LMFDB - Embedded newform 507.2.q.a.55.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(16,507)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(507, base_ring=CyclotomicField(78))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("507.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.q (of order $39$, degree $24$, 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:	$4.04841538248$
Analytic rank:	$0$
Dimension:	$360$
Relative dimension:	$15$ over $\Q(\zeta_{39})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{39}]$

Embedding invariants

Embedding label			55.3
Character	$\chi$	$=$	507.55
Dual form			507.2.q.a.295.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.28348 + 1.57198i) q^{2} +(0.996757 + 0.0804666i) q^{3} +(-0.423741 - 2.07562i) q^{4} +(-0.317374 - 2.61381i) q^{5} +(-1.40581 + 1.46360i) q^{6} +(0.313349 - 0.198150i) q^{7} +(0.212820 + 0.111697i) q^{8} +(0.987050 + 0.160411i) q^{9} +O(q^{10})$	\(q+(-1.28348 + 1.57198i) q^{2} +(0.996757 + 0.0804666i) q^{3} +(-0.423741 - 2.07562i) q^{4} +(-0.317374 - 2.61381i) q^{5} +(-1.40581 + 1.46360i) q^{6} +(0.313349 - 0.198150i) q^{7} +(0.212820 + 0.111697i) q^{8} +(0.987050 + 0.160411i) q^{9} +(4.51619 + 2.85586i) q^{10} +(-2.28885 + 0.371974i) q^{11} +(-0.255349 - 2.10299i) q^{12} +(-3.24366 + 1.57438i) q^{13} +(-0.0906900 + 0.746899i) q^{14} +(-0.106020 - 2.63087i) q^{15} +(3.44910 - 1.46952i) q^{16} +(3.41968 - 2.16247i) q^{17} +(-1.51902 + 1.34574i) q^{18} +(2.02248 - 3.50304i) q^{19} +(-5.29079 + 1.76633i) q^{20} +(0.328278 - 0.172293i) q^{21} +(2.35295 - 4.07544i) q^{22} +(-4.44854 - 7.70509i) q^{23} +(0.203142 + 0.128460i) q^{24} +(-1.87655 + 0.462527i) q^{25} +(1.68828 - 7.11965i) q^{26} +(0.970942 + 0.239316i) q^{27} +(-0.544064 - 0.566430i) q^{28} +(6.38735 - 7.82308i) q^{29} +(4.27174 + 3.21001i) q^{30} +(8.61099 + 2.12242i) q^{31} +(-2.25053 + 7.76973i) q^{32} +(-2.31136 + 0.186592i) q^{33} +(-0.989729 + 8.15115i) q^{34} +(-0.617374 - 0.756146i) q^{35} +(-0.0853008 - 2.11672i) q^{36} +(-1.78363 - 6.15782i) q^{37} +(2.91088 + 7.67537i) q^{38} +(-3.35983 + 1.30827i) q^{39} +(0.224410 - 0.591721i) q^{40} +(-12.4274 - 1.00324i) q^{41} +(-0.150496 + 0.737180i) q^{42} +(1.51636 - 5.23507i) q^{43} +(1.74196 + 4.59316i) q^{44} +(0.106020 - 2.63087i) q^{45} +(17.8218 + 2.89633i) q^{46} +(-1.94108 - 1.71965i) q^{47} +(3.55616 - 1.18722i) q^{48} +(-2.94192 + 6.19997i) q^{49} +(1.68143 - 3.54354i) q^{50} +(3.58260 - 1.88029i) q^{51} +(4.64230 + 6.06548i) q^{52} +(5.21732 + 2.73826i) q^{53} +(-1.62238 + 1.21914i) q^{54} +(1.69869 + 5.86455i) q^{55} +(0.0888198 - 0.00717028i) q^{56} +(2.29780 - 3.32894i) q^{57} +(4.09968 + 20.0815i) q^{58} +(-5.84457 - 2.49014i) q^{59} +(-5.41577 + 1.33487i) q^{60} +(-0.417361 + 10.3567i) q^{61} +(-14.3884 + 10.8122i) q^{62} +(0.341077 - 0.145319i) q^{63} +(-5.06587 - 7.33918i) q^{64} +(5.14458 + 7.97863i) q^{65} +(2.67326 - 3.87289i) q^{66} +(0.555757 - 2.72228i) q^{67} +(-5.93754 - 6.18163i) q^{68} +(-3.81411 - 8.03807i) q^{69} +1.98103 q^{70} +(6.11372 + 12.8844i) q^{71} +(0.192147 + 0.144389i) q^{72} +(2.01938 - 5.32466i) q^{73} +(11.9692 + 5.09961i) q^{74} +(-1.90768 + 0.310028i) q^{75} +(-8.12799 - 2.71352i) q^{76} +(-0.643502 + 0.570093i) q^{77} +(2.25570 - 6.96071i) q^{78} +(0.521599 + 0.462096i) q^{79} +(-4.93570 - 8.54888i) q^{80} +(0.948536 + 0.316668i) q^{81} +(17.5274 - 18.2479i) q^{82} +(7.51910 + 10.8933i) q^{83} +(-0.496721 - 0.608372i) q^{84} +(-6.73760 - 8.25206i) q^{85} +(6.28320 + 9.10279i) q^{86} +(6.99613 - 7.28375i) q^{87} +(-0.528662 - 0.176493i) q^{88} +(-4.87917 - 8.45097i) q^{89} +(3.99959 + 3.54333i) q^{90} +(-0.704434 + 1.13606i) q^{91} +(-14.1078 + 12.4985i) q^{92} +(8.41228 + 2.80843i) q^{93} +(5.19460 - 0.844204i) q^{94} +(-9.79814 - 4.17460i) q^{95} +(-2.86844 + 7.56344i) q^{96} +(-10.9134 - 8.20088i) q^{97} +(-5.97032 - 12.5822i) q^{98} -2.31888 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 360 q + q^{2} - 15 q^{3} + 15 q^{4} + 2 q^{5} - q^{6} + 2 q^{7} + 6 q^{8} + 15 q^{9}+O(q^{10}) $ 360 * q + q^2 - 15 * q^3 + 15 * q^4 + 2 * q^5 - q^6 + 2 * q^7 + 6 * q^8 + 15 * q^9	\( 360 q + q^{2} - 15 q^{3} + 15 q^{4} + 2 q^{5} - q^{6} + 2 q^{7} + 6 q^{8} + 15 q^{9} - q^{10} - 2 q^{11} + 30 q^{12} - 19 q^{13} + q^{15} + 15 q^{16} - 7 q^{17} - 2 q^{18} - 6 q^{19} + q^{20} + 4 q^{21} + 22 q^{22} + 46 q^{23} + 3 q^{24} + 28 q^{25} + 34 q^{26} + 30 q^{27} - 2 q^{28} + 36 q^{29} + q^{30} - 34 q^{31} - 190 q^{32} + 15 q^{33} - 51 q^{34} - 80 q^{35} + 15 q^{36} + q^{37} - 53 q^{38} + 5 q^{39} - 45 q^{40} + 9 q^{41} + 130 q^{42} + 78 q^{43} + 35 q^{44} - q^{45} - 318 q^{46} - 12 q^{47} - 15 q^{48} - 71 q^{49} + 48 q^{50} - 14 q^{51} - 63 q^{52} - 26 q^{53} - q^{54} - 61 q^{55} - 4 q^{56} - 38 q^{57} - 27 q^{58} + 208 q^{59} - 180 q^{60} - 3 q^{61} - 61 q^{62} + 2 q^{63} + 140 q^{64} + 45 q^{65} - 60 q^{66} - 80 q^{67} - 140 q^{68} + 6 q^{69} - 100 q^{70} + 84 q^{71} - 3 q^{72} + 134 q^{73} - 151 q^{74} - 12 q^{75} + 32 q^{76} + 82 q^{77} - 63 q^{78} + 4 q^{79} - 155 q^{80} + 15 q^{81} - 56 q^{82} + 106 q^{83} + 2 q^{84} - 19 q^{85} + q^{86} - 49 q^{87} + 8 q^{88} - 14 q^{89} + 2 q^{90} - 368 q^{91} + 36 q^{92} - 4 q^{93} - 59 q^{94} + 104 q^{95} + 75 q^{96} - 28 q^{97} + 101 q^{98} + 30 q^{99}+O(q^{100}) \) 360 * q + q^2 - 15 * q^3 + 15 * q^4 + 2 * q^5 - q^6 + 2 * q^7 + 6 * q^8 + 15 * q^9 - q^10 - 2 * q^11 + 30 * q^12 - 19 * q^13 + q^15 + 15 * q^16 - 7 * q^17 - 2 * q^18 - 6 * q^19 + q^20 + 4 * q^21 + 22 * q^22 + 46 * q^23 + 3 * q^24 + 28 * q^25 + 34 * q^26 + 30 * q^27 - 2 * q^28 + 36 * q^29 + q^30 - 34 * q^31 - 190 * q^32 + 15 * q^33 - 51 * q^34 - 80 * q^35 + 15 * q^36 + q^37 - 53 * q^38 + 5 * q^39 - 45 * q^40 + 9 * q^41 + 130 * q^42 + 78 * q^43 + 35 * q^44 - q^45 - 318 * q^46 - 12 * q^47 - 15 * q^48 - 71 * q^49 + 48 * q^50 - 14 * q^51 - 63 * q^52 - 26 * q^53 - q^54 - 61 * q^55 - 4 * q^56 - 38 * q^57 - 27 * q^58 + 208 * q^59 - 180 * q^60 - 3 * q^61 - 61 * q^62 + 2 * q^63 + 140 * q^64 + 45 * q^65 - 60 * q^66 - 80 * q^67 - 140 * q^68 + 6 * q^69 - 100 * q^70 + 84 * q^71 - 3 * q^72 + 134 * q^73 - 151 * q^74 - 12 * q^75 + 32 * q^76 + 82 * q^77 - 63 * q^78 + 4 * q^79 - 155 * q^80 + 15 * q^81 - 56 * q^82 + 106 * q^83 + 2 * q^84 - 19 * q^85 + q^86 - 49 * q^87 + 8 * q^88 - 14 * q^89 + 2 * q^90 - 368 * q^91 + 36 * q^92 - 4 * q^93 - 59 * q^94 + 104 * q^95 + 75 * q^96 - 28 * q^97 + 101 * q^98 + 30 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$1$	$e\left(\frac{28}{39}\right)$

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 $

$2$	−1.28348	+	1.57198i	−0.907557	+	1.11156i	0.0857800	+	0.996314i	$0.472662\pi$
$2$	−1.28348	+	1.57198i	−0.907557	+	1.11156i	−0.993337	+	0.115242i	$0.963236\pi$
$3$	0.996757	+	0.0804666i	0.575478	+	0.0464574i
$3$	0.996757	+	0.0804666i	0.575478	+	0.0464574i
$4$	−0.423741	−	2.07562i	−0.211871	−	1.03781i
$5$	−0.317374	−	2.61381i	−0.141934	−	1.16893i	−0.873383	−	0.487034i	$-0.838079\pi$
$5$	−0.317374	−	2.61381i	−0.141934	−	1.16893i	0.731449	−	0.681896i	$-0.238844\pi$
$6$	−1.40581	+	1.46360i	−0.573919	+	0.597513i
$7$	0.313349	−	0.198150i	0.118435	−	0.0748937i	−0.473935	−	0.880560i	$-0.657167\pi$
$7$	0.313349	−	0.198150i	0.118435	−	0.0748937i	0.592370	+	0.805666i	$0.298192\pi$
$8$	0.212820	+	0.111697i	0.0752434	+	0.0394908i
$9$	0.987050	+	0.160411i	0.329017	+	0.0534704i
$10$	4.51619	+	2.85586i	1.42814	+	0.903103i
$11$	−2.28885	+	0.371974i	−0.690113	+	0.112154i	−0.495347	−	0.868695i	$-0.664959\pi$
$11$	−2.28885	+	0.371974i	−0.690113	+	0.112154i	−0.194766	+	0.980850i	$0.562395\pi$
$12$	−0.255349	−	2.10299i	−0.0737129	−	0.607081i
$13$	−3.24366	+	1.57438i	−0.899629	+	0.436655i
$13$	−3.24366	+	1.57438i	−0.899629	+	0.436655i
$14$	−0.0906900	+	0.746899i	−0.0242379	+	0.199617i
$15$	−0.106020	−	2.63087i	−0.0273743	−	0.679287i
$16$	3.44910	−	1.46952i	0.862274	−	0.367381i
$17$	3.41968	−	2.16247i	0.829394	−	0.524477i	−0.0510119	−	0.998698i	$-0.516245\pi$
$17$	3.41968	−	2.16247i	0.829394	−	0.524477i	0.880406	+	0.474221i	$0.157270\pi$
$18$	−1.51902	+	1.34574i	−0.358037	+	0.317193i
$19$	2.02248	−	3.50304i	0.463989	−	0.803652i	−0.535167	−	0.844747i	$-0.679751\pi$
$19$	2.02248	−	3.50304i	0.463989	−	0.803652i	0.999155	+	0.0410946i	$0.0130845\pi$
$20$	−5.29079	+	1.76633i	−1.18306	+	0.394962i
$21$	0.328278	−	0.172293i	0.0716360	−	0.0375975i
$22$	2.35295	−	4.07544i	0.501652	−	0.868886i
$23$	−4.44854	−	7.70509i	−0.927584	−	1.60662i	−0.787351	−	0.616505i	$-0.788548\pi$
$23$	−4.44854	−	7.70509i	−0.927584	−	1.60662i	−0.140233	−	0.990119i	$-0.544785\pi$
$24$	0.203142	+	0.128460i	0.0414663	+	0.0262217i
$25$	−1.87655	+	0.462527i	−0.375309	+	0.0925055i
$26$	1.68828	−	7.11965i	0.331099	−	1.39628i
$27$	0.970942	+	0.239316i	0.186858	+	0.0460563i
$28$	−0.544064	−	0.566430i	−0.102818	−	0.107045i
$29$	6.38735	−	7.82308i	1.18610	−	1.45271i	0.323939	−	0.946078i	$-0.394993\pi$
$29$	6.38735	−	7.82308i	1.18610	−	1.45271i	0.862162	−	0.506632i	$-0.169110\pi$
$30$	4.27174	+	3.21001i	0.779910	+	0.586064i
$31$	8.61099	+	2.12242i	1.54658	+	0.381197i	0.918010	−	0.396557i	$-0.129795\pi$
$31$	8.61099	+	2.12242i	1.54658	+	0.381197i	0.628569	+	0.777754i	$0.283641\pi$
$32$	−2.25053	+	7.76973i	−0.397841	+	1.37351i
$33$	−2.31136	+	0.186592i	−0.402355	+	0.0324815i
$34$	−0.989729	+	8.15115i	−0.169737	+	1.39791i
$35$	−0.617374	−	0.756146i	−0.104355	−	0.127812i
$36$	−0.0853008	−	2.11672i	−0.0142168	−	0.352786i
$37$	−1.78363	−	6.15782i	−0.293228	−	1.01234i	−0.962939	−	0.269718i	$-0.913069\pi$
$37$	−1.78363	−	6.15782i	−0.293228	−	1.01234i	0.669712	−	0.742621i	$-0.266418\pi$
$38$	2.91088	+	7.67537i	0.472208	+	1.24511i
$39$	−3.35983	+	1.30827i	−0.538003	+	0.209491i
$40$	0.224410	−	0.591721i	0.0354824	−	0.0935593i
$41$	−12.4274	−	1.00324i	−1.94083	−	0.156680i	−0.952040	−	0.305974i	$-0.901018\pi$
$41$	−12.4274	−	1.00324i	−1.94083	−	0.156680i	−0.988793	+	0.149294i	$0.952300\pi$
$42$	−0.150496	+	0.737180i	−0.0232221	+	0.113749i
$43$	1.51636	−	5.23507i	0.231242	−	0.798341i	−0.758025	−	0.652225i	$-0.773836\pi$
$43$	1.51636	−	5.23507i	0.231242	−	0.798341i	0.989268	−	0.146116i	$-0.0466771\pi$
$44$	1.74196	+	4.59316i	0.262610	+	0.692445i
$45$	0.106020	−	2.63087i	0.0158046	−	0.392187i
$46$	17.8218	+	2.89633i	2.62769	+	0.427041i
$47$	−1.94108	−	1.71965i	−0.283136	−	0.250837i	0.509586	−	0.860420i	$-0.329799\pi$
$47$	−1.94108	−	1.71965i	−0.283136	−	0.250837i	−0.792722	+	0.609583i	$0.791337\pi$
$48$	3.55616	−	1.18722i	0.513288	−	0.171361i
$49$	−2.94192	+	6.19997i	−0.420275	+	0.885710i
$50$	1.68143	−	3.54354i	0.237790	−	0.501132i
$51$	3.58260	−	1.88029i	0.501664	−	0.263293i
$52$	4.64230	+	6.06548i	0.643770	+	0.841131i
$53$	5.21732	+	2.73826i	0.716655	+	0.376129i	0.783297	−	0.621648i	$-0.213536\pi$
$53$	5.21732	+	2.73826i	0.716655	+	0.376129i	−0.0666425	+	0.997777i	$0.521229\pi$
$54$	−1.62238	+	1.21914i	−0.220778	+	0.165904i
$55$	1.69869	+	5.86455i	0.229051	+	0.790775i
$56$	0.0888198	−	0.00717028i	0.0118690	−	0.000958169i
$57$	2.29780	−	3.32894i	0.304351	−	0.440928i
$58$	4.09968	+	20.0815i	0.538314	+	2.63684i
$59$	−5.84457	−	2.49014i	−0.760899	−	0.324189i	−0.0235693	−	0.999722i	$-0.507503\pi$
$59$	−5.84457	−	2.49014i	−0.760899	−	0.324189i	−0.737329	+	0.675534i	$0.763913\pi$
$60$	−5.41577	+	1.33487i	−0.699172	+	0.172330i
$61$	−0.417361	+	10.3567i	−0.0534376	+	1.32604i	0.720799	+	0.693144i	$0.243775\pi$
$61$	−0.417361	+	10.3567i	−0.0534376	+	1.32604i	−0.774237	+	0.632896i	$0.781866\pi$
$62$	−14.3884	+	10.8122i	−1.82733	+	1.37315i
$63$	0.341077	−	0.145319i	0.0429716	−	0.0183085i
$64$	−5.06587	−	7.33918i	−0.633234	−	0.917397i
$65$	5.14458	+	7.97863i	0.638107	+	0.989627i
$66$	2.67326	−	3.87289i	0.329056	−	0.476719i
$67$	0.555757	−	2.72228i	0.0678965	−	0.332579i	−0.931628	−	0.363413i	$-0.881611\pi$
$67$	0.555757	−	2.72228i	0.0678965	−	0.332579i	0.999525	+	0.0308343i	$0.00981642\pi$
$68$	−5.93754	−	6.18163i	−0.720032	−	0.749633i
$69$	−3.81411	−	8.03807i	−0.459165	−	0.967670i
$70$	1.98103			0.236779
$71$	6.11372	+	12.8844i	0.725566	+	1.52910i	0.844123	+	0.536150i	$0.180122\pi$
$71$	6.11372	+	12.8844i	0.725566	+	1.52910i	−0.118557	+	0.992947i	$0.537827\pi$
$72$	0.192147	+	0.144389i	0.0226447	+	0.0170164i
$73$	2.01938	−	5.32466i	0.236350	−	0.623205i	−0.763391	−	0.645936i	$-0.776467\pi$
$73$	2.01938	−	5.32466i	0.236350	−	0.623205i	0.999742	+	0.0227318i	$0.00723637\pi$
$74$	11.9692	+	5.09961i	1.39139	+	0.592817i
$75$	−1.90768	+	0.310028i	−0.220280	+	0.0357990i
$76$	−8.12799	−	2.71352i	−0.932345	−	0.311262i
$77$	−0.643502	+	0.570093i	−0.0733338	+	0.0649681i
$78$	2.25570	−	6.96071i	0.255407	−	0.788145i
$79$	0.521599	+	0.462096i	0.0586845	+	0.0519899i	0.691955	−	0.721940i	$-0.256750\pi$
$79$	0.521599	+	0.462096i	0.0586845	+	0.0519899i	−0.633271	+	0.773930i	$0.718288\pi$
$80$	−4.93570	−	8.54888i	−0.551828	−	0.955794i
$81$	0.948536	+	0.316668i	0.105393	+	0.0351853i
$82$	17.5274	−	18.2479i	1.93558	−	2.01515i
$83$	7.51910	+	10.8933i	0.825329	+	1.19570i	0.978244	+	0.207456i	$0.0665184\pi$
$83$	7.51910	+	10.8933i	0.825329	+	1.19570i	−0.152916	+	0.988239i	$0.548866\pi$
$84$	−0.496721	−	0.608372i	−0.0541967	−	0.0663789i
$85$	−6.73760	−	8.25206i	−0.730796	−	0.895062i
$86$	6.28320	+	9.10279i	0.677535	+	0.981579i
$87$	6.99613	−	7.28375i	0.750064	−	0.780900i
$88$	−0.528662	−	0.176493i	−0.0563555	−	0.0188142i
$89$	−4.87917	−	8.45097i	−0.517191	−	0.895801i	−0.999801	−	0.0199656i	$-0.993644\pi$
$89$	−4.87917	−	8.45097i	−0.517191	−	0.895801i	0.482610	−	0.875836i	$-0.339689\pi$
$90$	3.99959	+	3.54333i	0.421594	+	0.373500i
$91$	−0.704434	+	1.13606i	−0.0738448	+	0.119092i
$92$	−14.1078	+	12.4985i	−1.47084	+	1.30305i
$93$	8.41228	+	2.80843i	0.872313	+	0.291221i
$94$	5.19460	−	0.844204i	0.535782	−	0.0870730i
$95$	−9.79814	−	4.17460i	−1.00527	−	0.428305i
$96$	−2.86844	+	7.56344i	−0.292759	+	0.771941i
$97$	−10.9134	−	8.20088i	−1.10809	−	0.832674i	−0.120968	−	0.992656i	$-0.538600\pi$
$97$	−10.9134	−	8.20088i	−1.10809	−	0.832674i	−0.987120	+	0.159983i	$0.948856\pi$
$98$	−5.97032	−	12.5822i	−0.603093	−	1.27099i
$99$	−2.31888			−0.233056
$100$	1.75520	+	3.69901i	0.175520	+	0.369901i
$101$	5.59240	+	5.82230i	0.556464	+	0.579341i	0.938705	−	0.344722i	$-0.112027\pi$
$101$	5.59240	+	5.82230i	0.556464	+	0.579341i	−0.382240	+	0.924063i	$0.624847\pi$
$102$	−1.64241	+	8.04508i	−0.162623	+	0.796581i
$103$	4.65001	−	6.73671i	0.458179	−	0.663787i	−0.524003	−	0.851716i	$-0.675562\pi$
$103$	4.65001	−	6.73671i	0.458179	−	0.663787i	0.982183	+	0.187929i	$0.0601774\pi$
$104$	−0.866170	−	0.0272457i	−0.0849350	−	0.00267166i
$105$	−0.554528	−	0.803372i	−0.0541164	−	0.0784011i
$106$	−11.0008	+	4.68701i	−1.06849	+	0.455243i
$107$	−0.0734448	+	0.0551902i	−0.00710018	+	0.00533544i	−0.604286	−	0.796767i	$-0.706542\pi$
$107$	−0.0734448	+	0.0551902i	−0.00710018	+	0.00533544i	0.597186	+	0.802103i	$0.296285\pi$
$108$	0.0853008	−	2.11672i	0.00820807	−	0.203681i
$109$	−7.92301	+	1.95285i	−0.758887	+	0.187049i	−0.599728	−	0.800204i	$-0.704724\pi$
$109$	−7.92301	+	1.95285i	−0.758887	+	0.187049i	−0.159159	+	0.987253i	$0.550878\pi$
$110$	−11.3992	−	4.85673i	−1.08687	−	0.463071i
$111$	−1.28235	−	6.28137i	−0.121715	−	0.596202i
$112$	0.789586	−	1.14391i	0.0746088	−	0.108090i
$113$	−7.05058	+	0.569181i	−0.663262	+	0.0535441i	−0.407513	−	0.913199i	$-0.633604\pi$
$113$	−7.05058	+	0.569181i	−0.663262	+	0.0535441i	−0.255749	+	0.966743i	$0.582322\pi$
$114$	2.28383	+	7.88471i	0.213901	+	0.738471i
$115$	−18.7278	+	14.0730i	−1.74637	+	1.31231i
$116$	−18.9444	−	9.94277i	−1.75894	−	0.923163i
$117$	−3.45420	+	1.03367i	−0.319341	+	0.0955632i
$118$	11.4158	−	5.99149i	1.05091	−	0.551562i
$119$	0.643059	−	1.35522i	0.0589491	−	0.124233i
$120$	0.271296	−	0.571745i	0.0247658	−	0.0521929i
$121$	−5.33345	+	1.78057i	−0.484859	+	0.161870i
$122$	−15.7448	−	13.9487i	−1.42547	−	1.26286i
$123$	−12.3064	−	1.99998i	−1.10963	−	0.180332i
$124$	0.756507	−	18.7725i	0.0679363	−	1.68582i
$125$	−2.86386	−	7.55137i	−0.256151	−	0.675415i
$126$	−0.209327	+	0.722680i	−0.0186483	+	0.0643814i
$127$	−1.52515	+	7.47069i	−0.135335	+	0.662916i	0.854355	+	0.519690i	$0.173953\pi$
$127$	−1.52515	+	7.47069i	−0.135335	+	0.662916i	−0.989690	+	0.143226i	$0.954252\pi$
$128$	1.91321	+	0.154451i	0.169106	+	0.0136516i
$129$	1.93269	−	5.09608i	0.170164	−	0.448685i
$130$	−19.1452	−	2.15325i	−1.67914	−	0.188852i
$131$	7.36243	+	19.4131i	0.643258	+	1.69613i	0.715379	+	0.698737i	$0.246254\pi$
$131$	7.36243	+	19.4131i	0.643258	+	1.69613i	−0.0721207	+	0.997396i	$0.522977\pi$
$132$	1.36671	+	4.71844i	0.118957	+	0.410687i
$133$	−0.0603846	−	1.49843i	−0.00523601	−	0.129930i
$134$	3.56605	+	4.36762i	0.308060	+	0.377305i
$135$	0.317374	−	2.61381i	0.0273152	−	0.224961i
$136$	0.969319	−	0.0782515i	0.0831184	−	0.00671001i
$137$	−3.06575	+	10.5842i	−0.261925	+	0.904269i	0.716487	+	0.697601i	$0.245749\pi$
$137$	−3.06575	+	10.5842i	−0.261925	+	0.904269i	−0.978411	+	0.206668i	$0.933738\pi$
$138$	17.5310	+	4.32100i	1.49234	+	0.367828i
$139$	8.78715	+	6.60311i	0.745316	+	0.560069i	0.904139	−	0.427238i	$-0.140513\pi$
$139$	8.78715	+	6.60311i	0.745316	+	0.560069i	−0.158823	+	0.987307i	$0.550770\pi$
$140$	−1.30787	+	1.60185i	−0.110535	+	0.135381i
$141$	−1.79642	−	1.87027i	−0.151286	−	0.157505i
$142$	−28.1008	−	6.92623i	−2.35817	−	0.581237i
$143$	6.83861	−	4.81007i	0.571873	−	0.402239i
$144$	3.64016	−	0.897219i	0.303347	−	0.0747683i
$145$	−22.4752	−	14.2125i	−1.86646	−	1.18028i
$146$	5.77842	+	10.0085i	0.478225	+	0.828311i
$147$	−3.43127	+	5.94314i	−0.283007	+	0.490182i
$148$	−12.0255	+	6.31148i	−0.988491	+	0.518800i
$149$	14.2799	−	4.76733i	1.16985	−	0.390554i	0.335637	−	0.941991i	$-0.391048\pi$
$149$	14.2799	−	4.76733i	1.16985	−	0.390554i	0.834217	+	0.551437i	$0.185920\pi$
$150$	1.96111	−	3.39675i	0.160124	−	0.277343i
$151$	−4.00503	+	3.54815i	−0.325925	+	0.288744i	−0.810178	−	0.586184i	$-0.800630\pi$
$151$	−4.00503	+	3.54815i	−0.325925	+	0.288744i	0.484253	+	0.874928i	$0.339091\pi$
$152$	0.821703	−	0.519614i	0.0666489	−	0.0421462i
$153$	3.72228	−	1.58592i	0.300928	−	0.128214i
$154$	−0.0702515	−	1.74327i	−0.00566103	−	0.140477i
$155$	2.81469	−	23.1810i	0.226081	−	1.86195i
$156$	4.13917	+	6.41936i	0.331399	+	0.513960i
$157$	0.0870331	+	0.716782i	0.00694600	+	0.0572054i	0.995770	−	0.0918839i	$-0.0292889\pi$
$157$	0.0870331	+	0.716782i	0.00694600	+	0.0572054i	−0.988824	+	0.149089i	$0.952366\pi$
$158$	−1.39587	+	0.226850i	−0.111049	+	0.0180473i
$159$	4.98007	+	3.14920i	0.394945	+	0.249748i
$160$	21.0228	+	3.41654i	1.66200	+	0.270101i
$161$	−2.92071	−	1.53291i	−0.230184	−	0.120810i
$162$	−1.71522	+	1.08464i	−0.134761	+	0.0852175i
$163$	4.36743	−	4.54697i	0.342083	−	0.356146i	−0.527831	−	0.849349i	$-0.676995\pi$
$163$	4.36743	−	4.54697i	0.342083	−	0.356146i	0.869914	+	0.493203i	$0.164174\pi$
$164$	3.18365	+	26.2197i	0.248601	+	2.04741i
$165$	1.22128	+	5.98222i	0.0950764	+	0.465715i
$166$	−26.7746	−	2.16147i	−2.07812	−	0.167763i
$167$	7.56303	−	9.26303i	0.585245	−	0.716795i	−0.394083	−	0.919075i	$-0.628938\pi$
$167$	7.56303	−	9.26303i	0.585245	−	0.716795i	0.979328	+	0.202280i	$0.0648351\pi$
$168$	0.0891088			0.00687489
$169$	8.04265	−	10.2135i	0.618665	−	0.785655i
$170$	21.6196			1.65815
$171$	2.55822	−	3.13325i	0.195632	−	0.239605i
$172$	−11.5086	−	0.929068i	−0.877520	−	0.0708408i
$173$	1.46351	+	7.16876i	0.111269	+	0.545030i	0.996764	+	0.0803822i	$0.0256141\pi$
$173$	1.46351	+	7.16876i	0.111269	+	0.545030i	−0.885495	+	0.464648i	$0.846181\pi$
$174$	2.47049	+	20.3463i	0.187287	+	1.54245i
$175$	−0.496365	+	0.516770i	−0.0375216	+	0.0390642i
$176$	−7.34783	+	4.64649i	−0.553864	+	0.350242i
$177$	−5.62525	−	2.95236i	−0.422819	−	0.221913i
$178$	19.5471	+	3.17671i	1.46511	+	0.238104i
$179$	−2.40480	−	1.52071i	−0.179743	−	0.113663i	0.441564	−	0.897230i	$-0.354424\pi$
$179$	−2.40480	−	1.52071i	−0.179743	−	0.113663i	−0.621307	+	0.783567i	$0.713398\pi$
$180$	−5.50562	+	0.894750i	−0.410364	+	0.0666907i
$181$	−0.0330988	−	0.272593i	−0.00246021	−	0.0202617i	0.991427	−	0.130661i	$-0.0417100\pi$
$181$	−0.0330988	−	0.272593i	−0.00246021	−	0.0202617i	−0.993887	+	0.110400i	$0.964787\pi$
$182$	−0.881737	−	2.56547i	−0.0653587	−	0.190165i
$183$	−1.24938	+	10.2895i	−0.0923565	+	0.760624i
$184$	−0.0861056	−	2.13669i	−0.00634779	−	0.157519i
$185$	−15.5293	+	6.61640i	−1.14173	+	0.486448i
$186$	−15.2118	+	9.61935i	−1.11538	+	0.705325i
$187$	−7.02274	+	6.22160i	−0.513553	+	0.454969i
$188$	−2.74683	+	4.75765i	−0.200333	+	0.346987i
$189$	0.351664	−	0.117403i	0.0255798	−	0.00853979i
$190$	19.1381	−	10.0444i	1.38842	−	0.728701i
$191$	9.60592	−	16.6379i	0.695060	−	1.20388i	−0.275101	−	0.961415i	$-0.588711\pi$
$191$	9.60592	−	16.6379i	0.695060	−	1.20388i	0.970161	−	0.242463i	$-0.0779554\pi$
$192$	−4.45888	−	7.72301i	−0.321792	−	0.557360i
$193$	−2.75876	−	1.74454i	−0.198580	−	0.125574i	0.431475	−	0.902125i	$-0.357993\pi$
$193$	−2.75876	−	1.74454i	−0.198580	−	0.125574i	−0.630055	+	0.776550i	$0.716968\pi$
$194$	26.8987	−	6.62994i	1.93122	−	0.476002i
$195$	4.48588	+	8.36672i	0.321241	+	0.599153i
$196$	14.1154	+	3.47914i	1.00824	+	0.248510i
$197$	12.3858	+	12.8949i	0.882449	+	0.918727i	0.997209	−	0.0746667i	$-0.0237893\pi$
$197$	12.3858	+	12.8949i	0.882449	+	0.918727i	−0.114760	+	0.993393i	$0.536610\pi$
$198$	2.97623	−	3.64522i	0.211511	−	0.259055i
$199$	−7.53280	−	5.66053i	−0.533986	−	0.401264i	0.299256	−	0.954173i	$-0.403262\pi$
$199$	−7.53280	−	5.66053i	−0.533986	−	0.401264i	−0.833242	+	0.552908i	$0.813518\pi$
$200$	−0.451030	−	0.111169i	−0.0318927	−	0.00786084i
$201$	0.773007	−	2.66873i	0.0545237	−	0.188238i
$202$	−16.3303	+	1.31831i	−1.14899	+	0.0927563i
$203$	0.451327	−	3.71701i	0.0316769	−	0.260883i
$204$	−5.42087	−	6.63936i	−0.379537	−	0.464848i
$205$	1.32184	+	32.8012i	0.0923215	+	2.29094i
$206$	4.62175	+	15.9561i	0.322013	+	1.11172i
$207$	−3.15495	−	8.31891i	−0.219284	−	0.578204i
$208$	−8.87411	+	10.1968i	−0.615309	+	0.707023i
$209$	−3.32611	+	8.77022i	−0.230072	+	0.606649i
$210$	1.97461	+	0.159407i	0.136261	+	0.0110001i
$211$	3.33000	−	16.3114i	0.229247	−	1.12293i	−0.688339	−	0.725389i	$-0.741660\pi$
$211$	3.33000	−	16.3114i	0.229247	−	1.12293i	0.917586	−	0.397537i	$-0.130135\pi$
$212$	3.47280	−	11.9895i	0.238513	−	0.823443i
$213$	5.05714	+	13.3346i	0.346509	+	0.913670i
$214$	0.00750719	−	0.186289i	0.000513181	−	0.0127345i
$215$	−14.1647	−	2.30199i	−0.966025	−	0.156994i
$216$	0.179905	+	0.159382i	0.0122410	+	0.0108446i
$217$	3.11880	−	1.04121i	0.211718	−	0.0706819i
$218$	7.09920	−	14.9612i	0.480818	−	1.01330i
$219$	2.44129	−	5.14490i	0.164967	−	0.347660i
$220$	11.4528	−	6.01088i	0.772146	−	0.405254i
$221$	−7.68771	+	12.3982i	−0.517131	+	0.833994i
$222$	11.5201	+	6.04619i	0.773175	+	0.405794i
$223$	11.5005	−	8.64203i	0.770127	−	0.578713i	−0.141400	−	0.989953i	$-0.545160\pi$
$223$	11.5005	−	8.64203i	0.770127	−	0.578713i	0.911527	+	0.411240i	$0.134904\pi$
$224$	0.834371	+	2.88058i	0.0557487	+	0.192467i
$225$	−1.92644	+	0.155518i	−0.128429	+	0.0103679i
$226$	8.15453	−	11.8139i	0.542431	−	0.785848i
$227$	1.48804	+	7.28889i	0.0987645	+	0.483780i	0.998845	+	0.0480561i	$0.0153026\pi$
$227$	1.48804	+	7.28889i	0.0987645	+	0.483780i	−0.900080	+	0.435724i	$0.856492\pi$
$228$	−7.88329	−	3.35876i	−0.522084	−	0.222439i
$229$	13.8026	−	3.40204i	0.912102	−	0.224813i	0.244777	−	0.969579i	$-0.421285\pi$
$229$	13.8026	−	3.40204i	0.912102	−	0.224813i	0.667325	+	0.744767i	$0.267439\pi$
$230$	1.91427	−	47.5021i	0.126223	−	3.13219i
$231$	−0.687288	+	0.516464i	−0.0452202	+	0.0339808i
$232$	2.23317	−	0.951466i	0.146615	−	0.0624668i
$233$	9.16674	+	13.2803i	0.600533	+	0.870022i	0.998885	−	0.0472102i	$-0.0150331\pi$
$233$	9.16674	+	13.2803i	0.600533	+	0.870022i	−0.398352	+	0.917233i	$0.630418\pi$
$234$	2.80849	−	6.75663i	0.183597	−	0.441695i
$235$	−3.87879	+	5.61939i	−0.253024	+	0.366569i
$236$	−2.69200	+	13.1863i	−0.175234	+	0.858355i
$237$	0.482724	+	0.502569i	0.0313563	+	0.0326454i
$238$	1.30502	+	2.75027i	0.0845919	+	0.178274i
$239$	20.4925			1.32555			0.662773	−	0.748820i	$-0.269379\pi$
$239$	20.4925			1.32555			0.662773	+	0.748820i	$0.269379\pi$
$240$	−4.23180	−	8.91832i	−0.273161	−	0.575675i
$241$	14.0727	+	10.5750i	0.906505	+	0.681194i	0.948111	−	0.317940i	$-0.102991\pi$
$241$	14.0727	+	10.5750i	0.906505	+	0.681194i	−0.0416060	+	0.999134i	$0.513247\pi$
$242$	4.04636	−	10.6694i	0.260110	−	0.685854i
$243$	0.919979	+	0.391967i	0.0590167	+	0.0251447i
$244$	21.6735	−	3.52228i	1.38750	−	0.225491i
$245$	17.1392	+	5.72191i	1.09498	+	0.365559i
$246$	18.9389	−	16.7784i	1.20750	−	1.06975i
$247$	−1.04512	+	14.5468i	−0.0664992	+	0.925591i
$248$	1.59553	+	1.41351i	0.101316	+	0.0897582i
$249$	6.61817	+	11.4630i	0.419410	+	0.726439i
$250$	15.5463	+	5.19011i	0.983234	+	0.328252i
$251$	11.8035	−	12.2887i	0.745028	−	0.775656i	−0.235534	−	0.971866i	$-0.575684\pi$
$251$	11.8035	−	12.2887i	0.745028	−	0.775656i	0.980562	+	0.196210i	$0.0628633\pi$
$252$	−0.446156	−	0.646369i	−0.0281052	−	0.0407174i
$253$	13.0481	+	15.9810i	0.820328	+	1.00472i
$254$	−9.78625	−	11.9860i	−0.614044	−	0.752068i
$255$	−6.05174	−	8.76746i	−0.378975	−	0.549039i
$256$	9.65674	−	10.0537i	0.603546	−	0.628358i
$257$	−25.1013	−	8.38004i	−1.56578	−	0.522733i	−0.604096	−	0.796911i	$-0.706466\pi$
$257$	−25.1013	−	8.38004i	−1.56578	−	0.522733i	−0.961679	+	0.274179i	$0.911594\pi$
$258$	5.53036	+	9.57886i	0.344305	+	0.596354i
$259$	−1.77907	−	1.57612i	−0.110546	−	0.0979354i
$260$	14.3807	−	14.0591i	0.891850	−	0.871907i
$261$	7.55955	−	6.69717i	0.467924	−	0.414545i
$262$	−39.9665	−	13.3428i	−2.46914	−	0.824320i
$263$	−15.7559	+	2.56058i	−0.971551	+	0.157892i	−0.625415	−	0.780292i	$-0.715070\pi$
$263$	−15.7559	+	2.56058i	−0.971551	+	0.157892i	−0.346136	+	0.938184i	$0.612506\pi$
$264$	−0.512746	−	0.218460i	−0.0315573	−	0.0134453i
$265$	5.50145	−	14.5061i	0.337951	−	0.891104i
$266$	2.43300	+	1.82828i	0.149177	+	0.112099i
$267$	−4.18333	−	8.81618i	−0.256016	−	0.539541i
$268$	−5.88592			−0.359540
$269$	6.45110	+	13.5954i	0.393331	+	0.828927i	0.999437	+	0.0335434i	$0.0106792\pi$
$269$	6.45110	+	13.5954i	0.393331	+	0.828927i	−0.606107	+	0.795383i	$0.707270\pi$
$270$	3.70150	+	3.85367i	0.225266	+	0.234527i
$271$	−3.51192	+	17.2025i	−0.213334	+	1.04498i	0.722185	+	0.691700i	$0.243138\pi$
$271$	−3.51192	+	17.2025i	−0.213334	+	1.04498i	−0.935518	+	0.353278i	$0.885067\pi$
$272$	8.61700	−	12.4839i	0.522482	−	0.756946i
$273$	−0.793565	+	1.07569i	−0.0480287	+	0.0651040i
$274$	−12.7033	−	18.4039i	−0.767434	−	1.11182i
$275$	4.12308	−	1.75668i	0.248631	−	0.105932i
$276$	−15.0678	+	11.3227i	−0.906975	+	0.681547i
$277$	0.458852	−	11.3863i	0.0275697	−	0.684136i	−0.925027	−	0.379901i	$-0.875958\pi$
$277$	0.458852	−	11.3863i	0.0275697	−	0.684136i	0.952597	−	0.304235i	$-0.0984008\pi$
$278$	−21.6581	+	5.33824i	−1.29896	+	0.320166i
$279$	8.15902	+	3.47623i	0.488468	+	0.208117i
$280$	−0.0469308	−	0.229882i	−0.00280465	−	0.0137381i
$281$	−11.3707	+	16.4734i	−0.678322	+	0.982719i	0.321042	+	0.947065i	$0.395967\pi$
$281$	−11.3707	+	16.4734i	−0.678322	+	0.982719i	−0.999364	+	0.0356540i	$0.988649\pi$
$282$	5.24568	−	0.423475i	0.312376	−	0.0252176i
$283$	−4.06057	−	14.0187i	−0.241376	−	0.833326i	−0.986128	−	0.165985i	$-0.946920\pi$
$283$	−4.06057	−	14.0187i	−0.241376	−	0.833326i	0.744753	−	0.667341i	$-0.232567\pi$
$284$	24.1525	−	18.1494i	1.43319	−	1.07697i
$285$	−9.43045	−	4.94948i	−0.558612	−	0.293182i
$286$	−1.21589	+	16.9238i	−0.0718970	+	1.00072i
$287$	−4.09291	+	2.14812i	−0.241597	+	0.126800i
$288$	−3.46774	+	7.30811i	−0.204338	+	0.430634i
$289$	−0.269864	+	0.568727i	−0.0158744	+	0.0334545i
$290$	51.1881	−	17.0891i	3.00587	−	1.00351i
$291$	−10.2181	−	9.05246i	−0.598996	−	0.530664i
$292$	−11.9077	−	1.93519i	−0.696845	−	0.113248i
$293$	0.405623	−	10.0654i	0.0236968	−	0.588029i	−0.943104	−	0.332498i	$-0.892109\pi$
$293$	0.405623	−	10.0654i	0.0236968	−	0.588029i	0.966801	−	0.255531i	$-0.0822504\pi$
$294$	−4.93851	−	13.0218i	−0.288020	−	0.759446i
$295$	−4.65383	+	16.0669i	−0.270956	+	0.935450i
$296$	0.308215	−	1.50974i	0.0179146	−	0.0877516i
$297$	−2.31136	−	0.186592i	−0.134118	−	0.0108272i
$298$	−10.8338	+	28.5664i	−0.627586	+	1.65481i
$299$	26.5603	+	17.9890i	1.53602	+	1.04033i
$300$	1.45186	+	3.82825i	0.0838235	+	0.221024i
$301$	−0.562180	−	1.94087i	−0.0324035	−	0.111870i
$302$	−0.437232	−	10.8498i	−0.0251599	−	0.624336i
$303$	5.10576	+	6.25342i	0.293318	+	0.359250i
$304$	1.82793	−	15.0544i	0.104839	−	0.863429i
$305$	27.2029	−	2.19604i	1.55763	−	0.125745i
$306$	−2.28445	+	7.88683i	−0.130593	+	0.450860i
$307$	10.5253	+	2.59426i	0.600713	+	0.148062i	0.527934	−	0.849286i	$-0.322967\pi$
$307$	10.5253	+	2.59426i	0.600713	+	0.148062i	0.0727794	+	0.997348i	$0.476813\pi$
$308$	1.45598	+	1.09409i	0.0829619	+	0.0623418i
$309$	5.17701	−	6.34069i	0.294510	−	0.360709i
$310$	32.8275	+	34.1770i	1.86448	+	1.94113i
$311$	16.5057	+	4.06829i	0.935953	+	0.230692i	0.677660	−	0.735375i	$-0.262994\pi$
$311$	16.5057	+	4.06829i	0.935953	+	0.230692i	0.258293	+	0.966067i	$0.416840\pi$
$312$	−0.861169	−	0.0968551i	−0.0487541	−	0.00548334i
$313$	−4.05446	+	0.999336i	−0.229172	+	0.0564858i	−0.352229	−	0.935914i	$-0.614576\pi$
$313$	−4.05446	+	0.999336i	−0.229172	+	0.0564858i	0.123057	+	0.992400i	$0.460730\pi$
$314$	−1.23847	−	0.783161i	−0.0698909	−	0.0441963i
$315$	−0.488085	−	0.845388i	−0.0275005	−	0.0476322i
$316$	0.738114	−	1.27845i	0.0415222	−	0.0719185i
$317$	−15.8441	+	8.31564i	−0.889894	+	0.467053i	−0.846735	−	0.532016i	$-0.821435\pi$
$317$	−15.8441	+	8.31564i	−0.889894	+	0.467053i	−0.0431598	+	0.999068i	$0.513742\pi$
$318$	−11.3423	+	3.78661i	−0.636044	+	0.212343i
$319$	−11.7097	+	20.2818i	−0.655616	+	1.13556i
$320$	−17.5754	+	15.5705i	−0.982495	+	0.870415i
$321$	−0.0776476	+	0.0491014i	−0.00433387	+	0.00274057i
$322$	6.15837	−	2.62384i	0.343192	−	0.146221i
$323$	−0.658996	−	16.3528i	−0.0366675	−	0.909895i
$324$	0.255349	−	2.10299i	0.0141861	−	0.116833i
$325$	5.35868	−	4.45468i	0.297246	−	0.247101i
$326$	1.54224	+	12.7014i	0.0854165	+	0.703468i
$327$	−8.05446	+	1.30898i	−0.445413	+	0.0723866i
$328$	−2.53274	−	1.60161i	−0.139847	−	0.0884341i
$329$	−0.948986	−	0.154225i	−0.0523193	−	0.00850271i
$330$	−10.9714	−	5.75823i	−0.603956	−	0.316980i
$331$	6.38219	−	4.03585i	0.350797	−	0.221830i	−0.347432	−	0.937705i	$-0.612946\pi$
$331$	6.38219	−	4.03585i	0.350797	−	0.221830i	0.698229	+	0.715875i	$0.253972\pi$
$332$	19.4242	−	20.2228i	1.06604	−	1.10987i
$333$	−0.772753	−	6.36419i	−0.0423466	−	0.348756i
$334$	4.85428	+	23.7778i	0.265614	+	1.30107i
$335$	−7.29188	−	0.588662i	−0.398398	−	0.0321620i
$336$	0.879072	−	1.07667i	0.0479573	−	0.0587371i
$337$	−26.7345			−1.45632			−0.728161	−	0.685406i	$-0.759625\pi$
$337$	−26.7345			−1.45632			−0.728161	+	0.685406i	$0.759625\pi$
$338$	5.73284	+	25.7517i	0.311825	+	1.40071i
$339$	−7.07351			−0.384180
$340$	−14.2732	+	17.4815i	−0.774071	+	0.948065i
$341$	−20.4987	−	1.65483i	−1.11007	−	0.0896139i
$342$	1.64197	+	8.04292i	0.0887877	+	0.434911i
$343$	0.619493	+	5.10198i	0.0334495	+	0.275481i
$344$	0.907452	−	0.944758i	0.0489265	−	0.0509379i
$345$	−19.7995	+	12.5204i	−1.06597	+	0.674076i
$346$	−13.1475	−	6.90035i	−0.706815	−	0.370965i
$347$	−16.0207	−	2.60361i	−0.860035	−	0.139769i	−0.285629	−	0.958340i	$-0.592203\pi$
$347$	−16.0207	−	2.60361i	−0.860035	−	0.139769i	−0.574406	+	0.818571i	$0.694767\pi$
$348$	−18.0829	−	11.4349i	−0.969343	−	0.612976i
$349$	21.4468	−	3.48544i	1.14802	−	0.186571i	0.443513	−	0.896268i	$-0.353732\pi$
$349$	21.4468	−	3.48544i	1.14802	−	0.186571i	0.704507	+	0.709697i	$0.251168\pi$
$350$	−0.175277	−	1.44354i	−0.00936897	−	0.0771604i
$351$	−3.52618	+	0.752375i	−0.188213	+	0.0401588i
$352$	2.26098	−	18.6209i	0.120511	−	0.992495i
$353$	−0.326723	−	8.10755i	−0.0173897	−	0.431521i	−0.984311	−	0.176445i	$-0.943540\pi$
$353$	−0.326723	−	8.10755i	−0.0173897	−	0.431521i	0.966921	−	0.255077i	$-0.0821007\pi$
$354$	11.8609	−	5.05347i	0.630401	−	0.268589i
$355$	31.7370	−	20.0693i	1.68442	−	1.06517i
$356$	−15.4735	+	13.7083i	−0.820095	+	0.726541i
$357$	0.750024	−	1.29908i	0.0396955	−	0.0687546i
$358$	5.47703	−	1.82850i	0.289470	−	0.0966393i
$359$	11.2078	−	5.88229i	0.591523	−	0.310455i	−0.142271	−	0.989828i	$-0.545440\pi$
$359$	11.2078	−	5.88229i	0.591523	−	0.310455i	0.733793	+	0.679373i	$0.237748\pi$
$360$	0.316423	−	0.548060i	0.0166769	−	0.0288853i
$361$	1.31915	+	2.28484i	0.0694291	+	0.120255i
$362$	0.470992	+	0.297837i	0.0247548	+	0.0156540i
$363$	−5.45943	+	1.34563i	−0.286546	+	0.0706272i
$364$	2.65653	+	0.980743i	0.139240	+	0.0514049i
$365$	−14.5585	−	3.58836i	−0.762028	−	0.187823i
$366$	−14.5714	−	15.1704i	−0.761658	−	0.792970i
$367$	0.646052	−	0.791270i	0.0337236	−	0.0413040i	−0.757468	−	0.652873i	$-0.773564\pi$
$367$	0.646052	−	0.791270i	0.0337236	−	0.0413040i	0.791191	+	0.611569i	$0.209461\pi$
$368$	−26.6663	−	20.0384i	−1.39007	−	1.04457i
$369$	−12.1055	−	2.98375i	−0.630189	−	0.155328i
$370$	9.53067	−	32.9037i	0.495476	−	1.71058i
$371$	2.17743	−	0.175780i	0.113047	−	0.00912606i
$372$	2.26461	−	18.6508i	0.117415	−	0.966997i
$373$	−4.82616	−	5.91098i	−0.249889	−	0.306059i	0.634394	−	0.773010i	$-0.281250\pi$
$373$	−4.82616	−	5.91098i	−0.249889	−	0.306059i	−0.884283	+	0.466951i	$0.845352\pi$
$374$	−0.766677	−	19.0249i	−0.0396439	−	0.983753i
$375$	−2.24694	−	7.75733i	−0.116031	−	0.400587i
$376$	−0.221023	−	0.582790i	−0.0113984	−	0.0300551i
$377$	−8.40187	+	35.4315i	−0.432718	+	1.82482i
$378$	−0.266799	+	0.703492i	−0.0137227	+	0.0361837i
$379$	5.17967	+	0.418146i	0.266062	+	0.0214787i	0.212778	−	0.977101i	$-0.431749\pi$
$379$	5.17967	+	0.418146i	0.266062	+	0.0214787i	0.0532841	+	0.998579i	$0.483031\pi$
$380$	−4.51301	+	22.1062i	−0.231513	+	1.13402i
$381$	−2.12135	+	7.32374i	−0.108680	+	0.375207i
$382$	13.8255	+	36.4547i	0.707372	+	1.86519i
$383$	0.723100	−	17.9435i	0.0369487	−	0.916872i	−0.869340	−	0.494214i	$-0.835456\pi$
$383$	0.723100	−	17.9435i	0.0369487	−	0.916872i	0.906289	−	0.422658i	$-0.138903\pi$
$384$	1.89458	+	0.307900i	0.0966825	+	0.0157124i
$385$	1.69434	+	1.50106i	0.0863517	+	0.0765009i
$386$	6.28319	−	2.09764i	0.319806	−	0.106767i
$387$	2.33648	−	4.92404i	0.118770	−	0.250303i
$388$	−12.3975	+	26.1271i	−0.629387	+	1.32640i
$389$	18.5506	−	9.73609i	0.940551	−	0.493639i	0.0765146	−	0.997068i	$-0.475621\pi$
$389$	18.5506	−	9.73609i	0.940551	−	0.493639i	0.864037	+	0.503429i	$0.167929\pi$
$390$	−18.9098	−	3.68681i	−0.957537	−	0.186689i
$391$	−31.8746	−	16.7291i	−1.61197	−	0.846027i
$392$	−1.31862	+	0.990878i	−0.0666003	+	0.0500469i
$393$	5.77645	+	19.9426i	0.291383	+	1.00597i
$394$	−36.1674	+	2.91974i	−1.82209	+	0.147094i
$395$	1.04229	−	1.51002i	0.0524432	−	0.0759771i
$396$	0.982604	+	4.81311i	0.0493777	+	0.241868i
$397$	2.25248	+	0.959692i	0.113049	+	0.0481656i	0.447750	−	0.894159i	$-0.352225\pi$
$397$	2.25248	+	0.959692i	0.113049	+	0.0481656i	−0.334702	+	0.942324i	$0.608636\pi$
$398$	18.5664	−	4.57621i	0.930651	−	0.229385i
$399$	0.0603846	−	1.49843i	0.00302301	−	0.0750152i
$400$	−5.79270	+	4.35293i	−0.289635	+	0.217647i
$401$	−21.8034	+	9.28955i	−1.08881	+	0.463898i	−0.860375	−	0.509661i	$-0.829771\pi$
$401$	−21.8034	+	9.28955i	−1.08881	+	0.463898i	−0.228434	+	0.973559i	$0.573360\pi$
$402$	3.20304	+	4.64041i	0.159753	+	0.231443i
$403$	−31.2726	+	6.67258i	−1.55780	+	0.332385i
$404$	9.71517	−	14.0749i	0.483348	−	0.700250i
$405$	0.526668	−	2.57979i	0.0261704	−	0.128191i
$406$	5.26379	+	5.48018i	0.261237	+	0.271977i
$407$	6.37301	+	13.4308i	0.315898	+	0.665742i
$408$	0.972472			0.0481446
$409$	12.6671	+	26.6954i	0.626349	+	1.32000i	0.930120	+	0.367257i	$0.119703\pi$
$409$	12.6671	+	26.6954i	0.626349	+	1.32000i	−0.303771	+	0.952745i	$0.598246\pi$
$410$	−53.2593	−	40.0218i	−2.63029	−	1.97653i
$411$	−3.90748	+	10.3032i	−0.192742	+	0.508219i
$412$	−15.9533	−	6.79705i	−0.785961	−	0.334867i
$413$	−2.32481	+	0.377819i	−0.114397	+	0.0185913i
$414$	17.1265	+	5.71765i	0.841719	+	0.281007i
$415$	26.0866	−	23.1107i	1.28054	−	1.13446i
$416$	−4.93257	−	28.7456i	−0.241839	−	1.40937i
$417$	8.22732	+	7.28877i	0.402894	+	0.356933i
$418$	−9.51760	−	16.4850i	−0.465521	−	0.806306i
$419$	−13.3429	−	4.45450i	−0.651841	−	0.217617i	−0.0285331	−	0.999593i	$-0.509084\pi$
$419$	−13.3429	−	4.45450i	−0.651841	−	0.217617i	−0.623308	+	0.781976i	$0.714212\pi$
$420$	−1.43252	+	1.49141i	−0.0698999	+	0.0727735i
$421$	−18.6477	−	27.0159i	−0.908833	−	1.31667i	−0.948275	−	0.317451i	$-0.897173\pi$
$421$	−18.6477	−	27.0159i	−0.908833	−	1.31667i	0.0394413	−	0.999222i	$-0.487442\pi$
$422$	21.3672	+	26.1701i	1.04014	+	1.27394i
$423$	−1.64010	−	2.00875i	−0.0797442	−	0.0976690i
$424$	0.804498	+	1.16552i	0.0390699	+	0.0566025i
$425$	−5.41699	+	5.63968i	−0.262762	+	0.273565i
$426$	−27.4524	−	9.16495i	−1.33007	−	0.444043i
$427$	1.92140	+	3.32796i	0.0929831	+	0.161051i
$428$	0.145676	+	0.129057i	0.00704150	+	0.00623822i
$429$	7.20348	−	4.24420i	0.347787	−	0.204912i
$430$	21.7988	−	19.3120i	1.05123	−	0.931310i
$431$	12.6540	+	4.22451i	0.609520	+	0.203488i	0.604638	−	0.796500i	$-0.293318\pi$
$431$	12.6540	+	4.22451i	0.609520	+	0.203488i	0.00488195	+	0.999988i	$0.498446\pi$
$432$	3.70055	−	0.601398i	0.178043	−	0.0289348i
$433$	−2.53868	−	1.08163i	−0.122001	−	0.0519798i	0.330103	−	0.943945i	$-0.392916\pi$
$433$	−2.53868	−	1.08163i	−0.122001	−	0.0519798i	−0.452105	+	0.891965i	$0.649327\pi$
$434$	−2.36616	+	6.23906i	−0.113579	+	0.299484i
$435$	−21.2587	−	15.9749i	−1.01928	−	0.765936i
$436$	7.41068	+	15.6177i	0.354907	+	0.747951i
$437$	−35.9883			−1.72155
$438$	4.95433	+	10.4410i	0.236727	+	0.498892i
$439$	−5.44108	−	5.66476i	−0.259688	−	0.270364i	0.578576	−	0.815629i	$-0.303609\pi$
$439$	−5.44108	−	5.66476i	−0.259688	−	0.270364i	−0.838264	+	0.545264i	$0.816429\pi$
$440$	−0.293536	+	1.43783i	−0.0139938	+	0.0685460i
$441$	−3.89837	+	5.64777i	−0.185637	+	0.268941i
$442$	−9.62268	−	27.9978i	−0.457704	−	1.33172i
$443$	10.3693	+	15.0226i	0.492663	+	0.713745i	0.987914	−	0.155005i	$-0.0495394\pi$
$443$	10.3693	+	15.0226i	0.492663	+	0.713745i	−0.495251	+	0.868750i	$0.664924\pi$
$444$	−12.4944	+	5.32336i	−0.592957	+	0.252635i
$445$	−20.5407	+	15.4353i	−0.973722	+	0.731704i
$446$	−1.17552	+	29.1703i	−0.0556627	+	1.38125i
$447$	14.6172	−	3.60281i	0.691369	−	0.170407i
$448$	−3.04164	−	1.29592i	−0.143704	−	0.0612266i
$449$	3.65136	+	17.8855i	0.172318	+	0.844070i	0.970397	+	0.241517i	$0.0776448\pi$
$449$	3.65136	+	17.8855i	0.172318	+	0.844070i	−0.798079	+	0.602553i	$0.794150\pi$
$450$	2.22808	−	3.22793i	0.105033	−	0.152166i
$451$	28.8176	−	2.32640i	1.35697	−	0.109546i
$452$	4.16903	+	14.3931i	0.196095	+	0.676997i
$453$	−4.27755	+	3.21437i	−0.200977	+	0.151024i
$454$	−13.3678	−	7.01598i	−0.627384	−	0.329276i
$455$	3.19301	+	1.48070i	0.149691	+	0.0694162i
$456$	0.860850	−	0.451809i	0.0403130	−	0.0211579i
$457$	5.57811	−	11.7556i	0.260933	−	0.549904i	−0.730129	−	0.683310i	$-0.760540\pi$
$457$	5.57811	−	11.7556i	0.260933	−	0.549904i	0.991062	+	0.133405i	$0.0425912\pi$
$458$	−12.3674	+	26.0638i	−0.577893	+	1.21788i
$459$	3.83782	−	1.28125i	0.179134	−	0.0598038i
$460$	37.1460	+	32.9085i	1.73194	+	1.53437i
$461$	5.65515	+	0.919051i	0.263387	+	0.0428045i	0.290670	−	0.956823i	$-0.406122\pi$
$461$	5.65515	+	0.919051i	0.263387	+	0.0428045i	−0.0272839	+	0.999628i	$0.508686\pi$
$462$	0.0702515	−	1.74327i	0.00326839	−	0.0811044i
$463$	−7.35636	−	19.3971i	−0.341879	−	0.901461i	−0.990145	−	0.140047i	$-0.955275\pi$
$463$	−7.35636	−	19.3971i	−0.341879	−	0.901461i	0.648266	−	0.761414i	$-0.275494\pi$
$464$	10.5344	−	36.3689i	0.489047	−	1.68839i
$465$	4.67086	−	22.8794i	0.216606	−	1.06101i
$466$	−32.6417	−	2.63511i	−1.51210	−	0.122069i
$467$	−3.03695	+	8.00777i	−0.140533	+	0.370556i	−0.986742	−	0.162296i	$-0.948110\pi$
$467$	−3.03695	+	8.00777i	−0.140533	+	0.370556i	0.846209	+	0.532851i	$0.178879\pi$
$468$	3.60921	+	6.73161i	0.166836	+	0.311169i
$469$	−0.365273	−	0.963146i	−0.0168667	−	0.0444740i
$470$	−3.85521	−	13.3097i	−0.177828	−	0.613933i
$471$	0.0290739	+	0.721461i	0.00133965	+	0.0332432i
$472$	−0.965704	−	1.18277i	−0.0444501	−	0.0544415i
$473$	−1.52340	+	12.5463i	−0.0700459	+	0.576880i
$474$	−1.40959	+	0.113794i	−0.0647448	+	0.00522674i
$475$	−2.17503	+	7.50907i	−0.0997971	+	0.344540i
$476$	−3.08541	−	0.760486i	−0.141420	−	0.0348568i
$477$	4.71051	+	3.53972i	0.215680	+	0.162073i
$478$	−26.3017	+	32.2137i	−1.20301	+	1.47342i
$479$	14.8435	+	15.4537i	0.678215	+	0.706097i	0.967987	−	0.250999i	$-0.0807590\pi$
$479$	14.8435	+	15.4537i	0.678215	+	0.706097i	−0.289772	+	0.957096i	$0.593580\pi$
$480$	20.6797	+	5.09710i	0.943897	+	0.232650i
$481$	15.4803	+	17.1657i	0.705839	+	0.782691i
$482$	−34.6857	+	8.54926i	−1.57989	+	0.389408i
$483$	−2.78789	−	1.76296i	−0.126853	−	0.0802173i
$484$	5.95579	+	10.3157i	0.270718	+	0.468897i
$485$	−17.9719	+	31.1282i	−0.816062	+	1.41346i
$486$	−1.79694	+	0.943106i	−0.0815108	+	0.0427802i
$487$	22.1481	−	7.39413i	1.00363	−	0.335060i	0.233090	−	0.972455i	$-0.425116\pi$
$487$	22.1481	−	7.39413i	1.00363	−	0.335060i	0.770537	+	0.637395i	$0.219988\pi$
$488$	−1.24563	+	2.15750i	−0.0563872	+	0.0976654i
$489$	4.71914	−	4.18080i	0.213407	−	0.189062i
$490$	−30.9926	+	19.5985i	−1.40010	+	0.885370i
$491$	23.1991	−	9.88420i	1.04696	−	0.446068i	0.201154	−	0.979560i	$-0.435531\pi$
$491$	23.1991	−	9.88420i	1.04696	−	0.446068i	0.845805	+	0.533492i	$0.179121\pi$
$492$	1.06351	+	26.3909i	0.0479470	+	1.18979i
$493$	4.92547	−	40.5649i	0.221832	−	1.82695i
$494$	−21.5259	−	20.3134i	−0.968495	−	0.913945i
$495$	0.735950	+	6.06109i	0.0330785	+	0.272426i
$496$	32.8191	−	5.33362i	1.47362	−	0.239487i
$497$	4.46877	+	2.82588i	0.200452	+	0.126758i
$498$	−26.5139	−	4.30893i	−1.18812	−	0.193088i
$499$	−14.7557	−	7.74437i	−0.660554	−	0.346685i	0.100907	−	0.994896i	$-0.467825\pi$
$499$	−14.7557	−	7.74437i	−0.660554	−	0.346685i	−0.761461	+	0.648210i	$0.775518\pi$
$500$	−14.4603	+	9.14411i	−0.646682	+	0.408937i
$501$	8.28387	−	8.62442i	0.370096	−	0.385311i
$502$	4.16806	+	34.3271i	0.186030	+	1.53209i
$503$	−4.20172	−	20.5814i	−0.187345	−	0.917678i	−0.959384	−	0.282103i	$-0.908968\pi$
$503$	−4.20172	−	20.5814i	−0.187345	−	0.917678i	0.772039	−	0.635575i	$-0.219237\pi$
$504$	0.0888198	+	0.00717028i	0.00395635	+	0.000319390i
$505$	13.4435	−	16.4653i	0.598227	−	0.732696i
$506$	−41.8688			−1.86130
$507$	8.83841	−	9.53323i	0.392528	−	0.423386i
$508$	16.1526			0.716656
$509$	7.63615	−	9.35258i	0.338466	−	0.414546i	−0.577125	−	0.816656i	$-0.695826\pi$
$509$	7.63615	−	9.35258i	0.338466	−	0.414546i	0.915591	+	0.402110i	$0.131723\pi$
$510$	21.5495	+	1.73966i	0.954229	+	0.0770334i
$511$	−0.422311	−	2.06862i	−0.0186820	−	0.0915103i
$512$	3.87273	+	31.8948i	0.171152	+	1.40957i
$513$	2.80204	−	2.91723i	0.123713	−	0.128799i
$514$	45.3902	−	28.7030i	2.00208	−	1.26604i
$515$	−19.0842	−	10.0162i	−0.840952	−	0.441366i
$516$	−11.3965	−	1.85211i	−0.501703	−	0.0815346i
$517$	5.08251	+	3.21398i	0.223529	+	0.141351i
$518$	4.76103	−	0.773743i	0.209188	−	0.0339963i
$519$	0.881921	+	7.26327i	0.0387120	+	0.318822i
$520$	0.203685	+	2.27265i	0.00893216	+	0.0996622i
$521$	4.65520	−	38.3390i	0.203948	−	1.67966i	−0.427322	−	0.904100i	$-0.640543\pi$
$521$	4.65520	−	38.3390i	0.203948	−	1.67966i	0.631270	−	0.775563i	$-0.282534\pi$
$522$	0.825281	+	20.4791i	0.0361216	+	0.896347i
$523$	18.6727	−	7.95568i	0.816499	−	0.347878i	0.0569903	−	0.998375i	$-0.481850\pi$
$523$	18.6727	−	7.95568i	0.816499	−	0.347878i	0.759509	+	0.650497i	$0.225439\pi$
$524$	37.1746	−	23.5078i	1.62398	−	1.02694i
$525$	−0.536338	+	0.475154i	−0.0234077	+	0.0207374i
$526$	16.1972	−	28.0544i	0.706232	−	1.22323i
$527$	34.0365	−	11.3630i	1.48265	−	0.494982i
$528$	−7.69789	+	4.04017i	−0.335008	+	0.175826i
$529$	−28.0790	+	48.6342i	−1.22083	+	2.11453i
$530$	15.7423	+	27.2665i	0.683802	+	1.18438i
$531$	−5.36944	−	3.39543i	−0.233014	−	0.147349i
$532$	−3.08458	+	0.760282i	−0.133734	+	0.0329624i
$533$	41.8897	−	16.3113i	1.81444	−	0.706520i
$534$	19.2281	+	4.73929i	0.832079	+	0.205089i
$535$	0.167566	+	0.174455i	0.00724450	+	0.00754233i
$536$	0.422346	−	0.517280i	0.0182426	−	0.0223431i
$537$	−2.27464	−	1.70928i	−0.0981579	−	0.0737609i
$538$	−29.6515	−	7.30845i	−1.27837	−	0.315090i
$539$	4.42738	−	15.2851i	0.190701	−	0.658376i
$540$	−5.55976	+	0.448830i	−0.239254	+	0.0193146i
$541$	−4.69113	+	38.6349i	−0.201687	+	1.66104i	0.442943	+	0.896550i	$0.353934\pi$
$541$	−4.69113	+	38.6349i	−0.201687	+	1.66104i	−0.644631	+	0.764494i	$0.722989\pi$
$542$	−22.5345	−	27.5997i	−0.967939	−	1.18551i
$543$	−0.0110568	−	0.274372i	−0.000474494	−	0.0117744i
$544$	9.10575	+	31.4367i	0.390406	+	1.34784i
$545$	7.61892	+	20.0894i	0.326359	+	0.860537i
$546$	−0.672444	−	2.62810i	−0.0287779	−	0.112472i
$547$	3.67933	−	9.70160i	0.157317	−	0.414810i	−0.833064	−	0.553176i	$-0.813416\pi$
$547$	3.67933	−	9.70160i	0.157317	−	0.414810i	0.990381	+	0.138366i	$0.0441849\pi$
$548$	23.2679	+	1.87838i	0.993955	+	0.0802403i
$549$	−2.07329	+	10.1556i	−0.0884858	+	0.433432i
$550$	−2.53043	+	8.73606i	−0.107898	+	0.372507i
$551$	−14.4863	−	38.1972i	−0.617136	−	1.62725i
$552$	0.0861056	−	2.13669i	0.00366490	−	0.0909435i
$553$	0.255007	+	0.0414427i	0.0108440	+	0.00176232i
$554$	17.3101	+	15.3354i	0.735434	+	0.651538i
$555$	−16.0113	+	5.34536i	−0.679642	+	0.226898i
$556$	9.98209	−	21.0368i	0.423335	−	0.892160i
$557$	−4.74514	+	10.0002i	−0.201058	+	0.423721i	−0.978787	−	0.204878i	$-0.934320\pi$
$557$	−4.74514	+	10.0002i	−0.201058	+	0.423721i	0.777729	+	0.628599i	$0.216371\pi$
$558$	−15.9365	+	8.36412i	−0.674646	+	0.354081i
$559$	3.32345	+	19.3681i	0.140567	+	0.819183i
$560$	−3.24056	−	1.70078i	−0.136939	−	0.0718709i
$561$	−7.50059	+	5.63633i	−0.316675	+	0.237966i
$562$	−11.3016	−	39.0178i	−0.476731	−	1.64587i
$563$	−3.33481	+	0.269214i	−0.140545	+	0.0113460i	−0.150539	−	0.988604i	$-0.548101\pi$
$563$	−3.33481	+	0.269214i	−0.140545	+	0.0113460i	0.00999361	+	0.999950i	$0.496819\pi$
$564$	−3.12075	+	4.52119i	−0.131407	+	0.190377i
$565$	3.72540	+	18.2482i	0.156729	+	0.767707i
$566$	27.2488	+	11.6096i	1.14535	+	0.487988i
$567$	0.359971	−	0.0887248i	0.0151174	−	0.00372609i
$568$	−0.138021	+	3.42495i	−0.00579122	+	0.143708i
$569$	−13.7411	+	10.3258i	−0.576057	+	0.432879i	−0.848426	−	0.529314i	$-0.822449\pi$
$569$	−13.7411	+	10.3258i	−0.576057	+	0.432879i	0.272369	+	0.962193i	$0.412193\pi$
$570$	19.8843	−	8.47190i	0.832861	−	0.354849i
$571$	6.42278	+	9.30500i	0.268785	+	0.389402i	0.934014	−	0.357238i	$-0.116281\pi$
$571$	6.42278	+	9.30500i	0.268785	+	0.389402i	−0.665229	+	0.746640i	$0.731666\pi$
$572$	−12.8817	−	12.1561i	−0.538611	−	0.508274i
$573$	10.9136	−	15.8110i	0.455921	−	0.660515i
$574$	1.87636	−	9.19103i	0.0783178	−	0.383626i
$575$	11.9117	+	12.4014i	0.496753	+	0.517174i
$576$	−3.82298	−	8.05676i	−0.159291	−	0.335698i
$577$	−9.59859			−0.399594			−0.199797	−	0.979837i	$-0.564028\pi$
$577$	−9.59859			−0.399594			−0.199797	+	0.979837i	$0.564028\pi$
$578$	−0.547661	−	1.15417i	−0.0227797	−	0.0480072i
$579$	−2.60944	−	1.96087i	−0.108445	−	0.0814909i
$580$	−19.9760	+	52.6724i	−0.829459	+	2.18710i
$581$	4.51461	+	1.92350i	0.187298	+	0.0798001i
$582$	27.3450	−	4.44399i	1.13349	−	0.184210i
$583$	−12.9602	−	4.32676i	−0.536757	−	0.179196i
$584$	1.02451	−	0.907639i	0.0423946	−	0.0375584i
$585$	3.79810	+	8.70056i	0.157032	+	0.359724i
$586$	15.3020	+	13.5564i	0.632121	+	0.560011i
$587$	9.35576	+	16.2046i	0.386153	+	0.668837i	0.991928	−	0.126799i	$-0.0404702\pi$
$587$	9.35576	+	16.2046i	0.386153	+	0.668837i	−0.605775	+	0.795636i	$0.707137\pi$
$588$	13.7897	+	4.60368i	0.568677	+	0.189852i
$589$	24.8505	−	25.8721i	1.02395	−	1.06604i
$590$	−19.2837	−	27.9372i	−0.793897	−	1.15016i
$591$	11.3080	+	13.8498i	0.465148	+	0.569703i
$592$	−15.2010	−	18.6178i	−0.624757	−	0.765188i
$593$	13.4387	+	19.4693i	0.551861	+	0.799509i	0.995305	−	0.0967932i	$-0.0308585\pi$
$593$	13.4387	+	19.4693i	0.551861	+	0.799509i	−0.443443	+	0.896303i	$0.646243\pi$
$594$	3.25990	−	3.39391i	0.133755	−	0.139254i
$595$	−3.74637	−	1.25072i	−0.153586	−	0.0512746i
$596$	−15.9461	−	27.6195i	−0.653180	−	1.13134i
$597$	−7.05289	−	6.24831i	−0.288655	−	0.255726i
$598$	−62.3679	+	18.6637i	−2.55041	+	0.763214i
$599$	17.3437	−	15.3651i	0.708643	−	0.627803i	−0.229800	−	0.973238i	$-0.573807\pi$
$599$	17.3437	−	15.3651i	0.708643	−	0.627803i	0.938443	+	0.345435i	$0.112269\pi$
$600$	−0.440623	−	0.147101i	−0.0179883	−	0.00600539i
$601$	25.2924	−	4.11042i	1.03170	−	0.167668i	0.379089	−	0.925360i	$-0.376238\pi$
$601$	25.2924	−	4.11042i	1.03170	−	0.167668i	0.652611	+	0.757693i	$0.273673\pi$
$602$	3.77255	+	1.60733i	0.153758	+	0.0655101i
$603$	0.985244	−	2.59787i	0.0401222	−	0.105794i
$604$	9.06171	+	6.80944i	0.368716	+	0.277072i
$605$	6.34675	+	13.3755i	0.258032	+	0.543791i
$606$	−16.3834			−0.665529
$607$	2.89085	+	6.09233i	0.117336	+	0.247280i	0.953618	−	0.301019i	$-0.0973268\pi$
$607$	2.89085	+	6.09233i	0.117336	+	0.247280i	−0.836282	+	0.548299i	$0.815275\pi$
$608$	22.6660	+	23.5978i	0.919228	+	0.957018i
$609$	0.748958	−	3.66864i	0.0303493	−	0.148661i
$610$	−31.4622	+	45.5809i	−1.27387	+	1.84552i
$611$	9.00360	+	2.52195i	0.364247	+	0.102027i
$612$	−4.86905	−	7.05403i	−0.196820	−	0.285142i
$613$	−3.50632	+	1.49390i	−0.141619	+	0.0603382i	−0.461613	−	0.887081i	$-0.652729\pi$
$613$	−3.50632	+	1.49390i	−0.141619	+	0.0603382i	0.319994	+	0.947419i	$0.396319\pi$
$614$	−17.5872	+	13.2159i	−0.709761	+	0.533351i
$615$	−1.32184	+	32.8012i	−0.0533019	+	1.32267i
$616$	−0.200628	+	0.0494503i	−0.00808352	+	0.00199241i
$617$	22.2420	+	9.47643i	0.895429	+	0.381507i	0.790134	−	0.612934i	$-0.210011\pi$
$617$	22.2420	+	9.47643i	0.895429	+	0.381507i	0.105295	+	0.994441i	$0.466421\pi$
$618$	3.32283	+	16.2763i	0.133664	+	0.654729i
$619$	14.7297	−	21.3396i	0.592036	−	0.857712i	−0.406396	−	0.913697i	$-0.633215\pi$
$619$	14.7297	−	21.3396i	0.592036	−	0.857712i	0.998432	+	0.0559850i	$0.0178299\pi$
$620$	−49.3078	+	3.98054i	−1.98025	+	0.159862i
$621$	−2.47532	−	8.54580i	−0.0993313	−	0.342931i
$622$	−27.5800	+	20.7250i	−1.10586	+	0.830998i
$623$	−3.20344	−	1.68130i	−0.128343	−	0.0673597i
$624$	−9.66583	+	9.44969i	−0.386943	+	0.378291i
$625$	−27.3855	+	14.3730i	−1.09542	+	0.574922i
$626$	3.63289	−	7.65615i	0.145199	−	0.306001i
$627$	−4.02103	+	8.47414i	−0.160585	+	0.338425i
$628$	1.45089	−	0.484378i	0.0578968	−	0.0193288i
$629$	−19.4156	−	17.2007i	−0.774150	−	0.685837i
$630$	1.95538	+	0.317780i	0.0779042	+	0.0126607i
$631$	−0.296774	+	7.36438i	−0.0118144	+	0.293171i	0.982471	+	0.186416i	$0.0596872\pi$
$631$	−0.296774	+	7.36438i	−0.0118144	+	0.293171i	−0.994285	+	0.106755i	$0.965954\pi$
$632$	0.0593922	+	0.156604i	0.00236250	+	0.00622939i
$633$	4.63173	−	15.9906i	0.184095	−	0.635569i
$634$	7.26362	−	35.5796i	0.288475	−	1.41304i
$635$	20.0110	+	1.61545i	0.794111	+	0.0641073i
$636$	4.42630	−	11.6712i	0.175514	−	0.462793i
$637$	−0.218526	−	24.7423i	−0.00865832	−	0.980326i
$638$	−16.8533	−	44.4386i	−0.667230	−	1.75934i
$639$	3.96775	+	13.6983i	0.156962	+	0.541895i
$640$	−0.203500	−	5.04979i	−0.00804403	−	0.199610i
$641$	−3.03897	−	3.72206i	−0.120032	−	0.147013i	0.711093	−	0.703098i	$-0.248200\pi$
$641$	−3.03897	−	3.72206i	−0.120032	−	0.147013i	−0.831125	+	0.556085i	$0.812303\pi$
$642$	0.0224729	−	0.185081i	0.000886934	−	0.00730456i
$643$	28.9286	−	2.33536i	1.14083	−	0.0920976i	0.504429	−	0.863453i	$-0.331703\pi$
$643$	28.9286	−	2.33536i	1.14083	−	0.0920976i	0.636405	+	0.771355i	$0.280421\pi$
$644$	−1.94411	+	6.71185i	−0.0766087	+	0.264484i
$645$	−13.9335	−	3.43431i	−0.548633	−	0.135226i
$646$	26.5521	+	19.9526i	1.04468	+	0.785024i
$647$	−8.06355	+	9.87606i	−0.317011	+	0.388268i	−0.908389	−	0.418127i	$-0.862687\pi$
$647$	−8.06355	+	9.87606i	−0.317011	+	0.388268i	0.591378	+	0.806395i	$0.298584\pi$
$648$	0.166497	+	0.173342i	0.00654063	+	0.00680951i
$649$	14.3036	+	3.52552i	0.561465	+	0.138389i
$650$	0.124897	+	14.1412i	0.00489885	+	0.554665i
$651$	3.19247	−	0.786874i	0.125123	−	0.0308400i
$652$	−11.2885	−	7.13839i	−0.442090	−	0.279561i
$653$	15.1235	+	26.1946i	0.591826	+	1.02507i	0.993986	+	0.109504i	$0.0349263\pi$
$653$	15.1235	+	26.1946i	0.591826	+	1.02507i	−0.402160	+	0.915569i	$0.631740\pi$
$654$	8.28005	−	14.3415i	0.323776	−	0.560796i
$655$	48.4055	−	25.4052i	1.89136	−	0.992662i
$656$	−44.3376	+	14.8021i	−1.73109	+	0.577923i
$657$	2.84736	−	4.93178i	0.111086	−	0.192407i
$658$	1.46044	−	1.29384i	0.0569340	−	0.0504391i
$659$	31.5664	−	19.9614i	1.22965	−	0.777586i	0.248093	−	0.968736i	$-0.420196\pi$
$659$	31.5664	−	19.9614i	1.22965	−	0.777586i	0.981561	+	0.191150i	$0.0612217\pi$
$660$	11.8993	−	5.06983i	0.463180	−	0.197343i
$661$	0.406843	+	10.0957i	0.0158244	+	0.392677i	0.987621	+	0.156858i	$0.0501364\pi$
$661$	0.406843	+	10.0957i	0.0158244	+	0.392677i	−0.971797	+	0.235820i	$0.924223\pi$
$662$	−1.84714	+	15.2126i	−0.0717912	+	0.591254i
$663$	−8.66042	+	11.7394i	−0.336343	+	0.455920i
$664$	0.383472	+	3.15818i	0.0148816	+	0.122561i
$665$	−3.89744	+	0.633395i	−0.151136	+	0.0245620i
$666$	10.9962	+	6.95356i	0.426093	+	0.269445i
$667$	−88.6920	−	14.4138i	−3.43417	−	0.558106i
$668$	−22.4313	−	11.7729i	−0.867894	−	0.455506i
$669$	12.1586	−	7.68860i	0.470077	−	0.297259i
$670$	10.2844	−	10.7071i	0.397319	−	0.413653i
$671$	−2.89715	−	23.8601i	−0.111843	−	0.921111i
$672$	0.599874	+	2.93838i	0.0231407	+	0.113350i
$673$	−20.5975	−	1.66280i	−0.793974	−	0.0640962i	−0.323178	−	0.946338i	$-0.604751\pi$
$673$	−20.5975	−	1.66280i	−0.793974	−	0.0640962i	−0.470796	+	0.882242i	$0.656033\pi$
$674$	34.3132	−	42.0260i	1.32170	−	1.61878i
$675$	−1.93271			−0.0743900
$676$	−24.6074	−	12.3656i	−0.946439	−	0.475600i
$677$	−9.80515			−0.376842			−0.188421	−	0.982088i	$-0.560337\pi$
$677$	−9.80515			−0.376842			−0.188421	+	0.982088i	$0.560337\pi$
$678$	9.07871	−	11.1194i	0.348666	−	0.427038i
$679$	−5.04471	−	0.407251i	−0.193598	−	0.0156289i
$680$	−0.512170	−	2.50878i	−0.0196408	−	0.0962072i
$681$	0.896700	+	7.38499i	0.0343616	+	0.282993i
$682$	28.9110	−	30.0996i	1.10706	−	1.15257i
$683$	−23.1035	+	14.6097i	−0.884030	+	0.559027i	−0.897565	−	0.440882i	$-0.854666\pi$
$683$	−23.1035	+	14.6097i	−0.884030	+	0.559027i	0.0135354	+	0.999908i	$0.495691\pi$
$684$	−7.58746	−	3.98220i	−0.290114	−	0.152263i
$685$	28.6380	+	4.65413i	1.09420	+	0.177825i
$686$	−8.81531	−	5.57447i	−0.336570	−	0.212834i
$687$	14.0316	−	2.28036i	0.535339	−	0.0870010i
$688$	−2.46299	−	20.2846i	−0.0939008	−	0.773343i
$689$	−21.2343	−	0.667932i	−0.808962	−	0.0254462i
$690$	5.73039	−	47.1940i	0.218152	−	1.79664i
$691$	0.222552	+	5.52257i	0.00846628	+	0.210089i	0.997885	+	0.0650014i	$0.0207052\pi$
$691$	0.222552	+	5.52257i	0.00846628	+	0.210089i	−0.989419	+	0.145087i	$0.953654\pi$
$692$	14.2595	−	6.07540i	0.542064	−	0.230952i
$693$	−0.726618	+	0.459485i	−0.0276019	+	0.0174544i
$694$	24.6550	−	21.8425i	0.935893	−	0.829129i
$695$	14.4704	−	25.0636i	0.548895	−	0.950715i
$696$	2.30249	−	0.768685i	0.0872757	−	0.0291369i
$697$	−44.6672	+	23.4431i	−1.69189	+	0.887972i
$698$	−22.0475	+	38.1874i	−0.834510	+	1.44541i
$699$	8.06839	+	13.9749i	0.305175	+	0.528578i
$700$	1.28295	+	0.811289i	0.0484910	+	0.0306638i
$701$	−31.9933	+	7.88563i	−1.20837	+	0.297836i	−0.791522	−	0.611140i	$-0.790711\pi$
$701$	−31.9933	+	7.88563i	−1.20837	+	0.297836i	−0.416847	+	0.908977i	$0.636865\pi$
$702$	3.34306	−	6.50873i	0.126176	−	0.245656i
$703$	−25.1784	−	6.20593i	−0.949623	−	0.234061i
$704$	14.3250	+	14.9139i	0.539893	+	0.562088i
$705$	−4.31838	+	5.28906i	−0.162640	+	0.199197i
$706$	13.1642	+	9.89228i	0.495442	+	0.372301i
$707$	2.90606	+	0.716280i	0.109294	+	0.0269385i
$708$	−3.74433	+	12.9269i	−0.140721	+	0.485824i
$709$	11.9252	−	0.962699i	0.447859	−	0.0361549i	0.145520	−	0.989355i	$-0.453515\pi$
$709$	11.9252	−	0.962699i	0.447859	−	0.0361549i	0.302339	+	0.953200i	$0.402233\pi$
$710$	−9.18537	+	75.6483i	−0.344721	+	2.83903i
$711$	0.440719	+	0.539783i	0.0165282	+	0.0202434i
$712$	−0.0944409	−	2.34353i	−0.00353932	−	0.0878274i
$713$	−21.9529	−	75.7901i	−0.822142	−	2.83836i
$714$	1.07948	+	2.84636i	0.0403986	+	0.106522i
$715$	−14.7430	−	16.3482i	−0.551357	−	0.611388i
$716$	−2.13740	+	5.63585i	−0.0798782	+	0.210622i
$717$	20.4260	+	1.64896i	0.762823	+	0.0615815i
$718$	−5.13811	+	25.1681i	−0.191753	+	0.939267i
$719$	−9.83609	+	33.9581i	−0.366824	+	1.26642i	0.538833	+	0.842413i	$0.318866\pi$
$719$	−9.83609	+	33.9581i	−0.366824	+	1.26642i	−0.905657	+	0.424011i	$0.860622\pi$
$720$	−3.50045	−	9.22992i	−0.130454	−	0.343979i
$721$	0.122199	−	3.03234i	0.00455093	−	0.112930i
$722$	−5.28483	−	0.858868i	−0.196681	−	0.0319637i
$723$	13.1762	+	11.6731i	0.490027	+	0.434126i
$724$	−0.551775	+	0.184209i	−0.0205065	+	0.00684609i
$725$	−8.36777	+	17.6347i	−0.310771	+	0.654937i
$726$	4.89177	−	10.3092i	0.181551	−	0.382610i
$727$	9.56872	−	5.02205i	0.354884	−	0.186258i	−0.277854	−	0.960623i	$-0.589623\pi$
$727$	9.56872	−	5.02205i	0.354884	−	0.186258i	0.632738	+	0.774366i	$0.281931\pi$
$728$	−0.276812	+	0.163094i	−0.0102594	+	0.00604467i
$729$	0.885456	+	0.464723i	0.0327947	+	0.0172120i
$730$	24.3264	−	18.2801i	0.900360	−	0.676577i
$731$	−6.13525	−	21.1813i	−0.226920	−	0.783420i
$732$	21.8866	−	1.76687i	0.808952	−	0.0653054i
$733$	9.48809	−	13.7459i	0.350451	−	0.507715i	−0.607628	−	0.794222i	$-0.707879\pi$
$733$	9.48809	−	13.7459i	0.350451	−	0.507715i	0.958078	+	0.286507i	$0.0924941\pi$
$734$	0.414664	+	2.03116i	0.0153055	+	0.0749714i
$735$	16.6232	+	7.08249i	0.613157	+	0.261242i
$736$	69.8781	−	17.2234i	2.57574	−	0.634863i
$737$	−0.259426	+	6.43760i	−0.00955609	+	0.237132i
$738$	20.2276	−	15.2000i	0.744588	−	0.559521i
$739$	35.9610	−	15.3216i	1.32285	−	0.563613i	0.388986	−	0.921244i	$-0.372826\pi$
$739$	35.9610	−	15.3216i	1.32285	−	0.563613i	0.933863	+	0.357631i	$0.116415\pi$
$740$	20.3136	+	29.4293i	0.746741	+	1.08184i
$741$	−2.21226	+	14.4155i	−0.0812694	+	0.529568i
$742$	−2.51837	+	3.64848i	−0.0924521	+	0.133940i
$743$	−3.58933	+	17.5817i	−0.131680	+	0.645010i	0.859352	+	0.511384i	$0.170867\pi$
$743$	−3.58933	+	17.5817i	−0.131680	+	0.645010i	−0.991032	+	0.133626i	$0.957338\pi$
$744$	1.47661	+	1.53732i	0.0541352	+	0.0563608i
$745$	−16.9929	−	35.8118i	−0.622572	−	1.31204i
$746$	15.4862			0.566990
$747$	5.67432	+	11.9584i	0.207613	+	0.437534i
$748$	15.8895	+	11.9402i	0.580978	+	0.436577i
$749$	−0.0120779	+	0.0318469i	−0.000441318	+	0.00116366i
$750$	15.0782	+	6.42424i	0.550580	+	0.234580i
$751$	−14.5669	+	2.36736i	−0.531555	+	0.0863861i	−0.420264	−	0.907402i	$-0.638063\pi$
$751$	−14.5669	+	2.36736i	−0.531555	+	0.0863861i	−0.111291	+	0.993788i	$0.535498\pi$
$752$	−9.22206	−	3.07878i	−0.336294	−	0.112271i
$753$	12.7540	−	11.2991i	0.464782	−	0.411761i
$754$	−44.9140	−	58.6832i	−1.63567	−	2.13712i
$755$	10.5453	+	9.34229i	0.383781	+	0.340001i
$756$	−0.392699	−	0.680174i	−0.0142823	−	0.0247377i
$757$	38.2598	+	12.7730i	1.39058	+	0.464242i	0.910690	−	0.413089i	$-0.135550\pi$
$757$	38.2598	+	12.7730i	1.39058	+	0.464242i	0.479885	+	0.877332i	$0.340679\pi$
$758$	−7.30532	+	7.60564i	−0.265341	+	0.276249i
$759$	11.7199	+	16.9792i	0.425404	+	0.616304i
$760$	−1.61896	−	1.98286i	−0.0587257	−	0.0719259i
$761$	−17.8161	−	21.8207i	−0.645833	−	0.791001i	0.343111	−	0.939295i	$-0.388519\pi$
$761$	−17.8161	−	21.8207i	−0.645833	−	0.791001i	−0.988943	+	0.148294i	$0.952622\pi$
$762$	−8.79005	−	12.7346i	−0.318430	−	0.461325i
$763$	−2.09571	+	2.18187i	−0.0758699	+	0.0789889i
$764$	−38.6045	−	12.8881i	−1.39666	−	0.466274i
$765$	−5.32663	−	9.22599i	−0.192585	−	0.333566i
$766$	27.2788	+	24.1669i	0.985621	+	0.873184i
$767$	22.8782	−	1.12442i	0.826085	−	0.0406006i
$768$	10.4344	−	9.24409i	0.376520	−	0.333567i
$769$	−31.0630	−	10.3703i	−1.12016	−	0.373964i	−0.304510	−	0.952509i	$-0.598493\pi$
$769$	−31.0630	−	10.3703i	−1.12016	−	0.373964i	−0.815651	+	0.578545i	$0.803621\pi$
$770$	−4.53428	+	0.736892i	−0.163404	+	0.0265558i
$771$	−24.3456	−	10.3727i	−0.876784	−	0.373563i
$772$	−2.45200	+	6.46538i	−0.0882493	+	0.232694i
$773$	32.0983	+	24.1203i	1.15450	+	0.867547i	0.992858	−	0.119303i	$-0.0380660\pi$
$773$	32.0983	+	24.1203i	1.15450	+	0.867547i	0.161638	+	0.986850i	$0.448322\pi$
$774$	4.74164	+	9.99280i	0.170435	+	0.359184i
$775$	−17.1406			−0.615709
$776$	−1.40658	−	2.96431i	−0.0504933	−	0.106412i
$777$	−1.64648	−	1.71417i	−0.0590671	−	0.0614953i
$778$	−8.50437	+	41.6572i	−0.304896	+	1.49348i
$779$	−28.6485	+	41.5046i	−1.02644	+	1.48706i
$780$	15.4653	−	12.8563i	0.553747	−	0.460331i
$781$	−18.7860	−	27.2163i	−0.672217	−	0.973875i
$782$	67.2082	−	28.6347i	2.40336	−	1.02398i
$783$	8.07393	−	6.06717i	0.288539	−	0.216823i
$784$	−1.03598	+	25.7075i	−0.0369992	+	0.918126i
$785$	1.84591	−	0.454975i	0.0658832	−	0.0162388i
$786$	−38.7633	−	16.5155i	−1.38264	−	0.589088i
$787$	9.59402	+	46.9946i	0.341990	+	1.67518i	0.679360	+	0.733806i	$0.262258\pi$
$787$	9.59402	+	46.9946i	0.341990	+	1.67518i	−0.337369	+	0.941372i	$0.609537\pi$
$788$	21.5167	−	31.1723i	0.766500	−	1.11047i
$789$	−15.9109	+	1.28446i	−0.566441	+	0.0457279i
$790$	1.03595	+	3.57653i	0.0368576	+	0.127247i
$791$	−2.09651	+	1.57542i	−0.0745433	+	0.0560156i
$792$	−0.493504	−	0.259011i	−0.0175359	−	0.00920355i
$793$	−14.9516	−	34.2507i	−0.530948	−	1.21628i
$794$	−4.39963	+	2.30910i	−0.156137	+	0.0819470i
$795$	6.65087	−	14.0164i	0.235882	−	0.497111i
$796$	−8.55717	+	18.0338i	−0.303301	+	0.639193i
$797$	0.920751	−	0.307392i	0.0326147	−	0.0108884i	−0.300314	−	0.953840i	$-0.597091\pi$
$797$	0.920751	−	0.307392i	0.0326147	−	0.0108884i	0.332929	+	0.942952i	$0.391963\pi$
$798$	2.27799	+	2.01813i	0.0806401	+	0.0714409i
$799$	−10.3566	−	1.68311i	−0.366390	−	0.0595441i
$800$	0.629513	−	15.6212i	0.0222566	−	0.552293i
$801$	−3.46036	−	9.12421i	−0.122266	−	0.322388i
$802$	13.3812	−	46.1974i	0.472508	−	1.63129i
$803$	−2.64141	+	12.9385i	−0.0932134	+	0.456589i
$804$	−5.86683	−	0.473619i	−0.206907	−	0.0167033i
$805$	−3.07977	+	8.12067i	−0.108547	+	0.286216i
$806$	29.6486	−	57.7240i	1.04433	−	2.03324i
$807$	5.33621	+	14.0704i	0.187843	+	0.495302i
$808$	0.539844	+	1.86376i	0.0189916	+	0.0655668i
$809$	1.62779	+	40.3931i	0.0572299	+	1.42015i	0.731591	+	0.681744i	$0.238778\pi$
$809$	1.62779	+	40.3931i	0.0572299	+	1.42015i	−0.674361	+	0.738402i	$0.735581\pi$
$810$	3.37941	+	4.13902i	0.118740	+	0.145430i
$811$	5.30424	−	43.6844i	0.186257	−	1.53397i	−0.537116	−	0.843508i	$-0.680486\pi$
$811$	5.30424	−	43.6844i	0.186257	−	1.53397i	0.723373	−	0.690457i	$-0.242591\pi$
$812$	−7.90636	+	0.638267i	−0.277459	+	0.0223988i
$813$	−4.88476	+	16.8641i	−0.171316	+	0.591451i
$814$	−29.2926	−	7.21998i	−1.02671	−	0.253060i
$815$	−13.2710	−	9.97252i	−0.464863	−	0.349322i
$816$	9.59359	−	11.7500i	0.335843	−	0.411333i
$817$	−15.2718	−	15.8997i	−0.534294	−	0.556259i
$818$	−58.2226	−	14.3506i	−2.03570	−	0.501756i
$819$	−0.877549	+	1.00835i	−0.0306640	+	0.0352346i
$820$	67.5228	−	16.6429i	2.35800	−	0.581194i
$821$	−43.4269	−	27.4615i	−1.51561	−	0.958413i	−0.994479	−	0.104935i	$-0.966537\pi$
$821$	−43.4269	−	27.4615i	−1.51561	−	0.958413i	−0.521129	−	0.853478i	$-0.674489\pi$
$822$	−11.1812	−	19.3664i	−0.389989	−	0.675481i
$823$	−8.65502	+	14.9909i	−0.301695	+	0.522551i	−0.976520	−	0.215427i	$-0.930886\pi$
$823$	−8.65502	+	14.9909i	−0.301695	+	0.522551i	0.674825	+	0.737978i	$0.264219\pi$
$824$	1.74209	−	0.914317i	0.0606884	−	0.0318518i
$825$	4.25106	−	1.41921i	0.148003	−	0.0494107i
$826$	2.38993	−	4.13948i	0.0831562	−	0.144031i
$827$	−21.6411	+	19.1724i	−0.752536	+	0.666688i	−0.949516	−	0.313719i	$-0.898425\pi$
$827$	−21.6411	+	19.1724i	−0.752536	+	0.666688i	0.196980	+	0.980407i	$0.436887\pi$
$828$	−15.9300	+	10.0735i	−0.553607	+	0.350080i
$829$	−14.2818	+	6.08492i	−0.496028	+	0.211338i	−0.625469	−	0.780249i	$-0.715092\pi$
$829$	−14.2818	+	6.08492i	−0.496028	+	0.211338i	0.129440	+	0.991587i	$0.458682\pi$
$830$	2.84789	+	70.6697i	0.0988518	+	2.45298i
$831$	1.37358	−	11.3124i	0.0476489	−	0.392424i
$832$	27.9866	+	15.8302i	0.970261	+	0.548813i
$833$	3.34684	+	27.5637i	0.115961	+	0.955027i
$834$	−22.0174	+	3.57817i	−0.762400	+	0.123902i
$835$	−26.6121	−	16.8285i	−0.920949	−	0.582373i
$836$	19.6131	+	3.18744i	0.678333	+	0.110240i
$837$	7.85284	+	4.12149i	0.271434	+	0.142459i
$838$	24.1277	−	15.2574i	0.833476	−	0.527059i
$839$	9.60282	−	9.99760i	0.331526	−	0.345155i	−0.534487	−	0.845177i	$-0.679495\pi$
$839$	9.60282	−	9.99760i	0.331526	−	0.345155i	0.866013	+	0.500021i	$0.166675\pi$
$840$	−0.0282808	−	0.232913i	−0.000975779	−	0.00803626i
$841$	−14.6017	−	71.5236i	−0.503505	−	2.46633i
$842$	66.4023	+	5.36055i	2.28837	+	0.184737i
$843$	−12.6594	+	15.5050i	−0.436014	+	0.534020i
$844$	−35.2674			−1.21396
$845$	−29.2487	−	17.7804i	−1.00618	−	0.611665i
$846$	5.26275			0.180937
$847$	−1.31841	+	1.61476i	−0.0453012	+	0.0554839i
$848$	22.0190	+	1.77756i	0.756136	+	0.0610416i
$849$	−2.91936	−	14.3000i	−0.100192	−	0.490774i
$850$	−1.91286	−	15.7538i	−0.0656105	−	0.540351i
$851$	−39.5120	+	41.1364i	−1.35445	+	1.41014i
$852$	25.5346	−	16.1471i	0.874802	−	0.553191i
$853$	42.1816	+	22.1386i	1.44427	+	0.758011i	0.991063	−	0.133394i	$-0.0425875\pi$
$853$	42.1816	+	22.1386i	1.44427	+	0.758011i	0.453207	+	0.891405i	$0.350280\pi$
$854$	−7.69756	−	1.25098i	−0.263405	−	0.0428075i
$855$	−9.00161	−	5.69227i	−0.307848	−	0.194672i
$856$	−0.0217951	+	0.00354205i	−0.000744942	+	0.000121065i
$857$	0.522730	+	4.30507i	0.0178561	+	0.147058i	0.998910	−	0.0466765i	$-0.0148630\pi$
$857$	0.522730	+	4.30507i	0.0178561	+	0.147058i	−0.981054	+	0.193735i	$0.937940\pi$
$858$	−2.57374	+	16.7711i	−0.0878662	+	0.572554i
$859$	2.22279	−	18.3063i	0.0758405	−	0.624603i	−0.904385	−	0.426718i	$-0.859670\pi$
$859$	2.22279	−	18.3063i	0.0758405	−	0.624603i	0.980225	−	0.197885i	$-0.0634072\pi$
$860$	1.22411	+	30.3760i	0.0417419	+	1.03581i
$861$	−4.25249	+	1.81181i	−0.144924	+	0.0617465i
$862$	−22.8819	+	14.4697i	−0.779362	+	0.492839i
$863$	−0.611783	+	0.541992i	−0.0208253	+	0.0184496i	−0.673471	−	0.739214i	$-0.735197\pi$
$863$	−0.611783	+	0.541992i	−0.0208253	+	0.0184496i	0.652646	+	0.757663i	$0.273659\pi$
$864$	−4.04455	+	7.00537i	−0.137598	+	0.238328i
$865$	18.2733	−	6.10051i	0.621309	−	0.207424i
$866$	4.95864	−	2.60250i	0.168502	−	0.0884364i
$867$	−0.314753	+	0.545168i	−0.0106896	+	0.0185149i
$868$	−3.48272	−	6.03225i	−0.118211	−	0.204748i
$869$	−1.36575	−	0.863646i	−0.0463298	−	0.0292972i
$870$	52.3972	−	12.9148i	1.77643	−	0.437851i
$871$	2.48322	+	9.70511i	0.0841406	+	0.328845i
$872$	−1.90431	−	0.469369i	−0.0644879	−	0.0158948i
$873$	−9.45656	−	9.84532i	−0.320056	−	0.333213i
$874$	46.1903	−	56.5728i	1.56241	−	1.91360i
$875$	−2.39369	−	1.79874i	−0.0809215	−	0.0608086i
$876$	−11.7134	−	2.88708i	−0.395758	−	0.0975455i
$877$	−2.57464	+	8.88868i	−0.0869393	+	0.300149i	−0.992191	−	0.124726i	$-0.960195\pi$
$877$	−2.57464	+	8.88868i	−0.0869393	+	0.300149i	0.905252	+	0.424875i	$0.139682\pi$
$878$	15.8884	−	1.28264i	0.536207	−	0.0432871i
$879$	1.21424	−	10.0002i	0.0409553	−	0.337297i
$880$	14.4770	+	17.7311i	0.488020	+	0.597716i
$881$	−0.0818180	−	2.03029i	−0.00275652	−	0.0684023i	0.997225	−	0.0744435i	$-0.0237180\pi$
$881$	−0.0818180	−	2.03029i	−0.00275652	−	0.0684023i	−0.999982	+	0.00604118i	$0.998077\pi$
$882$	−3.87468	−	13.3770i	−0.130467	−	0.450425i
$883$	10.4102	+	27.4493i	0.350330	+	0.923744i	0.988141	+	0.153551i	$0.0490709\pi$
$883$	10.4102	+	27.4493i	0.350330	+	0.923744i	−0.637811	+	0.770193i	$0.720160\pi$
$884$	28.9916	+	10.7032i	0.975093	+	0.359986i
$885$	−5.93159	+	15.6403i	−0.199388	+	0.525743i
$886$	−36.9240	−	2.98082i	−1.24049	−	0.100142i
$887$	2.41108	−	11.8102i	0.0809561	−	0.396549i	−0.919041	−	0.394162i	$-0.871035\pi$
$887$	2.41108	−	11.8102i	0.0809561	−	0.396549i	0.999997	−	0.00238732i	$-0.000759910\pi$
$888$	0.428699	−	1.48004i	0.0143862	−	0.0496669i
$889$	1.00241	+	2.64314i	0.0336198	+	0.0886482i
$890$	2.09958	−	52.1004i	0.0703779	−	1.74641i
$891$	−2.28885	−	0.371974i	−0.0766792	−	0.0124616i
$892$	−22.8108	−	20.2086i	−0.763762	−	0.676634i
$893$	−9.94981	+	3.32173i	−0.332958	+	0.111158i
$894$	−13.0973	+	27.6020i	−0.438040	+	0.923150i
$895$	−3.21161	+	6.76832i	−0.107352	+	0.226240i
$896$	0.630108	−	0.330706i	0.0210504	−	0.0110481i
$897$	25.0267	+	20.0679i	0.835616	+	0.670047i
$898$	−32.8021	−	17.2159i	−1.09462	−	0.574501i
$899$	71.6052	−	53.8078i	2.38817	−	1.79459i
$900$	1.13911	+	3.93267i	0.0379703	+	0.131089i
$901$	23.7630	−	1.91835i	0.791660	−	0.0639094i
$902$	−33.3297	+	48.2865i	−1.10976	+	1.60776i
$903$	−0.404182	−	1.97981i	−0.0134503	−	0.0658841i
$904$	−1.56408	−	0.666393i	−0.0520206	−	0.0221639i
$905$	−0.702000	+	0.173028i	−0.0233353	+	0.00575163i
$906$	0.437232	−	10.8498i	0.0145261	−	0.360460i
$907$	−8.22133	+	6.17793i	−0.272985	+	0.205135i	−0.728414	−	0.685137i	$-0.759742\pi$
$907$	−8.22133	+	6.17793i	−0.272985	+	0.205135i	0.455429	+	0.890272i	$0.349486\pi$
$908$	14.4984	−	6.17721i	0.481148	−	0.204998i
$909$	4.58601	+	6.64399i	0.152108	+	0.220367i
$910$	−6.42579	+	3.11890i	−0.213013	+	0.103391i
$911$	2.51152	−	3.63856i	0.0832103	−	0.120551i	−0.779168	−	0.626815i	$-0.784358\pi$
$911$	2.51152	−	3.63856i	0.0832103	−	0.120551i	0.862379	+	0.506264i	$0.168974\pi$
$912$	3.03338	−	14.8585i	0.100445	−	0.492014i
$913$	−21.2621	−	22.1362i	−0.703673	−	0.732601i
$914$	11.3202	+	23.8567i	0.374438	+	0.789111i
$915$	27.2914			0.902225
$916$	−12.9101	−	27.2074i	−0.426561	−	0.898959i
$917$	6.15372	+	4.62422i	0.203214	+	0.152705i
$918$	−2.91167	+	7.67744i	−0.0960993	+	0.253393i
$919$	−40.9521	−	17.4481i	−1.35089	−	0.575559i	−0.409321	−	0.912390i	$-0.634234\pi$
$919$	−40.9521	−	17.4481i	−1.35089	−	0.575559i	−0.941565	+	0.336832i	$0.890645\pi$
$920$	−5.55756	+	0.903192i	−0.183227	+	0.0297774i
$921$	10.2825	+	3.43279i	0.338819	+	0.113114i
$922$	−8.70300	+	7.71018i	−0.286618	+	0.253921i
$923$	−40.1158	−	32.1673i	−1.32043	−	1.05880i
$924$	1.36322	+	1.20770i	0.0448465	+	0.0397306i
$925$	6.19523	+	10.7305i	0.203698	+	0.352815i
$926$	39.9336	+	13.3318i	1.31230	+	0.438110i
$927$	5.67044	−	5.90355i	0.186242	−	0.193898i
$928$	46.4083	+	67.2341i	1.52343	+	2.20707i
$929$	4.07965	+	4.99667i	0.133849	+	0.163935i	0.837180	−	0.546927i	$-0.184202\pi$
$929$	4.07965	+	4.99667i	0.133849	+	0.163935i	−0.703331	+	0.710862i	$0.748305\pi$
$930$	29.9709	+	36.7077i	0.982786	+	1.20369i
$931$	15.7688	+	22.8450i	0.516800	+	0.748714i
$932$	23.6806	−	24.6541i	0.775684	−	0.807572i
$933$	16.1248	+	5.38326i	0.527903	+	0.176240i
$934$	−8.69018	−	15.0518i	−0.284351	−	0.492511i
$935$	18.4909	+	16.3815i	0.604717	+	0.535732i
$936$	−0.850583	−	0.165836i	−0.0278022	−	0.00542053i
$937$	1.34272	−	1.18954i	0.0438646	−	0.0388607i	−0.640906	−	0.767620i	$-0.721441\pi$
$937$	1.34272	−	1.18954i	0.0438646	−	0.0388607i	0.684770	+	0.728759i	$0.259903\pi$
$938$	1.98287	+	0.661978i	0.0647428	+	0.0216143i
$939$	−4.12173	+	0.669846i	−0.134508	+	0.0218596i
$940$	13.3073	+	5.66973i	0.434038	+	0.184926i
$941$	−13.1657	+	34.7151i	−0.429189	+	1.13168i	0.529771	+	0.848140i	$0.322278\pi$
$941$	−13.1657	+	34.7151i	−0.429189	+	1.13168i	−0.958961	+	0.283539i	$0.908492\pi$
$942$	−1.17144	−	0.880277i	−0.0381674	−	0.0286810i
$943$	47.5537	+	100.217i	1.54856	+	3.26352i
$944$	−23.8178			−0.775204
$945$	−0.418477	−	0.881921i	−0.0136131	−	0.0286889i
$946$	−17.7673	−	18.4977i	−0.577664	−	0.601412i
$947$	4.86249	−	23.8180i	0.158010	−	0.773982i	−0.821122	−	0.570753i	$-0.806651\pi$
$947$	4.86249	−	23.8180i	0.158010	−	0.773982i	0.979131	−	0.203229i	$-0.0651436\pi$
$948$	0.838594	−	1.21491i	0.0272363	−	0.0394585i
$949$	1.83288	+	20.4507i	0.0594977	+	0.663856i
$950$	−9.01248	−	13.0568i	−0.292403	−	0.423620i
$951$	−16.4619	+	7.01375i	−0.533813	+	0.227436i
$952$	0.288230	−	0.216591i	0.00934158	−	0.00701974i
$953$	1.94663	−	48.3051i	0.0630575	−	1.56475i	−0.589973	−	0.807423i	$-0.700862\pi$
$953$	1.94663	−	48.3051i	0.0630575	−	1.56475i	0.653030	−	0.757332i	$-0.273497\pi$
$954$	−11.6102	+	2.86166i	−0.375895	+	0.0926497i
$955$	−46.5370	−	19.8276i	−1.50590	−	0.641605i
$956$	−8.68350	−	42.5346i	−0.280845	−	1.37567i
$957$	−13.3037	+	19.2738i	−0.430048	+	0.623032i
$958$	−43.3441	+	3.49910i	−1.40039	+	0.113051i
$959$	1.13661	+	3.92403i	0.0367030	+	0.126713i
$960$	−18.7713	+	14.1057i	−0.605842	+	0.455261i
$961$	42.1953	+	22.1458i	1.36114	+	0.714381i
$962$	−46.8528	+	2.30273i	−1.51059	+	0.0742430i
$963$	−0.0813468	+	0.0426941i	−0.00262137	+	0.00137580i
$964$	15.9865	−	33.6908i	0.514889	−	1.08511i
$965$	−3.68432	+	7.76454i	−0.118602	+	0.249949i
$966$	6.34953	−	2.11978i	0.204293	−	0.0682029i
$967$	−5.53924	−	4.90734i	−0.178130	−	0.157809i	0.569347	−	0.822098i	$-0.307196\pi$
$967$	−5.53924	−	4.90734i	−0.178130	−	0.157809i	−0.747476	+	0.664288i	$0.768735\pi$
$968$	−1.33395	−	0.216788i	−0.0428748	−	0.00696783i
$969$	0.658996	−	16.3528i	0.0211700	−	0.525328i
$970$	−25.8663	−	68.2039i	−0.830518	−	2.18990i
$971$	−8.94708	+	30.8889i	−0.287125	+	0.991272i	0.679201	+	0.733952i	$0.262326\pi$
$971$	−8.94708	+	30.8889i	−0.287125	+	0.991272i	−0.966326	+	0.257320i	$0.917161\pi$
$972$	0.423741	−	2.07562i	0.0135915	−	0.0665756i
$973$	4.06185	+	0.327907i	0.130217	+	0.0105122i
$974$	−16.8033	+	44.3065i	−0.538411	+	1.41967i
$975$	5.69976	−	4.00904i	0.182538	−	0.128392i
$976$	13.7799	+	36.3346i	0.441084	+	1.16304i
$977$	1.35778	+	4.68760i	0.0434393	+	0.149970i	0.979306	−	0.202384i	$-0.0648688\pi$
$977$	1.35778	+	4.68760i	0.0434393	+	0.149970i	−0.935867	+	0.352353i	$0.885382\pi$
$978$	0.515192	+	12.7844i	0.0164740	+	0.408799i
$979$	14.3112	+	17.5281i	0.457388	+	0.560199i
$980$	4.61393	−	37.9992i	0.147387	−	1.21384i
$981$	−8.13367	+	0.656618i	−0.259688	+	0.0209642i
$982$	−14.2378	+	49.1546i	−0.454346	+	1.56859i
$983$	32.1337	+	7.92025i	1.02491	+	0.252617i	0.715722	−	0.698385i	$-0.246098\pi$
$983$	32.1337	+	7.92025i	1.02491	+	0.252617i	0.309185	+	0.951002i	$0.399944\pi$
$984$	−2.39566	−	1.80022i	−0.0763707	−	0.0573889i
$985$	29.7740	−	36.4665i	0.948677	−	1.16192i
$986$	57.4454	+	59.8070i	1.82943	+	1.90464i
$987$	−0.933499	−	0.230087i	−0.0297136	−	0.00732374i
$988$	30.6366	−	3.99482i	0.974679	−	0.127092i
$989$	−47.0823	+	11.6047i	−1.49713	+	0.369009i
$990$	−10.4725	−	6.62239i	−0.332837	−	0.210473i
$991$	16.2433	+	28.1342i	0.515986	+	0.893713i	0.999828	+	0.0185581i	$0.00590757\pi$
$991$	16.2433	+	28.1342i	0.515986	+	0.893713i	−0.483842	+	0.875155i	$0.660759\pi$
$992$	−35.8699	+	62.1285i	−1.13887	+	1.97258i
$993$	6.68624	−	3.50921i	0.212181	−	0.111361i
$994$	−10.1778	+	3.39785i	−0.322820	+	0.107773i
$995$	−12.4048	+	21.4858i	−0.393259	+	0.681145i
$996$	20.9885	−	18.5942i	0.665046	−	0.589179i
$997$	46.2250	−	29.2309i	1.46396	−	0.925752i	0.464772	−	0.885430i	$-0.346136\pi$
$997$	46.2250	−	29.2309i	1.46396	−	0.925752i	0.999187	−	0.0403212i	$-0.0128381\pi$
$998$	31.1126	−	13.2558i	0.984851	−	0.419606i
$999$	−0.258142	−	6.40574i	−0.00816726	−	0.202669i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.q.a.55.3	✓	360
169.126	even	39	inner	507.2.q.a.295.3	yes	360

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.2.q.a.55.3	✓	360	1.1	even	1	trivial
507.2.q.a.295.3	yes	360	169.126	even	39	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:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.q (of order \(39\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.28348 + 1.57198i) q^{2} +(0.996757 + 0.0804666i) q^{3} +(-0.423741 - 2.07562i) q^{4} +(-0.317374 - 2.61381i) q^{5} +(-1.40581 + 1.46360i) q^{6} +(0.313349 - 0.198150i) q^{7} +(0.212820 + 0.111697i) q^{8} +(0.987050 + 0.160411i) q^{9} +O(q^{10})\)	\(q+(-1.28348 + 1.57198i) q^{2} +(0.996757 + 0.0804666i) q^{3} +(-0.423741 - 2.07562i) q^{4} +(-0.317374 - 2.61381i) q^{5} +(-1.40581 + 1.46360i) q^{6} +(0.313349 - 0.198150i) q^{7} +(0.212820 + 0.111697i) q^{8} +(0.987050 + 0.160411i) q^{9} +(4.51619 + 2.85586i) q^{10} +(-2.28885 + 0.371974i) q^{11} +(-0.255349 - 2.10299i) q^{12} +(-3.24366 + 1.57438i) q^{13} +(-0.0906900 + 0.746899i) q^{14} +(-0.106020 - 2.63087i) q^{15} +(3.44910 - 1.46952i) q^{16} +(3.41968 - 2.16247i) q^{17} +(-1.51902 + 1.34574i) q^{18} +(2.02248 - 3.50304i) q^{19} +(-5.29079 + 1.76633i) q^{20} +(0.328278 - 0.172293i) q^{21} +(2.35295 - 4.07544i) q^{22} +(-4.44854 - 7.70509i) q^{23} +(0.203142 + 0.128460i) q^{24} +(-1.87655 + 0.462527i) q^{25} +(1.68828 - 7.11965i) q^{26} +(0.970942 + 0.239316i) q^{27} +(-0.544064 - 0.566430i) q^{28} +(6.38735 - 7.82308i) q^{29} +(4.27174 + 3.21001i) q^{30} +(8.61099 + 2.12242i) q^{31} +(-2.25053 + 7.76973i) q^{32} +(-2.31136 + 0.186592i) q^{33} +(-0.989729 + 8.15115i) q^{34} +(-0.617374 - 0.756146i) q^{35} +(-0.0853008 - 2.11672i) q^{36} +(-1.78363 - 6.15782i) q^{37} +(2.91088 + 7.67537i) q^{38} +(-3.35983 + 1.30827i) q^{39} +(0.224410 - 0.591721i) q^{40} +(-12.4274 - 1.00324i) q^{41} +(-0.150496 + 0.737180i) q^{42} +(1.51636 - 5.23507i) q^{43} +(1.74196 + 4.59316i) q^{44} +(0.106020 - 2.63087i) q^{45} +(17.8218 + 2.89633i) q^{46} +(-1.94108 - 1.71965i) q^{47} +(3.55616 - 1.18722i) q^{48} +(-2.94192 + 6.19997i) q^{49} +(1.68143 - 3.54354i) q^{50} +(3.58260 - 1.88029i) q^{51} +(4.64230 + 6.06548i) q^{52} +(5.21732 + 2.73826i) q^{53} +(-1.62238 + 1.21914i) q^{54} +(1.69869 + 5.86455i) q^{55} +(0.0888198 - 0.00717028i) q^{56} +(2.29780 - 3.32894i) q^{57} +(4.09968 + 20.0815i) q^{58} +(-5.84457 - 2.49014i) q^{59} +(-5.41577 + 1.33487i) q^{60} +(-0.417361 + 10.3567i) q^{61} +(-14.3884 + 10.8122i) q^{62} +(0.341077 - 0.145319i) q^{63} +(-5.06587 - 7.33918i) q^{64} +(5.14458 + 7.97863i) q^{65} +(2.67326 - 3.87289i) q^{66} +(0.555757 - 2.72228i) q^{67} +(-5.93754 - 6.18163i) q^{68} +(-3.81411 - 8.03807i) q^{69} +1.98103 q^{70} +(6.11372 + 12.8844i) q^{71} +(0.192147 + 0.144389i) q^{72} +(2.01938 - 5.32466i) q^{73} +(11.9692 + 5.09961i) q^{74} +(-1.90768 + 0.310028i) q^{75} +(-8.12799 - 2.71352i) q^{76} +(-0.643502 + 0.570093i) q^{77} +(2.25570 - 6.96071i) q^{78} +(0.521599 + 0.462096i) q^{79} +(-4.93570 - 8.54888i) q^{80} +(0.948536 + 0.316668i) q^{81} +(17.5274 - 18.2479i) q^{82} +(7.51910 + 10.8933i) q^{83} +(-0.496721 - 0.608372i) q^{84} +(-6.73760 - 8.25206i) q^{85} +(6.28320 + 9.10279i) q^{86} +(6.99613 - 7.28375i) q^{87} +(-0.528662 - 0.176493i) q^{88} +(-4.87917 - 8.45097i) q^{89} +(3.99959 + 3.54333i) q^{90} +(-0.704434 + 1.13606i) q^{91} +(-14.1078 + 12.4985i) q^{92} +(8.41228 + 2.80843i) q^{93} +(5.19460 - 0.844204i) q^{94} +(-9.79814 - 4.17460i) q^{95} +(-2.86844 + 7.56344i) q^{96} +(-10.9134 - 8.20088i) q^{97} +(-5.97032 - 12.5822i) q^{98} -2.31888 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 360 q + q^{2} - 15 q^{3} + 15 q^{4} + 2 q^{5} - q^{6} + 2 q^{7} + 6 q^{8} + 15 q^{9}+O(q^{10}) \) 360 * q + q^2 - 15 * q^3 + 15 * q^4 + 2 * q^5 - q^6 + 2 * q^7 + 6 * q^8 + 15 * q^9	\( 360 q + q^{2} - 15 q^{3} + 15 q^{4} + 2 q^{5} - q^{6} + 2 q^{7} + 6 q^{8} + 15 q^{9} - q^{10} - 2 q^{11} + 30 q^{12} - 19 q^{13} + q^{15} + 15 q^{16} - 7 q^{17} - 2 q^{18} - 6 q^{19} + q^{20} + 4 q^{21} + 22 q^{22} + 46 q^{23} + 3 q^{24} + 28 q^{25} + 34 q^{26} + 30 q^{27} - 2 q^{28} + 36 q^{29} + q^{30} - 34 q^{31} - 190 q^{32} + 15 q^{33} - 51 q^{34} - 80 q^{35} + 15 q^{36} + q^{37} - 53 q^{38} + 5 q^{39} - 45 q^{40} + 9 q^{41} + 130 q^{42} + 78 q^{43} + 35 q^{44} - q^{45} - 318 q^{46} - 12 q^{47} - 15 q^{48} - 71 q^{49} + 48 q^{50} - 14 q^{51} - 63 q^{52} - 26 q^{53} - q^{54} - 61 q^{55} - 4 q^{56} - 38 q^{57} - 27 q^{58} + 208 q^{59} - 180 q^{60} - 3 q^{61} - 61 q^{62} + 2 q^{63} + 140 q^{64} + 45 q^{65} - 60 q^{66} - 80 q^{67} - 140 q^{68} + 6 q^{69} - 100 q^{70} + 84 q^{71} - 3 q^{72} + 134 q^{73} - 151 q^{74} - 12 q^{75} + 32 q^{76} + 82 q^{77} - 63 q^{78} + 4 q^{79} - 155 q^{80} + 15 q^{81} - 56 q^{82} + 106 q^{83} + 2 q^{84} - 19 q^{85} + q^{86} - 49 q^{87} + 8 q^{88} - 14 q^{89} + 2 q^{90} - 368 q^{91} + 36 q^{92} - 4 q^{93} - 59 q^{94} + 104 q^{95} + 75 q^{96} - 28 q^{97} + 101 q^{98} + 30 q^{99}+O(q^{100}) \) 360 * q + q^2 - 15 * q^3 + 15 * q^4 + 2 * q^5 - q^6 + 2 * q^7 + 6 * q^8 + 15 * q^9 - q^10 - 2 * q^11 + 30 * q^12 - 19 * q^13 + q^15 + 15 * q^16 - 7 * q^17 - 2 * q^18 - 6 * q^19 + q^20 + 4 * q^21 + 22 * q^22 + 46 * q^23 + 3 * q^24 + 28 * q^25 + 34 * q^26 + 30 * q^27 - 2 * q^28 + 36 * q^29 + q^30 - 34 * q^31 - 190 * q^32 + 15 * q^33 - 51 * q^34 - 80 * q^35 + 15 * q^36 + q^37 - 53 * q^38 + 5 * q^39 - 45 * q^40 + 9 * q^41 + 130 * q^42 + 78 * q^43 + 35 * q^44 - q^45 - 318 * q^46 - 12 * q^47 - 15 * q^48 - 71 * q^49 + 48 * q^50 - 14 * q^51 - 63 * q^52 - 26 * q^53 - q^54 - 61 * q^55 - 4 * q^56 - 38 * q^57 - 27 * q^58 + 208 * q^59 - 180 * q^60 - 3 * q^61 - 61 * q^62 + 2 * q^63 + 140 * q^64 + 45 * q^65 - 60 * q^66 - 80 * q^67 - 140 * q^68 + 6 * q^69 - 100 * q^70 + 84 * q^71 - 3 * q^72 + 134 * q^73 - 151 * q^74 - 12 * q^75 + 32 * q^76 + 82 * q^77 - 63 * q^78 + 4 * q^79 - 155 * q^80 + 15 * q^81 - 56 * q^82 + 106 * q^83 + 2 * q^84 - 19 * q^85 + q^86 - 49 * q^87 + 8 * q^88 - 14 * q^89 + 2 * q^90 - 368 * q^91 + 36 * q^92 - 4 * q^93 - 59 * q^94 + 104 * q^95 + 75 * q^96 - 28 * q^97 + 101 * q^98 + 30 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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