LMFDB - Embedded newform 425.2.p.a.16.5

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			16.5
Character	$\chi$	$=$	425.16
Dual form			425.2.p.a.186.5

$q$-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} +(2.16680 - 3.50785i) 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} +(-8.94703 + 3.66877i) 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} +(-4.32726 + 8.14093i) 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	−0.821271	−	0.570539i	$-0.806734\pi$
$3$	−1.99244	+	0.647384i	−1.15034	+	0.373768i	−0.329068	+	0.944306i	$0.606734\pi$
$4$	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	$0.414021\pi$
$7$			5.09964i			1.92748i	−0.266838	+	0.963741i	$0.585979\pi$
$8$	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	−0.761140	−	0.648588i	$-0.775360\pi$
$11$	0.301510	−	0.414993i	0.0909088	−	0.125125i	0.852049	+	0.523463i	$0.175360\pi$
$12$	−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
$17$	2.16680	−	3.50785i	0.525526	−	0.850777i
$17$	2.16680	−	3.50785i	0.525526	−	0.850777i
$18$	−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	$0.499361\pi$
$23$	−4.55445	+	6.26866i	−0.949668	+	1.30711i	−0.951675	+	0.307107i	$0.900639\pi$
$24$			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	−0.581256	−	0.813721i	$-0.697439\pi$
$29$	−3.08683	+	1.00297i	−0.573210	+	0.186247i	0.00804671	+	0.999968i	$0.497439\pi$
$30$	−10.6468	−	2.71165i	−1.94383	−	0.495076i
$31$	1.53447	+	0.498578i	0.275598	+	0.0895473i	0.443555	−	0.896247i	$-0.353717\pi$
$31$	1.53447	+	0.498578i	0.275598	+	0.0895473i	−0.167957	+	0.985794i	$0.553717\pi$
$32$	−4.10050			−0.724873
$33$	−0.332082	+	1.02204i	−0.0578081	+	0.177915i
$34$	−8.94703	+	3.66877i	−1.53440	+	0.629189i
$35$	−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	$-0.980261\pi$
$37$	−4.55351	−	6.26737i	−0.748593	−	1.03035i	0.249485	−	0.968379i	$-0.419739\pi$
$38$	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	0.795680	−	0.605717i	$-0.207114\pi$
$41$	−0.168209	−	0.231520i	−0.0262699	−	0.0361574i	−0.821950	+	0.569560i	$0.807114\pi$
$42$	−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	−0.768133	−	0.640290i	$-0.778814\pi$
$61$	0.610641	−	0.840475i	0.0781846	−	0.107612i	0.846318	+	0.532678i	$0.178814\pi$
$62$	−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	−0.625607	−	0.780138i	$-0.715149\pi$
$71$	−5.67232	+	1.84305i	−0.673181	+	0.218730i	−0.0475734	+	0.998868i	$0.515149\pi$
$72$	−1.51049	−	4.64880i	−0.178013	−	0.547867i
$73$	6.60310	−	9.08839i	0.772835	−	1.06372i	−0.223202	−	0.974772i	$-0.571651\pi$
$73$	6.60310	−	9.08839i	0.772835	−	1.06372i	0.996037	−	0.0889438i	$-0.0283491\pi$
$74$			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	0.143630	−	0.989631i	$-0.454123\pi$
$79$	7.47959	−	2.43027i	0.841519	−	0.273426i	0.697890	+	0.716205i	$0.254123\pi$
$80$	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
$85$	−4.32726	+	8.14093i	−0.469357	+	0.883008i
$86$	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	−0.0785547	−	0.996910i	$-0.525031\pi$
$97$	4.37153	−	1.42040i	0.443862	−	0.144220i	0.522417	+	0.852690i	$0.325031\pi$
$98$	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	$0.485997\pi$
$102$	15.4514	−	13.1020i	1.52991	−	1.29729i
$103$	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	$-0.777343\pi$
$107$		−	13.3197i		−	1.28767i	0.765166	−	0.643833i	$-0.222657\pi$
$108$	11.2365	+	3.65098i	1.08124	+	0.351315i
$109$	−3.66188	−	5.04015i	−0.350745	−	0.482759i	0.596796	−	0.802393i	$-0.296440\pi$
$109$	−3.66188	−	5.04015i	−0.350745	−	0.482759i	−0.947541	+	0.319634i	$0.896440\pi$
$110$	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	0.616642	−	0.787244i	$-0.288493\pi$
$113$	−3.42954	−	4.72036i	−0.322624	−	0.444054i	−0.939266	+	0.343190i	$0.888493\pi$
$114$	−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
$119$	17.8887	+	11.0499i	1.63986	+	1.01294i
$120$	−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	−0.124150	−	0.992263i	$-0.539621\pi$
$131$	−9.24601	−	3.00421i	−0.807828	−	0.262479i	−0.683678	+	0.729784i	$0.739621\pi$
$132$	−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
$136$	−9.38438	−	11.0671i	−0.804704	−	0.948998i
$137$	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	$0.489923\pi$
$139$	−10.9493	+	15.0704i	−0.928709	+	1.27826i	−0.960361	+	0.278760i	$0.910077\pi$
$140$	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
$153$	−0.429018	−	5.71066i	−0.0346841	−	0.461680i
$154$	−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	$0.0360602\pi$
$163$	10.1379	+	13.9537i	0.794065	+	1.09294i	−0.199525	+	0.979893i	$0.563940\pi$
$164$	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	0.128586	−	0.991698i	$-0.458956\pi$
$167$	−4.52677	−	1.47084i	−0.350292	−	0.113817i	−0.478878	+	0.877882i	$0.658956\pi$
$168$	−37.5985			−2.90079
$169$	−0.458413	+	1.41085i	−0.0352625	+	0.108527i
$170$	19.4332	−	9.48133i	1.49046	−	0.727185i
$171$	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	−0.825828	−	0.563922i	$-0.809292\pi$
$173$	−0.451304	+	0.621167i	−0.0343120	+	0.0472264i	0.791516	+	0.611148i	$0.209292\pi$
$174$	−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	−0.432862	−	0.901460i	$-0.642496\pi$
$181$	−17.6635	−	5.73923i	−1.31292	−	0.426593i	−0.880058	+	0.474867i	$0.842496\pi$
$182$			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
$187$	−0.802420	−	1.95686i	−0.0586787	−	0.143100i
$188$	−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	$0.215238\pi$
$193$			17.3885i			1.25165i	−0.779964	+	0.625825i	$0.784762\pi$
$194$	−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	−0.497719	−	0.867338i	$-0.665829\pi$
$197$	−5.48197	+	1.78120i	−0.390574	+	0.126905i	0.107145	+	0.994243i	$0.465829\pi$
$198$	−0.982175	+	1.35185i	−0.0698001	+	0.0960716i
$199$		−	19.5316i		−	1.38456i	−0.721631	−	0.692278i	$-0.756607\pi$
$199$		−	19.5316i		−	1.38456i	0.721631	−	0.692278i	$-0.243393\pi$
$200$	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
$204$	−30.1521	+	2.26520i	−2.11107	+	0.158596i
$205$	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	$-0.535215\pi$
$211$	12.6223	−	17.3731i	0.868953	−	1.19601i	0.979360	−	0.202125i	$-0.0647847\pi$
$212$	−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
$221$	1.04822	+	13.9529i	0.0705110	+	0.938571i
$222$	−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	−0.715123	−	0.698998i	$-0.753629\pi$
$227$	2.57108	−	3.53879i	0.170649	−	0.234878i	0.885772	+	0.464120i	$0.153629\pi$
$228$	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	0.381454	−	0.924388i	$-0.375423\pi$
$233$	2.23952	+	0.727663i	0.146716	+	0.0476708i	−0.234739	+	0.972059i	$0.575423\pi$
$234$	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
$238$	−18.7094	−	45.6266i	−1.21275	−	2.95753i
$239$	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	0.555128	−	0.831765i	$-0.312669\pi$
$241$	−6.32565	−	8.70652i	−0.407471	−	0.560836i	−0.962599	+	0.270929i	$0.912669\pi$
$242$	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
$255$	3.35151	−	19.0218i	0.209880	−	1.19119i
$256$	−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	0.946504	−	0.322692i	$-0.104588\pi$
$269$	24.9720	+	8.11389i	1.52257	+	0.494712i	0.576064	+	0.817404i	$0.304588\pi$
$270$	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	$-0.210259\pi$
$272$	0.386939	+	5.15055i	0.0234617	+	0.312298i
$273$	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	−0.965534	−	0.260276i	$-0.916187\pi$
$277$	−6.98405	+	9.61272i	−0.419631	+	0.577573i	0.545903	+	0.837848i	$0.316187\pi$
$278$	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	0.145832	−	0.989309i	$-0.453414\pi$
$283$	−5.34437	−	1.73649i	−0.317690	−	0.103224i	−0.463521	+	0.886086i	$0.653414\pi$
$284$	−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
$289$	−7.60995	−	15.2016i	−0.447644	−	0.894212i
$290$	−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
$306$	−7.05839	+	11.4269i	−0.403501	+	0.653230i
$307$	−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	−0.922206	−	0.386699i	$-0.873615\pi$
$311$	−4.75191	+	6.54044i	−0.269456	+	0.370874i	0.652750	+	0.757573i	$0.273615\pi$
$312$	−14.7065	−	20.2418i	−0.832594	−	1.14597i
$313$	1.93756	+	2.66682i	0.109517	+	0.150738i	0.860257	−	0.509860i	$-0.170303\pi$
$313$	1.93756	+	2.66682i	0.109517	+	0.150738i	−0.750740	+	0.660598i	$0.770303\pi$
$314$	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	0.268554	−	0.963265i	$-0.413454\pi$
$317$	−1.43102	−	0.464967i	−0.0803742	−	0.0261152i	−0.348928	+	0.937149i	$0.613454\pi$
$318$			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
$323$	10.1728	+	11.9970i	0.566032	+	0.667529i
$324$	−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	0.993578	−	0.113150i	$-0.0360939\pi$
$337$	10.6278	+	14.6279i	0.578934	+	0.796834i	−0.414644	+	0.909984i	$0.636094\pi$
$338$	2.81472	−	2.04501i	0.153100	−	0.111234i
$339$	9.88906	+	7.18482i	0.537100	+	0.390226i
$340$	−31.7838	−	5.60010i	−1.72372	−	0.303708i
$341$	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	−0.932201	−	0.361940i	$-0.882115\pi$
$347$	−27.4506	+	8.91924i	−1.47363	+	0.478810i	−0.541424	+	0.840750i	$0.682115\pi$
$348$	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	0.481202	−	0.876609i	$-0.340200\pi$
$367$	6.80552	+	2.21125i	0.355245	+	0.115426i	−0.125957	+	0.992036i	$0.540200\pi$
$368$		−	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	−0.130978	−	0.991385i	$-0.541812\pi$
$379$	6.73161	−	2.18723i	0.345779	−	0.112351i	0.476758	+	0.879035i	$0.341812\pi$
$380$	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
$391$	12.1209	+	29.5592i	0.612980	+	1.49487i
$392$	−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	0.128783	−	0.991673i	$-0.458893\pi$
$397$	16.2559	−	5.28187i	0.815862	−	0.265090i	0.687079	+	0.726583i	$0.258893\pi$
$398$	−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	$0.0690734\pi$
$401$			8.62281i			0.430603i	−0.976548	+	0.215301i	$0.930927\pi$
$402$	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
$408$	25.8625	+	15.9753i	1.28039	+	0.790897i
$409$	−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	0.572629	−	0.819815i	$-0.305924\pi$
$419$	11.3405	+	3.68476i	0.554021	+	0.180012i	−0.0186083	+	0.999827i	$0.505924\pi$
$420$	−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
$425$	8.47752	−	18.7918i	0.411220	−	0.911536i
$426$	−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	0.458160	−	0.888870i	$-0.348509\pi$
$431$	6.36010	+	2.06652i	0.306355	+	0.0995409i	−0.151805	+	0.988410i	$0.548509\pi$
$432$			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	−0.468617	−	0.883402i	$-0.655247\pi$
$439$	10.8189	−	14.8910i	0.516359	−	0.710707i	0.984975	+	0.172695i	$0.0552474\pi$
$440$	2.57907	+	3.10529i	0.122952	+	0.148039i
$441$	−21.3570	+	15.5168i	−1.01700	+	0.738893i
$442$	17.2458	−	27.9193i	0.820298	−	1.32798i
$443$	−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	$-0.975604\pi$
$449$		−	3.24492i		−	0.153137i	0.997064	−	0.0765686i	$-0.0243964\pi$
$450$	−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
$459$	−5.27970	−	12.8756i	−0.246435	−	0.600981i
$460$	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	−0.675260	−	0.737580i	$-0.735968\pi$
$479$	−17.2466	+	5.60376i	−0.788017	+	0.256042i	−0.112758	+	0.993623i	$0.535968\pi$
$480$	−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	0.841969	−	0.539526i	$-0.181396\pi$
$487$	1.51534	+	2.08569i	0.0686668	+	0.0945117i	−0.773302	+	0.634038i	$0.781396\pi$
$488$	−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	$0.215236\pi$
$499$			27.9596i			1.25164i	−0.779966	+	0.625822i	$0.784764\pi$
$500$	−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	−0.604589	−	0.796538i	$-0.706663\pi$
$503$	−14.0289	+	4.55827i	−0.625519	+	0.203243i	−0.0209296	+	0.999781i	$0.506663\pi$
$504$	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	$0.335574\pi$
$510$	−32.5816	+	31.4718i	−1.44274	+	1.39359i
$511$	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	−0.511150	−	0.859492i	$-0.670780\pi$
$521$	−9.57485	+	3.11106i	−0.419482	+	0.136298i	0.0916678	+	0.995790i	$0.470780\pi$
$522$	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
$527$	5.07382	−	4.30235i	0.221019	−	0.187413i
$528$	−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	$-0.876820\pi$
$541$	−23.2317	−	31.9757i	−0.998810	−	1.37474i	−0.0727580	−	0.997350i	$-0.523180\pi$
$542$	−8.10109	+	24.9326i	−0.347972	+	1.07095i
$543$	38.9091			1.66975
$544$	−8.88496	+	14.3839i	−0.380940	+	0.616705i
$545$	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	−0.272322	−	0.962206i	$-0.587792\pi$
$547$	1.70580	−	0.554247i	0.0729346	−	0.0236979i	0.345257	+	0.938508i	$0.387792\pi$
$548$	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
$561$	2.86562	+	3.37946i	0.120986	+	0.142681i
$562$	−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	−0.589873	−	0.807496i	$-0.700822\pi$
$571$	−14.1571	+	4.59993i	−0.592457	+	0.192501i	−0.00258351	+	0.999997i	$0.500822\pi$
$572$	−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	$0.733782\pi$
$578$	−6.51694	+	39.3343i	−0.271069	+	1.63609i
$579$	−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
$595$	−41.5158	−	22.0675i	−1.70198	−	0.904678i
$596$	−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	$-0.840054\pi$
$601$		−	23.6134i		−	0.963209i	0.876389	−	0.481605i	$-0.159946\pi$
$602$	−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	$0.00825814\pi$
$607$			1.27823i			0.0518816i	−0.999663	+	0.0259408i	$0.991742\pi$
$608$	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
$612$	18.5479	−	7.60567i	0.749756	−	0.307441i
$613$	−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	0.569305	−	0.822126i	$-0.307212\pi$
$617$	13.5785	+	4.41192i	0.546649	+	0.177617i	−0.0226561	+	0.999743i	$0.507212\pi$
$618$			22.0934i			0.888726i
$619$	14.7163	+	4.78162i	0.591498	+	0.192189i	0.589445	−	0.807808i	$-0.299346\pi$
$619$	14.7163	+	4.78162i	0.591498	+	0.192189i	0.00205326	+	0.999998i	$0.499346\pi$
$620$	−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
$629$	−31.8515	+	2.39287i	−1.27000	+	0.0954100i
$630$	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	0.989175	−	0.146737i	$-0.0468772\pi$
$641$	13.7717	+	18.9551i	0.543948	+	0.748680i	−0.445228	+	0.895417i	$0.646877\pi$
$642$	20.2237	−	62.2420i	0.798164	−	2.45650i
$643$			23.9636i			0.945033i	0.881322	+	0.472516i	$0.156654\pi$
$643$			23.9636i			0.945033i	−0.881322	+	0.472516i	$0.843346\pi$
$644$	42.7439	−	131.552i	1.68435	−	5.18388i
$645$	−19.4075	+	7.72754i	−0.764170	+	0.304272i
$646$	−2.76364	−	36.7869i	−0.108734	−	1.44736i
$647$	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	−0.372713	−	0.927947i	$-0.621572\pi$
$653$	−3.29162	+	1.06951i	−0.128811	+	0.0418533i	0.243902	+	0.969800i	$0.421572\pi$
$654$	−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
$663$	−11.1214	−	27.1217i	−0.431919	−	1.05332i
$664$	−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	−0.407181	−	0.913347i	$-0.633488\pi$
$673$	15.2356	−	20.9700i	0.587290	−	0.808335i	0.994471	+	0.105013i	$0.0334883\pi$
$674$		−	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	$-0.518982\pi$
$677$	23.6303	−	32.5243i	0.908185	−	1.25001i	0.967783	−	0.251787i	$-0.0810181\pi$
$678$	−8.85896	−	27.2651i	−0.340226	−	1.04711i
$679$	7.24352	+	22.2932i	0.277981	+	0.855536i
$680$	22.5419	+	23.3367i	0.864441	+	0.894923i
$681$	−2.83178	+	8.71533i	−0.108514	+	0.333972i
$682$	−1.94105			−0.0743267
$683$	−15.1472	−	4.92164i	−0.579593	−	0.188321i	0.00452516	−	0.999990i	$-0.498560\pi$
$683$	−15.1472	−	4.92164i	−0.579593	−	0.188321i	−0.584118	+	0.811669i	$0.698560\pi$
$684$	−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	0.865007	−	0.501760i	$-0.167314\pi$
$691$	3.16763	+	4.35987i	0.120502	+	0.165857i	−0.744504	+	0.667618i	$0.767314\pi$
$692$	−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
$697$	−1.17661	+	0.0883941i	−0.0445674	+	0.00334817i
$698$	−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	$-0.933878\pi$
$709$	−23.2260	−	31.9679i	−0.872271	−	1.20058i	0.106231	−	0.994341i	$-0.466122\pi$
$710$	−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
$714$	66.8155	+	78.7963i	2.50051	+	2.94888i
$715$	−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	−0.507146	−	0.861860i	$-0.669300\pi$
$719$	−38.1841	−	12.4068i	−1.42403	−	0.462694i	−0.916879	+	0.399166i	$0.869300\pi$
$720$	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
$731$	−9.66228	+	15.6423i	−0.357372	+	0.578552i
$732$	−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	$-0.894699\pi$
$743$		−	17.7074i		−	0.649621i	0.945779	−	0.324811i	$-0.105301\pi$
$744$	−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
$748$	5.64680	−	4.78821i	0.206468	−	0.175074i
$749$	67.9257			2.48195
$750$	−54.5395	−	6.56786i	−1.99150	−	0.239825i
$751$		−	12.1873i		−	0.444721i	−0.974965	−	0.222360i	$-0.928624\pi$
$751$		−	12.1873i		−	0.444721i	0.974965	−	0.222360i	$-0.0713761\pi$
$752$	−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
$765$	1.78381	+	12.6806i	0.0644938	+	0.458466i
$766$	−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
$772$

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} +(2.16680 - 3.50785i) 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} +(-8.94703 + 3.66877i) 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} +(-4.32726 + 8.14093i) 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

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