LMFDB - Embedded newform 575.2.k.g.26.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [575,2,Mod(26,575)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(575, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 16]))

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

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

chi := DirichletCharacter("575.26");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 575 = 5^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	575.k (of order $11$, degree $10$, 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:	$4.59139811622$
Analytic rank:	$0$
Dimension:	$100$
Relative dimension:	$10$ over $\Q(\zeta_{11})$
Twist minimal:	no (minimal twist has level 115)
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			26.5
Character	$\chi$	$=$	575.26
Dual form			575.2.k.g.376.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0448489 - 0.311931i) q^{2} +(0.875852 - 1.91785i) q^{3} +(1.82370 - 0.535486i) q^{4} +(-0.637517 - 0.187192i) q^{6} +(-1.15522 + 0.742416i) q^{7} +(-0.510652 - 1.11817i) q^{8} +(-0.946445 - 1.09226i) q^{9} +O(q^{10})$	\(q+(-0.0448489 - 0.311931i) q^{2} +(0.875852 - 1.91785i) q^{3} +(1.82370 - 0.535486i) q^{4} +(-0.637517 - 0.187192i) q^{6} +(-1.15522 + 0.742416i) q^{7} +(-0.510652 - 1.11817i) q^{8} +(-0.946445 - 1.09226i) q^{9} +(0.312084 - 2.17059i) q^{11} +(0.570308 - 3.96658i) q^{12} +(-3.65206 - 2.34704i) q^{13} +(0.283393 + 0.327053i) q^{14} +(2.87203 - 1.84574i) q^{16} +(-1.06457 - 0.312586i) q^{17} +(-0.298261 + 0.344212i) q^{18} +(0.315941 - 0.0927686i) q^{19} +(0.412038 + 2.86579i) q^{21} -0.691072 q^{22} +(2.64750 - 3.99884i) q^{23} -2.59174 q^{24} +(-0.568322 + 1.24445i) q^{26} +(3.14520 - 0.923513i) q^{27} +(-1.70922 + 1.97255i) q^{28} +(5.91592 + 1.73707i) q^{29} +(-0.922622 - 2.02026i) q^{31} +(-2.31454 - 2.67112i) q^{32} +(-3.88953 - 2.49965i) q^{33} +(-0.0497604 + 0.346091i) q^{34} +(-2.31092 - 1.48514i) q^{36} +(6.21098 + 7.16786i) q^{37} +(-0.0431070 - 0.0943912i) q^{38} +(-7.69992 + 4.94844i) q^{39} +(-6.50490 + 7.50706i) q^{41} +(0.875448 - 0.257055i) q^{42} +(-3.00242 + 6.57438i) q^{43} +(-0.593174 - 4.12562i) q^{44} +(-1.36610 - 0.646493i) q^{46} -4.44405 q^{47} +(-1.02438 - 7.12472i) q^{48} +(-2.12455 + 4.65211i) q^{49} +(-1.53190 + 1.76790i) q^{51} +(-7.91705 - 2.32466i) q^{52} +(10.6197 - 6.82485i) q^{53} +(-0.429131 - 0.939666i) q^{54} +(1.42006 + 0.912620i) q^{56} +(0.0988014 - 0.687179i) q^{57} +(0.276523 - 1.92326i) q^{58} +(0.863867 + 0.555174i) q^{59} +(4.43650 + 9.71459i) q^{61} +(-0.588803 + 0.378401i) q^{62} +(1.90426 + 0.559142i) q^{63} +(3.74197 - 4.31847i) q^{64} +(-0.605277 + 1.32537i) q^{66} +(0.00594089 + 0.0413198i) q^{67} -2.10884 q^{68} +(-5.35036 - 8.57990i) q^{69} +(-1.49444 - 10.3941i) q^{71} +(-0.738026 + 1.61605i) q^{72} +(-4.21680 + 1.23817i) q^{73} +(1.95732 - 2.25887i) q^{74} +(0.526504 - 0.338364i) q^{76} +(1.25096 + 2.73921i) q^{77} +(1.88891 + 2.17991i) q^{78} +(7.33076 + 4.71119i) q^{79} +(1.60062 - 11.1325i) q^{81} +(2.63342 + 1.69240i) q^{82} +(5.90540 + 6.81519i) q^{83} +(2.28602 + 5.00568i) q^{84} +(2.18541 + 0.641694i) q^{86} +(8.51290 - 9.82442i) q^{87} +(-2.58646 + 0.759454i) q^{88} +(2.24048 - 4.90597i) q^{89} +5.96141 q^{91} +(2.68691 - 8.71037i) q^{92} -4.68263 q^{93} +(0.199311 + 1.38624i) q^{94} +(-7.14999 + 2.09943i) q^{96} +(-4.18210 + 4.82640i) q^{97} +(1.54642 + 0.454071i) q^{98} +(-2.66621 + 1.71347i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 100 q + 14 q^{4} - 18 q^{6} + 12 q^{9}+O(q^{10}) $ 100 * q + 14 * q^4 - 18 * q^6 + 12 * q^9	$ 100 q + 14 q^{4} - 18 q^{6} + 12 q^{9} - 26 q^{11} + 26 q^{14} - 18 q^{16} + 14 q^{19} - 22 q^{21} + 68 q^{24} - 42 q^{26} + 24 q^{29} - 12 q^{31} - 8 q^{34} - 10 q^{36} - 14 q^{39} + 8 q^{41} - 166 q^{44} - 18 q^{46} - 32 q^{49} - 22 q^{51} - 116 q^{54} - 116 q^{56} - 50 q^{59} - 38 q^{61} - 10 q^{64} - 28 q^{66} - 80 q^{69} - 110 q^{71} - 22 q^{74} + 4 q^{76} - 42 q^{79} + 204 q^{81} - 56 q^{84} + 132 q^{86} + 66 q^{89} + 76 q^{91} + 70 q^{94} + 236 q^{96} + 60 q^{99}+O(q^{100}) $ 100 * q + 14 * q^4 - 18 * q^6 + 12 * q^9 - 26 * q^11 + 26 * q^14 - 18 * q^16 + 14 * q^19 - 22 * q^21 + 68 * q^24 - 42 * q^26 + 24 * q^29 - 12 * q^31 - 8 * q^34 - 10 * q^36 - 14 * q^39 + 8 * q^41 - 166 * q^44 - 18 * q^46 - 32 * q^49 - 22 * q^51 - 116 * q^54 - 116 * q^56 - 50 * q^59 - 38 * q^61 - 10 * q^64 - 28 * q^66 - 80 * q^69 - 110 * q^71 - 22 * q^74 + 4 * q^76 - 42 * q^79 + 204 * q^81 - 56 * q^84 + 132 * q^86 + 66 * q^89 + 76 * q^91 + 70 * q^94 + 236 * q^96 + 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/575\mathbb{Z}\right)^\times$.

$n$	$51$	$277$
$\chi(n)$	$e\left(\frac{8}{11}\right)$	$1$

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 $

$2$	−0.0448489	−	0.311931i	−0.0317130	−	0.220568i	0.967802	−	0.251713i	$-0.0809939\pi$
$2$	−0.0448489	−	0.311931i	−0.0317130	−	0.220568i	−0.999515	+	0.0311445i	$0.990085\pi$
$3$	0.875852	−	1.91785i	0.505674	−	1.10727i	−0.468910	−	0.883246i	$-0.655353\pi$
$3$	0.875852	−	1.91785i	0.505674	−	1.10727i	0.974583	−	0.224025i	$-0.0719196\pi$
$4$	1.82370	−	0.535486i	0.911848	−	0.267743i
$5$		0			0
$5$		0			0
$6$	−0.637517	−	0.187192i	−0.260265	−	0.0764208i
$7$	−1.15522	+	0.742416i	−0.436633	+	0.280607i	−0.740435	−	0.672128i	$-0.765380\pi$
$7$	−1.15522	+	0.742416i	−0.436633	+	0.280607i	0.303802	+	0.952735i	$0.401744\pi$
$8$	−0.510652	−	1.11817i	−0.180543	−	0.395333i
$9$	−0.946445	−	1.09226i	−0.315482	−	0.364085i
$10$		0			0
$11$	0.312084	−	2.17059i	0.0940969	−	0.654458i	−0.887118	−	0.461542i	$-0.847296\pi$
$11$	0.312084	−	2.17059i	0.0940969	−	0.654458i	0.981215	−	0.192916i	$-0.0617945\pi$
$12$	0.570308	−	3.96658i	0.164634	−	1.14505i
$13$	−3.65206	−	2.34704i	−1.01290	−	0.650951i	−0.0747571	−	0.997202i	$-0.523818\pi$
$13$	−3.65206	−	2.34704i	−1.01290	−	0.650951i	−0.938142	+	0.346251i	$0.887455\pi$
$14$	0.283393	+	0.327053i	0.0757399	+	0.0874085i
$15$		0			0
$16$	2.87203	−	1.84574i	0.718008	−	0.461435i
$17$	−1.06457	−	0.312586i	−0.258196	−	0.0758131i	0.150073	−	0.988675i	$-0.452049\pi$
$17$	−1.06457	−	0.312586i	−0.258196	−	0.0758131i	−0.408269	+	0.912862i	$0.633867\pi$
$18$	−0.298261	+	0.344212i	−0.0703009	+	0.0811315i
$19$	0.315941	−	0.0927686i	0.0724818	−	0.0212826i	−0.245291	−	0.969450i	$-0.578883\pi$
$19$	0.315941	−	0.0927686i	0.0724818	−	0.0212826i	0.317772	+	0.948167i	$0.397065\pi$
$20$		0			0
$21$	0.412038	+	2.86579i	0.0899140	+	0.625366i
$22$	−0.691072			−0.147337
$23$	2.64750	−	3.99884i	0.552042	−	0.833817i
$23$	2.64750	−	3.99884i	0.552042	−	0.833817i
$24$	−2.59174			−0.529037
$25$		0			0
$26$	−0.568322	+	1.24445i	−0.111457	+	0.244057i
$27$	3.14520	−	0.923513i	0.605293	−	0.177730i
$28$	−1.70922	+	1.97255i	−0.323012	+	0.372776i
$29$	5.91592	+	1.73707i	1.09856	+	0.322566i	0.780279	−	0.625431i	$-0.215077\pi$
$29$	5.91592	+	1.73707i	1.09856	+	0.322566i	0.318279	+	0.947997i	$0.396895\pi$
$30$		0			0
$31$	−0.922622	−	2.02026i	−0.165708	−	0.362849i	0.808502	−	0.588493i	$-0.200279\pi$
$31$	−0.922622	−	2.02026i	−0.165708	−	0.362849i	−0.974210	+	0.225644i	$0.927551\pi$
$32$	−2.31454	−	2.67112i	−0.409156	−	0.472191i
$33$	−3.88953	−	2.49965i	−0.677080	−	0.435133i
$34$	−0.0497604	+	0.346091i	−0.00853384	+	0.0593541i
$35$		0			0
$36$	−2.31092	−	1.48514i	−0.385153	−	0.247523i
$37$	6.21098	+	7.16786i	1.02108	+	1.17839i	0.983834	+	0.179083i	$0.0573129\pi$
$37$	6.21098	+	7.16786i	1.02108	+	1.17839i	0.0372455	+	0.999306i	$0.488142\pi$
$38$	−0.0431070	−	0.0943912i	−0.00699288	−	0.0153123i
$39$	−7.69992	+	4.94844i	−1.23297	+	0.792385i
$40$		0			0
$41$	−6.50490	+	7.50706i	−1.01589	+	1.17241i	−0.0309527	+	0.999521i	$0.509854\pi$
$41$	−6.50490	+	7.50706i	−1.01589	+	1.17241i	−0.984942	+	0.172884i	$0.944691\pi$
$42$	0.875448	−	0.257055i	0.135085	−	0.0396644i
$43$	−3.00242	+	6.57438i	−0.457865	+	1.00258i	0.530104	+	0.847932i	$0.322153\pi$
$43$	−3.00242	+	6.57438i	−0.457865	+	1.00258i	−0.987969	+	0.154652i	$0.950574\pi$
$44$	−0.593174	−	4.12562i	−0.0894244	−	0.621960i
$45$		0			0
$46$	−1.36610	−	0.646493i	−0.201421	−	0.0953202i
$47$	−4.44405			−0.648231			−0.324115	−	0.946018i	$-0.605067\pi$
$47$	−4.44405			−0.648231			−0.324115	+	0.946018i	$0.605067\pi$
$48$	−1.02438	−	7.12472i	−0.147856	−	1.02836i
$49$	−2.12455	+	4.65211i	−0.303507	+	0.664588i
$50$		0			0
$51$	−1.53190	+	1.76790i	−0.214508	+	0.247556i
$52$	−7.91705	−	2.32466i	−1.09790	−	0.322372i
$53$	10.6197	−	6.82485i	1.45872	−	0.937465i	0.459951	−	0.887944i	$-0.347867\pi$
$53$	10.6197	−	6.82485i	1.45872	−	0.937465i	0.998773	−	0.0495213i	$-0.0157696\pi$
$54$	−0.429131	−	0.939666i	−0.0583973	−	0.127872i
$55$		0			0
$56$	1.42006	+	0.912620i	0.189764	+	0.121954i
$57$	0.0988014	−	0.687179i	0.0130866	−	0.0910190i
$58$	0.276523	−	1.92326i	0.0363093	−	0.252537i
$59$	0.863867	+	0.555174i	0.112466	+	0.0722775i	0.595665	−	0.803233i	$-0.296889\pi$
$59$	0.863867	+	0.555174i	0.112466	+	0.0722775i	−0.483199	+	0.875511i	$0.660525\pi$
$60$		0			0
$61$	4.43650	+	9.71459i	0.568036	+	1.24383i	0.947837	+	0.318757i	$0.103265\pi$
$61$	4.43650	+	9.71459i	0.568036	+	1.24383i	−0.379801	+	0.925068i	$0.624007\pi$
$62$	−0.588803	+	0.378401i	−0.0747780	+	0.0480569i
$63$	1.90426	+	0.559142i	0.239914	+	0.0704452i
$64$	3.74197	−	4.31847i	0.467747	−	0.539809i
$65$		0			0
$66$	−0.605277	+	1.32537i	−0.0745044	+	0.163142i
$67$	0.00594089	+	0.0413198i	0.000725795	+	0.00504802i	0.990181	−	0.139790i	$-0.0446429\pi$
$67$	0.00594089	+	0.0413198i	0.000725795	+	0.00504802i	−0.989455	+	0.144838i	$0.953734\pi$
$68$	−2.10884			−0.255734
$69$	−5.35036	−	8.57990i	−0.644108	−	1.03290i
$70$		0			0
$71$	−1.49444	−	10.3941i	−0.177358	−	1.23355i	−0.862846	−	0.505467i	$-0.831320\pi$
$71$	−1.49444	−	10.3941i	−0.177358	−	1.23355i	0.685488	−	0.728084i	$-0.259589\pi$
$72$	−0.738026	+	1.61605i	−0.0869772	+	0.190453i
$73$	−4.21680	+	1.23817i	−0.493540	+	0.144916i	−0.519025	−	0.854759i	$-0.673705\pi$
$73$	−4.21680	+	1.23817i	−0.493540	+	0.144916i	0.0254857	+	0.999675i	$0.491887\pi$
$74$	1.95732	−	2.25887i	0.227534	−	0.262588i
$75$		0			0
$76$	0.526504	−	0.338364i	0.0603942	−	0.0388130i
$77$	1.25096	+	2.73921i	0.142560	+	0.312162i
$78$	1.88891	+	2.17991i	0.213876	+	0.246827i
$79$	7.33076	+	4.71119i	0.824775	+	0.530051i	0.883614	−	0.468217i	$-0.155103\pi$
$79$	7.33076	+	4.71119i	0.824775	+	0.530051i	−0.0588387	+	0.998268i	$0.518740\pi$
$80$		0			0
$81$	1.60062	−	11.1325i	0.177846	−	1.23695i
$82$	2.63342	+	1.69240i	0.290813	+	0.186894i
$83$	5.90540	+	6.81519i	0.648201	+	0.748064i	0.980803	−	0.195003i	$-0.0624718\pi$
$83$	5.90540	+	6.81519i	0.648201	+	0.748064i	−0.332601	+	0.943068i	$0.607926\pi$
$84$	2.28602	+	5.00568i	0.249425	+	0.546165i
$85$		0			0
$86$	2.18541	+	0.641694i	0.235659	+	0.0691956i
$87$	8.51290	−	9.82442i	0.912679	−	1.05329i
$88$	−2.58646	+	0.759454i	−0.275718	+	0.0809580i
$89$	2.24048	−	4.90597i	0.237490	−	0.520031i	−0.752933	−	0.658098i	$-0.771361\pi$
$89$	2.24048	−	4.90597i	0.237490	−	0.520031i	0.990423	+	0.138066i	$0.0440887\pi$
$90$		0			0
$91$	5.96141			0.624926
$92$	2.68691	−	8.71037i	0.280130	−	0.908119i
$93$	−4.68263			−0.485566
$94$	0.199311	+	1.38624i	0.0205573	+	0.142979i
$95$		0			0
$96$	−7.14999	+	2.09943i	−0.729743	+	0.214272i
$97$	−4.18210	+	4.82640i	−0.424628	+	0.490047i	−0.927241	−	0.374465i	$-0.877826\pi$
$97$	−4.18210	+	4.82640i	−0.424628	+	0.490047i	0.502613	+	0.864511i	$0.332372\pi$
$98$	1.54642	+	0.454071i	0.156212	+	0.0458681i
$99$	−2.66621	+	1.71347i	−0.267964	+	0.172210i
$100$		0			0
$101$	−4.64143	−	5.35649i	−0.461839	−	0.532991i	0.476285	−	0.879291i	$-0.341983\pi$
$101$	−4.64143	−	5.35649i	−0.461839	−	0.532991i	−0.938124	+	0.346300i	$0.887438\pi$
$102$	0.620168	+	0.398558i	0.0614057	+	0.0394631i
$103$	−2.28752	+	15.9100i	−0.225396	+	1.56766i	0.491748	+	0.870737i	$0.336358\pi$
$103$	−2.28752	+	15.9100i	−0.225396	+	1.56766i	−0.717144	+	0.696925i	$0.754551\pi$
$104$	−0.759458	+	5.28215i	−0.0744710	+	0.517957i
$105$		0			0
$106$	−2.60516	−	3.00652i	−0.253036	−	0.292019i
$107$	1.19060	+	2.60705i	0.115100	+	0.252033i	0.958411	−	0.285393i	$-0.0921240\pi$
$107$	1.19060	+	2.60705i	0.115100	+	0.252033i	−0.843311	+	0.537426i	$0.819397\pi$
$108$	5.24136	−	3.36841i	0.504350	−	0.324126i
$109$	−15.1393	−	4.44530i	−1.45008	−	0.425783i	−0.540514	−	0.841335i	$-0.681770\pi$
$109$	−15.1393	−	4.44530i	−1.45008	−	0.425783i	−0.909569	+	0.415552i	$0.863588\pi$
$110$		0			0
$111$	19.1868	−	5.63375i	1.82113	−	0.534731i
$112$	−1.94752	+	4.26448i	−0.184024	+	0.402956i
$113$	1.58807	+	11.0453i	0.149393	+	1.03905i	0.917217	+	0.398389i	$0.130431\pi$
$113$	1.58807	+	11.0453i	0.149393	+	1.03905i	−0.767824	+	0.640661i	$0.778660\pi$
$114$	−0.218783			−0.0204909
$115$		0			0
$116$	11.7190			1.08808
$117$	0.892910	+	6.21032i	0.0825495	+	0.574145i
$118$	0.134432	−	0.294366i	0.0123755	−	0.0270986i
$119$	1.46188	−	0.429247i	0.134010	−	0.0393490i
$120$		0			0
$121$	5.94035	+	1.74424i	0.540032	+	0.158568i
$122$	2.83131	−	1.81957i	0.256335	−	0.164736i
$123$	8.70007	+	19.0505i	0.784459	+	1.71772i
$124$	−2.76440	−	3.19029i	−0.248251	−	0.286496i
$125$		0			0
$126$	0.0890096	−	0.619075i	0.00792960	−	0.0551516i
$127$	−1.32385	+	9.20756i	−0.117472	+	0.817039i	0.842850	+	0.538148i	$0.180876\pi$
$127$	−1.32385	+	9.20756i	−0.117472	+	0.817039i	−0.960323	+	0.278891i	$0.910033\pi$
$128$	−7.46153	−	4.79523i	−0.659512	−	0.423843i
$129$	9.97900	+	11.5164i	0.878602	+	1.01396i
$130$		0			0
$131$	−4.57152	+	2.93794i	−0.399415	+	0.256689i	−0.724894	−	0.688861i	$-0.758111\pi$
$131$	−4.57152	+	2.93794i	−0.399415	+	0.256689i	0.325478	+	0.945550i	$0.394475\pi$
$132$	−8.43184	−	2.47581i	−0.733898	−	0.215492i
$133$	−0.296109	+	0.341728i	−0.0256759	+	0.0296316i
$134$	0.0126225	−	0.00370629i	0.00109042	−	0.000320175i
$135$		0			0
$136$	0.194100	+	1.34999i	0.0166439	+	0.115761i
$137$	11.8569			1.01301			0.506503	−	0.862238i	$-0.330938\pi$
$137$	11.8569			1.01301			0.506503	+	0.862238i	$0.330938\pi$
$138$	−2.43638	+	2.05374i	−0.207398	+	0.174826i
$139$	21.8203			1.85077			0.925387	−	0.379024i	$-0.123740\pi$
$139$	21.8203			1.85077			0.925387	+	0.379024i	$0.123740\pi$
$140$		0			0
$141$	−3.89233	+	8.52301i	−0.327793	+	0.717767i
$142$	−3.17521	+	0.932327i	−0.266458	+	0.0782391i
$143$	−6.23421	+	7.19466i	−0.521331	+	0.601648i
$144$	−4.73424	−	1.39010i	−0.394520	−	0.115842i
$145$		0			0
$146$	0.575341	+	1.25982i	0.0476156	+	0.104264i
$147$	7.06126	+	8.14913i	0.582403	+	0.672129i
$148$	15.1652	+	9.74611i	1.24657	+	0.801125i
$149$	0.187122	−	1.30146i	0.0153297	−	0.106620i	−0.980720	−	0.195418i	$-0.937394\pi$
$149$	0.187122	−	1.30146i	0.0153297	−	0.106620i	0.996050	+	0.0887982i	$0.0283026\pi$
$150$		0			0
$151$	−19.7805	−	12.7121i	−1.60971	−	1.03450i	−0.962162	−	0.272477i	$-0.912157\pi$
$151$	−19.7805	−	12.7121i	−1.60971	−	1.03450i	−0.647550	−	0.762023i	$-0.724206\pi$
$152$	−0.265067	−	0.305904i	−0.0214998	−	0.0248121i
$153$	0.666132	+	1.45863i	0.0538536	+	0.117923i
$154$	0.798341	−	0.513062i	0.0643321	−	0.0413437i
$155$		0			0
$156$	−11.3925	+	13.1477i	−0.912131	+	1.05265i
$157$	−16.3489	+	4.80046i	−1.30478	+	0.383119i	−0.858978	−	0.512012i	$-0.828900\pi$
$157$	−16.3489	+	4.80046i	−1.30478	+	0.383119i	−0.445804	+	0.895130i	$0.647082\pi$
$158$	1.14079	−	2.49798i	0.0907564	−	0.198729i
$159$	−3.78777	−	26.3445i	−0.300389	−	2.08925i
$160$		0			0
$161$	−0.0896427	+	6.58509i	−0.00706483	+	0.518978i
$162$	−3.54437			−0.278472
$163$	−0.905459	−	6.29760i	−0.0709210	−	0.493266i	−0.994063	−	0.108807i	$-0.965297\pi$
$163$	−0.905459	−	6.29760i	−0.0709210	−	0.493266i	0.923142	−	0.384459i	$-0.125612\pi$
$164$	−7.84304	+	17.1739i	−0.612439	+	1.34105i
$165$		0			0
$166$	1.86102	−	2.14773i	0.144443	−	0.166696i
$167$	17.6850	+	5.19279i	1.36851	+	0.401830i	0.881754	−	0.471709i	$-0.156363\pi$
$167$	17.6850	+	5.19279i	1.36851	+	0.401830i	0.486754	+	0.873539i	$0.338181\pi$
$168$	2.99403	−	1.92415i	0.230995	−	0.148451i
$169$	2.42856	+	5.31781i	0.186813	+	0.409063i
$170$		0			0
$171$	−0.400348	−	0.257288i	−0.0306154	−	0.0196753i
$172$	−1.95502	+	13.5974i	−0.149069	+	1.03679i
$173$	3.29067	−	22.8871i	0.250185	−	1.74007i	−0.346906	−	0.937900i	$-0.612768\pi$
$173$	3.29067	−	22.8871i	0.250185	−	1.74007i	0.597090	−	0.802174i	$-0.296323\pi$
$174$	−3.44633	−	2.21482i	−0.261266	−	0.167905i
$175$		0			0
$176$	−3.11004	−	6.81003i	−0.234428	−	0.513326i
$177$	1.82136	−	1.17052i	0.136902	−	0.0879814i
$178$	−1.63081	−	0.478848i	−0.122234	−	0.0358912i
$179$	3.19748	−	3.69008i	0.238991	−	0.275810i	−0.623566	−	0.781771i	$-0.714317\pi$
$179$	3.19748	−	3.69008i	0.238991	−	0.275810i	0.862556	+	0.505961i	$0.168862\pi$
$180$		0			0
$181$	−7.11867	+	15.5877i	−0.529127	+	1.15863i	0.436740	+	0.899588i	$0.356133\pi$
$181$	−7.11867	+	15.5877i	−0.529127	+	1.15863i	−0.965867	+	0.259038i	$0.916594\pi$
$182$	−0.267363	−	1.85955i	−0.0198183	−	0.137839i
$183$	22.5168			1.66449
$184$	−5.82334	−	0.918341i	−0.429303	−	0.0677010i
$185$		0			0
$186$	0.210011	+	1.46066i	0.0153987	+	0.107101i
$187$	−1.01073	+	2.21319i	−0.0739119	+	0.161845i
$188$	−8.10459	+	2.37972i	−0.591088	+	0.173559i
$189$	−2.94777	+	3.40191i	−0.214419	+	0.247452i
$190$		0			0
$191$	6.21983	−	3.99724i	0.450051	−	0.289230i	−0.295915	−	0.955214i	$-0.595624\pi$
$191$	6.21983	−	3.99724i	0.450051	−	0.289230i	0.745966	+	0.665984i	$0.231988\pi$
$192$	−5.00475	−	10.9589i	−0.361187	−	0.790889i
$193$	1.80537	+	2.08351i	0.129953	+	0.149974i	0.816997	−	0.576642i	$-0.195637\pi$
$193$	1.80537	+	2.08351i	0.129953	+	0.149974i	−0.687044	+	0.726616i	$0.741092\pi$
$194$	1.69307	+	1.08807i	0.121555	+	0.0781187i
$195$		0			0
$196$	−1.38339	+	9.62171i	−0.0988138	+	0.687265i
$197$	−13.8837	−	8.92252i	−0.989173	−	0.635703i	−0.0572506	−	0.998360i	$-0.518233\pi$
$197$	−13.8837	−	8.92252i	−0.989173	−	0.635703i	−0.931923	+	0.362657i	$0.881870\pi$
$198$	0.654061	+	0.754827i	0.0464821	+	0.0536432i
$199$	−2.45045	−	5.36575i	−0.173708	−	0.380368i	0.802674	−	0.596418i	$-0.203410\pi$
$199$	−2.45045	−	5.36575i	−0.173708	−	0.380368i	−0.976382	+	0.216050i	$0.930683\pi$
$200$		0			0
$201$	0.0844485	+	0.0247963i	0.00595653	+	0.00174900i
$202$	−1.46269	+	1.68804i	−0.102915	+	0.118770i
$203$	−8.12382	+	2.38537i	−0.570180	+	0.167420i
$204$	−1.84703	+	4.04443i	−0.129318	+	0.283167i
$205$		0			0
$206$	5.06543			0.352925
$207$	−6.87347	+	0.892940i	−0.477739	+	0.0620636i
$208$	−14.8208			−1.02764
$209$	−0.102763	−	0.714731i	−0.00710825	−	0.0494389i
$210$		0			0
$211$	−5.11866	+	1.50297i	−0.352383	+	0.103469i	−0.453133	−	0.891443i	$-0.649694\pi$
$211$	−5.11866	+	1.50297i	−0.352383	+	0.103469i	0.100750	+	0.994912i	$0.467876\pi$
$212$	15.7125	−	18.1331i	1.07914	−	1.24539i
$213$	−21.2432	−	6.23757i	−1.45556	−	0.427391i
$214$	0.759824	−	0.488309i	0.0519405	−	0.0333801i
$215$		0			0
$216$	−2.63875	−	3.04528i	−0.179544	−	0.207205i
$217$	2.56570	+	1.64888i	0.174171	+	0.111933i
$218$	−0.707646	+	4.92179i	−0.0479279	+	0.333346i
$219$	−1.31868	+	9.17164i	−0.0891083	+	0.619762i
$220$		0			0
$221$	3.15422	+	3.64016i	0.212176	+	0.244864i
$222$	−2.61785	−	5.73228i	−0.175698	−	0.384726i
$223$	20.2463	−	13.0115i	1.35579	−	0.871316i	0.357749	−	0.933818i	$-0.383544\pi$
$223$	20.2463	−	13.0115i	1.35579	−	0.871316i	0.998045	+	0.0625015i	$0.0199078\pi$
$224$	4.65688	+	1.36738i	0.311151	+	0.0913622i
$225$		0			0
$226$	3.37413	−	0.990735i	0.224444	−	0.0659027i
$227$	1.24243	−	2.72053i	0.0824627	−	0.180568i	−0.863909	−	0.503648i	$-0.831991\pi$
$227$	1.24243	−	2.72053i	0.0824627	−	0.180568i	0.946372	+	0.323080i	$0.104718\pi$
$228$	−0.187791	−	1.30611i	−0.0124367	−	0.0864994i
$229$	−5.44323			−0.359699			−0.179849	−	0.983694i	$-0.557561\pi$
$229$	−5.44323			−0.359699			−0.179849	+	0.983694i	$0.557561\pi$
$230$		0			0
$231$	6.34904			0.417736
$232$	−1.07863	−	7.50205i	−0.0708156	−	0.492534i
$233$	−3.02782	+	6.63000i	−0.198359	+	0.434346i	−0.982506	−	0.186229i	$-0.940373\pi$
$233$	−3.02782	+	6.63000i	−0.198359	+	0.434346i	0.784147	+	0.620575i	$0.213101\pi$
$234$	1.89715	−	0.557052i	0.124020	−	0.0364157i
$235$		0			0
$236$	1.87272	+	0.549880i	0.121904	+	0.0357941i
$237$	15.4560	−	9.93298i	1.00398	−	0.645216i
$238$	−0.199459	−	0.436755i	−0.0129290	−	0.0283106i
$239$	−5.17030	−	5.96685i	−0.334439	−	0.385963i	0.563476	−	0.826133i	$-0.309464\pi$
$239$	−5.17030	−	5.96685i	−0.334439	−	0.385963i	−0.897915	+	0.440169i	$0.854918\pi$
$240$		0			0
$241$	0.856700	−	5.95848i	0.0551849	−	0.383819i	−0.943447	−	0.331524i	$-0.892437\pi$
$241$	0.856700	−	5.95848i	0.0551849	−	0.383819i	0.998632	−	0.0522953i	$-0.0166537\pi$
$242$	0.277666	−	1.93121i	0.0178490	−	0.124143i
$243$	−11.6758	−	7.50356i	−0.749001	−	0.481354i
$244$	13.2929	+	15.3408i	0.850988	+	0.982092i
$245$		0			0
$246$	5.55225	−	3.56821i	0.353998	−	0.227501i
$247$	−1.37157	−	0.402728i	−0.0872707	−	0.0256250i
$248$	−1.78786	+	2.06330i	−0.113529	+	0.131020i
$249$	18.2428	−	5.35656i	1.15609	−	0.339458i
$250$		0			0
$251$	−0.291178	−	2.02519i	−0.0183790	−	0.127829i	0.978566	−	0.205932i	$-0.0660226\pi$
$251$	−0.291178	−	2.02519i	−0.0183790	−	0.127829i	−0.996945	+	0.0781034i	$0.975114\pi$
$252$	3.77221			0.237627
$253$	−7.85362	−	6.99461i	−0.493753	−	0.439748i
$254$	2.93150			0.183938
$255$		0			0
$256$	3.58635	−	7.85301i	0.224147	−	0.490813i
$257$	−9.77913	+	2.87141i	−0.610005	+	0.179114i	−0.572122	−	0.820168i	$-0.693880\pi$
$257$	−9.77913	+	2.87141i	−0.610005	+	0.179114i	−0.0378832	+	0.999282i	$0.512061\pi$
$258$	3.14477	−	3.62926i	0.195785	−	0.225948i
$259$	−12.4966	−	3.66933i	−0.776501	−	0.228001i
$260$		0			0
$261$	−3.70176	−	8.10573i	−0.229133	−	0.501732i
$262$	1.12146	+	1.29423i	0.0692841	+	0.0799581i
$263$	3.53734	+	2.27331i	0.218122	+	0.140178i	0.645139	−	0.764065i	$-0.276799\pi$
$263$	3.53734	+	2.27331i	0.218122	+	0.140178i	−0.427017	+	0.904243i	$0.640436\pi$
$264$	−0.808841	+	5.62561i	−0.0497807	+	0.346232i
$265$		0			0
$266$	0.119876	+	0.0770394i	0.00735005	+	0.00472359i
$267$	−7.44657	−	8.59380i	−0.455723	−	0.525932i
$268$	0.0329605	+	0.0721735i	0.00201338	+	0.00440870i
$269$	−13.2549	+	8.51841i	−0.808166	+	0.519376i	−0.878271	−	0.478163i	$-0.841303\pi$
$269$	−13.2549	+	8.51841i	−0.808166	+	0.519376i	0.0701055	+	0.997540i	$0.477666\pi$
$270$		0			0
$271$	9.48435	−	10.9455i	0.576133	−	0.664893i	−0.390636	−	0.920545i	$-0.627745\pi$
$271$	9.48435	−	10.9455i	0.576133	−	0.664893i	0.966769	+	0.255652i	$0.0822902\pi$
$272$	−3.63443	+	1.06716i	−0.220369	+	0.0647063i
$273$	5.22132	−	11.4331i	0.316009	−	0.691962i
$274$	−0.531770	−	3.69854i	−0.0321254	−	0.223437i
$275$		0			0
$276$	−14.3518	−	12.7821i	−0.863880	−	0.769391i
$277$	1.56984			0.0943227			0.0471613	−	0.998887i	$-0.484983\pi$
$277$	1.56984			0.0943227			0.0471613	+	0.998887i	$0.484983\pi$
$278$	−0.978617	−	6.80643i	−0.0586935	−	0.408222i
$279$	−1.33343	+	2.91980i	−0.0798303	+	0.174804i
$280$		0			0
$281$	−2.39255	+	2.76115i	−0.142728	+	0.164717i	−0.822612	−	0.568602i	$-0.807484\pi$
$281$	−2.39255	+	2.76115i	−0.142728	+	0.164717i	0.679885	+	0.733319i	$0.262030\pi$
$282$	2.83316	+	0.831890i	0.168712	+	0.0495383i
$283$	17.6759	−	11.3596i	1.05072	−	0.675258i	0.103106	−	0.994670i	$-0.467122\pi$
$283$	17.6759	−	11.3596i	1.05072	−	0.675258i	0.947616	+	0.319412i	$0.103485\pi$
$284$	−8.29130	−	18.1554i	−0.491998	−	1.07733i
$285$		0			0
$286$	2.52383	+	1.62197i	0.149237	+	0.0959091i
$287$	1.94124	−	13.5017i	0.114588	−	0.796977i
$288$	−0.726962	+	5.05613i	−0.0428366	+	0.297935i
$289$	−13.2657	−	8.52536i	−0.780336	−	0.501492i
$290$		0			0
$291$	5.59340	+	12.2478i	0.327891	+	0.717982i
$292$	−7.02715	+	4.51608i	−0.411233	+	0.264283i
$293$	−21.1179	−	6.20077i	−1.23372	−	0.362253i	−0.401067	−	0.916049i	$-0.631361\pi$
$293$	−21.1179	−	6.20077i	−1.23372	−	0.362253i	−0.832652	+	0.553796i	$0.813179\pi$
$294$	2.22528	−	2.56811i	0.129781	−	0.149775i
$295$		0			0
$296$	4.84325	−	10.6052i	0.281508	−	0.616416i
$297$	−1.02300	−	7.11515i	−0.0593607	−	0.412863i
$298$	−0.414359			−0.0240032
$299$	−19.0543	+	8.39024i	−1.10194	+	0.485220i
$300$		0			0
$301$	−1.41247	−	9.82391i	−0.0814132	−	0.566241i
$302$	−3.07818	+	6.74027i	−0.177129	+	0.387859i
$303$	−14.3381	+	4.21006i	−0.823705	+	0.241862i
$304$	0.736165	−	0.849580i	0.0422220	−	0.0487267i
$305$		0			0
$306$	0.425115	−	0.273205i	0.0243022	−	0.0156181i
$307$	9.94698	+	21.7808i	0.567704	+	1.24310i	0.948011	+	0.318238i	$0.103091\pi$
$307$	9.94698	+	21.7808i	0.567704	+	1.24310i	−0.380307	+	0.924860i	$0.624182\pi$
$308$	3.74817	+	4.32562i	0.213572	+	0.246475i
$309$	28.5095	+	18.3220i	1.62185	+	1.04230i
$310$		0			0
$311$	−1.31020	+	9.11267i	−0.0742949	+	0.516732i	0.918360	+	0.395747i	$0.129514\pi$
$311$	−1.31020	+	9.11267i	−0.0742949	+	0.516732i	−0.992654	+	0.120985i	$0.961395\pi$
$312$	9.46519	+	6.08291i	0.535861	+	0.344377i
$313$	−3.50453	−	4.04445i	−0.198088	−	0.228606i	0.648012	−	0.761630i	$-0.275601\pi$
$313$	−3.50453	−	4.04445i	−0.198088	−	0.228606i	−0.846100	+	0.533025i	$0.821055\pi$
$314$	2.23064	+	4.88443i	0.125882	+	0.275644i
$315$		0			0
$316$	15.8919	+	4.66627i	0.893987	+	0.262498i
$317$	−3.44223	+	3.97254i	−0.193335	+	0.223120i	−0.844138	−	0.536127i	$-0.819887\pi$
$317$	−3.44223	+	3.97254i	−0.193335	+	0.223120i	0.650803	+	0.759247i	$0.274432\pi$
$318$	−8.04779	+	2.36304i	−0.451297	+	0.132513i
$319$	5.61673	−	12.2989i	0.314477	−	0.688608i
$320$		0			0
$321$	6.04273			0.337272
$322$	2.05812	−	0.267372i	0.114694	−	0.0149001i
$323$	−0.365339			−0.0203280
$324$	−3.04227	−	21.1595i	−0.169015	−	1.17553i
$325$		0			0
$326$	−1.92381	+	0.564881i	−0.106550	+	0.0312859i
$327$	−21.7852	+	25.1415i	−1.20473	+	1.39033i
$328$	11.7159	+	3.44010i	0.646903	+	0.189948i
$329$	5.13386	−	3.29933i	0.283039	−	0.181898i
$330$		0			0
$331$	4.50235	+	5.19599i	0.247472	+	0.285597i	0.865872	−	0.500266i	$-0.166764\pi$
$331$	4.50235	+	5.19599i	0.247472	+	0.285597i	−0.618400	+	0.785863i	$0.712219\pi$
$332$	14.4191	+	9.26658i	0.791350	+	0.508570i
$333$	1.95078	−	13.5680i	0.106902	−	0.743520i
$334$	0.826639	−	5.74940i	0.0452316	−	0.314593i
$335$		0			0
$336$	6.47289	+	7.47011i	0.353125	+	0.407528i
$337$	−5.60260	−	12.2680i	−0.305193	−	0.668280i	0.693442	−	0.720513i	$-0.256093\pi$
$337$	−5.60260	−	12.2680i	−0.305193	−	0.668280i	−0.998635	+	0.0522330i	$0.983366\pi$
$338$	1.54987	−	0.996043i	0.0843019	−	0.0541776i
$339$	22.5740	+	6.62834i	1.22605	+	0.360002i
$340$		0			0
$341$	−4.67309	+	1.37214i	−0.253062	+	0.0743058i
$342$	−0.0623009	+	0.136420i	−0.00336885	+	0.00737675i
$343$	−2.36748	−	16.4662i	−0.127832	−	0.889090i
$344$	8.88448			0.479019
$345$		0			0
$346$	−7.28678			−0.391740
$347$	−1.02376	−	7.12040i	−0.0549582	−	0.382243i	−0.998674	−	0.0514848i	$-0.983605\pi$
$347$	−1.02376	−	7.12040i	−0.0549582	−	0.382243i	0.943716	−	0.330758i	$-0.107304\pi$
$348$	10.2641	−	22.4753i	0.550215	−	1.20480i
$349$	−2.18769	+	0.642363i	−0.117104	+	0.0343849i	−0.339760	−	0.940512i	$-0.610346\pi$
$349$	−2.18769	+	0.642363i	−0.117104	+	0.0343849i	0.222655	+	0.974897i	$0.428528\pi$
$350$		0			0
$351$	−13.6540	−	4.00917i	−0.728795	−	0.213993i
$352$	−6.52024	+	4.19030i	−0.347530	+	0.223344i
$353$	−0.00284239	−	0.00622396i	−0.000151285	−	0.000331268i	0.909556	−	0.415581i	$-0.136422\pi$
$353$	−0.00284239	−	0.00622396i	−0.000151285	−	0.000331268i	−0.909708	+	0.415249i	$0.863694\pi$
$354$	−0.446806	−	0.515642i	−0.0237475	−	0.0274061i
$355$		0			0
$356$	1.45888	−	10.1467i	0.0773205	−	0.537776i
$357$	0.457161	−	3.17962i	0.0241955	−	0.168284i
$358$	−1.29445	−	0.831895i	−0.0684140	−	0.0439670i
$359$	−14.5635	−	16.8071i	−0.768630	−	0.887046i	0.227604	−	0.973754i	$-0.426911\pi$
$359$	−14.5635	−	16.8071i	−0.768630	−	0.887046i	−0.996234	+	0.0867077i	$0.972365\pi$
$360$		0			0
$361$	−15.8926	+	10.2136i	−0.836453	+	0.537556i
$362$	5.18156	+	1.52144i	0.272337	+	0.0799652i
$363$	8.54806	−	9.86499i	0.448657	−	0.517778i
$364$	10.8718	−	3.19225i	0.569838	−	0.167319i
$365$		0			0
$366$	−1.00986	−	7.02370i	−0.0527860	−	0.367134i
$367$	−2.17421			−0.113493			−0.0567464	−	0.998389i	$-0.518073\pi$
$367$	−2.17421			−0.113493			−0.0567464	+	0.998389i	$0.518073\pi$
$368$	0.222863	−	16.3714i	0.0116176	−	0.853418i
$369$	14.3562			0.747352
$370$		0			0
$371$	−7.20120	+	15.7684i	−0.373868	+	0.818656i
$372$	−8.53970	+	2.50748i	−0.442763	+	0.130007i
$373$	−7.01421	+	8.09483i	−0.363182	+	0.419134i	−0.907703	−	0.419613i	$-0.862166\pi$
$373$	−7.01421	+	8.09483i	−0.363182	+	0.419134i	0.544521	+	0.838747i	$0.316711\pi$
$374$	0.735693	+	0.216019i	0.0380418	+	0.0111701i
$375$		0			0
$376$	2.26936	+	4.96921i	0.117033	+	0.256267i
$377$	−17.5283	−	20.2287i	−0.902754	−	1.04183i
$378$	1.19336	+	0.766928i	0.0613800	+	0.0394465i
$379$	−4.66642	+	32.4556i	−0.239698	+	1.66713i	0.413923	+	0.910312i	$0.364158\pi$
$379$	−4.66642	+	32.4556i	−0.239698	+	1.66713i	−0.653621	+	0.756822i	$0.726751\pi$
$380$		0			0
$381$	16.4992	+	10.6034i	0.845280	+	0.543229i
$382$	−1.52582	−	1.76089i	−0.0780676	−	0.0900948i
$383$	−4.06949	−	8.91094i	−0.207941	−	0.455328i	0.776711	−	0.629858i	$-0.216887\pi$
$383$	−4.06949	−	8.91094i	−0.207941	−	0.455328i	−0.984652	+	0.174530i	$0.944159\pi$
$384$	−15.7317	+	10.1102i	−0.802807	+	0.515933i
$385$		0			0
$386$	0.568941	−	0.656593i	0.0289583	−	0.0334197i
$387$	10.0225	−	2.94288i	0.509474	−	0.149595i
$388$	−5.04241	+	11.0413i	−0.255990	+	0.560539i
$389$	−4.08139	−	28.3867i	−0.206935	−	1.43926i	−0.783082	−	0.621918i	$-0.786354\pi$
$389$	−4.08139	−	28.3867i	−0.206935	−	1.43926i	0.576148	−	0.817346i	$-0.304555\pi$
$390$		0			0
$391$	−4.06843	+	3.42947i	−0.205749	+	0.173436i
$392$	6.28677			0.317530
$393$	1.63054	+	11.3407i	0.0822500	+	0.572061i
$394$	−2.16054	+	4.73092i	−0.108846	+	0.238341i
$395$		0			0
$396$	−3.94482	+	4.55257i	−0.198235	+	0.228775i
$397$	−18.6163	−	5.46625i	−0.934327	−	0.274343i	−0.221080	−	0.975256i	$-0.570958\pi$
$397$	−18.6163	−	5.46625i	−0.934327	−	0.274343i	−0.713247	+	0.700913i	$0.752776\pi$
$398$	−1.56384	+	1.00502i	−0.0783883	+	0.0503771i
$399$	0.396035	+	0.867195i	0.0198265	+	0.0434141i
$400$		0			0
$401$	−6.88455	−	4.42443i	−0.343798	−	0.220946i	0.357335	−	0.933976i	$-0.383686\pi$
$401$	−6.88455	−	4.42443i	−0.343798	−	0.220946i	−0.701133	+	0.713031i	$0.747322\pi$
$402$	0.00394731	−	0.0274542i	0.000196874	−	0.00136929i
$403$	−1.37215	+	9.54353i	−0.0683518	+	0.475397i
$404$	−11.3329	−	7.28320i	−0.563832	−	0.362353i
$405$		0			0
$406$	1.10841	+	2.42709i	0.0550097	+	0.120454i
$407$	17.4968	−	11.2445i	0.867286	−	0.557371i
$408$	2.75909	+	0.810141i	0.136595	+	0.0401079i
$409$	−17.2934	+	19.9577i	−0.855105	+	0.986843i	−0.999997	−	0.00260403i	$-0.999171\pi$
$409$	−17.2934	+	19.9577i	−0.855105	+	0.986843i	0.144892	+	0.989447i	$0.453717\pi$
$410$		0			0
$411$	10.3849	−	22.7398i	0.512250	−	1.12167i
$412$	4.34786	+	30.2400i	0.214204	+	1.48982i
$413$	−1.41013			−0.0693878
$414$	0.586803	+	2.10400i	0.0288398	+	0.103406i
$415$		0			0
$416$	2.18362	+	15.1874i	0.107061	+	0.744622i
$417$	19.1114	−	41.8480i	0.935887	−	2.04931i
$418$	−0.218338	+	0.0641098i	−0.0106793	+	0.00313571i
$419$	−21.9234	+	25.3009i	−1.07103	+	1.23603i	−0.100526	+	0.994934i	$0.532053\pi$
$419$	−21.9234	+	25.3009i	−1.07103	+	1.23603i	−0.970501	+	0.241097i	$0.922493\pi$
$420$		0			0
$421$	−3.50998	+	2.25573i	−0.171066	+	0.109937i	−0.623372	−	0.781925i	$-0.714238\pi$
$421$	−3.50998	+	2.25573i	−0.171066	+	0.109937i	0.452306	+	0.891863i	$0.350601\pi$
$422$	0.698391	+	1.52926i	0.0339971	+	0.0744433i
$423$	4.20605	+	4.85404i	0.204505	+	0.236011i
$424$	−13.0543	−	8.38950i	−0.633973	−	0.407430i
$425$		0			0
$426$	−0.992956	+	6.90616i	−0.0481089	+	0.334605i
$427$	−12.3374	−	7.92877i	−0.597049	−	0.383700i
$428$	3.56734	+	4.11692i	0.172434	+	0.198999i
$429$	8.33802	+	18.2577i	0.402564	+	0.881491i
$430$		0			0
$431$	−30.9314	−	9.08228i	−1.48991	−	0.437478i	−0.567399	−	0.823443i	$-0.692050\pi$
$431$	−30.9314	−	9.08228i	−1.48991	−	0.437478i	−0.922513	+	0.385965i	$0.873869\pi$
$432$	7.32853	−	8.45758i	0.352594	−	0.406915i
$433$	−8.64523	+	2.53847i	−0.415463	+	0.121991i	−0.482782	−	0.875741i	$-0.660374\pi$
$433$	−8.64523	+	2.53847i	−0.415463	+	0.121991i	0.0673189	+	0.997732i	$0.478555\pi$
$434$	0.399267	−	0.874273i	0.0191654	−	0.0419664i
$435$		0			0
$436$	−29.9899			−1.43626
$437$	0.465486	−	1.50900i	0.0222672	−	0.0721854i
$438$	2.92006			0.139526
$439$	−0.883245	−	6.14310i	−0.0421550	−	0.293194i	−0.999983	−	0.00585185i	$-0.998137\pi$
$439$	−0.883245	−	6.14310i	−0.0421550	−	0.293194i	0.957828	−	0.287343i	$-0.0927718\pi$
$440$		0			0
$441$	7.09207	−	2.08242i	0.337718	−	0.0991628i
$442$	0.994016	−	1.14716i	0.0472805	−	0.0545646i
$443$	21.1553	+	6.21176i	1.00512	+	0.295130i	0.742555	−	0.669785i	$-0.233614\pi$
$443$	21.1553	+	6.21176i	1.00512	+	0.295130i	0.262564	+	0.964914i	$0.415432\pi$
$444$	31.9741	−	20.5485i	1.51742	−	0.975188i
$445$		0			0
$446$	−4.96672	−	5.73190i	−0.235181	−	0.271414i
$447$	−2.33212	−	1.49876i	−0.110306	−	0.0708890i
$448$	−1.11671	+	7.76689i	−0.0527596	+	0.366951i
$449$	−4.54049	+	31.5798i	−0.214279	+	1.49034i	0.544372	+	0.838844i	$0.316768\pi$
$449$	−4.54049	+	31.5798i	−0.214279	+	1.49034i	−0.758650	+	0.651498i	$0.774141\pi$
$450$		0			0
$451$	14.2647	+	16.4623i	0.671698	+	0.775180i
$452$	8.81073	+	19.2928i	0.414422	+	0.907457i
$453$	−41.7047	+	26.8020i	−1.95946	+	1.25927i
$454$	−0.904340	−	0.265538i	−0.0424428	−	0.0124623i
$455$		0			0
$456$	−0.818837	+	0.240432i	−0.0383456	+	0.0112593i
$457$	6.63487	−	14.5283i	0.310366	−	0.679607i	−0.688597	−	0.725145i	$-0.741773\pi$
$457$	6.63487	−	14.5283i	0.310366	−	0.679607i	0.998963	+	0.0455379i	$0.0145002\pi$
$458$	0.244123	+	1.69791i	0.0114071	+	0.0793382i
$459$	−3.63695			−0.169758
$460$		0			0
$461$	20.0327			0.933014			0.466507	−	0.884517i	$-0.345512\pi$
$461$	20.0327			0.933014			0.466507	+	0.884517i	$0.345512\pi$
$462$	−0.284748	−	1.98046i	−0.0132477	−	0.0921395i
$463$	−1.88016	+	4.11698i	−0.0873785	+	0.191332i	−0.948277	−	0.317445i	$-0.897175\pi$
$463$	−1.88016	+	4.11698i	−0.0873785	+	0.191332i	0.860898	+	0.508777i	$0.169902\pi$
$464$	20.1969	−	5.93034i	0.937616	−	0.275309i
$465$		0			0
$466$	2.20390	+	0.647123i	0.102094	+	0.0299774i
$467$	−19.5538	+	12.5665i	−0.904844	+	0.581508i	−0.908223	−	0.418486i	$-0.862561\pi$
$467$	−19.5538	+	12.5665i	−0.904844	+	0.581508i	0.00337895	+	0.999994i	$0.498924\pi$
$468$	4.95394	+	10.8476i	0.228996	+	0.501431i
$469$	−0.0375395	−	0.0433229i	−0.00173341	−	0.00200047i
$470$		0			0
$471$	−5.11264	+	35.5592i	−0.235578	+	1.63848i
$472$	0.179644	−	1.24945i	0.00826879	−	0.0575107i
$473$	13.3333	+	8.56879i	0.613066	+	0.393993i
$474$	−3.79159	−	4.37573i	−0.174153	−	0.200984i
$475$		0			0
$476$	2.43617	−	1.56563i	0.111662	−	0.0717606i
$477$	−17.5054	−	5.14006i	−0.801518	−	0.235347i
$478$	−1.62936	+	1.88038i	−0.0745253	+	0.0860067i
$479$	36.8988	−	10.8345i	1.68595	−	0.495040i	0.708412	−	0.705799i	$-0.249412\pi$
$479$	36.8988	−	10.8345i	1.68595	−	0.495040i	0.977538	+	0.210759i	$0.0675936\pi$
$480$		0			0
$481$	−5.85966	−	40.7548i	−0.267178	−	1.85826i
$482$	−1.89706			−0.0864085
$483$	12.5507	+	5.93949i	0.571077	+	0.270256i
$484$	11.7674			0.534882
$485$		0			0
$486$	−1.81695	+	3.97856i	−0.0824184	+	0.180471i
$487$	30.8112	−	9.04698i	1.39619	−	0.409958i	0.504815	−	0.863228i	$-0.331561\pi$
$487$	30.8112	−	9.04698i	1.39619	−	0.409958i	0.891373	+	0.453270i	$0.149743\pi$
$488$	8.59707	−	9.92154i	0.389171	−	0.449127i
$489$	−12.8709	−	3.77924i	−0.582042	−	0.170903i
$490$		0			0
$491$	3.57944	+	7.83787i	0.161538	+	0.353718i	0.973042	−	0.230628i	$-0.0740781\pi$
$491$	3.57944	+	7.83787i	0.161538	+	0.353718i	−0.811504	+	0.584347i	$0.801351\pi$
$492$	26.0675	+	30.0835i	1.17522	+	1.35627i
$493$	−5.75492	−	3.69846i	−0.259188	−	0.166570i
$494$	−0.0641102	+	0.445896i	−0.00288445	+	0.0200618i
$495$		0			0
$496$	−6.37867	−	4.09932i	−0.286411	−	0.184065i
$497$	9.44315	+	10.8980i	0.423583	+	0.488841i
$498$	−2.48904	−	5.45025i	−0.111537	−	0.244231i
$499$	−4.04504	+	2.59959i	−0.181081	+	0.116374i	−0.628041	−	0.778180i	$-0.716143\pi$
$499$	−4.04504	+	2.59959i	−0.181081	+	0.116374i	0.446960	+	0.894554i	$0.352507\pi$
$500$		0			0
$501$	25.4485	−	29.3691i	1.13695	−	1.31211i
$502$	−0.618660	+	0.181655i	−0.0276122	+	0.00810766i
$503$	−12.3952	+	27.1417i	−0.552675	+	1.21019i	0.402846	+	0.915268i	$0.368021\pi$
$503$	−12.3952	+	27.1417i	−0.552675	+	1.21019i	−0.955521	+	0.294922i	$0.904706\pi$
$504$	−0.347198	−	2.41482i	−0.0154654	−	0.107565i
$505$		0			0
$506$	−1.82961	+	2.76349i	−0.0813361	+	0.122852i
$507$	12.3258			0.547409
$508$	2.51622	+	17.5007i	0.111639	+	0.776468i
$509$	0.343223	−	0.751553i	0.0152131	−	0.0333120i	−0.901873	−	0.432001i	$-0.857808\pi$
$509$	0.343223	−	0.751553i	0.0152131	−	0.0333120i	0.917086	+	0.398689i	$0.130535\pi$
$510$		0			0
$511$	3.95211	−	4.56098i	0.174831	−	0.201766i
$512$	−19.6310	−	5.76417i	−0.867574	−	0.254743i
$513$	0.908023	−	0.583551i	0.0400902	−	0.0257644i
$514$	1.33427	+	2.92163i	0.0588519	+	0.128868i
$515$		0			0
$516$	24.3655	+	15.6588i	1.07263	+	0.689339i
$517$	−1.38692	+	9.64621i	−0.0609965	+	0.424240i
$518$	−0.584119	+	4.06264i	−0.0256647	+	0.178502i
$519$	−41.0119	−	26.3567i	−1.80022	−	1.15693i
$520$		0			0
$521$	−4.66156	−	10.2074i	−0.204226	−	0.447194i	0.779609	−	0.626266i	$-0.215418\pi$
$521$	−4.66156	−	10.2074i	−0.204226	−	0.447194i	−0.983836	+	0.179072i	$0.942690\pi$
$522$	−2.36241	+	1.51823i	−0.103400	+	0.0664510i
$523$	12.2987	+	3.61123i	0.537786	+	0.157908i	0.539336	−	0.842091i	$-0.318675\pi$
$523$	12.2987	+	3.61123i	0.537786	+	0.157908i	−0.00155034	+	0.999999i	$0.500493\pi$
$524$	−6.76384	+	7.80588i	−0.295480	+	0.341002i
$525$		0			0
$526$	0.550470	−	1.20536i	0.0240017	−	0.0525563i
$527$	0.350690	+	2.43910i	0.0152763	+	0.106249i
$528$	−15.7845			−0.686934
$529$	−8.98150	−	21.1739i	−0.390500	−	0.920603i
$530$		0			0
$531$	−0.211211	−	1.46901i	−0.00916578	−	0.0637494i
$532$	−0.357022	+	0.781770i	−0.0154789	+	0.0338940i
$533$	41.3756	−	12.1490i	1.79218	−	0.526231i
$534$	−2.34670	+	2.70824i	−0.101552	+	0.117197i
$535$		0			0
$536$	0.0431689	−	0.0277430i	0.00186461	−	0.00119831i
$537$	−4.27651	−	9.36424i	−0.184545	−	0.404097i
$538$	3.25162	+	3.75257i	0.140187	+	0.161785i
$539$	9.43481	+	6.06338i	0.406386	+	0.261168i
$540$		0			0
$541$	1.57193	−	10.9330i	0.0675824	−	0.470046i	−0.927724	−	0.373268i	$-0.878237\pi$
$541$	1.57193	−	10.9330i	0.0675824	−	0.470046i	0.995306	−	0.0967778i	$-0.0308536\pi$
$542$	−3.83961	−	2.46757i	−0.164925	−	0.105991i
$543$	23.6600	+	27.3051i	1.01535	+	1.17177i
$544$	1.62903	+	3.56708i	0.0698441	+	0.152937i
$545$		0			0
$546$	−3.80051	−	1.11593i	−0.162647	−	0.0477574i
$547$	−21.9217	+	25.2990i	−0.937305	+	1.08171i	0.0592060	+	0.998246i	$0.481143\pi$
$547$	−21.9217	+	25.2990i	−0.937305	+	1.08171i	−0.996511	+	0.0834618i	$0.973402\pi$
$548$	21.6234	−	6.34921i	0.923707	−	0.271225i
$549$	6.41191	−	14.0401i	0.273654	−	0.599218i
$550$		0			0
$551$	2.03023			0.0864905
$552$	−6.86163	+	10.3640i	−0.292050	+	0.441120i
$553$	−11.9663			−0.508859
$554$	−0.0704057	−	0.489682i	−0.00299125	−	0.0208046i
$555$		0			0
$556$	39.7936	−	11.6845i	1.68762	−	0.495531i
$557$	−18.0587	+	20.8408i	−0.765170	+	0.883054i	−0.995946	−	0.0899533i	$-0.971328\pi$
$557$	−18.0587	+	20.8408i	−0.765170	+	0.883054i	0.230776	+	0.973007i	$0.425874\pi$
$558$	0.970580	+	0.284988i	0.0410879	+	0.0120645i
$559$	26.3953	−	16.9633i	1.11640	−	0.717469i
$560$		0			0
$561$	3.35932	+	3.87686i	0.141830	+	0.163681i
$562$	0.968592	+	0.622476i	0.0408576	+	0.0262576i
$563$	−0.245927	+	1.71046i	−0.0103646	+	0.0720874i	−0.994347	−	0.106177i	$-0.966139\pi$
$563$	−0.245927	+	1.71046i	−0.0103646	+	0.0720874i	0.983983	+	0.178264i	$0.0570482\pi$
$564$	−2.53448	+	17.6277i	−0.106721	+	0.742259i
$565$		0			0
$566$	−4.33616	−	5.00419i	−0.182262	−	0.210342i
$567$	6.41590	+	14.0489i	0.269442	+	0.589996i
$568$	−10.8592	+	6.97881i	−0.455643	+	0.292824i
$569$	7.47338	+	2.19438i	0.313301	+	0.0919934i	0.434603	−	0.900622i	$-0.356889\pi$
$569$	7.47338	+	2.19438i	0.313301	+	0.0919934i	−0.121302	+	0.992616i	$0.538707\pi$
$570$		0			0
$571$	−11.8904	+	3.49133i	−0.497597	+	0.146108i	−0.520895	−	0.853621i	$-0.674402\pi$
$571$	−11.8904	+	3.49133i	−0.497597	+	0.146108i	0.0232978	+	0.999729i	$0.492583\pi$
$572$	−7.51667	+	16.4592i	−0.314288	+	0.688194i
$573$	−2.21846	−	15.4297i	−0.0926773	−	0.644585i
$574$	−4.29865			−0.179422
$575$		0			0
$576$	−8.25845			−0.344102
$577$	4.79583	+	33.3557i	0.199653	+	1.38862i	0.805292	+	0.592878i	$0.202008\pi$
$577$	4.79583	+	33.3557i	0.199653	+	1.38862i	−0.605639	+	0.795739i	$0.707083\pi$
$578$	−2.06437	+	4.52034i	−0.0858665	+	0.188021i
$579$	5.57709	−	1.63758i	0.231776	−	0.0680555i
$580$		0			0
$581$	−11.8817	−	3.48879i	−0.492938	−	0.144740i
$582$	3.56962	−	2.29406i	0.147966	−	0.0950918i
$583$	−11.4997	−	25.1809i	−0.476270	−	1.04289i
$584$	3.53780	+	4.08284i	0.146395	+	0.168949i
$585$		0			0
$586$	−0.987098	+	6.86542i	−0.0407766	+	0.283608i
$587$	0.470259	−	3.27072i	0.0194097	−	0.134997i	−0.977812	−	0.209482i	$-0.932822\pi$
$587$	0.470259	−	3.27072i	0.0194097	−	0.134997i	0.997222	+	0.0744850i	$0.0237313\pi$
$588$	17.2413	+	11.0803i	0.711021	+	0.456945i
$589$	−0.478911	−	0.552692i	−0.0197332	−	0.0227733i
$590$		0			0
$591$	−29.2721	+	18.8121i	−1.20409	+	0.773824i
$592$	31.0682	+	9.12243i	1.27689	+	0.374930i
$593$	−5.08821	+	5.87210i	−0.208948	+	0.241138i	−0.850544	−	0.525904i	$-0.823727\pi$
$593$	−5.08821	+	5.87210i	−0.208948	+	0.241138i	0.641596	+	0.767043i	$0.278273\pi$
$594$	−2.17356	+	0.638214i	−0.0891821	+	0.0261862i
$595$		0			0
$596$	−0.355661	−	2.47368i	−0.0145684	−	0.101326i
$597$	−12.4369			−0.509009
$598$	3.47174	+	5.56732i	0.141970	+	0.227665i
$599$	42.0433			1.71784			0.858921	−	0.512107i	$-0.171135\pi$
$599$	42.0433			1.71784			0.858921	+	0.512107i	$0.171135\pi$
$600$		0			0
$601$	−3.97427	+	8.70244i	−0.162114	+	0.354980i	−0.973205	−	0.229940i	$-0.926147\pi$
$601$	−3.97427	+	8.70244i	−0.162114	+	0.354980i	0.811091	+	0.584920i	$0.198874\pi$
$602$	−3.00104	+	0.881183i	−0.122313	+	0.0359144i
$603$	0.0395091	−	0.0455959i	0.00160893	−	0.00185681i
$604$	−42.8808	−	12.5909i	−1.74479	−	0.512318i
$605$		0			0
$606$	1.95630	+	4.28369i	0.0794692	+	0.174013i
$607$	−16.7684	−	19.3517i	−0.680607	−	0.785463i	0.305389	−	0.952228i	$-0.401213\pi$
$607$	−16.7684	−	19.3517i	−0.680607	−	0.785463i	−0.985997	+	0.166765i	$0.946668\pi$
$608$	−0.979053	−	0.629199i	−0.0397058	−	0.0255174i
$609$	−2.54049	+	17.6695i	−0.102946	+	0.716004i
$610$		0			0
$611$	16.2299	+	10.4303i	0.656592	+	0.421966i
$612$	1.99590	+	2.30339i	0.0806793	+	0.0931089i
$613$	5.34157	+	11.6964i	0.215744	+	0.472413i	0.986301	−	0.164958i	$-0.0527489\pi$
$613$	5.34157	+	11.6964i	0.215744	+	0.472413i	−0.770557	+	0.637372i	$0.780022\pi$
$614$	6.34801	−	4.07962i	0.256185	−	0.164640i
$615$		0			0
$616$	2.42411	−	2.79757i	0.0976700	−	0.112717i
$617$	14.0415	−	4.12295i	0.565288	−	0.165984i	0.0134127	−	0.999910i	$-0.495730\pi$
$617$	14.0415	−	4.12295i	0.565288	−	0.165984i	0.551876	+	0.833926i	$0.313912\pi$
$618$	4.43656	−	9.71472i	0.178465	−	0.390783i
$619$	−0.803533	−	5.58869i	−0.0322967	−	0.224629i	0.967280	−	0.253710i	$-0.0816509\pi$
$619$	−0.803533	−	5.58869i	−0.0322967	−	0.224629i	−0.999577	+	0.0290814i	$0.990742\pi$
$620$		0			0
$621$	4.63392	−	15.0221i	0.185953	−	0.602818i
$622$	2.90128			0.116331
$623$	1.05402	+	7.33084i	0.0422283	+	0.293704i
$624$	−12.9809	+	28.4241i	−0.519651	+	1.13788i
$625$		0			0
$626$	−1.10441	+	1.27456i	−0.0441412	+	0.0509417i
$627$	−1.46075	−	0.428915i	−0.0583367	−	0.0171292i
$628$	−27.2448	+	17.5092i	−1.08719	+	0.698692i
$629$	−4.37145	−	9.57214i	−0.174301	−	0.381666i
$630$		0			0
$631$	22.5323	+	14.4806i	0.896996	+	0.576464i	0.905898	−	0.423496i	$-0.139197\pi$
$631$	22.5323	+	14.4806i	0.896996	+	0.576464i	−0.00890218	+	0.999960i	$0.502834\pi$
$632$	1.52446	−	10.6028i	0.0606396	−	0.421758i
$633$	−1.60071	+	11.1332i	−0.0636226	+	0.442505i
$634$	1.39354	+	0.895573i	0.0553445	+	0.0355678i
$635$		0			0
$636$	−21.0148	−	46.0161i	−0.833292	−	1.82466i
$637$	18.6777	−	12.0034i	0.740036	−	0.475592i
$638$	−4.08832	−	1.20044i	−0.161858	−	0.0475258i
$639$	−9.93860	+	11.4698i	−0.393165	+	0.453736i
$640$		0			0
$641$	7.24468	−	15.8636i	0.286147	−	0.626576i	−0.710906	−	0.703287i	$-0.751715\pi$
$641$	7.24468	−	15.8636i	0.286147	−	0.626576i	0.997053	+	0.0767116i	$0.0244421\pi$
$642$	−0.271010	−	1.88491i	−0.0106959	−	0.0743916i
$643$	−20.3245			−0.801519			−0.400759	−	0.916183i	$-0.631254\pi$
$643$	−20.3245			−0.801519			−0.400759	+	0.916183i	$0.631254\pi$
$644$	3.36274	+	12.0572i	0.132511	+	0.475121i
$645$		0			0
$646$	0.0163851	+	0.113961i	0.000644661	+	0.00448372i
$647$	−8.00399	+	17.5263i	−0.314669	+	0.689030i	−0.999202	−	0.0399528i	$-0.987279\pi$
$647$	−8.00399	+	17.5263i	−0.314669	+	0.689030i	0.684532	+	0.728983i	$0.260007\pi$
$648$	−13.2654	+	3.89508i	−0.521115	+	0.153013i
$649$	1.47465	−	1.70184i	0.0578853	−	0.0668032i
$650$		0			0
$651$	5.40948	−	3.47646i	0.212014	−	0.136253i
$652$	−5.02356	−	11.0001i	−0.196738	−	0.430796i
$653$	−10.1175	−	11.6762i	−0.395929	−	0.456926i	0.522426	−	0.852685i	$-0.325027\pi$
$653$	−10.1175	−	11.6762i	−0.395929	−	0.456926i	−0.918355	+	0.395759i	$0.870482\pi$
$654$	8.81945	+	5.66792i	0.344868	+	0.221633i
$655$		0			0
$656$	−4.82619	+	33.5669i	−0.188431	+	1.31057i
$657$	5.34337	+	3.43397i	0.208465	+	0.133972i
$658$	−1.25941	−	1.45344i	−0.0490970	−	0.0566609i
$659$	10.7902	+	23.6273i	0.420327	+	0.920388i	0.994798	+	0.101863i	$0.0324805\pi$
$659$	10.7902	+	23.6273i	0.420327	+	0.920388i	−0.574471	+	0.818525i	$0.694792\pi$
$660$		0			0
$661$	9.27329	+	2.72288i	0.360689	+	0.105908i	0.457056	−	0.889438i	$-0.348904\pi$
$661$	9.27329	+	2.72288i	0.360689	+	0.105908i	−0.0963666	+	0.995346i	$0.530722\pi$
$662$	1.41886	−	1.63746i	0.0551457	−	0.0636416i
$663$	9.74391	−	2.86107i	0.378422	−	0.111115i
$664$	4.60495	−	10.0834i	0.178707	−	0.391313i
$665$		0			0
$666$	−4.31976			−0.167387
$667$	22.6086	−	19.0579i	0.875410	−	0.737926i
$668$	35.0328			1.35546
$669$	−7.22135	−	50.2256i	−0.279193	−	1.94183i
$670$		0			0
$671$	22.4710	−	6.59807i	0.867482	−	0.254716i
$672$	6.70118	−	7.73357i	0.258503	−	0.298329i
$673$	10.1060	+	2.96740i	0.389559	+	0.114385i	0.470646	−	0.882322i	$-0.344021\pi$
$673$	10.1060	+	2.96740i	0.389559	+	0.114385i	−0.0810870	+	0.996707i	$0.525839\pi$
$674$	−3.57549	+	2.29783i	−0.137723	+	0.0885091i
$675$		0			0
$676$	7.27658	+	8.39762i	0.279868	+	0.322985i
$677$	−22.9911	−	14.7755i	−0.883622	−	0.567869i	0.0182692	−	0.999833i	$-0.494184\pi$
$677$	−22.9911	−	14.7755i	−0.883622	−	0.567869i	−0.901891	+	0.431964i	$0.857821\pi$
$678$	1.05516	−	7.33882i	0.0405233	−	0.281846i
$679$	1.24806	−	8.68042i	0.0478960	−	0.333124i
$680$		0			0
$681$	−4.12939	−	4.76557i	−0.158239	−	0.182617i
$682$	0.637597	+	1.39614i	0.0244149	+	0.0534611i
$683$	16.0398	−	10.3082i	0.613747	−	0.394431i	−0.196514	−	0.980501i	$-0.562962\pi$
$683$	16.0398	−	10.3082i	0.613747	−	0.394431i	0.810260	+	0.586070i	$0.199326\pi$
$684$	−0.867887	−	0.254835i	−0.0331845	−	0.00974385i
$685$		0			0
$686$	−5.03013	+	1.47698i	−0.192051	+	0.0563914i
$687$	−4.76746	+	10.4393i	−0.181890	+	0.398284i
$688$	3.51157	+	24.4235i	0.133877	+	0.931138i
$689$	−54.8019			−2.08778
$690$		0			0
$691$	−31.0594			−1.18156			−0.590778	−	0.806834i	$-0.701179\pi$
$691$	−31.0594			−1.18156			−0.590778	+	0.806834i	$0.701179\pi$
$692$	−6.25453	−	43.5012i	−0.237762	−	1.65367i
$693$	1.80796	−	3.95888i	0.0686787	−	0.150385i
$694$	−2.17516	+	0.638684i	−0.0825679	+	0.0242441i
$695$		0			0
$696$	−15.3325	−	4.50203i	−0.581178	−	0.170649i
$697$	9.27151	−	5.95844i	0.351184	−	0.225692i
$698$	0.298488	+	0.653598i	0.0112980	+	0.0247391i
$699$	10.0634	+	11.6138i	0.380633	+	0.439274i
$700$		0			0
$701$	−4.11925	+	28.6500i	−0.155582	+	1.08210i	0.751072	+	0.660221i	$0.229537\pi$
$701$	−4.11925	+	28.6500i	−0.155582	+	1.08210i	−0.906654	+	0.421876i	$0.861372\pi$
$702$	−0.638218	+	4.43890i	−0.0240880	+	0.167535i
$703$	2.62726	+	1.68844i	0.0990889	+	0.0636806i
$704$	−8.20582	−	9.47003i	−0.309269	−	0.356915i
$705$		0			0
$706$	−0.00181397	+	0.00116577i	−6.82696e−5	+	4.38742e-5i
$707$	9.33862	+	2.74207i	0.351215	+	0.103126i
$708$	2.69481	−	3.10998i	0.101277	−	0.116880i
$709$	27.0364	−	7.93861i	1.01537	−	0.298141i	0.268624	−	0.963245i	$-0.413431\pi$
$709$	27.0364	−	7.93861i	1.01537	−	0.298141i	0.746750	+	0.665104i	$0.231613\pi$
$710$		0			0
$711$	−1.79233	−	12.4660i	−0.0672177	−	0.467510i
$712$	−6.62982			−0.248463
$713$	−10.5213	−	1.65921i	−0.394027	−	0.0621381i
$714$	−1.01233			−0.0378854
$715$		0			0
$716$	3.85524	−	8.44179i	0.144077	−	0.315485i
$717$	−15.9719	+	4.68978i	−0.596483	+	0.175143i
$718$	−4.58951	+	5.29657i	−0.171279	+	0.197666i
$719$	−11.6099	−	3.40898i	−0.432977	−	0.127134i	0.0579789	−	0.998318i	$-0.481534\pi$
$719$	−11.6099	−	3.40898i	−0.432977	−	0.127134i	−0.490956	+	0.871184i	$0.663353\pi$
$720$		0			0
$721$	−9.16927	−	20.0779i	−0.341482	−	0.747740i
$722$	3.89869	+	4.49933i	0.145094	+	0.167448i
$723$	−10.6771	−	6.86177i	−0.397086	−	0.255192i
$724$	−4.63530	+	32.2392i	−0.172270	+	1.19816i
$725$		0			0
$726$	−3.46057	−	2.22397i	−0.128434	−	0.0825393i
$727$	−23.2237	−	26.8016i	−0.861320	−	0.994017i	−0.999993	−	0.00367836i	$-0.998829\pi$
$727$	−23.2237	−	26.8016i	−0.861320	−	0.994017i	0.138673	−	0.990338i	$-0.455716\pi$
$728$	−3.04421	−	6.66588i	−0.112826	−	0.247054i
$729$	3.76780	−	2.42142i	0.139548	−	0.0896822i
$730$		0			0
$731$	5.25134	−	6.06037i	0.194228	−	0.224151i
$732$	41.0639	−	12.0574i	1.51776	−	0.445656i
$733$	7.49374	−	16.4090i	0.276788	−	0.606080i	−0.719276	−	0.694725i	$-0.755526\pi$
$733$	7.49374	−	16.4090i	0.276788	−	0.606080i	0.996063	+	0.0886445i	$0.0282535\pi$
$734$	0.0975108	+	0.678203i	0.00359919	+	0.0250329i
$735$		0			0
$736$	−16.8091	+	2.18369i	−0.619592	+	0.0804919i
$737$	0.0915425			0.00337201
$738$	−0.643858	−	4.47813i	−0.0237007	−	0.164842i
$739$	−6.10010	+	13.3573i	−0.224396	+	0.491358i	−0.988024	−	0.154298i	$-0.950689\pi$
$739$	−6.10010	+	13.3573i	−0.224396	+	0.491358i	0.763629	+	0.645656i	$0.223416\pi$
$740$		0			0
$741$	−1.97366	+	2.27773i	−0.0725043	+	0.0836744i
$742$	5.24163	+	1.53908i	0.192426	+	0.0565014i
$743$	−43.2220	+	27.7771i	−1.58566	+	1.01904i	−0.612055	+	0.790815i	$0.709657\pi$
$743$	−43.2220	+	27.7771i	−1.58566	+	1.01904i	−0.973608	+	0.228228i	$0.926707\pi$
$744$	2.39120	+	5.23599i	0.0876655	+	0.191961i
$745$		0			0
$746$	2.83961	+	1.82490i	0.103965	+	0.0668145i
$747$	1.85480	−	12.9004i	0.0678635	−	0.472001i
$748$	−0.658134	+	4.57742i	−0.0240638	+	0.167367i
$749$	−3.31093	−	2.12780i	−0.120979	−	0.0777482i
$750$		0			0
$751$	14.4294	+	31.5959i	0.526536	+	1.15295i	0.966905	+	0.255136i	$0.0821202\pi$
$751$	14.4294	+	31.5959i	0.526536	+	1.15295i	−0.440369	+	0.897817i	$0.645153\pi$
$752$	−12.7634	+	8.20256i	−0.465435	+	0.299117i
$753$	−4.13904	−	1.21533i	−0.150835	−	0.0442891i
$754$	−5.52385	+	6.37486i	−0.201167	+	0.232159i
$755$		0			0
$756$	−3.55416	+	7.78253i	−0.129264	+	0.283048i
$757$	−4.32174	−	30.0583i	−0.157076	−	1.09249i	−0.903986	−	0.427563i	$-0.859372\pi$
$757$	−4.32174	−	30.0583i	−0.157076	−	1.09249i	0.746909	−	0.664926i	$-0.231537\pi$
$758$	10.3332			0.375319
$759$	−20.2932	+	8.93580i	−0.736597	+	0.324349i
$760$		0			0
$761$	3.52921	+	24.5462i	0.127934	+	0.889799i	0.948168	+	0.317770i	$0.102934\pi$
$761$	3.52921	+	24.5462i	0.127934	+	0.889799i	−0.820234	+	0.572028i	$0.806157\pi$
$762$	2.56756	−	5.62217i	0.0930128	−	0.203670i
$763$	20.7895	−	6.10436i	0.752631	−	0.220993i
$764$	9.20262	−	10.6204i	0.332939	−	0.384232i
$765$		0			0
$766$	−2.59709	+	1.66905i	−0.0938365	+	0.0603051i
$767$	−1.85188	−	4.05505i	−0.0668676	−	0.146420i
$768$	−11.9198	−	13.7562i	−0.430118	−	0.496382i
$769$	15.4172	+	9.90803i	0.555958	+	0.357293i	0.788252	−	0.615353i	$-0.210987\pi$
$769$	15.4172	+	9.90803i	0.555958	+	0.357293i	−0.232293	+	0.972646i	$0.574623\pi$
$770$		0			0
$771$	−3.05814	+	21.2698i	−0.110136	+	0.766014i
$772$	4.40813	+	2.83293i	0.158652	+	0.101960i
$773$	−35.4620	−	40.9253i	−1.27548	−	1.47198i	−0.809425	−	0.587223i	$-0.800221\pi$
$773$	−35.4620	−	40.9253i	−1.27548	−	1.47198i	−0.466053	−	0.884757i	$-0.654324\pi$
$774$	−1.36748	−	2.99435i	−0.0491529	−	0.107630i
$775$		0			0
$776$	7.53234	+	2.21169i	0.270395	+	0.0793952i
$777$	−17.9824	+	20.7528i	−0.645115	+	0.744502i
$778$	−8.67165	+	2.54623i	−0.310894	+	0.0912866i
$779$	−1.35875	+	2.97524i	−0.0486821	+	0.106599i
$780$		0			0
$781$	−23.0277			−0.823997
$782$	1.25222	+	1.11526i	0.0447794	+	0.0398816i
$783$	20.2109			0.722279
$784$	2.48483	+	17.2824i	0.0887440	+	0.617228i
$785$		0			0
$786$	3.46438	−	1.01723i	0.123570	−	0.0362835i
$787$	19.8309	−	22.8861i	0.706896	−	0.815801i	−0.282771	−	0.959187i	$-0.591254\pi$
$787$	19.8309	−	22.8861i	0.706896	−	0.815801i	0.989667	+	0.143386i	$0.0457991\pi$
$788$	−30.0976	−	8.83744i	−1.07218	−	0.314821i
$789$	7.45806	−	4.79300i	0.265514	−	0.170635i
$790$		0			0
$791$	−10.0347	−	11.5807i	−0.356794	−	0.411763i
$792$	3.27746	+	2.10630i	0.116460	+	0.0748440i
$793$	6.59811	−	45.8909i	0.234306	−	1.62963i
$794$	−0.870170	+	6.05216i	−0.0308812	+	0.214783i
$795$		0			0
$796$	−7.34216	−	8.47331i	−0.260236	−	0.300328i
$797$	−1.91551	−	4.19439i	−0.0678510	−	0.148573i	0.872668	−	0.488314i	$-0.162388\pi$
$797$	−1.91551	−	4.19439i	−0.0678510	−	0.148573i	−0.940519	+	0.339741i	$0.889661\pi$
$798$	0.252743	−	0.162428i	0.00894702	−	0.00574990i
$799$	4.73099	+	1.38915i	0.167371	+	0.0491444i
$800$		0			0
$801$	−7.47906	+	2.19605i	−0.264260	+	0.0775936i
$802$	−1.07135	+	2.34594i	−0.0378308	+	0.0828379i
$803$	1.37155	+	9.53937i	0.0484011	+	0.336637i
$804$	0.167286			0.00589974
$805$		0			0
$806$	3.03846			0.107025
$807$	4.72768	+	32.8818i	0.166422	+	1.15749i
$808$	−3.61932	+	7.92521i	−0.127327	+	0.278808i
$809$	26.4975	−	7.78037i	0.931602	−	0.273543i	0.219495	−	0.975614i	$-0.429559\pi$
$809$	26.4975	−	7.78037i	0.931602	−	0.273543i	0.712107	+	0.702071i	$0.247741\pi$
$810$		0			0
$811$	6.06504	+	1.78085i	0.212972	+	0.0625343i	0.386478	−	0.922299i	$-0.373691\pi$
$811$	6.06504	+	1.78085i	0.212972	+	0.0625343i	−0.173506	+	0.984833i	$0.555510\pi$
$812$	−13.5381	+	8.70038i	−0.475092	+	0.305323i
$813$	−12.6850	−	27.7762i	−0.444881	−	0.974154i
$814$	−4.29223	−	4.95350i	−0.150443	−	0.173620i
$815$		0			0
$816$	−1.13656	+	7.90496i	−0.0397876	+	0.276729i
$817$	−0.338691	+	2.35565i	−0.0118493	+	0.0824137i
$818$	7.00101	+	4.49927i	0.244784	+	0.157313i
$819$	−5.64215	−	6.51139i	−0.197153	−	0.227526i
$820$		0			0
$821$	−4.35389	+	2.79808i	−0.151952	+	0.0976535i	−0.614407	−	0.788989i	$-0.710605\pi$
$821$	−4.35389	+	2.79808i	−0.151952	+	0.0976535i	0.462456	+	0.886642i	$0.346968\pi$
$822$	−7.55899	−	2.21952i	−0.263650	−	0.0774147i
$823$	31.2142	−	36.0231i	1.08806	−	1.25568i	0.123349	−	0.992363i	$-0.460637\pi$
$823$	31.2142	−	36.0231i	1.08806	−	1.25568i	0.964708	−	0.263321i	$-0.0848179\pi$
$824$	18.9583	−	5.56665i	0.660443	−	0.193924i
$825$		0			0
$826$	0.0632427	+	0.439862i	0.00220049	+	0.0153048i
$827$	3.95471			0.137519			0.0687594	−	0.997633i	$-0.478096\pi$
$827$	3.95471			0.137519			0.0687594	+	0.997633i	$0.478096\pi$
$828$	−12.0570	+	5.30910i	−0.419009	+	0.184504i
$829$	23.0331			0.799972			0.399986	−	0.916521i	$-0.369015\pi$
$829$	23.0331			0.799972			0.399986	+	0.916521i	$0.369015\pi$
$830$		0			0
$831$	1.37495	−	3.01072i	0.0476965	−	0.104441i
$832$	−23.8015	+	6.98876i	−0.825169	+	0.242292i
$833$	3.71591	−	4.28839i	0.128749	−	0.148584i
$834$	−13.9108	−	4.08459i	−0.481692	−	0.141438i
$835$		0			0
$836$	−0.570136	−	1.24842i	−0.0197186	−	0.0431776i
$837$	−4.76756	−	5.50206i	−0.164791	−	0.190179i
$838$	8.87538	+	5.70386i	0.306595	+	0.197037i
$839$	2.97617	−	20.6997i	0.102749	−	0.714634i	−0.871703	−	0.490035i	$-0.836984\pi$
$839$	2.97617	−	20.6997i	0.102749	−	0.714634i	0.974451	−	0.224599i	$-0.0721071\pi$
$840$		0			0
$841$	7.58429	+	4.87413i	0.261527	+	0.168073i
$842$	0.861050	+	0.993705i	0.0296738	+	0.0342453i
$843$	3.19995	+	7.00691i	0.110212	+	0.241331i
$844$	−8.53006	+	5.48194i	−0.293617	+	0.188696i
$845$		0			0
$846$	1.32549	−	1.52969i	0.0455712	−	0.0525920i
$847$	−8.15737	+	2.39522i	−0.280291	+	0.0823008i
$848$	17.9031	−	39.2024i	0.614795	−	1.34621i
$849$	−6.30454	−	43.8490i	−0.216371	−	1.50489i
$850$		0			0
$851$	45.1067	−	5.85986i	1.54624	−	0.200873i
$852$	−42.0813			−1.44168
$853$	−0.320570	−	2.22962i	−0.0109761	−	0.0763406i	0.983597	−	0.180379i	$-0.0577325\pi$
$853$	−0.320570	−	2.22962i	−0.0109761	−	0.0763406i	−0.994573	+	0.104039i	$0.966823\pi$
$854$	−1.91991	+	4.20402i	−0.0656979	+	0.143858i
$855$		0			0
$856$	2.30715	−	2.66259i	0.0788568	−	0.0910056i
$857$	49.2148	+	14.4508i	1.68115	+	0.493629i	0.976425	−	0.215855i	$-0.0692538\pi$
$857$	49.2148	+	14.4508i	1.68115	+	0.493629i	0.704721	+	0.709484i	$0.251072\pi$
$858$	5.32120	−	3.41973i	0.181663	−	0.116748i
$859$	9.08775	+	19.8994i	0.310070	+	0.678959i	0.998945	−	0.0459215i	$-0.0146224\pi$
$859$	9.08775	+	19.8994i	0.310070	+	0.678959i	−0.688875	+	0.724880i	$0.741895\pi$
$860$		0			0
$861$	−24.1939	−	15.5485i	−0.824525	−	0.529890i
$862$	−1.44580	+	10.0558i	−0.0492443	+	0.342502i
$863$	−2.63034	+	18.2944i	−0.0895379	+	0.622750i	0.894801	+	0.446465i	$0.147317\pi$
$863$	−2.63034	+	18.2944i	−0.0895379	+	0.622750i	−0.984339	+	0.176285i	$0.943592\pi$
$864$	−9.74648	−	6.26368i	−0.331582	−	0.213095i
$865$		0			0
$866$	1.17956	+	2.58287i	0.0400829	+	0.0877694i
$867$	−27.9692	+	17.9747i	−0.949882	+	0.610452i
$868$	5.56202	+	1.63316i	0.188787	+	0.0554329i
$869$	12.5139	−	14.4418i	0.424505	−	0.489905i
$870$		0			0
$871$	0.0752826	−	0.164846i	0.00255085	−	0.00558559i
$872$	2.76031	+	19.1984i	0.0934758	+	0.650139i
$873$	9.22979			0.312381
$874$	−0.491581	−	0.0775223i	−0.0166280	−	0.00262223i
$875$		0			0
$876$	2.50640	+	17.4324i	0.0846836	+	0.588987i
$877$	−10.9995	+	24.0855i	−0.371425	+	0.813308i	0.627960	+	0.778246i	$0.283890\pi$
$877$	−10.9995	+	24.0855i	−0.371425	+	0.813308i	−0.999385	+	0.0350624i	$0.988837\pi$
$878$	−1.87661	+	0.551023i	−0.0633326	+	0.0185961i
$879$	−30.3883	+	35.0699i	−1.02497	+	1.18288i
$880$		0			0
$881$	5.60631	−	3.60296i	0.188882	−	0.121387i	−0.442782	−	0.896629i	$-0.646009\pi$
$881$	5.60631	−	3.60296i	0.188882	−	0.121387i	0.631664	+	0.775242i	$0.282372\pi$
$882$	−0.967643	−	2.11884i	−0.0325822	−	0.0713451i
$883$	−35.3341	−	40.7777i	−1.18909	−	1.37228i	−0.911355	−	0.411621i	$-0.864963\pi$
$883$	−35.3341	−	40.7777i	−1.18909	−	1.37228i	−0.277731	−	0.960659i	$-0.589583\pi$
$884$	7.70159	+	4.94951i	0.259033	+	0.166470i
$885$		0			0
$886$	0.988848	−	6.87759i	0.0332210	−	0.231057i
$887$	−2.78318	−	1.78864i	−0.0934501	−	0.0600568i	0.493081	−	0.869983i	$-0.335871\pi$
$887$	−2.78318	−	1.78864i	−0.0934501	−	0.0600568i	−0.586531	+	0.809927i	$0.699507\pi$
$888$	−16.0973	−	18.5772i	−0.540189	−	0.623411i
$889$	−5.30650	−	11.6196i	−0.177974	−	0.389709i
$890$		0			0
$891$	−23.6646	−	6.94857i	−0.792795	−	0.232786i
$892$	29.9557	−	34.5707i	1.00299	−	1.15751i
$893$	−1.40406	+	0.412268i	−0.0469850	+	0.0137960i
$894$	−0.362917	+	0.794678i	−0.0121378	+	0.0265780i
$895$		0			0
$896$	12.1798			0.406898
$897$	−0.597497	+	43.8918i	−0.0199499	+	1.46550i
$898$	10.0543			0.335518
$899$	−1.94882	−	13.5543i	−0.0649968	−	0.452063i
$900$		0			0
$901$	−13.4387	+	3.94597i	−0.447709	+	0.131459i
$902$	4.49535	−	5.18791i	0.149679	−	0.172739i
$903$	−20.0779	−	5.89540i	−0.668150	−	0.196187i
$904$	11.5395	−	7.41601i	0.383799	−	0.246653i
$905$		0			0
$906$	10.2308	+	11.8070i	0.339895	+	0.392260i
$907$	−38.2891	−	24.6069i	−1.27137	−	0.817059i	−0.281572	−	0.959540i	$-0.590856\pi$
$907$	−38.2891	−	24.6069i	−1.27137	−	0.817059i	−0.989798	+	0.142481i	$0.954492\pi$
$908$	0.809001	−	5.62673i	0.0268477	−	0.186730i
$909$	−1.45780	+	10.1392i	−0.0483523	+	0.336298i
$910$		0			0
$911$	−14.7732	−	17.0492i	−0.489457	−	0.564864i	0.456263	−	0.889845i	$-0.349187\pi$
$911$	−14.7732	−	17.0492i	−0.489457	−	0.564864i	−0.945720	+	0.324981i	$0.894642\pi$
$912$	−0.984594	−	2.15596i	−0.0326032	−	0.0713910i
$913$	16.6360	−	10.6913i	0.550570	−	0.353830i
$914$	−4.82940	−	1.41804i	−0.159742	−	0.0469046i
$915$		0			0
$916$	−9.92679	+	2.91477i	−0.327991	+	0.0963067i
$917$	3.09994	−	6.78793i	0.102369	−	0.224157i
$918$	0.163113	+	1.13448i	0.00538354	+	0.0374434i
$919$	31.1689			1.02817			0.514083	−	0.857740i	$-0.328132\pi$
$919$	31.1689			1.02817			0.514083	+	0.857740i	$0.328132\pi$
$920$		0			0
$921$	50.4844			1.66352
$922$	−0.898443	−	6.24881i	−0.0295886	−	0.205794i
$923$	−18.9375	+	41.4673i	−0.623335	+	1.36491i
$924$	11.5787	−	3.39982i	0.380912	−	0.111846i
$925$		0			0
$926$	1.36854	+	0.401839i	0.0449729	+	0.0132052i
$927$	19.5428	−	12.5594i	0.641871	−	0.412506i
$928$	−9.05268	−	19.8226i	−0.297169	−	0.650709i
$929$	−9.71976	−	11.2172i	−0.318895	−	0.368025i	0.573558	−	0.819165i	$-0.305563\pi$
$929$	−9.71976	−	11.2172i	−0.318895	−	0.368025i	−0.892453	+	0.451140i	$0.851017\pi$
$930$		0			0
$931$	−0.239662	+	1.66689i	−0.00785460	+	0.0546300i
$932$	−1.97155	+	13.7125i	−0.0645804	+	0.449167i
$933$	16.3292	+	10.4941i	0.534593	+	0.343562i
$934$	4.79685	+	5.53586i	0.156958	+	0.181139i
$935$		0			0
$936$	6.48824	−	4.16974i	0.212075	−	0.136292i
$937$	18.7372	+	5.50172i	0.612116	+	0.179734i	0.573073	−	0.819504i	$-0.305751\pi$
$937$	18.7372	+	5.50172i	0.612116	+	0.179734i	0.0390427	+	0.999238i	$0.487569\pi$
$938$	−0.0118301	+	0.0136527i	−0.000386268	+	0.000445777i
$939$	−10.8261	+	3.17883i	−0.353296	+	0.103737i
$940$		0			0
$941$	−8.33132	−	57.9456i	−0.271593	−	1.88897i	−0.431923	−	0.901910i	$-0.642165\pi$
$941$	−8.33132	−	57.9456i	−0.271593	−	1.88897i	0.160330	−	0.987063i	$-0.448744\pi$
$942$	11.3213			0.368868
$943$	12.7978	+	45.8870i	0.416755	+	1.49429i
$944$	3.50576			0.114103
$945$		0			0
$946$	2.07489	−	4.54337i	0.0674604	−	0.147718i
$947$	44.8355	−	13.1649i	1.45696	−	0.427802i	0.545123	−	0.838356i	$-0.316483\pi$
$947$	44.8355	−	13.1649i	1.45696	−	0.427802i	0.911836	+	0.410554i	$0.134665\pi$
$948$	22.8681	−	26.3912i	0.742722	−	0.857147i
$949$	18.3060	+	5.37514i	0.594239	+	0.174484i
$950$		0			0
$951$	4.60385	+	10.0810i	0.149290	+	0.326900i
$952$	−1.22648	−	1.41544i	−0.0397506	−	0.0458746i
$953$	−25.6608	−	16.4912i	−0.831234	−	0.534202i	0.0544358	−	0.998517i	$-0.482664\pi$
$953$	−25.6608	−	16.4912i	−0.831234	−	0.534202i	−0.885670	+	0.464316i	$0.846300\pi$
$954$	−0.818244	+	5.69101i	−0.0264916	+	0.184253i
$955$		0			0
$956$	−12.6242	−	8.11309i	−0.408296	−	0.262396i
$957$	−18.6681	−	21.5441i	−0.603453	−	0.696421i
$958$	−5.03448	−	11.0240i	−0.162657	−	0.356168i
$959$	−13.6974	+	8.80277i	−0.442311	+	0.284256i
$960$		0			0
$961$	17.0705	−	19.7004i	0.550660	−	0.635496i
$962$	−12.4499	+	3.65562i	−0.401401	+	0.117862i
$963$	1.72073	−	3.76787i	0.0554498	−	0.121418i
$964$	−1.62832	−	11.3252i	−0.0524446	−	0.364760i
$965$		0			0
$966$	1.28983	−	4.18133i	0.0414995	−	0.134532i
$967$	44.3081			1.42485			0.712426	−	0.701747i	$-0.247596\pi$
$967$	44.3081			1.42485			0.712426	+	0.701747i	$0.247596\pi$
$968$	−1.08309	−	7.53303i	−0.0348117	−	0.242121i
$969$	−0.319983	+	0.700665i	−0.0102793	+	0.0225086i
$970$		0			0
$971$	−12.1571	+	14.0300i	−0.390139	+	0.450244i	−0.916511	−	0.400010i	$-0.869007\pi$
$971$	−12.1571	+	14.0300i	−0.390139	+	0.450244i	0.526372	+	0.850255i	$0.323552\pi$
$972$	−25.3111	−	7.43201i	−0.811854	−	0.238382i
$973$	−25.2073	+	16.1997i	−0.808108	+	0.519340i
$974$	−4.20388	−	9.20521i	−0.134701	−	0.294954i
$975$		0			0
$976$	30.6724	+	19.7119i	0.981799	+	0.630964i
$977$	−2.80145	+	19.4845i	−0.0896264	+	0.623365i	0.894655	+	0.446758i	$0.147421\pi$
$977$	−2.80145	+	19.4845i	−0.0896264	+	0.623365i	−0.984281	+	0.176608i	$0.943488\pi$
$978$	−0.601615	+	4.18433i	−0.0192375	+	0.133800i
$979$	−9.94963	−	6.39424i	−0.317992	−	0.204361i
$980$		0			0
$981$	9.47312	+	20.7432i	0.302454	+	0.662281i
$982$	2.28434	−	1.46806i	0.0728963	−	0.0468476i
$983$	20.1094	+	5.90466i	0.641391	+	0.188329i	0.586226	−	0.810148i	$-0.300613\pi$
$983$	20.1094	+	5.90466i	0.641391	+	0.188329i	0.0551653	+	0.998477i	$0.482431\pi$
$984$	16.8590	−	19.4563i	0.537446	−	0.620245i
$985$		0			0
$986$	−0.895562	+	1.96101i	−0.0285205	+	0.0624512i
$987$	−1.83112	−	12.7357i	−0.0582851	−	0.405382i
$988$	−2.71698			−0.0864385
$989$	18.3410	+	29.4119i	0.583211	+	0.935243i
$990$		0			0
$991$	−7.32999	−	50.9812i	−0.232845	−	1.61947i	−0.685699	−	0.727886i	$-0.740503\pi$
$991$	−7.32999	−	50.9812i	−0.232845	−	1.61947i	0.452854	−	0.891585i	$-0.350406\pi$
$992$	−3.26091	+	7.14039i	−0.103534	+	0.226708i
$993$	13.9085	−	4.08391i	0.441373	−	0.129599i
$994$	2.97590	−	3.43437i	0.0943899	−	0.108932i
$995$		0			0
$996$	30.4009	−	19.5375i	0.963289	−	0.619068i
$997$	−11.1517	−	24.4188i	−0.353177	−	0.773350i	−0.999943	−	0.0106615i	$-0.996606\pi$
$997$	−11.1517	−	24.4188i	−0.353177	−	0.773350i	0.646766	−	0.762688i	$-0.276121\pi$
$998$	0.992308	+	1.14518i	0.0314110	+	0.0362502i
$999$	26.1544	+	16.8084i	0.827488	+	0.531794i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	575.2.k.g.26.5		100
5.2	odd	4		115.2.j.a.49.6	yes	100
5.3	odd	4		115.2.j.a.49.5	✓	100
5.4	even	2	inner	575.2.k.g.26.6		100
23.8	even	11	inner	575.2.k.g.376.5		100
115.8	odd	44		115.2.j.a.54.6	yes	100
115.54	even	22	inner	575.2.k.g.376.6		100
115.77	odd	44		115.2.j.a.54.5	yes	100

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.2.j.a.49.5	✓	100	5.3	odd	4
115.2.j.a.49.6	yes	100	5.2	odd	4
115.2.j.a.54.5	yes	100	115.77	odd	44
115.2.j.a.54.6	yes	100	115.8	odd	44
575.2.k.g.26.5		100	1.1	even	1	trivial
575.2.k.g.26.6		100	5.4	even	2	inner
575.2.k.g.376.5		100	23.8	even	11	inner
575.2.k.g.376.6		100	115.54	even	22	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:	\( N \)	\(=\)	\( 575 = 5^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	575.k (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0448489 - 0.311931i) q^{2} +(0.875852 - 1.91785i) q^{3} +(1.82370 - 0.535486i) q^{4} +(-0.637517 - 0.187192i) q^{6} +(-1.15522 + 0.742416i) q^{7} +(-0.510652 - 1.11817i) q^{8} +(-0.946445 - 1.09226i) q^{9} +O(q^{10})\)	\(q+(-0.0448489 - 0.311931i) q^{2} +(0.875852 - 1.91785i) q^{3} +(1.82370 - 0.535486i) q^{4} +(-0.637517 - 0.187192i) q^{6} +(-1.15522 + 0.742416i) q^{7} +(-0.510652 - 1.11817i) q^{8} +(-0.946445 - 1.09226i) q^{9} +(0.312084 - 2.17059i) q^{11} +(0.570308 - 3.96658i) q^{12} +(-3.65206 - 2.34704i) q^{13} +(0.283393 + 0.327053i) q^{14} +(2.87203 - 1.84574i) q^{16} +(-1.06457 - 0.312586i) q^{17} +(-0.298261 + 0.344212i) q^{18} +(0.315941 - 0.0927686i) q^{19} +(0.412038 + 2.86579i) q^{21} -0.691072 q^{22} +(2.64750 - 3.99884i) q^{23} -2.59174 q^{24} +(-0.568322 + 1.24445i) q^{26} +(3.14520 - 0.923513i) q^{27} +(-1.70922 + 1.97255i) q^{28} +(5.91592 + 1.73707i) q^{29} +(-0.922622 - 2.02026i) q^{31} +(-2.31454 - 2.67112i) q^{32} +(-3.88953 - 2.49965i) q^{33} +(-0.0497604 + 0.346091i) q^{34} +(-2.31092 - 1.48514i) q^{36} +(6.21098 + 7.16786i) q^{37} +(-0.0431070 - 0.0943912i) q^{38} +(-7.69992 + 4.94844i) q^{39} +(-6.50490 + 7.50706i) q^{41} +(0.875448 - 0.257055i) q^{42} +(-3.00242 + 6.57438i) q^{43} +(-0.593174 - 4.12562i) q^{44} +(-1.36610 - 0.646493i) q^{46} -4.44405 q^{47} +(-1.02438 - 7.12472i) q^{48} +(-2.12455 + 4.65211i) q^{49} +(-1.53190 + 1.76790i) q^{51} +(-7.91705 - 2.32466i) q^{52} +(10.6197 - 6.82485i) q^{53} +(-0.429131 - 0.939666i) q^{54} +(1.42006 + 0.912620i) q^{56} +(0.0988014 - 0.687179i) q^{57} +(0.276523 - 1.92326i) q^{58} +(0.863867 + 0.555174i) q^{59} +(4.43650 + 9.71459i) q^{61} +(-0.588803 + 0.378401i) q^{62} +(1.90426 + 0.559142i) q^{63} +(3.74197 - 4.31847i) q^{64} +(-0.605277 + 1.32537i) q^{66} +(0.00594089 + 0.0413198i) q^{67} -2.10884 q^{68} +(-5.35036 - 8.57990i) q^{69} +(-1.49444 - 10.3941i) q^{71} +(-0.738026 + 1.61605i) q^{72} +(-4.21680 + 1.23817i) q^{73} +(1.95732 - 2.25887i) q^{74} +(0.526504 - 0.338364i) q^{76} +(1.25096 + 2.73921i) q^{77} +(1.88891 + 2.17991i) q^{78} +(7.33076 + 4.71119i) q^{79} +(1.60062 - 11.1325i) q^{81} +(2.63342 + 1.69240i) q^{82} +(5.90540 + 6.81519i) q^{83} +(2.28602 + 5.00568i) q^{84} +(2.18541 + 0.641694i) q^{86} +(8.51290 - 9.82442i) q^{87} +(-2.58646 + 0.759454i) q^{88} +(2.24048 - 4.90597i) q^{89} +5.96141 q^{91} +(2.68691 - 8.71037i) q^{92} -4.68263 q^{93} +(0.199311 + 1.38624i) q^{94} +(-7.14999 + 2.09943i) q^{96} +(-4.18210 + 4.82640i) q^{97} +(1.54642 + 0.454071i) q^{98} +(-2.66621 + 1.71347i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 100 q + 14 q^{4} - 18 q^{6} + 12 q^{9}+O(q^{10}) \) 100 * q + 14 * q^4 - 18 * q^6 + 12 * q^9	\( 100 q + 14 q^{4} - 18 q^{6} + 12 q^{9} - 26 q^{11} + 26 q^{14} - 18 q^{16} + 14 q^{19} - 22 q^{21} + 68 q^{24} - 42 q^{26} + 24 q^{29} - 12 q^{31} - 8 q^{34} - 10 q^{36} - 14 q^{39} + 8 q^{41} - 166 q^{44} - 18 q^{46} - 32 q^{49} - 22 q^{51} - 116 q^{54} - 116 q^{56} - 50 q^{59} - 38 q^{61} - 10 q^{64} - 28 q^{66} - 80 q^{69} - 110 q^{71} - 22 q^{74} + 4 q^{76} - 42 q^{79} + 204 q^{81} - 56 q^{84} + 132 q^{86} + 66 q^{89} + 76 q^{91} + 70 q^{94} + 236 q^{96} + 60 q^{99}+O(q^{100}) \) 100 * q + 14 * q^4 - 18 * q^6 + 12 * q^9 - 26 * q^11 + 26 * q^14 - 18 * q^16 + 14 * q^19 - 22 * q^21 + 68 * q^24 - 42 * q^26 + 24 * q^29 - 12 * q^31 - 8 * q^34 - 10 * q^36 - 14 * q^39 + 8 * q^41 - 166 * q^44 - 18 * q^46 - 32 * q^49 - 22 * q^51 - 116 * q^54 - 116 * q^56 - 50 * q^59 - 38 * q^61 - 10 * q^64 - 28 * q^66 - 80 * q^69 - 110 * q^71 - 22 * q^74 + 4 * q^76 - 42 * q^79 + 204 * q^81 - 56 * q^84 + 132 * q^86 + 66 * q^89 + 76 * q^91 + 70 * q^94 + 236 * q^96 + 60 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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