LMFDB - Embedded newform 425.2.q.a.84.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [425,2,Mod(84,425)]

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([7, 5]))

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

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

chi := DirichletCharacter("425.84");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	425.q (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:	$176$
Relative dimension:	$44$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			84.3
Character	$\chi$	$=$	425.84
Dual form			425.2.q.a.339.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.47509 + 2.03029i) q^{2} +(-0.532962 - 1.64029i) q^{3} +(-1.32814 - 4.08760i) q^{4} +(0.886990 + 2.05262i) q^{5} +(4.11642 + 1.33751i) q^{6} -3.49211 q^{7} +(5.48463 + 1.78207i) q^{8} +(0.0205526 - 0.0149323i) q^{9} +(-5.47580 - 1.22696i) q^{10} +(1.63185 - 2.24605i) q^{11} +(-5.99699 + 4.35707i) q^{12} +(2.93728 + 4.04282i) q^{13} +(5.15117 - 7.08998i) q^{14} +(2.89416 - 2.54889i) q^{15} +(-4.75420 + 3.45413i) q^{16} +(-4.11813 + 0.202457i) q^{17} +0.0637542i q^{18} +(-2.01401 + 6.19849i) q^{19} +(7.21224 - 6.35183i) q^{20} +(1.86116 + 5.72806i) q^{21} +(2.15300 + 6.62625i) q^{22} +(-1.41733 - 1.02975i) q^{23} -9.94616i q^{24} +(-3.42650 + 3.64131i) q^{25} -12.5408 q^{26} +(-4.22139 - 3.06702i) q^{27} +(4.63801 + 14.2743i) q^{28} +(-6.38667 + 2.07516i) q^{29} +(0.905831 + 9.63581i) q^{30} +(-2.96543 - 0.963528i) q^{31} -3.21376i q^{32} +(-4.55389 - 1.47965i) q^{33} +(5.66357 - 8.65963i) q^{34} +(-3.09746 - 7.16797i) q^{35} +(-0.0883342 - 0.0641785i) q^{36} +(-5.66078 + 4.11280i) q^{37} +(-9.61387 - 13.2324i) q^{38} +(5.06593 - 6.97265i) q^{39} +(1.20691 + 12.8385i) q^{40} +(2.49719 + 3.43708i) q^{41} +(-14.3750 - 4.67072i) q^{42} +8.26881i q^{43} +(-11.3483 - 3.68728i) q^{44} +(0.0488804 + 0.0289419i) q^{45} +(4.18139 - 1.35862i) q^{46} +(9.09369 - 2.95472i) q^{47} +(8.19957 + 5.95734i) q^{48} +5.19481 q^{49} +(-2.33850 - 12.3280i) q^{50} +(2.52690 + 6.64702i) q^{51} +(12.6243 - 17.3758i) q^{52} +(-7.02371 + 2.28214i) q^{53} +(12.4538 - 4.04650i) q^{54} +(6.05772 + 1.35735i) q^{55} +(-19.1529 - 6.22316i) q^{56} +11.2407 q^{57} +(5.20775 - 16.0278i) q^{58} +(-3.87604 + 2.81611i) q^{59} +(-14.2627 - 8.44487i) q^{60} +(1.80274 - 2.48126i) q^{61} +(6.33052 - 4.59939i) q^{62} +(-0.0717719 + 0.0521453i) q^{63} +(-2.98354 - 2.16767i) q^{64} +(-5.69303 + 9.61505i) q^{65} +(9.72150 - 7.06308i) q^{66} +(-5.84210 - 1.89821i) q^{67} +(6.29703 + 16.5644i) q^{68} +(-0.933707 + 2.87365i) q^{69} +(19.1221 + 4.28466i) q^{70} +(8.77051 - 2.84971i) q^{71} +(0.139334 - 0.0452723i) q^{72} +(-1.91096 - 1.38839i) q^{73} -17.5597i q^{74} +(7.79899 + 3.67977i) q^{75} +28.0118 q^{76} +(-5.69860 + 7.84345i) q^{77} +(6.68378 + 20.5706i) q^{78} +(-4.67642 + 1.51946i) q^{79} +(-11.3069 - 6.69478i) q^{80} +(-2.75740 + 8.48641i) q^{81} -10.6618 q^{82} +(4.64204 + 1.50829i) q^{83} +(20.9421 - 15.2154i) q^{84} +(-4.06831 - 8.27338i) q^{85} +(-16.7881 - 12.1972i) q^{86} +(6.80771 + 9.37001i) q^{87} +(12.9527 - 9.41070i) q^{88} +(-8.50595 - 6.17994i) q^{89} +(-0.130863 + 0.0565493i) q^{90} +(-10.2573 - 14.1179i) q^{91} +(-2.32680 + 7.16115i) q^{92} +5.37769i q^{93} +(-7.41508 + 22.8213i) q^{94} +(-14.5096 + 1.36400i) q^{95} +(-5.27149 + 1.71281i) q^{96} +(5.29550 + 16.2979i) q^{97} +(-7.66281 + 10.5470i) q^{98} -0.0705295i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 176 q - 10 q^{2} + 38 q^{4} - 10 q^{8} - 50 q^{9} - 10 q^{13} + 6 q^{15} - 58 q^{16} - 8 q^{19} - 44 q^{21} - 20 q^{25} - 64 q^{26} + 78 q^{30} - 20 q^{33} - 23 q^{34} - 46 q^{35} + 52 q^{36} - 10 q^{38}+ \cdots - 250 q^{98}+O(q^{100}) $ 176 * q - 10 * q^2 + 38 * q^4 - 10 * q^8 - 50 * q^9 - 10 * q^13 + 6 * q^15 - 58 * q^16 - 8 * q^19 - 44 * q^21 - 20 * q^25 - 64 * q^26 + 78 * q^30 - 20 * q^33 - 23 * q^34 - 46 * q^35 + 52 * q^36 - 10 * q^38 - 20 * q^42 + 40 * q^47 + 164 * q^49 + 84 * q^50 + 20 * q^51 - 30 * q^52 - 40 * q^53 - 18 * q^55 - 18 * q^59 - 48 * q^60 + 66 * q^64 + 80 * q^66 - 50 * q^67 + 68 * q^69 - 152 * q^70 + 60 * q^72 - 72 * q^76 - 40 * q^77 - 38 * q^81 + 50 * q^83 - 52 * q^84 + 47 * q^85 - 94 * q^86 - 120 * q^87 + 60 * q^89 + 50 * q^94 - 250 * q^98

Character values

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

$n$	$52$	$326$
$\chi(n)$	$e\left(\frac{7}{10}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.47509	+	2.03029i	−1.04305	+	1.43563i	−0.148360	+	0.988933i	$0.547400\pi$
$2$	−1.47509	+	2.03029i	−1.04305	+	1.43563i	−0.894686	+	0.446696i	$0.852600\pi$
$3$	−0.532962	−	1.64029i	−0.307706	−	0.947021i	−0.978654	−	0.205517i	$-0.934113\pi$
$3$	−0.532962	−	1.64029i	−0.307706	−	0.947021i	0.670948	−	0.741505i	$-0.265887\pi$
$4$	−1.32814	−	4.08760i	−0.664071	−	2.04380i
$5$	0.886990	+	2.05262i	0.396674	+	0.917960i
$5$	0.886990	+	2.05262i	0.396674	+	0.917960i
$6$	4.11642	+	1.33751i	1.68052	+	0.546035i
$7$	−3.49211			−1.31989			−0.659946	−	0.751313i	$-0.729421\pi$
$7$	−3.49211			−1.31989			−0.659946	+	0.751313i	$0.729421\pi$
$8$	5.48463	+	1.78207i	1.93911	+	0.630055i
$9$	0.0205526	−	0.0149323i	0.00685087	−	0.00497745i
$10$	−5.47580	−	1.22696i	−1.73160	−	0.387997i
$11$	1.63185	−	2.24605i	0.492022	−	0.677210i	−0.488738	−	0.872431i	$-0.662542\pi$
$11$	1.63185	−	2.24605i	0.492022	−	0.677210i	0.980759	+	0.195221i	$0.0625425\pi$
$12$	−5.99699	+	4.35707i	−1.73118	+	1.25778i
$13$	2.93728	+	4.04282i	0.814654	+	1.12128i	0.990589	+	0.136873i	$0.0437054\pi$
$13$	2.93728	+	4.04282i	0.814654	+	1.12128i	−0.175934	+	0.984402i	$0.556295\pi$
$14$	5.15117	−	7.08998i	1.37671	−	1.89488i
$15$	2.89416	−	2.54889i	0.747268	−	0.658120i
$16$	−4.75420	+	3.45413i	−1.18855	+	0.863531i
$17$	−4.11813	+	0.202457i	−0.998794	+	0.0491031i
$17$	−4.11813	+	0.202457i	−0.998794	+	0.0491031i
$18$			0.0637542i			0.0150270i
$19$	−2.01401	+	6.19849i	−0.462046	+	1.42203i	0.400614	+	0.916247i	$0.368797\pi$
$19$	−2.01401	+	6.19849i	−0.462046	+	1.42203i	−0.862660	+	0.505785i	$0.831203\pi$
$20$	7.21224	−	6.35183i	1.61271	−	1.42031i
$21$	1.86116	+	5.72806i	0.406139	+	1.24997i
$22$	2.15300	+	6.62625i	0.459021	+	1.41272i
$23$	−1.41733	−	1.02975i	−0.295534	−	0.214718i	0.430130	−	0.902767i	$-0.358468\pi$
$23$	−1.41733	−	1.02975i	−0.295534	−	0.214718i	−0.725665	+	0.688049i	$0.758468\pi$
$24$		−	9.94616i		−	2.03025i
$25$	−3.42650	+	3.64131i	−0.685300	+	0.728261i
$26$	−12.5408			−2.45946
$27$	−4.22139	−	3.06702i	−0.812406	−	0.590248i
$28$	4.63801	+	14.2743i	0.876502	+	2.69760i
$29$	−6.38667	+	2.07516i	−1.18598	+	0.385347i	−0.834583	−	0.550882i	$-0.814292\pi$
$29$	−6.38667	+	2.07516i	−1.18598	+	0.385347i	−0.351392	+	0.936228i	$0.614292\pi$
$30$	0.905831	+	9.63581i	0.165381	+	1.75925i
$31$	−2.96543	−	0.963528i	−0.532608	−	0.173055i	0.0303518	−	0.999539i	$-0.490337\pi$
$31$	−2.96543	−	0.963528i	−0.532608	−	0.173055i	−0.562959	+	0.826485i	$0.690337\pi$
$32$		−	3.21376i		−	0.568117i
$33$	−4.55389	−	1.47965i	−0.792730	−	0.257573i
$34$	5.66357	−	8.65963i	0.971294	−	1.48511i
$35$	−3.09746	−	7.16797i	−0.523567	−	1.21161i
$36$	−0.0883342	−	0.0641785i	−0.0147224	−	0.0106964i
$37$	−5.66078	+	4.11280i	−0.930626	+	0.676140i	−0.946146	−	0.323740i	$-0.895060\pi$
$37$	−5.66078	+	4.11280i	−0.930626	+	0.676140i	0.0155199	+	0.999880i	$0.495060\pi$
$38$	−9.61387	−	13.2324i	−1.55958	−	2.14657i
$39$	5.06593	−	6.97265i	0.811198	−	1.11652i
$40$	1.20691	+	12.8385i	0.190829	+	2.02995i
$41$	2.49719	+	3.43708i	0.389995	+	0.536782i	0.958198	−	0.286107i	$-0.0923612\pi$
$41$	2.49719	+	3.43708i	0.389995	+	0.536782i	−0.568203	+	0.822888i	$0.692361\pi$
$42$	−14.3750	−	4.67072i	−2.21811	−	0.720707i
$43$			8.26881i			1.26098i	0.776197	+	0.630491i	$0.217146\pi$
$43$			8.26881i			1.26098i	−0.776197	+	0.630491i	$0.782854\pi$
$44$	−11.3483	−	3.68728i	−1.71082	−	0.555878i
$45$	0.0488804	+	0.0289419i	0.00728666	+	0.00431440i
$46$	4.18139	−	1.35862i	0.616512	−	0.200317i
$47$	9.09369	−	2.95472i	1.32645	−	0.430990i	0.441745	−	0.897141i	$-0.354359\pi$
$47$	9.09369	−	2.95472i	1.32645	−	0.430990i	0.884705	+	0.466151i	$0.154359\pi$
$48$	8.19957	+	5.95734i	1.18351	+	0.859867i
$49$	5.19481			0.742116
$50$	−2.33850	−	12.3280i	−0.330714	−	1.74345i
$51$	2.52690	+	6.64702i	0.353836	+	0.930769i
$52$	12.6243	−	17.3758i	1.75067	−	2.40960i
$53$	−7.02371	+	2.28214i	−0.964781	+	0.313476i	−0.748707	−	0.662901i	$-0.769325\pi$
$53$	−7.02371	+	2.28214i	−0.964781	+	0.313476i	−0.216074	+	0.976377i	$0.569325\pi$
$54$	12.4538	−	4.04650i	1.69475	−	0.550659i
$55$	6.05772	+	1.35735i	0.816823	+	0.183025i
$56$	−19.1529	−	6.22316i	−2.55942	−	0.831605i
$57$	11.2407			1.48887
$58$	5.20775	−	16.0278i	0.683812	−	2.10456i
$59$	−3.87604	+	2.81611i	−0.504617	+	0.366626i	−0.810778	−	0.585354i	$-0.800956\pi$
$59$	−3.87604	+	2.81611i	−0.504617	+	0.366626i	0.306160	+	0.951980i	$0.400956\pi$
$60$	−14.2627	−	8.44487i	−1.84130	−	1.09023i
$61$	1.80274	−	2.48126i	0.230817	−	0.317692i	−0.677861	−	0.735190i	$-0.737093\pi$
$61$	1.80274	−	2.48126i	0.230817	−	0.317692i	0.908678	+	0.417498i	$0.137093\pi$
$62$	6.33052	−	4.59939i	0.803977	−	0.584123i
$63$	−0.0717719	+	0.0521453i	−0.00904241	+	0.00656969i
$64$	−2.98354	−	2.16767i	−0.372943	−	0.270959i
$65$	−5.69303	+	9.61505i	−0.706133	+	1.19260i
$66$	9.72150	−	7.06308i	1.19663	−	0.869405i
$67$	−5.84210	−	1.89821i	−0.713726	−	0.231904i	−0.0704252	−	0.997517i	$-0.522436\pi$
$67$	−5.84210	−	1.89821i	−0.713726	−	0.231904i	−0.643301	+	0.765613i	$0.722436\pi$
$68$	6.29703	+	16.5644i	0.763627	+	2.00873i
$69$	−0.933707	+	2.87365i	−0.112405	+	0.345947i
$70$	19.1221	+	4.28466i	2.28552	+	0.512115i
$71$	8.77051	−	2.84971i	1.04087	−	0.338199i	0.261790	−	0.965125i	$-0.415687\pi$
$71$	8.77051	−	2.84971i	1.04087	−	0.338199i	0.779079	+	0.626926i	$0.215687\pi$
$72$	0.139334	−	0.0452723i	0.0164207	−	0.00533540i
$73$	−1.91096	−	1.38839i	−0.223660	−	0.162499i	0.470312	−	0.882500i	$-0.344141\pi$
$73$	−1.91096	−	1.38839i	−0.223660	−	0.162499i	−0.693973	+	0.720001i	$0.744141\pi$
$74$		−	17.5597i		−	2.04128i
$75$	7.79899	+	3.67977i	0.900549	+	0.424903i
$76$	28.0118			3.21318
$77$	−5.69860	+	7.84345i	−0.649415	+	0.893844i
$78$	6.68378	+	20.5706i	0.756790	+	2.32916i
$79$	−4.67642	+	1.51946i	−0.526138	+	0.170953i	−0.560029	−	0.828473i	$-0.689210\pi$
$79$	−4.67642	+	1.51946i	−0.526138	+	0.170953i	0.0338911	+	0.999426i	$0.489210\pi$
$80$	−11.3069	−	6.69478i	−1.26415	−	0.748500i
$81$	−2.75740	+	8.48641i	−0.306378	+	0.942935i
$82$	−10.6618			−1.17740
$83$	4.64204	+	1.50829i	0.509530	+	0.165556i	0.552489	−	0.833520i	$-0.313678\pi$
$83$	4.64204	+	1.50829i	0.509530	+	0.165556i	−0.0429584	+	0.999077i	$0.513678\pi$
$84$	20.9421	−	15.2154i	2.28497	−	1.66013i
$85$	−4.06831	−	8.27338i	−0.441270	−	0.897374i
$86$	−16.7881	−	12.1972i	−1.81030	−	1.31526i
$87$	6.80771	+	9.37001i	0.729863	+	1.00457i
$88$	12.9527	−	9.41070i	1.38076	−	1.00318i
$89$	−8.50595	−	6.17994i	−0.901629	−	0.655072i	0.0372548	−	0.999306i	$-0.488139\pi$
$89$	−8.50595	−	6.17994i	−0.901629	−	0.655072i	−0.938884	+	0.344234i	$0.888139\pi$
$90$	−0.130863	+	0.0565493i	−0.0137942	+	0.00596082i
$91$	−10.2573	−	14.1179i	−1.07526	−	1.47996i
$92$	−2.32680	+	7.16115i	−0.242585	+	0.746601i
$93$			5.37769i			0.557641i
$94$	−7.41508	+	22.8213i	−0.764807	+	2.35383i
$95$	−14.5096	+	1.36400i	−1.48865	+	0.139943i
$96$	−5.27149	+	1.71281i	−0.538019	+	0.174813i
$97$	5.29550	+	16.2979i	0.537677	+	1.65480i	0.737793	+	0.675027i	$0.235868\pi$
$97$	5.29550	+	16.2979i	0.537677	+	1.65480i	−0.200116	+	0.979772i	$0.564132\pi$
$98$	−7.66281	+	10.5470i	−0.774061	+	1.06540i
$99$		−	0.0705295i		−	0.00708848i
$100$	19.4351	+	9.16998i	1.94351	+	0.916998i
$101$	12.5176			1.24555			0.622776	−	0.782400i	$-0.286005\pi$
$101$	12.5176			1.24555			0.622776	+	0.782400i	$0.286005\pi$
$102$	−17.2228	−	4.67463i	−1.70531	−	0.462857i
$103$	3.49616	−	1.13597i	0.344487	−	0.111931i	−0.131663	−	0.991294i	$-0.542032\pi$
$103$	3.49616	−	1.13597i	0.344487	−	0.111931i	0.476150	+	0.879364i	$0.342032\pi$
$104$	8.90533	+	27.4078i	0.873240	+	2.68755i
$105$	−10.1067	+	8.90099i	−0.986314	+	0.868648i
$106$	5.72720	−	17.6265i	0.556275	−	1.71204i
$107$	−6.32548			−0.611507			−0.305754	−	0.952111i	$-0.598908\pi$
$107$	−6.32548			−0.611507			−0.305754	+	0.952111i	$0.598908\pi$
$108$	−6.93013	+	21.3288i	−0.666853	+	2.05236i
$109$	10.8364	+	14.9151i	1.03794	+	1.42861i	0.898813	+	0.438332i	$0.144431\pi$
$109$	10.8364	+	14.9151i	1.03794	+	1.42861i	0.139130	+	0.990274i	$0.455569\pi$
$110$	−11.6915	+	10.2967i	−1.11474	+	0.981752i
$111$	9.76315	+	7.09335i	0.926677	+	0.673271i
$112$	16.6022	−	12.0622i	1.56876	−	1.13977i
$113$	−0.0220850	+	0.0160457i	−0.00207759	+	0.00150946i	−0.588824	−	0.808262i	$-0.700409\pi$
$113$	−0.0220850	+	0.0160457i	−0.00207759	+	0.00150946i	0.586746	+	0.809771i	$0.300409\pi$
$114$	−16.5811	+	22.8219i	−1.55296	+	2.13746i
$115$	0.856531	−	3.82263i	0.0798720	−	0.356462i
$116$	16.9648	+	23.3500i	1.57514	+	2.16800i
$117$	0.120737	+	0.0392300i	0.0111622	+	0.00362681i
$118$		−	12.0235i		−	1.10685i
$119$	14.3810	−	0.707003i	1.31830	−	0.0648109i
$120$	20.4157	−	8.82214i	1.86369	−	0.805347i
$121$	1.01738	+	3.13118i	0.0924894	+	0.284653i
$122$	2.37846	+	7.32015i	0.215336	+	0.662736i
$123$	4.30690	−	5.92794i	0.388340	−	0.534504i
$124$			13.4012i			1.20346i
$125$	−10.5135	−	3.80350i	−0.940355	−	0.340195i
$126$		−	0.222637i		−	0.0198340i
$127$	7.32741	−	10.0853i	0.650202	−	0.894927i	−0.348906	−	0.937158i	$-0.613447\pi$
$127$	7.32741	−	10.0853i	0.650202	−	0.894927i	0.999108	+	0.0422312i	$0.0134466\pi$
$128$	14.9149	−	4.84615i	1.31831	−	0.428343i
$129$	13.5632	−	4.40696i	1.19418	−	0.388011i
$130$	−11.1236	−	25.7415i	−0.975603	−	2.25768i
$131$	−5.82741	−	1.89344i	−0.509143	−	0.165431i	0.0431693	−	0.999068i	$-0.486255\pi$
$131$	−5.82741	−	1.89344i	−0.509143	−	0.165431i	−0.552313	+	0.833637i	$0.686255\pi$
$132$			20.5796i			1.79123i
$133$	7.03315	−	21.6458i	0.609851	−	1.87693i
$134$	12.4715	−	9.06111i	1.07738	−	0.782760i
$135$	2.55109	−	11.3853i	0.219563	−	0.979892i
$136$	−22.9472	−	6.22838i	−1.96771	−	0.534079i
$137$	5.95745	+	8.19973i	0.508980	+	0.700550i	0.983747	−	0.179561i	$-0.0574677\pi$
$137$	5.95745	+	8.19973i	0.508980	+	0.700550i	−0.474767	+	0.880111i	$0.657468\pi$
$138$	−4.45704	−	6.13459i	−0.379409	−	0.522211i
$139$	−4.00987	+	5.51911i	−0.340113	+	0.468125i	−0.944474	−	0.328585i	$-0.893428\pi$
$139$	−4.00987	+	5.51911i	−0.340113	+	0.468125i	0.604362	+	0.796710i	$0.293428\pi$
$140$	−25.1859	+	22.1813i	−2.12860	+	1.87466i
$141$	−9.69318	−	13.3415i	−0.816313	−	1.12356i
$142$	−7.15156	+	22.0102i	−0.600146	+	1.84706i
$143$	13.8736			1.16017
$144$	−0.0461329	+	0.141983i	−0.00384441	+	0.0118319i
$145$	−9.92442	−	11.2688i	−0.824178	−	0.935820i
$146$	5.63766	−	1.83179i	0.466576	−	0.151600i
$147$	−2.76864	−	8.52099i	−0.228353	−	0.702799i
$148$	24.3298	+	17.6766i	1.99989	+	1.45301i
$149$	3.64889			0.298928			0.149464	−	0.988767i	$-0.452245\pi$
$149$	3.64889			0.298928			0.149464	+	0.988767i	$0.452245\pi$
$150$	−18.9752	+	10.4062i	−1.54932	+	0.849662i
$151$	−14.6451			−1.19180			−0.595900	−	0.803059i	$-0.703204\pi$
$151$	−14.6451			−1.19180			−0.595900	+	0.803059i	$0.703204\pi$
$152$	−22.0922	+	30.4074i	−1.79192	+	2.46636i
$153$	−0.0816152	+	0.0656544i	−0.00659820	+	0.00530784i
$154$	−7.51850	−	23.1396i	−0.605858	−	1.86464i
$155$	−0.652553	−	6.94155i	−0.0524143	−	0.557559i
$156$	−35.2297	−	11.4468i	−2.82063	−	0.916478i
$157$		−	19.9707i		−	1.59384i	−0.604087	−	0.796918i	$-0.706462\pi$
$157$		−	19.9707i		−	1.59384i	0.604087	−	0.796918i	$-0.293538\pi$
$158$	3.81320	−	11.7358i	0.303362	−	0.933651i
$159$	7.48674	+	10.3046i	0.593737	+	0.817209i
$160$	6.59662	−	2.85057i	0.521509	−	0.225357i
$161$	4.94948	+	3.59601i	0.390074	+	0.283405i
$162$	−13.1624	−	18.1165i	−1.03414	−	1.42337i
$163$	1.72127	−	1.25058i	0.134820	−	0.0979528i	−0.518331	−	0.855180i	$-0.673446\pi$
$163$	1.72127	−	1.25058i	0.134820	−	0.0979528i	0.653151	+	0.757227i	$0.273446\pi$
$164$	10.7328	−	14.7724i	0.838090	−	1.15353i
$165$	−1.00210	−	10.6598i	−0.0780131	−	0.829866i
$166$	−9.90969	+	7.19981i	−0.769141	+	0.558814i
$167$	7.50297	−	23.0918i	0.580597	−	1.78689i	−0.0356779	−	0.999363i	$-0.511359\pi$
$167$	7.50297	−	23.0918i	0.580597	−	1.78689i	0.616275	−	0.787531i	$-0.288641\pi$
$168$			34.7330i			2.67971i
$169$	−3.69954	+	11.3860i	−0.284580	+	0.875847i
$170$	22.7985	+	3.94415i	1.74856	+	0.302502i
$171$	0.0511648	+	0.157469i	0.00391267	+	0.0120420i
$172$	33.7996	−	10.9821i	2.57719	−	0.837381i
$173$	−13.7065	−	9.95835i	−1.04209	−	0.757119i	−0.0713937	−	0.997448i	$-0.522745\pi$
$173$	−13.7065	−	9.95835i	−1.04209	−	0.757119i	−0.970691	+	0.240329i	$0.922745\pi$
$174$	−29.0658			−2.20347
$175$	11.9657	−	12.7158i	0.904522	−	0.961226i
$176$			16.3148i			1.22977i
$177$	6.68501	+	4.85695i	0.502476	+	0.365070i
$178$	25.0941	−	8.15356i	1.88088	−	0.611135i
$179$	−1.19209	−	3.66888i	−0.0891012	−	0.274225i	0.896570	−	0.442901i	$-0.146051\pi$
$179$	−1.19209	−	3.66888i	−0.0891012	−	0.274225i	−0.985672	+	0.168676i	$0.946051\pi$
$180$	0.0533826	−	0.238242i	0.00397891	−	0.0177575i
$181$	13.6144	+	4.42358i	1.01195	+	0.328802i	0.767630	−	0.640893i	$-0.221436\pi$
$181$	13.6144	+	4.42358i	1.01195	+	0.328802i	0.244318	+	0.969695i	$0.421436\pi$
$182$	43.7939			3.24622
$183$	−5.03077	−	1.63460i	−0.371885	−	0.120833i
$184$	−5.93847	−	8.17360i	−0.437790	−	0.602566i
$185$	−13.4631	−	7.97142i	−0.989824	−	0.586070i
$186$	−10.9183	−	7.93258i	−0.800565	−	0.581645i
$187$	−6.26545	+	9.57991i	−0.458175	+	0.700552i
$188$	−24.1554	−	33.2471i	−1.76171	−	2.42479i
$189$	14.7415	+	10.7103i	1.07229	+	0.779063i
$190$	18.6336	−	31.4706i	1.35182	−	2.28312i
$191$	1.68683	−	1.22555i	0.122055	−	0.0886778i	−0.525083	−	0.851051i	$-0.675966\pi$
$191$	1.68683	−	1.22555i	0.122055	−	0.0886778i	0.647138	+	0.762373i	$0.275966\pi$
$192$	−1.96549	+	6.04916i	−0.141847	+	0.436561i
$193$	−4.69405			−0.337885			−0.168943	−	0.985626i	$-0.554035\pi$
$193$	−4.69405			−0.337885			−0.168943	+	0.985626i	$0.554035\pi$
$194$	−40.9007	−	13.2894i	−2.93650	−	0.954127i
$195$	18.8056	+	4.21375i	1.34670	+	0.301753i
$196$	−6.89944	−	21.2343i	−0.492817	−	1.51674i
$197$	−1.77263	−	5.45559i	−0.126295	−	0.388695i	0.867840	−	0.496844i	$-0.165508\pi$
$197$	−1.77263	−	5.45559i	−0.126295	−	0.388695i	−0.994135	+	0.108149i	$0.965508\pi$
$198$	0.143195	+	0.104037i	0.0101764	+	0.00739362i
$199$			23.5282i			1.66787i	0.551865	+	0.833934i	$0.313917\pi$
$199$			23.5282i			1.66787i	−0.551865	+	0.833934i	$0.686083\pi$
$200$	−25.2821	+	13.8650i	−1.78772	+	0.980403i
$201$			10.5944i			0.747272i
$202$	−18.4646	+	25.4144i	−1.29917	+	1.78815i
$203$	22.3029	−	7.24666i	1.56536	−	0.508616i
$204$	23.8143	−	19.1571i	1.66733	−	1.34127i
$205$	−4.84004	+	8.17443i	−0.338043	+	0.570927i
$206$	−2.85080	+	8.77387i	−0.198625	+	0.611304i
$207$	−0.0445065			−0.00309342
$208$	−27.9288	−	9.07461i	−1.93651	−	0.629211i
$209$	10.6356	+	14.6386i	0.735677	+	1.01257i
$210$	−3.16326	−	33.6493i	−0.218286	−	2.32202i
$211$	−5.15468	+	7.09480i	−0.354863	+	0.488426i	−0.948708	−	0.316152i	$-0.897609\pi$
$211$	−5.15468	+	7.09480i	−0.354863	+	0.488426i	0.593846	+	0.804579i	$0.297609\pi$
$212$	18.6570	+	25.6791i	1.28137	+	1.76365i
$213$	−9.34870	−	12.8674i	−0.640562	−	0.881659i
$214$	9.33065	−	12.8425i	0.637830	−	0.877898i
$215$	−16.9727	+	7.33435i	−1.15753	+	0.500198i
$216$	−17.6871	−	24.3443i	−1.20346	−	1.65642i
$217$	10.3556	+	3.36474i	0.702985	+	0.228414i
$218$	−46.2666			−3.13357
$219$	−1.25889	+	3.87448i	−0.0850682	+	0.261813i
$220$	−2.49722	−	26.5643i	−0.168363	−	1.79096i
$221$	−12.9146	−	16.0542i	−0.868730	−	1.07992i
$222$	−28.8031	+	9.35868i	−1.93313	+	0.628114i
$223$	8.92258	−	12.2809i	0.597500	−	0.822389i	−0.397976	−	0.917396i	$-0.630287\pi$
$223$	8.92258	−	12.2809i	0.597500	−	0.822389i	0.995477	+	0.0950071i	$0.0302874\pi$
$224$			11.2228i			0.749854i
$225$	−0.0160502	+	0.126004i	−0.00107002	+	0.00840026i
$226$		−	0.0685079i		−	0.00455708i
$227$	6.02225	+	4.37542i	0.399711	+	0.290407i	0.769423	−	0.638739i	$-0.220544\pi$
$227$	6.02225	+	4.37542i	0.399711	+	0.290407i	−0.369712	+	0.929146i	$0.620544\pi$
$228$	−14.9293	−	45.9475i	−0.988714	−	3.04295i
$229$	−0.525326	−	1.61679i	−0.0347145	−	0.106840i	0.932198	−	0.361949i	$-0.117889\pi$
$229$	−0.525326	−	1.61679i	−0.0347145	−	0.106840i	−0.966912	+	0.255109i	$0.917889\pi$
$230$	6.49757	+	7.37772i	0.428437	+	0.486473i
$231$	15.9027	+	5.16709i	1.04632	+	0.339969i
$232$	−38.7266			−2.54253
$233$	4.96362	−	15.2764i	0.325177	−	1.00079i	−0.646183	−	0.763182i	$-0.723636\pi$
$233$	4.96362	−	15.2764i	0.325177	−	1.00079i	0.971361	−	0.237610i	$-0.0763642\pi$
$234$	−0.257747	+	0.187264i	−0.0168494	+	0.0122418i
$235$	14.1309	+	16.0451i	0.921800	+	1.04667i
$236$	16.6590	+	12.1035i	1.08441	+	0.787871i
$237$	4.98471	+	6.86086i	0.323791	+	0.445661i
$238$	−19.7778	+	30.2404i	−1.28200	+	1.96019i
$239$	−14.2647	−	10.3639i	−0.922705	−	0.670385i	0.0214905	−	0.999769i	$-0.493159\pi$
$239$	−14.2647	−	10.3639i	−0.922705	−	0.670385i	−0.944196	+	0.329384i	$0.893159\pi$
$240$	−4.95521	+	22.1147i	−0.319858	+	1.42750i
$241$	−0.925378	−	1.27367i	−0.0596089	−	0.0820446i	0.778172	−	0.628051i	$-0.216147\pi$
$241$	−0.925378	−	1.27367i	−0.0596089	−	0.0820446i	−0.837781	+	0.546007i	$0.816147\pi$
$242$	−7.85794	−	2.55320i	−0.505127	−	0.164126i
$243$	−0.264003			−0.0169358
$244$	−12.5367	−	4.07341i	−0.802578	−	0.260773i
$245$	4.60774	+	10.6630i	0.294378	+	0.681232i
$246$	5.68235	+	17.4885i	0.362294	+	1.11503i
$247$	−30.9751	+	10.0644i	−1.97090	+	0.640383i
$248$	−14.5473	−	10.5692i	−0.923751	−	0.671145i
$249$		−	8.41815i		−	0.533479i
$250$	23.2305	−	15.7349i	1.46923	−	0.995162i
$251$	−22.9666			−1.44964			−0.724820	−	0.688938i	$-0.758077\pi$
$251$	−22.9666			−1.44964			−0.724820	+	0.688938i	$0.758077\pi$
$252$	0.308472	+	0.224118i	0.0194319	+	0.0141181i
$253$	−4.62575	+	1.50300i	−0.290819	+	0.0944927i
$254$	9.66749	+	29.7535i	0.606592	+	1.86690i
$255$	−11.4025	+	11.0826i	−0.714051	+	0.694019i
$256$	−9.88254	+	30.4153i	−0.617659	+	1.90096i
$257$		−	11.3852i		−	0.710192i	−0.934830	−	0.355096i	$-0.884448\pi$
$257$		−	11.3852i		−	0.710192i	0.934830	−	0.355096i	$-0.115552\pi$
$258$	−11.0596	+	34.0379i	−0.688540	+	2.11911i
$259$	19.7680	−	14.3623i	1.22833	−	0.892431i
$260$	46.8636	+	10.5007i	2.90636	+	0.651224i
$261$	−0.100276	+	0.138018i	−0.00620692	+	0.00854309i
$262$	12.4402	−	9.03832i	0.768557	−	0.558389i
$263$	−8.20341	−	11.2910i	−0.505844	−	0.696235i	0.477368	−	0.878704i	$-0.341591\pi$
$263$	−8.20341	−	11.2910i	−0.505844	−	0.696235i	−0.983212	+	0.182469i	$0.941591\pi$
$264$	−22.3396	−	16.2306i	−1.37491	−	0.998927i
$265$	−10.9143	−	12.3928i	−0.670462	−	0.761282i
$266$	33.5727	+	46.2088i	2.05847	+	2.83324i
$267$	−5.60353	+	17.2459i	−0.342930	+	1.05543i
$268$			26.4013i			1.61271i
$269$	17.1156	+	5.56119i	1.04355	+	0.339071i	0.780136	−	0.625610i	$-0.215150\pi$
$269$	17.1156	+	5.56119i	1.04355	+	0.339071i	0.263419	+	0.964682i	$0.415150\pi$
$270$	19.3524	+	21.9738i	1.17775	+	1.33728i
$271$	−3.55814	−	10.9508i	−0.216142	−	0.665216i	−0.999071	−	0.0431047i	$-0.986275\pi$
$271$	−3.55814	−	10.9508i	−0.216142	−	0.665216i	0.782929	−	0.622111i	$-0.213725\pi$
$272$	18.8791	−	15.1871i	1.14471	−	0.920851i
$273$	−17.6908	+	24.3492i	−1.07069	+	1.47368i
$274$	−25.4356			−1.53662
$275$	2.58702	+	13.6382i	0.156003	+	0.822412i
$276$	12.9864			0.781692
$277$	7.05121	+	5.12301i	0.423666	+	0.307812i	0.779111	−	0.626886i	$-0.215671\pi$
$277$	7.05121	+	5.12301i	0.423666	+	0.307812i	−0.355445	+	0.934697i	$0.615671\pi$
$278$	−5.29046	−	16.2824i	−0.317301	−	0.976552i
$279$	−0.0753351	+	0.0244779i	−0.00451019	+	0.00146545i
$280$	−4.21466	−	44.8336i	−0.251874	−	2.67932i
$281$	2.56031	−	7.87983i	0.152735	−	0.470071i	−0.845189	−	0.534468i	$-0.820512\pi$
$281$	2.56031	−	7.87983i	0.152735	−	0.470071i	0.997924	+	0.0643963i	$0.0205122\pi$
$282$	41.3854			2.46447
$283$	−9.50965	+	29.2677i	−0.565290	+	1.73978i	0.101798	+	0.994805i	$0.467540\pi$
$283$	−9.50965	+	29.2677i	−0.565290	+	1.73978i	−0.667088	+	0.744979i	$0.732460\pi$
$284$	−23.2970	−	32.0655i	−1.38242	−	1.90274i
$285$	9.97039	+	23.0729i	0.590595	+	1.36672i
$286$	−20.4648	+	28.1673i	−1.21011	+	1.66557i
$287$	−8.72044	−	12.0027i	−0.514751	−	0.708494i
$288$	−0.0479889	−	0.0660511i	−0.00282777	−	0.00389210i
$289$	16.9180	−	1.66749i	0.995178	−	0.0980878i
$290$	37.5182	−	3.52697i	2.20315	−	0.207111i
$291$	23.9109	−	17.3723i	1.40168	−	1.01838i
$292$	−3.13716	+	9.65520i	−0.183589	+	0.565028i
$293$			7.73475i			0.451869i	0.974143	+	0.225934i	$0.0725435\pi$
$293$			7.73475i			0.451869i	−0.974143	+	0.225934i	$0.927457\pi$
$294$	21.3840	+	6.94810i	1.24714	+	0.405221i
$295$	−9.21841	−	5.45818i	−0.536716	−	0.317787i
$296$	−38.3766	+	12.4693i	−2.23059	+	0.724764i
$297$	−13.7773	+	4.47653i	−0.799443	+	0.259755i
$298$	−5.38244	+	7.40829i	−0.311796	+	0.429151i
$299$		−	8.75469i		−	0.506297i
$300$	4.68326	−	36.7664i	0.270388	−	2.12271i
$301$		−	28.8756i		−	1.66436i
$302$	21.6028	−	29.7337i	1.24310	−	1.71098i
$303$	−6.67143	−	20.5325i	−0.383264	−	1.17956i
$304$	−11.8354	−	36.4255i	−0.678805	−	2.08915i
$305$	6.69209	+	1.49949i	0.383188	+	0.0858604i
$306$	−0.0129075	−	0.262548i	−0.000737874	−	0.0150089i
$307$		−	15.2071i		−	0.867917i	−0.900933	−	0.433959i	$-0.857116\pi$
$307$		−	15.2071i		−	0.867917i	0.900933	−	0.433959i	$-0.142884\pi$
$308$	39.6294	+	12.8764i	2.25809	+	0.733700i
$309$	−3.72664	−	5.12928i	−0.212001	−	0.291795i
$310$	15.0559	+	8.91454i	0.855118	+	0.506312i
$311$	−4.83802	+	6.65896i	−0.274339	+	0.377595i	−0.923849	−	0.382758i	$-0.874974\pi$
$311$	−4.83802	+	6.65896i	−0.274339	+	0.377595i	0.649510	+	0.760353i	$0.274974\pi$
$312$	40.2105	−	29.2146i	2.27647	−	1.65395i
$313$	13.1045	−	9.52101i	0.740713	−	0.538159i	−0.152221	−	0.988346i	$-0.548643\pi$
$313$	13.1045	−	9.52101i	0.740713	−	0.538159i	0.892934	+	0.450187i	$0.148643\pi$
$314$	40.5463	+	29.4586i	2.28816	+	1.66244i
$315$	−0.170695	−	0.101068i	−0.00961760	−	0.00569454i
$316$	12.4219	+	17.0973i	0.698786	+	0.961796i
$317$	−1.43517	+	4.41700i	−0.0806071	+	0.248083i	−0.983236	−	0.182336i	$-0.941634\pi$
$317$	−1.43517	+	4.41700i	−0.0806071	+	0.248083i	0.902629	+	0.430419i	$0.141634\pi$
$318$	−31.9650			−1.79251
$319$	−5.76119	+	17.7311i	−0.322565	+	0.992753i
$320$	1.80303	−	8.04679i	0.100793	−	0.449829i
$321$	3.37124	+	10.3756i	0.188164	+	0.579110i
$322$	−14.6019	+	4.74443i	−0.813729	+	0.264397i
$323$	7.03904	−	25.9340i	0.391663	−	1.44300i
$324$	38.3513			2.13063
$325$	−24.7857	−	3.15718i	−1.37486	−	0.175129i
$326$			5.33939i			0.295722i
$327$	18.6896	−	25.7241i	1.03354	−	1.42254i
$328$	7.57105	+	23.3013i	0.418041	+	1.28660i
$329$	−31.7561	+	10.3182i	−1.75077	+	0.568860i
$330$	23.1207	+	13.6897i	1.27275	+	0.753591i
$331$	−4.87029	+	14.9892i	−0.267695	+	0.823881i	0.723365	+	0.690466i	$0.242594\pi$
$331$	−4.87029	+	14.9892i	−0.267695	+	0.823881i	−0.991060	+	0.133415i	$0.957406\pi$
$332$		−	20.9780i		−	1.15132i
$333$	−0.0549301	+	0.169057i	−0.00301015	+	0.00926428i
$334$	35.8154	+	49.2956i	1.95973	+	2.69734i
$335$	−1.28557	−	13.6753i	−0.0702383	−	0.747162i
$336$	−28.6338	−	20.8037i	−1.56210	−	1.13493i
$337$	−9.85651	+	7.16118i	−0.536919	+	0.390094i	−0.822939	−	0.568129i	$-0.807667\pi$
$337$	−9.85651	+	7.16118i	−0.536919	+	0.390094i	0.286021	+	0.958223i	$0.407667\pi$
$338$	−17.6597	−	24.3065i	−0.960562	−	1.32210i
$339$	0.0380901	+	0.0276741i	0.00206877	+	0.00150305i
$340$	−28.4150	+	27.6178i	−1.54102	+	1.49779i
$341$	−7.00328	+	5.08818i	−0.379249	+	0.275540i
$342$	−0.395180	−	0.128402i	−0.0213689	−	0.00694317i
$343$	6.30391			0.340379
$344$	−14.7356	+	45.3514i	−0.794488	+	2.44518i
$345$	−6.72671	+	0.632356i	−0.362154	+	0.0340449i
$346$	40.4366	−	13.1387i	2.17389	−	0.706338i
$347$	11.1440	+	34.2976i	0.598240	+	1.84119i	0.537888	+	0.843016i	$0.319222\pi$
$347$	11.1440	+	34.2976i	0.598240	+	1.84119i	0.0603517	+	0.998177i	$0.480778\pi$
$348$	29.2592	−	40.2719i	1.56846	−	2.15880i
$349$	20.6106			1.10326			0.551631	−	0.834088i	$-0.314006\pi$
$349$	20.6106			1.10326			0.551631	+	0.834088i	$0.314006\pi$
$350$	8.16630	+	43.0508i	0.436507	+	2.30116i
$351$		−	26.0750i		−	1.39178i
$352$	−7.21826	−	5.24437i	−0.384734	−	0.279526i
$353$	9.45045	−	3.07064i	0.502997	−	0.163434i	−0.0465182	−	0.998917i	$-0.514813\pi$
$353$	9.45045	−	3.07064i	0.502997	−	0.163434i	0.549515	+	0.835484i	$0.314813\pi$
$354$	−19.7220	+	6.40806i	−1.04821	+	0.340585i
$355$	13.6287	+	15.4749i	0.723338	+	0.821321i
$356$	−13.9640	+	42.9767i	−0.740090	+	2.27776i
$357$	−8.82419	−	23.2121i	−0.467026	−	1.22852i
$358$	9.20733	+	2.99164i	0.486623	+	0.158113i
$359$	−2.91109	+	2.11503i	−0.153641	+	0.111627i	−0.661950	−	0.749548i	$-0.730271\pi$
$359$	−2.91109	+	2.11503i	−0.153641	+	0.111627i	0.508309	+	0.861175i	$0.330271\pi$
$360$	0.216515	+	0.245844i	0.0114113	+	0.0129571i
$361$	−18.9937	−	13.7998i	−0.999671	−	0.726303i
$362$	−29.0636	+	21.1159i	−1.52755	+	1.10983i
$363$	4.59382	−	3.33761i	0.241113	−	0.175179i
$364$	−44.0854	+	60.6783i	−2.31070	+	3.18041i
$365$	1.15484	−	5.15396i	0.0604471	−	0.269770i
$366$	10.7395	−	7.80273i	0.561364	−	0.407855i
$367$	8.15074	−	25.0854i	0.425465	−	1.30945i	−0.477082	−	0.878859i	$-0.658306\pi$
$367$	8.15074	−	25.0854i	0.425465	−	1.30945i	0.902548	−	0.430589i	$-0.141694\pi$
$368$	10.2952			0.536673
$369$	0.102647	+	0.0333521i	0.00534361	+	0.00173624i
$370$	36.0435	−	15.5753i	1.87381	−	0.809722i
$371$	24.5276	−	7.96949i	1.27341	−	0.413755i
$372$	21.9818	−	7.14233i	1.13971	−	0.370313i
$373$	−5.98347	+	8.23554i	−0.309812	+	0.426420i	−0.935323	−	0.353796i	$-0.884891\pi$
$373$	−5.98347	+	8.23554i	−0.309812	+	0.426420i	0.625510	+	0.780216i	$0.284891\pi$
$374$	−10.2079	−	26.8519i	−0.527836	−	1.38848i
$375$	−0.635546	+	19.2723i	−0.0328195	+	0.995216i
$376$	55.1411			2.84368
$377$	−27.1489	−	19.7248i	−1.39824	−	1.01588i
$378$	−43.4902	+	14.1308i	−2.23689	+	0.726811i
$379$	−20.7723	+	6.74933i	−1.06700	+	0.346690i	−0.789319	−	0.613983i	$-0.789566\pi$
$379$	−20.7723	+	6.74933i	−1.06700	+	0.346690i	−0.277682	+	0.960673i	$0.589566\pi$
$380$	24.8462	+	57.4977i	1.27458	+	2.94957i
$381$	−20.4481	−	6.64398i	−1.04759	−	0.340381i
$382$			5.23254i			0.267720i
$383$	−4.41151	−	1.43339i	−0.225418	−	0.0732427i	0.194130	−	0.980976i	$-0.437811\pi$
$383$	−4.41151	−	1.43339i	−0.225418	−	0.0732427i	−0.419548	+	0.907733i	$0.637811\pi$
$384$	−15.8982	−	21.8820i	−0.811300	−	1.11666i
$385$	−21.1542	−	4.74000i	−1.07812	−	0.241573i
$386$	6.92415	−	9.53027i	0.352430	−	0.485078i
$387$	0.123473	+	0.169946i	0.00627647	+	0.00863882i
$388$	59.5860	−	43.2918i	3.02502	−	2.19781i
$389$	20.0247	+	14.5488i	1.01529	+	0.737654i	0.965313	−	0.261097i	$-0.0840841\pi$
$389$	20.0247	+	14.5488i	1.01529	+	0.737654i	0.0499805	+	0.998750i	$0.484084\pi$
$390$	−36.2951	+	31.9652i	−1.83788	+	1.61862i
$391$	6.04525	+	3.95371i	0.305721	+	0.199948i
$392$	28.4916	+	9.25750i	1.43905	+	0.467574i
$393$			10.5678i			0.533073i
$394$	13.6912	+	4.44854i	0.689753	+	0.224114i
$395$	−7.26681	−	8.25116i	−0.365633	−	0.415161i
$396$	−0.288296	+	0.0936732i	−0.0144874	+	0.00470725i
$397$	−6.41268	−	19.7362i	−0.321843	−	0.990532i	−0.972845	−	0.231456i	$-0.925651\pi$
$397$	−6.41268	−	19.7362i	−0.321843	−	0.990532i	0.651002	−	0.759076i	$-0.274349\pi$
$398$	−47.7689	−	34.7062i	−2.39444	−	1.73966i
$399$	−39.2538			−1.96515
$400$	3.71272	−	29.1470i	0.185636	−	1.45735i
$401$			11.5552i			0.577038i	0.957474	+	0.288519i	$0.0931629\pi$
$401$			11.5552i			0.577038i	−0.957474	+	0.288519i	$0.906837\pi$
$402$	−21.5097	−	15.6277i	−1.07281	−	0.779439i
$403$	−4.81494	−	14.8189i	−0.239849	−	0.738180i
$404$	−16.6252	−	51.1671i	−0.827134	−	2.54566i
$405$	−19.8652	+	1.86746i	−0.987108	+	0.0927949i
$406$	−18.1860	+	55.9709i	−0.902558	+	2.77779i
$407$			19.4259i			0.962904i
$408$	2.01367	+	40.9596i	0.0996917	+	2.02780i
$409$	−27.5718	+	20.0321i	−1.36334	+	0.990524i	−0.365115	+	0.930963i	$0.618970\pi$
$409$	−27.5718	+	20.0321i	−1.36334	+	0.990524i	−0.998225	+	0.0595614i	$0.981030\pi$
$410$	−9.45694	−	21.8847i	−0.467045	−	1.08081i
$411$	10.2748	−	14.1421i	0.506820	−	0.697578i
$412$	−9.28679	−	12.7822i	−0.457527	−	0.629732i
$413$	13.5355	−	9.83415i	0.666041	−	0.483907i
$414$	0.0656511	−	0.0903610i	0.00322658	−	0.00444100i
$415$	1.02150	+	10.8662i	0.0501432	+	0.533400i
$416$	12.9926	−	9.43969i	0.637016	−	0.462819i
$417$	11.1900	+	3.63587i	0.547979	+	0.178049i
$418$	−45.4089			−2.22102
$419$	10.0997	+	3.28158i	0.493402	+	0.160316i	0.545140	−	0.838345i	$-0.316476\pi$
$419$	10.0997	+	3.28158i	0.493402	+	0.160316i	−0.0517388	+	0.998661i	$0.516476\pi$
$420$	49.8068	+	29.4904i	2.43032	+	1.43898i
$421$	−9.07115	−	27.9181i	−0.442101	−	1.36065i	−0.885632	−	0.464387i	$-0.846275\pi$
$421$	−9.07115	−	27.9181i	−0.442101	−	1.36065i	0.443531	−	0.896259i	$-0.353725\pi$
$422$	−6.80088	−	20.9309i	−0.331061	−	1.01890i
$423$	0.142778	−	0.196517i	0.00694211	−	0.00955499i
$424$	−42.5894			−2.06833
$425$	13.3736	−	15.6891i	0.648713	−	0.761033i
$426$	39.9147			1.93387
$427$	−6.29536	+	8.66481i	−0.304654	+	0.419320i
$428$	8.40113	+	25.8560i	0.406084	+	1.24980i
$429$	−7.39408	−	22.7567i	−0.356990	−	1.09870i
$430$	10.1455	−	45.2783i	0.489257	−	2.18351i
$431$	14.8692	+	4.83131i	0.716226	+	0.232716i	0.644386	−	0.764700i	$-0.277113\pi$
$431$	14.8692	+	4.83131i	0.716226	+	0.232716i	0.0718400	+	0.997416i	$0.477113\pi$
$432$	30.6632			1.47528
$433$	−8.58871	−	2.79064i	−0.412747	−	0.134110i	0.0952806	−	0.995450i	$-0.469625\pi$
$433$	−8.58871	−	2.79064i	−0.412747	−	0.134110i	−0.508027	+	0.861341i	$0.669625\pi$
$434$	−22.1069	+	16.0616i	−1.06116	+	0.770980i
$435$	−13.1947	+	22.2847i	−0.632637	+	1.06847i
$436$	46.5746	−	64.1044i	2.23052	−	3.07004i
$437$	9.23744	−	6.71139i	0.441887	−	0.321050i
$438$	−6.00932	−	8.27112i	−0.287137	−	0.395210i
$439$	−3.46837	+	4.77380i	−0.165536	+	0.227841i	−0.883724	−	0.468008i	$-0.844972\pi$
$439$	−3.46837	+	4.77380i	−0.165536	+	0.227841i	0.718188	+	0.695849i	$0.244972\pi$
$440$	30.8055	+	18.2398i	1.46860	+	0.869549i
$441$	0.106767	−	0.0775707i	0.00508414	−	0.00369384i
$442$	51.6448	−	2.53898i	2.45649	−	0.120767i
$443$			22.9693i			1.09131i	0.838012	+	0.545653i	$0.183718\pi$
$443$			22.9693i			1.09131i	−0.838012	+	0.545653i	$0.816282\pi$
$444$	16.0279	−	49.3288i	0.760651	−	2.34104i
$445$	5.14037	−	22.9410i	0.243677	−	1.08751i
$446$	11.7721	+	36.2308i	0.557425	+	1.71558i
$447$	−1.94472	−	5.98523i	−0.0919820	−	0.283092i
$448$	10.4189	+	7.56974i	0.492245	+	0.357637i
$449$		−	6.34155i		−	0.299276i	−0.988741	−	0.149638i	$-0.952189\pi$
$449$		−	6.34155i		−	0.299276i	0.988741	−	0.149638i	$-0.0478109\pi$
$450$	−0.232149	−	0.218454i	−0.0109436	−	0.0102980i
$451$	11.7949			0.555400
$452$	0.0949206	+	0.0689638i	0.00446469	+	0.00324379i
$453$	7.80527	+	24.0221i	0.366723	+	1.12866i
$454$	−17.7667	+	5.77276i	−0.833833	+	0.270929i
$455$	19.8807	−	33.5768i	0.932020	−	1.57410i
$456$	61.6512	+	20.0317i	2.88708	+	0.938070i
$457$			32.0435i			1.49893i	0.662044	+	0.749465i	$0.269689\pi$
$457$			32.0435i			1.49893i	−0.662044	+	0.749465i	$0.730311\pi$
$458$	4.05744	+	1.31834i	0.189592	+	0.0616021i
$459$	18.0052	+	11.7757i	0.840409	+	0.549644i
$460$	−16.7630	+	1.57583i	−0.781577	+	0.0734735i
$461$	6.02771	+	4.37939i	0.280738	+	0.203968i	0.719239	−	0.694762i	$-0.244490\pi$
$461$	6.02771	+	4.37939i	0.280738	+	0.203968i	−0.438501	+	0.898731i	$0.644490\pi$
$462$	−33.9485	+	24.6650i	−1.57943	+	1.14752i
$463$	18.7162	+	25.7607i	0.869816	+	1.19720i	0.979139	+	0.203193i	$0.0651320\pi$
$463$	18.7162	+	25.7607i	0.869816	+	1.19720i	−0.109322	+	0.994006i	$0.534868\pi$
$464$	23.1956	−	31.9261i	1.07683	−	1.48213i
$465$	−11.0384	+	4.76996i	−0.511892	+	0.221201i
$466$	23.6938	+	32.6117i	1.09759	+	1.51071i
$467$	−7.14215	−	2.32062i	−0.330499	−	0.107386i	0.139067	−	0.990283i	$-0.455590\pi$
$467$	−7.14215	−	2.32062i	−0.330499	−	0.107386i	−0.469566	+	0.882897i	$0.655590\pi$
$468$		−	0.545629i		−	0.0252217i
$469$	20.4012	+	6.62876i	0.942042	+	0.306088i
$470$	−53.4205	+	5.02189i	−2.46410	+	0.231642i
$471$	−32.7577	+	10.6436i	−1.50940	+	0.490433i
$472$	−26.2772	+	8.53797i	−1.20950	+	0.392992i
$473$	18.5722	+	13.4935i	0.853949	+	0.620430i
$474$	−21.2824			−0.977533
$475$	−15.6696	−	28.5728i	−0.718970	−	1.31101i
$476$	−21.9899	−	57.8446i	−1.00790	−	2.65130i
$477$	−0.110278	+	0.151784i	−0.00504928	+	0.00694973i
$478$	42.0834	−	13.6737i	1.92485	−	0.625421i
$479$	23.8710	−	7.75617i	1.09070	−	0.354388i	0.292180	−	0.956363i	$-0.405619\pi$
$479$	23.8710	−	7.75617i	1.09070	−	0.354388i	0.798515	+	0.601975i	$0.205619\pi$
$480$	−8.19150	−	9.30112i	−0.373889	−	0.424536i
$481$	−33.2546	−	10.8051i	−1.51628	−	0.492668i
$482$	3.95094			0.179960
$483$	3.26060	−	10.0351i	0.148363	−	0.456613i
$484$	11.4478	−	8.31731i	0.520354	−	0.378060i
$485$	−28.7563	+	25.3257i	−1.30576	+	1.14998i
$486$	0.389429	−	0.536002i	0.0176648	−	0.0243136i
$487$	10.9214	−	7.93484i	0.494894	−	0.359562i	−0.312169	−	0.950027i	$-0.601056\pi$
$487$	10.9214	−	7.93484i	0.494894	−	0.359562i	0.807063	+	0.590465i	$0.201056\pi$
$488$	14.3091	−	10.3962i	0.647744	−	0.470613i
$489$	−2.96868	−	2.15687i	−0.134248	−	0.0975372i
$490$	−28.4457	−	6.37380i	−1.28505	−	0.287939i
$491$	18.0603	−	13.1216i	0.815051	−	0.592169i	−0.100240	−	0.994963i	$-0.531961\pi$
$491$	18.0603	−	13.1216i	0.815051	−	0.592169i	0.915291	+	0.402794i	$0.131961\pi$
$492$	−29.9512	−	9.73174i	−1.35030	−	0.438741i
$493$	25.8810	−	9.83879i	1.16562	−	0.443117i
$494$	25.2574	−	77.7342i	1.13638	−	3.49743i
$495$	0.144770	−	0.0625590i	0.00650694	−	0.00281182i
$496$	17.4264	−	5.66218i	0.782468	−	0.254239i
$497$	−30.6276	+	9.95150i	−1.37383	+	0.446386i
$498$	17.0913	+	12.4175i	0.765878	+	0.556443i
$499$			5.02549i			0.224972i	0.993653	+	0.112486i	$0.0358813\pi$
$499$			5.02549i			0.224972i	−0.993653	+	0.112486i	$0.964119\pi$
$500$	−1.58378	+	48.0265i	−0.0708289	+	2.14781i
$501$	−41.8760			−1.87088
$502$	33.8778	−	46.6288i	1.51204	−	2.08115i
$503$	8.57329	+	26.3859i	0.382264	+	1.17649i	0.938446	+	0.345427i	$0.112266\pi$
$503$	8.57329	+	26.3859i	0.382264	+	1.17649i	−0.556182	+	0.831061i	$0.687734\pi$
$504$	−0.486569	+	0.158096i	−0.0216735	+	0.00704215i
$505$	11.1030	+	25.6940i	0.494078	+	1.14337i
$506$	3.77188	−	11.6087i	0.167681	−	0.516068i
$507$	20.6481			0.917012
$508$	−50.9565	−	16.5568i	−2.26083	−	0.734588i
$509$	2.38406	−	1.73212i	0.105672	−	0.0767749i	−0.533695	−	0.845677i	$-0.679197\pi$
$509$	2.38406	−	1.73212i	0.105672	−	0.0767749i	0.639366	+	0.768902i	$0.279197\pi$
$510$	−5.68117	−	39.4981i	−0.251567	−	1.74901i
$511$	6.67326	+	4.84841i	0.295208	+	0.214481i
$512$	−28.7384	−	39.5550i	−1.27007	−	1.74810i
$513$	27.5128	−	19.9892i	1.21472	−	0.882546i
$514$	23.1153	+	16.7943i	1.01957	+	0.740763i
$515$	5.43277	+	6.16869i	0.239397	+	0.271825i
$516$	−36.0278	−	49.5880i	−1.58603	−	2.18299i
$517$	8.20310	−	25.2465i	0.360772	−	1.11034i
$518$			61.3205i			2.69427i
$519$	−9.02953	+	27.7900i	−0.396352	+	1.21985i
$520$	−48.3588	+	42.5897i	−2.12068	+	1.86768i
$521$	−30.4917	+	9.90736i	−1.33587	+	0.434049i	−0.887914	−	0.460009i	$-0.847846\pi$
$521$	−30.4917	+	9.90736i	−1.33587	+	0.434049i	−0.447951	+	0.894058i	$0.647846\pi$
$522$	−0.132300	−	0.407177i	−0.00579061	−	0.0178217i
$523$	−2.72893	+	3.75604i	−0.119328	+	0.164240i	−0.864502	−	0.502629i	$-0.832366\pi$
$523$	−2.72893	+	3.75604i	−0.119328	+	0.164240i	0.745175	+	0.666869i	$0.232366\pi$
$524$			26.3349i			1.15044i
$525$	−27.2349	−	12.8501i	−1.18863	−	0.560826i
$526$	35.0248			1.52715
$527$	12.4071	+	3.36756i	0.540463	+	0.146693i
$528$	26.7610	−	8.69516i	1.16462	−	0.378408i
$529$	−6.15895	−	18.9553i	−0.267780	−	0.824143i
$530$	41.2605	−	3.87877i	1.79224	−	0.168483i
$531$	−0.0376116	+	0.115757i	−0.00163221	+	0.00502341i
$532$	−97.8204			−4.24105
$533$	−6.56056	+	20.1913i	−0.284169	+	0.874583i
$534$	−26.7484	−	36.8160i	−1.15752	−	1.59318i
$535$	−5.61064	−	12.9838i	−0.242569	−	0.561339i
$536$	−28.6590	−	20.8220i	−1.23788	−	0.899374i
$537$	−5.38269	+	3.91075i	−0.232280	+	0.168761i
$538$	−36.5378	+	26.5463i	−1.57526	+	1.14449i
$539$	8.47716	−	11.6678i	0.365137	−	0.502568i
$540$	−49.9268	+	4.69346i	−2.14851	+	0.201974i
$541$	16.0730	+	22.1225i	0.691030	+	0.951122i	1.00000		4.97855e-5i	$1.58472e-5\pi$
$541$	16.0730	+	22.1225i	0.691030	+	0.951122i	−0.308970	+	0.951072i	$0.599984\pi$
$542$	27.4819	+	8.92942i	1.18045	+	0.383551i
$543$		−	24.6891i		−	1.05951i
$544$	0.650649	+	13.2347i	0.0278963	+	0.567432i
$545$	−21.0032	+	35.4726i	−0.899678	+	1.51948i
$546$	−23.3405	−	71.8346i	−0.998881	−	3.07424i
$547$	−2.36062	−	7.26524i	−0.100933	−	0.310639i	0.887822	−	0.460188i	$-0.152218\pi$
$547$	−2.36062	−	7.26524i	−0.100933	−	0.310639i	−0.988754	+	0.149549i	$0.952218\pi$
$548$	25.6049	−	35.2421i	1.09379	−	1.50547i
$549$		−	0.0779154i		−	0.00332535i
$550$	−31.5055	−	14.8651i	−1.34340	−	0.633850i
$551$		−	43.7671i		−	1.86454i
$552$	−10.2421	+	14.0970i	−0.435932	+	0.600009i
$553$	16.3305	−	5.30612i	0.694446	−	0.225639i
$554$	−20.8023	+	6.75909i	−0.883807	+	0.287166i
$555$	−5.90013	+	26.3318i	−0.250446	+	1.11772i
$556$	27.8856	+	9.06058i	1.18261	+	0.384254i
$557$			16.0733i			0.681046i	0.940236	+	0.340523i	$0.110604\pi$
$557$			16.0733i			0.681046i	−0.940236	+	0.340523i	$0.889396\pi$
$558$	0.0614290	−	0.189059i	0.00260050	−	0.00800350i
$559$	−33.4293	+	24.2878i	−1.41391	+	1.02726i
$560$	39.4850	+	23.3789i	1.66855	+	0.987939i
$561$	19.0531	+	5.17141i	0.804421	+	0.218337i
$562$	12.2216	+	16.8216i	0.515538	+	0.709577i
$563$	10.0309	+	13.8063i	0.422750	+	0.581866i	0.966270	−	0.257530i	$-0.0829088\pi$
$563$	10.0309	+	13.8063i	0.422750	+	0.581866i	−0.543520	+	0.839396i	$0.682909\pi$
$564$	−41.6609	+	57.3413i	−1.75424	+	2.41450i
$565$	−0.0525250	−	0.0310998i	−0.00220974	−	0.00130838i
$566$	−45.3942	−	62.4798i	−1.90806	−	2.62622i
$567$	9.62914	−	29.6355i	0.404386	−	1.24457i
$568$	53.1814			2.23144
$569$	9.96690	−	30.6750i	0.417834	−	1.28596i	−0.491857	−	0.870676i	$-0.663682\pi$
$569$	9.96690	−	30.6750i	0.417834	−	1.28596i	0.909691	−	0.415285i	$-0.136318\pi$
$570$	−61.5518	−	13.7918i	−2.57812	−	0.577677i
$571$	7.33498	−	2.38328i	0.306959	−	0.0997371i	−0.151487	−	0.988459i	$-0.548406\pi$
$571$	7.33498	−	2.38328i	0.306959	−	0.0997371i	0.458446	+	0.888722i	$0.348406\pi$
$572$	−18.4261	−	56.7096i	−0.770432	−	2.37115i
$573$	−2.90927	−	2.11371i	−0.121537	−	0.0883016i
$574$	37.2323			1.55404
$575$	8.60613	−	1.63250i	0.358901	−	0.0680798i
$576$	−0.0936880			−0.00390367
$577$	−6.93058	+	9.53912i	−0.288524	+	0.397119i	−0.928534	−	0.371248i	$-0.878930\pi$
$577$	−6.93058	+	9.53912i	−0.288524	+	0.397119i	0.640010	+	0.768366i	$0.278930\pi$
$578$	−21.5701	+	36.8081i	−0.897198	+	1.53102i
$579$	2.50175	+	7.69960i	0.103969	+	0.319984i
$580$	−32.8812	+	55.5336i	−1.36532	+	2.30591i
$581$	−16.2105	−	5.26711i	−0.672525	−	0.218517i
$582$			74.1718i			3.07452i
$583$	−6.33584	+	19.4997i	−0.262404	+	0.807596i
$584$	−8.00669	−	11.0203i	−0.331319	−	0.456022i
$585$	0.0265686	+	0.282625i	0.00109848	+	0.0116851i
$586$	−15.7038	−	11.4094i	−0.648716	−	0.471320i
$587$	11.7880	+	16.2249i	0.486545	+	0.669671i	0.979746	−	0.200244i	$-0.0641734\pi$
$587$	11.7880	+	16.2249i	0.486545	+	0.669671i	−0.493201	+	0.869915i	$0.664173\pi$
$588$	−31.1532	+	22.6342i	−1.28474	+	0.933417i
$589$	11.9448	−	16.4407i	0.492179	−	0.677426i
$590$	24.6797	−	10.6647i	1.01605	−	0.439059i
$591$	−8.00400	+	5.81525i	−0.329241	+	0.239207i
$592$	12.7063	−	39.1061i	0.522227	−	1.60725i
$593$		−	38.9918i		−	1.60120i	−0.599198	−	0.800601i	$-0.704514\pi$
$593$		−	38.9918i		−	1.60120i	0.599198	−	0.800601i	$-0.295486\pi$
$594$	11.2342	−	34.5752i	0.460944	−	1.41864i
$595$	14.2070	+	28.8915i	0.582429	+	1.18444i
$596$	−4.84624	−	14.9152i	−0.198510	−	0.610950i
$597$	38.5930	−	12.5396i	1.57951	−	0.513212i
$598$	17.7745	+	12.9139i	0.726854	+	0.528091i
$599$	25.0761			1.02458			0.512290	−	0.858812i	$-0.328797\pi$
$599$	25.0761			1.02458			0.512290	+	0.858812i	$0.328797\pi$
$600$	36.2170	+	34.0805i	1.47855	+	1.39133i
$601$			41.3734i			1.68766i	0.536613	+	0.843829i	$0.319704\pi$
$601$			41.3734i			1.68766i	−0.536613	+	0.843829i	$0.680296\pi$
$602$	58.6257	+	42.5940i	2.38940	+	1.73600i
$603$	−0.148415	+	0.0482230i	−0.00604393	+	0.00196379i
$604$	19.4507	+	59.8632i	0.791439	+	2.43580i
$605$	−5.52472	+	4.86563i	−0.224612	+	0.197816i
$606$	51.5279	+	16.7424i	2.09318	+	0.680115i
$607$	−30.3007			−1.22987			−0.614934	−	0.788579i	$-0.710817\pi$
$607$	−30.3007			−1.22987			−0.614934	+	0.788579i	$0.710817\pi$
$608$	19.9204	+	6.47255i	0.807881	+	0.262496i
$609$	−23.7732	−	32.7211i	−0.963340	−	1.32592i
$610$	−12.9158	+	11.3750i	−0.522946	+	0.460559i
$611$	38.6561	+	28.0853i	1.56386	+	1.13621i
$612$	0.376765	+	0.246412i	0.0152298	+	0.00996060i
$613$	18.9107	+	26.0283i	0.763795	+	1.05127i	0.996889	+	0.0788193i	$0.0251150\pi$
$613$	18.9107	+	26.0283i	0.763795	+	1.05127i	−0.233094	+	0.972454i	$0.574885\pi$
$614$	30.8749	+	22.4319i	1.24601	+	0.905278i
$615$	15.9880	+	3.58241i	0.644698	+	0.144457i
$616$	−45.2323	+	32.8632i	−1.82246	+	1.32409i
$617$	3.99232	−	12.2871i	0.160725	−	0.494660i	−0.837971	−	0.545714i	$-0.816258\pi$
$617$	3.99232	−	12.2871i	0.160725	−	0.494660i	0.998696	+	0.0510548i	$0.0162583\pi$
$618$	15.9110			0.640036
$619$	−21.4210	−	6.96012i	−0.860984	−	0.279751i	−0.154945	−	0.987923i	$-0.549520\pi$
$619$	−21.4210	−	6.96012i	−0.860984	−	0.279751i	−0.706040	+	0.708172i	$0.749520\pi$
$620$	−27.5076	+	11.8867i	−1.10473	+	0.477383i
$621$	2.82484	+	8.69397i	0.113357	+	0.348877i
$622$	−6.38309	−	19.6451i	−0.255939	−	0.787698i
$623$	29.7037	+	21.5810i	1.19005	+	0.864624i
$624$			50.6477i			2.02753i
$625$	−1.51822	−	24.9539i	−0.0607286	−	0.998154i
$626$			40.6503i			1.62471i
$627$	18.3432	−	25.2472i	0.732555	−	1.00828i
$628$	−81.6322	+	26.5239i	−3.25748	+	1.05842i
$629$	22.4792	−	18.0831i	0.896303	−	0.721021i
$630$	0.456988	−	0.197476i	0.0182069	−	0.00786765i
$631$	−13.0168	+	40.0617i	−0.518191	+	1.59483i	0.259208	+	0.965822i	$0.416539\pi$
$631$	−13.0168	+	40.0617i	−0.518191	+	1.59483i	−0.777399	+	0.629008i	$0.783461\pi$
$632$	−28.3562			−1.12795
$633$	14.3848	+	4.67390i	0.571743	+	0.185771i
$634$	−6.85077	−	9.42927i	−0.272079	−	0.374484i
$635$	27.2006	+	6.09482i	1.07942	+	0.241865i
$636$	32.1777	−	44.2888i	1.27593	−	1.75616i
$637$	15.2586	+	21.0017i	0.604568	+	0.832116i
$638$	−27.5010	−	37.8519i	−1.08878	−	1.49857i
$639$	0.137704	−	0.189533i	0.00544749	−	0.00749782i
$640$	23.1767	+	26.3162i	0.916139	+	1.04024i
$641$	9.10908	+	12.5376i	0.359787	+	0.495204i	0.950089	−	0.311978i	$-0.100992\pi$
$641$	9.10908	+	12.5376i	0.359787	+	0.495204i	−0.590302	+	0.807182i	$0.700992\pi$
$642$	−26.0384	−	8.46038i	−1.02765	−	0.333904i
$643$	−0.455776			−0.0179740			−0.00898702	−	0.999960i	$-0.502861\pi$
$643$	−0.455776			−0.0179740			−0.00898702	+	0.999960i	$0.502861\pi$
$644$	8.12543	−	25.0075i	0.320187	−	0.985433i
$645$	21.0763	+	23.9312i	0.829877	+	0.942291i
$646$	42.2702	+	52.5462i	1.66310	+	2.06740i
$647$	−16.9589	+	5.51027i	−0.666722	+	0.216631i	−0.622773	−	0.782403i	$-0.713994\pi$
$647$	−16.9589	+	5.51027i	−0.666722	+	0.216631i	−0.0439492	+	0.999034i	$0.513994\pi$
$648$	−30.2467	+	41.6310i	−1.18820	+	1.63542i
$649$			13.3012i			0.522120i
$650$	42.9711	−	45.6650i	1.68547	−	1.79113i
$651$		−	18.7795i		−	0.736026i
$652$	−7.39795	−	5.37493i	−0.289726	−	0.210498i
$653$	0.655107	+	2.01621i	0.0256363	+	0.0789005i	0.963056	−	0.269301i	$-0.0867926\pi$
$653$	0.655107	+	2.01621i	0.0256363	+	0.0789005i	−0.937420	+	0.348201i	$0.886793\pi$
$654$	24.6584	+	75.8906i	0.964218	+	2.96756i
$655$	−1.28234	−	13.6409i	−0.0501051	−	0.532995i
$656$	−23.7442	−	7.71496i	−0.927056	−	0.301219i
$657$	−0.0600070			−0.00234110
$658$	25.8943	−	79.6943i	1.00946	−	3.10681i
$659$	−0.948920	+	0.689430i	−0.0369647	+	0.0268564i	−0.606114	−	0.795378i	$-0.707273\pi$
$659$	−0.948920	+	0.689430i	−0.0369647	+	0.0268564i	0.569150	+	0.822234i	$0.307273\pi$
$660$	−42.2422	+	18.2539i	−1.64427	+	0.710533i
$661$	−3.64975	−	2.65170i	−0.141959	−	0.103139i	0.514539	−	0.857467i	$-0.327963\pi$
$661$	−3.64975	−	2.65170i	−0.141959	−	0.103139i	−0.656498	+	0.754328i	$0.727963\pi$
$662$	−23.2483	−	31.9985i	−0.903570	−	1.24366i
$663$	−19.4505	+	29.7399i	−0.755395	+	1.15500i
$664$	22.7720	+	16.5448i	0.883726	+	0.642065i
$665$	50.6689	−	4.76322i	1.96486	−	0.184710i
$666$	−0.262208	−	0.360899i	−0.0101604	−	0.0139845i
$667$	11.1889	+	3.63551i	0.433237	+	0.140767i
$668$	−104.355			−4.03761
$669$	−24.8996	−	8.09037i	−0.962674	−	0.312792i
$670$	29.6611	+	17.5622i	1.14591	+	0.678488i
$671$	−2.63123	−	8.09808i	−0.101577	−	0.312623i
$672$	18.4086	−	5.98132i	0.710127	−	0.230734i
$673$	−19.6268	−	14.2597i	−0.756556	−	0.549670i	0.141296	−	0.989967i	$-0.454873\pi$
$673$	−19.6268	−	14.2597i	−0.756556	−	0.549670i	−0.897852	+	0.440297i	$0.854873\pi$
$674$		−	30.5749i		−	1.17770i
$675$	25.6325	−	4.86223i	0.986596	−	0.187147i
$676$	51.4549			1.97904
$677$	16.3260	+	11.8616i	0.627461	+	0.455877i	0.855520	−	0.517770i	$-0.173238\pi$
$677$	16.3260	+	11.8616i	0.627461	+	0.455877i	−0.228059	+	0.973647i	$0.573238\pi$
$678$	−0.112373	+	0.0365121i	−0.00431565	+	0.00140224i
$679$	−18.4925	−	56.9139i	−0.709676	−	2.18416i
$680$	−7.56948	−	52.6265i	−0.290276	−	2.01813i
$681$	3.96732	−	12.2102i	0.152028	−	0.467894i
$682$		−	21.7242i		−	0.831862i
$683$	−7.04897	+	21.6945i	−0.269721	+	0.830117i	0.720847	+	0.693095i	$0.243753\pi$
$683$	−7.04897	+	21.6945i	−0.269721	+	0.830117i	−0.990568	+	0.137022i	$0.956247\pi$
$684$	0.575716	−	0.418282i	0.0220131	−	0.0159934i
$685$	−11.5467	+	19.5015i	−0.441178	+	0.745113i
$686$	−9.29884	+	12.7987i	−0.355031	+	0.488659i
$687$	−2.37202	+	1.72337i	−0.0904981	+	0.0657507i
$688$	−28.5615	−	39.3115i	−1.08890	−	1.49874i
$689$	−29.8569	−	21.6923i	−1.13746	−	0.826410i
$690$	8.63864	−	14.5899i	0.328867	−	0.555429i
$691$	−12.3268	−	16.9664i	−0.468935	−	0.645434i	0.507396	−	0.861713i	$-0.330608\pi$
$691$	−12.3268	−	16.9664i	−0.468935	−	0.645434i	−0.976332	+	0.216279i	$0.930608\pi$
$692$	−22.5016	+	69.2527i	−0.855382	+	2.63259i
$693$			0.246297i			0.00935604i
$694$	−86.0724	−	27.9666i	−3.26726	−	1.06160i
$695$	−14.8854	−	3.33534i	−0.564634	−	0.126517i
$696$	20.6398	+	63.5228i	0.782350	+	2.40783i
$697$	−10.9796	−	13.6488i	−0.415882	−	0.516984i
$698$	−30.4025	+	41.8455i	−1.15075	+	1.58388i
$699$	−27.7032			−1.04783
$700$	−67.8693	−	32.0226i	−2.56522	−	1.21034i
$701$	11.5317			0.435546			0.217773	−	0.975999i	$-0.430121\pi$
$701$	11.5317			0.435546			0.217773	+	0.975999i	$0.430121\pi$
$702$	52.9397	+	38.4629i	1.99808	+	1.45169i
$703$	−14.0923	−	43.3715i	−0.531500	−	1.63579i
$704$	−9.73740	+	3.16387i	−0.366992	+	0.119243i
$705$	18.7873	−	31.7302i	0.707571	−	1.19503i
$706$	−7.70599	+	23.7166i	−0.290019	+	0.892586i
$707$	−43.7129			−1.64399
$708$	10.9746	−	33.7764i	0.412451	−	1.26939i
$709$	−11.6113	−	15.9815i	−0.436070	−	0.600198i	0.533263	−	0.845949i	$-0.320965\pi$
$709$	−11.6113	−	15.9815i	−0.436070	−	0.600198i	−0.969333	+	0.245751i	$0.920965\pi$
$710$	−51.5220	+	4.84342i	−1.93359	+	0.181770i
$711$	−0.0734234	+	0.101059i	−0.00275359	+	0.00379000i
$712$	−35.6390	−	49.0529i	−1.33563	−	1.83833i
$713$	3.21081	+	4.41930i	0.120246	+	0.165504i
$714$	60.1437	+	16.3243i	2.25082	+	0.610922i
$715$	12.3057	+	28.4772i	0.460207	+	1.06499i
$716$	−13.4137	+	9.74559i	−0.501292	+	0.364210i
$717$	−9.39725	+	28.9218i	−0.350947	+	1.08010i
$718$		−	9.03021i		−	0.337004i
$719$	15.6535	+	5.08613i	0.583777	+	0.189681i	0.585992	−	0.810317i	$-0.300705\pi$
$719$	15.6535	+	5.08613i	0.583777	+	0.189681i	−0.00221472	+	0.999998i	$0.500705\pi$
$720$	−0.332356	+	0.0312437i	−0.0123862	+	0.00116438i
$721$	−12.2090	+	3.96693i	−0.454685	+	0.147736i
$722$	56.0350	−	18.2069i	2.08541	−	0.677589i
$723$	−1.59600	+	2.19671i	−0.0593559	+	0.0816964i
$724$		−	61.5252i		−	2.28657i
$725$	14.3276	−	30.3663i	0.532115	−	1.12778i
$726$			14.2500i			0.528869i
$727$	19.4165	−	26.7245i	0.720118	−	0.991157i	−0.279402	−	0.960174i	$-0.590136\pi$
$727$	19.4165	−	26.7245i	0.720118	−	0.991157i	0.999520	−	0.0309828i	$-0.00986372\pi$
$728$	−31.0984	−	95.7109i	−1.15258	−	3.54728i
$729$	8.41291	+	25.8923i	0.311589	+	0.958973i
$730$	8.76051	+	9.94720i	0.324241	+	0.368163i
$731$	−1.67408	−	34.0520i	−0.0619181	−	1.25946i
$732$			22.7347i			0.840300i
$733$	−39.0470	−	12.6871i	−1.44223	−	0.468610i	−0.519640	−	0.854386i	$-0.673934\pi$
$733$	−39.0470	−	12.6871i	−1.44223	−	0.468610i	−0.922592	+	0.385776i	$0.873934\pi$
$734$	38.9075	+	53.5516i	1.43610	+	1.97663i
$735$	15.0346	−	13.2410i	0.554560	−	0.488401i
$736$	−3.30937	+	4.55496i	−0.121985	+	0.167898i
$737$	−13.7969	+	10.0240i	−0.508216	+	0.369241i
$738$	−0.219128	+	0.159206i	−0.00806623	+	0.00586046i
$739$	0.650862	+	0.472879i	0.0239423	+	0.0173951i	0.599692	−	0.800231i	$-0.295290\pi$
$739$	0.650862	+	0.472879i	0.0239423	+	0.0173951i	−0.575750	+	0.817626i	$0.695290\pi$
$740$	−14.7031	+	65.6188i	−0.540497	+	2.41219i
$741$	33.0171	+	45.4441i	1.21291	+	1.66943i
$742$	−20.0000	+	61.5537i	−0.734223	+	2.25971i
$743$	2.40294			0.0881552			0.0440776	−	0.999028i	$-0.485965\pi$
$743$	2.40294			0.0881552			0.0440776	+	0.999028i	$0.485965\pi$
$744$	−9.58340	+	29.4947i	−0.351344	+	1.08133i
$745$	3.23652	+	7.48978i	0.118577	+	0.274404i
$746$	−7.89435	−	24.2963i	−0.289033	−	0.889551i
$747$	0.117928	−	0.0383172i	0.00431477	−	0.00140195i
$748$	47.4802	+	12.8872i	1.73605	+	0.471201i
$749$	22.0893			0.807124
$750$	−38.1908	−	29.7187i	−1.39453	−	1.08517i
$751$			44.2671i			1.61533i	0.589642	+	0.807665i	$0.299269\pi$
$751$			44.2671i			1.61533i	−0.589642	+	0.807665i	$0.700731\pi$
$752$	−33.0272	+	45.4581i	−1.20438	+	1.65768i
$753$	12.2403	+	37.6719i	0.446063	+	1.37284i
$754$	80.0941	−	26.0242i	2.91686	−	0.947744i
$755$	−12.9900	−	30.0608i	−0.472756	−	1.09402i
$756$	24.2008	−	74.4823i	0.880174	−	2.70890i
$757$			35.2667i			1.28179i	0.767628	+	0.640895i	$0.221437\pi$
$757$			35.2667i			1.28179i	−0.767628	+	0.640895i	$0.778563\pi$
$758$	16.9379	−	52.1296i	0.615213	−	1.89343i
$759$	4.93070	+	6.78653i	0.178973	+	0.246335i
$760$	−82.0104	−	18.3760i	−2.97483	−	0.666566i
$761$	−25.3841	−	18.4427i	−0.920174	−	0.668546i	0.0233932	−	0.999726i	$-0.492553\pi$
$761$	−25.3841	−	18.4427i	−0.920174	−	0.668546i	−0.943567	+	0.331181i	$0.892553\pi$
$762$	43.6519	−	31.7150i	1.58134	−	1.14891i
$763$	−37.8420	−	52.0851i	−1.36997	−	1.88561i
$764$	−7.24991	−	5.26737i	−0.262293	−	0.190567i
$765$	−0.207155	−	0.109290i	−0.00748972	−	0.00395139i
$766$	9.41757	−	6.84226i	0.340271	−	0.247221i
$767$	−22.7700	−	7.39843i	−0.822178	−	0.267142i
$768$	55.1570			1.99031
$769$	2.01951	−	6.21542i	0.0728255	−	0.224134i	−0.908018	−	0.418931i	$-0.862405\pi$
$769$	2.01951	−	6.21542i	0.0728255	−	0.224134i	0.980844	+	0.194797i	$0.0624049\pi$
$770$	40.8279	−	35.9572i	1.47134	−	1.29581i
$771$	−18.6751	+	6.06790i	−0.672567	+	0.218530i

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

\(f(q)\)	\(=\)	\(q+(-1.47509 + 2.03029i) q^{2} +(-0.532962 - 1.64029i) q^{3} +(-1.32814 - 4.08760i) q^{4} +(0.886990 + 2.05262i) q^{5} +(4.11642 + 1.33751i) q^{6} -3.49211 q^{7} +(5.48463 + 1.78207i) q^{8} +(0.0205526 - 0.0149323i) q^{9} +(-5.47580 - 1.22696i) q^{10} +(1.63185 - 2.24605i) q^{11} +(-5.99699 + 4.35707i) q^{12} +(2.93728 + 4.04282i) q^{13} +(5.15117 - 7.08998i) q^{14} +(2.89416 - 2.54889i) q^{15} +(-4.75420 + 3.45413i) q^{16} +(-4.11813 + 0.202457i) q^{17} +0.0637542i q^{18} +(-2.01401 + 6.19849i) q^{19} +(7.21224 - 6.35183i) q^{20} +(1.86116 + 5.72806i) q^{21} +(2.15300 + 6.62625i) q^{22} +(-1.41733 - 1.02975i) q^{23} -9.94616i q^{24} +(-3.42650 + 3.64131i) q^{25} -12.5408 q^{26} +(-4.22139 - 3.06702i) q^{27} +(4.63801 + 14.2743i) q^{28} +(-6.38667 + 2.07516i) q^{29} +(0.905831 + 9.63581i) q^{30} +(-2.96543 - 0.963528i) q^{31} -3.21376i q^{32} +(-4.55389 - 1.47965i) q^{33} +(5.66357 - 8.65963i) q^{34} +(-3.09746 - 7.16797i) q^{35} +(-0.0883342 - 0.0641785i) q^{36} +(-5.66078 + 4.11280i) q^{37} +(-9.61387 - 13.2324i) q^{38} +(5.06593 - 6.97265i) q^{39} +(1.20691 + 12.8385i) q^{40} +(2.49719 + 3.43708i) q^{41} +(-14.3750 - 4.67072i) q^{42} +8.26881i q^{43} +(-11.3483 - 3.68728i) q^{44} +(0.0488804 + 0.0289419i) q^{45} +(4.18139 - 1.35862i) q^{46} +(9.09369 - 2.95472i) q^{47} +(8.19957 + 5.95734i) q^{48} +5.19481 q^{49} +(-2.33850 - 12.3280i) q^{50} +(2.52690 + 6.64702i) q^{51} +(12.6243 - 17.3758i) q^{52} +(-7.02371 + 2.28214i) q^{53} +(12.4538 - 4.04650i) q^{54} +(6.05772 + 1.35735i) q^{55} +(-19.1529 - 6.22316i) q^{56} +11.2407 q^{57} +(5.20775 - 16.0278i) q^{58} +(-3.87604 + 2.81611i) q^{59} +(-14.2627 - 8.44487i) q^{60} +(1.80274 - 2.48126i) q^{61} +(6.33052 - 4.59939i) q^{62} +(-0.0717719 + 0.0521453i) q^{63} +(-2.98354 - 2.16767i) q^{64} +(-5.69303 + 9.61505i) q^{65} +(9.72150 - 7.06308i) q^{66} +(-5.84210 - 1.89821i) q^{67} +(6.29703 + 16.5644i) q^{68} +(-0.933707 + 2.87365i) q^{69} +(19.1221 + 4.28466i) q^{70} +(8.77051 - 2.84971i) q^{71} +(0.139334 - 0.0452723i) q^{72} +(-1.91096 - 1.38839i) q^{73} -17.5597i q^{74} +(7.79899 + 3.67977i) q^{75} +28.0118 q^{76} +(-5.69860 + 7.84345i) q^{77} +(6.68378 + 20.5706i) q^{78} +(-4.67642 + 1.51946i) q^{79} +(-11.3069 - 6.69478i) q^{80} +(-2.75740 + 8.48641i) q^{81} -10.6618 q^{82} +(4.64204 + 1.50829i) q^{83} +(20.9421 - 15.2154i) q^{84} +(-4.06831 - 8.27338i) q^{85} +(-16.7881 - 12.1972i) q^{86} +(6.80771 + 9.37001i) q^{87} +(12.9527 - 9.41070i) q^{88} +(-8.50595 - 6.17994i) q^{89} +(-0.130863 + 0.0565493i) q^{90} +(-10.2573 - 14.1179i) q^{91} +(-2.32680 + 7.16115i) q^{92} +5.37769i q^{93} +(-7.41508 + 22.8213i) q^{94} +(-14.5096 + 1.36400i) q^{95} +(-5.27149 + 1.71281i) q^{96} +(5.29550 + 16.2979i) q^{97} +(-7.66281 + 10.5470i) q^{98} -0.0705295i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 176 q - 10 q^{2} + 38 q^{4} - 10 q^{8} - 50 q^{9} - 10 q^{13} + 6 q^{15} - 58 q^{16} - 8 q^{19} - 44 q^{21} - 20 q^{25} - 64 q^{26} + 78 q^{30} - 20 q^{33} - 23 q^{34} - 46 q^{35} + 52 q^{36} - 10 q^{38}+ \cdots - 250 q^{98}+O(q^{100}) \) 176 * q - 10 * q^2 + 38 * q^4 - 10 * q^8 - 50 * q^9 - 10 * q^13 + 6 * q^15 - 58 * q^16 - 8 * q^19 - 44 * q^21 - 20 * q^25 - 64 * q^26 + 78 * q^30 - 20 * q^33 - 23 * q^34 - 46 * q^35 + 52 * q^36 - 10 * q^38 - 20 * q^42 + 40 * q^47 + 164 * q^49 + 84 * q^50 + 20 * q^51 - 30 * q^52 - 40 * q^53 - 18 * q^55 - 18 * q^59 - 48 * q^60 + 66 * q^64 + 80 * q^66 - 50 * q^67 + 68 * q^69 - 152 * q^70 + 60 * q^72 - 72 * q^76 - 40 * q^77 - 38 * q^81 + 50 * q^83 - 52 * q^84 + 47 * q^85 - 94 * q^86 - 120 * q^87 + 60 * q^89 + 50 * q^94 - 250 * q^98

Introduction

L-functions

Modular forms

Varieties

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