LMFDB - Embedded newform 576.2.bm.a.133.80

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [576,2,Mod(13,576)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(576, base_ring=CyclotomicField(48))

chi = DirichletCharacter(H, H._module([0, 45, 16]))

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

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

chi := DirichletCharacter("576.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 576 = 2^{6} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	576.bm (of order $48$, degree $16$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.59938315643$
Analytic rank:	$0$
Dimension:	$1504$
Relative dimension:	$94$ over $\Q(\zeta_{48})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{48}]$

Embedding invariants

Embedding label			133.80
Character	$\chi$	$=$	576.133
Dual form			576.2.bm.a.13.80

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.25108 - 0.659399i) q^{2} +(0.977923 - 1.42957i) q^{3} +(1.13039 - 1.64992i) q^{4} +(-0.765671 - 2.25560i) q^{5} +(0.280800 - 2.43334i) q^{6} +(1.05377 + 1.37330i) q^{7} +(0.326245 - 2.80955i) q^{8} +(-1.08733 - 2.79602i) q^{9} +O(q^{10})$	\(q+(1.25108 - 0.659399i) q^{2} +(0.977923 - 1.42957i) q^{3} +(1.13039 - 1.64992i) q^{4} +(-0.765671 - 2.25560i) q^{5} +(0.280800 - 2.43334i) q^{6} +(1.05377 + 1.37330i) q^{7} +(0.326245 - 2.80955i) q^{8} +(-1.08733 - 2.79602i) q^{9} +(-2.44525 - 2.31704i) q^{10} +(-0.555516 + 0.0364104i) q^{11} +(-1.25324 - 3.22946i) q^{12} +(4.12433 + 4.70290i) q^{13} +(2.22389 + 1.02324i) q^{14} +(-3.97330 - 1.11122i) q^{15} +(-1.44446 - 3.73009i) q^{16} +(-4.04767 + 4.04767i) q^{17} +(-3.20403 - 2.78104i) q^{18} +(0.619179 + 3.11282i) q^{19} +(-4.58705 - 1.28640i) q^{20} +(2.99372 - 0.163455i) q^{21} +(-0.670984 + 0.411859i) q^{22} +(-2.14962 - 1.64946i) q^{23} +(-3.69740 - 3.21391i) q^{24} +(-0.534691 + 0.410283i) q^{25} +(8.26094 + 3.16410i) q^{26} +(-5.06043 - 1.17987i) q^{27} +(3.45699 - 0.186275i) q^{28} +(0.508442 + 1.03102i) q^{29} +(-5.70363 + 1.22977i) q^{30} +(2.53342 - 1.46267i) q^{31} +(-4.26674 - 3.71415i) q^{32} +(-0.491200 + 0.829755i) q^{33} +(-2.39491 + 7.73297i) q^{34} +(2.29076 - 3.42836i) q^{35} +(-5.84230 - 1.36656i) q^{36} +(1.55289 - 7.80690i) q^{37} +(2.82723 + 3.48610i) q^{38} +(10.7564 - 1.29694i) q^{39} +(-6.58700 + 1.41531i) q^{40} +(6.43239 + 4.93574i) q^{41} +(3.63759 - 2.17855i) q^{42} +(0.753577 + 11.4974i) q^{43} +(-0.567873 + 0.957714i) q^{44} +(-5.47414 + 4.59342i) q^{45} +(-3.77699 - 0.646145i) q^{46} +(-1.75166 - 6.53727i) q^{47} +(-6.74498 - 1.58279i) q^{48} +(1.03622 - 3.86722i) q^{49} +(-0.398399 + 0.865870i) q^{50} +(1.82811 + 9.74472i) q^{51} +(12.4215 - 1.48872i) q^{52} +(-2.94043 - 4.40066i) q^{53} +(-7.10898 + 1.86074i) q^{54} +(0.507470 + 1.22514i) q^{55} +(4.20213 - 2.51258i) q^{56} +(5.05551 + 2.15894i) q^{57} +(1.31595 + 0.954617i) q^{58} +(2.78077 + 8.19189i) q^{59} +(-6.32477 + 5.29951i) q^{60} +(-6.59370 + 3.25166i) q^{61} +(2.20502 - 3.50045i) q^{62} +(2.69396 - 4.43958i) q^{63} +(-7.78713 - 1.83320i) q^{64} +(7.44995 - 12.9037i) q^{65} +(-0.0673897 + 1.36198i) q^{66} +(-0.254497 + 3.88288i) q^{67} +(2.10289 + 11.2537i) q^{68} +(-4.46018 + 1.45998i) q^{69} +(0.605256 - 5.79967i) q^{70} +(-1.77930 + 4.29560i) q^{71} +(-8.21028 + 2.14273i) q^{72} +(-5.93905 - 14.3381i) q^{73} +(-3.20508 - 10.7910i) q^{74} +(0.0636412 + 1.16560i) q^{75} +(5.83581 + 2.49710i) q^{76} +(-0.635386 - 0.724519i) q^{77} +(12.6019 - 8.71533i) q^{78} +(9.13053 - 2.44652i) q^{79} +(-7.30759 + 6.11413i) q^{80} +(-6.63541 + 6.08041i) q^{81} +(11.3020 + 1.93348i) q^{82} +(13.0525 + 4.43074i) q^{83} +(3.11437 - 5.12416i) q^{84} +(12.2291 + 6.03071i) q^{85} +(8.52414 + 13.8872i) q^{86} +(1.97113 + 0.281403i) q^{87} +(-0.0789374 + 1.57263i) q^{88} +(-1.86775 - 0.773649i) q^{89} +(-3.81967 + 9.35636i) q^{90} +(-2.11238 + 10.6197i) q^{91} +(-5.15137 + 1.68217i) q^{92} +(0.386500 - 5.05208i) q^{93} +(-6.50212 - 7.02358i) q^{94} +(6.54718 - 3.78002i) q^{95} +(-9.48218 + 2.46745i) q^{96} +(11.7390 + 6.77752i) q^{97} +(-1.25365 - 5.52147i) q^{98} +(0.705836 + 1.51364i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1504 q - 8 q^{2} - 16 q^{3} - 8 q^{4} - 8 q^{5} - 16 q^{6} - 8 q^{7} - 32 q^{8} - 16 q^{9}+O(q^{10}) $ 1504 * q - 8 * q^2 - 16 * q^3 - 8 * q^4 - 8 * q^5 - 16 * q^6 - 8 * q^7 - 32 * q^8 - 16 * q^9	\( 1504 q - 8 q^{2} - 16 q^{3} - 8 q^{4} - 8 q^{5} - 16 q^{6} - 8 q^{7} - 32 q^{8} - 16 q^{9} - 32 q^{10} - 8 q^{11} - 16 q^{12} - 8 q^{13} - 8 q^{14} - 16 q^{15} - 8 q^{16} - 32 q^{17} - 16 q^{18} - 32 q^{19} - 8 q^{20} - 16 q^{21} - 8 q^{22} - 8 q^{23} + 64 q^{24} - 8 q^{25} - 32 q^{26} - 16 q^{27} - 32 q^{28} - 8 q^{29} - 96 q^{30} - 8 q^{32} - 8 q^{34} - 32 q^{35} - 96 q^{36} - 32 q^{37} - 8 q^{38} - 16 q^{39} - 8 q^{40} - 8 q^{41} + 64 q^{42} - 8 q^{43} - 32 q^{44} - 16 q^{45} - 32 q^{46} - 8 q^{47} - 16 q^{48} - 8 q^{49} - 8 q^{50} - 16 q^{51} - 8 q^{52} - 32 q^{53} - 16 q^{54} - 32 q^{55} - 8 q^{56} - 16 q^{57} - 80 q^{58} - 8 q^{59} - 16 q^{60} - 8 q^{61} - 64 q^{62} - 32 q^{63} - 32 q^{64} - 16 q^{65} - 32 q^{66} - 8 q^{67} - 8 q^{68} - 16 q^{69} - 8 q^{70} - 32 q^{71} - 16 q^{72} - 32 q^{73} - 8 q^{74} - 16 q^{75} + 40 q^{76} - 8 q^{77} - 40 q^{78} - 8 q^{79} - 160 q^{80} - 16 q^{81} - 32 q^{82} - 8 q^{83} - 128 q^{84} - 8 q^{85} - 216 q^{86} - 16 q^{87} - 8 q^{88} - 32 q^{89} - 160 q^{90} - 32 q^{91} + 144 q^{92} - 40 q^{93} - 8 q^{94} - 152 q^{96} - 304 q^{98} - 16 q^{99}+O(q^{100}) \) 1504 * q - 8 * q^2 - 16 * q^3 - 8 * q^4 - 8 * q^5 - 16 * q^6 - 8 * q^7 - 32 * q^8 - 16 * q^9 - 32 * q^10 - 8 * q^11 - 16 * q^12 - 8 * q^13 - 8 * q^14 - 16 * q^15 - 8 * q^16 - 32 * q^17 - 16 * q^18 - 32 * q^19 - 8 * q^20 - 16 * q^21 - 8 * q^22 - 8 * q^23 + 64 * q^24 - 8 * q^25 - 32 * q^26 - 16 * q^27 - 32 * q^28 - 8 * q^29 - 96 * q^30 - 8 * q^32 - 8 * q^34 - 32 * q^35 - 96 * q^36 - 32 * q^37 - 8 * q^38 - 16 * q^39 - 8 * q^40 - 8 * q^41 + 64 * q^42 - 8 * q^43 - 32 * q^44 - 16 * q^45 - 32 * q^46 - 8 * q^47 - 16 * q^48 - 8 * q^49 - 8 * q^50 - 16 * q^51 - 8 * q^52 - 32 * q^53 - 16 * q^54 - 32 * q^55 - 8 * q^56 - 16 * q^57 - 80 * q^58 - 8 * q^59 - 16 * q^60 - 8 * q^61 - 64 * q^62 - 32 * q^63 - 32 * q^64 - 16 * q^65 - 32 * q^66 - 8 * q^67 - 8 * q^68 - 16 * q^69 - 8 * q^70 - 32 * q^71 - 16 * q^72 - 32 * q^73 - 8 * q^74 - 16 * q^75 + 40 * q^76 - 8 * q^77 - 40 * q^78 - 8 * q^79 - 160 * q^80 - 16 * q^81 - 32 * q^82 - 8 * q^83 - 128 * q^84 - 8 * q^85 - 216 * q^86 - 16 * q^87 - 8 * q^88 - 32 * q^89 - 160 * q^90 - 32 * q^91 + 144 * q^92 - 40 * q^93 - 8 * q^94 - 152 * q^96 - 304 * q^98 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/576\mathbb{Z}\right)^\times$.

$n$	$65$	$127$	$325$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{1}{16}\right)$

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 $

$2$	1.25108	−	0.659399i	0.884645	−	0.466266i
$2$	1.25108	−	0.659399i	0.884645	−	0.466266i
$3$	0.977923	−	1.42957i	0.564604	−	0.825362i
$3$	0.977923	−	1.42957i	0.564604	−	0.825362i
$4$	1.13039	−	1.64992i	0.565193	−	0.824959i
$5$	−0.765671	−	2.25560i	−0.342419	−	1.00873i	−0.972640	−	0.232317i	$-0.925369\pi$
$5$	−0.765671	−	2.25560i	−0.342419	−	1.00873i	0.630221	−	0.776416i	$-0.282964\pi$
$6$	0.280800	−	2.43334i	0.114636	−	0.993408i
$7$	1.05377	+	1.37330i	0.398286	+	0.519057i	0.948846	−	0.315739i	$-0.102252\pi$
$7$	1.05377	+	1.37330i	0.398286	+	0.519057i	−0.550560	+	0.834796i	$0.685586\pi$
$8$	0.326245	−	2.80955i	0.115345	−	0.993325i
$9$	−1.08733	−	2.79602i	−0.362445	−	0.932005i
$10$	−2.44525	−	2.31704i	−0.773256	−	0.732712i
$11$	−0.555516	+	0.0364104i	−0.167494	+	0.0109782i	−0.148920	−	0.988849i	$-0.547580\pi$
$11$	−0.555516	+	0.0364104i	−0.167494	+	0.0109782i	−0.0185748	+	0.999827i	$0.505913\pi$
$12$	−1.25324	−	3.22946i	−0.361780	−	0.932264i
$13$	4.12433	+	4.70290i	1.14388	+	1.30435i	0.946016	+	0.324120i	$0.105068\pi$
$13$	4.12433	+	4.70290i	1.14388	+	1.30435i	0.197867	+	0.980229i	$0.436599\pi$
$14$	2.22389	+	1.02324i	0.594360	+	0.273474i
$15$	−3.97330	−	1.11122i	−1.02590	−	0.286915i
$16$	−1.44446	−	3.73009i	−0.361114	−	0.932522i
$17$	−4.04767	+	4.04767i	−0.981703	+	0.981703i	−0.999836	−	0.0181323i	$-0.994228\pi$
$17$	−4.04767	+	4.04767i	−0.981703	+	0.981703i	0.0181323	+	0.999836i	$0.494228\pi$
$18$	−3.20403	−	2.78104i	−0.755197	−	0.655498i
$19$	0.619179	+	3.11282i	0.142049	+	0.714131i	0.984504	+	0.175363i	$0.0561099\pi$
$19$	0.619179	+	3.11282i	0.142049	+	0.714131i	−0.842454	+	0.538768i	$0.818890\pi$
$20$	−4.58705	−	1.28640i	−1.02570	−	0.287647i
$21$	2.99372	−	0.163455i	0.653284	−	0.0356689i
$22$	−0.670984	+	0.411859i	−0.143054	+	0.0878086i
$23$	−2.14962	−	1.64946i	−0.448227	−	0.343936i	0.359854	−	0.933009i	$-0.382827\pi$
$23$	−2.14962	−	1.64946i	−0.448227	−	0.343936i	−0.808080	+	0.589072i	$0.799493\pi$
$24$	−3.69740	−	3.21391i	−0.754729	−	0.656037i
$25$	−0.534691	+	0.410283i	−0.106938	+	0.0820565i
$26$	8.26094	+	3.16410i	1.62010	+	0.620532i
$27$	−5.06043	−	1.17987i	−0.973880	−	0.227065i
$28$	3.45699	−	0.186275i	0.653309	−	0.0352026i
$29$	0.508442	+	1.03102i	0.0944153	+	0.191455i	0.938957	−	0.344034i	$-0.111794\pi$
$29$	0.508442	+	1.03102i	0.0944153	+	0.191455i	−0.844542	+	0.535490i	$0.820127\pi$
$30$	−5.70363	+	1.22977i	−1.04134	+	0.224524i
$31$	2.53342	−	1.46267i	0.455016	−	0.262703i	−0.254930	−	0.966959i	$-0.582053\pi$
$31$	2.53342	−	1.46267i	0.455016	−	0.262703i	0.709946	+	0.704256i	$0.248719\pi$
$32$	−4.26674	−	3.71415i	−0.754260	−	0.656575i
$33$	−0.491200	+	0.829755i	−0.0855070	+	0.144442i
$34$	−2.39491	+	7.73297i	−0.410724	+	1.32619i
$35$	2.29076	−	3.42836i	0.387209	−	0.579499i
$36$	−5.84230	−	1.36656i	−0.973717	−	0.227760i
$37$	1.55289	−	7.80690i	0.255293	−	1.28345i	−0.614062	−	0.789258i	$-0.710465\pi$
$37$	1.55289	−	7.80690i	0.255293	−	1.28345i	0.869355	−	0.494188i	$-0.164535\pi$
$38$	2.82723	+	3.48610i	0.458638	+	0.565519i
$39$	10.7564	−	1.29694i	1.72240	−	0.207677i
$40$	−6.58700	+	1.41531i	−1.04150	+	0.223781i
$41$	6.43239	+	4.93574i	1.00457	+	0.770834i	0.973501	−	0.228684i	$-0.0734421\pi$
$41$	6.43239	+	4.93574i	1.00457	+	0.770834i	0.0310692	+	0.999517i	$0.490109\pi$
$42$	3.63759	−	2.17855i	0.561293	−	0.336158i
$43$	0.753577	+	11.4974i	0.114919	+	1.75333i	0.534093	+	0.845426i	$0.320653\pi$
$43$	0.753577	+	11.4974i	0.114919	+	1.75333i	−0.419173	+	0.907906i	$0.637680\pi$
$44$	−0.567873	+	0.957714i	−0.0856101	+	0.144381i
$45$	−5.47414	+	4.59342i	−0.816036	+	0.684746i
$46$	−3.77699	−	0.646145i	−0.556887	−	0.0952689i
$47$	−1.75166	−	6.53727i	−0.255505	−	0.953558i	−0.967809	−	0.251687i	$-0.919015\pi$
$47$	−1.75166	−	6.53727i	−0.255505	−	0.953558i	0.712304	−	0.701872i	$-0.247652\pi$
$48$	−6.74498	−	1.58279i	−0.973554	−	0.228455i
$49$	1.03622	−	3.86722i	0.148031	−	0.552460i
$50$	−0.398399	+	0.865870i	−0.0563421	+	0.122452i
$51$	1.82811	+	9.74472i	0.255987	+	1.36453i
$52$	12.4215	−	1.48872i	1.72255	−	0.206448i
$53$	−2.94043	−	4.40066i	−0.403899	−	0.604477i	0.572643	−	0.819805i	$-0.305918\pi$
$53$	−2.94043	−	4.40066i	−0.403899	−	0.604477i	−0.976542	+	0.215328i	$0.930918\pi$
$54$	−7.10898	+	1.86074i	−0.967410	+	0.253214i
$55$	0.507470	+	1.22514i	0.0684272	+	0.165198i
$56$	4.20213	−	2.51258i	0.561533	−	0.335757i
$57$	5.05551	+	2.15894i	0.669618	+	0.285959i
$58$	1.31595	+	0.954617i	0.172793	+	0.125347i
$59$	2.78077	+	8.19189i	0.362026	+	1.06649i	0.963525	+	0.267619i	$0.0862370\pi$
$59$	2.78077	+	8.19189i	0.362026	+	1.06649i	−0.601499	+	0.798873i	$0.705430\pi$
$60$	−6.32477	+	5.29951i	−0.816525	+	0.684163i
$61$	−6.59370	+	3.25166i	−0.844237	+	0.416332i	−0.812357	−	0.583160i	$-0.801816\pi$
$61$	−6.59370	+	3.25166i	−0.844237	+	0.416332i	−0.0318800	+	0.999492i	$0.510149\pi$
$62$	2.20502	−	3.50045i	0.280038	−	0.444557i
$63$	2.69396	−	4.43958i	0.339407	−	0.559334i
$64$	−7.78713	−	1.83320i	−0.973391	−	0.229150i
$65$	7.44995	−	12.9037i	0.924052	−	1.60051i
$66$	−0.0673897	+	1.36198i	−0.00829509	+	0.167649i
$67$	−0.254497	+	3.88288i	−0.0310918	+	0.474369i	0.953715	+	0.300713i	$0.0972248\pi$
$67$	−0.254497	+	3.88288i	−0.0310918	+	0.474369i	−0.984806	+	0.173656i	$0.944442\pi$
$68$	2.10289	+	11.2537i	0.255013	+	1.36472i
$69$	−4.46018	+	1.45998i	−0.536943	+	0.175761i
$70$	0.605256	−	5.79967i	0.0723419	−	0.693193i
$71$	−1.77930	+	4.29560i	−0.211164	+	0.509795i	−0.993603	−	0.112933i	$-0.963975\pi$
$71$	−1.77930	+	4.29560i	−0.211164	+	0.509795i	0.782439	+	0.622727i	$0.213975\pi$
$72$	−8.21028	+	2.14273i	−0.967591	+	0.252524i
$73$	−5.93905	−	14.3381i	−0.695114	−	1.67815i	−0.734214	−	0.678918i	$-0.762449\pi$
$73$	−5.93905	−	14.3381i	−0.695114	−	1.67815i	0.0391005	−	0.999235i	$-0.487551\pi$
$74$	−3.20508	−	10.7910i	−0.372583	−	1.25443i
$75$	0.0636412	+	1.16560i	0.00734865	+	0.134592i
$76$	5.83581	+	2.49710i	0.669414	+	0.286437i
$77$	−0.635386	−	0.724519i	−0.0724090	−	0.0825666i
$78$	12.6019	−	8.71533i	1.42688	−	0.986817i
$79$	9.13053	−	2.44652i	1.02726	−	0.275255i	0.294438	−	0.955671i	$-0.404867\pi$
$79$	9.13053	−	2.44652i	1.02726	−	0.275255i	0.732826	+	0.680416i	$0.238201\pi$
$80$	−7.30759	+	6.11413i	−0.817013	+	0.683580i
$81$	−6.63541	+	6.08041i	−0.737267	+	0.675601i
$82$	11.3020	+	1.93348i	1.24810	+	0.213518i
$83$	13.0525	+	4.43074i	1.43270	+	0.486337i	0.926571	−	0.376119i	$-0.122742\pi$
$83$	13.0525	+	4.43074i	1.43270	+	0.486337i	0.506132	+	0.862456i	$0.331075\pi$
$84$	3.11437	−	5.12416i	0.339806	−	0.559092i
$85$	12.2291	+	6.03071i	1.32643	+	0.654123i
$86$	8.52414	+	13.8872i	0.919181	+	1.49749i
$87$	1.97113	+	0.281403i	0.211327	+	0.0301696i
$88$	−0.0789374	+	1.57263i	−0.00841476	+	0.167643i
$89$	−1.86775	−	0.773649i	−0.197981	−	0.0820066i	0.281490	−	0.959564i	$-0.409171\pi$
$89$	−1.86775	−	0.773649i	−0.197981	−	0.0820066i	−0.479471	+	0.877558i	$0.659171\pi$
$90$	−3.81967	+	9.35636i	−0.402629	+	0.986247i
$91$	−2.11238	+	10.6197i	−0.221438	+	1.11324i
$92$	−5.15137	+	1.68217i	−0.537068	+	0.175378i
$93$	0.386500	−	5.05208i	0.0400782	−	0.523876i
$94$	−6.50212	−	7.02358i	−0.670643	−	0.724427i
$95$	6.54718	−	3.78002i	0.671727	−	0.387822i
$96$	−9.48218	+	2.46745i	−0.967771	+	0.251833i
$97$	11.7390	+	6.77752i	1.19192	+	0.688153i	0.958741	−	0.284281i	$-0.0917550\pi$
$97$	11.7390	+	6.77752i	1.19192	+	0.688153i	0.233175	+	0.972435i	$0.425088\pi$
$98$	−1.25365	−	5.52147i	−0.126638	−	0.557752i
$99$	0.705836	+	1.51364i	0.0709392	+	0.152127i
$100$	0.0725258	+	1.34597i	0.00725258	+	0.134597i
$101$	−9.42192	−	8.26280i	−0.937516	−	0.822179i	0.0467441	−	0.998907i	$-0.485115\pi$
$101$	−9.42192	−	8.26280i	−0.937516	−	0.822179i	−0.984260	+	0.176728i	$0.943449\pi$
$102$	8.71277	+	10.9859i	0.862693	+	1.08777i
$103$	1.22676	+	9.31819i	0.120877	+	0.918149i	0.939195	+	0.343384i	$0.111573\pi$
$103$	1.22676	+	9.31819i	0.120877	+	0.918149i	−0.818319	+	0.574765i	$0.805094\pi$
$104$	14.5586	−	10.0532i	1.42758	−	0.985798i
$105$	−2.66090	−	6.62747i	−0.259677	−	0.646775i
$106$	−6.58049	−	3.56665i	−0.639154	−	0.346423i
$107$	−8.11283	+	5.42082i	−0.784297	+	0.524050i	−0.882047	−	0.471161i	$-0.843835\pi$
$107$	−8.11283	+	5.42082i	−0.784297	+	0.524050i	0.0977508	+	0.995211i	$0.468835\pi$
$108$	−7.66692	+	7.01558i	−0.737749	+	0.675075i
$109$	−0.931381	−	4.68237i	−0.0892101	−	0.448490i	−0.999411	−	0.0343221i	$-0.989073\pi$
$109$	−0.931381	−	4.68237i	−0.0892101	−	0.448490i	0.910201	−	0.414167i	$-0.135927\pi$
$110$	1.44274	+	1.19812i	0.137560	+	0.114236i
$111$	−9.64189	−	9.85450i	−0.915168	−	0.935348i
$112$	3.60039	−	5.91430i	0.340205	−	0.558849i
$113$	0.818038	−	3.05296i	0.0769545	−	0.287198i	−0.916715	−	0.399542i	$-0.869169\pi$
$113$	0.818038	−	3.05296i	0.0769545	−	0.287198i	0.993669	+	0.112344i	$0.0358358\pi$
$114$	7.74843	−	0.632595i	0.725707	−	0.0592479i
$115$	−2.07461	+	6.11162i	−0.193459	+	0.569911i
$116$	2.27583	+	0.326561i	0.211306	+	0.0303204i
$117$	8.66484	−	16.6453i	0.801065	−	1.53886i
$118$	8.88068	+	8.41504i	0.817533	+	0.774667i
$119$	−9.82393	−	1.29335i	−0.900559	−	0.118561i
$120$	−4.41829	+	10.8006i	−0.403333	+	0.985959i
$121$	−10.5986	+	1.39533i	−0.963511	+	0.126849i
$122$	−6.10509	+	8.41595i	−0.552729	+	0.761945i
$123$	13.3464	−	4.36876i	1.20340	−	0.393918i
$124$	0.450456	−	5.83332i	0.0404521	−	0.523847i
$125$	−8.56801	−	5.72496i	−0.766346	−	0.512056i
$126$	0.442893	−	7.33065i	0.0394561	−	0.653066i
$127$	−12.9883			−1.15253			−0.576264	−	0.817263i	$-0.695490\pi$
$127$	−12.9883			−1.15253			−0.576264	+	0.817263i	$0.695490\pi$
$128$	−10.9511	+	2.84135i	−0.967950	+	0.251142i
$129$	17.1732	+	10.1662i	1.51202	+	0.895088i
$130$	0.811776	−	21.0560i	0.0711975	−	1.84673i
$131$	0.158470	−	2.41779i	0.0138456	−	0.211243i	−0.985330	−	0.170657i	$-0.945411\pi$
$131$	0.158470	−	2.41779i	0.0138456	−	0.211243i	0.999176	−	0.0405858i	$-0.0129224\pi$
$132$	0.813782	+	1.74838i	0.0708306	+	0.152177i
$133$	−3.62236	+	4.13050i	−0.314098	+	0.358160i
$134$	2.24197	+	5.02560i	0.193677	+	0.434145i
$135$	1.21332	+	12.3177i	0.104426	+	1.06014i
$136$	10.0516	+	12.6926i	0.861916	+	1.08839i
$137$	3.94854	+	0.519836i	0.337347	+	0.0444126i	0.297297	−	0.954785i	$-0.403915\pi$
$137$	3.94854	+	0.519836i	0.337347	+	0.0444126i	0.0400501	+	0.999198i	$0.487248\pi$
$138$	−4.61731	+	4.76759i	−0.393052	+	0.405844i
$139$	−3.32239	+	6.73714i	−0.281802	+	0.571437i	−0.991045	−	0.133526i	$-0.957370\pi$
$139$	−3.32239	+	6.73714i	−0.281802	+	0.571437i	0.709244	+	0.704963i	$0.249037\pi$
$140$	−3.06708	−	7.65494i	−0.259215	−	0.646960i
$141$	−11.0585	−	3.88883i	−0.931290	−	0.327498i
$142$	0.606480	+	6.54740i	0.0508947	+	0.549445i
$143$	−2.46237	−	2.46237i	−0.205913	−	0.205913i
$144$	−8.85877	+	8.09458i	−0.738231	+	0.674548i
$145$	1.93626	−	1.93626i	0.160798	−	0.160798i
$146$	−16.8848	−	14.0219i	−1.39739	−	1.16046i
$147$	−4.51511	−	5.26318i	−0.372400	−	0.434100i
$148$	−11.1254	−	11.3869i	−0.914500	−	0.936001i
$149$	9.80170	+	4.83366i	0.802987	+	0.395989i	0.796990	−	0.603993i	$-0.206424\pi$
$149$	9.80170	+	4.83366i	0.802987	+	0.395989i	0.00599682	+	0.999982i	$0.498091\pi$
$150$	0.848217	+	1.41629i	0.0692566	+	0.115640i
$151$	−1.57887	+	11.9927i	−0.128487	+	0.975952i	0.798799	+	0.601598i	$0.205469\pi$
$151$	−1.57887	+	11.9927i	−0.128487	+	0.975952i	−0.927286	+	0.374354i	$0.877864\pi$
$152$	8.94763	−	0.724071i	0.725749	−	0.0587299i
$153$	15.7185	+	6.91617i	1.27077	+	0.559139i
$154$	−1.27266	−	0.487456i	−0.102554	−	0.0392803i
$155$	−5.23896	−	4.59445i	−0.420804	−	0.369035i
$156$	10.0190	−	19.2132i	0.802163	−	1.53829i
$157$	7.24350	+	0.474764i	0.578094	+	0.0378903i	0.351646	−	0.936133i	$-0.385622\pi$
$157$	7.24350	+	0.474764i	0.578094	+	0.0378903i	0.226448	+	0.974023i	$0.427289\pi$
$158$	9.80976	−	9.08144i	0.780422	−	0.722481i
$159$	−9.16656	−	0.0999615i	−0.726955	−	0.00792747i
$160$	−5.11070	+	12.4679i	−0.404036	+	0.985671i
$161$		−	4.69021i		−	0.369640i
$162$	−4.29198	+	11.9824i	−0.337210	+	0.941429i
$163$	−10.2642	+	15.3615i	−0.803956	+	1.20321i	0.171969	+	0.985102i	$0.444987\pi$
$163$	−10.2642	+	15.3615i	−0.803956	+	1.20321i	−0.975926	+	0.218104i	$0.930013\pi$
$164$	15.4146	−	5.03361i	1.20368	−	0.393059i
$165$	2.24769	+	0.472630i	0.174982	+	0.0367942i
$166$	19.2514	−	3.06364i	1.49420	−	0.237784i
$167$	−0.590107	−	4.48231i	−0.0456638	−	0.346851i	−0.998991	−	0.0449118i	$-0.985699\pi$
$167$	−0.590107	−	4.48231i	−0.0456638	−	0.346851i	0.953327	−	0.301939i	$-0.0976340\pi$
$168$	0.517451	−	8.46433i	0.0399222	−	0.653038i
$169$	−3.41030	+	25.9038i	−0.262331	+	1.99260i
$170$	19.2762	−	0.518957i	1.47841	−	0.0398022i
$171$	8.03025	−	5.11592i	0.614088	−	0.391224i
$172$	19.8215	+	11.7531i	1.51138	+	0.896167i
$173$	15.6095	+	5.29870i	1.18677	+	0.402853i	0.843884	−	0.536525i	$-0.180263\pi$
$173$	15.6095	+	5.29870i	1.18677	+	0.402853i	0.342882	+	0.939378i	$0.388597\pi$
$174$	2.65159	−	0.947704i	0.201017	−	0.0718452i
$175$	−1.12688	−	0.301946i	−0.0851840	−	0.0228250i
$176$	0.938233	+	2.01953i	0.0707220	+	0.152228i
$177$	14.4302	+	4.03573i	1.08464	+	0.303344i
$178$	−2.84685	+	0.263701i	−0.213380	+	0.0197652i
$179$	−9.44178	+	1.87809i	−0.705712	+	0.140375i	−0.534883	−	0.844926i	$-0.679644\pi$
$179$	−9.44178	+	1.87809i	−0.705712	+	0.140375i	−0.170829	+	0.985301i	$0.554644\pi$
$180$	1.39087	+	14.2242i	0.103669	+	1.06021i
$181$	1.68086	+	2.51558i	0.124937	+	0.186982i	0.888665	−	0.458556i	$-0.151633\pi$
$181$	1.68086	+	2.51558i	0.124937	+	0.186982i	−0.763728	+	0.645538i	$0.776633\pi$
$182$	4.35985	+	14.6789i	0.323173	+	1.08807i
$183$	−1.79967	+	12.6060i	−0.133035	+	0.931864i
$184$	−5.33554	+	5.50133i	−0.393342	+	0.405564i
$185$	−18.7982	+	2.47483i	−1.38207	+	0.181953i
$186$	−2.84779	−	6.57540i	−0.208810	−	0.482131i
$187$	2.10117	−	2.39592i	0.153652	−	0.175207i
$188$	−12.7660	−	4.49955i	−0.931056	−	0.328163i
$189$	−3.71220	−	8.19276i	−0.270023	−	0.595936i
$190$	5.69849	−	9.04630i	0.413412	−	0.656288i
$191$	6.79274	−	11.7654i	0.491506	−	0.851313i	−0.508446	−	0.861094i	$-0.669780\pi$
$191$	6.79274	−	11.7654i	0.491506	−	0.851313i	0.999952	+	0.00978071i	$0.00311335\pi$
$192$	−10.2359	+	9.33951i	−0.738712	+	0.674021i
$193$	−9.93674	−	17.2109i	−0.715263	−	1.23887i	−0.962858	−	0.270008i	$-0.912974\pi$
$193$	−9.93674	−	17.2109i	−0.715263	−	1.23887i	0.247596	−	0.968863i	$-0.420360\pi$
$194$	19.1555	+	0.738506i	1.37528	+	0.0530216i
$195$	−11.1612	−	23.2690i	−0.799273	−	1.66633i
$196$	−5.20926	−	6.08112i	−0.372090	−	0.434366i
$197$	−0.513417	−	0.102125i	−0.0365794	−	0.00727610i	0.176767	−	0.984253i	$-0.443436\pi$
$197$	−0.513417	−	0.102125i	−0.0365794	−	0.00727610i	−0.213346	+	0.976977i	$0.568436\pi$
$198$	1.88115	+	1.42825i	0.133687	+	0.101502i
$199$	4.30335	−	10.3892i	0.305057	−	0.736472i	−0.694794	−	0.719208i	$-0.744505\pi$
$199$	4.30335	−	10.3892i	0.305057	−	0.736472i	0.999851	−	0.0172633i	$-0.00549536\pi$
$200$	0.978269	+	1.63609i	0.0691741	+	0.115689i
$201$	5.30197	+	4.16098i	0.373972	+	0.293493i
$202$	−17.2360	−	4.12459i	−1.21272	−	0.290205i
$203$	−0.880114	+	1.78469i	−0.0617719	+	0.125261i
$204$	18.1445	+	7.99906i	1.27037	+	0.560046i
$205$	6.20795	−	18.2880i	0.433582	−	1.27729i
$206$	7.67918	+	10.8488i	0.535034	+	0.755875i
$207$	−2.27456	+	7.80389i	−0.158093	+	0.542408i
$208$	11.5848	−	22.1772i	0.803261	−	1.53771i
$209$	−0.457303	−	1.70668i	−0.0316323	−	0.118053i
$210$	−7.69913	−	6.53688i	−0.531291	−	0.451088i
$211$	−11.6219	+	10.1921i	−0.800082	+	0.701653i	−0.958304	−	0.285750i	$-0.907757\pi$
$211$	−11.6219	+	10.1921i	−0.800082	+	0.701653i	0.158222	+	0.987404i	$0.449424\pi$
$212$	−10.5845	−	0.122981i	−0.726949	−	0.00844635i
$213$	4.40085	+	6.74440i	0.301541	+	0.462119i
$214$	−6.57529	+	12.1314i	−0.449477	+	0.829289i
$215$	25.3564	−	10.5030i	1.72929	−	0.716297i
$216$	−4.96583	+	13.8326i	−0.337882	+	0.941188i
$217$	4.67831	+	1.93782i	0.317585	+	0.131548i
$218$	−4.25278	−	5.24385i	−0.288035	−	0.355158i
$219$	−26.3053	−	5.53131i	−1.77755	−	0.373771i
$220$	2.59502	+	0.547598i	0.174956	+	0.0369191i
$221$	−35.7297	−	2.34185i	−2.40344	−	0.157530i
$222$	−18.5608	−	5.97088i	−1.24572	−	0.400739i
$223$	−12.8210	−	7.40223i	−0.858561	−	0.495690i	0.00496938	−	0.999988i	$-0.498418\pi$
$223$	−12.8210	−	7.40223i	−0.858561	−	0.495690i	−0.863530	+	0.504297i	$0.831752\pi$
$224$	0.604477	−	9.77334i	0.0403883	−	0.653009i
$225$	1.72854	+	1.04889i	0.115236	+	0.0699259i
$226$	−0.989690	−	4.35890i	−0.0658332	−	0.289950i
$227$	−3.06508	−	6.21536i	−0.203436	−	0.412528i	0.771114	−	0.636697i	$-0.219700\pi$
$227$	−3.06508	−	6.21536i	−0.203436	−	0.412528i	−0.974550	+	0.224169i	$0.928033\pi$
$228$	9.27675	−	5.90073i	0.614368	−	0.390785i
$229$	−5.67410	+	1.92610i	−0.374955	+	0.127280i	−0.502554	−	0.864546i	$-0.667606\pi$
$229$	−5.67410	+	1.92610i	−0.374955	+	0.127280i	0.127599	+	0.991826i	$0.459273\pi$
$230$	1.43449	+	9.01410i	0.0945877	+	0.594372i
$231$	−1.65711	+	0.199805i	−0.109030	+	0.0131462i
$232$	3.06257	−	1.09213i	0.201068	−	0.0717017i
$233$	−17.4537	+	7.22957i	−1.14343	+	0.473625i	−0.872326	−	0.488924i	$-0.837389\pi$
$233$	−17.4537	+	7.22957i	−1.14343	+	0.473625i	−0.271106	+	0.962549i	$0.587389\pi$
$234$	−0.135519	−	26.5381i	−0.00885918	−	1.73485i
$235$	−13.4042	+	8.95642i	−0.874396	+	0.584253i
$236$	16.6593	+	4.67195i	1.08443	+	0.304118i
$237$	5.43148	−	15.4452i	0.352813	−	1.00327i
$238$	−13.1433	+	4.85982i	−0.851955	+	0.315015i
$239$	23.1884	+	6.21332i	1.49993	+	0.401906i	0.913078	−	0.407785i	$-0.133699\pi$
$239$	23.1884	+	6.21332i	1.49993	+	0.401906i	0.586856	+	0.809691i	$0.300365\pi$
$240$	1.59432	+	16.4258i	0.102913	+	1.06028i
$241$	−0.432149	+	0.115794i	−0.0278372	+	0.00745895i	−0.272711	−	0.962096i	$-0.587920\pi$
$241$	−0.432149	+	0.115794i	−0.0278372	+	0.00745895i	0.244874	+	0.969555i	$0.421254\pi$
$242$	−12.3396	+	8.73439i	−0.793220	+	0.561468i
$243$	2.20345	+	15.4319i	0.141352	+	0.989959i
$244$	−2.08847	+	14.5547i	−0.133700	+	0.931769i
$245$	−9.51628	+	0.623730i	−0.607973	+	0.0398486i
$246$	13.8166	−	14.2662i	0.880912	−	0.909582i
$247$	−12.0856	+	15.7502i	−0.768987	+	1.00216i
$248$	−3.28293	−	7.59496i	−0.208466	−	0.482280i
$249$	19.0984	−	14.3266i	1.21031	−	0.907911i
$250$	−14.4943	−	1.51263i	−0.916698	−	0.0956669i
$251$	−8.06992	−	1.60521i	−0.509369	−	0.101320i	−0.0662864	−	0.997801i	$-0.521115\pi$
$251$	−8.06992	−	1.60521i	−0.509369	−	0.101320i	−0.443082	+	0.896481i	$0.646115\pi$
$252$	−4.27973	−	9.46324i	−0.269598	−	0.596128i
$253$	1.25421	+	0.838033i	0.0788512	+	0.0526867i
$254$	−16.2494	+	8.56450i	−1.01958	+	0.537384i
$255$	20.5804	−	11.5847i	1.28880	−	0.725465i
$256$	−11.8271	+	10.7759i	−0.739193	+	0.673493i
$257$	−8.28955	−	14.3579i	−0.517088	−	0.895622i	−0.999803	−	0.0198449i	$-0.993683\pi$
$257$	−8.28955	−	14.3579i	−0.517088	−	0.895622i	0.482715	−	0.875777i	$-0.339651\pi$
$258$	28.1886	+	1.39475i	1.75495	+	0.0868331i
$259$	12.3576	−	6.09407i	0.767861	−	0.378667i
$260$	−12.8687	−	26.8779i	−0.798083	−	1.66690i
$261$	2.32990	−	2.54267i	0.144217	−	0.157388i
$262$	−1.39603	−	3.12933i	−0.0862469	−	0.193331i
$263$	9.49509	+	12.3742i	0.585492	+	0.763029i	0.988344	−	0.152237i	$-0.0486476\pi$
$263$	9.49509	+	12.3742i	0.585492	+	0.763029i	−0.402852	+	0.915265i	$0.631981\pi$
$264$	2.17099	+	1.65075i	0.133615	+	0.101597i
$265$	−7.67471	+	10.0019i	−0.471453	+	0.614410i
$266$	−1.80819	+	7.55616i	−0.110867	+	0.463298i
$267$	−2.93250	+	1.91351i	−0.179466	+	0.117105i
$268$	6.11875	+	4.80905i	0.373762	+	0.293760i
$269$	5.05669	−	1.00584i	0.308312	−	0.0613270i	−0.0385096	−	0.999258i	$-0.512261\pi$
$269$	5.05669	−	1.00584i	0.308312	−	0.0613270i	0.346821	+	0.937931i	$0.387261\pi$
$270$	9.64022	+	14.6103i	0.586685	+	0.889153i
$271$	0.0628361	+	0.0628361i	0.00381702	+	0.00381702i	0.709013	−	0.705196i	$-0.249141\pi$
$271$	0.0628361	+	0.0628361i	0.00381702	+	0.00381702i	−0.705196	+	0.709013i	$0.749141\pi$
$272$	20.9448	+	9.25147i	1.26997	+	0.560953i
$273$	13.1158	+	13.4050i	0.793805	+	0.811309i
$274$	5.28271	−	1.95331i	0.319140	−	0.118004i
$275$	0.282091	−	0.247387i	0.0170107	−	0.0149180i
$276$	−2.63287	+	9.00927i	−0.158480	+	0.542295i
$277$	−1.72003	−	26.2425i	−0.103346	−	1.57676i	−0.663375	−	0.748287i	$-0.730877\pi$
$277$	−1.72003	−	26.2425i	−0.103346	−	1.57676i	0.560029	−	0.828473i	$-0.310790\pi$
$278$	0.285900	+	10.6195i	0.0171471	+	0.636913i
$279$	−6.84433	−	5.49307i	−0.409759	−	0.328862i
$280$	−8.88481	−	7.55449i	−0.530969	−	0.451467i
$281$	6.21873	−	4.77180i	0.370978	−	0.284662i	−0.406400	−	0.913695i	$-0.633216\pi$
$281$	6.21873	−	4.77180i	0.370978	−	0.284662i	0.777378	+	0.629034i	$0.216549\pi$
$282$	−16.3993	+	2.42671i	−0.976562	+	0.144509i
$283$	22.3858	−	7.59897i	1.33070	−	0.451712i	0.436631	−	0.899641i	$-0.356172\pi$
$283$	22.3858	−	7.59897i	1.33070	−	0.451712i	0.894069	+	0.447929i	$0.147838\pi$
$284$	5.07610	+	7.79139i	0.301211	+	0.462334i
$285$	0.998842	−	13.0562i	0.0591663	−	0.773383i
$286$	−4.70429	−	1.45693i	−0.278170	−	0.0861499i
$287$			14.0347i			0.828441i
$288$	−5.74545	+	15.9684i	−0.338554	+	0.940947i
$289$		−	15.7672i		−	0.927483i
$290$	1.14564	−	3.69918i	0.0672744	−	0.217223i
$291$	21.1688	−	10.1538i	1.24094	−	0.595229i
$292$	−30.3702	−	6.40868i	−1.77728	−	0.375040i
$293$	−11.4555	+	3.88863i	−0.669240	+	0.227176i	−0.635321	−	0.772248i	$-0.719132\pi$
$293$	−11.4555	+	3.88863i	−0.669240	+	0.227176i	−0.0339192	+	0.999425i	$0.510799\pi$
$294$	−9.11929	−	3.60738i	−0.531848	−	0.210387i
$295$	16.3484	−	12.5446i	0.951842	−	0.730374i
$296$	−21.4272	−	6.90988i	−1.24543	−	0.401628i
$297$	2.85411	+	0.471182i	0.165612	+	0.0273408i
$298$	15.4500	−	0.415948i	0.894994	−	0.0240952i
$299$	−1.10849	−	16.9124i	−0.0641059	−	0.978067i
$300$	1.99509	+	1.21258i	0.115186	+	0.0700082i
$301$	−14.9952	+	13.1504i	−0.864308	+	0.757978i
$302$	5.93269	+	16.0449i	0.341388	+	0.923280i
$303$	−21.0261	+	5.38890i	−1.20792	+	0.309584i
$304$	10.7167	−	6.80593i	0.614646	−	0.390347i
$305$	12.3830	+	12.3830i	0.709050	+	0.709050i
$306$	24.2256	−	1.71211i	1.38488	−	0.0978749i
$307$	−30.3434	+	6.03567i	−1.73179	+	0.344474i	−0.957516	−	0.288379i	$-0.906884\pi$
$307$	−30.3434	+	6.03567i	−1.73179	+	0.344474i	−0.774272	+	0.632853i	$0.781884\pi$
$308$	−1.91363	+	0.229349i	−0.109039	+	0.0130684i
$309$	14.5207	+	7.35873i	0.826052	+	0.418623i
$310$	−9.58392	−	2.29344i	−0.544330	−	0.130259i
$311$	9.85966	−	12.8494i	0.559090	−	0.728620i	−0.425216	−	0.905092i	$-0.639802\pi$
$311$	9.85966	−	12.8494i	0.559090	−	0.728620i	0.984306	+	0.176472i	$0.0564685\pi$
$312$	−0.134611	−	30.6437i	−0.00762087	−	1.73486i
$313$	−10.1569	−	13.2368i	−0.574103	−	0.748186i	0.412566	−	0.910928i	$-0.364633\pi$
$313$	−10.1569	−	13.2368i	−0.574103	−	0.748186i	−0.986669	+	0.162742i	$0.947966\pi$
$314$	9.37523	−	4.18239i	0.529075	−	0.236026i
$315$	−12.0766	−	2.67722i	−0.680438	−	0.150844i
$316$	6.28446	−	17.8301i	0.353529	−	1.00302i
$317$	−17.6109	+	8.68476i	−0.989129	+	0.487784i	−0.863530	−	0.504297i	$-0.831752\pi$
$317$	−17.6109	+	8.68476i	−0.989129	+	0.487784i	−0.125599	+	0.992081i	$0.540085\pi$
$318$	−11.5340	+	5.91936i	−0.646793	+	0.331941i
$319$	−0.319988	−	0.554235i	−0.0179159	−	0.0310312i
$320$	1.82742	+	18.9682i	0.102156	+	1.06036i
$321$	−0.184284	+	16.8990i	−0.0102857	+	0.943209i
$322$	−3.09272	−	5.86781i	−0.172350	−	0.327000i
$323$	−15.1059	−	10.0934i	−0.840515	−	0.561614i
$324$	2.53161	+	17.8211i	0.140645	+	0.990060i
$325$	−4.13476	−	0.822454i	−0.229355	−	0.0456216i
$326$	−2.71198	+	25.9866i	−0.150202	+	1.43927i
$327$	−7.60459	−	3.24752i	−0.420535	−	0.179588i
$328$	15.9657	−	16.4618i	0.881561	−	0.908953i
$329$	7.13176	−	9.29429i	0.393187	−	0.512411i
$330$	3.12368	−	0.890829i	0.171953	−	0.0490385i
$331$	−12.1643	+	0.797288i	−0.668608	+	0.0438229i	−0.395928	−	0.918282i	$-0.629577\pi$
$331$	−12.1643	+	0.797288i	−0.668608	+	0.0438229i	−0.272681	+	0.962105i	$0.587910\pi$
$332$	22.0648	−	16.5272i	1.21096	−	0.907047i
$333$	−23.5167	+	4.14681i	−1.28871	+	0.227244i
$334$	−3.69390	−	5.21859i	−0.202121	−	0.285549i
$335$	8.95307	−	2.39897i	0.489158	−	0.131070i
$336$	−4.93400	−	10.9307i	−0.269172	−	0.596321i
$337$	−3.27078	−	0.876403i	−0.178171	−	0.0477407i	0.168631	−	0.985679i	$-0.446066\pi$
$337$	−3.27078	−	0.876403i	−0.178171	−	0.0477407i	−0.346801	+	0.937939i	$0.612732\pi$
$338$	12.8144	+	34.6564i	0.697011	+	1.88506i
$339$	−3.56444	−	4.15500i	−0.193594	−	0.225669i
$340$	23.7738	−	13.3599i	1.28931	−	0.724545i
$341$	−1.35410	+	0.904780i	−0.0733286	+	0.0489966i
$342$	6.67303	−	11.6955i	0.360836	−	0.632423i
$343$	17.5974	−	7.28909i	0.950171	−	0.393574i
$344$	32.5483	+	1.63375i	1.75488	+	0.0880857i
$345$	6.70817	+	8.94249i	0.361155	+	0.481448i
$346$	23.0226	−	3.66379i	1.23770	−	0.196967i
$347$	−9.05715	+	3.07449i	−0.486213	+	0.165047i	−0.553772	−	0.832668i	$-0.686812\pi$
$347$	−9.05715	+	3.07449i	−0.486213	+	0.165047i	0.0675591	+	0.997715i	$0.478479\pi$
$348$	2.69243	−	2.93411i	0.144329	−	0.157285i
$349$	−6.02400	−	12.2155i	−0.322457	−	0.653879i	0.673931	−	0.738795i	$-0.264605\pi$
$349$	−6.02400	−	12.2155i	−0.322457	−	0.653879i	−0.996388	+	0.0849156i	$0.972938\pi$
$350$	−1.60891	+	0.365305i	−0.0860001	+	0.0195264i
$351$	−15.3221	−	28.6648i	−0.817832	−	1.53001i
$352$	2.50548	+	1.90792i	0.133542	+	0.101692i
$353$	−0.190057	−	0.109729i	−0.0101157	−	0.00584030i	0.494934	−	0.868931i	$-0.335192\pi$
$353$	−0.190057	−	0.109729i	−0.0101157	−	0.00584030i	−0.505049	+	0.863090i	$0.668526\pi$
$354$	20.7145	−	4.46629i	1.10096	−	0.237380i
$355$	11.0515	+	0.724354i	0.586553	+	0.0384447i
$356$	−3.38774	+	2.20712i	−0.179550	+	0.116977i
$357$	−11.4560	+	12.7792i	−0.606314	+	0.676347i
$358$	−10.5740	+	8.57553i	−0.558852	+	0.453231i
$359$	−28.4547	−	11.7863i	−1.50178	−	0.622058i	−0.527938	−	0.849283i	$-0.677035\pi$
$359$	−28.4547	−	11.7863i	−1.50178	−	0.622058i	−0.973842	+	0.227225i	$0.927035\pi$
$360$	11.1195	+	16.8784i	0.586050	+	0.889572i
$361$	8.24742	−	3.41619i	0.434075	−	0.179800i
$362$	3.76165	+	2.03883i	0.197708	+	0.107159i
$363$	−8.36990	+	16.5160i	−0.439306	+	0.866865i
$364$	15.1338	+	15.4896i	0.793225	+	0.811875i
$365$	−27.7937	+	24.3744i	−1.45479	+	1.27582i
$366$	6.06088	+	16.9578i	0.316807	+	0.886398i
$367$	−6.15471	−	22.9697i	−0.321273	−	1.19901i	−0.918006	−	0.396568i	$-0.870201\pi$
$367$	−6.15471	−	22.9697i	−0.321273	−	1.19901i	0.596732	−	0.802440i	$-0.296465\pi$
$368$	−3.04760	+	10.4008i	−0.158867	+	0.542181i
$369$	6.80626	−	23.3519i	0.354320	−	1.21565i
$370$	−21.8861	+	15.4917i	−1.13780	+	0.805376i
$371$	2.94488	−	8.67534i	0.152891	−	0.450401i
$372$	−7.89862	−	6.34849i	−0.409524	−	0.329154i
$373$	6.17233	−	12.5163i	0.319591	−	0.648067i	−0.676496	−	0.736447i	$-0.736502\pi$
$373$	6.17233	−	12.5163i	0.319591	−	0.648067i	0.996087	+	0.0883796i	$0.0281689\pi$
$374$	1.04885	−	4.38299i	0.0542348	−	0.226639i
$375$	−16.5631	+	6.64999i	−0.855313	+	0.343404i
$376$	−18.9382	+	2.78861i	−0.976665	+	0.143812i
$377$	−2.75179	+	6.64341i	−0.141724	+	0.342153i
$378$	−10.0465	−	7.80195i	−0.516739	−	0.401289i
$379$	30.8406	+	6.13457i	1.58417	+	0.315112i	0.907136	−	0.420838i	$-0.138264\pi$
$379$	30.8406	+	6.13457i	1.58417	+	0.315112i	0.677037	+	0.735949i	$0.263264\pi$
$380$	1.16412	−	15.0752i	0.0597183	−	0.773341i
$381$	−12.7016	+	18.5677i	−0.650722	+	0.951253i
$382$	0.740164	−	19.1985i	0.0378701	−	0.982282i
$383$	−1.36953	−	2.37210i	−0.0699799	−	0.121209i	0.828912	−	0.559379i	$-0.188960\pi$
$383$	−1.36953	−	2.37210i	−0.0699799	−	0.121209i	−0.898892	+	0.438170i	$0.855627\pi$
$384$	−6.64743	+	18.4340i	−0.339225	+	0.940705i
$385$	−1.14773	+	1.98792i	−0.0584935	+	0.101314i
$386$	−23.7805	−	14.9799i	−1.21040	−	0.762459i
$387$	31.3274	−	14.6085i	1.59246	−	0.742592i
$388$	24.4520	−	11.7072i	1.24136	−	0.594343i
$389$	−23.7647	+	27.0985i	−1.20492	+	1.37395i	−0.296961	+	0.954890i	$0.595973\pi$
$389$	−23.7647	+	27.0985i	−1.20492	+	1.37395i	−0.907959	+	0.419058i	$0.862360\pi$
$390$	−29.3071	−	21.7516i	−1.48402	−	1.10144i
$391$	15.3774	−	2.02447i	0.777669	−	0.102382i
$392$	−10.5271	−	4.17296i	−0.531697	−	0.210766i
$393$	−3.30142	−	2.59095i	−0.166535	−	0.130696i
$394$	−0.709665	+	0.210780i	−0.0357524	+	0.0106190i
$395$	−12.5093	−	18.7215i	−0.629413	−	0.941983i
$396$	3.29525	+	0.546427i	0.165593	+	0.0274590i
$397$	17.7280	−	3.52632i	0.889744	−	0.176981i	0.271005	−	0.962578i	$-0.412644\pi$
$397$	17.7280	−	3.52632i	0.889744	−	0.176981i	0.618739	+	0.785597i	$0.287644\pi$
$398$	−1.46681	−	15.8353i	−0.0735247	−	0.793753i
$399$	2.36246	+	9.21772i	0.118271	+	0.461463i
$400$	2.30273	+	1.40181i	0.115136	+	0.0700904i
$401$	−24.2976	−	6.51052i	−1.21336	−	0.325120i	−0.405282	−	0.914192i	$-0.632827\pi$
$401$	−24.2976	−	6.51052i	−1.21336	−	0.325120i	−0.808081	+	0.589072i	$0.799493\pi$
$402$	9.37691	+	1.70959i	0.467678	+	0.0852666i
$403$	17.3274	+	5.88188i	0.863142	+	0.292997i
$404$	−24.2833	+	6.20524i	−1.20814	+	0.308722i
$405$	18.7955	+	10.3112i	0.933955	+	0.512367i
$406$	0.0757359	+	2.81314i	0.00375871	+	0.139614i
$407$	−0.578402	+	4.39340i	−0.0286703	+	0.217773i
$408$	27.9747	−	1.95701i	1.38495	−	0.0968863i
$409$	3.95411	+	30.0345i	0.195518	+	1.48511i	0.754703	+	0.656066i	$0.227781\pi$
$409$	3.95411	+	30.0345i	0.195518	+	1.48511i	−0.559185	+	0.829043i	$0.688886\pi$
$410$	−4.29249	−	26.9732i	−0.211991	−	1.33211i
$411$	4.60451	−	5.13636i	0.227124	−	0.253358i
$412$	16.7610	+	8.50909i	0.825753	+	0.419213i
$413$	−8.31959	+	12.4512i	−0.409380	+	0.612681i
$414$	2.30022	+	11.2631i	0.113050	+	0.553551i
$415$		−	32.8338i		−	1.61175i
$416$	−0.130179	−	35.3844i	−0.00638256	−	1.73486i
$417$	6.38217	+	11.3380i	0.312536	+	0.555224i
$418$	−1.69750	−	1.83364i	−0.0830276	−	0.0896863i
$419$	35.9109	+	2.35373i	1.75436	+	0.114987i	0.908360	−	0.418189i	$-0.137335\pi$
$419$	35.9109	+	2.35373i	1.75436	+	0.114987i	0.846004	+	0.533177i	$0.179002\pi$
$420$	−13.9426	−	3.10134i	−0.680330	−	0.151330i
$421$	9.52126	+	8.34992i	0.464038	+	0.406950i	0.859183	−	0.511669i	$-0.170972\pi$
$421$	9.52126	+	8.34992i	0.464038	+	0.406950i	−0.395145	+	0.918619i	$0.629306\pi$
$422$	−7.81918	+	20.4146i	−0.380632	+	0.993765i
$423$	−16.3737	+	12.0059i	−0.796115	+	0.583745i
$424$	−13.3232	+	6.82558i	−0.647030	+	0.331479i
$425$	0.503563	−	3.82494i	0.0244264	−	0.185537i
$426$	9.95305	+	5.53584i	0.482227	+	0.268213i
$427$	−11.4137	−	5.62862i	−0.552348	−	0.272388i
$428$	−0.226721	+	19.5131i	−0.0109590	+	0.943202i
$429$	−5.92812	+	1.11212i	−0.286212	+	0.0536936i
$430$	24.7972	−	29.8600i	1.19583	−	1.43998i
$431$	−22.6605	+	22.6605i	−1.09152	+	1.09152i	−0.0961502	+	0.995367i	$0.530653\pi$
$431$	−22.6605	+	22.6605i	−1.09152	+	1.09152i	−0.995367	+	0.0961502i	$0.969347\pi$
$432$	2.90856	+	20.5801i	0.139938	+	0.990160i
$433$	−21.8872	−	21.8872i	−1.05183	−	1.05183i	−0.998581	−	0.0532502i	$-0.983042\pi$
$433$	−21.8872	−	21.8872i	−1.05183	−	1.05183i	−0.0532502	−	0.998581i	$-0.516958\pi$
$434$	7.13072	−	0.660513i	0.342286	−	0.0317056i
$435$	−0.874505	−	4.66153i	−0.0419293	−	0.223503i
$436$	−8.77834	−	3.75618i	−0.420406	−	0.179888i
$437$	3.80348	−	7.71270i	0.181945	−	0.368948i
$438$	−36.5573	+	10.4256i	−1.74678	+	0.498155i
$439$	−3.42925	−	0.451470i	−0.163669	−	0.0215475i	0.0482461	−	0.998835i	$-0.484637\pi$
$439$	−3.42925	−	0.451470i	−0.163669	−	0.0215475i	−0.211915	+	0.977288i	$0.567970\pi$
$440$	3.60765	−	1.02607i	0.171988	−	0.0489158i
$441$	−11.9395	+	1.30768i	−0.568548	+	0.0622704i
$442$	−46.2448	+	20.6303i	−2.19964	+	0.981282i
$443$	−11.2457	+	12.8233i	−0.534300	+	0.609253i	−0.954512	−	0.298174i	$-0.903623\pi$
$443$	−11.2457	+	12.8233i	−0.534300	+	0.609253i	0.420211	+	0.907426i	$0.361956\pi$
$444$	−27.1582	+	4.76894i	−1.28887	+	0.226324i
$445$	−0.314953	+	4.80526i	−0.0149302	+	0.227791i
$446$	−20.9211	−	0.806577i	−0.990644	−	0.0381925i
$447$	16.4954	−	9.28526i	0.780204	−	0.439178i
$448$	−5.68829	−	12.6258i	−0.268746	−	0.596513i
$449$	27.3990			1.29304			0.646521	−	0.762897i	$-0.276223\pi$
$449$	27.3990			1.29304			0.646521	+	0.762897i	$0.276223\pi$
$450$	2.85418	+	0.172440i	0.134547	+	0.00812889i
$451$	−3.75301	−	2.50768i	−0.176722	−	0.118082i
$452$	−4.11243	−	4.80072i	−0.193433	−	0.225807i
$453$	15.6004	+	13.9850i	0.732970	+	0.657074i
$454$	−7.93305	−	5.75478i	−0.372316	−	0.270085i
$455$	25.5711	−	3.36650i	1.19879	−	0.157824i
$456$	7.71498	−	13.4993i	0.361287	−	0.632165i
$457$	9.50296	+	1.25109i	0.444530	+	0.0585234i	0.349469	−	0.936948i	$-0.386362\pi$
$457$	9.50296	+	1.25109i	0.444530	+	0.0585234i	0.0950608	+	0.995471i	$0.469695\pi$
$458$	−5.82866	+	6.15119i	−0.272356	+	0.287426i
$459$	25.2586	−	15.7072i	1.17897	−	0.733150i
$460$	7.73855	+	10.3314i	0.360812	+	0.481705i
$461$	9.32268	−	27.4637i	0.434201	−	1.27911i	−0.481215	−	0.876603i	$-0.659804\pi$
$461$	9.32268	−	27.4637i	0.434201	−	1.27911i	0.915415	−	0.402511i	$-0.131862\pi$
$462$	−1.94142	+	1.34267i	−0.0903230	+	0.0624665i
$463$	6.82162	−	25.4586i	0.317027	−	1.18316i	−0.605060	−	0.796180i	$-0.706851\pi$
$463$	6.82162	−	25.4586i	0.317027	−	1.18316i	0.922087	−	0.386982i	$-0.126483\pi$
$464$	3.11137	−	3.38579i	0.144442	−	0.157182i
$465$	−11.6914	+	2.99644i	−0.542175	+	0.138957i
$466$	−17.0688	+	20.5537i	−0.790696	+	0.952133i
$467$	3.08217	+	15.4951i	0.142626	+	0.717029i	0.984224	+	0.176925i	$0.0566151\pi$
$467$	3.08217	+	15.4951i	0.142626	+	0.717029i	−0.841598	+	0.540104i	$0.818385\pi$
$468$	−17.6688	−	33.1119i	−0.816739	−	1.53060i
$469$	−5.60052	+	3.74215i	−0.258608	+	0.172796i
$470$	−10.8639	+	20.0439i	−0.501113	+	0.924557i
$471$	7.76229	−	9.89080i	0.357667	−	0.455744i
$472$	23.9227	−	5.14015i	1.10113	−	0.236595i
$473$	−0.837248	−	6.35953i	−0.0384967	−	0.292412i
$474$	−3.38936	−	22.9047i	−0.155679	−	1.05205i
$475$	−1.60821	−	1.41036i	−0.0737896	−	0.0647117i
$476$	−13.2387	+	14.7467i	−0.606797	+	0.675914i
$477$	−9.10708	+	13.0065i	−0.416985	+	0.595525i
$478$	33.1075	−	7.51708i	1.51430	−	0.343823i
$479$	29.2854	+	16.9079i	1.33809	+	0.772544i	0.986523	−	0.163621i	$-0.0523174\pi$
$479$	29.2854	+	16.9079i	1.33809	+	0.772544i	0.351562	+	0.936165i	$0.385651\pi$
$480$	12.8258	+	19.4987i	0.585415	+	0.889990i
$481$	43.1196	−	24.8951i	1.96609	−	1.13512i
$482$	−0.464297	+	0.429826i	−0.0211482	+	0.0195780i
$483$	−6.70498	−	4.58666i	−0.305087	−	0.208700i
$484$	−9.67834	+	19.0641i	−0.439925	+	0.866551i
$485$	6.29912	−	31.6678i	0.286028	−	1.43796i
$486$	12.9325	+	17.8536i	0.586630	+	0.809855i
$487$	−13.0389	−	5.40088i	−0.590848	−	0.244737i	0.0671673	−	0.997742i	$-0.478604\pi$
$487$	−13.0389	−	5.40088i	−0.590848	−	0.244737i	−0.658015	+	0.753004i	$0.728604\pi$
$488$	6.98452	+	19.5862i	0.316174	+	0.886624i
$489$	11.9227	+	29.6958i	0.539163	+	1.34289i
$490$	−11.4943	+	7.05536i	−0.519260	+	0.318729i
$491$	6.06287	+	2.98988i	0.273613	+	0.134931i	0.573920	−	0.818912i	$-0.305422\pi$
$491$	6.06287	+	2.98988i	0.273613	+	0.134931i	−0.300306	+	0.953843i	$0.597089\pi$
$492$	7.87843	−	26.9588i	0.355187	−	1.21540i
$493$	−6.23122	−	2.11522i	−0.280640	−	0.0952645i
$494$	−4.73430	+	27.6740i	−0.213006	+	1.24511i
$495$	2.87372	−	2.75103i	0.129164	−	0.123650i
$496$	−9.11531	−	7.33711i	−0.409289	−	0.329446i
$497$	−7.77410	+	2.08306i	−0.348716	+	0.0934381i
$498$	14.4467	−	30.5172i	0.647370	−	1.36751i
$499$	−7.96612	−	9.08362i	−0.356612	−	0.406639i	0.545520	−	0.838098i	$-0.316332\pi$
$499$	−7.96612	−	9.08362i	−0.356612	−	0.406639i	−0.902132	+	0.431459i	$0.857999\pi$
$500$	−19.1309	+	7.66509i	−0.855558	+	0.342793i
$501$	−6.98484	−	3.53975i	−0.312060	−	0.158144i
$502$	−11.1546	+	3.31306i	−0.497852	+	0.147869i
$503$	16.0329	+	38.7069i	0.714873	+	1.72585i	0.687451	+	0.726231i	$0.258730\pi$
$503$	16.0329	+	38.7069i	0.714873	+	1.72585i	0.0274218	+	0.999624i	$0.491270\pi$
$504$	−11.5943	−	9.01719i	−0.516452	−	0.401658i
$505$	−11.4234	+	27.5786i	−0.508336	+	1.22723i
$506$	2.12171	+	0.221422i	0.0943213	+	0.00984341i
$507$	33.6962	+	30.2072i	1.49650	+	1.34155i
$508$	−14.6818	+	21.4297i	−0.651401	+	0.950788i
$509$	1.28475	−	19.6016i	0.0569457	−	0.868824i	−0.869864	−	0.493292i	$-0.835793\pi$
$509$	1.28475	−	19.6016i	0.0569457	−	0.868824i	0.926810	−	0.375532i	$-0.122540\pi$
$510$	18.1087	−	28.0641i	0.801867	−	1.24270i
$511$	13.4321	−	23.2651i	0.594202	−	1.02919i
$512$	−7.69098	+	21.2802i	−0.339897	+	0.940463i
$513$	0.539406	−	16.4828i	0.0238154	−	0.727732i
$514$	−19.8385	−	12.4967i	−0.875037	−	0.551207i
$515$	20.0788	−	9.90175i	0.884776	−	0.436323i
$516$	36.1858	−	16.8426i	1.59299	−	0.741455i
$517$	1.21110	+	3.56778i	0.0532640	+	0.156911i
$518$	11.4418	−	15.7727i	0.502725	−	0.693013i
$519$	22.8397	−	17.1331i	1.00255	−	0.752060i
$520$	−33.8230	−	25.1408i	−1.48324	−	1.10250i
$521$	12.5535	+	30.3068i	0.549979	+	1.32777i	0.917495	+	0.397748i	$0.130208\pi$
$521$	12.5535	+	30.3068i	0.549979	+	1.32777i	−0.367516	+	0.930017i	$0.619792\pi$
$522$	1.23824	−	4.71741i	0.0541964	−	0.206476i
$523$	−3.85072	−	5.76301i	−0.168380	−	0.251999i	0.737677	−	0.675154i	$-0.235923\pi$
$523$	−3.85072	−	5.76301i	−0.168380	−	0.251999i	−0.906057	+	0.423155i	$0.860923\pi$
$524$	−3.81002	−	2.99449i	−0.166441	−	0.130815i
$525$	−1.53365	+	1.31567i	−0.0669341	+	0.0574206i
$526$	20.0387	+	9.22007i	0.873727	+	0.402014i
$527$	−4.33404	+	16.1748i	−0.188794	+	0.704587i
$528$	3.80458	+	0.633675i	0.165573	+	0.0275772i
$529$	−4.05270	−	15.1249i	−0.176204	−	0.657603i
$530$	−3.00642	+	17.5738i	−0.130591	+	0.763357i
$531$	19.8810	−	16.6824i	0.862762	−	0.723955i
$532$	2.72033	+	10.6457i	0.117941	+	0.461548i
$533$	3.31699	+	50.6075i	0.143675	+	2.19205i
$534$	−2.40702	+	4.32764i	−0.104162	+	0.187275i
$535$	18.4389	+	14.1487i	0.797184	+	0.611701i
$536$	10.8261	+	1.98179i	0.467617	+	0.0856004i
$537$	−6.54848	+	15.3343i	−0.282588	+	0.661724i
$538$	5.66306	−	4.59276i	0.244152	−	0.198008i
$539$	−0.434828	+	2.18603i	−0.0187294	+	0.0941590i
$540$	21.6947	+	11.9218i	0.933589	+	0.513034i
$541$	6.71295	−	10.0466i	0.288612	−	0.431939i	−0.658625	−	0.752471i	$-0.728862\pi$
$541$	6.71295	−	10.0466i	0.288612	−	0.431939i	0.947238	+	0.320532i	$0.103862\pi$
$542$	0.120047	+	0.0371787i	0.00515645	+	0.00159696i
$543$	5.23995	+	0.0571418i	0.224868	+	0.00245219i
$544$	32.3040	−	2.23670i	1.38502	−	0.0958978i
$545$	−9.84840	+	5.68597i	−0.421859	+	0.243560i
$546$	25.2481	+	8.12215i	1.08052	+	0.347596i
$547$	7.81531	+	15.8479i	0.334159	+	0.677607i	0.997497	−	0.0707131i	$-0.0225275\pi$
$547$	7.81531	+	15.8479i	0.334159	+	0.677607i	−0.663338	+	0.748320i	$0.730861\pi$
$548$	5.32106	−	5.92716i	0.227305	−	0.253196i
$549$	16.2612	+	14.9005i	0.694013	+	0.635936i
$550$	0.189790	−	0.495510i	0.00809269	−	0.0211286i
$551$	−2.89456	+	2.22108i	−0.123313	+	0.0946210i
$552$	2.64679	+	13.0074i	0.112655	+	0.553632i
$553$	12.9812	+	9.96085i	0.552018	+	0.423578i
$554$	−19.4562	−	31.6972i	−0.826614	−	1.34669i
$555$	−14.8452	+	29.2935i	−0.630146	+	1.24344i
$556$	7.36015	+	13.0972i	0.312140	+	0.555447i
$557$	1.85741	+	9.33784i	0.0787011	+	0.395657i	0.999977	+	0.00674798i	$0.00214797\pi$
$557$	1.85741	+	9.33784i	0.0787011	+	0.395657i	−0.921276	+	0.388909i	$0.872852\pi$
$558$	−12.1849	−	2.35911i	−0.515828	−	0.0998690i
$559$	−50.9629	+	50.9629i	−2.15550	+	2.15550i
$560$	−16.0970	−	3.59261i	−0.680222	−	0.151815i
$561$	−1.37036	−	5.34679i	−0.0578565	−	0.225742i
$562$	4.63359	−	10.0705i	0.195456	−	0.424799i
$563$	6.84387	+	7.80394i	0.288435	+	0.328897i	0.877852	−	0.478932i	$-0.158976\pi$
$563$	6.84387	+	7.80394i	0.288435	+	0.328897i	−0.589417	+	0.807829i	$0.700643\pi$
$564$	−18.9166	+	13.8497i	−0.796531	+	0.583176i
$565$	−7.51259	+	0.492401i	−0.316057	+	0.0207155i
$566$	22.9956	−	24.2681i	0.966579	−	1.02006i
$567$	−15.3424	−	2.70504i	−0.644319	−	0.113601i
$568$	11.4882	+	6.40044i	0.482035	+	0.268557i
$569$	14.2004	+	18.5063i	0.595310	+	0.775823i	0.989706	−	0.143118i	$-0.0457128\pi$
$569$	14.2004	+	18.5063i	0.595310	+	0.775823i	−0.394396	+	0.918941i	$0.629046\pi$
$570$	−7.35963	−	16.9930i	−0.308261	−	0.711757i
$571$	−6.28615	−	18.5184i	−0.263067	−	0.774970i	−0.995554	−	0.0941897i	$-0.969974\pi$
$571$	−6.28615	−	18.5184i	−0.263067	−	0.774970i	0.732487	−	0.680781i	$-0.238359\pi$
$572$	−6.84612	+	1.27928i	−0.286251	+	0.0534893i
$573$	−10.1766	−	21.2163i	−0.425135	−	0.886325i
$574$	9.25446	+	17.5585i	0.386274	+	0.732876i
$575$	1.82613			0.0761548
$576$	3.34155	+	23.7662i	0.139231	+	0.990260i
$577$	7.60665			0.316669			0.158334	−	0.987386i	$-0.449388\pi$
$577$	7.60665			0.316669			0.158334	+	0.987386i	$0.449388\pi$
$578$	−10.3969	−	19.7260i	−0.432453	−	0.820493i
$579$	−34.3216	−	2.62571i	−1.42636	−	0.109121i
$580$	−1.00595	−	5.38339i	−0.0417698	−	0.223533i
$581$	7.66962	+	22.5940i	0.318189	+	0.937356i
$582$	19.7883	−	26.6619i	0.820253	−	1.10517i
$583$	1.79368	+	2.33757i	0.0742868	+	0.0968124i
$584$	−42.2213	+	12.0083i	−1.74713	+	0.496908i
$585$	−44.1795	−	6.79954i	−1.82660	−	0.281126i
$586$	−11.7676	+	12.4188i	−0.486115	+	0.513014i
$587$	−33.2547	+	2.17963i	−1.37257	+	0.0899629i	−0.733763	−	0.679406i	$-0.762238\pi$
$587$	−33.2547	+	2.17963i	−1.37257	+	0.0899629i	−0.638805	+	0.769368i	$0.720571\pi$
$588$	−13.7876	+	1.50014i	−0.568593	+	0.0618646i
$589$	6.12168	+	6.98044i	0.252239	+	0.287624i
$590$	12.1812	−	26.4744i	0.501494	−	1.08993i
$591$	−0.648077	+	0.634095i	−0.0266583	+	0.0260832i
$592$	−31.3635	+	5.48432i	−1.28903	+	0.225404i
$593$	5.93396	−	5.93396i	0.243678	−	0.243678i	−0.574692	−	0.818370i	$-0.694878\pi$
$593$	5.93396	−	5.93396i	0.243678	−	0.243678i	0.818370	+	0.574692i	$0.194878\pi$
$594$	3.88140	−	1.29251i	0.159256	−	0.0530323i
$595$	4.60464	+	23.1491i	0.188772	+	0.949021i
$596$	19.0548	−	10.7081i	0.780517	−	0.438621i
$597$	−10.6437	−	16.3118i	−0.435620	−	0.667597i
$598$	−12.5388	−	20.4277i	−0.512750	−	0.835351i
$599$	17.0913	+	13.1146i	0.698331	+	0.535848i	0.895798	−	0.444461i	$-0.146605\pi$
$599$	17.0913	+	13.1146i	0.698331	+	0.535848i	−0.197467	+	0.980310i	$0.563272\pi$
$600$	3.29558	+	0.201469i	0.134541	+	0.00822493i
$601$	12.6143	−	9.67927i	0.514547	−	0.394826i	−0.318590	−	0.947893i	$-0.603209\pi$
$601$	12.6143	−	9.67927i	0.514547	−	0.394826i	0.833137	+	0.553067i	$0.186543\pi$
$602$	−10.0887	+	26.3400i	−0.411187	+	1.07354i
$603$	11.1333	−	3.51041i	0.453384	−	0.142955i
$604$	18.0022	+	16.1614i	0.732501	+	0.657597i
$605$	11.2624	+	22.8378i	0.457881	+	0.928490i
$606$	−22.7519	+	20.6066i	−0.924232	+	0.837084i
$607$	−16.6065	+	9.58776i	−0.674036	+	0.389155i	−0.797604	−	0.603181i	$-0.793900\pi$
$607$	−16.6065	+	9.58776i	−0.674036	+	0.389155i	0.123568	+	0.992336i	$0.460566\pi$
$608$	8.91962	−	15.5813i	0.361738	−	0.631907i
$609$	1.69066	+	3.00348i	0.0685090	+	0.121707i
$610$	23.6575	+	7.32676i	0.957863	+	0.296652i
$611$	23.5197	−	35.1997i	0.951504	−	1.42403i
$612$	29.1791	−	18.1163i	1.17949	−	0.732308i
$613$	−8.72091	+	43.8430i	−0.352234	+	1.77080i	0.245790	+	0.969323i	$0.420953\pi$
$613$	−8.72091	+	43.8430i	−0.352234	+	1.77080i	−0.598024	+	0.801478i	$0.704047\pi$
$614$	−33.9820	+	27.5595i	−1.37140	+	1.11221i
$615$	−20.0731	−	26.7590i	−0.809425	−	1.07903i
$616$	−2.24286	+	1.54878i	−0.0903676	+	0.0624021i
$617$	2.70948	+	2.07906i	0.109080	+	0.0836998i	0.661861	−	0.749627i	$-0.269767\pi$
$617$	2.70948	+	2.07906i	0.109080	+	0.0836998i	−0.552781	+	0.833326i	$0.686434\pi$
$618$	23.0188	−	0.368589i	0.925953	−	0.0148268i
$619$	0.835080	+	12.7409i	0.0335647	+	0.512098i	0.981231	+	0.192836i	$0.0617685\pi$
$619$	0.835080	+	12.7409i	0.0335647	+	0.512098i	−0.947666	+	0.319263i	$0.896565\pi$
$620$	−13.5025	+	3.45036i	−0.542274	+	0.138570i
$621$	8.93185	+	10.8832i	0.358423	+	0.436729i
$622$	3.86233	−	22.5770i	0.154865	−	0.905254i
$623$	−0.905728	−	3.38022i	−0.0362872	−	0.135426i
$624$	−20.3748	−	38.2489i	−0.815647	−	1.53118i
$625$	−7.22509	+	26.9644i	−0.289003	+	1.07858i
$626$	−21.4354	−	9.86273i	−0.856731	−	0.394194i
$627$	−2.88702	−	1.01525i	−0.115297	−	0.0405453i
$628$	8.97127	−	11.4145i	0.357992	−	0.455488i
$629$	25.3141	+	37.8853i	1.00934	+	1.51059i
$630$	−16.8741	+	4.61388i	−0.672280	+	0.183821i
$631$	−10.3752	−	25.0479i	−0.413029	−	0.997141i	−0.984320	−	0.176393i	$-0.943557\pi$
$631$	−10.3752	−	25.0479i	−0.413029	−	0.997141i	0.571290	−	0.820748i	$-0.306443\pi$
$632$	−3.89482	−	26.4508i	−0.154928	−	1.05216i
$633$	3.20503	+	26.5813i	0.127388	+	1.05651i
$634$	−16.3059	+	22.4779i	−0.647591	+	0.892713i
$635$	9.94480	+	29.2964i	0.394647	+	1.16259i
$636$	−10.5267	+	15.0111i	−0.417410	+	0.595228i
$637$	22.4608	−	11.0764i	0.889930	−	0.438865i
$638$	−0.765791	−	0.482391i	−0.0303180	−	0.0190980i
$639$	13.9453	+	0.304183i	0.551666	+	0.0120333i
$640$	14.7939	+	22.5257i	0.584780	+	0.890407i
$641$	13.6857	−	23.7044i	0.540553	−	0.936266i	−0.458319	−	0.888788i	$-0.651548\pi$
$641$	13.6857	−	23.7044i	0.540553	−	0.936266i	0.998872	−	0.0474779i	$-0.0151184\pi$
$642$	10.9126	+	21.2634i	0.430687	+	0.839201i
$643$	−0.983277	+	15.0019i	−0.0387767	+	0.591617i	0.933617	+	0.358272i	$0.116634\pi$
$643$	−0.983277	+	15.0019i	−0.0387767	+	0.591617i	−0.972394	+	0.233345i	$0.925033\pi$
$644$	−7.73846	−	5.30174i	−0.304938	−	0.208918i
$645$	9.78189	−	46.5198i	0.385161	−	1.83172i
$646$	−25.5543	−	2.66685i	−1.00542	−	0.104926i
$647$	16.4307	−	39.6673i	0.645959	−	1.55948i	−0.172557	−	0.985000i	$-0.555203\pi$
$647$	16.4307	−	39.6673i	0.645959	−	1.55948i	0.818516	−	0.574484i	$-0.194797\pi$
$648$	14.9184	+	20.6262i	0.586052	+	0.810274i
$649$	−1.84303	−	4.44948i	−0.0723454	−	0.174657i
$650$	−5.71522	+	1.69750i	−0.224170	+	0.0665815i
$651$	7.34528	−	4.79293i	0.287884	−	0.187850i
$652$	13.7427	+	34.2996i	0.538205	+	1.34327i
$653$	24.0220	+	27.3918i	0.940053	+	1.07193i	0.997290	+	0.0735646i	$0.0234375\pi$
$653$	24.0220	+	27.3918i	0.940053	+	1.07193i	−0.0572373	+	0.998361i	$0.518229\pi$
$654$	−11.6553	+	0.951561i	−0.455760	+	0.0372090i
$655$	−5.57489	+	1.49379i	−0.217829	+	0.0583670i
$656$	9.11945	−	31.1228i	0.356055	−	1.21514i
$657$	−33.6319	+	32.1961i	−1.31211	+	1.25609i
$658$	2.79373	−	16.3305i	0.108911	−	0.636631i
$659$	−12.1319	−	4.11823i	−0.472593	−	0.160424i	0.0749743	−	0.997185i	$-0.476113\pi$
$659$	−12.1319	−	4.11823i	−0.472593	−	0.160424i	−0.547567	+	0.836762i	$0.684446\pi$
$660$	3.32056	−	3.17425i	0.129252	−	0.123557i
$661$	21.1540	+	10.4320i	0.822794	+	0.405757i	0.804410	−	0.594074i	$-0.202481\pi$
$661$	21.1540	+	10.4320i	0.822794	+	0.405757i	0.0183835	+	0.999831i	$0.494148\pi$
$662$	−14.6927	+	9.01857i	−0.571048	+	0.350517i
$663$	−38.2887	+	48.7879i	−1.48701	+	1.89476i
$664$	16.7067	−	35.2263i	0.648346	−	1.36704i
$665$	12.0903	+	5.00796i	0.468841	+	0.194200i
$666$	−26.6868	+	20.6949i	−1.03409	+	0.801910i
$667$	0.607668	−	3.05495i	0.0235290	−	0.118288i
$668$	−8.06248	−	4.09311i	−0.311947	−	0.158367i
$669$	−23.1200	+	11.0898i	−0.893871	+	0.428755i
$670$	9.61910	−	8.90494i	0.371618	−	0.344028i
$671$	3.54451	−	2.04643i	0.136834	−	0.0790014i
$672$	−13.3805	−	10.4217i	−0.516165	−	0.402026i
$673$	18.4880	+	10.6740i	0.712658	+	0.411453i	0.812044	−	0.583596i	$-0.198355\pi$
$673$	18.4880	+	10.6740i	0.712658	+	0.411453i	−0.0993863	+	0.995049i	$0.531688\pi$
$674$	−4.66990	+	1.06030i	−0.179878	+	0.0408413i
$675$	3.18984	−	1.44534i	0.122777	−	0.0556312i
$676$	38.8842	+	34.9080i	1.49554	+	1.34261i
$677$	24.0952	+	21.1309i	0.926053	+	0.812127i	0.982497	−	0.186279i	$-0.0596429\pi$
$677$	24.0952	+	21.1309i	0.926053	+	0.812127i	−0.0564440	+	0.998406i	$0.517976\pi$
$678$	−7.19919	−	2.84784i	−0.276483	−	0.109370i
$679$	3.06264	+	23.2631i	0.117533	+	0.892754i
$680$	20.9333	−	32.3907i	0.802754	−	1.24213i
$681$	−11.8827	−	1.69640i	−0.455346	−	0.0650063i
$682$	−1.09747	+	2.02484i	−0.0420243	+	0.0775352i
$683$	0.779177	−	0.520630i	0.0298144	−	0.0199213i	−0.540574	−	0.841297i	$-0.681793\pi$
$683$	0.779177	−	0.520630i	0.0298144	−	0.0199213i	0.570388	+	0.821375i	$0.306793\pi$
$684$	0.636437	−	19.0322i	0.0243348	−	0.727715i
$685$	−1.85075	−	9.30434i	−0.0707135	−	0.355501i
$686$	17.2093	−	20.7229i	0.657054	−	0.791205i
$687$	−2.79534	+	9.99508i	−0.106649	+	0.381336i
$688$	41.7977	−	19.4184i	1.59352	−	0.740318i
$689$	8.56856	−	31.9783i	0.326436	−	1.21828i
$690$	14.2891	+	6.76439i	0.543977	+	0.257516i
$691$	10.6658	−	31.4203i	0.405745	−	1.19529i	−0.531634	−	0.846974i	$-0.678422\pi$
$691$	10.6658	−	31.4203i	0.405745	−	1.19529i	0.937379	−	0.348312i	$-0.113245\pi$
$692$	26.3872	−	19.7648i	1.00309	−	0.751344i
$693$	−1.33489	+	2.56435i	−0.0507083	+	0.0974114i
$694$	−9.30387	+	9.81869i	−0.353170	+	0.372713i
$695$	17.7401	+	2.33553i	0.672921	+	0.0885918i
$696$	1.43369	−	5.44618i	0.0543438	−	0.206437i
$697$	−46.0144	+	6.05791i	−1.74292	+	0.229460i
$698$	−15.5914	−	11.3103i	−0.590142	−	0.428100i
$699$	−6.73323	+	32.0213i	−0.254674	+	1.21116i
$700$	−1.77199	+	1.51794i	−0.0669751	+	0.0573728i
$701$	−26.3339	−	17.5958i	−0.994619	−	0.664583i	−0.0520672	−	0.998644i	$-0.516581\pi$
$701$	−26.3339	−	17.5958i	−0.994619	−	0.664583i	−0.942552	+	0.334061i	$0.891581\pi$
$702$	−38.0706	−	25.7585i	−1.43688	−	0.972193i
$703$	25.2630			0.952813
$704$	4.39262	+	0.734841i	0.165553	+	0.0276953i
$705$	−0.304479	+	27.9210i	−0.0114673	+	1.05156i
$706$	−0.310131	−	0.0119565i	−0.0116719	−	0.000449990i
$707$	1.41876	−	21.6461i	0.0533581	−	0.814087i
$708$	22.9704	−	19.2468i	0.863279	−	0.723339i
$709$	31.6534	−	36.0938i	1.18877	−	1.35553i	0.268966	−	0.963150i	$-0.413318\pi$
$709$	31.6534	−	36.0938i	1.18877	−	1.35553i	0.919803	−	0.392381i	$-0.128349\pi$
$710$	14.3039	−	6.38113i	0.536816	−	0.239480i
$711$	−16.7684	−	22.8689i	−0.628866	−	0.857651i
$712$	−2.78295	+	4.99514i	−0.104295	+	0.187201i
$713$	−7.85851	−	1.03459i	−0.294303	−	0.0387458i
$714$	−5.90571	+	23.5418i	−0.221016	+	0.881030i
$715$	−3.66874	+	7.43946i	−0.137203	+	0.278220i
$716$	−7.57417	+	17.7011i	−0.283060	+	0.661522i
$717$	31.5588	−	27.0733i	1.17859	−	1.01107i
$718$	−43.3709	+	4.01741i	−1.61859	+	0.149928i
$719$	−11.5346	−	11.5346i	−0.430169	−	0.430169i	0.458517	−	0.888686i	$-0.348381\pi$
$719$	−11.5346	−	11.5346i	−0.430169	−	0.430169i	−0.888686	+	0.458517i	$0.848381\pi$
$720$	25.0410	+	13.7840i	0.933223	+	0.513700i
$721$	−11.5039	+	11.5039i	−0.428428	+	0.428428i
$722$	8.06552	−	9.71226i	0.300168	−	0.361453i
$723$	−0.257073	+	0.731024i	−0.00956064	+	0.0271871i
$724$	6.05052	+	0.0703004i	0.224866	+	0.00261269i
$725$	−0.694868	−	0.342671i	−0.0258068	−	0.0127265i
$726$	0.419238	+	26.1819i	0.0155594	+	0.971701i
$727$	−3.30209	+	25.0819i	−0.122468	+	0.930236i	0.814339	+	0.580389i	$0.197100\pi$
$727$	−3.30209	+	25.0819i	−0.122468	+	0.930236i	−0.936807	+	0.349847i	$0.886234\pi$
$728$	29.1473	+	9.39946i	1.08027	+	0.348367i
$729$	24.2158	+	11.9413i	0.896883	+	0.442269i
$730$	−18.6996	+	48.8214i	−0.692102	+	1.80696i
$731$	−49.5877	−	43.4873i	−1.83407	−	1.60843i
$732$	18.7646	+	17.2190i	0.693559	+	0.636431i
$733$	10.9137	+	0.715325i	0.403108	+	0.0264211i	0.265609	−	0.964081i	$-0.414427\pi$
$733$	10.9137	+	0.715325i	0.403108	+	0.0264211i	0.137499	+	0.990502i	$0.456094\pi$
$734$	−22.8462	−	24.6784i	−0.843269	−	0.910898i
$735$	−8.41452	+	14.2141i	−0.310374	+	0.524296i
$736$	3.04552	+	15.0218i	0.112259	+	0.553712i
$737$		−	2.16627i		−	0.0797955i
$738$	−6.88304	−	33.7030i	−0.253368	−	1.24062i
$739$	10.2243	−	15.3017i	0.376106	−	0.562882i	−0.594336	−	0.804217i	$-0.702585\pi$
$739$	10.2243	−	15.3017i	0.376106	−	0.562882i	0.970442	+	0.241334i	$0.0775851\pi$
$740$	−17.1660	+	33.8130i	−0.631033	+	1.24299i
$741$	10.6973	+	32.6797i	0.392975	+	1.20052i
$742$	−2.03624	−	12.7954i	−0.0747527	−	0.469733i
$743$	−3.70091	−	28.1112i	−0.135773	−	1.03130i	−0.914685	−	0.404167i	$-0.867562\pi$
$743$	−3.70091	−	28.1112i	−0.135773	−	1.03130i	0.778912	−	0.627133i	$-0.215772\pi$
$744$	−14.0680	−	2.73411i	−0.515757	−	0.100237i
$745$	3.39791	−	25.8097i	0.124490	−	0.945593i
$746$	−0.531144	−	19.7288i	−0.0194466	−	0.722324i
$747$	−1.80406	−	41.3128i	−0.0660073	−	1.51156i
$748$	−1.57794	−	6.17507i	−0.0576953	−	0.225783i
$749$	−15.9934	−	5.42903i	−0.584386	−	0.198372i
$750$	−16.3367	+	19.2413i	−0.596531	+	0.702594i
$751$	−32.3156	−	8.65895i	−1.17921	−	0.315970i	−0.384600	−	0.923083i	$-0.625660\pi$
$751$	−32.3156	−	8.65895i	−1.17921	−	0.315970i	−0.794615	+	0.607114i	$0.792327\pi$
$752$	−21.8544	+	15.9766i	−0.796947	+	0.582607i
$753$	−10.1865	+	9.96674i	−0.371217	+	0.363208i
$754$	0.937958	+	10.1259i	0.0341584	+	0.368765i
$755$	28.2596	−	5.62118i	1.02847	−	0.204576i
$756$	−17.7136	−	3.13615i	−0.644238	−	0.114061i
$757$	−20.3294	−	30.4250i	−0.738883	−	1.10582i	−0.990436	−	0.137973i	$-0.955941\pi$
$757$	−20.3294	−	30.4250i	−0.738883	−	1.10582i	0.251553	−	0.967844i	$-0.419059\pi$
$758$	42.6290	−	12.6614i	1.54836	−	0.459883i
$759$	2.42454	−	0.973442i	0.0880053	−	0.0353337i
$760$	−8.48416	−	19.6278i	−0.307753	−	0.711977i
$761$	20.0013	−	2.63321i	0.725045	−	0.0954540i	0.241035	−	0.970516i	$-0.422513\pi$
$761$	20.0013	−	2.63321i	0.725045	−	0.0954540i	0.484010	+	0.875062i	$0.339180\pi$
$762$	−3.64712	+	31.6051i	−0.132121	+	1.14493i
$763$	5.44882	−	6.21318i	0.197260	−	0.224932i
$764$	−11.7335	−	24.5069i	−0.424503	−	0.886628i
$765$	3.56487	−	40.7501i	0.128888	−	1.47332i
$766$	−3.27755	−	2.06461i	−0.118423	−	0.0745975i
$767$	−27.0568	+	46.8637i	−0.976963	+	1.69215i
$768$	3.83890	+	27.4456i	0.138525	+	0.990359i
$769$	−2.07614	−	3.59598i	−0.0748676	−	0.129674i	0.826161	−	0.563434i	$-0.190520\pi$
$769$	−2.07614	−	3.59598i	−0.0748676	−	0.129674i	−0.901029	+	0.433760i	$0.857187\pi$
$770$	−0.125061	+	3.24385i	−0.00450687	+	0.116900i
$771$	−28.6322	−	2.19045i	−1.03116	−	0.0788872i
$772$	−39.6290	−	3.06020i	−1.42628	−	0.110139i
$773$	−5.25194	−	1.04468i	−0.188899	−	0.0375744i	0.0997340	−	0.995014i	$-0.468201\pi$
$773$	−5.25194	−	1.04468i	−0.188899	−	0.0375744i	−0.288633	+	0.957440i	$0.593201\pi$
$774$	29.5602	−	38.9336i	1.06252	−	1.39944i
$775$	−0.754488	+	1.82150i	−0.0271020	+	0.0654300i
$776$	22.8716	−	30.7702i	0.821042	−	1.10459i
$777$	3.37284	−	23.6255i	0.121000	−	0.847560i
$778$	−11.8628	+	49.5727i	−0.425302	+	1.77727i
$779$	−11.3813	+	23.0790i	−0.407777	+	0.826891i
$780$	−51.0085	−	7.88784i	−1.82640	−	0.282430i
$781$	0.832024	−	2.45106i	0.0297721	−	0.0877059i
$782$	17.9034	−	12.6726i	0.640224	−	0.453172i
$783$	−1.35647	−	5.81729i	−0.0484763	−	0.207893i
$784$	−15.9218	+	1.72084i	−0.568637	+	0.0614587i
$785$	−4.47526	−	16.7019i	−0.159729	−	0.596117i
$786$	−5.83880	−	1.06453i	−0.208263	−	0.0379704i
$787$	−22.3314	+	19.5841i	−0.796028	+	0.698098i	−0.957390	−	0.288797i	$-0.906745\pi$
$787$	−22.3314	+	19.5841i	−0.796028	+	0.698098i	0.161362	+	0.986895i	$0.448411\pi$
$788$	−0.748857	+	0.731655i	−0.0266769	+	0.0260641i
$789$	26.9753	−	1.47284i	0.960346	−	0.0524343i
$790$	−27.9951	−	15.1734i	−0.996021	−	0.539847i
$791$	5.05463	−	2.09370i	0.179722	−	0.0744433i
$792$	4.48292	−	1.48926i	0.159294	−	0.0529187i
$793$	−42.4868	−	17.5986i	−1.50875	−	0.624945i
$794$	19.8539	−	16.1016i	0.704588	−	0.571423i
$795$	6.79310	+	20.7526i	0.240926	+	0.736018i
$796$	−12.2769	−	18.8440i	−0.435143	−	0.667908i
$797$	20.2557	+	1.32763i	0.717493	+	0.0470270i	0.419777	−	0.907627i	$-0.362108\pi$
$797$	20.2557	+	1.32763i	0.717493	+	0.0470270i	0.297716	+	0.954654i	$0.403775\pi$
$798$	9.03377	+	9.97427i	0.319792	+	0.353085i
$799$	33.5508	+	19.3706i	1.18694	+	0.685281i
$800$	3.80524	+	0.235352i	0.134536	+	0.00832096i
$801$	−0.132261	+	6.06348i	−0.00467320	+	0.214243i
$802$	−34.6912	+	7.87664i	−1.22499	+	0.278134i
$803$	3.82130	+	7.74883i	0.134851	+	0.273450i
$804$	12.8585	−	4.04430i	0.453486	−	0.142631i
$805$	−10.5792	+	3.59116i	−0.372868	+	0.126572i
$806$	25.5565	−	4.06703i	0.900188	−	0.143255i
$807$	3.50714	−	8.21252i	0.123457	−	0.289094i
$808$	−26.2886	+	23.7756i	−0.924829	+	0.836424i
$809$	33.6897	−	13.9547i	1.18447	−	0.490622i	0.298517	−	0.954404i	$-0.403508\pi$
$809$	33.6897	−	13.9547i	1.18447	−	0.490622i	0.885949	+	0.463783i	$0.153508\pi$
$810$	30.3138	+	0.506367i	1.06512	+	0.0177919i
$811$	−20.4166	+	13.6420i	−0.716925	+	0.479034i	−0.859751	−	0.510714i	$-0.829381\pi$
$811$	−20.4166	+	13.6420i	−0.716925	+	0.479034i	0.142825	+	0.989748i	$0.454381\pi$
$812$	1.94973	+	3.46951i	0.0684221	+	0.121756i
$813$	0.151277	−	0.0283797i	0.00530553	−	0.000995319i
$814$	2.17338	+	5.87788i	0.0761769	+	0.206019i
$815$	42.5084	+	11.3901i	1.48900	+	0.398977i
$816$	33.7080	−	20.8948i	1.18002	−	0.731466i
$817$	−35.3227	+	9.46468i	−1.23578	+	0.331127i
$818$	24.7516	+	34.9681i	0.865420	+	1.22263i
$819$	31.9896	−	5.64088i	1.11781	−	0.197108i
$820$	−23.1564	−	30.9151i	−0.808655	−	1.07960i
$821$	−29.1515	+	1.91069i	−1.01740	+	0.0666836i	−0.564964	−	0.825116i	$-0.691110\pi$
$821$	−29.1515	+	1.91069i	−1.01740	+	0.0666836i	−0.452431	+	0.891799i	$0.649443\pi$
$822$	2.37369	−	9.46219i	0.0827919	−	0.330032i
$823$	11.8081	−	15.3886i	0.411605	−	0.536414i	−0.540840	−	0.841126i	$-0.681894\pi$
$823$	11.8081	−	15.3886i	0.411605	−	0.536414i	0.952445	+	0.304712i	$0.0985602\pi$
$824$	26.5801	−	0.406638i	0.925963	−	0.0141659i
$825$	−0.0777938	−	0.645193i	−0.00270843	−	0.0224628i
$826$	−2.19817	+	21.0633i	−0.0764842	+	0.732885i
$827$	−14.0867	−	2.80202i	−0.489842	−	0.0974357i	−0.0560116	−	0.998430i	$-0.517838\pi$
$827$	−14.0867	−	2.80202i	−0.489842	−	0.0974357i	−0.433831	+	0.900994i	$0.642838\pi$
$828$	10.3046	+	12.5742i	0.358111	+	0.436985i
$829$	29.0505	+	19.4109i	1.00897	+	0.674169i	0.946107	−	0.323853i	$-0.104978\pi$
$829$	29.0505	+	19.4109i	1.00897	+	0.674169i	0.0628584	+	0.998022i	$0.479978\pi$
$830$	−21.6506	−	41.0775i	−0.751502	−	1.42582i
$831$	−39.1975	−	23.2043i	−1.35975	−	0.804947i
$832$	−23.4953	−	44.1828i	−0.814554	−	1.53176i
$833$	11.4589	+	19.8475i	0.397029	+	0.687674i
$834$	15.4608	+	9.97630i	0.535365	+	0.345451i
$835$	−9.65844	+	4.76301i	−0.334244	+	0.164831i
$836$	−3.33281	−	1.17469i	−0.115268	−	0.0406276i
$837$	−14.5459	+	4.41264i	−0.502781	+	0.152523i
$838$	46.4794	−	20.7349i	1.60560	−	0.716277i
$839$	−18.3136	−	23.8667i	−0.632254	−	0.823970i	0.361868	−	0.932229i	$-0.382139\pi$
$839$	−18.3136	−	23.8667i	−0.632254	−	0.823970i	−0.994123	+	0.108259i	$0.965472\pi$
$840$	−19.4883	+	5.31374i	−0.672411	+	0.183341i
$841$	16.8496	−	21.9588i	0.581021	−	0.757201i
$842$	17.4177	+	4.16808i	0.600255	+	0.143642i
$843$	−0.740180	−	13.5565i	−0.0254931	−	0.466912i
$844$	3.67894	+	30.6961i	0.126634	+	1.05660i
$845$	61.0396	−	12.1415i	2.09983	−	0.417682i
$846$	−12.5681	+	25.8170i	−0.432099	+	0.887607i
$847$	−13.0847	−	13.0847i	−0.449595	−	0.449595i
$848$	−12.1675	+	17.3246i	−0.417834	+	0.594929i
$849$	11.0284	−	39.4333i	0.378493	−	1.35335i
$850$	−1.89216	−	5.11734i	−0.0649007	−	0.175523i
$851$	−16.2153	+	14.2204i	−0.555853	+	0.487470i
$852$	16.1024	+	0.362734i	0.551658	+	0.0124271i
$853$	−2.80478	−	42.7927i	−0.0960340	−	1.46520i	−0.725529	−	0.688191i	$-0.758405\pi$
$853$	−2.80478	−	42.7927i	−0.0960340	−	1.46520i	0.629496	−	0.777004i	$-0.283262\pi$
$854$	−17.9909	+	0.484356i	−0.615637	+	0.0165743i
$855$	−17.6880	−	14.1959i	−0.604916	−	0.485489i
$856$	12.5833	+	24.5619i	0.430088	+	0.839508i
$857$	−15.1263	+	11.6068i	−0.516705	+	0.396482i	−0.833931	−	0.551868i	$-0.813915\pi$
$857$	−15.1263	+	11.6068i	−0.516705	+	0.396482i	0.317226	+	0.948350i	$0.397249\pi$
$858$	−6.68321	+	5.30034i	−0.228161	+	0.180951i
$859$	33.8545	−	11.4920i	1.15510	−	0.392103i	0.322820	−	0.946460i	$-0.395369\pi$
$859$	33.8545	−	11.4920i	1.15510	−	0.392103i	0.832279	+	0.554357i	$0.187036\pi$
$860$	11.3335	−	53.7084i	0.386469	−	1.83144i
$861$	20.0636	+	13.7248i	0.683764	+	0.467741i
$862$	−13.4077	+	43.2923i	−0.456668	+	1.47454i
$863$		−	14.4145i		−	0.490675i	−0.969438	−	0.245338i	$-0.921101\pi$
$863$		−	14.4145i		−	0.490675i	0.969438	−	0.245338i	$-0.0788988\pi$
$864$	17.2093	+	23.8294i	0.585473	+	0.810692i
$865$		−	39.2657i		−	1.33507i
$866$	−41.8150	−	12.9502i	−1.42093	−	0.440064i
$867$	−22.5403	−	15.4191i	−0.765509	−	0.523660i
$868$	8.48554	−	5.52835i	0.288018	−	0.187644i
$869$	−4.98308	+	1.69153i	−0.169039	+	0.0573811i
$870$	−4.16788	−	5.25529i	−0.141305	−	0.178171i
$871$	−19.3104	+	14.8174i	−0.654308	+	0.502069i
$872$	−13.4592	+	1.08916i	−0.455786	+	0.0368836i
$873$	6.18582	−	40.1919i	0.209358	−	1.36029i
$874$	−0.327299	−	12.1572i	−0.0110710	−	0.411223i
$875$	−1.16662	−	17.7992i	−0.0394389	−	0.601722i
$876$	−38.8613	+	37.1491i	−1.31300	+	1.25515i
$877$	−28.7249	+	25.1910i	−0.969970	+	0.850641i	−0.988810	−	0.149182i	$-0.952336\pi$
$877$	−28.7249	+	25.1910i	−0.969970	+	0.850641i	0.0188401	+	0.999823i	$0.494003\pi$
$878$	−4.58796	+	1.69642i	−0.154836	+	0.0572515i
$879$	−5.64357	+	20.1793i	−0.190353	+	0.680630i
$880$	3.83686	−	3.66257i	0.129341	−	0.123465i
$881$	−31.6694	−	31.6694i	−1.06697	−	1.06697i	−0.997590	−	0.0693790i	$-0.977898\pi$
$881$	−31.6694	−	31.6694i	−1.06697	−	1.06697i	−0.0693790	−	0.997590i	$-0.522102\pi$
$882$	−14.0750	+	9.50891i	−0.473929	+	0.320182i
$883$	46.1141	−	9.17266i	1.55186	−	0.308685i	0.656605	−	0.754234i	$-0.271992\pi$
$883$	46.1141	−	9.17266i	1.55186	−	0.308685i	0.895257	+	0.445550i	$0.146992\pi$
$884$	−44.2521	+	56.3038i	−1.48836	+	1.89370i
$885$	−1.94586	−	35.6388i	−0.0654093	−	1.19799i
$886$	−5.61360	+	23.4583i	−0.188592	+	0.788098i
$887$	0.760797	−	0.991490i	0.0255451	−	0.0332910i	−0.780406	−	0.625273i	$-0.784988\pi$
$887$	0.760797	−	0.991490i	0.0255451	−	0.0332910i	0.805951	+	0.591982i	$0.201654\pi$
$888$	−30.8323	+	23.8744i	−1.03467	+	0.801172i
$889$	−13.6867	−	17.8368i	−0.459036	−	0.598228i
$890$	2.77455	+	6.21942i	0.0930032	+	0.208476i
$891$	3.46468	−	3.61936i	0.116071	−	0.121253i
$892$	−26.7058	+	12.7863i	−0.894176	+	0.428117i
$893$	19.2648	−	9.50033i	0.644671	−	0.317917i
$894$	14.5143	−	22.4936i	0.485430	−	0.752298i
$895$	11.4655	+	19.8588i	0.383250	+	0.663808i
$896$	−15.4419	−	12.0450i	−0.515878	−	0.402395i
$897$	−25.2614	−	14.9543i	−0.843454	−	0.499310i
$898$	34.2783	−	18.0669i	1.14388	−	0.602901i
$899$	2.79614	+	1.86832i	0.0932565	+	0.0623120i
$900$	3.68450	−	1.66631i	0.122817	−	0.0555436i
$901$	29.7143	+	5.91054i	0.989926	+	0.196908i
$902$	−6.34886	−	0.662569i	−0.211394	−	0.0220611i
$903$	4.13531	+	34.2967i	0.137614	+	1.14132i
$904$	−8.31056	−	3.29433i	−0.276405	−	0.109568i
$905$	4.38715	−	5.71745i	0.145834	−	0.190054i
$906$	28.7390	+	7.20948i	0.954789	+	0.239519i
$907$	13.8983	−	0.910941i	0.461485	−	0.0302473i	0.167112	−	0.985938i	$-0.446556\pi$
$907$	13.8983	−	0.910941i	0.461485	−	0.0302473i	0.294373	+	0.955691i	$0.404889\pi$
$908$	−13.7195	−	1.96863i	−0.455299	−	0.0653313i
$909$	−12.8581	+	35.3283i	−0.426477	+	1.17176i
$910$	29.7715	−	21.0733i	0.986916	−	0.698573i
$911$	13.6404	−	3.65492i	0.451925	−	0.121093i	−0.0256748	−	0.999670i	$-0.508173\pi$
$911$	13.6404	−	3.65492i	0.451925	−	0.121093i	0.477600	+	0.878577i	$0.341507\pi$
$912$	0.750581	−	21.9760i	0.0248542	−	0.727697i
$913$	−7.41222	−	1.98610i	−0.245309	−	0.0657303i
$914$	12.7139	−	4.70103i	0.420538	−	0.155496i
$915$	29.8120	−	5.59275i	0.985556	−	0.184891i
$916$	−3.23602	+	11.5390i	−0.106921	+	0.381260i
$917$	3.48733	−	2.33016i	0.115162	−	0.0769485i
$918$	21.2432	−	36.3064i	0.701129	−	1.19829i
$919$	41.7029	−	17.2739i	1.37565	−	0.569814i	0.432337	−	0.901712i	$-0.357689\pi$
$919$	41.7029	−	17.2739i	1.37565	−	0.569814i	0.943315	+	0.331898i	$0.107689\pi$
$920$	16.4941	+	7.82261i	0.543793	+	0.257904i
$921$	−21.0451	+	49.2804i	−0.693458	+	1.62384i
$922$	−6.44617	−	40.5066i	−0.212293	−	1.33401i
$923$	−27.5402	+	9.34863i	−0.906496	+	0.307714i
$924$	−1.54351	+	2.95995i	−0.0507778	+	0.0973752i
$925$	2.37272	+	4.81140i	0.0780145	+	0.158198i
$926$	−8.25302	−	36.3488i	−0.271211	−	1.19450i
$927$	24.7199	−	13.5620i	0.811908	−	0.445436i
$928$	1.65997	−	6.28752i	0.0544911	−	0.206398i
$929$	−13.1474	−	7.59063i	−0.431351	−	0.249041i	0.268571	−	0.963260i	$-0.413449\pi$
$929$	−13.1474	−	7.59063i	−0.431351	−	0.249041i	−0.699922	+	0.714219i	$0.746782\pi$
$930$	−12.6510	+	11.4581i	−0.414841	+	0.375725i
$931$	12.6796	+	0.831063i	0.415556	+	0.0272370i
$932$	−7.80125	+	36.9694i	−0.255538	+	1.21097i
$933$	−8.72706	−	26.6607i	−0.285711	−	0.872833i
$934$	14.0735	+	17.3532i	0.460499	+	0.567815i
$935$	−7.01303	−	2.90489i	−0.229351	−	0.0950001i
$936$	−43.9389	−	29.7747i	−1.43619	−	0.973218i
$937$	−23.1047	+	9.57026i	−0.754796	+	0.312647i	−0.726697	−	0.686958i	$-0.758946\pi$
$937$	−23.1047	+	9.57026i	−0.754796	+	0.312647i	−0.0280994	+	0.999605i	$0.508946\pi$
$938$	−4.53911	+	8.37470i	−0.148207	+	0.273443i
$939$	−28.8555	+	1.57550i	−0.941665	+	0.0514144i
$940$	−0.374594	+	32.2401i	−0.0122179	+	1.05156i
$941$	20.7553	−	18.2019i	0.676602	−	0.593364i	−0.250526	−	0.968110i	$-0.580603\pi$
$941$	20.7553	−	18.2019i	0.676602	−	0.593364i	0.927128	+	0.374746i	$0.122270\pi$
$942$	3.18923	−	17.4926i	0.103911	−	0.569939i
$943$	−5.68587	−	21.2199i	−0.185157	−	0.691016i
$944$	26.5397	−	22.2053i	0.863795	−	0.722722i
$945$	−15.6372	+	14.6462i	−0.508679	+	0.476441i
$946$	−5.24093	−	7.40418i	−0.170397	−	0.240731i
$947$	11.8185	−	34.8162i	0.384050	−	1.13137i	−0.567366	−	0.823466i	$-0.692037\pi$
$947$	11.8185	−	34.8162i	0.384050	−	1.13137i	0.951416	−	0.307909i	$-0.0996292\pi$
$948$	−19.3437	−	26.4206i	−0.628253	−	0.858100i
$949$	42.9362	−	87.0660i	1.39377	−	2.82628i
$950$	−2.94198	−	0.704018i	−0.0954504	−	0.0228414i
$951$	−4.80668	+	33.6691i	−0.155867	+	1.09179i
$952$	−6.83873	+	27.1789i	−0.221644	+	0.880872i
$953$	11.2379	−	27.1307i	0.364032	−	0.878851i	−0.630670	−	0.776051i	$-0.717220\pi$
$953$	11.2379	−	27.1307i	0.364032	−	0.878851i	0.994702	−	0.102800i	$-0.0327802\pi$
$954$	−2.81721	+	22.2773i	−0.0912104	+	0.721254i
$955$	−31.7389	−	6.31327i	−1.02705	−	0.204293i
$956$	36.4633	−	31.2355i	1.17931	−	1.01023i
$957$	−1.10524	−	0.0845544i	−0.0357273	−	0.00273325i
$958$	47.7874	+	1.84236i	1.54394	+	0.0595238i
$959$	3.44696	+	5.97030i	0.111308	+	0.192791i
$960$	28.9035	+	15.9370i	0.932856	+	0.514366i
$961$	−11.2212	+	19.4357i	−0.361974	+	0.626957i
$962$	37.5302	−	59.5788i	1.21002	−	1.92090i
$963$	23.9780	+	16.7893i	0.772682	+	0.541029i
$964$	−0.297445	+	0.843902i	−0.00958004	+	0.0271803i
$965$	−31.2126	+	35.5912i	−1.00477	+	1.14572i
$966$	−11.4129	−	1.31701i	−0.367203	−	0.0423741i
$967$	−19.2114	+	2.52923i	−0.617798	+	0.0813347i	−0.432928	−	0.901428i	$-0.642520\pi$
$967$	−19.2114	+	2.52923i	−0.617798	+	0.0813347i	−0.184870	+	0.982763i	$0.559186\pi$
$968$	0.462514	+	30.2326i	0.0148658	+	0.971711i
$969$	−29.2017	+	11.7243i	−0.938093	+	0.376640i
$970$	−13.0010	−	43.7725i	−0.417439	−	1.40545i
$971$	7.61274	+	11.3933i	0.244304	+	0.365627i	0.933275	−	0.359161i	$-0.116937\pi$
$971$	7.61274	+	11.3933i	0.244304	+	0.365627i	−0.688971	+	0.724789i	$0.741937\pi$
$972$	27.9522	+	13.8085i	0.896567	+	0.442909i
$973$	−12.7531	+	2.53675i	−0.408846	+	0.0813245i
$974$	−19.8740	+	1.84091i	−0.636803	+	0.0589866i
$975$	−5.21923	+	5.10662i	−0.167149	+	0.163543i
$976$	21.6533	+	19.8982i	0.693104	+	0.636926i
$977$	−52.7233	−	14.1272i	−1.68677	−	0.451968i	−0.717216	−	0.696851i	$-0.754584\pi$
$977$	−52.7233	−	14.1272i	−1.68677	−	0.451968i	−0.969553	+	0.244883i	$0.921250\pi$
$978$	34.4976	+	29.2899i	1.10311	+	0.936587i
$979$	1.06574	+	0.361769i	0.0340611	+	0.0115622i
$980$	−9.72796	+	16.4061i	−0.310748	+	0.524075i
$981$	−12.0793	+	7.69546i	−0.385661	+	0.245697i
$982$	9.55664	−	0.257286i	0.304965	−	0.00821033i
$983$	3.05546	−	23.2086i	0.0974542	−	0.740238i	−0.871042	−	0.491209i	$-0.836555\pi$
$983$	3.05546	−	23.2086i	0.0974542	−	0.740238i	0.968496	−	0.249029i	$-0.0801115\pi$
$984$	−7.92007	−	38.9225i	−0.252483	−	1.24081i
$985$	0.162756	+	1.23626i	0.00518584	+	0.0393904i
$986$	−9.19051	+	1.46257i	−0.292685	+	0.0465776i
$987$	−6.31252	−	19.2844i	−0.200930	−	0.613830i
$988$	12.3252	+	37.7441i	0.392118	+	1.20080i
$989$	17.3446	−	25.9580i	0.551525	−	0.825415i
$990$	1.78122	−	5.33668i	0.0566109	−	0.169611i
$991$		−	45.5712i		−	1.44762i	−0.690001	−	0.723808i	$-0.742390\pi$
$991$		−	45.5712i		−	1.44762i	0.690001	−	0.723808i	$-0.257610\pi$
$992$	−16.2420	−	3.16867i	−0.515685	−	0.100605i
$993$	−10.7559	+	18.1693i	−0.341329	+	0.576587i
$994$	−8.35242	+	7.73230i	−0.264923	+	0.245254i
$995$	−26.7288	−	1.75190i	−0.847360	−	0.0555389i
$996$	−2.04910	−	47.7054i	−0.0649283	−	1.51160i
$997$	29.2805	+	25.6783i	0.927324	+	0.813241i	0.982696	−	0.185225i	$-0.0593013\pi$
$997$	29.2805	+	25.6783i	0.927324	+	0.813241i	−0.0553724	+	0.998466i	$0.517635\pi$
$998$	−15.9560	−	6.11145i	−0.505077	−	0.193455i
$999$	−17.0694	+	37.6740i	−0.540051	+	1.19195i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	576.2.bm.a.133.80	yes	1504
9.4	even	3	inner	576.2.bm.a.517.46	yes	1504
64.13	even	16	inner	576.2.bm.a.205.46	yes	1504
576.13	even	48	inner	576.2.bm.a.13.80	✓	1504

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
576.2.bm.a.13.80	✓	1504	576.13	even	48	inner
576.2.bm.a.133.80	yes	1504	1.1	even	1	trivial
576.2.bm.a.205.46	yes	1504	64.13	even	16	inner
576.2.bm.a.517.46	yes	1504	9.4	even	3	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:	\( N \)	\(=\)	\( 576 = 2^{6} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	576.bm (of order \(48\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(1.25108 - 0.659399i) q^{2} +(0.977923 - 1.42957i) q^{3} +(1.13039 - 1.64992i) q^{4} +(-0.765671 - 2.25560i) q^{5} +(0.280800 - 2.43334i) q^{6} +(1.05377 + 1.37330i) q^{7} +(0.326245 - 2.80955i) q^{8} +(-1.08733 - 2.79602i) q^{9} +O(q^{10})\)	\(q+(1.25108 - 0.659399i) q^{2} +(0.977923 - 1.42957i) q^{3} +(1.13039 - 1.64992i) q^{4} +(-0.765671 - 2.25560i) q^{5} +(0.280800 - 2.43334i) q^{6} +(1.05377 + 1.37330i) q^{7} +(0.326245 - 2.80955i) q^{8} +(-1.08733 - 2.79602i) q^{9} +(-2.44525 - 2.31704i) q^{10} +(-0.555516 + 0.0364104i) q^{11} +(-1.25324 - 3.22946i) q^{12} +(4.12433 + 4.70290i) q^{13} +(2.22389 + 1.02324i) q^{14} +(-3.97330 - 1.11122i) q^{15} +(-1.44446 - 3.73009i) q^{16} +(-4.04767 + 4.04767i) q^{17} +(-3.20403 - 2.78104i) q^{18} +(0.619179 + 3.11282i) q^{19} +(-4.58705 - 1.28640i) q^{20} +(2.99372 - 0.163455i) q^{21} +(-0.670984 + 0.411859i) q^{22} +(-2.14962 - 1.64946i) q^{23} +(-3.69740 - 3.21391i) q^{24} +(-0.534691 + 0.410283i) q^{25} +(8.26094 + 3.16410i) q^{26} +(-5.06043 - 1.17987i) q^{27} +(3.45699 - 0.186275i) q^{28} +(0.508442 + 1.03102i) q^{29} +(-5.70363 + 1.22977i) q^{30} +(2.53342 - 1.46267i) q^{31} +(-4.26674 - 3.71415i) q^{32} +(-0.491200 + 0.829755i) q^{33} +(-2.39491 + 7.73297i) q^{34} +(2.29076 - 3.42836i) q^{35} +(-5.84230 - 1.36656i) q^{36} +(1.55289 - 7.80690i) q^{37} +(2.82723 + 3.48610i) q^{38} +(10.7564 - 1.29694i) q^{39} +(-6.58700 + 1.41531i) q^{40} +(6.43239 + 4.93574i) q^{41} +(3.63759 - 2.17855i) q^{42} +(0.753577 + 11.4974i) q^{43} +(-0.567873 + 0.957714i) q^{44} +(-5.47414 + 4.59342i) q^{45} +(-3.77699 - 0.646145i) q^{46} +(-1.75166 - 6.53727i) q^{47} +(-6.74498 - 1.58279i) q^{48} +(1.03622 - 3.86722i) q^{49} +(-0.398399 + 0.865870i) q^{50} +(1.82811 + 9.74472i) q^{51} +(12.4215 - 1.48872i) q^{52} +(-2.94043 - 4.40066i) q^{53} +(-7.10898 + 1.86074i) q^{54} +(0.507470 + 1.22514i) q^{55} +(4.20213 - 2.51258i) q^{56} +(5.05551 + 2.15894i) q^{57} +(1.31595 + 0.954617i) q^{58} +(2.78077 + 8.19189i) q^{59} +(-6.32477 + 5.29951i) q^{60} +(-6.59370 + 3.25166i) q^{61} +(2.20502 - 3.50045i) q^{62} +(2.69396 - 4.43958i) q^{63} +(-7.78713 - 1.83320i) q^{64} +(7.44995 - 12.9037i) q^{65} +(-0.0673897 + 1.36198i) q^{66} +(-0.254497 + 3.88288i) q^{67} +(2.10289 + 11.2537i) q^{68} +(-4.46018 + 1.45998i) q^{69} +(0.605256 - 5.79967i) q^{70} +(-1.77930 + 4.29560i) q^{71} +(-8.21028 + 2.14273i) q^{72} +(-5.93905 - 14.3381i) q^{73} +(-3.20508 - 10.7910i) q^{74} +(0.0636412 + 1.16560i) q^{75} +(5.83581 + 2.49710i) q^{76} +(-0.635386 - 0.724519i) q^{77} +(12.6019 - 8.71533i) q^{78} +(9.13053 - 2.44652i) q^{79} +(-7.30759 + 6.11413i) q^{80} +(-6.63541 + 6.08041i) q^{81} +(11.3020 + 1.93348i) q^{82} +(13.0525 + 4.43074i) q^{83} +(3.11437 - 5.12416i) q^{84} +(12.2291 + 6.03071i) q^{85} +(8.52414 + 13.8872i) q^{86} +(1.97113 + 0.281403i) q^{87} +(-0.0789374 + 1.57263i) q^{88} +(-1.86775 - 0.773649i) q^{89} +(-3.81967 + 9.35636i) q^{90} +(-2.11238 + 10.6197i) q^{91} +(-5.15137 + 1.68217i) q^{92} +(0.386500 - 5.05208i) q^{93} +(-6.50212 - 7.02358i) q^{94} +(6.54718 - 3.78002i) q^{95} +(-9.48218 + 2.46745i) q^{96} +(11.7390 + 6.77752i) q^{97} +(-1.25365 - 5.52147i) q^{98} +(0.705836 + 1.51364i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1504 q - 8 q^{2} - 16 q^{3} - 8 q^{4} - 8 q^{5} - 16 q^{6} - 8 q^{7} - 32 q^{8} - 16 q^{9}+O(q^{10}) \) 1504 * q - 8 * q^2 - 16 * q^3 - 8 * q^4 - 8 * q^5 - 16 * q^6 - 8 * q^7 - 32 * q^8 - 16 * q^9	\( 1504 q - 8 q^{2} - 16 q^{3} - 8 q^{4} - 8 q^{5} - 16 q^{6} - 8 q^{7} - 32 q^{8} - 16 q^{9} - 32 q^{10} - 8 q^{11} - 16 q^{12} - 8 q^{13} - 8 q^{14} - 16 q^{15} - 8 q^{16} - 32 q^{17} - 16 q^{18} - 32 q^{19} - 8 q^{20} - 16 q^{21} - 8 q^{22} - 8 q^{23} + 64 q^{24} - 8 q^{25} - 32 q^{26} - 16 q^{27} - 32 q^{28} - 8 q^{29} - 96 q^{30} - 8 q^{32} - 8 q^{34} - 32 q^{35} - 96 q^{36} - 32 q^{37} - 8 q^{38} - 16 q^{39} - 8 q^{40} - 8 q^{41} + 64 q^{42} - 8 q^{43} - 32 q^{44} - 16 q^{45} - 32 q^{46} - 8 q^{47} - 16 q^{48} - 8 q^{49} - 8 q^{50} - 16 q^{51} - 8 q^{52} - 32 q^{53} - 16 q^{54} - 32 q^{55} - 8 q^{56} - 16 q^{57} - 80 q^{58} - 8 q^{59} - 16 q^{60} - 8 q^{61} - 64 q^{62} - 32 q^{63} - 32 q^{64} - 16 q^{65} - 32 q^{66} - 8 q^{67} - 8 q^{68} - 16 q^{69} - 8 q^{70} - 32 q^{71} - 16 q^{72} - 32 q^{73} - 8 q^{74} - 16 q^{75} + 40 q^{76} - 8 q^{77} - 40 q^{78} - 8 q^{79} - 160 q^{80} - 16 q^{81} - 32 q^{82} - 8 q^{83} - 128 q^{84} - 8 q^{85} - 216 q^{86} - 16 q^{87} - 8 q^{88} - 32 q^{89} - 160 q^{90} - 32 q^{91} + 144 q^{92} - 40 q^{93} - 8 q^{94} - 152 q^{96} - 304 q^{98} - 16 q^{99}+O(q^{100}) \) 1504 * q - 8 * q^2 - 16 * q^3 - 8 * q^4 - 8 * q^5 - 16 * q^6 - 8 * q^7 - 32 * q^8 - 16 * q^9 - 32 * q^10 - 8 * q^11 - 16 * q^12 - 8 * q^13 - 8 * q^14 - 16 * q^15 - 8 * q^16 - 32 * q^17 - 16 * q^18 - 32 * q^19 - 8 * q^20 - 16 * q^21 - 8 * q^22 - 8 * q^23 + 64 * q^24 - 8 * q^25 - 32 * q^26 - 16 * q^27 - 32 * q^28 - 8 * q^29 - 96 * q^30 - 8 * q^32 - 8 * q^34 - 32 * q^35 - 96 * q^36 - 32 * q^37 - 8 * q^38 - 16 * q^39 - 8 * q^40 - 8 * q^41 + 64 * q^42 - 8 * q^43 - 32 * q^44 - 16 * q^45 - 32 * q^46 - 8 * q^47 - 16 * q^48 - 8 * q^49 - 8 * q^50 - 16 * q^51 - 8 * q^52 - 32 * q^53 - 16 * q^54 - 32 * q^55 - 8 * q^56 - 16 * q^57 - 80 * q^58 - 8 * q^59 - 16 * q^60 - 8 * q^61 - 64 * q^62 - 32 * q^63 - 32 * q^64 - 16 * q^65 - 32 * q^66 - 8 * q^67 - 8 * q^68 - 16 * q^69 - 8 * q^70 - 32 * q^71 - 16 * q^72 - 32 * q^73 - 8 * q^74 - 16 * q^75 + 40 * q^76 - 8 * q^77 - 40 * q^78 - 8 * q^79 - 160 * q^80 - 16 * q^81 - 32 * q^82 - 8 * q^83 - 128 * q^84 - 8 * q^85 - 216 * q^86 - 16 * q^87 - 8 * q^88 - 32 * q^89 - 160 * q^90 - 32 * q^91 + 144 * q^92 - 40 * q^93 - 8 * q^94 - 152 * q^96 - 304 * q^98 - 16 * q^99

Introduction

L-functions

Modular forms

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