	$0.0421914\pi$
$151$	13.8044	+	13.8044i	1.12339	+	1.12339i	0.132160	+	0.991228i	$0.457809\pi$
$152$	10.9502	−	18.6396i	0.888176	−	1.51187i
$153$	−20.5966	+	3.65317i	−1.66514	+	0.295341i
$154$	0.00924066	+	0.108776i	0.000744634	+	0.00876539i
$155$	6.23180	+	2.58130i	0.500550	+	0.207335i
$156$	0.582025	−	4.27123i	0.0465993	−	0.341972i
$157$	−5.56363	−	13.4318i	−0.444026	−	1.07197i	−0.974523	−	0.224287i	$-0.927995\pi$
$157$	−5.56363	−	13.4318i	−0.444026	−	1.07197i	0.530497	−	0.847687i	$-0.322005\pi$
$158$	18.4184	+	5.85835i	1.46529	+	0.466065i
$159$	1.56956	−	4.98679i	0.124475	−	0.395478i
$160$	−11.7423	−	4.44208i	−0.928310	−	0.351177i
$161$		−	2.28332i		−	0.179951i
$162$	−12.7161	+	0.548815i	−0.999070	+	0.0431190i
$163$	9.16540	−	3.79643i	0.717890	−	0.297360i	0.00632469	−	0.999980i	$-0.497987\pi$
$163$	9.16540	−	3.79643i	0.717890	−	0.297360i	0.711565	+	0.702620i	$0.247987\pi$
$164$	0.266126	+	1.55504i	0.0207810	+	0.121428i
$165$	−0.190619	+	0.227404i	−0.0148397	+	0.0177034i
$166$	6.82155	−	0.579501i	0.529455	−	0.0449780i
$167$	−6.39470	−	6.39470i	−0.494837	−	0.494837i	0.414989	−	0.909826i	$-0.363785\pi$
$167$	−6.39470	−	6.39470i	−0.494837	−	0.494837i	−0.909826	+	0.414989i	$0.863785\pi$
$168$	−0.248194	+	4.89269i	−0.0191486	+	0.377479i
$169$	−8.09742	+	8.09742i	−0.622879	+	0.622879i
$170$	−14.1093	+	16.7291i	−1.08213	+	1.28306i
$171$	−12.3395	−	19.3260i	−0.943623	−	1.47790i
$172$	13.7415	+	21.8115i	1.04778	+	1.66311i
$173$	−9.45686	−	22.8309i	−0.718992	−	1.73580i	−0.676203	−	0.736715i	$-0.736376\pi$
$173$	−9.45686	−	22.8309i	−0.718992	−	1.73580i	−0.0427889	−	0.999084i	$-0.513624\pi$
$174$	0.0333466	+	0.191371i	0.00252800	+	0.0145078i
$175$	−0.0745758			−0.00563740
$176$	−0.308327	−	0.0165752i	−0.0232410	−	0.00124941i
$177$	−0.327278	+	1.03982i	−0.0245997	+	0.0781577i
$178$	7.35224	−	3.80383i	0.551074	−	0.285109i
$179$	−18.7224	+	7.75507i	−1.39938	+	0.579641i	−0.949590	−	0.313494i	$-0.898500\pi$
$179$	−18.7224	+	7.75507i	−1.39938	+	0.579641i	−0.449788	+	0.893135i	$0.648500\pi$
$180$	−9.85373	+	8.95653i	−0.734453	+	0.667580i
$181$	6.59223	−	15.9151i	0.489997	−	1.18296i	−0.464725	−	0.885455i	$-0.653847\pi$
$181$	6.59223	−	15.9151i	0.489997	−	1.18296i	0.954721	−	0.297501i	$-0.0961533\pi$
$182$	−1.13459	+	1.34526i	−0.0841017	+	0.0997174i
$183$	−1.67519	+	0.873125i	−0.123834	+	0.0645432i
$184$	6.39641	+	0.891317i	0.471549	+	0.0657088i
$185$	−4.44686	+	4.44686i	−0.326939	+	0.326939i
$186$	7.26505	+	1.62598i	0.532699	+	0.119223i
$187$	−0.205977	+	0.497272i	−0.0150625	+	0.0363642i
$188$	−8.87436	+	12.5390i	−0.647229	+	0.914500i
$189$	4.50393	+	2.59126i	0.327612	+	0.188487i
$190$	−22.8603	−	7.27117i	−1.65846	−	0.527506i
$191$	16.1767			1.17050			0.585251	−	0.810852i	$-0.300996\pi$
$191$	16.1767			1.17050			0.585251	+	0.810852i	$0.300996\pi$
$192$	−13.6093	−	2.60519i	−0.982166	−	0.188013i
$193$	13.0467			0.939121			0.469560	−	0.882900i	$-0.344412\pi$
$193$	13.0467			0.939121			0.469560	+	0.882900i	$0.344412\pi$
$194$	−1.63764	−	0.520884i	−0.117576	−	0.0373973i
$195$	−4.76502	+	0.419308i	−0.341230	+	0.0300272i
$196$	1.15539	−	1.63251i	0.0825279	−	0.116608i
$197$	3.95344	−	9.54444i	0.281671	−	0.680014i	−0.718204	−	0.695833i	$-0.755036\pi$
$197$	3.95344	−	9.54444i	0.281671	−	0.680014i	0.999875	+	0.0158190i	$0.00503556\pi$
$198$	−0.164179	+	0.283378i	−0.0116677	+	0.0201388i
$199$	6.65764	−	6.65764i	0.471947	−	0.471947i	−0.430597	−	0.902544i	$-0.641697\pi$
$199$	6.65764	−	6.65764i	0.471947	−	0.471947i	0.902544	+	0.430597i	$0.141697\pi$
$200$	0.0291114	−	0.208914i	0.00205849	−	0.0147724i
$201$	5.09784	+	9.78081i	0.359574	+	0.689885i
$202$	6.62186	−	7.85139i	0.465913	−	0.552422i
$203$	0.0303484	−	0.0732676i	0.00213004	−	0.00514237i
$204$	−12.1717	+	20.8631i	−0.852193	+	1.46071i
$205$	1.61740	−	0.669948i	0.112964	−	0.0467912i
$206$	−20.7873	+	10.7547i	−1.44832	+	0.749317i
$207$	3.92332	−	5.61512i	0.272689	−	0.390278i
$208$	−3.32566	−	3.70354i	−0.230593	−	0.256794i
$209$	−0.589997			−0.0408110
$210$	5.35553	−	0.933206i	0.369566	−	0.0643974i
$211$	1.24087	+	2.99572i	0.0854248	+	0.206234i	0.960819	−	0.277175i	$-0.0893983\pi$
$211$	1.24087	+	2.99572i	0.0854248	+	0.206234i	−0.875394	+	0.483409i	$0.839398\pi$
$212$	−3.21785	−	5.10760i	−0.221003	−	0.350791i
$213$	−7.79561	+	9.29997i	−0.534147	+	0.637224i
$214$	2.30358	−	2.73130i	0.157470	−	0.186708i
$215$	20.2278	−	20.2278i	1.37952	−	1.37952i
$216$	−9.01722	+	11.6056i	−0.613544	+	0.789661i
$217$	−2.14912	−	2.14912i	−0.145892	−	0.145892i
$218$	13.9151	−	1.18211i	0.942452	−	0.0800627i
$219$	1.60956	+	1.34920i	0.108764	+	0.0911703i
$220$	0.0577974	+	0.337724i	0.00389670	+	0.0227693i
$221$	−8.01630	+	3.32046i	−0.539234	+	0.223358i
$222$	−3.99264	+	5.67770i	−0.267968	+	0.381063i
$223$			26.9139i			1.80229i	0.433521	+	0.901143i	$0.357271\pi$
$223$			26.9139i			1.80229i	−0.433521	+	0.901143i	$0.642729\pi$
$224$	4.12222	+	3.87393i	0.275427	+	0.258838i
$225$	−0.183396	−	0.128140i	−0.0122264	−	0.00854265i
$226$	−0.576643	−	0.183413i	−0.0383577	−	0.0122004i
$227$	−5.48685	−	13.2464i	−0.364175	−	0.879196i	−0.994680	−	0.103011i	$-0.967152\pi$
$227$	−5.48685	−	13.2464i	−0.364175	−	0.879196i	0.630505	−	0.776185i	$-0.282848\pi$
$228$	−26.2342	−	3.57483i	−1.73740	−	0.236749i
$229$	13.9662	+	5.78498i	0.922911	+	0.382282i	0.792985	−	0.609241i	$-0.208526\pi$
$229$	13.9662	+	5.78498i	0.922911	+	0.382282i	0.129926	+	0.991524i	$0.458526\pi$
$230$	−0.606616	−	7.14073i	−0.0399990	−	0.470846i
$231$	0.118564	−	0.0617967i	0.00780096	−	0.00406592i
$232$	0.193402	+	0.113618i	0.0126975	+	0.00745936i
$233$	−12.0908	−	12.0908i	−0.792094	−	0.792094i	0.189741	−	0.981834i	$-0.439235\pi$
$233$	−12.0908	−	12.0908i	−0.792094	−	0.792094i	−0.981834	+	0.189741i	$0.939235\pi$
$234$	−5.10168	+	1.35874i	−0.333507	+	0.0888235i
$235$	15.7487	+	6.52333i	1.02733	+	0.425535i
$236$	0.670970	+	1.06501i	0.0436764	+	0.0693263i
$237$	−2.07500	−	23.5803i	−0.134786	−	1.53171i
$238$	8.75815	−	4.53121i	0.567706	−	0.293714i
$239$			10.6356i			0.687960i	0.938977	+	0.343980i	$0.111775\pi$
$239$			10.6356i			0.687960i	−0.938977	+	0.343980i	$0.888225\pi$
$240$	0.523664	+	15.3670i	0.0338024	+	0.991939i
$241$		−	5.57725i		−	0.359262i	−0.983734	−	0.179631i	$-0.942510\pi$
$241$		−	5.57725i		−	0.359262i	0.983734	−	0.179631i	$-0.0574904\pi$
$242$	−7.14448	−	13.8092i	−0.459264	−	0.887690i
$243$	6.62358	+	14.1113i	0.424903	+	0.905239i
$244$	−0.482845	+	2.12721i	−0.0309110	+	0.136181i
$245$	−2.05039	−	0.849301i	−0.130995	−	0.0542598i
$246$	1.63170	−	1.03489i	0.104033	−	0.0659824i
$247$	−6.72534	−	6.72534i	−0.427923	−	0.427923i
$248$	6.85940	−	5.18154i	0.435572	−	0.329028i
$249$	−3.87540	−	7.43542i	−0.245594	−	0.471200i
$250$	−15.8699	+	1.34817i	−1.00370	+	0.0852661i
$251$	−18.1519	−	7.51877i	−1.14574	−	0.474580i	−0.272636	−	0.962117i	$-0.587895\pi$
$251$	−18.1519	−	7.51877i	−1.14574	−	0.474580i	−0.873102	+	0.487537i	$0.837895\pi$
$252$	5.64638	−	2.02939i	0.355688	−	0.127840i
$253$	−0.0674505	−	0.162840i	−0.00424058	−	0.0102377i
$254$	−6.50867	+	20.4630i	−0.408390	+	1.28396i
$255$	25.5665	+	8.04692i	1.60104	+	0.503918i
$256$	−12.4614	+	10.0356i	−0.778839	+	0.627224i
$257$		−	21.3745i		−	1.33330i	−0.745369	−	0.666652i	$-0.767727\pi$
$257$		−	21.3745i		−	1.33330i	0.745369	−	0.666652i	$-0.232273\pi$
$258$	18.1616	−	25.8266i	1.13069	−	1.60790i
$259$	2.61795	−	1.08439i	0.162672	−	0.0673808i
$260$	−3.19086	+	4.50852i	−0.197889	+	0.279607i
$261$	0.200524	−	0.128033i	0.0124122	−	0.00792503i
$262$	2.64377	+	31.1209i	0.163333	+	1.92266i
$263$	12.4380	+	12.4380i	0.766958	+	0.766958i	0.977570	−	0.210612i	$-0.0675456\pi$
$263$	12.4380	+	12.4380i	0.766958	+	0.766958i	−0.210612	+	0.977570i	$0.567546\pi$
$264$	0.126832	+	0.356264i	0.00780597	+	0.0219265i
$265$	−4.73673	+	4.73673i	−0.290975	+	0.290975i
$266$	8.26267	+	6.96874i	0.506617	+	0.427281i
$267$	−7.76974	−	6.51291i	−0.475500	−	0.398584i
$268$	12.4200	+	2.81914i	0.758670	+	0.172207i
$269$	3.33594	+	8.05367i	0.203396	+	0.491041i	0.992357	−	0.123403i	$-0.0393806\pi$
$269$	3.33594	+	8.05367i	0.203396	+	0.491041i	−0.788961	+	0.614443i	$0.789381\pi$
$270$	14.7737	+	6.90720i	0.899101	+	0.420359i
$271$	17.9556			1.09073			0.545364	−	0.838200i	$-0.316392\pi$
$271$	17.9556			1.09073			0.545364	+	0.838200i	$0.316392\pi$
$272$	9.27471	+	26.3035i	0.562362	+	1.59489i
$273$	2.05592	+	0.647090i	0.124430	+	0.0391637i
$274$	−10.1136	−	19.5480i	−0.610983	−	1.18094i
$275$	−0.00531853	+	0.00220301i	−0.000320719	+	0.000132846i
$276$	−2.01252	−	7.64934i	−0.121140	−	0.460436i
$277$	−2.93268	+	7.08012i	−0.176208	+	0.425403i	−0.987165	−	0.159702i	$-0.948947\pi$
$277$	−2.93268	+	7.08012i	−0.176208	+	0.425403i	0.810958	+	0.585105i	$0.198947\pi$
$278$	15.1237	+	12.7553i	0.907060	+	0.765015i
$279$	−1.59237	−	8.97783i	−0.0953330	−	0.537489i
$280$	3.17959	−	5.41236i	0.190017	−	0.323450i
$281$	10.1942	−	10.1942i	0.608133	−	0.608133i	−0.334325	−	0.942458i	$-0.608508\pi$
$281$	10.1942	−	10.1942i	0.608133	−	0.608133i	0.942458	+	0.334325i	$0.108508\pi$
$282$	18.3599	+	4.10911i	1.09332	+	0.244694i
$283$	11.0511	−	26.6797i	0.656920	−	1.58595i	−0.145615	−	0.989341i	$-0.546516\pi$
$283$	11.0511	−	26.6797i	0.656920	−	1.58595i	0.802535	−	0.596605i	$-0.203484\pi$
$284$	2.36369	+	13.8116i	0.140259	+	0.819569i
$285$	2.57541	+	29.2671i	0.152554	+	1.73363i
$286$	−0.0411762	+	0.129457i	−0.00243480	+	0.00765493i
$287$	−0.788823			−0.0465628
$288$	3.48094	+	16.6097i	0.205117	+	0.978738i
$289$	31.6185			1.85991
$290$	0.0754447	−	0.237195i	0.00443027	−	0.0139286i
$291$	0.184495	+	2.09660i	0.0108153	+	0.122905i
$292$	2.39040	−	0.409088i	0.139887	−	0.0239401i
$293$	4.27905	−	10.3305i	0.249985	−	0.603517i	−0.748217	−	0.663454i	$-0.769090\pi$
$293$	4.27905	−	10.3305i	0.249985	−	0.603517i	0.998202	+	0.0599370i	$0.0190900\pi$
$294$	−2.39035	−	0.534982i	−0.139408	−	0.0312008i
$295$	0.987679	−	0.987679i	0.0575049	−	0.0575049i
$296$	2.01583	+	7.75713i	0.117168	+	0.450874i
$297$	0.397754	+	0.0517531i	0.0230800	+	0.00300302i
$298$	15.6087	+	13.1644i	0.904186	+	0.762591i
$299$	1.08734	−	2.62507i	0.0628824	−	0.151811i
$300$	−0.249836	+	0.0657311i	−0.0144243	+	0.00379499i
$301$	−11.9085	+	4.93266i	−0.686394	+	0.284314i
$302$	−12.6866	−	24.5214i	−0.730034	−	1.41105i
$303$	−11.9990	−	3.77663i	−0.689327	−	0.216962i
$304$	−22.7474	+	20.4264i	−1.30465	+	1.17153i
$305$	2.42053			0.138599
$306$	29.3237	+	3.90558i	1.67632	+	0.223267i
$307$	3.17891	+	7.67457i	0.181430	+	0.438011i	0.988262	−	0.152771i	$-0.0488196\pi$
$307$	3.17891	+	7.67457i	0.181430	+	0.438011i	−0.806832	+	0.590781i	$0.798820\pi$
$308$	0.0341740	−	0.150556i	0.00194725	−	0.00857874i
$309$	21.9677	+	18.4142i	1.24970	+	1.04755i
$310$	−7.29201	−	6.15008i	−0.414158	−	0.349301i
$311$	12.4675	−	12.4675i	0.706968	−	0.706968i	−0.258928	−	0.965897i	$-0.583369\pi$
$311$	12.4675	−	12.4675i	0.706968	−	0.706968i	0.965897	+	0.258928i	$0.0833693\pi$
$312$	−2.61528	+	5.50678i	−0.148061	+	0.311760i
$313$	−13.6424	−	13.6424i	−0.771116	−	0.771116i	0.207186	−	0.978302i	$-0.433569\pi$
$313$	−13.6424	−	13.6424i	−0.771116	−	0.771116i	−0.978302	+	0.207186i	$0.933569\pi$
$314$	1.74038	+	20.4867i	0.0982151	+	1.15613i
$315$	−3.58300	−	5.61168i	−0.201879	−	0.316182i
$316$	−22.3110	−	15.7904i	−1.25509	−	0.888279i
$317$	24.0752	−	9.97229i	1.35220	−	0.560100i	0.415296	−	0.909686i	$-0.363678\pi$
$317$	24.0752	−	9.97229i	1.35220	−	0.560100i	0.936904	+	0.349587i	$0.113678\pi$
$318$	−4.25290	+	6.04781i	−0.238491	+	0.339144i
$319$		−	0.00612174i		−	0.000342751i
$320$	13.9208	+	11.0199i	0.778195	+	0.616033i
$321$	−4.17417	−	1.31380i	−0.232980	−	0.0733290i
$322$	−0.978763	+	3.07720i	−0.0545443	+	0.171485i
$323$	20.3945	+	49.2366i	1.13478	+	2.73960i
$324$	17.3725	+	4.71122i	0.965140	+	0.261734i
$325$	−0.0857375	−	0.0355136i	−0.00475586	−	0.00196994i
$326$	−13.9794	+	1.18757i	−0.774249	+	0.0657736i
$327$	−7.90535	−	15.1673i	−0.437167	−	0.838756i
$328$	0.307925	−	2.20978i	0.0170023	−	0.122015i
$329$	−5.43117	−	5.43117i	−0.299430	−	0.299430i
$330$	0.354373	−	0.224759i	0.0195076	−	0.0123726i
$331$	−21.8914	−	9.06772i	−1.20326	−	0.498407i	−0.311210	−	0.950341i	$-0.600734\pi$
$331$	−21.8914	−	9.06772i	−1.20326	−	0.498407i	−0.892051	+	0.451934i	$0.850734\pi$
$332$	−9.44171	−	2.14313i	−0.518181	−	0.117619i
$333$	8.30130	+	1.83157i	0.454908	+	0.100369i
$334$	5.87690	+	11.3592i	0.321570	+	0.621546i
$335$		−	14.1326i		−	0.772145i
$336$	2.43178	−	6.48741i	0.132664	−	0.353917i
$337$		−	14.7223i		−	0.801973i	−0.916084	−	0.400986i	$-0.868667\pi$
$337$		−	14.7223i		−	0.801973i	0.916084	−	0.400986i	$-0.131333\pi$
$338$	14.3838	−	7.44175i	0.782375	−	0.404778i
$339$	0.0649639	+	0.738252i	0.00352835	+	0.0400963i
$340$	26.1859	−	16.4974i	1.42013	−	0.894699i
$341$	−0.216755	−	0.0897830i	−0.0117380	−	0.00486202i
$342$	8.34545	+	31.3348i	0.451271	+	1.69439i
$343$	0.707107	+	0.707107i	0.0381802	+	0.0381802i
$344$	−9.16956	−	35.2855i	−0.494389	−	1.90247i
$345$	−7.78331	+	4.05673i	−0.419039	+	0.218407i
$346$	2.95823	+	34.8226i	0.159035	+	1.87207i
$347$	−18.1120	−	7.50223i	−0.972302	−	0.402741i	−0.160733	−	0.986998i	$-0.551386\pi$
$347$	−18.1120	−	7.50223i	−0.972302	−	0.402741i	−0.811569	+	0.584257i	$0.801386\pi$
$348$	0.0370920	−	0.272202i	0.00198834	−	0.0145916i
$349$	3.63314	+	8.77119i	0.194478	+	0.469511i	0.990795	−	0.135368i	$-0.0432216\pi$
$349$	3.63314	+	8.77119i	0.194478	+	0.469511i	−0.796318	+	0.604879i	$0.793222\pi$
$350$	0.100505	+	0.0319675i	0.00537220	+	0.00170873i
$351$	3.94404	+	5.12391i	0.210518	+	0.273494i
$352$	0.408422	+	0.154505i	0.0217690	+	0.00823514i
$353$			32.4813i			1.72881i	0.502798	+	0.864404i	$0.332304\pi$
$353$			32.4813i			1.72881i	−0.502798	+	0.864404i	$0.667696\pi$
$354$	0.886794	−	1.26106i	0.0471326	−	0.0670246i
$355$	14.3655	−	5.95038i	0.762441	−	0.315813i
$356$	−11.5390	+	1.97477i	−0.611568	+	0.104663i
$357$	−9.25548	−	7.75832i	−0.489852	−	0.410614i
$358$	28.5562	−	2.42589i	1.50924	−	0.128212i
$359$	9.52119	+	9.52119i	0.502509	+	0.502509i	0.912217	−	0.409708i	$-0.134369\pi$
$359$	9.52119	+	9.52119i	0.502509	+	0.502509i	−0.409708	+	0.912217i	$0.634369\pi$
$360$	17.1190	−	7.84669i	0.902250	−	0.413557i
$361$	−27.8724	+	27.8724i	−1.46697	+	1.46697i
$362$	−15.7064	+	18.6227i	−0.825508	+	0.978785i
$363$	−12.2328	+	14.5934i	−0.642053	+	0.765953i
$364$	2.10573	−	1.32663i	0.110370	−	0.0695346i
$365$	−1.02984	−	2.48625i	−0.0539043	−	0.130136i
$366$	2.63190	−	0.458612i	0.137572	−	0.0239720i
$367$	−20.4341			−1.06665			−0.533326	−	0.845910i	$-0.679058\pi$
$367$	−20.4341			−1.06665			−0.533326	+	0.845910i	$0.679058\pi$
$368$	−8.23827	−	3.94308i	−0.429449	−	0.205547i
$369$	−1.93987	−	1.35540i	−0.100985	−	0.0705591i
$370$	7.89914	−	4.08678i	0.410657	−	0.212462i
$371$	2.78861	−	1.15508i	0.144777	−	0.0599687i
$372$	−9.09400	−	5.30553i	−0.471502	−	0.275079i
$373$	5.57510	−	13.4595i	0.288668	−	0.696906i	−0.711314	−	0.702874i	$-0.751900\pi$
$373$	5.57510	−	13.4595i	0.288668	−	0.696906i	0.999982	+	0.00596820i	$0.00189975\pi$
$374$	0.490752	−	0.581873i	0.0253762	−	0.0300879i
$375$	9.01588	+	17.2980i	0.465578	+	0.893267i
$376$	17.3348	−	13.0945i	0.893972	−	0.675300i
$377$	0.0697813	−	0.0697813i	0.00359392	−	0.00359392i
$378$	−4.95911	−	5.42285i	−0.255069	−	0.278921i
$379$	−3.16943	+	7.65167i	−0.162802	+	0.393040i	−0.984138	−	0.177406i	$-0.943229\pi$
$379$	−3.16943	+	7.65167i	−0.162802	+	0.393040i	0.821335	+	0.570446i	$0.193229\pi$
$380$	27.6916	+	19.5985i	1.42055	+	1.00538i
$381$	26.1979	−	2.30534i	1.34216	−	0.118106i
$382$	−21.8010	−	6.93425i	−1.11544	−	0.354787i
$383$	−26.9488			−1.37702			−0.688509	−	0.725228i	$-0.741734\pi$
$383$	−26.9488			−1.37702			−0.688509	+	0.725228i	$0.741734\pi$
$384$	17.2243	+	9.34470i	0.878974	+	0.476870i
$385$	−0.171317			−0.00873112
$386$	−17.5828	−	5.59256i	−0.894941	−	0.284654i
$387$	−37.7608	−	8.33141i	−1.91949	−	0.423509i
$388$	1.98374	+	1.40397i	0.100709	+	0.0712760i
$389$	6.80266	−	16.4231i	0.344909	−	0.832683i	−0.652296	−	0.757964i	$-0.726194\pi$
$389$	6.80266	−	16.4231i	0.344909	−	0.832683i	0.997205	−	0.0747188i	$-0.0238059\pi$
$390$	6.60149	+	1.47747i	0.334279	+	0.0748146i
$391$	−11.2578	+	11.2578i	−0.569330	+	0.569330i
$392$	−2.25689	+	1.70483i	−0.113990	+	0.0861072i
$393$	33.9215	−	17.6801i	1.71111	−	0.891846i
$394$	−9.41929	+	11.1682i	−0.474537	+	0.562647i
$395$	−11.6072	+	28.0222i	−0.584019	+	1.40995i
$396$	0.342734	−	0.311527i	0.0172230	−	0.0156548i
$397$	−31.9392	+	13.2296i	−1.60298	+	0.663977i	−0.991834	−	0.127539i	$-0.959292\pi$
$397$	−31.9392	+	13.2296i	−1.60298	+	0.663977i	−0.611148	+	0.791516i	$0.709292\pi$
$398$	−11.8262	+	6.11855i	−0.592796	+	0.306695i
$399$	3.97447	−	12.6276i	0.198972	−	0.632171i
$400$	−0.128785	+	0.269071i	−0.00643927	+	0.0134535i
$401$	−5.69103			−0.284197			−0.142098	−	0.989853i	$-0.545385\pi$
$401$	−5.69103			−0.284197			−0.142098	+	0.989853i	$0.545385\pi$
$402$	−2.67766	−	15.3667i	−0.133549	−	0.766420i
$403$	−1.44735	−	3.49421i	−0.0720976	−	0.174059i
$404$	−12.2897	+	7.74268i	−0.611437	+	0.385213i
$405$	0.830990	−	19.9567i	0.0412922	−	0.991655i
$406$	−0.0723068	+	0.0857324i	−0.00358852	+	0.00425483i
$407$	0.154671	−	0.154671i	0.00766677	−	0.00766677i
$408$	25.3468	−	22.8994i	1.25485	−	1.13369i
$409$	1.20996	+	1.20996i	0.0598286	+	0.0598286i	0.736388	−	0.676559i	$-0.236530\pi$
$409$	1.20996	+	1.20996i	0.0598286	+	0.0598286i	−0.676559	+	0.736388i	$0.736530\pi$
$410$	−2.46692	+	0.209569i	−0.121833	+	0.0103499i
$411$	−17.3164	+	20.6581i	−0.854156	+	1.01899i
$412$	32.6248	−	5.58334i	1.60731	−	0.275071i
$413$	−0.581466	+	0.240851i	−0.0286121	+	0.0118515i
$414$	−7.69436	+	5.88565i	−0.378157	+	0.289264i
$415$			10.7436i			0.527385i
$416$	2.89439	+	6.41677i	0.141909	+	0.314608i
$417$	7.27473	−	23.1131i	0.356245	−	1.13185i
$418$	0.795130	+	0.252907i	0.0388911	+	0.0123701i
$419$	8.43112	+	20.3545i	0.411887	+	0.994383i	0.984631	+	0.174649i	$0.0558790\pi$
$419$	8.43112	+	20.3545i	0.411887	+	0.994383i	−0.572744	+	0.819735i	$0.694121\pi$
$420$	−7.61759	−	1.03802i	−0.371700	−	0.0506502i
$421$	−0.275683	−	0.114192i	−0.0134360	−	0.00556537i	0.375955	−	0.926638i	$-0.377315\pi$
$421$	−0.275683	−	0.114192i	−0.0134360	−	0.00556537i	−0.389391	+	0.921072i	$0.627315\pi$
$422$	−0.388160	−	4.56919i	−0.0188953	−	0.222425i
$423$	−4.02418	−	22.6884i	−0.195662	−	1.10315i
$424$	2.14723	+	8.26279i	0.104279	+	0.401276i
$425$	0.367691	+	0.367691i	0.0178357	+	0.0178357i
$426$	14.4925	−	9.19178i	0.702165	−	0.445343i
$427$	−1.00764	−	0.417378i	−0.0487631	−	0.0201983i
$428$	−4.27530	+	2.69349i	−0.206654	+	0.130195i
$429$	0.165738	−	0.0145844i	0.00800190	−	0.000704143i
$430$	−35.9315	+	18.5899i	−1.73277	+	0.896483i
$431$			32.6112i			1.57083i	0.618971	+	0.785414i	$0.287550\pi$
$431$			32.6112i			1.57083i	−0.618971	+	0.785414i	$0.712450\pi$
$432$	17.1272	−	11.7754i	0.824032	−	0.566543i
$433$			29.4357i			1.41459i	0.706919	+	0.707295i	$0.250085\pi$
$433$			29.4357i			1.41459i	−0.706919	+	0.707295i	$0.749915\pi$
$434$	1.97510	+	3.81758i	0.0948079	+	0.183250i
$435$	−0.303671	+	0.0267221i	−0.0145599	+	0.00128123i
$436$	−19.2599	−	4.37172i	−0.922384	−	0.209367i
$437$	−16.1233	−	6.67849i	−0.771283	−	0.319476i
$438$	−1.59083	−	2.50824i	−0.0760129	−	0.119848i
$439$	−13.1578	−	13.1578i	−0.627989	−	0.627989i	0.319573	−	0.947562i	$-0.396461\pi$
$439$	−13.1578	−	13.1578i	−0.627989	−	0.627989i	−0.947562	+	0.319573i	$0.896461\pi$
$440$	0.0668752	−	0.479920i	0.00318815	−	0.0228793i
$441$	0.523925	+	2.95390i	0.0249488	+	0.140662i
$442$	12.2268	−	1.03868i	0.581568	−	0.0494051i
$443$	4.54262	+	1.88161i	0.215826	+	0.0893982i	0.487977	−	0.872856i	$-0.337735\pi$
$443$	4.54262	+	1.88161i	0.215826	+	0.0893982i	−0.272151	+	0.962255i	$0.587735\pi$
$444$	7.81460	−	5.94028i	0.370865	−	0.281913i
$445$	4.97130	+	12.0018i	0.235662	+	0.568939i
$446$	11.5368	−	36.2714i	0.546285	−	1.71750i
$447$	7.50799	−	23.8543i	0.355116	−	1.12827i
$448$	−3.89486	−	6.98785i	−0.184015	−	0.330145i
$449$		−	2.13873i		−	0.100933i	−0.998726	−	0.0504666i	$-0.983929\pi$
$449$		−	2.13873i		−	0.100933i	0.998726	−	0.0504666i	$-0.0160708\pi$
$450$	0.192232	+	0.251306i	0.00906190	+	0.0118467i
$451$	−0.0562566	+	0.0233022i	−0.00264902	+	0.00109726i
$452$	0.698511	+	0.494365i	0.0328552	+	0.0232530i
$453$	−21.7220	+	25.9138i	−1.02059	+	1.21754i
$454$	1.71636	+	20.2040i	0.0805527	+	0.948219i
$455$	−1.95283	−	1.95283i	−0.0915501	−	0.0915501i
$456$	33.8230	+	16.0632i	1.58391	+	0.752229i
$457$	19.8775	−	19.8775i	0.929833	−	0.929833i	−0.0678622	−	0.997695i	$-0.521618\pi$
$457$	19.8775	−	19.8775i	0.929833	−	0.929833i	0.997695	+	0.0678622i	$0.0216178\pi$
$458$	−16.3422	−	13.7830i	−0.763622	−	0.644039i
$459$	−9.43027	−	34.9824i	−0.440167	−	1.63284i
$460$	−2.24340	+	9.88348i	−0.104599	+	0.460819i
$461$	−7.61484	−	18.3838i	−0.354658	−	0.856221i	−0.996032	−	0.0889927i	$-0.971635\pi$
$461$	−7.61484	−	18.3838i	−0.354658	−	0.856221i	0.641374	−	0.767229i	$-0.278365\pi$
$462$	−0.186277	+	0.0324589i	−0.00866638	+	0.00151013i
$463$	−32.9991			−1.53360			−0.766800	−	0.641886i	$-0.778152\pi$
$463$	−32.9991			−1.53360			−0.766800	+	0.641886i	$0.778152\pi$
$464$	−0.211942	−	0.236024i	−0.00983915	−	0.0109571i
$465$	−3.50756	+	11.1442i	−0.162659	+	0.516798i
$466$	11.1118	+	21.4774i	0.514742	+	0.994920i
$467$	7.43819	−	3.08100i	0.344199	−	0.142572i	−0.203886	−	0.978995i	$-0.565357\pi$
$467$	7.43819	−	3.08100i	0.344199	−	0.142572i	0.548085	+	0.836423i	$0.315357\pi$
$468$	7.45788	+	0.355722i	0.344741	+	0.0164432i
$469$	−2.43691	+	5.88321i	−0.112526	+	0.271662i
$470$	−18.4280	−	15.5422i	−0.850022	−	0.716908i
$471$	22.3303	−	11.6387i	1.02892	−	0.536284i
$472$	−0.447730	−	1.72292i	−0.0206084	−	0.0793036i
$473$	−0.703566	+	0.703566i	−0.0323500	+	0.0323500i
$474$	−7.31145	+	32.6683i	−0.335826	+	1.50051i
$475$	−0.218127	+	0.526605i	−0.0100083	+	0.0241623i
$476$	−13.7456	+	2.35239i	−0.630026	+	0.107821i
$477$	8.84243	+	1.95096i	0.404867	+	0.0893284i
$478$	4.55903	−	14.3334i	0.208525	−	0.655596i
$479$	−39.4501			−1.80252			−0.901261	−	0.433276i	$-0.857358\pi$
$479$	−39.4501			−1.80252			−0.901261	+	0.433276i	$0.857358\pi$
$480$	5.88147	−	20.9344i	0.268451	−	0.955520i
$481$	3.52618			0.160780
$482$	−2.39073	+	7.51637i	−0.108895	+	0.342361i
$483$	3.93961	−	0.346673i	0.179258	−	0.0157742i
$484$	3.70907	+	21.6730i	0.168594	+	0.985136i
$485$	1.03203	−	2.49154i	0.0468620	−	0.113135i
$486$	−2.87758	−	21.8568i	−0.130530	−	0.991444i
$487$	17.6592	−	17.6592i	0.800216	−	0.800216i	−0.182913	−	0.983129i	$-0.558553\pi$
$487$	17.6592	−	17.6592i	0.800216	−	0.800216i	0.983129	+	0.182913i	$0.0585526\pi$
$488$	1.56257	−	2.65983i	0.0707341	−	0.120405i
$489$	7.94187	+	15.2374i	0.359144	+	0.689060i
$490$	2.39922	+	2.02351i	0.108386	+	0.0914127i
$491$	−10.1365	+	24.4716i	−0.457453	+	1.10439i	0.511972	+	0.859002i	$0.328915\pi$
$491$	−10.1365	+	24.4716i	−0.457453	+	1.10439i	−0.969425	+	0.245387i	$0.921085\pi$
$492$	−2.64263	+	0.695269i	−0.119139	+	0.0313452i
$493$	−0.510872	+	0.211610i	−0.0230085	+	0.00953045i
$494$	6.18077	+	11.9465i	0.278086	+	0.537499i
$495$	−0.421301	−	0.294365i	−0.0189361	−	0.0132307i
$496$	−11.4654	+	4.04274i	−0.514812	+	0.181524i
$497$	−7.00621			−0.314272
$498$	2.03557	+	11.6818i	0.0912160	+	0.523474i
$499$	4.72640	+	11.4105i	0.211583	+	0.510806i	0.993667	−	0.112367i	$-0.0358432\pi$
$499$	4.72640	+	11.4105i	0.211583	+	0.510806i	−0.782084	+	0.623173i	$0.785843\pi$
$500$	21.9656	+	4.98585i	0.982330	+	0.222974i
$501$	10.0624	−	12.0042i	0.449556	−	0.536309i
$502$	21.2401	+	17.9139i	0.947990	+	0.799535i
$503$	−1.11827	+	1.11827i	−0.0498611	+	0.0498611i	−0.731598	−	0.681737i	$-0.761225\pi$
$503$	−1.11827	+	1.11827i	−0.0498611	+	0.0498611i	0.681737	+	0.731598i	$0.261225\pi$
$504$	−8.47945	+	0.314619i	−0.377705	+	0.0140143i
$505$	11.3974	+	11.3974i	0.507176	+	0.507176i
$506$	0.0210994	+	0.248370i	0.000937983	+	0.0110414i
$507$	−15.2006	−	12.7417i	−0.675081	−	0.565881i
$508$	17.5433	−	24.7877i	0.778356	−	1.09978i
$509$	7.94172	−	3.28957i	0.352011	−	0.145808i	−0.199670	−	0.979863i	$-0.563987\pi$
$509$	7.94172	−	3.28957i	0.352011	−	0.145808i	0.551680	+	0.834056i	$0.313987\pi$
$510$	−31.0062	−	21.8040i	−1.37298	−	0.965497i
$511$			1.21257i			0.0536411i
$512$	21.0959	−	8.18312i	0.932315	−	0.361646i
$513$	31.4713	−	24.2246i	1.38949	−	1.06954i
$514$	−9.16233	+	28.8060i	−0.404133	+	1.27058i
$515$	−14.0555	−	33.9331i	−0.619361	−	1.49527i
$516$	−35.5469	+	27.0210i	−1.56487	+	1.18953i
$517$	−0.547775	−	0.226896i	−0.0240911	−	0.00997886i
$518$	−3.99301	+	0.339212i	−0.175443	+	0.0149041i
$519$	37.9562	−	19.7831i	1.66609	−	0.868381i
$520$	6.23289	−	4.70827i	0.273330	−	0.206471i
$521$	−1.76555	−	1.76555i	−0.0773500	−	0.0773500i	0.667373	−	0.744723i	$-0.267419\pi$
$521$	−1.76555	−	1.76555i	−0.0773500	−	0.0773500i	−0.744723	+	0.667373i	$0.767419\pi$
$522$	−0.325126	+	0.0865914i	−0.0142304	+	0.00379000i
$523$	−27.8984	−	11.5559i	−1.21991	−	0.505305i	−0.322532	−	0.946559i	$-0.604534\pi$
$523$	−27.8984	−	11.5559i	−1.21991	−	0.505305i	−0.897382	+	0.441254i	$0.854534\pi$
$524$	9.77726	−	43.0745i	0.427122	−	1.88172i
$525$	−0.0113227	−	0.128672i	−0.000494164	−	0.00561570i
$526$	−11.4308	−	22.0941i	−0.498408	−	0.963348i
$527$			21.1922i			0.923149i
$528$	−0.0182142	−	0.534499i	−0.000792670	−	0.0232611i
$529$			17.7864i			0.773324i
$530$	8.41405	−	4.35318i	0.365483	−	0.189090i
$531$	−1.84378	−	0.406805i	−0.0800132	−	0.0176538i
$532$	−8.14827	−	12.9335i	−0.353272	−	0.560739i
$533$	−0.906886	−	0.375645i	−0.0392816	−	0.0162710i
$534$	7.67935	+	12.1079i	0.332318	+	0.523960i
$535$	3.96486	+	3.96486i	0.171416	+	0.171416i
$536$	−15.5297	−	9.12322i	−0.670782	−	0.394063i
$537$	−16.2231	−	31.1259i	−0.700077	−	1.34318i
$538$	−1.04353	−	12.2838i	−0.0449896	−	0.529591i
$539$	0.0713171	+	0.0295405i	0.00307184	+	0.00127240i
$540$	−16.9495	−	15.6416i	−0.729391	−	0.673107i
$541$	−0.417450	−	1.00781i	−0.0179476	−	0.0433293i	0.914652	−	0.404243i	$-0.132465\pi$
$541$	−0.417450	−	1.00781i	−0.0179476	−	0.0433293i	−0.932599	+	0.360914i	$0.882465\pi$
$542$	−24.1985	−	7.69682i	−1.03942	−	0.330607i
$543$	28.4605	+	8.95777i	1.22136	+	0.384415i
$544$	−1.22417	−	39.4245i	−0.0524860	−	1.69031i
$545$			21.9157i			0.938767i
$546$	−2.49335	−	1.75336i	−0.106706	−	0.0750369i
$547$	−12.8577	+	5.32585i	−0.549757	+	0.227717i	−0.640232	−	0.768182i	$-0.721162\pi$
$547$	−12.8577	+	5.32585i	−0.549757	+	0.227717i	0.0904747	+	0.995899i	$0.471162\pi$
$548$	5.25048	+	30.6798i	0.224289	+	1.31058i
$549$	−1.76082	−	2.75779i	−0.0751498	−	0.117699i
$550$	0.00811203		0.000689129i	0.000345898		2.93846e-5i
$551$	−0.428601	−	0.428601i	−0.0182590	−	0.0182590i
$552$	−0.566707	+	11.1716i	−0.0241207	+	0.475494i
$553$	9.66383	−	9.66383i	0.410948	−	0.410948i
$554$	6.98727	−	8.28465i	0.296861	−	0.351981i
$555$	−8.34769	−	6.99737i	−0.354340	−	0.297022i
$556$	−14.9143	−	23.6731i	−0.632508	−	1.00396i
$557$	6.97990	+	16.8510i	0.295748	+	0.713999i	0.999992	+	0.00404049i	$0.00128613\pi$
$557$	6.97990	+	16.8510i	0.295748	+	0.713999i	−0.704244	+	0.709958i	$0.748714\pi$
$558$	−1.70240	+	12.7819i	−0.0720683	+	0.541100i
$559$	−16.0398			−0.678411
$560$	−6.60513	+	5.93119i	−0.279118	+	0.250639i
$561$	−0.889259	−	0.279889i	−0.0375445	−	0.0118169i
$562$	−18.1083	+	9.36871i	−0.763854	+	0.395195i
$563$	−14.3460	+	5.94232i	−0.604613	+	0.250439i	−0.663923	−	0.747801i	$-0.731110\pi$
$563$	−14.3460	+	5.94232i	−0.604613	+	0.250439i	0.0593102	+	0.998240i	$0.481110\pi$
$564$	−22.9820	−	13.4079i	−0.967715	−	0.564574i
$565$	0.363396	−	0.877316i	0.0152882	−	0.0369089i
$566$	−26.3299	+	31.2187i	−1.10673	+	1.31222i
$567$	−3.78710	+	8.16443i	−0.159043	+	0.342874i
$568$	2.73494	−	19.6269i	0.114756	−	0.823527i
$569$	13.8640	−	13.8640i	0.581210	−	0.581210i	−0.354026	−	0.935236i	$-0.615188\pi$
$569$	13.8640	−	13.8640i	0.581210	−	0.581210i	0.935236	+	0.354026i	$0.115188\pi$
$570$	9.07471	−	40.5467i	0.380098	−	1.69832i
$571$	9.27216	−	22.3850i	0.388028	−	0.936782i	−0.602330	−	0.798247i	$-0.705761\pi$
$571$	9.27216	−	22.3850i	0.388028	−	0.936782i	0.990358	−	0.138535i	$-0.0442392\pi$
$572$	0.110985	−	0.156816i	0.00464052	−	0.00655681i
$573$	2.45608	+	27.9109i	0.102604	+	1.16600i
$574$	1.06308	+	0.338135i	0.0443723	+	0.0141135i
$575$	−0.170280			−0.00710119
$576$	2.42867	−	23.8768i	0.101195	−	0.994867i
$577$	38.1721			1.58912			0.794562	−	0.607183i	$-0.207700\pi$
$577$	38.1721			1.58912			0.794562	+	0.607183i	$0.207700\pi$
$578$	−42.6117	−	13.5535i	−1.77241	−	0.563751i
$579$	1.98086	+	22.5105i	0.0823217	+	0.935506i
$580$	−0.203351	+	0.287325i	−0.00844370	+	0.0119305i
$581$	1.85255	−	4.47245i	0.0768566	−	0.185548i
$582$	0.650084	−	2.90464i	0.0269468	−	0.120401i
$583$	0.164754	−	0.164754i	0.00682340	−	0.00682340i
$584$	−3.39686	−	0.473340i	−0.140563	−	0.0195870i
$585$	−1.44693	−	8.15783i	−0.0598233	−	0.337285i
$586$	−10.1951	+	12.0881i	−0.421155	+	0.499353i
$587$	−3.77132	+	9.10476i	−0.155659	+	0.375794i	−0.982400	−	0.186789i	$-0.940192\pi$
$587$	−3.77132	+	9.10476i	−0.155659	+	0.375794i	0.826741	+	0.562582i	$0.190192\pi$
$588$	2.99212	+	1.74563i	0.123393	+	0.0719886i
$589$	−21.4617	+	8.88971i	−0.884313	+	0.366294i
$590$	−1.75446	+	0.907704i	−0.0722298	+	0.0373696i
$591$	17.0681	+	5.37208i	0.702087	+	0.220978i
$592$	0.608454	−	11.3183i	0.0250073	−	0.465178i
$593$	−33.8756			−1.39110			−0.695552	−	0.718476i	$-0.744840\pi$
$593$	−33.8756			−1.39110			−0.695552	+	0.718476i	$0.744840\pi$
$594$	−0.513863	−	0.240247i	−0.0210840	−	0.00985746i
$595$	5.92192	+	14.2968i	0.242775	+	0.586110i
$596$	−15.3926	−	24.4322i	−0.630503	−	1.00078i
$597$	12.4978	+	10.4762i	0.511501	+	0.428761i
$598$	−2.59064	+	3.07166i	−0.105939	+	0.125610i
$599$	0.00423417	−	0.00423417i	0.000173003	−	0.000173003i	−0.707020	−	0.707193i	$-0.749961\pi$
$599$	0.00423417	−	0.00423417i	0.000173003	−	0.000173003i	0.707193	+	0.707020i	$0.249961\pi$
$600$	0.364876	+	0.0185093i	0.0148960	+	0.000755638i
$601$	−8.33485	−	8.33485i	−0.339985	−	0.339985i	0.516376	−	0.856362i	$-0.327281\pi$
$601$	−8.33485	−	8.33485i	−0.339985	−	0.339985i	−0.856362	+	0.516376i	$0.827281\pi$
$602$	18.1633	−	1.54300i	0.740281	−	0.0628880i
$603$	−16.1016	+	10.2807i	−0.655710	+	0.418664i
$604$	6.58630	+	38.4853i	0.267993	+	1.56595i
$605$	22.5421	−	9.33725i	0.916467	−	0.379613i
$606$	14.5520	+	10.2332i	0.591136	+	0.415695i
$607$			1.45781i			0.0591707i	0.999562	+	0.0295854i	$0.00941869\pi$
$607$			1.45781i			0.0591707i	−0.999562	+	0.0295854i	$0.990581\pi$
$608$	39.4122	−	17.7775i	1.59838	−	0.720973i
$609$	0.131022	+	0.0412386i	0.00530929	+	0.00167107i
$610$	−3.26212	−	1.03758i	−0.132079	−	0.0420104i
$611$	−3.65768	−	8.83042i	−0.147974	−	0.357240i
$612$	−37.8449	−	17.8333i	−1.52979	−	0.720869i
$613$	1.81409	+	0.751421i	0.0732704	+	0.0303496i	0.419018	−	0.907978i	$-0.362375\pi$
$613$	1.81409	+	0.751421i	0.0732704	+	0.0303496i	−0.345747	+	0.938328i	$0.612375\pi$
$614$	−0.994405	−	11.7056i	−0.0401309	−	0.472398i
$615$	1.40148	+	2.68892i	0.0565133	+	0.108428i
$616$	−0.110593	+	0.188253i	−0.00445592	+	0.00758495i
$617$	23.4418	+	23.4418i	0.943731	+	0.943731i	0.998499	−	0.0547685i	$-0.0174421\pi$
$617$	23.4418	+	23.4418i	0.943731	+	0.943731i	−0.0547685	+	0.998499i	$0.517442\pi$
$618$	−21.7121	−	34.2331i	−0.873389	−	1.37706i
$619$	39.6688	+	16.4313i	1.59442	+	0.660431i	0.990613	−	0.136697i	$-0.0436488\pi$
$619$	39.6688	+	16.4313i	1.59442	+	0.660431i	0.603809	+	0.797129i	$0.293649\pi$
$620$	7.19104	+	11.4141i	0.288799	+	0.458403i
$621$	10.2839	+	5.91669i	0.412679	+	0.237429i
$622$	−22.1466	+	11.4580i	−0.887997	+	0.459423i
$623$		−	5.85340i		−	0.234512i
$624$	5.88510	−	6.30034i	0.235592	−	0.252216i
$625$		−	24.6216i		−	0.984862i
$626$	12.5378	+	24.2336i	0.501109	+	0.968570i
$627$	−0.0895784	−	1.01797i	−0.00357742	−	0.0406539i
$628$	6.43631	−	28.3556i	0.256837	−	1.13151i
$629$	−18.2542	−	7.56113i	−0.727842	−	0.301482i
$630$	2.42326	+	9.09865i	0.0965450	+	0.362499i
$631$	−2.84253	−	2.84253i	−0.113159	−	0.113159i	0.648260	−	0.761419i	$-0.275497\pi$
$631$	−2.84253	−	2.84253i	−0.113159	−	0.113159i	−0.761419	+	0.648260i	$0.775497\pi$
$632$	23.2995	+	30.8442i	0.926805	+	1.22692i
$633$	−4.98037	+	2.59581i	−0.197952	+	0.103174i
$634$	−36.7205	+	3.11946i	−1.45836	+	0.123890i
$635$	−31.1328	−	12.8956i	−1.23547	−	0.511748i
$636$	8.32401	−	6.32750i	0.330068	−	0.250902i
$637$	0.476209	+	1.14967i	0.0188681	+	0.0455516i
$638$	−0.00262413	+	0.00825017i	−0.000103890	+	0.000326627i
$639$	−17.2296	−	12.0384i	−0.681593	−	0.476233i
$640$	−14.0370	−	20.8186i	−0.554862	−	0.822929i
$641$		−	29.3828i		−	1.16055i	−0.814421	−	0.580275i	$-0.802945\pi$
$641$		−	29.3828i		−	1.16055i	0.814421	−	0.580275i	$-0.197055\pi$
$642$	5.06230	+	3.55987i	0.199793	+	0.140497i
$643$	−1.36995	+	0.567450i	−0.0540254	+	0.0223781i	−0.409533	−	0.912296i	$-0.634308\pi$
$643$	−1.36995	+	0.567450i	−0.0540254	+	0.0223781i	0.355507	+	0.934674i	$0.384308\pi$
$644$	2.63813	−	3.72753i	0.103957	−	0.146885i
$645$	37.9718	+	31.8295i	1.49514	+	1.25329i
$646$	−6.37965	−	75.0976i	−0.251004	−	2.95468i
$647$	3.69587	+	3.69587i	0.145300	+	0.145300i	0.776015	−	0.630715i	$-0.217238\pi$
$647$	3.69587	+	3.69587i	0.145300	+	0.145300i	−0.630715	+	0.776015i	$0.717238\pi$
$648$	−21.3932	−	13.7961i	−0.840403	−	0.541962i
$649$	−0.0343536	+	0.0343536i	−0.00134850	+	0.00134850i
$650$	0.100324	+	0.0846132i	0.00393503	+	0.00331880i
$651$	3.38176	−	4.03436i	0.132542	−	0.158119i
$652$	19.3489	+	4.39192i	0.757762	+	0.172001i
$653$	15.0188	+	36.2585i	0.587730	+	1.41891i	0.885667	+	0.464320i	$0.153701\pi$
$653$	15.0188	+	36.2585i	0.587730	+	1.41891i	−0.297938	+	0.954585i	$0.596299\pi$
$654$	4.15231	+	23.8295i	0.162368	+	0.931806i
$655$	−49.0141			−1.91514
$656$	−1.36222	+	2.84609i	−0.0531859	+	0.111121i
$657$	−2.08351	+	2.98195i	−0.0812853	+	0.116337i
$658$	4.99139	+	9.64761i	0.194585	+	0.376103i
$659$	39.0594	−	16.1789i	1.52154	−	0.630242i	0.543639	−	0.839319i	$-0.317046\pi$
$659$	39.0594	−	16.1789i	1.52154	−	0.630242i	0.977899	+	0.209077i	$0.0670460\pi$
$660$	−0.573928	+	0.150999i	−0.0223401	+	0.00587762i
$661$	16.4454	−	39.7027i	0.639652	−	1.54426i	−0.187491	−	0.982266i	$-0.560036\pi$
$661$	16.4454	−	39.7027i	0.639652	−	1.54426i	0.827143	−	0.561991i	$-0.189964\pi$
$662$	25.6158	+	21.6044i	0.995585	+	0.839677i
$663$	−6.94617	−	13.3270i	−0.269767	−	0.517579i
$664$	11.8058	+	6.93552i	0.458153	+	0.269150i
$665$	−11.9944	+	11.9944i	−0.465123	+	0.465123i
$666$	−10.4024	−	6.02679i	−0.403085	−	0.233533i
$667$	0.0692952	−	0.167293i	0.00268312	−	0.00647763i
$668$	−3.05101	−	17.8278i	−0.118047	−	0.689777i
$669$	−46.4368	+	4.08629i	−1.79535	+	0.157985i
$670$	−6.05803	+	19.0462i	−0.234042	+	0.735820i
$671$	−0.0841914			−0.00325017
$672$	−6.05814	+	7.70058i	−0.233698	+	0.297056i
$673$	39.0077			1.50363			0.751817	−	0.659371i	$-0.229177\pi$
$673$	39.0077			1.50363			0.751817	+	0.659371i	$0.229177\pi$
$674$	−6.31081	+	19.8410i	−0.243083	+	0.764245i
$675$	0.193246	−	0.335884i	0.00743802	−	0.0129282i
$676$	−22.5748	+	3.86340i	−0.868260	+	0.148592i
$677$	−3.69368	+	8.91734i	−0.141960	+	0.342721i	−0.978828	−	0.204683i	$-0.934384\pi$
$677$	−3.69368	+	8.91734i	−0.141960	+	0.342721i	0.836869	+	0.547404i	$0.184384\pi$
$678$	0.228906	−	1.02278i	0.00879110	−	0.0392795i
$679$	−0.859242	+	0.859242i	−0.0329747	+	0.0329747i
$680$	−42.3621	+	11.0085i	−1.62451	+	0.422158i
$681$	22.0221	−	11.4781i	0.843889	−	0.439842i
$682$	0.253632	+	0.213913i	0.00971206	+	0.00819115i
$683$	−17.4263	+	42.0708i	−0.666798	+	1.60979i	0.120137	+	0.992757i	$0.461667\pi$
$683$	−17.4263	+	42.0708i	−0.666798	+	1.60979i	−0.786935	+	0.617036i	$0.788333\pi$
$684$	2.18486	−	45.8068i	0.0835404	−	1.75147i
$685$	31.9101	−	13.2176i	1.21922	−	0.505018i
$686$	−0.649850	−	1.25606i	−0.0248114	−	0.0479567i
$687$	−7.86085	+	24.9753i	−0.299910	+	0.952869i
$688$	−2.76773	+	51.4843i	−0.105519	+	1.96282i
$689$	3.75603			0.143094
$690$	12.2284	−	2.13081i	0.465527	−	0.0811186i
$691$	2.34291	+	5.65628i	0.0891284	+	0.215175i	0.962158	−	0.272492i	$-0.0878479\pi$
$691$	2.34291	+	5.65628i	0.0891284	+	0.215175i	−0.873030	+	0.487667i	$0.837848\pi$
$692$	10.9402	−	48.1979i	0.415884	−	1.83221i
$693$	0.124624	+	0.195186i	0.00473409	+	0.00741451i
$694$	21.1933	+	17.8745i	0.804488	+	0.678506i
$695$	−21.9541	+	21.9541i	−0.832768	+	0.832768i
$696$	−0.166670	+	0.350943i	−0.00631761	+	0.0133025i
$697$	3.88925	+	3.88925i	0.147316	+	0.147316i
$698$	−1.13650	−	13.3782i	−0.0430170	−	0.506371i
$699$	19.0255	−	22.6970i	0.719611	−	0.858478i
$700$	−0.121745	−	0.0861641i	−0.00460154	−	0.00325670i
$701$	3.21226	−	1.33056i	0.121325	−	0.0502546i	−0.321195	−	0.947013i	$-0.604084\pi$
$701$	3.21226	−	1.33056i	0.121325	−	0.0502546i	0.442520	+	0.896759i	$0.354084\pi$
$702$	−3.11892	−	8.59605i	−0.117716	−	0.324437i
$703$		−	21.6580i		−	0.816847i
$704$	−0.484195	−	0.383297i	−0.0182488	−	0.0144461i
$705$	−8.86415	+	28.1630i	−0.333843	+	1.06068i
$706$	13.9234	−	43.7746i	0.524013	−	1.64748i
$707$	−2.77931	−	6.70985i	−0.104527	−	0.252350i
$708$	−1.73568	+	1.31938i	−0.0652309	+	0.0495853i
$709$	−9.53367	−	3.94898i	−0.358045	−	0.148307i	0.196408	−	0.980522i	$-0.437072\pi$
$709$	−9.53367	−	3.94898i	−0.358045	−	0.148307i	−0.554453	+	0.832215i	$0.687072\pi$
$710$	−21.9108	+	1.86136i	−0.822298	+	0.0698555i
$711$	40.3701	−	7.16033i	1.51400	−	0.268533i
$712$	16.3975	+	2.28493i	0.614522	+	0.0856315i
$713$	−4.90714	−	4.90714i	−0.183774	−	0.183774i
$714$	9.14780	+	14.4232i	0.342348	+	0.539775i
$715$	−0.196958	−	0.0815826i	−0.00736580	−	0.00305102i
$716$	−39.5246	−	8.97148i	−1.47710	−	0.335280i
$717$	−18.3505	+	1.61479i	−0.685312	+	0.0603054i
$718$	−8.75023	−	16.9129i	−0.326556	−	0.631183i
$719$			27.5910i			1.02897i	0.857499	+	0.514486i	$0.172017\pi$
$719$			27.5910i			1.02897i	−0.857499	+	0.514486i	$0.827983\pi$
$720$	−26.4345	+	3.23668i	−0.985157	+	0.120624i
$721$			16.5495i			0.616337i
$722$	49.5110	−	25.6155i	1.84261	−	0.953311i
$723$	9.62290	−	0.846786i	0.357879	−	0.0314923i
$724$	29.1499	−	18.3648i	1.08335	−	0.682523i
$725$	−0.00546398	−	0.00226326i	−0.000202927	−	8.40552e-5i
$726$	22.7415	−	14.4236i	0.844014	−	0.535310i
$727$	−1.46332	−	1.46332i	−0.0542714	−	0.0542714i	0.679450	−	0.733722i	$-0.262218\pi$
$727$	−1.46332	−	1.46332i	−0.0542714	−	0.0542714i	−0.733722	+	0.679450i	$0.762218\pi$
$728$	−3.40653	+	0.885247i	−0.126254	+	0.0328094i
$729$	−23.3417	+	13.5707i	−0.864508	+	0.502619i
$730$	0.322148	+	3.79213i	0.0119232	+	0.140353i
$731$	83.0343	+	34.3939i	3.07113	+	1.27211i
$732$	−3.74356	−	0.510121i	−0.138366	−	0.0188546i
$733$	−7.97120	−	19.2442i	−0.294423	−	0.710800i	−0.999998	−	0.00216461i	$-0.999311\pi$
$733$	−7.97120	−	19.2442i	−0.294423	−	0.710800i	0.705575	−	0.708636i	$-0.250689\pi$
$734$	27.5387	+	8.75924i	1.01647	+	0.323309i
$735$	1.15406	−	3.66666i	0.0425682	−	0.135247i
$736$	9.41235	+	8.84543i	0.346944	+	0.326047i
$737$			0.491561i			0.0181069i
$738$	2.03333	+	2.65818i	0.0748478	+	0.0978491i
$739$	2.23877	−	0.927329i	0.0823545	−	0.0341123i	−0.341126	−	0.940018i	$-0.610808\pi$
$739$	2.23877	−	0.927329i	0.0823545	−	0.0341123i	0.423480	+	0.905905i	$0.360808\pi$
$740$	−12.3974	+	2.12166i	−0.455736	+	0.0779939i
$741$	10.5827	−	12.6249i	0.388765	−	0.463787i
$742$	−4.25329	+	0.361324i	−0.156143	+	0.0132646i
$743$	−12.9505	−	12.9505i	−0.475107	−	0.475107i	0.428456	−	0.903563i	$-0.359058\pi$
$743$	−12.9505	−	12.9505i	−0.475107	−	0.475107i	−0.903563	+	0.428456i	$0.859058\pi$
$744$	9.98159	+	11.0484i	0.365943	+	0.405054i
$745$	−22.6581	+	22.6581i	−0.830129	+	0.830129i
$746$	−13.2830	+	15.7493i	−0.486325	+	0.576624i
$747$	12.2405	−	7.81546i	0.447858	−	0.285953i
$748$	−0.910802	+	0.573816i	−0.0333022	+	0.0209808i
$749$	−0.966854	−	2.33419i	−0.0353281	−	0.0852895i
$750$	−4.73563	−	27.1770i	−0.172921	−	0.992365i
$751$	−29.5476			−1.07821			−0.539104	−	0.842239i	$-0.681237\pi$
$751$	−29.5476			−1.07821			−0.539104	+	0.842239i	$0.681237\pi$
$752$	−28.9749	+	10.2166i	−1.05660	+	0.372562i
$753$	10.2168	−	32.4606i	0.372320	−	1.18293i
$754$	−0.123955	+	0.0641309i	−0.00451419	+	0.00233551i
$755$	40.0286	−	16.5804i	1.45679	−	0.603422i
$756$	4.35876	+	9.43404i	0.158527	+	0.343113i
$757$	6.23821	−	15.0604i	0.226732	−	0.547379i	−0.769044	−	0.639196i	$-0.779267\pi$
$757$	6.23821	−	15.0604i	0.226732	−	0.547379i	0.995776	+	0.0918169i	$0.0292674\pi$
$758$	7.55133	−	8.95344i	0.274277	−	0.325203i
$759$	0.270720	−	0.141102i	0.00982653	−	0.00512167i
$760$	−28.9185	−	38.2828i	−1.04898	−	1.38866i
$761$	36.4856	−	36.4856i	1.32260	−	1.32260i	0.410937	−	0.911664i	$-0.365202\pi$
$761$	36.4856	−	36.4856i	1.32260	−	1.32260i	0.911664	−	0.410937i	$-0.134798\pi$
$762$	−36.2947	−	8.12308i	−1.31482	−	0.294268i
$763$	3.77897	−	9.12325i	0.136808	−	0.330284i
$764$	26.4085	+	18.6904i	0.955425	+	0.676193i
$765$	−10.0023	+	45.3338i	−0.361634	+	1.63905i
$766$	36.3184	+	11.5518i	1.31224	+	0.417383i
$767$	−0.783190			−0.0282793
$768$	−19.2072	−	19.9770i	−0.693082	−	0.720859i
$769$	−9.03461			−0.325796			−0.162898	−	0.986643i	$-0.552084\pi$
$769$	−9.03461			−0.325796			−0.162898	+	0.986643i	$0.552084\pi$
$770$	0.230881	+	0.0734363i	0.00832038	+	0.00264646i
$771$	36.8792	−	3.24525i	1.32817	−	0.116875i
$772$	21.2988	+	15.0740i	0.766560	+	0.542526i
$773$	5.32734	−	12.8613i	0.191611	−	0.462590i	−0.798653	−	0.601792i	$-0.794454\pi$
$773$	5.32734	−	12.8613i	0.191611	−	0.462590i	0.990264	+	0.139202i	$0.0444536\pi$
$774$	47.3183	+	27.4146i	1.70082	+	0.985396i
$775$	−0.160273	+	0.160273i	−0.00575716	+	0.00575716i
$776$	−2.07163	−	2.74246i	−0.0743672	−	0.0984485i
$777$	2.26847	+	4.35233i	0.0813809	+	0.156139i
$778$	−16.2077	+	19.2171i	−0.581075	+	0.688967i
$779$	−2.30723	+	5.57015i	−0.0826652	+	0.199571i
$780$	−8.26339	−	4.82094i	−0.295877	−	0.172617i
$781$	−0.499663	+	0.206967i	−0.0178793	+	0.00740586i
$782$	19.9977	−	10.3462i	0.715115	−	0.369979i
$783$	0.251351	+	0.326543i	0.00898255	+	0.0116697i
$784$	3.77236	−	1.33015i	0.134727	−	0.0475052i
$785$	−32.2657			−1.15161
$786$	−53.2942	+	9.28656i	−1.90094	+	0.331241i
$787$	−9.63770	−	23.2675i	−0.343547	−	0.829395i	−0.997352	−	0.0727321i	$-0.976828\pi$
$787$	−9.63770	−	23.2675i	−0.343547	−	0.829395i	0.653805	−	0.756663i	$-0.273172\pi$
$788$	17.4816	−	11.0136i	0.622755	−	0.392343i
$789$	−19.5718	+	23.3487i	−0.696776	+	0.831236i
$790$	27.6547	−	32.7895i	0.983910	−	1.16660i
$791$	−0.302555	+	0.302555i	−0.0107576	+	0.0107576i
$792$	−0.595436	+	0.272925i	−0.0211579	+	0.00969796i
$793$	−0.959693	−	0.959693i	−0.0340797	−	0.0340797i
$794$	48.7149	−	4.13841i	1.72883	−	0.146867i
$795$	−8.89185	−	7.45351i	−0.315361	−	0.264349i
$796$	18.5608	−	3.17646i	0.657870	−	0.112587i
$797$	28.9116	−	11.9756i	1.02410	−	0.424197i	0.193522	−	0.981096i	$-0.438009\pi$
$797$	28.9116	−	11.9756i	1.02410	−	0.424197i	0.830580	+	0.556899i	$0.188009\pi$
$798$	−10.7692	+	15.3143i	−0.381227	+	0.542122i
$799$			53.5561i			1.89468i
$800$	0.288901	−	0.307418i	0.0102142	−	0.0108689i
$801$	10.0576	−	14.3946i	0.355368	−	0.508609i
$802$	7.66971	+	2.43950i	0.270827	+	0.0861419i
$803$	0.0358201	+	0.0864773i	0.00126406	+	0.00305172i
$804$	−2.97840	+	21.8572i	−0.105040	+	0.770844i
$805$	−4.68171	−	1.93923i	−0.165009	−	0.0683488i
$806$	0.452750	+	5.32951i	0.0159474	+	0.187724i
$807$	−13.3892	+	6.97855i	−0.471321	+	0.245657i
$808$	19.8816	−	5.16660i	0.699434	−	0.181760i
$809$	13.4536	+	13.4536i	0.473003	+	0.473003i	0.902885	−	0.429882i	$-0.141445\pi$
$809$	13.4536	+	13.4536i	0.473003	+	0.473003i	−0.429882	+	0.902885i	$0.641445\pi$
$810$	−9.67449	+	26.5391i	−0.339927	+	0.932488i
$811$	−32.9412	−	13.6447i	−1.15672	−	0.479131i	−0.279941	−	0.960017i	$-0.590315\pi$
$811$	−32.9412	−	13.6447i	−1.15672	−	0.479131i	−0.876783	+	0.480887i	$0.840315\pi$
$812$	0.134197	−	0.0845454i	0.00470938	−	0.00296696i
$813$	2.72618	+	30.9804i	0.0956112	+	1.08653i
$814$	−0.274749	+	0.142147i	−0.00962995	+	0.00498225i
$815$		−	22.0170i		−	0.771221i
$816$	−43.9755	+	19.9961i	−1.53945	+	0.700002i
$817$			98.5175i			3.44669i
$818$	−1.11198	−	2.14930i	−0.0388796	−	0.0751485i
$819$	−0.804331	+	3.64550i	−0.0281056	+	0.127384i
$820$	3.41446	+	0.775032i	0.119238	+	0.0270653i
$821$	−44.1836	−	18.3014i	−1.54202	−	0.638725i	−0.560167	−	0.828380i	$-0.689263\pi$
$821$	−44.1836	−	18.3014i	−1.54202	−	0.638725i	−0.981851	+	0.189655i	$0.939263\pi$
$822$	32.1923	−	20.4177i	1.12284	−	0.712150i
$823$	2.64268	+	2.64268i	0.0921180	+	0.0921180i	0.751664	−	0.659546i	$-0.229251\pi$
$823$	2.64268	+	2.64268i	0.0921180	+	0.0921180i	−0.659546	+	0.751664i	$0.729251\pi$
$824$	−46.3612	−	6.46028i	−1.61507	−	0.225054i
$825$	−0.00460853	−	0.00884202i	−0.000160449	−	0.000307840i
$826$	0.886876	−	0.0753414i	0.0308583	−	0.00262146i
$827$	0.329250	+	0.136380i	0.0114491	+	0.00474239i	0.388401	−	0.921491i	$-0.373028\pi$
$827$	0.329250	+	0.136380i	0.0114491	+	0.00474239i	−0.376952	+	0.926233i	$0.623028\pi$
$828$	12.8925	−	4.63376i	0.448045	−	0.161034i
$829$	10.6999	+	25.8320i	0.371625	+	0.897181i	0.993476	+	0.114045i	$0.0363809\pi$
$829$	10.6999	+	25.8320i	0.371625	+	0.897181i	−0.621851	+	0.783136i	$0.713619\pi$
$830$	4.60534	−	14.4790i	0.159854	−	0.502575i
$831$	−12.6612	−	3.98503i	−0.439211	−	0.138239i
$832$	−1.15012	−	9.88849i	−0.0398734	−	0.342822i
$833$		−	6.97270i		−	0.241590i
$834$	−19.7117	+	28.0308i	−0.682559	+	0.970628i
$835$	−18.5427	+	7.68063i	−0.641696	+	0.265799i
$836$	−0.963174	−	0.681677i	−0.0333121	−	0.0235763i
$837$	15.2484	−	4.11055i	0.527063	−	0.142081i
$838$	−2.63736	−	31.0455i	−0.0911062	−	1.07245i
$839$	2.95571	+	2.95571i	0.102043	+	0.102043i	0.756285	−	0.654242i	$-0.227012\pi$
$839$	2.95571	+	2.95571i	0.102043	+	0.102043i	−0.654242	+	0.756285i	$0.727012\pi$
$840$	9.82114	+	4.66426i	0.338862	+	0.160932i
$841$	−20.5016	+	20.5016i	−0.706953	+	0.706953i
$842$	0.322585	+	0.272068i	0.0111170	+	0.00937609i
$843$	19.1366	+	16.0411i	0.659100	+	0.552484i
$844$	−1.43550	+	6.32421i	−0.0494120	+	0.217688i
$845$	9.72575	+	23.4800i	0.334576	+	0.807738i
$846$	−4.30223	+	32.3018i	−0.147914	+	1.11056i
$847$	−10.9940			−0.377760
$848$	0.648117	−	12.0561i	0.0222564	−	0.414007i
$849$	47.7107	+	15.0167i	1.63743	+	0.515370i
$850$	−0.337918	−	0.653146i	−0.0115905	−	0.0224027i
$851$	5.97763	−	2.47601i	0.204910	−	0.0848767i
$852$	−23.4715	+	6.17528i	−0.804119	+	0.211562i
$853$	4.02753	−	9.72333i	0.137900	−	0.332920i	−0.839810	−	0.542881i	$-0.817334\pi$
$853$	4.02753	−	9.72333i	0.137900	−	0.332920i	0.977710	+	0.209960i	$0.0673335\pi$
$854$	1.17907	+	0.994425i	0.0403468	+	0.0340285i
$855$	−50.1059	+	8.88715i	−1.71359	+	0.303934i
$856$	6.91633	−	1.79733i	0.236395	−	0.0614315i
$857$	−8.78361	+	8.78361i	−0.300042	+	0.300042i	−0.841030	−	0.540988i	$-0.818050\pi$
$857$	−8.78361	+	8.78361i	−0.300042	+	0.300042i	0.540988	+	0.841030i	$0.318050\pi$
$858$	−0.229614	−	0.0513896i	−0.00783889	−	0.00175441i
$859$	2.89606	−	6.99170i	0.0988122	−	0.238554i	−0.866741	−	0.498758i	$-0.833790\pi$
$859$	2.89606	−	6.99170i	0.0988122	−	0.238554i	0.965554	+	0.260204i	$0.0837898\pi$
$860$	56.3929	−	9.65098i	1.92298	−	0.329096i
$861$	−0.119766	−	1.36102i	−0.00408161	−	0.0463835i
$862$	13.9790	−	43.9496i	0.476128	−	1.49693i
$863$	−31.8743			−1.08501			−0.542507	−	0.840051i	$-0.682525\pi$
$863$	−31.8743			−1.08501			−0.542507	+	0.840051i	$0.682525\pi$
$864$	−28.1296	+	8.52779i	−0.956990	+	0.290121i
$865$	−54.8440			−1.86475
$866$	12.6178	−	39.6700i	0.428771	−	1.34804i
$867$	4.80059	+	54.5540i	0.163036	+	1.85275i
$868$	−1.02538	−	5.99153i	−0.0348036	−	0.203366i
$869$	0.403722	−	0.974671i	0.0136953	−	0.0330635i
$870$	0.420708	+	0.0941580i	0.0142633	+	0.00319226i
$871$	−5.60328	+	5.60328i	−0.189860	+	0.189860i
$872$	24.0823	+	14.1476i	0.815531	+	0.479099i
$873$	−3.58943	+	0.636648i	−0.121484	+	0.0215473i
$874$	18.8663	+	15.9119i	0.638164	+	0.538227i
$875$	−4.30984	+	10.4049i	−0.145699	+	0.351749i
$876$	1.06876	+	4.06224i	0.0361102	+	0.137250i
$877$	44.1770	−	18.2987i	1.49175	−	0.617904i	0.520054	−	0.854133i	$-0.325912\pi$
$877$	44.1770	−	18.2987i	1.49175	−	0.617904i	0.971697	+	0.236229i	$0.0759117\pi$
$878$	12.0924	+	23.3728i	0.408098	+	0.788794i
$879$	18.4738	+	5.81453i	0.623107	+	0.196119i
$880$	−0.295848	+	0.618114i	−0.00997304	+	0.0208366i
$881$	−32.4398			−1.09292			−0.546462	−	0.837484i	$-0.684026\pi$
$881$	−32.4398			−1.09292			−0.546462	+	0.837484i	$0.684026\pi$
$882$	0.560125	−	4.20550i	0.0188604	−	0.141607i
$883$	−9.16610	−	22.1289i	−0.308464	−	0.744698i	−0.999755	−	0.0221215i	$-0.992958\pi$
$883$	−9.16610	−	22.1289i	−0.308464	−	0.744698i	0.691291	−	0.722576i	$-0.257042\pi$
$884$	−16.9231	−	3.84128i	−0.569184	−	0.129196i
$885$	1.85408	+	1.55417i	0.0623243	+	0.0522428i
$886$	−5.31545	−	4.48305i	−0.178576	−	0.150611i
$887$	−2.08563	+	2.08563i	−0.0700288	+	0.0700288i	−0.741254	−	0.671225i	$-0.765768\pi$
$887$	−2.08563	+	2.08563i	−0.0700288	+	0.0700288i	0.671225	+	0.741254i	$0.265768\pi$
$888$	−13.0780	+	4.65583i	−0.438868	+	0.156239i
$889$	10.7366	+	10.7366i	0.360094	+	0.360094i
$890$	−1.55509	−	18.3056i	−0.0521266	−	0.613605i
$891$	−0.0289036	+	0.694136i	−0.000968307	+	0.0232544i
$892$	−31.0960	+	43.9370i	−1.04117	+	1.47112i
$893$	−54.2370	+	22.4657i	−1.81497	+	0.751785i
$894$	−20.3437	+	28.9297i	−0.680396	+	0.967552i
$895$			44.9747i			1.50334i
$896$	2.25364	+	11.0870i	0.0752889	+	0.370390i
$897$	4.69433	+	1.47751i	0.156739	+	0.0493328i
$898$	−0.916785	+	2.88234i	−0.0305935	+	0.0961849i
$899$	−0.0922385	−	0.222683i	−0.00307633	−	0.00742691i
$900$	−0.151344	−	0.421083i	−0.00504479	−	0.0140361i
$901$	−19.4441	−	8.05401i	−0.647777	−	0.268318i
$902$	0.0858048	−	0.00728925i	0.00285699	−	0.000242705i
$903$	−10.3188	−	19.7978i	−0.343387	−	0.658829i
$904$	−0.729459	−	0.965669i	−0.0242615	−	0.0321177i
$905$	−27.0333	−	27.0333i	−0.898618	−	0.898618i
$906$	40.3826	−	25.6124i	1.34162	−	0.850914i
$907$	−7.84764	−	3.25060i	−0.260577	−	0.107934i	0.248571	−	0.968614i	$-0.420039\pi$
$907$	−7.84764	−	3.25060i	−0.260577	−	0.107934i	−0.509147	+	0.860679i	$0.670039\pi$
$908$	6.34748	−	27.9643i	0.210648	−	0.928028i
$909$	4.69434	−	21.2764i	0.155701	−	0.705692i
$910$	1.79470	+	3.46889i	0.0594938	+	0.114993i
$911$		−	30.6158i		−	1.01435i	−0.861844	−	0.507173i	$-0.830691\pi$
$911$		−	30.6158i		−	1.01435i	0.861844	−	0.507173i	$-0.169309\pi$
$912$	−38.6971	−	36.1466i	−1.28139	−	1.19693i
$913$		−	0.373687i		−	0.0123672i
$914$	−35.3093	+	18.2680i	−1.16793	+	0.604252i
$915$	0.367506	+	4.17635i	0.0121494	+	0.138066i
$916$	16.1160	+	25.5804i	0.532486	+	0.845200i
$917$	20.4040	+	8.45160i	0.673798	+	0.279096i
$918$	−2.28646	+	51.1876i	−0.0754643	+	1.68944i
$919$	−32.1225	−	32.1225i	−1.05962	−	1.05962i	−0.998106	−	0.0615189i	$-0.980406\pi$
$919$	−32.1225	−	32.1225i	−1.05962	−	1.05962i	−0.0615189	−	0.998106i	$-0.519594\pi$
$920$	7.26002	−	12.3582i	0.239356	−	0.407436i
$921$	−12.7589	+	6.65006i	−0.420421	+	0.219127i
$922$	2.38202	+	28.0398i	0.0784477	+	0.923441i
$923$	−8.05483	−	3.33642i	−0.265128	−	0.109820i
$924$	0.264956	+	0.0361046i	0.00871641	+	0.00118775i
$925$	−0.0808693	−	0.195236i	−0.00265897	−	0.00641931i
$926$	44.4724	+	14.1453i	1.46145	+	0.464844i
$927$	−28.4362	+	40.6985i	−0.933969	+	1.33671i
$928$	0.184457	+	0.408936i	0.00605510	+	0.0134240i
$929$			13.2216i			0.433786i	0.976195	+	0.216893i	$0.0695923\pi$
$929$			13.2216i			0.433786i	−0.976195	+	0.216893i	$0.930408\pi$
$930$	9.50411	−	13.5153i	0.311652	−	0.443183i
$931$	7.06134	−	2.92490i	0.231426	−	0.0958598i
$932$	−5.76870	−	33.7078i	−0.188960	−	1.10414i
$933$	23.4042	+	19.6183i	0.766219	+	0.642275i
$934$	−11.3450	+	0.963778i	−0.371221	+	0.0315358i
$935$	0.844668	+	0.844668i	0.0276236	+	0.0276236i
$936$	−9.89839	−	3.67628i	−0.323539	−	0.120163i
$937$	16.0314	−	16.0314i	0.523724	−	0.523724i	−0.394970	−	0.918694i	$-0.629245\pi$
$937$	16.0314	−	16.0314i	0.523724	−	0.523724i	0.918694	+	0.394970i	$0.129245\pi$
$938$	5.80607	−	6.88412i	0.189575	−	0.224774i
$939$	21.4671	−	25.6097i	0.700553	−	0.835742i
$940$	18.1729	+	28.8453i	0.592734	+	0.940830i
$941$	17.9294	+	43.2854i	0.584482	+	1.41106i	0.888712	+	0.458465i	$0.151601\pi$
$941$	17.9294	+	43.2854i	0.584482	+	1.41106i	−0.304231	+	0.952598i	$0.598399\pi$
$942$	−35.0832	+	6.11328i	−1.14307	+	0.199182i
$943$	−1.80114			−0.0586531
$944$	−0.135142	+	2.51387i	−0.00439850	+	0.0818194i
$945$	9.13830	−	7.03406i	0.297269	−	0.228818i
$946$	1.24977	−	0.646596i	0.0406336	−	0.0210226i
$947$	−11.6023	+	4.80582i	−0.377023	+	0.156168i	−0.563144	−	0.826359i	$-0.690408\pi$
$947$	−11.6023	+	4.80582i	−0.377023	+	0.156168i	0.186121	+	0.982527i	$0.440408\pi$
$948$	23.8570	−	40.8925i	0.774841	−	1.32813i
$949$	−0.577438	+	1.39406i	−0.0187444	+	0.0452531i
$950$	0.519699	−	0.616195i	0.0168613	−	0.0199920i
$951$	20.8613	+	40.0249i	0.676475	+	1.29790i
$952$	19.5330	+	2.72186i	0.633069	+	0.0882160i
$953$	23.4165	−	23.4165i	0.758534	−	0.758534i	−0.217522	−	0.976055i	$-0.569797\pi$
$953$	23.4165	−	23.4165i	0.758534	−	0.758534i	0.976055	+	0.217522i	$0.0697973\pi$
$954$	−11.0805	−	6.41966i	−0.358745	−	0.207844i
$955$	13.7388	−	33.1685i	0.444579	−	1.07331i
$956$	−12.2883	+	17.3627i	−0.397431	+	0.561549i
$957$	0.0105623		0.000929454i	0.000341432		3.00450e-5i
$958$	53.1663	+	16.9106i	1.71773	+	0.546357i
$959$	−15.5629			−0.502553
$960$	−16.9001	+	25.6918i	−0.545447	+	0.829200i
$961$	21.7625			0.702017
$962$	−4.75217	−	1.51152i	−0.153216	−	0.0487334i
$963$	1.63305	−	7.40152i	0.0526242	−	0.238511i
$964$	6.44390	−	9.10489i	0.207544	−	0.293249i
$965$	11.0806	−	26.7508i	0.356696	−	0.861140i
$966$	−5.45795	−	1.22154i	−0.175607	−	0.0393023i
$967$	12.0205	−	12.0205i	0.386553	−	0.386553i	−0.486903	−	0.873456i	$-0.661874\pi$
$967$	12.0205	−	12.0205i	0.386553	−	0.386553i	0.873456	+	0.486903i	$0.161874\pi$
$968$	4.29163	−	30.7983i	0.137938	−	0.989894i
$969$	−81.8555	+	42.6638i	−2.62958	+	1.37056i
$970$	−2.45887	+	2.91542i	−0.0789494	+	0.0936085i
$971$	7.98084	−	19.2675i	0.256118	−	0.618322i	−0.742558	−	0.669782i	$-0.766387\pi$
$971$	7.98084	−	19.2675i	0.256118	−	0.618322i	0.998675	+	0.0514599i	$0.0163874\pi$
$972$	−5.49101	+	30.6896i	−0.176124	+	0.984368i
$973$	12.9248	−	5.35364i	0.414351	−	0.171630i
$974$	−31.3688	+	16.2293i	−1.00512	+	0.520021i
$975$	0.0482572	−	0.153322i	0.00154547	−	0.00491023i
$976$	−3.24600	+	2.91481i	−0.103902	+	0.0933007i
$977$	56.7098			1.81431			0.907153	−	0.420800i	$-0.138251\pi$
$977$	56.7098			1.81431			0.907153	+	0.420800i	$0.138251\pi$
$978$	−4.17150	−	23.9396i	−0.133390	−	0.765503i
$979$	−0.172912	−	0.417448i	−0.00552631	−	0.0133417i
$980$	−2.36600	−	3.75549i	−0.0755792	−	0.119965i
$981$	24.9692	−	15.9426i	0.797206	−	0.509008i
$982$	24.1507	−	28.6350i	0.770681	−	0.913778i
$983$	16.3231	−	16.3231i	0.520627	−	0.520627i	−0.397134	−	0.917761i	$-0.629995\pi$
$983$	16.3231	−	16.3231i	0.520627	−	0.520627i	0.917761	+	0.397134i	$0.129995\pi$
$984$	3.85947	+	0.195781i	0.123035	+	0.00624128i
$985$	−16.2122	−	16.2122i	−0.516564	−	0.516564i
$986$	0.779203	−	0.0661945i	0.0248149	−	0.00210806i
$987$	8.54624	−	10.1955i	0.272030	−	0.324525i
$988$	−3.20876	−	18.7496i	−0.102084	−	0.596503i
$989$	−27.1909	+	11.2628i	−0.864621	+	0.358138i
$990$	0.441599	+	0.577305i	0.0140349	+	0.0183480i
$991$		−	18.1750i		−	0.577349i	−0.957427	−	0.288675i	$-0.906785\pi$
$991$		−	18.1750i		−	0.577349i	0.957427	−	0.288675i	$-0.0932146\pi$
$992$	17.1847	−	0.533603i	0.545615	−	0.0169419i
$993$	12.3216	−	39.1478i	0.391013	−	1.24232i
$994$	9.44216	+	3.00327i	0.299487	+	0.0952578i
$995$	−7.99644	−	19.3051i	−0.253504	−	0.612013i
$996$	2.26419	−	16.6160i	0.0717438	−	0.526497i
$997$	−30.8990	−	12.7988i	−0.978582	−	0.405342i	−0.164682	−	0.986347i	$-0.552660\pi$
$997$	−30.8990	−	12.7988i	−0.978582	−	0.405342i	−0.813900	+	0.581005i	$0.802660\pi$
$998$	−1.47848	−	17.4038i	−0.0468005	−	0.550908i
$999$	−1.89979	+	14.6010i	−0.0601066	+	0.461955i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	672.2.bs.a.155.5	✓	192
3.2	odd	2	inner	672.2.bs.a.155.44	yes	192
32.19	odd	8	inner	672.2.bs.a.659.44	yes	192
96.83	even	8	inner	672.2.bs.a.659.5	yes	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
672.2.bs.a.155.5	✓	192	1.1	even	1	trivial
672.2.bs.a.155.44	yes	192	3.2	odd	2	inner
672.2.bs.a.659.5	yes	192	96.83	even	8	inner
672.2.bs.a.659.44	yes	192	32.19	odd	8	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:	\( N \)	\(=\)	\( 672 = 2^{5} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	672.bs (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.34768 - 0.428658i) q^{2} +(0.151828 + 1.72538i) q^{3} +(1.63251 + 1.15539i) q^{4} +(0.849301 - 2.05039i) q^{5} +(0.534982 - 2.39035i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(-1.70483 - 2.25689i) q^{8} +(-2.95390 + 0.523925i) q^{9} +O(q^{10})\)	\(q+(-1.34768 - 0.428658i) q^{2} +(0.151828 + 1.72538i) q^{3} +(1.63251 + 1.15539i) q^{4} +(0.849301 - 2.05039i) q^{5} +(0.534982 - 2.39035i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(-1.70483 - 2.25689i) q^{8} +(-2.95390 + 0.523925i) q^{9} +(-2.02351 + 2.39922i) q^{10} +(-0.0295405 + 0.0713171i) q^{11} +(-1.74563 + 2.99212i) q^{12} +(-1.14967 + 0.476209i) q^{13} +(1.25606 - 0.649850i) q^{14} +(3.66666 + 1.15406i) q^{15} +(1.33015 + 3.77236i) q^{16} +6.97270 q^{17} +(4.20550 + 0.560125i) q^{18} +(2.92490 + 7.06134i) q^{19} +(3.75549 - 2.36600i) q^{20} +(-1.32739 - 1.11267i) q^{21} +(0.0703819 - 0.0834502i) q^{22} +(-1.61455 + 1.61455i) q^{23} +(3.63515 - 3.28415i) q^{24} +(0.0527330 + 0.0527330i) q^{25} +(1.75352 - 0.148964i) q^{26} +(-1.35246 - 5.01706i) q^{27} +(-1.97134 + 0.337371i) q^{28} +(-0.0732676 + 0.0303484i) q^{29} +(-4.44681 - 3.12705i) q^{30} +3.03932i q^{31} +(-0.175567 - 5.65413i) q^{32} +(-0.127534 - 0.0401407i) q^{33} +(-9.39699 - 2.98890i) q^{34} +(0.849301 + 2.05039i) q^{35} +(-5.42759 - 2.55759i) q^{36} +(-2.61795 - 1.08439i) q^{37} +(-0.914948 - 10.7702i) q^{38} +(-0.996195 - 1.91132i) q^{39} +(-6.07542 + 1.57881i) q^{40} +(0.557782 + 0.557782i) q^{41} +(1.31195 + 2.06853i) q^{42} +(11.9085 + 4.93266i) q^{43} +(-0.130624 + 0.0822947i) q^{44} +(-1.43449 + 6.50162i) q^{45} +(2.86800 - 1.48382i) q^{46} +7.68083i q^{47} +(-6.30682 + 2.86777i) q^{48} -1.00000i q^{49} +(-0.0484631 - 0.0936719i) q^{50} +(1.05865 + 12.0306i) q^{51} +(-2.42705 - 0.550904i) q^{52} +(-2.78861 - 1.15508i) q^{53} +(-0.327916 + 7.34115i) q^{54} +(0.121139 + 0.121139i) q^{55} +(2.80136 + 0.390360i) q^{56} +(-11.7394 + 6.11869i) q^{57} +(0.111751 - 0.00949338i) q^{58} +(0.581466 + 0.240851i) q^{59} +(4.65246 + 6.12044i) q^{60} +(0.417378 + 1.00764i) q^{61} +(1.30283 - 4.09604i) q^{62} +(1.71825 - 2.45919i) q^{63} +(-2.18708 + 7.69524i) q^{64} +2.76172i q^{65} +(0.154670 + 0.108766i) q^{66} +(5.88321 - 2.43691i) q^{67} +(11.3830 + 8.05618i) q^{68} +(-3.03086 - 2.54059i) q^{69} +(-0.265672 - 3.12734i) q^{70} +(4.95414 + 4.95414i) q^{71} +(6.21834 + 5.77340i) q^{72} +(0.857420 - 0.857420i) q^{73} +(3.06334 + 2.58362i) q^{74} +(-0.0829783 + 0.0989911i) q^{75} +(-3.38368 + 14.9071i) q^{76} +(-0.0295405 - 0.0713171i) q^{77} +(0.523255 + 3.00288i) q^{78} -13.6667 q^{79} +(8.86452 + 0.476545i) q^{80} +(8.45101 - 3.09524i) q^{81} +(-0.512617 - 0.990812i) q^{82} +(-4.47245 + 1.85255i) q^{83} +(-0.881400 - 3.35009i) q^{84} +(5.92192 - 14.2968i) q^{85} +(-13.9345 - 11.7523i) q^{86} +(-0.0634868 - 0.121807i) q^{87} +(0.211316 - 0.0549143i) q^{88} +(-4.13898 + 4.13898i) q^{89} +(4.72021 - 8.14722i) q^{90} +(0.476209 - 1.14967i) q^{91} +(-4.50120 + 0.770327i) q^{92} +(-5.24399 + 0.461455i) q^{93} +(3.29245 - 10.3513i) q^{94} +16.9626 q^{95} +(9.72888 - 1.16138i) q^{96} +1.21515 q^{97} +(-0.428658 + 1.34768i) q^{98} +(0.0498948 - 0.226140i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q - 16 q^{4}+O(q^{10}) \) 192 * q - 16 * q^4	\( 192 q - 16 q^{4} + 8 q^{10} + 16 q^{16} + 16 q^{22} + 24 q^{27} - 84 q^{30} + 40 q^{36} + 32 q^{37} + 24 q^{39} - 96 q^{46} - 72 q^{48} + 16 q^{52} - 32 q^{55} - 72 q^{58} - 28 q^{60} - 16 q^{61} - 64 q^{64} - 12 q^{66} - 32 q^{67} + 56 q^{69} - 24 q^{70} + 60 q^{72} + 80 q^{75} - 56 q^{76} + 100 q^{78} - 32 q^{79} - 120 q^{82} - 56 q^{87} + 40 q^{88} + 60 q^{90} - 80 q^{93} + 216 q^{94} + 96 q^{96} - 64 q^{99}+O(q^{100}) \) 192 * q - 16 * q^4 + 8 * q^10 + 16 * q^16 + 16 * q^22 + 24 * q^27 - 84 * q^30 + 40 * q^36 + 32 * q^37 + 24 * q^39 - 96 * q^46 - 72 * q^48 + 16 * q^52 - 32 * q^55 - 72 * q^58 - 28 * q^60 - 16 * q^61 - 64 * q^64 - 12 * q^66 - 32 * q^67 + 56 * q^69 - 24 * q^70 + 60 * q^72 + 80 * q^75 - 56 * q^76 + 100 * q^78 - 32 * q^79 - 120 * q^82 - 56 * q^87 + 40 * q^88 + 60 * q^90 - 80 * q^93 + 216 * q^94 + 96 * q^96 - 64 * q^99

Introduction

L-functions

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