LMFDB - Embedded newform 507.2.t.b.355.2

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			355.2
Character	$\chi$	$=$	507.355
Dual form			507.2.t.b.10.2

$q$-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 $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$1$	$e\left(\frac{73}{78}\right)$

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	−0.954084	−	0.299538i	$-0.903167\pi$
$2$	−2.42455	+	0.494975i	−1.71441	+	0.350000i	−0.760329	+	0.649538i	$0.774962\pi$
$3$	−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	0.985269	−	0.171014i	$-0.0547043\pi$
$5$	0.0746454	+	0.302848i	0.0333824	+	0.135438i	−0.951886	+	0.306452i	$0.900858\pi$
$6$	2.47255	−	0.0996403i	1.00941	−	0.0406780i
$7$	−4.01396	−	1.90465i	−1.51713	−	0.719889i	−0.525721	−	0.850657i	$-0.676205\pi$
$7$	−4.01396	−	1.90465i	−1.51713	−	0.719889i	−0.991413	+	0.130768i	$0.958256\pi$
$8$	−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	0.947027	+	0.321153i	$0.104070\pi$
$11$	1.26981	+	3.80356i	0.382863	+	1.14682i	−0.564164	+	0.825662i	$0.690802\pi$
$12$	−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	−0.973472	−	0.228807i	$-0.926517\pi$
$17$	−0.744504	+	1.56901i	−0.180569	+	0.380541i	0.792903	+	0.609348i	$0.208569\pi$
$18$	−2.45651	−	0.298275i	−0.579006	−	0.0703040i
$19$	−2.40942	+	1.39108i	−0.552759	+	0.319136i	−0.750234	−	0.661172i	$-0.770059\pi$
$19$	−2.40942	+	1.39108i	−0.552759	+	0.319136i	0.197475	+	0.980308i	$0.436726\pi$
$20$	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	−0.783329	−	0.621607i	$-0.786480\pi$
$23$	0.703372	−	1.21828i	0.146663	−	0.254028i	0.929992	+	0.367579i	$0.119813\pi$
$24$	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	−0.963796	−	0.266641i	$-0.914086\pi$
$29$	−0.978149	−	4.79129i	−0.181638	−	0.889720i	0.782158	−	0.623080i	$-0.214119\pi$
$30$	0.214740	+	0.741369i	0.0392060	+	0.135355i
$31$	2.45367	−	4.67508i	0.440693	−	0.839669i	−0.559251	−	0.828999i	$-0.688911\pi$
$31$	2.45367	−	4.67508i	0.440693	−	0.839669i	0.999943	−	0.0106708i	$-0.00339668\pi$
$32$	−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	0.897122	+	0.441783i	$0.145654\pi$
$37$	5.54542	+	8.76938i	0.911661	+	1.44168i	0.0145394	+	0.999894i	$0.495372\pi$
$38$	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	0.333581	+	0.942722i	$0.391743\pi$
$41$	−1.80160	+	11.0857i	−0.281362	+	1.73129i	−0.614943	+	0.788571i	$0.710821\pi$
$42$	−10.1145	−	4.30938i	−1.56070	−	0.664952i
$43$	5.54325	+	3.50534i	0.845338	+	0.534560i	0.885503	−	0.464633i	$-0.153814\pi$
$43$	5.54325	+	3.50534i	0.845338	+	0.534560i	−0.0401647	+	0.999193i	$0.512788\pi$
$44$	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	−0.343349	−	0.939208i	$-0.611561\pi$
$47$	−3.09844	+	0.376218i	−0.451953	+	0.0548771i	−0.108605	+	0.994085i	$0.534638\pi$
$48$	−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	0.984357	+	0.176183i	$0.0563750\pi$
$53$	5.82433	+	8.43800i	0.800033	+	1.15905i	−0.184324	+	0.982865i	$0.559010\pi$
$54$	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	−0.555905	−	0.831246i	$-0.687628\pi$
$59$	1.93782	−	1.86130i	0.252283	−	0.242321i	0.808188	+	0.588925i	$0.200449\pi$
$60$	−0.597701	−	1.13882i	−0.0771629	−	0.147022i
$61$	12.1873	+	0.983861i	1.56042	+	0.125970i	0.830289	−	0.557333i	$-0.188175\pi$
$61$	12.1873	+	0.983861i	1.56042	+	0.125970i	0.730135	+	0.683303i	$0.239457\pi$
$62$	−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	0.609069	+	0.793118i	$0.291543\pi$
$67$	−3.15010	+	7.39356i	−0.384846	+	0.903268i	−0.993915	+	0.110150i	$0.964867\pi$
$68$	−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	0.996649	−	0.0817925i	$-0.0260645\pi$
$71$	9.40245	+	7.67686i	1.11587	+	0.911076i	0.119216	+	0.992868i	$0.461962\pi$
$72$	−5.04708	+	1.46190i	−0.594804	+	0.172287i
$73$	8.26333	−	9.32737i	0.967149	−	1.09169i	−0.0286008	−	0.999591i	$-0.509105\pi$
$73$	8.26333	−	9.32737i	0.967149	−	1.09169i	0.995750	−	0.0920951i	$-0.0293564\pi$
$74$	−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	−0.999463	−	0.0327587i	$-0.989571\pi$
$79$	−0.327817	−	2.69981i	−0.0368823	−	0.303753i	0.962581	−	0.270994i	$-0.0873524\pi$
$80$	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	0.00180085	−	0.999998i	$-0.499427\pi$
$83$	−6.01264	−	2.28029i	−0.659973	−	0.250295i	−0.661774	+	0.749704i	$0.730196\pi$
$84$	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	0.362543	−	0.931967i	$-0.381909\pi$
$89$	−2.48391	−	1.43408i	−0.263293	−	0.152013i	−0.625836	+	0.779955i	$0.715242\pi$
$90$	−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	−0.266979	−	0.963702i	$-0.586026\pi$
$97$	0.220992	−	0.0640112i	0.0224384	−	0.00649936i	0.289418	+	0.957203i	$0.406538\pi$
$98$	−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	−0.923085	−	0.384595i	$-0.874341\pi$
$101$	0.280932	−	6.97125i	0.0279537	−	0.693665i	0.951039	−	0.309070i	$-0.100018\pi$
$102$	−1.68449	+	3.95363i	−0.166789	+	0.391468i
$103$	1.07172	+	2.82588i	0.105599	+	0.278442i	0.977393	−	0.211431i	$-0.0678123\pi$
$103$	1.07172	+	2.82588i	0.105599	+	0.278442i	−0.871794	+	0.489873i	$0.837043\pi$
$104$	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	0.507688	+	0.861541i	$0.330500\pi$
$107$	−3.95008	+	13.6373i	−0.381869	+	1.31836i	−0.889557	+	0.456824i	$0.848987\pi$
$108$	−4.11006	−	0.331798i	−0.395490	−	0.0319273i
$109$	−0.685704	−	1.30650i	−0.0656786	−	0.125140i	0.850403	−	0.526131i	$-0.176358\pi$
$109$	−0.685704	−	1.30650i	−0.0656786	−	0.125140i	−0.916082	+	0.400991i	$0.868666\pi$
$110$	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	0.673306	−	0.739364i	$-0.264874\pi$
$113$	16.4352	−	2.67098i	1.54609	−	0.251265i	0.872788	+	0.488100i	$0.162310\pi$
$114$	−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	−0.274426	−	0.961608i	$-0.588488\pi$
$127$	−13.0505	−	5.56029i	−1.15804	−	0.493396i	−0.883616	+	0.468212i	$0.844898\pi$
$128$	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	−0.573607	−	0.819131i	$-0.694456\pi$
$131$	1.95044	−	1.72794i	0.170411	−	0.150971i	0.744018	+	0.668160i	$0.232918\pi$
$132$	−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	−0.893435	−	0.449193i	$-0.851712\pi$
$137$	−1.22434	+	1.93615i	−0.104603	+	0.165416i	0.788832	+	0.614609i	$0.210686\pi$
$138$	1.61773	−	3.08233i	0.137710	−	0.262385i
$139$	4.78221	+	16.5101i	0.405622	+	1.40037i	0.860334	+	0.509730i	$0.170255\pi$
$139$	4.78221	+	16.5101i	0.405622	+	1.40037i	−0.454713	+	0.890638i	$0.650258\pi$
$140$	−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	0.518645	−	0.854990i	$-0.326437\pi$
$149$	−5.45492	−	7.25918i	−0.446885	−	0.594696i	−0.965529	+	0.260294i	$0.916180\pi$
$150$	10.5066	−	6.06602i	0.857864	−	0.495288i
$151$	1.19552	+	0.145163i	0.0972904	+	0.0118132i	0.169037	−	0.985610i	$-0.445934\pi$
$151$	1.19552	+	0.145163i	0.0972904	+	0.0118132i	−0.0717467	+	0.997423i	$0.522857\pi$
$152$	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	0.476516	−	0.879166i	$-0.341900\pi$
$157$	16.3769	−	4.03654i	1.30702	−	0.322151i	0.830502	+	0.557015i	$0.188053\pi$
$158$	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	−0.0155123	−	0.999880i	$-0.504938\pi$
$163$	0.631752	−	0.0254588i	0.0494827	−	0.00199408i	0.0649949	+	0.997886i	$0.479297\pi$
$164$	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	−0.262002	−	0.965067i	$-0.584383\pi$
$167$	−1.61230	+	0.329153i	−0.124763	+	0.0254706i	0.137238	+	0.990538i	$0.456177\pi$
$168$	−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	−0.658690	−	0.752415i	$-0.728889\pi$
$173$	−7.52791	+	3.20734i	−0.572337	+	0.243850i	0.0863530	+	0.996265i	$0.472479\pi$
$174$	−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	0.837697	−	0.546135i	$-0.183901\pi$
$179$	−1.54046	−	3.24645i	−0.115139	−	0.242651i	−0.952837	+	0.303484i	$0.901850\pi$
$180$	0.407281	+	1.21996i	0.0303569	+	0.0909301i
$181$	−3.21635	+	0.792759i	−0.239069	+	0.0589253i	−0.357030	−	0.934093i	$-0.616211\pi$
$181$	−3.21635	+	0.792759i	−0.239069	+	0.0589253i	0.117960	+	0.993018i	$0.462364\pi$
$182$	−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	0.589210	−	0.807980i	$-0.299439\pi$
$191$	−5.59896	−	9.69768i	−0.405126	−	0.701699i	−0.994336	+	0.106281i	$0.966106\pi$
$192$	3.19756	−	5.53834i	0.230764	−	0.399695i
$193$	4.80060	−	2.27791i	0.345555	−	0.163968i	−0.248003	−	0.968759i	$-0.579774\pi$
$193$	4.80060	−	2.27791i	0.345555	−	0.163968i	0.593557	+	0.804792i	$0.297723\pi$
$194$	−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	0.811964	−	0.583708i	$-0.198399\pi$
$197$	22.0967	+	0.890467i	1.57433	+	0.0634431i	0.762362	+	0.647151i	$0.224040\pi$
$198$	−1.98481	−	9.72224i	−0.141054	−	0.690929i
$199$	0.576370	+	1.98986i	0.0408578	+	0.141057i	0.978354	−	0.206938i	$-0.0663497\pi$
$199$	0.576370	+	1.98986i	0.0408578	+	0.141057i	−0.937496	+	0.347995i	$0.886863\pi$
$200$	−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	0.0690371	−	0.997614i	$-0.478007\pi$
$211$	−8.75358	−	3.72955i	−0.602621	−	0.256753i	−0.671658	+	0.740861i	$0.734418\pi$
$212$	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	−0.143066	−	0.989713i	$-0.545696\pi$
$223$	−11.8413	−	3.42987i	−0.792952	−	0.229681i	−0.649886	+	0.760032i	$0.725183\pi$
$224$	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	0.841683	−	0.539972i	$-0.181565\pi$
$227$	−1.97070	−	4.62540i	−0.130800	−	0.306999i	−0.972483	+	0.232973i	$0.925155\pi$
$228$	8.27365	−	7.94695i	0.547936	−	0.526300i
$229$	−9.35112	−	17.8171i	−0.617940	−	1.17739i	−0.970387	−	0.241554i	$-0.922343\pi$
$229$	−9.35112	−	17.8171i	−0.617940	−	1.17739i	0.352448	−	0.935831i	$-0.385349\pi$
$230$	−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	0.448596	+	0.893735i	$0.351924\pi$
$233$	−7.32442	+	19.3129i	−0.479839	+	1.26523i	−0.928435	+	0.371496i	$0.878845\pi$
$234$	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	$0.351877\pi$
$239$			27.6316i			1.78734i	−0.448728	+	0.893668i	$0.648123\pi$
$240$	−1.14904	−	0.938162i	−0.0741702	−	0.0605581i
$241$	24.5249	−	7.10372i	1.57979	−	0.457591i	0.631597	−	0.775297i	$-0.282400\pi$
$241$	24.5249	−	7.10372i	1.57979	−	0.457591i	0.948189	+	0.317706i	$0.102913\pi$
$242$	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	−0.999978	−	0.00669922i	$-0.997868\pi$
$251$	−0.0599131	−	1.48673i	−0.00378168	−	0.0938415i	0.996196	−	0.0871423i	$-0.0277735\pi$
$252$	−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	−0.996309	−	0.0858379i	$-0.972643\pi$
$257$	−21.7375	−	16.3347i	−1.35595	−	1.01893i	−0.359639	−	0.933091i	$-0.617100\pi$
$258$	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	0.619430	−	0.785052i	$-0.287364\pi$
$263$	25.7245	−	8.58811i	1.58624	−	0.529566i	0.966813	+	0.255486i	$0.0822354\pi$
$264$	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	−0.895419	−	0.445224i	$-0.853124\pi$
$269$	−4.59376	+	5.62634i	−0.280087	+	0.343044i	0.615333	+	0.788267i	$0.289022\pi$
$270$	−0.0310790	+	0.771217i	−0.00189141	+	0.0469348i
$271$	5.69249	−	13.3608i	0.345794	−	0.811608i	−0.652745	−	0.757577i	$-0.726383\pi$
$271$	5.69249	−	13.3608i	0.345794	−	0.811608i	0.998539	−	0.0540308i	$-0.0172069\pi$
$272$	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	0.586750	−	0.809768i	$-0.300407\pi$
$277$	17.2426	+	1.39196i	1.03601	+	0.0836350i	0.449255	+	0.893403i	$0.351689\pi$
$278$	−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	−0.231050	−	0.972942i	$-0.574216\pi$
$281$	4.04302	−	1.53332i	0.241187	−	0.0914700i	0.472237	+	0.881472i	$0.343447\pi$
$282$	−7.62355	+	1.23895i	−0.453976	+	0.0737782i
$283$	−1.73247	+	1.09555i	−0.102985	+	0.0651235i	−0.584965	−	0.811058i	$-0.698892\pi$
$283$	−1.73247	+	1.09555i	−0.102985	+	0.0651235i	0.481981	+	0.876182i	$0.339918\pi$
$284$	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	0.593805	+	0.804609i	$0.297625\pi$
$293$	−2.07767	+	25.7366i	−0.121379	+	1.50355i	−0.715184	+	0.698937i	$0.753657\pi$
$294$	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	0.552085	+	0.833788i	$0.313832\pi$
$307$	−7.84485	+	14.9471i	−0.447729	+	0.853077i	−0.999814	+	0.0192888i	$0.993860\pi$
$308$	−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	−0.260919	−	0.965361i	$-0.584025\pi$
$311$	−21.2260	−	11.1402i	−1.20361	−	0.631705i	−0.942695	+	0.333656i	$0.891718\pi$
$312$	−13.6301	−	13.1588i	−0.771652	−	0.744968i
$313$	−2.03275	+	1.06687i	−0.114898	+	0.0603029i	−0.521193	−	0.853439i	$-0.674513\pi$
$313$	−2.03275	+	1.06687i	−0.114898	+	0.0603029i	0.406295	+	0.913742i	$0.366820\pi$
$314$	−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	0.101736	−	0.994811i	$-0.467560\pi$
$317$	−14.1074	−	9.73767i	−0.792353	−	0.546922i	−0.894089	+	0.447890i	$0.852176\pi$
$318$	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	0.953601	−	0.301074i	$-0.0973453\pi$
$331$	24.0787	+	11.4255i	1.32349	+	0.628003i	0.369887	+	0.929077i	$0.379397\pi$
$332$	−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	−0.313343	−	0.949640i	$-0.601449\pi$
$347$	−21.1302	−	7.05431i	−1.13433	−	0.378695i	−0.820988	+	0.570945i	$0.806577\pi$
$348$	8.64417	+	18.2172i	0.463376	+	0.976545i
$349$	7.41294	+	22.2045i	0.396805	+	1.18858i	0.937688	+	0.347479i	$0.112962\pi$
$349$	7.41294	+	22.2045i	0.396805	+	1.18858i	−0.540882	+	0.841098i	$0.681910\pi$
$350$	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	0.847752	+	0.530393i	$0.177956\pi$
$353$	1.80479	+	22.3563i	0.0960593	+	1.18991i	−0.751692	+	0.659514i	$0.770762\pi$
$354$	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	0.781871	−	0.623440i	$-0.214266\pi$
$359$	9.02269	+	6.22791i	0.476199	+	0.328697i	−0.305672	+	0.952137i	$0.598881\pi$
$360$	−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	0.499942	+	0.866059i	$0.333355\pi$
$367$	7.26963	+	35.6090i	0.379472	+	1.85878i	−0.120470	+	0.992717i	$0.538440\pi$
$368$	−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	0.630828	+	0.775923i	$0.282716\pi$
$373$	−4.89893	+	23.9965i	−0.253657	+	1.24249i	−0.884484	+	0.466570i	$0.845490\pi$
$374$	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	−0.931685	−	0.363267i	$-0.881661\pi$
$379$	1.30605	−	8.03645i	0.0670873	−	0.412805i	0.998772	−	0.0495374i	$-0.0157747\pi$
$380$	−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	−0.996431	−	0.0844149i	$-0.973098\pi$
$383$	0.0124779	−	0.154567i	0.000637593	−	0.00789800i	0.997068	+	0.0765169i	$0.0243799\pi$
$384$	−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	−0.480571	−	0.876956i	$-0.659571\pi$
$389$	10.0550	−	14.5672i	0.509810	−	0.738587i	0.990381	+	0.138369i	$0.0441860\pi$
$390$	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	−0.601893	−	0.798577i	$-0.705587\pi$
$397$	3.42309	−	3.28792i	0.171800	−	0.165016i	0.773693	+	0.633560i	$0.218407\pi$
$398$	−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	−0.983301	−	0.181988i	$-0.941747\pi$
$401$	−24.1248	−	23.1722i	−1.20473	−	1.15716i	−0.221434	−	0.975175i	$-0.571074\pi$
$402$	−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	0.599392	−	0.800456i	$-0.295409\pi$
$409$	−1.31441	−	1.07319i	−0.0649936	−	0.0530656i	−0.664385	+	0.747390i	$0.731307\pi$
$410$	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	0.919202	−	0.393786i	$-0.128835\pi$
$419$	16.3081	+	12.2547i	0.796702	+	0.598683i	−0.122500	+	0.992468i	$0.539091\pi$
$420$	0.230089	+	5.70961i	0.0112272	+	0.278600i
$421$	−13.5343	−	5.13287i	−0.659620	−	0.250161i	0.00200260	−	0.999998i	$-0.499363\pi$
$421$	−13.5343	−	5.13287i	−0.659620	−	0.250161i	−0.661622	+	0.749837i	$0.730132\pi$
$422$	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	0.181510	−	0.983389i	$-0.441902\pi$
$431$	22.3295	−	29.7152i	1.07557	−	1.43133i	0.894064	−	0.447939i	$-0.147842\pi$
$432$	−4.51104	+	1.50601i	−0.217038	+	0.0724578i
$433$	10.5692	+	11.0037i	0.507923	+	0.528804i	0.924949	−	0.380091i	$-0.124107\pi$
$433$	10.5692	+	11.0037i	0.507923	+	0.528804i	−0.417026	+	0.908894i	$0.636928\pi$
$434$	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	−0.926230	−	0.376958i	$-0.876970\pi$
$439$	0.572607	−	14.2091i	0.0273290	−	0.678163i	0.953559	−	0.301205i	$-0.0973888\pi$
$440$	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	−0.944053	−	0.329795i	$-0.893020\pi$
$443$	−0.394105	+	1.03917i	−0.0187245	+	0.0493724i	0.925328	+	0.379167i	$0.123790\pi$
$444$	−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	0.993669	−	0.112348i	$-0.0358370\pi$
$449$	4.75294	+	11.1556i	0.224305	+	0.526463i	−0.769364	+	0.638811i	$0.779427\pi$
$450$	−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	−0.422605	−	0.906314i	$-0.638884\pi$
$457$	8.14187	−	6.64763i	0.380860	−	0.310963i	0.803466	+	0.595351i	$0.202987\pi$
$458$	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	−0.908844	−	0.417136i	$-0.863034\pi$
$461$	1.46680	−	4.39360i	0.0683157	−	0.204630i	0.977160	+	0.212505i	$0.0681622\pi$
$462$	3.54746	−	43.9431i	0.165043	−	2.04442i
$463$	15.4952	+	17.4904i	0.720122	+	0.812850i	0.988621	−	0.150430i	$-0.0480659\pi$
$463$	15.4952	+	17.4904i	0.720122	+	0.812850i	−0.268499	+	0.963280i	$0.586527\pi$
$464$	−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	0.997456	−	0.0712796i	$-0.0227083\pi$
$467$	22.6243	+	20.0434i	1.04693	+	0.927496i	0.0494702	+	0.998776i	$0.484247\pi$
$468$	−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	−0.774186	−	0.632959i	$-0.781840\pi$
$479$	−34.9475	−	1.40834i	−1.59679	−	0.0643485i	−0.822607	+	0.568610i	$0.807481\pi$
$480$	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	0.325807	−	0.945436i	$-0.394364\pi$
$487$	−14.8506	−	19.7626i	−0.672947	−	0.895529i	−0.998754	+	0.0499070i	$0.984108\pi$
$488$	−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	−0.920006	−	0.391905i	$-0.871816\pi$
$491$	−10.8881	+	11.3357i	−0.491374	+	0.511574i	0.428632	+	0.903479i	$0.358996\pi$
$492$	−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	0.339164	−	0.940727i	$-0.389856\pi$
$499$	29.9116	−	20.6465i	1.33903	−	0.924265i	0.999864	+	0.0164627i	$0.00524048\pi$
$500$	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	0.0479170	−	0.998851i	$-0.484742\pi$
$503$	17.9754	−	7.65861i	0.801484	−	0.341481i	0.753567	+	0.657371i	$0.228331\pi$
$504$	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	0.319084	−	0.947727i	$-0.396625\pi$
$509$	22.2026	−	4.53269i	0.984111	−	0.200908i	0.665028	+	0.746819i	$0.268420\pi$
$510$	−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	−0.259216	−	0.965819i	$-0.583464\pi$
$521$	−21.4006	−	5.27479i	−0.937579	−	0.231093i	−0.678363	+	0.734727i	$0.737310\pi$
$522$	0.973715	+	12.0616i	0.0426184	+	0.527923i
$523$	10.8796	−	11.3268i	0.475730	−	0.495287i	−0.439487	−	0.898249i	$-0.644840\pi$
$523$	10.8796	−	11.3268i	0.475730	−	0.495287i	0.915217	+	0.402962i	$0.132019\pi$
$524$	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	−0.985093	−	0.172025i	$-0.944969\pi$
$541$	−0.765053	+	3.10394i	−0.0328922	+	0.133449i	0.952200	+	0.305474i	$0.0988150\pi$
$542$	−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	0.982228	−	0.187691i	$-0.0601002\pi$
$547$	21.3837	+	18.9443i	0.914301	+	0.810000i	−0.0679276	+	0.997690i	$0.521639\pi$
$548$	−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	−0.434527	−	0.900659i	$-0.643084\pi$
$557$	8.52022	−	6.95655i	0.361013	−	0.294758i	0.795541	+	0.605900i	$0.207187\pi$
$558$	−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	0.111117	−	0.993807i	$-0.464557\pi$
$563$	12.6047	−	2.04846i	0.531223	−	0.0863321i	0.420106	+	0.907475i	$0.361993\pi$
$564$	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	0.735217	+	0.677832i	$0.237080\pi$
$569$	−5.92667	+	20.4612i	−0.248459	+	0.857780i	−0.983676	+	0.179948i	$0.942407\pi$
$570$	−1.54870	−	1.48755i	−0.0648680	−	0.0623066i
$571$	14.9495	−	39.4186i	0.625617	−	1.64962i	−0.127584	−	0.991828i	$-0.540722\pi$
$571$	14.9495	−	39.4186i	0.625617	−	1.64962i	0.753202	−	0.657790i	$-0.228508\pi$
$572$	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	$-0.962314\pi$
$577$		−	5.67461i		−	0.236237i	0.993000	−	0.118118i	$-0.0376863\pi$
$578$	−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	0.668564	−	0.743654i	$-0.266909\pi$
$587$	8.69359	+	5.01925i	0.358823	+	0.207167i	−0.309741	+	0.950821i	$0.600242\pi$
$588$	−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	0.671957	−	0.740590i	$-0.265454\pi$
$593$	16.6522	+	6.31533i	0.683822	+	0.259340i	0.0118650	+	0.999930i	$0.496223\pi$
$594$	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	0.613131	+	0.789981i	$0.289910\pi$
$599$	−4.19097	+	34.5157i	−0.171238	+	1.41027i	−0.784370	+	0.620294i	$0.787013\pi$
$600$	15.4760	−	20.5948i	0.631805	−	0.840780i
$601$	−7.48534	+	2.49897i	−0.305333	+	0.101935i	−0.465206	−	0.885202i	$-0.654020\pi$
$601$	−7.48534	+	2.49897i	−0.305333	+	0.101935i	0.159873	+	0.987138i	$0.448892\pi$
$602$	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	−0.994996	−	0.0999174i	$-0.968142\pi$
$607$	−17.1987	+	21.0646i	−0.698073	+	0.854984i	0.296923	+	0.954901i	$0.404040\pi$
$608$	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	0.844472	−	0.535600i	$-0.179914\pi$
$613$	8.49995	+	8.16432i	0.343310	+	0.329754i	−0.501162	+	0.865353i	$0.667094\pi$
$614$	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	0.255865	−	0.966712i	$-0.417640\pi$
$617$	30.6046	−	29.3962i	1.23210	−	1.18344i	0.976231	−	0.216732i	$-0.0695398\pi$
$618$	2.93144	+	6.88034i	0.117920	+	0.276768i
$619$	25.9781	−	9.85218i	1.04415	−	0.395993i	0.227893	−	0.973686i	$-0.426816\pi$
$619$	25.9781	−	9.85218i	1.04415	−	0.395993i	0.816254	+	0.577694i	$0.196047\pi$
$620$	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	0.819531	+	0.573034i	$0.194234\pi$
$631$	−2.04244	+	25.3002i	−0.0813084	+	1.00719i	−0.900840	+	0.434152i	$0.857048\pi$
$632$	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	−0.973088	−	0.230434i	$-0.925985\pi$
$641$	0.315346	−	1.54467i	0.0124554	−	0.0610107i	0.985543	+	0.169423i	$0.0541905\pi$
$642$	−8.40795	+	34.1124i	−0.331835	+	1.34631i
$643$	−3.75382	−	23.0982i	−0.148036	−	0.910904i	−0.949707	−	0.313139i	$-0.898620\pi$
$643$	−3.75382	−	23.0982i	−0.148036	−	0.910904i	0.801671	−	0.597765i	$-0.203945\pi$
$644$	−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	0.879828	+	0.475293i	$0.157658\pi$
$647$	6.52955	+	31.9839i	0.256703	+	1.25742i	−0.623124	+	0.782123i	$0.714137\pi$
$648$	−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	−0.969335	−	0.245744i	$-0.920968\pi$
$653$	−6.94673	+	12.0321i	−0.271847	+	0.470852i	0.697488	+	0.716596i	$0.254301\pi$
$654$	−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	−0.532402	−	0.846492i	$-0.678710\pi$
$659$	11.8089	−	24.8868i	0.460010	−	0.969451i	0.992412	−	0.122959i	$-0.0392384\pi$
$660$	3.57261	−	3.71949i	0.139064	−	0.144781i
$661$	−0.648386	−	8.03171i	−0.0252193	−	0.312397i	−0.997052	−	0.0767262i	$-0.975553\pi$
$661$	−0.648386	−	8.03171i	−0.0252193	−	0.312397i	0.971833	−	0.235671i	$-0.0757288\pi$
$662$	−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	−0.647287	−	0.762247i	$-0.724096\pi$
$673$	−38.9819	−	6.33517i	−1.50264	−	0.244203i	−0.855354	+	0.518044i	$0.826660\pi$
$674$	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	0.543716	−	0.839269i	$-0.317017\pi$
$683$	6.20647	+	2.94501i	0.237484	+	0.112688i	−0.306232	+	0.951957i	$0.599068\pi$
$684$	−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	−0.880935	−	0.473237i	$-0.843086\pi$
$691$	−2.29538	−	28.4334i	−0.0873204	−	1.08166i	0.793615	−	0.608420i	$-0.208196\pi$
$692$	−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	−0.713231	−	0.700929i	$-0.752769\pi$
$701$	−14.3380	+	7.52518i	−0.541540	+	0.284222i	0.171691	+	0.985151i	$0.445077\pi$
$702$	−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	0.973877	+	0.227075i	$0.0729161\pi$
$709$	3.24920	+	19.9932i	0.122026	+	0.750859i	−0.851851	+	0.523784i	$0.824520\pi$
$710$	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	0.225877	−	0.974156i	$-0.427475\pi$
$719$	−14.9460	−	9.45130i	−0.557393	−	0.352474i	−0.783270	+	0.621682i	$0.786450\pi$
$720$	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	−0.0122049	+	0.999926i	$0.503885\pi$
$727$	−25.4213	+	36.8291i	−0.942824	+	1.36592i	−0.930619	+	0.365990i	$0.880730\pi$
$728$	−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	−0.897668	−	0.440672i	$-0.854740\pi$
$733$	−34.5833	+	13.1157i	−1.27736	+	0.484440i	−0.379695	+	0.925112i	$0.623971\pi$
$734$	−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	0.990226	−	0.139472i	$-0.0445404\pi$
$739$	24.2144	+	23.2582i	0.890740	+	0.855567i	−0.0994861	+	0.995039i	$0.531720\pi$
$740$	−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	−0.472604	−	0.881275i	$-0.656686\pi$
$743$	13.3662	−	31.3716i	0.490358	−	1.15091i	0.962962	−	0.269637i	$-0.0869037\pi$
$744$	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	−0.548072	−	0.836431i	$-0.684638\pi$
$751$	−13.2567	+	4.42575i	−0.483745	+	0.161498i	0.0643272	+	0.997929i	$0.479510\pi$
$752$	−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	0.925520	−	0.378700i	$-0.123629\pi$
$757$	22.5410	+	16.9385i	0.819267	+	0.615639i	−0.106252	+	0.994339i	$0.533885\pi$
$758$	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	0.519032	−	0.854755i	$-0.326293\pi$
$761$	18.2481	+	3.72539i	0.661495	+	0.135045i	0.142463	+	0.989800i	$0.454498\pi$
$762$	−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	0.177672	+	0.984090i	$0.443143\pi$
$769$	−22.6560	+	30.1496i	−0.816996	+	1.08722i	−0.994667	+	0.103134i	$0.967113\pi$
$770$	−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	0.265103	−	0.964220i	$-0.414594\pi$
$773$	27.9282	−	8.08951i	1.00451	−	0.290959i	0.739405	+	0.673261i	$0.235107\pi$
$774$	−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	−0.994460	−	0.105116i	$-0.966478\pi$
$787$	−10.6992	−	25.1118i	−0.381384	−	0.895140i	0.613076	−	0.790024i	$-0.289932\pi$
$788$	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	0.0214803	−	0.999769i	$-0.493162\pi$
$797$	27.8854	−	20.9545i	0.987753	−	0.742248i	0.966273	+	0.257521i	$0.0829057\pi$
$798$	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	−0.912829	−	0.408342i	$-0.866107\pi$
$809$	−49.7278	+	4.01444i	−1.74833	+	0.141140i	−0.835506	+	0.549482i	$0.814825\pi$
$810$	0.154388	−	0.756245i	0.00542466	−	0.0265717i
$811$	7.33508	−	29.7596i	0.257569	−	1.04500i	−0.689581	−	0.724209i	$-0.742205\pi$
$811$	7.33508	−	29.7596i	0.257569	−	1.04500i	0.947150	−	0.320791i	$-0.103949\pi$
$812$	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	−0.826280	−	0.563259i	$-0.809547\pi$
$821$	−26.1475	+	12.4071i	−0.912554	+	0.433012i	−0.0862739	+	0.996271i	$0.527496\pi$
$822$	−2.83433	+	4.90921i	−0.0988587	+	0.171228i
$823$	−3.77140	−	6.53226i	−0.131463	−	0.227700i	0.792778	−	0.609511i	$-0.208634\pi$
$823$	−3.77140	−	6.53226i	−0.131463	−	0.227700i	−0.924241	+	0.381810i	$0.875301\pi$
$824$	−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	−0.131096	−	0.991370i	$-0.541850\pi$
$827$	−14.2532	−	1.73065i	−0.495633	−	0.0601807i	−0.364537	+	0.931189i	$0.618773\pi$
$828$	2.48667	−	5.24056i	0.0864179	−	0.182122i
$829$	−11.7130	+	12.1945i	−0.406808	+	0.423532i	−0.892815	−	0.450423i	$-0.851273\pi$
$829$	−11.7130	+	12.1945i	−0.406808	+	0.423532i	0.486007	+	0.873955i	$0.338453\pi$
$830$	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	0.265816	−	0.964024i	$-0.414359\pi$
$839$	17.6209	−	0.710099i	0.608342	−	0.0245153i	0.342526	+	0.939508i	$0.388718\pi$
$840$	−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	0.230559	−	0.973058i	$-0.425944\pi$
$853$	35.6941	−	24.6378i	1.22214	−	0.843584i	0.991583	+	0.129474i	$0.0413290\pi$
$854$	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	−0.415454	−	0.909614i	$-0.636377\pi$
$857$	−10.5565	+	2.60194i	−0.360602	+	0.0888805i	0.0548521	+	0.998494i	$0.482531\pi$
$858$	26.8398	−	23.6563i	0.916297	−	0.807614i
$859$	55.0297	+	13.5636i	1.87759	+	0.462784i	0.999866	−	0.0163828i	$-0.00521503\pi$
$859$	55.0297	+	13.5636i	1.87759	+	0.462784i	0.877724	+	0.479167i	$0.159061\pi$
$860$	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	0.718415	−	0.695615i	$-0.244868\pi$
$863$	36.7059	+	4.45690i	1.24948	+	0.151715i	0.531067	+	0.847330i	$0.321791\pi$
$864$	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	0.166335	+	0.986069i	$0.446807\pi$
$877$	−23.5681	+	37.2699i	−0.795837	+	1.25851i	−0.962171	+	0.272445i	$0.912168\pi$
$878$	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	−0.153582	−	0.988136i	$-0.549081\pi$
$881$	−4.35332	+	0.351437i	−0.146667	+	0.0118402i	0.00691490	+	0.999976i	$0.497799\pi$
$882$	−16.8489	−	26.6444i	−0.567332	−	0.897164i
$883$	−6.43349	+	5.69958i	−0.216504	+	0.191806i	−0.764403	−	0.644738i	$-0.776966\pi$
$883$	−6.43349	+	5.69958i	−0.216504	+	0.191806i	0.547899	+	0.836545i	$0.315428\pi$
$884$	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	0.490618	−	0.871375i	$-0.336771\pi$
$887$	6.01734	+	2.56375i	0.202042	+	0.0860823i	−0.288575	+	0.957457i	$0.593181\pi$
$888$	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	−0.698143	−	0.715959i	$-0.745990\pi$
$907$	8.26925	−	28.5488i	0.274576	−	0.947947i	0.972719	−	0.231988i	$-0.0745230\pi$
$908$	−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	0.922013	−	0.387159i	$-0.126544\pi$
$911$	−0.750279	−	1.97832i	−0.0248579	−	0.0655448i	−0.946871	+	0.321615i	$0.895774\pi$
$912$	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	0.731474	−	0.681869i	$-0.238833\pi$
$919$	0.627675	+	0.653479i	0.0207051	+	0.0215563i	−0.710769	+	0.703425i	$0.751653\pi$
$920$	−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	−0.517971	−	0.855398i	$-0.673312\pi$
$929$	−40.5311	−	8.27448i	−1.32978	−	0.271477i	−0.811810	+	0.583922i	$0.801518\pi$
$930$	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	0.896440	+	0.443166i	$0.146145\pi$
$937$	−2.44907	+	20.1699i	−0.0800076	+	0.658922i	−0.976447	+	0.215756i	$0.930778\pi$
$938$	−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	−0.391941	−	0.919990i	$-0.628196\pi$
$941$	17.4418	−	19.6877i	0.568585	−	0.641800i	0.960526	+	0.278190i	$0.0897346\pi$
$942$	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	−0.898460	−	0.439055i	$-0.855313\pi$
$947$	1.24855	−	2.93045i	0.0405723	−	0.0952268i	0.939033	+	0.343828i	$0.111724\pi$
$948$	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	−0.128975	−	0.991648i	$-0.541169\pi$
$953$	−12.8222	−	1.03511i	−0.415352	−	0.0335306i	−0.286376	+	0.958117i	$0.592451\pi$
$954$	−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	0.262440	−	0.964948i	$-0.415473\pi$
$967$	23.2659	−	2.82499i	0.748181	−	0.0908456i	0.485741	+	0.874103i	$0.338550\pi$
$968$	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	0.999136	+	0.0415575i	$0.0132320\pi$
$971$	45.6508	+	28.8678i	1.46500	+	0.926412i	0.465867	+	0.884855i	$0.345742\pi$
$972$	−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	0.997034	−	0.0769594i	$-0.0245212\pi$
$977$	15.6311	+	24.7186i	0.500084	+	0.790820i	−0.496950	+	0.867779i	$0.665547\pi$
$978$	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	−0.759260	−	0.650788i	$-0.774439\pi$
$983$	6.50999	−	12.4038i	0.207637	−	0.395618i	0.966896	+	0.255169i	$0.0821311\pi$
$984$	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	0.280492	+	0.959856i	$0.409502\pi$
$991$	−21.7532	+	37.6777i	−0.691014	+	1.19687i	−0.971506	+	0.237015i	$0.923831\pi$
$992$	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	−0.597678	−	0.801736i	$-0.703910\pi$
$997$	12.6727	−	26.7072i	0.401349	−	0.845825i	0.999028	−	0.0440895i	$-0.0140387\pi$
$998$	−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.355.2	yes	360
169.10	even	78	inner	507.2.t.b.10.2	✓	360

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.2.t.b.10.2	✓	360	169.10	even	78	inner
507.2.t.b.355.2	yes	360	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.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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Representations

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