LMFDB - Embedded newform 310.2.s.a.277.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [310,2,Mod(23,310)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(310, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([15, 18]))

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

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

chi := DirichletCharacter("310.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 310 = 2 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	310.s (of order $20$, degree $8$, 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:	$2.47536246266$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$16$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			277.2
Character	$\chi$	$=$	310.277
Dual form			310.2.s.a.263.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.156434 - 0.987688i) q^{2} +(-2.26401 - 0.358585i) q^{3} +(-0.951057 + 0.309017i) q^{4} +(-1.29145 - 1.82542i) q^{5} +2.29224i q^{6} +(-2.04651 + 4.01650i) q^{7} +(0.453990 + 0.891007i) q^{8} +(2.14401 + 0.696631i) q^{9} +O(q^{10})$	\(q+(-0.156434 - 0.987688i) q^{2} +(-2.26401 - 0.358585i) q^{3} +(-0.951057 + 0.309017i) q^{4} +(-1.29145 - 1.82542i) q^{5} +2.29224i q^{6} +(-2.04651 + 4.01650i) q^{7} +(0.453990 + 0.891007i) q^{8} +(2.14401 + 0.696631i) q^{9} +(-1.60092 + 1.56111i) q^{10} +(3.76196 - 1.22234i) q^{11} +(2.26401 - 0.358585i) q^{12} +(4.43788 + 0.702891i) q^{13} +(4.28719 + 1.39299i) q^{14} +(2.26930 + 4.59587i) q^{15} +(0.809017 - 0.587785i) q^{16} +(-0.689777 - 1.35376i) q^{17} +(0.352657 - 2.22659i) q^{18} +(-2.65485 + 3.65408i) q^{19} +(1.79233 + 1.33700i) q^{20} +(6.07358 - 8.35957i) q^{21} +(-1.79579 - 3.52443i) q^{22} +(-3.67789 + 1.87398i) q^{23} +(-0.708340 - 2.18005i) q^{24} +(-1.66430 + 4.71488i) q^{25} -4.49320i q^{26} +(1.52292 + 0.775968i) q^{27} +(0.705179 - 4.45232i) q^{28} +(3.51317 + 2.55247i) q^{29} +(4.18429 - 2.96031i) q^{30} +(5.42681 + 1.24487i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(-8.95545 + 1.41840i) q^{33} +(-1.22919 + 0.893060i) q^{34} +(9.97476 - 1.45138i) q^{35} -2.25435 q^{36} +(-5.91166 + 5.91166i) q^{37} +(4.02440 + 2.05054i) q^{38} +(-9.79537 - 3.18271i) q^{39} +(1.04015 - 1.97941i) q^{40} +(3.28478 + 2.38653i) q^{41} +(-9.20676 - 4.69108i) q^{42} +(1.60240 + 10.1171i) q^{43} +(-3.20012 + 2.32502i) q^{44} +(-1.49724 - 4.81338i) q^{45} +(2.42626 + 3.33945i) q^{46} +(-3.57518 - 0.566253i) q^{47} +(-2.04240 + 1.04065i) q^{48} +(-7.82957 - 10.7765i) q^{49} +(4.91719 + 0.906243i) q^{50} +(1.07623 + 3.31229i) q^{51} +(-4.43788 + 0.702891i) q^{52} +(-3.49158 + 1.77905i) q^{53} +(0.528177 - 1.62556i) q^{54} +(-7.08967 - 5.28857i) q^{55} -4.50782 q^{56} +(7.32091 - 7.32091i) q^{57} +(1.97146 - 3.86921i) q^{58} +(2.45196 + 3.37484i) q^{59} +(-3.57843 - 3.66968i) q^{60} -9.90839i q^{61} +(0.380608 - 5.55474i) q^{62} +(-7.18575 + 7.18575i) q^{63} +(-0.587785 + 0.809017i) q^{64} +(-4.44824 - 9.00873i) q^{65} +(2.80188 + 8.62331i) q^{66} +(-2.92785 - 2.92785i) q^{67} +(1.07435 + 1.07435i) q^{68} +(8.99878 - 2.92388i) q^{69} +(-2.99391 - 9.62491i) q^{70} +(-3.95467 + 12.1712i) q^{71} +(0.352657 + 2.22659i) q^{72} +(0.390755 - 0.766899i) q^{73} +(6.76367 + 4.91409i) q^{74} +(5.45869 - 10.0778i) q^{75} +(1.39573 - 4.29563i) q^{76} +(-2.78938 + 17.6114i) q^{77} +(-1.61119 + 10.1727i) q^{78} +(-2.07659 + 6.39107i) q^{79} +(-2.11776 - 0.717698i) q^{80} +(-8.64108 - 6.27811i) q^{81} +(1.84330 - 3.61767i) q^{82} +(-0.632745 - 3.99499i) q^{83} +(-3.19307 + 9.82726i) q^{84} +(-1.58037 + 3.00745i) q^{85} +(9.74190 - 3.16533i) q^{86} +(-7.03860 - 7.03860i) q^{87} +(2.79700 + 2.79700i) q^{88} +(-1.22664 - 3.77522i) q^{89} +(-4.51990 + 2.23179i) q^{90} +(-11.9053 + 16.3863i) q^{91} +(2.91879 - 2.91879i) q^{92} +(-11.8400 - 4.76439i) q^{93} +3.61975i q^{94} +(10.0988 + 0.127132i) q^{95} +(1.34734 + 1.85446i) q^{96} +(6.53357 - 12.8229i) q^{97} +(-9.41899 + 9.41899i) q^{98} +8.91720 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q + 12 q^{7}+O(q^{10}) $ 128 * q + 12 * q^7	$ 128 q + 12 q^{7} + 8 q^{10} + 32 q^{16} + 8 q^{20} - 80 q^{21} - 20 q^{22} - 20 q^{23} + 40 q^{25} + 8 q^{28} - 32 q^{31} + 20 q^{33} - 48 q^{35} - 128 q^{36} + 52 q^{38} + 8 q^{41} - 20 q^{42} + 64 q^{45} - 40 q^{46} - 20 q^{47} - 20 q^{48} + 24 q^{50} - 16 q^{51} - 40 q^{53} - 40 q^{55} + 20 q^{60} - 8 q^{62} + 256 q^{63} - 160 q^{65} + 56 q^{66} + 8 q^{67} - 32 q^{70} + 56 q^{71} - 80 q^{73} - 160 q^{75} + 48 q^{76} - 20 q^{77} + 4 q^{78} - 96 q^{81} + 16 q^{82} - 240 q^{83} + 120 q^{85} + 40 q^{87} - 64 q^{90} + 80 q^{91} - 160 q^{93} + 32 q^{95} - 56 q^{97} - 176 q^{98}+O(q^{100}) $ 128 * q + 12 * q^7 + 8 * q^10 + 32 * q^16 + 8 * q^20 - 80 * q^21 - 20 * q^22 - 20 * q^23 + 40 * q^25 + 8 * q^28 - 32 * q^31 + 20 * q^33 - 48 * q^35 - 128 * q^36 + 52 * q^38 + 8 * q^41 - 20 * q^42 + 64 * q^45 - 40 * q^46 - 20 * q^47 - 20 * q^48 + 24 * q^50 - 16 * q^51 - 40 * q^53 - 40 * q^55 + 20 * q^60 - 8 * q^62 + 256 * q^63 - 160 * q^65 + 56 * q^66 + 8 * q^67 - 32 * q^70 + 56 * q^71 - 80 * q^73 - 160 * q^75 + 48 * q^76 - 20 * q^77 + 4 * q^78 - 96 * q^81 + 16 * q^82 - 240 * q^83 + 120 * q^85 + 40 * q^87 - 64 * q^90 + 80 * q^91 - 160 * q^93 + 32 * q^95 - 56 * q^97 - 176 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/310\mathbb{Z}\right)^\times$.

$n$	$187$	$251$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{3}{10}\right)$

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 $

$2$	−0.156434	−	0.987688i	−0.110616	−	0.698401i
$2$	−0.156434	−	0.987688i	−0.110616	−	0.698401i
$3$	−2.26401	−	0.358585i	−1.30713	−	0.207029i	−0.536277	−	0.844042i	$-0.680170\pi$
$3$	−2.26401	−	0.358585i	−1.30713	−	0.207029i	−0.770853	+	0.637013i	$0.780170\pi$
$4$	−0.951057	+	0.309017i	−0.475528	+	0.154508i
$5$	−1.29145	−	1.82542i	−0.577555	−	0.816352i
$5$	−1.29145	−	1.82542i	−0.577555	−	0.816352i
$6$			2.29224i			0.935801i
$7$	−2.04651	+	4.01650i	−0.773507	+	1.51809i	0.0798729	+	0.996805i	$0.474549\pi$
$7$	−2.04651	+	4.01650i	−0.773507	+	1.51809i	−0.853380	+	0.521289i	$0.825451\pi$
$8$	0.453990	+	0.891007i	0.160510	+	0.315018i
$9$	2.14401	+	0.696631i	0.714670	+	0.232210i
$10$	−1.60092	+	1.56111i	−0.506254	+	0.493666i
$11$	3.76196	−	1.22234i	1.13427	−	0.368548i	0.319076	−	0.947729i	$-0.396628\pi$
$11$	3.76196	−	1.22234i	1.13427	−	0.368548i	0.815199	+	0.579181i	$0.196628\pi$
$12$	2.26401	−	0.358585i	0.653565	−	0.103514i
$13$	4.43788	+	0.702891i	1.23085	+	0.194947i	0.737778	−	0.675044i	$-0.235875\pi$
$13$	4.43788	+	0.702891i	1.23085	+	0.194947i	0.493068	+	0.869991i	$0.335875\pi$
$14$	4.28719	+	1.39299i	1.14580	+	0.372293i
$15$	2.26930	+	4.59587i	0.585931	+	1.18665i
$16$	0.809017	−	0.587785i	0.202254	−	0.146946i
$17$	−0.689777	−	1.35376i	−0.167296	−	0.328336i	0.792104	−	0.610386i	$-0.208986\pi$
$17$	−0.689777	−	1.35376i	−0.167296	−	0.328336i	−0.959400	+	0.282050i	$0.908986\pi$
$18$	0.352657	−	2.22659i	0.0831221	−	0.524812i
$19$	−2.65485	+	3.65408i	−0.609063	+	0.838304i	−0.996500	−	0.0835926i	$-0.973361\pi$
$19$	−2.65485	+	3.65408i	−0.609063	+	0.838304i	0.387437	+	0.921896i	$0.373361\pi$
$20$	1.79233	+	1.33700i	0.400777	+	0.298961i
$21$	6.07358	−	8.35957i	1.32536	−	1.82421i
$22$	−1.79579	−	3.52443i	−0.382863	−	0.751411i
$23$	−3.67789	+	1.87398i	−0.766893	+	0.390752i	−0.793246	−	0.608901i	$-0.791611\pi$
$23$	−3.67789	+	1.87398i	−0.766893	+	0.390752i	0.0263531	+	0.999653i	$0.491611\pi$
$24$	−0.708340	−	2.18005i	−0.144589	−	0.445000i
$25$	−1.66430	+	4.71488i	−0.332861	+	0.942976i
$26$		−	4.49320i		−	0.881188i
$27$	1.52292	+	0.775968i	0.293087	+	0.149335i
$28$	0.705179	−	4.45232i	0.133266	−	0.841410i
$29$	3.51317	+	2.55247i	0.652380	+	0.473982i	0.864081	−	0.503353i	$-0.167900\pi$
$29$	3.51317	+	2.55247i	0.652380	+	0.473982i	−0.211701	+	0.977334i	$0.567900\pi$
$30$	4.18429	−	2.96031i	0.763943	−	0.540477i
$31$	5.42681	+	1.24487i	0.974684	+	0.223586i
$31$	5.42681	+	1.24487i	0.974684	+	0.223586i
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	−8.95545	+	1.41840i	−1.55894	+	0.246912i
$34$	−1.22919	+	0.893060i	−0.210805	+	0.153159i
$35$	9.97476	−	1.45138i	1.68604	−	0.245328i
$36$	−2.25435			−0.375724
$37$	−5.91166	+	5.91166i	−0.971871	+	0.971871i	−0.999615	−	0.0277441i	$-0.991168\pi$
$37$	−5.91166	+	5.91166i	−0.971871	+	0.971871i	0.0277441	+	0.999615i	$0.491168\pi$
$38$	4.02440	+	2.05054i	0.652844	+	0.332641i
$39$	−9.79537	−	3.18271i	−1.56852	−	0.509641i
$40$	1.04015	−	1.97941i	0.164463	−	0.312973i
$41$	3.28478	+	2.38653i	0.512996	+	0.372713i	0.813959	−	0.580922i	$-0.197308\pi$
$41$	3.28478	+	2.38653i	0.512996	+	0.372713i	−0.300963	+	0.953636i	$0.597308\pi$
$42$	−9.20676	−	4.69108i	−1.42063	−	0.723849i
$43$	1.60240	+	10.1171i	0.244363	+	1.54285i	0.738975	+	0.673733i	$0.235310\pi$
$43$	1.60240	+	10.1171i	0.244363	+	1.54285i	−0.494612	+	0.869114i	$0.664690\pi$
$44$	−3.20012	+	2.32502i	−0.482436	+	0.350510i
$45$	−1.49724	−	4.81338i	−0.223196	−	0.717536i
$46$	2.42626	+	3.33945i	0.357732	+	0.492376i
$47$	−3.57518	−	0.566253i	−0.521494	−	0.0825965i	−0.109862	−	0.993947i	$-0.535041\pi$
$47$	−3.57518	−	0.566253i	−0.521494	−	0.0825965i	−0.411632	+	0.911350i	$0.635041\pi$
$48$	−2.04240	+	1.04065i	−0.294795	+	0.150205i
$49$	−7.82957	−	10.7765i	−1.11851	−	1.53950i
$50$	4.91719	+	0.906243i	0.695395	+	0.128162i
$51$	1.07623	+	3.31229i	0.150702	+	0.463813i
$52$	−4.43788	+	0.702891i	−0.615423	+	0.0974734i
$53$	−3.49158	+	1.77905i	−0.479605	+	0.244371i	−0.677042	−	0.735945i	$-0.736738\pi$
$53$	−3.49158	+	1.77905i	−0.479605	+	0.244371i	0.197437	+	0.980316i	$0.436738\pi$
$54$	0.528177	−	1.62556i	0.0718758	−	0.221211i
$55$	−7.08967	−	5.28857i	−0.955971	−	0.713110i
$56$	−4.50782			−0.602383
$57$	7.32091	−	7.32091i	0.969678	−	0.969678i
$58$	1.97146	−	3.86921i	0.258866	−	0.508053i
$59$	2.45196	+	3.37484i	0.319219	+	0.439367i	0.938228	−	0.346017i	$-0.112466\pi$
$59$	2.45196	+	3.37484i	0.319219	+	0.439367i	−0.619010	+	0.785383i	$0.712466\pi$
$60$	−3.57843	−	3.66968i	−0.461974	−	0.473753i
$61$		−	9.90839i		−	1.26864i	−0.773071	−	0.634320i	$-0.781280\pi$
$61$		−	9.90839i		−	1.26864i	0.773071	−	0.634320i	$-0.218720\pi$
$62$	0.380608	−	5.55474i	0.0483373	−	0.705453i
$63$	−7.18575	+	7.18575i	−0.905320	+	0.905320i
$64$	−0.587785	+	0.809017i	−0.0734732	+	0.101127i
$65$	−4.44824	−	9.00873i	−0.551736	−	1.11740i
$66$	2.80188	+	8.62331i	0.344888	+	1.06146i
$67$	−2.92785	−	2.92785i	−0.357694	−	0.357694i	0.505268	−	0.862962i	$-0.331394\pi$
$67$	−2.92785	−	2.92785i	−0.357694	−	0.357694i	−0.862962	+	0.505268i	$0.831394\pi$
$68$	1.07435	+	1.07435i	0.130284	+	0.130284i
$69$	8.99878	−	2.92388i	1.08333	−	0.351994i
$70$	−2.99391	−	9.62491i	−0.357841	−	1.15040i
$71$	−3.95467	+	12.1712i	−0.469333	+	1.44446i	0.384117	+	0.923284i	$0.374506\pi$
$71$	−3.95467	+	12.1712i	−0.469333	+	1.44446i	−0.853450	+	0.521174i	$0.825494\pi$
$72$	0.352657	+	2.22659i	0.0415611	+	0.262406i
$73$	0.390755	−	0.766899i	0.0457344	−	0.0897588i	−0.867008	−	0.498294i	$-0.833960\pi$
$73$	0.390755	−	0.766899i	0.0457344	−	0.0897588i	0.912743	+	0.408535i	$0.133960\pi$
$74$	6.76367	+	4.91409i	0.786260	+	0.571251i
$75$	5.45869	−	10.0778i	0.630315	−	1.16368i
$76$	1.39573	−	4.29563i	0.160102	−	0.492743i
$77$	−2.78938	+	17.6114i	−0.317879	+	2.00701i
$78$	−1.61119	+	10.1727i	−0.182432	+	1.15183i
$79$	−2.07659	+	6.39107i	−0.233634	+	0.719052i	0.763666	+	0.645612i	$0.223398\pi$
$79$	−2.07659	+	6.39107i	−0.233634	+	0.719052i	−0.997300	+	0.0734398i	$0.976602\pi$
$80$	−2.11776	−	0.717698i	−0.236773	−	0.0802411i
$81$	−8.64108	−	6.27811i	−0.960120	−	0.697568i
$82$	1.84330	−	3.61767i	0.203558	−	0.399505i
$83$	−0.632745	−	3.99499i	−0.0694528	−	0.438508i	−0.997772	−	0.0667224i	$-0.978746\pi$
$83$	−0.632745	−	3.99499i	−0.0694528	−	0.438508i	0.928319	−	0.371785i	$-0.121254\pi$
$84$	−3.19307	+	9.82726i	−0.348392	+	1.07224i
$85$	−1.58037	+	3.00745i	−0.171415	+	0.326204i
$86$	9.74190	−	3.16533i	1.05050	−	0.341327i
$87$	−7.03860	−	7.03860i	−0.754617	−	0.754617i
$88$	2.79700	+	2.79700i	0.298162	+	0.298162i
$89$	−1.22664	−	3.77522i	−0.130024	−	0.400173i	0.864759	−	0.502187i	$-0.167471\pi$
$89$	−1.22664	−	3.77522i	−0.130024	−	0.400173i	−0.994783	+	0.102014i	$0.967471\pi$
$90$	−4.51990	+	2.23179i	−0.476439	+	0.235251i
$91$	−11.9053	+	16.3863i	−1.24802	+	1.71775i
$92$	2.91879	−	2.91879i	0.304305	−	0.304305i
$93$	−11.8400	−	4.76439i	−1.22775	−	0.494044i
$94$			3.61975i			0.373348i
$95$	10.0988	+	0.127132i	1.03612	+	0.0130435i
$96$	1.34734	+	1.85446i	0.137513	+	0.189270i
$97$	6.53357	−	12.8229i	0.663384	−	1.30196i	−0.276679	−	0.960962i	$-0.589234\pi$
$97$	6.53357	−	12.8229i	0.663384	−	1.30196i	0.940063	−	0.341001i	$-0.110766\pi$
$98$	−9.41899	+	9.41899i	−0.951461	+	0.951461i
$99$	8.91720			0.896213
$100$	0.125868	−	4.99842i	0.0125868	−	0.499842i
$101$	−3.96082	+	12.1901i	−0.394116	+	1.21296i	0.535532	+	0.844515i	$0.320111\pi$
$101$	−3.96082	+	12.1901i	−0.394116	+	1.21296i	−0.929648	+	0.368449i	$0.879889\pi$
$102$	3.10315	−	1.58113i	0.307257	−	0.156555i
$103$	8.74980	−	1.38583i	0.862143	−	0.136550i	0.290323	−	0.956929i	$-0.406237\pi$
$103$	8.74980	−	1.38583i	0.862143	−	0.136550i	0.571820	+	0.820379i	$0.306237\pi$
$104$	1.38847	+	4.27328i	0.136151	+	0.419030i
$105$	−23.1034	−	0.290845i	−2.25466	−	0.0283835i
$106$	2.30335	+	3.17029i	0.223721	+	0.307925i
$107$	15.6128	−	7.95514i	1.50935	−	0.769052i	0.513331	−	0.858191i	$-0.328411\pi$
$107$	15.6128	−	7.95514i	1.50935	−	0.769052i	0.996019	+	0.0891387i	$0.0284114\pi$
$108$	−1.68817	−	0.267380i	−0.162445	−	0.0257287i
$109$	7.54510	+	10.3849i	0.722689	+	0.994697i	0.999430	+	0.0337520i	$0.0107456\pi$
$109$	7.54510	+	10.3849i	0.722689	+	0.994697i	−0.276741	+	0.960945i	$0.589254\pi$
$110$	−4.11439	+	7.82970i	−0.392291	+	0.746532i
$111$	15.5039	−	11.2643i	1.47157	−	1.06916i
$112$	0.705179	+	4.45232i	0.0666331	+	0.420705i
$113$	8.60988	+	4.38695i	0.809949	+	0.412690i	0.809362	−	0.587310i	$-0.199813\pi$
$113$	8.60988	+	4.38695i	0.809949	+	0.412690i	0.000587215		1.00000i	$0.499813\pi$
$114$	−8.37602	−	6.08553i	−0.784486	−	0.569962i
$115$	8.17061	+	4.29353i	0.761914	+	0.400374i
$116$	−4.12998	−	1.34191i	−0.383459	−	0.124593i
$117$	9.02520	+	4.59857i	0.834380	+	0.425138i
$118$	2.94972	−	2.94972i	0.271544	−	0.271544i
$119$	6.84903			0.627849
$120$	−3.06471	+	4.10844i	−0.279768	+	0.375048i
$121$	3.75907	−	2.73113i	0.341734	−	0.248284i
$122$	−9.78640	+	1.55001i	−0.886019	+	0.140332i
$123$	−6.58101	−	6.58101i	−0.593390	−	0.593390i
$124$	−5.54589	+	0.493031i	−0.498036	+	0.0442755i
$125$	10.7560	−	3.05099i	0.962045	−	0.272889i
$126$	8.22138	+	5.97318i	0.732419	+	0.532134i
$127$	1.02599	−	6.47784i	0.0910417	−	0.574815i	−0.899426	−	0.437072i	$-0.856015\pi$
$127$	1.02599	−	6.47784i	0.0910417	−	0.574815i	0.990468	−	0.137743i	$-0.0439847\pi$
$128$	0.891007	+	0.453990i	0.0787546	+	0.0401275i
$129$		−	23.4799i		−	2.06729i
$130$	−8.20196	+	5.80275i	−0.719360	+	0.508935i
$131$	−4.76645	−	14.6696i	−0.416446	−	1.28169i	−0.910951	−	0.412515i	$-0.864650\pi$
$131$	−4.76645	−	14.6696i	−0.416446	−	1.28169i	0.494504	−	0.869175i	$-0.335350\pi$
$132$	8.07883	−	4.11637i	0.703172	−	0.358284i
$133$	−9.24345	−	18.1413i	−0.801509	−	1.57305i
$134$	−2.43379	+	3.34982i	−0.210247	+	0.289381i
$135$	−0.550316	−	3.78210i	−0.0473637	−	0.325511i
$136$	0.893060	−	1.22919i	0.0765793	−	0.105402i
$137$	−2.84513	+	17.9634i	−0.243076	+	1.53472i	0.500303	+	0.865850i	$0.333222\pi$
$137$	−2.84513	+	17.9634i	−0.243076	+	1.53472i	−0.743379	+	0.668870i	$0.766778\pi$
$138$	−4.29560	−	8.43059i	−0.365666	−	0.717660i
$139$	−13.0907	+	9.51095i	−1.11034	+	0.806708i	−0.982717	−	0.185114i	$-0.940734\pi$
$139$	−13.0907	+	9.51095i	−1.11034	+	0.806708i	−0.127622	+	0.991823i	$0.540734\pi$
$140$	−9.03806	+	4.46272i	−0.763855	+	0.377168i
$141$	7.89121	+	2.56401i	0.664560	+	0.215929i
$142$	12.6400	+	2.00198i	1.06073	+	0.168003i
$143$	17.5543	−	2.78033i	1.46796	−	0.232503i
$144$	2.14401	−	0.696631i	0.178667	−	0.0580526i
$145$	0.122230	−	9.70940i	0.0101506	−	0.806322i
$146$	−0.818585	−	0.265974i	−0.0677466	−	0.0220122i
$147$	13.8620	+	27.2057i	1.14332	+	2.24389i
$148$	3.79552	−	7.44913i	0.311990	−	0.612314i
$149$		−	0.803110i		−	0.0657934i	−0.999459	−	0.0328967i	$-0.989527\pi$
$149$		−	0.803110i		−	0.0657934i	0.999459	−	0.0328967i	$-0.0104732\pi$
$150$	−10.8076	−	3.81498i	−0.882438	−	0.311491i
$151$	−11.9363	+	3.87835i	−0.971366	+	0.315616i	−0.751367	−	0.659884i	$-0.770605\pi$
$151$	−11.9363	+	3.87835i	−0.971366	+	0.315616i	−0.219998	+	0.975500i	$0.570605\pi$
$152$	−4.46108	−	0.706566i	−0.361842	−	0.0573101i
$153$	−0.535815	−	3.38300i	−0.0433181	−	0.273500i
$154$	17.8310			1.43686
$155$	−4.73605	−	11.5139i	−0.380409	−	0.924818i
$156$	10.2995			0.824617
$157$	−1.37648	−	8.69073i	−0.109855	−	0.693596i	−0.979730	−	0.200324i	$-0.935801\pi$
$157$	−1.37648	−	8.69073i	−0.109855	−	0.693596i	0.869875	−	0.493272i	$-0.164199\pi$
$158$	6.63724	+	1.05124i	0.528030	+	0.0836318i
$159$	8.54292	−	2.77576i	0.677498	−	0.220132i
$160$	−0.377571	+	2.20396i	−0.0298496	+	0.174238i
$161$		−	18.6074i		−	1.46646i
$162$	−4.84906	+	9.51681i	−0.380978	+	0.747711i
$163$	5.64954	+	11.0878i	0.442506	+	0.868467i	0.999285	+	0.0378062i	$0.0120369\pi$
$163$	5.64954	+	11.0878i	0.442506	+	0.868467i	−0.556779	+	0.830661i	$0.687963\pi$
$164$	−3.86149	−	1.25467i	−0.301531	−	0.0979735i
$165$	14.1547	+	14.5156i	1.10194	+	1.13004i
$166$	−3.84683	+	1.24991i	−0.298572	+	0.0970118i
$167$	−6.76296	+	1.07115i	−0.523334	+	0.0828879i	−0.412512	−	0.910952i	$-0.635348\pi$
$167$	−6.76296	+	1.07115i	−0.523334	+	0.0828879i	−0.110822	+	0.993840i	$0.535348\pi$
$168$	10.2058	+	1.61644i	0.787393	+	0.124711i
$169$	6.83697	+	2.22147i	0.525921	+	0.170882i
$170$	3.21765	+	1.09044i	0.246783	+	0.0836333i
$171$	−8.23756	+	5.98494i	−0.629942	+	0.457680i
$172$	−4.65033	−	9.12679i	−0.354585	−	0.695911i
$173$	−0.663137	+	4.18688i	−0.0504174	+	0.318323i	0.949571	+	0.313551i	$0.101519\pi$
$173$	−0.663137	+	4.18688i	−0.0504174	+	0.318323i	−0.999989	+	0.00477139i	$0.998481\pi$
$174$	−5.85086	+	8.05302i	−0.443553	+	0.610498i
$175$	−15.5313	−	16.3337i	−1.17406	−	1.23471i
$176$	2.32502	−	3.20012i	0.175255	−	0.241218i
$177$	−4.34112	−	8.51992i	−0.326298	−	0.640397i
$178$	−3.53686	+	1.80212i	−0.265099	+	0.135074i
$179$	0.504423	+	1.55246i	0.0377024	+	0.116036i	0.968136	−	0.250423i	$-0.0805698\pi$
$179$	0.504423	+	1.55246i	0.0377024	+	0.116036i	−0.930434	+	0.366459i	$0.880570\pi$
$180$	2.91138	+	4.11512i	0.217001	+	0.306723i
$181$			6.23609i			0.463525i	0.972772	+	0.231762i	$0.0744491\pi$
$181$			6.23609i			0.463525i	−0.972772	+	0.231762i	$0.925551\pi$
$182$	18.0469	+	9.19536i	1.33773	+	0.681606i
$183$	−3.55300	+	22.4327i	−0.262645	+	1.65828i
$184$	−3.33945	−	2.42626i	−0.246188	−	0.178866i
$185$	18.4259	+	3.15663i	1.35470	+	0.232080i
$186$	−2.85355	+	12.4395i	−0.209232	+	0.912111i
$187$	−4.24967	−	4.24967i	−0.310767	−	0.310767i
$188$	3.57518	−	0.566253i	0.260747	−	0.0412983i
$189$	−6.23335	+	4.52879i	−0.453409	+	0.329421i
$190$	−1.45424	−	9.99439i	−0.105502	−	0.725069i
$191$	−13.9072			−1.00629			−0.503145	−	0.864202i	$-0.667824\pi$
$191$	−13.9072			−1.00629			−0.503145	+	0.864202i	$0.667824\pi$
$192$	1.62086	−	1.62086i	0.116975	−	0.116975i
$193$	7.00296	+	3.56819i	0.504084	+	0.256844i	0.687490	−	0.726194i	$-0.258712\pi$
$193$	7.00296	+	3.56819i	0.504084	+	0.256844i	−0.183406	+	0.983037i	$0.558712\pi$
$194$	−13.6871	−	4.44720i	−0.982674	−	0.319290i
$195$	6.84048	+	21.9910i	0.489857	+	1.57481i
$196$	10.7765	+	7.82957i	0.769748	+	0.559255i
$197$	13.5013	+	6.87924i	0.961926	+	0.490126i	0.863130	−	0.504982i	$-0.168501\pi$
$197$	13.5013	+	6.87924i	0.961926	+	0.490126i	0.0987958	+	0.995108i	$0.468501\pi$
$198$	−1.39496	−	8.80742i	−0.0991353	−	0.625916i
$199$	−13.7051	+	9.95732i	−0.971527	+	0.705856i	−0.955799	−	0.294020i	$-0.905007\pi$
$199$	−13.7051	+	9.95732i	−0.971527	+	0.705856i	−0.0157282	+	0.999876i	$0.505007\pi$
$200$	−4.95657	+	0.657606i	−0.350482	+	0.0464998i
$201$	5.57882	+	7.67858i	0.393499	+	0.541605i
$202$	12.6597	+	2.00509i	0.890731	+	0.141078i
$203$	−17.4417	+	8.88700i	−1.22417	+	0.623745i
$204$	−2.04710	−	2.81760i	−0.143326	−	0.197271i
$205$	0.114283	−	9.07818i	0.00798190	−	0.634048i
$206$	−2.73754	−	8.42528i	−0.190733	−	0.587017i
$207$	−9.19090	+	1.45570i	−0.638812	+	0.101178i
$208$	4.00347	−	2.03987i	0.277591	−	0.141439i
$209$	−5.52091	+	16.9916i	−0.381890	+	1.17534i
$210$	3.32691	+	22.8645i	0.229579	+	1.57780i
$211$	10.7639			0.741015			0.370507	−	0.928830i	$-0.379184\pi$
$211$	10.7639			0.741015			0.370507	+	0.928830i	$0.379184\pi$
$212$	2.77093	−	2.77093i	0.190308	−	0.190308i
$213$	13.3178	−	26.1377i	0.912524	−	1.79093i
$214$	−10.2996	−	14.1762i	−0.704065	−	0.969062i
$215$	16.3986	−	15.9908i	1.11837	−	1.09057i
$216$			1.70922i			0.116297i
$217$	−16.1061	+	19.2491i	−1.09335	+	1.30672i
$218$	9.07677	−	9.07677i	0.614756	−	0.614756i
$219$	−1.15967	+	1.59615i	−0.0783634	+	0.107858i
$220$	8.37693	+	2.83890i	0.564773	+	0.191398i
$221$	−2.10960	−	6.49268i	−0.141907	−	0.436745i
$222$	−13.5509	−	13.5509i	−0.909478	−	0.909478i
$223$	−14.5449	−	14.5449i	−0.974002	−	0.974002i	0.0256690	−	0.999670i	$-0.491828\pi$
$223$	−14.5449	−	14.5449i	−0.974002	−	0.974002i	−0.999670	+	0.0256690i	$0.991828\pi$
$224$	4.28719	−	1.39299i	0.286450	−	0.0930733i
$225$	−6.85281	+	8.94934i	−0.456854	+	0.596623i
$226$	2.98606	−	9.19015i	0.198630	−	0.611319i
$227$	−2.64646	−	16.7091i	−0.175652	−	1.10902i	−0.905167	−	0.425056i	$-0.860254\pi$
$227$	−2.64646	−	16.7091i	−0.175652	−	1.10902i	0.729515	−	0.683965i	$-0.239746\pi$
$228$	−4.70031	+	9.22488i	−0.311286	+	0.610933i
$229$	22.2035	+	16.1318i	1.46725	+	1.06602i	0.981400	+	0.191973i	$0.0614888\pi$
$229$	22.2035	+	16.1318i	1.46725	+	1.06602i	0.485847	+	0.874044i	$0.338511\pi$
$230$	2.96251	−	8.74168i	0.195342	−	0.576409i
$231$	12.6304	−	38.8723i	0.831018	−	2.55761i
$232$	−0.679320	+	4.28906i	−0.0445995	+	0.281590i
$233$	−0.0838260	+	0.529257i	−0.00549162	+	0.0346728i	−0.990282	−	0.139074i	$-0.955587\pi$
$233$	−0.0838260	+	0.529257i	−0.00549162	+	0.0346728i	0.984790	+	0.173747i	$0.0555874\pi$
$234$	3.13010	−	9.63346i	0.204621	−	0.629759i
$235$	3.58353	+	7.25749i	0.233764	+	0.473426i
$236$	−3.37484	−	2.45196i	−0.219683	−	0.159609i
$237$	6.99316	−	13.7248i	0.454255	−	0.891525i
$238$	−1.07142	−	6.76470i	−0.0694501	−	0.438491i
$239$	4.68610	−	14.4223i	0.303119	−	0.932904i	−0.677254	−	0.735749i	$-0.736830\pi$
$239$	4.68610	−	14.4223i	0.303119	−	0.932904i	0.980373	−	0.197154i	$-0.0631699\pi$
$240$	4.53729	+	2.38427i	0.292881	+	0.153904i
$241$	−12.3144	+	4.00119i	−0.793239	+	0.257739i	−0.677483	−	0.735538i	$-0.736929\pi$
$241$	−12.3144	+	4.00119i	−0.793239	+	0.257739i	−0.115757	+	0.993278i	$0.536929\pi$
$242$	−3.28555	−	3.28555i	−0.211203	−	0.211203i
$243$	13.6865	+	13.6865i	0.877990	+	0.877990i
$244$	3.06186	+	9.42344i	0.196016	+	0.603274i
$245$	−9.56006	+	28.2095i	−0.610770	+	1.80224i
$246$	−5.47049	+	7.52948i	−0.348786	+	0.480062i
$247$	−14.3503	+	14.3503i	−0.913088	+	0.913088i
$248$	1.35453	+	5.40049i	0.0860127	+	0.342931i
$249$			9.27162i			0.587565i
$250$	−4.69604	−	10.1463i	−0.297004	−	0.641708i
$251$	6.03572	+	8.30745i	0.380971	+	0.524362i	0.955841	−	0.293883i	$-0.0949475\pi$
$251$	6.03572	+	8.30745i	0.380971	+	0.524362i	−0.574870	+	0.818244i	$0.694948\pi$
$252$	4.61354	−	9.05458i	0.290625	−	0.570385i
$253$	−11.5455	+	11.5455i	−0.725856	+	0.725856i
$254$	−6.55858			−0.411522
$255$	4.65641	−	6.24222i	0.291596	−	0.390903i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	−4.37455	+	2.22895i	−0.272877	+	0.139038i	−0.585075	−	0.810979i	$-0.698935\pi$
$257$	−4.37455	+	2.22895i	−0.272877	+	0.139038i	0.312198	+	0.950017i	$0.398935\pi$
$258$	−23.1908	+	3.67307i	−1.44380	+	0.228675i
$259$	−11.6459	−	35.8424i	−0.723642	−	2.22714i
$260$	7.01438	+	7.19323i	0.435013	+	0.446105i
$261$	5.75415	+	7.91990i	0.356173	+	0.490230i
$262$	−13.7434	+	7.00260i	−0.849068	+	0.432622i
$263$	−6.73844	−	1.06726i	−0.415510	−	0.0658104i	−0.0548206	−	0.998496i	$-0.517459\pi$
$263$	−6.73844	−	1.06726i	−0.415510	−	0.0658104i	−0.360690	+	0.932686i	$0.617459\pi$
$264$	−5.32950	−	7.33542i	−0.328008	−	0.451464i
$265$	7.75671	+	4.07603i	0.476491	+	0.250389i
$266$	−16.4719	+	11.9676i	−1.00996	+	0.733779i
$267$	1.42340	+	8.98702i	0.0871109	+	0.549997i
$268$	3.68931	+	1.87980i	0.225360	+	0.114827i
$269$	7.33659	+	5.33035i	0.447320	+	0.324997i	0.788537	−	0.614988i	$-0.210839\pi$
$269$	7.33659	+	5.33035i	0.447320	+	0.324997i	−0.341217	+	0.939985i	$0.610839\pi$
$270$	−3.64944	+	1.13519i	−0.222098	+	0.0690855i
$271$	3.15023	+	1.02357i	0.191363	+	0.0621776i	0.403131	−	0.915142i	$-0.367922\pi$
$271$	3.15023	+	1.02357i	0.191363	+	0.0621776i	−0.211768	+	0.977320i	$0.567922\pi$
$272$	−1.35376	−	0.689777i	−0.0820840	−	0.0418239i
$273$	32.8297	−	32.8297i	1.98694	−	1.98694i
$274$	18.1874			1.09874
$275$	−0.497879	+	19.7715i	−0.0300232	+	1.19227i
$276$	−7.65482	+	5.56155i	−0.460766	+	0.334766i
$277$	11.2141	−	1.77614i	0.673789	−	0.106718i	0.189841	−	0.981815i	$-0.439203\pi$
$277$	11.2141	−	1.77614i	0.673789	−	0.106718i	0.483947	+	0.875097i	$0.339203\pi$
$278$	11.4417	+	11.4417i	0.686227	+	0.686227i
$279$	10.7679	+	6.44951i	0.644658	+	0.386122i
$280$	5.82164	+	8.22866i	0.347909	+	0.491757i
$281$	−16.3091	−	11.8492i	−0.972918	−	0.706866i	−0.0168030	−	0.999859i	$-0.505349\pi$
$281$	−16.3091	−	11.8492i	−0.972918	−	0.706866i	−0.956115	+	0.292993i	$0.905349\pi$
$282$	1.29799	−	8.19516i	0.0772939	−	0.488015i
$283$	−18.5406	−	9.44689i	−1.10212	−	0.561559i	−0.194312	−	0.980940i	$-0.562247\pi$
$283$	−18.5406	−	9.44689i	−1.10212	−	0.561559i	−0.907810	+	0.419381i	$0.862247\pi$
$284$		−	12.7976i		−	0.759397i
$285$	−22.8183	−	3.90912i	−1.35164	−	0.231556i
$286$	−5.49219	−	16.9032i	−0.324760	−	0.999509i
$287$	−16.3078	+	8.30925i	−0.962620	+	0.490479i
$288$	−1.02345	−	2.00864i	−0.0603074	−	0.118360i
$289$	8.63546	−	11.8857i	0.507969	−	0.699159i
$290$	−9.60898	+	1.39816i	−0.564259	+	0.0821028i
$291$	−19.3902	+	26.6883i	−1.13667	+	1.56450i
$292$	−0.134645	+	0.850114i	−0.00787950	+	0.0497492i
$293$	0.515346	+	1.01142i	0.0301068	+	0.0590880i	0.905570	−	0.424197i	$-0.139444\pi$
$293$	0.515346	+	1.01142i	0.0301068	+	0.0590880i	−0.875463	+	0.483285i	$0.839444\pi$
$294$	24.7022	−	17.9472i	1.44066	−	1.04670i
$295$	2.99390	−	8.83431i	0.174312	−	0.514353i
$296$	−7.95117	−	2.58349i	−0.462152	−	0.150162i
$297$	6.67767	+	1.05764i	0.387478	+	0.0613705i
$298$	−0.793223	+	0.125634i	−0.0459502	+	0.00727779i
$299$	−17.6392	+	5.73133i	−1.02010	+	0.331452i
$300$	−2.07732	+	11.2714i	−0.119934	+	0.650752i
$301$	−43.9147	−	14.2688i	−2.53120	−	0.822438i
$302$	5.69786	+	11.1827i	0.327875	+	0.643491i
$303$	13.3385	−	26.1784i	0.766279	−	1.50391i
$304$			4.51669i			0.259050i
$305$	−18.0870	+	12.7962i	−1.03566	+	0.732709i
$306$	−3.25753	+	1.05844i	−0.186221	+	0.0605068i
$307$	−23.1223	−	3.66222i	−1.31966	−	0.209014i	−0.543426	−	0.839457i	$-0.682873\pi$
$307$	−23.1223	−	3.66222i	−1.31966	−	0.209014i	−0.776235	+	0.630444i	$0.782873\pi$
$308$	−2.78938	−	17.6114i	−0.158940	−	1.00350i
$309$	−20.3066			−1.15520
$310$	−10.6313	+	6.47891i	−0.603815	+	0.367977i
$311$	27.1502			1.53954			0.769772	−	0.638319i	$-0.220370\pi$
$311$	27.1502			1.53954			0.769772	+	0.638319i	$0.220370\pi$
$312$	−1.61119	−	10.1727i	−0.0912158	−	0.575914i
$313$	−8.81344	−	1.39591i	−0.498165	−	0.0789016i	−0.0977042	−	0.995216i	$-0.531150\pi$
$313$	−8.81344	−	1.39591i	−0.498165	−	0.0789016i	−0.400461	+	0.916314i	$0.631150\pi$
$314$	−8.36841	+	2.71906i	−0.472257	+	0.153445i
$315$	22.3971	+	3.83695i	1.26193	+	0.216188i
$316$		−	6.71997i		−	0.378028i
$317$	1.00454	−	1.97153i	0.0564207	−	0.110732i	−0.861074	−	0.508479i	$-0.830208\pi$
$317$	1.00454	−	1.97153i	0.0564207	−	0.110732i	0.917495	+	0.397747i	$0.130208\pi$
$318$	−4.07800	−	8.00352i	−0.228683	−	0.448815i
$319$	16.3364	+	5.30802i	0.914662	+	0.297192i
$320$	2.23589	+	0.0281472i	0.124990	+	0.00157348i
$321$	−38.2003	+	12.4120i	−2.13213	+	0.692772i
$322$	−18.3783	+	2.91083i	−1.02418	+	0.162214i
$323$	6.77801	+	1.07353i	0.377139	+	0.0597329i
$324$	10.1582	+	3.30060i	0.564344	+	0.183367i
$325$	−10.7000	+	19.7542i	−0.593530	+	1.09577i
$326$	10.0675	−	7.31450i	0.557590	−	0.405113i
$327$	−13.3583	−	26.2172i	−0.738718	−	1.44981i
$328$	−0.635156	+	4.01022i	−0.0350706	+	0.221427i
$329$	9.59099	−	13.2009i	0.528769	−	0.727788i
$330$	12.1226	−	16.2512i	0.667330	−	0.894599i
$331$	−9.98451	+	13.7425i	−0.548799	+	0.755356i	−0.989849	−	0.142126i	$-0.954606\pi$
$331$	−9.98451	+	13.7425i	−0.548799	+	0.755356i	0.441050	+	0.897483i	$0.354606\pi$
$332$	1.83630	+	3.60394i	0.100780	+	0.197792i
$333$	−16.7929	+	8.55641i	−0.920245	+	0.468888i
$334$	2.11592	+	6.51213i	0.115778	+	0.356328i
$335$	−1.56337	+	9.12574i	−0.0854162	+	0.498592i
$336$		−	10.3330i		−	0.563711i
$337$	5.58936	+	2.84792i	0.304472	+	0.155136i	0.599551	−	0.800337i	$-0.295346\pi$
$337$	5.58936	+	2.84792i	0.304472	+	0.155136i	−0.295079	+	0.955473i	$0.595346\pi$
$338$	1.12458	−	7.10031i	0.0611690	−	0.386206i
$339$	−17.9198	−	13.0195i	−0.973270	−	0.707122i
$340$	0.573668	−	3.34862i	0.0311115	−	0.181604i
$341$	21.9371	−	1.95021i	1.18796	−	0.105610i
$342$	7.19989	+	7.19989i	0.389326	+	0.389326i
$343$	28.1407	−	4.45705i	1.51946	−	0.240658i
$344$	−8.28695	+	6.02082i	−0.446803	+	0.324621i
$345$	−16.9588	−	12.6505i	−0.913031	−	0.681079i
$346$	4.23907			0.227894
$347$	10.0331	−	10.0331i	0.538606	−	0.538606i	−0.384513	−	0.923120i	$-0.625631\pi$
$347$	10.0331	−	10.0331i	0.538606	−	0.538606i	0.923120	+	0.384513i	$0.125631\pi$
$348$	8.86915	+	4.51906i	0.475436	+	0.242247i
$349$	25.7262	+	8.35895i	1.37709	+	0.447444i	0.901713	−	0.432336i	$-0.142311\pi$
$349$	25.7262	+	8.35895i	1.37709	+	0.447444i	0.475380	+	0.879781i	$0.342311\pi$
$350$	−13.7030	+	17.8952i	−0.732455	+	0.956541i
$351$	6.21313	+	4.51410i	0.331632	+	0.240945i
$352$	−3.52443	−	1.79579i	−0.187853	−	0.0957158i
$353$	−5.45292	−	34.4284i	−0.290230	−	1.83244i	−0.513992	−	0.857795i	$-0.671834\pi$
$353$	−5.45292	−	34.4284i	−0.290230	−	1.83244i	0.223763	−	0.974644i	$-0.428166\pi$
$354$	−7.73593	+	5.62048i	−0.411160	+	0.298725i
$355$	27.3248	−	8.49962i	1.45025	−	0.451113i
$356$	2.33322	+	3.21140i	0.123660	+	0.170204i
$357$	−15.5063	−	2.45596i	−0.820680	−	0.129983i
$358$	1.45443	−	0.741071i	0.0768692	−	0.0391668i
$359$	−17.5717	−	24.1854i	−0.927400	−	1.27646i	−0.960865	−	0.277017i	$-0.910654\pi$
$359$	−17.5717	−	24.1854i	−0.927400	−	1.27646i	0.0334648	−	0.999440i	$-0.489346\pi$
$360$	3.60902	−	3.51928i	0.190212	−	0.185482i
$361$	−0.432781	−	1.33196i	−0.0227780	−	0.0701033i
$362$	6.15931	−	0.975539i	0.323726	−	0.0512732i
$363$	−9.48993	+	4.83536i	−0.498092	+	0.253791i
$364$	6.25899	−	19.2632i	0.328060	−	1.00967i
$365$	−1.90455	+	0.277123i	−0.0996889	+	0.0145053i
$366$	22.7124			1.18719
$367$	11.0087	−	11.0087i	0.574647	−	0.574647i	−0.358776	−	0.933424i	$-0.616806\pi$
$367$	11.0087	−	11.0087i	0.574647	−	0.574647i	0.933424	+	0.358776i	$0.116806\pi$
$368$	−1.87398	+	3.67789i	−0.0976879	+	0.191723i
$369$	5.38006	+	7.40502i	0.280075	+	0.385490i
$370$	0.235320	−	18.6928i	0.0122337	−	0.971794i
$371$		−	17.6648i		−	0.917108i
$372$	12.7328	+	0.872443i	0.660164	+	0.0452341i
$373$	5.85735	−	5.85735i	0.303282	−	0.303282i	−0.539015	−	0.842296i	$-0.681203\pi$
$373$	5.85735	−	5.85735i	0.303282	−	0.303282i	0.842296	+	0.539015i	$0.181203\pi$
$374$	−3.53255	+	4.86214i	−0.182664	+	0.251416i
$375$	−25.4458	+	3.05056i	−1.31401	+	0.157530i
$376$	−1.11856	−	3.44258i	−0.0576855	−	0.177538i
$377$	13.7969	+	13.7969i	0.710578	+	0.710578i
$378$	5.44815	+	5.44815i	0.280222	+	0.280222i
$379$	4.73326	−	1.53793i	0.243131	−	0.0789981i	−0.184917	−	0.982754i	$-0.559202\pi$
$379$	4.73326	−	1.53793i	0.243131	−	0.0789981i	0.428048	+	0.903756i	$0.359202\pi$
$380$	−9.64384	+	2.99980i	−0.494719	+	0.153887i
$381$	−4.64571	+	14.2980i	−0.238007	+	0.732509i
$382$	2.17557	+	13.7360i	0.111312	+	0.702794i
$383$	−10.5299	+	20.6661i	−0.538053	+	1.05599i	0.448688	+	0.893689i	$0.351891\pi$
$383$	−10.5299	+	20.6661i	−0.538053	+	1.05599i	−0.986741	+	0.162301i	$0.948109\pi$
$384$	−1.85446	−	1.34734i	−0.0946349	−	0.0687563i
$385$	35.7506	−	17.6525i	1.82202	−	0.899657i
$386$	2.42875	−	7.47493i	0.123620	−	0.380464i
$387$	−3.61235	+	22.8075i	−0.183626	+	1.15937i
$388$	−2.25132	+	14.2142i	−0.114293	+	0.721619i
$389$	1.63451	−	5.03050i	0.0828729	−	0.255057i	−0.901031	−	0.433755i	$-0.857188\pi$
$389$	1.63451	−	5.03050i	0.0828729	−	0.255057i	0.983904	+	0.178698i	$0.0571885\pi$
$390$	20.6501	−	10.1964i	1.04566	−	0.516315i
$391$	5.07385	+	3.68637i	0.256596	+	0.186428i
$392$	6.04736	−	11.8686i	0.305438	−	0.599456i
$393$	5.53101	+	34.9214i	0.279002	+	1.76155i
$394$	4.68248	−	14.4112i	0.235900	−	0.726026i
$395$	14.3482	−	4.46313i	0.721936	−	0.224564i
$396$	−8.48076	+	2.75557i	−0.426174	+	0.138472i
$397$	12.4378	+	12.4378i	0.624236	+	0.624236i	0.946612	−	0.322376i	$-0.104481\pi$
$397$	12.4378	+	12.4378i	0.624236	+	0.624236i	−0.322376	+	0.946612i	$0.604481\pi$
$398$	11.9787	+	11.9787i	0.600437	+	0.600437i
$399$	14.4221	+	44.3867i	0.722009	+	2.22211i
$400$	1.42489	+	4.79267i	0.0712444	+	0.239634i
$401$	−1.56948	+	2.16020i	−0.0783760	+	0.107875i	−0.846405	−	0.532540i	$-0.821238\pi$
$401$	−1.56948	+	2.16020i	−0.0783760	+	0.107875i	0.768029	+	0.640415i	$0.221238\pi$
$402$	6.71133	−	6.71133i	0.334731	−	0.334731i
$403$	23.2085	+	9.33906i	1.15610	+	0.465212i
$404$		−	12.8175i		−	0.637693i
$405$	−0.300639	+	23.8815i	−0.0149389	+	1.18668i
$406$	11.5061	+	15.8368i	0.571037	+	0.785965i
$407$	−15.0134	+	29.4655i	−0.744187	+	1.46055i
$408$	−2.46267	+	2.46267i	−0.121920	+	0.121920i
$409$	7.04932			0.348566			0.174283	−	0.984696i	$-0.444239\pi$
$409$	7.04932			0.348566			0.174283	+	0.984696i	$0.444239\pi$
$410$	−8.98429	+	1.30726i	−0.443702	+	0.0645612i
$411$	12.8828	−	39.6493i	0.635463	−	1.95575i
$412$	−7.89331	+	4.02184i	−0.388875	+	0.198142i
$413$	−18.5730	+	2.94168i	−0.913918	+	0.144750i
$414$	2.87555	+	8.85003i	0.141325	+	0.434955i
$415$	−6.47538	+	6.31437i	−0.317864	+	0.309960i
$416$	−2.64103	−	3.63507i	−0.129487	−	0.178224i
$417$	33.0480	−	16.8388i	1.61837	−	0.824600i
$418$	17.6461	+	2.79487i	0.863099	+	0.136701i
$419$	−21.7328	−	29.9126i	−1.06172	−	1.46133i	−0.878190	−	0.478311i	$-0.841249\pi$
$419$	−21.7328	−	29.9126i	−1.06172	−	1.46133i	−0.183525	−	0.983015i	$-0.558751\pi$
$420$	22.0626	−	6.86275i	1.07654	−	0.334868i
$421$	−12.9953	+	9.44163i	−0.633351	+	0.460157i	−0.857560	−	0.514385i	$-0.828020\pi$
$421$	−12.9953	+	9.44163i	−0.633351	+	0.460157i	0.224208	+	0.974541i	$0.428020\pi$
$422$	−1.68384	−	10.6313i	−0.0819680	−	0.517526i
$423$	−7.27075	−	3.70463i	−0.353516	−	0.180125i
$424$	−3.17029	−	2.30335i	−0.153963	−	0.111860i
$425$	7.53083	−	0.999143i	0.365299	−	0.0484656i
$426$	−27.8993	−	9.06504i	−1.35173	−	0.439202i
$427$	39.7970	+	20.2776i	1.92591	+	0.981302i
$428$	−12.3904	+	12.3904i	−0.598913	+	0.598913i
$429$	−40.7402			−1.96695
$430$	−18.3593	−	13.6952i	−0.885362	−	0.660439i
$431$	−3.06924	+	2.22993i	−0.147840	+	0.107412i	−0.659247	−	0.751927i	$-0.729125\pi$
$431$	−3.06924	+	2.22993i	−0.147840	+	0.107412i	0.511406	+	0.859339i	$0.329125\pi$
$432$	1.68817	−	0.267380i	0.0812223	−	0.0128643i
$433$	0.209442	+	0.209442i	0.0100651	+	0.0100651i	0.712121	−	0.702056i	$-0.247735\pi$
$433$	0.209442	+	0.209442i	0.0100651	+	0.0100651i	−0.702056	+	0.712121i	$0.747735\pi$
$434$	21.5317	+	12.8965i	1.03355	+	0.619053i
$435$	−3.75837	+	21.9384i	−0.180200	+	1.05187i
$436$	−10.3849	−	7.54510i	−0.497348	−	0.361345i
$437$	2.91656	−	18.4144i	0.139518	−	0.880882i
$438$	1.75791	+	0.895702i	0.0839964	+	0.0427983i
$439$		−	2.02804i		−	0.0967928i	−0.998828	−	0.0483964i	$-0.984589\pi$
$439$		−	2.02804i		−	0.0967928i	0.998828	−	0.0483964i	$-0.0154111\pi$
$440$	1.49351	−	8.71790i	0.0712001	−	0.415610i
$441$	−9.27945	−	28.5592i	−0.441878	−	1.35996i
$442$	−6.08273	+	3.09930i	−0.289326	+	0.147419i
$443$	−15.5886	−	30.5944i	−0.740638	−	1.45358i	−0.885747	−	0.464168i	$-0.846353\pi$
$443$	−15.5886	−	30.5944i	−0.740638	−	1.45358i	0.145110	−	0.989416i	$-0.453647\pi$
$444$	−11.2643	+	15.5039i	−0.534578	+	0.735783i
$445$	−5.30721	+	7.11466i	−0.251586	+	0.337267i
$446$	−12.0905	+	16.6412i	−0.572504	+	0.787984i
$447$	−0.287983	+	1.81825i	−0.0136211	+	0.0860004i
$448$	−2.04651	−	4.01650i	−0.0966884	−	0.189762i
$449$	−1.82299	+	1.32448i	−0.0860324	+	0.0625062i	−0.629970	−	0.776619i	$-0.716933\pi$
$449$	−1.82299	+	1.32448i	−0.0860324	+	0.0625062i	0.543938	+	0.839126i	$0.316933\pi$
$450$	9.91118	+	5.36846i	0.467217	+	0.253072i
$451$	15.2743	+	4.96294i	0.719241	+	0.233696i
$452$	−9.54412	−	1.51164i	−0.448918	−	0.0711016i
$453$	28.4148	−	4.50046i	1.33504	−	0.211450i
$454$	−16.0894	+	5.22775i	−0.755112	+	0.245351i
$455$	45.2869	+	0.570108i	2.12308	+	0.0267271i
$456$	9.84660	+	3.19935i	0.461109	+	0.149823i
$457$	−2.07609	−	4.07456i	−0.0971155	−	0.190600i	0.837338	−	0.546686i	$-0.184111\pi$
$457$	−2.07609	−	4.07456i	−0.0971155	−	0.190600i	−0.934453	+	0.356086i	$0.884111\pi$
$458$	12.4598	−	24.4537i	0.582207	−	1.14265i
$459$		−	2.59692i		−	0.121214i
$460$	−9.09749	−	1.55853i	−0.424173	−	0.0726671i
$461$	21.2061	−	6.89027i	0.987665	−	0.320912i	0.229739	−	0.973252i	$-0.426213\pi$
$461$	21.2061	−	6.89027i	0.987665	−	0.320912i	0.757926	+	0.652341i	$0.226213\pi$
$462$	−40.3696	−	6.39391i	−1.87816	−	0.297472i
$463$	4.71663	+	29.7797i	0.219201	+	1.38398i	0.814355	+	0.580367i	$0.197091\pi$
$463$	4.71663	+	29.7797i	0.219201	+	1.38398i	−0.595155	+	0.803611i	$0.702909\pi$
$464$	4.34252			0.201596
$465$	6.59378	+	27.7659i	0.305779	+	1.28761i
$466$	0.535854			0.0248229
$467$	6.16903	+	38.9497i	0.285469	+	1.80238i	0.546945	+	0.837169i	$0.315791\pi$
$467$	6.16903	+	38.9497i	0.285469	+	1.80238i	−0.261476	+	0.965210i	$0.584209\pi$
$468$	−10.0045	−	1.58456i	−0.462459	−	0.0732462i
$469$	17.7516	−	5.76784i	0.819692	−	0.266334i
$470$	6.60755	−	4.67473i	0.304784	−	0.215629i
$471$			20.1695i			0.929363i
$472$	−1.89384	+	3.71686i	−0.0871709	+	0.171082i
$473$	18.3947	+	36.1016i	0.845788	+	1.65995i
$474$	−14.6498	−	4.76002i	−0.672890	−	0.218635i
$475$	−12.8101	−	18.5988i	−0.587767	−	0.853370i
$476$	−6.51381	+	2.11647i	−0.298560	+	0.0970080i
$477$	−8.72532	+	1.38195i	−0.399505	+	0.0632754i
$478$	−14.9778	−	2.37226i	−0.685071	−	0.108505i
$479$	−5.11499	−	1.66196i	−0.233710	−	0.0759369i	0.189821	−	0.981819i	$-0.439209\pi$
$479$	−5.11499	−	1.66196i	−0.233710	−	0.0759369i	−0.423530	+	0.905882i	$0.639209\pi$
$480$	1.64513	−	4.85441i	0.0750897	−	0.221572i
$481$	−30.3905	+	22.0800i	−1.38569	+	1.00676i
$482$	5.87832	+	11.5369i	0.267750	+	0.525489i
$483$	−6.67231	+	42.1273i	−0.303601	+	1.91686i
$484$	−2.73113	+	3.75907i	−0.124142	+	0.170867i
$485$	−31.8449	+	4.63360i	−1.44600	+	0.210401i
$486$	11.3770	−	15.6590i	0.516069	−	0.710308i
$487$	13.5768	+	26.6460i	0.615223	+	1.20744i	0.962907	+	0.269832i	$0.0869681\pi$
$487$	13.5768	+	26.6460i	0.615223	+	1.20744i	−0.347684	+	0.937612i	$0.613032\pi$
$488$	8.82844	−	4.49832i	0.399645	−	0.203629i
$489$	−8.81470	−	27.1289i	−0.398615	−	1.22681i
$490$	29.3578	+	5.02942i	1.32625	+	0.227206i
$491$			1.67870i			0.0757589i	0.999282	+	0.0378794i	$0.0120603\pi$
$491$			1.67870i			0.0757589i	−0.999282	+	0.0378794i	$0.987940\pi$
$492$	8.29256	+	4.22527i	0.373857	+	0.190490i
$493$	1.03213	−	6.51664i	0.0464850	−	0.293495i
$494$	16.4185	+	11.9287i	0.738703	+	0.536699i
$495$	−11.5161	−	16.2776i	−0.517612	−	0.731625i
$496$	5.12210	−	2.18267i	0.229989	−	0.0980050i
$497$	−40.7924	−	40.7924i	−1.82979	−	1.82979i
$498$	9.15747	−	1.45040i	0.410356	−	0.0649940i
$499$	26.7013	−	19.3996i	1.19531	−	0.868445i	0.201497	−	0.979489i	$-0.435419\pi$
$499$	26.7013	−	19.3996i	1.19531	−	0.868445i	0.993816	+	0.111044i	$0.0354193\pi$
$500$	−9.28675	+	6.22545i	−0.415316	+	0.278411i
$501$	15.6955			0.701225
$502$	7.26098	−	7.26098i	0.324073	−	0.324073i
$503$	6.93761	+	3.53489i	0.309333	+	0.157613i	0.601765	−	0.798673i	$-0.294464\pi$
$503$	6.93761	+	3.53489i	0.309333	+	0.157613i	−0.292432	+	0.956286i	$0.594464\pi$
$504$	−9.66481	−	3.14029i	−0.430505	−	0.139880i
$505$	27.3673	−	8.51283i	1.21783	−	0.378816i
$506$	13.2094	+	9.59720i	0.587230	+	0.426648i
$507$	−14.6824	−	7.48106i	−0.652069	−	0.332246i
$508$	1.02599	+	6.47784i	0.0455209	+	0.287407i
$509$	−24.1926	+	17.5769i	−1.07232	+	0.779083i	−0.976327	−	0.216299i	$-0.930601\pi$
$509$	−24.1926	+	17.5769i	−1.07232	+	0.779083i	−0.0959891	+	0.995382i	$0.530601\pi$
$510$	−6.89379	−	3.62258i	−0.305262	−	0.160411i
$511$	2.28057	+	3.13893i	0.100886	+	0.138858i
$512$	−0.987688	−	0.156434i	−0.0436501	−	0.00691349i
$513$	−6.87857	+	3.50481i	−0.303696	+	0.154741i
$514$	2.88583	+	3.97201i	0.127289	+	0.175198i
$515$	−13.8297	−	14.1823i	−0.609408	−	0.624947i
$516$	7.25569	+	22.3307i	0.319414	+	0.983055i
$517$	−14.1419	+	2.23985i	−0.621958	+	0.0985085i
$518$	−33.5793	+	17.1095i	−1.47539	+	0.751749i
$519$	3.00270	−	9.24137i	0.131804	−	0.405651i
$520$	6.00738	−	8.05329i	0.263441	−	0.353160i
$521$	36.5545			1.60148			0.800741	−	0.599010i	$-0.204439\pi$
$521$	36.5545			1.60148			0.800741	+	0.599010i	$0.204439\pi$
$522$	6.92225	−	6.92225i	0.302979	−	0.302979i
$523$	9.80274	−	19.2390i	0.428644	−	0.841261i	−0.571148	−	0.820847i	$-0.693502\pi$
$523$	9.80274	−	19.2390i	0.428644	−	0.841261i	0.999792	−	0.0204138i	$-0.00649838\pi$
$524$	9.06632	+	12.4787i	0.396064	+	0.545136i
$525$	29.3061	+	42.5491i	1.27902	+	1.85699i
$526$			6.82244i			0.297473i
$527$	−2.05802	−	8.20531i	−0.0896489	−	0.357429i
$528$	−6.41139	+	6.41139i	−0.279020	+	0.279020i
$529$	−3.50398	+	4.82282i	−0.152347	+	0.209688i
$530$	2.81244	−	8.29885i	0.122164	−	0.360479i
$531$	2.90602	+	8.94381i	0.126110	+	0.388128i
$532$	14.3970	+	14.3970i	0.624189	+	0.624189i
$533$	12.9000	+	12.9000i	0.558760	+	0.558760i
$534$	8.65370	−	2.81176i	0.374482	−	0.121677i
$535$	−34.6847	−	18.2263i	−1.49955	−	0.787991i
$536$	1.27952	−	3.93795i	0.0552668	−	0.170094i
$537$	−0.585335	−	3.69566i	−0.0252591	−	0.159480i
$538$	4.11703	−	8.08012i	0.177498	−	0.348359i
$539$	−42.6270	−	30.9703i	−1.83608	−	1.33399i
$540$	1.69211	+	3.42693i	0.0728170	+	0.147472i
$541$	−8.45536	+	26.0229i	−0.363524	+	1.11881i	0.587375	+	0.809315i	$0.300161\pi$
$541$	−8.45536	+	26.0229i	−0.363524	+	1.11881i	−0.950900	+	0.309499i	$0.899839\pi$
$542$	0.518165	−	3.27157i	0.0222571	−	0.140526i
$543$	2.23616	−	14.1186i	0.0959630	−	0.605887i
$544$	−0.469510	+	1.44500i	−0.0201301	+	0.0619539i
$545$	9.21272	−	27.1846i	0.394630	−	1.16446i
$546$	−37.5612	−	27.2898i	−1.60747	−	1.16790i
$547$	14.3797	−	28.2217i	0.614830	−	1.20667i	−0.348236	−	0.937407i	$-0.613219\pi$
$547$	14.3797	−	28.2217i	0.614830	−	1.20667i	0.963066	−	0.269265i	$-0.0867806\pi$
$548$	−2.84513	−	17.9634i	−0.121538	−	0.767360i
$549$	6.90249	−	21.2437i	0.294591	−	0.906659i
$550$	19.6060	−	2.60120i	0.836003	−	0.110916i
$551$	−18.6539	+	6.06100i	−0.794681	+	0.258207i
$552$	6.69055	+	6.69055i	0.284769	+	0.284769i
$553$	−21.4200	−	21.4200i	−0.910870	−	0.910870i
$554$	−3.50854	−	10.7982i	−0.149063	−	0.458770i
$555$	−40.5845	−	13.7539i	−1.72272	−	0.583820i
$556$	9.51095	−	13.0907i	0.403354	−	0.555169i
$557$	18.9096	−	18.9096i	0.801224	−	0.801224i	−0.182063	−	0.983287i	$-0.558277\pi$
$557$	18.9096	−	18.9096i	0.801224	−	0.801224i	0.983287	+	0.182063i	$0.0582775\pi$
$558$	4.68563	−	11.6443i	0.198359	−	0.492941i
$559$			46.0249i			1.94664i
$560$	7.21665	−	7.03721i	0.304959	−	0.297376i
$561$	8.09745	+	11.1452i	0.341875	+	0.470550i
$562$	−9.15205	+	17.9619i	−0.386056	+	0.757677i
$563$	−1.34845	+	1.34845i	−0.0568305	+	0.0568305i	−0.734951	−	0.678120i	$-0.762795\pi$
$563$	−1.34845	+	1.34845i	−0.0568305	+	0.0568305i	0.678120	+	0.734951i	$0.262795\pi$
$564$	−8.29731			−0.349380
$565$	−3.11122	−	21.3822i	−0.130890	−	0.899555i
$566$	−6.43020	+	19.7901i	−0.270281	+	0.831841i
$567$	42.9001	−	21.8587i	1.80163	−	0.917978i
$568$	−12.6400	+	2.00198i	−0.530363	+	0.0840013i
$569$	−10.5413	−	32.4429i	−0.441916	−	1.36008i	−0.885830	−	0.464009i	$-0.846410\pi$
$569$	−10.5413	−	32.4429i	−0.441916	−	1.36008i	0.443914	−	0.896069i	$-0.353590\pi$
$570$	−0.291417	+	23.1489i	−0.0122061	+	0.969601i
$571$	16.3611	+	22.5192i	0.684693	+	0.942399i	0.999978	−	0.00659830i	$-0.00210032\pi$
$571$	16.3611	+	22.5192i	0.684693	+	0.942399i	−0.315286	+	0.948997i	$0.602100\pi$
$572$	−15.8360	+	8.06883i	−0.662135	+	0.337375i
$573$	31.4861	+	4.98691i	1.31535	+	0.208331i
$574$	10.7581	+	14.8072i	0.449032	+	0.618040i
$575$	−2.71446	−	20.4597i	−0.113201	−	0.853228i
$576$	−1.82380	+	1.32507i	−0.0759918	+	0.0552113i
$577$	4.57678	+	28.8966i	0.190534	+	1.20298i	0.878680	+	0.477411i	$0.158425\pi$
$577$	4.57678	+	28.8966i	0.190534	+	1.20298i	−0.688146	+	0.725572i	$0.741575\pi$
$578$	−13.0902	−	6.66982i	−0.544483	−	0.277428i
$579$	−14.5753	−	10.5896i	−0.605729	−	0.440088i
$580$	2.88412	+	9.27196i	0.119757	+	0.384997i
$581$	17.3408	+	5.63437i	0.719418	+	0.233753i
$582$	29.3930	+	14.9765i	1.21838	+	0.620795i
$583$	−10.9606	+	10.9606i	−0.453941	+	0.453941i
$584$	0.860711			0.0356165
$585$	−3.26130	−	22.4136i	−0.134838	−	0.926688i
$586$	0.918353	−	0.667222i	0.0379368	−	0.0275627i
$587$	17.7838	−	2.81668i	0.734017	−	0.116257i	0.221775	−	0.975098i	$-0.428815\pi$
$587$	17.7838	−	2.81668i	0.734017	−	0.116257i	0.512242	+	0.858841i	$0.328815\pi$
$588$	−21.5905	−	21.5905i	−0.890379	−	0.890379i
$589$	−18.9562	+	16.5251i	−0.781077	+	0.680903i
$590$	−9.19389	−	1.57505i	−0.378506	−	0.0648438i
$591$	−28.1003	−	20.4160i	−1.15589	−	0.839804i
$592$	−1.30785	+	8.25742i	−0.0537522	+	0.339378i
$593$	0.0530063	+	0.0270081i	0.00217671	+	0.00110909i	0.455079	−	0.890451i	$-0.349611\pi$
$593$	0.0530063	+	0.0270081i	0.00217671	+	0.00110909i	−0.452902	+	0.891560i	$0.649611\pi$
$594$		−	6.76091i		−	0.277404i
$595$	−8.84519	−	12.5023i	−0.362617	−	0.512546i
$596$	0.248175	+	0.763803i	0.0101656	+	0.0312866i
$597$	34.5990	−	17.6291i	1.41604	−	0.721511i
$598$	8.42015	+	16.5255i	0.344326	+	0.675777i
$599$	18.6821	−	25.7137i	0.763329	−	1.05063i	−0.233601	−	0.972333i	$-0.575051\pi$
$599$	18.6821	−	25.7137i	0.763329	−	1.05063i	0.996930	−	0.0783000i	$-0.0249492\pi$
$600$	11.4575	+	0.288519i	0.467752	+	0.0117788i
$601$	2.62398	−	3.61160i	0.107034	−	0.147320i	−0.752139	−	0.659004i	$-0.770978\pi$
$601$	2.62398	−	3.61160i	0.107034	−	0.147320i	0.859174	+	0.511684i	$0.170978\pi$
$602$	−7.22331	+	45.6062i	−0.294400	+	1.85877i
$603$	−4.23771	−	8.31698i	−0.172573	−	0.338693i
$604$	10.1537	−	7.37706i	0.413146	−	0.300168i
$605$	−9.84011	−	3.33476i	−0.400057	−	0.135577i
$606$	−27.9427	−	9.07912i	−1.13509	−	0.368814i
$607$	10.1876	+	1.61356i	0.413502	+	0.0654923i	0.359720	−	0.933060i	$-0.382872\pi$
$607$	10.1876	+	1.61356i	0.413502	+	0.0654923i	0.0537823	+	0.998553i	$0.482872\pi$
$608$	4.46108	−	0.706566i	0.180921	−	0.0286550i
$609$	42.6751	−	13.8660i	1.72928	−	0.561877i
$610$	15.4681	+	15.8625i	0.626285	+	0.642254i
$611$	−15.4682	−	5.02592i	−0.625777	−	0.203327i
$612$	1.55500	+	3.05185i	0.0628570	+	0.123364i
$613$	10.9618	−	21.5138i	0.442744	−	0.868933i	−0.556530	−	0.830827i	$-0.687868\pi$
$613$	10.9618	−	21.5138i	0.442744	−	0.868933i	0.999274	−	0.0381057i	$-0.0121324\pi$
$614$			23.4105i			0.944773i
$615$	−3.51404	+	20.5122i	−0.141700	+	0.827130i
$616$	−16.9583	+	5.51007i	−0.683268	+	0.222007i
$617$	−9.79984	−	1.55214i	−0.394527	−	0.0624869i	−0.0439806	−	0.999032i	$-0.514004\pi$
$617$	−9.79984	−	1.55214i	−0.394527	−	0.0624869i	−0.350546	+	0.936546i	$0.614004\pi$
$618$	3.17665	+	20.0566i	0.127784	+	0.806795i
$619$	−28.3211			−1.13832			−0.569160	−	0.822227i	$-0.692732\pi$
$619$	−28.3211			−1.13832			−0.569160	+	0.822227i	$0.692732\pi$
$620$	8.06224	+	9.48685i	0.323787	+	0.381001i
$621$	−7.05529			−0.283119
$622$	−4.24722	−	26.8159i	−0.170298	−	1.07522i
$623$	17.6735	+	2.79921i	0.708075	+	0.112148i
$624$	−9.79537	+	3.18271i	−0.392129	+	0.127410i
$625$	−19.4602	−	15.6940i	−0.778408	−	0.627759i
$626$			8.92330i			0.356647i
$627$	18.5924	−	36.4896i	0.742508	−	1.45725i
$628$	3.99469	+	7.84002i	0.159406	+	0.312851i
$629$	12.0807	+	3.92526i	0.481690	+	0.156511i
$630$	0.286037	−	22.7215i	0.0113960	−	0.905248i
$631$	22.8208	−	7.41493i	0.908483	−	0.295184i	0.182749	−	0.983160i	$-0.441500\pi$
$631$	22.8208	−	7.41493i	0.908483	−	0.295184i	0.725734	+	0.687976i	$0.241500\pi$
$632$	−6.63724	+	1.05124i	−0.264015	+	0.0418159i
$633$	−24.3695	−	3.85976i	−0.968602	−	0.153412i
$634$	−2.10440	−	0.683760i	−0.0835763	−	0.0271556i
$635$	−13.1498	+	6.49296i	−0.521833	+	0.257665i
$636$	−7.26704	+	5.27982i	−0.288157	+	0.209358i
$637$	−27.1720	−	53.3280i	−1.07659	−	2.11293i
$638$	2.68709	−	16.9656i	0.106383	−	0.671675i
$639$	−16.9577	+	23.3403i	−0.670836	+	0.923327i
$640$	−0.321970	−	2.21277i	−0.0127270	−	0.0874673i
$641$	12.0064	−	16.5254i	0.474224	−	0.652713i	−0.503158	−	0.864194i	$-0.667829\pi$
$641$	12.0064	−	16.5254i	0.474224	−	0.652713i	0.977382	+	0.211481i	$0.0678287\pi$
$642$	18.2351	+	35.7883i	0.719680	+	1.41245i
$643$	14.6564	−	7.46779i	0.577990	−	0.294501i	−0.140452	−	0.990088i	$-0.544856\pi$
$643$	14.6564	−	7.46779i	0.577990	−	0.294501i	0.718442	+	0.695587i	$0.244856\pi$
$644$	5.74999	+	17.6966i	0.226581	+	0.697345i
$645$	−42.8607	+	30.3232i	−1.68764	+	1.19397i
$646$		−	6.86250i		−	0.270002i
$647$	−4.72464	−	2.40733i	−0.185745	−	0.0946418i	0.358645	−	0.933474i	$-0.383239\pi$
$647$	−4.72464	−	2.40733i	−0.185745	−	0.0946418i	−0.544390	+	0.838832i	$0.683239\pi$
$648$	1.67087	−	10.5495i	0.0656380	−	0.414422i
$649$	13.3494	+	9.69890i	0.524009	+	0.380715i
$650$	21.1849	+	7.47804i	0.830939	+	0.293313i
$651$	43.3668	−	37.8049i	1.69968	−	1.48169i
$652$	−8.79936	−	8.79936i	−0.344610	−	0.344610i
$653$	−14.3445	+	2.27194i	−0.561344	+	0.0889081i	−0.430657	−	0.902516i	$-0.641718\pi$
$653$	−14.3445	+	2.27194i	−0.561344	+	0.0889081i	−0.130686	+	0.991424i	$0.541718\pi$
$654$	−23.8047	+	17.2951i	−0.930838	+	0.676294i
$655$	−20.6225	+	27.6459i	−0.805790	+	1.08021i
$656$	4.06021			0.158524
$657$	1.37203	−	1.37203i	0.0535279	−	0.0535279i
$658$	−14.5387	−	7.40784i	−0.566778	−	0.288788i
$659$	1.70857	+	0.555148i	0.0665564	+	0.0216255i	0.342106	−	0.939661i	$-0.388860\pi$
$659$	1.70857	+	0.555148i	0.0665564	+	0.0216255i	−0.275550	+	0.961287i	$0.588860\pi$
$660$	−17.9475	−	9.43115i	−0.698606	−	0.367107i
$661$	18.7978	+	13.6574i	0.731149	+	0.531211i	0.889927	−	0.456103i	$-0.150755\pi$
$661$	18.7978	+	13.6574i	0.731149	+	0.531211i	−0.158777	+	0.987314i	$0.550755\pi$
$662$	15.1352	+	7.71179i	0.588248	+	0.299727i
$663$	2.44799	+	15.4560i	0.0950720	+	0.600261i
$664$	3.27231	−	2.37747i	0.126990	−	0.0922637i
$665$	−21.1780	+	40.3018i	−0.821246	+	1.56284i
$666$	11.0781	+	15.2476i	0.429266	+	0.590834i
$667$	−17.7043	−	2.80409i	−0.685514	−	0.108575i
$668$	6.10096	−	3.10859i	0.236053	−	0.120275i
$669$	27.7144	+	38.1456i	1.07150	+	1.47479i
$670$	9.25795	+	0.116547i	0.357666	+	0.00450258i
$671$	−12.1114	−	37.2750i	−0.467555	−	1.43899i
$672$	−10.2058	+	1.61644i	−0.393696	+	0.0623554i
$673$	−38.9098	+	19.8255i	−1.49986	+	0.764217i	−0.995084	−	0.0990325i	$-0.968425\pi$
$673$	−38.9098	+	19.8255i	−1.49986	+	0.764217i	−0.504777	+	0.863250i	$0.668425\pi$
$674$	1.93849	−	5.96606i	0.0746678	−	0.229804i
$675$	−6.19320	+	5.88895i	−0.238376	+	0.226666i
$676$	−7.18881			−0.276493
$677$	7.69790	−	7.69790i	0.295854	−	0.295854i	−0.543533	−	0.839388i	$-0.682914\pi$
$677$	7.69790	−	7.69790i	0.295854	−	0.295854i	0.839388	+	0.543533i	$0.182914\pi$
$678$	−10.0559	+	19.7359i	−0.386196	+	0.757952i
$679$	38.1320	+	52.4842i	1.46337	+	2.01416i
$680$	−3.39713	−	0.0427659i	−0.130274	−	0.00164000i
$681$			38.7786i			1.48600i
$682$	−5.35792	−	21.3620i	−0.205166	−	0.817992i
$683$	26.8917	−	26.8917i	1.02898	−	1.02898i	0.0294160	−	0.999567i	$-0.490635\pi$
$683$	26.8917	−	26.8917i	1.02898	−	1.02898i	0.999567	−	0.0294160i	$-0.00936477\pi$
$684$	5.98494	−	8.23756i	0.228840	−	0.314971i
$685$	36.4651	−	18.0054i	1.39326	−	0.687950i
$686$	−8.80436	−	27.0970i	−0.336152	−	1.03457i
$687$	−44.4844	−	44.4844i	−1.69719	−	1.69719i
$688$	7.24306	+	7.24306i	0.276139	+	0.276139i
$689$	−16.7457	+	5.44100i	−0.637959	+	0.207286i
$690$	−9.84179	+	18.7290i	−0.374671	+	0.713000i
$691$	14.6666	−	45.1392i	0.557944	−	1.71717i	−0.130096	−	0.991501i	$-0.541529\pi$
$691$	14.6666	−	45.1392i	0.557944	−	1.71717i	0.688040	−	0.725673i	$-0.258471\pi$
$692$	−0.663137	−	4.18688i	−0.0252087	−	0.159161i
$693$	−18.2491	+	35.8159i	−0.693227	+	1.36053i
$694$	−11.4791	−	8.34008i	−0.435742	−	0.316585i
$695$	34.2675	+	11.6131i	1.29984	+	0.440509i
$696$	3.07598	−	9.46689i	0.116595	−	0.358842i
$697$	0.965034	−	6.09299i	0.0365533	−	0.230788i
$698$	4.23157	−	26.7171i	0.160167	−	1.01126i
$699$	0.379567	−	1.16819i	0.0143565	−	0.0441848i
$700$	19.8185	+	10.7348i	0.749070	+	0.405739i
$701$	5.50845	+	4.00212i	0.208051	+	0.151158i	0.686932	−	0.726722i	$-0.258957\pi$
$701$	5.50845	+	4.00212i	0.208051	+	0.151158i	−0.478880	+	0.877880i	$0.658957\pi$
$702$	3.48658	−	6.84279i	0.131592	−	0.258265i
$703$	−5.90714	−	37.2962i	−0.222792	−	1.40665i
$704$	−1.22234	+	3.76196i	−0.0460685	+	0.141784i
$705$	−5.51073	−	17.7161i	−0.207546	−	0.667225i
$706$	−33.1515	+	10.7716i	−1.24767	+	0.405394i
$707$	−40.8558	−	40.8558i	−1.53654	−	1.53654i
$708$	6.76145	+	6.76145i	0.254111	+	0.254111i
$709$	0.0358543	+	0.110348i	0.00134654	+	0.00414421i	0.951728	−	0.306944i	$-0.0993065\pi$
$709$	0.0358543	+	0.110348i	0.00134654	+	0.00414421i	−0.950381	+	0.311088i	$0.899306\pi$
$710$	−12.6695	−	25.6588i	−0.475479	−	0.962957i
$711$	−8.90444	+	12.2559i	−0.333943	+	0.459632i
$712$	2.80686	−	2.80686i	0.105192	−	0.105192i
$713$	−22.2921	+	5.59122i	−0.834845	+	0.209393i
$714$			15.6996i			0.587542i
$715$	−27.7458	−	28.4533i	−1.03763	−	1.06409i
$716$	−0.959470	−	1.32060i	−0.0358571	−	0.0493531i
$717$	−15.7810	+	30.9720i	−0.589353	+	1.15667i
$718$	−21.1388	+	21.1388i	−0.788894	+	0.788894i
$719$	42.1400			1.57156			0.785778	−	0.618509i	$-0.212263\pi$
$719$	42.1400			1.57156			0.785778	+	0.618509i	$0.212263\pi$
$720$	−4.04053	−	3.01405i	−0.150582	−	0.112327i
$721$	−12.3403	+	37.9797i	−0.459578	+	1.41444i
$722$	−1.24786	+	0.635818i	−0.0464407	+	0.0236627i
$723$	29.3147	−	4.64300i	1.09023	−	0.172675i
$724$	−1.92706	−	5.93087i	−0.0716185	−	0.220419i
$725$	−17.8816	+	12.3161i	−0.664105	+	0.457409i
$726$	6.26038	+	8.61668i	0.232345	+	0.319795i
$727$	−45.0928	+	22.9759i	−1.67240	+	0.852130i	−0.679432	+	0.733739i	$0.737774\pi$
$727$	−45.0928	+	22.9759i	−1.67240	+	0.852130i	−0.992967	+	0.118391i	$0.962226\pi$
$728$	−20.0052	−	3.16851i	−0.741441	−	0.117433i
$729$	−7.24433	−	9.97097i	−0.268309	−	0.369295i
$730$	0.571649	+	1.83775i	0.0211577	+	0.0680183i
$731$	12.5909	−	9.14783i	0.465691	−	0.338345i
$732$	−3.55300	−	22.4327i	−0.131323	−	0.829138i
$733$	41.8415	+	21.3193i	1.54545	+	0.787446i	0.998755	−	0.0498850i	$-0.0158855\pi$
$733$	41.8415	+	21.3193i	1.54545	+	0.787446i	0.546696	+	0.837331i	$0.315885\pi$
$734$	−12.5953	−	9.15099i	−0.464899	−	0.337769i
$735$	31.7596	−	60.4387i	1.17147	−	2.22932i
$736$	3.92576	+	1.27556i	0.144706	+	0.0470177i
$737$	−14.5933	−	7.43565i	−0.537551	−	0.273896i
$738$	6.47223	−	6.47223i	0.238246	−	0.238246i
$739$	−10.1635			−0.373870			−0.186935	−	0.982372i	$-0.559855\pi$
$739$	−10.1635			−0.373870			−0.186935	+	0.982372i	$0.559855\pi$
$740$	−18.4995	+	2.69178i	−0.680055	+	0.0989518i
$741$	37.6351	−	27.3435i	1.38256	−	1.00449i
$742$	−17.4473	+	2.76338i	−0.640510	+	0.101447i
$743$	−15.9333	−	15.9333i	−0.584535	−	0.584535i	0.351611	−	0.936146i	$-0.385634\pi$
$743$	−15.9333	−	15.9333i	−0.584535	−	0.584535i	−0.936146	+	0.351611i	$0.885634\pi$
$744$	−1.13014	−	12.7125i	−0.0414330	−	0.466063i
$745$	−1.46601	+	1.03718i	−0.0537105	+	0.0379993i
$746$	−6.70152	−	4.86894i	−0.245360	−	0.178265i
$747$	1.42643	−	9.00610i	0.0521902	−	0.329516i
$748$	5.35490	+	2.72846i	0.195794	+	0.0997622i
$749$			78.9892i			2.88620i
$750$	6.99360	+	24.6553i	0.255370	+	0.900284i
$751$	0.420856	+	1.29526i	0.0153573	+	0.0472648i	0.958441	−	0.285289i	$-0.0920896\pi$
$751$	0.420856	+	1.29526i	0.0153573	+	0.0472648i	−0.943084	+	0.332554i	$0.892090\pi$
$752$	−3.22522	+	1.64333i	−0.117612	+	0.0599261i
$753$	−10.6860	−	20.9725i	−0.389420	−	0.764281i
$754$	11.4687	−	15.7854i	0.417667	−	0.574869i
$755$	22.4948	+	16.7801i	0.818670	+	0.610691i
$756$	4.52879	−	6.23335i	0.164711	−	0.226705i
$757$	−6.69539	+	42.2730i	−0.243348	+	1.53644i	0.499105	+	0.866542i	$0.333662\pi$
$757$	−6.69539	+	42.2730i	−0.243348	+	1.53644i	−0.742453	+	0.669898i	$0.766338\pi$
$758$	−2.25944	−	4.43440i	−0.0820665	−	0.161065i
$759$	30.2791	−	21.9991i	1.09906	−	0.798515i
$760$	4.47150	+	9.05584i	0.162198	+	0.328490i
$761$	−5.31495	−	1.72693i	−0.192667	−	0.0626012i	0.211094	−	0.977466i	$-0.432297\pi$
$761$	−5.31495	−	1.72693i	−0.192667	−	0.0626012i	−0.403761	+	0.914864i	$0.632297\pi$
$762$	14.8487	+	2.35181i	0.537913	+	0.0851970i
$763$	−57.1522	+	9.05202i	−2.06905	+	0.327705i
$764$	13.2265	−	4.29756i	0.478519	−	0.155480i
$765$	−5.48342	+	5.34707i	−0.198253	+	0.193324i
$766$	22.0589	+	7.16738i	0.797021	+	0.258968i
$767$	8.50938	+	16.7006i	0.307256	+	0.603023i
$768$	−1.04065	+	2.04240i	−0.0375513	+	0.0736987i
$769$		−	0.344040i		−	0.0124064i	−0.999981	−	0.00620320i	$-0.998025\pi$
$769$		−	0.344040i		−	0.0124064i	0.999981	−	0.00620320i	$-0.00197455\pi$
$770$	−23.0278	−	32.5490i	−0.829866	−	1.17298i
$771$	10.7033	−	3.47772i	0.385471	−	0.125247i
$772$	−7.76284	−	1.22951i	−0.279391	−	0.0442511i
$773$	−3.90863	−	24.6781i	−0.140584	−	0.887611i	−0.952655	−	0.304053i	$-0.901660\pi$
$773$	−3.90863	−	24.6781i	−0.140584	−	0.887611i	0.812071	−	0.583558i	$-0.198340\pi$
$774$	23.0918			0.830017
$775$	−14.9013	+	23.5149i	−0.535270	+	0.844681i
$776$	14.3914			0.516622
$777$	13.5140	+	85.3239i	0.484811	+	3.06098i
$778$	−5.22426	−	0.827442i	−0.187299	−	0.0296652i
$779$	−17.4411	+	5.66697i	−0.624894	+	0.203040i
$780$	−13.3013	−	18.8008i	−0.476262	−	0.673178i
$781$			50.6216i			1.81138i
$782$	2.84726	−	5.58806i	0.101818	−	0.199828i
$783$	3.36966	+	6.61332i	0.120422	+	0.236341i
$784$	−12.6685	−	4.11625i	−0.452447	−	0.147009i
$785$	−14.0866	+	13.7363i	−0.502771	+	0.490270i
$786$	33.6262	−	10.9258i	1.19941	−	0.389711i
$787$	−9.43427	+	1.49424i	−0.336295	+	0.0532640i	−0.322299	−	0.946638i	$-0.604455\pi$
$787$	−9.43427	+	1.49424i	−0.336295	+	0.0532640i	−0.0139969	+	0.999902i	$0.504455\pi$
$788$	−14.9663	−	2.37042i	−0.533151	−	0.0844429i
$789$	14.8732	+	4.83261i	0.529501	+	0.172045i
$790$	−6.65273	−	13.4734i	−0.236694	−	0.479360i
$791$	−35.2404	+	25.6036i	−1.25300	+	0.910360i
$792$	4.04832	+	7.94529i	0.143851	+	0.282323i
$793$	6.96452	−	43.9722i	0.247317	−	1.56150i
$794$	10.3390	−	14.2304i	0.366917	−	0.505018i
$795$	−16.0997	−	12.0096i	−0.570998	−	0.425938i
$796$	9.95732	−	13.7051i	0.352928	−	0.485764i
$797$	−21.8400	−	42.8634i	−0.773612	−	1.51830i	−0.853265	−	0.521477i	$-0.825381\pi$
$797$	−21.8400	−	42.8634i	−0.773612	−	1.51830i	0.0796533	−	0.996823i	$-0.474619\pi$
$798$	41.5841	−	21.1882i	1.47206	−	0.750053i
$799$	1.69951	+	5.23054i	0.0601242	+	0.185043i
$800$	4.51076	−	2.15708i	0.159480	−	0.0762644i
$801$		−	8.94864i		−	0.316185i
$802$	2.37913	+	1.21223i	0.0840099	+	0.0428052i
$803$	0.532596	−	3.36268i	0.0187949	−	0.118666i
$804$	−7.67858	−	5.57882i	−0.270803	−	0.196750i
$805$	−33.9662	+	24.0305i	−1.19715	+	0.846964i
$806$	5.59347	−	24.3837i	0.197021	−	0.858880i
$807$	−14.6988	−	14.6988i	−0.517421	−	0.517421i
$808$	−12.6597	+	2.00509i	−0.445365	+	0.0705390i
$809$	−32.2854	+	23.4567i	−1.13509	+	0.824694i	−0.986428	−	0.164193i	$-0.947498\pi$
$809$	−32.2854	+	23.4567i	−1.13509	+	0.824694i	−0.148666	+	0.988887i	$0.547498\pi$
$810$	23.6345	−	3.43895i	0.830431	−	0.120832i
$811$	14.8320			0.520820			0.260410	−	0.965498i	$-0.416142\pi$
$811$	14.8320			0.520820			0.260410	+	0.965498i	$0.416142\pi$
$812$	13.8418	−	13.8418i	0.485753	−	0.485753i
$813$	−6.76513	−	3.44701i	−0.237263	−	0.120892i
$814$	31.4513	+	10.2192i	1.10237	+	0.358181i
$815$	12.9438	−	24.6322i	0.453403	−	0.862828i
$816$	2.81760	+	2.04710i	0.0986357	+	0.0716630i
$817$	−41.2229	−	21.0041i	−1.44221	−	0.734841i
$818$	−1.10276	−	6.96253i	−0.0385570	−	0.243439i
$819$	−36.9403	+	26.8387i	−1.29080	+	0.937820i
$820$	2.69662	+	8.66918i	0.0941701	+	0.302741i
$821$	19.1006	+	26.2897i	0.666616	+	0.917518i	0.999678	−	0.0253869i	$-0.00808176\pi$
$821$	19.1006	+	26.2897i	0.666616	+	0.917518i	−0.333062	+	0.942905i	$0.608082\pi$
$822$	−41.1764	−	6.52171i	−1.43619	−	0.227471i
$823$	−35.2498	+	17.9607i	−1.22873	+	0.626069i	−0.943176	−	0.332294i	$-0.892178\pi$
$823$	−35.2498	+	17.9607i	−1.22873	+	0.626069i	−0.285554	+	0.958363i	$0.592178\pi$
$824$	5.20711	+	7.16697i	0.181398	+	0.249673i
$825$	8.21698	−	44.5845i	0.286078	−	1.55223i
$826$	5.81092	+	17.8842i	0.202188	+	0.622270i
$827$	3.80734	−	0.603023i	0.132394	−	0.0209692i	−0.0898857	−	0.995952i	$-0.528650\pi$
$827$	3.80734	−	0.603023i	0.132394	−	0.0209692i	0.222280	+	0.974983i	$0.428650\pi$
$828$	8.29123	−	4.22459i	0.288140	−	0.146815i
$829$	12.6101	−	38.8100i	0.437968	−	1.34793i	−0.452046	−	0.891994i	$-0.649306\pi$
$829$	12.6101	−	38.8100i	0.437968	−	1.34793i	0.890014	−	0.455932i	$-0.150694\pi$
$830$	7.24960	+	5.40787i	0.251637	+	0.187710i
$831$	−26.0257			−0.902823
$832$	−3.17717	+	3.17717i	−0.110149	+	0.110149i
$833$	−9.18815	+	18.0328i	−0.318350	+	0.624798i
$834$	−21.8013	−	30.0070i	−0.754919	−	1.03906i
$835$	10.6893	+	10.9619i	0.369920	+	0.379352i
$836$		−	17.8661i		−	0.617910i
$837$	7.29863	+	6.10688i	0.252278	+	0.211085i
$838$	−26.1446	+	26.1446i	−0.903149	+	0.903149i
$839$	−2.13422	+	2.93751i	−0.0736816	+	0.101414i	−0.844267	−	0.535923i	$-0.819964\pi$
$839$	−2.13422	+	2.93751i	−0.0736816	+	0.101414i	0.770586	+	0.637337i	$0.219964\pi$
$840$	−10.2296	−	20.7174i	−0.352955	−	0.714817i
$841$	−3.13421	−	9.64612i	−0.108076	−	0.332625i
$842$	11.3583	+	11.3583i	0.391433	+	0.391433i
$843$	32.6750	+	32.6750i	1.12539	+	1.12539i
$844$	−10.2370	+	3.32622i	−0.352374	+	0.114493i
$845$	−4.77451	−	15.3492i	−0.164248	−	0.528030i
$846$	−2.52163	+	7.76077i	−0.0866953	+	0.266821i
$847$	3.27659	+	20.6876i	0.112585	+	0.710834i
$848$	−1.77905	+	3.49158i	−0.0610928	+	0.119901i
$849$	38.5886	+	28.0363i	1.32436	+	0.962202i
$850$	−2.16492	−	7.28182i	−0.0742563	−	0.249764i
$851$	10.6641	−	32.8208i	0.365561	−	1.12508i
$852$	−4.58902	+	28.9739i	−0.157217	+	0.992630i
$853$	−0.135660	+	0.856523i	−0.00464491	+	0.0293268i	−0.989902	−	0.141754i	$-0.954726\pi$
$853$	−0.135660	+	0.856523i	−0.00464491	+	0.0293268i	0.985257	+	0.171081i	$0.0547259\pi$
$854$	13.8023	−	42.4792i	0.472306	−	1.45361i
$855$	21.5634	+	7.30773i	0.737454	+	0.249919i
$856$	14.1762	+	10.2996i	0.484531	+	0.352032i
$857$	4.38562	−	8.60725i	0.149810	−	0.294018i	−0.803890	−	0.594778i	$-0.797240\pi$
$857$	4.38562	−	8.60725i	0.149810	−	0.294018i	0.953700	+	0.300759i	$0.0972401\pi$
$858$	6.37317	+	40.2386i	0.217576	+	1.37372i
$859$	−0.474007	+	1.45884i	−0.0161729	+	0.0497751i	−0.958817	−	0.284024i	$-0.908331\pi$
$859$	−0.474007	+	1.45884i	−0.0161729	+	0.0497751i	0.942644	+	0.333799i	$0.108331\pi$
$860$	−10.6545	+	20.2756i	−0.363316	+	0.691393i
$861$	39.9007	−	12.9645i	1.35981	−	0.441830i
$862$	2.68261	+	2.68261i	0.0913702	+	0.0913702i
$863$	8.18231	+	8.18231i	0.278529	+	0.278529i	0.832522	−	0.553992i	$-0.186896\pi$
$863$	8.18231	+	8.18231i	0.278529	+	0.278529i	−0.553992	+	0.832522i	$0.686896\pi$
$864$	−0.528177	−	1.62556i	−0.0179689	−	0.0553027i
$865$	8.49922	−	4.19665i	0.288982	−	0.142691i
$866$	0.174099	−	0.239627i	0.00591613	−	0.00814286i
$867$	−23.8128	+	23.8128i	−0.808727	+	0.808727i
$868$	9.36946	−	23.2841i	0.318020	−	0.790313i
$869$			26.5813i			0.901707i
$870$	22.2562	+	0.280179i	0.754557	+	0.00949897i
$871$	−10.9355	−	15.0514i	−0.370535	−	0.509998i
$872$	−5.82764	+	11.4374i	−0.197349	+	0.387319i
$873$	22.9408	−	22.9408i	0.776430	−	0.776430i
$874$	−18.6440			−0.630642
$875$	−9.75793	+	49.4453i	−0.329878	+	1.67156i
$876$	0.609676	−	1.87639i	0.0205990	−	0.0633973i
$877$	−3.13074	+	1.59519i	−0.105718	+	0.0538659i	−0.506050	−	0.862504i	$-0.668895\pi$
$877$	−3.13074	+	1.59519i	−0.105718	+	0.0538659i	0.400332	+	0.916370i	$0.368895\pi$
$878$	−2.00307	+	0.317255i	−0.0676002	+	0.0107068i
$879$	−0.804070	−	2.47467i	−0.0271206	−	0.0834686i
$880$	−8.84420	−	0.111338i	−0.298138	−	0.00375320i
$881$	−4.94661	−	6.80842i	−0.166656	−	0.229382i	0.717518	−	0.696540i	$-0.245278\pi$
$881$	−4.94661	−	6.80842i	−0.166656	−	0.229382i	−0.884174	+	0.467158i	$0.845278\pi$
$882$	−26.7560	+	13.6328i	−0.900920	+	0.459042i
$883$	2.89352	+	0.458288i	0.0973747	+	0.0154226i	0.204932	−	0.978776i	$-0.434303\pi$
$883$	2.89352	+	0.458288i	0.0973747	+	0.0154226i	−0.107557	+	0.994199i	$0.534303\pi$
$884$	4.01270	+	5.52300i	0.134962	+	0.185759i
$885$	−9.94608	+	18.9274i	−0.334334	+	0.636239i
$886$	−27.7791	+	20.1827i	−0.933258	+	0.678052i
$887$	7.71966	+	48.7400i	0.259201	+	1.63653i	0.682746	+	0.730655i	$0.260785\pi$
$887$	7.71966	+	48.7400i	0.259201	+	1.63653i	−0.423545	+	0.905875i	$0.639215\pi$
$888$	17.0752	+	8.70023i	0.573005	+	0.291960i
$889$	23.9185	+	17.3778i	0.802202	+	0.582834i
$890$	7.85730	+	4.12889i	0.263377	+	0.138401i
$891$	−40.1814	−	13.0557i	−1.34613	−	0.437383i
$892$	18.3277	+	9.33843i	0.613657	+	0.312674i
$893$	11.5607	−	11.5607i	0.386864	−	0.386864i
$894$	1.84092			0.0615695
$895$	2.18244	−	2.92571i	0.0729510	−	0.0977956i
$896$	−3.64690	+	2.64963i	−0.121835	+	0.0885180i
$897$	41.9906	−	6.65066i	1.40203	−	0.222059i
$898$	1.59336	+	1.59336i	0.0531710	+	0.0531710i
$899$	15.8878	+	18.2252i	0.529888	+	0.607845i
$900$	3.75191	−	10.6290i	0.125064	−	0.354299i
$901$	4.81682	+	3.49963i	0.160472	+	0.116589i
$902$	2.51240	−	15.8627i	0.0836538	−	0.528169i
$903$	94.3070	+	48.0518i	3.13834	+	1.59907i
$904$			9.66309i			0.321390i
$905$	11.3835	−	8.05361i	0.378399	−	0.267711i
$906$	−8.89010	−	27.3609i	−0.295354	−	0.909005i
$907$	41.5317	−	21.1615i	1.37904	−	0.702655i	0.401984	−	0.915647i	$-0.368321\pi$
$907$	41.5317	−	21.1615i	1.37904	−	0.702655i	0.977054	+	0.212992i	$0.0683209\pi$
$908$	7.68033	+	15.0735i	0.254881	+	0.500231i
$909$	−16.9841	+	23.3765i	−0.563326	+	0.775351i
$910$	−6.52135	−	44.8185i	−0.216180	−	1.48572i
$911$	−3.08517	+	4.24637i	−0.102216	+	0.140688i	−0.857061	−	0.515215i	$-0.827712\pi$
$911$	−3.08517	+	4.24637i	−0.102216	+	0.140688i	0.754845	+	0.655903i	$0.227712\pi$
$912$	1.61962	−	10.2259i	0.0536309	−	0.338612i
$913$	−7.26359	−	14.2556i	−0.240390	−	0.471791i
$914$	−3.69962	+	2.68793i	−0.122373	+	0.0889089i
$915$	45.5377	−	22.4851i	1.50543	−	0.743335i
$916$	−26.1018	−	8.48097i	−0.862426	−	0.280219i
$917$	68.6751	+	10.8771i	2.26785	+	0.359192i
$918$	−2.56495	+	0.406248i	−0.0846560	+	0.0134082i
$919$	−11.2223	+	3.64636i	−0.370191	+	0.120282i	−0.488203	−	0.872730i	$-0.662348\pi$
$919$	−11.2223	+	3.64636i	−0.370191	+	0.120282i	0.118013	+	0.993012i	$0.462348\pi$
$920$	−0.116186	+	9.22929i	−0.00383053	+	0.304281i
$921$	51.0361	+	16.5826i	1.68170	+	0.546416i
$922$	−10.1228	−	19.8671i	−0.333377	−	0.654288i
$923$	−26.1054	+	51.2347i	−0.859269	+	1.68641i
$924$			40.8728i			1.34462i
$925$	−18.0340	−	37.7116i	−0.592954	−	1.23995i
$926$	28.6752	−	9.31713i	0.942325	−	0.306180i
$927$	19.7251	+	3.12414i	0.647856	+	0.102610i
$928$	−0.679320	−	4.28906i	−0.0222998	−	0.140795i
$929$	10.8038			0.354462			0.177231	−	0.984169i	$-0.443286\pi$
$929$	10.8038			0.354462			0.177231	+	0.984169i	$0.443286\pi$
$930$	26.3926	−	10.8561i	0.865446	−	0.355987i
$931$	60.1644			1.97181
$932$	−0.0838260	−	0.529257i	−0.00274581	−	0.0173364i
$933$	−61.4684	−	9.73563i	−2.01238	−	0.318730i
$934$	37.5051	−	12.1862i	1.22721	−	0.398743i
$935$	−2.26918	+	13.2457i	−0.0742101	+	0.433180i
$936$			10.1292i			0.331084i
$937$	22.4228	−	44.0071i	0.732519	−	1.43765i	−0.160222	−	0.987081i	$-0.551221\pi$
$937$	22.4228	−	44.0071i	0.732519	−	1.43765i	0.892741	−	0.450569i	$-0.148779\pi$
$938$	−8.47379	−	16.6307i	−0.276679	−	0.543013i
$939$	19.4532	+	6.32073i	0.634831	+	0.206269i
$940$	−5.65082	−	5.79491i	−0.184310	−	0.189009i
$941$	25.8324	−	8.39347i	0.842114	−	0.273619i	0.143974	−	0.989581i	$-0.454012\pi$
$941$	25.8324	−	8.39347i	0.842114	−	0.273619i	0.698139	+	0.715962i	$0.254012\pi$
$942$	19.9212	−	3.15521i	0.649068	−	0.102802i
$943$	−16.5534	−	2.62179i	−0.539051	−	0.0853773i
$944$	3.96736	+	1.28907i	0.129127	+	0.0419558i
$945$	16.3170	+	5.52975i	0.530792	+	0.179883i
$946$	32.7796	−	23.8157i	1.06576	−	0.774316i
$947$	2.91551	+	5.72201i	0.0947413	+	0.185940i	0.933514	−	0.358542i	$-0.116726\pi$
$947$	2.91551	+	5.72201i	0.0947413	+	0.185940i	−0.838772	+	0.544483i	$0.816726\pi$
$948$	−2.40968	+	15.2141i	−0.0782627	+	0.494131i
$949$	2.27317	−	3.12875i	0.0737902	−	0.101563i
$950$	−16.3659	+	15.5619i	−0.530978	+	0.504893i
$951$	−2.98126	+	4.10335i	−0.0966739	+	0.133060i
$952$	3.10939	+	6.10253i	0.100776	+	0.197784i
$953$	−4.18531	+	2.13252i	−0.135575	+	0.0690791i	−0.520462	−	0.853885i	$-0.674240\pi$
$953$	−4.18531	+	2.13252i	−0.135575	+	0.0690791i	0.384887	+	0.922964i	$0.374240\pi$
$954$	2.72988	+	8.40171i	0.0883832	+	0.272015i
$955$	17.9605	+	25.3865i	0.581188	+	0.821487i
$956$			15.1645i			0.490456i
$957$	−35.0825	−	17.8754i	−1.13405	−	0.577830i
$958$	−0.841339	+	5.31200i	−0.0271824	+	0.171623i
$959$	−66.3276	−	48.1898i	−2.14183	−	1.55613i
$960$	−5.05200	−	0.865482i	−0.163052	−	0.0279333i
$961$	27.9006	+	13.5114i	0.900018	+	0.435852i
$962$	26.5623	+	26.5623i	0.856401	+	0.856401i
$963$	39.0159	−	6.17951i	1.25727	−	0.199132i
$964$	10.4752	−	7.61071i	0.337385	−	0.245124i
$965$	−2.53055	−	17.3915i	−0.0814614	−	0.559851i
$966$	42.6524			1.37232
$967$	−12.4742	+	12.4742i	−0.401143	+	0.401143i	−0.878636	−	0.477493i	$-0.841546\pi$
$967$	−12.4742	+	12.4742i	−0.401143	+	0.401143i	0.477493	+	0.878636i	$0.341546\pi$
$968$	4.14003	+	2.10945i	0.133066	+	0.0678004i
$969$	−14.9606	−	4.86098i	−0.480603	−	0.156157i
$970$	9.55819	+	30.7279i	0.306895	+	0.986615i
$971$	−23.5311	−	17.0964i	−0.755150	−	0.548649i	0.142269	−	0.989828i	$-0.454560\pi$
$971$	−23.5311	−	17.0964i	−0.755150	−	0.548649i	−0.897419	+	0.441179i	$0.854560\pi$
$972$	−17.2460	−	8.78728i	−0.553166	−	0.281852i
$973$	−11.4105	−	72.0430i	−0.365804	−	2.30959i
$974$	24.1940	−	17.5780i	0.775226	−	0.563235i
$975$	31.3086	−	40.8870i	1.00268	−	1.30943i
$976$	−5.82401	−	8.01606i	−0.186422	−	0.256588i
$977$	5.20312	+	0.824093i	0.166462	+	0.0263651i	0.239109	−	0.970993i	$-0.423145\pi$
$977$	5.20312	+	0.824093i	0.166462	+	0.0263651i	−0.0726468	+	0.997358i	$0.523145\pi$
$978$	−25.4159	+	12.9501i	−0.812712	+	0.414098i
$979$	−9.22918	−	12.7029i	−0.294966	−	0.405986i
$980$	0.374934	−	29.7831i	0.0119768	−	0.951386i
$981$	8.94230	+	27.5216i	0.285506	+	0.878696i
$982$	1.65804	−	0.262607i	0.0529101	−	0.00838013i
$983$	12.2330	−	6.23301i	0.390171	−	0.198802i	−0.247889	−	0.968788i	$-0.579737\pi$
$983$	12.2330	−	6.23301i	0.390171	−	0.198802i	0.638061	+	0.769986i	$0.279737\pi$
$984$	2.87601	−	8.85144i	0.0916837	−	0.282174i
$985$	−4.87875	−	33.5297i	−0.155450	−	1.06834i
$986$	−6.59787			−0.210119
$987$	−26.4478	+	26.4478i	−0.841842	+	0.841842i
$988$	9.21346	−	18.0824i	0.293119	−	0.575279i
$989$	−24.8527	−	34.2068i	−0.790270	−	1.08771i
$990$	−14.2757	+	13.9207i	−0.453711	+	0.442430i
$991$			17.9482i			0.570143i	0.958506	+	0.285072i	$0.0920174\pi$
$991$			17.9482i			0.570143i	−0.958506	+	0.285072i	$0.907983\pi$
$992$	−2.95708	−	4.71759i	−0.0938873	−	0.149784i
$993$	27.5329	−	27.5329i	0.873731	−	0.873731i
$994$	−33.9089	+	46.6716i	−1.07552	+	1.48033i
$995$	35.8757	+	12.1581i	1.13734	+	0.385438i
$996$	−2.86509	−	8.81783i	−0.0907838	−	0.279404i
$997$	−0.0587356	−	0.0587356i	−0.00186017	−	0.00186017i	0.706176	−	0.708036i	$-0.250419\pi$
$997$	−0.0587356	−	0.0587356i	−0.00186017	−	0.00186017i	−0.708036	+	0.706176i	$0.750419\pi$
$998$	−23.3378	−	23.3378i	−0.738744	−	0.738744i
$999$	−13.5903	+	4.41574i	−0.429977	+	0.139708i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	310.2.s.a.277.2	yes	128
5.3	odd	4	inner	310.2.s.a.153.7	yes	128
31.15	odd	10	inner	310.2.s.a.77.7	✓	128
155.108	even	20	inner	310.2.s.a.263.2	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
310.2.s.a.77.7	✓	128	31.15	odd	10	inner
310.2.s.a.153.7	yes	128	5.3	odd	4	inner
310.2.s.a.263.2	yes	128	155.108	even	20	inner
310.2.s.a.277.2	yes	128	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 310 = 2 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	310.s (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.156434 - 0.987688i) q^{2} +(-2.26401 - 0.358585i) q^{3} +(-0.951057 + 0.309017i) q^{4} +(-1.29145 - 1.82542i) q^{5} +2.29224i q^{6} +(-2.04651 + 4.01650i) q^{7} +(0.453990 + 0.891007i) q^{8} +(2.14401 + 0.696631i) q^{9} +O(q^{10})\)	\(q+(-0.156434 - 0.987688i) q^{2} +(-2.26401 - 0.358585i) q^{3} +(-0.951057 + 0.309017i) q^{4} +(-1.29145 - 1.82542i) q^{5} +2.29224i q^{6} +(-2.04651 + 4.01650i) q^{7} +(0.453990 + 0.891007i) q^{8} +(2.14401 + 0.696631i) q^{9} +(-1.60092 + 1.56111i) q^{10} +(3.76196 - 1.22234i) q^{11} +(2.26401 - 0.358585i) q^{12} +(4.43788 + 0.702891i) q^{13} +(4.28719 + 1.39299i) q^{14} +(2.26930 + 4.59587i) q^{15} +(0.809017 - 0.587785i) q^{16} +(-0.689777 - 1.35376i) q^{17} +(0.352657 - 2.22659i) q^{18} +(-2.65485 + 3.65408i) q^{19} +(1.79233 + 1.33700i) q^{20} +(6.07358 - 8.35957i) q^{21} +(-1.79579 - 3.52443i) q^{22} +(-3.67789 + 1.87398i) q^{23} +(-0.708340 - 2.18005i) q^{24} +(-1.66430 + 4.71488i) q^{25} -4.49320i q^{26} +(1.52292 + 0.775968i) q^{27} +(0.705179 - 4.45232i) q^{28} +(3.51317 + 2.55247i) q^{29} +(4.18429 - 2.96031i) q^{30} +(5.42681 + 1.24487i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(-8.95545 + 1.41840i) q^{33} +(-1.22919 + 0.893060i) q^{34} +(9.97476 - 1.45138i) q^{35} -2.25435 q^{36} +(-5.91166 + 5.91166i) q^{37} +(4.02440 + 2.05054i) q^{38} +(-9.79537 - 3.18271i) q^{39} +(1.04015 - 1.97941i) q^{40} +(3.28478 + 2.38653i) q^{41} +(-9.20676 - 4.69108i) q^{42} +(1.60240 + 10.1171i) q^{43} +(-3.20012 + 2.32502i) q^{44} +(-1.49724 - 4.81338i) q^{45} +(2.42626 + 3.33945i) q^{46} +(-3.57518 - 0.566253i) q^{47} +(-2.04240 + 1.04065i) q^{48} +(-7.82957 - 10.7765i) q^{49} +(4.91719 + 0.906243i) q^{50} +(1.07623 + 3.31229i) q^{51} +(-4.43788 + 0.702891i) q^{52} +(-3.49158 + 1.77905i) q^{53} +(0.528177 - 1.62556i) q^{54} +(-7.08967 - 5.28857i) q^{55} -4.50782 q^{56} +(7.32091 - 7.32091i) q^{57} +(1.97146 - 3.86921i) q^{58} +(2.45196 + 3.37484i) q^{59} +(-3.57843 - 3.66968i) q^{60} -9.90839i q^{61} +(0.380608 - 5.55474i) q^{62} +(-7.18575 + 7.18575i) q^{63} +(-0.587785 + 0.809017i) q^{64} +(-4.44824 - 9.00873i) q^{65} +(2.80188 + 8.62331i) q^{66} +(-2.92785 - 2.92785i) q^{67} +(1.07435 + 1.07435i) q^{68} +(8.99878 - 2.92388i) q^{69} +(-2.99391 - 9.62491i) q^{70} +(-3.95467 + 12.1712i) q^{71} +(0.352657 + 2.22659i) q^{72} +(0.390755 - 0.766899i) q^{73} +(6.76367 + 4.91409i) q^{74} +(5.45869 - 10.0778i) q^{75} +(1.39573 - 4.29563i) q^{76} +(-2.78938 + 17.6114i) q^{77} +(-1.61119 + 10.1727i) q^{78} +(-2.07659 + 6.39107i) q^{79} +(-2.11776 - 0.717698i) q^{80} +(-8.64108 - 6.27811i) q^{81} +(1.84330 - 3.61767i) q^{82} +(-0.632745 - 3.99499i) q^{83} +(-3.19307 + 9.82726i) q^{84} +(-1.58037 + 3.00745i) q^{85} +(9.74190 - 3.16533i) q^{86} +(-7.03860 - 7.03860i) q^{87} +(2.79700 + 2.79700i) q^{88} +(-1.22664 - 3.77522i) q^{89} +(-4.51990 + 2.23179i) q^{90} +(-11.9053 + 16.3863i) q^{91} +(2.91879 - 2.91879i) q^{92} +(-11.8400 - 4.76439i) q^{93} +3.61975i q^{94} +(10.0988 + 0.127132i) q^{95} +(1.34734 + 1.85446i) q^{96} +(6.53357 - 12.8229i) q^{97} +(-9.41899 + 9.41899i) q^{98} +8.91720 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q + 12 q^{7}+O(q^{10}) \) 128 * q + 12 * q^7	\( 128 q + 12 q^{7} + 8 q^{10} + 32 q^{16} + 8 q^{20} - 80 q^{21} - 20 q^{22} - 20 q^{23} + 40 q^{25} + 8 q^{28} - 32 q^{31} + 20 q^{33} - 48 q^{35} - 128 q^{36} + 52 q^{38} + 8 q^{41} - 20 q^{42} + 64 q^{45} - 40 q^{46} - 20 q^{47} - 20 q^{48} + 24 q^{50} - 16 q^{51} - 40 q^{53} - 40 q^{55} + 20 q^{60} - 8 q^{62} + 256 q^{63} - 160 q^{65} + 56 q^{66} + 8 q^{67} - 32 q^{70} + 56 q^{71} - 80 q^{73} - 160 q^{75} + 48 q^{76} - 20 q^{77} + 4 q^{78} - 96 q^{81} + 16 q^{82} - 240 q^{83} + 120 q^{85} + 40 q^{87} - 64 q^{90} + 80 q^{91} - 160 q^{93} + 32 q^{95} - 56 q^{97} - 176 q^{98}+O(q^{100}) \) 128 * q + 12 * q^7 + 8 * q^10 + 32 * q^16 + 8 * q^20 - 80 * q^21 - 20 * q^22 - 20 * q^23 + 40 * q^25 + 8 * q^28 - 32 * q^31 + 20 * q^33 - 48 * q^35 - 128 * q^36 + 52 * q^38 + 8 * q^41 - 20 * q^42 + 64 * q^45 - 40 * q^46 - 20 * q^47 - 20 * q^48 + 24 * q^50 - 16 * q^51 - 40 * q^53 - 40 * q^55 + 20 * q^60 - 8 * q^62 + 256 * q^63 - 160 * q^65 + 56 * q^66 + 8 * q^67 - 32 * q^70 + 56 * q^71 - 80 * q^73 - 160 * q^75 + 48 * q^76 - 20 * q^77 + 4 * q^78 - 96 * q^81 + 16 * q^82 - 240 * q^83 + 120 * q^85 + 40 * q^87 - 64 * q^90 + 80 * q^91 - 160 * q^93 + 32 * q^95 - 56 * q^97 - 176 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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