LMFDB - Embedded newform 510.2.l.g.137.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [510,2,Mod(137,510)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(510, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0]))

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

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

chi := DirichletCharacter("510.137");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 510 = 2 \cdot 3 \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	510.l (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.07237050309$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			137.4
Character	$\chi$	$=$	510.137
Dual form			510.2.l.g.443.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(0.209343 + 1.71935i) q^{3} -1.00000i q^{4} +(-1.22996 + 1.86740i) q^{5} +(-1.36379 - 1.06774i) q^{6} +(1.96777 + 1.96777i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.91235 + 0.719870i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(0.209343 + 1.71935i) q^{3} -1.00000i q^{4} +(-1.22996 + 1.86740i) q^{5} +(-1.36379 - 1.06774i) q^{6} +(1.96777 + 1.96777i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.91235 + 0.719870i) q^{9} +(-0.450736 - 2.19017i) q^{10} +2.52895i q^{11} +(1.71935 - 0.209343i) q^{12} +(0.989239 - 0.989239i) q^{13} -2.78285 q^{14} +(-3.46821 - 1.72382i) q^{15} -1.00000 q^{16} +(-0.707107 + 0.707107i) q^{17} +(1.55032 - 2.56837i) q^{18} -1.20796i q^{19} +(1.86740 + 1.22996i) q^{20} +(-2.97136 + 3.79523i) q^{21} +(-1.78824 - 1.78824i) q^{22} +(2.54000 + 2.54000i) q^{23} +(-1.06774 + 1.36379i) q^{24} +(-1.97438 - 4.59367i) q^{25} +1.39900i q^{26} +(-1.84739 - 4.85666i) q^{27} +(1.96777 - 1.96777i) q^{28} -4.48489 q^{29} +(3.67131 - 1.23347i) q^{30} -2.67060 q^{31} +(0.707107 - 0.707107i) q^{32} +(-4.34815 + 0.529418i) q^{33} -1.00000i q^{34} +(-6.09491 + 1.25433i) q^{35} +(0.719870 + 2.91235i) q^{36} +(-0.953720 - 0.953720i) q^{37} +(0.854153 + 0.854153i) q^{38} +(1.90794 + 1.49376i) q^{39} +(-2.19017 + 0.450736i) q^{40} +8.82636i q^{41} +(-0.582571 - 4.78470i) q^{42} +(0.0549708 - 0.0549708i) q^{43} +2.52895 q^{44} +(2.23780 - 6.32394i) q^{45} -3.59210 q^{46} +(8.35634 - 8.35634i) q^{47} +(-0.209343 - 1.71935i) q^{48} +0.744252i q^{49} +(4.64431 + 1.85212i) q^{50} +(-1.36379 - 1.06774i) q^{51} +(-0.989239 - 0.989239i) q^{52} +(-7.21125 - 7.21125i) q^{53} +(4.74048 + 2.12787i) q^{54} +(-4.72256 - 3.11051i) q^{55} +2.78285i q^{56} +(2.07690 - 0.252877i) q^{57} +(3.17130 - 3.17130i) q^{58} -7.12840 q^{59} +(-1.72382 + 3.46821i) q^{60} +7.63437 q^{61} +(1.88840 - 1.88840i) q^{62} +(-7.14738 - 4.31430i) q^{63} +1.00000i q^{64} +(0.630578 + 3.06404i) q^{65} +(2.70025 - 3.44896i) q^{66} +(9.61120 + 9.61120i) q^{67} +(0.707107 + 0.707107i) q^{68} +(-3.83542 + 4.89889i) q^{69} +(3.42281 - 5.19670i) q^{70} +6.19766i q^{71} +(-2.56837 - 1.55032i) q^{72} +(-4.99754 + 4.99754i) q^{73} +1.34876 q^{74} +(7.48483 - 4.35630i) q^{75} -1.20796 q^{76} +(-4.97639 + 4.97639i) q^{77} +(-2.40537 + 0.292870i) q^{78} +6.89543i q^{79} +(1.22996 - 1.86740i) q^{80} +(7.96357 - 4.19303i) q^{81} +(-6.24118 - 6.24118i) q^{82} +(-6.01743 - 6.01743i) q^{83} +(3.79523 + 2.97136i) q^{84} +(-0.450736 - 2.19017i) q^{85} +0.0777404i q^{86} +(-0.938882 - 7.71112i) q^{87} +(-1.78824 + 1.78824i) q^{88} +8.16385 q^{89} +(2.88934 + 6.05407i) q^{90} +3.89319 q^{91} +(2.54000 - 2.54000i) q^{92} +(-0.559072 - 4.59171i) q^{93} +11.8177i q^{94} +(2.25574 + 1.48574i) q^{95} +(1.36379 + 1.06774i) q^{96} +(12.1755 + 12.1755i) q^{97} +(-0.526266 - 0.526266i) q^{98} +(-1.82051 - 7.36518i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 4 q^{7}+O(q^{10}) $ 28 * q + 4 * q^7	$ 28 q + 4 q^{7} - 12 q^{10} - 8 q^{13} + 8 q^{15} - 28 q^{16} - 16 q^{18} + 48 q^{21} + 20 q^{22} + 40 q^{25} - 36 q^{27} + 4 q^{28} - 12 q^{30} + 16 q^{31} + 8 q^{33} + 8 q^{37} - 8 q^{40} - 48 q^{42} + 48 q^{43} + 36 q^{45} - 64 q^{46} + 8 q^{52} - 36 q^{55} - 32 q^{57} + 20 q^{58} + 12 q^{60} - 16 q^{61} - 56 q^{63} + 32 q^{66} + 112 q^{67} - 28 q^{70} + 16 q^{72} + 12 q^{73} + 16 q^{75} - 8 q^{76} - 32 q^{78} - 48 q^{81} + 24 q^{82} - 12 q^{85} - 44 q^{87} + 20 q^{88} - 20 q^{90} - 80 q^{91} + 28 q^{93} + 60 q^{97}+O(q^{100}) $ 28 * q + 4 * q^7 - 12 * q^10 - 8 * q^13 + 8 * q^15 - 28 * q^16 - 16 * q^18 + 48 * q^21 + 20 * q^22 + 40 * q^25 - 36 * q^27 + 4 * q^28 - 12 * q^30 + 16 * q^31 + 8 * q^33 + 8 * q^37 - 8 * q^40 - 48 * q^42 + 48 * q^43 + 36 * q^45 - 64 * q^46 + 8 * q^52 - 36 * q^55 - 32 * q^57 + 20 * q^58 + 12 * q^60 - 16 * q^61 - 56 * q^63 + 32 * q^66 + 112 * q^67 - 28 * q^70 + 16 * q^72 + 12 * q^73 + 16 * q^75 - 8 * q^76 - 32 * q^78 - 48 * q^81 + 24 * q^82 - 12 * q^85 - 44 * q^87 + 20 * q^88 - 20 * q^90 - 80 * q^91 + 28 * q^93 + 60 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/510\mathbb{Z}\right)^\times$.

$n$	$241$	$307$	$341$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$	0.209343	+	1.71935i	0.120864	+	0.992669i
$3$	0.209343	+	1.71935i	0.120864	+	0.992669i
$4$		−	1.00000i		−	0.500000i
$5$	−1.22996	+	1.86740i	−0.550057	+	0.835127i
$5$	−1.22996	+	1.86740i	−0.550057	+	0.835127i
$6$	−1.36379	−	1.06774i	−0.556767	−	0.435902i
$7$	1.96777	+	1.96777i	0.743748	+	0.743748i	0.973297	−	0.229549i	$-0.0737252\pi$
$7$	1.96777	+	1.96777i	0.743748	+	0.743748i	−0.229549	+	0.973297i	$0.573725\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	−2.91235	+	0.719870i	−0.970784	+	0.239957i
$10$	−0.450736	−	2.19017i	−0.142535	−	0.692592i
$11$			2.52895i			0.762506i	0.924471	+	0.381253i	$0.124507\pi$
$11$			2.52895i			0.762506i	−0.924471	+	0.381253i	$0.875493\pi$
$12$	1.71935	−	0.209343i	0.496335	−	0.0604322i
$13$	0.989239	−	0.989239i	0.274366	−	0.274366i	−0.556489	−	0.830855i	$-0.687852\pi$
$13$	0.989239	−	0.989239i	0.274366	−	0.274366i	0.830855	+	0.556489i	$0.187852\pi$
$14$	−2.78285			−0.743748
$15$	−3.46821	−	1.72382i	−0.895487	−	0.445087i
$16$	−1.00000			−0.250000
$17$	−0.707107	+	0.707107i	−0.171499	+	0.171499i
$17$	−0.707107	+	0.707107i	−0.171499	+	0.171499i
$18$	1.55032	−	2.56837i	0.365413	−	0.605370i
$19$		−	1.20796i		−	0.277124i	−0.990354	−	0.138562i	$-0.955752\pi$
$19$		−	1.20796i		−	0.277124i	0.990354	−	0.138562i	$-0.0442480\pi$
$20$	1.86740	+	1.22996i	0.417564	+	0.275028i
$21$	−2.97136	+	3.79523i	−0.648403	+	0.828188i
$22$	−1.78824	−	1.78824i	−0.381253	−	0.381253i
$23$	2.54000	+	2.54000i	0.529626	+	0.529626i	0.920461	−	0.390835i	$-0.127814\pi$
$23$	2.54000	+	2.54000i	0.529626	+	0.529626i	−0.390835	+	0.920461i	$0.627814\pi$
$24$	−1.06774	+	1.36379i	−0.217951	+	0.278383i
$25$	−1.97438	−	4.59367i	−0.394875	−	0.918735i
$26$			1.39900i			0.274366i
$27$	−1.84739	−	4.85666i	−0.355531	−	0.934665i
$28$	1.96777	−	1.96777i	0.371874	−	0.371874i
$29$	−4.48489			−0.832824			−0.416412	−	0.909176i	$-0.636713\pi$
$29$	−4.48489			−0.832824			−0.416412	+	0.909176i	$0.636713\pi$
$30$	3.67131	−	1.23347i	0.670287	−	0.225200i
$31$	−2.67060			−0.479654			−0.239827	−	0.970816i	$-0.577091\pi$
$31$	−2.67060			−0.479654			−0.239827	+	0.970816i	$0.577091\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	−4.34815	+	0.529418i	−0.756916	+	0.0921598i
$34$		−	1.00000i		−	0.171499i
$35$	−6.09491	+	1.25433i	−1.03023	+	0.212021i
$36$	0.719870	+	2.91235i	0.119978	+	0.485392i
$37$	−0.953720	−	0.953720i	−0.156791	−	0.156791i	0.624352	−	0.781143i	$-0.285363\pi$
$37$	−0.953720	−	0.953720i	−0.156791	−	0.156791i	−0.781143	+	0.624352i	$0.785363\pi$
$38$	0.854153	+	0.854153i	0.138562	+	0.138562i
$39$	1.90794	+	1.49376i	0.305515	+	0.239193i
$40$	−2.19017	+	0.450736i	−0.346296	+	0.0712676i
$41$			8.82636i			1.37845i	0.724549	+	0.689223i	$0.242048\pi$
$41$			8.82636i			1.37845i	−0.724549	+	0.689223i	$0.757952\pi$
$42$	−0.582571	−	4.78470i	−0.0898926	−	0.738295i
$43$	0.0549708	−	0.0549708i	0.00838296	−	0.00838296i	−0.702903	−	0.711286i	$-0.748113\pi$
$43$	0.0549708	−	0.0549708i	0.00838296	−	0.00838296i	0.711286	+	0.702903i	$0.248113\pi$
$44$	2.52895			0.381253
$45$	2.23780	−	6.32394i	0.333592	−	0.942718i
$46$	−3.59210			−0.529626
$47$	8.35634	−	8.35634i	1.21890	−	1.21890i	0.250879	−	0.968018i	$-0.419280\pi$
$47$	8.35634	−	8.35634i	1.21890	−	1.21890i	0.968018	−	0.250879i	$-0.0807198\pi$
$48$	−0.209343	−	1.71935i	−0.0302161	−	0.248167i
$49$			0.744252i			0.106322i
$50$	4.64431	+	1.85212i	0.656805	+	0.261930i
$51$	−1.36379	−	1.06774i	−0.190969	−	0.149513i
$52$	−0.989239	−	0.989239i	−0.137183	−	0.137183i
$53$	−7.21125	−	7.21125i	−0.990541	−	0.990541i	0.00941435	−	0.999956i	$-0.497003\pi$
$53$	−7.21125	−	7.21125i	−0.990541	−	0.990541i	−0.999956	+	0.00941435i	$0.997003\pi$
$54$	4.74048	+	2.12787i	0.645098	+	0.289567i
$55$	−4.72256	−	3.11051i	−0.636790	−	0.419422i
$56$			2.78285i			0.371874i
$57$	2.07690	−	0.252877i	0.275092	−	0.0334944i
$58$	3.17130	−	3.17130i	0.416412	−	0.416412i
$59$	−7.12840			−0.928039			−0.464020	−	0.885825i	$-0.653593\pi$
$59$	−7.12840			−0.928039			−0.464020	+	0.885825i	$0.653593\pi$
$60$	−1.72382	+	3.46821i	−0.222544	+	0.447744i
$61$	7.63437			0.977481			0.488741	−	0.872429i	$-0.337456\pi$
$61$	7.63437			0.977481			0.488741	+	0.872429i	$0.337456\pi$
$62$	1.88840	−	1.88840i	0.239827	−	0.239827i
$63$	−7.14738	−	4.31430i	−0.900485	−	0.543551i
$64$			1.00000i			0.125000i
$65$	0.630578	+	3.06404i	0.0782135	+	0.380047i
$66$	2.70025	−	3.44896i	0.332378	−	0.424538i
$67$	9.61120	+	9.61120i	1.17419	+	1.17419i	0.981200	+	0.192995i	$0.0618202\pi$
$67$	9.61120	+	9.61120i	1.17419	+	1.17419i	0.192995	+	0.981200i	$0.438180\pi$
$68$	0.707107	+	0.707107i	0.0857493	+	0.0857493i
$69$	−3.83542	+	4.89889i	−0.461731	+	0.589757i
$70$	3.42281	−	5.19670i	0.409104	−	0.621124i
$71$			6.19766i			0.735527i	0.929919	+	0.367763i	$0.119876\pi$
$71$			6.19766i			0.735527i	−0.929919	+	0.367763i	$0.880124\pi$
$72$	−2.56837	−	1.55032i	−0.302685	−	0.182707i
$73$	−4.99754	+	4.99754i	−0.584918	+	0.584918i	−0.936251	−	0.351333i	$-0.885729\pi$
$73$	−4.99754	+	4.99754i	−0.584918	+	0.584918i	0.351333	+	0.936251i	$0.385729\pi$
$74$	1.34876			0.156791
$75$	7.48483	−	4.35630i	0.864273	−	0.503023i
$76$	−1.20796			−0.138562
$77$	−4.97639	+	4.97639i	−0.567112	+	0.567112i
$78$	−2.40537	+	0.292870i	−0.272354	+	0.0331610i
$79$			6.89543i			0.775797i	0.921702	+	0.387898i	$0.126799\pi$
$79$			6.89543i			0.775797i	−0.921702	+	0.387898i	$0.873201\pi$
$80$	1.22996	−	1.86740i	0.137514	−	0.208782i
$81$	7.96357	−	4.19303i	0.884842	−	0.465892i
$82$	−6.24118	−	6.24118i	−0.689223	−	0.689223i
$83$	−6.01743	−	6.01743i	−0.660498	−	0.660498i	0.294999	−	0.955498i	$-0.404681\pi$
$83$	−6.01743	−	6.01743i	−0.660498	−	0.660498i	−0.955498	+	0.294999i	$0.904681\pi$
$84$	3.79523	+	2.97136i	0.414094	+	0.324201i
$85$	−0.450736	−	2.19017i	−0.0488892	−	0.237557i
$86$			0.0777404i			0.00838296i
$87$	−0.938882	−	7.71112i	−0.100659	−	0.826718i
$88$	−1.78824	+	1.78824i	−0.190627	+	0.190627i
$89$	8.16385			0.865366			0.432683	−	0.901546i	$-0.357567\pi$
$89$	8.16385			0.865366			0.432683	+	0.901546i	$0.357567\pi$
$90$	2.88934	+	6.05407i	0.304563	+	0.638155i
$91$	3.89319			0.408118
$92$	2.54000	−	2.54000i	0.264813	−	0.264813i
$93$	−0.559072	−	4.59171i	−0.0579731	−	0.476138i
$94$			11.8177i			1.21890i
$95$	2.25574	+	1.48574i	0.231434	+	0.152434i
$96$	1.36379	+	1.06774i	0.139192	+	0.108976i
$97$	12.1755	+	12.1755i	1.23623	+	1.23623i	0.961530	+	0.274700i	$0.0885784\pi$
$97$	12.1755	+	12.1755i	1.23623	+	1.23623i	0.274700	+	0.961530i	$0.411422\pi$
$98$	−0.526266	−	0.526266i	−0.0531608	−	0.0531608i
$99$	−1.82051	−	7.36518i	−0.182968	−	0.740228i
$100$	−4.59367	+	1.97438i	−0.459367	+	0.197438i
$101$			7.62404i			0.758621i	0.925269	+	0.379310i	$0.123839\pi$
$101$			7.62404i			0.758621i	−0.925269	+	0.379310i	$0.876161\pi$
$102$	1.71935	−	0.209343i	0.170241	−	0.0207281i
$103$	−8.95809	+	8.95809i	−0.882667	+	0.882667i	−0.993805	−	0.111138i	$-0.964550\pi$
$103$	−8.95809	+	8.95809i	−0.882667	+	0.882667i	0.111138	+	0.993805i	$0.464550\pi$
$104$	1.39900			0.137183
$105$	−3.43256	−	10.2167i	−0.334984	−	0.997049i
$106$	10.1982			0.990541
$107$	10.2145	−	10.2145i	0.987472	−	0.987472i	−0.0124505	−	0.999922i	$-0.503963\pi$
$107$	10.2145	−	10.2145i	0.987472	−	0.987472i	0.999922	+	0.0124505i	$0.00396323\pi$
$108$	−4.85666	+	1.84739i	−0.467332	+	0.177765i
$109$			11.0093i			1.05450i	0.849710	+	0.527251i	$0.176777\pi$
$109$			11.0093i			1.05450i	−0.849710	+	0.527251i	$0.823223\pi$
$110$	5.53882	−	1.13989i	0.528106	−	0.108684i
$111$	1.44013	−	1.83944i	0.136691	−	0.174592i
$112$	−1.96777	−	1.96777i	−0.185937	−	0.185937i
$113$	11.0369	+	11.0369i	1.03826	+	1.03826i	0.999238	+	0.0390248i	$0.0124251\pi$
$113$	11.0369	+	11.0369i	1.03826	+	1.03826i	0.0390248	+	0.999238i	$0.487575\pi$
$114$	−1.28978	+	1.64740i	−0.120799	+	0.154293i
$115$	−7.86731	+	1.61909i	−0.733630	+	0.150981i
$116$			4.48489i			0.416412i
$117$	−2.16889	+	3.59313i	−0.200514	+	0.332185i
$118$	5.04054	−	5.04054i	0.464020	−	0.464020i
$119$	−2.78285			−0.255103
$120$	−1.23347	−	3.67131i	−0.112600	−	0.335144i
$121$	4.60443			0.418585
$122$	−5.39832	+	5.39832i	−0.488741	+	0.488741i
$123$	−15.1756	+	1.84774i	−1.36834	+	0.166605i
$124$			2.67060i			0.239827i
$125$	11.0066	+	1.96310i	0.984464	+	0.175585i
$126$	8.10463	−	2.00329i	0.722018	−	0.178467i
$127$	4.77180	+	4.77180i	0.423429	+	0.423429i	0.886382	−	0.462954i	$-0.153210\pi$
$127$	4.77180	+	4.77180i	0.423429	+	0.423429i	−0.462954	+	0.886382i	$0.653210\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	0.106022	+	0.0830064i	0.00933471	+	0.00730831i
$130$	−2.61249	−	1.72071i	−0.229130	−	0.150917i
$131$		−	4.32841i		−	0.378175i	−0.981960	−	0.189087i	$-0.939447\pi$
$131$		−	4.32841i		−	0.378175i	0.981960	−	0.189087i	$-0.0605529\pi$
$132$	0.529418	+	4.34815i	0.0460799	+	0.378458i
$133$	2.37698	−	2.37698i	0.206110	−	0.206110i
$134$	−13.5923			−1.17419
$135$	11.3416	+	2.52370i	0.976126	+	0.217205i
$136$	−1.00000			−0.0857493
$137$	−0.710284	+	0.710284i	−0.0606837	+	0.0606837i	−0.736797	−	0.676114i	$-0.763663\pi$
$137$	−0.710284	+	0.710284i	−0.0606837	+	0.0606837i	0.676114	+	0.736797i	$0.263663\pi$
$138$	−0.751982	−	6.17609i	−0.0640130	−	0.525744i
$139$		−	14.4568i		−	1.22621i	−0.790001	−	0.613106i	$-0.789920\pi$
$139$		−	14.4568i		−	1.22621i	0.790001	−	0.613106i	$-0.210080\pi$
$140$	1.25433	+	6.09491i	0.106010	+	0.515114i
$141$	16.1168	+	12.6182i	1.35728	+	1.06264i
$142$	−4.38241	−	4.38241i	−0.367763	−	0.367763i
$143$	2.50173	+	2.50173i	0.209205	+	0.209205i
$144$	2.91235	−	0.719870i	0.242696	−	0.0599892i
$145$	5.51626	−	8.37510i	0.458100	−	0.695514i
$146$		−	7.06759i		−	0.584918i
$147$	−1.27963	+	0.155804i	−0.105542	+	0.0128505i
$148$	−0.953720	+	0.953720i	−0.0783953	+	0.0783953i
$149$	8.47958			0.694674			0.347337	−	0.937740i	$-0.387086\pi$
$149$	8.47958			0.694674			0.347337	+	0.937740i	$0.387086\pi$
$150$	−2.21220	+	8.37294i	−0.180625	+	0.683648i
$151$	5.31468			0.432503			0.216251	−	0.976338i	$-0.430617\pi$
$151$	5.31468			0.432503			0.216251	+	0.976338i	$0.430617\pi$
$152$	0.854153	−	0.854153i	0.0692810	−	0.0692810i
$153$	1.55032	−	2.56837i	0.125336	−	0.207640i
$154$		−	7.03768i		−	0.567112i
$155$	3.28475	−	4.98709i	0.263837	−	0.400572i
$156$	1.49376	−	1.90794i	0.119597	−	0.152758i
$157$	7.02850	+	7.02850i	0.560936	+	0.560936i	0.929573	−	0.368638i	$-0.120176\pi$
$157$	7.02850	+	7.02850i	0.560936	+	0.560936i	−0.368638	+	0.929573i	$0.620176\pi$
$158$	−4.87581	−	4.87581i	−0.387898	−	0.387898i
$159$	10.8891	−	13.9083i	0.863559	−	1.10300i
$160$	0.450736	+	2.19017i	0.0356338	+	0.173148i
$161$			9.99628i			0.787817i
$162$	−2.66618	+	8.59602i	−0.209475	+	0.675367i
$163$	9.32418	−	9.32418i	0.730326	−	0.730326i	−0.240358	−	0.970684i	$-0.577265\pi$
$163$	9.32418	−	9.32418i	0.730326	−	0.730326i	0.970684	+	0.240358i	$0.0772648\pi$
$164$	8.82636			0.689223
$165$	4.35944	−	8.77091i	0.339382	−	0.682814i
$166$	8.50993			0.660498
$167$	−0.878378	+	0.878378i	−0.0679709	+	0.0679709i	−0.740275	−	0.672304i	$-0.765305\pi$
$167$	−0.878378	+	0.878378i	−0.0679709	+	0.0679709i	0.672304	+	0.740275i	$0.265305\pi$
$168$	−4.78470	+	0.582571i	−0.369148	+	0.0449463i
$169$			11.0428i			0.849447i
$170$	1.86740	+	1.22996i	0.143223	+	0.0943340i
$171$	0.869570	+	3.51799i	0.0664977	+	0.269027i
$172$	−0.0549708	−	0.0549708i	−0.00419148	−	0.00419148i
$173$	14.4146	+	14.4146i	1.09592	+	1.09592i	0.994882	+	0.101043i	$0.0322179\pi$
$173$	14.4146	+	14.4146i	1.09592	+	1.09592i	0.101043	+	0.994882i	$0.467782\pi$
$174$	6.11647	+	4.78869i	0.463689	+	0.363030i
$175$	5.15418	−	12.9244i	0.389620	−	0.976995i
$176$		−	2.52895i		−	0.190627i
$177$	−1.49228	−	12.2562i	−0.112167	−	0.921236i
$178$	−5.77271	+	5.77271i	−0.432683	+	0.432683i
$179$	−24.7375			−1.84897			−0.924484	−	0.381220i	$-0.875504\pi$
$179$	−24.7375			−1.84897			−0.924484	+	0.381220i	$0.875504\pi$
$180$	−6.32394	−	2.23780i	−0.471359	−	0.166796i
$181$	−16.2804			−1.21012			−0.605058	−	0.796182i	$-0.706850\pi$
$181$	−16.2804			−1.21012			−0.605058	+	0.796182i	$0.706850\pi$
$182$	−2.75290	+	2.75290i	−0.204059	+	0.204059i
$183$	1.59820	+	13.1262i	0.118143	+	0.970315i
$184$			3.59210i			0.264813i
$185$	2.95402	−	0.607936i	0.217184	−	0.0446964i
$186$	3.64215	+	2.85150i	0.267056	+	0.209082i
$187$	−1.78824	−	1.78824i	−0.130769	−	0.130769i
$188$	−8.35634	−	8.35634i	−0.609449	−	0.609449i
$189$	5.92155	−	13.1920i	0.430730	−	0.959580i
$190$	−2.64562	+	0.544469i	−0.191934	+	0.0394999i
$191$		−	18.9004i		−	1.36758i	−0.729677	−	0.683792i	$-0.760330\pi$
$191$		−	18.9004i		−	1.36758i	0.729677	−	0.683792i	$-0.239670\pi$
$192$	−1.71935	+	0.209343i	−0.124084	+	0.0151080i
$193$	14.6605	−	14.6605i	1.05529	−	1.05529i	0.0569086	−	0.998379i	$-0.481876\pi$
$193$	14.6605	−	14.6605i	1.05529	−	1.05529i	0.998379	−	0.0569086i	$-0.0181244\pi$
$194$	−17.2187			−1.23623
$195$	−5.13615	+	1.72562i	−0.367807	+	0.123574i
$196$	0.744252			0.0531608
$197$	−14.2642	+	14.2642i	−1.01628	+	1.01628i	−0.0164186	+	0.999865i	$0.505226\pi$
$197$	−14.2642	+	14.2642i	−1.01628	+	1.01628i	−0.999865	+	0.0164186i	$0.994774\pi$
$198$	6.49526	+	3.92067i	0.461598	+	0.278630i
$199$		−	3.37444i		−	0.239208i	−0.992822	−	0.119604i	$-0.961838\pi$
$199$		−	3.37444i		−	0.239208i	0.992822	−	0.119604i	$-0.0381624\pi$
$200$	1.85212	−	4.64431i	0.130965	−	0.328402i
$201$	−14.5130	+	18.5371i	−1.02367	+	1.30751i
$202$	−5.39101	−	5.39101i	−0.379310	−	0.379310i
$203$	−8.82525	−	8.82525i	−0.619411	−	0.619411i
$204$	−1.06774	+	1.36379i	−0.0747566	+	0.0954847i
$205$	−16.4824	−	10.8561i	−1.15118	−	0.758224i
$206$		−	12.6686i		−	0.882667i
$207$	−9.22584	−	5.56890i	−0.641240	−	0.387065i
$208$	−0.989239	+	0.989239i	−0.0685914	+	0.0685914i
$209$	3.05485			0.211309
$210$	9.65150	+	4.79712i	0.666017	+	0.331033i
$211$	−16.2292			−1.11726			−0.558631	−	0.829416i	$-0.688673\pi$
$211$	−16.2292			−1.11726			−0.558631	+	0.829416i	$0.688673\pi$
$212$	−7.21125	+	7.21125i	−0.495271	+	0.495271i
$213$	−10.6560	+	1.29744i	−0.730135	+	0.0888990i
$214$			14.4455i			0.987472i
$215$	0.0350404	+	0.170265i	0.00238973	+	0.0116119i
$216$	2.12787	−	4.74048i	0.144783	−	0.322549i
$217$	−5.25514	−	5.25514i	−0.356742	−	0.356742i
$218$	−7.78477	−	7.78477i	−0.527251	−	0.527251i
$219$	−9.63874	−	7.54634i	−0.651326	−	0.509934i
$220$	−3.11051	+	4.72256i	−0.209711	+	0.318395i
$221$			1.39900i			0.0941066i
$222$	0.282355	+	2.31900i	0.0189504	+	0.155641i
$223$	−0.926391	+	0.926391i	−0.0620357	+	0.0620357i	−0.737444	−	0.675408i	$-0.763967\pi$
$223$	−0.926391	+	0.926391i	−0.0620357	+	0.0620357i	0.675408	+	0.737444i	$0.263967\pi$
$224$	2.78285			0.185937
$225$	9.05692	+	11.9571i	0.603795	+	0.797140i
$226$	−15.6085			−1.03826
$227$	7.98766	−	7.98766i	0.530159	−	0.530159i	−0.390460	−	0.920620i	$-0.627684\pi$
$227$	7.98766	−	7.98766i	0.530159	−	0.530159i	0.920620	+	0.390460i	$0.127684\pi$
$228$	−0.252877	−	2.07690i	−0.0167472	−	0.137546i
$229$			22.5679i			1.49133i	0.666322	+	0.745664i	$0.267868\pi$
$229$			22.5679i			1.49133i	−0.666322	+	0.745664i	$0.732132\pi$
$230$	4.41816	−	6.70789i	0.291325	−	0.442305i
$231$	−9.59794	−	7.51440i	−0.631498	−	0.494411i
$232$	−3.17130	−	3.17130i	−0.208206	−	0.208206i
$233$	−16.6026	−	16.6026i	−1.08767	−	1.08767i	−0.995768	−	0.0919037i	$-0.970705\pi$
$233$	−16.6026	−	16.6026i	−1.08767	−	1.08767i	−0.0919037	−	0.995768i	$-0.529295\pi$
$234$	−1.00709	−	4.07437i	−0.0658358	−	0.266350i
$235$	5.32664	+	25.8826i	0.347472	+	1.68840i
$236$			7.12840i			0.464020i
$237$	−11.8557	+	1.44351i	−0.770109	+	0.0937662i
$238$	1.96777	−	1.96777i	0.127552	−	0.127552i
$239$	0.481252			0.0311296			0.0155648	−	0.999879i	$-0.495045\pi$
$239$	0.481252			0.0311296			0.0155648	+	0.999879i	$0.495045\pi$
$240$	3.46821	+	1.72382i	0.223872	+	0.111272i
$241$	−15.6008			−1.00493			−0.502467	−	0.864597i	$-0.667574\pi$
$241$	−15.6008			−1.00493			−0.502467	+	0.864597i	$0.667574\pi$
$242$	−3.25582	+	3.25582i	−0.209292	+	0.209292i
$243$	8.87642	+	12.8144i	0.569422	+	0.822045i
$244$		−	7.63437i		−	0.488741i
$245$	−1.38982	−	0.915403i	−0.0887921	−	0.0584830i
$246$	9.42425	−	12.0373i	0.600868	−	0.767473i
$247$	−1.19496	−	1.19496i	−0.0760333	−	0.0760333i
$248$	−1.88840	−	1.88840i	−0.119914	−	0.119914i
$249$	9.08637	−	11.6058i	0.575826	−	0.735487i
$250$	−9.17100	+	6.39475i	−0.580025	+	0.404439i
$251$		−	2.69892i		−	0.170355i	−0.996366	−	0.0851773i	$-0.972854\pi$
$251$		−	2.69892i		−	0.170355i	0.996366	−	0.0851773i	$-0.0271457\pi$
$252$	−4.31430	+	7.14738i	−0.271775	+	0.450243i
$253$	−6.42352	+	6.42352i	−0.403843	+	0.403843i
$254$	−6.74834			−0.423429
$255$	3.67131	−	1.23347i	0.229907	−	0.0772430i
$256$	1.00000			0.0625000
$257$	21.9691	−	21.9691i	1.37039	−	1.37039i	0.510538	−	0.859855i	$-0.329446\pi$
$257$	21.9691	−	21.9691i	1.37039	−	1.37039i	0.859855	−	0.510538i	$-0.170554\pi$
$258$	−0.133663	+	0.0162744i	−0.00832151	+	0.00101320i
$259$		−	3.75341i		−	0.233225i
$260$	3.06404	−	0.630578i	0.190023	−	0.0391068i
$261$	13.0616	−	3.22854i	0.808492	−	0.199842i
$262$	3.06065	+	3.06065i	0.189087	+	0.189087i
$263$	14.2617	+	14.2617i	0.879415	+	0.879415i	0.993474	−	0.114059i	$-0.0363853\pi$
$263$	14.2617	+	14.2617i	0.879415	+	0.879415i	−0.114059	+	0.993474i	$0.536385\pi$
$264$	−3.44896	−	2.70025i	−0.212269	−	0.166189i
$265$	22.3359	−	4.59672i	1.37208	−	0.282374i
$266$			3.36156i			0.206110i
$267$	1.70905	+	14.0365i	0.104592	+	0.859022i
$268$	9.61120	−	9.61120i	0.587097	−	0.587097i
$269$	−22.6787			−1.38275			−0.691373	−	0.722498i	$-0.742994\pi$
$269$	−22.6787			−1.38275			−0.691373	+	0.722498i	$0.742994\pi$
$270$	−9.80422	+	6.23517i	−0.596666	+	0.379460i
$271$	−3.05948			−0.185850			−0.0929249	−	0.995673i	$-0.529622\pi$
$271$	−3.05948			−0.185850			−0.0929249	+	0.995673i	$0.529622\pi$
$272$	0.707107	−	0.707107i	0.0428746	−	0.0428746i
$273$	0.815014	+	6.69378i	0.0493269	+	0.405126i
$274$		−	1.00449i		−	0.0606837i
$275$	11.6172	−	4.99309i	0.700541	−	0.301095i
$276$	4.89889	+	3.83542i	0.294878	+	0.230865i
$277$	−12.3544	−	12.3544i	−0.742301	−	0.742301i	0.230719	−	0.973020i	$-0.425892\pi$
$277$	−12.3544	−	12.3544i	−0.742301	−	0.742301i	−0.973020	+	0.230719i	$0.925892\pi$
$278$	10.2225	+	10.2225i	0.613106	+	0.613106i
$279$	7.77773	−	1.92249i	0.465641	−	0.115096i
$280$	−5.19670	−	3.42281i	−0.310562	−	0.204552i
$281$		−	24.4558i		−	1.45891i	−0.684027	−	0.729456i	$-0.739773\pi$
$281$		−	24.4558i		−	1.45891i	0.684027	−	0.729456i	$-0.260227\pi$
$282$	−20.3187	+	2.47395i	−1.20996	+	0.147321i
$283$	−0.00141764	+	0.00141764i	−8.42702e−5	+	8.42702e-5i	−0.707149	−	0.707065i	$-0.750019\pi$
$283$	−0.00141764	+	0.00141764i	−8.42702e−5	+	8.42702e-5i	0.707065	+	0.707149i	$0.250019\pi$
$284$	6.19766			0.367763
$285$	−2.08229	+	4.18944i	−0.123344	+	0.248161i
$286$	−3.53798			−0.209205
$287$	−17.3683	+	17.3683i	−1.02522	+	1.02522i
$288$	−1.55032	+	2.56837i	−0.0913534	+	0.151343i
$289$		−	1.00000i		−	0.0588235i
$290$	2.02150	+	9.82267i	0.118707	+	0.576807i
$291$	−18.3851	+	23.4827i	−1.07775	+	1.37658i
$292$	4.99754	+	4.99754i	0.292459	+	0.292459i
$293$	−9.47960	−	9.47960i	−0.553804	−	0.553804i	0.373732	−	0.927537i	$-0.378078\pi$
$293$	−9.47960	−	9.47960i	−0.553804	−	0.553804i	−0.927537	+	0.373732i	$0.878078\pi$
$294$	0.794666	−	1.01501i	0.0463459	−	0.0591964i
$295$	8.76768	−	13.3116i	0.510474	−	0.775031i
$296$		−	1.34876i		−	0.0783953i
$297$	12.2822	−	4.67195i	0.712687	−	0.271094i
$298$	−5.99597	+	5.99597i	−0.347337	+	0.347337i
$299$	5.02533			0.290623
$300$	−4.35630	−	7.48483i	−0.251511	−	0.432137i
$301$	0.216340			0.0124696
$302$	−3.75805	+	3.75805i	−0.216251	+	0.216251i
$303$	−13.1084	+	1.59604i	−0.753059	+	0.0916902i
$304$			1.20796i			0.0692810i
$305$	−9.39001	+	14.2564i	−0.537670	+	0.816321i
$306$	0.719870	+	2.91235i	0.0411522	+	0.166488i
$307$	−16.2626	−	16.2626i	−0.928153	−	0.928153i	0.0694338	−	0.997587i	$-0.477881\pi$
$307$	−16.2626	−	16.2626i	−0.928153	−	0.928153i	−0.997587	+	0.0694338i	$0.977881\pi$
$308$	4.97639	+	4.97639i	0.283556	+	0.283556i
$309$	−17.2774	−	13.5268i	−0.982879	−	0.769513i
$310$	1.20374	+	5.84907i	0.0683676	+	0.332205i
$311$			8.85175i			0.501937i	0.967995	+	0.250968i	$0.0807490\pi$
$311$			8.85175i			0.501937i	−0.967995	+	0.250968i	$0.919251\pi$
$312$	0.292870	+	2.40537i	0.0165805	+	0.136177i
$313$	−15.4004	+	15.4004i	−0.870483	+	0.870483i	−0.992525	−	0.122042i	$-0.961056\pi$
$313$	−15.4004	+	15.4004i	−0.870483	+	0.870483i	0.122042	+	0.992525i	$0.461056\pi$
$314$	−9.93980			−0.560936
$315$	16.8476	−	8.04059i	0.949252	−	0.453036i
$316$	6.89543			0.387898
$317$	14.7669	−	14.7669i	0.829389	−	0.829389i	−0.158043	−	0.987432i	$-0.550518\pi$
$317$	14.7669	−	14.7669i	0.829389	−	0.829389i	0.987432	+	0.158043i	$0.0505184\pi$
$318$	2.13493	+	17.5344i	0.119721	+	0.983280i
$319$		−	11.3421i		−	0.635033i
$320$	−1.86740	−	1.22996i	−0.104391	−	0.0687571i
$321$	19.7006	+	15.4240i	1.09958	+	0.860883i
$322$	−7.06844	−	7.06844i	−0.393909	−	0.393909i
$323$	0.854153	+	0.854153i	0.0475264	+	0.0475264i
$324$	−4.19303	−	7.96357i	−0.232946	−	0.442421i
$325$	−6.49737	−	2.59111i	−0.360409	−	0.143729i
$326$			13.1864i			0.730326i
$327$	−18.9289	+	2.30473i	−1.04677	+	0.127452i
$328$	−6.24118	+	6.24118i	−0.344612	+	0.344612i
$329$	32.8867			1.81311
$330$	3.11938	+	9.28456i	0.171716	+	0.511098i
$331$	17.9050			0.984150			0.492075	−	0.870553i	$-0.336239\pi$
$331$	17.9050			0.984150			0.492075	+	0.870553i	$0.336239\pi$
$332$	−6.01743	+	6.01743i	−0.330249	+	0.330249i
$333$	3.46412	+	2.09101i	0.189833	+	0.114587i
$334$		−	1.24221i		−	0.0679709i
$335$	−29.7694	+	6.12653i	−1.62648	+	0.334728i
$336$	2.97136	−	3.79523i	0.162101	−	0.207047i
$337$	16.4569	+	16.4569i	0.896465	+	0.896465i	0.995122	−	0.0986568i	$-0.0314546\pi$
$337$	16.4569	+	16.4569i	0.896465	+	0.896465i	−0.0986568	+	0.995122i	$0.531455\pi$
$338$	−7.80845	−	7.80845i	−0.424724	−	0.424724i
$339$	−16.6658	+	21.2868i	−0.905163	+	1.15614i
$340$	−2.19017	+	0.450736i	−0.118779	+	0.0244446i
$341$		−	6.75381i		−	0.365739i
$342$	−3.10247	−	1.87271i	−0.167763	−	0.101265i
$343$	12.3099	−	12.3099i	0.664671	−	0.664671i
$344$	0.0777404			0.00419148
$345$	−4.43075	−	13.1877i	−0.238544	−	0.710004i
$346$	−20.3854			−1.09592
$347$	8.31483	−	8.31483i	0.446364	−	0.446364i	−0.447780	−	0.894144i	$-0.647785\pi$
$347$	8.31483	−	8.31483i	0.446364	−	0.446364i	0.894144	+	0.447780i	$0.147785\pi$
$348$	−7.71112	+	0.938882i	−0.413359	+	0.0503294i
$349$			28.6639i			1.53434i	0.641442	+	0.767172i	$0.278337\pi$
$349$			28.6639i			1.53434i	−0.641442	+	0.767172i	$0.721663\pi$
$350$	5.49439	+	12.7835i	0.293687	+	0.683307i
$351$	−6.63191	−	2.97689i	−0.353985	−	0.158894i
$352$	1.78824	+	1.78824i	0.0953133	+	0.0953133i
$353$	12.3209	+	12.3209i	0.655774	+	0.655774i	0.954377	−	0.298603i	$-0.0965208\pi$
$353$	12.3209	+	12.3209i	0.655774	+	0.655774i	−0.298603	+	0.954377i	$0.596521\pi$
$354$	9.72168	+	7.61127i	0.516701	+	0.404534i
$355$	−11.5735	−	7.62290i	−0.614258	−	0.404581i
$356$		−	8.16385i		−	0.432683i
$357$	−0.582571	−	4.78470i	−0.0308329	−	0.253233i
$358$	17.4921	−	17.4921i	0.924484	−	0.924484i
$359$	2.97871			0.157210			0.0786052	−	0.996906i	$-0.474953\pi$
$359$	2.97871			0.157210			0.0786052	+	0.996906i	$0.474953\pi$
$360$	6.05407	−	2.88934i	0.319077	−	0.152281i
$361$	17.5408			0.923202
$362$	11.5120	−	11.5120i	0.605058	−	0.605058i
$363$	0.963906	+	7.91664i	0.0505920	+	0.415516i
$364$		−	3.89319i		−	0.204059i
$365$	−3.18562	−	15.4792i	−0.166743	−	0.810219i
$366$	−10.4117	−	8.15151i	−0.544229	−	0.426086i
$367$	−19.9832	−	19.9832i	−1.04311	−	1.04311i	−0.999028	−	0.0440845i	$-0.985963\pi$
$367$	−19.9832	−	19.9832i	−1.04311	−	1.04311i	−0.0440845	−	0.999028i	$-0.514037\pi$
$368$	−2.54000	−	2.54000i	−0.132407	−	0.132407i
$369$	−6.35383	−	25.7055i	−0.330767	−	1.33817i
$370$	−1.65893	+	2.51868i	−0.0862437	+	0.130940i
$371$		−	28.3802i		−	1.47343i
$372$	−4.59171	+	0.559072i	−0.238069	+	0.0289866i
$373$	14.5108	−	14.5108i	0.751339	−	0.751339i	−0.223390	−	0.974729i	$-0.571712\pi$
$373$	14.5108	−	14.5108i	0.751339	−	0.751339i	0.974729	+	0.223390i	$0.0717123\pi$
$374$	2.52895			0.130769
$375$	−1.07110	+	19.3353i	−0.0553116	+	0.998469i
$376$	11.8177			0.609449
$377$	−4.43663	+	4.43663i	−0.228498	+	0.228498i
$378$	5.14101	+	13.5154i	0.264425	+	0.695155i
$379$		−	18.5197i		−	0.951292i	−0.879637	−	0.475646i	$-0.842214\pi$
$379$		−	18.5197i		−	0.951292i	0.879637	−	0.475646i	$-0.157786\pi$
$380$	1.48574	−	2.25574i	0.0762169	−	0.115717i
$381$	−7.20546	+	9.20335i	−0.369147	+	0.471502i
$382$	13.3646	+	13.3646i	0.683792	+	0.683792i
$383$	21.0263	+	21.0263i	1.07439	+	1.07439i	0.997001	+	0.0773910i	$0.0246590\pi$
$383$	21.0263	+	21.0263i	1.07439	+	1.07439i	0.0773910	+	0.997001i	$0.475341\pi$
$384$	1.06774	−	1.36379i	0.0544878	−	0.0695958i
$385$	−3.17213	−	15.4137i	−0.161667	−	0.785555i
$386$			20.7331i			1.05529i
$387$	−0.120522	+	0.199666i	−0.00612650	+	0.0101496i
$388$	12.1755	−	12.1755i	0.618115	−	0.618115i
$389$	−2.56661			−0.130132			−0.0650660	−	0.997881i	$-0.520726\pi$
$389$	−2.56661			−0.130132			−0.0650660	+	0.997881i	$0.520726\pi$
$390$	2.41161	−	4.85201i	0.122117	−	0.245691i
$391$	−3.59210			−0.181660
$392$	−0.526266	+	0.526266i	−0.0265804	+	0.0265804i
$393$	7.44206	−	0.906123i	0.375402	−	0.0457079i
$394$		−	20.1727i		−	1.01628i
$395$	−12.8765	−	8.48114i	−0.647889	−	0.426732i
$396$	−7.36518	+	1.82051i	−0.370114	+	0.0914842i
$397$	−2.68629	−	2.68629i	−0.134821	−	0.134821i	0.636476	−	0.771297i	$-0.280392\pi$
$397$	−2.68629	−	2.68629i	−0.134821	−	0.134821i	−0.771297	+	0.636476i	$0.780392\pi$
$398$	2.38609	+	2.38609i	0.119604	+	0.119604i
$399$	4.58447	+	3.58926i	0.229511	+	0.179688i
$400$	1.97438	+	4.59367i	0.0987188	+	0.229684i
$401$		−	10.9308i		−	0.545857i	−0.962034	−	0.272929i	$-0.912008\pi$
$401$		−	10.9308i		−	0.545857i	0.962034	−	0.272929i	$-0.0879923\pi$
$402$	−2.84545	−	23.3699i	−0.141918	−	1.16559i
$403$	−2.64186	+	2.64186i	−0.131601	+	0.131601i
$404$	7.62404			0.379310
$405$	−1.96485	+	20.0285i	−0.0976341	+	0.995222i
$406$	12.4808			0.619411
$407$	2.41191	−	2.41191i	0.119554	−	0.119554i
$408$	−0.209343	−	1.71935i	−0.0103640	−	0.0851207i
$409$		−	2.89808i		−	0.143301i	−0.997430	−	0.0716503i	$-0.977173\pi$
$409$		−	2.89808i		−	0.143301i	0.997430	−	0.0716503i	$-0.0228266\pi$
$410$	19.3312	−	3.97836i	0.954701	−	0.196477i
$411$	−1.36992	−	1.07254i	−0.0675733	−	0.0529043i
$412$	8.95809	+	8.95809i	0.441333	+	0.441333i
$413$	−14.0271	−	14.0271i	−0.690227	−	0.690227i
$414$	10.4615	−	2.58585i	0.514153	−	0.127087i
$415$	18.6382	−	3.83573i	0.914912	−	0.188289i
$416$		−	1.39900i		−	0.0685914i
$417$	24.8564	−	3.02644i	1.21722	−	0.148205i
$418$	−2.16011	+	2.16011i	−0.105654	+	0.105654i
$419$	−5.18051			−0.253085			−0.126542	−	0.991961i	$-0.540388\pi$
$419$	−5.18051			−0.253085			−0.126542	+	0.991961i	$0.540388\pi$
$420$	−10.2167	+	3.43256i	−0.498525	+	0.167492i
$421$	4.77086			0.232518			0.116259	−	0.993219i	$-0.462910\pi$
$421$	4.77086			0.232518			0.116259	+	0.993219i	$0.462910\pi$
$422$	11.4758	−	11.4758i	0.558631	−	0.558631i
$423$	−18.3211	+	30.3521i	−0.890803	+	1.47577i
$424$		−	10.1982i		−	0.495271i
$425$	4.64431	+	1.85212i	0.225282	+	0.0898412i
$426$	6.61748	−	8.45233i	0.320618	−	0.409517i
$427$	15.0227	+	15.0227i	0.726999	+	0.726999i
$428$	−10.2145	−	10.2145i	−0.493736	−	0.493736i
$429$	−3.77764	+	4.82508i	−0.182386	+	0.232957i
$430$	−0.145173	−	0.0956179i	−0.00700084	−	0.00461111i
$431$		−	29.6950i		−	1.43036i	−0.698941	−	0.715179i	$-0.746345\pi$
$431$		−	29.6950i		−	1.43036i	0.698941	−	0.715179i	$-0.253655\pi$
$432$	1.84739	+	4.85666i	0.0888827	+	0.233666i
$433$	10.6381	−	10.6381i	0.511234	−	0.511234i	−0.403670	−	0.914904i	$-0.632266\pi$
$433$	10.6381	−	10.6381i	0.511234	−	0.511234i	0.914904	+	0.403670i	$0.132266\pi$
$434$	7.43188			0.356742
$435$	15.5545	+	7.73113i	0.745783	+	0.370679i
$436$	11.0093			0.527251
$437$	3.06820	−	3.06820i	0.146772	−	0.146772i
$438$	12.1517	−	1.47955i	0.580630	−	0.0706958i
$439$			18.8619i			0.900227i	0.892971	+	0.450113i	$0.148616\pi$
$439$			18.8619i			0.900227i	−0.892971	+	0.450113i	$0.851384\pi$
$440$	−1.13989	−	5.53882i	−0.0543420	−	0.264053i
$441$	−0.535764	−	2.16752i	−0.0255126	−	0.103215i
$442$	−0.989239	−	0.989239i	−0.0470533	−	0.0470533i
$443$	16.1813	+	16.1813i	0.768795	+	0.768795i	0.977894	−	0.209099i	$-0.0670531\pi$
$443$	16.1813	+	16.1813i	0.768795	+	0.768795i	−0.209099	+	0.977894i	$0.567053\pi$
$444$	−1.83944	−	1.44013i	−0.0872958	−	0.0683454i
$445$	−10.0412	+	15.2452i	−0.476001	+	0.722691i
$446$		−	1.31011i		−	0.0620357i
$447$	1.77514	+	14.5794i	0.0839614	+	0.689582i
$448$	−1.96777	+	1.96777i	−0.0929685	+	0.0929685i
$449$	−9.61811			−0.453907			−0.226953	−	0.973906i	$-0.572877\pi$
$449$	−9.61811			−0.453907			−0.226953	+	0.973906i	$0.572877\pi$
$450$	−14.8592	−	2.05073i	−0.700467	−	0.0966725i
$451$	−22.3214			−1.05107
$452$	11.0369	−	11.0369i	0.519132	−	0.519132i
$453$	1.11259	+	9.13782i	0.0522742	+	0.429332i
$454$			11.2963i			0.530159i
$455$	−4.78849	+	7.27016i	−0.224488	+	0.340830i
$456$	1.64740	+	1.28978i	0.0771467	+	0.0603995i
$457$	17.3874	+	17.3874i	0.813349	+	0.813349i	0.985134	−	0.171785i	$-0.0549536\pi$
$457$	17.3874	+	17.3874i	0.813349	+	0.813349i	−0.171785	+	0.985134i	$0.554954\pi$
$458$	−15.9579	−	15.9579i	−0.745664	−	0.745664i
$459$	4.74048	+	2.12787i	0.221267	+	0.0993207i
$460$	1.61909	+	7.86731i	0.0754904	+	0.366815i
$461$			8.39149i			0.390831i	0.980721	+	0.195415i	$0.0626055\pi$
$461$			8.39149i			0.390831i	−0.980721	+	0.195415i	$0.937395\pi$
$462$	12.1003	−	1.47329i	0.562955	−	0.0685437i
$463$	5.66585	−	5.66585i	0.263314	−	0.263314i	−0.563085	−	0.826399i	$-0.690386\pi$
$463$	5.66585	−	5.66585i	0.263314	−	0.263314i	0.826399	+	0.563085i	$0.190386\pi$
$464$	4.48489			0.208206
$465$	9.26220	+	4.60363i	0.429524	+	0.213488i
$466$	23.4796			1.08767
$467$	2.68728	−	2.68728i	0.124353	−	0.124353i	−0.642192	−	0.766544i	$-0.721975\pi$
$467$	2.68728	−	2.68728i	0.124353	−	0.124353i	0.766544	+	0.642192i	$0.221975\pi$
$468$	3.59313	+	2.16889i	0.166093	+	0.100257i
$469$			37.8253i			1.74661i
$470$	−22.0683	−	14.5353i	−1.01793	−	0.670463i
$471$	−10.6131	+	13.5558i	−0.489026	+	0.624620i
$472$	−5.04054	−	5.04054i	−0.232010	−	0.232010i
$473$	0.139018	+	0.139018i	0.00639206	+	0.00639206i
$474$	7.36252	−	9.40395i	0.338172	−	0.431938i
$475$	−5.54895	+	2.38496i	−0.254603	+	0.109429i
$476$			2.78285i			0.127552i
$477$	26.1929	+	15.8105i	1.19929	+	0.723914i
$478$	−0.340297	+	0.340297i	−0.0155648	+	0.0155648i
$479$	4.91424			0.224537			0.112269	−	0.993678i	$-0.464188\pi$
$479$	4.91424			0.224537			0.112269	+	0.993678i	$0.464188\pi$
$480$	−3.67131	+	1.23347i	−0.167572	+	0.0563000i
$481$	−1.88691			−0.0860359
$482$	11.0314	−	11.0314i	0.502467	−	0.502467i
$483$	−17.1871	+	2.09265i	−0.782042	+	0.0952190i
$484$		−	4.60443i		−	0.209292i
$485$	−37.7118	+	7.76108i	−1.71241	+	0.352413i
$486$	−15.3377	−	2.78459i	−0.695734	−	0.126311i
$487$	27.2528	+	27.2528i	1.23494	+	1.23494i	0.962043	+	0.272898i	$0.0879821\pi$
$487$	27.2528	+	27.2528i	1.23494	+	1.23494i	0.272898	+	0.962043i	$0.412018\pi$
$488$	5.39832	+	5.39832i	0.244370	+	0.244370i
$489$	17.9835	+	14.0796i	0.813243	+	0.636702i
$490$	1.63004	−	0.335461i	0.0736376	−	0.0151546i
$491$		−	0.0661004i		−	0.00298307i	−0.999999	−	0.00149154i	$-0.999525\pi$
$491$		−	0.0661004i		−	0.00298307i	0.999999	−	0.00149154i	$-0.000474771\pi$
$492$	1.84774	+	15.1756i	0.0833025	+	0.684171i
$493$	3.17130	−	3.17130i	0.142828	−	0.142828i
$494$	1.68992			0.0760333
$495$	15.9929	+	5.65928i	0.718828	+	0.254366i
$496$	2.67060			0.119914
$497$	−12.1956	+	12.1956i	−0.547046	+	0.547046i
$498$	1.78150	+	14.6316i	0.0798307	+	0.655656i
$499$		−	41.8265i		−	1.87241i	−0.351454	−	0.936205i	$-0.614313\pi$
$499$		−	41.8265i		−	1.87241i	0.351454	−	0.936205i	$-0.385687\pi$
$500$	1.96310	−	11.0066i	0.0877927	−	0.492232i
$501$	−1.69412	−	1.32636i	−0.0756879	−	0.0592574i
$502$	1.90843	+	1.90843i	0.0851773	+	0.0851773i
$503$	−0.975914	−	0.975914i	−0.0435138	−	0.0435138i	0.685015	−	0.728529i	$-0.259796\pi$
$503$	−0.975914	−	0.975914i	−0.0435138	−	0.0435138i	−0.728529	+	0.685015i	$0.759796\pi$
$504$	−2.00329	−	8.10463i	−0.0892336	−	0.361009i
$505$	−14.2371	−	9.37730i	−0.633545	−	0.417284i
$506$		−	9.08423i		−	0.403843i
$507$	−18.9865	+	2.31174i	−0.843220	+	0.102668i
$508$	4.77180	−	4.77180i	0.211714	−	0.211714i
$509$	9.47611			0.420021			0.210011	−	0.977699i	$-0.432650\pi$
$509$	9.47611			0.420021			0.210011	+	0.977699i	$0.432650\pi$
$510$	−1.72382	+	3.46821i	−0.0763318	+	0.153575i
$511$	−19.6680			−0.870063
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	−5.86663	+	2.23157i	−0.259018	+	0.0985260i
$514$			31.0690i			1.37039i
$515$	−5.71022	−	27.7465i	−0.251622	−	1.22266i
$516$	0.0830064	−	0.106022i	0.00365415	−	0.00466735i
$517$	21.1327	+	21.1327i	0.929417	+	0.929417i
$518$	2.65406	+	2.65406i	0.116613	+	0.116613i
$519$	−21.7663	+	27.8015i	−0.955432	+	1.22035i
$520$	−1.72071	+	2.61249i	−0.0754583	+	0.114565i
$521$			7.51285i			0.329144i	0.986365	+	0.164572i	$0.0526243\pi$
$521$			7.51285i			0.329144i	−0.986365	+	0.164572i	$0.947376\pi$
$522$	−6.95301	+	11.5189i	−0.304325	+	0.504167i
$523$	14.7767	−	14.7767i	0.646140	−	0.646140i	−0.305918	−	0.952058i	$-0.598963\pi$
$523$	14.7767	−	14.7767i	0.646140	−	0.646140i	0.952058	+	0.305918i	$0.0989633\pi$
$524$	−4.32841			−0.189087
$525$	23.3006	+	6.15622i	1.01692	+	0.268679i
$526$	−20.1691			−0.879415
$527$	1.88840	−	1.88840i	0.0822600	−	0.0822600i
$528$	4.34815	−	0.529418i	0.189229	−	0.0230400i
$529$		−	10.0968i		−	0.438992i
$530$	−12.5435	+	19.0442i	−0.544854	+	0.827228i
$531$	20.7604	−	5.13152i	0.900925	−	0.222689i
$532$	−2.37698	−	2.37698i	−0.103055	−	0.103055i
$533$	8.73138	+	8.73138i	0.378198	+	0.378198i
$534$	−11.1338	−	8.71686i	−0.481807	−	0.377215i
$535$	6.51109	+	31.6380i	0.281499	+	1.36783i
$536$			13.5923i			0.587097i
$537$	−5.17863	−	42.5325i	−0.223474	−	1.83541i
$538$	16.0363	−	16.0363i	0.691373	−	0.691373i
$539$	−1.88217			−0.0810709
$540$	2.52370	−	11.3416i	0.108603	−	0.488063i
$541$	−14.8224			−0.637263			−0.318632	−	0.947879i	$-0.603223\pi$
$541$	−14.8224			−0.637263			−0.318632	+	0.947879i	$0.603223\pi$
$542$	2.16338	−	2.16338i	0.0929249	−	0.0929249i
$543$	−3.40820	−	27.9918i	−0.146260	−	1.20124i
$544$			1.00000i			0.0428746i
$545$	−20.5588	−	13.5411i	−0.880643	−	0.580036i
$546$	−5.30952	−	4.15691i	−0.227226	−	0.177899i
$547$	13.5320	+	13.5320i	0.578586	+	0.578586i	0.934514	−	0.355927i	$-0.115835\pi$
$547$	13.5320	+	13.5320i	0.578586	+	0.578586i	−0.355927	+	0.934514i	$0.615835\pi$
$548$	0.710284	+	0.710284i	0.0303418	+	0.0303418i
$549$	−22.2340	+	5.49575i	−0.948923	+	0.234553i
$550$	−4.68392	+	11.7452i	−0.199723	+	0.500818i
$551$			5.41755i			0.230795i
$552$	−6.17609	+	0.751982i	−0.262872	+	0.0320065i
$553$	−13.5686	+	13.5686i	−0.576997	+	0.576997i
$554$	17.4717			0.742301
$555$	1.66366	+	4.95174i	0.0706185	+	0.210189i
$556$	−14.4568			−0.613106
$557$	−7.27672	+	7.27672i	−0.308325	+	0.308325i	−0.844259	−	0.535935i	$-0.819959\pi$
$557$	−7.27672	+	7.27672i	−0.308325	+	0.308325i	0.535935	+	0.844259i	$0.319959\pi$
$558$	−4.14028	+	6.85909i	−0.175272	+	0.290368i
$559$		−	0.108758i		−	0.00459999i
$560$	6.09491	−	1.25433i	0.257557	−	0.0530051i
$561$	2.70025	−	3.44896i	0.114005	−	0.145615i
$562$	17.2929	+	17.2929i	0.729456	+	0.729456i
$563$	27.5220	+	27.5220i	1.15991	+	1.15991i	0.984494	+	0.175419i	$0.0561281\pi$
$563$	27.5220	+	27.5220i	1.15991	+	1.15991i	0.175419	+	0.984494i	$0.443872\pi$
$564$	12.6182	−	16.1168i	0.531320	−	0.678642i
$565$	−34.1853	+	7.03532i	−1.43819	+	0.295978i
$566$		−	0.00200485i		−	8.42702e-5i
$567$	23.9214	+	7.41958i	1.00461	+	0.311593i
$568$	−4.38241	+	4.38241i	−0.183882	+	0.183882i
$569$	6.26861			0.262794			0.131397	−	0.991330i	$-0.458054\pi$
$569$	6.26861			0.262794			0.131397	+	0.991330i	$0.458054\pi$
$570$	−1.48998	−	4.43478i	−0.0624083	−	0.185753i
$571$	−19.0308			−0.796413			−0.398206	−	0.917296i	$-0.630367\pi$
$571$	−19.0308			−0.796413			−0.398206	+	0.917296i	$0.630367\pi$
$572$	2.50173	−	2.50173i	0.104603	−	0.104603i
$573$	32.4964	−	3.95667i	1.35756	−	0.165292i
$574$		−	24.5624i		−	1.02522i
$575$	6.65302	−	16.6828i	0.277450	−	0.695723i
$576$	−0.719870	−	2.91235i	−0.0299946	−	0.121348i
$577$	−30.7072	−	30.7072i	−1.27836	−	1.27836i	−0.941586	−	0.336774i	$-0.890664\pi$
$577$	−30.7072	−	30.7072i	−1.27836	−	1.27836i	−0.336774	−	0.941586i	$-0.609336\pi$
$578$	0.707107	+	0.707107i	0.0294118	+	0.0294118i
$579$	28.2757	+	22.1375i	1.17510	+	0.920005i
$580$	−8.37510	−	5.51626i	−0.347757	−	0.229050i
$581$		−	23.6818i		−	0.982488i
$582$	−3.60462	−	29.6050i	−0.149416	−	1.22717i
$583$	18.2369	−	18.2369i	0.755294	−	0.755294i
$584$	−7.06759			−0.292459
$585$	−4.04217	−	8.46961i	−0.167123	−	0.350175i
$586$	13.4062			0.553804
$587$	−21.1119	+	21.1119i	−0.871383	+	0.871383i	−0.992623	−	0.121240i	$-0.961313\pi$
$587$	−21.1119	+	21.1119i	−0.871383	+	0.871383i	0.121240	+	0.992623i	$0.461313\pi$
$588$	0.155804	+	1.27963i	0.00642525	+	0.0527711i
$589$			3.22597i			0.132924i
$590$	3.21303	+	15.6124i	0.132278	+	0.642752i
$591$	−27.5114	−	21.5391i	−1.13167	−	0.886001i
$592$	0.953720	+	0.953720i	0.0391977	+	0.0391977i
$593$	0.188868	+	0.188868i	0.00775588	+	0.00775588i	0.710974	−	0.703218i	$-0.248254\pi$
$593$	0.188868	+	0.188868i	0.00775588	+	0.00775588i	−0.703218	+	0.710974i	$0.748254\pi$
$594$	−5.38128	+	11.9884i	−0.220797	+	0.491891i
$595$	3.42281	−	5.19670i	0.140321	−	0.213044i
$596$		−	8.47958i		−	0.347337i
$597$	5.80185	−	0.706416i	0.237454	−	0.0289117i
$598$	−3.55345	+	3.55345i	−0.145311	+	0.145311i
$599$	9.37844			0.383193			0.191596	−	0.981474i	$-0.438634\pi$
$599$	9.37844			0.383193			0.191596	+	0.981474i	$0.438634\pi$
$600$	8.37294	+	2.21220i	0.341824	+	0.0903127i
$601$	−41.3465			−1.68656			−0.843280	−	0.537474i	$-0.819379\pi$
$601$	−41.3465			−1.68656			−0.843280	+	0.537474i	$0.819379\pi$
$602$	−0.152975	+	0.152975i	−0.00623481	+	0.00623481i
$603$	−34.9100	−	21.0724i	−1.42164	−	0.858133i
$604$		−	5.31468i		−	0.216251i
$605$	−5.66328	+	8.59832i	−0.230245	+	0.349571i
$606$	8.14048	−	10.3976i	0.330685	−	0.422375i
$607$	25.1616	+	25.1616i	1.02128	+	1.02128i	0.999769	+	0.0215072i	$0.00684649\pi$
$607$	25.1616	+	25.1616i	1.02128	+	1.02128i	0.0215072	+	0.999769i	$0.493154\pi$
$608$	−0.854153	−	0.854153i	−0.0346405	−	0.0346405i
$609$	13.3262	−	17.0212i	0.540005	−	0.689735i
$610$	−3.44109	−	16.7206i	−0.139326	−	0.676996i
$611$		−	16.5328i		−	0.668847i
$612$	−2.56837	−	1.55032i	−0.103820	−	0.0626679i
$613$	−9.51982	+	9.51982i	−0.384502	+	0.384502i	−0.872721	−	0.488219i	$-0.837647\pi$
$613$	−9.51982	+	9.51982i	−0.384502	+	0.384502i	0.488219	+	0.872721i	$0.337647\pi$
$614$	22.9987			0.928153
$615$	15.2150	−	30.6117i	0.613529	−	1.23438i
$616$	−7.03768			−0.283556
$617$	13.5000	−	13.5000i	0.543488	−	0.543488i	−0.381062	−	0.924550i	$-0.624441\pi$
$617$	13.5000	−	13.5000i	0.543488	−	0.543488i	0.924550	+	0.381062i	$0.124441\pi$
$618$	21.7819	−	2.65210i	0.876196	−	0.106683i
$619$		−	2.80658i		−	0.112806i	−0.998408	−	0.0564029i	$-0.982037\pi$
$619$		−	2.80658i		−	0.112806i	0.998408	−	0.0564029i	$-0.0179631\pi$
$620$	−4.98709	−	3.28475i	−0.200286	−	0.131919i
$621$	7.64354	−	17.0283i	0.306725	−	0.683322i
$622$	−6.25913	−	6.25913i	−0.250968	−	0.250968i
$623$	16.0646	+	16.0646i	0.643614	+	0.643614i
$624$	−1.90794	−	1.49376i	−0.0763788	−	0.0597983i
$625$	−17.2037	+	18.1393i	−0.688147	+	0.725571i
$626$		−	21.7795i		−	0.870483i
$627$	0.639513	+	5.25237i	0.0255397	+	0.209760i
$628$	7.02850	−	7.02850i	0.280468	−	0.280468i
$629$	1.34876			0.0537787
$630$	−6.22747	+	17.5986i	−0.248108	+	0.701144i
$631$	11.1830			0.445190			0.222595	−	0.974911i	$-0.428547\pi$
$631$	11.1830			0.445190			0.222595	+	0.974911i	$0.428547\pi$
$632$	−4.87581	+	4.87581i	−0.193949	+	0.193949i
$633$	−3.39747	−	27.9037i	−0.135037	−	1.10907i
$634$			20.8835i			0.829389i
$635$	−14.7800	+	3.04172i	−0.586527	+	0.120707i
$636$	−13.9083	−	10.8891i	−0.551500	−	0.431779i
$637$	0.736243	+	0.736243i	0.0291710	+	0.0291710i
$638$	8.02004	+	8.02004i	0.317517	+	0.317517i
$639$	−4.46151	−	18.0498i	−0.176495	−	0.714037i
$640$	2.19017	−	0.450736i	0.0865740	−	0.0178169i
$641$			13.5257i			0.534233i	0.963664	+	0.267116i	$0.0860709\pi$
$641$			13.5257i			0.534233i	−0.963664	+	0.267116i	$0.913929\pi$
$642$	−24.8369	+	3.02406i	−0.980233	+	0.119350i
$643$	23.9728	−	23.9728i	0.945395	−	0.945395i	−0.0531897	−	0.998584i	$-0.516939\pi$
$643$	23.9728	−	23.9728i	0.945395	−	0.945395i	0.998584	+	0.0531897i	$0.0169388\pi$
$644$	9.99628			0.393909
$645$	−0.285409	+	0.0958905i	−0.0112380	+	0.00377569i
$646$	−1.20796			−0.0475264
$647$	−20.1028	+	20.1028i	−0.790324	+	0.790324i	−0.981547	−	0.191222i	$-0.938755\pi$
$647$	−20.1028	+	20.1028i	−0.790324	+	0.790324i	0.191222	+	0.981547i	$0.438755\pi$
$648$	8.59602	+	2.66618i	0.337683	+	0.104737i
$649$		−	18.0274i		−	0.707635i
$650$	6.42653	−	2.76214i	0.252069	−	0.108340i
$651$	7.93531	−	10.1356i	0.311009	−	0.397244i
$652$	−9.32418	−	9.32418i	−0.365163	−	0.365163i
$653$	−19.2853	−	19.2853i	−0.754693	−	0.754693i	0.220658	−	0.975351i	$-0.429179\pi$
$653$	−19.2853	−	19.2853i	−0.754693	−	0.754693i	−0.975351	+	0.220658i	$0.929179\pi$
$654$	11.7551	−	15.0145i	0.459660	−	0.587112i
$655$	8.08287	+	5.32379i	0.315824	+	0.208018i
$656$		−	8.82636i		−	0.344612i
$657$	10.9570	−	18.1522i	0.427474	−	0.708184i
$658$	−23.2544	+	23.2544i	−0.906553	+	0.906553i
$659$	44.4380			1.73106			0.865529	−	0.500859i	$-0.166982\pi$
$659$	44.4380			1.73106			0.865529	+	0.500859i	$0.166982\pi$
$660$	−8.77091	−	4.35944i	−0.341407	−	0.169691i
$661$	15.6995			0.610640			0.305320	−	0.952250i	$-0.401237\pi$
$661$	15.6995			0.610640			0.305320	+	0.952250i	$0.401237\pi$
$662$	−12.6608	+	12.6608i	−0.492075	+	0.492075i
$663$	−2.40537	+	0.292870i	−0.0934167	+	0.0113741i
$664$		−	8.50993i		−	0.330249i
$665$	1.51517	+	7.36238i	0.0587560	+	0.285501i
$666$	−3.92807	+	0.970934i	−0.152210	+	0.0376229i
$667$	−11.3916	−	11.3916i	−0.441086	−	0.441086i
$668$	0.878378	+	0.878378i	0.0339855	+	0.0339855i
$669$	−1.78673	−	1.39886i	−0.0690788	−	0.0540830i
$670$	16.7180	−	25.3823i	0.645874	−	0.980602i
$671$			19.3069i			0.745335i
$672$	0.582571	+	4.78470i	0.0224732	+	0.184574i
$673$	25.9201	−	25.9201i	0.999147	−	0.999147i	−0.000852425	−	1.00000i	$-0.500271\pi$
$673$	25.9201	−	25.9201i	0.999147	−	0.999147i	1.00000		0.000852425i	$0.000271335\pi$
$674$	−23.2736			−0.896465
$675$	−18.6625	+	18.0752i	−0.718319	+	0.695714i
$676$	11.0428			0.424724
$677$	−31.4702	+	31.4702i	−1.20950	+	1.20950i	−0.238308	+	0.971190i	$0.576593\pi$
$677$	−31.4702	+	31.4702i	−1.20950	+	1.20950i	−0.971190	+	0.238308i	$0.923407\pi$
$678$	−3.26754	−	26.8366i	−0.125489	−	1.03065i
$679$			47.9170i			1.83889i
$680$	1.22996	−	1.86740i	0.0471670	−	0.0716116i
$681$	15.4058	+	12.0614i	0.590350	+	0.462195i
$682$	4.77567	+	4.77567i	0.182870	+	0.182870i
$683$	3.28670	+	3.28670i	0.125762	+	0.125762i	0.767186	−	0.641424i	$-0.221656\pi$
$683$	3.28670	+	3.28670i	0.125762	+	0.125762i	−0.641424	+	0.767186i	$0.721656\pi$
$684$	3.51799	−	0.869570i	0.134514	−	0.0332489i
$685$	−0.452761	−	2.20001i	−0.0172991	−	0.0840581i
$686$			17.4088i			0.664671i
$687$	−38.8022	+	4.72443i	−1.48040	+	0.180248i
$688$	−0.0549708	+	0.0549708i	−0.00209574	+	0.00209574i
$689$	−14.2673			−0.543541
$690$	12.4582	+	6.19212i	0.474274	+	0.235730i
$691$	−24.1265			−0.917815			−0.458907	−	0.888484i	$-0.651759\pi$
$691$	−24.1265			−0.917815			−0.458907	+	0.888484i	$0.651759\pi$
$692$	14.4146	−	14.4146i	0.547962	−	0.547962i
$693$	10.9106	−	18.0753i	0.414461	−	0.686626i
$694$			11.7590i			0.446364i
$695$	26.9967	+	17.7814i	1.02404	+	0.674486i
$696$	4.78869	−	6.11647i	0.181515	−	0.231844i
$697$	−6.24118	−	6.24118i	−0.236402	−	0.236402i
$698$	−20.2684	−	20.2684i	−0.767172	−	0.767172i
$699$	25.0701	−	32.0213i	0.948237	−	1.21116i
$700$	−12.9244	−	5.15418i	−0.488497	−	0.194810i
$701$		−	16.3755i		−	0.618496i	−0.950981	−	0.309248i	$-0.899923\pi$
$701$		−	16.3755i		−	0.618496i	0.950981	−	0.309248i	$-0.100077\pi$
$702$	6.79444	−	2.58449i	0.256440	−	0.0975454i
$703$	−1.15205	+	1.15205i	−0.0434504	+	0.0434504i
$704$	−2.52895			−0.0953133
$705$	−43.3863	+	14.5767i	−1.63402	+	0.548992i
$706$	−17.4243			−0.655774
$707$	−15.0024	+	15.0024i	−0.564223	+	0.564223i
$708$	−12.2562	+	1.49228i	−0.460618	+	0.0560834i
$709$		−	10.6366i		−	0.399466i	−0.979850	−	0.199733i	$-0.935992\pi$
$709$		−	10.6366i		−	0.399466i	0.979850	−	0.199733i	$-0.0640075\pi$
$710$	13.5739	−	2.79351i	0.509420	−	0.104838i
$711$	−4.96381	−	20.0819i	−0.186158	−	0.753131i
$712$	5.77271	+	5.77271i	0.216342	+	0.216342i
$713$	−6.78333	−	6.78333i	−0.254038	−	0.254038i
$714$	3.79523	+	2.97136i	0.142033	+	0.111200i
$715$	−7.74878	+	1.59470i	−0.289788	+	0.0596383i
$716$			24.7375i			0.924484i
$717$	0.100747	+	0.827442i	0.00376246	+	0.0309014i
$718$	−2.10627	+	2.10627i	−0.0786052	+	0.0786052i
$719$	−31.8489			−1.18776			−0.593882	−	0.804552i	$-0.702406\pi$
$719$	−31.8489			−1.18776			−0.593882	+	0.804552i	$0.702406\pi$
$720$	−2.23780	+	6.32394i	−0.0833980	+	0.235679i
$721$	−35.2549			−1.31296
$722$	−12.4033	+	12.4033i	−0.461601	+	0.461601i
$723$	−3.26591	−	26.8232i	−0.121461	−	0.997566i
$724$			16.2804i			0.605058i
$725$	8.85486	+	20.6021i	0.328861	+	0.765144i
$726$	−6.27949	−	4.91633i	−0.233054	−	0.182462i
$727$	−36.9258	−	36.9258i	−1.36950	−	1.36950i	−0.861150	−	0.508351i	$-0.830255\pi$
$727$	−36.9258	−	36.9258i	−1.36950	−	1.36950i	−0.508351	−	0.861150i	$-0.669745\pi$
$728$	2.75290	+	2.75290i	0.102029	+	0.102029i
$729$	−20.1743	+	17.9443i	−0.747196	+	0.664604i
$730$	13.1980	+	8.69289i	0.488481	+	0.321738i
$731$			0.0777404i			0.00287533i
$732$	13.1262	−	1.59820i	0.485158	−	0.0590713i
$733$	−11.2787	+	11.2787i	−0.416588	+	0.416588i	−0.884026	−	0.467438i	$-0.845177\pi$
$733$	−11.2787	+	11.2787i	−0.416588	+	0.416588i	0.467438	+	0.884026i	$0.345177\pi$
$734$	28.2605			1.04311
$735$	1.28295	−	2.58122i	0.0473224	−	0.0952097i
$736$	3.59210			0.132407
$737$	−24.3062	+	24.3062i	−0.895331	+	0.895331i
$738$	22.6693	+	13.6837i	0.834470	+	0.503703i
$739$		−	44.3775i		−	1.63245i	−0.577733	−	0.816226i	$-0.696062\pi$
$739$		−	44.3775i		−	1.63245i	0.577733	−	0.816226i	$-0.303938\pi$
$740$	−0.607936	−	2.95402i	−0.0223482	−	0.108592i
$741$	1.80440	−	2.30471i	0.0662861	−	0.0846656i
$742$	20.0678	+	20.0678i	0.736713	+	0.736713i
$743$	1.13462	+	1.13462i	0.0416250	+	0.0416250i	0.727613	−	0.685988i	$-0.240630\pi$
$743$	1.13462	+	1.13462i	0.0416250	+	0.0416250i	−0.685988	+	0.727613i	$0.740630\pi$
$744$	2.85150	−	3.64215i	0.104541	−	0.133528i
$745$	−10.4296	+	15.8348i	−0.382110	+	0.580141i
$746$			20.5213i			0.751339i
$747$	21.8566	+	13.1931i	0.799692	+	0.482710i
$748$	−1.78824	+	1.78824i	−0.0653844	+	0.0653844i
$749$	40.1996			1.46886
$750$	−12.9147	−	14.4295i	−0.471579	−	0.526890i
$751$	34.8890			1.27312			0.636559	−	0.771228i	$-0.280357\pi$
$751$	34.8890			1.27312			0.636559	+	0.771228i	$0.280357\pi$
$752$	−8.35634	+	8.35634i	−0.304724	+	0.304724i
$753$	4.64040	−	0.565001i	0.169106	−	0.0205898i
$754$		−	6.27435i		−	0.228498i
$755$	−6.53687	+	9.92464i	−0.237901	+	0.361195i
$756$	−13.1920	−	5.92155i	−0.479790	−	0.215365i
$757$	−6.74622	−	6.74622i	−0.245196	−	0.245196i	0.573800	−	0.818996i	$-0.305469\pi$
$757$	−6.74622	−	6.74622i	−0.245196	−	0.245196i	−0.818996	+	0.573800i	$0.805469\pi$
$758$	13.0954	+	13.0954i	0.475646	+	0.475646i
$759$	−12.3890	−	9.69958i	−0.449693	−	0.352073i
$760$	0.544469	+	2.64562i	0.0197500	+	0.0959669i
$761$			27.2060i			0.986217i	0.869968	+	0.493109i	$0.164140\pi$
$761$			27.2060i			0.986217i	−0.869968	+	0.493109i	$0.835860\pi$
$762$	−1.41272	−	11.6028i	−0.0511774	−	0.420325i
$763$	−21.6638	+	21.6638i	−0.784284	+	0.784284i
$764$	−18.9004			−0.683792
$765$	2.88934	+	6.05407i	0.104464	+	0.218885i
$766$	−29.7356			−1.07439
$767$	−7.05170	+	7.05170i	−0.254622	+	0.254622i
$768$	0.209343	+	1.71935i	0.00755402	+	0.0620418i
$769$		−	41.2250i		−	1.48661i	−0.668952	−	0.743306i	$-0.733257\pi$
$769$		−	41.2250i		−	1.48661i	0.668952	−	0.743306i	$-0.266743\pi$
$770$	13.1422	+	8.65609i	0.473611	+	0.311944i
$771$	42.3717	+	33.1735i	1.52598	+	1.19472i
$772$	−14.6605	−	14.6605i	−0.527644	−	0.527644i
$773$	−9.99203	−	9.99203i	−0.359388	−	0.359388i	0.504199	−	0.863587i	$-0.331788\pi$
$773$	−9.99203	−	9.99203i	−0.359388	−	0.359388i	−0.863587	+	0.504199i	$0.831788\pi$
$774$	−0.0559630	−	0.226407i	−0.00201155	−	0.00813804i
$775$	5.27277	+	12.2679i	0.189404	+	0.440675i
$776$			17.2187i			0.618115i
$777$	6.45343	−	0.785750i	0.231516	−	0.0281886i
$778$	1.81486	−	1.81486i	0.0650660	−	0.0650660i
$779$	10.6619			0.382000
$780$	1.72562	+	5.13615i	0.0617871	+	0.183904i
$781$	−15.6735			−0.560844
$782$	2.54000	−	2.54000i	0.0908302	−	0.0908302i
$783$	8.28535	+	21.7816i	0.296094	+	0.778411i
$784$		−	0.744252i		−	0.0265804i
$785$	−21.7698	+	4.48023i	−0.776999	+	0.159906i
$786$	−4.62161	+	5.90306i	−0.164847	+	0.210555i
$787$	−6.46873	−	6.46873i	−0.230585	−	0.230585i	0.582352	−	0.812937i	$-0.302133\pi$
$787$	−6.46873	−	6.46873i	−0.230585	−	0.230585i	−0.812937	+	0.582352i	$0.802133\pi$
$788$	14.2642	+	14.2642i	0.508142	+	0.508142i
$789$	−21.5353	+	27.5065i	−0.766678	+	0.979258i
$790$	15.1022	−	3.10802i	0.537311	−	0.110578i
$791$			43.4362i			1.54441i
$792$	3.92067	−	6.49526i	0.139315	−	0.230799i
$793$	7.55222	−	7.55222i	0.268187	−	0.268187i
$794$	3.79899			0.134821
$795$	12.5792	+	37.4410i	0.446140	+	1.32789i
$796$	−3.37444			−0.119604
$797$	−15.6462	+	15.6462i	−0.554218	+	0.554218i	−0.927655	−	0.373437i	$-0.878179\pi$
$797$	−15.6462	+	15.6462i	−0.554218	+	0.554218i	0.373437	+	0.927655i	$0.378179\pi$
$798$	−5.77970	+	0.703719i	−0.204599	+	0.0249114i
$799$			11.8177i			0.418078i
$800$	−4.64431	−	1.85212i	−0.164201	−	0.0654825i
$801$	−23.7760	+	5.87691i	−0.840083	+	0.207650i
$802$	7.72923	+	7.72923i	0.272929	+	0.272929i
$803$	−12.6385	−	12.6385i	−0.446004	−	0.446004i
$804$	18.5371	+	14.5130i	0.653753	+	0.511834i
$805$	−18.6671	−	12.2951i	−0.657927	−	0.433344i
$806$		−	3.73616i		−	0.131601i
$807$	−4.74764	−	38.9927i	−0.167125	−	1.37261i
$808$	−5.39101	+	5.39101i	−0.189655	+	0.189655i
$809$	43.2206			1.51956			0.759778	−	0.650183i	$-0.225308\pi$
$809$	43.2206			1.51956			0.759778	+	0.650183i	$0.225308\pi$
$810$	−12.7729	−	15.5516i	−0.448794	−	0.546428i
$811$	43.1822			1.51633			0.758166	−	0.652062i	$-0.226096\pi$
$811$	43.1822			1.51633			0.758166	+	0.652062i	$0.226096\pi$
$812$	−8.82525	+	8.82525i	−0.309705	+	0.309705i
$813$	−0.640480	−	5.26032i	−0.0224626	−	0.184487i
$814$			3.41095i			0.119554i
$815$	5.94358	+	28.8804i	0.208194	+	1.01164i
$816$	1.36379	+	1.06774i	0.0477424	+	0.0373783i
$817$	−0.0664022	−	0.0664022i	−0.00232312	−	0.00232312i
$818$	2.04925	+	2.04925i	0.0716503	+	0.0716503i
$819$	−11.3383	+	2.80259i	−0.396194	+	0.0979305i
$820$	−10.8561	+	16.4824i	−0.379112	+	0.575589i
$821$		−	1.73603i		−	0.0605877i	−0.999541	−	0.0302939i	$-0.990356\pi$
$821$		−	1.73603i		−	0.0605877i	0.999541	−	0.0302939i	$-0.00964431\pi$
$822$	1.72708	−	0.210284i	0.0602388	−	0.00733449i
$823$	−2.91686	+	2.91686i	−0.101675	+	0.101675i	−0.756115	−	0.654439i	$-0.772905\pi$
$823$	−2.91686	+	2.91686i	−0.101675	+	0.101675i	0.654439	+	0.756115i	$0.272905\pi$
$824$	−12.6686			−0.441333
$825$	11.0169	+	18.9287i	0.383558	+	0.659014i
$826$	19.8373			0.690227
$827$	−9.68706	+	9.68706i	−0.336852	+	0.336852i	−0.855181	−	0.518329i	$-0.826554\pi$
$827$	−9.68706	+	9.68706i	−0.336852	+	0.336852i	0.518329	+	0.855181i	$0.326554\pi$
$828$	−5.56890	+	9.22584i	−0.193533	+	0.320620i
$829$			13.7128i			0.476264i	0.971233	+	0.238132i	$0.0765351\pi$
$829$			13.7128i			0.476264i	−0.971233	+	0.238132i	$0.923465\pi$
$830$	−10.4669	+	15.8914i	−0.363312	+	0.551600i
$831$	18.6552	−	23.8278i	0.647142	−	0.826577i
$832$	0.989239	+	0.989239i	0.0342957	+	0.0342957i
$833$	−0.526266	−	0.526266i	−0.0182340	−	0.0182340i
$834$	−15.4361	+	19.7161i	−0.534508	+	0.682714i
$835$	−0.559911	−	2.72066i	−0.0193765	−	0.0941523i
$836$		−	3.05485i		−	0.105654i
$837$	4.93365	+	12.9702i	0.170532	+	0.448316i
$838$	3.66318	−	3.66318i	0.126542	−	0.126542i
$839$	−5.68715			−0.196342			−0.0981711	−	0.995170i	$-0.531299\pi$
$839$	−5.68715			−0.196342			−0.0981711	+	0.995170i	$0.531299\pi$
$840$	4.79712	−	9.65150i	0.165516	−	0.333008i
$841$	−8.88573			−0.306404
$842$	−3.37351	+	3.37351i	−0.116259	+	0.116259i
$843$	42.0482	−	5.11966i	1.44822	−	0.176331i
$844$			16.2292i			0.558631i
$845$	−20.6214	−	13.5823i	−0.709396	−	0.467244i
$846$	−8.50717	−	34.4171i	−0.292483	−	1.18329i
$847$	9.06047	+	9.06047i	0.311321	+	0.311321i
$848$	7.21125	+	7.21125i	0.247635	+	0.247635i
$849$	−0.00273421	−	0.00214066i	−9.38377e−5	−	7.34672e-5i
$850$	−4.59367	+	1.97438i	−0.157562	+	0.0677205i
$851$		−	4.84490i		−	0.166081i
$852$	1.29744	+	10.6560i	0.0444495	+	0.365067i
$853$	−12.7324	+	12.7324i	−0.435948	+	0.435948i	−0.890646	−	0.454698i	$-0.849747\pi$
$853$	−12.7324	+	12.7324i	−0.435948	+	0.435948i	0.454698	+	0.890646i	$0.349747\pi$
$854$	−21.2453			−0.726999
$855$	−7.63904	−	2.70316i	−0.261250	−	0.0924463i
$856$	14.4455			0.493736
$857$	18.0972	−	18.0972i	0.618189	−	0.618189i	−0.326878	−	0.945067i	$-0.605997\pi$
$857$	18.0972	−	18.0972i	0.618189	−	0.618189i	0.945067	+	0.326878i	$0.105997\pi$
$858$	−0.740653	−	6.08305i	−0.0252855	−	0.207672i
$859$		−	40.4694i		−	1.38080i	−0.723429	−	0.690399i	$-0.757435\pi$
$859$		−	40.4694i		−	1.38080i	0.723429	−	0.690399i	$-0.242565\pi$
$860$	0.170265	−	0.0350404i	0.00580597	−	0.00119487i
$861$	−33.4981	−	26.2263i	−1.14161	−	0.893789i
$862$	20.9975	+	20.9975i	0.715179	+	0.715179i
$863$	−33.5317	−	33.5317i	−1.14143	−	1.14143i	−0.988189	−	0.153242i	$-0.951029\pi$
$863$	−33.5317	−	33.5317i	−1.14143	−	1.14143i	−0.153242	−	0.988189i	$-0.548971\pi$
$864$	−4.74048	−	2.12787i	−0.161274	−	0.0723917i
$865$	−44.6474	+	9.18843i	−1.51806	+	0.312416i
$866$			15.0445i			0.511234i
$867$	1.71935	−	0.209343i	0.0583923	−	0.00710967i
$868$	−5.25514	+	5.25514i	−0.178371	+	0.178371i
$869$	−17.4382			−0.591550
$870$	−16.4655	+	5.53199i	−0.558231	+	0.187552i
$871$	19.0155			0.644317
$872$	−7.78477	+	7.78477i	−0.263626	+	0.263626i
$873$	−44.2239	−	26.6944i	−1.49675	−	0.903470i
$874$			4.33910i			0.146772i
$875$	17.7956	+	25.5215i	0.601602	+	0.862784i
$876$	−7.54634	+	9.63874i	−0.254967	+	0.325663i
$877$	15.9710	+	15.9710i	0.539301	+	0.539301i	0.923324	−	0.384023i	$-0.125462\pi$
$877$	15.9710	+	15.9710i	0.539301	+	0.539301i	−0.384023	+	0.923324i	$0.625462\pi$
$878$	−13.3373	−	13.3373i	−0.450113	−	0.450113i
$879$	14.3143	−	18.2833i	0.482809	−	0.616680i
$880$	4.72256	+	3.11051i	0.159197	+	0.104855i
$881$		−	28.3552i		−	0.955312i	−0.878547	−	0.477656i	$-0.841487\pi$
$881$		−	28.3552i		−	0.955312i	0.878547	−	0.477656i	$-0.158513\pi$
$882$	1.91151	+	1.15383i	0.0643640	+	0.0388514i
$883$	−22.6946	+	22.6946i	−0.763735	+	0.763735i	−0.976995	−	0.213260i	$-0.931592\pi$
$883$	−22.6946	+	22.6946i	−0.763735	+	0.763735i	0.213260	+	0.976995i	$0.431592\pi$
$884$	1.39900			0.0470533
$885$	24.7228	+	12.2881i	0.831047	+	0.413058i
$886$	−22.8838			−0.768795
$887$	29.9212	−	29.9212i	1.00466	−	1.00466i	0.00466796	−	0.999989i	$-0.498514\pi$
$887$	29.9212	−	29.9212i	1.00466	−	1.00466i	0.999989	−	0.00466796i	$-0.00148586\pi$
$888$	2.31900	−	0.282355i	0.0778206	−	0.00947520i
$889$			18.7796i			0.629848i
$890$	−3.67974	−	17.8802i	−0.123345	−	0.599346i
$891$	10.6039	+	20.1395i	0.355245	+	0.674697i
$892$	0.926391	+	0.926391i	0.0310179	+	0.0310179i
$893$	−10.0941	−	10.0941i	−0.337786	−	0.337786i
$894$	−11.5644	−	9.05397i	−0.386771	−	0.302810i
$895$	30.4263	−	46.1949i	1.01704	−	1.54412i
$896$		−	2.78285i		−	0.0929685i
$897$	1.05202	+	8.64032i	0.0351259	+	0.288492i
$898$	6.80103	−	6.80103i	0.226953	−	0.226953i
$899$	11.9774			0.399468
$900$	11.9571	−	9.05692i	0.398570	−	0.301897i
$901$	10.1982			0.339753
$902$	15.7836	−	15.7836i	0.525537	−	0.525537i
$903$	0.0452893	+	0.371965i	0.00150713	+	0.0123782i
$904$			15.6085i			0.519132i
$905$	20.0244	−	30.4021i	0.665632	−	1.01060i
$906$	−7.24813	−	5.67469i	−0.240803	−	0.188529i
$907$	−25.6603	−	25.6603i	−0.852036	−	0.852036i	0.138347	−	0.990384i	$-0.455821\pi$
$907$	−25.6603	−	25.6603i	−0.852036	−	0.852036i	−0.990384	+	0.138347i	$0.955821\pi$
$908$	−7.98766	−	7.98766i	−0.265080	−	0.265080i
$909$	−5.48832	−	22.2039i	−0.182036	−	0.736457i
$910$	−1.75480	−	8.52675i	−0.0581711	−	0.282659i
$911$		−	42.1356i		−	1.39601i	−0.716091	−	0.698007i	$-0.754070\pi$
$911$		−	42.1356i		−	1.39601i	0.716091	−	0.698007i	$-0.245930\pi$
$912$	−2.07690	+	0.252877i	−0.0687731	+	0.00837360i
$913$	15.2177	−	15.2177i	0.503634	−	0.503634i
$914$	−24.5895			−0.813349
$915$	−26.4776	−	13.1602i	−0.875322	−	0.435064i
$916$	22.5679			0.745664
$917$	8.51732	−	8.51732i	0.281267	−	0.281267i
$918$	−4.85666	+	1.84739i	−0.160294	+	0.0609730i
$919$		−	22.8415i		−	0.753471i	−0.926321	−	0.376735i	$-0.877047\pi$
$919$		−	22.8415i		−	0.753471i	0.926321	−	0.376735i	$-0.122953\pi$
$920$	−6.70789	−	4.41816i	−0.221153	−	0.145662i
$921$	24.5566	−	31.3655i	0.809168	−	1.03353i
$922$	−5.93368	−	5.93368i	−0.195415	−	0.195415i
$923$	6.13097	+	6.13097i	0.201803	+	0.201803i
$924$	−7.51440	+	9.59794i	−0.247206	+	0.315749i
$925$	−2.49808	+	6.26408i	−0.0821363	+	0.205962i
$926$			8.01272i			0.263314i
$927$	19.6404	−	32.5377i	0.645077	−	1.06868i
$928$	−3.17130	+	3.17130i	−0.104103	+	0.104103i
$929$	59.4712			1.95119			0.975594	−	0.219584i	$-0.0704701\pi$
$929$	59.4712			1.95119			0.975594	+	0.219584i	$0.0704701\pi$
$930$	−9.80462	+	3.29411i	−0.321506	+	0.108018i
$931$	0.899023			0.0294643
$932$	−16.6026	+	16.6026i	−0.543836	+	0.543836i
$933$	−15.2193	+	1.85305i	−0.498257	+	0.0606662i
$934$			3.80039i			0.124353i
$935$	5.53882	−	1.13989i	0.181139	−	0.0372783i
$936$	−4.07437	+	1.00709i	−0.133175	+	0.0329179i
$937$	−10.4705	−	10.4705i	−0.342058	−	0.342058i	0.515083	−	0.857140i	$-0.327761\pi$
$937$	−10.4705	−	10.4705i	−0.342058	−	0.342058i	−0.857140	+	0.515083i	$0.827761\pi$
$938$	−26.7465	−	26.7465i	−0.873305	−	0.873305i
$939$	−29.7027	−	23.2548i	−0.969312	−	0.758891i
$940$	25.8826	−	5.32664i	0.844199	−	0.173736i
$941$		−	19.1807i		−	0.625272i	−0.949873	−	0.312636i	$-0.898788\pi$
$941$		−	19.1807i		−	0.625272i	0.949873	−	0.312636i	$-0.101212\pi$
$942$	−2.08083	−	17.0900i	−0.0677971	−	0.556823i
$943$	−22.4190	+	22.4190i	−0.730062	+	0.730062i
$944$	7.12840			0.232010
$945$	17.3515	+	27.2837i	0.564446	+	0.887538i
$946$	−0.196601			−0.00639206
$947$	13.2375	−	13.2375i	0.430161	−	0.430161i	−0.458522	−	0.888683i	$-0.651621\pi$
$947$	13.2375	−	13.2375i	0.430161	−	0.430161i	0.888683	+	0.458522i	$0.151621\pi$
$948$	1.44351	+	11.8557i	0.0468831	+	0.385055i
$949$			9.88753i			0.320963i
$950$	2.23728	−	5.61012i	0.0725870	−	0.182016i
$951$	28.4808	+	22.2981i	0.923553	+	0.723066i
$952$	−1.96777	−	1.96777i	−0.0637759	−	0.0637759i
$953$	13.0276	+	13.0276i	0.422007	+	0.422007i	0.885894	−	0.463887i	$-0.153546\pi$
$953$	13.0276	+	13.0276i	0.422007	+	0.422007i	−0.463887	+	0.885894i	$0.653546\pi$
$954$	−29.7009	+	7.34141i	−0.961601	+	0.237687i
$955$	35.2946	+	23.2468i	1.14211	+	0.752249i
$956$		−	0.481252i		−	0.0155648i
$957$	19.5010	−	2.37438i	0.630378	−	0.0767529i
$958$	−3.47489	+	3.47489i	−0.112269	+	0.112269i
$959$	−2.79535			−0.0902667
$960$	1.72382	−	3.46821i	0.0556359	−	0.111936i
$961$	−23.8679			−0.769932
$962$	1.33425	−	1.33425i	0.0430179	−	0.0430179i
$963$	−22.3951	+	37.1013i	−0.721671	+	1.19557i
$964$			15.6008i			0.502467i
$965$	9.34516	+	45.4090i	0.300831	+	1.46177i
$966$	10.6734	−	13.6329i	0.343411	−	0.438630i
$967$	−41.7514	−	41.7514i	−1.34264	−	1.34264i	−0.893427	−	0.449208i	$-0.851706\pi$
$967$	−41.7514	−	41.7514i	−1.34264	−	1.34264i	−0.449208	−	0.893427i	$-0.648294\pi$
$968$	3.25582	+	3.25582i	0.104646	+	0.104646i
$969$	−1.28978	+	1.64740i	−0.0414337	+	0.0529222i
$970$	21.1784	−	32.1542i	0.679997	−	1.03241i
$971$			8.25464i			0.264904i	0.991189	+	0.132452i	$0.0422851\pi$
$971$			8.25464i			0.264904i	−0.991189	+	0.132452i	$0.957715\pi$
$972$	12.8144	−	8.87642i	0.411023	−	0.284711i
$973$	28.4477	−	28.4477i	0.911992	−	0.911992i
$974$	−38.5412			−1.23494
$975$	3.09486	−	11.7137i	0.0991148	−	0.375139i
$976$	−7.63437			−0.244370
$977$	−12.2913	+	12.2913i	−0.393233	+	0.393233i	−0.875838	−	0.482605i	$-0.839691\pi$
$977$	−12.2913	+	12.2913i	−0.393233	+	0.393233i	0.482605	+	0.875838i	$0.339691\pi$
$978$	−22.6721	+	2.76048i	−0.724972	+	0.0882704i
$979$			20.6459i			0.659847i
$980$	−0.915403	+	1.38982i	−0.0292415	+	0.0443961i
$981$	−7.92528	−	32.0630i	−0.253035	−	1.02369i
$982$	0.0467401	+	0.0467401i	0.00149154	+	0.00149154i
$983$	40.0891	+	40.0891i	1.27864	+	1.27864i	0.941427	+	0.337215i	$0.109485\pi$
$983$	40.0891	+	40.0891i	1.27864	+	1.27864i	0.337215	+	0.941427i	$0.390515\pi$
$984$	−12.0373	−	9.42425i	−0.383737	−	0.300434i
$985$	−9.09254	−	44.1815i	−0.289712	−	1.40774i
$986$			4.48489i			0.142828i
$987$	6.88462	+	56.5439i	0.219140	+	1.79981i
$988$	−1.19496	+	1.19496i	−0.0380166	+	0.0380166i
$989$	0.279251			0.00887968
$990$	−15.3104	+	7.30698i	−0.486597	+	0.232231i
$991$	16.5865			0.526888			0.263444	−	0.964675i	$-0.415142\pi$
$991$	16.5865			0.526888			0.263444	+	0.964675i	$0.415142\pi$
$992$	−1.88840	+	1.88840i	−0.0599568	+	0.0599568i
$993$	3.74830	+	30.7851i	0.118949	+	0.976935i
$994$		−	17.2472i		−	0.547046i
$995$	6.30143	+	4.15044i	0.199769	+	0.131578i
$996$	−11.6058	−	9.08637i	−0.367743	−	0.287913i
$997$	24.0317	+	24.0317i	0.761090	+	0.761090i	0.976519	−	0.215429i	$-0.0691150\pi$
$997$	24.0317	+	24.0317i	0.761090	+	0.761090i	−0.215429	+	0.976519i	$0.569115\pi$
$998$	29.5758	+	29.5758i	0.936205	+	0.936205i
$999$	−2.87000	+	6.39379i	−0.0908028	+	0.202291i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	510.2.l.g.137.4	✓	28
3.2	odd	2	inner	510.2.l.g.137.8	yes	28
5.3	odd	4	inner	510.2.l.g.443.8	yes	28
15.8	even	4	inner	510.2.l.g.443.4	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
510.2.l.g.137.4	✓	28	1.1	even	1	trivial
510.2.l.g.137.8	yes	28	3.2	odd	2	inner
510.2.l.g.443.4	yes	28	15.8	even	4	inner
510.2.l.g.443.8	yes	28	5.3	odd	4	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:	\( N \)	\(=\)	\( 510 = 2 \cdot 3 \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	510.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(0.209343 + 1.71935i) q^{3} -1.00000i q^{4} +(-1.22996 + 1.86740i) q^{5} +(-1.36379 - 1.06774i) q^{6} +(1.96777 + 1.96777i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.91235 + 0.719870i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(0.209343 + 1.71935i) q^{3} -1.00000i q^{4} +(-1.22996 + 1.86740i) q^{5} +(-1.36379 - 1.06774i) q^{6} +(1.96777 + 1.96777i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.91235 + 0.719870i) q^{9} +(-0.450736 - 2.19017i) q^{10} +2.52895i q^{11} +(1.71935 - 0.209343i) q^{12} +(0.989239 - 0.989239i) q^{13} -2.78285 q^{14} +(-3.46821 - 1.72382i) q^{15} -1.00000 q^{16} +(-0.707107 + 0.707107i) q^{17} +(1.55032 - 2.56837i) q^{18} -1.20796i q^{19} +(1.86740 + 1.22996i) q^{20} +(-2.97136 + 3.79523i) q^{21} +(-1.78824 - 1.78824i) q^{22} +(2.54000 + 2.54000i) q^{23} +(-1.06774 + 1.36379i) q^{24} +(-1.97438 - 4.59367i) q^{25} +1.39900i q^{26} +(-1.84739 - 4.85666i) q^{27} +(1.96777 - 1.96777i) q^{28} -4.48489 q^{29} +(3.67131 - 1.23347i) q^{30} -2.67060 q^{31} +(0.707107 - 0.707107i) q^{32} +(-4.34815 + 0.529418i) q^{33} -1.00000i q^{34} +(-6.09491 + 1.25433i) q^{35} +(0.719870 + 2.91235i) q^{36} +(-0.953720 - 0.953720i) q^{37} +(0.854153 + 0.854153i) q^{38} +(1.90794 + 1.49376i) q^{39} +(-2.19017 + 0.450736i) q^{40} +8.82636i q^{41} +(-0.582571 - 4.78470i) q^{42} +(0.0549708 - 0.0549708i) q^{43} +2.52895 q^{44} +(2.23780 - 6.32394i) q^{45} -3.59210 q^{46} +(8.35634 - 8.35634i) q^{47} +(-0.209343 - 1.71935i) q^{48} +0.744252i q^{49} +(4.64431 + 1.85212i) q^{50} +(-1.36379 - 1.06774i) q^{51} +(-0.989239 - 0.989239i) q^{52} +(-7.21125 - 7.21125i) q^{53} +(4.74048 + 2.12787i) q^{54} +(-4.72256 - 3.11051i) q^{55} +2.78285i q^{56} +(2.07690 - 0.252877i) q^{57} +(3.17130 - 3.17130i) q^{58} -7.12840 q^{59} +(-1.72382 + 3.46821i) q^{60} +7.63437 q^{61} +(1.88840 - 1.88840i) q^{62} +(-7.14738 - 4.31430i) q^{63} +1.00000i q^{64} +(0.630578 + 3.06404i) q^{65} +(2.70025 - 3.44896i) q^{66} +(9.61120 + 9.61120i) q^{67} +(0.707107 + 0.707107i) q^{68} +(-3.83542 + 4.89889i) q^{69} +(3.42281 - 5.19670i) q^{70} +6.19766i q^{71} +(-2.56837 - 1.55032i) q^{72} +(-4.99754 + 4.99754i) q^{73} +1.34876 q^{74} +(7.48483 - 4.35630i) q^{75} -1.20796 q^{76} +(-4.97639 + 4.97639i) q^{77} +(-2.40537 + 0.292870i) q^{78} +6.89543i q^{79} +(1.22996 - 1.86740i) q^{80} +(7.96357 - 4.19303i) q^{81} +(-6.24118 - 6.24118i) q^{82} +(-6.01743 - 6.01743i) q^{83} +(3.79523 + 2.97136i) q^{84} +(-0.450736 - 2.19017i) q^{85} +0.0777404i q^{86} +(-0.938882 - 7.71112i) q^{87} +(-1.78824 + 1.78824i) q^{88} +8.16385 q^{89} +(2.88934 + 6.05407i) q^{90} +3.89319 q^{91} +(2.54000 - 2.54000i) q^{92} +(-0.559072 - 4.59171i) q^{93} +11.8177i q^{94} +(2.25574 + 1.48574i) q^{95} +(1.36379 + 1.06774i) q^{96} +(12.1755 + 12.1755i) q^{97} +(-0.526266 - 0.526266i) q^{98} +(-1.82051 - 7.36518i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 4 q^{7}+O(q^{10}) \) 28 * q + 4 * q^7	\( 28 q + 4 q^{7} - 12 q^{10} - 8 q^{13} + 8 q^{15} - 28 q^{16} - 16 q^{18} + 48 q^{21} + 20 q^{22} + 40 q^{25} - 36 q^{27} + 4 q^{28} - 12 q^{30} + 16 q^{31} + 8 q^{33} + 8 q^{37} - 8 q^{40} - 48 q^{42} + 48 q^{43} + 36 q^{45} - 64 q^{46} + 8 q^{52} - 36 q^{55} - 32 q^{57} + 20 q^{58} + 12 q^{60} - 16 q^{61} - 56 q^{63} + 32 q^{66} + 112 q^{67} - 28 q^{70} + 16 q^{72} + 12 q^{73} + 16 q^{75} - 8 q^{76} - 32 q^{78} - 48 q^{81} + 24 q^{82} - 12 q^{85} - 44 q^{87} + 20 q^{88} - 20 q^{90} - 80 q^{91} + 28 q^{93} + 60 q^{97}+O(q^{100}) \) 28 * q + 4 * q^7 - 12 * q^10 - 8 * q^13 + 8 * q^15 - 28 * q^16 - 16 * q^18 + 48 * q^21 + 20 * q^22 + 40 * q^25 - 36 * q^27 + 4 * q^28 - 12 * q^30 + 16 * q^31 + 8 * q^33 + 8 * q^37 - 8 * q^40 - 48 * q^42 + 48 * q^43 + 36 * q^45 - 64 * q^46 + 8 * q^52 - 36 * q^55 - 32 * q^57 + 20 * q^58 + 12 * q^60 - 16 * q^61 - 56 * q^63 + 32 * q^66 + 112 * q^67 - 28 * q^70 + 16 * q^72 + 12 * q^73 + 16 * q^75 - 8 * q^76 - 32 * q^78 - 48 * q^81 + 24 * q^82 - 12 * q^85 - 44 * q^87 + 20 * q^88 - 20 * q^90 - 80 * q^91 + 28 * q^93 + 60 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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