LMFDB - Embedded newform 800.2.ba.f.749.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [800,2,Mod(149,800)]

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, 5, 4]))

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

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

chi := DirichletCharacter("800.149");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 800 = 2^{5} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	800.ba (of order $8$, degree $4$, not 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			749.10
Character	$\chi$	$=$	800.749
Dual form			800.2.ba.f.549.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.315126 - 1.37866i) q^{2} +(-3.12667 - 1.29511i) q^{3} +(-1.80139 - 0.868900i) q^{4} +(-2.77080 + 3.90248i) q^{6} +(1.02642 + 1.02642i) q^{7} +(-1.76558 + 2.20969i) q^{8} +(5.97742 + 5.97742i) q^{9} +O(q^{10})$	\(q+(0.315126 - 1.37866i) q^{2} +(-3.12667 - 1.29511i) q^{3} +(-1.80139 - 0.868900i) q^{4} +(-2.77080 + 3.90248i) q^{6} +(1.02642 + 1.02642i) q^{7} +(-1.76558 + 2.20969i) q^{8} +(5.97742 + 5.97742i) q^{9} +(0.473788 + 1.14383i) q^{11} +(4.50703 + 5.04976i) q^{12} +(2.14423 - 5.17663i) q^{13} +(1.73854 - 1.09164i) q^{14} +(2.49002 + 3.13046i) q^{16} +4.22533 q^{17} +(10.1245 - 6.35718i) q^{18} +(3.63519 + 1.50574i) q^{19} +(-1.87996 - 4.53862i) q^{21} +(1.72625 - 0.292743i) q^{22} +(-5.53379 + 5.53379i) q^{23} +(8.38217 - 4.62234i) q^{24} +(-6.46110 - 4.58745i) q^{26} +(-7.06268 - 17.0508i) q^{27} +(-0.957132 - 2.74085i) q^{28} +(-0.848854 + 2.04932i) q^{29} -0.964876 q^{31} +(5.10050 - 2.44640i) q^{32} -4.18997i q^{33} +(1.33151 - 5.82528i) q^{34} +(-5.57389 - 15.9615i) q^{36} +(0.998488 + 2.41056i) q^{37} +(3.22145 - 4.53718i) q^{38} +(-13.4086 + 13.4086i) q^{39} +(4.62808 + 4.62808i) q^{41} +(-6.84962 + 1.16158i) q^{42} +(0.951273 - 0.394030i) q^{43} +(0.140393 - 2.47215i) q^{44} +(5.88536 + 9.37304i) q^{46} +2.36232 q^{47} +(-3.73119 - 13.0128i) q^{48} -4.89290i q^{49} +(-13.2112 - 5.47226i) q^{51} +(-8.36058 + 7.46202i) q^{52} +(3.65259 - 1.51295i) q^{53} +(-25.7329 + 4.36386i) q^{54} +(-4.08032 + 0.455844i) q^{56} +(-9.41592 - 9.41592i) q^{57} +(2.55781 + 1.81607i) q^{58} +(0.648566 - 0.268645i) q^{59} +(3.01738 - 7.28461i) q^{61} +(-0.304057 + 1.33023i) q^{62} +12.2708i q^{63} +(-1.76545 - 7.80277i) q^{64} +(-5.77653 - 1.32037i) q^{66} +(1.65215 + 0.684344i) q^{67} +(-7.61147 - 3.67139i) q^{68} +(24.4692 - 10.1355i) q^{69} +(6.24109 - 6.24109i) q^{71} +(-23.7619 + 2.65462i) q^{72} +(-5.70275 + 5.70275i) q^{73} +(3.63799 - 0.616942i) q^{74} +(-5.24006 - 5.87105i) q^{76} +(-0.687743 + 1.66036i) q^{77} +(14.2605 + 22.7113i) q^{78} -14.9022i q^{79} +37.0991i q^{81} +(7.83896 - 4.92211i) q^{82} +(1.38975 - 3.35516i) q^{83} +(-0.557068 + 9.80933i) q^{84} +(-0.243462 - 1.43565i) q^{86} +(5.30817 - 5.30817i) q^{87} +(-3.36401 - 0.972592i) q^{88} +(9.90375 - 9.90375i) q^{89} +(7.51432 - 3.11253i) q^{91} +(14.7768 - 5.16021i) q^{92} +(3.01685 + 1.24962i) q^{93} +(0.744427 - 3.25683i) q^{94} +(-19.1159 + 1.04338i) q^{96} +13.1798i q^{97} +(-6.74564 - 1.54188i) q^{98} +(-4.00510 + 9.66916i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q+O(q^{10}) $ 64 * q	$ 64 q - 24 q^{12} + 16 q^{14} + 20 q^{16} + 40 q^{18} + 24 q^{22} - 8 q^{23} + 28 q^{24} - 48 q^{28} - 20 q^{32} + 20 q^{34} + 12 q^{36} + 16 q^{37} - 24 q^{39} - 40 q^{44} + 32 q^{46} + 80 q^{47} + 40 q^{48} + 16 q^{51} - 76 q^{54} + 48 q^{56} - 8 q^{58} - 32 q^{59} - 32 q^{61} - 44 q^{62} - 48 q^{64} + 16 q^{66} - 32 q^{68} + 32 q^{69} + 32 q^{71} + 96 q^{72} - 8 q^{74} + 52 q^{78} - 116 q^{82} - 56 q^{84} - 84 q^{86} + 20 q^{88} + 48 q^{91} + 88 q^{92} - 48 q^{93} - 32 q^{94} - 100 q^{96} - 72 q^{98} + 64 q^{99}+O(q^{100}) $ 64 * q - 24 * q^12 + 16 * q^14 + 20 * q^16 + 40 * q^18 + 24 * q^22 - 8 * q^23 + 28 * q^24 - 48 * q^28 - 20 * q^32 + 20 * q^34 + 12 * q^36 + 16 * q^37 - 24 * q^39 - 40 * q^44 + 32 * q^46 + 80 * q^47 + 40 * q^48 + 16 * q^51 - 76 * q^54 + 48 * q^56 - 8 * q^58 - 32 * q^59 - 32 * q^61 - 44 * q^62 - 48 * q^64 + 16 * q^66 - 32 * q^68 + 32 * q^69 + 32 * q^71 + 96 * q^72 - 8 * q^74 + 52 * q^78 - 116 * q^82 - 56 * q^84 - 84 * q^86 + 20 * q^88 + 48 * q^91 + 88 * q^92 - 48 * q^93 - 32 * q^94 - 100 * q^96 - 72 * 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 $

$2$	0.315126	−	1.37866i	0.222827	−	0.974858i
$2$	0.315126	−	1.37866i	0.222827	−	0.974858i
$3$	−3.12667	−	1.29511i	−1.80518	−	0.747731i	−0.984269	−	0.176678i	$-0.943465\pi$
$3$	−3.12667	−	1.29511i	−1.80518	−	0.747731i	−0.820913	−	0.571053i	$-0.806535\pi$
$4$	−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	$-0.161546\pi$
$7$	1.02642	+	1.02642i	0.387952	+	0.387952i	−0.486004	+	0.873956i	$0.661546\pi$
$8$	−1.76558	+	2.20969i	−0.624227	+	0.781243i
$9$	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	$0.815238\pi$
$12$	4.50703	+	5.04976i	1.30107	+	1.45774i
$13$	2.14423	−	5.17663i	0.594703	−	1.43574i	−0.284212	−	0.958761i	$-0.591732\pi$
$13$	2.14423	−	5.17663i	0.594703	−	1.43574i	0.878915	−	0.476979i	$-0.158268\pi$
$14$	1.73854	−	1.09164i	0.464645	−	0.291752i
$15$		0			0
$16$	2.49002	+	3.13046i	0.622506	+	0.782615i
$17$	4.22533			1.02479			0.512396	−	0.858749i	$-0.328758\pi$
$17$	4.22533			1.02479			0.512396	+	0.858749i	$0.328758\pi$
$18$	10.1245	−	6.35718i	2.38636	−	1.49840i
$19$	3.63519	+	1.50574i	0.833969	+	0.345441i	0.758473	−	0.651705i	$-0.225946\pi$
$19$	3.63519	+	1.50574i	0.833969	+	0.345441i	0.0754966	+	0.997146i	$0.475946\pi$
$20$		0			0
$21$	−1.87996	−	4.53862i	−0.410240	−	0.990408i
$22$	1.72625	−	0.292743i	0.368037	−	0.0624130i
$23$	−5.53379	+	5.53379i	−1.15388	+	1.15388i	−0.168107	+	0.985769i	$0.553765\pi$
$23$	−5.53379	+	5.53379i	−1.15388	+	1.15388i	−0.985769	+	0.168107i	$0.946235\pi$
$24$	8.38217	−	4.62234i	1.71100	−	0.943532i
$25$		0			0
$26$	−6.46110	−	4.58745i	−1.26713	−	0.899673i
$27$	−7.06268	−	17.0508i	−1.35921	−	3.28143i
$28$	−0.957132	−	2.74085i	−0.180881	−	0.517973i
$29$	−0.848854	+	2.04932i	−0.157628	+	0.380548i	−0.982888	−	0.184205i	$-0.941029\pi$
$29$	−0.848854	+	2.04932i	−0.157628	+	0.380548i	0.825259	+	0.564754i	$0.191029\pi$
$30$		0			0
$31$	−0.964876			−0.173297			−0.0866484	−	0.996239i	$-0.527616\pi$
$31$	−0.964876			−0.173297			−0.0866484	+	0.996239i	$0.527616\pi$
$32$	5.10050	−	2.44640i	0.901650	−	0.432467i
$33$		−	4.18997i		−	0.729380i
$34$	1.33151	−	5.82528i	0.228352	−	0.999027i
$35$		0			0
$36$	−5.57389	−	15.9615i	−0.928982	−	2.66024i
$37$	0.998488	+	2.41056i	0.164150	+	0.396294i	0.984456	−	0.175631i	$-0.0561967\pi$
$37$	0.998488	+	2.41056i	0.164150	+	0.396294i	−0.820306	+	0.571925i	$0.806197\pi$
$38$	3.22145	−	4.53718i	0.522588	−	0.736028i
$39$	−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	$0.579243\pi$
$42$	−6.84962	+	1.16158i	−1.05692	+	0.179236i
$43$	0.951273	−	0.394030i	0.145068	−	0.0600890i	−0.308968	−	0.951072i	$-0.599984\pi$
$43$	0.951273	−	0.394030i	0.145068	−	0.0600890i	0.454036	+	0.890983i	$0.349984\pi$
$44$	0.140393	−	2.47215i	0.0211650	−	0.372691i
$45$		0			0
$46$	5.88536	+	9.37304i	0.867750	+	1.38198i
$47$	2.36232			0.344580			0.172290	−	0.985046i	$-0.444883\pi$
$47$	2.36232			0.344580			0.172290	+	0.985046i	$0.444883\pi$
$48$	−3.73119	−	13.0128i	−0.538551	−	1.87823i
$49$		−	4.89290i		−	0.698986i
$50$		0			0
$51$	−13.2112	−	5.47226i	−1.84994	−	0.766269i
$52$	−8.36058	+	7.46202i	−1.15940	+	1.03480i
$53$	3.65259	−	1.51295i	0.501722	−	0.207820i	−0.117445	−	0.993079i	$-0.537470\pi$
$53$	3.65259	−	1.51295i	0.501722	−	0.207820i	0.619167	+	0.785259i	$0.287470\pi$
$54$	−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
$58$	2.55781	+	1.81607i	0.335857	+	0.238462i
$59$	0.648566	−	0.268645i	0.0844361	−	0.0349746i	−0.340066	−	0.940402i	$-0.610449\pi$
$59$	0.648566	−	0.268645i	0.0844361	−	0.0349746i	0.424502	+	0.905427i	$0.360449\pi$
$60$		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	$-0.0434237\pi$
$62$	−0.304057	+	1.33023i	−0.0386153	+	0.168940i
$63$			12.2708i			1.54597i
$64$	−1.76545	−	7.80277i	−0.220681	−	0.975346i
$65$		0			0
$66$	−5.77653	−	1.32037i	−0.711042	−	0.162526i
$67$	1.65215	+	0.684344i	0.201843	+	0.0836059i	0.481315	−	0.876548i	$-0.340159\pi$
$67$	1.65215	+	0.684344i	0.201843	+	0.0836059i	−0.279472	+	0.960154i	$0.590159\pi$
$68$	−7.61147	−	3.67139i	−0.923027	−	0.445222i
$69$	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	$0.0745362\pi$
$72$	−23.7619	+	2.65462i	−2.80036	+	0.312850i
$73$	−5.70275	+	5.70275i	−0.667457	+	0.667457i	−0.957127	−	0.289670i	$-0.906454\pi$
$73$	−5.70275	+	5.70275i	−0.667457	+	0.667457i	0.289670	+	0.957127i	$0.406454\pi$
$74$	3.63799	−	0.616942i	0.422908	−	0.0717181i
$75$		0			0
$76$	−5.24006	−	5.87105i	−0.601076	−	0.673456i
$77$	−0.687743	+	1.66036i	−0.0783756	+	0.189216i
$78$	14.2605	+	22.7113i	1.61468	+	2.57154i
$79$		−	14.9022i		−	1.67663i	−0.545186	−	0.838315i	$-0.683541\pi$
$79$		−	14.9022i		−	1.67663i	0.545186	−	0.838315i	$-0.316459\pi$
$80$		0			0
$81$			37.0991i			4.12212i
$82$	7.83896	−	4.92211i	0.865669	−	0.543556i
$83$	1.38975	−	3.35516i	0.152545	−	0.368277i	−0.829071	−	0.559144i	$-0.811130\pi$
$83$	1.38975	−	3.35516i	0.152545	−	0.368277i	0.981616	+	0.190867i	$0.0611299\pi$
$84$	−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
$88$	−3.36401	−	0.972592i	−0.358605	−	0.103679i
$89$	9.90375	−	9.90375i	1.04980	−	1.04980i	0.0511025	−	0.998693i	$-0.483726\pi$
$89$	9.90375	−	9.90375i	1.04980	−	1.04980i	0.998693	−	0.0511025i	$-0.0162735\pi$
$90$		0			0
$91$	7.51432	−	3.11253i	0.787715	−	0.326282i
$92$	14.7768	−	5.16021i	1.54059	−	0.537989i
$93$	3.01685	+	1.24962i	0.312832	+	0.129579i
$94$	0.744427	−	3.25683i	0.0767818	−	0.335916i
$95$		0			0
$96$	−19.1159	+	1.04338i	−1.95101	+	0.106490i
$97$			13.1798i			1.33820i	0.743171	+	0.669101i	$0.233321\pi$
$97$			13.1798i			1.33820i	−0.743171	+	0.669101i	$0.766679\pi$
$98$	−6.74564	−	1.54188i	−0.681412	−	0.155753i
$99$	−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	$0.311661\pi$
$102$	−11.7076	+	16.4893i	−1.15922	+	1.63268i
$103$	5.18393	+	5.18393i	0.510788	+	0.510788i	0.914768	−	0.403980i	$-0.132374\pi$
$103$	5.18393	+	5.18393i	0.510788	+	0.510788i	−0.403980	+	0.914768i	$0.632374\pi$
$104$	7.65294	+	13.8779i	0.750432	+	1.36084i
$105$		0			0
$106$	−0.934818	−	5.51244i	−0.0907975	−	0.535415i
$107$	10.3254	−	4.27693i	0.998197	−	0.413467i	0.177061	−	0.984200i	$-0.443341\pi$
$107$	10.3254	−	4.27693i	0.998197	−	0.413467i	0.821136	+	0.570733i	$0.193341\pi$
$108$	−2.09281	+	36.8520i	−0.201381	+	3.54608i
$109$	−12.7925	−	5.29882i	−1.22530	−	0.507534i	−0.326207	−	0.945298i	$-0.605771\pi$
$109$	−12.7925	−	5.29882i	−1.22530	−	0.507534i	−0.899090	+	0.437764i	$0.855771\pi$
$110$		0			0
$111$		−	8.83018i		−	0.838123i
$112$	−0.657360	+	5.76901i	−0.0621146	+	0.545120i
$113$	6.33910			0.596332			0.298166	−	0.954514i	$-0.403625\pi$
$113$	6.33910			0.596332			0.298166	+	0.954514i	$0.403625\pi$
$114$	−15.9485	+	10.0141i	−1.49372	+	0.937909i
$115$		0			0
$116$	3.30977	−	2.95405i	0.307305	−	0.274277i
$117$	43.7599	−	18.1259i	4.04561	−	1.67574i
$118$	−0.165989	−	0.978807i	−0.0152806	−	0.0901065i
$119$	4.33698	+	4.33698i	0.397571	+	0.397571i
$120$		0			0
$121$	6.69431	−	6.69431i	0.608574	−	0.608574i
$122$	−9.09212	−	6.45550i	−0.823162	−	0.584454i
$123$	−8.47660	−	20.4643i	−0.764310	−	1.84521i
$124$	1.73812	+	0.838381i	0.156088	+	0.0752888i
$125$		0			0
$126$	16.9172	+	3.86683i	1.50710	+	0.344484i
$127$		−	11.3243i		−	1.00487i	−0.864615	−	0.502435i	$-0.832438\pi$
$127$		−	11.3243i		−	1.00487i	0.864615	−	0.502435i	$-0.167562\pi$
$128$	−11.3137	−	0.0249011i	−0.999998	−	0.00220097i
$129$	−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	$0.233398\pi$
$132$	−3.64067	+	7.54778i	−0.316879	+	0.656950i
$133$	2.18571	+	5.27678i	0.189526	+	0.457555i
$134$	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	−0.981654	−	0.190670i	$-0.938934\pi$
$137$	−9.25823	+	9.25823i	−0.790984	+	0.790984i	0.190670	+	0.981654i	$0.438934\pi$
$138$	−6.26247	−	36.9286i	−0.533097	−	3.14357i
$139$	0.956760	+	2.30982i	0.0811513	+	0.195917i	0.959247	−	0.282568i	$-0.0911863\pi$
$139$	0.956760	+	2.30982i	0.0811513	+	0.195917i	−0.878096	+	0.478485i	$0.841186\pi$
$140$		0			0
$141$	−7.38619	−	3.05946i	−0.622029	−	0.257653i
$142$	−6.63759	−	10.5710i	−0.557014	−	0.887102i
$143$	6.93708			0.580108
$144$	−3.82816	+	33.5960i	−0.319013	+	2.79967i
$145$		0			0
$146$	6.06506	+	9.65922i	0.501948	+	0.799403i
$147$	−6.33684	+	15.2985i	−0.522654	+	1.26180i
$148$	0.295872	−	5.20996i	0.0243205	−	0.428256i
$149$	7.06329	+	17.0523i	0.578647	+	1.39698i	0.894027	+	0.448012i	$0.147868\pi$
$149$	7.06329	+	17.0523i	0.578647	+	1.39698i	−0.315380	+	0.948965i	$0.602132\pi$
$150$		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	$0.474083\pi$
$152$	−9.74545	+	5.37412i	−0.790460	+	0.435899i
$153$	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
$157$	10.5325	+	4.36271i	0.840586	+	0.348182i	0.761085	−	0.648652i	$-0.224667\pi$
$157$	10.5325	+	4.36271i	0.840586	+	0.348182i	0.0795017	+	0.996835i	$0.474667\pi$
$158$	−20.5451	−	4.69607i	−1.63448	−	0.373599i
$159$	−13.3799			−1.06109
$160$		0			0
$161$	−11.3600			−0.895297
$162$	51.1469	+	11.6909i	4.01848	+	0.918522i
$163$	−11.9523	−	4.95082i	−0.936179	−	0.387778i	−0.138160	−	0.990410i	$-0.544119\pi$
$163$	−11.9523	−	4.95082i	−0.936179	−	0.387778i	−0.798019	+	0.602632i	$0.794119\pi$
$164$	−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	$-0.135011\pi$
$167$	6.45942	+	6.45942i	0.499845	+	0.499845i	−0.411545	+	0.911390i	$0.635011\pi$
$168$	13.3482	+	3.85918i	1.02983	+	0.297742i
$169$	−13.0074	−	13.0074i	−1.00057	−	1.00057i
$170$		0			0
$171$	12.7286	+	30.7295i	0.973379	+	2.34995i
$172$	−2.05599	−	0.116759i	−0.156768	−	0.00890278i
$173$	−4.83167	+	11.6647i	−0.367345	+	0.886849i	0.626838	+	0.779149i	$0.284349\pi$
$173$	−4.83167	+	11.6647i	−0.367345	+	0.886849i	−0.994183	+	0.107700i	$0.965651\pi$
$174$	−5.64541	−	8.99089i	−0.427977	−	0.681598i
$175$		0			0
$176$	−2.40096	+	4.33133i	−0.180979	+	0.326486i
$177$	−2.37577			−0.178574
$178$	−10.5330	−	16.7748i	−0.789478	−	1.25733i
$179$	−1.39173	−	0.576474i	−0.104023	−	0.0430877i	0.330065	−	0.943958i	$-0.392929\pi$
$179$	−1.39173	−	0.576474i	−0.104023	−	0.0430877i	−0.434088	+	0.900870i	$0.642929\pi$
$180$		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	$0.904148\pi$
$182$	−1.92316	−	11.3405i	−0.142554	−	0.840615i
$183$	−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
$187$	2.00191	+	4.83304i	0.146394	+	0.353427i
$188$	−4.25546	−	2.05262i	−0.310362	−	0.149703i
$189$	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	$0.316142\pi$
$192$	−4.58545	+	26.6831i	−0.330926	+	1.92569i
$193$			2.95918i			0.213007i	0.994312	+	0.106503i	$0.0339655\pi$
$193$			2.95918i			0.213007i	−0.994312	+	0.106503i	$0.966035\pi$
$194$	18.1704	+	4.15328i	1.30456	+	0.298188i
$195$		0			0
$196$	−4.25145	+	8.81404i	−0.303675	+	0.629574i
$197$	−5.14189	−	12.4136i	−0.366344	−	0.884433i	−0.994343	−	0.106219i	$-0.966126\pi$
$197$	−5.14189	−	12.4136i	−0.366344	−	0.884433i	0.627998	−	0.778215i	$-0.283874\pi$
$198$	12.0684	+	8.56866i	0.857660	+	0.608948i
$199$	−7.68494	+	7.68494i	−0.544771	+	0.544771i	−0.924924	−	0.380153i	$-0.875871\pi$
$199$	−7.68494	+	7.68494i	−0.544771	+	0.544771i	0.380153	+	0.924924i	$0.375871\pi$
$200$		0			0
$201$	−4.27943	−	4.27943i	−0.301848	−	0.301848i
$202$	−0.939476	−	5.53991i	−0.0661013	−	0.389787i
$203$	−2.97475	+	1.23218i	−0.208787	+	0.0864823i
$204$	19.0437	+	21.3369i	1.33333	+	1.49388i
$205$		0			0
$206$	8.78045	−	5.51327i	0.611763	−	0.384128i
$207$	−66.1556			−4.59813
$208$	21.5444	−	6.17751i	1.49384	−	0.428333i
$209$			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	$0.661500\pi$
$212$	−7.89435	−	0.448317i	−0.542186	−	0.0307906i
$213$	−27.5967	+	11.4309i	−1.89089	+	0.783234i
$214$	−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
$218$	−11.3365	+	15.9666i	−0.767804	+	1.08140i
$219$	25.2163	−	10.4449i	1.70396	−	0.705803i
$220$		0			0
$221$	9.06009	−	21.8730i	0.609447	−	1.47134i
$222$	−12.1738	−	2.78262i	−0.817051	−	0.186757i
$223$		−	23.3670i		−	1.56477i	−0.622796	−	0.782384i	$-0.714004\pi$
$223$		−	23.3670i		−	1.56477i	0.622796	−	0.782384i	$-0.285996\pi$
$224$	7.74633	+	2.72423i	0.517573	+	0.182021i
$225$		0			0
$226$	1.99761	−	8.73945i	0.132879	−	0.581339i
$227$	10.1954	+	4.22308i	0.676693	+	0.280295i	0.694444	−	0.719547i	$-0.255651\pi$
$227$	10.1954	+	4.22308i	0.676693	+	0.280295i	−0.0177508	+	0.999842i	$0.505651\pi$
$228$	8.78027	+	25.1433i	0.581487	+	1.66515i
$229$	−16.7615	+	6.94283i	−1.10763	+	0.458795i	−0.860121	−	0.510090i	$-0.829612\pi$
$229$	−16.7615	+	6.94283i	−1.10763	+	0.458795i	−0.247509	+	0.968886i	$0.579612\pi$
$230$		0			0
$231$	4.30069	−	4.30069i	0.282965	−	0.282965i
$232$	−3.02963	−	5.49394i	−0.198905	−	0.360695i
$233$	19.1508	−	19.1508i	1.25461	−	1.25461i	0.300978	−	0.953631i	$-0.402687\pi$
$233$	19.1508	−	19.1508i	1.25461	−	1.25461i	0.953631	−	0.300978i	$-0.0973131\pi$
$234$	−11.1996	−	66.0419i	−0.732141	−	4.31729i
$235$		0			0
$236$	−1.40175	−	0.0796047i	−0.0912460	−	0.00518183i
$237$	−19.3000	+	46.5943i	−1.25367	+	3.02662i
$238$	7.34591	−	4.61252i	0.476165	−	0.298985i
$239$			19.5640i			1.26549i	0.774360	+	0.632745i	$0.218072\pi$
$239$			19.5640i			1.26549i	−0.774360	+	0.632745i	$0.781928\pi$
$240$		0			0
$241$		−	4.63126i		−	0.298325i	−0.988813	−	0.149163i	$-0.952342\pi$
$241$		−	4.63126i		−	0.298325i	0.988813	−	0.149163i	$-0.0476578\pi$
$242$	−7.11961	−	11.3387i	−0.457666	−	0.728880i
$243$	26.8593	−	64.8441i	1.72302	−	4.15975i
$244$	−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
$248$	1.70357	−	2.13208i	0.108177	−	0.135387i
$249$	−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	$0.255244\pi$
$252$	10.6621	−	22.1044i	0.671647	−	1.39245i
$253$	−8.95154	−	3.70785i	−0.562779	−	0.233111i
$254$	−15.6123	−	3.56858i	−0.979605	−	0.223913i
$255$		0			0
$256$	−3.59956	+	15.5898i	−0.224973	+	0.974365i
$257$			4.04829i			0.252525i	0.991997	+	0.126263i	$0.0402982\pi$
$257$			4.04829i			0.252525i	−0.991997	+	0.126263i	$0.959702\pi$
$258$	−1.09809	+	4.80410i	−0.0683644	+	0.299090i
$259$	−1.44939	+	3.49914i	−0.0900607	+	0.217426i
$260$		0			0
$261$	−17.3236	+	7.17567i	−1.07230	+	0.444163i
$262$	8.81629	+	6.25966i	0.544672	+	0.386723i
$263$	1.60540	+	1.60540i	0.0989933	+	0.0989933i	0.754869	−	0.655876i	$-0.227700\pi$
$263$	1.60540	+	1.60540i	0.0989933	+	0.0989933i	−0.655876	+	0.754869i	$0.727700\pi$
$264$	9.25853	+	7.39773i	0.569823	+	0.455299i
$265$		0			0
$266$	7.96365	−	1.35050i	0.488283	−	0.0828046i
$267$	−43.7922	+	18.1393i	−2.68004	+	1.11011i
$268$	−2.38155	−	2.66833i	−0.145476	−	0.162994i
$269$	−3.38365	−	1.40155i	−0.206305	−	0.0854542i	0.277138	−	0.960830i	$-0.410614\pi$
$269$	−3.38365	−	1.40155i	−0.206305	−	0.0854542i	−0.483443	+	0.875376i	$0.660614\pi$
$270$		0			0
$271$		−	22.4256i		−	1.36226i	−0.732165	−	0.681128i	$-0.761490\pi$
$271$		−	22.4256i		−	1.36226i	0.732165	−	0.681128i	$-0.238510\pi$
$272$	10.5212	+	13.2272i	0.637940	+	0.802018i
$273$	−27.5258			−1.66594
$274$	9.84642	+	15.6814i	0.594844	+	0.947350i
$275$		0			0
$276$	−52.8853	−	3.00334i	−3.18332	−	0.180780i
$277$	−5.32210	+	2.20449i	−0.319774	+	0.132455i	−0.536796	−	0.843712i	$-0.680366\pi$
$277$	−5.32210	+	2.20449i	−0.319774	+	0.132455i	0.217022	+	0.976167i	$0.430366\pi$
$278$	3.48595	−	0.591160i	0.209074	−	0.0354554i
$279$	−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	$0.225595\pi$
$282$	−6.54552	+	9.21891i	−0.389780	+	0.548978i
$283$	6.30082	+	15.2115i	0.374545	+	0.904232i	0.992968	+	0.118386i	$0.0377720\pi$
$283$	6.30082	+	15.2115i	0.374545	+	0.904232i	−0.618423	+	0.785846i	$0.712228\pi$
$284$	−16.6655	+	5.81976i	−0.988917	+	0.345339i
$285$		0			0
$286$	2.18605	−	9.56386i	0.129264	−	0.565523i
$287$			9.50075i			0.560812i
$288$	45.1110	+	15.8647i	2.65819	+	0.934835i
$289$	0.853410			0.0502006
$290$		0			0
$291$	17.0692	−	41.2087i	1.00062	−	2.41570i
$292$	15.2280	−	5.31777i	0.891152	−	0.311199i
$293$	−6.53752	−	15.7830i	−0.381926	−	0.922051i	−0.991593	−	0.129394i	$-0.958697\pi$
$293$	−6.53752	−	15.7830i	−0.381926	−	0.922051i	0.609667	−	0.792658i	$-0.291303\pi$
$294$	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
$298$	25.7351	−	4.36424i	1.49079	−	0.252814i
$299$	16.7807	+	40.5122i	0.970452	+	2.34288i
$300$		0			0
$301$	1.38085	+	0.571968i	0.0795910	+	0.0329677i
$302$	22.4374	−	14.0885i	1.29113	−	0.810703i
$303$	−13.4465			−0.772484
$304$	4.33803	+	15.1292i	0.248803	+	0.867716i
$305$		0			0
$306$	42.7792	−	26.8612i	2.44552	−	1.53555i
$307$	−0.203315	+	0.490845i	−0.0116038	+	0.0280140i	−0.929575	−	0.368632i	$-0.879826\pi$
$307$	−0.203315	+	0.490845i	−0.0116038	+	0.0280140i	0.917971	+	0.396646i	$0.129826\pi$
$308$	2.68158	−	2.39338i	0.152797	−	0.136375i
$309$	−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	$0.715942\pi$
$312$	−5.95487	−	53.3028i	−0.337128	−	3.01768i
$313$	13.7553	+	13.7553i	0.777493	+	0.777493i	0.979404	−	0.201911i	$-0.0647150\pi$
$313$	13.7553	+	13.7553i	0.777493	+	0.777493i	−0.201911	+	0.979404i	$0.564715\pi$
$314$	9.33375	−	13.1459i	0.526734	−	0.741868i
$315$		0			0
$316$	−12.9485	+	26.8447i	−0.728413	+	1.51013i
$317$	−20.0122	−	8.28931i	−1.12399	−	0.465574i	−0.258259	−	0.966076i	$-0.583149\pi$
$317$	−20.0122	−	8.28931i	−1.12399	−	0.465574i	−0.865736	+	0.500502i	$0.833149\pi$
$318$	−4.21634	+	18.4462i	−0.236440	+	1.03441i
$319$	−2.74624			−0.153760
$320$		0			0
$321$	−37.8233			−2.11109
$322$	−3.57984	+	15.6616i	−0.199497	+	0.872787i
$323$	15.3599	+	6.36227i	0.854646	+	0.354006i
$324$	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
$328$	−18.3979	+	2.05537i	−1.01585	+	0.113489i
$329$	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	$0.954704\pi$
$332$	−5.41879	+	4.83641i	−0.297395	+	0.265432i
$333$	−8.44057	+	20.3773i	−0.462540	+	1.11667i
$334$	10.9409	−	6.86980i	0.598657	−	0.375899i
$335$		0			0
$336$	9.52683	−	17.1864i	0.519731	−	0.937595i
$337$	−12.2658			−0.668162			−0.334081	−	0.942544i	$-0.608426\pi$
$337$	−12.2658			−0.668162			−0.334081	+	0.942544i	$0.608426\pi$
$338$	−22.0318	+	13.8338i	−1.19837	+	0.752460i
$339$	−19.8203	−	8.20982i	−1.07649	−	0.445896i
$340$		0			0
$341$	−0.457147	−	1.10365i	−0.0247559	−	0.0597660i
$342$	46.3766	−	7.86470i	2.50776	−	0.425274i
$343$	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
$347$	−6.72820	−	16.2433i	−0.361189	−	0.871987i	−0.995127	−	0.0986033i	$-0.968563\pi$
$347$	−6.72820	−	16.2433i	−0.361189	−	0.871987i	0.633938	−	0.773384i	$-0.281437\pi$
$348$	−14.1744	+	4.94982i	−0.759826	+	0.265338i
$349$	10.6274	−	25.6568i	0.568871	−	1.37338i	−0.333636	−	0.942702i	$-0.608275\pi$
$349$	10.6274	−	25.6568i	0.568871	−	1.37338i	0.902507	−	0.430675i	$-0.141725\pi$
$350$		0			0
$351$	−103.410			−5.51961
$352$	5.21481	+	4.67501i	0.277951	+	0.249179i
$353$			21.9232i			1.16686i	0.812165	+	0.583428i	$0.198289\pi$
$353$			21.9232i			1.16686i	−0.812165	+	0.583428i	$0.801711\pi$
$354$	−0.748667	+	3.27538i	−0.0397912	+	0.174084i
$355$		0			0
$356$	−26.4459	+	9.23516i	−1.40163	+	0.489463i
$357$	−7.94344	−	19.1772i	−0.420412	−	1.01496i
$358$	−1.23333	+	1.73706i	−0.0651835	+	0.0918064i
$359$	−4.02137	+	4.02137i	−0.212240	+	0.212240i	−0.805218	−	0.592978i	$-0.797952\pi$
$359$	−4.02137	+	4.02137i	−0.212240	+	0.212240i	0.592978	+	0.805218i	$0.297952\pi$
$360$		0			0
$361$	−2.48770	−	2.48770i	−0.130931	−	0.130931i
$362$	−3.43063	+	0.581777i	−0.180310	+	0.0305775i
$363$	−29.6007	+	12.2610i	−1.55364	+	0.643537i
$364$	−16.2407	−	0.922305i	−0.851245	−	0.0483419i
$365$		0			0
$366$	20.0675	+	31.9595i	1.04894	+	1.67055i
$367$	28.1923			1.47163			0.735814	−	0.677183i	$-0.236800\pi$
$367$	28.1923			1.47163			0.735814	+	0.677183i	$0.236800\pi$
$368$	−31.1026	−	3.54404i	−1.62133	−	0.184746i
$369$			55.3280i			2.88026i
$370$		0			0
$371$	5.30204	+	2.19618i	0.275268	+	0.114020i
$372$	−4.34873	−	4.87239i	−0.225471	−	0.252622i
$373$	1.14096	−	0.472600i	0.0590765	−	0.0244703i	−0.352950	−	0.935642i	$-0.614821\pi$
$373$	1.14096	−	0.472600i	0.0590765	−	0.0244703i	0.412026	+	0.911172i	$0.364821\pi$
$374$	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
$378$	−30.8920	−	21.9337i	−1.58891	−	1.12815i
$379$	6.22454	−	2.57829i	0.319733	−	0.132438i	−0.217044	−	0.976162i	$-0.569642\pi$
$379$	6.22454	−	2.57829i	0.319733	−	0.132438i	0.536777	+	0.843724i	$0.319642\pi$
$380$		0			0
$381$	−14.6662	+	35.4073i	−0.751372	+	1.81397i
$382$	4.75597	−	20.8071i	0.243337	−	1.06458i
$383$			6.12827i			0.313140i	0.987667	+	0.156570i	$0.0500437\pi$
$383$			6.12827i			0.313140i	−0.987667	+	0.156570i	$0.949956\pi$
$384$	35.3419	+	14.7303i	1.80353	+	0.751702i
$385$		0			0
$386$	4.07970	+	0.932514i	0.207651	+	0.0474637i
$387$	8.04144	+	3.33087i	0.408769	+	0.169318i
$388$	11.4519	−	23.7419i	0.581382	−	1.20531i
$389$	−15.9683	+	6.61427i	−0.809623	+	0.335357i	−0.748804	−	0.662792i	$-0.769371\pi$
$389$	−15.9683	+	6.61427i	−0.809623	+	0.335357i	−0.0608194	+	0.998149i	$0.519371\pi$
$390$		0			0
$391$	−23.3821	+	23.3821i	−1.18248	+	1.18248i
$392$	10.8118	+	8.63882i	0.546078	+	0.436326i
$393$	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
$397$	−6.14033	+	14.8241i	−0.308174	+	0.743999i	0.691590	+	0.722290i	$0.256911\pi$
$397$	−6.14033	+	14.8241i	−0.308174	+	0.743999i	−0.999764	+	0.0217084i	$0.993089\pi$
$398$	8.17318	+	13.0166i	0.409684	+	0.652464i
$399$		−	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	$0.761053\pi$
$402$	−7.24843	+	4.55131i	−0.361519	+	0.226999i
$403$	−2.06892	+	4.99481i	−0.103060	+	0.248809i
$404$	−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
$408$	35.4174	−	19.5309i	1.75342	−	0.966925i
$409$	2.23691	−	2.23691i	0.110608	−	0.110608i	−0.649637	−	0.760245i	$-0.725079\pi$
$409$	2.23691	−	2.23691i	0.110608	−	0.110608i	0.760245	+	0.649637i	$0.225079\pi$
$410$		0			0
$411$	40.9378	−	16.9570i	2.01931	−	0.836427i
$412$	−4.83397	−	13.8426i	−0.238152	−	0.681976i
$413$	0.941448	+	0.389961i	0.0463256	+	0.0191887i
$414$	−20.8473	+	91.2059i	−1.02459	+	4.48253i
$415$		0			0
$416$	−1.72747	−	31.6491i	−0.0846960	−	1.55172i
$417$		−	8.46115i		−	0.414344i
$418$	6.71603	+	1.53511i	0.328492	+	0.0750848i
$419$	−3.88329	+	9.37508i	−0.189711	+	0.458003i	−0.989904	−	0.141740i	$-0.954730\pi$
$419$	−3.88329	+	9.37508i	−0.189711	+	0.458003i	0.800193	+	0.599743i	$0.204730\pi$
$420$		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	$0.348087\pi$
$422$	−2.72144	+	3.83296i	−0.132478	+	0.186586i
$423$	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
$427$	10.5742	−	4.37998i	0.511722	−	0.211962i
$428$	−22.3164	−	1.26734i	−1.07870	−	0.0612591i
$429$	−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	$0.770566\pi$
$432$	35.7907	−	64.5664i	1.72198	−	3.10645i
$433$	31.7483			1.52573			0.762864	−	0.646560i	$-0.223793\pi$
$433$	31.7483			1.52573			0.762864	+	0.646560i	$0.223793\pi$
$434$	−1.67748	+	1.05329i	−0.0805214	+	0.0505597i
$435$		0			0
$436$	18.4401	+	20.6606i	0.883121	+	0.989465i
$437$	−28.4489	+	11.7839i	−1.36089	+	0.563701i
$438$	−6.45368	−	38.0561i	−0.308369	−	1.81839i
$439$	−7.15702	−	7.15702i	−0.341586	−	0.341586i	0.515377	−	0.856963i	$-0.327652\pi$
$439$	−7.15702	−	7.15702i	−0.341586	−	0.341586i	−0.856963	+	0.515377i	$0.827652\pi$
$440$		0			0
$441$	29.2469	−	29.2469i	1.39271	−	1.39271i
$442$	−27.3003	−	19.3835i	−1.29854	−	0.921979i
$443$	2.48722	+	6.00467i	0.118171	+	0.285290i	0.971887	−	0.235449i	$-0.0756562\pi$
$443$	2.48722	+	6.00467i	0.118171	+	0.285290i	−0.853715	+	0.520740i	$0.825656\pi$
$444$	−7.67255	+	15.9066i	−0.364123	+	0.754894i
$445$		0			0
$446$	−32.2150	−	7.36353i	−1.52543	−	0.348673i
$447$		−	62.4645i		−	2.95447i
$448$	6.19685	−	9.82106i	0.292774	−	0.464001i
$449$	−8.48000			−0.400196			−0.200098	−	0.979776i	$-0.564126\pi$
$449$	−8.48000			−0.400196			−0.200098	+	0.979776i	$0.564126\pi$
$450$		0			0
$451$	−3.10099	+	7.48645i	−0.146020	+	0.352523i
$452$	−11.4192	−	5.50805i	−0.537114	−	0.259077i
$453$	−24.2625	−	58.5749i	−1.13995	−	2.75209i
$454$	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	−0.153548	−	0.988141i	$-0.549070\pi$
$457$	17.8416	−	17.8416i	0.834593	−	0.834593i	0.988141	+	0.153548i	$0.0490701\pi$
$458$	4.28981	+	25.2962i	0.200450	+	1.18201i
$459$	−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	$0.645436\pi$
$462$	−4.57392	−	7.28443i	−0.212798	−	0.338903i
$463$	−26.6297			−1.23759			−0.618793	−	0.785554i	$-0.712378\pi$
$463$	−26.6297			−1.23759			−0.618793	+	0.785554i	$0.712378\pi$
$464$	−8.52897	+	2.44554i	−0.395947	+	0.113531i
$465$		0			0
$466$	−20.3675	−	32.4373i	−0.943504	−	1.50263i
$467$	−2.41096	+	5.82058i	−0.111566	+	0.269344i	−0.969794	−	0.243924i	$-0.921565\pi$
$467$	−2.41096	+	5.82058i	−0.111566	+	0.269344i	0.858228	+	0.513268i	$0.171565\pi$
$468$	−94.5784	−	5.37107i	−4.37189	−	0.248278i
$469$	0.993383	+	2.39824i	0.0458702	+	0.110740i
$470$		0			0
$471$	−27.2815	−	27.2815i	−1.25706	−	1.25706i
$472$	−0.551474	+	1.90744i	−0.0253836	+	0.0877972i
$473$	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
$477$	30.8766	+	12.7895i	1.41374	+	0.585592i
$478$	26.9721	+	6.16512i	1.23367	+	0.281986i
$479$	−8.91801			−0.407474			−0.203737	−	0.979026i	$-0.565309\pi$
$479$	−8.91801			−0.407474			−0.203737	+	0.979026i	$0.565309\pi$
$480$		0			0
$481$	14.6196			0.666596
$482$	−6.38492	−	1.45943i	−0.290825	−	0.0664751i
$483$	35.5191	+	14.7125i	1.61617	+	0.669441i
$484$	−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	$-0.404583\pi$
$487$	−14.5675	−	14.5675i	−0.660115	−	0.660115i	−0.955407	+	0.295292i	$0.904583\pi$
$488$	10.7693	+	19.5290i	0.487502	+	0.884038i
$489$	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	$0.621815\pi$
$492$	−2.51178	+	44.2296i	−0.113240	+	1.99402i
$493$	−3.58669	+	8.65904i	−0.161536	+	0.389983i
$494$	−16.5798	−	26.4050i	−0.745960	−	1.18802i
$495$		0			0
$496$	−2.40256	−	3.02051i	−0.107878	−	0.135625i
$497$	12.8120			0.574697
$498$	9.24273	+	14.7200i	0.414176	+	0.659618i
$499$	10.0229	+	4.15164i	0.448689	+	0.185853i	0.595574	−	0.803301i	$-0.296925\pi$
$499$	10.0229	+	4.15164i	0.448689	+	0.185853i	−0.146885	+	0.989154i	$0.546925\pi$
$500$		0			0
$501$	−11.8308	−	28.5621i	−0.528562	−	1.27606i
$502$	−2.75272	−	16.2323i	−0.122860	−	0.724481i
$503$	15.5986	−	15.5986i	0.695505	−	0.695505i	−0.267932	−	0.963438i	$-0.586340\pi$
$503$	15.5986	−	15.5986i	0.695505	−	0.695505i	0.963438	+	0.267932i	$0.0863404\pi$
$504$	−27.1145	−	21.6650i	−1.20778	−	0.965036i
$505$		0			0
$506$	−7.93271	+	11.1727i	−0.352652	+	0.496686i
$507$	23.8239	+	57.5159i	1.05806	+	2.55437i
$508$	−9.83969	+	20.3995i	−0.436566	+	0.905082i
$509$	−1.06698	+	2.57591i	−0.0472930	+	0.114175i	−0.945761	−	0.324864i	$-0.894681\pi$
$509$	−1.06698	+	2.57591i	−0.0472930	+	0.114175i	0.898468	+	0.439040i	$0.144681\pi$
$510$		0			0
$511$	−11.7069			−0.517883
$512$	20.3587	+	9.87532i	0.899737	+	0.436432i
$513$		−	72.6175i		−	3.20614i
$514$	5.58120	+	1.27572i	0.246176	+	0.0562696i
$515$		0			0
$516$	6.27717	+	3.02779i	0.276337	+	0.133291i
$517$	1.11924	+	2.70208i	0.0492241	+	0.118837i
$518$	4.36737	+	3.10088i	0.191891	+	0.136245i
$519$	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	$0.871009\pi$
$522$	4.43368	+	26.1445i	0.194057	+	1.14431i
$523$	10.7057	−	4.43446i	0.468129	−	0.193905i	−0.136134	−	0.990690i	$-0.543468\pi$
$523$	10.7057	−	4.43446i	0.468129	−	0.193905i	0.604263	+	0.796785i	$0.293468\pi$
$524$	11.4082	−	10.1821i	0.498368	−	0.444805i
$525$		0			0
$526$	2.71920	−	1.70739i	0.118563	−	0.0744459i
$527$	−4.07692			−0.177593
$528$	13.1165	−	10.4331i	0.570824	−	0.454043i
$529$		−	38.2457i		−	1.66286i
$530$		0			0
$531$	5.48256	+	2.27095i	0.237923	+	0.0985508i
$532$	0.647670	−	11.4047i	0.0280801	−	0.494457i
$533$	33.8816	−	14.0342i	1.46757	−	0.607889i
$534$	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
$538$	−2.99853	+	4.22323i	−0.129276	+	0.182076i
$539$	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	$-0.0290153\pi$
$542$	−30.9172	−	7.06687i	−1.32801	−	0.303548i
$543$			8.32686i			0.357340i
$544$	21.5513	−	10.3369i	0.924004	−	0.443189i
$545$		0			0
$546$	−8.67410	+	37.9487i	−0.371217	+	1.62405i
$547$	29.4527	+	12.1997i	1.25931	+	0.521623i	0.909697	−	0.415272i	$-0.136314\pi$
$547$	29.4527	+	12.1997i	1.25931	+	0.521623i	0.349611	+	0.936895i	$0.386314\pi$
$548$	24.7222	−	8.63322i	1.05608	−	0.368793i
$549$	61.5793	−	25.5070i	2.62814	−	1.08861i
$550$		0			0
$551$	−6.17149	+	6.17149i	−0.262914	+	0.262914i
$552$	−20.8061	+	71.9643i	−0.885566	+	3.06300i
$553$	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
$557$	−0.454492	+	1.09724i	−0.0192574	+	0.0464916i	−0.933216	−	0.359316i	$-0.883010\pi$
$557$	−0.454492	+	1.09724i	−0.0192574	+	0.0464916i	0.913958	+	0.405808i	$0.133010\pi$
$558$	−9.76884	+	6.13389i	−0.413548	+	0.259668i
$559$		−	5.76928i		−	0.244015i
$560$		0			0
$561$		−	17.7040i		−	0.747464i
$562$	−1.93118	−	3.07561i	−0.0814621	−	0.129737i
$563$	−16.2116	+	39.1382i	−0.683236	+	1.64948i	0.0747465	+	0.997203i	$0.476185\pi$
$563$	−16.2116	+	39.1382i	−0.683236	+	1.64948i	−0.757982	+	0.652275i	$0.773815\pi$
$564$	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
$568$	2.77172	+	24.8100i	0.116299	+	1.04100i
$569$	−4.33822	+	4.33822i	−0.181868	+	0.181868i	−0.792169	−	0.610301i	$-0.791048\pi$
$569$	−4.33822	+	4.33822i	−0.181868	+	0.181868i	0.610301	+	0.792169i	$0.291048\pi$
$570$		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	$0.694552\pi$
$572$	−12.4964	−	6.02763i	−0.522501	−	0.252028i
$573$	−47.1886	−	19.5462i	−1.97133	−	0.816553i
$574$	13.0983	+	2.99393i	0.546712	+	0.124964i
$575$		0			0
$576$	36.0876	−	57.1933i	1.50365	−	2.38305i
$577$		−	4.17488i		−	0.173802i	−0.996217	−	0.0869012i	$-0.972304\pi$
$577$		−	4.17488i		−	0.173802i	0.996217	−	0.0869012i	$-0.0276965\pi$
$578$	0.268931	−	1.17656i	0.0111861	−	0.0489384i
$579$	3.83246	−	9.25238i	0.159272	−	0.384516i
$580$		0			0
$581$	4.87030	−	2.01735i	0.202054	−	0.0836936i
$582$	−51.4338	−	36.5185i	−2.13200	−	1.51374i
$583$	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
$587$	−17.3964	+	7.20581i	−0.718024	+	0.297415i	−0.711621	−	0.702564i	$-0.752038\pi$
$587$	−17.3964	+	7.20581i	−0.718024	+	0.297415i	−0.00640387	+	0.999979i	$0.502038\pi$
$588$	24.7080	−	22.0525i	1.01894	−	0.909429i
$589$	−3.50751	−	1.45286i	−0.144524	−	0.0598639i
$590$		0			0
$591$			45.4725i			1.87049i
$592$	−5.05991	+	9.12809i	−0.207961	+	0.375162i
$593$	9.27068			0.380701			0.190351	−	0.981716i	$-0.439038\pi$
$593$	9.27068			0.380701			0.190351	+	0.981716i	$0.439038\pi$
$594$	−17.1834	−	27.3664i	−0.705045	−	1.12286i
$595$		0			0
$596$	2.09299	−	36.8551i	0.0857322	−	1.50965i
$597$	33.9811	−	14.0754i	1.39075	−	0.576069i
$598$	61.1404	−	10.3684i	2.50022	−	0.423995i
$599$	−22.3629	−	22.3629i	−0.913723	−	0.913723i	0.0828402	−	0.996563i	$-0.473601\pi$
$599$	−22.3629	−	22.3629i	−0.913723	−	0.913723i	−0.996563	+	0.0828402i	$0.973601\pi$
$600$		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	$-0.0193923\pi$
$602$	1.22369	−	1.72348i	0.0498739	−	0.0702438i
$603$	5.78500	+	13.9662i	0.235583	+	0.568749i
$604$	−12.3526	−	35.3732i	−0.502622	−	1.43931i
$605$		0			0
$606$	−4.23735	+	18.5382i	−0.172131	+	0.753062i
$607$		−	3.46490i		−	0.140636i	−0.997525	−	0.0703179i	$-0.977599\pi$
$607$		−	3.46490i		−	0.140636i	0.997525	−	0.0703179i	$-0.0224014\pi$
$608$	22.2249	−	1.21308i	0.901340	−	0.0491968i
$609$	10.8969			0.441564
$610$		0			0
$611$	5.06536	−	12.2289i	0.204923	−	0.494727i
$612$	−23.5515	−	67.4424i	−0.952014	−	2.72620i
$613$	13.7592	+	33.2177i	0.555730	+	1.34165i	0.913118	+	0.407695i	$0.133667\pi$
$613$	13.7592	+	33.2177i	0.555730	+	1.34165i	−0.357388	+	0.933956i	$0.616333\pi$
$614$	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	−0.260799	+	0.965393i	$0.583986\pi$
$617$	−30.4580	+	30.4580i	−1.22619	+	1.22619i	−0.965393	+	0.260799i	$0.916014\pi$
$618$	−34.5938	+	5.86654i	−1.39157	+	0.235987i
$619$	−4.97518	−	12.0112i	−0.199969	−	0.482769i	0.791804	−	0.610775i	$-0.209142\pi$
$619$	−4.97518	−	12.0112i	−0.199969	−	0.482769i	−0.991773	+	0.128006i	$0.959142\pi$
$620$		0			0
$621$	133.439	+	55.2723i	5.35473	+	2.21800i
$622$	4.51127	−	2.83264i	0.180885	−	0.113578i
$623$	20.3309			0.814541
$624$	−75.3628	−	8.58735i	−3.01693	−	0.343769i
$625$		0			0
$626$	23.2984	−	14.6292i	0.931192	−	0.584699i
$627$	6.30902	−	15.2313i	0.251958	−	0.608281i
$628$	−15.1824	−	17.0107i	−0.605845	−	0.678799i
$629$	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	$0.813825\pi$
$632$	32.9293	+	26.3111i	1.30986	+	1.04660i
$633$	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
$637$	−25.3288	−	10.4915i	−1.00356	−	0.415689i
$638$	−0.865410	+	3.78612i	−0.0342619	+	0.149894i
$639$	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	$0.700292\pi$
$642$	−11.9191	+	52.1453i	−0.470409	+	2.05801i
$643$	−13.5899	−	5.62912i	−0.535933	−	0.221991i	0.0982665	−	0.995160i	$-0.468670\pi$
$643$	−13.5899	−	5.62912i	−0.535933	−	0.221991i	−0.634200	+	0.773169i	$0.718670\pi$
$644$	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	−0.984525	−	0.175247i	$-0.943928\pi$
$647$	−29.5002	−	29.5002i	−1.15977	−	1.15977i	−0.175247	−	0.984525i	$-0.556072\pi$
$648$	−81.9775	−	65.5014i	−3.22038	−	2.57314i
$649$	0.614566	+	0.614566i	0.0241238	+	0.0241238i
$650$		0			0
$651$	1.81393	+	4.37921i	0.0710934	+	0.171635i
$652$	17.2291	+	19.3037i	0.674742	+	0.755993i
$653$	12.9516	−	31.2680i	0.506836	−	1.22361i	−0.438859	−	0.898556i	$-0.644617\pi$
$653$	12.9516	−	31.2680i	0.506836	−	1.22361i	0.945695	−	0.325054i	$-0.105383\pi$
$654$	56.1239	−	35.2404i	2.19462	−	1.37801i
$655$		0			0
$656$	−2.96399	+	26.0121i	−0.115724	+	1.01560i
$657$	−68.1755			−2.65978
$658$	4.10699	−	2.57879i	0.160107	−	0.100532i
$659$	38.4825	+	15.9400i	1.49907	+	0.620933i	0.973267	−	0.229676i	$-0.0737666\pi$
$659$	38.4825	+	15.9400i	1.49907	+	0.620933i	0.525799	+	0.850609i	$0.323767\pi$
$660$		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	$0.745568\pi$
$662$	−12.5714	+	2.13189i	−0.488600	+	0.0828584i
$663$	−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
$667$	−6.64311	−	16.0379i	−0.257222	−	0.620989i
$668$	−6.02335	−	17.2485i	−0.233051	−	0.667366i
$669$	−30.2627	+	73.0607i	−1.17003	+	2.82469i
$670$		0			0
$671$	9.76192			0.376855
$672$	−20.6920	−	18.5501i	−0.798212	−	0.715586i
$673$			33.3993i			1.28745i	0.765257	+	0.643725i	$0.222612\pi$
$673$			33.3993i			1.28745i	−0.765257	+	0.643725i	$0.777388\pi$
$674$	−3.86527	+	16.9104i	−0.148885	+	0.651363i
$675$		0			0
$676$	12.1293	+	34.7336i	0.466512	+	1.33591i
$677$	−0.788676	−	1.90403i	−0.0303113	−	0.0731779i	0.907999	−	0.418972i	$-0.137610\pi$
$677$	−0.788676	−	1.90403i	−0.0303113	−	0.0731779i	−0.938310	+	0.345794i	$0.887610\pi$
$678$	−17.5644	+	24.7382i	−0.674557	+	0.950065i
$679$	−13.5280	+	13.5280i	−0.519158	+	0.519158i
$680$		0			0
$681$	−26.4083	−	26.4083i	−1.01197	−	1.01197i
$682$	−1.66561	+	0.282460i	−0.0637796	+	0.0108160i
$683$	5.16393	−	2.13897i	0.197592	−	0.0818454i	−0.281693	−	0.959505i	$-0.590896\pi$
$683$	5.16393	−	2.13897i	0.197592	−	0.0818454i	0.479285	+	0.877659i	$0.340896\pi$
$684$	3.77173	−	66.4158i	0.144216	−	2.53947i
$685$		0			0
$686$	−12.9827	−	20.6763i	−0.495682	−	0.789425i
$687$	61.3993			2.34253
$688$	3.60219	+	1.99678i	0.137332	+	0.0761264i
$689$		−	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	$0.773383\pi$
$692$	18.8392	−	16.8144i	0.716158	−	0.639188i
$693$	−14.0356	+	5.81374i	−0.533168	+	0.220846i
$694$	−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
$698$	−32.0230	−	22.7367i	−1.21209	−	0.860595i
$699$	−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	$0.971788\pi$
$702$	−32.5871	+	142.567i	−1.22992	+	5.38084i
$703$			10.2663i			0.387202i
$704$	8.08856	−	5.71623i	0.304849	−	0.215438i
$705$		0			0
$706$	30.2246	+	6.90857i	1.13752	+	0.260007i
$707$	5.32846	+	2.20712i	0.200397	+	0.0830073i
$708$	4.27970	+	2.06431i	0.160841	+	0.0775816i
$709$	−34.4885	+	14.2856i	−1.29524	+	0.536506i	−0.920543	−	0.390640i	$-0.872254\pi$
$709$	−34.4885	+	14.2856i	−1.29524	+	0.536506i	−0.374698	+	0.927147i	$0.622254\pi$
$710$		0			0
$711$	89.0769	−	89.0769i	3.34064	−	3.34064i
$712$	4.39834	+	39.3701i	0.164835	+	1.47546i
$713$	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
$717$	25.3375	−	61.1701i	0.946246	−	2.28444i
$718$	4.27686	+	6.81133i	0.159611	+	0.254197i
$719$		−	47.1132i		−	1.75702i	−0.477719	−	0.878512i	$-0.658536\pi$
$719$		−	47.1132i		−	1.75702i	0.477719	−	0.878512i	$-0.341464\pi$
$720$		0			0
$721$			10.6418i			0.396322i
$722$	−4.21362	+	2.64575i	−0.156815	+	0.0984645i
$723$	−5.99798	+	14.4804i	−0.223067	+	0.538532i
$724$	−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	0.221885	−	0.975073i	$-0.428779\pi$
$727$	32.2735	−	32.2735i	1.19696	−	1.19696i	0.975073	−	0.221885i	$-0.0712210\pi$
$728$	−6.38941	+	22.0997i	−0.236807	+	0.819071i
$729$	−89.2611	+	89.2611i	−3.30597	+	3.30597i
$730$		0			0
$731$	4.01944	−	1.66491i	0.148664	−	0.0615788i
$732$	50.3849	−	17.5949i	1.86228	−	0.650326i
$733$	−38.8138	−	16.0772i	−1.43362	−	0.593825i	−0.475378	−	0.879782i	$-0.657689\pi$
$733$	−38.8138	−	16.0772i	−1.43362	−	0.593825i	−0.958243	+	0.285956i	$0.907689\pi$
$734$	8.88413	−	38.8676i	0.327919	−	1.43463i
$735$		0			0
$736$	−14.6872	+	41.7630i	−0.541379	+	1.53940i
$737$			2.21401i			0.0815541i
$738$	76.2783	+	17.4353i	2.80784	+	0.641801i
$739$	3.96376	−	9.56937i	0.145809	−	0.352015i	−0.834054	−	0.551682i	$-0.813986\pi$
$739$	3.96376	−	9.56937i	0.145809	−	0.352015i	0.979864	+	0.199667i	$0.0639861\pi$
$740$		0			0
$741$	−68.9327	+	28.5529i	−2.53231	+	1.04892i
$742$	4.69858	−	6.61762i	0.172490	−	0.242941i
$743$	27.5088	+	27.5088i	1.00920	+	1.00920i	0.999957	+	0.00924260i	$0.00294205\pi$
$743$	27.5088	+	27.5088i	1.00920	+	1.00920i	0.00924260	+	0.999957i	$0.497058\pi$
$744$	−8.08775	+	4.45999i	−0.296511	+	0.163511i
$745$		0			0
$746$	−0.292008	−	1.72192i	−0.0106912	−	0.0630439i
$747$	28.3624	−	11.7481i	1.03773	−	0.429840i
$748$	0.593205	−	10.4457i	0.0216897	−	0.381931i
$749$	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	$0.818149\pi$
$752$	5.88223	+	7.39515i	0.214503	+	0.269673i
$753$	−39.3992			−1.43579
$754$	14.8857	−	9.34676i	0.542104	−	0.340389i
$755$		0			0
$756$	−39.9739	+	35.6777i	−1.45384	+	1.29758i
$757$	−48.4128	+	20.0533i	−1.75959	+	0.728848i	−0.762999	+	0.646399i	$0.776274\pi$
$757$	−48.4128	+	20.0533i	−1.75959	+	0.728848i	−0.996595	+	0.0824488i	$0.973726\pi$
$758$	−1.59306	−	9.39399i	−0.0578627	−	0.341205i
$759$	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	$0.957354\pi$
$762$	44.1929	+	31.3774i	1.60094	+	1.13668i
$763$	−7.69168	−	18.5694i	−0.278457	−	0.672256i
$764$	−27.1872	−	13.1137i	−0.983597	−	0.474437i
$765$		0			0
$766$	8.44878	+	1.93118i	0.305267	+	0.0697762i
$767$		−	3.93343i		−	0.142028i
$768$	31.4452	−	44.0824i	1.13468	−	1.59069i
$769$	9.26292			0.334029			0.167015	−	0.985954i	$-0.446587\pi$
$769$	9.26292			0.334029			0.167015	+	0.985954i	$0.446587\pi$
$770$		0			0
$771$	5.24297	−	12.6576i	0.188821	−	0.455854i
$772$	2.57124	−	5.33065i	0.0925408	−	0.191854i
$773$	8.47782	+	20.4673i	0.304926	+	0.736156i	0.999854	+	0.0170771i	$0.00543608\pi$
$773$	8.47782	+	20.4673i	0.304926	+	0.736156i	−0.694928	+	0.719079i	$0.744564\pi$
$774$	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
$778$	4.08680	+	24.0991i	0.146519	+	0.863994i
$779$	9.85524	+	23.7927i	0.353101	+	0.852460i
$780$		0			0
$781$	10.0957	+	4.18176i	0.361251	+	0.149635i
$782$	24.8676	+	39.6042i	0.889264	+	1.41624i
$783$	40.9377			1.46299
$784$	15.3170	−	12.1834i	0.547037	−	0.435123i
$785$		0			0
$786$	−19.4587	−	30.9899i	−0.694068	−	1.10537i
$787$	9.46364	−	22.8472i	0.337342	−	0.814416i	−0.660627	−	0.750715i	$-0.729709\pi$
$787$	9.46364	−	22.8472i	0.337342	−	0.814416i	0.997969	−	0.0637018i	$-0.0202906\pi$
$788$	−1.52364	+	26.8296i	−0.0542775	+	0.955764i
$789$	−2.94039	−	7.09872i	−0.104681	−	0.252721i
$790$		0			0
$791$	6.50661	+	6.50661i	0.231348	+	0.231348i
$792$	−14.2945	−	25.9217i	−0.507934	−	0.921088i
$793$	−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
$797$	−26.0050	−	10.7716i	−0.921145	−	0.381551i	−0.128833	−	0.991666i	$-0.541123\pi$
$797$	−26.0050	−	10.7716i	−0.921145	−	0.381551i	−0.792313	+	0.610115i	$0.791123\pi$
$798$	−26.6487	−	6.09121i	−0.943355	−	0.215627i
$799$	9.98158			0.353123
$800$		0			0
$801$	118.398			4.18338
$802$	37.6640	+	8.60902i	1.32996	+	0.303995i
$803$	−9.22485	−	3.82106i	−0.325538	−	0.134842i
$804$	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
$808$	−3.12126	+	10.7959i	−0.109806	+	0.379797i
$809$	24.2885	+	24.2885i	0.853938	+	0.853938i	0.990616	−	0.136678i	$-0.0436426\pi$
$809$	24.2885	+	24.2885i	0.853938	+	0.853938i	−0.136678	+	0.990616i	$0.543643\pi$
$810$		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	$0.674600\pi$
$812$	6.42934	+	0.365120i	0.225626	+	0.0128132i
$813$	−29.0435	+	70.1173i	−1.01860	+	2.45912i
$814$	2.42931	+	3.86893i	0.0851473	+	0.135606i
$815$		0			0
$816$	−15.7655	−	54.9832i	−0.551904	−	1.92480i
$817$	4.05136			0.141739
$818$	−2.37903	−	3.78885i	−0.0831808	−	0.132474i
$819$	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	$0.929934\pi$
$822$	−10.4773	−	61.7828i	−0.365439	−	2.15492i
$823$	9.16017	−	9.16017i	0.319304	−	0.319304i	−0.529196	−	0.848500i	$-0.677506\pi$
$823$	9.16017	−	9.16017i	0.319304	−	0.319304i	0.848500	+	0.529196i	$0.177506\pi$
$824$	−20.6075	+	2.30223i	−0.717897	+	0.0802018i
$825$		0			0
$826$	0.834296	−	1.17505i	0.0290289	−	0.0408851i
$827$	16.5936	+	40.0605i	0.577017	+	1.39304i	0.895478	+	0.445106i	$0.146834\pi$
$827$	16.5936	+	40.0605i	0.577017	+	1.39304i	−0.318461	+	0.947936i	$0.603166\pi$
$828$	119.172	+	57.4827i	4.14152	+	1.99766i
$829$	−9.71946	+	23.4648i	−0.337571	+	0.814968i	0.660377	+	0.750934i	$0.270396\pi$
$829$	−9.71946	+	23.4648i	−0.337571	+	0.814968i	−0.997948	+	0.0640336i	$0.979604\pi$
$830$		0			0
$831$	19.4955			0.676291
$832$	−44.1776	−	7.59186i	−1.53158	−	0.263200i
$833$		−	20.6741i		−	0.716316i
$834$	−11.6650	−	2.66633i	−0.403927	−	0.0923273i
$835$		0			0
$836$	4.23278	−	8.77535i	0.146394	−	0.303502i
$837$	6.81461	+	16.4519i	0.235547	+	0.568662i
$838$	11.7013	+	8.30805i	0.404215	+	0.286997i
$839$	−32.2653	+	32.2653i	−1.11392	+	1.11392i	−0.121307	+	0.992615i	$0.538708\pi$
$839$	−32.2653	+	32.2653i	−1.11392	+	1.11392i	−0.992615	+	0.121307i	$0.961292\pi$
$840$		0			0
$841$	17.0270	+	17.0270i	0.587136	+	0.587136i
$842$	−0.819424	−	4.83198i	−0.0282392	−	0.166521i
$843$	−8.02915	+	3.32578i	−0.276539	+	0.114546i
$844$	4.42675	+	4.95980i	0.152375	+	0.170723i
$845$		0			0
$846$	23.9172	−	15.0177i	0.822290	−	0.516319i
$847$	13.7424			0.472195
$848$	13.8313	+	7.66700i	0.474968	+	0.263286i
$849$		−	55.7216i		−	1.91236i
$850$		0			0
$851$	−18.8650	−	7.81413i	−0.646683	−	0.267865i
$852$	59.6448	+	3.38721i	2.04340	+	0.116044i
$853$	−4.41898	+	1.83040i	−0.151303	+	0.0626718i	−0.457050	−	0.889441i	$-0.651094\pi$
$853$	−4.41898	+	1.83040i	−0.151303	+	0.0626718i	0.305747	+	0.952113i	$0.401094\pi$
$854$	−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	$-0.142433\pi$
$857$	13.7258	+	13.7258i	0.468864	+	0.468864i	−0.432683	+	0.901546i	$0.642433\pi$
$858$	−19.2213	+	27.0718i	−0.656204	+	0.924217i
$859$	35.3096	−	14.6257i	1.20475	−	0.499023i	0.312217	−	0.950011i	$-0.398928\pi$
$859$	35.3096	−	14.6257i	1.20475	−	0.499023i	0.892530	+	0.450988i	$0.148928\pi$
$860$		0			0
$861$	12.3045	−	29.7057i	0.419336	−	1.01237i
$862$	37.7793	+	8.63538i	1.28677	+	0.294122i
$863$		−	52.6541i		−	1.79237i	−0.443685	−	0.896183i	$-0.646329\pi$
$863$		−	52.6541i		−	1.79237i	0.443685	−	0.896183i	$-0.353671\pi$
$864$	−77.7363	−	69.6896i	−2.64464	−	2.37089i
$865$		0			0
$866$	10.0047	−	43.7701i	0.339974	−	1.48737i
$867$	−2.66833	−	1.10526i	−0.0906212	−	0.0375365i
$868$	0.923514	+	2.64458i	0.0313461	+	0.0897630i
$869$	17.0455	−	7.06050i	0.578231	−	0.239511i
$870$		0			0
$871$	7.08520	−	7.08520i	0.240073	−	0.240073i
$872$	34.2949	−	18.9119i	1.16137	−	0.640438i
$873$	−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
$877$	12.2342	−	29.5360i	0.413120	−	0.997359i	−0.571175	−	0.820828i	$-0.693512\pi$
$877$	12.2342	−	29.5360i	0.413120	−	0.997359i	0.984295	−	0.176531i	$-0.0564876\pi$
$878$	−12.1224	+	7.61172i	−0.409113	+	0.256883i
$879$			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	$-0.0439617\pi$
$882$	−31.1051	−	49.5380i	−1.04736	−	1.66803i
$883$	−4.83737	+	11.6784i	−0.162790	+	0.393011i	−0.984135	−	0.177422i	$-0.943224\pi$
$883$	−4.83737	+	11.6784i	−0.162790	+	0.393011i	0.821345	+	0.570432i	$0.193224\pi$
$884$	−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	−0.987935	−	0.154868i	$-0.950505\pi$
$887$	−24.8109	+	24.8109i	−0.833067	+	0.833067i	0.154868	+	0.987935i	$0.450505\pi$
$888$	19.5119	+	15.5904i	0.654778	+	0.523179i
$889$	11.6236	−	11.6236i	0.389841	−	0.389841i
$890$		0			0
$891$	−42.4349	+	17.5771i	−1.42162	+	0.588855i
$892$	−20.3036	+	42.0931i	−0.679814	+	1.40938i
$893$	8.58748	+	3.55705i	0.287369	+	0.119032i
$894$	−86.1172	−	19.6842i	−2.88019	−	0.658337i
$895$		0			0
$896$	−11.5871	−	11.6382i	−0.387097	−	0.388805i
$897$		−	148.401i		−	4.95496i
$898$	−2.67227	+	11.6910i	−0.0891747	+	0.390134i
$899$	0.819039	−	1.97734i	0.0273165	−	0.0659478i
$900$		0			0
$901$	15.4334	−	6.39272i	0.514161	−	0.212972i
$902$	9.34405	+	6.63437i	0.311123	+	0.220900i
$903$	−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
$907$	−32.3281	+	13.3908i	−1.07344	+	0.444633i	−0.848203	−	0.529672i	$-0.822315\pi$
$907$	−32.3281	+	13.3908i	−1.07344	+	0.444633i	−0.225236	+	0.974304i	$0.572315\pi$
$908$	−14.6965	−	16.4662i	−0.487720	−	0.546450i
$909$	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	$-0.103057\pi$
$912$	6.03030	−	52.9220i	0.199683	−	1.75242i
$913$	4.49617			0.148802
$914$	−18.9751	−	30.2197i	−0.627639	−	0.999579i
$915$		0			0
$916$	36.2266	+	2.05730i	1.19696	+	0.0679750i
$917$	−10.2534	+	4.24711i	−0.338598	+	0.140252i
$918$	−108.730	+	18.4388i	−3.58862	+	0.608570i
$919$	7.47911	+	7.47911i	0.246713	+	0.246713i	0.819620	−	0.572907i	$-0.194184\pi$
$919$	7.47911	+	7.47911i	0.246713	+	0.246713i	−0.572907	+	0.819620i	$0.694184\pi$
$920$		0			0
$921$	1.27140	−	1.27140i	0.0418939	−	0.0418939i
$922$	−2.25566	+	3.17693i	−0.0742861	+	0.104627i
$923$	−18.9255	−	45.6902i	−0.622940	−	1.50391i
$924$	−11.4841	+	4.01036i	−0.377799	+	0.131931i
$925$		0			0
$926$	−8.39169	+	36.7132i	−0.275768	+	1.20647i
$927$			61.9731i			2.03546i
$928$	0.683866	+	12.5292i	0.0224490	+	0.411290i
$929$	−33.1810			−1.08863			−0.544317	−	0.838880i	$-0.683211\pi$
$929$	−33.1810			−1.08863			−0.544317	+	0.838880i	$0.683211\pi$
$930$		0			0
$931$	7.36746	−	17.7866i	0.241459	−	0.582933i
$932$	−51.1382	+	17.8579i	−1.67509	+	0.584956i
$933$	−4.87822	−	11.7771i	−0.159706	−	0.385564i
$934$	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	−0.774444	−	0.632643i	$-0.781970\pi$
$937$	−4.34060	+	4.34060i	−0.141801	+	0.141801i	0.632643	+	0.774444i	$0.281970\pi$
$938$	3.61939	−	0.613788i	0.118177	−	0.0200409i
$939$	−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	$0.778490\pi$
$942$	−46.2089	+	29.0147i	−1.50557	+	0.945351i
$943$	−51.2217			−1.66801
$944$	2.45593	+	1.36138i	0.0799336	+	0.0443091i
$945$		0			0
$946$	1.52678	−	0.958671i	0.0496400	−	0.0311691i
$947$	14.7887	−	35.7030i	0.480567	−	1.16019i	−0.478773	−	0.877939i	$-0.658918\pi$
$947$	14.7887	−	35.7030i	0.480567	−	1.16019i	0.959340	−	0.282252i	$-0.0910816\pi$
$948$	75.2526	−	67.1648i	2.44409	−	2.18141i
$949$	17.2930	+	41.7491i	0.561356	+	1.35523i
$950$		0			0
$951$	51.8358	+	51.8358i	1.68089	+	1.68089i
$952$	−17.2407	+	1.92609i	−0.558774	+	0.0624250i
$953$	−16.4270	−	16.4270i	−0.532122	−	0.532122i	0.389081	−	0.921204i	$-0.372793\pi$
$953$	−16.4270	−	16.4270i	−0.532122	−	0.532122i	−0.921204	+	0.389081i	$0.872793\pi$
$954$	27.3624	−	38.5380i	0.885889	−	1.24771i
$955$		0			0
$956$	16.9992	−	35.2424i	0.549793	−	1.13982i
$957$	8.58657	+	3.55667i	0.277564	+	0.114971i
$958$	−2.81029	+	12.2949i	−0.0907965	+	0.397229i
$959$	−19.0058			−0.613728
$960$		0			0
$961$	−30.0690			−0.969968
$962$	4.60701	−	20.1554i	0.148536	−	0.649837i
$963$	87.2845	+	36.1544i	2.81270	+	1.16506i
$964$	−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	$-0.300412\pi$
$967$	−6.93584	−	6.93584i	−0.223042	−	0.223042i	−0.809778	+	0.586736i	$0.800412\pi$
$968$	2.97300	+	26.6117i	0.0955558	+	0.855332i
$969$	−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	$0.667475\pi$
$972$	−104.727	+	93.4715i	−3.35913	+	2.99810i
$973$	−1.38882	+	3.35290i	−0.0445234	+	0.107489i
$974$	−24.6741	+	15.4930i	−0.790610	+	0.496427i
$975$		0			0
$976$	30.3175	−	8.69305i	0.970440	−	0.278258i
$977$	−21.7591			−0.696134			−0.348067	−	0.937470i	$-0.613162\pi$
$977$	−21.7591			−0.696134			−0.348067	+	0.937470i	$0.613162\pi$
$978$	52.4380	−	32.9260i	1.67678	−	1.05286i
$979$	16.0205	+	6.63589i	0.512016	+	0.212084i
$980$		0			0
$981$	−44.7928	−	108.139i	−1.43012	−	3.45262i
$982$	44.1282	−	7.48341i	1.40819	−	0.238805i
$983$	31.8111	−	31.8111i	1.01462	−	1.01462i	0.0147254	−	0.999892i	$-0.495313\pi$
$983$	31.8111	−	31.8111i	1.01462	−	1.01462i	0.999892	−	0.0147254i	$-0.00468739\pi$
$984$	60.1859	+	17.4008i	1.91866	+	0.554716i
$985$		0			0
$986$	10.8076	+	7.67350i	0.344184	+	0.244374i
$987$	−4.44106	−	10.7217i	−0.141361	−	0.341275i
$988$	−41.6282	+	14.5370i	−1.32437	+	0.462482i
$989$	−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	$0.523313\pi$
$992$	−4.92135	+	2.36047i	−0.156253	+	0.0749451i
$993$			30.5134i			0.968313i
$994$	4.03739	−	17.6634i	0.128058	−	0.560248i
$995$		0			0
$996$	23.2064	−	8.10391i	0.735324	−	0.256782i
$997$	12.3407	+	29.7932i	0.390835	+	0.943559i	0.989758	+	0.142752i	$0.0455953\pi$
$997$	12.3407	+	29.7932i	0.390835	+	0.943559i	−0.598924	+	0.800806i	$0.704405\pi$
$998$	8.88218	−	12.5099i	0.281160	−	0.395995i
$999$	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.ba.f.749.10		64
5.2	odd	4		800.2.y.e.301.15	yes	64
5.3	odd	4		800.2.y.d.301.2	yes	64
5.4	even	2		800.2.ba.h.749.7		64
32.5	even	8		800.2.ba.h.549.7		64
160.37	odd	8		800.2.y.e.101.15	yes	64
160.69	even	8	inner	800.2.ba.f.549.10		64
160.133	odd	8		800.2.y.d.101.2	✓	64

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

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.ba (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.315126 - 1.37866i) q^{2} +(-3.12667 - 1.29511i) q^{3} +(-1.80139 - 0.868900i) q^{4} +(-2.77080 + 3.90248i) q^{6} +(1.02642 + 1.02642i) q^{7} +(-1.76558 + 2.20969i) q^{8} +(5.97742 + 5.97742i) q^{9} +O(q^{10})\)	\(q+(0.315126 - 1.37866i) q^{2} +(-3.12667 - 1.29511i) q^{3} +(-1.80139 - 0.868900i) q^{4} +(-2.77080 + 3.90248i) q^{6} +(1.02642 + 1.02642i) q^{7} +(-1.76558 + 2.20969i) q^{8} +(5.97742 + 5.97742i) q^{9} +(0.473788 + 1.14383i) q^{11} +(4.50703 + 5.04976i) q^{12} +(2.14423 - 5.17663i) q^{13} +(1.73854 - 1.09164i) q^{14} +(2.49002 + 3.13046i) q^{16} +4.22533 q^{17} +(10.1245 - 6.35718i) q^{18} +(3.63519 + 1.50574i) q^{19} +(-1.87996 - 4.53862i) q^{21} +(1.72625 - 0.292743i) q^{22} +(-5.53379 + 5.53379i) q^{23} +(8.38217 - 4.62234i) q^{24} +(-6.46110 - 4.58745i) q^{26} +(-7.06268 - 17.0508i) q^{27} +(-0.957132 - 2.74085i) q^{28} +(-0.848854 + 2.04932i) q^{29} -0.964876 q^{31} +(5.10050 - 2.44640i) q^{32} -4.18997i q^{33} +(1.33151 - 5.82528i) q^{34} +(-5.57389 - 15.9615i) q^{36} +(0.998488 + 2.41056i) q^{37} +(3.22145 - 4.53718i) q^{38} +(-13.4086 + 13.4086i) q^{39} +(4.62808 + 4.62808i) q^{41} +(-6.84962 + 1.16158i) q^{42} +(0.951273 - 0.394030i) q^{43} +(0.140393 - 2.47215i) q^{44} +(5.88536 + 9.37304i) q^{46} +2.36232 q^{47} +(-3.73119 - 13.0128i) q^{48} -4.89290i q^{49} +(-13.2112 - 5.47226i) q^{51} +(-8.36058 + 7.46202i) q^{52} +(3.65259 - 1.51295i) q^{53} +(-25.7329 + 4.36386i) q^{54} +(-4.08032 + 0.455844i) q^{56} +(-9.41592 - 9.41592i) q^{57} +(2.55781 + 1.81607i) q^{58} +(0.648566 - 0.268645i) q^{59} +(3.01738 - 7.28461i) q^{61} +(-0.304057 + 1.33023i) q^{62} +12.2708i q^{63} +(-1.76545 - 7.80277i) q^{64} +(-5.77653 - 1.32037i) q^{66} +(1.65215 + 0.684344i) q^{67} +(-7.61147 - 3.67139i) q^{68} +(24.4692 - 10.1355i) q^{69} +(6.24109 - 6.24109i) q^{71} +(-23.7619 + 2.65462i) q^{72} +(-5.70275 + 5.70275i) q^{73} +(3.63799 - 0.616942i) q^{74} +(-5.24006 - 5.87105i) q^{76} +(-0.687743 + 1.66036i) q^{77} +(14.2605 + 22.7113i) q^{78} -14.9022i q^{79} +37.0991i q^{81} +(7.83896 - 4.92211i) q^{82} +(1.38975 - 3.35516i) q^{83} +(-0.557068 + 9.80933i) q^{84} +(-0.243462 - 1.43565i) q^{86} +(5.30817 - 5.30817i) q^{87} +(-3.36401 - 0.972592i) q^{88} +(9.90375 - 9.90375i) q^{89} +(7.51432 - 3.11253i) q^{91} +(14.7768 - 5.16021i) q^{92} +(3.01685 + 1.24962i) q^{93} +(0.744427 - 3.25683i) q^{94} +(-19.1159 + 1.04338i) q^{96} +13.1798i q^{97} +(-6.74564 - 1.54188i) q^{98} +(-4.00510 + 9.66916i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q+O(q^{10}) \) 64 * q	\( 64 q - 24 q^{12} + 16 q^{14} + 20 q^{16} + 40 q^{18} + 24 q^{22} - 8 q^{23} + 28 q^{24} - 48 q^{28} - 20 q^{32} + 20 q^{34} + 12 q^{36} + 16 q^{37} - 24 q^{39} - 40 q^{44} + 32 q^{46} + 80 q^{47} + 40 q^{48} + 16 q^{51} - 76 q^{54} + 48 q^{56} - 8 q^{58} - 32 q^{59} - 32 q^{61} - 44 q^{62} - 48 q^{64} + 16 q^{66} - 32 q^{68} + 32 q^{69} + 32 q^{71} + 96 q^{72} - 8 q^{74} + 52 q^{78} - 116 q^{82} - 56 q^{84} - 84 q^{86} + 20 q^{88} + 48 q^{91} + 88 q^{92} - 48 q^{93} - 32 q^{94} - 100 q^{96} - 72 q^{98} + 64 q^{99}+O(q^{100}) \) 64 * q - 24 * q^12 + 16 * q^14 + 20 * q^16 + 40 * q^18 + 24 * q^22 - 8 * q^23 + 28 * q^24 - 48 * q^28 - 20 * q^32 + 20 * q^34 + 12 * q^36 + 16 * q^37 - 24 * q^39 - 40 * q^44 + 32 * q^46 + 80 * q^47 + 40 * q^48 + 16 * q^51 - 76 * q^54 + 48 * q^56 - 8 * q^58 - 32 * q^59 - 32 * q^61 - 44 * q^62 - 48 * q^64 + 16 * q^66 - 32 * q^68 + 32 * q^69 + 32 * q^71 + 96 * q^72 - 8 * q^74 + 52 * q^78 - 116 * q^82 - 56 * q^84 - 84 * q^86 + 20 * q^88 + 48 * q^91 + 88 * q^92 - 48 * q^93 - 32 * q^94 - 100 * q^96 - 72 * q^98 + 64 * q^99

Introduction

L-functions

Modular forms

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