LMFDB - Embedded newform 520.2.ca.b.381.4

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			381.4
Character	$\chi$	$=$	520.381
Dual form			520.2.ca.b.101.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.32269 - 0.500493i) q^{2} +(0.815452 + 0.470802i) q^{3} +(1.49901 + 1.32399i) q^{4} +1.00000 q^{5} +(-0.842957 - 1.03085i) q^{6} +(-2.82007 + 1.62817i) q^{7} +(-1.32008 - 2.50148i) q^{8} +(-1.05669 - 1.83024i) q^{9} +O(q^{10})$	\(q+(-1.32269 - 0.500493i) q^{2} +(0.815452 + 0.470802i) q^{3} +(1.49901 + 1.32399i) q^{4} +1.00000 q^{5} +(-0.842957 - 1.03085i) q^{6} +(-2.82007 + 1.62817i) q^{7} +(-1.32008 - 2.50148i) q^{8} +(-1.05669 - 1.83024i) q^{9} +(-1.32269 - 0.500493i) 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} +(0.494087 + 3.96937i) q^{16} +(3.64340 + 6.31055i) q^{17} +(0.481651 + 2.94971i) q^{18} +(-3.24655 - 5.62320i) q^{19} +(1.49901 + 1.32399i) q^{20} -3.06618 q^{21} +(5.00960 - 4.09650i) q^{22} +(-3.65810 + 6.33601i) q^{23} +(0.101236 - 2.66133i) q^{24} +1.00000 q^{25} +(-1.48516 - 4.87794i) q^{26} -4.81478i q^{27} +(-6.38301 - 1.29310i) q^{28} +(-3.33584 - 1.92595i) q^{29} +(-0.842957 - 1.03085i) q^{30} +2.78436i q^{31} +(1.33312 - 5.49753i) q^{32} +(-3.73142 + 2.15433i) q^{33} +(-1.66070 - 10.1704i) q^{34} +(-2.82007 + 1.62817i) q^{35} +(0.839233 - 4.14261i) 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} +(4.05560 + 1.53460i) q^{42} +(6.09210 - 3.51727i) q^{43} +(-8.67642 + 2.91112i) q^{44} +(-1.05669 - 1.83024i) q^{45} +(8.00965 - 6.54972i) q^{46} +7.32283i q^{47} +(-1.46588 + 3.46945i) q^{48} +(1.80186 - 3.12092i) q^{49} +(-1.32269 - 0.500493i) q^{50} +6.86127i q^{51} +(-0.476971 + 7.19531i) q^{52} +3.33709i q^{53} +(-2.40976 + 6.36846i) q^{54} +(-2.28794 + 3.96283i) q^{55} +(7.79555 + 4.90502i) q^{56} -6.11393i q^{57} +(3.44836 + 4.21699i) q^{58} +(-0.960988 - 1.66448i) q^{59} +(0.599037 + 1.78539i) q^{60} +(4.19212 - 2.42032i) q^{61} +(1.39355 - 3.68284i) 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} +(-2.89362 + 14.2834i) q^{68} +(-5.96601 + 3.44448i) q^{69} +(4.54496 - 0.742136i) q^{70} +(-5.29581 + 3.05754i) q^{71} +(-3.18339 + 5.05936i) q^{72} -7.65793i q^{73} +(5.63964 - 4.61170i) q^{74} +(0.815452 + 0.470802i) q^{75} +(2.57844 - 12.7277i) q^{76} -14.9006i q^{77} +(1.08547 - 4.67694i) q^{78} +14.7003 q^{79} +(0.494087 + 3.96937i) q^{80} +(-0.903270 + 1.56451i) q^{81} +(-3.58989 - 4.39008i) q^{82} -7.55031 q^{83} +(-4.59624 - 4.05959i) q^{84} +(3.64340 + 6.31055i) q^{85} +(-9.81832 + 1.60321i) q^{86} +(-1.81348 - 3.14104i) q^{87} +(12.9332 + 0.491972i) 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} +(3.66502 - 9.68583i) q^{94} +(-3.24655 - 5.62320i) q^{95} +(3.67534 - 3.85534i) q^{96} +(7.27269 - 4.19889i) q^{97} +(-3.94530 + 3.22618i) q^{98} +9.67060 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 6 q^{4} + 56 q^{5} - 13 q^{6} + 28 q^{9}+O(q^{10}) $ 56 * q + 6 * q^4 + 56 * q^5 - 13 * q^6 + 28 * q^9	$ 56 q + 6 q^{4} + 56 q^{5} - 13 q^{6} + 28 q^{9} - 8 q^{11} + 6 q^{12} - 4 q^{14} + 14 q^{16} + 18 q^{18} - 16 q^{19} + 6 q^{20} - 6 q^{22} + 12 q^{23} + 22 q^{24} + 56 q^{25} - 37 q^{26} - 12 q^{28} - 13 q^{30} - 30 q^{32} - 16 q^{34} + 15 q^{36} + 4 q^{37} - 24 q^{39} - 61 q^{42} + 24 q^{44} + 28 q^{45} - 19 q^{46} - 51 q^{48} + 20 q^{49} - 64 q^{52} - 5 q^{54} - 8 q^{55} - 23 q^{56} - q^{58} - 16 q^{59} + 6 q^{60} + 10 q^{62} - 30 q^{64} + 14 q^{66} - 36 q^{67} - 51 q^{68} - 4 q^{70} - 81 q^{72} + 70 q^{74} - 60 q^{76} + 143 q^{78} + 14 q^{80} - 28 q^{81} + 21 q^{82} + 40 q^{83} + 31 q^{84} - 28 q^{86} - 36 q^{87} - 19 q^{88} + 18 q^{90} + 16 q^{91} - 18 q^{92} + 43 q^{94} - 16 q^{95} - 48 q^{96} + 24 q^{97} + 56 q^{98} - 48 q^{99}+O(q^{100}) $ 56 * q + 6 * q^4 + 56 * q^5 - 13 * q^6 + 28 * q^9 - 8 * q^11 + 6 * q^12 - 4 * q^14 + 14 * q^16 + 18 * q^18 - 16 * q^19 + 6 * q^20 - 6 * q^22 + 12 * q^23 + 22 * q^24 + 56 * q^25 - 37 * q^26 - 12 * q^28 - 13 * q^30 - 30 * q^32 - 16 * q^34 + 15 * q^36 + 4 * q^37 - 24 * q^39 - 61 * q^42 + 24 * q^44 + 28 * q^45 - 19 * q^46 - 51 * q^48 + 20 * q^49 - 64 * q^52 - 5 * q^54 - 8 * q^55 - 23 * q^56 - q^58 - 16 * q^59 + 6 * q^60 + 10 * q^62 - 30 * q^64 + 14 * q^66 - 36 * q^67 - 51 * q^68 - 4 * q^70 - 81 * q^72 + 70 * q^74 - 60 * q^76 + 143 * q^78 + 14 * q^80 - 28 * q^81 + 21 * q^82 + 40 * q^83 + 31 * q^84 - 28 * q^86 - 36 * q^87 - 19 * q^88 + 18 * q^90 + 16 * q^91 - 18 * q^92 + 43 * q^94 - 16 * q^95 - 48 * q^96 + 24 * q^97 + 56 * q^98 - 48 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−1.32269	−	0.500493i	−0.935283	−	0.353902i
$2$	−1.32269	−	0.500493i	−0.935283	−	0.353902i
$3$	0.815452	+	0.470802i	0.470802	+	0.271817i	0.716575	−	0.697510i	$-0.245709\pi$
$3$	0.815452	+	0.470802i	0.470802	+	0.271817i	−0.245774	+	0.969327i	$0.579042\pi$
$4$	1.49901	+	1.32399i	0.749507	+	0.661996i
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$	−0.842957	−	1.03085i	−0.344136	−	0.420844i
$7$	−2.82007	+	1.62817i	−1.06589	+	0.615390i	−0.927055	−	0.374926i	$-0.877668\pi$
$7$	−2.82007	+	1.62817i	−1.06589	+	0.615390i	−0.138832	+	0.990316i	$0.544335\pi$
$8$	−1.32008	−	2.50148i	−0.466719	−	0.884405i
$9$	−1.05669	−	1.83024i	−0.352231	−	0.610081i
$10$	−1.32269	−	0.500493i	−0.418271	−	0.158270i
$11$	−2.28794	+	3.96283i	−0.689840	+	1.19484i	0.282049	+	0.959400i	$0.408986\pi$
$11$	−2.28794	+	3.96283i	−0.689840	+	1.19484i	−0.971889	+	0.235439i	$0.924347\pi$
$12$	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
$16$	0.494087	+	3.96937i	0.123522	+	0.992342i
$17$	3.64340	+	6.31055i	0.883654	+	1.53053i	0.847249	+	0.531196i	$0.178257\pi$
$17$	3.64340	+	6.31055i	0.883654	+	1.53053i	0.0364049	+	0.999337i	$0.488409\pi$
$18$	0.481651	+	2.94971i	0.113526	+	0.695253i
$19$	−3.24655	−	5.62320i	−0.744811	−	1.29005i	−0.950283	−	0.311387i	$-0.899206\pi$
$19$	−3.24655	−	5.62320i	−0.744811	−	1.29005i	0.205472	−	0.978663i	$-0.434127\pi$
$20$	1.49901	+	1.32399i	0.335190	+	0.296054i
$21$	−3.06618			−0.669095
$22$	5.00960	−	4.09650i	1.06805	−	0.873376i
$23$	−3.65810	+	6.33601i	−0.762766	+	1.32115i	0.178654	+	0.983912i	$0.442826\pi$
$23$	−3.65810	+	6.33601i	−0.762766	+	1.32115i	−0.941420	+	0.337237i	$0.890507\pi$
$24$	0.101236	−	2.66133i	0.0206646	−	0.543242i
$25$	1.00000			0.200000
$26$	−1.48516	−	4.87794i	−0.291263	−	0.956643i
$27$		−	4.81478i		−	0.926605i
$28$	−6.38301	−	1.29310i	−1.20627	−	0.244374i
$29$	−3.33584	−	1.92595i	−0.619450	−	0.357640i	0.157205	−	0.987566i	$-0.449752\pi$
$29$	−3.33584	−	1.92595i	−0.619450	−	0.357640i	−0.776655	+	0.629926i	$0.783085\pi$
$30$	−0.842957	−	1.03085i	−0.153902	−	0.188207i
$31$			2.78436i			0.500086i	0.968235	+	0.250043i	$0.0804448\pi$
$31$			2.78436i			0.500086i	−0.968235	+	0.250043i	$0.919555\pi$
$32$	1.33312	−	5.49753i	0.235664	−	0.971835i
$33$	−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
$36$	0.839233	−	4.14261i	0.139872	−	0.690436i
$37$	−2.57569	+	4.46122i	−0.423440	+	0.733420i	−0.996273	−	0.0862519i	$-0.972511\pi$
$37$	−2.57569	+	4.46122i	−0.423440	+	0.733420i	0.572833	+	0.819672i	$0.305844\pi$
$38$	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	0.746032	−	0.665910i	$-0.231956\pi$
$41$	3.47276	+	2.00500i	0.542354	+	0.313128i	−0.203679	+	0.979038i	$0.565290\pi$
$42$	4.05560	+	1.53460i	0.625793	+	0.236794i
$43$	6.09210	−	3.51727i	0.929036	−	0.536379i	0.0425296	−	0.999095i	$-0.486458\pi$
$43$	6.09210	−	3.51727i	0.929036	−	0.536379i	0.886507	+	0.462716i	$0.153125\pi$
$44$	−8.67642	+	2.91112i	−1.30802	+	0.438868i
$45$	−1.05669	−	1.83024i	−0.157522	−	0.272837i
$46$	8.00965	−	6.54972i	1.18096	−	0.965704i
$47$			7.32283i			1.06814i	0.845439	+	0.534072i	$0.179339\pi$
$47$			7.32283i			1.06814i	−0.845439	+	0.534072i	$0.820661\pi$
$48$	−1.46588	+	3.46945i	−0.211582	+	0.500772i
$49$	1.80186	−	3.12092i	0.257409	−	0.445845i
$50$	−1.32269	−	0.500493i	−0.187057	−	0.0707803i
$51$			6.86127i			0.960770i
$52$	−0.476971	+	7.19531i	−0.0661439	+	0.997810i
$53$			3.33709i			0.458385i	0.973381	+	0.229192i	$0.0736085\pi$
$53$			3.33709i			0.458385i	−0.973381	+	0.229192i	$0.926392\pi$
$54$	−2.40976	+	6.36846i	−0.327927	+	0.866637i
$55$	−2.28794	+	3.96283i	−0.308506	+	0.534348i
$56$	7.79555	+	4.90502i	1.04172	+	0.655461i
$57$		−	6.11393i		−	0.809810i
$58$	3.44836	+	4.21699i	0.452792	+	0.553719i
$59$	−0.960988	−	1.66448i	−0.125110	−	0.216697i	0.796666	−	0.604420i	$-0.206595\pi$
$59$	−0.960988	−	1.66448i	−0.125110	−	0.216697i	−0.921776	+	0.387723i	$0.873262\pi$
$60$	0.599037	+	1.78539i	0.0773353	+	0.230493i
$61$	4.19212	−	2.42032i	0.536745	−	0.309890i	−0.207014	−	0.978338i	$-0.566374\pi$
$61$	4.19212	−	2.42032i	0.536745	−	0.309890i	0.743759	+	0.668448i	$0.233041\pi$
$62$	1.39355	−	3.68284i	0.176981	−	0.467722i
$63$	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	$-0.837441\pi$
$67$	−0.105635	+	0.182965i	−0.0129054	+	0.0223528i	0.859501	+	0.511135i	$0.170775\pi$
$68$	−2.89362	+	14.2834i	−0.350903	+	1.73212i
$69$	−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	−0.780170	−	0.625568i	$-0.784867\pi$
$71$	−5.29581	+	3.05754i	−0.628497	+	0.362863i	0.151673	+	0.988431i	$0.451534\pi$
$72$	−3.18339	+	5.05936i	−0.375166	+	0.596251i
$73$		−	7.65793i		−	0.896293i	−0.893960	−	0.448146i	$-0.852084\pi$
$73$		−	7.65793i		−	0.896293i	0.893960	−	0.448146i	$-0.147916\pi$
$74$	5.63964	−	4.61170i	0.655595	−	0.536099i
$75$	0.815452	+	0.470802i	0.0941603	+	0.0543635i
$76$	2.57844	−	12.7277i	0.295767	−	1.45996i
$77$		−	14.9006i		−	1.69808i
$78$	1.08547	−	4.67694i	0.122905	−	0.529560i
$79$	14.7003			1.65392			0.826959	−	0.562262i	$-0.190069\pi$
$79$	14.7003			1.65392			0.826959	+	0.562262i	$0.190069\pi$
$80$	0.494087	+	3.96937i	0.0552407	+	0.443789i
$81$	−0.903270	+	1.56451i	−0.100363	+	0.173834i
$82$	−3.58989	−	4.39008i	−0.396437	−	0.484803i
$83$	−7.55031			−0.828754			−0.414377	−	0.910105i	$-0.636001\pi$
$83$	−7.55031			−0.828754			−0.414377	+	0.910105i	$0.636001\pi$
$84$	−4.59624	−	4.05959i	−0.501491	−	0.442938i
$85$	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
$88$	12.9332	+	0.491972i	1.37868	+	0.0524443i
$89$	−4.09878	−	2.36643i	−0.434470	−	0.250841i	0.266779	−	0.963758i	$-0.414041\pi$
$89$	−4.09878	−	2.36643i	−0.434470	−	0.250841i	−0.701249	+	0.712916i	$0.747374\pi$
$90$	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
$94$	3.66502	−	9.68583i	0.378018	−	0.999017i
$95$	−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	−0.0830682	−	0.996544i	$-0.526472\pi$
$97$	7.27269	−	4.19889i	0.738430	−	0.426333i	0.821498	+	0.570211i	$0.193139\pi$
$98$	−3.94530	+	3.22618i	−0.398535	+	0.325894i
$99$	9.67060			0.971932
$100$	1.49901	+	1.32399i	0.149901	+	0.132399i
$101$	8.39604	+	4.84746i	0.835437	+	0.482340i	0.855711	−	0.517455i	$-0.173120\pi$
$101$	8.39604	+	4.84746i	0.835437	+	0.482340i	−0.0202735	+	0.999794i	$0.506454\pi$
$102$	3.43402	−	9.07533i	0.340018	−	0.898592i
$103$	−9.65843			−0.951673			−0.475837	−	0.879534i	$-0.657855\pi$
$103$	−9.65843			−0.951673			−0.475837	+	0.879534i	$0.657855\pi$
$104$	4.23208	−	9.27844i	0.414990	−	0.909826i
$105$	−3.06618			−0.299228
$106$	1.67019	−	4.41393i	0.162223	−	0.428719i
$107$	2.53186	+	1.46177i	0.244764	+	0.141314i	0.617364	−	0.786677i	$-0.288200\pi$
$107$	2.53186	+	1.46177i	0.244764	+	0.141314i	−0.372601	+	0.927992i	$0.621534\pi$
$108$	6.37473	−	7.21742i	0.613409	−	0.694497i
$109$	−1.12321			−0.107584			−0.0537921	−	0.998552i	$-0.517131\pi$
$109$	−1.12321			−0.107584			−0.0537921	+	0.998552i	$0.517131\pi$
$110$	5.00960	−	4.09650i	0.477647	−	0.390586i
$111$	−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	0.991933	−	0.126764i	$-0.0404591\pi$
$113$	4.10521	+	7.11043i	0.386186	+	0.668893i	−0.605747	+	0.795657i	$0.707126\pi$
$114$	−3.05998	+	8.08683i	−0.286593	+	0.757401i
$115$	−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
$120$	0.101236	−	2.66133i	0.00924150	−	0.242945i
$121$	−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
$124$	−3.68647	+	4.17380i	−0.331055	+	0.374818i
$125$	1.00000			0.0894427
$126$	−6.16091	−	7.53418i	−0.548858	−	0.671198i
$127$	−2.26541	+	3.92381i	−0.201023	+	0.348182i	−0.948858	−	0.315702i	$-0.897760\pi$
$127$	−2.26541	+	3.92381i	−0.201023	+	0.348182i	0.747835	+	0.663884i	$0.231093\pi$
$128$	9.27704	−	6.47584i	0.819983	−	0.572389i
$129$	6.62375			0.583189
$130$	−1.48516	−	4.87794i	−0.130257	−	0.427824i
$131$		−	18.1375i		−	1.58468i	−0.610078	−	0.792342i	$-0.708862\pi$
$131$		−	18.1375i		−	1.58468i	0.610078	−	0.792342i	$-0.291138\pi$
$132$	−8.44577	−	1.71099i	−0.735110	−	0.148923i
$133$	18.3110	+	10.5719i	1.58777	+	0.916698i
$134$	0.231295	−	0.189137i	0.0199808	−	0.0163389i
$135$		−	4.81478i		−	0.414390i
$136$	10.9761	−	17.4443i	0.941194	−	1.49584i
$137$	10.3515	−	5.97644i	0.884389	−	0.510602i	0.0122856	−	0.999925i	$-0.496089\pi$
$137$	10.3515	−	5.97644i	0.884389	−	0.510602i	0.872103	+	0.489323i	$0.162756\pi$
$138$	9.61511	−	1.57003i	0.818493	−	0.133650i
$139$	17.3034	−	9.99011i	1.46765	−	0.847350i	0.468310	−	0.883564i	$-0.344863\pi$
$139$	17.3034	−	9.99011i	1.46765	−	0.847350i	0.999344	+	0.0362139i	$0.0115298\pi$
$140$	−6.38301	−	1.29310i	−0.539463	−	0.109287i
$141$	−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
$146$	−3.83274	+	10.1291i	−0.317200	+	0.838287i
$147$	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	$-0.332359\pi$
$149$	−6.07088	−	10.5151i	−0.497346	−	0.861429i	−0.999995	+	0.00306162i	$0.999025\pi$
$150$	−0.842957	−	1.03085i	−0.0688272	−	0.0841687i
$151$			2.19357i			0.178510i	0.996009	+	0.0892550i	$0.0284486\pi$
$151$			2.19357i			0.178510i	−0.996009	+	0.0892550i	$0.971551\pi$
$152$	−9.78058	+	15.5443i	−0.793310	+	1.26081i
$153$	7.69990	−	13.3366i	0.622500	−	1.07820i
$154$	−7.45765	+	19.7089i	−0.600954	+	1.58819i
$155$			2.78436i			0.223645i
$156$	−3.77651	+	5.64287i	−0.302363	+	0.451792i
$157$		−	21.5797i		−	1.72225i	−0.508395	−	0.861124i	$-0.669761\pi$
$157$		−	21.5797i		−	1.72225i	0.508395	−	0.861124i	$-0.330239\pi$
$158$	−19.4440	−	7.35741i	−1.54688	−	0.585324i
$159$	−1.57111	+	2.72124i	−0.124597	+	0.215808i
$160$	1.33312	−	5.49753i	0.105392	−	0.434618i
$161$		−	23.8240i		−	1.87759i
$162$	1.97777	−	1.61728i	0.155388	−	0.127065i
$163$	7.84916	+	13.5951i	0.614794	+	1.06485i	0.990421	+	0.138083i	$0.0440941\pi$
$163$	7.84916	+	13.5951i	0.614794	+	1.06485i	−0.375627	+	0.926771i	$0.622573\pi$
$164$	2.55111	+	7.60342i	0.199208	+	0.593728i
$165$	−3.73142	+	2.15433i	−0.290490	+	0.167715i
$166$	9.98672	+	3.77888i	0.775120	+	0.293298i
$167$	8.80939	+	5.08611i	0.681691	+	0.393575i	0.800492	−	0.599343i	$-0.204572\pi$
$167$	8.80939	+	5.08611i	0.681691	+	0.393575i	−0.118801	+	0.992918i	$0.537905\pi$
$168$	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
$172$	13.7890	+	2.79345i	1.05140	+	0.212998i
$173$	−15.2799	+	8.82187i	−1.16171	+	0.670714i	−0.951714	−	0.306987i	$-0.900679\pi$
$173$	−15.2799	+	8.82187i	−1.16171	+	0.670714i	−0.209998	+	0.977702i	$0.567346\pi$
$174$	0.826603	+	5.06225i	0.0626646	+	0.383768i
$175$	−2.82007	+	1.62817i	−0.213177	+	0.123078i
$176$	−16.8604	−	7.12370i	−1.27090	−	0.536969i
$177$		−	1.80974i		−	0.136028i
$178$	4.23703	+	5.18146i	0.317579	+	0.388367i
$179$	−1.09869	−	0.634330i	−0.0821201	−	0.0474120i	0.458378	−	0.888758i	$-0.348431\pi$
$179$	−1.09869	−	0.634330i	−0.0821201	−	0.0474120i	−0.540498	+	0.841345i	$0.681764\pi$
$180$	0.839233	−	4.14261i	0.0625527	−	0.308772i
$181$		−	13.4062i		−	0.996473i	−0.867041	−	0.498237i	$-0.833981\pi$
$181$		−	13.4062i		−	0.996473i	0.867041	−	0.498237i	$-0.166019\pi$
$182$	12.1304	+	11.3380i	0.899162	+	0.840432i
$183$	4.55796			0.336934
$184$	20.6784	+	0.786593i	1.52443	+	0.0579884i
$185$	−2.57569	+	4.46122i	−0.189368	+	0.327995i
$186$	2.87026	−	2.34710i	0.210458	−	0.172098i
$187$	−33.3435			−2.43832
$188$	−9.69537	+	10.9770i	−0.707108	+	0.800582i
$189$	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	0.885130	−	0.465343i	$-0.154069\pi$
$191$	0.546815	+	0.947111i	0.0395661	+	0.0685306i	−0.845564	+	0.533874i	$0.820736\pi$
$192$	−6.79090	+	3.25994i	−0.490091	+	0.235266i
$193$	−17.4409	−	10.0695i	−1.25543	−	0.724821i	−0.283244	−	0.959048i	$-0.591411\pi$
$193$	−17.4409	−	10.0695i	−1.25543	−	0.724821i	−0.972182	+	0.234227i	$0.924744\pi$
$194$	−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	$-0.680148\pi$
$197$	6.49688	−	11.2529i	0.462884	−	0.801738i	0.999103	+	0.0423403i	$0.0134814\pi$
$198$	−12.7912	−	4.84006i	−0.909031	−	0.343968i
$199$	−2.01275	−	3.48619i	−0.142680	−	0.247130i	0.785825	−	0.618449i	$-0.212239\pi$
$199$	−2.01275	−	3.48619i	−0.142680	−	0.247130i	−0.928505	+	0.371320i	$0.878905\pi$
$200$	−1.32008	−	2.50148i	−0.0933439	−	0.176881i
$201$	−0.172281	+	0.0994662i	−0.0121517	+	0.00701581i
$202$	−8.67924	−	10.6138i	−0.610669	−	0.746787i
$203$	12.5431			0.880351
$204$	−9.08427	+	10.2851i	−0.636026	+	0.720104i
$205$	3.47276	+	2.00500i	0.242548	+	0.140035i
$206$	12.7751	+	4.83397i	0.890083	+	0.336799i
$207$	15.4619			1.07468
$208$	−10.2415	+	10.1544i	−0.710122	+	0.704079i
$209$	29.7117			2.05520
$210$	4.05560	+	1.53460i	0.279863	+	0.105897i
$211$	18.4537	+	10.6543i	1.27041	+	0.733469i	0.975064	−	0.221922i	$-0.0712332\pi$
$211$	18.4537	+	10.6543i	1.27041	+	0.733469i	0.295342	+	0.955392i	$0.404566\pi$
$212$	−4.41828	+	5.00235i	−0.303449	+	0.343563i
$213$	−5.75797			−0.394530
$214$	−2.61725	−	3.20064i	−0.178912	−	0.218791i
$215$	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
$218$	1.48566	+	0.562159i	0.100622	+	0.0380742i
$219$	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	0.755294	−	0.655386i	$-0.227494\pi$
$223$	8.44262	+	4.87435i	0.565359	+	0.326410i	−0.189934	+	0.981797i	$0.560828\pi$
$224$	5.19142	+	17.6739i	0.346866	+	1.18089i
$225$	−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	$-0.0402878\pi$
$227$	5.82595	+	10.0908i	0.386682	+	0.669753i	−0.605319	+	0.795983i	$0.706954\pi$
$228$	8.09480	−	9.16487i	0.536091	−	0.606958i
$229$	21.6811			1.43273			0.716365	−	0.697726i	$-0.245805\pi$
$229$	21.6811			1.43273			0.716365	+	0.697726i	$0.245805\pi$
$230$	8.00965	−	6.54972i	0.528141	−	0.431876i
$231$	7.01523	−	12.1507i	0.461569	−	0.799460i
$232$	−0.414133	+	10.8869i	−0.0271891	+	0.714762i
$233$	16.1554			1.05838			0.529188	−	0.848505i	$-0.322497\pi$
$233$	16.1554			1.05838			0.529188	+	0.848505i	$0.322497\pi$
$234$	−7.35847	+	7.87268i	−0.481038	+	0.514653i
$235$			7.32283i			0.477689i
$236$	0.763224	−	3.76742i	0.0496817	−	0.245238i
$237$	11.9874	+	6.92095i	0.778667	+	0.449564i
$238$	21.2424	+	25.9773i	1.37694	+	1.68386i
$239$			0.979222i			0.0633406i	0.999498	+	0.0316703i	$0.0100827\pi$
$239$			0.979222i			0.0633406i	−0.999498	+	0.0316703i	$0.989917\pi$
$240$	−1.46588	+	3.46945i	−0.0946221	+	0.223952i
$241$	9.26265	−	5.34779i	0.596660	−	0.344482i	−0.171067	−	0.985259i	$-0.554721\pi$
$241$	9.26265	−	5.34779i	0.596660	−	0.344482i	0.767726	+	0.640778i	$0.221388\pi$
$242$	2.26509	+	13.8718i	0.145605	+	0.891710i
$243$	−13.9823	+	8.07269i	−0.896965	+	0.517863i
$244$	9.48852	+	1.92224i	0.607441	+	0.123059i
$245$	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
$250$	−1.32269	−	0.500493i	−0.0836542	−	0.0316539i
$251$	−1.41559	+	0.817291i	−0.0893512	+	0.0515869i	−0.544010	−	0.839079i	$-0.683095\pi$
$251$	−1.41559	+	0.817291i	−0.0893512	+	0.0515869i	0.454659	+	0.890666i	$0.349761\pi$
$252$	4.37817	+	13.0489i	0.275799	+	0.822002i
$253$	−16.7390	−	28.9928i	−1.05237	−	1.82276i
$254$	4.96028	−	4.05616i	0.311235	−	0.254506i
$255$			6.86127i			0.429669i
$256$	−15.5118	+	3.92243i	−0.969485	+	0.245152i
$257$	−14.2913	+	24.7533i	−0.891469	+	1.54407i	−0.0533543	+	0.998576i	$0.516991\pi$
$257$	−14.2913	+	24.7533i	−0.891469	+	1.54407i	−0.838115	+	0.545494i	$0.816342\pi$
$258$	−8.76117	−	3.31514i	−0.545447	−	0.206392i
$259$		−	16.7746i		−	1.04232i
$260$	−0.476971	+	7.19531i	−0.0295805	+	0.446234i
$261$			8.14053i			0.503886i
$262$	−9.07770	+	23.9903i	−0.560822	+	1.48213i
$263$	−0.592661	+	1.02652i	−0.0365451	+	0.0632979i	−0.883719	−	0.468017i	$-0.844969\pi$
$263$	−0.592661	+	1.02652i	−0.0365451	+	0.0632979i	0.847174	+	0.531315i	$0.178302\pi$
$264$	10.3148	+	6.49015i	0.634831	+	0.399441i
$265$			3.33709i			0.204996i
$266$	−18.9286	−	23.1478i	−1.16059	−	1.41928i
$267$	−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	$-0.884615\pi$
$269$	−17.9663	+	10.3729i	−1.09543	+	0.632444i	−0.160410	+	0.987051i	$0.551281\pi$
$270$	−2.40976	+	6.36846i	−0.146653	+	0.387572i
$271$	−3.99411	−	2.30600i	−0.242625	−	0.140079i	0.373758	−	0.927526i	$-0.378069\pi$
$271$	−3.99411	−	2.30600i	−0.242625	−	0.140079i	−0.616383	+	0.787447i	$0.711402\pi$
$272$	−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
$276$	−13.5036	−	2.73563i	−0.812821	−	0.164666i
$277$	17.0409	−	9.83855i	1.02389	−	0.591141i	0.108659	−	0.994079i	$-0.465344\pi$
$277$	17.0409	−	9.83855i	1.02389	−	0.591141i	0.915227	+	0.402938i	$0.132011\pi$
$278$	−27.8870	+	4.55360i	−1.67255	+	0.273107i
$279$	5.09606	−	2.94221i	0.305093	−	0.176146i
$280$	7.79555	+	4.90502i	0.465873	+	0.293131i
$281$			22.9775i			1.37072i	0.728203	+	0.685361i	$0.240356\pi$
$281$			22.9775i			1.37072i	−0.728203	+	0.685361i	$0.759644\pi$
$282$	7.54876	−	6.17283i	0.449522	−	0.367587i
$283$	−15.4338	−	8.91072i	−0.917446	−	0.529688i	−0.0346264	−	0.999400i	$-0.511024\pi$
$283$	−15.4338	−	8.91072i	−0.917446	−	0.529688i	−0.882819	+	0.469713i	$0.844357\pi$
$284$	−11.9866	−	2.42832i	−0.711276	−	0.144094i
$285$		−	6.11393i		−	0.362158i
$286$	22.7284	+	5.27501i	1.34396	+	0.311918i
$287$	−13.0579			−0.770783
$288$	−11.4705	+	3.36927i	−0.675906	+	0.198536i
$289$	−18.0487	+	31.2613i	−1.06169	+	1.83890i
$290$	3.44836	+	4.21699i	0.202495	+	0.247630i
$291$	7.90738			0.463539
$292$	10.1390	−	11.4793i	0.593343	−	0.671778i
$293$	1.92052	+	3.32644i	0.112198	+	0.194333i	0.916656	−	0.399677i	$-0.130878\pi$
$293$	1.92052	+	3.32644i	0.112198	+	0.194333i	−0.804458	+	0.594009i	$0.797544\pi$
$294$	−4.73610	+	0.773346i	−0.276215	+	0.0451025i
$295$	−0.960988	−	1.66448i	−0.0559509	−	0.0969098i
$296$	14.5598	+	0.553845i	0.846269	+	0.0321916i
$297$	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
$302$	1.09786	−	2.90141i	0.0631750	−	0.166957i
$303$	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
$306$	−16.8594	+	13.7865i	−0.963790	+	0.788119i
$307$	0.0398307			0.00227326			0.00113663	−	0.999999i	$-0.499638\pi$
$307$	0.0398307			0.00227326			0.00113663	+	0.999999i	$0.499638\pi$
$308$	19.7283	−	22.3362i	1.12412	−	1.27273i
$309$	−7.87599	−	4.54720i	−0.448049	−	0.258681i
$310$	1.39355	−	3.68284i	0.0791484	−	0.209172i
$311$	11.5568			0.655328			0.327664	−	0.944794i	$-0.393739\pi$
$311$	11.5568			0.655328			0.327664	+	0.944794i	$0.393739\pi$
$312$	7.81937	−	5.57365i	0.442685	−	0.315546i
$313$	−15.1522			−0.856451			−0.428226	−	0.903672i	$-0.640861\pi$
$313$	−15.1522			−0.856451			−0.428226	+	0.903672i	$0.640861\pi$
$314$	−10.8005	+	28.5432i	−0.609506	+	1.61079i
$315$	5.95989	+	3.44094i	0.335802	+	0.193875i
$316$	22.0360	+	19.4631i	1.23962	+	1.09489i
$317$	21.4371			1.20403			0.602013	−	0.798486i	$-0.294365\pi$
$317$	21.4371			1.20403			0.602013	+	0.798486i	$0.294365\pi$
$318$	3.44005	−	2.81302i	0.192908	−	0.157747i
$319$	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
$322$	−11.9237	+	31.5117i	−0.664484	+	1.75608i
$323$	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
$328$	0.431131	−	11.3338i	0.0238052	−	0.625803i
$329$	−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	0.984914	+	0.173046i	$0.0553609\pi$
$331$	11.6860	+	20.2407i	0.642319	+	1.11253i	−0.342595	+	0.939483i	$0.611306\pi$
$332$	−11.3180	−	9.99656i	−0.621157	−	0.548632i
$333$	10.8868			0.596594
$334$	−9.10653	−	11.1364i	−0.498287	−	0.609355i
$335$	−0.105635	+	0.182965i	−0.00577146	+	0.00999645i
$336$	−1.51496	−	12.1708i	−0.0826478	−	0.663971i
$337$	−32.2953			−1.75924			−0.879619	−	0.475680i	$-0.842202\pi$
$337$	−32.2953			−1.75924			−0.879619	+	0.475680i	$0.842202\pi$
$338$	10.6517	−	14.9847i	0.579375	−	0.815061i
$339$			7.73096i			0.419888i
$340$	−2.89362	+	14.2834i	−0.156928	+	0.774628i
$341$	−11.0340	−	6.37046i	−0.597522	−	0.344980i
$342$	15.0231	−	12.2848i	0.812356	−	0.664287i
$343$		−	11.0594i		−	0.597152i
$344$	−16.8404	−	10.5962i	−0.907976	−	0.571306i
$345$	−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	$-0.707267\pi$
$347$	−4.10416	+	2.36954i	−0.220323	+	0.127203i	0.385777	+	0.922592i	$0.373933\pi$
$348$	1.44028	−	7.10949i	0.0772071	−	0.381109i
$349$	−11.1002	+	19.2260i	−0.594177	+	1.02915i	0.399485	+	0.916740i	$0.369189\pi$
$349$	−11.1002	+	19.2260i	−0.594177	+	1.02915i	−0.993662	+	0.112406i	$0.964144\pi$
$350$	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	0.883080	−	0.469223i	$-0.155466\pi$
$353$	17.2525	+	9.96076i	0.918260	+	0.530158i	0.0351807	+	0.999381i	$0.488799\pi$
$354$	−0.905761	+	2.39372i	−0.0481407	+	0.127225i
$355$	−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
$358$	1.13575	+	1.38891i	0.0600263	+	0.0734061i
$359$			8.08438i			0.426677i	0.976978	+	0.213339i	$0.0684337\pi$
$359$			8.08438i			0.426677i	−0.976978	+	0.213339i	$0.931566\pi$
$360$	−3.18339	+	5.05936i	−0.167779	+	0.266652i
$361$	−11.5802	+	20.0576i	−0.609486	+	1.05566i
$362$	−6.70969	+	17.7322i	−0.352654	+	0.931984i
$363$		−	9.35833i		−	0.491185i
$364$	−10.3701	−	21.0679i	−0.543540	−	1.10426i
$365$		−	7.65793i		−	0.400834i
$366$	−6.02877	−	2.28123i	−0.315129	−	0.119242i
$367$	0.926465	−	1.60468i	0.0483611	−	0.0837638i	−0.840832	−	0.541297i	$-0.817934\pi$
$367$	0.926465	−	1.60468i	0.0483611	−	0.0837638i	0.889193	+	0.457533i	$0.151267\pi$
$368$	−26.9574	−	11.3898i	−1.40525	−	0.593734i
$369$		−	8.47466i		−	0.441173i
$370$	5.63964	−	4.61170i	0.293191	−	0.239751i
$371$	−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	$-0.780369\pi$
$373$	−11.6966	+	6.75302i	−0.605625	+	0.349658i	0.165626	+	0.986189i	$0.447036\pi$
$374$	44.1031	+	16.6882i	2.28052	+	0.862926i
$375$	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	−0.0772193	−	0.997014i	$-0.524604\pi$
$379$	16.0577	−	27.8128i	0.824830	−	1.42865i	0.902049	−	0.431633i	$-0.142063\pi$
$380$	2.57844	−	12.7277i	0.132271	−	0.652916i
$381$	−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	0.635424	−	0.772163i	$-0.280825\pi$
$383$	31.7402	−	18.3252i	1.62185	−	0.936375i	0.986425	−	0.164212i	$-0.0525082\pi$
$384$	10.6138	−	0.913089i	0.541634	−	0.0465959i
$385$		−	14.9006i		−	0.759406i
$386$	18.0292	+	22.0479i	0.917663	+	1.12221i
$387$	−12.8749	−	7.43335i	−0.654470	−	0.377858i
$388$	16.4612	+	3.33479i	0.835689	+	0.169298i
$389$			19.7184i			0.999763i	0.866094	+	0.499881i	$0.166623\pi$
$389$			19.7184i			0.999763i	−0.866094	+	0.499881i	$0.833377\pi$
$390$	1.08547	−	4.67694i	0.0549647	−	0.236826i
$391$	−53.3116			−2.69608
$392$	−10.1855	−	0.387451i	−0.514446	−	0.0195692i
$393$	8.53918	−	14.7903i	0.430745	−	0.746072i
$394$	−14.2254	+	11.6325i	−0.716664	+	0.586036i
$395$	14.7003			0.739655
$396$	14.4964	+	12.8038i	0.728470	+	0.643415i
$397$	−5.90055	−	10.2200i	−0.296140	−	0.512929i	0.679109	−	0.734037i	$-0.262366\pi$
$397$	−5.90055	−	10.2200i	−0.296140	−	0.512929i	−0.975249	+	0.221108i	$0.929033\pi$
$398$	0.917435	+	5.61852i	0.0459869	+	0.281631i
$399$	9.95451	+	17.2417i	0.498349	+	0.863165i
$400$	0.494087	+	3.96937i	0.0247044	+	0.198468i
$401$	−15.0742	−	8.70308i	−0.752769	−	0.434611i	0.0739247	−	0.997264i	$-0.476448\pi$
$401$	−15.0742	−	8.70308i	−0.752769	−	0.434611i	−0.826693	+	0.562653i	$0.809781\pi$
$402$	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
$406$	−16.5906	−	6.27771i	−0.823377	−	0.311558i
$407$	−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	−0.639177	−	0.769060i	$-0.720725\pi$
$409$	−5.92031	+	3.41809i	−0.292740	+	0.169014i	0.346437	+	0.938073i	$0.387392\pi$
$410$	−3.58989	−	4.39008i	−0.177292	−	0.216811i
$411$	11.2549			0.555162
$412$	−14.4781	−	12.7877i	−0.713286	−	0.630004i
$413$	5.42011	+	3.12930i	0.266706	+	0.153983i
$414$	−20.4513	−	7.73858i	−1.00513	−	0.380330i
$415$	−7.55031			−0.370630
$416$	18.6285	−	8.30527i	0.913339	−	0.407199i
$417$	18.8134			0.921298
$418$	−39.2994	−	14.8705i	−1.92220	−	0.727340i
$419$	19.7820	+	11.4211i	0.966412	+	0.557958i	0.898140	−	0.439709i	$-0.144918\pi$
$419$	19.7820	+	11.4211i	0.966412	+	0.557958i	0.0682714	+	0.997667i	$0.478252\pi$
$420$	−4.59624	−	4.05959i	−0.224274	−	0.198088i
$421$	−30.1915			−1.47144			−0.735722	−	0.677283i	$-0.763157\pi$
$421$	−30.1915			−1.47144			−0.735722	+	0.677283i	$0.763157\pi$
$422$	−19.0762	−	23.3282i	−0.928613	−	1.13560i
$423$	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
$426$	7.61601	+	2.88182i	0.368997	+	0.139625i
$427$	−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	0.642339	−	0.766421i	$-0.277964\pi$
$431$	6.22337	+	3.59306i	0.299769	+	0.173072i	−0.342570	+	0.939492i	$0.611297\pi$
$432$	19.1116	−	2.37892i	0.919508	−	0.114456i
$433$	17.2895	+	29.9463i	0.830882	+	1.43913i	0.897340	+	0.441340i	$0.145497\pi$
$433$	17.2895	+	29.9463i	0.830882	+	1.43913i	−0.0664584	+	0.997789i	$0.521170\pi$
$434$	2.06638	+	12.6548i	0.0991892	+	0.607451i
$435$	−1.81348	−	3.14104i	−0.0869497	−	0.150601i
$436$	−1.68371	−	1.48712i	−0.0806351	−	0.0712203i
$437$	47.5049			2.27247
$438$	−7.89419	+	6.45531i	−0.377199	+	0.308447i
$439$	1.44165	−	2.49701i	0.0688063	−	0.119176i	−0.829570	−	0.558403i	$-0.811414\pi$
$439$	1.44165	−	2.49701i	0.0688063	−	0.119176i	0.898376	+	0.439227i	$0.144748\pi$
$440$	12.9332	+	0.491972i	0.616566	+	0.0234538i
$441$	−7.61605			−0.362669
$442$	25.3715	−	27.1444i	1.20680	−	1.29113i
$443$		−	1.83786i		−	0.0873193i	−0.999046	−	0.0436596i	$-0.986098\pi$
$443$		−	1.83786i		−	0.0873193i	0.999046	−	0.0436596i	$-0.0139017\pi$
$444$	−9.50795	−	1.92617i	−0.451228	−	0.0914121i
$445$	−4.09878	−	2.36643i	−0.194301	−	0.112180i
$446$	−8.72738	−	10.6727i	−0.413254	−	0.505368i
$447$		−	11.4327i		−	0.540750i
$448$	1.97904	−	25.9754i	0.0935010	−	1.22722i
$449$	−9.68862	+	5.59373i	−0.457234	+	0.263984i	−0.710881	−	0.703313i	$-0.751703\pi$
$449$	−9.68862	+	5.59373i	−0.457234	+	0.263984i	0.253646	+	0.967297i	$0.418370\pi$
$450$	0.481651	+	2.94971i	0.0227053	+	0.139051i
$451$	−15.8909	+	9.17464i	−0.748275	+	0.432017i
$452$	−3.26039	+	16.0939i	−0.153356	+	0.756994i
$453$	−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	0.838042	−	0.545605i	$-0.183700\pi$
$457$	16.7719	+	9.68325i	0.784555	+	0.452963i	−0.0534869	+	0.998569i	$0.517034\pi$
$458$	−28.6774	−	10.8512i	−1.34001	−	0.507046i
$459$	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	$-0.000328703\pi$
$461$	10.7162	+	18.5611i	0.499105	+	0.864476i	−0.500894	+	0.865509i	$0.666995\pi$
$462$	−15.3603	+	12.5606i	−0.714627	+	0.584371i
$463$			23.6913i			1.10103i	0.834825	+	0.550515i	$0.185569\pi$
$463$			23.6913i			1.10103i	−0.834825	+	0.550515i	$0.814431\pi$
$464$	5.99660	−	14.1928i	0.278385	−	0.658882i
$465$	−1.31088	+	2.27051i	−0.0607907	+	0.105293i
$466$	−21.3686	−	8.08566i	−0.989880	−	0.374561i
$467$			1.19692i			0.0553869i	0.999616	+	0.0276934i	$0.00881622\pi$
$467$			1.19692i			0.0553869i	−0.999616	+	0.0276934i	$0.991184\pi$
$468$	13.6732	−	6.73025i	0.632043	−	0.311106i
$469$		−	0.687966i		−	0.0317673i
$470$	3.66502	−	9.68583i	0.169055	−	0.446774i
$471$	10.1598	−	17.5972i	0.468137	−	0.810837i
$472$	−2.89507	+	4.60114i	−0.133257	+	0.211785i
$473$			32.1893i			1.48006i
$474$	−12.3918	−	15.1539i	−0.569173	−	0.696041i
$475$	−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
$478$	0.490093	−	1.29521i	0.0224163	−	0.0592413i
$479$	9.74703	+	5.62745i	0.445353	+	0.257125i	0.705866	−	0.708346i	$-0.250558\pi$
$479$	9.74703	+	5.62745i	0.445353	+	0.257125i	−0.260513	+	0.965470i	$0.583892\pi$
$480$	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
$484$	3.94670	−	19.4817i	0.179396	−	0.885531i
$485$	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	−0.718401	−	0.695629i	$-0.755126\pi$
$487$	−10.4861	+	6.05415i	−0.475170	+	0.274340i	0.243231	+	0.969968i	$0.421793\pi$
$488$	−11.5883	−	7.29146i	−0.524578	−	0.330069i
$489$			14.7816i			0.668447i
$490$	−3.94530	+	3.22618i	−0.178230	+	0.145744i
$491$	2.03007	+	1.17206i	0.0916159	+	0.0528945i	0.545108	−	0.838366i	$-0.316489\pi$
$491$	2.03007	+	1.17206i	0.0916159	+	0.0528945i	−0.453492	+	0.891260i	$0.649822\pi$
$492$	−1.49940	+	7.40130i	−0.0675980	+	0.333676i
$493$		−	28.0680i		−	1.26412i
$494$	−22.6080	+	24.1878i	−1.01718	+	1.08826i
$495$	9.67060			0.434661
$496$	−11.0522	+	1.37572i	−0.496256	+	0.0617715i
$497$	9.95636	−	17.2449i	0.446604	−	0.773541i
$498$	6.36459	+	7.78326i	0.285204	+	0.348776i
$499$	−0.0649069			−0.00290563			−0.00145282	−	0.999999i	$-0.500462\pi$
$499$	−0.0649069			−0.00290563			−0.00145282	+	0.999999i	$0.500462\pi$
$500$	1.49901	+	1.32399i	0.0670380	+	0.0592107i
$501$	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	−0.937256	−	0.348641i	$-0.886643\pi$
$503$	−17.2819	−	29.9331i	−0.770560	−	1.33465i	0.166697	−	0.986008i	$-0.446690\pi$
$504$	0.739899	−	19.4508i	0.0329577	−	0.866410i
$505$	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	$-0.767043\pi$
$509$	4.66463	−	8.07937i	0.206756	−	0.358112i	0.950691	+	0.310140i	$0.100376\pi$
$510$	3.43402	−	9.07533i	0.152061	−	0.401862i
$511$	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
$514$	31.2919	−	25.5882i	1.38022	−	1.12865i
$515$	−9.65843			−0.425601
$516$	9.92910	+	8.76980i	0.437104	+	0.386069i
$517$	−29.0191	−	16.7542i	−1.27626	−	0.736849i
$518$	−8.39557	+	22.1876i	−0.368880	+	0.974867i
$519$	−16.6134			−0.729247
$520$	4.23208	−	9.27844i	0.185589	−	0.406887i
$521$	12.9021			0.565251			0.282626	−	0.959230i	$-0.408795\pi$
$521$	12.9021			0.565251			0.282626	+	0.959230i	$0.408795\pi$
$522$	4.07428	−	10.7674i	0.178326	−	0.471276i
$523$	6.38548	+	3.68666i	0.279218	+	0.161206i	0.633069	−	0.774095i	$-0.281795\pi$
$523$	6.38548	+	3.68666i	0.279218	+	0.161206i	−0.353852	+	0.935302i	$0.615128\pi$
$524$	24.0140	−	27.1884i	1.04905	−	1.18773i
$525$	−3.06618			−0.133819
$526$	1.29767	−	1.06114i	0.0565812	−	0.0462681i
$527$	−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
$530$	1.67019	−	4.41393i	0.0725484	−	0.191729i
$531$	−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
$536$	0.597130	+	0.0227145i	0.0257921	+	0.000981116i
$537$	−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
$540$	6.37473	−	7.21742i	0.274325	−	0.310588i
$541$	10.9267			0.469775			0.234888	−	0.972023i	$-0.424528\pi$
$541$	10.9267			0.469775			0.234888	+	0.972023i	$0.424528\pi$
$542$	4.12883	+	5.04914i	0.177348	+	0.216879i
$543$	6.31165	−	10.9321i	0.270859	−	0.469141i
$544$	39.5495	−	11.6170i	1.69567	−	0.498074i
$545$	−1.12321			−0.0481131
$546$	4.55376	+	14.9566i	0.194883	+	0.640085i
$547$			37.9154i			1.62114i	0.585639	+	0.810572i	$0.300843\pi$
$547$			37.9154i			1.62114i	−0.585639	+	0.810572i	$0.699157\pi$
$548$	23.4298	+	4.74654i	1.00087	+	0.202762i
$549$	−8.85955	−	5.11506i	−0.378116	−	0.218306i
$550$	5.00960	−	4.09650i	0.213610	−	0.174675i
$551$			25.0108i			1.06550i
$552$	16.4919	+	10.3768i	0.701942	+	0.441668i
$553$	−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
$556$	39.1649	+	7.93423i	1.66096	+	0.336486i
$557$	−7.58932	+	13.1451i	−0.321570	+	0.556975i	−0.980812	−	0.194955i	$-0.937544\pi$
$557$	−7.58932	+	13.1451i	−0.321570	+	0.556975i	0.659242	+	0.751931i	$0.270877\pi$
$558$	−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
$562$	11.5001	−	30.3921i	0.485101	−	1.28201i
$563$	−9.61390	+	5.55059i	−0.405178	+	0.233929i	−0.688716	−	0.725032i	$-0.741825\pi$
$563$	−9.61390	+	5.55059i	−0.405178	+	0.233929i	0.283538	+	0.958961i	$0.408492\pi$
$564$	−13.0741	+	4.38664i	−0.550520	+	0.184711i
$565$	4.10521	+	7.11043i	0.172707	+	0.299138i
$566$	15.9544	+	19.5106i	0.670614	+	0.820093i
$567$		−	5.88270i		−	0.247050i
$568$	14.6393	+	9.21114i	0.614249	+	0.386491i
$569$	−2.01815	+	3.49553i	−0.0846051	+	0.146540i	−0.905223	−	0.424937i	$-0.860296\pi$
$569$	−2.01815	+	3.49553i	−0.0846051	+	0.146540i	0.820618	+	0.571477i	$0.193630\pi$
$570$	−3.05998	+	8.08683i	−0.128168	+	0.338720i
$571$			12.7832i			0.534960i	0.963563	+	0.267480i	$0.0861909\pi$
$571$			12.7832i			0.534960i	−0.963563	+	0.267480i	$0.913809\pi$
$572$	−27.4225	−	18.3526i	−1.14659	−	0.767361i
$573$			1.02977i			0.0430191i
$574$	17.2715	+	6.53538i	0.720900	+	0.272781i
$575$	−3.65810	+	6.33601i	−0.152553	+	0.264230i
$576$	16.8582	+	1.28441i	0.702425	+	0.0535172i
$577$			25.9751i			1.08136i	0.841229	+	0.540679i	$0.181832\pi$
$577$			25.9751i			1.08136i	−0.841229	+	0.540679i	$0.818168\pi$
$578$	39.5188	−	32.3157i	1.64377	−	1.34416i
$579$	−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
$582$	−10.4590	−	3.95758i	−0.433540	−	0.164047i
$583$	−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	0.392597	+	0.919711i	$0.371577\pi$
$587$	−14.5416	+	25.1867i	−0.600194	+	1.03957i	−0.992791	+	0.119856i	$0.961757\pi$
$588$	6.65144	+	1.34748i	0.274301	+	0.0555693i
$589$	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
$592$	−18.9808	−	8.01961i	−0.780108	−	0.329604i
$593$		−	25.3253i		−	1.03998i	−0.854171	−	0.519992i	$-0.825935\pi$
$593$		−	25.3253i		−	1.03998i	0.854171	−	0.519992i	$-0.174065\pi$
$594$	−19.7237	−	24.1201i	−0.809274	−	0.989661i
$595$	−20.5493	−	11.8641i	−0.842438	−	0.486382i
$596$	4.82155	−	23.8001i	0.197498	−	0.974888i
$597$		−	3.79043i		−	0.155132i
$598$	36.3395	+	8.43400i	1.48603	+	0.344892i
$599$	17.8764			0.730409			0.365205	−	0.930927i	$-0.380999\pi$
$599$	17.8764			0.730409			0.365205	+	0.930927i	$0.380999\pi$
$600$	0.101236	−	2.66133i	0.00413292	−	0.108648i
$601$	−10.6079	+	18.3734i	−0.432705	+	0.749467i	−0.997105	−	0.0760342i	$-0.975774\pi$
$601$	−10.6079	+	18.3734i	−0.432705	+	0.749467i	0.564400	+	0.825501i	$0.309108\pi$
$602$	25.0781	−	20.5070i	1.02211	−	0.835805i
$603$	0.446494			0.0181827
$604$	−2.90427	+	3.28819i	−0.118173	+	0.133794i
$605$	−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	0.929910	−	0.367786i	$-0.119884\pi$
$607$	3.60796	+	6.24918i	0.146443	+	0.253646i	−0.783468	+	0.621433i	$0.786551\pi$
$608$	−35.2417	+	10.3517i	−1.42924	+	0.419815i
$609$	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	$-0.916815\pi$
$613$	−6.41919	+	11.1184i	−0.259269	+	0.449067i	0.706777	+	0.707436i	$0.250148\pi$
$614$	−0.0526836	−	0.0199350i	−0.00212614	−	0.000804510i
$615$	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	−0.778550	−	0.627583i	$-0.784044\pi$
$617$	−15.5078	+	8.95345i	−0.624322	+	0.360452i	0.154228	+	0.988035i	$0.450711\pi$
$618$	8.14164	+	9.95641i	0.327505	+	0.400506i
$619$	−21.6358			−0.869618			−0.434809	−	0.900523i	$-0.643184\pi$
$619$	−21.6358			−0.869618			−0.434809	+	0.900523i	$0.643184\pi$
$620$	−3.68647	+	4.17380i	−0.148052	+	0.167624i
$621$	30.5065	+	17.6129i	1.22418	+	0.706782i
$622$	−15.2861	−	5.78411i	−0.612916	−	0.231922i
$623$	15.4118			0.617461
$624$	−13.1322	+	3.45868i	−0.525707	+	0.138458i
$625$	1.00000			0.0400000
$626$	20.0416	+	7.58355i	0.801024	+	0.303100i
$627$	24.2285	+	13.9883i	0.967593	+	0.558640i
$628$	28.5714	−	32.3483i	1.14012	−	1.29084i
$629$	−37.5370			−1.49670
$630$	−6.16091	−	7.53418i	−0.245457	−	0.300169i
$631$	11.0070	−	6.35490i	0.438182	−	0.252985i	−0.264644	−	0.964346i	$-0.585254\pi$
$631$	11.0070	−	6.35490i	0.438182	−	0.252985i	0.702826	+	0.711361i	$0.251921\pi$
$632$	−19.4057	−	36.7726i	−0.771916	−	1.46273i
$633$	10.0321	+	17.3761i	0.398739	+	0.690637i
$634$	−28.3546	−	10.7291i	−1.12610	−	0.426107i
$635$	−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
$640$	9.27704	−	6.47584i	0.366707	−	0.255980i
$641$	23.4415	+	40.6018i	0.925882	+	1.60367i	0.790137	+	0.612931i	$0.210009\pi$
$641$	23.4415	+	40.6018i	0.925882	+	1.60367i	0.135745	+	0.990744i	$0.456657\pi$
$642$	−0.627380	−	3.84218i	−0.0247607	−	0.151639i
$643$	−4.08952	−	7.08325i	−0.161275	−	0.279336i	0.774051	−	0.633123i	$-0.218227\pi$
$643$	−4.08952	−	7.08325i	−0.161275	−	0.279336i	−0.935326	+	0.353787i	$0.884894\pi$
$644$	31.5428	−	35.7125i	1.24296	−	1.40727i
$645$	6.62375			0.260810
$646$	−51.7986	+	42.3572i	−2.03799	+	1.66652i
$647$	0.875253	−	1.51598i	0.0344097	−	0.0595994i	−0.848308	−	0.529504i	$-0.822378\pi$
$647$	0.875253	−	1.51598i	0.0344097	−	0.0595994i	0.882717	+	0.469904i	$0.155712\pi$
$648$	5.10597	+	0.194228i	0.200582	+	0.00763001i
$649$	8.79474			0.345224
$650$	−1.48516	−	4.87794i	−0.0582527	−	0.191329i
$651$		−	8.53734i		−	0.334605i
$652$	−6.23387	+	30.7716i	−0.244137	+	1.20511i
$653$	−28.9507	−	16.7147i	−1.13293	−	0.654096i	−0.188258	−	0.982120i	$-0.560284\pi$
$653$	−28.9507	−	16.7147i	−1.13293	−	0.654096i	−0.944669	+	0.328024i	$0.893617\pi$
$654$	0.946820	+	1.15787i	0.0370236	+	0.0452761i
$655$		−	18.1375i		−	0.708692i
$656$	−6.24273	+	14.7753i	−0.243737	+	0.576878i
$657$	−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	$-0.853200\pi$
$659$	−24.5902	+	14.1972i	−0.957899	+	0.553043i	−0.0623733	+	0.998053i	$0.519867\pi$
$660$	−8.44577	−	1.71099i	−0.328751	−	0.0666002i
$661$	−16.0451	+	27.7908i	−0.624080	+	1.08094i	0.364638	+	0.931149i	$0.381193\pi$
$661$	−16.0451	+	27.7908i	−0.624080	+	1.08094i	−0.988718	+	0.149789i	$0.952140\pi$
$662$	−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
$666$	−14.3999	−	5.44878i	−0.557984	−	0.211136i
$667$	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
$670$	0.231295	−	0.189137i	0.00893570	−	0.00730698i
$671$			22.1502i			0.855099i
$672$	−4.08757	+	16.8564i	−0.157681	+	0.650249i
$673$	22.3377	−	38.6901i	0.861056	−	1.49139i	−0.00985491	−	0.999951i	$-0.503137\pi$
$673$	22.3377	−	38.6901i	0.861056	−	1.49139i	0.870911	−	0.491441i	$-0.163530\pi$
$674$	42.7166	+	16.1636i	1.64538	+	0.622597i
$675$		−	4.81478i		−	0.185321i
$676$	−21.5886	+	14.4890i	−0.830331	+	0.557270i
$677$		−	38.4184i		−	1.47654i	−0.674506	−	0.738270i	$-0.735643\pi$
$677$		−	38.4184i		−	1.47654i	0.674506	−	0.738270i	$-0.264357\pi$
$678$	3.86929	−	10.2257i	0.148599	−	0.392714i
$679$	−13.6730	+	23.6823i	−0.524722	+	0.908844i
$680$	10.9761	−	17.4443i	0.420915	−	0.668959i
$681$			10.9715i			0.420428i
$682$	11.4061	+	13.9485i	0.436763	+	0.534117i
$683$	−11.6110	−	20.1108i	−0.444281	−	0.769518i	0.553721	−	0.832703i	$-0.313208\pi$
$683$	−11.6110	−	20.1108i	−0.444281	−	0.769518i	−0.998002	+	0.0631848i	$0.979874\pi$
$684$	−26.0193	+	8.73005i	−0.994875	+	0.333802i
$685$	10.3515	−	5.97644i	0.395511	−	0.228348i
$686$	−5.53516	+	14.6282i	−0.211333	+	0.558506i
$687$	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	0.110917	−	0.993830i	$-0.464621\pi$
$691$	24.0825	−	41.7121i	0.916140	−	1.58680i	0.805223	−	0.592972i	$-0.202045\pi$
$692$	−34.5849	−	7.00640i	−1.31472	−	0.266343i
$693$	−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
$696$	−5.46329	+	8.68280i	−0.207086	+	0.329121i
$697$			29.2200i			1.10679i
$698$	24.3045	−	19.8745i	0.919940	−	0.752262i
$699$	13.1740	+	7.60599i	0.498285	+	0.287685i
$700$	−6.38301	−	1.29310i	−0.241255	−	0.0488747i
$701$		−	40.5311i		−	1.53084i	−0.643533	−	0.765419i	$-0.722532\pi$
$701$		−	40.5311i		−	1.53084i	0.643533	−	0.765419i	$-0.277468\pi$
$702$	−23.4862	+	7.15071i	−0.886430	+	0.269886i
$703$	33.4484			1.26153
$704$	−15.8422	−	33.0015i	−0.597076	−	1.24379i
$705$	−3.44760	+	5.97142i	−0.129844	+	0.224897i
$706$	−17.8345	−	21.8098i	−0.671209	−	0.820821i
$707$	−31.5699			−1.18731
$708$	2.39608	−	2.71282i	0.0900502	−	0.101954i
$709$	18.1735	+	31.4774i	0.682520	+	1.18216i	0.974209	+	0.225646i	$0.0724491\pi$
$709$	18.1735	+	31.4774i	0.682520	+	1.18216i	−0.291690	+	0.956513i	$0.594218\pi$
$710$	8.53498	−	1.39366i	0.320312	−	0.0523030i
$711$	−15.5337	−	26.9052i	−0.582560	−	1.00902i
$712$	−0.508849	+	13.3769i	−0.0190699	+	0.501320i
$713$	−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
$718$	4.04617	−	10.6931i	0.151002	−	0.399064i
$719$	−21.8623	−	37.8667i	−0.815327	−	1.41219i	−0.909093	−	0.416594i	$-0.863224\pi$
$719$	−21.8623	−	37.8667i	−0.815327	−	1.41219i	0.0937658	−	0.995594i	$-0.470110\pi$
$720$	6.74281	−	5.09870i	0.251290	−	0.190017i
$721$	27.2374	−	15.7255i	1.01438	−	0.585650i
$722$	25.3557	−	20.7341i	0.943642	−	0.771643i
$723$	10.0710			0.374544
$724$	17.7497	−	20.0960i	0.659662	−	0.746864i
$725$	−3.33584	−	1.92595i	−0.123890	−	0.0715279i
$726$	−4.68377	+	12.3782i	−0.173831	+	0.459397i
$727$	−4.55677			−0.169001			−0.0845005	−	0.996423i	$-0.526929\pi$
$727$	−4.55677			−0.169001			−0.0845005	+	0.996423i	$0.526929\pi$
$728$	3.17209	+	33.0564i	0.117565	+	1.22515i
$729$	−9.78292			−0.362330
$730$	−3.83274	+	10.1291i	−0.141856	+	0.374893i
$731$	44.3919	+	25.6297i	1.64189	+	0.947947i
$732$	6.83245	+	6.03471i	0.252535	+	0.223049i
$733$	−12.6156			−0.465968			−0.232984	−	0.972481i	$-0.574849\pi$
$733$	−12.6156			−0.465968			−0.232984	+	0.972481i	$0.574849\pi$
$734$	−2.02856	+	1.65881i	−0.0748754	+	0.0612278i
$735$	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
$738$	−4.24150	+	11.2093i	−0.156132	+	0.412621i
$739$	16.5996	−	28.7514i	0.610626	−	1.05764i	−0.380509	−	0.924777i	$-0.624251\pi$
$739$	16.5996	−	28.7514i	0.610626	−	1.05764i	0.991135	−	0.132858i	$-0.0424156\pi$
$740$	−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	0.267940	−	0.963436i	$-0.413657\pi$
$743$	−11.7877	−	6.80565i	−0.432450	−	0.249675i	−0.700390	+	0.713760i	$0.746991\pi$
$744$	7.41011	+	0.281876i	0.271668	+	0.0103341i
$745$	−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
$748$	−49.9824	−	44.1466i	−1.82754	−	1.61416i
$749$	−9.52001			−0.347854
$750$	−0.842957	−	1.03085i	−0.0307805	−	0.0376414i
$751$	1.60795	−	2.78505i	0.0586748	−	0.101628i	−0.835196	−	0.549952i	$-0.814646\pi$
$751$	1.60795	−	2.78505i	0.0586748	−	0.101628i	0.893871	+	0.448325i	$0.147979\pi$
$752$	−29.0670	+	3.61812i	−1.05996	+	0.131939i
$753$	−1.53913			−0.0560889
$754$	−4.44041	+	19.1324i	−0.161710	+	0.696760i
$755$			2.19357i			0.0798321i
$756$	−6.22601	+	30.7328i	−0.226438	+	1.11774i
$757$	−18.8023	−	10.8555i	−0.683381	−	0.394550i	0.117746	−	0.993044i	$-0.462433\pi$
$757$	−18.8023	−	10.8555i	−0.683381	−	0.394550i	−0.801128	+	0.598493i	$0.795766\pi$
$758$	−35.1595	+	28.7509i	−1.27705	+	1.04428i
$759$		−	31.5230i		−	1.14421i
$760$	−9.78058	+	15.5443i	−0.354779	+	0.563850i
$761$	9.68269	−	5.59031i	0.350997	−	0.202648i	−0.314127	−	0.949381i	$-0.601712\pi$
$761$	9.68269	−	5.59031i	0.350997	−	0.202648i	0.665124	+	0.746733i	$0.268378\pi$
$762$	5.95452	−	0.972299i	0.215709	−	0.0352227i
$763$	3.16754	−	1.82878i	0.114672	−	0.0662062i
$764$	−0.434285	+	2.14371i	−0.0157119	+	0.0775568i
$765$	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	0.782513	−	0.622634i	$-0.213937\pi$

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)

\(f(q)\)	\(=\)	\(q+(-1.32269 - 0.500493i) q^{2} +(0.815452 + 0.470802i) q^{3} +(1.49901 + 1.32399i) q^{4} +1.00000 q^{5} +(-0.842957 - 1.03085i) q^{6} +(-2.82007 + 1.62817i) q^{7} +(-1.32008 - 2.50148i) q^{8} +(-1.05669 - 1.83024i) q^{9} +O(q^{10})\)	\(q+(-1.32269 - 0.500493i) q^{2} +(0.815452 + 0.470802i) q^{3} +(1.49901 + 1.32399i) q^{4} +1.00000 q^{5} +(-0.842957 - 1.03085i) q^{6} +(-2.82007 + 1.62817i) q^{7} +(-1.32008 - 2.50148i) q^{8} +(-1.05669 - 1.83024i) q^{9} +(-1.32269 - 0.500493i) 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} +(0.494087 + 3.96937i) q^{16} +(3.64340 + 6.31055i) q^{17} +(0.481651 + 2.94971i) q^{18} +(-3.24655 - 5.62320i) q^{19} +(1.49901 + 1.32399i) q^{20} -3.06618 q^{21} +(5.00960 - 4.09650i) q^{22} +(-3.65810 + 6.33601i) q^{23} +(0.101236 - 2.66133i) q^{24} +1.00000 q^{25} +(-1.48516 - 4.87794i) q^{26} -4.81478i q^{27} +(-6.38301 - 1.29310i) q^{28} +(-3.33584 - 1.92595i) q^{29} +(-0.842957 - 1.03085i) q^{30} +2.78436i q^{31} +(1.33312 - 5.49753i) q^{32} +(-3.73142 + 2.15433i) q^{33} +(-1.66070 - 10.1704i) q^{34} +(-2.82007 + 1.62817i) q^{35} +(0.839233 - 4.14261i) 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} +(4.05560 + 1.53460i) q^{42} +(6.09210 - 3.51727i) q^{43} +(-8.67642 + 2.91112i) q^{44} +(-1.05669 - 1.83024i) q^{45} +(8.00965 - 6.54972i) q^{46} +7.32283i q^{47} +(-1.46588 + 3.46945i) q^{48} +(1.80186 - 3.12092i) q^{49} +(-1.32269 - 0.500493i) q^{50} +6.86127i q^{51} +(-0.476971 + 7.19531i) q^{52} +3.33709i q^{53} +(-2.40976 + 6.36846i) q^{54} +(-2.28794 + 3.96283i) q^{55} +(7.79555 + 4.90502i) q^{56} -6.11393i q^{57} +(3.44836 + 4.21699i) q^{58} +(-0.960988 - 1.66448i) q^{59} +(0.599037 + 1.78539i) q^{60} +(4.19212 - 2.42032i) q^{61} +(1.39355 - 3.68284i) 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} +(-2.89362 + 14.2834i) q^{68} +(-5.96601 + 3.44448i) q^{69} +(4.54496 - 0.742136i) q^{70} +(-5.29581 + 3.05754i) q^{71} +(-3.18339 + 5.05936i) q^{72} -7.65793i q^{73} +(5.63964 - 4.61170i) q^{74} +(0.815452 + 0.470802i) q^{75} +(2.57844 - 12.7277i) q^{76} -14.9006i q^{77} +(1.08547 - 4.67694i) q^{78} +14.7003 q^{79} +(0.494087 + 3.96937i) q^{80} +(-0.903270 + 1.56451i) q^{81} +(-3.58989 - 4.39008i) q^{82} -7.55031 q^{83} +(-4.59624 - 4.05959i) q^{84} +(3.64340 + 6.31055i) q^{85} +(-9.81832 + 1.60321i) q^{86} +(-1.81348 - 3.14104i) q^{87} +(12.9332 + 0.491972i) 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} +(3.66502 - 9.68583i) q^{94} +(-3.24655 - 5.62320i) q^{95} +(3.67534 - 3.85534i) q^{96} +(7.27269 - 4.19889i) q^{97} +(-3.94530 + 3.22618i) q^{98} +9.67060 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 6 q^{4} + 56 q^{5} - 13 q^{6} + 28 q^{9}+O(q^{10}) \) 56 * q + 6 * q^4 + 56 * q^5 - 13 * q^6 + 28 * q^9	\( 56 q + 6 q^{4} + 56 q^{5} - 13 q^{6} + 28 q^{9} - 8 q^{11} + 6 q^{12} - 4 q^{14} + 14 q^{16} + 18 q^{18} - 16 q^{19} + 6 q^{20} - 6 q^{22} + 12 q^{23} + 22 q^{24} + 56 q^{25} - 37 q^{26} - 12 q^{28} - 13 q^{30} - 30 q^{32} - 16 q^{34} + 15 q^{36} + 4 q^{37} - 24 q^{39} - 61 q^{42} + 24 q^{44} + 28 q^{45} - 19 q^{46} - 51 q^{48} + 20 q^{49} - 64 q^{52} - 5 q^{54} - 8 q^{55} - 23 q^{56} - q^{58} - 16 q^{59} + 6 q^{60} + 10 q^{62} - 30 q^{64} + 14 q^{66} - 36 q^{67} - 51 q^{68} - 4 q^{70} - 81 q^{72} + 70 q^{74} - 60 q^{76} + 143 q^{78} + 14 q^{80} - 28 q^{81} + 21 q^{82} + 40 q^{83} + 31 q^{84} - 28 q^{86} - 36 q^{87} - 19 q^{88} + 18 q^{90} + 16 q^{91} - 18 q^{92} + 43 q^{94} - 16 q^{95} - 48 q^{96} + 24 q^{97} + 56 q^{98} - 48 q^{99}+O(q^{100}) \) 56 * q + 6 * q^4 + 56 * q^5 - 13 * q^6 + 28 * q^9 - 8 * q^11 + 6 * q^12 - 4 * q^14 + 14 * q^16 + 18 * q^18 - 16 * q^19 + 6 * q^20 - 6 * q^22 + 12 * q^23 + 22 * q^24 + 56 * q^25 - 37 * q^26 - 12 * q^28 - 13 * q^30 - 30 * q^32 - 16 * q^34 + 15 * q^36 + 4 * q^37 - 24 * q^39 - 61 * q^42 + 24 * q^44 + 28 * q^45 - 19 * q^46 - 51 * q^48 + 20 * q^49 - 64 * q^52 - 5 * q^54 - 8 * q^55 - 23 * q^56 - q^58 - 16 * q^59 + 6 * q^60 + 10 * q^62 - 30 * q^64 + 14 * q^66 - 36 * q^67 - 51 * q^68 - 4 * q^70 - 81 * q^72 + 70 * q^74 - 60 * q^76 + 143 * q^78 + 14 * q^80 - 28 * q^81 + 21 * q^82 + 40 * q^83 + 31 * q^84 - 28 * q^86 - 36 * q^87 - 19 * q^88 + 18 * q^90 + 16 * q^91 - 18 * q^92 + 43 * q^94 - 16 * q^95 - 48 * q^96 + 24 * q^97 + 56 * q^98 - 48 * q^99

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