LMFDB - Embedded newform 605.2.s.a.16.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [605,2,Mod(16,605)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(605, base_ring=CyclotomicField(110))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("605.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 605 = 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	605.s (of order $55$, degree $40$, 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:	$4.83094932229$
Analytic rank:	$0$
Dimension:	$880$
Relative dimension:	$22$ over $\Q(\zeta_{55})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{55}]$

Embedding invariants

Embedding label			16.11
Character	$\chi$	$=$	605.16
Dual form			605.2.s.a.416.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.217809 + 0.0249913i) q^{2} +(1.53233 + 1.11330i) q^{3} +(-1.90121 - 0.442107i) q^{4} +(0.564443 - 0.825472i) q^{5} +(0.305933 + 0.280782i) q^{6} +(-1.17803 - 1.21217i) q^{7} +(-0.816028 - 0.291158i) q^{8} +(0.181542 + 0.558728i) q^{9} +O(q^{10})$	\(q+(0.217809 + 0.0249913i) q^{2} +(1.53233 + 1.11330i) q^{3} +(-1.90121 - 0.442107i) q^{4} +(0.564443 - 0.825472i) q^{5} +(0.305933 + 0.280782i) q^{6} +(-1.17803 - 1.21217i) q^{7} +(-0.816028 - 0.291158i) q^{8} +(0.181542 + 0.558728i) q^{9} +(0.143570 - 0.165689i) q^{10} +(3.24723 + 0.674888i) q^{11} +(-2.42108 - 2.79407i) q^{12} +(0.545382 - 0.904415i) q^{13} +(-0.226293 - 0.293461i) q^{14} +(1.78391 - 0.636499i) q^{15} +(3.33286 + 1.63866i) q^{16} +(6.25148 - 5.11181i) q^{17} +(0.0255781 + 0.126233i) q^{18} +(6.80850 + 0.389324i) q^{19} +(-1.43807 + 1.31985i) q^{20} +(-0.455626 - 3.16895i) q^{21} +(0.690411 + 0.228149i) q^{22} +(-0.825207 + 5.73944i) q^{23} +(-0.926277 - 1.35464i) q^{24} +(-0.362808 - 0.931864i) q^{25} +(0.141392 - 0.183360i) q^{26} +(1.41204 - 4.34582i) q^{27} +(1.70378 + 2.82540i) q^{28} +(-0.560803 + 1.44041i) q^{29} +(0.404460 - 0.0940530i) q^{30} +(-6.10466 - 2.57985i) q^{31} +(2.14272 + 1.37705i) q^{32} +(4.22448 + 4.64931i) q^{33} +(1.48938 - 0.957167i) q^{34} +(-1.66554 + 0.288233i) q^{35} +(-0.0981310 - 1.14252i) q^{36} +(0.484158 - 5.63695i) q^{37} +(1.47322 + 0.254951i) q^{38} +(1.84259 - 0.778687i) q^{39} +(-0.700944 + 0.509266i) q^{40} +(-3.30684 + 1.86746i) q^{41} +(-0.0200434 - 0.701612i) q^{42} +(-9.98072 + 2.93060i) q^{43} +(-5.87529 - 2.71873i) q^{44} +(0.563684 + 0.165513i) q^{45} +(-0.323173 + 1.22948i) q^{46} +(-1.63710 + 8.07938i) q^{47} +(3.28273 + 6.22146i) q^{48} +(0.118305 - 4.14120i) q^{49} +(-0.0557343 - 0.212035i) q^{50} +(15.2703 - 0.873189i) q^{51} +(-1.43673 + 1.47836i) q^{52} +(9.76924 - 4.80321i) q^{53} +(0.416163 - 0.911270i) q^{54} +(2.38998 - 2.29956i) q^{55} +(0.608375 + 1.33216i) q^{56} +(9.99943 + 8.17649i) q^{57} +(-0.158146 + 0.299719i) q^{58} +(-3.24744 - 1.83391i) q^{59} +(-3.67299 + 0.421437i) q^{60} +(-6.67479 + 0.765860i) q^{61} +(-1.26518 - 0.714478i) q^{62} +(0.463409 - 0.878258i) q^{63} +(-5.31791 - 4.34843i) q^{64} +(-0.438732 - 0.960689i) q^{65} +(0.803938 + 1.11824i) q^{66} +(-0.564415 + 1.23590i) q^{67} +(-14.1453 + 6.95479i) q^{68} +(-7.65422 + 7.87601i) q^{69} +(-0.369973 + 0.0211558i) q^{70} +(-1.05389 - 4.00940i) q^{71} +(0.0145351 - 0.508795i) q^{72} +(4.85343 + 9.19828i) q^{73} +(0.246329 - 1.21568i) q^{74} +(0.481506 - 1.83184i) q^{75} +(-12.7722 - 3.75027i) q^{76} +(-3.00727 - 4.73123i) q^{77} +(0.420794 - 0.123556i) q^{78} +(0.236443 + 8.27659i) q^{79} +(3.23388 - 1.82626i) q^{80} +(8.42778 - 6.12314i) q^{81} +(-0.766930 + 0.324107i) q^{82} +(8.26498 + 1.43031i) q^{83} +(-0.534774 + 6.22626i) q^{84} +(-0.691050 - 8.04575i) q^{85} +(-2.24713 + 0.388881i) q^{86} +(-2.46295 + 1.58284i) q^{87} +(-2.45333 - 1.49619i) q^{88} +(3.35072 + 2.15338i) q^{89} +(0.118639 + 0.0501373i) q^{90} +(-1.73878 + 0.404336i) q^{91} +(4.10633 - 10.5470i) q^{92} +(-6.48220 - 10.7495i) q^{93} +(-0.558488 + 1.71885i) q^{94} +(4.16439 - 5.40047i) q^{95} +(1.75029 + 4.49559i) q^{96} +(-3.95857 - 5.78923i) q^{97} +(0.129262 - 0.899035i) q^{98} +(0.212429 + 1.93684i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 880 q + 2 q^{2} + 5 q^{3} + 24 q^{4} - 22 q^{5} + 7 q^{6} + q^{7} - 4 q^{8} - 217 q^{9}+O(q^{10}) $ 880 * q + 2 * q^2 + 5 * q^3 + 24 * q^4 - 22 * q^5 + 7 * q^6 + q^7 - 4 * q^8 - 217 * q^9	\( 880 q + 2 q^{2} + 5 q^{3} + 24 q^{4} - 22 q^{5} + 7 q^{6} + q^{7} - 4 q^{8} - 217 q^{9} - 2 q^{10} - 3 q^{11} - 49 q^{12} + 2 q^{13} + 60 q^{14} - 16 q^{15} + 18 q^{16} + 13 q^{17} - 15 q^{19} - 19 q^{20} + 42 q^{21} - 301 q^{22} + 31 q^{23} - 409 q^{24} + 22 q^{25} - 4 q^{26} - 4 q^{27} + 6 q^{28} + 9 q^{29} + 19 q^{30} - 10 q^{31} + 94 q^{32} - 5 q^{33} + 12 q^{34} + 4 q^{35} + 35 q^{36} + 73 q^{37} - 8 q^{38} - 21 q^{39} + 4 q^{40} - 8 q^{41} - 17 q^{42} + 93 q^{43} + q^{44} + 80 q^{45} + 129 q^{46} - 178 q^{47} + 153 q^{48} - 177 q^{49} + 2 q^{50} - 12 q^{51} - 126 q^{52} - 99 q^{53} - 93 q^{54} - 7 q^{55} - 25 q^{56} + 100 q^{57} - 26 q^{58} + 25 q^{59} - 4 q^{60} - 6 q^{61} + 63 q^{62} - 25 q^{63} + 8 q^{64} - 2 q^{65} + 64 q^{66} + 47 q^{67} - 11 q^{68} + 67 q^{69} - 60 q^{70} + 18 q^{71} - 641 q^{72} - 35 q^{73} - 108 q^{74} - 5 q^{75} - 132 q^{76} - 166 q^{77} + 115 q^{78} - 103 q^{79} - 23 q^{80} - 230 q^{81} - 72 q^{82} + 149 q^{83} - 28 q^{84} - 21 q^{85} + 49 q^{86} + 6 q^{87} - 85 q^{88} + 44 q^{89} - 34 q^{90} - 135 q^{92} - 172 q^{93} + 49 q^{94} - 106 q^{95} - 115 q^{96} - 421 q^{97} - 192 q^{98} - 156 q^{99}+O(q^{100}) \) 880 * q + 2 * q^2 + 5 * q^3 + 24 * q^4 - 22 * q^5 + 7 * q^6 + q^7 - 4 * q^8 - 217 * q^9 - 2 * q^10 - 3 * q^11 - 49 * q^12 + 2 * q^13 + 60 * q^14 - 16 * q^15 + 18 * q^16 + 13 * q^17 - 15 * q^19 - 19 * q^20 + 42 * q^21 - 301 * q^22 + 31 * q^23 - 409 * q^24 + 22 * q^25 - 4 * q^26 - 4 * q^27 + 6 * q^28 + 9 * q^29 + 19 * q^30 - 10 * q^31 + 94 * q^32 - 5 * q^33 + 12 * q^34 + 4 * q^35 + 35 * q^36 + 73 * q^37 - 8 * q^38 - 21 * q^39 + 4 * q^40 - 8 * q^41 - 17 * q^42 + 93 * q^43 + q^44 + 80 * q^45 + 129 * q^46 - 178 * q^47 + 153 * q^48 - 177 * q^49 + 2 * q^50 - 12 * q^51 - 126 * q^52 - 99 * q^53 - 93 * q^54 - 7 * q^55 - 25 * q^56 + 100 * q^57 - 26 * q^58 + 25 * q^59 - 4 * q^60 - 6 * q^61 + 63 * q^62 - 25 * q^63 + 8 * q^64 - 2 * q^65 + 64 * q^66 + 47 * q^67 - 11 * q^68 + 67 * q^69 - 60 * q^70 + 18 * q^71 - 641 * q^72 - 35 * q^73 - 108 * q^74 - 5 * q^75 - 132 * q^76 - 166 * q^77 + 115 * q^78 - 103 * q^79 - 23 * q^80 - 230 * q^81 - 72 * q^82 + 149 * q^83 - 28 * q^84 - 21 * q^85 + 49 * q^86 + 6 * q^87 - 85 * q^88 + 44 * q^89 - 34 * q^90 - 135 * q^92 - 172 * q^93 + 49 * q^94 - 106 * q^95 - 115 * q^96 - 421 * q^97 - 192 * q^98 - 156 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/605\mathbb{Z}\right)^\times$.

$n$	$122$	$486$
$\chi(n)$	$1$	$e\left(\frac{2}{55}\right)$

Coefficient data

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

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

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

$2$	0.217809	+	0.0249913i	0.154014	+	0.0176715i	0.190656	−	0.981657i	$-0.438939\pi$
$2$	0.217809	+	0.0249913i	0.154014	+	0.0176715i	−0.0366413	+	0.999328i	$0.511666\pi$
$3$	1.53233	+	1.11330i	0.884691	+	0.642766i	0.934488	−	0.355993i	$-0.115857\pi$
$3$	1.53233	+	1.11330i	0.884691	+	0.642766i	−0.0497970	+	0.998759i	$0.515857\pi$
$4$	−1.90121	−	0.442107i	−0.950604	−	0.221053i
$5$	0.564443	−	0.825472i	0.252427	−	0.369162i
$5$	0.564443	−	0.825472i	0.252427	−	0.369162i
$6$	0.305933	+	0.280782i	0.124896	+	0.114629i
$7$	−1.17803	−	1.21217i	−0.445254	−	0.458156i	0.456932	−	0.889501i	$-0.348948\pi$
$7$	−1.17803	−	1.21217i	−0.445254	−	0.458156i	−0.902187	+	0.431345i	$0.858039\pi$
$8$	−0.816028	−	0.291158i	−0.288509	−	0.102940i
$9$	0.181542	+	0.558728i	0.0605139	+	0.186243i
$10$	0.143570	−	0.165689i	0.0454010	−	0.0523955i
$11$	3.24723	+	0.674888i	0.979078	+	0.203487i
$11$	3.24723	+	0.674888i	0.979078	+	0.203487i
$12$	−2.42108	−	2.79407i	−0.698905	−	0.806580i
$13$	0.545382	−	0.904415i	0.151262	−	0.250840i	−0.771484	−	0.636249i	$-0.780485\pi$
$13$	0.545382	−	0.904415i	0.151262	−	0.250840i	0.922746	+	0.385409i	$0.125940\pi$
$14$	−0.226293	−	0.293461i	−0.0604792	−	0.0784309i
$15$	1.78391	−	0.636499i	0.460605	−	0.164343i
$16$	3.33286	+	1.63866i	0.833216	+	0.409665i
$17$	6.25148	−	5.11181i	1.51621	−	1.23980i	0.629921	−	0.776660i	$-0.283087\pi$
$17$	6.25148	−	5.11181i	1.51621	−	1.23980i	0.886287	−	0.463137i	$-0.153276\pi$
$18$	0.0255781	+	0.126233i	0.00602882	+	0.0297534i
$19$	6.80850	+	0.389324i	1.56198	+	0.0893170i	0.816551	−	0.577273i	$-0.195883\pi$
$19$	6.80850	+	0.389324i	1.56198	+	0.0893170i	0.745425	+	0.666590i	$0.232247\pi$
$20$	−1.43807	+	1.31985i	−0.321562	+	0.295127i
$21$	−0.455626	−	3.16895i	−0.0994257	−	0.691521i
$22$	0.690411	+	0.228149i	0.147196	+	0.0486416i
$23$	−0.825207	+	5.73944i	−0.172067	+	1.19676i	0.702440	+	0.711743i	$0.252094\pi$
$23$	−0.825207	+	5.73944i	−0.172067	+	1.19676i	−0.874507	+	0.485012i	$0.838815\pi$
$24$	−0.926277	−	1.35464i	−0.189076	−	0.276514i
$25$	−0.362808	−	0.931864i	−0.0725615	−	0.186373i
$26$	0.141392	−	0.183360i	0.0277292	−	0.0359598i
$27$	1.41204	−	4.34582i	0.271748	−	0.836354i
$28$	1.70378	+	2.82540i	0.321984	+	0.533950i
$29$	−0.560803	+	1.44041i	−0.104138	+	0.267478i	−0.974286	−	0.225313i	$-0.927660\pi$
$29$	−0.560803	+	1.44041i	−0.104138	+	0.267478i	0.870148	+	0.492791i	$0.164023\pi$
$30$	0.404460	−	0.0940530i	0.0738439	−	0.0171717i
$31$	−6.10466	−	2.57985i	−1.09643	−	0.463355i	−0.235394	−	0.971900i	$-0.575638\pi$
$31$	−6.10466	−	2.57985i	−1.09643	−	0.463355i	−0.861035	+	0.508545i	$0.830183\pi$
$32$	2.14272	+	1.37705i	0.378784	+	0.243430i
$33$	4.22448	+	4.64931i	0.735388	+	0.809341i
$34$	1.48938	−	0.957167i	0.255427	−	0.164153i
$35$	−1.66554	+	0.288233i	−0.281528	+	0.0487203i
$36$	−0.0981310	−	1.14252i	−0.0163552	−	0.190420i
$37$	0.484158	−	5.63695i	0.0795952	−	0.926710i	−0.842234	−	0.539113i	$-0.818760\pi$
$37$	0.484158	−	5.63695i	0.0795952	−	0.926710i	0.921829	−	0.387597i	$-0.126695\pi$
$38$	1.47322	+	0.254951i	0.238988	+	0.0413585i
$39$	1.84259	−	0.778687i	0.295051	−	0.124690i
$40$	−0.700944	+	0.509266i	−0.110829	+	0.0805220i
$41$	−3.30684	+	1.86746i	−0.516442	+	0.291648i	−0.727834	−	0.685753i	$-0.759473\pi$
$41$	−3.30684	+	1.86746i	−0.516442	+	0.291648i	0.211392	+	0.977401i	$0.432200\pi$
$42$	−0.0200434	−	0.701612i	−0.00309277	−	0.108261i
$43$	−9.98072	+	2.93060i	−1.52205	+	0.446913i	−0.932605	−	0.360898i	$-0.882470\pi$
$43$	−9.98072	+	2.93060i	−1.52205	+	0.446913i	−0.589441	+	0.807811i	$0.700652\pi$
$44$	−5.87529	−	2.71873i	−0.885734	−	0.409864i
$45$	0.563684	+	0.165513i	0.0840291	+	0.0246732i
$46$	−0.323173	+	1.22948i	−0.0476493	+	0.181277i
$47$	−1.63710	+	8.07938i	−0.238795	+	1.17850i	0.663767	+	0.747939i	$0.268957\pi$
$47$	−1.63710	+	8.07938i	−0.238795	+	1.17850i	−0.902562	+	0.430560i	$0.858316\pi$
$48$	3.28273	+	6.22146i	0.473821	+	0.897990i
$49$	0.118305	−	4.14120i	0.0169007	−	0.591600i
$50$	−0.0557343	−	0.212035i	−0.00788203	−	0.0299863i
$51$	15.2703	−	0.873189i	2.13827	−	0.122271i
$52$	−1.43673	+	1.47836i	−0.199239	+	0.205012i
$53$	9.76924	−	4.80321i	1.34191	−	0.659772i	0.377950	−	0.925826i	$-0.376629\pi$
$53$	9.76924	−	4.80321i	1.34191	−	0.659772i	0.963958	+	0.266054i	$0.0857200\pi$
$54$	0.416163	−	0.911270i	0.0566326	−	0.124008i
$55$	2.38998	−	2.29956i	0.322265	−	0.310073i
$56$	0.608375	+	1.33216i	0.0812975	+	0.178017i
$57$	9.99943	+	8.17649i	1.32446	+	1.08300i
$58$	−0.158146	+	0.299719i	−0.0207655	+	0.0393551i
$59$	−3.24744	−	1.83391i	−0.422780	−	0.238755i	0.265632	−	0.964074i	$-0.414419\pi$
$59$	−3.24744	−	1.83391i	−0.422780	−	0.238755i	−0.688413	+	0.725319i	$0.741692\pi$
$60$	−3.67299	+	0.421437i	−0.474181	+	0.0544072i
$61$	−6.67479	+	0.765860i	−0.854619	+	0.0980584i	−0.530218	−	0.847861i	$-0.677890\pi$
$61$	−6.67479	+	0.765860i	−0.854619	+	0.0980584i	−0.324401	+	0.945920i	$0.605163\pi$
$62$	−1.26518	−	0.714478i	−0.160678	−	0.0907388i
$63$	0.463409	−	0.878258i	0.0583841	−	0.110650i
$64$	−5.31791	−	4.34843i	−0.664738	−	0.543554i
$65$	−0.438732	−	0.960689i	−0.0544180	−	0.119159i
$66$	0.803938	+	1.11824i	0.0989579	+	0.137645i
$67$	−0.564415	+	1.23590i	−0.0689543	+	0.150989i	−0.940971	−	0.338487i	$-0.890085\pi$
$67$	−0.564415	+	1.23590i	−0.0689543	+	0.150989i	0.872017	+	0.489476i	$0.162812\pi$
$68$	−14.1453	+	6.95479i	−1.71537	+	0.843392i
$69$	−7.65422	+	7.87601i	−0.921460	+	0.948160i
$70$	−0.369973	+	0.0211558i	−0.0442203	+	0.00252861i
$71$	−1.05389	−	4.00940i	−0.125073	−	0.475828i	0.874891	−	0.484320i	$-0.160933\pi$
$71$	−1.05389	−	4.00940i	−0.125073	−	0.475828i	−0.999964	+	0.00849262i	$0.997297\pi$
$72$	0.0145351	−	0.508795i	0.00171298	−	0.0599620i
$73$	4.85343	+	9.19828i	0.568051	+	1.07658i	0.985786	+	0.168008i	$0.0537334\pi$
$73$	4.85343	+	9.19828i	0.568051	+	1.07658i	−0.417734	+	0.908569i	$0.637176\pi$
$74$	0.246329	−	1.21568i	0.0286351	−	0.141320i
$75$	0.481506	−	1.83184i	0.0555995	−	0.211523i
$76$	−12.7722	−	3.75027i	−1.46508	−	0.430185i
$77$	−3.00727	−	4.73123i	−0.342710	−	0.539174i
$78$	0.420794	−	0.123556i	0.0476455	−	0.0139900i
$79$	0.236443	+	8.27659i	0.0266019	+	0.931190i	0.897838	+	0.440326i	$0.145137\pi$
$79$	0.236443	+	8.27659i	0.0266019	+	0.931190i	−0.871236	+	0.490864i	$0.836681\pi$
$80$	3.23388	−	1.82626i	0.361559	−	0.204182i
$81$	8.42778	−	6.12314i	0.936420	−	0.680349i
$82$	−0.766930	+	0.324107i	−0.0846933	+	0.0357917i
$83$	8.26498	+	1.43031i	0.907199	+	0.156997i	0.604979	−	0.796241i	$-0.293181\pi$
$83$	8.26498	+	1.43031i	0.907199	+	0.156997i	0.302220	+	0.953238i	$0.402272\pi$
$84$	−0.534774	+	6.22626i	−0.0583486	+	0.679341i
$85$	−0.691050	−	8.04575i	−0.0749549	−	0.872684i
$86$	−2.24713	+	0.388881i	−0.242314	+	0.0419342i
$87$	−2.46295	+	1.58284i	−0.264056	+	0.169698i
$88$	−2.45333	−	1.49619i	−0.261526	−	0.159494i
$89$	3.35072	+	2.15338i	0.355176	+	0.228258i	0.706045	−	0.708167i	$-0.250477\pi$
$89$	3.35072	+	2.15338i	0.355176	+	0.228258i	−0.350869	+	0.936424i	$0.614114\pi$
$90$	0.118639	+	0.0501373i	0.0125057	+	0.00528494i
$91$	−1.73878	+	0.404336i	−0.182274	+	0.0423859i
$92$	4.10633	−	10.5470i	0.428115	−	1.09960i
$93$	−6.48220	−	10.7495i	−0.672173	−	1.11467i
$94$	−0.558488	+	1.71885i	−0.0576037	+	0.177286i
$95$	4.16439	−	5.40047i	0.427257	−	0.554077i
$96$	1.75029	+	4.49559i	0.178639	+	0.458829i
$97$	−3.95857	−	5.78923i	−0.401932	−	0.587807i	0.570412	−	0.821358i	$-0.306783\pi$
$97$	−3.95857	−	5.78923i	−0.401932	−	0.587807i	−0.972344	+	0.233552i	$0.924965\pi$
$98$	0.129262	−	0.899035i	0.0130574	−	0.0908162i
$99$	0.212429	+	1.93684i	0.0213499	+	0.194660i
$100$	0.277789	+	1.93207i	0.0277789	+	0.193207i
$101$	−12.9747	+	11.9081i	−1.29103	+	1.18490i	−0.319607	+	0.947550i	$0.603551\pi$
$101$	−12.9747	+	11.9081i	−1.29103	+	1.18490i	−0.971425	+	0.237348i	$0.923722\pi$
$102$	3.34784	+	0.191436i	0.331486	+	0.0189550i
$103$	−1.10908	−	5.47350i	−0.109280	−	0.539320i	−0.996896	−	0.0787345i	$-0.974912\pi$
$103$	−1.10908	−	5.47350i	−0.109280	−	0.539320i	0.887615	−	0.460586i	$-0.152361\pi$
$104$	−0.708375	+	0.579235i	−0.0694619	+	0.0567987i
$105$	−2.87305	−	1.41258i	−0.280381	−	0.137854i
$106$	2.24787	−	0.802037i	0.218332	−	0.0779008i
$107$	−5.73653	−	7.43926i	−0.554571	−	0.719181i	0.428267	−	0.903652i	$-0.359124\pi$
$107$	−5.73653	−	7.43926i	−0.554571	−	0.719181i	−0.982838	+	0.184472i	$0.940943\pi$
$108$	−4.60590	+	7.63803i	−0.443203	+	0.734970i
$109$	4.82647	+	5.57004i	0.462292	+	0.533513i	0.938251	−	0.345954i	$-0.112445\pi$
$109$	4.82647	+	5.57004i	0.462292	+	0.533513i	−0.475960	+	0.879467i	$0.657899\pi$
$110$	0.578028	−	0.441137i	0.0551128	−	0.0420608i
$111$	7.01753	−	8.09866i	0.666075	−	0.768691i
$112$	−1.93989	−	5.97038i	−0.183303	−	0.564148i
$113$	6.98776	+	2.49323i	0.657353	+	0.234543i	0.643600	−	0.765362i	$-0.277440\pi$
$113$	6.98776	+	2.49323i	0.657353	+	0.234543i	0.0137534	+	0.999905i	$0.495622\pi$
$114$	1.97363	+	2.03081i	0.184847	+	0.190203i
$115$	4.27196	+	3.92077i	0.398363	+	0.365614i
$116$	1.70302	−	2.49058i	0.158121	−	0.231245i
$117$	0.604331	+	0.140531i	0.0558705	+	0.0129921i
$118$	−0.661490	−	0.480600i	−0.0608951	−	0.0442429i
$119$	−13.5608	−	1.55596i	−1.24312	−	0.142635i
$120$	−1.64105			−0.149806
$121$	10.0891	+	4.38304i	0.917186	+	0.398458i
$122$	−1.47297			−0.133356
$123$	−7.14622	−	0.819953i	−0.644353	−	0.0739327i
$124$	10.4657	+	7.60374i	0.939843	+	0.682836i
$125$	−0.974012	−	0.226497i	−0.0871183	−	0.0202585i
$126$	0.122884	−	0.179711i	0.0109473	−	0.0160100i
$127$	12.7405	+	11.6931i	1.13053	+	1.03760i	0.998928	+	0.0462932i	$0.0147409\pi$
$127$	12.7405	+	11.6931i	1.13053	+	1.03760i	0.131607	+	0.991302i	$0.457986\pi$
$128$	−4.59990	−	4.73319i	−0.406578	−	0.418359i
$129$	−18.5564	−	6.62092i	−1.63380	−	0.582939i
$130$	−0.0715509	−	0.220211i	−0.00627543	−	0.0193138i
$131$	−1.14432	+	1.32061i	−0.0999793	+	0.115382i	−0.803534	−	0.595259i	$-0.797050\pi$
$131$	−1.14432	+	1.32061i	−0.0999793	+	0.115382i	0.703555	+	0.710641i	$0.251595\pi$
$132$	−5.97612	−	10.7070i	−0.520155	−	0.931922i
$133$	−7.54871	−	8.71167i	−0.654556	−	0.755398i
$134$	−0.153821	+	0.255084i	−0.0132881	+	0.0220359i
$135$	−2.79034	−	3.61857i	−0.240154	−	0.311437i
$136$	−6.58973	+	2.35121i	−0.565065	+	0.201615i
$137$	−12.1188	−	5.95843i	−1.03538	−	0.509063i	−0.157289	−	0.987553i	$-0.550276\pi$
$137$	−12.1188	−	5.95843i	−1.03538	−	0.509063i	−0.878093	+	0.478489i	$0.841185\pi$
$138$	−1.86399	+	1.52418i	−0.158673	+	0.129747i
$139$	2.53899	+	12.5304i	0.215354	+	1.06282i	0.931186	+	0.364543i	$0.118775\pi$
$139$	2.53899	+	12.5304i	0.215354	+	1.06282i	−0.715832	+	0.698273i	$0.753952\pi$
$140$	3.29397	+	0.188356i	0.278391	+	0.0159190i
$141$	−11.5034	+	10.5577i	−0.968759	+	0.889119i
$142$	−0.129346	−	0.899620i	−0.0108545	−	0.0754945i
$143$	2.38136	−	2.56877i	0.199140	−	0.214812i
$144$	−0.310511	+	2.15965i	−0.0258759	+	0.179971i
$145$	0.872477	+	1.27596i	0.0724553	+	0.105962i
$146$	0.827245	+	2.12476i	0.0684633	+	0.175847i
$147$	4.79170	−	6.21398i	0.395212	−	0.512520i
$148$	−3.41262	+	10.5030i	−0.280516	+	0.863339i
$149$	−2.20510	−	3.65675i	−0.180649	−	0.299573i	0.752823	−	0.658223i	$-0.228692\pi$
$149$	−2.20510	−	3.65675i	−0.180649	−	0.299573i	−0.933472	+	0.358650i	$0.883237\pi$
$150$	0.150656	−	0.386958i	0.0123010	−	0.0315950i
$151$	−1.13942	+	0.264961i	−0.0927247	+	0.0215622i	−0.272602	−	0.962127i	$-0.587884\pi$
$151$	−1.13942	+	0.264961i	−0.0927247	+	0.0215622i	0.179878	+	0.983689i	$0.442430\pi$
$152$	−5.44257	−	2.30005i	−0.441451	−	0.186559i
$153$	3.99102	+	2.56487i	0.322655	+	0.207358i
$154$	−0.536771	−	1.10566i	−0.0432542	−	0.0890966i
$155$	−5.57533	+	3.58304i	−0.447821	+	0.287797i
$156$	−3.84742	+	0.665822i	−0.308040	+	0.0533084i
$157$	0.374184	+	4.35654i	0.0298631	+	0.347690i	0.995979	+	0.0895826i	$0.0285533\pi$
$157$	0.374184	+	4.35654i	0.0298631	+	0.347690i	−0.966116	+	0.258107i	$0.916901\pi$
$158$	−0.155343	+	1.80863i	−0.0123584	+	0.143887i
$159$	20.3171	+	3.51602i	1.61125	+	0.278838i
$160$	2.34616	−	0.991495i	0.185480	−	0.0783846i
$161$	7.92928	−	5.76096i	0.624915	−	0.454027i
$162$	1.98867	−	1.12305i	0.156245	−	0.0882355i
$163$	−0.193005	−	6.75606i	−0.0151173	−	0.529175i	−0.971497	−	0.237050i	$-0.923819\pi$
$163$	−0.193005	−	6.75606i	−0.0151173	−	0.529175i	0.956380	−	0.292125i	$-0.0943624\pi$
$164$	7.11261	−	2.08845i	0.555402	−	0.163081i
$165$	6.22235	−	0.862919i	0.484409	−	0.0671781i
$166$	1.76444	+	0.518087i	0.136947	+	0.0402113i
$167$	−0.0966154	+	0.367563i	−0.00747633	+	0.0284429i	−0.970780	−	0.239969i	$-0.922863\pi$
$167$	−0.0966154	+	0.367563i	−0.00747633	+	0.0284429i	0.963304	+	0.268412i	$0.0864990\pi$
$168$	−0.550862	+	2.71861i	−0.0424999	+	0.209745i
$169$	5.54615	+	10.5111i	0.426627	+	0.808548i
$170$	0.0505565	−	1.76971i	0.00387750	−	0.135730i
$171$	1.01850	+	3.87478i	0.0778866	+	0.296311i
$172$	20.2711	−	1.15914i	1.54565	−	0.0883837i
$173$	−2.33486	+	2.40252i	−0.177516	+	0.182660i	−0.800051	−	0.599933i	$-0.795194\pi$
$173$	−2.33486	+	2.40252i	−0.177516	+	0.182660i	0.622534	+	0.782593i	$0.286103\pi$
$174$	−0.576010	+	0.283205i	−0.0436672	+	0.0214697i
$175$	−0.702175	+	1.53755i	−0.0530795	+	0.116228i
$176$	9.71668	+	7.57042i	0.732422	+	0.570642i
$177$	−2.93445	−	6.42554i	−0.220567	−	0.482974i
$178$	0.676002	+	0.552764i	0.0506685	+	0.0414314i
$179$	−11.6267	+	22.0350i	−0.869018	+	1.64697i	−0.111876	+	0.993722i	$0.535686\pi$
$179$	−11.6267	+	22.0350i	−0.869018	+	1.64697i	−0.757142	+	0.653250i	$0.773405\pi$
$180$	−0.998506	−	0.563882i	−0.0744243	−	0.0420293i
$181$	−16.1743	+	1.85583i	−1.20223	+	0.137943i	−0.691872	−	0.722020i	$-0.743214\pi$
$181$	−16.1743	+	1.85583i	−1.20223	+	0.137943i	−0.510356	+	0.859963i	$0.670486\pi$
$182$	−0.388827	+	0.0446137i	−0.0288218	+	0.00330699i
$183$	−11.0806	−	6.25751i	−0.819103	−	0.462569i
$184$	2.34448	−	4.44328i	0.172837	−	0.327563i
$185$	−4.37987	−	3.58140i	−0.322014	−	0.263310i
$186$	−1.14324	−	2.50334i	−0.0838262	−	0.183554i
$187$	23.7499	−	12.3802i	1.73677	−	0.905329i
$188$	6.68441	−	14.6368i	0.487511	−	1.06750i
$189$	−6.93129	+	3.40789i	−0.504177	+	0.247887i
$190$	1.04201	−	1.07220i	0.0755950	−	0.0777854i
$191$	−19.8432	+	1.13467i	−1.43580	+	0.0821022i	−0.757574	−	0.652749i	$-0.773616\pi$
$191$	−19.8432	+	1.13467i	−1.43580	+	0.0821022i	−0.678229	+	0.734851i	$0.737252\pi$
$192$	−3.30767	−	12.5837i	−0.238710	−	0.908149i
$193$	−0.0970327	+	3.39659i	−0.00698457	+	0.244492i	0.988597	+	0.150588i	$0.0481165\pi$
$193$	−0.0970327	+	3.39659i	−0.00698457	+	0.244492i	−0.995581	+	0.0939042i	$0.970065\pi$
$194$	−0.717533	−	1.35988i	−0.0515158	−	0.0976334i
$195$	0.397256	−	1.96053i	0.0284481	−	0.140397i
$196$	−2.05578	+	7.82098i	−0.146841	+	0.558641i
$197$	6.74122	+	1.97940i	0.480292	+	0.141027i	0.512912	−	0.858441i	$-0.328567\pi$
$197$	6.74122	+	1.97940i	0.480292	+	0.141027i	−0.0326196	+	0.999468i	$0.510385\pi$
$198$	−0.00213506	+	0.427170i	−0.000151732	+	0.0303577i
$199$	−21.2269	+	6.23277i	−1.50473	+	0.441829i	−0.927209	−	0.374545i	$-0.877799\pi$
$199$	−21.2269	+	6.23277i	−1.50473	+	0.441829i	−0.577523	+	0.816374i	$0.695981\pi$
$200$	0.0247414	+	0.866061i	0.00174948	+	0.0612398i
$201$	−2.24080	+	1.26544i	−0.158054	+	0.0892571i
$202$	−3.12361	+	2.26943i	−0.219776	+	0.159677i
$203$	2.40666	−	1.01706i	0.168915	−	0.0713839i
$204$	−29.4181	−	5.09101i	−2.05968	−	0.356442i
$205$	−0.324989	+	3.78378i	−0.0226982	+	0.264271i
$206$	−0.104777	−	1.21990i	−0.00730016	−	0.0849942i
$207$	−3.35659	+	0.580881i	−0.233299	+	0.0403740i
$208$	3.29971	−	2.12060i	0.228794	−	0.147037i
$209$	21.8460	+	5.85920i	1.51112	+	0.405289i
$210$	−0.590475	−	0.379475i	−0.0407466	−	0.0261863i
$211$	21.5840	+	9.12146i	1.48590	+	0.627947i	0.973063	−	0.230538i	$-0.0740485\pi$
$211$	21.5840	+	9.12146i	1.48590	+	0.627947i	0.512838	+	0.858485i	$0.328594\pi$
$212$	−20.6969	+	4.81285i	−1.42147	+	0.330548i
$213$	2.84877	−	7.31701i	0.195195	−	0.501353i
$214$	−1.06355	−	1.76370i	−0.0727029	−	0.120564i
$215$	−3.21442	+	9.89297i	−0.219222	+	0.674695i
$216$	−2.41759	+	3.13518i	−0.164496	+	0.213322i
$217$	4.06428	+	10.4390i	0.275901	+	0.708646i
$218$	0.912046	+	1.33382i	0.0617715	+	0.0903380i
$219$	−2.80341	+	19.4981i	−0.189437	+	1.31756i
$220$	−5.56050	+	3.31532i	−0.374889	+	0.223519i
$221$	−1.21375	−	8.44183i	−0.0816458	−	0.567859i
$222$	1.73088	−	1.58859i	0.116169	−	0.106619i
$223$	11.4849	+	0.656731i	0.769086	+	0.0439779i	0.437227	−	0.899351i	$-0.355961\pi$
$223$	11.4849	+	0.656731i	0.769086	+	0.0439779i	0.331859	+	0.943329i	$0.392324\pi$
$224$	−0.854990	−	4.21954i	−0.0571265	−	0.281930i
$225$	0.454794	−	0.371883i	0.0303196	−	0.0247922i
$226$	1.45969	+	0.717680i	0.0970970	+	0.0477394i
$227$	−26.5649	+	9.47834i	−1.76318	+	0.629100i	−0.999857	−	0.0169229i	$-0.994613\pi$
$227$	−26.5649	+	9.47834i	−1.76318	+	0.629100i	−0.763318	+	0.646022i	$0.776431\pi$
$228$	−15.3961	−	19.9660i	−1.01963	−	1.32228i
$229$	−7.27604	+	12.0660i	−0.480814	+	0.797341i	−0.998296	−	0.0583532i	$-0.981415\pi$
$229$	−7.27604	+	12.0660i	−0.480814	+	0.797341i	0.517482	+	0.855694i	$0.326870\pi$
$230$	0.832487	+	0.960741i	0.0548926	+	0.0633494i
$231$	0.659162	−	10.5978i	0.0433697	−	0.697285i
$232$	0.877018	−	1.01213i	0.0575791	−	0.0664498i
$233$	−7.71243	−	23.7364i	−0.505258	−	1.55503i	−0.800336	−	0.599552i	$-0.795345\pi$
$233$	−7.71243	−	23.7364i	−0.505258	−	1.55503i	0.295078	−	0.955473i	$-0.404655\pi$
$234$	0.128117	+	0.0457120i	0.00837526	+	0.00298829i
$235$	5.74526	+	5.91173i	0.374779	+	0.385639i
$236$	5.36327	+	4.92236i	0.349119	+	0.320419i
$237$	−8.85205	+	12.9457i	−0.575002	+	0.840914i
$238$	−2.91478	−	0.677804i	−0.188937	−	0.0439355i
$239$	16.5365	+	12.0145i	1.06966	+	0.777153i	0.975851	−	0.218438i	$-0.0700960\pi$
$239$	16.5365	+	12.0145i	1.06966	+	0.777153i	0.0938080	+	0.995590i	$0.470096\pi$
$240$	6.98855	+	0.801861i	0.451109	+	0.0517599i
$241$	−7.72474			−0.497594			−0.248797	−	0.968556i	$-0.580035\pi$
$241$	−7.72474			−0.497594			−0.248797	+	0.968556i	$0.580035\pi$
$242$	2.08795	+	1.20680i	0.134218	+	0.0775763i
$243$	6.02266			0.386354
$244$	13.0287	+	1.49491i	0.834080	+	0.0957018i
$245$	−3.35167	−	2.43513i	−0.214130	−	0.155575i
$246$	−1.53602	−	0.357186i	−0.0979331	−	0.0227734i
$247$	4.06534	−	5.94538i	0.258672	−	0.378295i
$248$	4.23043	+	3.88265i	0.268632	+	0.246548i
$249$	11.0723	+	11.3931i	0.701679	+	0.722011i
$250$	−0.206488	−	0.0736748i	−0.0130595	−	0.00465961i
$251$	−5.49127	−	16.9004i	−0.346606	−	1.06674i	−0.960719	−	0.277525i	$-0.910486\pi$
$251$	−5.49127	−	16.9004i	−0.346606	−	1.06674i	0.614113	−	0.789218i	$-0.289514\pi$
$252$	−1.26932	+	1.46488i	−0.0799597	+	0.0922785i
$253$	−6.55312	+	18.0804i	−0.411991	+	1.13670i
$254$	2.48277	+	2.86526i	0.155783	+	0.179783i
$255$	7.89844	−	13.0981i	0.494620	−	0.820235i
$256$	7.50599	+	9.73394i	0.469124	+	0.608371i
$257$	8.06743	−	2.87845i	0.503233	−	0.179553i	−0.0722192	−	0.997389i	$-0.523008\pi$
$257$	8.06743	−	2.87845i	0.503233	−	0.179553i	0.575452	+	0.817836i	$0.304826\pi$
$258$	−3.87629	−	1.90584i	−0.241327	−	0.118653i
$259$	−7.40328	+	6.05363i	−0.460018	+	0.376155i
$260$	0.409393	+	2.02043i	0.0253895	+	0.125302i
$261$	−0.906607	−	0.0518416i	−0.0561175	−	0.00320892i
$262$	−0.282246	+	0.259043i	−0.0174372	+	0.0160037i
$263$	0.113823	+	0.791659i	0.00701865	+	0.0488158i	0.993030	−	0.117864i	$-0.0376046\pi$
$263$	0.113823	+	0.791659i	0.00701865	+	0.0488158i	−0.986011	+	0.166679i	$0.946695\pi$
$264$	−2.09361	−	5.02396i	−0.128853	−	0.309203i
$265$	1.54926	−	10.7754i	0.0951706	−	0.661926i
$266$	−1.42646	−	2.08613i	−0.0874619	−	0.127909i
$267$	2.73705	+	7.03006i	0.167505	+	0.430233i
$268$	1.61947	−	2.10016i	0.0989248	−	0.128288i
$269$	6.95351	−	21.4007i	0.423963	−	1.30482i	−0.480020	−	0.877257i	$-0.659371\pi$
$269$	6.95351	−	21.4007i	0.423963	−	1.30482i	0.903983	−	0.427567i	$-0.140629\pi$
$270$	−0.517328	−	0.857892i	−0.0314836	−	0.0522096i
$271$	−4.70959	+	12.0965i	−0.286087	+	0.734810i	0.713335	+	0.700823i	$0.247184\pi$
$271$	−4.70959	+	12.0965i	−0.286087	+	0.734810i	−0.999422	+	0.0339862i	$0.989180\pi$
$272$	29.2119	−	6.79293i	1.77123	−	0.411882i
$273$	−3.11453	−	1.31621i	−0.188500	−	0.0796608i
$274$	−2.49069	−	1.60067i	−0.150468	−	0.0966998i
$275$	−0.549217	−	3.27083i	−0.0331190	−	0.197239i
$276$	18.0343	−	11.5899i	1.08554	−	0.697633i
$277$	−14.2365	+	2.46373i	−0.855390	+	0.148031i	−0.581316	−	0.813678i	$-0.697462\pi$
$277$	−14.2365	+	2.46373i	−0.855390	+	0.148031i	−0.274074	+	0.961709i	$0.588371\pi$
$278$	0.239864	+	2.79269i	0.0143861	+	0.167494i
$279$	0.333184	−	3.87919i	0.0199472	−	0.232241i
$280$	1.44305	+	0.249730i	0.0862387	+	0.0149242i
$281$	4.44056	−	1.87660i	0.264902	−	0.111948i	−0.252774	−	0.967525i	$-0.581343\pi$
$281$	4.44056	−	1.87660i	0.264902	−	0.111948i	0.517676	+	0.855577i	$0.326797\pi$
$282$	−2.76939	+	2.01208i	−0.164915	+	0.119818i
$283$	17.3429	−	9.79397i	1.03093	−	0.582191i	0.119149	−	0.992876i	$-0.461983\pi$
$283$	17.3429	−	9.79397i	1.03093	−	0.582191i	0.911777	+	0.410686i	$0.134711\pi$
$284$	0.231073	+	8.08862i	0.0137117	+	0.479971i
$285$	12.3936	−	3.63908i	0.734132	−	0.215561i
$286$	0.582879	−	0.499989i	0.0344664	−	0.0295650i
$287$	6.15924	+	1.80852i	0.363568	+	0.106753i
$288$	−0.380400	+	1.44719i	−0.0224153	+	0.0852766i
$289$	9.57438	−	47.2514i	0.563199	−	2.77949i
$290$	0.158146	+	0.299719i	0.00928663	+	0.0176001i
$291$	0.379325	−	13.2781i	0.0222364	−	0.778376i
$292$	−5.16076	−	19.6336i	−0.302011	−	1.14897i
$293$	6.72028	−	0.384280i	0.392603	−	0.0224499i	0.140327	−	0.990105i	$-0.455185\pi$
$293$	6.72028	−	0.384280i	0.392603	−	0.0224499i	0.252276	+	0.967655i	$0.418821\pi$
$294$	1.19897	−	1.23371i	0.0699253	−	0.0719515i
$295$	−3.34684	+	1.64553i	−0.194860	+	0.0958064i
$296$	−2.03633	+	4.45894i	−0.118359	+	0.259171i
$297$	7.51818	−	13.1589i	0.436249	−	0.763558i
$298$	−0.388904	−	0.851582i	−0.0225286	−	0.0493308i
$299$	4.74078	+	3.87652i	0.274166	+	0.224185i
$300$	−1.72531	+	3.26983i	−0.0996109	+	0.188784i
$301$	15.3100	+	8.64595i	0.882454	+	0.498345i
$302$	−0.254798	+	0.0292353i	−0.0146620	+	0.00168230i
$303$	−33.1388	+	3.80233i	−1.90378	+	0.218438i
$304$	22.0538	+	12.4544i	1.26487	+	0.714307i
$305$	−3.13534	+	5.94213i	−0.179529	+	0.340246i
$306$	0.805180	+	0.658393i	0.0460291	+	0.0376378i
$307$	3.96087	+	8.67309i	0.226059	+	0.494999i	0.988343	−	0.152243i	$-0.0486496\pi$
$307$	3.96087	+	8.67309i	0.226059	+	0.494999i	−0.762285	+	0.647242i	$0.775922\pi$
$308$	3.62573	+	10.3246i	0.206595	+	0.588298i
$309$	4.39420	−	9.62196i	0.249977	−	0.547374i
$310$	−1.30390	+	0.641085i	−0.0740566	+	0.0364112i
$311$	7.12376	−	7.33018i	0.403951	−	0.415656i	−0.484381	−	0.874857i	$-0.660955\pi$
$311$	7.12376	−	7.33018i	0.403951	−	0.415656i	0.888332	+	0.459201i	$0.151864\pi$
$312$	−1.73033	+	0.0989438i	−0.0979606	+	0.00560159i
$313$	7.23168	+	27.5122i	0.408759	+	1.55508i	0.779536	+	0.626357i	$0.215455\pi$
$313$	7.23168	+	27.5122i	0.408759	+	1.55508i	−0.370777	+	0.928722i	$0.620909\pi$
$314$	−0.0273749	+	0.958245i	−0.00154485	+	0.0540769i
$315$	−0.463409	−	0.878258i	−0.0261102	−	0.0494843i
$316$	3.20961	−	15.8401i	0.180555	−	0.891073i
$317$	8.49797	−	32.3296i	0.477294	−	1.81581i	−0.0946371	−	0.995512i	$-0.530169\pi$
$317$	8.49797	−	32.3296i	0.477294	−	1.81581i	0.571931	−	0.820302i	$-0.306195\pi$
$318$	4.33739	+	1.27357i	0.243229	+	0.0714183i
$319$	−2.79317	+	4.29887i	−0.156388	+	0.240691i
$320$	−6.59116	+	1.93534i	−0.368457	+	0.108189i
$321$	−0.508102	−	17.7859i	−0.0283595	−	0.992712i
$322$	1.87104	−	1.05663i	0.104269	−	0.0588835i
$323$	44.5534	−	32.3699i	2.47901	−	1.80111i
$324$	−18.7300	+	7.91538i	−1.04056	+	0.439743i
$325$	−1.04066	−	0.180093i	−0.0577255	−	0.00998979i
$326$	0.126804	−	1.47635i	0.00702303	−	0.0817677i
$327$	1.19460	+	13.9085i	0.0660615	+	0.769140i
$328$	3.24220	−	0.561085i	0.179021	−	0.0309807i
$329$	11.7221	−	7.53334i	0.646261	−	0.415327i
$330$	1.37685	−	0.0324471i	0.0757931	−	0.00178615i
$331$	14.7004	+	9.44737i	0.808007	+	0.519274i	0.878220	−	0.478258i	$-0.158732\pi$
$331$	14.7004	+	9.44737i	0.808007	+	0.519274i	−0.0702130	+	0.997532i	$0.522368\pi$
$332$	−15.0811	−	6.37332i	−0.827682	−	0.349781i
$333$	3.23742	−	0.752829i	0.177409	−	0.0412548i
$334$	−0.0302296	+	0.0776441i	−0.00165409	+	0.00424849i
$335$	0.701618	+	1.16350i	0.0383335	+	0.0635689i
$336$	3.67429	−	11.3083i	0.200449	−	0.616918i
$337$	18.2784	−	23.7038i	0.995687	−	1.29123i	0.0392689	−	0.999229i	$-0.487497\pi$
$337$	18.2784	−	23.7038i	0.995687	−	1.29123i	0.956418	−	0.292001i	$-0.0943211\pi$
$338$	0.945316	+	2.42802i	0.0514184	+	0.132067i
$339$	7.93184	+	11.5999i	0.430798	+	0.630022i
$340$	−2.24325	+	15.6022i	−0.121657	+	0.846146i
$341$	−18.0821	−	12.4973i	−0.979203	−	0.676769i
$342$	0.125003	+	0.869415i	0.00675939	+	0.0470126i
$343$	−13.8764	+	12.7356i	−0.749254	+	0.687659i
$344$	8.99782	+	0.514514i	0.485130	+	0.0277407i
$345$	2.18105	+	10.7639i	0.117424	+	0.579509i
$346$	−0.568597	+	0.464939i	−0.0305679	+	0.0249953i
$347$	−6.02388	−	2.96174i	−0.323379	−	0.158995i	0.272311	−	0.962209i	$-0.412212\pi$
$347$	−6.02388	−	2.96174i	−0.323379	−	0.158995i	−0.595690	+	0.803215i	$0.703121\pi$
$348$	5.38236	−	1.92042i	0.288525	−	0.102945i
$349$	−10.0289	−	13.0057i	−0.536835	−	0.696180i	0.442879	−	0.896581i	$-0.353957\pi$
$349$	−10.0289	−	13.0057i	−0.536835	−	0.696180i	−0.979714	+	0.200402i	$0.935775\pi$
$350$	−0.191365	+	0.317344i	−0.0102289	+	0.0169627i
$351$	−3.16032	−	3.64721i	−0.168686	−	0.194673i
$352$	6.02858	+	5.91769i	0.321324	+	0.315414i
$353$	−0.886618	+	1.02321i	−0.0471899	+	0.0544601i	−0.778854	−	0.627205i	$-0.784199\pi$
$353$	−0.886618	+	1.02321i	−0.0471899	+	0.0544601i	0.731664	+	0.681666i	$0.238744\pi$
$354$	−0.478567	−	1.47288i	−0.0254355	−	0.0782826i
$355$	−3.90450	−	1.39312i	−0.207229	−	0.0739393i
$356$	−5.41840	−	5.57540i	−0.287175	−	0.295496i
$357$	−19.0474	−	17.4815i	−1.00810	−	0.925222i
$358$	−3.08308	+	4.50885i	−0.162946	+	0.238300i
$359$	11.4750	+	2.66839i	0.605625	+	0.140832i	0.518085	−	0.855329i	$-0.326645\pi$
$359$	11.4750	+	2.66839i	0.605625	+	0.140832i	0.0875399	+	0.996161i	$0.472099\pi$
$360$	−0.411792	−	0.299184i	−0.0217033	−	0.0157684i
$361$	27.3279	+	3.13558i	1.43831	+	0.165031i
$362$	−3.56929			−0.187598
$363$	10.5801	+	17.9484i	0.555312	+	0.942049i
$364$	3.48454			0.182640
$365$	10.3324	+	1.18553i	0.540823	+	0.0620536i
$366$	−2.25708	−	1.63986i	−0.117979	−	0.0857169i
$367$	27.0340	+	6.28650i	1.41117	+	0.328152i	0.861723	−	0.507379i	$-0.169386\pi$
$367$	27.0340	+	6.28650i	1.41117	+	0.328152i	0.549443	+	0.835531i	$0.314840\pi$
$368$	−12.1553	+	17.7765i	−0.633638	+	0.926666i
$369$	−1.64373	−	1.50860i	−0.0855692	−	0.0785347i
$370$	−0.864471	−	0.889520i	−0.0449417	−	0.0462439i
$371$	−17.3308	−	6.18361i	−0.899769	−	0.321037i
$372$	7.57157	+	23.3029i	0.392567	+	1.20820i
$373$	−2.93992	+	3.39285i	−0.152223	+	0.175675i	−0.826739	−	0.562585i	$-0.809807\pi$
$373$	−2.93992	+	3.39285i	−0.152223	+	0.175675i	0.674516	+	0.738260i	$0.264352\pi$
$374$	5.48235	−	2.10298i	0.283485	−	0.108742i
$375$	−1.24035	−	1.43144i	−0.0640513	−	0.0739192i
$376$	3.68829	−	6.11635i	0.190209	−	0.315427i
$377$	0.996877	+	1.29277i	0.0513418	+	0.0665812i
$378$	−1.59487	+	0.569047i	−0.0820310	+	0.0292686i
$379$	−15.9053	−	7.82012i	−0.817002	−	0.401693i	−0.0156438	−	0.999878i	$-0.504980\pi$
$379$	−15.9053	−	7.82012i	−0.817002	−	0.401693i	−0.801358	+	0.598185i	$0.795889\pi$
$380$	−10.3049	+	8.42631i	−0.528633	+	0.432261i
$381$	6.50465	+	32.1017i	0.333243	+	1.64462i
$382$	−4.35038	−	0.248764i	−0.222585	−	0.0127279i
$383$	17.0360	−	15.6355i	0.870498	−	0.798936i	−0.110313	−	0.993897i	$-0.535185\pi$
$383$	17.0360	−	15.6355i	0.870498	−	0.798936i	0.980811	+	0.194961i	$0.0624581\pi$
$384$	−1.77910	−	12.3739i	−0.0907892	−	0.631453i
$385$	−5.60293	−	0.188094i	−0.285552	−	0.00958615i
$386$	−0.106020	+	0.737383i	−0.00539626	+	0.0375318i
$387$	−3.44933	−	5.04448i	−0.175339	−	0.256425i
$388$	4.96661	+	12.7566i	0.252141	+	0.647620i
$389$	−13.4091	+	17.3893i	−0.679870	+	0.881671i	−0.997790	−	0.0664465i	$-0.978834\pi$
$389$	−13.4091	+	17.3893i	−0.679870	+	0.881671i	0.317920	+	0.948118i	$0.397016\pi$
$390$	0.135522	−	0.417094i	0.00686243	−	0.0211204i
$391$	24.1802	+	40.0983i	1.22284	+	2.02786i
$392$	−1.30228	+	3.34489i	−0.0657753	+	0.168942i
$393$	−3.22371	+	0.749642i	−0.162615	+	0.0378144i
$394$	1.41883	+	0.599603i	0.0714797	+	0.0302076i
$395$	6.96555	+	4.47649i	0.350475	+	0.225237i
$396$	0.452418	−	3.77625i	0.0227349	−	0.189764i
$397$	−1.80220	+	1.15821i	−0.0904500	+	0.0581287i	−0.585084	−	0.810973i	$-0.698938\pi$
$397$	−1.80220	+	1.15821i	−0.0904500	+	0.0581287i	0.494634	+	0.869101i	$0.335302\pi$
$398$	−4.77917	+	0.827067i	−0.239558	+	0.0414571i
$399$	−1.86838	−	21.7532i	−0.0935360	−	1.08902i
$400$	0.317819	−	3.70029i	0.0158909	−	0.185015i
$401$	−33.7224	−	5.83590i	−1.68402	−	0.291431i	−0.753438	−	0.657519i	$-0.771606\pi$
$401$	−33.7224	−	5.83590i	−1.68402	−	0.291431i	−0.930580	+	0.366088i	$0.880697\pi$
$402$	−0.519691	+	0.219623i	−0.0259198	+	0.0109538i
$403$	−5.66263	+	4.11414i	−0.282076	+	0.204940i
$404$	29.9323	−	16.9035i	1.48919	−	0.840982i
$405$	−0.297477	−	10.4131i	−0.0147818	−	0.517429i
$406$	0.549610	−	0.161380i	0.0272767	−	0.00800916i
$407$	5.37649	−	17.9778i	0.266503	−	0.891124i
$408$	−12.7153	−	3.73354i	−0.629499	−	0.184838i
$409$	−1.55436	+	5.91339i	−0.0768581	+	0.292399i	−0.994462	−	0.105098i	$-0.966484\pi$
$409$	−1.55436	+	5.91339i	−0.0768581	+	0.292399i	0.917604	+	0.397496i	$0.130121\pi$
$410$	−0.165347	+	0.816020i	−0.00816591	+	0.0403003i
$411$	−11.9365	−	22.6222i	−0.588786	−	1.11587i
$412$	−0.311291	+	10.8966i	−0.0153362	+	0.536837i
$413$	1.60258	+	6.09685i	0.0788578	+	0.300006i
$414$	−0.745613	+	0.0426357i	−0.0366449	+	0.00209543i
$415$	5.84579	−	6.01518i	0.286959	−	0.295273i
$416$	2.41402	−	1.18690i	0.118357	−	0.0581924i
$417$	−10.0596	+	22.0274i	−0.492620	+	1.07869i
$418$	4.61183	+	1.82215i	0.225572	+	0.0891241i
$419$	−13.0795	−	28.6402i	−0.638977	−	1.39916i	−0.900879	−	0.434070i	$-0.857077\pi$
$419$	−13.0795	−	28.6402i	−0.638977	−	1.39916i	0.261902	−	0.965095i	$-0.415650\pi$
$420$	4.83776	+	3.95581i	0.236058	+	0.193024i
$421$	−17.0622	+	32.3364i	−0.831559	+	1.57598i	−0.0141660	+	0.999900i	$0.504509\pi$
$421$	−17.0622	+	32.3364i	−0.831559	+	1.57598i	−0.817393	+	0.576080i	$0.804582\pi$
$422$	4.47323	+	2.52615i	0.217753	+	0.122971i
$423$	−4.81138	+	0.552054i	−0.233937	+	0.0268418i
$424$	−9.37046	+	1.07516i	−0.455070	+	0.0522144i
$425$	−7.03160	−	3.97093i	−0.341083	−	0.192618i
$426$	0.803350	−	1.52252i	0.0389224	−	0.0737662i
$427$	8.79147	+	7.18875i	0.425449	+	0.347888i
$428$	7.61738	+	16.6797i	0.368200	+	0.806246i
$429$	6.50886	−	1.28503i	0.314251	−	0.0620419i
$430$	−0.947367	+	2.07445i	−0.0456861	+	0.100039i
$431$	−5.36211	+	2.63637i	−0.258284	+	0.126989i	−0.565770	−	0.824563i	$-0.691421\pi$
$431$	−5.36211	+	2.63637i	−0.258284	+	0.126989i	0.307487	+	0.951552i	$0.400512\pi$
$432$	11.8275	−	12.1702i	0.569049	−	0.585538i
$433$	−13.2759	+	0.759144i	−0.638000	+	0.0364821i	−0.373096	−	0.927793i	$-0.621704\pi$
$433$	−13.2759	+	0.759144i	−0.638000	+	0.0364821i	−0.264904	+	0.964275i	$0.585340\pi$
$434$	0.624352	+	2.37528i	0.0299699	+	0.114017i
$435$	−0.0836039	+	2.92652i	−0.00400850	+	0.140316i
$436$	−6.71356	−	12.7236i	−0.321521	−	0.609351i
$437$	−7.85292	+	38.7557i	−0.375656	+	1.85394i
$438$	−1.09789	+	4.17681i	−0.0524593	+	0.199576i
$439$	23.0061	+	6.75520i	1.09802	+	0.322408i	0.780066	−	0.625698i	$-0.215186\pi$
$439$	23.0061	+	6.75520i	1.09802	+	0.322408i	0.317955	+	0.948106i	$0.397004\pi$
$440$	−2.61983	+	1.18065i	−0.124895	+	0.0562851i
$441$	2.33528	−	0.685701i	0.111204	−	0.0326524i
$442$	−0.0533942	−	1.86904i	−0.00253970	−	0.0889011i
$443$	10.2563	−	5.79201i	0.487293	−	0.275187i	−0.228444	−	0.973557i	$-0.573364\pi$
$443$	10.2563	−	5.79201i	0.487293	−	0.275187i	0.715737	+	0.698370i	$0.246091\pi$
$444$	−16.9223	+	12.2947i	−0.803095	+	0.583483i
$445$	3.66885	−	1.55047i	0.173920	−	0.0734992i
$446$	2.48510	+	0.430064i	0.117673	+	0.0203641i
$447$	0.692128	−	8.05830i	0.0327365	−	0.381144i
$448$	0.993644	+	11.5688i	0.0469452	+	0.546574i
$449$	−38.7635	+	6.70829i	−1.82936	+	0.316584i	−0.978097	−	0.208150i	$-0.933256\pi$
$449$	−38.7635	+	6.70829i	−1.82936	+	0.316584i	−0.851266	+	0.524734i	$0.824165\pi$
$450$	0.108352	−	0.0696336i	0.00510776	−	0.00328256i
$451$	−11.9984	+	3.83233i	−0.564983	+	0.180457i
$452$	−12.1829	−	7.82948i	−0.573036	−	0.368268i
$453$	−2.04095	−	0.862513i	−0.0958922	−	0.0405244i
$454$	−6.02295	+	1.40058i	−0.282671	+	0.0657324i
$455$	−0.647675	+	1.66354i	−0.0303635	+	0.0779879i
$456$	−5.77916	−	9.58366i	−0.270634	−	0.448796i
$457$	−4.01494	+	12.3567i	−0.187811	+	0.578022i	−0.999985	−	0.00539215i	$-0.998284\pi$
$457$	−4.01494	+	12.3567i	−0.187811	+	0.578022i	0.812175	+	0.583414i	$0.198284\pi$
$458$	−1.88633	+	2.44624i	−0.0881425	+	0.114305i
$459$	−13.3877	−	34.3859i	−0.624882	−	1.60500i
$460$	−6.38849	−	9.34287i	−0.297865	−	0.435613i
$461$	−3.17070	+	22.0527i	−0.147674	+	1.02710i	0.772339	+	0.635210i	$0.219087\pi$
$461$	−3.17070	+	22.0527i	−0.147674	+	1.02710i	−0.920014	+	0.391887i	$0.871823\pi$
$462$	0.408424	−	2.29183i	0.0190016	−	0.106625i
$463$	−2.29619	−	15.9703i	−0.106713	−	0.742205i	−0.970978	−	0.239168i	$-0.923125\pi$
$463$	−2.29619	−	15.9703i	−0.106713	−	0.742205i	0.864265	−	0.503036i	$-0.167784\pi$
$464$	−4.22942	+	3.88173i	−0.196346	+	0.180205i
$465$	−12.5323	−	0.716620i	−0.581170	−	0.0332325i
$466$	−1.08663	−	5.36275i	−0.0503374	−	0.248425i
$467$	−13.5984	+	11.1193i	−0.629257	+	0.514541i	−0.893003	−	0.450051i	$-0.851406\pi$
$467$	−13.5984	+	11.1193i	−0.629257	+	0.514541i	0.263746	+	0.964592i	$0.415042\pi$
$468$	−1.08683	−	0.534358i	−0.0502387	−	0.0247007i
$469$	2.16301	−	0.771761i	0.0998786	−	0.0356366i
$470$	1.10363	+	1.43121i	0.0509065	+	0.0660168i
$471$	−4.27678	+	7.09224i	−0.197064	+	0.326793i
$472$	2.11604	+	2.44204i	0.0973987	+	0.112404i
$473$	−34.3876	+	2.78048i	−1.58114	+	0.127847i
$474$	−2.25159	+	2.59847i	−0.103419	+	0.119352i
$475$	−2.10738	−	6.48584i	−0.0966931	−	0.297591i
$476$	25.0940	+	8.95353i	1.15018	+	0.410385i
$477$	4.45721	+	4.58636i	0.204082	+	0.209995i
$478$	3.30155	+	3.03013i	0.151009	+	0.138595i
$479$	0.387467	−	0.566652i	0.0177038	−	0.0258910i	−0.816518	−	0.577319i	$-0.804099\pi$
$479$	0.387467	−	0.566652i	0.0177038	−	0.0258910i	0.834222	+	0.551428i	$0.185917\pi$
$480$	4.69893	+	1.09269i	0.214476	+	0.0498742i
$481$	−4.83409	−	3.51218i	−0.220416	−	0.160141i
$482$	−1.68252	−	0.193051i	−0.0766366	−	0.00879323i
$483$	18.5640			0.844690
$484$	−17.2436	−	12.7935i	−0.783800	−	0.581523i
$485$	−7.01323			−0.318455
$486$	1.31179	+	0.150514i	0.0595040	+	0.00682745i
$487$	−0.367833	−	0.267246i	−0.0166681	−	0.0121101i	0.579420	−	0.815029i	$-0.303279\pi$
$487$	−0.367833	−	0.267246i	−0.0166681	−	0.0121101i	−0.596088	+	0.802919i	$0.703279\pi$
$488$	5.66980	+	1.31845i	0.256660	+	0.0596837i
$489$	7.22579	−	10.5674i	0.326762	−	0.477874i
$490$	−0.669167	−	0.614156i	−0.0302299	−	0.0277447i
$491$	−6.87034	−	7.06941i	−0.310054	−	0.319038i	0.544138	−	0.838996i	$-0.316857\pi$
$491$	−6.87034	−	7.06941i	−0.310054	−	0.319038i	−0.854192	+	0.519958i	$0.825948\pi$
$492$	13.2239	+	4.71830i	0.596182	+	0.212717i
$493$	3.85726	+	11.8714i	0.173722	+	0.534662i
$494$	1.03405	−	1.19336i	0.0465242	−	0.0536917i
$495$	1.71871	+	0.917882i	0.0772503	+	0.0412557i
$496$	−16.1185	−	18.6017i	−0.723742	−	0.835243i
$497$	−3.61854	+	6.00068i	−0.162314	+	0.269167i
$498$	2.12692	+	2.75824i	0.0953096	+	0.123600i
$499$	20.3941	−	7.27661i	0.912966	−	0.325746i	0.162542	−	0.986702i	$-0.448031\pi$
$499$	20.3941	−	7.27661i	0.912966	−	0.325746i	0.750425	+	0.660956i	$0.229849\pi$
$500$	1.75166	+	0.861235i	0.0783368	+	0.0385156i
$501$	−0.557256	+	0.455666i	−0.0248964	+	0.0203577i
$502$	−0.773686	−	3.81829i	−0.0345313	−	0.170419i
$503$	7.30510	+	0.417721i	0.325718	+	0.0186252i	0.219183	−	0.975684i	$-0.429661\pi$
$503$	7.30510	+	0.417721i	0.325718	+	0.0186252i	0.106535	+	0.994309i	$0.466024\pi$
$504$	−0.633867	+	0.581758i	−0.0282347	+	0.0259136i
$505$	2.50630	+	17.4317i	0.111529	+	0.775700i
$506$	−1.87918	+	3.77430i	−0.0835397	+	0.167788i
$507$	−3.20353	+	22.2811i	−0.142274	+	0.989537i
$508$	−19.0527	−	27.8637i	−0.845326	−	1.23625i
$509$	3.03569	+	7.79710i	0.134555	+	0.345601i	0.982980	−	0.183715i	$-0.0588124\pi$
$509$	3.03569	+	7.79710i	0.134555	+	0.345601i	−0.848425	+	0.529316i	$0.822449\pi$
$510$	2.04769	−	2.65549i	0.0906733	−	0.117587i
$511$	5.43235	−	16.7190i	0.240313	−	0.739607i
$512$	8.20822	+	13.6118i	0.362756	+	0.601563i
$513$	11.3058	−	29.0388i	0.499164	−	1.28209i
$514$	1.82910	−	0.425338i	0.0806780	−	0.0187609i
$515$	−5.14423	−	2.17397i	−0.226682	−	0.0957966i
$516$	32.3525	+	20.7917i	1.42424	+	0.915302i
$517$	−10.7687	+	25.1308i	−0.473607	+	1.10525i
$518$	−1.76379	+	1.13352i	−0.0774965	+	0.0498040i
$519$	−6.25252	+	1.08204i	−0.274455	+	0.0474963i
$520$	0.0783050	+	0.911689i	0.00343390	+	0.0399802i
$521$	1.24370	−	14.4801i	0.0544874	−	0.634386i	−0.917249	−	0.398315i	$-0.869595\pi$
$521$	1.24370	−	14.4801i	0.0544874	−	0.634386i	0.971736	−	0.236070i	$-0.0758596\pi$
$522$	−0.196172	−	0.0339488i	−0.00858620	−	0.00148590i
$523$	−11.9321	+	5.04255i	−0.521754	+	0.220495i	−0.634209	−	0.773162i	$-0.718674\pi$
$523$	−11.9321	+	5.04255i	−0.521754	+	0.220495i	0.112455	+	0.993657i	$0.464129\pi$
$524$	2.75943	−	2.00485i	0.120546	−	0.0875821i
$525$	−2.78772	+	1.57430i	−0.121666	+	0.0687081i
$526$	0.00500721	+	0.175275i	0.000218325	+	0.00764236i
$527$	−51.3509	+	15.0780i	−2.23688	+	0.656807i
$528$	6.46099	+	22.4180i	0.281178	+	0.975618i
$529$	−10.1918	−	2.99260i	−0.443124	−	0.130113i
$530$	0.606734	−	2.30826i	0.0263548	−	0.100264i
$531$	0.435113	−	2.14737i	0.0188823	−	0.0931878i
$532$	10.5002	+	19.9000i	0.455240	+	0.862776i
$533$	−0.114535	+	4.00924i	−0.00496105	+	0.173659i
$534$	0.420465	+	1.59961i	0.0181953	+	0.0692220i
$535$	−9.37885	+	0.536302i	−0.405483	+	0.0231863i
$536$	0.820420	−	0.844192i	0.0354367	−	0.0364635i
$537$	−42.3475	+	20.8209i	−1.82743	+	0.898487i
$538$	2.04937	−	4.48749i	0.0883546	−	0.193470i
$539$	3.17901	−	13.3676i	0.136930	−	0.575784i
$540$	3.70521	+	8.11328i	0.159447	+	0.349140i
$541$	−23.5659	−	19.2697i	−1.01318	−	0.828471i	−0.0279300	−	0.999610i	$-0.508892\pi$
$541$	−23.5659	−	19.2697i	−1.01318	−	0.828471i	−0.985247	+	0.171139i	$0.945255\pi$
$542$	−1.32810	+	2.51703i	−0.0570467	+	0.108116i
$543$	−26.8505	−	15.1632i	−1.15227	−	0.650714i
$544$	20.4344	−	2.34463i	0.876118	−	0.100525i
$545$	7.32218	−	0.840142i	0.313648	−	0.0359877i
$546$	−0.645480	−	0.364519i	−0.0276240	−	0.0156000i
$547$	6.50683	−	12.3318i	0.278212	−	0.527271i	−0.705120	−	0.709088i	$-0.749107\pi$
$547$	6.50683	−	12.3318i	0.278212	−	0.527271i	0.983332	+	0.181817i	$0.0581979\pi$
$548$	20.4062	+	16.6860i	0.871709	+	0.712793i
$549$	−1.63966	−	3.59035i	−0.0699790	−	0.153233i
$550$	−0.0378822	−	0.726143i	−0.00161530	−	0.0309628i
$551$	−4.37901	+	9.58870i	−0.186552	+	0.408492i
$552$	8.53922	−	4.19845i	0.363454	−	0.178698i
$553$	9.75407	−	10.0367i	0.414785	−	0.426804i
$554$	−3.16242	+	0.180834i	−0.134358	+	0.00768288i
$555$	−2.72422	−	10.3640i	−0.115637	−	0.439928i
$556$	0.712634	−	24.9454i	0.0302224	−	1.05792i
$557$	0.904781	+	1.71475i	0.0383368	+	0.0726563i	0.902855	−	0.429945i	$-0.141467\pi$
$557$	0.904781	+	1.71475i	0.0383368	+	0.0726563i	−0.864518	+	0.502602i	$0.832376\pi$
$558$	0.169516	−	0.836597i	0.00717620	−	0.0354160i
$559$	−2.79283	+	10.6250i	−0.118124	+	0.449390i
$560$	−6.02334	−	1.76861i	−0.254533	−	0.0747375i
$561$	50.1757	+	7.47032i	2.11842	+	0.315397i
$562$	1.01409	−	0.297765i	0.0427770	−	0.0125604i
$563$	0.217425	+	7.61086i	0.00916336	+	0.320759i	0.991224	+	0.132194i	$0.0422021\pi$
$563$	0.217425	+	7.61086i	0.00916336	+	0.320759i	−0.982061	+	0.188566i	$0.939616\pi$
$564$	26.5379	−	14.9867i	1.11745	−	0.631052i
$565$	6.00228	−	4.36091i	0.252518	−	0.183465i
$566$	4.02220	−	1.69979i	0.169066	−	0.0714477i
$567$	−17.3505	−	3.00262i	−0.728651	−	0.126098i
$568$	−0.307368	+	3.57863i	−0.0128969	+	0.150156i
$569$	−3.12488	−	36.3823i	−0.131002	−	1.52522i	−0.706672	−	0.707542i	$-0.749804\pi$
$569$	−3.12488	−	36.3823i	−0.131002	−	1.52522i	0.575670	−	0.817682i	$-0.304741\pi$
$570$	2.79038	−	0.482894i	0.116876	−	0.0202262i
$571$	10.3678	−	6.66297i	0.433878	−	0.278836i	−0.305416	−	0.952219i	$-0.598796\pi$
$571$	10.3678	−	6.66297i	0.433878	−	0.278836i	0.739294	+	0.673382i	$0.235159\pi$
$572$	−5.66314	+	3.83096i	−0.236788	+	0.160180i
$573$	−31.6696	−	20.3528i	−1.32302	−	0.850250i
$574$	1.29634	+	0.547838i	0.0541082	+	0.0228663i
$575$	5.64777	−	1.31333i	0.235528	−	0.0547697i
$576$	1.46417	−	3.76068i	0.0610070	−	0.156695i
$577$	0.824486	+	1.36726i	0.0343238	+	0.0569197i	0.873038	−	0.487652i	$-0.162147\pi$
$577$	0.824486	+	1.36726i	0.0343238	+	0.0569197i	−0.838714	+	0.544572i	$0.816692\pi$
$578$	3.26626	−	10.0525i	0.135858	−	0.418129i
$579$	−3.93012	+	5.09667i	−0.163330	+	0.211810i
$580$	−1.09465	−	2.81159i	−0.0454529	−	0.116745i
$581$	−8.00264	−	11.7035i	−0.332005	−	0.485542i
$582$	0.414457	−	2.88261i	0.0171798	−	0.119488i
$583$	34.9646	−	9.00400i	1.44809	−	0.372908i
$584$	−1.28238	−	8.91917i	−0.0530654	−	0.369078i
$585$	0.457115	−	0.419537i	0.0188994	−	0.0173457i
$586$	1.47334	+	0.0842487i	0.0608632	+	0.00348028i
$587$	−3.45981	−	17.0748i	−0.142802	−	0.704754i	−0.985946	−	0.167066i	$-0.946571\pi$
$587$	−3.45981	−	17.0748i	−0.142802	−	0.704754i	0.843144	−	0.537688i	$-0.180702\pi$
$588$	−11.8573	+	9.69563i	−0.488985	+	0.399841i
$589$	−40.5591	−	19.9416i	−1.67121	−	0.821679i
$590$	−0.770096	+	0.274770i	−0.0317043	+	0.0113121i
$591$	8.12611	+	10.5381i	0.334263	+	0.433480i
$592$	10.8507	−	17.9938i	0.445960	−	0.739542i
$593$	−5.45160	−	6.29148i	−0.223870	−	0.258360i	0.632692	−	0.774403i	$-0.281950\pi$
$593$	−5.45160	−	6.29148i	−0.223870	−	0.258360i	−0.856563	+	0.516043i	$0.827404\pi$
$594$	1.96639	−	2.67824i	0.0806818	−	0.109890i
$595$	−8.93871	+	10.3158i	−0.366452	+	0.422908i
$596$	2.57568	+	7.92713i	0.105504	+	0.324708i
$597$	−39.4655	−	14.0813i	−1.61522	−	0.576308i
$598$	0.935706	+	0.962819i	0.0382639	+	0.0393726i
$599$	28.4169	+	26.0808i	1.16108	+	1.06563i	0.996858	+	0.0792082i	$0.0252392\pi$
$599$	28.4169	+	26.0808i	1.16108	+	1.06563i	0.164224	+	0.986423i	$0.447488\pi$
$600$	−0.926277	+	1.35464i	−0.0378151	+	0.0553028i
$601$	1.82830	+	0.425152i	0.0745777	+	0.0173423i	0.263620	−	0.964627i	$-0.415084\pi$
$601$	1.82830	+	0.425152i	0.0745777	+	0.0173423i	−0.189042	+	0.981969i	$0.560538\pi$
$602$	3.11858	+	2.26578i	0.127104	+	0.0923464i
$603$	−0.792995	−	0.0909877i	−0.0322932	−	0.00370530i
$604$	2.28342			0.0929109
$605$	9.31277	−	5.85425i	0.378618	−	0.238009i
$606$	−7.31297			−0.297069
$607$	22.8433	+	2.62103i	0.927181	+	0.106384i	0.564410	−	0.825494i	$-0.309104\pi$
$607$	22.8433	+	2.62103i	0.927181	+	0.106384i	0.362771	+	0.931878i	$0.381831\pi$
$608$	14.0526	+	10.2098i	0.569909	+	0.414063i
$609$	4.82010	+	1.12087i	0.195320	+	0.0454198i
$610$	−0.831407	+	1.21589i	−0.0336627	+	0.0492301i
$611$	6.41427	+	5.88697i	0.259494	+	0.238161i
$612$	−6.45380	−	6.64081i	−0.260880	−	0.268439i
$613$	−3.72523	−	1.32916i	−0.150461	−	0.0536842i	0.259745	−	0.965677i	$-0.416361\pi$
$613$	−3.72523	−	1.32916i	−0.150461	−	0.0536842i	−0.410206	+	0.911993i	$0.634543\pi$
$614$	0.645961	+	1.98806i	0.0260689	+	0.0802317i
$615$	−4.71049	+	5.43619i	−0.189945	+	0.219208i
$616$	1.07648	+	4.73641i	0.0433726	+	0.190835i
$617$	16.6095	+	19.1684i	0.668675	+	0.771692i	0.984168	−	0.177235i	$-0.0567154\pi$
$617$	16.6095	+	19.1684i	0.668675	+	0.771692i	−0.315493	+	0.948928i	$0.602170\pi$
$618$	1.19756	−	1.98593i	0.0481730	−	0.0798859i
$619$	2.16632	+	2.80933i	0.0870717	+	0.112917i	0.833423	−	0.552636i	$-0.186378\pi$
$619$	2.16632	+	2.80933i	0.0870717	+	0.112917i	−0.746351	+	0.665552i	$0.768196\pi$
$620$	12.1839	−	4.34722i	0.489319	−	0.174589i
$621$	23.7773	+	11.6905i	0.954152	+	0.469125i
$622$	1.73481	−	1.41855i	0.0695595	−	0.0568786i
$623$	−1.33701	−	6.59839i	−0.0535660	−	0.264359i
$624$	7.41712	+	0.424126i	0.296922	+	0.0169786i
$625$	−0.736741	+	0.676175i	−0.0294696	+	0.0270470i
$626$	0.887562	+	6.17313i	0.0354741	+	0.246728i
$627$	26.9523	+	33.2995i	1.07637	+	1.32985i
$628$	1.21466	−	8.44812i	0.0484700	−	0.337117i
$629$	−25.7883	−	37.7143i	−1.02825	−	1.50377i
$630$	−0.0789860	−	0.202874i	−0.00314688	−	0.00808269i
$631$	−23.4855	+	30.4565i	−0.934943	+	1.21246i	0.0420350	+	0.999116i	$0.486616\pi$
$631$	−23.4855	+	30.4565i	−0.934943	+	1.21246i	−0.976978	+	0.213340i	$0.931566\pi$
$632$	2.21685	−	6.82277i	0.0881817	−	0.271395i
$633$	22.9188	+	38.0066i	0.910941	+	1.51063i
$634$	2.65889	−	6.82931i	0.105598	−	0.271227i
$635$	16.8436	−	3.91681i	0.668418	−	0.155434i
$636$	−37.0726	−	15.6670i	−1.47003	−	0.621238i
$637$	−3.68084	−	2.36553i	−0.145840	−	0.0937259i
$638$	−0.715813	+	0.866528i	−0.0283393	+	0.0343062i
$639$	2.04884	−	1.31671i	0.0810507	−	0.0520881i
$640$	−6.50350	+	1.12547i	−0.257073	+	0.0444883i
$641$	3.24199	+	37.7458i	0.128051	+	1.49087i	0.725088	+	0.688656i	$0.241799\pi$
$641$	3.24199	+	37.7458i	0.128051	+	1.49087i	−0.597037	+	0.802213i	$0.703656\pi$
$642$	0.333823	−	3.88663i	0.0131749	−	0.153393i
$643$	−14.0401	−	2.42974i	−0.553689	−	0.0958197i	−0.113191	−	0.993573i	$-0.536107\pi$
$643$	−14.0401	−	2.42974i	−0.553689	−	0.0958197i	−0.440498	+	0.897754i	$0.645198\pi$
$644$	−17.6222	+	7.44719i	−0.694410	+	0.293460i
$645$	−15.9394	+	11.5807i	−0.627614	+	0.455989i
$646$	10.5131	−	5.93701i	0.413632	−	0.233589i
$647$	−0.122607	−	4.29182i	−0.00482019	−	0.168729i	−0.998436	−	0.0559102i	$-0.982194\pi$
$647$	−0.122607	−	4.29182i	−0.00482019	−	0.168729i	0.993616	−	0.112819i	$-0.0359879\pi$
$648$	−8.66011	+	2.54284i	−0.340201	+	0.0998920i
$649$	−9.30750	−	8.14680i	−0.365352	−	0.319790i
$650$	−0.222165	−	0.0652334i	−0.00871401	−	0.00255866i
$651$	−5.39397	+	20.5208i	−0.211406	+	0.804273i
$652$	−2.61996	+	12.9300i	−0.102605	+	0.506378i
$653$	11.2156	+	21.2560i	0.438901	+	0.831810i	0.999992	+	0.00405577i	$0.00129099\pi$
$653$	11.2156	+	21.2560i	0.438901	+	0.831810i	−0.561091	+	0.827754i	$0.689618\pi$
$654$	−0.0873956	+	3.05924i	−0.00341744	+	0.119626i
$655$	0.444226	+	1.69001i	0.0173573	+	0.0660342i
$656$	−14.0814	+	0.805203i	−0.549786	+	0.0314379i
$657$	−4.25823	+	4.38162i	−0.166130	+	0.170943i
$658$	2.74145	−	1.34788i	0.106873	−	0.0525458i
$659$	0.617693	−	1.35256i	0.0240619	−	0.0526882i	−0.897219	−	0.441585i	$-0.854416\pi$
$659$	0.617693	−	1.35256i	0.0240619	−	0.0526882i	0.921281	+	0.388897i	$0.127144\pi$
$660$	−12.2115	−	1.11036i	−0.475331	−	0.0432206i
$661$	−3.62279	−	7.93280i	−0.140910	−	0.308550i	0.825999	−	0.563672i	$-0.190612\pi$
$661$	−3.62279	−	7.93280i	−0.140910	−	0.308550i	−0.966909	+	0.255122i	$0.917884\pi$
$662$	2.96578	+	2.42510i	0.115268	+	0.0942543i
$663$	7.53844	−	14.2869i	0.292769	−	0.554859i
$664$	−6.32801	−	3.57359i	−0.245574	−	0.138682i
$665$	−11.4521	+	1.31400i	−0.444092	+	0.0509548i
$666$	0.723953	−	0.0830659i	0.0280526	−	0.00321874i
$667$	−7.80437	−	4.40733i	−0.302186	−	0.170653i
$668$	0.346188	−	0.656100i	0.0133944	−	0.0253853i
$669$	16.8675	+	13.7925i	0.652136	+	0.533249i
$670$	0.123741	+	0.270956i	0.00478054	+	0.0104679i
$671$	−22.1915	−	2.01781i	−0.856692	−	0.0778966i
$672$	3.38750	−	7.41760i	0.130676	−	0.286140i
$673$	−12.8922	+	6.33867i	−0.496958	+	0.244338i	−0.672449	−	0.740143i	$-0.734758\pi$
$673$	−12.8922	+	6.33867i	−0.496958	+	0.244338i	0.175491	+	0.984481i	$0.443849\pi$
$674$	4.57359	−	4.70611i	0.176168	−	0.181273i
$675$	−4.56201	+	0.260865i	−0.175592	+	0.0100407i
$676$	−5.89734	−	22.4358i	−0.226821	−	0.862916i
$677$	−0.514322	+	18.0036i	−0.0197670	+	0.691936i	0.927928	+	0.372759i	$0.121588\pi$
$677$	−0.514322	+	18.0036i	−0.0197670	+	0.691936i	−0.947695	+	0.319177i	$0.896594\pi$
$678$	1.43773	+	2.72480i	0.0552156	+	0.104645i
$679$	−2.35418	+	11.6183i	−0.0903452	+	0.445871i
$680$	−1.77867	+	6.76676i	−0.0682089	+	0.259493i
$681$	−51.2585	−	15.0509i	−1.96423	−	0.576750i
$682$	−3.62613	−	3.17393i	−0.138852	−	0.121536i
$683$	39.9480	−	11.7298i	1.52857	−	0.448828i	0.593957	−	0.804497i	$-0.297565\pi$
$683$	39.9480	−	11.7298i	1.52857	−	0.448828i	0.934612	+	0.355668i	$0.115747\pi$
$684$	−0.223315	−	7.81704i	−0.00853866	−	0.298892i
$685$	−11.7589	+	6.64057i	−0.449285	+	0.253723i
$686$	−3.34068	+	2.42715i	−0.127548	+	0.0926689i
$687$	−24.5824	+	10.3886i	−0.937876	+	0.396350i
$688$	−38.0667	−	6.58769i	−1.45128	−	0.251154i
$689$	0.983874	−	11.4550i	0.0374826	−	0.436402i
$690$	0.206049	+	2.39898i	0.00784415	+	0.0913278i
$691$	30.3739	−	5.25640i	1.15548	−	0.199963i	0.439602	−	0.898193i	$-0.355119\pi$
$691$	30.3739	−	5.25640i	1.15548	−	0.199963i	0.715874	+	0.698229i	$0.246028\pi$
$692$	5.50123	−	3.53543i	0.209125	−	0.134397i
$693$	2.09752	−	2.53916i	0.0796784	−	0.0964547i
$694$	−1.23804	−	0.795639i	−0.0469953	−	0.0302020i
$695$	11.7766	+	4.97684i	0.446713	+	0.188782i
$696$	2.47069	−	0.574535i	0.0936513	−	0.0217777i
$697$	−11.1266	+	28.5783i	−0.421449	+	1.08248i
$698$	−1.85936	−	3.08340i	−0.0703777	−	0.116708i
$699$	14.6078	−	44.9583i	0.552520	−	1.70048i
$700$	2.01474	−	2.61276i	0.0761501	−	0.0987532i
$701$	9.39401	+	24.1283i	0.354807	+	0.911314i	0.990267	+	0.139180i	$0.0444468\pi$
$701$	9.39401	+	24.1283i	0.354807	+	0.911314i	−0.635460	+	0.772134i	$0.719190\pi$
$702$	−0.597199	−	0.873375i	−0.0225398	−	0.0329634i
$703$	5.49099	−	38.1907i	0.207097	−	1.44039i
$704$	−14.3338	−	17.7094i	−0.540225	−	0.667447i
$705$	2.22208	+	15.4549i	0.0836885	+	0.582067i
$706$	−0.218685	+	0.200707i	−0.00823031	+	0.00755371i
$707$	29.7192	+	1.69941i	1.11771	+	0.0639127i
$708$	2.73822	+	13.5136i	0.102909	+	0.507873i
$709$	28.5633	−	23.3561i	1.07272	−	0.877155i	0.0798994	−	0.996803i	$-0.474540\pi$
$709$	28.5633	−	23.3561i	1.07272	−	0.877155i	0.992816	+	0.119648i	$0.0381765\pi$
$710$	−0.815620	−	0.401013i	−0.0306097	−	0.0150498i
$711$	−4.58144	+	1.63465i	−0.171817	+	0.0613043i
$712$	−2.10731	−	2.73281i	−0.0789748	−	0.102416i
$713$	19.8445	−	32.9084i	0.743182	−	1.23243i
$714$	−3.71181	−	4.28366i	−0.138911	−	0.160312i
$715$	−0.776307	−	3.41568i	−0.0290322	−	0.127739i
$716$	31.8465	−	36.7529i	1.19016	−	1.37352i
$717$	11.9637	+	36.8203i	0.446791	+	1.37508i
$718$	2.43266	+	0.867973i	0.0907862	+	0.0323925i
$719$	−30.2874	−	31.1650i	−1.12953	−	1.16226i	−0.984964	−	0.172762i	$-0.944731\pi$
$719$	−30.2874	−	31.1650i	−1.12953	−	1.16226i	−0.144565	−	0.989495i	$-0.546178\pi$
$720$	1.60746	+	1.47532i	0.0599066	+	0.0549818i
$721$	−5.32827	+	7.79235i	−0.198435	+	0.290202i
$722$	5.87390	+	1.36592i	0.218604	+	0.0508342i
$723$	−11.8369	−	8.59998i	−0.440217	−	0.319837i
$724$	31.5712	+	3.62246i	1.17334	+	0.134628i
$725$	1.54573			0.0574070
$726$	1.85589	+	4.17374i	0.0688785	+	0.154902i
$727$	−37.3071			−1.38365			−0.691823	−	0.722067i	$-0.743192\pi$
$727$	−37.3071			−1.38365			−0.691823	+	0.722067i	$0.743192\pi$
$728$	1.53662	+	0.176311i	0.0569509	+	0.00653450i
$729$	−16.0546	−	11.6644i	−0.594616	−	0.432014i
$730$	2.22086	+	0.516440i	0.0821979	+	0.0191143i
$731$	−47.4136	+	69.3402i	−1.75366	+	2.56464i
$732$	18.3001	+	16.7956i	0.676390	+	0.620785i
$733$	−23.5127	−	24.1940i	−0.868463	−	0.893627i	0.126692	−	0.991942i	$-0.459564\pi$
$733$	−23.5127	−	24.1940i	−0.868463	−	0.893627i	−0.995155	+	0.0983146i	$0.968655\pi$
$734$	5.73115	+	2.04487i	0.211541	+	0.0754776i
$735$	−2.42483	−	7.46285i	−0.0894411	−	0.275271i
$736$	−9.67166	+	11.1617i	−0.356502	+	0.411425i
$737$	−2.66688	+	3.63233i	−0.0982358	+	0.133799i
$738$	−0.320318	−	0.369666i	−0.0117911	−	0.0136076i
$739$	−22.7134	+	37.6659i	−0.835524	+	1.38556i	0.0856153	+	0.996328i	$0.472714\pi$
$739$	−22.7134	+	37.6659i	−0.835524	+	1.38556i	−0.921139	+	0.389233i	$0.872740\pi$
$740$	6.74368	+	8.74535i	0.247902	+	0.321486i
$741$	12.8485	−	4.58432i	0.472000	−	0.168409i
$742$	−3.62026	−	1.77996i	−0.132904	−	0.0653445i
$743$	26.1585	−	21.3897i	0.959662	−	0.784712i	−0.0169201	−	0.999857i	$-0.505386\pi$
$743$	26.1585	−	21.3897i	0.959662	−	0.784712i	0.976582	+	0.215145i	$0.0690225\pi$
$744$	2.15984	+	10.6592i	0.0791837	+	0.390787i
$745$	−4.26320	−	0.243779i	−0.156192	−	0.00893136i
$746$	−0.725132	+	0.665521i	−0.0265490	+	0.0243664i
$747$	0.701284	+	4.87754i	0.0256586	+	0.178460i
$748$	−50.6269	+	13.0373i	−1.85110	+	0.476691i
$749$	−2.25981	+	15.7173i	−0.0825716	+	0.574298i
$750$	−0.234386	−	0.342778i	−0.00855856	−	0.0125165i
$751$	−1.47663	−	3.79270i	−0.0538830	−	0.138397i	0.902350	−	0.431005i	$-0.141841\pi$
$751$	−1.47663	−	3.79270i	−0.0538830	−	0.138397i	−0.956233	+	0.292607i	$0.905477\pi$
$752$	−18.6956	+	24.2448i	−0.681757	+	0.884119i
$753$	10.4008	−	32.0104i	0.379027	−	1.16652i
$754$	0.184821	+	0.306491i	0.00673078	+	0.0111617i
$755$	−0.424420	+	1.09011i	−0.0154462	+	0.0396733i
$756$	14.6845	−	3.41473i	0.534069	−	0.124192i
$757$	−13.4008	−	5.66321i	−0.487059	−	0.205833i	0.131889	−	0.991264i	$-0.457896\pi$
$757$	−13.4008	−	5.66321i	−0.487059	−	0.205833i	−0.618949	+	0.785431i	$0.712441\pi$
$758$	−3.26889	−	2.10079i	−0.118731	−	0.0763041i
$759$	−30.1705	+	20.4095i	−1.09512	+	0.740818i
$760$	−4.97065	+	3.19444i	−0.180304	+	0.115875i
$761$	−29.7531	+	5.14897i	−1.07855	+	0.186650i	−0.681992	−	0.731360i	$-0.738886\pi$
$761$	−29.7531	+	5.14897i	−1.07855	+	0.186650i	−0.396557	+	0.918010i	$0.629795\pi$
$762$	0.614509	+	7.15460i	0.0222613	+	0.259184i
$763$	1.06608	−	12.4122i	0.0385948	−	0.449351i
$764$	38.2277	+	6.61556i	1.38303	+	0.239343i
$765$	4.36993	−	1.84675i	0.157995	−	0.0667693i
$766$	4.10134	−	2.97980i	0.148187	−	0.107664i
$767$	−3.42971	+	1.93685i	−0.123840	+	0.0699355i
$768$	0.664829	+	23.2720i	0.0239899	+	0.839758i
$769$	12.6605	−	3.71746i	0.456549	−	0.134055i	−0.0453687	−	0.998970i	$-0.514446\pi$
$769$	12.6605	−	3.71746i	0.456549	−	0.134055i	0.501918	+	0.864915i	$0.332628\pi$
$770$	−1.21567	−	0.180993i	−0.0438096	−	0.00652253i
$771$	15.5666	+	4.57076i	0.560616	+	0.164612i
$772$	1.68613	−	6.41472i	0.0606853	−	0.230871i
$773$	5.07639	−	25.0530i	0.182585	−	0.901093i	−0.779092	−	0.626909i	$-0.784320\pi$
$773$	5.07639	−	25.0530i	0.182585	−	0.901093i	0.961677	−	0.274184i	$-0.0884077\pi$
$774$	−0.625227	−	1.18494i	−0.0224733	−	0.0425917i
$775$	−0.189252	+	6.62470i	−0.00679815	+	0.237966i
$776$	1.54472	+	5.87674i	0.0554524	+	0.210963i
$777$	−18.0838	+	1.03407i	−0.648753	+	0.0370970i
$778$	−3.35521	+	3.45243i	−0.120290	+	0.123776i
$779$	−23.2417	+	11.4272i	−0.832719	+	0.409420i
$780$	−1.62203	+	3.55175i	−0.0580780	+	0.127173i
$781$	−0.716317	−	13.7307i	−0.0256318	−	0.491323i
$782$	4.26455	+	9.33807i	0.152500	+	0.333929i
$783$	5.46789	+	4.47107i	0.195406	+	0.159783i
$784$	7.18031	−	13.6082i	0.256440	−	0.486007i
$785$	3.80741	+	2.15014i	0.135892	+	0.0767418i
$786$	−0.720888	+	0.0827142i	−0.0257132	+	0.00295032i
$787$	49.5654	−	5.68710i	1.76681	−	0.202723i	0.831255	−	0.555891i	$-0.187623\pi$
$787$	49.5654	−	5.68710i	1.76681	−	0.202723i	0.935560	+	0.353168i	$0.114896\pi$
$788$	−11.9414	−	6.74359i	−0.425393	−	0.240231i
$789$	−0.706942	+	1.33980i	−0.0251678	+	0.0476983i
$790$	1.40529	+	1.14910i	0.0499979	+	0.0408831i
$791$	−5.20960	−	11.4074i	−0.185232	−	0.405602i
$792$	0.390579	−	1.64237i	0.0138786	−	0.0583589i
$793$	−2.94765	+	6.45446i	−0.104674	+	0.229205i
$794$	−0.421481	+	0.207228i	−0.0149578	+	0.00735426i
$795$	14.3702	−	14.7866i	0.509660	−	0.524428i
$796$	43.1122	−	2.46525i	1.52807	−	0.0873783i
$797$	−5.71577	−	21.7451i	−0.202463	−	0.770249i	−0.988391	−	0.151931i	$-0.951451\pi$
$797$	−5.71577	−	21.7451i	−0.202463	−	0.770249i	0.785928	−	0.618318i	$-0.212186\pi$
$798$	0.136689	−	4.78473i	0.00483873	−	0.169378i
$799$	31.0660	+	58.8767i	1.09904	+	2.08291i
$800$	0.505822	−	2.49633i	0.0178835	−	0.0882586i
$801$	−0.594857	+	2.26307i	−0.0210182	+	0.0799617i
$802$	−7.19921	−	2.11388i	−0.254213	−	0.0746436i
$803$	9.55242	+	33.1445i	0.337097	+	1.16964i
$804$	4.81968	−	1.41519i	0.169977	−	0.0499098i
$805$	−0.279881	−	9.79713i	−0.00986452	−	0.345303i
$806$	−1.33619	+	0.754581i	−0.0470652	+	0.0265790i
$807$	34.4806	−	25.0516i	1.21377	−	0.881858i
$808$	14.0549	−	5.93963i	0.494448	−	0.208956i
$809$	23.6066	+	4.08529i	0.829965	+	0.143631i	0.569644	−	0.821891i	$-0.307081\pi$
$809$	23.6066	+	4.08529i	0.829965	+	0.143631i	0.260320	+	0.965522i	$0.416172\pi$
$810$	0.195442	−	2.27549i	0.00686714	−	0.0799527i
$811$	3.04815	+	35.4889i	0.107035	+	1.24618i	0.830970	+	0.556317i	$0.187786\pi$
$811$	3.04815	+	35.4889i	0.107035	+	1.24618i	−0.723936	+	0.689868i	$0.757669\pi$
$812$	−5.02522	+	0.869648i	−0.176350	+	0.0305187i
$813$	−20.6837	+	13.2926i	−0.725410	+	0.466193i
$814$	1.62034	−	3.78135i	0.0567927	−	0.132536i
$815$	−5.68588	−	3.65409i	−0.199168	−	0.127997i
$816$	52.3248	+	22.1127i	1.83173	+	0.774098i
$817$	−69.0947	+	16.0673i	−2.41732	+	0.562123i
$818$	−0.486337	+	1.24915i	−0.0170044	+	0.0436754i
$819$	−0.541575	−	0.898101i	−0.0189242	−	0.0313822i
$820$	2.29071	−	7.05007i	0.0799950	−	0.246199i
$821$	1.81369	−	2.35203i	0.0632981	−	0.0820865i	−0.759189	−	0.650870i	$-0.774404\pi$
$821$	1.81369	−	2.35203i	0.0632981	−	0.0820865i	0.822487	+	0.568784i	$0.192586\pi$
$822$	−2.03453	−	5.22564i	−0.0709622	−	0.182265i
$823$	−14.5660	−	21.3022i	−0.507741	−	0.742547i	0.483395	−	0.875402i	$-0.339404\pi$
$823$	−14.5660	−	21.3022i	−0.507741	−	0.742547i	−0.991135	+	0.132856i	$0.957585\pi$
$824$	−0.688619	+	4.78945i	−0.0239892	+	0.166848i
$825$	2.79985	−	5.62345i	0.0974782	−	0.195783i
$826$	0.196689	+	1.36800i	0.00684367	+	0.0475988i
$827$	20.5945	−	18.9015i	0.716142	−	0.657270i	−0.232870	−	0.972508i	$-0.574812\pi$
$827$	20.5945	−	18.9015i	0.716142	−	0.657270i	0.949013	+	0.315238i	$0.102084\pi$
$828$	6.63839	+	0.379597i	0.230700	+	0.0131919i
$829$	−1.85558	−	9.15763i	−0.0644468	−	0.318058i	0.934871	−	0.354988i	$-0.115515\pi$
$829$	−1.85558	−	9.15763i	−0.0644468	−	0.318058i	−0.999318	+	0.0369299i	$0.988242\pi$
$830$	1.42359	−	1.16407i	0.0494137	−	0.0404053i
$831$	−24.5579	−	12.0743i	−0.851906	−	0.418854i
$832$	−6.83308	+	2.43804i	−0.236894	+	0.0845237i
$833$	−20.4295	−	26.4934i	−0.707839	−	0.917942i
$834$	−2.74156	+	4.54637i	−0.0949325	+	0.157428i
$835$	0.248879	+	0.287222i	0.00861282	+	0.00993973i
$836$	−38.9434	−	20.7978i	−1.34689	−	0.719308i
$837$	−19.8316	+	22.8869i	−0.685480	+	0.791087i
$838$	−2.13309	−	6.56497i	−0.0736863	−	0.226783i
$839$	4.38407	+	1.56423i	0.151355	+	0.0540033i	0.410640	−	0.911797i	$-0.365305\pi$
$839$	4.38407	+	1.56423i	0.151355	+	0.0540033i	−0.259285	+	0.965801i	$0.583487\pi$
$840$	1.93320	+	1.98922i	0.0667019	+	0.0686346i
$841$	19.6052	+	17.9935i	0.676042	+	0.620465i
$842$	−4.52442	+	6.61676i	−0.155922	+	0.228028i
$843$	8.89364	+	2.06813i	0.306313	+	0.0712301i
$844$	−37.0029	−	26.8842i	−1.27369	−	0.925393i
$845$	11.8071	+	1.35474i	0.406177	+	0.0466045i
$846$	−1.06176			−0.0365040
$847$	−6.57225	−	17.3930i	−0.225825	−	0.597630i
$848$	40.4304			1.38838
$849$	37.4787	+	4.30028i	1.28626	+	0.147585i
$850$	−1.43231	−	1.04063i	−0.0491277	−	0.0356934i
$851$	31.9534	+	7.43045i	1.09535	+	0.254713i
$852$	−8.65101	+	12.6517i	−0.296379	+	0.433440i
$853$	−22.7631	−	20.8918i	−0.779394	−	0.715321i	0.184142	−	0.982900i	$-0.441049\pi$
$853$	−22.7631	−	20.8918i	−0.779394	−	0.715321i	−0.963536	+	0.267578i	$0.913777\pi$
$854$	1.73521	+	1.78548i	0.0593775	+	0.0610980i
$855$	3.77340	+	1.34635i	0.129048	+	0.0460441i
$856$	2.51516	+	7.74088i	0.0859666	+	0.264578i
$857$	−1.79726	+	2.07415i	−0.0613931	+	0.0708515i	−0.785615	−	0.618715i	$-0.787654\pi$
$857$	−1.79726	+	2.07415i	−0.0613931	+	0.0708515i	0.724222	+	0.689567i	$0.242199\pi$
$858$	1.44980	−	0.117227i	0.0494955	−	0.00400207i
$859$	25.0991	+	28.9659i	0.856372	+	0.988305i	0.999999	−	0.00132640i	$-0.000422208\pi$
$859$	25.0991	+	28.9659i	0.856372	+	0.988305i	−0.143628	+	0.989632i	$0.545877\pi$
$860$	10.4850	−	17.3875i	0.357537	−	0.592908i
$861$	7.42456	+	9.62835i	0.253028	+	0.328133i
$862$	−1.23380	+	0.440219i	−0.0420234	+	0.0149939i
$863$	15.2018	+	7.47421i	0.517475	+	0.254425i	0.681222	−	0.732077i	$-0.261449\pi$
$863$	15.2018	+	7.47421i	0.517475	+	0.254425i	−0.163747	+	0.986502i	$0.552358\pi$
$864$	9.01001	−	7.36745i	0.306527	−	0.250646i
$865$	0.665313	+	3.28345i	0.0226213	+	0.111641i
$866$	−2.91059	−	0.166433i	−0.0989057	−	0.00565564i
$867$	67.2763	−	61.7456i	2.28482	−	2.09699i
$868$	−3.11188	−	21.6436i	−0.105624	−	0.734631i
$869$	−4.81799	+	27.0356i	−0.163439	+	0.917120i
$870$	−0.0913471	+	0.635333i	−0.00309696	+	0.0215398i
$871$	0.809941	+	1.18450i	0.0274438	+	0.0401353i
$872$	−2.31677	−	5.95057i	−0.0784557	−	0.201512i
$873$	2.51596	−	3.26275i	0.0851522	−	0.110427i
$874$	−2.67899	+	8.24508i	−0.0906182	+	0.278894i
$875$	0.872866	+	1.44749i	0.0295083	+	0.0489339i
$876$	13.9501	−	35.8306i	0.471331	−	1.21060i
$877$	−50.9977	+	11.8590i	−1.72207	+	0.400450i	−0.966915	−	0.255097i	$-0.917892\pi$
$877$	−50.9977	+	11.8590i	−1.72207	+	0.400450i	−0.755154	+	0.655547i	$0.772438\pi$
$878$	4.84211	+	2.04629i	0.163413	+	0.0690591i
$879$	10.7255	+	6.89287i	0.361763	+	0.232491i
$880$	11.7337	−	3.74777i	0.395542	−	0.126337i
$881$	−36.4315	+	23.4131i	−1.22741	+	0.788807i	−0.983485	−	0.180988i	$-0.942071\pi$
$881$	−36.4315	+	23.4131i	−1.22741	+	0.788807i	−0.243922	+	0.969795i	$0.578434\pi$
$882$	0.525782	−	0.0909902i	0.0177040	−	0.00306380i
$883$	0.195788	+	2.27952i	0.00658880	+	0.0767120i	0.998888	−	0.0471556i	$-0.0150157\pi$
$883$	0.195788	+	2.27952i	0.00658880	+	0.0767120i	−0.992299	+	0.123868i	$0.960470\pi$
$884$	−1.42460	+	16.5863i	−0.0479144	+	0.557857i
$885$	−6.96044	−	1.20455i	−0.233972	−	0.0404905i
$886$	2.37867	−	1.00523i	0.0799130	−	0.0337715i
$887$	7.56576	−	5.49684i	0.254033	−	0.184566i	−0.453479	−	0.891267i	$-0.649817\pi$
$887$	7.56576	−	5.49684i	0.254033	−	0.184566i	0.707512	+	0.706701i	$0.249817\pi$
$888$	−8.08449	+	4.56552i	−0.271298	+	0.153209i
$889$	−0.834704	−	29.2184i	−0.0279951	−	0.979955i
$890$	0.837856	−	0.246017i	0.0280850	−	0.00824650i
$891$	31.4994	−	14.1955i	1.05527	−	0.475566i
$892$	−21.5448	−	6.32614i	−0.721375	−	0.211815i
$893$	−14.2917	+	54.3711i	−0.478252	+	1.81946i
$894$	0.352139	−	1.73787i	0.0117773	−	0.0581232i
$895$	11.6267	+	22.0350i	0.388637	+	0.736548i
$896$	−0.318578	+	11.1517i	−0.0106430	+	0.372552i
$897$	2.94870	+	11.2180i	0.0984543	+	0.374559i
$898$	−8.61069	+	0.492377i	−0.287343	+	0.0164308i
$899$	7.13955	−	7.34643i	0.238117	−	0.245017i
$900$	−1.02907	+	0.505959i	−0.0343023	+	0.0168653i
$901$	36.5191	−	79.9657i	1.21663	−	2.66404i
$902$	−2.70914	+	0.534860i	−0.0902044	+	0.0178089i
$903$	13.8344	+	30.2931i	0.460380	+	1.00809i
$904$	−4.97628	−	4.06909i	−0.165509	−	0.135336i
$905$	−7.59755	+	14.3990i	−0.252551	+	0.478638i
$906$	−0.422982	−	0.238869i	−0.0140526	−	0.00793589i
$907$	22.9282	−	2.63077i	0.761318	−	0.0873531i	0.275367	−	0.961339i	$-0.411201\pi$
$907$	22.9282	−	2.63077i	0.761318	−	0.0873531i	0.485951	+	0.873986i	$0.338473\pi$
$908$	54.6959	−	6.27576i	1.81515	−	0.208269i
$909$	−9.00883	−	5.08752i	−0.298804	−	0.168742i
$910$	−0.182643	+	0.346148i	−0.00605457	+	0.0114747i
$911$	−30.1624	−	24.6637i	−0.999326	−	0.817145i	−0.0161621	−	0.999869i	$-0.505145\pi$
$911$	−30.1624	−	24.6637i	−0.999326	−	0.817145i	−0.983164	+	0.182724i	$0.941508\pi$
$912$	19.9283	+	43.6368i	0.659891	+	1.44496i
$913$	25.8730	+	10.2225i	0.856272	+	0.338315i
$914$	−1.18330	+	2.59106i	−0.0391401	+	0.0857048i
$915$	−11.4198	+	5.61473i	−0.377526	+	0.185617i
$916$	19.1677	−	19.7231i	0.633319	−	0.651670i
$917$	2.94884	−	0.168621i	0.0973793	−	0.00556835i
$918$	−2.05661	−	7.82414i	−0.0678781	−	0.258235i
$919$	0.114636	−	4.01278i	0.00378149	−	0.132369i	−0.995508	−	0.0946781i	$-0.969818\pi$
$919$	0.114636	−	4.01278i	0.00378149	−	0.132369i	0.999289	−	0.0376913i	$-0.0120004\pi$
$920$	−2.34448	−	4.44328i	−0.0772951	−	0.146490i
$921$	−3.58642	+	17.6997i	−0.118177	+	0.583224i
$922$	−1.24173	+	4.72404i	−0.0408943	+	0.155578i
$923$	−4.20093	−	1.23350i	−0.138275	−	0.0406013i
$924$	−5.93857	+	19.8572i	−0.195365	+	0.653254i
$925$	−5.42853	+	1.59396i	−0.178489	+	0.0524091i
$926$	−0.101012	−	3.53587i	−0.00331945	−	0.116196i
$927$	2.85686	−	1.61334i	0.0938315	−	0.0529891i
$928$	−3.18516	+	2.31415i	−0.104558	+	0.0759658i
$929$	−8.11491	+	3.42939i	−0.266242	+	0.112515i	−0.518304	−	0.855196i	$-0.673437\pi$
$929$	−8.11491	+	3.42939i	−0.266242	+	0.112515i	0.252063	+	0.967711i	$0.418891\pi$
$930$	−2.71173	−	0.469283i	−0.0889211	−	0.0153884i
$931$	2.41775	−	28.1493i	0.0792384	−	0.922556i
$932$	4.16890	+	48.5376i	0.136557	+	1.58990i
$933$	19.0767	−	3.30135i	0.624542	−	0.108081i
$934$	−3.23973	+	2.08205i	−0.106007	+	0.0681267i
$935$	3.18598	−	26.5928i	0.104193	−	0.869678i
$936$	−0.452234	−	0.290633i	−0.0147817	−	0.00949965i
$937$	25.4826	+	10.7690i	0.832480	+	0.351809i	0.763499	−	0.645809i	$-0.223480\pi$
$937$	25.4826	+	10.7690i	0.832480	+	0.351809i	0.0689807	+	0.997618i	$0.478025\pi$
$938$	0.490411	−	0.114040i	0.0160125	−	0.00372354i
$939$	−19.5481	+	50.2088i	−0.637927	+	1.63850i
$940$	−8.30931	−	13.7794i	−0.271020	−	0.449436i
$941$	8.39885	−	25.8490i	0.273795	−	0.842653i	−0.715741	−	0.698366i	$-0.753911\pi$
$941$	8.39885	−	25.8490i	0.273795	−	0.842653i	0.989536	−	0.144288i	$-0.0460891\pi$
$942$	−1.10876	+	1.43787i	−0.0361255	+	0.0468484i
$943$	−7.98934	−	20.5205i	−0.260169	−	0.668238i
$944$	−7.81811	−	11.4336i	−0.254458	−	0.372133i
$945$	−1.09921	+	7.64515i	−0.0357572	+	0.248697i
$946$	−7.55941	−	0.253774i	−0.245778	−	0.00825091i
$947$	−0.705884	−	4.90953i	−0.0229381	−	0.159538i	0.975133	−	0.221621i	$-0.0711348\pi$
$947$	−0.705884	−	4.90953i	−0.0229381	−	0.159538i	−0.998071	+	0.0620828i	$0.980226\pi$
$948$	22.5530	−	20.6989i	0.732487	−	0.672270i
$949$	10.9660	+	0.627061i	0.355973	+	0.0203552i
$950$	−0.296917	−	1.46534i	−0.00963325	−	0.0475420i
$951$	49.0144	−	40.0789i	1.58940	−	1.29965i
$952$	10.6130	+	5.21805i	0.343968	+	0.169118i
$953$	26.2128	−	9.35271i	0.849116	−	0.302964i	0.124588	−	0.992209i	$-0.460239\pi$
$953$	26.2128	−	9.35271i	0.849116	−	0.302964i	0.724529	+	0.689244i	$0.242057\pi$
$954$	0.856202	+	1.11034i	0.0277206	+	0.0359487i
$955$	−10.2637	+	17.0205i	−0.332126	+	0.550769i
$956$	−26.1277	−	30.1529i	−0.845030	−	0.975216i
$957$	−9.06601	+	3.47764i	−0.293063	+	0.112416i
$958$	0.0985551	−	0.113739i	0.00318417	−	0.00367473i
$959$	7.05378	+	21.7093i	0.227778	+	0.701030i
$960$	−12.2545	−	4.37238i	−0.395511	−	0.141118i
$961$	9.00615	+	9.26711i	0.290521	+	0.298939i
$962$	−0.965136	−	0.885794i	−0.0311172	−	0.0285591i
$963$	3.11510	−	4.55569i	0.100383	−	0.146805i
$964$	14.6863	+	3.41516i	0.473015	+	0.109995i
$965$	2.74902	+	1.99728i	0.0884940	+	0.0642947i
$966$	4.04340	+	0.463937i	0.130094	+	0.0149269i
$967$	31.4958			1.01284			0.506418	−	0.862288i	$-0.330969\pi$
$967$	31.4958			1.01284			0.506418	+	0.862288i	$0.330969\pi$
$968$	−6.95679	−	6.51419i	−0.223600	−	0.209374i
$969$	104.308			3.35086
$970$	−1.52755	−	0.175270i	−0.0490465	−	0.00562757i
$971$	−16.5455	−	12.0210i	−0.530970	−	0.385772i	0.289750	−	0.957102i	$-0.406428\pi$
$971$	−16.5455	−	12.0210i	−0.530970	−	0.385772i	−0.820720	+	0.571330i	$0.806428\pi$
$972$	−11.4503	−	2.66266i	−0.367269	−	0.0854048i
$973$	12.1979	−	17.8389i	0.391048	−	0.571890i
$974$	−0.0734385	−	0.0674012i	−0.00235312	−	0.00215967i
$975$	−1.39414	−	1.43453i	−0.0446481	−	0.0459418i
$976$	−23.5011	−	8.38519i	−0.752253	−	0.268403i
$977$	1.11838	+	3.44201i	0.0357800	+	0.110120i	0.967351	−	0.253439i	$-0.0815617\pi$
$977$	1.11838	+	3.44201i	0.0357800	+	0.110120i	−0.931571	+	0.363558i	$0.881562\pi$
$978$	1.83794	−	2.12109i	0.0587707	−	0.0678250i
$979$	9.42729	+	9.25389i	0.301298	+	0.295756i
$980$	5.29563	+	6.11148i	0.169163	+	0.195224i
$981$	−2.23593	+	3.70788i	−0.0713878	+	0.118383i
$982$	−1.31975	−	1.71148i	−0.0421149	−	0.0546155i
$983$	−18.4511	+	6.58332i	−0.588497	+	0.209975i	−0.613477	−	0.789713i	$-0.710230\pi$
$983$	−18.4511	+	6.58332i	−0.588497	+	0.209975i	0.0249799	+	0.999688i	$0.492048\pi$
$984$	5.59278	+	2.74979i	0.178291	+	0.0876600i
$985$	5.43898	−	4.44743i	0.173300	−	0.141707i
$986$	0.543464	+	2.68210i	0.0173074	+	0.0854155i
$987$	26.3490	+	1.50669i	0.838699	+	0.0479586i
$988$	−10.3576	+	9.50608i	−0.329518	+	0.302429i
$989$	−8.58387	−	59.7021i	−0.272951	−	1.89842i
$990$	0.351412	+	0.242876i	0.0111686	+	0.00771910i
$991$	4.86858	−	33.8617i	0.154656	−	1.07565i	−0.753629	−	0.657300i	$-0.771698\pi$
$991$	4.86858	−	33.8617i	0.154656	−	1.07565i	0.908285	−	0.418353i	$-0.137392\pi$
$992$	−9.52803	−	13.9343i	−0.302515	−	0.442414i
$993$	12.0081	+	30.8425i	0.381065	+	0.978757i
$994$	−0.938116	+	1.21657i	−0.0297552	+	0.0385873i
$995$	−6.83638	+	21.0402i	−0.216728	+	0.667020i
$996$	−16.0138	−	26.5559i	−0.507416	−	0.841455i
$997$	16.8446	−	43.2650i	0.533473	−	1.37022i	−0.364926	−	0.931036i	$-0.618906\pi$
$997$	16.8446	−	43.2650i	0.533473	−	1.37022i	0.898400	−	0.439179i	$-0.144731\pi$
$998$	4.62388	−	1.07524i	0.146366	−	0.0340360i
$999$	−23.8135	−	10.0637i	−0.753427	−	0.318401i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.2.s.a.16.11	✓	880
121.53	even	55	inner	605.2.s.a.416.11	yes	880

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
605.2.s.a.16.11	✓	880	1.1	even	1	trivial
605.2.s.a.416.11	yes	880	121.53	even	55	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:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	605.s (of order \(55\), degree \(40\), minimal)

\(f(q)\)	\(=\)	\(q+(0.217809 + 0.0249913i) q^{2} +(1.53233 + 1.11330i) q^{3} +(-1.90121 - 0.442107i) q^{4} +(0.564443 - 0.825472i) q^{5} +(0.305933 + 0.280782i) q^{6} +(-1.17803 - 1.21217i) q^{7} +(-0.816028 - 0.291158i) q^{8} +(0.181542 + 0.558728i) q^{9} +O(q^{10})\)	\(q+(0.217809 + 0.0249913i) q^{2} +(1.53233 + 1.11330i) q^{3} +(-1.90121 - 0.442107i) q^{4} +(0.564443 - 0.825472i) q^{5} +(0.305933 + 0.280782i) q^{6} +(-1.17803 - 1.21217i) q^{7} +(-0.816028 - 0.291158i) q^{8} +(0.181542 + 0.558728i) q^{9} +(0.143570 - 0.165689i) q^{10} +(3.24723 + 0.674888i) q^{11} +(-2.42108 - 2.79407i) q^{12} +(0.545382 - 0.904415i) q^{13} +(-0.226293 - 0.293461i) q^{14} +(1.78391 - 0.636499i) q^{15} +(3.33286 + 1.63866i) q^{16} +(6.25148 - 5.11181i) q^{17} +(0.0255781 + 0.126233i) q^{18} +(6.80850 + 0.389324i) q^{19} +(-1.43807 + 1.31985i) q^{20} +(-0.455626 - 3.16895i) q^{21} +(0.690411 + 0.228149i) q^{22} +(-0.825207 + 5.73944i) q^{23} +(-0.926277 - 1.35464i) q^{24} +(-0.362808 - 0.931864i) q^{25} +(0.141392 - 0.183360i) q^{26} +(1.41204 - 4.34582i) q^{27} +(1.70378 + 2.82540i) q^{28} +(-0.560803 + 1.44041i) q^{29} +(0.404460 - 0.0940530i) q^{30} +(-6.10466 - 2.57985i) q^{31} +(2.14272 + 1.37705i) q^{32} +(4.22448 + 4.64931i) q^{33} +(1.48938 - 0.957167i) q^{34} +(-1.66554 + 0.288233i) q^{35} +(-0.0981310 - 1.14252i) q^{36} +(0.484158 - 5.63695i) q^{37} +(1.47322 + 0.254951i) q^{38} +(1.84259 - 0.778687i) q^{39} +(-0.700944 + 0.509266i) q^{40} +(-3.30684 + 1.86746i) q^{41} +(-0.0200434 - 0.701612i) q^{42} +(-9.98072 + 2.93060i) q^{43} +(-5.87529 - 2.71873i) q^{44} +(0.563684 + 0.165513i) q^{45} +(-0.323173 + 1.22948i) q^{46} +(-1.63710 + 8.07938i) q^{47} +(3.28273 + 6.22146i) q^{48} +(0.118305 - 4.14120i) q^{49} +(-0.0557343 - 0.212035i) q^{50} +(15.2703 - 0.873189i) q^{51} +(-1.43673 + 1.47836i) q^{52} +(9.76924 - 4.80321i) q^{53} +(0.416163 - 0.911270i) q^{54} +(2.38998 - 2.29956i) q^{55} +(0.608375 + 1.33216i) q^{56} +(9.99943 + 8.17649i) q^{57} +(-0.158146 + 0.299719i) q^{58} +(-3.24744 - 1.83391i) q^{59} +(-3.67299 + 0.421437i) q^{60} +(-6.67479 + 0.765860i) q^{61} +(-1.26518 - 0.714478i) q^{62} +(0.463409 - 0.878258i) q^{63} +(-5.31791 - 4.34843i) q^{64} +(-0.438732 - 0.960689i) q^{65} +(0.803938 + 1.11824i) q^{66} +(-0.564415 + 1.23590i) q^{67} +(-14.1453 + 6.95479i) q^{68} +(-7.65422 + 7.87601i) q^{69} +(-0.369973 + 0.0211558i) q^{70} +(-1.05389 - 4.00940i) q^{71} +(0.0145351 - 0.508795i) q^{72} +(4.85343 + 9.19828i) q^{73} +(0.246329 - 1.21568i) q^{74} +(0.481506 - 1.83184i) q^{75} +(-12.7722 - 3.75027i) q^{76} +(-3.00727 - 4.73123i) q^{77} +(0.420794 - 0.123556i) q^{78} +(0.236443 + 8.27659i) q^{79} +(3.23388 - 1.82626i) q^{80} +(8.42778 - 6.12314i) q^{81} +(-0.766930 + 0.324107i) q^{82} +(8.26498 + 1.43031i) q^{83} +(-0.534774 + 6.22626i) q^{84} +(-0.691050 - 8.04575i) q^{85} +(-2.24713 + 0.388881i) q^{86} +(-2.46295 + 1.58284i) q^{87} +(-2.45333 - 1.49619i) q^{88} +(3.35072 + 2.15338i) q^{89} +(0.118639 + 0.0501373i) q^{90} +(-1.73878 + 0.404336i) q^{91} +(4.10633 - 10.5470i) q^{92} +(-6.48220 - 10.7495i) q^{93} +(-0.558488 + 1.71885i) q^{94} +(4.16439 - 5.40047i) q^{95} +(1.75029 + 4.49559i) q^{96} +(-3.95857 - 5.78923i) q^{97} +(0.129262 - 0.899035i) q^{98} +(0.212429 + 1.93684i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 880 q + 2 q^{2} + 5 q^{3} + 24 q^{4} - 22 q^{5} + 7 q^{6} + q^{7} - 4 q^{8} - 217 q^{9}+O(q^{10}) \) 880 * q + 2 * q^2 + 5 * q^3 + 24 * q^4 - 22 * q^5 + 7 * q^6 + q^7 - 4 * q^8 - 217 * q^9	\( 880 q + 2 q^{2} + 5 q^{3} + 24 q^{4} - 22 q^{5} + 7 q^{6} + q^{7} - 4 q^{8} - 217 q^{9} - 2 q^{10} - 3 q^{11} - 49 q^{12} + 2 q^{13} + 60 q^{14} - 16 q^{15} + 18 q^{16} + 13 q^{17} - 15 q^{19} - 19 q^{20} + 42 q^{21} - 301 q^{22} + 31 q^{23} - 409 q^{24} + 22 q^{25} - 4 q^{26} - 4 q^{27} + 6 q^{28} + 9 q^{29} + 19 q^{30} - 10 q^{31} + 94 q^{32} - 5 q^{33} + 12 q^{34} + 4 q^{35} + 35 q^{36} + 73 q^{37} - 8 q^{38} - 21 q^{39} + 4 q^{40} - 8 q^{41} - 17 q^{42} + 93 q^{43} + q^{44} + 80 q^{45} + 129 q^{46} - 178 q^{47} + 153 q^{48} - 177 q^{49} + 2 q^{50} - 12 q^{51} - 126 q^{52} - 99 q^{53} - 93 q^{54} - 7 q^{55} - 25 q^{56} + 100 q^{57} - 26 q^{58} + 25 q^{59} - 4 q^{60} - 6 q^{61} + 63 q^{62} - 25 q^{63} + 8 q^{64} - 2 q^{65} + 64 q^{66} + 47 q^{67} - 11 q^{68} + 67 q^{69} - 60 q^{70} + 18 q^{71} - 641 q^{72} - 35 q^{73} - 108 q^{74} - 5 q^{75} - 132 q^{76} - 166 q^{77} + 115 q^{78} - 103 q^{79} - 23 q^{80} - 230 q^{81} - 72 q^{82} + 149 q^{83} - 28 q^{84} - 21 q^{85} + 49 q^{86} + 6 q^{87} - 85 q^{88} + 44 q^{89} - 34 q^{90} - 135 q^{92} - 172 q^{93} + 49 q^{94} - 106 q^{95} - 115 q^{96} - 421 q^{97} - 192 q^{98} - 156 q^{99}+O(q^{100}) \) 880 * q + 2 * q^2 + 5 * q^3 + 24 * q^4 - 22 * q^5 + 7 * q^6 + q^7 - 4 * q^8 - 217 * q^9 - 2 * q^10 - 3 * q^11 - 49 * q^12 + 2 * q^13 + 60 * q^14 - 16 * q^15 + 18 * q^16 + 13 * q^17 - 15 * q^19 - 19 * q^20 + 42 * q^21 - 301 * q^22 + 31 * q^23 - 409 * q^24 + 22 * q^25 - 4 * q^26 - 4 * q^27 + 6 * q^28 + 9 * q^29 + 19 * q^30 - 10 * q^31 + 94 * q^32 - 5 * q^33 + 12 * q^34 + 4 * q^35 + 35 * q^36 + 73 * q^37 - 8 * q^38 - 21 * q^39 + 4 * q^40 - 8 * q^41 - 17 * q^42 + 93 * q^43 + q^44 + 80 * q^45 + 129 * q^46 - 178 * q^47 + 153 * q^48 - 177 * q^49 + 2 * q^50 - 12 * q^51 - 126 * q^52 - 99 * q^53 - 93 * q^54 - 7 * q^55 - 25 * q^56 + 100 * q^57 - 26 * q^58 + 25 * q^59 - 4 * q^60 - 6 * q^61 + 63 * q^62 - 25 * q^63 + 8 * q^64 - 2 * q^65 + 64 * q^66 + 47 * q^67 - 11 * q^68 + 67 * q^69 - 60 * q^70 + 18 * q^71 - 641 * q^72 - 35 * q^73 - 108 * q^74 - 5 * q^75 - 132 * q^76 - 166 * q^77 + 115 * q^78 - 103 * q^79 - 23 * q^80 - 230 * q^81 - 72 * q^82 + 149 * q^83 - 28 * q^84 - 21 * q^85 + 49 * q^86 + 6 * q^87 - 85 * q^88 + 44 * q^89 - 34 * q^90 - 135 * q^92 - 172 * q^93 + 49 * q^94 - 106 * q^95 - 115 * q^96 - 421 * q^97 - 192 * q^98 - 156 * q^99

Introduction

L-functions

Modular forms

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Database

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