LMFDB - Embedded newform 425.2.p.a.16.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([2, 5]))

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

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

chi := DirichletCharacter("425.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.39364208590$
Analytic rank:	$0$
Dimension:	$168$
Relative dimension:	$42$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			16.3
Character	$\chi$	$=$	425.16
Dual form			425.2.p.a.186.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.10617 - 1.53022i) q^{2} +(-2.96838 + 0.964486i) q^{3} +(1.47633 + 4.54369i) q^{4} +(1.79897 + 1.32805i) q^{5} +(7.72779 + 2.51091i) q^{6} -1.45026i q^{7} +(2.23447 - 6.87699i) q^{8} +(5.45401 - 3.96257i) q^{9} +(-1.75672 - 5.54991i) q^{10} +(-2.07972 + 2.86249i) q^{11} +(-8.76465 - 12.0635i) q^{12} +(-1.51257 + 1.09895i) q^{13} +(-2.21922 + 3.05450i) q^{14} +(-6.62091 - 2.20708i) q^{15} +(-7.49928 + 5.44855i) q^{16} +(4.02507 + 0.893775i) q^{17} -17.5507 q^{18} +(2.37199 - 7.30024i) q^{19} +(-3.37836 + 10.1346i) q^{20} +(1.39876 + 4.30494i) q^{21} +(8.76048 - 2.84645i) q^{22} +(0.279000 - 0.384010i) q^{23} +22.5686i q^{24} +(1.47257 + 4.77824i) q^{25} +4.86736 q^{26} +(-6.86407 + 9.44758i) q^{27} +(6.58955 - 2.14107i) q^{28} +(-6.95806 + 2.26081i) q^{29} +(10.5674 + 14.7799i) q^{30} +(2.63346 + 0.855662i) q^{31} +9.67045 q^{32} +(3.41258 - 10.5028i) q^{33} +(-7.10979 - 8.04168i) q^{34} +(1.92602 - 2.60898i) q^{35} +(26.0566 + 18.9312i) q^{36} +(0.933506 + 1.28486i) q^{37} +(-16.1668 + 11.7459i) q^{38} +(3.42997 - 4.72095i) q^{39} +(13.1527 - 9.40399i) q^{40} +(4.01518 + 5.52642i) q^{41} +(3.64149 - 11.2073i) q^{42} +2.33403 q^{43} +(-16.0766 - 5.22361i) q^{44} +(15.0741 + 0.114656i) q^{45} +(-1.17524 + 0.381859i) q^{46} +(0.721991 + 2.22206i) q^{47} +(17.0057 - 23.4063i) q^{48} +4.89673 q^{49} +(4.21027 - 12.3171i) q^{50} +(-12.8100 + 1.22906i) q^{51} +(-7.22634 - 5.25024i) q^{52} +(3.05079 + 9.38937i) q^{53} +(28.9137 - 9.39464i) q^{54} +(-7.54288 + 2.38756i) q^{55} +(-9.97345 - 3.24057i) q^{56} +23.9577i q^{57} +(18.1144 + 5.88572i) q^{58} +(-11.6536 + 8.46682i) q^{59} +(0.253602 - 33.3417i) q^{60} +(3.34074 - 4.59813i) q^{61} +(-4.23715 - 5.83194i) q^{62} +(-5.74678 - 7.90976i) q^{63} +(-5.36902 - 3.90082i) q^{64} +(-4.18053 - 0.0317977i) q^{65} +(-23.2591 + 16.8987i) q^{66} +(-3.26587 + 10.0513i) q^{67} +(1.88131 + 19.6082i) q^{68} +(-0.457806 + 1.40898i) q^{69} +(-8.04884 + 2.54771i) q^{70} +(-7.17479 + 2.33123i) q^{71} +(-15.0637 - 46.3614i) q^{72} +(-4.74144 + 6.52603i) q^{73} -4.13460i q^{74} +(-8.97970 - 12.7634i) q^{75} +36.6718 q^{76} +(4.15137 + 3.01615i) q^{77} +(-14.4482 + 4.69450i) q^{78} +(-0.468426 + 0.152201i) q^{79} +(-20.7269 - 0.157652i) q^{80} +(5.01338 - 15.4296i) q^{81} -17.7837i q^{82} +(-1.62330 + 4.99602i) q^{83} +(-17.4953 + 12.7111i) q^{84} +(6.05399 + 6.95336i) q^{85} +(-4.91585 - 3.57158i) q^{86} +(18.4737 - 13.4219i) q^{87} +(15.0382 + 20.6984i) q^{88} +(9.51902 + 6.91597i) q^{89} +(-31.5731 - 23.3081i) q^{90} +(1.59377 + 2.19363i) q^{91} +(2.15672 + 0.700761i) q^{92} -8.64238 q^{93} +(1.87961 - 5.78483i) q^{94} +(13.9622 - 9.98277i) q^{95} +(-28.7056 + 9.32701i) q^{96} +(-3.12491 + 1.01534i) q^{97} +(-10.3133 - 7.49308i) q^{98} +23.8531i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 168 q - 8 q^{2} - 44 q^{4} - 4 q^{8} + 28 q^{9} - 18 q^{13} - 10 q^{15} - 28 q^{16} + 2 q^{17} - 60 q^{18} - 8 q^{19} + 32 q^{21} + 6 q^{25} + 52 q^{26} - 54 q^{30} + 44 q^{32} - 24 q^{33} + 26 q^{35} + 34 q^{36}+ \cdots - 36 q^{98}+O(q^{100}) $ 168 * q - 8 * q^2 - 44 * q^4 - 4 * q^8 + 28 * q^9 - 18 * q^13 - 10 * q^15 - 28 * q^16 + 2 * q^17 - 60 * q^18 - 8 * q^19 + 32 * q^21 + 6 * q^25 + 52 * q^26 - 54 * q^30 + 44 * q^32 - 24 * q^33 + 26 * q^35 + 34 * q^36 - 18 * q^38 + 80 * q^42 - 8 * q^43 - 40 * q^47 - 84 * q^49 - 82 * q^50 - 36 * q^51 - 30 * q^52 - 42 * q^53 - 18 * q^55 - 18 * q^59 + 28 * q^60 - 16 * q^64 - 140 * q^66 - 62 * q^67 + 144 * q^68 + 44 * q^69 + 4 * q^70 - 6 * q^72 + 72 * q^76 + 48 * q^77 - 28 * q^81 - 14 * q^83 + 24 * q^84 + 62 * q^85 + 82 * q^86 + 48 * q^87 + 90 * q^89 - 224 * q^93 + 26 * q^94 - 36 * q^98

Character values

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

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

Coefficient data

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

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

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

$2$	−2.10617	−	1.53022i	−1.48929	−	1.08203i	−0.974414	−	0.224762i	$-0.927840\pi$
$2$	−2.10617	−	1.53022i	−1.48929	−	1.08203i	−0.514872	−	0.857267i	$-0.672160\pi$
$3$	−2.96838	+	0.964486i	−1.71380	+	0.556846i	−0.990958	−	0.134171i	$-0.957163\pi$
$3$	−2.96838	+	0.964486i	−1.71380	+	0.556846i	−0.722838	+	0.691017i	$0.757163\pi$
$4$	1.47633	+	4.54369i	0.738167	+	2.27184i
$5$	1.79897	+	1.32805i	0.804523	+	0.593922i
$5$	1.79897	+	1.32805i	0.804523	+	0.593922i
$6$	7.72779	+	2.51091i	3.15486	+	1.02507i
$7$		−	1.45026i		−	0.548149i	−0.961709	−	0.274074i	$-0.911629\pi$
$7$		−	1.45026i		−	0.548149i	0.961709	−	0.274074i	$-0.0883714\pi$
$8$	2.23447	−	6.87699i	0.790004	−	2.43138i
$9$	5.45401	−	3.96257i	1.81800	−	1.32086i
$10$	−1.75672	−	5.54991i	−0.555524	−	1.75504i
$11$	−2.07972	+	2.86249i	−0.627060	+	0.863073i	−0.997843	−	0.0656459i	$-0.979089\pi$
$11$	−2.07972	+	2.86249i	−0.627060	+	0.863073i	0.370783	+	0.928719i	$0.379089\pi$
$12$	−8.76465	−	12.0635i	−2.53014	−	3.48243i
$13$	−1.51257	+	1.09895i	−0.419512	+	0.304793i	−0.777441	−	0.628955i	$-0.783483\pi$
$13$	−1.51257	+	1.09895i	−0.419512	+	0.304793i	0.357929	+	0.933749i	$0.383483\pi$
$14$	−2.21922	+	3.05450i	−0.593113	+	0.816350i
$15$	−6.62091	−	2.20708i	−1.70951	−	0.569865i
$16$	−7.49928	+	5.44855i	−1.87482	+	1.36214i
$17$	4.02507	+	0.893775i	0.976222	+	0.216772i
$17$	4.02507	+	0.893775i	0.976222	+	0.216772i
$18$	−17.5507			−4.13673
$19$	2.37199	−	7.30024i	0.544172	−	1.67479i	−0.178778	−	0.983889i	$-0.557214\pi$
$19$	2.37199	−	7.30024i	0.544172	−	1.67479i	0.722950	−	0.690900i	$-0.242786\pi$
$20$	−3.37836	+	10.1346i	−0.755425	+	2.26616i
$21$	1.39876	+	4.30494i	0.305235	+	0.939415i
$22$	8.76048	−	2.84645i	1.86774	−	0.606866i
$23$	0.279000	−	0.384010i	0.0581755	−	0.0800717i	−0.778938	−	0.627101i	$-0.784241\pi$
$23$	0.279000	−	0.384010i	0.0581755	−	0.0800717i	0.837113	+	0.547029i	$0.184241\pi$
$24$			22.5686i			4.60680i
$25$	1.47257	+	4.77824i	0.294514	+	0.955647i
$26$	4.86736			0.954568
$27$	−6.86407	+	9.44758i	−1.32099	+	1.81819i
$28$	6.58955	−	2.14107i	1.24531	−	0.404625i
$29$	−6.95806	+	2.26081i	−1.29208	+	0.419822i	−0.872819	−	0.488044i	$-0.837710\pi$
$29$	−6.95806	+	2.26081i	−1.29208	+	0.419822i	−0.419260	+	0.907866i	$0.637710\pi$
$30$	10.5674	+	14.7799i	1.92934	+	2.69843i
$31$	2.63346	+	0.855662i	0.472983	+	0.153681i	0.535802	−	0.844343i	$-0.320009\pi$
$31$	2.63346	+	0.855662i	0.472983	+	0.153681i	−0.0628194	+	0.998025i	$0.520009\pi$
$32$	9.67045			1.70951
$33$	3.41258	−	10.5028i	0.594053	−	1.82831i
$34$	−7.10979	−	8.04168i	−1.21932	−	1.37914i
$35$	1.92602	−	2.60898i	0.325557	−	0.440998i
$36$	26.0566	+	18.9312i	4.34277	+	3.15521i
$37$	0.933506	+	1.28486i	0.153467	+	0.211230i	0.878827	−	0.477140i	$-0.158327\pi$
$37$	0.933506	+	1.28486i	0.153467	+	0.211230i	−0.725360	+	0.688370i	$0.758327\pi$
$38$	−16.1668	+	11.7459i	−2.62260	+	1.90543i
$39$	3.42997	−	4.72095i	0.549235	−	0.755957i
$40$	13.1527	−	9.40399i	2.07963	−	1.48690i
$41$	4.01518	+	5.52642i	0.627066	+	0.863082i	0.997843	−	0.0656394i	$-0.0209087\pi$
$41$	4.01518	+	5.52642i	0.627066	+	0.863082i	−0.370777	+	0.928722i	$0.620909\pi$
$42$	3.64149	−	11.2073i	0.561893	−	1.72933i
$43$	2.33403			0.355936			0.177968	−	0.984036i	$-0.443048\pi$
$43$	2.33403			0.355936			0.177968	+	0.984036i	$0.443048\pi$
$44$	−16.0766	−	5.22361i	−2.42364	−	0.787489i
$45$	15.0741	+	0.114656i	2.24711	+	0.0170919i
$46$	−1.17524	+	0.381859i	−0.173280	+	0.0563020i
$47$	0.721991	+	2.22206i	0.105313	+	0.324121i	0.989804	−	0.142437i	$-0.0454939\pi$
$47$	0.721991	+	2.22206i	0.105313	+	0.324121i	−0.884491	+	0.466558i	$0.845494\pi$
$48$	17.0057	−	23.4063i	2.45456	−	3.37841i
$49$	4.89673			0.699533
$50$	4.21027	−	12.3171i	0.595422	−	1.74190i
$51$	−12.8100	+	1.22906i	−1.79376	+	0.172102i
$52$	−7.22634	−	5.25024i	−1.00211	−	0.728077i
$53$	3.05079	+	9.38937i	0.419058	+	1.28973i	0.908570	+	0.417732i	$0.137175\pi$
$53$	3.05079	+	9.38937i	0.419058	+	1.28973i	−0.489512	+	0.871997i	$0.662825\pi$
$54$	28.9137	−	9.39464i	3.93466	−	1.27845i
$55$	−7.54288	+	2.38756i	−1.01708	+	0.321938i
$56$	−9.97345	−	3.24057i	−1.33276	−	0.433039i
$57$			23.9577i			3.17327i
$58$	18.1144	+	5.88572i	2.37853	+	0.772832i
$59$	−11.6536	+	8.46682i	−1.51717	+	1.10229i	−0.554298	+	0.832318i	$0.687013\pi$
$59$	−11.6536	+	8.46682i	−1.51717	+	1.10229i	−0.962869	+	0.269968i	$0.912987\pi$
$60$	0.253602	−	33.3417i	0.0327399	−	4.30440i
$61$	3.34074	−	4.59813i	0.427738	−	0.588730i	−0.539695	−	0.841861i	$-0.681460\pi$
$61$	3.34074	−	4.59813i	0.427738	−	0.588730i	0.967432	+	0.253131i	$0.0814602\pi$
$62$	−4.23715	−	5.83194i	−0.538119	−	0.740657i
$63$	−5.74678	−	7.90976i	−0.724026	−	0.996536i
$64$	−5.36902	−	3.90082i	−0.671127	−	0.487602i
$65$	−4.18053	−	0.0317977i	−0.518530	−	0.00394402i
$66$	−23.2591	+	16.8987i	−2.86300	+	2.08009i
$67$	−3.26587	+	10.0513i	−0.398989	+	1.22796i	0.526822	+	0.849976i	$0.323383\pi$
$67$	−3.26587	+	10.0513i	−0.398989	+	1.22796i	−0.925811	+	0.377987i	$0.876617\pi$
$68$	1.88131	+	19.6082i	0.228142	+	2.37784i
$69$	−0.457806	+	1.40898i	−0.0551133	+	0.169621i
$70$	−8.04884	+	2.54771i	−0.962021	+	0.304510i
$71$	−7.17479	+	2.33123i	−0.851490	+	0.276666i	−0.702070	−	0.712108i	$-0.747741\pi$
$71$	−7.17479	+	2.33123i	−0.851490	+	0.276666i	−0.149420	+	0.988774i	$0.547741\pi$
$72$	−15.0637	−	46.3614i	−1.77528	−	5.46374i
$73$	−4.74144	+	6.52603i	−0.554943	+	0.763814i	−0.990673	−	0.136264i	$-0.956490\pi$
$73$	−4.74144	+	6.52603i	−0.554943	+	0.763814i	0.435729	+	0.900078i	$0.356490\pi$
$74$		−	4.13460i		−	0.480638i
$75$	−8.97970	−	12.7634i	−1.03689	−	1.47379i
$76$	36.6718			4.20655
$77$	4.15137	+	3.01615i	0.473093	+	0.343722i
$78$	−14.4482	+	4.69450i	−1.63594	+	0.531548i
$79$	−0.468426	+	0.152201i	−0.0527020	+	0.0171239i	−0.335249	−	0.942129i	$-0.608821\pi$
$79$	−0.468426	+	0.152201i	−0.0527020	+	0.0171239i	0.282547	+	0.959253i	$0.408821\pi$
$80$	−20.7269	−	0.157652i	−2.31734	−	0.0176260i
$81$	5.01338	−	15.4296i	0.557042	−	1.71440i
$82$		−	17.7837i		−	1.96388i
$83$	−1.62330	+	4.99602i	−0.178181	+	0.548384i	−0.999764	−	0.0217038i	$-0.993091\pi$
$83$	−1.62330	+	4.99602i	−0.178181	+	0.548384i	0.821584	+	0.570088i	$0.193091\pi$
$84$	−17.4953	+	12.7111i	−1.90889	+	1.38689i
$85$	6.05399	+	6.95336i	0.656647	+	0.754198i
$86$	−4.91585	−	3.57158i	−0.530090	−	0.385133i
$87$	18.4737	−	13.4219i	1.98058	−	1.43898i
$88$	15.0382	+	20.6984i	1.60308	+	2.20645i
$89$	9.51902	+	6.91597i	1.00901	+	0.733092i	0.964002	−	0.265895i	$-0.0856674\pi$
$89$	9.51902	+	6.91597i	1.00901	+	0.733092i	0.0450121	+	0.998986i	$0.485667\pi$
$90$	−31.5731	−	23.3081i	−3.32810	−	2.45689i
$91$	1.59377	+	2.19363i	0.167072	+	0.229955i
$92$	2.15672	+	0.700761i	0.224854	+	0.0730593i
$93$	−8.64238			−0.896173
$94$	1.87961	−	5.78483i	0.193867	−	0.596660i
$95$	13.9622	−	9.98277i	1.43249	−	1.02421i
$96$	−28.7056	+	9.32701i	−2.92975	+	0.951934i
$97$	−3.12491	+	1.01534i	−0.317286	+	0.103092i	−0.463331	−	0.886186i	$-0.653346\pi$
$97$	−3.12491	+	1.01534i	−0.317286	+	0.103092i	0.146045	+	0.989278i	$0.453346\pi$
$98$	−10.3133	−	7.49308i	−1.04180	−	0.756915i
$99$			23.8531i			2.39733i
$100$	−19.5368	+	13.7452i	−1.95368	+	1.37452i
$101$	−10.5602			−1.05078			−0.525392	−	0.850861i	$-0.676081\pi$
$101$	−10.5602			−1.05078			−0.525392	+	0.850861i	$0.676081\pi$
$102$	28.8607	+	17.0135i	2.85763	+	1.68459i
$103$	−0.103595	−	0.318834i	−0.0102075	−	0.0314156i	0.945823	−	0.324683i	$-0.105257\pi$
$103$	−0.103595	−	0.318834i	−0.0102075	−	0.0314156i	−0.956031	+	0.293267i	$0.905257\pi$
$104$	4.17766	+	12.8575i	0.409653	+	1.26078i
$105$	−3.20085	+	9.60207i	−0.312371	+	0.937066i
$106$	7.94232	−	24.4440i	0.771427	−	2.37421i
$107$			1.17274i			0.113373i	0.998392	+	0.0566866i	$0.0180536\pi$
$107$			1.17274i			0.113373i	−0.998392	+	0.0566866i	$0.981946\pi$
$108$	−53.0605	−	17.2404i	−5.10575	−	1.65896i
$109$	−8.80266	−	12.1158i	−0.843142	−	1.16049i	−0.985332	−	0.170646i	$-0.945414\pi$
$109$	−8.80266	−	12.1158i	−0.843142	−	1.16049i	0.142190	−	0.989839i	$-0.454586\pi$
$110$	19.5401	+	6.51367i	1.86307	+	0.621054i
$111$	−4.01023	−	2.91360i	−0.380634	−	0.276547i
$112$	7.90184	+	10.8759i	0.746654	+	1.02768i
$113$	−3.43046	−	4.72162i	−0.322710	−	0.444173i	0.616582	−	0.787291i	$-0.288517\pi$
$113$	−3.43046	−	4.72162i	−0.322710	−	0.444173i	−0.939292	+	0.343118i	$0.888517\pi$
$114$	36.6605	−	50.4588i	3.43357	−	4.72590i
$115$	1.01190	−	0.320297i	0.0943598	−	0.0298678i
$116$	−20.5448	−	28.2775i	−1.90754	−	2.62550i
$117$	−3.89493	+	11.9873i	−0.360086	+	1.10823i
$118$	37.5005			3.45220
$119$	1.29621	−	5.83741i	0.118823	−	0.535115i
$120$	−29.9723	+	40.6003i	−2.73608	+	3.70628i
$121$	−0.469426	−	1.44474i	−0.0426751	−	0.131340i
$122$	−14.0723	+	4.57237i	−1.27405	+	0.413963i
$123$	−17.2488	−	12.5320i	−1.55527	−	1.12997i
$124$			13.2288i			1.18799i
$125$	−3.69662	+	10.5515i	−0.330636	+	0.943758i
$126$			25.4531i			2.26754i
$127$	1.21992	+	0.886327i	0.108251	+	0.0786488i	0.640594	−	0.767880i	$-0.278688\pi$
$127$	1.21992	+	0.886327i	0.108251	+	0.0786488i	−0.532343	+	0.846529i	$0.678688\pi$
$128$	−0.637731	−	1.96273i	−0.0563680	−	0.173483i
$129$	−6.92829	+	2.25114i	−0.610002	+	0.198202i
$130$	8.75623	+	6.46410i	0.767972	+	0.566939i
$131$	5.66674	+	1.84123i	0.495105	+	0.160869i	0.545918	−	0.837839i	$-0.316181\pi$
$131$	5.66674	+	1.84123i	0.495105	+	0.160869i	−0.0508126	+	0.998708i	$0.516181\pi$
$132$	52.7597			4.59214
$133$	−10.5873	−	3.44002i	−0.918033	−	0.298287i
$134$	22.2592	−	16.1722i	1.92290	−	1.39707i
$135$	−24.8951	+	7.88007i	−2.14263	+	0.678208i
$136$	15.1404	−	25.6832i	1.29828	−	2.20232i
$137$	15.8897	−	11.5445i	1.35755	−	0.986315i	0.358950	−	0.933357i	$-0.383135\pi$
$137$	15.8897	−	11.5445i	1.35755	−	0.986315i	0.998597	−	0.0529581i	$-0.0168650\pi$
$138$	3.12027	−	2.26701i	0.265615	−	0.192980i
$139$	−6.42381	+	8.84161i	−0.544860	+	0.749936i	−0.989304	−	0.145871i	$-0.953401\pi$
$139$	−6.42381	+	8.84161i	−0.544860	+	0.749936i	0.444443	+	0.895807i	$0.353401\pi$
$140$	14.6978	+	4.89952i	1.24219	+	0.414085i
$141$	−4.28629	−	5.89957i	−0.360971	−	0.496834i
$142$	18.6786	+	6.06904i	1.56747	+	0.509303i
$143$		−	6.61523i		−	0.553193i
$144$	−19.3109	+	59.4329i	−1.60924	+	4.95274i
$145$	−15.5198	−	5.17352i	−1.28885	−	0.429637i
$146$	19.9725	−	6.48946i	1.65294	−	0.537072i
$147$	−14.5354	+	4.72283i	−1.19886	+	0.389532i
$148$	−4.45984	+	6.13844i	−0.366596	+	0.504577i
$149$	5.40732			0.442985			0.221493	−	0.975162i	$-0.428907\pi$
$149$	5.40732			0.442985			0.221493	+	0.975162i	$0.428907\pi$
$150$	−0.618000	+	40.6227i	−0.0504595	+	3.31683i
$151$	17.3406			1.41115			0.705577	−	0.708633i	$-0.250688\pi$
$151$	17.3406			1.41115			0.705577	+	0.708633i	$0.250688\pi$
$152$	−44.9035	−	32.6243i	−3.64215	−	2.64618i
$153$	25.4944	−	11.0750i	2.06110	−	0.895357i
$154$	−4.12811	−	12.7050i	−0.332653	−	1.02380i
$155$	3.60114	+	5.03667i	0.289251	+	0.404555i
$156$	26.5143	+	8.61502i	2.12284	+	0.689754i
$157$	−8.06165			−0.643390			−0.321695	−	0.946843i	$-0.604253\pi$
$157$	−8.06165			−0.643390			−0.321695	+	0.946843i	$0.604253\pi$
$158$	1.21948	+	0.396234i	0.0970169	+	0.0315227i
$159$	−18.1118	−	24.9288i	−1.43636	−	1.97698i
$160$	17.3968	+	12.8428i	1.37534	+	1.01531i
$161$	−0.556917	−	0.404624i	−0.0438912	−	0.0318888i
$162$	−34.1697	+	24.8257i	−2.68462	+	1.95049i
$163$	5.59949	+	7.70704i	0.438586	+	0.603662i	0.969897	−	0.243515i	$-0.0783004\pi$
$163$	5.59949	+	7.70704i	0.438586	+	0.603662i	−0.531311	+	0.847177i	$0.678300\pi$
$164$	−19.1826	+	26.4026i	−1.49791	+	2.06169i
$165$	20.0874	−	14.3622i	1.56380	−	1.11809i
$166$	11.0640	−	8.03844i	0.858730	−	0.623904i
$167$	4.84705	+	1.57490i	0.375076	+	0.121870i	0.490488	−	0.871448i	$-0.336819\pi$
$167$	4.84705	+	1.57490i	0.375076	+	0.121870i	−0.115412	+	0.993318i	$0.536819\pi$
$168$	32.7305			2.52521
$169$	−2.93703	+	9.03926i	−0.225926	+	0.695328i
$170$	−2.11055	−	23.9089i	−0.161872	−	1.83373i
$171$	−15.9908	−	49.2148i	−1.22285	−	3.76355i
$172$	3.44580	+	10.6051i	0.262740	+	0.808631i
$173$	−1.40446	+	1.93308i	−0.106779	+	0.146969i	−0.859062	−	0.511871i	$-0.828953\pi$
$173$	−1.40446	+	1.93308i	−0.106779	+	0.146969i	0.752283	+	0.658840i	$0.228953\pi$
$174$	−59.4471			−4.50667
$175$	6.92971	−	2.13562i	0.523837	−	0.161438i
$176$		−	32.7981i		−	2.47225i
$177$	26.4262	−	36.3725i	1.98631	−	2.73392i
$178$	−9.46569	−	29.1324i	−0.709483	−	2.18357i
$179$	4.41172	+	13.5779i	0.329748	+	1.01486i	0.969252	+	0.246071i	$0.0791398\pi$
$179$	4.41172	+	13.5779i	0.329748	+	1.01486i	−0.639504	+	0.768788i	$0.720860\pi$
$180$	21.7334	+	68.6612i	1.61991	+	5.11770i
$181$	−14.6260	−	4.75228i	−1.08714	−	0.353234i	−0.290001	−	0.957026i	$-0.593656\pi$
$181$	−14.6260	−	4.75228i	−1.08714	−	0.353234i	−0.797142	+	0.603792i	$0.793656\pi$
$182$		−	7.05897i		−	0.523245i
$183$	−5.48175	+	16.8711i	−0.405223	+	1.24715i
$184$	−2.01742	−	2.77674i	−0.148726	−	0.204704i
$185$	−0.0270107	+	3.55116i	−0.00198586	+	0.261087i
$186$	18.2023	+	13.2248i	1.33466	+	0.969686i
$187$	−10.9294	+	9.66291i	−0.799240	+	0.706622i
$188$	−9.03044	+	6.56100i	−0.658613	+	0.478510i
$189$	13.7015	+	9.95471i	0.996637	+	0.724099i
$190$	−44.6826	−	0.339862i	−3.24162	−	0.0246562i
$191$	−1.36505	+	0.991768i	−0.0987716	+	0.0717618i	−0.636075	−	0.771627i	$-0.719443\pi$
$191$	−1.36505	+	0.991768i	−0.0987716	+	0.0717618i	0.537303	+	0.843389i	$0.319443\pi$
$192$	19.6996	+	6.40078i	1.42169	+	0.461937i
$193$		−	7.82417i		−	0.563196i	−0.959532	−	0.281598i	$-0.909135\pi$
$193$		−	7.82417i		−	0.563196i	0.959532	−	0.281598i	$-0.0908645\pi$
$194$	8.13527	+	2.64331i	0.584079	+	0.189779i
$195$	12.4401	−	3.93767i	0.890852	−	0.281982i
$196$	7.22921	+	22.2492i	0.516372	+	1.58923i
$197$	17.9951	−	5.84696i	1.28210	−	0.416579i	0.412779	−	0.910831i	$-0.364558\pi$
$197$	17.9951	−	5.84696i	1.28210	−	0.416579i	0.869318	+	0.494253i	$0.164558\pi$
$198$	36.5005	−	50.2386i	2.59398	−	3.57030i
$199$			19.5265i			1.38419i	0.721804	+	0.692097i	$0.243313\pi$
$199$			19.5265i			1.38419i	−0.721804	+	0.692097i	$0.756687\pi$
$200$	36.1503	+	0.549960i	2.55621	+	0.0388881i
$201$		−	32.9860i		−	2.32665i
$202$	22.2416	+	16.1595i	1.56492	+	1.13698i
$203$	3.27877	+	10.0910i	0.230125	+	0.708251i
$204$	−24.4962	−	56.3900i	−1.71508	−	3.94809i
$205$	−0.116178	+	15.2742i	−0.00811422	+	1.06680i
$206$	−0.269697	+	0.830041i	−0.0187906	+	0.0578317i
$207$		−	3.19995i		−	0.222412i
$208$	5.35554	−	16.4826i	0.371340	−	1.14287i
$209$	15.9638	+	21.9723i	1.10424	+	1.51985i
$210$	21.4348	−	15.3256i	1.47914	−	1.05757i
$211$	14.1090	−	19.4193i	0.971302	−	1.33688i	0.0299150	−	0.999552i	$-0.490476\pi$
$211$	14.1090	−	19.4193i	0.971302	−	1.33688i	0.941387	−	0.337330i	$-0.109524\pi$
$212$	−38.1584	+	27.7237i	−2.62073	+	1.90407i
$213$	19.0491	−	13.8400i	1.30522	−	0.948299i
$214$	1.79455	−	2.46999i	0.122673	−	0.168845i
$215$	4.19884	+	3.09970i	0.286359	+	0.211398i
$216$	49.6333	+	68.3144i	3.37712	+	4.64821i
$217$	1.24094	−	3.81921i	0.0842403	−	0.259265i
$218$			38.9880i			2.64060i
$219$	7.78013	−	23.9448i	0.525733	−	1.61804i
$220$	−21.9841	−	30.7477i	−1.48217	−	2.07301i
$221$	−7.07042	+	3.07144i	−0.475608	+	0.206607i
$222$	3.98776	+	12.2731i	0.267641	+	0.823715i
$223$	10.4768	+	7.61187i	0.701581	+	0.509729i	0.880447	−	0.474145i	$-0.157243\pi$
$223$	10.4768	+	7.61187i	0.701581	+	0.509729i	−0.178865	+	0.983874i	$0.557243\pi$
$224$		−	14.0247i		−	0.937066i
$225$	26.9655	+	20.2254i	1.79770	+	1.34836i
$226$			15.1939i			1.01068i
$227$	−7.35246	+	10.1198i	−0.488000	+	0.671674i	−0.980018	−	0.198911i	$-0.936259\pi$
$227$	−7.35246	+	10.1198i	−0.488000	+	0.671674i	0.492018	+	0.870585i	$0.336259\pi$
$228$	−108.856	+	35.3695i	−7.20917	+	2.34240i
$229$	−2.38818	−	7.35007i	−0.157816	−	0.485707i	0.840620	−	0.541626i	$-0.182191\pi$
$229$	−2.38818	−	7.35007i	−0.157816	−	0.485707i	−0.998435	+	0.0559193i	$0.982191\pi$
$230$	−2.62135	−	0.873825i	−0.172847	−	0.0576183i
$231$	−15.2319	−	4.94914i	−1.00218	−	0.325629i
$232$			52.9022i			3.47320i
$233$	−18.2558	−	5.93166i	−1.19597	−	0.388596i	−0.357696	−	0.933838i	$-0.616438\pi$
$233$	−18.2558	−	5.93166i	−1.19597	−	0.388596i	−0.838279	+	0.545242i	$0.816438\pi$
$234$	26.5467	−	19.2873i	1.73541	−	1.26085i
$235$	−1.65217	+	4.95625i	−0.107775	+	0.323310i
$236$	−55.6752	−	40.4504i	−3.62415	−	2.63310i
$237$	1.24367	−	0.903580i	0.0807851	−	0.0586938i
$238$	−11.6626	+	10.3111i	−0.755972	+	0.668368i
$239$	−6.27591	−	4.55972i	−0.405955	−	0.294944i	0.366007	−	0.930612i	$-0.380725\pi$
$239$	−6.27591	−	4.55972i	−0.405955	−	0.294944i	−0.771962	+	0.635668i	$0.780725\pi$
$240$	61.6775	−	19.5228i	3.98126	−	1.26019i
$241$	3.86212	+	5.31575i	0.248781	+	0.342417i	0.915084	−	0.403264i	$-0.132124\pi$
$241$	3.86212	+	5.31575i	0.248781	+	0.342417i	−0.666303	+	0.745681i	$0.732124\pi$
$242$	−1.22209	+	3.76120i	−0.0785587	+	0.241779i
$243$			15.6027i			1.00091i
$244$	25.8245	+	8.39089i	1.65324	+	0.537172i
$245$	8.80906	+	6.50310i	0.562790	+	0.415468i
$246$	17.1521	+	52.7888i	1.09358	+	3.36569i
$247$	4.43477	+	13.6488i	0.282178	+	0.868454i
$248$	11.7688	−	16.1983i	0.747317	−	1.02859i
$249$		−	16.3957i		−	1.03904i
$250$	23.9319	−	16.5667i	1.51359	−	1.04777i
$251$	7.35280			0.464105			0.232052	−	0.972703i	$-0.425456\pi$
$251$	7.35280			0.464105			0.232052	+	0.972703i	$0.425456\pi$
$252$	27.4553	−	37.7890i	1.72952	−	2.38048i
$253$	0.518984	+	1.59727i	0.0326282	+	0.100419i
$254$	−1.21309	−	3.73351i	−0.0761160	−	0.234261i
$255$	−24.6770	−	14.8012i	−1.54533	−	0.926890i
$256$	−5.76181	+	17.7330i	−0.360113	+	1.10831i
$257$	−19.7835			−1.23406			−0.617031	−	0.786939i	$-0.711665\pi$
$257$	−19.7835			−1.23406			−0.617031	+	0.786939i	$0.711665\pi$
$258$	18.0369	+	5.86053i	1.12293	+	0.364861i
$259$	1.86339	−	1.35383i	0.115785	−	0.0841229i
$260$	−6.02737	−	19.0419i	−0.373802	−	1.18093i
$261$	−28.9907	+	39.9023i	−1.79448	+	2.46989i
$262$	−9.11760	−	12.5493i	−0.563287	−	0.775298i
$263$	−4.81028	+	3.49488i	−0.296615	+	0.215503i	−0.726132	−	0.687556i	$-0.758684\pi$
$263$	−4.81028	+	3.49488i	−0.296615	+	0.215503i	0.429517	+	0.903059i	$0.358684\pi$
$264$	−64.6025	−	46.9365i	−3.97601	−	2.88874i
$265$	−6.98126	+	20.9428i	−0.428856	+	1.28650i
$266$	17.0346	+	23.4461i	1.04446	+	1.43757i
$267$	−34.9265	−	11.3483i	−2.13746	−	0.694504i
$268$	−50.4915			−3.08426
$269$	7.24152	+	2.35291i	0.441523	+	0.143460i	0.521338	−	0.853350i	$-0.325433\pi$
$269$	7.24152	+	2.35291i	0.441523	+	0.143460i	−0.0798151	+	0.996810i	$0.525433\pi$
$270$	64.4914	+	21.4982i	3.92482	+	1.30834i
$271$	5.01456	+	15.4332i	0.304613	+	0.937502i	0.979821	+	0.199875i	$0.0640536\pi$
$271$	5.01456	+	15.4332i	0.304613	+	0.937502i	−0.675209	+	0.737627i	$0.735946\pi$
$272$	−35.0549	+	15.2281i	−2.12552	+	0.923339i
$273$	−6.84663	−	4.97437i	−0.414377	−	0.301063i
$274$	−51.1320			−3.08900
$275$	−16.7402	−	5.72217i	−1.00947	−	0.345060i
$276$	−7.07784			−0.426036
$277$	6.97614	−	9.60183i	0.419155	−	0.576918i	−0.546266	−	0.837612i	$-0.683951\pi$
$277$	6.97614	−	9.60183i	0.419155	−	0.576918i	0.965422	+	0.260694i	$0.0839513\pi$
$278$	27.0592	−	8.79208i	1.62290	−	0.527314i
$279$	17.7535	−	5.76847i	1.06288	−	0.345349i
$280$	−13.6383	−	19.0749i	−0.815043	−	1.13994i
$281$	0.848314	−	2.61084i	0.0506062	−	0.155750i	−0.922560	−	0.385854i	$-0.873907\pi$
$281$	0.848314	−	2.61084i	0.0506062	−	0.155750i	0.973166	+	0.230104i	$0.0739068\pi$
$282$			18.9845i			1.13051i
$283$	9.19794	+	2.98859i	0.546761	+	0.177653i	0.569355	−	0.822091i	$-0.307193\pi$
$283$	9.19794	+	2.98859i	0.546761	+	0.177653i	−0.0225950	+	0.999745i	$0.507193\pi$
$284$	−21.1848	−	29.1583i	−1.25708	−	1.73023i
$285$	−31.8169	+	43.0990i	−1.88467	+	2.55297i
$286$	−10.1228	+	13.9328i	−0.598571	+	0.823863i
$287$	8.01478	−	5.82308i	0.473097	−	0.343725i
$288$	52.7427	−	38.3198i	3.10790	−	2.25802i
$289$	15.4023	+	7.19501i	0.906020	+	0.423236i
$290$	24.7707	+	34.6450i	1.45458	+	2.03442i
$291$	8.29663	−	6.02785i	0.486357	−	0.353359i
$292$	−36.6522	−	11.9090i	−2.14491	−	0.696922i
$293$	4.17009			0.243619			0.121810	−	0.992553i	$-0.461130\pi$
$293$	4.17009			0.243619			0.121810	+	0.992553i	$0.461130\pi$
$294$	37.8409	+	12.2953i	2.20693	+	0.717074i
$295$	−32.2088	−	0.244985i	−1.87527	−	0.0142636i
$296$	10.9219	−	3.54873i	0.634820	−	0.206266i
$297$	−12.7683	−	39.2966i	−0.740889	−	2.28022i
$298$	−11.3887	−	8.27440i	−0.659732	−	0.479323i
$299$			0.887449i			0.0513225i
$300$	44.7357	−	59.6439i	2.58282	−	3.44354i
$301$		−	3.38496i		−	0.195106i
$302$	−36.5221	−	26.5349i	−2.10161	−	1.52691i
$303$	31.3468	−	10.1852i	1.80083	−	0.585125i
$304$	21.9875	+	67.6705i	1.26107	+	3.88117i
$305$	12.1164	−	3.83523i	0.693784	−	0.219604i
$306$	−70.6426	−	15.6863i	−4.03837	−	0.896729i
$307$	5.86961			0.334996			0.167498	−	0.985872i	$-0.446431\pi$
$307$	5.86961			0.334996			0.167498	+	0.985872i	$0.446431\pi$
$308$	−7.57562	+	23.3154i	−0.431661	+	1.32852i
$309$	0.615021	+	0.846504i	0.0349873	+	0.0481559i
$310$	0.122601	−	16.1186i	0.00696324	−	0.915476i
$311$	8.97430	−	12.3521i	0.508886	−	0.700421i	−0.474845	−	0.880069i	$-0.657496\pi$
$311$	8.97430	−	12.3521i	0.508886	−	0.700421i	0.983731	+	0.179648i	$0.0574959\pi$
$312$	−24.8018	−	34.1367i	−1.40412	−	1.93261i
$313$	0.254769	+	0.350660i	0.0144004	+	0.0198205i	0.816157	−	0.577831i	$-0.196101\pi$
$313$	0.254769	+	0.350660i	0.0144004	+	0.0198205i	−0.801756	+	0.597651i	$0.796101\pi$
$314$	16.9792	+	12.3361i	0.958191	+	0.696166i
$315$	0.166281	−	21.8614i	0.00936888	−	1.23175i
$316$	−1.38310	−	1.90368i	−0.0778057	−	0.107090i
$317$	25.7986	+	8.38247i	1.44899	+	0.470806i	0.924689	−	0.380724i	$-0.124325\pi$
$317$	25.7986	+	8.38247i	1.44899	+	0.470806i	0.524305	+	0.851531i	$0.324325\pi$
$318$			80.2193i			4.49847i
$319$	7.99927	−	24.6192i	0.447873	−	1.37841i
$320$	−4.47821	−	14.1478i	−0.250340	−	0.790884i
$321$	−1.13109	−	3.48115i	−0.0631314	−	0.194299i
$322$	0.553796	+	1.70441i	0.0308619	+	0.0949831i
$323$	16.0722	−	27.2639i	0.894281	−	1.51701i
$324$	77.5086			4.30604
$325$	−7.47840	−	5.60915i	−0.414827	−	0.311139i
$326$		−	24.8008i		−	1.37359i
$327$	37.8152	+	27.4744i	2.09119	+	1.51934i
$328$	46.9769	−	15.2637i	2.59387	−	0.842799i
$329$	3.22257	−	1.04708i	0.177666	−	0.0577273i
$330$	−64.2847	−	0.488959i	−3.53876	−	0.0269163i
$331$	6.47931	−	19.9413i	0.356135	−	1.09607i	−0.599213	−	0.800590i	$-0.704520\pi$
$331$	6.47931	−	19.9413i	0.356135	−	1.09607i	0.955348	−	0.295482i	$-0.0954802\pi$
$332$	−25.0969			−1.37737
$333$	10.1827	+	3.30856i	0.558009	+	0.181308i
$334$	−7.79875	−	10.7341i	−0.426729	−	0.587342i
$335$	−19.2238	+	13.7447i	−1.05031	+	0.750956i
$336$	−33.9454	−	24.6628i	−1.85187	−	1.34546i
$337$	8.07018	+	11.1077i	0.439611	+	0.605072i	0.970126	−	0.242603i	$-0.0780013\pi$
$337$	8.07018	+	11.1077i	0.439611	+	0.605072i	−0.530515	+	0.847676i	$0.678001\pi$
$338$	20.0179	−	14.5439i	1.08883	−	0.791083i
$339$	14.7369	+	10.7070i	0.800396	+	0.581522i
$340$	−22.6562	+	37.7729i	−1.22870	+	2.04852i
$341$	−7.92618	+	5.75871i	−0.429227	+	0.311852i
$342$	−41.6300	+	128.124i	−2.25109	+	6.92816i
$343$		−	17.2534i		−	0.931597i
$344$	5.21531	−	16.0511i	0.281191	−	0.865416i
$345$	−2.69477	+	1.92672i	−0.145082	+	0.103731i
$346$	5.91607	−	1.92225i	0.318050	−	0.103341i
$347$	12.5475	−	4.07692i	0.673584	−	0.218861i	0.0477996	−	0.998857i	$-0.484779\pi$
$347$	12.5475	−	4.07692i	0.673584	−	0.218861i	0.625784	+	0.779996i	$0.284779\pi$
$348$	88.2582	+	64.1233i	4.73114	+	3.43737i
$349$	−26.6114			−1.42447			−0.712237	−	0.701940i	$-0.752318\pi$
$349$	−26.6114			−1.42447			−0.712237	+	0.701940i	$0.752318\pi$
$350$	−17.8631	−	6.10601i	−0.954822	−	0.326380i
$351$		−	21.8334i		−	1.16538i
$352$	−20.1118	+	27.6816i	−1.07196	+	1.47543i
$353$	3.17191	+	9.76213i	0.168824	+	0.519586i	0.999298	−	0.0374716i	$-0.0119304\pi$
$353$	3.17191	+	9.76213i	0.168824	+	0.519586i	−0.830474	+	0.557057i	$0.811930\pi$
$354$	−111.316	+	36.1687i	−5.91637	+	1.92235i
$355$	−16.0032	−	5.33466i	−0.849362	−	0.283134i
$356$	−17.3708	+	53.4617i	−0.920649	+	2.83347i
$357$	1.78246	+	18.5779i	0.0943376	+	0.983244i
$358$	11.4853	−	35.3482i	0.607019	−	1.86821i
$359$	−12.7076	+	9.23262i	−0.670682	+	0.487279i	−0.870254	−	0.492604i	$-0.836045\pi$
$359$	−12.7076	+	9.23262i	−0.670682	+	0.487279i	0.199571	+	0.979883i	$0.436045\pi$
$360$	34.4710	−	103.408i	1.81678	−	5.45008i
$361$	−32.2958	−	23.4643i	−1.69978	−	1.23496i
$362$	23.5328	+	32.3901i	1.23686	+	1.70239i
$363$	2.78687	+	3.83580i	0.146273	+	0.201327i
$364$	−7.61424	+	10.4801i	−0.399095	+	0.549307i
$365$	−17.1966	+	5.44325i	−0.900110	+	0.284913i
$366$	37.3620	−	27.1451i	1.95294	−	1.41890i
$367$	−35.5228	−	11.5420i	−1.85427	−	0.602490i	−0.996006	−	0.0892875i	$-0.971541\pi$
$367$	−35.5228	−	11.5420i	−1.85427	−	0.602490i	−0.858268	−	0.513203i	$-0.828459\pi$
$368$			4.39995i			0.229363i
$369$	43.7977	+	14.2307i	2.28002	+	0.740822i
$370$	5.49095	−	7.43801i	0.285461	−	0.386684i
$371$	13.6171	−	4.42445i	0.706963	−	0.229706i
$372$	−12.7590	−	39.2683i	−0.661525	−	2.03597i
$373$	−9.26977	−	6.73488i	−0.479971	−	0.348719i	0.321344	−	0.946963i	$-0.395866\pi$
$373$	−9.26977	−	6.73488i	−0.479971	−	0.348719i	−0.801314	+	0.598244i	$0.795866\pi$
$374$	37.8056	−	3.62727i	1.95488	−	0.187561i
$375$	0.796175	−	34.8863i	0.0411143	−	1.80152i
$376$	16.8943			0.871259
$377$	8.04005	−	11.0662i	0.414084	−	0.569937i
$378$	−13.6247	−	41.9326i	−0.700780	−	2.15678i
$379$	−1.05461	+	0.342662i	−0.0541715	+	0.0176014i	−0.335977	−	0.941870i	$-0.609067\pi$
$379$	−1.05461	+	0.342662i	−0.0541715	+	0.0176014i	0.281806	+	0.959471i	$0.409067\pi$
$380$	65.9715	+	48.7020i	3.38427	+	2.49836i
$381$	−4.47605	−	1.45436i	−0.229315	−	0.0745090i
$382$	4.39265			0.224748
$383$	4.62339	−	14.2293i	0.236244	−	0.727085i	−0.760710	−	0.649092i	$-0.775149\pi$
$383$	4.62339	−	14.2293i	0.236244	−	0.727085i	0.996954	−	0.0779925i	$-0.0248510\pi$
$384$	3.78606	+	5.21106i	0.193206	+	0.265926i
$385$	3.46259	+	10.9392i	0.176470	+	0.557512i
$386$	−11.9727	+	16.4790i	−0.609395	+	0.838760i
$387$	12.7298	−	9.24875i	0.647093	−	0.470140i
$388$	−9.22680	−	12.6996i	−0.468420	−	0.644725i
$389$	12.8421	+	9.33031i	0.651119	+	0.473066i	0.863652	−	0.504088i	$-0.168171\pi$
$389$	12.8421	+	9.33031i	0.651119	+	0.473066i	−0.212533	+	0.977154i	$0.568171\pi$
$390$	−32.2264	−	10.7426i	−1.63185	−	0.543975i
$391$	1.46621	−	1.29630i	0.0741495	−	0.0655569i
$392$	10.9416	−	33.6748i	0.552634	−	1.70083i
$393$	−18.5969			−0.938089
$394$	−46.8478	−	15.2218i	−2.36016	−	0.766862i
$395$	−1.04481	−	0.348288i	−0.0525702	−	0.0175243i
$396$	−108.381	+	35.2151i	−5.44635	+	1.76963i
$397$	24.0574	−	7.81674i	1.20741	−	0.392311i	0.364927	−	0.931036i	$-0.381094\pi$
$397$	24.0574	−	7.81674i	1.20741	−	0.392311i	0.842481	+	0.538725i	$0.181094\pi$
$398$	29.8798	−	41.1260i	1.49774	−	2.06146i
$399$	34.7449			1.73942
$400$	−37.0777	−	27.8100i	−1.85388	−	1.39050i
$401$		−	23.2929i		−	1.16319i	−0.813478	−	0.581596i	$-0.802428\pi$
$401$		−	23.2929i		−	1.16319i	0.813478	−	0.581596i	$-0.197572\pi$
$402$	−50.4759	+	69.4741i	−2.51751	+	3.46505i
$403$	−4.92362	+	1.59978i	−0.245263	+	0.0796908i
$404$	−15.5904	−	47.9824i	−0.775653	−	2.38722i
$405$	29.5102	−	21.0993i	1.46637	−	1.04843i
$406$	8.53585	−	26.2706i	0.423627	−	1.30379i
$407$	−5.61933			−0.278540
$408$	−20.1713	+	90.8403i	−0.998627	+	4.49726i
$409$	−17.0655	+	12.3988i	−0.843835	+	0.613082i	−0.923439	−	0.383744i	$-0.874634\pi$
$409$	−17.0655	+	12.3988i	−0.843835	+	0.613082i	0.0796042	+	0.996827i	$0.474634\pi$
$410$	23.6176	−	31.9923i	1.16639	−	1.57999i
$411$	−36.0321	+	49.5939i	−1.77733	+	2.44629i
$412$	1.29574	−	0.941409i	0.0638365	−	0.0463799i
$413$	12.2791	+	16.9008i	0.604217	+	0.831633i
$414$	−4.89663	+	6.73964i	−0.240656	+	0.331235i
$415$	−9.55523	+	6.83185i	−0.469048	+	0.335362i
$416$	−14.6272	+	10.6273i	−0.717160	+	0.521047i
$417$	10.5407	−	32.4410i	0.516181	−	1.58864i
$418$		−	70.7054i		−	3.45831i
$419$	−23.9529	−	7.78276i	−1.17017	−	0.380213i	−0.341467	−	0.939894i	$-0.610924\pi$
$419$	−23.9529	−	7.78276i	−1.17017	−	0.380213i	−0.828708	+	0.559681i	$0.810924\pi$
$420$	−48.3543	−	0.367790i	−2.35945	−	0.0179463i
$421$	1.88743	+	5.80891i	0.0919877	+	0.283109i	0.986457	−	0.164020i	$-0.0524463\pi$
$421$	1.88743	+	5.80891i	0.0919877	+	0.283109i	−0.894469	+	0.447130i	$0.852446\pi$
$422$	−59.4317	+	19.3105i	−2.89309	+	0.940022i
$423$	12.7428	+	9.25820i	0.619577	+	0.450149i
$424$	71.3874			3.46688
$425$	1.65653	+	20.5489i	0.0803537	+	0.996766i
$426$	−61.2987			−2.96993
$427$	−6.66851	−	4.84495i	−0.322712	−	0.234464i
$428$	−5.32857	+	1.73136i	−0.257566	+	0.0836883i
$429$	6.38030	+	19.6365i	0.308044	+	0.948061i
$430$	−4.10023	−	12.9536i	−0.197731	−	0.624680i
$431$	25.9685	+	8.43768i	1.25086	+	0.406429i	0.858229	−	0.513268i	$-0.171565\pi$
$431$	25.9685	+	8.43768i	1.25086	+	0.406429i	0.392630	+	0.919696i	$0.371565\pi$
$432$		−	108.249i		−	5.20814i
$433$	12.6068	−	38.7996i	0.605842	−	1.86459i	0.114949	−	0.993371i	$-0.463330\pi$
$433$	12.6068	−	38.7996i	0.605842	−	1.86459i	0.490894	−	0.871220i	$-0.336670\pi$
$434$	−8.45785	+	6.14499i	−0.405990	+	0.294969i
$435$	51.0585	+	0.388358i	2.44807	+	0.0186203i
$436$	42.0549	−	57.8835i	2.01406	−	2.77212i
$437$	−2.14158	−	2.94763i	−0.102446	−	0.141004i
$438$	−53.0271	+	38.5264i	−2.53373	+	1.84086i
$439$	−15.0543	+	20.7205i	−0.718503	+	0.988935i	0.281069	+	0.959688i	$0.409311\pi$
$439$	−15.0543	+	20.7205i	−0.718503	+	0.988935i	−0.999572	+	0.0292475i	$0.990689\pi$
$440$	−0.435126	+	57.2072i	−0.0207438	+	2.72725i
$441$	26.7068	−	19.4036i	1.27175	−	0.923983i
$442$	19.5915	+	4.35033i	0.931871	+	0.206924i
$443$	−12.3322			−0.585920			−0.292960	−	0.956125i	$-0.594640\pi$
$443$	−12.3322			−0.585920			−0.292960	+	0.956125i	$0.594640\pi$
$444$	7.31807	−	22.5227i	0.347300	−	1.06888i
$445$	7.93966	+	25.0833i	0.376376	+	1.18906i
$446$	−10.4181	−	32.0638i	−0.493314	−	1.51826i
$447$	−16.0510	+	5.21529i	−0.759187	+	0.246675i
$448$	−5.65722	+	7.78649i	−0.267279	+	0.367877i
$449$		−	23.0430i		−	1.08747i	−0.839257	−	0.543734i	$-0.817010\pi$
$449$		−	23.0430i		−	1.08747i	0.839257	−	0.543734i	$-0.182990\pi$
$450$	−25.8446	−	83.8612i	−1.21833	−	3.95326i
$451$	−24.1698			−1.13811
$452$	16.3891	−	22.5576i	0.770877	−	1.06102i
$453$	−51.4734	+	16.7247i	−2.41843	+	0.785796i
$454$	30.9710	−	10.0631i	1.45354	−	0.472284i
$455$	−0.0461151	+	6.06287i	−0.00216191	+	0.284232i
$456$	164.756	+	53.5326i	7.71543	+	2.50689i
$457$	1.20747			0.0564831			0.0282416	−	0.999601i	$-0.491009\pi$
$457$	1.20747			0.0564831			0.0282416	+	0.999601i	$0.491009\pi$
$458$	−6.21732	+	19.1349i	−0.290516	+	0.894117i
$459$	−36.0723	+	31.8922i	−1.68371	+	1.48860i
$460$	2.94922	+	4.12487i	0.137508	+	0.192323i
$461$	−11.2164	−	8.14919i	−0.522400	−	0.379546i	0.295107	−	0.955464i	$-0.404645\pi$
$461$	−11.2164	−	8.14919i	−0.522400	−	0.379546i	−0.817507	+	0.575918i	$0.804645\pi$
$462$	24.5076	+	33.7319i	1.14020	+	1.56935i
$463$	25.2737	−	18.3624i	1.17457	−	0.853374i	0.183020	−	0.983109i	$-0.441413\pi$
$463$	25.2737	−	18.3624i	1.17457	−	0.853374i	0.991549	+	0.129736i	$0.0414128\pi$
$464$	39.8623	−	54.8658i	1.85056	−	2.54708i
$465$	−15.5474	−	11.4775i	−0.720992	−	0.532257i
$466$	29.3730	+	40.4284i	1.36068	+	1.87281i
$467$	−6.80663	+	20.9486i	−0.314973	+	0.969388i	0.660792	+	0.750569i	$0.270220\pi$
$467$	−6.80663	+	20.9486i	−0.314973	+	0.969388i	−0.975765	+	0.218819i	$0.929780\pi$
$468$	−60.2170			−2.78353
$469$	14.5771	+	4.73637i	0.673106	+	0.218705i
$470$	11.0639	−	7.91052i	0.510339	−	0.364885i
$471$	23.9301	−	7.77535i	1.10264	−	0.358269i
$472$	32.1867	+	99.0604i	1.48151	+	4.55962i
$473$	−4.85413	+	6.68113i	−0.223193	+	0.307199i
$474$	−4.00206			−0.183820
$475$	38.3752	+	0.583808i	1.76077	+	0.0267870i
$476$	28.4370	−	2.72840i	1.30341	−	0.125056i
$477$	53.8451	+	39.1207i	2.46540	+	1.79122i
$478$	6.24075	+	19.2071i	0.285445	+	0.878510i
$479$	17.7783	−	5.77652i	0.812311	−	0.263936i	0.126735	−	0.991937i	$-0.459550\pi$
$479$	17.7783	−	5.77652i	0.812311	−	0.263936i	0.685576	+	0.728001i	$0.259550\pi$
$480$	−64.0272	−	21.3434i	−2.92243	−	0.974190i
$481$	−2.82399	−	0.917570i	−0.128763	−	0.0418376i
$482$		−	17.1057i		−	0.779145i
$483$	2.04340	+	0.663939i	0.0929777	+	0.0302103i
$484$	5.87143	−	4.26585i	0.266883	−	0.193902i
$485$	−6.97003	−	2.32346i	−0.316493	−	0.105503i
$486$	23.8756	−	32.8619i	1.08302	−	1.49065i
$487$	2.40845	+	3.31494i	0.109137	+	0.150214i	0.860092	−	0.510140i	$-0.170406\pi$
$487$	2.40845	+	3.31494i	0.109137	+	0.150214i	−0.750955	+	0.660354i	$0.770406\pi$
$488$	−24.1565	−	33.2486i	−1.09351	−	1.50509i
$489$	−24.0548	−	17.4768i	−1.08779	−	0.790329i
$490$	−8.60219	−	27.1764i	−0.388607	−	1.22771i
$491$	14.4890	−	10.5269i	0.653880	−	0.475072i	−0.210710	−	0.977549i	$-0.567578\pi$
$491$	14.4890	−	10.5269i	0.653880	−	0.475072i	0.864591	+	0.502477i	$0.167578\pi$
$492$	31.4764	−	96.8743i	1.41906	−	4.36743i
$493$	−30.0273	+	2.88097i	−1.35236	+	0.129753i
$494$	11.5453	−	35.5329i	0.519449	−	1.59870i
$495$	−31.6781	+	42.9110i	−1.42382	+	1.92870i
$496$	−24.4112	+	7.93167i	−1.09609	+	0.356142i
$497$	3.38090	+	10.4053i	0.151654	+	0.466743i
$498$	−25.0891	+	34.5322i	−1.12427	+	1.54742i
$499$			12.2757i			0.549534i	0.961511	+	0.274767i	$0.0886008\pi$
$499$			12.2757i			0.549534i	−0.961511	+	0.274767i	$0.911399\pi$
$500$	−53.4003	−	1.21870i	−2.38814	−	0.0545019i
$501$	−15.9069			−0.710666
$502$	−15.4862	−	11.2514i	−0.691185	−	0.502175i
$503$	−20.6856	+	6.72115i	−0.922325	+	0.299681i	−0.731420	−	0.681927i	$-0.761142\pi$
$503$	−20.6856	+	6.72115i	−0.922325	+	0.299681i	−0.190905	+	0.981609i	$0.561142\pi$
$504$	−67.2363	+	21.8464i	−2.99494	+	0.973116i
$505$	−18.9975	−	14.0245i	−0.845379	−	0.624083i
$506$	1.35111	−	4.15827i	0.0600640	−	0.184858i
$507$		−	29.6647i		−	1.31746i
$508$	−2.22618	+	6.85147i	−0.0987707	+	0.303985i
$509$	−11.8574	+	8.61491i	−0.525570	+	0.381849i	−0.818698	−	0.574224i	$-0.805304\pi$
$509$	−11.8574	+	8.61491i	−0.525570	+	0.381849i	0.293128	+	0.956073i	$0.405304\pi$
$510$	29.3247	+	68.9351i	1.29852	+	3.05250i
$511$	9.46447	+	6.87634i	0.418683	+	0.304191i
$512$	35.9316	−	26.1058i	1.58797	−	1.15372i
$513$	52.6880	+	72.5189i	2.32623	+	3.20179i
$514$	41.6674	+	30.2732i	1.83787	+	1.33529i
$515$	0.237062	−	0.711151i	0.0104462	−	0.0313371i
$516$	−20.4569	−	28.1565i	−0.900566	−	1.23952i
$517$	−7.86216	−	2.55457i	−0.345778	−	0.112350i
$518$	−5.99627			−0.263461
$519$	2.30456	−	7.09270i	0.101159	−	0.311335i
$520$	−9.55992	+	28.6784i	−0.419230	+	1.25763i
$521$	9.78031	−	3.17782i	0.428483	−	0.139223i	−0.0868327	−	0.996223i	$-0.527675\pi$
$521$	9.78031	−	3.17782i	0.428483	−	0.139223i	0.515316	+	0.857000i	$0.327675\pi$
$522$	122.119	−	39.6787i	5.34498	−	1.73669i
$523$	25.4494	+	18.4901i	1.11282	+	0.808513i	0.983106	−	0.183038i	$-0.0585930\pi$
$523$	25.4494	+	18.4901i	1.11282	+	0.808513i	0.129717	+	0.991551i	$0.458593\pi$
$524$			28.4662i			1.24355i
$525$	−18.5102	+	13.0229i	−0.807853	+	0.568368i
$526$	15.4792			0.674925
$527$	9.83507	+	5.79782i	0.428423	+	0.252557i
$528$	31.6333	+	97.3573i	1.37666	+	4.23693i
$529$	7.03777	+	21.6600i	0.305990	+	0.941740i
$530$	46.7508	−	33.4261i	2.03072	−	1.45194i
$531$	−30.0084	+	92.3563i	−1.30225	+	4.00792i
$532$		−	53.1839i		−	2.30581i
$533$	−12.1465	−	3.94664i	−0.526123	−	0.170948i
$534$	56.1956	+	77.3466i	2.43182	+	3.34711i
$535$	−1.55746	+	2.10972i	−0.0673348	+	0.0912113i
$536$	61.8252	+	44.9186i	2.67044	+	1.94019i
$537$	−26.1914	−	36.0493i	−1.13024	−	1.55564i
$538$	−11.6514	−	16.0367i	−0.502327	−	0.691393i
$539$	−10.1838	+	14.0168i	−0.438649	+	0.603748i
$540$	−72.5580	−	101.482i	−3.12240	−	4.36708i
$541$	11.2320	+	15.4595i	0.482901	+	0.664657i	0.979059	−	0.203576i	$-0.0652563\pi$
$541$	11.2320	+	15.4595i	0.482901	+	0.664657i	−0.496158	+	0.868232i	$0.665256\pi$
$542$	13.0547	−	40.1783i	0.560749	−	1.72581i
$543$	47.9991			2.05984
$544$	38.9242	+	8.64320i	1.66886	+	0.370574i
$545$	0.254702	−	33.4864i	0.0109102	−	1.43440i
$546$	6.80827	+	20.9537i	0.291367	+	0.896736i
$547$	10.9145	−	3.54634i	0.466670	−	0.151630i	−0.0662371	−	0.997804i	$-0.521099\pi$
$547$	10.9145	−	3.54634i	0.466670	−	0.151630i	0.532907	+	0.846174i	$0.321099\pi$
$548$	75.9132	+	55.1541i	3.24285	+	2.35607i
$549$		−	38.3162i		−	1.63529i
$550$	26.5015	+	37.6680i	1.13003	+	1.60617i
$551$			56.1581i			2.39241i
$552$	8.66659	+	6.29664i	0.368874	+	0.268003i
$553$	0.220731	+	0.679341i	0.00938645	+	0.0288885i
$554$	−29.3858	+	9.54803i	−1.24848	+	0.405657i
$555$	−3.34487	−	10.5673i	−0.141982	−	0.448555i
$556$	−49.6572	−	16.1346i	−2.10593	−	0.684260i
$557$	15.2455			0.645971			0.322986	−	0.946404i	$-0.395313\pi$
$557$	15.2455			0.645971			0.322986	+	0.946404i	$0.395313\pi$
$558$	−46.2189	−	15.0174i	−1.95660	−	0.635739i
$559$	−3.53039	+	2.56497i	−0.149319	+	0.108487i
$560$	−0.228637	+	30.0595i	−0.00966168	+	1.27025i
$561$	23.1230	−	39.2245i	0.976254	−	1.65606i
$562$	−5.78186	+	4.20076i	−0.243893	+	0.177199i
$563$	7.38949	−	5.36878i	0.311430	−	0.226267i	−0.421080	−	0.907024i	$-0.638349\pi$
$563$	7.38949	−	5.36878i	0.311430	−	0.226267i	0.732510	+	0.680757i	$0.238349\pi$
$564$	20.4778	−	28.1853i	0.862272	−	1.18682i
$565$	0.0992592	−	13.0499i	0.00417587	−	0.549012i
$566$	−14.7992	−	20.3693i	−0.622056	−	0.856187i
$567$	−22.3770	−	7.27072i	−0.939745	−	0.305342i
$568$			54.5500i			2.28887i
$569$	8.87589	−	27.3172i	0.372097	−	1.14520i	−0.573320	−	0.819332i	$-0.694345\pi$
$569$	8.87589	−	27.3172i	0.372097	−	1.14520i	0.945417	−	0.325864i	$-0.105655\pi$
$570$	132.963	−	42.0869i	5.56920	−	1.76283i
$571$	1.67143	−	0.543081i	0.0699472	−	0.0227272i	−0.273834	−	0.961777i	$-0.588292\pi$
$571$	1.67143	−	0.543081i	0.0699472	−	0.0227272i	0.343782	+	0.939050i	$0.388292\pi$
$572$	30.0575	−	9.76628i	1.25677	−	0.408349i
$573$	3.09545	−	4.26052i	0.129314	−	0.177986i
$574$	−25.7911			−1.07650
$575$	2.24574	+	0.767644i	0.0936538	+	0.0320130i
$576$	−44.7399			−1.86416
$577$	−12.1016	−	8.79236i	−0.503798	−	0.366031i	0.306668	−	0.951817i	$-0.400786\pi$
$577$	−12.1016	−	8.79236i	−0.503798	−	0.366031i	−0.810466	+	0.585786i	$0.800786\pi$
$578$	−21.4299	−	38.7229i	−0.891368	−	1.61066i
$579$	7.54631	+	23.2251i	0.313614	+	0.965204i
$580$	0.594458	−	78.1549i	0.0246835	−	3.24521i
$581$	7.24555	+	2.35422i	0.300596	+	0.0976696i
$582$	−26.6980			−1.10667
$583$	−33.2218	−	10.7944i	−1.37590	−	0.447059i
$584$	34.2848	+	47.1890i	1.41872	+	1.95269i
$585$	−22.9266	+	16.3922i	−0.947900	+	0.677734i
$586$	−8.78291	−	6.38115i	−0.362818	−	0.263603i
$587$	15.7078	−	11.4124i	0.648329	−	0.471038i	−0.214373	−	0.976752i	$-0.568771\pi$
$587$	15.7078	−	11.4124i	0.648329	−	0.471038i	0.862701	+	0.505714i	$0.168771\pi$
$588$	−42.9181	−	59.0717i	−1.76991	−	2.43608i
$589$	12.4931	−	17.1952i	0.514768	−	0.708518i
$590$	67.4622	+	49.8025i	2.77737	+	2.05034i
$591$	−47.7770	+	34.7120i	−1.96528	+	1.42786i
$592$	−14.0013	−	4.54928i	−0.575448	−	0.186974i
$593$	−38.2132			−1.56923			−0.784613	−	0.619986i	$-0.787138\pi$
$593$	−38.2132			−1.56923			−0.784613	+	0.619986i	$0.787138\pi$
$594$	−33.2404	+	102.304i	−1.36387	+	4.19757i
$595$	10.0842	−	8.77989i	0.413412	−	0.359940i
$596$	7.98302	+	24.5692i	0.326997	+	1.00639i
$597$	−18.8330	−	57.9620i	−0.770784	−	2.37223i
$598$	1.35799	−	1.86912i	0.0555325	−	0.0764339i
$599$	−46.2615			−1.89019			−0.945097	−	0.326791i	$-0.894033\pi$
$599$	−46.2615			−1.89019			−0.945097	+	0.326791i	$0.894033\pi$
$600$	−107.838	+	33.2339i	−4.40248	+	1.35677i
$601$			13.8025i			0.563016i	0.959559	+	0.281508i	$0.0908347\pi$
$601$			13.8025i			0.563016i	−0.959559	+	0.281508i	$0.909165\pi$
$602$	−5.17973	+	7.12929i	−0.211110	+	0.290568i
$603$	22.0169	+	67.7612i	0.896599	+	2.75945i
$604$	25.6005	+	78.7901i	1.04167	+	3.20592i
$605$	1.07421	−	3.22247i	0.0436728	−	0.131012i
$606$	−81.6073	−	26.5158i	−3.31507	−	1.07713i
$607$			6.39444i			0.259542i	0.991544	+	0.129771i	$0.0414243\pi$
$607$			6.39444i			0.259542i	−0.991544	+	0.129771i	$0.958576\pi$
$608$	22.9382	−	70.5966i	0.930268	−	2.86307i
$609$	−19.4653	−	26.7917i	−0.788774	−	1.08565i
$610$	−31.3880	−	10.4632i	−1.27086	−	0.423641i
$611$	−3.53399	−	2.56759i	−0.142970	−	0.103874i
$612$	87.9594	+	99.4883i	3.55555	+	4.02158i
$613$	19.2869	−	14.0128i	0.778991	−	0.565970i	−0.125685	−	0.992070i	$-0.540113\pi$
$613$	19.2869	−	14.0128i	0.778991	−	0.565970i	0.904676	+	0.426100i	$0.140113\pi$
$614$	−12.3624	−	8.98179i	−0.498905	−	0.362476i
$615$	−14.3869	−	45.4518i	−0.580136	−	1.83279i
$616$	30.0181	−	21.8094i	1.20946	−	0.878727i
$617$	−4.91898	−	1.59827i	−0.198031	−	0.0643441i	0.208322	−	0.978060i	$-0.433200\pi$
$617$	−4.91898	−	1.59827i	−0.198031	−	0.0643441i	−0.406353	+	0.913716i	$0.633200\pi$
$618$		−	2.72400i		−	0.109575i
$619$	−0.376030	−	0.122180i	−0.0151139	−	0.00491081i	0.301450	−	0.953482i	$-0.402529\pi$
$619$	−0.376030	−	0.122180i	−0.0151139	−	0.00491081i	−0.316564	+	0.948571i	$0.602529\pi$
$620$	−17.5686	+	23.7983i	−0.705570	+	0.955762i
$621$	1.71289	+	5.27174i	0.0687360	+	0.211548i
$622$	−37.8028	+	12.2829i	−1.51575	+	0.492498i
$623$	10.0300	−	13.8051i	0.401843	−	0.553090i
$624$			54.0921i			2.16542i
$625$	−20.6631	+	14.0726i	−0.826523	+	0.562904i
$626$		−	1.12840i		−	0.0451000i
$627$	−68.5786	−	49.8252i	−2.73876	−	1.98983i
$628$	−11.9017	−	36.6296i	−0.474929	−	1.46168i
$629$	2.60905	+	6.00599i	0.104030	+	0.239475i
$630$	−33.8030	+	45.7893i	−1.34674	+	1.82429i
$631$	2.99529	−	9.21854i	0.119240	−	0.366984i	−0.873567	−	0.486703i	$-0.838199\pi$
$631$	2.99529	−	9.21854i	0.119240	−	0.366984i	0.992808	+	0.119719i	$0.0381993\pi$
$632$			3.56144i			0.141667i
$633$	−23.1512	+	71.2519i	−0.920176	+	2.83201i
$634$	−41.5091	−	57.1324i	−1.64854	−	2.26902i
$635$	1.01752	+	3.21459i	0.0403790	+	0.127567i
$636$	86.5295	−	119.098i	3.43112	−	4.72253i
$637$	−7.40666	+	5.38125i	−0.293463	+	0.213213i
$638$	−54.5206	+	39.6116i	−2.15849	+	1.56824i
$639$	−29.8937	+	41.1452i	−1.18258	+	1.62768i
$640$	1.45935	−	4.37783i	0.0576858	−	0.173049i
$641$	15.1633	+	20.8705i	0.598914	+	0.824334i	0.995608	−	0.0936163i	$-0.0298427\pi$
$641$	15.1633	+	20.8705i	0.598914	+	0.824334i	−0.396694	+	0.917951i	$0.629843\pi$
$642$	−2.94465	+	9.06270i	−0.116216	+	0.357676i
$643$		−	29.7961i		−	1.17504i	−0.809208	−	0.587522i	$-0.800104\pi$
$643$		−	29.7961i		−	1.17504i	0.809208	−	0.587522i	$-0.199896\pi$
$644$	1.01629	−	3.12781i	0.0400474	−	0.123253i
$645$	−15.4534	−	5.15138i	−0.608477	−	0.202835i
$646$	−75.5705	+	32.8284i	−2.97328	+	1.29162i
$647$	−5.50856	−	16.9536i	−0.216564	−	0.666515i	−0.999039	−	0.0438328i	$-0.986043\pi$
$647$	−5.50856	−	16.9536i	−0.216564	−	0.666515i	0.782475	−	0.622682i	$-0.213957\pi$
$648$	−94.9068	−	68.9538i	−3.72829	−	2.70876i
$649$		−	50.9669i		−	2.00063i
$650$	7.16754	+	23.2574i	0.281134	+	0.912230i
$651$			12.5337i			0.491236i
$652$	−26.7517	+	36.8205i	−1.04768	+	1.44200i
$653$	−20.4127	+	6.63248i	−0.798810	+	0.259549i	−0.679851	−	0.733350i	$-0.737956\pi$
$653$	−20.4127	+	6.63248i	−0.798810	+	0.259549i	−0.118959	+	0.992899i	$0.537956\pi$
$654$	−37.6034	−	115.731i	−1.47041	−	4.52545i
$655$	7.74903	+	10.8380i	0.302780	+	0.423477i
$656$	−60.2220	−	19.5673i	−2.35127	−	0.763975i
$657$			54.3813i			2.12162i
$658$	−8.38954	−	2.72593i	−0.327058	−	0.106268i
$659$	36.7605	−	26.7080i	1.43198	−	1.04040i	0.442341	−	0.896847i	$-0.354148\pi$
$659$	36.7605	−	26.7080i	1.43198	−	1.04040i	0.989643	−	0.143551i	$-0.0458520\pi$
$660$	94.9130	+	70.0674i	3.69448	+	2.72737i
$661$	39.5174	+	28.7111i	1.53705	+	1.11673i	0.952152	+	0.305626i	$0.0988657\pi$
$661$	39.5174	+	28.7111i	1.53705	+	1.11673i	0.584899	+	0.811106i	$0.301134\pi$
$662$	−44.1611	+	32.0849i	−1.71637	+	1.24701i
$663$	18.0253	−	15.9365i	0.700046	−	0.618923i
$664$	30.7303	+	22.3269i	1.19257	+	0.866451i
$665$	−14.4777	−	20.2489i	−0.561420	−	0.785219i
$666$	−16.3837	−	22.5502i	−0.634854	−	0.873801i
$667$	−1.07312	+	3.30273i	−0.0415515	+	0.127882i
$668$			24.3486i			0.942074i
$669$	−38.4408	−	12.4902i	−1.48621	−	0.482898i
$670$	61.5211	+	0.467938i	2.37677	+	0.0180780i
$671$	6.21430	+	19.1257i	0.239901	+	0.738338i
$672$	13.5266	+	41.6307i	0.521801	+	1.60594i
$673$	−12.5866	+	17.3240i	−0.485179	+	0.667791i	−0.979490	−	0.201494i	$-0.935420\pi$
$673$	−12.5866	+	17.3240i	−0.485179	+	0.667791i	0.494311	+	0.869285i	$0.335420\pi$
$674$		−	35.7437i		−	1.37680i
$675$	−55.2506	−	18.8859i	−2.12660	−	0.726918i
$676$	−45.4076			−1.74645
$677$	−12.8226	+	17.6487i	−0.492811	+	0.678296i	−0.980903	−	0.194496i	$-0.937693\pi$
$677$	−12.8226	+	17.6487i	−0.492811	+	0.678296i	0.488092	+	0.872792i	$0.337693\pi$
$678$	−14.6543	−	45.1013i	−0.562795	−	1.73210i
$679$	1.47252	+	4.53194i	0.0565100	+	0.173920i
$680$	61.3456	−	26.0961i	2.35250	−	1.00074i
$681$	12.0645	−	37.1307i	0.462313	−	1.42285i
$682$	25.5060			0.976674
$683$	−10.4304	−	3.38906i	−0.399110	−	0.129679i	0.102583	−	0.994724i	$-0.467289\pi$
$683$	−10.4304	−	3.38906i	−0.399110	−	0.129679i	−0.501693	+	0.865046i	$0.667289\pi$
$684$	200.009	−	145.315i	7.64752	−	5.55625i
$685$	43.9167	+	0.334037i	1.67797	+	0.0127629i
$686$	−26.4015	+	36.3386i	−1.00801	+	1.38741i
$687$	14.1781	+	19.5145i	0.540928	+	0.744523i
$688$	−17.5035	+	12.7171i	−0.667316	+	0.484834i
$689$	−14.9330	−	10.8494i	−0.568901	−	0.413330i
$690$	8.62395	+	0.0655951i	0.328308	+	0.00249716i
$691$	15.5951	+	21.4648i	0.593266	+	0.816561i	0.995071	−	0.0991646i	$-0.0316170\pi$
$691$	15.5951	+	21.4648i	0.593266	+	0.816561i	−0.401805	+	0.915725i	$0.631617\pi$
$692$	−10.8568	−	3.52758i	−0.412712	−	0.134098i
$693$	34.5933			1.31409
$694$	−32.6657	−	10.6137i	−1.23997	−	0.402891i
$695$	−23.2983	+	7.37465i	−0.883755	+	0.279736i
$696$	−51.0234	−	157.034i	−1.93404	−	5.95235i
$697$	11.2220	+	25.8329i	0.425064	+	0.978491i
$698$	56.0480	+	40.7212i	2.12145	+	1.54132i
$699$	59.9111			2.26605
$700$	19.9341	+	28.3335i	0.753440	+	1.07091i
$701$	−11.6679			−0.440692			−0.220346	−	0.975422i	$-0.570719\pi$
$701$	−11.6679			−0.440692			−0.220346	+	0.975422i	$0.570719\pi$
$702$	−33.4099	+	45.9848i	−1.26098	+	1.73558i
$703$	11.5941	−	3.76714i	0.437278	−	0.142080i
$704$	22.3321	−	7.25614i	0.841673	−	0.273476i
$705$	0.124022	−	16.3055i	0.00467095	−	0.614102i
$706$	8.25764	−	25.4144i	0.310780	−	0.956484i
$707$			15.3151i			0.575985i
$708$	204.279	+	66.3743i	7.67728	+	2.49450i
$709$	21.8040	+	30.0107i	0.818867	+	1.12707i	0.989894	+	0.141808i	$0.0452915\pi$
$709$	21.8040	+	30.0107i	0.818867	+	1.12707i	−0.171027	+	0.985266i	$0.554708\pi$
$710$	25.5422	+	35.7241i	0.958582	+	1.34070i
$711$	−1.95169	+	2.68627i	−0.0731942	+	0.100743i
$712$	68.8310	−	50.0086i	2.57955	−	1.87415i
$713$	1.06332	−	0.772545i	0.0398215	−	0.0289320i
$714$	24.6741	−	41.8556i	0.923404	−	1.56641i
$715$	8.78535	−	11.9006i	0.328553	−	0.445057i
$716$	−55.1805	+	40.0910i	−2.06219	+	1.49827i
$717$	23.0271	+	7.48196i	0.859963	+	0.279419i
$718$	40.8923			1.52609
$719$	5.16243	+	1.67738i	0.192526	+	0.0625556i	0.403693	−	0.914894i	$-0.367726\pi$
$719$	5.16243	+	1.67738i	0.192526	+	0.0625556i	−0.211167	+	0.977450i	$0.567726\pi$
$720$	−113.670	+	81.2720i	−4.23621	+	3.02883i
$721$	−0.462393	+	0.150241i	−0.0172204	+	0.00559525i
$722$	32.1149	+	98.8394i	1.19519	+	3.67842i
$723$	−16.5912	−	12.0542i	−0.617033	−	0.448301i
$724$		−	73.4720i		−	2.73057i
$725$	−21.0489	−	29.9180i	−0.781737	−	1.11113i
$726$		−	12.3434i		−	0.458105i
$727$	−30.3009	−	22.0149i	−1.12380	−	0.816486i	−0.139017	−	0.990290i	$-0.544394\pi$
$727$	−30.3009	−	22.0149i	−1.12380	−	0.816486i	−0.984780	+	0.173804i	$0.944394\pi$
$728$	18.6468	−	6.05871i	0.691096	−	0.224551i
$729$	−0.00847193	−	0.0260739i	−0.000313775	−	0.000965700i
$730$	44.5482	+	14.8501i	1.64880	+	0.549628i
$731$	9.39462	+	2.08610i	0.347473	+	0.0771570i
$732$	−84.7499			−3.13245
$733$	−9.64304	+	29.6782i	−0.356174	+	1.09619i	0.599152	+	0.800635i	$0.295504\pi$
$733$	−9.64304	+	29.6782i	−0.356174	+	1.09619i	−0.955326	+	0.295555i	$0.904496\pi$
$734$	57.1550	+	78.6671i	2.10963	+	2.90366i
$735$	−32.4208	−	10.8075i	−1.19586	−	0.398640i
$736$	2.69805	−	3.71355i	0.0994515	−	0.136883i
$737$	−21.9797	−	30.2524i	−0.809632	−	1.11436i
$738$	−70.4691	−	96.9924i	−2.59400	−	3.57034i
$739$	6.71017	+	4.87522i	0.246838	+	0.179338i	0.704324	−	0.709879i	$-0.251250\pi$
$739$	6.71017	+	4.87522i	0.246838	+	0.179338i	−0.457487	+	0.889217i	$0.651250\pi$
$740$	−16.1753	+	5.11998i	−0.594614	+	0.188214i
$741$	−26.3282	−	36.2377i	−0.967191	−	1.33122i
$742$	−35.4502	−	11.5185i	−1.30142	−	0.422856i
$743$			27.7913i			1.01956i	0.860304	+	0.509781i	$0.170274\pi$
$743$			27.7913i			1.01956i	−0.860304	+	0.509781i	$0.829726\pi$
$744$	−19.3111	+	59.4335i	−0.707980	+	2.17894i
$745$	9.72760	+	7.18119i	0.356392	+	0.263099i
$746$	9.21784	+	28.3696i	0.337489	+	1.03868i
$747$	10.9436	+	33.6808i	0.400404	+	1.23232i
$748$	−60.0408	−	35.3943i	−2.19531	−	1.29414i
$749$	1.70079			0.0621454
$750$	−55.0607	+	72.2582i	−2.01053	+	2.63850i
$751$		−	47.4546i		−	1.73164i	−0.500353	−	0.865822i	$-0.666796\pi$
$751$		−	47.4546i		−	1.73164i	0.500353	−	0.865822i	$-0.333204\pi$
$752$	−17.5214	−	12.7301i	−0.638940	−	0.464217i
$753$	−21.8259	+	7.09168i	−0.795381	+	0.258435i
$754$	−33.8674	+	11.0042i	−1.23338	+	0.400749i
$755$	31.1951	+	23.0291i	1.13531	+	0.838115i
$756$	−25.0031	+	76.9518i	−0.909355	+	2.79871i
$757$	−2.23404			−0.0811974			−0.0405987	−	0.999176i	$-0.512927\pi$
$757$	−2.23404			−0.0811974			−0.0405987	+	0.999176i	$0.512927\pi$
$758$	2.74552	+	0.892075i	0.0997220	+	0.0324016i
$759$	−3.08109	−	4.24075i	−0.111836	−	0.153930i
$760$	−37.4533	−	118.324i	−1.35857	−	4.29207i
$761$	26.6219	+	19.3419i	0.965041	+	0.701144i	0.954316	−	0.298799i	$-0.0965860\pi$
$761$	26.6219	+	19.3419i	0.965041	+	0.701144i	0.0107253	+	0.999942i	$0.496586\pi$
$762$	7.20183	+	9.91247i	0.260895	+	0.359091i
$763$	−17.5712	+	12.7662i	−0.636119	+	0.462167i
$764$	−6.52155	−	4.73819i	−0.235942	−	0.171422i
$765$	60.5717	+	13.9343i	2.18997	+	0.503797i
$766$	−31.5116	+	22.8945i	−1.13856	+	0.827213i
$767$	8.32229	−	25.6134i	0.300500	−	0.924845i
$768$		−	58.1956i		−	2.09995i
$769$	−0.611658	+	1.88249i	−0.0220570	+	0.0678844i	−0.961479	−	0.274878i	$-0.911363\pi$
$769$	−0.611658	+	1.88249i	−0.0220570	+	0.0678844i	0.939422	+	0.342762i	$0.111363\pi$
$770$	9.44655	−	28.3383i	0.340430	−	1.02124i
$771$	58.7251	−	19.0809i	2.11493	−	0.687183i
$772$	35.5506	−	11.5511i	1.27949	−	0.415733i </

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-2.10617 - 1.53022i) q^{2} +(-2.96838 + 0.964486i) q^{3} +(1.47633 + 4.54369i) q^{4} +(1.79897 + 1.32805i) q^{5} +(7.72779 + 2.51091i) q^{6} -1.45026i q^{7} +(2.23447 - 6.87699i) q^{8} +(5.45401 - 3.96257i) q^{9} +(-1.75672 - 5.54991i) q^{10} +(-2.07972 + 2.86249i) q^{11} +(-8.76465 - 12.0635i) q^{12} +(-1.51257 + 1.09895i) q^{13} +(-2.21922 + 3.05450i) q^{14} +(-6.62091 - 2.20708i) q^{15} +(-7.49928 + 5.44855i) q^{16} +(4.02507 + 0.893775i) q^{17} -17.5507 q^{18} +(2.37199 - 7.30024i) q^{19} +(-3.37836 + 10.1346i) q^{20} +(1.39876 + 4.30494i) q^{21} +(8.76048 - 2.84645i) q^{22} +(0.279000 - 0.384010i) q^{23} +22.5686i q^{24} +(1.47257 + 4.77824i) q^{25} +4.86736 q^{26} +(-6.86407 + 9.44758i) q^{27} +(6.58955 - 2.14107i) q^{28} +(-6.95806 + 2.26081i) q^{29} +(10.5674 + 14.7799i) q^{30} +(2.63346 + 0.855662i) q^{31} +9.67045 q^{32} +(3.41258 - 10.5028i) q^{33} +(-7.10979 - 8.04168i) q^{34} +(1.92602 - 2.60898i) q^{35} +(26.0566 + 18.9312i) q^{36} +(0.933506 + 1.28486i) q^{37} +(-16.1668 + 11.7459i) q^{38} +(3.42997 - 4.72095i) q^{39} +(13.1527 - 9.40399i) q^{40} +(4.01518 + 5.52642i) q^{41} +(3.64149 - 11.2073i) q^{42} +2.33403 q^{43} +(-16.0766 - 5.22361i) q^{44} +(15.0741 + 0.114656i) q^{45} +(-1.17524 + 0.381859i) q^{46} +(0.721991 + 2.22206i) q^{47} +(17.0057 - 23.4063i) q^{48} +4.89673 q^{49} +(4.21027 - 12.3171i) q^{50} +(-12.8100 + 1.22906i) q^{51} +(-7.22634 - 5.25024i) q^{52} +(3.05079 + 9.38937i) q^{53} +(28.9137 - 9.39464i) q^{54} +(-7.54288 + 2.38756i) q^{55} +(-9.97345 - 3.24057i) q^{56} +23.9577i q^{57} +(18.1144 + 5.88572i) q^{58} +(-11.6536 + 8.46682i) q^{59} +(0.253602 - 33.3417i) q^{60} +(3.34074 - 4.59813i) q^{61} +(-4.23715 - 5.83194i) q^{62} +(-5.74678 - 7.90976i) q^{63} +(-5.36902 - 3.90082i) q^{64} +(-4.18053 - 0.0317977i) q^{65} +(-23.2591 + 16.8987i) q^{66} +(-3.26587 + 10.0513i) q^{67} +(1.88131 + 19.6082i) q^{68} +(-0.457806 + 1.40898i) q^{69} +(-8.04884 + 2.54771i) q^{70} +(-7.17479 + 2.33123i) q^{71} +(-15.0637 - 46.3614i) q^{72} +(-4.74144 + 6.52603i) q^{73} -4.13460i q^{74} +(-8.97970 - 12.7634i) q^{75} +36.6718 q^{76} +(4.15137 + 3.01615i) q^{77} +(-14.4482 + 4.69450i) q^{78} +(-0.468426 + 0.152201i) q^{79} +(-20.7269 - 0.157652i) q^{80} +(5.01338 - 15.4296i) q^{81} -17.7837i q^{82} +(-1.62330 + 4.99602i) q^{83} +(-17.4953 + 12.7111i) q^{84} +(6.05399 + 6.95336i) q^{85} +(-4.91585 - 3.57158i) q^{86} +(18.4737 - 13.4219i) q^{87} +(15.0382 + 20.6984i) q^{88} +(9.51902 + 6.91597i) q^{89} +(-31.5731 - 23.3081i) q^{90} +(1.59377 + 2.19363i) q^{91} +(2.15672 + 0.700761i) q^{92} -8.64238 q^{93} +(1.87961 - 5.78483i) q^{94} +(13.9622 - 9.98277i) q^{95} +(-28.7056 + 9.32701i) q^{96} +(-3.12491 + 1.01534i) q^{97} +(-10.3133 - 7.49308i) q^{98} +23.8531i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 168 q - 8 q^{2} - 44 q^{4} - 4 q^{8} + 28 q^{9} - 18 q^{13} - 10 q^{15} - 28 q^{16} + 2 q^{17} - 60 q^{18} - 8 q^{19} + 32 q^{21} + 6 q^{25} + 52 q^{26} - 54 q^{30} + 44 q^{32} - 24 q^{33} + 26 q^{35} + 34 q^{36}+ \cdots - 36 q^{98}+O(q^{100}) \) 168 * q - 8 * q^2 - 44 * q^4 - 4 * q^8 + 28 * q^9 - 18 * q^13 - 10 * q^15 - 28 * q^16 + 2 * q^17 - 60 * q^18 - 8 * q^19 + 32 * q^21 + 6 * q^25 + 52 * q^26 - 54 * q^30 + 44 * q^32 - 24 * q^33 + 26 * q^35 + 34 * q^36 - 18 * q^38 + 80 * q^42 - 8 * q^43 - 40 * q^47 - 84 * q^49 - 82 * q^50 - 36 * q^51 - 30 * q^52 - 42 * q^53 - 18 * q^55 - 18 * q^59 + 28 * q^60 - 16 * q^64 - 140 * q^66 - 62 * q^67 + 144 * q^68 + 44 * q^69 + 4 * q^70 - 6 * q^72 + 72 * q^76 + 48 * q^77 - 28 * q^81 - 14 * q^83 + 24 * q^84 + 62 * q^85 + 82 * q^86 + 48 * q^87 + 90 * q^89 - 224 * q^93 + 26 * q^94 - 36 * q^98

Introduction

L-functions

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