LMFDB - Embedded newform 425.2.p.a.16.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [425,2,Mod(16,425)]

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([2, 5]))

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

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

chi := DirichletCharacter("425.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	425.p (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:	$168$
Relative dimension:	$42$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			16.6
Character	$\chi$	$=$	425.16
Dual form			425.2.p.a.186.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.89741 - 1.37855i) q^{2} +(1.99244 - 0.647384i) q^{3} +(1.08173 + 3.32921i) q^{4} +(2.23138 - 0.144731i) q^{5} +(-4.67293 - 1.51833i) q^{6} -5.09964i q^{7} +(1.08751 - 3.34701i) q^{8} +(1.12368 - 0.816399i) q^{9} +(-4.43335 - 2.80145i) q^{10} +(-0.301510 + 0.414993i) q^{11} +(4.31056 + 5.93298i) q^{12} +(-2.74548 + 1.99471i) q^{13} +(-7.03009 + 9.67609i) q^{14} +(4.35220 - 1.73293i) q^{15} +(-1.01347 + 0.736326i) q^{16} +(0.308881 - 4.11152i) q^{17} -3.25752 q^{18} +(-1.17888 + 3.62822i) q^{19} +(2.89558 + 7.27218i) q^{20} +(-3.30143 - 10.1607i) q^{21} +(1.14417 - 0.371765i) q^{22} +(4.55445 - 6.26866i) q^{23} -7.37277i q^{24} +(4.95811 - 0.645898i) q^{25} +7.95910 q^{26} +(-1.98385 + 2.73054i) q^{27} +(16.9778 - 5.51642i) q^{28} +(3.08683 - 1.00297i) q^{29} +(-10.6468 - 2.71165i) q^{30} +(-1.53447 - 0.498578i) q^{31} -4.10050 q^{32} +(-0.332082 + 1.02204i) q^{33} +(-6.25399 + 7.37542i) q^{34} +(-0.738074 - 11.3792i) q^{35} +(3.93348 + 2.85784i) q^{36} +(4.55351 + 6.26737i) q^{37} +(7.23849 - 5.25907i) q^{38} +(-4.17888 + 5.75173i) q^{39} +(1.94223 - 7.62585i) q^{40} +(0.168209 + 0.231520i) q^{41} +(-7.74292 + 23.8302i) q^{42} -4.45924 q^{43} +(-1.70775 - 0.554883i) q^{44} +(2.38919 - 1.98433i) q^{45} +(-17.2833 + 5.61567i) q^{46} +(0.566017 + 1.74202i) q^{47} +(-1.54259 + 2.12319i) q^{48} -19.0063 q^{49} +(-10.2979 - 5.60945i) q^{50} +(-2.04630 - 8.39194i) q^{51} +(-9.61068 - 6.98257i) q^{52} +(2.41330 + 7.42738i) q^{53} +(7.52836 - 2.44611i) q^{54} +(-0.612721 + 0.969645i) q^{55} +(-17.0686 - 5.54591i) q^{56} +7.99222i q^{57} +(-7.23961 - 2.35229i) q^{58} +(6.62047 - 4.81005i) q^{59} +(10.4772 + 12.6149i) q^{60} +(-0.610641 + 0.840475i) q^{61} +(2.22419 + 3.06134i) q^{62} +(-4.16334 - 5.73035i) q^{63} +(9.80725 + 7.12538i) q^{64} +(-5.83752 + 4.84831i) q^{65} +(2.03903 - 1.48144i) q^{66} +(2.08409 - 6.41416i) q^{67} +(14.0223 - 3.41921i) q^{68} +(5.01625 - 15.4384i) q^{69} +(-14.2864 + 22.6085i) q^{70} +(5.67232 - 1.84305i) q^{71} +(-1.51049 - 4.64880i) q^{72} +(-6.60310 + 9.08839i) q^{73} -18.1690i q^{74} +(9.46061 - 4.49672i) q^{75} -13.3544 q^{76} +(2.11632 + 1.53759i) q^{77} +(15.8581 - 5.15260i) q^{78} +(-7.47959 + 2.43027i) q^{79} +(-2.15486 + 1.78970i) q^{80} +(-3.47263 + 10.6877i) q^{81} -0.671173i q^{82} +(4.81624 - 14.8229i) q^{83} +(30.2561 - 21.9823i) q^{84} +(0.0941685 - 9.21906i) q^{85} +(8.46099 + 6.14727i) q^{86} +(5.50103 - 3.99673i) q^{87} +(1.06109 + 1.46047i) q^{88} +(-3.21356 - 2.33478i) q^{89} +(-7.26876 + 0.471463i) q^{90} +(10.1723 + 14.0010i) q^{91} +(25.7964 + 8.38175i) q^{92} -3.38011 q^{93} +(1.32749 - 4.08560i) q^{94} +(-2.10541 + 8.26656i) q^{95} +(-8.17002 + 2.65460i) q^{96} +(-4.37153 + 1.42040i) q^{97} +(36.0627 + 26.2011i) q^{98} +0.712471i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 168 q - 8 q^{2} - 44 q^{4} - 4 q^{8} + 28 q^{9} - 18 q^{13} - 10 q^{15} - 28 q^{16} + 2 q^{17} - 60 q^{18} - 8 q^{19} + 32 q^{21} + 6 q^{25} + 52 q^{26} - 54 q^{30} + 44 q^{32} - 24 q^{33} + 26 q^{35} + 34 q^{36}+ \cdots - 36 q^{98}+O(q^{100}) $ 168 * q - 8 * q^2 - 44 * q^4 - 4 * q^8 + 28 * q^9 - 18 * q^13 - 10 * q^15 - 28 * q^16 + 2 * q^17 - 60 * q^18 - 8 * q^19 + 32 * q^21 + 6 * q^25 + 52 * q^26 - 54 * q^30 + 44 * q^32 - 24 * q^33 + 26 * q^35 + 34 * q^36 - 18 * q^38 + 80 * q^42 - 8 * q^43 - 40 * q^47 - 84 * q^49 - 82 * q^50 - 36 * q^51 - 30 * q^52 - 42 * q^53 - 18 * q^55 - 18 * q^59 + 28 * q^60 - 16 * q^64 - 140 * q^66 - 62 * q^67 + 144 * q^68 + 44 * q^69 + 4 * q^70 - 6 * q^72 + 72 * q^76 + 48 * q^77 - 28 * q^81 - 14 * q^83 + 24 * q^84 + 62 * q^85 + 82 * q^86 + 48 * q^87 + 90 * q^89 - 224 * q^93 + 26 * q^94 - 36 * q^98

Character values

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

$n$	$52$	$326$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$-1$

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 $

$2$	−1.89741	−	1.37855i	−1.34167	−	0.974780i	−0.999381	−	0.0351846i	$-0.988798\pi$
$2$	−1.89741	−	1.37855i	−1.34167	−	0.974780i	−0.342288	−	0.939595i	$-0.611202\pi$
$3$	1.99244	−	0.647384i	1.15034	−	0.373768i	0.329068	−	0.944306i	$-0.393266\pi$
$3$	1.99244	−	0.647384i	1.15034	−	0.373768i	0.821271	+	0.570539i	$0.193266\pi$
$4$	1.08173	+	3.32921i	0.540864	+	1.66461i
$5$	2.23138	−	0.144731i	0.997903	−	0.0647255i
$5$	2.23138	−	0.144731i	0.997903	−	0.0647255i
$6$	−4.67293	−	1.51833i	−1.90771	−	0.619854i
$7$		−	5.09964i		−	1.92748i	−0.266838	−	0.963741i	$-0.585979\pi$
$7$		−	5.09964i		−	1.92748i	0.266838	−	0.963741i	$-0.414021\pi$
$8$	1.08751	−	3.34701i	0.384493	−	1.18335i
$9$	1.12368	−	0.816399i	0.374559	−	0.272133i
$10$	−4.43335	−	2.80145i	−1.40195	−	0.885895i
$11$	−0.301510	+	0.414993i	−0.0909088	+	0.125125i	−0.852049	−	0.523463i	$-0.824640\pi$
$11$	−0.301510	+	0.414993i	−0.0909088	+	0.125125i	0.761140	+	0.648588i	$0.224640\pi$
$12$	4.31056	+	5.93298i	1.24435	+	1.71270i
$13$	−2.74548	+	1.99471i	−0.761460	+	0.553233i	−0.899358	−	0.437213i	$-0.855965\pi$
$13$	−2.74548	+	1.99471i	−0.761460	+	0.553233i	0.137898	+	0.990446i	$0.455965\pi$
$14$	−7.03009	+	9.67609i	−1.87887	+	2.58604i
$15$	4.35220	−	1.73293i	1.12373	−	0.447440i
$16$	−1.01347	+	0.736326i	−0.253366	+	0.184081i
$17$	0.308881	−	4.11152i	0.0749147	−	0.997190i
$17$	0.308881	−	4.11152i	0.0749147	−	0.997190i
$18$	−3.25752			−0.767804
$19$	−1.17888	+	3.62822i	−0.270454	+	0.832371i	0.719933	+	0.694044i	$0.244173\pi$
$19$	−1.17888	+	3.62822i	−0.270454	+	0.832371i	−0.990387	+	0.138327i	$0.955827\pi$
$20$	2.89558	+	7.27218i	0.647472	+	1.62611i
$21$	−3.30143	−	10.1607i	−0.720431	−	2.21726i
$22$	1.14417	−	0.371765i	0.243939	−	0.0792606i
$23$	4.55445	−	6.26866i	0.949668	−	1.30711i	−0.00200741	−	0.999998i	$-0.500639\pi$
$23$	4.55445	−	6.26866i	0.949668	−	1.30711i	0.951675	−	0.307107i	$-0.0993610\pi$
$24$		−	7.37277i		−	1.50496i
$25$	4.95811	−	0.645898i	0.991621	−	0.129180i
$26$	7.95910			1.56091
$27$	−1.98385	+	2.73054i	−0.381793	+	0.525493i
$28$	16.9778	−	5.51642i	3.20850	−	1.04251i
$29$	3.08683	−	1.00297i	0.573210	−	0.186247i	−0.00804671	−	0.999968i	$-0.502561\pi$
$29$	3.08683	−	1.00297i	0.573210	−	0.186247i	0.581256	+	0.813721i	$0.302561\pi$
$30$	−10.6468	−	2.71165i	−1.94383	−	0.495076i
$31$	−1.53447	−	0.498578i	−0.275598	−	0.0895473i	0.167957	−	0.985794i	$-0.446283\pi$
$31$	−1.53447	−	0.498578i	−0.275598	−	0.0895473i	−0.443555	+	0.896247i	$0.646283\pi$
$32$	−4.10050			−0.724873
$33$	−0.332082	+	1.02204i	−0.0578081	+	0.177915i
$34$	−6.25399	+	7.37542i	−1.07255	+	1.26487i
$35$	−0.738074	−	11.3792i	−0.124757	−	1.92344i
$36$	3.93348	+	2.85784i	0.655580	+	0.476307i
$37$	4.55351	+	6.26737i	0.748593	+	1.03035i	0.998078	+	0.0619707i	$0.0197385\pi$
$37$	4.55351	+	6.26737i	0.748593	+	1.03035i	−0.249485	+	0.968379i	$0.580261\pi$
$38$	7.23849	−	5.25907i	1.17424	−	0.853134i
$39$	−4.17888	+	5.75173i	−0.669156	+	0.921014i
$40$	1.94223	−	7.62585i	0.307094	−	1.20575i
$41$	0.168209	+	0.231520i	0.0262699	+	0.0361574i	0.821950	−	0.569560i	$-0.192886\pi$
$41$	0.168209	+	0.231520i	0.0262699	+	0.0361574i	−0.795680	+	0.605717i	$0.792886\pi$
$42$	−7.74292	+	23.8302i	−1.19476	+	3.67709i
$43$	−4.45924			−0.680028			−0.340014	−	0.940420i	$-0.610432\pi$
$43$	−4.45924			−0.680028			−0.340014	+	0.940420i	$0.610432\pi$
$44$	−1.70775	−	0.554883i	−0.257453	−	0.0836517i
$45$	2.38919	−	1.98433i	0.356160	−	0.295806i
$46$	−17.2833	+	5.61567i	−2.54828	+	0.827986i
$47$	0.566017	+	1.74202i	0.0825621	+	0.254100i	0.983813	−	0.179197i	$-0.0573501\pi$
$47$	0.566017	+	1.74202i	0.0825621	+	0.254100i	−0.901251	+	0.433297i	$0.857350\pi$
$48$	−1.54259	+	2.12319i	−0.222653	+	0.306456i
$49$	−19.0063			−2.71519
$50$	−10.2979	−	5.60945i	−1.45635	−	0.793296i
$51$	−2.04630	−	8.39194i	−0.286540	−	1.17511i
$52$	−9.61068	−	6.98257i	−1.33276	−	0.968308i
$53$	2.41330	+	7.42738i	0.331493	+	1.02023i	0.968424	+	0.249309i	$0.0802035\pi$
$53$	2.41330	+	7.42738i	0.331493	+	1.02023i	−0.636931	+	0.770921i	$0.719797\pi$
$54$	7.52836	−	2.44611i	1.02448	−	0.332874i
$55$	−0.612721	+	0.969645i	−0.0826193	+	0.130747i
$56$	−17.0686	−	5.54591i	−2.28088	−	0.741104i
$57$			7.99222i			1.05860i
$58$	−7.23961	−	2.35229i	−0.950607	−	0.308871i
$59$	6.62047	−	4.81005i	0.861912	−	0.626216i	−0.0664926	−	0.997787i	$-0.521181\pi$
$59$	6.62047	−	4.81005i	0.861912	−	0.626216i	0.928404	+	0.371571i	$0.121181\pi$
$60$	10.4772	+	12.6149i	1.35260	+	1.62857i
$61$	−0.610641	+	0.840475i	−0.0781846	+	0.107612i	−0.846318	−	0.532678i	$-0.821186\pi$
$61$	−0.610641	+	0.840475i	−0.0781846	+	0.107612i	0.768133	+	0.640290i	$0.221186\pi$
$62$	2.22419	+	3.06134i	0.282473	+	0.388790i
$63$	−4.16334	−	5.73035i	−0.524532	−	0.721956i
$64$	9.80725	+	7.12538i	1.22591	+	0.890673i
$65$	−5.83752	+	4.84831i	−0.724055	+	0.601359i
$66$	2.03903	−	1.48144i	0.250987	−	0.182353i
$67$	2.08409	−	6.41416i	0.254612	−	0.783614i	−0.739294	−	0.673383i	$-0.764841\pi$
$67$	2.08409	−	6.41416i	0.254612	−	0.783614i	0.993906	−	0.110232i	$-0.0351593\pi$
$68$	14.0223	−	3.41921i	1.70045	−	0.414640i
$69$	5.01625	−	15.4384i	0.603885	−	1.85857i
$70$	−14.2864	+	22.6085i	−1.70755	+	2.70223i
$71$	5.67232	−	1.84305i	0.673181	−	0.218730i	0.0475734	−	0.998868i	$-0.484851\pi$
$71$	5.67232	−	1.84305i	0.673181	−	0.218730i	0.625607	+	0.780138i	$0.284851\pi$
$72$	−1.51049	−	4.64880i	−0.178013	−	0.547867i
$73$	−6.60310	+	9.08839i	−0.772835	+	1.06372i	0.223202	+	0.974772i	$0.428349\pi$
$73$	−6.60310	+	9.08839i	−0.772835	+	1.06372i	−0.996037	+	0.0889438i	$0.971651\pi$
$74$		−	18.1690i		−	2.11210i
$75$	9.46061	−	4.49672i	1.09242	−	0.519236i
$76$	−13.3544			−1.53185
$77$	2.11632	+	1.53759i	0.241177	+	0.175225i
$78$	15.8581	−	5.15260i	1.79557	−	0.583417i
$79$	−7.47959	+	2.43027i	−0.841519	+	0.273426i	−0.697890	−	0.716205i	$-0.745877\pi$
$79$	−7.47959	+	2.43027i	−0.841519	+	0.273426i	−0.143630	+	0.989631i	$0.545877\pi$
$80$	−2.15486	+	1.78970i	−0.240920	+	0.200095i
$81$	−3.47263	+	10.6877i	−0.385848	+	1.18752i
$82$		−	0.671173i		−	0.0741186i
$83$	4.81624	−	14.8229i	0.528651	−	1.62702i	−0.228331	−	0.973584i	$-0.573327\pi$
$83$	4.81624	−	14.8229i	0.528651	−	1.62702i	0.756982	−	0.653436i	$-0.226673\pi$
$84$	30.2561	−	21.9823i	3.30121	−	2.39847i
$85$	0.0941685	−	9.21906i	0.0102140	−	0.999948i
$86$	8.46099	+	6.14727i	0.912372	+	0.662877i
$87$	5.50103	−	3.99673i	0.589772	−	0.428494i
$88$	1.06109	+	1.46047i	0.113113	+	0.155686i
$89$	−3.21356	−	2.33478i	−0.340636	−	0.247487i	0.404294	−	0.914629i	$-0.367517\pi$
$89$	−3.21356	−	2.33478i	−0.340636	−	0.247487i	−0.744930	+	0.667142i	$0.767517\pi$
$90$	−7.26876	+	0.471463i	−0.766194	+	0.0496965i
$91$	10.1723	+	14.0010i	1.06635	+	1.46770i
$92$	25.7964	+	8.38175i	2.68946	+	0.873857i
$93$	−3.38011			−0.350501
$94$	1.32749	−	4.08560i	0.136920	−	0.421398i
$95$	−2.10541	+	8.26656i	−0.216011	+	0.848131i
$96$	−8.17002	+	2.65460i	−0.833849	+	0.270934i
$97$	−4.37153	+	1.42040i	−0.443862	+	0.144220i	−0.522417	−	0.852690i	$-0.674969\pi$
$97$	−4.37153	+	1.42040i	−0.443862	+	0.144220i	0.0785547	+	0.996910i	$0.474969\pi$
$98$	36.0627	+	26.2011i	3.64289	+	2.64671i
$99$			0.712471i			0.0716061i
$100$	7.51365	+	15.8079i	0.751365	+	1.58079i
$101$	0.883930			0.0879543			0.0439771	−	0.999033i	$-0.485997\pi$
$101$	0.883930			0.0879543			0.0439771	+	0.999033i	$0.485997\pi$
$102$	−7.68601	+	18.7438i	−0.761028	+	1.85592i
$103$	1.38951	+	4.27648i	0.136913	+	0.421374i	0.995883	−	0.0906522i	$-0.0288952\pi$
$103$	1.38951	+	4.27648i	0.136913	+	0.421374i	−0.858970	+	0.512026i	$0.828895\pi$
$104$	3.69058	+	11.3584i	0.361891	+	1.11379i
$105$	−8.83731	−	22.1947i	−0.862433	−	2.16598i
$106$	5.65998	−	17.4196i	0.549745	−	1.69194i
$107$			13.3197i			1.28767i	0.765166	+	0.643833i	$0.222657\pi$
$107$			13.3197i			1.28767i	−0.765166	+	0.643833i	$0.777343\pi$
$108$	−11.2365	−	3.65098i	−1.08124	−	0.351315i
$109$	3.66188	+	5.04015i	0.350745	+	0.482759i	0.947541	−	0.319634i	$-0.103560\pi$
$109$	3.66188	+	5.04015i	0.350745	+	0.482759i	−0.596796	+	0.802393i	$0.703560\pi$
$110$	2.49928	−	0.995146i	0.238297	−	0.0948834i
$111$	13.1300	+	9.53951i	1.24625	+	0.905451i
$112$	3.75500	+	5.16831i	0.354814	+	0.488359i
$113$	3.42954	+	4.72036i	0.322624	+	0.444054i	0.939266	−	0.343190i	$-0.111507\pi$
$113$	3.42954	+	4.72036i	0.322624	+	0.444054i	−0.616642	+	0.787244i	$0.711507\pi$
$114$	11.0176	−	15.1645i	1.03190	−	1.42028i
$115$	9.25543	−	14.6469i	0.863073	−	1.36583i
$116$	6.67821	+	9.19177i	0.620056	+	0.853434i
$117$	−1.45656	+	4.48282i	−0.134659	+	0.414437i
$118$	−19.1926			−1.76682
$119$	−20.9673	−	1.57518i	−1.92207	−	0.144397i
$120$	−1.06707	−	16.4515i	−0.0974094	−	1.50181i
$121$	3.31788	+	10.2114i	0.301625	+	0.928307i
$122$	2.31727	−	0.752926i	0.209796	−	0.0681667i
$123$	0.485031	+	0.352395i	0.0437337	+	0.0317744i
$124$		−	5.64789i		−	0.507196i
$125$	10.9699	−	2.15883i	0.981181	−	0.193092i
$126$			16.6122i			1.47993i
$127$	16.1938	+	11.7655i	1.43697	+	1.04402i	0.988665	+	0.150138i	$0.0479718\pi$
$127$	16.1938	+	11.7655i	1.43697	+	1.04402i	0.448304	+	0.893881i	$0.352028\pi$
$128$	−6.25141	−	19.2399i	−0.552552	−	1.70058i
$129$	−8.88479	+	2.88684i	−0.782262	+	0.254172i
$130$	17.7598	−	1.15193i	1.55763	−	0.101031i
$131$	9.24601	+	3.00421i	0.807828	+	0.262479i	0.683678	−	0.729784i	$-0.260379\pi$
$131$	9.24601	+	3.00421i	0.807828	+	0.262479i	0.124150	+	0.992263i	$0.460379\pi$
$132$	−3.76183			−0.327425
$133$	18.5026	+	6.01187i	1.60438	+	0.521295i
$134$	−12.7966	+	9.29726i	−1.10546	+	0.803161i
$135$	−4.03154	+	6.38000i	−0.346980	+	0.549103i
$136$	−13.4254	−	5.50515i	−1.15122	−	0.472063i
$137$	5.19699	−	3.77583i	0.444008	−	0.322591i	−0.343217	−	0.939256i	$-0.611517\pi$
$137$	5.19699	−	3.77583i	0.444008	−	0.322591i	0.787226	+	0.616665i	$0.211517\pi$
$138$	−30.8005	+	22.3778i	−2.62191	+	1.90493i
$139$	10.9493	−	15.0704i	0.928709	−	1.27826i	−0.0316514	−	0.999499i	$-0.510077\pi$
$139$	10.9493	−	15.0704i	0.928709	−	1.27826i	0.960361	−	0.278760i	$-0.0899234\pi$
$140$	37.0855	−	14.7664i	3.13430	−	1.24799i
$141$	2.25551	+	3.10445i	0.189949	+	0.261442i
$142$	−13.3034	−	4.32255i	−1.11640	−	0.362740i
$143$		−	1.74078i		−	0.145572i
$144$	−0.537672	+	1.65479i	−0.0448060	+	0.137899i
$145$	6.74272	−	2.68477i	0.559953	−	0.222958i
$146$	25.0575	−	8.14169i	2.07378	−	0.673811i
$147$	−37.8691	+	12.3044i	−3.12339	+	1.01485i
$148$	−15.9398	+	21.9392i	−1.31024	+	1.80339i
$149$	−12.5650			−1.02937			−0.514683	−	0.857380i	$-0.672090\pi$
$149$	−12.5650			−1.02937			−0.514683	+	0.857380i	$0.672090\pi$
$150$	−24.1496	−	4.50979i	−1.97180	−	0.368223i
$151$	6.00838			0.488955			0.244477	−	0.969655i	$-0.421384\pi$
$151$	6.00838			0.488955			0.244477	+	0.969655i	$0.421384\pi$
$152$	10.8617	+	7.89146i	0.880997	+	0.640082i
$153$	−3.00956	−	4.87219i	−0.243308	−	0.393893i
$154$	−1.89587	−	5.83488i	−0.152773	−	0.470188i
$155$	−3.49613	−	0.890433i	−0.280816	−	0.0715213i
$156$	−23.6692	−	7.69057i	−1.89505	−	0.615739i
$157$	−5.81595			−0.464163			−0.232081	−	0.972696i	$-0.574554\pi$
$157$	−5.81595			−0.464163			−0.232081	+	0.972696i	$0.574554\pi$
$158$	17.5421	+	5.69976i	1.39557	+	0.453448i
$159$	9.61674	+	13.2363i	0.762657	+	1.04971i
$160$	−9.14977	+	0.593468i	−0.723353	+	0.0469178i
$161$	−31.9679	−	23.2260i	−2.51942	−	1.83047i
$162$	21.3224	−	15.4916i	1.67525	−	1.21714i
$163$	−10.1379	−	13.9537i	−0.794065	−	1.09294i	−0.993590	−	0.113044i	$-0.963940\pi$
$163$	−10.1379	−	13.9537i	−0.794065	−	1.09294i	0.199525	−	0.979893i	$-0.436060\pi$
$164$	−0.588824	+	0.810447i	−0.0459794	+	0.0632853i
$165$	−0.593080	+	2.32863i	−0.0461712	+	0.181284i
$166$	−29.5724	+	21.4856i	−2.29526	+	1.66760i
$167$	4.52677	+	1.47084i	0.350292	+	0.113817i	0.478878	−	0.877882i	$-0.341044\pi$
$167$	4.52677	+	1.47084i	0.350292	+	0.113817i	−0.128586	+	0.991698i	$0.541044\pi$
$168$	−37.5985			−2.90079
$169$	−0.458413	+	1.41085i	−0.0352625	+	0.108527i
$170$	−12.8876	+	17.3625i	−0.988433	+	1.33164i
$171$	1.63740	+	5.03939i	0.125215	+	0.385372i
$172$	−4.82368	−	14.8458i	−0.367802	−	1.13198i
$173$	0.451304	−	0.621167i	0.0343120	−	0.0472264i	−0.791516	−	0.611148i	$-0.790708\pi$
$173$	0.451304	−	0.621167i	0.0343120	−	0.0472264i	0.825828	+	0.563922i	$0.190708\pi$
$174$	−15.9474			−1.20897
$175$	−3.29385	−	25.2846i	−0.248991	−	1.91133i
$176$		−	0.642591i		−	0.0484371i
$177$	10.0770	−	13.8698i	0.757431	−	1.04251i
$178$	2.87881	+	8.86007i	0.215776	+	0.664090i
$179$	6.51619	+	20.0548i	0.487043	+	1.49896i	0.829000	+	0.559248i	$0.188910\pi$
$179$	6.51619	+	20.0548i	0.487043	+	1.49896i	−0.341957	+	0.939716i	$0.611090\pi$
$180$	9.19070	+	5.80763i	0.685035	+	0.432875i
$181$	17.6635	+	5.73923i	1.31292	+	0.426593i	0.880058	−	0.474867i	$-0.157504\pi$
$181$	17.6635	+	5.73923i	1.31292	+	0.426593i	0.432862	+	0.901460i	$0.357504\pi$
$182$		−	40.5885i		−	3.00862i
$183$	−0.672558	+	2.06992i	−0.0497169	+	0.153013i
$184$	−16.0283	−	22.0610i	−1.18162	−	1.62636i
$185$	11.0677	+	13.3258i	0.813713	+	0.979736i
$186$	6.41344	+	4.65964i	0.470256	+	0.341661i
$187$	1.61312	+	1.36785i	0.117963	+	0.100027i
$188$	−5.18728	+	3.76878i	−0.378322	+	0.274867i
$189$	13.9248	+	10.1169i	1.01288	+	0.735900i
$190$	15.3907	−	12.7826i	1.11656	−	0.927348i
$191$	−16.3077	+	11.8483i	−1.17999	+	0.857310i	−0.992170	−	0.124895i	$-0.960141\pi$
$191$	−16.3077	+	11.8483i	−1.17999	+	0.857310i	−0.187815	+	0.982204i	$0.560141\pi$
$192$	24.1533	+	7.84787i	1.74311	+	0.566371i
$193$		−	17.3885i		−	1.25165i	−0.779964	−	0.625825i	$-0.784762\pi$
$193$		−	17.3885i		−	1.25165i	0.779964	−	0.625825i	$-0.215238\pi$
$194$	10.2527	+	3.33129i	0.736098	+	0.239173i
$195$	−8.49221	+	13.4391i	−0.608140	+	0.962394i
$196$	−20.5597	−	63.2761i	−1.46855	−	4.51972i
$197$	5.48197	−	1.78120i	0.390574	−	0.126905i	−0.107145	−	0.994243i	$-0.534171\pi$
$197$	5.48197	−	1.78120i	0.390574	−	0.126905i	0.497719	+	0.867338i	$0.334171\pi$
$198$	0.982175	−	1.35185i	0.0698001	−	0.0960716i
$199$			19.5316i			1.38456i	0.721631	+	0.692278i	$0.243393\pi$
$199$			19.5316i			1.38456i	−0.721631	+	0.692278i	$0.756607\pi$
$200$	3.23016	−	17.2973i	0.228407	−	1.22310i
$201$		−	14.1291i		−	0.996587i
$202$	−1.67717	−	1.21854i	−0.118006	−	0.0857360i
$203$	−5.11479	−	15.7417i	−0.358988	−	1.10485i
$204$	25.7250	−	15.8904i	1.80111	−	1.11255i
$205$	0.408847	+	0.492265i	0.0285551	+	0.0343813i
$206$	3.25885	−	10.0297i	0.227055	−	0.698804i
$207$		−	10.7622i		−	0.748024i
$208$	1.31370	−	4.04314i	0.0910884	−	0.280341i
$209$	−1.15024	−	1.58317i	−0.0795640	−	0.109510i
$210$	−13.8284	+	54.2950i	−0.954251	+	3.74671i
$211$	−12.6223	+	17.3731i	−0.868953	+	1.19601i	0.110407	+	0.993886i	$0.464785\pi$
$211$	−12.6223	+	17.3731i	−0.868953	+	1.19601i	−0.979360	+	0.202125i	$0.935215\pi$
$212$	−22.1168	+	16.0688i	−1.51899	+	1.10361i
$213$	10.1086	−	7.34435i	0.692632	−	0.503226i
$214$	18.3618	−	25.2729i	1.25519	−	1.72762i
$215$	−9.95025	+	0.645389i	−0.678602	+	0.0440151i
$216$	6.98170	+	9.60948i	0.475044	+	0.653842i
$217$	−2.54257	+	7.82522i	−0.172601	+	0.531211i
$218$		−	14.6113i		−	0.989601i
$219$	−7.27263	+	22.3829i	−0.491439	+	1.51249i
$220$	−3.89095	−	0.990989i	−0.262328	−	0.0668125i
$221$	7.35326	+	11.9042i	0.494634	+	0.800766i
$222$	−11.7623	−	36.2007i	−0.789435	−	2.42963i
$223$	−15.1438	−	11.0026i	−1.01410	−	0.736788i	−0.0490363	−	0.998797i	$-0.515615\pi$
$223$	−15.1438	−	11.0026i	−1.01410	−	0.736788i	−0.965065	+	0.262009i	$0.915615\pi$
$224$			20.9111i			1.39718i
$225$	5.04400	−	4.77358i	0.336267	−	0.318238i
$226$		−	13.6842i		−	0.910261i
$227$	−2.57108	+	3.53879i	−0.170649	+	0.234878i	−0.885772	−	0.464120i	$-0.846371\pi$
$227$	−2.57108	+	3.53879i	−0.170649	+	0.234878i	0.715123	+	0.698998i	$0.246371\pi$
$228$	−26.6078	+	8.64540i	−1.76214	+	0.572556i
$229$	−1.38748	−	4.27022i	−0.0916871	−	0.282184i	0.894689	−	0.446690i	$-0.147397\pi$
$229$	−1.38748	−	4.27022i	−0.0916871	−	0.282184i	−0.986376	+	0.164506i	$0.947397\pi$
$230$	−37.7528	+	15.0321i	−2.48934	+	0.991189i
$231$	5.21206	+	1.69350i	0.342928	+	0.111424i
$232$		−	11.4224i		−	0.749917i
$233$	−2.23952	−	0.727663i	−0.146716	−	0.0476708i	0.234739	−	0.972059i	$-0.424577\pi$
$233$	−2.23952	−	0.727663i	−0.146716	−	0.0476708i	−0.381454	+	0.924388i	$0.624577\pi$
$234$	8.94346	−	6.49780i	0.584652	−	0.424775i
$235$	1.51512	+	3.80519i	0.0988357	+	0.248223i
$236$	23.1752	+	16.8378i	1.50858	+	1.09605i
$237$	−13.3293	+	9.68434i	−0.865834	+	0.629065i
$238$	37.6120	+	31.8931i	2.43802	+	2.06732i
$239$	15.6067	+	11.3389i	1.00951	+	0.733453i	0.964106	−	0.265516i	$-0.0855424\pi$
$239$	15.6067	+	11.3389i	1.00951	+	0.733453i	0.0454044	+	0.998969i	$0.485542\pi$
$240$	−3.13481	+	4.96090i	−0.202351	+	0.320225i
$241$	6.32565	+	8.70652i	0.407471	+	0.560836i	0.962599	−	0.270929i	$-0.0873308\pi$
$241$	6.32565	+	8.70652i	0.407471	+	0.560836i	−0.555128	+	0.831765i	$0.687331\pi$
$242$	7.78149	−	23.9490i	0.500213	−	1.53950i
$243$			13.4173i			0.860719i
$244$	−3.45867	−	1.12379i	−0.221419	−	0.0719433i
$245$	−42.4103	+	2.75080i	−2.70950	+	0.175742i
$246$	−0.434507	−	1.33727i	−0.0277031	−	0.0852615i
$247$	−4.00065	−	12.3127i	−0.254556	−	0.783441i
$248$	−3.33750	+	4.59367i	−0.211931	+	0.291698i
$249$		−	32.6517i		−	2.06922i
$250$	−23.7905	−	11.0264i	−1.50464	−	0.697369i
$251$	16.7582			1.05777			0.528883	−	0.848695i	$-0.322611\pi$
$251$	16.7582			1.05777			0.528883	+	0.848695i	$0.322611\pi$
$252$	14.5740	−	20.0593i	0.918073	−	1.26362i
$253$	1.22824	+	3.78013i	0.0772187	+	0.237655i
$254$	−14.5070	−	44.6479i	−0.910248	−	2.80146i
$255$	−5.78065	−	18.4294i	−0.361999	−	1.15410i
$256$	−7.16952	+	22.0655i	−0.448095	+	1.37909i
$257$	−11.1329			−0.694454			−0.347227	−	0.937781i	$-0.612877\pi$
$257$	−11.1329			−0.694454			−0.347227	+	0.937781i	$0.612877\pi$
$258$	20.8377	+	6.77058i	1.29730	+	0.421518i
$259$	31.9613	−	23.2213i	1.98598	−	1.44290i
$260$	−22.4557	−	14.1898i	−1.39264	−	0.880014i
$261$	2.64977	−	3.64710i	0.164017	−	0.225750i
$262$	−13.4020	−	18.4463i	−0.827979	−	1.13961i
$263$	−6.09645	+	4.42933i	−0.375923	+	0.273124i	−0.759663	−	0.650317i	$-0.774636\pi$
$263$	−6.09645	+	4.42933i	−0.375923	+	0.273124i	0.383739	+	0.923441i	$0.374636\pi$
$264$	3.05965	+	2.22297i	0.188309	+	0.136814i
$265$	6.45996	+	16.2240i	0.396832	+	0.996634i
$266$	−26.8194	−	36.9137i	−1.64440	−	2.26332i
$267$	−7.91433	−	2.57152i	−0.484349	−	0.157375i
$268$	23.6085			1.44212
$269$	−24.9720	−	8.11389i	−1.52257	−	0.494712i	−0.576064	−	0.817404i	$-0.695412\pi$
$269$	−24.9720	−	8.11389i	−1.52257	−	0.494712i	−0.946504	+	0.322692i	$0.895412\pi$
$270$	16.4446	−	6.54779i	1.00079	−	0.398486i
$271$	−3.45415	−	10.6308i	−0.209825	−	0.645773i	−0.999481	−	0.0322238i	$-0.989741\pi$
$271$	−3.45415	−	10.6308i	−0.209825	−	0.645773i	0.789656	−	0.613550i	$-0.210259\pi$
$272$	2.71438	+	4.39432i	0.164583	+	0.266445i
$273$	29.3318	+	21.3108i	1.77524	+	1.28979i
$274$	−15.0660			−0.910168
$275$	−1.22688	+	2.25233i	−0.0739834	+	0.135820i
$276$	56.8240			3.42040
$277$	6.98405	−	9.61272i	0.419631	−	0.577573i	−0.545903	−	0.837848i	$-0.683813\pi$
$277$	6.98405	−	9.61272i	0.419631	−	0.577573i	0.965534	+	0.260276i	$0.0838134\pi$
$278$	−41.5506	+	13.5006i	−2.49204	+	0.809713i
$279$	−2.13128	+	0.692496i	−0.127597	+	0.0414586i
$280$	−38.8891	−	9.90469i	−2.32407	−	0.591918i
$281$	3.92085	−	12.0671i	0.233898	−	0.719864i	−0.763368	−	0.645964i	$-0.776455\pi$
$281$	3.92085	−	12.0671i	0.233898	−	0.719864i	0.997266	−	0.0738999i	$-0.0235445\pi$
$282$		−	8.99973i		−	0.535926i
$283$	5.34437	+	1.73649i	0.317690	+	0.103224i	0.463521	−	0.886086i	$-0.346586\pi$
$283$	5.34437	+	1.73649i	0.317690	+	0.103224i	−0.145832	+	0.989309i	$0.546586\pi$
$284$	12.2718	+	16.8907i	0.728198	+	1.00228i
$285$	1.15672	+	17.8337i	0.0685181	+	1.05638i
$286$	−2.39975	+	3.30297i	−0.141900	+	0.195309i
$287$	1.18067	−	0.857807i	0.0696928	−	0.0506348i
$288$	−4.60764	+	3.34764i	−0.271508	+	0.197262i
$289$	−16.8092	−	2.53994i	−0.988776	−	0.149408i
$290$	−16.4948	−	4.20106i	−0.968606	−	0.246695i
$291$	−7.79050	+	5.66013i	−0.456687	+	0.331802i
$292$	−37.4000	−	12.1520i	−2.18867	−	0.711141i
$293$	−31.5463			−1.84296			−0.921478	−	0.388431i	$-0.873017\pi$
$293$	−31.5463			−1.84296			−0.921478	+	0.388431i	$0.873017\pi$
$294$	88.8152	+	28.8578i	5.17981	+	1.68302i
$295$	14.0766	−	11.6912i	0.819572	−	0.680690i
$296$	25.9290	−	8.42483i	1.50709	−	0.489683i
$297$	−0.535004	−	1.64657i	−0.0310441	−	0.0955438i
$298$	23.8409	+	17.3215i	1.38107	+	1.00341i
$299$			26.2953i			1.52070i
$300$	25.2043	+	26.6322i	1.45517	+	1.53761i
$301$			22.7405i			1.31074i
$302$	−11.4003	−	8.28283i	−0.656016	−	0.476623i
$303$	1.76118	−	0.572242i	0.101177	−	0.0328745i
$304$	−1.47680	−	4.54512i	−0.0847002	−	0.260680i
$305$	−1.24093	+	1.96380i	−0.0710554	+	0.112447i
$306$	−1.00619	+	13.3933i	−0.0575198	+	0.765647i
$307$	−0.393657			−0.0224672			−0.0112336	−	0.999937i	$-0.503576\pi$
$307$	−0.393657			−0.0224672			−0.0112336	+	0.999937i	$0.503576\pi$
$308$	−2.82970	+	8.70893i	−0.161237	+	0.496237i
$309$	5.53705	+	7.62109i	0.314992	+	0.433549i
$310$	5.40609	+	6.50910i	0.307045	+	0.369692i
$311$	4.75191	−	6.54044i	0.269456	−	0.370874i	−0.652750	−	0.757573i	$-0.726385\pi$
$311$	4.75191	−	6.54044i	0.269456	−	0.370874i	0.922206	+	0.386699i	$0.126385\pi$
$312$	14.7065	+	20.2418i	0.832594	+	1.14597i
$313$	−1.93756	−	2.66682i	−0.109517	−	0.150738i	0.750740	−	0.660598i	$-0.229697\pi$
$313$	−1.93756	−	2.66682i	−0.109517	−	0.150738i	−0.860257	+	0.509860i	$0.829697\pi$
$314$	11.0352	+	8.01755i	0.622753	+	0.452457i
$315$	−10.1194	−	12.1840i	−0.570161	−	0.686492i
$316$	−16.1817	−	22.2723i	−0.910294	−	1.25291i
$317$	1.43102	+	0.464967i	0.0803742	+	0.0261152i	0.348928	−	0.937149i	$-0.386546\pi$
$317$	1.43102	+	0.464967i	0.0803742	+	0.0261152i	−0.268554	+	0.963265i	$0.586546\pi$
$318$		−	38.3718i		−	2.15178i
$319$	−0.514484	+	1.58342i	−0.0288056	+	0.0886544i
$320$	22.9149	+	14.4800i	1.28098	+	0.809458i
$321$	8.62297	+	26.5388i	0.481287	+	1.48125i
$322$	28.6379	+	88.1385i	1.59593	+	4.91176i
$323$	14.5534	+	5.96768i	0.809771	+	0.332051i
$324$	−39.3379			−2.18544
$325$	−12.3240	+	11.6633i	−0.683613	+	0.646963i
$326$			40.4514i			2.24040i
$327$	10.5590	+	7.67157i	0.583915	+	0.424239i
$328$	0.957831	−	0.311218i	0.0528874	−	0.0171841i
$329$	8.88368	−	2.88648i	0.489773	−	0.159137i
$330$	4.33544	−	3.60077i	0.238658	−	0.198216i
$331$	2.02104	−	6.22012i	0.111086	−	0.341889i	−0.880024	−	0.474929i	$-0.842474\pi$
$331$	2.02104	−	6.22012i	0.111086	−	0.341889i	0.991111	+	0.133040i	$0.0424738\pi$
$332$	54.5583			2.99428
$333$	10.2334	+	3.32502i	0.560784	+	0.182210i
$334$	−6.56150	−	9.03113i	−0.359029	−	0.494162i
$335$	3.72206	−	14.6141i	0.203358	−	0.798451i
$336$	10.8275	+	7.86664i	0.590689	+	0.429161i
$337$	−10.6278	−	14.6279i	−0.578934	−	0.796834i	0.414644	−	0.909984i	$-0.363906\pi$
$337$	−10.6278	−	14.6279i	−0.578934	−	0.796834i	−0.993578	+	0.113150i	$0.963906\pi$
$338$	2.81472	−	2.04501i	0.153100	−	0.111234i
$339$	9.88906	+	7.18482i	0.537100	+	0.390226i
$340$	30.7941	−	9.65900i	1.67004	−	0.523833i
$341$	0.669564	−	0.486467i	0.0362589	−	0.0263436i
$342$	3.84022	−	11.8190i	0.207656	−	0.639098i
$343$			61.2280i			3.30600i
$344$	−4.84947	+	14.9251i	−0.261466	+	0.804709i
$345$	8.95874	−	35.1750i	0.482322	−	1.89376i
$346$	−1.71261	+	0.556462i	−0.0920707	+	0.0299156i
$347$	27.4506	−	8.91924i	1.47363	−	0.478810i	0.541424	−	0.840750i	$-0.317885\pi$
$347$	27.4506	−	8.91924i	1.47363	−	0.478810i	0.932201	+	0.361940i	$0.117885\pi$
$348$	19.2566	+	13.9907i	1.03226	+	0.749981i
$349$	12.9081			0.690955			0.345478	−	0.938427i	$-0.387717\pi$
$349$	12.9081			0.690955			0.345478	+	0.938427i	$0.387717\pi$
$350$	−28.6062	+	52.5158i	−1.52906	+	2.80709i
$351$		−	11.4539i		−	0.611362i
$352$	1.23634	−	1.70168i	0.0658973	−	0.0906998i
$353$	−2.32780	−	7.16424i	−0.123896	−	0.381314i	0.869802	−	0.493401i	$-0.164246\pi$
$353$	−2.32780	−	7.16424i	−0.123896	−	0.381314i	−0.993698	+	0.112087i	$0.964246\pi$
$354$	−38.2402	+	12.4250i	−2.03244	+	0.660381i
$355$	12.3904	−	4.93350i	0.657612	−	0.261843i
$356$	4.29681	−	13.2242i	0.227730	−	0.700882i
$357$	−42.7959	+	10.4354i	−2.26500	+	0.552301i
$358$	15.2826	−	47.0349i	0.807709	−	2.48587i
$359$	−22.9112	+	16.6460i	−1.20921	+	0.878540i	−0.995159	−	0.0982829i	$-0.968665\pi$
$359$	−22.9112	+	16.6460i	−1.20921	+	0.878540i	−0.214048	+	0.976823i	$0.568665\pi$
$360$	−4.04330	−	10.1546i	−0.213100	−	0.535196i
$361$	3.59709	+	2.61344i	0.189321	+	0.137549i
$362$	−25.6031	−	35.2396i	−1.34567	−	1.85215i
$363$	13.2214	+	18.1977i	0.693942	+	0.955129i
$364$	−35.6086	+	49.0110i	−1.86640	+	2.56887i
$365$	−13.4187	+	21.2353i	−0.702365	+	1.11151i
$366$	4.12960	−	3.00033i	0.215857	−	0.156830i
$367$	−6.80552	−	2.21125i	−0.355245	−	0.115426i	0.125957	−	0.992036i	$-0.459800\pi$
$367$	−6.80552	−	2.21125i	−0.355245	−	0.115426i	−0.481202	+	0.876609i	$0.659800\pi$
$368$			9.70662i			0.505993i
$369$	0.378026	+	0.122828i	0.0196793	+	0.00639418i
$370$	−2.62961	−	40.5419i	−0.136707	−	2.10767i
$371$	37.8770	−	12.3070i	1.96647	−	0.638946i
$372$	−3.65636	−	11.2531i	−0.189573	−	0.583446i
$373$	4.14021	+	3.00804i	0.214372	+	0.155750i	0.689790	−	0.724010i	$-0.257703\pi$
$373$	4.14021	+	3.00804i	0.214372	+	0.155750i	−0.475418	+	0.879760i	$0.657703\pi$
$374$	−1.17510	−	4.81913i	−0.0607632	−	0.249191i
$375$	20.4594	−	11.4031i	1.05652	−	0.588855i
$376$	6.44612			0.332433
$377$	−6.47420	+	8.91097i	−0.333438	+	0.458938i
$378$	−12.4743	−	38.3919i	−0.641608	−	1.97467i
$379$	−6.73161	+	2.18723i	−0.345779	+	0.112351i	−0.476758	−	0.879035i	$-0.658188\pi$
$379$	−6.73161	+	2.18723i	−0.345779	+	0.112351i	0.130978	+	0.991385i	$0.458188\pi$
$380$	−29.7986	+	1.93278i	−1.52864	+	0.0991497i
$381$	39.8821	+	12.9585i	2.04322	+	0.663883i
$382$	47.2757			2.41884
$383$	8.33306	−	25.6465i	0.425800	−	1.31048i	−0.476427	−	0.879214i	$-0.658068\pi$
$383$	8.33306	−	25.6465i	0.425800	−	1.31048i	0.902226	−	0.431263i	$-0.141932\pi$
$384$	−24.9112	−	34.2873i	−1.27124	−	1.74972i
$385$	4.94484	+	3.12466i	0.252012	+	0.159247i
$386$	−23.9708	+	32.9930i	−1.22008	+	1.67930i
$387$	−5.01075	+	3.64052i	−0.254711	+	0.185058i
$388$	−9.45761	−	13.0173i	−0.480138	−	0.660853i
$389$	−9.73570	−	7.07340i	−0.493619	−	0.358635i	0.312955	−	0.949768i	$-0.398681\pi$
$389$	−9.73570	−	7.07340i	−0.493619	−	0.358635i	−0.806574	+	0.591132i	$0.798681\pi$
$390$	34.6396	−	13.7925i	1.75404	−	0.698413i
$391$	−24.3669	−	20.6620i	−1.23229	−	1.04492i
$392$	−20.6696	+	63.6144i	−1.04397	+	3.21301i
$393$	20.3671			1.02738
$394$	−12.8570	−	4.17749i	−0.647726	−	0.210459i
$395$	−16.3381	+	6.50537i	−0.822057	+	0.327321i
$396$	−2.37197	+	0.770699i	−0.119196	+	0.0387291i
$397$	−16.2559	+	5.28187i	−0.815862	+	0.265090i	−0.687079	−	0.726583i	$-0.741107\pi$
$397$	−16.2559	+	5.28187i	−0.815862	+	0.265090i	−0.128783	+	0.991673i	$0.541107\pi$
$398$	26.9252	−	37.0593i	1.34964	−	1.85762i
$399$	40.7574			2.04042
$400$	−4.54928	+	4.30538i	−0.227464	+	0.215269i
$401$		−	8.62281i		−	0.430603i	−0.976548	−	0.215301i	$-0.930927\pi$
$401$		−	8.62281i		−	0.430603i	0.976548	−	0.215301i	$-0.0690734\pi$
$402$	−19.4776	+	26.8086i	−0.971453	+	1.33709i
$403$	5.20737	−	1.69198i	0.259398	−	0.0842834i
$404$	0.956171	+	2.94279i	0.0475713	+	0.146409i
$405$	−6.20192	+	24.3508i	−0.308176	+	1.21000i
$406$	−11.9958	+	36.9194i	−0.595344	+	1.83228i
$407$	−3.97385			−0.196976
$408$	−30.3133	−	2.27731i	−1.50073	−	0.112744i
$409$	−12.2074	+	8.86917i	−0.603615	+	0.438552i	−0.847160	−	0.531337i	$-0.821690\pi$
$409$	−12.2074	+	8.86917i	−0.603615	+	0.438552i	0.243545	+	0.969890i	$0.421690\pi$
$410$	−0.0971393	−	1.49764i	−0.00479737	−	0.0739632i
$411$	7.91029	−	10.8876i	0.390186	−	0.537045i
$412$	−12.7342	+	9.25196i	−0.627370	+	0.455811i
$413$	−24.5295	−	33.7620i	−1.20702	−	1.66132i
$414$	−14.8362	+	20.4203i	−0.729159	+	1.00360i
$415$	8.60153	−	33.7725i	0.422233	−	1.65783i
$416$	11.2579	−	8.17931i	0.551962	−	0.401024i
$417$	12.0595	−	37.1155i	0.590558	−	1.81755i
$418$			4.58959i			0.224484i
$419$	−11.3405	−	3.68476i	−0.554021	−	0.180012i	0.0186083	−	0.999827i	$-0.494076\pi$
$419$	−11.3405	−	3.68476i	−0.554021	−	0.180012i	−0.572629	+	0.819815i	$0.694076\pi$
$420$	64.3312	−	53.4299i	3.13904	−	2.60711i
$421$	−7.74100	−	23.8243i	−0.377273	−	1.16113i	−0.941932	−	0.335803i	$-0.890992\pi$
$421$	−7.74100	−	23.8243i	−0.377273	−	1.16113i	0.564659	−	0.825324i	$-0.309008\pi$
$422$	47.8992	−	15.5634i	2.33169	−	0.757614i
$423$	2.05821	+	1.49537i	0.100073	+	0.0727076i
$424$	27.4840			1.33474
$425$	−1.12416	−	20.5849i	−0.0545295	−	0.998512i
$426$	−29.3047			−1.41982
$427$	4.28612	+	3.11405i	0.207420	+	0.150699i
$428$	−44.3442	+	14.4083i	−2.14346	+	0.696451i
$429$	−1.12696	−	3.46841i	−0.0544099	−	0.167457i
$430$	19.7694	+	12.4923i	0.953364	+	0.602433i
$431$	−6.36010	−	2.06652i	−0.306355	−	0.0995409i	0.151805	−	0.988410i	$-0.451491\pi$
$431$	−6.36010	−	2.06652i	−0.306355	−	0.0995409i	−0.458160	+	0.888870i	$0.651491\pi$
$432$		−	4.22807i		−	0.203423i
$433$	2.49133	−	7.66754i	0.119726	−	0.368478i	−0.873177	−	0.487402i	$-0.837944\pi$
$433$	2.49133	−	7.66754i	0.119726	−	0.368478i	0.992903	+	0.118924i	$0.0379445\pi$
$434$	15.6117	−	11.3426i	0.749387	−	0.544461i
$435$	11.6964	−	9.71438i	0.560801	−	0.465769i
$436$	−12.8186	+	17.6433i	−0.613898	+	0.844959i
$437$	17.3749	+	23.9145i	0.831155	+	1.14399i
$438$	44.6550	−	32.4437i	2.13370	−	1.55022i
$439$	−10.8189	+	14.8910i	−0.516359	+	0.710707i	−0.984975	−	0.172695i	$-0.944753\pi$
$439$	−10.8189	+	14.8910i	−0.516359	+	0.710707i	0.468617	+	0.883402i	$0.344753\pi$
$440$	2.57907	+	3.10529i	0.122952	+	0.148039i
$441$	−21.3570	+	15.5168i	−1.01700	+	0.738893i
$442$	2.45842	−	32.7240i	0.116935	−	1.55652i
$443$	−22.3801			−1.06331			−0.531655	−	0.846961i	$-0.678430\pi$
$443$	−22.3801			−1.06331			−0.531655	+	0.846961i	$0.678430\pi$
$444$	−17.5560	+	54.0318i	−0.833170	+	2.56423i
$445$	−7.50858	−	4.74469i	−0.355941	−	0.224920i
$446$	13.5663	+	41.7528i	0.642383	+	1.97705i
$447$	−25.0351	+	8.13440i	−1.18412	+	0.384744i
$448$	36.3369	−	50.0134i	1.71676	−	2.36291i
$449$			3.24492i			0.153137i	0.997064	+	0.0765686i	$0.0243964\pi$
$449$			3.24492i			0.153137i	−0.997064	+	0.0765686i	$0.975604\pi$
$450$	−16.1511	+	2.10402i	−0.761371	+	0.0991846i
$451$	−0.146796			−0.00691236
$452$	−12.0053	+	16.5238i	−0.564680	+	0.777215i
$453$	11.9714	−	3.88973i	0.562464	−	0.182756i
$454$	9.75678	−	3.17017i	0.457909	−	0.148784i
$455$	24.7246	+	29.7692i	1.15911	+	1.39560i
$456$	26.7501	+	8.69162i	1.25269	+	0.407022i
$457$	−35.7574			−1.67266			−0.836331	−	0.548224i	$-0.815304\pi$
$457$	−35.7574			−1.67266			−0.836331	+	0.548224i	$0.815304\pi$
$458$	−3.25408	+	10.0150i	−0.152053	+	0.467972i
$459$	10.6139	+	9.00007i	0.495414	+	0.420087i
$460$	58.7746	+	14.9693i	2.74038	+	0.697949i
$461$	−25.7775	−	18.7285i	−1.20058	−	0.872271i	−0.206237	−	0.978502i	$-0.566122\pi$
$461$	−25.7775	−	18.7285i	−1.20058	−	0.872271i	−0.994341	+	0.106231i	$0.966122\pi$
$462$	−7.55482	−	10.3983i	−0.351482	−	0.483774i
$463$	−21.2453	+	15.4356i	−0.987351	+	0.717353i	−0.959339	−	0.282255i	$-0.908918\pi$
$463$	−21.2453	+	15.4356i	−0.987351	+	0.717353i	−0.0280118	+	0.999608i	$0.508918\pi$
$464$	−2.38988	+	3.28939i	−0.110947	+	0.152706i
$465$	−7.54231	+	0.489206i	−0.349766	+	0.0226864i
$466$	3.24615	+	4.46795i	0.150375	+	0.206974i
$467$	−0.610526	+	1.87901i	−0.0282518	+	0.0869501i	−0.964188	−	0.265219i	$-0.914556\pi$
$467$	−0.610526	+	1.87901i	−0.0282518	+	0.0869501i	0.935936	+	0.352169i	$0.114556\pi$
$468$	−16.4999			−0.762707
$469$	−32.7099	−	10.6281i	−1.51040	−	0.490760i
$470$	2.37083	−	9.30866i	0.109358	−	0.429376i
$471$	−11.5879	+	3.76515i	−0.533944	+	0.173489i
$472$	−8.89948	−	27.3898i	−0.409632	−	1.26072i
$473$	1.34451	−	1.85055i	0.0618205	−	0.0850886i
$474$	38.6415			1.77486
$475$	−3.50155	+	18.7505i	−0.160662	+	0.860334i
$476$	−17.4367	−	71.5084i	−0.799212	−	3.27758i
$477$	8.77548	+	6.37576i	0.401802	+	0.291926i
$478$	−13.9810	−	43.0290i	−0.639475	−	1.96810i
$479$	17.2466	−	5.60376i	0.788017	−	0.256042i	0.112758	−	0.993623i	$-0.464032\pi$
$479$	17.2466	−	5.60376i	0.788017	−	0.256042i	0.675260	+	0.737580i	$0.264032\pi$
$480$	−17.8462	+	7.10587i	−0.814564	+	0.324337i
$481$	−25.0032	−	8.12402i	−1.14005	−	0.370424i
$482$		−	25.2400i		−	1.14965i
$483$	−78.7304	−	25.5811i	−3.58236	−	1.16398i
$484$	−30.4068	+	22.0918i	−1.38213	+	1.00417i
$485$	−9.54897	+	3.80214i	−0.433597	+	0.172646i
$486$	18.4963	−	25.4580i	0.839011	−	1.15480i
$487$	−1.51534	−	2.08569i	−0.0686668	−	0.0945117i	0.773302	−	0.634038i	$-0.218604\pi$
$487$	−1.51534	−	2.08569i	−0.0686668	−	0.0945117i	−0.841969	+	0.539526i	$0.818604\pi$
$488$	2.14900	+	2.95785i	0.0972808	+	0.133896i
$489$	−29.2327	−	21.2388i	−1.32195	−	0.960452i
$490$	84.2617	+	53.2452i	3.80656	+	2.40537i
$491$	5.14337	−	3.73688i	0.232117	−	0.168643i	−0.465647	−	0.884971i	$-0.654178\pi$
$491$	5.14337	−	3.73688i	0.232117	−	0.168643i	0.697764	+	0.716328i	$0.254178\pi$
$492$	−0.648529	+	1.99597i	−0.0292379	+	0.0899851i
$493$	−3.17027	−	13.0014i	−0.142782	−	0.585551i
$494$	−9.38283	+	28.8774i	−0.422153	+	1.29925i
$495$	0.103116	+	1.58979i	0.00463474	+	0.0714559i
$496$	1.92224	−	0.624575i	0.0863113	−	0.0280442i
$497$	−9.39889	−	28.9268i	−0.421598	−	1.29754i
$498$	−45.0118	+	61.9535i	−2.01703	+	2.77620i
$499$		−	27.9596i		−	1.25164i	−0.779966	−	0.625822i	$-0.784764\pi$
$499$		−	27.9596i		−	1.25164i	0.779966	−	0.625822i	$-0.215236\pi$
$500$	19.0537	+	34.1860i	0.852107	+	1.52884i
$501$	9.97153			0.445495
$502$	−31.7970	−	23.1019i	−1.41917	−	1.03109i
$503$	14.0289	−	4.55827i	0.625519	−	0.203243i	0.0209296	−	0.999781i	$-0.493337\pi$
$503$	14.0289	−	4.55827i	0.625519	−	0.203243i	0.604589	+	0.796538i	$0.293337\pi$
$504$	−23.7072	+	7.70295i	−1.05600	+	0.343117i
$505$	1.97238	−	0.127932i	0.0877698	−	0.00569289i
$506$	2.88062	−	8.86562i	0.128059	−	0.394125i
$507$			3.10781i			0.138023i
$508$	−21.6526	+	66.6397i	−0.960677	+	2.95666i
$509$	−4.07124	+	2.95793i	−0.180454	+	0.131108i	−0.674346	−	0.738416i	$-0.735574\pi$
$509$	−4.07124	+	2.95793i	−0.180454	+	0.131108i	0.493891	+	0.869524i	$0.335574\pi$
$510$	−14.4376	+	42.9370i	−0.639307	+	1.90128i
$511$	46.3475	+	33.6735i	2.05029	+	1.48963i
$512$	11.2890	−	8.20194i	0.498908	−	0.362478i
$513$	−7.56828	−	10.4168i	−0.334148	−	0.459915i
$514$	21.1237	+	15.3473i	0.931727	+	0.676939i
$515$	3.71946	+	9.34133i	0.163899	+	0.411628i
$516$	−19.2218	−	26.4566i	−0.846194	−	1.16469i
$517$	−0.893587	−	0.290344i	−0.0392999	−	0.0127693i
$518$	−92.6552			−4.07104
$519$	0.497065	−	1.52981i	0.0218187	−	0.0671511i
$520$	9.87899	+	24.8108i	0.433223	+	1.08803i
$521$	9.57485	−	3.11106i	0.419482	−	0.136298i	−0.0916678	−	0.995790i	$-0.529220\pi$
$521$	9.57485	−	3.11106i	0.419482	−	0.136298i	0.511150	+	0.859492i	$0.329220\pi$
$522$	−10.0554	+	3.26720i	−0.440113	+	0.143001i
$523$	−22.9271	−	16.6575i	−1.00253	−	0.728381i	−0.0399008	−	0.999204i	$-0.512704\pi$
$523$	−22.9271	−	16.6575i	−1.00253	−	0.728381i	−0.962629	+	0.270823i	$0.912704\pi$
$524$			34.0317i			1.48668i
$525$	−22.9316	−	48.2457i	−1.00082	−	2.10561i
$526$	17.6735			0.770601
$527$	−2.52388	+	6.15499i	−0.109942	+	0.268115i
$528$	−0.416003	−	1.28033i	−0.0181042	−	0.0557191i
$529$	−11.4457	−	35.2262i	−0.497639	−	1.53157i
$530$	10.1084	−	39.6889i	0.439081	−	1.72398i
$531$	3.51235	−	10.8099i	0.152423	−	0.469109i
$532$			68.1024i			2.95261i
$533$	−0.923632	−	0.300106i	−0.0400069	−	0.0129990i
$534$	11.4717	+	15.7895i	0.496431	+	0.683279i
$535$	1.92777	+	29.7213i	0.0833448	+	1.28496i
$536$	−19.2018	−	13.9509i	−0.829392	−	0.602588i
$537$	25.9663	+	35.7395i	1.12053	+	1.54227i
$538$	36.1966	+	49.8204i	1.56055	+	2.14791i
$539$	5.73060	−	7.88750i	0.246835	−	0.339739i
$540$	−25.6014	−	6.52044i	−1.10171	−	0.280595i
$541$	23.2317	+	31.9757i	0.998810	+	1.37474i	0.926052	+	0.377395i	$0.123180\pi$
$541$	23.2317	+	31.9757i	0.998810	+	1.37474i	0.0727580	+	0.997350i	$0.476820\pi$
$542$	−8.10109	+	24.9326i	−0.347972	+	1.07095i
$543$	38.9091			1.66975
$544$	−1.26657	+	16.8593i	−0.0543036	+	0.722836i
$545$	8.90051	+	10.7165i	0.381256	+	0.459044i
$546$	−26.2764	−	80.8704i	−1.12453	−	3.46093i
$547$	−1.70580	+	0.554247i	−0.0729346	+	0.0236979i	−0.345257	−	0.938508i	$-0.612208\pi$
$547$	−1.70580	+	0.554247i	−0.0729346	+	0.0236979i	0.272322	+	0.962206i	$0.412208\pi$
$548$	18.1923	+	13.2175i	0.777135	+	0.564622i
$549$			1.44295i			0.0615836i
$550$	5.43282	−	2.58227i	0.231656	−	0.110108i
$551$			12.3821i			0.527494i
$552$	−46.2174	−	33.5789i	−1.96714	−	1.42921i
$553$	12.3935	+	38.1432i	0.527024	+	1.62201i
$554$	−26.5032	+	8.61140i	−1.12601	+	0.365863i
$555$	30.6787	+	19.3860i	1.30224	+	0.822888i
$556$	62.0169	+	20.1505i	2.63010	+	0.854572i
$557$	37.4116			1.58518			0.792590	−	0.609755i	$-0.208732\pi$
$557$	37.4116			1.58518			0.792590	+	0.609755i	$0.208732\pi$
$558$	4.99855	+	1.62413i	0.211605	+	0.0687548i
$559$	12.2428	−	8.89489i	0.517814	−	0.376214i
$560$	9.12683	+	10.9890i	0.385679	+	0.464370i
$561$	4.09958	+	1.68105i	0.173084	+	0.0709741i
$562$	−24.0745	+	17.4912i	−1.01552	+	0.737821i
$563$	28.3676	−	20.6103i	1.19555	−	0.868620i	0.201713	−	0.979445i	$-0.435349\pi$
$563$	28.3676	−	20.6103i	1.19555	−	0.868620i	0.993840	+	0.110824i	$0.0353490\pi$
$564$	−7.89552	+	10.8673i	−0.332462	+	0.457594i
$565$	8.33579	+	10.0366i	0.350689	+	0.422241i
$566$	−7.74661	−	10.6623i	−0.325614	−	0.448169i
$567$	54.5032	+	17.7092i	2.28892	+	0.743715i
$568$		−	20.9897i		−	0.880707i
$569$	5.52986	−	17.0192i	0.231824	−	0.713480i	−0.765703	−	0.643194i	$-0.777609\pi$
$569$	5.52986	−	17.0192i	0.231824	−	0.713480i	0.997527	−	0.0702859i	$-0.0223912\pi$
$570$	22.3898	−	35.4323i	0.937805	−	1.48410i
$571$	14.1571	−	4.59993i	0.592457	−	0.192501i	0.00258351	−	0.999997i	$-0.499178\pi$
$571$	14.1571	−	4.59993i	0.592457	−	0.192501i	0.589873	+	0.807496i	$0.299178\pi$
$572$	5.79544	−	1.88305i	0.242319	−	0.0787343i
$573$	−24.8219	+	34.1644i	−1.03695	+	1.42724i
$574$	−3.42274			−0.142862
$575$	18.5325	−	34.0224i	0.772859	−	1.41883i
$576$	16.8373			0.701556
$577$	−4.11709	−	2.99124i	−0.171397	−	0.124527i	0.498780	−	0.866729i	$-0.333782\pi$
$577$	−4.11709	−	2.99124i	−0.171397	−	0.124527i	−0.670177	+	0.742202i	$0.733782\pi$
$578$	28.3924	+	27.9915i	1.18097	+	1.16429i
$579$	−11.2570	−	34.6456i	−0.467826	−	1.43982i
$580$	16.2320	+	19.5438i	0.673995	+	0.811511i
$581$	−75.5912	−	24.5611i	−3.13605	−	1.01897i
$582$	22.5845			0.936157
$583$	−3.80995	−	1.23793i	−0.157792	−	0.0512697i
$584$	23.2380	+	31.9844i	0.961596	+	1.32352i
$585$	−2.60133	+	10.2137i	−0.107552	+	0.422284i
$586$	59.8562	+	43.4881i	2.47264	+	1.79648i
$587$	−31.5372	+	22.9131i	−1.30168	+	0.945727i	−0.999971	−	0.00767294i	$-0.997558\pi$
$587$	−31.5372	+	22.9131i	−1.30168	+	0.945727i	−0.301710	+	0.953400i	$0.597558\pi$
$588$	−81.9280	−	112.764i	−3.37865	−	4.65032i
$589$	3.61790	−	4.97962i	0.149073	−	0.205182i
$590$	−42.8260	+	2.77776i	−1.76312	+	0.114359i
$591$	9.76940	−	7.09788i	0.401859	−	0.291968i
$592$	−9.22965	−	2.99890i	−0.379336	−	0.123254i
$593$	1.68514			0.0692004			0.0346002	−	0.999401i	$-0.488984\pi$
$593$	1.68514			0.0692004			0.0346002	+	0.999401i	$0.488984\pi$
$594$	−1.25476	+	3.86175i	−0.0514833	+	0.158449i
$595$	−47.0139	−	0.480226i	−1.92738	−	0.0196873i
$596$	−13.5919	−	41.8316i	−0.556747	−	1.71349i
$597$	12.6444	+	38.9156i	0.517502	+	1.59271i
$598$	36.2493	−	49.8929i	1.48234	−	2.04027i
$599$	−38.9862			−1.59293			−0.796466	−	0.604683i	$-0.793300\pi$
$599$	−38.9862			−1.59293			−0.796466	+	0.604683i	$0.793300\pi$
$600$	−4.76206	−	36.5550i	−0.194410	−	1.49235i
$601$			23.6134i			0.963209i	0.876389	+	0.481605i	$0.159946\pi$
$601$			23.6134i			0.963209i	−0.876389	+	0.481605i	$0.840054\pi$
$602$	31.3489	−	43.1480i	1.27768	−	1.75858i
$603$	−2.89467	−	8.90889i	−0.117880	−	0.362798i
$604$	6.49943	+	20.0032i	0.264458	+	0.813918i
$605$	8.88134	+	22.3052i	0.361078	+	0.906837i
$606$	−4.13054	−	1.34209i	−0.167792	−	0.0545188i
$607$		−	1.27823i		−	0.0518816i	−0.999663	−	0.0259408i	$-0.991742\pi$
$607$		−	1.27823i		−	0.0518816i	0.999663	−	0.0259408i	$-0.00825814\pi$
$608$	4.83400	−	14.8775i	0.196045	−	0.603363i
$609$	−20.3819	−	28.0533i	−0.825915	−	1.13678i
$610$	5.06173	−	2.01544i	0.204944	−	0.0816029i
$611$	−5.02882	−	3.65365i	−0.203444	−	0.147811i
$612$	12.9650	−	15.2898i	0.524081	−	0.618055i
$613$	−26.0496	+	18.9261i	−1.05213	+	0.764419i	−0.972617	−	0.232415i	$-0.925337\pi$
$613$	−26.0496	+	18.9261i	−1.05213	+	0.764419i	−0.0795156	+	0.996834i	$0.525337\pi$
$614$	0.746927	+	0.542674i	0.0301435	+	0.0219005i
$615$	1.13329	+	0.716129i	0.0456986	+	0.0288771i
$616$	7.44786	−	5.41119i	0.300083	−	0.218023i
$617$	−13.5785	−	4.41192i	−0.546649	−	0.177617i	0.0226561	−	0.999743i	$-0.492788\pi$
$617$	−13.5785	−	4.41192i	−0.546649	−	0.177617i	−0.569305	+	0.822126i	$0.692788\pi$
$618$		−	22.0934i		−	0.888726i
$619$	−14.7163	−	4.78162i	−0.591498	−	0.192189i	−0.00205326	−	0.999998i	$-0.500654\pi$
$619$	−14.7163	−	4.78162i	−0.591498	−	0.192189i	−0.589445	+	0.807808i	$0.700654\pi$
$620$	−0.817423	−	12.6026i	−0.0328285	−	0.506132i
$621$	8.08147	+	24.8722i	0.324298	+	0.998087i
$622$	−18.0326	+	5.85915i	−0.723042	+	0.234931i
$623$	−11.9066	+	16.3880i	−0.477026	+	0.656570i
$624$		−	8.90620i		−	0.356533i
$625$	24.1656	−	6.40486i	0.966625	−	0.256194i
$626$			7.73107i			0.308996i
$627$	−3.31672	−	2.40974i	−0.132457	−	0.0962356i
$628$	−6.29127	−	19.3625i	−0.251049	−	0.772649i
$629$	27.1749	−	16.7860i	1.08353	−	0.669301i
$630$	2.40429	+	37.0680i	0.0957892	+	1.47683i
$631$	10.3484	−	31.8491i	0.411963	−	1.26789i	−0.502977	−	0.864300i	$-0.667762\pi$
$631$	10.3484	−	31.8491i	0.411963	−	1.26789i	0.914939	−	0.403591i	$-0.132238\pi$
$632$			27.6772i			1.10094i
$633$	−13.9021	+	42.7863i	−0.552560	+	1.70060i
$634$	−2.07425	−	2.85496i	−0.0823791	−	0.113385i
$635$	37.8374	+	23.9095i	1.50153	+	0.948821i
$636$	−33.6638	+	46.3343i	−1.33486	+	1.83727i
$637$	52.1816	−	37.9121i	2.06751	−	1.50213i
$638$	3.15900	−	2.29515i	0.125066	−	0.0908658i
$639$	4.86920	−	6.70187i	0.192622	−	0.265122i
$640$	−16.7339	−	42.0267i	−0.661465	−	1.66125i
$641$	−13.7717	−	18.9551i	−0.543948	−	0.748680i	0.445228	−	0.895417i	$-0.353123\pi$
$641$	−13.7717	−	18.9551i	−0.543948	−	0.748680i	−0.989175	+	0.146737i	$0.953123\pi$
$642$	20.2237	−	62.2420i	0.798164	−	2.45650i
$643$		−	23.9636i		−	0.945033i	−0.881322	−	0.472516i	$-0.843346\pi$
$643$		−	23.9636i		−	0.945033i	0.881322	−	0.472516i	$-0.156654\pi$
$644$	42.7439	−	131.552i	1.68435	−	5.18388i
$645$	−19.4075	+	7.72754i	−0.764170	+	0.304272i
$646$	−19.3869	−	31.3856i	−0.762769	−	1.23485i
$647$	13.9763	+	43.0147i	0.549465	+	1.69108i	0.710129	+	0.704071i	$0.248636\pi$
$647$	13.9763	+	43.0147i	0.549465	+	1.69108i	−0.160664	+	0.987009i	$0.551364\pi$
$648$	31.9952	+	23.2459i	1.25689	+	0.913184i
$649$			4.19773i			0.164775i
$650$	39.4621	−	5.14077i	1.54783	−	0.201637i
$651$			17.2373i			0.675585i
$652$	35.4883	−	48.8455i	1.38983	−	1.91294i
$653$	3.29162	−	1.06951i	0.128811	−	0.0418533i	−0.243902	−	0.969800i	$-0.578428\pi$
$653$	3.29162	−	1.06951i	0.128811	−	0.0418533i	0.372713	+	0.927947i	$0.378428\pi$
$654$	−9.45912	−	29.1122i	−0.369881	−	1.13838i
$655$	21.0662	+	5.36536i	0.823123	+	0.209642i
$656$	−0.340949	−	0.110781i	−0.0133118	−	0.00432527i
$657$			15.6032i			0.608739i
$658$	−20.8351	−	6.76974i	−0.812237	−	0.263912i
$659$	−16.4442	+	11.9474i	−0.640577	+	0.465406i	−0.860048	−	0.510213i	$-0.829567\pi$
$659$	−16.4442	+	11.9474i	−0.640577	+	0.465406i	0.219472	+	0.975619i	$0.429567\pi$
$660$	−8.39406	+	0.544451i	−0.326738	+	0.0211927i
$661$	−8.04104	−	5.84216i	−0.312760	−	0.227234i	0.420320	−	0.907376i	$-0.361918\pi$
$661$	−8.04104	−	5.84216i	−0.312760	−	0.227234i	−0.733080	+	0.680142i	$0.761918\pi$
$662$	−12.4095	+	9.01601i	−0.482308	+	0.350417i
$663$	22.3576	+	18.9581i	0.868296	+	0.736273i
$664$	−44.3746	−	32.2400i	−1.72207	−	1.25116i
$665$	42.1565	+	10.7369i	1.63476	+	0.416358i
$666$	−14.8331	−	20.4161i	−0.574772	−	0.791106i
$667$	7.77151	−	23.9182i	0.300914	−	0.926118i
$668$			16.6616i			0.644657i
$669$	−37.2960	−	12.1182i	−1.44195	−	0.468517i
$670$	−27.2084	+	22.5978i	−1.05115	+	0.873028i
$671$	−0.164677	−	0.506824i	−0.00635729	−	0.0195657i
$672$	13.5375	+	41.6641i	0.522220	+	1.60723i
$673$	−15.2356	+	20.9700i	−0.587290	+	0.808335i	−0.994471	−	0.105013i	$-0.966512\pi$
$673$	−15.2356	+	20.9700i	−0.587290	+	0.808335i	0.407181	+	0.913347i	$0.366512\pi$
$674$			42.4061i			1.63342i
$675$	−8.07251	+	14.8197i	−0.310711	+	0.570410i
$676$	−5.19290			−0.199727
$677$	−23.6303	+	32.5243i	−0.908185	+	1.25001i	0.0595980	+	0.998222i	$0.481018\pi$
$677$	−23.6303	+	32.5243i	−0.908185	+	1.25001i	−0.967783	+	0.251787i	$0.918982\pi$
$678$	−8.85896	−	27.2651i	−0.340226	−	1.04711i
$679$	7.24352	+	22.2932i	0.277981	+	0.855536i
$680$	−30.7539	−	10.3410i	−1.17936	−	0.396560i
$681$	−2.83178	+	8.71533i	−0.108514	+	0.333972i
$682$	−1.94105			−0.0743267
$683$	15.1472	+	4.92164i	0.579593	+	0.188321i	0.584118	−	0.811669i	$-0.301440\pi$
$683$	15.1472	+	4.92164i	0.579593	+	0.188321i	−0.00452516	+	0.999990i	$0.501440\pi$
$684$	−15.0060	+	10.9025i	−0.573768	+	0.416867i
$685$	11.0500	−	9.17747i	0.422198	−	0.350653i
$686$	84.4056	−	116.174i	3.22262	−	4.43556i
$687$	−5.52894	−	7.60994i	−0.210942	−	0.290337i
$688$	4.51928	−	3.28345i	0.172296	−	0.125180i
$689$	−21.4412	−	15.5779i	−0.816843	−	0.593471i
$690$	−65.4887	+	54.3912i	−2.49311	+	2.07064i
$691$	−3.16763	−	4.35987i	−0.120502	−	0.165857i	0.744504	−	0.667618i	$-0.232686\pi$
$691$	−3.16763	−	4.35987i	−0.120502	−	0.165857i	−0.865007	+	0.501760i	$0.832686\pi$
$692$	2.55618	+	0.830555i	0.0971716	+	0.0315730i
$693$	3.63335			0.138019
$694$	−64.3805	−	20.9185i	−2.44385	−	0.794055i
$695$	22.2509	−	35.2126i	0.844026	−	1.33569i
$696$	−7.39468	−	22.7585i	−0.280295	−	0.862658i
$697$	1.00386	−	0.620084i	0.0380238	−	0.0234873i
$698$	−24.4919	−	17.7944i	−0.927033	−	0.673529i
$699$	−4.93319			−0.186590
$700$	80.6146	−	38.3169i	3.04695	−	1.44824i
$701$	−12.5945			−0.475688			−0.237844	−	0.971303i	$-0.576441\pi$
$701$	−12.5945			−0.475688			−0.237844	+	0.971303i	$0.576441\pi$
$702$	−15.7897	+	21.7327i	−0.595944	+	0.820246i
$703$	−28.1075	+	9.13266i	−1.06009	+	0.344445i
$704$	−5.91397	+	1.92157i	−0.222891	+	0.0724217i
$705$	5.48222	+	6.60076i	0.206472	+	0.248599i
$706$	−5.45945	+	16.8025i	−0.205469	+	0.632369i
$707$		−	4.50772i		−	0.169530i
$708$	57.0759	+	18.5451i	2.14504	+	0.696967i
$709$	23.2260	+	31.9679i	0.872271	+	1.20058i	0.978502	+	0.206237i	$0.0661218\pi$
$709$	23.2260	+	31.9679i	0.872271	+	1.20058i	−0.106231	+	0.994341i	$0.533878\pi$
$710$	−30.3106	−	7.71983i	−1.13754	−	0.289720i
$711$	−6.42058	+	8.83716i	−0.240790	+	0.331420i
$712$	−11.3093	+	8.21671i	−0.423835	+	0.307934i
$713$	−10.1141	+	7.34829i	−0.378774	+	0.275196i
$714$	95.5869	+	39.1959i	3.57725	+	1.46687i
$715$	−0.251945	−	3.88435i	−0.00942219	−	0.145266i
$716$	−59.7179	+	43.3876i	−2.23176	+	1.62147i
$717$	38.4360	+	12.4886i	1.43542	+	0.466396i
$718$	66.4191			2.47874
$719$	38.1841	+	12.4068i	1.42403	+	0.462694i	0.916879	−	0.399166i	$-0.130700\pi$
$719$	38.1841	+	12.4068i	1.42403	+	0.462694i	0.507146	+	0.861860i	$0.330700\pi$
$720$	−0.960253	+	3.77027i	−0.0357865	+	0.140510i
$721$	21.8085	−	7.08601i	0.812191	−	0.263897i
$722$	−3.22239	−	9.91751i	−0.119925	−	0.369092i
$723$	18.2400	+	13.2521i	0.678352	+	0.492852i
$724$			65.0139i			2.41622i
$725$	14.6570	−	6.96661i	0.544347	−	0.258734i
$726$		−	52.7546i		−	1.95791i
$727$	1.73819	+	1.26287i	0.0644659	+	0.0468372i	0.619552	−	0.784956i	$-0.287314\pi$
$727$	1.73819	+	1.26287i	0.0644659	+	0.0468372i	−0.555086	+	0.831793i	$0.687314\pi$
$728$	57.9239	−	18.8206i	2.14680	−	0.697539i
$729$	−1.73175	−	5.32978i	−0.0641389	−	0.197399i
$730$	54.7345	−	21.7938i	2.02582	−	0.806625i
$731$	−1.37738	+	18.3342i	−0.0509441	+	0.678117i
$732$	−7.61873			−0.281596
$733$	9.96117	−	30.6573i	0.367924	−	1.13235i	−0.580205	−	0.814470i	$-0.697028\pi$
$733$	9.96117	−	30.6573i	0.367924	−	1.13235i	0.948130	−	0.317884i	$-0.102972\pi$
$734$	9.86453	+	13.5774i	0.364107	+	0.501150i
$735$	−82.7194	+	32.9366i	−3.05115	+	1.21488i
$736$	−18.6755	+	25.7046i	−0.688388	+	0.947485i
$737$	2.03346	+	2.79882i	0.0749034	+	0.103096i
$738$	−0.547945	−	0.754182i	−0.0201701	−	0.0277618i
$739$	−36.0655	−	26.2031i	−1.32669	−	0.963897i	−0.999823	−	0.0188272i	$-0.994007\pi$
$739$	−36.0655	−	26.2031i	−1.32669	−	0.963897i	−0.326868	−	0.945070i	$-0.605993\pi$
$740$	−32.3924	+	51.2616i	−1.19077	+	1.88441i
$741$	−15.9422	−	21.9425i	−0.585650	−	0.806078i
$742$	−88.8338	−	28.8638i	−3.26119	−	1.05962i
$743$			17.7074i			0.649621i	0.945779	+	0.324811i	$0.105301\pi$
$743$			17.7074i			0.649621i	−0.945779	+	0.324811i	$0.894699\pi$
$744$	−3.67590	+	11.3133i	−0.134765	+	0.414765i
$745$	−28.0373	+	1.81854i	−1.02721	+	0.0666263i
$746$	−3.70894	−	11.4149i	−0.135794	−	0.417931i
$747$	−6.68947	−	20.5881i	−0.244755	−	0.753278i
$748$	−2.80890	+	6.85007i	−0.102704	+	0.250463i
$749$	67.9257			2.48195
$750$	−54.5395	−	6.56786i	−1.99150	−	0.239825i
$751$			12.1873i			0.444721i	0.974965	+	0.222360i	$0.0713761\pi$
$751$			12.1873i			0.444721i	−0.974965	+	0.222360i	$0.928624\pi$
$752$	−1.85633	−	1.34871i	−0.0676935	−	0.0491822i
$753$	33.3897	−	10.8490i	1.21679	−	0.395359i
$754$	24.5684	−	7.98275i	0.894727	−	0.290714i
$755$	13.4070	−	0.869597i	0.487930	−	0.0316479i
$756$	−18.6187	+	57.3023i	−0.677154	+	2.08407i
$757$	0.922765			0.0335385			0.0167692	−	0.999859i	$-0.494662\pi$
$757$	0.922765			0.0335385			0.0167692	+	0.999859i	$0.494662\pi$
$758$	15.7878	+	5.12977i	0.573439	+	0.186321i
$759$	4.89439	+	6.73655i	0.177655	+	0.244521i
$760$	25.3786	+	16.0368i	0.920579	+	0.581717i
$761$	−0.733937	−	0.533236i	−0.0266052	−	0.0193298i	0.574403	−	0.818573i	$-0.305234\pi$
$761$	−0.733937	−	0.533236i	−0.0266052	−	0.0193298i	−0.601008	+	0.799243i	$0.705234\pi$
$762$	−57.8087	−	79.5668i	−2.09419	−	2.88240i
$763$	25.7029	−	18.6743i	0.930509	−	0.676054i
$764$	−57.0859	−	41.4753i	−2.06529	−	1.50052i
$765$	−7.42062	−	10.4361i	−0.268293	−	0.377319i
$766$	−51.1662	+	37.1744i	−1.84871	+	1.34317i
$767$	−8.58173	+	26.4118i	−0.309868	+	0.953676i
$768$			48.6058i			1.75391i
$769$	−5.90424	+	18.1714i	−0.212912	+	0.655276i	0.786383	+	0.617739i	$0.211951\pi$
$769$	−5.90424	+	18.1714i	−0.212912	+	0.655276i	−0.999295	+	0.0375372i	$0.988049\pi$
$770$	−5.07489	−	12.7454i	−0.182886	−	0.459314i
$771$	−22.1818	+	7.20729i	−0.798857	+	0.259564i

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.p (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.89741 - 1.37855i) q^{2} +(1.99244 - 0.647384i) q^{3} +(1.08173 + 3.32921i) q^{4} +(2.23138 - 0.144731i) q^{5} +(-4.67293 - 1.51833i) q^{6} -5.09964i q^{7} +(1.08751 - 3.34701i) q^{8} +(1.12368 - 0.816399i) q^{9} +(-4.43335 - 2.80145i) q^{10} +(-0.301510 + 0.414993i) q^{11} +(4.31056 + 5.93298i) q^{12} +(-2.74548 + 1.99471i) q^{13} +(-7.03009 + 9.67609i) q^{14} +(4.35220 - 1.73293i) q^{15} +(-1.01347 + 0.736326i) q^{16} +(0.308881 - 4.11152i) q^{17} -3.25752 q^{18} +(-1.17888 + 3.62822i) q^{19} +(2.89558 + 7.27218i) q^{20} +(-3.30143 - 10.1607i) q^{21} +(1.14417 - 0.371765i) q^{22} +(4.55445 - 6.26866i) q^{23} -7.37277i q^{24} +(4.95811 - 0.645898i) q^{25} +7.95910 q^{26} +(-1.98385 + 2.73054i) q^{27} +(16.9778 - 5.51642i) q^{28} +(3.08683 - 1.00297i) q^{29} +(-10.6468 - 2.71165i) q^{30} +(-1.53447 - 0.498578i) q^{31} -4.10050 q^{32} +(-0.332082 + 1.02204i) q^{33} +(-6.25399 + 7.37542i) q^{34} +(-0.738074 - 11.3792i) q^{35} +(3.93348 + 2.85784i) q^{36} +(4.55351 + 6.26737i) q^{37} +(7.23849 - 5.25907i) q^{38} +(-4.17888 + 5.75173i) q^{39} +(1.94223 - 7.62585i) q^{40} +(0.168209 + 0.231520i) q^{41} +(-7.74292 + 23.8302i) q^{42} -4.45924 q^{43} +(-1.70775 - 0.554883i) q^{44} +(2.38919 - 1.98433i) q^{45} +(-17.2833 + 5.61567i) q^{46} +(0.566017 + 1.74202i) q^{47} +(-1.54259 + 2.12319i) q^{48} -19.0063 q^{49} +(-10.2979 - 5.60945i) q^{50} +(-2.04630 - 8.39194i) q^{51} +(-9.61068 - 6.98257i) q^{52} +(2.41330 + 7.42738i) q^{53} +(7.52836 - 2.44611i) q^{54} +(-0.612721 + 0.969645i) q^{55} +(-17.0686 - 5.54591i) q^{56} +7.99222i q^{57} +(-7.23961 - 2.35229i) q^{58} +(6.62047 - 4.81005i) q^{59} +(10.4772 + 12.6149i) q^{60} +(-0.610641 + 0.840475i) q^{61} +(2.22419 + 3.06134i) q^{62} +(-4.16334 - 5.73035i) q^{63} +(9.80725 + 7.12538i) q^{64} +(-5.83752 + 4.84831i) q^{65} +(2.03903 - 1.48144i) q^{66} +(2.08409 - 6.41416i) q^{67} +(14.0223 - 3.41921i) q^{68} +(5.01625 - 15.4384i) q^{69} +(-14.2864 + 22.6085i) q^{70} +(5.67232 - 1.84305i) q^{71} +(-1.51049 - 4.64880i) q^{72} +(-6.60310 + 9.08839i) q^{73} -18.1690i q^{74} +(9.46061 - 4.49672i) q^{75} -13.3544 q^{76} +(2.11632 + 1.53759i) q^{77} +(15.8581 - 5.15260i) q^{78} +(-7.47959 + 2.43027i) q^{79} +(-2.15486 + 1.78970i) q^{80} +(-3.47263 + 10.6877i) q^{81} -0.671173i q^{82} +(4.81624 - 14.8229i) q^{83} +(30.2561 - 21.9823i) q^{84} +(0.0941685 - 9.21906i) q^{85} +(8.46099 + 6.14727i) q^{86} +(5.50103 - 3.99673i) q^{87} +(1.06109 + 1.46047i) q^{88} +(-3.21356 - 2.33478i) q^{89} +(-7.26876 + 0.471463i) q^{90} +(10.1723 + 14.0010i) q^{91} +(25.7964 + 8.38175i) q^{92} -3.38011 q^{93} +(1.32749 - 4.08560i) q^{94} +(-2.10541 + 8.26656i) q^{95} +(-8.17002 + 2.65460i) q^{96} +(-4.37153 + 1.42040i) q^{97} +(36.0627 + 26.2011i) q^{98} +0.712471i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 168 q - 8 q^{2} - 44 q^{4} - 4 q^{8} + 28 q^{9} - 18 q^{13} - 10 q^{15} - 28 q^{16} + 2 q^{17} - 60 q^{18} - 8 q^{19} + 32 q^{21} + 6 q^{25} + 52 q^{26} - 54 q^{30} + 44 q^{32} - 24 q^{33} + 26 q^{35} + 34 q^{36}+ \cdots - 36 q^{98}+O(q^{100}) \) 168 * q - 8 * q^2 - 44 * q^4 - 4 * q^8 + 28 * q^9 - 18 * q^13 - 10 * q^15 - 28 * q^16 + 2 * q^17 - 60 * q^18 - 8 * q^19 + 32 * q^21 + 6 * q^25 + 52 * q^26 - 54 * q^30 + 44 * q^32 - 24 * q^33 + 26 * q^35 + 34 * q^36 - 18 * q^38 + 80 * q^42 - 8 * q^43 - 40 * q^47 - 84 * q^49 - 82 * q^50 - 36 * q^51 - 30 * q^52 - 42 * q^53 - 18 * q^55 - 18 * q^59 + 28 * q^60 - 16 * q^64 - 140 * q^66 - 62 * q^67 + 144 * q^68 + 44 * q^69 + 4 * q^70 - 6 * q^72 + 72 * q^76 + 48 * q^77 - 28 * q^81 - 14 * q^83 + 24 * q^84 + 62 * q^85 + 82 * q^86 + 48 * q^87 + 90 * q^89 - 224 * q^93 + 26 * q^94 - 36 * q^98

Introduction

L-functions

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