LMFDB - Embedded newform 520.2.ca.a.101.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [520,2,Mod(101,520)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(520, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 0, 5]))

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

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

chi := DirichletCharacter("520.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 520 = 2^{3} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	520.ca (of order $6$, degree $2$, 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:	$4.15222090511$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$28$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.6
Character	$\chi$	$=$	520.101
Dual form			520.2.ca.a.381.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.09478 + 0.895236i) q^{2} +(-0.815452 + 0.470802i) q^{3} +(0.397104 - 1.96018i) q^{4} -1.00000 q^{5} +(0.471265 - 1.24545i) q^{6} +(-2.82007 - 1.62817i) q^{7} +(1.32008 + 2.50148i) q^{8} +(-1.05669 + 1.83024i) q^{9} +(1.09478 - 0.895236i) q^{10} +(2.28794 + 3.96283i) q^{11} +(0.599037 + 1.78539i) q^{12} +(-2.20289 + 2.85434i) q^{13} +(4.54496 - 0.742136i) q^{14} +(0.815452 - 0.470802i) q^{15} +(-3.68462 - 1.55679i) q^{16} +(3.64340 - 6.31055i) q^{17} +(-0.481651 - 2.94971i) q^{18} +(3.24655 - 5.62320i) q^{19} +(-0.397104 + 1.96018i) q^{20} +3.06618 q^{21} +(-6.05247 - 2.29020i) q^{22} +(-3.65810 - 6.33601i) q^{23} +(-2.25416 - 1.41834i) q^{24} +1.00000 q^{25} +(-0.143626 - 5.09700i) q^{26} -4.81478i q^{27} +(-4.31136 + 4.88129i) q^{28} +(3.33584 - 1.92595i) q^{29} +(-0.471265 + 1.24545i) q^{30} -2.78436i q^{31} +(5.42756 - 1.59425i) q^{32} +(-3.73142 - 2.15433i) q^{33} +(1.66070 + 10.1704i) q^{34} +(2.82007 + 1.62817i) q^{35} +(3.16799 + 2.79810i) q^{36} +(2.57569 + 4.46122i) q^{37} +(1.47981 + 9.06262i) q^{38} +(0.452520 - 3.36471i) q^{39} +(-1.32008 - 2.50148i) q^{40} +(3.47276 - 2.00500i) q^{41} +(-3.35680 + 2.74495i) q^{42} +(-6.09210 - 3.51727i) q^{43} +(8.67642 - 2.91112i) q^{44} +(1.05669 - 1.83024i) q^{45} +(9.67705 + 3.66170i) q^{46} -7.32283i q^{47} +(3.73757 - 0.465234i) q^{48} +(1.80186 + 3.12092i) q^{49} +(-1.09478 + 0.895236i) q^{50} +6.86127i q^{51} +(4.72026 + 5.45153i) q^{52} +3.33709i q^{53} +(4.31036 + 5.27114i) q^{54} +(-2.28794 - 3.96283i) q^{55} +(0.350102 - 9.20365i) q^{56} +6.11393i q^{57} +(-1.92785 + 5.09486i) q^{58} +(0.960988 - 1.66448i) q^{59} +(-0.599037 - 1.78539i) q^{60} +(-4.19212 - 2.42032i) q^{61} +(2.49266 + 3.04827i) q^{62} +(5.95989 - 3.44094i) q^{63} +(-4.51477 + 6.60431i) q^{64} +(2.20289 - 2.85434i) q^{65} +(6.01373 - 0.981968i) q^{66} +(0.105635 + 0.182965i) q^{67} +(-10.9230 - 9.64766i) q^{68} +(5.96601 + 3.44448i) q^{69} +(-4.54496 + 0.742136i) q^{70} +(-5.29581 - 3.05754i) q^{71} +(-5.97323 - 0.227218i) q^{72} +7.65793i q^{73} +(-6.81367 - 2.57822i) q^{74} +(-0.815452 + 0.470802i) q^{75} +(-9.73326 - 8.59683i) q^{76} -14.9006i q^{77} +(2.51679 + 4.08874i) q^{78} +14.7003 q^{79} +(3.68462 + 1.55679i) q^{80} +(-0.903270 - 1.56451i) q^{81} +(-2.00697 + 5.30398i) q^{82} +7.55031 q^{83} +(1.21759 - 6.01026i) q^{84} +(-3.64340 + 6.31055i) q^{85} +(9.81832 - 1.60321i) q^{86} +(-1.81348 + 3.14104i) q^{87} +(-6.89266 + 10.9545i) q^{88} +(-4.09878 + 2.36643i) q^{89} +(0.481651 + 2.94971i) q^{90} +(10.8597 - 4.46278i) q^{91} +(-13.8724 + 4.65448i) q^{92} +(1.31088 + 2.27051i) q^{93} +(6.55566 + 8.01692i) q^{94} +(-3.24655 + 5.62320i) q^{95} +(-3.67534 + 3.85534i) q^{96} +(7.27269 + 4.19889i) q^{97} +(-4.76661 - 1.80364i) q^{98} -9.67060 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 6 q^{4} - 56 q^{5} - 5 q^{6} + 28 q^{9} + 8 q^{11} + 6 q^{12} - 4 q^{14} - 10 q^{16} - 18 q^{18} + 16 q^{19} + 6 q^{20} - 6 q^{22} + 12 q^{23} + 2 q^{24} + 56 q^{25} + 11 q^{26} + 6 q^{28} + 5 q^{30}+ \cdots + 48 q^{99}+O(q^{100}) $ 56 * q - 6 * q^4 - 56 * q^5 - 5 * q^6 + 28 * q^9 + 8 * q^11 + 6 * q^12 - 4 * q^14 - 10 * q^16 - 18 * q^18 + 16 * q^19 + 6 * q^20 - 6 * q^22 + 12 * q^23 + 2 * q^24 + 56 * q^25 + 11 * q^26 + 6 * q^28 + 5 * q^30 + 16 * q^34 - 21 * q^36 - 4 * q^37 - 24 * q^39 + 29 * q^42 - 24 * q^44 - 28 * q^45 - 11 * q^46 + 3 * q^48 + 20 * q^49 + 18 * q^52 - 49 * q^54 - 8 * q^55 + 61 * q^56 - 47 * q^58 + 16 * q^59 - 6 * q^60 - 2 * q^62 - 30 * q^64 + 14 * q^66 + 36 * q^67 + 33 * q^68 + 4 * q^70 - 51 * q^72 - 2 * q^74 - 48 * q^76 - 35 * q^78 + 10 * q^80 - 28 * q^81 - 21 * q^82 - 40 * q^83 - 61 * q^84 + 28 * q^86 - 36 * q^87 + 41 * q^88 + 18 * q^90 - 16 * q^91 - 18 * q^92 - 41 * q^94 - 16 * q^95 + 48 * q^96 + 24 * q^97 + 28 * q^98 + 48 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/520\mathbb{Z}\right)^\times$.

$n$	$41$	$261$	$391$	$417$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$1$	$1$

Coefficient data

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

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

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

$2$	−1.09478	+	0.895236i	−0.774129	+	0.633028i
$2$	−1.09478	+	0.895236i	−0.774129	+	0.633028i
$3$	−0.815452	+	0.470802i	−0.470802	+	0.271817i	−0.716575	−	0.697510i	$-0.754291\pi$
$3$	−0.815452	+	0.470802i	−0.470802	+	0.271817i	0.245774	+	0.969327i	$0.420958\pi$
$4$	0.397104	−	1.96018i	0.198552	−	0.980090i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$	0.471265	−	1.24545i	0.192393	−	0.508452i
$7$	−2.82007	−	1.62817i	−1.06589	−	0.615390i	−0.138832	−	0.990316i	$-0.544335\pi$
$7$	−2.82007	−	1.62817i	−1.06589	−	0.615390i	−0.927055	+	0.374926i	$0.877668\pi$
$8$	1.32008	+	2.50148i	0.466719	+	0.884405i
$9$	−1.05669	+	1.83024i	−0.352231	+	0.610081i
$10$	1.09478	−	0.895236i	0.346201	−	0.283099i
$11$	2.28794	+	3.96283i	0.689840	+	1.19484i	0.971889	+	0.235439i	$0.0756527\pi$
$11$	2.28794	+	3.96283i	0.689840	+	1.19484i	−0.282049	+	0.959400i	$0.591014\pi$
$12$	0.599037	+	1.78539i	0.172927	+	0.515398i
$13$	−2.20289	+	2.85434i	−0.610971	+	0.791653i
$13$	−2.20289	+	2.85434i	−0.610971	+	0.791653i
$14$	4.54496	−	0.742136i	1.21469	−	0.198344i
$15$	0.815452	−	0.470802i	0.210549	−	0.121560i
$16$	−3.68462	−	1.55679i	−0.921154	−	0.389198i
$17$	3.64340	−	6.31055i	0.883654	−	1.53053i	0.0364049	−	0.999337i	$-0.488409\pi$
$17$	3.64340	−	6.31055i	0.883654	−	1.53053i	0.847249	−	0.531196i	$-0.178257\pi$
$18$	−0.481651	−	2.94971i	−0.113526	−	0.695253i
$19$	3.24655	−	5.62320i	0.744811	−	1.29005i	−0.205472	−	0.978663i	$-0.565873\pi$
$19$	3.24655	−	5.62320i	0.744811	−	1.29005i	0.950283	−	0.311387i	$-0.100794\pi$
$20$	−0.397104	+	1.96018i	−0.0887952	+	0.438310i
$21$	3.06618			0.669095
$22$	−6.05247	−	2.29020i	−1.29039	−	0.488271i
$23$	−3.65810	−	6.33601i	−0.762766	−	1.32115i	−0.941420	−	0.337237i	$-0.890507\pi$
$23$	−3.65810	−	6.33601i	−0.762766	−	1.32115i	0.178654	−	0.983912i	$-0.442826\pi$
$24$	−2.25416	−	1.41834i	−0.460129	−	0.289517i
$25$	1.00000			0.200000
$26$	−0.143626	−	5.09700i	−0.0281674	−	0.999603i
$27$		−	4.81478i		−	0.926605i
$28$	−4.31136	+	4.88129i	−0.814771	+	0.922478i
$29$	3.33584	−	1.92595i	0.619450	−	0.357640i	−0.157205	−	0.987566i	$-0.550248\pi$
$29$	3.33584	−	1.92595i	0.619450	−	0.357640i	0.776655	+	0.629926i	$0.216915\pi$
$30$	−0.471265	+	1.24545i	−0.0860409	+	0.227387i
$31$		−	2.78436i		−	0.500086i	−0.968235	−	0.250043i	$-0.919555\pi$
$31$		−	2.78436i		−	0.500086i	0.968235	−	0.250043i	$-0.0804448\pi$
$32$	5.42756	−	1.59425i	0.959465	−	0.281827i
$33$	−3.73142	−	2.15433i	−0.649556	−	0.375021i
$34$	1.66070	+	10.1704i	0.284808	+	1.74421i
$35$	2.82007	+	1.62817i	0.476679	+	0.275211i
$36$	3.16799	+	2.79810i	0.527999	+	0.466351i
$37$	2.57569	+	4.46122i	0.423440	+	0.733420i	0.996273	−	0.0862519i	$-0.0274890\pi$
$37$	2.57569	+	4.46122i	0.423440	+	0.733420i	−0.572833	+	0.819672i	$0.694156\pi$
$38$	1.47981	+	9.06262i	0.240058	+	1.47015i
$39$	0.452520	−	3.36471i	0.0724612	−	0.538784i
$40$	−1.32008	−	2.50148i	−0.208723	−	0.395518i
$41$	3.47276	−	2.00500i	0.542354	−	0.313128i	−0.203679	−	0.979038i	$-0.565290\pi$
$41$	3.47276	−	2.00500i	0.542354	−	0.313128i	0.746032	+	0.665910i	$0.231956\pi$
$42$	−3.35680	+	2.74495i	−0.517966	+	0.423555i
$43$	−6.09210	−	3.51727i	−0.929036	−	0.536379i	−0.0425296	−	0.999095i	$-0.513542\pi$
$43$	−6.09210	−	3.51727i	−0.929036	−	0.536379i	−0.886507	+	0.462716i	$0.846875\pi$
$44$	8.67642	−	2.91112i	1.30802	−	0.438868i
$45$	1.05669	−	1.83024i	0.157522	−	0.272837i
$46$	9.67705	+	3.66170i	1.42680	+	0.539888i
$47$		−	7.32283i		−	1.06814i	−0.845439	−	0.534072i	$-0.820661\pi$
$47$		−	7.32283i		−	1.06814i	0.845439	−	0.534072i	$-0.179339\pi$
$48$	3.73757	−	0.465234i	0.539472	−	0.0671508i
$49$	1.80186	+	3.12092i	0.257409	+	0.445845i
$50$	−1.09478	+	0.895236i	−0.154826	+	0.126606i
$51$			6.86127i			0.960770i
$52$	4.72026	+	5.45153i	0.654582	+	0.755991i
$53$			3.33709i			0.458385i	0.973381	+	0.229192i	$0.0736085\pi$
$53$			3.33709i			0.458385i	−0.973381	+	0.229192i	$0.926392\pi$
$54$	4.31036	+	5.27114i	0.586566	+	0.717312i
$55$	−2.28794	−	3.96283i	−0.308506	−	0.534348i
$56$	0.350102	−	9.20365i	0.0467843	−	1.22989i
$57$			6.11393i			0.809810i
$58$	−1.92785	+	5.09486i	−0.253139	+	0.668988i
$59$	0.960988	−	1.66448i	0.125110	−	0.216697i	−0.796666	−	0.604420i	$-0.793405\pi$
$59$	0.960988	−	1.66448i	0.125110	−	0.216697i	0.921776	+	0.387723i	$0.126738\pi$
$60$	−0.599037	−	1.78539i	−0.0773353	−	0.230493i
$61$	−4.19212	−	2.42032i	−0.536745	−	0.309890i	0.207014	−	0.978338i	$-0.433626\pi$
$61$	−4.19212	−	2.42032i	−0.536745	−	0.309890i	−0.743759	+	0.668448i	$0.766959\pi$
$62$	2.49266	+	3.04827i	0.316568	+	0.387131i
$63$	5.95989	−	3.44094i	0.750875	−	0.433518i
$64$	−4.51477	+	6.60431i	−0.564346	+	0.825538i
$65$	2.20289	−	2.85434i	0.273235	−	0.354038i
$66$	6.01373	−	0.981968i	0.740239	−	0.120872i
$67$	0.105635	+	0.182965i	0.0129054	+	0.0223528i	0.872406	−	0.488782i	$-0.162559\pi$
$67$	0.105635	+	0.182965i	0.0129054	+	0.0223528i	−0.859501	+	0.511135i	$0.829225\pi$
$68$	−10.9230	−	9.64766i	−1.32461	−	1.16995i
$69$	5.96601	+	3.44448i	0.718223	+	0.414666i
$70$	−4.54496	+	0.742136i	−0.543227	+	0.0887023i
$71$	−5.29581	−	3.05754i	−0.628497	−	0.362863i	0.151673	−	0.988431i	$-0.451534\pi$
$71$	−5.29581	−	3.05754i	−0.628497	−	0.362863i	−0.780170	+	0.625568i	$0.784867\pi$
$72$	−5.97323	−	0.227218i	−0.703952	−	0.0267779i
$73$			7.65793i			0.896293i	0.893960	+	0.448146i	$0.147916\pi$
$73$			7.65793i			0.896293i	−0.893960	+	0.448146i	$0.852084\pi$
$74$	−6.81367	−	2.57822i	−0.792073	−	0.299713i
$75$	−0.815452	+	0.470802i	−0.0941603	+	0.0543635i
$76$	−9.73326	−	8.59683i	−1.11648	−	0.986124i
$77$		−	14.9006i		−	1.69808i
$78$	2.51679	+	4.08874i	0.284971	+	0.462958i
$79$	14.7003			1.65392			0.826959	−	0.562262i	$-0.190069\pi$
$79$	14.7003			1.65392			0.826959	+	0.562262i	$0.190069\pi$
$80$	3.68462	+	1.55679i	0.411953	+	0.174055i
$81$	−0.903270	−	1.56451i	−0.100363	−	0.173834i
$82$	−2.00697	+	5.30398i	−0.221633	+	0.585726i
$83$	7.55031			0.828754			0.414377	−	0.910105i	$-0.363999\pi$
$83$	7.55031			0.828754			0.414377	+	0.910105i	$0.363999\pi$
$84$	1.21759	−	6.01026i	0.132850	−	0.655773i
$85$	−3.64340	+	6.31055i	−0.395182	+	0.684475i
$86$	9.81832	−	1.60321i	1.05874	−	0.172879i
$87$	−1.81348	+	3.14104i	−0.194425	+	0.336755i
$88$	−6.89266	+	10.9545i	−0.734760	+	1.16775i
$89$	−4.09878	+	2.36643i	−0.434470	+	0.250841i	−0.701249	−	0.712916i	$-0.747374\pi$
$89$	−4.09878	+	2.36643i	−0.434470	+	0.250841i	0.266779	+	0.963758i	$0.414041\pi$
$90$	0.481651	+	2.94971i	0.0507705	+	0.310927i
$91$	10.8597	−	4.46278i	1.13840	−	0.467826i
$92$	−13.8724	+	4.65448i	−1.44629	+	0.485263i
$93$	1.31088	+	2.27051i	0.135932	+	0.235441i
$94$	6.55566	+	8.01692i	0.676165	+	0.826882i
$95$	−3.24655	+	5.62320i	−0.333089	+	0.576928i
$96$	−3.67534	+	3.85534i	−0.375112	+	0.393484i
$97$	7.27269	+	4.19889i	0.738430	+	0.426333i	0.821498	−	0.570211i	$-0.193139\pi$
$97$	7.27269	+	4.19889i	0.738430	+	0.426333i	−0.0830682	+	0.996544i	$0.526472\pi$
$98$	−4.76661	−	1.80364i	−0.481500	−	0.182195i
$99$	−9.67060			−0.971932
$100$	0.397104	−	1.96018i	0.0397104	−	0.196018i
$101$	−8.39604	+	4.84746i	−0.835437	+	0.482340i	−0.855711	−	0.517455i	$-0.826880\pi$
$101$	−8.39604	+	4.84746i	−0.835437	+	0.482340i	0.0202735	+	0.999794i	$0.493546\pi$
$102$	−6.14246	−	7.51161i	−0.608194	−	0.743760i
$103$	−9.65843			−0.951673			−0.475837	−	0.879534i	$-0.657855\pi$
$103$	−9.65843			−0.951673			−0.475837	+	0.879534i	$0.657855\pi$
$104$	−10.0481	−	1.74250i	−0.985294	−	0.170867i
$105$	−3.06618			−0.299228
$106$	−2.98748	−	3.65339i	−0.290170	−	0.354849i
$107$	−2.53186	+	1.46177i	−0.244764	+	0.141314i	−0.617364	−	0.786677i	$-0.711800\pi$
$107$	−2.53186	+	1.46177i	−0.244764	+	0.141314i	0.372601	+	0.927992i	$0.378466\pi$
$108$	−9.43784	−	1.91197i	−0.908156	−	0.183979i
$109$	1.12321			0.107584			0.0537921	−	0.998552i	$-0.482869\pi$
$109$	1.12321			0.107584			0.0537921	+	0.998552i	$0.482869\pi$
$110$	6.05247	+	2.29020i	0.577081	+	0.218362i
$111$	−4.20070	−	2.42528i	−0.398713	−	0.230197i
$112$	7.85616	+	10.3894i	0.742337	+	0.981709i
$113$	4.10521	−	7.11043i	0.386186	−	0.668893i	−0.605747	−	0.795657i	$-0.707126\pi$
$113$	4.10521	−	7.11043i	0.386186	−	0.668893i	0.991933	+	0.126764i	$0.0404591\pi$
$114$	−5.47341	−	6.69344i	−0.512632	−	0.626898i
$115$	3.65810	+	6.33601i	0.341119	+	0.590836i
$116$	−2.45053	−	7.30365i	−0.227526	−	0.678127i
$117$	−2.89637	−	7.04798i	−0.267770	−	0.651586i
$118$	0.438029	+	2.68256i	0.0403238	+	0.246949i
$119$	−20.5493	+	11.8641i	−1.88375	+	1.08758i
$120$	2.25416	+	1.41834i	0.205776	+	0.129476i
$121$	−4.96936	+	8.60718i	−0.451760	+	0.782471i
$122$	6.75622	−	1.10321i	0.611679	−	0.0998797i
$123$	−1.88791	+	3.26996i	−0.170227	+	0.294842i
$124$	−5.45785	−	1.10568i	−0.490129	−	0.0992931i
$125$	−1.00000			−0.0894427
$126$	−3.44433	+	9.10260i	−0.306846	+	0.810924i
$127$	−2.26541	−	3.92381i	−0.201023	−	0.348182i	0.747835	−	0.663884i	$-0.231093\pi$
$127$	−2.26541	−	3.92381i	−0.201023	−	0.348182i	−0.948858	+	0.315702i	$0.897760\pi$
$128$	−0.969718	−	11.2721i	−0.0857117	−	0.996320i
$129$	6.62375			0.583189
$130$	0.143626	+	5.09700i	0.0125969	+	0.447036i
$131$		−	18.1375i		−	1.58468i	−0.610078	−	0.792342i	$-0.708862\pi$
$131$		−	18.1375i		−	1.58468i	0.610078	−	0.792342i	$-0.291138\pi$
$132$	−5.70464	+	6.45875i	−0.496525	+	0.562162i
$133$	−18.3110	+	10.5719i	−1.58777	+	0.916698i
$134$	−0.279445	−	0.105739i	−0.0241403	−	0.00913446i
$135$			4.81478i			0.414390i
$136$	20.5953	+	0.783432i	1.76603	+	0.0671788i
$137$	10.3515	+	5.97644i	0.884389	+	0.510602i	0.872103	−	0.489323i	$-0.162756\pi$
$137$	10.3515	+	5.97644i	0.884389	+	0.510602i	0.0122856	+	0.999925i	$0.496089\pi$
$138$	−9.61511	+	1.57003i	−0.818493	+	0.133650i
$139$	−17.3034	−	9.99011i	−1.46765	−	0.847350i	−0.468310	−	0.883564i	$-0.655137\pi$
$139$	−17.3034	−	9.99011i	−1.46765	−	0.847350i	−0.999344	+	0.0362139i	$0.988470\pi$
$140$	4.31136	−	4.88129i	0.364377	−	0.412545i
$141$	3.44760	+	5.97142i	0.290340	+	0.502884i
$142$	8.53498	−	1.39366i	0.716240	−	0.116953i
$143$	−16.3514	−	2.19910i	−1.36737	−	0.183898i
$144$	6.74281	−	5.09870i	0.561901	−	0.424891i
$145$	−3.33584	+	1.92595i	−0.277026	+	0.159941i
$146$	−6.85566	−	8.38378i	−0.567378	−	0.693846i
$147$	−2.93867	−	1.69664i	−0.242377	−	0.139936i
$148$	9.76761	−	3.27724i	0.802893	−	0.269388i
$149$	6.07088	−	10.5151i	0.497346	−	0.861429i	−0.502649	−	0.864491i	$-0.667641\pi$
$149$	6.07088	−	10.5151i	0.497346	−	0.861429i	0.999995	+	0.00306162i	$0.000974545\pi$
$150$	0.471265	−	1.24545i	0.0384787	−	0.101690i
$151$		−	2.19357i		−	0.178510i	−0.996009	−	0.0892550i	$-0.971551\pi$
$151$		−	2.19357i		−	0.178510i	0.996009	−	0.0892550i	$-0.0284486\pi$
$152$	18.3520	+	0.698100i	1.48854	+	0.0566234i
$153$	7.69990	+	13.3366i	0.622500	+	1.07820i
$154$	13.3396	+	16.3130i	1.07493	+	1.31454i
$155$			2.78436i			0.223645i
$156$	−6.41573	−	2.22316i	−0.513670	−	0.177995i
$157$		−	21.5797i		−	1.72225i	−0.508395	−	0.861124i	$-0.669761\pi$
$157$		−	21.5797i		−	1.72225i	0.508395	−	0.861124i	$-0.330239\pi$
$158$	−16.0937	+	13.1603i	−1.28035	+	1.04698i
$159$	−1.57111	−	2.72124i	−0.124597	−	0.215808i
$160$	−5.42756	+	1.59425i	−0.429086	+	0.126037i
$161$			23.8240i			1.87759i
$162$	2.38949	+	0.904160i	0.187736	+	0.0710375i
$163$	−7.84916	+	13.5951i	−0.614794	+	1.06485i	0.375627	+	0.926771i	$0.377427\pi$
$163$	−7.84916	+	13.5951i	−0.614794	+	1.06485i	−0.990421	+	0.138083i	$0.955906\pi$
$164$	−2.55111	−	7.60342i	−0.199208	−	0.593728i
$165$	3.73142	+	2.15433i	0.290490	+	0.167715i
$166$	−8.26596	+	6.75931i	−0.641563	+	0.524624i
$167$	8.80939	−	5.08611i	0.681691	−	0.393575i	−0.118801	−	0.992918i	$-0.537905\pi$
$167$	8.80939	−	5.08611i	0.681691	−	0.393575i	0.800492	+	0.599343i	$0.204572\pi$
$168$	4.04760	+	7.66997i	0.312279	+	0.591751i
$169$	−3.29457	−	12.5756i	−0.253428	−	0.967354i
$170$	−1.66070	−	10.1704i	−0.127370	−	0.780033i
$171$	6.86121	+	11.8840i	0.524690	+	0.908790i
$172$	−9.31369	+	10.5449i	−0.710162	+	0.804040i
$173$	15.2799	+	8.82187i	1.16171	+	0.670714i	0.951714	−	0.306987i	$-0.0993210\pi$
$173$	15.2799	+	8.82187i	1.16171	+	0.670714i	0.209998	+	0.977702i	$0.432654\pi$
$174$	−0.826603	−	5.06225i	−0.0626646	−	0.383768i
$175$	−2.82007	−	1.62817i	−0.213177	−	0.123078i
$176$	−2.26089	−	18.1634i	−0.170421	−	1.36912i
$177$			1.80974i			0.136028i
$178$	2.36876	−	6.26011i	0.177546	−	0.469215i
$179$	1.09869	−	0.634330i	0.0821201	−	0.0474120i	−0.458378	−	0.888758i	$-0.651569\pi$
$179$	1.09869	−	0.634330i	0.0821201	−	0.0474120i	0.540498	+	0.841345i	$0.318236\pi$
$180$	−3.16799	−	2.79810i	−0.236128	−	0.208558i
$181$		−	13.4062i		−	0.996473i	−0.867041	−	0.498237i	$-0.833981\pi$
$181$		−	13.4062i		−	0.996473i	0.867041	−	0.498237i	$-0.166019\pi$
$182$	−7.89373	+	14.6077i	−0.585122	+	1.08280i
$183$	4.55796			0.336934
$184$	11.0204	−	17.5147i	0.812434	−	1.29120i
$185$	−2.57569	−	4.46122i	−0.189368	−	0.327995i
$186$	−3.46778	−	1.31217i	−0.254270	−	0.0962132i
$187$	33.3435			2.43832
$188$	−14.3541	−	2.90793i	−1.04688	−	0.212082i
$189$	−7.83927	+	13.5780i	−0.570223	+	0.987655i
$190$	−1.47981	−	9.06262i	−0.107357	−	0.657472i
$191$	0.546815	−	0.947111i	0.0395661	−	0.0685306i	−0.845564	−	0.533874i	$-0.820736\pi$
$191$	0.546815	−	0.947111i	0.0395661	−	0.0685306i	0.885130	+	0.465343i	$0.154069\pi$
$192$	0.572261	−	7.51106i	0.0412994	−	0.542064i
$193$	−17.4409	+	10.0695i	−1.25543	+	0.724821i	−0.972182	−	0.234227i	$-0.924744\pi$
$193$	−17.4409	+	10.0695i	−1.25543	+	0.724821i	−0.283244	+	0.959048i	$0.591411\pi$
$194$	−11.7210	+	1.91390i	−0.841521	+	0.137410i
$195$	−0.452520	+	3.36471i	−0.0324056	+	0.240952i
$196$	6.83309	−	2.29265i	0.488078	−	0.163760i
$197$	−6.49688	−	11.2529i	−0.462884	−	0.801738i	0.536219	−	0.844079i	$-0.319852\pi$
$197$	−6.49688	−	11.2529i	−0.462884	−	0.801738i	−0.999103	+	0.0423403i	$0.986519\pi$
$198$	10.5872	−	8.65747i	0.752401	−	0.615260i
$199$	−2.01275	+	3.48619i	−0.142680	+	0.247130i	−0.928505	−	0.371320i	$-0.878905\pi$
$199$	−2.01275	+	3.48619i	−0.142680	+	0.247130i	0.785825	+	0.618449i	$0.212239\pi$
$200$	1.32008	+	2.50148i	0.0933439	+	0.176881i
$201$	−0.172281	−	0.0994662i	−0.0121517	−	0.00701581i
$202$	4.85223	−	12.8234i	0.341402	−	0.902248i
$203$	−12.5431			−0.880351
$204$	13.4493	+	2.72464i	0.941641	+	0.190763i
$205$	−3.47276	+	2.00500i	−0.242548	+	0.140035i
$206$	10.5739	−	8.64658i	0.736718	−	0.602435i
$207$	15.4619			1.07468
$208$	12.5604	−	7.08773i	0.870908	−	0.491446i
$209$	29.7117			2.05520
$210$	3.35680	−	2.74495i	0.231641	−	0.189420i
$211$	−18.4537	+	10.6543i	−1.27041	+	0.733469i	−0.975064	−	0.221922i	$-0.928767\pi$
$211$	−18.4537	+	10.6543i	−1.27041	+	0.733469i	−0.295342	+	0.955392i	$0.595434\pi$
$212$	6.54130	+	1.32517i	0.449258	+	0.0910132i
$213$	5.75797			0.394530
$214$	1.46321	−	3.86693i	0.100023	−	0.264338i
$215$	6.09210	+	3.51727i	0.415478	+	0.239876i
$216$	12.0441	−	6.35590i	0.819494	−	0.432464i
$217$	−4.53341	+	7.85209i	−0.307748	+	0.533035i
$218$	−1.22967	+	1.00554i	−0.0832841	+	0.0681038i
$219$	−3.60537	−	6.24468i	−0.243628	−	0.421976i
$220$	−8.67642	+	2.91112i	−0.584964	+	0.196268i
$221$	9.98649	+	24.3010i	0.671764	+	1.63466i
$222$	6.77005	−	1.10547i	0.454376	−	0.0741940i
$223$	8.44262	−	4.87435i	0.565359	−	0.326410i	−0.189934	−	0.981797i	$-0.560828\pi$
$223$	8.44262	−	4.87435i	0.565359	−	0.326410i	0.755294	+	0.655386i	$0.227494\pi$
$224$	−17.9018	−	4.34107i	−1.19611	−	0.290050i
$225$	−1.05669	+	1.83024i	−0.0704461	+	0.122016i
$226$	1.87120	+	11.4595i	0.124470	+	0.762276i
$227$	−5.82595	+	10.0908i	−0.386682	+	0.669753i	−0.992001	−	0.126230i	$-0.959712\pi$
$227$	−5.82595	+	10.0908i	−0.386682	+	0.669753i	0.605319	+	0.795983i	$0.293046\pi$
$228$	11.9844	+	2.42787i	0.793687	+	0.160789i
$229$	−21.6811			−1.43273			−0.716365	−	0.697726i	$-0.754195\pi$
$229$	−21.6811			−1.43273			−0.716365	+	0.697726i	$0.754195\pi$
$230$	−9.67705	−	3.66170i	−0.638086	−	0.241445i
$231$	7.01523	+	12.1507i	0.461569	+	0.799460i
$232$	9.22130	+	5.80212i	0.605408	+	0.380928i
$233$	16.1554			1.05838			0.529188	−	0.848505i	$-0.322497\pi$
$233$	16.1554			1.05838			0.529188	+	0.848505i	$0.322497\pi$
$234$	9.48051	+	5.12308i	0.619761	+	0.334906i
$235$			7.32283i			0.477689i
$236$	−2.88107	−	2.54468i	−0.187542	−	0.165645i
$237$	−11.9874	+	6.92095i	−0.778667	+	0.449564i
$238$	11.8758	−	31.3851i	0.769795	−	2.03439i
$239$		−	0.979222i		−	0.0633406i	−0.999498	−	0.0316703i	$-0.989917\pi$
$239$		−	0.979222i		−	0.0633406i	0.999498	−	0.0316703i	$-0.0100827\pi$
$240$	−3.73757	+	0.465234i	−0.241259	+	0.0300307i
$241$	9.26265	+	5.34779i	0.596660	+	0.344482i	0.767726	−	0.640778i	$-0.221388\pi$
$241$	9.26265	+	5.34779i	0.596660	+	0.344482i	−0.171067	+	0.985259i	$0.554721\pi$
$242$	−2.26509	−	13.8718i	−0.145605	−	0.891710i
$243$	13.9823	+	8.07269i	0.896965	+	0.517863i
$244$	−6.40897	+	7.25619i	−0.410292	+	0.464530i
$245$	−1.80186	−	3.12092i	−0.115117	−	0.199388i
$246$	−0.860530	−	5.27003i	−0.0548654	−	0.336005i
$247$	8.89875	+	21.6541i	0.566214	+	1.37781i
$248$	6.96501	−	3.67558i	0.442279	−	0.233400i
$249$	−6.15692	+	3.55470i	−0.390179	+	0.225270i
$250$	1.09478	−	0.895236i	0.0692402	−	0.0566197i
$251$	1.41559	+	0.817291i	0.0893512	+	0.0515869i	0.544010	−	0.839079i	$-0.316905\pi$
$251$	1.41559	+	0.817291i	0.0893512	+	0.0515869i	−0.454659	+	0.890666i	$0.650239\pi$
$252$	−4.37817	−	13.0489i	−0.275799	−	0.822002i
$253$	16.7390	−	28.9928i	1.05237	−	1.82276i
$254$	5.99288	+	2.26765i	0.376027	+	0.142285i
$255$		−	6.86127i		−	0.429669i
$256$	11.1528	+	11.4724i	0.697050	+	0.717022i
$257$	−14.2913	−	24.7533i	−0.891469	−	1.54407i	−0.838115	−	0.545494i	$-0.816342\pi$
$257$	−14.2913	−	24.7533i	−0.891469	−	1.54407i	−0.0533543	−	0.998576i	$-0.516991\pi$
$258$	−7.25158	+	5.92983i	−0.451464	+	0.369175i
$259$		−	16.7746i		−	1.04232i
$260$	−4.72026	−	5.45153i	−0.292738	−	0.338090i
$261$			8.14053i			0.503886i
$262$	16.2374	+	19.8567i	1.00315	+	1.22675i
$263$	−0.592661	−	1.02652i	−0.0365451	−	0.0632979i	0.847174	−	0.531315i	$-0.178302\pi$
$263$	−0.592661	−	1.02652i	−0.0365451	−	0.0632979i	−0.883719	+	0.468017i	$0.844969\pi$
$264$	0.463242	−	12.1779i	0.0285106	−	0.749501i
$265$		−	3.33709i		−	0.204996i
$266$	10.5823	−	27.9666i	0.648842	−	1.71474i
$267$	2.22824	−	3.85943i	0.136366	−	0.236193i
$268$	0.400593	−	0.134407i	0.0244701	−	0.00821024i
$269$	17.9663	+	10.3729i	1.09543	+	0.632444i	0.935016	−	0.354607i	$-0.115385\pi$
$269$	17.9663	+	10.3729i	1.09543	+	0.632444i	0.160410	+	0.987051i	$0.448719\pi$
$270$	−4.31036	−	5.27114i	−0.262320	−	0.320792i
$271$	−3.99411	+	2.30600i	−0.242625	+	0.140079i	−0.616383	−	0.787447i	$-0.711402\pi$
$271$	−3.99411	+	2.30600i	−0.242625	+	0.140079i	0.373758	+	0.927526i	$0.378069\pi$
$272$	−23.2487	+	17.5799i	−1.40966	+	1.06594i
$273$	−6.75444	+	8.75192i	−0.408798	+	0.529691i
$274$	−16.6830	+	2.72413i	−1.00786	+	0.164570i
$275$	2.28794	+	3.96283i	0.137968	+	0.238968i
$276$	9.12092	−	10.3266i	0.549015	−	0.621591i
$277$	−17.0409	−	9.83855i	−1.02389	−	0.591141i	−0.108659	−	0.994079i	$-0.534656\pi$
$277$	−17.0409	−	9.83855i	−1.02389	−	0.591141i	−0.915227	+	0.402938i	$0.867989\pi$
$278$	27.8870	−	4.55360i	1.67255	−	0.273107i
$279$	5.09606	+	2.94221i	0.305093	+	0.176146i
$280$	−0.350102	+	9.20365i	−0.0209226	+	0.550023i
$281$		−	22.9775i		−	1.37072i	−0.728203	−	0.685361i	$-0.759644\pi$
$281$		−	22.9775i		−	1.37072i	0.728203	−	0.685361i	$-0.240356\pi$
$282$	−9.12021	−	3.45100i	−0.543101	−	0.205504i
$283$	15.4338	−	8.91072i	0.917446	−	0.529688i	0.0346264	−	0.999400i	$-0.488976\pi$
$283$	15.4338	−	8.91072i	0.917446	−	0.529688i	0.882819	+	0.469713i	$0.155643\pi$
$284$	−8.09631	+	9.16658i	−0.480428	+	0.543936i
$285$		−	6.11393i		−	0.362158i
$286$	19.8699	−	12.2308i	1.17493	−	0.723222i
$287$	−13.0579			−0.770783
$288$	−2.81738	+	11.6184i	−0.166016	+	0.684620i
$289$	−18.0487	−	31.2613i	−1.06169	−	1.83890i
$290$	1.92785	−	5.09486i	0.113207	−	0.299181i
$291$	−7.90738			−0.463539
$292$	15.0109	+	3.04100i	0.878448	+	0.177961i
$293$	−1.92052	+	3.32644i	−0.112198	+	0.194333i	−0.916656	−	0.399677i	$-0.869122\pi$
$293$	−1.92052	+	3.32644i	−0.112198	+	0.194333i	0.804458	+	0.594009i	$0.202456\pi$
$294$	4.73610	−	0.773346i	0.276215	−	0.0451025i
$295$	−0.960988	+	1.66448i	−0.0559509	+	0.0969098i
$296$	−7.75952	+	12.3322i	−0.451013	+	0.716794i
$297$	19.0802	−	11.0159i	1.10714	−	0.639209i
$298$	2.76717	+	16.9466i	0.160298	+	0.981691i
$299$	26.1435	+	3.51605i	1.51192	+	0.203339i
$300$	0.599037	+	1.78539i	0.0345854	+	0.103080i
$301$	11.4534	+	19.8379i	0.660165	+	1.14344i
$302$	1.96376	+	2.40148i	0.113002	+	0.138190i
$303$	4.56438	−	7.90574i	0.262217	−	0.454173i
$304$	−20.7165	+	15.6651i	−1.18817	+	0.898456i
$305$	4.19212	+	2.42032i	0.240040	+	0.138587i
$306$	−20.3691	−	7.70748i	−1.16443	−	0.440607i
$307$	−0.0398307			−0.00227326			−0.00113663	−	0.999999i	$-0.500362\pi$
$307$	−0.0398307			−0.00227326			−0.00113663	+	0.999999i	$0.500362\pi$
$308$	−29.2079	−	5.91710i	−1.66427	−	0.337158i
$309$	7.87599	−	4.54720i	0.448049	−	0.258681i
$310$	−2.49266	−	3.04827i	−0.141574	−	0.173130i
$311$	11.5568			0.655328			0.327664	−	0.944794i	$-0.393739\pi$
$311$	11.5568			0.655328			0.327664	+	0.944794i	$0.393739\pi$
$312$	9.01409	−	3.30972i	0.510323	−	0.187376i
$313$	−15.1522			−0.856451			−0.428226	−	0.903672i	$-0.640861\pi$
$313$	−15.1522			−0.856451			−0.428226	+	0.903672i	$0.640861\pi$
$314$	19.3189	+	23.6251i	1.09023	+	1.33324i
$315$	−5.95989	+	3.44094i	−0.335802	+	0.193875i
$316$	5.83757	−	28.8153i	0.328389	−	1.62099i
$317$	−21.4371			−1.20403			−0.602013	−	0.798486i	$-0.705635\pi$
$317$	−21.4371			−1.20403			−0.602013	+	0.798486i	$0.705635\pi$
$318$	4.15617	+	1.57266i	0.233067	+	0.0881901i
$319$	15.2644	+	8.81292i	0.854643	+	0.493429i
$320$	4.51477	−	6.60431i	0.252383	−	0.369192i
$321$	1.37640	−	2.38400i	0.0768234	−	0.133062i
$322$	−21.3281	−	26.0821i	−1.18857	−	1.45350i
$323$	−23.6570	−	40.9751i	−1.31631	−	2.27992i
$324$	−3.42541	+	1.14930i	−0.190301	+	0.0638499i
$325$	−2.20289	+	2.85434i	−0.122194	+	0.158331i
$326$	−3.57773	−	21.9106i	−0.198152	−	1.21352i
$327$	−0.915926	+	0.528810i	−0.0506508	+	0.0292433i
$328$	9.59978	+	6.04026i	0.530059	+	0.333518i
$329$	−11.9228	+	20.6509i	−0.657325	+	1.13852i
$330$	−6.01373	+	0.981968i	−0.331045	+	0.0540556i
$331$	−11.6860	+	20.2407i	−0.642319	+	1.11253i	0.342595	+	0.939483i	$0.388694\pi$
$331$	−11.6860	+	20.2407i	−0.642319	+	1.11253i	−0.984914	+	0.173046i	$0.944639\pi$
$332$	2.99826	−	14.8000i	0.164551	−	0.812254i
$333$	−10.8868			−0.596594
$334$	−5.09112	+	13.4547i	−0.278574	+	0.736207i
$335$	−0.105635	−	0.182965i	−0.00577146	−	0.00999645i
$336$	−11.2977	−	4.77340i	−0.616339	−	0.260410i
$337$	−32.2953			−1.75924			−0.879619	−	0.475680i	$-0.842202\pi$
$337$	−32.2953			−1.75924			−0.879619	+	0.475680i	$0.842202\pi$
$338$	14.8650	+	10.8182i	0.808548	+	0.588430i
$339$			7.73096i			0.419888i
$340$	10.9230	+	9.64766i	0.592383	+	0.523218i
$341$	11.0340	−	6.37046i	0.597522	−	0.344980i
$342$	−18.1505	−	6.86797i	−0.981467	−	0.371378i
$343$			11.0594i			0.597152i
$344$	0.756312	−	19.8823i	0.0407776	−	1.07198i
$345$	−5.96601	−	3.44448i	−0.321199	−	0.185444i
$346$	−24.6259	+	4.02110i	−1.32390	+	0.216176i
$347$	4.10416	+	2.36954i	0.220323	+	0.127203i	0.606100	−	0.795389i	$-0.292733\pi$
$347$	4.10416	+	2.36954i	0.220323	+	0.127203i	−0.385777	+	0.922592i	$0.626067\pi$
$348$	5.43686	+	4.80207i	0.291446	+	0.257418i
$349$	11.1002	+	19.2260i	0.594177	+	1.02915i	0.993662	+	0.112406i	$0.0358557\pi$
$349$	11.1002	+	19.2260i	0.594177	+	1.02915i	−0.399485	+	0.916740i	$0.630811\pi$
$350$	4.54496	−	0.742136i	0.242938	−	0.0396689i
$351$	13.7430	+	10.6064i	0.733549	+	0.566129i
$352$	18.7357	+	17.8609i	0.998615	+	0.951991i
$353$	17.2525	−	9.96076i	0.918260	−	0.530158i	0.0351807	−	0.999381i	$-0.488799\pi$
$353$	17.2525	−	9.96076i	0.918260	−	0.530158i	0.883080	+	0.469223i	$0.155466\pi$
$354$	−1.62014	−	1.98127i	−0.0861097	−	0.105303i
$355$	5.29581	+	3.05754i	0.281072	+	0.162277i
$356$	3.01099	+	8.97407i	0.159582	+	0.475625i
$357$	11.1713	−	19.3493i	0.591248	−	1.02407i
$358$	−0.634955	+	1.67804i	−0.0335584	+	0.0886873i
$359$		−	8.08438i		−	0.426677i	−0.976978	−	0.213339i	$-0.931566\pi$
$359$		−	8.08438i		−	0.426677i	0.976978	−	0.213339i	$-0.0684337\pi$
$360$	5.97323	+	0.227218i	0.314817	+	0.0119755i
$361$	−11.5802	−	20.0576i	−0.609486	−	1.05566i
$362$	12.0017	+	14.6769i	0.630795	+	0.771399i
$363$		−	9.35833i		−	0.491185i
$364$	−4.43544	−	23.0591i	−0.232480	−	1.20862i
$365$		−	7.65793i		−	0.400834i
$366$	−4.98998	+	4.08045i	−0.260831	+	0.213289i
$367$	0.926465	+	1.60468i	0.0483611	+	0.0837638i	0.889193	−	0.457533i	$-0.151267\pi$
$367$	0.926465	+	1.60468i	0.0483611	+	0.0837638i	−0.840832	+	0.541297i	$0.817934\pi$
$368$	3.61484	+	29.0407i	0.188437	+	1.51385i
$369$			8.47466i			0.441173i
$370$	6.81367	+	2.57822i	0.354226	+	0.134036i
$371$	5.43334	−	9.41083i	0.282085	−	0.488586i
$372$	4.97117	−	1.66793i	0.257743	−	0.0864784i
$373$	11.6966	+	6.75302i	0.605625	+	0.349658i	0.771251	−	0.636531i	$-0.219631\pi$
$373$	11.6966	+	6.75302i	0.605625	+	0.349658i	−0.165626	+	0.986189i	$0.552964\pi$
$374$	−36.5040	+	29.8503i	−1.88758	+	1.54352i
$375$	0.815452	−	0.470802i	0.0421098	−	0.0243121i
$376$	18.3179	−	9.66673i	0.944673	−	0.498524i
$377$	−1.85116	+	13.7643i	−0.0953397	+	0.708897i
$378$	−3.57322	−	21.8830i	−0.183787	−	1.12554i
$379$	−16.0577	−	27.8128i	−0.824830	−	1.42865i	−0.902049	−	0.431633i	$-0.857937\pi$
$379$	−16.0577	−	27.8128i	−0.824830	−	1.42865i	0.0772193	−	0.997014i	$-0.475396\pi$
$380$	9.73326	+	8.59683i	0.499306	+	0.441008i
$381$	3.69467	+	2.13312i	0.189284	+	0.109283i
$382$	0.249244	+	1.52641i	0.0127524	+	0.0780980i
$383$	31.7402	+	18.3252i	1.62185	+	0.936375i	0.986425	+	0.164212i	$0.0525082\pi$
$383$	31.7402	+	18.3252i	1.62185	+	0.936375i	0.635424	+	0.772163i	$0.280825\pi$
$384$	6.09767	+	8.73529i	0.311170	+	0.445771i
$385$			14.9006i			0.759406i
$386$	10.0794	−	26.6377i	0.513030	−	1.35582i
$387$	12.8749	−	7.43335i	0.654470	−	0.377858i
$388$	11.1186	−	12.5884i	0.564461	−	0.639079i
$389$			19.7184i			0.999763i	0.866094	+	0.499881i	$0.166623\pi$
$389$			19.7184i			0.999763i	−0.866094	+	0.499881i	$0.833377\pi$
$390$	−2.51679	−	4.08874i	−0.127443	−	0.207041i
$391$	−53.3116			−2.69608
$392$	−5.42829	+	8.62718i	−0.274170	+	0.435738i
$393$	8.53918	+	14.7903i	0.430745	+	0.746072i
$394$	17.1867	+	6.50329i	0.865854	+	0.327631i
$395$	−14.7003			−0.739655
$396$	−3.84023	+	18.9561i	−0.192979	+	0.952581i
$397$	5.90055	−	10.2200i	0.296140	−	0.512929i	−0.679109	−	0.734037i	$-0.737634\pi$
$397$	5.90055	−	10.2200i	0.296140	−	0.512929i	0.975249	+	0.221108i	$0.0709672\pi$
$398$	−0.917435	−	5.61852i	−0.0459869	−	0.281631i
$399$	9.95451	−	17.2417i	0.498349	−	0.863165i
$400$	−3.68462	−	1.55679i	−0.184231	−	0.0778396i
$401$	−15.0742	+	8.70308i	−0.752769	+	0.434611i	−0.826693	−	0.562653i	$-0.809781\pi$
$401$	−15.0742	+	8.70308i	−0.752769	+	0.434611i	0.0739247	+	0.997264i	$0.476448\pi$
$402$	0.277656	−	0.0453378i	0.0138482	−	0.00226124i
$403$	7.94753	+	6.13364i	0.395894	+	0.305538i
$404$	6.16779	+	18.3827i	0.306859	+	0.914573i
$405$	0.903270	+	1.56451i	0.0448838	+	0.0777411i
$406$	13.7320	−	11.2290i	0.681505	−	0.557286i
$407$	−11.7860	+	20.4140i	−0.584213	+	1.01189i
$408$	−17.1633	+	9.05744i	−0.849710	+	0.448410i
$409$	−5.92031	−	3.41809i	−0.292740	−	0.169014i	0.346437	−	0.938073i	$-0.387392\pi$
$409$	−5.92031	−	3.41809i	−0.292740	−	0.169014i	−0.639177	+	0.769060i	$0.720725\pi$
$410$	2.00697	−	5.30398i	0.0991173	−	0.261945i
$411$	−11.2549			−0.555162
$412$	−3.83540	+	18.9323i	−0.188957	+	0.932726i
$413$	−5.42011	+	3.12930i	−0.266706	+	0.153983i
$414$	−16.9275	+	13.8421i	−0.831940	+	0.680301i
$415$	−7.55031			−0.370630
$416$	−7.40575	+	19.0041i	−0.363097	+	0.931751i
$417$	18.8134			0.921298
$418$	−32.5279	+	26.5990i	−1.59099	+	1.30100i
$419$	−19.7820	+	11.4211i	−0.966412	+	0.557958i	−0.898140	−	0.439709i	$-0.855082\pi$
$419$	−19.7820	+	11.4211i	−0.966412	+	0.557958i	−0.0682714	+	0.997667i	$0.521748\pi$
$420$	−1.21759	+	6.01026i	−0.0594124	+	0.293271i
$421$	30.1915			1.47144			0.735722	−	0.677283i	$-0.236843\pi$
$421$	30.1915			1.47144			0.735722	+	0.677283i	$0.236843\pi$
$422$	10.6648	−	28.1845i	0.519152	−	1.37200i
$423$	13.4026	+	7.73797i	0.651655	+	0.376233i
$424$	−8.34765	+	4.40523i	−0.405398	+	0.213937i
$425$	3.64340	−	6.31055i	0.176731	−	0.306107i
$426$	−6.30373	+	5.15474i	−0.305417	+	0.249748i
$427$	7.88137	+	13.6509i	0.381406	+	0.660615i
$428$	1.85992	+	5.54337i	0.0899025	+	0.267949i
$429$	14.3691	−	5.90499i	0.693747	−	0.285096i
$430$	−9.81832	+	1.60321i	−0.473482	+	0.0773137i
$431$	6.22337	−	3.59306i	0.299769	−	0.173072i	−0.342570	−	0.939492i	$-0.611297\pi$
$431$	6.22337	−	3.59306i	0.299769	−	0.173072i	0.642339	+	0.766421i	$0.277964\pi$
$432$	−7.49561	+	17.7406i	−0.360633	+	0.853546i
$433$	17.2895	−	29.9463i	0.830882	−	1.43913i	−0.0664584	−	0.997789i	$-0.521170\pi$
$433$	17.2895	−	29.9463i	0.830882	−	1.43913i	0.897340	−	0.441340i	$-0.145497\pi$
$434$	−2.06638	−	12.6548i	−0.0991892	−	0.607451i
$435$	1.81348	−	3.14104i	0.0869497	−	0.150601i
$436$	0.446032	−	2.20170i	0.0213611	−	0.105442i
$437$	−47.5049			−2.27247
$438$	9.53756	+	3.60892i	0.455722	+	0.172441i
$439$	1.44165	+	2.49701i	0.0688063	+	0.119176i	0.898376	−	0.439227i	$-0.144748\pi$
$439$	1.44165	+	2.49701i	0.0688063	+	0.119176i	−0.829570	+	0.558403i	$0.811414\pi$
$440$	6.89266	−	10.9545i	0.328595	−	0.522235i
$441$	−7.61605			−0.362669
$442$	−32.6881	−	17.6640i	−1.55482	−	0.840192i
$443$		−	1.83786i		−	0.0873193i	−0.999046	−	0.0436596i	$-0.986098\pi$
$443$		−	1.83786i		−	0.0873193i	0.999046	−	0.0436596i	$-0.0139017\pi$
$444$	−6.42209	+	7.27104i	−0.304779	+	0.345068i
$445$	4.09878	−	2.36643i	0.194301	−	0.112180i
$446$	−4.87915	+	12.8945i	−0.231034	+	0.610572i
$447$			11.4327i			0.540750i
$448$	23.4849	−	11.2738i	1.10956	−	0.532637i
$449$	−9.68862	−	5.59373i	−0.457234	−	0.263984i	0.253646	−	0.967297i	$-0.418370\pi$
$449$	−9.68862	−	5.59373i	−0.457234	−	0.263984i	−0.710881	+	0.703313i	$0.751703\pi$
$450$	−0.481651	−	2.94971i	−0.0227053	−	0.139051i
$451$	15.8909	+	9.17464i	0.748275	+	0.432017i
$452$	−12.3075	−	10.8705i	−0.578898	−	0.511307i
$453$	1.03273	+	1.78875i	0.0485221	+	0.0840428i
$454$	−2.65553	−	16.2629i	−0.124630	−	0.763256i
$455$	−10.8597	+	4.46278i	−0.509108	+	0.209218i
$456$	−15.2939	+	8.07089i	−0.716201	+	0.377954i
$457$	16.7719	−	9.68325i	0.784555	−	0.452963i	−0.0534869	−	0.998569i	$-0.517034\pi$
$457$	16.7719	−	9.68325i	0.784555	−	0.452963i	0.838042	+	0.545605i	$0.183700\pi$
$458$	23.7362	−	19.4097i	1.10912	−	0.906957i
$459$	−30.3839	−	17.5422i	−1.41820	−	0.818798i
$460$	13.8724	−	4.65448i	0.646803	−	0.217016i
$461$	−10.7162	+	18.5611i	−0.499105	+	0.864476i	−0.999999	−	0.00103265i	$-0.999671\pi$
$461$	−10.7162	+	18.5611i	−0.499105	+	0.864476i	0.500894	+	0.865509i	$0.333005\pi$
$462$	−18.5580	−	7.02215i	−0.863394	−	0.326700i
$463$		−	23.6913i		−	1.10103i	−0.834825	−	0.550515i	$-0.814431\pi$
$463$		−	23.6913i		−	1.10103i	0.834825	−	0.550515i	$-0.185569\pi$
$464$	−15.2896	+	1.90317i	−0.709802	+	0.0883526i
$465$	−1.31088	−	2.27051i	−0.0607907	−	0.105293i
$466$	−17.6867	+	14.4629i	−0.819319	+	0.669981i
$467$			1.19692i			0.0553869i	0.999616	+	0.0276934i	$0.00881622\pi$
$467$			1.19692i			0.0553869i	−0.999616	+	0.0276934i	$0.991184\pi$
$468$	−14.9655	+	2.87863i	−0.691780	+	0.133065i
$469$		−	0.687966i		−	0.0317673i
$470$	−6.55566	−	8.01692i	−0.302390	−	0.369793i
$471$	10.1598	+	17.5972i	0.468137	+	0.810837i
$472$	5.43224	+	0.206639i	0.250039	+	0.00951134i
$473$		−	32.1893i		−	1.48006i
$474$	6.92777	−	18.3085i	0.318203	−	0.840938i
$475$	3.24655	−	5.62320i	0.148962	−	0.258010i
$476$	15.0956	+	44.9916i	0.691907	+	2.06219i
$477$	−6.10769	−	3.52628i	−0.279652	−	0.161457i
$478$	0.876635	+	1.07204i	0.0400963	+	0.0490338i
$479$	9.74703	−	5.62745i	0.445353	−	0.257125i	−0.260513	−	0.965470i	$-0.583892\pi$
$479$	9.74703	−	5.62745i	0.445353	−	0.257125i	0.705866	+	0.708346i	$0.250558\pi$
$480$	3.67534	−	3.85534i	0.167755	−	0.175971i
$481$	−18.4078	−	2.47567i	−0.839324	−	0.112881i
$482$	−14.9281	+	2.43758i	−0.679958	+	0.111029i
$483$	−11.2164	−	19.4273i	−0.510363	−	0.883974i
$484$	14.8983	+	13.1588i	0.677194	+	0.598127i
$485$	−7.27269	−	4.19889i	−0.330236	−	0.190662i
$486$	−22.5346	+	3.67962i	−1.02219	+	0.166911i
$487$	−10.4861	−	6.05415i	−0.475170	−	0.274340i	0.243231	−	0.969968i	$-0.421793\pi$
$487$	−10.4861	−	6.05415i	−0.475170	−	0.274340i	−0.718401	+	0.695629i	$0.755126\pi$
$488$	0.520436	−	13.6815i	0.0235590	−	0.619332i
$489$		−	14.7816i		−	0.668447i
$490$	4.76661	+	1.80364i	0.215333	+	0.0814800i
$491$	−2.03007	+	1.17206i	−0.0916159	+	0.0528945i	−0.545108	−	0.838366i	$-0.683511\pi$
$491$	−2.03007	+	1.17206i	−0.0916159	+	0.0528945i	0.453492	+	0.891260i	$0.350178\pi$
$492$	5.66001	+	4.99916i	0.255173	+	0.225380i
$493$		−	28.0680i		−	1.26412i
$494$	−29.1277	−	15.7400i	−1.31052	−	0.708178i
$495$	9.67060			0.434661
$496$	−4.33467	+	10.2593i	−0.194632	+	0.460656i
$497$	9.95636	+	17.2449i	0.446604	+	0.773541i
$498$	3.55820	−	9.40353i	0.159447	−	0.421382i
$499$	0.0649069			0.00290563			0.00145282	−	0.999999i	$-0.499538\pi$
$499$	0.0649069			0.00290563			0.00145282	+	0.999999i	$0.499538\pi$
$500$	−0.397104	+	1.96018i	−0.0177590	+	0.0876619i
$501$	−4.78909	+	8.29495i	−0.213961	+	0.370591i
$502$	−2.28143	+	0.372530i	−0.101825	+	0.0166268i
$503$	−17.2819	+	29.9331i	−0.770560	+	1.33465i	0.166697	+	0.986008i	$0.446690\pi$
$503$	−17.2819	+	29.9331i	−0.770560	+	1.33465i	−0.937256	+	0.348641i	$0.886643\pi$
$504$	16.4750	+	10.3662i	0.733854	+	0.461747i
$505$	8.39604	−	4.84746i	0.373619	−	0.215709i
$506$	7.62983	+	46.7263i	0.339187	+	2.07724i
$507$	8.60718	+	8.70372i	0.382258	+	0.386546i
$508$	−8.59098	+	2.88246i	−0.381163	+	0.127888i
$509$	−4.66463	−	8.07937i	−0.206756	−	0.358112i	0.743935	−	0.668252i	$-0.232957\pi$
$509$	−4.66463	−	8.07937i	−0.206756	−	0.358112i	−0.950691	+	0.310140i	$0.899624\pi$
$510$	6.14246	+	7.51161i	0.271993	+	0.332620i
$511$	12.4684	−	21.5959i	0.551569	−	0.955346i
$512$	−22.4804	−	2.57536i	−0.993502	−	0.113816i
$513$	−27.0745	−	15.6314i	−1.19537	−	0.690145i
$514$	37.8060	+	14.3054i	1.66755	+	0.630985i
$515$	9.65843			0.425601
$516$	2.63032	−	12.9838i	0.115793	−	0.571578i
$517$	29.0191	−	16.7542i	1.27626	−	0.736849i
$518$	15.0172	+	18.3646i	0.659819	+	0.806893i
$519$	−16.6134			−0.729247
$520$	10.0481	+	1.74250i	0.440637	+	0.0764139i
$521$	12.9021			0.565251			0.282626	−	0.959230i	$-0.408795\pi$
$521$	12.9021			0.565251			0.282626	+	0.959230i	$0.408795\pi$
$522$	−7.28770	−	8.91213i	−0.318974	−	0.390073i
$523$	−6.38548	+	3.68666i	−0.279218	+	0.161206i	−0.633069	−	0.774095i	$-0.718205\pi$
$523$	−6.38548	+	3.68666i	−0.279218	+	0.161206i	0.353852	+	0.935302i	$0.384872\pi$
$524$	−35.5528	−	7.20249i	−1.55313	−	0.314642i
$525$	3.06618			0.133819
$526$	1.56781	+	0.593245i	0.0683599	+	0.0258667i
$527$	−17.5708	−	10.1445i	−0.765398	−	0.441903i
$528$	10.3950	+	13.7469i	0.452384	+	0.598258i
$529$	−15.2634	+	26.4369i	−0.663624	+	1.14943i
$530$	2.98748	+	3.65339i	0.129768	+	0.158693i
$531$	2.03094	+	3.51768i	0.0881351	+	0.152654i
$532$	13.4514	+	40.0910i	0.583192	+	1.73817i
$533$	−1.92714	+	14.3292i	−0.0834738	+	0.620668i
$534$	1.01566	+	6.22004i	0.0439517	+	0.269167i
$535$	2.53186	−	1.46177i	0.109462	−	0.0631977i
$536$	−0.318236	+	0.505772i	−0.0137457	+	0.0218460i
$537$	−0.597287	+	1.03453i	−0.0257748	+	0.0446433i
$538$	−28.9554	+	4.72806i	−1.24836	+	0.203841i
$539$	−8.24511	+	14.2810i	−0.355142	+	0.615124i
$540$	9.43784	+	1.91197i	0.406140	+	0.0822780i
$541$	−10.9267			−0.469775			−0.234888	−	0.972023i	$-0.575472\pi$
$541$	−10.9267			−0.469775			−0.234888	+	0.972023i	$0.575472\pi$
$542$	2.30827	−	6.10024i	0.0991487	−	0.262028i
$543$	6.31165	+	10.9321i	0.270859	+	0.469141i
$544$	9.71414	−	40.0594i	0.416490	−	1.71753i
$545$	−1.12321			−0.0481131
$546$	−0.440383	−	15.6283i	−0.0188467	−	0.668829i
$547$			37.9154i			1.62114i	0.585639	+	0.810572i	$0.300843\pi$
$547$			37.9154i			1.62114i	−0.585639	+	0.810572i	$0.699157\pi$
$548$	15.8255	−	17.9175i	0.676033	−	0.765400i
$549$	8.85955	−	5.11506i	0.378116	−	0.218306i
$550$	−6.05247	−	2.29020i	−0.258078	−	0.0976543i
$551$		−	25.0108i		−	1.06550i
$552$	−0.740659	+	19.4708i	−0.0315245	+	0.828733i
$553$	−41.4560	−	23.9346i	−1.76289	−	1.01780i
$554$	27.4639	−	4.48451i	1.16683	−	0.190529i
$555$	4.20070	+	2.42528i	0.178310	+	0.102947i
$556$	−26.4537	+	29.9506i	−1.12189	+	1.27019i
$557$	7.58932	+	13.1451i	0.321570	+	0.556975i	0.980812	−	0.194955i	$-0.0624562\pi$
$557$	7.58932	+	13.1451i	0.321570	+	0.556975i	−0.659242	+	0.751931i	$0.729123\pi$
$558$	−8.21306	+	1.34109i	−0.347686	+	0.0567729i
$559$	23.4597	−	9.64079i	0.992241	−	0.407762i
$560$	−7.85616	−	10.3894i	−0.331983	−	0.439034i
$561$	−27.1901	+	15.6982i	−1.14797	+	0.662778i
$562$	20.5703	+	25.1554i	0.867705	+	1.06112i
$563$	9.61390	+	5.55059i	0.405178	+	0.233929i	0.688716	−	0.725032i	$-0.258175\pi$
$563$	9.61390	+	5.55059i	0.405178	+	0.233929i	−0.283538	+	0.958961i	$0.591508\pi$
$564$	13.0741	−	4.38664i	0.550520	−	0.184711i
$565$	−4.10521	+	7.11043i	−0.172707	+	0.299138i
$566$	−8.91950	+	23.5722i	−0.374915	+	0.990815i
$567$			5.88270i			0.247050i
$568$	0.657456	−	17.2835i	0.0275862	−	0.725201i
$569$	−2.01815	−	3.49553i	−0.0846051	−	0.146540i	0.820618	−	0.571477i	$-0.193630\pi$
$569$	−2.01815	−	3.49553i	−0.0846051	−	0.146540i	−0.905223	+	0.424937i	$0.860296\pi$
$570$	5.47341	+	6.69344i	0.229256	+	0.280357i
$571$			12.7832i			0.534960i	0.963563	+	0.267480i	$0.0861909\pi$
$571$			12.7832i			0.534960i	−0.963563	+	0.267480i	$0.913809\pi$
$572$	−10.8038	+	31.1784i	−0.451731	+	1.30363i
$573$			1.02977i			0.0430191i
$574$	14.2956	−	11.6899i	0.596686	−	0.487927i
$575$	−3.65810	−	6.33601i	−0.152553	−	0.264230i
$576$	−7.31677	−	15.2418i	−0.304865	−	0.635077i
$577$		−	25.9751i		−	1.08136i	−0.841229	−	0.540679i	$-0.818168\pi$
$577$		−	25.9751i		−	1.08136i	0.841229	−	0.540679i	$-0.181832\pi$
$578$	47.7456	+	18.0665i	1.98596	+	0.751466i
$579$	9.48150	−	16.4224i	0.394038	−	0.682493i
$580$	2.45053	+	7.30365i	0.101753	+	0.303268i
$581$	−21.2924	−	12.2932i	−0.883358	−	0.510007i
$582$	8.65687	−	7.07897i	0.358839	−	0.293433i
$583$	−13.2243	+	7.63507i	−0.547696	+	0.316212i
$584$	−19.1561	+	10.1091i	−0.792686	+	0.418317i
$585$	2.89637	+	7.04798i	0.119750	+	0.291398i
$586$	−0.875393	−	5.36105i	−0.0361622	−	0.221463i
$587$	14.5416	+	25.1867i	0.600194	+	1.03957i	0.992791	+	0.119856i	$0.0382434\pi$
$587$	14.5416	+	25.1867i	0.600194	+	1.03957i	−0.392597	+	0.919711i	$0.628423\pi$
$588$	−4.49268	+	5.08657i	−0.185275	+	0.209767i
$589$	−15.6570	−	9.03958i	−0.645136	−	0.372469i
$590$	−0.438029	−	2.68256i	−0.0180334	−	0.110439i
$591$	10.5958	+	6.11749i	0.435853	+	0.251640i
$592$	−2.54523	−	20.4477i	−0.104608	−	0.840395i
$593$			25.3253i			1.03998i	0.854171	+	0.519992i	$0.174065\pi$
$593$			25.3253i			1.03998i	−0.854171	+	0.519992i	$0.825935\pi$
$594$	−11.0268	+	29.1413i	−0.452435	+	1.19568i
$595$	20.5493	−	11.8641i	0.842438	−	0.486382i
$596$	−18.2007	−	16.0756i	−0.745529	−	0.658483i
$597$		−	3.79043i		−	0.155132i
$598$	−31.7692	+	19.5553i	−1.29914	+	0.799677i
$599$	17.8764			0.730409			0.365205	−	0.930927i	$-0.380999\pi$
$599$	17.8764			0.730409			0.365205	+	0.930927i	$0.380999\pi$
$600$	−2.25416	−	1.41834i	−0.0920258	−	0.0579034i
$601$	−10.6079	−	18.3734i	−0.432705	−	0.749467i	0.564400	−	0.825501i	$-0.309108\pi$
$601$	−10.6079	−	18.3734i	−0.432705	−	0.749467i	−0.997105	+	0.0760342i	$0.975774\pi$
$602$	−30.2987	−	11.4647i	−1.23488	−	0.467267i
$603$	−0.446494			−0.0181827
$604$	−4.29979	−	0.871074i	−0.174956	−	0.0354435i
$605$	4.96936	−	8.60718i	0.202033	−	0.349932i
$606$	2.08049	+	12.7413i	0.0845142	+	0.517579i
$607$	3.60796	−	6.24918i	0.146443	−	0.253646i	−0.783468	−	0.621433i	$-0.786551\pi$
$607$	3.60796	−	6.24918i	0.146443	−	0.253646i	0.929910	+	0.367786i	$0.119884\pi$
$608$	8.65606	−	35.6960i	0.351050	−	1.44767i
$609$	10.2283	−	5.90530i	0.414471	−	0.239295i
$610$	−6.75622	+	1.10321i	−0.273551	+	0.0446676i
$611$	20.9019	+	16.1314i	0.845600	+	0.652606i
$612$	29.1998	−	9.79717i	1.18033	−	0.396027i
$613$	6.41919	+	11.1184i	0.259269	+	0.449067i	0.966046	−	0.258369i	$-0.0831851\pi$
$613$	6.41919	+	11.1184i	0.259269	+	0.449067i	−0.706777	+	0.707436i	$0.749852\pi$
$614$	0.0436060	−	0.0356579i	0.00175979	−	0.00143903i
$615$	1.88791	−	3.26996i	0.0761280	−	0.131858i
$616$	37.2735	−	19.6700i	1.50179	−	0.792528i
$617$	−15.5078	−	8.95345i	−0.624322	−	0.360452i	0.154228	−	0.988035i	$-0.450711\pi$
$617$	−15.5078	−	8.95345i	−0.624322	−	0.360452i	−0.778550	+	0.627583i	$0.784044\pi$
$618$	−4.55168	+	12.0291i	−0.183096	+	0.483880i
$619$	21.6358			0.869618			0.434809	−	0.900523i	$-0.356816\pi$
$619$	21.6358			0.869618			0.434809	+	0.900523i	$0.356816\pi$
$620$	5.45785	+	1.10568i	0.219193	+	0.0444052i
$621$	−30.5065	+	17.6129i	−1.22418	+	0.706782i
$622$	−12.6522	+	10.3461i	−0.507308	+	0.414840i
$623$	15.4118			0.617461
$624$	−6.90551	+	11.6932i	−0.276442	+	0.468101i
$625$	1.00000			0.0400000
$626$	16.5884	−	13.5648i	0.663004	−	0.542157i
$627$	−24.2285	+	13.9883i	−0.967593	+	0.558640i
$628$	−42.3001	−	8.56939i	−1.68796	−	0.341956i
$629$	37.5370			1.49670
$630$	3.44433	−	9.10260i	0.137226	−	0.362656i
$631$	11.0070	+	6.35490i	0.438182	+	0.252985i	0.702826	−	0.711361i	$-0.251921\pi$
$631$	11.0070	+	6.35490i	0.438182	+	0.252985i	−0.264644	+	0.964346i	$0.585254\pi$
$632$	19.4057	+	36.7726i	0.771916	+	1.46273i
$633$	10.0321	−	17.3761i	0.398739	−	0.690637i
$634$	23.4690	−	19.1913i	0.932072	−	0.762182i
$635$	2.26541	+	3.92381i	0.0899002	+	0.155712i
$636$	−5.95801	+	1.99904i	−0.236251	+	0.0792671i
$637$	−12.8775	−	1.73189i	−0.510224	−	0.0686202i
$638$	−24.6009	+	4.01702i	−0.973958	+	0.159035i
$639$	11.1921	−	6.46174i	0.442751	−	0.255623i
$640$	0.969718	+	11.2721i	0.0383315	+	0.445568i
$641$	23.4415	−	40.6018i	0.925882	−	1.60367i	0.135745	−	0.990744i	$-0.456657\pi$
$641$	23.4415	−	40.6018i	0.925882	−	1.60367i	0.790137	−	0.612931i	$-0.210009\pi$
$642$	0.627380	+	3.84218i	0.0247607	+	0.151639i
$643$	4.08952	−	7.08325i	0.161275	−	0.279336i	−0.774051	−	0.633123i	$-0.781773\pi$
$643$	4.08952	−	7.08325i	0.161275	−	0.279336i	0.935326	+	0.353787i	$0.115106\pi$
$644$	46.6993	+	9.46060i	1.84021	+	0.372800i
$645$	−6.62375			−0.260810
$646$	62.5817	+	23.6803i	2.46224	+	0.931689i
$647$	0.875253	+	1.51598i	0.0344097	+	0.0595994i	0.882717	−	0.469904i	$-0.155712\pi$
$647$	0.875253	+	1.51598i	0.0344097	+	0.0595994i	−0.848308	+	0.529504i	$0.822378\pi$
$648$	2.72119	−	4.32479i	0.106899	−	0.169894i
$649$	8.79474			0.345224
$650$	−0.143626	−	5.09700i	−0.00563348	−	0.199921i
$651$		−	8.53734i		−	0.334605i
$652$	23.5320	+	20.7845i	0.921585	+	0.813983i
$653$	28.9507	−	16.7147i	1.13293	−	0.654096i	0.188258	−	0.982120i	$-0.439716\pi$
$653$	28.9507	−	16.7147i	1.13293	−	0.654096i	0.944669	+	0.328024i	$0.106383\pi$
$654$	0.529331	−	1.39890i	0.0206985	−	0.0547014i
$655$			18.1375i			0.708692i
$656$	−15.9171	+	1.98129i	−0.621460	+	0.0773563i
$657$	−14.0159	−	8.09207i	−0.546811	−	0.315702i
$658$	−5.43454	−	33.2820i	−0.211860	−	1.29747i
$659$	24.5902	+	14.1972i	0.957899	+	0.553043i	0.895526	−	0.445010i	$-0.146800\pi$
$659$	24.5902	+	14.1972i	0.957899	+	0.553043i	0.0623733	+	0.998053i	$0.480133\pi$
$660$	5.70464	−	6.45875i	0.222053	−	0.251407i
$661$	16.0451	+	27.7908i	0.624080	+	1.08094i	0.988718	+	0.149789i	$0.0478595\pi$
$661$	16.0451	+	27.7908i	0.624080	+	1.08094i	−0.364638	+	0.931149i	$0.618807\pi$
$662$	−5.32659	−	32.6209i	−0.207024	−	1.26785i
$663$	−19.5844	−	15.1146i	−0.760596	−	0.587003i
$664$	9.96703	+	18.8869i	0.386796	+	0.732955i
$665$	18.3110	−	10.5719i	0.710071	−	0.409960i
$666$	11.9187	−	9.74628i	0.461841	−	0.377661i
$667$	−24.4057	−	14.0906i	−0.944991	−	0.545591i
$668$	−6.47144	−	19.2877i	−0.250388	−	0.746264i
$669$	−4.58970	+	7.94959i	−0.177448	+	0.307349i
$670$	0.279445	+	0.105739i	0.0107959	+	0.00408506i
$671$		−	22.1502i		−	0.855099i
$672$	16.6418	−	4.88826i	0.641973	−	0.188569i
$673$	22.3377	+	38.6901i	0.861056	+	1.49139i	0.870911	+	0.491441i	$0.163530\pi$
$673$	22.3377	+	38.6901i	0.861056	+	1.49139i	−0.00985491	+	0.999951i	$0.503137\pi$
$674$	35.3564	−	28.9119i	1.36188	−	1.11365i
$675$		−	4.81478i		−	0.185321i
$676$	−25.9587	+	1.46412i	−0.998413	+	0.0563125i
$677$		−	38.4184i		−	1.47654i	−0.674506	−	0.738270i	$-0.735643\pi$
$677$		−	38.4184i		−	1.47654i	0.674506	−	0.738270i	$-0.264357\pi$
$678$	−6.92103	−	8.46373i	−0.265801	−	0.325048i
$679$	−13.6730	−	23.6823i	−0.524722	−	0.908844i
$680$	−20.5953	−	0.783432i	−0.789793	−	0.0300433i
$681$		−	10.9715i		−	0.420428i
$682$	−6.37673	+	16.8523i	−0.244178	+	0.645307i
$683$	11.6110	−	20.1108i	0.444281	−	0.769518i	−0.553721	−	0.832703i	$-0.686792\pi$
$683$	11.6110	−	20.1108i	0.444281	−	0.769518i	0.998002	+	0.0631848i	$0.0201258\pi$
$684$	26.0193	−	8.73005i	0.994875	−	0.333802i
$685$	−10.3515	−	5.97644i	−0.395511	−	0.228348i
$686$	−9.90079	−	12.1077i	−0.378014	−	0.462273i
$687$	17.6799	−	10.2075i	0.674531	−	0.389441i
$688$	16.9714	+	22.4439i	0.647028	+	0.855667i
$689$	−9.52521	−	7.35124i	−0.362881	−	0.280060i
$690$	9.61511	−	1.57003i	0.366041	−	0.0597700i
$691$	−24.0825	−	41.7121i	−0.916140	−	1.58680i	−0.805223	−	0.592972i	$-0.797955\pi$
$691$	−24.0825	−	41.7121i	−0.916140	−	1.58680i	−0.110917	−	0.993830i	$-0.535379\pi$
$692$	23.3602	−	26.4482i	0.888021	−	1.00541i
$693$	27.2718	+	15.7454i	1.03597	+	0.598117i
$694$	−6.61446	+	1.08006i	−0.251081	+	0.0409985i
$695$	17.3034	+	9.99011i	0.656355	+	0.378947i
$696$	−10.2512	−	0.389949i	−0.388570	−	0.0147810i
$697$		−	29.2200i		−	1.10679i
$698$	−29.3641	−	11.1111i	−1.11145	−	0.420561i
$699$	−13.1740	+	7.60599i	−0.498285	+	0.287685i
$700$	−4.31136	+	4.88129i	−0.162954	+	0.184496i
$701$		−	40.5311i		−	1.53084i	−0.643533	−	0.765419i	$-0.722532\pi$
$701$		−	40.5311i		−	1.53084i	0.643533	−	0.765419i	$-0.277468\pi$
$702$	−24.5409	+	0.691528i	−0.926237	+	0.0261001i
$703$	33.4484			1.26153
$704$	−36.5013	−	2.78100i	−1.37569	−	0.104813i
$705$	−3.44760	−	5.97142i	−0.129844	−	0.224897i
$706$	−9.97058	+	26.3500i	−0.375248	+	0.991695i
$707$	31.5699			1.18731
$708$	3.54742	+	0.718655i	0.133320	+	0.0270087i
$709$	−18.1735	+	31.4774i	−0.682520	+	1.18216i	0.291690	+	0.956513i	$0.405782\pi$
$709$	−18.1735	+	31.4774i	−0.682520	+	1.18216i	−0.974209	+	0.225646i	$0.927551\pi$
$710$	−8.53498	+	1.39366i	−0.320312	+	0.0523030i
$711$	−15.5337	+	26.9052i	−0.582560	+	1.00902i
$712$	−11.3303	−	7.12912i	−0.424621	−	0.267175i
$713$	−17.6417	+	10.1855i	−0.660688	+	0.381449i
$714$	5.09200	+	31.1842i	0.190563	+	1.16704i
$715$	16.3514	+	2.19910i	0.611507	+	0.0822417i
$716$	−0.807106	−	2.40553i	−0.0301630	−	0.0898988i
$717$	0.461019	+	0.798509i	0.0172171	+	0.0298208i
$718$	7.23743	+	8.85065i	0.270098	+	0.330303i
$719$	−21.8623	+	37.8667i	−0.815327	+	1.41219i	0.0937658	+	0.995594i	$0.470110\pi$
$719$	−21.8623	+	37.8667i	−0.815327	+	1.41219i	−0.909093	+	0.416594i	$0.863224\pi$
$720$	−6.74281	+	5.09870i	−0.251290	+	0.190017i
$721$	27.2374	+	15.7255i	1.01438	+	0.585650i
$722$	30.6341	+	11.5916i	1.14008	+	0.431396i
$723$	−10.0710			−0.374544
$724$	−26.2785	−	5.32365i	−0.976634	−	0.197852i
$725$	3.33584	−	1.92595i	0.123890	−	0.0715279i
$726$	8.37791	+	10.2453i	0.310934	+	0.380240i
$727$	−4.55677			−0.169001			−0.0845005	−	0.996423i	$-0.526929\pi$
$727$	−4.55677			−0.169001			−0.0845005	+	0.996423i	$0.526929\pi$
$728$	25.4992	+	21.2739i	0.945062	+	0.788464i
$729$	−9.78292			−0.362330
$730$	6.85566	+	8.38378i	0.253739	+	0.310298i
$731$	−44.3919	+	25.6297i	−1.64189	+	0.947947i
$732$	1.80998	−	8.93443i	0.0668990	−	0.330226i
$733$	12.6156			0.465968			0.232984	−	0.972481i	$-0.425151\pi$
$733$	12.6156			0.465968			0.232984	+	0.972481i	$0.425151\pi$
$734$	−2.45085	−	0.927378i	−0.0904625	−	0.0342301i
$735$	2.93867	+	1.69664i	0.108394	+	0.0625815i
$736$	−29.9557	−	28.5571i	−1.10418	−	1.05263i
$737$	−0.483373	+	0.837227i	−0.0178053	+	0.0308397i
$738$	−7.58682	−	9.27792i	−0.279275	−	0.341525i
$739$	−16.5996	−	28.7514i	−0.610626	−	1.05764i	−0.991135	−	0.132858i	$-0.957584\pi$
$739$	−16.5996	−	28.7514i	−0.610626	−	1.05764i	0.380509	−	0.924777i	$-0.375749\pi$
$740$	−9.76761	+	3.27724i	−0.359065	+	0.120474i
$741$	−17.4513	−	13.4683i	−0.641088	−	0.494771i
$742$	2.47658	+	15.1670i	0.0909180	+	0.556796i
$743$	−11.7877	+	6.80565i	−0.432450	+	0.249675i	−0.700390	−	0.713760i	$-0.746991\pi$
$743$	−11.7877	+	6.80565i	−0.432450	+	0.249675i	0.267940	+	0.963436i	$0.413657\pi$
$744$	−3.94917	+	6.27640i	−0.144783	+	0.230104i
$745$	−6.07088	+	10.5151i	−0.222420	+	0.385243i
$746$	−18.8508	+	3.07810i	−0.690175	+	0.112697i
$747$	−7.97835	+	13.8189i	−0.291913	+	0.505607i
$748$	13.2409	−	65.3593i	0.484134	−	2.38977i
$749$	9.52001			0.347854
$750$	−0.471265	+	1.24545i	−0.0172082	+	0.0454774i
$751$	1.60795	+	2.78505i	0.0586748	+	0.101628i	0.893871	−	0.448325i	$-0.147979\pi$
$751$	1.60795	+	2.78505i	0.0586748	+	0.101628i	−0.835196	+	0.549952i	$0.814646\pi$
$752$	−11.4001	+	26.9818i	−0.415720	+	0.983926i
$753$	−1.53913			−0.0560889
$754$	−10.2957	−	16.7261i	−0.374946	−	0.609130i
$755$			2.19357i			0.0798321i
$756$	23.5023	+	20.7583i	0.854772	+	0.754971i
$757$	18.8023	−	10.8555i	0.683381	−	0.394550i	−0.117746	−	0.993044i	$-0.537567\pi$
$757$	18.8023	−	10.8555i	0.683381	−	0.394550i	0.801128	+	0.598493i	$0.204234\pi$
$758$	42.4788	+	16.0735i	1.54290	+	0.583817i
$759$			31.5230i			1.14421i
$760$	−18.3520	−	0.698100i	−0.665698	−	0.0253227i
$761$	9.68269	+	5.59031i	0.350997	+	0.202648i	0.665124	−	0.746733i	$-0.268378\pi$
$761$	9.68269	+	5.59031i	0.350997	+	0.202648i	−0.314127	+	0.949381i	$0.601712\pi$
$762$	−5.95452	+	0.972299i	−0.215709	+	0.0352227i
$763$	−3.16754	−	1.82878i	−0.114672	−	0.0662062i
$764$	−1.63937	−	1.44796i	−0.0593102	−	0.0523853i
$765$	−7.69990	−	13.3366i	−0.278390	−	0.482186i
$766$	−51.1541	+	8.35283i	−1.84827	+	0.301800i
$767$	2.63405	+	6.40965i	0.0951101	+	0.231439i
$768$	−14.4958	−	4.10441i	−0.523072	−	0.148105i
$769$	17.5967	−	10.1595i	0.634553	−	0.366360i	−0.147960	−	0.988993i	$-0.547271\pi$
$769$	17.5967	−	10.1595i	0.634553	−	0.366360i	0.782513	+	0.622634i	$0.213937\pi$
$770$	−13.3396	−	16.3130i	−0.480725	−	0.587878i

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:	\( N \)	\(=\)	\( 520 = 2^{3} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	520.ca (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.09478 + 0.895236i) q^{2} +(-0.815452 + 0.470802i) q^{3} +(0.397104 - 1.96018i) q^{4} -1.00000 q^{5} +(0.471265 - 1.24545i) q^{6} +(-2.82007 - 1.62817i) q^{7} +(1.32008 + 2.50148i) q^{8} +(-1.05669 + 1.83024i) q^{9} +(1.09478 - 0.895236i) q^{10} +(2.28794 + 3.96283i) q^{11} +(0.599037 + 1.78539i) q^{12} +(-2.20289 + 2.85434i) q^{13} +(4.54496 - 0.742136i) q^{14} +(0.815452 - 0.470802i) q^{15} +(-3.68462 - 1.55679i) q^{16} +(3.64340 - 6.31055i) q^{17} +(-0.481651 - 2.94971i) q^{18} +(3.24655 - 5.62320i) q^{19} +(-0.397104 + 1.96018i) q^{20} +3.06618 q^{21} +(-6.05247 - 2.29020i) q^{22} +(-3.65810 - 6.33601i) q^{23} +(-2.25416 - 1.41834i) q^{24} +1.00000 q^{25} +(-0.143626 - 5.09700i) q^{26} -4.81478i q^{27} +(-4.31136 + 4.88129i) q^{28} +(3.33584 - 1.92595i) q^{29} +(-0.471265 + 1.24545i) q^{30} -2.78436i q^{31} +(5.42756 - 1.59425i) q^{32} +(-3.73142 - 2.15433i) q^{33} +(1.66070 + 10.1704i) q^{34} +(2.82007 + 1.62817i) q^{35} +(3.16799 + 2.79810i) q^{36} +(2.57569 + 4.46122i) q^{37} +(1.47981 + 9.06262i) q^{38} +(0.452520 - 3.36471i) q^{39} +(-1.32008 - 2.50148i) q^{40} +(3.47276 - 2.00500i) q^{41} +(-3.35680 + 2.74495i) q^{42} +(-6.09210 - 3.51727i) q^{43} +(8.67642 - 2.91112i) q^{44} +(1.05669 - 1.83024i) q^{45} +(9.67705 + 3.66170i) q^{46} -7.32283i q^{47} +(3.73757 - 0.465234i) q^{48} +(1.80186 + 3.12092i) q^{49} +(-1.09478 + 0.895236i) q^{50} +6.86127i q^{51} +(4.72026 + 5.45153i) q^{52} +3.33709i q^{53} +(4.31036 + 5.27114i) q^{54} +(-2.28794 - 3.96283i) q^{55} +(0.350102 - 9.20365i) q^{56} +6.11393i q^{57} +(-1.92785 + 5.09486i) q^{58} +(0.960988 - 1.66448i) q^{59} +(-0.599037 - 1.78539i) q^{60} +(-4.19212 - 2.42032i) q^{61} +(2.49266 + 3.04827i) q^{62} +(5.95989 - 3.44094i) q^{63} +(-4.51477 + 6.60431i) q^{64} +(2.20289 - 2.85434i) q^{65} +(6.01373 - 0.981968i) q^{66} +(0.105635 + 0.182965i) q^{67} +(-10.9230 - 9.64766i) q^{68} +(5.96601 + 3.44448i) q^{69} +(-4.54496 + 0.742136i) q^{70} +(-5.29581 - 3.05754i) q^{71} +(-5.97323 - 0.227218i) q^{72} +7.65793i q^{73} +(-6.81367 - 2.57822i) q^{74} +(-0.815452 + 0.470802i) q^{75} +(-9.73326 - 8.59683i) q^{76} -14.9006i q^{77} +(2.51679 + 4.08874i) q^{78} +14.7003 q^{79} +(3.68462 + 1.55679i) q^{80} +(-0.903270 - 1.56451i) q^{81} +(-2.00697 + 5.30398i) q^{82} +7.55031 q^{83} +(1.21759 - 6.01026i) q^{84} +(-3.64340 + 6.31055i) q^{85} +(9.81832 - 1.60321i) q^{86} +(-1.81348 + 3.14104i) q^{87} +(-6.89266 + 10.9545i) q^{88} +(-4.09878 + 2.36643i) q^{89} +(0.481651 + 2.94971i) q^{90} +(10.8597 - 4.46278i) q^{91} +(-13.8724 + 4.65448i) q^{92} +(1.31088 + 2.27051i) q^{93} +(6.55566 + 8.01692i) q^{94} +(-3.24655 + 5.62320i) q^{95} +(-3.67534 + 3.85534i) q^{96} +(7.27269 + 4.19889i) q^{97} +(-4.76661 - 1.80364i) q^{98} -9.67060 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 6 q^{4} - 56 q^{5} - 5 q^{6} + 28 q^{9} + 8 q^{11} + 6 q^{12} - 4 q^{14} - 10 q^{16} - 18 q^{18} + 16 q^{19} + 6 q^{20} - 6 q^{22} + 12 q^{23} + 2 q^{24} + 56 q^{25} + 11 q^{26} + 6 q^{28} + 5 q^{30}+ \cdots + 48 q^{99}+O(q^{100}) \) 56 * q - 6 * q^4 - 56 * q^5 - 5 * q^6 + 28 * q^9 + 8 * q^11 + 6 * q^12 - 4 * q^14 - 10 * q^16 - 18 * q^18 + 16 * q^19 + 6 * q^20 - 6 * q^22 + 12 * q^23 + 2 * q^24 + 56 * q^25 + 11 * q^26 + 6 * q^28 + 5 * q^30 + 16 * q^34 - 21 * q^36 - 4 * q^37 - 24 * q^39 + 29 * q^42 - 24 * q^44 - 28 * q^45 - 11 * q^46 + 3 * q^48 + 20 * q^49 + 18 * q^52 - 49 * q^54 - 8 * q^55 + 61 * q^56 - 47 * q^58 + 16 * q^59 - 6 * q^60 - 2 * q^62 - 30 * q^64 + 14 * q^66 + 36 * q^67 + 33 * q^68 + 4 * q^70 - 51 * q^72 - 2 * q^74 - 48 * q^76 - 35 * q^78 + 10 * q^80 - 28 * q^81 - 21 * q^82 - 40 * q^83 - 61 * q^84 + 28 * q^86 - 36 * q^87 + 41 * q^88 + 18 * q^90 - 16 * q^91 - 18 * q^92 - 41 * q^94 - 16 * q^95 + 48 * q^96 + 24 * q^97 + 28 * q^98 + 48 * q^99

Introduction

L-functions

Modular forms

Varieties

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