LMFDB - Embedded newform 825.2.bi.h.101.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [825,2,Mod(101,825)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(825, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 0, 1]))

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

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

chi := DirichletCharacter("825.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 825 = 3 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	825.bi (of order $10$, 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:	$6.58765816676$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$20$ over $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 165)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			101.13
Character	$\chi$	$=$	825.101
Dual form			825.2.bi.h.776.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.270252 - 0.831751i) q^{2} +(-1.57542 + 0.719767i) q^{3} +(0.999260 + 0.726005i) q^{4} +(0.172907 + 1.50487i) q^{6} +(1.92808 - 2.65378i) q^{7} +(2.28897 - 1.66303i) q^{8} +(1.96387 - 2.26786i) q^{9} +O(q^{10})$	\(q+(0.270252 - 0.831751i) q^{2} +(-1.57542 + 0.719767i) q^{3} +(0.999260 + 0.726005i) q^{4} +(0.172907 + 1.50487i) q^{6} +(1.92808 - 2.65378i) q^{7} +(2.28897 - 1.66303i) q^{8} +(1.96387 - 2.26786i) q^{9} +(-3.23205 - 0.744199i) q^{11} +(-2.09681 - 0.424525i) q^{12} +(-1.90577 - 0.619221i) q^{13} +(-1.68622 - 2.32088i) q^{14} +(-0.00126317 - 0.00388765i) q^{16} +(-1.24609 - 3.83508i) q^{17} +(-1.35556 - 2.24635i) q^{18} +(3.42983 + 4.72076i) q^{19} +(-1.12743 + 5.56858i) q^{21} +(-1.49246 + 2.48714i) q^{22} -6.57716i q^{23} +(-2.40908 + 4.26749i) q^{24} +(-1.03008 + 1.41778i) q^{26} +(-1.46158 + 4.98636i) q^{27} +(3.85332 - 1.25202i) q^{28} +(-0.795704 - 0.578113i) q^{29} +(1.51506 - 4.66286i) q^{31} +5.65506 q^{32} +(5.62748 - 1.15390i) q^{33} -3.52660 q^{34} +(3.60890 - 0.840407i) q^{36} +(-1.00274 - 0.728533i) q^{37} +(4.85341 - 1.57697i) q^{38} +(3.44807 - 0.396177i) q^{39} +(4.47200 - 3.24910i) q^{41} +(4.32698 + 2.44266i) q^{42} -1.88388i q^{43} +(-2.68937 - 3.09014i) q^{44} +(-5.47056 - 1.77749i) q^{46} +(2.21245 + 3.04517i) q^{47} +(0.00478823 + 0.00521547i) q^{48} +(-1.16192 - 3.57602i) q^{49} +(4.72348 + 5.14495i) q^{51} +(-1.45480 - 2.00236i) q^{52} +(-7.66260 - 2.48973i) q^{53} +(3.75242 + 2.56325i) q^{54} -9.28088i q^{56} +(-8.80125 - 4.96848i) q^{57} +(-0.695887 + 0.505591i) q^{58} +(7.11811 - 9.79724i) q^{59} +(3.98985 - 1.29638i) q^{61} +(-3.46890 - 2.52030i) q^{62} +(-2.23191 - 9.58431i) q^{63} +(1.53082 - 4.71138i) q^{64} +(0.561079 - 4.99251i) q^{66} +13.2069 q^{67} +(1.53912 - 4.73692i) q^{68} +(4.73402 + 10.3618i) q^{69} +(1.57757 - 0.512584i) q^{71} +(0.723704 - 8.45705i) q^{72} +(-2.47649 + 3.40860i) q^{73} +(-0.876951 + 0.637142i) q^{74} +7.20734i q^{76} +(-8.20661 + 7.14228i) q^{77} +(0.602329 - 2.97501i) q^{78} +(-10.1467 - 3.29686i) q^{79} +(-1.28642 - 8.90759i) q^{81} +(-1.49387 - 4.59766i) q^{82} +(4.73919 + 14.5857i) q^{83} +(-5.16941 + 4.74594i) q^{84} +(-1.56692 - 0.509122i) q^{86} +(1.66967 + 0.338047i) q^{87} +(-8.63569 + 3.67156i) q^{88} -2.87598i q^{89} +(-5.31776 + 3.86358i) q^{91} +(4.77505 - 6.57229i) q^{92} +(0.969332 + 8.43644i) q^{93} +(3.13074 - 1.01724i) q^{94} +(-8.90908 + 4.07033i) q^{96} +(-0.938473 + 2.88832i) q^{97} -3.28837 q^{98} +(-8.03508 + 5.86835i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 4 q^{4} - 10 q^{6} + 10 q^{9}+O(q^{10}) $ 80 * q - 4 * q^4 - 10 * q^6 + 10 * q^9	$ 80 q - 4 q^{4} - 10 q^{6} + 10 q^{9} - 60 q^{16} + 20 q^{19} + 30 q^{24} - 20 q^{31} + 56 q^{34} + 2 q^{36} + 50 q^{39} - 40 q^{46} - 72 q^{49} + 30 q^{51} - 96 q^{64} - 42 q^{66} - 30 q^{69} - 66 q^{81} - 140 q^{84} + 48 q^{91} - 60 q^{94} - 70 q^{96} - 60 q^{99}+O(q^{100}) $ 80 * q - 4 * q^4 - 10 * q^6 + 10 * q^9 - 60 * q^16 + 20 * q^19 + 30 * q^24 - 20 * q^31 + 56 * q^34 + 2 * q^36 + 50 * q^39 - 40 * q^46 - 72 * q^49 + 30 * q^51 - 96 * q^64 - 42 * q^66 - 30 * q^69 - 66 * q^81 - 140 * q^84 + 48 * q^91 - 60 * q^94 - 70 * q^96 - 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/825\mathbb{Z}\right)^\times$.

$n$	$376$	$551$	$727$
$\chi(n)$	$e\left(\frac{1}{10}\right)$	$-1$	$1$

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 $

$2$	0.270252	−	0.831751i	0.191097	−	0.588137i	−0.808903	−	0.587942i	$-0.799938\pi$
$2$	0.270252	−	0.831751i	0.191097	−	0.588137i	1.00000		0.000194370i	$-6.18700e-5\pi$
$3$	−1.57542	+	0.719767i	−0.909567	+	0.415558i
$3$	−1.57542	+	0.719767i	−0.909567	+	0.415558i
$4$	0.999260	+	0.726005i	0.499630	+	0.363003i
$5$		0			0
$5$		0			0
$6$	0.172907	+	1.50487i	0.0705891	+	0.614362i
$7$	1.92808	−	2.65378i	0.728747	−	1.00303i	−0.270441	−	0.962737i	$-0.587169\pi$
$7$	1.92808	−	2.65378i	0.728747	−	1.00303i	0.999188	−	0.0402978i	$-0.0128307\pi$
$8$	2.28897	−	1.66303i	0.809272	−	0.587971i
$9$	1.96387	−	2.26786i	0.654624	−	0.755955i
$10$		0			0
$11$	−3.23205	−	0.744199i	−0.974501	−	0.224384i
$11$	−3.23205	−	0.744199i	−0.974501	−	0.224384i
$12$	−2.09681	−	0.424525i	−0.605296	−	0.122550i
$13$	−1.90577	−	0.619221i	−0.528565	−	0.171741i	0.0325639	−	0.999470i	$-0.489633\pi$
$13$	−1.90577	−	0.619221i	−0.528565	−	0.171741i	−0.561129	+	0.827729i	$0.689633\pi$
$14$	−1.68622	−	2.32088i	−0.450660	−	0.620280i
$15$		0			0
$16$	−0.00126317	−	0.00388765i	−0.000315793	−	0.000971912i
$17$	−1.24609	−	3.83508i	−0.302222	−	0.930144i	−0.980699	−	0.195523i	$-0.937360\pi$
$17$	−1.24609	−	3.83508i	−0.302222	−	0.930144i	0.678477	−	0.734622i	$-0.262640\pi$
$18$	−1.35556	−	2.24635i	−0.319508	−	0.529469i
$19$	3.42983	+	4.72076i	0.786857	+	1.08302i	0.994492	+	0.104809i	$0.0334232\pi$
$19$	3.42983	+	4.72076i	0.786857	+	1.08302i	−0.207635	+	0.978206i	$0.566577\pi$
$20$		0			0
$21$	−1.12743	+	5.56858i	−0.246026	+	1.21516i
$22$	−1.49246	+	2.48714i	−0.318193	+	0.530261i
$23$		−	6.57716i		−	1.37143i	−0.727869	−	0.685716i	$-0.759489\pi$
$23$		−	6.57716i		−	1.37143i	0.727869	−	0.685716i	$-0.240511\pi$
$24$	−2.40908	+	4.26749i	−0.491751	+	0.871098i
$25$		0			0
$26$	−1.03008	+	1.41778i	−0.202015	+	0.278049i
$27$	−1.46158	+	4.98636i	−0.281281	+	0.959625i
$28$	3.85332	−	1.25202i	0.728208	−	0.236609i
$29$	−0.795704	−	0.578113i	−0.147758	−	0.107353i	0.511450	−	0.859313i	$-0.329109\pi$
$29$	−0.795704	−	0.578113i	−0.147758	−	0.107353i	−0.659209	+	0.751960i	$0.729109\pi$
$30$		0			0
$31$	1.51506	−	4.66286i	0.272112	−	0.837475i	−0.717857	−	0.696191i	$-0.754877\pi$
$31$	1.51506	−	4.66286i	0.272112	−	0.837475i	0.989969	−	0.141284i	$-0.0451232\pi$
$32$	5.65506			0.999684
$33$	5.62748	−	1.15390i	0.979618	−	0.200869i
$34$	−3.52660			−0.604806
$35$		0			0
$36$	3.60890	−	0.840407i	0.601483	−	0.140068i
$37$	−1.00274	−	0.728533i	−0.164849	−	0.119770i	0.502302	−	0.864692i	$-0.332487\pi$
$37$	−1.00274	−	0.728533i	−0.164849	−	0.119770i	−0.667151	+	0.744922i	$0.732487\pi$
$38$	4.85341	−	1.57697i	0.787328	−	0.255818i
$39$	3.44807	−	0.396177i	0.552133	−	0.0634391i
$40$		0			0
$41$	4.47200	−	3.24910i	0.698408	−	0.507423i	−0.181005	−	0.983482i	$-0.557935\pi$
$41$	4.47200	−	3.24910i	0.698408	−	0.507423i	0.879414	+	0.476059i	$0.157935\pi$
$42$	4.32698	+	2.44266i	0.667668	+	0.376911i
$43$		−	1.88388i		−	0.287289i	−0.989629	−	0.143644i	$-0.954118\pi$
$43$		−	1.88388i		−	0.287289i	0.989629	−	0.143644i	$-0.0458821\pi$
$44$	−2.68937	−	3.09014i	−0.405438	−	0.465855i
$45$		0			0
$46$	−5.47056	−	1.77749i	−0.806590	−	0.262077i
$47$	2.21245	+	3.04517i	0.322718	+	0.444184i	0.939295	−	0.343111i	$-0.111481\pi$
$47$	2.21245	+	3.04517i	0.322718	+	0.444184i	−0.616576	+	0.787295i	$0.711481\pi$
$48$	0.00478823	+	0.00521547i	0.000691121	+	0.000752789i
$49$	−1.16192	−	3.57602i	−0.165989	−	0.510861i
$50$		0			0
$51$	4.72348	+	5.14495i	0.661420	+	0.720438i
$52$	−1.45480	−	2.00236i	−0.201744	−	0.277677i
$53$	−7.66260	−	2.48973i	−1.05254	−	0.341990i	−0.268874	−	0.963175i	$-0.586652\pi$
$53$	−7.66260	−	2.48973i	−1.05254	−	0.341990i	−0.783664	+	0.621185i	$0.786652\pi$
$54$	3.75242	+	2.56325i	0.510639	+	0.348814i
$55$		0			0
$56$		−	9.28088i		−	1.24021i
$57$	−8.80125	−	4.96848i	−1.16575	−	0.658091i
$58$	−0.695887	+	0.505591i	−0.0913744	+	0.0663874i
$59$	7.11811	−	9.79724i	0.926699	−	1.27549i	−0.0344338	−	0.999407i	$-0.510963\pi$
$59$	7.11811	−	9.79724i	0.926699	−	1.27549i	0.961133	−	0.276085i	$-0.0890372\pi$
$60$		0			0
$61$	3.98985	−	1.29638i	0.510848	−	0.165984i	−0.0422400	−	0.999107i	$-0.513449\pi$
$61$	3.98985	−	1.29638i	0.510848	−	0.165984i	0.553088	+	0.833123i	$0.313449\pi$
$62$	−3.46890	−	2.52030i	−0.440550	−	0.320078i
$63$	−2.23191	−	9.58431i	−0.281194	−	1.20751i
$64$	1.53082	−	4.71138i	0.191353	−	0.588923i
$65$		0			0
$66$	0.561079	−	4.99251i	0.0690641	−	0.614535i
$67$	13.2069			1.61348			0.806741	−	0.590905i	$-0.201229\pi$
$67$	13.2069			1.61348			0.806741	+	0.590905i	$0.201229\pi$
$68$	1.53912	−	4.73692i	0.186645	−	0.574436i
$69$	4.73402	+	10.3618i	0.569909	+	1.24741i
$70$		0			0
$71$	1.57757	−	0.512584i	0.187223	−	0.0608325i	−0.213905	−	0.976854i	$-0.568618\pi$
$71$	1.57757	−	0.512584i	0.187223	−	0.0608325i	0.401128	+	0.916022i	$0.368618\pi$
$72$	0.723704	−	8.45705i	0.0852894	−	0.996673i
$73$	−2.47649	+	3.40860i	−0.289851	+	0.398946i	−0.928966	−	0.370165i	$-0.879301\pi$
$73$	−2.47649	+	3.40860i	−0.289851	+	0.398946i	0.639114	+	0.769112i	$0.279301\pi$
$74$	−0.876951	+	0.637142i	−0.101944	+	0.0740663i
$75$		0			0
$76$			7.20734i			0.826738i
$77$	−8.20661	+	7.14228i	−0.935230	+	0.813938i
$78$	0.602329	−	2.97501i	0.0682003	−	0.336853i
$79$	−10.1467	−	3.29686i	−1.14159	−	0.370926i	−0.323622	−	0.946187i	$-0.604901\pi$
$79$	−10.1467	−	3.29686i	−1.14159	−	0.370926i	−0.817970	+	0.575261i	$0.804901\pi$
$80$		0			0
$81$	−1.28642	−	8.90759i	−0.142936	−	0.989732i
$82$	−1.49387	−	4.59766i	−0.164971	−	0.507727i
$83$	4.73919	+	14.5857i	0.520194	+	1.60099i	0.773629	+	0.633639i	$0.218439\pi$
$83$	4.73919	+	14.5857i	0.520194	+	1.60099i	−0.253435	+	0.967352i	$0.581561\pi$
$84$	−5.16941	+	4.74594i	−0.564029	+	0.517824i
$85$		0			0
$86$	−1.56692	−	0.509122i	−0.168965	−	0.0549001i
$87$	1.66967	+	0.338047i	0.179008	+	0.0362424i
$88$	−8.63569	+	3.67156i	−0.920568	+	0.391390i
$89$		−	2.87598i		−	0.304853i	−0.988315	−	0.152427i	$-0.951291\pi$
$89$		−	2.87598i		−	0.304853i	0.988315	−	0.152427i	$-0.0487088\pi$
$90$		0			0
$91$	−5.31776	+	3.86358i	−0.557452	+	0.405013i
$92$	4.77505	−	6.57229i	0.497833	−	0.685209i
$93$	0.969332	+	8.43644i	0.100515	+	0.874818i
$94$	3.13074	−	1.01724i	0.322911	−	0.104920i
$95$		0			0
$96$	−8.90908	+	4.07033i	−0.909279	+	0.415426i
$97$	−0.938473	+	2.88832i	−0.0952875	+	0.293265i	−0.987329	−	0.158690i	$-0.949273\pi$
$97$	−0.938473	+	2.88832i	−0.0952875	+	0.293265i	0.892041	+	0.451954i	$0.149273\pi$
$98$	−3.28837			−0.332176
$99$	−8.03508	+	5.86835i	−0.807556	+	0.589791i
$100$		0			0
$101$	−3.68651	+	11.3459i	−0.366822	+	1.12896i	0.582011	+	0.813181i	$0.302266\pi$
$101$	−3.68651	+	11.3459i	−0.366822	+	1.12896i	−0.948832	+	0.315780i	$0.897734\pi$
$102$	5.55585	−	2.53833i	0.550112	−	0.251332i
$103$	6.52446	+	4.74030i	0.642875	+	0.467076i	0.860837	−	0.508882i	$-0.169941\pi$
$103$	6.52446	+	4.74030i	0.642875	+	0.467076i	−0.217962	+	0.975957i	$0.569941\pi$
$104$	−5.39203	+	1.75198i	−0.528732	+	0.171795i
$105$		0			0
$106$	−4.14167	+	5.70052i	−0.402274	+	0.553683i
$107$	−4.57853	+	3.32650i	−0.442623	+	0.321585i	−0.786676	−	0.617366i	$-0.788200\pi$
$107$	−4.57853	+	3.32650i	−0.442623	+	0.321585i	0.344053	+	0.938950i	$0.388200\pi$
$108$	−5.08062	+	3.92156i	−0.488883	+	0.377352i
$109$			5.45613i			0.522602i	0.965257	+	0.261301i	$0.0841515\pi$
$109$			5.45613i			0.522602i	−0.965257	+	0.261301i	$0.915848\pi$
$110$		0			0
$111$	2.10411	+	0.426004i	0.199713	+	0.0404345i
$112$	−0.0127525	−	0.00414353i	−0.00120500	−	0.000391527i
$113$	−4.30936	−	5.93132i	−0.405390	−	0.557972i	0.556696	−	0.830716i	$-0.312069\pi$
$113$	−4.30936	−	5.93132i	−0.405390	−	0.557972i	−0.962087	+	0.272744i	$0.912069\pi$
$114$	−6.51109	+	5.97771i	−0.609820	+	0.559864i
$115$		0			0
$116$	−0.375402	−	1.15537i	−0.0348552	−	0.107273i
$117$	−5.14699	+	3.10595i	−0.475840	+	0.287145i
$118$	−6.22518	−	8.56823i	−0.573074	−	0.788769i
$119$	−12.5800	−	4.08750i	−1.15321	−	0.374701i
$120$		0			0
$121$	9.89234	+	4.81058i	0.899303	+	0.437325i
$122$		−	3.66891i		−	0.332168i
$123$	−4.70666	+	8.33747i	−0.424385	+	0.751765i
$124$	4.89920	−	3.55948i	0.439961	−	0.319650i
$125$		0			0
$126$	−8.57494	−	0.733793i	−0.763917	−	0.0653715i
$127$	−5.99114	+	1.94664i	−0.531628	+	0.172736i	−0.562516	−	0.826786i	$-0.690166\pi$
$127$	−5.99114	+	1.94664i	−0.531628	+	0.172736i	0.0308880	+	0.999523i	$0.490166\pi$
$128$	5.64510	+	4.10140i	0.498961	+	0.362516i
$129$	1.35595	+	2.96789i	0.119385	+	0.261308i
$130$		0			0
$131$	9.97712			0.871705			0.435852	−	0.900018i	$-0.356447\pi$
$131$	9.97712			0.871705			0.435852	+	0.900018i	$0.356447\pi$
$132$	6.46106	+	2.93253i	0.562363	+	0.255244i
$133$	19.1408			1.65972
$134$	3.56920	−	10.9849i	0.308332	−	0.948949i
$135$		0			0
$136$	−9.23014	−	6.70609i	−0.791478	−	0.575042i
$137$	−7.53879	+	2.44950i	−0.644082	+	0.209275i	−0.612803	−	0.790236i	$-0.709958\pi$
$137$	−7.53879	+	2.44950i	−0.644082	+	0.209275i	−0.0312791	+	0.999511i	$0.509958\pi$
$138$	9.89778	−	1.13724i	0.842555	−	0.0968081i
$139$	−0.205139	+	0.282349i	−0.0173996	+	0.0239485i	−0.817628	−	0.575747i	$-0.804711\pi$
$139$	−0.205139	+	0.282349i	−0.0173996	+	0.0239485i	0.800229	+	0.599695i	$0.204711\pi$
$140$		0			0
$141$	−5.67734	−	3.20496i	−0.478118	−	0.269907i
$142$		−	1.45067i		−	0.121738i
$143$	5.69872	+	3.41963i	0.476551	+	0.285964i
$144$	−0.0112974	−	0.00477013i	−0.000941448	−	0.000397511i
$145$		0			0
$146$	2.16583	+	2.98101i	0.179245	+	0.246710i
$147$	4.40441	+	4.79741i	0.363270	+	0.395684i
$148$	−0.473079	−	1.45599i	−0.0388869	−	0.119682i
$149$	1.62130	+	4.98986i	0.132822	+	0.408785i	0.995245	−	0.0974039i	$-0.0310539\pi$
$149$	1.62130	+	4.98986i	0.132822	+	0.408785i	−0.862423	+	0.506189i	$0.831054\pi$
$150$		0			0
$151$	5.49973	+	7.56973i	0.447562	+	0.616016i	0.971872	−	0.235511i	$-0.0756765\pi$
$151$	5.49973	+	7.56973i	0.447562	+	0.616016i	−0.524310	+	0.851528i	$0.675677\pi$
$152$	15.7015	+	5.10174i	1.27356	+	0.413806i
$153$	−11.1446	−	4.70564i	−0.900989	−	0.380428i
$154$	3.72274	+	8.75607i	0.299987	+	0.705585i
$155$		0			0
$156$	3.73315	+	2.10743i	0.298891	+	0.168730i
$157$	−4.20006	+	3.05152i	−0.335201	+	0.243538i	−0.742634	−	0.669697i	$-0.766424\pi$
$157$	−4.20006	+	3.05152i	−0.335201	+	0.243538i	0.407433	+	0.913235i	$0.366424\pi$
$158$	−5.48433	+	7.54854i	−0.436310	+	0.600529i
$159$	13.8638	−	1.59293i	1.09947	−	0.126327i
$160$		0			0
$161$	−17.4543	−	12.6813i	−1.37559	−	0.999427i
$162$	−7.75655	−	1.33731i	−0.609412	−	0.105069i
$163$	4.25756	−	13.1034i	0.333478	−	1.02634i	−0.633989	−	0.773342i	$-0.718584\pi$
$163$	4.25756	−	13.1034i	0.333478	−	1.02634i	0.967467	−	0.252997i	$-0.0814162\pi$
$164$	6.82755			0.533142
$165$		0			0
$166$	13.4125			1.04101
$167$	−0.0484080	+	0.148984i	−0.00374592	+	0.0115288i	−0.952912	−	0.303247i	$-0.901929\pi$
$167$	−0.0484080	+	0.148984i	−0.00374592	+	0.0115288i	0.949166	+	0.314776i	$0.101929\pi$
$168$	6.68007	+	14.6212i	0.515379	+	1.12805i
$169$	−7.26871	−	5.28102i	−0.559131	−	0.406233i
$170$		0			0
$171$	17.4418	+	1.49256i	1.33381	+	0.114139i
$172$	1.36770	−	1.88248i	0.104287	−	0.143538i
$173$	−15.5033	+	11.2638i	−1.17869	+	0.856372i	−0.992024	−	0.126051i	$-0.959770\pi$
$173$	−15.5033	+	11.2638i	−1.17869	+	0.856372i	−0.186671	+	0.982423i	$0.559770\pi$
$174$	0.732403	−	1.29739i	0.0555233	−	0.0983551i
$175$		0			0
$176$	0.00118946	+	0.0135051i	8.96590e−5	+	0.00101799i
$177$	−4.16226	+	20.5581i	−0.312854	+	1.54524i
$178$	−2.39210	−	0.777240i	−0.179295	−	0.0582566i
$179$	1.32649	+	1.82575i	0.0991462	+	0.136463i	0.855708	−	0.517460i	$-0.173122\pi$
$179$	1.32649	+	1.82575i	0.0991462	+	0.136463i	−0.756561	+	0.653923i	$0.773122\pi$
$180$		0			0
$181$	−2.62715	−	8.08554i	−0.195275	−	0.600993i	−0.999973	−	0.00730983i	$-0.997673\pi$
$181$	−2.62715	−	8.08554i	−0.195275	−	0.600993i	0.804699	−	0.593683i	$-0.202327\pi$
$182$	1.77640	+	5.46719i	0.131675	+	0.405255i
$183$	−5.35258	+	4.91410i	−0.395674	+	0.363261i
$184$	−10.9380	−	15.0549i	−0.806362	−	1.10986i
$185$		0			0
$186$	7.27898	+	1.47372i	0.533721	+	0.108059i
$187$	1.17338	+	13.3225i	0.0858059	+	0.974240i
$188$			4.64917i			0.339075i
$189$	10.4147	+	13.4928i	0.757555	+	0.981459i
$190$		0			0
$191$	−5.37971	+	7.40453i	−0.389262	+	0.535773i	−0.958009	−	0.286740i	$-0.907428\pi$
$191$	−5.37971	+	7.40453i	−0.389262	+	0.535773i	0.568747	+	0.822513i	$0.307428\pi$
$192$	0.979418	+	8.52422i	0.0706834	+	0.615183i
$193$	9.20446	−	2.99071i	0.662551	−	0.215276i	0.0416111	−	0.999134i	$-0.486751\pi$
$193$	9.20446	−	2.99071i	0.662551	−	0.215276i	0.620940	+	0.783858i	$0.286751\pi$
$194$	2.14874	+	1.56115i	0.154271	+	0.112084i
$195$		0			0
$196$	1.43515	−	4.41694i	0.102511	−	0.315496i
$197$	−11.9641			−0.852408			−0.426204	−	0.904627i	$-0.640149\pi$
$197$	−11.9641			−0.852408			−0.426204	+	0.904627i	$0.640149\pi$
$198$	2.70951	+	8.26912i	0.192556	+	0.587661i
$199$	26.5730			1.88371			0.941854	−	0.336023i	$-0.109082\pi$
$199$	26.5730			1.88371			0.941854	+	0.336023i	$0.109082\pi$
$200$		0			0
$201$	−20.8064	+	9.50591i	−1.46757	+	0.670495i
$202$	8.44069	+	6.13252i	0.593885	+	0.431483i
$203$	−3.06837	+	0.996973i	−0.215357	+	0.0699738i
$204$	0.984726	+	8.57042i	0.0689446	+	0.600050i
$205$		0			0
$206$	5.70600	−	4.14565i	0.397556	−	0.288841i
$207$	−14.9161	−	12.9167i	−1.03674	−	0.897772i
$208$			0.00819114i			0.000567953i
$209$	−7.57221	−	17.8102i	−0.523781	−	1.23196i
$210$		0			0
$211$	−14.6673	−	4.76569i	−1.00974	−	0.328084i	−0.242988	−	0.970029i	$-0.578128\pi$
$211$	−14.6673	−	4.76569i	−1.00974	−	0.328084i	−0.766750	+	0.641945i	$0.778128\pi$
$212$	−5.84937	−	8.05097i	−0.401737	−	0.552943i
$213$	−2.11639	+	1.94302i	−0.145013	+	0.133133i
$214$	1.52946	+	4.70719i	0.104552	+	0.321777i
$215$		0			0
$216$	4.94697	+	13.8443i	0.336599	+	0.941983i
$217$	−9.45306	−	13.0110i	−0.641716	−	0.883246i
$218$	4.53814	+	1.47453i	0.307362	+	0.0998678i
$219$	1.44811	−	7.15246i	0.0978541	−	0.483318i
$220$		0			0
$221$			8.08039i			0.543546i
$222$	0.922969	−	1.63496i	0.0619456	−	0.109732i
$223$	−20.6013	+	14.9677i	−1.37956	+	1.00231i	−0.382644	+	0.923896i	$0.624986\pi$
$223$	−20.6013	+	14.9677i	−1.37956	+	1.00231i	−0.996921	+	0.0784164i	$0.975014\pi$
$224$	10.9034	−	15.0073i	0.728517	−	1.00272i
$225$		0			0
$226$	−6.09800	+	1.98136i	−0.405633	+	0.131798i
$227$	17.9642	+	13.0518i	1.19233	+	0.866277i	0.993508	−	0.113759i	$-0.0362891\pi$
$227$	17.9642	+	13.0518i	1.19233	+	0.866277i	0.198820	+	0.980036i	$0.436289\pi$
$228$	−5.18760	−	11.3546i	−0.343557	−	0.751974i
$229$	−5.90023	+	18.1590i	−0.389898	+	1.19998i	0.542966	+	0.839754i	$0.317301\pi$
$229$	−5.90023	+	18.1590i	−0.389898	+	1.19998i	−0.932864	+	0.360228i	$0.882699\pi$
$230$		0			0
$231$	7.78805	−	17.1589i	0.512416	−	1.12897i
$232$	−2.78276			−0.182697
$233$	−5.85108	+	18.0078i	−0.383317	+	1.17973i	0.554377	+	0.832266i	$0.312957\pi$
$233$	−5.85108	+	18.0078i	−0.383317	+	1.17973i	−0.937694	+	0.347462i	$0.887043\pi$
$234$	1.19239	+	5.12041i	0.0779492	+	0.334732i
$235$		0			0
$236$	14.2257	−	4.62221i	0.926014	−	0.300880i
$237$	18.3582	−	2.10933i	1.19250	−	0.137016i
$238$	−6.79957	+	9.35881i	−0.440751	+	0.606641i
$239$	−15.2628	+	11.0891i	−0.987270	+	0.717294i	−0.959322	−	0.282315i	$-0.908898\pi$
$239$	−15.2628	+	11.0891i	−0.987270	+	0.717294i	−0.0279488	+	0.999609i	$0.508898\pi$
$240$		0			0
$241$			2.15494i			0.138812i	0.997589	+	0.0694059i	$0.0221104\pi$
$241$			2.15494i			0.138812i	−0.997589	+	0.0694059i	$0.977890\pi$
$242$	6.67463	−	6.92789i	0.429062	−	0.445342i
$243$	8.43804	+	13.1072i	0.541300	+	0.840829i
$244$	4.92808	+	1.60123i	0.315488	+	0.102508i
$245$		0			0
$246$	5.66272	+	6.16799i	0.361042	+	0.393257i
$247$	−3.61327	−	11.1205i	−0.229907	−	0.707580i
$248$	−4.28658	−	13.1927i	−0.272198	−	0.837739i
$249$	−17.9645	−	19.5675i	−1.13846	−	1.24004i
$250$		0			0
$251$	2.22750	+	0.723758i	0.140598	+	0.0456832i	0.378471	−	0.925613i	$-0.376450\pi$
$251$	2.22750	+	0.723758i	0.140598	+	0.0456832i	−0.237872	+	0.971296i	$0.576450\pi$
$252$	4.72801	−	11.1976i	0.297836	−	0.705383i
$253$	−4.89471	+	21.2577i	−0.307728	+	1.33646i
$254$			5.50922i			0.345679i
$255$		0			0
$256$	12.9524	−	9.41049i	0.809527	−	0.588156i
$257$	−6.04504	+	8.32028i	−0.377079	+	0.519005i	−0.954808	−	0.297224i	$-0.903939\pi$
$257$	−6.04504	+	8.32028i	−0.377079	+	0.519005i	0.577729	+	0.816229i	$0.303939\pi$
$258$	2.83500	−	0.325736i	0.176499	−	0.0202794i
$259$	−3.86673	+	1.25638i	−0.240267	+	0.0780675i
$260$		0			0
$261$	−2.87374	+	0.669210i	−0.177880	+	0.0414231i
$262$	2.69634	−	8.29848i	0.166580	−	0.512682i
$263$	12.1665			0.750219			0.375110	−	0.926980i	$-0.377605\pi$
$263$	12.1665			0.750219			0.375110	+	0.926980i	$0.377605\pi$
$264$	10.9621	−	11.9999i	0.674673	−	0.738544i
$265$		0			0
$266$	5.17286	−	15.9204i	0.317168	−	0.976144i
$267$	2.07004	+	4.53087i	0.126684	+	0.277284i
$268$	13.1972	+	9.58830i	0.806145	+	0.585698i
$269$	2.56774	−	0.834310i	0.156558	−	0.0508688i	−0.229689	−	0.973264i	$-0.573771\pi$
$269$	2.56774	−	0.834310i	0.156558	−	0.0508688i	0.386248	+	0.922395i	$0.373771\pi$
$270$		0			0
$271$	7.12643	−	9.80869i	0.432900	−	0.595836i	−0.535716	−	0.844398i	$-0.679958\pi$
$271$	7.12643	−	9.80869i	0.432900	−	0.595836i	0.968616	+	0.248563i	$0.0799582\pi$
$272$	−0.0133354	+	0.00968875i	−0.000808579	+	0.000587467i
$273$	5.59680	−	9.91429i	0.338734	−	0.600040i
$274$			6.93238i			0.418800i
$275$		0			0
$276$	−2.79217	+	13.7910i	−0.168069	+	0.830122i
$277$	13.4331	+	4.36469i	0.807119	+	0.262249i	0.683377	−	0.730065i	$-0.260510\pi$
$277$	13.4331	+	4.36469i	0.807119	+	0.262249i	0.123742	+	0.992314i	$0.460510\pi$
$278$	0.179405	+	0.246930i	0.0107600	+	0.0148099i
$279$	−7.59937	−	12.5932i	−0.454962	−	0.753936i
$280$		0			0
$281$	−5.06988	−	15.6035i	−0.302444	−	0.930827i	−0.980619	−	0.195926i	$-0.937229\pi$
$281$	−5.06988	−	15.6035i	−0.302444	−	0.930827i	0.678175	−	0.734901i	$-0.262771\pi$
$282$	−4.20005	+	3.85598i	−0.250109	+	0.229620i
$283$	−18.5806	−	25.5739i	−1.10450	−	1.52021i	−0.829281	−	0.558832i	$-0.811250\pi$
$283$	−18.5806	−	25.5739i	−1.10450	−	1.52021i	−0.275218	−	0.961382i	$-0.588750\pi$
$284$	1.94854	+	0.633120i	0.115625	+	0.0375687i
$285$		0			0
$286$	4.38437	−	3.81575i	0.259253	−	0.225630i
$287$		−	18.1322i		−	1.07031i
$288$	11.1058	−	12.8249i	0.654416	−	0.755716i
$289$	0.598172	−	0.434598i	0.0351866	−	0.0255646i
$290$		0			0
$291$	−0.600434	−	5.22579i	−0.0351981	−	0.306341i
$292$	−4.94932	+	1.60813i	−0.289637	+	0.0941088i
$293$	2.58332	+	1.87689i	0.150919	+	0.109649i	0.660682	−	0.750665i	$-0.270267\pi$
$293$	2.58332	+	1.87689i	0.150919	+	0.109649i	−0.509763	+	0.860315i	$0.670267\pi$
$294$	5.18056	−	2.36686i	0.302136	−	0.138038i
$295$		0			0
$296$	−3.50681			−0.203829
$297$	8.43475	−	15.0285i	0.489434	−	0.872041i
$298$	4.58848			0.265803
$299$	−4.07272	+	12.5345i	−0.235531	+	0.724891i
$300$		0			0
$301$	−4.99940	−	3.63227i	−0.288160	−	0.209361i
$302$	7.78245	−	2.52867i	0.447830	−	0.145509i
$303$	−2.35863	−	20.5280i	−0.135500	−	1.17930i
$304$	0.0140202	−	0.0192971i	0.000804112	−	0.00110677i
$305$		0			0
$306$	−6.92578	+	7.99784i	−0.395920	+	0.457206i
$307$			15.2157i			0.868408i	0.900814	+	0.434204i	$0.142970\pi$
$307$			15.2157i			0.868408i	−0.900814	+	0.434204i	$0.857030\pi$
$308$	−13.3859	+	1.17896i	−0.762731	+	0.0671773i
$309$	−13.6907	−	2.77185i	−0.778834	−	0.157685i
$310$		0			0
$311$	12.3446	+	16.9909i	0.700001	+	0.963468i	0.999955	+	0.00951471i	$0.00302867\pi$
$311$	12.3446	+	16.9909i	0.700001	+	0.963468i	−0.299954	+	0.953954i	$0.596971\pi$
$312$	7.23367	−	6.64109i	0.409526	−	0.375978i
$313$	5.74415	+	17.6787i	0.324679	+	0.999258i	0.971585	+	0.236689i	$0.0760622\pi$
$313$	5.74415	+	17.6787i	0.324679	+	0.999258i	−0.646907	+	0.762569i	$0.723938\pi$
$314$	1.40303	+	4.31808i	0.0791776	+	0.243684i
$315$		0			0
$316$	−7.74565	−	10.6610i	−0.435727	−	0.599726i
$317$	−21.5259	−	6.99418i	−1.20901	−	0.392832i	−0.365944	−	0.930637i	$-0.619254\pi$
$317$	−21.5259	−	6.99418i	−1.20901	−	0.392832i	−0.843070	+	0.537804i	$0.819254\pi$
$318$	2.42181	−	11.9617i	0.135808	−	0.670780i
$319$	2.14153	+	2.46065i	0.119902	+	0.137770i
$320$		0			0
$321$	4.81879	−	8.53609i	0.268958	−	0.476438i
$322$	−15.2648	+	11.0905i	−0.850672	+	0.618049i
$323$	13.8306	−	19.0362i	0.769555	−	1.05920i
$324$	5.18148	−	9.83495i	0.287860	−	0.546386i
$325$		0			0
$326$	−9.74816	−	7.08246i	−0.539901	−	0.392261i
$327$	−3.92714	−	8.59567i	−0.217171	−	0.475342i
$328$	4.83290	−	14.8741i	0.266852	−	0.821287i
$329$	12.3470			0.680712
$330$		0			0
$331$	0.654516			0.0359754			0.0179877	−	0.999838i	$-0.494274\pi$
$331$	0.654516			0.0359754			0.0179877	+	0.999838i	$0.494274\pi$
$332$	−5.85363	+	18.0156i	−0.321260	+	0.988735i
$333$	−3.62147	+	0.843334i	−0.198455	+	0.0462144i
$334$	0.110836	+	0.0805268i	0.00606466	+	0.00440623i
$335$		0			0
$336$	0.0230728	−	0.00265103i	0.00125873	−	0.000144625i
$337$	−9.90839	+	13.6377i	−0.539745	+	0.742895i	−0.988576	−	0.150722i	$-0.951840\pi$
$337$	−9.90839	+	13.6377i	−0.539745	+	0.742895i	0.448832	+	0.893616i	$0.351840\pi$
$338$	−6.35688	+	4.61854i	−0.345769	+	0.251216i
$339$	11.0582	+	6.24257i	0.600599	+	0.339050i
$340$		0			0
$341$	−8.36684	+	13.9431i	−0.453090	+	0.755063i
$342$	5.95512	−	14.1038i	0.322016	−	0.762649i
$343$	10.1077	+	3.28418i	0.545763	+	0.177329i
$344$	−3.13295	−	4.31213i	−0.168917	−	0.232495i
$345$		0			0
$346$	5.17888	+	15.9390i	0.278419	+	0.856884i
$347$	1.96396	+	6.04444i	0.105431	+	0.324482i	0.989831	−	0.142246i	$-0.0454325\pi$
$347$	1.96396	+	6.04444i	0.105431	+	0.324482i	−0.884401	+	0.466729i	$0.845432\pi$
$348$	1.42301	+	1.54999i	0.0762815	+	0.0830880i
$349$	−0.899962	−	1.23869i	−0.0481738	−	0.0663056i	0.784251	−	0.620444i	$-0.213048\pi$
$349$	−0.899962	−	1.23869i	−0.0481738	−	0.0663056i	−0.832424	+	0.554139i	$0.813048\pi$
$350$		0			0
$351$	5.87309	−	8.59780i	0.313482	−	0.458917i
$352$	−18.2775	−	4.20849i	−0.974192	−	0.224313i
$353$		−	17.7930i		−	0.947024i	−0.880787	−	0.473512i	$-0.842986\pi$
$353$		−	17.7930i		−	0.947024i	0.880787	−	0.473512i	$-0.157014\pi$
$354$	15.9744	+	9.01784i	0.849028	+	0.479293i
$355$		0			0
$356$	2.08798	−	2.87385i	0.110663	−	0.152314i
$357$	22.7608	−	2.61518i	1.20463	−	0.138410i
$358$	1.87706	−	0.609892i	0.0992055	−	0.0322338i
$359$	8.01407	+	5.82257i	0.422967	+	0.307303i	0.778830	−	0.627235i	$-0.215813\pi$
$359$	8.01407	+	5.82257i	0.422967	+	0.307303i	−0.355864	+	0.934538i	$0.615813\pi$
$360$		0			0
$361$	−4.65048	+	14.3127i	−0.244762	+	0.753300i
$362$	−7.43515			−0.390783
$363$	−19.0470	−	0.458487i	−0.999710	−	0.0240643i
$364$	−8.11880			−0.425541
$365$		0			0
$366$	2.64076	+	5.78006i	0.138035	+	0.302129i
$367$	−13.0818	−	9.50450i	−0.682866	−	0.496131i	0.191441	−	0.981504i	$-0.438684\pi$
$367$	−13.0818	−	9.50450i	−0.682866	−	0.496131i	−0.874307	+	0.485373i	$0.838684\pi$
$368$	−0.0255697	+	0.00830809i	−0.00133291	+	0.000433089i
$369$	1.41391	−	16.5227i	0.0736054	−	0.860137i
$370$		0			0
$371$	−21.3813	+	15.5344i	−1.11006	+	0.806508i
$372$	−5.15628	+	9.13394i	−0.267341	+	0.473573i
$373$		−	23.6579i		−	1.22496i	−0.790487	−	0.612479i	$-0.790172\pi$
$373$		−	23.6579i		−	1.22496i	0.790487	−	0.612479i	$-0.209828\pi$
$374$	11.3981	+	2.62449i	0.589384	+	0.135709i
$375$		0			0
$376$	10.1284	+	3.29093i	0.522334	+	0.169717i
$377$	1.15845	+	1.59447i	0.0596630	+	0.0821191i
$378$	14.0373	−	5.01593i	0.721999	−	0.257992i
$379$	−2.77374	−	8.53671i	−0.142478	−	0.438501i	0.854200	−	0.519944i	$-0.174047\pi$
$379$	−2.77374	−	8.53671i	−0.142478	−	0.438501i	−0.996678	+	0.0814428i	$0.974047\pi$
$380$		0			0
$381$	8.03741	−	7.37899i	0.411769	−	0.378037i
$382$	4.70485	+	6.47567i	0.240721	+	0.331324i
$383$	27.0846	+	8.80032i	1.38396	+	0.449675i	0.903969	−	0.427598i	$-0.140640\pi$
$383$	27.0846	+	8.80032i	1.38396	+	0.449675i	0.479990	+	0.877274i	$0.340640\pi$
$384$	−11.8454	−	2.39826i	−0.604485	−	0.122386i
$385$		0			0
$386$		−	8.46406i		−	0.430810i
$387$	−4.27238	−	3.69969i	−0.217177	−	0.188066i
$388$	−3.03472	+	2.20485i	−0.154064	+	0.111934i
$389$	−7.85595	+	10.8128i	−0.398312	+	0.548230i	−0.960319	−	0.278903i	$-0.910029\pi$
$389$	−7.85595	+	10.8128i	−0.398312	+	0.548230i	0.562007	+	0.827132i	$0.310029\pi$
$390$		0			0
$391$	−25.2239	+	8.19576i	−1.27563	+	0.414477i
$392$	−8.60664	−	6.25309i	−0.434701	−	0.315829i
$393$	−15.7181	+	7.18120i	−0.792874	+	0.362244i
$394$	−3.23333	+	9.95117i	−0.162893	+	0.501333i
$395$		0			0
$396$	−12.2896	+	0.0305015i	−0.617575	+	0.00153276i
$397$	14.3972			0.722574			0.361287	−	0.932455i	$-0.382338\pi$
$397$	14.3972			0.722574			0.361287	+	0.932455i	$0.382338\pi$
$398$	7.18140	−	22.1021i	0.359971	−	1.10788i
$399$	−30.1548	+	13.7769i	−1.50963	+	0.689710i
$400$		0			0
$401$	14.0903	−	4.57823i	0.703637	−	0.228626i	0.0647228	−	0.997903i	$-0.479384\pi$
$401$	14.0903	−	4.57823i	0.703637	−	0.228626i	0.638915	+	0.769278i	$0.279384\pi$
$402$	2.28357	+	19.8747i	0.113894	+	0.991262i
$403$	−5.77469	+	7.94818i	−0.287658	+	0.395927i
$404$	−11.9210	+	8.66110i	−0.593091	+	0.430906i
$405$		0			0
$406$			2.82155i			0.140031i
$407$	2.69874	+	3.10090i	0.133771	+	0.153706i
$408$	19.3681	+	3.92133i	0.958865	+	0.194135i
$409$	−23.2795	−	7.56395i	−1.15109	−	0.374013i	−0.329539	−	0.944142i	$-0.606893\pi$
$409$	−23.2795	−	7.56395i	−1.15109	−	0.374013i	−0.821556	+	0.570128i	$0.806893\pi$
$410$		0			0
$411$	10.1137	−	9.28515i	0.498870	−	0.458003i
$412$	3.07816	+	9.47359i	0.151650	+	0.466730i
$413$	−12.2754	−	37.7798i	−0.604033	−	1.85902i
$414$	−14.7746	+	8.91572i	−0.726131	+	0.438184i
$415$		0			0
$416$	−10.7772	−	3.50174i	−0.528398	−	0.171687i
$417$	0.119953	−	0.592470i	0.00587413	−	0.0290134i
$418$	−16.8601	+	1.48495i	−0.824653	+	0.0726311i
$419$			3.66657i			0.179123i	0.995981	+	0.0895617i	$0.0285466\pi$
$419$			3.66657i			0.179123i	−0.995981	+	0.0895617i	$0.971453\pi$
$420$		0			0
$421$	10.1620	−	7.38315i	0.495267	−	0.359833i	−0.311939	−	0.950102i	$-0.600978\pi$
$421$	10.1620	−	7.38315i	0.495267	−	0.359833i	0.807206	+	0.590269i	$0.200978\pi$
$422$	−7.92774	+	10.9116i	−0.385916	+	0.531168i
$423$	11.2510	+	0.962794i	0.547042	+	0.0468126i
$424$	−21.6799	+	7.04424i	−1.05287	+	0.342098i
$425$		0			0
$426$	1.04415	+	2.28541i	0.0505891	+	0.110729i
$427$	4.25245	−	13.0877i	0.205791	−	0.633359i
$428$	−6.99020			−0.337884
$429$	−11.4392	−	1.28558i	−0.552289	−	0.0620686i
$430$		0			0
$431$	−7.04575	+	21.6846i	−0.339382	+	1.04451i	0.625141	+	0.780512i	$0.285041\pi$
$431$	−7.04575	+	21.6846i	−0.339382	+	1.04451i	−0.964523	+	0.263999i	$0.914959\pi$
$432$	0.0212314		0.000616532i	0.00102150		2.96629e-5i
$433$	−23.0195	−	16.7246i	−1.10624	−	0.803734i	−0.124177	−	0.992260i	$-0.539629\pi$
$433$	−23.0195	−	16.7246i	−1.10624	−	0.803734i	−0.982068	+	0.188526i	$0.939629\pi$
$434$	−13.3766	+	4.34633i	−0.642099	+	0.208631i
$435$		0			0
$436$	−3.96118	+	5.45209i	−0.189706	+	0.261108i
$437$	31.0491	−	22.5585i	1.48528	−	1.07912i
$438$	−5.55771	−	3.13743i	−0.265558	−	0.149912i
$439$		−	16.4681i		−	0.785979i	−0.919543	−	0.392989i	$-0.871441\pi$
$439$		−	16.4681i		−	0.785979i	0.919543	−	0.392989i	$-0.128559\pi$
$440$		0			0
$441$	−10.3918	−	4.38777i	−0.494848	−	0.208941i
$442$	6.72087	+	2.18374i	0.319679	+	0.103870i
$443$	−0.154522	−	0.212682i	−0.00734157	−	0.0101048i	0.805330	−	0.592826i	$-0.201988\pi$
$443$	−0.154522	−	0.212682i	−0.00734157	−	0.0101048i	−0.812672	+	0.582721i	$0.801988\pi$
$444$	1.79327	+	1.95328i	0.0851048	+	0.0926986i
$445$		0			0
$446$	6.88187	+	21.1802i	0.325866	+	1.00291i
$447$	−6.14576	−	6.69414i	−0.290684	−	0.316622i
$448$	−9.55142	−	13.1464i	−0.451262	−	0.621109i
$449$	−7.95876	−	2.58596i	−0.375597	−	0.122039i	0.115134	−	0.993350i	$-0.463270\pi$
$449$	−7.95876	−	2.58596i	−0.375597	−	0.122039i	−0.490731	+	0.871311i	$0.663270\pi$
$450$		0			0
$451$	−16.8717	+	7.17320i	−0.794457	+	0.337773i
$452$		−	9.05555i		−	0.425937i
$453$	−14.1128	−	7.96695i	−0.663078	−	0.374320i
$454$	15.7107	−	11.4145i	0.737340	−	0.535709i
$455$		0			0
$456$	−28.4085	+	3.26409i	−1.33035	+	0.152855i
$457$	28.6709	−	9.31574i	1.34117	−	0.435772i	0.451455	−	0.892294i	$-0.350905\pi$
$457$	28.6709	−	9.31574i	1.34117	−	0.435772i	0.889712	+	0.456522i	$0.150905\pi$
$458$	13.5092	+	9.81504i	0.631245	+	0.458627i
$459$	20.9444	−	0.608196i	0.977600	−	0.0283881i
$460$		0			0
$461$	−18.8046			−0.875819			−0.437909	−	0.899019i	$-0.644281\pi$
$461$	−18.8046			−0.875819			−0.437909	+	0.899019i	$0.644281\pi$
$462$	−12.1672	−	11.1150i	−0.566070	−	0.517114i
$463$	33.3418			1.54953			0.774763	−	0.632252i	$-0.217869\pi$
$463$	33.3418			1.54953			0.774763	+	0.632252i	$0.217869\pi$
$464$	−0.00124239	+	0.00382367i	−5.76764e−5	+	0.000177510i
$465$		0			0
$466$	13.3967	+	9.73328i	0.620591	+	0.450886i
$467$	27.2421	−	8.85149i	1.26061	−	0.409598i	0.398900	−	0.916994i	$-0.369392\pi$
$467$	27.2421	−	8.85149i	1.26061	−	0.409598i	0.861713	+	0.507396i	$0.169392\pi$
$468$	−7.39812	−	0.633088i	−0.341978	−	0.0292645i
$469$	25.4641	−	35.0483i	1.17582	−	1.61838i
$470$		0			0
$471$	4.42046	−	7.83048i	0.203684	−	0.360809i
$472$		−	34.2632i		−	1.57709i
$473$	−1.40198	+	6.08879i	−0.0644631	+	0.279963i
$474$	3.20692	−	15.8395i	0.147299	−	0.727534i
$475$		0			0
$476$	−9.60319	−	13.2177i	−0.440161	−	0.605830i
$477$	−20.6947	+	12.4882i	−0.947546	+	0.571797i
$478$	5.09855	+	15.6917i	0.233202	+	0.717723i
$479$	12.8091	+	39.4224i	0.585264	+	1.80126i	0.598210	+	0.801340i	$0.295879\pi$
$479$	12.8091	+	39.4224i	0.585264	+	1.80126i	−0.0129461	+	0.999916i	$0.504121\pi$
$480$		0			0
$481$	1.45987	+	2.00933i	0.0665642	+	0.0916177i
$482$	1.79237	+	0.582377i	0.0816403	+	0.0265265i
$483$	36.6254	+	7.41529i	1.66651	+	0.337407i
$484$	6.39251	+	11.9889i	0.290569	+	0.544950i
$485$		0			0
$486$	13.1824	−	3.47609i	0.597964	−	0.157679i
$487$	−8.10463	+	5.88836i	−0.367256	+	0.266827i	−0.756072	−	0.654488i	$-0.772884\pi$
$487$	−8.10463	+	5.88836i	−0.367256	+	0.266827i	0.388816	+	0.921315i	$0.372884\pi$
$488$	6.97671	−	9.60262i	0.315821	−	0.434690i
$489$	2.72398	+	23.7078i	0.123183	+	1.07210i
$490$		0			0
$491$	17.6468	+	12.8212i	0.796390	+	0.578611i	0.909853	−	0.414931i	$-0.136194\pi$
$491$	17.6468	+	12.8212i	0.796390	+	0.578611i	−0.113463	+	0.993542i	$0.536194\pi$
$492$	−10.7562	+	4.91424i	−0.484928	+	0.221551i
$493$	−1.22559	+	3.77197i	−0.0551977	+	0.169881i
$494$	−10.2260			−0.460088
$495$		0			0
$496$	−0.0200414			−0.000899884
$497$	1.68140	−	5.17483i	0.0754213	−	0.232123i
$498$	−21.1302	+	9.65385i	−0.946868	+	0.432599i
$499$	15.9416	+	11.5823i	0.713644	+	0.518493i	0.884347	−	0.466830i	$-0.154604\pi$
$499$	15.9416	+	11.5823i	0.713644	+	0.518493i	−0.170703	+	0.985323i	$0.554604\pi$
$500$		0			0
$501$	−0.0309714	−	0.269555i	−0.00138370	−	0.0120428i
$502$	1.20397	−	1.65713i	0.0537359	−	0.0739612i
$503$	18.2609	−	13.2673i	0.814215	−	0.591562i	−0.100835	−	0.994903i	$-0.532151\pi$
$503$	18.2609	−	13.2673i	0.814215	−	0.591562i	0.915050	+	0.403342i	$0.132151\pi$
$504$	−21.0478	−	18.2265i	−0.937543	−	0.811871i
$505$		0			0
$506$	16.3583	+	9.81613i	0.727216	+	0.436380i
$507$	15.2523	+	3.08803i	0.677380	+	0.137144i
$508$	−7.39998	−	2.40440i	−0.328321	−	0.106678i
$509$	12.0546	+	16.5917i	0.534310	+	0.735414i	0.987780	−	0.155857i	$-0.0498140\pi$
$509$	12.0546	+	16.5917i	0.534310	+	0.735414i	−0.453470	+	0.891272i	$0.649814\pi$
$510$		0			0
$511$	4.27079	+	13.1441i	0.188928	+	0.581462i
$512$	−0.0142912	−	0.0439837i	−0.000631587	−	0.00194382i
$513$	−28.5524	+	10.2026i	−1.26062	+	0.450456i
$514$	5.28672	+	7.27654i	0.233187	+	0.320954i
$515$		0			0
$516$	−0.799754	+	3.95012i	−0.0352072	+	0.173895i
$517$	−4.88453	−	11.4887i	−0.214821	−	0.505270i
$518$			3.55570i			0.156228i
$519$	16.3168	−	28.9040i	0.716230	−	1.26874i
$520$		0			0
$521$	2.41526	−	3.32432i	0.105814	−	0.145641i	−0.752826	−	0.658220i	$-0.771310\pi$
$521$	2.41526	−	3.32432i	0.105814	−	0.145641i	0.858640	+	0.512579i	$0.171310\pi$
$522$	−0.220019	+	2.57109i	−0.00962997	+	0.112534i
$523$	26.9924	−	8.77036i	1.18030	−	0.383501i	0.347819	−	0.937562i	$-0.386922\pi$
$523$	26.9924	−	8.77036i	1.18030	−	0.383501i	0.832476	+	0.554061i	$0.186922\pi$
$524$	9.96974	+	7.24344i	0.435530	+	0.316431i
$525$		0			0
$526$	3.28803	−	10.1195i	0.143365	−	0.441232i
$527$	−19.7704			−0.861211
$528$	−0.0115945	−	0.0204201i	−0.000504584	−	0.000888670i
$529$	−20.2590			−0.880826
$530$		0			0
$531$	−8.23977	−	35.3834i	−0.357575	−	1.53551i
$532$	19.1267	+	13.8964i	0.829247	+	0.602483i
$533$	−10.5345	+	3.42287i	−0.456300	+	0.148261i
$534$	4.32798	−	0.497278i	0.187290	−	0.0215193i
$535$		0			0
$536$	30.2302	−	21.9635i	1.30575	−	0.948681i
$537$	−3.40388	−	1.92156i	−0.146888	−	0.0829213i
$538$		−	2.36120i		−	0.101798i
$539$	1.09412	+	12.4226i	0.0471269	+	0.535079i
$540$		0			0
$541$	7.19528	+	2.33789i	0.309349	+	0.100514i	0.459577	−	0.888138i	$-0.348001\pi$
$541$	7.19528	+	2.33789i	0.309349	+	0.100514i	−0.150228	+	0.988651i	$0.548001\pi$
$542$	−6.23246	−	8.57824i	−0.267707	−	0.368467i
$543$	9.95856	+	10.8471i	0.427363	+	0.465496i
$544$	−7.04674	−	21.6876i	−0.302127	−	0.929850i
$545$		0			0
$546$	−6.73367	−	7.33451i	−0.288174	−	0.313888i
$547$	−4.11064	−	5.65781i	−0.175758	−	0.241911i	0.712045	−	0.702134i	$-0.247769\pi$
$547$	−4.11064	−	5.65781i	−0.175758	−	0.241911i	−0.887803	+	0.460223i	$0.847769\pi$
$548$	−9.31156	−	3.02551i	−0.397770	−	0.129243i
$549$	4.89553	−	11.5944i	0.208936	−	0.494835i
$550$		0			0
$551$		−	5.73915i		−	0.244496i
$552$	28.0680	+	15.8449i	1.19465	+	0.674404i
$553$	−28.3128	+	20.5705i	−1.20398	+	0.874745i
$554$	7.26068	−	9.99346i	0.308477	−	0.424582i
$555$		0			0
$556$	−0.409974	+	0.133209i	−0.0173868	+	0.00564930i
$557$	9.46385	+	6.87589i	0.400996	+	0.291341i	0.769947	−	0.638108i	$-0.220283\pi$
$557$	9.46385	+	6.87589i	0.400996	+	0.291341i	−0.368950	+	0.929449i	$0.620283\pi$
$558$	−12.5282	+	2.91744i	−0.530359	+	0.123505i
$559$	−1.16654	+	3.59023i	−0.0493393	+	0.151851i
$560$		0			0
$561$	−11.4377	−	20.1440i	−0.482899	−	0.850479i
$562$	−14.3484			−0.605250
$563$	2.06731	−	6.36251i	0.0871266	−	0.268148i	−0.897995	−	0.440005i	$-0.854977\pi$
$563$	2.06731	−	6.36251i	0.0871266	−	0.268148i	0.985122	+	0.171857i	$0.0549767\pi$
$564$	−3.34632	−	7.32437i	−0.140905	−	0.308412i
$565$		0			0
$566$	−26.2926	+	8.54298i	−1.10516	+	0.359088i
$567$	−26.1191	−	13.7607i	−1.09690	−	0.577895i
$568$	2.75856	−	3.79684i	0.115747	−	0.159312i
$569$	30.8612	−	22.4220i	1.29377	−	0.939978i	0.293894	−	0.955838i	$-0.405049\pi$
$569$	30.8612	−	22.4220i	1.29377	−	0.939978i	0.999874	+	0.0158600i	$0.00504861\pi$
$570$		0			0
$571$		−	31.7168i		−	1.32731i	−0.748041	−	0.663653i	$-0.769005\pi$
$571$		−	31.7168i		−	1.32731i	0.748041	−	0.663653i	$-0.230995\pi$
$572$	3.21184	+	7.55440i	0.134294	+	0.315865i
$573$	3.14574	−	15.5374i	0.131415	−	0.649082i
$574$	−15.0815	−	4.90028i	−0.629489	−	0.204534i
$575$		0			0
$576$	−7.67844	−	12.7242i	−0.319935	−	0.530177i
$577$	11.0964	+	34.1511i	0.461947	+	1.42173i	0.862782	+	0.505577i	$0.168720\pi$
$577$	11.0964	+	34.1511i	0.461947	+	1.42173i	−0.400834	+	0.916151i	$0.631280\pi$
$578$	−0.199820	−	0.614982i	−0.00831140	−	0.0255799i
$579$	−12.3482	+	11.3367i	−0.513175	+	0.471136i
$580$		0			0
$581$	47.8449	+	15.5457i	1.98494	+	0.644946i
$582$	−4.50883	−	0.912871i	−0.186897	−	0.0378397i
$583$	22.9131	+	13.7494i	0.948962	+	0.569443i
$584$			11.9207i			0.493280i
$585$		0			0
$586$	2.25926	−	1.64145i	0.0933291	−	0.0678075i
$587$	16.3686	−	22.5294i	0.675603	−	0.929888i	−0.324267	−	0.945965i	$-0.605118\pi$
$587$	16.3686	−	22.5294i	0.675603	−	0.929888i	0.999871	+	0.0160773i	$0.00511778\pi$
$588$	0.918208	+	7.99149i	0.0378663	+	0.329564i
$589$	27.2086	−	8.84062i	1.12111	−	0.364271i
$590$		0			0
$591$	18.8485	−	8.61138i	0.775322	−	0.354225i
$592$	−0.00156565	+	0.00481857i	−6.43477e−5	+	0.000198042i
$593$	−23.0788			−0.947731			−0.473865	−	0.880597i	$-0.657142\pi$
$593$	−23.0788			−0.947731			−0.473865	+	0.880597i	$0.657142\pi$
$594$	−10.2204	−	11.0771i	−0.419350	−	0.454498i
$595$		0			0
$596$	−2.00256	+	6.16324i	−0.0820280	+	0.252456i
$597$	−41.8635	+	19.1263i	−1.71336	+	0.782789i
$598$	9.32495	+	6.77497i	0.381326	+	0.277049i
$599$	14.7956	−	4.80738i	0.604532	−	0.196424i	0.00927118	−	0.999957i	$-0.497049\pi$
$599$	14.7956	−	4.80738i	0.604532	−	0.196424i	0.595261	+	0.803533i	$0.297049\pi$
$600$		0			0
$601$	6.32878	−	8.71081i	0.258156	−	0.355322i	−0.660191	−	0.751098i	$-0.729525\pi$
$601$	6.32878	−	8.71081i	0.258156	−	0.355322i	0.918347	+	0.395777i	$0.129525\pi$
$602$	−4.37225	+	3.17662i	−0.178199	+	0.129469i
$603$	25.9367	−	29.9515i	1.05622	−	1.21972i
$604$			11.5570i			0.470246i
$605$		0			0
$606$	−17.7116	−	3.58594i	−0.719484	−	0.145669i
$607$	−29.4641	−	9.57347i	−1.19591	−	0.388575i	−0.357656	−	0.933853i	$-0.616424\pi$
$607$	−29.4641	−	9.57347i	−1.19591	−	0.388575i	−0.838255	+	0.545278i	$0.816424\pi$
$608$	19.3959	+	26.6962i	0.786608	+	1.08267i
$609$	4.11637	−	3.77916i	0.166804	−	0.153139i
$610$		0			0
$611$	−2.33077	−	7.17338i	−0.0942930	−	0.290204i
$612$	−7.72006	−	12.7932i	−0.312065	−	0.517135i
$613$	−17.1995	−	23.6731i	−0.694683	−	0.956149i	−0.999992	−	0.00389577i	$-0.998760\pi$
$613$	−17.1995	−	23.6731i	−0.694683	−	0.956149i	0.305310	−	0.952253i	$-0.401240\pi$
$614$	12.6557	+	4.11209i	0.510743	+	0.165950i
$615$		0			0
$616$	−6.90682	+	29.9963i	−0.278284	+	1.20859i
$617$		−	19.3771i		−	0.780095i	−0.920795	−	0.390047i	$-0.872459\pi$
$617$		−	19.3771i		−	0.780095i	0.920795	−	0.390047i	$-0.127541\pi$
$618$	−6.00542	+	10.6381i	−0.241574	+	0.427928i
$619$	28.5199	−	20.7209i	1.14631	−	0.832844i	0.158325	−	0.987387i	$-0.449390\pi$
$619$	28.5199	−	20.7209i	1.14631	−	0.832844i	0.987986	+	0.154543i	$0.0493905\pi$
$620$		0			0
$621$	32.7961	+	9.61304i	1.31606	+	0.385758i
$622$	17.4684	−	5.67583i	0.700419	−	0.227580i
$623$	−7.63222	−	5.54513i	−0.305778	−	0.222161i
$624$	−0.00589571	−	0.0129045i	−0.000236017	−	0.000516592i
$625$		0			0
$626$	16.2566			0.649746
$627$	24.7486	+	22.6083i	0.988363	+	0.902887i
$628$	−6.41237			−0.255882
$629$	−1.54448	+	4.75341i	−0.0615823	+	0.189531i
$630$		0			0
$631$	13.3120	+	9.67175i	0.529943	+	0.385026i	0.820337	−	0.571881i	$-0.193786\pi$
$631$	13.3120	+	9.67175i	0.529943	+	0.385026i	−0.290393	+	0.956907i	$0.593786\pi$
$632$	−28.7082	+	9.32787i	−1.14195	+	0.371043i
$633$	26.5373	−	3.04909i	1.05476	−	0.121190i
$634$	−11.6348	+	16.0140i	−0.462079	+	0.635996i
$635$		0			0
$636$	15.0100	+	8.47344i	0.595186	+	0.335994i
$637$			7.53456i			0.298530i
$638$	2.62540	−	1.11622i	0.103941	−	0.0441916i
$639$	1.93567	−	4.58436i	0.0765741	−	0.181355i
$640$		0			0
$641$	1.52097	+	2.09343i	0.0600746	+	0.0826856i	0.837997	−	0.545674i	$-0.183726\pi$
$641$	1.52097	+	2.09343i	0.0600746	+	0.0826856i	−0.777923	+	0.628360i	$0.783726\pi$
$642$	−5.79762	−	6.31493i	−0.228814	−	0.249230i
$643$	−2.44092	−	7.51238i	−0.0962605	−	0.296259i	0.891320	−	0.453376i	$-0.149780\pi$
$643$	−2.44092	−	7.51238i	−0.0962605	−	0.296259i	−0.987580	+	0.157116i	$0.949780\pi$
$644$	−8.23472	−	25.3439i	−0.324493	−	0.998688i
$645$		0			0
$646$	−12.0956	−	16.6482i	−0.475896	−	0.655014i
$647$	19.7674	+	6.42281i	0.777136	+	0.252507i	0.670617	−	0.741804i	$-0.266030\pi$
$647$	19.7674	+	6.42281i	0.777136	+	0.252507i	0.106519	+	0.994311i	$0.466030\pi$
$648$	−17.7582	−	18.2498i	−0.697607	−	0.716921i
$649$	−30.2972	+	26.3679i	−1.18927	+	1.03503i
$650$		0			0
$651$	24.2574	+	13.6938i	0.950723	+	0.536701i
$652$	13.7676	−	10.0027i	0.539179	−	0.391736i
$653$	−6.19152	+	8.52190i	−0.242293	+	0.333488i	−0.912793	−	0.408421i	$-0.866079\pi$
$653$	−6.19152	+	8.52190i	−0.242293	+	0.333488i	0.670501	+	0.741909i	$0.266079\pi$
$654$	−8.21078	+	0.943403i	−0.321067	+	0.0368900i
$655$		0			0
$656$	−0.0182803	−	0.0132814i	−0.000713724	−	0.000518551i
$657$	2.86673	+	12.3104i	0.111842	+	0.480274i
$658$	3.33680	−	10.2696i	0.130082	−	0.400352i
$659$	−37.3557			−1.45517			−0.727586	−	0.686016i	$-0.759358\pi$
$659$	−37.3557			−1.45517			−0.727586	+	0.686016i	$0.759358\pi$
$660$		0			0
$661$	−17.0519			−0.663241			−0.331621	−	0.943413i	$-0.607595\pi$
$661$	−17.0519			−0.663241			−0.331621	+	0.943413i	$0.607595\pi$
$662$	0.176884	−	0.544394i	0.00687481	−	0.0211585i
$663$	−5.81600	−	12.7300i	−0.225875	−	0.494391i
$664$	35.1044	+	25.5048i	1.36231	+	0.989779i
$665$		0			0
$666$	−0.277266	+	3.24007i	−0.0107438	+	0.125550i
$667$	−3.80234	+	5.23347i	−0.147227	+	0.202641i
$668$	−0.156536	+	0.113730i	−0.00605655	+	0.00440034i
$669$	21.6823	−	38.4085i	0.838288	−	1.48496i
$670$		0			0
$671$	−13.8602	+	1.22073i	−0.535066	+	0.0471258i
$672$	−6.37569	+	31.4907i	−0.245948	+	1.21478i
$673$	16.1118	+	5.23505i	0.621066	+	0.201796i	0.602613	−	0.798033i	$-0.294126\pi$
$673$	16.1118	+	5.23505i	0.621066	+	0.201796i	0.0184523	+	0.999830i	$0.494126\pi$
$674$	8.66544	+	11.9269i	0.333780	+	0.459409i
$675$		0			0
$676$	−3.42928	−	10.5542i	−0.131895	−	0.405932i
$677$	5.67258	+	17.4584i	0.218015	+	0.670981i	0.998926	+	0.0463387i	$0.0147553\pi$
$677$	5.67258	+	17.4584i	0.218015	+	0.670981i	−0.780911	+	0.624643i	$0.785245\pi$
$678$	8.18077	−	7.51060i	0.314180	−	0.288443i
$679$	5.85552	+	8.05943i	0.224714	+	0.309293i
$680$		0			0
$681$	−37.6954	−	7.63192i	−1.44449	−	0.292456i
$682$	9.33605	+	10.7273i	0.357496	+	0.410769i
$683$			15.6834i			0.600109i	0.953922	+	0.300055i	$0.0970049\pi$
$683$			15.6834i			0.600109i	−0.953922	+	0.300055i	$0.902995\pi$
$684$	16.3453	+	14.1543i	0.624977	+	0.541202i
$685$		0			0
$686$	5.46325	−	7.51951i	0.208588	−	0.287096i
$687$	−3.77496	−	32.8548i	−0.144024	−	1.25349i
$688$	−0.00732386	+	0.00237966i	−0.000279219	+	9.07239e-5i
$689$	13.0614	+	9.48969i	0.497601	+	0.361528i
$690$		0			0
$691$	−3.15318	+	9.70449i	−0.119953	+	0.369176i	−0.992948	−	0.118553i	$-0.962175\pi$
$691$	−3.15318	+	9.70449i	−0.119953	+	0.369176i	0.872995	+	0.487729i	$0.162175\pi$
$692$	−23.6694			−0.899777
$693$	0.0810042	+	32.6380i	0.00307709	+	1.23981i
$694$	5.55823			0.210988
$695$		0			0
$696$	4.38400	−	2.00294i	0.166175	−	0.0759212i
$697$	−18.0331	−	13.1018i	−0.683052	−	0.496266i
$698$	−1.27350	+	0.413785i	−0.0482027	+	0.0156620i
$699$	−3.74351	−	32.5811i	−0.141593	−	1.23233i
$700$		0			0
$701$	−18.1727	+	13.2032i	−0.686373	+	0.498679i	−0.875466	−	0.483280i	$-0.839445\pi$
$701$	−18.1727	+	13.2032i	−0.686373	+	0.498679i	0.189093	+	0.981959i	$0.439445\pi$
$702$	−5.56402	−	7.20853i	−0.210000	−	0.272068i
$703$		−	7.23244i		−	0.272776i
$704$	−8.45390	+	14.0882i	−0.318618	+	0.530969i
$705$		0			0
$706$	−14.7993	−	4.80859i	−0.556980	−	0.180974i
$707$	23.0017	+	31.6591i	0.865067	+	1.19066i
$708$	−19.0845	+	17.5211i	−0.717238	+	0.658483i
$709$	8.10883	+	24.9564i	0.304533	+	0.937258i	0.979851	+	0.199730i	$0.0640066\pi$
$709$	8.10883	+	24.9564i	0.304533	+	0.937258i	−0.675317	+	0.737527i	$0.735993\pi$
$710$		0			0
$711$	−27.4036	+	16.5367i	−1.02772	+	0.620175i
$712$	−4.78285	−	6.58303i	−0.179245	−	0.246709i
$713$	−30.6684	−	9.96476i	−1.14854	−	0.373183i
$714$	3.97599	−	19.6381i	0.148798	−	0.734938i
$715$		0			0
$716$			2.78744i			0.104171i
$717$	16.0637	−	28.4556i	0.599911	−	1.06269i
$718$	7.00875	−	5.09215i	0.261564	−	0.190037i
$719$	−20.8046	+	28.6351i	−0.775880	+	1.06791i	0.219844	+	0.975535i	$0.429445\pi$
$719$	−20.8046	+	28.6351i	−0.775880	+	1.06791i	−0.995724	+	0.0923728i	$0.970555\pi$
$720$		0			0
$721$	25.1594	−	8.17479i	0.936986	−	0.304445i
$722$	10.6478	+	7.73608i	0.396270	+	0.287907i
$723$	−1.55105	−	3.39492i	−0.0576843	−	0.126259i
$724$	3.24493	−	9.98688i	0.120597	−	0.371159i
$725$		0			0
$726$	−5.52885	+	15.7185i	−0.205195	+	0.583368i
$727$	3.78385			0.140335			0.0701675	−	0.997535i	$-0.477647\pi$
$727$	3.78385			0.140335			0.0701675	+	0.997535i	$0.477647\pi$
$728$	−5.74692	+	17.6872i	−0.212995	+	0.655531i
$729$	−22.7276	−	14.5759i	−0.841762	−	0.539849i
$730$		0			0
$731$	−7.22483	+	2.34749i	−0.267220	+	0.0868250i
$732$	−8.91628	+	1.02446i	−0.329555	+	0.0378653i
$733$	−3.48496	+	4.79663i	−0.128720	+	0.177168i	−0.868513	−	0.495667i	$-0.834924\pi$
$733$	−3.48496	+	4.79663i	−0.128720	+	0.177168i	0.739793	+	0.672835i	$0.234924\pi$
$734$	−11.4408	+	8.31221i	−0.422287	+	0.306809i
$735$		0			0
$736$		−	37.1942i		−	1.37100i
$737$	−42.6855	−	9.82858i	−1.57234	−	0.362040i
$738$	−13.3607	−	5.64132i	−0.491812	−	0.207660i
$739$	−41.7616	−	13.5692i	−1.53622	−	0.499150i	−0.585893	−	0.810389i	$-0.699256\pi$
$739$	−41.7616	−	13.5692i	−1.53622	−	0.499150i	−0.950332	+	0.311239i	$0.899256\pi$
$740$		0			0
$741$	13.6966	+	14.9187i	0.503156	+	0.548052i
$742$	7.14243	+	21.9822i	0.262207	+	0.806990i
$743$	15.5121	+	47.7414i	0.569084	+	1.75146i	0.655493	+	0.755201i	$0.272461\pi$
$743$	15.5121	+	47.7414i	0.569084	+	1.75146i	−0.0864090	+	0.996260i	$0.527539\pi$
$744$	16.2488	+	17.6987i	0.595711	+	0.648866i
$745$		0			0
$746$	−19.6775	−	6.39360i	−0.720443	−	0.234086i
$747$	42.3856	+	17.8966i	1.55081	+	0.654804i
$748$	−8.49972	+	14.1646i	−0.310781	+	0.517908i
$749$			18.5642i			0.678320i
$750$		0			0
$751$	7.12816	−	5.17891i	0.260110	−	0.188981i	−0.450085	−	0.892986i	$-0.648606\pi$
$751$	7.12816	−	5.17891i	0.260110	−	0.188981i	0.710196	+	0.704004i	$0.248606\pi$
$752$	0.00904385	−	0.0124478i	0.000329795	−	0.000453924i
$753$	−4.03017	+	0.463060i	−0.146868	+	0.0168748i
$754$	1.63927	−	0.532632i	0.0596987	−	0.0193973i
$755$		0			0
$756$	0.611087	+	21.0439i	0.0222250	+	0.765361i
$757$	8.14397	−	25.0646i	0.295998	−	0.910988i	−0.686887	−	0.726765i	$-0.741023\pi$
$757$	8.14397	−	25.0646i	0.295998	−	0.910988i	0.982884	−	0.184223i	$-0.0589769\pi$
$758$	−7.85003			−0.285126
$759$	−7.58940	−	37.0128i	−0.275478	−	1.34348i
$760$		0			0
$761$	4.81075	−	14.8060i	0.174390	−	0.536716i	−0.825215	−	0.564818i	$-0.808946\pi$
$761$	4.81075	−	14.8060i	0.174390	−	0.536716i	0.999605	+	0.0281019i	$0.00894629\pi$
$762$	−3.96536	−	8.67932i	−0.143650	−	0.314419i
$763$	14.4794	+	10.5199i	0.524188	+	0.380845i
$764$	−10.7515	+	3.49336i	−0.388974	+	0.126385i
$765$		0			0
$766$	14.6394	−	20.1493i	0.528941	−	0.728025i
$767$	−19.6321	+	14.2636i	−0.708875	+	0.515028i
$768$	−13.6321	+	24.1482i	−0.491906	+	0.871372i
$769$			41.5808i			1.49944i	0.661753	+	0.749722i	$0.269813\pi$
$769$			41.5808i			1.49944i	−0.661753	+	0.749722i	$0.730187\pi$
$770$		0			0
$771$	3.53478	−	17.4589i	0.127302	−	0.628767i
$772$	11.3689	+	3.69399i	0.409176	+	0.132949i
$773$	24.9738	+	34.3735i	0.898247	+	1.23633i	0.971024	+	0.238982i	$0.0768137\pi$
$773$	24.9738	+	34.3735i	0.898247	+	1.23633i	−0.0727775	+	0.997348i	$0.523186\pi$
$774$	−4.23184	+	2.55371i	−0.152110	+	0.0917911i
$775$		0			0
$776$	2.65524	+	8.17199i	0.0953176	+	0.293357i
$777$	5.18741	−	4.76247i	0.186097	−	0.170852i
$778$	6.87046	+	9.45637i	0.246318	+	0.339027i
$779$	30.6764	+	9.96736i	1.09910	+	0.357118i
$780$		0			0
$781$	−5.48025	+	0.482672i	−0.196099	+	0.0172714i
$782$			23.1950i			0.829450i
$783$	4.04566	−	3.12271i	0.144580	−	0.111596i
$784$	−0.0124346	+	0.00903428i	−0.000444094	+	0.000322653i
$785$		0			0
$786$	1.72512	+	15.0143i	0.0615328	+	0.535542i
$787$	22.8825	−	7.43499i	0.815674	−	0.265029i	0.128675	−	0.991687i	$-0.458928\pi$
$787$	22.8825	−	7.43499i	0.815674	−	0.265029i	0.686999	+	0.726658i	$0.258928\pi$
$788$	−11.9553	−	8.68601i	−0.425889	−	0.309426i
$789$	−19.1673	+	8.75706i	−0.682375	+	0.311759i
$790$		0			0
$791$	−24.0492			−0.855092
$792$	−8.63278	+	26.7951i	−0.306752	+	0.952121i
$793$	−8.40647			−0.298523
$794$	3.89087	−	11.9749i	0.138082	−	0.424972i
$795$		0			0
$796$	26.5533	+	19.2921i	0.941157	+	0.683791i
$797$	−40.2177	+	13.0675i	−1.42459	+	0.462876i	−0.917056	−	0.398759i	$-0.869441\pi$
$797$	−40.2177	+	13.0675i	−1.42459	+	0.462876i	−0.507529	+	0.861634i	$0.669441\pi$
$798$	3.30959	+	28.8045i	0.117158	+	1.01967i
$799$	8.92157	−	12.2795i	0.315622	−	0.434417i
$800$		0			0
$801$	−6.52234	−	5.64805i	−0.230455	−	0.199564i
$802$		−	12.9569i		−	0.457525i
$803$	10.5408	−	9.17377i	0.371978	−	0.323735i
$804$	−27.6924	−	5.60668i	−0.976634	−	0.197732i
$805$		0			0
$806$	5.05029	+	6.95112i	0.177889	+	0.244843i
$807$	−3.44475	+	3.16256i	−0.121261	+	0.111327i
$808$	10.4303	+	32.1012i	0.366938	+	1.12932i
$809$	−10.5925	−	32.6003i	−0.372412	−	1.14617i	−0.945208	−	0.326468i	$-0.894141\pi$
$809$	−10.5925	−	32.6003i	−0.372412	−	1.14617i	0.572796	−	0.819698i	$-0.305859\pi$
$810$		0			0
$811$	21.8253	+	30.0400i	0.766391	+	1.05485i	0.996655	+	0.0817183i	$0.0260408\pi$
$811$	21.8253	+	30.0400i	0.766391	+	1.05485i	−0.230265	+	0.973128i	$0.573959\pi$
$812$	−3.78991	−	1.23141i	−0.133000	−	0.0432142i
$813$	−4.16712	+	20.5821i	−0.146147	+	0.721847i
$814$	3.30851	−	1.40665i	0.115963	−	0.0493031i
$815$		0			0
$816$	0.0140352	−	0.0248622i	0.000491330	−	0.000870352i
$817$	8.89333	−	6.46138i	0.311138	−	0.226055i
$818$	−12.5827	+	17.3185i	−0.439942	+	0.605528i
$819$	−1.68132	+	19.6475i	−0.0587500	+	0.686540i
$820$		0			0
$821$	23.8031	+	17.2940i	0.830733	+	0.603563i	0.919767	−	0.392466i	$-0.128378\pi$
$821$	23.8031	+	17.2940i	0.830733	+	0.603563i	−0.0890334	+	0.996029i	$0.528378\pi$
$822$	−4.98970	−	10.9214i	−0.174036	−	0.380927i
$823$	−9.10727	+	28.0293i	−0.317459	+	0.977040i	0.657271	+	0.753654i	$0.271711\pi$
$823$	−9.10727	+	28.0293i	−0.317459	+	0.977040i	−0.974730	+	0.223385i	$0.928289\pi$
$824$	22.8176			0.794887
$825$		0			0
$826$	−34.7409			−1.20879
$827$	−4.92467	+	15.1566i	−0.171248	+	0.527046i	−0.999442	−	0.0333946i	$-0.989368\pi$
$827$	−4.92467	+	15.1566i	−0.171248	+	0.527046i	0.828195	+	0.560441i	$0.189368\pi$
$828$	−5.52749	−	23.7363i	−0.192094	−	0.824893i
$829$	−4.50537	−	3.27334i	−0.156478	−	0.113688i	0.506791	−	0.862069i	$-0.330832\pi$
$829$	−4.50537	−	3.27334i	−0.156478	−	0.113688i	−0.663269	+	0.748381i	$0.730832\pi$
$830$		0			0
$831$	−24.3044	+	2.79253i	−0.843109	+	0.0968717i
$832$	−5.83478	+	8.03088i	−0.202284	+	0.278421i
$833$	−12.2665	+	8.91213i	−0.425009	+	0.308787i
$834$	−0.460370	−	0.259887i	−0.0159413	−	0.00899917i
$835$		0			0
$836$	5.36369	−	23.2945i	0.185507	−	0.805657i
$837$	21.0363	+	14.3698i	0.727123	+	0.496692i
$838$	3.04967	+	0.990898i	0.105349	+	0.0342300i
$839$	−32.5303	−	44.7742i	−1.12307	−	1.54578i	−0.800602	−	0.599196i	$-0.795487\pi$
$839$	−32.5303	−	44.7742i	−1.12307	−	1.54578i	−0.322470	−	0.946580i	$-0.604513\pi$
$840$		0			0
$841$	−8.66256	−	26.6606i	−0.298709	−	0.919332i
$842$	−3.39463	−	10.4476i	−0.116987	−	0.360048i
$843$	19.2181	+	20.9329i	0.661905	+	0.720966i
$844$	−11.1965	−	15.4107i	−0.385400	−	0.530458i
$845$		0			0
$846$	3.84141	−	9.09783i	0.132070	−	0.312790i
$847$	31.8395	−	16.9769i	1.09402	−	0.583333i
$848$			0.0329344i			0.00113097i
$849$	47.6794	+	26.9159i	1.63635	+	0.923752i
$850$		0			0
$851$	−4.79168	+	6.59518i	−0.164257	+	0.226080i
$852$	−3.52546	+	0.405069i	−0.120780	+	0.0138774i
$853$	2.23637	−	0.726641i	0.0765719	−	0.0248797i	−0.270481	−	0.962725i	$-0.587183\pi$
$853$	2.23637	−	0.726641i	0.0765719	−	0.0248797i	0.347052	+	0.937846i	$0.387183\pi$
$854$	−9.73648	−	7.07397i	−0.333176	−	0.242066i
$855$		0			0
$856$	−4.94804	+	15.2285i	−0.169120	+	0.520499i
$857$	43.7806			1.49552			0.747759	−	0.663970i	$-0.231130\pi$
$857$	43.7806			1.49552			0.747759	+	0.663970i	$0.231130\pi$
$858$	−4.16075	+	9.16712i	−0.142046	+	0.312960i
$859$	16.1286			0.550302			0.275151	−	0.961401i	$-0.411272\pi$
$859$	16.1286			0.550302			0.275151	+	0.961401i	$0.411272\pi$
$860$		0			0
$861$	13.0510	+	28.5658i	0.444776	+	0.973520i
$862$	16.1321	+	11.7206i	0.549460	+	0.399206i
$863$	−2.81745	+	0.915446i	−0.0959072	+	0.0311621i	−0.356578	−	0.934266i	$-0.616056\pi$
$863$	−2.81745	+	0.915446i	−0.0959072	+	0.0311621i	0.260670	+	0.965428i	$0.416056\pi$
$864$	−8.26532	+	28.1982i	−0.281192	+	0.959322i
$865$		0			0
$866$	−20.1318	+	14.6266i	−0.684106	+	0.497032i
$867$	−0.629561	+	1.11522i	−0.0213810	+	0.0378748i
$868$		−	19.8644i		−	0.674241i
$869$	30.3411	+	18.2068i	1.02925	+	0.617623i
$870$		0			0
$871$	−25.1693	−	8.17801i	−0.852830	−	0.277101i
$872$	9.07371	+	12.4889i	0.307275	+	0.422927i
$873$	4.70729	+	7.80062i	0.159318	+	0.264011i
$874$	−10.3720	−	31.9217i	−0.350837	−	1.07977i
$875$		0			0
$876$	6.63976	−	6.09583i	0.224337	−	0.205959i
$877$	−1.87055	−	2.57459i	−0.0631640	−	0.0869378i	0.776266	−	0.630405i	$-0.217111\pi$
$877$	−1.87055	−	2.57459i	−0.0631640	−	0.0869378i	−0.839430	+	0.543467i	$0.817111\pi$
$878$	−13.6973	−	4.45054i	−0.462263	−	0.150198i
$879$	−5.42073	−	1.09750i	−0.182837	−	0.0370177i
$880$		0			0
$881$			43.7637i			1.47444i	0.675655	+	0.737218i	$0.263861\pi$
$881$			43.7637i			1.47444i	−0.675655	+	0.737218i	$0.736139\pi$
$882$	−6.45794	+	7.45759i	−0.217450	+	0.251110i
$883$	8.64999	−	6.28458i	0.291095	−	0.211493i	−0.432647	−	0.901563i	$-0.642420\pi$
$883$	8.64999	−	6.28458i	0.291095	−	0.211493i	0.723742	+	0.690070i	$0.242420\pi$
$884$	−5.86640	+	8.07441i	−0.197308	+	0.271572i
$885$		0			0
$886$	−0.218658	+	0.0710463i	−0.00734596	+	0.00238685i
$887$	−2.95019	−	2.14344i	−0.0990577	−	0.0719696i	0.537154	−	0.843484i	$-0.319499\pi$
$887$	−2.95019	−	2.14344i	−0.0990577	−	0.0719696i	−0.636212	+	0.771515i	$0.719499\pi$
$888$	5.52469	−	2.52409i	0.185396	−	0.0847029i
$889$	−6.38547	+	19.6525i	−0.214162	+	0.659122i
$890$		0			0
$891$	−2.47123	+	29.7472i	−0.0827894	+	0.996567i
$892$	−31.4527			−1.05311
$893$	−6.78719	+	20.8888i	−0.227125	+	0.699018i
$894$	−7.22876	+	3.30264i	−0.241766	+	0.110457i
$895$		0			0
$896$	21.7684	−	7.07300i	0.727233	−	0.236292i
$897$	−2.60572	−	22.6785i	−0.0870025	−	0.757213i
$898$	−4.30175	+	5.92084i	−0.143551	+	0.197581i
$899$	−3.90120	+	2.83439i	−0.130112	+	0.0945321i
$900$		0			0
$901$			32.4891i			1.08237i
$902$	1.40670	+	15.9716i	0.0468379	+	0.531797i
$903$	10.4905	+	2.12394i	0.349103	+	0.0706804i
$904$	−19.7280	−	6.41000i	−0.656142	−	0.213194i
$905$		0			0
$906$	−10.4405	+	9.58526i	−0.346864	+	0.318449i
$907$	−6.42498	−	19.7741i	−0.213338	−	0.656587i	−0.999267	−	0.0382705i	$-0.987815\pi$
$907$	−6.42498	−	19.7741i	−0.213338	−	0.656587i	0.785929	−	0.618316i	$-0.212185\pi$
$908$	8.47529	+	26.0843i	0.281262	+	0.865637i
$909$	18.4912	+	30.6424i	0.613314	+	1.01635i
$910$		0			0
$911$	−37.3651	−	12.1406i	−1.23796	−	0.402237i	−0.384368	−	0.923180i	$-0.625581\pi$
$911$	−37.3651	−	12.1406i	−1.23796	−	0.402237i	−0.853592	+	0.520943i	$0.825581\pi$
$912$	−0.00819818	+	0.0404922i	−0.000271469	+	0.00134083i
$913$	−4.46263	−	50.6687i	−0.147692	−	1.67689i
$914$		−	26.3646i		−	0.872065i
$915$		0			0
$916$	−19.0794	+	13.8620i	−0.630401	+	0.458013i
$917$	19.2367	−	26.4771i	0.635252	−	0.874350i
$918$	5.15440	−	17.5849i	0.170120	−	0.580387i
$919$	−35.8105	+	11.6355i	−1.18128	+	0.383821i	−0.832842	−	0.553511i	$-0.813288\pi$
$919$	−35.8105	+	11.6355i	−1.18128	+	0.383821i	−0.348438	+	0.937332i	$0.613288\pi$
$920$		0			0
$921$	−10.9518	−	23.9711i	−0.360874	−	0.789876i
$922$	−5.08199	+	15.6408i	−0.167367	+	0.515101i
$923$	−3.32389			−0.109407
$924$	20.2397	−	11.4921i	0.665839	−	0.378061i
$925$		0			0
$926$	9.01070	−	27.7321i	0.296110	−	0.911333i
$927$	23.5636	−	5.48726i	0.773929	−	0.180225i
$928$	−4.49976	−	3.26926i	−0.147712	−	0.107319i
$929$	19.7724	−	6.42444i	0.648712	−	0.210779i	0.0338656	−	0.999426i	$-0.489218\pi$
$929$	19.7724	−	6.42444i	0.648712	−	0.210779i	0.614846	+	0.788647i	$0.289218\pi$
$930$		0			0
$931$	12.8963	−	17.7503i	0.422661	−	0.581743i
$932$	−18.9205	+	13.7465i	−0.619761	+	0.450283i
$933$	−31.6775	−	17.8825i	−1.03707	−	0.585448i
$934$		−	25.0508i		−	0.819686i
$935$		0			0
$936$	−6.61600	+	15.6690i	−0.216251	+	0.512159i
$937$	−31.1623	−	10.1252i	−1.01803	−	0.330777i	−0.247981	−	0.968765i	$-0.579767\pi$
$937$	−31.1623	−	10.1252i	−1.01803	−	0.330777i	−0.770047	+	0.637987i	$0.779767\pi$
$938$	−22.2697	−	30.6516i	−0.727132	−	1.00081i
$939$	−21.7740	−	23.7168i	−0.710566	−	0.773969i
$940$		0			0
$941$	−1.83270	−	5.64048i	−0.0597444	−	0.183874i	0.916730	−	0.399507i	$-0.130819\pi$
$941$	−1.83270	−	5.64048i	−0.0597444	−	0.183874i	−0.976475	+	0.215633i	$0.930819\pi$
$942$	−5.31837	−	5.79292i	−0.173282	−	0.188744i
$943$	−21.3698	−	29.4130i	−0.695897	−	0.957820i
$944$	−0.0470797	−	0.0152971i	−0.00153231	−	0.000497878i
$945$		0			0
$946$	4.68547	+	2.81161i	0.152338	+	0.0914133i
$947$		−	26.1300i		−	0.849110i	−0.905402	−	0.424555i	$-0.860431\pi$
$947$		−	26.1300i		−	0.849110i	0.905402	−	0.424555i	$-0.139569\pi$
$948$	19.8760	+	11.2204i	0.645544	+	0.364422i
$949$	6.83030	−	4.96250i	0.221721	−	0.161090i
$950$		0			0
$951$	38.9464	−	4.47487i	1.26292	−	0.145108i
$952$	−35.5930	+	11.5649i	−1.15357	+	0.374819i
$953$	3.28163	+	2.38424i	0.106302	+	0.0772331i	0.639666	−	0.768653i	$-0.279072\pi$
$953$	3.28163	+	2.38424i	0.106302	+	0.0772331i	−0.533364	+	0.845886i	$0.679072\pi$
$954$	4.79430	+	20.5878i	0.155221	+	0.666555i
$955$		0			0
$956$	−23.3023			−0.753650
$957$	−5.14489	−	2.33515i	−0.166311	−	0.0754847i
$958$	36.2513			1.17123
$959$	−8.03498	+	24.7291i	−0.259463	+	0.798545i
$960$		0			0
$961$	5.63261	+	4.09233i	0.181697	+	0.132011i
$962$	2.06580	−	0.671218i	0.0666040	−	0.0216409i
$963$	−1.44760	+	16.9163i	−0.0466482	+	0.545120i
$964$	−1.56450	+	2.15334i	−0.0503890	+	0.0693545i
$965$		0			0
$966$	16.0658	−	28.4592i	0.516908	−	0.915661i
$967$			11.3476i			0.364914i	0.983214	+	0.182457i	$0.0584050\pi$
$967$			11.3476i			0.364914i	−0.983214	+	0.182457i	$0.941595\pi$
$968$	30.6434	−	5.44001i	0.984916	−	0.174849i
$969$	−8.08733	+	39.9447i	−0.259802	+	1.28321i
$970$		0			0
$971$	−29.8652	−	41.1059i	−0.958419	−	1.31915i	−0.947685	−	0.319208i	$-0.896583\pi$
$971$	−29.8652	−	41.1059i	−0.958419	−	1.31915i	−0.0107342	−	0.999942i	$-0.503417\pi$
$972$	−1.08412	+	19.2236i	−0.0347732	+	0.616597i
$973$	0.353768	+	1.08879i	0.0113413	+	0.0349049i
$974$	2.70736	+	8.33238i	0.0867493	+	0.266987i
$975$		0			0
$976$	−0.0100797	−	0.0138736i	−0.000322645	−	0.000444082i
$977$	43.0442	+	13.9859i	1.37711	+	0.447449i	0.901717	−	0.432327i	$-0.142308\pi$
$977$	43.0442	+	13.9859i	1.37711	+	0.447449i	0.475388	+	0.879776i	$0.342308\pi$
$978$	20.4551	+	4.14141i	0.654083	+	0.132428i
$979$	−2.14030	+	9.29532i	−0.0684043	+	0.297080i
$980$		0			0
$981$	12.3738	+	10.7151i	0.395064	+	0.342108i
$982$	15.4331	−	11.2128i	0.492491	−	0.357815i
$983$	3.51639	−	4.83989i	0.112155	−	0.154369i	−0.749249	−	0.662288i	$-0.769585\pi$
$983$	3.51639	−	4.83989i	0.112155	−	0.154369i	0.861404	+	0.507920i	$0.169585\pi$
$984$	3.09209	+	26.9115i	0.0985721	+	0.857908i
$985$		0			0
$986$	2.80612	+	2.03877i	0.0893652	+	0.0649276i
$987$	−19.4517	+	8.88696i	−0.619153	+	0.282875i
$988$	4.46294	−	13.7355i	0.141985	−	0.436985i
$989$	−12.3906			−0.393997
$990$		0			0
$991$	38.3458			1.21809			0.609047	−	0.793134i	$-0.291552\pi$
$991$	38.3458			1.21809			0.609047	+	0.793134i	$0.291552\pi$
$992$	8.56774	−	26.3688i	0.272026	−	0.837210i
$993$	−1.03113	+	0.471099i	−0.0327221	+	0.0149499i
$994$	−3.84977	−	2.79702i	−0.122107	−	0.0887160i
$995$		0			0
$996$	−3.74515	−	32.5953i	−0.118669	−	1.03282i
$997$	−21.3512	+	29.3874i	−0.676198	+	0.930707i	−0.999881	−	0.0154587i	$-0.995079\pi$
$997$	−21.3512	+	29.3874i	−0.676198	+	0.930707i	0.323682	+	0.946166i	$0.395079\pi$
$998$	13.9418	−	10.1293i	0.441320	−	0.320638i
$999$	5.09831	−	3.93521i	0.161303	−	0.124505i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	825.2.bi.h.101.13		80
3.2	odd	2	inner	825.2.bi.h.101.7		80
5.2	odd	4		165.2.r.a.134.14	yes	80
5.3	odd	4		165.2.r.a.134.7	✓	80
5.4	even	2	inner	825.2.bi.h.101.8		80
11.6	odd	10	inner	825.2.bi.h.776.7		80
15.2	even	4		165.2.r.a.134.8	yes	80
15.8	even	4		165.2.r.a.134.13	yes	80
15.14	odd	2	inner	825.2.bi.h.101.14		80
33.17	even	10	inner	825.2.bi.h.776.13		80
55.17	even	20		165.2.r.a.149.13	yes	80
55.28	even	20		165.2.r.a.149.8	yes	80
55.39	odd	10	inner	825.2.bi.h.776.14		80
165.17	odd	20		165.2.r.a.149.7	yes	80
165.83	odd	20		165.2.r.a.149.14	yes	80
165.149	even	10	inner	825.2.bi.h.776.8		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.2.r.a.134.7	✓	80	5.3	odd	4
165.2.r.a.134.8	yes	80	15.2	even	4
165.2.r.a.134.13	yes	80	15.8	even	4
165.2.r.a.134.14	yes	80	5.2	odd	4
165.2.r.a.149.7	yes	80	165.17	odd	20
165.2.r.a.149.8	yes	80	55.28	even	20
165.2.r.a.149.13	yes	80	55.17	even	20
165.2.r.a.149.14	yes	80	165.83	odd	20
825.2.bi.h.101.7		80	3.2	odd	2	inner
825.2.bi.h.101.8		80	5.4	even	2	inner
825.2.bi.h.101.13		80	1.1	even	1	trivial
825.2.bi.h.101.14		80	15.14	odd	2	inner
825.2.bi.h.776.7		80	11.6	odd	10	inner
825.2.bi.h.776.8		80	165.149	even	10	inner
825.2.bi.h.776.13		80	33.17	even	10	inner
825.2.bi.h.776.14		80	55.39	odd	10	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	825.bi (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.270252 - 0.831751i) q^{2} +(-1.57542 + 0.719767i) q^{3} +(0.999260 + 0.726005i) q^{4} +(0.172907 + 1.50487i) q^{6} +(1.92808 - 2.65378i) q^{7} +(2.28897 - 1.66303i) q^{8} +(1.96387 - 2.26786i) q^{9} +O(q^{10})\)	\(q+(0.270252 - 0.831751i) q^{2} +(-1.57542 + 0.719767i) q^{3} +(0.999260 + 0.726005i) q^{4} +(0.172907 + 1.50487i) q^{6} +(1.92808 - 2.65378i) q^{7} +(2.28897 - 1.66303i) q^{8} +(1.96387 - 2.26786i) q^{9} +(-3.23205 - 0.744199i) q^{11} +(-2.09681 - 0.424525i) q^{12} +(-1.90577 - 0.619221i) q^{13} +(-1.68622 - 2.32088i) q^{14} +(-0.00126317 - 0.00388765i) q^{16} +(-1.24609 - 3.83508i) q^{17} +(-1.35556 - 2.24635i) q^{18} +(3.42983 + 4.72076i) q^{19} +(-1.12743 + 5.56858i) q^{21} +(-1.49246 + 2.48714i) q^{22} -6.57716i q^{23} +(-2.40908 + 4.26749i) q^{24} +(-1.03008 + 1.41778i) q^{26} +(-1.46158 + 4.98636i) q^{27} +(3.85332 - 1.25202i) q^{28} +(-0.795704 - 0.578113i) q^{29} +(1.51506 - 4.66286i) q^{31} +5.65506 q^{32} +(5.62748 - 1.15390i) q^{33} -3.52660 q^{34} +(3.60890 - 0.840407i) q^{36} +(-1.00274 - 0.728533i) q^{37} +(4.85341 - 1.57697i) q^{38} +(3.44807 - 0.396177i) q^{39} +(4.47200 - 3.24910i) q^{41} +(4.32698 + 2.44266i) q^{42} -1.88388i q^{43} +(-2.68937 - 3.09014i) q^{44} +(-5.47056 - 1.77749i) q^{46} +(2.21245 + 3.04517i) q^{47} +(0.00478823 + 0.00521547i) q^{48} +(-1.16192 - 3.57602i) q^{49} +(4.72348 + 5.14495i) q^{51} +(-1.45480 - 2.00236i) q^{52} +(-7.66260 - 2.48973i) q^{53} +(3.75242 + 2.56325i) q^{54} -9.28088i q^{56} +(-8.80125 - 4.96848i) q^{57} +(-0.695887 + 0.505591i) q^{58} +(7.11811 - 9.79724i) q^{59} +(3.98985 - 1.29638i) q^{61} +(-3.46890 - 2.52030i) q^{62} +(-2.23191 - 9.58431i) q^{63} +(1.53082 - 4.71138i) q^{64} +(0.561079 - 4.99251i) q^{66} +13.2069 q^{67} +(1.53912 - 4.73692i) q^{68} +(4.73402 + 10.3618i) q^{69} +(1.57757 - 0.512584i) q^{71} +(0.723704 - 8.45705i) q^{72} +(-2.47649 + 3.40860i) q^{73} +(-0.876951 + 0.637142i) q^{74} +7.20734i q^{76} +(-8.20661 + 7.14228i) q^{77} +(0.602329 - 2.97501i) q^{78} +(-10.1467 - 3.29686i) q^{79} +(-1.28642 - 8.90759i) q^{81} +(-1.49387 - 4.59766i) q^{82} +(4.73919 + 14.5857i) q^{83} +(-5.16941 + 4.74594i) q^{84} +(-1.56692 - 0.509122i) q^{86} +(1.66967 + 0.338047i) q^{87} +(-8.63569 + 3.67156i) q^{88} -2.87598i q^{89} +(-5.31776 + 3.86358i) q^{91} +(4.77505 - 6.57229i) q^{92} +(0.969332 + 8.43644i) q^{93} +(3.13074 - 1.01724i) q^{94} +(-8.90908 + 4.07033i) q^{96} +(-0.938473 + 2.88832i) q^{97} -3.28837 q^{98} +(-8.03508 + 5.86835i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 4 q^{4} - 10 q^{6} + 10 q^{9}+O(q^{10}) \) 80 * q - 4 * q^4 - 10 * q^6 + 10 * q^9	\( 80 q - 4 q^{4} - 10 q^{6} + 10 q^{9} - 60 q^{16} + 20 q^{19} + 30 q^{24} - 20 q^{31} + 56 q^{34} + 2 q^{36} + 50 q^{39} - 40 q^{46} - 72 q^{49} + 30 q^{51} - 96 q^{64} - 42 q^{66} - 30 q^{69} - 66 q^{81} - 140 q^{84} + 48 q^{91} - 60 q^{94} - 70 q^{96} - 60 q^{99}+O(q^{100}) \) 80 * q - 4 * q^4 - 10 * q^6 + 10 * q^9 - 60 * q^16 + 20 * q^19 + 30 * q^24 - 20 * q^31 + 56 * q^34 + 2 * q^36 + 50 * q^39 - 40 * q^46 - 72 * q^49 + 30 * q^51 - 96 * q^64 - 42 * q^66 - 30 * q^69 - 66 * q^81 - 140 * q^84 + 48 * q^91 - 60 * q^94 - 70 * q^96 - 60 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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