LMFDB - Embedded newform 510.2.l.g.443.8

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			443.8
Character	$\chi$	$=$	510.443
Dual form			510.2.l.g.137.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{2} +(-1.71935 + 0.209343i) q^{3} +1.00000i q^{4} +(1.22996 + 1.86740i) q^{5} +(-1.36379 - 1.06774i) q^{6} +(1.96777 - 1.96777i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.91235 - 0.719870i) q^{9} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{2} +(-1.71935 + 0.209343i) 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} +(-0.209343 - 1.71935i) q^{12} +(0.989239 + 0.989239i) q^{13} +2.78285 q^{14} +(-2.50567 - 2.95324i) q^{15} -1.00000 q^{16} +(0.707107 + 0.707107i) q^{17} +(2.56837 + 1.55032i) 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} +(-4.85666 + 1.84739i) q^{27} +(1.96777 + 1.96777i) q^{28} +4.48489 q^{29} +(0.316477 - 3.86003i) q^{30} -2.67060 q^{31} +(-0.707107 - 0.707107i) q^{32} +(-0.529418 - 4.34815i) 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} +(-4.78470 + 0.582571i) q^{42} +(0.0549708 + 0.0549708i) q^{43} -2.52895 q^{44} +(4.92637 + 4.55311i) q^{45} -3.59210 q^{46} +(-8.35634 - 8.35634i) q^{47} +(1.71935 - 0.209343i) 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} +(-0.252877 - 2.07690i) q^{57} +(3.17130 + 3.17130i) q^{58} +7.12840 q^{59} +(2.95324 - 2.50567i) q^{60} +7.63437 q^{61} +(-1.88840 - 1.88840i) q^{62} +(4.31430 - 7.14738i) 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} +(-1.55032 + 2.56837i) q^{72} +(-4.99754 - 4.99754i) q^{73} -1.34876 q^{74} +(2.43299 - 8.31147i) q^{75} -1.20796 q^{76} +(4.97639 + 4.97639i) q^{77} +(-0.292870 - 2.40537i) 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} +(-7.71112 + 0.938882i) q^{87} +(-1.78824 - 1.78824i) q^{88} -8.16385 q^{89} +(0.263935 + 6.70301i) q^{90} +3.89319 q^{91} +(-2.54000 - 2.54000i) q^{92} +(4.59171 - 0.559072i) 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 $\left(\mathbb{Z}/510\mathbb{Z}\right)^\times$.

$n$	$241$	$307$	$341$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$-1$

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
$3$	−1.71935	+	0.209343i	−0.992669	+	0.120864i
$3$	−1.71935	+	0.209343i	−0.992669	+	0.120864i
$4$			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	−0.229549	−	0.973297i	$-0.573725\pi$
$7$	1.96777	−	1.96777i	0.743748	−	0.743748i	0.973297	+	0.229549i	$0.0737252\pi$
$8$	−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	$0.875493\pi$
$12$	−0.209343	−	1.71935i	−0.0604322	−	0.496335i
$13$	0.989239	+	0.989239i	0.274366	+	0.274366i	0.830855	−	0.556489i	$-0.187852\pi$
$13$	0.989239	+	0.989239i	0.274366	+	0.274366i	−0.556489	+	0.830855i	$0.687852\pi$
$14$	2.78285			0.743748
$15$	−2.50567	−	2.95324i	−0.646961	−	0.762523i
$16$	−1.00000			−0.250000
$17$	0.707107	+	0.707107i	0.171499	+	0.171499i
$17$	0.707107	+	0.707107i	0.171499	+	0.171499i
$18$	2.56837	+	1.55032i	0.605370	+	0.365413i
$19$			1.20796i			0.277124i	0.990354	+	0.138562i	$0.0442480\pi$
$19$			1.20796i			0.277124i	−0.990354	+	0.138562i	$0.955752\pi$
$20$	−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	$-0.872186\pi$
$23$	−2.54000	+	2.54000i	−0.529626	+	0.529626i	0.390835	+	0.920461i	$0.372186\pi$
$24$	1.06774	−	1.36379i	0.217951	−	0.278383i
$25$	−1.97438	+	4.59367i	−0.394875	+	0.918735i
$26$			1.39900i			0.274366i
$27$	−4.85666	+	1.84739i	−0.934665	+	0.355531i
$28$	1.96777	+	1.96777i	0.371874	+	0.371874i
$29$	4.48489			0.832824			0.416412	−	0.909176i	$-0.363287\pi$
$29$	4.48489			0.832824			0.416412	+	0.909176i	$0.363287\pi$
$30$	0.316477	−	3.86003i	0.0577806	−	0.704742i
$31$	−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
$33$	−0.529418	−	4.34815i	−0.0921598	−	0.756916i
$34$			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	−0.781143	−	0.624352i	$-0.785363\pi$
$37$	−0.953720	+	0.953720i	−0.156791	+	0.156791i	0.624352	+	0.781143i	$0.285363\pi$
$38$	−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	$0.757952\pi$
$42$	−4.78470	+	0.582571i	−0.738295	+	0.0898926i
$43$	0.0549708	+	0.0549708i	0.00838296	+	0.00838296i	0.711286	−	0.702903i	$-0.248113\pi$
$43$	0.0549708	+	0.0549708i	0.00838296	+	0.00838296i	−0.702903	+	0.711286i	$0.748113\pi$
$44$	−2.52895			−0.381253
$45$	4.92637	+	4.55311i	0.734380	+	0.678738i
$46$	−3.59210			−0.529626
$47$	−8.35634	−	8.35634i	−1.21890	−	1.21890i	−0.968018	−	0.250879i	$-0.919280\pi$
$47$	−8.35634	−	8.35634i	−1.21890	−	1.21890i	−0.250879	−	0.968018i	$-0.580720\pi$
$48$	1.71935	−	0.209343i	0.248167	−	0.0302161i
$49$		−	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	$-0.502997\pi$
$53$	7.21125	−	7.21125i	0.990541	−	0.990541i	0.999956	+	0.00941435i	$0.00299672\pi$
$54$	−4.74048	−	2.12787i	−0.645098	−	0.289567i
$55$	−4.72256	+	3.11051i	−0.636790	+	0.419422i
$56$			2.78285i			0.371874i
$57$	−0.252877	−	2.07690i	−0.0334944	−	0.275092i
$58$	3.17130	+	3.17130i	0.416412	+	0.416412i
$59$	7.12840			0.928039			0.464020	−	0.885825i	$-0.346407\pi$
$59$	7.12840			0.928039			0.464020	+	0.885825i	$0.346407\pi$
$60$	2.95324	−	2.50567i	0.381261	−	0.323481i
$61$	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
$63$	4.31430	−	7.14738i	0.543551	−	0.900485i
$64$		−	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	0.192995	−	0.981200i	$-0.438180\pi$
$67$	9.61120	−	9.61120i	1.17419	−	1.17419i	0.981200	−	0.192995i	$-0.0618202\pi$
$68$	−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	$0.880124\pi$
$72$	−1.55032	+	2.56837i	−0.182707	+	0.302685i
$73$	−4.99754	−	4.99754i	−0.584918	−	0.584918i	0.351333	−	0.936251i	$-0.385729\pi$
$73$	−4.99754	−	4.99754i	−0.584918	−	0.584918i	−0.936251	+	0.351333i	$0.885729\pi$
$74$	−1.34876			−0.156791
$75$	2.43299	−	8.31147i	0.280938	−	0.959726i
$76$	−1.20796			−0.138562
$77$	4.97639	+	4.97639i	0.567112	+	0.567112i
$78$	−0.292870	−	2.40537i	−0.0331610	−	0.272354i
$79$		−	6.89543i		−	0.775797i	−0.921702	−	0.387898i	$-0.873201\pi$
$79$		−	6.89543i		−	0.775797i	0.921702	−	0.387898i	$-0.126799\pi$
$80$	−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	$-0.595319\pi$
$83$	6.01743	−	6.01743i	0.660498	−	0.660498i	0.955498	+	0.294999i	$0.0953194\pi$
$84$	−3.79523	−	2.97136i	−0.414094	−	0.324201i
$85$	−0.450736	+	2.19017i	−0.0488892	+	0.237557i
$86$			0.0777404i			0.00838296i
$87$	−7.71112	+	0.938882i	−0.826718	+	0.100659i
$88$	−1.78824	−	1.78824i	−0.190627	−	0.190627i
$89$	−8.16385			−0.865366			−0.432683	−	0.901546i	$-0.642433\pi$
$89$	−8.16385			−0.865366			−0.432683	+	0.901546i	$0.642433\pi$
$90$	0.263935	+	6.70301i	0.0278212	+	0.706559i
$91$	3.89319			0.408118
$92$	−2.54000	−	2.54000i	−0.264813	−	0.264813i
$93$	4.59171	−	0.559072i	0.476138	−	0.0579731i
$94$		−	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	0.274700	−	0.961530i	$-0.411422\pi$
$97$	12.1755	−	12.1755i	1.23623	−	1.23623i	0.961530	−	0.274700i	$-0.0885784\pi$
$98$	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	$0.876161\pi$
$102$	−0.209343	−	1.71935i	−0.0207281	−	0.170241i
$103$	−8.95809	−	8.95809i	−0.882667	−	0.882667i	0.111138	−	0.993805i	$-0.464550\pi$
$103$	−8.95809	−	8.95809i	−0.882667	−	0.882667i	−0.993805	+	0.111138i	$0.964550\pi$
$104$	−1.39900			−0.137183
$105$	−10.7419	−	0.880709i	−1.04830	−	0.0859484i
$106$	10.1982			0.990541
$107$	−10.2145	−	10.2145i	−0.987472	−	0.987472i	0.0124505	−	0.999922i	$-0.496037\pi$
$107$	−10.2145	−	10.2145i	−0.987472	−	0.987472i	−0.999922	+	0.0124505i	$0.996037\pi$
$108$	−1.84739	−	4.85666i	−0.177765	−	0.467332i
$109$		−	11.0093i		−	1.05450i	−0.849710	−	0.527251i	$-0.823223\pi$
$109$		−	11.0093i		−	1.05450i	0.849710	−	0.527251i	$-0.176777\pi$
$110$	−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	−0.0390248	+	0.999238i	$0.512425\pi$
$113$	−11.0369	+	11.0369i	−1.03826	+	1.03826i	−0.999238	+	0.0390248i	$0.987575\pi$
$114$	1.28978	−	1.64740i	0.120799	−	0.154293i
$115$	−7.86731	−	1.61909i	−0.733630	−	0.150981i
$116$			4.48489i			0.416412i
$117$	3.59313	+	2.16889i	0.332185	+	0.200514i
$118$	5.04054	+	5.04054i	0.464020	+	0.464020i
$119$	2.78285			0.255103
$120$	3.86003	+	0.316477i	0.352371	+	0.0288903i
$121$	4.60443			0.418585
$122$	5.39832	+	5.39832i	0.488741	+	0.488741i
$123$	−1.84774	−	15.1756i	−0.166605	−	1.36834i
$124$		−	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	−0.462954	−	0.886382i	$-0.653210\pi$
$127$	4.77180	−	4.77180i	0.423429	−	0.423429i	0.886382	+	0.462954i	$0.153210\pi$
$128$	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	$-0.0605529\pi$
$132$	4.34815	−	0.529418i	0.378458	−	0.0460799i
$133$	2.37698	+	2.37698i	0.206110	+	0.206110i
$134$	13.5923			1.17419
$135$	−9.42334	−	6.79711i	−0.811032	−	0.585002i
$136$	−1.00000			−0.0857493
$137$	0.710284	+	0.710284i	0.0606837	+	0.0606837i	0.736797	−	0.676114i	$-0.236337\pi$
$137$	0.710284	+	0.710284i	0.0606837	+	0.0606837i	−0.676114	+	0.736797i	$0.736337\pi$
$138$	6.17609	−	0.751982i	0.525744	−	0.0640130i
$139$			14.4568i			1.22621i	0.790001	+	0.613106i	$0.210080\pi$
$139$			14.4568i			1.22621i	−0.790001	+	0.613106i	$0.789920\pi$
$140$	−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
$147$	0.155804	+	1.27963i	0.0128505	+	0.105542i
$148$	−0.953720	−	0.953720i	−0.0783953	−	0.0783953i
$149$	−8.47958			−0.694674			−0.347337	−	0.937740i	$-0.612914\pi$
$149$	−8.47958			−0.694674			−0.347337	+	0.937740i	$0.612914\pi$
$150$	7.59748	−	4.15671i	0.620332	−	0.339394i
$151$	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
$153$	2.56837	+	1.55032i	0.207640	+	0.125336i
$154$			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	−0.368638	−	0.929573i	$-0.620176\pi$
$157$	7.02850	−	7.02850i	0.560936	−	0.560936i	0.929573	+	0.368638i	$0.120176\pi$
$158$	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
$162$	8.59602	+	2.66618i	0.675367	+	0.209475i
$163$	9.32418	+	9.32418i	0.730326	+	0.730326i	0.970684	−	0.240358i	$-0.0772648\pi$
$163$	9.32418	+	9.32418i	0.730326	+	0.730326i	−0.240358	+	0.970684i	$0.577265\pi$
$164$	−8.82636			−0.689223
$165$	7.46858	−	6.33671i	0.581428	−	0.493312i
$166$	8.50993			0.660498
$167$	0.878378	+	0.878378i	0.0679709	+	0.0679709i	0.740275	−	0.672304i	$-0.234695\pi$
$167$	0.878378	+	0.878378i	0.0679709	+	0.0679709i	−0.672304	+	0.740275i	$0.734695\pi$
$168$	−0.582571	−	4.78470i	−0.0449463	−	0.369148i
$169$		−	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	−0.101043	+	0.994882i	$0.532218\pi$
$173$	−14.4146	+	14.4146i	−1.09592	+	1.09592i	−0.994882	+	0.101043i	$0.967782\pi$
$174$	−6.11647	−	4.78869i	−0.463689	−	0.363030i
$175$	5.15418	+	12.9244i	0.389620	+	0.976995i
$176$		−	2.52895i		−	0.190627i
$177$	−12.2562	+	1.49228i	−0.921236	+	0.112167i
$178$	−5.77271	−	5.77271i	−0.432683	−	0.432683i
$179$	24.7375			1.84897			0.924484	−	0.381220i	$-0.124496\pi$
$179$	24.7375			1.84897			0.924484	+	0.381220i	$0.124496\pi$
$180$	−4.55311	+	4.92637i	−0.339369	+	0.367190i
$181$	−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
$183$	−13.1262	+	1.59820i	−0.970315	+	0.118143i
$184$		−	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	$-0.239670\pi$
$192$	0.209343	+	1.71935i	0.0151080	+	0.124084i
$193$	14.6605	+	14.6605i	1.05529	+	1.05529i	0.998379	+	0.0569086i	$0.0181244\pi$
$193$	14.6605	+	14.6605i	1.05529	+	1.05529i	0.0569086	+	0.998379i	$0.481876\pi$
$194$	17.2187			1.23623
$195$	0.442751	−	5.40017i	0.0317060	−	0.386714i
$196$	0.744252			0.0531608
$197$	14.2642	+	14.2642i	1.01628	+	1.01628i	0.999865	+	0.0164186i	$0.00522643\pi$
$197$	14.2642	+	14.2642i	1.01628	+	1.01628i	0.0164186	+	0.999865i	$0.494774\pi$
$198$	−3.92067	+	6.49526i	−0.278630	+	0.461598i
$199$			3.37444i			0.239208i	0.992822	+	0.119604i	$0.0381624\pi$
$199$			3.37444i			0.239208i	−0.992822	+	0.119604i	$0.961838\pi$
$200$	−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
$207$	−5.56890	+	9.22584i	−0.387065	+	0.641240i
$208$	−0.989239	−	0.989239i	−0.0685914	−	0.0685914i
$209$	−3.05485			−0.211309
$210$	−6.97291	−	8.21842i	−0.481176	−	0.567125i
$211$	−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
$213$	−1.29744	−	10.6560i	−0.0888990	−	0.730135i
$214$		−	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
$222$	2.31900	−	0.282355i	0.155641	−	0.0189504i
$223$	−0.926391	−	0.926391i	−0.0620357	−	0.0620357i	0.675408	−	0.737444i	$-0.263967\pi$
$223$	−0.926391	−	0.926391i	−0.0620357	−	0.0620357i	−0.737444	+	0.675408i	$0.763967\pi$
$224$	−2.78285			−0.185937
$225$	−2.44323	+	14.7997i	−0.162882	+	0.986646i
$226$	−15.6085			−1.03826
$227$	−7.98766	−	7.98766i	−0.530159	−	0.530159i	0.390460	−	0.920620i	$-0.372316\pi$
$227$	−7.98766	−	7.98766i	−0.530159	−	0.530159i	−0.920620	+	0.390460i	$0.872316\pi$
$228$	2.07690	−	0.252877i	0.137546	−	0.0167472i
$229$		−	22.5679i		−	1.49133i	−0.666322	−	0.745664i	$-0.732132\pi$
$229$		−	22.5679i		−	1.49133i	0.666322	−	0.745664i	$-0.267868\pi$
$230$	−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	0.0919037	−	0.995768i	$-0.470705\pi$
$233$	16.6026	−	16.6026i	1.08767	−	1.08767i	0.995768	−	0.0919037i	$-0.0292952\pi$
$234$	1.00709	+	4.07437i	0.0658358	+	0.266350i
$235$	5.32664	−	25.8826i	0.347472	−	1.68840i
$236$			7.12840i			0.464020i
$237$	1.44351	+	11.8557i	0.0937662	+	0.770109i
$238$	1.96777	+	1.96777i	0.127552	+	0.127552i
$239$	−0.481252			−0.0311296			−0.0155648	−	0.999879i	$-0.504955\pi$
$239$	−0.481252			−0.0311296			−0.0155648	+	0.999879i	$0.504955\pi$
$240$	2.50567	+	2.95324i	0.161740	+	0.190631i
$241$	−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
$243$	−12.8144	+	8.87642i	−0.822045	+	0.569422i
$244$			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	$-0.0271457\pi$
$252$	7.14738	+	4.31430i	0.450243	+	0.271775i
$253$	−6.42352	−	6.42352i	−0.403843	−	0.403843i
$254$	6.74834			0.423429
$255$	0.316477	−	3.86003i	0.0198186	−	0.241725i
$256$	1.00000			0.0625000
$257$	−21.9691	−	21.9691i	−1.37039	−	1.37039i	−0.859855	−	0.510538i	$-0.829446\pi$
$257$	−21.9691	−	21.9691i	−1.37039	−	1.37039i	−0.510538	−	0.859855i	$-0.670554\pi$
$258$	−0.0162744	−	0.133663i	−0.00101320	−	0.00832151i
$259$			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	$-0.963615\pi$
$263$	−14.2617	+	14.2617i	−0.879415	+	0.879415i	0.114059	+	0.993474i	$0.463615\pi$
$264$	3.44896	+	2.70025i	0.212269	+	0.166189i
$265$	22.3359	+	4.59672i	1.37208	+	0.282374i
$266$			3.36156i			0.206110i
$267$	14.0365	−	1.70905i	0.859022	−	0.104592i
$268$	9.61120	+	9.61120i	0.587097	+	0.587097i
$269$	22.6787			1.38275			0.691373	−	0.722498i	$-0.257006\pi$
$269$	22.6787			1.38275			0.691373	+	0.722498i	$0.257006\pi$
$270$	−1.85703	−	11.4696i	−0.113015	−	0.698017i
$271$	−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
$273$	−6.69378	+	0.815014i	−0.405126	+	0.0493269i
$274$			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	−0.973020	−	0.230719i	$-0.925892\pi$
$277$	−12.3544	+	12.3544i	−0.742301	+	0.742301i	0.230719	+	0.973020i	$0.425892\pi$
$278$	−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	$-0.260227\pi$
$282$	2.47395	+	20.3187i	0.147321	+	1.20996i
$283$	−0.00141764	−	0.00141764i	−8.42702e−5	−	8.42702e-5i	0.707065	−	0.707149i	$-0.250019\pi$
$283$	−0.00141764	−	0.00141764i	−8.42702e−5	−	8.42702e-5i	−0.707149	+	0.707065i	$0.750019\pi$
$284$	−6.19766			−0.367763
$285$	3.56738	−	3.02674i	0.211313	−	0.179288i
$286$	−3.53798			−0.209205
$287$	17.3683	+	17.3683i	1.02522	+	1.02522i
$288$	−2.56837	−	1.55032i	−0.151343	−	0.0913534i
$289$			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	$-0.621922\pi$
$293$	9.47960	−	9.47960i	0.553804	−	0.553804i	0.927537	+	0.373732i	$0.121922\pi$
$294$	−0.794666	+	1.01501i	−0.0463459	+	0.0591964i
$295$	8.76768	+	13.3116i	0.510474	+	0.775031i
$296$		−	1.34876i		−	0.0783953i
$297$	−4.67195	−	12.2822i	−0.271094	−	0.712687i
$298$	−5.99597	−	5.99597i	−0.347337	−	0.347337i
$299$	−5.02533			−0.290623
$300$	8.31147	+	2.43299i	0.479863	+	0.140469i
$301$	0.216340			0.0124696
$302$	3.75805	+	3.75805i	0.216251	+	0.216251i
$303$	−1.59604	−	13.1084i	−0.0916902	−	0.753059i
$304$		−	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	−0.997587	−	0.0694338i	$-0.977881\pi$
$307$	−16.2626	+	16.2626i	−0.928153	+	0.928153i	0.0694338	+	0.997587i	$0.477881\pi$
$308$	−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	$0.919251\pi$
$312$	2.40537	−	0.292870i	0.136177	−	0.0165805i
$313$	−15.4004	−	15.4004i	−0.870483	−	0.870483i	0.122042	−	0.992525i	$-0.461056\pi$
$313$	−15.4004	−	15.4004i	−0.870483	−	0.870483i	−0.992525	+	0.122042i	$0.961056\pi$
$314$	9.93980			0.560936
$315$	18.6535	−	0.734491i	1.05100	−	0.0413839i
$316$	6.89543			0.387898
$317$	−14.7669	−	14.7669i	−0.829389	−	0.829389i	0.158043	−	0.987432i	$-0.449482\pi$
$317$	−14.7669	−	14.7669i	−0.829389	−	0.829389i	−0.987432	+	0.158043i	$0.949482\pi$
$318$	−17.5344	+	2.13493i	−0.983280	+	0.119721i
$319$			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
$327$	2.30473	+	18.9289i	0.127452	+	1.04677i
$328$	−6.24118	−	6.24118i	−0.344612	−	0.344612i
$329$	−32.8867			−1.81311
$330$	9.76181	+	0.800355i	0.537370	+	0.0440581i
$331$	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
$333$	−2.09101	+	3.46412i	−0.114587	+	0.189833i
$334$			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	−0.0986568	−	0.995122i	$-0.531455\pi$
$337$	16.4569	−	16.4569i	0.896465	−	0.896465i	0.995122	+	0.0986568i	$0.0314546\pi$
$338$	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
$342$	−1.87271	+	3.10247i	−0.101265	+	0.167763i
$343$	12.3099	+	12.3099i	0.664671	+	0.664671i
$344$	−0.0777404			−0.00419148
$345$	13.8656	+	1.13682i	0.746500	+	0.0612043i
$346$	−20.3854			−1.09592
$347$	−8.31483	−	8.31483i	−0.446364	−	0.446364i	0.447780	−	0.894144i	$-0.352215\pi$
$347$	−8.31483	−	8.31483i	−0.446364	−	0.446364i	−0.894144	+	0.447780i	$0.852215\pi$
$348$	−0.938882	−	7.71112i	−0.0503294	−	0.413359i
$349$		−	28.6639i		−	1.53434i	−0.641442	−	0.767172i	$-0.721663\pi$
$349$		−	28.6639i		−	1.53434i	0.641442	−	0.767172i	$-0.278337\pi$
$350$	−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	$-0.903479\pi$
$353$	−12.3209	+	12.3209i	−0.655774	+	0.655774i	0.298603	+	0.954377i	$0.403479\pi$
$354$	−9.72168	−	7.61127i	−0.516701	−	0.404534i
$355$	−11.5735	+	7.62290i	−0.614258	+	0.404581i
$356$		−	8.16385i		−	0.432683i
$357$	−4.78470	+	0.582571i	−0.253233	+	0.0308329i
$358$	17.4921	+	17.4921i	0.924484	+	0.924484i
$359$	−2.97871			−0.157210			−0.0786052	−	0.996906i	$-0.525047\pi$
$359$	−2.97871			−0.157210			−0.0786052	+	0.996906i	$0.525047\pi$
$360$	−6.70301	+	0.263935i	−0.353280	+	0.0139106i
$361$	17.5408			0.923202
$362$	−11.5120	−	11.5120i	−0.605058	−	0.605058i
$363$	−7.91664	+	0.963906i	−0.415516	+	0.0505920i
$364$			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	−0.0440845	+	0.999028i	$0.514037\pi$
$367$	−19.9832	+	19.9832i	−1.04311	+	1.04311i	−0.999028	+	0.0440845i	$0.985963\pi$
$368$	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
$372$	0.559072	+	4.59171i	0.0289866	+	0.238069i
$373$	14.5108	+	14.5108i	0.751339	+	0.751339i	0.974729	−	0.223390i	$-0.0717123\pi$
$373$	14.5108	+	14.5108i	0.751339	+	0.751339i	−0.223390	+	0.974729i	$0.571712\pi$
$374$	−2.52895			−0.130769
$375$	18.5133	−	5.67944i	0.956025	−	0.293285i
$376$	11.8177			0.609449
$377$	4.43663	+	4.43663i	0.228498	+	0.228498i
$378$	−13.5154	+	5.14101i	−0.695155	+	0.264425i
$379$			18.5197i			0.951292i	0.879637	+	0.475646i	$0.157786\pi$
$379$			18.5197i			0.951292i	−0.879637	+	0.475646i	$0.842214\pi$
$380$	−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	−0.0773910	+	0.997001i	$0.524659\pi$
$383$	−21.0263	+	21.0263i	−1.07439	+	1.07439i	−0.997001	+	0.0773910i	$0.975341\pi$
$384$	−1.06774	+	1.36379i	−0.0544878	+	0.0695958i
$385$	−3.17213	+	15.4137i	−0.161667	+	0.785555i
$386$			20.7331i			1.05529i
$387$	0.199666	+	0.120522i	0.0101496	+	0.00612650i
$388$	12.1755	+	12.1755i	0.618115	+	0.618115i
$389$	2.56661			0.130132			0.0650660	−	0.997881i	$-0.479274\pi$
$389$	2.56661			0.130132			0.0650660	+	0.997881i	$0.479274\pi$
$390$	4.13157	−	3.50542i	0.209210	−	0.177504i
$391$	−3.59210			−0.181660
$392$	0.526266	+	0.526266i	0.0265804	+	0.0265804i
$393$	0.906123	+	7.44206i	0.0457079	+	0.375402i
$394$			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	−0.771297	−	0.636476i	$-0.780392\pi$
$397$	−2.68629	+	2.68629i	−0.134821	+	0.134821i	0.636476	+	0.771297i	$0.280392\pi$
$398$	−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	$-0.0879923\pi$
$402$	−23.3699	+	2.84545i	−1.16559	+	0.141918i
$403$	−2.64186	−	2.64186i	−0.131601	−	0.131601i
$404$	−7.62404			−0.379310
$405$	17.6250	+	9.71392i	0.875792	+	0.482688i
$406$	12.4808			0.619411
$407$	−2.41191	−	2.41191i	−0.119554	−	0.119554i
$408$	1.71935	−	0.209343i	0.0851207	−	0.0103640i
$409$			2.89808i			0.143301i	0.997430	+	0.0716503i	$0.0228266\pi$
$409$			2.89808i			0.143301i	−0.997430	+	0.0716503i	$0.977173\pi$
$410$	−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
$417$	−3.02644	−	24.8564i	−0.148205	−	1.21722i
$418$	−2.16011	−	2.16011i	−0.105654	−	0.105654i
$419$	5.18051			0.253085			0.126542	−	0.991961i	$-0.459612\pi$
$419$	5.18051			0.253085			0.126542	+	0.991961i	$0.459612\pi$
$420$	0.880709	−	10.7419i	0.0429742	−	0.524150i
$421$	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
$423$	−30.3521	−	18.3211i	−1.47577	−	0.890803i
$424$			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	$-0.253655\pi$
$432$	4.85666	−	1.84739i	0.233666	−	0.0888827i
$433$	10.6381	+	10.6381i	0.511234	+	0.511234i	0.914904	−	0.403670i	$-0.132266\pi$
$433$	10.6381	+	10.6381i	0.511234	+	0.511234i	−0.403670	+	0.914904i	$0.632266\pi$
$434$	−7.43188			−0.356742
$435$	−11.2377	−	13.2450i	−0.538805	−	0.635047i
$436$	11.0093			0.527251
$437$	−3.06820	−	3.06820i	−0.146772	−	0.146772i
$438$	1.47955	+	12.1517i	0.0706958	+	0.580630i
$439$		−	18.8619i		−	0.900227i	−0.892971	−	0.450113i	$-0.851384\pi$
$439$		−	18.8619i		−	0.900227i	0.892971	−	0.450113i	$-0.148616\pi$
$440$	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	$-0.932947\pi$
$443$	−16.1813	+	16.1813i	−0.768795	+	0.768795i	0.209099	+	0.977894i	$0.432947\pi$
$444$	1.83944	+	1.44013i	0.0872958	+	0.0683454i
$445$	−10.0412	−	15.2452i	−0.476001	−	0.722691i
$446$		−	1.31011i		−	0.0620357i
$447$	14.5794	−	1.77514i	0.689582	−	0.0839614i
$448$	−1.96777	−	1.96777i	−0.0929685	−	0.0929685i
$449$	9.61811			0.453907			0.226953	−	0.973906i	$-0.427123\pi$
$449$	9.61811			0.453907			0.226953	+	0.973906i	$0.427123\pi$
$450$	−12.1926	+	8.73734i	−0.574764	+	0.411882i
$451$	−22.3214			−1.05107
$452$	−11.0369	−	11.0369i	−0.519132	−	0.519132i
$453$	−9.13782	+	1.11259i	−0.429332	+	0.0522742i
$454$		−	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	−0.171785	−	0.985134i	$-0.554954\pi$
$457$	17.3874	−	17.3874i	0.813349	−	0.813349i	0.985134	+	0.171785i	$0.0549536\pi$
$458$	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	$0.937395\pi$
$462$	−1.47329	−	12.1003i	−0.0685437	−	0.562955i
$463$	5.66585	+	5.66585i	0.263314	+	0.263314i	0.826399	−	0.563085i	$-0.190386\pi$
$463$	5.66585	+	5.66585i	0.263314	+	0.263314i	−0.563085	+	0.826399i	$0.690386\pi$
$464$	−4.48489			−0.208206
$465$	6.69165	+	7.88692i	0.310318	+	0.365747i
$466$	23.4796			1.08767
$467$	−2.68728	−	2.68728i	−0.124353	−	0.124353i	0.642192	−	0.766544i	$-0.278025\pi$
$467$	−2.68728	−	2.68728i	−0.124353	−	0.124353i	−0.766544	+	0.642192i	$0.778025\pi$
$468$	−2.16889	+	3.59313i	−0.100257	+	0.166093i
$469$		−	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
$477$	15.8105	−	26.1929i	0.723914	−	1.19929i
$478$	−0.340297	−	0.340297i	−0.0155648	−	0.0155648i
$479$	−4.91424			−0.224537			−0.112269	−	0.993678i	$-0.535812\pi$
$479$	−4.91424			−0.224537			−0.112269	+	0.993678i	$0.535812\pi$
$480$	−0.316477	+	3.86003i	−0.0144452	+	0.176186i
$481$	−1.88691			−0.0860359
$482$	−11.0314	−	11.0314i	−0.502467	−	0.502467i
$483$	−2.09265	−	17.1871i	−0.0952190	−	0.782042i
$484$			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	0.272898	−	0.962043i	$-0.412018\pi$
$487$	27.2528	−	27.2528i	1.23494	−	1.23494i	0.962043	−	0.272898i	$-0.0879821\pi$
$488$	−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	$-0.000474771\pi$
$492$	15.1756	−	1.84774i	0.684171	−	0.0833025i
$493$	3.17130	+	3.17130i	0.142828	+	0.142828i
$494$	−1.68992			−0.0760333
$495$	−11.5146	+	12.4585i	−0.517542	+	0.559970i
$496$	2.67060			0.119914
$497$	12.1956	+	12.1956i	0.547046	+	0.547046i
$498$	−14.6316	+	1.78150i	−0.655656	+	0.0798307i
$499$			41.8265i			1.87241i	0.351454	+	0.936205i	$0.385687\pi$
$499$			41.8265i			1.87241i	−0.351454	+	0.936205i	$0.614313\pi$
$500$	−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	$-0.740204\pi$
$503$	0.975914	−	0.975914i	0.0435138	−	0.0435138i	0.728529	+	0.685015i	$0.240204\pi$
$504$	2.00329	+	8.10463i	0.0892336	+	0.361009i
$505$	−14.2371	+	9.37730i	−0.633545	+	0.417284i
$506$		−	9.08423i		−	0.403843i
$507$	2.31174	+	18.9865i	0.102668	+	0.843220i
$508$	4.77180	+	4.77180i	0.211714	+	0.211714i
$509$	−9.47611			−0.420021			−0.210011	−	0.977699i	$-0.567350\pi$
$509$	−9.47611			−0.420021			−0.210011	+	0.977699i	$0.567350\pi$
$510$	2.95324	−	2.50567i	0.130772	−	0.110953i
$511$	−19.6680			−0.870063
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	−2.23157	−	5.86663i	−0.0985260	−	0.259018i
$514$		−	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	$0.947376\pi$
$522$	11.5189	+	6.95301i	0.504167	+	0.304325i
$523$	14.7767	+	14.7767i	0.646140	+	0.646140i	0.952058	−	0.305918i	$-0.0989633\pi$
$523$	14.7767	+	14.7767i	0.646140	+	0.646140i	−0.305918	+	0.952058i	$0.598963\pi$
$524$	4.32841			0.189087
$525$	−11.5675	−	21.1427i	−0.504847	−	0.922741i
$526$	−20.1691			−0.879415
$527$	−1.88840	−	1.88840i	−0.0822600	−	0.0822600i
$528$	0.529418	+	4.34815i	0.0230400	+	0.189229i
$529$			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
$537$	−42.5325	+	5.17863i	−1.83541	+	0.223474i
$538$	16.0363	+	16.0363i	0.691373	+	0.691373i
$539$	1.88217			0.0810709
$540$	6.79711	−	9.42334i	0.292501	−	0.405516i
$541$	−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
$543$	27.9918	−	3.40820i	1.20124	−	0.146260i
$544$		−	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	−0.355927	−	0.934514i	$-0.615835\pi$
$547$	13.5320	−	13.5320i	0.578586	−	0.578586i	0.934514	+	0.355927i	$0.115835\pi$
$548$	−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
$552$	0.751982	+	6.17609i	0.0320065	+	0.262872i
$553$	−13.5686	−	13.5686i	−0.576997	−	0.576997i
$554$	−17.4717			−0.742301
$555$	5.20627	+	0.426853i	0.220994	+	0.0181189i
$556$	−14.4568			−0.613106
$557$	7.27672	+	7.27672i	0.308325	+	0.308325i	0.844259	−	0.535935i	$-0.180041\pi$
$557$	7.27672	+	7.27672i	0.308325	+	0.308325i	−0.535935	+	0.844259i	$0.680041\pi$
$558$	−6.85909	−	4.14028i	−0.290368	−	0.175272i
$559$			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	−0.175419	+	0.984494i	$0.556128\pi$
$563$	−27.5220	+	27.5220i	−1.15991	+	1.15991i	−0.984494	+	0.175419i	$0.943872\pi$
$564$	−12.6182	+	16.1168i	−0.531320	+	0.678642i
$565$	−34.1853	−	7.03532i	−1.43819	−	0.295978i
$566$		−	0.00200485i		−	8.42702e-5i
$567$	7.41958	−	23.9214i	0.311593	−	1.00461i
$568$	−4.38241	−	4.38241i	−0.183882	−	0.183882i
$569$	−6.26861			−0.262794			−0.131397	−	0.991330i	$-0.541946\pi$
$569$	−6.26861			−0.262794			−0.131397	+	0.991330i	$0.541946\pi$
$570$	4.66274	+	0.382291i	0.195301	+	0.0160124i
$571$	−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
$573$	3.95667	+	32.4964i	0.165292	+	1.35756i
$574$			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	−0.336774	+	0.941586i	$0.609336\pi$
$577$	−30.7072	+	30.7072i	−1.27836	+	1.27836i	−0.941586	+	0.336774i	$0.890664\pi$
$578$	−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
$582$	−29.6050	+	3.60462i	−1.22717	+	0.149416i
$583$	18.2369	+	18.2369i	0.755294	+	0.755294i
$584$	7.06759			0.292459
$585$	0.369244	+	9.37748i	0.0152663	+	0.387711i
$586$	13.4062			0.553804
$587$	21.1119	+	21.1119i	0.871383	+	0.871383i	0.992623	−	0.121240i	$-0.0386871\pi$
$587$	21.1119	+	21.1119i	0.871383	+	0.871383i	−0.121240	+	0.992623i	$0.538687\pi$
$588$	−1.27963	+	0.155804i	−0.0527711	+	0.00642525i
$589$		−	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	$-0.751746\pi$
$593$	−0.188868	+	0.188868i	−0.00775588	+	0.00775588i	0.703218	+	0.710974i	$0.251746\pi$
$594$	5.38128	−	11.9884i	0.220797	−	0.491891i
$595$	3.42281	+	5.19670i	0.140321	+	0.213044i
$596$		−	8.47958i		−	0.347337i
$597$	−0.706416	−	5.80185i	−0.0289117	−	0.237454i
$598$	−3.55345	−	3.55345i	−0.145311	−	0.145311i
$599$	−9.37844			−0.383193			−0.191596	−	0.981474i	$-0.561366\pi$
$599$	−9.37844			−0.383193			−0.191596	+	0.981474i	$0.561366\pi$
$600$	4.15671	+	7.59748i	0.169697	+	0.310166i
$601$	−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
$603$	21.0724	−	34.9100i	0.858133	−	1.42164i
$604$			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	0.0215072	−	0.999769i	$-0.493154\pi$
$607$	25.1616	−	25.1616i	1.02128	−	1.02128i	0.999769	−	0.0215072i	$-0.00684649\pi$
$608$	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
$612$	−1.55032	+	2.56837i	−0.0626679	+	0.103820i
$613$	−9.51982	−	9.51982i	−0.384502	−	0.384502i	0.488219	−	0.872721i	$-0.337647\pi$
$613$	−9.51982	−	9.51982i	−0.384502	−	0.384502i	−0.872721	+	0.488219i	$0.837647\pi$
$614$	−22.9987			−0.928153
$615$	26.0664	−	22.1160i	1.05110	−	0.891802i
$616$	−7.03768			−0.283556
$617$	−13.5000	−	13.5000i	−0.543488	−	0.543488i	0.381062	−	0.924550i	$-0.375559\pi$
$617$	−13.5000	−	13.5000i	−0.543488	−	0.543488i	−0.924550	+	0.381062i	$0.875559\pi$
$618$	2.65210	+	21.7819i	0.106683	+	0.876196i
$619$			2.80658i			0.112806i	0.998408	+	0.0564029i	$0.0179631\pi$
$619$			2.80658i			0.112806i	−0.998408	+	0.0564029i	$0.982037\pi$
$620$	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
$627$	5.25237	−	0.639513i	0.209760	−	0.0255397i
$628$	7.02850	+	7.02850i	0.280468	+	0.280468i
$629$	−1.34876			−0.0537787
$630$	13.7094	+	12.6706i	0.546194	+	0.504810i
$631$	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
$633$	27.9037	−	3.39747i	1.10907	−	0.135037i
$634$		−	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	$0.913929\pi$
$642$	3.02406	+	24.8369i	0.119350	+	0.980233i
$643$	23.9728	+	23.9728i	0.945395	+	0.945395i	0.998584	−	0.0531897i	$-0.0169388\pi$
$643$	23.9728	+	23.9728i	0.945395	+	0.945395i	−0.0531897	+	0.998584i	$0.516939\pi$
$644$	−9.99628			−0.393909
$645$	0.0246031	−	0.300080i	0.000968745	−	0.0118157i
$646$	−1.20796			−0.0475264
$647$	20.1028	+	20.1028i	0.790324	+	0.790324i	0.981547	−	0.191222i	$-0.0612452\pi$
$647$	20.1028	+	20.1028i	0.790324	+	0.790324i	−0.191222	+	0.981547i	$0.561245\pi$
$648$	−2.66618	+	8.59602i	−0.104737	+	0.337683i
$649$			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	$-0.570821\pi$
$653$	19.2853	−	19.2853i	0.754693	−	0.754693i	0.975351	+	0.220658i	$0.0708206\pi$
$654$	−11.7551	+	15.0145i	−0.459660	+	0.587112i
$655$	8.08287	−	5.32379i	0.315824	−	0.208018i
$656$		−	8.82636i		−	0.344612i
$657$	−18.1522	−	10.9570i	−0.708184	−	0.427474i
$658$	−23.2544	−	23.2544i	−0.906553	−	0.906553i
$659$	−44.4380			−1.73106			−0.865529	−	0.500859i	$-0.833018\pi$
$659$	−44.4380			−1.73106			−0.865529	+	0.500859i	$0.833018\pi$
$660$	6.33671	+	7.46858i	0.246656	+	0.290714i
$661$	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
$663$	−0.292870	−	2.40537i	−0.0113741	−	0.0934167i
$664$			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
$672$	4.78470	−	0.582571i	0.184574	−	0.0224732i
$673$	25.9201	+	25.9201i	0.999147	+	0.999147i	1.00000		0.000852425i	$-0.000271335\pi$
$673$	25.9201	+	25.9201i	0.999147	+	0.999147i	−0.000852425		1.00000i	$0.500271\pi$
$674$	23.2736			0.896465
$675$	1.10255	−	25.9574i	0.0424373	−	0.999099i
$676$	11.0428			0.424724
$677$	31.4702	+	31.4702i	1.20950	+	1.20950i	0.971190	+	0.238308i	$0.0765927\pi$
$677$	31.4702	+	31.4702i	1.20950	+	1.20950i	0.238308	+	0.971190i	$0.423407\pi$
$678$	26.8366	−	3.26754i	1.03065	−	0.125489i
$679$		−	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	$-0.778344\pi$
$683$	−3.28670	+	3.28670i	−0.125762	+	0.125762i	0.641424	+	0.767186i	$0.278344\pi$
$684$	−3.51799	+	0.869570i	−0.134514	+	0.0332489i
$685$	−0.452761	+	2.20001i	−0.0172991	+	0.0840581i
$686$			17.4088i			0.664671i
$687$	4.72443	+	38.8022i	0.180248	+	1.48040i
$688$	−0.0549708	−	0.0549708i	−0.00209574	−	0.00209574i
$689$	14.2673			0.543541
$690$	9.00062	+	10.6083i	0.342648	+	0.403852i
$691$	−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
$693$	18.0753	+	10.9106i	0.686626	+	0.414461i
$694$		−	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	$-0.100077\pi$
$702$	−2.58449	−	6.79444i	−0.0975454	−	0.256440i
$703$	−1.15205	−	1.15205i	−0.0434504	−	0.0434504i
$704$	2.52895			0.0953133
$705$	−3.74002	+	45.6165i	−0.140857	+	1.71802i
$706$	−17.4243			−0.655774
$707$	15.0024	+	15.0024i	0.564223	+	0.564223i
$708$	−1.49228	−	12.2562i	−0.0560834	−	0.460618i
$709$			10.6366i			0.399466i	0.979850	+	0.199733i	$0.0640075\pi$
$709$			10.6366i			0.399466i	−0.979850	+	0.199733i	$0.935992\pi$
$710$	−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
$717$	0.827442	−	0.100747i	0.0309014	−	0.00376246i
$718$	−2.10627	−	2.10627i	−0.0786052	−	0.0786052i
$719$	31.8489			1.18776			0.593882	−	0.804552i	$-0.297594\pi$
$719$	31.8489			1.18776			0.593882	+	0.804552i	$0.297594\pi$
$720$	−4.92637	−	4.55311i	−0.183595	−	0.169685i
$721$	−35.2549			−1.31296
$722$	12.4033	+	12.4033i	0.461601	+	0.461601i
$723$	26.8232	−	3.26591i	0.997566	−	0.121461i
$724$		−	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	−0.508351	+	0.861150i	$0.669745\pi$
$727$	−36.9258	+	36.9258i	−1.36950	+	1.36950i	−0.861150	+	0.508351i	$0.830255\pi$
$728$	−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
$732$	−1.59820	−	13.1262i	−0.0590713	−	0.485158i
$733$	−11.2787	−	11.2787i	−0.416588	−	0.416588i	0.467438	−	0.884026i	$-0.345177\pi$
$733$	−11.2787	−	11.2787i	−0.416588	−	0.416588i	−0.884026	+	0.467438i	$0.845177\pi$
$734$	−28.2605			−1.04311
$735$	−2.19795	+	1.86485i	−0.0810727	+	0.0687860i
$736$	3.59210			0.132407
$737$	24.3062	+	24.3062i	0.895331	+	0.895331i
$738$	−13.6837	+	22.6693i	−0.503703	+	0.834470i
$739$			44.3775i			1.63245i	0.577733	+	0.816226i	$0.303938\pi$
$739$			44.3775i			1.63245i	−0.577733	+	0.816226i	$0.696062\pi$
$740$	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	$-0.759370\pi$
$743$	−1.13462	+	1.13462i	−0.0416250	+	0.0416250i	0.685988	+	0.727613i	$0.259370\pi$
$744$	−2.85150	+	3.64215i	−0.104541	+	0.133528i
$745$	−10.4296	−	15.8348i	−0.382110	−	0.580141i
$746$			20.5213i			0.751339i
$747$	13.1931	−	21.8566i	0.482710	−	0.799692i
$748$	−1.78824	−	1.78824i	−0.0653844	−	0.0653844i
$749$	−40.1996			−1.46886
$750$	17.1069	+	9.07494i	0.624655	+	0.331370i
$751$	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
$753$	0.565001	+	4.64040i	0.0205898	+	0.169106i
$754$			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	−0.818996	−	0.573800i	$-0.805469\pi$
$757$	−6.74622	+	6.74622i	−0.245196	+	0.245196i	0.573800	+	0.818996i	$0.305469\pi$
$758$	−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	$0.835860\pi$
$762$	−11.6028	+	1.41272i	−0.420325	+	0.0511774i
$763$	−21.6638	−	21.6638i	−0.784284	−	0.784284i
$764$	18.9004			0.683792
$765$	0.263935	+	6.70301i	0.00954258	+	0.242348i
$766$	−29.7356			−1.07439
$767$	7.05170	+	7.05170i	0.254622	+	0.254622i
$768$	−1.71935	+	0.209343i	−0.0620418	+	0.00755402i
$769$			41.2250i			1.48661i	0.668952	+	0.743306i	$0.266743\pi$
$769$			41.2250i			1.48661i	−0.668952	+	0.743306i	$0.733257\pi$
$770$	−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	$-0.668212\pi$
$773$	9.99203	−	9.99203i	0.359388	−	0.359388i	0.863587	+	0.504199i	$0.168212\pi$
$774$	0.0559630	+	0.226407i	0.00201155	+	0.00813804i
$775$	5.27277	−	12.2679i	0.189404	−	0.440675i
$776$			17.2187i			0.618115i
$777$	−0.785750	−	6.45343i	−0.0281886	−	0.231516i
$778$	1.81486	+	1.81486i	0.0650660	+	0.0650660i
$779$	−10.6619			−0.382000
$780$	5.40017	+	0.442751i	0.193357	+	0.0158530i
$781$	−15.6735			−0.560844
$782$	−2.54000	−	2.54000i	−0.0908302	−	0.0908302i
$783$	−21.7816	+	8.28535i	−0.778411	+	0.296094i
$784$			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	−0.812937	−	0.582352i	$-0.802133\pi$
$787$	−6.46873	+	6.46873i	−0.230585	+	0.230585i	0.582352	+	0.812937i	$0.302133\pi$
$788$	−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
$792$	−6.49526	−	3.92067i	−0.230799	−	0.139315i
$793$	7.55222	+	7.55222i	0.268187	+	0.268187i
$794$	−3.79899			−0.134821
$795$	−39.3656	−	3.22752i	−1.39615	−	0.114468i
$796$	−3.37444			−0.119604
$797$	15.6462	+	15.6462i	0.554218	+	0.554218i	0.927655	−	0.373437i	$-0.121821\pi$
$797$	15.6462	+	15.6462i	0.554218	+	0.554218i	−0.373437	+	0.927655i	$0.621821\pi$
$798$	−0.703719	−	5.77970i	−0.0249114	−	0.204599i
$799$		−	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
$807$	−38.9927	+	4.74764i	−1.37261	+	0.167125i
$808$	−5.39101	−	5.39101i	−0.189655	−	0.189655i
$809$	−43.2206			−1.51956			−0.759778	−	0.650183i	$-0.774692\pi$
$809$	−43.2206			−1.51956			−0.759778	+	0.650183i	$0.774692\pi$
$810$	5.59397	+	19.3315i	0.196552	+	0.679240i
$811$	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
$813$	5.26032	−	0.640480i	0.184487	−	0.0224626i
$814$		−	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	$-0.00964431\pi$
$822$	−0.210284	−	1.72708i	−0.00733449	−	0.0602388i
$823$	−2.91686	−	2.91686i	−0.101675	−	0.101675i	0.654439	−	0.756115i	$-0.272905\pi$
$823$	−2.91686	−	2.91686i	−0.101675	−	0.101675i	−0.756115	+	0.654439i	$0.772905\pi$
$824$	12.6686			0.441333
$825$	21.0193	+	6.15291i	0.731797	+	0.214217i
$826$	19.8373			0.690227
$827$	9.68706	+	9.68706i	0.336852	+	0.336852i	0.855181	−	0.518329i	$-0.173446\pi$
$827$	9.68706	+	9.68706i	0.336852	+	0.336852i	−0.518329	+	0.855181i	$0.673446\pi$
$828$	−9.22584	−	5.56890i	−0.320620	−	0.193533i
$829$		−	13.7128i		−	0.476264i	−0.971233	−	0.238132i	$-0.923465\pi$
$829$		−	13.7128i		−	0.476264i	0.971233	−	0.238132i	$-0.0765351\pi$
$830$	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
$837$	12.9702	−	4.93365i	0.448316	−	0.170532i
$838$	3.66318	+	3.66318i	0.126542	+	0.126542i
$839$	5.68715			0.196342			0.0981711	−	0.995170i	$-0.468701\pi$
$839$	5.68715			0.196342			0.0981711	+	0.995170i	$0.468701\pi$
$840$	8.21842	−	6.97291i	0.283562	−	0.240588i
$841$	−8.88573			−0.306404
$842$	3.37351	+	3.37351i	0.116259	+	0.116259i
$843$	5.11966	+	42.0482i	0.176331	+	1.44822i
$844$		−	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
$852$	10.6560	−	1.29744i	0.365067	−	0.0444495i
$853$	−12.7324	−	12.7324i	−0.435948	−	0.435948i	0.454698	−	0.890646i	$-0.349747\pi$
$853$	−12.7324	−	12.7324i	−0.435948	−	0.435948i	−0.890646	+	0.454698i	$0.849747\pi$
$854$	21.2453			0.726999
$855$	−5.49996	+	5.95084i	−0.188095	+	0.203514i
$856$	14.4455			0.493736
$857$	−18.0972	−	18.0972i	−0.618189	−	0.618189i	0.326878	−	0.945067i	$-0.394003\pi$
$857$	−18.0972	−	18.0972i	−0.618189	−	0.618189i	−0.945067	+	0.326878i	$0.894003\pi$
$858$	6.08305	−	0.740653i	0.207672	−	0.0252855i
$859$			40.4694i			1.38080i	0.723429	+	0.690399i	$0.242565\pi$
$859$			40.4694i			1.38080i	−0.723429	+	0.690399i	$0.757435\pi$
$860$	−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	0.153242	−	0.988189i	$-0.451029\pi$
$863$	33.5317	−	33.5317i	1.14143	−	1.14143i	0.988189	−	0.153242i	$-0.0489714\pi$
$864$	4.74048	+	2.12787i	0.161274	+	0.0723917i
$865$	−44.6474	−	9.18843i	−1.51806	−	0.312416i
$866$			15.0445i			0.511234i
$867$	−0.209343	−	1.71935i	−0.00710967	−	0.0583923i
$868$	−5.25514	−	5.25514i	−0.178371	−	0.178371i
$869$	17.4382			0.591550
$870$	1.41937	−	17.3118i	0.0481211	−	0.586926i
$871$	19.0155			0.644317
$872$	7.78477	+	7.78477i	0.263626	+	0.263626i
$873$	26.6944	−	44.2239i	0.903470	−	1.49675i
$874$		−	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	−0.384023	−	0.923324i	$-0.625462\pi$
$877$	15.9710	−	15.9710i	0.539301	−	0.539301i	0.923324	+	0.384023i	$0.125462\pi$
$878$	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	$-0.158513\pi$
$882$	1.15383	−	1.91151i	0.0388514	−	0.0643640i
$883$	−22.6946	−	22.6946i	−0.763735	−	0.763735i	0.213260	−	0.976995i	$-0.431592\pi$
$883$	−22.6946	−	22.6946i	−0.763735	−	0.763735i	−0.976995	+	0.213260i	$0.931592\pi$
$884$	−1.39900			−0.0470533
$885$	−17.8614	−	21.0519i	−0.600406	−	0.707651i
$886$	−22.8838			−0.768795
$887$	−29.9212	−	29.9212i	−1.00466	−	1.00466i	−0.999989	−	0.00466796i	$-0.998514\pi$
$887$	−29.9212	−	29.9212i	−1.00466	−	1.00466i	−0.00466796	−	0.999989i	$-0.501486\pi$
$888$	0.282355	+	2.31900i	0.00947520	+	0.0778206i
$889$		−	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
$897$	8.64032	−	1.05202i	0.288492	−	0.0351259i
$898$	6.80103	+	6.80103i	0.226953	+	0.226953i
$899$	−11.9774			−0.399468
$900$	−14.7997	−	2.44323i	−0.493323	−	0.0814409i
$901$	10.1982			0.339753
$902$	−15.7836	−	15.7836i	−0.525537	−	0.525537i
$903$	−0.371965	+	0.0452893i	−0.0123782	+	0.00150713i
$904$		−	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	−0.990384	−	0.138347i	$-0.955821\pi$
$907$	−25.6603	+	25.6603i	−0.852036	+	0.852036i	0.138347	+	0.990384i	$0.455821\pi$
$908$	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	$-0.245930\pi$
$912$	0.252877	+	2.07690i	0.00837360	+	0.0687731i
$913$	15.2177	+	15.2177i	0.503634	+	0.503634i
$914$	24.5895			0.813349
$915$	−19.1292	−	22.5461i	−0.632393	−	0.745352i
$916$	22.5679			0.745664
$917$	−8.51732	−	8.51732i	−0.281267	−	0.281267i
$918$	−1.84739	−	4.85666i	−0.0609730	−	0.160294i
$919$			22.8415i			0.753471i	0.926321	+	0.376735i	$0.122953\pi$
$919$			22.8415i			0.753471i	−0.926321	+	0.376735i	$0.877047\pi$
$920$	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
$927$	−32.5377	−	19.6404i	−1.06868	−	0.645077i
$928$	−3.17130	−	3.17130i	−0.104103	−	0.104103i
$929$	−59.4712			−1.95119			−0.975594	−	0.219584i	$-0.929530\pi$
$929$	−59.4712			−1.95119			−0.975594	+	0.219584i	$0.929530\pi$
$930$	−0.845185	+	10.3086i	−0.0277147	+	0.338033i
$931$	0.899023			0.0294643
$932$	16.6026	+	16.6026i	0.543836	+	0.543836i
$933$	−1.85305	−	15.2193i	−0.0606662	−	0.498257i
$934$		−	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	−0.857140	−	0.515083i	$-0.827761\pi$
$937$	−10.4705	+	10.4705i	−0.342058	+	0.342058i	0.515083	+	0.857140i	$0.327761\pi$
$938$	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	$-0.101212\pi$
$942$	−17.0900	+	2.08083i	−0.556823	+	0.0677971i
$943$	−22.4190	−	22.4190i	−0.730062	−	0.730062i
$944$	−7.12840			−0.232010
$945$	−31.9181	+	5.16783i	−1.03830	+	0.168109i
$946$	−0.196601			−0.00639206
$947$	−13.2375	−	13.2375i	−0.430161	−	0.430161i	0.458522	−	0.888683i	$-0.348379\pi$
$947$	−13.2375	−	13.2375i	−0.430161	−	0.430161i	−0.888683	+	0.458522i	$0.848379\pi$
$948$	−11.8557	+	1.44351i	−0.385055	+	0.0468831i
$949$		−	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	$-0.846454\pi$
$953$	−13.0276	+	13.0276i	−0.422007	+	0.422007i	0.463887	+	0.885894i	$0.346454\pi$
$954$	29.7009	−	7.34141i	0.961601	−	0.237687i
$955$	35.2946	−	23.2468i	1.14211	−	0.752249i
$956$		−	0.481252i		−	0.0155648i
$957$	−2.37438	−	19.5010i	−0.0767529	−	0.630378i
$958$	−3.47489	−	3.47489i	−0.112269	−	0.112269i
$959$	2.79535			0.0902667
$960$	−2.95324	+	2.50567i	−0.0953153	+	0.0808702i
$961$	−23.8679			−0.769932
$962$	−1.33425	−	1.33425i	−0.0430179	−	0.0430179i
$963$	−37.1013	−	22.3951i	−1.19557	−	0.721671i
$964$		−	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	−0.449208	+	0.893427i	$0.648294\pi$
$967$	−41.7514	+	41.7514i	−1.34264	+	1.34264i	−0.893427	+	0.449208i	$0.851706\pi$
$968$	−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	$0.957715\pi$
$972$	−8.87642	−	12.8144i	−0.284711	−	0.411023i
$973$	28.4477	+	28.4477i	0.911992	+	0.911992i
$974$	38.5412			1.23494
$975$	10.6288	−	5.81522i	0.340395	−	0.186236i
$976$	−7.63437			−0.244370
$977$	12.2913	+	12.2913i	0.393233	+	0.393233i	0.875838	−	0.482605i	$-0.160309\pi$
$977$	12.2913	+	12.2913i	0.393233	+	0.393233i	−0.482605	+	0.875838i	$0.660309\pi$
$978$	−2.76048	−	22.6721i	−0.0882704	−	0.724972i
$979$		−	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	−0.337215	+	0.941427i	$0.609485\pi$
$983$	−40.0891	+	40.0891i	−1.27864	+	1.27864i	−0.941427	+	0.337215i	$0.890515\pi$
$984$	12.0373	+	9.42425i	0.383737	+	0.300434i
$985$	−9.09254	+	44.1815i	−0.289712	+	1.40774i
$986$			4.48489i			0.142828i
$987$	56.5439	−	6.88462i	1.79981	−	0.219140i
$988$	−1.19496	−	1.19496i	−0.0380166	−	0.0380166i
$989$	−0.279251			−0.00887968
$990$	−16.9516	+	0.667477i	−0.538756	+	0.0212138i
$991$	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
$993$	−30.7851	+	3.74830i	−0.976935	+	0.118949i
$994$			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	−0.215429	−	0.976519i	$-0.569115\pi$
$997$	24.0317	−	24.0317i	0.761090	−	0.761090i	0.976519	+	0.215429i	$0.0691150\pi$
$998$	−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.443.8	yes	28
3.2	odd	2	inner	510.2.l.g.443.4	yes	28
5.2	odd	4	inner	510.2.l.g.137.4	✓	28
15.2	even	4	inner	510.2.l.g.137.8	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
510.2.l.g.137.4	✓	28	5.2	odd	4	inner
510.2.l.g.137.8	yes	28	15.2	even	4	inner
510.2.l.g.443.4	yes	28	3.2	odd	2	inner
510.2.l.g.443.8	yes	28	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +(-1.71935 + 0.209343i) q^{3} +1.00000i q^{4} +(1.22996 + 1.86740i) q^{5} +(-1.36379 - 1.06774i) q^{6} +(1.96777 - 1.96777i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.91235 - 0.719870i) q^{9} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{2} +(-1.71935 + 0.209343i) 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} +(-0.209343 - 1.71935i) q^{12} +(0.989239 + 0.989239i) q^{13} +2.78285 q^{14} +(-2.50567 - 2.95324i) q^{15} -1.00000 q^{16} +(0.707107 + 0.707107i) q^{17} +(2.56837 + 1.55032i) 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} +(-4.85666 + 1.84739i) q^{27} +(1.96777 + 1.96777i) q^{28} +4.48489 q^{29} +(0.316477 - 3.86003i) q^{30} -2.67060 q^{31} +(-0.707107 - 0.707107i) q^{32} +(-0.529418 - 4.34815i) 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} +(-4.78470 + 0.582571i) q^{42} +(0.0549708 + 0.0549708i) q^{43} -2.52895 q^{44} +(4.92637 + 4.55311i) q^{45} -3.59210 q^{46} +(-8.35634 - 8.35634i) q^{47} +(1.71935 - 0.209343i) 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} +(-0.252877 - 2.07690i) q^{57} +(3.17130 + 3.17130i) q^{58} +7.12840 q^{59} +(2.95324 - 2.50567i) q^{60} +7.63437 q^{61} +(-1.88840 - 1.88840i) q^{62} +(4.31430 - 7.14738i) 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} +(-1.55032 + 2.56837i) q^{72} +(-4.99754 - 4.99754i) q^{73} -1.34876 q^{74} +(2.43299 - 8.31147i) q^{75} -1.20796 q^{76} +(4.97639 + 4.97639i) q^{77} +(-0.292870 - 2.40537i) 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} +(-7.71112 + 0.938882i) q^{87} +(-1.78824 - 1.78824i) q^{88} -8.16385 q^{89} +(0.263935 + 6.70301i) q^{90} +3.89319 q^{91} +(-2.54000 - 2.54000i) q^{92} +(4.59171 - 0.559072i) 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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