LMFDB - Embedded newform 507.2.m.b.313.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(40,507)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(507, base_ring=CyclotomicField(26))

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("507.40");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.m (of order $13$, degree $12$, 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:	$204$
Relative dimension:	$17$ over $\Q(\zeta_{13})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{13}]$

Embedding invariants

Embedding label			313.6
Character	$\chi$	$=$	507.313
Dual form			507.2.m.b.196.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.509495 + 1.34343i) q^{2} +(0.568065 + 0.822984i) q^{3} +(-0.0481910 - 0.0426935i) q^{4} +(-0.0880026 + 0.724766i) q^{5} +(-1.39505 + 0.343848i) q^{6} +(-4.13500 + 2.17021i) q^{7} +(-2.46253 + 1.29244i) q^{8} +(-0.354605 + 0.935016i) q^{9} +O(q^{10})$	\(q+(-0.509495 + 1.34343i) q^{2} +(0.568065 + 0.822984i) q^{3} +(-0.0481910 - 0.0426935i) q^{4} +(-0.0880026 + 0.724766i) q^{5} +(-1.39505 + 0.343848i) q^{6} +(-4.13500 + 2.17021i) q^{7} +(-2.46253 + 1.29244i) q^{8} +(-0.354605 + 0.935016i) q^{9} +(-0.928834 - 0.487490i) q^{10} +(-0.821521 - 2.16617i) q^{11} +(0.00776045 - 0.0639131i) q^{12} +(-0.931628 - 3.48311i) q^{13} +(-0.808765 - 6.66078i) q^{14} +(-0.646462 + 0.339289i) q^{15} +(-0.497168 - 4.09455i) q^{16} +(-1.28795 + 0.675970i) q^{17} +(-1.07546 - 0.952772i) q^{18} +7.36767 q^{19} +(0.0351837 - 0.0311701i) q^{20} +(-4.13500 - 2.17021i) q^{21} +3.32866 q^{22} -2.78764 q^{23} +(-2.46253 - 1.29244i) q^{24} +(4.33717 + 1.06902i) q^{25} +(5.15397 + 0.523053i) q^{26} +(-0.970942 + 0.239316i) q^{27} +(0.291924 + 0.0719527i) q^{28} +(-3.46888 + 9.14668i) q^{29} +(-0.126442 - 1.04134i) q^{30} +(-7.12347 + 1.75578i) q^{31} +(0.353483 + 0.0871258i) q^{32} +(1.31605 - 1.90663i) q^{33} +(-0.251911 - 2.07468i) q^{34} +(-1.20901 - 3.18789i) q^{35} +(0.0570079 - 0.0299200i) q^{36} +(-1.60283 + 0.395061i) q^{37} +(-3.75379 + 9.89793i) q^{38} +(2.33732 - 2.74535i) q^{39} +(-0.720005 - 1.89850i) q^{40} +(2.02452 + 2.93303i) q^{41} +(5.02229 - 4.44936i) q^{42} +(9.35953 + 2.30692i) q^{43} +(-0.0528916 + 0.139464i) q^{44} +(-0.646462 - 0.339289i) q^{45} +(1.42029 - 3.74499i) q^{46} +(-9.30360 + 8.24227i) q^{47} +(3.08732 - 2.73513i) q^{48} +(8.41192 - 12.1868i) q^{49} +(-3.64591 + 5.28201i) q^{50} +(-1.28795 - 0.675970i) q^{51} +(-0.103810 + 0.207629i) q^{52} +(0.773796 - 0.406119i) q^{53} +(0.173187 - 1.42632i) q^{54} +(1.64227 - 0.404782i) q^{55} +(7.37770 - 10.6884i) q^{56} +(4.18531 + 6.06348i) q^{57} +(-10.5205 - 9.32037i) q^{58} +(-0.500316 + 4.12048i) q^{59} +(0.0456391 + 0.0112490i) q^{60} +(-0.434040 - 0.227802i) q^{61} +(1.27061 - 10.4644i) q^{62} +(-0.562895 - 4.63586i) q^{63} +(4.38896 - 6.35850i) q^{64} +(2.60643 - 0.368690i) q^{65} +(1.89089 + 2.73943i) q^{66} +(-9.66559 + 8.56296i) q^{67} +(0.0909273 + 0.0224116i) q^{68} +(-1.58356 - 2.29418i) q^{69} +4.89868 q^{70} +(-5.89128 - 8.53499i) q^{71} +(-0.335223 - 2.76081i) q^{72} +(0.355963 + 0.938597i) q^{73} +(0.285896 - 2.35456i) q^{74} +(1.58401 + 4.17669i) q^{75} +(-0.355055 - 0.314552i) q^{76} +(8.09805 + 7.17425i) q^{77} +(2.49732 + 4.53876i) q^{78} +(-3.46321 + 3.06814i) q^{79} +3.01134 q^{80} +(-0.748511 - 0.663123i) q^{81} +(-4.97179 + 1.22544i) q^{82} +(1.05041 - 1.52178i) q^{83} +(0.106616 + 0.281122i) q^{84} +(-0.376577 - 0.992952i) q^{85} +(-7.86781 + 11.3985i) q^{86} +(-9.49812 + 2.34108i) q^{87} +(4.82266 + 4.27251i) q^{88} -9.35530 q^{89} +(0.785180 - 0.695609i) q^{90} +(11.4114 + 12.3808i) q^{91} +(0.134339 + 0.119014i) q^{92} +(-5.49157 - 4.86511i) q^{93} +(-6.33275 - 16.6981i) q^{94} +(-0.648374 + 5.33984i) q^{95} +(0.129098 + 0.340404i) q^{96} +(0.765884 + 6.30762i) q^{97} +(12.0862 + 17.5099i) q^{98} +2.31672 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 204 q - q^{2} - 17 q^{3} - 21 q^{4} - 6 q^{5} - q^{6} - 8 q^{7} - 9 q^{8} - 17 q^{9}+O(q^{10}) $ 204 * q - q^2 - 17 * q^3 - 21 * q^4 - 6 * q^5 - q^6 - 8 * q^7 - 9 * q^8 - 17 * q^9	\( 204 q - q^{2} - 17 q^{3} - 21 q^{4} - 6 q^{5} - q^{6} - 8 q^{7} - 9 q^{8} - 17 q^{9} - 6 q^{10} - 8 q^{11} - 21 q^{12} + 54 q^{13} - 30 q^{14} - 6 q^{15} - 45 q^{16} - 18 q^{17} - q^{18} - 20 q^{19} - 58 q^{20} - 8 q^{21} + 44 q^{22} + 40 q^{23} - 9 q^{24} + 7 q^{25} - 2 q^{26} - 17 q^{27} - 40 q^{28} + 11 q^{29} - 6 q^{30} + 2 q^{31} + 61 q^{32} + 5 q^{33} - q^{34} + 11 q^{35} - 21 q^{36} - 34 q^{37} + 17 q^{38} - 11 q^{39} - 31 q^{40} - 58 q^{41} + 35 q^{42} + 32 q^{43} - 41 q^{44} - 6 q^{45} + 76 q^{46} - 36 q^{47} - 45 q^{48} + 9 q^{49} - 35 q^{50} - 18 q^{51} - 24 q^{52} + 66 q^{53} - q^{54} + 7 q^{55} - 114 q^{56} - 7 q^{57} - 60 q^{58} + 40 q^{59} + 59 q^{60} - 54 q^{61} - 31 q^{62} - 8 q^{63} + 75 q^{64} - 26 q^{65} + 18 q^{66} + 2 q^{67} + 26 q^{68} - 12 q^{69} - 56 q^{70} - 37 q^{71} - 9 q^{72} + 70 q^{73} + 174 q^{74} - 45 q^{75} - 26 q^{76} + 24 q^{78} - 66 q^{79} + 126 q^{80} - 17 q^{81} - 17 q^{82} - 2 q^{83} - 40 q^{84} + 54 q^{85} + 61 q^{86} + 24 q^{87} + 94 q^{88} - 114 q^{89} - 6 q^{90} + 104 q^{91} - 78 q^{92} + 67 q^{93} - 63 q^{94} - 70 q^{95} - 4 q^{96} + 36 q^{97} - 65 q^{98} + 18 q^{99}+O(q^{100}) \) 204 * q - q^2 - 17 * q^3 - 21 * q^4 - 6 * q^5 - q^6 - 8 * q^7 - 9 * q^8 - 17 * q^9 - 6 * q^10 - 8 * q^11 - 21 * q^12 + 54 * q^13 - 30 * q^14 - 6 * q^15 - 45 * q^16 - 18 * q^17 - q^18 - 20 * q^19 - 58 * q^20 - 8 * q^21 + 44 * q^22 + 40 * q^23 - 9 * q^24 + 7 * q^25 - 2 * q^26 - 17 * q^27 - 40 * q^28 + 11 * q^29 - 6 * q^30 + 2 * q^31 + 61 * q^32 + 5 * q^33 - q^34 + 11 * q^35 - 21 * q^36 - 34 * q^37 + 17 * q^38 - 11 * q^39 - 31 * q^40 - 58 * q^41 + 35 * q^42 + 32 * q^43 - 41 * q^44 - 6 * q^45 + 76 * q^46 - 36 * q^47 - 45 * q^48 + 9 * q^49 - 35 * q^50 - 18 * q^51 - 24 * q^52 + 66 * q^53 - q^54 + 7 * q^55 - 114 * q^56 - 7 * q^57 - 60 * q^58 + 40 * q^59 + 59 * q^60 - 54 * q^61 - 31 * q^62 - 8 * q^63 + 75 * q^64 - 26 * q^65 + 18 * q^66 + 2 * q^67 + 26 * q^68 - 12 * q^69 - 56 * q^70 - 37 * q^71 - 9 * q^72 + 70 * q^73 + 174 * q^74 - 45 * q^75 - 26 * q^76 + 24 * q^78 - 66 * q^79 + 126 * q^80 - 17 * q^81 - 17 * q^82 - 2 * q^83 - 40 * q^84 + 54 * q^85 + 61 * q^86 + 24 * q^87 + 94 * q^88 - 114 * q^89 - 6 * q^90 + 104 * q^91 - 78 * q^92 + 67 * q^93 - 63 * q^94 - 70 * q^95 - 4 * q^96 + 36 * q^97 - 65 * q^98 + 18 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$170$	$340$
$\chi(n)$	$1$	$e\left(\frac{8}{13}\right)$

Coefficient data

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

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

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

$2$	−0.509495	+	1.34343i	−0.360267	+	0.949947i	0.625258	+	0.780418i	$0.284994\pi$
$2$	−0.509495	+	1.34343i	−0.360267	+	0.949947i	−0.985525	+	0.169529i	$0.945775\pi$
$3$	0.568065	+	0.822984i	0.327972	+	0.475150i
$3$	0.568065	+	0.822984i	0.327972	+	0.475150i
$4$	−0.0481910	−	0.0426935i	−0.0240955	−	0.0213467i
$5$	−0.0880026	+	0.724766i	−0.0393559	+	0.324125i	0.959713	+	0.280982i	$0.0906602\pi$
$5$	−0.0880026	+	0.724766i	−0.0393559	+	0.324125i	−0.999069	+	0.0431431i	$0.986263\pi$
$6$	−1.39505	+	0.343848i	−0.569525	+	0.140375i
$7$	−4.13500	+	2.17021i	−1.56288	+	0.820264i	−0.999980	−	0.00625976i	$-0.998007\pi$
$7$	−4.13500	+	2.17021i	−1.56288	+	0.820264i	−0.562902	+	0.826524i	$0.690315\pi$
$8$	−2.46253	+	1.29244i	−0.870636	+	0.456945i
$9$	−0.354605	+	0.935016i	−0.118202	+	0.311672i
$10$	−0.928834	−	0.487490i	−0.293723	−	0.154158i
$11$	−0.821521	−	2.16617i	−0.247698	−	0.653126i	0.752286	−	0.658837i	$-0.228951\pi$
$11$	−0.821521	−	2.16617i	−0.247698	−	0.653126i	−0.999984	+	0.00571109i	$0.998182\pi$
$12$	0.00776045	−	0.0639131i	0.00224025	−	0.0184501i
$13$	−0.931628	−	3.48311i	−0.258387	−	0.966041i
$13$	−0.931628	−	3.48311i	−0.258387	−	0.966041i
$14$	−0.808765	−	6.66078i	−0.216152	−	1.78017i
$15$	−0.646462	+	0.339289i	−0.166916	+	0.0876042i
$16$	−0.497168	−	4.09455i	−0.124292	−	1.02364i
$17$	−1.28795	+	0.675970i	−0.312375	+	0.163947i	−0.613624	−	0.789599i	$-0.710289\pi$
$17$	−1.28795	+	0.675970i	−0.312375	+	0.163947i	0.301249	+	0.953546i	$0.402596\pi$
$18$	−1.07546	−	0.952772i	−0.253488	−	0.224570i
$19$	7.36767			1.69026			0.845130	−	0.534561i	$-0.179523\pi$
$19$	7.36767			1.69026			0.845130	+	0.534561i	$0.179523\pi$
$20$	0.0351837	−	0.0311701i	0.00786732	−	0.00696984i
$21$	−4.13500	−	2.17021i	−0.902331	−	0.473580i
$22$	3.32866			0.709672
$23$	−2.78764			−0.581264			−0.290632	−	0.956835i	$-0.593865\pi$
$23$	−2.78764			−0.581264			−0.290632	+	0.956835i	$0.593865\pi$
$24$	−2.46253	−	1.29244i	−0.502662	−	0.263817i
$25$	4.33717	+	1.06902i	0.867433	+	0.213803i
$26$	5.15397	+	0.523053i	1.01078	+	0.102579i
$27$	−0.970942	+	0.239316i	−0.186858	+	0.0460563i
$28$	0.291924	+	0.0719527i	0.0551684	+	0.0135978i
$29$	−3.46888	+	9.14668i	−0.644155	+	1.69850i	0.0691174	+	0.997609i	$0.477982\pi$
$29$	−3.46888	+	9.14668i	−0.644155	+	1.69850i	−0.713272	+	0.700887i	$0.752788\pi$
$30$	−0.126442	−	1.04134i	−0.0230850	−	0.190122i
$31$	−7.12347	+	1.75578i	−1.27941	+	0.315347i	−0.819737	−	0.572739i	$-0.805881\pi$
$31$	−7.12347	+	1.75578i	−1.27941	+	0.315347i	−0.459676	+	0.888087i	$0.652035\pi$
$32$	0.353483	+	0.0871258i	0.0624876	+	0.0154018i
$33$	1.31605	−	1.90663i	0.229095	−	0.331901i
$34$	−0.251911	−	2.07468i	−0.0432024	−	0.355804i
$35$	−1.20901	−	3.18789i	−0.204360	−	0.538852i
$36$	0.0570079	−	0.0299200i	0.00950131	−	0.00498667i
$37$	−1.60283	+	0.395061i	−0.263503	+	0.0649477i	−0.368854	−	0.929487i	$-0.620250\pi$
$37$	−1.60283	+	0.395061i	−0.263503	+	0.0649477i	0.105351	+	0.994435i	$0.466404\pi$
$38$	−3.75379	+	9.89793i	−0.608945	+	1.60566i
$39$	2.33732	−	2.74535i	0.374271	−	0.439607i
$40$	−0.720005	−	1.89850i	−0.113843	−	0.300179i
$41$	2.02452	+	2.93303i	0.316177	+	0.458062i	0.948561	−	0.316593i	$-0.102539\pi$
$41$	2.02452	+	2.93303i	0.316177	+	0.458062i	−0.632384	+	0.774655i	$0.717924\pi$
$42$	5.02229	−	4.44936i	0.774956	−	0.686551i
$43$	9.35953	+	2.30692i	1.42731	+	0.351801i	0.875925	−	0.482447i	$-0.160252\pi$
$43$	9.35953	+	2.30692i	1.42731	+	0.351801i	0.551389	+	0.834248i	$0.314098\pi$
$44$	−0.0528916	+	0.139464i	−0.00797371	+	0.0210249i
$45$	−0.646462	−	0.339289i	−0.0963689	−	0.0505783i
$46$	1.42029	−	3.74499i	0.209410	−	0.552169i
$47$	−9.30360	+	8.24227i	−1.35707	+	1.20226i	−0.398579	+	0.917134i	$0.630496\pi$
$47$	−9.30360	+	8.24227i	−1.35707	+	1.20226i	−0.958491	+	0.285124i	$0.907965\pi$
$48$	3.08732	−	2.73513i	0.445617	−	0.394782i
$49$	8.41192	−	12.1868i	1.20170	−	1.74097i
$50$	−3.64591	+	5.28201i	−0.515609	+	0.746989i
$51$	−1.28795	−	0.675970i	−0.180350	−	0.0946548i
$52$	−0.103810	+	0.207629i	−0.0143959	+	0.0287930i
$53$	0.773796	−	0.406119i	0.106289	−	0.0557848i	−0.410741	−	0.911752i	$-0.634730\pi$
$53$	0.773796	−	0.406119i	0.106289	−	0.0557848i	0.517030	+	0.855967i	$0.327038\pi$
$54$	0.173187	−	1.42632i	0.0235677	−	0.194098i
$55$	1.64227	−	0.404782i	0.221443	−	0.0545808i
$56$	7.37770	−	10.6884i	0.985886	−	1.42830i
$57$	4.18531	+	6.06348i	0.554358	+	0.803127i
$58$	−10.5205	−	9.32037i	−1.38141	−	1.22382i
$59$	−0.500316	+	4.12048i	−0.0651356	+	0.536440i	0.923219	+	0.384274i	$0.125548\pi$
$59$	−0.500316	+	4.12048i	−0.0651356	+	0.536440i	−0.988355	+	0.152167i	$0.951375\pi$
$60$	0.0456391	+	0.0112490i	0.00589198	+	0.00145224i
$61$	−0.434040	−	0.227802i	−0.0555731	−	0.0291670i	0.436708	−	0.899603i	$-0.356144\pi$
$61$	−0.434040	−	0.227802i	−0.0555731	−	0.0291670i	−0.492281	+	0.870436i	$0.663837\pi$
$62$	1.27061	−	10.4644i	0.161368	−	1.32898i
$63$	−0.562895	−	4.63586i	−0.0709181	−	0.584063i
$64$	4.38896	−	6.35850i	0.548620	−	0.794813i
$65$	2.60643	−	0.368690i	0.323288	−	0.0457303i
$66$	1.89089	+	2.73943i	0.232753	+	0.337201i
$67$	−9.66559	+	8.56296i	−1.18084	+	1.04613i	−0.182825	+	0.983145i	$0.558524\pi$
$67$	−9.66559	+	8.56296i	−1.18084	+	1.04613i	−0.998014	+	0.0629869i	$0.979937\pi$
$68$	0.0909273	+	0.0224116i	0.0110266	+	0.00271780i
$69$	−1.58356	−	2.29418i	−0.190638	−	0.276187i
$70$	4.89868			0.585505
$71$	−5.89128	−	8.53499i	−0.699166	−	1.01292i	−0.998276	−	0.0586979i	$-0.981305\pi$
$71$	−5.89128	−	8.53499i	−0.699166	−	1.01292i	0.299110	−	0.954219i	$-0.403310\pi$
$72$	−0.335223	−	2.76081i	−0.0395064	−	0.325365i
$73$	0.355963	+	0.938597i	0.0416623	+	0.109854i	0.954233	−	0.299065i	$-0.0966748\pi$
$73$	0.355963	+	0.938597i	0.0416623	+	0.109854i	−0.912570	+	0.408920i	$0.865906\pi$
$74$	0.285896	−	2.35456i	0.0332347	−	0.273712i
$75$	1.58401	+	4.17669i	0.182906	+	0.482283i
$76$	−0.355055	−	0.314552i	−0.0407276	−	0.0360815i
$77$	8.09805	+	7.17425i	0.922858	+	0.817581i
$78$	2.49732	+	4.53876i	0.282766	+	0.513913i
$79$	−3.46321	+	3.06814i	−0.389642	+	0.345192i	−0.835088	−	0.550116i	$-0.814583\pi$
$79$	−3.46321	+	3.06814i	−0.389642	+	0.345192i	0.445447	+	0.895309i	$0.353045\pi$
$80$	3.01134			0.336678
$81$	−0.748511	−	0.663123i	−0.0831679	−	0.0736803i
$82$	−4.97179	+	1.22544i	−0.549043	+	0.135327i
$83$	1.05041	−	1.52178i	0.115298	−	0.167037i	−0.761086	−	0.648651i	$-0.775334\pi$
$83$	1.05041	−	1.52178i	0.115298	−	0.167037i	0.876384	+	0.481613i	$0.159949\pi$
$84$	0.106616	+	0.281122i	0.0116327	+	0.0306729i
$85$	−0.376577	−	0.992952i	−0.0408455	−	0.107701i
$86$	−7.86781	+	11.3985i	−0.848407	+	1.22913i
$87$	−9.49812	+	2.34108i	−1.01831	+	0.250990i
$88$	4.82266	+	4.27251i	0.514097	+	0.455451i
$89$	−9.35530			−0.991660			−0.495830	−	0.868420i	$-0.665136\pi$
$89$	−9.35530			−0.991660			−0.495830	+	0.868420i	$0.665136\pi$
$90$	0.785180	−	0.695609i	0.0827652	−	0.0733236i
$91$	11.4114	+	12.3808i	1.19624	+	1.29786i
$92$	0.134339	+	0.119014i	0.0140058	+	0.0124081i
$93$	−5.49157	−	4.86511i	−0.569449	−	0.504488i
$94$	−6.33275	−	16.6981i	−0.653174	−	1.72228i
$95$	−0.648374	+	5.33984i	−0.0665218	+	0.547856i
$96$	0.129098	+	0.340404i	0.0131760	+	0.0347424i
$97$	0.765884	+	6.30762i	0.0777638	+	0.640442i	0.978525	+	0.206128i	$0.0660863\pi$
$97$	0.765884	+	6.30762i	0.0777638	+	0.640442i	−0.900761	+	0.434314i	$0.856991\pi$
$98$	12.0862	+	17.5099i	1.22089	+	1.76877i
$99$	2.31672			0.232839
$100$	−0.163372	−	0.236686i	−0.0163372	−	0.0236686i
$101$	7.88605	+	1.94374i	0.784692	+	0.193409i	0.611253	−	0.791435i	$-0.290666\pi$
$101$	7.88605	+	1.94374i	0.784692	+	0.193409i	0.173439	+	0.984845i	$0.444512\pi$
$102$	1.56432	−	1.38587i	0.154891	−	0.137221i
$103$	−2.95655	−	4.28330i	−0.291318	−	0.422046i	0.649811	−	0.760096i	$-0.274848\pi$
$103$	−2.95655	−	4.28330i	−0.291318	−	0.422046i	−0.941128	+	0.338050i	$0.890233\pi$
$104$	6.79586	+	7.37320i	0.666389	+	0.723002i
$105$	1.93679	−	2.80592i	0.189011	−	0.273830i
$106$	0.151347	+	1.24645i	0.0147001	+	0.121066i
$107$	−2.08163	+	17.1437i	−0.201238	+	1.65735i	0.445980	+	0.895043i	$0.352855\pi$
$107$	−2.08163	+	17.1437i	−0.201238	+	1.65735i	−0.647218	+	0.762305i	$0.724068\pi$
$108$	0.0570079	+	0.0299200i	0.00548558	+	0.00287906i
$109$	13.3130	+	3.28137i	1.27516	+	0.314298i	0.818068	−	0.575122i	$-0.195045\pi$
$109$	13.3130	+	3.28137i	1.27516	+	0.314298i	0.457091	+	0.889420i	$0.348891\pi$
$110$	−0.292930	+	2.41250i	−0.0279298	+	0.230023i
$111$	−1.23564	−	1.09468i	−0.117282	−	0.103902i
$112$	10.9418	+	15.8520i	1.03391	+	1.49787i
$113$	8.37996	−	12.1405i	0.788320	−	1.14208i	−0.198475	−	0.980106i	$-0.563599\pi$
$113$	8.37996	−	12.1405i	0.788320	−	1.14208i	0.986795	−	0.161973i	$-0.0517857\pi$
$114$	−10.2782	+	2.53336i	−0.962645	+	0.237271i
$115$	0.245320	−	2.02039i	0.0228762	−	0.188402i
$116$	0.557672	−	0.292689i	0.0517786	−	0.0271755i
$117$	3.58713	+	0.364041i	0.331630	+	0.0336556i
$118$	−5.28065	−	2.77150i	−0.486123	−	0.255137i
$119$	3.85869	−	5.59027i	0.353725	−	0.512459i
$120$	1.15342	−	1.67102i	0.105293	−	0.152543i
$121$	4.21621	−	3.73523i	0.383292	−	0.339567i
$122$	0.527176	−	0.467038i	0.0477283	−	0.0422836i
$123$	−1.26377	+	3.33230i	−0.113951	+	0.300463i
$124$	0.418247	+	0.219513i	0.0375597	+	0.0197129i
$125$	−2.45093	+	6.46258i	−0.219218	+	0.578031i
$126$	6.51473	+	1.60574i	0.580379	+	0.143050i
$127$	−10.6613	+	9.44506i	−0.946034	+	0.838113i	−0.986946	−	0.161049i	$-0.948512\pi$
$127$	−10.6613	+	9.44506i	−0.946034	+	0.838113i	0.0409120	+	0.999163i	$0.486974\pi$
$128$	6.71966	+	9.73510i	0.593939	+	0.860470i
$129$	3.41826	+	9.01322i	0.300961	+	0.793570i
$130$	−0.832654	+	3.68939i	−0.0730285	+	0.323581i
$131$	0.217828	−	0.574366i	0.0190318	−	0.0501826i	−0.925164	−	0.379568i	$-0.876072\pi$
$131$	0.217828	−	0.574366i	0.0190318	−	0.0501826i	0.944195	+	0.329386i	$0.106842\pi$
$132$	−0.144822	+	0.0356955i	−0.0126052	+	0.00310689i
$133$	−30.4653	+	15.9894i	−2.64168	+	1.38646i
$134$	−6.57915	−	17.3478i	−0.568352	−	1.49862i
$135$	−0.0880026	−	0.724766i	−0.00757405	−	0.0623779i
$136$	2.29798	−	3.32919i	0.197050	−	0.285476i
$137$	1.35441	+	0.333832i	0.115715	+	0.0285212i	0.296748	−	0.954956i	$-0.404098\pi$
$137$	1.35441	+	0.333832i	0.115715	+	0.0285212i	−0.181033	+	0.983477i	$0.557944\pi$
$138$	3.88889	−	0.958524i	0.331044	−	0.0815950i
$139$	−0.544658	−	4.48566i	−0.0461973	−	0.380469i	−0.997410	−	0.0719317i	$-0.977084\pi$
$139$	−0.544658	−	4.48566i	−0.0461973	−	0.380469i	0.951212	−	0.308537i	$-0.0998394\pi$
$140$	−0.0778389	+	0.205244i	−0.00657859	+	0.0173463i
$141$	−12.0683	−	2.97457i	−1.01633	−	0.250504i
$142$	14.4677	−	3.56597i	1.21410	−	0.299250i
$143$	−6.77967	+	4.87952i	−0.566945	+	0.408046i
$144$	4.00477	+	0.987086i	0.333730	+	0.0822572i
$145$	−6.32393	−	3.31906i	−0.525174	−	0.275633i
$146$	−1.44230			−0.119365
$147$	14.8080			1.22135
$148$	0.0941083	+	0.0493919i	0.00773566	+	0.00405999i
$149$	12.1510	−	10.7648i	0.995447	−	0.881889i	0.00244591	−	0.999997i	$-0.499221\pi$
$149$	12.1510	−	10.7648i	0.995447	−	0.881889i	0.993001	+	0.118108i	$0.0376830\pi$
$150$	−6.41812			−0.524038
$151$	14.8888	+	13.1903i	1.21163	+	1.07341i	0.995275	+	0.0970967i	$0.0309556\pi$
$151$	14.8888	+	13.1903i	1.21163	+	1.07341i	0.216356	+	0.976315i	$0.430583\pi$
$152$	−18.1431	+	9.52224i	−1.47160	+	0.772356i
$153$	−0.175328	−	1.44396i	−0.0141745	−	0.116737i
$154$	−13.7640	+	7.22390i	−1.10913	+	0.582119i
$155$	−0.645645	−	5.31737i	−0.0518595	−	0.427101i
$156$	−0.229846	+	0.0325127i	−0.0184024	+	0.00260310i
$157$	1.86132	−	15.3293i	0.148549	−	1.22341i	−0.707573	−	0.706640i	$-0.750210\pi$
$157$	1.86132	−	15.3293i	0.148549	−	1.22341i	0.856122	−	0.516773i	$-0.172867\pi$
$158$	−2.35733	−	6.21577i	−0.187539	−	0.494500i
$159$	0.773796	+	0.406119i	0.0613660	+	0.0322074i
$160$	−0.0942533	+	0.248525i	−0.00745138	+	0.0196477i
$161$	11.5269	−	6.04978i	0.908446	−	0.476789i
$162$	1.27222	−	0.667712i	0.0999550	−	0.0524604i
$163$	9.08641	−	2.23960i	0.711703	−	0.175419i	0.133188	−	0.991091i	$-0.457479\pi$
$163$	9.08641	−	2.23960i	0.711703	−	0.175419i	0.578515	+	0.815672i	$0.303632\pi$
$164$	0.0276574	−	0.227779i	0.00215968	−	0.0177866i
$165$	1.26604	+	1.12162i	0.0985613	+	0.0873177i
$166$	1.50923	+	2.18649i	0.117139	+	0.169705i
$167$	4.02649	−	10.6170i	0.311579	−	0.821566i	−0.684159	−	0.729333i	$-0.739830\pi$
$167$	4.02649	−	10.6170i	0.311579	−	0.821566i	0.995737	−	0.0922326i	$-0.0294003\pi$
$168$	12.9874			1.00200
$169$	−11.2641	+	6.48993i	−0.866472	+	0.499225i
$170$	1.52582			0.117025
$171$	−2.61261	+	6.88889i	−0.199791	+	0.526807i
$172$	−0.352554	−	0.510763i	−0.0268820	−	0.0389453i
$173$	18.0481	+	15.9892i	1.37217	+	1.21564i	0.951205	+	0.308560i	$0.0998472\pi$
$173$	18.0481	+	15.9892i	1.37217	+	1.21564i	0.420966	+	0.907077i	$0.361691\pi$
$174$	1.69418	−	13.9528i	0.128435	−	1.05776i
$175$	−20.2542	+	4.99221i	−1.53107	+	0.377375i
$176$	−8.46107	+	4.44071i	−0.637777	+	0.334731i
$177$	−3.67530	+	1.92894i	−0.276252	+	0.144988i
$178$	4.76648	−	12.5682i	0.357263	−	0.942024i
$179$	1.08681	+	0.570403i	0.0812322	+	0.0426340i	0.504850	−	0.863207i	$-0.331548\pi$
$179$	1.08681	+	0.570403i	0.0812322	+	0.0426340i	−0.423618	+	0.905841i	$0.639240\pi$
$180$	0.0166682	+	0.0439504i	0.00124237	+	0.00327587i
$181$	−0.389808	+	3.21035i	−0.0289742	+	0.238624i	−1.00000		0.000351069i	$-0.999888\pi$
$181$	−0.389808	+	3.21035i	−0.0289742	+	0.238624i	0.971026	+	0.238975i	$0.0768113\pi$
$182$	−22.4468	+	9.02239i	−1.66387	+	0.668784i
$183$	−0.0590857	−	0.486614i	−0.00436774	−	0.0359716i
$184$	6.86465	−	3.60285i	0.506069	−	0.265605i
$185$	−0.145274	−	1.19644i	−0.0106808	−	0.0879641i
$186$	9.33385	−	4.89878i	0.684391	−	0.359196i
$187$	2.52235	+	2.23461i	0.184453	+	0.163411i
$188$	0.800241			0.0583635
$189$	3.49548	−	3.09672i	0.254258	−	0.225253i
$190$	−6.84334	−	3.59166i	−0.496468	−	0.260567i
$191$	23.9152			1.73044			0.865222	−	0.501389i	$-0.167177\pi$
$191$	23.9152			1.73044			0.865222	+	0.501389i	$0.167177\pi$
$192$	7.72616			0.557587
$193$	−9.86120	−	5.17556i	−0.709825	−	0.372545i	0.0708460	−	0.997487i	$-0.477430\pi$
$193$	−9.86120	−	5.17556i	−0.709825	−	0.372545i	−0.780671	+	0.624942i	$0.785122\pi$
$194$	−8.86405	−	2.18479i	−0.636402	−	0.156859i
$195$	1.78405	+	1.93561i	0.127758	+	0.138612i
$196$	−0.925675	+	0.228158i	−0.0661196	+	0.0162970i
$197$	15.5574	+	3.83455i	1.10842	+	0.273200i	0.750709	−	0.660633i	$-0.229712\pi$
$197$	15.5574	+	3.83455i	1.10842	+	0.273200i	0.357708	+	0.933833i	$0.383558\pi$
$198$	−1.18036	+	3.11235i	−0.0838844	+	0.221185i
$199$	1.15873	+	9.54301i	0.0821403	+	0.676486i	0.974377	+	0.224919i	$0.0722118\pi$
$199$	1.15873	+	9.54301i	0.0821403	+	0.676486i	−0.892237	+	0.451567i	$0.850865\pi$
$200$	−12.0620	+	2.97303i	−0.852915	+	0.210225i
$201$	−12.5379	−	3.09030i	−0.884352	−	0.217973i
$202$	−6.62917	+	9.60402i	−0.466427	+	0.675736i
$203$	−5.50645	−	45.3497i	−0.386477	−	3.18293i
$204$	0.0332082	+	0.0875629i	0.00232504	+	0.00613063i
$205$	−2.30392	+	1.20919i	−0.160913	+	0.0844536i
$206$	7.26066	−	1.78959i	0.505874	−	0.124687i
$207$	0.988511	−	2.60649i	0.0687063	−	0.181164i
$208$	−13.7986	+	5.54629i	−0.956760	+	0.384566i
$209$	−6.05270	−	15.9597i	−0.418674	−	1.10395i
$210$	2.78277	+	4.03154i	0.192029	+	0.278203i
$211$	−2.41842	+	2.14253i	−0.166491	+	0.147498i	−0.742254	−	0.670118i	$-0.766243\pi$
$211$	−2.41842	+	2.14253i	−0.166491	+	0.147498i	0.575764	+	0.817616i	$0.304705\pi$
$212$	−0.0546286	−	0.0134648i	−0.00375191	−	0.000924763i
$213$	3.67753	−	9.69685i	0.251980	−	0.664417i
$214$	−21.9708	−	11.5312i	−1.50189	−	0.788254i
$215$	−2.49564	+	6.58045i	−0.170201	+	0.448783i
$216$	2.08167	−	1.84420i	0.141640	−	0.125482i
$217$	25.6451	−	22.7196i	1.74091	−	1.54231i
$218$	−11.1912	+	16.2133i	−0.757965	+	1.09810i
$219$	−0.570240	+	0.826135i	−0.0385333	+	0.0558251i
$220$	−0.0964239	−	0.0506072i	−0.00650090	−	0.00341194i
$221$	3.55437	+	3.85633i	0.239093	+	0.259405i
$222$	2.10017	−	1.10226i	0.140955	−	0.0739786i
$223$	1.51497	−	12.4769i	0.101450	−	0.835517i	−0.849802	−	0.527102i	$-0.823278\pi$
$223$	1.51497	−	12.4769i	0.101450	−	0.835517i	0.951252	−	0.308415i	$-0.0997985\pi$
$224$	−1.65073	+	0.406869i	−0.110294	+	0.0271851i
$225$	−2.53753	+	3.67624i	−0.169169	+	0.245083i
$226$	12.0403	+	17.4434i	0.800908	+	1.16032i
$227$	4.69789	+	4.16197i	0.311810	+	0.276240i	0.804484	−	0.593974i	$-0.202442\pi$
$227$	4.69789	+	4.16197i	0.311810	+	0.276240i	−0.492674	+	0.870214i	$0.663980\pi$
$228$	0.0571765	−	0.470890i	0.00378660	−	0.0311855i
$229$	15.6230	+	3.85072i	1.03240	+	0.254463i	0.718891	−	0.695123i	$-0.244650\pi$
$229$	15.6230	+	3.85072i	1.03240	+	0.254463i	0.313506	+	0.949586i	$0.398496\pi$
$230$	2.58926	+	1.35895i	0.170731	+	0.0896063i
$231$	−1.30407	+	10.7400i	−0.0858017	+	0.706640i
$232$	−3.27928	−	27.0073i	−0.215295	−	1.77311i
$233$	−7.85880	+	11.3854i	−0.514847	+	0.745885i	−0.991056	−	0.133447i	$-0.957395\pi$
$233$	−7.85880	+	11.3854i	−0.514847	+	0.745885i	0.476209	+	0.879332i	$0.342011\pi$
$234$	−2.31669	+	4.63357i	−0.151446	+	0.302906i
$235$	−5.15498	−	7.46827i	−0.336274	−	0.487176i
$236$	0.200028	−	0.177209i	0.0130207	−	0.0115354i
$237$	−4.49235	−	1.10727i	−0.291810	−	0.0719246i
$238$	5.54414	+	8.03208i	0.359373	+	0.520642i
$239$	−3.55800			−0.230148			−0.115074	−	0.993357i	$-0.536710\pi$
$239$	−3.55800			−0.230148			−0.115074	+	0.993357i	$0.536710\pi$
$240$	1.71064	+	2.47829i	0.110421	+	0.159973i
$241$	2.62825	+	21.6456i	0.169301	+	1.39432i	0.791362	+	0.611347i	$0.209372\pi$
$241$	2.62825	+	21.6456i	0.169301	+	1.39432i	−0.622062	+	0.782968i	$0.713705\pi$
$242$	2.86988	+	7.56725i	0.184483	+	0.486441i
$243$	0.120537	−	0.992709i	0.00773243	−	0.0636823i
$244$	0.0111912	+	0.0295087i	0.000716441	+	0.00188910i
$245$	8.09229	+	7.16915i	0.516998	+	0.458020i
$246$	−3.83281	−	3.39558i	−0.244371	−	0.216494i
$247$	−6.86393	−	25.6624i	−0.436741	−	1.63286i
$248$	15.2725	−	13.5303i	0.969807	−	0.859174i
$249$	1.84910			0.117182
$250$	−7.43327	−	6.58531i	−0.470122	−	0.416491i
$251$	−12.4225	+	3.06188i	−0.784104	+	0.193264i	−0.610991	−	0.791638i	$-0.709229\pi$
$251$	−12.4225	+	3.06188i	−0.784104	+	0.193264i	−0.173113	+	0.984902i	$0.555383\pi$
$252$	−0.170794	+	0.247439i	−0.0107590	+	0.0155872i
$253$	2.29011	+	6.03852i	0.143978	+	0.379638i
$254$	−7.25689	−	19.1348i	−0.455338	−	1.20063i
$255$	0.603264	−	0.873978i	0.0377778	−	0.0547306i
$256$	−1.49874	+	0.369407i	−0.0936713	+	0.0230879i
$257$	−5.09926	−	4.51755i	−0.318083	−	0.281797i	0.488940	−	0.872318i	$-0.337384\pi$
$257$	−5.09926	−	4.51755i	−0.318083	−	0.281797i	−0.807022	+	0.590521i	$0.798922\pi$
$258$	−13.8502			−0.862275
$259$	5.77032	−	5.11206i	0.358550	−	0.317648i
$260$	−0.141347	−	0.0935100i	−0.00876597	−	0.00579924i
$261$	−7.32221	−	6.48692i	−0.453234	−	0.401530i
$262$	0.660637	+	0.585273i	0.0408143	+	0.0361583i
$263$	−8.48802	−	22.3811i	−0.523394	−	1.38008i	−0.892651	−	0.450749i	$-0.851157\pi$
$263$	−8.48802	−	22.3811i	−0.523394	−	1.38008i	0.369257	−	0.929327i	$-0.379612\pi$
$264$	−0.776619	+	6.39603i	−0.0477976	+	0.393649i
$265$	0.226246	+	0.596561i	0.0138982	+	0.0366464i
$266$	−5.95872	−	49.0745i	−0.365352	−	3.00895i
$267$	−5.31442	−	7.69926i	−0.325237	−	0.471187i
$268$	0.831377			0.0507844
$269$	−12.7724	−	18.5040i	−0.778744	−	1.12821i	−0.988614	−	0.150477i	$-0.951919\pi$
$269$	−12.7724	−	18.5040i	−0.778744	−	1.12821i	0.209869	−	0.977729i	$-0.432696\pi$
$270$	1.01851	+	0.251040i	0.0619844	+	0.0152778i
$271$	5.62393	−	4.98237i	0.341629	−	0.302657i	−0.474810	−	0.880088i	$-0.657483\pi$
$271$	5.62393	−	4.98237i	0.341629	−	0.302657i	0.816439	+	0.577431i	$0.195945\pi$
$272$	3.40812	+	4.93752i	0.206648	+	0.299381i
$273$	−3.70682	+	16.4245i	−0.224347	+	0.994056i
$274$	−1.13854	+	1.64946i	−0.0687819	+	0.0996478i
$275$	−1.24740	−	10.2733i	−0.0752212	−	0.619502i
$276$	−0.0216334	+	0.178167i	−0.00130218	+	0.0107244i
$277$	−8.63301	−	4.53095i	−0.518707	−	0.272238i	0.184988	−	0.982741i	$-0.440775\pi$
$277$	−8.63301	−	4.53095i	−0.518707	−	0.272238i	−0.703695	+	0.710502i	$0.748468\pi$
$278$	6.30366	+	1.55371i	0.378069	+	0.0931855i
$279$	0.884337	−	7.28317i	0.0529439	−	0.436032i
$280$	7.09736	+	6.28771i	0.424149	+	0.375763i
$281$	−7.42106	−	10.7513i	−0.442703	−	0.641366i	0.536583	−	0.843848i	$-0.319715\pi$
$281$	−7.42106	−	10.7513i	−0.442703	−	0.641366i	−0.979286	+	0.202481i	$0.935100\pi$
$282$	10.1449	−	14.6974i	0.604117	−	0.875215i
$283$	−0.731294	+	0.180248i	−0.0434709	+	0.0107146i	−0.260991	−	0.965341i	$-0.584049\pi$
$283$	−0.731294	+	0.180248i	−0.0434709	+	0.0107146i	0.217520	+	0.976056i	$0.430203\pi$
$284$	−0.0804819	+	0.662828i	−0.00477572	+	0.0393316i
$285$	−4.76292	+	2.49977i	−0.282131	+	0.148074i
$286$	−3.10107	−	11.5941i	−0.183370	−	0.685573i
$287$	−14.7367	−	7.73441i	−0.869879	−	0.456548i
$288$	−0.206811	+	0.299617i	−0.0121865	+	0.0176551i
$289$	−8.45521	+	12.2495i	−0.497365	+	0.720558i
$290$	7.68092	−	6.80471i	0.451039	−	0.399586i
$291$	−4.75600	+	4.21345i	−0.278802	+	0.246997i
$292$	0.0229178	−	0.0604292i	0.00134116	−	0.00353635i
$293$	25.0780	+	13.1620i	1.46507	+	0.768930i	0.993601	−	0.112951i	$-0.0360302\pi$
$293$	25.0780	+	13.1620i	1.46507	+	0.768930i	0.471473	+	0.881880i	$0.343722\pi$
$294$	−7.54462	+	19.8935i	−0.440011	+	1.16021i
$295$	−2.94235	−	0.725225i	−0.171310	−	0.0422242i
$296$	3.43642	−	3.04440i	0.199738	−	0.176952i
$297$	1.31605	+	1.90663i	0.0763649	+	0.110634i
$298$	8.27090	+	21.8086i	0.479120	+	1.26334i
$299$	2.59705	+	9.70967i	0.150191	+	0.561525i
$300$	0.101982	−	0.268906i	0.00588796	−	0.0155253i
$301$	−43.7081	+	10.7731i	−2.51929	+	0.620950i
$302$	−25.3060	+	13.2816i	−1.45619	+	0.764270i
$303$	2.88012	+	7.59426i	0.165459	+	0.436279i
$304$	−3.66297	−	30.1673i	−0.210086	−	1.73021i
$305$	0.203300	−	0.294530i	0.0116409	−	0.0168648i
$306$	2.02918	+	0.500149i	0.116001	+	0.0285916i
$307$	−9.54051	+	2.35152i	−0.544505	+	0.134209i	−0.501968	−	0.864886i	$-0.667390\pi$
$307$	−9.54051	+	2.35152i	−0.544505	+	0.134209i	−0.0425377	+	0.999095i	$0.513544\pi$
$308$	−0.0839594	−	0.691468i	−0.00478403	−	0.0394000i
$309$	1.84558	−	4.86639i	0.104991	−	0.276839i
$310$	7.47245	+	1.84179i	0.424407	+	0.104607i
$311$	3.40348	−	0.838882i	0.192993	−	0.0475686i	−0.141634	−	0.989919i	$-0.545236\pi$
$311$	3.40348	−	0.838882i	0.192993	−	0.0475686i	0.334628	+	0.942350i	$0.391389\pi$
$312$	−2.20754	+	9.78134i	−0.124977	+	0.553759i
$313$	13.1493	+	3.24101i	0.743241	+	0.183193i	0.592714	−	0.805413i	$-0.298057\pi$
$313$	13.1493	+	3.24101i	0.743241	+	0.183193i	0.150528	+	0.988606i	$0.451903\pi$
$314$	19.6455	+	10.3108i	1.10866	+	0.581870i
$315$	3.40945			0.192101
$316$	0.297885			0.0167573
$317$	−9.79732	−	5.14203i	−0.550273	−	0.288805i	0.166583	−	0.986028i	$-0.446727\pi$
$317$	−9.79732	−	5.14203i	−0.550273	−	0.288805i	−0.716855	+	0.697222i	$0.754419\pi$
$318$	−0.939837	+	0.832623i	−0.0527035	+	0.0466912i
$319$	22.6631			1.26889
$320$	4.22219	+	3.74053i	0.236027	+	0.209102i
$321$	−15.2915	+	8.02561i	−0.853489	+	0.447946i
$322$	2.25455	+	18.5679i	0.125641	+	1.03475i
$323$	−9.48922	+	4.98033i	−0.527994	+	0.277113i
$324$	0.00776045	+	0.0639131i	0.000431136	+	0.00355073i
$325$	−0.317125	−	16.1028i	−0.0175909	−	0.893221i
$326$	−1.62074	+	13.3480i	−0.0897645	+	0.739278i
$327$	4.86216	+	12.8205i	0.268878	+	0.708973i
$328$	−8.77620	−	4.60610i	−0.484584	−	0.254329i
$329$	20.5829	−	54.2726i	1.13477	−	2.99214i
$330$	−2.15185	+	1.12938i	−0.118456	+	0.0621702i
$331$	13.3295	−	6.99584i	0.732653	−	0.384526i	−0.0567602	−	0.998388i	$-0.518077\pi$
$331$	13.3295	−	6.99584i	0.732653	−	0.384526i	0.789414	+	0.613862i	$0.210385\pi$
$332$	−0.115590	+	0.0284905i	−0.00634385	+	0.00156362i
$333$	0.198981	−	1.63876i	0.0109041	−	0.0898035i
$334$	12.2117	+	10.8186i	0.668192	+	0.591967i
$335$	−5.35555	−	7.75885i	−0.292605	−	0.423911i
$336$	−6.83026	+	18.0099i	−0.372621	+	0.982521i
$337$	−8.85678			−0.482460			−0.241230	−	0.970468i	$-0.577551\pi$
$337$	−8.85678			−0.482460			−0.241230	+	0.970468i	$0.577551\pi$
$338$	−2.97973	−	18.4391i	−0.162076	−	1.00296i
$339$	14.7518			0.801206
$340$	−0.0242450	+	0.0639287i	−0.00131487	+	0.00346702i
$341$	9.65541	+	13.9883i	0.522870	+	0.757507i
$342$	−7.92362	−	7.01971i	−0.428460	−	0.379582i
$343$	−4.39511	+	36.1970i	−0.237313	+	1.95445i
$344$	−26.0297	+	6.41574i	−1.40343	+	0.345913i
$345$	1.80210	−	0.945817i	0.0970221	−	0.0509211i
$346$	−30.6757	+	16.0999i	−1.64914	+	0.865535i
$347$	−10.3894	+	27.3945i	−0.557731	+	1.47061i	0.298697	+	0.954348i	$0.403448\pi$
$347$	−10.3894	+	27.3945i	−0.557731	+	1.47061i	−0.856428	+	0.516267i	$0.827321\pi$
$348$	0.557672	+	0.292689i	0.0298944	+	0.0156898i
$349$	−4.85159	−	12.7926i	−0.259700	−	0.684772i	−0.999923	−	0.0124109i	$-0.996049\pi$
$349$	−4.85159	−	12.7926i	−0.259700	−	0.684772i	0.740223	−	0.672361i	$-0.234720\pi$
$350$	3.61273	−	29.7535i	0.193109	−	1.59039i
$351$	1.73812	+	3.15895i	0.0927740	+	0.168612i
$352$	−0.101664	−	0.837282i	−0.00541873	−	0.0446273i
$353$	23.9393	−	12.5643i	1.27416	−	0.668730i	0.314329	−	0.949314i	$-0.398220\pi$
$353$	23.9393	−	12.5643i	1.27416	−	0.668730i	0.959829	+	0.280584i	$0.0905281\pi$
$354$	−0.718852	−	5.92028i	−0.0382066	−	0.314659i
$355$	6.70432	−	3.51870i	0.355828	−	0.186753i
$356$	0.450841	+	0.399411i	0.0238945	+	0.0211687i
$357$	6.79269			0.359507
$358$	−1.32002	+	1.16944i	−0.0697653	+	0.0618067i
$359$	9.97143	+	5.23341i	0.526272	+	0.276209i	0.706864	−	0.707349i	$-0.250109\pi$
$359$	9.97143	+	5.23341i	0.526272	+	0.276209i	−0.180592	+	0.983558i	$0.557802\pi$
$360$	2.03044			0.107014
$361$	35.2826			1.85698
$362$	−4.11427	−	2.15934i	−0.216241	−	0.113492i
$363$	5.46912	+	1.34802i	0.287054	+	0.0707525i
$364$	−0.0213449	−	1.08384i	−0.00111877	−	0.0568084i
$365$	−0.711589	+	0.175391i	−0.0372463	+	0.00918038i
$366$	0.683835	+	0.168550i	0.0357446	+	0.00881026i
$367$	−10.3374	+	27.2574i	−0.539606	+	1.42282i	0.336950	+	0.941523i	$0.390605\pi$
$367$	−10.3374	+	27.2574i	−0.539606	+	1.42282i	−0.876556	+	0.481301i	$0.840165\pi$
$368$	1.38593	+	11.4141i	0.0722464	+	0.595003i
$369$	−3.46033	+	0.852895i	−0.180138	+	0.0444000i
$370$	1.68135	+	0.414415i	0.0874091	+	0.0215444i
$371$	−2.31828	+	3.35861i	−0.120359	+	0.174370i
$372$	0.0569358	+	0.468909i	0.00295198	+	0.0243118i
$373$	−3.32244	−	8.76054i	−0.172029	−	0.453604i	0.821078	−	0.570817i	$-0.193373\pi$
$373$	−3.32244	−	8.76054i	−0.172029	−	0.453604i	−0.993107	+	0.117213i	$0.962604\pi$
$374$	−4.28716	+	2.25007i	−0.221684	+	0.116349i
$375$	−6.71089	+	1.65409i	−0.346549	+	0.0854166i
$376$	12.2578	−	32.3211i	0.632147	−	1.66684i
$377$	35.0906	+	3.56119i	1.80726	+	0.183411i
$378$	2.37929	+	6.27368i	0.122378	+	0.322683i
$379$	4.88403	+	7.07574i	0.250876	+	0.363457i	0.928107	−	0.372314i	$-0.121436\pi$
$379$	4.88403	+	7.07574i	0.250876	+	0.363457i	−0.677231	+	0.735771i	$0.736820\pi$
$380$	0.259222	−	0.229651i	0.0132978	−	0.0117808i
$381$	−13.8294	−	3.40865i	−0.708503	−	0.174630i
$382$	−12.1847	+	32.1284i	−0.623422	+	1.64383i
$383$	7.97819	+	4.18728i	0.407667	+	0.213960i	0.656075	−	0.754695i	$-0.272215\pi$
$383$	7.97819	+	4.18728i	0.407667	+	0.213960i	−0.248409	+	0.968655i	$0.579908\pi$
$384$	−4.19463	+	11.0603i	−0.214056	+	0.564421i
$385$	−5.91230	+	5.23784i	−0.301319	+	0.266945i
$386$	11.9772	−	10.6109i	0.609624	−	0.540080i
$387$	−5.47594	+	7.93327i	−0.278358	+	0.403271i
$388$	0.232386	−	0.336669i	0.0117976	−	0.0170918i
$389$	−2.80348	−	1.47138i	−0.142142	−	0.0746020i	0.392153	−	0.919900i	$-0.371731\pi$
$389$	−2.80348	−	1.47138i	−0.142142	−	0.0746020i	−0.534295	+	0.845298i	$0.679423\pi$
$390$	−3.50931	+	1.41055i	−0.177701	+	0.0714261i
$391$	3.59035	−	1.88436i	0.181572	−	0.0952963i
$392$	−4.96400	+	40.8822i	−0.250720	+	2.06486i
$393$	0.596435	−	0.147008i	0.0300862	−	0.00741557i
$394$	−13.0778	+	18.9465i	−0.658852	+	0.954512i
$395$	−1.91891	−	2.78002i	−0.0965508	−	0.139878i
$396$	−0.111645	−	0.0989090i	−0.00561038	−	0.00497036i
$397$	3.93689	−	32.4232i	0.197587	−	1.62727i	−0.469947	−	0.882695i	$-0.655727\pi$
$397$	3.93689	−	32.4232i	0.197587	−	1.62727i	0.667534	−	0.744579i	$-0.267350\pi$
$398$	−13.4107	−	3.30544i	−0.672218	−	0.165687i
$399$	−30.4653	−	15.9894i	−1.52517	−	0.800473i
$400$	2.22083	−	18.2902i	0.111042	−	0.914511i
$401$	−0.342155	−	2.81790i	−0.0170864	−	0.140719i	0.981669	−	0.190593i	$-0.0610411\pi$
$401$	−0.342155	−	2.81790i	−0.0170864	−	0.140719i	−0.998756	+	0.0498740i	$0.984118\pi$
$402$	10.5396	−	15.2692i	0.525666	−	0.761559i
$403$	12.7520	+	23.1761i	0.635222	+	1.15448i
$404$	−0.297052	−	0.430354i	−0.0147789	−	0.0214109i
$405$	0.546480	−	0.484139i	0.0271548	−	0.0240571i
$406$	63.7296	+	15.7079i	3.16285	+	0.779571i
$407$	2.17253	+	3.14745i	0.107688	+	0.156013i
$408$	4.04527			0.200271
$409$	14.9624	+	21.6767i	0.739841	+	1.07185i	0.994492	+	0.104812i	$0.0334241\pi$
$409$	14.9624	+	21.6767i	0.739841	+	1.07185i	−0.254651	+	0.967033i	$0.581961\pi$
$410$	−0.450625	−	3.71123i	−0.0222548	−	0.183285i
$411$	0.494654	+	1.30429i	0.0243995	+	0.0643361i
$412$	−0.0403901	+	0.332642i	−0.00198988	+	0.0163881i
$413$	−6.87351	−	18.1239i	−0.338223	−	0.891821i
$414$	2.99799	+	2.65599i	0.147343	+	0.130535i
$415$	1.01050	+	0.895223i	0.0496034	+	0.0439447i
$416$	−0.0258460	−	1.31239i	−0.00126720	−	0.0643453i
$417$	3.38223	−	2.99639i	0.165628	−	0.146734i
$418$	24.5245			1.19953
$419$	−26.0483	−	23.0768i	−1.27254	−	1.12737i	−0.985540	−	0.169444i	$-0.945803\pi$
$419$	−26.0483	−	23.0768i	−1.27254	−	1.12737i	−0.287002	−	0.957930i	$-0.592659\pi$
$420$	−0.213130	+	0.0525319i	−0.0103997	+	0.00256329i
$421$	−2.32430	+	3.36733i	−0.113280	+	0.164114i	−0.875523	−	0.483177i	$-0.839483\pi$
$421$	−2.32430	+	3.36733i	−0.113280	+	0.164114i	0.762243	+	0.647291i	$0.224098\pi$
$422$	−1.64616	−	4.34058i	−0.0801340	−	0.211296i
$423$	−4.40755	−	11.6218i	−0.214303	−	0.565069i
$424$	−1.38061	+	2.00016i	−0.0670485	+	0.0971365i
$425$	−6.30869	+	1.55495i	−0.306017	+	0.0754263i
$426$	11.1533	+	9.88099i	0.540381	+	0.478736i
$427$	2.28913			0.110779
$428$	0.832242	−	0.737302i	0.0402279	−	0.0356388i
$429$	−7.86706	−	2.80768i	−0.379825	−	0.135556i
$430$	−7.56885	−	6.70542i	−0.365002	−	0.323364i
$431$	4.27548	+	3.78774i	0.205942	+	0.182449i	0.759789	−	0.650170i	$-0.225302\pi$
$431$	4.27548	+	3.78774i	0.205942	+	0.182449i	−0.553847	+	0.832619i	$0.686841\pi$
$432$	1.46261	+	3.85659i	0.0703699	+	0.185550i
$433$	0.518271	−	4.26835i	0.0249065	−	0.205124i	−0.974943	−	0.222454i	$-0.928593\pi$
$433$	0.518271	−	4.26835i	0.0249065	−	0.205124i	0.999850	+	0.0173298i	$0.00551652\pi$
$434$	17.4561	+	46.0279i	0.837919	+	2.20941i
$435$	−0.860874	−	7.08994i	−0.0412758	−	0.339936i
$436$	−0.501476	−	0.726513i	−0.0240163	−	0.0347937i
$437$	−20.5384			−0.982486
$438$	−0.819319	−	1.18699i	−0.0391486	−	0.0567165i
$439$	−1.66343	−	0.409998i	−0.0793910	−	0.0195681i	0.199420	−	0.979914i	$-0.436094\pi$
$439$	−1.66343	−	0.409998i	−0.0793910	−	0.0195681i	−0.278811	+	0.960346i	$0.589940\pi$
$440$	−3.52097	+	3.11931i	−0.167856	+	0.148707i
$441$	8.41192	+	12.1868i	0.400568	+	0.580323i
$442$	−6.99164	+	2.81026i	−0.332558	+	0.133670i
$443$	−17.8199	+	25.8165i	−0.846647	+	1.22658i	0.125473	+	0.992097i	$0.459955\pi$
$443$	−17.8199	+	25.8165i	−0.846647	+	1.22658i	−0.972120	+	0.234483i	$0.924660\pi$
$444$	0.0128109	+	0.105507i	0.000607979	+	0.00500716i
$445$	0.823291	−	6.78041i	0.0390277	−	0.321422i
$446$	15.9900	+	8.39219i	0.757148	+	0.397382i
$447$	15.7618	+	3.88494i	0.745508	+	0.183751i
$448$	−4.34902	+	35.8174i	−0.205472	+	1.69221i
$449$	−18.2835	−	16.1978i	−0.862853	−	0.764421i	0.110466	−	0.993880i	$-0.464766\pi$
$449$	−18.2835	−	16.1978i	−0.862853	−	0.764421i	−0.973318	+	0.229459i	$0.926304\pi$
$450$	−3.64591	−	5.28201i	−0.171870	−	0.248996i
$451$	4.69026	−	6.79501i	0.220856	−	0.319965i
$452$	−0.922157	+	0.227291i	−0.0433746	+	0.0106909i
$453$	−2.39762	+	19.7462i	−0.112650	+	0.927756i
$454$	−7.98486	+	4.19078i	−0.374748	+	0.196683i
$455$	−9.97744	+	7.18104i	−0.467749	+	0.336652i
$456$	−18.1431	−	9.52224i	−0.849629	−	0.445920i
$457$	−2.91669	+	4.22556i	−0.136437	+	0.197663i	−0.885247	−	0.465122i	$-0.846010\pi$
$457$	−2.91669	+	4.22556i	−0.136437	+	0.197663i	0.748809	+	0.662785i	$0.230626\pi$
$458$	−13.1330	+	19.0264i	−0.613665	+	0.889047i
$459$	1.08876	−	0.964555i	0.0508189	−	0.0450216i
$460$	−0.0980796	+	0.0868910i	−0.00457299	+	0.00405131i
$461$	4.66176	−	12.2921i	0.217120	−	0.572498i	−0.781562	−	0.623828i	$-0.785577\pi$
$461$	4.66176	−	12.2921i	0.217120	−	0.572498i	0.998682	+	0.0513295i	$0.0163459\pi$
$462$	−13.7640	−	7.22390i	−0.640359	−	0.336086i
$463$	−2.13841	+	5.63852i	−0.0993803	+	0.262044i	−0.975481	−	0.220084i	$-0.929367\pi$
$463$	−2.13841	+	5.63852i	−0.0993803	+	0.262044i	0.876101	+	0.482128i	$0.160136\pi$
$464$	39.1761	+	9.65605i	1.81871	+	0.448271i
$465$	4.00934	−	3.55196i	0.185929	−	0.164718i
$466$	−11.2915	−	16.3585i	−0.523068	−	0.757795i
$467$	−1.55210	−	4.09256i	−0.0718228	−	0.189381i	0.894298	−	0.447472i	$-0.147676\pi$
$467$	−1.55210	−	4.09256i	−0.0718228	−	0.189381i	−0.966121	+	0.258091i	$0.916907\pi$
$468$	−0.157325	−	0.170690i	−0.00727235	−	0.00789017i
$469$	21.3837	−	56.3842i	0.987408	−	2.60358i
$470$	12.6595	−	3.12029i	0.583940	−	0.143928i
$471$	13.6731	−	7.17622i	0.630025	−	0.330663i
$472$	−4.09341	−	10.7934i	−0.188414	−	0.496808i
$473$	−2.69187	−	22.1695i	−0.123772	−	1.01936i
$474$	3.77636	−	5.47101i	0.173454	−	0.251292i
$475$	31.9548	+	7.87616i	1.46619	+	0.361383i
$476$	−0.424622	+	0.104660i	−0.0194625	+	0.00479708i
$477$	0.105336	+	0.867524i	0.00482303	+	0.0397212i
$478$	1.81278	−	4.77991i	0.0829146	−	0.218628i
$479$	−29.6996	−	7.32030i	−1.35701	−	0.334473i	−0.507321	−	0.861757i	$-0.669364\pi$
$479$	−29.6996	−	7.32030i	−1.35701	−	0.334473i	−0.849689	+	0.527284i	$0.823210\pi$
$480$	−0.258074	+	0.0636096i	−0.0117794	+	0.00290337i
$481$	2.86928	+	5.21477i	0.130828	+	0.237773i
$482$	−30.4184	−	7.49746i	−1.38552	−	0.341500i
$483$	11.5269	+	6.04978i	0.524492	+	0.275275i
$484$	−0.362653			−0.0164842
$485$	−4.63895			−0.210644
$486$	1.27222	+	0.667712i	0.0577091	+	0.0302880i
$487$	−21.2462	+	18.8225i	−0.962759	+	0.852930i	−0.989178	−	0.146721i	$-0.953128\pi$
$487$	−21.2462	+	18.8225i	−0.962759	+	0.852930i	0.0264193	+	0.999651i	$0.491589\pi$
$488$	1.36326			0.0617117
$489$	7.00483	+	6.20573i	0.316769	+	0.280633i
$490$	−13.7542	+	7.21877i	−0.621352	+	0.326111i
$491$	1.86665	+	15.3732i	0.0842408	+	0.693785i	0.972248	+	0.233955i	$0.0751667\pi$
$491$	1.86665	+	15.3732i	0.0842408	+	0.693785i	−0.888007	+	0.459830i	$0.847910\pi$
$492$	0.203170	−	0.106632i	0.00915961	−	0.00480733i
$493$	−1.71513	−	14.1254i	−0.0772455	−	0.636174i
$494$	37.9727	+	3.85368i	1.70847	+	0.173385i
$495$	−0.203878	+	1.67908i	−0.00916361	+	0.0754692i
$496$	10.7307	+	28.2945i	0.481822	+	1.27046i
$497$	42.8832	+	22.5068i	1.92357	+	1.00957i
$498$	−0.942109	+	2.48414i	−0.0422169	+	0.111317i
$499$	−24.9250	+	13.0817i	−1.11580	+	0.585616i	−0.918774	−	0.394783i	$-0.870820\pi$
$499$	−24.9250	+	13.0817i	−1.11580	+	0.585616i	−0.197023	+	0.980399i	$0.563127\pi$
$500$	0.394023	−	0.206799i	0.0176213	−	0.00924835i
$501$	11.0249	−	2.71739i	0.492556	−	0.121404i
$502$	2.21580	−	18.2488i	0.0988962	−	0.814483i
$503$	−2.79835	−	2.47912i	−0.124772	−	0.110539i	0.598429	−	0.801176i	$-0.295792\pi$
$503$	−2.79835	−	2.47912i	−0.124772	−	0.110539i	−0.723202	+	0.690637i	$0.757330\pi$
$504$	7.37770	+	10.6884i	0.328629	+	0.476101i
$505$	−2.10275	+	5.54449i	−0.0935711	+	0.246727i
$506$	−9.27911			−0.412507
$507$	−11.7399	−	5.58350i	−0.521386	−	0.247972i
$508$	0.917019			0.0406862
$509$	10.9507	−	28.8746i	0.485381	−	1.27985i	−0.439038	−	0.898468i	$-0.644681\pi$
$509$	10.9507	−	28.8746i	0.485381	−	1.27985i	0.924420	−	0.381377i	$-0.124550\pi$
$510$	0.866767	+	1.25573i	0.0383811	+	0.0556046i
$511$	−3.50886	−	3.10858i	−0.155223	−	0.137515i
$512$	−2.58434	+	21.2839i	−0.114213	+	0.940625i
$513$	−7.15358	+	1.76320i	−0.315838	+	0.0778472i
$514$	8.66704	−	4.54881i	0.382287	−	0.200640i
$515$	3.36458	−	1.76587i	0.148261	−	0.0778134i
$516$	0.220076	−	0.580293i	0.00968832	−	0.0255460i
$517$	25.4973	+	13.3820i	1.12137	+	0.588540i
$518$	3.92773	+	10.3566i	0.172574	+	0.455042i
$519$	−2.90638	+	23.9362i	−0.127576	+	1.05068i
$520$	−5.94190	+	4.27655i	−0.260570	+	0.187539i
$521$	−0.569690	−	4.69182i	−0.0249586	−	0.205552i	0.974895	−	0.222665i	$-0.0714756\pi$
$521$	−0.569690	−	4.69182i	−0.0249586	−	0.205552i	−0.999854	+	0.0171129i	$0.994553\pi$
$522$	12.4453	−	6.53181i	0.544717	−	0.285890i
$523$	0.975583	+	8.03465i	0.0426593	+	0.351331i	0.998372	+	0.0570309i	$0.0181634\pi$
$523$	0.975583	+	8.03465i	0.0426593	+	0.351331i	−0.955713	+	0.294300i	$0.904914\pi$
$524$	−0.0350191	+	0.0183794i	−0.00152982	+	0.000802909i
$525$	−15.6142	−	13.8330i	−0.681459	−	0.603720i
$526$	34.3919			1.49956
$527$	7.98785	−	7.07662i	0.347956	−	0.308262i
$528$	−8.46107	−	4.44071i	−0.368221	−	0.193257i
$529$	−15.2291			−0.662133
$530$	−0.916707			−0.0398192
$531$	−3.67530	−	1.92894i	−0.159494	−	0.0837091i
$532$	2.15080	+	0.530124i	0.0932489	+	0.0229838i
$533$	8.32996	−	9.78413i	0.360811	−	0.423798i
$534$	13.0511	−	3.21680i	0.564775	−	0.139205i
$535$	−12.2420	−	3.01739i	−0.529268	−	0.130453i
$536$	12.7347	−	33.5787i	0.550056	−	1.45038i
$537$	0.147947	+	1.21846i	0.00638440	+	0.0525802i
$538$	31.3662	−	7.73107i	1.35229	−	0.333310i
$539$	−33.3093	−	8.20999i	−1.43473	−	0.353629i
$540$	−0.0267019	+	0.0386843i	−0.00114907	+	0.00166471i
$541$	−0.0901764	−	0.742669i	−0.00387699	−	0.0319298i	0.990642	−	0.136486i	$-0.0435809\pi$
$541$	−0.0901764	−	0.742669i	−0.00387699	−	0.0319298i	−0.994519	+	0.104556i	$0.966658\pi$
$542$	3.82808	+	10.0938i	0.164430	+	0.433567i
$543$	−2.86351	+	1.50288i	−0.122885	+	0.0644949i
$544$	−0.514165	+	0.126730i	−0.0220446	+	0.00543351i
$545$	−3.54981	+	9.36008i	−0.152057	+	0.400942i
$546$	−20.1765	−	13.3480i	−0.863475	−	0.571243i
$547$	−12.0696	−	31.8249i	−0.516059	−	1.36073i	−0.899400	−	0.437128i	$-0.855996\pi$
$547$	−12.0696	−	31.8249i	−0.516059	−	1.36073i	0.383341	−	0.923607i	$-0.374773\pi$
$548$	−0.0510178	−	0.0739121i	−0.00217937	−	0.00315737i
$549$	0.366911	−	0.325055i	0.0156594	−	0.0138730i
$550$	14.4369	+	3.55839i	0.615594	+	0.151730i
$551$	−25.5576	+	67.3897i	−1.08879	+	2.87090i
$552$	6.86465	+	3.60285i	0.292179	+	0.153347i
$553$	7.66185	−	20.2026i	0.325815	−	0.859104i
$554$	10.4855	−	9.28932i	0.445485	−	0.394665i
$555$	0.902127	−	0.799214i	0.0382931	−	0.0339248i
$556$	−0.165261	+	0.239422i	−0.00700863	+	0.0101537i
$557$	0.400470	−	0.580182i	0.0169685	−	0.0245831i	−0.814408	−	0.580293i	$-0.802938\pi$
$557$	0.400470	−	0.580182i	0.0169685	−	0.0245831i	0.831376	+	0.555710i	$0.187553\pi$
$558$	9.33385	+	4.89878i	0.395133	+	0.207382i
$559$	−0.684349	−	34.7495i	−0.0289449	−	1.46975i
$560$	−12.4519	+	6.53526i	−0.526188	+	0.276165i
$561$	−0.406188	+	3.34526i	−0.0171493	+	0.141237i
$562$	18.2245	−	4.49194i	0.768755	−	0.189481i
$563$	3.73398	−	5.40960i	0.157368	−	0.227988i	−0.736367	−	0.676583i	$-0.763460\pi$
$563$	3.73398	−	5.40960i	0.157368	−	0.227988i	0.893735	+	0.448595i	$0.148075\pi$
$564$	0.454588	+	0.658585i	0.0191416	+	0.0277314i
$565$	8.06154	+	7.14190i	0.339152	+	0.300462i
$566$	0.130441	−	1.07428i	0.00548283	−	0.0451552i
$567$	4.53421	+	1.11758i	0.190419	+	0.0469340i
$568$	25.5384	+	13.4036i	1.07157	+	0.562401i
$569$	−4.82649	+	39.7497i	−0.202337	+	1.66640i	0.438509	+	0.898727i	$0.355507\pi$
$569$	−4.82649	+	39.7497i	−0.202337	+	1.66640i	−0.640846	+	0.767669i	$0.721416\pi$
$570$	−0.931581	−	7.67226i	−0.0390196	−	0.321356i
$571$	0.680894	−	0.986446i	0.0284945	−	0.0412815i	−0.808478	−	0.588527i	$-0.799708\pi$
$571$	0.680894	−	0.986446i	0.0284945	−	0.0412815i	0.836972	+	0.547245i	$0.184324\pi$
$572$	0.535043	+	0.0542991i	0.0223713	+	0.00227036i
$573$	13.5854	+	19.6818i	0.567538	+	0.822220i
$574$	17.8989	−	15.8570i	0.747085	−	0.661860i
$575$	−12.0905	−	2.98003i	−0.504207	−	0.124276i
$576$	4.38896	+	6.35850i	0.182873	+	0.264938i
$577$	−21.9418			−0.913448			−0.456724	−	0.889608i	$-0.650977\pi$
$577$	−21.9418			−0.913448			−0.456724	+	0.889608i	$0.650977\pi$
$578$	−12.1484	−	17.6000i	−0.505307	−	0.732064i
$579$	−1.34240	−	11.0557i	−0.0557883	−	0.459458i
$580$	0.163055	+	0.429939i	0.00677047	+	0.0178523i
$581$	−1.04085	+	8.57218i	−0.0431818	+	0.355634i
$582$	−3.23731	−	8.53607i	−0.134191	−	0.353832i
$583$	−1.51542	−	1.34254i	−0.0627621	−	0.0556024i
$584$	−2.08965	−	1.85126i	−0.0864701	−	0.0766059i
$585$	−0.579521	+	2.56779i	−0.0239602	+	0.106165i
$586$	−30.4593	+	26.9846i	−1.25826	+	1.11472i
$587$	11.3880			0.470033			0.235016	−	0.971991i	$-0.424486\pi$
$587$	11.3880			0.470033			0.235016	+	0.971991i	$0.424486\pi$
$588$	−0.713614	−	0.632207i	−0.0294289	−	0.0260718i
$589$	−52.4834	+	12.9360i	−2.16254	+	0.533019i
$590$	2.47340	−	3.58334i	0.101828	−	0.147524i
$591$	5.68182	+	14.9817i	0.233719	+	0.616266i
$592$	2.41447	+	6.36644i	0.0992342	+	0.261659i
$593$	1.23977	−	1.79612i	0.0509113	−	0.0737578i	−0.796702	−	0.604373i	$-0.793424\pi$
$593$	1.23977	−	1.79612i	0.0509113	−	0.0737578i	0.847613	+	0.530615i	$0.178039\pi$
$594$	−3.23193	+	0.796600i	−0.132608	+	0.0326849i
$595$	3.71207	+	3.28860i	0.152180	+	0.134820i
$596$	−1.04516			−0.0428112
$597$	−7.19551	+	6.37467i	−0.294493	+	0.260898i
$598$	−14.3674	−	1.45808i	−0.587527	−	0.0596255i
$599$	12.8629	+	11.3955i	0.525563	+	0.465608i	0.883695	−	0.468063i	$-0.155048\pi$
$599$	12.8629	+	11.3955i	0.525563	+	0.465608i	−0.358132	+	0.933671i	$0.616586\pi$
$600$	−9.29877	−	8.23799i	−0.379621	−	0.336315i
$601$	−13.7761	−	36.3246i	−0.561939	−	1.48171i	−0.851397	−	0.524522i	$-0.824244\pi$
$601$	−13.7761	−	36.3246i	−0.561939	−	1.48171i	0.289458	−	0.957191i	$-0.406525\pi$
$602$	7.79621	−	64.2075i	0.317750	−	2.61690i
$603$	−4.57904	−	12.0739i	−0.186473	−	0.491689i
$604$	−0.154365	−	1.27131i	−0.00628101	−	0.0517287i
$605$	2.33613	+	3.38447i	0.0949774	+	0.137598i
$606$	−11.6698			−0.474051
$607$	6.24358	+	9.04538i	0.253419	+	0.367141i	0.928959	−	0.370183i	$-0.120705\pi$
$607$	6.24358	+	9.04538i	0.253419	+	0.367141i	−0.675540	+	0.737323i	$0.736089\pi$
$608$	2.60435	+	0.641914i	0.105620	+	0.0260331i
$609$	34.1941	−	30.2933i	1.38561	−	1.22755i
$610$	0.292100	+	0.423180i	0.0118268	+	0.0171341i
$611$	37.3762	+	24.7267i	1.51208	+	1.00034i
$612$	−0.0531984	+	0.0770712i	−0.00215042	+	0.00311542i
$613$	2.34993	+	19.3534i	0.0949129	+	0.781678i	0.959989	+	0.280038i	$0.0903469\pi$
$613$	2.34993	+	19.3534i	0.0949129	+	0.781678i	−0.865076	+	0.501641i	$0.832730\pi$
$614$	1.70174	−	14.0151i	0.0686765	−	0.565602i
$615$	−2.30392	−	1.20919i	−0.0929031	−	0.0487593i
$616$	−29.2139	−	7.20059i	−1.17706	−	0.290120i
$617$	2.62442	−	21.6141i	0.105655	−	0.870149i	−0.839462	−	0.543418i	$-0.817130\pi$
$617$	2.62442	−	21.6141i	0.105655	−	0.870149i	0.945117	−	0.326731i	$-0.105947\pi$
$618$	5.59733	+	4.95880i	0.225158	+	0.199472i
$619$	−19.8803	−	28.8015i	−0.799055	−	1.15763i	−0.984570	−	0.174990i	$-0.944011\pi$
$619$	−19.8803	−	28.8015i	−0.799055	−	1.15763i	0.185515	−	0.982641i	$-0.440605\pi$
$620$	−0.195903	+	0.283814i	−0.00786764	+	0.0113982i
$621$	2.70664	−	0.667126i	0.108614	−	0.0267709i
$622$	−0.607077	+	4.99973i	−0.0243416	+	0.200471i
$623$	38.6842	−	20.3030i	1.54985	−	0.813423i
$624$	−12.4030	−	8.20537i	−0.496517	−	0.328478i
$625$	15.3084	+	8.03444i	0.612334	+	0.321378i
$626$	−11.0535	+	16.0138i	−0.441789	+	0.640041i
$627$	9.69621	−	14.0474i	0.387230	−	0.560999i
$628$	−0.744161	+	0.659269i	−0.0296953	+	0.0263077i
$629$	1.79732	−	1.59228i	0.0716637	−	0.0634885i
$630$	−1.73710	+	4.58035i	−0.0692076	+	0.182485i
$631$	−11.0758	−	5.81302i	−0.440920	−	0.231413i	0.229629	−	0.973278i	$-0.426249\pi$
$631$	−11.0758	−	5.81302i	−0.440920	−	0.231413i	−0.670548	+	0.741866i	$0.733941\pi$
$632$	4.56289	−	12.0314i	0.181502	−	0.478582i
$633$	−3.13709	−	0.773223i	−0.124688	−	0.0307328i
$634$	11.8996	−	10.5422i	0.472595	−	0.418682i
$635$	−5.90724	−	8.55811i	−0.234422	−	0.339618i
$636$	−0.0199513	−	0.0526073i	−0.000791122	−	0.00208602i
$637$	−50.2847	−	17.9461i	−1.99235	−	0.711052i
$638$	−11.5467	+	30.4462i	−0.457139	+	1.20538i
$639$	10.0694	−	2.48189i	0.398340	−	0.0981821i
$640$	−7.64702	+	4.01347i	−0.302275	+	0.158646i
$641$	3.85772	+	10.1720i	0.152371	+	0.401769i	0.989367	−	0.145440i	$-0.0464597\pi$
$641$	3.85772	+	10.1720i	0.152371	+	0.401769i	−0.836996	+	0.547209i	$0.815690\pi$
$642$	−2.99087	−	24.6321i	−0.118040	−	0.972150i
$643$	−2.35810	+	3.41630i	−0.0929944	+	0.134726i	−0.866720	−	0.498796i	$-0.833776\pi$
$643$	−2.35810	+	3.41630i	−0.0929944	+	0.134726i	0.773725	+	0.633521i	$0.218391\pi$
$644$	−0.813779	−	0.200578i	−0.0320674	−	0.00790390i
$645$	−6.83329	+	1.68425i	−0.269061	+	0.0663175i
$646$	−1.85600	−	15.2855i	−0.0730233	−	0.601401i
$647$	−6.53898	+	17.2419i	−0.257074	+	0.677848i	0.742891	+	0.669413i	$0.233454\pi$
$647$	−6.53898	+	17.2419i	−0.257074	+	0.677848i	−0.999964	+	0.00843518i	$0.997315\pi$
$648$	2.70027	+	0.665558i	0.106077	+	0.0261456i
$649$	9.33668	−	2.30129i	0.366497	−	0.0903334i
$650$	21.7945	+	7.77824i	0.854849	+	0.305088i
$651$	33.2660	+	8.19932i	1.30380	+	0.321357i
$652$	−0.533500	−	0.280002i	−0.0208935	−	0.0109657i
$653$	13.2595			0.518882			0.259441	−	0.965759i	$-0.416462\pi$
$653$	13.2595			0.518882			0.259441	+	0.965759i	$0.416462\pi$
$654$	−19.7006			−0.770354
$655$	0.397112	+	0.208420i	0.0155164	+	0.00814366i
$656$	11.0029	−	9.74771i	0.429591	−	0.380584i
$657$	−1.00383			−0.0391631
$658$	62.4244	+	55.3032i	2.43356	+	2.15594i
$659$	−12.8564	+	6.74758i	−0.500816	+	0.262848i	−0.696160	−	0.717886i	$-0.745110\pi$
$659$	−12.8564	+	6.74758i	−0.500816	+	0.262848i	0.195345	+	0.980735i	$0.437417\pi$
$660$	−0.0131261	−	0.108104i	−0.000510934	−	0.00420792i
$661$	−12.4345	+	6.52613i	−0.483646	+	0.253837i	−0.688879	−	0.724876i	$-0.741897\pi$
$661$	−12.4345	+	6.52613i	−0.483646	+	0.253837i	0.205233	+	0.978713i	$0.434205\pi$
$662$	2.60711	+	21.4715i	0.101328	+	0.834514i
$663$	−1.15459	+	5.11584i	−0.0448404	+	0.198683i
$664$	−0.619862	+	5.10502i	−0.0240553	+	0.198113i
$665$	−8.90757	−	23.4873i	−0.345421	−	0.910800i
$666$	2.10017	+	1.10226i	0.0813801	+	0.0427116i
$667$	9.66999	−	25.4977i	0.374424	−	0.987274i
$668$	−0.647316	+	0.339738i	−0.0250454	+	0.0131448i
$669$	11.1289	−	5.84091i	0.430269	−	0.225822i
$670$	13.1521	−	3.24170i	0.508109	−	0.125238i
$671$	−0.136885	+	1.12735i	−0.00528439	+	0.0435209i
$672$	−1.27257	−	1.12740i	−0.0490905	−	0.0434904i
$673$	18.4176	+	26.6825i	0.709946	+	1.02853i	0.997493	+	0.0707679i	$0.0225450\pi$
$673$	18.4176	+	26.6825i	0.709946	+	1.02853i	−0.287547	+	0.957767i	$0.592840\pi$
$674$	4.51248	−	11.8984i	0.173814	−	0.458311i
$675$	−4.46697			−0.171934
$676$	0.819908	+	0.168149i	0.0315349	+	0.00646728i
$677$	25.6449			0.985613			0.492806	−	0.870139i	$-0.335971\pi$
$677$	25.6449			0.985613			0.492806	+	0.870139i	$0.335971\pi$
$678$	−7.51595	+	19.8179i	−0.288648	+	0.761103i
$679$	−16.8558	−	24.4199i	−0.646867	−	0.937149i
$680$	2.21066	+	1.95847i	0.0847749	+	0.0751040i
$681$	−0.756527	+	6.23056i	−0.0289902	+	0.238756i
$682$	−23.7116	+	5.84439i	−0.907964	+	0.223793i
$683$	42.0759	−	22.0832i	1.60999	−	0.844988i	0.611434	−	0.791296i	$-0.290593\pi$
$683$	42.0759	−	22.0832i	1.60999	−	0.844988i	0.998558	−	0.0536927i	$-0.0170991\pi$
$684$	0.420015	−	0.220441i	0.0160597	−	0.00842877i
$685$	−0.361141	+	0.952252i	−0.0137985	+	0.0363837i
$686$	−46.3887	−	24.3467i	−1.77113	−	0.929560i
$687$	5.70579	+	15.0449i	0.217690	+	0.574000i
$688$	4.79252	−	39.4699i	0.182713	−	1.50478i
$689$	−2.13545	−	2.31687i	−0.0813542	−	0.0882656i
$690$	0.352474	+	2.90289i	0.0134185	+	0.110511i
$691$	−2.90178	+	1.52297i	−0.110389	+	0.0579366i	−0.519014	−	0.854766i	$-0.673701\pi$
$691$	−2.90178	+	1.52297i	−0.110389	+	0.0579366i	0.408625	+	0.912702i	$0.366008\pi$
$692$	−0.187120	−	1.54107i	−0.00711323	−	0.0585827i
$693$	−9.57965	+	5.02779i	−0.363901	+	0.190990i
$694$	−31.5092	−	27.9147i	−1.19607	−	1.05963i
$695$	3.29899			0.125138
$696$	20.3637	−	18.0407i	0.771885	−	0.683830i
$697$	−4.59013	−	2.40909i	−0.173864	−	0.0912506i
$698$	19.6578			0.744058
$699$	−13.8343			−0.523263
$700$	1.18920	+	0.624142i	0.0449477	+	0.0235903i
$701$	−42.2288	−	10.4085i	−1.59496	−	0.393122i	−0.660968	−	0.750415i	$-0.729854\pi$
$701$	−42.2288	−	10.4085i	−1.59496	−	0.393122i	−0.933993	+	0.357292i	$0.883700\pi$
$702$	−5.12938	+	0.725571i	−0.193596	+	0.0273849i
$703$	−11.8091	+	2.91068i	−0.445389	+	0.109778i
$704$	−17.3792	−	4.28360i	−0.655005	−	0.161444i
$705$	3.21791	−	8.48493i	0.121193	−	0.319561i
$706$	4.68229	+	38.5621i	0.176220	+	1.45130i
$707$	−36.8271	+	9.07708i	−1.38503	+	0.341379i
$708$	0.259469	+	0.0639535i	0.00975146	+	0.00240352i
$709$	−17.3689	+	25.1633i	−0.652304	+	0.945026i	0.347668	+	0.937618i	$0.386974\pi$
$709$	−17.3689	+	25.1633i	−0.652304	+	0.945026i	−0.999973	+	0.00740845i	$0.997642\pi$
$710$	1.31130	+	10.7995i	0.0492122	+	0.405299i
$711$	−1.64069	−	4.32613i	−0.0615305	−	0.162243i
$712$	23.0377	−	12.0911i	0.863375	−	0.453134i
$713$	19.8577	−	4.89448i	0.743676	−	0.183300i
$714$	−3.46084	+	9.12548i	−0.129519	+	0.341513i
$715$	−2.93988	−	5.34309i	−0.109945	−	0.199820i
$716$	−0.0280221	−	0.0738881i	−0.00104723	−	0.00276133i
$717$	−2.02117	−	2.92817i	−0.0754820	−	0.109355i
$718$	−12.1111	+	10.7295i	−0.451982	+	0.400421i
$719$	44.8907	+	11.0646i	1.67414	+	0.412639i	0.958332	−	0.285656i	$-0.0922116\pi$
$719$	44.8907	+	11.0646i	1.67414	+	0.412639i	0.715810	+	0.698295i	$0.246058\pi$
$720$	−1.06784	+	2.81565i	−0.0397959	+	0.104933i
$721$	21.5210	+	11.2951i	0.801485	+	0.420652i
$722$	−17.9763	+	47.3996i	−0.669009	+	1.76403i
$723$	−16.3210	+	14.4591i	−0.606983	+	0.537740i
$724$	0.155846	−	0.138068i	0.00579199	−	0.00513125i
$725$	−24.8231	+	35.9624i	−0.921905	+	1.33561i
$726$	−4.59745	+	6.66055i	−0.170627	+	0.247196i
$727$	−11.2031	−	5.87982i	−0.415498	−	0.218070i	0.244002	−	0.969775i	$-0.421540\pi$
$727$	−11.2031	−	5.87982i	−0.415498	−	0.218070i	−0.659500	+	0.751704i	$0.729232\pi$
$728$	−44.1023	−	15.7397i	−1.63454	−	0.583352i
$729$	0.885456	−	0.464723i	0.0327947	−	0.0172120i
$730$	0.126926	−	1.04533i	0.00469774	−	0.0386894i
$731$	−13.6140	+	3.35556i	−0.503534	+	0.124110i
$732$	−0.0179279	+	0.0259730i	−0.000662633	+	0.000959989i
$733$	−14.9092	−	21.5997i	−0.550683	−	0.797801i	0.444506	−	0.895776i	$-0.353379\pi$
$733$	−14.9092	−	21.5997i	−0.550683	−	0.797801i	−0.995189	+	0.0979743i	$0.968764\pi$
$734$	−31.3515	−	27.7750i	−1.15720	−	1.02519i
$735$	−1.30315	+	10.7324i	−0.0480672	+	0.395869i
$736$	−0.985385	−	0.242876i	−0.0363218	−	0.00895251i
$737$	26.4893	+	13.9027i	0.975748	+	0.512112i
$738$	0.617219	−	5.08325i	0.0227201	−	0.187117i
$739$	−0.649324	−	5.34766i	−0.0238858	−	0.196717i	0.975881	−	0.218302i	$-0.0700518\pi$
$739$	−0.649324	−	5.34766i	−0.0238858	−	0.196717i	−0.999767	+	0.0215851i	$0.993129\pi$
$740$	−0.0440793	+	0.0638599i	−0.00162039	+	0.00234754i
$741$	17.2206	−	20.2268i	0.632615	−	0.743051i
$742$	−3.33089	−	4.82563i	−0.122281	−	0.177155i
$743$	−5.95902	+	5.27923i	−0.218615	+	0.193676i	−0.765321	−	0.643648i	$-0.777420\pi$
$743$	−5.95902	+	5.27923i	−0.218615	+	0.193676i	0.546706	+	0.837324i	$0.315881\pi$
$744$	19.8110	+	4.88297i	0.726307	+	0.179018i
$745$	6.73266	+	9.75395i	0.246666	+	0.357357i
$746$	13.4619			0.492876
$747$	1.05041	+	1.52178i	0.0384325	+	0.0556791i
$748$	−0.0261514	−	0.215376i	−0.000956189	−	0.00787492i
$749$	−28.5981	−	75.4069i	−1.04495	−	2.75531i
$750$	1.19702	−	9.85834i	0.0437090	−	0.359976i
$751$	1.28873	+	3.39811i	0.0470265	+	0.123999i	0.956472	−	0.291825i	$-0.0942625\pi$
$751$	1.28873	+	3.39811i	0.0470265	+	0.123999i	−0.909445	+	0.415824i	$0.863493\pi$
$752$	38.3738	+	33.9962i	1.39935	+	1.23971i
$753$	−9.57668	−	8.48420i	−0.348994	−	0.309182i
$754$	−22.6627	+	45.3273i	−0.825326	+	1.65072i
$755$	−10.8701	+	9.63010i	−0.395605	+	0.350475i
$756$	−0.300660			−0.0109349
$757$	−14.9759	−	13.2675i	−0.544309	−	0.482216i	0.345582	−	0.938388i	$-0.387681\pi$
$757$	−14.9759	−	13.2675i	−0.544309	−	0.482216i	−0.889891	+	0.456173i	$0.849220\pi$
$758$	−11.9941	+	2.95629i	−0.435647	+	0.107377i
$759$	−3.66867	+	5.31499i	−0.133164	+	0.192922i
$760$	−5.30476	−	13.9875i	−0.192424	−	0.507380i
$761$	2.84921	+	7.51276i	0.103284	+	0.272337i	0.976690	−	0.214656i	$-0.0688630\pi$
$761$	2.84921	+	7.51276i	0.103284	+	0.272337i	−0.873406	+	0.486993i	$0.838094\pi$
$762$	11.6253	−	16.8421i	0.421140	−	0.610126i
$763$	−62.1707	+	15.3237i	−2.25073	+	0.554755i
$764$	−1.15250	−	1.02102i	−0.0416959	−	0.0369393i
$765$	1.06196			0.0383953
$766$	−9.69015	+	8.58473i	−0.350119	+	0.310179i
$767$	14.8182	−	2.09609i	0.535054	−	0.0756855i
$768$	−1.15540	−	1.02359i	−0.0416918	−	0.0369357i
$769$	−1.09416	−	0.969345i	−0.0394566	−	0.0349555i	0.643164	−	0.765728i	$-0.277621\pi$
$769$	−1.09416	−	0.969345i	−0.0394566	−	0.0349555i	−0.682621	+	0.730773i	$0.739160\pi$
$770$	−4.02437	−	10.6114i	−0.145028	−	0.382408i
$771$	0.821160	−	6.76286i	0.0295734	−	0.243559i
$772$	0.254258	+	0.670424i	0.00915096	+	0.0241291i
$773$	4.39285	+	36.1784i	0.158000	+	1.30125i	0.828773	+	0.559585i	$0.189039\pi$
$773$	4.39285	+	36.1784i	0.158000	+	1.30125i	−0.670773	+	0.741662i	$0.734038\pi$
$774$	−7.86781	−	11.3985i	−0.282802	−	0.409710i
$775$	−32.7727			−1.17723
$776$	−10.0382	−	14.5429i	−0.360351	−	0.522058i
$777$	7.48505	+	1.84490i	0.268525	+	0.0661854i
$778$	3.40505	−	3.01662i	0.122077	−	0.108151i
$779$	14.9160	+	21.6096i	0.534422	+	0.774243i
$780$	−0.00333704	−	0.169446i	−0.000119485	−	0.00606714i
$781$	−13.6485	+	19.7732i	−0.488380	+	0.707541i
$782$	0.702238	+	5.78345i	0.0251120	+	0.206816i
$783$	1.17914	−	9.71105i	0.0421389	−	0.347045i
$784$	−54.0815	−	28.3841i	−1.93148	−	1.01372i
$785$	10.9464	+	2.69804i	0.390693	+	0.0962972i
$786$	−0.106386	+	0.876167i	−0.00379466	+	0.0312518i
$787$	−41.0736	−	36.3881i	−1.46412	−	1.29709i	−0.870327	−	0.492474i	$-0.836092\pi$
$787$	−41.0736	−	36.3881i	−1.46412	−	1.29709i	−0.593790	−	0.804620i	$-0.702369\pi$
$788$	−0.586015	−	0.848989i	−0.0208759	−	0.0302440i
$789$	13.5975	−	19.6994i	0.484084	−	0.701317i
$790$	4.71243	−	1.16151i	0.167661	−	0.0413247i
$791$	−8.30370	+	68.3871i	−0.295246	+	2.43157i
$792$	−5.70500	+	2.99422i	−0.202718	+	0.106395i
$793$	−0.389095	+	1.72404i	−0.0138172	+	0.0612224i
$794$	41.5524	+	21.8084i	1.47464	+	0.773951i
$795$	−0.362438	+	0.525082i	−0.0128543	+	0.0186227i
$796$	0.351584	−	0.509357i	0.0124616	−	0.0180537i
$797$	−13.0896	+	11.5964i	−0.463657	+	0.410764i	−0.862344	−	0.506323i	$-0.831004\pi$
$797$	−13.0896	+	11.5964i	−0.463657	+	0.410764i	0.398687	+	0.917087i	$0.369466\pi$
$798$	37.0026	−	32.7814i	1.30988	−	1.16045i
$799$	6.41107	−	16.9046i	0.226808	−	0.598042i
$800$	1.43998	+	0.755758i	0.0509109	+	0.0267201i
$801$	3.31744	−	8.74736i	0.117216	−	0.309073i
$802$	3.95997	+	0.976045i	0.139831	+	0.0344653i
$803$	1.74073	−	1.54215i	0.0614291	−	0.0544214i
$804$	0.472276	+	0.684210i	0.0166559	+	0.0241302i
$805$	3.37028	+	8.88670i	0.118787	+	0.313215i
$806$	−37.6325	+	5.32327i	−1.32555	+	0.187504i
$807$	7.97293	−	21.0229i	0.280660	−	0.740041i
$808$	−21.9318	+	5.40570i	−0.771558	+	0.190172i
$809$	−7.52530	+	3.94958i	−0.264576	+	0.138860i	−0.591795	−	0.806088i	$-0.701581\pi$
$809$	−7.52530	+	3.94958i	−0.264576	+	0.138860i	0.327220	+	0.944948i	$0.393888\pi$
$810$	0.371977	+	0.980822i	0.0130699	+	0.0344626i
$811$	3.34890	+	27.5806i	0.117596	+	0.968487i	0.925388	+	0.379021i	$0.123739\pi$
$811$	3.34890	+	27.5806i	0.117596	+	0.968487i	−0.807793	+	0.589467i	$0.799338\pi$
$812$	−1.67078	+	2.42054i	−0.0586327	+	0.0849442i
$813$	7.29516	+	1.79810i	0.255853	+	0.0630620i
$814$	−5.33526	+	1.31502i	−0.187001	+	0.0460916i
$815$	0.823559	+	6.78262i	0.0288480	+	0.237585i
$816$	−2.12746	+	5.60966i	−0.0744761	+	0.196377i
$817$	68.9579	+	16.9966i	2.41253	+	0.594636i
$818$	−36.7444	+	9.05667i	−1.28474	+	0.316659i
$819$	−15.6228	+	6.27952i	−0.545905	+	0.219424i
$820$	0.162653	+	0.0400903i	0.00568008	+	0.00140001i
$821$	−11.1347	−	5.84392i	−0.388602	−	0.203954i	0.259095	−	0.965852i	$-0.416576\pi$
$821$	−11.1347	−	5.84392i	−0.388602	−	0.203954i	−0.647698	+	0.761898i	$0.724268\pi$
$822$	−2.00425			−0.0699062
$823$	19.4712			0.678722			0.339361	−	0.940656i	$-0.389789\pi$
$823$	19.4712			0.678722			0.339361	+	0.940656i	$0.389789\pi$
$824$	12.8165	+	6.72661i	0.446484	+	0.234333i
$825$	7.74614	−	6.86248i	0.269686	−	0.238921i
$826$	27.8502			0.969033
$827$	−3.43484	−	3.04300i	−0.119441	−	0.105816i	0.601288	−	0.799032i	$-0.294654\pi$
$827$	−3.43484	−	3.04300i	−0.119441	−	0.105816i	−0.720729	+	0.693217i	$0.756193\pi$
$828$	−0.158917	+	0.0834063i	−0.00552276	+	0.00289857i
$829$	−0.131149	−	1.08011i	−0.00455500	−	0.0375138i	0.990254	−	0.139272i	$-0.0444763\pi$
$829$	−0.131149	−	1.08011i	−0.00455500	−	0.0375138i	−0.994809	+	0.101758i	$0.967553\pi$
$830$	−1.71751	+	0.901419i	−0.0596156	+	0.0312887i
$831$	−1.17521	−	9.67870i	−0.0407675	−	0.335750i
$832$	−26.2363	−	9.36347i	−0.909578	−	0.324620i
$833$	−2.59627	+	21.3822i	−0.0899555	+	0.740850i
$834$	2.30221	+	6.07042i	0.0797189	+	0.210202i
$835$	7.34048	+	3.85258i	0.254028	+	0.133324i
$836$	−0.389688	+	1.02752i	−0.0134776	+	0.0355376i
$837$	6.49629	−	3.40952i	0.224545	−	0.117850i
$838$	44.2734	−	23.2365i	1.52940	−	0.802691i
$839$	15.7410	−	3.87982i	0.543441	−	0.133946i	0.0419672	−	0.999119i	$-0.486638\pi$
$839$	15.7410	−	3.87982i	0.543441	−	0.133946i	0.501474	+	0.865173i	$0.332791\pi$
$840$	−1.14293	+	9.41284i	−0.0394347	+	0.324774i
$841$	−49.9218	−	44.2269i	−1.72144	−	1.52507i
$842$	−3.33955	−	4.83817i	−0.115088	−	0.166734i
$843$	4.63247	−	12.2148i	0.159551	−	0.420701i
$844$	0.208018			0.00716028
$845$	−3.71241	−	8.73500i	−0.127711	−	0.300493i
$846$	17.8586			0.613992
$847$	−9.32775	+	24.5953i	−0.320505	+	0.845103i
$848$	−2.04758	−	2.96643i	−0.0703143	−	0.101868i
$849$	−0.563764	−	0.499451i	−0.0193483	−	0.0171411i
$850$	1.12528	−	9.26751i	0.0385968	−	0.317873i
$851$	4.46811	−	1.10129i	0.153165	−	0.0377517i
$852$	−0.591216	+	0.310294i	−0.0202547	+	0.0106305i
$853$	29.5905	−	15.5303i	1.01316	−	0.531747i	0.125426	−	0.992103i	$-0.459970\pi$
$853$	29.5905	−	15.5303i	1.01316	−	0.531747i	0.887735	+	0.460356i	$0.152278\pi$
$854$	−1.16630	+	3.07529i	−0.0399100	+	0.105234i
$855$	−4.76292	−	2.49977i	−0.162888	−	0.0854904i
$856$	−17.0311	−	44.9074i	−0.582111	−	1.53490i
$857$	4.67661	−	38.5154i	0.159750	−	1.31566i	−0.663583	−	0.748102i	$-0.730965\pi$
$857$	4.67661	−	38.5154i	0.159750	−	1.31566i	0.823334	−	0.567558i	$-0.192112\pi$
$858$	7.78014	−	9.13832i	0.265610	−	0.311977i
$859$	−1.43824	−	11.8450i	−0.0490721	−	0.404145i	−0.996461	−	0.0840597i	$-0.973211\pi$
$859$	−1.43824	−	11.8450i	−0.0490721	−	0.404145i	0.947389	−	0.320086i	$-0.103712\pi$
$860$	0.401210	−	0.210571i	0.0136811	−	0.00718041i
$861$	−2.00610	−	16.5217i	−0.0683676	−	0.563058i
$862$	−7.26689	+	3.81396i	−0.247511	+	0.129904i
$863$	10.9772	+	9.72494i	0.373668	+	0.331041i	0.828967	−	0.559298i	$-0.188929\pi$
$863$	10.9772	+	9.72494i	0.373668	+	0.331041i	−0.455299	+	0.890339i	$0.650468\pi$
$864$	−0.364062			−0.0123857
$865$	−13.1767	+	11.6736i	−0.448022	+	0.396913i
$866$	5.47016	+	2.87096i	0.185884	+	0.0975592i
$867$	−14.8842			−0.505495
$868$	−2.20584			−0.0748712
$869$	9.49122	+	4.98137i	0.321967	+	0.168982i
$870$	9.96343	+	2.45576i	0.337792	+	0.0832582i
$871$	38.8305	+	25.6888i	1.31572	+	0.870433i
$872$	−37.0247	+	9.12578i	−1.25382	+	0.309038i
$873$	−6.16932	−	1.52060i	−0.208800	−	0.0514645i
$874$	10.4642	−	27.5919i	0.353958	−	0.933310i
$875$	−3.89058	−	32.0418i	−0.131526	−	1.08321i
$876$	0.0627510	−	0.0154667i	0.00212016	−	0.000522573i
$877$	43.4114	+	10.6999i	1.46590	+	0.361311i	0.889906	−	0.456144i	$-0.150770\pi$
$877$	43.4114	+	10.6999i	1.46590	+	0.361311i	0.575992	+	0.817456i	$0.304616\pi$
$878$	1.39831	−	2.02580i	0.0471907	−	0.0683675i
$879$	3.41386	+	28.1157i	0.115147	+	0.948317i
$880$	−2.47388	−	6.52309i	−0.0833945	−	0.219893i
$881$	−0.457093	+	0.239901i	−0.0153998	+	0.00808246i	−0.472406	−	0.881381i	$-0.656614\pi$
$881$	−0.457093	+	0.239901i	−0.0153998	+	0.00808246i	0.457006	+	0.889464i	$0.348922\pi$
$882$	−20.6579	+	5.09171i	−0.695587	+	0.171447i
$883$	−6.08541	+	16.0459i	−0.204790	+	0.539988i	−0.997582	−	0.0695054i	$-0.977858\pi$
$883$	−6.08541	+	16.0459i	−0.204790	+	0.539988i	0.792791	+	0.609493i	$0.208627\pi$
$884$	−0.00664841	−	0.337589i	−0.000223610	−	0.0113544i
$885$	−1.07460	−	2.83348i	−0.0361222	−	0.0952465i
$886$	−25.6035	−	37.0931i	−0.860166	−	1.24617i
$887$	−9.39125	+	8.31992i	−0.315327	+	0.279356i	−0.805909	−	0.592040i	$-0.798323\pi$
$887$	−9.39125	+	8.31992i	−0.315327	+	0.279356i	0.490582	+	0.871395i	$0.336784\pi$
$888$	4.45760	+	1.09870i	0.149587	+	0.0368700i
$889$	23.5865	−	62.1925i	0.791066	−	2.08587i
$890$	8.68953	+	4.56061i	0.291274	+	0.152872i
$891$	−0.821521	+	2.16617i	−0.0275220	+	0.0725695i
$892$	−0.605692	+	0.536596i	−0.0202801	+	0.0179666i
$893$	−68.5459	+	60.7263i	−2.29380	+	2.03213i
$894$	−13.2497	+	19.1955i	−0.443136	+	0.641994i
$895$	−0.509052	+	0.737488i	−0.0170157	+	0.0246515i
$896$	−48.9130	−	25.6715i	−1.63407	−	0.857626i
$897$	−6.51561	+	7.65305i	−0.217550	+	0.255528i
$898$	31.0759	−	16.3099i	1.03702	−	0.544268i
$899$	8.65092	−	71.2467i	0.288524	−	2.37621i
$900$	0.279238	−	0.0688259i	0.00930792	−	0.00229420i
$901$	−0.722089	+	1.04613i	−0.0240563	+	0.0348515i
$902$	6.73894	+	9.76304i	0.224382	+	0.325074i
$903$	−33.6951	−	29.8513i	−1.12130	−	0.993388i
$904$	−4.94513	+	40.7268i	−0.164473	+	1.35455i
$905$	−2.29245	−	0.565039i	−0.0762037	−	0.0187825i
$906$	−25.3060	−	13.2816i	−0.840734	−	0.441251i
$907$	−4.33513	+	35.7030i	−0.143946	+	1.18550i	0.724343	+	0.689439i	$0.242143\pi$
$907$	−4.33513	+	35.7030i	−0.143946	+	1.18550i	−0.868289	+	0.496059i	$0.834780\pi$
$908$	−0.0487071	−	0.401139i	−0.00161640	−	0.0133123i
$909$	−4.61386	+	6.68433i	−0.153032	+	0.221705i
$910$	−4.56375	−	17.0627i	−0.151287	−	0.565622i
$911$	−3.66711	−	5.31272i	−0.121497	−	0.176018i	0.757516	−	0.652816i	$-0.226413\pi$
$911$	−3.66711	−	5.31272i	−0.121497	−	0.176018i	−0.879013	+	0.476798i	$0.841797\pi$
$912$	22.7464	−	20.1515i	0.753208	−	0.667284i
$913$	−4.15938	−	1.02519i	−0.137655	−	0.0339290i
$914$	−4.19069	−	6.07127i	−0.138616	−	0.200820i
$915$	0.357881			0.0118312
$916$	−0.588487	−	0.852570i	−0.0194442	−	0.0281697i
$917$	0.345778	+	2.84774i	0.0114186	+	0.0940406i
$918$	0.741094	+	1.95410i	0.0244597	+	0.0644950i
$919$	−4.29561	+	35.3775i	−0.141699	+	1.16700i	0.732269	+	0.681015i	$0.238461\pi$
$919$	−4.29561	+	35.3775i	−0.141699	+	1.16700i	−0.873969	+	0.485982i	$0.838462\pi$
$920$	2.00712	+	5.29233i	0.0661726	+	0.174483i
$921$	−7.35489	−	6.51587i	−0.242352	−	0.214705i
$922$	14.1383	+	12.5255i	0.465622	+	0.412505i
$923$	−24.2398	+	28.4714i	−0.797864	+	0.937148i
$924$	0.521373	−	0.461896i	0.0171519	−	0.0151953i
$925$	−7.37405			−0.242457
$926$	−6.48544	−	5.74560i	−0.213125	−	0.188812i
$927$	5.05337	−	1.24554i	0.165974	−	0.0409090i
$928$	−2.02310	+	2.93097i	−0.0664116	+	0.0962138i
$929$	17.0018	+	44.8301i	0.557811	+	1.47083i	0.856333	+	0.516424i	$0.172737\pi$
$929$	17.0018	+	44.8301i	0.557811	+	1.47083i	−0.298522	+	0.954403i	$0.596494\pi$
$930$	2.72907	+	7.19596i	0.0894897	+	0.235965i
$931$	61.9763	−	89.7882i	2.03119	−	2.94269i
$932$	0.864807	−	0.213156i	0.0283277	−	0.00698215i
$933$	2.62378	+	2.32447i	0.0858988	+	0.0760997i
$934$	6.28885			0.205778
$935$	−1.84154	+	1.63146i	−0.0602248	+	0.0533546i
$936$	−9.30391	+	3.73967i	−0.304108	+	0.122235i
$937$	5.37835	+	4.76481i	0.175703	+	0.155659i	0.746391	−	0.665508i	$-0.231785\pi$
$937$	5.37835	+	4.76481i	0.175703	+	0.155659i	−0.570688	+	0.821167i	$0.693323\pi$
$938$	64.8532	+	57.4549i	2.11753	+	1.87597i
$939$	4.80235	+	12.6627i	0.156719	+	0.413233i
$940$	−0.0704232	+	0.579987i	−0.00229695	+	0.0189171i
$941$	8.84937	+	23.3339i	0.288481	+	0.760663i	0.998409	+	0.0563880i	$0.0179584\pi$
$941$	8.84937	+	23.3339i	0.288481	+	0.760663i	−0.709928	+	0.704275i	$0.751272\pi$
$942$	2.67433	+	22.0251i	0.0871345	+	0.717617i
$943$	−5.64364	−	8.17623i	−0.183782	−	0.266255i
$944$	17.1202			0.557216
$945$	1.93679	+	2.80592i	0.0630037	+	0.0912767i
$946$	31.1547	+	7.67894i	1.01293	+	0.249664i
$947$	35.7373	−	31.6604i	1.16130	−	1.02883i	0.162190	−	0.986760i	$-0.448144\pi$
$947$	35.7373	−	31.6604i	1.16130	−	1.02883i	0.999115	−	0.0420668i	$-0.0133942\pi$
$948$	0.169218	+	0.245154i	0.00549594	+	0.00796225i
$949$	2.93761	−	2.11428i	0.0953589	−	0.0686325i
$950$	−26.8619	+	38.9161i	−0.871514	+	1.26261i
$951$	−1.33370	−	10.9840i	−0.0432483	−	0.356182i
$952$	−2.27706	+	18.7533i	−0.0738001	+	0.607798i
$953$	−19.7654	−	10.3737i	−0.640263	−	0.336036i	0.113155	−	0.993577i	$-0.463904\pi$
$953$	−19.7654	−	10.3737i	−0.640263	−	0.336036i	−0.753418	+	0.657541i	$0.771597\pi$
$954$	−1.21912	−	0.300487i	−0.0394706	−	0.00972863i
$955$	−2.10460	+	17.3329i	−0.0681032	+	0.560881i
$956$	0.171463	+	0.151903i	0.00554552	+	0.00491290i
$957$	12.8741	+	18.6513i	0.416160	+	0.602912i
$958$	24.9661	−	36.1696i	0.806618	−	1.16859i
$959$	−6.32496	+	1.55896i	−0.204244	+	0.0503416i
$960$	−0.679921	+	5.59966i	−0.0219444	+	0.180728i
$961$	20.2120	−	10.6081i	0.651999	−	0.342196i
$962$	−8.46756	+	1.19777i	−0.273005	+	0.0386177i
$963$	−15.2915	−	8.02561i	−0.492762	−	0.258622i
$964$	0.797468	−	1.15533i	0.0256847	−	0.0372107i
$965$	4.61888	−	6.69160i	0.148687	−	0.215410i
$966$	−14.0003	+	12.4032i	−0.450453	+	0.399067i
$967$	44.4771	−	39.4033i	1.43029	−	1.26712i	0.519359	−	0.854556i	$-0.326171\pi$
$967$	44.4771	−	39.4033i	1.43029	−	1.26712i	0.910927	−	0.412567i	$-0.135368\pi$
$968$	−5.55499	+	14.6473i	−0.178544	+	0.470782i
$969$	−9.48922	−	4.98033i	−0.304838	−	0.159991i
$970$	2.36352	−	6.23210i	0.0758881	−	0.200101i
$971$	26.0930	+	6.43134i	0.837363	+	0.206391i	0.634604	−	0.772837i	$-0.281163\pi$
$971$	26.0930	+	6.43134i	0.837363	+	0.206391i	0.202759	+	0.979229i	$0.435009\pi$
$972$	−0.0481910	+	0.0426935i	−0.00154573	+	0.00136939i
$973$	11.9870	+	17.3662i	0.384286	+	0.556734i
$974$	−14.4618	−	38.1327i	−0.463387	−	1.22185i
$975$	13.0722	−	9.40840i	0.418644	−	0.301310i
$976$	−0.716954	+	1.89045i	−0.0229492	+	0.0605119i
$977$	38.6052	−	9.51534i	1.23509	−	0.304423i	0.432874	−	0.901455i	$-0.357500\pi$
$977$	38.6052	−	9.51534i	1.23509	−	0.304423i	0.802217	+	0.597032i	$0.203653\pi$
$978$	−11.9059	+	6.24869i	−0.380708	+	0.199811i
$979$	7.68558	+	20.2652i	0.245632	+	0.647679i
$980$	−0.0838997	−	0.690976i	−0.00268008	−	0.0220724i
$981$	−7.78901	+	11.2843i	−0.248684	+	0.360281i
$982$	−21.6039	−	5.32488i	−0.689408	−	0.169924i
$983$	−21.4822	+	5.29490i	−0.685177	+	0.168881i	−0.566512	−	0.824053i	$-0.691708\pi$
$983$	−21.4822	+	5.29490i	−0.685177	+	0.168881i	−0.118665	+	0.992934i	$0.537861\pi$
$984$	−1.19470	−	9.83923i	−0.0380856	−	0.313663i
$985$	−4.14824	+	10.9380i	−0.132174	+	0.348514i
$986$	19.8502	+	4.89265i	0.632161	+	0.155814i
$987$	56.3578	−	13.8910i	1.79389	−	0.442154i
$988$	−0.764839	+	1.52974i	−0.0243328	+	0.0486676i
$989$	−26.0910	−	6.43086i	−0.829646	−	0.204489i
$990$	−2.15185	−	1.12938i	−0.0683903	−	0.0358940i
$991$	24.8207			0.788455			0.394228	−	0.919013i	$-0.371012\pi$
$991$	24.8207			0.788455			0.394228	+	0.919013i	$0.371012\pi$
$992$	−2.67100			−0.0848044
$993$	13.3295	+	6.99584i	0.422998	+	0.222006i
$994$	−52.0850	+	46.1433i	−1.65204	+	1.46358i
$995$	−7.01842			−0.222499
$996$	−0.0891101	−	0.0789447i	−0.00282356	−	0.00250146i
$997$	18.1868	−	9.54517i	0.575982	−	0.302298i	−0.151465	−	0.988463i	$-0.548399\pi$
$997$	18.1868	−	9.54517i	0.575982	−	0.302298i	0.727447	+	0.686164i	$0.240707\pi$
$998$	−4.87509	−	40.1500i	−0.154318	−	1.27093i
$999$	1.46171	−	0.767163i	0.0462464	−	0.0242720i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.m.b.313.6	yes	204
169.27	even	13	inner	507.2.m.b.196.6	✓	204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.2.m.b.196.6	✓	204	169.27	even	13	inner
507.2.m.b.313.6	yes	204	1.1	even	1	trivial

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.m (of order \(13\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.509495 + 1.34343i) q^{2} +(0.568065 + 0.822984i) q^{3} +(-0.0481910 - 0.0426935i) q^{4} +(-0.0880026 + 0.724766i) q^{5} +(-1.39505 + 0.343848i) q^{6} +(-4.13500 + 2.17021i) q^{7} +(-2.46253 + 1.29244i) q^{8} +(-0.354605 + 0.935016i) q^{9} +O(q^{10})\)	\(q+(-0.509495 + 1.34343i) q^{2} +(0.568065 + 0.822984i) q^{3} +(-0.0481910 - 0.0426935i) q^{4} +(-0.0880026 + 0.724766i) q^{5} +(-1.39505 + 0.343848i) q^{6} +(-4.13500 + 2.17021i) q^{7} +(-2.46253 + 1.29244i) q^{8} +(-0.354605 + 0.935016i) q^{9} +(-0.928834 - 0.487490i) q^{10} +(-0.821521 - 2.16617i) q^{11} +(0.00776045 - 0.0639131i) q^{12} +(-0.931628 - 3.48311i) q^{13} +(-0.808765 - 6.66078i) q^{14} +(-0.646462 + 0.339289i) q^{15} +(-0.497168 - 4.09455i) q^{16} +(-1.28795 + 0.675970i) q^{17} +(-1.07546 - 0.952772i) q^{18} +7.36767 q^{19} +(0.0351837 - 0.0311701i) q^{20} +(-4.13500 - 2.17021i) q^{21} +3.32866 q^{22} -2.78764 q^{23} +(-2.46253 - 1.29244i) q^{24} +(4.33717 + 1.06902i) q^{25} +(5.15397 + 0.523053i) q^{26} +(-0.970942 + 0.239316i) q^{27} +(0.291924 + 0.0719527i) q^{28} +(-3.46888 + 9.14668i) q^{29} +(-0.126442 - 1.04134i) q^{30} +(-7.12347 + 1.75578i) q^{31} +(0.353483 + 0.0871258i) q^{32} +(1.31605 - 1.90663i) q^{33} +(-0.251911 - 2.07468i) q^{34} +(-1.20901 - 3.18789i) q^{35} +(0.0570079 - 0.0299200i) q^{36} +(-1.60283 + 0.395061i) q^{37} +(-3.75379 + 9.89793i) q^{38} +(2.33732 - 2.74535i) q^{39} +(-0.720005 - 1.89850i) q^{40} +(2.02452 + 2.93303i) q^{41} +(5.02229 - 4.44936i) q^{42} +(9.35953 + 2.30692i) q^{43} +(-0.0528916 + 0.139464i) q^{44} +(-0.646462 - 0.339289i) q^{45} +(1.42029 - 3.74499i) q^{46} +(-9.30360 + 8.24227i) q^{47} +(3.08732 - 2.73513i) q^{48} +(8.41192 - 12.1868i) q^{49} +(-3.64591 + 5.28201i) q^{50} +(-1.28795 - 0.675970i) q^{51} +(-0.103810 + 0.207629i) q^{52} +(0.773796 - 0.406119i) q^{53} +(0.173187 - 1.42632i) q^{54} +(1.64227 - 0.404782i) q^{55} +(7.37770 - 10.6884i) q^{56} +(4.18531 + 6.06348i) q^{57} +(-10.5205 - 9.32037i) q^{58} +(-0.500316 + 4.12048i) q^{59} +(0.0456391 + 0.0112490i) q^{60} +(-0.434040 - 0.227802i) q^{61} +(1.27061 - 10.4644i) q^{62} +(-0.562895 - 4.63586i) q^{63} +(4.38896 - 6.35850i) q^{64} +(2.60643 - 0.368690i) q^{65} +(1.89089 + 2.73943i) q^{66} +(-9.66559 + 8.56296i) q^{67} +(0.0909273 + 0.0224116i) q^{68} +(-1.58356 - 2.29418i) q^{69} +4.89868 q^{70} +(-5.89128 - 8.53499i) q^{71} +(-0.335223 - 2.76081i) q^{72} +(0.355963 + 0.938597i) q^{73} +(0.285896 - 2.35456i) q^{74} +(1.58401 + 4.17669i) q^{75} +(-0.355055 - 0.314552i) q^{76} +(8.09805 + 7.17425i) q^{77} +(2.49732 + 4.53876i) q^{78} +(-3.46321 + 3.06814i) q^{79} +3.01134 q^{80} +(-0.748511 - 0.663123i) q^{81} +(-4.97179 + 1.22544i) q^{82} +(1.05041 - 1.52178i) q^{83} +(0.106616 + 0.281122i) q^{84} +(-0.376577 - 0.992952i) q^{85} +(-7.86781 + 11.3985i) q^{86} +(-9.49812 + 2.34108i) q^{87} +(4.82266 + 4.27251i) q^{88} -9.35530 q^{89} +(0.785180 - 0.695609i) q^{90} +(11.4114 + 12.3808i) q^{91} +(0.134339 + 0.119014i) q^{92} +(-5.49157 - 4.86511i) q^{93} +(-6.33275 - 16.6981i) q^{94} +(-0.648374 + 5.33984i) q^{95} +(0.129098 + 0.340404i) q^{96} +(0.765884 + 6.30762i) q^{97} +(12.0862 + 17.5099i) q^{98} +2.31672 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q - q^{2} - 17 q^{3} - 21 q^{4} - 6 q^{5} - q^{6} - 8 q^{7} - 9 q^{8} - 17 q^{9}+O(q^{10}) \) 204 * q - q^2 - 17 * q^3 - 21 * q^4 - 6 * q^5 - q^6 - 8 * q^7 - 9 * q^8 - 17 * q^9	\( 204 q - q^{2} - 17 q^{3} - 21 q^{4} - 6 q^{5} - q^{6} - 8 q^{7} - 9 q^{8} - 17 q^{9} - 6 q^{10} - 8 q^{11} - 21 q^{12} + 54 q^{13} - 30 q^{14} - 6 q^{15} - 45 q^{16} - 18 q^{17} - q^{18} - 20 q^{19} - 58 q^{20} - 8 q^{21} + 44 q^{22} + 40 q^{23} - 9 q^{24} + 7 q^{25} - 2 q^{26} - 17 q^{27} - 40 q^{28} + 11 q^{29} - 6 q^{30} + 2 q^{31} + 61 q^{32} + 5 q^{33} - q^{34} + 11 q^{35} - 21 q^{36} - 34 q^{37} + 17 q^{38} - 11 q^{39} - 31 q^{40} - 58 q^{41} + 35 q^{42} + 32 q^{43} - 41 q^{44} - 6 q^{45} + 76 q^{46} - 36 q^{47} - 45 q^{48} + 9 q^{49} - 35 q^{50} - 18 q^{51} - 24 q^{52} + 66 q^{53} - q^{54} + 7 q^{55} - 114 q^{56} - 7 q^{57} - 60 q^{58} + 40 q^{59} + 59 q^{60} - 54 q^{61} - 31 q^{62} - 8 q^{63} + 75 q^{64} - 26 q^{65} + 18 q^{66} + 2 q^{67} + 26 q^{68} - 12 q^{69} - 56 q^{70} - 37 q^{71} - 9 q^{72} + 70 q^{73} + 174 q^{74} - 45 q^{75} - 26 q^{76} + 24 q^{78} - 66 q^{79} + 126 q^{80} - 17 q^{81} - 17 q^{82} - 2 q^{83} - 40 q^{84} + 54 q^{85} + 61 q^{86} + 24 q^{87} + 94 q^{88} - 114 q^{89} - 6 q^{90} + 104 q^{91} - 78 q^{92} + 67 q^{93} - 63 q^{94} - 70 q^{95} - 4 q^{96} + 36 q^{97} - 65 q^{98} + 18 q^{99}+O(q^{100}) \) 204 * q - q^2 - 17 * q^3 - 21 * q^4 - 6 * q^5 - q^6 - 8 * q^7 - 9 * q^8 - 17 * q^9 - 6 * q^10 - 8 * q^11 - 21 * q^12 + 54 * q^13 - 30 * q^14 - 6 * q^15 - 45 * q^16 - 18 * q^17 - q^18 - 20 * q^19 - 58 * q^20 - 8 * q^21 + 44 * q^22 + 40 * q^23 - 9 * q^24 + 7 * q^25 - 2 * q^26 - 17 * q^27 - 40 * q^28 + 11 * q^29 - 6 * q^30 + 2 * q^31 + 61 * q^32 + 5 * q^33 - q^34 + 11 * q^35 - 21 * q^36 - 34 * q^37 + 17 * q^38 - 11 * q^39 - 31 * q^40 - 58 * q^41 + 35 * q^42 + 32 * q^43 - 41 * q^44 - 6 * q^45 + 76 * q^46 - 36 * q^47 - 45 * q^48 + 9 * q^49 - 35 * q^50 - 18 * q^51 - 24 * q^52 + 66 * q^53 - q^54 + 7 * q^55 - 114 * q^56 - 7 * q^57 - 60 * q^58 + 40 * q^59 + 59 * q^60 - 54 * q^61 - 31 * q^62 - 8 * q^63 + 75 * q^64 - 26 * q^65 + 18 * q^66 + 2 * q^67 + 26 * q^68 - 12 * q^69 - 56 * q^70 - 37 * q^71 - 9 * q^72 + 70 * q^73 + 174 * q^74 - 45 * q^75 - 26 * q^76 + 24 * q^78 - 66 * q^79 + 126 * q^80 - 17 * q^81 - 17 * q^82 - 2 * q^83 - 40 * q^84 + 54 * q^85 + 61 * q^86 + 24 * q^87 + 94 * q^88 - 114 * q^89 - 6 * q^90 + 104 * q^91 - 78 * q^92 + 67 * q^93 - 63 * q^94 - 70 * q^95 - 4 * q^96 + 36 * q^97 - 65 * q^98 + 18 * q^99

Introduction

L-functions

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