LMFDB - Embedded newform 462.2.bf.a.5.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,2,Mod(5,462)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(462, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([15, 25, 12]))

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

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

chi := DirichletCharacter("462.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.bf (of order $30$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.68908857338$
Analytic rank:	$0$
Dimension:	$256$
Relative dimension:	$32$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			5.5
Character	$\chi$	$=$	462.5
Dual form			462.2.bf.a.185.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.207912 + 0.978148i) q^{2} +(-1.26644 - 1.18158i) q^{3} +(-0.913545 - 0.406737i) q^{4} +(2.46318 + 2.73564i) q^{5} +(1.41907 - 0.993102i) q^{6} +(2.33823 - 1.23802i) q^{7} +(0.587785 - 0.809017i) q^{8} +(0.207743 + 2.99280i) q^{9} +O(q^{10})$	\(q+(-0.207912 + 0.978148i) q^{2} +(-1.26644 - 1.18158i) q^{3} +(-0.913545 - 0.406737i) q^{4} +(2.46318 + 2.73564i) q^{5} +(1.41907 - 0.993102i) q^{6} +(2.33823 - 1.23802i) q^{7} +(0.587785 - 0.809017i) q^{8} +(0.207743 + 2.99280i) q^{9} +(-3.18798 + 1.84058i) q^{10} +(-0.587723 - 3.26414i) q^{11} +(0.676360 + 1.59453i) q^{12} +(-4.24304 + 1.37865i) q^{13} +(0.724816 + 2.54453i) q^{14} +(0.112901 - 6.37496i) q^{15} +(0.669131 + 0.743145i) q^{16} +(5.49056 - 1.16705i) q^{17} +(-2.97059 - 0.419034i) q^{18} +(0.959028 + 2.15401i) q^{19} +(-1.13754 - 3.50099i) q^{20} +(-4.42404 - 1.19493i) q^{21} +(3.31500 + 0.103772i) q^{22} +(7.07989 + 4.08758i) q^{23} +(-1.70031 + 0.330057i) q^{24} +(-0.893819 + 8.50412i) q^{25} +(-0.466343 - 4.43696i) q^{26} +(3.27313 - 4.03567i) q^{27} +(-2.63963 + 0.179939i) q^{28} +(-1.15621 - 1.59138i) q^{29} +(6.21218 + 1.43586i) q^{30} +(1.73371 + 1.56104i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(-3.11252 + 4.82827i) q^{33} +5.61322i q^{34} +(9.14624 + 3.34710i) q^{35} +(1.02750 - 2.81855i) q^{36} +(0.725533 + 6.90299i) q^{37} +(-2.30633 + 0.490227i) q^{38} +(7.00254 + 3.26751i) q^{39} +(3.66100 - 0.384786i) q^{40} +(6.25012 + 4.54098i) q^{41} +(2.08863 - 4.07893i) q^{42} -4.72775 q^{43} +(-0.790732 + 3.22098i) q^{44} +(-7.67550 + 7.94011i) q^{45} +(-5.47024 + 6.07532i) q^{46} +(0.294049 - 0.130919i) q^{47} +(0.0306700 - 1.73178i) q^{48} +(3.93464 - 5.78953i) q^{49} +(-8.13245 - 2.64239i) q^{50} +(-8.33243 - 5.00952i) q^{51} +(4.43696 + 0.466343i) q^{52} +(-4.38235 - 3.94588i) q^{53} +(3.26695 + 4.04067i) q^{54} +(7.48183 - 9.64795i) q^{55} +(0.372802 - 2.61935i) q^{56} +(1.33058 - 3.86110i) q^{57} +(1.79699 - 0.800073i) q^{58} +(5.40495 + 2.40644i) q^{59} +(-2.69607 + 5.77790i) q^{60} +(2.22618 - 2.00446i) q^{61} +(-1.88739 + 1.37127i) q^{62} +(4.19088 + 6.74066i) q^{63} +(-0.309017 - 0.951057i) q^{64} +(-14.2229 - 8.21157i) q^{65} +(-4.07564 - 4.04836i) q^{66} +(-5.92281 - 10.2586i) q^{67} +(-5.49056 - 1.16705i) q^{68} +(-4.13647 - 13.5421i) q^{69} +(-5.17556 + 8.25047i) q^{70} +(-5.81664 - 1.88994i) q^{71} +(2.54333 + 1.59105i) q^{72} +(2.42435 - 5.44517i) q^{73} +(-6.90299 - 0.725533i) q^{74} +(11.1803 - 9.71385i) q^{75} -2.35786i q^{76} +(-5.41528 - 6.90469i) q^{77} +(-4.65202 + 6.17017i) q^{78} +(-4.63124 - 0.984401i) q^{79} +(-0.384786 + 3.66100i) q^{80} +(-8.91369 + 1.24347i) q^{81} +(-5.74122 + 5.16942i) q^{82} +(-1.88570 + 5.80360i) q^{83} +(3.55554 + 2.89104i) q^{84} +(16.7169 + 12.1455i) q^{85} +(0.982954 - 4.62443i) q^{86} +(-0.416076 + 3.38154i) q^{87} +(-2.98620 - 1.44313i) q^{88} +(0.217259 - 0.376303i) q^{89} +(-6.17077 - 9.15862i) q^{90} +(-8.21442 + 8.47655i) q^{91} +(-4.80523 - 6.61384i) q^{92} +(-0.351150 - 4.02548i) q^{93} +(0.0669219 + 0.314843i) q^{94} +(-3.53034 + 7.92927i) q^{95} +(1.68756 + 0.390057i) q^{96} +(-12.1030 + 3.93249i) q^{97} +(4.84496 + 5.05237i) q^{98} +(9.64680 - 2.43704i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 256 q - 32 q^{4} + 4 q^{7} - 12 q^{9}+O(q^{10}) $ 256 * q - 32 * q^4 + 4 * q^7 - 12 * q^9	$ 256 q - 32 q^{4} + 4 q^{7} - 12 q^{9} + 12 q^{10} + 24 q^{15} + 32 q^{16} - 8 q^{18} - 16 q^{21} - 12 q^{22} + 48 q^{25} + 6 q^{28} + 18 q^{31} - 132 q^{33} + 16 q^{36} + 4 q^{37} - 18 q^{40} - 4 q^{42} + 64 q^{43} - 48 q^{45} + 8 q^{46} + 76 q^{49} - 8 q^{51} - 88 q^{57} + 46 q^{58} - 8 q^{60} - 12 q^{63} + 64 q^{64} - 120 q^{66} - 32 q^{67} - 58 q^{70} - 12 q^{72} - 96 q^{73} - 204 q^{75} - 32 q^{78} - 4 q^{79} - 64 q^{81} + 24 q^{82} - 36 q^{84} + 232 q^{85} - 228 q^{87} - 6 q^{88} + 40 q^{91} - 2 q^{93} - 144 q^{94} + 160 q^{99}+O(q^{100}) $ 256 * q - 32 * q^4 + 4 * q^7 - 12 * q^9 + 12 * q^10 + 24 * q^15 + 32 * q^16 - 8 * q^18 - 16 * q^21 - 12 * q^22 + 48 * q^25 + 6 * q^28 + 18 * q^31 - 132 * q^33 + 16 * q^36 + 4 * q^37 - 18 * q^40 - 4 * q^42 + 64 * q^43 - 48 * q^45 + 8 * q^46 + 76 * q^49 - 8 * q^51 - 88 * q^57 + 46 * q^58 - 8 * q^60 - 12 * q^63 + 64 * q^64 - 120 * q^66 - 32 * q^67 - 58 * q^70 - 12 * q^72 - 96 * q^73 - 204 * q^75 - 32 * q^78 - 4 * q^79 - 64 * q^81 + 24 * q^82 - 36 * q^84 + 232 * q^85 - 228 * q^87 - 6 * q^88 + 40 * q^91 - 2 * q^93 - 144 * q^94 + 160 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/462\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{5}\right)$

Coefficient data

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

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

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

$2$	−0.207912	+	0.978148i	−0.147016	+	0.691655i
$2$	−0.207912	+	0.978148i	−0.147016	+	0.691655i
$3$	−1.26644	−	1.18158i	−0.731180	−	0.682185i
$3$	−1.26644	−	1.18158i	−0.731180	−	0.682185i
$4$	−0.913545	−	0.406737i	−0.456773	−	0.203368i
$5$	2.46318	+	2.73564i	1.10157	+	1.22341i	0.972777	+	0.231743i	$0.0744427\pi$
$5$	2.46318	+	2.73564i	1.10157	+	1.22341i	0.128790	+	0.991672i	$0.458891\pi$
$6$	1.41907	−	0.993102i	0.579331	−	0.405432i
$7$	2.33823	−	1.23802i	0.883768	−	0.467926i
$7$	2.33823	−	1.23802i	0.883768	−	0.467926i
$8$	0.587785	−	0.809017i	0.207813	−	0.286031i
$9$	0.207743	+	2.99280i	0.0692478	+	0.997599i
$10$	−3.18798	+	1.84058i	−1.00813	+	0.582043i
$11$	−0.587723	−	3.26414i	−0.177205	−	0.984174i
$11$	−0.587723	−	3.26414i	−0.177205	−	0.984174i
$12$	0.676360	+	1.59453i	0.195248	+	0.460302i
$13$	−4.24304	+	1.37865i	−1.17681	+	0.382368i	−0.831180	−	0.556003i	$-0.812334\pi$
$13$	−4.24304	+	1.37865i	−1.17681	+	0.382368i	−0.345628	+	0.938371i	$0.612334\pi$
$14$	0.724816	+	2.54453i	0.193715	+	0.680055i
$15$	0.112901	−	6.37496i	0.0291510	−	1.64601i
$16$	0.669131	+	0.743145i	0.167283	+	0.185786i
$17$	5.49056	−	1.16705i	1.33166	−	0.283052i	0.513520	−	0.858078i	$-0.328341\pi$
$17$	5.49056	−	1.16705i	1.33166	−	0.283052i	0.818135	+	0.575026i	$0.195008\pi$
$18$	−2.97059	−	0.419034i	−0.700175	−	0.0987673i
$19$	0.959028	+	2.15401i	0.220016	+	0.494164i	0.989505	−	0.144495i	$-0.0461559\pi$
$19$	0.959028	+	2.15401i	0.220016	+	0.494164i	−0.769489	+	0.638660i	$0.779489\pi$
$20$	−1.13754	−	3.50099i	−0.254362	−	0.782846i
$21$	−4.42404	−	1.19493i	−0.965405	−	0.260755i
$22$	3.31500	+	0.103772i	0.706761	+	0.0221243i
$23$	7.07989	+	4.08758i	1.47626	+	0.852318i	0.999641	−	0.0267921i	$-0.00852920\pi$
$23$	7.07989	+	4.08758i	1.47626	+	0.852318i	0.476618	+	0.879111i	$0.341863\pi$
$24$	−1.70031	+	0.330057i	−0.347075	+	0.0673727i
$25$	−0.893819	+	8.50412i	−0.178764	+	1.70082i
$26$	−0.466343	−	4.43696i	−0.0914574	−	0.870159i
$27$	3.27313	−	4.03567i	0.629915	−	0.776664i
$28$	−2.63963	+	0.179939i	−0.498842	+	0.0340053i
$29$	−1.15621	−	1.59138i	−0.214702	−	0.295512i	0.688059	−	0.725655i	$-0.258463\pi$
$29$	−1.15621	−	1.59138i	−0.214702	−	0.295512i	−0.902761	+	0.430143i	$0.858463\pi$
$30$	6.21218	+	1.43586i	1.13418	+	0.262152i
$31$	1.73371	+	1.56104i	0.311384	+	0.280371i	0.809973	−	0.586467i	$-0.199482\pi$
$31$	1.73371	+	1.56104i	0.311384	+	0.280371i	−0.498589	+	0.866838i	$0.666148\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$	−3.11252	+	4.82827i	−0.541820	+	0.840495i
$34$			5.61322i			0.962659i
$35$	9.14624	+	3.34710i	1.54600	+	0.565763i
$36$	1.02750	−	2.81855i	0.171250	−	0.469759i
$37$	0.725533	+	6.90299i	0.119277	+	1.13484i	0.876404	+	0.481576i	$0.159936\pi$
$37$	0.725533	+	6.90299i	0.119277	+	1.13484i	−0.757127	+	0.653267i	$0.773398\pi$
$38$	−2.30633	+	0.490227i	−0.374137	+	0.0795253i
$39$	7.00254	+	3.26751i	1.12130	+	0.523221i
$40$	3.66100	−	0.384786i	0.578855	−	0.0608401i
$41$	6.25012	+	4.54098i	0.976105	+	0.709182i	0.956835	−	0.290632i	$-0.0938657\pi$
$41$	6.25012	+	4.54098i	0.976105	+	0.709182i	0.0192704	+	0.999814i	$0.493866\pi$
$42$	2.08863	−	4.07893i	0.322282	−	0.629392i
$43$	−4.72775			−0.720974			−0.360487	−	0.932764i	$-0.617390\pi$
$43$	−4.72775			−0.720974			−0.360487	+	0.932764i	$0.617390\pi$
$44$	−0.790732	+	3.22098i	−0.119207	+	0.485582i
$45$	−7.67550	+	7.94011i	−1.14420	+	1.18364i
$46$	−5.47024	+	6.07532i	−0.806544	+	0.895757i
$47$	0.294049	−	0.130919i	0.0428914	−	0.0190965i	−0.385179	−	0.922842i	$-0.625860\pi$
$47$	0.294049	−	0.130919i	0.0428914	−	0.0190965i	0.428070	+	0.903745i	$0.359194\pi$
$48$	0.0306700	−	1.73178i	0.00442683	−	0.249961i
$49$	3.93464	−	5.78953i	0.562091	−	0.827075i
$50$	−8.13245	−	2.64239i	−1.15010	−	0.373691i
$51$	−8.33243	−	5.00952i	−1.16677	−	0.701473i
$52$	4.43696	+	0.466343i	0.615296	+	0.0646702i
$53$	−4.38235	−	3.94588i	−0.601962	−	0.542009i	0.310814	−	0.950471i	$-0.399398\pi$
$53$	−4.38235	−	3.94588i	−0.601962	−	0.542009i	−0.912775	+	0.408462i	$0.866065\pi$
$54$	3.26695	+	4.04067i	0.444576	+	0.549865i
$55$	7.48183	−	9.64795i	1.00885	−	1.30093i
$56$	0.372802	−	2.61935i	0.0498177	−	0.350026i
$57$	1.33058	−	3.86110i	0.176240	−	0.511415i
$58$	1.79699	−	0.800073i	0.235957	−	0.105055i
$59$	5.40495	+	2.40644i	0.703665	+	0.313292i	0.727195	−	0.686431i	$-0.240824\pi$
$59$	5.40495	+	2.40644i	0.703665	+	0.313292i	−0.0235299	+	0.999723i	$0.507490\pi$
$60$	−2.69607	+	5.77790i	−0.348061	+	0.745923i
$61$	2.22618	−	2.00446i	0.285034	−	0.256645i	−0.514194	−	0.857674i	$-0.671909\pi$
$61$	2.22618	−	2.00446i	0.285034	−	0.256645i	0.799228	+	0.601029i	$0.205242\pi$
$62$	−1.88739	+	1.37127i	−0.239698	+	0.174151i
$63$	4.19088	+	6.74066i	0.528001	+	0.849243i
$64$	−0.309017	−	0.951057i	−0.0386271	−	0.118882i
$65$	−14.2229	−	8.21157i	−1.76413	−	1.01852i
$66$	−4.07564	−	4.04836i	−0.501676	−	0.498318i
$67$	−5.92281	−	10.2586i	−0.723587	−	1.25329i	−0.959553	−	0.281528i	$-0.909159\pi$
$67$	−5.92281	−	10.2586i	−0.723587	−	1.25329i	0.235966	−	0.971761i	$-0.424175\pi$
$68$	−5.49056	−	1.16705i	−0.665828	−	0.141526i
$69$	−4.13647	−	13.5421i	−0.497972	−	1.63028i
$70$	−5.17556	+	8.25047i	−0.618598	+	0.986120i
$71$	−5.81664	−	1.88994i	−0.690308	−	0.224295i	−0.0572055	−	0.998362i	$-0.518219\pi$
$71$	−5.81664	−	1.88994i	−0.690308	−	0.224295i	−0.633103	+	0.774068i	$0.718219\pi$
$72$	2.54333	+	1.59105i	0.299735	+	0.187508i
$73$	2.42435	−	5.44517i	0.283748	−	0.637309i	−0.714294	−	0.699845i	$-0.753252\pi$
$73$	2.42435	−	5.44517i	0.283748	−	0.637309i	0.998043	+	0.0625361i	$0.0199188\pi$
$74$	−6.90299	−	0.725533i	−0.802456	−	0.0843415i
$75$	11.1803	−	9.71385i	1.29099	−	1.12166i
$76$		−	2.35786i		−	0.270465i
$77$	−5.41528	−	6.90469i	−0.617129	−	0.786862i
$78$	−4.65202	+	6.17017i	−0.526738	+	0.698634i
$79$	−4.63124	−	0.984401i	−0.521056	−	0.110754i	−0.0601266	−	0.998191i	$-0.519150\pi$
$79$	−4.63124	−	0.984401i	−0.521056	−	0.110754i	−0.460929	+	0.887437i	$0.652484\pi$
$80$	−0.384786	+	3.66100i	−0.0430204	+	0.409312i
$81$	−8.91369	+	1.24347i	−0.990409	+	0.138163i
$82$	−5.74122	+	5.16942i	−0.634012	+	0.570867i
$83$	−1.88570	+	5.80360i	−0.206983	+	0.637028i	0.792643	+	0.609686i	$0.208704\pi$
$83$	−1.88570	+	5.80360i	−0.206983	+	0.637028i	−0.999626	+	0.0273421i	$0.991296\pi$
$84$	3.55554	+	2.89104i	0.387941	+	0.315439i
$85$	16.7169	+	12.1455i	1.81320	+	1.31737i
$86$	0.982954	−	4.62443i	0.105995	−	0.498665i
$87$	−0.416076	+	3.38154i	−0.0446080	+	0.362539i
$88$	−2.98620	−	1.44313i	−0.318330	−	0.153838i
$89$	0.217259	−	0.376303i	0.0230294	−	0.0398880i	−0.854281	−	0.519811i	$-0.826002\pi$
$89$	0.217259	−	0.376303i	0.0230294	−	0.0398880i	0.877310	+	0.479923i	$0.159336\pi$
$90$	−6.17077	−	9.15862i	−0.650457	−	0.965403i
$91$	−8.21442	+	8.47655i	−0.861106	+	0.888584i
$92$	−4.80523	−	6.61384i	−0.500980	−	0.689540i
$93$	−0.351150	−	4.02548i	−0.0364125	−	0.417423i
$94$	0.0669219	+	0.314843i	0.00690246	+	0.0324735i
$95$	−3.53034	+	7.92927i	−0.362205	+	0.813526i
$96$	1.68756	+	0.390057i	0.172236	+	0.0398100i
$97$	−12.1030	+	3.93249i	−1.22887	+	0.399284i	−0.850305	−	0.526290i	$-0.823583\pi$
$97$	−12.1030	+	3.93249i	−1.22887	+	0.399284i	−0.378566	+	0.925574i	$0.623583\pi$
$98$	4.84496	+	5.05237i	0.489414	+	0.510366i
$99$	9.64680	−	2.43704i	0.969540	−	0.244932i
$100$	4.27548	−	7.40535i	0.427548	−	0.740535i
$101$	6.79431	−	7.54584i	0.676059	−	0.750839i	−0.303316	−	0.952890i	$-0.598094\pi$
$101$	6.79431	−	7.54584i	0.676059	−	0.750839i	0.979375	+	0.202051i	$0.0647606\pi$
$102$	6.63246	−	7.10881i	0.656711	−	0.703877i
$103$	−0.403522	+	0.0424119i	−0.0397602	+	0.00417896i	−0.124388	−	0.992234i	$-0.539697\pi$
$103$	−0.403522	+	0.0424119i	−0.0397602	+	0.00417896i	0.0846275	+	0.996413i	$0.473030\pi$
$104$	−1.37865	+	4.24304i	−0.135188	+	0.416065i
$105$	−7.62831	−	15.0459i	−0.744447	−	1.46833i
$106$	4.77080	−	3.46619i	0.463381	−	0.336666i
$107$	−2.00829	−	4.51070i	−0.194149	−	0.436066i	0.790071	−	0.613015i	$-0.210044\pi$
$107$	−2.00829	−	4.51070i	−0.194149	−	0.436066i	−0.984220	+	0.176950i	$0.943377\pi$
$108$	−4.63161	+	2.35546i	−0.445677	+	0.226654i
$109$	−6.22931	−	10.7895i	−0.596660	−	1.03344i	−0.993310	−	0.115475i	$-0.963161\pi$
$109$	−6.22931	−	10.7895i	−0.596660	−	1.03344i	0.396651	−	0.917970i	$-0.370172\pi$
$110$	7.88156	+	9.32425i	0.751477	+	0.889032i
$111$	7.23758	−	9.59950i	0.686960	−	0.911144i
$112$	2.48461	+	0.909250i	0.234773	+	0.0859160i
$113$	−8.73868	+	12.0278i	−0.822066	+	1.13148i	0.167282	+	0.985909i	$0.446501\pi$
$113$	−8.73868	+	12.0278i	−0.822066	+	1.13148i	−0.989348	+	0.145568i	$0.953499\pi$
$114$	3.50008	+	2.10427i	0.327812	+	0.197083i
$115$	6.25691	+	29.4364i	0.583460	+	2.74496i
$116$	0.408974	+	1.92407i	0.0379723	+	0.178645i
$117$	−5.00748	−	12.4122i	−0.462942	−	1.14751i
$118$	−3.47761	+	4.78651i	−0.320140	+	0.440634i
$119$	11.3934	−	9.52623i	1.04443	−	0.873268i
$120$	−5.09109	−	3.83845i	−0.464751	−	0.350401i
$121$	−10.3092	+	3.83682i	−0.937197	+	0.348801i
$122$	1.49781	+	2.59429i	0.135606	+	0.234876i
$123$	−2.54988	−	13.1359i	−0.229915	−	1.18442i
$124$	−0.948891	−	2.13124i	−0.0852129	−	0.191391i
$125$	−10.5752	+	7.68334i	−0.945876	+	0.687219i
$126$	−7.46469	+	2.69784i	−0.665008	+	0.240343i
$127$	1.54603	−	4.75820i	0.137188	−	0.422222i	−0.858736	−	0.512419i	$-0.828750\pi$
$127$	1.54603	−	4.75820i	0.137188	−	0.422222i	0.995924	+	0.0901968i	$0.0287496\pi$
$128$	0.994522	−	0.104528i	0.0879041	−	0.00923910i
$129$	5.98741	+	5.58620i	0.527162	+	0.491838i
$130$	10.9892	−	12.2048i	0.963819	−	1.07043i
$131$	2.33974	−	4.05255i	0.204424	−	0.354073i	−0.745525	−	0.666478i	$-0.767801\pi$
$131$	2.33974	−	4.05255i	0.204424	−	0.354073i	0.949949	+	0.312405i	$0.101135\pi$
$132$	4.80726	−	3.14487i	0.418418	−	0.273726i
$133$	4.90913	+	3.84928i	0.425675	+	0.333775i
$134$	11.2659	−	3.66050i	0.973222	−	0.316219i
$135$	19.1024	−	0.986465i	1.64408	−	0.0849014i
$136$	2.28310	−	5.12793i	0.195774	−	0.439716i
$137$	1.38102	+	6.49721i	0.117989	+	0.555094i	0.996939	+	0.0781807i	$0.0249111\pi$
$137$	1.38102	+	6.49721i	0.117989	+	0.555094i	−0.878950	+	0.476913i	$0.841756\pi$
$138$	14.1062	−	1.23051i	1.20080	−	0.104748i
$139$	−7.76895	−	10.6930i	−0.658954	−	0.906972i	0.340492	−	0.940247i	$-0.389406\pi$
$139$	−7.76895	−	10.6930i	−0.658954	−	0.906972i	−0.999446	+	0.0332751i	$0.989406\pi$
$140$	−6.99412	−	6.77784i	−0.591111	−	0.572832i
$141$	−0.527086	−	0.181641i	−0.0443887	−	0.0152969i
$142$	3.05799	−	5.29659i	0.256621	−	0.444480i
$143$	6.99383	+	13.0396i	0.584853	+	1.09043i
$144$	−2.08508	+	2.15696i	−0.173756	+	0.179746i
$145$	1.50550	−	7.08282i	0.125025	−	0.588196i
$146$	4.82213	+	3.50349i	0.399083	+	0.289951i
$147$	−11.8238	+	2.68301i	−0.975208	+	0.221291i
$148$	2.14489	−	6.60129i	0.176309	−	0.542623i
$149$	13.9415	−	12.5529i	1.14213	−	1.02838i	0.142875	−	0.989741i	$-0.454365\pi$
$149$	13.9415	−	12.5529i	1.14213	−	1.02838i	0.999253	−	0.0386365i	$-0.0123014\pi$
$150$	7.17707	+	12.9556i	0.586005	+	1.05782i
$151$	1.35271	−	12.8701i	0.110082	−	1.04736i	−0.790438	−	0.612542i	$-0.790147\pi$
$151$	1.35271	−	12.8701i	0.110082	−	1.04736i	0.900520	−	0.434815i	$-0.143186\pi$
$152$	2.30633	+	0.490227i	0.187068	+	0.0397626i
$153$	4.63338	+	16.1897i	0.374587	+	1.30886i
$154$	7.87971	−	3.86138i	0.634965	−	0.311159i
$155$			8.58792i			0.689799i
$156$	−5.06812	−	5.83321i	−0.405775	−	0.467031i
$157$	−5.53722	−	0.581985i	−0.441918	−	0.0464474i	−0.119043	−	0.992889i	$-0.537983\pi$
$157$	−5.53722	−	0.581985i	−0.441918	−	0.0464474i	−0.322875	+	0.946442i	$0.604649\pi$
$158$	1.92578	−	4.32537i	0.153207	−	0.344108i
$159$	0.887610	+	10.1753i	0.0703921	+	0.806955i
$160$	−3.50099	−	1.13754i	−0.276778	−	0.0899306i
$161$	21.6149	+	0.792683i	1.70349	+	0.0624721i
$162$	0.636964	−	8.97743i	0.0500446	−	0.705334i
$163$	−18.8959	−	4.01645i	−1.48004	−	0.314593i	−0.604062	−	0.796937i	$-0.706452\pi$
$163$	−18.8959	−	4.01645i	−1.48004	−	0.314593i	−0.875982	+	0.482345i	$0.839785\pi$
$164$	−3.86279	−	6.69055i	−0.301633	−	0.522444i
$165$	−20.8751	+	3.37819i	−1.62512	+	0.262992i
$166$	−5.28472	−	3.05113i	−0.410174	−	0.236814i
$167$	0.296343	+	0.912051i	0.0229317	+	0.0705767i	0.961867	−	0.273516i	$-0.0881866\pi$
$167$	0.296343	+	0.912051i	0.0229317	+	0.0705767i	−0.938936	+	0.344093i	$0.888187\pi$
$168$	−3.56711	+	2.87676i	−0.275208	+	0.221947i
$169$	5.58553	−	4.05812i	0.429656	−	0.312163i
$170$	−15.3557	+	13.8264i	−1.17773	+	1.06043i
$171$	−6.24729	+	3.31766i	−0.477742	+	0.253708i
$172$	4.31901	+	1.92295i	0.329321	+	0.146623i
$173$	3.62337	−	1.61323i	0.275479	−	0.122651i	−0.264347	−	0.964428i	$-0.585156\pi$
$173$	3.62337	−	1.61323i	0.275479	−	0.122651i	0.539827	+	0.841776i	$0.318490\pi$
$174$	−3.22114	−	1.11004i	−0.244194	−	0.0841523i
$175$	8.43828	+	20.9912i	0.637874	+	1.58678i
$176$	2.03246	−	2.62090i	0.153203	−	0.197558i
$177$	−4.00165	−	9.43399i	−0.300783	−	0.709102i
$178$	0.322909	+	0.290749i	0.0242031	+	0.0217925i
$179$	3.78162	+	0.397464i	0.282651	+	0.0297079i	0.244793	−	0.969575i	$-0.421280\pi$
$179$	3.78162	+	0.397464i	0.282651	+	0.0297079i	0.0378580	+	0.999283i	$0.487947\pi$
$180$	10.2415	−	4.13174i	0.763353	−	0.307962i
$181$	20.5877	+	6.68935i	1.53027	+	0.497216i	0.948673	−	0.316259i	$-0.102427\pi$
$181$	20.5877	+	6.68935i	1.53027	+	0.497216i	0.581600	+	0.813475i	$0.302427\pi$
$182$	−6.58344	−	9.79729i	−0.487997	−	0.726224i
$183$	−5.18776	−	0.0918758i	−0.383490	−	0.00679165i
$184$	7.46837	−	3.32513i	0.550576	−	0.245132i
$185$	−17.0970	+	18.9881i	−1.25699	+	1.39603i
$186$	4.01052	+	0.493468i	0.294066	+	0.0361828i
$187$	−7.03635	−	17.2360i	−0.514549	−	1.26042i
$188$	−0.321876			−0.0234752
$189$	2.65712	−	13.4885i	0.193277	−	0.981144i
$190$	−7.02200	−	5.10178i	−0.509429	−	0.370122i
$191$	−25.2003	+	2.64866i	−1.82343	+	0.191650i	−0.953472	−	0.301481i	$-0.902519\pi$
$191$	−25.2003	+	2.64866i	−1.82343	+	0.191650i	−0.869955	+	0.493130i	$0.835853\pi$
$192$	−0.732397	+	1.56958i	−0.0528562	+	0.113275i
$193$	−24.5058	+	5.20887i	−1.76397	+	0.374943i	−0.971882	−	0.235468i	$-0.924338\pi$
$193$	−24.5058	+	5.20887i	−1.76397	+	0.374943i	−0.792085	+	0.610411i	$0.791004\pi$
$194$	−1.33021	−	12.6561i	−0.0955035	−	0.908655i
$195$	8.30979	+	27.2049i	0.595076	+	1.94818i
$196$	−5.94928	+	3.68864i	−0.424949	+	0.263474i
$197$		−	8.20277i		−	0.584423i	−0.956354	−	0.292212i	$-0.905609\pi$
$197$		−	8.20277i		−	0.584423i	0.956354	−	0.292212i	$-0.0943911\pi$
$198$	0.378101	+	9.94269i	0.0268704	+	0.706596i
$199$	9.54974	−	5.51355i	0.676963	−	0.390845i	−0.121747	−	0.992561i	$-0.538850\pi$
$199$	9.54974	−	5.51355i	0.676963	−	0.390845i	0.798710	+	0.601716i	$0.205516\pi$
$200$	6.35461	+	5.72171i	0.449339	+	0.404586i
$201$	−4.62047	+	19.9902i	−0.325903	+	1.41000i
$202$	5.96833	+	8.21470i	0.419930	+	0.577984i
$203$	−4.67363	−	2.28961i	−0.328024	−	0.160699i
$204$	5.57450	+	7.96553i	0.390293	+	0.557698i
$205$	2.97270	+	28.2833i	0.207622	+	1.97539i
$206$	0.0424119	−	0.403522i	0.00295497	−	0.0281147i
$207$	−10.7625	+	22.0378i	−0.748045	+	1.53174i
$208$	−3.86369	−	2.23070i	−0.267898	−	0.154671i
$209$	6.46734	−	4.39636i	0.447356	−	0.304103i
$210$	16.3031	−	4.33340i	1.12502	−	0.299033i
$211$	4.91558	+	15.1286i	0.338403	+	1.04150i	0.965022	+	0.262171i	$0.0844383\pi$
$211$	4.91558	+	15.1286i	0.338403	+	1.04150i	−0.626619	+	0.779326i	$0.715562\pi$
$212$	2.39854	+	5.38720i	0.164732	+	0.369995i
$213$	5.13332	+	9.26632i	0.351729	+	0.634918i
$214$	4.82968	−	1.02658i	0.330150	−	0.0701755i
$215$	−11.6453	−	12.9334i	−0.794202	−	0.882050i
$216$	−1.34102	−	5.02013i	−0.0912451	−	0.341576i
$217$	5.98640	+	1.50371i	0.406384	+	0.102079i
$218$	11.8489	−	3.84993i	0.802506	−	0.260750i
$219$	−9.50419	+	4.03143i	−0.642234	+	0.272419i
$220$	−10.7592	+	5.77071i	−0.725383	+	0.389061i
$221$	−21.6877	+	12.5214i	−1.45887	+	0.842281i
$222$	7.88495	+	9.07527i	0.529203	+	0.609092i
$223$	8.57934	−	11.8084i	0.574515	−	0.790752i	−0.418566	−	0.908187i	$-0.637467\pi$
$223$	8.57934	−	11.8084i	0.574515	−	0.790752i	0.993081	+	0.117435i	$0.0374670\pi$
$224$	−1.40596	+	2.24127i	−0.0939396	+	0.149751i
$225$	−25.6368	−	0.908346i	−1.70912	−	0.0605564i
$226$	−9.94806	−	11.0484i	−0.661735	−	0.734931i
$227$	−14.1449	−	6.29773i	−0.938832	−	0.417995i	−0.120482	−	0.992716i	$-0.538444\pi$
$227$	−14.1449	−	6.29773i	−0.938832	−	0.417995i	−0.818350	+	0.574721i	$0.805111\pi$
$228$	−2.78600	+	2.98609i	−0.184507	+	0.197759i
$229$	−2.40571	+	11.3180i	−0.158974	+	0.747914i	0.824354	+	0.566074i	$0.191538\pi$
$229$	−2.40571	+	11.3180i	−0.158974	+	0.747914i	−0.983328	+	0.181840i	$0.941795\pi$
$230$	−30.0941			−1.98434
$231$	−1.30030	+	15.1430i	−0.0855536	+	0.996334i
$232$	−1.96706			−0.129143
$233$	3.20924	−	15.0983i	0.210244	−	0.989120i	−0.738787	−	0.673939i	$-0.764601\pi$
$233$	3.20924	−	15.0983i	0.210244	−	0.989120i	0.949031	−	0.315182i	$-0.102065\pi$
$234$	13.1820	−	2.31742i	0.861737	−	0.151495i
$235$	1.08244	+	0.481934i	0.0706107	+	0.0314379i
$236$	−3.95888	−	4.39678i	−0.257701	−	0.286206i
$237$	4.70205	+	6.71887i	0.305431	+	0.436437i
$238$	6.94925	+	13.1250i	0.450453	+	0.850767i
$239$	−2.58665	+	3.56022i	−0.167316	+	0.230291i	−0.884439	−	0.466656i	$-0.845459\pi$
$239$	−2.58665	+	3.56022i	−0.167316	+	0.230291i	0.717123	+	0.696947i	$0.245459\pi$
$240$	4.81307	−	4.18178i	0.310682	−	0.269933i
$241$	−2.76116	+	1.59416i	−0.177862	+	0.102689i	−0.586288	−	0.810103i	$-0.699411\pi$
$241$	−2.76116	+	1.59416i	−0.177862	+	0.102689i	0.408426	+	0.912792i	$0.366078\pi$
$242$	−1.60958	−	10.8816i	−0.103468	−	0.699496i
$243$	12.7579	+	8.95744i	0.818420	+	0.574620i
$244$	−2.84901	+	0.925699i	−0.182389	+	0.0592618i
$245$	25.5298	−	3.49690i	1.63104	−	0.223409i
$246$	13.3790	+	0.236943i	0.853013	+	0.0151070i
$247$	−7.03882	−	7.81740i	−0.447870	−	0.497410i
$248$	2.28196	−	0.485045i	0.144904	−	0.0308004i
$249$	9.24554	−	5.12181i	0.585912	−	0.324581i
$250$	−5.31673	−	11.9416i	−0.336260	−	0.755252i
$251$	6.49259	+	19.9821i	0.409809	+	1.26126i	0.916813	+	0.399317i	$0.130753\pi$
$251$	6.49259	+	19.9821i	0.409809	+	1.26126i	−0.507004	+	0.861944i	$0.669247\pi$
$252$	−1.08689	−	7.86249i	−0.0684674	−	0.495290i
$253$	9.18139	−	25.5121i	0.577229	−	1.60393i
$254$	4.33278	+	2.50153i	0.271863	+	0.156960i
$255$	−6.82003	−	35.1338i	−0.427087	−	2.20017i
$256$	−0.104528	+	0.994522i	−0.00653303	+	0.0621576i
$257$	−1.14621	−	10.9055i	−0.0714986	−	0.680264i	−0.970299	−	0.241907i	$-0.922227\pi$
$257$	−1.14621	−	10.9055i	−0.0714986	−	0.680264i	0.898801	−	0.438357i	$-0.144440\pi$
$258$	−6.70898	+	4.69513i	−0.417683	+	0.292306i
$259$	10.2425	+	15.2425i	0.636436	+	0.947126i
$260$	9.65328	+	13.2866i	0.598671	+	0.824000i
$261$	4.52249	−	3.79089i	0.279935	−	0.234650i
$262$	3.47753	+	3.13118i	0.214843	+	0.193445i
$263$	9.99503	−	5.77064i	0.616320	−	0.355833i	−0.159115	−	0.987260i	$-0.550864\pi$
$263$	9.99503	−	5.77064i	0.616320	−	0.355833i	0.775435	+	0.631427i	$0.217531\pi$
$264$	2.07666	+	5.35607i	0.127810	+	0.329643i
$265$		−	21.7079i		−	1.33351i
$266$	−4.78583	+	4.00154i	−0.293438	+	0.245350i
$267$	−0.719777	+	0.219857i	−0.0440496	+	0.0134550i
$268$	1.23821	+	11.7807i	0.0756354	+	0.719623i
$269$	−12.3284	+	2.62048i	−0.751676	+	0.159774i	−0.567790	−	0.823174i	$-0.692201\pi$
$269$	−12.3284	+	2.62048i	−0.751676	+	0.159774i	−0.183887	+	0.982947i	$0.558868\pi$
$270$	−3.00671	+	18.8901i	−0.182983	+	1.14961i
$271$	28.5336	−	2.99900i	1.73329	−	0.182176i	0.815371	−	0.578939i	$-0.196533\pi$
$271$	28.5336	−	2.99900i	1.73329	−	0.182176i	0.917921	+	0.396763i	$0.129866\pi$
$272$	4.54119	+	3.29937i	0.275350	+	0.200053i
$273$	20.4188	−	1.02906i	1.23580	−	0.0622814i
$274$	−6.64236			−0.401280
$275$	28.2839	−	2.08052i	1.70559	−	0.125460i
$276$	−1.72923	+	14.0538i	−0.104087	+	0.845939i
$277$	9.05983	−	10.0620i	0.544353	−	0.604565i	−0.406712	−	0.913556i	$-0.633325\pi$
$277$	9.05983	−	10.0620i	0.544353	−	0.604565i	0.951065	+	0.308992i	$0.0999915\pi$
$278$	12.0746	−	5.37597i	0.724188	−	0.322429i
$279$	−4.31171	+	5.51294i	−0.258135	+	0.330051i
$280$	8.08388	−	5.43209i	0.483104	−	0.324629i
$281$	11.9316	+	3.87681i	0.711779	+	0.231271i	0.642455	−	0.766323i	$-0.277916\pi$
$281$	11.9316	+	3.87681i	0.711779	+	0.231271i	0.0693237	+	0.997594i	$0.477916\pi$
$282$	0.287259	−	0.477803i	0.0171060	−	0.0284527i
$283$	−23.0936	−	2.42724i	−1.37277	−	0.144284i	−0.610744	−	0.791828i	$-0.709130\pi$
$283$	−23.0936	−	2.42724i	−1.37277	−	0.144284i	−0.762028	+	0.647544i	$0.775796\pi$
$284$	4.54506	+	4.09239i	0.269700	+	0.242839i
$285$	13.8400	−	5.87058i	0.819812	−	0.347743i
$286$	−14.2088	+	4.12991i	−0.840182	+	0.244207i
$287$	20.2360	+	2.88011i	1.19449	+	0.170007i
$288$	−1.67631	−	2.48797i	−0.0987775	−	0.146605i
$289$	13.2539	−	5.90102i	0.779642	−	0.347119i
$290$	6.61503	+	2.94520i	0.388448	+	0.172948i
$291$	19.9742	+	9.32034i	1.17091	+	0.546368i
$292$	−4.42950	+	3.98834i	−0.259217	+	0.233400i
$293$	−16.8427	+	12.2369i	−0.983961	+	0.714890i	−0.958590	−	0.284788i	$-0.908077\pi$
$293$	−16.8427	+	12.2369i	−0.983961	+	0.714890i	−0.0253709	+	0.999678i	$0.508077\pi$
$294$	−0.166079	−	12.1232i	−0.00968592	−	0.707040i
$295$	6.73022	+	20.7135i	0.391848	+	1.20599i
$296$	6.01109	+	3.47050i	0.349388	+	0.201719i
$297$	−15.0967	−	8.31209i	−0.875997	−	0.482317i
$298$	9.38004	+	16.2467i	0.543371	+	0.941146i
$299$	−35.6756	−	7.58308i	−2.06317	−	0.438541i
$300$	−14.1647	+	4.32662i	−0.817797	+	0.249798i
$301$	−11.0546	+	5.85302i	−0.637174	+	0.337362i
$302$	12.3076	+	3.99900i	0.708226	+	0.230116i
$303$	−17.5206	+	1.52835i	−1.00653	+	0.0878015i
$304$	−0.959028	+	2.15401i	−0.0550040	+	0.123541i
$305$	10.9670	+	1.15268i	0.627967	+	0.0660020i
$306$	−16.7992	+	1.16611i	−0.960348	+	0.0666620i
$307$		−	9.75485i		−	0.556739i	−0.960474	−	0.278369i	$-0.910206\pi$
$307$		−	9.75485i		−	0.556739i	0.960474	−	0.278369i	$-0.0897939\pi$
$308$	2.13872	+	8.51034i	0.121865	+	0.484922i
$309$	0.561149	+	0.423081i	0.0319227	+	0.0240682i
$310$	−8.40026	−	1.78553i	−0.477103	−	0.101411i
$311$	2.75222	−	26.1856i	0.156064	−	1.48485i	−0.583692	−	0.811975i	$-0.698392\pi$
$311$	2.75222	−	26.1856i	0.156064	−	1.48485i	0.739756	−	0.672876i	$-0.234941\pi$
$312$	6.75947	−	3.74458i	0.382679	−	0.211995i
$313$	−18.3052	+	16.4820i	−1.03467	+	0.931621i	−0.997706	−	0.0676961i	$-0.978435\pi$
$313$	−18.3052	+	16.4820i	−1.03467	+	0.931621i	−0.0369634	+	0.999317i	$0.511769\pi$
$314$	1.72052	−	5.29521i	0.0970945	−	0.298826i
$315$	−8.11712	+	28.0682i	−0.457348	+	1.58146i
$316$	3.83046	+	2.78299i	0.215480	+	0.156556i
$317$	−2.47228	+	11.6312i	−0.138857	+	0.653272i	0.852570	+	0.522613i	$0.175043\pi$
$317$	−2.47228	+	11.6312i	−0.138857	+	0.653272i	−0.991427	+	0.130659i	$0.958291\pi$
$318$	−10.1375	−	1.24735i	−0.568483	−	0.0699481i
$319$	−4.51495	+	4.70930i	−0.252789	+	0.263670i
$320$	1.84058	−	3.18798i	0.102892	−	0.178214i
$321$	−2.78636	+	8.08549i	−0.155520	+	0.451288i
$322$	−5.26935	+	20.9777i	−0.293649	+	1.16904i
$323$	7.77944	+	10.7075i	0.432860	+	0.595780i
$324$	8.64882	+	2.48956i	0.480490	+	0.138309i
$325$	−7.93168	−	37.3156i	−0.439971	−	2.06990i
$326$	7.85737	−	17.6479i	0.435179	−	0.977429i
$327$	−4.85957	+	21.0247i	−0.268735	+	1.16267i
$328$	7.34746	−	2.38733i	0.405696	−	0.131818i
$329$	0.525474	−	0.670155i	0.0289703	−	0.0369469i
$330$	1.03581	−	21.1213i	0.0570195	−	1.16269i
$331$	5.34065	−	9.25027i	0.293548	−	0.508441i	−0.681098	−	0.732193i	$-0.738497\pi$
$331$	5.34065	−	9.25027i	0.293548	−	0.508441i	0.974646	+	0.223752i	$0.0718305\pi$
$332$	4.08321	−	4.53487i	0.224095	−	0.248883i
$333$	−20.5085	+	3.60542i	−1.12386	+	0.197576i
$334$	−0.953734	+	0.100242i	−0.0521860	+	0.00548497i
$335$	13.4749	−	41.4715i	0.736212	−	2.26583i
$336$	−2.07226	−	4.08727i	−0.113051	−	0.222979i
$337$	−7.98701	+	5.80290i	−0.435080	+	0.316104i	−0.783677	−	0.621169i	$-0.786658\pi$
$337$	−7.98701	+	5.80290i	−0.435080	+	0.316104i	0.348597	+	0.937273i	$0.386658\pi$
$338$	2.80815	+	6.30720i	0.152743	+	0.343066i
$339$	25.2788	−	4.90701i	1.37295	−	0.266512i
$340$	−10.3316	−	17.8948i	−0.560309	−	0.970484i
$341$	4.07650	−	6.57653i	0.220755	−	0.356139i
$342$	−1.94628	−	6.80055i	−0.105243	−	0.367732i
$343$	2.03256	−	18.4084i	0.109748	−	0.993959i
$344$	−2.77890	+	3.82483i	−0.149828	+	0.206221i
$345$	26.8575	−	44.6725i	1.44596	−	2.40509i
$346$	0.824633	+	3.87959i	0.0443326	+	0.208568i
$347$	−2.30339	−	10.8366i	−0.123652	−	0.581738i	−0.995725	−	0.0923627i	$-0.970558\pi$
$347$	−2.30339	−	10.8366i	−0.123652	−	0.581738i	0.872073	−	0.489376i	$-0.162775\pi$
$348$	1.75550	−	2.91996i	0.0941047	−	0.156526i
$349$	−4.94705	+	6.80903i	−0.264810	+	0.364479i	−0.920629	−	0.390439i	$-0.872323\pi$
$349$	−4.94705	+	6.80903i	−0.264810	+	0.364479i	0.655819	+	0.754918i	$0.272323\pi$
$350$	−22.2869	+	3.88957i	−1.19128	+	0.207906i
$351$	−8.32428	+	21.6360i	−0.444317	+	1.15484i
$352$	2.14105	+	2.53296i	0.114118	+	0.135007i
$353$	8.54150	+	14.7943i	0.454618	+	0.787422i	0.998666	−	0.0516323i	$-0.0164424\pi$
$353$	8.54150	+	14.7943i	0.454618	+	0.787422i	−0.544048	+	0.839054i	$0.683109\pi$
$354$	10.0598	−	1.95277i	0.534674	−	0.103789i
$355$	−9.15724	−	20.5675i	−0.486016	−	1.09161i
$356$	−0.351532	+	0.255403i	−0.0186311	+	0.0135363i
$357$	−25.6850	−	1.39774i	−1.35939	−	0.0739761i
$358$	−1.17502	+	3.61634i	−0.0621018	+	0.191130i
$359$	−8.36433	+	0.879127i	−0.441452	+	0.0463985i	−0.322648	−	0.946519i	$-0.604573\pi$
$359$	−8.36433	+	0.879127i	−0.441452	+	0.0463985i	−0.118805	+	0.992918i	$0.537906\pi$
$360$	1.91214	+	10.8767i	0.100778	+	0.573252i
$361$	8.99345	−	9.98824i	0.473339	−	0.525697i
$362$	−10.8236	+	18.7470i	−0.568876	+	0.985322i
$363$	17.5894	+	7.32199i	0.923206	+	0.384305i
$364$	10.9520	−	4.40261i	0.574039	−	0.230759i
$365$	20.8676	−	6.78030i	1.09226	−	0.354897i
$366$	1.16846	−	5.05529i	0.0610766	−	0.264244i
$367$	1.56971	−	3.52562i	0.0819381	−	0.184036i	−0.867930	−	0.496686i	$-0.834550\pi$
$367$	1.56971	−	3.52562i	0.0819381	−	0.184036i	0.949868	+	0.312650i	$0.101217\pi$
$368$	1.69971	+	7.99651i	0.0886035	+	0.416847i
$369$	−12.2918	+	19.6487i	−0.639886	+	1.02287i
$370$	−15.0185	−	20.6712i	−0.780774	−	1.07464i
$371$	−15.1320	−	3.80097i	−0.785614	−	0.197336i
$372$	−1.31652	+	3.82028i	−0.0682583	+	0.198073i
$373$	−11.1782	+	19.3611i	−0.578783	+	1.00248i	0.416837	+	0.908981i	$0.363139\pi$
$373$	−11.1782	+	19.3611i	−0.578783	+	1.00248i	−0.995619	+	0.0934996i	$0.970195\pi$
$374$	18.3223	−	3.29902i	0.947424	−	0.170588i
$375$	22.4714	+	2.76495i	1.16042	+	0.142782i
$376$	0.0669219	−	0.314843i	0.00345123	−	0.0162368i
$377$	7.09979	+	5.15830i	0.365658	+	0.265666i
$378$	12.6413	+	5.40347i	0.650198	+	0.277925i
$379$	3.54075	−	10.8973i	0.181876	−	0.559757i	−0.818005	−	0.575212i	$-0.804920\pi$
$379$	3.54075	−	10.8973i	0.181876	−	0.559757i	0.999881	+	0.0154551i	$0.00491970\pi$
$380$	6.45025	−	5.80783i	0.330891	−	0.297935i
$381$	−7.58014	+	4.19922i	−0.388343	+	0.215132i
$382$	2.64866	−	25.2003i	0.135517	−	1.28936i
$383$	−29.1357	−	6.19298i	−1.48876	−	0.316447i	−0.609502	−	0.792785i	$-0.708630\pi$
$383$	−29.1357	−	6.19298i	−1.48876	−	0.316447i	−0.879262	+	0.476338i	$0.841964\pi$
$384$	−1.38301	−	1.04273i	−0.0705765	−	0.0532114i
$385$	5.54992	−	31.8217i	0.282850	−	1.62179i
$386$		−	25.0533i		−	1.27518i
$387$	−0.982158	−	14.1492i	−0.0499259	−	0.719244i
$388$	12.6561	+	1.33021i	0.642516	+	0.0675312i
$389$	−11.0531	+	24.8257i	−0.560416	+	1.25871i	0.381966	+	0.924176i	$0.375247\pi$
$389$	−11.0531	+	24.8257i	−0.560416	+	1.25871i	−0.942382	+	0.334538i	$0.891420\pi$
$390$	−28.3381	+	2.47198i	−1.43496	+	0.125174i
$391$	43.6429	+	14.1805i	2.20712	+	0.717136i
$392$	−2.37110	−	6.58619i	−0.119759	−	0.332653i
$393$	−7.75154	+	2.36772i	−0.391014	+	0.119436i
$394$	8.02352	+	1.70545i	0.404219	+	0.0859194i
$395$	−8.71462	−	15.0942i	−0.438480	−	0.759470i
$396$	−9.80403	−	1.69736i	−0.492671	−	0.0852957i
$397$	−4.67421	−	2.69866i	−0.234592	−	0.135442i	0.378097	−	0.925766i	$-0.376579\pi$
$397$	−4.67421	−	2.69866i	−0.234592	−	0.135442i	−0.612689	+	0.790324i	$0.709912\pi$
$398$	3.40756	+	10.4874i	0.170805	+	0.525685i
$399$	−1.66889	−	10.6754i	−0.0835488	−	0.534439i
$400$	−6.91788	+	5.02613i	−0.345894	+	0.251307i
$401$	−0.645634	+	0.581332i	−0.0322414	+	0.0290303i	−0.685094	−	0.728455i	$-0.740239\pi$
$401$	−0.645634	+	0.581332i	−0.0322414	+	0.0290303i	0.652852	+	0.757485i	$0.273572\pi$
$402$	−18.5927	−	8.67570i	−0.927320	−	0.432704i
$403$	−9.50833	−	4.23338i	−0.473644	−	0.210880i
$404$	−9.27608	+	4.12998i	−0.461502	+	0.205474i
$405$	−25.3577	−	21.3217i	−1.26003	−	1.05949i
$406$	3.21128	−	4.09546i	0.159373	−	0.203254i
$407$	22.1059	−	6.42528i	1.09575	−	0.318489i
$408$	−8.95046	+	3.79655i	−0.443114	+	0.187957i
$409$	26.8007	+	24.1314i	1.32521	+	1.19322i	0.965574	+	0.260129i	$0.0837652\pi$
$409$	26.8007	+	24.1314i	1.32521	+	1.19322i	0.359634	+	0.933093i	$0.382901\pi$
$410$	−28.2833	−	2.97270i	−1.39681	−	0.146811i
$411$	5.92798	−	9.86012i	0.292406	−	0.486364i
$412$	0.385886	+	0.125382i	0.0190112	+	0.00617713i
$413$	15.6172	−	1.06460i	0.768473	−	0.0523857i
$414$	−19.3186	−	15.1092i	−0.949458	−	0.742578i
$415$	−20.5214	+	9.13670i	−1.00735	+	0.448503i
$416$	2.98526	−	3.31547i	0.146364	−	0.162554i
$417$	−2.79576	+	22.7217i	−0.136909	+	1.11269i
$418$	2.95565	+	7.24007i	0.144566	+	0.354124i
$419$	−0.666338			−0.0325528			−0.0162764	−	0.999868i	$-0.505181\pi$
$419$	−0.666338			−0.0325528			−0.0162764	+	0.999868i	$0.505181\pi$
$420$	0.849089	+	16.8478i	0.0414313	+	0.822090i
$421$	−22.8238	−	16.5825i	−1.11236	−	0.808179i	−0.129329	−	0.991602i	$-0.541282\pi$
$421$	−22.8238	−	16.5825i	−1.11236	−	0.808179i	−0.983034	+	0.183423i	$0.941282\pi$
$422$	−15.8200	+	1.66275i	−0.770107	+	0.0809415i
$423$	0.452901	+	0.852831i	0.0220208	+	0.0414661i
$424$	−5.76816	+	1.22606i	−0.280127	+	0.0595428i
$425$	5.01720	+	47.7355i	0.243370	+	2.31551i
$426$	−10.1311	+	3.09457i	−0.490854	+	0.149932i
$427$	2.72377	−	7.44295i	0.131813	−	0.360189i
$428$			4.93757i			0.238667i
$429$	6.55005	−	24.7776i	0.316239	−	1.19628i
$430$	15.0720	−	8.70180i	0.726835	−	0.419638i
$431$	15.1346	+	13.6273i	0.729008	+	0.656402i	0.947616	−	0.319411i	$-0.103485\pi$
$431$	15.1346	+	13.6273i	0.729008	+	0.656402i	−0.218608	+	0.975813i	$0.570152\pi$
$432$	5.18924	−	0.267977i	0.249667	−	0.0128930i
$433$	−3.64287	−	5.01399i	−0.175065	−	0.240957i	0.712463	−	0.701709i	$-0.247580\pi$
$433$	−3.64287	−	5.01399i	−0.175065	−	0.240957i	−0.887529	+	0.460753i	$0.847580\pi$
$434$	−2.71549	+	5.54295i	−0.130348	+	0.266070i
$435$	−10.2755	+	7.19110i	−0.492674	+	0.344787i
$436$	1.30228	+	12.3904i	0.0623679	+	0.593391i
$437$	−2.01488	+	19.1703i	−0.0963846	+	0.917038i
$438$	−1.96730	−	10.1347i	−0.0940013	−	0.484254i
$439$	10.8710	+	6.27640i	0.518846	+	0.299556i	0.736463	−	0.676478i	$-0.236495\pi$
$439$	10.8710	+	6.27640i	0.518846	+	0.299556i	−0.217616	+	0.976034i	$0.569828\pi$
$440$	−3.40765	−	11.7238i	−0.162453	−	0.558912i
$441$	18.1443	+	10.5728i	0.864014	+	0.503469i
$442$	−7.73865	−	23.8171i	−0.368090	−	1.13287i
$443$	16.7510	+	37.6234i	0.795864	+	1.78754i	0.586985	+	0.809598i	$0.300315\pi$
$443$	16.7510	+	37.6234i	0.795864	+	1.78754i	0.208879	+	0.977942i	$0.433019\pi$
$444$	−10.5163	+	5.82579i	−0.499083	+	0.276480i
$445$	1.56458	−	0.332561i	0.0741680	−	0.0157649i
$446$	9.76666	+	10.8470i	0.462465	+	0.513619i
$447$	−32.4883	−	0.575371i	−1.53664	−	0.0272141i
$448$	−1.89998	−	1.84122i	−0.0897654	−	0.0869895i
$449$	20.0019	−	6.49900i	0.943947	−	0.306707i	0.203693	−	0.979035i	$-0.434706\pi$
$449$	20.0019	−	6.49900i	0.943947	−	0.306707i	0.740253	+	0.672328i	$0.234706\pi$
$450$	6.21869	−	24.8877i	0.293152	−	1.17322i
$451$	11.1490	−	23.0701i	0.524987	−	1.08633i
$452$	12.8753	−	7.43357i	0.605604	−	0.349646i
$453$	−16.9202	+	14.7009i	−0.794980	+	0.690710i
$454$	9.10100	−	12.5265i	0.427131	−	0.587896i
$455$	−43.4224	−	1.59243i	−2.03567	−	0.0746542i
$456$	−2.34159	−	3.34596i	−0.109655	−	0.156689i
$457$	21.9871	+	24.4192i	1.02851	+	1.14228i	0.989718	+	0.143034i	$0.0456857\pi$
$457$	21.9871	+	24.4192i	1.02851	+	1.14228i	0.0387963	+	0.999247i	$0.487648\pi$
$458$	−10.5705	−	4.70629i	−0.493927	−	0.219910i
$459$	13.2615	−	25.9780i	0.618993	−	1.21255i
$460$	6.25691	−	29.4364i	0.291730	−	1.37248i
$461$	−0.143485			−0.00668277			−0.00334138	−	0.999994i	$-0.501064\pi$
$461$	−0.143485			−0.00668277			−0.00334138	+	0.999994i	$0.501064\pi$
$462$	−14.5417	−	4.42029i	−0.676541	−	0.205650i
$463$	−22.0979			−1.02698			−0.513489	−	0.858096i	$-0.671647\pi$
$463$	−22.0979			−1.02698			−0.513489	+	0.858096i	$0.671647\pi$
$464$	0.408974	−	1.92407i	0.0189861	−	0.0893227i
$465$	10.1473	−	10.8761i	0.470570	−	0.504367i
$466$	14.1011	+	6.27821i	0.653221	+	0.290833i
$467$	13.1740	+	14.6313i	0.609622	+	0.677054i	0.966373	−	0.257146i	$-0.0827821\pi$
$467$	13.1740	+	14.6313i	0.609622	+	0.677054i	−0.356751	+	0.934200i	$0.616115\pi$
$468$	−0.473923	+	13.3758i	−0.0219071	+	0.618297i
$469$	−26.5492	−	16.6545i	−1.22593	−	0.769032i
$470$	−0.696455	+	0.958588i	−0.0321251	+	0.0442164i
$471$	6.32489	+	7.27971i	0.291436	+	0.335431i
$472$	5.12380	−	2.95823i	0.235842	−	0.136163i
$473$	2.77861	+	15.4320i	0.127760	+	0.709564i
$474$	−7.54965	+	3.20237i	−0.346767	+	0.147090i
$475$	−19.1752	+	6.23039i	−0.879818	+	0.285870i
$476$	−14.2830	+	4.06855i	−0.654661	+	0.186482i
$477$	10.8988	−	13.9352i	0.499023	−	0.638049i
$478$	−2.94462	−	3.27034i	−0.134684	−	0.149582i
$479$	13.5733	−	2.88509i	0.620179	−	0.131823i	0.112902	−	0.993606i	$-0.463985\pi$
$479$	13.5733	−	2.88509i	0.620179	−	0.131823i	0.507277	+	0.861783i	$0.330652\pi$
$480$	3.08971	+	5.57733i	0.141025	+	0.254569i
$481$	−12.5953	−	28.2894i	−0.574294	−	1.28989i
$482$	−0.985243	−	3.03227i	−0.0448766	−	0.138116i
$483$	−26.4374	−	26.5436i	−1.20294	−	1.20777i
$484$	10.9785	+	0.688009i	0.499021	+	0.0312731i
$485$	−40.5697	−	23.4229i	−1.84217	−	1.06358i
$486$	−11.4142	+	10.6168i	−0.517760	+	0.481586i
$487$	−0.618908	+	5.88852i	−0.0280454	+	0.266834i	0.971509	+	0.237001i	$0.0761644\pi$
$487$	−0.618908	+	5.88852i	−0.0280454	+	0.266834i	−0.999555	+	0.0298335i	$0.990502\pi$
$488$	−0.313128	−	2.97921i	−0.0141746	−	0.134863i
$489$	19.1848	+	27.4136i	0.867567	+	1.23969i
$490$	−1.88745	+	25.6989i	−0.0852664	+	1.16096i
$491$	−20.8109	−	28.6437i	−0.939183	−	1.29267i	−0.956168	−	0.292819i	$-0.905407\pi$
$491$	−20.8109	−	28.6437i	−0.939183	−	1.29267i	0.0169852	−	0.999856i	$-0.494593\pi$
$492$	−3.01341	+	13.0374i	−0.135855	+	0.587770i
$493$	−8.20544	−	7.38821i	−0.369554	−	0.332748i
$494$	9.11003	−	5.25968i	0.409880	−	0.236644i
$495$	30.4287	+	20.3873i	1.36767	+	0.916341i
$496$			2.33294i			0.104752i
$497$	−15.9404	+	2.78197i	−0.715026	+	0.124789i
$498$	3.08763	+	10.1084i	0.138360	+	0.452968i
$499$	−0.635236	−	6.04387i	−0.0284371	−	0.270561i	−0.999497	−	0.0317235i	$-0.989900\pi$
$499$	−0.635236	−	6.04387i	−0.0284371	−	0.270561i	0.971060	−	0.238837i	$-0.0767663\pi$
$500$	12.7860	−	2.71776i	0.571809	−	0.121542i
$501$	0.702359	−	1.50521i	0.0313791	−	0.0672479i
$502$	−20.8954	+	2.19619i	−0.932606	+	0.0980208i
$503$	−19.6080	−	14.2461i	−0.874278	−	0.635200i	0.0574532	−	0.998348i	$-0.481702\pi$
$503$	−19.6080	−	14.2461i	−0.874278	−	0.635200i	−0.931732	+	0.363148i	$0.881702\pi$
$504$	7.91665	+	0.571567i	0.352636	+	0.0254596i
$505$	37.3783			1.66331
$506$	23.0457	+	14.2850i	1.02450	+	0.635046i
$507$	−11.8687	−	1.46037i	−0.527109	−	0.0648572i
$508$	−3.34770	+	3.71800i	−0.148530	+	0.164960i
$509$	27.3066	−	12.1577i	1.21035	−	0.538881i	0.300482	−	0.953788i	$-0.402853\pi$
$509$	27.3066	−	12.1577i	1.21035	−	0.538881i	0.909864	+	0.414907i	$0.136186\pi$
$510$	35.7841	+	0.633739i	1.58454	+	0.0280624i
$511$	−1.07253	−	15.7334i	−0.0474457	−	0.696007i
$512$	−0.951057	−	0.309017i	−0.0420312	−	0.0136568i
$513$	11.8319	+	3.18005i	0.522391	+	0.140403i
$514$	10.9055	+	1.14621i	0.481019	+	0.0505572i
$515$	−1.10997	−	0.999422i	−0.0489111	−	0.0440398i
$516$	−3.19766	−	7.53855i	−0.140769	−	0.331866i
$517$	−0.600156	−	0.882871i	−0.0263948	−	0.0388286i
$518$	−17.0390	+	6.84954i	−0.748650	+	0.300951i
$519$	−6.49493	−	2.23824i	−0.285096	−	0.0982477i
$520$	−15.0033	+	6.67989i	−0.657938	+	0.292933i
$521$	−10.4989	−	4.67439i	−0.459963	−	0.204789i	0.163655	−	0.986518i	$-0.447671\pi$
$521$	−10.4989	−	4.67439i	−0.459963	−	0.204789i	−0.623619	+	0.781729i	$0.714338\pi$
$522$	2.76777	+	5.21183i	0.121142	+	0.228116i
$523$	−10.3058	+	9.27940i	−0.450642	+	0.405760i	−0.862954	−	0.505283i	$-0.831388\pi$
$523$	−10.3058	+	9.27940i	−0.450642	+	0.405760i	0.412312	+	0.911043i	$0.364721\pi$
$524$	−3.78578	+	2.75053i	−0.165382	+	0.120157i
$525$	14.1161	−	36.5545i	0.616078	−	1.59537i
$526$	3.56645	+	10.9764i	0.155505	+	0.478594i
$527$	11.3409	+	6.54764i	0.494015	+	0.285220i
$528$	−5.67079	+	0.917696i	−0.246789	+	0.0399376i
$529$	21.9166	+	37.9606i	0.952894	+	1.65046i
$530$	21.2336	+	4.51333i	0.922327	+	0.196047i
$531$	−6.07914	+	16.6759i	−0.263812	+	0.723670i
$532$	−2.91907	−	5.51322i	−0.126558	−	0.239028i
$533$	−32.7800	−	10.6509i	−1.41986	−	0.461340i
$534$	−0.0654028	−	0.749759i	−0.00283025	−	0.0324452i
$535$	7.39285	−	16.6046i	0.319621	−	0.717880i
$536$	−11.7807	−	1.23821i	−0.508850	−	0.0534823i
$537$	−4.31956	−	4.97164i	−0.186403	−	0.214542i
$538$		−	12.6038i		−	0.543390i
$539$	−21.2103	−	9.44055i	−0.913591	−	0.406633i
$540$	−17.8522	−	6.86848i	−0.768235	−	0.295572i
$541$	−30.4510	−	6.47255i	−1.30919	−	0.278277i	−0.500102	−	0.865966i	$-0.666704\pi$
$541$	−30.4510	−	6.47255i	−1.30919	−	0.278277i	−0.809086	+	0.587690i	$0.800038\pi$
$542$	−2.99900	+	28.5336i	−0.128818	+	1.22562i
$543$	−18.1691	−	32.7977i	−0.779711	−	1.40748i
$544$	−4.17143	+	3.75598i	−0.178849	+	0.161036i
$545$	14.1722	−	43.6176i	0.607071	−	1.86837i
$546$	−3.23874	+	20.1865i	−0.138605	+	0.863904i
$547$	15.8403	+	11.5087i	0.677283	+	0.492075i	0.872455	−	0.488694i	$-0.162527\pi$
$547$	15.8403	+	11.5087i	0.677283	+	0.492075i	−0.195172	+	0.980769i	$0.562527\pi$
$548$	1.38102	−	6.49721i	0.0589944	−	0.277547i
$549$	6.46143	+	6.24610i	0.275767	+	0.266577i
$550$	−3.84550	+	28.0984i	−0.163973	+	1.19812i
$551$	2.31902	−	4.01666i	0.0987936	−	0.171115i
$552$	−13.3872	−	4.61339i	−0.569795	−	0.196359i
$553$	−12.0476	+	3.43179i	−0.512317	+	0.145935i
$554$	7.95844	+	10.9539i	0.338122	+	0.465385i
$555$	44.0882	−	3.84589i	1.87144	−	0.163249i
$556$	2.74804	+	12.9285i	0.116543	+	0.548291i
$557$	13.3076	−	29.8893i	0.563859	−	1.26645i	−0.376548	−	0.926397i	$-0.622889\pi$
$557$	13.3076	−	29.8893i	0.563859	−	1.26645i	0.940407	−	0.340051i	$-0.110444\pi$
$558$	−4.49602	−	5.36369i	−0.190332	−	0.227063i
$559$	20.0600	−	6.51790i	0.848449	−	0.275678i
$560$	3.63265	+	9.03663i	0.153508	+	0.381867i
$561$	−11.4546	+	30.1424i	−0.483613	+	1.27261i
$562$	−6.27281	+	10.8648i	−0.264602	+	0.458305i
$563$	−12.5537	+	13.9423i	−0.529075	+	0.587597i	−0.947140	−	0.320820i	$-0.896042\pi$
$563$	−12.5537	+	13.9423i	−0.529075	+	0.587597i	0.418065	+	0.908417i	$0.362708\pi$
$564$	0.407637	+	0.380322i	0.0171646	+	0.0160145i
$565$	−54.4286	+	5.72067i	−2.28983	+	0.240670i
$566$	7.17563	−	22.0843i	0.301614	−	0.928273i
$567$	−19.3028	+	13.9428i	−0.810642	+	0.585542i
$568$	−4.94793	+	3.59488i	−0.207611	+	0.150838i
$569$	−7.72615	−	17.3532i	−0.323897	−	0.727485i	0.676059	−	0.736848i	$-0.263686\pi$
$569$	−7.72615	−	17.3532i	−0.323897	−	0.727485i	−0.999956	+	0.00936243i	$0.997020\pi$
$570$	2.86479	+	14.7581i	0.119993	+	0.618151i
$571$	11.8339	+	20.4970i	0.495235	+	0.857772i	0.999985	−	0.00549323i	$-0.00174856\pi$
$571$	11.8339	+	20.4970i	0.495235	+	0.857772i	−0.504750	+	0.863266i	$0.668415\pi$
$572$	−1.08550	−	14.7569i	−0.0453869	−	0.617018i
$573$	35.0442	+	26.4217i	1.46399	+	1.10378i
$574$	−7.02448	+	19.1950i	−0.293196	+	0.801184i
$575$	−41.0894	+	56.5547i	−1.71355	+	2.35849i
$576$	2.78212	−	1.12240i	0.115922	−	0.0467667i
$577$	5.26062	+	24.7493i	0.219003	+	1.03033i	0.940994	+	0.338424i	$0.109894\pi$
$577$	5.26062	+	24.7493i	0.219003	+	1.03033i	−0.721991	+	0.691902i	$0.756773\pi$
$578$	3.01643	+	14.1912i	0.125467	+	0.590275i
$579$	37.1899	+	22.3588i	1.54556	+	0.929201i
$580$	−4.25618	+	5.85813i	−0.176728	+	0.243246i
$581$	2.77573	+	15.9047i	0.115157	+	0.659837i
$582$	−13.2696	+	17.6000i	−0.550041	+	0.729541i
$583$	−10.3043	+	16.6237i	−0.426760	+	0.688482i
$584$	−2.98024	−	5.16193i	−0.123323	−	0.213602i
$585$	21.6209	−	44.2721i	0.893913	−	1.83042i
$586$	−8.46774	−	19.0189i	−0.349799	−	0.785662i
$587$	−2.79600	+	2.03141i	−0.115403	+	0.0838454i	−0.643990	−	0.765034i	$-0.722722\pi$
$587$	−2.79600	+	2.03141i	−0.115403	+	0.0838454i	0.528587	+	0.848879i	$0.322722\pi$
$588$	11.8928	+	2.35811i	0.490452	+	0.0972468i
$589$	−1.69982	+	5.23151i	−0.0700399	+	0.215561i
$590$	−21.6601	+	2.27657i	−0.891733	+	0.0937250i
$591$	−9.69222	+	10.3883i	−0.398685	+	0.427318i
$592$	−4.64444	+	5.15818i	−0.190885	+	0.212000i
$593$	12.6041	−	21.8310i	0.517590	−	0.896492i	−0.482201	−	0.876060i	$-0.660163\pi$
$593$	12.6041	−	21.8310i	0.517590	−	0.896492i	0.999791	−	0.0204317i	$-0.00650406\pi$
$594$	11.2692	−	13.0386i	0.462382	−	0.534979i
$595$	54.1242	+	7.70327i	2.21887	+	0.315803i
$596$	−17.8419	+	5.79718i	−0.730833	+	0.237462i
$597$	−18.6089	−	4.30119i	−0.761610	−	0.176036i
$598$	14.8348	−	33.3194i	0.606638	−	1.36253i
$599$	−2.82100	−	13.2718i	−0.115263	−	0.542270i	−0.997450	−	0.0713706i	$-0.977263\pi$
$599$	−2.82100	−	13.2718i	−0.115263	−	0.542270i	0.882187	−	0.470900i	$-0.156071\pi$
$600$	−1.28708	−	14.7547i	−0.0525447	−	0.602357i
$601$	2.21011	+	3.04195i	0.0901522	+	0.124084i	0.851711	−	0.524012i	$-0.175565\pi$
$601$	2.21011	+	3.04195i	0.0901522	+	0.124084i	−0.761558	+	0.648096i	$0.775565\pi$
$602$	−3.42675	−	12.0299i	−0.139664	−	0.490302i
$603$	29.4715	−	19.8569i	1.20017	−	0.808637i
$604$	−6.47051	+	11.2073i	−0.263281	+	0.456017i
$605$	−35.8895	−	18.7514i	−1.45911	−	0.762352i
$606$	2.14778	−	17.4555i	0.0872477	−	0.709081i
$607$	−0.715800	+	3.36758i	−0.0290534	+	0.136686i	−0.990284	−	0.139061i	$-0.955592\pi$
$607$	−0.715800	+	3.36758i	−0.0290534	+	0.136686i	0.961230	+	0.275746i	$0.0889250\pi$
$608$	−1.90755	−	1.38592i	−0.0773613	−	0.0562063i
$609$	3.21351	+	8.42192i	0.130218	+	0.341273i
$610$	−3.40765	+	10.4877i	−0.137972	+	0.424633i
$611$	−1.06717	+	0.960884i	−0.0431731	+	0.0388732i
$612$	2.35213	−	16.6746i	0.0950792	−	0.674030i
$613$	−0.204590	+	1.94654i	−0.00826330	+	0.0786200i	−0.997876	−	0.0651368i	$-0.979252\pi$
$613$	−0.204590	+	1.94654i	−0.00826330	+	0.0786200i	0.989613	+	0.143757i	$0.0459183\pi$
$614$	9.54168	+	2.02815i	0.385071	+	0.0818494i
$615$	29.6542	−	39.3316i	1.19577	−	1.58600i
$616$	−8.76903	+	0.322580i	−0.353314	+	0.0129971i
$617$			22.5224i			0.906718i	0.891328	+	0.453359i	$0.149774\pi$
$617$			22.5224i			0.906718i	−0.891328	+	0.453359i	$0.850226\pi$
$618$	−0.530505	+	0.460924i	−0.0213400	+	0.0185411i
$619$	15.9969	+	1.68134i	0.642968	+	0.0675787i	0.420401	−	0.907339i	$-0.361889\pi$
$619$	15.9969	+	1.68134i	0.642968	+	0.0675787i	0.222568	+	0.974917i	$0.428556\pi$
$620$	3.49302	−	7.84546i	0.140283	−	0.315081i
$621$	39.6695	−	15.1929i	1.59188	−	0.609670i
$622$	25.0412	+	8.13638i	1.00406	+	0.326239i
$623$	0.0421318	−	1.14885i	0.00168798	−	0.0460278i
$624$	2.25738	+	7.39030i	0.0903675	+	0.295849i
$625$	−5.24697	−	1.11528i	−0.209879	−	0.0446111i
$626$	−12.3160	−	21.3320i	−0.492247	−	0.852597i
$627$	−13.3852	−	2.07395i	−0.534552	−	0.0828255i
$628$	4.82178	+	2.78386i	0.192410	+	0.111088i
$629$	12.0397	+	37.0545i	0.480056	+	1.47746i
$630$	−25.7672	−	13.7754i	−1.02659	−	0.548827i
$631$	−26.0065	+	18.8949i	−1.03530	+	0.752193i	−0.969363	−	0.245631i	$-0.921005\pi$
$631$	−26.0065	+	18.8949i	−1.03530	+	0.752193i	−0.0659408	+	0.997824i	$0.521005\pi$
$632$	−3.51857	+	3.16814i	−0.139961	+	0.126022i
$633$	11.6503	−	24.9676i	0.463060	−	0.992374i
$634$	−10.8630	−	4.83652i	−0.431425	−	0.192083i
$635$	16.8249	−	7.49091i	0.667674	−	0.297268i
$636$	3.32780	−	9.65664i	0.131956	−	0.382910i
$637$	−8.71312	+	29.9897i	−0.345226	+	1.18824i
$638$	−3.66768	−	5.39541i	−0.145205	−	0.213606i
$639$	4.44785	−	17.8007i	0.175954	−	0.704183i
$640$	2.73564	+	2.46318i	0.108136	+	0.0973657i
$641$	35.7102	+	3.75329i	1.41047	+	0.148246i	0.778936	−	0.627104i	$-0.215760\pi$
$641$	35.7102	+	3.75329i	1.41047	+	0.148246i	0.631532	+	0.775350i	$0.282426\pi$
$642$	−7.32948	−	4.40654i	−0.289272	−	0.173912i
$643$	−15.3634	−	4.99187i	−0.605873	−	0.196860i	−0.0100149	−	0.999950i	$-0.503188\pi$
$643$	−15.3634	−	4.99187i	−0.605873	−	0.196860i	−0.595858	+	0.803090i	$0.703188\pi$
$644$	−19.4238	−	9.51572i	−0.765404	−	0.374972i
$645$	−0.533768	+	30.1392i	−0.0210171	+	1.18673i
$646$	−12.0909	+	5.38323i	−0.475712	+	0.211800i
$647$	4.78747	−	5.31702i	0.188215	−	0.209034i	−0.641651	−	0.766997i	$-0.721750\pi$
$647$	4.78747	−	5.31702i	0.188215	−	0.209034i	0.829866	+	0.557963i	$0.188417\pi$
$648$	−4.23335	+	7.94222i	−0.166302	+	0.312000i
$649$	4.67833	−	19.0568i	0.183640	−	0.748045i
$650$	38.1493			1.49634
$651$	−5.80467	−	8.97777i	−0.227503	−	0.351866i
$652$	15.6287	+	11.3549i	0.612065	+	0.444691i
$653$	24.1077	−	2.53382i	0.943406	−	0.0991560i	0.379680	−	0.925118i	$-0.376034\pi$
$653$	24.1077	−	2.53382i	0.943406	−	0.0991560i	0.563726	+	0.825962i	$0.309367\pi$
$654$	−19.5549	−	9.12465i	−0.764655	−	0.356802i
$655$	16.8495	−	3.58147i	0.658364	−	0.139940i
$656$	0.807543	+	7.68326i	0.0315292	+	0.299981i
$657$	16.8000	+	6.12439i	0.655429	+	0.238935i
$658$	0.546259	+	0.653324i	0.0212954	+	0.0254692i
$659$		−	0.650596i		−	0.0253436i	−0.999920	−	0.0126718i	$-0.995966\pi$
$659$		−	0.650596i		−	0.0253436i	0.999920	−	0.0126718i	$-0.00403367\pi$
$660$	20.4444	+	5.40454i	0.795797	+	0.210371i
$661$	−9.00617	+	5.19972i	−0.350299	+	0.202245i	−0.664817	−	0.747006i	$-0.731491\pi$
$661$	−9.00617	+	5.19972i	−0.350299	+	0.202245i	0.314518	+	0.949252i	$0.398157\pi$
$662$	7.93775	+	7.14718i	0.308509	+	0.277783i
$663$	42.2612	+	9.76812i	1.64129	+	0.379362i
$664$	3.58682	+	4.93684i	0.139196	+	0.191586i
$665$	1.56181	+	22.9111i	0.0605645	+	0.888453i
$666$	0.737325	−	20.8100i	0.0285708	−	0.806370i
$667$	−1.68092	−	15.9929i	−0.0650855	−	0.619247i
$668$	0.100242	−	0.953734i	0.00387846	−	0.0369011i
$669$	−24.8178	+	4.81753i	−0.959513	+	0.186257i
$670$	37.7636	+	21.8028i	1.45894	+	0.842317i
$671$	−7.85122	−	6.08849i	−0.303093	−	0.235044i
$672$	4.42880	−	1.17718i	0.170845	−	0.0454107i
$673$	−15.6644	−	48.2101i	−0.603819	−	1.85836i	−0.504716	−	0.863285i	$-0.668403\pi$
$673$	−15.6644	−	48.2101i	−0.603819	−	1.85836i	−0.0991021	−	0.995077i	$-0.531597\pi$
$674$	−4.01550	−	9.01896i	−0.154671	−	0.347397i
$675$	31.3942	+	31.4423i	1.20836	+	1.21021i
$676$	−6.75322	+	1.43544i	−0.259739	+	0.0552093i
$677$	11.9520	+	13.2740i	0.459352	+	0.510162i	0.927672	−	0.373397i	$-0.121807\pi$
$677$	11.9520	+	13.2740i	0.459352	+	0.510162i	−0.468320	+	0.883559i	$0.655140\pi$
$678$	−0.455975	+	25.7466i	−0.0175116	+	0.988792i
$679$	−23.4310	+	24.1787i	−0.899201	+	0.927895i
$680$	19.6518	−	6.38527i	0.753614	−	0.244864i
$681$	10.4724	+	24.6890i	0.401305	+	0.946086i
$682$	5.58526	+	5.35476i	0.213871	+	0.205044i
$683$	12.9494	−	7.47636i	0.495497	−	0.286075i	−0.231355	−	0.972869i	$-0.574316\pi$
$683$	12.9494	−	7.47636i	0.495497	−	0.286075i	0.726852	+	0.686794i	$0.240983\pi$
$684$	7.05660	−	0.489830i	0.269816	−	0.0187291i
$685$	−14.3723	+	19.7818i	−0.549137	+	0.755823i
$686$	17.5835	+	5.81547i	0.671342	+	0.222036i
$687$	16.4198	−	11.4910i	0.626454	−	0.438410i
$688$	−3.16348	−	3.51340i	−0.120607	−	0.133947i
$689$	24.0345	+	10.7008i	0.915640	+	0.407669i
$690$	38.1124	+	35.5585i	1.45091	+	1.35369i
$691$	−3.29205	+	15.4879i	−0.125235	+	0.589187i	0.870113	+	0.492851i	$0.164045\pi$
$691$	−3.29205	+	15.4879i	−0.125235	+	0.589187i	−0.995349	+	0.0963352i	$0.969288\pi$
$692$	−3.96627			−0.150775
$693$	19.5394	−	17.6412i	0.742239	−	0.670136i
$694$	11.0787			0.420541
$695$	10.1160	−	47.5919i	0.383721	−	1.80526i
$696$	2.49116	+	2.32423i	0.0944271	+	0.0880997i
$697$	39.6162	+	17.6383i	1.50057	+	0.668097i
$698$	−5.63169	−	6.25462i	−0.213163	−	0.236741i
$699$	−21.9041	+	15.3291i	−0.828489	+	0.579800i
$700$	0.829122	−	22.6085i	0.0313379	−	0.854522i
$701$	5.43451	−	7.47996i	0.205259	−	0.282514i	−0.693960	−	0.720013i	$-0.744136\pi$
$701$	5.43451	−	7.47996i	0.205259	−	0.282514i	0.899219	+	0.437499i	$0.144136\pi$
$702$	−19.4325	−	12.6408i	−0.733432	−	0.477094i
$703$	−14.1733	+	8.18296i	−0.534556	+	0.308626i
$704$	−2.92276	+	1.56763i	−0.110156	+	0.0590823i
$705$	−0.801405	−	1.88933i	−0.0301826	−	0.0711563i
$706$	−16.2469	+	5.27894i	−0.611460	+	0.198675i
$707$	6.54478	−	26.0554i	0.246142	−	0.979913i
$708$	−0.181458	+	10.2460i	−0.00681960	+	0.385068i
$709$	−14.6095	−	16.2255i	−0.548672	−	0.609362i	0.403479	−	0.914989i	$-0.367801\pi$
$709$	−14.6095	−	16.2255i	−0.548672	−	0.609362i	−0.952151	+	0.305627i	$0.901134\pi$
$710$	22.0219	−	4.68091i	0.826469	−	0.175671i
$711$	1.98400	−	14.0649i	0.0744060	−	0.527474i
$712$	−0.176734	−	0.396951i	−0.00662339	−	0.0148764i
$713$	5.89361	+	18.1387i	0.220717	+	0.679298i
$714$	6.70740	−	24.8331i	0.251018	−	0.929356i
$715$	−18.4446	+	51.2515i	−0.689788	+	1.91670i
$716$	−3.29302	−	1.90122i	−0.123066	−	0.0710521i
$717$	7.48252	−	1.45247i	0.279440	−	0.0542436i
$718$	0.879127	−	8.36433i	0.0328087	−	0.312154i
$719$	3.00343	+	28.5758i	0.112009	+	1.06570i	0.895735	+	0.444589i	$0.146650\pi$
$719$	3.00343	+	28.5758i	0.112009	+	1.06570i	−0.783726	+	0.621107i	$0.786683\pi$
$720$	−11.0366	−	0.391040i	−0.411309	−	0.0145732i
$721$	−0.891020	+	0.598735i	−0.0331833	+	0.0222981i
$722$	7.90013	+	10.8736i	0.294012	+	0.404673i
$723$	5.38047	+	1.24362i	0.200102	+	0.0462509i
$724$	−16.0870	−	14.4848i	−0.597869	−	0.538324i
$725$	14.5667	−	8.41011i	0.540995	−	0.312344i
$726$	−10.8190	+	15.6827i	−0.401532	+	0.582041i
$727$		−	12.2626i		−	0.454796i	−0.973802	−	0.227398i	$-0.926978\pi$
$727$		−	12.2626i		−	0.454796i	0.973802	−	0.227398i	$-0.0730218\pi$
$728$	2.02935	+	11.6280i	0.0752129	+	0.430962i
$729$	−5.57321	−	26.4185i	−0.206415	−	0.978465i
$730$	2.29351	+	21.8213i	0.0848867	+	0.807643i
$731$	−25.9579	+	5.51753i	−0.960089	+	0.204073i
$732$	4.70189	+	2.19399i	0.173787	+	0.0810920i
$733$	31.1637	−	3.27544i	1.15106	−	0.120981i	0.490281	−	0.871564i	$-0.336894\pi$
$733$	31.1637	−	3.27544i	1.15106	−	0.120981i	0.660776	+	0.750583i	$0.270227\pi$
$734$	3.12222	+	2.26842i	0.115243	+	0.0837290i
$735$	−36.4638	−	25.7368i	−1.34499	−	0.949317i
$736$	−8.17515			−0.301340
$737$	−30.0045	+	25.3621i	−1.10523	+	0.934225i
$738$	−16.6637	−	16.1084i	−0.613400	−	0.592959i
$739$	−1.49487	+	1.66022i	−0.0549897	+	0.0610723i	−0.770012	−	0.638029i	$-0.779750\pi$
$739$	−1.49487	+	1.66022i	−0.0549897	+	0.0610723i	0.715022	+	0.699102i	$0.246417\pi$
$740$	23.3420	−	10.3925i	0.858069	−	0.382037i
$741$	−0.322629	+	18.2172i	−0.0118521	+	0.669226i
$742$	6.86403	−	14.0111i	0.251986	−	0.514362i
$743$	−1.97610	−	0.642074i	−0.0724960	−	0.0235554i	0.272544	−	0.962143i	$-0.412135\pi$
$743$	−1.97610	−	0.642074i	−0.0724960	−	0.0235554i	−0.345040	+	0.938588i	$0.612135\pi$
$744$	−3.46308	−	2.08203i	−0.126963	−	0.0763310i
$745$	68.6806	+	7.21862i	2.51626	+	0.264470i
$746$	−16.6140	−	14.9593i	−0.608281	−	0.547698i
$747$	−17.7607	−	4.43787i	−0.649832	−	0.162373i
$748$	−0.582495	+	18.6078i	−0.0212981	+	0.680369i
$749$	−10.2802	−	8.06075i	−0.375629	−	0.294534i
$750$	−7.37659	+	21.4054i	−0.269355	+	0.781616i
$751$	24.5794	−	10.9435i	0.896916	−	0.399333i	0.0941025	−	0.995563i	$-0.470002\pi$
$751$	24.5794	−	10.9435i	0.896916	−	0.399333i	0.802814	+	0.596230i	$0.203335\pi$
$752$	0.294049	+	0.130919i	0.0107229	+	0.00477412i
$753$	15.3880	−	32.9777i	0.560769	−	1.20177i
$754$	−6.52170	+	5.87217i	−0.237506	+	0.213852i
$755$	38.5400	−	28.0009i	1.40261	−	1.01906i
$756$	−7.91367	+	11.2416i	−0.287817	+	0.408853i
$757$	9.78801	+	30.1244i	0.355751	+	1.09489i	0.955573	+	0.294756i	$0.0952383\pi$
$757$	9.78801	+	30.1244i	0.355751	+	1.09489i	−0.599821	+	0.800134i	$0.704762\pi$
$758$	9.92300	+	5.72905i	0.360420	+	0.208088i
$759$	−41.7722	+	21.4610i	−1.51624	+	0.778985i
$760$	4.33983	+	7.51681i	0.157422	+	0.272663i
$761$	−44.8967	−	9.54308i	−1.62750	−	0.345936i	−0.698386	−	0.715722i	$-0.746098\pi$
$761$	−44.8967	−	9.54308i	−1.62750	−	0.345936i	−0.929117	+	0.369785i	$0.879431\pi$
$762$	−2.53145	−	8.28757i	−0.0917049	−	0.300227i
$763$	−27.9231	−	17.5163i	−1.01088	−	0.634133i
$764$	24.0989	+	7.83021i	0.871868	+	0.283287i
$765$	−32.8762	+	52.5533i	−1.18864	+	1.90007i
$766$	12.1153	−	27.2114i	0.437744	−	0.983188i
$767$	−26.2511	−	2.75910i	−0.947871	−	0.0996253i
$768$	1.30749	−	1.13599i	0.0471798	−	0.0409917i
$769$		−	6.74456i		−	0.243215i	−0.992578	−	0.121608i	$-0.961195\pi$
$769$		−	6.74456i		−	0.243215i	0.992578	−	0.121608i	$-0.0388049\pi$
$770$	29.9725	+	12.0448i	1.08013	+	0.434063i
$771$	−11.4341	+	15.1655i	−0.411787	+	0.546171i
$772$	24.5058	+	5.20887i	0.881984	+	0.187471i
$773$	−1.10380	+	10.5019i	−0.0397008	+	0.377728i	0.956574	+	0.291490i	$0.0941511\pi$
$773$	−1.10380	+	10.5019i	−0.0397008	+	0.377728i	−0.996275	+	0.0862376i	$0.972516\pi$
$774$	14.0442	+	1.98109i	0.504808	+	0.0712087i
$775$	−14.8249	+	13.3484i	−0.532526	+	0.479489i
$776$	−3.93249	+	12.1030i	−0.141168	+	0.434471i
$777$	5.03880	−	31.4061i	0.180766	−	1.12669i
$778$	−21.9852	−	15.9731i	−0.788206	−	0.572665i
$779$	−3.78728	+	17.8178i	−0.135694	+	0.638388i
$780$	3.47386	−	28.2328i	0.124384	−	1.01090i
$781$	−2.75045	+	20.0971i	−0.0984189	+	0.719130i
$782$	−22.9445	+	39.7410i	−0.820492	+	1.42113i
$783$	−10.2067	−	0.542739i	−0.364758	−	0.0193959i
$784$	6.93524	−	0.949945i	0.247687	−	0.0339266i
$785$	−12.0471	−	16.5813i	−0.429978	−	0.591814i
$786$	−0.704347	−	8.07443i	−0.0251232	−	0.288005i
$787$	−7.21631	−	33.9501i	−0.257234	−	1.21019i	−0.897143	−	0.441739i	$-0.854362\pi$
$787$	−7.21631	−	33.9501i	−0.257234	−	1.21019i	0.639910	−	0.768450i	$-0.278972\pi$
$788$	−3.33637	+	7.49360i	−0.118853	+	0.266948i
$789$	−19.4766	−	4.50175i	−0.693384	−	0.160267i
$790$	16.5762	−	5.38593i	0.589754	−	0.191623i
$791$	−5.54249	+	38.9423i	−0.197068	+	1.38463i
$792$	3.69864	−	9.23688i	0.131426	−	0.328218i
$793$	−6.68234	+	11.5742i	−0.237297	+	0.411010i
$794$	3.61151	−	4.01098i	0.128168	−	0.142345i
$795$	−25.6496	+	27.4918i	−0.909699	+	0.975034i
$796$	−10.9667	+	1.15264i	−0.388704	+	0.0408544i
$797$	−6.90719	+	21.2582i	−0.244665	+	0.753002i	0.751026	+	0.660273i	$0.229559\pi$
$797$	−6.90719	+	21.2582i	−0.244665	+	0.753002i	−0.995691	+	0.0927297i	$0.970441\pi$
$798$	10.7891	+	0.587126i	0.381930	+	0.0207840i
$799$	1.46170	−	1.06199i	0.0517113	−	0.0375704i
$800$	−3.47799	−	7.81170i	−0.122966	−	0.276185i
$801$	1.17133	+	0.572037i	0.0413870	+	0.0202119i
$802$	−0.434393	−	0.752391i	−0.0153390	−	0.0265679i
$803$	−19.1986	−	4.71315i	−0.677505	−	0.166323i
$804$	12.3518	−	16.3826i	0.435613	−	0.577771i
$805$	51.0729	+	61.0830i	1.80008	+	2.15289i
$806$	6.11777	−	8.42038i	0.215489	−	0.296595i
$807$	18.7095	+	11.2483i	0.658606	+	0.395959i
$808$	−2.11112	−	9.93204i	−0.0742690	−	0.349408i
$809$	−2.12663	−	10.0050i	−0.0747685	−	0.351758i	0.924821	−	0.380402i	$-0.124214\pi$
$809$	−2.12663	−	10.0050i	−0.0747685	−	0.351758i	−0.999590	+	0.0286441i	$0.990881\pi$
$810$	26.1280	−	20.3705i	0.918043	−	0.715747i
$811$	−28.7291	+	39.5421i	−1.00881	+	1.38851i	−0.0890554	+	0.996027i	$0.528385\pi$
$811$	−28.7291	+	39.5421i	−1.00881	+	1.38851i	−0.919758	+	0.392486i	$0.871615\pi$
$812$	3.33830	+	3.99260i	0.117151	+	0.140113i
$813$	−39.6796	−	29.9166i	−1.39163	−	1.04922i
$814$	1.68881	+	22.9587i	0.0591926	+	0.804702i
$815$	−35.5565	−	61.5857i	−1.24549	−	2.15725i
$816$	−1.85268	−	9.54422i	−0.0648569	−	0.334115i
$817$	−4.53404	−	10.1836i	−0.158626	−	0.356280i
$818$	−29.1763	+	21.1978i	−1.02012	+	0.741164i
$819$	−27.0751	−	22.8232i	−0.946080	−	0.797506i
$820$	8.78817	−	27.0472i	0.306896	−	0.944529i
$821$	23.1180	−	2.42980i	0.806825	−	0.0848008i	0.307870	−	0.951428i	$-0.400384\pi$
$821$	23.1180	−	2.42980i	0.806825	−	0.0848008i	0.498955	+	0.866628i	$0.333717\pi$
$822$	8.41215	+	7.84847i	0.293408	+	0.273747i
$823$	−25.8014	+	28.6554i	−0.899380	+	0.998863i	0.100612	+	0.994926i	$0.467920\pi$
$823$	−25.8014	+	28.6554i	−0.899380	+	0.998863i	−0.999992	+	0.00393704i	$0.998747\pi$
$824$	−0.202872	+	0.351385i	−0.00706739	+	0.0122411i
$825$	−38.2782	−	30.7848i	−1.33268	−	1.07179i
$826$	−2.20567	+	15.4973i	−0.0767449	+	0.539220i
$827$	−34.4694	+	11.1998i	−1.19862	+	0.389455i	−0.839253	−	0.543741i	$-0.817007\pi$
$827$	−34.4694	+	11.1998i	−1.19862	+	0.389455i	−0.359367	+	0.933196i	$0.617007\pi$
$828$	18.7956	−	15.7551i	0.653193	−	0.547527i
$829$	17.8238	−	40.0330i	0.619047	−	1.39040i	−0.283148	−	0.959076i	$-0.591379\pi$
$829$	17.8238	−	40.0330i	0.619047	−	1.39040i	0.902196	−	0.431327i	$-0.141954\pi$
$830$	−4.67041	−	21.9726i	−0.162112	−	0.762679i
$831$	−23.3627	+	2.03797i	−0.810445	+	0.0706965i
$832$	2.62235	+	3.60935i	0.0909135	+	0.125132i
$833$	14.8467	−	36.3797i	0.514406	−	1.26048i
$834$	−21.6439	−	7.45878i	−0.749468	−	0.258276i
$835$	−1.76510	+	3.05723i	−0.0610836	+	0.105800i
$836$	−7.69637	+	1.38577i	−0.266185	+	0.0479278i
$837$	11.9745	−	1.88719i	0.413899	−	0.0652307i
$838$	0.138540	−	0.651777i	0.00478577	−	0.0225153i
$839$	−37.8907	−	27.5292i	−1.30813	−	0.950414i	−0.308133	−	0.951343i	$-0.599704\pi$
$839$	−37.8907	−	27.5292i	−1.30813	−	0.950414i	−1.00000		0.000929658i	$0.999704\pi$
$840$	−16.6562	−	2.67233i	−0.574693	−	0.0922040i
$841$	7.76581	−	23.9007i	0.267787	−	0.824162i
$842$	20.9654	−	18.8773i	0.722516	−	0.650556i
$843$	−10.5299	−	19.0079i	−0.362669	−	0.654665i
$844$	1.66275	−	15.8200i	0.0572343	−	0.544548i
$845$	24.8597	+	5.28409i	0.855200	+	0.181778i
$846$	−0.928358	+	0.265690i	−0.0319176	+	0.00913461i
$847$	−19.3552	+	21.7343i	−0.665051	+	0.746798i
$848$		−	5.89703i		−	0.202505i
$849$	26.3787	+	30.3609i	0.905315	+	1.04198i
$850$	−47.7355	−	5.01720i	−1.63731	−	0.172089i
$851$	−23.0798	+	51.8380i	−0.791165	+	1.77699i
$852$	−0.920566	−	10.5531i	−0.0315381	−	0.361544i
$853$	−6.94279	−	2.25585i	−0.237717	−	0.0772388i	0.187736	−	0.982220i	$-0.439885\pi$
$853$	−6.94279	−	2.25585i	−0.237717	−	0.0772388i	−0.425453	+	0.904981i	$0.639885\pi$
$854$	6.71400	+	4.21173i	0.229748	+	0.144122i
$855$	−24.4641	−	8.91834i	−0.836655	−	0.305001i
$856$	−4.82968	−	1.02658i	−0.165075	−	0.0350878i
$857$	18.2095	+	31.5397i	0.622024	+	1.07738i	0.989108	+	0.147189i	$0.0470226\pi$
$857$	18.2095	+	31.5397i	0.622024	+	1.07738i	−0.367085	+	0.930188i	$0.619644\pi$
$858$	22.8744	+	11.5585i	0.780918	+	0.394600i
$859$	−39.2598	−	22.6666i	−1.33953	−	0.773375i	−0.352789	−	0.935703i	$-0.614767\pi$
$859$	−39.2598	−	22.6666i	−1.33953	−	0.773375i	−0.986737	+	0.162328i	$0.948100\pi$
$860$	5.37801	+	16.5518i	0.183389	+	0.564412i
$861$	−22.2246	−	27.5579i	−0.757414	−	0.939172i
$862$	−16.4761	+	11.9706i	−0.561179	+	0.407721i
$863$	8.87325	−	7.98951i	0.302049	−	0.271966i	−0.504143	−	0.863620i	$-0.668192\pi$
$863$	8.87325	−	7.98951i	0.302049	−	0.271966i	0.806192	+	0.591654i	$0.201525\pi$
$864$	−0.816783	+	5.13156i	−0.0277875	+	0.174579i
$865$	13.3382	+	5.93855i	0.453512	+	0.201917i
$866$	5.66181	−	2.52080i	0.192396	−	0.0856603i
$867$	−23.7578	−	8.18725i	−0.806858	−	0.278053i
$868$	−4.85724	−	3.80860i	−0.164865	−	0.129272i
$869$	−0.491330	+	15.6956i	−0.0166672	+	0.532436i
$870$	−4.89756	−	11.5461i	−0.166043	−	0.391449i
$871$	39.2738	+	35.3623i	1.33074	+	1.19820i
$872$	−12.3904	−	1.30228i	−0.419591	−	0.0441008i
$873$	−14.2835	−	35.4048i	−0.483422	−	1.19827i
$874$	−18.3324	−	5.95657i	−0.620104	−	0.201484i
$875$	−15.2152	+	31.0577i	−0.514367	+	1.04994i
$876$	10.3222	+	0.182808i	0.348756	+	0.00617651i
$877$	14.0584	−	6.25919i	0.474718	−	0.211358i	−0.155409	−	0.987850i	$-0.549670\pi$
$877$	14.0584	−	6.25919i	0.474718	−	0.211358i	0.630127	+	0.776492i	$0.283003\pi$
$878$	−8.39946	+	9.32855i	−0.283468	+	0.314823i
$879$	35.7892	+	4.40362i	1.20714	+	0.148531i
$880$	12.1761	−	0.895658i	0.410458	−	0.0301926i
$881$	18.7431			0.631472			0.315736	−	0.948847i	$-0.397749\pi$
$881$	18.7431			0.631472			0.315736	+	0.948847i	$0.397749\pi$
$882$	−14.1142	+	15.5496i	−0.475250	+	0.523581i
$883$	34.2038	+	24.8505i	1.15105	+	0.836286i	0.988620	−	0.150434i	$-0.0480671\pi$
$883$	34.2038	+	24.8505i	1.15105	+	0.836286i	0.162429	+	0.986720i	$0.448067\pi$
$884$	24.9056	−	2.61769i	0.837667	−	0.0880423i
$885$	15.9512	−	34.1847i	0.536193	−	1.14911i
$886$	−40.2839	+	8.56261i	−1.35336	+	0.287667i
$887$	1.28956	+	12.2693i	0.0432992	+	0.411964i	0.994607	+	0.103720i	$0.0330746\pi$
$887$	1.28956	+	12.2693i	0.0432992	+	0.411964i	−0.951307	+	0.308244i	$0.900259\pi$
$888$	−3.51201	−	11.4978i	−0.117855	−	0.385840i
$889$	−2.27574	−	13.0398i	−0.0763259	−	0.437340i
$890$			1.59953i			0.0536163i
$891$	9.29763	+	28.3647i	0.311482	+	0.950252i
$892$	−12.6405	+	7.29802i	−0.423237	+	0.244356i
$893$	0.564002	+	0.507830i	0.0188736	+	0.0169939i
$894$	7.31750	−	31.6587i	0.244734	−	1.05883i
$895$	8.22749	+	11.3242i	0.275015	+	0.378525i
$896$	2.19601	−	1.47564i	0.0733636	−	0.0492978i
$897$	36.2210	+	51.7571i	1.20938	+	1.72812i
$898$	2.19836	+	20.9160i	0.0733602	+	0.697976i
$899$	0.479683	−	4.56388i	0.0159983	−	0.152214i
$900$	23.0509	+	11.2572i	0.768364	+	0.375242i
$901$	−28.6666	−	16.5507i	−0.955022	−	0.551382i
$902$	20.2479	+	15.7019i	0.674183	+	0.522817i
$903$	20.9157	+	5.64933i	0.696032	+	0.187998i
$904$	4.59420	+	14.1395i	0.152801	+	0.470272i
$905$	32.4116	+	72.7976i	1.07740	+	2.41987i
$906$	−10.8618	−	19.6069i	−0.360858	−	0.651397i
$907$	17.0470	−	3.62346i	0.566038	−	0.120315i	0.0840003	−	0.996466i	$-0.473230\pi$
$907$	17.0470	−	3.62346i	0.566038	−	0.120315i	0.482037	+	0.876151i	$0.339897\pi$
$908$	10.3605	+	11.5065i	0.343826	+	0.381857i
$909$	23.9947	+	18.7664i	0.795852	+	0.622442i
$910$	10.5856	−	42.1424i	0.350911	−	1.39701i
$911$	−5.87838	+	1.91000i	−0.194759	+	0.0632811i	−0.404773	−	0.914417i	$-0.632649\pi$
$911$	−5.87838	+	1.91000i	−0.194759	+	0.0632811i	0.210013	+	0.977699i	$0.432649\pi$
$912$	3.75969	−	1.59476i	0.124496	−	0.0528078i
$913$	20.0520	+	2.74428i	0.663625	+	0.0908225i
$914$	−28.4569	+	16.4296i	−0.941272	+	0.543443i
$915$	−12.5270	−	14.4181i	−0.414131	−	0.476649i
$916$	6.80117	−	9.36101i	0.224717	−	0.309296i
$917$	0.453734	−	12.3724i	0.0149836	−	0.408573i
$918$	22.6531	+	18.3728i	0.747663	+	0.606393i
$919$	−1.49093	−	1.65585i	−0.0491812	−	0.0546213i	0.718052	−	0.695989i	$-0.245034\pi$
$919$	−1.49093	−	1.65585i	−0.0491812	−	0.0546213i	−0.767233	+	0.641368i	$0.778367\pi$
$920$	27.4923	+	12.2404i	0.906394	+	0.403553i
$921$	−11.5261	+	12.3539i	−0.379799	+	0.407076i
$922$	0.0298322	−	0.140350i	0.000982472	−	0.00462217i
$923$	27.2858			0.898124
$924$	7.34708	−	13.3049i	0.241701	−	0.437699i
$925$	−59.3523			−1.95149
$926$	4.59442	−	21.6151i	0.150982	−	0.710315i
$927$	−0.210759	−	1.19885i	−0.00692224	−	0.0393754i
$928$	1.79699	+	0.800073i	0.0589892	+	0.0262637i
$929$	−13.2956	−	14.7662i	−0.436214	−	0.484464i	0.484451	−	0.874818i	$-0.339019\pi$
$929$	−13.2956	−	14.7662i	−0.436214	−	0.484464i	−0.920665	+	0.390354i	$0.872353\pi$
$930$	8.52868	+	12.1868i	0.279667	+	0.399622i
$931$	16.2441	+	2.92294i	0.532380	+	0.0957954i
$932$	−9.07280	+	12.4876i	−0.297189	+	0.409046i
$933$	−34.4259	+	29.9106i	−1.12705	+	0.979228i
$934$	−17.0506	+	9.84415i	−0.557912	+	0.322110i
$935$	29.8197	−	61.7043i	0.975209	−	2.01795i
$936$	−12.9850	−	3.24455i	−0.424427	−	0.106052i
$937$	27.5570	−	8.95380i	0.900247	−	0.292508i	0.177908	−	0.984047i	$-0.443067\pi$
$937$	27.5570	−	8.95380i	0.900247	−	0.292508i	0.722339	+	0.691539i	$0.243067\pi$
$938$	21.8104	−	22.5064i	0.712135	−	0.734860i
$939$	42.6573	+	0.755464i	1.39207	+	0.0246536i
$940$	−0.792839	−	0.880537i	−0.0258596	−	0.0287200i
$941$	2.64599	−	0.562423i	0.0862569	−	0.0183345i	−0.164581	−	0.986364i	$-0.552627\pi$
$941$	2.64599	−	0.562423i	0.0862569	−	0.0183345i	0.250838	+	0.968029i	$0.419294\pi$
$942$	−8.43565	+	4.67314i	−0.274848	+	0.152259i
$943$	25.6886	+	57.6975i	0.836535	+	1.87889i
$944$	1.82829	+	5.62688i	0.0595056	+	0.183139i
$945$	43.4446	−	25.9557i	1.41325	−	0.844338i
$946$	−15.6725	−	0.490608i	−0.509556	−	0.0159510i
$947$	−27.1959	−	15.7016i	−0.883748	−	0.510232i	−0.0118553	−	0.999930i	$-0.503774\pi$
$947$	−27.1959	−	15.7016i	−0.883748	−	0.510232i	−0.871892	+	0.489698i	$0.837107\pi$
$948$	−1.56273	−	8.05048i	−0.0507550	−	0.261468i
$949$	−2.77963	+	26.4464i	−0.0902307	+	0.858488i
$950$	−2.10750	−	20.0515i	−0.0683763	−	0.650558i
$951$	16.8742	−	11.8090i	0.547182	−	0.382933i
$952$	−1.01004	−	14.8168i	−0.0327355	−	0.480215i
$953$	−18.5907	−	25.5879i	−0.602212	−	0.828874i	0.393696	−	0.919240i	$-0.371196\pi$
$953$	−18.5907	−	25.5879i	−0.602212	−	0.828874i	−0.995909	+	0.0903667i	$0.971196\pi$
$954$	11.3647	+	13.5580i	0.367946	+	0.438955i
$955$	−69.3185	−	62.4147i	−2.24310	−	2.01969i
$956$	3.81109	−	2.20034i	0.123260	−	0.0711640i
$957$	11.2823	−	0.629280i	0.364706	−	0.0203417i
$958$			13.8765i			0.448330i
$959$	11.2728	+	13.4822i	0.364017	+	0.435364i
$960$	−6.09784	+	1.86260i	−0.196807	+	0.0601150i
$961$	−2.67148	−	25.4174i	−0.0861766	−	0.819916i
$962$	30.2899	−	6.43832i	0.976586	−	0.207580i
$963$	13.0824	−	6.94748i	0.421575	−	0.223879i
$964$	3.17085	−	0.333270i	0.102126	−	0.0107339i
$965$	−74.6118	−	54.2086i	−2.40184	−	1.74504i
$966$	31.4602	−	20.3409i	1.01221	−	0.654458i
$967$	31.8095			1.02292			0.511462	−	0.859306i	$-0.329104\pi$
$967$	31.8095			1.02292			0.511462	+	0.859306i	$0.329104\pi$
$968$	−2.95552	+	10.5955i	−0.0949942	+	0.340553i
$969$	2.79953	−	22.7524i	0.0899340	−	0.730913i
$970$	31.3460	−	34.8132i	1.00646	−	1.11779i
$971$	−19.5745	+	8.71513i	−0.628176	+	0.279682i	−0.696029	−	0.718013i	$-0.745052\pi$
$971$	−19.5745	+	8.71513i	−0.628176	+	0.279682i	0.0678535	+	0.997695i	$0.478385\pi$
$972$	−8.01161	−	13.3721i	−0.256972	−	0.428912i
$973$	−31.4037	−	15.3847i	−1.00676	−	0.493211i
$974$	−5.63116	−	1.82968i	−0.180434	−	0.0586266i
$975$	−34.0463	+	56.6299i	−1.09036	+	1.81361i
$976$	2.97921	+	0.313128i	0.0953623	+	0.0100230i
$977$	7.21318	+	6.49478i	0.230770	+	0.207786i	0.776401	−	0.630239i	$-0.217043\pi$
$977$	7.21318	+	6.49478i	0.230770	+	0.207786i	−0.545631	+	0.838026i	$0.683710\pi$
$978$	−30.8033	+	13.0660i	−0.984982	+	0.417804i
$979$	−1.35599	−	0.488000i	−0.0433377	−	0.0155965i
$980$	−24.7449	−	7.18931i	−0.790447	−	0.229654i
$981$	30.9966	−	20.8845i	0.989647	−	0.666791i
$982$	32.3446	−	14.4008i	1.03216	−	0.459547i
$983$	−51.4935	−	22.9264i	−1.64239	−	0.731237i	−0.642986	−	0.765878i	$-0.722305\pi$
$983$	−51.4935	−	22.9264i	−1.64239	−	0.731237i	−0.999400	+	0.0346401i	$0.988971\pi$
$984$	−12.1259	−	5.65819i	−0.386561	−	0.180376i
$985$	22.4398	−	20.2049i	0.714992	−	0.643781i
$986$	8.93277	−	6.49004i	0.284477	−	0.206685i
$987$	−1.45732	+	0.227823i	−0.0463871	+	0.00725169i
$988$	3.25066	+	10.0045i	0.103417	+	0.318286i
$989$	−33.4719	−	19.3250i	−1.06434	−	0.614500i
$990$	−26.2683	+	25.5250i	−0.834860	+	0.811237i
$991$	−27.6620	−	47.9120i	−0.878712	−	1.52197i	−0.852755	−	0.522311i	$-0.825070\pi$
$991$	−27.6620	−	47.9120i	−0.878712	−	1.52197i	−0.0259571	−	0.999663i	$-0.508263\pi$
$992$	−2.28196	−	0.485045i	−0.0724522	−	0.0154002i
$993$	−17.6935	+	5.40452i	−0.561487	+	0.171507i
$994$	0.593020	−	16.1705i	0.0188095	−	0.512897i
$995$	38.6058	+	12.5438i	1.22389	+	0.397665i
$996$	−10.5294	+	0.918502i	−0.333638	+	0.0291039i
$997$	−17.9424	+	40.2992i	−0.568241	+	1.27629i	0.369589	+	0.929195i	$0.379498\pi$
$997$	−17.9424	+	40.2992i	−0.568241	+	1.27629i	−0.937830	+	0.347095i	$0.887168\pi$
$998$	6.04387	+	0.635236i	0.191315	+	0.0201081i
$999$	30.2329	+	19.6664i	0.956527	+	0.622217i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.bf.a.5.5	✓	256
3.2	odd	2	inner	462.2.bf.a.5.19	yes	256
7.3	odd	6	inner	462.2.bf.a.269.10	yes	256
11.9	even	5	inner	462.2.bf.a.383.19	yes	256
21.17	even	6	inner	462.2.bf.a.269.19	yes	256
33.20	odd	10	inner	462.2.bf.a.383.10	yes	256
77.31	odd	30	inner	462.2.bf.a.185.19	yes	256
231.185	even	30	inner	462.2.bf.a.185.5	yes	256

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.bf.a.5.5	✓	256	1.1	even	1	trivial
462.2.bf.a.5.19	yes	256	3.2	odd	2	inner
462.2.bf.a.185.5	yes	256	231.185	even	30	inner
462.2.bf.a.185.19	yes	256	77.31	odd	30	inner
462.2.bf.a.269.10	yes	256	7.3	odd	6	inner
462.2.bf.a.269.19	yes	256	21.17	even	6	inner
462.2.bf.a.383.10	yes	256	33.20	odd	10	inner
462.2.bf.a.383.19	yes	256	11.9	even	5	inner

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:	\( N \)	\(=\)	\( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	462.bf (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.207912 + 0.978148i) q^{2} +(-1.26644 - 1.18158i) q^{3} +(-0.913545 - 0.406737i) q^{4} +(2.46318 + 2.73564i) q^{5} +(1.41907 - 0.993102i) q^{6} +(2.33823 - 1.23802i) q^{7} +(0.587785 - 0.809017i) q^{8} +(0.207743 + 2.99280i) q^{9} +O(q^{10})\)	\(q+(-0.207912 + 0.978148i) q^{2} +(-1.26644 - 1.18158i) q^{3} +(-0.913545 - 0.406737i) q^{4} +(2.46318 + 2.73564i) q^{5} +(1.41907 - 0.993102i) q^{6} +(2.33823 - 1.23802i) q^{7} +(0.587785 - 0.809017i) q^{8} +(0.207743 + 2.99280i) q^{9} +(-3.18798 + 1.84058i) q^{10} +(-0.587723 - 3.26414i) q^{11} +(0.676360 + 1.59453i) q^{12} +(-4.24304 + 1.37865i) q^{13} +(0.724816 + 2.54453i) q^{14} +(0.112901 - 6.37496i) q^{15} +(0.669131 + 0.743145i) q^{16} +(5.49056 - 1.16705i) q^{17} +(-2.97059 - 0.419034i) q^{18} +(0.959028 + 2.15401i) q^{19} +(-1.13754 - 3.50099i) q^{20} +(-4.42404 - 1.19493i) q^{21} +(3.31500 + 0.103772i) q^{22} +(7.07989 + 4.08758i) q^{23} +(-1.70031 + 0.330057i) q^{24} +(-0.893819 + 8.50412i) q^{25} +(-0.466343 - 4.43696i) q^{26} +(3.27313 - 4.03567i) q^{27} +(-2.63963 + 0.179939i) q^{28} +(-1.15621 - 1.59138i) q^{29} +(6.21218 + 1.43586i) q^{30} +(1.73371 + 1.56104i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(-3.11252 + 4.82827i) q^{33} +5.61322i q^{34} +(9.14624 + 3.34710i) q^{35} +(1.02750 - 2.81855i) q^{36} +(0.725533 + 6.90299i) q^{37} +(-2.30633 + 0.490227i) q^{38} +(7.00254 + 3.26751i) q^{39} +(3.66100 - 0.384786i) q^{40} +(6.25012 + 4.54098i) q^{41} +(2.08863 - 4.07893i) q^{42} -4.72775 q^{43} +(-0.790732 + 3.22098i) q^{44} +(-7.67550 + 7.94011i) q^{45} +(-5.47024 + 6.07532i) q^{46} +(0.294049 - 0.130919i) q^{47} +(0.0306700 - 1.73178i) q^{48} +(3.93464 - 5.78953i) q^{49} +(-8.13245 - 2.64239i) q^{50} +(-8.33243 - 5.00952i) q^{51} +(4.43696 + 0.466343i) q^{52} +(-4.38235 - 3.94588i) q^{53} +(3.26695 + 4.04067i) q^{54} +(7.48183 - 9.64795i) q^{55} +(0.372802 - 2.61935i) q^{56} +(1.33058 - 3.86110i) q^{57} +(1.79699 - 0.800073i) q^{58} +(5.40495 + 2.40644i) q^{59} +(-2.69607 + 5.77790i) q^{60} +(2.22618 - 2.00446i) q^{61} +(-1.88739 + 1.37127i) q^{62} +(4.19088 + 6.74066i) q^{63} +(-0.309017 - 0.951057i) q^{64} +(-14.2229 - 8.21157i) q^{65} +(-4.07564 - 4.04836i) q^{66} +(-5.92281 - 10.2586i) q^{67} +(-5.49056 - 1.16705i) q^{68} +(-4.13647 - 13.5421i) q^{69} +(-5.17556 + 8.25047i) q^{70} +(-5.81664 - 1.88994i) q^{71} +(2.54333 + 1.59105i) q^{72} +(2.42435 - 5.44517i) q^{73} +(-6.90299 - 0.725533i) q^{74} +(11.1803 - 9.71385i) q^{75} -2.35786i q^{76} +(-5.41528 - 6.90469i) q^{77} +(-4.65202 + 6.17017i) q^{78} +(-4.63124 - 0.984401i) q^{79} +(-0.384786 + 3.66100i) q^{80} +(-8.91369 + 1.24347i) q^{81} +(-5.74122 + 5.16942i) q^{82} +(-1.88570 + 5.80360i) q^{83} +(3.55554 + 2.89104i) q^{84} +(16.7169 + 12.1455i) q^{85} +(0.982954 - 4.62443i) q^{86} +(-0.416076 + 3.38154i) q^{87} +(-2.98620 - 1.44313i) q^{88} +(0.217259 - 0.376303i) q^{89} +(-6.17077 - 9.15862i) q^{90} +(-8.21442 + 8.47655i) q^{91} +(-4.80523 - 6.61384i) q^{92} +(-0.351150 - 4.02548i) q^{93} +(0.0669219 + 0.314843i) q^{94} +(-3.53034 + 7.92927i) q^{95} +(1.68756 + 0.390057i) q^{96} +(-12.1030 + 3.93249i) q^{97} +(4.84496 + 5.05237i) q^{98} +(9.64680 - 2.43704i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 256 q - 32 q^{4} + 4 q^{7} - 12 q^{9}+O(q^{10}) \) 256 * q - 32 * q^4 + 4 * q^7 - 12 * q^9	\( 256 q - 32 q^{4} + 4 q^{7} - 12 q^{9} + 12 q^{10} + 24 q^{15} + 32 q^{16} - 8 q^{18} - 16 q^{21} - 12 q^{22} + 48 q^{25} + 6 q^{28} + 18 q^{31} - 132 q^{33} + 16 q^{36} + 4 q^{37} - 18 q^{40} - 4 q^{42} + 64 q^{43} - 48 q^{45} + 8 q^{46} + 76 q^{49} - 8 q^{51} - 88 q^{57} + 46 q^{58} - 8 q^{60} - 12 q^{63} + 64 q^{64} - 120 q^{66} - 32 q^{67} - 58 q^{70} - 12 q^{72} - 96 q^{73} - 204 q^{75} - 32 q^{78} - 4 q^{79} - 64 q^{81} + 24 q^{82} - 36 q^{84} + 232 q^{85} - 228 q^{87} - 6 q^{88} + 40 q^{91} - 2 q^{93} - 144 q^{94} + 160 q^{99}+O(q^{100}) \) 256 * q - 32 * q^4 + 4 * q^7 - 12 * q^9 + 12 * q^10 + 24 * q^15 + 32 * q^16 - 8 * q^18 - 16 * q^21 - 12 * q^22 + 48 * q^25 + 6 * q^28 + 18 * q^31 - 132 * q^33 + 16 * q^36 + 4 * q^37 - 18 * q^40 - 4 * q^42 + 64 * q^43 - 48 * q^45 + 8 * q^46 + 76 * q^49 - 8 * q^51 - 88 * q^57 + 46 * q^58 - 8 * q^60 - 12 * q^63 + 64 * q^64 - 120 * q^66 - 32 * q^67 - 58 * q^70 - 12 * q^72 - 96 * q^73 - 204 * q^75 - 32 * q^78 - 4 * q^79 - 64 * q^81 + 24 * q^82 - 36 * q^84 + 232 * q^85 - 228 * q^87 - 6 * q^88 + 40 * q^91 - 2 * q^93 - 144 * q^94 + 160 * q^99

Introduction

L-functions

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