LMFDB - Embedded newform 507.2.t.b.10.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(4,507)]

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, 1]))

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

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

chi := DirichletCharacter("507.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.t (of order $78$, 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 $\Q(\zeta_{78})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{78}]$

Embedding invariants

Embedding label			10.2
Character	$\chi$	$=$	507.10
Dual form			507.2.t.b.355.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.42455 - 0.494975i) q^{2} +(-0.987050 + 0.160411i) q^{3} +(3.79347 + 1.61625i) q^{4} +(0.0746454 - 0.302848i) q^{5} +(2.47255 + 0.0996403i) q^{6} +(-4.01396 + 1.90465i) q^{7} +(-4.32440 - 2.98492i) q^{8} +(0.948536 - 0.316668i) q^{9} +O(q^{10})$	\(q+(-2.42455 - 0.494975i) q^{2} +(-0.987050 + 0.160411i) q^{3} +(3.79347 + 1.61625i) q^{4} +(0.0746454 - 0.302848i) q^{5} +(2.47255 + 0.0996403i) q^{6} +(-4.01396 + 1.90465i) q^{7} +(-4.32440 - 2.98492i) q^{8} +(0.948536 - 0.316668i) q^{9} +(-0.330883 + 0.697322i) q^{10} +(1.26981 - 3.80356i) q^{11} +(-4.00361 - 0.986801i) q^{12} +(-1.26996 + 3.37449i) q^{13} +(10.6748 - 2.63110i) q^{14} +(-0.0250985 + 0.310900i) q^{15} +(3.29445 + 3.42989i) q^{16} +(-0.744504 - 1.56901i) q^{17} +(-2.45651 + 0.298275i) q^{18} +(-2.40942 - 1.39108i) q^{19} +(0.772642 - 1.02820i) q^{20} +(3.65645 - 2.52387i) q^{21} +(-4.96139 + 8.59337i) q^{22} +(0.703372 + 1.21828i) q^{23} +(4.74721 + 2.25258i) q^{24} +(4.34114 + 2.27840i) q^{25} +(4.74936 - 7.55302i) q^{26} +(-0.885456 + 0.464723i) q^{27} +(-18.3052 + 0.737675i) q^{28} +(-0.978149 + 4.79129i) q^{29} +(0.214740 - 0.741369i) q^{30} +(2.45367 + 4.67508i) q^{31} +(-0.673107 - 1.06443i) q^{32} +(-0.643236 + 3.95799i) q^{33} +(1.02847 + 4.17265i) q^{34} +(0.277196 + 1.35779i) q^{35} +(4.11006 + 0.331798i) q^{36} +(5.54542 - 8.76938i) q^{37} +(5.15320 + 4.56534i) q^{38} +(0.712206 - 3.53451i) q^{39} +(-1.22677 + 1.08683i) q^{40} +(-1.80160 - 11.0857i) q^{41} +(-10.1145 + 4.30938i) q^{42} +(5.54325 - 3.50534i) q^{43} +(10.9645 - 12.3763i) q^{44} +(-0.0250985 - 0.310900i) q^{45} +(-1.10234 - 3.30192i) q^{46} +(-3.09844 - 0.376218i) q^{47} +(-3.80198 - 2.85701i) q^{48} +(8.05708 - 9.86813i) q^{49} +(-9.39753 - 7.67285i) q^{50} +(0.986550 + 1.42926i) q^{51} +(-10.2716 + 10.7485i) q^{52} +(5.82433 - 8.43800i) q^{53} +(2.37686 - 0.688465i) q^{54} +(-1.05711 - 0.668478i) q^{55} +(23.0432 + 3.74488i) q^{56} +(2.60136 + 0.986567i) q^{57} +(4.74314 - 11.1325i) q^{58} +(1.93782 + 1.86130i) q^{59} +(-0.597701 + 1.13882i) q^{60} +(12.1873 - 0.983861i) q^{61} +(-3.63500 - 12.5495i) q^{62} +(-3.20425 + 3.07772i) q^{63} +(-2.26774 - 5.97955i) q^{64} +(0.927162 + 0.636495i) q^{65} +(3.51866 - 9.27795i) q^{66} +(-3.15010 - 7.39356i) q^{67} +(-0.288348 - 7.15529i) q^{68} +(-0.889688 - 1.08967i) q^{69} -3.42924i q^{70} +(9.40245 - 7.67686i) q^{71} +(-5.04708 - 1.46190i) q^{72} +(8.26333 + 9.32737i) q^{73} +(-17.7858 + 18.5169i) q^{74} +(-4.65040 - 1.55253i) q^{75} +(-6.89173 - 9.17123i) q^{76} +(2.14745 + 17.6859i) q^{77} +(-3.47627 + 8.21706i) q^{78} +(-0.327817 + 2.69981i) q^{79} +(1.28465 - 0.741694i) q^{80} +(0.799443 - 0.600742i) q^{81} +(-1.11907 + 27.7695i) q^{82} +(-6.01264 + 2.28029i) q^{83} +(17.9498 - 3.66448i) q^{84} +(-0.530745 + 0.108352i) q^{85} +(-15.1749 + 5.75509i) q^{86} +(0.196905 - 4.88615i) q^{87} +(-16.8445 + 12.6578i) q^{88} +(-2.48391 + 1.43408i) q^{89} +(-0.0930354 + 0.766215i) q^{90} +(-1.32966 - 15.9639i) q^{91} +(0.699185 + 5.75831i) q^{92} +(-3.17183 - 4.22094i) q^{93} +(7.32608 + 2.44581i) q^{94} +(-0.601138 + 0.625851i) q^{95} +(0.835138 + 0.942676i) q^{96} +(0.220992 + 0.0640112i) q^{97} +(-24.4192 + 19.9377i) q^{98} -4.00992i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 360 q - 15 q^{3} - 14 q^{4} + 3 q^{7} + 15 q^{9}+O(q^{10}) $ 360 * q - 15 * q^3 - 14 * q^4 + 3 * q^7 + 15 * q^9	$ 360 q - 15 q^{3} - 14 q^{4} + 3 q^{7} + 15 q^{9} + 6 q^{11} - 28 q^{12} + 6 q^{13} + 4 q^{14} - 6 q^{15} + 20 q^{16} - 6 q^{19} - 12 q^{20} - 28 q^{22} + 46 q^{23} - 6 q^{25} - 39 q^{26} + 30 q^{27} - 6 q^{28} + 43 q^{29} + 26 q^{31} - 195 q^{32} + 19 q^{33} + 65 q^{34} + 84 q^{35} - 14 q^{36} - 65 q^{38} - 2 q^{39} + 12 q^{41} - 128 q^{42} + 83 q^{43} - 39 q^{44} - 6 q^{45} - 20 q^{48} + 72 q^{49} - 52 q^{50} - 55 q^{52} + 49 q^{53} - 49 q^{55} - 2 q^{56} + 26 q^{57} + 26 q^{58} - 202 q^{59} - 182 q^{60} - 3 q^{61} - 65 q^{62} - 3 q^{63} - 14 q^{64} - 58 q^{65} + 48 q^{66} - 41 q^{67} + 139 q^{68} + 6 q^{69} - 60 q^{71} - 52 q^{73} - 269 q^{74} + 23 q^{75} - 14 q^{76} + 70 q^{77} - 65 q^{78} + 18 q^{79} + 492 q^{80} + 15 q^{81} - 65 q^{82} + 78 q^{83} - 6 q^{84} - 91 q^{85} - 169 q^{86} + 48 q^{87} - 522 q^{88} - 12 q^{89} + 373 q^{91} + 72 q^{92} - 3 q^{93} - 13 q^{94} - 110 q^{95} + 65 q^{96} - 121 q^{97} - 104 q^{98}+O(q^{100}) $ 360 * q - 15 * q^3 - 14 * q^4 + 3 * q^7 + 15 * q^9 + 6 * q^11 - 28 * q^12 + 6 * q^13 + 4 * q^14 - 6 * q^15 + 20 * q^16 - 6 * q^19 - 12 * q^20 - 28 * q^22 + 46 * q^23 - 6 * q^25 - 39 * q^26 + 30 * q^27 - 6 * q^28 + 43 * q^29 + 26 * q^31 - 195 * q^32 + 19 * q^33 + 65 * q^34 + 84 * q^35 - 14 * q^36 - 65 * q^38 - 2 * q^39 + 12 * q^41 - 128 * q^42 + 83 * q^43 - 39 * q^44 - 6 * q^45 - 20 * q^48 + 72 * q^49 - 52 * q^50 - 55 * q^52 + 49 * q^53 - 49 * q^55 - 2 * q^56 + 26 * q^57 + 26 * q^58 - 202 * q^59 - 182 * q^60 - 3 * q^61 - 65 * q^62 - 3 * q^63 - 14 * q^64 - 58 * q^65 + 48 * q^66 - 41 * q^67 + 139 * q^68 + 6 * q^69 - 60 * q^71 - 52 * q^73 - 269 * q^74 + 23 * q^75 - 14 * q^76 + 70 * q^77 - 65 * q^78 + 18 * q^79 + 492 * q^80 + 15 * q^81 - 65 * q^82 + 78 * q^83 - 6 * q^84 - 91 * q^85 - 169 * q^86 + 48 * q^87 - 522 * q^88 - 12 * q^89 + 373 * q^91 + 72 * q^92 - 3 * q^93 - 13 * q^94 - 110 * q^95 + 65 * q^96 - 121 * q^97 - 104 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$170$	$340$
$\chi(n)$	$1$	$e\left(\frac{5}{78}\right)$

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 $

$2$	−2.42455	−	0.494975i	−1.71441	−	0.350000i	−0.760329	−	0.649538i	$-0.774962\pi$
$2$	−2.42455	−	0.494975i	−1.71441	−	0.350000i	−0.954084	+	0.299538i	$0.903167\pi$
$3$	−0.987050	+	0.160411i	−0.569874	+	0.0926135i
$3$	−0.987050	+	0.160411i	−0.569874	+	0.0926135i
$4$	3.79347	+	1.61625i	1.89673	+	0.808123i
$5$	0.0746454	−	0.302848i	0.0333824	−	0.135438i	−0.951886	−	0.306452i	$-0.900858\pi$
$5$	0.0746454	−	0.302848i	0.0333824	−	0.135438i	0.985269	+	0.171014i	$0.0547043\pi$
$6$	2.47255	+	0.0996403i	1.00941	+	0.0406780i
$7$	−4.01396	+	1.90465i	−1.51713	+	0.719889i	−0.991413	−	0.130768i	$-0.958256\pi$
$7$	−4.01396	+	1.90465i	−1.51713	+	0.719889i	−0.525721	+	0.850657i	$0.676205\pi$
$8$	−4.32440	−	2.98492i	−1.52891	−	1.05533i
$9$	0.948536	−	0.316668i	0.316179	−	0.105556i
$10$	−0.330883	+	0.697322i	−0.104635	+	0.220513i
$11$	1.26981	−	3.80356i	0.382863	−	1.14682i	−0.564164	−	0.825662i	$-0.690802\pi$
$11$	1.26981	−	3.80356i	0.382863	−	1.14682i	0.947027	−	0.321153i	$-0.104070\pi$
$12$	−4.00361	−	0.986801i	−1.15574	−	0.284865i
$13$	−1.26996	+	3.37449i	−0.352223	+	0.935916i
$13$	−1.26996	+	3.37449i	−0.352223	+	0.935916i
$14$	10.6748	−	2.63110i	2.85296	−	0.703191i
$15$	−0.0250985	+	0.310900i	−0.00648040	+	0.0802741i
$16$	3.29445	+	3.42989i	0.823614	+	0.857472i
$17$	−0.744504	−	1.56901i	−0.180569	−	0.380541i	0.792903	−	0.609348i	$-0.208569\pi$
$17$	−0.744504	−	1.56901i	−0.180569	−	0.380541i	−0.973472	+	0.228807i	$0.926517\pi$
$18$	−2.45651	+	0.298275i	−0.579006	+	0.0703040i
$19$	−2.40942	−	1.39108i	−0.552759	−	0.319136i	0.197475	−	0.980308i	$-0.436726\pi$
$19$	−2.40942	−	1.39108i	−0.552759	−	0.319136i	−0.750234	+	0.661172i	$0.770059\pi$
$20$	0.772642	−	1.02820i	0.172768	−	0.229912i
$21$	3.65645	−	2.52387i	0.797904	−	0.550753i
$22$	−4.96139	+	8.59337i	−1.05777	+	1.83211i
$23$	0.703372	+	1.21828i	0.146663	+	0.254028i	0.929992	−	0.367579i	$-0.119813\pi$
$23$	0.703372	+	1.21828i	0.146663	+	0.254028i	−0.783329	+	0.621607i	$0.786480\pi$
$24$	4.74721	+	2.25258i	0.969021	+	0.459806i
$25$	4.34114	+	2.27840i	0.868227	+	0.455681i
$26$	4.74936	−	7.55302i	0.931427	−	1.48127i
$27$	−0.885456	+	0.464723i	−0.170406	+	0.0894360i
$28$	−18.3052	+	0.737675i	−3.45936	+	0.139407i
$29$	−0.978149	+	4.79129i	−0.181638	+	0.889720i	0.782158	+	0.623080i	$0.214119\pi$
$29$	−0.978149	+	4.79129i	−0.181638	+	0.889720i	−0.963796	+	0.266641i	$0.914086\pi$
$30$	0.214740	−	0.741369i	0.0392060	−	0.135355i
$31$	2.45367	+	4.67508i	0.440693	+	0.839669i	0.999943	+	0.0106708i	$0.00339668\pi$
$31$	2.45367	+	4.67508i	0.440693	+	0.839669i	−0.559251	+	0.828999i	$0.688911\pi$
$32$	−0.673107	−	1.06443i	−0.118990	−	0.188167i
$33$	−0.643236	+	3.95799i	−0.111973	+	0.688998i
$34$	1.02847	+	4.17265i	0.176380	+	0.715603i
$35$	0.277196	+	1.35779i	0.0468546	+	0.229509i
$36$	4.11006	+	0.331798i	0.685009	+	0.0552997i
$37$	5.54542	−	8.76938i	0.911661	−	1.44168i	0.0145394	−	0.999894i	$-0.495372\pi$
$37$	5.54542	−	8.76938i	0.911661	−	1.44168i	0.897122	−	0.441783i	$-0.145654\pi$
$38$	5.15320	+	4.56534i	0.835960	+	0.740596i
$39$	0.712206	−	3.53451i	0.114044	−	0.565975i
$40$	−1.22677	+	1.08683i	−0.193970	+	0.171842i
$41$	−1.80160	−	11.0857i	−0.281362	−	1.73129i	−0.614943	−	0.788571i	$-0.710821\pi$
$41$	−1.80160	−	11.0857i	−0.281362	−	1.73129i	0.333581	−	0.942722i	$-0.391743\pi$
$42$	−10.1145	+	4.30938i	−1.56070	+	0.664952i
$43$	5.54325	−	3.50534i	0.845338	−	0.534560i	−0.0401647	−	0.999193i	$-0.512788\pi$
$43$	5.54325	−	3.50534i	0.845338	−	0.534560i	0.885503	+	0.464633i	$0.153814\pi$
$44$	10.9645	−	12.3763i	1.65296	−	1.86580i
$45$	−0.0250985	−	0.310900i	−0.00374146	−	0.0463463i
$46$	−1.10234	−	3.30192i	−0.162531	−	0.486841i
$47$	−3.09844	−	0.376218i	−0.451953	−	0.0548771i	−0.108605	−	0.994085i	$-0.534638\pi$
$47$	−3.09844	−	0.376218i	−0.451953	−	0.0548771i	−0.343349	+	0.939208i	$0.611561\pi$
$48$	−3.80198	−	2.85701i	−0.548769	−	0.412373i
$49$	8.05708	−	9.86813i	1.15101	−	1.40973i
$50$	−9.39753	−	7.67285i	−1.32901	−	1.08510i
$51$	0.986550	+	1.42926i	0.138145	+	0.200137i
$52$	−10.2716	+	10.7485i	−1.42441	+	1.49054i
$53$	5.82433	−	8.43800i	0.800033	−	1.15905i	−0.184324	−	0.982865i	$-0.559010\pi$
$53$	5.82433	−	8.43800i	0.800033	−	1.15905i	0.984357	−	0.176183i	$-0.0563750\pi$
$54$	2.37686	−	0.688465i	0.323449	−	0.0936882i
$55$	−1.05711	−	0.668478i	−0.142541	−	0.0901376i
$56$	23.0432	+	3.74488i	3.07928	+	0.500431i
$57$	2.60136	+	0.986567i	0.344559	+	0.130674i
$58$	4.74314	−	11.1325i	0.622804	−	1.46178i
$59$	1.93782	+	1.86130i	0.252283	+	0.242321i	0.808188	−	0.588925i	$-0.200449\pi$
$59$	1.93782	+	1.86130i	0.252283	+	0.242321i	−0.555905	+	0.831246i	$0.687628\pi$
$60$	−0.597701	+	1.13882i	−0.0771629	+	0.147022i
$61$	12.1873	−	0.983861i	1.56042	−	0.125970i	0.730135	−	0.683303i	$-0.239457\pi$
$61$	12.1873	−	0.983861i	1.56042	−	0.125970i	0.830289	+	0.557333i	$0.188175\pi$
$62$	−3.63500	−	12.5495i	−0.461645	−	1.59378i
$63$	−3.20425	+	3.07772i	−0.403697	+	0.387756i
$64$	−2.26774	−	5.97955i	−0.283468	−	0.747444i
$65$	0.927162	+	0.636495i	0.115000	+	0.0789475i
$66$	3.51866	−	9.27795i	0.433117	−	1.14204i
$67$	−3.15010	−	7.39356i	−0.384846	−	0.903268i	−0.993915	−	0.110150i	$-0.964867\pi$
$67$	−3.15010	−	7.39356i	−0.384846	−	0.903268i	0.609069	−	0.793118i	$-0.291543\pi$
$68$	−0.288348	−	7.15529i	−0.0349674	−	0.867706i
$69$	−0.889688	−	1.08967i	−0.107106	−	0.131181i
$70$		−	3.42924i		−	0.409872i
$71$	9.40245	−	7.67686i	1.11587	−	0.911076i	0.119216	−	0.992868i	$-0.461962\pi$
$71$	9.40245	−	7.67686i	1.11587	−	0.911076i	0.996649	+	0.0817925i	$0.0260645\pi$
$72$	−5.04708	−	1.46190i	−0.594804	−	0.172287i
$73$	8.26333	+	9.32737i	0.967149	+	1.09169i	0.995750	+	0.0920951i	$0.0293564\pi$
$73$	8.26333	+	9.32737i	0.967149	+	1.09169i	−0.0286008	+	0.999591i	$0.509105\pi$
$74$	−17.7858	+	18.5169i	−2.06755	+	2.15255i
$75$	−4.65040	−	1.55253i	−0.536982	−	0.179271i
$76$	−6.89173	−	9.17123i	−0.790536	−	1.05201i
$77$	2.14745	+	17.6859i	0.244725	+	2.01549i
$78$	−3.47627	+	8.21706i	−0.393610	+	0.930399i
$79$	−0.327817	+	2.69981i	−0.0368823	+	0.303753i	0.962581	+	0.270994i	$0.0873524\pi$
$79$	−0.327817	+	2.69981i	−0.0368823	+	0.303753i	−0.999463	+	0.0327587i	$0.989571\pi$
$80$	1.28465	−	0.741694i	0.143628	−	0.0829239i
$81$	0.799443	−	0.600742i	0.0888270	−	0.0667491i
$82$	−1.11907	+	27.7695i	−0.123581	+	3.06663i
$83$	−6.01264	+	2.28029i	−0.659973	+	0.250295i	−0.661774	−	0.749704i	$-0.730196\pi$
$83$	−6.01264	+	2.28029i	−0.659973	+	0.250295i	0.00180085	+	0.999998i	$0.499427\pi$
$84$	17.9498	−	3.66448i	1.95849	−	0.399828i
$85$	−0.530745	+	0.108352i	−0.0575674	+	0.0117525i
$86$	−15.1749	+	5.75509i	−1.63636	+	0.620588i
$87$	0.196905	−	4.88615i	0.0211104	−	0.523850i
$88$	−16.8445	+	12.6578i	−1.79563	+	1.34933i
$89$	−2.48391	+	1.43408i	−0.263293	+	0.152013i	−0.625836	−	0.779955i	$-0.715242\pi$
$89$	−2.48391	+	1.43408i	−0.263293	+	0.152013i	0.362543	+	0.931967i	$0.381909\pi$
$90$	−0.0930354	+	0.766215i	−0.00980679	+	0.0807662i
$91$	−1.32966	−	15.9639i	−0.139386	−	1.67347i
$92$	0.699185	+	5.75831i	0.0728951	+	0.600345i
$93$	−3.17183	−	4.22094i	−0.328904	−	0.437691i
$94$	7.32608	+	2.44581i	0.755628	+	0.252266i
$95$	−0.601138	+	0.625851i	−0.0616754	+	0.0642109i
$96$	0.835138	+	0.942676i	0.0852359	+	0.0962114i
$97$	0.220992	+	0.0640112i	0.0224384	+	0.00649936i	0.289418	−	0.957203i	$-0.406538\pi$
$97$	0.220992	+	0.0640112i	0.0224384	+	0.00649936i	−0.266979	+	0.963702i	$0.586026\pi$
$98$	−24.4192	+	19.9377i	−2.46671	+	2.01401i
$99$		−	4.00992i		−	0.403012i
$100$	12.7855	+	15.6594i	1.27855	+	1.56594i
$101$	0.280932	+	6.97125i	0.0279537	+	0.693665i	0.951039	+	0.309070i	$0.100018\pi$
$101$	0.280932	+	6.97125i	0.0279537	+	0.693665i	−0.923085	+	0.384595i	$0.874341\pi$
$102$	−1.68449	−	3.95363i	−0.166789	−	0.391468i
$103$	1.07172	−	2.82588i	0.105599	−	0.278442i	−0.871794	−	0.489873i	$-0.837043\pi$
$103$	1.07172	−	2.82588i	0.105599	−	0.278442i	0.977393	+	0.211431i	$0.0678123\pi$
$104$	15.5644	−	10.8019i	1.52621	−	1.05922i
$105$	−0.491411	−	1.29575i	−0.0479568	−	0.126452i
$106$	−18.2980	+	17.5754i	−1.77725	+	1.70708i
$107$	−3.95008	−	13.6373i	−0.381869	−	1.31836i	−0.889557	−	0.456824i	$-0.848987\pi$
$107$	−3.95008	−	13.6373i	−0.381869	−	1.31836i	0.507688	−	0.861541i	$-0.330500\pi$
$108$	−4.11006	+	0.331798i	−0.395490	+	0.0319273i
$109$	−0.685704	+	1.30650i	−0.0656786	+	0.125140i	−0.916082	−	0.400991i	$-0.868666\pi$
$109$	−0.685704	+	1.30650i	−0.0656786	+	0.125140i	0.850403	+	0.526131i	$0.176358\pi$
$110$	2.23214	+	2.14400i	0.212826	+	0.204423i
$111$	−4.06690	+	9.54537i	−0.386013	+	0.906006i
$112$	−19.7565	−	7.49267i	−1.86682	−	0.707991i
$113$	16.4352	+	2.67098i	1.54609	+	0.251265i	0.872788	−	0.488100i	$-0.162310\pi$
$113$	16.4352	+	2.67098i	1.54609	+	0.251265i	0.673306	+	0.739364i	$0.264874\pi$
$114$	−5.81880	−	3.67959i	−0.544981	−	0.344625i
$115$	0.421456	−	0.122076i	0.0393010	−	0.0113837i
$116$	−11.4545	+	16.5947i	−1.06352	+	1.54078i
$117$	−0.136008	+	3.60299i	−0.0125740	+	0.333096i
$118$	−3.77704	−	5.47198i	−0.347704	−	0.503737i
$119$	5.97682	+	4.87992i	0.547894	+	0.447342i
$120$	1.03655	−	1.26954i	0.0946234	−	0.115893i
$121$	−4.06074	−	3.05144i	−0.369158	−	0.277404i
$122$	−30.0357	−	3.64699i	−2.71930	−	0.330183i
$123$	3.55654	+	10.6531i	0.320682	+	0.960560i
$124$	1.75185	+	21.7005i	0.157320	+	1.94876i
$125$	2.04823	−	2.31198i	0.183200	−	0.206790i
$126$	9.29224	−	5.87606i	0.827818	−	0.523481i
$127$	−13.0505	+	5.56029i	−1.15804	+	0.493396i	−0.883616	−	0.468212i	$-0.844898\pi$
$127$	−13.0505	+	5.56029i	−1.15804	+	0.493396i	−0.274426	+	0.961608i	$0.588488\pi$
$128$	2.94257	+	18.1064i	0.260089	+	1.60039i
$129$	−4.90917	+	4.34915i	−0.432229	+	0.382921i
$130$	−1.93290	−	2.00213i	−0.169527	−	0.175599i
$131$	1.95044	+	1.72794i	0.170411	+	0.150971i	0.744018	−	0.668160i	$-0.232918\pi$
$131$	1.95044	+	1.72794i	0.170411	+	0.150971i	−0.573607	+	0.819131i	$0.694456\pi$
$132$	−8.83718	+	13.9749i	−0.769178	+	1.21636i
$133$	12.3208	+	0.994641i	1.06835	+	0.0862463i
$134$	3.97794	+	19.4853i	0.343642	+	1.68327i
$135$	0.0746454	+	0.302848i	0.00642445	+	0.0260650i
$136$	−1.46383	+	9.00731i	−0.125522	+	0.772370i
$137$	−1.22434	−	1.93615i	−0.104603	−	0.165416i	0.788832	−	0.614609i	$-0.210686\pi$
$137$	−1.22434	−	1.93615i	−0.104603	−	0.165416i	−0.893435	+	0.449193i	$0.851712\pi$
$138$	1.61773	+	3.08233i	0.137710	+	0.262385i
$139$	4.78221	−	16.5101i	0.405622	−	1.40037i	−0.454713	−	0.890638i	$-0.650258\pi$
$139$	4.78221	−	16.5101i	0.405622	−	1.40037i	0.860334	−	0.509730i	$-0.170255\pi$
$140$	−1.14300	+	5.59876i	−0.0966008	+	0.473182i
$141$	3.11866	−	0.125678i	0.262639	−	0.0105840i
$142$	−26.5965	+	13.9589i	−2.23193	+	1.17141i
$143$	11.2225	+	9.11534i	0.938469	+	0.762263i
$144$	4.21105	+	2.21013i	0.350921	+	0.184177i
$145$	1.37802	+	0.653878i	0.114438	+	0.0543016i
$146$	−15.4180	−	26.7048i	−1.27600	−	2.21010i
$147$	−6.36978	+	11.0328i	−0.525371	+	0.909969i
$148$	35.2098	−	24.3036i	2.89423	−	1.99774i
$149$	−5.45492	+	7.25918i	−0.446885	+	0.594696i	−0.965529	−	0.260294i	$-0.916180\pi$
$149$	−5.45492	+	7.25918i	−0.446885	+	0.594696i	0.518645	+	0.854990i	$0.326437\pi$
$150$	10.5066	+	6.06602i	0.857864	+	0.495288i
$151$	1.19552	−	0.145163i	0.0972904	−	0.0118132i	−0.0717467	−	0.997423i	$-0.522857\pi$
$151$	1.19552	−	0.145163i	0.0972904	−	0.0118132i	0.169037	+	0.985610i	$0.445934\pi$
$152$	6.26704	+	13.2075i	0.508324	+	1.07127i
$153$	−1.20304	−	1.25250i	−0.0972604	−	0.101259i
$154$	3.54746	−	43.9431i	0.285862	−	3.54104i
$155$	1.59900	−	0.394117i	0.128434	−	0.0316562i
$156$	8.41437	−	12.2569i	0.673689	−	0.981341i
$157$	16.3769	+	4.03654i	1.30702	+	0.322151i	0.830502	−	0.557015i	$-0.188053\pi$
$157$	16.3769	+	4.03654i	1.30702	+	0.322151i	0.476516	+	0.879166i	$0.341900\pi$
$158$	2.13115	−	6.38356i	0.169545	−	0.507849i
$159$	−4.39536	+	9.26302i	−0.348574	+	0.734605i
$160$	−0.372606	+	0.124394i	−0.0294571	+	0.00983422i
$161$	−5.14369	−	3.55043i	−0.405380	−	0.279813i
$162$	−2.23564	+	1.06082i	−0.175648	+	0.0833462i
$163$	0.631752	+	0.0254588i	0.0494827	+	0.00199408i	0.0649949	−	0.997886i	$-0.479297\pi$
$163$	0.631752	+	0.0254588i	0.0494827	+	0.00199408i	−0.0155123	+	0.999880i	$0.504938\pi$
$164$	11.0829	−	44.9650i	0.865427	−	3.51118i
$165$	1.15066	+	0.490249i	0.0895785	+	0.0381658i
$166$	15.7066	−	2.55257i	1.21907	−	0.198118i
$167$	−1.61230	−	0.329153i	−0.124763	−	0.0254706i	0.137238	−	0.990538i	$-0.456177\pi$
$167$	−1.61230	−	0.329153i	−0.124763	−	0.0254706i	−0.262002	+	0.965067i	$0.584383\pi$
$168$	−23.3455			−1.80114
$169$	−9.77441	−	8.57094i	−0.751878	−	0.659303i
$170$	1.34045			0.102808
$171$	−2.72593	−	0.556503i	−0.208457	−	0.0425569i
$172$	26.6936	−	4.33814i	2.03537	−	0.330780i
$173$	−7.52791	−	3.20734i	−0.572337	−	0.243850i	0.0863530	−	0.996265i	$-0.472479\pi$
$173$	−7.52791	−	3.20734i	−0.572337	−	0.243850i	−0.658690	+	0.752415i	$0.728889\pi$
$174$	−2.89593	+	11.7492i	−0.219540	+	0.890707i
$175$	−21.7647	−	0.877087i	−1.64526	−	0.0663016i
$176$	17.2291	−	8.17532i	1.29869	−	0.616238i
$177$	−2.21130	−	1.52635i	−0.166211	−	0.114727i
$178$	6.73218	−	2.24753i	0.504598	−	0.168460i
$179$	−1.54046	+	3.24645i	−0.115139	+	0.242651i	−0.952837	−	0.303484i	$-0.901850\pi$
$179$	−1.54046	+	3.24645i	−0.115139	+	0.242651i	0.837697	+	0.546135i	$0.183901\pi$
$180$	0.407281	−	1.21996i	0.0303569	−	0.0909301i
$181$	−3.21635	−	0.792759i	−0.239069	−	0.0589253i	0.117960	−	0.993018i	$-0.462364\pi$
$181$	−3.21635	−	0.792759i	−0.239069	−	0.0589253i	−0.357030	+	0.934093i	$0.616211\pi$
$182$	−4.67792	+	39.3634i	−0.346750	+	2.91781i
$183$	−11.8717	+	2.92610i	−0.877578	+	0.216304i
$184$	0.594792	−	7.36782i	0.0438486	−	0.543163i
$185$	−2.24185	−	2.33401i	−0.164824	−	0.171600i
$186$	5.60100	+	11.8039i	0.410685	+	0.865501i
$187$	−6.91319	+	0.839414i	−0.505543	+	0.0613840i
$188$	−11.1458	−	6.43501i	−0.812888	−	0.469321i
$189$	2.66905	−	3.55186i	0.194145	−	0.258360i
$190$	1.76727	−	1.21986i	0.128211	−	0.0884977i
$191$	−5.59896	+	9.69768i	−0.405126	+	0.701699i	−0.994336	−	0.106281i	$-0.966106\pi$
$191$	−5.59896	+	9.69768i	−0.405126	+	0.701699i	0.589210	+	0.807980i	$0.299439\pi$
$192$	3.19756	+	5.53834i	0.230764	+	0.399695i
$193$	4.80060	+	2.27791i	0.345555	+	0.163968i	0.593557	−	0.804792i	$-0.297723\pi$
$193$	4.80060	+	2.27791i	0.345555	+	0.163968i	−0.248003	+	0.968759i	$0.579774\pi$
$194$	−0.504122	−	0.264584i	−0.0361939	−	0.0189960i
$195$	−1.01726	−	0.479525i	−0.0728473	−	0.0343395i
$196$	46.5136	−	24.4122i	3.32240	−	1.74373i
$197$	22.0967	−	0.890467i	1.57433	−	0.0634431i	0.762362	−	0.647151i	$-0.224040\pi$
$197$	22.0967	−	0.890467i	1.57433	−	0.0634431i	0.811964	+	0.583708i	$0.198399\pi$
$198$	−1.98481	+	9.72224i	−0.141054	+	0.690929i
$199$	0.576370	−	1.98986i	0.0408578	−	0.141057i	−0.937496	−	0.347995i	$-0.886863\pi$
$199$	0.576370	−	1.98986i	0.0408578	−	0.141057i	0.978354	+	0.206938i	$0.0663497\pi$
$200$	−11.9720	−	22.8107i	−0.846545	−	1.61296i
$201$	4.29532	+	6.79251i	0.302969	+	0.479107i
$202$	2.76946	−	17.0412i	0.194858	−	1.19901i
$203$	−5.19947	−	21.0951i	−0.364931	−	1.48058i
$204$	1.43240	+	7.01637i	0.100288	+	0.491244i
$205$	−3.49176	−	0.281884i	−0.243875	−	0.0196876i
$206$	−3.99716	+	6.32101i	−0.278496	+	0.440406i
$207$	1.05296	+	0.932843i	0.0731859	+	0.0648371i
$208$	−15.7580	+	6.76129i	−1.09262	+	0.468811i
$209$	−8.35056	+	7.39795i	−0.577620	+	0.511727i
$210$	0.550089	+	3.38483i	0.0379597	+	0.233576i
$211$	−8.75358	+	3.72955i	−0.602621	+	0.256753i	−0.671658	−	0.740861i	$-0.734418\pi$
$211$	−8.75358	+	3.72955i	−0.602621	+	0.256753i	0.0690371	+	0.997614i	$0.478007\pi$
$212$	35.7323	−	22.5957i	2.45410	−	1.55188i
$213$	−8.04923	+	9.08571i	−0.551524	+	0.622542i
$214$	2.82706	+	35.0194i	0.193254	+	2.39388i
$215$	−0.647808	−	1.94042i	−0.0441801	−	0.132336i
$216$	5.21623	+	0.633365i	0.354919	+	0.0430950i
$217$	−18.7533	−	14.0922i	−1.27306	−	0.956642i
$218$	2.30921	−	2.82826i	0.156399	−	0.191554i
$219$	−9.65254	−	7.88105i	−0.652258	−	0.532552i
$220$	−2.92970	−	4.24441i	−0.197521	−	0.286158i
$221$	6.24010	−	0.519747i	0.419755	−	0.0349620i
$222$	14.5851	−	21.1302i	0.978888	−	1.41816i
$223$	−11.8413	+	3.42987i	−0.792952	+	0.229681i	−0.649886	−	0.760032i	$-0.725183\pi$
$223$	−11.8413	+	3.42987i	−0.792952	+	0.229681i	−0.143066	+	0.989713i	$0.545696\pi$
$224$	4.72920	+	2.99056i	0.315983	+	0.199815i
$225$	4.83922	+	0.786450i	0.322615	+	0.0524300i
$226$	−38.5258	−	14.6109i	−2.56270	−	0.971904i
$227$	−1.97070	+	4.62540i	−0.130800	+	0.306999i	−0.972483	−	0.232973i	$-0.925155\pi$
$227$	−1.97070	+	4.62540i	−0.130800	+	0.306999i	0.841683	+	0.539972i	$0.181565\pi$
$228$	8.27365	+	7.94695i	0.547936	+	0.526300i
$229$	−9.35112	+	17.8171i	−0.617940	+	1.17739i	0.352448	+	0.935831i	$0.385349\pi$
$229$	−9.35112	+	17.8171i	−0.617940	+	1.17739i	−0.970387	+	0.241554i	$0.922343\pi$
$230$	−1.08226	+	0.0873694i	−0.0713624	+	0.00576097i
$231$	−4.95666	−	17.1124i	−0.326124	−	1.12591i
$232$	18.5315	−	17.7998i	1.21665	−	1.16861i
$233$	−7.32442	−	19.3129i	−0.479839	−	1.26523i	−0.928435	−	0.371496i	$-0.878845\pi$
$233$	−7.32442	−	19.3129i	−0.479839	−	1.26523i	0.448596	−	0.893735i	$-0.351924\pi$
$234$	2.11315	−	8.66828i	0.138141	−	0.566664i
$235$	−0.345221	+	0.910273i	−0.0225197	+	0.0593796i
$236$	4.34273	+	10.1928i	0.282688	+	0.663493i
$237$	−0.109509	−	2.71744i	−0.00711337	−	0.176517i
$238$	−12.0756	−	14.7900i	−0.782748	−	0.958692i
$239$		−	27.6316i		−	1.78734i	−0.448728	−	0.893668i	$-0.648123\pi$
$239$		−	27.6316i		−	1.78734i	0.448728	−	0.893668i	$-0.351877\pi$
$240$	−1.14904	+	0.938162i	−0.0741702	+	0.0605581i
$241$	24.5249	+	7.10372i	1.57979	+	0.457591i	0.948189	−	0.317706i	$-0.102913\pi$
$241$	24.5249	+	7.10372i	1.57979	+	0.457591i	0.631597	+	0.775297i	$0.282400\pi$
$242$	8.33505	+	9.40833i	0.535798	+	0.604790i
$243$	−0.692724	+	0.721202i	−0.0444383	+	0.0462652i
$244$	47.8223	+	15.9654i	3.06151	+	1.02208i
$245$	−2.38712	−	3.17668i	−0.152508	−	0.202951i
$246$	−3.34996	−	27.5894i	−0.213586	−	1.75904i
$247$	7.75405	−	6.36396i	0.493379	−	0.404929i
$248$	3.34407	−	27.5409i	0.212349	−	1.74885i
$249$	5.56899	−	3.21526i	0.352920	−	0.203759i
$250$	−6.11041	+	4.59168i	−0.386456	+	0.290403i
$251$	−0.0599131	+	1.48673i	−0.00378168	+	0.0938415i	0.996196	+	0.0871423i	$0.0277735\pi$
$251$	−0.0599131	+	1.48673i	−0.00378168	+	0.0938415i	−0.999978	+	0.00669922i	$0.997868\pi$
$252$	−17.1296	+	6.49638i	−1.07906	+	0.409234i
$253$	5.52693	−	1.12833i	0.347475	−	0.0709375i
$254$	34.3937	−	7.02152i	2.15805	−	0.440569i
$255$	0.506491	−	0.192087i	0.0317177	−	0.0120289i
$256$	1.31278	−	32.5763i	0.0820488	−	2.03602i
$257$	−21.7375	+	16.3347i	−1.35595	+	1.01893i	−0.359639	+	0.933091i	$0.617100\pi$
$257$	−21.7375	+	16.3347i	−1.35595	+	1.01893i	−0.996309	+	0.0858379i	$0.972643\pi$
$258$	14.0552	−	8.11480i	0.875041	−	0.505205i
$259$	−5.55651	+	45.7620i	−0.345265	+	2.84351i
$260$	2.48843	+	3.91305i	0.154326	+	0.242677i
$261$	0.589438	+	4.85446i	0.0364853	+	0.300484i
$262$	−3.87365	−	5.15490i	−0.239315	−	0.318471i
$263$	25.7245	+	8.58811i	1.58624	+	0.529566i	0.966813	−	0.255486i	$-0.0822354\pi$
$263$	25.7245	+	8.58811i	1.58624	+	0.529566i	0.619430	+	0.785052i	$0.287364\pi$
$264$	14.5959	−	15.1959i	0.898315	−	0.935245i
$265$	−2.12067	−	2.39375i	−0.130272	−	0.147047i
$266$	−29.3801	−	8.51005i	−1.80141	−	0.521785i
$267$	2.22170	−	1.81396i	0.135966	−	0.111012i
$268$		−	33.1386i		−	2.02426i
$269$	−4.59376	−	5.62634i	−0.280087	−	0.343044i	0.615333	−	0.788267i	$-0.289022\pi$
$269$	−4.59376	−	5.62634i	−0.280087	−	0.343044i	−0.895419	+	0.445224i	$0.853124\pi$
$270$	−0.0310790	−	0.771217i	−0.00189141	−	0.0469348i
$271$	5.69249	+	13.3608i	0.345794	+	0.811608i	0.998539	+	0.0540308i	$0.0172069\pi$
$271$	5.69249	+	13.3608i	0.345794	+	0.811608i	−0.652745	+	0.757577i	$0.726383\pi$
$272$	2.92879	−	7.72260i	0.177584	−	0.468251i
$273$	3.87323	+	15.5439i	0.234418	+	0.940759i
$274$	2.01014	+	5.30030i	0.121437	+	0.320203i
$275$	14.1785	−	13.6186i	0.854994	−	0.821232i
$276$	−1.61383	−	5.57158i	−0.0971411	−	0.335370i
$277$	17.2426	−	1.39196i	1.03601	−	0.0836350i	0.449255	−	0.893403i	$-0.351689\pi$
$277$	17.2426	−	1.39196i	1.03601	−	0.0836350i	0.586750	+	0.809768i	$0.300407\pi$
$278$	−19.7668	+	37.6624i	−1.18553	+	2.25884i
$279$	3.80785	+	3.65749i	0.227970	+	0.218968i
$280$	2.85420	−	6.69905i	0.170571	−	0.400345i
$281$	4.04302	+	1.53332i	0.241187	+	0.0914700i	0.472237	−	0.881472i	$-0.343447\pi$
$281$	4.04302	+	1.53332i	0.241187	+	0.0914700i	−0.231050	+	0.972942i	$0.574216\pi$
$282$	−7.62355	−	1.23895i	−0.453976	−	0.0737782i
$283$	−1.73247	−	1.09555i	−0.102985	−	0.0651235i	0.481981	−	0.876182i	$-0.339918\pi$
$283$	−1.73247	−	1.09555i	−0.102985	−	0.0651235i	−0.584965	+	0.811058i	$0.698892\pi$
$284$	48.0756	−	13.9253i	2.85276	−	0.826312i
$285$	0.492960	−	0.714176i	0.0292004	−	0.0423041i
$286$	−22.6975	−	27.6554i	−1.34213	−	1.63530i
$287$	28.3459	+	41.0661i	1.67320	+	2.42405i
$288$	−0.975539	−	0.796503i	−0.0574842	−	0.0469344i
$289$	8.84407	−	10.8320i	0.520239	−	0.637177i
$290$	−3.01742	−	2.26744i	−0.177189	−	0.133149i
$291$	−0.228399	−	0.0277326i	−0.0133890	−	0.00162572i
$292$	16.2713	+	48.7386i	0.952209	+	2.85221i
$293$	−2.07767	−	25.7366i	−0.121379	−	1.50355i	−0.715184	−	0.698937i	$-0.753657\pi$
$293$	−2.07767	−	25.7366i	−0.121379	−	1.50355i	0.593805	−	0.804609i	$-0.297625\pi$
$294$	20.9048	−	23.5966i	1.21919	−	1.37618i
$295$	0.708341	−	0.447927i	0.0412412	−	0.0260793i
$296$	−50.1565	+	21.3697i	−2.91529	+	1.24209i
$297$	0.643236	+	3.95799i	0.0373244	+	0.229666i
$298$	16.8188	−	14.9002i	0.974289	−	0.863144i
$299$	−5.00431	+	0.826363i	−0.289407	+	0.0477898i
$300$	−15.1319	−	13.4057i	−0.873639	−	0.773977i
$301$	−15.5740	+	24.6282i	−0.897668	+	1.41955i
$302$	−2.97046	−	0.239800i	−0.170931	−	0.0137989i
$303$	−1.39556	−	6.83591i	−0.0801728	−	0.392713i
$304$	−3.16648	−	12.8469i	−0.181610	−	0.736820i
$305$	0.611765	−	3.76434i	0.0350296	−	0.215546i
$306$	2.29688	+	3.63223i	0.131304	+	0.207641i
$307$	−7.84485	−	14.9471i	−0.447729	−	0.853077i	−0.999814	−	0.0192888i	$-0.993860\pi$
$307$	−7.84485	−	14.9471i	−0.447729	−	0.853077i	0.552085	−	0.833788i	$-0.313832\pi$
$308$	−20.4384	+	70.5616i	−1.16459	+	4.02062i
$309$	−0.604534	+	2.96120i	−0.0343907	+	0.168457i
$310$	−4.07192	+	0.164093i	−0.231269	+	0.00931983i
$311$	−21.2260	+	11.1402i	−1.20361	+	0.631705i	−0.942695	−	0.333656i	$-0.891718\pi$
$311$	−21.2260	+	11.1402i	−1.20361	+	0.631705i	−0.260919	+	0.965361i	$0.584025\pi$
$312$	−13.6301	+	13.1588i	−0.771652	+	0.744968i
$313$	−2.03275	−	1.06687i	−0.114898	−	0.0603029i	0.406295	−	0.913742i	$-0.366820\pi$
$313$	−2.03275	−	1.06687i	−0.114898	−	0.0603029i	−0.521193	+	0.853439i	$0.674513\pi$
$314$	−37.7085	−	17.8929i	−2.12802	−	1.00976i
$315$	0.692900	+	1.20014i	0.0390405	+	0.0676201i
$316$	−5.60712	+	9.71182i	−0.315425	+	0.546333i
$317$	−14.1074	+	9.73767i	−0.792353	+	0.546922i	−0.894089	−	0.447890i	$-0.852176\pi$
$317$	−14.1074	+	9.73767i	−0.792353	+	0.546922i	0.101736	+	0.994811i	$0.467560\pi$
$318$	15.2417	−	20.2830i	0.854712	−	1.13742i
$319$	16.9819	+	9.80449i	0.950802	+	0.548946i
$320$	−1.98017	+	0.240436i	−0.110695	+	0.0134408i
$321$	6.08650	+	12.8270i	0.339715	+	0.715935i
$322$	10.7137	+	11.1542i	0.597054	+	0.621599i
$323$	−0.388793	+	4.81607i	−0.0216330	+	0.267973i
$324$	4.00361	−	0.986801i	0.222423	−	0.0548223i
$325$	−13.2015	+	11.7557i	−0.732289	+	0.652086i
$326$	−1.51911	−	0.374427i	−0.0841358	−	0.0207376i
$327$	0.467247	−	1.39958i	0.0258388	−	0.0773967i
$328$	−25.2990	+	53.3165i	−1.39690	+	2.94391i
$329$	13.1536	−	4.39130i	0.725179	−	0.242100i
$330$	−2.54716	−	1.75818i	−0.140216	−	0.0967844i
$331$	24.0787	−	11.4255i	1.32349	−	0.628003i	0.369887	−	0.929077i	$-0.379397\pi$
$331$	24.0787	−	11.4255i	1.32349	−	0.628003i	0.953601	+	0.301074i	$0.0973453\pi$
$332$	−26.4943	−	1.06768i	−1.45406	−	0.0585967i
$333$	2.48305	−	10.0741i	0.136070	−	0.552059i
$334$	3.74617	+	1.59609i	0.204981	+	0.0873344i
$335$	−2.47427	+	0.402108i	−0.135184	+	0.0219695i
$336$	20.7026	+	4.22647i	1.12942	+	0.230573i
$337$	−36.4027			−1.98298			−0.991490	−	0.130184i	$-0.958443\pi$
$337$	−36.4027			−1.98298			−0.991490	+	0.130184i	$0.958443\pi$
$338$	19.4561	+	25.6187i	1.05827	+	1.39347i
$339$	−16.6508			−0.904349
$340$	−2.18849	−	0.446783i	−0.118687	−	0.0242302i
$341$	20.8976	−	3.39620i	1.13167	−	0.183914i
$342$	6.33370	+	2.69854i	0.342487	+	0.145920i
$343$	−6.10265	+	24.7594i	−0.329512	+	1.33688i
$344$	−34.4344	−	1.38766i	−1.85658	−	0.0748176i
$345$	−0.396416	+	0.188102i	−0.0213423	+	0.0101270i
$346$	16.6642	+	11.5025i	0.895874	+	0.618377i
$347$	−21.1302	+	7.05431i	−1.13433	+	0.378695i	−0.820988	−	0.570945i	$-0.806577\pi$
$347$	−21.1302	+	7.05431i	−1.13433	+	0.378695i	−0.313343	+	0.949640i	$0.601449\pi$
$348$	8.64417	−	18.2172i	0.463376	−	0.976545i
$349$	7.41294	−	22.2045i	0.396805	−	1.18858i	−0.540882	−	0.841098i	$-0.681910\pi$
$349$	7.41294	−	22.2045i	0.396805	−	1.18858i	0.937688	−	0.347479i	$-0.112962\pi$
$350$	52.3354	+	12.8995i	2.79744	+	0.689508i
$351$	−0.443712	−	3.57814i	−0.0236836	−	0.190987i
$352$	−4.90335	+	1.20857i	−0.261350	+	0.0644169i
$353$	1.80479	−	22.3563i	0.0960593	−	1.18991i	−0.751692	−	0.659514i	$-0.770762\pi$
$353$	1.80479	−	22.3563i	0.0960593	−	1.18991i	0.847752	−	0.530393i	$-0.177956\pi$
$354$	4.60589	+	4.79524i	0.244800	+	0.254864i
$355$	−1.62307	−	3.42056i	−0.0861438	−	0.181544i
$356$	−11.7404	+	1.42555i	−0.622242	+	0.0755539i
$357$	−6.68222	−	3.85798i	−0.353660	−	0.204186i
$358$	5.34183	−	7.10869i	0.282325	−	0.375706i
$359$	9.02269	−	6.22791i	0.476199	−	0.328697i	−0.305672	−	0.952137i	$-0.598881\pi$
$359$	9.02269	−	6.22791i	0.476199	−	0.328697i	0.781871	+	0.623440i	$0.214266\pi$
$360$	−0.819476	+	1.41937i	−0.0431902	+	0.0748076i
$361$	−5.62980	−	9.75109i	−0.296305	−	0.513215i
$362$	7.40579	+	3.51409i	0.389240	+	0.184697i
$363$	4.49764	+	2.36054i	0.236065	+	0.123896i
$364$	20.7576	−	62.7076i	1.08799	−	3.28677i
$365$	3.44160	−	1.80629i	0.180141	−	0.0945455i
$366$	30.2317	−	1.21830i	1.58024	−	0.0636814i
$367$	7.26963	−	35.6090i	0.379472	−	1.85878i	−0.120470	−	0.992717i	$-0.538440\pi$
$367$	7.26963	−	35.6090i	0.379472	−	1.85878i	0.499942	−	0.866059i	$-0.333355\pi$
$368$	−1.86132	+	6.42604i	−0.0970283	+	0.334980i
$369$	−5.21936	−	9.94467i	−0.271709	−	0.517699i
$370$	4.28019	+	6.76858i	0.222517	+	0.351882i
$371$	−7.30721	+	44.9631i	−0.379372	+	2.33437i
$372$	−5.21017	−	21.1385i	−0.270135	−	1.09598i
$373$	−4.89893	−	23.9965i	−0.253657	−	1.24249i	−0.884484	−	0.466570i	$-0.845490\pi$
$373$	−4.89893	−	23.9965i	−0.253657	−	1.24249i	0.630828	−	0.775923i	$-0.282716\pi$
$374$	17.1769	+	1.38666i	0.888194	+	0.0717024i
$375$	−1.65084	+	2.61060i	−0.0852492	+	0.134811i
$376$	12.2759	+	10.8755i	0.633081	+	0.560861i
$377$	−14.9260	−	9.38550i	−0.768727	−	0.483378i
$378$	−8.22932	+	7.29054i	−0.423271	+	0.374985i
$379$	1.30605	+	8.03645i	0.0670873	+	0.412805i	0.998772	+	0.0495374i	$0.0157747\pi$
$379$	1.30605	+	8.03645i	0.0670873	+	0.412805i	−0.931685	+	0.363267i	$0.881661\pi$
$380$	−3.29193	+	1.40256i	−0.168872	+	0.0719497i
$381$	11.9895	−	7.58173i	0.614243	−	0.388424i
$382$	18.3750	−	20.7411i	0.940149	−	1.06121i
$383$	0.0124779	+	0.154567i	0.000637593	+	0.00789800i	0.997068	−	0.0765169i	$-0.0243799\pi$
$383$	0.0124779	+	0.154567i	0.000637593	+	0.00789800i	−0.996431	+	0.0844149i	$0.973098\pi$
$384$	−5.80893	−	17.3999i	−0.296436	−	0.887933i
$385$	5.51643	+	0.669816i	0.281143	+	0.0341370i
$386$	−10.5118	−	7.89908i	−0.535035	−	0.402052i
$387$	4.14795	−	5.08032i	0.210852	−	0.258247i
$388$	0.734870	+	0.600003i	0.0373074	+	0.0304605i
$389$	10.0550	+	14.5672i	0.509810	+	0.738587i	0.990381	−	0.138369i	$-0.0441860\pi$
$389$	10.0550	+	14.5672i	0.509810	+	0.738587i	−0.480571	+	0.876956i	$0.659571\pi$
$390$	2.22903	+	1.66615i	0.112872	+	0.0843687i
$391$	1.38782	−	2.01061i	0.0701852	−	0.101681i
$392$	−64.2976	+	18.6240i	−3.24752	+	0.940655i
$393$	−2.20237	−	1.39269i	−0.111095	−	0.0702521i
$394$	−54.0153	−	8.77833i	−2.72125	−	0.442246i
$395$	0.793164	+	0.300807i	0.0399084	+	0.0151353i
$396$	6.48102	−	15.2115i	0.325683	−	0.764407i
$397$	3.42309	+	3.28792i	0.171800	+	0.165016i	0.773693	−	0.633560i	$-0.218407\pi$
$397$	3.42309	+	3.28792i	0.171800	+	0.165016i	−0.601893	+	0.798577i	$0.705587\pi$
$398$	−2.38237	+	4.53922i	−0.119417	+	0.227531i
$399$	−12.3208	+	0.994641i	−0.616813	+	0.0497943i
$400$	6.48700	+	22.3957i	0.324350	+	1.11979i
$401$	−24.1248	+	23.1722i	−1.20473	+	1.15716i	−0.221434	+	0.975175i	$0.571074\pi$
$401$	−24.1248	+	23.1722i	−1.20473	+	1.15716i	−0.983301	+	0.181988i	$0.941747\pi$
$402$	−7.05209	−	18.5948i	−0.351726	−	0.927426i
$403$	−18.8921	+	2.34274i	−0.941082	+	0.116700i
$404$	−10.2015	+	26.8993i	−0.507546	+	1.33829i
$405$	−0.122259	−	0.286952i	−0.00607510	−	0.0142588i
$406$	2.16483	+	53.7196i	0.107439	+	2.66606i
$407$	−26.3132	−	32.2278i	−1.30430	−	1.59747i
$408$		−	9.12548i		−	0.451779i
$409$	−1.31441	+	1.07319i	−0.0649936	+	0.0530656i	−0.664385	−	0.747390i	$-0.731307\pi$
$409$	−1.31441	+	1.07319i	−0.0649936	+	0.0530656i	0.599392	+	0.800456i	$0.295409\pi$
$410$	8.32641	+	2.41177i	0.411212	+	0.119109i
$411$	1.51907	+	1.71467i	0.0749301	+	0.0845787i
$412$	8.63283	−	8.98773i	0.425309	−	0.442794i
$413$	−11.3234	−	3.78032i	−0.557190	−	0.186018i
$414$	−2.09122	−	2.78291i	−0.102778	−	0.136773i
$415$	0.241767	+	1.99113i	0.0118679	+	0.0977407i
$416$	4.44674	−	0.919608i	0.218019	−	0.0450875i
$417$	−2.07187	+	17.0634i	−0.101460	+	0.835599i
$418$	23.9081	−	13.8034i	1.16938	−	0.675145i
$419$	16.3081	−	12.2547i	0.796702	−	0.598683i	−0.122500	−	0.992468i	$-0.539091\pi$
$419$	16.3081	−	12.2547i	0.796702	−	0.598683i	0.919202	+	0.393786i	$0.128835\pi$
$420$	0.230089	−	5.70961i	0.0112272	−	0.278600i
$421$	−13.5343	+	5.13287i	−0.659620	+	0.250161i	−0.661622	−	0.749837i	$-0.730132\pi$
$421$	−13.5343	+	5.13287i	−0.659620	+	0.250161i	0.00200260	+	0.999998i	$0.499363\pi$
$422$	23.0695	−	4.70967i	1.12301	−	0.229263i
$423$	−3.05812	+	0.624319i	−0.148691	+	0.0303554i
$424$	−50.3735	+	19.1041i	−2.44635	+	0.927779i
$425$	0.342843	−	8.50756i	0.0166303	−	0.412677i
$426$	24.0129	−	18.0446i	1.16343	−	0.874261i
$427$	−47.0454	+	27.1617i	−2.27669	+	1.31445i
$428$	7.05666	−	58.1169i	0.341097	−	2.80918i
$429$	−12.5393	−	7.19708i	−0.605405	−	0.347479i
$430$	0.610181	+	5.02529i	0.0294255	+	0.242341i
$431$	22.3295	+	29.7152i	1.07557	+	1.43133i	0.894064	+	0.447939i	$0.147842\pi$
$431$	22.3295	+	29.7152i	1.07557	+	1.43133i	0.181510	+	0.983389i	$0.441902\pi$
$432$	−4.51104	−	1.50601i	−0.217038	−	0.0724578i
$433$	10.5692	−	11.0037i	0.507923	−	0.528804i	−0.417026	−	0.908894i	$-0.636928\pi$
$433$	10.5692	−	11.0037i	0.507923	−	0.528804i	0.924949	+	0.380091i	$0.124107\pi$
$434$	38.4930	+	43.4496i	1.84772	+	2.08565i
$435$	−1.46506	−	0.424361i	−0.0702444	−	0.0203465i
$436$	−4.71282	+	3.84790i	−0.225703	+	0.184281i
$437$		−	3.91378i		−	0.187222i
$438$	19.5021	+	23.8857i	0.931846	+	1.14130i
$439$	0.572607	+	14.2091i	0.0273290	+	0.678163i	0.953559	+	0.301205i	$0.0973888\pi$
$439$	0.572607	+	14.2091i	0.0273290	+	0.678163i	−0.926230	+	0.376958i	$0.876970\pi$
$440$	2.57603	+	6.04617i	0.122807	+	0.288240i
$441$	4.51751	−	11.9117i	0.215120	−	0.567224i
$442$	−15.3867	−	1.82854i	−0.731870	−	0.0869749i
$443$	−0.394105	−	1.03917i	−0.0187245	−	0.0493724i	0.925328	−	0.379167i	$-0.123790\pi$
$443$	−0.394105	−	1.03917i	−0.0187245	−	0.0493724i	−0.944053	+	0.329795i	$0.893020\pi$
$444$	−30.8553	+	29.6369i	−1.46433	+	1.40651i
$445$	0.248897	+	0.859294i	0.0117989	+	0.0407344i
$446$	30.4075	−	2.45475i	1.43984	−	0.116236i
$447$	4.21983	−	8.04021i	0.199591	−	0.380289i
$448$	20.4916	+	19.6824i	0.968136	+	0.929907i
$449$	4.75294	−	11.1556i	0.224305	−	0.526463i	−0.769364	−	0.638811i	$-0.779427\pi$
$449$	4.75294	−	11.1556i	0.224305	−	0.526463i	0.993669	+	0.112348i	$0.0358370\pi$
$450$	−11.3436	−	4.30208i	−0.534745	−	0.202802i
$451$	−44.4527	−	7.22427i	−2.09320	−	0.340177i
$452$	58.0294	+	36.6956i	2.72948	+	1.72602i
$453$	−1.15676	+	0.335059i	−0.0543492	+	0.0157424i
$454$	7.06751	−	10.2391i	0.331695	−	0.480543i
$455$	−4.93389	−	0.788948i	−0.231304	−	0.0369864i
$456$	−8.30452	−	12.0312i	−0.388895	−	0.563411i
$457$	8.14187	+	6.64763i	0.380860	+	0.310963i	0.803466	−	0.595351i	$-0.202987\pi$
$457$	8.14187	+	6.64763i	0.380860	+	0.310963i	−0.422605	+	0.906314i	$0.638884\pi$
$458$	31.4912	−	38.5698i	1.47149	−	1.80225i
$459$	1.38838	+	1.04330i	0.0648041	+	0.0486971i
$460$	1.79608	+	0.218084i	0.0837429	+	0.0101682i
$461$	1.46680	+	4.39360i	0.0683157	+	0.204630i	0.977160	−	0.212505i	$-0.0681622\pi$
$461$	1.46680	+	4.39360i	0.0683157	+	0.204630i	−0.908844	+	0.417136i	$0.863034\pi$
$462$	3.54746	+	43.9431i	0.165043	+	2.04442i
$463$	15.4952	−	17.4904i	0.720122	−	0.812850i	−0.268499	−	0.963280i	$-0.586527\pi$
$463$	15.4952	−	17.4904i	0.720122	−	0.812850i	0.988621	+	0.150430i	$0.0480659\pi$
$464$	−19.6561	+	12.4297i	−0.912510	+	0.577036i
$465$	−1.51507	+	0.645510i	−0.0702596	+	0.0299348i
$466$	8.19900	+	50.4504i	0.379811	+	2.33707i
$467$	22.6243	−	20.0434i	1.04693	−	0.927496i	0.0494702	−	0.998776i	$-0.484247\pi$
$467$	22.6243	−	20.0434i	1.04693	−	0.927496i	0.997456	+	0.0712796i	$0.0227083\pi$
$468$	−6.33925	+	13.4480i	−0.293032	+	0.621633i
$469$	26.7265	+	23.6776i	1.23412	+	1.09333i
$470$	1.28757	−	2.03612i	0.0593910	−	0.0939193i
$471$	−16.8123	−	1.35723i	−0.774671	−	0.0625379i
$472$	−2.82408	−	13.8332i	−0.129989	−	0.636726i
$473$	−6.29386	−	25.5352i	−0.289392	−	1.17411i
$474$	−1.07955	+	6.64276i	−0.0495855	+	0.305112i
$475$	−7.29018	−	11.5285i	−0.334496	−	0.528964i
$476$	14.7857	+	28.1718i	0.677702	+	1.29125i
$477$	2.85255	−	9.84813i	0.130609	−	0.450915i
$478$	−13.6769	+	66.9940i	−0.625568	+	3.06423i
$479$	−34.9475	+	1.40834i	−1.59679	+	0.0643485i	−0.822607	−	0.568610i	$-0.807481\pi$
$479$	−34.9475	+	1.40834i	−1.59679	+	0.0643485i	−0.774186	+	0.632959i	$0.781840\pi$
$480$	0.347827	−	0.182554i	0.0158760	−	0.00833239i
$481$	22.5498	+	29.8497i	1.02818	+	1.36103i
$482$	−55.9455	−	29.3625i	−2.54825	−	1.33742i
$483$	5.64661	+	2.67935i	0.256930	+	0.121915i
$484$	−10.4724	−	18.1387i	−0.476018	−	0.824487i
$485$	0.0358817	−	0.0621490i	0.00162931	−	0.00282204i
$486$	2.03652	−	1.40571i	0.0923784	−	0.0637642i
$487$	−14.8506	+	19.7626i	−0.672947	+	0.895529i	−0.998754	−	0.0499070i	$-0.984108\pi$
$487$	−14.8506	+	19.7626i	−0.672947	+	0.895529i	0.325807	+	0.945436i	$0.394364\pi$
$488$	−55.6395	−	32.1235i	−2.51868	−	1.45416i
$489$	−0.627655	+	0.0762112i	−0.0283836	+	0.00344639i
$490$	4.21531	+	8.88358i	0.190428	+	0.401319i
$491$	−10.8881	−	11.3357i	−0.491374	−	0.511574i	0.428632	−	0.903479i	$-0.358996\pi$
$491$	−10.8881	−	11.3357i	−0.491374	−	0.511574i	−0.920006	+	0.391905i	$0.871816\pi$
$492$	−3.72646	+	46.1605i	−0.168002	+	2.08108i
$493$	8.24581	−	2.03241i	0.371373	−	0.0915352i
$494$	−21.9501	+	11.5917i	−0.987580	+	0.521533i
$495$	−1.21440	−	0.299322i	−0.0545831	−	0.0134535i
$496$	−7.95151	+	23.8177i	−0.357033	+	1.06944i
$497$	−23.1193	+	48.7230i	−1.03704	+	2.18552i
$498$	−15.0938	+	5.03903i	−0.676367	+	0.225805i
$499$	29.9116	+	20.6465i	1.33903	+	0.924265i	0.999864	−	0.0164627i	$-0.00524048\pi$
$499$	29.9116	+	20.6465i	1.33903	+	0.924265i	0.339164	+	0.940727i	$0.389856\pi$
$500$	11.5066	−	5.45997i	0.514592	−	0.244177i
$501$	1.64422	+	0.0662598i	0.0734583	+	0.00296027i
$502$	0.881155	−	3.57499i	0.0393279	−	0.159559i
$503$	17.9754	+	7.65861i	0.801484	+	0.341481i	0.753567	−	0.657371i	$-0.228331\pi$
$503$	17.9754	+	7.65861i	0.801484	+	0.341481i	0.0479170	+	0.998851i	$0.484742\pi$
$504$	23.0432	−	3.74488i	1.02643	−	0.166810i
$505$	2.13220	+	0.435292i	0.0948816	+	0.0193702i
$506$	−13.9588			−0.620544
$507$	11.0227	+	6.89202i	0.489536	+	0.306085i
$508$	−58.4933			−2.59522
$509$	22.2026	+	4.53269i	0.984111	+	0.200908i	0.665028	−	0.746819i	$-0.268420\pi$
$509$	22.2026	+	4.53269i	0.984111	+	0.200908i	0.319084	+	0.947727i	$0.396625\pi$
$510$	−1.32309	+	0.215023i	−0.0585874	+	0.00952138i
$511$	−50.9340	−	21.7010i	−2.25319	−	0.959994i
$512$	−10.5274	+	42.7113i	−0.465249	+	1.88759i
$513$	2.77990	+	0.112026i	0.122736	+	0.00494608i
$514$	60.7889	−	28.8447i	2.68128	−	1.27228i
$515$	−0.775814	−	0.535506i	−0.0341865	−	0.0235972i
$516$	−25.6521	+	8.56392i	−1.12927	+	0.377006i
$517$	−5.36540	+	11.3073i	−0.235970	+	0.497296i
$518$	36.1231	−	108.202i	1.58716	−	4.75411i
$519$	7.94492	+	1.95825i	0.348743	+	0.0859575i
$520$	−2.10954	−	5.51996i	−0.0925093	−	0.242066i
$521$	−21.4006	+	5.27479i	−0.937579	+	0.231093i	−0.678363	−	0.734727i	$-0.737310\pi$
$521$	−21.4006	+	5.27479i	−0.937579	+	0.231093i	−0.259216	+	0.965819i	$0.583464\pi$
$522$	0.973715	−	12.0616i	0.0426184	−	0.527923i
$523$	10.8796	+	11.3268i	0.475730	+	0.495287i	0.915217	−	0.402962i	$-0.132019\pi$
$523$	10.8796	+	11.3268i	0.475730	+	0.495287i	−0.439487	+	0.898249i	$0.644840\pi$
$524$	4.60617	+	9.70729i	0.201221	+	0.424065i
$525$	21.6235	−	2.62557i	0.943729	−	0.114589i
$526$	−58.1194	−	33.5553i	−2.53413	−	1.46308i
$527$	5.50848	−	7.33045i	0.239953	−	0.319319i
$528$	−15.6946	+	10.8332i	−0.683019	+	0.471454i
$529$	10.5105	−	18.2048i	0.456980	−	0.791512i
$530$	3.95683	+	6.85343i	0.171874	+	0.297694i
$531$	2.42751	+	1.15187i	0.105345	+	0.0499867i
$532$	45.1311	+	23.6866i	1.95668	+	1.02695i
$533$	39.6965	+	7.99888i	1.71945	+	0.346470i
$534$	−6.28447	+	3.29834i	−0.271956	+	0.142733i
$535$	−4.42488	+	0.178316i	−0.191304	+	0.00770929i
$536$	−8.44687	+	41.3755i	−0.364849	+	1.78715i
$537$	0.999745	−	3.45152i	0.0431422	−	0.148944i
$538$	8.35290	+	15.9151i	0.360119	+	0.686149i
$539$	−27.3030	−	43.1762i	−1.17602	−	1.85973i
$540$	−0.206312	+	1.26949i	−0.00887826	+	0.0546301i
$541$	−0.765053	−	3.10394i	−0.0328922	−	0.133449i	0.952200	−	0.305474i	$-0.0988150\pi$
$541$	−0.765053	−	3.10394i	−0.0328922	−	0.133449i	−0.985093	+	0.172025i	$0.944969\pi$
$542$	−7.18846	−	35.2114i	−0.308771	−	1.51246i
$543$	3.30186	+	0.266554i	0.141697	+	0.0114389i
$544$	−1.16898	+	1.84859i	−0.0501194	+	0.0792575i
$545$	0.344487	+	0.305188i	0.0147562	+	0.0130728i
$546$	−1.69699	−	39.6040i	−0.0726246	−	1.69490i
$547$	21.3837	−	18.9443i	0.914301	−	0.810000i	−0.0679276	−	0.997690i	$-0.521639\pi$
$547$	21.3837	−	18.9443i	0.914301	−	0.810000i	0.982228	+	0.187691i	$0.0601002\pi$
$548$	−1.51522	−	9.32355i	−0.0647272	−	0.398282i
$549$	11.2485	−	4.79256i	0.480076	−	0.204541i
$550$	−41.1172	+	26.0009i	−1.75324	+	1.10868i
$551$	9.02184	−	10.1836i	0.384343	−	0.433834i
$552$	0.594792	+	7.36782i	0.0253160	+	0.313595i
$553$	−3.82635	−	11.4613i	−0.162713	−	0.487385i
$554$	−42.4944	−	5.15975i	−1.80541	−	0.219217i
$555$	2.58722	+	1.94417i	0.109821	+	0.0825254i
$556$	44.8255	−	54.9013i	1.90103	−	2.32833i
$557$	8.52022	+	6.95655i	0.361013	+	0.294758i	0.795541	−	0.605900i	$-0.207187\pi$
$557$	8.52022	+	6.95655i	0.361013	+	0.294758i	−0.434527	+	0.900659i	$0.643084\pi$
$558$	−7.42194	−	10.7525i	−0.314196	−	0.455191i
$559$	4.78905	+	23.1573i	0.202555	+	0.979450i
$560$	−3.74387	+	5.42394i	−0.158208	+	0.229203i
$561$	6.68902	−	1.93750i	0.282411	−	0.0818012i
$562$	−9.04355	−	5.71879i	−0.381479	−	0.241233i
$563$	12.6047	+	2.04846i	0.531223	+	0.0863321i	0.420106	−	0.907475i	$-0.361993\pi$
$563$	12.6047	+	2.04846i	0.531223	+	0.0863321i	0.111117	+	0.993807i	$0.464557\pi$
$564$	12.0337	+	4.56377i	0.506709	+	0.192169i
$565$	2.03571	−	4.77799i	0.0856431	−	0.201012i
$566$	3.65818	+	3.51373i	0.153765	+	0.147693i
$567$	−2.06473	+	3.93401i	−0.0867105	+	0.165213i
$568$	−63.5747	+	5.13228i	−2.66754	+	0.215346i
$569$	−5.92667	−	20.4612i	−0.248459	−	0.857780i	−0.983676	−	0.179948i	$-0.942407\pi$
$569$	−5.92667	−	20.4612i	−0.248459	−	0.857780i	0.735217	−	0.677832i	$-0.237080\pi$
$570$	−1.54870	+	1.48755i	−0.0648680	+	0.0623066i
$571$	14.9495	+	39.4186i	0.625617	+	1.64962i	0.753202	+	0.657790i	$0.228508\pi$
$571$	14.9495	+	39.4186i	0.625617	+	1.64962i	−0.127584	+	0.991828i	$0.540722\pi$
$572$	27.8394	+	52.7170i	1.16402	+	2.20421i
$573$	3.97084	−	10.4702i	0.165884	−	0.437400i
$574$	−48.3992	−	113.597i	−2.02014	−	4.74145i
$575$	0.277708	+	6.89126i	0.0115812	+	0.287385i
$576$	−4.04457	−	4.95370i	−0.168524	−	0.206404i
$577$			5.67461i			0.236237i	0.993000	+	0.118118i	$0.0376863\pi$
$577$			5.67461i			0.236237i	−0.993000	+	0.118118i	$0.962314\pi$
$578$	−26.8044	+	21.8851i	−1.11492	+	0.910302i
$579$	−5.10383	−	1.47834i	−0.212108	−	0.0614379i
$580$	4.17064	+	4.70768i	0.173177	+	0.195476i
$581$	19.7913	−	20.6050i	0.821083	−	0.854838i
$582$	0.540036	+	0.180291i	0.0223852	+	0.00747329i
$583$	−24.6986	−	32.8678i	−1.02291	−	1.36125i
$584$	−7.89250	−	65.0006i	−0.326594	−	2.68975i
$585$	1.08101	+	0.310136i	0.0446941	+	0.0128225i
$586$	−7.70154	+	63.4279i	−0.318148	+	2.62018i
$587$	8.69359	−	5.01925i	0.358823	−	0.207167i	−0.309741	−	0.950821i	$-0.600242\pi$
$587$	8.69359	−	5.01925i	0.358823	−	0.207167i	0.668564	+	0.743654i	$0.266909\pi$
$588$	−41.9952	+	31.5574i	−1.73185	+	1.30140i
$589$	0.591483	−	14.6775i	0.0243716	−	0.604775i
$590$	−1.93912	+	0.735410i	−0.0798322	+	0.0302764i
$591$	−21.6677	+	4.42350i	−0.891291	+	0.181958i
$592$	48.3471	−	9.87014i	1.98706	−	0.405660i
$593$	16.6522	−	6.31533i	0.683822	−	0.259340i	0.0118650	−	0.999930i	$-0.496223\pi$
$593$	16.6522	−	6.31533i	0.683822	−	0.259340i	0.671957	+	0.740590i	$0.265454\pi$
$594$	0.399550	−	9.91472i	0.0163937	−	0.406806i
$595$	1.92402	−	1.44581i	0.0788770	−	0.0592722i
$596$	−32.4257	+	18.7210i	−1.32821	+	0.766841i
$597$	−0.249710	+	2.05655i	−0.0102200	+	0.0841689i
$598$	12.5422	+	0.473454i	0.512890	+	0.0193610i
$599$	−4.19097	−	34.5157i	−0.171238	−	1.41027i	−0.784370	−	0.620294i	$-0.787013\pi$
$599$	−4.19097	−	34.5157i	−0.171238	−	1.41027i	0.613131	−	0.789981i	$-0.289910\pi$
$600$	15.4760	+	20.5948i	0.631805	+	0.840780i
$601$	−7.48534	−	2.49897i	−0.305333	−	0.101935i	0.159873	−	0.987138i	$-0.448892\pi$
$601$	−7.48534	−	2.49897i	−0.305333	−	0.101935i	−0.465206	+	0.885202i	$0.654020\pi$
$602$	49.9502	−	52.0036i	2.03582	−	2.11951i
$603$	−5.32929	−	6.01553i	−0.217026	−	0.244971i
$604$	4.76980	+	1.38159i	0.194080	+	0.0562161i
$605$	−1.22724	+	1.00201i	−0.0498944	+	0.0407375i
$606$			17.2647i			0.701332i
$607$	−17.1987	−	21.0646i	−0.698073	−	0.854984i	0.296923	−	0.954901i	$-0.404040\pi$
$607$	−17.1987	−	21.0646i	−0.698073	−	0.854984i	−0.994996	+	0.0999174i	$0.968142\pi$
$608$	0.141086	+	3.50101i	0.00572179	+	0.141985i
$609$	8.51603	+	19.9879i	0.345087	+	0.809949i
$610$	−3.34651	+	8.82402i	−0.135496	+	0.357274i
$611$	5.20443	−	9.97787i	0.210549	−	0.403661i
$612$	−2.53936	−	6.69574i	−0.102648	−	0.270659i
$613$	8.49995	−	8.16432i	0.343310	−	0.329754i	−0.501162	−	0.865353i	$-0.667094\pi$
$613$	8.49995	−	8.16432i	0.343310	−	0.329754i	0.844472	+	0.535600i	$0.179914\pi$
$614$	11.6218	+	40.1230i	0.469016	+	1.61923i
$615$	3.49176	−	0.281884i	0.140801	−	0.0113667i
$616$	43.5044	−	82.8907i	1.75284	−	3.33976i
$617$	30.6046	+	29.3962i	1.23210	+	1.18344i	0.976231	+	0.216732i	$0.0695398\pi$
$617$	30.6046	+	29.3962i	1.23210	+	1.18344i	0.255865	+	0.966712i	$0.417640\pi$
$618$	2.93144	−	6.88034i	0.117920	−	0.276768i
$619$	25.9781	+	9.85218i	1.04415	+	0.395993i	0.816254	−	0.577694i	$-0.196047\pi$
$619$	25.9781	+	9.85218i	1.04415	+	0.395993i	0.227893	+	0.973686i	$0.426816\pi$
$620$	6.70273	+	1.08930i	0.269188	+	0.0437473i
$621$	−1.18897	−	0.751856i	−0.0477115	−	0.0301709i
$622$	56.9775	−	16.5037i	2.28459	−	0.661739i
$623$	7.23887	−	10.4873i	0.290019	−	0.420166i
$624$	14.4693	−	9.20149i	0.579236	−	0.368354i
$625$	13.3780	+	19.3814i	0.535120	+	0.775255i
$626$	4.40041	+	3.59283i	0.175876	+	0.143598i
$627$	7.05571	−	8.64167i	0.281778	−	0.345115i
$628$	55.6012	+	41.7816i	2.21873	+	1.66727i
$629$	−17.8878	−	2.17198i	−0.713234	−	0.0866023i
$630$	−1.08593	−	3.25276i	−0.0432645	−	0.129593i
$631$	−2.04244	−	25.3002i	−0.0813084	−	1.00719i	−0.900840	−	0.434152i	$-0.857048\pi$
$631$	−2.04244	−	25.3002i	−0.0813084	−	1.00719i	0.819531	−	0.573034i	$-0.194234\pi$
$632$	9.47633	−	10.6966i	0.376948	−	0.425487i
$633$	8.04196	−	5.08543i	0.319639	−	0.202128i
$634$	39.0241	−	16.6266i	1.54984	−	0.660326i
$635$	0.709765	+	4.36736i	0.0281662	+	0.173313i
$636$	−31.6450	+	28.0350i	−1.25480	+	1.11166i
$637$	23.0678	+	39.7207i	0.913978	+	1.57379i
$638$	−36.3204	−	32.1770i	−1.43794	−	1.27390i
$639$	6.48755	−	10.2592i	0.256643	−	0.405849i
$640$	5.70313	+	0.460404i	0.225436	+	0.0181991i
$641$	0.315346	+	1.54467i	0.0124554	+	0.0610107i	0.985543	−	0.169423i	$-0.0541905\pi$
$641$	0.315346	+	1.54467i	0.0124554	+	0.0610107i	−0.973088	+	0.230434i	$0.925985\pi$
$642$	−8.40795	−	34.1124i	−0.331835	−	1.34631i
$643$	−3.75382	+	23.0982i	−0.148036	+	0.910904i	0.801671	+	0.597765i	$0.203945\pi$
$643$	−3.75382	+	23.0982i	−0.148036	+	0.910904i	−0.949707	+	0.313139i	$0.898620\pi$
$644$	−13.7741	−	21.7819i	−0.542774	−	0.858328i
$645$	0.950685	+	1.81138i	0.0374332	+	0.0713229i
$646$	3.32648	−	11.4843i	0.130879	−	0.451845i
$647$	6.52955	−	31.9839i	0.256703	−	1.25742i	−0.623124	−	0.782123i	$-0.714137\pi$
$647$	6.52955	−	31.9839i	0.256703	−	1.25742i	0.879828	−	0.475293i	$-0.157658\pi$
$648$	−5.25028	+	0.211579i	−0.206250	+	0.00831160i
$649$	9.54023	−	5.00710i	0.374487	−	0.196546i
$650$	37.8265	−	21.9677i	1.48368	−	0.861644i
$651$	20.7710	+	10.9015i	0.814081	+	0.427263i
$652$	2.35538	+	1.11764i	0.0922440	+	0.0437703i
$653$	−6.94673	−	12.0321i	−0.271847	−	0.470852i	0.697488	−	0.716596i	$-0.254301\pi$
$653$	−6.94673	−	12.0321i	−0.271847	−	0.470852i	−0.969335	+	0.245744i	$0.920968\pi$
$654$	−1.82562	+	3.16206i	−0.0713873	+	0.123646i
$655$	0.668896	−	0.461705i	0.0261359	−	0.0180403i
$656$	32.0874	−	42.7006i	1.25280	−	1.66718i
$657$	10.7917	+	6.23062i	0.421026	+	0.243080i
$658$	−34.0650	+	4.13624i	−1.32799	+	0.161247i
$659$	11.8089	+	24.8868i	0.460010	+	0.969451i	0.992412	+	0.122959i	$0.0392384\pi$
$659$	11.8089	+	24.8868i	0.460010	+	0.969451i	−0.532402	+	0.846492i	$0.678710\pi$
$660$	3.57261	+	3.71949i	0.139064	+	0.144781i
$661$	−0.648386	+	8.03171i	−0.0252193	+	0.312397i	0.971833	+	0.235671i	$0.0757288\pi$
$661$	−0.648386	+	8.03171i	−0.0252193	+	0.312397i	−0.997052	+	0.0767262i	$0.975553\pi$
$662$	−64.0354	+	15.7833i	−2.48881	+	0.613435i
$663$	−6.07592	+	1.51400i	−0.235969	+	0.0587988i
$664$	32.8075	+	8.08633i	1.27318	+	0.313811i
$665$	1.22092	−	3.65710i	0.0473452	−	0.141816i
$666$	−11.0067	+	23.1962i	−0.426502	+	0.898833i
$667$	−6.52511	+	2.17840i	−0.252653	+	0.0843481i
$668$	−5.58421	−	3.85450i	−0.216060	−	0.149135i
$669$	11.1378	−	5.28494i	0.430611	−	0.204327i
$670$	6.19801	+	0.249771i	0.239450	+	0.00964951i
$671$	11.7334	−	47.6044i	0.452964	−	1.83775i
$672$	−5.14767	−	2.19322i	−0.198576	−	0.0846053i
$673$	−38.9819	+	6.33517i	−1.50264	+	0.244203i	−0.855354	−	0.518044i	$-0.826660\pi$
$673$	−38.9819	+	6.33517i	−1.50264	+	0.244203i	−0.647287	+	0.762247i	$0.724096\pi$
$674$	88.2600	+	18.0184i	3.39965	+	0.694043i
$675$	−4.90271			−0.188705
$676$	−23.2262	−	48.3114i	−0.893314	−	1.85813i
$677$	21.3687			0.821266			0.410633	−	0.911801i	$-0.365308\pi$
$677$	21.3687			0.821266			0.410633	+	0.911801i	$0.365308\pi$
$678$	40.3707	+	8.24174i	1.55043	+	0.316522i
$679$	−1.00897	+	0.163974i	−0.0387209	+	0.00629275i
$680$	2.61858	+	1.11567i	0.100418	+	0.0427841i
$681$	1.20321	−	4.88163i	0.0461072	−	0.187064i
$682$	−52.3483	−	2.10957i	−2.00452	−	0.0807794i
$683$	6.20647	−	2.94501i	0.237484	−	0.112688i	−0.306232	−	0.951957i	$-0.599068\pi$
$683$	6.20647	−	2.94501i	0.237484	−	0.112688i	0.543716	+	0.839269i	$0.317017\pi$
$684$	−9.44129	−	6.51685i	−0.360997	−	0.249178i
$685$	−0.677750	+	0.226266i	−0.0258955	+	0.00864518i
$686$	27.0515	−	57.0097i	1.03283	−	2.17664i
$687$	6.37197	−	19.0864i	0.243106	−	0.728191i
$688$	30.2849	+	7.46457i	1.15460	+	0.284584i
$689$	21.0773	+	30.3701i	0.802982	+	1.15701i
$690$	1.05423	−	0.259845i	0.0401340	−	0.00989214i
$691$	−2.29538	+	28.4334i	−0.0873204	+	1.08166i	0.793615	+	0.608420i	$0.208196\pi$
$691$	−2.29538	+	28.4334i	−0.0873204	+	1.08166i	−0.880935	+	0.473237i	$0.843086\pi$
$692$	−23.3730	−	24.3339i	−0.888510	−	0.925036i
$693$	7.63749	+	16.0957i	0.290124	+	0.611424i
$694$	54.7230	−	6.64457i	2.07726	−	0.252225i
$695$	−4.64308	−	2.68069i	−0.176122	−	0.101684i
$696$	−15.4363	+	20.5419i	−0.585110	+	0.778640i
$697$	−16.0522	+	11.0801i	−0.608022	+	0.419687i
$698$	−28.9637	+	50.1665i	−1.09629	+	1.89883i
$699$	10.3276	+	17.8879i	0.390625	+	0.676582i
$700$	−81.1461	−	38.5043i	−3.06703	−	1.45533i
$701$	−14.3380	−	7.52518i	−0.541540	−	0.284222i	0.171691	−	0.985151i	$-0.445077\pi$
$701$	−14.3380	−	7.52518i	−0.541540	−	0.284222i	−0.713231	+	0.700929i	$0.752769\pi$
$702$	−0.695290	+	8.89501i	−0.0262420	+	0.335720i
$703$	−25.5602	+	13.4150i	−0.964019	+	0.505956i
$704$	−25.6232	+	1.03258i	−0.965709	+	0.0389167i
$705$	0.194732	−	0.953862i	0.00733405	−	0.0359245i
$706$	−15.4416	+	53.3106i	−0.581153	+	2.00637i
$707$	−14.4054	−	27.4472i	−0.541772	−	1.03226i
$708$	−5.92153	−	9.36416i	−0.222545	−	0.351927i
$709$	3.24920	−	19.9932i	0.122026	−	0.750859i	−0.851851	−	0.523784i	$-0.824520\pi$
$709$	3.24920	−	19.9932i	0.122026	−	0.750859i	0.973877	−	0.227075i	$-0.0729161\pi$
$710$	2.24213	+	9.09668i	0.0841456	+	0.341392i
$711$	0.543999	+	2.66468i	0.0204015	+	0.0999333i
$712$	15.0220	+	1.21270i	0.562974	+	0.0454480i
$713$	−3.96969	+	6.27757i	−0.148666	+	0.235097i
$714$	14.2917	+	12.6614i	0.534855	+	0.473840i
$715$	3.59827	−	2.71828i	0.134568	−	0.101658i
$716$	−11.0908	+	9.82555i	−0.414481	+	0.367198i
$717$	4.43241	+	27.2737i	0.165531	+	1.01856i
$718$	−24.9586	+	10.6339i	−0.931446	+	0.396852i
$719$	−14.9460	+	9.45130i	−0.557393	+	0.352474i	−0.783270	−	0.621682i	$-0.786450\pi$
$719$	−14.9460	+	9.45130i	−0.557393	+	0.352474i	0.225877	+	0.974156i	$0.427475\pi$
$720$	0.983668	−	1.11033i	0.0366591	−	0.0413796i
$721$	1.08049	+	13.3842i	0.0402394	+	0.498454i
$722$	8.82316	+	26.4286i	0.328364	+	0.983570i
$723$	−25.3468	−	3.07766i	−0.942658	−	0.114459i
$724$	−10.9198	−	8.20571i	−0.405832	−	0.304963i
$725$	−15.1628	+	18.5710i	−0.563131	+	0.689710i
$726$	−9.73632	−	7.94946i	−0.361349	−	0.295032i
$727$	−25.4213	−	36.8291i	−0.942824	−	1.36592i	−0.930619	−	0.365990i	$-0.880730\pi$
$727$	−25.4213	−	36.8291i	−0.942824	−	1.36592i	−0.0122049	−	0.999926i	$-0.503885\pi$
$728$	−41.9010	+	73.0032i	−1.55295	+	2.70568i
$729$	0.568065	−	0.822984i	0.0210394	−	0.0304809i
$730$	−9.23838	+	2.67593i	−0.341928	+	0.0990406i
$731$	−9.62689	−	6.08768i	−0.356063	−	0.225161i
$732$	−49.7640	−	8.08745i	−1.83933	−	0.298921i
$733$	−34.5833	−	13.1157i	−1.27736	−	0.484440i	−0.379695	−	0.925112i	$-0.623971\pi$
$733$	−34.5833	−	13.1157i	−1.27736	−	0.484440i	−0.897668	+	0.440672i	$0.854740\pi$
$734$	−35.2511	+	82.7375i	−1.30114	+	3.05390i
$735$	2.86578	+	2.75262i	0.105706	+	0.101532i
$736$	0.823329	−	1.56872i	0.0303483	−	0.0578239i
$737$	−32.1219	+	2.59315i	−1.18322	+	0.0955197i
$738$	7.73223	+	26.6948i	0.284627	+	0.982648i
$739$	24.2144	−	23.2582i	0.890740	−	0.855567i	−0.0994861	−	0.995039i	$-0.531720\pi$
$739$	24.2144	−	23.2582i	0.890740	−	0.855567i	0.990226	+	0.139472i	$0.0445404\pi$
$740$	−4.73205	−	12.4774i	−0.173954	−	0.458678i
$741$	−6.63279	+	7.52538i	−0.243662	+	0.276452i
$742$	39.9723	−	105.398i	1.46743	−	3.86929i
$743$	13.3662	+	31.3716i	0.490358	+	1.15091i	0.962962	+	0.269637i	$0.0869037\pi$
$743$	13.3662	+	31.3716i	0.490358	+	1.15091i	−0.472604	+	0.881275i	$0.656686\pi$
$744$	1.11711	+	27.7207i	0.0409551	+	1.01629i
$745$	1.79125	+	2.19388i	0.0656262	+	0.0803775i
$746$			60.6055i			2.21893i
$747$	−4.98111	+	4.06695i	−0.182249	+	0.148802i
$748$	−27.5817	−	7.98913i	−1.00849	−	0.292112i
$749$	41.8297	+	47.2159i	1.52842	+	1.72523i
$750$	5.29473	−	5.51239i	0.193336	−	0.201284i
$751$	−13.2567	−	4.42575i	−0.483745	−	0.161498i	0.0643272	−	0.997929i	$-0.479510\pi$
$751$	−13.2567	−	4.42575i	−0.483745	−	0.161498i	−0.548072	+	0.836431i	$0.684638\pi$
$752$	−8.91727	−	11.8667i	−0.325179	−	0.432735i
$753$	−0.179351	−	1.47709i	−0.00653591	−	0.0538280i
$754$	31.5431	+	30.1436i	1.14873	+	1.09776i
$755$	0.0452780	−	0.372898i	0.00164784	−	0.0135711i
$756$	15.8656	−	9.16003i	0.577028	−	0.333147i
$757$	22.5410	−	16.9385i	0.819267	−	0.615639i	−0.106252	−	0.994339i	$-0.533885\pi$
$757$	22.5410	−	16.9385i	0.819267	−	0.615639i	0.925520	+	0.378700i	$0.123629\pi$
$758$	0.811260	−	20.1312i	0.0294663	−	0.731199i
$759$	−5.27436	+	2.00030i	−0.191447	+	0.0726063i
$760$	4.46767	−	0.912082i	0.162060	−	0.0330847i
$761$	18.2481	−	3.72539i	0.661495	−	0.135045i	0.142463	−	0.989800i	$-0.454498\pi$
$761$	18.2481	−	3.72539i	0.661495	−	0.135045i	0.519032	+	0.854755i	$0.326293\pi$
$762$	−32.8220	+	12.4477i	−1.18901	+	0.450934i
$763$	0.263967	−	6.55027i	0.00955623	−	0.237136i
$764$	−36.9133	+	27.7385i	−1.33548	+	1.00355i
$765$	−0.469120	+	0.270846i	−0.0169611	+	0.00979247i
$766$	0.0462534	−	0.380931i	0.00167120	−	0.0137636i
$767$	−8.74189	+	4.17538i	−0.315652	+	0.150764i
$768$	3.92983	+	32.3650i	0.141805	+	1.16787i
$769$	−22.6560	−	30.1496i	−0.816996	−	1.08722i	−0.994667	−	0.103134i	$-0.967113\pi$
$769$	−22.6560	−	30.1496i	−0.816996	−	1.08722i	0.177672	−	0.984090i	$-0.443143\pi$
$770$	−13.0433	−	4.35449i	−0.470048	−	0.156925i
$771$	18.8357	−	19.6101i	0.678353	−	0.706240i
$772$	14.5292	+	16.4001i	0.522919	+	0.590254i
$773$	27.9282	+	8.08951i	1.00451	+	0.290959i	0.739405	−	0.673261i	$-0.235107\pi$
$773$	27.9282	+	8.08951i	1.00451	+	0.290959i	0.265103	+	0.964220i	$0.414594\pi$
$774$	−12.5715	+	10.2643i	−0.451874	+	0.368944i
$775$			25.8856i			0.929839i
$776$	−0.764591	−	0.936454i	−0.0274472	−	0.0336167i
$777$	−1.85618	−	46.0607i	−0.0665902	−	1.65242i
$778$	−17.1685	−	40.2959i	−0.615519	−	1.44468i
$779$	−11.0803	+	29.2162i	−0.396991	+	1.04678i
$780$	−3.08390	−	3.46320i	−0.110421	−	0.124002i
$781$	−17.2600	−	45.5109i	−0.617612	−	1.62851i
$782$	−4.36004	+	4.18787i	−0.155915	+	0.149758i
$783$	−1.36052	−	4.69705i	−0.0486209	−	0.167859i
$784$	60.3903	−	4.87521i	2.15679	−	0.174114i
$785$	2.44492	−	4.65840i	0.0872629	−	0.166265i
$786$	4.65039	+	4.46676i	0.165874	+	0.159324i
$787$	−10.6992	+	25.1118i	−0.381384	+	0.895140i	0.613076	+	0.790024i	$0.289932\pi$
$787$	−10.6992	+	25.1118i	−0.381384	+	0.895140i	−0.994460	+	0.105116i	$0.966478\pi$
$788$	85.2624	+	32.3357i	3.03735	+	1.15191i
$789$	−26.7690	−	4.35039i	−0.953003	−	0.154878i
$790$	−1.77417	−	1.12192i	−0.0631221	−	0.0399160i
$791$	−71.0575	+	20.5821i	−2.52651	+	0.731814i
$792$	−11.9693	+	17.3405i	−0.425310	+	0.616168i
$793$	−12.1573	+	42.3754i	−0.431720	+	1.50480i
$794$	−6.67200	−	9.66607i	−0.236781	−	0.343036i
$795$	2.47719	+	2.02257i	0.0878570	+	0.0717331i
$796$	5.40254	−	6.61692i	0.191488	−	0.234530i
$797$	27.8854	+	20.9545i	0.987753	+	0.742248i	0.966273	−	0.257521i	$-0.0829057\pi$
$797$	27.8854	+	20.9545i	0.987753	+	0.742248i	0.0214803	+	0.999769i	$0.493162\pi$
$798$	30.3648	+	3.68695i	1.07490	+	0.130517i
$799$	1.71651	+	5.14157i	0.0607257	+	0.181896i
$800$	−0.496839	−	6.15446i	−0.0175659	−	0.217593i
$801$	−1.90195	+	2.14685i	−0.0672020	+	0.0758553i
$802$	69.9613	−	44.2409i	2.47042	−	1.56220i
$803$	45.9700	−	19.5860i	1.62225	−	0.691175i
$804$	5.31580	+	32.7095i	0.187474	+	1.15357i
$805$	−1.45919	+	1.29273i	−0.0514299	+	0.0455629i
$806$	46.9644	+	3.67103i	1.65425	+	0.129307i
$807$	5.43680	+	4.81659i	0.191385	+	0.169552i
$808$	19.5937	−	30.9850i	0.689305	−	1.09005i
$809$	−49.7278	−	4.01444i	−1.74833	−	0.141140i	−0.835506	−	0.549482i	$-0.814825\pi$
$809$	−49.7278	−	4.01444i	−1.74833	−	0.141140i	−0.912829	+	0.408342i	$0.866107\pi$
$810$	0.154388	+	0.756245i	0.00542466	+	0.0265717i
$811$	7.33508	+	29.7596i	0.257569	+	1.04500i	0.947150	+	0.320791i	$0.103949\pi$
$811$	7.33508	+	29.7596i	0.257569	+	1.04500i	−0.689581	+	0.724209i	$0.742205\pi$
$812$	14.3708	−	88.4271i	0.504316	−	3.10318i
$813$	−7.76199	−	12.2746i	−0.272225	−	0.430489i
$814$	47.8456	+	91.1621i	1.67699	+	3.19523i
$815$	0.0548675	−	0.189425i	0.00192193	−	0.00663526i
$816$	−1.65208	+	8.09240i	−0.0578342	+	0.283291i
$817$	−18.2322	+	0.734734i	−0.637865	+	0.0257051i
$818$	3.71806	−	1.95139i	0.129999	−	0.0682287i
$819$	−6.31649	−	14.7213i	−0.220716	−	0.514403i
$820$	−12.7903	−	6.71286i	−0.446656	−	0.234423i
$821$	−26.1475	−	12.4071i	−0.912554	−	0.433012i	−0.0862739	−	0.996271i	$-0.527496\pi$
$821$	−26.1475	−	12.4071i	−0.912554	−	0.433012i	−0.826280	+	0.563259i	$0.809547\pi$
$822$	−2.83433	−	4.90921i	−0.0988587	−	0.171228i
$823$	−3.77140	+	6.53226i	−0.131463	+	0.227700i	−0.924241	−	0.381810i	$-0.875301\pi$
$823$	−3.77140	+	6.53226i	−0.131463	+	0.227700i	0.792778	+	0.609511i	$0.208634\pi$
$824$	−13.0695	+	9.02126i	−0.455299	+	0.314270i
$825$	−11.8103	+	15.7166i	−0.411181	+	0.547183i
$826$	25.5831	+	14.7704i	0.890149	+	0.513928i
$827$	−14.2532	+	1.73065i	−0.495633	+	0.0601807i	−0.364537	−	0.931189i	$-0.618773\pi$
$827$	−14.2532	+	1.73065i	−0.495633	+	0.0601807i	−0.131096	+	0.991370i	$0.541850\pi$
$828$	2.48667	+	5.24056i	0.0864179	+	0.182122i
$829$	−11.7130	−	12.1945i	−0.406808	−	0.423532i	0.486007	−	0.873955i	$-0.338453\pi$
$829$	−11.7130	−	12.1945i	−0.406808	−	0.423532i	−0.892815	+	0.450423i	$0.851273\pi$
$830$	0.399384	−	4.94726i	0.0138628	−	0.171722i
$831$	−16.7960	+	4.13984i	−0.582646	+	0.143609i
$832$	23.0579	−	0.0587045i	0.799388	−	0.00203521i
$833$	−21.4817	−	5.29477i	−0.744297	−	0.183453i
$834$	13.4693	−	40.3455i	0.466404	−	1.39705i
$835$	−0.220034	+	0.463712i	−0.00761459	+	0.0160474i
$836$	−43.6345	+	14.5673i	−1.50913	+	0.503822i
$837$	−4.34524	−	2.99930i	−0.150193	−	0.103671i
$838$	−45.6055	+	21.6401i	−1.57542	+	0.747544i
$839$	17.6209	+	0.710099i	0.608342	+	0.0245153i	0.342526	−	0.939508i	$-0.388718\pi$
$839$	17.6209	+	0.710099i	0.608342	+	0.0245153i	0.265816	+	0.964024i	$0.414359\pi$
$840$	−1.74263	+	7.07014i	−0.0601266	+	0.243943i
$841$	4.67971	+	1.99384i	0.161369	+	0.0687531i
$842$	35.3551	−	5.74576i	1.21842	−	0.198012i
$843$	−4.23663	−	0.864914i	−0.145917	−	0.0297892i
$844$	−39.2343			−1.35050
$845$	−3.32531	+	2.32038i	−0.114394	+	0.0798235i
$846$	7.72357			0.265542
$847$	22.1116	+	4.51411i	0.759762	+	0.155107i
$848$	48.1294	−	7.82179i	1.65277	−	0.268601i
$849$	1.88577	+	0.803452i	0.0647195	+	0.0275744i
$850$	−5.04227	+	20.4573i	−0.172948	+	0.701679i
$851$	14.5840	+	0.587715i	0.499933	+	0.0201466i
$852$	−45.2192	+	21.4568i	−1.54919	+	0.735098i
$853$	35.6941	+	24.6378i	1.22214	+	0.843584i	0.991583	−	0.129474i	$-0.0413290\pi$
$853$	35.6941	+	24.6378i	1.22214	+	0.843584i	0.230559	+	0.973058i	$0.425944\pi$
$854$	127.508	−	42.5685i	4.36324	−	1.45666i
$855$	−0.372014	+	0.784004i	−0.0127226	+	0.0268124i
$856$	−23.6244	+	70.7637i	−0.807465	+	2.41865i
$857$	−10.5565	−	2.60194i	−0.360602	−	0.0888805i	0.0548521	−	0.998494i	$-0.482531\pi$
$857$	−10.5565	−	2.60194i	−0.360602	−	0.0888805i	−0.415454	+	0.909614i	$0.636377\pi$
$858$	26.8398	+	23.6563i	0.916297	+	0.807614i
$859$	55.0297	−	13.5636i	1.87759	−	0.462784i	0.877724	−	0.479167i	$-0.159061\pi$
$859$	55.0297	−	13.5636i	1.87759	−	0.462784i	0.999866	+	0.0163828i	$0.00521503\pi$
$860$	0.678759	−	8.40794i	0.0231455	−	0.286709i
$861$	−34.5663	−	35.9873i	−1.17802	−	1.22644i
$862$	−39.4306	−	83.0983i	−1.34301	−	2.83034i
$863$	36.7059	−	4.45690i	1.24948	−	0.151715i	0.531067	−	0.847330i	$-0.321791\pi$
$863$	36.7059	−	4.45690i	1.24948	−	0.151715i	0.718415	+	0.695615i	$0.244868\pi$
$864$	1.09067	+	0.629701i	0.0371055	+	0.0214229i
$865$	−1.53326	+	2.04040i	−0.0521325	+	0.0693757i
$866$	−31.0720	+	21.4475i	−1.05587	+	0.728815i
$867$	−6.99196	+	12.1104i	−0.237459	+	0.411292i
$868$	−48.3637	−	83.7683i	−1.64157	−	2.84328i
$869$	9.85263	+	4.67513i	0.334227	+	0.158593i
$870$	3.34207	+	1.75405i	0.113307	+	0.0594679i
$871$	28.9500	−	1.24048i	0.980934	−	0.0420320i
$872$	6.86505	−	3.60306i	0.232480	−	0.122015i
$873$	0.229890	−	0.00926424i	0.00778059	−	0.000313547i
$874$	−1.93722	+	9.48915i	−0.0655276	+	0.320975i
$875$	−3.81803	+	13.1814i	−0.129073	+	0.445611i
$876$	−23.8789	−	45.4974i	−0.806792	−	1.53721i
$877$	−23.5681	−	37.2699i	−0.795837	−	1.25851i	−0.962171	−	0.272445i	$-0.912168\pi$
$877$	−23.5681	−	37.2699i	−0.795837	−	1.25851i	0.166335	−	0.986069i	$-0.446807\pi$
$878$	5.64483	−	34.7340i	0.190504	−	1.17222i
$879$	6.17920	+	25.0700i	0.208419	+	0.845590i
$880$	−1.18981	−	5.82806i	−0.0401084	−	0.196464i
$881$	−4.35332	−	0.351437i	−0.146667	−	0.0118402i	0.00691490	−	0.999976i	$-0.497799\pi$
$881$	−4.35332	−	0.351437i	−0.146667	−	0.0118402i	−0.153582	+	0.988136i	$0.549081\pi$
$882$	−16.8489	+	26.6444i	−0.567332	+	0.897164i
$883$	−6.43349	−	5.69958i	−0.216504	−	0.191806i	0.547899	−	0.836545i	$-0.315428\pi$
$883$	−6.43349	−	5.69958i	−0.216504	−	0.191806i	−0.764403	+	0.644738i	$0.776966\pi$
$884$	24.5117	+	8.11389i	0.824416	+	0.272900i
$885$	−0.627315	+	0.555753i	−0.0210870	+	0.0186814i
$886$	0.441163	+	2.71459i	0.0148212	+	0.0911983i
$887$	6.01734	−	2.56375i	0.202042	−	0.0860823i	−0.288575	−	0.957457i	$-0.593181\pi$
$887$	6.01734	−	2.56375i	0.202042	−	0.0860823i	0.490618	+	0.871375i	$0.336771\pi$
$888$	46.0790	−	29.1386i	1.54631	−	0.977828i
$889$	41.7937	−	47.1753i	1.40172	−	1.58221i
$890$	−0.178135	−	2.20660i	−0.00597109	−	0.0739653i
$891$	−1.26981	−	3.80356i	−0.0425403	−	0.127424i
$892$	−50.4631	−	6.12733i	−1.68963	−	0.205158i
$893$	6.94209	+	5.21664i	0.232308	+	0.174568i
$894$	−14.2109	+	17.4052i	−0.475283	+	0.582116i
$895$	0.868194	+	0.708859i	0.0290205	+	0.0236945i
$896$	−46.2976	−	67.0736i	−1.54669	−	2.24077i
$897$	4.80695	−	1.61841i	0.160499	−	0.0540371i
$898$	−17.0454	+	24.6946i	−0.568814	+	0.824069i
$899$	−24.7997	+	7.18333i	−0.827117	+	0.239577i
$900$	17.0863	+	10.8047i	0.569545	+	0.360158i
$901$	−17.5755	−	2.85630i	−0.585526	−	0.0951572i
$902$	104.202	+	39.5185i	3.46954	+	1.31582i
$903$	11.4216	−	26.8076i	0.380088	−	0.892100i
$904$	−63.0997	−	60.6081i	−2.09867	−	2.01580i
$905$	−0.480171	+	0.914889i	−0.0159614	+	0.0304120i
$906$	2.97046	−	0.239800i	0.0986868	−	0.00796682i
$907$	8.26925	+	28.5488i	0.274576	+	0.947947i	0.972719	+	0.231988i	$0.0745230\pi$
$907$	8.26925	+	28.5488i	0.274576	+	0.947947i	−0.698143	+	0.715959i	$0.745990\pi$
$908$	−14.9516	+	14.3612i	−0.496186	+	0.476593i
$909$	2.47404	+	6.52352i	0.0820589	+	0.216372i
$910$	11.5719	+	4.35499i	0.383606	+	0.144367i
$911$	−0.750279	+	1.97832i	−0.0248579	+	0.0655448i	−0.946871	−	0.321615i	$-0.895774\pi$
$911$	−0.750279	+	1.97832i	−0.0248579	+	0.0655448i	0.922013	+	0.387159i	$0.126544\pi$
$912$	5.18626	+	12.1726i	0.171734	+	0.403075i
$913$	1.03829	+	25.7649i	0.0343624	+	0.852695i
$914$	−16.4499	−	20.1475i	−0.544115	−	0.666420i
$915$			3.81373i			0.126078i
$916$	−64.2699	+	52.4748i	−2.12354	+	1.73382i
$917$	−11.1201	−	3.22098i	−0.367219	−	0.106366i
$918$	−2.84979	−	3.21674i	−0.0940570	−	0.106168i
$919$	0.627675	−	0.653479i	0.0207051	−	0.0215563i	−0.710769	−	0.703425i	$-0.751653\pi$
$919$	0.627675	−	0.653479i	0.0207051	−	0.0215563i	0.731474	+	0.681869i	$0.238833\pi$
$920$	−2.18693	−	0.730105i	−0.0721010	−	0.0240708i
$921$	10.1409	+	13.4951i	0.334156	+	0.444680i
$922$	−1.38160	−	11.3785i	−0.0455007	−	0.374732i
$923$	13.9648	+	41.4778i	0.459657	+	1.36526i
$924$	8.85486	−	72.9264i	0.291304	−	2.39910i
$925$	44.0536	−	25.4344i	1.44847	−	0.836277i
$926$	−46.2261	+	34.7367i	−1.51908	+	1.14152i
$927$	0.121695	−	3.01983i	0.00399699	−	0.0991842i
$928$	5.75841	−	2.18388i	0.189029	−	0.0716893i
$929$	−40.5311	+	8.27448i	−1.32978	+	0.271477i	−0.811810	−	0.583922i	$-0.801518\pi$
$929$	−40.5311	+	8.27448i	−1.32978	+	0.271477i	−0.517971	+	0.855398i	$0.673312\pi$
$930$	3.99286	−	0.815149i	0.130931	−	0.0267298i
$931$	−33.1402	+	12.5684i	−1.08613	+	0.411914i
$932$	3.42945	−	85.1009i	0.112335	−	2.78757i
$933$	19.1641	−	14.4009i	0.627403	−	0.471463i
$934$	−64.7746	+	37.3976i	−2.11949	+	1.22369i
$935$	−0.261823	+	2.15631i	−0.00856253	+	0.0705188i
$936$	11.3428	−	15.1748i	0.370750	−	0.496003i
$937$	−2.44907	−	20.1699i	−0.0800076	−	0.658922i	−0.976447	−	0.215756i	$-0.930778\pi$
$937$	−2.44907	−	20.1699i	−0.0800076	−	0.658922i	0.896440	−	0.443166i	$-0.146145\pi$
$938$	−53.0799	−	70.6365i	−1.73312	−	2.30636i
$939$	2.17756	+	0.726976i	0.0710620	+	0.0237240i
$940$	−2.78081	+	2.89513i	−0.0907000	+	0.0944287i
$941$	17.4418	+	19.6877i	0.568585	+	0.641800i	0.960526	−	0.278190i	$-0.0897346\pi$
$941$	17.4418	+	19.6877i	0.568585	+	0.641800i	−0.391941	+	0.919990i	$0.628196\pi$
$942$	40.0905	+	11.6123i	1.30622	+	0.378351i
$943$	12.2382	−	9.99220i	0.398531	−	0.325391i
$944$			12.7785i			0.415904i
$945$	−0.876443	−	1.07345i	−0.0285107	−	0.0349192i
$946$	2.62048	+	65.0266i	0.0851992	+	2.11420i
$947$	1.24855	+	2.93045i	0.0405723	+	0.0952268i	0.939033	−	0.343828i	$-0.111724\pi$
$947$	1.24855	+	2.93045i	0.0405723	+	0.0952268i	−0.898460	+	0.439055i	$0.855313\pi$
$948$	3.97663	−	10.4855i	0.129155	−	0.340553i
$949$	−41.9692	+	16.0392i	−1.36238	+	0.520653i
$950$	11.9691	+	31.5598i	0.388328	+	1.02394i
$951$	12.3627	−	11.8746i	0.400889	−	0.385059i
$952$	−11.2800	−	38.9430i	−0.365587	−	1.26215i
$953$	−12.8222	+	1.03511i	−0.415352	+	0.0335306i	−0.286376	−	0.958117i	$-0.592451\pi$
$953$	−12.8222	+	1.03511i	−0.415352	+	0.0335306i	−0.128975	+	0.991648i	$0.541169\pi$
$954$	−11.7907	+	22.4653i	−0.381738	+	0.727341i
$955$	2.51899	+	2.41952i	0.0815125	+	0.0782939i
$956$	44.6594	−	104.819i	1.44439	−	3.39010i
$957$	−18.3347	−	6.95344i	−0.592677	−	0.224773i
$958$	85.4290	+	13.8836i	2.76008	+	0.448557i
$959$	8.60215	+	5.43967i	0.277778	+	0.175656i
$960$	1.91596	−	0.554965i	0.0618374	−	0.0179114i
$961$	1.77413	−	2.57026i	0.0572298	−	0.0829117i
$962$	−39.8981	−	83.5336i	−1.28637	−	2.69323i
$963$	−8.06529	−	11.6846i	−0.259900	−	0.376530i
$964$	81.5530	+	66.5859i	2.62664	+	2.14459i
$965$	1.04820	−	1.28382i	0.0337429	−	0.0413275i
$966$	−12.3643	−	9.29114i	−0.397814	−	0.298938i
$967$	23.2659	+	2.82499i	0.748181	+	0.0908456i	0.485741	−	0.874103i	$-0.338550\pi$
$967$	23.2659	+	2.82499i	0.748181	+	0.0908456i	0.262440	+	0.964948i	$0.415473\pi$
$968$	8.45193	+	25.3166i	0.271655	+	0.813707i
$969$	−0.388793	−	4.81607i	−0.0124898	−	0.154714i
$970$	−0.117759	+	0.132923i	−0.00378102	+	0.00426789i
$971$	45.6508	−	28.8678i	1.46500	−	0.926412i	0.465867	−	0.884855i	$-0.345742\pi$
$971$	45.6508	−	28.8678i	1.46500	−	0.926412i	0.999136	−	0.0415575i	$-0.0132320\pi$
$972$	−3.79347	+	1.61625i	−0.121676	+	0.0518411i
$973$	12.2503	+	75.3793i	0.392728	+	2.41655i
$974$	45.7880	−	40.5647i	1.46714	−	1.29978i
$975$	11.1448	−	13.7211i	0.356920	−	0.439427i
$976$	43.5250	+	38.5598i	1.39320	+	1.23427i
$977$	15.6311	−	24.7186i	0.500084	−	0.790820i	−0.496950	−	0.867779i	$-0.665547\pi$
$977$	15.6311	−	24.7186i	0.500084	−	0.790820i	0.997034	+	0.0769594i	$0.0245212\pi$
$978$	1.55950	+	0.125896i	0.0498674	+	0.00402571i
$979$	2.30052	+	11.2687i	0.0735249	+	0.360149i
$980$	−3.92117	−	15.9088i	−0.125257	−	0.508188i
$981$	−0.236689	+	1.45640i	−0.00755689	+	0.0464994i
$982$	20.7878	+	32.8733i	0.663367	+	1.04903i
$983$	6.50999	+	12.4038i	0.207637	+	0.395618i	0.966896	−	0.255169i	$-0.0821311\pi$
$983$	6.50999	+	12.4038i	0.207637	+	0.395618i	−0.759260	+	0.650788i	$0.774439\pi$
$984$	16.4188	−	56.6844i	0.523413	−	1.80703i
$985$	1.37974	−	6.75842i	0.0439622	−	0.215341i
$986$	−20.9984	+	0.846205i	−0.668724	+	0.0269487i
$987$	−12.2788	+	6.44442i	−0.390839	+	0.205128i
$988$	39.7005	−	11.6090i	1.26304	−	0.369332i
$989$	8.16944	+	4.28765i	0.259773	+	0.136339i
$990$	2.79621	+	1.32682i	0.0888692	+	0.0421690i
$991$	−21.7532	−	37.6777i	−0.691014	−	1.19687i	−0.971506	−	0.237015i	$-0.923831\pi$
$991$	−21.7532	−	37.6777i	−0.691014	−	1.19687i	0.280492	−	0.959856i	$-0.409502\pi$
$992$	3.32473	−	5.75860i	0.105560	−	0.182836i
$993$	−21.9341	+	15.1400i	−0.696059	+	0.480455i
$994$	80.1706	−	106.688i	2.54286	−	3.38393i
$995$	−0.559602	−	0.323087i	−0.0177406	−	0.0102425i
$996$	26.3224	−	3.19612i	0.834058	−	0.101273i
$997$	12.6727	+	26.7072i	0.401349	+	0.845825i	0.999028	+	0.0440895i	$0.0140387\pi$
$997$	12.6727	+	26.7072i	0.401349	+	0.845825i	−0.597678	+	0.801736i	$0.703910\pi$
$998$	−62.3026	−	64.8639i	−1.97216	−	2.05323i
$999$	−0.834891	+	10.3420i	−0.0264148	+	0.327206i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.t.b.10.2	✓	360
169.17	even	78	inner	507.2.t.b.355.2	yes	360

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.2.t.b.10.2	✓	360	1.1	even	1	trivial
507.2.t.b.355.2	yes	360	169.17	even	78	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.t (of order \(78\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.42455 - 0.494975i) q^{2} +(-0.987050 + 0.160411i) q^{3} +(3.79347 + 1.61625i) q^{4} +(0.0746454 - 0.302848i) q^{5} +(2.47255 + 0.0996403i) q^{6} +(-4.01396 + 1.90465i) q^{7} +(-4.32440 - 2.98492i) q^{8} +(0.948536 - 0.316668i) q^{9} +O(q^{10})\)	\(q+(-2.42455 - 0.494975i) q^{2} +(-0.987050 + 0.160411i) q^{3} +(3.79347 + 1.61625i) q^{4} +(0.0746454 - 0.302848i) q^{5} +(2.47255 + 0.0996403i) q^{6} +(-4.01396 + 1.90465i) q^{7} +(-4.32440 - 2.98492i) q^{8} +(0.948536 - 0.316668i) q^{9} +(-0.330883 + 0.697322i) q^{10} +(1.26981 - 3.80356i) q^{11} +(-4.00361 - 0.986801i) q^{12} +(-1.26996 + 3.37449i) q^{13} +(10.6748 - 2.63110i) q^{14} +(-0.0250985 + 0.310900i) q^{15} +(3.29445 + 3.42989i) q^{16} +(-0.744504 - 1.56901i) q^{17} +(-2.45651 + 0.298275i) q^{18} +(-2.40942 - 1.39108i) q^{19} +(0.772642 - 1.02820i) q^{20} +(3.65645 - 2.52387i) q^{21} +(-4.96139 + 8.59337i) q^{22} +(0.703372 + 1.21828i) q^{23} +(4.74721 + 2.25258i) q^{24} +(4.34114 + 2.27840i) q^{25} +(4.74936 - 7.55302i) q^{26} +(-0.885456 + 0.464723i) q^{27} +(-18.3052 + 0.737675i) q^{28} +(-0.978149 + 4.79129i) q^{29} +(0.214740 - 0.741369i) q^{30} +(2.45367 + 4.67508i) q^{31} +(-0.673107 - 1.06443i) q^{32} +(-0.643236 + 3.95799i) q^{33} +(1.02847 + 4.17265i) q^{34} +(0.277196 + 1.35779i) q^{35} +(4.11006 + 0.331798i) q^{36} +(5.54542 - 8.76938i) q^{37} +(5.15320 + 4.56534i) q^{38} +(0.712206 - 3.53451i) q^{39} +(-1.22677 + 1.08683i) q^{40} +(-1.80160 - 11.0857i) q^{41} +(-10.1145 + 4.30938i) q^{42} +(5.54325 - 3.50534i) q^{43} +(10.9645 - 12.3763i) q^{44} +(-0.0250985 - 0.310900i) q^{45} +(-1.10234 - 3.30192i) q^{46} +(-3.09844 - 0.376218i) q^{47} +(-3.80198 - 2.85701i) q^{48} +(8.05708 - 9.86813i) q^{49} +(-9.39753 - 7.67285i) q^{50} +(0.986550 + 1.42926i) q^{51} +(-10.2716 + 10.7485i) q^{52} +(5.82433 - 8.43800i) q^{53} +(2.37686 - 0.688465i) q^{54} +(-1.05711 - 0.668478i) q^{55} +(23.0432 + 3.74488i) q^{56} +(2.60136 + 0.986567i) q^{57} +(4.74314 - 11.1325i) q^{58} +(1.93782 + 1.86130i) q^{59} +(-0.597701 + 1.13882i) q^{60} +(12.1873 - 0.983861i) q^{61} +(-3.63500 - 12.5495i) q^{62} +(-3.20425 + 3.07772i) q^{63} +(-2.26774 - 5.97955i) q^{64} +(0.927162 + 0.636495i) q^{65} +(3.51866 - 9.27795i) q^{66} +(-3.15010 - 7.39356i) q^{67} +(-0.288348 - 7.15529i) q^{68} +(-0.889688 - 1.08967i) q^{69} -3.42924i q^{70} +(9.40245 - 7.67686i) q^{71} +(-5.04708 - 1.46190i) q^{72} +(8.26333 + 9.32737i) q^{73} +(-17.7858 + 18.5169i) q^{74} +(-4.65040 - 1.55253i) q^{75} +(-6.89173 - 9.17123i) q^{76} +(2.14745 + 17.6859i) q^{77} +(-3.47627 + 8.21706i) q^{78} +(-0.327817 + 2.69981i) q^{79} +(1.28465 - 0.741694i) q^{80} +(0.799443 - 0.600742i) q^{81} +(-1.11907 + 27.7695i) q^{82} +(-6.01264 + 2.28029i) q^{83} +(17.9498 - 3.66448i) q^{84} +(-0.530745 + 0.108352i) q^{85} +(-15.1749 + 5.75509i) q^{86} +(0.196905 - 4.88615i) q^{87} +(-16.8445 + 12.6578i) q^{88} +(-2.48391 + 1.43408i) q^{89} +(-0.0930354 + 0.766215i) q^{90} +(-1.32966 - 15.9639i) q^{91} +(0.699185 + 5.75831i) q^{92} +(-3.17183 - 4.22094i) q^{93} +(7.32608 + 2.44581i) q^{94} +(-0.601138 + 0.625851i) q^{95} +(0.835138 + 0.942676i) q^{96} +(0.220992 + 0.0640112i) q^{97} +(-24.4192 + 19.9377i) q^{98} -4.00992i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 360 q - 15 q^{3} - 14 q^{4} + 3 q^{7} + 15 q^{9}+O(q^{10}) \) 360 * q - 15 * q^3 - 14 * q^4 + 3 * q^7 + 15 * q^9	\( 360 q - 15 q^{3} - 14 q^{4} + 3 q^{7} + 15 q^{9} + 6 q^{11} - 28 q^{12} + 6 q^{13} + 4 q^{14} - 6 q^{15} + 20 q^{16} - 6 q^{19} - 12 q^{20} - 28 q^{22} + 46 q^{23} - 6 q^{25} - 39 q^{26} + 30 q^{27} - 6 q^{28} + 43 q^{29} + 26 q^{31} - 195 q^{32} + 19 q^{33} + 65 q^{34} + 84 q^{35} - 14 q^{36} - 65 q^{38} - 2 q^{39} + 12 q^{41} - 128 q^{42} + 83 q^{43} - 39 q^{44} - 6 q^{45} - 20 q^{48} + 72 q^{49} - 52 q^{50} - 55 q^{52} + 49 q^{53} - 49 q^{55} - 2 q^{56} + 26 q^{57} + 26 q^{58} - 202 q^{59} - 182 q^{60} - 3 q^{61} - 65 q^{62} - 3 q^{63} - 14 q^{64} - 58 q^{65} + 48 q^{66} - 41 q^{67} + 139 q^{68} + 6 q^{69} - 60 q^{71} - 52 q^{73} - 269 q^{74} + 23 q^{75} - 14 q^{76} + 70 q^{77} - 65 q^{78} + 18 q^{79} + 492 q^{80} + 15 q^{81} - 65 q^{82} + 78 q^{83} - 6 q^{84} - 91 q^{85} - 169 q^{86} + 48 q^{87} - 522 q^{88} - 12 q^{89} + 373 q^{91} + 72 q^{92} - 3 q^{93} - 13 q^{94} - 110 q^{95} + 65 q^{96} - 121 q^{97} - 104 q^{98}+O(q^{100}) \) 360 * q - 15 * q^3 - 14 * q^4 + 3 * q^7 + 15 * q^9 + 6 * q^11 - 28 * q^12 + 6 * q^13 + 4 * q^14 - 6 * q^15 + 20 * q^16 - 6 * q^19 - 12 * q^20 - 28 * q^22 + 46 * q^23 - 6 * q^25 - 39 * q^26 + 30 * q^27 - 6 * q^28 + 43 * q^29 + 26 * q^31 - 195 * q^32 + 19 * q^33 + 65 * q^34 + 84 * q^35 - 14 * q^36 - 65 * q^38 - 2 * q^39 + 12 * q^41 - 128 * q^42 + 83 * q^43 - 39 * q^44 - 6 * q^45 - 20 * q^48 + 72 * q^49 - 52 * q^50 - 55 * q^52 + 49 * q^53 - 49 * q^55 - 2 * q^56 + 26 * q^57 + 26 * q^58 - 202 * q^59 - 182 * q^60 - 3 * q^61 - 65 * q^62 - 3 * q^63 - 14 * q^64 - 58 * q^65 + 48 * q^66 - 41 * q^67 + 139 * q^68 + 6 * q^69 - 60 * q^71 - 52 * q^73 - 269 * q^74 + 23 * q^75 - 14 * q^76 + 70 * q^77 - 65 * q^78 + 18 * q^79 + 492 * q^80 + 15 * q^81 - 65 * q^82 + 78 * q^83 - 6 * q^84 - 91 * q^85 - 169 * q^86 + 48 * q^87 - 522 * q^88 - 12 * q^89 + 373 * q^91 + 72 * q^92 - 3 * q^93 - 13 * q^94 - 110 * q^95 + 65 * q^96 - 121 * q^97 - 104 * q^98

Introduction

L-functions

Modular forms

Varieties

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