LMFDB - Embedded newform 800.2.y.e.301.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [800,2,Mod(101,800)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(800, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

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

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

chi := DirichletCharacter("800.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 800 = 2^{5} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	800.y (of order $8$, degree $4$, 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:	$6.38803216170$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			301.15
Character	$\chi$	$=$	800.301
Dual form			800.2.y.e.101.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.37866 + 0.315126i) q^{2} +(-1.29511 + 3.12667i) q^{3} +(1.80139 + 0.868900i) q^{4} +(-2.77080 + 3.90248i) q^{6} +(-1.02642 + 1.02642i) q^{7} +(2.20969 + 1.76558i) q^{8} +(-5.97742 - 5.97742i) q^{9} +O(q^{10})$	\(q+(1.37866 + 0.315126i) q^{2} +(-1.29511 + 3.12667i) q^{3} +(1.80139 + 0.868900i) q^{4} +(-2.77080 + 3.90248i) q^{6} +(-1.02642 + 1.02642i) q^{7} +(2.20969 + 1.76558i) q^{8} +(-5.97742 - 5.97742i) q^{9} +(0.473788 + 1.14383i) q^{11} +(-5.04976 + 4.50703i) q^{12} +(-5.17663 - 2.14423i) q^{13} +(-1.73854 + 1.09164i) q^{14} +(2.49002 + 3.13046i) q^{16} +4.22533i q^{17} +(-6.35718 - 10.1245i) q^{18} +(-3.63519 - 1.50574i) q^{19} +(-1.87996 - 4.53862i) q^{21} +(0.292743 + 1.72625i) q^{22} +(5.53379 + 5.53379i) q^{23} +(-8.38217 + 4.62234i) q^{24} +(-6.46110 - 4.58745i) q^{26} +(17.0508 - 7.06268i) q^{27} +(-2.74085 + 0.957132i) q^{28} +(0.848854 - 2.04932i) q^{29} -0.964876 q^{31} +(2.44640 + 5.10050i) q^{32} -4.18997 q^{33} +(-1.33151 + 5.82528i) q^{34} +(-5.57389 - 15.9615i) q^{36} +(-2.41056 + 0.998488i) q^{37} +(-4.53718 - 3.22145i) q^{38} +(13.4086 - 13.4086i) q^{39} +(4.62808 + 4.62808i) q^{41} +(-1.16158 - 6.84962i) q^{42} +(-0.394030 - 0.951273i) q^{43} +(-0.140393 + 2.47215i) q^{44} +(5.88536 + 9.37304i) q^{46} +2.36232i q^{47} +(-13.0128 + 3.73119i) q^{48} +4.89290i q^{49} +(-13.2112 - 5.47226i) q^{51} +(-7.46202 - 8.36058i) q^{52} +(-1.51295 - 3.65259i) q^{53} +(25.7329 - 4.36386i) q^{54} +(-4.08032 + 0.455844i) q^{56} +(9.41592 - 9.41592i) q^{57} +(1.81607 - 2.55781i) q^{58} +(-0.648566 + 0.268645i) q^{59} +(3.01738 - 7.28461i) q^{61} +(-1.33023 - 0.304057i) q^{62} +12.2708 q^{63} +(1.76545 + 7.80277i) q^{64} +(-5.77653 - 1.32037i) q^{66} +(-0.684344 + 1.65215i) q^{67} +(-3.67139 + 7.61147i) q^{68} +(-24.4692 + 10.1355i) q^{69} +(6.24109 - 6.24109i) q^{71} +(-2.65462 - 23.7619i) q^{72} +(5.70275 + 5.70275i) q^{73} +(-3.63799 + 0.616942i) q^{74} +(-5.24006 - 5.87105i) q^{76} +(-1.66036 - 0.687743i) q^{77} +(22.7113 - 14.2605i) q^{78} +14.9022i q^{79} +37.0991i q^{81} +(4.92211 + 7.83896i) q^{82} +(-3.35516 - 1.38975i) q^{83} +(0.557068 - 9.80933i) q^{84} +(-0.243462 - 1.43565i) q^{86} +(5.30817 + 5.30817i) q^{87} +(-0.972592 + 3.36401i) q^{88} +(-9.90375 + 9.90375i) q^{89} +(7.51432 - 3.11253i) q^{91} +(5.16021 + 14.7768i) q^{92} +(1.24962 - 3.01685i) q^{93} +(-0.744427 + 3.25683i) q^{94} +(-19.1159 + 1.04338i) q^{96} -13.1798 q^{97} +(-1.54188 + 6.74564i) q^{98} +(4.00510 - 9.66916i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q+O(q^{10}) $ 64 * q	$ 64 q - 16 q^{14} + 20 q^{16} + 20 q^{18} - 4 q^{22} + 8 q^{23} - 28 q^{24} + 24 q^{27} - 20 q^{28} - 20 q^{32} - 20 q^{34} + 12 q^{36} - 20 q^{38} + 24 q^{39} - 100 q^{42} + 8 q^{43} + 40 q^{44} + 32 q^{46} + 16 q^{51} - 88 q^{52} - 32 q^{53} + 76 q^{54} + 48 q^{56} + 72 q^{58} + 32 q^{59} - 32 q^{61} - 48 q^{62} + 80 q^{63} + 48 q^{64} + 16 q^{66} - 40 q^{67} + 48 q^{68} - 32 q^{69} + 32 q^{71} - 36 q^{72} + 8 q^{74} + 16 q^{77} + 36 q^{78} + 40 q^{83} + 56 q^{84} - 84 q^{86} - 40 q^{88} + 48 q^{91} + 4 q^{92} + 32 q^{94} - 100 q^{96} - 40 q^{98} - 64 q^{99}+O(q^{100}) $ 64 * q - 16 * q^14 + 20 * q^16 + 20 * q^18 - 4 * q^22 + 8 * q^23 - 28 * q^24 + 24 * q^27 - 20 * q^28 - 20 * q^32 - 20 * q^34 + 12 * q^36 - 20 * q^38 + 24 * q^39 - 100 * q^42 + 8 * q^43 + 40 * q^44 + 32 * q^46 + 16 * q^51 - 88 * q^52 - 32 * q^53 + 76 * q^54 + 48 * q^56 + 72 * q^58 + 32 * q^59 - 32 * q^61 - 48 * q^62 + 80 * q^63 + 48 * q^64 + 16 * q^66 - 40 * q^67 + 48 * q^68 - 32 * q^69 + 32 * q^71 - 36 * q^72 + 8 * q^74 + 16 * q^77 + 36 * q^78 + 40 * q^83 + 56 * q^84 - 84 * q^86 - 40 * q^88 + 48 * q^91 + 4 * q^92 + 32 * q^94 - 100 * q^96 - 40 * q^98 - 64 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/800\mathbb{Z}\right)^\times$.

$n$	$101$	$351$	$577$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$1$	$1$

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 $

$2$	1.37866	+	0.315126i	0.974858	+	0.222827i
$2$	1.37866	+	0.315126i	0.974858	+	0.222827i
$3$	−1.29511	+	3.12667i	−0.747731	+	1.80518i	−0.176678	+	0.984269i	$0.556535\pi$
$3$	−1.29511	+	3.12667i	−0.747731	+	1.80518i	−0.571053	+	0.820913i	$0.693465\pi$
$4$	1.80139	+	0.868900i	0.900696	+	0.434450i
$5$		0			0
$5$		0			0
$6$	−2.77080	+	3.90248i	−1.13118	+	1.59318i
$7$	−1.02642	+	1.02642i	−0.387952	+	0.387952i	−0.873956	−	0.486004i	$-0.838454\pi$
$7$	−1.02642	+	1.02642i	−0.387952	+	0.387952i	0.486004	+	0.873956i	$0.338454\pi$
$8$	2.20969	+	1.76558i	0.781243	+	0.624227i
$9$	−5.97742	−	5.97742i	−1.99247	−	1.99247i
$10$		0			0
$11$	0.473788	+	1.14383i	0.142853	+	0.344876i	0.979071	−	0.203520i	$-0.0652383\pi$
$11$	0.473788	+	1.14383i	0.142853	+	0.344876i	−0.836218	+	0.548397i	$0.815238\pi$
$12$	−5.04976	+	4.50703i	−1.45774	+	1.30107i
$13$	−5.17663	−	2.14423i	−1.43574	−	0.594703i	−0.476979	−	0.878915i	$-0.658268\pi$
$13$	−5.17663	−	2.14423i	−1.43574	−	0.594703i	−0.958761	+	0.284212i	$0.908268\pi$
$14$	−1.73854	+	1.09164i	−0.464645	+	0.291752i
$15$		0			0
$16$	2.49002	+	3.13046i	0.622506	+	0.782615i
$17$			4.22533i			1.02479i	0.858749	+	0.512396i	$0.171242\pi$
$17$			4.22533i			1.02479i	−0.858749	+	0.512396i	$0.828758\pi$
$18$	−6.35718	−	10.1245i	−1.49840	−	2.38636i
$19$	−3.63519	−	1.50574i	−0.833969	−	0.345441i	−0.0754966	−	0.997146i	$-0.524054\pi$
$19$	−3.63519	−	1.50574i	−0.833969	−	0.345441i	−0.758473	+	0.651705i	$0.774054\pi$
$20$		0			0
$21$	−1.87996	−	4.53862i	−0.410240	−	0.990408i
$22$	0.292743	+	1.72625i	0.0624130	+	0.368037i
$23$	5.53379	+	5.53379i	1.15388	+	1.15388i	0.985769	+	0.168107i	$0.0537653\pi$
$23$	5.53379	+	5.53379i	1.15388	+	1.15388i	0.168107	+	0.985769i	$0.446235\pi$
$24$	−8.38217	+	4.62234i	−1.71100	+	0.943532i
$25$		0			0
$26$	−6.46110	−	4.58745i	−1.26713	−	0.899673i
$27$	17.0508	−	7.06268i	3.28143	−	1.35921i
$28$	−2.74085	+	0.957132i	−0.517973	+	0.180881i
$29$	0.848854	−	2.04932i	0.157628	−	0.380548i	−0.825259	−	0.564754i	$-0.808971\pi$
$29$	0.848854	−	2.04932i	0.157628	−	0.380548i	0.982888	+	0.184205i	$0.0589711\pi$
$30$		0			0
$31$	−0.964876			−0.173297			−0.0866484	−	0.996239i	$-0.527616\pi$
$31$	−0.964876			−0.173297			−0.0866484	+	0.996239i	$0.527616\pi$
$32$	2.44640	+	5.10050i	0.432467	+	0.901650i
$33$	−4.18997			−0.729380
$34$	−1.33151	+	5.82528i	−0.228352	+	0.999027i
$35$		0			0
$36$	−5.57389	−	15.9615i	−0.928982	−	2.66024i
$37$	−2.41056	+	0.998488i	−0.396294	+	0.164150i	−0.571925	−	0.820306i	$-0.693803\pi$
$37$	−2.41056	+	0.998488i	−0.396294	+	0.164150i	0.175631	+	0.984456i	$0.443803\pi$
$38$	−4.53718	−	3.22145i	−0.736028	−	0.522588i
$39$	13.4086	−	13.4086i	2.14709	−	2.14709i
$40$		0			0
$41$	4.62808	+	4.62808i	0.722785	+	0.722785i	0.969172	−	0.246387i	$-0.0792434\pi$
$41$	4.62808	+	4.62808i	0.722785	+	0.722785i	−0.246387	+	0.969172i	$0.579243\pi$
$42$	−1.16158	−	6.84962i	−0.179236	−	1.05692i
$43$	−0.394030	−	0.951273i	−0.0600890	−	0.145068i	0.890983	−	0.454036i	$-0.150016\pi$
$43$	−0.394030	−	0.951273i	−0.0600890	−	0.145068i	−0.951072	+	0.308968i	$0.900016\pi$
$44$	−0.140393	+	2.47215i	−0.0211650	+	0.372691i
$45$		0			0
$46$	5.88536	+	9.37304i	0.867750	+	1.38198i
$47$			2.36232i			0.344580i	0.985046	+	0.172290i	$0.0551166\pi$
$47$			2.36232i			0.344580i	−0.985046	+	0.172290i	$0.944883\pi$
$48$	−13.0128	+	3.73119i	−1.87823	+	0.538551i
$49$			4.89290i			0.698986i
$50$		0			0
$51$	−13.2112	−	5.47226i	−1.84994	−	0.766269i
$52$	−7.46202	−	8.36058i	−1.03480	−	1.15940i
$53$	−1.51295	−	3.65259i	−0.207820	−	0.501722i	0.785259	−	0.619167i	$-0.212530\pi$
$53$	−1.51295	−	3.65259i	−0.207820	−	0.501722i	−0.993079	+	0.117445i	$0.962530\pi$
$54$	25.7329	−	4.36386i	3.50180	−	0.593847i
$55$		0			0
$56$	−4.08032	+	0.455844i	−0.545255	+	0.0609147i
$57$	9.41592	−	9.41592i	1.24717	−	1.24717i
$58$	1.81607	−	2.55781i	0.238462	−	0.335857i
$59$	−0.648566	+	0.268645i	−0.0844361	+	0.0349746i	−0.424502	−	0.905427i	$-0.639551\pi$
$59$	−0.648566	+	0.268645i	−0.0844361	+	0.0349746i	0.340066	+	0.940402i	$0.389551\pi$
$60$		0			0
$61$	3.01738	−	7.28461i	0.386336	−	0.932698i	−0.604373	−	0.796701i	$-0.706576\pi$
$61$	3.01738	−	7.28461i	0.386336	−	0.932698i	0.990709	−	0.135997i	$-0.0434237\pi$
$62$	−1.33023	−	0.304057i	−0.168940	−	0.0386153i
$63$	12.2708			1.54597
$64$	1.76545	+	7.80277i	0.220681	+	0.975346i
$65$		0			0
$66$	−5.77653	−	1.32037i	−0.711042	−	0.162526i
$67$	−0.684344	+	1.65215i	−0.0836059	+	0.201843i	−0.960154	−	0.279472i	$-0.909841\pi$
$67$	−0.684344	+	1.65215i	−0.0836059	+	0.201843i	0.876548	+	0.481315i	$0.159841\pi$
$68$	−3.67139	+	7.61147i	−0.445222	+	0.923027i
$69$	−24.4692	+	10.1355i	−2.94574	+	1.22017i
$70$		0			0
$71$	6.24109	−	6.24109i	0.740681	−	0.740681i	−0.232028	−	0.972709i	$-0.574536\pi$
$71$	6.24109	−	6.24109i	0.740681	−	0.740681i	0.972709	+	0.232028i	$0.0745362\pi$
$72$	−2.65462	−	23.7619i	−0.312850	−	2.80036i
$73$	5.70275	+	5.70275i	0.667457	+	0.667457i	0.957127	−	0.289670i	$-0.0935455\pi$
$73$	5.70275	+	5.70275i	0.667457	+	0.667457i	−0.289670	+	0.957127i	$0.593546\pi$
$74$	−3.63799	+	0.616942i	−0.422908	+	0.0717181i
$75$		0			0
$76$	−5.24006	−	5.87105i	−0.601076	−	0.673456i
$77$	−1.66036	−	0.687743i	−0.189216	−	0.0783756i
$78$	22.7113	−	14.2605i	2.57154	−	1.61468i
$79$			14.9022i			1.67663i	0.545186	+	0.838315i	$0.316459\pi$
$79$			14.9022i			1.67663i	−0.545186	+	0.838315i	$0.683541\pi$
$80$		0			0
$81$			37.0991i			4.12212i
$82$	4.92211	+	7.83896i	0.543556	+	0.865669i
$83$	−3.35516	−	1.38975i	−0.368277	−	0.152545i	0.190867	−	0.981616i	$-0.438870\pi$
$83$	−3.35516	−	1.38975i	−0.368277	−	0.152545i	−0.559144	+	0.829071i	$0.688870\pi$
$84$	0.557068	−	9.80933i	0.0607811	−	1.07029i
$85$		0			0
$86$	−0.243462	−	1.43565i	−0.0262532	−	0.154810i
$87$	5.30817	+	5.30817i	0.569096	+	0.569096i
$88$	−0.972592	+	3.36401i	−0.103679	+	0.358605i
$89$	−9.90375	+	9.90375i	−1.04980	+	1.04980i	−0.0511025	+	0.998693i	$0.516274\pi$
$89$	−9.90375	+	9.90375i	−1.04980	+	1.04980i	−0.998693	+	0.0511025i	$0.983726\pi$
$90$		0			0
$91$	7.51432	−	3.11253i	0.787715	−	0.326282i
$92$	5.16021	+	14.7768i	0.537989	+	1.54059i
$93$	1.24962	−	3.01685i	0.129579	−	0.312832i
$94$	−0.744427	+	3.25683i	−0.0767818	+	0.335916i
$95$		0			0
$96$	−19.1159	+	1.04338i	−1.95101	+	0.106490i
$97$	−13.1798			−1.33820			−0.669101	−	0.743171i	$-0.733321\pi$
$97$	−13.1798			−1.33820			−0.669101	+	0.743171i	$0.733321\pi$
$98$	−1.54188	+	6.74564i	−0.155753	+	0.681412i
$99$	4.00510	−	9.66916i	0.402528	−	0.971787i
$100$		0			0
$101$	3.67079	−	1.52049i	0.365257	−	0.151295i	−0.192503	−	0.981296i	$-0.561661\pi$
$101$	3.67079	−	1.52049i	0.365257	−	0.151295i	0.557761	+	0.830002i	$0.311661\pi$
$102$	−16.4893	−	11.7076i	−1.63268	−	1.15922i
$103$	5.18393	−	5.18393i	0.510788	−	0.510788i	−0.403980	−	0.914768i	$-0.632374\pi$
$103$	5.18393	−	5.18393i	0.510788	−	0.510788i	0.914768	+	0.403980i	$0.132374\pi$
$104$	−7.65294	−	13.8779i	−0.750432	−	1.36084i
$105$		0			0
$106$	−0.934818	−	5.51244i	−0.0907975	−	0.535415i
$107$	4.27693	+	10.3254i	0.413467	+	0.998197i	0.984200	+	0.177061i	$0.0566590\pi$
$107$	4.27693	+	10.3254i	0.413467	+	0.998197i	−0.570733	+	0.821136i	$0.693341\pi$
$108$	36.8520	+	2.09281i	3.54608	+	0.201381i
$109$	12.7925	+	5.29882i	1.22530	+	0.507534i	0.899090	−	0.437764i	$-0.144229\pi$
$109$	12.7925	+	5.29882i	1.22530	+	0.507534i	0.326207	+	0.945298i	$0.394229\pi$
$110$		0			0
$111$		−	8.83018i		−	0.838123i
$112$	−5.76901	−	0.657360i	−0.545120	−	0.0621146i
$113$		−	6.33910i		−	0.596332i	−0.954514	−	0.298166i	$-0.903625\pi$
$113$		−	6.33910i		−	0.596332i	0.954514	−	0.298166i	$-0.0963750\pi$
$114$	15.9485	−	10.0141i	1.49372	−	0.937909i
$115$		0			0
$116$	3.30977	−	2.95405i	0.307305	−	0.274277i
$117$	18.1259	+	43.7599i	1.67574	+	4.04561i
$118$	−0.978807	+	0.165989i	−0.0901065	+	0.0152806i
$119$	−4.33698	−	4.33698i	−0.397571	−	0.397571i
$120$		0			0
$121$	6.69431	−	6.69431i	0.608574	−	0.608574i
$122$	6.45550	−	9.09212i	0.584454	−	0.823162i
$123$	−20.4643	+	8.47660i	−1.84521	+	0.764310i
$124$	−1.73812	−	0.838381i	−0.156088	−	0.0752888i
$125$		0			0
$126$	16.9172	+	3.86683i	1.50710	+	0.344484i
$127$	11.3243			1.00487			0.502435	−	0.864615i	$-0.332438\pi$
$127$	11.3243			1.00487			0.502435	+	0.864615i	$0.332438\pi$
$128$	−0.0249011	+	11.3137i	−0.00220097	+	0.999998i
$129$	3.48462			0.306804
$130$		0			0
$131$	−2.92584	+	7.06361i	−0.255632	+	0.617151i	−0.998640	−	0.0521319i	$-0.983398\pi$
$131$	−2.92584	+	7.06361i	−0.255632	+	0.617151i	0.743008	+	0.669282i	$0.233398\pi$
$132$	−7.54778	−	3.64067i	−0.656950	−	0.316879i
$133$	5.27678	−	2.18571i	0.457555	−	0.189526i
$134$	−1.46411	+	2.06210i	−0.126480	+	0.178138i
$135$		0			0
$136$	−7.46016	+	9.33666i	−0.639703	+	0.800612i
$137$	−9.25823	−	9.25823i	−0.790984	−	0.790984i	0.190670	−	0.981654i	$-0.438934\pi$
$137$	−9.25823	−	9.25823i	−0.790984	−	0.790984i	−0.981654	+	0.190670i	$0.938934\pi$
$138$	−36.9286	+	6.26247i	−3.14357	+	0.533097i
$139$	−0.956760	−	2.30982i	−0.0811513	−	0.195917i	0.878096	−	0.478485i	$-0.158814\pi$
$139$	−0.956760	−	2.30982i	−0.0811513	−	0.195917i	−0.959247	+	0.282568i	$0.908814\pi$
$140$		0			0
$141$	−7.38619	−	3.05946i	−0.622029	−	0.257653i
$142$	10.5710	−	6.63759i	0.887102	−	0.557014i
$143$		−	6.93708i		−	0.580108i
$144$	3.82816	−	33.5960i	0.319013	−	2.79967i
$145$		0			0
$146$	6.06506	+	9.65922i	0.501948	+	0.799403i
$147$	−15.2985	−	6.33684i	−1.26180	−	0.522654i
$148$	−5.20996	−	0.295872i	−0.428256	−	0.0243205i
$149$	−7.06329	−	17.0523i	−0.578647	−	1.39698i	−0.894027	−	0.448012i	$-0.852132\pi$
$149$	−7.06329	−	17.0523i	−0.578647	−	1.39698i	0.315380	−	0.948965i	$-0.397868\pi$
$150$		0			0
$151$	13.2469	+	13.2469i	1.07802	+	1.07802i	0.996687	+	0.0813322i	$0.0259175\pi$
$151$	13.2469	+	13.2469i	1.07802	+	1.07802i	0.0813322	+	0.996687i	$0.474083\pi$
$152$	−5.37412	−	9.74545i	−0.435899	−	0.790460i
$153$	25.2566	−	25.2566i	2.04187	−	2.04187i
$154$	−2.07234	−	1.47138i	−0.166994	−	0.118568i
$155$		0			0
$156$	35.8049	−	12.5034i	2.86668	−	1.00107i
$157$	−4.36271	+	10.5325i	−0.348182	+	0.840586i	0.648652	+	0.761085i	$0.275333\pi$
$157$	−4.36271	+	10.5325i	−0.348182	+	0.840586i	−0.996835	+	0.0795017i	$0.974667\pi$
$158$	−4.69607	+	20.5451i	−0.373599	+	1.63448i
$159$	13.3799			1.06109
$160$		0			0
$161$	−11.3600			−0.895297
$162$	−11.6909	+	51.1469i	−0.918522	+	4.01848i
$163$	−4.95082	+	11.9523i	−0.387778	+	0.936179i	0.602632	+	0.798019i	$0.294119\pi$
$163$	−4.95082	+	11.9523i	−0.387778	+	0.936179i	−0.990410	+	0.138160i	$0.955881\pi$
$164$	4.31564	+	12.3583i	0.336995	+	0.965023i
$165$		0			0
$166$	−4.18767	−	2.97329i	−0.325026	−	0.230772i
$167$	−6.45942	+	6.45942i	−0.499845	+	0.499845i	−0.911390	−	0.411545i	$-0.864989\pi$
$167$	−6.45942	+	6.45942i	−0.499845	+	0.499845i	0.411545	+	0.911390i	$0.364989\pi$
$168$	3.85918	−	13.3482i	0.297742	−	1.02983i
$169$	13.0074	+	13.0074i	1.00057	+	1.00057i
$170$		0			0
$171$	12.7286	+	30.7295i	0.973379	+	2.34995i
$172$	0.116759	−	2.05599i	0.00890278	−	0.156768i
$173$	11.6647	+	4.83167i	0.886849	+	0.367345i	0.779149	−	0.626838i	$-0.215651\pi$
$173$	11.6647	+	4.83167i	0.886849	+	0.367345i	0.107700	+	0.994183i	$0.465651\pi$
$174$	5.64541	+	8.99089i	0.427977	+	0.681598i
$175$		0			0
$176$	−2.40096	+	4.33133i	−0.180979	+	0.326486i
$177$		−	2.37577i		−	0.178574i
$178$	−16.7748	+	10.5330i	−1.25733	+	0.789478i
$179$	1.39173	+	0.576474i	0.104023	+	0.0430877i	0.434088	−	0.900870i	$-0.357071\pi$
$179$	1.39173	+	0.576474i	0.104023	+	0.0430877i	−0.330065	+	0.943958i	$0.607071\pi$
$180$		0			0
$181$	−0.941575	−	2.27316i	−0.0699867	−	0.168963i	0.885016	−	0.465562i	$-0.154148\pi$
$181$	−0.941575	−	2.27316i	−0.0699867	−	0.168963i	−0.955002	+	0.296599i	$0.904148\pi$
$182$	11.3405	−	1.92316i	0.840615	−	0.142554i
$183$	18.8687	+	18.8687i	1.39481	+	1.39481i
$184$	2.45760	+	21.9983i	0.181177	+	1.62174i
$185$		0			0
$186$	2.67348	−	3.76541i	0.196029	−	0.276093i
$187$	−4.83304	+	2.00191i	−0.353427	+	0.146394i
$188$	−2.05262	+	4.25546i	−0.149703	+	0.310362i
$189$	−10.2521	+	24.7507i	−0.745729	+	1.80035i
$190$		0			0
$191$	15.0923			1.09204			0.546020	−	0.837772i	$-0.316142\pi$
$191$	15.0923			1.09204			0.546020	+	0.837772i	$0.316142\pi$
$192$	−26.6831	−	4.58545i	−1.92569	−	0.330926i
$193$	2.95918			0.213007			0.106503	−	0.994312i	$-0.466035\pi$
$193$	2.95918			0.213007			0.106503	+	0.994312i	$0.466035\pi$
$194$	−18.1704	−	4.15328i	−1.30456	−	0.298188i
$195$		0			0
$196$	−4.25145	+	8.81404i	−0.303675	+	0.629574i
$197$	12.4136	−	5.14189i	0.884433	−	0.366344i	0.106219	−	0.994343i	$-0.466126\pi$
$197$	12.4136	−	5.14189i	0.884433	−	0.366344i	0.778215	+	0.627998i	$0.216126\pi$
$198$	8.56866	−	12.0684i	0.608948	−	0.857660i
$199$	7.68494	−	7.68494i	0.544771	−	0.544771i	−0.380153	−	0.924924i	$-0.624129\pi$
$199$	7.68494	−	7.68494i	0.544771	−	0.544771i	0.924924	+	0.380153i	$0.124129\pi$
$200$		0			0
$201$	−4.27943	−	4.27943i	−0.301848	−	0.301848i
$202$	5.53991	−	0.939476i	0.389787	−	0.0661013i
$203$	1.23218	+	2.97475i	0.0864823	+	0.208787i
$204$	−19.0437	−	21.3369i	−1.33333	−	1.49388i
$205$		0			0
$206$	8.78045	−	5.51327i	0.611763	−	0.384128i
$207$		−	66.1556i		−	4.59813i
$208$	−6.17751	−	21.5444i	−0.428333	−	1.49384i
$209$		−	4.87143i		−	0.336964i
$210$		0			0
$211$	−3.07097	−	1.27204i	−0.211414	−	0.0875707i	0.274463	−	0.961598i	$-0.411500\pi$
$211$	−3.07097	−	1.27204i	−0.211414	−	0.0875707i	−0.485877	+	0.874027i	$0.661500\pi$
$212$	0.448317	−	7.89435i	0.0307906	−	0.542186i
$213$	11.4309	+	27.5967i	0.783234	+	1.89089i
$214$	2.64262	+	15.5830i	0.180646	+	1.06523i
$215$		0			0
$216$	50.1467	+	14.4983i	3.41205	+	0.986482i
$217$	0.990373	−	0.990373i	0.0672309	−	0.0672309i
$218$	15.9666	+	11.3365i	1.08140	+	0.767804i
$219$	−25.2163	+	10.4449i	−1.70396	+	0.705803i
$220$		0			0
$221$	9.06009	−	21.8730i	0.609447	−	1.47134i
$222$	2.78262	−	12.1738i	0.186757	−	0.817051i
$223$	−23.3670			−1.56477			−0.782384	−	0.622796i	$-0.785996\pi$
$223$	−23.3670			−1.56477			−0.782384	+	0.622796i	$0.785996\pi$
$224$	−7.74633	−	2.72423i	−0.517573	−	0.182021i
$225$		0			0
$226$	1.99761	−	8.73945i	0.132879	−	0.581339i
$227$	−4.22308	+	10.1954i	−0.280295	+	0.676693i	−0.999842	−	0.0177508i	$-0.994349\pi$
$227$	−4.22308	+	10.1954i	−0.280295	+	0.676693i	0.719547	+	0.694444i	$0.244349\pi$
$228$	25.1433	−	8.78027i	1.66515	−	0.581487i
$229$	16.7615	−	6.94283i	1.10763	−	0.458795i	0.247509	−	0.968886i	$-0.420388\pi$
$229$	16.7615	−	6.94283i	1.10763	−	0.458795i	0.860121	+	0.510090i	$0.170388\pi$
$230$		0			0
$231$	4.30069	−	4.30069i	0.282965	−	0.282965i
$232$	5.49394	−	3.02963i	0.360695	−	0.198905i
$233$	−19.1508	−	19.1508i	−1.25461	−	1.25461i	−0.953631	−	0.300978i	$-0.902687\pi$
$233$	−19.1508	−	19.1508i	−1.25461	−	1.25461i	−0.300978	−	0.953631i	$-0.597313\pi$
$234$	11.1996	+	66.0419i	0.732141	+	4.31729i
$235$		0			0
$236$	−1.40175	−	0.0796047i	−0.0912460	−	0.00518183i
$237$	−46.5943	−	19.3000i	−3.02662	−	1.25367i
$238$	−4.61252	−	7.34591i	−0.298985	−	0.476165i
$239$		−	19.5640i		−	1.26549i	−0.774360	−	0.632745i	$-0.781928\pi$
$239$		−	19.5640i		−	1.26549i	0.774360	−	0.632745i	$-0.218072\pi$
$240$		0			0
$241$		−	4.63126i		−	0.298325i	−0.988813	−	0.149163i	$-0.952342\pi$
$241$		−	4.63126i		−	0.298325i	0.988813	−	0.149163i	$-0.0476578\pi$
$242$	11.3387	−	7.11961i	0.728880	−	0.457666i
$243$	−64.8441	−	26.8593i	−4.15975	−	1.72302i
$244$	11.7651	−	10.5006i	0.753182	−	0.672233i
$245$		0			0
$246$	−30.8845	+	5.23750i	−1.96912	+	0.333931i
$247$	15.5894	+	15.5894i	0.991928	+	0.991928i
$248$	−2.13208	−	1.70357i	−0.135387	−	0.108177i
$249$	8.69060	−	8.69060i	0.550744	−	0.550744i
$250$		0			0
$251$	10.7556	−	4.45513i	0.678890	−	0.281205i	−0.0164729	−	0.999864i	$-0.505244\pi$
$251$	10.7556	−	4.45513i	0.678890	−	0.281205i	0.695363	+	0.718659i	$0.255244\pi$
$252$	22.1044	+	10.6621i	1.39245	+	0.671647i
$253$	−3.70785	+	8.95154i	−0.233111	+	0.562779i
$254$	15.6123	+	3.56858i	0.979605	+	0.223913i
$255$		0			0
$256$	−3.59956	+	15.5898i	−0.224973	+	0.974365i
$257$	−4.04829			−0.252525			−0.126263	−	0.991997i	$-0.540298\pi$
$257$	−4.04829			−0.252525			−0.126263	+	0.991997i	$0.540298\pi$
$258$	4.80410	+	1.09809i	0.299090	+	0.0683644i
$259$	1.44939	−	3.49914i	0.0900607	−	0.217426i
$260$		0			0
$261$	−17.3236	+	7.17567i	−1.07230	+	0.444163i
$262$	−6.25966	+	8.81629i	−0.386723	+	0.544672i
$263$	1.60540	−	1.60540i	0.0989933	−	0.0989933i	−0.655876	−	0.754869i	$-0.727700\pi$
$263$	1.60540	−	1.60540i	0.0989933	−	0.0989933i	0.754869	+	0.655876i	$0.227700\pi$
$264$	−9.25853	−	7.39773i	−0.569823	−	0.455299i
$265$		0			0
$266$	7.96365	−	1.35050i	0.488283	−	0.0828046i
$267$	−18.1393	−	43.7922i	−1.11011	−	2.68004i
$268$	−2.66833	+	2.38155i	−0.162994	+	0.145476i
$269$	3.38365	+	1.40155i	0.206305	+	0.0854542i	0.483443	−	0.875376i	$-0.339386\pi$
$269$	3.38365	+	1.40155i	0.206305	+	0.0854542i	−0.277138	+	0.960830i	$0.589386\pi$
$270$		0			0
$271$		−	22.4256i		−	1.36226i	−0.732165	−	0.681128i	$-0.761490\pi$
$271$		−	22.4256i		−	1.36226i	0.732165	−	0.681128i	$-0.238510\pi$
$272$	−13.2272	+	10.5212i	−0.802018	+	0.637940i
$273$			27.5258i			1.66594i
$274$	−9.84642	−	15.6814i	−0.594844	−	0.947350i
$275$		0			0
$276$	−52.8853	−	3.00334i	−3.18332	−	0.180780i
$277$	−2.20449	−	5.32210i	−0.132455	−	0.319774i	0.843712	−	0.536796i	$-0.180366\pi$
$277$	−2.20449	−	5.32210i	−0.132455	−	0.319774i	−0.976167	+	0.217022i	$0.930366\pi$
$278$	−0.591160	−	3.48595i	−0.0354554	−	0.209074i
$279$	5.76747	+	5.76747i	0.345289	+	0.345289i
$280$		0			0
$281$	1.81582	−	1.81582i	0.108323	−	0.108323i	−0.650868	−	0.759191i	$-0.725595\pi$
$281$	1.81582	−	1.81582i	0.108323	−	0.108323i	0.759191	+	0.650868i	$0.225595\pi$
$282$	−9.21891	−	6.54552i	−0.548978	−	0.389780i
$283$	15.2115	−	6.30082i	0.904232	−	0.374545i	0.118386	−	0.992968i	$-0.462228\pi$
$283$	15.2115	−	6.30082i	0.904232	−	0.374545i	0.785846	+	0.618423i	$0.212228\pi$
$284$	16.6655	−	5.81976i	0.988917	−	0.345339i
$285$		0			0
$286$	2.18605	−	9.56386i	0.129264	−	0.565523i
$287$	−9.50075			−0.560812
$288$	15.8647	−	45.1110i	0.934835	−	2.65819i
$289$	−0.853410			−0.0502006
$290$		0			0
$291$	17.0692	−	41.2087i	1.00062	−	2.41570i
$292$	5.31777	+	15.2280i	0.311199	+	0.891152i
$293$	−15.7830	+	6.53752i	−0.922051	+	0.381926i	−0.792658	−	0.609667i	$-0.791303\pi$
$293$	−15.7830	+	6.53752i	−0.922051	+	0.381926i	−0.129394	+	0.991593i	$0.541303\pi$
$294$	−19.0945	−	13.5573i	−1.11361	−	0.790676i
$295$		0			0
$296$	−7.08951	−	2.04970i	−0.412069	−	0.119136i
$297$	16.1569	+	16.1569i	0.937521	+	0.937521i
$298$	−4.36424	−	25.7351i	−0.252814	−	1.49079i
$299$	−16.7807	−	40.5122i	−0.970452	−	2.34288i
$300$		0			0
$301$	1.38085	+	0.571968i	0.0795910	+	0.0329677i
$302$	14.0885	+	22.4374i	0.810703	+	1.29113i
$303$			13.4465i			0.772484i
$304$	−4.33803	−	15.1292i	−0.248803	−	0.867716i
$305$		0			0
$306$	42.7792	−	26.8612i	2.44552	−	1.53555i
$307$	−0.490845	−	0.203315i	−0.0280140	−	0.0116038i	0.368632	−	0.929575i	$-0.379826\pi$
$307$	−0.490845	−	0.203315i	−0.0280140	−	0.0116038i	−0.396646	+	0.917971i	$0.629826\pi$
$308$	−2.39338	−	2.68158i	−0.136375	−	0.152797i
$309$	9.49467	+	22.9222i	0.540133	+	1.30400i
$310$		0			0
$311$	2.66343	+	2.66343i	0.151029	+	0.151029i	0.778578	−	0.627548i	$-0.215942\pi$
$311$	2.66343	+	2.66343i	0.151029	+	0.151029i	−0.627548	+	0.778578i	$0.715942\pi$
$312$	53.3028	−	5.95487i	3.01768	−	0.337128i
$313$	13.7553	−	13.7553i	0.777493	−	0.777493i	−0.201911	−	0.979404i	$-0.564715\pi$
$313$	13.7553	−	13.7553i	0.777493	−	0.777493i	0.979404	+	0.201911i	$0.0647150\pi$
$314$	−9.33375	+	13.1459i	−0.526734	+	0.741868i
$315$		0			0
$316$	−12.9485	+	26.8447i	−0.728413	+	1.51013i
$317$	8.28931	−	20.0122i	0.465574	−	1.12399i	−0.500502	−	0.865736i	$-0.666851\pi$
$317$	8.28931	−	20.0122i	0.465574	−	1.12399i	0.966076	−	0.258259i	$-0.0831489\pi$
$318$	18.4462	+	4.21634i	1.03441	+	0.236440i
$319$	2.74624			0.153760
$320$		0			0
$321$	−37.8233			−2.11109
$322$	−15.6616	−	3.57984i	−0.872787	−	0.199497i
$323$	6.36227	−	15.3599i	0.354006	−	0.854646i
$324$	−32.2354	+	66.8300i	−1.79086	+	3.71278i
$325$		0			0
$326$	−10.5920	+	14.9180i	−0.586635	+	0.826234i
$327$	−33.1353	+	33.1353i	−1.83238	+	1.83238i
$328$	2.05537	+	18.3979i	0.113489	+	1.01585i
$329$	−2.42474	−	2.42474i	−0.133680	−	0.133680i
$330$		0			0
$331$	−3.45036	−	8.32990i	−0.189649	−	0.457853i	0.800243	−	0.599675i	$-0.204704\pi$
$331$	−3.45036	−	8.32990i	−0.189649	−	0.457853i	−0.989892	+	0.141823i	$0.954704\pi$
$332$	−4.83641	−	5.41879i	−0.265432	−	0.297395i
$333$	20.3773	+	8.44057i	1.11667	+	0.462540i
$334$	−10.9409	+	6.86980i	−0.598657	+	0.375899i
$335$		0			0
$336$	9.52683	−	17.1864i	0.519731	−	0.937595i
$337$		−	12.2658i		−	0.668162i	−0.942544	−	0.334081i	$-0.891574\pi$
$337$		−	12.2658i		−	0.668162i	0.942544	−	0.334081i	$-0.108426\pi$
$338$	13.8338	+	22.0318i	0.752460	+	1.19837i
$339$	19.8203	+	8.20982i	1.07649	+	0.445896i
$340$		0			0
$341$	−0.457147	−	1.10365i	−0.0247559	−	0.0597660i
$342$	7.86470	+	46.3766i	0.425274	+	2.50776i
$343$	−12.2072	−	12.2072i	−0.659125	−	0.659125i
$344$	0.808865	−	2.79771i	0.0436111	−	0.150842i
$345$		0			0
$346$	14.5590	+	10.3371i	0.782698	+	0.555724i
$347$	16.2433	−	6.72820i	0.871987	−	0.361189i	0.0986033	−	0.995127i	$-0.468563\pi$
$347$	16.2433	−	6.72820i	0.871987	−	0.361189i	0.773384	+	0.633938i	$0.218563\pi$
$348$	4.94982	+	14.1744i	0.265338	+	0.759826i
$349$	−10.6274	+	25.6568i	−0.568871	+	1.37338i	0.333636	+	0.942702i	$0.391725\pi$
$349$	−10.6274	+	25.6568i	−0.568871	+	1.37338i	−0.902507	+	0.430675i	$0.858275\pi$
$350$		0			0
$351$	−103.410			−5.51961
$352$	−4.67501	+	5.21481i	−0.249179	+	0.277951i
$353$	21.9232			1.16686			0.583428	−	0.812165i	$-0.301711\pi$
$353$	21.9232			1.16686			0.583428	+	0.812165i	$0.301711\pi$
$354$	0.748667	−	3.27538i	0.0397912	−	0.174084i
$355$		0			0
$356$	−26.4459	+	9.23516i	−1.40163	+	0.489463i
$357$	19.1772	−	7.94344i	1.01496	−	0.420412i
$358$	1.73706	+	1.23333i	0.0918064	+	0.0651835i
$359$	4.02137	−	4.02137i	0.212240	−	0.212240i	−0.592978	−	0.805218i	$-0.702048\pi$
$359$	4.02137	−	4.02137i	0.212240	−	0.212240i	0.805218	+	0.592978i	$0.202048\pi$
$360$		0			0
$361$	−2.48770	−	2.48770i	−0.130931	−	0.130931i
$362$	−0.581777	−	3.43063i	−0.0305775	−	0.180310i
$363$	12.2610	+	29.6007i	0.643537	+	1.55364i
$364$	16.2407	+	0.922305i	0.851245	+	0.0483419i
$365$		0			0
$366$	20.0675	+	31.9595i	1.04894	+	1.67055i
$367$			28.1923i			1.47163i	0.677183	+	0.735814i	$0.263200\pi$
$367$			28.1923i			1.47163i	−0.677183	+	0.735814i	$0.736800\pi$
$368$	−3.54404	+	31.1026i	−0.184746	+	1.62133i
$369$		−	55.3280i		−	2.88026i
$370$		0			0
$371$	5.30204	+	2.19618i	0.275268	+	0.114020i
$372$	4.87239	−	4.34873i	0.252622	−	0.225471i
$373$	−0.472600	−	1.14096i	−0.0244703	−	0.0590765i	0.911172	−	0.412026i	$-0.135179\pi$
$373$	−0.472600	−	1.14096i	−0.0244703	−	0.0590765i	−0.935642	+	0.352950i	$0.885179\pi$
$374$	−7.29396	+	1.23693i	−0.377162	+	0.0639604i
$375$		0			0
$376$	−4.17087	+	5.21999i	−0.215096	+	0.269201i
$377$	−8.78842	+	8.78842i	−0.452627	+	0.452627i
$378$	−21.9337	+	30.8920i	−1.12815	+	1.58891i
$379$	−6.22454	+	2.57829i	−0.319733	+	0.132438i	−0.536777	−	0.843724i	$-0.680358\pi$
$379$	−6.22454	+	2.57829i	−0.319733	+	0.132438i	0.217044	+	0.976162i	$0.430358\pi$
$380$		0			0
$381$	−14.6662	+	35.4073i	−0.751372	+	1.81397i
$382$	20.8071	+	4.75597i	1.06458	+	0.243337i
$383$	6.12827			0.313140			0.156570	−	0.987667i	$-0.449956\pi$
$383$	6.12827			0.313140			0.156570	+	0.987667i	$0.449956\pi$
$384$	−35.3419	−	14.7303i	−1.80353	−	0.751702i
$385$		0			0
$386$	4.07970	+	0.932514i	0.207651	+	0.0474637i
$387$	−3.33087	+	8.04144i	−0.169318	+	0.408769i
$388$	−23.7419	−	11.4519i	−1.20531	−	0.581382i
$389$	15.9683	−	6.61427i	0.809623	−	0.335357i	0.0608194	−	0.998149i	$-0.480629\pi$
$389$	15.9683	−	6.61427i	0.809623	−	0.335357i	0.748804	+	0.662792i	$0.230629\pi$
$390$		0			0
$391$	−23.3821	+	23.3821i	−1.18248	+	1.18248i
$392$	−8.63882	+	10.8118i	−0.436326	+	0.546078i
$393$	−18.2963	−	18.2963i	−0.922925	−	0.922925i
$394$	18.7345	−	3.17705i	0.943828	−	0.160058i
$395$		0			0
$396$	15.6163	−	13.9379i	0.784748	−	0.700407i
$397$	−14.8241	−	6.14033i	−0.743999	−	0.308174i	−0.0217084	−	0.999764i	$-0.506911\pi$
$397$	−14.8241	−	6.14033i	−0.743999	−	0.308174i	−0.722290	+	0.691590i	$0.756911\pi$
$398$	13.0166	−	8.17318i	0.652464	−	0.409684i
$399$			19.3295i			0.967684i
$400$		0			0
$401$			27.3193i			1.36426i	0.731230	+	0.682131i	$0.238947\pi$
$401$			27.3193i			1.36426i	−0.731230	+	0.682131i	$0.761053\pi$
$402$	−4.55131	−	7.24843i	−0.226999	−	0.361519i
$403$	4.99481	+	2.06892i	0.248809	+	0.103060i
$404$	7.93369	+	0.450551i	0.394716	+	0.0224158i
$405$		0			0
$406$	0.761338	+	4.48946i	0.0377846	+	0.222808i
$407$	−2.28419	−	2.28419i	−0.113223	−	0.113223i
$408$	−19.5309	−	35.4174i	−0.966925	−	1.75342i
$409$	−2.23691	+	2.23691i	−0.110608	+	0.110608i	−0.760245	−	0.649637i	$-0.774921\pi$
$409$	−2.23691	+	2.23691i	−0.110608	+	0.110608i	0.649637	+	0.760245i	$0.274921\pi$
$410$		0			0
$411$	40.9378	−	16.9570i	2.01931	−	0.836427i
$412$	13.8426	−	4.83397i	0.681976	−	0.238152i
$413$	0.389961	−	0.941448i	0.0191887	−	0.0463256i
$414$	20.8473	−	91.2059i	1.02459	−	4.48253i
$415$		0			0
$416$	−1.72747	−	31.6491i	−0.0846960	−	1.55172i
$417$	8.46115			0.414344
$418$	1.53511	−	6.71603i	0.0750848	−	0.328492i
$419$	3.88329	−	9.37508i	0.189711	−	0.458003i	−0.800193	−	0.599743i	$-0.795270\pi$
$419$	3.88329	−	9.37508i	0.189711	−	0.458003i	0.989904	+	0.141740i	$0.0452696\pi$
$420$		0			0
$421$	3.20171	−	1.32619i	0.156042	−	0.0646347i	−0.303295	−	0.952897i	$-0.598087\pi$
$421$	3.20171	−	1.32619i	0.156042	−	0.0646347i	0.459337	+	0.888262i	$0.348087\pi$
$422$	−3.83296	−	2.72144i	−0.186586	−	0.132478i
$423$	14.1206	−	14.1206i	0.686566	−	0.686566i
$424$	3.10579	−	10.7423i	0.150830	−	0.521693i
$425$		0			0
$426$	7.06290	+	41.6485i	0.342199	+	2.01788i
$427$	4.37998	+	10.5742i	0.211962	+	0.511722i
$428$	−1.26734	+	22.3164i	−0.0612591	+	1.07870i
$429$	21.6899	+	8.98427i	1.04720	+	0.433765i
$430$		0			0
$431$			27.4030i			1.31996i	0.751285	+	0.659978i	$0.229434\pi$
$431$			27.4030i			1.31996i	−0.751285	+	0.659978i	$0.770566\pi$
$432$	64.5664	+	35.7907i	3.10645	+	1.72198i
$433$		−	31.7483i		−	1.52573i	−0.646560	−	0.762864i	$-0.723793\pi$
$433$		−	31.7483i		−	1.52573i	0.646560	−	0.762864i	$-0.276207\pi$
$434$	1.67748	−	1.05329i	0.0805214	−	0.0505597i
$435$		0			0
$436$	18.4401	+	20.6606i	0.883121	+	0.989465i
$437$	−11.7839	−	28.4489i	−0.563701	−	1.36089i
$438$	−38.0561	+	6.45368i	−1.81839	+	0.308369i
$439$	7.15702	+	7.15702i	0.341586	+	0.341586i	0.856963	−	0.515377i	$-0.172348\pi$
$439$	7.15702	+	7.15702i	0.341586	+	0.341586i	−0.515377	+	0.856963i	$0.672348\pi$
$440$		0			0
$441$	29.2469	−	29.2469i	1.39271	−	1.39271i
$442$	19.3835	−	27.3003i	0.921979	−	1.29854i
$443$	6.00467	−	2.48722i	0.285290	−	0.118171i	−0.235449	−	0.971887i	$-0.575656\pi$
$443$	6.00467	−	2.48722i	0.285290	−	0.118171i	0.520740	+	0.853715i	$0.325656\pi$
$444$	7.67255	−	15.9066i	0.364123	−	0.754894i
$445$		0			0
$446$	−32.2150	−	7.36353i	−1.52543	−	0.348673i
$447$	62.4645			2.95447
$448$	−9.82106	−	6.19685i	−0.464001	−	0.292774i
$449$	8.48000			0.400196			0.200098	−	0.979776i	$-0.435874\pi$
$449$	8.48000			0.400196			0.200098	+	0.979776i	$0.435874\pi$
$450$		0			0
$451$	−3.10099	+	7.48645i	−0.146020	+	0.352523i
$452$	5.50805	−	11.4192i	0.259077	−	0.537114i
$453$	−58.5749	+	24.2625i	−2.75209	+	1.13995i
$454$	−9.03501	+	12.7252i	−0.424034	+	0.597222i
$455$		0			0
$456$	37.4308	−	4.18169i	1.75286	−	0.195826i
$457$	17.8416	+	17.8416i	0.834593	+	0.834593i	0.988141	−	0.153548i	$-0.0490701\pi$
$457$	17.8416	+	17.8416i	0.834593	+	0.834593i	−0.153548	+	0.988141i	$0.549070\pi$
$458$	25.2962	−	4.28981i	1.18201	−	0.200450i
$459$	29.8421	+	72.0453i	1.39291	+	3.36279i
$460$		0			0
$461$	−2.54536	−	1.05432i	−0.118549	−	0.0491047i	0.322620	−	0.946528i	$-0.395436\pi$
$461$	−2.54536	−	1.05432i	−0.118549	−	0.0491047i	−0.441170	+	0.897424i	$0.645436\pi$
$462$	7.28443	−	4.57392i	0.338903	−	0.212798i
$463$			26.6297i			1.23759i	0.785554	+	0.618793i	$0.212378\pi$
$463$			26.6297i			1.23759i	−0.785554	+	0.618793i	$0.787622\pi$
$464$	8.52897	−	2.44554i	0.395947	−	0.113531i
$465$		0			0
$466$	−20.3675	−	32.4373i	−0.943504	−	1.50263i
$467$	−5.82058	−	2.41096i	−0.269344	−	0.111566i	0.243924	−	0.969794i	$-0.421565\pi$
$467$	−5.82058	−	2.41096i	−0.269344	−	0.111566i	−0.513268	+	0.858228i	$0.671565\pi$
$468$	−5.37107	+	94.5784i	−0.248278	+	4.37189i
$469$	−0.993383	−	2.39824i	−0.0458702	−	0.110740i
$470$		0			0
$471$	−27.2815	−	27.2815i	−1.25706	−	1.25706i
$472$	−1.90744	−	0.551474i	−0.0877972	−	0.0253836i
$473$	0.901403	−	0.901403i	0.0414466	−	0.0414466i
$474$	−58.1556	−	41.2911i	−2.67118	−	1.89656i
$475$		0			0
$476$	−4.04420	−	11.5810i	−0.185366	−	0.530815i
$477$	−12.7895	+	30.8766i	−0.585592	+	1.41374i
$478$	6.16512	−	26.9721i	0.281986	−	1.23367i
$479$	8.91801			0.407474			0.203737	−	0.979026i	$-0.434691\pi$
$479$	8.91801			0.407474			0.203737	+	0.979026i	$0.434691\pi$
$480$		0			0
$481$	14.6196			0.666596
$482$	1.45943	−	6.38492i	0.0664751	−	0.290825i
$483$	14.7125	−	35.5191i	0.669441	−	1.61617i
$484$	17.8758	−	6.24239i	0.812535	−	0.283745i
$485$		0			0
$486$	−80.9337	−	57.4638i	−3.67123	−	2.60661i
$487$	14.5675	−	14.5675i	0.660115	−	0.660115i	−0.295292	−	0.955407i	$-0.595417\pi$
$487$	14.5675	−	14.5675i	0.660115	−	0.660115i	0.955407	+	0.295292i	$0.0954169\pi$
$488$	19.5290	−	10.7693i	0.884038	−	0.487502i
$489$	−30.9591	−	30.9591i	−1.40002	−	1.40002i
$490$		0			0
$491$	12.1115	+	29.2397i	0.546584	+	1.31957i	0.920004	+	0.391908i	$0.128185\pi$
$491$	12.1115	+	29.2397i	0.546584	+	1.31957i	−0.373420	+	0.927662i	$0.621815\pi$
$492$	−44.2296	−	2.51178i	−1.99402	−	0.113240i
$493$	8.65904	+	3.58669i	0.389983	+	0.161536i
$494$	16.5798	+	26.4050i	0.745960	+	1.18802i
$495$		0			0
$496$	−2.40256	−	3.02051i	−0.107878	−	0.135625i
$497$			12.8120i			0.574697i
$498$	14.7200	−	9.24273i	0.659618	−	0.414176i
$499$	−10.0229	−	4.15164i	−0.448689	−	0.185853i	0.146885	−	0.989154i	$-0.453075\pi$
$499$	−10.0229	−	4.15164i	−0.448689	−	0.185853i	−0.595574	+	0.803301i	$0.703075\pi$
$500$		0			0
$501$	−11.8308	−	28.5621i	−0.528562	−	1.27606i
$502$	16.2323	−	2.75272i	0.724481	−	0.122860i
$503$	−15.5986	−	15.5986i	−0.695505	−	0.695505i	0.267932	−	0.963438i	$-0.413660\pi$
$503$	−15.5986	−	15.5986i	−0.695505	−	0.695505i	−0.963438	+	0.267932i	$0.913660\pi$
$504$	27.1145	+	21.6650i	1.20778	+	0.965036i
$505$		0			0
$506$	−7.93271	+	11.1727i	−0.352652	+	0.496686i
$507$	−57.5159	+	23.8239i	−2.55437	+	1.05806i
$508$	20.3995	+	9.83969i	0.905082	+	0.436566i
$509$	1.06698	−	2.57591i	0.0472930	−	0.114175i	−0.898468	−	0.439040i	$-0.855319\pi$
$509$	1.06698	−	2.57591i	0.0472930	−	0.114175i	0.945761	+	0.324864i	$0.105319\pi$
$510$		0			0
$511$	−11.7069			−0.517883
$512$	−9.87532	+	20.3587i	−0.436432	+	0.899737i
$513$	−72.6175			−3.20614
$514$	−5.58120	−	1.27572i	−0.246176	−	0.0562696i
$515$		0			0
$516$	6.27717	+	3.02779i	0.276337	+	0.133291i
$517$	−2.70208	+	1.11924i	−0.118837	+	0.0492241i
$518$	3.10088	−	4.36737i	0.136245	−	0.191891i
$519$	−30.2140	+	30.2140i	−1.32625	+	1.32625i
$520$		0			0
$521$	−11.9781	−	11.9781i	−0.524771	−	0.524771i	0.394238	−	0.919009i	$-0.371009\pi$
$521$	−11.9781	−	11.9781i	−0.524771	−	0.524771i	−0.919009	+	0.394238i	$0.871009\pi$
$522$	−26.1445	+	4.43368i	−1.14431	+	0.194057i
$523$	−4.43446	−	10.7057i	−0.193905	−	0.468129i	0.796785	−	0.604263i	$-0.206532\pi$
$523$	−4.43446	−	10.7057i	−0.193905	−	0.468129i	−0.990690	+	0.136134i	$0.956532\pi$
$524$	−11.4082	+	10.1821i	−0.498368	+	0.444805i
$525$		0			0
$526$	2.71920	−	1.70739i	0.118563	−	0.0744459i
$527$		−	4.07692i		−	0.177593i
$528$	−10.4331	−	13.1165i	−0.454043	−	0.570824i
$529$			38.2457i			1.66286i
$530$		0			0
$531$	5.48256	+	2.27095i	0.237923	+	0.0985508i
$532$	11.4047	+	0.647670i	0.494457	+	0.0280801i
$533$	−14.0342	−	33.8816i	−0.607889	−	1.46757i
$534$	−11.2079	−	66.0906i	−0.485011	−	2.86002i
$535$		0			0
$536$	−4.42920	+	2.44248i	−0.191312	+	0.105499i
$537$	−3.60488	+	3.60488i	−0.155562	+	0.155562i
$538$	4.22323	+	2.99853i	0.182076	+	0.129276i
$539$	−5.59663	+	2.31820i	−0.241064	+	0.0998519i
$540$		0			0
$541$	8.28137	−	19.9930i	0.356044	−	0.859566i	−0.639804	−	0.768538i	$-0.720985\pi$
$541$	8.28137	−	19.9930i	0.356044	−	0.859566i	0.995848	−	0.0910282i	$-0.0290153\pi$
$542$	7.06687	−	30.9172i	0.303548	−	1.32801i
$543$	8.32686			0.357340
$544$	−21.5513	+	10.3369i	−0.924004	+	0.443189i
$545$		0			0
$546$	−8.67410	+	37.9487i	−0.371217	+	1.62405i
$547$	−12.1997	+	29.4527i	−0.521623	+	1.25931i	0.415272	+	0.909697i	$0.363686\pi$
$547$	−12.1997	+	29.4527i	−0.521623	+	1.25931i	−0.936895	+	0.349611i	$0.886314\pi$
$548$	−8.63322	−	24.7222i	−0.368793	−	1.05608i
$549$	−61.5793	+	25.5070i	−2.62814	+	1.08861i
$550$		0			0
$551$	−6.17149	+	6.17149i	−0.262914	+	0.262914i
$552$	−71.9643	−	20.8061i	−3.06300	−	0.885566i
$553$	−15.2960	−	15.2960i	−0.650453	−	0.650453i
$554$	−1.36210	−	8.03205i	−0.0578701	−	0.341249i
$555$		0			0
$556$	0.283507	−	4.99222i	0.0120234	−	0.211717i
$557$	−1.09724	−	0.454492i	−0.0464916	−	0.0192574i	0.359316	−	0.933216i	$-0.383010\pi$
$557$	−1.09724	−	0.454492i	−0.0464916	−	0.0192574i	−0.405808	+	0.913958i	$0.633010\pi$
$558$	6.13389	+	9.76884i	0.259668	+	0.413548i
$559$			5.76928i			0.244015i
$560$		0			0
$561$		−	17.7040i		−	0.747464i
$562$	3.07561	−	1.93118i	0.129737	−	0.0814621i
$563$	39.1382	+	16.2116i	1.64948	+	0.683236i	0.997203	−	0.0747465i	$-0.0238148\pi$
$563$	39.1382	+	16.2116i	1.64948	+	0.683236i	0.652275	+	0.757982i	$0.273815\pi$
$564$	−10.6471	−	11.9291i	−0.448322	−	0.502308i
$565$		0			0
$566$	22.9570	−	3.89313i	0.964956	−	0.163641i
$567$	−38.0794	−	38.0794i	−1.59919	−	1.59919i
$568$	24.8100	−	2.77172i	1.04100	−	0.116299i
$569$	4.33822	−	4.33822i	0.181868	−	0.181868i	−0.610301	−	0.792169i	$-0.708952\pi$
$569$	4.33822	−	4.33822i	0.181868	−	0.181868i	0.792169	+	0.610301i	$0.208952\pi$
$570$		0			0
$571$	−37.2465	+	15.4280i	−1.55872	+	0.645643i	−0.984866	−	0.173316i	$-0.944552\pi$
$571$	−37.2465	+	15.4280i	−1.55872	+	0.645643i	−0.573853	+	0.818958i	$0.694552\pi$
$572$	6.02763	−	12.4964i	0.252028	−	0.522501i
$573$	−19.5462	+	47.1886i	−0.816553	+	1.97133i
$574$	−13.0983	−	2.99393i	−0.546712	−	0.124964i
$575$		0			0
$576$	36.0876	−	57.1933i	1.50365	−	2.38305i
$577$	4.17488			0.173802			0.0869012	−	0.996217i	$-0.472304\pi$
$577$	4.17488			0.173802			0.0869012	+	0.996217i	$0.472304\pi$
$578$	−1.17656	−	0.268931i	−0.0489384	−	0.0111861i
$579$	−3.83246	+	9.25238i	−0.159272	+	0.384516i
$580$		0			0
$581$	4.87030	−	2.01735i	0.202054	−	0.0836936i
$582$	36.5185	−	51.4338i	1.51374	−	2.13200i
$583$	3.46111	−	3.46111i	0.143344	−	0.143344i
$584$	2.53264	+	22.6700i	0.104801	+	0.938090i
$585$		0			0
$586$	−23.8195	+	4.03938i	−0.983973	+	0.166865i
$587$	−7.20581	−	17.3964i	−0.297415	−	0.718024i	−0.999979	−	0.00640387i	$-0.997962\pi$
$587$	−7.20581	−	17.3964i	−0.297415	−	0.718024i	0.702564	−	0.711621i	$-0.252038\pi$
$588$	−22.0525	−	24.7080i	−0.909429	−	1.01894i
$589$	3.50751	+	1.45286i	0.144524	+	0.0598639i
$590$		0			0
$591$			45.4725i			1.87049i
$592$	−9.12809	−	5.05991i	−0.375162	−	0.207961i
$593$		−	9.27068i		−	0.380701i	−0.981716	−	0.190351i	$-0.939038\pi$
$593$		−	9.27068i		−	0.380701i	0.981716	−	0.190351i	$-0.0609625\pi$
$594$	17.1834	+	27.3664i	0.705045	+	1.12286i
$595$		0			0
$596$	2.09299	−	36.8551i	0.0857322	−	1.50965i
$597$	14.0754	+	33.9811i	0.576069	+	1.39075i
$598$	−10.3684	−	61.1404i	−0.423995	−	2.50022i
$599$	22.3629	+	22.3629i	0.913723	+	0.913723i	0.996563	−	0.0828402i	$-0.0263991\pi$
$599$	22.3629	+	22.3629i	0.913723	+	0.913723i	−0.0828402	+	0.996563i	$0.526399\pi$
$600$		0			0
$601$	25.9624	−	25.9624i	1.05903	−	1.05903i	0.0608851	−	0.998145i	$-0.480608\pi$
$601$	25.9624	−	25.9624i	1.05903	−	1.05903i	0.998145	−	0.0608851i	$-0.0193923\pi$
$602$	1.72348	+	1.22369i	0.0702438	+	0.0498739i
$603$	13.9662	−	5.78500i	0.568749	−	0.235583i
$604$	12.3526	+	35.3732i	0.502622	+	1.43931i
$605$		0			0
$606$	−4.23735	+	18.5382i	−0.172131	+	0.753062i
$607$	3.46490			0.140636			0.0703179	−	0.997525i	$-0.477599\pi$
$607$	3.46490			0.140636			0.0703179	+	0.997525i	$0.477599\pi$
$608$	−1.21308	−	22.2249i	−0.0491968	−	0.901340i
$609$	−10.8969			−0.441564
$610$		0			0
$611$	5.06536	−	12.2289i	0.204923	−	0.494727i
$612$	67.4424	−	23.5515i	2.72620	−	0.952014i
$613$	33.2177	−	13.7592i	1.34165	−	0.555730i	0.407695	−	0.913118i	$-0.366333\pi$
$613$	33.2177	−	13.7592i	1.34165	−	0.555730i	0.933956	+	0.357388i	$0.116333\pi$
$614$	−0.612638	−	0.434979i	−0.0247241	−	0.0175543i
$615$		0			0
$616$	−2.45461	−	4.45120i	−0.0988991	−	0.179344i
$617$	−30.4580	−	30.4580i	−1.22619	−	1.22619i	−0.965393	−	0.260799i	$-0.916014\pi$
$617$	−30.4580	−	30.4580i	−1.22619	−	1.22619i	−0.260799	−	0.965393i	$-0.583986\pi$
$618$	5.86654	+	34.5938i	0.235987	+	1.39157i
$619$	4.97518	+	12.0112i	0.199969	+	0.482769i	0.991773	−	0.128006i	$-0.0408578\pi$
$619$	4.97518	+	12.0112i	0.199969	+	0.482769i	−0.791804	+	0.610775i	$0.790858\pi$
$620$		0			0
$621$	133.439	+	55.2723i	5.35473	+	2.21800i
$622$	2.83264	+	4.51127i	0.113578	+	0.180885i
$623$		−	20.3309i		−	0.814541i
$624$	75.3628	+	8.58735i	3.01693	+	0.343769i
$625$		0			0
$626$	23.2984	−	14.6292i	0.931192	−	0.584699i
$627$	15.2313	+	6.30902i	0.608281	+	0.251958i
$628$	−17.0107	+	15.1824i	−0.678799	+	0.605845i
$629$	−4.21894	−	10.1854i	−0.168220	−	0.406119i
$630$		0			0
$631$	−7.07552	−	7.07552i	−0.281672	−	0.281672i	0.552103	−	0.833776i	$-0.313825\pi$
$631$	−7.07552	−	7.07552i	−0.281672	−	0.281672i	−0.833776	+	0.552103i	$0.813825\pi$
$632$	−26.3111	+	32.9293i	−1.04660	+	1.30986i
$633$	7.95447	−	7.95447i	0.316162	−	0.316162i
$634$	17.7345	−	24.9777i	0.704325	−	0.991993i
$635$		0			0
$636$	24.1024	+	11.6258i	0.955721	+	0.460992i
$637$	10.4915	−	25.3288i	0.415689	−	1.00356i
$638$	3.78612	+	0.865410i	0.149894	+	0.0342619i
$639$	−74.6112			−2.95157
$640$		0			0
$641$	−29.8007			−1.17706			−0.588528	−	0.808477i	$-0.700292\pi$
$641$	−29.8007			−1.17706			−0.588528	+	0.808477i	$0.700292\pi$
$642$	−52.1453	−	11.9191i	−2.05801	−	0.470409i
$643$	−5.62912	+	13.5899i	−0.221991	+	0.535933i	−0.995160	−	0.0982665i	$-0.968670\pi$
$643$	−5.62912	+	13.5899i	−0.221991	+	0.535933i	0.773169	+	0.634200i	$0.218670\pi$
$644$	−20.4639	−	9.87075i	−0.806390	−	0.388962i
$645$		0			0
$646$	13.6117	−	19.1711i	0.535544	−	0.754276i
$647$	29.5002	−	29.5002i	1.15977	−	1.15977i	0.175247	−	0.984525i	$-0.443928\pi$
$647$	29.5002	−	29.5002i	1.15977	−	1.15977i	0.984525	−	0.175247i	$-0.0560723\pi$
$648$	−65.5014	+	81.9775i	−2.57314	+	3.22038i
$649$	−0.614566	−	0.614566i	−0.0241238	−	0.0241238i
$650$		0			0
$651$	1.81393	+	4.37921i	0.0710934	+	0.171635i
$652$	−19.3037	+	17.2291i	−0.755993	+	0.674742i
$653$	−31.2680	−	12.9516i	−1.22361	−	0.506836i	−0.325054	−	0.945695i	$-0.605383\pi$
$653$	−31.2680	−	12.9516i	−1.22361	−	0.506836i	−0.898556	+	0.438859i	$0.855383\pi$
$654$	−56.1239	+	35.2404i	−2.19462	+	1.37801i
$655$		0			0
$656$	−2.96399	+	26.0121i	−0.115724	+	1.01560i
$657$		−	68.1755i		−	2.65978i
$658$	−2.57879	−	4.10699i	−0.100532	−	0.160107i
$659$	−38.4825	−	15.9400i	−1.49907	−	0.620933i	−0.525799	−	0.850609i	$-0.676233\pi$
$659$	−38.4825	−	15.9400i	−1.49907	−	0.620933i	−0.973267	+	0.229676i	$0.926233\pi$
$660$		0			0
$661$	7.78263	+	18.7889i	0.302709	+	0.730805i	0.999903	+	0.0139222i	$0.00443172\pi$
$661$	7.78263	+	18.7889i	0.302709	+	0.730805i	−0.697194	+	0.716883i	$0.745568\pi$
$662$	−2.13189	−	12.5714i	−0.0828584	−	0.488600i
$663$	56.6558	+	56.6558i	2.20033	+	2.20033i
$664$	−4.96014	−	8.99474i	−0.192491	−	0.349063i
$665$		0			0
$666$	25.4335	+	18.0581i	0.985529	+	0.699736i
$667$	16.0379	−	6.64311i	0.620989	−	0.257222i
$668$	−17.2485	+	6.02335i	−0.667366	+	0.233051i
$669$	30.2627	−	73.0607i	1.17003	−	2.82469i
$670$		0			0
$671$	9.76192			0.376855
$672$	18.5501	−	20.6920i	0.715586	−	0.798212i
$673$	33.3993			1.28745			0.643725	−	0.765257i	$-0.277388\pi$
$673$	33.3993			1.28745			0.643725	+	0.765257i	$0.277388\pi$
$674$	3.86527	−	16.9104i	0.148885	−	0.651363i
$675$		0			0
$676$	12.1293	+	34.7336i	0.466512	+	1.33591i
$677$	1.90403	−	0.788676i	0.0731779	−	0.0303113i	−0.345794	−	0.938310i	$-0.612390\pi$
$677$	1.90403	−	0.788676i	0.0731779	−	0.0303113i	0.418972	+	0.907999i	$0.362390\pi$
$678$	24.7382	+	17.5644i	0.950065	+	0.674557i
$679$	13.5280	−	13.5280i	0.519158	−	0.519158i
$680$		0			0
$681$	−26.4083	−	26.4083i	−1.01197	−	1.01197i
$682$	−0.282460	−	1.66561i	−0.0108160	−	0.0637796i
$683$	−2.13897	−	5.16393i	−0.0818454	−	0.197592i	0.877659	−	0.479285i	$-0.159104\pi$
$683$	−2.13897	−	5.16393i	−0.0818454	−	0.197592i	−0.959505	+	0.281693i	$0.909104\pi$
$684$	−3.77173	+	66.4158i	−0.144216	+	2.53947i
$685$		0			0
$686$	−12.9827	−	20.6763i	−0.495682	−	0.789425i
$687$			61.3993i			2.34253i
$688$	1.99678	−	3.60219i	0.0761264	−	0.137332i
$689$			22.1522i			0.843933i
$690$		0			0
$691$	−21.8310	−	9.04271i	−0.830492	−	0.344001i	−0.0733946	−	0.997303i	$-0.523383\pi$
$691$	−21.8310	−	9.04271i	−0.830492	−	0.344001i	−0.757097	+	0.653302i	$0.773383\pi$
$692$	16.8144	+	18.8392i	0.639188	+	0.716158i
$693$	5.81374	+	14.0356i	0.220846	+	0.533168i
$694$	24.5142	−	4.15720i	0.930546	−	0.157805i
$695$		0			0
$696$	2.35740	+	21.1014i	0.0893571	+	0.799847i
$697$	−19.5552	+	19.5552i	−0.740705	+	0.740705i
$698$	−22.7367	+	32.0230i	−0.860595	+	1.21209i
$699$	84.6804	−	35.0758i	3.20291	−	1.32669i
$700$		0			0
$701$	−9.38145	+	22.6488i	−0.354332	+	0.855434i	0.641743	+	0.766920i	$0.278212\pi$
$701$	−9.38145	+	22.6488i	−0.354332	+	0.855434i	−0.996075	+	0.0885139i	$0.971788\pi$
$702$	−142.567	−	32.5871i	−5.38084	−	1.22992i
$703$	10.2663			0.387202
$704$	−8.08856	+	5.71623i	−0.304849	+	0.215438i
$705$		0			0
$706$	30.2246	+	6.90857i	1.13752	+	0.260007i
$707$	−2.20712	+	5.32846i	−0.0830073	+	0.200397i
$708$	2.06431	−	4.27970i	0.0775816	−	0.160841i
$709$	34.4885	−	14.2856i	1.29524	−	0.536506i	0.374698	−	0.927147i	$-0.377746\pi$
$709$	34.4885	−	14.2856i	1.29524	−	0.536506i	0.920543	+	0.390640i	$0.127746\pi$
$710$		0			0
$711$	89.0769	−	89.0769i	3.34064	−	3.34064i
$712$	−39.3701	+	4.39834i	−1.47546	+	0.164835i
$713$	−5.33942	−	5.33942i	−0.199963	−	0.199963i
$714$	28.9419	−	4.90807i	1.08312	−	0.183680i
$715$		0			0
$716$	2.00615	+	2.24773i	0.0749735	+	0.0840017i
$717$	61.1701	+	25.3375i	2.28444	+	0.946246i
$718$	6.81133	−	4.27686i	0.254197	−	0.159611i
$719$			47.1132i			1.75702i	0.477719	+	0.878512i	$0.341464\pi$
$719$			47.1132i			1.75702i	−0.477719	+	0.878512i	$0.658536\pi$
$720$		0			0
$721$			10.6418i			0.396322i
$722$	−2.64575	−	4.21362i	−0.0984645	−	0.156815i
$723$	14.4804	+	5.99798i	0.538532	+	0.223067i
$724$	0.279007	−	4.91299i	0.0103692	−	0.182590i
$725$		0			0
$726$	7.57580	+	44.6730i	0.281164	+	1.65797i
$727$	32.2735	+	32.2735i	1.19696	+	1.19696i	0.975073	+	0.221885i	$0.0712210\pi$
$727$	32.2735	+	32.2735i	1.19696	+	1.19696i	0.221885	+	0.975073i	$0.428779\pi$
$728$	22.0997	+	6.38941i	0.819071	+	0.236807i
$729$	89.2611	−	89.2611i	3.30597	−	3.30597i
$730$		0			0
$731$	4.01944	−	1.66491i	0.148664	−	0.0615788i
$732$	17.5949	+	50.3849i	0.650326	+	1.86228i
$733$	−16.0772	+	38.8138i	−0.593825	+	1.43362i	0.285956	+	0.958243i	$0.407689\pi$
$733$	−16.0772	+	38.8138i	−0.593825	+	1.43362i	−0.879782	+	0.475378i	$0.842311\pi$
$734$	−8.88413	+	38.8676i	−0.327919	+	1.43463i
$735$		0			0
$736$	−14.6872	+	41.7630i	−0.541379	+	1.53940i
$737$	−2.21401			−0.0815541
$738$	17.4353	−	76.2783i	0.641801	−	2.80784i
$739$	−3.96376	+	9.56937i	−0.145809	+	0.352015i	−0.979864	−	0.199667i	$-0.936014\pi$
$739$	−3.96376	+	9.56937i	−0.145809	+	0.352015i	0.834054	+	0.551682i	$0.186014\pi$
$740$		0			0
$741$	−68.9327	+	28.5529i	−2.53231	+	1.04892i
$742$	6.61762	+	4.69858i	0.242941	+	0.172490i
$743$	27.5088	−	27.5088i	1.00920	−	1.00920i	0.00924260	−	0.999957i	$-0.497058\pi$
$743$	27.5088	−	27.5088i	1.00920	−	1.00920i	0.999957	−	0.00924260i	$-0.00294205\pi$
$744$	8.08775	−	4.45999i	0.296511	−	0.163511i
$745$		0			0
$746$	−0.292008	−	1.72192i	−0.0106912	−	0.0630439i
$747$	11.7481	+	28.3624i	0.429840	+	1.03773i
$748$	−10.4457	−	0.593205i	−0.381931	−	0.0216897i
$749$	−14.9882	−	6.20833i	−0.547658	−	0.226847i
$750$		0			0
$751$			29.6365i			1.08145i	0.841199	+	0.540726i	$0.181851\pi$
$751$			29.6365i			1.08145i	−0.841199	+	0.540726i	$0.818149\pi$
$752$	−7.39515	+	5.88223i	−0.269673	+	0.214503i
$753$			39.3992i			1.43579i
$754$	−14.8857	+	9.34676i	−0.542104	+	0.340389i
$755$		0			0
$756$	−39.9739	+	35.6777i	−1.45384	+	1.29758i
$757$	−20.0533	−	48.4128i	−0.728848	−	1.75959i	−0.646399	−	0.762999i	$-0.723726\pi$
$757$	−20.0533	−	48.4128i	−0.728848	−	1.75959i	−0.0824488	−	0.996595i	$-0.526274\pi$
$758$	−9.39399	+	1.59306i	−0.341205	+	0.0578627i
$759$	−23.1864	−	23.1864i	−0.841614	−	0.841614i
$760$		0			0
$761$	−31.0239	+	31.0239i	−1.12461	+	1.12461i	−0.133576	+	0.991039i	$0.542646\pi$
$761$	−31.0239	+	31.0239i	−1.12461	+	1.12461i	−0.991039	+	0.133576i	$0.957354\pi$
$762$	−31.3774	+	44.1929i	−1.13668	+	1.60094i
$763$	−18.5694	+	7.69168i	−0.672256	+	0.278457i
$764$	27.1872	+	13.1137i	0.983597	+	0.474437i
$765$		0			0
$766$	8.44878	+	1.93118i	0.305267	+	0.0697762i
$767$	3.93343			0.142028
$768$	−44.0824	−	31.4452i	−1.59069	−	1.13468i
$769$	−9.26292			−0.334029			−0.167015	−	0.985954i	$-0.553413\pi$
$769$	−9.26292			−0.334029			−0.167015	+	0.985954i	$0.553413\pi$
$770$		0			0
$771$	5.24297	−	12.6576i	0.188821	−	0.455854i
$772$	5.33065	+	2.57124i	0.191854	+	0.0925408i
$773$	20.4673	−	8.47782i	0.736156	−	0.304926i	0.0170771	−	0.999854i	$-0.494564\pi$
$773$	20.4673	−	8.47782i	0.736156	−	0.304926i	0.719079	+	0.694928i	$0.244564\pi$
$774$	−7.12620	+	10.0367i	−0.256146	+	0.360763i
$775$		0			0
$776$	−29.1232	−	23.2699i	−1.04546	−	0.835342i
$777$	9.06352	+	9.06352i	0.325152	+	0.325152i
$778$	24.0991	−	4.08680i	0.863994	−	0.146519i
$779$	−9.85524	−	23.7927i	−0.353101	−	0.852460i
$780$		0			0
$781$	10.0957	+	4.18176i	0.361251	+	0.149635i
$782$	−39.6042	+	24.8676i	−1.41624	+	0.889264i
$783$		−	40.9377i		−	1.46299i
$784$	−15.3170	+	12.1834i	−0.547037	+	0.435123i
$785$		0			0
$786$	−19.4587	−	30.9899i	−0.694068	−	1.10537i
$787$	22.8472	+	9.46364i	0.814416	+	0.337342i	0.750715	−	0.660627i	$-0.229709\pi$
$787$	22.8472	+	9.46364i	0.814416	+	0.337342i	0.0637018	+	0.997969i	$0.479709\pi$
$788$	26.8296	+	1.52364i	0.955764	+	0.0542775i
$789$	2.94039	+	7.09872i	0.104681	+	0.252721i
$790$		0			0
$791$	6.50661	+	6.50661i	0.231348	+	0.231348i
$792$	25.9217	−	14.2945i	0.921088	−	0.507934i
$793$	−31.2398	+	31.2398i	−1.10936	+	1.10936i
$794$	−18.5023	−	13.1369i	−0.656623	−	0.466210i
$795$		0			0
$796$	20.5210	−	7.16614i	0.727349	−	0.253997i
$797$	10.7716	−	26.0050i	0.381551	−	0.921145i	−0.610115	−	0.792313i	$-0.708877\pi$
$797$	10.7716	−	26.0050i	0.381551	−	0.921145i	0.991666	−	0.128833i	$-0.0411230\pi$
$798$	−6.09121	+	26.6487i	−0.215627	+	0.943355i
$799$	−9.98158			−0.353123
$800$		0			0
$801$	118.398			4.18338
$802$	−8.60902	+	37.6640i	−0.303995	+	1.32996i
$803$	−3.82106	+	9.22485i	−0.134842	+	0.325538i
$804$	−3.99053	−	11.4273i	−0.140735	−	0.403011i
$805$		0			0
$806$	6.23416	+	4.42632i	0.219589	+	0.155911i
$807$	−8.76438	+	8.76438i	−0.308521	+	0.308521i
$808$	10.7959	+	3.12126i	0.379797	+	0.109806i
$809$	−24.2885	−	24.2885i	−0.853938	−	0.853938i	0.136678	−	0.990616i	$-0.456357\pi$
$809$	−24.2885	−	24.2885i	−0.853938	−	0.853938i	−0.990616	+	0.136678i	$0.956357\pi$
$810$		0			0
$811$	12.8336	+	30.9831i	0.450649	+	1.08796i	0.972076	+	0.234667i	$0.0754001\pi$
$811$	12.8336	+	30.9831i	0.450649	+	1.08796i	−0.521426	+	0.853296i	$0.674600\pi$
$812$	−0.365120	+	6.42934i	−0.0128132	+	0.225626i
$813$	70.1173	+	29.0435i	2.45912	+	1.01860i
$814$	−2.42931	−	3.86893i	−0.0851473	−	0.135606i
$815$		0			0
$816$	−15.7655	−	54.9832i	−0.551904	−	1.92480i
$817$			4.05136i			0.141739i
$818$	−3.78885	+	2.37903i	−0.132474	+	0.0831808i
$819$	−63.5212	−	26.3113i	−2.21961	−	0.919393i
$820$		0			0
$821$	−3.76592	−	9.09173i	−0.131431	−	0.317304i	0.844440	−	0.535651i	$-0.179934\pi$
$821$	−3.76592	−	9.09173i	−0.131431	−	0.317304i	−0.975871	+	0.218347i	$0.929934\pi$
$822$	61.7828	−	10.4773i	2.15492	−	0.365439i
$823$	−9.16017	−	9.16017i	−0.319304	−	0.319304i	0.529196	−	0.848500i	$-0.322494\pi$
$823$	−9.16017	−	9.16017i	−0.319304	−	0.319304i	−0.848500	+	0.529196i	$0.822494\pi$
$824$	20.6075	−	2.30223i	0.717897	−	0.0802018i
$825$		0			0
$826$	0.834296	−	1.17505i	0.0290289	−	0.0408851i
$827$	−40.0605	+	16.5936i	−1.39304	+	0.577017i	−0.947936	−	0.318461i	$-0.896834\pi$
$827$	−40.0605	+	16.5936i	−1.39304	+	0.577017i	−0.445106	+	0.895478i	$0.646834\pi$
$828$	57.4827	−	119.172i	1.99766	−	4.14152i
$829$	9.71946	−	23.4648i	0.337571	−	0.814968i	−0.660377	−	0.750934i	$-0.729604\pi$
$829$	9.71946	−	23.4648i	0.337571	−	0.814968i	0.997948	−	0.0640336i	$-0.0203965\pi$
$830$		0			0
$831$	19.4955			0.676291
$832$	7.59186	−	44.1776i	0.263200	−	1.53158i
$833$	−20.6741			−0.716316
$834$	11.6650	+	2.66633i	0.403927	+	0.0923273i
$835$		0			0
$836$	4.23278	−	8.77535i	0.146394	−	0.303502i
$837$	−16.4519	+	6.81461i	−0.568662	+	0.235547i
$838$	8.30805	−	11.7013i	0.286997	−	0.404215i
$839$	32.2653	−	32.2653i	1.11392	−	1.11392i	0.121307	−	0.992615i	$-0.461292\pi$
$839$	32.2653	−	32.2653i	1.11392	−	1.11392i	0.992615	−	0.121307i	$-0.0387085\pi$
$840$		0			0
$841$	17.0270	+	17.0270i	0.587136	+	0.587136i
$842$	4.83198	−	0.819424i	0.166521	−	0.0282392i
$843$	3.32578	+	8.02915i	0.114546	+	0.276539i
$844$	−4.42675	−	4.95980i	−0.152375	−	0.170723i
$845$		0			0
$846$	23.9172	−	15.0177i	0.822290	−	0.516319i
$847$			13.7424i			0.472195i
$848$	7.66700	−	13.8313i	0.263286	−	0.474968i
$849$			55.7216i			1.91236i
$850$		0			0
$851$	−18.8650	−	7.81413i	−0.646683	−	0.267865i
$852$	−3.38721	+	59.6448i	−0.116044	+	2.04340i
$853$	1.83040	+	4.41898i	0.0626718	+	0.151303i	0.952113	−	0.305747i	$-0.0989061\pi$
$853$	1.83040	+	4.41898i	0.0626718	+	0.151303i	−0.889441	+	0.457050i	$0.848906\pi$
$854$	2.70629	+	15.9585i	0.0926073	+	0.546087i
$855$		0			0
$856$	−8.77968	+	30.3673i	−0.300083	+	1.03793i
$857$	−13.7258	+	13.7258i	−0.468864	+	0.468864i	−0.901546	−	0.432683i	$-0.857567\pi$
$857$	−13.7258	+	13.7258i	−0.468864	+	0.468864i	0.432683	+	0.901546i	$0.357567\pi$
$858$	27.0718	+	19.2213i	0.924217	+	0.656204i
$859$	−35.3096	+	14.6257i	−1.20475	+	0.499023i	−0.892530	−	0.450988i	$-0.851072\pi$
$859$	−35.3096	+	14.6257i	−1.20475	+	0.499023i	−0.312217	+	0.950011i	$0.601072\pi$
$860$		0			0
$861$	12.3045	−	29.7057i	0.419336	−	1.01237i
$862$	−8.63538	+	37.7793i	−0.294122	+	1.28677i
$863$	−52.6541			−1.79237			−0.896183	−	0.443685i	$-0.853671\pi$
$863$	−52.6541			−1.79237			−0.896183	+	0.443685i	$0.853671\pi$
$864$	77.7363	+	69.6896i	2.64464	+	2.37089i
$865$		0			0
$866$	10.0047	−	43.7701i	0.339974	−	1.48737i
$867$	1.10526	−	2.66833i	0.0375365	−	0.0906212i
$868$	2.64458	−	0.923514i	0.0897630	−	0.0313461i
$869$	−17.0455	+	7.06050i	−0.578231	+	0.239511i
$870$		0			0
$871$	7.08520	−	7.08520i	0.240073	−	0.240073i
$872$	18.9119	+	34.2949i	0.640438	+	1.16137i
$873$	78.7810	+	78.7810i	2.66633	+	2.66633i
$874$	−7.28100	−	42.9346i	−0.246283	−	1.45229i
$875$		0			0
$876$	−54.5000	−	3.09504i	−1.84138	−	0.104572i
$877$	29.5360	+	12.2342i	0.997359	+	0.413120i	0.820828	−	0.571175i	$-0.193512\pi$
$877$	29.5360	+	12.2342i	0.997359	+	0.413120i	0.176531	+	0.984295i	$0.443512\pi$
$878$	7.61172	+	12.1224i	0.256883	+	0.409113i
$879$		−	57.8149i		−	1.95005i
$880$		0			0
$881$		−	8.17260i		−	0.275342i	−0.990478	−	0.137671i	$-0.956038\pi$
$881$		−	8.17260i		−	0.275342i	0.990478	−	0.137671i	$-0.0439617\pi$
$882$	49.5380	−	31.1051i	1.66803	−	1.04736i
$883$	11.6784	+	4.83737i	0.393011	+	0.162790i	0.570432	−	0.821345i	$-0.306776\pi$
$883$	11.6784	+	4.83737i	0.393011	+	0.162790i	−0.177422	+	0.984135i	$0.556776\pi$
$884$	35.3262	−	31.5295i	1.18815	−	1.06045i
$885$		0			0
$886$	9.06216	−	1.53679i	0.304449	−	0.0516295i
$887$	−24.8109	−	24.8109i	−0.833067	−	0.833067i	0.154868	−	0.987935i	$-0.450505\pi$
$887$	−24.8109	−	24.8109i	−0.833067	−	0.833067i	−0.987935	+	0.154868i	$0.950505\pi$
$888$	15.5904	−	19.5119i	0.523179	−	0.654778i
$889$	−11.6236	+	11.6236i	−0.389841	+	0.389841i
$890$		0			0
$891$	−42.4349	+	17.5771i	−1.42162	+	0.588855i
$892$	−42.0931	−	20.3036i	−1.40938	−	0.679814i
$893$	3.55705	−	8.58748i	0.119032	−	0.287369i
$894$	86.1172	+	19.6842i	2.88019	+	0.658337i
$895$		0			0
$896$	−11.5871	−	11.6382i	−0.387097	−	0.388805i
$897$	148.401			4.95496
$898$	11.6910	+	2.67227i	0.390134	+	0.0891747i
$899$	−0.819039	+	1.97734i	−0.0273165	+	0.0659478i
$900$		0			0
$901$	15.4334	−	6.39272i	0.514161	−	0.212972i
$902$	−6.63437	+	9.34405i	−0.220900	+	0.311123i
$903$	−3.57671	+	3.57671i	−0.119025	+	0.119025i
$904$	11.1922	−	14.0074i	0.372247	−	0.465881i
$905$		0			0
$906$	−88.4005	+	14.9912i	−2.93691	+	0.498051i
$907$	−13.3908	−	32.3281i	−0.444633	−	1.07344i	−0.974304	−	0.225236i	$-0.927685\pi$
$907$	−13.3908	−	32.3281i	−0.444633	−	1.07344i	0.529672	−	0.848203i	$-0.322315\pi$
$908$	−16.4662	+	14.6965i	−0.546450	+	0.487720i
$909$	−31.0305	−	12.8533i	−1.02922	−	0.426315i
$910$		0			0
$911$		−	19.2045i		−	0.636273i	−0.948045	−	0.318137i	$-0.896943\pi$
$911$		−	19.2045i		−	0.636273i	0.948045	−	0.318137i	$-0.103057\pi$
$912$	52.9220	+	6.03030i	1.75242	+	0.199683i
$913$		−	4.49617i		−	0.148802i
$914$	18.9751	+	30.2197i	0.627639	+	0.999579i
$915$		0			0
$916$	36.2266	+	2.05730i	1.19696	+	0.0679750i
$917$	−4.24711	−	10.2534i	−0.140252	−	0.338598i
$918$	18.4388	+	108.730i	0.608570	+	3.58862i
$919$	−7.47911	−	7.47911i	−0.246713	−	0.246713i	0.572907	−	0.819620i	$-0.305816\pi$
$919$	−7.47911	−	7.47911i	−0.246713	−	0.246713i	−0.819620	+	0.572907i	$0.805816\pi$
$920$		0			0
$921$	1.27140	−	1.27140i	0.0418939	−	0.0418939i
$922$	−3.17693	−	2.25566i	−0.104627	−	0.0742861i
$923$	−45.6902	+	18.9255i	−1.50391	+	0.622940i
$924$	11.4841	−	4.01036i	0.377799	−	0.131931i
$925$		0			0
$926$	−8.39169	+	36.7132i	−0.275768	+	1.20647i
$927$	−61.9731			−2.03546
$928$	12.5292	−	0.683866i	0.411290	−	0.0224490i
$929$	33.1810			1.08863			0.544317	−	0.838880i	$-0.316789\pi$
$929$	33.1810			1.08863			0.544317	+	0.838880i	$0.316789\pi$
$930$		0			0
$931$	7.36746	−	17.7866i	0.241459	−	0.582933i
$932$	−17.8579	−	51.1382i	−0.584956	−	1.67509i
$933$	−11.7771	+	4.87822i	−0.385564	+	0.159706i
$934$	−7.26482	−	5.15810i	−0.237712	−	0.168778i
$935$		0			0
$936$	−37.2089	+	128.699i	−1.21621	+	4.20665i
$937$	−4.34060	−	4.34060i	−0.141801	−	0.141801i	0.632643	−	0.774444i	$-0.281970\pi$
$937$	−4.34060	−	4.34060i	−0.141801	−	0.141801i	−0.774444	+	0.632643i	$0.781970\pi$
$938$	−0.613788	−	3.61939i	−0.0200409	−	0.118177i
$939$	25.1936	+	60.8227i	0.822161	+	1.98487i
$940$		0			0
$941$	−26.2850	−	10.8876i	−0.856866	−	0.354925i	−0.0893847	−	0.995997i	$-0.528490\pi$
$941$	−26.2850	−	10.8876i	−0.856866	−	0.354925i	−0.767481	+	0.641072i	$0.778490\pi$
$942$	−29.0147	−	46.2089i	−0.945351	−	1.50557i
$943$			51.2217i			1.66801i
$944$	−2.45593	−	1.36138i	−0.0799336	−	0.0443091i
$945$		0			0
$946$	1.52678	−	0.958671i	0.0496400	−	0.0311691i
$947$	35.7030	+	14.7887i	1.16019	+	0.480567i	0.877939	−	0.478773i	$-0.158918\pi$
$947$	35.7030	+	14.7887i	1.16019	+	0.480567i	0.282252	+	0.959340i	$0.408918\pi$
$948$	−67.1648	−	75.2526i	−2.18141	−	2.44409i
$949$	−17.2930	−	41.7491i	−0.561356	−	1.35523i
$950$		0			0
$951$	51.8358	+	51.8358i	1.68089	+	1.68089i
$952$	−1.92609	−	17.2407i	−0.0624250	−	0.558774i
$953$	−16.4270	+	16.4270i	−0.532122	+	0.532122i	−0.921204	−	0.389081i	$-0.872793\pi$
$953$	−16.4270	+	16.4270i	−0.532122	+	0.532122i	0.389081	+	0.921204i	$0.372793\pi$
$954$	−27.3624	+	38.5380i	−0.885889	+	1.24771i
$955$		0			0
$956$	16.9992	−	35.2424i	0.549793	−	1.13982i
$957$	−3.55667	+	8.58657i	−0.114971	+	0.277564i
$958$	12.2949	+	2.81029i	0.397229	+	0.0907965i
$959$	19.0058			0.613728
$960$		0			0
$961$	−30.0690			−0.969968
$962$	20.1554	+	4.60701i	0.649837	+	0.148536i
$963$	36.1544	−	87.2845i	1.16506	−	2.81270i
$964$	4.02410	−	8.34271i	0.129608	−	0.268701i
$965$		0			0
$966$	31.4764	−	44.3324i	1.01274	−	1.42637i
$967$	6.93584	−	6.93584i	0.223042	−	0.223042i	−0.586736	−	0.809778i	$-0.699588\pi$
$967$	6.93584	−	6.93584i	0.223042	−	0.223042i	0.809778	+	0.586736i	$0.199588\pi$
$968$	26.6117	−	2.97300i	0.855332	−	0.0955558i
$969$	39.7854	+	39.7854i	1.27809	+	1.27809i
$970$		0			0
$971$	14.4706	+	34.9351i	0.464383	+	1.12112i	0.966580	+	0.256366i	$0.0825253\pi$
$971$	14.4706	+	34.9351i	0.464383	+	1.12112i	−0.502197	+	0.864753i	$0.667475\pi$
$972$	−93.4715	−	104.727i	−2.99810	−	3.35913i
$973$	3.35290	+	1.38882i	0.107489	+	0.0445234i
$974$	24.6741	−	15.4930i	0.790610	−	0.496427i
$975$		0			0
$976$	30.3175	−	8.69305i	0.970440	−	0.278258i
$977$		−	21.7591i		−	0.696134i	−0.937470	−	0.348067i	$-0.886838\pi$
$977$		−	21.7591i		−	0.696134i	0.937470	−	0.348067i	$-0.113162\pi$
$978$	−32.9260	−	52.4380i	−1.05286	−	1.67678i
$979$	−16.0205	−	6.63589i	−0.512016	−	0.212084i
$980$		0			0
$981$	−44.7928	−	108.139i	−1.43012	−	3.45262i
$982$	7.48341	+	44.1282i	0.238805	+	1.40819i
$983$	−31.8111	−	31.8111i	−1.01462	−	1.01462i	−0.999892	−	0.0147254i	$-0.995313\pi$
$983$	−31.8111	−	31.8111i	−1.01462	−	1.01462i	−0.0147254	−	0.999892i	$-0.504687\pi$
$984$	−60.1859	−	17.4008i	−1.91866	−	0.554716i
$985$		0			0
$986$	10.8076	+	7.67350i	0.344184	+	0.244374i
$987$	10.7217	−	4.44106i	0.341275	−	0.141361i
$988$	14.5370	+	41.6282i	0.462482	+	1.32437i
$989$	3.08366	−	7.44463i	0.0980548	−	0.236725i
$990$		0			0
$991$	−4.60717			−0.146352			−0.0731758	−	0.997319i	$-0.523313\pi$
$991$	−4.60717			−0.146352			−0.0731758	+	0.997319i	$0.523313\pi$
$992$	−2.36047	−	4.92135i	−0.0749451	−	0.156253i
$993$	30.5134			0.968313
$994$	−4.03739	+	17.6634i	−0.128058	+	0.560248i
$995$		0			0
$996$	23.2064	−	8.10391i	0.735324	−	0.256782i
$997$	−29.7932	+	12.3407i	−0.943559	+	0.390835i	−0.800806	−	0.598924i	$-0.795595\pi$
$997$	−29.7932	+	12.3407i	−0.943559	+	0.390835i	−0.142752	+	0.989758i	$0.545595\pi$
$998$	−12.5099	−	8.88218i	−0.395995	−	0.281160i
$999$	−34.0501	+	34.0501i	−1.07730	+	1.07730i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	800.2.y.e.301.15	yes	64
5.2	odd	4		800.2.ba.h.749.7		64
5.3	odd	4		800.2.ba.f.749.10		64
5.4	even	2		800.2.y.d.301.2	yes	64
32.5	even	8	inner	800.2.y.e.101.15	yes	64
160.37	odd	8		800.2.ba.f.549.10		64
160.69	even	8		800.2.y.d.101.2	✓	64
160.133	odd	8		800.2.ba.h.549.7		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
800.2.y.d.101.2	✓	64	160.69	even	8
800.2.y.d.301.2	yes	64	5.4	even	2
800.2.y.e.101.15	yes	64	32.5	even	8	inner
800.2.y.e.301.15	yes	64	1.1	even	1	trivial
800.2.ba.f.549.10		64	160.37	odd	8
800.2.ba.f.749.10		64	5.3	odd	4
800.2.ba.h.549.7		64	160.133	odd	8
800.2.ba.h.749.7		64	5.2	odd	4

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:	\( N \)	\(=\)	\( 800 = 2^{5} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	800.y (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.37866 + 0.315126i) q^{2} +(-1.29511 + 3.12667i) q^{3} +(1.80139 + 0.868900i) q^{4} +(-2.77080 + 3.90248i) q^{6} +(-1.02642 + 1.02642i) q^{7} +(2.20969 + 1.76558i) q^{8} +(-5.97742 - 5.97742i) q^{9} +O(q^{10})\)	\(q+(1.37866 + 0.315126i) q^{2} +(-1.29511 + 3.12667i) q^{3} +(1.80139 + 0.868900i) q^{4} +(-2.77080 + 3.90248i) q^{6} +(-1.02642 + 1.02642i) q^{7} +(2.20969 + 1.76558i) q^{8} +(-5.97742 - 5.97742i) q^{9} +(0.473788 + 1.14383i) q^{11} +(-5.04976 + 4.50703i) q^{12} +(-5.17663 - 2.14423i) q^{13} +(-1.73854 + 1.09164i) q^{14} +(2.49002 + 3.13046i) q^{16} +4.22533i q^{17} +(-6.35718 - 10.1245i) q^{18} +(-3.63519 - 1.50574i) q^{19} +(-1.87996 - 4.53862i) q^{21} +(0.292743 + 1.72625i) q^{22} +(5.53379 + 5.53379i) q^{23} +(-8.38217 + 4.62234i) q^{24} +(-6.46110 - 4.58745i) q^{26} +(17.0508 - 7.06268i) q^{27} +(-2.74085 + 0.957132i) q^{28} +(0.848854 - 2.04932i) q^{29} -0.964876 q^{31} +(2.44640 + 5.10050i) q^{32} -4.18997 q^{33} +(-1.33151 + 5.82528i) q^{34} +(-5.57389 - 15.9615i) q^{36} +(-2.41056 + 0.998488i) q^{37} +(-4.53718 - 3.22145i) q^{38} +(13.4086 - 13.4086i) q^{39} +(4.62808 + 4.62808i) q^{41} +(-1.16158 - 6.84962i) q^{42} +(-0.394030 - 0.951273i) q^{43} +(-0.140393 + 2.47215i) q^{44} +(5.88536 + 9.37304i) q^{46} +2.36232i q^{47} +(-13.0128 + 3.73119i) q^{48} +4.89290i q^{49} +(-13.2112 - 5.47226i) q^{51} +(-7.46202 - 8.36058i) q^{52} +(-1.51295 - 3.65259i) q^{53} +(25.7329 - 4.36386i) q^{54} +(-4.08032 + 0.455844i) q^{56} +(9.41592 - 9.41592i) q^{57} +(1.81607 - 2.55781i) q^{58} +(-0.648566 + 0.268645i) q^{59} +(3.01738 - 7.28461i) q^{61} +(-1.33023 - 0.304057i) q^{62} +12.2708 q^{63} +(1.76545 + 7.80277i) q^{64} +(-5.77653 - 1.32037i) q^{66} +(-0.684344 + 1.65215i) q^{67} +(-3.67139 + 7.61147i) q^{68} +(-24.4692 + 10.1355i) q^{69} +(6.24109 - 6.24109i) q^{71} +(-2.65462 - 23.7619i) q^{72} +(5.70275 + 5.70275i) q^{73} +(-3.63799 + 0.616942i) q^{74} +(-5.24006 - 5.87105i) q^{76} +(-1.66036 - 0.687743i) q^{77} +(22.7113 - 14.2605i) q^{78} +14.9022i q^{79} +37.0991i q^{81} +(4.92211 + 7.83896i) q^{82} +(-3.35516 - 1.38975i) q^{83} +(0.557068 - 9.80933i) q^{84} +(-0.243462 - 1.43565i) q^{86} +(5.30817 + 5.30817i) q^{87} +(-0.972592 + 3.36401i) q^{88} +(-9.90375 + 9.90375i) q^{89} +(7.51432 - 3.11253i) q^{91} +(5.16021 + 14.7768i) q^{92} +(1.24962 - 3.01685i) q^{93} +(-0.744427 + 3.25683i) q^{94} +(-19.1159 + 1.04338i) q^{96} -13.1798 q^{97} +(-1.54188 + 6.74564i) q^{98} +(4.00510 - 9.66916i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q+O(q^{10}) \) 64 * q	\( 64 q - 16 q^{14} + 20 q^{16} + 20 q^{18} - 4 q^{22} + 8 q^{23} - 28 q^{24} + 24 q^{27} - 20 q^{28} - 20 q^{32} - 20 q^{34} + 12 q^{36} - 20 q^{38} + 24 q^{39} - 100 q^{42} + 8 q^{43} + 40 q^{44} + 32 q^{46} + 16 q^{51} - 88 q^{52} - 32 q^{53} + 76 q^{54} + 48 q^{56} + 72 q^{58} + 32 q^{59} - 32 q^{61} - 48 q^{62} + 80 q^{63} + 48 q^{64} + 16 q^{66} - 40 q^{67} + 48 q^{68} - 32 q^{69} + 32 q^{71} - 36 q^{72} + 8 q^{74} + 16 q^{77} + 36 q^{78} + 40 q^{83} + 56 q^{84} - 84 q^{86} - 40 q^{88} + 48 q^{91} + 4 q^{92} + 32 q^{94} - 100 q^{96} - 40 q^{98} - 64 q^{99}+O(q^{100}) \) 64 * q - 16 * q^14 + 20 * q^16 + 20 * q^18 - 4 * q^22 + 8 * q^23 - 28 * q^24 + 24 * q^27 - 20 * q^28 - 20 * q^32 - 20 * q^34 + 12 * q^36 - 20 * q^38 + 24 * q^39 - 100 * q^42 + 8 * q^43 + 40 * q^44 + 32 * q^46 + 16 * q^51 - 88 * q^52 - 32 * q^53 + 76 * q^54 + 48 * q^56 + 72 * q^58 + 32 * q^59 - 32 * q^61 - 48 * q^62 + 80 * q^63 + 48 * q^64 + 16 * q^66 - 40 * q^67 + 48 * q^68 - 32 * q^69 + 32 * q^71 - 36 * q^72 + 8 * q^74 + 16 * q^77 + 36 * q^78 + 40 * q^83 + 56 * q^84 - 84 * q^86 - 40 * q^88 + 48 * q^91 + 4 * q^92 + 32 * q^94 - 100 * q^96 - 40 * q^98 - 64 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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