LMFDB - Embedded newform 425.2.q.a.84.16

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			84.16
Character	$\chi$	$=$	425.84
Dual form			425.2.q.a.339.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.677444 + 0.932422i) q^{2} +(1.03346 + 3.18065i) q^{3} +(0.207554 + 0.638786i) q^{4} +(-2.01329 + 0.972965i) q^{5} +(-3.66582 - 1.19110i) q^{6} +4.10770 q^{7} +(-2.92848 - 0.951521i) q^{8} +(-6.62147 + 4.81078i) q^{9} +(0.456678 - 2.53636i) q^{10} +(1.41394 - 1.94612i) q^{11} +(-1.81726 + 1.32032i) q^{12} +(0.302563 + 0.416442i) q^{13} +(-2.78274 + 3.83011i) q^{14} +(-5.17531 - 5.39806i) q^{15} +(1.78433 - 1.29639i) q^{16} +(4.00104 - 0.995833i) q^{17} -9.43303i q^{18} +(-0.992682 + 3.05516i) q^{19} +(-1.03938 - 1.08412i) q^{20} +(4.24513 + 13.0652i) q^{21} +(0.856742 + 2.63678i) q^{22} +(0.444953 + 0.323277i) q^{23} -10.2978i q^{24} +(3.10668 - 3.91772i) q^{25} -0.593269 q^{26} +(-14.0275 - 10.1916i) q^{27} +(0.852571 + 2.62394i) q^{28} +(1.70891 - 0.555258i) q^{29} +(8.53925 - 1.16869i) q^{30} +(4.70334 + 1.52821i) q^{31} -3.61639i q^{32} +(7.65119 + 2.48602i) q^{33} +(-1.78194 + 4.40528i) q^{34} +(-8.26999 + 3.99665i) q^{35} +(-4.44737 - 3.23121i) q^{36} +(7.70860 - 5.60063i) q^{37} +(-2.17621 - 2.99530i) q^{38} +(-1.01187 + 1.39272i) q^{39} +(6.82168 - 0.933619i) q^{40} +(-0.481169 - 0.662273i) q^{41} +(-15.0581 - 4.89267i) q^{42} -3.79889i q^{43} +(1.53663 + 0.499280i) q^{44} +(8.65022 - 16.1279i) q^{45} +(-0.602861 + 0.195881i) q^{46} +(-7.90580 + 2.56875i) q^{47} +(5.96740 + 4.33557i) q^{48} +9.87320 q^{49} +(1.54837 + 5.55077i) q^{50} +(7.30230 + 11.6968i) q^{51} +(-0.203219 + 0.279707i) q^{52} +(-5.69406 + 1.85011i) q^{53} +(19.0057 - 6.17534i) q^{54} +(-0.953166 + 5.29383i) q^{55} +(-12.0293 - 3.90856i) q^{56} -10.7433 q^{57} +(-0.639955 + 1.96958i) q^{58} +(-1.99351 + 1.44837i) q^{59} +(2.37405 - 4.42631i) q^{60} +(-4.29318 + 5.90906i) q^{61} +(-4.61118 + 3.35022i) q^{62} +(-27.1990 + 19.7612i) q^{63} +(6.94066 + 5.04269i) q^{64} +(-1.01433 - 0.544036i) q^{65} +(-7.50128 + 5.45000i) q^{66} +(-9.58242 - 3.11352i) q^{67} +(1.46656 + 2.34912i) q^{68} +(-0.568392 + 1.74933i) q^{69} +(1.87590 - 10.4186i) q^{70} +(13.8098 - 4.48708i) q^{71} +(23.9684 - 7.78780i) q^{72} +(0.226203 + 0.164346i) q^{73} +10.9818i q^{74} +(15.6715 + 5.83247i) q^{75} -2.15763 q^{76} +(5.80805 - 7.99410i) q^{77} +(-0.613118 - 1.88698i) q^{78} +(-16.0405 + 5.21188i) q^{79} +(-2.33103 + 4.34610i) q^{80} +(10.3316 - 31.7973i) q^{81} +0.943483 q^{82} +(0.180325 + 0.0585910i) q^{83} +(-7.46476 + 5.42346i) q^{84} +(-7.08634 + 5.89777i) q^{85} +(3.54216 + 2.57353i) q^{86} +(3.53216 + 4.86161i) q^{87} +(-5.99248 + 4.35379i) q^{88} +(0.532227 + 0.386686i) q^{89} +(9.17801 + 18.9914i) q^{90} +(1.24284 + 1.71062i) q^{91} +(-0.114153 + 0.351327i) q^{92} +16.5390i q^{93} +(2.96058 - 9.11172i) q^{94} +(-0.974007 - 7.11677i) q^{95} +(11.5025 - 3.73738i) q^{96} +(0.579938 + 1.78487i) q^{97} +(-6.68854 + 9.20599i) q^{98} +19.6884i 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 $

$2$	−0.677444	+	0.932422i	−0.479025	+	0.659322i	−0.978317	−	0.207112i	$-0.933593\pi$
$2$	−0.677444	+	0.932422i	−0.479025	+	0.659322i	0.499292	+	0.866434i	$0.333593\pi$
$3$	1.03346	+	3.18065i	0.596666	+	1.83635i	0.546250	+	0.837622i	$0.316055\pi$
$3$	1.03346	+	3.18065i	0.596666	+	1.83635i	0.0504168	+	0.998728i	$0.483945\pi$
$4$	0.207554	+	0.638786i	0.103777	+	0.319393i
$5$	−2.01329	+	0.972965i	−0.900371	+	0.435123i
$5$	−2.01329	+	0.972965i	−0.900371	+	0.435123i
$6$	−3.66582	−	1.19110i	−1.49656	−	0.486263i
$7$	4.10770			1.55256			0.776282	−	0.630385i	$-0.217103\pi$
$7$	4.10770			1.55256			0.776282	+	0.630385i	$0.217103\pi$
$8$	−2.92848	−	0.951521i	−1.03537	−	0.336413i
$9$	−6.62147	+	4.81078i	−2.20716	+	1.60359i
$10$	0.456678	−	2.53636i	0.144414	−	0.802069i
$11$	1.41394	−	1.94612i	0.426320	−	0.586779i	−0.540784	−	0.841161i	$-0.681872\pi$
$11$	1.41394	−	1.94612i	0.426320	−	0.586779i	0.967104	+	0.254383i	$0.0818724\pi$
$12$	−1.81726	+	1.32032i	−0.524597	+	0.381142i
$13$	0.302563	+	0.416442i	0.0839158	+	0.115500i	0.848911	−	0.528536i	$-0.177259\pi$
$13$	0.302563	+	0.416442i	0.0839158	+	0.115500i	−0.764995	+	0.644036i	$0.777259\pi$
$14$	−2.78274	+	3.83011i	−0.743718	+	1.02364i
$15$	−5.17531	−	5.39806i	−1.33626	−	1.39377i
$16$	1.78433	−	1.29639i	0.446083	−	0.324098i
$17$	4.00104	−	0.995833i	0.970395	−	0.241525i
$17$	4.00104	−	0.995833i	0.970395	−	0.241525i
$18$		−	9.43303i		−	2.22339i
$19$	−0.992682	+	3.05516i	−0.227737	+	0.700902i	0.770265	+	0.637723i	$0.220124\pi$
$19$	−0.992682	+	3.05516i	−0.227737	+	0.700902i	−0.998002	+	0.0631785i	$0.979876\pi$
$20$	−1.03938	−	1.08412i	−0.232413	−	0.242417i
$21$	4.24513	+	13.0652i	0.926363	+	2.85105i
$22$	0.856742	+	2.63678i	0.182658	+	0.562163i
$23$	0.444953	+	0.323277i	0.0927790	+	0.0674079i	0.633208	−	0.773982i	$-0.281738\pi$
$23$	0.444953	+	0.323277i	0.0927790	+	0.0674079i	−0.540429	+	0.841390i	$0.681738\pi$
$24$		−	10.2978i		−	2.10204i
$25$	3.10668	−	3.91772i	0.621336	−	0.783544i
$26$	−0.593269			−0.116350
$27$	−14.0275	−	10.1916i	−2.69960	−	1.96137i
$28$	0.852571	+	2.62394i	0.161121	+	0.495879i
$29$	1.70891	−	0.555258i	0.317336	−	0.103109i	−0.146018	−	0.989282i	$-0.546646\pi$
$29$	1.70891	−	0.555258i	0.317336	−	0.103109i	0.463354	+	0.886173i	$0.346646\pi$
$30$	8.53925	−	1.16869i	1.55905	−	0.213372i
$31$	4.70334	+	1.52821i	0.844744	+	0.274474i	0.699243	−	0.714884i	$-0.253521\pi$
$31$	4.70334	+	1.52821i	0.844744	+	0.274474i	0.145501	+	0.989358i	$0.453521\pi$
$32$		−	3.61639i		−	0.639293i
$33$	7.65119	+	2.48602i	1.33190	+	0.432761i
$34$	−1.78194	+	4.40528i	−0.305601	+	0.755499i
$35$	−8.26999	+	3.99665i	−1.39788	+	0.675557i
$36$	−4.44737	−	3.23121i	−0.741229	−	0.538534i
$37$	7.70860	−	5.60063i	1.26729	−	0.920737i	0.268195	−	0.963365i	$-0.413573\pi$
$37$	7.70860	−	5.60063i	1.26729	−	0.920737i	0.999091	+	0.0426271i	$0.0135727\pi$
$38$	−2.17621	−	2.99530i	−0.353028	−	0.485902i
$39$	−1.01187	+	1.39272i	−0.162029	+	0.223014i
$40$	6.82168	−	0.933619i	1.07860	−	0.147618i
$41$	−0.481169	−	0.662273i	−0.0751460	−	0.103430i	0.769789	−	0.638298i	$-0.220361\pi$
$41$	−0.481169	−	0.662273i	−0.0751460	−	0.103430i	−0.844935	+	0.534868i	$0.820361\pi$
$42$	−15.0581	−	4.89267i	−2.32351	−	0.754955i
$43$		−	3.79889i		−	0.579325i	−0.957129	−	0.289662i	$-0.906457\pi$
$43$		−	3.79889i		−	0.579325i	0.957129	−	0.289662i	$-0.0935430\pi$
$44$	1.53663	+	0.499280i	0.231655	+	0.0752694i
$45$	8.65022	−	16.1279i	1.28950	−	2.40421i
$46$	−0.602861	+	0.195881i	−0.0888870	+	0.0288811i
$47$	−7.90580	+	2.56875i	−1.15318	+	0.374691i	−0.822340	−	0.568996i	$-0.807332\pi$
$47$	−7.90580	+	2.56875i	−1.15318	+	0.374691i	−0.330839	+	0.943687i	$0.607332\pi$
$48$	5.96740	+	4.33557i	0.861320	+	0.625786i
$49$	9.87320			1.41046
$50$	1.54837	+	5.55077i	0.218972	+	0.784998i
$51$	7.30230	+	11.6968i	1.02253	+	1.63787i
$52$	−0.203219	+	0.279707i	−0.0281814	+	0.0387884i
$53$	−5.69406	+	1.85011i	−0.782139	+	0.254132i	−0.672753	−	0.739867i	$-0.734888\pi$
$53$	−5.69406	+	1.85011i	−0.782139	+	0.254132i	−0.109386	+	0.993999i	$0.534888\pi$
$54$	19.0057	−	6.17534i	2.58635	−	0.840357i
$55$	−0.953166	+	5.29383i	−0.128525	+	0.713820i
$56$	−12.0293	−	3.90856i	−1.60748	−	0.522303i
$57$	−10.7433			−1.42298
$58$	−0.639955	+	1.96958i	−0.0840302	+	0.258618i
$59$	−1.99351	+	1.44837i	−0.259534	+	0.188562i	−0.709941	−	0.704261i	$-0.751279\pi$
$59$	−1.99351	+	1.44837i	−0.259534	+	0.188562i	0.450408	+	0.892823i	$0.351279\pi$
$60$	2.37405	−	4.42631i	0.306489	−	0.571434i
$61$	−4.29318	+	5.90906i	−0.549686	+	0.756577i	−0.989969	−	0.141281i	$-0.954878\pi$
$61$	−4.29318	+	5.90906i	−0.549686	+	0.756577i	0.440284	+	0.897859i	$0.354878\pi$
$62$	−4.61118	+	3.35022i	−0.585620	+	0.425478i
$63$	−27.1990	+	19.7612i	−3.42675	+	2.48968i
$64$	6.94066	+	5.04269i	0.867583	+	0.630336i
$65$	−1.01433	−	0.544036i	−0.125812	−	0.0674794i
$66$	−7.50128	+	5.45000i	−0.923343	+	0.670848i
$67$	−9.58242	−	3.11352i	−1.17068	−	0.380377i	−0.341783	−	0.939779i	$-0.611031\pi$
$67$	−9.58242	−	3.11352i	−1.17068	−	0.380377i	−0.828896	+	0.559402i	$0.811031\pi$
$68$	1.46656	+	2.34912i	0.177846	+	0.284873i
$69$	−0.568392	+	1.74933i	−0.0684264	+	0.210595i
$70$	1.87590	−	10.4186i	0.224213	−	1.24526i
$71$	13.8098	−	4.48708i	1.63892	−	0.532518i	0.662624	−	0.748952i	$-0.269443\pi$
$71$	13.8098	−	4.48708i	1.63892	−	0.532518i	0.976297	+	0.216434i	$0.0694427\pi$
$72$	23.9684	−	7.78780i	2.82470	−	0.917801i
$73$	0.226203	+	0.164346i	0.0264750	+	0.0192352i	0.600944	−	0.799291i	$-0.294791\pi$
$73$	0.226203	+	0.164346i	0.0264750	+	0.0192352i	−0.574469	+	0.818526i	$0.694791\pi$
$74$			10.9818i			1.27661i
$75$	15.6715	+	5.83247i	1.80959	+	0.673476i
$76$	−2.15763			−0.247497
$77$	5.80805	−	7.99410i	0.661889	−	0.911012i
$78$	−0.613118	−	1.88698i	−0.0694219	−	0.213659i
$79$	−16.0405	+	5.21188i	−1.80470	+	0.586383i	−0.999974	−	0.00726275i	$-0.997688\pi$
$79$	−16.0405	+	5.21188i	−1.80470	+	0.586383i	−0.804727	+	0.593645i	$0.797688\pi$
$80$	−2.33103	+	4.34610i	−0.260617	+	0.485909i
$81$	10.3316	−	31.7973i	1.14795	−	3.53303i
$82$	0.943483			0.104190
$83$	0.180325	+	0.0585910i	0.0197932	+	0.00643120i	0.318897	−	0.947789i	$-0.396688\pi$
$83$	0.180325	+	0.0585910i	0.0197932	+	0.00643120i	−0.299104	+	0.954221i	$0.596688\pi$
$84$	−7.46476	+	5.42346i	−0.814472	+	0.591748i
$85$	−7.08634	+	5.89777i	−0.768622	+	0.639703i
$86$	3.54216	+	2.57353i	0.381961	+	0.277511i
$87$	3.53216	+	4.86161i	0.378688	+	0.521219i
$88$	−5.99248	+	4.35379i	−0.638800	+	0.464116i
$89$	0.532227	+	0.386686i	0.0564160	+	0.0409886i	0.615636	−	0.788031i	$-0.288899\pi$
$89$	0.532227	+	0.386686i	0.0564160	+	0.0409886i	−0.559220	+	0.829019i	$0.688899\pi$
$90$	9.17801	+	18.9914i	0.967447	+	2.00187i
$91$	1.24284	+	1.71062i	0.130285	+	0.179322i
$92$	−0.114153	+	0.351327i	−0.0119013	+	0.0366284i
$93$			16.5390i			1.71502i
$94$	2.96058	−	9.11172i	0.305360	−	0.939802i
$95$	−0.974007	−	7.11677i	−0.0999310	−	0.730165i
$96$	11.5025	−	3.73738i	1.17397	−	0.381445i
$97$	0.579938	+	1.78487i	0.0588838	+	0.181226i	0.976172	−	0.216998i	$-0.0696266\pi$
$97$	0.579938	+	1.78487i	0.0588838	+	0.181226i	−0.917288	+	0.398224i	$0.869627\pi$
$98$	−6.68854	+	9.20599i	−0.675645	+	0.929945i
$99$			19.6884i			1.97875i
$100$	3.14739	+	1.17136i	0.314739	+	0.117136i
$101$	−12.4654			−1.24035			−0.620175	−	0.784463i	$-0.712939\pi$
$101$	−12.4654			−1.24035			−0.620175	+	0.784463i	$0.712939\pi$
$102$	−15.8532	−	1.11508i	−1.56970	−	0.110409i
$103$	2.47524	−	0.804255i	0.243893	−	0.0792456i	−0.184520	−	0.982829i	$-0.559073\pi$
$103$	2.47524	−	0.804255i	0.243893	−	0.0792456i	0.428413	+	0.903583i	$0.359073\pi$
$104$	−0.489796	−	1.50744i	−0.0480284	−	0.147816i
$105$	−21.2586	−	22.1736i	−2.07463	−	2.16392i
$106$	2.13232	−	6.56261i	0.207109	−	0.637417i
$107$	2.22423			0.215025			0.107512	−	0.994204i	$-0.465711\pi$
$107$	2.22423			0.215025			0.107512	+	0.994204i	$0.465711\pi$
$108$	3.59878	−	11.0759i	0.346293	−	1.06578i
$109$	8.98608	+	12.3683i	0.860711	+	1.18467i	0.981400	+	0.191976i	$0.0614896\pi$
$109$	8.98608	+	12.3683i	0.860711	+	1.18467i	−0.120689	+	0.992690i	$0.538510\pi$
$110$	−4.29036	−	4.47503i	−0.409070	−	0.426677i
$111$	25.7802	+	18.7304i	2.44694	+	1.77781i
$112$	7.32950	−	5.32519i	0.692572	−	0.503183i
$113$	11.4020	−	8.28407i	1.07261	−	0.779300i	0.0962336	−	0.995359i	$-0.469320\pi$
$113$	11.4020	−	8.28407i	1.07261	−	0.779300i	0.976380	+	0.216059i	$0.0693204\pi$
$114$	7.27798	−	10.0173i	0.681646	−	0.938205i
$115$	−1.21036	−	0.217927i	−0.112866	−	0.0203218i
$116$	0.709382	+	0.976381i	0.0658645	+	0.0906547i
$117$	−4.00682	−	1.30189i	−0.370431	−	0.120360i
$118$		−	2.83999i		−	0.261442i
$119$	16.4351	−	4.09058i	1.50660	−	0.374983i
$120$	10.0194	+	20.7325i	0.914644	+	1.89261i
$121$	1.61102	+	4.95821i	0.146456	+	0.450746i
$122$	−2.60134	−	8.00611i	−0.235515	−	0.724839i
$123$	1.60919	−	2.21486i	0.145096	−	0.199707i
$124$			3.32161i			0.298290i
$125$	−2.44284	+	10.9102i	−0.218495	+	0.975838i
$126$		−	38.7481i		−	3.45195i
$127$	12.8283	−	17.6567i	1.13833	−	1.56678i	0.367149	−	0.930162i	$-0.380334\pi$
$127$	12.8283	−	17.6567i	1.13833	−	1.56678i	0.771181	−	0.636615i	$-0.219666\pi$
$128$	−2.52504	+	0.820434i	−0.223184	+	0.0725168i
$129$	12.0829	−	3.92598i	1.06384	−	0.345664i
$130$	1.19442	−	0.577230i	0.104758	−	0.0506264i
$131$	−3.56331	−	1.15779i	−0.311328	−	0.101157i	0.149186	−	0.988809i	$-0.452335\pi$
$131$	−3.56331	−	1.15779i	−0.311328	−	0.101157i	−0.460514	+	0.887653i	$0.652335\pi$
$132$			5.40346i			0.470311i
$133$	−4.07764	+	12.5497i	−0.353576	+	1.08820i
$134$	9.39467	−	6.82562i	0.811576	−	0.589644i
$135$	38.1576	+	6.87036i	3.28408	+	0.591306i
$136$	−12.6645	−	0.890794i	−1.08597	−	0.0763850i
$137$	7.36901	+	10.1426i	0.629577	+	0.866538i	0.998006	−	0.0631175i	$-0.0201043\pi$
$137$	7.36901	+	10.1426i	0.629577	+	0.866538i	−0.368429	+	0.929656i	$0.620104\pi$
$138$	−1.24606	−	1.71506i	−0.106072	−	0.145995i
$139$	1.36816	−	1.88311i	0.116046	−	0.159724i	−0.747043	−	0.664776i	$-0.768527\pi$
$139$	1.36816	−	1.88311i	0.116046	−	0.159724i	0.863089	+	0.505053i	$0.168527\pi$
$140$	−4.26948	−	4.45324i	−0.360837	−	0.376367i
$141$	−16.3406	−	22.4909i	−1.37613	−	1.89408i
$142$	−5.17152	+	15.9163i	−0.433984	+	1.33567i
$143$	1.23825			0.103548
$144$	−5.57823	+	17.1680i	−0.464853	+	1.43067i
$145$	−2.90028	+	2.78060i	−0.240855	+	0.230916i
$146$	−0.306479	+	0.0995812i	−0.0253644	+	0.00824140i
$147$	10.2035	+	31.4032i	0.841573	+	2.59009i
$148$	5.17756	+	3.76172i	0.425593	+	0.309211i
$149$	2.93746			0.240646			0.120323	−	0.992735i	$-0.461607\pi$
$149$	2.93746			0.240646			0.120323	+	0.992735i	$0.461607\pi$
$150$	−16.0549	+	10.6613i	−1.31088	+	0.870492i
$151$	−9.59135			−0.780533			−0.390267	−	0.920702i	$-0.627617\pi$
$151$	−9.59135			−0.780533			−0.390267	+	0.920702i	$0.627617\pi$
$152$	5.81410	−	8.00242i	0.471586	−	0.649082i
$153$	−21.7020	+	25.8420i	−1.75450	+	2.08920i
$154$	3.51924	+	10.8311i	0.283588	+	0.872795i
$155$	−10.9561	+	1.49946i	−0.880013	+	0.120439i
$156$	−1.09967	−	0.357305i	−0.0880441	−	0.0286073i
$157$		−	3.20724i		−	0.255966i	−0.991776	−	0.127983i	$-0.959150\pi$
$157$		−	3.20724i		−	0.255966i	0.991776	−	0.127983i	$-0.0408503\pi$
$158$	6.00689	−	18.4873i	0.477882	−	1.47077i
$159$	−11.7691	−	16.1988i	−0.933352	−	1.28465i
$160$	3.51862	+	7.28084i	0.278171	+	0.575601i
$161$	1.82773	+	1.32792i	0.144045	+	0.104655i
$162$	22.6494	+	31.1743i	1.77951	+	2.44928i
$163$	11.9803	−	8.70417i	0.938367	−	0.681763i	−0.00966027	−	0.999953i	$-0.503075\pi$
$163$	11.9803	−	8.70417i	0.938367	−	0.681763i	0.948027	+	0.318190i	$0.103075\pi$
$164$	0.323182	−	0.444822i	0.0252363	−	0.0347348i
$165$	−17.8229	+	2.43925i	−1.38751	+	0.189896i
$166$	−0.176791	+	0.128446i	−0.0137217	+	0.00996937i
$167$	−3.74774	+	11.5344i	−0.290009	+	0.892556i	0.694843	+	0.719161i	$0.255474\pi$
$167$	−3.74774	+	11.5344i	−0.290009	+	0.892556i	−0.984852	+	0.173395i	$0.944526\pi$
$168$		−	42.3004i		−	3.26355i
$169$	3.93534	−	12.1117i	0.302719	−	0.931672i
$170$	−0.698609	−	10.6029i	−0.0535808	−	0.813203i
$171$	−8.12469	−	25.0052i	−0.621310	−	1.91220i
$172$	2.42668	−	0.788475i	0.185032	−	0.0601207i
$173$	−8.34301	−	6.06155i	−0.634307	−	0.460851i	0.223583	−	0.974685i	$-0.428225\pi$
$173$	−8.34301	−	6.06155i	−0.634307	−	0.460851i	−0.857890	+	0.513834i	$0.828225\pi$
$174$	−6.92591			−0.525052
$175$	12.7613	−	16.0928i	0.964664	−	1.21650i
$176$		−	5.30555i		−	0.399921i
$177$	−6.66698	−	4.84385i	−0.501121	−	0.364086i
$178$	−0.721108	+	0.234302i	−0.0540493	+	0.0175617i
$179$	2.00146	+	6.15985i	0.149596	+	0.460409i	0.997573	−	0.0696234i	$-0.0221797\pi$
$179$	2.00146	+	6.15985i	0.149596	+	0.460409i	−0.847977	+	0.530032i	$0.822180\pi$
$180$	12.0977	+	2.17822i	0.901710	+	0.162355i
$181$	−19.7829	−	6.42786i	−1.47045	−	0.477779i	−0.539208	−	0.842172i	$-0.681276\pi$
$181$	−19.7829	−	6.42786i	−1.47045	−	0.477779i	−0.931245	+	0.364393i	$0.881276\pi$
$182$	−2.43697			−0.180640
$183$	−23.2315	−	7.54837i	−1.71732	−	0.557991i
$184$	−0.995430	−	1.37009i	−0.0733840	−	0.101004i
$185$	−10.0704	+	18.7759i	−0.740394	+	1.38043i
$186$	−15.4213	−	11.2043i	−1.13075	−	0.821536i
$187$	3.71922	−	9.19457i	0.271976	−	0.672374i
$188$	−3.28176	−	4.51696i	−0.239347	−	0.329433i
$189$	−57.6209	−	41.8640i	−4.19131	−	3.04516i
$190$	7.29567	+	3.91303i	0.529283	+	0.283881i
$191$	−11.2666	+	8.18568i	−0.815225	+	0.592295i	−0.915341	−	0.402680i	$-0.868079\pi$
$191$	−11.2666	+	8.18568i	−0.815225	+	0.592295i	0.100116	+	0.994976i	$0.468079\pi$
$192$	−8.86616	+	27.2872i	−0.639860	+	1.96929i
$193$	−8.16670			−0.587852			−0.293926	−	0.955828i	$-0.594962\pi$
$193$	−8.16670			−0.587852			−0.293926	+	0.955828i	$0.594962\pi$
$194$	−2.05712	−	0.668400i	−0.147693	−	0.0479883i
$195$	0.682123	−	3.78847i	0.0488478	−	0.271298i
$196$	2.04922	+	6.30687i	0.146373	+	0.450490i
$197$	−3.65752	−	11.2567i	−0.260587	−	0.802006i	−0.992677	−	0.120798i	$-0.961455\pi$
$197$	−3.65752	−	11.2567i	−0.260587	−	0.802006i	0.732090	−	0.681208i	$-0.238545\pi$
$198$	−18.3579	−	13.3378i	−1.30464	−	0.947873i
$199$		−	7.40608i		−	0.525003i	−0.964932	−	0.262502i	$-0.915452\pi$
$199$		−	7.40608i		−	0.525003i	0.964932	−	0.262502i	$-0.0845475\pi$
$200$	−12.8256	+	8.51690i	−0.906910	+	0.602236i
$201$		−	33.6960i		−	2.37674i
$202$	8.44459	−	11.6230i	0.594159	−	0.817790i
$203$	7.01968	−	2.28083i	0.492685	−	0.160083i
$204$	−5.95611	+	7.09232i	−0.417011	+	0.496562i
$205$	1.61310	+	0.865187i	0.112664	+	0.0604273i
$206$	−0.926933	+	2.85281i	−0.0645825	+	0.198764i
$207$	−4.50145			−0.312873
$208$	1.07974	+	0.350830i	0.0748668	+	0.0243257i
$209$	4.54213	+	6.25170i	0.314186	+	0.432439i
$210$	35.0767	−	4.80062i	2.42052	−	0.331274i
$211$	−7.43911	+	10.2391i	−0.512130	+	0.704886i	−0.984277	−	0.176634i	$-0.943479\pi$
$211$	−7.43911	+	10.2391i	−0.512130	+	0.704886i	0.472147	+	0.881520i	$0.343479\pi$
$212$	−2.36365	−	3.25329i	−0.162336	−	0.223437i
$213$	28.5437	+	39.2870i	1.95578	+	2.69190i
$214$	−1.50679	+	2.07392i	−0.103002	+	0.141771i
$215$	3.69618	+	7.64826i	0.252078	+	0.521607i
$216$	31.3818	+	43.1934i	2.13526	+	2.93894i
$217$	19.3199	+	6.27742i	1.31152	+	0.426139i
$218$	−17.6200			−1.19338
$219$	−0.288956	+	0.889317i	−0.0195259	+	0.0600944i
$220$	−3.57946	+	0.489887i	−0.241327	+	0.0330282i
$221$	1.62527	+	1.36490i	0.109328	+	0.0918130i
$222$	−34.9292	+	11.3492i	−2.34430	+	0.761708i
$223$	2.35819	−	3.24577i	0.157916	−	0.217353i	−0.722726	−	0.691134i	$-0.757111\pi$
$223$	2.35819	−	3.24577i	0.157916	−	0.217353i	0.880642	+	0.473781i	$0.157111\pi$
$224$		−	14.8550i		−	0.992544i
$225$	−1.72349	+	40.8866i	−0.114899	+	2.72577i
$226$			16.2435i			1.08050i
$227$	10.5975	+	7.69953i	0.703381	+	0.511036i	0.881031	−	0.473058i	$-0.156850\pi$
$227$	10.5975	+	7.69953i	0.703381	+	0.511036i	−0.177651	+	0.984094i	$0.556850\pi$
$228$	−2.22982	−	6.86267i	−0.147673	−	0.454492i
$229$	−5.05135	−	15.5464i	−0.333802	−	1.02734i	−0.967309	−	0.253601i	$-0.918385\pi$
$229$	−5.05135	−	15.5464i	−0.333802	−	1.02734i	0.633507	−	0.773737i	$-0.281615\pi$
$230$	1.02315	−	0.980928i	0.0674644	−	0.0646805i
$231$	31.4288	+	10.2118i	2.06786	+	0.671890i
$232$	−5.53284			−0.363249
$233$	3.47735	−	10.7022i	0.227809	−	0.701123i	−0.770186	−	0.637820i	$-0.779837\pi$
$233$	3.47735	−	10.7022i	0.227809	−	0.701123i	0.997994	−	0.0633031i	$-0.0201635\pi$
$234$	3.92831	−	2.85409i	0.256802	−	0.186577i
$235$	13.4174	−	12.8637i	0.875253	−	0.839136i
$236$	−1.33896	−	0.972814i	−0.0871591	−	0.0633248i
$237$	−33.1544	−	45.6331i	−2.15361	−	2.96419i
$238$	−7.31969	+	18.0956i	−0.474465	+	1.17296i
$239$	21.5009	+	15.6213i	1.39077	+	1.01046i	0.995780	+	0.0917737i	$0.0292536\pi$
$239$	21.5009	+	15.6213i	1.39077	+	1.01046i	0.394995	+	0.918683i	$0.370746\pi$
$240$	−16.2325	−	2.92269i	−1.04780	−	0.188659i
$241$	4.51935	+	6.22036i	0.291117	+	0.400688i	0.929377	−	0.369133i	$-0.120345\pi$
$241$	4.51935	+	6.22036i	0.291117	+	0.400688i	−0.638259	+	0.769821i	$0.720345\pi$
$242$	−5.71452	−	1.85676i	−0.367343	−	0.119357i
$243$	59.7964			3.83594
$244$	−4.66569	−	1.51598i	−0.298690	−	0.0970504i
$245$	−19.8776	+	9.60628i	−1.26993	+	0.613723i
$246$	0.975049	+	3.00089i	0.0621668	+	0.191330i
$247$	−1.57265	+	0.510984i	−0.100065	+	0.0325131i
$248$	−12.3195	−	8.95064i	−0.782289	−	0.568366i
$249$			0.634101i			0.0401845i
$250$	−8.51802	−	9.66881i	−0.538727	−	0.611509i
$251$	13.3558			0.843008			0.421504	−	0.906827i	$-0.361502\pi$
$251$	13.3558			0.843008			0.421504	+	0.906827i	$0.361502\pi$
$252$	−18.2685	−	13.2728i	−1.15081	−	0.836109i
$253$	1.25827	−	0.408838i	0.0791070	−	0.0257034i
$254$	7.77300	+	23.9228i	0.487721	+	1.50105i
$255$	−26.0822	−	16.4441i	−1.63333	−	1.02977i
$256$	−4.35661	+	13.4083i	−0.272288	+	0.838017i
$257$			2.87054i			0.179060i	0.995984	+	0.0895298i	$0.0285364\pi$
$257$			2.87054i			0.179060i	−0.995984	+	0.0895298i	$0.971464\pi$
$258$	−4.52484	+	13.9260i	−0.281704	+	0.866996i
$259$	31.6646	−	23.0057i	1.96754	−	1.42950i
$260$	0.136994	−	0.760857i	0.00849601	−	0.0471864i
$261$	−8.64425	+	11.8978i	−0.535066	+	0.736455i
$262$	3.49349	−	2.53817i	0.215829	−	0.156809i
$263$	−8.22765	−	11.3244i	−0.507339	−	0.698292i	0.476129	−	0.879375i	$-0.342040\pi$
$263$	−8.22765	−	11.3244i	−0.507339	−	0.698292i	−0.983468	+	0.181084i	$0.942040\pi$
$264$	−20.0409	−	14.5605i	−1.23343	−	0.896139i
$265$	9.66370	−	9.26493i	0.593636	−	0.569140i
$266$	−8.93923	−	12.3038i	−0.548099	−	0.754394i
$267$	−0.679879	+	2.09245i	−0.0416079	+	0.128056i
$268$		−	6.76735i		−	0.413381i
$269$	18.4265	+	5.98715i	1.12349	+	0.365043i	0.811097	−	0.584912i	$-0.198871\pi$
$269$	18.4265	+	5.98715i	1.12349	+	0.365043i	0.312389	+	0.949954i	$0.398871\pi$
$270$	−32.2557	+	30.9247i	−1.96302	+	1.88202i
$271$	7.84434	+	24.1424i	0.476510	+	1.46655i	0.843911	+	0.536484i	$0.180248\pi$
$271$	7.84434	+	24.1424i	0.476510	+	1.46655i	−0.367401	+	0.930063i	$0.619752\pi$
$272$	5.84819	−	6.96381i	0.354598	−	0.422243i
$273$	−4.15647	+	5.72089i	−0.251561	+	0.346244i
$274$	−14.4492			−0.872911
$275$	−3.23171	−	11.5854i	−0.194879	−	0.698627i
$276$	−1.23542			−0.0743637
$277$	−3.79182	−	2.75492i	−0.227828	−	0.165527i	0.468015	−	0.883720i	$-0.344969\pi$
$277$	−3.79182	−	2.75492i	−0.227828	−	0.165527i	−0.695843	+	0.718193i	$0.744969\pi$
$278$	0.829003	+	2.55141i	0.0497203	+	0.153023i
$279$	−38.4949	+	12.5077i	−2.30463	+	0.748819i
$280$	28.0214	−	3.83503i	1.67460	−	0.229187i
$281$	5.15298	−	15.8592i	0.307401	−	0.946083i	−0.671369	−	0.741123i	$-0.734293\pi$
$281$	5.15298	−	15.8592i	0.307401	−	0.946083i	0.978770	−	0.204960i	$-0.0657065\pi$
$282$	32.0409			1.90801
$283$	3.87610	−	11.9294i	0.230410	−	0.709130i	−0.767287	−	0.641304i	$-0.778394\pi$
$283$	3.87610	−	11.9294i	0.230410	−	0.709130i	0.997697	−	0.0678262i	$-0.0216063\pi$
$284$	5.73256	+	7.89020i	0.340165	+	0.468197i
$285$	21.6294	−	10.4529i	1.28121	−	0.619174i
$286$	−0.838848	+	1.15458i	−0.0496021	+	0.0682715i
$287$	−1.97650	−	2.72042i	−0.116669	−	0.160581i
$288$	17.3976	+	23.9458i	1.02517	+	1.41102i
$289$	15.0166	−	7.96874i	0.883331	−	0.468749i
$290$	−0.627915	−	4.58799i	−0.0368724	−	0.269416i
$291$	−5.07770	+	3.68916i	−0.297660	+	0.216263i
$292$	−0.0580326	+	0.178606i	−0.00339610	+	0.0104521i
$293$			9.68644i			0.565888i	0.959136	+	0.282944i	$0.0913111\pi$
$293$			9.68644i			0.565888i	−0.959136	+	0.282944i	$0.908689\pi$
$294$	−36.1934	−	11.7599i	−2.11084	−	0.685853i
$295$	2.60431	−	4.85562i	0.151629	−	0.282705i
$296$	−27.9036	+	9.06643i	−1.62186	+	0.526975i
$297$	−39.6683	+	12.8890i	−2.30179	+	0.747895i
$298$	−1.98997	+	2.73895i	−0.115276	+	0.158663i
$299$			0.283109i			0.0163726i
$300$	−0.473010	+	11.2213i	−0.0273092	+	0.647863i
$301$		−	15.6047i		−	0.899439i
$302$	6.49760	−	8.94318i	0.373895	−	0.514622i
$303$	−12.8824	−	39.6480i	−0.740076	−	2.27772i
$304$	2.18941	+	6.73832i	0.125571	+	0.386469i
$305$	2.89412	−	16.0738i	0.165717	−	0.920381i
$306$	−9.39373	−	37.7419i	−0.537004	−	2.15756i
$307$		−	7.21570i		−	0.411822i	−0.978571	−	0.205911i	$-0.933984\pi$
$307$		−	7.21570i		−	0.411822i	0.978571	−	0.205911i	$-0.0660157\pi$
$308$	6.31200	+	2.05089i	0.359660	+	0.116861i
$309$	5.11611	+	7.04172i	0.291045	+	0.400589i
$310$	6.02400	−	11.2315i	0.342140	−	0.637905i
$311$	5.52199	−	7.60036i	0.313123	−	0.430977i	−0.623229	−	0.782039i	$-0.714179\pi$
$311$	5.52199	−	7.60036i	0.313123	−	0.430977i	0.936352	+	0.351062i	$0.114179\pi$
$312$	4.28845	−	3.11574i	0.242786	−	0.176394i
$313$	16.8843	−	12.2671i	0.954355	−	0.693379i	0.00252206	−	0.999997i	$-0.499197\pi$
$313$	16.8843	−	12.2671i	0.954355	−	0.693379i	0.951833	+	0.306617i	$0.0991972\pi$
$314$	2.99050	+	2.17273i	0.168764	+	0.122614i
$315$	35.5325	−	66.2488i	2.00203	−	3.73270i
$316$	−6.65856	−	9.16472i	−0.374573	−	0.515556i
$317$	−0.217641	+	0.669830i	−0.0122239	+	0.0376214i	−0.956982	−	0.290146i	$-0.906296\pi$
$317$	−0.217641	+	0.669830i	−0.0122239	+	0.0376214i	0.944759	+	0.327767i	$0.106296\pi$
$318$	23.0770			1.29410
$319$	1.33570	−	4.11085i	0.0747846	−	0.230163i
$320$	−18.8799	−	3.39937i	−1.05542	−	0.190031i
$321$	2.29865	+	7.07452i	0.128298	+	0.394861i
$322$	−2.47637	+	0.804622i	−0.138003	+	0.0448398i
$323$	−0.929329	+	13.2124i	−0.0517092	+	0.735156i
$324$	22.4560			1.24756
$325$	2.57147	+	0.108395i	0.142639	+	0.00601266i
$326$			17.0672i			0.945267i
$327$	−30.0525	+	41.3637i	−1.66191	+	2.28742i
$328$	0.778928	+	2.39729i	0.0430091	+	0.132368i
$329$	−32.4747	+	10.5517i	−1.79039	+	0.581732i
$330$	9.79960	−	18.2709i	0.539450	−	1.00578i
$331$	−2.83203	+	8.71609i	−0.155662	+	0.479080i	−0.998227	−	0.0595151i	$-0.981045\pi$
$331$	−2.83203	+	8.71609i	−0.155662	+	0.479080i	0.842565	+	0.538595i	$0.181045\pi$
$332$			0.127350i			0.00698922i
$333$	−24.0989	+	74.1687i	−1.32061	+	4.06442i
$334$	−8.21601	−	11.3084i	−0.449560	−	0.618766i
$335$	22.3215	−	3.05494i	1.21956	−	0.166909i
$336$	24.5123	+	17.8092i	1.33726	+	0.971573i
$337$	22.6096	−	16.4268i	1.23162	−	0.894825i	0.234611	−	0.972089i	$-0.424618\pi$
$337$	22.6096	−	16.4268i	1.23162	−	0.894825i	0.997011	+	0.0772639i	$0.0246184\pi$
$338$	8.62727	+	11.8744i	0.469262	+	0.645883i
$339$	38.1323	+	27.7047i	2.07106	+	1.50471i
$340$	−5.23822	−	3.30255i	−0.284082	−	0.179106i
$341$	9.62433	−	6.99248i	0.521186	−	0.378664i
$342$	28.8194	+	9.36400i	1.55838	+	0.506347i
$343$	11.8022			0.637262
$344$	−3.61472	+	11.1250i	−0.194893	+	0.599818i
$345$	−0.557699	−	4.07494i	−0.0300255	−	0.219387i
$346$	11.3038	−	3.67284i	0.607698	−	0.197453i
$347$	−7.43501	−	22.8826i	−0.399132	−	1.22840i	−0.925696	−	0.378267i	$-0.876520\pi$
$347$	−7.43501	−	22.8826i	−0.399132	−	1.22840i	0.526564	−	0.850135i	$-0.323480\pi$
$348$	−2.37241	+	3.26534i	−0.127175	+	0.175041i
$349$	−16.4985			−0.883146			−0.441573	−	0.897225i	$-0.645579\pi$
$349$	−16.4985			−0.883146			−0.441573	+	0.897225i	$0.645579\pi$
$350$	6.36023	+	22.8009i	0.339969	+	1.21876i
$351$		−	8.92526i		−	0.476395i
$352$	−7.03794	−	5.11336i	−0.375124	−	0.272543i
$353$	11.8718	−	3.85738i	0.631872	−	0.205308i	0.0244677	−	0.999701i	$-0.492211\pi$
$353$	11.8718	−	3.85738i	0.631872	−	0.205308i	0.607404	+	0.794393i	$0.292211\pi$
$354$	9.03301	−	2.93500i	0.480099	−	0.155994i
$355$	−23.4374	+	22.4702i	−1.24393	+	1.19260i
$356$	−0.136544	+	0.420238i	−0.00723679	+	0.0222726i
$357$	29.9957	+	48.0468i	1.58754	+	2.54291i
$358$	−7.09946	−	2.30675i	−0.375218	−	0.121916i
$359$	−4.41493	+	3.20763i	−0.233011	+	0.169292i	−0.698164	−	0.715938i	$-0.745999\pi$
$359$	−4.41493	+	3.20763i	−0.233011	+	0.169292i	0.465153	+	0.885230i	$0.345999\pi$
$360$	−40.6781	+	38.9995i	−2.14392	+	2.05545i
$361$	7.02273	+	5.10231i	0.369617	+	0.268543i
$362$	19.3953	−	14.0915i	1.01939	−	0.740633i
$363$	−14.1054	+	10.2482i	−0.740342	+	0.537890i
$364$	−0.834764	+	1.14895i	−0.0437535	+	0.0602216i
$365$	−0.615315	−	0.110789i	−0.0322070	−	0.00579895i
$366$	22.7763	−	16.5479i	1.19054	−	0.864975i
$367$	5.90976	−	18.1884i	0.308487	−	0.949425i	−0.669866	−	0.742482i	$-0.733648\pi$
$367$	5.90976	−	18.1884i	0.308487	−	0.949425i	0.978353	−	0.206943i	$-0.0663515\pi$
$368$	1.21304			0.0632339
$369$	6.37209	+	2.07042i	0.331718	+	0.107782i
$370$	−10.6849	−	22.1095i	−0.555481	−	1.14942i
$371$	−23.3895	+	7.59970i	−1.21432	+	0.394557i
$372$	−10.5649	+	3.43274i	−0.547764	+	0.177979i
$373$	−5.14434	+	7.08057i	−0.266364	+	0.366618i	−0.921158	−	0.389189i	$-0.872755\pi$
$373$	−5.14434	+	7.08057i	−0.266364	+	0.366618i	0.654794	+	0.755807i	$0.272755\pi$
$374$	6.05365	+	9.69669i	0.313027	+	0.501404i
$375$	−37.2261	+	3.50539i	−1.92235	+	0.181017i
$376$	25.5962			1.32002
$377$	0.748285	+	0.543661i	0.0385386	+	0.0279999i
$378$	78.0699	−	25.3664i	4.01548	−	1.30471i
$379$	−22.6708	+	7.36618i	−1.16452	+	0.378375i	−0.826595	−	0.562798i	$-0.809725\pi$
$379$	−22.6708	+	7.36618i	−1.16452	+	0.378375i	−0.337925	+	0.941173i	$0.609725\pi$
$380$	4.34394	−	2.09930i	0.222839	−	0.107692i
$381$	69.4173	+	22.5551i	3.55636	+	1.15553i
$382$		−	16.0506i		−	0.821220i
$383$	9.92378	+	3.22443i	0.507081	+	0.164761i	0.551375	−	0.834258i	$-0.314104\pi$
$383$	9.92378	+	3.22443i	0.507081	+	0.164761i	−0.0442931	+	0.999019i	$0.514104\pi$
$384$	−5.21903	−	7.18338i	−0.266333	−	0.366575i
$385$	−3.91532	+	21.7455i	−0.199543	+	1.10825i
$386$	5.53248	−	7.61481i	0.281596	−	0.387584i
$387$	18.2756	+	25.1542i	0.929001	+	1.27866i
$388$	−1.01978	+	0.740913i	−0.0517715	+	0.0376142i
$389$	−21.4199	−	15.5624i	−1.08603	−	0.789047i	−0.107306	−	0.994226i	$-0.534222\pi$
$389$	−21.4199	−	15.5624i	−1.08603	−	0.789047i	−0.978725	+	0.205179i	$0.934222\pi$
$390$	3.07035	+	3.20250i	0.155473	+	0.162165i
$391$	2.10220	+	0.850345i	0.106313	+	0.0430038i
$392$	−28.9135	−	9.39455i	−1.46035	−	0.474497i
$393$		−	12.5302i		−	0.632064i
$394$	12.9737	+	4.21542i	0.653608	+	0.212370i
$395$	27.2233	−	26.0999i	1.36975	−	1.31323i
$396$	−12.5767	+	4.08640i	−0.632001	+	0.205349i
$397$	5.57578	+	17.1605i	0.279840	+	0.861260i	0.987898	+	0.155106i	$0.0495718\pi$
$397$	5.57578	+	17.1605i	0.279840	+	0.861260i	−0.708057	+	0.706155i	$0.750428\pi$
$398$	6.90559	+	5.01721i	0.346146	+	0.251490i
$399$	−44.1303			−2.20928
$400$	0.464439	−	11.0180i	0.0232220	−	0.550899i
$401$		−	16.2482i		−	0.811398i	−0.914007	−	0.405699i	$-0.867028\pi$
$401$		−	16.2482i		−	0.811398i	0.914007	−	0.405699i	$-0.132972\pi$
$402$	31.4189	+	22.8272i	1.56703	+	1.13852i
$403$	0.786646	+	2.42105i	0.0391856	+	0.120601i
$404$	−2.58724	−	7.96271i	−0.128720	−	0.396160i
$405$	10.1372	+	74.0695i	0.503722	+	3.68054i
$406$	−2.62874	+	8.09044i	−0.130462	+	0.401522i
$407$		−	22.9209i		−	1.13614i
$408$	−10.2549	−	41.2020i	−0.507694	−	2.03980i
$409$	14.2801	−	10.3751i	0.706107	−	0.513017i	−0.175809	−	0.984424i	$-0.556254\pi$
$409$	14.2801	−	10.3751i	0.706107	−	0.513017i	0.881915	+	0.471408i	$0.156254\pi$
$410$	−1.89951	+	0.917975i	−0.0938099	+	0.0453356i
$411$	−24.6444	+	33.9202i	−1.21562	+	1.67316i
$412$	1.02749	+	1.41422i	0.0506210	+	0.0696738i
$413$	−8.18876	+	5.94948i	−0.402943	+	0.292755i
$414$	3.04948	−	4.19725i	0.149874	−	0.206284i
$415$	−0.420053	+	0.0574887i	−0.0206196	+	0.00282201i
$416$	1.50602	−	1.09419i	0.0738385	−	0.0536468i
$417$	7.40347	+	2.40553i	0.362550	+	0.117799i
$418$	−8.90626			−0.435619
$419$	22.6906	+	7.37264i	1.10851	+	0.360177i	0.805372	−	0.592770i	$-0.201966\pi$
$419$	22.6906	+	7.37264i	1.10851	+	0.360177i	0.303138	+	0.952947i	$0.401966\pi$
$420$	9.75189	−	18.1820i	0.475843	−	0.887188i
$421$	−7.39289	−	22.7530i	−0.360307	−	1.10891i	−0.952868	−	0.303386i	$-0.901883\pi$
$421$	−7.39289	−	22.7530i	−0.360307	−	1.10891i	0.592560	−	0.805526i	$-0.298117\pi$
$422$	−4.50754	−	13.8728i	−0.219424	−	0.675316i
$423$	39.9903	−	55.0419i	1.94440	−	2.67623i
$424$	18.4353			0.895300
$425$	8.52855	−	18.7687i	0.413695	−	0.910415i
$426$	−55.9687			−2.71169
$427$	−17.6351	+	24.2726i	−0.853423	+	1.17464i
$428$	0.461649	+	1.42081i	0.0223147	+	0.0686775i
$429$	1.27968	+	3.93846i	0.0617836	+	0.190151i
$430$	−9.63536	−	1.73487i	−0.464658	−	0.0836628i
$431$	1.10914	+	0.360381i	0.0534253	+	0.0173589i	0.335608	−	0.942002i	$-0.391058\pi$
$431$	1.10914	+	0.360381i	0.0534253	+	0.0173589i	−0.282182	+	0.959361i	$0.591058\pi$
$432$	−38.2421			−1.83992
$433$	−18.9017	−	6.14155i	−0.908360	−	0.295144i	−0.182677	−	0.983173i	$-0.558476\pi$
$433$	−18.9017	−	6.14155i	−0.908360	−	0.295144i	−0.725683	+	0.688029i	$0.758476\pi$
$434$	−18.9413	+	13.7617i	−0.909214	+	0.660582i
$435$	−11.8414	−	6.35116i	−0.567754	−	0.304515i
$436$	−6.03559	+	8.30728i	−0.289052	+	0.397846i
$437$	−1.42936	+	1.03849i	−0.0683755	+	0.0496777i
$438$	−0.633466	−	0.871891i	−0.0302682	−	0.0416606i
$439$	5.32684	−	7.33177i	0.254236	−	0.349926i	−0.662753	−	0.748838i	$-0.730612\pi$
$439$	5.32684	−	7.33177i	0.254236	−	0.349926i	0.916989	+	0.398912i	$0.130612\pi$
$440$	7.82852	−	14.5959i	0.373210	−	0.695833i
$441$	−65.3751	+	47.4978i	−3.11310	+	2.26180i
$442$	−2.37369	+	0.590797i	−0.112905	+	0.0281013i
$443$		−	19.9378i		−	0.947272i	−0.880721	−	0.473636i	$-0.842941\pi$
$443$		−	19.9378i		−	0.947272i	0.880721	−	0.473636i	$-0.157059\pi$
$444$	−6.61393	+	20.3556i	−0.313883	+	0.966033i
$445$	−1.44776	−	0.260672i	−0.0686304	−	0.0123571i
$446$	1.42888	+	4.39765i	0.0676596	+	0.208235i
$447$	3.03574	+	9.34304i	0.143586	+	0.441911i
$448$	28.5102	+	20.7138i	1.34698	+	0.978637i
$449$			33.1584i			1.56484i	0.622749	+	0.782422i	$0.286016\pi$
$449$			33.1584i			1.56484i	−0.622749	+	0.782422i	$0.713984\pi$
$450$	−36.9560	−	29.3054i	−1.74212	−	1.38147i
$451$	−1.96921			−0.0927265
$452$	7.65829	+	5.56407i	0.360216	+	0.261712i
$453$	−9.91225	−	30.5068i	−0.465718	−	1.43333i
$454$	−14.3584	+	4.66533i	−0.673874	+	0.218955i
$455$	−4.16657	−	2.23474i	−0.195332	−	0.104766i
$456$	31.4615	+	10.2225i	1.47332	+	0.478711i
$457$		−	11.9759i		−	0.560210i	−0.959969	−	0.280105i	$-0.909631\pi$
$457$		−	11.9759i		−	0.560210i	0.959969	−	0.280105i	$-0.0903693\pi$
$458$	17.9178	+	5.82186i	0.837246	+	0.272038i
$459$	−66.2739	−	26.8079i	−3.09340	−	1.25129i
$460$	−0.112006	−	0.818391i	−0.00522228	−	0.0381577i
$461$	18.6210	+	13.5290i	0.867269	+	0.630107i	0.929853	−	0.367932i	$-0.119934\pi$
$461$	18.6210	+	13.5290i	0.867269	+	0.630107i	−0.0625841	+	0.998040i	$0.519934\pi$
$462$	−30.8130	+	22.3870i	−1.43355	+	1.04154i
$463$	−3.01029	−	4.14331i	−0.139900	−	0.192556i	0.733318	−	0.679886i	$-0.237971\pi$
$463$	−3.01029	−	4.14331i	−0.139900	−	0.192556i	−0.873218	+	0.487330i	$0.837971\pi$
$464$	2.32942	−	3.20618i	0.108141	−	0.148843i
$465$	−16.0919	−	33.2978i	−0.746243	−	1.54415i
$466$	7.62323	+	10.4925i	0.353139	+	0.486055i
$467$	24.1215	+	7.83755i	1.11621	+	0.362679i	0.808320	−	0.588743i	$-0.200377\pi$
$467$	24.1215	+	7.83755i	1.11621	+	0.362679i	0.307890	+	0.951422i	$0.400377\pi$
$468$		−	2.82972i		−	0.130804i
$469$	−39.3617	−	12.7894i	−1.81756	−	0.590560i
$470$	2.90488	+	21.2251i	0.133992	+	0.979040i
$471$	10.2011	−	3.31455i	0.470043	−	0.152726i
$472$	7.21612	−	2.34466i	0.332149	−	0.107922i
$473$	−7.39310	−	5.37140i	−0.339935	−	0.246977i
$474$	65.0095			2.98599
$475$	8.88533	+	13.3805i	0.407687	+	0.613937i
$476$	6.02418	+	9.64948i	0.276118	+	0.442283i
$477$	28.8025	−	39.6433i	1.31878	−	1.81514i
$478$	−29.1312	+	9.46532i	−1.33243	+	0.432934i
$479$	−15.0439	+	4.88806i	−0.687374	+	0.223341i	−0.631821	−	0.775114i	$-0.717692\pi$
$479$	−15.0439	+	4.88806i	−0.687374	+	0.223341i	−0.0555529	+	0.998456i	$0.517692\pi$
$480$	−19.5215	+	18.7159i	−0.891030	+	0.854262i
$481$	4.66467	+	1.51564i	0.212691	+	0.0691074i
$482$	−8.86161			−0.403635
$483$	−2.33479	+	7.18573i	−0.106236	+	0.326962i
$484$	−2.83286	+	2.05819i	−0.128766	+	0.0935543i
$485$	−2.90420	−	3.02920i	−0.131873	−	0.137549i
$486$	−40.5087	+	55.7555i	−1.83751	+	2.52912i
$487$	−17.5598	+	12.7580i	−0.795712	+	0.578119i	−0.909653	−	0.415369i	$-0.863653\pi$
$487$	−17.5598	+	12.7580i	−0.795712	+	0.578119i	0.113941	+	0.993488i	$0.463653\pi$
$488$	18.1951	−	13.2195i	0.823653	−	0.598419i
$489$	40.0660	+	29.1097i	1.81185	+	1.31638i
$490$	4.50888	−	25.0420i	0.203690	−	1.13128i
$491$	−11.0279	+	8.01221i	−0.497680	+	0.361586i	−0.808130	−	0.589004i	$-0.799520\pi$
$491$	−11.0279	+	8.01221i	−0.497680	+	0.361586i	0.310450	+	0.950590i	$0.399520\pi$
$492$	1.74882	+	0.568226i	0.0788428	+	0.0256176i
$493$	6.28446	−	3.92339i	0.283038	−	0.176701i
$494$	0.588927	−	1.81253i	0.0264971	−	0.0815497i
$495$	−19.1561	−	39.6384i	−0.861002	−	1.78161i
$496$	10.3735	−	3.37054i	0.465782	−	0.151342i
$497$	56.7265	−	18.4316i	2.54453	−	0.826768i
$498$	−0.591249	−	0.429568i	−0.0264945	−	0.0192494i
$499$		−	20.1815i		−	0.903447i	−0.892158	−	0.451724i	$-0.850809\pi$
$499$		−	20.1815i		−	0.903447i	0.892158	−	0.451724i	$-0.149191\pi$
$500$	−7.47631	+	0.704004i	−0.334351	+	0.0314840i
$501$	−40.5600			−1.81208
$502$	−9.04778	+	12.4532i	−0.403822	+	0.555813i
$503$	−3.87831	−	11.9362i	−0.172925	−	0.532210i	0.826607	−	0.562779i	$-0.190268\pi$
$503$	−3.87831	−	11.9362i	−0.172925	−	0.532210i	−0.999533	+	0.0305696i	$0.990268\pi$
$504$	98.4549	−	31.9899i	4.38553	−	1.42495i
$505$	25.0964	−	12.1284i	1.11678	−	0.539705i
$506$	−0.471201	+	1.45021i	−0.0209474	+	0.0644696i
$507$	42.5902			1.89150
$508$	13.9414	+	4.52984i	0.618551	+	0.200979i
$509$	−19.4688	+	14.1449i	−0.862941	+	0.626963i	−0.928683	−	0.370874i	$-0.879058\pi$
$509$	−19.4688	+	14.1449i	−0.862941	+	0.626963i	0.0657427	+	0.997837i	$0.479058\pi$
$510$	33.0021	−	13.1796i	1.46136	−	0.583604i
$511$	0.929173	+	0.675084i	0.0411042	+	0.0298639i
$512$	−12.6719	−	17.4414i	−0.560025	−	0.770808i
$513$	45.0619	−	32.7394i	1.98953	−	1.44548i
$514$	−2.67656	−	1.94463i	−0.118058	−	0.0857741i
$515$	−4.20087	+	4.02752i	−0.185112	+	0.177474i
$516$	5.01573	+	6.90356i	0.220805	+	0.303912i
$517$	−6.17924	+	19.0177i	−0.271762	+	0.836399i
$518$			45.1099i			1.98201i
$519$	10.6575	−	32.8005i	0.467814	−	1.43978i
$520$	2.45278	+	2.55835i	0.107562	+	0.112191i
$521$	−18.4736	+	6.00245i	−0.809345	+	0.262972i	−0.684320	−	0.729181i	$-0.739901\pi$
$521$	−18.4736	+	6.00245i	−0.809345	+	0.262972i	−0.125025	+	0.992154i	$0.539901\pi$
$522$	−5.23776	−	16.1202i	−0.229251	−	0.705561i
$523$	−20.6224	+	28.3843i	−0.901756	+	1.24116i	0.0681488	+	0.997675i	$0.478291\pi$
$523$	−20.6224	+	28.3843i	−0.901756	+	1.24116i	−0.969905	+	0.243485i	$0.921709\pi$
$524$		−	2.51650i		−	0.109934i
$525$	64.3739	+	23.9580i	2.80951	+	1.04561i
$526$	16.1329			0.703427
$527$	20.3401	+	1.43068i	0.886028	+	0.0623212i
$528$	16.8751	−	5.48306i	0.734395	−	0.238619i
$529$	−7.01392	−	21.5866i	−0.304953	−	0.938548i
$530$	2.09221	+	15.2871i	0.0908796	+	0.664030i
$531$	6.23219	−	19.1807i	0.270454	−	0.832372i
$532$	−8.86290			−0.384255
$533$	0.130214	−	0.400758i	0.00564021	−	0.0173588i
$534$	−1.49047	−	2.05145i	−0.0644989	−	0.0887751i
$535$	−4.47803	+	2.16410i	−0.193602	+	0.0935623i
$536$	25.0994	+	18.2357i	1.08413	+	0.787664i
$537$	−17.5239	+	12.7319i	−0.756214	+	0.549421i
$538$	−18.0655	+	13.1253i	−0.778859	+	0.565874i
$539$	13.9601	−	19.2145i	0.601306	−	0.827626i
$540$	3.53108	+	25.8005i	0.151953	+	1.11028i
$541$	0.435796	+	0.599822i	0.0187363	+	0.0257884i	0.818282	−	0.574816i	$-0.194927\pi$
$541$	0.435796	+	0.599822i	0.0187363	+	0.0257884i	−0.799546	+	0.600605i	$0.794927\pi$
$542$	−27.8250	−	9.04089i	−1.19519	−	0.388339i
$543$		−	69.5655i		−	2.98534i
$544$	−3.60132	−	14.4693i	−0.154405	−	0.620367i
$545$	−30.1255	−	16.1578i	−1.29043	−	0.692124i
$546$	−2.51850	−	7.75116i	−0.107782	−	0.331719i
$547$	8.20646	+	25.2569i	0.350883	+	1.07991i	0.958358	+	0.285568i	$0.0921824\pi$
$547$	8.20646	+	25.2569i	0.350883	+	1.07991i	−0.607475	+	0.794339i	$0.707818\pi$
$548$	−4.94947	+	6.81236i	−0.211431	+	0.291009i
$549$		−	59.7802i		−	2.55136i
$550$	12.9918	+	4.83515i	0.553972	+	0.206172i
$551$			5.77218i			0.245903i
$552$	3.32905	−	4.58205i	0.141694	−	0.195025i
$553$	−65.8897	+	21.4089i	−2.80191	+	0.910397i
$554$	5.13749	−	1.66927i	0.218271	−	0.0709206i
$555$	−70.1270	−	12.6265i	−2.97672	−	0.535966i
$556$	1.48688	+	0.483115i	0.0630576	+	0.0204887i
$557$			37.5658i			1.59171i	0.605486	+	0.795856i	$0.292979\pi$
$557$			37.5658i			1.59171i	−0.605486	+	0.795856i	$0.707021\pi$
$558$	14.4156	−	44.3667i	0.610262	−	1.87819i
$559$	1.58202	−	1.14940i	0.0669121	−	0.0486145i
$560$	−9.57518	+	17.8525i	−0.404625	+	0.754406i
$561$	33.0884	+	2.32736i	1.39699	+	0.0982614i
$562$	11.2966	+	15.5485i	0.476520	+	0.655874i
$563$	14.5537	+	20.0314i	0.613365	+	0.844225i	0.996849	−	0.0793229i	$-0.0252758\pi$
$563$	14.5537	+	20.0314i	0.613365	+	0.844225i	−0.383484	+	0.923548i	$0.625276\pi$
$564$	10.9753	−	15.1062i	0.462145	−	0.636087i
$565$	−14.8955	+	27.7720i	−0.626659	+	1.16838i
$566$	8.49741	+	11.6957i	0.357173	+	0.491606i
$567$	42.4390	−	130.614i	1.78227	−	5.48526i
$568$	−44.7112			−1.87604
$569$	−4.38764	+	13.5038i	−0.183939	+	0.566107i	−0.999928	−	0.0119602i	$-0.996193\pi$
$569$	−4.38764	+	13.5038i	−0.183939	+	0.566107i	0.815989	+	0.578067i	$0.196193\pi$
$570$	−4.90623	+	27.2489i	−0.205499	+	1.14133i
$571$	2.45756	−	0.798509i	0.102846	−	0.0334166i	−0.257142	−	0.966374i	$-0.582781\pi$
$571$	2.45756	−	0.798509i	0.102846	−	0.0334166i	0.359988	+	0.932957i	$0.382781\pi$
$572$	0.257005	+	0.790980i	0.0107459	+	0.0330725i
$573$	−37.6794	−	27.3757i	−1.57408	−	1.14364i
$574$	3.87554			0.161762
$575$	2.64883	−	0.738883i	0.110464	−	0.0308135i
$576$	−70.2166			−2.92569
$577$	−11.0906	+	15.2649i	−0.461708	+	0.635487i	−0.974862	−	0.222810i	$-0.928477\pi$
$577$	−11.0906	+	15.2649i	−0.461708	+	0.635487i	0.513154	+	0.858297i	$0.328477\pi$
$578$	−2.74270	+	19.4002i	−0.114081	+	0.806942i
$579$	−8.43993	−	25.9754i	−0.350752	−	1.07950i
$580$	−2.37818	−	1.27553i	−0.0987484	−	0.0529637i
$581$	0.740719	+	0.240674i	0.0307302	+	0.00998485i
$582$		−	7.23376i		−	0.299849i
$583$	−4.45052	+	13.6973i	−0.184322	+	0.567284i
$584$	−0.506051	−	0.696520i	−0.0209406	−	0.0288222i
$585$	9.33359	−	1.27740i	0.385897	−	0.0528141i
$586$	−9.03185	−	6.56202i	−0.373102	−	0.271075i
$587$	20.5147	+	28.2361i	0.846734	+	1.16543i	0.984573	+	0.174975i	$0.0559844\pi$
$587$	20.5147	+	28.2361i	0.846734	+	1.16543i	−0.137839	+	0.990455i	$0.544016\pi$
$588$	−17.9422	+	13.0357i	−0.739922	+	0.537585i
$589$	−9.33784	+	12.8524i	−0.384759	+	0.529575i
$590$	2.76321	+	5.71772i	0.113759	+	0.235395i
$591$	32.0237	−	23.2666i	1.31728	−	0.957060i
$592$	6.49409	−	19.9867i	0.266905	−	0.821450i
$593$		−	22.9598i		−	0.942847i	−0.881907	−	0.471423i	$-0.843740\pi$
$593$		−	22.9598i		−	0.942847i	0.881907	−	0.471423i	$-0.156260\pi$
$594$	14.8550	−	45.7191i	0.609510	−	1.87588i
$595$	−29.1086	+	24.2263i	−1.19334	+	0.993181i
$596$	0.609683	+	1.87641i	0.0249736	+	0.0768608i
$597$	23.5562	−	7.65386i	0.964090	−	0.313252i
$598$	−0.263977	−	0.191790i	−0.0107948	−	0.00784288i
$599$	−13.5057			−0.551827			−0.275913	−	0.961182i	$-0.588980\pi$
$599$	−13.5057			−0.551827			−0.275913	+	0.961182i	$0.588980\pi$
$600$	−40.3440	−	31.9921i	−1.64704	−	1.30607i
$601$		−	5.23284i		−	0.213452i	−0.994288	−	0.106726i	$-0.965963\pi$
$601$		−	5.23284i		−	0.213452i	0.994288	−	0.106726i	$-0.0340367\pi$
$602$	14.5501	+	10.5713i	0.593020	+	0.430854i
$603$	78.4282	−	25.4829i	3.19384	−	1.03774i
$604$	−1.99073	−	6.12682i	−0.0810015	−	0.249297i
$605$	−8.06761	−	8.41485i	−0.327995	−	0.342112i
$606$	45.6958	+	14.8475i	1.85626	+	0.603137i
$607$	−36.2870			−1.47284			−0.736422	−	0.676522i	$-0.763486\pi$
$607$	−36.2870			−1.47284			−0.736422	+	0.676522i	$0.763486\pi$
$608$	11.0487	+	3.58992i	0.448082	+	0.145591i
$609$	14.5091	+	19.9700i	0.587937	+	0.809226i
$610$	13.0269	+	13.5876i	0.527445	+	0.550146i
$611$	−3.46174	−	2.51510i	−0.140047	−	0.101750i
$612$	−21.0119	−	8.49934i	−0.849354	−	0.343565i
$613$	−10.1996	−	14.0385i	−0.411958	−	0.567011i	0.551737	−	0.834018i	$-0.313965\pi$
$613$	−10.1996	−	14.0385i	−0.411958	−	0.567011i	−0.963695	+	0.267007i	$0.913965\pi$
$614$	6.72807	+	4.88823i	0.271523	+	0.197273i
$615$	−1.08479	+	6.02485i	−0.0437429	+	0.242945i
$616$	−24.6153	+	17.8841i	−0.991779	+	0.720569i
$617$	1.60766	−	4.94785i	0.0647218	−	0.199193i	−0.913466	−	0.406914i	$-0.866605\pi$
$617$	1.60766	−	4.94785i	0.0647218	−	0.199193i	0.978188	+	0.207721i	$0.0666047\pi$
$618$	−10.0317			−0.403535
$619$	−11.1823	−	3.63336i	−0.449456	−	0.146037i	0.0755384	−	0.997143i	$-0.475932\pi$
$619$	−11.1823	−	3.63336i	−0.449456	−	0.146037i	−0.524994	+	0.851106i	$0.675932\pi$
$620$	−3.23181	−	6.68737i	−0.129793	−	0.268571i
$621$	−2.94688	−	9.06956i	−0.118254	−	0.363949i
$622$	3.34591	+	10.2976i	0.134159	+	0.412898i
$623$	2.18623	+	1.58839i	0.0875895	+	0.0636375i
$624$			3.79686i			0.151996i
$625$	−5.69709	−	24.3422i	−0.227884	−	0.973688i
$626$			24.0535i			0.961373i
$627$	−15.1904	+	20.9078i	−0.606646	+	0.834977i
$628$	2.04874	−	0.665677i	0.0817537	−	0.0265634i
$629$	25.2651	−	30.0848i	1.00739	−	1.19956i
$630$	37.7005	+	78.0111i	1.50202	+	3.10804i
$631$	5.53461	−	17.0338i	0.220329	−	0.678104i	−0.778403	−	0.627765i	$-0.783970\pi$
$631$	5.53461	−	17.0338i	0.220329	−	0.678104i	0.998732	−	0.0503391i	$-0.0160302\pi$
$632$	51.9336			2.06581
$633$	−40.2549	−	13.0796i	−1.59999	−	0.519868i
$634$	−0.477124	−	0.656705i	−0.0189490	−	0.0260811i
$635$	−8.64783	+	48.0296i	−0.343179	+	1.90599i
$636$	7.90485	−	10.8801i	0.313448	−	0.431424i
$637$	2.98726	+	4.11162i	0.118360	+	0.162908i
$638$	2.92818	+	4.03030i	0.115928	+	0.159561i
$639$	−69.8548	+	96.1469i	−2.76341	+	3.80351i
$640$	4.28538	−	4.10854i	0.169394	−	0.162404i
$641$	−25.7214	−	35.4024i	−1.01593	−	1.39831i	−0.915017	−	0.403416i	$-0.867823\pi$
$641$	−25.7214	−	35.4024i	−1.01593	−	1.39831i	−0.100916	−	0.994895i	$-0.532177\pi$
$642$	−8.15364	−	2.64928i	−0.321798	−	0.104559i
$643$	−6.09314			−0.240290			−0.120145	−	0.992756i	$-0.538336\pi$
$643$	−6.09314			−0.240290			−0.120145	+	0.992756i	$0.538336\pi$
$644$	−0.468907	+	1.44315i	−0.0184775	+	0.0568679i
$645$	−20.5066	+	19.6604i	−0.807447	+	0.774128i
$646$	−11.6899	−	9.81716i	−0.459934	−	0.386251i
$647$	17.2186	−	5.59466i	0.676933	−	0.219949i	0.0496807	−	0.998765i	$-0.484180\pi$
$647$	17.2186	−	5.59466i	0.676933	−	0.219949i	0.627252	+	0.778816i	$0.284180\pi$
$648$	−60.5116	+	83.2870i	−2.37712	+	3.27182i
$649$			5.92754i			0.232676i
$650$	−1.84310	+	2.32426i	−0.0722922	+	0.0911651i
$651$			67.9373i			2.66267i
$652$	8.04666	+	5.84624i	0.315132	+	0.228956i
$653$	10.7561	+	33.1038i	0.420918	+	1.29545i	0.906850	+	0.421454i	$0.138480\pi$
$653$	10.7561	+	33.1038i	0.420918	+	1.29545i	−0.485932	+	0.873997i	$0.661520\pi$
$654$	−18.2095	−	56.0432i	−0.712049	−	2.19146i
$655$	8.30048	−	1.13601i	0.324326	−	0.0443875i
$656$	−1.71713	−	0.557930i	−0.0670427	−	0.0217835i
$657$	−2.28843			−0.0892800
$658$	12.1612	−	37.4282i	0.474092	−	1.45910i
$659$	−22.4626	+	16.3200i	−0.875019	+	0.635738i	−0.931929	−	0.362641i	$-0.881875\pi$
$659$	−22.4626	+	16.3200i	−0.875019	+	0.635738i	0.0569101	+	0.998379i	$0.481875\pi$
$660$	−5.25738	−	10.8787i	−0.204643	−	0.423454i
$661$	−21.9719	−	15.9635i	−0.854606	−	0.620908i	0.0718061	−	0.997419i	$-0.477124\pi$
$661$	−21.9719	−	15.9635i	−0.854606	−	0.620908i	−0.926412	+	0.376511i	$0.877124\pi$
$662$	−6.20853	−	8.54531i	−0.241301	−	0.332123i
$663$	−2.66162	+	6.57999i	−0.103369	+	0.255546i
$664$	−0.472326	−	0.343165i	−0.0183298	−	0.0133174i
$665$	−4.00093	−	29.2336i	−0.155149	−	1.13363i
$666$	−52.8309	−	72.7155i	−2.04716	−	2.81767i
$667$	0.939885	+	0.305387i	0.0363925	+	0.0118246i
$668$	−8.14586			−0.315173
$669$	12.7607	+	4.14622i	0.493359	+	0.160302i
$670$	−12.2731	+	22.8826i	−0.474151	+	0.884034i
$671$	5.42945	+	16.7101i	0.209602	+	0.645087i
$672$	47.2487	−	15.3520i	1.82266	−	0.592218i
$673$	13.7682	+	10.0032i	0.530724	+	0.385593i	0.820628	−	0.571462i	$-0.193624\pi$
$673$	13.7682	+	10.0032i	0.530724	+	0.385593i	−0.289905	+	0.957056i	$0.593624\pi$
$674$			32.2099i			1.24068i
$675$	−83.5069	+	23.2940i	−3.21418	+	0.896585i
$676$	8.55361			0.328985
$677$	−17.5216	−	12.7302i	−0.673408	−	0.489260i	0.197756	−	0.980251i	$-0.436635\pi$
$677$	−17.5216	−	12.7302i	−0.673408	−	0.489260i	−0.871164	+	0.490992i	$0.836635\pi$
$678$	−51.6649	+	16.7870i	−1.98418	+	0.644699i
$679$	2.38221	+	7.33170i	0.0914209	+	0.281365i
$680$	26.3641	−	10.5287i	1.01102	−	0.403757i
$681$	−13.5375	+	41.6641i	−0.518757	+	1.59657i
$682$			13.7109i			0.525019i
$683$	6.00726	−	18.4884i	0.229861	−	0.707441i	−0.767900	−	0.640569i	$-0.778698\pi$
$683$	6.00726	−	18.4884i	0.229861	−	0.707441i	0.997762	−	0.0668711i	$-0.0213016\pi$
$684$	14.2867	−	10.3799i	0.546265	−	0.396885i
$685$	−24.7043	−	13.2502i	−0.943904	−	0.506262i
$686$	−7.99536	+	11.0047i	−0.305264	+	0.420160i
$687$	44.2275	−	32.1332i	1.68738	−	1.22596i
$688$	−4.92485	−	6.77847i	−0.187758	−	0.258427i
$689$	−2.49327	−	1.81147i	−0.0949862	−	0.0690115i
$690$	4.17737	+	2.24053i	0.159030	+	0.0852956i
$691$	22.6170	+	31.1296i	0.860391	+	1.18423i	0.981476	+	0.191585i	$0.0613628\pi$
$691$	22.6170	+	31.1296i	0.860391	+	1.18423i	−0.121085	+	0.992642i	$0.538637\pi$
$692$	2.14041	−	6.58750i	0.0813661	−	0.250419i
$693$			80.8739i			3.07214i
$694$	26.3730	+	8.56912i	1.00111	+	0.325279i
$695$	−0.922305	+	5.12243i	−0.0349850	+	0.194305i
$696$	−5.71795	−	17.5980i	−0.216738	−	0.667052i
$697$	−2.58469	−	2.17062i	−0.0979021	−	0.0822179i
$698$	11.1768	−	15.3836i	0.423049	−	0.582277i
$699$	37.6336			1.42343
$700$	12.9285	+	4.81161i	0.488653	+	0.181862i
$701$	−13.4964			−0.509752			−0.254876	−	0.966974i	$-0.582035\pi$
$701$	−13.4964			−0.509752			−0.254876	+	0.966974i	$0.582035\pi$
$702$	8.32210	+	6.04636i	0.314098	+	0.228205i
$703$	9.45863	+	29.1107i	0.356739	+	1.09793i
$704$	19.6274	−	6.37732i	0.739735	−	0.240354i
$705$	54.7813	+	29.3819i	2.06318	+	1.10659i
$706$	−4.44577	+	13.6827i	−0.167319	+	0.514954i
$707$	−51.2040			−1.92573
$708$	1.71042	−	5.26414i	0.0642816	−	0.197838i
$709$	−12.6457	−	17.4053i	−0.474920	−	0.653671i	0.502599	−	0.864520i	$-0.332377\pi$
$709$	−12.6457	−	17.4053i	−0.474920	−	0.653671i	−0.977519	+	0.210848i	$0.932377\pi$
$710$	−5.07423	−	37.0758i	−0.190432	−	1.39143i
$711$	81.1386	−	111.678i	3.04294	−	4.18824i
$712$	−1.19068	−	1.63883i	−0.0446225	−	0.0614176i
$713$	1.59873	+	2.20046i	0.0598728	+	0.0824079i
$714$	−65.1203	−	4.58042i	−2.43706	−	0.171418i
$715$	−2.49297	+	1.20478i	−0.0932317	+	0.0450561i
$716$	−3.51942	+	2.55701i	−0.131527	+	0.0955599i
$717$	−27.4657	+	84.5307i	−1.02572	+	3.15686i
$718$		−	6.28957i		−	0.234725i
$719$	42.5986	+	13.8411i	1.58866	+	0.516187i	0.964269	−	0.264924i	$-0.0853470\pi$
$719$	42.5986	+	13.8411i	1.58866	+	0.516187i	0.624392	+	0.781112i	$0.285347\pi$
$720$	−5.47329	−	39.9917i	−0.203977	−	1.49040i
$721$	10.1675	−	3.30364i	0.378659	−	0.123034i
$722$	−9.51501	+	3.09162i	−0.354112	+	0.115058i
$723$	−15.1142	+	20.8030i	−0.562105	+	0.773671i
$724$		−	13.9712i		−	0.519235i
$725$	3.13368	−	8.42003i	0.116382	−	0.312712i
$726$		−	20.0948i		−	0.745787i
$727$	−8.78504	+	12.0916i	−0.325819	+	0.448451i	−0.940233	−	0.340533i	$-0.889393\pi$
$727$	−8.78504	+	12.0916i	−0.325819	+	0.448451i	0.614414	+	0.788984i	$0.289393\pi$
$728$	−2.01193	−	6.19210i	−0.0745673	−	0.229494i
$729$	30.8023	+	94.7997i	1.14083	+	3.51110i
$730$	0.520143	−	0.498679i	0.0192514	−	0.0184570i
$731$	−3.78306	−	15.1995i	−0.139921	−	0.562174i
$732$		−	16.4066i		−	0.606407i
$733$	−46.8287	−	15.2156i	−1.72966	−	0.562000i	−0.736257	−	0.676701i	$-0.763409\pi$
$733$	−46.8287	−	15.2156i	−1.72966	−	0.562000i	−0.993400	+	0.114702i	$0.963409\pi$
$734$	12.9557	+	17.8320i	0.478204	+	0.658191i
$735$	−51.0969	−	53.2961i	−1.88474	−	1.96586i
$736$	1.16910	−	1.60912i	0.0430934	−	0.0593130i
$737$	−19.6083	+	14.2463i	−0.722280	+	0.524767i
$738$	−6.24724	+	4.53889i	−0.229964	+	0.167079i
$739$	27.6823	+	20.1124i	1.01831	+	0.739846i	0.965936	−	0.258781i	$-0.0833209\pi$
$739$	27.6823	+	20.1124i	1.01831	+	0.739846i	0.0523750	+	0.998627i	$0.483321\pi$
$740$	−14.0839	−	2.53585i	−0.517736	−	0.0932196i
$741$	−3.25052	−	4.47396i	−0.119411	−	0.164355i
$742$	8.75894	−	26.9572i	0.321551	−	0.989631i
$743$	21.6907			0.795755			0.397878	−	0.917438i	$-0.369747\pi$
$743$	21.6907			0.795755			0.397878	+	0.917438i	$0.369747\pi$
$744$	15.7372	−	48.4342i	0.576954	−	1.77568i
$745$	−5.91396	+	2.85805i	−0.216671	+	0.104711i
$746$	−3.11708	−	9.59338i	−0.114124	−	0.351239i
$747$	−1.47588	+	0.479543i	−0.0539997	+	0.0175456i
$748$	6.64531	+	0.467416i	0.242976	+	0.0170904i
$749$	9.13649			0.333840
$750$	21.9501	−	37.0852i	0.801505	−	1.35416i
$751$		−	9.63105i		−	0.351442i	−0.984440	−	0.175721i	$-0.943774\pi$
$751$		−	9.63105i		−	0.351442i	0.984440	−	0.175721i	$-0.0562257\pi$
$752$	−10.7765	+	14.8325i	−0.392977	+	0.540886i
$753$	13.8026	+	42.4800i	0.502995	+	1.54806i
$754$	−1.01384	+	0.329417i	−0.0369219	+	0.0119967i
$755$	19.3102	−	9.33205i	0.702769	−	0.339628i
$756$	14.7827	−	45.4965i	0.537642	−	1.65469i
$757$		−	26.2140i		−	0.952765i	−0.879238	−	0.476382i	$-0.841948\pi$
$757$		−	26.2140i		−	0.952765i	0.879238	−	0.476382i	$-0.158052\pi$
$758$	8.48979	−	26.1289i	0.308363	−	0.949044i
$759$	2.60074	+	3.57962i	0.0944010	+	0.129932i
$760$	−3.91940	+	21.7681i	−0.142171	+	0.789612i
$761$	−41.1541	−	29.9002i	−1.49184	−	1.08388i	−0.973495	−	0.228707i	$-0.926550\pi$
$761$	−41.1541	−	29.9002i	−1.49184	−	1.08388i	−0.518340	−	0.855175i	$-0.673450\pi$
$762$	−68.0572	+	49.4464i	−2.46545	+	1.79125i
$763$	36.9121	+	50.8052i	1.33631	+	1.83927i
$764$	−7.56734	−	5.49799i	−0.273777	−	0.198910i
$765$	18.5491	−	73.1427i	0.670645	−	2.64448i
$766$	−9.72933	+	7.06877i	−0.351535	+	0.255405i
$767$	−1.20633	−	0.391959i	−0.0435579	−	0.0141528i
$768$	−47.1494			−1.70136
$769$	−8.63906	+	26.5883i	−0.311532	+	0.958798i	0.665626	+	0.746285i	$0.268165\pi$
$769$	−8.63906	+	26.5883i	−0.311532	+	0.958798i	−0.977158	+	0.212513i	$0.931835\pi$
$770$	−17.6235	−	18.3821i	−0.635108	−	0.662444i
$771$	−9.13020	+	2.96658i	−0.328816	+	0.106839i

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+(-0.677444 + 0.932422i) q^{2} +(1.03346 + 3.18065i) q^{3} +(0.207554 + 0.638786i) q^{4} +(-2.01329 + 0.972965i) q^{5} +(-3.66582 - 1.19110i) q^{6} +4.10770 q^{7} +(-2.92848 - 0.951521i) q^{8} +(-6.62147 + 4.81078i) q^{9} +(0.456678 - 2.53636i) q^{10} +(1.41394 - 1.94612i) q^{11} +(-1.81726 + 1.32032i) q^{12} +(0.302563 + 0.416442i) q^{13} +(-2.78274 + 3.83011i) q^{14} +(-5.17531 - 5.39806i) q^{15} +(1.78433 - 1.29639i) q^{16} +(4.00104 - 0.995833i) q^{17} -9.43303i q^{18} +(-0.992682 + 3.05516i) q^{19} +(-1.03938 - 1.08412i) q^{20} +(4.24513 + 13.0652i) q^{21} +(0.856742 + 2.63678i) q^{22} +(0.444953 + 0.323277i) q^{23} -10.2978i q^{24} +(3.10668 - 3.91772i) q^{25} -0.593269 q^{26} +(-14.0275 - 10.1916i) q^{27} +(0.852571 + 2.62394i) q^{28} +(1.70891 - 0.555258i) q^{29} +(8.53925 - 1.16869i) q^{30} +(4.70334 + 1.52821i) q^{31} -3.61639i q^{32} +(7.65119 + 2.48602i) q^{33} +(-1.78194 + 4.40528i) q^{34} +(-8.26999 + 3.99665i) q^{35} +(-4.44737 - 3.23121i) q^{36} +(7.70860 - 5.60063i) q^{37} +(-2.17621 - 2.99530i) q^{38} +(-1.01187 + 1.39272i) q^{39} +(6.82168 - 0.933619i) q^{40} +(-0.481169 - 0.662273i) q^{41} +(-15.0581 - 4.89267i) q^{42} -3.79889i q^{43} +(1.53663 + 0.499280i) q^{44} +(8.65022 - 16.1279i) q^{45} +(-0.602861 + 0.195881i) q^{46} +(-7.90580 + 2.56875i) q^{47} +(5.96740 + 4.33557i) q^{48} +9.87320 q^{49} +(1.54837 + 5.55077i) q^{50} +(7.30230 + 11.6968i) q^{51} +(-0.203219 + 0.279707i) q^{52} +(-5.69406 + 1.85011i) q^{53} +(19.0057 - 6.17534i) q^{54} +(-0.953166 + 5.29383i) q^{55} +(-12.0293 - 3.90856i) q^{56} -10.7433 q^{57} +(-0.639955 + 1.96958i) q^{58} +(-1.99351 + 1.44837i) q^{59} +(2.37405 - 4.42631i) q^{60} +(-4.29318 + 5.90906i) q^{61} +(-4.61118 + 3.35022i) q^{62} +(-27.1990 + 19.7612i) q^{63} +(6.94066 + 5.04269i) q^{64} +(-1.01433 - 0.544036i) q^{65} +(-7.50128 + 5.45000i) q^{66} +(-9.58242 - 3.11352i) q^{67} +(1.46656 + 2.34912i) q^{68} +(-0.568392 + 1.74933i) q^{69} +(1.87590 - 10.4186i) q^{70} +(13.8098 - 4.48708i) q^{71} +(23.9684 - 7.78780i) q^{72} +(0.226203 + 0.164346i) q^{73} +10.9818i q^{74} +(15.6715 + 5.83247i) q^{75} -2.15763 q^{76} +(5.80805 - 7.99410i) q^{77} +(-0.613118 - 1.88698i) q^{78} +(-16.0405 + 5.21188i) q^{79} +(-2.33103 + 4.34610i) q^{80} +(10.3316 - 31.7973i) q^{81} +0.943483 q^{82} +(0.180325 + 0.0585910i) q^{83} +(-7.46476 + 5.42346i) q^{84} +(-7.08634 + 5.89777i) q^{85} +(3.54216 + 2.57353i) q^{86} +(3.53216 + 4.86161i) q^{87} +(-5.99248 + 4.35379i) q^{88} +(0.532227 + 0.386686i) q^{89} +(9.17801 + 18.9914i) q^{90} +(1.24284 + 1.71062i) q^{91} +(-0.114153 + 0.351327i) q^{92} +16.5390i q^{93} +(2.96058 - 9.11172i) q^{94} +(-0.974007 - 7.11677i) q^{95} +(11.5025 - 3.73738i) q^{96} +(0.579938 + 1.78487i) q^{97} +(-6.68854 + 9.20599i) q^{98} +19.6884i 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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Database

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