LMFDB - Embedded newform 245.2.x.a.103.23

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [245,2,Mod(3,245)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(245, base_ring=CyclotomicField(84)) chi = DirichletCharacter(H, H._module([63, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("245.3"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 245 = 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	245.x (of order $84$, degree $24$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$1.95633484952$
Analytic rank:	$0$
Dimension:	$624$
Relative dimension:	$26$ over $\Q(\zeta_{84})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{84}]$

Embedding invariants

Embedding label			103.23
Character	$\chi$	$=$	245.103
Dual form			245.2.x.a.157.23

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.25589 - 1.70168i) q^{2} +(-1.93387 + 0.365908i) q^{3} +(-0.728921 - 2.36310i) q^{4} +(-1.72957 - 1.41725i) q^{5} +(-1.80608 + 3.75036i) q^{6} +(-2.39971 - 1.11418i) q^{7} +(-0.944171 - 0.330380i) q^{8} +(0.813339 - 0.319212i) q^{9} +(-4.58385 + 1.16325i) q^{10} +(0.0928530 - 0.236585i) q^{11} +(2.27432 + 4.30321i) q^{12} +(-2.22965 - 0.251221i) q^{13} +(-4.90975 + 2.68423i) q^{14} +(3.86334 + 2.10791i) q^{15} +(2.33855 - 1.59440i) q^{16} +(-3.82813 - 0.143238i) q^{17} +(0.478272 - 1.78494i) q^{18} +(1.87492 - 3.24746i) q^{19} +(-2.08838 + 5.12021i) q^{20} +(5.04841 + 1.27661i) q^{21} +(-0.285978 - 0.455132i) q^{22} +(-0.169500 - 4.52997i) q^{23} +(1.94679 + 0.293432i) q^{24} +(0.982817 + 4.90246i) q^{25} +(-3.22770 + 3.47863i) q^{26} +(3.54343 - 2.22649i) q^{27} +(-0.883728 + 6.48291i) q^{28} +(-0.249778 + 0.0570102i) q^{29} +(8.43893 - 3.92684i) q^{30} +(6.33821 - 3.65937i) q^{31} +(0.298630 - 7.98106i) q^{32} +(-0.0929970 + 0.491501i) q^{33} +(-5.05147 + 6.33434i) q^{34} +(2.57139 + 5.32803i) q^{35} +(-1.34719 - 1.68932i) q^{36} +(0.555290 - 0.293479i) q^{37} +(-3.17142 - 7.26897i) q^{38} +(4.40377 - 0.330017i) q^{39} +(1.16478 + 1.90954i) q^{40} +(-3.39316 - 7.04597i) q^{41} +(8.51264 - 6.98747i) q^{42} +(0.0831519 + 0.237634i) q^{43} +(-0.626758 - 0.0469691i) q^{44} +(-1.85913 - 0.600604i) q^{45} +(-7.92142 - 5.40073i) q^{46} +(7.95053 + 5.86776i) q^{47} +(-3.93905 + 3.93905i) q^{48} +(4.51720 + 5.34742i) q^{49} +(9.57670 + 4.48453i) q^{50} +(7.45551 - 1.12374i) q^{51} +(1.03158 + 5.45201i) q^{52} +(-9.66117 - 5.10608i) q^{53} +(0.661417 - 8.82600i) q^{54} +(-0.495896 + 0.277595i) q^{55} +(1.89763 + 1.84479i) q^{56} +(-2.43758 + 6.96621i) q^{57} +(-0.216682 + 0.496640i) q^{58} +(0.928629 + 12.3917i) q^{59} +(2.16514 - 10.6660i) q^{60} +(-2.88820 + 9.36330i) q^{61} +(1.73306 - 15.3814i) q^{62} +(-2.30744 - 0.140191i) q^{63} +(-8.78041 - 7.00214i) q^{64} +(3.50029 + 3.59447i) q^{65} +(0.719581 + 0.775524i) q^{66} +(-11.0191 - 2.95256i) q^{67} +(2.45192 + 9.15067i) q^{68} +(1.98534 + 8.69835i) q^{69} +(12.2960 + 2.31578i) q^{70} +(2.31287 - 10.1333i) q^{71} +(-0.873392 + 0.0326800i) q^{72} +(0.123161 - 0.0908966i) q^{73} +(0.197979 - 1.31350i) q^{74} +(-3.69449 - 9.12109i) q^{75} +(-9.04075 - 2.06349i) q^{76} +(-0.486419 + 0.464281i) q^{77} +(4.96909 - 7.90826i) q^{78} +(-0.348481 - 0.201196i) q^{79} +(-6.30434 - 0.556687i) q^{80} +(-7.95933 + 7.38518i) q^{81} +(-16.2514 - 3.07493i) q^{82} +(-1.84272 - 16.3546i) q^{83} +(-0.663132 - 12.8605i) q^{84} +(6.41801 + 5.67315i) q^{85} +(0.508807 + 0.156946i) q^{86} +(0.462178 - 0.201646i) q^{87} +(-0.165832 + 0.192700i) q^{88} +(-0.234099 - 0.596475i) q^{89} +(-3.35690 + 2.40934i) q^{90} +(5.07060 + 3.08709i) q^{91} +(-10.5812 + 3.70254i) q^{92} +(-10.9183 + 9.39594i) q^{93} +(19.9700 - 6.15994i) q^{94} +(-7.84526 + 2.95948i) q^{95} +(2.34282 + 15.5436i) q^{96} +(-0.348307 - 0.348307i) q^{97} +(14.7727 - 0.971017i) q^{98} -0.222064i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 624 q - 26 q^{2} - 22 q^{3} - 28 q^{5} - 28 q^{6} - 18 q^{7} - 24 q^{8} - 34 q^{10} - 56 q^{11} - 34 q^{12} - 28 q^{13} + 12 q^{15} - 100 q^{16} - 26 q^{17} - 10 q^{18} - 28 q^{20} - 76 q^{21} - 48 q^{22}+ \cdots + 304 q^{98}+O(q^{100}) $ 624 * q - 26 * q^2 - 22 * q^3 - 28 * q^5 - 28 * q^6 - 18 * q^7 - 24 * q^8 - 34 * q^10 - 56 * q^11 - 34 * q^12 - 28 * q^13 + 12 * q^15 - 100 * q^16 - 26 * q^17 - 10 * q^18 - 28 * q^20 - 76 * q^21 - 48 * q^22 - 34 * q^23 - 24 * q^25 - 60 * q^26 - 28 * q^27 - 46 * q^28 - 10 * q^30 - 60 * q^31 + 54 * q^32 - 28 * q^33 - 20 * q^35 + 116 * q^36 - 20 * q^37 + 12 * q^38 - 46 * q^40 - 114 * q^42 - 24 * q^43 + 60 * q^45 + 108 * q^46 - 94 * q^47 - 296 * q^50 + 52 * q^51 - 52 * q^52 - 106 * q^53 + 14 * q^55 + 96 * q^56 + 72 * q^57 - 142 * q^58 - 26 * q^60 + 80 * q^61 - 56 * q^62 - 24 * q^63 - 20 * q^65 - 240 * q^66 - 8 * q^67 - 30 * q^68 + 180 * q^70 + 48 * q^71 + 138 * q^72 - 4 * q^73 - 106 * q^75 + 56 * q^76 - 8 * q^77 - 204 * q^78 - 18 * q^80 - 284 * q^81 - 162 * q^82 + 182 * q^83 - 36 * q^85 - 76 * q^86 - 74 * q^87 + 288 * q^88 - 112 * q^90 + 44 * q^91 - 8 * q^92 + 368 * q^93 + 26 * q^95 + 136 * q^96 + 304 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/245\mathbb{Z}\right)^\times$.

$n$	$101$	$197$
$\chi(n)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	1.25589	−	1.70168i	0.888051	−	1.20327i	−0.0902168	−	0.995922i	$-0.528756\pi$
$2$	1.25589	−	1.70168i	0.888051	−	1.20327i	0.978268	−	0.207344i	$-0.0664821\pi$
$3$	−1.93387	+	0.365908i	−1.11652	+	0.211257i	−0.711249	−	0.702940i	$-0.751870\pi$
$3$	−1.93387	+	0.365908i	−1.11652	+	0.211257i	−0.405270	+	0.914197i	$0.632823\pi$
$4$	−0.728921	−	2.36310i	−0.364460	−	1.18155i
$5$	−1.72957	−	1.41725i	−0.773487	−	0.633813i
$5$	−1.72957	−	1.41725i	−0.773487	−	0.633813i
$6$	−1.80608	+	3.75036i	−0.737328	+	1.53108i
$7$	−2.39971	−	1.11418i	−0.907004	−	0.421121i
$7$	−2.39971	−	1.11418i	−0.907004	−	0.421121i
$8$	−0.944171	−	0.330380i	−0.333815	−	0.116807i
$9$	0.813339	−	0.319212i	0.271113	−	0.106404i
$10$	−4.58385	+	1.16325i	−1.44954	+	0.367853i
$11$	0.0928530	−	0.236585i	0.0279962	−	0.0713332i	−0.916192	−	0.400739i	$-0.868753\pi$
$11$	0.0928530	−	0.236585i	0.0279962	−	0.0713332i	0.944188	+	0.329406i	$0.106849\pi$
$12$	2.27432	+	4.30321i	0.656538	+	1.24223i
$13$	−2.22965	−	0.251221i	−0.618394	−	0.0696762i	−0.202790	−	0.979222i	$-0.565001\pi$
$13$	−2.22965	−	0.251221i	−0.618394	−	0.0696762i	−0.415603	+	0.909546i	$0.636430\pi$
$14$	−4.90975	+	2.68423i	−1.31219	+	0.717391i
$15$	3.86334	+	2.10791i	0.997510	+	0.544260i
$16$	2.33855	−	1.59440i	0.584638	−	0.398599i
$17$	−3.82813	−	0.143238i	−0.928457	−	0.0347404i	−0.431117	−	0.902296i	$-0.641880\pi$
$17$	−3.82813	−	0.143238i	−0.928457	−	0.0347404i	−0.497340	+	0.867556i	$0.665690\pi$
$18$	0.478272	−	1.78494i	0.112730	−	0.420713i
$19$	1.87492	−	3.24746i	0.430136	−	0.745018i	−0.566748	−	0.823891i	$-0.691799\pi$
$19$	1.87492	−	3.24746i	0.430136	−	0.745018i	0.996885	+	0.0788729i	$0.0251321\pi$
$20$	−2.08838	+	5.12021i	−0.466977	+	1.14491i
$21$	5.04841	+	1.27661i	1.10165	+	0.278579i
$22$	−0.285978	−	0.455132i	−0.0609708	−	0.0970344i
$23$	−0.169500	−	4.52997i	−0.0353431	−	0.944565i	−0.898326	−	0.439331i	$-0.855216\pi$
$23$	−0.169500	−	4.52997i	−0.0353431	−	0.944565i	0.862982	−	0.505234i	$-0.168594\pi$
$24$	1.94679	+	0.293432i	0.397387	+	0.0598965i
$25$	0.982817	+	4.90246i	0.196563	+	0.980491i
$26$	−3.22770	+	3.47863i	−0.633004	+	0.682216i
$27$	3.54343	−	2.22649i	0.681934	−	0.428487i
$28$	−0.883728	+	6.48291i	−0.167009	+	1.22515i
$29$	−0.249778	+	0.0570102i	−0.0463826	+	0.0105865i	−0.245649	−	0.969359i	$-0.579001\pi$
$29$	−0.249778	+	0.0570102i	−0.0463826	+	0.0105865i	0.199267	+	0.979945i	$0.436144\pi$
$30$	8.43893	−	3.92684i	1.54073	−	0.716940i
$31$	6.33821	−	3.65937i	1.13838	−	0.657242i	0.192348	−	0.981327i	$-0.438390\pi$
$31$	6.33821	−	3.65937i	1.13838	−	0.657242i	0.946028	+	0.324085i	$0.105056\pi$
$32$	0.298630	−	7.98106i	0.0527909	−	1.41087i
$33$	−0.0929970	+	0.491501i	−0.0161887	+	0.0855593i
$34$	−5.05147	+	6.33434i	−0.866320	+	1.08633i
$35$	2.57139	+	5.32803i	0.434644	+	0.900602i
$36$	−1.34719	−	1.68932i	−0.224532	−	0.281554i
$37$	0.555290	−	0.293479i	0.0912891	−	0.0482477i	−0.421001	−	0.907060i	$-0.638321\pi$
$37$	0.555290	−	0.293479i	0.0912891	−	0.0482477i	0.512290	+	0.858813i	$0.328797\pi$
$38$	−3.17142	−	7.26897i	−0.514472	−	1.17918i
$39$	4.40377	−	0.330017i	0.705168	−	0.0528451i
$40$	1.16478	+	1.90954i	0.184168	+	0.301925i
$41$	−3.39316	−	7.04597i	−0.529923	−	1.10040i	−0.978423	−	0.206613i	$-0.933756\pi$
$41$	−3.39316	−	7.04597i	−0.529923	−	1.10040i	0.448500	−	0.893783i	$-0.351958\pi$
$42$	8.51264	−	6.98747i	1.31353	−	1.07819i
$43$	0.0831519	+	0.237634i	0.0126805	+	0.0362389i	0.950050	−	0.312099i	$-0.101032\pi$
$43$	0.0831519	+	0.237634i	0.0126805	+	0.0362389i	−0.937369	+	0.348338i	$0.886746\pi$
$44$	−0.626758	−	0.0469691i	−0.0944874	−	0.00708085i
$45$	−1.85913	−	0.600604i	−0.277143	−	0.0895327i
$46$	−7.92142	−	5.40073i	−1.16795	−	0.796294i
$47$	7.95053	+	5.86776i	1.15970	+	0.855900i	0.991533	−	0.129857i	$-0.0414520\pi$
$47$	7.95053	+	5.86776i	1.15970	+	0.855900i	0.168171	+	0.985758i	$0.446214\pi$
$48$	−3.93905	+	3.93905i	−0.568553	+	0.568553i
$49$	4.51720	+	5.34742i	0.645314	+	0.763917i
$50$	9.57670	+	4.48453i	1.35435	+	0.634208i
$51$	7.45551	−	1.12374i	1.04398	−	0.157355i
$52$	1.03158	+	5.45201i	0.143054	+	0.756058i
$53$	−9.66117	−	5.10608i	−1.32706	−	0.701374i	−0.354730	−	0.934969i	$-0.615427\pi$
$53$	−9.66117	−	5.10608i	−1.32706	−	0.701374i	−0.972334	+	0.233595i	$0.924951\pi$
$54$	0.661417	−	8.82600i	0.0900075	−	1.20107i
$55$	−0.495896	+	0.277595i	−0.0668666	+	0.0374309i
$56$	1.89763	+	1.84479i	0.253582	+	0.246521i
$57$	−2.43758	+	6.96621i	−0.322866	+	0.922697i
$58$	−0.216682	+	0.496640i	−0.0284517	+	0.0652120i
$59$	0.928629	+	12.3917i	0.120897	+	1.61326i	0.646761	+	0.762693i	$0.276123\pi$
$59$	0.928629	+	12.3917i	0.120897	+	1.61326i	−0.525864	+	0.850569i	$0.676258\pi$
$60$	2.16514	−	10.6660i	0.279518	−	1.37697i
$61$	−2.88820	+	9.36330i	−0.369796	+	1.19885i	0.559287	+	0.828974i	$0.311075\pi$
$61$	−2.88820	+	9.36330i	−0.369796	+	1.19885i	−0.929082	+	0.369873i	$0.879401\pi$
$62$	1.73306	−	15.3814i	0.220099	−	1.95343i
$63$	−2.30744	−	0.140191i	−0.290710	−	0.0176625i
$64$	−8.78041	−	7.00214i	−1.09755	−	0.875267i
$65$	3.50029	+	3.59447i	0.434158	+	0.445839i
$66$	0.719581	+	0.775524i	0.0885743	+	0.0954604i
$67$	−11.0191	−	2.95256i	−1.34620	−	0.360713i	−0.487468	−	0.873141i	$-0.662079\pi$
$67$	−11.0191	−	2.95256i	−1.34620	−	0.360713i	−0.858730	+	0.512428i	$0.828746\pi$
$68$	2.45192	+	9.15067i	0.297338	+	1.10968i
$69$	1.98534	+	8.69835i	0.239007	+	1.04716i
$70$	12.2960	+	2.31578i	1.46965	+	0.276788i
$71$	2.31287	−	10.1333i	0.274487	−	1.20261i	−0.630168	−	0.776459i	$-0.717014\pi$
$71$	2.31287	−	10.1333i	0.274487	−	1.20261i	0.904654	−	0.426146i	$-0.140129\pi$
$72$	−0.873392	+	0.0326800i	−0.102930	+	0.00385138i
$73$	0.123161	−	0.0908966i	0.0144148	−	0.0106386i	−0.586589	−	0.809885i	$-0.699530\pi$
$73$	0.123161	−	0.0908966i	0.0144148	−	0.0106386i	0.601004	+	0.799246i	$0.294768\pi$
$74$	0.197979	−	1.31350i	0.0230145	−	0.152691i
$75$	−3.69449	−	9.12109i	−0.426602	−	1.05321i
$76$	−9.04075	−	2.06349i	−1.03705	−	0.236699i
$77$	−0.486419	+	0.464281i	−0.0554326	+	0.0529097i
$78$	4.96909	−	7.90826i	0.562639	−	0.895435i
$79$	−0.348481	−	0.201196i	−0.0392072	−	0.0226363i	0.480268	−	0.877122i	$-0.340539\pi$
$79$	−0.348481	−	0.201196i	−0.0392072	−	0.0226363i	−0.519475	+	0.854485i	$0.673873\pi$
$80$	−6.30434	−	0.556687i	−0.704847	−	0.0622395i
$81$	−7.95933	+	7.38518i	−0.884370	+	0.820575i
$82$	−16.2514	−	3.07493i	−1.79467	−	0.339569i
$83$	−1.84272	−	16.3546i	−0.202264	−	1.79515i	−0.527543	−	0.849529i	$-0.676887\pi$
$83$	−1.84272	−	16.3546i	−0.202264	−	1.79515i	0.325278	−	0.945618i	$-0.394542\pi$
$84$	−0.663132	−	12.8605i	−0.0723536	−	1.40319i
$85$	6.41801	+	5.67315i	0.696131	+	0.615339i
$86$	0.508807	+	0.156946i	0.0548660	+	0.0169239i
$87$	0.462178	−	0.201646i	0.0495506	−	0.0216187i
$88$	−0.165832	+	0.192700i	−0.0176778	+	0.0205419i
$89$	−0.234099	−	0.596475i	−0.0248145	−	0.0632262i	0.917930	−	0.396743i	$-0.129860\pi$
$89$	−0.234099	−	0.596475i	−0.0248145	−	0.0632262i	−0.942744	+	0.333517i	$0.891764\pi$
$90$	−3.35690	+	2.40934i	−0.353849	+	0.253967i
$91$	5.07060	+	3.08709i	0.531544	+	0.323615i
$92$	−10.5812	+	3.70254i	−1.10317	+	0.386016i
$93$	−10.9183	+	9.39594i	−1.13217	+	0.974313i
$94$	19.9700	−	6.15994i	2.05975	−	0.635350i
$95$	−7.84526	+	2.95948i	−0.804907	+	0.303636i
$96$	2.34282	+	15.5436i	0.239113	+	1.58641i
$97$	−0.348307	−	0.348307i	−0.0353652	−	0.0353652i	0.689203	−	0.724568i	$-0.257961\pi$
$97$	−0.348307	−	0.348307i	−0.0353652	−	0.0353652i	−0.724568	+	0.689203i	$0.757961\pi$
$98$	14.7727	−	0.971017i	1.49227	−	0.0980875i
$99$		−	0.222064i		−	0.0223183i
$100$	10.8686	−	5.89600i	1.08686	−	0.589600i
$101$	−0.571120	+	0.837680i	−0.0568286	+	0.0833522i	−0.853601	−	0.520927i	$-0.825586\pi$
$101$	−0.571120	+	0.837680i	−0.0568286	+	0.0833522i	0.796773	+	0.604279i	$0.206539\pi$
$102$	7.45109	−	14.0982i	0.737768	−	1.39593i
$103$	6.65184	+	7.72958i	0.655426	+	0.761618i	0.983080	−	0.183179i	$-0.0586389\pi$
$103$	6.65184	+	7.72958i	0.655426	+	0.761618i	−0.327654	+	0.944798i	$0.606258\pi$
$104$	2.02217	+	0.973827i	0.198290	+	0.0954916i
$105$	−6.92230	−	9.36283i	−0.675547	−	0.913719i
$106$	−20.8223	+	10.0275i	−2.02244	+	0.973956i
$107$	−5.42844	−	2.36840i	−0.524787	−	0.228962i	0.120761	−	0.992682i	$-0.461466\pi$
$107$	−5.42844	−	2.36840i	−0.524787	−	0.228962i	−0.645549	+	0.763719i	$0.723371\pi$
$108$	−7.84430	−	6.75056i	−0.754818	−	0.649573i
$109$	9.15062	+	3.59135i	0.876471	+	0.343989i	0.760558	−	0.649270i	$-0.224925\pi$
$109$	9.15062	+	3.59135i	0.876471	+	0.343989i	0.115913	+	0.993259i	$0.463021\pi$
$110$	−0.150416	+	1.19248i	−0.0143416	+	0.113699i
$111$	−0.966471	+	0.770735i	−0.0917334	+	0.0731549i
$112$	−7.38829	+	1.22052i	−0.698127	+	0.115328i
$113$	−4.77605	+	0.538131i	−0.449293	+	0.0506231i	−0.333712	−	0.942675i	$-0.608301\pi$
$113$	−4.77605	+	0.538131i	−0.449293	+	0.0506231i	−0.115580	+	0.993298i	$0.536873\pi$
$114$	8.79288	+	12.8968i	0.823529	+	1.20790i
$115$	−6.12693	+	8.07512i	−0.571339	+	0.753009i
$116$	0.316789	+	0.548695i	0.0294132	+	0.0509451i
$117$	−1.89365	+	0.507403i	−0.175068	+	0.0469094i
$118$	22.2529	+	13.9824i	2.04855	+	1.28719i
$119$	9.02680	+	4.60896i	0.827485	+	0.422503i
$120$	−2.95124	−	3.26660i	−0.269411	−	0.298198i
$121$	8.01622	+	7.43796i	0.728747	+	0.676179i
$122$	12.3060	+	16.6741i	1.11414	+	1.50960i
$123$	9.14010	+	12.3844i	0.824135	+	1.11666i
$124$	−13.2675	−	12.3105i	−1.19146	−	1.10551i
$125$	5.24815	−	9.87203i	0.469408	−	0.882981i
$126$	−3.13646	+	3.75044i	−0.279418	+	0.334116i
$127$	17.2303	+	10.8265i	1.52895	+	0.960700i	0.993213	+	0.116313i	$0.0371076\pi$
$127$	17.2303	+	10.8265i	1.52895	+	0.960700i	0.535733	+	0.844387i	$0.320035\pi$
$128$	−7.51362	+	2.01327i	−0.664116	+	0.177949i
$129$	−0.247757	−	0.429128i	−0.0218138	−	0.0377826i
$130$	10.5126	−	1.44209i	0.922018	−	0.126479i
$131$	−4.56780	−	6.69973i	−0.399090	−	0.585358i	0.573119	−	0.819472i	$-0.305733\pi$
$131$	−4.56780	−	6.69973i	−0.399090	−	0.585358i	−0.972209	+	0.234114i	$0.924781\pi$
$132$	1.22926	−	0.138504i	0.106993	−	0.0120552i
$133$	−8.11752	+	5.70395i	−0.703878	+	0.494595i
$134$	−18.8631	+	15.0428i	−1.62953	+	1.29950i
$135$	−9.28409	−	1.17106i	−0.799047	−	0.100789i
$136$	3.56708	+	1.39998i	0.305875	+	0.120047i
$137$	13.6011	+	11.7047i	1.16202	+	0.999997i	0.999913	+	0.0132231i	$0.00420916\pi$
$137$	13.6011	+	11.7047i	1.16202	+	0.999997i	0.162105	+	0.986774i	$0.448172\pi$
$138$	17.2952	+	7.54580i	1.47226	+	0.642341i
$139$	−3.08412	+	1.48523i	−0.261591	+	0.125976i	−0.560083	−	0.828436i	$-0.689231\pi$
$139$	−3.08412	+	1.48523i	−0.261591	+	0.125976i	0.298492	+	0.954412i	$0.403517\pi$
$140$	10.7164	−	9.96018i	0.905698	−	0.841789i
$141$	−17.5223	−	8.43831i	−1.47565	−	0.710634i
$142$	−14.3389	−	16.6621i	−1.20330	−	1.39826i
$143$	−0.266465	+	0.504176i	−0.0222829	+	0.0421613i
$144$	1.39308	−	2.04328i	0.116090	−	0.170273i
$145$	0.512806	+	0.255394i	0.0425862	+	0.0212093i
$146$		−	0.323736i		−	0.0267926i
$147$	−10.6923	−	8.68833i	−0.881889	−	0.716602i
$148$	−1.09828	−	1.09828i	−0.0902784	−	0.0902784i
$149$	−3.39917	−	22.5520i	−0.278470	−	1.84753i	−0.492001	−	0.870594i	$-0.663734\pi$
$149$	−3.39917	−	22.5520i	−0.278470	−	1.84753i	0.213531	−	0.976936i	$-0.431504\pi$
$150$	−20.1610	−	5.16830i	−1.64614	−	0.421990i
$151$	8.61664	−	2.65788i	0.701212	−	0.216295i	0.0764079	−	0.997077i	$-0.475655\pi$
$151$	8.61664	−	2.65788i	0.701212	−	0.216295i	0.624804	+	0.780781i	$0.285179\pi$
$152$	−2.84314	+	2.44672i	−0.230609	+	0.198455i
$153$	−3.15929	+	1.10548i	−0.255413	+	0.0893730i
$154$	0.179165	+	1.41082i	0.0144375	+	0.113687i
$155$	−16.1486	−	2.65369i	−1.29709	−	0.213149i
$156$	−3.98987	−	10.1660i	−0.319445	−	0.813933i
$157$	4.28267	−	4.97655i	0.341794	−	0.397172i	−0.560598	−	0.828088i	$-0.689429\pi$
$157$	4.28267	−	4.97655i	0.341794	−	0.397172i	0.902392	+	0.430916i	$0.141810\pi$
$158$	−0.780025	+	0.340321i	−0.0620554	+	0.0270745i
$159$	20.5518	+	6.33939i	1.62986	+	0.502746i
$160$	−11.8276	+	13.3806i	−0.935057	+	1.05783i
$161$	−4.64046	+	11.0595i	−0.365720	+	0.871608i
$162$	2.57111	+	22.8192i	0.202005	+	1.79285i
$163$	−11.7355	−	2.22048i	−0.919197	−	0.173921i	−0.295279	−	0.955411i	$-0.595413\pi$
$163$	−11.7355	−	2.22048i	−0.919197	−	0.173921i	−0.623918	+	0.781490i	$0.714460\pi$
$164$	−14.1770	+	13.1543i	−1.10704	+	1.02718i
$165$	0.857423	−	0.718285i	0.0667503	−	0.0559184i
$166$	−30.1444	−	17.4039i	−2.33966	−	1.35080i
$167$	13.2865	−	21.1454i	1.02814	−	1.63628i	0.295916	−	0.955214i	$-0.404375\pi$
$167$	13.2865	−	21.1454i	1.02814	−	1.63628i	0.732225	−	0.681063i	$-0.238482\pi$
$168$	−4.34480	−	2.87323i	−0.335208	−	0.221674i
$169$	−7.76584	−	1.77250i	−0.597372	−	0.136346i
$170$	17.7142	−	3.79650i	1.35862	−	0.291178i
$171$	0.488319	−	3.23978i	0.0373427	−	0.247752i
$172$	0.500944	−	0.369713i	0.0381966	−	0.0281904i
$173$	13.4609	−	0.503672i	1.02342	−	0.0382935i	0.479591	−	0.877492i	$-0.340785\pi$
$173$	13.4609	−	0.503672i	1.02342	−	0.0382935i	0.543825	+	0.839199i	$0.316976\pi$
$174$	0.237310	−	1.03972i	0.0179904	−	0.0788211i
$175$	3.10375	−	12.8595i	0.234622	−	0.972087i
$176$	−0.160070	−	0.701312i	−0.0120657	−	0.0528633i
$177$	−6.33007	−	23.6241i	−0.475797	−	1.77570i
$178$	−1.30901	−	0.350748i	−0.0981145	−	0.0262897i
$179$	−5.17088	−	5.57288i	−0.386490	−	0.416537i	0.509599	−	0.860412i	$-0.329794\pi$
$179$	−5.17088	−	5.57288i	−0.386490	−	0.416537i	−0.896089	+	0.443875i	$0.853603\pi$
$180$	−0.0641315	+	4.83111i	−0.00478008	+	0.360089i
$181$	−17.5627	−	14.0058i	−1.30542	−	1.04104i	−0.995929	−	0.0901374i	$-0.971269\pi$
$181$	−17.5627	−	14.0058i	−1.30542	−	1.04104i	−0.309493	−	0.950902i	$-0.600159\pi$
$182$	11.6214	−	4.75146i	0.861433	−	0.352202i
$183$	2.15929	−	19.1642i	0.159619	−	1.41666i
$184$	−1.33657	+	4.33307i	−0.0985336	+	0.319438i
$185$	−1.37634	−	0.279391i	−0.101191	−	0.0205412i
$186$	2.27664	+	30.3797i	0.166931	+	2.22755i
$187$	−0.389341	+	0.892379i	−0.0284714	+	0.0652572i
$188$	8.07081	−	23.0651i	0.588624	−	1.68219i
$189$	−10.9839	+	1.39489i	−0.798962	+	0.101463i
$190$	−4.81675	+	17.0669i	−0.349444	+	1.23816i
$191$	−1.23028	+	16.4170i	−0.0890202	+	1.18789i	0.756516	+	0.653975i	$0.226900\pi$
$191$	−1.23028	+	16.4170i	−0.0890202	+	1.18789i	−0.845537	+	0.533917i	$0.820719\pi$
$192$	19.5423	+	10.3284i	1.41034	+	0.745388i
$193$	1.65449	+	8.74417i	0.119092	+	0.629419i	0.990350	+	0.138592i	$0.0442576\pi$
$193$	1.65449	+	8.74417i	0.119092	+	0.629419i	−0.871257	+	0.490827i	$0.836695\pi$
$194$	−1.03014	+	0.155269i	−0.0739599	+	0.0111477i
$195$	−8.08435	−	5.67045i	−0.578932	−	0.406070i
$196$	9.34383	−	14.5725i	0.667416	−	1.04089i
$197$	6.97032	−	6.97032i	0.496615	−	0.496615i	−0.413768	−	0.910383i	$-0.635787\pi$
$197$	6.97032	−	6.97032i	0.496615	−	0.496615i	0.910383	+	0.413768i	$0.135787\pi$
$198$	−0.377881	−	0.278889i	−0.0268548	−	0.0198198i
$199$	−3.32613	−	2.26772i	−0.235783	−	0.160754i	0.439665	−	0.898162i	$-0.355097\pi$
$199$	−3.32613	−	2.26772i	−0.235783	−	0.160754i	−0.675448	+	0.737408i	$0.736050\pi$
$200$	0.691725	−	4.95346i	0.0489123	−	0.350262i
$201$	22.3899	+	1.67789i	1.57926	+	0.118349i
$202$	0.708193	+	2.02390i	0.0498283	+	0.142401i
$203$	0.662914	+	0.141490i	0.0465275	+	0.00993066i
$204$	−8.08999	−	16.7990i	−0.566412	−	1.17617i
$205$	−4.11718	+	16.9954i	−0.287556	+	1.18701i
$206$	21.5073	−	1.61175i	1.49848	−	0.112296i
$207$	−1.58388	−	3.63030i	−0.110087	−	0.252323i
$208$	−5.61470	+	2.96745i	−0.389309	+	0.205756i
$209$	−0.594210	−	0.745115i	−0.0411023	−	0.0515407i
$210$	−24.6262	+	0.0207884i	−1.69937	+	0.00143454i
$211$	6.86801	−	8.61221i	0.472813	−	0.592889i	−0.487044	−	0.873377i	$-0.661925\pi$
$211$	6.86801	−	8.61221i	0.472813	−	0.592889i	0.959857	+	0.280488i	$0.0904963\pi$
$212$	−5.02396	+	26.5523i	−0.345047	+	1.82362i
$213$	−0.764917	+	20.4428i	−0.0524112	+	1.40072i
$214$	−10.8478	+	6.26298i	−0.741541	+	0.428129i
$215$	0.192970	−	0.528852i	0.0131604	−	0.0360674i
$216$	−4.08119	+	0.931505i	−0.277690	+	0.0633809i
$217$	−19.2871	+	1.71950i	−1.30929	+	0.116727i
$218$	17.6035	−	11.0610i	1.19226	−	0.749148i
$219$	−0.204917	+	0.220847i	−0.0138470	+	0.0149235i
$220$	1.01746	+	0.969508i	0.0685968	+	0.0653642i
$221$	8.49940	+	1.28108i	0.571732	+	0.0861747i
$222$	0.0977559	+	2.61258i	0.00656095	+	0.175345i
$223$	−0.994562	−	1.58284i	−0.0666008	−	0.105995i	0.811764	−	0.583986i	$-0.198508\pi$
$223$	−0.994562	−	1.58284i	−0.0666008	−	0.105995i	−0.878364	+	0.477992i	$0.841365\pi$
$224$	−9.60897	+	18.8195i	−0.642027	+	1.25743i
$225$	2.36429	+	3.67363i	0.157619	+	0.244909i
$226$	−5.08248	+	8.80312i	−0.338082	+	0.585575i
$227$	0.636753	−	2.37639i	0.0422628	−	0.157727i	−0.941570	−	0.336818i	$-0.890649\pi$
$227$	0.636753	−	2.37639i	0.0422628	−	0.157727i	0.983832	+	0.179092i	$0.0573158\pi$
$228$	18.2387	+	0.682443i	1.20789	+	0.0451959i
$229$	15.6269	−	10.6542i	1.03265	−	0.704052i	0.0765460	−	0.997066i	$-0.475611\pi$
$229$	15.6269	−	10.6542i	1.03265	−	0.704052i	0.956108	+	0.293014i	$0.0946584\pi$
$230$	6.04646	+	20.5676i	0.398692	+	1.35618i
$231$	0.770787	−	1.07584i	0.0507140	−	0.0707853i
$232$	0.254668	+	0.0286942i	0.0167198	+	0.00188387i
$233$	−7.04943	−	13.3382i	−0.461824	−	0.873813i	−0.999529	−	0.0306804i	$-0.990233\pi$
$233$	−7.04943	−	13.3382i	−0.461824	−	0.873813i	0.537706	−	0.843133i	$-0.319291\pi$
$234$	−1.51479	+	3.85963i	−0.0990251	+	0.252312i
$235$	−5.43492	−	21.4166i	−0.354535	−	1.39706i
$236$	28.6060	−	11.2270i	1.86209	−	0.730817i
$237$	0.747535	+	0.261574i	0.0485576	+	0.0169910i
$238$	19.1797	−	9.57232i	1.24323	−	0.620481i
$239$	−6.93863	+	14.4082i	−0.448823	+	0.931990i	0.546687	+	0.837337i	$0.315889\pi$
$239$	−6.93863	+	14.4082i	−0.448823	+	0.931990i	−0.995510	+	0.0946535i	$0.969826\pi$
$240$	12.3955	−	1.23025i	0.800124	−	0.0794121i
$241$	−1.23578	−	4.00629i	−0.0796034	−	0.258068i	0.907019	−	0.421089i	$-0.138352\pi$
$241$	−1.23578	−	4.00629i	−0.0796034	−	0.258068i	−0.986622	+	0.163022i	$0.947876\pi$
$242$	22.7245	−	4.29971i	1.46079	−	0.276396i
$243$	5.23482	−	7.09293i	0.335814	−	0.455012i
$244$	24.2317			1.55128
$245$	−0.234187	−	15.6507i	−0.0149617	−	0.999888i
$246$	32.5532			2.07552
$247$	−4.99625	+	6.76968i	−0.317904	+	0.430744i
$248$	−7.19334	+	1.36105i	−0.456777	+	0.0864269i
$249$	9.54784	+	30.9533i	0.605070	+	1.96159i
$250$	−10.2079	−	21.3289i	−0.645603	−	1.34896i
$251$	11.5533	−	23.9906i	0.729236	−	1.51427i	−0.123734	−	0.992315i	$-0.539487\pi$
$251$	11.5533	−	23.9906i	0.729236	−	1.51427i	0.852970	−	0.521959i	$-0.174799\pi$
$252$	1.35065	+	5.55490i	0.0850831	+	0.349926i
$253$	−1.08746	−	0.380520i	−0.0683683	−	0.0239231i
$254$	40.0628	−	15.7235i	2.51376	−	0.986578i
$255$	−14.4874	−	8.62272i	−0.907238	−	0.539976i
$256$	2.19559	−	5.59427i	0.137224	−	0.349642i
$257$	8.22006	+	15.5531i	0.512753	+	0.970177i	0.995531	+	0.0944337i	$0.0301040\pi$
$257$	8.22006	+	15.5531i	0.512753	+	0.970177i	−0.482778	+	0.875743i	$0.660372\pi$
$258$	−1.04139	−	0.117337i	−0.0648343	−	0.00730507i
$259$	−1.65952	+	0.0855710i	−0.103118	+	0.00531712i
$260$	5.94267	−	10.8916i	0.368549	−	0.675470i
$261$	−0.184956	+	0.126101i	−0.0114485	+	0.00780544i
$262$	−17.1374	−	0.641237i	−1.05875	−	0.0396158i
$263$	1.19668	−	4.46607i	0.0737904	−	0.275390i	−0.919166	−	0.393871i	$-0.871136\pi$
$263$	1.19668	−	4.46607i	0.0737904	−	0.275390i	0.992956	+	0.118481i	$0.0378025\pi$
$264$	0.250187	−	0.433337i	0.0153979	−	0.0266700i
$265$	9.47308	+	22.5236i	0.581927	+	1.38361i
$266$	−0.488470	+	20.9770i	−0.0299500	+	1.28618i
$267$	0.670972	+	1.06785i	0.0410628	+	0.0653511i
$268$	1.05485	+	28.1915i	0.0644352	+	1.72207i
$269$	−24.1993	−	3.64746i	−1.47546	−	0.222390i	−0.638486	−	0.769633i	$-0.720439\pi$
$269$	−24.1993	−	3.64746i	−1.47546	−	0.222390i	−0.836974	+	0.547243i	$0.815677\pi$
$270$	−13.6526	+	14.3278i	−0.830871	+	0.871961i
$271$	20.7513	−	22.3645i	1.26055	−	1.35855i	0.354682	−	0.934987i	$-0.384589\pi$
$271$	20.7513	−	22.3645i	1.26055	−	1.35855i	0.905867	−	0.423562i	$-0.139220\pi$
$272$	−9.18065	+	5.76858i	−0.556659	+	0.349772i
$273$	−10.9355	−	4.11466i	−0.661845	−	0.249030i
$274$	36.9990	−	8.44479i	2.23519	−	0.510168i
$275$	1.25111	+	0.222687i	0.0754446	+	0.0134286i
$276$	19.1079	−	11.0320i	1.15016	−	0.664047i
$277$	−0.592674	+	15.8395i	−0.0356103	+	0.951706i	0.860925	+	0.508733i	$0.169886\pi$
$277$	−0.592674	+	15.8395i	−0.0356103	+	0.951706i	−0.896535	+	0.442973i	$0.853924\pi$
$278$	−1.34594	+	7.11346i	−0.0807241	+	0.426637i
$279$	3.98700	−	4.99954i	0.238695	−	0.299315i
$280$	−0.667557	−	5.88011i	−0.0398941	−	0.351404i
$281$	1.49322	+	1.87243i	0.0890778	+	0.111700i	0.824373	−	0.566047i	$-0.191528\pi$
$281$	1.49322	+	1.87243i	0.0890778	+	0.111700i	−0.735295	+	0.677747i	$0.762956\pi$
$282$	−36.3655	+	19.2197i	−2.16553	+	1.14452i
$283$	7.64685	+	17.5268i	0.454558	+	1.04186i	0.981414	+	0.191904i	$0.0614662\pi$
$283$	7.64685	+	17.5268i	0.454558	+	1.04186i	−0.526855	+	0.849955i	$0.676629\pi$
$284$	−25.6320	+	1.92085i	−1.52098	+	0.113982i
$285$	14.0888	−	8.59388i	0.834549	−	0.509057i
$286$	0.523293	+	1.08663i	0.0309429	+	0.0642537i
$287$	0.292106	+	20.6889i	0.0172425	+	1.22123i
$288$	−2.30476	−	6.58663i	−0.135809	−	0.388121i
$289$	−2.31842	−	0.173741i	−0.136377	−	0.0102201i
$290$	1.07863	−	0.551881i	0.0633392	−	0.0324076i
$291$	0.801028	+	0.546132i	0.0469571	+	0.0320148i
$292$	−0.304572	−	0.224785i	−0.0178237	−	0.0131545i
$293$	−17.7230	+	17.7230i	−1.03539	+	1.03539i	−0.0360400	+	0.999350i	$0.511474\pi$
$293$	−17.7230	+	17.7230i	−1.03539	+	1.03539i	−0.999350	+	0.0360400i	$0.988526\pi$
$294$	−28.2132	+	7.28326i	−1.64543	+	0.424769i
$295$	15.9560	−	22.7484i	0.928993	−	1.32446i
$296$	−0.621248	+	0.0936381i	−0.0361093	+	0.00544260i
$297$	−0.197736	−	1.04506i	−0.0114738	−	0.0606405i
$298$	−42.6452	−	22.5386i	−2.47037	−	1.30563i
$299$	−0.760100	+	10.1428i	−0.0439577	+	0.586575i
$300$	−18.8611	+	15.3790i	−1.08895	+	0.887907i
$301$	0.0652276	−	0.662900i	0.00375966	−	0.0382089i
$302$	6.29873	−	18.0008i	0.362451	−	1.03583i
$303$	0.797958	−	1.82894i	0.0458415	−	0.105070i
$304$	−0.793140	−	10.5837i	−0.0454897	−	0.607018i
$305$	18.2655	−	12.1012i	1.04588	−	0.692912i
$306$	−2.08656	+	6.76446i	−0.119281	+	0.386698i
$307$	−0.678704	+	6.02366i	−0.0387357	+	0.343789i	0.959364	+	0.282171i	$0.0910545\pi$
$307$	−0.678704	+	6.02366i	−0.0387357	+	0.343789i	−0.998100	+	0.0616177i	$0.980374\pi$
$308$	1.45171	+	0.811035i	0.0827186	+	0.0462130i
$309$	−15.6921	−	12.5140i	−0.892693	−	0.711899i
$310$	−24.7966	+	24.1469i	−1.40835	+	1.37145i
$311$	−1.01401	−	1.09284i	−0.0574990	−	0.0619692i	0.703647	−	0.710549i	$-0.251554\pi$
$311$	−1.01401	−	1.09284i	−0.0574990	−	0.0619692i	−0.761146	+	0.648580i	$0.775363\pi$
$312$	−4.26695	−	1.14333i	−0.241568	−	0.0647280i
$313$	2.04531	+	7.63321i	0.115608	+	0.431454i	0.999332	−	0.0365544i	$-0.0116382\pi$
$313$	2.04531	+	7.63321i	0.115608	+	0.431454i	−0.883724	+	0.468009i	$0.844972\pi$
$314$	−3.08990	−	13.5377i	−0.174373	−	0.763978i
$315$	3.79218	+	3.51268i	0.213665	+	0.197917i
$316$	−0.221431	+	0.970152i	−0.0124565	+	0.0545753i
$317$	14.9713	−	0.560186i	0.840871	−	0.0314632i	0.386515	−	0.922283i	$-0.373679\pi$
$317$	14.9713	−	0.560186i	0.840871	−	0.0314632i	0.454356	+	0.890820i	$0.349869\pi$
$318$	36.5984	−	27.0109i	2.05234	−	1.51470i
$319$	−0.00970484	+	0.0643874i	−0.000543367	+	0.00360500i
$320$	5.26255	+	24.5547i	0.294185	+	1.37265i
$321$	11.3645	+	2.59388i	0.634305	+	0.144776i
$322$	12.9917	+	21.7861i	0.723999	+	1.21409i
$323$	−7.64260	+	12.1631i	−0.425246	+	0.676775i
$324$	23.2537	+	13.4255i	1.29187	+	0.745861i
$325$	−0.959736	−	11.1777i	−0.0532366	−	0.620025i
$326$	−18.5171	+	17.1814i	−1.02557	+	0.951588i
$327$	−19.0102	−	3.59693i	−1.05127	−	0.198910i
$328$	0.875878	+	7.77363i	0.0483623	+	0.429227i
$329$	−12.5412	−	22.9392i	−0.691419	−	1.26468i
$330$	−0.145455	−	2.36115i	−0.00800705	−	0.129977i
$331$	−14.4883	−	4.46904i	−0.796348	−	0.245641i	−0.130227	−	0.991484i	$-0.541570\pi$
$331$	−14.4883	−	4.46904i	−0.796348	−	0.245641i	−0.666121	+	0.745843i	$0.732047\pi$
$332$	−37.3043	+	16.2757i	−2.04734	+	0.893246i
$333$	0.357957	−	0.415953i	0.0196159	−	0.0227941i
$334$	−19.2961	−	49.1657i	−1.05584	−	2.69023i
$335$	14.8738	+	20.7235i	0.812642	+	1.13224i
$336$	13.8414	−	5.06375i	0.755109	−	0.276250i
$337$	−4.28004	+	1.49765i	−0.233148	+	0.0815821i	−0.444325	−	0.895866i	$-0.646556\pi$
$337$	−4.28004	+	1.49765i	−0.233148	+	0.0815821i	0.211176	+	0.977448i	$0.432271\pi$
$338$	−12.7693	+	10.9889i	−0.694558	+	0.597715i
$339$	9.03934	−	2.78827i	0.490950	−	0.151438i
$340$	8.72802	−	19.3017i	0.473343	−	1.04678i
$341$	−0.277232	−	1.83931i	−0.0150129	−	0.0996043i
$342$	−4.89978	−	4.89978i	−0.264950	−	0.264950i
$343$	−4.88197	−	17.8652i	−0.263601	−	0.964632i
$344$		−	0.251839i		−	0.0135783i
$345$	8.89393	−	17.8581i	0.478833	−	0.961449i
$346$	16.0484	−	23.5387i	0.862768	−	1.26545i
$347$	−0.728776	+	1.37891i	−0.0391227	+	0.0740239i	−0.902902	−	0.429847i	$-0.858567\pi$
$347$	−0.728776	+	1.37891i	−0.0391227	+	0.0740239i	0.863779	+	0.503871i	$0.168091\pi$
$348$	−0.813401	−	0.945189i	−0.0436029	−	0.0506675i
$349$	12.0645	+	5.80994i	0.645796	+	0.310999i	0.727960	−	0.685620i	$-0.240469\pi$
$349$	12.0645	+	5.80994i	0.645796	+	0.310999i	−0.0821637	+	0.996619i	$0.526183\pi$
$350$	−17.9847	−	21.4317i	−0.961324	−	1.14558i
$351$	−8.45995	+	4.07410i	−0.451559	+	0.217459i
$352$	−1.86047	−	0.811717i	−0.0991636	−	0.0432646i
$353$	0.984391	+	0.847137i	0.0523939	+	0.0450886i	0.678095	−	0.734975i	$-0.262806\pi$
$353$	0.984391	+	0.847137i	0.0523939	+	0.0450886i	−0.625701	+	0.780063i	$0.715187\pi$
$354$	−48.1505	−	18.8977i	−2.55917	−	1.00440i
$355$	−18.3617	+	14.2484i	−0.974538	+	0.756226i
$356$	−1.23889	+	0.987984i	−0.0656612	+	0.0523630i
$357$	−19.1431	−	5.61015i	−1.01316	−	0.296921i
$358$	−15.9773	+	1.80021i	−0.844427	+	0.0951441i
$359$	12.0560	+	17.6830i	0.636293	+	0.933271i	0.999998	+	0.00175691i	$0.000559242\pi$
$359$	12.0560	+	17.6830i	0.636293	+	0.933271i	−0.363705	+	0.931514i	$0.618488\pi$
$360$	1.55691	+	1.18129i	0.0820563	+	0.0622595i
$361$	2.46934	+	4.27702i	0.129965	+	0.225106i
$362$	−45.8901	+	12.2962i	−2.41193	+	0.646274i
$363$	−18.2239	−	11.4509i	−0.956508	−	0.601014i
$364$	3.59905	−	14.2326i	0.188641	−	0.745991i
$365$	−0.341838	−	0.0173371i	−0.0178926	−	0.000907463i
$366$	−29.8994	−	27.7426i	−1.56287	−	1.45013i
$367$	9.85501	+	13.3531i	0.514427	+	0.697024i	0.982415	−	0.186711i	$-0.0597827\pi$
$367$	9.85501	+	13.3531i	0.514427	+	0.697024i	−0.467988	+	0.883735i	$0.655021\pi$
$368$	−7.61896	−	10.3233i	−0.397166	−	0.538140i
$369$	−5.00895	−	4.64763i	−0.260755	−	0.241946i
$370$	−2.20398	+	1.99121i	−0.114579	+	0.103518i
$371$	17.4949	+	23.0174i	0.908289	+	1.19500i
$372$	30.1621	+	18.9521i	1.56383	+	0.982622i
$373$	21.8050	−	5.84262i	1.12902	−	0.302519i	0.354490	−	0.935060i	$-0.384654\pi$
$373$	21.8050	−	5.84262i	1.12902	−	0.302519i	0.774527	+	0.632540i	$0.217988\pi$
$374$	1.02957	+	1.78327i	0.0532378	+	0.0922105i
$375$	−6.53697	+	21.0115i	−0.337568	+	1.08503i
$376$	−5.56807	−	8.16686i	−0.287151	−	0.421174i
$377$	0.571240	−	0.0643633i	0.0294203	−	0.00331488i
$378$	−11.4210	+	20.4429i	−0.587432	+	1.05147i
$379$	−4.59144	+	3.66155i	−0.235847	+	0.188081i	−0.734280	−	0.678846i	$-0.762480\pi$
$379$	−4.59144	+	3.66155i	−0.235847	+	0.188081i	0.498434	+	0.866928i	$0.333909\pi$
$380$	12.7121	+	16.3819i	0.652118	+	0.840376i
$381$	−37.2827	−	14.6324i	−1.91005	−	0.749641i
$382$	26.3913	+	22.7115i	1.35030	+	1.16202i
$383$	−23.9290	−	10.4401i	−1.22272	−	0.533465i	−0.313419	−	0.949615i	$-0.601474\pi$
$383$	−23.9290	−	10.4401i	−1.22272	−	0.533465i	−0.909296	+	0.416150i	$0.863379\pi$
$384$	13.7937	−	6.64269i	0.703906	−	0.338983i
$385$	1.49930	−	0.113630i	0.0764112	−	0.00579110i
$386$	16.9576	+	8.16635i	0.863119	+	0.415656i
$387$	0.143486	+	0.166734i	0.00729383	+	0.00847558i
$388$	−0.569197	+	1.07697i	−0.0288966	+	0.0546751i
$389$	17.1013	−	25.0830i	0.867069	−	1.27176i	−0.0940344	−	0.995569i	$-0.529976\pi$
$389$	17.1013	−	25.0830i	0.867069	−	1.27176i	0.961104	−	0.276188i	$-0.0890713\pi$
$390$	−19.8024	+	6.63545i	−1.00273	+	0.335999i
$391$			17.3656i			0.878216i
$392$	−2.49833	−	6.54127i	−0.126185	−	0.330384i
$393$	11.2850	+	11.2850i	0.569253	+	0.569253i
$394$	−3.10724	−	20.6152i	−0.156541	−	1.03858i
$395$	0.317578	+	0.841865i	0.0159791	+	0.0423588i
$396$	−0.524760	+	0.161867i	−0.0263702	+	0.00813413i
$397$	−9.76618	+	8.40447i	−0.490150	+	0.421808i	−0.862326	−	0.506354i	$-0.830993\pi$
$397$	−9.76618	+	8.40447i	−0.490150	+	0.421808i	0.372175	+	0.928162i	$0.378612\pi$
$398$	−8.03618	+	2.81198i	−0.402817	+	0.140952i
$399$	13.6111	−	14.0010i	0.681407	−	0.700925i
$400$	10.1148	+	9.89764i	0.505741	+	0.494882i
$401$	−1.72388	−	4.39236i	−0.0860863	−	0.219344i	0.881347	−	0.472469i	$-0.156637\pi$
$401$	−1.72388	−	4.39236i	−0.0860863	−	0.219344i	−0.967434	+	0.253124i	$0.918542\pi$
$402$	30.9745	−	35.9930i	1.54487	−	1.79517i
$403$	−15.0513	+	6.56682i	−0.749759	+	0.327116i
$404$	2.39583	+	0.739014i	0.119197	+	0.0367673i
$405$	24.2328	−	1.49283i	1.20414	−	0.0741794i
$406$	1.07332	−	0.950368i	0.0532680	−	0.0471660i
$407$	−0.0178726	−	0.158624i	−0.000885913	−	0.00786269i
$408$	−7.41054	−	1.40215i	−0.366876	−	0.0694167i
$409$	−2.03133	+	1.88480i	−0.100443	+	0.0931972i	−0.728796	−	0.684731i	$-0.759920\pi$
$409$	−2.03133	+	1.88480i	−0.100443	+	0.0931972i	0.628353	+	0.777928i	$0.283729\pi$
$410$	23.7500	+	28.3506i	1.17293	+	1.40014i
$411$	−30.5855	−	17.6585i	−1.50867	−	0.871032i
$412$	13.4171	−	21.3533i	0.661015	−	1.05200i
$413$	11.5782	−	30.7711i	0.569724	−	1.51415i
$414$	−8.16678	−	1.86401i	−0.401375	−	0.0916113i
$415$	−19.9914	+	30.8979i	−0.981338	+	1.51672i
$416$	−2.67085	+	17.7199i	−0.130949	+	0.868792i
$417$	5.42082	−	4.00075i	0.265459	−	0.195917i
$418$	−2.01421	+	0.0753664i	−0.0985182	+	0.00368629i
$419$	−1.78701	+	7.82938i	−0.0873010	+	0.382490i	−0.999637	−	0.0269524i	$-0.991420\pi$
$419$	−1.78701	+	7.82938i	−0.0873010	+	0.382490i	0.912336	+	0.409443i	$0.134277\pi$
$420$	−17.0795	+	23.1829i	−0.833396	+	1.13121i
$421$	7.55555	+	33.1030i	0.368235	+	1.61334i	0.731626	+	0.681706i	$0.238762\pi$
$421$	7.55555	+	33.1030i	0.368235	+	1.61334i	−0.363391	+	0.931637i	$0.618381\pi$
$422$	−6.02970	−	22.5032i	−0.293521	−	1.09544i
$423$	8.33954	+	2.23457i	0.405482	+	0.108649i
$424$	7.43485	+	8.01286i	0.361068	+	0.389139i
$425$	−3.06013	−	18.9080i	−0.148438	−	0.917173i
$426$	33.8264	+	26.9757i	1.63890	+	1.30698i
$427$	17.3632	−	19.2512i	0.840266	−	0.931632i
$428$	−1.63988	+	14.5543i	−0.0792666	+	0.703511i
$429$	0.330826	−	1.07251i	0.0159724	−	0.0517814i
$430$	−0.657585	−	0.992554i	−0.0317116	−	0.0478652i
$431$	−2.26007	−	30.1585i	−0.108864	−	1.45268i	−0.737691	−	0.675139i	$-0.764084\pi$
$431$	−2.26007	−	30.1585i	−0.108864	−	1.45268i	0.628827	−	0.777545i	$-0.283535\pi$
$432$	4.73659	−	10.8564i	0.227889	−	0.522328i
$433$	−6.26312	+	17.8990i	−0.300987	+	0.860170i	0.689711	+	0.724085i	$0.257738\pi$
$433$	−6.26312	+	17.8990i	−0.300987	+	0.860170i	−0.990697	+	0.136085i	$0.956548\pi$
$434$	−21.2965	+	34.9798i	−1.02226	+	1.67909i
$435$	−1.08515	−	0.306260i	−0.0520290	−	0.0146840i
$436$	1.81666	−	24.2417i	0.0870024	−	1.16097i
$437$	−15.0287	−	7.94290i	−0.718920	−	0.379960i
$438$	0.118457	+	0.626063i	0.00566011	+	0.0299144i
$439$	−4.16027	+	0.627060i	−0.198559	+	0.0299279i	−0.247569	−	0.968870i	$-0.579632\pi$
$439$	−4.16027	+	0.627060i	−0.198559	+	0.0299279i	0.0490097	+	0.998798i	$0.484393\pi$
$440$	0.559922	−	0.0982634i	0.0266933	−	0.00468452i
$441$	5.38098	+	2.90732i	0.256237	+	0.138444i
$442$	12.8543	−	12.8543i	0.611418	−	0.611418i
$443$	30.2666	+	22.3378i	1.43801	+	1.06130i	0.985526	+	0.169527i	$0.0542239\pi$
$443$	30.2666	+	22.3378i	1.43801	+	1.06130i	0.452484	+	0.891773i	$0.350538\pi$
$444$	2.52581	+	1.72207i	0.119870	+	0.0817257i
$445$	−0.440462	+	1.36342i	−0.0208799	+	0.0646324i
$446$	−3.94254	−	0.295452i	−0.186685	−	0.0139901i
$447$	14.8255	+	42.3688i	0.701221	+	2.00398i
$448$	13.2688	+	26.5861i	0.626890	+	1.25607i
$449$	1.09417	+	2.27207i	0.0516372	+	0.107226i	0.925191	−	0.379502i	$-0.123905\pi$
$449$	1.09417	+	2.27207i	0.0516372	+	0.107226i	−0.873554	+	0.486728i	$0.838190\pi$
$450$	9.22062	+	0.590443i	0.434664	+	0.0278338i
$451$	−1.98204	+	0.148533i	−0.0933306	+	0.00699416i
$452$	4.75302	+	10.8940i	0.223563	+	0.512413i
$453$	−15.6909	+	8.29289i	−0.737224	+	0.389634i
$454$	−3.24416	−	4.06805i	−0.152256	−	0.190923i
$455$	−4.39478	−	12.5256i	−0.206031	−	0.587211i
$456$	4.60299	−	5.77196i	0.215555	−	0.270297i
$457$	3.57411	−	18.8896i	0.167190	−	0.883619i	−0.794039	−	0.607867i	$-0.792025\pi$
$457$	3.57411	−	18.8896i	0.167190	−	0.883619i	0.961229	−	0.275752i	$-0.0889269\pi$
$458$	1.49567	−	39.9725i	0.0698878	−	1.86779i
$459$	−13.8836	+	8.01572i	−0.648032	+	0.374142i
$460$	23.5484	+	8.59245i	1.09795	+	0.400625i
$461$	−26.0978	+	5.95665i	−1.21549	+	0.277429i	−0.781741	−	0.623603i	$-0.785668\pi$
$461$	−26.0978	+	5.95665i	−1.21549	+	0.277429i	−0.433753	+	0.901032i	$0.642811\pi$
$462$	−0.862710	−	2.66277i	−0.0401369	−	0.123883i
$463$	25.8620	−	16.2502i	1.20191	−	0.755209i	0.226157	−	0.974091i	$-0.427384\pi$
$463$	25.8620	−	16.2502i	1.20191	−	0.755209i	0.975751	+	0.218881i	$0.0702408\pi$
$464$	−0.493222	+	0.531567i	−0.0228972	+	0.0246774i
$465$	32.2003	−	0.777015i	1.49325	−	0.0360332i
$466$	−31.5506	−	4.75549i	−1.46155	−	0.220294i
$467$	1.59798	+	42.7069i	0.0739456	+	1.97624i	0.186047	+	0.982541i	$0.440432\pi$
$467$	1.59798	+	42.7069i	0.0739456	+	1.97624i	−0.112101	+	0.993697i	$0.535758\pi$
$468$	2.57937	+	4.10504i	0.119231	+	0.189756i
$469$	23.1529	+	19.3626i	1.06910	+	0.894080i
$470$	−43.2697	−	17.6485i	−1.99588	−	0.814063i
$471$	−6.46116	+	11.1911i	−0.297714	+	0.515657i
$472$	3.21718	−	12.0067i	0.148083	−	0.552652i
$473$	0.0639418	+	0.00239253i	0.00294004	+	0.000110009i
$474$	1.38394	−	0.943554i	0.0635664	−	0.0433389i
$475$	17.7632	+	6.00006i	0.815033	+	0.275302i
$476$	4.31163	−	24.6908i	0.197623	−	1.13170i
$477$	−9.48773	−	1.06901i	−0.434413	−	0.0489466i
$478$	15.8039	+	29.9025i	0.722855	+	1.36771i
$479$	−7.94706	+	20.2488i	−0.363110	+	0.925190i	0.626239	+	0.779631i	$0.284593\pi$
$479$	−7.94706	+	20.2488i	−0.363110	+	0.925190i	−0.989350	+	0.145559i	$0.953502\pi$
$480$	17.9771	−	30.2041i	0.820537	−	1.37862i
$481$	−1.31183	+	0.514855i	−0.0598143	+	0.0234754i
$482$	−8.36941	−	2.92858i	−0.381216	−	0.133393i
$483$	4.92730	−	23.0855i	0.224200	−	1.05043i
$484$	11.7335	−	24.3648i	0.533341	−	1.10749i
$485$	0.108784	+	1.09606i	0.00493961	+	0.0497695i
$486$	−5.49549	−	17.8159i	−0.249280	−	0.808147i
$487$	14.0188	−	2.65250i	0.635252	−	0.120196i	0.141696	−	0.989910i	$-0.454744\pi$
$487$	14.0188	−	2.65250i	0.635252	−	0.120196i	0.493556	+	0.869714i	$0.335697\pi$
$488$	5.82040	−	7.88636i	0.263477	−	0.356999i
$489$	23.5075			1.06304
$490$	−26.9266	−	19.2571i	−1.21642	−	0.869949i
$491$	−14.5681			−0.657448			−0.328724	−	0.944426i	$-0.606619\pi$
$491$	−14.5681			−0.657448			−0.328724	+	0.944426i	$0.606619\pi$
$492$	22.6032	−	30.6263i	1.01903	−	1.38074i
$493$	0.964348	−	0.182465i	0.0434321	−	0.00821779i
$494$	5.24504	+	17.0040i	0.235985	+	0.765046i
$495$	−0.314720	+	0.384075i	−0.0141456	+	0.0172629i
$496$	8.98774	−	18.6632i	0.403562	−	0.838004i
$497$	−16.8406	+	21.7401i	−0.755403	+	0.975176i
$498$	64.6636	+	22.6268i	2.89765	+	1.01393i
$499$	−2.28791	+	0.897938i	−0.102421	+	0.0401972i	−0.415998	−	0.909365i	$-0.636568\pi$
$499$	−2.28791	+	0.897938i	−0.102421	+	0.0401972i	0.313577	+	0.949563i	$0.398473\pi$
$500$	−27.1541	−	5.20598i	−1.21437	−	0.232819i
$501$	−17.9571	+	45.7540i	−0.802265	+	2.04414i
$502$	−26.3146	−	49.7896i	−1.17448	−	2.22222i
$503$	−2.79431	−	0.314843i	−0.124592	−	0.0140382i	0.0494482	−	0.998777i	$-0.484254\pi$
$503$	−2.79431	−	0.314843i	−0.124592	−	0.0140382i	−0.174040	+	0.984739i	$0.555682\pi$
$504$	2.13230	+	0.894695i	0.0949801	+	0.0398529i
$505$	2.17499	−	0.639406i	0.0967859	−	0.0284532i
$506$	−2.01326	+	1.37262i	−0.0895004	+	0.0610203i
$507$	15.6667	+	0.586206i	0.695782	+	0.0260343i
$508$	13.0247	−	48.6088i	0.577877	−	2.15667i
$509$	−0.831483	+	1.44017i	−0.0368548	+	0.0638344i	−0.883864	−	0.467743i	$-0.845067\pi$
$509$	−0.831483	+	1.44017i	−0.0368548	+	0.0638344i	0.847010	+	0.531578i	$0.178401\pi$
$510$	−32.8678	+	13.8237i	−1.45541	+	0.612123i
$511$	−0.396825	+	0.0809022i	−0.0175545	+	0.00357890i
$512$	−15.0392	−	23.9348i	−0.664646	−	1.05778i
$513$	−0.586765	−	15.6816i	−0.0259063	−	0.692361i
$514$	36.7899	+	5.54518i	1.62273	+	0.244588i
$515$	−0.550087	−	22.7962i	−0.0242397	−	1.00452i
$516$	−0.833478	+	0.898276i	−0.0366918	+	0.0395444i
$517$	2.12646	−	1.33614i	0.0935214	−	0.0587634i
$518$	−1.93857	+	2.93144i	−0.0851759	+	0.128800i
$519$	−25.8474	+	5.89949i	−1.13457	+	0.258959i
$520$	−2.11733	−	4.55022i	−0.0928512	−	0.199540i
$521$	6.65506	−	3.84230i	0.291564	−	0.168334i	−0.347083	−	0.937834i	$-0.612828\pi$
$521$	6.65506	−	3.84230i	0.291564	−	0.168334i	0.638647	+	0.769500i	$0.279495\pi$
$522$	−0.0177023	+	0.473104i	−0.000774809	+	0.0207072i
$523$	−2.12968	+	11.2556i	−0.0931244	+	0.492174i	0.904689	+	0.426074i	$0.140104\pi$
$523$	−2.12968	+	11.2556i	−0.0931244	+	0.492174i	−0.997813	+	0.0661009i	$0.978944\pi$
$524$	−12.5026	+	15.6777i	−0.546178	+	0.684886i
$525$	−1.29686	+	26.0043i	−0.0565995	+	1.13492i
$526$	−6.09690	−	7.64527i	−0.265837	−	0.333350i
$527$	−24.7876	+	13.1007i	−1.07977	+	0.570673i
$528$	0.566169	+	1.29767i	0.0246394	+	0.0564740i
$529$	2.44377	−	0.183135i	0.106251	−	0.00796240i
$530$	50.2250	+	12.1671i	2.18164	+	0.528506i
$531$	4.71087	+	9.78222i	0.204434	+	0.424512i
$532$	19.3961	+	15.0248i	0.840926	+	0.651408i
$533$	5.79546	+	16.5625i	0.251029	+	0.717401i
$534$	2.65980	+	0.199324i	0.115101	+	0.00862560i
$535$	6.03225	+	11.7898i	0.260797	+	0.509716i
$536$	9.42845	+	6.42821i	0.407247	+	0.277656i
$537$	12.0390	+	8.88516i	0.519520	+	0.383423i
$538$	−36.5986	+	36.5986i	−1.57788	+	1.57788i
$539$	1.68456	−	0.572180i	0.0725590	−	0.0246455i
$540$	4.00003	+	22.7929i	0.172134	+	0.980849i
$541$	−1.62033	+	0.244226i	−0.0696636	+	0.0105001i	−0.183782	−	0.982967i	$-0.558834\pi$
$541$	−1.62033	+	0.244226i	−0.0696636	+	0.0105001i	0.114118	+	0.993467i	$0.463596\pi$
$542$	−11.9958	−	63.3994i	−0.515264	−	2.72324i
$543$	39.0887	+	20.6590i	1.67746	+	0.886561i
$544$	−2.28639	+	30.5097i	−0.0980281	+	1.30809i
$545$	−10.7368	−	19.1802i	−0.459914	−	0.821589i
$546$	−20.7356	+	13.4411i	−0.887402	+	0.575224i
$547$	0.0449914	−	0.128578i	0.00192369	−	0.00549760i	−0.942917	−	0.333026i	$-0.891930\pi$
$547$	0.0449914	−	0.128578i	0.00192369	−	0.00549760i	0.944841	+	0.327529i	$0.106216\pi$
$548$	17.7452	−	40.6725i	0.758039	−	1.73744i
$549$	0.639796	+	8.53749i	0.0273058	+	0.364371i
$550$	1.95020	−	1.84931i	0.0831568	−	0.0788547i
$551$	−0.283176	+	0.918034i	−0.0120637	+	0.0391095i
$552$	0.999257	−	8.86865i	0.0425312	−	0.377475i
$553$	0.612084	+	0.871081i	0.0260285	+	0.0370421i
$554$	26.2094	+	20.9013i	1.11353	+	0.888012i
$555$	2.76390	+	0.0366900i	0.117321	+	0.00155740i
$556$	5.75784	+	6.20547i	0.244187	+	0.263171i
$557$	−35.5291	−	9.51999i	−1.50542	−	0.403375i	−0.590506	−	0.807034i	$-0.701072\pi$
$557$	−35.5291	−	9.51999i	−1.50542	−	0.403375i	−0.914910	+	0.403659i	$0.867738\pi$
$558$	−3.50035	−	13.0635i	−0.148182	−	0.553021i
$559$	−0.125701	−	0.550731i	−0.00531658	−	0.0232934i
$560$	14.5083	+	8.36006i	0.613089	+	0.353277i
$561$	0.426406	−	1.86821i	0.0180029	−	0.0788758i
$562$	5.06159	−	0.189392i	0.213510	−	0.00798900i
$563$	−7.29379	+	5.38306i	−0.307396	+	0.226869i	−0.736583	−	0.676347i	$-0.763562\pi$
$563$	−7.29379	+	5.38306i	−0.307396	+	0.226869i	0.429187	+	0.903216i	$0.358800\pi$
$564$	−7.16821	+	47.5580i	−0.301836	+	2.00255i
$565$	9.02317	+	5.83811i	0.379608	+	0.245611i
$566$	39.4285	+	8.99931i	1.65730	+	0.378269i
$567$	27.3285	−	8.85413i	1.14769	−	0.371839i
$568$	−5.53159	+	8.80347i	−0.232100	+	0.369386i
$569$	7.69748	+	4.44414i	0.322695	+	0.186308i	0.652593	−	0.757708i	$-0.273681\pi$
$569$	7.69748	+	4.44414i	0.322695	+	0.186308i	−0.329898	+	0.944017i	$0.607014\pi$
$570$	3.07005	−	34.7676i	0.128590	−	1.45625i
$571$	7.96417	−	7.38967i	0.333290	−	0.309248i	−0.495719	−	0.868483i	$-0.665095\pi$
$571$	7.96417	−	7.38967i	0.333290	−	0.309248i	0.829009	+	0.559235i	$0.188905\pi$
$572$	1.38565	+	0.262180i	0.0579370	+	0.0109623i
$573$	−3.62790	−	32.1985i	−0.151558	−	1.34511i
$574$	35.5726	+	25.4860i	1.48477	+	1.06376i
$575$	22.0414	−	5.28310i	0.919190	−	0.220320i
$576$	−9.37661	−	2.89230i	−0.390692	−	0.120513i
$577$	28.1810	−	12.2952i	1.17319	−	0.511858i	0.279327	−	0.960196i	$-0.409889\pi$
$577$	28.1810	−	12.2952i	1.17319	−	0.511858i	0.893864	+	0.448338i	$0.147984\pi$
$578$	−3.20734	+	3.72699i	−0.133408	+	0.155022i
$579$	−6.39912	−	16.3047i	−0.265938	−	0.677599i
$580$	0.229728	−	1.39798i	0.00953895	−	0.0580478i
$581$	−13.8000	+	41.2993i	−0.572519	+	1.71338i
$582$	1.93535	−	0.677207i	0.0802227	−	0.0280711i
$583$	−2.10509	+	1.81158i	−0.0871840	+	0.0750279i
$584$	−0.146315	+	0.0451322i	−0.00605456	+	0.00186758i
$585$	3.99432	+	1.80619i	0.165145	+	0.0746767i
$586$	7.90061	+	52.4171i	0.326371	+	2.16533i
$587$	−16.0460	−	16.0460i	−0.662289	−	0.662289i	0.293630	−	0.955919i	$-0.405137\pi$
$587$	−16.0460	−	16.0460i	−0.662289	−	0.662289i	−0.955919	+	0.293630i	$0.905137\pi$
$588$	−12.7376	+	31.6002i	−0.525288	+	1.30317i
$589$		−	27.4441i		−	1.13081i
$590$	−18.6714	−	55.7215i	−0.768688	−	2.29402i
$591$	−10.9292	+	16.0302i	−0.449567	+	0.659394i
$592$	0.830651	−	1.57167i	0.0341395	−	0.0645952i
$593$	−9.55218	−	11.0998i	−0.392261	−	0.455815i	0.526766	−	0.850010i	$-0.323404\pi$
$593$	−9.55218	−	11.0998i	−0.392261	−	0.455815i	−0.919027	+	0.394195i	$0.871023\pi$
$594$	−2.02669	−	0.976002i	−0.0831561	−	0.0400458i
$595$	−9.08043	−	20.7647i	−0.372261	−	0.851271i
$596$	−50.8150	+	24.4712i	−2.08146	+	1.00238i
$597$	7.26207	+	3.16841i	0.297217	+	0.129674i
$598$	16.3052	+	14.0318i	0.666770	+	0.573802i
$599$	−40.8497	−	16.0323i	−1.66907	−	0.655063i	−0.672681	−	0.739933i	$-0.734857\pi$
$599$	−40.8497	−	16.0323i	−1.66907	−	0.655063i	−0.996392	+	0.0848703i	$0.972952\pi$
$600$	0.474804	+	9.83245i	0.0193838	+	0.401408i
$601$	0.954511	−	0.761197i	0.0389353	−	0.0310499i	−0.603829	−	0.797114i	$-0.706359\pi$
$601$	0.954511	−	0.761197i	0.0389353	−	0.0310499i	0.642764	+	0.766064i	$0.277788\pi$
$602$	−1.04612	−	0.943528i	−0.0426367	−	0.0384553i
$603$	−9.90476	+	1.11600i	−0.403353	+	0.0454470i
$604$	−12.5617	−	18.4246i	−0.511128	−	0.749688i
$605$	−3.32316	−	24.2254i	−0.135106	−	0.984904i
$606$	−2.11011	−	3.65482i	−0.0857175	−	0.148467i
$607$	21.5156	−	5.76509i	0.873291	−	0.233998i	0.205781	−	0.978598i	$-0.434027\pi$
$607$	21.5156	−	5.76509i	0.873291	−	0.233998i	0.667510	+	0.744601i	$0.267360\pi$
$608$	−25.3583	−	15.9336i	−1.02841	−	0.646195i
$609$	−1.33376	−	0.0310580i	−0.0540467	−	0.00125853i
$610$	2.34718	−	46.2797i	0.0950345	−	1.87381i
$611$	−16.2528	−	15.0804i	−0.657518	−	0.610087i
$612$	4.91524	+	6.65992i	0.198687	+	0.269211i
$613$	−8.34300	−	11.3044i	−0.336971	−	0.456579i	0.603047	−	0.797706i	$-0.293953\pi$
$613$	−8.34300	−	11.3044i	−0.336971	−	0.456579i	−0.940017	+	0.341127i	$0.889191\pi$
$614$	9.39795	+	8.72002i	0.379270	+	0.351911i
$615$	1.74333	−	34.3735i	0.0702977	−	1.38607i
$616$	0.612652	−	0.277658i	0.0246845	−	0.0111871i
$617$	−10.3582	−	6.50846i	−0.417003	−	0.262021i	0.307148	−	0.951662i	$-0.400625\pi$
$617$	−10.3582	−	6.50846i	−0.417003	−	0.262021i	−0.724151	+	0.689641i	$0.757768\pi$
$618$	−41.0025	+	10.9866i	−1.64936	+	0.441945i
$619$	−13.6782	−	23.6914i	−0.549774	−	0.952236i	−0.998290	−	0.0584613i	$-0.981381\pi$
$619$	−13.6782	−	23.6914i	−0.549774	−	0.952236i	0.448516	−	0.893775i	$-0.351953\pi$
$620$	5.50012	+	40.0951i	0.220890	+	1.61026i
$621$	−10.6865	−	15.6743i	−0.428836	−	0.628986i
$622$	−3.13314	+	0.353020i	−0.125627	+	0.0141548i
$623$	−0.102812	+	1.69220i	−0.00411906	+	0.0677964i
$624$	9.77227	−	7.79313i	0.391204	−	0.311975i
$625$	−23.0681	+	9.63643i	−0.922726	+	0.385457i
$626$	15.5579	+	6.10604i	0.621820	+	0.244047i
$627$	1.42177	+	1.22353i	0.0567799	+	0.0488631i
$628$	−14.8818	−	6.49288i	−0.593850	−	0.259094i
$629$	−2.16776	+	1.04394i	−0.0864342	+	0.0416245i
$630$	10.7400	−	2.04151i	0.427893	−	0.0813359i
$631$	16.0211	+	7.71537i	0.637791	+	0.307144i	0.724692	−	0.689073i	$-0.241982\pi$
$631$	16.0211	+	7.71537i	0.637791	+	0.307144i	−0.0869010	+	0.996217i	$0.527696\pi$
$632$	0.262555	+	0.305094i	0.0104439	+	0.0121360i
$633$	−10.1306	+	19.1680i	−0.402654	+	0.761858i
$634$	17.8491	−	26.1798i	0.708878	−	1.03973i
$635$	−14.4572	−	43.1449i	−0.573715	−	1.71215i
$636$		−	53.1869i		−	2.10900i
$637$	−8.72839	−	13.0577i	−0.345831	−	0.517365i
$638$	0.0973783	+	0.0973783i	0.00385524	+	0.00385524i
$639$	−1.35354	−	8.98013i	−0.0535451	−	0.355248i
$640$	15.8486	+	7.16657i	0.626472	+	0.283284i
$641$	24.2745	−	7.48768i	0.958784	−	0.295746i	0.224413	−	0.974494i	$-0.427953\pi$
$641$	24.2745	−	7.48768i	0.958784	−	0.295746i	0.734371	+	0.678748i	$0.237477\pi$
$642$	18.6866	−	16.0811i	0.737500	−	0.634670i
$643$	19.8723	−	6.95361i	0.783686	−	0.274224i	0.0913693	−	0.995817i	$-0.470876\pi$
$643$	19.8723	−	6.95361i	0.783686	−	0.274224i	0.692317	+	0.721593i	$0.256590\pi$
$644$	29.5172	+	2.90441i	1.16314	+	0.114450i
$645$	−0.179668	+	1.09334i	−0.00707441	+	0.0430502i
$646$	11.0994	+	28.2808i	0.436700	+	1.11269i
$647$	3.04699	−	3.54067i	0.119790	−	0.139198i	−0.694875	−	0.719131i	$-0.744540\pi$
$647$	3.04699	−	3.54067i	0.119790	−	0.139198i	0.814664	+	0.579933i	$0.196921\pi$
$648$	9.95488	−	4.34327i	0.391065	−	0.170620i
$649$	3.01792	+	0.930906i	0.118464	+	0.0365412i
$650$	−20.2261	−	12.4048i	−0.793332	−	0.486556i
$651$	36.6695	−	10.3826i	1.43719	−	0.406925i
$652$	3.30704	+	29.3508i	0.129514	+	1.14947i
$653$	29.5996	+	5.60056i	1.15832	+	0.219167i	0.729344	−	0.684147i	$-0.239825\pi$
$653$	29.5996	+	5.60056i	1.15832	+	0.219167i	0.428980	+	0.903314i	$0.358873\pi$
$654$	−29.9956	+	27.8319i	−1.17292	+	1.08831i
$655$	−1.59486	+	18.0613i	−0.0623162	+	0.705715i
$656$	−19.1692	−	11.0673i	−0.748430	−	0.432106i
$657$	0.0711560	−	0.113244i	0.00277606	−	0.00441807i
$658$	−54.7856	−	7.46819i	−2.13576	−	0.291140i
$659$	−2.61922	−	0.597820i	−0.102030	−	0.0232878i	0.171201	−	0.985236i	$-0.445235\pi$
$659$	−2.61922	−	0.597820i	−0.102030	−	0.0232878i	−0.273231	+	0.961948i	$0.588092\pi$
$660$	−2.32238	−	1.50261i	−0.0903983	−	0.0584889i
$661$	−3.56236	+	23.6347i	−0.138560	+	0.919285i	0.806229	+	0.591604i	$0.201505\pi$
$661$	−3.56236	+	23.6347i	−0.138560	+	0.919285i	−0.944788	+	0.327681i	$0.893733\pi$
$662$	−25.8006	+	19.0417i	−1.00277	+	0.740077i
$663$	−16.9055	+	0.632559i	−0.656555	+	0.0245665i
$664$	−3.66338	+	16.0503i	−0.142167	+	0.622873i
$665$	22.1237	+	1.63916i	0.857921	+	0.0635641i
$666$	−0.258262	−	1.13152i	−0.0100074	−	0.0438455i
$667$	0.300592	+	1.12182i	0.0116390	+	0.0434372i
$668$	−59.6535	−	15.9841i	−2.30806	−	0.618444i
$669$	2.50252	+	2.69708i	0.0967532	+	0.104275i
$670$	53.9445	+	0.716097i	2.08406	+	0.0276652i
$671$	1.94704	+	1.55272i	0.0751648	+	0.0599419i
$672$	11.6963	−	39.9104i	0.451195	−	1.53958i
$673$	2.75855	−	24.4828i	0.106334	−	0.943742i	−0.821362	−	0.570407i	$-0.806786\pi$
$673$	2.75855	−	24.4828i	0.106334	−	0.943742i	0.927696	−	0.373335i	$-0.121786\pi$
$674$	−2.82676	+	9.16412i	−0.108883	+	0.352989i
$675$	14.3978	+	15.1833i	0.554171	+	0.584405i
$676$	1.47208	+	19.6435i	0.0566183	+	0.755519i
$677$	−0.551546	+	1.26416i	−0.0211976	+	0.0485855i	−0.926839	−	0.375459i	$-0.877485\pi$
$677$	−0.551546	+	1.26416i	−0.0211976	+	0.0485855i	0.905641	+	0.424044i	$0.139390\pi$
$678$	6.60773	−	18.8838i	0.253768	−	0.725228i
$679$	0.447758	+	1.22391i	0.0171834	+	0.0469695i
$680$	−4.18540	−	7.47680i	−0.160503	−	0.286722i
$681$	−0.361855	+	4.82863i	−0.0138663	+	0.185033i
$682$	−3.47809	−	1.83822i	−0.133183	−	0.0703892i
$683$	7.61639	+	40.2536i	0.291433	+	1.54026i	0.755911	+	0.654675i	$0.227194\pi$
$683$	7.61639	+	40.2536i	0.291433	+	1.54026i	−0.464478	+	0.885585i	$0.653758\pi$
$684$	−8.01189	+	1.20760i	−0.306342	+	0.0461737i
$685$	−6.93557	−	39.5201i	−0.264994	−	1.50999i
$686$	−36.5321	−	14.1293i	−1.39480	−	0.539460i
$687$	−26.3219	+	26.3219i	−1.00424	+	1.00424i
$688$	0.573339	+	0.423143i	0.0218583	+	0.0161322i
$689$	20.2583	+	13.8119i	0.771779	+	0.526190i
$690$	−19.2189	−	37.5625i	−0.731651	−	1.42998i
$691$	5.76994	+	0.432397i	0.219499	+	0.0164492i	0.184026	−	0.982921i	$-0.441087\pi$
$691$	5.76994	+	0.432397i	0.219499	+	0.0164492i	0.0354733	+	0.999371i	$0.488706\pi$
$692$	−11.0022	−	31.4424i	−0.418240	−	1.19526i
$693$	−0.247420	+	0.532889i	−0.00939869	+	0.0202428i
$694$	1.43120	+	2.97191i	0.0543274	+	0.112812i
$695$	7.43914	+	1.80215i	0.282183	+	0.0683593i
$696$	−0.502994	+	0.0376942i	−0.0190660	+	0.00142880i
$697$	11.9802	+	27.4589i	0.453782	+	1.04008i
$698$	25.0383	−	13.2331i	0.947715	−	0.500882i
$699$	18.5132	+	23.2148i	0.700234	+	0.878066i
$700$	−32.6507	+	2.03907i	−1.23408	+	0.0770697i
$701$	4.17050	−	5.22964i	0.157518	−	0.197521i	−0.696810	−	0.717256i	$-0.745398\pi$
$701$	4.17050	−	5.22964i	0.157518	−	0.197521i	0.854328	+	0.519735i	$0.173969\pi$
$702$	−3.69201	+	19.5127i	−0.139346	+	0.736461i
$703$	0.0880629	−	2.35353i	0.00332136	−	0.0887651i
$704$	−2.47189	+	1.42715i	−0.0931629	+	0.0537876i
$705$	18.3469	+	39.4281i	0.690985	+	1.48495i
$706$	2.67784	−	0.611200i	0.100782	−	0.0230028i
$707$	2.30385	−	1.37386i	0.0866452	−	0.0516691i
$708$	−51.2121	+	32.1787i	−1.92467	+	1.20935i
$709$	−19.4353	+	20.9462i	−0.729906	+	0.786652i	−0.983548	−	0.180646i	$-0.942181\pi$
$709$	−19.4353	+	20.9462i	−0.729906	+	0.786652i	0.253642	+	0.967298i	$0.418372\pi$
$710$	1.18578	+	49.1401i	0.0445017	+	1.84420i
$711$	−0.347657	−	0.0524009i	−0.0130382	−	0.00196519i
$712$	0.0239664	+	0.640516i	0.000898180	+	0.0240044i
$713$	−17.6512	−	28.0917i	−0.661041	−	1.05204i
$714$	−33.5884	+	25.5296i	−1.25701	+	0.955421i
$715$	1.17541	−	0.494361i	0.0439579	−	0.0184880i
$716$	−9.40014	+	16.2815i	−0.351300	+	0.608469i
$717$	8.14633	−	30.4025i	0.304230	−	1.13540i
$718$	45.2318	+	1.69245i	1.68804	+	0.0631618i
$719$	−11.4410	+	7.80037i	−0.426679	+	0.290905i	−0.757557	−	0.652769i	$-0.773607\pi$
$719$	−11.4410	+	7.80037i	−0.426679	+	0.290905i	0.330879	+	0.943673i	$0.392655\pi$
$720$	−5.30527	+	1.55965i	−0.197716	+	0.0581246i
$721$	−7.35033	−	25.9601i	−0.273741	−	0.966805i
$722$	10.3793	+	1.16947i	0.386279	+	0.0435232i
$723$	3.85576	+	7.29546i	0.143397	+	0.271321i
$724$	−20.2953	+	51.7115i	−0.754267	+	1.92184i
$725$	−0.524976	−	1.16850i	−0.0194971	−	0.0433968i
$726$	−42.3730	+	16.6302i	−1.57261	+	0.617203i
$727$	9.25314	+	3.23781i	0.343180	+	0.120084i	0.496366	−	0.868114i	$-0.334668\pi$
$727$	9.25314	+	3.23781i	0.343180	+	0.120084i	−0.153186	+	0.988197i	$0.548953\pi$
$728$	−3.76760	−	4.58997i	−0.139637	−	0.170116i
$729$	6.60496	−	13.7153i	0.244628	−	0.507976i
$730$	−0.458814	+	0.559923i	−0.0169815	+	0.0207237i
$731$	−0.284278	−	0.921606i	−0.0105144	−	0.0340868i
$732$	−46.8610	+	8.86657i	−1.73203	+	0.327718i
$733$	19.4993	−	26.4207i	0.720224	−	0.975869i	−0.279651	−	0.960102i	$-0.590219\pi$
$733$	19.4993	−	26.4207i	0.720224	−	0.975869i	0.999876	−	0.0157677i	$-0.00501921\pi$
$734$	35.0994			1.29554
$735$	6.17961	+	30.1808i	0.227938	+	1.11323i
$736$	−36.2046			−1.33452
$737$	−1.72169	+	2.33281i	−0.0634192	+	0.0859300i
$738$	−14.1995	+	2.68668i	−0.522689	+	0.0988982i
$739$	0.211761	+	0.686513i	0.00778977	+	0.0252538i	0.959384	−	0.282103i	$-0.0910318\pi$
$739$	0.211761	+	0.686513i	0.00778977	+	0.0252538i	−0.951594	+	0.307356i	$0.900556\pi$
$740$	0.343017	+	3.45610i	0.0126096	+	0.127049i
$741$	7.18501	−	14.9198i	0.263948	−	0.548094i
$742$	61.1399	−	0.863235i	2.24451	−	0.0316903i
$743$	41.5604	+	14.5426i	1.52470	+	0.533516i	0.957093	−	0.289782i	$-0.0935827\pi$
$743$	41.5604	+	14.5426i	1.52470	+	0.533516i	0.567609	+	0.823298i	$0.307868\pi$
$744$	13.4129	−	5.26419i	0.491743	−	0.192995i
$745$	−26.0827	+	43.8227i	−0.955595	+	1.60554i
$746$	17.4425	−	44.4427i	0.638614	−	1.62716i
$747$	−6.71933	−	12.7136i	−0.245847	−	0.465166i
$748$	2.39258	+	0.269579i	0.0874815	+	0.00985680i
$749$	10.3878	+	11.7317i	0.379563	+	0.428669i
$750$	27.5451	+	37.5121i	1.00580	+	1.36975i
$751$	−35.4686	+	24.1821i	−1.29427	+	0.882418i	−0.997369	−	0.0724905i	$-0.976905\pi$
$751$	−35.4686	+	24.1821i	−1.29427	+	0.882418i	−0.296900	+	0.954908i	$0.595953\pi$
$752$	27.9482	+	1.04575i	1.01917	+	0.0381346i
$753$	−13.5642	+	50.6222i	−0.494306	+	1.84477i
$754$	0.607891	−	1.05290i	0.0221381	−	0.0383443i
$755$	−18.6700	−	7.61493i	−0.679469	−	0.277136i
$756$	11.3027	+	24.9394i	0.411074	+	0.907035i
$757$	−1.22470	−	1.94910i	−0.0445124	−	0.0708411i	0.823727	−	0.566987i	$-0.191891\pi$
$757$	−1.22470	−	1.94910i	−0.0445124	−	0.0708411i	−0.868239	+	0.496146i	$0.834748\pi$
$758$	0.464412	+	12.4117i	0.0168682	+	0.450812i
$759$	2.24225	+	0.337965i	0.0813885	+	0.0122673i
$760$	8.38502	−	0.202336i	0.304157	−	0.00733950i
$761$	4.02980	−	4.34309i	0.146080	−	0.157437i	−0.655773	−	0.754958i	$-0.727657\pi$
$761$	4.02980	−	4.34309i	0.146080	−	0.157437i	0.801853	+	0.597521i	$0.203848\pi$
$762$	−71.7228	+	45.0664i	−2.59824	+	1.63258i
$763$	−17.9574	−	18.8137i	−0.650102	−	0.681100i
$764$	39.6918	−	9.05940i	1.43600	−	0.327758i
$765$	7.03095	+	2.56549i	0.254205	+	0.0927554i
$766$	−47.8180	+	27.6077i	−1.72773	+	0.997508i
$767$	1.04254	−	27.8624i	0.0376439	−	1.00605i
$768$	−2.19900	+	11.6220i	−0.0793494	+	0.419372i
$769$	−17.7573	+	22.2669i	−0.640345	+	0.802967i	−0.991046	−	0.133521i	$-0.957372\pi$
$769$	−17.7573	+	22.2669i	−0.640345	+	0.802967i	0.350701	+	0.936487i	$0.385943\pi$
$770$	1.68960	−	2.69402i	0.0608889	−	0.0970859i
$771$	−21.5875	−	27.0699i	−0.777456	−	0.974899i
$772$	19.4574	−	10.2835i	0.700287	−	0.370112i
$773$	2.90379	+	6.65557i	0.104442	+	0.239384i	0.960935	−	0.276776i	$-0.0892659\pi$
$773$	2.90379	+	6.65557i	0.104442	+	0.239384i	−0.856492	+	0.516160i	$0.827361\pi$
$774$	0.463932	−	0.0347669i	0.0166757	−	0.00124967i
$775$	24.1692	+	27.4763i	0.868183	+	0.986978i
$776$	0.213788	+	0.443935i	0.00767454	+	0.0159363i
$777$	3.17799	−	0.772715i	0.114010	−	0.0277210i
$778$	−21.2057	−	60.6024i	−0.760261	−	2.17270i
$779$	−29.2434	−	2.19149i	−1.04775	−	0.0785183i
$780$	−7.50702	+	23.2375i	−0.268794	+	0.832035i
$781$	−2.18264	−	1.48810i	−0.0781011	−	0.0532484i
$782$	29.5506	+	21.8093i	1.05673	+	0.779901i
$783$	−0.758139	+	0.758139i	−0.0270937	+	0.0270937i
$784$	19.0896	+	5.30300i	0.681772	+	0.189393i
$785$	−14.4602	+	2.53768i	−0.516106	+	0.0905738i
$786$	33.3762	−	5.03065i	1.19049	−	0.179437i
$787$	2.26548	+	11.9734i	0.0807558	+	0.426805i	0.999490	+	0.0319285i	$0.0101649\pi$
$787$	2.26548	+	11.9734i	0.0807558	+	0.426805i	−0.918734	+	0.394876i	$0.870787\pi$
$788$	−21.5524	−	11.3908i	−0.767773	−	0.405780i
$789$	−0.680052	+	9.07467i	−0.0242105	+	0.323067i
$790$	1.83143	+	0.516879i	0.0651592	+	0.0183897i
$791$	12.0607	+	4.03002i	0.428829	+	0.143291i
$792$	−0.0733655	+	0.209666i	−0.00260693	+	0.00745017i
$793$	8.79192	−	20.1513i	0.312210	−	0.715594i
$794$	2.03641	+	27.1740i	0.0722695	+	0.964369i
$795$	−26.5612	−	40.0914i	−0.942030	−	1.42189i
$796$	−2.93436	+	9.51297i	−0.104006	+	0.337178i
$797$	−1.70893	+	15.1671i	−0.0605333	+	0.537248i	0.926449	+	0.376420i	$0.122845\pi$
$797$	−1.70893	+	15.1671i	−0.0605333	+	0.537248i	−0.986982	+	0.160828i	$0.948584\pi$
$798$	−6.73099	−	40.7454i	−0.238275	−	1.44237i
$799$	−29.5952	−	23.6013i	−1.04700	−	0.834956i
$800$	39.4203	−	6.37990i	1.39372	−	0.225563i
$801$	−0.380804	−	0.410409i	−0.0134550	−	0.0145011i
$802$	−9.63939	−	2.58287i	−0.340379	−	0.0912042i
$803$	−0.0100690	−	0.0375780i	−0.000355327	−	0.00132610i
$804$	−12.3554	−	54.1326i	−0.435742	−	1.90911i
$805$	23.7000	−	12.5514i	0.835315	−	0.442380i
$806$	−7.72825	+	33.8597i	−0.272216	+	1.19266i
$807$	48.1330	−	1.80101i	1.69436	−	0.0633985i
$808$	0.815988	−	0.602226i	0.0287064	−	0.0211863i
$809$	4.54870	−	30.1787i	0.159924	−	1.06103i	−0.754510	−	0.656289i	$-0.772125\pi$
$809$	4.54870	−	30.1787i	0.159924	−	1.06103i	0.914433	−	0.404736i	$-0.132637\pi$
$810$	27.8936	−	43.1113i	0.980079	−	1.51478i
$811$	23.0205	+	5.25427i	0.808358	+	0.184503i	0.606677	−	0.794949i	$-0.292502\pi$
$811$	23.0205	+	5.25427i	0.808358	+	0.184503i	0.201682	+	0.979451i	$0.435359\pi$
$812$	−0.148856	−	1.66967i	−0.00522382	−	0.0585939i
$813$	−31.9469	+	50.8431i	−1.12043	+	1.78315i
$814$	−0.292373	−	0.168801i	−0.0102477	−	0.00591649i
$815$	17.1504	+	20.4726i	0.600753	+	0.717125i
$816$	15.6434	−	14.5150i	0.547629	−	0.508125i
$817$	0.927611	+	0.175514i	0.0324530	+	0.00614044i
$818$	0.656181	+	5.82377i	0.0229428	+	0.203623i
$819$	5.10956	+	0.892255i	0.178542	+	0.0311779i
$820$	43.1631	−	2.65900i	1.50732	−	0.0928565i
$821$	35.8825	+	11.0683i	1.25231	+	0.386286i	0.848811	−	0.528696i	$-0.177319\pi$
$821$	35.8825	+	11.0683i	1.25231	+	0.386286i	0.403496	+	0.914981i	$0.367795\pi$
$822$	−68.4613	+	29.8693i	−2.38786	+	1.04181i
$823$	30.2118	−	35.1068i	1.05312	−	1.22375i	0.0791969	−	0.996859i	$-0.474764\pi$
$823$	30.2118	−	35.1068i	1.05312	−	1.22375i	0.973921	−	0.226886i	$-0.0728546\pi$
$824$	−3.72678	−	9.49568i	−0.129829	−	0.330798i
$825$	−2.50096	+	0.0271417i	−0.0870723	+	0.000944952i
$826$	−37.8215	−	58.3475i	−1.31598	−	2.03017i
$827$	−3.07204	+	1.07495i	−0.106825	+	0.0373798i	−0.383162	−	0.923681i	$-0.625165\pi$
$827$	−3.07204	+	1.07495i	−0.106825	+	0.0373798i	0.276337	+	0.961061i	$0.410879\pi$
$828$	−7.42424	+	6.38908i	−0.258010	+	0.222036i
$829$	40.7335	−	12.5646i	1.41473	−	0.436387i	0.509193	−	0.860652i	$-0.329944\pi$
$829$	40.7335	−	12.5646i	1.41473	−	0.436387i	0.905538	+	0.424265i	$0.139468\pi$
$830$	27.4712	+	72.8234i	0.953540	+	2.52774i
$831$	−4.64966	−	30.8485i	−0.161295	−	1.07012i
$832$	17.8181	+	17.8181i	0.617733	+	0.617733i
$833$	−16.5265	−	21.1176i	−0.572608	−	0.731683i
$834$		−	14.2490i		−	0.493402i
$835$	−52.9481	+	17.7421i	−1.83235	+	0.613990i
$836$	−1.32765	+	1.94731i	−0.0459178	+	0.0673491i
$837$	14.3115	−	27.0786i	0.494677	−	0.935975i
$838$	11.0788	+	12.8738i	0.382710	+	0.444717i
$839$	24.0017	+	11.5586i	0.828632	+	0.399048i	0.799602	−	0.600530i	$-0.205044\pi$
$839$	24.0017	+	11.5586i	0.828632	+	0.399048i	0.0290301	+	0.999579i	$0.490758\pi$
$840$	3.44255	+	11.1271i	0.118779	+	0.383921i
$841$	−26.0690	+	12.5541i	−0.898930	+	0.432902i
$842$	65.8196	+	28.7168i	2.26829	+	0.989646i
$843$	−3.57282	−	3.07466i	−0.123054	−	0.105897i
$844$	−25.3578	−	9.95220i	−0.872851	−	0.342569i
$845$	10.9195	+	14.0718i	0.375641	+	0.484084i
$846$	14.2761	−	11.3848i	0.490822	−	0.391418i
$847$	−10.9493	−	26.7805i	−0.376224	−	0.920188i
$848$	−30.7342	+	3.46292i	−1.05542	+	0.118917i
$849$	−21.2012	−	31.0964i	−0.727623	−	1.06723i
$850$	−36.0185	−	18.5391i	−1.23542	−	0.635886i
$851$	−1.42357	−	2.46570i	−0.0487995	−	0.0845232i
$852$	48.8661	−	13.0936i	1.67412	−	0.448580i
$853$	43.5991	+	27.3951i	1.49280	+	0.937991i	0.997602	+	0.0692125i	$0.0220487\pi$
$853$	43.5991	+	27.3951i	1.49280	+	0.937991i	0.495202	+	0.868778i	$0.335094\pi$
$854$	−10.9529	−	53.7241i	−0.374802	−	1.83840i
$855$	−5.43616	+	4.91136i	−0.185913	+	0.167965i
$856$	4.34290	+	4.02963i	0.148437	+	0.137730i
$857$	−28.0885	−	38.0585i	−0.959484	−	1.30006i	−0.953917	−	0.300071i	$-0.902990\pi$
$857$	−28.0885	−	38.0585i	−0.959484	−	1.30006i	−0.00556723	−	0.999985i	$-0.501772\pi$
$858$	−1.40959	−	1.90992i	−0.0481225	−	0.0652036i
$859$	−34.8050	−	32.2943i	−1.18753	−	1.10187i	−0.992648	−	0.121041i	$-0.961377\pi$
$859$	−34.8050	−	32.2943i	−1.18753	−	1.10187i	−0.194883	−	0.980827i	$-0.562433\pi$
$860$	−1.39039	−	0.0705169i	−0.0474120	−	0.00240460i
$861$	−8.13511	−	39.9027i	−0.277244	−	1.35988i
$862$	−54.1584	−	34.0300i	−1.84464	−	1.15907i
$863$	18.4473	−	4.94295i	0.627955	−	0.168260i	0.0692134	−	0.997602i	$-0.477951\pi$
$863$	18.4473	−	4.94295i	0.627955	−	0.168260i	0.558742	+	0.829342i	$0.311284\pi$
$864$	−16.7115	−	28.9452i	−0.568538	−	0.984737i
$865$	−23.9954	−	18.2063i	−0.815869	−	0.619034i
$866$	22.5924	+	33.1370i	0.767723	+	1.12604i
$867$	4.54709	−	0.512334i	0.154427	−	0.0173998i
$868$	18.1221	+	44.3239i	0.615104	+	1.50445i
$869$	−0.0799574	+	0.0637639i	−0.00271237	+	0.00216304i
$870$	−1.88399	+	1.46194i	−0.0638732	+	0.0495646i
$871$	23.8270	+	9.35141i	0.807347	+	0.316860i
$872$	−7.45324	−	6.41403i	−0.252399	−	0.217207i
$873$	−0.394476	−	0.172108i	−0.0133510	−	0.00582497i
$874$	−32.3907	+	15.5985i	−1.09563	+	0.527628i
$875$	−23.5933	+	17.8426i	−0.797597	+	0.603190i
$876$	0.671253	+	0.323259i	0.0226796	+	0.0109219i
$877$	−33.7758	−	39.2481i	−1.14053	−	1.32532i	−0.938238	−	0.345989i	$-0.887543\pi$
$877$	−33.7758	−	39.2481i	−1.14053	−	1.32532i	−0.202288	−	0.979326i	$-0.564838\pi$
$878$	−4.15781	+	7.86695i	−0.140319	+	0.265497i
$879$	27.7890	−	40.7590i	0.937300	−	1.37477i
$880$	−0.717081	+	1.43983i	−0.0241728	+	0.0485365i
$881$			12.1128i			0.408091i	0.978961	+	0.204046i	$0.0654091\pi$
$881$			12.1128i			0.408091i	−0.978961	+	0.204046i	$0.934591\pi$
$882$	11.7053	−	5.50539i	0.394136	−	0.185376i
$883$	−37.0414	−	37.0414i	−1.24654	−	1.24654i	−0.957236	−	0.289308i	$-0.906575\pi$
$883$	−37.0414	−	37.0414i	−1.24654	−	1.24654i	−0.289308	−	0.957236i	$-0.593425\pi$
$884$	−3.16807	−	21.0188i	−0.106554	−	0.706938i
$885$	−22.5330	+	49.8308i	−0.757437	+	1.67504i
$886$	76.0233	−	23.4501i	2.55405	−	0.787821i
$887$	3.92353	−	3.37647i	0.131739	−	0.113371i	−0.583950	−	0.811790i	$-0.698494\pi$
$887$	3.92353	−	3.37647i	0.131739	−	0.113371i	0.715689	+	0.698419i	$0.246113\pi$
$888$	1.16715	−	0.408403i	0.0391670	−	0.0137051i
$889$	−29.2851	−	45.1783i	−0.982190	−	1.51523i
$890$	1.76693	+	2.46184i	0.0592275	+	0.0825210i
$891$	1.00818	+	2.56880i	0.0337752	+	0.0860579i
$892$	−3.01545	+	3.50401i	−0.100965	+	0.117323i
$893$	33.9619	−	14.8174i	1.13649	−	0.495846i
$894$	90.7172	+	27.9826i	3.03404	+	0.935877i
$895$	1.04524	+	16.9671i	0.0349384	+	0.567148i
$896$	20.2736	+	3.54028i	0.677295	+	0.118272i
$897$	−2.24141	−	19.8930i	−0.0748384	−	0.664209i
$898$	5.24050	+	0.991555i	0.174878	+	0.0330886i
$899$	−1.37452	+	1.27537i	−0.0458430	+	0.0425360i
$900$	6.95780	−	8.26484i	0.231927	−	0.275495i
$901$	36.2528	+	20.9306i	1.20776	+	0.697298i
$902$	−2.23648	+	3.55933i	−0.0744665	+	0.118513i
$903$	0.116418	+	1.30583i	0.00387416	+	0.0434552i
$904$	4.68719	+	1.06982i	0.155894	+	0.0355817i
$905$	10.5262	+	49.1145i	0.349903	+	1.63262i
$906$	−5.59431	+	37.1158i	−0.185859	+	1.23309i
$907$	3.01798	−	2.22737i	0.100210	−	0.0739585i	−0.542563	−	0.840015i	$-0.682546\pi$
$907$	3.01798	−	2.22737i	0.100210	−	0.0739585i	0.642773	+	0.766057i	$0.277784\pi$
$908$	−6.07981	+	0.227490i	−0.201765	+	0.00754953i
$909$	−0.197117	+	0.863626i	−0.00653796	+	0.0286447i
$910$	−26.8340	−	8.25238i	−0.889537	−	0.273564i
$911$	4.01101	+	17.5734i	0.132891	+	0.582232i	0.996895	+	0.0787469i	$0.0250919\pi$
$911$	4.01101	+	17.5734i	0.132891	+	0.582232i	−0.864004	+	0.503485i	$0.832051\pi$
$912$	5.40649	+	20.1773i	0.179027	+	0.668137i
$913$	−4.04035	−	1.08261i	−0.133716	−	0.0358292i
$914$	−27.6553	−	29.8053i	−0.914756	−	0.985872i
$915$	−30.8951	+	30.0856i	−1.02136	+	0.994598i
$916$	−36.5678	−	29.1619i	−1.20823	−	0.963535i
$917$	3.49667	+	21.1667i	0.115470	+	0.698987i
$918$	−3.79621	+	33.6923i	−0.125294	+	1.11201i
$919$	10.7506	−	34.8526i	0.354629	−	1.14968i	−0.586019	−	0.810297i	$-0.699306\pi$
$919$	10.7506	−	34.8526i	0.354629	−	1.14968i	0.940648	−	0.339383i	$-0.110218\pi$
$920$	8.45273	−	5.60008i	0.278678	−	0.184629i
$921$	−0.891581	−	11.8973i	−0.0293786	−	0.392030i
$922$	−22.6398	+	51.8909i	−0.745601	+	1.70894i
$923$	−7.70259	+	22.0127i	−0.253534	+	0.724558i
$924$	−3.10417	−	1.03724i	−0.102120	−	0.0341228i
$925$	1.98452	+	2.43385i	0.0652505	+	0.0800244i
$926$	4.82740	−	64.4172i	0.158638	−	2.11688i
$927$	7.87758	+	4.16342i	0.258734	+	0.136745i
$928$	0.380411	+	2.01052i	0.0124876	+	0.0659985i
$929$	−27.4640	+	4.13953i	−0.901064	+	0.135814i	−0.583206	−	0.812325i	$-0.698202\pi$
$929$	−27.4640	+	4.13953i	−0.901064	+	0.135814i	−0.317859	+	0.948138i	$0.602964\pi$
$930$	39.1179	−	55.7703i	1.28273	−	1.82878i
$931$	25.8349	−	4.64343i	0.846705	−	0.152182i
$932$	−26.3810	+	26.3810i	−0.864139	+	0.864139i
$933$	2.36083	+	1.74237i	0.0772901	+	0.0570427i
$934$	74.6801	+	50.9160i	2.44361	+	1.66602i
$935$	1.93812	−	0.991639i	0.0633831	−	0.0324301i
$936$	1.95557	+	0.146550i	0.0639198	+	0.00479013i
$937$	−6.25863	−	17.8861i	−0.204461	−	0.584315i	0.795299	−	0.606217i	$-0.207314\pi$
$937$	−6.25863	−	17.8861i	−0.204461	−	0.584315i	−0.999760	+	0.0219018i	$0.993028\pi$
$938$	62.0264	−	15.0815i	2.02524	−	0.492428i
$939$	−6.74841	−	14.0132i	−0.220226	−	0.457304i
$940$	−46.6479	+	28.4543i	−1.52149	+	0.928076i
$941$	2.15796	−	0.161716i	0.0703473	−	0.00527180i	−0.0395099	−	0.999219i	$-0.512580\pi$
$941$	2.15796	−	0.161716i	0.0703473	−	0.00527180i	0.109857	+	0.993947i	$0.464961\pi$
$942$	10.9290	+	25.0496i	0.356087	+	0.816159i
$943$	−31.3429	+	16.5652i	−1.02067	+	0.539438i
$944$	21.9289	+	27.4980i	0.713726	+	0.894984i
$945$	20.9743	+	13.1544i	0.682295	+	0.427911i
$946$	0.0843754	−	0.105803i	0.00274328	−	0.00343996i
$947$	−7.50889	+	39.6854i	−0.244006	+	1.28960i	0.619393	+	0.785081i	$0.287379\pi$
$947$	−7.50889	+	39.6854i	−0.244006	+	1.28960i	−0.863399	+	0.504522i	$0.831669\pi$
$948$	0.0732321	−	1.95717i	0.00237847	−	0.0635659i
$949$	−0.297440	+	0.171727i	−0.00965531	+	0.00557450i
$950$	32.5189	−	22.6918i	1.05505	−	0.736220i
$951$	−28.7475	+	6.56143i	−0.932202	+	0.212769i
$952$	−7.00013	−	7.33392i	−0.226876	−	0.237694i
$953$	−7.77944	+	4.88815i	−0.252001	+	0.158343i	−0.652109	−	0.758125i	$-0.726115\pi$
$953$	−7.77944	+	4.88815i	−0.252001	+	0.158343i	0.400108	+	0.916468i	$0.368973\pi$
$954$	−13.7347	+	14.8025i	−0.444677	+	0.479248i
$955$	25.3948	−	26.6507i	0.821757	−	0.862397i
$956$	39.1058	+	5.89426i	1.26477	+	0.190634i
$957$	−0.00479196	−	0.128068i	−0.000154902	−	0.00413985i
$958$	24.4762	+	38.9536i	0.790790	+	1.25853i
$959$	−19.5975	−	43.2418i	−0.632835	−	1.39635i
$960$	−19.1618	−	45.5599i	−0.618445	−	1.47044i
$961$	11.2819	−	19.5409i	0.363934	−	0.630351i
$962$	−0.771402	+	2.87891i	−0.0248710	+	0.0928199i
$963$	−5.17119	−	0.193492i	−0.166639	−	0.00623520i
$964$	−8.56649	+	5.84054i	−0.275908	+	0.188111i
$965$	9.53110	−	17.4685i	0.306817	−	0.562329i
$966$	−33.0959	−	37.3777i	−1.06484	−	1.20261i
$967$	−45.9937	−	5.18225i	−1.47906	−	0.166650i	−0.664743	−	0.747072i	$-0.731459\pi$
$967$	−45.9937	−	5.18225i	−1.47906	−	0.166650i	−0.814316	+	0.580422i	$0.802888\pi$
$968$	−5.11133	−	9.67111i	−0.164284	−	0.310841i
$969$	10.3292	−	26.3184i	0.331822	−	0.845468i
$970$	2.00176	+	1.19142i	0.0642725	+	0.0382542i
$971$	−15.0692	+	5.91421i	−0.483593	+	0.189796i	−0.594597	−	0.804024i	$-0.702688\pi$
$971$	−15.0692	+	5.91421i	−0.483593	+	0.189796i	0.111005	+	0.993820i	$0.464593\pi$
$972$	−20.5771	−	7.20024i	−0.660011	−	0.230948i
$973$	9.05580	−	0.127859i	0.290316	−	0.00409897i
$974$	13.0924	−	27.1867i	0.419508	−	0.871118i
$975$	5.94600	+	21.2650i	0.190424	+	0.681024i
$976$	8.17462	+	26.5015i	0.261663	+	0.848292i
$977$	−18.3690	+	3.47561i	−0.587677	+	0.111195i	−0.471242	−	0.882004i	$-0.656194\pi$
$977$	−18.3690	+	3.47561i	−0.587677	+	0.111195i	−0.116435	+	0.993198i	$0.537147\pi$
$978$	29.5229	−	40.0021i	0.944037	−	1.27913i
$979$	−0.162854			−0.00520484
$980$	−36.8136	+	11.9615i	−1.17597	+	0.382098i
$981$	8.58896			0.274224
$982$	−18.2960	+	24.7901i	−0.583847	+	0.791085i
$983$	−17.5913	+	3.32845i	−0.561075	+	0.106161i	−0.458710	−	0.888586i	$-0.651688\pi$
$983$	−17.5913	+	3.32845i	−0.561075	+	0.106161i	−0.102365	+	0.994747i	$0.532641\pi$
$984$	−4.53827	−	14.7127i	−0.144675	−	0.469024i
$985$	−21.9343	+	2.17698i	−0.698886	+	0.0693643i
$986$	0.900624	−	1.87016i	0.0286817	−	0.0595582i
$987$	32.6467	+	39.7726i	1.03916	+	1.26597i
$988$	19.6393	+	6.87209i	0.624810	+	0.218630i
$989$	1.06238	−	0.416955i	0.0337818	−	0.0132584i
$990$	0.258317	+	1.01791i	0.00820984	+	0.0323513i
$991$	−14.6638	+	37.3628i	−0.465812	+	1.18687i	0.484284	+	0.874911i	$0.339080\pi$
$991$	−14.6638	+	37.3628i	−0.465812	+	1.18687i	−0.950096	+	0.311958i	$0.899015\pi$
$992$	−27.3128	−	51.6784i	−0.867184	−	1.64079i
$993$	29.6537	+	3.34117i	0.941031	+	0.106029i
$994$	15.8446	+	55.9604i	0.502560	+	1.77496i
$995$	2.53885	+	8.63612i	0.0804870	+	0.273783i
$996$	66.1863	−	45.1251i	2.09719	−	1.42984i
$997$	−9.31559	−	0.348565i	−0.295028	−	0.0110392i	−0.110532	−	0.993873i	$-0.535256\pi$
$997$	−9.31559	−	0.348565i	−0.295028	−	0.0110392i	−0.184495	+	0.982833i	$0.559065\pi$
$998$	−1.34537	+	5.02100i	−0.0425870	+	0.158937i
$999$	1.31420	−	2.27627i	0.0415796	−	0.0720179i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	245.2.x.a.103.23	✓	624
5.2	odd	4	inner	245.2.x.a.152.23	yes	624
49.10	odd	42	inner	245.2.x.a.108.23	yes	624
245.157	even	84	inner	245.2.x.a.157.23	yes	624

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
245.2.x.a.103.23	✓	624	1.1	even	1	trivial
245.2.x.a.108.23	yes	624	49.10	odd	42	inner
245.2.x.a.152.23	yes	624	5.2	odd	4	inner
245.2.x.a.157.23	yes	624	245.157	even	84	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 245 = 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	245.x (of order \(84\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(1.25589 - 1.70168i) q^{2} +(-1.93387 + 0.365908i) q^{3} +(-0.728921 - 2.36310i) q^{4} +(-1.72957 - 1.41725i) q^{5} +(-1.80608 + 3.75036i) q^{6} +(-2.39971 - 1.11418i) q^{7} +(-0.944171 - 0.330380i) q^{8} +(0.813339 - 0.319212i) q^{9} +(-4.58385 + 1.16325i) q^{10} +(0.0928530 - 0.236585i) q^{11} +(2.27432 + 4.30321i) q^{12} +(-2.22965 - 0.251221i) q^{13} +(-4.90975 + 2.68423i) q^{14} +(3.86334 + 2.10791i) q^{15} +(2.33855 - 1.59440i) q^{16} +(-3.82813 - 0.143238i) q^{17} +(0.478272 - 1.78494i) q^{18} +(1.87492 - 3.24746i) q^{19} +(-2.08838 + 5.12021i) q^{20} +(5.04841 + 1.27661i) q^{21} +(-0.285978 - 0.455132i) q^{22} +(-0.169500 - 4.52997i) q^{23} +(1.94679 + 0.293432i) q^{24} +(0.982817 + 4.90246i) q^{25} +(-3.22770 + 3.47863i) q^{26} +(3.54343 - 2.22649i) q^{27} +(-0.883728 + 6.48291i) q^{28} +(-0.249778 + 0.0570102i) q^{29} +(8.43893 - 3.92684i) q^{30} +(6.33821 - 3.65937i) q^{31} +(0.298630 - 7.98106i) q^{32} +(-0.0929970 + 0.491501i) q^{33} +(-5.05147 + 6.33434i) q^{34} +(2.57139 + 5.32803i) q^{35} +(-1.34719 - 1.68932i) q^{36} +(0.555290 - 0.293479i) q^{37} +(-3.17142 - 7.26897i) q^{38} +(4.40377 - 0.330017i) q^{39} +(1.16478 + 1.90954i) q^{40} +(-3.39316 - 7.04597i) q^{41} +(8.51264 - 6.98747i) q^{42} +(0.0831519 + 0.237634i) q^{43} +(-0.626758 - 0.0469691i) q^{44} +(-1.85913 - 0.600604i) q^{45} +(-7.92142 - 5.40073i) q^{46} +(7.95053 + 5.86776i) q^{47} +(-3.93905 + 3.93905i) q^{48} +(4.51720 + 5.34742i) q^{49} +(9.57670 + 4.48453i) q^{50} +(7.45551 - 1.12374i) q^{51} +(1.03158 + 5.45201i) q^{52} +(-9.66117 - 5.10608i) q^{53} +(0.661417 - 8.82600i) q^{54} +(-0.495896 + 0.277595i) q^{55} +(1.89763 + 1.84479i) q^{56} +(-2.43758 + 6.96621i) q^{57} +(-0.216682 + 0.496640i) q^{58} +(0.928629 + 12.3917i) q^{59} +(2.16514 - 10.6660i) q^{60} +(-2.88820 + 9.36330i) q^{61} +(1.73306 - 15.3814i) q^{62} +(-2.30744 - 0.140191i) q^{63} +(-8.78041 - 7.00214i) q^{64} +(3.50029 + 3.59447i) q^{65} +(0.719581 + 0.775524i) q^{66} +(-11.0191 - 2.95256i) q^{67} +(2.45192 + 9.15067i) q^{68} +(1.98534 + 8.69835i) q^{69} +(12.2960 + 2.31578i) q^{70} +(2.31287 - 10.1333i) q^{71} +(-0.873392 + 0.0326800i) q^{72} +(0.123161 - 0.0908966i) q^{73} +(0.197979 - 1.31350i) q^{74} +(-3.69449 - 9.12109i) q^{75} +(-9.04075 - 2.06349i) q^{76} +(-0.486419 + 0.464281i) q^{77} +(4.96909 - 7.90826i) q^{78} +(-0.348481 - 0.201196i) q^{79} +(-6.30434 - 0.556687i) q^{80} +(-7.95933 + 7.38518i) q^{81} +(-16.2514 - 3.07493i) q^{82} +(-1.84272 - 16.3546i) q^{83} +(-0.663132 - 12.8605i) q^{84} +(6.41801 + 5.67315i) q^{85} +(0.508807 + 0.156946i) q^{86} +(0.462178 - 0.201646i) q^{87} +(-0.165832 + 0.192700i) q^{88} +(-0.234099 - 0.596475i) q^{89} +(-3.35690 + 2.40934i) q^{90} +(5.07060 + 3.08709i) q^{91} +(-10.5812 + 3.70254i) q^{92} +(-10.9183 + 9.39594i) q^{93} +(19.9700 - 6.15994i) q^{94} +(-7.84526 + 2.95948i) q^{95} +(2.34282 + 15.5436i) q^{96} +(-0.348307 - 0.348307i) q^{97} +(14.7727 - 0.971017i) q^{98} -0.222064i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 624 q - 26 q^{2} - 22 q^{3} - 28 q^{5} - 28 q^{6} - 18 q^{7} - 24 q^{8} - 34 q^{10} - 56 q^{11} - 34 q^{12} - 28 q^{13} + 12 q^{15} - 100 q^{16} - 26 q^{17} - 10 q^{18} - 28 q^{20} - 76 q^{21} - 48 q^{22}+ \cdots + 304 q^{98}+O(q^{100}) \) 624 * q - 26 * q^2 - 22 * q^3 - 28 * q^5 - 28 * q^6 - 18 * q^7 - 24 * q^8 - 34 * q^10 - 56 * q^11 - 34 * q^12 - 28 * q^13 + 12 * q^15 - 100 * q^16 - 26 * q^17 - 10 * q^18 - 28 * q^20 - 76 * q^21 - 48 * q^22 - 34 * q^23 - 24 * q^25 - 60 * q^26 - 28 * q^27 - 46 * q^28 - 10 * q^30 - 60 * q^31 + 54 * q^32 - 28 * q^33 - 20 * q^35 + 116 * q^36 - 20 * q^37 + 12 * q^38 - 46 * q^40 - 114 * q^42 - 24 * q^43 + 60 * q^45 + 108 * q^46 - 94 * q^47 - 296 * q^50 + 52 * q^51 - 52 * q^52 - 106 * q^53 + 14 * q^55 + 96 * q^56 + 72 * q^57 - 142 * q^58 - 26 * q^60 + 80 * q^61 - 56 * q^62 - 24 * q^63 - 20 * q^65 - 240 * q^66 - 8 * q^67 - 30 * q^68 + 180 * q^70 + 48 * q^71 + 138 * q^72 - 4 * q^73 - 106 * q^75 + 56 * q^76 - 8 * q^77 - 204 * q^78 - 18 * q^80 - 284 * q^81 - 162 * q^82 + 182 * q^83 - 36 * q^85 - 76 * q^86 - 74 * q^87 + 288 * q^88 - 112 * q^90 + 44 * q^91 - 8 * q^92 + 368 * q^93 + 26 * q^95 + 136 * q^96 + 304 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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