LMFDB - Embedded newform 310.2.s.a.77.7

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			77.7
Character	$\chi$	$=$	310.77
Dual form			310.2.s.a.153.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.987688 - 0.156434i) q^{2} +(0.358585 + 2.26401i) q^{3} +(0.951057 + 0.309017i) q^{4} +(-1.29145 - 1.82542i) q^{5} -2.29224i q^{6} +(4.01650 - 2.04651i) q^{7} +(-0.891007 - 0.453990i) q^{8} +(-2.14401 + 0.696631i) q^{9} +O(q^{10})$	\(q+(-0.987688 - 0.156434i) q^{2} +(0.358585 + 2.26401i) q^{3} +(0.951057 + 0.309017i) q^{4} +(-1.29145 - 1.82542i) q^{5} -2.29224i q^{6} +(4.01650 - 2.04651i) q^{7} +(-0.891007 - 0.453990i) q^{8} +(-2.14401 + 0.696631i) q^{9} +(0.989994 + 2.00497i) q^{10} +(3.76196 + 1.22234i) q^{11} +(-0.358585 + 2.26401i) q^{12} +(-0.702891 - 4.43788i) q^{13} +(-4.28719 + 1.39299i) q^{14} +(3.66968 - 3.57843i) q^{15} +(0.809017 + 0.587785i) q^{16} +(-1.35376 - 0.689777i) q^{17} +(2.22659 - 0.352657i) q^{18} +(2.65485 + 3.65408i) q^{19} +(-0.664159 - 2.13516i) q^{20} +(6.07358 + 8.35957i) q^{21} +(-3.52443 - 1.79579i) q^{22} +(-1.87398 + 3.67789i) q^{23} +(0.708340 - 2.18005i) q^{24} +(-1.66430 + 4.71488i) q^{25} +4.49320i q^{26} +(0.775968 + 1.52292i) q^{27} +(4.45232 - 0.705179i) 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} +(-1.41840 + 8.95545i) q^{33} +(1.22919 + 0.893060i) q^{34} +(-8.92285 - 4.68882i) q^{35} -2.25435 q^{36} +(5.91166 - 5.91166i) q^{37} +(-2.05054 - 4.02440i) q^{38} +(9.79537 - 3.18271i) q^{39} +(0.321970 + 2.21277i) q^{40} +(3.28478 - 2.38653i) q^{41} +(-4.69108 - 9.20676i) q^{42} +(-10.1171 - 1.60240i) q^{43} +(3.20012 + 2.32502i) q^{44} +(4.04053 + 3.01405i) q^{45} +(2.42626 - 3.33945i) q^{46} +(-0.566253 - 3.57518i) q^{47} +(-1.04065 + 2.04240i) q^{48} +(7.82957 - 10.7765i) q^{49} +(2.38138 - 4.39648i) q^{50} +(1.07623 - 3.31229i) q^{51} +(0.702891 - 4.43788i) q^{52} +(-1.77905 + 3.49158i) q^{53} +(-0.528177 - 1.62556i) q^{54} +(-2.62712 - 8.44574i) q^{55} -4.50782 q^{56} +(-7.32091 + 7.32091i) q^{57} +(3.86921 - 1.97146i) q^{58} +(-2.45196 + 3.37484i) q^{59} +(4.59587 - 2.26930i) q^{60} +9.90839i q^{61} +(-5.55474 + 0.380608i) q^{62} +(-7.18575 + 7.18575i) q^{63} +(0.587785 + 0.809017i) q^{64} +(-7.19323 + 7.01438i) 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} +(8.07950 + 6.02694i) q^{70} +(-3.95467 - 12.1712i) q^{71} +(2.22659 + 0.352657i) q^{72} +(0.766899 - 0.390755i) q^{73} +(-6.76367 + 4.91409i) q^{74} +(-11.2714 - 2.07732i) q^{75} +(1.39573 + 4.29563i) q^{76} +(17.6114 - 2.78938i) q^{77} +(-10.1727 + 1.61119i) q^{78} +(2.07659 + 6.39107i) q^{79} +(0.0281472 - 2.23589i) q^{80} +(-8.64108 + 6.27811i) q^{81} +(-3.61767 + 1.84330i) q^{82} +(3.99499 + 0.632745i) q^{83} +(3.19307 + 9.82726i) q^{84} +(0.489189 + 3.36200i) 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} +(-3.51928 - 3.60902i) q^{90} +(-11.9053 - 16.3863i) q^{91} +(-2.91879 + 2.91879i) q^{92} +(4.76439 + 11.8400i) q^{93} +3.61975i q^{94} +(3.24162 - 9.56527i) q^{95} +(1.34734 - 1.85446i) q^{96} +(-12.8229 + 6.53357i) 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 $\left(\mathbb{Z}/310\mathbb{Z}\right)^\times$.

$n$	$187$	$251$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{7}{10}\right)$

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 $

$2$	−0.987688	−	0.156434i	−0.698401	−	0.110616i
$2$	−0.987688	−	0.156434i	−0.698401	−	0.110616i
$3$	0.358585	+	2.26401i	0.207029	+	1.30713i	0.844042	+	0.536277i	$0.180170\pi$
$3$	0.358585	+	2.26401i	0.207029	+	1.30713i	−0.637013	+	0.770853i	$0.719830\pi$
$4$	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
$7$	4.01650	−	2.04651i	1.51809	−	0.773507i	0.521289	−	0.853380i	$-0.325451\pi$
$7$	4.01650	−	2.04651i	1.51809	−	0.773507i	0.996805	+	0.0798729i	$0.0254514\pi$
$8$	−0.891007	−	0.453990i	−0.315018	−	0.160510i
$9$	−2.14401	+	0.696631i	−0.714670	+	0.232210i
$10$	0.989994	+	2.00497i	0.313064	+	0.634028i
$11$	3.76196	+	1.22234i	1.13427	+	0.368548i	0.815199	−	0.579181i	$-0.196628\pi$
$11$	3.76196	+	1.22234i	1.13427	+	0.368548i	0.319076	+	0.947729i	$0.396628\pi$
$12$	−0.358585	+	2.26401i	−0.103514	+	0.653565i
$13$	−0.702891	−	4.43788i	−0.194947	−	1.23085i	−0.869991	−	0.493068i	$-0.835875\pi$
$13$	−0.702891	−	4.43788i	−0.194947	−	1.23085i	0.675044	−	0.737778i	$-0.264125\pi$
$14$	−4.28719	+	1.39299i	−1.14580	+	0.372293i
$15$	3.66968	−	3.57843i	0.947507	−	0.923948i
$16$	0.809017	+	0.587785i	0.202254	+	0.146946i
$17$	−1.35376	−	0.689777i	−0.328336	−	0.167296i	0.282050	−	0.959400i	$-0.408986\pi$
$17$	−1.35376	−	0.689777i	−0.328336	−	0.167296i	−0.610386	+	0.792104i	$0.708986\pi$
$18$	2.22659	−	0.352657i	0.524812	−	0.0831221i
$19$	2.65485	+	3.65408i	0.609063	+	0.838304i	0.996500	−	0.0835926i	$-0.0266395\pi$
$19$	2.65485	+	3.65408i	0.609063	+	0.838304i	−0.387437	+	0.921896i	$0.626639\pi$
$20$	−0.664159	−	2.13516i	−0.148510	−	0.477436i
$21$	6.07358	+	8.35957i	1.32536	+	1.82421i
$22$	−3.52443	−	1.79579i	−0.751411	−	0.382863i
$23$	−1.87398	+	3.67789i	−0.390752	+	0.766893i	−0.999653	−	0.0263531i	$-0.991611\pi$
$23$	−1.87398	+	3.67789i	−0.390752	+	0.766893i	0.608901	+	0.793246i	$0.291611\pi$
$24$	0.708340	−	2.18005i	0.144589	−	0.445000i
$25$	−1.66430	+	4.71488i	−0.332861	+	0.942976i
$26$			4.49320i			0.881188i
$27$	0.775968	+	1.52292i	0.149335	+	0.293087i
$28$	4.45232	−	0.705179i	0.841410	−	0.133266i
$29$	−3.51317	+	2.55247i	−0.652380	+	0.473982i	−0.864081	−	0.503353i	$-0.832100\pi$
$29$	−3.51317	+	2.55247i	−0.652380	+	0.473982i	0.211701	+	0.977334i	$0.432100\pi$
$30$	−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
$33$	−1.41840	+	8.95545i	−0.246912	+	1.55894i
$34$	1.22919	+	0.893060i	0.210805	+	0.153159i
$35$	−8.92285	−	4.68882i	−1.50824	−	0.792556i
$36$	−2.25435			−0.375724
$37$	5.91166	−	5.91166i	0.971871	−	0.971871i	−0.0277441	−	0.999615i	$-0.508832\pi$
$37$	5.91166	−	5.91166i	0.971871	−	0.971871i	0.999615	+	0.0277441i	$0.00883234\pi$
$38$	−2.05054	−	4.02440i	−0.332641	−	0.652844i
$39$	9.79537	−	3.18271i	1.56852	−	0.509641i
$40$	0.321970	+	2.21277i	0.0509079	+	0.349869i
$41$	3.28478	−	2.38653i	0.512996	−	0.372713i	−0.300963	−	0.953636i	$-0.597308\pi$
$41$	3.28478	−	2.38653i	0.512996	−	0.372713i	0.813959	+	0.580922i	$0.197308\pi$
$42$	−4.69108	−	9.20676i	−0.723849	−	1.42063i
$43$	−10.1171	−	1.60240i	−1.54285	−	0.244363i	−0.673733	−	0.738975i	$-0.735310\pi$
$43$	−10.1171	−	1.60240i	−1.54285	−	0.244363i	−0.869114	+	0.494612i	$0.835310\pi$
$44$	3.20012	+	2.32502i	0.482436	+	0.350510i
$45$	4.04053	+	3.01405i	0.602326	+	0.449308i
$46$	2.42626	−	3.33945i	0.357732	−	0.492376i
$47$	−0.566253	−	3.57518i	−0.0825965	−	0.521494i	−0.993947	−	0.109862i	$-0.964959\pi$
$47$	−0.566253	−	3.57518i	−0.0825965	−	0.521494i	0.911350	−	0.411632i	$-0.135041\pi$
$48$	−1.04065	+	2.04240i	−0.150205	+	0.294795i
$49$	7.82957	−	10.7765i	1.11851	−	1.53950i
$50$	2.38138	−	4.39648i	0.336778	−	0.621756i
$51$	1.07623	−	3.31229i	0.150702	−	0.463813i
$52$	0.702891	−	4.43788i	0.0974734	−	0.615423i
$53$	−1.77905	+	3.49158i	−0.244371	+	0.479605i	−0.980316	−	0.197437i	$-0.936738\pi$
$53$	−1.77905	+	3.49158i	−0.244371	+	0.479605i	0.735945	+	0.677042i	$0.236738\pi$
$54$	−0.528177	−	1.62556i	−0.0718758	−	0.221211i
$55$	−2.62712	−	8.44574i	−0.354241	−	1.13882i
$56$	−4.50782			−0.602383
$57$	−7.32091	+	7.32091i	−0.969678	+	0.969678i
$58$	3.86921	−	1.97146i	0.508053	−	0.258866i
$59$	−2.45196	+	3.37484i	−0.319219	+	0.439367i	−0.938228	−	0.346017i	$-0.887534\pi$
$59$	−2.45196	+	3.37484i	−0.319219	+	0.439367i	0.619010	+	0.785383i	$0.287534\pi$
$60$	4.59587	−	2.26930i	0.593324	−	0.292965i
$61$			9.90839i			1.26864i	0.773071	+	0.634320i	$0.218720\pi$
$61$			9.90839i			1.26864i	−0.773071	+	0.634320i	$0.781280\pi$
$62$	−5.55474	+	0.380608i	−0.705453	+	0.0483373i
$63$	−7.18575	+	7.18575i	−0.905320	+	0.905320i
$64$	0.587785	+	0.809017i	0.0734732	+	0.101127i
$65$	−7.19323	+	7.01438i	−0.892211	+	0.870026i
$66$	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
$70$	8.07950	+	6.02694i	0.965685	+	0.720357i
$71$	−3.95467	−	12.1712i	−0.469333	−	1.44446i	−0.853450	−	0.521174i	$-0.825494\pi$
$71$	−3.95467	−	12.1712i	−0.469333	−	1.44446i	0.384117	−	0.923284i	$-0.374506\pi$
$72$	2.22659	+	0.352657i	0.262406	+	0.0415611i
$73$	0.766899	−	0.390755i	0.0897588	−	0.0457344i	−0.408535	−	0.912743i	$-0.633960\pi$
$73$	0.766899	−	0.390755i	0.0897588	−	0.0457344i	0.498294	+	0.867008i	$0.333960\pi$
$74$	−6.76367	+	4.91409i	−0.786260	+	0.571251i
$75$	−11.2714	−	2.07732i	−1.30150	−	0.239869i
$76$	1.39573	+	4.29563i	0.160102	+	0.492743i
$77$	17.6114	−	2.78938i	2.00701	−	0.317879i
$78$	−10.1727	+	1.61119i	−1.15183	+	0.182432i
$79$	2.07659	+	6.39107i	0.233634	+	0.719052i	0.997300	+	0.0734398i	$0.0233977\pi$
$79$	2.07659	+	6.39107i	0.233634	+	0.719052i	−0.763666	+	0.645612i	$0.776602\pi$
$80$	0.0281472	−	2.23589i	0.00314695	−	0.249980i
$81$	−8.64108	+	6.27811i	−0.960120	+	0.697568i
$82$	−3.61767	+	1.84330i	−0.399505	+	0.203558i
$83$	3.99499	+	0.632745i	0.438508	+	0.0694528i	0.371785	−	0.928319i	$-0.378746\pi$
$83$	3.99499	+	0.632745i	0.438508	+	0.0694528i	0.0667224	+	0.997772i	$0.478746\pi$
$84$	3.19307	+	9.82726i	0.348392	+	1.07224i
$85$	0.489189	+	3.36200i	0.0530600	+	0.364660i
$86$	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	$-0.832529\pi$
$89$	1.22664	−	3.77522i	0.130024	−	0.400173i	0.994783	+	0.102014i	$0.0325288\pi$
$90$	−3.51928	−	3.60902i	−0.370965	−	0.380424i
$91$	−11.9053	−	16.3863i	−1.24802	−	1.71775i
$92$	−2.91879	+	2.91879i	−0.304305	+	0.304305i
$93$	4.76439	+	11.8400i	0.494044	+	1.22775i
$94$			3.61975i			0.373348i
$95$	3.24162	−	9.56527i	0.332583	−	0.981376i
$96$	1.34734	−	1.85446i	0.137513	−	0.189270i
$97$	−12.8229	+	6.53357i	−1.30196	+	0.663384i	−0.960962	−	0.276679i	$-0.910766\pi$
$97$	−12.8229	+	6.53357i	−1.30196	+	0.663384i	−0.341001	+	0.940063i	$0.610766\pi$
$98$	−9.41899	+	9.41899i	−0.951461	+	0.951461i
$99$	−8.91720			−0.896213
$100$	−3.03982	+	3.96982i	−0.303982	+	0.396982i
$101$	−3.96082	−	12.1901i	−0.394116	−	1.21296i	−0.929648	−	0.368449i	$-0.879889\pi$
$101$	−3.96082	−	12.1901i	−0.394116	−	1.21296i	0.535532	−	0.844515i	$-0.320111\pi$
$102$	−1.58113	+	3.10315i	−0.156555	+	0.307257i
$103$	1.38583	−	8.74980i	0.136550	−	0.862143i	−0.820379	−	0.571820i	$-0.806237\pi$
$103$	1.38583	−	8.74980i	0.136550	−	0.862143i	0.956929	−	0.290323i	$-0.0937626\pi$
$104$	−1.38847	+	4.27328i	−0.136151	+	0.419030i
$105$	7.41597	−	21.8828i	0.723724	−	2.13554i
$106$	2.30335	−	3.17029i	0.223721	−	0.307925i
$107$	−7.95514	+	15.6128i	−0.769052	+	1.50935i	0.0891387	+	0.996019i	$0.471589\pi$
$107$	−7.95514	+	15.6128i	−0.769052	+	1.50935i	−0.858191	+	0.513331i	$0.828411\pi$
$108$	0.267380	+	1.68817i	0.0257287	+	0.162445i
$109$	−7.54510	+	10.3849i	−0.722689	+	0.994697i	0.276741	+	0.960945i	$0.410746\pi$
$109$	−7.54510	+	10.3849i	−0.722689	+	0.994697i	−0.999430	+	0.0337520i	$0.989254\pi$
$110$	1.27357	+	8.75273i	0.121430	+	0.834540i
$111$	15.5039	+	11.2643i	1.47157	+	1.06916i
$112$	4.45232	+	0.705179i	0.420705	+	0.0666331i
$113$	−4.38695	−	8.60988i	−0.412690	−	0.809949i	−1.00000		0.000587215i	$-0.999813\pi$
$113$	−4.38695	−	8.60988i	−0.412690	−	0.809949i	0.587310	−	0.809362i	$-0.300187\pi$
$114$	8.37602	−	6.08553i	0.784486	−	0.569962i
$115$	9.13384	−	1.32902i	0.851735	−	0.123932i
$116$	−4.12998	+	1.34191i	−0.383459	+	0.124593i
$117$	4.59857	+	9.02520i	0.425138	+	0.834380i
$118$	2.94972	−	2.94972i	0.271544	−	0.271544i
$119$	−6.84903			−0.627849
$120$	−4.89428	+	1.52241i	−0.446785	+	0.138976i
$121$	3.75907	+	2.73113i	0.341734	+	0.248284i
$122$	1.55001	−	9.78640i	0.140332	−	0.886019i
$123$	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
$127$	−6.47784	+	1.02599i	−0.574815	+	0.0910417i	−0.437072	−	0.899426i	$-0.643985\pi$
$127$	−6.47784	+	1.02599i	−0.574815	+	0.0910417i	−0.137743	+	0.990468i	$0.543985\pi$
$128$	−0.453990	−	0.891007i	−0.0401275	−	0.0787546i
$129$		−	23.4799i		−	2.06729i
$130$	8.20196	−	5.80275i	0.719360	−	0.508935i
$131$	−4.76645	+	14.6696i	−0.416446	+	1.28169i	0.494504	+	0.869175i	$0.335350\pi$
$131$	−4.76645	+	14.6696i	−0.416446	+	1.28169i	−0.910951	+	0.412515i	$0.864650\pi$
$132$	−4.11637	+	8.07883i	−0.358284	+	0.703172i
$133$	18.1413	+	9.24345i	1.57305	+	0.801509i
$134$	2.43379	+	3.34982i	0.210247	+	0.289381i
$135$	1.77785	−	3.38325i	0.153013	−	0.291184i
$136$	0.893060	+	1.22919i	0.0765793	+	0.105402i
$137$	17.9634	−	2.84513i	1.53472	−	0.243076i	0.668870	−	0.743379i	$-0.266778\pi$
$137$	17.9634	−	2.84513i	1.53472	−	0.243076i	0.865850	+	0.500303i	$0.166778\pi$
$138$	8.43059	+	4.29560i	0.717660	+	0.365666i
$139$	13.0907	+	9.51095i	1.11034	+	0.806708i	0.982717	−	0.185114i	$-0.0592656\pi$
$139$	13.0907	+	9.51095i	1.11034	+	0.806708i	0.127622	+	0.991823i	$0.459266\pi$
$140$	−7.03721	−	7.21665i	−0.594753	−	0.609918i
$141$	7.89121	−	2.56401i	0.664560	−	0.215929i
$142$	2.00198	+	12.6400i	0.168003	+	1.06073i
$143$	2.78033	−	17.5543i	0.232503	−	1.46796i
$144$	−2.14401	−	0.696631i	−0.178667	−	0.0580526i
$145$	9.19642	+	3.11662i	0.763721	+	0.258821i
$146$	−0.818585	+	0.265974i	−0.0677466	+	0.0220122i
$147$	27.2057	+	13.8620i	2.24389	+	1.14332i
$148$	7.44913	−	3.79552i	0.612314	−	0.311990i
$149$		−	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	−0.219998	−	0.975500i	$-0.570605\pi$
$151$	−11.9363	−	3.87835i	−0.971366	−	0.315616i	−0.751367	+	0.659884i	$0.770605\pi$
$152$	−0.706566	−	4.46108i	−0.0573101	−	0.361842i
$153$	3.38300	+	0.535815i	0.273500	+	0.0433181i
$154$	−17.8310			−1.43686
$155$	−9.28088	−	8.29850i	−0.745459	−	0.666552i
$156$	10.2995			0.824617
$157$	−8.69073	−	1.37648i	−0.693596	−	0.109855i	−0.200324	−	0.979730i	$-0.564199\pi$
$157$	−8.69073	−	1.37648i	−0.693596	−	0.109855i	−0.493272	+	0.869875i	$0.664199\pi$
$158$	−1.05124	−	6.63724i	−0.0836318	−	0.528030i
$159$	−8.54292	−	2.77576i	−0.677498	−	0.220132i
$160$	−0.377571	+	2.20396i	−0.0298496	+	0.174238i
$161$			18.6074i			1.46646i
$162$	9.51681	−	4.84906i	0.747711	−	0.380978i
$163$	−11.0878	−	5.64954i	−0.868467	−	0.442506i	−0.0378062	−	0.999285i	$-0.512037\pi$
$163$	−11.0878	−	5.64954i	−0.868467	−	0.442506i	−0.830661	+	0.556779i	$0.812037\pi$
$164$	3.86149	−	1.25467i	0.301531	−	0.0979735i
$165$	18.1792	−	8.97635i	1.41525	−	0.698808i
$166$	−3.84683	−	1.24991i	−0.298572	−	0.0970118i
$167$	1.07115	−	6.76296i	0.0828879	−	0.523334i	−0.910952	−	0.412512i	$-0.864652\pi$
$167$	1.07115	−	6.76296i	0.0828879	−	0.523334i	0.993840	−	0.110822i	$-0.0353484\pi$
$168$	−1.61644	−	10.2058i	−0.124711	−	0.787393i
$169$	−6.83697	+	2.22147i	−0.525921	+	0.170882i
$170$	0.0427659	−	3.39713i	0.00327999	−	0.260548i
$171$	−8.23756	−	5.98494i	−0.629942	−	0.457680i
$172$	−9.12679	−	4.65033i	−0.695911	−	0.354585i
$173$	−4.18688	+	0.663137i	−0.318323	+	0.0504174i	−0.313551	−	0.949571i	$-0.601519\pi$
$173$	−4.18688	+	0.663137i	−0.318323	+	0.0504174i	−0.00477139	+	0.999989i	$0.501519\pi$
$174$	5.85086	+	8.05302i	0.443553	+	0.610498i
$175$	2.96437	+	22.3433i	0.224085	+	1.68900i
$176$	2.32502	+	3.20012i	0.175255	+	0.241218i
$177$	−8.51992	−	4.34112i	−0.640397	−	0.326298i
$178$	−1.80212	+	3.53686i	−0.135074	+	0.265099i
$179$	−0.504423	+	1.55246i	−0.0377024	+	0.116036i	−0.968136	−	0.250423i	$-0.919430\pi$
$179$	−0.504423	+	1.55246i	−0.0377024	+	0.116036i	0.930434	+	0.366459i	$0.119430\pi$
$180$	2.91138	+	4.11512i	0.217001	+	0.306723i
$181$		−	6.23609i		−	0.463525i	−0.972772	−	0.231762i	$-0.925551\pi$
$181$		−	6.23609i		−	0.463525i	0.972772	−	0.231762i	$-0.0744491\pi$
$182$	9.19536	+	18.0469i	0.681606	+	1.33773i
$183$	−22.4327	+	3.55300i	−1.65828	+	0.262645i
$184$	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
$188$	0.566253	−	3.57518i	0.0412983	−	0.260747i
$189$	6.23335	+	4.52879i	0.453409	+	0.329421i
$190$	−4.69805	+	8.94041i	−0.340832	+	0.648605i
$191$	−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
$193$	−3.56819	−	7.00296i	−0.256844	−	0.504084i	0.726194	−	0.687490i	$-0.241288\pi$
$193$	−3.56819	−	7.00296i	−0.256844	−	0.504084i	−0.983037	+	0.183406i	$0.941288\pi$
$194$	13.6871	−	4.44720i	0.982674	−	0.319290i
$195$	−18.4600	−	13.7703i	−1.32195	−	0.986114i
$196$	10.7765	−	7.82957i	0.769748	−	0.559255i
$197$	6.87924	+	13.5013i	0.490126	+	0.961926i	0.995108	+	0.0987958i	$0.0314991\pi$
$197$	6.87924	+	13.5013i	0.490126	+	0.961926i	−0.504982	+	0.863130i	$0.668501\pi$
$198$	8.80742	+	1.39496i	0.625916	+	0.0991353i
$199$	13.7051	+	9.95732i	0.971527	+	0.705856i	0.955799	−	0.294020i	$-0.0949934\pi$
$199$	13.7051	+	9.95732i	0.971527	+	0.705856i	0.0157282	+	0.999876i	$0.494993\pi$
$200$	3.62342	−	3.44541i	0.256214	−	0.243627i
$201$	5.57882	−	7.67858i	0.393499	−	0.541605i
$202$	2.00509	+	12.6597i	0.141078	+	0.890731i
$203$	−8.88700	+	17.4417i	−0.623745	+	1.22417i
$204$	2.04710	−	2.81760i	0.143326	−	0.197271i
$205$	−8.59855	−	2.91400i	−0.600549	−	0.203523i
$206$	−2.73754	+	8.42528i	−0.190733	+	0.587017i
$207$	1.45570	−	9.19090i	0.101178	−	0.638812i
$208$	2.03987	−	4.00347i	0.141439	−	0.277591i
$209$	5.52091	+	16.9916i	0.381890	+	1.17534i
$210$	−10.7479	+	20.4533i	−0.741675	+	1.41141i
$211$	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
$213$	26.1377	−	13.3178i	1.79093	−	0.912524i
$214$	10.2996	−	14.1762i	0.704065	−	0.969062i
$215$	10.1407	+	20.5374i	0.691593	+	1.40064i
$216$		−	1.70922i		−	0.116297i
$217$	19.2491	−	16.1061i	1.30672	−	1.09335i
$218$	9.07677	−	9.07677i	0.614756	−	0.614756i
$219$	1.15967	+	1.59615i	0.0783634	+	0.107858i
$220$	0.111338	−	8.84420i	0.00750640	−	0.596276i
$221$	−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	0.999670	−	0.0256690i	$-0.00817159\pi$
$223$	14.5449	+	14.5449i	0.974002	+	0.974002i	−0.0256690	+	0.999670i	$0.508172\pi$
$224$	−4.28719	−	1.39299i	−0.286450	−	0.0930733i
$225$	0.283750	−	11.2682i	0.0189167	−	0.751210i
$226$	2.98606	+	9.19015i	0.198630	+	0.611319i
$227$	−16.7091	−	2.64646i	−1.10902	−	0.175652i	−0.425056	−	0.905167i	$-0.639746\pi$
$227$	−16.7091	−	2.64646i	−1.10902	−	0.175652i	−0.683965	+	0.729515i	$0.739746\pi$
$228$	−9.22488	+	4.70031i	−0.610933	+	0.311286i
$229$	−22.2035	+	16.1318i	−1.46725	+	1.06602i	−0.485847	+	0.874044i	$0.661489\pi$
$229$	−22.2035	+	16.1318i	−1.46725	+	1.06602i	−0.981400	+	0.191973i	$0.938511\pi$
$230$	−9.22929	−	0.116186i	−0.608562	−	0.00766106i
$231$	12.6304	+	38.8723i	0.831018	+	2.55761i
$232$	4.28906	−	0.679320i	0.281590	−	0.0445995i
$233$	−0.529257	+	0.0838260i	−0.0346728	+	0.00549162i	−0.173747	−	0.984790i	$-0.555587\pi$
$233$	−0.529257	+	0.0838260i	−0.0346728	+	0.00549162i	0.139074	+	0.990282i	$0.455587\pi$
$234$	−3.13010	−	9.63346i	−0.204621	−	0.629759i
$235$	−5.79491	+	5.65082i	−0.378018	+	0.368619i
$236$	−3.37484	+	2.45196i	−0.219683	+	0.159609i
$237$	−13.7248	+	6.99316i	−0.891525	+	0.454255i
$238$	6.76470	+	1.07142i	0.438491	+	0.0694501i
$239$	−4.68610	−	14.4223i	−0.303119	−	0.932904i	−0.980373	−	0.197154i	$-0.936830\pi$
$239$	−4.68610	−	14.4223i	−0.303119	−	0.932904i	0.677254	−	0.735749i	$-0.263170\pi$
$240$	5.07218	−	0.738031i	0.327408	−	0.0476397i
$241$	−12.3144	−	4.00119i	−0.793239	−	0.257739i	−0.115757	−	0.993278i	$-0.536929\pi$
$241$	−12.3144	−	4.00119i	−0.793239	−	0.257739i	−0.677483	+	0.735538i	$0.736929\pi$
$242$	−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
$245$	−29.7831	−	0.374934i	−1.90277	−	0.0239536i
$246$	−5.47049	−	7.52948i	−0.348786	−	0.480062i
$247$	14.3503	−	14.3503i	0.913088	−	0.913088i
$248$	−5.40049	−	1.35453i	−0.342931	−	0.0860127i
$249$			9.27162i			0.587565i
$250$	−11.1009	+	1.33082i	−0.702080	+	0.0841686i
$251$	6.03572	−	8.30745i	0.380971	−	0.524362i	−0.574870	−	0.818244i	$-0.694948\pi$
$251$	6.03572	−	8.30745i	0.380971	−	0.524362i	0.955841	+	0.293883i	$0.0949475\pi$
$252$	−9.05458	+	4.61354i	−0.570385	+	0.290625i
$253$	−11.5455	+	11.5455i	−0.725856	+	0.725856i
$254$	6.55858			0.411522
$255$	−7.43620	+	2.31309i	−0.465673	+	0.144852i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	2.22895	−	4.37455i	0.139038	−	0.272877i	−0.810979	−	0.585075i	$-0.801065\pi$
$257$	2.22895	−	4.37455i	0.139038	−	0.272877i	0.950017	+	0.312198i	$0.101065\pi$
$258$	−3.67307	+	23.1908i	−0.228675	+	1.44380i
$259$	11.6459	−	35.8424i	0.723642	−	2.22714i
$260$	−9.00873	+	4.44824i	−0.558698	+	0.275868i
$261$	5.75415	−	7.91990i	0.356173	−	0.490230i
$262$	7.00260	−	13.7434i	0.432622	−	0.849068i
$263$	1.06726	+	6.73844i	0.0658104	+	0.415510i	0.998496	+	0.0548206i	$0.0174587\pi$
$263$	1.06726	+	6.73844i	0.0658104	+	0.415510i	−0.932686	+	0.360690i	$0.882541\pi$
$264$	5.32950	−	7.33542i	0.328008	−	0.451464i
$265$	8.67115	−	1.26170i	0.532664	−	0.0775056i
$266$	−16.4719	−	11.9676i	−1.00996	−	0.733779i
$267$	8.98702	+	1.42340i	0.549997	+	0.0871109i
$268$	−1.87980	−	3.68931i	−0.114827	−	0.225360i
$269$	−7.33659	+	5.33035i	−0.447320	+	0.324997i	−0.788537	−	0.614988i	$-0.789161\pi$
$269$	−7.33659	+	5.33035i	−0.447320	+	0.324997i	0.341217	+	0.939985i	$0.389161\pi$
$270$	−2.28521	+	3.06348i	−0.139074	+	0.186437i
$271$	3.15023	−	1.02357i	0.191363	−	0.0621776i	−0.211768	−	0.977320i	$-0.567922\pi$
$271$	3.15023	−	1.02357i	0.191363	−	0.0621776i	0.403131	+	0.915142i	$0.367922\pi$
$272$	−0.689777	−	1.35376i	−0.0418239	−	0.0820840i
$273$	32.8297	−	32.8297i	1.98694	−	1.98694i
$274$	−18.1874			−1.09874
$275$	−12.0242	+	15.7029i	−0.725087	+	0.946918i
$276$	−7.65482	−	5.56155i	−0.460766	−	0.334766i
$277$	−1.77614	+	11.2141i	−0.106718	+	0.673789i	0.875097	+	0.483947i	$0.160797\pi$
$277$	−1.77614	+	11.2141i	−0.106718	+	0.673789i	−0.981815	+	0.189841i	$0.939203\pi$
$278$	−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	−0.956115	−	0.292993i	$-0.905349\pi$
$281$	−16.3091	+	11.8492i	−0.972918	+	0.706866i	−0.0168030	+	0.999859i	$0.505349\pi$
$282$	−8.19516	+	1.29799i	−0.488015	+	0.0772939i
$283$	9.44689	+	18.5406i	0.561559	+	1.10212i	0.980940	+	0.194312i	$0.0622473\pi$
$283$	9.44689	+	18.5406i	0.561559	+	1.10212i	−0.419381	+	0.907810i	$0.637753\pi$
$284$		−	12.7976i		−	0.759397i
$285$	22.8183	+	3.90912i	1.35164	+	0.231556i
$286$	−5.49219	+	16.9032i	−0.324760	+	0.999509i
$287$	8.30925	−	16.3078i	0.490479	−	0.962620i
$288$	2.00864	+	1.02345i	0.118360	+	0.0603074i
$289$	−8.63546	−	11.8857i	−0.507969	−	0.699159i
$290$	−8.59565	−	4.51688i	−0.504754	−	0.265240i
$291$	−19.3902	−	26.6883i	−1.13667	−	1.56450i
$292$	0.850114	−	0.134645i	0.0497492	−	0.00787950i
$293$	−1.01142	−	0.515346i	−0.0590880	−	0.0301068i	0.424197	−	0.905570i	$-0.360556\pi$
$293$	−1.01142	−	0.515346i	−0.0590880	−	0.0301068i	−0.483285	+	0.875463i	$0.660556\pi$
$294$	−24.7022	−	17.9472i	−1.44066	−	1.04670i
$295$	9.32709	+	0.117417i	0.543044	+	0.00683628i
$296$	−7.95117	+	2.58349i	−0.462152	+	0.150162i
$297$	1.05764	+	6.67767i	0.0613705	+	0.387478i
$298$	−0.125634	+	0.793223i	−0.00727779	+	0.0459502i
$299$	17.6392	+	5.73133i	1.02010	+	0.331452i
$300$	−10.0778	−	5.45869i	−0.581840	−	0.315158i
$301$	−43.9147	+	14.2688i	−2.53120	+	0.822438i
$302$	11.1827	+	5.69786i	0.643491	+	0.327875i
$303$	26.1784	−	13.3385i	1.50391	−	0.766279i
$304$			4.51669i			0.259050i
$305$	18.0870	−	12.7962i	1.03566	−	0.732709i
$306$	−3.25753	−	1.05844i	−0.186221	−	0.0605068i
$307$	−3.66222	−	23.1223i	−0.209014	−	1.31966i	−0.839457	−	0.543426i	$-0.817127\pi$
$307$	−3.66222	−	23.1223i	−0.209014	−	1.31966i	0.630444	−	0.776235i	$-0.282873\pi$
$308$	17.6114	+	2.78938i	1.00350	+	0.158940i
$309$	20.3066			1.15520
$310$	7.86845	+	9.64819i	0.446898	+	0.547980i
$311$	27.1502			1.53954			0.769772	−	0.638319i	$-0.220370\pi$
$311$	27.1502			1.53954			0.769772	+	0.638319i	$0.220370\pi$
$312$	−10.1727	−	1.61119i	−0.575914	−	0.0912158i
$313$	1.39591	+	8.81344i	0.0789016	+	0.498165i	0.995216	+	0.0977042i	$0.0311499\pi$
$313$	1.39591	+	8.81344i	0.0789016	+	0.498165i	−0.916314	+	0.400461i	$0.868850\pi$
$314$	8.36841	+	2.71906i	0.472257	+	0.153445i
$315$	22.3971	+	3.83695i	1.26193	+	0.216188i
$316$			6.71997i			0.378028i
$317$	−1.97153	+	1.00454i	−0.110732	+	0.0564207i	−0.508479	−	0.861074i	$-0.669792\pi$
$317$	−1.97153	+	1.00454i	−0.110732	+	0.0564207i	0.397747	+	0.917495i	$0.369792\pi$
$318$	8.00352	+	4.07800i	0.448815	+	0.228683i
$319$	−16.3364	+	5.30802i	−0.914662	+	0.297192i
$320$	0.717698	−	2.11776i	0.0401205	−	0.118386i
$321$	−38.2003	−	12.4120i	−2.13213	−	0.692772i
$322$	2.91083	−	18.3783i	0.162214	−	1.02418i
$323$	−1.07353	−	6.77801i	−0.0597329	−	0.377139i
$324$	−10.1582	+	3.30060i	−0.564344	+	0.183367i
$325$	22.0939	+	4.07193i	1.22555	+	0.225870i
$326$	10.0675	+	7.31450i	0.557590	+	0.405113i
$327$	−26.2172	−	13.3583i	−1.44981	−	0.738718i
$328$	−4.01022	+	0.635156i	−0.221427	+	0.0350706i
$329$	−9.59099	−	13.2009i	−0.528769	−	0.727788i
$330$	−19.3596	+	6.02198i	−1.06571	+	0.331499i
$331$	−9.98451	−	13.7425i	−0.548799	−	0.755356i	0.441050	−	0.897483i	$-0.354606\pi$
$331$	−9.98451	−	13.7425i	−0.548799	−	0.755356i	−0.989849	+	0.142126i	$0.954606\pi$
$332$	3.60394	+	1.83630i	0.197792	+	0.100780i
$333$	−8.55641	+	16.7929i	−0.468888	+	0.920245i
$334$	−2.11592	+	6.51213i	−0.115778	+	0.356328i
$335$	−1.56337	+	9.12574i	−0.0854162	+	0.498592i
$336$			10.3330i			0.563711i
$337$	2.84792	+	5.58936i	0.155136	+	0.304472i	0.955473	−	0.295079i	$-0.0953460\pi$
$337$	2.84792	+	5.58936i	0.155136	+	0.304472i	−0.800337	+	0.599551i	$0.795346\pi$
$338$	7.10031	−	1.12458i	0.386206	−	0.0611690i
$339$	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
$343$	4.45705	−	28.1407i	0.240658	−	1.51946i
$344$	8.28695	+	6.02082i	0.446803	+	0.324621i
$345$	6.28419	+	20.2026i	0.338329	+	1.08767i
$346$	4.23907			0.227894
$347$	−10.0331	+	10.0331i	−0.538606	+	0.538606i	−0.923120	−	0.384513i	$-0.874369\pi$
$347$	−10.0331	+	10.0331i	−0.538606	+	0.538606i	0.384513	+	0.923120i	$0.374369\pi$
$348$	−4.51906	−	8.86915i	−0.242247	−	0.475436i
$349$	−25.7262	+	8.35895i	−1.37709	+	0.447444i	−0.901713	−	0.432336i	$-0.857689\pi$
$349$	−25.7262	+	8.35895i	−1.37709	+	0.447444i	−0.475380	+	0.879781i	$0.657689\pi$
$350$	0.567391	−	22.5320i	0.0303283	−	1.20438i
$351$	6.21313	−	4.51410i	0.331632	−	0.240945i
$352$	−1.79579	−	3.52443i	−0.0957158	−	0.187853i
$353$	34.4284	+	5.45292i	1.83244	+	0.290230i	0.974644	−	0.223763i	$-0.0718340\pi$
$353$	34.4284	+	5.45292i	1.83244	+	0.290230i	0.857795	+	0.513992i	$0.171834\pi$
$354$	7.73593	+	5.62048i	0.411160	+	0.298725i
$355$	−17.1103	+	22.9375i	−0.908121	+	1.21739i
$356$	2.33322	−	3.21140i	0.123660	−	0.170204i
$357$	−2.45596	−	15.5063i	−0.129983	−	0.820680i
$358$	0.741071	−	1.45443i	0.0391668	−	0.0768692i
$359$	17.5717	−	24.1854i	0.927400	−	1.27646i	−0.0334648	−	0.999440i	$-0.510654\pi$
$359$	17.5717	−	24.1854i	0.927400	−	1.27646i	0.960865	−	0.277017i	$-0.0893458\pi$
$360$	−2.23179	−	4.51990i	−0.117626	−	0.238220i
$361$	−0.432781	+	1.33196i	−0.0227780	+	0.0701033i
$362$	−0.975539	+	6.15931i	−0.0512732	+	0.323726i
$363$	−4.83536	+	9.48993i	−0.253791	+	0.498092i
$364$	−6.25899	−	19.2632i	−0.328060	−	1.00967i
$365$	−1.70370	−	0.895271i	−0.0891760	−	0.0468606i
$366$	22.7124			1.18719
$367$	−11.0087	+	11.0087i	−0.574647	+	0.574647i	−0.933424	−	0.358776i	$-0.883194\pi$
$367$	−11.0087	+	11.0087i	−0.574647	+	0.574647i	0.358776	+	0.933424i	$0.383194\pi$
$368$	−3.67789	+	1.87398i	−0.191723	+	0.0976879i
$369$	−5.38006	+	7.40502i	−0.280075	+	0.385490i
$370$	17.7052	+	6.00021i	0.920451	+	0.311936i
$371$			17.6648i			0.917108i
$372$	0.872443	+	12.7328i	0.0452341	+	0.660164i
$373$	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
$375$	10.7644	+	23.2577i	0.555873	+	1.20102i
$376$	−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	$-0.440798\pi$
$379$	−4.73326	−	1.53793i	−0.243131	−	0.0789981i	−0.428048	+	0.903756i	$0.640798\pi$
$380$	6.03880	−	8.09540i	0.309784	−	0.415285i
$381$	−4.64571	−	14.2980i	−0.238007	−	0.732509i
$382$	13.7360	+	2.17557i	0.702794	+	0.111312i
$383$	−20.6661	+	10.5299i	−1.05599	+	0.538053i	−0.893689	−	0.448688i	$-0.851891\pi$
$383$	−20.6661	+	10.5299i	−1.05599	+	0.538053i	−0.162301	+	0.986741i	$0.551891\pi$
$384$	1.85446	−	1.34734i	0.0946349	−	0.0687563i
$385$	−27.8361	−	28.5459i	−1.41866	−	1.45483i
$386$	2.42875	+	7.47493i	0.123620	+	0.380464i
$387$	22.8075	−	3.61235i	1.15937	−	0.183626i
$388$	−14.2142	+	2.25132i	−0.721619	+	0.114293i
$389$	−1.63451	−	5.03050i	−0.0828729	−	0.255057i	0.901031	−	0.433755i	$-0.142812\pi$
$389$	−1.63451	−	5.03050i	−0.0828729	−	0.255057i	−0.983904	+	0.178698i	$0.942812\pi$
$390$	16.0786	+	16.4886i	0.814172	+	0.834932i
$391$	5.07385	−	3.68637i	0.256596	−	0.186428i
$392$	−11.8686	+	6.04736i	−0.599456	+	0.305438i
$393$	−34.9214	−	5.53101i	−1.76155	−	0.279002i
$394$	−4.68248	−	14.4112i	−0.235900	−	0.726026i
$395$	8.98457	−	12.0444i	0.452063	−	0.606020i
$396$	−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
$400$	−4.11779	+	2.83617i	−0.205889	+	0.141808i
$401$	−1.56948	−	2.16020i	−0.0783760	−	0.107875i	0.768029	−	0.640415i	$-0.221238\pi$
$401$	−1.56948	−	2.16020i	−0.0783760	−	0.107875i	−0.846405	+	0.532540i	$0.821238\pi$
$402$	−6.71133	+	6.71133i	−0.334731	+	0.334731i
$403$	−9.33906	−	23.2085i	−0.465212	−	1.15610i
$404$		−	12.8175i		−	0.637693i
$405$	22.6197	+	7.66570i	1.12398	+	0.380912i
$406$	11.5061	−	15.8368i	0.571037	−	0.785965i
$407$	29.4655	−	15.0134i	1.46055	−	0.744187i
$408$	−2.46267	+	2.46267i	−0.121920	+	0.121920i
$409$	−7.04932			−0.348566			−0.174283	−	0.984696i	$-0.555761\pi$
$409$	−7.04932			−0.348566			−0.174283	+	0.984696i	$0.555761\pi$
$410$	8.03683	+	4.22323i	0.396911	+	0.208571i
$411$	12.8828	+	39.6493i	0.635463	+	1.95575i
$412$	4.02184	−	7.89331i	0.198142	−	0.388875i
$413$	−2.94168	+	18.5730i	−0.144750	+	0.913918i
$414$	−2.87555	+	8.85003i	−0.141325	+	0.434955i
$415$	−4.00432	−	8.10970i	−0.196564	−	0.398089i
$416$	−2.64103	+	3.63507i	−0.129487	+	0.178224i
$417$	−16.8388	+	33.0480i	−0.824600	+	1.61837i
$418$	−2.79487	−	17.6461i	−0.136701	−	0.863099i
$419$	21.7328	−	29.9126i	1.06172	−	1.46133i	0.183525	−	0.983015i	$-0.441249\pi$
$419$	21.7328	−	29.9126i	1.06172	−	1.46133i	0.878190	−	0.478311i	$-0.158751\pi$
$420$	13.8152	−	18.5201i	0.674111	−	0.903689i
$421$	−12.9953	−	9.44163i	−0.633351	−	0.460157i	0.224208	−	0.974541i	$-0.428020\pi$
$421$	−12.9953	−	9.44163i	−0.633351	−	0.460157i	−0.857560	+	0.514385i	$0.828020\pi$
$422$	−10.6313	−	1.68384i	−0.517526	−	0.0819680i
$423$	3.70463	+	7.27075i	0.180125	+	0.353516i
$424$	3.17029	−	2.30335i	0.153963	−	0.111860i
$425$	5.50529	−	5.23484i	0.267046	−	0.253927i
$426$	−27.8993	+	9.06504i	−1.35173	+	0.439202i
$427$	20.2776	+	39.7970i	0.981302	+	1.92591i
$428$	−12.3904	+	12.3904i	−0.598913	+	0.598913i
$429$	40.7402			1.96695
$430$	−6.80313	−	21.8709i	−0.328076	−	1.05471i
$431$	−3.06924	−	2.22993i	−0.147840	−	0.107412i	0.511406	−	0.859339i	$-0.329125\pi$
$431$	−3.06924	−	2.22993i	−0.147840	−	0.107412i	−0.659247	+	0.751927i	$0.729125\pi$
$432$	−0.267380	+	1.68817i	−0.0128643	+	0.0812223i
$433$	−0.209442	−	0.209442i	−0.0100651	−	0.0100651i	0.702056	−	0.712121i	$-0.252265\pi$
$433$	−0.209442	−	0.209442i	−0.0100651	−	0.0100651i	−0.712121	+	0.702056i	$0.752265\pi$
$434$	−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
$437$	−18.4144	+	2.91656i	−0.880882	+	0.139518i
$438$	−0.895702	−	1.75791i	−0.0427983	−	0.0839964i
$439$		−	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
$442$	3.09930	−	6.08273i	0.147419	−	0.289326i
$443$	30.5944	+	15.5886i	1.45358	+	0.740638i	0.989416	−	0.145110i	$-0.0463535\pi$
$443$	30.5944	+	15.5886i	1.45358	+	0.740638i	0.464168	+	0.885747i	$0.346353\pi$
$444$	11.2643	+	15.5039i	0.534578	+	0.735783i
$445$	−8.47552	+	2.63638i	−0.401778	+	0.124976i
$446$	−12.0905	−	16.6412i	−0.572504	−	0.787984i
$447$	1.81825	−	0.287983i	0.0860004	−	0.0136211i
$448$	4.01650	+	2.04651i	0.189762	+	0.0966884i
$449$	1.82299	+	1.32448i	0.0860324	+	0.0625062i	0.629970	−	0.776619i	$-0.283067\pi$
$449$	1.82299	+	1.32448i	0.0860324	+	0.0625062i	−0.543938	+	0.839126i	$0.683067\pi$
$450$	−2.04298	+	11.0850i	−0.0963072	+	0.522554i
$451$	15.2743	−	4.96294i	0.719241	−	0.233696i
$452$	−1.51164	−	9.54412i	−0.0711016	−	0.448918i
$453$	4.50046	−	28.4148i	0.211450	−	1.33504i
$454$	16.0894	+	5.22775i	0.755112	+	0.245351i
$455$	−14.5366	+	42.8942i	−0.681488	+	2.01091i
$456$	9.84660	−	3.19935i	0.461109	−	0.149823i
$457$	−4.07456	−	2.07609i	−0.190600	−	0.0971155i	0.356086	−	0.934453i	$-0.384111\pi$
$457$	−4.07456	−	2.07609i	−0.190600	−	0.0971155i	−0.546686	+	0.837338i	$0.684111\pi$
$458$	24.4537	−	12.4598i	1.14265	−	0.582207i
$459$		−	2.59692i		−	0.121214i
$460$	9.09749	+	1.55853i	0.424173	+	0.0726671i
$461$	21.2061	+	6.89027i	0.987665	+	0.320912i	0.757926	−	0.652341i	$-0.226213\pi$
$461$	21.2061	+	6.89027i	0.987665	+	0.320912i	0.229739	+	0.973252i	$0.426213\pi$
$462$	−6.39391	−	40.3696i	−0.297472	−	1.87816i
$463$	−29.7797	−	4.71663i	−1.38398	−	0.219201i	−0.580367	−	0.814355i	$-0.697091\pi$
$463$	−29.7797	−	4.71663i	−1.38398	−	0.219201i	−0.803611	+	0.595155i	$0.797091\pi$
$464$	−4.34252			−0.201596
$465$	15.4600	−	23.9878i	0.716938	−	1.11241i
$466$	0.535854			0.0248229
$467$	38.9497	+	6.16903i	1.80238	+	0.285469i	0.965210	−	0.261476i	$-0.0842092\pi$
$467$	38.9497	+	6.16903i	1.80238	+	0.285469i	0.837169	+	0.546945i	$0.184209\pi$
$468$	1.58456	+	10.0045i	0.0732462	+	0.462459i
$469$	−17.7516	−	5.76784i	−0.819692	−	0.266334i
$470$	6.60755	−	4.67473i	0.304784	−	0.215629i
$471$		−	20.1695i		−	0.929363i
$472$	3.71686	−	1.89384i	0.171082	−	0.0871709i
$473$	−36.1016	−	18.3947i	−1.65995	−	0.845788i
$474$	14.6498	−	4.76002i	0.672890	−	0.218635i
$475$	−21.6470	+	6.43578i	−0.993233	+	0.295294i
$476$	−6.51381	−	2.11647i	−0.298560	−	0.0970080i
$477$	1.38195	−	8.72532i	0.0632754	−	0.399505i
$478$	2.37226	+	14.9778i	0.108505	+	0.685071i
$479$	5.11499	−	1.66196i	0.233710	−	0.0759369i	−0.189821	−	0.981819i	$-0.560791\pi$
$479$	5.11499	−	1.66196i	0.233710	−	0.0759369i	0.423530	+	0.905882i	$0.360791\pi$
$480$	−5.12519	−	0.0645200i	−0.233932	−	0.00294492i
$481$	−30.3905	−	22.0800i	−1.38569	−	1.00676i
$482$	11.5369	+	5.87832i	0.525489	+	0.267750i
$483$	−42.1273	+	6.67231i	−1.91686	+	0.303601i
$484$	2.73113	+	3.75907i	0.124142	+	0.170867i
$485$	28.4866	+	14.9693i	1.29351	+	0.679720i
$486$	11.3770	+	15.6590i	0.516069	+	0.710308i
$487$	26.6460	+	13.5768i	1.20744	+	0.615223i	0.937612	−	0.347684i	$-0.113032\pi$
$487$	26.6460	+	13.5768i	1.20744	+	0.615223i	0.269832	+	0.962907i	$0.413032\pi$
$488$	4.49832	−	8.82844i	0.203629	−	0.399645i
$489$	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	$-0.987940\pi$
$491$		−	1.67870i		−	0.0757589i	0.999282	−	0.0378794i	$-0.0120603\pi$
$492$	4.22527	+	8.29256i	0.190490	+	0.373857i
$493$	6.51664	−	1.03213i	0.293495	−	0.0464850i
$494$	−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
$498$	1.45040	−	9.15747i	0.0649940	−	0.410356i
$499$	−26.7013	−	19.3996i	−1.19531	−	0.868445i	−0.201497	−	0.979489i	$-0.564581\pi$
$499$	−26.7013	−	19.3996i	−1.19531	−	0.868445i	−0.993816	+	0.111044i	$0.964581\pi$
$500$	11.1724	+	0.422119i	0.499644	+	0.0188777i
$501$	15.6955			0.701225
$502$	−7.26098	+	7.26098i	−0.324073	+	0.324073i
$503$	−3.53489	−	6.93761i	−0.157613	−	0.309333i	0.798673	−	0.601765i	$-0.205536\pi$
$503$	−3.53489	−	6.93761i	−0.157613	−	0.309333i	−0.956286	+	0.292432i	$0.905536\pi$
$504$	9.66481	−	3.14029i	0.430505	−	0.139880i
$505$	−17.1369	+	22.9731i	−0.762582	+	1.02229i
$506$	13.2094	−	9.59720i	0.587230	−	0.426648i
$507$	−7.48106	−	14.6824i	−0.332246	−	0.652069i
$508$	−6.47784	−	1.02599i	−0.287407	−	0.0455209i
$509$	24.1926	+	17.5769i	1.07232	+	0.779083i	0.976327	−	0.216299i	$-0.0693986\pi$
$509$	24.1926	+	17.5769i	1.07232	+	0.779083i	0.0959891	+	0.995382i	$0.469399\pi$
$510$	7.70650	−	1.12134i	0.341249	−	0.0496537i
$511$	2.28057	−	3.13893i	0.100886	−	0.138858i
$512$	−0.156434	−	0.987688i	−0.00691349	−	0.0436501i
$513$	−3.50481	+	6.87857i	−0.154741	+	0.303696i
$514$	−2.88583	+	3.97201i	−0.127289	+	0.175198i
$515$	−17.7618	+	8.77022i	−0.782677	+	0.386462i
$516$	7.25569	−	22.3307i	0.319414	−	0.983055i
$517$	2.23985	−	14.1419i	0.0985085	−	0.621958i
$518$	−17.1095	+	33.5793i	−0.751749	+	1.47539i
$519$	−3.00270	−	9.24137i	−0.131804	−	0.405651i
$520$	9.59368	−	2.98420i	0.420711	−	0.130866i
$521$	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
$523$	19.2390	−	9.80274i	0.841261	−	0.428644i	0.0204138	−	0.999792i	$-0.493502\pi$
$523$	19.2390	−	9.80274i	0.841261	−	0.428644i	0.820847	+	0.571148i	$0.193502\pi$
$524$	−9.06632	+	12.4787i	−0.396064	+	0.545136i
$525$	−49.5226	+	14.7234i	−2.16134	+	0.642580i
$526$		−	6.82244i		−	0.297473i
$527$	−8.20531	−	2.05802i	−0.357429	−	0.0896489i
$528$	−6.41139	+	6.41139i	−0.279020	+	0.279020i
$529$	3.50398	+	4.82282i	0.152347	+	0.209688i
$530$	−8.76176	−	0.110300i	−0.380587	−	0.00479113i
$531$	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
$535$	38.7736	−	5.64178i	1.67633	−	0.243915i
$536$	1.27952	+	3.93795i	0.0552668	+	0.170094i
$537$	−3.69566	−	0.585335i	−0.159480	−	0.0252591i
$538$	8.08012	−	4.11703i	0.348359	−	0.177498i
$539$	42.6270	−	30.9703i	1.83608	−	1.33399i
$540$	2.73631	−	2.66828i	0.117752	−	0.114824i
$541$	−8.45536	−	26.0229i	−0.363524	−	1.11881i	−0.950900	−	0.309499i	$-0.899839\pi$
$541$	−8.45536	−	26.0229i	−0.363524	−	1.11881i	0.587375	−	0.809315i	$-0.300161\pi$
$542$	−3.27157	+	0.518165i	−0.140526	+	0.0222571i
$543$	14.1186	−	2.23616i	0.605887	−	0.0959630i
$544$	0.469510	+	1.44500i	0.0201301	+	0.0619539i
$545$	28.7010	+	0.361311i	1.22942	+	0.0154769i
$546$	−37.5612	+	27.2898i	−1.60747	+	1.16790i
$547$	−28.2217	+	14.3797i	−1.20667	+	0.614830i	−0.937407	−	0.348236i	$-0.886781\pi$
$547$	−28.2217	+	14.3797i	−1.20667	+	0.614830i	−0.269265	+	0.963066i	$0.586781\pi$
$548$	17.9634	+	2.84513i	0.767360	+	0.121538i
$549$	−6.90249	−	21.2437i	−0.294591	−	0.906659i
$550$	14.3326	−	13.6285i	0.611146	−	0.581123i
$551$	−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
$555$	0.539410	−	42.8484i	0.0228967	−	1.81881i
$556$	9.51095	+	13.0907i	0.403354	+	0.555169i
$557$	−18.9096	+	18.9096i	−0.801224	+	0.801224i	−0.983287	−	0.182063i	$-0.941723\pi$
$557$	−18.9096	+	18.9096i	−0.801224	+	0.801224i	0.182063	+	0.983287i	$0.441723\pi$
$558$	11.6443	−	4.68563i	0.492941	−	0.198359i
$559$			46.0249i			1.94664i
$560$	−4.46272	−	9.03806i	−0.188584	−	0.381928i
$561$	8.09745	−	11.1452i	0.341875	−	0.470550i
$562$	17.9619	−	9.15205i	0.757677	−	0.386056i
$563$	−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
$565$	−10.0511	+	19.1273i	−0.422853	+	0.804690i
$566$	−6.43020	−	19.7901i	−0.270281	−	0.831841i
$567$	−21.8587	+	42.9001i	−0.917978	+	1.80163i
$568$	−2.00198	+	12.6400i	−0.0840013	+	0.530363i
$569$	10.5413	−	32.4429i	0.441916	−	1.36008i	−0.443914	−	0.896069i	$-0.646410\pi$
$569$	10.5413	−	32.4429i	0.441916	−	1.36008i	0.885830	−	0.464009i	$-0.153590\pi$
$570$	−21.9259	−	7.43056i	−0.918373	−	0.311232i
$571$	16.3611	−	22.5192i	0.684693	−	0.942399i	−0.315286	−	0.948997i	$-0.602100\pi$
$571$	16.3611	−	22.5192i	0.684693	−	0.942399i	0.999978	+	0.00659830i	$0.00210032\pi$
$572$	8.06883	−	15.8360i	0.337375	−	0.662135i
$573$	−4.98691	−	31.4861i	−0.208331	−	1.31535i
$574$	−10.7581	+	14.8072i	−0.449032	+	0.618040i
$575$	−14.2219	−	14.9567i	−0.593096	−	0.623738i
$576$	−1.82380	−	1.32507i	−0.0759918	−	0.0552113i
$577$	28.8966	+	4.57678i	1.20298	+	0.190534i	0.725572	−	0.688146i	$-0.241575\pi$
$577$	28.8966	+	4.57678i	1.20298	+	0.190534i	0.477411	+	0.878680i	$0.341575\pi$
$578$	6.66982	+	13.0902i	0.277428	+	0.544483i
$579$	14.5753	−	10.5896i	0.605729	−	0.440088i
$580$	7.78322	+	5.80593i	0.323181	+	0.241078i
$581$	17.3408	−	5.63437i	0.719418	−	0.233753i
$582$	14.9765	+	29.3930i	0.620795	+	1.21838i
$583$	−10.9606	+	10.9606i	−0.453941	+	0.453941i
$584$	−0.860711			−0.0356165
$585$	10.5359	−	20.0499i	0.435607	−	0.828962i
$586$	0.918353	+	0.667222i	0.0379368	+	0.0275627i
$587$	−2.81668	+	17.7838i	−0.116257	+	0.734017i	0.858841	+	0.512242i	$0.171185\pi$
$587$	−2.81668	+	17.7838i	−0.116257	+	0.734017i	−0.975098	+	0.221775i	$0.928815\pi$
$588$	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
$592$	8.25742	−	1.30785i	0.339378	−	0.0537522i
$593$	−0.0270081	−	0.0530063i	−0.00110909	−	0.00217671i	0.890451	−	0.455079i	$-0.150389\pi$
$593$	−0.0270081	−	0.0530063i	−0.00110909	−	0.00217671i	−0.891560	+	0.452902i	$0.850389\pi$
$594$		−	6.76091i		−	0.277404i
$595$	8.84519	+	12.5023i	0.362617	+	0.512546i
$596$	0.248175	−	0.763803i	0.0101656	−	0.0312866i
$597$	−17.6291	+	34.5990i	−0.721511	+	1.41604i
$598$	−16.5255	−	8.42015i	−0.675777	−	0.344326i
$599$	−18.6821	−	25.7137i	−0.763329	−	1.05063i	−0.996930	−	0.0783000i	$-0.975051\pi$
$599$	−18.6821	−	25.7137i	−0.763329	−	1.05063i	0.233601	−	0.972333i	$-0.424949\pi$
$600$	9.09976	+	6.96799i	0.371496	+	0.284467i
$601$	2.62398	+	3.61160i	0.107034	+	0.147320i	0.859174	−	0.511684i	$-0.170978\pi$
$601$	2.62398	+	3.61160i	0.107034	+	0.147320i	−0.752139	+	0.659004i	$0.770978\pi$
$602$	45.6062	−	7.22331i	1.85877	−	0.294400i
$603$	8.31698	+	4.23771i	0.338693	+	0.172573i
$604$	−10.1537	−	7.37706i	−0.413146	−	0.300168i
$605$	0.130785	−	10.3890i	0.00531717	−	0.422373i
$606$	−27.9427	+	9.07912i	−1.13509	+	0.368814i
$607$	1.61356	+	10.1876i	0.0654923	+	0.413502i	0.998553	+	0.0537823i	$0.0171277\pi$
$607$	1.61356	+	10.1876i	0.0654923	+	0.413502i	−0.933060	+	0.359720i	$0.882872\pi$
$608$	0.706566	−	4.46108i	0.0286550	−	0.180921i
$609$	−42.6751	−	13.8660i	−1.72928	−	0.561877i
$610$	−19.8660	+	9.80925i	−0.804353	+	0.397165i
$611$	−15.4682	+	5.02592i	−0.625777	+	0.203327i
$612$	3.05185	+	1.55500i	0.123364	+	0.0628570i
$613$	21.5138	−	10.9618i	0.868933	−	0.442744i	0.0381057	−	0.999274i	$-0.487868\pi$
$613$	21.5138	−	10.9618i	0.868933	−	0.442744i	0.830827	+	0.556530i	$0.187868\pi$
$614$			23.4105i			0.944773i
$615$	3.51404	−	20.5122i	0.141700	−	0.827130i
$616$	−16.9583	−	5.51007i	−0.683268	−	0.222007i
$617$	−1.55214	−	9.79984i	−0.0624869	−	0.394527i	−0.999032	−	0.0439806i	$-0.985996\pi$
$617$	−1.55214	−	9.79984i	−0.0624869	−	0.394527i	0.936546	−	0.350546i	$-0.114004\pi$
$618$	−20.0566	−	3.17665i	−0.806795	−	0.127784i
$619$	28.3211			1.13832			0.569160	−	0.822227i	$-0.307268\pi$
$619$	28.3211			1.13832			0.569160	+	0.822227i	$0.307268\pi$
$620$	−6.26227	−	10.7603i	−0.251499	−	0.432144i
$621$	−7.05529			−0.283119
$622$	−26.8159	−	4.24722i	−1.07522	−	0.170298i
$623$	−2.79921	−	17.6735i	−0.112148	−	0.708075i
$624$	9.79537	+	3.18271i	0.392129	+	0.127410i
$625$	−19.4602	−	15.6940i	−0.778408	−	0.627759i
$626$		−	8.92330i		−	0.356647i
$627$	−36.4896	+	18.5924i	−1.45725	+	0.742508i
$628$	−7.84002	−	3.99469i	−0.312851	−	0.159406i
$629$	−12.0807	+	3.92526i	−0.481690	+	0.156511i
$630$	−21.5211	−	7.29338i	−0.857420	−	0.290575i
$631$	22.8208	+	7.41493i	0.908483	+	0.295184i	0.725734	−	0.687976i	$-0.241500\pi$
$631$	22.8208	+	7.41493i	0.908483	+	0.295184i	0.182749	+	0.983160i	$0.441500\pi$
$632$	1.05124	−	6.63724i	0.0418159	−	0.264015i
$633$	3.85976	+	24.3695i	0.153412	+	0.968602i
$634$	2.10440	−	0.683760i	0.0835763	−	0.0271556i
$635$	10.2387	+	10.4997i	0.406309	+	0.416670i
$636$	−7.26704	−	5.27982i	−0.288157	−	0.209358i
$637$	−53.3280	−	27.1720i	−2.11293	−	1.07659i
$638$	16.9656	−	2.68709i	0.671675	−	0.106383i
$639$	16.9577	+	23.3403i	0.670836	+	0.923327i
$640$	−1.04015	+	1.97941i	−0.0411156	+	0.0782432i
$641$	12.0064	+	16.5254i	0.474224	+	0.652713i	0.977382	−	0.211481i	$-0.0678287\pi$
$641$	12.0064	+	16.5254i	0.474224	+	0.652713i	−0.503158	+	0.864194i	$0.667829\pi$
$642$	35.7883	+	18.2351i	1.41245	+	0.719680i
$643$	7.46779	−	14.6564i	0.294501	−	0.577990i	−0.695587	−	0.718442i	$-0.744856\pi$
$643$	7.46779	−	14.6564i	0.294501	−	0.577990i	0.990088	+	0.140452i	$0.0448555\pi$
$644$	−5.74999	+	17.6966i	−0.226581	+	0.697345i
$645$	−42.8607	+	30.3232i	−1.68764	+	1.19397i
$646$			6.86250i			0.270002i
$647$	−2.40733	−	4.72464i	−0.0946418	−	0.185745i	0.838832	−	0.544390i	$-0.183239\pi$
$647$	−2.40733	−	4.72464i	−0.0946418	−	0.185745i	−0.933474	+	0.358645i	$0.883239\pi$
$648$	10.5495	−	1.67087i	0.414422	−	0.0656380i
$649$	−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
$653$	−2.27194	+	14.3445i	−0.0889081	+	0.561344i	0.902516	+	0.430657i	$0.141718\pi$
$653$	−2.27194	+	14.3445i	−0.0889081	+	0.561344i	−0.991424	+	0.130686i	$0.958282\pi$
$654$	23.8047	+	17.2951i	0.930838	+	0.676294i
$655$	32.9338	−	10.2443i	1.28683	−	0.400280i
$656$	4.06021			0.158524
$657$	−1.37203	+	1.37203i	−0.0535279	+	0.0535279i
$658$	7.40784	+	14.5387i	0.288788	+	0.566778i
$659$	−1.70857	+	0.555148i	−0.0665564	+	0.0216255i	−0.342106	−	0.939661i	$-0.611140\pi$
$659$	−1.70857	+	0.555148i	−0.0665564	+	0.0216255i	0.275550	+	0.961287i	$0.411140\pi$
$660$	20.0633	−	2.91933i	0.780964	−	0.113635i
$661$	18.7978	−	13.6574i	0.731149	−	0.531211i	−0.158777	−	0.987314i	$-0.550755\pi$
$661$	18.7978	−	13.6574i	0.731149	−	0.531211i	0.889927	+	0.456103i	$0.150755\pi$
$662$	7.71179	+	15.1352i	0.299727	+	0.588248i
$663$	−15.4560	−	2.44799i	−0.600261	−	0.0950720i
$664$	−3.27231	−	2.37747i	−0.126990	−	0.0922637i
$665$	−6.55545	−	45.0529i	−0.254209	−	1.74708i
$666$	11.0781	−	15.2476i	0.429266	−	0.590834i
$667$	−2.80409	−	17.7043i	−0.108575	−	0.685514i
$668$	3.10859	−	6.10096i	0.120275	−	0.236053i
$669$	−27.7144	+	38.1456i	−1.07150	+	1.47479i
$670$	2.97171	−	8.76882i	0.114807	−	0.338769i
$671$	−12.1114	+	37.2750i	−0.467555	+	1.43899i
$672$	1.61644	−	10.2058i	0.0623554	−	0.393696i
$673$	−19.8255	+	38.9098i	−0.764217	+	1.49986i	0.0990325	+	0.995084i	$0.468425\pi$
$673$	−19.8255	+	38.9098i	−0.764217	+	1.49986i	−0.863250	+	0.504777i	$0.831575\pi$
$674$	−1.93849	−	5.96606i	−0.0746678	−	0.229804i
$675$	−8.47185	+	1.12399i	−0.326081	+	0.0432624i
$676$	−7.18881			−0.276493
$677$	−7.69790	+	7.69790i	−0.295854	+	0.295854i	−0.839388	−	0.543533i	$-0.817086\pi$
$677$	−7.69790	+	7.69790i	−0.295854	+	0.295854i	0.543533	+	0.839388i	$0.317086\pi$
$678$	−19.7359	+	10.0559i	−0.757952	+	0.386196i
$679$	−38.1320	+	52.4842i	−1.46337	+	2.01416i
$680$	1.09044	−	3.21765i	0.0418167	−	0.123391i
$681$		−	38.7786i		−	1.48600i
$682$	−21.3620	−	5.35792i	−0.817992	−	0.205166i
$683$	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
$685$	−28.3925	−	29.1164i	−1.08482	−	1.11248i
$686$	−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
$690$	−3.04644	−	20.9369i	−0.115976	−	0.797055i
$691$	14.6666	+	45.1392i	0.557944	+	1.71717i	0.688040	+	0.725673i	$0.258471\pi$
$691$	14.6666	+	45.1392i	0.557944	+	1.71717i	−0.130096	+	0.991501i	$0.541529\pi$
$692$	−4.18688	−	0.663137i	−0.159161	−	0.0252087i
$693$	−35.8159	+	18.2491i	−1.36053	+	0.693227i
$694$	11.4791	−	8.34008i	0.435742	−	0.316585i
$695$	0.455450	−	36.1789i	0.0172762	−	1.37235i
$696$	3.07598	+	9.46689i	0.116595	+	0.358842i
$697$	−6.09299	+	0.965034i	−0.230788	+	0.0365533i
$698$	26.7171	−	4.23157i	1.01126	−	0.160167i
$699$	−0.379567	−	1.16819i	−0.0143565	−	0.0441848i
$700$	−4.08518	+	22.1658i	−0.154405	+	0.837789i
$701$	5.50845	−	4.00212i	0.208051	−	0.151158i	−0.478880	−	0.877880i	$-0.658957\pi$
$701$	5.50845	−	4.00212i	0.208051	−	0.151158i	0.686932	+	0.726722i	$0.258957\pi$
$702$	−6.84279	+	3.48658i	−0.258265	+	0.131592i
$703$	37.2962	+	5.90714i	1.40665	+	0.222792i
$704$	1.22234	+	3.76196i	0.0460685	+	0.141784i
$705$	−14.8715	−	11.0935i	−0.560094	−	0.417804i
$706$	−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	$-0.900694\pi$
$709$	−0.0358543	+	0.110348i	−0.00134654	+	0.00414421i	0.950381	+	0.311088i	$0.100694\pi$
$710$	20.4879	−	19.9784i	0.768896	−	0.749777i
$711$	−8.90444	−	12.2559i	−0.333943	−	0.459632i
$712$	−2.80686	+	2.80686i	−0.105192	+	0.105192i
$713$	−5.59122	+	22.2921i	−0.209393	+	0.834845i
$714$			15.6996i			0.587542i
$715$	−35.6346	+	17.5953i	−1.33266	+	0.658026i
$716$	−0.959470	+	1.32060i	−0.0358571	+	0.0493531i
$717$	30.9720	−	15.7810i	1.15667	−	0.589353i
$718$	−21.1388	+	21.1388i	−0.788894	+	0.788894i
$719$	−42.1400			−1.57156			−0.785778	−	0.618509i	$-0.787737\pi$
$719$	−42.1400			−1.57156			−0.785778	+	0.618509i	$0.787737\pi$
$720$	1.49724	+	4.81338i	0.0557990	+	0.179384i
$721$	−12.3403	−	37.9797i	−0.459578	−	1.41444i
$722$	0.635818	−	1.24786i	0.0236627	−	0.0464407i
$723$	4.64300	−	29.3147i	0.172675	−	1.09023i
$724$	1.92706	−	5.93087i	0.0716185	−	0.220419i
$725$	−6.18760	−	20.8123i	−0.229802	−	0.772948i
$726$	6.26038	−	8.61668i	0.232345	−	0.319795i
$727$	22.9759	−	45.0928i	0.852130	−	1.67240i	0.118391	−	0.992967i	$-0.462226\pi$
$727$	22.9759	−	45.0928i	0.852130	−	1.67240i	0.733739	−	0.679432i	$-0.237774\pi$
$728$	3.16851	+	20.0052i	0.117433	+	0.741441i
$729$	7.24433	−	9.97097i	0.268309	−	0.369295i
$730$	1.54268	+	1.15077i	0.0570971	+	0.0425918i
$731$	12.5909	+	9.14783i	0.465691	+	0.338345i
$732$	−22.4327	−	3.55300i	−0.829138	−	0.131323i
$733$	−21.3193	−	41.8415i	−0.787446	−	1.54545i	−0.837331	−	0.546696i	$-0.815885\pi$
$733$	−21.3193	−	41.8415i	−0.787446	−	1.54545i	0.0498850	−	0.998755i	$-0.484115\pi$
$734$	12.5953	−	9.15099i	0.464899	−	0.337769i
$735$	−9.83091	−	67.5638i	−0.362618	−	2.49213i
$736$	3.92576	−	1.27556i	0.144706	−	0.0470177i
$737$	−7.43565	−	14.5933i	−0.273896	−	0.537551i
$738$	6.47223	−	6.47223i	0.238246	−	0.238246i
$739$	10.1635			0.373870			0.186935	−	0.982372i	$-0.440145\pi$
$739$	10.1635			0.373870			0.186935	+	0.982372i	$0.440145\pi$
$740$	−16.5486	−	8.69604i	−0.608339	−	0.319673i
$741$	37.6351	+	27.3435i	1.38256	+	1.00449i
$742$	2.76338	−	17.4473i	0.101447	−	0.640510i
$743$	15.9333	+	15.9333i	0.584535	+	0.584535i	0.936146	−	0.351611i	$-0.114366\pi$
$743$	15.9333	+	15.9333i	0.584535	+	0.584535i	−0.351611	+	0.936146i	$0.614366\pi$
$744$	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
$747$	−9.00610	+	1.42643i	−0.329516	+	0.0521902i
$748$	−2.72846	−	5.35490i	−0.0997622	−	0.195794i
$749$			78.9892i			2.88620i
$750$	−6.99360	−	24.6553i	−0.255370	−	0.900284i
$751$	0.420856	−	1.29526i	0.0153573	−	0.0472648i	−0.943084	−	0.332554i	$-0.892090\pi$
$751$	0.420856	−	1.29526i	0.0153573	−	0.0472648i	0.958441	+	0.285289i	$0.0920896\pi$
$752$	1.64333	−	3.22522i	0.0599261	−	0.117612i
$753$	20.9725	+	10.6860i	0.764281	+	0.389420i
$754$	−11.4687	−	15.7854i	−0.417667	−	0.574869i
$755$	8.33560	+	26.7975i	0.303363	+	0.975262i
$756$	4.52879	+	6.23335i	0.164711	+	0.226705i
$757$	42.2730	−	6.69539i	1.53644	−	0.243348i	0.669898	−	0.742453i	$-0.266338\pi$
$757$	42.2730	−	6.69539i	1.53644	−	0.243348i	0.866542	+	0.499105i	$0.166338\pi$
$758$	4.43440	+	2.25944i	0.161065	+	0.0820665i
$759$	−30.2791	−	21.9991i	−1.09906	−	0.798515i
$760$	−7.23085	+	7.05106i	−0.262290	+	0.255769i
$761$	−5.31495	+	1.72693i	−0.192667	+	0.0626012i	−0.403761	−	0.914864i	$-0.632297\pi$
$761$	−5.31495	+	1.72693i	−0.192667	+	0.0626012i	0.211094	+	0.977466i	$0.432297\pi$
$762$	2.35181	+	14.8487i	0.0851970	+	0.537913i
$763$	−9.05202	+	57.1522i	−0.327705	+	2.06905i
$764$	−13.2265	−	4.29756i	−0.478519	−	0.155480i
$765$	−3.39090	−	6.86738i	−0.122598	−	0.248290i
$766$	22.0589	−	7.16738i	0.797021	−	0.258968i
$767$	16.7006	+	8.50938i	0.603023	+	0.307256i
$768$	−2.04240	+	1.04065i	−0.0736987	+	0.0375513i
$769$		−	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
$772$	−1.22951	−	7.76284i	−0.0442511	−	0.279391i
$773$	24.6781	+	3.90863i	0.887611	+	0.140584i	0.583558	−	0.812071i	$-0.301660\pi$
$773$	24.6781	+	3.90863i	0.887611	+	0.140584i	0.304053	+	0.952655i	$0.401660\pi$
$774$	−23.0918			−0.830017
$775$	−3.16242	+	27.6586i	−0.113598	+	0.993527i
$776$	14.3914			0.516622
$777$	85.3239	+	13.5140i	3.06098	+	0.484811i
$778$	0.827442	+	5.22426i	0.0296652	+	0.187299i
$779$	17.4411	+	5.66697i	0.624894	+	0.203040i
$780$	−13.3013	−	18.8008i	−0.476262	−	0.673178i
$781$		−	50.6216i		−	1.81138i
$782$	−5.58806	+	2.84726i	−0.199828	+	0.101818i
$783$	−6.61332	−	3.36966i	−0.236341	−	0.120422i
$784$	12.6685	−	4.11625i	0.452447	−	0.147009i
$785$	8.71102	+	17.6419i	0.310910	+	0.629666i
$786$	33.6262	+	10.9258i	1.19941	+	0.389711i
$787$	1.49424	−	9.43427i	0.0532640	−	0.336295i	−0.946638	−	0.322299i	$-0.895545\pi$
$787$	1.49424	−	9.43427i	0.0532640	−	0.336295i	0.999902	−	0.0139969i	$-0.00445548\pi$
$788$	2.37042	+	14.9663i	0.0844429	+	0.533151i
$789$	−14.8732	+	4.83261i	−0.529501	+	0.172045i
$790$	−10.7581	+	10.4906i	−0.382756	+	0.373239i
$791$	−35.2404	−	25.6036i	−1.25300	−	0.910360i
$792$	7.94529	+	4.04832i	0.282323	+	0.143851i
$793$	43.9722	−	6.96452i	1.56150	−	0.247317i
$794$	−10.3390	−	14.2304i	−0.366917	−	0.505018i
$795$	5.96585	+	19.1792i	0.211587	+	0.680215i
$796$	9.95732	+	13.7051i	0.352928	+	0.485764i
$797$	−42.8634	−	21.8400i	−1.51830	−	0.773612i	−0.521477	−	0.853265i	$-0.674619\pi$
$797$	−42.8634	−	21.8400i	−1.51830	−	0.773612i	−0.996823	+	0.0796533i	$0.974619\pi$
$798$	21.1882	−	41.5841i	0.750053	−	1.47206i
$799$	−1.69951	+	5.23054i	−0.0601242	+	0.185043i
$800$	4.51076	−	2.15708i	0.159480	−	0.0762644i
$801$			8.94864i			0.316185i
$802$	1.21223	+	2.37913i	0.0428052	+	0.0840099i
$803$	3.36268	−	0.532596i	0.118666	−	0.0187949i
$804$	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
$808$	−2.00509	+	12.6597i	−0.0705390	+	0.445365i
$809$	32.2854	+	23.4567i	1.13509	+	0.824694i	0.986428	−	0.164193i	$-0.0525021\pi$
$809$	32.2854	+	23.4567i	1.13509	+	0.824694i	0.148666	+	0.988887i	$0.452502\pi$
$810$	−21.1421	−	11.1098i	−0.742856	−	0.390360i
$811$	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
$813$	3.44701	+	6.76513i	0.120892	+	0.237263i
$814$	−31.4513	+	10.2192i	−1.10237	+	0.358181i
$815$	4.00665	+	27.5361i	0.140347	+	0.964546i
$816$	2.81760	−	2.04710i	0.0986357	−	0.0716630i
$817$	−21.0041	−	41.2229i	−0.734841	−	1.44221i
$818$	6.96253	+	1.10276i	0.243439	+	0.0385570i
$819$	36.9403	+	26.8387i	1.29080	+	0.937820i
$820$	−7.27723	−	5.42848i	−0.254132	−	0.189571i
$821$	19.1006	−	26.2897i	0.666616	−	0.917518i	−0.333062	−	0.942905i	$-0.608082\pi$
$821$	19.1006	−	26.2897i	0.666616	−	0.917518i	0.999678	+	0.0253869i	$0.00808176\pi$
$822$	−6.52171	−	41.1764i	−0.227471	−	1.43619i
$823$	−17.9607	+	35.2498i	−0.626069	+	1.22873i	0.332294	+	0.943176i	$0.392178\pi$
$823$	−17.9607	+	35.2498i	−0.626069	+	1.22873i	−0.958363	+	0.285554i	$0.907822\pi$
$824$	−5.20711	+	7.16697i	−0.181398	+	0.249673i
$825$	−39.8632	−	21.5922i	−1.38786	−	0.751743i
$826$	5.81092	−	17.8842i	0.202188	−	0.622270i
$827$	−0.603023	+	3.80734i	−0.0209692	+	0.132394i	−0.995952	−	0.0898857i	$-0.971350\pi$
$827$	−0.603023	+	3.80734i	−0.0209692	+	0.132394i	0.974983	+	0.222280i	$0.0713498\pi$
$828$	4.22459	−	8.29123i	0.146815	−	0.288140i
$829$	−12.6101	−	38.8100i	−0.437968	−	1.34793i	−0.890014	−	0.455932i	$-0.849306\pi$
$829$	−12.6101	−	38.8100i	−0.437968	−	1.34793i	0.452046	−	0.891994i	$-0.350694\pi$
$830$	2.68638	+	8.63627i	0.0932458	+	0.299769i
$831$	−26.0257			−0.902823
$832$	3.17717	−	3.17717i	0.110149	−	0.110149i
$833$	−18.0328	+	9.18815i	−0.624798	+	0.318350i
$834$	21.8013	−	30.0070i	0.754919	−	1.03906i
$835$	−13.7286	+	6.77875i	−0.475097	+	0.234588i
$836$			17.8661i			0.617910i
$837$	6.10688	+	7.29863i	0.211085	+	0.252278i
$838$	−26.1446	+	26.1446i	−0.903149	+	0.903149i
$839$	2.13422	+	2.93751i	0.0736816	+	0.101414i	0.844267	−	0.535923i	$-0.180036\pi$
$839$	2.13422	+	2.93751i	0.0736816	+	0.101414i	−0.770586	+	0.637337i	$0.780036\pi$
$840$	−16.5423	+	16.1309i	−0.570762	+	0.556570i
$841$	−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
$845$	12.8847	+	9.61141i	0.443248	+	0.330643i
$846$	−2.52163	−	7.76077i	−0.0866953	−	0.266821i
$847$	20.6876	+	3.27659i	0.710834	+	0.112585i
$848$	−3.49158	+	1.77905i	−0.119901	+	0.0610928i
$849$	−38.5886	+	28.0363i	−1.32436	+	0.962202i
$850$	−6.25642	+	4.30917i	−0.214593	+	0.147803i
$851$	10.6641	+	32.8208i	0.365561	+	1.12508i
$852$	28.9739	−	4.58902i	0.992630	−	0.157217i
$853$	−0.856523	+	0.135660i	−0.0293268	+	0.00464491i	−0.171081	−	0.985257i	$-0.554726\pi$
$853$	−0.856523	+	0.135660i	−0.0293268	+	0.00464491i	0.141754	+	0.989902i	$0.454726\pi$
$854$	−13.8023	−	42.4792i	−0.472306	−	1.45361i
$855$	−0.286600	+	22.7663i	−0.00980151	+	0.778589i
$856$	14.1762	−	10.2996i	0.484531	−	0.352032i
$857$	−8.60725	+	4.38562i	−0.294018	+	0.149810i	−0.594778	−	0.803890i	$-0.702760\pi$
$857$	−8.60725	+	4.38562i	−0.294018	+	0.149810i	0.300759	+	0.953700i	$0.402760\pi$
$858$	−40.2386	−	6.37317i	−1.37372	−	0.217576i
$859$	0.474007	+	1.45884i	0.0161729	+	0.0497751i	0.958817	−	0.284024i	$-0.0916694\pi$
$859$	0.474007	+	1.45884i	0.0161729	+	0.0497751i	−0.942644	+	0.333799i	$0.891669\pi$
$860$	3.29801	+	22.6659i	0.112461	+	0.772900i
$861$	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	0.553992	−	0.832522i	$-0.313104\pi$
$863$	−8.18231	−	8.18231i	−0.278529	−	0.278529i	−0.832522	+	0.553992i	$0.813104\pi$
$864$	0.528177	−	1.62556i	0.0179689	−	0.0553027i
$865$	6.61766	+	6.78640i	0.225007	+	0.230745i
$866$	0.174099	+	0.239627i	0.00591613	+	0.00814286i
$867$	23.8128	−	23.8128i	0.808727	−	0.808727i
$868$	23.2841	−	9.36946i	0.790313	−	0.318020i
$869$			26.5813i			0.901707i
$870$	7.14402	−	21.0804i	0.242205	−	0.714691i
$871$	−10.9355	+	15.0514i	−0.370535	+	0.509998i
$872$	11.4374	−	5.82764i	0.387319	−	0.197349i
$873$	22.9408	−	22.9408i	0.776430	−	0.776430i
$874$	18.6440			0.630642
$875$	36.9576	−	34.2665i	1.24939	−	1.15842i
$876$	0.609676	+	1.87639i	0.0205990	+	0.0633973i
$877$	1.59519	−	3.13074i	0.0538659	−	0.105718i	−0.862504	−	0.506050i	$-0.831105\pi$
$877$	1.59519	−	3.13074i	0.0538659	−	0.105718i	0.916370	+	0.400332i	$0.131105\pi$
$878$	−0.317255	+	2.00307i	−0.0107068	+	0.0676002i
$879$	0.804070	−	2.47467i	0.0271206	−	0.0834686i
$880$	2.83890	−	8.37693i	0.0956992	−	0.282386i
$881$	−4.94661	+	6.80842i	−0.166656	+	0.229382i	−0.884174	−	0.467158i	$-0.845278\pi$
$881$	−4.94661	+	6.80842i	−0.166656	+	0.229382i	0.717518	+	0.696540i	$0.245278\pi$
$882$	13.6328	−	26.7560i	0.459042	−	0.900920i
$883$	−0.458288	−	2.89352i	−0.0154226	−	0.0973747i	0.978776	−	0.204932i	$-0.0656972\pi$
$883$	−0.458288	−	2.89352i	−0.0154226	−	0.0973747i	−0.994199	+	0.107557i	$0.965697\pi$
$884$	−4.01270	+	5.52300i	−0.134962	+	0.185759i
$885$	3.07872	+	21.1588i	0.103490	+	0.711244i
$886$	−27.7791	−	20.1827i	−0.933258	−	0.678052i
$887$	48.7400	+	7.71966i	1.63653	+	0.259201i	0.905875	−	0.423545i	$-0.139215\pi$
$887$	48.7400	+	7.71966i	1.63653	+	0.259201i	0.730655	+	0.682746i	$0.239215\pi$
$888$	−8.70023	−	17.0752i	−0.291960	−	0.573005i
$889$	−23.9185	+	17.3778i	−0.802202	+	0.582834i
$890$	8.78359	−	1.27806i	0.294427	−	0.0428407i
$891$	−40.1814	+	13.0557i	−1.34613	+	0.437383i
$892$	9.33843	+	18.3277i	0.312674	+	0.613657i
$893$	11.5607	−	11.5607i	0.386864	−	0.386864i
$894$	−1.84092			−0.0615695
$895$	3.48532	−	1.08414i	0.116501	−	0.0362388i
$896$	−3.64690	−	2.64963i	−0.121835	−	0.0885180i
$897$	−6.65066	+	41.9906i	−0.222059	+	1.40203i
$898$	−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
$902$	−15.8627	+	2.51240i	−0.528169	+	0.0836538i
$903$	−48.0518	−	94.3070i	−1.59907	−	3.13834i
$904$			9.66309i			0.321390i
$905$	−11.3835	+	8.05361i	−0.378399	+	0.267711i
$906$	−8.89010	+	27.3609i	−0.295354	+	0.909005i
$907$	−21.1615	+	41.5317i	−0.702655	+	1.37904i	0.212992	+	0.977054i	$0.431679\pi$
$907$	−21.1615	+	41.5317i	−0.702655	+	1.37904i	−0.915647	+	0.401984i	$0.868321\pi$
$908$	−15.0735	−	7.68033i	−0.500231	−	0.254881i
$909$	16.9841	+	23.3765i	0.563326	+	0.775351i
$910$	21.0678	−	40.0921i	0.698391	−	1.32904i
$911$	−3.08517	−	4.24637i	−0.102216	−	0.140688i	0.754845	−	0.655903i	$-0.227712\pi$
$911$	−3.08517	−	4.24637i	−0.102216	−	0.140688i	−0.857061	+	0.515215i	$0.827712\pi$
$912$	−10.2259	+	1.61962i	−0.338612	+	0.0536309i
$913$	14.2556	+	7.26359i	0.471791	+	0.240390i
$914$	3.69962	+	2.68793i	0.122373	+	0.0889089i
$915$	35.4565	+	36.3606i	1.17216	+	1.20204i
$916$	−26.1018	+	8.48097i	−0.862426	+	0.280219i
$917$	10.8771	+	68.6751i	0.359192	+	2.26785i
$918$	−0.406248	+	2.56495i	−0.0134082	+	0.0846560i
$919$	11.2223	+	3.64636i	0.370191	+	0.120282i	0.488203	−	0.872730i	$-0.337652\pi$
$919$	11.2223	+	3.64636i	0.370191	+	0.120282i	−0.118013	+	0.993012i	$0.537652\pi$
$920$	−8.74168	−	2.96251i	−0.288204	−	0.0976710i
$921$	51.0361	−	16.5826i	1.68170	−	0.546416i
$922$	−19.8671	−	10.1228i	−0.654288	−	0.333377i
$923$	−51.2347	+	26.1054i	−1.68641	+	0.859269i
$924$			40.8728i			1.34462i
$925$	18.0340	+	37.7116i	0.592954	+	1.23995i
$926$	28.6752	+	9.31713i	0.942325	+	0.306180i
$927$	3.12414	+	19.7251i	0.102610	+	0.647856i
$928$	4.28906	+	0.679320i	0.140795	+	0.0222998i
$929$	−10.8038			−0.354462			−0.177231	−	0.984169i	$-0.556714\pi$
$929$	−10.8038			−0.354462			−0.177231	+	0.984169i	$0.556714\pi$
$930$	−19.0221	+	21.2740i	−0.623760	+	0.697601i
$931$	60.1644			1.97181
$932$	−0.529257	−	0.0838260i	−0.0173364	−	0.00274581i
$933$	9.73563	+	61.4684i	0.318730	+	2.01238i
$934$	−37.5051	−	12.1862i	−1.22721	−	0.398743i
$935$	−2.26918	+	13.2457i	−0.0742101	+	0.433180i
$936$		−	10.1292i		−	0.331084i
$937$	−44.0071	+	22.4228i	−1.43765	+	0.732519i	−0.987081	−	0.160222i	$-0.948779\pi$
$937$	−44.0071	+	22.4228i	−1.43765	+	0.732519i	−0.450569	+	0.892741i	$0.648779\pi$
$938$	16.6307	+	8.47379i	0.543013	+	0.276679i
$939$	−19.4532	+	6.32073i	−0.634831	+	0.206269i
$940$	−7.25749	+	3.58353i	−0.236713	+	0.116882i
$941$	25.8324	+	8.39347i	0.842114	+	0.273619i	0.698139	−	0.715962i	$-0.254012\pi$
$941$	25.8324	+	8.39347i	0.842114	+	0.273619i	0.143974	+	0.989581i	$0.454012\pi$
$942$	−3.15521	+	19.9212i	−0.102802	+	0.649068i
$943$	2.62179	+	16.5534i	0.0853773	+	0.539051i
$944$	−3.96736	+	1.28907i	−0.129127	+	0.0419558i
$945$	0.216870	−	17.2272i	0.00705477	−	0.560400i
$946$	32.7796	+	23.8157i	1.06576	+	0.774316i
$947$	5.72201	+	2.91551i	0.185940	+	0.0947413i	0.544483	−	0.838772i	$-0.316726\pi$
$947$	5.72201	+	2.91551i	0.185940	+	0.0947413i	−0.358542	+	0.933514i	$0.616726\pi$
$948$	−15.2141	+	2.40968i	−0.494131	+	0.0782627i
$949$	−2.27317	−	3.12875i	−0.0737902	−	0.101563i
$950$	22.3873	−	2.97020i	0.726340	−	0.0963661i
$951$	−2.98126	−	4.10335i	−0.0966739	−	0.133060i
$952$	6.10253	+	3.10939i	0.197784	+	0.100776i
$953$	−2.13252	+	4.18531i	−0.0690791	+	0.135575i	−0.922964	−	0.384887i	$-0.874240\pi$
$953$	−2.13252	+	4.18531i	−0.0690791	+	0.135575i	0.853885	+	0.520462i	$0.174240\pi$
$954$	−2.72988	+	8.40171i	−0.0883832	+	0.272015i
$955$	17.9605	+	25.3865i	0.581188	+	0.821487i
$956$		−	15.1645i		−	0.490456i
$957$	−17.8754	−	35.0825i	−0.577830	−	1.13405i
$958$	−5.31200	+	0.841339i	−0.171623	+	0.0271824i
$959$	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
$963$	6.17951	−	39.0159i	0.199132	−	1.25727i
$964$	−10.4752	−	7.61071i	−0.337385	−	0.245124i
$965$	−8.17519	+	15.5574i	−0.263169	+	0.500811i
$966$	42.6524			1.37232
$967$	12.4742	−	12.4742i	0.401143	−	0.401143i	−0.477493	−	0.878636i	$-0.658454\pi$
$967$	12.4742	−	12.4742i	0.401143	−	0.401143i	0.878636	+	0.477493i	$0.158454\pi$
$968$	−2.10945	−	4.14003i	−0.0678004	−	0.133066i
$969$	14.9606	−	4.86098i	0.480603	−	0.156157i
$970$	−25.7942	−	19.2413i	−0.828201	−	0.617800i
$971$	−23.5311	+	17.0964i	−0.755150	+	0.548649i	−0.897419	−	0.441179i	$-0.854560\pi$
$971$	−23.5311	+	17.0964i	−0.755150	+	0.548649i	0.142269	+	0.989828i	$0.454560\pi$
$972$	−8.78728	−	17.2460i	−0.281852	−	0.553166i
$973$	72.0430	+	11.4105i	2.30959	+	0.365804i
$974$	−24.1940	−	17.5780i	−0.775226	−	0.563235i
$975$	−1.29637	+	51.4810i	−0.0415172	+	1.64871i
$976$	−5.82401	+	8.01606i	−0.186422	+	0.256588i
$977$	0.824093	+	5.20312i	0.0263651	+	0.166462i	0.997358	−	0.0726468i	$-0.0231446\pi$
$977$	0.824093	+	5.20312i	0.0263651	+	0.166462i	−0.970993	+	0.239109i	$0.923145\pi$
$978$	−12.9501	+	25.4159i	−0.414098	+	0.812712i
$979$	9.22918	−	12.7029i	0.294966	−	0.405986i
$980$	−28.2095	−	9.56006i	−0.901121	−	0.305385i
$981$	8.94230	−	27.5216i	0.285506	−	0.878696i
$982$	−0.262607	+	1.65804i	−0.00838013	+	0.0529101i
$983$	6.23301	−	12.2330i	0.198802	−	0.390171i	−0.769986	−	0.638061i	$-0.779737\pi$
$983$	6.23301	−	12.2330i	0.198802	−	0.390171i	0.968788	+	0.247889i	$0.0797369\pi$
$984$	−2.87601	−	8.85144i	−0.0916837	−	0.282174i
$985$	15.7613	−	29.9937i	0.502195	−	0.955680i
$986$	−6.59787			−0.210119
$987$	26.4478	−	26.4478i	0.841842	−	0.841842i
$988$	18.0824	−	9.21346i	0.575279	−	0.293119i
$989$	24.8527	−	34.2068i	0.790270	−	1.08771i
$990$	−8.82798	−	17.8787i	−0.280571	−	0.568224i
$991$		−	17.9482i		−	0.570143i	−0.958506	−	0.285072i	$-0.907983\pi$
$991$		−	17.9482i		−	0.570143i	0.958506	−	0.285072i	$-0.0920174\pi$
$992$	−4.71759	−	2.95708i	−0.149784	−	0.0938873i
$993$	27.5329	−	27.5329i	0.873731	−	0.873731i
$994$	33.9089	+	46.6716i	1.07552	+	1.48033i
$995$	0.476825	−	37.8769i	0.0151164	−	1.20078i
$996$	−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.77.7	✓	128
5.3	odd	4	inner	310.2.s.a.263.2	yes	128
31.29	odd	10	inner	310.2.s.a.277.2	yes	128
155.153	even	20	inner	310.2.s.a.153.7	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
310.2.s.a.77.7	✓	128	1.1	even	1	trivial
310.2.s.a.153.7	yes	128	155.153	even	20	inner
310.2.s.a.263.2	yes	128	5.3	odd	4	inner
310.2.s.a.277.2	yes	128	31.29	odd	10	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:	\( N \)	\(=\)	\( 310 = 2 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	310.s (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.987688 - 0.156434i) q^{2} +(0.358585 + 2.26401i) q^{3} +(0.951057 + 0.309017i) q^{4} +(-1.29145 - 1.82542i) q^{5} -2.29224i q^{6} +(4.01650 - 2.04651i) q^{7} +(-0.891007 - 0.453990i) q^{8} +(-2.14401 + 0.696631i) q^{9} +O(q^{10})\)	\(q+(-0.987688 - 0.156434i) q^{2} +(0.358585 + 2.26401i) q^{3} +(0.951057 + 0.309017i) q^{4} +(-1.29145 - 1.82542i) q^{5} -2.29224i q^{6} +(4.01650 - 2.04651i) q^{7} +(-0.891007 - 0.453990i) q^{8} +(-2.14401 + 0.696631i) q^{9} +(0.989994 + 2.00497i) q^{10} +(3.76196 + 1.22234i) q^{11} +(-0.358585 + 2.26401i) q^{12} +(-0.702891 - 4.43788i) q^{13} +(-4.28719 + 1.39299i) q^{14} +(3.66968 - 3.57843i) q^{15} +(0.809017 + 0.587785i) q^{16} +(-1.35376 - 0.689777i) q^{17} +(2.22659 - 0.352657i) q^{18} +(2.65485 + 3.65408i) q^{19} +(-0.664159 - 2.13516i) q^{20} +(6.07358 + 8.35957i) q^{21} +(-3.52443 - 1.79579i) q^{22} +(-1.87398 + 3.67789i) q^{23} +(0.708340 - 2.18005i) q^{24} +(-1.66430 + 4.71488i) q^{25} +4.49320i q^{26} +(0.775968 + 1.52292i) q^{27} +(4.45232 - 0.705179i) 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} +(-1.41840 + 8.95545i) q^{33} +(1.22919 + 0.893060i) q^{34} +(-8.92285 - 4.68882i) q^{35} -2.25435 q^{36} +(5.91166 - 5.91166i) q^{37} +(-2.05054 - 4.02440i) q^{38} +(9.79537 - 3.18271i) q^{39} +(0.321970 + 2.21277i) q^{40} +(3.28478 - 2.38653i) q^{41} +(-4.69108 - 9.20676i) q^{42} +(-10.1171 - 1.60240i) q^{43} +(3.20012 + 2.32502i) q^{44} +(4.04053 + 3.01405i) q^{45} +(2.42626 - 3.33945i) q^{46} +(-0.566253 - 3.57518i) q^{47} +(-1.04065 + 2.04240i) q^{48} +(7.82957 - 10.7765i) q^{49} +(2.38138 - 4.39648i) q^{50} +(1.07623 - 3.31229i) q^{51} +(0.702891 - 4.43788i) q^{52} +(-1.77905 + 3.49158i) q^{53} +(-0.528177 - 1.62556i) q^{54} +(-2.62712 - 8.44574i) q^{55} -4.50782 q^{56} +(-7.32091 + 7.32091i) q^{57} +(3.86921 - 1.97146i) q^{58} +(-2.45196 + 3.37484i) q^{59} +(4.59587 - 2.26930i) q^{60} +9.90839i q^{61} +(-5.55474 + 0.380608i) q^{62} +(-7.18575 + 7.18575i) q^{63} +(0.587785 + 0.809017i) q^{64} +(-7.19323 + 7.01438i) 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} +(8.07950 + 6.02694i) q^{70} +(-3.95467 - 12.1712i) q^{71} +(2.22659 + 0.352657i) q^{72} +(0.766899 - 0.390755i) q^{73} +(-6.76367 + 4.91409i) q^{74} +(-11.2714 - 2.07732i) q^{75} +(1.39573 + 4.29563i) q^{76} +(17.6114 - 2.78938i) q^{77} +(-10.1727 + 1.61119i) q^{78} +(2.07659 + 6.39107i) q^{79} +(0.0281472 - 2.23589i) q^{80} +(-8.64108 + 6.27811i) q^{81} +(-3.61767 + 1.84330i) q^{82} +(3.99499 + 0.632745i) q^{83} +(3.19307 + 9.82726i) q^{84} +(0.489189 + 3.36200i) 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} +(-3.51928 - 3.60902i) q^{90} +(-11.9053 - 16.3863i) q^{91} +(-2.91879 + 2.91879i) q^{92} +(4.76439 + 11.8400i) q^{93} +3.61975i q^{94} +(3.24162 - 9.56527i) q^{95} +(1.34734 - 1.85446i) q^{96} +(-12.8229 + 6.53357i) 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

Related objects

Downloads

Learn more