LMFDB - Embedded newform 190.2.i.a.49.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [190,2,Mod(49,190)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(190, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 4]))

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

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

chi := DirichletCharacter("190.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 190 = 2 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	190.i (of order $6$, 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:	$1.51715763840$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 20 x^{18} + 270 x^{16} - 1928 x^{14} + 9835 x^{12} - 29980 x^{10} + 66046 x^{8} - 89920 x^{6} + \cdots + 10000 $ x^20 - 20x^18 + 270x^16 - 1928x^14 + 9835x^12 - 29980x^10 + 66046x^8 - 89920x^6 + 85425x^4 - 34500*x^2 + 10000
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			49.9
Root			$-1.28416 - 0.741409i$ of defining polynomial
Character	$\chi$	$=$	190.49
Dual form			190.2.i.a.159.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(1.28416 + 0.741409i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.25308 - 1.85197i) q^{5} +(0.741409 + 1.28416i) q^{6} -0.482818i q^{7} +1.00000i q^{8} +(-0.400626 - 0.693904i) q^{9} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(1.28416 + 0.741409i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.25308 - 1.85197i) q^{5} +(0.741409 + 1.28416i) q^{6} -0.482818i q^{7} +1.00000i q^{8} +(-0.400626 - 0.693904i) q^{9} +(2.01118 - 0.977310i) q^{10} -4.43782 q^{11} +1.48282i q^{12} +(-3.58738 + 2.07118i) q^{13} +(0.241409 - 0.418132i) q^{14} +(2.98222 - 1.44917i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(6.84039 + 3.94930i) q^{17} -0.801252i q^{18} +(-4.31875 - 0.590253i) q^{19} +(2.23039 + 0.159217i) q^{20} +(0.357965 - 0.620014i) q^{21} +(-3.84326 - 2.21891i) q^{22} +(-4.90130 + 2.82977i) q^{23} +(-0.741409 + 1.28416i) q^{24} +(-1.85957 - 4.64134i) q^{25} -4.14235 q^{26} -5.63656i q^{27} +(0.418132 - 0.241409i) q^{28} +(1.91196 + 3.31161i) q^{29} +(3.30727 + 0.236090i) q^{30} +7.58017 q^{31} +(-0.866025 + 0.500000i) q^{32} +(-5.69885 - 3.29024i) q^{33} +(3.94930 + 6.84039i) q^{34} +(-0.894163 - 0.605010i) q^{35} +(0.400626 - 0.693904i) q^{36} -3.50579i q^{37} +(-3.44502 - 2.67055i) q^{38} -6.14235 q^{39} +(1.85197 + 1.25308i) q^{40} +(4.44930 - 7.70641i) q^{41} +(0.620014 - 0.357965i) q^{42} +(-0.551544 - 0.318434i) q^{43} +(-2.21891 - 3.84326i) q^{44} +(-1.78711 - 0.127573i) q^{45} -5.65953 q^{46} +(-3.69022 + 2.13055i) q^{47} +(-1.28416 + 0.741409i) q^{48} +6.76689 q^{49} +(0.710233 - 4.94930i) q^{50} +(5.85609 + 10.1430i) q^{51} +(-3.58738 - 2.07118i) q^{52} +(-2.76033 + 1.59368i) q^{53} +(2.81828 - 4.88141i) q^{54} +(-5.56095 + 8.21869i) q^{55} +0.482818 q^{56} +(-5.10834 - 3.95994i) q^{57} +3.82392i q^{58} +(0.812584 - 1.40744i) q^{59} +(2.74613 + 1.85809i) q^{60} +(-0.735243 - 1.27348i) q^{61} +(6.56462 + 3.79008i) q^{62} +(-0.335029 + 0.193429i) q^{63} -1.00000 q^{64} +(-0.659533 + 9.23907i) q^{65} +(-3.29024 - 5.69885i) q^{66} +(11.4272 - 6.59750i) q^{67} +7.89860i q^{68} -8.39206 q^{69} +(-0.471863 - 0.971036i) q^{70} +(-1.41164 + 2.44504i) q^{71} +(0.693904 - 0.400626i) q^{72} +(-5.95528 - 3.43828i) q^{73} +(1.75289 - 3.03610i) q^{74} +(1.05315 - 7.33891i) q^{75} +(-1.64820 - 4.03527i) q^{76} +2.14266i q^{77} +(-5.31943 - 3.07118i) q^{78} +(-0.576026 + 0.997706i) q^{79} +(0.977310 + 2.01118i) q^{80} +(2.97712 - 5.15652i) q^{81} +(7.70641 - 4.44930i) q^{82} +12.4044i q^{83} +0.715931 q^{84} +(15.8855 - 7.71938i) q^{85} +(-0.318434 - 0.551544i) q^{86} +5.67017i q^{87} -4.43782i q^{88} +(4.37859 + 7.58395i) q^{89} +(-1.48389 - 1.00403i) q^{90} +(1.00000 + 1.73205i) q^{91} +(-4.90130 - 2.82977i) q^{92} +(9.73413 + 5.62000i) q^{93} -4.26110 q^{94} +(-6.50488 + 7.25855i) q^{95} -1.48282 q^{96} +(0.825585 + 0.476652i) q^{97} +(5.86030 + 3.38344i) q^{98} +(1.77790 + 3.07942i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 10 q^{4} - 2 q^{5} + 10 q^{9}+O(q^{10}) $ 20 * q + 10 * q^4 - 2 * q^5 + 10 * q^9	$ 20 q + 10 q^{4} - 2 q^{5} + 10 q^{9} - 12 q^{11} - 10 q^{14} - 2 q^{15} - 10 q^{16} - 22 q^{19} - 4 q^{20} + 40 q^{21} - 6 q^{25} + 8 q^{26} - 4 q^{29} + 12 q^{30} - 16 q^{31} - 8 q^{34} - 2 q^{35} - 10 q^{36} - 32 q^{39} + 2 q^{41} - 6 q^{44} - 56 q^{45} - 52 q^{46} + 40 q^{49} + 40 q^{50} + 8 q^{51} + 36 q^{54} + 18 q^{55} - 20 q^{56} - 44 q^{59} + 2 q^{60} - 4 q^{61} - 20 q^{64} + 48 q^{65} + 4 q^{66} + 48 q^{69} - 8 q^{70} - 44 q^{71} + 10 q^{74} - 56 q^{75} + 4 q^{76} - 4 q^{79} - 2 q^{80} - 10 q^{81} + 80 q^{84} + 12 q^{85} + 2 q^{89} + 42 q^{90} + 20 q^{91} - 40 q^{94} - 4 q^{95} - 26 q^{99}+O(q^{100}) $ 20 * q + 10 * q^4 - 2 * q^5 + 10 * q^9 - 12 * q^11 - 10 * q^14 - 2 * q^15 - 10 * q^16 - 22 * q^19 - 4 * q^20 + 40 * q^21 - 6 * q^25 + 8 * q^26 - 4 * q^29 + 12 * q^30 - 16 * q^31 - 8 * q^34 - 2 * q^35 - 10 * q^36 - 32 * q^39 + 2 * q^41 - 6 * q^44 - 56 * q^45 - 52 * q^46 + 40 * q^49 + 40 * q^50 + 8 * q^51 + 36 * q^54 + 18 * q^55 - 20 * q^56 - 44 * q^59 + 2 * q^60 - 4 * q^61 - 20 * q^64 + 48 * q^65 + 4 * q^66 + 48 * q^69 - 8 * q^70 - 44 * q^71 + 10 * q^74 - 56 * q^75 + 4 * q^76 - 4 * q^79 - 2 * q^80 - 10 * q^81 + 80 * q^84 + 12 * q^85 + 2 * q^89 + 42 * q^90 + 20 * q^91 - 40 * q^94 - 4 * q^95 - 26 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/190\mathbb{Z}\right)^\times$.

$n$	$21$	$77$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$

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 $

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$	1.28416	+	0.741409i	0.741409	+	0.428053i	0.822581	−	0.568647i	$-0.192533\pi$
$3$	1.28416	+	0.741409i	0.741409	+	0.428053i	−0.0811725	+	0.996700i	$0.525866\pi$
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	1.25308	−	1.85197i	0.560395	−	0.828225i
$5$	1.25308	−	1.85197i	0.560395	−	0.828225i
$6$	0.741409	+	1.28416i	0.302679	+	0.524255i
$7$		−	0.482818i		−	0.182488i	−0.995829	−	0.0912440i	$-0.970916\pi$
$7$		−	0.482818i		−	0.182488i	0.995829	−	0.0912440i	$-0.0290843\pi$
$8$			1.00000i			0.353553i
$9$	−0.400626	−	0.693904i	−0.133542	−	0.231301i
$10$	2.01118	−	0.977310i	0.635993	−	0.309053i
$11$	−4.43782			−1.33805			−0.669026	−	0.743239i	$-0.733288\pi$
$11$	−4.43782			−1.33805			−0.669026	+	0.743239i	$0.733288\pi$
$12$			1.48282i			0.428053i
$13$	−3.58738	+	2.07118i	−0.994960	+	0.574441i	−0.906753	−	0.421661i	$-0.861447\pi$
$13$	−3.58738	+	2.07118i	−0.994960	+	0.574441i	−0.0882071	+	0.996102i	$0.528114\pi$
$14$	0.241409	−	0.418132i	0.0645192	−	0.111751i
$15$	2.98222	−	1.44917i	0.770006	−	0.374175i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	6.84039	+	3.94930i	1.65904	+	0.957846i	0.973160	+	0.230129i	$0.0739148\pi$
$17$	6.84039	+	3.94930i	1.65904	+	0.957846i	0.685878	+	0.727717i	$0.259419\pi$
$18$		−	0.801252i		−	0.188857i
$19$	−4.31875	−	0.590253i	−0.990789	−	0.135413i
$19$	−4.31875	−	0.590253i	−0.990789	−	0.135413i
$20$	2.23039	+	0.159217i	0.498731	+	0.0356020i
$21$	0.357965	−	0.620014i	0.0781144	−	0.135298i
$22$	−3.84326	−	2.21891i	−0.819386	−	0.473073i
$23$	−4.90130	+	2.82977i	−1.02199	+	0.590047i	−0.914680	−	0.404178i	$-0.867557\pi$
$23$	−4.90130	+	2.82977i	−1.02199	+	0.590047i	−0.107311	+	0.994225i	$0.534224\pi$
$24$	−0.741409	+	1.28416i	−0.151339	+	0.262128i
$25$	−1.85957	−	4.64134i	−0.371914	−	0.928267i
$26$	−4.14235			−0.812382
$27$		−	5.63656i		−	1.08476i
$28$	0.418132	−	0.241409i	0.0790196	−	0.0456220i
$29$	1.91196	+	3.31161i	0.355042	+	0.614950i	0.987125	−	0.159950i	$-0.0511333\pi$
$29$	1.91196	+	3.31161i	0.355042	+	0.614950i	−0.632083	+	0.774900i	$0.717800\pi$
$30$	3.30727	+	0.236090i	0.603821	+	0.0431039i
$31$	7.58017			1.36144			0.680719	−	0.732545i	$-0.261667\pi$
$31$	7.58017			1.36144			0.680719	+	0.732545i	$0.261667\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$	−5.69885	−	3.29024i	−0.992043	−	0.572756i
$34$	3.94930	+	6.84039i	0.677299	+	1.17312i
$35$	−0.894163	−	0.605010i	−0.151141	−	0.102265i
$36$	0.400626	−	0.693904i	0.0667710	−	0.115651i
$37$		−	3.50579i		−	0.576348i	−0.957578	−	0.288174i	$-0.906952\pi$
$37$		−	3.50579i		−	0.576348i	0.957578	−	0.288174i	$-0.0930481\pi$
$38$	−3.44502	−	2.67055i	−0.558856	−	0.433220i
$39$	−6.14235			−0.983563
$40$	1.85197	+	1.25308i	0.292822	+	0.198130i
$41$	4.44930	−	7.70641i	0.694864	−	1.20354i	−0.275363	−	0.961340i	$-0.588798\pi$
$41$	4.44930	−	7.70641i	0.694864	−	1.20354i	0.970227	−	0.242199i	$-0.0778687\pi$
$42$	0.620014	−	0.357965i	0.0956702	−	0.0552352i
$43$	−0.551544	−	0.318434i	−0.0841097	−	0.0485607i	0.457355	−	0.889284i	$-0.348797\pi$
$43$	−0.551544	−	0.318434i	−0.0841097	−	0.0485607i	−0.541465	+	0.840723i	$0.682130\pi$
$44$	−2.21891	−	3.84326i	−0.334513	−	0.579393i
$45$	−1.78711	−	0.127573i	−0.266406	−	0.0190175i
$46$	−5.65953			−0.834453
$47$	−3.69022	+	2.13055i	−0.538274	+	0.310773i	−0.744379	−	0.667757i	$-0.767254\pi$
$47$	−3.69022	+	2.13055i	−0.538274	+	0.310773i	0.206105	+	0.978530i	$0.433921\pi$
$48$	−1.28416	+	0.741409i	−0.185352	+	0.107013i
$49$	6.76689			0.966698
$50$	0.710233	−	4.94930i	0.100442	−	0.699937i
$51$	5.85609	+	10.1430i	0.820017	+	1.42031i
$52$	−3.58738	−	2.07118i	−0.497480	−	0.287220i
$53$	−2.76033	+	1.59368i	−0.379160	+	0.218908i	−0.677453	−	0.735566i	$-0.736916\pi$
$53$	−2.76033	+	1.59368i	−0.379160	+	0.218908i	0.298293	+	0.954474i	$0.403583\pi$
$54$	2.81828	−	4.88141i	0.383520	−	0.664275i
$55$	−5.56095	+	8.21869i	−0.749838	+	1.10821i
$56$	0.482818			0.0645192
$57$	−5.10834	−	3.95994i	−0.676616	−	0.524507i
$58$			3.82392i			0.502105i
$59$	0.812584	−	1.40744i	0.105789	−	0.183233i	−0.808271	−	0.588811i	$-0.799596\pi$
$59$	0.812584	−	1.40744i	0.105789	−	0.183233i	0.914060	+	0.405578i	$0.132930\pi$
$60$	2.74613	+	1.85809i	0.354524	+	0.239879i
$61$	−0.735243	−	1.27348i	−0.0941382	−	0.163052i	0.815110	−	0.579306i	$-0.196676\pi$
$61$	−0.735243	−	1.27348i	−0.0941382	−	0.163052i	−0.909249	+	0.416253i	$0.863343\pi$
$62$	6.56462	+	3.79008i	0.833707	+	0.481341i
$63$	−0.335029	+	0.193429i	−0.0422097	+	0.0243698i
$64$	−1.00000			−0.125000
$65$	−0.659533	+	9.23907i	−0.0818050	+	1.14597i
$66$	−3.29024	−	5.69885i	−0.405000	−	0.701481i
$67$	11.4272	−	6.59750i	1.39606	−	0.806013i	0.402079	−	0.915605i	$-0.368288\pi$
$67$	11.4272	−	6.59750i	1.39606	−	0.806013i	0.993977	+	0.109592i	$0.0349545\pi$
$68$			7.89860i			0.957846i
$69$	−8.39206			−1.01028
$70$	−0.471863	−	0.971036i	−0.0563984	−	0.116061i
$71$	−1.41164	+	2.44504i	−0.167531	+	0.290172i	−0.937551	−	0.347847i	$-0.886913\pi$
$71$	−1.41164	+	2.44504i	−0.167531	+	0.290172i	0.770020	+	0.638020i	$0.220246\pi$
$72$	0.693904	−	0.400626i	0.0817774	−	0.0472142i
$73$	−5.95528	−	3.43828i	−0.697013	−	0.402421i	0.109221	−	0.994017i	$-0.465164\pi$
$73$	−5.95528	−	3.43828i	−0.697013	−	0.402421i	−0.806234	+	0.591597i	$0.798498\pi$
$74$	1.75289	−	3.03610i	0.203770	−	0.352940i
$75$	1.05315	−	7.33891i	0.121607	−	0.847424i
$76$	−1.64820	−	4.03527i	−0.189062	−	0.462878i
$77$			2.14266i			0.244178i
$78$	−5.31943	−	3.07118i	−0.602307	−	0.347742i
$79$	−0.576026	+	0.997706i	−0.0648080	+	0.112251i	−0.896609	−	0.442824i	$-0.853977\pi$
$79$	−0.576026	+	0.997706i	−0.0648080	+	0.112251i	0.831801	+	0.555074i	$0.187310\pi$
$80$	0.977310	+	2.01118i	0.109267	+	0.224857i
$81$	2.97712	−	5.15652i	0.330791	−	0.572947i
$82$	7.70641	−	4.44930i	0.851031	−	0.491343i
$83$			12.4044i			1.36156i	0.732489	+	0.680779i	$0.238359\pi$
$83$			12.4044i			1.36156i	−0.732489	+	0.680779i	$0.761641\pi$
$84$	0.715931			0.0781144
$85$	15.8855	−	7.71938i	1.72303	−	0.837284i
$86$	−0.318434	−	0.551544i	−0.0343376	−	0.0594745i
$87$			5.67017i			0.607906i
$88$		−	4.43782i		−	0.473073i
$89$	4.37859	+	7.58395i	0.464130	+	0.803897i	0.999162	−	0.0409353i	$-0.0130337\pi$
$89$	4.37859	+	7.58395i	0.464130	+	0.803897i	−0.535032	+	0.844832i	$0.679700\pi$
$90$	−1.48389	−	1.00403i	−0.156416	−	0.105835i
$91$	1.00000	+	1.73205i	0.104828	+	0.181568i
$92$	−4.90130	−	2.82977i	−0.510996	−	0.295024i
$93$	9.73413	+	5.62000i	1.00938	+	0.582767i
$94$	−4.26110			−0.439499
$95$	−6.50488	+	7.25855i	−0.667386	+	0.744712i
$96$	−1.48282			−0.151339
$97$	0.825585	+	0.476652i	0.0838255	+	0.0483967i	0.541327	−	0.840812i	$-0.317922\pi$
$97$	0.825585	+	0.476652i	0.0838255	+	0.0483967i	−0.457501	+	0.889209i	$0.651256\pi$
$98$	5.86030	+	3.38344i	0.591979	+	0.341779i
$99$	1.77790	+	3.07942i	0.178686	+	0.309493i
$100$	3.08973	−	3.93110i	0.308973	−	0.393110i
$101$	3.32360	+	5.75665i	0.330711	+	0.572808i	0.982651	−	0.185462i	$-0.0593783\pi$
$101$	3.32360	+	5.75665i	0.330711	+	0.572808i	−0.651941	+	0.758270i	$0.726045\pi$
$102$			11.7122i			1.15968i
$103$			4.13171i			0.407110i	0.979064	+	0.203555i	$0.0652495\pi$
$103$			4.13171i			0.407110i	−0.979064	+	0.203555i	$0.934750\pi$
$104$	−2.07118	−	3.58738i	−0.203095	−	0.351772i
$105$	−0.699686	−	1.43987i	−0.0682824	−	0.140517i
$106$	−3.18735			−0.309583
$107$			10.0000i			0.966736i	0.875417	+	0.483368i	$0.160587\pi$
$107$			10.0000i			0.966736i	−0.875417	+	0.483368i	$0.839413\pi$
$108$	4.88141	−	2.81828i	0.469714	−	0.271189i
$109$	9.10799	−	15.7755i	0.872387	−	1.51102i	0.0128662	−	0.999917i	$-0.495904\pi$
$109$	9.10799	−	15.7755i	0.872387	−	1.51102i	0.859521	−	0.511101i	$-0.170762\pi$
$110$	−8.92527	+	4.33712i	−0.850991	+	0.413528i
$111$	2.59922	−	4.50198i	0.246707	−	0.427309i
$112$	0.418132	+	0.241409i	0.0395098	+	0.0228110i
$113$		−	8.29703i		−	0.780519i	−0.920705	−	0.390260i	$-0.872385\pi$
$113$		−	8.29703i		−	0.780519i	0.920705	−	0.390260i	$-0.127615\pi$
$114$	−2.44398	−	5.98358i	−0.228900	−	0.560413i
$115$	−0.901094	+	12.6230i	−0.0840275	+	1.17710i
$116$	−1.91196	+	3.31161i	−0.177521	+	0.307475i
$117$	2.87440	+	1.65953i	0.265738	+	0.153424i
$118$	1.40744	−	0.812584i	0.129565	−	0.0748044i
$119$	1.90679	−	3.30266i	0.174795	−	0.302754i
$120$	1.44917	+	2.98222i	0.132291	+	0.272238i
$121$	8.69420			0.790382
$122$		−	1.47049i		−	0.133132i
$123$	11.4272	−	6.59750i	1.03036	−	0.594877i
$124$	3.79008	+	6.56462i	0.340359	+	0.589520i
$125$	−10.9258	−	2.37211i	−0.977233	−	0.212168i
$126$	−0.386859			−0.0344641
$127$	−12.4255	+	7.17384i	−1.10258	+	0.636576i	−0.936898	−	0.349603i	$-0.886316\pi$
$127$	−12.4255	+	7.17384i	−1.10258	+	0.636576i	−0.165683	+	0.986179i	$0.552983\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$	−0.472180	−	0.817839i	−0.0415731	−	0.0720067i
$130$	−5.19071	+	7.67150i	−0.455255	+	0.672835i
$131$	−5.00032	+	8.66080i	−0.436880	+	0.756698i	−0.997447	−	0.0714111i	$-0.977250\pi$
$131$	−5.00032	+	8.66080i	−0.436880	+	0.756698i	0.560567	+	0.828109i	$0.310583\pi$
$132$		−	6.58047i		−	0.572756i
$133$	−0.284985	+	2.08517i	−0.0247113	+	0.180807i
$134$	13.1950			1.13987
$135$	−10.4387	−	7.06308i	−0.898423	−	0.607893i
$136$	−3.94930	+	6.84039i	−0.338650	+	0.586558i
$137$	3.16870	−	1.82945i	0.270720	−	0.156301i	−0.358495	−	0.933532i	$-0.616710\pi$
$137$	3.16870	−	1.82945i	0.270720	−	0.156301i	0.629215	+	0.777231i	$0.283377\pi$
$138$	−7.26773	−	4.19603i	−0.618671	−	0.357190i
$139$	−3.17602	−	5.50103i	−0.269387	−	0.466591i	0.699317	−	0.714812i	$-0.253488\pi$
$139$	−3.17602	−	5.50103i	−0.269387	−	0.466591i	−0.968704	+	0.248220i	$0.920154\pi$
$140$	0.0768728	−	1.07687i	0.00649694	−	0.0910124i
$141$	−6.31843			−0.532108
$142$	−2.44504	+	1.41164i	−0.205183	+	0.118462i
$143$	15.9201	−	9.19149i	1.33131	−	0.768631i
$144$	0.801252			0.0667710
$145$	8.52883	+	0.608833i	0.708281	+	0.0505608i
$146$	−3.43828	−	5.95528i	−0.284554	−	0.492863i
$147$	8.68975	+	5.01703i	0.716719	+	0.413798i
$148$	3.03610	−	1.75289i	0.249566	−	0.144087i
$149$	−6.02101	+	10.4287i	−0.493260	+	0.854351i	−0.999970	−	0.00776522i	$-0.997528\pi$
$149$	−6.02101	+	10.4287i	−0.493260	+	0.854351i	0.506710	+	0.862117i	$0.330862\pi$
$150$	4.58151	−	5.82911i	0.374078	−	0.475945i
$151$	−1.53484			−0.124903			−0.0624516	−	0.998048i	$-0.519892\pi$
$151$	−1.53484			−0.124903			−0.0624516	+	0.998048i	$0.519892\pi$
$152$	0.590253	−	4.31875i	0.0478759	−	0.350297i
$153$		−	6.32877i		−	0.511650i
$154$	−1.07133	+	1.85559i	−0.0863300	+	0.149528i
$155$	9.49857	−	14.0382i	0.762944	−	1.12758i
$156$	−3.07118	−	5.31943i	−0.245891	−	0.425895i
$157$	−16.5006	−	9.52664i	−1.31689	−	0.760309i	−0.333666	−	0.942691i	$-0.608286\pi$
$157$	−16.5006	−	9.52664i	−1.31689	−	0.760309i	−0.983228	+	0.182383i	$0.941619\pi$
$158$	−0.997706	+	0.576026i	−0.0793732	+	0.0458262i
$159$	−4.72626			−0.374817
$160$	−0.159217	+	2.23039i	−0.0125872	+	0.176328i
$161$	1.36626	+	2.36643i	0.107676	+	0.186501i
$162$	5.15652	−	2.97712i	0.405135	−	0.233905i
$163$		−	9.96533i		−	0.780545i	−0.920699	−	0.390272i	$-0.872381\pi$
$163$		−	9.96533i		−	0.780545i	0.920699	−	0.390272i	$-0.127619\pi$
$164$	8.89860			0.694864
$165$	−13.2345	+	6.43116i	−1.03031	+	0.500665i
$166$	−6.20219	+	10.7425i	−0.481384	+	0.833781i
$167$	−6.41331	+	3.70272i	−0.496277	+	0.286525i	−0.727175	−	0.686453i	$-0.759167\pi$
$167$	−6.41331	+	3.70272i	−0.496277	+	0.286525i	0.230898	+	0.972978i	$0.425834\pi$
$168$	0.620014	+	0.357965i	0.0478351	+	0.0276176i
$169$	2.07953	−	3.60186i	0.159964	−	0.277066i
$170$	17.6170	+	1.25759i	1.35116	+	0.0964529i
$171$	1.32062	+	3.23327i	0.100991	+	0.247254i
$172$		−	0.636868i		−	0.0485607i
$173$	−13.5667	−	7.83274i	−1.03146	−	0.595512i	−0.114056	−	0.993474i	$-0.536384\pi$
$173$	−13.5667	−	7.83274i	−1.03146	−	0.595512i	−0.917402	+	0.397962i	$0.869718\pi$
$174$	−2.83509	+	4.91051i	−0.214927	+	0.372265i
$175$	−2.24092	+	0.897833i	−0.169398	+	0.0678698i
$176$	2.21891	−	3.84326i	0.167256	−	0.289697i
$177$	2.08697	−	1.20491i	0.156866	−	0.0905669i
$178$			8.75719i			0.656379i
$179$	−4.61284			−0.344780			−0.172390	−	0.985029i	$-0.555149\pi$
$179$	−4.61284			−0.344780			−0.172390	+	0.985029i	$0.555149\pi$
$180$	−0.783071	−	1.61147i	−0.0583667	−	0.120112i
$181$	−0.605224	−	1.04828i	−0.0449860	−	0.0779180i	0.842656	−	0.538453i	$-0.180991\pi$
$181$	−0.605224	−	1.04828i	−0.0449860	−	0.0779180i	−0.887642	+	0.460535i	$0.847658\pi$
$182$			2.00000i			0.148250i
$183$		−	2.18046i		−	0.161184i
$184$	−2.82977	−	4.90130i	−0.208613	−	0.361329i
$185$	−6.49261	−	4.39304i	−0.477346	−	0.322983i
$186$	5.62000	+	9.73413i	0.412079	+	0.713741i
$187$	−30.3564	−	17.5263i	−2.21988	−	1.28165i
$188$	−3.69022	−	2.13055i	−0.269137	−	0.155386i
$189$	−2.72143			−0.197955
$190$	−9.26267	+	3.03365i	−0.671984	+	0.220084i
$191$	−7.64783			−0.553378			−0.276689	−	0.960960i	$-0.589237\pi$
$191$	−7.64783			−0.553378			−0.276689	+	0.960960i	$0.589237\pi$
$192$	−1.28416	−	0.741409i	−0.0926761	−	0.0535066i
$193$	15.5220	+	8.96163i	1.11730	+	0.645072i	0.940710	−	0.339212i	$-0.110161\pi$
$193$	15.5220	+	8.96163i	1.11730	+	0.645072i	0.176588	+	0.984285i	$0.443494\pi$
$194$	0.476652	+	0.825585i	0.0342216	+	0.0592736i
$195$	−7.69687	+	11.3754i	−0.551184	+	0.814612i
$196$	3.38344	+	5.86030i	0.241675	+	0.418593i
$197$			18.5697i			1.32304i	0.749929	+	0.661518i	$0.230088\pi$
$197$			18.5697i			1.32304i	−0.749929	+	0.661518i	$0.769912\pi$
$198$			3.55581i			0.252700i
$199$	−6.76689	−	11.7206i	−0.479692	−	0.830851i	0.520037	−	0.854144i	$-0.325918\pi$
$199$	−6.76689	−	11.7206i	−0.479692	−	0.830851i	−0.999729	+	0.0232931i	$0.992585\pi$
$200$	4.64134	−	1.85957i	0.328192	−	0.131491i
$201$	19.5658			1.38006
$202$			6.64720i			0.467695i
$203$	1.59890	−	0.923127i	0.112221	−	0.0647908i
$204$	−5.85609	+	10.1430i	−0.410008	+	0.710155i
$205$	−8.69669	−	17.8967i	−0.607403	−	1.24996i
$206$	−2.06586	+	3.57817i	−0.143935	+	0.249303i
$207$	3.92717	+	2.26736i	0.272958	+	0.157592i
$208$		−	4.14235i		−	0.287220i
$209$	19.1658	+	2.61944i	1.32573	+	0.181190i
$210$	0.113988	−	1.59681i	0.00786594	−	0.110190i
$211$	6.67055	−	11.5537i	0.459220	−	0.795392i	−0.539700	−	0.841857i	$-0.681462\pi$
$211$	6.67055	−	11.5537i	0.459220	−	0.795392i	0.998920	+	0.0464656i	$0.0147958\pi$
$212$	−2.76033	−	1.59368i	−0.189580	−	0.109454i
$213$	−3.62554	+	2.09321i	−0.248418	+	0.143424i
$214$	−5.00000	+	8.66025i	−0.341793	+	0.592003i
$215$	−1.28086	+	0.622418i	−0.0873539	+	0.0424485i
$216$	5.63656			0.383520
$217$		−	3.65984i		−	0.248446i
$218$	15.7755	−	9.10799i	1.06845	−	0.616871i
$219$	−5.09835	−	8.83060i	−0.344514	−	0.596716i
$220$	−9.89807	−	0.706576i	−0.667328	−	0.0476373i
$221$	−32.7188			−2.20090
$222$	4.50198	−	2.59922i	0.302153	−	0.174448i
$223$	−4.77802	−	2.75859i	−0.319960	−	0.184729i	0.331415	−	0.943485i	$-0.392474\pi$
$223$	−4.77802	−	2.75859i	−0.319960	−	0.184729i	−0.651375	+	0.758756i	$0.725807\pi$
$224$	0.241409	+	0.418132i	0.0161298	+	0.0279376i
$225$	−2.47565	+	3.14980i	−0.165043	+	0.209987i
$226$	4.14852	−	7.18544i	0.275955	−	0.477968i
$227$		−	22.2457i		−	1.47650i	−0.674529	−	0.738248i	$-0.735653\pi$
$227$		−	22.2457i		−	1.47650i	0.674529	−	0.738248i	$-0.264347\pi$
$228$	0.875238	−	6.40392i	0.0579641	−	0.424110i
$229$	−16.4341			−1.08599			−0.542997	−	0.839735i	$-0.682710\pi$
$229$	−16.4341			−1.08599			−0.542997	+	0.839735i	$0.682710\pi$
$230$	−7.09186	+	10.4813i	−0.467623	+	0.691115i
$231$	−1.58858	+	2.75151i	−0.104521	+	0.181036i
$232$	−3.31161	+	1.91196i	−0.217418	+	0.125526i
$233$	9.15309	+	5.28454i	0.599639	+	0.346202i	0.768899	−	0.639370i	$-0.220805\pi$
$233$	9.15309	+	5.28454i	0.599639	+	0.346202i	−0.169261	+	0.985571i	$0.554138\pi$
$234$	1.65953	+	2.87440i	0.108487	+	0.187905i
$235$	−0.678440	+	9.50392i	−0.0442565	+	0.619968i
$236$	1.62517			0.105789
$237$	−1.47942	+	0.854141i	−0.0960984	+	0.0554824i
$238$	3.30266	−	1.90679i	0.214080	−	0.123599i
$239$	15.8625			1.02606			0.513031	−	0.858370i	$-0.328522\pi$
$239$	15.8625			1.02606			0.513031	+	0.858370i	$0.328522\pi$
$240$	−0.236090	+	3.30727i	−0.0152395	+	0.213483i
$241$	−2.19672	−	3.80483i	−0.141503	−	0.245091i	0.786560	−	0.617514i	$-0.211860\pi$
$241$	−2.19672	−	3.80483i	−0.141503	−	0.245091i	−0.928063	+	0.372423i	$0.878527\pi$
$242$	7.52940	+	4.34710i	0.484008	+	0.279442i
$243$	−6.99804	+	4.04032i	−0.448924	+	0.259187i
$244$	0.735243	−	1.27348i	0.0470691	−	0.0815261i
$245$	8.47947	−	12.5321i	0.541733	−	0.800644i
$246$	13.1950			0.841283
$247$	16.7155	−	6.82742i	1.06358	−	0.434419i
$248$			7.58017i			0.481341i
$249$	−9.19672	+	15.9292i	−0.582819	+	1.00947i
$250$	−8.27596	−	7.51721i	−0.523418	−	0.475430i
$251$	−7.21853	−	12.5029i	−0.455630	−	0.789173i	0.543095	−	0.839671i	$-0.317252\pi$
$251$	−7.21853	−	12.5029i	−0.455630	−	0.789173i	−0.998724	+	0.0504980i	$0.983919\pi$
$252$	−0.335029	−	0.193429i	−0.0211049	−	0.0121849i
$253$	21.7511	−	12.5580i	1.36748	−	0.789513i
$254$	−14.3477			−0.900254
$255$	26.1228	+	1.86478i	1.63587	+	0.116777i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	9.55685	−	5.51765i	0.596140	−	0.344182i	−0.171382	−	0.985205i	$-0.554823\pi$
$257$	9.55685	−	5.51765i	0.596140	−	0.344182i	0.767522	+	0.641023i	$0.221490\pi$
$258$		−	0.944359i		−	0.0587933i
$259$	−1.69266			−0.105177
$260$	−8.33103	+	4.04836i	−0.516669	+	0.251069i
$261$	1.53196	−	2.65343i	0.0948259	−	0.164243i
$262$	−8.66080	+	5.00032i	−0.535066	+	0.308921i
$263$	18.2957	+	10.5630i	1.12816	+	0.651345i	0.943472	−	0.331451i	$-0.107538\pi$
$263$	18.2957	+	10.5630i	1.12816	+	0.651345i	0.184691	+	0.982797i	$0.440872\pi$
$264$	3.29024	−	5.69885i	0.202500	−	0.350740i
$265$	−0.507481	+	7.10905i	−0.0311743	+	0.436705i
$266$	−1.28939	+	1.66332i	−0.0790575	+	0.101984i
$267$			12.9853i			0.794688i
$268$	11.4272	+	6.59750i	0.698028	+	0.403006i
$269$	−14.1483	+	24.5056i	−0.862637	+	1.49413i	0.00673681	+	0.999977i	$0.497856\pi$
$269$	−14.1483	+	24.5056i	−0.862637	+	1.49413i	−0.869374	+	0.494154i	$0.835478\pi$
$270$	−5.50867	−	11.3362i	−0.335247	−	0.689897i
$271$	6.15672	−	10.6638i	0.373994	−	0.647777i	−0.616182	−	0.787604i	$-0.711321\pi$
$271$	6.15672	−	10.6638i	0.373994	−	0.647777i	0.990176	+	0.139827i	$0.0446546\pi$
$272$	−6.84039	+	3.94930i	−0.414759	+	0.239461i
$273$			2.96564i			0.179488i
$274$	3.65890			0.221042
$275$	8.25243	+	20.5974i	0.497640	+	1.24207i
$276$	−4.19603	−	7.26773i	−0.252571	−	0.437466i
$277$			27.2677i			1.63836i	0.573539	+	0.819178i	$0.305570\pi$
$277$			27.2677i			1.63836i	−0.573539	+	0.819178i	$0.694430\pi$
$278$		−	6.35204i		−	0.380970i
$279$	−3.03681	−	5.25991i	−0.181809	−	0.314903i
$280$	0.605010	−	0.894163i	0.0361563	−	0.0534364i
$281$	−4.63665	−	8.03092i	−0.276600	−	0.479084i	0.693938	−	0.720035i	$-0.255874\pi$
$281$	−4.63665	−	8.03092i	−0.276600	−	0.479084i	−0.970537	+	0.240950i	$0.922541\pi$
$282$	−5.47192	−	3.15922i	−0.325848	−	0.188129i
$283$	22.5226	+	13.0034i	1.33883	+	0.772975i	0.986634	−	0.162951i	$-0.0521013\pi$
$283$	22.5226	+	13.0034i	1.33883	+	0.772975i	0.352197	+	0.935926i	$0.385435\pi$
$284$	−2.82328			−0.167531
$285$	−13.7348	+	4.49835i	−0.813582	+	0.266459i
$286$	18.3830			1.08701
$287$	−3.72079	−	2.14820i	−0.219631	−	0.126804i
$288$	0.693904	+	0.400626i	0.0408887	+	0.0236071i
$289$	22.6939	+	39.3071i	1.33494	+	2.31218i
$290$	7.08177	+	4.79168i	0.415856	+	0.281377i
$291$	0.706788	+	1.22419i	0.0414326	+	0.0717634i
$292$		−	6.87657i		−	0.402421i
$293$		−	17.4435i		−	1.01906i	−0.860453	−	0.509529i	$-0.829820\pi$
$293$		−	17.4435i		−	1.01906i	0.860453	−	0.509529i	$-0.170180\pi$
$294$	5.01703	+	8.68975i	0.292599	+	0.506797i
$295$	−1.58829	−	3.26851i	−0.0924740	−	0.190300i
$296$	3.50579			0.203770
$297$			25.0140i			1.45146i
$298$	−10.4287	+	6.02101i	−0.604118	+	0.348788i
$299$	11.7219	−	20.3029i	0.677894	−	1.17415i
$300$	6.88225	−	2.75740i	0.397347	−	0.159199i
$301$	−0.153746	+	0.266295i	−0.00886175	+	0.0153490i
$302$	−1.32921	−	0.767418i	−0.0764873	−	0.0441600i
$303$			9.85659i			0.566246i
$304$	2.67055	−	3.44502i	0.153167	−	0.197585i
$305$	−3.27976	−	0.234126i	−0.187799	−	0.0134060i
$306$	3.16438	−	5.48087i	0.180896	−	0.313321i
$307$	−0.965067	−	0.557182i	−0.0550793	−	0.0318000i	0.472207	−	0.881487i	$-0.343457\pi$
$307$	−0.965067	−	0.557182i	−0.0550793	−	0.0318000i	−0.527287	+	0.849687i	$0.676791\pi$
$308$	−1.85559	+	1.07133i	−0.105732	+	0.0610446i
$309$	−3.06329	+	5.30577i	−0.174264	+	0.301835i
$310$	15.2451	−	7.40817i	0.865864	−	0.420756i
$311$	33.8032			1.91680			0.958400	−	0.285427i	$-0.0921354\pi$
$311$	33.8032			1.91680			0.958400	+	0.285427i	$0.0921354\pi$
$312$		−	6.14235i		−	0.347742i
$313$	−12.7842	+	7.38095i	−0.722605	+	0.417196i	−0.815711	−	0.578460i	$-0.803654\pi$
$313$	−12.7842	+	7.38095i	−0.722605	+	0.417196i	0.0931060	+	0.995656i	$0.470320\pi$
$314$	−9.52664	−	16.5006i	−0.537619	−	0.931184i
$315$	−0.0615945	+	0.862846i	−0.00347046	+	0.0486159i
$316$	−1.15205			−0.0648080
$317$	22.6350	−	13.0683i	1.27131	−	0.733989i	0.296072	−	0.955165i	$-0.404323\pi$
$317$	22.6350	−	13.0683i	1.27131	−	0.733989i	0.975234	+	0.221177i	$0.0709897\pi$
$318$	−4.09306	−	2.36313i	−0.229528	−	0.132518i
$319$	−8.48492	−	14.6963i	−0.475064	−	0.822835i
$320$	−1.25308	+	1.85197i	−0.0700494	+	0.103528i
$321$	−7.41409	+	12.8416i	−0.413814	+	0.716747i
$322$			2.73252i			0.152278i
$323$	−27.2108	−	21.0936i	−1.51405	−	1.17368i
$324$	5.95424			0.330791
$325$	16.2840	+	12.7987i	0.903274	+	0.709947i
$326$	4.98267	−	8.63023i	0.275964	−	0.477984i
$327$	23.3922	−	13.5055i	1.29359	−	0.746855i
$328$	7.70641	+	4.44930i	0.425515	+	0.245671i
$329$	1.02867	+	1.78170i	0.0567123	+	0.0982285i
$330$	−14.6770	−	1.04772i	−0.807944	−	0.0576753i
$331$	2.17127			0.119344			0.0596720	−	0.998218i	$-0.480995\pi$
$331$	2.17127			0.119344			0.0596720	+	0.998218i	$0.480995\pi$
$332$	−10.7425	+	6.20219i	−0.589572	+	0.340390i
$333$	−2.43268	+	1.40451i	−0.133310	+	0.0769666i
$334$	−7.40545			−0.405208
$335$	2.10087	−	29.4300i	0.114783	−	1.60793i
$336$	0.357965	+	0.620014i	0.0195286	+	0.0338245i
$337$	−11.3697	−	6.56430i	−0.619347	−	0.357580i	0.157268	−	0.987556i	$-0.449731\pi$
$337$	−11.3697	−	6.56430i	−0.619347	−	0.357580i	−0.776615	+	0.629976i	$0.783065\pi$
$338$	3.60186	−	2.07953i	0.195915	−	0.113112i
$339$	6.15149	−	10.6547i	0.334103	−	0.578684i
$340$	14.6280	+	9.89759i	0.793312	+	0.536772i
$341$	−33.6394			−1.82167
$342$	−0.472942	+	3.46041i	−0.0255738	+	0.187117i
$343$		−	6.64690i		−	0.358899i
$344$	0.318434	−	0.551544i	0.0171688	−	0.0297373i
$345$	−10.5159	+	15.5418i	−0.566159	+	0.836743i
$346$	−7.83274	−	13.5667i	−0.421091	−	0.729351i
$347$	12.9352	+	7.46811i	0.694395	+	0.400909i	0.805257	−	0.592927i	$-0.202028\pi$
$347$	12.9352	+	7.46811i	0.694395	+	0.400909i	−0.110861	+	0.993836i	$0.535361\pi$
$348$	−4.91051	+	2.83509i	−0.263231	+	0.151977i
$349$	18.8611			1.00961			0.504806	−	0.863233i	$-0.331564\pi$
$349$	18.8611			1.00961			0.504806	+	0.863233i	$0.331564\pi$
$350$	−2.38961	−	0.342913i	−0.127730	−	0.0183295i
$351$	11.6743	+	20.2205i	0.623129	+	1.07929i
$352$	3.84326	−	2.21891i	0.204846	−	0.118268i
$353$			2.01172i			0.107073i	0.998566	+	0.0535366i	$0.0170494\pi$
$353$			2.01172i			0.107073i	−0.998566	+	0.0535366i	$0.982951\pi$
$354$	2.40983			0.128081
$355$	2.75922	+	5.67815i	0.146444	+	0.301365i
$356$	−4.37859	+	7.58395i	−0.232065	+	0.401948i
$357$	4.89724	−	2.82742i	0.259190	−	0.149643i
$358$	−3.99483	−	2.30642i	−0.211134	−	0.121898i
$359$	−3.29938	+	5.71469i	−0.174135	+	0.301610i	−0.939861	−	0.341556i	$-0.889046\pi$
$359$	−3.29938	+	5.71469i	−0.174135	+	0.301610i	0.765727	+	0.643166i	$0.222379\pi$
$360$	0.127573	−	1.78711i	0.00672368	−	0.0941887i
$361$	18.3032	+	5.09831i	0.963326	+	0.268332i
$362$		−	1.21045i		−	0.0636197i
$363$	11.1647	+	6.44596i	0.585996	+	0.338325i
$364$	−1.00000	+	1.73205i	−0.0524142	+	0.0907841i
$365$	−13.8300	+	6.72054i	−0.723898	+	0.351769i
$366$	1.09023	−	1.88834i	0.0569873	−	0.0987049i
$367$	−9.69814	+	5.59922i	−0.506239	+	0.292277i	−0.731286	−	0.682071i	$-0.761080\pi$
$367$	−9.69814	+	5.59922i	−0.506239	+	0.292277i	0.225048	+	0.974348i	$0.427746\pi$
$368$		−	5.65953i		−	0.295024i
$369$	−7.13002			−0.371174
$370$	−3.42624	−	7.05079i	−0.178122	−	0.366553i
$371$	0.769455	+	1.33274i	0.0399481	+	0.0691922i
$372$			11.2400i			0.582767i
$373$		−	3.19437i		−	0.165398i	−0.996575	−	0.0826991i	$-0.973646\pi$
$373$		−	3.19437i		−	0.165398i	0.996575	−	0.0826991i	$-0.0263540\pi$
$374$	−17.5263	−	30.3564i	−0.906261	−	1.56969i
$375$	−12.2717	−	11.1466i	−0.633710	−	0.575610i
$376$	−2.13055	−	3.69022i	−0.109875	−	0.190309i
$377$	−13.7178	−	7.92000i	−0.706505	−	0.407901i
$378$	−2.35683	−	1.36072i	−0.121222	−	0.0699877i
$379$	−17.2666			−0.886927			−0.443463	−	0.896292i	$-0.646250\pi$
$379$	−17.2666			−0.886927			−0.443463	+	0.896292i	$0.646250\pi$
$380$	−9.53853	−	2.00412i	−0.489316	−	0.102809i
$381$	−21.2750			−1.08995
$382$	−6.62322	−	3.82392i	−0.338873	−	0.195649i
$383$	−27.8729	−	16.0924i	−1.42424	−	0.822285i	−0.427582	−	0.903977i	$-0.640634\pi$
$383$	−27.8729	−	16.0924i	−1.42424	−	0.822285i	−0.996658	+	0.0816914i	$0.973968\pi$
$384$	−0.741409	−	1.28416i	−0.0378349	−	0.0655319i
$385$	3.96813	+	2.68492i	0.202235	+	0.136836i
$386$	8.96163	+	15.5220i	0.456135	+	0.790049i
$387$			0.510292i			0.0259396i
$388$			0.953304i			0.0483967i
$389$	−5.03587	−	8.72239i	−0.255329	−	0.442243i	0.709656	−	0.704548i	$-0.248850\pi$
$389$	−5.03587	−	8.72239i	−0.255329	−	0.442243i	−0.964985	+	0.262306i	$0.915517\pi$
$390$	−12.3534	+	6.00298i	−0.625539	+	0.303973i
$391$	−44.7024			−2.26070
$392$			6.76689i			0.341779i
$393$	−12.8424	+	7.41456i	−0.647813	+	0.374015i
$394$	−9.28485	+	16.0818i	−0.467764	+	0.810191i
$395$	1.12591	+	2.31699i	0.0566508	+	0.116580i
$396$	−1.77790	+	3.07942i	−0.0893430	+	0.154747i
$397$	−30.6949	−	17.7217i	−1.54053	−	0.889428i	−0.998805	−	0.0488757i	$-0.984436\pi$
$397$	−30.6949	−	17.7217i	−1.54053	−	0.889428i	−0.541730	−	0.840553i	$-0.682230\pi$
$398$		−	13.5338i		−	0.678387i
$399$	−1.91193	+	2.46640i	−0.0957161	+	0.123474i
$400$	4.94930	+	0.710233i	0.247465	+	0.0355117i
$401$	15.4751	−	26.8036i	0.772789	−	1.33851i	−0.163239	−	0.986587i	$-0.552194\pi$
$401$	15.4751	−	26.8036i	0.772789	−	1.33851i	0.936029	−	0.351924i	$-0.114472\pi$
$402$	16.9445	+	9.78289i	0.845113	+	0.487926i
$403$	−27.1929	+	15.6999i	−1.35458	+	0.782065i
$404$	−3.32360	+	5.75665i	−0.165355	+	0.286404i
$405$	−5.81914	−	11.9751i	−0.289155	−	0.595046i
$406$	1.84625			0.0916281
$407$			15.5580i			0.771183i
$408$	−10.1430	+	5.85609i	−0.502156	+	0.289920i
$409$	13.5583	+	23.4837i	0.670417	+	1.16120i	0.977786	+	0.209606i	$0.0672182\pi$
$409$	13.5583	+	23.4837i	0.670417	+	1.16120i	−0.307369	+	0.951590i	$0.599449\pi$
$410$	1.41681	−	19.8474i	0.0699712	−	0.980192i
$411$	5.42548			0.267619
$412$	−3.57817	+	2.06586i	−0.176284	+	0.101777i
$413$	−0.679535	−	0.392330i	−0.0334378	−	0.0193053i
$414$	2.26736	+	3.92717i	0.111434	+	0.193010i
$415$	22.9725	+	15.5437i	1.12768	+	0.763011i
$416$	2.07118	−	3.58738i	0.101548	−	0.175886i
$417$		−	9.41892i		−	0.461246i
$418$	15.2884	+	11.8514i	0.747778	+	0.579671i
$419$	8.28108			0.404557			0.202279	−	0.979328i	$-0.435165\pi$
$419$	8.28108			0.404557			0.202279	+	0.979328i	$0.435165\pi$
$420$	0.897120	−	1.32588i	0.0437750	−	0.0646963i
$421$	−2.95790	+	5.12323i	−0.144159	+	0.249691i	−0.929059	−	0.369932i	$-0.879381\pi$
$421$	−2.95790	+	5.12323i	−0.144159	+	0.249691i	0.784900	+	0.619623i	$0.212714\pi$
$422$	11.5537	−	6.67055i	0.562427	−	0.324717i
$423$	2.95680	+	1.70711i	0.143764	+	0.0830024i
$424$	−1.59368	−	2.76033i	−0.0773958	−	0.134053i
$425$	5.60985	−	39.0925i	0.272118	−	1.89627i
$426$	−4.18642			−0.202833
$427$	−0.614858	+	0.354988i	−0.0297551	+	0.0171791i
$428$	−8.66025	+	5.00000i	−0.418609	+	0.241684i
$429$	27.2586			1.31606
$430$	−1.42047	−	0.101400i	−0.0685010	−	0.00488996i
$431$	7.48526	+	12.9649i	0.360552	+	0.624495i	0.988052	−	0.154122i	$-0.0492548\pi$
$431$	7.48526	+	12.9649i	0.360552	+	0.624495i	−0.627499	+	0.778617i	$0.715922\pi$
$432$	4.88141	+	2.81828i	0.234857	+	0.135595i
$433$	2.90269	−	1.67587i	0.139494	−	0.0805371i	−0.428629	−	0.903481i	$-0.641003\pi$
$433$	2.90269	−	1.67587i	0.139494	−	0.0805371i	0.568123	+	0.822944i	$0.307670\pi$
$434$	1.82992	−	3.16951i	0.0878389	−	0.152141i
$435$	10.5010	+	7.10519i	0.503483	+	0.340668i
$436$	18.2160			0.872387
$437$	22.8378	−	9.32805i	1.09248	−	0.446221i
$438$		−	10.1967i		−	0.487217i
$439$	6.00116	−	10.3943i	0.286420	−	0.496094i	−0.686533	−	0.727099i	$-0.740868\pi$
$439$	6.00116	−	10.3943i	0.286420	−	0.496094i	0.972953	+	0.231005i	$0.0742014\pi$
$440$	−8.21869	−	5.56095i	−0.391811	−	0.265108i
$441$	−2.71099	−	4.69557i	−0.129095	−	0.223599i
$442$	−28.3353	−	16.3594i	−1.34777	−	0.778137i
$443$	−23.2046	+	13.3972i	−1.10248	+	0.636520i	−0.936873	−	0.349671i	$-0.886293\pi$
$443$	−23.2046	+	13.3972i	−1.10248	+	0.636520i	−0.165612	+	0.986191i	$0.552960\pi$
$444$	5.19844			0.246707
$445$	19.5320	+	1.39429i	0.925904	+	0.0660958i
$446$	−2.75859	−	4.77802i	−0.130623	−	0.226246i
$447$	−15.4638	+	8.92805i	−0.731415	+	0.422282i
$448$			0.482818i			0.0228110i
$449$	−3.53608			−0.166878			−0.0834389	−	0.996513i	$-0.526590\pi$
$449$	−3.53608			−0.166878			−0.0834389	+	0.996513i	$0.526590\pi$
$450$	−3.71888	+	1.48998i	−0.175310	+	0.0702385i
$451$	−19.7452	+	34.1996i	−0.929764	+	1.61040i
$452$	7.18544	−	4.14852i	0.337975	−	0.195130i
$453$	−1.97097	−	1.13794i	−0.0926043	−	0.0534651i
$454$	11.1228	−	19.2653i	0.522020	−	0.904165i
$455$	4.46078	+	0.318434i	0.209125	+	0.0149284i
$456$	3.95994	−	5.10834i	0.185441	−	0.239220i
$457$		−	21.5147i		−	1.00642i	−0.864166	−	0.503208i	$-0.832153\pi$
$457$		−	21.5147i		−	1.00642i	0.864166	−	0.503208i	$-0.167847\pi$
$458$	−14.2323	−	8.21703i	−0.665033	−	0.383957i
$459$	22.2605	−	38.5563i	1.03903	−	1.79965i
$460$	−11.3824	+	5.53112i	−0.530706	+	0.257890i
$461$	−20.1971	+	34.9825i	−0.940675	+	1.62930i	−0.176486	+	0.984303i	$0.556473\pi$
$461$	−20.1971	+	34.9825i	−0.940675	+	1.62930i	−0.764188	+	0.644993i	$0.776860\pi$
$462$	−2.75151	+	1.58858i	−0.128012	+	0.0739076i
$463$		−	19.6448i		−	0.912972i	−0.889731	−	0.456486i	$-0.849108\pi$
$463$		−	19.6448i		−	0.912972i	0.889731	−	0.456486i	$-0.150892\pi$
$464$	−3.82392			−0.177521
$465$	22.6057	−	10.9850i	1.04832	−	0.509416i
$466$	5.28454	+	9.15309i	0.244801	+	0.424009i
$467$		−	15.1929i		−	0.703042i	−0.936180	−	0.351521i	$-0.885665\pi$
$467$		−	15.1929i		−	0.703042i	0.936180	−	0.351521i	$-0.114335\pi$
$468$			3.31907i			0.153424i
$469$	−3.18539	−	5.51726i	−0.147088	−	0.254763i
$470$	−5.33951	+	7.89142i	−0.246293	+	0.364004i
$471$	−14.1263	−	24.4674i	−0.650904	−	1.12740i
$472$	1.40744	+	0.812584i	0.0647825	+	0.0374022i
$473$	2.44765	+	1.41315i	0.112543	+	0.0649768i
$474$	−1.70828			−0.0784640
$475$	5.29145	+	21.1424i	0.242789	+	0.970079i
$476$	3.81358			0.174795
$477$	2.21172	+	1.27694i	0.101268	+	0.0584669i
$478$	13.7374	+	7.93127i	0.628332	+	0.362768i
$479$	−2.12032	−	3.67250i	−0.0968798	−	0.167801i	0.813512	−	0.581548i	$-0.197553\pi$
$479$	−2.12032	−	3.67250i	−0.0968798	−	0.167801i	−0.910392	+	0.413748i	$0.864220\pi$
$480$	−1.85809	+	2.74613i	−0.0848099	+	0.125343i
$481$	7.26110	+	12.5766i	0.331078	+	0.573443i
$482$		−	4.39344i		−	0.200116i
$483$			4.05183i			0.184365i
$484$	4.34710	+	7.52940i	0.197596	+	0.342245i
$485$	1.91727	−	0.931673i	0.0870587	−	0.0423051i
$486$	−8.08064			−0.366545
$487$			8.00831i			0.362891i	0.983401	+	0.181446i	$0.0580776\pi$
$487$			8.00831i			0.362891i	−0.983401	+	0.181446i	$0.941922\pi$
$488$	1.27348	−	0.735243i	0.0576477	−	0.0332829i
$489$	7.38838	−	12.7971i	0.334114	−	0.578703i
$490$	13.6095	−	6.61335i	0.614813	−	0.298761i
$491$	8.53834	−	14.7888i	0.385330	−	0.667411i	−0.606485	−	0.795095i	$-0.707421\pi$
$491$	8.53834	−	14.7888i	0.385330	−	0.667411i	0.991815	+	0.127684i	$0.0407543\pi$
$492$	11.4272	+	6.59750i	0.515178	+	0.297438i
$493$			30.2036i			1.36030i
$494$	17.8898	+	2.44504i	0.804899	+	0.110007i
$495$	7.93085	+	0.566145i	0.356465	+	0.0254463i
$496$	−3.79008	+	6.56462i	−0.170180	+	0.294760i
$497$	1.18051	+	0.681566i	0.0529530	+	0.0305724i
$498$	−15.9292	+	9.19672i	−0.713804	+	0.412115i
$499$	5.63718	−	9.76389i	0.252355	−	0.437092i	−0.711819	−	0.702363i	$-0.752128\pi$
$499$	5.63718	−	9.76389i	0.252355	−	0.437092i	0.964174	+	0.265272i	$0.0854616\pi$
$500$	−3.40859	−	10.6481i	−0.152437	−	0.476196i
$501$	−10.9809			−0.490592
$502$		−	14.4371i		−	0.644357i
$503$	−7.36586	+	4.25268i	−0.328427	+	0.189618i	−0.655143	−	0.755505i	$-0.727391\pi$
$503$	−7.36586	+	4.25268i	−0.328427	+	0.189618i	0.326715	+	0.945123i	$0.394058\pi$
$504$	−0.193429	−	0.335029i	−0.00861602	−	0.0149234i
$505$	14.8259	+	1.05835i	0.659742	+	0.0470959i
$506$	25.1160			1.11654
$507$	5.34090	−	3.08357i	0.237198	−	0.136946i
$508$	−12.4255	−	7.17384i	−0.551291	−	0.318288i
$509$	15.4306	+	26.7265i	0.683948	+	1.18463i	0.973766	+	0.227550i	$0.0730716\pi$
$509$	15.4306	+	26.7265i	0.683948	+	1.18463i	−0.289819	+	0.957082i	$0.593595\pi$
$510$	21.6906	+	14.6763i	0.960475	+	0.649879i
$511$	−1.66006	+	2.87532i	−0.0734369	+	0.127196i
$512$		−	1.00000i		−	0.0441942i
$513$	−3.32700	+	24.3429i	−0.146891	+	1.07477i
$514$	11.0353			0.486746
$515$	7.65180	+	5.17738i	0.337179	+	0.228142i
$516$	0.472180	−	0.817839i	0.0207866	−	0.0360034i
$517$	16.3765	−	9.45499i	0.720238	−	0.415830i
$518$	−1.46588	−	0.846328i	−0.0644072	−	0.0371855i
$519$	−11.6145	−	20.1170i	−0.509821	−	0.883036i
$520$	−9.23907	−	0.659533i	−0.405160	−	0.0289224i
$521$	−8.09735			−0.354751			−0.177376	−	0.984143i	$-0.556761\pi$
$521$	−8.09735			−0.354751			−0.177376	+	0.984143i	$0.556761\pi$
$522$	2.65343	−	1.53196i	0.116138	−	0.0670521i
$523$	−12.7352	+	7.35267i	−0.556872	+	0.321510i	−0.751889	−	0.659290i	$-0.770857\pi$
$523$	−12.7352	+	7.35267i	−0.556872	+	0.321510i	0.195017	+	0.980800i	$0.437524\pi$
$524$	−10.0006			−0.436880
$525$	−3.54336	−	0.508478i	−0.154645	−	0.0221918i
$526$	10.5630	+	18.2957i	0.460571	+	0.797732i
$527$	51.8513	+	29.9363i	2.25868	+	1.30405i
$528$	5.69885	−	3.29024i	0.248011	−	0.143189i
$529$	4.51516	−	7.82048i	0.196311	−	0.340021i
$530$	−3.99402	+	5.90288i	−0.173489	+	0.256405i
$531$	−1.30217			−0.0565093
$532$	−1.94830	+	0.795780i	−0.0844696	+	0.0345015i
$533$			36.8611i			1.59663i
$534$	−6.49265	+	11.2456i	−0.280965	+	0.486645i
$535$	18.5197	+	12.5308i	0.800676	+	0.541755i
$536$	6.59750	+	11.4272i	0.284969	+	0.493580i
$537$	−5.92361	−	3.42000i	−0.255623	−	0.147584i
$538$	−24.5056	+	14.1483i	−1.05651	+	0.609977i
$539$	−30.0302			−1.29349
$540$	0.897437	−	12.5717i	0.0386195	−	0.541002i
$541$	−5.50993	−	9.54347i	−0.236890	−	0.410306i	0.722930	−	0.690921i	$-0.242795\pi$
$541$	−5.50993	−	9.54347i	−0.236890	−	0.410306i	−0.959820	+	0.280615i	$0.909462\pi$
$542$	10.6638	−	6.15672i	0.458048	−	0.264454i
$543$		−	1.79487i		−	0.0770254i
$544$	−7.89860			−0.338650
$545$	−17.8027	−	36.6357i	−0.762582	−	1.56930i
$546$	−1.48282	+	2.56832i	−0.0634587	+	0.109914i
$547$	2.24490	−	1.29610i	0.0959852	−	0.0554171i	−0.451239	−	0.892403i	$-0.649018\pi$
$547$	2.24490	−	1.29610i	0.0959852	−	0.0554171i	0.547224	+	0.836986i	$0.315684\pi$
$548$	3.16870	+	1.82945i	0.135360	+	0.0781503i
$549$	−0.589115	+	1.02038i	−0.0251428	+	0.0435486i
$550$	−3.15188	+	21.9641i	−0.134397	+	0.936551i
$551$	−6.30258	−	15.4305i	−0.268499	−	0.657364i
$552$		−	8.39206i		−	0.357190i
$553$	0.481710	+	0.278115i	0.0204844	+	0.0118267i
$554$	−13.6338	+	23.6145i	−0.579246	+	1.00328i
$555$	−5.08049	−	10.4550i	−0.215655	−	0.443791i
$556$	3.17602	−	5.50103i	0.134693	−	0.233296i
$557$	7.30563	−	4.21791i	0.309550	−	0.178719i	−0.337175	−	0.941442i	$-0.609472\pi$
$557$	7.30563	−	4.21791i	0.309550	−	0.178719i	0.646725	+	0.762723i	$0.276138\pi$
$558$		−	6.07362i		−	0.257117i
$559$	2.63813			0.111581
$560$	0.971036	−	0.471863i	0.0410337	−	0.0199398i
$561$	−25.9883	−	45.0130i	−1.09722	−	1.90045i
$562$		−	9.27331i		−	0.391171i
$563$		−	27.9415i		−	1.17760i	−0.808280	−	0.588798i	$-0.799601\pi$
$563$		−	27.9415i		−	1.17760i	0.808280	−	0.588798i	$-0.200399\pi$
$564$	−3.15922	−	5.47192i	−0.133027	−	0.230410i
$565$	−15.3658	−	10.3969i	−0.646446	−	0.437399i
$566$	13.0034	+	22.5226i	0.546576	+	0.946697i
$567$	−2.48966	−	1.43741i	−0.104556	−	0.0603654i
$568$	−2.44504	−	1.41164i	−0.102591	−	0.0592312i
$569$	−10.7931			−0.452472			−0.226236	−	0.974072i	$-0.572642\pi$
$569$	−10.7931			−0.452472			−0.226236	+	0.974072i	$0.572642\pi$
$570$	−14.1439	−	2.97174i	−0.592423	−	0.124472i
$571$	6.26581			0.262216			0.131108	−	0.991368i	$-0.458147\pi$
$571$	6.26581			0.262216			0.131108	+	0.991368i	$0.458147\pi$
$572$	15.9201	+	9.19149i	0.665654	+	0.384316i
$573$	−9.82102	−	5.67017i	−0.410279	−	0.236875i
$574$	−2.14820	−	3.72079i	−0.0896642	−	0.155303i
$575$	22.2482	+	17.4864i	0.927814	+	0.729234i
$576$	0.400626	+	0.693904i	0.0166927	+	0.0289127i
$577$			42.3965i			1.76499i	0.470324	+	0.882494i	$0.344137\pi$
$577$			42.3965i			1.76499i	−0.470324	+	0.882494i	$0.655863\pi$
$578$			45.3879i			1.88789i
$579$	13.2885	+	23.0163i	0.552250	+	0.956525i
$580$	3.73715	+	7.69060i	0.155177	+	0.319335i
$581$	5.98906			0.248468
$582$			1.41358i			0.0585946i
$583$	12.2498	−	7.07244i	0.507336	−	0.292911i
$584$	3.43828	−	5.95528i	0.142277	−	0.246431i
$585$	6.67526	−	3.24376i	0.275988	−	0.134113i
$586$	8.72173	−	15.1065i	0.360291	−	0.624043i
$587$	−37.8513	−	21.8535i	−1.56229	−	0.901989i	−0.997025	−	0.0770809i	$-0.975440\pi$
$587$	−37.8513	−	21.8535i	−1.56229	−	0.901989i	−0.565266	−	0.824908i	$-0.691227\pi$
$588$			10.0341i			0.413798i
$589$	−32.7368	−	4.47422i	−1.34890	−	0.184357i
$590$	0.258755	−	3.62476i	0.0106528	−	0.149229i
$591$	−13.7677	+	23.8464i	−0.566329	+	0.980911i
$592$	3.03610	+	1.75289i	0.124783	+	0.0720435i
$593$	24.7329	−	14.2795i	1.01566	−	0.586391i	0.102815	−	0.994700i	$-0.467215\pi$
$593$	24.7329	−	14.2795i	1.01566	−	0.586391i	0.912843	+	0.408310i	$0.133882\pi$
$594$	−12.5070	+	21.6628i	−0.513169	+	0.888835i
$595$	−3.72705	−	7.66982i	−0.152794	−	0.314432i
$596$	−12.0420			−0.493260
$597$		−	20.0681i		−	0.821333i
$598$	20.3029	−	11.7219i	0.830247	−	0.479344i
$599$	6.25875	+	10.8405i	0.255726	+	0.442930i	0.965092	−	0.261910i	$-0.0843522\pi$
$599$	6.25875	+	10.8405i	0.255726	+	0.442930i	−0.709367	+	0.704840i	$0.751019\pi$
$600$	7.33891	+	1.05315i	0.299610	+	0.0429945i
$601$	9.44734			0.385365			0.192682	−	0.981261i	$-0.438281\pi$
$601$	9.44734			0.385365			0.192682	+	0.981261i	$0.438281\pi$
$602$	−0.266295	+	0.153746i	−0.0108534	+	0.00626620i
$603$	−9.15607	−	5.28626i	−0.372864	−	0.215273i
$604$	−0.767418	−	1.32921i	−0.0312258	−	0.0540847i
$605$	10.8946	−	16.1014i	0.442926	−	0.654614i
$606$	−4.92829	+	8.53606i	−0.200198	+	0.346754i
$607$			15.1486i			0.614864i	0.951570	+	0.307432i	$0.0994697\pi$
$607$			15.1486i			0.614864i	−0.951570	+	0.307432i	$0.900530\pi$
$608$	4.03527	−	1.64820i	0.163652	−	0.0668434i
$609$	2.73766			0.110936
$610$	−2.72329	−	1.84264i	−0.110263	−	0.0746063i
$611$	8.82548	−	15.2862i	0.357041	−	0.618413i
$612$	5.48087	−	3.16438i	0.221551	−	0.127913i
$613$	−6.36907	−	3.67718i	−0.257244	−	0.148520i	0.365833	−	0.930681i	$-0.380784\pi$
$613$	−6.36907	−	3.67718i	−0.257244	−	0.148520i	−0.623077	+	0.782161i	$0.714118\pi$
$614$	−0.557182	−	0.965067i	−0.0224860	−	0.0389469i
$615$	2.10087	−	29.4300i	0.0847152	−	1.18673i
$616$	−2.14266			−0.0863300
$617$	−26.1606	+	15.1038i	−1.05319	+	0.608057i	−0.923539	−	0.383504i	$-0.874717\pi$
$617$	−26.1606	+	15.1038i	−1.05319	+	0.608057i	−0.129646	+	0.991560i	$0.541384\pi$
$618$	−5.30577	+	3.06329i	−0.213429	+	0.123224i
$619$	−32.0889			−1.28976			−0.644881	−	0.764283i	$-0.723093\pi$
$619$	−32.0889			−1.28976			−0.644881	+	0.764283i	$0.723093\pi$
$620$	16.9067	+	1.20689i	0.678991	+	0.0484699i
$621$	15.9502	+	27.6265i	0.640058	+	1.10861i
$622$	29.2744	+	16.9016i	1.17380	+	0.677691i
$623$	3.66166	−	2.11406i	0.146701	−	0.0846981i
$624$	3.07118	−	5.31943i	0.122945	−	0.212948i
$625$	−18.0840	+	17.2618i	−0.723360	+	0.690471i
$626$	−14.7619			−0.590004
$627$	22.6699	+	17.5735i	0.905347	+	0.701817i
$628$		−	19.0533i		−	0.760309i
$629$	13.8454	−	23.9809i	0.552052	−	0.956183i
$630$	−0.484766	+	0.716450i	−0.0193135	+	0.0285440i
$631$	−5.03414	−	8.71938i	−0.200406	−	0.347113i	0.748253	−	0.663413i	$-0.230893\pi$
$631$	−5.03414	−	8.71938i	−0.200406	−	0.347113i	−0.948659	+	0.316300i	$0.897559\pi$
$632$	−0.997706	−	0.576026i	−0.0396866	−	0.0229131i
$633$	17.1321	−	9.89121i	0.680939	−	0.393140i
$634$	26.1366			1.03802
$635$	−2.28440	+	32.0010i	−0.0906535	+	1.26992i
$636$	−2.36313	−	4.09306i	−0.0937043	−	0.162301i
$637$	−24.2754	+	14.0154i	−0.961826	+	0.555311i
$638$		−	16.9698i		−	0.671842i
$639$	2.26216			0.0894897
$640$	−2.01118	+	0.977310i	−0.0794991	+	0.0386316i
$641$	15.9198	−	27.5740i	0.628796	−	1.08911i	−0.358997	−	0.933339i	$-0.616881\pi$
$641$	15.9198	−	27.5740i	0.628796	−	1.08911i	0.987794	−	0.155768i	$-0.0497854\pi$
$642$	−12.8416	+	7.41409i	−0.506817	+	0.292611i
$643$	34.6879	+	20.0270i	1.36796	+	0.789790i	0.990667	−	0.136306i	$-0.0435230\pi$
$643$	34.6879	+	20.0270i	1.36796	+	0.789790i	0.377289	+	0.926096i	$0.376856\pi$
$644$	−1.36626	+	2.36643i	−0.0538382	+	0.0932506i
$645$	−2.10629	−	0.150358i	−0.0829352	−	0.00592035i
$646$	−13.0185	−	31.8730i	−0.512205	−	1.25403i
$647$		−	5.37891i		−	0.211467i	−0.994395	−	0.105733i	$-0.966281\pi$
$647$		−	5.37891i		−	0.211467i	0.994395	−	0.105733i	$-0.0337190\pi$
$648$	5.15652	+	2.97712i	0.202567	+	0.116952i
$649$	−3.60610	+	6.24594i	−0.141552	+	0.245175i
$650$	7.70299	+	19.2260i	0.302136	+	0.754107i
$651$	2.71344	−	4.69981i	0.106348	−	0.184200i
$652$	8.63023	−	4.98267i	0.337986	−	0.195136i
$653$		−	19.0958i		−	0.747278i	−0.927574	−	0.373639i	$-0.878110\pi$
$653$		−	19.0958i		−	0.747278i	0.927574	−	0.373639i	$-0.121890\pi$
$654$	27.0110			1.05621
$655$	9.77372	+	20.1131i	0.381891	+	0.785885i
$656$	4.44930	+	7.70641i	0.173716	+	0.300885i
$657$			5.50986i			0.214960i
$658$			2.05733i			0.0802032i
$659$	20.3162	+	35.1887i	0.791407	+	1.37076i	0.925096	+	0.379733i	$0.123984\pi$
$659$	20.3162	+	35.1887i	0.791407	+	1.37076i	−0.133690	+	0.991023i	$0.542683\pi$
$660$	−12.1868	−	8.24587i	−0.474371	−	0.320970i
$661$	9.76205	+	16.9084i	0.379700	+	0.657659i	0.991018	−	0.133725i	$-0.0426940\pi$
$661$	9.76205	+	16.9084i	0.379700	+	0.657659i	−0.611319	+	0.791384i	$0.709361\pi$
$662$	1.88038	+	1.08564i	0.0730830	+	0.0421945i
$663$	−42.0161	−	24.2580i	−1.63177	−	0.942102i
$664$	−12.4044			−0.481384
$665$	3.50456	+	3.14067i	0.135901	+	0.121790i
$666$	−2.80902			−0.108847
$667$	−18.7422	−	10.8208i	−0.725699	−	0.418983i
$668$	−6.41331	−	3.70272i	−0.248138	−	0.143263i
$669$	−4.09049	−	7.08493i	−0.158147	−	0.273919i
$670$	16.5344	−	24.4367i	0.638780	−	0.944073i
$671$	3.26287	+	5.65146i	0.125962	+	0.218172i
$672$			0.715931i			0.0276176i
$673$		−	1.79517i		−	0.0691988i	−0.999401	−	0.0345994i	$-0.988984\pi$
$673$		−	1.79517i		−	0.0691988i	0.999401	−	0.0345994i	$-0.0110155\pi$
$674$	−6.56430	−	11.3697i	−0.252847	−	0.437944i
$675$	−26.1612	+	10.4816i	−1.00694	+	0.403436i
$676$	4.15907			0.159964
$677$			6.92605i			0.266190i	0.991103	+	0.133095i	$0.0424915\pi$
$677$			6.92605i			0.266190i	−0.991103	+	0.133095i	$0.957508\pi$
$678$	10.6547	−	6.15149i	0.409191	−	0.236247i
$679$	0.230136	−	0.398607i	0.00883181	−	0.0152971i
$680$	7.71938	+	15.8855i	0.296025	+	0.609183i
$681$	16.4931	−	28.5669i	0.632018	−	1.09469i
$682$	−29.1326	−	16.8197i	−1.11554	−	0.644059i
$683$			11.7972i			0.451407i	0.974196	+	0.225704i	$0.0724681\pi$
$683$			11.7972i			0.451407i	−0.974196	+	0.225704i	$0.927532\pi$
$684$	−2.13978	+	2.76033i	−0.0818166	+	0.105544i
$685$	0.582559	−	8.16079i	0.0222585	−	0.311808i
$686$	3.32345	−	5.75638i	0.126890	−	0.219780i
$687$	−21.1039	−	12.1844i	−0.805165	−	0.464862i
$688$	0.551544	−	0.318434i	0.0210274	−	0.0121402i
$689$	6.60157	−	11.4342i	0.251500	−	0.435610i
$690$	−16.8780	+	8.20164i	−0.642534	+	0.312231i
$691$	15.3361			0.583413			0.291707	−	0.956508i	$-0.405777\pi$
$691$	15.3361			0.583413			0.291707	+	0.956508i	$0.405777\pi$
$692$		−	15.6655i		−	0.595512i
$693$	1.48680	−	0.858403i	0.0564788	−	0.0326080i
$694$	7.46811	+	12.9352i	0.283486	+	0.491012i
$695$	−14.1675	−	1.01135i	−0.537406	−	0.0383628i
$696$	−5.67017			−0.214927
$697$	60.8699	−	35.1432i	2.30561	−	1.33115i
$698$	16.3342	+	9.43056i	0.618259	+	0.356952i
$699$	7.83601	+	13.5724i	0.296385	+	0.513354i
$700$	−1.89801	−	1.49178i	−0.0717379	−	0.0563838i
$701$	5.57300	−	9.65272i	0.210489	−	0.364578i	−0.741378	−	0.671087i	$-0.765828\pi$
$701$	5.57300	−	9.65272i	0.210489	−	0.364578i	0.951868	+	0.306509i	$0.0991609\pi$
$702$			23.3486i			0.881237i
$703$	−2.06930	+	15.1406i	−0.0780452	+	0.571039i
$704$	4.43782			0.167256
$705$	−7.91752	+	11.7015i	−0.298191	+	0.440705i
$706$	−1.00586	+	1.74220i	−0.0378561	+	0.0655686i
$707$	2.77941	−	1.60469i	0.104530	−	0.0603507i
$708$	2.08697	+	1.20491i	0.0784332	+	0.0452834i
$709$	−8.65757	−	14.9954i	−0.325142	−	0.563162i	0.656399	−	0.754414i	$-0.272079\pi$
$709$	−8.65757	−	14.9954i	−0.325142	−	0.563162i	−0.981541	+	0.191252i	$0.938745\pi$
$710$	−0.449515	+	6.29703i	−0.0168700	+	0.236323i
$711$	0.923084			0.0346183
$712$	−7.58395	+	4.37859i	−0.284220	+	0.164095i
$713$	−37.1527	+	21.4501i	−1.39138	+	0.803312i
$714$	5.65485			0.211627
$715$	2.92688	−	41.0013i	0.109459	−	1.53336i
$716$	−2.30642	−	3.99483i	−0.0861949	−	0.149294i
$717$	20.3700	+	11.7606i	0.760732	+	0.439209i
$718$	−5.71469	+	3.29938i	−0.213270	+	0.123132i
$719$	−18.7052	+	32.3983i	−0.697585	+	1.20825i	0.271716	+	0.962377i	$0.412409\pi$
$719$	−18.7052	+	32.3983i	−0.697585	+	1.20825i	−0.969301	+	0.245875i	$0.920925\pi$
$720$	1.00403	−	1.48389i	0.0374182	−	0.0553014i
$721$	1.99486			0.0742926
$722$	13.3019	+	13.5669i	0.495045	+	0.504907i
$723$		−	6.51468i		−	0.242283i
$724$	0.605224	−	1.04828i	0.0224930	−	0.0389590i
$725$	11.8149	−	15.0322i	0.438793	−	0.558282i
$726$	6.44596	+	11.1647i	0.239232	+	0.414362i
$727$	−31.0202	−	17.9095i	−1.15048	−	0.664228i	−0.201474	−	0.979494i	$-0.564573\pi$
$727$	−31.0202	−	17.9095i	−1.15048	−	0.664228i	−0.949003	+	0.315266i	$0.897906\pi$
$728$	−1.73205	+	1.00000i	−0.0641941	+	0.0370625i
$729$	−29.8448			−1.10536
$730$	−15.3374	−	1.09487i	−0.567664	−	0.0405228i
$731$	−2.51518	−	4.35643i	−0.0930274	−	0.161128i
$732$	1.88834	−	1.09023i	0.0697949	−	0.0402961i
$733$		−	20.1867i		−	0.745614i	−0.927909	−	0.372807i	$-0.878395\pi$
$733$		−	20.1867i		−	0.745614i	0.927909	−	0.372807i	$-0.121605\pi$
$734$	−11.1984			−0.413342
$735$	20.1803	−	9.80639i	0.744363	−	0.361714i
$736$	2.82977	−	4.90130i	0.104307	−	0.180664i
$737$	−50.7118	+	29.2785i	−1.86799	+	1.07849i
$738$	−6.17478	−	3.56501i	−0.227297	−	0.131230i
$739$	−19.1178	+	33.1130i	−0.703260	+	1.21808i	0.264056	+	0.964507i	$0.414940\pi$
$739$	−19.1178	+	33.1130i	−0.703260	+	1.21808i	−0.967316	+	0.253575i	$0.918394\pi$
$740$	0.558181	−	7.81928i	0.0205191	−	0.287442i
$741$	26.5273	+	3.62554i	0.974504	+	0.133188i
$742$			1.53891i			0.0564952i
$743$	13.6258	+	7.86688i	0.499884	+	0.288608i	0.728665	−	0.684870i	$-0.240141\pi$
$743$	13.6258	+	7.86688i	0.499884	+	0.288608i	−0.228782	+	0.973478i	$0.573474\pi$
$744$	−5.62000	+	9.73413i	−0.206039	+	0.356870i
$745$	11.7688	+	24.2187i	0.431175	+	0.887305i
$746$	1.59718	−	2.76640i	0.0584771	−	0.101285i
$747$	8.60746	−	4.96952i	0.314930	−	0.181825i
$748$		−	35.0525i		−	1.28165i
$749$	4.82818			0.176418
$750$	−5.05432	−	15.7892i	−0.184558	−	0.576538i
$751$	12.1150	+	20.9838i	0.442083	+	0.765710i	0.997844	−	0.0656323i	$-0.0209064\pi$
$751$	12.1150	+	20.9838i	0.442083	+	0.765710i	−0.555761	+	0.831342i	$0.687573\pi$
$752$		−	4.26110i		−	0.155386i
$753$		−	21.4075i		−	0.780134i
$754$	−7.92000	−	13.7178i	−0.288429	−	0.499574i
$755$	−1.92328	+	2.84247i	−0.0699952	+	0.103448i
$756$	−1.36072	−	2.35683i	−0.0494888	−	0.0857171i
$757$	−12.8226	−	7.40312i	−0.466045	−	0.269071i	0.248538	−	0.968622i	$-0.420050\pi$
$757$	−12.8226	−	7.40312i	−0.466045	−	0.269071i	−0.714582	+	0.699551i	$0.753383\pi$
$758$	−14.9533	−	8.63331i	−0.543130	−	0.313576i
$759$	37.2424			1.35181
$760$	−7.25855	−	6.50488i	−0.263295	−	0.235957i
$761$	−1.98843			−0.0720804			−0.0360402	−	0.999350i	$-0.511474\pi$
$761$	−1.98843			−0.0720804			−0.0360402	+	0.999350i	$0.511474\pi$
$762$	−18.4247	−	10.6375i	−0.667456	−	0.385356i
$763$	−7.61669	−	4.39750i	−0.275743	−	0.159200i
$764$	−3.82392	−	6.62322i	−0.138344	−	0.239620i
$765$	−11.7207	−	7.93047i	−0.423762	−	0.286727i
$766$	−16.0924	−	27.8729i	−0.581443	−	1.00709i
$767$			6.73202i			0.243079i
$768$		−	1.48282i		−	0.0535066i
$769$	−14.9388	−	25.8748i	−0.538708	−	0.933070i	−0.998974	−	0.0452890i	$-0.985579\pi$
$769$	−14.9388	−	25.8748i	−0.538708	−	0.933070i	0.460266	−	0.887781i	$-0.347754\pi$
$770$	2.09404	+	4.30928i	0.0754639	+	0.155296i
$771$	16.3633			0.589311
$772$			17.9233i			0.645072i
$773$	−10.9462	+	6.31979i	−0.393707	+	0.227307i	−0.683765	−	0.729702i	$-0.739659\pi$
$773$	−10.9462	+	6.31979i	−0.393707	+	0.227307i	0.290058	+	0.957009i	$0.406325\pi$
$774$	−0.255146	+	0.441926i	−0.00917103	+	0.0158847i
$775$	−14.0958	−	35.1821i	−0.506338	−	1.26378i
$776$	−0.476652	+	0.825585i	−0.0171108	+	0.0296368i
$777$	−2.17364	−	1.25495i	−0.0779788	−	0.0450211i
$778$		−	10.0717i		−	0.361090i
$779$	−23.7641	+	30.6559i	−0.851439	+	1.09836i
$780$	−13.6999	−	0.977967i	−0.490533	−	0.0350168i
$781$	6.26461	−	10.8506i	0.224165	−	0.388266i
$782$	−38.7134	−	22.3512i	−1.38439	−	0.799277i
$783$	18.6661	−	10.7769i	0.667072	−	0.385134i
$784$	−3.38344	+	5.86030i	−0.120837	+	0.209296i
$785$	−38.3197	+	18.6210i	−1.36769	+	0.664611i
$786$	−14.8291			−0.528937
$787$		−	46.4316i		−	1.65511i	−0.561387	−	0.827554i	$-0.689732\pi$
$787$		−	46.4316i		−	1.65511i	0.561387	−	0.827554i	$-0.310268\pi$
$788$	−16.0818	+	9.28485i	−0.572892	+	0.330759i
$789$	15.6631	+	27.1292i	0.557620	+	0.965826i
$790$	−0.183426	+	2.56953i	−0.00652602	+	0.0914197i
$791$	−4.00595			−0.142435
$792$	−3.07942	+	1.77790i	−0.109422	+	0.0631751i
$793$	5.27519	+	3.04563i	0.187328	+	0.108154i
$794$	−17.7217	−	30.6949i	−0.628921	−	1.08932i
$795$	−5.92240	+	8.75289i	−0.210046	+	0.310433i
$796$	6.76689	−	11.7206i	0.239846	−	0.415425i
$797$			51.4600i			1.82281i	0.411513	+	0.911404i	$0.365000\pi$
$797$			51.4600i			1.82281i	−0.411513	+	0.911404i	$0.635000\pi$
$798$	−2.88898	+	1.18000i	−0.102269	+	0.0417714i
$799$	−33.6567			−1.19069
$800$	3.93110	+	3.08973i	0.138985	+	0.109238i
$801$	3.50836	−	6.07665i	0.123962	−	0.214708i
$802$	26.8036	−	15.4751i	0.946470	−	0.546445i
$803$	26.4284	+	15.2585i	0.932639	+	0.538460i
$804$	9.78289	+	16.9445i	0.345016	+	0.597585i
$805$	6.09460	+	0.435064i	0.214806	+	0.0153340i
$806$	−31.3997			−1.10601
$807$	−36.3373	+	20.9794i	−1.27913	+	0.738508i
$808$	−5.75665	+	3.32360i	−0.202518	+	0.116924i
$809$	−14.0066			−0.492446			−0.246223	−	0.969213i	$-0.579189\pi$
$809$	−14.0066			−0.492446			−0.246223	+	0.969213i	$0.579189\pi$
$810$	0.948017	−	13.2803i	0.0333099	−	0.466622i
$811$	−21.9071	−	37.9442i	−0.769263	−	1.33240i	−0.937963	−	0.346735i	$-0.887290\pi$
$811$	−21.9071	−	37.9442i	−0.769263	−	1.33240i	0.168700	−	0.985667i	$-0.446043\pi$
$812$	1.59890	+	0.923127i	0.0561105	+	0.0323954i
$813$	15.8124	−	9.12930i	0.554565	−	0.320178i
$814$	−7.77902	+	13.4737i	−0.272654	+	0.472251i
$815$	−18.4555	−	12.4874i	−0.646467	−	0.437414i
$816$	−11.7122			−0.410008
$817$	2.19402	+	1.70079i	0.0767592	+	0.0595030i
$818$			27.1167i			0.948113i
$819$	0.801252	−	1.38781i	0.0279980	−	0.0484940i
$820$	11.1507	−	16.4799i	0.389399	−	0.575504i
$821$	15.0983	+	26.1510i	0.526934	+	0.912676i	0.999507	+	0.0313848i	$0.00999175\pi$
$821$	15.0983	+	26.1510i	0.526934	+	0.912676i	−0.472574	+	0.881291i	$0.656675\pi$
$822$	4.69861	+	2.71274i	0.163883	+	0.0946177i
$823$	8.29314	−	4.78805i	0.289081	−	0.166901i	−0.348447	−	0.937329i	$-0.613291\pi$
$823$	8.29314	−	4.78805i	0.289081	−	0.166901i	0.637527	+	0.770428i	$0.279957\pi$
$824$	−4.13171			−0.143935
$825$	−4.67367	+	32.5687i	−0.162716	+	1.13390i
$826$	−0.392330	−	0.679535i	−0.0136509	−	0.0236441i
$827$	44.0158	−	25.4125i	1.53058	−	0.883681i	0.531245	−	0.847218i	$-0.321724\pi$
$827$	44.0158	−	25.4125i	1.53058	−	0.883681i	0.999335	−	0.0364625i	$-0.0116089\pi$
$828$			4.53471i			0.157592i
$829$	40.5305			1.40768			0.703841	−	0.710358i	$-0.251467\pi$
$829$	40.5305			1.40768			0.703841	+	0.710358i	$0.251467\pi$
$830$	12.1229	+	24.9475i	0.420793	+	0.865941i
$831$	−20.2165	+	35.0160i	−0.701303	+	1.21469i
$832$	3.58738	−	2.07118i	0.124370	−	0.0718051i
$833$	46.2881	+	26.7245i	1.60379	+	0.925948i
$834$	4.70946	−	8.15702i	0.163075	−	0.282455i
$835$	−1.17907	+	16.5171i	−0.0408035	+	0.571596i
$836$	7.31441	+	17.9078i	0.252974	+	0.619354i
$837$		−	42.7261i		−	1.47683i
$838$	7.17162	+	4.14054i	0.247740	+	0.143033i
$839$	12.9569	−	22.4420i	0.447322	−	0.774785i	−0.550888	−	0.834579i	$-0.685711\pi$
$839$	12.9569	−	22.4420i	0.447322	−	0.774785i	0.998211	+	0.0597940i	$0.0190444\pi$
$840$	1.43987	−	0.699686i	0.0496802	−	0.0241415i
$841$	7.18883	−	12.4514i	0.247891	−	0.429359i
$842$	−5.12323	+	2.95790i	−0.176558	+	0.101936i
$843$		−	13.7506i		−	0.473597i
$844$	13.3411			0.459220
$845$	−4.06470	−	8.36465i	−0.139830	−	0.287753i
$846$	1.70711	+	2.95680i	0.0586915	+	0.101657i
$847$		−	4.19771i		−	0.144235i
$848$		−	3.18735i		−	0.109454i
$849$	19.2817	+	33.3970i	0.661748	+	1.14618i
$850$	24.4045	−	31.0502i	0.837069	−	1.06501i
$851$	9.92056	+	17.1829i	0.340072	+	0.589023i
$852$	−3.62554	−	2.09321i	−0.124209	−	0.0717121i
$853$	18.3182	+	10.5760i	0.627204	+	0.362116i	0.779668	−	0.626193i	$-0.215388\pi$
$853$	18.3182	+	10.5760i	0.627204	+	0.362116i	−0.152465	+	0.988309i	$0.548721\pi$
$854$	−0.709977			−0.0242949
$855$	7.64276	+	1.60580i	0.261377	+	0.0549172i
$856$	−10.0000			−0.341793
$857$	−15.1082	−	8.72273i	−0.516087	−	0.297963i	0.219245	−	0.975670i	$-0.429640\pi$
$857$	−15.1082	−	8.72273i	−0.516087	−	0.297963i	−0.735332	+	0.677707i	$0.762974\pi$
$858$	23.6067	+	13.6293i	0.805918	+	0.465297i
$859$	−21.0863	−	36.5225i	−0.719454	−	1.24613i	−0.961216	−	0.275796i	$-0.911059\pi$
$859$	−21.0863	−	36.5225i	−0.719454	−	1.24613i	0.241762	−	0.970336i	$-0.422275\pi$
$860$	−1.17946	−	0.798048i	−0.0402192	−	0.0272132i
$861$	−3.18539	−	5.51726i	−0.108558	−	0.188028i
$862$			14.9705i			0.509898i
$863$		−	29.1252i		−	0.991434i	−0.868484	−	0.495717i	$-0.834905\pi$
$863$		−	29.1252i		−	0.991434i	0.868484	−	0.495717i	$-0.165095\pi$
$864$	2.81828	+	4.88141i	0.0958799	+	0.166069i
$865$	−31.5062	+	15.3100i	−1.07124	+	0.520557i
$866$	3.35174			0.113897
$867$			67.3019i			2.28569i
$868$	3.16951	−	1.82992i	0.107580	−	0.0621115i
$869$	2.55630	−	4.42764i	0.0867164	−	0.150197i
$870$	5.54152	+	11.4038i	0.187875	+	0.386624i
$871$	−27.3292	+	47.3355i	−0.926013	+	1.60390i
$872$	15.7755	+	9.10799i	0.534226	+	0.308435i
$873$		−	0.763836i		−	0.0258519i
$874$	24.4421	+	3.34056i	0.826767	+	0.112996i
$875$	−1.14530	+	5.27517i	−0.0387181	+	0.178333i
$876$	5.09835	−	8.83060i	0.172257	−	0.298358i
$877$	8.82966	+	5.09781i	0.298156	+	0.172141i	0.641614	−	0.767027i	$-0.278265\pi$
$877$	8.82966	+	5.09781i	0.298156	+	0.172141i	−0.343458	+	0.939168i	$0.611598\pi$
$878$	10.3943	−	6.00116i	0.350791	−	0.202529i
$879$	12.9327	−	22.4002i	0.436210	−	0.755539i
$880$	−4.33712	−	8.92527i	−0.146204	−	0.300871i
$881$	2.18109			0.0734829			0.0367415	−	0.999325i	$-0.488302\pi$
$881$	2.18109			0.0734829			0.0367415	+	0.999325i	$0.488302\pi$
$882$		−	5.42198i		−	0.182568i
$883$	5.76125	−	3.32626i	0.193881	−	0.111938i	−0.399917	−	0.916551i	$-0.630961\pi$
$883$	5.76125	−	3.32626i	0.193881	−	0.111938i	0.593798	+	0.804614i	$0.297628\pi$
$884$	−16.3594	−	28.3353i	−0.550226	−	0.953019i
$885$	0.383686	−	5.37486i	0.0128975	−	0.180674i
$886$	−26.7944			−0.900175
$887$	−0.308694	+	0.178225i	−0.0103649	+	0.00598419i	−0.505174	−	0.863018i	$-0.668572\pi$
$887$	−0.308694	+	0.178225i	−0.0103649	+	0.00598419i	0.494809	+	0.869002i	$0.335238\pi$
$888$	4.50198	+	2.59922i	0.151077	+	0.0872242i
$889$	3.46366	+	5.99923i	0.116167	+	0.201208i
$890$	16.2180	+	10.9735i	0.543629	+	0.367832i
$891$	−13.2119	+	22.8837i	−0.442616	+	0.766633i
$892$		−	5.51718i		−	0.184729i
$893$	17.1947	−	7.02315i	0.575399	−	0.235021i
$894$	−17.8561			−0.597198
$895$	−5.78026	+	8.54283i	−0.193213	+	0.285555i
$896$	−0.241409	+	0.418132i	−0.00806490	+	0.0139688i
$897$	30.1055	−	17.3814i	1.00519	−	0.580349i
$898$	−3.06233	−	1.76804i	−0.102191	−	0.0590002i
$899$	14.4930	+	25.1025i	0.483367	+	0.837217i
$900$	−3.96564	−	0.569075i	−0.132188	−	0.0189692i
$901$	−25.1756			−0.838722
$902$	−34.1996	+	19.7452i	−1.13872	+	0.657442i
$903$	−0.394867	+	0.227977i	−0.0131404	+	0.00758659i
$904$	8.29703			0.275955
$905$	−2.69977	−	0.192724i	−0.0897435	−	0.00640636i
$906$	−1.13794	−	1.97097i	−0.0378056	−	0.0654812i
$907$	15.4418	+	8.91530i	0.512735	+	0.296028i	0.733957	−	0.679196i	$-0.237671\pi$
$907$	15.4418	+	8.91530i	0.512735	+	0.296028i	−0.221222	+	0.975223i	$0.571005\pi$
$908$	19.2653	−	11.1228i	0.639341	−	0.369124i
$909$	2.66304	−	4.61252i	0.0883275	−	0.152988i
$910$	3.70394	+	2.50616i	0.122784	+	0.0830785i
$911$	44.1391			1.46239			0.731196	−	0.682167i	$-0.238962\pi$
$911$	44.1391			1.46239			0.731196	+	0.682167i	$0.238962\pi$
$912$	5.98358	−	2.44398i	0.198136	−	0.0809283i
$913$		−	55.0484i		−	1.82184i
$914$	10.7573	−	18.6323i	0.355821	−	0.616301i
$915$	−4.03815	−	2.73230i	−0.133497	−	0.0903270i
$916$	−8.21703	−	14.2323i	−0.271498	−	0.470249i
$917$	4.18159	+	2.41424i	0.138088	+	0.0797253i
$918$	38.5563	−	22.2605i	1.27255	−	0.734705i
$919$	19.5399			0.644563			0.322281	−	0.946644i	$-0.395550\pi$
$919$	19.5399			0.644563			0.322281	+	0.946644i	$0.395550\pi$
$920$	−12.6230	−	0.901094i	−0.416167	−	0.0297082i
$921$	−0.826199	−	1.43102i	−0.0272242	−	0.0471537i
$922$	−34.9825	+	20.1971i	−1.15209	+	0.665157i
$923$		−	11.6950i		−	0.384947i
$924$	−3.17717			−0.104521
$925$	−16.2715	+	6.51926i	−0.535005	+	0.214352i
$926$	9.82241	−	17.0129i	0.322784	−	0.559079i
$927$	2.86701	−	1.65527i	0.0941651	−	0.0543662i
$928$	−3.31161	−	1.91196i	−0.108709	−	0.0627631i
$929$	9.78639	−	16.9505i	0.321081	−	0.556129i	−0.659630	−	0.751590i	$-0.729287\pi$
$929$	9.78639	−	16.9505i	0.321081	−	0.556129i	0.980711	+	0.195461i	$0.0626204\pi$
$930$	25.0696	+	1.78960i	0.822065	+	0.0586833i
$931$	−29.2245	−	3.99418i	−0.957794	−	0.130904i
$932$			10.5691i			0.346202i
$933$	43.4086	+	25.0620i	1.42113	+	0.820492i
$934$	7.59644	−	13.1574i	0.248563	−	0.430524i
$935$	−70.4971	+	34.2572i	−2.30550	+	1.12033i
$936$	−1.65953	+	2.87440i	−0.0542435	+	0.0939525i
$937$	−8.41560	+	4.85875i	−0.274926	+	0.158728i	−0.631124	−	0.775682i	$-0.717406\pi$
$937$	−8.41560	+	4.85875i	−0.274926	+	0.158728i	0.356198	+	0.934410i	$0.384073\pi$
$938$		−	6.37078i		−	0.208013i
$939$	−21.8892			−0.714327
$940$	−8.56986	+	4.16442i	−0.279518	+	0.135828i
$941$	20.1536	+	34.9071i	0.656989	+	1.13794i	0.981391	+	0.192019i	$0.0615037\pi$
$941$	20.1536	+	34.9071i	0.656989	+	1.13794i	−0.324402	+	0.945919i	$0.605163\pi$
$942$		−	28.2525i		−	0.920518i
$943$			50.3619i			1.64001i
$944$	0.812584	+	1.40744i	0.0264474	+	0.0458082i
$945$	−3.41018	+	5.04001i	−0.110933	+	0.163951i
$946$	1.41315	+	2.44765i	0.0459455	+	0.0795800i
$947$	13.8707	+	8.00828i	0.450739	+	0.260234i	0.708142	−	0.706070i	$-0.249534\pi$
$947$	13.8707	+	8.00828i	0.450739	+	0.260234i	−0.257403	+	0.966304i	$0.582867\pi$
$948$	−1.47942	−	0.854141i	−0.0480492	−	0.0277412i
$949$	28.4851			0.924667
$950$	−5.98866	+	20.9556i	−0.194298	+	0.679889i
$951$	38.7558			1.25674
$952$	3.30266	+	1.90679i	0.107040	+	0.0617995i
$953$	−20.7652	−	11.9888i	−0.672649	−	0.388354i	0.124430	−	0.992228i	$-0.460290\pi$
$953$	−20.7652	−	11.9888i	−0.672649	−	0.388354i	−0.797080	+	0.603874i	$0.793623\pi$
$954$	1.27694	+	2.21172i	0.0413423	+	0.0716070i
$955$	−9.58336	+	14.1635i	−0.310110	+	0.458321i
$956$	7.93127	+	13.7374i	0.256516	+	0.444298i
$957$		−	25.1632i		−	0.813410i
$958$		−	4.24064i		−	0.137009i
$959$	−0.883291	−	1.52991i	−0.0285230	−	0.0494032i
$960$	−2.98222	+	1.44917i	−0.0962508	+	0.0467718i
$961$	26.4589			0.853513
$962$			14.5222i			0.468215i
$963$	6.93904	−	4.00626i	0.223608	−	0.129100i
$964$	2.19672	−	3.80483i	0.0707517	−	0.122545i
$965$	36.0470	−	17.5166i	1.16039	−	0.563879i
$966$	−2.02592	+	3.50899i	−0.0651828	+	0.112900i
$967$	20.6783	+	11.9386i	0.664969	+	0.383920i	0.794168	−	0.607699i	$-0.207907\pi$
$967$	20.6783	+	11.9386i	0.664969	+	0.383920i	−0.129199	+	0.991619i	$0.541241\pi$
$968$			8.69420i			0.279442i
$969$	−19.3040	−	47.2619i	−0.620135	−	1.51827i
$970$	2.12624	+	0.151782i	0.0682695	+	0.00487343i
$971$	5.71587	−	9.90017i	0.183431	−	0.317712i	−0.759616	−	0.650372i	$-0.774613\pi$
$971$	5.71587	−	9.90017i	0.183431	−	0.317712i	0.943047	+	0.332660i	$0.107946\pi$
$972$	−6.99804	−	4.04032i	−0.224462	−	0.129593i
$973$	−2.65599	+	1.53344i	−0.0851473	+	0.0491598i
$974$	−4.00416	+	6.93540i	−0.128301	+	0.222225i
$975$	11.4221	+	28.5087i	0.365801	+	0.913009i
$976$	1.47049			0.0470691
$977$		−	22.3158i		−	0.713947i	−0.934115	−	0.356973i	$-0.883809\pi$
$977$		−	22.3158i		−	0.713947i	0.934115	−	0.356973i	$-0.116191\pi$
$978$	12.7971	−	7.38838i	0.409205	−	0.236254i
$979$	−19.4314	−	33.6561i	−0.621030	−	1.07566i
$980$	15.0928	+	1.07740i	0.482122	+	0.0344164i
$981$	−14.5956			−0.466001
$982$	14.7888	−	8.53834i	0.471931	−	0.272469i
$983$	32.7268	+	18.8948i	1.04382	+	0.602652i	0.920914	−	0.389766i	$-0.127444\pi$
$983$	32.7268	+	18.8948i	1.04382	+	0.602652i	0.122910	+	0.992418i	$0.460777\pi$
$984$	6.59750	+	11.4272i	0.210321	+	0.364286i
$985$	34.3905	+	23.2694i	1.09577	+	0.741424i
$986$	−15.1018	+	26.1571i	−0.480939	+	0.833011i
$987$			3.05065i			0.0971033i
$988$	14.2705	+	11.0624i	0.454005	+	0.351940i
$989$	3.60438			0.114613
$990$	6.58524	+	4.45572i	0.209293	+	0.141612i
$991$	−22.4330	+	38.8551i	−0.712608	+	1.23427i	0.251267	+	0.967918i	$0.419153\pi$
$991$	−22.4330	+	38.8551i	−0.712608	+	1.23427i	−0.963875	+	0.266355i	$0.914181\pi$
$992$	−6.56462	+	3.79008i	−0.208427	+	0.120335i
$993$	2.78826	+	1.60980i	0.0884827	+	0.0510855i
$994$	0.681566	+	1.18051i	0.0216180	+	0.0374434i
$995$	−30.1856	−	2.15481i	−0.956949	−	0.0683120i
$996$	−18.3934			−0.582819
$997$	−49.1961	+	28.4034i	−1.55806	+	0.899544i	−0.560612	+	0.828079i	$0.689434\pi$
$997$	−49.1961	+	28.4034i	−1.55806	+	0.899544i	−0.997443	+	0.0714649i	$0.977233\pi$
$998$	9.76389	−	5.63718i	0.309071	−	0.178442i
$999$	−19.7606			−0.625197

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	190.2.i.a.49.9	yes	20
3.2	odd	2		1710.2.t.d.1189.2		20
5.2	odd	4		950.2.e.n.201.4		10
5.3	odd	4		950.2.e.o.201.2		10
5.4	even	2	inner	190.2.i.a.49.2	✓	20
15.14	odd	2		1710.2.t.d.1189.7		20
19.7	even	3	inner	190.2.i.a.159.2	yes	20
57.26	odd	6		1710.2.t.d.919.7		20
95.7	odd	12		950.2.e.n.501.4		10
95.64	even	6	inner	190.2.i.a.159.9	yes	20
95.83	odd	12		950.2.e.o.501.2		10
285.254	odd	6		1710.2.t.d.919.2		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.2.i.a.49.2	✓	20	5.4	even	2	inner
190.2.i.a.49.9	yes	20	1.1	even	1	trivial
190.2.i.a.159.2	yes	20	19.7	even	3	inner
190.2.i.a.159.9	yes	20	95.64	even	6	inner
950.2.e.n.201.4		10	5.2	odd	4
950.2.e.n.501.4		10	95.7	odd	12
950.2.e.o.201.2		10	5.3	odd	4
950.2.e.o.501.2		10	95.83	odd	12
1710.2.t.d.919.2		20	285.254	odd	6
1710.2.t.d.919.7		20	57.26	odd	6
1710.2.t.d.1189.2		20	3.2	odd	2
1710.2.t.d.1189.7		20	15.14	odd	2

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:	\( N \)	\(=\)	\( 190 = 2 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	190.i (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(1.28416 + 0.741409i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.25308 - 1.85197i) q^{5} +(0.741409 + 1.28416i) q^{6} -0.482818i q^{7} +1.00000i q^{8} +(-0.400626 - 0.693904i) q^{9} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(1.28416 + 0.741409i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.25308 - 1.85197i) q^{5} +(0.741409 + 1.28416i) q^{6} -0.482818i q^{7} +1.00000i q^{8} +(-0.400626 - 0.693904i) q^{9} +(2.01118 - 0.977310i) q^{10} -4.43782 q^{11} +1.48282i q^{12} +(-3.58738 + 2.07118i) q^{13} +(0.241409 - 0.418132i) q^{14} +(2.98222 - 1.44917i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(6.84039 + 3.94930i) q^{17} -0.801252i q^{18} +(-4.31875 - 0.590253i) q^{19} +(2.23039 + 0.159217i) q^{20} +(0.357965 - 0.620014i) q^{21} +(-3.84326 - 2.21891i) q^{22} +(-4.90130 + 2.82977i) q^{23} +(-0.741409 + 1.28416i) q^{24} +(-1.85957 - 4.64134i) q^{25} -4.14235 q^{26} -5.63656i q^{27} +(0.418132 - 0.241409i) q^{28} +(1.91196 + 3.31161i) q^{29} +(3.30727 + 0.236090i) q^{30} +7.58017 q^{31} +(-0.866025 + 0.500000i) q^{32} +(-5.69885 - 3.29024i) q^{33} +(3.94930 + 6.84039i) q^{34} +(-0.894163 - 0.605010i) q^{35} +(0.400626 - 0.693904i) q^{36} -3.50579i q^{37} +(-3.44502 - 2.67055i) q^{38} -6.14235 q^{39} +(1.85197 + 1.25308i) q^{40} +(4.44930 - 7.70641i) q^{41} +(0.620014 - 0.357965i) q^{42} +(-0.551544 - 0.318434i) q^{43} +(-2.21891 - 3.84326i) q^{44} +(-1.78711 - 0.127573i) q^{45} -5.65953 q^{46} +(-3.69022 + 2.13055i) q^{47} +(-1.28416 + 0.741409i) q^{48} +6.76689 q^{49} +(0.710233 - 4.94930i) q^{50} +(5.85609 + 10.1430i) q^{51} +(-3.58738 - 2.07118i) q^{52} +(-2.76033 + 1.59368i) q^{53} +(2.81828 - 4.88141i) q^{54} +(-5.56095 + 8.21869i) q^{55} +0.482818 q^{56} +(-5.10834 - 3.95994i) q^{57} +3.82392i q^{58} +(0.812584 - 1.40744i) q^{59} +(2.74613 + 1.85809i) q^{60} +(-0.735243 - 1.27348i) q^{61} +(6.56462 + 3.79008i) q^{62} +(-0.335029 + 0.193429i) q^{63} -1.00000 q^{64} +(-0.659533 + 9.23907i) q^{65} +(-3.29024 - 5.69885i) q^{66} +(11.4272 - 6.59750i) q^{67} +7.89860i q^{68} -8.39206 q^{69} +(-0.471863 - 0.971036i) q^{70} +(-1.41164 + 2.44504i) q^{71} +(0.693904 - 0.400626i) q^{72} +(-5.95528 - 3.43828i) q^{73} +(1.75289 - 3.03610i) q^{74} +(1.05315 - 7.33891i) q^{75} +(-1.64820 - 4.03527i) q^{76} +2.14266i q^{77} +(-5.31943 - 3.07118i) q^{78} +(-0.576026 + 0.997706i) q^{79} +(0.977310 + 2.01118i) q^{80} +(2.97712 - 5.15652i) q^{81} +(7.70641 - 4.44930i) q^{82} +12.4044i q^{83} +0.715931 q^{84} +(15.8855 - 7.71938i) q^{85} +(-0.318434 - 0.551544i) q^{86} +5.67017i q^{87} -4.43782i q^{88} +(4.37859 + 7.58395i) q^{89} +(-1.48389 - 1.00403i) q^{90} +(1.00000 + 1.73205i) q^{91} +(-4.90130 - 2.82977i) q^{92} +(9.73413 + 5.62000i) q^{93} -4.26110 q^{94} +(-6.50488 + 7.25855i) q^{95} -1.48282 q^{96} +(0.825585 + 0.476652i) q^{97} +(5.86030 + 3.38344i) q^{98} +(1.77790 + 3.07942i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 10 q^{4} - 2 q^{5} + 10 q^{9}+O(q^{10}) \) 20 * q + 10 * q^4 - 2 * q^5 + 10 * q^9	\( 20 q + 10 q^{4} - 2 q^{5} + 10 q^{9} - 12 q^{11} - 10 q^{14} - 2 q^{15} - 10 q^{16} - 22 q^{19} - 4 q^{20} + 40 q^{21} - 6 q^{25} + 8 q^{26} - 4 q^{29} + 12 q^{30} - 16 q^{31} - 8 q^{34} - 2 q^{35} - 10 q^{36} - 32 q^{39} + 2 q^{41} - 6 q^{44} - 56 q^{45} - 52 q^{46} + 40 q^{49} + 40 q^{50} + 8 q^{51} + 36 q^{54} + 18 q^{55} - 20 q^{56} - 44 q^{59} + 2 q^{60} - 4 q^{61} - 20 q^{64} + 48 q^{65} + 4 q^{66} + 48 q^{69} - 8 q^{70} - 44 q^{71} + 10 q^{74} - 56 q^{75} + 4 q^{76} - 4 q^{79} - 2 q^{80} - 10 q^{81} + 80 q^{84} + 12 q^{85} + 2 q^{89} + 42 q^{90} + 20 q^{91} - 40 q^{94} - 4 q^{95} - 26 q^{99}+O(q^{100}) \) 20 * q + 10 * q^4 - 2 * q^5 + 10 * q^9 - 12 * q^11 - 10 * q^14 - 2 * q^15 - 10 * q^16 - 22 * q^19 - 4 * q^20 + 40 * q^21 - 6 * q^25 + 8 * q^26 - 4 * q^29 + 12 * q^30 - 16 * q^31 - 8 * q^34 - 2 * q^35 - 10 * q^36 - 32 * q^39 + 2 * q^41 - 6 * q^44 - 56 * q^45 - 52 * q^46 + 40 * q^49 + 40 * q^50 + 8 * q^51 + 36 * q^54 + 18 * q^55 - 20 * q^56 - 44 * q^59 + 2 * q^60 - 4 * q^61 - 20 * q^64 + 48 * q^65 + 4 * q^66 + 48 * q^69 - 8 * q^70 - 44 * q^71 + 10 * q^74 - 56 * q^75 + 4 * q^76 - 4 * q^79 - 2 * q^80 - 10 * q^81 + 80 * q^84 + 12 * q^85 + 2 * q^89 + 42 * q^90 + 20 * q^91 - 40 * q^94 - 4 * q^95 - 26 * q^99

Introduction

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