LMFDB - Embedded newform 425.2.r.a.69.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [425,2,Mod(69,425)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(425, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([9, 0]))

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

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

chi := DirichletCharacter("425.69");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	425.r (of order $10$, degree $4$, 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:	$3.39364208590$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$40$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			69.9
Character	$\chi$	$=$	425.69
Dual form			425.2.r.a.154.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.63738 + 0.532018i) q^{2} +(-1.52304 - 2.09629i) q^{3} +(0.779945 - 0.566663i) q^{4} +(2.20989 - 0.341170i) q^{5} +(3.60906 + 2.62214i) q^{6} -0.996248i q^{7} +(1.04832 - 1.44289i) q^{8} +(-1.14771 + 3.53228i) q^{9} +(-3.43692 + 1.73433i) q^{10} +(1.27455 + 3.92267i) q^{11} +(-2.37577 - 0.771936i) q^{12} +(4.61707 + 1.50018i) q^{13} +(0.530022 + 1.63124i) q^{14} +(-4.08094 - 4.11294i) q^{15} +(-1.54469 + 4.75405i) q^{16} +(0.587785 - 0.809017i) q^{17} -6.39430i q^{18} +(-2.33736 - 1.69819i) q^{19} +(1.53026 - 1.51836i) q^{20} +(-2.08842 + 1.51733i) q^{21} +(-4.17386 - 5.74482i) q^{22} +(1.89422 - 0.615470i) q^{23} -4.62135 q^{24} +(4.76721 - 1.50790i) q^{25} -8.35804 q^{26} +(1.75969 - 0.571757i) q^{27} +(-0.564537 - 0.777019i) q^{28} +(3.25890 - 2.36773i) q^{29} +(8.87021 + 4.56332i) q^{30} +(1.47575 + 1.07219i) q^{31} -5.03898i q^{32} +(6.28183 - 8.64620i) q^{33} +(-0.532018 + 1.63738i) q^{34} +(-0.339890 - 2.20160i) q^{35} +(1.10647 + 3.40535i) q^{36} +(5.22873 + 1.69892i) q^{37} +(4.73062 + 1.53707i) q^{38} +(-3.88719 - 11.9635i) q^{39} +(1.82440 - 3.54629i) q^{40} +(3.35669 - 10.3308i) q^{41} +(2.61230 - 3.59552i) q^{42} -2.44766i q^{43} +(3.21691 + 2.33722i) q^{44} +(-1.33120 + 8.19751i) q^{45} +(-2.77412 + 2.01552i) q^{46} +(-3.13496 - 4.31490i) q^{47} +(12.3185 - 4.00251i) q^{48} +6.00749 q^{49} +(-7.00351 + 5.00524i) q^{50} -2.59115 q^{51} +(4.45116 - 1.44627i) q^{52} +(-8.30687 - 11.4334i) q^{53} +(-2.57710 + 1.87237i) q^{54} +(4.15491 + 8.23381i) q^{55} +(-1.43748 - 1.04439i) q^{56} +7.48619i q^{57} +(-4.07639 + 5.61067i) q^{58} +(-1.19379 + 3.67410i) q^{59} +(-5.51356 - 0.895349i) q^{60} +(2.68092 + 8.25103i) q^{61} +(-2.98679 - 0.970468i) q^{62} +(3.51903 + 1.14340i) q^{63} +(-0.408545 - 1.25737i) q^{64} +(10.7150 + 1.74002i) q^{65} +(-5.68583 + 17.4992i) q^{66} +(1.24040 - 1.70726i) q^{67} -0.964065i q^{68} +(-4.17517 - 3.03344i) q^{69} +(1.72782 + 3.42403i) q^{70} +(3.69156 - 2.68208i) q^{71} +(3.89354 + 5.35899i) q^{72} +(-13.3880 + 4.35002i) q^{73} -9.46529 q^{74} +(-10.4216 - 7.69684i) q^{75} -2.78532 q^{76} +(3.90795 - 1.26977i) q^{77} +(12.7296 + 17.5208i) q^{78} +(-9.28545 + 6.74628i) q^{79} +(-1.79164 + 11.0329i) q^{80} +(5.13558 + 3.73122i) q^{81} +18.7013i q^{82} +(-2.02930 + 2.79309i) q^{83} +(-0.769040 + 2.36686i) q^{84} +(1.02293 - 1.98837i) q^{85} +(1.30220 + 4.00775i) q^{86} +(-9.92686 - 3.22543i) q^{87} +(6.99613 + 2.27318i) q^{88} +(-1.36801 - 4.21031i) q^{89} +(-2.18154 - 14.1307i) q^{90} +(1.49455 - 4.59975i) q^{91} +(1.12862 - 1.55342i) q^{92} -4.72659i q^{93} +(7.42873 + 5.39729i) q^{94} +(-5.74468 - 2.95538i) q^{95} +(-10.5631 + 7.67457i) q^{96} +(-3.16413 - 4.35506i) q^{97} +(-9.83656 + 3.19609i) q^{98} -15.3188 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q + 40 q^{4} - 8 q^{5} + 4 q^{6} - 30 q^{8} + 36 q^{9} - 6 q^{10} + 8 q^{11} - 40 q^{12} - 20 q^{14} - 40 q^{15} - 64 q^{16} + 6 q^{19} + 2 q^{20} - 50 q^{22} + 20 q^{23} + 20 q^{24} + 32 q^{25} + 20 q^{26}+ \cdots + 44 q^{99}+O(q^{100}) $ 160 * q + 40 * q^4 - 8 * q^5 + 4 * q^6 - 30 * q^8 + 36 * q^9 - 6 * q^10 + 8 * q^11 - 40 * q^12 - 20 * q^14 - 40 * q^15 - 64 * q^16 + 6 * q^19 + 2 * q^20 - 50 * q^22 + 20 * q^23 + 20 * q^24 + 32 * q^25 + 20 * q^26 + 30 * q^27 + 60 * q^28 + 16 * q^30 + 12 * q^31 - 40 * q^33 - 4 * q^34 - 54 * q^36 - 40 * q^38 - 12 * q^39 - 52 * q^40 - 2 * q^41 + 30 * q^42 - 20 * q^44 + 42 * q^45 + 48 * q^46 + 40 * q^47 - 100 * q^48 - 184 * q^49 + 46 * q^50 - 32 * q^51 - 10 * q^52 - 20 * q^53 - 40 * q^54 + 18 * q^55 + 24 * q^56 - 120 * q^58 + 6 * q^59 - 40 * q^60 + 12 * q^61 - 10 * q^62 + 90 * q^63 + 58 * q^64 - 20 * q^65 + 48 * q^66 - 90 * q^67 - 74 * q^69 - 120 * q^70 - 16 * q^71 - 10 * q^72 + 52 * q^74 + 76 * q^75 + 96 * q^76 + 80 * q^77 + 40 * q^78 - 60 * q^79 - 24 * q^80 - 118 * q^81 - 76 * q^84 + 2 * q^85 + 44 * q^86 + 40 * q^87 + 140 * q^88 + 50 * q^89 + 224 * q^90 + 28 * q^91 - 170 * q^92 + 96 * q^94 - 44 * q^95 - 116 * q^96 + 110 * q^97 + 70 * q^98 + 44 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/425\mathbb{Z}\right)^\times$.

$n$	$52$	$326$
$\chi(n)$	$e\left(\frac{9}{10}\right)$	$1$

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 $

$2$	−1.63738	+	0.532018i	−1.15780	+	0.376193i	−0.824078	−	0.566477i	$-0.808306\pi$
$2$	−1.63738	+	0.532018i	−1.15780	+	0.376193i	−0.333726	+	0.942670i	$0.608306\pi$
$3$	−1.52304	−	2.09629i	−0.879328	−	1.21029i	−0.976607	−	0.215034i	$-0.931014\pi$
$3$	−1.52304	−	2.09629i	−0.879328	−	1.21029i	0.0972789	−	0.995257i	$-0.468986\pi$
$4$	0.779945	−	0.566663i	0.389972	−	0.283332i
$5$	2.20989	−	0.341170i	0.988292	−	0.152576i
$5$	2.20989	−	0.341170i	0.988292	−	0.152576i
$6$	3.60906	+	2.62214i	1.47339	+	1.07048i
$7$		−	0.996248i		−	0.376546i	−0.982117	−	0.188273i	$-0.939711\pi$
$7$		−	0.996248i		−	0.376546i	0.982117	−	0.188273i	$-0.0602890\pi$
$8$	1.04832	−	1.44289i	0.370638	−	0.510140i
$9$	−1.14771	+	3.53228i	−0.382570	+	1.17743i
$10$	−3.43692	+	1.73433i	−1.08685	+	0.548442i
$11$	1.27455	+	3.92267i	0.384292	+	1.18273i	0.936993	+	0.349349i	$0.113597\pi$
$11$	1.27455	+	3.92267i	0.384292	+	1.18273i	−0.552701	+	0.833380i	$0.686403\pi$
$12$	−2.37577	−	0.771936i	−0.685827	−	0.222839i
$13$	4.61707	+	1.50018i	1.28055	+	0.416074i	0.868772	−	0.495212i	$-0.164910\pi$
$13$	4.61707	+	1.50018i	1.28055	+	0.416074i	0.411773	+	0.911286i	$0.364910\pi$
$14$	0.530022	+	1.63124i	0.141654	+	0.435967i
$15$	−4.08094	−	4.11294i	−1.05369	−	1.06196i
$16$	−1.54469	+	4.75405i	−0.386171	+	1.18851i
$17$	0.587785	−	0.809017i	0.142559	−	0.196215i
$17$	0.587785	−	0.809017i	0.142559	−	0.196215i
$18$		−	6.39430i		−	1.50715i
$19$	−2.33736	−	1.69819i	−0.536228	−	0.389592i	0.286455	−	0.958094i	$-0.407523\pi$
$19$	−2.33736	−	1.69819i	−0.536228	−	0.389592i	−0.822682	+	0.568502i	$0.807523\pi$
$20$	1.53026	−	1.51836i	0.342177	−	0.339515i
$21$	−2.08842	+	1.51733i	−0.455731	+	0.331108i
$22$	−4.17386	−	5.74482i	−0.889869	−	1.22480i
$23$	1.89422	−	0.615470i	0.394972	−	0.128334i	−0.104795	−	0.994494i	$-0.533419\pi$
$23$	1.89422	−	0.615470i	0.394972	−	0.128334i	0.499768	+	0.866160i	$0.333419\pi$
$24$	−4.62135			−0.943330
$25$	4.76721	−	1.50790i	0.953441	−	0.301579i
$26$	−8.35804			−1.63915
$27$	1.75969	−	0.571757i	0.338652	−	0.110035i
$28$	−0.564537	−	0.777019i	−0.106687	−	0.146843i
$29$	3.25890	−	2.36773i	0.605162	−	0.439676i	−0.242545	−	0.970140i	$-0.577982\pi$
$29$	3.25890	−	2.36773i	0.605162	−	0.439676i	0.847707	+	0.530464i	$0.177982\pi$
$30$	8.87021	+	4.56332i	1.61947	+	0.833145i
$31$	1.47575	+	1.07219i	0.265052	+	0.192572i	0.712371	−	0.701803i	$-0.247621\pi$
$31$	1.47575	+	1.07219i	0.265052	+	0.192572i	−0.447319	+	0.894374i	$0.647621\pi$
$32$		−	5.03898i		−	0.890774i
$33$	6.28183	−	8.64620i	1.09353	−	1.50511i
$34$	−0.532018	+	1.63738i	−0.0912403	+	0.280809i
$35$	−0.339890	−	2.20160i	−0.0574519	−	0.372138i
$36$	1.10647	+	3.40535i	0.184411	+	0.567558i
$37$	5.22873	+	1.69892i	0.859599	+	0.279301i	0.705461	−	0.708749i	$-0.250740\pi$
$37$	5.22873	+	1.69892i	0.859599	+	0.279301i	0.154138	+	0.988049i	$0.450740\pi$
$38$	4.73062	+	1.53707i	0.767409	+	0.249346i
$39$	−3.88719	−	11.9635i	−0.622448	−	1.91570i
$40$	1.82440	−	3.54629i	0.288464	−	0.560717i
$41$	3.35669	−	10.3308i	0.524226	−	1.61340i	−0.241614	−	0.970372i	$-0.577677\pi$
$41$	3.35669	−	10.3308i	0.524226	−	1.61340i	0.765841	−	0.643030i	$-0.222323\pi$
$42$	2.61230	−	3.59552i	0.403086	−	0.554801i
$43$		−	2.44766i		−	0.373264i	−0.982430	−	0.186632i	$-0.940243\pi$
$43$		−	2.44766i		−	0.373264i	0.982430	−	0.186632i	$-0.0597572\pi$
$44$	3.21691	+	2.33722i	0.484968	+	0.352350i
$45$	−1.33120	+	8.19751i	−0.198443	+	1.22201i
$46$	−2.77412	+	2.01552i	−0.409022	+	0.297172i
$47$	−3.13496	−	4.31490i	−0.457281	−	0.629393i	0.516661	−	0.856190i	$-0.327175\pi$
$47$	−3.13496	−	4.31490i	−0.457281	−	0.629393i	−0.973942	+	0.226797i	$0.927175\pi$
$48$	12.3185	−	4.00251i	1.77802	−	0.577713i
$49$	6.00749			0.858213
$50$	−7.00351	+	5.00524i	−0.990446	+	0.707848i
$51$	−2.59115			−0.362834
$52$	4.45116	−	1.44627i	0.617265	−	0.200561i
$53$	−8.30687	−	11.4334i	−1.14104	−	1.57050i	−0.765171	−	0.643827i	$-0.777346\pi$
$53$	−8.30687	−	11.4334i	−1.14104	−	1.57050i	−0.375865	−	0.926675i	$-0.622654\pi$
$54$	−2.57710	+	1.87237i	−0.350698	+	0.254797i
$55$	4.15491	+	8.23381i	0.560248	+	1.11025i
$56$	−1.43748	−	1.04439i	−0.192091	−	0.139562i
$57$			7.48619i			0.991570i
$58$	−4.07639	+	5.61067i	−0.535256	+	0.736717i
$59$	−1.19379	+	3.67410i	−0.155418	+	0.478327i	−0.998203	−	0.0599230i	$-0.980914\pi$
$59$	−1.19379	+	3.67410i	−0.155418	+	0.478327i	0.842785	+	0.538250i	$0.180914\pi$
$60$	−5.51356	−	0.895349i	−0.711797	−	0.115589i
$61$	2.68092	+	8.25103i	0.343257	+	1.05644i	0.962510	+	0.271245i	$0.0874352\pi$
$61$	2.68092	+	8.25103i	0.343257	+	1.05644i	−0.619254	+	0.785191i	$0.712565\pi$
$62$	−2.98679	−	0.970468i	−0.379323	−	0.123250i
$63$	3.51903	+	1.14340i	0.443356	+	0.144055i
$64$	−0.408545	−	1.25737i	−0.0510681	−	0.157171i
$65$	10.7150	+	1.74002i	1.32904	+	0.215823i
$66$	−5.68583	+	17.4992i	−0.699878	+	2.15400i
$67$	1.24040	−	1.70726i	0.151539	−	0.208575i	−0.726498	−	0.687169i	$-0.758853\pi$
$67$	1.24040	−	1.70726i	0.151539	−	0.208575i	0.878037	+	0.478593i	$0.158853\pi$
$68$		−	0.964065i		−	0.116910i
$69$	−4.17517	−	3.03344i	−0.502632	−	0.365183i
$70$	1.72782	+	3.42403i	0.206514	+	0.409250i
$71$	3.69156	−	2.68208i	0.438108	−	0.318304i	−0.346775	−	0.937948i	$-0.612723\pi$
$71$	3.69156	−	2.68208i	0.438108	−	0.318304i	0.784883	+	0.619645i	$0.212723\pi$
$72$	3.89354	+	5.35899i	0.458858	+	0.631564i
$73$	−13.3880	+	4.35002i	−1.56694	+	0.509131i	−0.958652	−	0.284581i	$-0.908145\pi$
$73$	−13.3880	+	4.35002i	−1.56694	+	0.509131i	−0.608293	+	0.793713i	$0.708145\pi$
$74$	−9.46529			−1.10032
$75$	−10.4216	−	7.69684i	−1.20339	−	0.888754i
$76$	−2.78532			−0.319498
$77$	3.90795	−	1.26977i	0.445352	−	0.144704i
$78$	12.7296	+	17.5208i	1.44135	+	1.98384i
$79$	−9.28545	+	6.74628i	−1.04470	+	0.759015i	−0.971197	−	0.238280i	$-0.923416\pi$
$79$	−9.28545	+	6.74628i	−1.04470	+	0.759015i	−0.0734987	+	0.997295i	$0.523416\pi$
$80$	−1.79164	+	11.0329i	−0.200312	+	1.23352i
$81$	5.13558	+	3.73122i	0.570620	+	0.414580i
$82$			18.7013i			2.06522i
$83$	−2.02930	+	2.79309i	−0.222745	+	0.306582i	−0.905734	−	0.423847i	$-0.860680\pi$
$83$	−2.02930	+	2.79309i	−0.222745	+	0.306582i	0.682989	+	0.730428i	$0.260680\pi$
$84$	−0.769040	+	2.36686i	−0.0839091	+	0.258246i
$85$	1.02293	−	1.98837i	0.110952	−	0.215669i
$86$	1.30220	+	4.00775i	0.140419	+	0.432167i
$87$	−9.92686	−	3.22543i	−1.06427	−	0.345803i
$88$	6.99613	+	2.27318i	0.745790	+	0.242322i
$89$	−1.36801	−	4.21031i	−0.145009	−	0.446292i	0.852003	−	0.523537i	$-0.175388\pi$
$89$	−1.36801	−	4.21031i	−0.145009	−	0.446292i	−0.997012	+	0.0772447i	$0.975388\pi$
$90$	−2.18154	−	14.1307i	−0.229955	−	1.48951i
$91$	1.49455	−	4.59975i	0.156671	−	0.482185i
$92$	1.12862	−	1.55342i	0.117667	−	0.161955i
$93$		−	4.72659i		−	0.490124i
$94$	7.42873	+	5.39729i	0.766215	+	0.556688i
$95$	−5.74468	−	2.95538i	−0.589392	−	0.303215i
$96$	−10.5631	+	7.67457i	−1.07810	+	0.783282i
$97$	−3.16413	−	4.35506i	−0.321269	−	0.442189i	0.617585	−	0.786504i	$-0.288111\pi$
$97$	−3.16413	−	4.35506i	−0.321269	−	0.442189i	−0.938854	+	0.344315i	$0.888111\pi$
$98$	−9.83656	+	3.19609i	−0.993642	+	0.322854i
$99$	−15.3188			−1.53960
$100$	2.86369	−	3.87747i	0.286369	−	0.387747i
$101$	7.00010			0.696536			0.348268	−	0.937395i	$-0.386770\pi$
$101$	7.00010			0.696536			0.348268	+	0.937395i	$0.386770\pi$
$102$	4.24271	−	1.37854i	0.420090	−	0.136496i
$103$	4.41072	+	6.07084i	0.434602	+	0.598178i	0.969002	−	0.247054i	$-0.0794624\pi$
$103$	4.41072	+	6.07084i	0.434602	+	0.598178i	−0.534400	+	0.845232i	$0.679462\pi$
$104$	7.00478	−	5.08927i	0.686875	−	0.499044i
$105$	−4.09751	+	4.06563i	−0.399876	+	0.396765i
$106$	19.6843	+	14.3015i	1.91191	+	1.38908i
$107$		−	13.5578i		−	1.31069i	−0.755331	−	0.655343i	$-0.772524\pi$
$107$		−	13.5578i		−	1.31069i	0.755331	−	0.655343i	$-0.227476\pi$
$108$	1.04847	−	1.44309i	0.100889	−	0.138861i
$109$	−4.32646	+	13.3155i	−0.414399	+	1.27539i	0.498388	+	0.866954i	$0.333926\pi$
$109$	−4.32646	+	13.3155i	−0.414399	+	1.27539i	−0.912787	+	0.408436i	$0.866074\pi$
$110$	−11.1837	−	11.2714i	−1.06633	−	1.07469i
$111$	−4.40216	−	13.5484i	−0.417834	−	1.28596i
$112$	4.73622	+	1.53889i	0.447531	+	0.145411i
$113$	−3.40851	−	1.10749i	−0.320646	−	0.104184i	0.144272	−	0.989538i	$-0.453916\pi$
$113$	−3.40851	−	1.10749i	−0.320646	−	0.104184i	−0.464918	+	0.885354i	$0.653916\pi$
$114$	−3.98279	−	12.2578i	−0.373022	−	1.14804i
$115$	3.97603	−	2.00637i	0.370767	−	0.187095i
$116$	1.20006	−	3.69339i	0.111422	−	0.342923i
$117$	−10.5981	+	14.5870i	−0.979795	+	1.34857i
$118$		−	6.65103i		−	0.612277i
$119$	−0.805982	−	0.585580i	−0.0738842	−	0.0536800i
$120$	−10.2127	+	1.57667i	−0.932285	+	0.143929i
$121$	−4.86365	+	3.53365i	−0.442150	+	0.321241i
$122$	−8.77939	−	12.0838i	−0.794848	−	1.09401i
$123$	−26.7687	+	8.69768i	−2.41365	+	0.784243i
$124$	1.75858			0.157925
$125$	10.0205	−	4.95871i	0.896264	−	0.443520i
$126$	−6.37031			−0.567512
$127$	16.8193	−	5.46491i	1.49247	−	0.484932i	0.554658	−	0.832079i	$-0.312849\pi$
$127$	16.8193	−	5.46491i	1.49247	−	0.484932i	0.937811	+	0.347146i	$0.112849\pi$
$128$	7.26156	+	9.99469i	0.641838	+	0.883414i
$129$	−5.13098	+	3.72788i	−0.451758	+	0.328221i
$130$	−18.4703	+	2.85151i	−1.61995	+	0.250094i
$131$	−4.02240	−	2.92245i	−0.351439	−	0.255335i	0.398034	−	0.917371i	$-0.369693\pi$
$131$	−4.02240	−	2.92245i	−0.351439	−	0.255335i	−0.749472	+	0.662036i	$0.769693\pi$
$132$		−	10.3032i		−	0.896782i
$133$	−1.69182	+	2.32859i	−0.146700	+	0.201915i
$134$	−1.12271	+	3.45536i	−0.0969877	+	0.298498i
$135$	3.69364	−	1.86387i	0.317898	−	0.160417i
$136$	−0.551136	−	1.69622i	−0.0472595	−	0.145450i
$137$	−2.85915	−	0.928994i	−0.244274	−	0.0793693i	0.184321	−	0.982866i	$-0.440991\pi$
$137$	−2.85915	−	0.928994i	−0.244274	−	0.0793693i	−0.428595	+	0.903497i	$0.640991\pi$
$138$	8.45020	+	2.74564i	0.719329	+	0.233724i
$139$	−3.12164	−	9.60743i	−0.264774	−	0.814892i	−0.991745	−	0.128224i	$-0.959072\pi$
$139$	−3.12164	−	9.60743i	−0.264774	−	0.814892i	0.726971	−	0.686668i	$-0.240928\pi$
$140$	−1.51266	−	1.52452i	−0.127843	−	0.128846i
$141$	−4.27059	+	13.1435i	−0.359649	+	1.10689i
$142$	−4.61758	+	6.35556i	−0.387499	+	0.533347i
$143$			20.0233i			1.67443i
$144$	−15.0198	−	10.9125i	−1.25165	−	0.909378i
$145$	6.39400	−	6.34425i	0.530993	−	0.526861i
$146$	19.6070	−	14.2453i	1.62268	−	1.17895i
$147$	−9.14965	−	12.5934i	−0.754650	−	1.03869i
$148$	5.04084	−	1.63787i	0.414354	−	0.134632i
$149$	14.0121			1.14792			0.573959	−	0.818884i	$-0.305407\pi$
$149$	14.0121			1.14792			0.573959	+	0.818884i	$0.305407\pi$
$150$	21.1590	+	7.05818i	1.72763	+	0.576298i
$151$	23.8375			1.93987			0.969933	−	0.243373i	$-0.0782538\pi$
$151$	23.8375			1.93987			0.969933	+	0.243373i	$0.0782538\pi$
$152$	−4.90062	+	1.59231i	−0.397493	+	0.129153i
$153$	2.18307	+	3.00474i	0.176491	+	0.242919i
$154$	−5.72327	+	4.15820i	−0.461194	+	0.335077i
$155$	3.62704	+	1.86595i	0.291331	+	0.149877i
$156$	−9.81108	−	7.12817i	−0.785515	−	0.570710i
$157$			3.29376i			0.262871i	0.991325	+	0.131435i	$0.0419586\pi$
$157$			3.29376i			0.262871i	−0.991325	+	0.131435i	$0.958041\pi$
$158$	11.6147	−	15.9863i	0.924016	−	1.27180i
$159$	−11.3160	+	34.8271i	−0.897419	+	2.76197i
$160$	−1.71915	−	11.1356i	−0.135911	−	0.880345i
$161$	−0.613161	−	1.88711i	−0.0483238	−	0.148725i
$162$	−10.3940	−	3.37721i	−0.816628	−	0.265339i
$163$	15.4756	+	5.02834i	1.21214	+	0.393850i	0.844215	−	0.536004i	$-0.180067\pi$
$163$	15.4756	+	5.02834i	1.21214	+	0.393850i	0.367929	+	0.929854i	$0.380067\pi$
$164$	−3.23606	−	9.95958i	−0.252694	−	0.777712i
$165$	10.9323	−	21.2503i	0.851080	−	1.65433i
$166$	1.83677	−	5.65299i	0.142561	−	0.438757i
$167$	−6.99323	+	9.62535i	−0.541152	+	0.744832i	−0.988779	−	0.149389i	$-0.952269\pi$
$167$	−6.99323	+	9.62535i	−0.541152	+	0.744832i	0.447626	+	0.894221i	$0.352269\pi$
$168$			4.60401i			0.355207i
$169$	8.54961	+	6.21165i	0.657662	+	0.477819i
$170$	−0.617074	+	3.79994i	−0.0473274	+	0.291442i
$171$	8.68111	−	6.30719i	0.663861	−	0.482323i
$172$	−1.38700	−	1.90904i	−0.105757	−	0.145563i
$173$	−7.77414	+	2.52597i	−0.591057	+	0.192046i	−0.589248	−	0.807952i	$-0.700576\pi$
$173$	−7.77414	+	2.52597i	−0.591057	+	0.192046i	−0.00180904	+	0.999998i	$0.500576\pi$
$174$	17.9701			1.36231
$175$	−1.50224	−	4.74932i	−0.113558	−	0.359015i
$176$	−20.6174			−1.55409
$177$	9.52015	−	3.09328i	0.715578	−	0.232505i
$178$	4.47992	+	6.16608i	0.335784	+	0.462168i
$179$	7.15344	−	5.19728i	0.534673	−	0.388463i	−0.287430	−	0.957802i	$-0.592801\pi$
$179$	7.15344	−	5.19728i	0.534673	−	0.388463i	0.822103	+	0.569339i	$0.192801\pi$
$180$	3.60697	+	7.14795i	0.268848	+	0.532777i
$181$	19.5159	+	14.1792i	1.45061	+	1.05393i	0.985689	+	0.168575i	$0.0539164\pi$
$181$	19.5159	+	14.1792i	1.45061	+	1.05393i	0.464919	+	0.885353i	$0.346084\pi$
$182$			8.32668i			0.617214i
$183$	13.2134	−	18.1866i	0.976759	−	1.34439i
$184$	1.09770	−	3.37837i	0.0809234	−	0.249057i
$185$	12.1345	+	1.97053i	0.892149	+	0.144876i
$186$	2.51463	+	7.73923i	0.184382	+	0.567468i
$187$	3.92267	+	1.27455i	0.286854	+	0.0932045i
$188$	−4.89019	−	1.58892i	−0.356654	−	0.115884i
$189$	−0.569612	−	1.75309i	−0.0414332	−	0.127518i
$190$	10.9786	+	1.78281i	0.796468	+	0.129339i
$191$	−3.26357	+	10.0442i	−0.236144	+	0.726776i	0.760824	+	0.648959i	$0.224795\pi$
$191$	−3.26357	+	10.0442i	−0.236144	+	0.726776i	−0.996968	+	0.0778175i	$0.975205\pi$
$192$	−2.01358	+	2.77145i	−0.145318	+	0.200012i
$193$			17.9808i			1.29429i	0.762367	+	0.647144i	$0.224037\pi$
$193$			17.9808i			1.29429i	−0.762367	+	0.647144i	$0.775963\pi$
$194$	7.49786	+	5.44752i	0.538315	+	0.391109i
$195$	−12.6718	−	25.1119i	−0.907450	−	1.79830i
$196$	4.68551	−	3.40422i	0.334679	−	0.243159i
$197$	−8.97970	−	12.3595i	−0.639777	−	0.880577i	0.358827	−	0.933404i	$-0.383177\pi$
$197$	−8.97970	−	12.3595i	−0.639777	−	0.880577i	−0.998604	+	0.0528268i	$0.983177\pi$
$198$	25.0827	−	8.14987i	1.78255	−	0.579186i
$199$	−27.1415			−1.92401			−0.962006	−	0.273028i	$-0.911975\pi$
$199$	−27.1415			−1.92401			−0.962006	+	0.273028i	$0.911975\pi$
$200$	2.82184	−	8.45933i	0.199534	−	0.598165i
$201$	−5.46809			−0.385689
$202$	−11.4618	+	3.72418i	−0.806452	+	0.262032i
$203$	−2.35884	−	3.24667i	−0.165558	−	0.227872i
$204$	−2.02095	+	1.46831i	−0.141495	+	0.102802i
$205$	3.89333	−	23.9751i	0.271922	−	1.67450i
$206$	−10.4518	−	7.59371i	−0.728214	−	0.529079i
$207$			7.39730i			0.514148i
$208$	−14.2639	+	19.6325i	−0.989020	+	1.36127i
$209$	3.68236	−	11.3331i	0.254714	−	0.783929i
$210$	4.54620	−	8.83693i	0.313718	−	0.609806i
$211$	−7.79707	−	23.9969i	−0.536772	−	1.65202i	−0.739788	−	0.672840i	$-0.765074\pi$
$211$	−7.79707	−	23.9969i	−0.536772	−	1.65202i	0.203015	−	0.979176i	$-0.434926\pi$
$212$	−12.9578	−	4.21024i	−0.889945	−	0.289161i
$213$	−11.2448	−	3.65365i	−0.770480	−	0.250344i
$214$	7.21301	+	22.1994i	0.493071	+	1.51752i
$215$	−0.835067	−	5.40904i	−0.0569511	−	0.368894i
$216$	1.01974	−	3.13843i	0.0693843	−	0.213543i
$217$	1.06817	−	1.47021i	0.0725122	−	0.0998045i
$218$		−	24.1043i		−	1.63255i
$219$	29.5093	+	21.4398i	1.99405	+	1.44877i
$220$	7.90640	+	4.06749i	0.533049	+	0.274230i
$221$	3.92752	−	2.85351i	0.264193	−	0.191948i
$222$	14.4160	+	19.8420i	0.967540	+	1.33170i
$223$	−4.93111	+	1.60222i	−0.330212	+	0.107292i	−0.469431	−	0.882969i	$-0.655541\pi$
$223$	−4.93111	+	1.60222i	−0.330212	+	0.107292i	0.139219	+	0.990262i	$0.455541\pi$
$224$	−5.02007			−0.335418
$225$	−0.145050	+	18.5697i	−0.00967000	+	1.23798i
$226$	6.17024			0.410439
$227$	10.7763	−	3.50144i	0.715249	−	0.232399i	0.0712871	−	0.997456i	$-0.477289\pi$
$227$	10.7763	−	3.50144i	0.715249	−	0.232399i	0.643962	+	0.765057i	$0.277289\pi$
$228$	4.24215	+	5.83882i	0.280943	+	0.386685i
$229$	−15.9469	+	11.5861i	−1.05380	+	0.765633i	−0.972932	−	0.231091i	$-0.925770\pi$
$229$	−15.9469	+	11.5861i	−1.05380	+	0.765633i	−0.0808718	+	0.996725i	$0.525770\pi$
$230$	−5.44287	+	5.40052i	−0.358892	+	0.356100i
$231$	−8.61377	−	6.25827i	−0.566744	−	0.411764i
$232$		−	7.18438i		−	0.471678i
$233$	−11.3289	+	15.5929i	−0.742182	+	1.02153i	0.256308	+	0.966595i	$0.417494\pi$
$233$	−11.3289	+	15.5929i	−0.742182	+	1.02153i	−0.998490	+	0.0549309i	$0.982506\pi$
$234$	9.59259	−	29.5230i	0.627087	−	1.92998i
$235$	−8.40002	−	8.46589i	−0.547957	−	0.552254i
$236$	1.15089	+	3.54207i	0.0749165	+	0.230569i
$237$	28.2842	+	9.19011i	1.83726	+	0.596962i
$238$	1.63124	+	0.530022i	0.105738	+	0.0343562i
$239$	0.593268	+	1.82589i	0.0383753	+	0.118107i	0.968409	−	0.249367i	$-0.0802226\pi$
$239$	0.593268	+	1.82589i	0.0383753	+	0.118107i	−0.930034	+	0.367474i	$0.880223\pi$
$240$	25.8569	−	13.0478i	1.66906	−	0.842232i
$241$	2.84218	−	8.74732i	0.183081	−	0.563465i	−0.816829	−	0.576879i	$-0.804270\pi$
$241$	2.84218	−	8.74732i	0.183081	−	0.563465i	0.999910	+	0.0134149i	$0.00427022\pi$
$242$	6.08369	−	8.37348i	0.391074	−	0.538268i
$243$		−	21.9992i		−	1.41125i
$244$	6.76652	+	4.91617i	0.433182	+	0.314725i
$245$	13.2759	−	2.04958i	0.848165	−	0.130943i
$246$	39.2033	−	28.4829i	2.49951	−	1.81600i
$247$	−8.24418	−	11.3471i	−0.524564	−	0.722001i
$248$	3.09412	−	1.00534i	0.196477	−	0.0638393i
$249$	8.94583			0.566919
$250$	−13.7693	+	13.4504i	−0.870849	+	0.850678i
$251$	−24.4576			−1.54375			−0.771875	−	0.635774i	$-0.780681\pi$
$251$	−24.4576			−1.54375			−0.771875	+	0.635774i	$0.780681\pi$
$252$	3.39257	−	1.10231i	0.213712	−	0.0694393i
$253$	4.82856	+	6.64595i	0.303569	+	0.417827i
$254$	−24.6321	+	17.8963i	−1.54556	+	1.12291i
$255$	−5.72615	+	0.884023i	−0.358586	+	0.0553597i
$256$	−15.0681	−	10.9476i	−0.941759	−	0.684228i
$257$			23.5156i			1.46686i	0.679762	+	0.733432i	$0.262083\pi$
$257$			23.5156i			1.46686i	−0.679762	+	0.733432i	$0.737917\pi$
$258$	6.41809	−	8.83374i	0.399573	−	0.549965i
$259$	1.69254	−	5.20912i	0.105170	−	0.323679i
$260$	9.34313	−	4.71469i	0.579437	−	0.292393i
$261$	4.62322	+	14.2288i	0.286170	+	0.880741i
$262$	8.14100	+	2.64517i	0.502953	+	0.163419i
$263$	18.1047	+	5.88258i	1.11638	+	0.362735i	0.808387	−	0.588652i	$-0.200341\pi$
$263$	18.1047	+	5.88258i	1.11638	+	0.362735i	0.307998	+	0.951387i	$0.400341\pi$
$264$	−5.89015	−	18.1280i	−0.362514	−	1.11570i
$265$	−22.2580	−	22.4325i	−1.36730	−	1.37802i
$266$	1.53131	−	4.71288i	0.0938904	−	0.288965i
$267$	−6.74247	+	9.28022i	−0.412633	+	0.567940i
$268$		−	2.03446i		−	0.124274i
$269$	−6.42792	−	4.67016i	−0.391917	−	0.284745i	0.374323	−	0.927298i	$-0.377875\pi$
$269$	−6.42792	−	4.67016i	−0.391917	−	0.284745i	−0.766241	+	0.642554i	$0.777875\pi$
$270$	−5.05630	+	5.01696i	−0.307716	+	0.305322i
$271$	−7.85272	+	5.70533i	−0.477019	+	0.346574i	−0.800170	−	0.599773i	$-0.795258\pi$
$271$	−7.85272	+	5.70533i	−0.477019	+	0.346574i	0.323152	+	0.946347i	$0.395258\pi$
$272$	2.93817	+	4.04404i	0.178153	+	0.245206i
$273$	−11.9186	+	3.87260i	−0.721349	+	0.234381i
$274$	5.17576			0.312679
$275$	11.9910	+	16.7783i	0.723086	+	1.01177i
$276$	−4.97535			−0.299481
$277$	15.4088	−	5.00664i	0.925828	−	0.300820i	0.192972	−	0.981204i	$-0.438187\pi$
$277$	15.4088	−	5.00664i	0.925828	−	0.300820i	0.732855	+	0.680384i	$0.238187\pi$
$278$	10.2227	+	14.0703i	0.613114	+	0.843879i
$279$	−5.48103	+	3.98220i	−0.328140	+	0.238408i
$280$	−3.53298	−	1.81756i	−0.211136	−	0.108620i
$281$	6.98050	+	5.07163i	0.416422	+	0.302548i	0.776197	−	0.630491i	$-0.217146\pi$
$281$	6.98050	+	5.07163i	0.416422	+	0.302548i	−0.359775	+	0.933039i	$0.617146\pi$
$282$		−	23.7930i		−	1.41685i
$283$	−17.9509	+	24.7073i	−1.06707	+	1.46870i	−0.194064	+	0.980989i	$0.562167\pi$
$283$	−17.9509	+	24.7073i	−1.06707	+	1.46870i	−0.873007	+	0.487708i	$0.837833\pi$
$284$	1.35938	−	4.18374i	0.0806644	−	0.248259i
$285$	2.55406	+	16.5436i	0.151290	+	0.979961i
$286$	−10.6527	−	32.7858i	−0.629910	−	1.93866i
$287$	−10.2921	−	3.34409i	−0.607521	−	0.197396i
$288$	17.7991	+	5.78328i	1.04882	+	0.340783i
$289$	−0.309017	−	0.951057i	−0.0181775	−	0.0559445i
$290$	−7.09417	+	13.7897i	−0.416584	+	0.809758i
$291$	−4.31034	+	13.2658i	−0.252676	+	0.777658i
$292$	−7.97689	+	10.9793i	−0.466812	+	0.642512i
$293$			2.93070i			0.171213i	0.996329	+	0.0856067i	$0.0272829\pi$
$293$			2.93070i			0.171213i	−0.996329	+	0.0856067i	$0.972717\pi$
$294$	21.6814	+	15.7525i	1.26448	+	0.918702i
$295$	−1.38464	+	8.52663i	−0.0806171	+	0.496440i
$296$	7.93276	−	5.76349i	0.461082	−	0.334996i
$297$	4.48563	+	6.17393i	0.260282	+	0.358248i
$298$	−22.9432	+	7.45470i	−1.32906	+	0.431839i
$299$	9.66907			0.559177
$300$	−12.4898	−	0.0975591i	−0.721099	−	0.00563257i
$301$	−2.43847			−0.140551
$302$	−39.0311	+	12.6820i	−2.24598	+	0.729765i
$303$	−10.6614	−	14.6742i	−0.612483	−	0.843011i
$304$	11.6838	−	8.48877i	0.670111	−	0.486864i
$305$	8.73954	+	17.3192i	0.500424	+	0.991694i
$306$	−5.17310	−	3.75848i	−0.295726	−	0.214858i
$307$		−	15.5853i		−	0.889501i	−0.895655	−	0.444750i	$-0.853292\pi$
$307$		−	15.5853i		−	0.889501i	0.895655	−	0.444750i	$-0.146708\pi$
$308$	2.32845	−	3.20484i	0.132676	−	0.182613i
$309$	6.00850	−	18.4923i	0.341812	−	1.05199i
$310$	−6.93157	−	1.12562i	−0.393687	−	0.0639310i
$311$	0.542278	+	1.66896i	0.0307498	+	0.0946381i	0.965254	−	0.261315i	$-0.0841562\pi$
$311$	0.542278	+	1.66896i	0.0307498	+	0.0946381i	−0.934504	+	0.355953i	$0.884156\pi$
$312$	−21.3371	−	6.93285i	−1.20798	−	0.392495i
$313$	−20.7391	−	6.73853i	−1.17224	−	0.380884i	−0.342762	−	0.939422i	$-0.611363\pi$
$313$	−20.7391	−	6.73853i	−1.17224	−	0.380884i	−0.829479	+	0.558538i	$0.811363\pi$
$314$	−1.75234	−	5.39315i	−0.0988903	−	0.304353i
$315$	8.16676	+	1.32620i	0.460145	+	0.0747231i
$316$	−3.41928	+	10.5234i	−0.192349	+	0.591990i
$317$	−1.77673	+	2.44546i	−0.0997912	+	0.137351i	−0.855992	−	0.516988i	$-0.827053\pi$
$317$	−1.77673	+	2.44546i	−0.0997912	+	0.137351i	0.756201	+	0.654339i	$0.227053\pi$
$318$		−	63.0457i		−	3.53542i
$319$	13.4414	+	9.76578i	0.752576	+	0.546779i
$320$	−1.33182	−	2.63927i	−0.0744507	−	0.147539i
$321$	−28.4211	+	20.6491i	−1.58631	+	1.15252i
$322$	2.00796	+	2.76372i	0.111899	+	0.154016i
$323$	−2.74773	+	0.892793i	−0.152888	+	0.0496763i
$324$	6.11981			0.339990
$325$	24.2726	+	0.189596i	1.34640	+	0.0105169i
$326$	−28.0147			−1.55159
$327$	34.5024	−	11.2105i	1.90799	−	0.619942i
$328$	−11.3874	−	15.6734i	−0.628762	−	0.865417i
$329$	−4.29871	+	3.12320i	−0.236996	+	0.172187i
$330$	−6.59485	+	40.6111i	−0.363034	+	2.23557i
$331$	13.4918	+	9.80233i	0.741574	+	0.538785i	0.893204	−	0.449652i	$-0.148452\pi$
$331$	13.4918	+	9.80233i	0.741574	+	0.538785i	−0.151630	+	0.988437i	$0.548452\pi$
$332$			3.32839i			0.182669i
$333$	−12.0021	+	16.5195i	−0.657713	+	0.905264i
$334$	6.32973	−	19.4809i	0.346347	−	1.06595i
$335$	2.15868	−	4.19605i	0.117941	−	0.229255i
$336$	−3.98750	−	12.2723i	−0.217536	−	0.669506i
$337$	−32.2576	−	10.4811i	−1.75718	−	0.570943i	−0.760279	−	0.649597i	$-0.774938\pi$
$337$	−32.2576	−	10.4811i	−1.75718	−	0.570943i	−0.996902	+	0.0786542i	$0.974938\pi$
$338$	−17.3037	−	5.62231i	−0.941197	−	0.305813i
$339$	2.86968	+	8.83197i	0.155860	+	0.479687i
$340$	−0.328910	−	2.13047i	−0.0178377	−	0.115541i
$341$	−2.32494	+	7.15544i	−0.125903	+	0.387489i
$342$	−10.8588	+	14.9458i	−0.587174	+	0.808176i
$343$		−	12.9587i		−	0.699703i
$344$	−3.53170	−	2.56593i	−0.190417	−	0.138346i
$345$	−10.2616	−	5.27912i	−0.552465	−	0.284218i
$346$	11.3854	−	8.27196i	0.612082	−	0.444703i
$347$	17.4944	+	24.0789i	0.939147	+	1.29262i	0.956183	+	0.292770i	$0.0945770\pi$
$347$	17.4944	+	24.0789i	0.939147	+	1.29262i	−0.0170359	+	0.999855i	$0.505423\pi$
$348$	−9.57014	+	3.10953i	−0.513013	+	0.166688i
$349$	26.2161			1.40332			0.701659	−	0.712513i	$-0.252443\pi$
$349$	26.2161			1.40332			0.701659	+	0.712513i	$0.252443\pi$
$350$	4.98646	+	6.97724i	0.266538	+	0.372949i
$351$	8.98234			0.479442
$352$	19.7662	−	6.42244i	1.05354	−	0.342317i
$353$	−8.27175	−	11.3851i	−0.440261	−	0.605967i	0.530009	−	0.847992i	$-0.322188\pi$
$353$	−8.27175	−	11.3851i	−0.440261	−	0.605967i	−0.970270	+	0.242025i	$0.922188\pi$
$354$	−13.9424	+	10.1298i	−0.741033	+	0.538392i
$355$	7.24289	−	7.18653i	0.384413	−	0.381422i
$356$	−3.45280	−	2.50861i	−0.182998	−	0.132956i
$357$			2.58143i			0.136624i
$358$	−8.94788	+	12.3157i	−0.472910	+	0.650905i
$359$	9.90025	−	30.4698i	0.522515	−	1.60814i	−0.246662	−	0.969102i	$-0.579334\pi$
$359$	9.90025	−	30.4698i	0.522515	−	1.60814i	0.769177	−	0.639036i	$-0.220666\pi$
$360$	10.4326	+	10.5144i	0.549847	+	0.554158i
$361$	−3.29192	−	10.1315i	−0.173259	−	0.533236i
$362$	−39.4986	−	12.8339i	−2.07600	−	0.674533i
$363$	14.8151	+	4.81371i	0.777589	+	0.252654i
$364$	−1.44084	−	4.43446i	−0.0755207	−	0.232429i
$365$	−28.1018	+	14.1806i	−1.47092	+	0.742248i
$366$	−11.9597	+	36.8082i	−0.625144	+	1.92400i
$367$	−8.31622	+	11.4463i	−0.434103	+	0.597492i	−0.968889	−	0.247496i	$-0.920392\pi$
$367$	−8.31622	+	11.4463i	−0.434103	+	0.597492i	0.534786	+	0.844988i	$0.320392\pi$
$368$			9.95594i			0.518989i
$369$	32.6389	+	23.7135i	1.69911	+	1.23448i
$370$	−20.9172	+	3.22928i	−1.08744	+	0.167882i
$371$	−11.3905	+	8.27570i	−0.591367	+	0.429653i
$372$	−2.67838	−	3.68648i	−0.138868	−	0.191135i
$373$	−13.1970	+	4.28795i	−0.683313	+	0.222022i	−0.630045	−	0.776558i	$-0.716964\pi$
$373$	−13.1970	+	4.28795i	−0.683313	+	0.222022i	−0.0532677	+	0.998580i	$0.516964\pi$
$374$	−7.10099			−0.367184
$375$	−25.6565	−	13.4536i	−1.32490	−	0.694741i
$376$	−9.51239			−0.490564
$377$	18.5986	−	6.04304i	0.957875	−	0.311233i
$378$	1.86535	+	2.56743i	0.0959430	+	0.132054i
$379$	9.45013	−	6.86592i	0.485421	−	0.352679i	−0.318000	−	0.948091i	$-0.603011\pi$
$379$	9.45013	−	6.86592i	0.485421	−	0.352679i	0.803421	+	0.595412i	$0.203011\pi$
$380$	−6.15524	+	0.950267i	−0.315757	+	0.0487476i
$381$	−37.0724	−	26.9347i	−1.89928	−	1.37991i
$382$		−	18.1825i		−	0.930300i
$383$	−3.26923	+	4.49971i	−0.167050	+	0.229924i	−0.884332	−	0.466858i	$-0.845386\pi$
$383$	−3.26923	+	4.49971i	−0.167050	+	0.229924i	0.717282	+	0.696783i	$0.245386\pi$
$384$	9.89206	−	30.4446i	0.504802	−	1.55362i
$385$	8.20292	−	4.13932i	0.418060	−	0.210960i
$386$	−9.56613	−	29.4415i	−0.486903	−	1.49853i
$387$	8.64581	+	2.80920i	0.439491	+	0.142799i
$388$	−4.93570	−	1.60371i	−0.250572	−	0.0814158i
$389$	1.30094	+	4.00388i	0.0659603	+	0.203005i	0.978605	−	0.205750i	$-0.0659632\pi$
$389$	1.30094	+	4.00388i	0.0659603	+	0.203005i	−0.912644	+	0.408755i	$0.865963\pi$
$390$	34.1086	+	34.3761i	1.72716	+	1.74070i
$391$	0.615470	−	1.89422i	0.0311256	−	0.0957949i
$392$	6.29779	−	8.66816i	0.318086	−	0.437808i
$393$			12.8831i			0.649867i
$394$	21.2787	+	15.4599i	1.07200	+	0.778856i
$395$	−18.2182	+	18.0764i	−0.916656	+	0.909524i
$396$	−11.9478	+	8.68059i	−0.600400	+	0.436216i
$397$	5.94994	+	8.18939i	0.298619	+	0.411014i	0.931790	−	0.362998i	$-0.118247\pi$
$397$	5.94994	+	8.18939i	0.298619	+	0.411014i	−0.633171	+	0.774012i	$0.718247\pi$
$398$	44.4411	−	14.4398i	2.22763	−	0.723801i
$399$	7.45811			0.373372
$400$	−0.195221	+	24.9928i	−0.00976105	+	1.24964i
$401$	−15.7449			−0.786262			−0.393131	−	0.919482i	$-0.628608\pi$
$401$	−15.7449			−0.786262			−0.393131	+	0.919482i	$0.628608\pi$
$402$	8.95336	−	2.90912i	0.446553	−	0.145094i
$403$	5.20516	+	7.16429i	0.259287	+	0.356879i
$404$	5.45969	−	3.96670i	0.271630	−	0.197351i
$405$	12.6220	+	6.49346i	0.627194	+	0.322663i
$406$	5.58962	+	4.06109i	0.277408	+	0.201549i
$407$			22.6759i			1.12400i
$408$	−2.71636	+	3.73875i	−0.134480	+	0.185096i
$409$	0.814092	−	2.50552i	0.0402542	−	0.123890i	−0.928910	−	0.370306i	$-0.879253\pi$
$409$	0.814092	−	2.50552i	0.0402542	−	0.123890i	0.969164	+	0.246416i	$0.0792529\pi$
$410$	6.38033	+	41.3278i	0.315102	+	2.04104i
$411$	2.40716	+	7.40848i	0.118737	+	0.365434i
$412$	6.88024	+	2.23553i	0.338965	+	0.110137i
$413$	3.66032	+	1.18931i	0.180112	+	0.0585221i
$414$	−3.93550	−	12.1122i	−0.193419	−	0.595283i
$415$	−3.53161	+	6.86476i	−0.173360	+	0.336978i
$416$	7.55937	−	23.2653i	0.370628	−	1.14068i
$417$	−15.3855	+	21.1764i	−0.753433	+	1.03701i
$418$			20.5157i			1.00346i
$419$	12.6727	+	9.20726i	0.619102	+	0.449804i	0.852608	−	0.522551i	$-0.175020\pi$
$419$	12.6727	+	9.20726i	0.619102	+	0.449804i	−0.233505	+	0.972355i	$0.575020\pi$
$420$	−0.891989	+	5.49287i	−0.0435246	+	0.268025i
$421$	−11.9788	+	8.70312i	−0.583812	+	0.424164i	−0.840096	−	0.542437i	$-0.817502\pi$
$421$	−11.9788	+	8.70312i	−0.583812	+	0.424164i	0.256284	+	0.966601i	$0.417502\pi$
$422$	25.5336	+	35.1440i	1.24296	+	1.71078i
$423$	18.8395	−	6.12132i	0.916007	−	0.297629i
$424$	−25.2055			−1.22409
$425$	1.58218	−	4.74307i	0.0767470	−	0.230073i
$426$	20.3558			0.986243
$427$	8.22007	−	2.67086i	0.397797	−	0.129252i
$428$	−7.68273	−	10.5744i	−0.371359	−	0.511131i
$429$	41.9745	−	30.4963i	2.02655	−	1.47237i
$430$	4.24503	+	8.41240i	0.204714	+	0.405682i
$431$	27.8081	+	20.2037i	1.33947	+	0.973180i	0.999463	+	0.0327553i	$0.0104282\pi$
$431$	27.8081	+	20.2037i	1.33947	+	0.973180i	0.340003	+	0.940424i	$0.389572\pi$
$432$			9.24883i			0.444985i
$433$	−13.8252	+	19.0287i	−0.664396	+	0.914462i	−0.999617	−	0.0276773i	$-0.991189\pi$
$433$	−13.8252	+	19.0287i	−0.664396	+	0.914462i	0.335221	+	0.942139i	$0.391189\pi$
$434$	−0.966827	+	2.97559i	−0.0464092	+	0.142833i
$435$	−23.0377	−	3.74110i	−1.10457	−	0.179372i
$436$	4.17098	+	12.8370i	0.199754	+	0.614779i
$437$	−5.47266	−	1.77818i	−0.261793	−	0.0850617i
$438$	−59.7244	−	19.4056i	−2.85374	−	0.927237i
$439$	4.83553	+	14.8822i	0.230787	+	0.710290i	0.997652	+	0.0684817i	$0.0218155\pi$
$439$	4.83553	+	14.8822i	0.230787	+	0.710290i	−0.766865	+	0.641808i	$0.778185\pi$
$440$	16.2362	+	2.63660i	0.774031	+	0.125695i
$441$	−6.89485	+	21.2202i	−0.328326	+	1.01048i
$442$	−4.91273	+	6.76179i	−0.233675	+	0.321626i
$443$			26.9637i			1.28108i	0.767924	+	0.640541i	$0.221290\pi$
$443$			26.9637i			1.28108i	−0.767924	+	0.640541i	$0.778710\pi$
$444$	−11.1108	−	8.07250i	−0.527297	−	0.383104i
$445$	−4.45959	−	8.83759i	−0.211405	−	0.418942i
$446$	7.22171	−	5.24688i	0.341958	−	0.248447i
$447$	−21.3410	−	29.3734i	−1.00940	−	1.38931i
$448$	−1.25265	+	0.407012i	−0.0591823	+	0.0192295i
$449$	0.733545			0.0346181			0.0173091	−	0.999850i	$-0.494490\pi$
$449$	0.733545			0.0346181			0.0173091	+	0.999850i	$0.494490\pi$
$450$	−9.64194	−	30.4830i	−0.454525	−	1.43698i
$451$	44.8026			2.10967
$452$	−3.28603	+	1.06769i	−0.154562	+	0.0502201i
$453$	−36.3054	−	49.9701i	−1.70578	−	2.34780i
$454$	−15.7821	+	11.4664i	−0.740692	+	0.538144i
$455$	1.73349	−	10.6748i	0.0812672	−	0.500444i
$456$	10.8018	+	7.84795i	0.505839	+	0.367514i
$457$		−	3.34008i		−	0.156243i	−0.996944	−	0.0781213i	$-0.975108\pi$
$457$		−	3.34008i		−	0.156243i	0.996944	−	0.0781213i	$-0.0248921\pi$
$458$	19.9472	−	27.4550i	0.932072	−	1.28289i
$459$	0.571757	−	1.75969i	0.0266873	−	0.0821352i
$460$	1.96415	−	3.81793i	0.0915791	−	0.178012i
$461$	−0.353790	−	1.08885i	−0.0164776	−	0.0507130i	0.942480	−	0.334264i	$-0.108488\pi$
$461$	−0.353790	−	1.08885i	−0.0164776	−	0.0507130i	−0.958957	+	0.283551i	$0.908488\pi$
$462$	17.4335	+	5.66450i	0.811082	+	0.263536i
$463$	2.26840	+	0.737048i	0.105421	+	0.0342535i	0.361253	−	0.932468i	$-0.382349\pi$
$463$	2.26840	+	0.737048i	0.105421	+	0.0342535i	−0.255831	+	0.966721i	$0.582349\pi$
$464$	6.22233	+	19.1504i	0.288865	+	0.889034i
$465$	−1.61257	−	10.4452i	−0.0747811	−	0.484386i
$466$	10.2541	−	31.5588i	0.475010	−	1.46193i
$467$	2.12701	−	2.92758i	0.0984265	−	0.135472i	−0.756963	−	0.653458i	$-0.773318\pi$
$467$	2.12701	−	2.92758i	0.0984265	−	0.135472i	0.855390	+	0.517985i	$0.173318\pi$
$468$			17.3826i			0.803513i
$469$	−1.70086	−	1.23575i	−0.0785384	−	0.0570615i
$470$	18.2581	+	9.39294i	0.842181	+	0.433264i
$471$	6.90467	−	5.01653i	0.318150	−	0.231150i
$472$	4.04986	+	5.57415i	0.186410	+	0.256571i
$473$	9.60134	−	3.11966i	0.441470	−	0.143442i
$474$	−51.2014			−2.35176
$475$	−13.7034	−	4.57114i	−0.628754	−	0.209738i
$476$	−0.960448			−0.0440221
$477$	49.9200	−	16.2200i	2.28568	−	0.742662i
$478$	−1.94281	−	2.67405i	−0.0888622	−	0.122308i
$479$	−28.1016	+	20.4170i	−1.28399	+	0.932877i	−0.999666	−	0.0258501i	$-0.991771\pi$
$479$	−28.1016	+	20.4170i	−1.28399	+	0.932877i	−0.284329	+	0.958727i	$0.591771\pi$
$480$	−20.7250	+	20.5638i	−0.945963	+	0.938603i
$481$	21.5928	+	15.6881i	0.984545	+	0.715314i
$482$			15.8348i			0.721256i
$483$	−3.02206	+	4.15951i	−0.137509	+	0.189264i
$484$	−1.79099	+	5.51210i	−0.0814086	+	0.250550i
$485$	−8.47819	−	8.54468i	−0.384975	−	0.387994i
$486$	11.7039	+	36.0211i	0.530902	+	1.63395i
$487$	−9.38291	−	3.04869i	−0.425180	−	0.138149i	0.0886077	−	0.996067i	$-0.471758\pi$
$487$	−9.38291	−	3.04869i	−0.425180	−	0.138149i	−0.513788	+	0.857917i	$0.671758\pi$
$488$	14.7158	+	4.78146i	0.666154	+	0.216446i
$489$	−13.0292	−	40.0997i	−0.589200	−	1.81337i
$490$	−20.6473	+	10.4189i	−0.932749	+	0.470680i
$491$	7.52388	−	23.1561i	0.339548	−	1.04502i	−0.624890	−	0.780713i	$-0.714856\pi$
$491$	7.52388	−	23.1561i	0.339548	−	1.04502i	0.964438	−	0.264309i	$-0.0851437\pi$
$492$	−15.9495	+	21.9526i	−0.719057	+	0.989697i
$493$		−	4.02822i		−	0.181422i
$494$	19.5358	+	14.1936i	0.878955	+	0.638598i
$495$	−33.8528	+	5.22631i	−1.52157	+	0.234905i
$496$	−7.37684	+	5.35959i	−0.331230	+	0.240653i
$497$	−2.67201	−	3.67771i	−0.119856	−	0.164968i
$498$	−14.6477	+	4.75934i	−0.656381	+	0.213271i
$499$	−26.7917			−1.19936			−0.599680	−	0.800240i	$-0.704706\pi$
$499$	−26.7917			−1.19936			−0.599680	+	0.800240i	$0.704706\pi$
$500$	5.00555	−	9.54579i	0.223855	−	0.426901i
$501$	30.8284			1.37731
$502$	40.0464	−	13.0119i	1.78736	−	0.580749i
$503$	−19.9667	−	27.4817i	−0.890269	−	1.22535i	−0.973469	−	0.228817i	$-0.926514\pi$
$503$	−19.9667	−	27.4817i	−0.890269	−	1.22535i	0.0832004	−	0.996533i	$-0.473486\pi$
$504$	5.33889	−	3.87893i	0.237813	−	0.172781i
$505$	15.4694	−	2.38822i	0.688380	−	0.106275i
$506$	−11.4420	−	8.31308i	−0.508658	−	0.369561i
$507$		−	27.3830i		−	1.21612i
$508$	10.0213	−	13.7932i	0.444625	−	0.611974i
$509$	0.716411	−	2.20489i	0.0317544	−	0.0977299i	−0.933923	−	0.357474i	$-0.883638\pi$
$509$	0.716411	−	2.20489i	0.0317544	−	0.0977299i	0.965678	+	0.259744i	$0.0836381\pi$
$510$	8.90559	−	4.49390i	0.394346	−	0.198993i
$511$	4.33370	+	13.3378i	0.191712	+	0.590027i
$512$	6.99774	+	2.27370i	0.309259	+	0.100484i
$513$	−5.08398	−	1.65189i	−0.224463	−	0.0729325i
$514$	−12.5107	−	38.5041i	−0.551825	−	1.69834i
$515$	11.8184	+	11.9111i	0.520781	+	0.524864i
$516$	−1.88943	+	5.81508i	−0.0831777	+	0.255995i
$517$	12.9303	−	17.7970i	0.568672	−	0.782710i
$518$			9.42978i			0.414321i
$519$	17.1355	+	12.4497i	0.752164	+	0.546479i
$520$	13.7435	−	13.6365i	0.602691	−	0.598002i
$521$	−6.36669	+	4.62567i	−0.278930	+	0.202654i	−0.718450	−	0.695578i	$-0.755148\pi$
$521$	−6.36669	+	4.62567i	−0.278930	+	0.202654i	0.439521	+	0.898232i	$0.355148\pi$
$522$	−15.1400	−	20.8384i	−0.662658	−	0.912071i
$523$	−0.362872	+	0.117904i	−0.0158673	+	0.00515560i	−0.316940	−	0.948446i	$-0.602655\pi$
$523$	−0.362872	+	0.117904i	−0.0158673	+	0.00515560i	0.301073	+	0.953601i	$0.402655\pi$
$524$	−4.79329			−0.209396
$525$	−7.66796	+	10.3825i	−0.334657	+	0.453131i
$526$	−32.7740			−1.42901
$527$	1.73485	−	0.563686i	0.0755711	−	0.0245546i
$528$	31.4011	+	43.2199i	1.36656	+	1.88090i
$529$	−15.3981	+	11.1874i	−0.669484	+	0.486408i
$530$	48.3793	+	24.8890i	2.10146	+	1.08111i
$531$	−11.6078	−	8.43359i	−0.503738	−	0.365987i
$532$			2.77487i			0.120306i
$533$	30.9961	−	42.6625i	1.34259	−	1.84792i
$534$	6.10277	−	18.7824i	0.264093	−	0.812793i
$535$	−4.62553	−	29.9613i	−0.199979	−	1.29534i
$536$	−1.16306	−	3.57953i	−0.0502365	−	0.154612i
$537$	−21.7900	−	7.07999i	−0.940306	−	0.305524i
$538$	13.0096	+	4.22707i	0.560883	+	0.182242i
$539$	7.65686	+	23.5654i	0.329804	+	1.01503i
$540$	1.82465	−	3.54677i	0.0785205	−	0.152629i
$541$	3.52758	−	10.8568i	0.151662	−	0.466769i	−0.846145	−	0.532953i	$-0.821082\pi$
$541$	3.52758	−	10.8568i	0.151662	−	0.466769i	0.997807	+	0.0661840i	$0.0210824\pi$
$542$	9.82256	−	13.5196i	0.421915	−	0.580716i
$543$		−	62.5064i		−	2.68241i
$544$	−4.07662	−	2.96184i	−0.174784	−	0.126988i
$545$	−5.01814	+	30.9017i	−0.214954	+	1.32368i
$546$	17.4551	−	12.6819i	0.747009	−	0.542734i
$547$	20.9422	+	28.8244i	0.895422	+	1.23244i	0.971905	+	0.235371i	$0.0756307\pi$
$547$	20.9422	+	28.8244i	0.895422	+	1.23244i	−0.0764838	+	0.997071i	$0.524369\pi$
$548$	−2.75640	+	0.895610i	−0.117748	+	0.0382586i
$549$	−32.2219			−1.37520
$550$	−28.5602	−	21.0930i	−1.21781	−	0.899409i
$551$	−11.6381			−0.495799
$552$	−8.75386	+	2.84430i	−0.372589	+	0.121062i
$553$	6.72097	+	9.25062i	0.285805	+	0.393376i
$554$	−22.5666	+	16.3956i	−0.958761	+	0.696581i
$555$	−14.3506	−	28.4386i	−0.609149	−	1.20715i
$556$	−7.87889	−	5.72435i	−0.334139	−	0.242766i
$557$		−	10.3782i		−	0.439737i	−0.975530	−	0.219868i	$-0.929437\pi$
$557$		−	10.3782i		−	0.439737i	0.975530	−	0.219868i	$-0.0705628\pi$
$558$	6.85594	−	9.43639i	0.290235	−	0.399474i
$559$	3.67192	−	11.3010i	0.155306	−	0.477982i
$560$	10.9915	+	1.78492i	0.464477	+	0.0754266i
$561$	−3.30256	−	10.1642i	−0.139434	−	0.429134i
$562$	−14.1280	−	4.59045i	−0.595952	−	0.193636i
$563$	7.68215	+	2.49608i	0.323764	+	0.105197i	0.466390	−	0.884579i	$-0.345554\pi$
$563$	7.68215	+	2.49608i	0.323764	+	0.105197i	−0.142626	+	0.989777i	$0.545554\pi$
$564$	4.11713	+	12.6712i	0.173362	+	0.533555i
$565$	−7.91027	−	1.28455i	−0.332788	−	0.0540415i
$566$	16.2478	−	50.0055i	0.682945	−	2.10189i
$567$	3.71722	−	5.11631i	0.156108	−	0.214865i
$568$		−	8.13821i		−	0.341472i
$569$	−32.7623	−	23.8032i	−1.37347	−	0.997881i	−0.997457	−	0.0712646i	$-0.977297\pi$
$569$	−32.7623	−	23.8032i	−1.37347	−	0.997881i	−0.376008	−	0.926616i	$-0.622703\pi$
$570$	−12.9835	−	25.7295i	−0.543819	−	1.07769i
$571$	−0.642063	+	0.466486i	−0.0268695	+	0.0195218i	−0.601139	−	0.799145i	$-0.705286\pi$
$571$	−0.642063	+	0.466486i	−0.0268695	+	0.0195218i	0.574269	+	0.818666i	$0.305286\pi$
$572$	11.3465	+	15.6171i	0.474419	+	0.652982i
$573$	26.0262	−	8.45641i	1.08726	−	0.353272i
$574$	18.6312			0.777649
$575$	8.10208	−	5.79036i	0.337880	−	0.241475i
$576$	4.91028			0.204595
$577$	−32.4304	+	10.5373i	−1.35009	+	0.438672i	−0.892724	−	0.450605i	$-0.851208\pi$
$577$	−32.4304	+	10.5373i	−1.35009	+	0.438672i	−0.457370	+	0.889277i	$0.651208\pi$
$578$	1.01196	+	1.39284i	0.0420919	+	0.0579345i
$579$	37.6930	−	27.3855i	1.56647	−	1.13810i
$580$	1.39191	−	8.57141i	0.0577961	−	0.355908i
$581$	2.78262	+	2.02169i	0.115442	+	0.0838738i
$582$		−	24.0144i		−	0.995431i
$583$	34.2620	−	47.1576i	1.41899	−	1.95307i
$584$	−7.75832	+	23.8776i	−0.321041	+	0.988064i
$585$	−18.4440	+	35.8515i	−0.762564	+	1.48228i
$586$	−1.55919	−	4.79868i	−0.0644094	−	0.198232i
$587$	24.0984	+	7.83003i	0.994646	+	0.323180i	0.760724	−	0.649075i	$-0.224844\pi$
$587$	24.0984	+	7.83003i	0.994646	+	0.323180i	0.233922	+	0.972255i	$0.424844\pi$
$588$	−14.2724	−	4.63740i	−0.588586	−	0.191243i
$589$	−1.62857	−	5.01221i	−0.0671039	−	0.206525i
$590$	−2.26913	−	14.6980i	−0.0934186	−	0.605108i
$591$	−12.2326	+	37.6480i	−0.503181	+	1.54863i
$592$	−16.1535	+	22.2334i	−0.663905	+	0.913787i
$593$		−	5.67993i		−	0.233247i	−0.993176	−	0.116623i	$-0.962793\pi$
$593$		−	5.67993i		−	0.233247i	0.993176	−	0.116623i	$-0.0372071\pi$
$594$	−10.6293	−	7.72266i	−0.436127	−	0.316865i
$595$	−1.98091	−	1.01909i	−0.0812095	−	0.0417786i
$596$	10.9287	−	7.94016i	0.447656	−	0.325241i
$597$	41.3376	+	56.8964i	1.69184	+	2.32861i
$598$	−15.8320	+	5.14412i	−0.647417	+	0.210359i
$599$	−12.9594			−0.529508			−0.264754	−	0.964316i	$-0.585291\pi$
$599$	−12.9594			−0.529508			−0.264754	+	0.964316i	$0.585291\pi$
$600$	−22.0309	+	6.96851i	−0.899409	+	0.284488i
$601$	20.0400			0.817450			0.408725	−	0.912658i	$-0.365974\pi$
$601$	20.0400			0.817450			0.408725	+	0.912658i	$0.365974\pi$
$602$	3.99271	−	1.29731i	0.162731	−	0.0528744i
$603$	4.60692	+	6.34089i	0.187608	+	0.258221i
$604$	18.5919	−	13.5078i	0.756494	−	0.549625i
$605$	−9.54254	+	9.46829i	−0.387959	+	0.384941i
$606$	25.2638	+	18.3552i	1.02627	+	0.745629i
$607$			19.6696i			0.798365i	0.916872	+	0.399182i	$0.130706\pi$
$607$			19.6696i			0.798365i	−0.916872	+	0.399182i	$0.869294\pi$
$608$	−8.55716	+	11.7779i	−0.347039	+	0.477658i
$609$	−3.21333	+	9.88962i	−0.130211	+	0.400748i
$610$	−23.5241	−	23.7085i	−0.952462	−	0.959931i
$611$	−8.00122	−	24.6252i	−0.323695	−	0.996229i
$612$	3.40535	+	1.10647i	0.137653	+	0.0447262i
$613$	−13.5677	−	4.40843i	−0.547996	−	0.178055i	0.0219169	−	0.999760i	$-0.493023\pi$
$613$	−13.5677	−	4.40843i	−0.547996	−	0.178055i	−0.569913	+	0.821705i	$0.693023\pi$
$614$	8.29167	+	25.5191i	0.334624	+	1.02987i
$615$	−56.1884	+	28.3536i	−2.26574	+	1.14333i
$616$	2.26465	−	6.96988i	0.0912454	−	0.280825i
$617$	−19.6851	+	27.0942i	−0.792492	+	1.09077i	0.201301	+	0.979529i	$0.435483\pi$
$617$	−19.6851	+	27.0942i	−0.792492	+	1.09077i	−0.993793	+	0.111243i	$0.964517\pi$
$618$			33.4756i			1.34658i
$619$	−27.0878	−	19.6804i	−1.08875	−	0.791023i	−0.109562	−	0.993980i	$-0.534945\pi$
$619$	−27.0878	−	19.6804i	−1.08875	−	0.791023i	−0.979188	+	0.202957i	$0.934945\pi$
$620$	3.88626	−	0.599974i	0.156076	−	0.0240955i
$621$	2.98134	−	2.16607i	0.119637	−	0.0869213i
$622$	−1.77583	−	2.44423i	−0.0712045	−	0.0980046i
$623$	−4.19452	+	1.36288i	−0.168050	+	0.0546027i
$624$	62.8798			2.51721
$625$	20.4525	−	14.3769i	0.818100	−	0.575076i
$626$	37.5428			1.50051
$627$	−29.3658	+	9.54154i	−1.17276	+	0.381052i
$628$	1.86645	+	2.56895i	0.0744796	+	0.102512i
$629$	4.44783	−	3.23154i	0.177346	−	0.128850i
$630$	−14.0777	+	2.17336i	−0.560868	+	0.0865887i
$631$	−36.5261	−	26.5378i	−1.45408	−	1.05645i	−0.984856	−	0.173372i	$-0.944534\pi$
$631$	−36.5261	−	26.5378i	−1.45408	−	1.05645i	−0.469224	−	0.883079i	$-0.655466\pi$
$632$			20.4702i			0.814261i
$633$	−38.4291	+	52.8932i	−1.52742	+	2.10231i
$634$	1.60816	−	4.94941i	0.0638682	−	0.196566i
$635$	35.3042	−	17.8151i	1.40101	−	0.706969i
$636$	10.9094	+	33.5756i	0.432585	+	1.33136i
$637$	27.7370	+	9.01230i	1.09898	+	0.357080i
$638$	−27.2043	−	8.83923i	−1.07703	−	0.349948i
$639$	5.23702	+	16.1179i	0.207173	+	0.637613i
$640$	19.4571	+	19.6097i	0.769110	+	0.775142i
$641$	−15.2820	+	47.0331i	−0.603601	+	1.85769i	−0.0974677	+	0.995239i	$0.531074\pi$
$641$	−15.2820	+	47.0331i	−0.603601	+	1.85769i	−0.506134	+	0.862455i	$0.668926\pi$
$642$	35.5505	−	48.9311i	1.40307	−	1.93116i
$643$			29.9126i			1.17964i	0.807535	+	0.589819i	$0.200801\pi$
$643$			29.9126i			1.17964i	−0.807535	+	0.589819i	$0.799199\pi$
$644$	−1.54759	−	1.12439i	−0.0609836	−	0.0443072i
$645$	−10.0671	+	9.98873i	−0.396390	+	0.393306i
$646$	4.02411	−	2.92369i	0.158326	−	0.115031i
$647$	1.55888	+	2.14562i	0.0612860	+	0.0843530i	0.838560	−	0.544809i	$-0.183398\pi$
$647$	1.55888	+	2.14562i	0.0612860	+	0.0843530i	−0.777274	+	0.629162i	$0.783398\pi$
$648$	10.7675	−	3.49857i	0.422987	−	0.137437i
$649$	−15.9338			−0.625457
$650$	−39.8445	+	12.6030i	−1.56283	+	0.494332i
$651$	−4.70885			−0.184555
$652$	14.9195	−	4.84764i	0.584293	−	0.189848i
$653$	2.16369	+	2.97807i	0.0846719	+	0.116541i	0.849252	−	0.527988i	$-0.177053\pi$
$653$	2.16369	+	2.97807i	0.0846719	+	0.116541i	−0.764580	+	0.644529i	$0.777053\pi$
$654$	−50.5294	+	36.7118i	−1.97586	+	1.43554i
$655$	−9.88611	−	5.08595i	−0.386282	−	0.198725i
$656$	43.9282	+	31.9157i	1.71511	+	1.24610i
$657$		−	52.2827i		−	2.03974i
$658$	5.37704	−	7.40086i	0.209619	−	0.288516i
$659$	−3.72886	+	11.4762i	−0.145256	+	0.447051i	−0.997044	−	0.0768355i	$-0.975518\pi$
$659$	−3.72886	+	11.4762i	−0.145256	+	0.447051i	0.851788	+	0.523886i	$0.175518\pi$
$660$	−3.51516	−	22.7690i	−0.136827	−	0.886283i
$661$	−4.94652	−	15.2238i	−0.192397	−	0.592139i	−0.999997	−	0.00240737i	$-0.999234\pi$
$661$	−4.94652	−	15.2238i	−0.192397	−	0.592139i	0.807600	−	0.589731i	$-0.200766\pi$
$662$	−27.3062	−	8.87231i	−1.06128	−	0.344832i
$663$	−11.9635	−	3.88719i	−0.464625	−	0.150966i
$664$	1.90277	+	5.85613i	0.0738419	+	0.227262i
$665$	−2.94429	+	5.72313i	−0.114175	+	0.221933i
$666$	10.8634	−	33.4341i	0.420948	−	1.29555i
$667$	4.71581	−	6.49075i	0.182597	−	0.251323i
$668$			11.4700i			0.443789i
$669$	10.8690	+	7.89678i	0.420219	+	0.305307i
$670$	−1.30221	+	8.01899i	−0.0503087	+	0.309801i
$671$	−28.9491	+	21.0327i	−1.11757	+	0.811959i
$672$	7.64578	+	10.5235i	0.294942	+	0.405953i
$673$	39.0306	−	12.6818i	1.50452	−	0.488848i	0.563187	−	0.826330i	$-0.309575\pi$
$673$	39.0306	−	12.6818i	1.50452	−	0.488848i	0.941332	+	0.337482i	$0.109575\pi$
$674$	58.3941			2.24926
$675$	7.52664	−	5.37911i	0.289701	−	0.207042i
$676$	10.1881			0.391851
$677$	6.89698	−	2.24097i	0.265073	−	0.0861273i	−0.173465	−	0.984840i	$-0.555496\pi$
$677$	6.89698	−	2.24097i	0.265073	−	0.0861273i	0.438538	+	0.898713i	$0.355496\pi$
$678$	−9.39753	−	12.9346i	−0.360910	−	0.496750i
$679$	−4.33872	+	3.15226i	−0.166505	+	0.120973i
$680$	−1.79665	−	3.56043i	−0.0688983	−	0.136536i
$681$	−23.7528	−	17.2574i	−0.910209	−	0.661305i
$682$		−	12.9531i		−	0.496000i
$683$	18.4777	−	25.4324i	0.707030	−	0.973143i	−0.292826	−	0.956166i	$-0.594596\pi$
$683$	18.4777	−	25.4324i	0.707030	−	0.973143i	0.999856	−	0.0169771i	$-0.00540422\pi$
$684$	3.19673	−	9.83853i	0.122230	−	0.376186i
$685$	−6.63534	−	1.07752i	−0.253523	−	0.0411697i
$686$	6.89425	+	21.2183i	0.263224	+	0.810120i
$687$	48.5757	+	15.7832i	1.85328	+	0.602166i
$688$	11.6363	+	3.78086i	0.443629	+	0.144144i
$689$	−21.2012	−	65.2507i	−0.807703	−	2.48585i
$690$	19.6107	+	3.18459i	0.746568	+	0.121235i
$691$	10.0158	−	30.8254i	0.381018	−	1.17265i	−0.558310	−	0.829633i	$-0.688550\pi$
$691$	10.0158	−	30.8254i	0.381018	−	1.17265i	0.939328	−	0.343021i	$-0.111450\pi$
$692$	−4.63203	+	6.37544i	−0.176083	+	0.242358i
$693$			15.2613i			0.579729i
$694$	−41.4554	−	30.1191i	−1.57363	−	1.14331i
$695$	−10.1763	−	20.1663i	−0.386007	−	0.764953i
$696$	−15.0605	+	10.9421i	−0.570867	+	0.414759i
$697$	−6.38480	−	8.78792i	−0.241841	−	0.332866i
$698$	−42.9259	+	13.9475i	−1.62477	+	0.527919i
$699$	49.9416			1.88896
$700$	−3.86293	−	2.85295i	−0.146005	−	0.107831i
$701$	10.6773			0.403278			0.201639	−	0.979460i	$-0.435373\pi$
$701$	10.6773			0.403278			0.201639	+	0.979460i	$0.435373\pi$
$702$	−14.7075	+	4.77877i	−0.555100	+	0.180363i
$703$	−9.33635	−	12.8504i	−0.352127	−	0.484662i
$704$	4.41154	−	3.20517i	0.166266	−	0.120799i
$705$	−4.95335	+	30.5027i	−0.186554	+	1.14880i
$706$	19.6011	+	14.2410i	0.737696	+	0.535968i
$707$		−	6.97383i		−	0.262278i
$708$	5.67234	−	7.80731i	0.213180	−	0.293417i
$709$	0.969163	−	2.98278i	0.0363977	−	0.112021i	−0.931207	−	0.364491i	$-0.881243\pi$
$709$	0.969163	−	2.98278i	0.0363977	−	0.112021i	0.967605	+	0.252470i	$0.0812430\pi$
$710$	−8.03601	+	15.6205i	−0.301586	+	0.586225i
$711$	−13.1728	−	40.5416i	−0.494017	−	1.52043i
$712$	−7.50915	−	2.43987i	−0.281417	−	0.0914380i
$713$	3.45530	+	1.12269i	0.129402	+	0.0420452i
$714$	−1.37337	−	4.22679i	−0.0513970	−	0.158184i
$715$	6.83135	+	44.2492i	0.255478	+	1.65483i
$716$	2.63418	−	8.10718i	0.0984441	−	0.302980i
$717$	2.92402	−	4.02456i	0.109199	−	0.150300i
$718$			55.1579i			2.05848i
$719$	−29.2514	−	21.2524i	−1.09089	−	0.792580i	−0.111342	−	0.993782i	$-0.535515\pi$
$719$	−29.2514	−	21.2524i	−1.09089	−	0.792580i	−0.979550	+	0.201203i	$0.935515\pi$
$720$	−36.9151	−	18.9912i	−1.37575	−	0.707759i
$721$	6.04807	−	4.39418i	0.225242	−	0.163648i
$722$	10.7803	+	14.8378i	0.401200	+	0.552205i
$723$	−22.6656	+	7.36451i	−0.842944	+	0.273889i
$724$	23.2562			0.864308
$725$	11.9655	−	16.2015i	0.444389	−	0.601709i
$726$	−26.8189			−0.995343
$727$	23.3108	−	7.57415i	0.864551	−	0.280910i	0.157023	−	0.987595i	$-0.449810\pi$
$727$	23.3108	−	7.57415i	0.864551	−	0.280910i	0.707528	+	0.706685i	$0.249810\pi$
$728$	−5.07018	−	6.97850i	−0.187913	−	0.258640i
$729$	−30.7098	+	22.3120i	−1.13740	+	0.826369i
$730$	38.4691	−	38.1698i	1.42381	−	1.41273i
$731$	−1.98020	−	1.43870i	−0.0732402	−	0.0532121i
$732$		−	21.6721i		−	0.801023i
$733$	−10.2880	+	14.1602i	−0.379995	+	0.523019i	−0.955583	−	0.294721i	$-0.904773\pi$
$733$	−10.2880	+	14.1602i	−0.379995	+	0.523019i	0.575588	+	0.817740i	$0.304773\pi$
$734$	7.52720	−	23.1664i	0.277834	−	0.855086i
$735$	−24.5162	−	24.7084i	−0.904293	−	0.911384i
$736$	−3.10134	−	9.54494i	−0.114317	−	0.351831i
$737$	8.27798	+	2.68968i	0.304923	+	0.0990756i
$738$	−66.0584	−	21.4637i	−2.43164	−	0.790088i
$739$	11.4621	+	35.2767i	0.421640	+	1.29767i	0.906175	+	0.422902i	$0.138989\pi$
$739$	11.4621	+	35.2767i	0.421640	+	1.29767i	−0.484536	+	0.874771i	$0.661011\pi$
$740$	10.5809	−	5.33929i	0.388962	−	0.196276i
$741$	−11.2306	+	34.5643i	−0.412567	+	1.26975i
$742$	14.2478	−	19.6105i	0.523054	−	0.719922i
$743$		−	4.75933i		−	0.174603i	−0.996182	−	0.0873014i	$-0.972176\pi$
$743$		−	4.75933i		−	0.174603i	0.996182	−	0.0873014i	$-0.0278243\pi$
$744$	−6.81996	−	4.95499i	−0.250032	−	0.181659i
$745$	30.9652	−	4.78052i	1.13448	−	0.175145i
$746$	19.3272	−	14.0420i	0.707620	−	0.514116i
$747$	−7.53695	−	10.3737i	−0.275763	−	0.379555i
$748$	3.78171	−	1.22875i	0.138273	−	0.0449276i
$749$	−13.5070			−0.493534
$750$	49.1671	+	8.37895i	1.79533	+	0.305956i
$751$	−25.3217			−0.924003			−0.462002	−	0.886879i	$-0.652869\pi$
$751$	−25.3217			−0.924003			−0.462002	+	0.886879i	$0.652869\pi$
$752$	25.3558	−	8.23860i	0.924631	−	0.300431i
$753$	37.2499	+	51.2701i	1.35746	+	1.86839i
$754$	−27.2380	+	19.7896i	−0.991949	+	0.720693i
$755$	52.6781	−	8.13263i	1.91715	−	0.295977i
$756$	−1.43767	−	1.04453i	−0.0522877	−	0.0379893i
$757$			38.6881i			1.40614i	0.711119	+	0.703071i	$0.248188\pi$
$757$			38.6881i			1.40614i	−0.711119	+	0.703071i	$0.751812\pi$
$758$	−11.8207	+	16.2698i	−0.429347	+	0.590945i
$759$	6.57771	−	20.2441i	0.238756	−	0.734814i
$760$	−10.2866	+	5.19077i	−0.373133	+	0.188289i
$761$	−3.78469	−	11.6481i	−0.137195	−	0.422242i	0.858730	−	0.512428i	$-0.171254\pi$
$761$	−3.78469	−	11.6481i	−0.137195	−	0.422242i	−0.995925	+	0.0901858i	$0.971254\pi$
$762$	75.0315	+	24.3792i	2.71810	+	0.883166i
$763$	13.2655	+	4.31022i	0.480244	+	0.156041i
$764$	3.14630	+	9.68330i	0.113829	+	0.350330i
$765$	5.84947	+	5.89534i	0.211488	+	0.213146i
$766$	2.95905	−	9.10703i	0.106915	−	0.329051i
$767$	−11.0236	+	15.1727i	−0.398039	+	0.547854i
$768$			48.2608i			1.74146i
$769$	35.9308	+	26.1052i	1.29570	+	0.941379i	0.999904	−	0.0138726i	$-0.00441594\pi$
$769$	35.9308	+	26.1052i	1.29570	+	0.941379i	0.295794	+	0.955252i	$0.404416\pi$
$770$	−11.2291	+	11.1418i	−0.404670	+	0.401521i
$771$	49.2955	−	35.8153i	1.77533	−	1.28986i

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:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	425.r (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.63738 + 0.532018i) q^{2} +(-1.52304 - 2.09629i) q^{3} +(0.779945 - 0.566663i) q^{4} +(2.20989 - 0.341170i) q^{5} +(3.60906 + 2.62214i) q^{6} -0.996248i q^{7} +(1.04832 - 1.44289i) q^{8} +(-1.14771 + 3.53228i) q^{9} +(-3.43692 + 1.73433i) q^{10} +(1.27455 + 3.92267i) q^{11} +(-2.37577 - 0.771936i) q^{12} +(4.61707 + 1.50018i) q^{13} +(0.530022 + 1.63124i) q^{14} +(-4.08094 - 4.11294i) q^{15} +(-1.54469 + 4.75405i) q^{16} +(0.587785 - 0.809017i) q^{17} -6.39430i q^{18} +(-2.33736 - 1.69819i) q^{19} +(1.53026 - 1.51836i) q^{20} +(-2.08842 + 1.51733i) q^{21} +(-4.17386 - 5.74482i) q^{22} +(1.89422 - 0.615470i) q^{23} -4.62135 q^{24} +(4.76721 - 1.50790i) q^{25} -8.35804 q^{26} +(1.75969 - 0.571757i) q^{27} +(-0.564537 - 0.777019i) q^{28} +(3.25890 - 2.36773i) q^{29} +(8.87021 + 4.56332i) q^{30} +(1.47575 + 1.07219i) q^{31} -5.03898i q^{32} +(6.28183 - 8.64620i) q^{33} +(-0.532018 + 1.63738i) q^{34} +(-0.339890 - 2.20160i) q^{35} +(1.10647 + 3.40535i) q^{36} +(5.22873 + 1.69892i) q^{37} +(4.73062 + 1.53707i) q^{38} +(-3.88719 - 11.9635i) q^{39} +(1.82440 - 3.54629i) q^{40} +(3.35669 - 10.3308i) q^{41} +(2.61230 - 3.59552i) q^{42} -2.44766i q^{43} +(3.21691 + 2.33722i) q^{44} +(-1.33120 + 8.19751i) q^{45} +(-2.77412 + 2.01552i) q^{46} +(-3.13496 - 4.31490i) q^{47} +(12.3185 - 4.00251i) q^{48} +6.00749 q^{49} +(-7.00351 + 5.00524i) q^{50} -2.59115 q^{51} +(4.45116 - 1.44627i) q^{52} +(-8.30687 - 11.4334i) q^{53} +(-2.57710 + 1.87237i) q^{54} +(4.15491 + 8.23381i) q^{55} +(-1.43748 - 1.04439i) q^{56} +7.48619i q^{57} +(-4.07639 + 5.61067i) q^{58} +(-1.19379 + 3.67410i) q^{59} +(-5.51356 - 0.895349i) q^{60} +(2.68092 + 8.25103i) q^{61} +(-2.98679 - 0.970468i) q^{62} +(3.51903 + 1.14340i) q^{63} +(-0.408545 - 1.25737i) q^{64} +(10.7150 + 1.74002i) q^{65} +(-5.68583 + 17.4992i) q^{66} +(1.24040 - 1.70726i) q^{67} -0.964065i q^{68} +(-4.17517 - 3.03344i) q^{69} +(1.72782 + 3.42403i) q^{70} +(3.69156 - 2.68208i) q^{71} +(3.89354 + 5.35899i) q^{72} +(-13.3880 + 4.35002i) q^{73} -9.46529 q^{74} +(-10.4216 - 7.69684i) q^{75} -2.78532 q^{76} +(3.90795 - 1.26977i) q^{77} +(12.7296 + 17.5208i) q^{78} +(-9.28545 + 6.74628i) q^{79} +(-1.79164 + 11.0329i) q^{80} +(5.13558 + 3.73122i) q^{81} +18.7013i q^{82} +(-2.02930 + 2.79309i) q^{83} +(-0.769040 + 2.36686i) q^{84} +(1.02293 - 1.98837i) q^{85} +(1.30220 + 4.00775i) q^{86} +(-9.92686 - 3.22543i) q^{87} +(6.99613 + 2.27318i) q^{88} +(-1.36801 - 4.21031i) q^{89} +(-2.18154 - 14.1307i) q^{90} +(1.49455 - 4.59975i) q^{91} +(1.12862 - 1.55342i) q^{92} -4.72659i q^{93} +(7.42873 + 5.39729i) q^{94} +(-5.74468 - 2.95538i) q^{95} +(-10.5631 + 7.67457i) q^{96} +(-3.16413 - 4.35506i) q^{97} +(-9.83656 + 3.19609i) q^{98} -15.3188 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q + 40 q^{4} - 8 q^{5} + 4 q^{6} - 30 q^{8} + 36 q^{9} - 6 q^{10} + 8 q^{11} - 40 q^{12} - 20 q^{14} - 40 q^{15} - 64 q^{16} + 6 q^{19} + 2 q^{20} - 50 q^{22} + 20 q^{23} + 20 q^{24} + 32 q^{25} + 20 q^{26}+ \cdots + 44 q^{99}+O(q^{100}) \) 160 * q + 40 * q^4 - 8 * q^5 + 4 * q^6 - 30 * q^8 + 36 * q^9 - 6 * q^10 + 8 * q^11 - 40 * q^12 - 20 * q^14 - 40 * q^15 - 64 * q^16 + 6 * q^19 + 2 * q^20 - 50 * q^22 + 20 * q^23 + 20 * q^24 + 32 * q^25 + 20 * q^26 + 30 * q^27 + 60 * q^28 + 16 * q^30 + 12 * q^31 - 40 * q^33 - 4 * q^34 - 54 * q^36 - 40 * q^38 - 12 * q^39 - 52 * q^40 - 2 * q^41 + 30 * q^42 - 20 * q^44 + 42 * q^45 + 48 * q^46 + 40 * q^47 - 100 * q^48 - 184 * q^49 + 46 * q^50 - 32 * q^51 - 10 * q^52 - 20 * q^53 - 40 * q^54 + 18 * q^55 + 24 * q^56 - 120 * q^58 + 6 * q^59 - 40 * q^60 + 12 * q^61 - 10 * q^62 + 90 * q^63 + 58 * q^64 - 20 * q^65 + 48 * q^66 - 90 * q^67 - 74 * q^69 - 120 * q^70 - 16 * q^71 - 10 * q^72 + 52 * q^74 + 76 * q^75 + 96 * q^76 + 80 * q^77 + 40 * q^78 - 60 * q^79 - 24 * q^80 - 118 * q^81 - 76 * q^84 + 2 * q^85 + 44 * q^86 + 40 * q^87 + 140 * q^88 + 50 * q^89 + 224 * q^90 + 28 * q^91 - 170 * q^92 + 96 * q^94 - 44 * q^95 - 116 * q^96 + 110 * q^97 + 70 * q^98 + 44 * q^99

Introduction

L-functions

Modular forms

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