LMFDB - Embedded newform 520.2.ca.b.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.b.381.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.28768 - 0.584700i) q^{2} +(1.00895 - 0.582519i) q^{3} +(1.31625 + 1.50582i) q^{4} +1.00000 q^{5} +(-1.63981 + 0.160165i) q^{6} +(0.786953 + 0.454347i) q^{7} +(-0.814463 - 2.70863i) q^{8} +(-0.821344 + 1.42261i) q^{9} +O(q^{10})$	\(q+(-1.28768 - 0.584700i) q^{2} +(1.00895 - 0.582519i) q^{3} +(1.31625 + 1.50582i) q^{4} +1.00000 q^{5} +(-1.63981 + 0.160165i) q^{6} +(0.786953 + 0.454347i) q^{7} +(-0.814463 - 2.70863i) q^{8} +(-0.821344 + 1.42261i) q^{9} +(-1.28768 - 0.584700i) q^{10} +(2.01803 + 3.49532i) q^{11} +(2.20520 + 0.752555i) q^{12} +(1.21154 + 3.39590i) q^{13} +(-0.747688 - 1.04519i) q^{14} +(1.00895 - 0.582519i) q^{15} +(-0.534964 + 3.96407i) q^{16} +(1.41984 - 2.45923i) q^{17} +(1.88943 - 1.35163i) q^{18} +(0.810340 - 1.40355i) q^{19} +(1.31625 + 1.50582i) q^{20} +1.05866 q^{21} +(-0.554860 - 5.68081i) q^{22} +(-0.494250 - 0.856067i) q^{23} +(-2.39958 - 2.25843i) q^{24} +1.00000 q^{25} +(0.425507 - 5.08123i) q^{26} +5.40891i q^{27} +(0.351664 + 1.78304i) q^{28} +(-7.87290 + 4.54542i) q^{29} +(-1.63981 + 0.160165i) q^{30} +3.84896i q^{31} +(3.00665 - 4.79166i) q^{32} +(4.07218 + 2.35108i) q^{33} +(-3.26621 + 2.33653i) q^{34} +(0.786953 + 0.454347i) q^{35} +(-3.22328 + 0.635719i) q^{36} +(-0.538020 - 0.931878i) q^{37} +(-1.86412 + 1.33352i) q^{38} +(3.20056 + 2.72056i) q^{39} +(-0.814463 - 2.70863i) q^{40} +(7.68661 - 4.43786i) q^{41} +(-1.36322 - 0.619001i) q^{42} +(9.23470 + 5.33166i) q^{43} +(-2.60708 + 7.63950i) q^{44} +(-0.821344 + 1.42261i) q^{45} +(0.135895 + 1.39133i) q^{46} -11.5567i q^{47} +(1.76939 + 4.31118i) q^{48} +(-3.08714 - 5.34708i) q^{49} +(-1.28768 - 0.584700i) q^{50} -3.30832i q^{51} +(-3.51892 + 6.29422i) q^{52} -10.1285i q^{53} +(3.16259 - 6.96495i) q^{54} +(2.01803 + 3.49532i) q^{55} +(0.589713 - 2.50161i) q^{56} -1.88815i q^{57} +(12.7955 - 1.24977i) q^{58} +(4.67358 - 8.09488i) q^{59} +(2.20520 + 0.752555i) q^{60} +(0.159169 + 0.0918962i) q^{61} +(2.25049 - 4.95624i) q^{62} +(-1.29272 + 0.746351i) q^{63} +(-6.67330 + 4.41215i) q^{64} +(1.21154 + 3.39590i) q^{65} +(-3.86900 - 5.40844i) q^{66} +(5.74510 + 9.95080i) q^{67} +(5.57201 - 1.09895i) q^{68} +(-0.997350 - 0.575820i) q^{69} +(-0.747688 - 1.04519i) q^{70} +(4.27599 + 2.46874i) q^{71} +(4.52227 + 1.06605i) q^{72} -5.44599i q^{73} +(0.147930 + 1.51454i) q^{74} +(1.00895 - 0.582519i) q^{75} +(3.18010 - 0.627202i) q^{76} +3.66754i q^{77} +(-2.53060 - 5.37459i) q^{78} -14.8307 q^{79} +(-0.534964 + 3.96407i) q^{80} +(0.686757 + 1.18950i) q^{81} +(-12.4927 + 1.22020i) q^{82} +14.8263 q^{83} +(1.39347 + 1.59415i) q^{84} +(1.41984 - 2.45923i) q^{85} +(-8.77394 - 12.2650i) q^{86} +(-5.29559 + 9.17223i) q^{87} +(7.82391 - 8.31289i) q^{88} +(-2.39372 + 1.38202i) q^{89} +(1.88943 - 1.35163i) q^{90} +(-0.589495 + 3.22288i) q^{91} +(0.638521 - 1.87105i) q^{92} +(2.24209 + 3.88342i) q^{93} +(-6.75719 + 14.8813i) q^{94} +(0.810340 - 1.40355i) q^{95} +(0.242336 - 6.58599i) q^{96} +(-9.80772 - 5.66249i) q^{97} +(0.848814 + 8.69039i) q^{98} -6.62997 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 $\left(\mathbb{Z}/520\mathbb{Z}\right)^\times$.

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

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 $

$2$	−1.28768	−	0.584700i	−0.910529	−	0.413445i
$2$	−1.28768	−	0.584700i	−0.910529	−	0.413445i
$3$	1.00895	−	0.582519i	0.582519	−	0.336317i	−0.179615	−	0.983737i	$-0.557485\pi$
$3$	1.00895	−	0.582519i	0.582519	−	0.336317i	0.762134	+	0.647420i	$0.224152\pi$
$4$	1.31625	+	1.50582i	0.658126	+	0.752908i
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$	−1.63981	+	0.160165i	−0.669449	+	0.0653869i
$7$	0.786953	+	0.454347i	0.297440	+	0.171727i	0.641292	−	0.767297i	$-0.278399\pi$
$7$	0.786953	+	0.454347i	0.297440	+	0.171727i	−0.343852	+	0.939024i	$0.611732\pi$
$8$	−0.814463	−	2.70863i	−0.287956	−	0.957644i
$9$	−0.821344	+	1.42261i	−0.273781	+	0.474203i
$10$	−1.28768	−	0.584700i	−0.407201	−	0.184898i
$11$	2.01803	+	3.49532i	0.608458	+	1.05388i	0.991495	+	0.130147i	$0.0415448\pi$
$11$	2.01803	+	3.49532i	0.608458	+	1.05388i	−0.383037	+	0.923733i	$0.625122\pi$
$12$	2.20520	+	0.752555i	0.636587	+	0.217244i
$13$	1.21154	+	3.39590i	0.336021	+	0.941855i
$13$	1.21154	+	3.39590i	0.336021	+	0.941855i
$14$	−0.747688	−	1.04519i	−0.199828	−	0.279338i
$15$	1.00895	−	0.582519i	0.260510	−	0.150406i
$16$	−0.534964	+	3.96407i	−0.133741	+	0.991016i
$17$	1.41984	−	2.45923i	0.344361	−	0.596450i	−0.640877	−	0.767644i	$-0.721429\pi$
$17$	1.41984	−	2.45923i	0.344361	−	0.596450i	0.985237	+	0.171194i	$0.0547623\pi$
$18$	1.88943	−	1.35163i	0.445343	−	0.318582i
$19$	0.810340	−	1.40355i	0.185905	−	0.321996i	−0.757976	−	0.652282i	$-0.773812\pi$
$19$	0.810340	−	1.40355i	0.185905	−	0.321996i	0.943881	+	0.330286i	$0.107145\pi$
$20$	1.31625	+	1.50582i	0.294323	+	0.336711i
$21$	1.05866			0.231019
$22$	−0.554860	−	5.68081i	−0.118297	−	1.21115i
$23$	−0.494250	−	0.856067i	−0.103058	−	0.178502i	0.809885	−	0.586589i	$-0.199530\pi$
$23$	−0.494250	−	0.856067i	−0.103058	−	0.178502i	−0.912943	+	0.408087i	$0.866196\pi$
$24$	−2.39958	−	2.25843i	−0.489812	−	0.461001i
$25$	1.00000			0.200000
$26$	0.425507	−	5.08123i	0.0834488	−	0.996512i
$27$			5.40891i			1.04094i
$28$	0.351664	+	1.78304i	0.0664582	+	0.336963i
$29$	−7.87290	+	4.54542i	−1.46196	+	0.844064i	−0.999102	−	0.0423678i	$-0.986510\pi$
$29$	−7.87290	+	4.54542i	−1.46196	+	0.844064i	−0.462859	+	0.886432i	$0.653177\pi$
$30$	−1.63981	+	0.160165i	−0.299387	+	0.0292419i
$31$			3.84896i			0.691294i	0.938365	+	0.345647i	$0.112341\pi$
$31$			3.84896i			0.691294i	−0.938365	+	0.345647i	$0.887659\pi$
$32$	3.00665	−	4.79166i	0.531506	−	0.847054i
$33$	4.07218	+	2.35108i	0.708876	+	0.409270i
$34$	−3.26621	+	2.33653i	−0.560150	+	0.400711i
$35$	0.786953	+	0.454347i	0.133019	+	0.0767987i
$36$	−3.22328	+	0.635719i	−0.537214	+	0.105953i
$37$	−0.538020	−	0.931878i	−0.0884500	−	0.153200i	0.818406	−	0.574640i	$-0.194858\pi$
$37$	−0.538020	−	0.931878i	−0.0884500	−	0.153200i	−0.906856	+	0.421440i	$0.861525\pi$
$38$	−1.86412	+	1.33352i	−0.302400	+	0.216326i
$39$	3.20056	+	2.72056i	0.512500	+	0.435638i
$40$	−0.814463	−	2.70863i	−0.128778	−	0.428271i
$41$	7.68661	−	4.43786i	1.20045	−	0.693078i	0.239792	−	0.970824i	$-0.422921\pi$
$41$	7.68661	−	4.43786i	1.20045	−	0.693078i	0.960654	+	0.277747i	$0.0895875\pi$
$42$	−1.36322	−	0.619001i	−0.210350	−	0.0955139i
$43$	9.23470	+	5.33166i	1.40828	+	0.813070i	0.995222	−	0.0976356i	$-0.0311280\pi$
$43$	9.23470	+	5.33166i	1.40828	+	0.813070i	0.413056	+	0.910706i	$0.364461\pi$
$44$	−2.60708	+	7.63950i	−0.393033	+	1.15170i
$45$	−0.821344	+	1.42261i	−0.122439	+	0.212070i
$46$	0.135895	+	1.39133i	0.0200366	+	0.205140i
$47$		−	11.5567i		−	1.68571i	−0.538138	−	0.842857i	$-0.680872\pi$
$47$		−	11.5567i		−	1.68571i	0.538138	−	0.842857i	$-0.319128\pi$
$48$	1.76939	+	4.31118i	0.255389	+	0.622265i
$49$	−3.08714	−	5.34708i	−0.441020	−	0.763868i
$50$	−1.28768	−	0.584700i	−0.182106	−	0.0826891i
$51$		−	3.30832i		−	0.463258i
$52$	−3.51892	+	6.29422i	−0.487986	+	0.872851i
$53$		−	10.1285i		−	1.39126i	−0.718399	−	0.695631i	$-0.755125\pi$
$53$		−	10.1285i		−	1.39126i	0.718399	−	0.695631i	$-0.244875\pi$
$54$	3.16259	−	6.96495i	0.430374	−	0.947810i
$55$	2.01803	+	3.49532i	0.272111	+	0.471309i
$56$	0.589713	−	2.50161i	0.0788037	−	0.334291i
$57$		−	1.88815i		−	0.250092i
$58$	12.7955	−	1.24977i	1.68013	−	0.164103i
$59$	4.67358	−	8.09488i	0.608449	−	1.05386i	−0.383048	−	0.923729i	$-0.625125\pi$
$59$	4.67358	−	8.09488i	0.608449	−	1.05386i	0.991496	−	0.130135i	$-0.0415412\pi$
$60$	2.20520	+	0.752555i	0.284690	+	0.0971545i
$61$	0.159169	+	0.0918962i	0.0203795	+	0.0117661i	0.510155	−	0.860082i	$-0.329588\pi$
$61$	0.159169	+	0.0918962i	0.0203795	+	0.0117661i	−0.489776	+	0.871849i	$0.662921\pi$
$62$	2.25049	−	4.95624i	0.285812	−	0.629443i
$63$	−1.29272	+	0.746351i	−0.162867	+	0.0940313i
$64$	−6.67330	+	4.41215i	−0.834163	+	0.551519i
$65$	1.21154	+	3.39590i	0.150273	+	0.421210i
$66$	−3.86900	−	5.40844i	−0.476241	−	0.665733i
$67$	5.74510	+	9.95080i	0.701875	+	1.21568i	0.967807	+	0.251692i	$0.0809870\pi$
$67$	5.74510	+	9.95080i	0.701875	+	1.21568i	−0.265932	+	0.963992i	$0.585680\pi$
$68$	5.57201	−	1.09895i	0.675705	−	0.133267i
$69$	−0.997350	−	0.575820i	−0.120067	−	0.0693206i
$70$	−0.747688	−	1.04519i	−0.0893658	−	0.124924i
$71$	4.27599	+	2.46874i	0.507467	+	0.292986i	0.731792	−	0.681528i	$-0.238684\pi$
$71$	4.27599	+	2.46874i	0.507467	+	0.292986i	−0.224325	+	0.974514i	$0.572018\pi$
$72$	4.52227	+	1.06605i	0.532955	+	0.125635i
$73$		−	5.44599i		−	0.637405i	−0.947855	−	0.318703i	$-0.896753\pi$
$73$		−	5.44599i		−	0.637405i	0.947855	−	0.318703i	$-0.103247\pi$
$74$	0.147930	+	1.51454i	0.0171965	+	0.176062i
$75$	1.00895	−	0.582519i	0.116504	−	0.0672635i
$76$	3.18010	−	0.627202i	0.364782	−	0.0719450i
$77$			3.66754i			0.417955i
$78$	−2.53060	−	5.37459i	−0.286534	−	0.608552i
$79$	−14.8307			−1.66859			−0.834294	−	0.551320i	$-0.814124\pi$
$79$	−14.8307			−1.66859			−0.834294	+	0.551320i	$0.814124\pi$
$80$	−0.534964	+	3.96407i	−0.0598108	+	0.443196i
$81$	0.686757	+	1.18950i	0.0763064	+	0.132167i
$82$	−12.4927	+	1.22020i	−1.37959	+	0.134748i
$83$	14.8263			1.62740			0.813701	−	0.581284i	$-0.197449\pi$
$83$	14.8263			1.62740			0.813701	+	0.581284i	$0.197449\pi$
$84$	1.39347	+	1.59415i	0.152040	+	0.173936i
$85$	1.41984	−	2.45923i	0.154003	−	0.266741i
$86$	−8.77394	−	12.2650i	−0.946118	−	1.32257i
$87$	−5.29559	+	9.17223i	−0.567747	+	0.983366i
$88$	7.82391	−	8.31289i	0.834032	−	0.886157i
$89$	−2.39372	+	1.38202i	−0.253734	+	0.146494i	−0.621473	−	0.783436i	$-0.713465\pi$
$89$	−2.39372	+	1.38202i	−0.253734	+	0.146494i	0.367739	+	0.929929i	$0.380132\pi$
$90$	1.88943	−	1.35163i	0.199163	−	0.142474i
$91$	−0.589495	+	3.22288i	−0.0617959	+	0.337849i
$92$	0.638521	−	1.87105i	0.0665705	−	0.195070i
$93$	2.24209	+	3.88342i	0.232494	+	0.402692i
$94$	−6.75719	+	14.8813i	−0.696951	+	1.53489i
$95$	0.810340	−	1.40355i	0.0831391	−	0.144001i
$96$	0.242336	−	6.58599i	0.0247333	−	0.672180i
$97$	−9.80772	−	5.66249i	−0.995823	−	0.574939i	−0.0888131	−	0.996048i	$-0.528307\pi$
$97$	−9.80772	−	5.66249i	−0.995823	−	0.574939i	−0.907010	+	0.421110i	$0.861641\pi$
$98$	0.848814	+	8.69039i	0.0857432	+	0.877862i
$99$	−6.62997			−0.666337
$100$	1.31625	+	1.50582i	0.131625	+	0.150582i
$101$	−15.2516	+	8.80549i	−1.51759	+	0.876179i	−0.517801	+	0.855501i	$0.673249\pi$
$101$	−15.2516	+	8.80549i	−1.51759	+	0.876179i	−0.999786	+	0.0206778i	$0.993418\pi$
$102$	−1.93438	+	4.26007i	−0.191532	+	0.421810i
$103$	−4.00462			−0.394587			−0.197293	−	0.980344i	$-0.563215\pi$
$103$	−4.00462			−0.394587			−0.197293	+	0.980344i	$0.563215\pi$
$104$	8.21148	−	6.04745i	0.805202	−	0.593001i
$105$	1.05866			0.103315
$106$	−5.92216	+	13.0423i	−0.575211	+	1.26678i
$107$	−10.4667	+	6.04294i	−1.01185	+	0.584193i	−0.911733	−	0.410783i	$-0.865255\pi$
$107$	−10.4667	+	6.04294i	−1.01185	+	0.584193i	−0.100118	+	0.994976i	$0.531922\pi$
$108$	−8.14482	+	7.11948i	−0.783735	+	0.685072i
$109$	4.69338			0.449544			0.224772	−	0.974411i	$-0.427836\pi$
$109$	4.69338			0.449544			0.224772	+	0.974411i	$0.427836\pi$
$110$	−0.554860	−	5.68081i	−0.0529038	−	0.541644i
$111$	−1.08567	−	0.626814i	−0.103048	−	0.0594945i
$112$	−2.22205	+	2.87647i	−0.209964	+	0.271801i
$113$	5.70070	−	9.87391i	0.536277	−	0.928859i	−0.462823	−	0.886450i	$-0.653164\pi$
$113$	5.70070	−	9.87391i	0.536277	−	0.928859i	0.999100	−	0.0424084i	$-0.0135031\pi$
$114$	−1.10400	+	2.43134i	−0.103399	+	0.227716i
$115$	−0.494250	−	0.856067i	−0.0460891	−	0.0798286i
$116$	−17.2073	−	5.87223i	−1.59766	−	0.545222i
$117$	−5.82614	−	1.06566i	−0.538627	−	0.0985200i
$118$	−10.7512	+	7.69099i	−0.989725	+	0.708013i
$119$	2.23469	−	1.29020i	0.204853	−	0.118272i
$120$	−2.39958	−	2.25843i	−0.219051	−	0.206166i
$121$	−2.64485	+	4.58102i	−0.240441	+	0.416457i
$122$	−0.151227	−	0.211399i	−0.0136915	−	0.0191392i
$123$	5.17028	−	8.95518i	0.466188	−	0.807462i
$124$	−5.79583	+	5.06620i	−0.520481	+	0.454959i
$125$	1.00000			0.0894427
$126$	2.10100	−	0.205211i	0.187172	−	0.0182816i
$127$	5.13384	+	8.89208i	0.455555	+	0.789044i	0.998720	−	0.0505816i	$-0.0161075\pi$
$127$	5.13384	+	8.89208i	0.455555	+	0.789044i	−0.543165	+	0.839626i	$0.682774\pi$
$128$	11.1729	−	1.77957i	0.987552	−	0.157293i
$129$	12.4232			1.09380
$130$	0.425507	−	5.08123i	0.0373194	−	0.445654i
$131$		−	5.02397i		−	0.438946i	−0.975619	−	0.219473i	$-0.929566\pi$
$131$		−	5.02397i		−	0.438946i	0.975619	−	0.219473i	$-0.0704339\pi$
$132$	1.81973	+	9.22656i	0.158387	+	0.803069i
$133$	1.27540	−	0.736352i	0.110591	−	0.0638498i
$134$	−1.57963	−	16.1726i	−0.136459	−	1.39710i
$135$			5.40891i			0.465524i
$136$	−7.81753	−	1.84285i	−0.670348	−	0.158023i
$137$	−18.9228	−	10.9251i	−1.61668	−	0.933393i	−0.987770	−	0.155918i	$-0.950166\pi$
$137$	−18.9228	−	10.9251i	−1.61668	−	0.933393i	−0.628914	−	0.777475i	$-0.716500\pi$
$138$	0.947588	+	1.32462i	0.0806640	+	0.112760i
$139$	−1.79457	−	1.03610i	−0.152214	−	0.0878807i	0.421959	−	0.906615i	$-0.361343\pi$
$139$	−1.79457	−	1.03610i	−0.152214	−	0.0878807i	−0.574172	+	0.818734i	$0.694676\pi$
$140$	0.351664	+	1.78304i	0.0297210	+	0.150694i
$141$	−6.73198	−	11.6601i	−0.566935	−	0.981960i
$142$	−4.06264	−	5.67913i	−0.340929	−	0.476582i
$143$	−9.42486	+	11.0877i	−0.788147	+	0.927204i
$144$	−5.19993	−	4.01691i	−0.433327	−	0.334742i
$145$	−7.87290	+	4.54542i	−0.653809	+	0.377477i
$146$	−3.18427	+	7.01271i	−0.263532	+	0.580376i
$147$	−6.22955	−	3.59663i	−0.513804	−	0.296645i
$148$	0.695067	−	2.03675i	0.0571342	−	0.167419i
$149$	1.07638	−	1.86435i	0.0881809	−	0.152734i	−0.818561	−	0.574419i	$-0.805228\pi$
$149$	1.07638	−	1.86435i	0.0881809	−	0.152734i	0.906742	+	0.421685i	$0.138561\pi$
$150$	−1.63981	+	0.160165i	−0.133890	+	0.0130774i
$151$			7.39857i			0.602087i	0.953610	+	0.301043i	$0.0973349\pi$
$151$			7.39857i			0.602087i	−0.953610	+	0.301043i	$0.902665\pi$
$152$	−4.46168	−	1.05177i	−0.361890	−	0.0853097i
$153$	2.33235	+	4.03974i	0.188559	+	0.326594i
$154$	2.14441	−	4.72262i	0.172801	−	0.380560i
$155$			3.84896i			0.309156i
$156$	0.116084	+	8.40040i	0.00929415	+	0.672571i
$157$		−	7.81527i		−	0.623726i	−0.950127	−	0.311863i	$-0.899047\pi$
$157$		−	7.81527i		−	0.623726i	0.950127	−	0.311863i	$-0.100953\pi$
$158$	19.0973	+	8.67153i	1.51930	+	0.689870i
$159$	−5.90006	−	10.2192i	−0.467906	−	0.810436i
$160$	3.00665	−	4.79166i	0.237697	−	0.378814i
$161$		−	0.898245i		−	0.0707916i
$162$	−0.188825	−	1.93324i	−0.0148355	−	0.151890i
$163$	−3.49430	+	6.05231i	−0.273695	+	0.474054i	−0.969805	−	0.243881i	$-0.921579\pi$
$163$	−3.49430	+	6.05231i	−0.273695	+	0.474054i	0.696110	+	0.717935i	$0.254913\pi$
$164$	16.8001	+	5.73327i	1.31187	+	0.447693i
$165$	4.07218	+	2.35108i	0.317019	+	0.183031i
$166$	−19.0916	−	8.66896i	−1.48180	−	0.672842i
$167$	6.37387	−	3.67996i	0.493225	−	0.284763i	−0.232686	−	0.972552i	$-0.574752\pi$
$167$	6.37387	−	3.67996i	0.493225	−	0.284763i	0.725911	+	0.687788i	$0.241418\pi$
$168$	−0.862242	−	2.86752i	−0.0665234	−	0.221234i
$169$	−10.0643	+	8.22855i	−0.774180	+	0.632965i
$170$	−3.26621	+	2.33653i	−0.250507	+	0.179203i
$171$	1.33114	+	2.30559i	0.101794	+	0.176313i
$172$	4.12669	+	20.9236i	0.314657	+	1.59541i
$173$	−11.6569	−	6.73009i	−0.886255	−	0.511679i	−0.0135391	−	0.999908i	$-0.504310\pi$
$173$	−11.6569	−	6.73009i	−0.886255	−	0.511679i	−0.872716	+	0.488229i	$0.837643\pi$
$174$	12.1820	−	8.71458i	0.923518	−	0.660651i
$175$	0.786953	+	0.454347i	0.0594880	+	0.0343454i
$176$	−14.9353	+	6.12971i	−1.12579	+	0.462044i
$177$		−	10.8898i		−	0.818527i
$178$	3.89042	−	0.379988i	0.291599	−	0.0284813i
$179$	−5.65198	+	3.26317i	−0.422449	+	0.243901i	−0.696125	−	0.717921i	$-0.745094\pi$
$179$	−5.65198	+	3.26317i	−0.422449	+	0.243901i	0.273676	+	0.961822i	$0.411761\pi$
$180$	−3.22328	+	0.635719i	−0.240249	+	0.0473837i
$181$		−	11.3825i		−	0.846055i	−0.906117	−	0.423028i	$-0.860967\pi$
$181$		−	11.3825i		−	0.846055i	0.906117	−	0.423028i	$-0.139033\pi$
$182$	2.64350	−	3.80536i	0.195949	−	0.282072i
$183$	0.214125			0.0158286
$184$	−1.91622	+	2.03597i	−0.141265	+	0.150094i
$185$	−0.538020	−	0.931878i	−0.0395560	−	0.0685131i
$186$	−0.616468	−	6.31156i	−0.0452016	−	0.462786i
$187$	11.4611			0.838116
$188$	17.4022	−	15.2115i	1.26919	−	1.10941i
$189$	−2.45752	+	4.25655i	−0.178758	+	0.309619i
$190$	−1.86412	+	1.33352i	−0.135237	+	0.0967438i
$191$	−5.34414	+	9.25631i	−0.386688	+	0.669763i	−0.992002	−	0.126224i	$-0.959714\pi$
$191$	−5.34414	+	9.25631i	−0.386688	+	0.669763i	0.605314	+	0.795987i	$0.293048\pi$
$192$	−4.16288	+	8.33897i	−0.300430	+	0.601813i
$193$	−11.5999	+	6.69719i	−0.834977	+	0.482074i	−0.855554	−	0.517714i	$-0.826783\pi$
$193$	−11.5999	+	6.69719i	−0.834977	+	0.482074i	0.0205769	+	0.999788i	$0.493450\pi$
$194$	9.31837	+	13.0261i	0.669020	+	0.935217i
$195$	3.20056	+	2.72056i	0.229197	+	0.194823i
$196$	3.98827	−	11.6868i	0.284876	−	0.834769i
$197$	−5.72584	−	9.91745i	−0.407950	−	0.706589i	0.586710	−	0.809797i	$-0.300423\pi$
$197$	−5.72584	−	9.91745i	−0.407950	−	0.706589i	−0.994660	+	0.103208i	$0.967089\pi$
$198$	8.53730	+	3.87655i	0.606719	+	0.275494i
$199$	4.98119	−	8.62768i	0.353108	−	0.611600i	−0.633685	−	0.773591i	$-0.718458\pi$
$199$	4.98119	−	8.62768i	0.353108	−	0.611600i	0.986792	+	0.161991i	$0.0517916\pi$
$200$	−0.814463	−	2.70863i	−0.0575912	−	0.191529i
$201$	11.5931	+	6.69325i	0.817711	+	0.472106i
$202$	24.7877	−	2.42109i	1.74406	−	0.170347i
$203$	−8.26080			−0.579795
$204$	4.98173	−	4.35459i	0.348791	−	0.304882i
$205$	7.68661	−	4.43786i	0.536856	−	0.309954i
$206$	5.15668	+	2.34150i	0.359283	+	0.163140i
$207$	1.62380			0.112862
$208$	−14.1097	+	2.98594i	−0.978333	+	0.207037i
$209$	6.54115			0.452461
$210$	−1.36322	−	0.619001i	−0.0940712	−	0.0427151i
$211$	3.72205	−	2.14892i	0.256236	−	0.147938i	−0.366380	−	0.930465i	$-0.619403\pi$
$211$	3.72205	−	2.14892i	0.256236	−	0.147938i	0.622616	+	0.782527i	$0.286070\pi$
$212$	15.2517	−	13.3317i	1.04749	−	0.915625i
$213$	5.75236			0.394145
$214$	17.0111	−	1.66152i	1.16285	−	0.113579i
$215$	9.23470	+	5.33166i	0.629801	+	0.363616i
$216$	14.6507	−	4.40535i	0.996854	−	0.299746i
$217$	−1.74877	+	3.02895i	−0.118714	+	0.205619i
$218$	−6.04358	−	2.74422i	−0.409323	−	0.185862i
$219$	−3.17239	−	5.49474i	−0.214370	−	0.371300i
$220$	−2.60708	+	7.63950i	−0.175770	+	0.515055i
$221$	10.0715	+	1.84217i	0.677482	+	0.123918i
$222$	1.03150	+	1.44193i	0.0692300	+	0.0967760i
$223$	6.29404	−	3.63386i	0.421480	−	0.243342i	−0.274230	−	0.961664i	$-0.588423\pi$
$223$	6.29404	−	3.63386i	0.421480	−	0.243342i	0.695710	+	0.718322i	$0.255090\pi$
$224$	4.54317	−	2.40475i	0.303553	−	0.160674i
$225$	−0.821344	+	1.42261i	−0.0547563	+	0.0948406i
$226$	−13.1140	+	9.38125i	−0.872328	+	0.624032i
$227$	1.11578	−	1.93259i	0.0740568	−	0.128270i	−0.826619	−	0.562762i	$-0.809739\pi$
$227$	1.11578	−	1.93259i	0.0740568	−	0.128270i	0.900676	+	0.434492i	$0.143072\pi$
$228$	2.84321	−	2.48528i	0.188296	−	0.164592i
$229$	−5.95549			−0.393550			−0.196775	−	0.980449i	$-0.563047\pi$
$229$	−5.95549			−0.393550			−0.196775	+	0.980449i	$0.563047\pi$
$230$	0.135895	+	1.39133i	0.00896066	+	0.0917416i
$231$	2.13641	+	3.70037i	0.140565	+	0.243466i
$232$	18.7240	+	17.6227i	1.22929	+	1.15698i
$233$	0.994961			0.0651821			0.0325910	−	0.999469i	$-0.489624\pi$
$233$	0.994961			0.0651821			0.0325910	+	0.999469i	$0.489624\pi$
$234$	6.87912	+	4.77877i	0.449702	+	0.312398i
$235$		−	11.5567i		−	0.753874i
$236$	18.3410	−	3.61735i	1.19390	−	0.235469i
$237$	−14.9635	+	8.63918i	−0.971983	+	0.561175i
$238$	−3.63194	+	0.354742i	−0.235424	+	0.0229945i
$239$			2.10697i			0.136288i	0.997675	+	0.0681442i	$0.0217078\pi$
$239$			2.10697i			0.136288i	−0.997675	+	0.0681442i	$0.978292\pi$
$240$	1.76939	+	4.31118i	0.114214	+	0.278285i
$241$	12.4843	+	7.20780i	0.804183	+	0.464295i	0.844932	−	0.534874i	$-0.179641\pi$
$241$	12.4843	+	7.20780i	0.804183	+	0.464295i	−0.0407487	+	0.999169i	$0.512974\pi$
$242$	6.08426	−	4.35245i	0.391111	−	0.279786i
$243$	−12.6669	−	7.31326i	−0.812584	−	0.469146i
$244$	0.0711275	+	0.360638i	0.00455347	+	0.0230875i
$245$	−3.08714	−	5.34708i	−0.197230	−	0.341612i
$246$	−11.8938	+	8.50837i	−0.758319	+	0.542474i
$247$	5.74808	+	1.05138i	0.365742	+	0.0668977i
$248$	10.4254	−	3.13484i	0.662014	−	0.199062i
$249$	14.9591	−	8.63662i	0.947992	−	0.547324i
$250$	−1.28768	−	0.584700i	−0.0814402	−	0.0369797i
$251$	2.37866	+	1.37332i	0.150139	+	0.0866830i	0.573188	−	0.819424i	$-0.305707\pi$
$251$	2.37866	+	1.37332i	0.150139	+	0.0866830i	−0.423048	+	0.906107i	$0.639040\pi$
$252$	−2.82541	−	0.964209i	−0.177984	−	0.0607395i
$253$	1.99482	−	3.45513i	0.125413	−	0.217222i
$254$	−1.41156	−	14.4519i	−0.0885692	−	0.906795i
$255$		−	3.30832i		−	0.207175i
$256$	−15.4276	−	4.24127i	−0.964227	−	0.265079i
$257$	−3.27795	−	5.67758i	−0.204473	−	0.354158i	0.745492	−	0.666515i	$-0.232215\pi$
$257$	−3.27795	−	5.67758i	−0.204473	−	0.354158i	−0.949965	+	0.312357i	$0.898881\pi$
$258$	−15.9971	−	7.26382i	−0.995935	−	0.452226i
$259$		−	0.977792i		−	0.0607570i
$260$	−3.51892	+	6.29422i	−0.218234	+	0.390351i
$261$		−	14.9334i		−	0.924356i
$262$	−2.93752	+	6.46928i	−0.181480	+	0.399673i
$263$	0.410453	+	0.710926i	0.0253096	+	0.0438376i	0.878403	−	0.477921i	$-0.158609\pi$
$263$	0.410453	+	0.710926i	0.0253096	+	0.0438376i	−0.853093	+	0.521759i	$0.825276\pi$
$264$	3.05154	−	12.9449i	0.187809	−	0.796702i
$265$		−	10.1285i		−	0.622191i
$266$	−2.07285	+	0.202461i	−0.127095	+	0.0124137i
$267$	−1.61010	+	2.78878i	−0.0985367	+	0.170670i
$268$	−7.42208	+	21.7488i	−0.453376	+	1.32852i
$269$	15.4691	+	8.93107i	0.943166	+	0.544537i	0.890951	−	0.454099i	$-0.150039\pi$
$269$	15.4691	+	8.93107i	0.943166	+	0.544537i	0.0522145	+	0.998636i	$0.483372\pi$
$270$	3.16259	−	6.96495i	0.192469	−	0.423873i
$271$	8.02412	−	4.63273i	0.487431	−	0.281418i	−0.236077	−	0.971734i	$-0.575862\pi$
$271$	8.02412	−	4.63273i	0.487431	−	0.281418i	0.723508	+	0.690316i	$0.242529\pi$
$272$	8.98898	+	6.94392i	0.545037	+	0.421037i
$273$	1.28261	+	3.59512i	0.0776273	+	0.217587i
$274$	17.9787	+	25.1322i	1.08613	+	1.51829i
$275$	2.01803	+	3.49532i	0.121692	+	0.210776i
$276$	−0.445684	−	2.25975i	−0.0268270	−	0.136021i
$277$	−5.69939	−	3.29054i	−0.342443	−	0.197710i	0.318909	−	0.947785i	$-0.396684\pi$
$277$	−5.69939	−	3.29054i	−0.342443	−	0.197710i	−0.661352	+	0.750076i	$0.730017\pi$
$278$	1.70503	+	2.38345i	0.102261	+	0.142950i
$279$	−5.47557	−	3.16132i	−0.327814	−	0.189263i
$280$	0.589713	−	2.50161i	0.0352421	−	0.149500i
$281$		−	0.628207i		−	0.0374757i	−0.999824	−	0.0187378i	$-0.994035\pi$
$281$		−	0.628207i		−	0.0374757i	0.999824	−	0.0187378i	$-0.00596479\pi$
$282$	1.85097	+	18.9507i	0.110224	+	1.12850i
$283$	3.25394	−	1.87866i	0.193427	−	0.111675i	−0.400159	−	0.916446i	$-0.631045\pi$
$283$	3.25394	−	1.87866i	0.193427	−	0.111675i	0.593586	+	0.804771i	$0.297712\pi$
$284$	1.91080	+	9.68834i	0.113385	+	0.574897i
$285$		−	1.88815i		−	0.111845i
$286$	18.6192	−	8.76678i	1.10098	−	0.518390i
$287$	8.06532			0.476081
$288$	4.34717	+	8.21290i	0.256159	+	0.483950i
$289$	4.46813	+	7.73903i	0.262831	+	0.455237i
$290$	12.7955	−	1.24977i	0.751378	−	0.0733892i
$291$	−13.1940			−0.773447
$292$	8.20066	−	7.16829i	0.479907	−	0.419493i
$293$	−10.2140	+	17.6911i	−0.596707	+	1.03353i	0.396597	+	0.917993i	$0.370191\pi$
$293$	−10.2140	+	17.6911i	−0.596707	+	1.03353i	−0.993304	+	0.115534i	$0.963142\pi$
$294$	5.91873	+	8.27373i	0.345187	+	0.482534i
$295$	4.67358	−	8.09488i	0.272107	−	0.471302i
$296$	−2.08591	+	2.21628i	−0.121241	+	0.128818i
$297$	−18.9059	+	10.9153i	−1.09703	+	0.633370i
$298$	−2.47613	+	1.77133i	−0.143438	+	0.102611i
$299$	2.30832	−	2.71559i	0.133493	−	0.157046i
$300$	2.20520	+	0.752555i	0.127317	+	0.0434488i
$301$	4.84485	+	8.39152i	0.279252	+	0.483679i
$302$	4.32594	−	9.52700i	0.248930	−	0.548217i
$303$	−10.2587	+	17.7686i	−0.589349	+	1.02078i
$304$	5.13026	+	3.96309i	0.294241	+	0.227299i
$305$	0.159169	+	0.0918962i	0.00911399	+	0.00526196i
$306$	−0.641283	−	6.56563i	−0.0366597	−	0.375332i
$307$	−29.0460			−1.65774			−0.828870	−	0.559441i	$-0.811016\pi$
$307$	−29.0460			−1.65774			−0.828870	+	0.559441i	$0.811016\pi$
$308$	−5.52264	+	4.82740i	−0.314681	+	0.275067i
$309$	−4.04047	+	2.33277i	−0.229854	+	0.132706i
$310$	2.25049	−	4.95624i	0.127819	−	0.281496i
$311$	29.6373			1.68057			0.840287	−	0.542141i	$-0.182386\pi$
$311$	29.6373			1.68057			0.840287	+	0.542141i	$0.182386\pi$
$312$	4.76224	−	10.8849i	0.269609	−	0.616238i
$313$	21.2962			1.20373			0.601867	−	0.798597i	$-0.294424\pi$
$313$	21.2962			1.20373			0.601867	+	0.798597i	$0.294424\pi$
$314$	−4.56959	+	10.0636i	−0.257877	+	0.567921i
$315$	−1.29272	+	0.746351i	−0.0728364	+	0.0420521i
$316$	−19.5210	−	22.3324i	−1.09814	−	1.25629i
$317$	13.7154			0.770334			0.385167	−	0.922847i	$-0.374144\pi$
$317$	13.7154			0.770334			0.385167	+	0.922847i	$0.374144\pi$
$318$	1.62223	+	16.6089i	0.0909704	+	0.931379i
$319$	−31.7754	−	18.3456i	−1.77908	−	1.02715i
$320$	−6.67330	+	4.41215i	−0.373049	+	0.246647i
$321$	−7.04025	+	12.1941i	−0.392948	+	0.680607i
$322$	−0.525204	+	1.15665i	−0.0292685	+	0.0644578i
$323$	−2.30110	−	3.98562i	−0.128037	−	0.221766i
$324$	−0.887221	+	2.59981i	−0.0492900	+	0.144434i
$325$	1.21154	+	3.39590i	0.0672042	+	0.188371i
$326$	8.03834	−	5.75034i	0.445203	−	0.318482i
$327$	4.73539	−	2.73398i	0.261868	−	0.151189i
$328$	−18.2810	−	17.2057i	−1.00940	−	0.950024i
$329$	5.25074	−	9.09455i	0.289483	−	0.501399i
$330$	−3.86900	−	5.40844i	−0.212982	−	0.297725i
$331$	11.7962	−	20.4317i	0.648380	−	1.12303i	−0.335130	−	0.942172i	$-0.608780\pi$
$331$	11.7962	−	20.4317i	0.648380	−	1.12303i	0.983510	−	0.180855i	$-0.0578865\pi$
$332$	19.5152	+	22.3257i	1.07104	+	1.22528i
$333$	1.76760			0.0968638
$334$	−10.3592	+	1.01181i	−0.566830	+	0.0553638i
$335$	5.74510	+	9.95080i	0.313888	+	0.543670i
$336$	−0.566347	+	4.19661i	−0.0308968	+	0.228944i
$337$	10.2973			0.560931			0.280465	−	0.959864i	$-0.409511\pi$
$337$	10.2973			0.560931			0.280465	+	0.959864i	$0.409511\pi$
$338$	17.7709	−	4.71114i	0.966610	−	0.256252i
$339$		−	13.2831i		−	0.721437i
$340$	5.57201	−	1.09895i	0.302184	−	0.0595990i
$341$	−13.4534	+	7.76731i	−0.728541	+	0.420623i
$342$	−0.365998	−	3.74719i	−0.0197909	−	0.202625i
$343$		−	11.9714i		−	0.646394i
$344$	6.92014	−	29.3558i	0.373109	−	1.58276i
$345$	−0.997350	−	0.575820i	−0.0536955	−	0.0310011i
$346$	11.0752	+	15.4820i	0.595409	+	0.832317i
$347$	8.66358	+	5.00192i	0.465085	+	0.268517i	0.714180	−	0.699962i	$-0.246800\pi$
$347$	8.66358	+	5.00192i	0.465085	+	0.268517i	−0.249095	+	0.968479i	$0.580133\pi$
$348$	−20.7820	+	4.09878i	−1.11403	+	0.219717i
$349$	10.9211	+	18.9158i	0.584591	+	1.01254i	0.994926	+	0.100607i	$0.0320785\pi$
$349$	10.9211	+	18.9158i	0.584591	+	1.01254i	−0.410335	+	0.911935i	$0.634588\pi$
$350$	−0.747688	−	1.04519i	−0.0399656	−	0.0558676i
$351$	−18.3681	+	6.55311i	−0.980418	+	0.349779i
$352$	22.8159	+	0.839527i	1.21609	+	0.0447469i
$353$	4.63051	−	2.67343i	0.246457	−	0.142292i	−0.371684	−	0.928359i	$-0.621219\pi$
$353$	4.63051	−	2.67343i	0.246457	−	0.142292i	0.618141	+	0.786067i	$0.287886\pi$
$354$	−6.36727	+	14.0226i	−0.338416	+	0.745293i
$355$	4.27599	+	2.46874i	0.226946	+	0.131027i
$356$	−5.23181	−	1.78543i	−0.277285	−	0.0946274i
$357$	1.50313	−	2.60349i	0.0795540	−	0.137792i
$358$	9.18594	−	0.897216i	0.485492	−	0.0474193i
$359$		−	15.3255i		−	0.808851i	−0.914571	−	0.404426i	$-0.867471\pi$
$359$		−	15.3255i		−	0.808851i	0.914571	−	0.404426i	$-0.132529\pi$
$360$	4.52227	+	1.06605i	0.238345	+	0.0561858i
$361$	8.18670	+	14.1798i	0.430879	+	0.746304i
$362$	−6.65535	+	14.6571i	−0.349798	+	0.770358i
$363$			6.16271i			0.323458i
$364$	−5.62898	+	3.35444i	−0.295039	+	0.175821i
$365$		−	5.44599i		−	0.285056i
$366$	−0.275725	−	0.125199i	−0.0144124	−	0.00654426i
$367$	−17.4724	−	30.2631i	−0.912053	−	1.57972i	−0.811159	−	0.584826i	$-0.801163\pi$
$367$	−17.4724	−	30.2631i	−0.912053	−	1.57972i	−0.100895	−	0.994897i	$-0.532170\pi$
$368$	3.65791	−	1.50128i	0.190682	−	0.0782594i
$369$			14.5800i			0.759007i
$370$	0.147930	+	1.51454i	0.00769050	+	0.0787374i
$371$	4.60187	−	7.97068i	0.238917	−	0.413817i
$372$	−2.89656	+	8.48774i	−0.150179	+	0.440069i
$373$	−13.8440	−	7.99284i	−0.716815	−	0.413854i	0.0967640	−	0.995307i	$-0.469151\pi$
$373$	−13.8440	−	7.99284i	−0.716815	−	0.413854i	−0.813579	+	0.581454i	$0.802484\pi$
$374$	−14.7582	−	6.70128i	−0.763128	−	0.346515i
$375$	1.00895	−	0.582519i	0.0521021	−	0.0300811i
$376$	−31.3027	+	9.41248i	−1.61431	+	0.485412i
$377$	−24.9742	−	21.2287i	−1.28623	−	1.09333i
$378$	5.65331	−	4.04417i	0.290775	−	0.208010i
$379$	−0.360892	−	0.625083i	−0.0185378	−	0.0321084i	0.856608	−	0.515968i	$-0.172568\pi$
$379$	−0.360892	−	0.625083i	−0.0185378	−	0.0321084i	−0.875145	+	0.483860i	$0.839234\pi$
$380$	3.18010	−	0.627202i	0.163136	−	0.0321748i
$381$	10.3596	+	5.98112i	0.530739	+	0.306422i
$382$	12.2937	−	8.79447i	0.629001	−	0.449964i
$383$	−29.8976	−	17.2614i	−1.52769	−	0.882015i	−0.999458	−	0.0329171i	$-0.989520\pi$
$383$	−29.8976	−	17.2614i	−1.52769	−	0.882015i	−0.528236	−	0.849098i	$-0.677146\pi$
$384$	10.2363	−	8.30391i	0.522367	−	0.423757i
$385$			3.66754i			0.186915i
$386$	18.8528	−	1.84140i	0.959582	−	0.0937250i
$387$	−15.1697	+	8.75825i	−0.771121	+	0.445207i
$388$	−4.38276	−	22.2219i	−0.222501	−	1.12814i
$389$			28.3941i			1.43964i	0.694163	+	0.719818i	$0.255775\pi$
$389$			28.3941i			1.43964i	−0.694163	+	0.719818i	$0.744225\pi$
$390$	−2.53060	−	5.37459i	−0.128142	−	0.272153i
$391$	−2.80702			−0.141957
$392$	−11.9689	+	12.7169i	−0.604519	+	0.642300i
$393$	−2.92656	−	5.06895i	−0.147625	−	0.255695i
$394$	1.57433	+	16.1184i	0.0793137	+	0.812035i
$395$	−14.8307			−0.746215
$396$	−8.72671	−	9.98352i	−0.438534	−	0.501691i
$397$	19.2805	−	33.3949i	0.967662	−	1.67604i	0.265378	−	0.964145i	$-0.414503\pi$
$397$	19.2805	−	33.3949i	0.967662	−	1.67604i	0.702285	−	0.711896i	$-0.252163\pi$
$398$	−11.4588	+	8.19721i	−0.574378	+	0.410889i
$399$	0.857877	−	1.48589i	0.0429476	−	0.0743874i
$400$	−0.534964	+	3.96407i	−0.0267482	+	0.198203i
$401$	−24.7230	+	14.2738i	−1.23461	+	0.712802i	−0.967987	−	0.251000i	$-0.919241\pi$
$401$	−24.7230	+	14.2738i	−1.23461	+	0.712802i	−0.266622	+	0.963801i	$0.585907\pi$
$402$	−11.0146	−	15.3972i	−0.549360	−	0.767945i
$403$	−13.0707	+	4.66317i	−0.651099	+	0.232289i
$404$	−33.3343	−	11.3758i	−1.65845	−	0.565967i
$405$	0.686757	+	1.18950i	0.0341252	+	0.0591067i
$406$	10.6373	+	4.83009i	0.527920	+	0.239713i
$407$	2.17148	−	3.76111i	0.107636	−	0.186431i
$408$	−8.96101	+	2.69451i	−0.443636	+	0.133398i
$409$	16.0645	+	9.27487i	0.794341	+	0.458613i	0.841488	−	0.540275i	$-0.181680\pi$
$409$	16.0645	+	9.27487i	0.794341	+	0.458613i	−0.0471479	+	0.998888i	$0.515013\pi$
$410$	−12.4927	+	1.22020i	−0.616972	+	0.0602613i
$411$	−25.4563			−1.25567
$412$	−5.27108	−	6.03022i	−0.259688	−	0.297088i
$413$	7.35578	−	4.24686i	0.361954	−	0.208974i
$414$	−2.09094	−	0.949435i	−0.102764	−	0.0466622i
$415$	14.8263			0.727796
$416$	19.9147	+	4.40502i	0.976399	+	0.215974i
$417$	−2.41419			−0.118223
$418$	−8.42292	−	3.82461i	−0.411978	−	0.187068i
$419$	14.6025	−	8.43073i	0.713377	−	0.411868i	−0.0989333	−	0.995094i	$-0.531543\pi$
$419$	14.6025	−	8.43073i	0.713377	−	0.411868i	0.812310	+	0.583226i	$0.198210\pi$
$420$	1.39347	+	1.59415i	0.0679942	+	0.0777867i
$421$	27.8277			1.35624			0.678120	−	0.734951i	$-0.262795\pi$
$421$	27.8277			1.35624			0.678120	+	0.734951i	$0.262795\pi$
$422$	−6.04929	+	0.590851i	−0.294475	+	0.0287622i
$423$	16.4406	+	9.49200i	0.799371	+	0.461517i
$424$	−27.4344	+	8.24932i	−1.33233	+	0.400622i
$425$	1.41984	−	2.45923i	0.0688721	−	0.119290i
$426$	−7.40721	−	3.36340i	−0.358880	−	0.162957i
$427$	0.0835056	+	0.144636i	0.00404112	+	0.00699943i
$428$	−22.8763	−	7.80686i	−1.10577	−	0.377359i
$429$	−3.05042	+	16.6772i	−0.147275	+	0.805181i
$430$	−8.77394	−	12.2650i	−0.423117	−	0.591471i
$431$	7.01128	−	4.04796i	0.337721	−	0.194984i	−0.321543	−	0.946895i	$-0.604201\pi$
$431$	7.01128	−	4.04796i	0.337721	−	0.194984i	0.659264	+	0.751912i	$0.270868\pi$
$432$	−21.4413	−	2.89357i	−1.03159	−	0.139217i
$433$	−4.48649	+	7.77083i	−0.215607	+	0.373442i	−0.953460	−	0.301519i	$-0.902506\pi$
$433$	−4.48649	+	7.77083i	−0.215607	+	0.373442i	0.737853	+	0.674961i	$0.235840\pi$
$434$	4.02288	−	2.87782i	0.193105	−	0.138140i
$435$	−5.29559	+	9.17223i	−0.253904	+	0.439775i
$436$	6.17766	+	7.06736i	0.295856	+	0.338465i
$437$	−1.60204			−0.0766361
$438$	0.872255	+	8.93038i	0.0416780	+	0.426710i
$439$	3.21962	+	5.57654i	0.153664	+	0.266154i	0.932572	−	0.360985i	$-0.117559\pi$
$439$	3.21962	+	5.57654i	0.153664	+	0.266154i	−0.778908	+	0.627139i	$0.784226\pi$
$440$	7.82391	−	8.31289i	0.372990	−	0.396301i
$441$	10.1424			0.482972
$442$	−11.8918	−	8.26094i	−0.565633	−	0.392933i
$443$		−	10.0241i		−	0.476260i	−0.971233	−	0.238130i	$-0.923466\pi$
$443$		−	10.0241i		−	0.476260i	0.971233	−	0.238130i	$-0.0765344\pi$
$444$	−0.485153	−	2.45987i	−0.0230243	−	0.116740i
$445$	−2.39372	+	1.38202i	−0.113473	+	0.0655139i
$446$	−10.2294	+	0.999138i	−0.484378	+	0.0473106i
$447$		−	2.50806i		−	0.118627i
$448$	−7.25622	+	0.440156i	−0.342824	+	0.0207954i
$449$	−35.4627	−	20.4744i	−1.67359	−	0.966247i	−0.965603	−	0.260020i	$-0.916271\pi$
$449$	−35.4627	−	20.4744i	−1.67359	−	0.966247i	−0.707985	−	0.706227i	$-0.750396\pi$
$450$	1.88943	−	1.35163i	0.0890686	−	0.0637164i
$451$	31.0235	+	17.9114i	1.46084	+	0.843417i
$452$	22.3718	−	4.41233i	1.05228	−	0.207539i
$453$	4.30980	+	7.46480i	0.202492	+	0.350727i
$454$	−2.56675	+	1.83616i	−0.120464	+	0.0861753i
$455$	−0.589495	+	3.22288i	−0.0276360	+	0.151091i
$456$	−5.11430	+	1.53783i	−0.239499	+	0.0720155i
$457$	−17.0300	+	9.83229i	−0.796631	+	0.459935i	−0.842292	−	0.539022i	$-0.818794\pi$
$457$	−17.0300	+	9.83229i	−0.796631	+	0.459935i	0.0456608	+	0.998957i	$0.485461\pi$
$458$	7.66878	+	3.48218i	0.358338	+	0.162711i
$459$	13.3017	+	7.67976i	0.620872	+	0.358460i
$460$	0.638521	−	1.87105i	0.0297712	−	0.0872381i
$461$	−9.15438	+	15.8559i	−0.426362	+	0.738481i	−0.996547	−	0.0830360i	$-0.973538\pi$
$461$	−9.15438	+	15.8559i	−0.426362	+	0.738481i	0.570185	+	0.821517i	$0.306872\pi$
$462$	−0.587410	−	6.01406i	−0.0273288	−	0.279799i
$463$		−	34.7475i		−	1.61485i	−0.589968	−	0.807426i	$-0.700860\pi$
$463$		−	34.7475i		−	1.61485i	0.589968	−	0.807426i	$-0.299140\pi$
$464$	−13.8066	−	33.6403i	−0.640957	−	1.56171i
$465$	2.24209	+	3.88342i	0.103975	+	0.180089i
$466$	−1.28119	−	0.581754i	−0.0593501	−	0.0269492i
$467$		−	12.6309i		−	0.584489i	−0.956344	−	0.292245i	$-0.905598\pi$
$467$		−	12.6309i		−	0.584489i	0.956344	−	0.292245i	$-0.0944021\pi$
$468$	−6.06398	−	10.1758i	−0.280307	−	0.470375i
$469$			10.4411i			0.482124i
$470$	−6.75719	+	14.8813i	−0.311686	+	0.686424i
$471$	−4.55254	−	7.88523i	−0.209770	−	0.363332i
$472$	−25.7325	−	6.06600i	−1.18443	−	0.279210i
$473$			43.0377i			1.97887i
$474$	24.3196	−	2.37536i	1.11703	−	0.109104i
$475$	0.810340	−	1.40355i	0.0371810	−	0.0643993i
$476$	4.88421	+	1.66680i	0.223867	+	0.0763978i
$477$	14.4090	+	8.31901i	0.659741	+	0.380901i
$478$	1.23194	−	2.71311i	0.0563478	−	0.124095i
$479$	1.01749	−	0.587451i	0.0464905	−	0.0268413i	−0.476575	−	0.879134i	$-0.658122\pi$
$479$	1.01749	−	0.587451i	0.0464905	−	0.0268413i	0.523065	+	0.852293i	$0.324788\pi$
$480$	0.242336	−	6.58599i	0.0110611	−	0.300608i
$481$	2.51274	−	2.95607i	0.114571	−	0.134785i
$482$	−11.8614	−	16.5809i	−0.540271	−	0.755240i
$483$	−0.523245	−	0.906286i	−0.0238085	−	0.0412375i
$484$	−10.3795	+	2.04711i	−0.471794	+	0.0930506i
$485$	−9.80772	−	5.66249i	−0.445345	−	0.257120i
$486$	12.0349	+	16.8235i	0.545915	+	0.763130i
$487$	12.8997	+	7.44763i	0.584540	+	0.337484i	0.762936	−	0.646475i	$-0.223757\pi$
$487$	12.8997	+	7.44763i	0.584540	+	0.337484i	−0.178396	+	0.983959i	$0.557091\pi$
$488$	0.119275	−	0.505975i	0.00539934	−	0.0229044i
$489$			8.14199i			0.368194i
$490$	0.848814	+	8.69039i	0.0383455	+	0.392592i
$491$	−29.0986	+	16.8001i	−1.31320	+	0.758178i	−0.982625	−	0.185600i	$-0.940577\pi$
$491$	−29.0986	+	16.8001i	−1.31320	+	0.758178i	−0.330578	+	0.943779i	$0.607244\pi$
$492$	20.2902	−	4.00179i	0.914755	−	0.180414i
$493$			25.8150i			1.16265i
$494$	−6.78696	−	4.71475i	−0.305360	−	0.212127i
$495$	−6.62997			−0.297995
$496$	−15.2575	−	2.05906i	−0.685084	−	0.0924544i
$497$	2.24333	+	3.88557i	0.100627	+	0.174292i
$498$	−24.3124	+	2.37466i	−1.08946	+	0.106411i
$499$	17.4987			0.783349			0.391674	−	0.920104i	$-0.371896\pi$
$499$	17.4987			0.783349			0.391674	+	0.920104i	$0.371896\pi$
$500$	1.31625	+	1.50582i	0.0588646	+	0.0673421i
$501$	4.28729	−	7.42580i	0.191542	−	0.331760i
$502$	−2.25997	−	3.15920i	−0.100868	−	0.141002i
$503$	−7.33267	+	12.7006i	−0.326948	+	0.566290i	−0.981905	−	0.189376i	$-0.939353\pi$
$503$	−7.33267	+	12.7006i	−0.326948	+	0.566290i	0.654957	+	0.755666i	$0.272687\pi$
$504$	3.07445	+	2.89361i	0.136947	+	0.128892i
$505$	−15.2516	+	8.80549i	−0.678685	+	0.391839i
$506$	−4.58891	+	3.28274i	−0.204002	+	0.145935i
$507$	−5.36115	+	14.1649i	−0.238097	+	0.629084i
$508$	−6.63241	+	19.4348i	−0.294265	+	0.862282i
$509$	−17.8928	−	30.9912i	−0.793084	−	1.37366i	−0.924048	−	0.382275i	$-0.875141\pi$
$509$	−17.8928	−	30.9912i	−0.793084	−	1.37366i	0.130964	−	0.991387i	$-0.458193\pi$
$510$	−1.93438	+	4.26007i	−0.0856557	+	0.188639i
$511$	2.47437	−	4.28574i	0.109460	−	0.189590i
$512$	17.3860	+	14.4819i	0.768360	+	0.640017i
$513$	7.59167	+	4.38305i	0.335180	+	0.193516i
$514$	0.901279	+	9.22754i	0.0397537	+	0.407009i
$515$	−4.00462			−0.176465
$516$	16.3520	+	18.7070i	0.719857	+	0.823529i
$517$	40.3943	−	23.3217i	1.77654	−	1.02569i
$518$	−0.571715	+	1.25909i	−0.0251197	+	0.0553210i
$519$	−15.6816			−0.688347
$520$	8.21148	−	6.04745i	0.360097	−	0.265198i
$521$	33.7099			1.47686			0.738428	−	0.674332i	$-0.235568\pi$
$521$	33.7099			1.47686			0.738428	+	0.674332i	$0.235568\pi$
$522$	−8.73157	+	19.2295i	−0.382171	+	0.841652i
$523$	−3.92771	+	2.26767i	−0.171747	+	0.0991581i	−0.583409	−	0.812178i	$-0.698282\pi$
$523$	−3.92771	+	2.26767i	−0.171747	+	0.0991581i	0.411662	+	0.911336i	$0.364948\pi$
$524$	7.56518	−	6.61281i	0.330486	−	0.288882i
$525$	1.05866			0.0462039
$526$	−0.112855	−	1.15544i	−0.00492071	−	0.0503795i
$527$	9.46548	+	5.46490i	0.412323	+	0.238055i
$528$	−11.4983	+	14.8847i	−0.500399	+	0.647771i
$529$	11.0114	−	19.0724i	0.478758	−	0.829233i
$530$	−5.92216	+	13.0423i	−0.257242	+	0.566523i
$531$	7.67724	+	13.2974i	0.333164	+	0.577056i
$532$	2.78755	+	0.951292i	0.120856	+	0.0412437i
$533$	24.3832	+	20.7263i	1.05615	+	0.897757i
$534$	3.70390	−	2.64963i	0.160283	−	0.114661i
$535$	−10.4667	+	6.04294i	−0.452514	+	0.261259i
$536$	22.2738	−	23.6659i	0.962083	−	1.02221i
$537$	−3.80172	+	6.58477i	−0.164056	+	0.284154i
$538$	−14.6972	−	20.5452i	−0.633643	−	0.885764i
$539$	12.4598	−	21.5811i	0.536683	−	0.929563i
$540$	−8.14482	+	7.11948i	−0.350497	+	0.306374i
$541$	28.0708			1.20686			0.603430	−	0.797416i	$-0.293800\pi$
$541$	28.0708			1.20686			0.603430	+	0.797416i	$0.293800\pi$
$542$	−13.0413	+	1.27378i	−0.560171	+	0.0547134i
$543$	−6.63052	−	11.4844i	−0.284543	−	0.492843i
$544$	−7.51484	−	14.1974i	−0.322196	−	0.608709i
$545$	4.69338			0.201042
$546$	0.450469	−	5.37932i	0.0192783	−	0.230213i
$547$			8.48845i			0.362940i	0.983396	+	0.181470i	$0.0580855\pi$
$547$			8.48845i			0.362940i	−0.983396	+	0.181470i	$0.941914\pi$
$548$	−8.45600	−	42.8744i	−0.361222	−	1.83150i
$549$	−0.261465	+	0.150957i	−0.0111590	+	0.00644268i
$550$	−0.554860	−	5.68081i	−0.0236593	−	0.242230i
$551$			14.7334i			0.627662i
$552$	−0.747377	+	3.17043i	−0.0318105	+	0.134943i
$553$	−11.6711	−	6.73830i	−0.496305	−	0.286542i
$554$	5.41502	+	7.56961i	0.230062	+	0.321602i
$555$	−1.08567	−	0.626814i	−0.0460843	−	0.0266068i
$556$	−0.801938	−	4.06606i	−0.0340097	−	0.172440i
$557$	6.60522	+	11.4406i	0.279872	+	0.484753i	0.971353	−	0.237642i	$-0.0763746\pi$
$557$	6.60522	+	11.4406i	0.279872	+	0.484753i	−0.691481	+	0.722395i	$0.743041\pi$
$558$	5.20237	+	7.27235i	0.220234	+	0.307863i
$559$	−6.91759	+	37.8197i	−0.292583	+	1.59960i
$560$	−2.22205	+	2.87647i	−0.0938989	+	0.121553i
$561$	11.5637	−	6.67628i	0.488218	−	0.281873i
$562$	−0.367313	+	0.808931i	−0.0154942	+	0.0341227i
$563$	−13.6293	−	7.86886i	−0.574405	−	0.331633i	0.184502	−	0.982832i	$-0.440933\pi$
$563$	−13.6293	−	7.86886i	−0.574405	−	0.331633i	−0.758907	+	0.651199i	$0.774266\pi$
$564$	8.69703	−	25.4848i	0.366211	−	1.07310i
$565$	5.70070	−	9.87391i	0.239830	−	0.415398i
$566$	−5.28850	+	0.516542i	−0.222292	+	0.0217119i
$567$			1.24811i			0.0524155i
$568$	3.20427	−	13.5928i	0.134448	−	0.570339i
$569$	17.8062	+	30.8412i	0.746475	+	1.29293i	0.949503	+	0.313759i	$0.101588\pi$
$569$	17.8062	+	30.8412i	0.746475	+	1.29293i	−0.203028	+	0.979173i	$0.565078\pi$
$570$	−1.10400	+	2.43134i	−0.0462416	+	0.101838i
$571$		−	22.5745i		−	0.944715i	−0.881407	−	0.472357i	$-0.843403\pi$
$571$		−	22.5745i		−	0.944715i	0.881407	−	0.472357i	$-0.156597\pi$
$572$	−29.1016	+	0.402151i	−1.21680	+	0.0168148i
$573$			12.4522i			0.520200i
$574$	−10.3856	−	4.71580i	−0.433486	−	0.196834i
$575$	−0.494250	−	0.856067i	−0.0206117	−	0.0357005i
$576$	−0.795689	−	13.1174i	−0.0331537	−	0.546558i
$577$			5.11683i			0.213016i	0.994312	+	0.106508i	$0.0339670\pi$
$577$			5.11683i			0.213016i	−0.994312	+	0.106508i	$0.966033\pi$
$578$	−1.22852	−	12.5779i	−0.0510998	−	0.523173i
$579$	−7.80247	+	13.5143i	−0.324260	+	0.561634i
$580$	−17.2073	−	5.87223i	−0.714494	−	0.243831i
$581$	11.6676	+	6.73631i	0.484055	+	0.279469i
$582$	16.9897	+	7.71455i	0.704246	+	0.319778i
$583$	35.4025	−	20.4397i	1.46622	−	0.846524i
$584$	−14.7511	+	4.43556i	−0.610407	+	0.183545i
$585$	−5.82614	−	1.06566i	−0.240881	−	0.0440595i
$586$	23.4964	−	16.8084i	0.970626	−	0.694350i
$587$	8.14685	+	14.1108i	0.336256	+	0.582413i	0.983725	−	0.179679i	$-0.0575058\pi$
$587$	8.14685	+	14.1108i	0.336256	+	0.582413i	−0.647469	+	0.762092i	$0.724172\pi$
$588$	−2.78379	−	14.1146i	−0.114801	−	0.582077i
$589$	5.40221	+	3.11897i	0.222594	+	0.128515i
$590$	−10.7512	+	7.69099i	−0.442619	+	0.316633i
$591$	−11.5542	−	6.67082i	−0.475276	−	0.274401i
$592$	3.98185	−	1.63423i	0.163653	−	0.0671662i
$593$		−	45.0181i		−	1.84867i	−0.381581	−	0.924335i	$-0.624620\pi$
$593$		−	45.0181i		−	1.84867i	0.381581	−	0.924335i	$-0.375380\pi$
$594$	30.7269	−	3.00119i	1.26074	−	0.123140i
$595$	2.23469	−	1.29020i	0.0916132	−	0.0528929i
$596$	4.22417	−	0.833120i	0.173029	−	0.0341259i
$597$		−	11.6066i		−	0.475025i
$598$	−4.56018	+	2.14714i	−0.186480	+	0.0878031i
$599$	17.8885			0.730903			0.365452	−	0.930830i	$-0.380915\pi$
$599$	17.8885			0.730903			0.365452	+	0.930830i	$0.380915\pi$
$600$	−2.39958	−	2.25843i	−0.0979624	−	0.0922001i
$601$	−17.9649	−	31.1161i	−0.732803	−	1.26925i	−0.955681	−	0.294406i	$-0.904878\pi$
$601$	−17.9649	−	31.1161i	−0.732803	−	1.26925i	0.222877	−	0.974846i	$-0.428455\pi$
$602$	−1.33210	−	13.6384i	−0.0542923	−	0.555860i
$603$	−18.8748			−0.768641
$604$	−11.1409	+	9.73837i	−0.453316	+	0.396249i
$605$	−2.64485	+	4.58102i	−0.107529	+	0.186245i
$606$	23.5993	−	16.8821i	0.958656	−	0.685788i
$607$	−4.90763	+	8.50026i	−0.199194	+	0.345015i	−0.948267	−	0.317473i	$-0.897166\pi$
$607$	−4.90763	+	8.50026i	−0.199194	+	0.345015i	0.749073	+	0.662487i	$0.230499\pi$
$608$	−4.28893	−	8.10287i	−0.173939	−	0.328615i
$609$	−8.33475	+	4.81207i	−0.337741	+	0.194995i
$610$	−0.151227	−	0.211399i	−0.00612302	−	0.00855931i
$611$	39.2454	−	14.0014i	1.58770	−	0.566435i
$612$	−3.01316	+	8.82940i	−0.121800	+	0.356907i
$613$	−7.95475	−	13.7780i	−0.321289	−	0.556489i	0.659465	−	0.751735i	$-0.270783\pi$
$613$	−7.95475	−	13.7780i	−0.321289	−	0.556489i	−0.980754	+	0.195246i	$0.937449\pi$
$614$	37.4020	+	16.9832i	1.50942	+	0.685385i
$615$	5.17028	−	8.95518i	0.208486	−	0.361108i
$616$	9.93398	−	2.98707i	0.400252	−	0.120353i
$617$	−29.7504	−	17.1764i	−1.19771	−	0.691496i	−0.237663	−	0.971348i	$-0.576381\pi$
$617$	−29.7504	−	17.1764i	−1.19771	−	0.691496i	−0.960043	+	0.279852i	$0.909715\pi$
$618$	6.56681	−	0.641398i	0.264156	−	0.0258008i
$619$	−36.9709			−1.48599			−0.742994	−	0.669298i	$-0.766595\pi$
$619$	−36.9709			−1.48599			−0.742994	+	0.669298i	$0.766595\pi$
$620$	−5.79583	+	5.06620i	−0.232766	+	0.203464i
$621$	4.63038	−	2.67335i	0.185811	−	0.107278i
$622$	−38.1634	−	17.3289i	−1.53021	−	0.694826i
$623$	−2.51166			−0.100628
$624$	−12.4967	+	11.2318i	−0.500267	+	0.449634i
$625$	1.00000			0.0400000
$626$	−27.4228	−	12.4519i	−1.09603	−	0.497678i
$627$	6.59970	−	3.81034i	0.263567	−	0.152170i
$628$	11.7684	−	10.2869i	0.469609	−	0.410490i
$629$	−3.05560			−0.121835
$630$	2.10100	−	0.205211i	0.0837059	−	0.00817578i
$631$	22.4180	+	12.9431i	0.892448	+	0.515255i	0.874742	−	0.484588i	$-0.161030\pi$
$631$	22.4180	+	12.9431i	0.892448	+	0.515255i	0.0177056	+	0.999843i	$0.494364\pi$
$632$	12.0791	+	40.1709i	0.480480	+	1.59791i
$633$	2.50358	−	4.33632i	0.0995083	−	0.172353i
$634$	−17.6611	−	8.01940i	−0.701411	−	0.318491i
$635$	5.13384	+	8.89208i	0.203730	+	0.352871i
$636$	7.62228	−	22.3355i	0.302243	−	0.885659i
$637$	14.4180	−	16.9618i	0.571261	−	0.672052i
$638$	30.1900	+	42.2024i	1.19523	+	1.67081i
$639$	−7.02411	+	4.05537i	−0.277870	+	0.160428i
$640$	11.1729	−	1.77957i	0.441647	−	0.0703435i
$641$	−22.0205	+	38.1406i	−0.869757	+	1.50646i	−0.00751163	+	0.999972i	$0.502391\pi$
$641$	−22.0205	+	38.1406i	−0.869757	+	1.50646i	−0.862245	+	0.506491i	$0.830942\pi$
$642$	16.1955	−	11.5857i	0.639185	−	0.457249i
$643$	3.63461	−	6.29534i	0.143335	−	0.248264i	−0.785415	−	0.618969i	$-0.787551\pi$
$643$	3.63461	−	6.29534i	0.143335	−	0.248264i	0.928751	+	0.370705i	$0.120884\pi$
$644$	1.35259	−	1.18232i	0.0532996	−	0.0465898i
$645$	12.4232			0.489161
$646$	0.632692	+	6.47767i	0.0248929	+	0.254860i
$647$	22.3305	+	38.6775i	0.877902	+	1.52057i	0.853639	+	0.520865i	$0.174391\pi$
$647$	22.3305	+	38.6775i	0.877902	+	1.52057i	0.0242628	+	0.999706i	$0.492276\pi$
$648$	2.66257	−	2.82897i	0.104596	−	0.111132i
$649$	37.7256			1.48086
$650$	0.425507	−	5.08123i	0.0166898	−	0.199302i
$651$			4.07476i			0.159702i
$652$	−13.7131	+	2.70459i	−0.537045	+	0.105920i
$653$	−28.1392	+	16.2462i	−1.10117	+	0.635762i	−0.936528	−	0.350592i	$-0.885981\pi$
$653$	−28.1392	+	16.2462i	−1.10117	+	0.635762i	−0.164643	+	0.986353i	$0.552647\pi$
$654$	−7.69624	+	0.751713i	−0.300947	+	0.0293943i
$655$		−	5.02397i		−	0.196303i
$656$	13.4799	+	32.8443i	0.526302	+	1.28235i
$657$	7.74752	+	4.47303i	0.302259	+	0.174510i
$658$	−12.0789	+	8.64078i	−0.470884	+	0.336853i
$659$	−25.1640	−	14.5284i	−0.980251	−	0.565948i	−0.0779048	−	0.996961i	$-0.524823\pi$
$659$	−25.1640	−	14.5284i	−0.980251	−	0.565948i	−0.902346	+	0.431013i	$0.858156\pi$
$660$	1.81973	+	9.22656i	0.0708328	+	0.359144i
$661$	3.00066	+	5.19730i	0.116712	+	0.202151i	0.918463	−	0.395507i	$-0.129431\pi$
$661$	3.00066	+	5.19730i	0.116712	+	0.202151i	−0.801751	+	0.597659i	$0.796098\pi$
$662$	−27.1362	+	19.4123i	−1.05468	+	0.754479i
$663$	11.2348	−	4.00817i	0.436322	−	0.155664i
$664$	−12.0755	−	40.1590i	−0.468620	−	1.55847i
$665$	1.27540	−	0.736352i	0.0494578	−	0.0285545i
$666$	−2.27610	−	1.03351i	−0.0881973	−	0.0400479i
$667$	7.78237	+	4.49315i	0.301335	+	0.173976i
$668$	13.9310	+	4.75413i	0.539005	+	0.183943i
$669$	4.23359	−	7.33279i	0.163680	−	0.283502i
$670$	−1.57963	−	16.1726i	−0.0610263	−	0.624803i
$671$			0.741796i			0.0286367i
$672$	3.18303	−	5.07276i	0.122788	−	0.195686i
$673$	−3.97923	−	6.89223i	−0.153388	−	0.265676i	0.779083	−	0.626921i	$-0.215685\pi$
$673$	−3.97923	−	6.89223i	−0.153388	−	0.265676i	−0.932471	+	0.361245i	$0.882352\pi$
$674$	−13.2597	−	6.02085i	−0.510744	−	0.231914i
$675$			5.40891i			0.208189i
$676$	−25.6379	−	4.32420i	−0.986073	−	0.166315i
$677$			34.9163i			1.34194i	0.741483	+	0.670972i	$0.234123\pi$
$677$			34.9163i			1.34194i	−0.741483	+	0.670972i	$0.765877\pi$
$678$	−7.76661	+	17.1044i	−0.298275	+	0.656889i
$679$	−5.14547	−	8.91222i	−0.197465	−	0.342020i
$680$	−7.81753	−	1.84285i	−0.299789	−	0.0706702i
$681$		−	2.59985i		−	0.0996264i
$682$	21.8652	−	2.13564i	0.837262	−	0.0817777i
$683$	−8.39031	+	14.5324i	−0.321046	+	0.556068i	−0.980704	−	0.195498i	$-0.937368\pi$
$683$	−8.39031	+	14.5324i	−0.321046	+	0.556068i	0.659658	+	0.751566i	$0.270701\pi$
$684$	−1.71969	+	5.03919i	−0.0657541	+	0.192678i
$685$	−18.9228	−	10.9251i	−0.723003	−	0.417426i
$686$	−6.99967	+	15.4153i	−0.267249	+	0.588561i
$687$	−6.00880	+	3.46918i	−0.229250	+	0.132358i
$688$	−26.0753	+	33.7547i	−0.994110	+	1.28689i
$689$	34.3956	−	12.2711i	1.31037	−	0.467493i
$690$	0.947588	+	1.32462i	0.0360740	+	0.0504276i
$691$	−1.56844	−	2.71661i	−0.0596661	−	0.103345i	0.834649	−	0.550782i	$-0.185670\pi$
$691$	−1.56844	−	2.71661i	−0.0596661	−	0.103345i	−0.894316	+	0.447437i	$0.852337\pi$
$692$	−5.20908	−	26.4116i	−0.198019	−	1.00402i
$693$	−5.21747	−	3.01231i	−0.198195	−	0.114428i
$694$	−8.23132	−	11.5065i	−0.312456	−	0.436780i
$695$	−1.79457	−	1.03610i	−0.0680721	−	0.0393014i
$696$	29.1572	+	6.87333i	1.10520	+	0.260533i
$697$		−	25.2041i		−	0.954675i
$698$	−3.00277	−	30.7432i	−0.113656	−	1.16365i
$699$	1.00387	−	0.579583i	0.0379698	−	0.0219219i
$700$	0.351664	+	1.78304i	0.0132916	+	0.0673926i
$701$		−	15.2711i		−	0.576782i	−0.957513	−	0.288391i	$-0.906880\pi$
$701$		−	15.2711i		−	0.576782i	0.957513	−	0.288391i	$-0.0931203\pi$
$702$	27.4839	+	2.30153i	1.03731	+	0.0868656i
$703$	−1.74392			−0.0657731
$704$	−28.8888	−	14.4215i	−1.08879	−	0.543531i
$705$	−6.73198	−	11.6601i	−0.253541	−	0.439146i
$706$	−7.52578	+	0.735064i	−0.283236	+	0.0276645i
$707$	−16.0030			−0.601855
$708$	16.3980	−	14.3337i	0.616276	−	0.538694i
$709$	3.41446	−	5.91402i	0.128233	−	0.222106i	−0.794759	−	0.606925i	$-0.792403\pi$
$709$	3.41446	−	5.91402i	0.128233	−	0.222106i	0.922992	+	0.384819i	$0.125736\pi$
$710$	−4.06264	−	5.67913i	−0.152468	−	0.213134i
$711$	12.1811	−	21.0983i	0.456828	−	0.791249i
$712$	5.69297	+	5.35810i	0.213353	+	0.200803i
$713$	3.29497	−	1.90235i	0.123398	−	0.0712436i
$714$	−3.45781	+	2.47359i	−0.129405	+	0.0925719i
$715$	−9.42486	+	11.0877i	−0.352470	+	0.414658i
$716$	−12.3532	−	4.21569i	−0.461660	−	0.157548i
$717$	1.22735	+	2.12583i	0.0458362	+	0.0793906i
$718$	−8.96085	+	19.7344i	−0.334416	+	0.736482i
$719$	1.44358	−	2.50036i	0.0538366	−	0.0932477i	−0.837851	−	0.545899i	$-0.816188\pi$
$719$	1.44358	−	2.50036i	0.0538366	−	0.0932477i	0.891688	+	0.452651i	$0.149522\pi$
$720$	−5.19993	−	4.01691i	−0.193790	−	0.149701i
$721$	−3.15144	−	1.81949i	−0.117366	−	0.0677612i
$722$	−2.25095	−	23.0458i	−0.0837716	−	0.857676i
$723$	16.7947			0.624602
$724$	17.1400	−	14.9822i	0.637002	−	0.556811i
$725$	−7.87290	+	4.54542i	−0.292392	+	0.168813i
$726$	3.60334	−	7.93561i	0.133732	−	0.294518i
$727$	43.6301			1.61815			0.809075	−	0.587705i	$-0.199968\pi$
$727$	43.6301			1.61815			0.809075	+	0.587705i	$0.199968\pi$
$728$	9.20969	−	1.02819i	0.341334	−	0.0381073i
$729$	−21.1610			−0.783740
$730$	−3.18427	+	7.01271i	−0.117855	+	0.259552i
$731$	26.2235	−	15.1402i	0.969912	−	0.559979i
$732$	0.281843	+	0.322433i	0.0104172	+	0.0119175i
$733$	0.536145			0.0198030			0.00990149	−	0.999951i	$-0.496848\pi$
$733$	0.536145			0.0198030			0.00990149	+	0.999951i	$0.496848\pi$
$734$	4.80408	+	49.1854i	0.177322	+	1.81547i
$735$	−6.22955	−	3.59663i	−0.229780	−	0.132664i
$736$	−5.58802	−	0.205615i	−0.205977	−	0.00757907i
$737$	−23.1875	+	40.1619i	−0.854123	+	1.47938i
$738$	8.52496	−	18.7745i	0.313808	−	0.691098i
$739$	25.8337	+	44.7452i	0.950307	+	1.64598i	0.744760	+	0.667333i	$0.232564\pi$
$739$	25.8337	+	44.7452i	0.950307	+	1.64598i	0.205547	+	0.978647i	$0.434103\pi$
$740$	0.695067	−	2.03675i	0.0255512	−	0.0748723i
$741$	6.41199	−	2.28757i	0.235550	−	0.0840361i
$742$	−10.5862	+	7.57299i	−0.388632	+	0.278013i
$743$	6.05907	−	3.49821i	0.222286	−	0.128337i	−0.384722	−	0.923032i	$-0.625703\pi$
$743$	6.05907	−	3.49821i	0.222286	−	0.128337i	0.607008	+	0.794696i	$0.292369\pi$
$744$	8.69263	−	9.23589i	0.318687	−	0.338604i
$745$	1.07638	−	1.86435i	0.0394357	−	0.0683046i
$746$	13.1533	+	18.3868i	0.481575	+	0.673190i
$747$	−12.1775	+	21.0921i	−0.445552	+	0.771719i
$748$	15.0856	+	17.2582i	0.551585	+	0.631024i
$749$	−10.9824			−0.401287
$750$	−1.63981	+	0.160165i	−0.0598773	+	0.00584839i
$751$	−17.9187	−	31.0362i	−0.653864	−	1.13253i	−0.982177	−	0.187957i	$-0.939814\pi$
$751$	−17.9187	−	31.0362i	−0.653864	−	1.13253i	0.328313	−	0.944569i	$-0.393520\pi$
$752$	45.8114	+	6.18241i	1.67057	+	0.225449i
$753$	3.19993			0.116612
$754$	19.7464	+	41.9382i	0.719121	+	1.52730i
$755$			7.39857i			0.269261i
$756$	−9.64430	+	1.90212i	−0.350760	+	0.0691793i
$757$	−2.11175	+	1.21922i	−0.0767528	+	0.0443133i	−0.537885	−	0.843018i	$-0.680777\pi$
$757$	−2.11175	+	1.21922i	−0.0767528	+	0.0443133i	0.461132	+	0.887331i	$0.347443\pi$
$758$	0.0992279	+	1.01592i	0.00360412	+	0.0368999i
$759$		−	4.64808i		−	0.168715i
$760$	−4.46168	−	1.05177i	−0.161842	−	0.0381516i
$761$	−20.1359	−	11.6254i	−0.729924	−	0.421422i	0.0884703	−	0.996079i	$-0.471802\pi$
$761$	−20.1359	−	11.6254i	−0.729924	−	0.421422i	−0.818394	+	0.574657i	$0.805135\pi$
$762$	−9.84272	−	13.7590i	−0.356564	−	0.498438i
$763$	3.69346	+	2.13242i	0.133712	+	0.0771989i
$764$	−20.9725	+	4.13635i	−0.758760	+	0.149648i
$765$	2.33235	+	4.03974i	0.0843262	+	0.146057i
$766$	28.4058	+	39.7083i	1.02634	+	1.43472i
$767$	33.1517	+	6.06377i	1.19704	+	0.218950i
$768$	−18.0364	+	4.70765i	−0.650831	+	0.169873i
$769$	−8.79396	+	5.07719i	−0.317118	+

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)

\(f(q)\)	\(=\)	\(q+(-1.28768 - 0.584700i) q^{2} +(1.00895 - 0.582519i) q^{3} +(1.31625 + 1.50582i) q^{4} +1.00000 q^{5} +(-1.63981 + 0.160165i) q^{6} +(0.786953 + 0.454347i) q^{7} +(-0.814463 - 2.70863i) q^{8} +(-0.821344 + 1.42261i) q^{9} +O(q^{10})\)	\(q+(-1.28768 - 0.584700i) q^{2} +(1.00895 - 0.582519i) q^{3} +(1.31625 + 1.50582i) q^{4} +1.00000 q^{5} +(-1.63981 + 0.160165i) q^{6} +(0.786953 + 0.454347i) q^{7} +(-0.814463 - 2.70863i) q^{8} +(-0.821344 + 1.42261i) q^{9} +(-1.28768 - 0.584700i) q^{10} +(2.01803 + 3.49532i) q^{11} +(2.20520 + 0.752555i) q^{12} +(1.21154 + 3.39590i) q^{13} +(-0.747688 - 1.04519i) q^{14} +(1.00895 - 0.582519i) q^{15} +(-0.534964 + 3.96407i) q^{16} +(1.41984 - 2.45923i) q^{17} +(1.88943 - 1.35163i) q^{18} +(0.810340 - 1.40355i) q^{19} +(1.31625 + 1.50582i) q^{20} +1.05866 q^{21} +(-0.554860 - 5.68081i) q^{22} +(-0.494250 - 0.856067i) q^{23} +(-2.39958 - 2.25843i) q^{24} +1.00000 q^{25} +(0.425507 - 5.08123i) q^{26} +5.40891i q^{27} +(0.351664 + 1.78304i) q^{28} +(-7.87290 + 4.54542i) q^{29} +(-1.63981 + 0.160165i) q^{30} +3.84896i q^{31} +(3.00665 - 4.79166i) q^{32} +(4.07218 + 2.35108i) q^{33} +(-3.26621 + 2.33653i) q^{34} +(0.786953 + 0.454347i) q^{35} +(-3.22328 + 0.635719i) q^{36} +(-0.538020 - 0.931878i) q^{37} +(-1.86412 + 1.33352i) q^{38} +(3.20056 + 2.72056i) q^{39} +(-0.814463 - 2.70863i) q^{40} +(7.68661 - 4.43786i) q^{41} +(-1.36322 - 0.619001i) q^{42} +(9.23470 + 5.33166i) q^{43} +(-2.60708 + 7.63950i) q^{44} +(-0.821344 + 1.42261i) q^{45} +(0.135895 + 1.39133i) q^{46} -11.5567i q^{47} +(1.76939 + 4.31118i) q^{48} +(-3.08714 - 5.34708i) q^{49} +(-1.28768 - 0.584700i) q^{50} -3.30832i q^{51} +(-3.51892 + 6.29422i) q^{52} -10.1285i q^{53} +(3.16259 - 6.96495i) q^{54} +(2.01803 + 3.49532i) q^{55} +(0.589713 - 2.50161i) q^{56} -1.88815i q^{57} +(12.7955 - 1.24977i) q^{58} +(4.67358 - 8.09488i) q^{59} +(2.20520 + 0.752555i) q^{60} +(0.159169 + 0.0918962i) q^{61} +(2.25049 - 4.95624i) q^{62} +(-1.29272 + 0.746351i) q^{63} +(-6.67330 + 4.41215i) q^{64} +(1.21154 + 3.39590i) q^{65} +(-3.86900 - 5.40844i) q^{66} +(5.74510 + 9.95080i) q^{67} +(5.57201 - 1.09895i) q^{68} +(-0.997350 - 0.575820i) q^{69} +(-0.747688 - 1.04519i) q^{70} +(4.27599 + 2.46874i) q^{71} +(4.52227 + 1.06605i) q^{72} -5.44599i q^{73} +(0.147930 + 1.51454i) q^{74} +(1.00895 - 0.582519i) q^{75} +(3.18010 - 0.627202i) q^{76} +3.66754i q^{77} +(-2.53060 - 5.37459i) q^{78} -14.8307 q^{79} +(-0.534964 + 3.96407i) q^{80} +(0.686757 + 1.18950i) q^{81} +(-12.4927 + 1.22020i) q^{82} +14.8263 q^{83} +(1.39347 + 1.59415i) q^{84} +(1.41984 - 2.45923i) q^{85} +(-8.77394 - 12.2650i) q^{86} +(-5.29559 + 9.17223i) q^{87} +(7.82391 - 8.31289i) q^{88} +(-2.39372 + 1.38202i) q^{89} +(1.88943 - 1.35163i) q^{90} +(-0.589495 + 3.22288i) q^{91} +(0.638521 - 1.87105i) q^{92} +(2.24209 + 3.88342i) q^{93} +(-6.75719 + 14.8813i) q^{94} +(0.810340 - 1.40355i) q^{95} +(0.242336 - 6.58599i) q^{96} +(-9.80772 - 5.66249i) q^{97} +(0.848814 + 8.69039i) q^{98} -6.62997 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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