LMFDB - Embedded newform 825.2.bi.h.101.7

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			101.7
Character	$\chi$	$=$	825.101
Dual form			825.2.bi.h.776.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.270252 + 0.831751i) q^{2} +(-1.17137 + 1.27589i) q^{3} +(0.999260 + 0.726005i) q^{4} +(-0.744657 - 1.31910i) q^{6} +(1.92808 - 2.65378i) q^{7} +(-2.28897 + 1.66303i) q^{8} +(-0.255787 - 2.98908i) q^{9} +O(q^{10})$	\(q+(-0.270252 + 0.831751i) q^{2} +(-1.17137 + 1.27589i) q^{3} +(0.999260 + 0.726005i) q^{4} +(-0.744657 - 1.31910i) q^{6} +(1.92808 - 2.65378i) q^{7} +(-2.28897 + 1.66303i) q^{8} +(-0.255787 - 2.98908i) 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} +(2.55529 + 0.595053i) q^{18} +(3.42983 + 4.72076i) q^{19} +(1.12743 + 5.56858i) q^{21} +(-1.49246 + 2.48714i) q^{22} +6.57716i q^{23} +(0.559381 - 4.86849i) q^{24} +(1.03008 - 1.41778i) q^{26} +(4.11335 + 3.17496i) q^{27} +(3.85332 - 1.25202i) q^{28} +(0.795704 + 0.578113i) q^{29} +(1.51506 - 4.66286i) q^{31} -5.65506 q^{32} +(-4.73544 + 3.25201i) q^{33} -3.52660 q^{34} +(1.91449 - 3.17257i) q^{36} +(-1.00274 - 0.728533i) q^{37} +(-4.85341 + 1.57697i) q^{38} +(3.02242 - 1.70621i) q^{39} +(-4.47200 + 3.24910i) q^{41} +(-4.93636 - 0.567179i) q^{42} -1.88388i q^{43} +(2.68937 + 3.09014i) q^{44} +(-5.47056 - 1.77749i) q^{46} +(-2.21245 - 3.04517i) q^{47} +(0.00643985 + 0.00294220i) q^{48} +(-1.16192 - 3.57602i) q^{49} +(-6.35278 - 2.90242i) q^{51} +(-1.45480 - 2.00236i) q^{52} +(7.66260 + 2.48973i) q^{53} +(-3.75242 + 2.56325i) q^{54} +9.28088i q^{56} +(-10.0408 - 1.15367i) 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} +(-8.42553 - 5.08438i) q^{63} +(1.53082 - 4.71138i) q^{64} +(-1.42510 - 4.81757i) q^{66} +13.2069 q^{67} +(-1.53912 + 4.73692i) q^{68} +(-8.39172 - 7.70428i) q^{69} +(-1.57757 + 0.512584i) q^{71} +(5.55642 + 6.41651i) 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} +(-8.86915 + 1.52914i) q^{81} +(-1.49387 - 4.59766i) q^{82} +(-4.73919 - 14.5857i) q^{83} +(-2.91622 + 6.38298i) 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} +(4.17461 + 7.39498i) q^{93} +(3.13074 - 1.01724i) q^{94} +(6.62417 - 7.21524i) q^{96} +(-0.938473 + 2.88832i) q^{97} +3.28837 q^{98} +(1.39775 - 9.85121i) 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	$0.200062\pi$
$2$	−0.270252	+	0.831751i	−0.191097	+	0.588137i	−1.00000		0.000194370i	$0.999938\pi$
$3$	−1.17137	+	1.27589i	−0.676290	+	0.736635i
$3$	−1.17137	+	1.27589i	−0.676290	+	0.736635i
$4$	0.999260	+	0.726005i	0.499630	+	0.363003i
$5$		0			0
$5$		0			0
$6$	−0.744657	−	1.31910i	−0.304005	−	0.538520i
$7$	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
$9$	−0.255787	−	2.98908i	−0.0852625	−	0.996359i
$10$		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	$0.0626403\pi$
$17$	1.24609	+	3.83508i	0.302222	+	0.930144i	−0.678477	+	0.734622i	$0.737360\pi$
$18$	2.55529	+	0.595053i	0.602289	+	0.140255i
$19$	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	$0.240511\pi$
$23$			6.57716i			1.37143i	−0.727869	+	0.685716i	$0.759489\pi$
$24$	0.559381	−	4.86849i	0.114183	−	0.993777i
$25$		0			0
$26$	1.03008	−	1.41778i	0.202015	−	0.278049i
$27$	4.11335	+	3.17496i	0.791615	+	0.611020i
$28$	3.85332	−	1.25202i	0.728208	−	0.236609i
$29$	0.795704	+	0.578113i	0.147758	+	0.107353i	0.659209	−	0.751960i	$-0.270891\pi$
$29$	0.795704	+	0.578113i	0.147758	+	0.107353i	−0.511450	+	0.859313i	$0.670891\pi$
$30$		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
$33$	−4.73544	+	3.25201i	−0.824335	+	0.566102i
$34$	−3.52660			−0.604806
$35$		0			0
$36$	1.91449	−	3.17257i	0.319081	−	0.528761i
$37$	−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
$39$	3.02242	−	1.70621i	0.483974	−	0.273213i
$40$		0			0
$41$	−4.47200	+	3.24910i	−0.698408	+	0.507423i	−0.879414	−	0.476059i	$-0.842065\pi$
$41$	−4.47200	+	3.24910i	−0.698408	+	0.507423i	0.181005	+	0.983482i	$0.442065\pi$
$42$	−4.93636	−	0.567179i	−0.761697	−	0.0875177i
$43$		−	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	0.616576	−	0.787295i	$-0.288519\pi$
$47$	−2.21245	−	3.04517i	−0.322718	−	0.444184i	−0.939295	+	0.343111i	$0.888519\pi$
$48$	0.00643985	+	0.00294220i	0.000929513	+	0.000424670i
$49$	−1.16192	−	3.57602i	−0.165989	−	0.510861i
$50$		0			0
$51$	−6.35278	−	2.90242i	−0.889567	−	0.406420i
$52$	−1.45480	−	2.00236i	−0.201744	−	0.277677i
$53$	7.66260	+	2.48973i	1.05254	+	0.341990i	0.783664	−	0.621185i	$-0.213348\pi$
$53$	7.66260	+	2.48973i	1.05254	+	0.341990i	0.268874	+	0.963175i	$0.413348\pi$
$54$	−3.75242	+	2.56325i	−0.510639	+	0.348814i
$55$		0			0
$56$			9.28088i			1.24021i
$57$	−10.0408	−	1.15367i	−1.32993	−	0.152807i
$58$	−0.695887	+	0.505591i	−0.0913744	+	0.0663874i
$59$	−7.11811	+	9.79724i	−0.926699	+	1.27549i	0.0344338	+	0.999407i	$0.489037\pi$
$59$	−7.11811	+	9.79724i	−0.926699	+	1.27549i	−0.961133	+	0.276085i	$0.910963\pi$
$60$		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
$63$	−8.42553	−	5.08438i	−1.06152	−	0.640572i
$64$	1.53082	−	4.71138i	0.191353	−	0.588923i
$65$		0			0
$66$	−1.42510	−	4.81757i	−0.175418	−	0.593002i
$67$	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
$69$	−8.39172	−	7.70428i	−1.01024	−	0.927486i
$70$		0			0
$71$	−1.57757	+	0.512584i	−0.187223	+	0.0608325i	−0.401128	−	0.916022i	$-0.631382\pi$
$71$	−1.57757	+	0.512584i	−0.187223	+	0.0608325i	0.213905	+	0.976854i	$0.431382\pi$
$72$	5.55642	+	6.41651i	0.654830	+	0.756193i
$73$	−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
$81$	−8.86915	+	1.52914i	−0.985461	+	0.169904i
$82$	−1.49387	−	4.59766i	−0.164971	−	0.507727i
$83$	−4.73919	−	14.5857i	−0.520194	−	1.60099i	−0.773629	−	0.633639i	$-0.781561\pi$
$83$	−4.73919	−	14.5857i	−0.520194	−	1.60099i	0.253435	−	0.967352i	$-0.418439\pi$
$84$	−2.91622	+	6.38298i	−0.318186	+	0.696440i
$85$		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	$0.0487088\pi$
$89$			2.87598i			0.304853i	−0.988315	+	0.152427i	$0.951291\pi$
$90$		0			0
$91$	−5.31776	+	3.86358i	−0.557452	+	0.405013i
$92$	−4.77505	+	6.57229i	−0.497833	+	0.685209i
$93$	4.17461	+	7.39498i	0.432887	+	0.766824i
$94$	3.13074	−	1.01724i	0.322911	−	0.104920i
$95$		0			0
$96$	6.62417	−	7.21524i	0.676076	−	0.736402i
$97$	−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
$99$	1.39775	−	9.85121i	0.140479	−	0.990084i
$100$		0			0
$101$	3.68651	−	11.3459i	0.366822	−	1.12896i	−0.582011	−	0.813181i	$-0.697734\pi$
$101$	3.68651	−	11.3459i	0.366822	−	1.12896i	0.948832	−	0.315780i	$-0.102266\pi$
$102$	4.13095	−	4.49955i	0.409025	−	0.445521i
$103$	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	−0.344053	−	0.938950i	$-0.611800\pi$
$107$	4.57853	−	3.32650i	0.442623	−	0.321585i	0.786676	+	0.617366i	$0.211800\pi$
$108$	1.80528	+	6.15892i	0.173713	+	0.592642i
$109$			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	0.962087	−	0.272744i	$-0.0879313\pi$
$113$	4.30936	+	5.93132i	0.405390	+	0.557972i	−0.556696	+	0.830716i	$0.687931\pi$
$114$	3.67310	−	8.03963i	0.344017	−	0.752981i
$115$		0			0
$116$	0.375402	+	1.15537i	0.0348552	+	0.107273i
$117$	−1.36343	+	5.85487i	−0.126049	+	0.541283i
$118$	−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
$123$	1.09287	−	9.51166i	0.0985411	−	0.857638i
$124$	4.89920	−	3.55948i	0.439961	−	0.319650i
$125$		0			0
$126$	6.50596	−	5.63388i	0.579597	−	0.501906i
$127$	−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
$129$	2.40362	+	2.20672i	0.211627	+	0.194291i
$130$		0			0
$131$	−9.97712			−0.871705			−0.435852	−	0.900018i	$-0.643553\pi$
$131$	−9.97712			−0.871705			−0.435852	+	0.900018i	$0.643553\pi$
$132$	−7.09292	−	0.188351i	−0.617359	−	0.0163939i
$133$	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	0.0312791	−	0.999511i	$-0.490042\pi$
$137$	7.53879	−	2.44950i	0.644082	−	0.209275i	0.612803	+	0.790236i	$0.290042\pi$
$138$	8.67593	−	4.89773i	0.738544	−	0.416922i
$139$	−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
$141$	6.47689	+	0.744183i	0.545453	+	0.0626716i
$142$		−	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
$147$	5.92365	+	2.70636i	0.488574	+	0.223217i
$148$	−0.473079	−	1.45599i	−0.0388869	−	0.119682i
$149$	−1.62130	−	4.98986i	−0.132822	−	0.408785i	0.862423	−	0.506189i	$-0.168946\pi$
$149$	−1.62130	−	4.98986i	−0.132822	−	0.408785i	−0.995245	+	0.0974039i	$0.968946\pi$
$150$		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
$156$	4.25890	+	0.489340i	0.340985	+	0.0391786i
$157$	−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
$159$	−12.1523	+	6.86023i	−0.963744	+	0.544052i
$160$		0			0
$161$	17.4543	+	12.6813i	1.37559	+	0.999427i
$162$	1.12505	−	7.79017i	0.0883920	−	0.612054i
$163$	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	−0.949166	−	0.314776i	$-0.898071\pi$
$167$	0.0484080	−	0.148984i	0.00374592	−	0.0115288i	0.952912	+	0.303247i	$0.0980707\pi$
$168$	−11.8414	−	10.8713i	−0.913582	−	0.838742i
$169$	−7.26871	−	5.28102i	−0.559131	−	0.406233i
$170$		0			0
$171$	13.2334	−	11.4595i	1.01198	−	0.876332i
$172$	1.36770	−	1.88248i	0.104287	−	0.143538i
$173$	15.5033	−	11.2638i	1.17869	−	0.856372i	0.186671	−	0.982423i	$-0.440230\pi$
$173$	15.5033	−	11.2638i	1.17869	−	0.856372i	0.992024	+	0.126051i	$0.0402302\pi$
$174$	0.170062	−	1.48011i	0.0128924	−	0.112207i
$175$		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	0.756561	−	0.653923i	$-0.226878\pi$
$179$	−1.32649	−	1.82575i	−0.0991462	−	0.136463i	−0.855708	+	0.517460i	$0.826878\pi$
$180$		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
$183$	−3.01955	+	6.60915i	−0.223211	+	0.488562i
$184$	−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
$189$	16.3565	−	4.79435i	1.18976	−	0.348738i
$190$		0			0
$191$	5.37971	−	7.40453i	0.389262	−	0.535773i	−0.568747	−	0.822513i	$-0.692572\pi$
$191$	5.37971	−	7.40453i	0.389262	−	0.535773i	0.958009	+	0.286740i	$0.0925715\pi$
$192$	4.21804	+	7.47193i	0.304411	+	0.539240i
$193$	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	$-0.359851\pi$
$197$	11.9641			0.852408			0.426204	+	0.904627i	$0.359851\pi$
$198$	7.81601	+	3.82489i	0.555460	+	0.271823i
$199$	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
$201$	−15.4702	+	16.8506i	−1.09118	+	1.18855i
$202$	8.44069	+	6.13252i	0.593885	+	0.431483i
$203$	3.06837	−	0.996973i	0.215357	−	0.0699738i
$204$	−4.24091	−	7.51243i	−0.296923	−	0.525975i
$205$		0			0
$206$	−5.70600	+	4.14565i	−0.397556	+	0.288841i
$207$	19.6596	−	1.68235i	1.36644	−	0.116932i
$208$			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
$213$	1.19392	−	2.61323i	0.0818059	−	0.179056i
$214$	1.52946	+	4.70719i	0.104552	+	0.321777i
$215$		0			0
$216$	−14.6954	−	0.426733i	−0.999894	−	0.0290355i
$217$	−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
$222$	−0.214311	+	1.86522i	−0.0143836	+	0.125185i
$223$	−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	−0.198820	−	0.980036i	$-0.563711\pi$
$227$	−17.9642	−	13.0518i	−1.19233	−	0.866277i	−0.993508	+	0.113759i	$0.963711\pi$
$228$	−9.19577	−	8.44245i	−0.609004	−	0.559115i
$229$	−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
$231$	−0.500212	+	18.8370i	−0.0329115	+	1.23938i
$232$	−2.78276			−0.182697
$233$	5.85108	−	18.0078i	0.383317	−	1.17973i	−0.554377	−	0.832266i	$-0.687043\pi$
$233$	5.85108	−	18.0078i	0.383317	−	1.17973i	0.937694	−	0.347462i	$-0.112957\pi$
$234$	−4.50133	−	2.71633i	−0.294261	−	0.177572i
$235$		0			0
$236$	−14.2257	+	4.62221i	−0.926014	+	0.300880i
$237$	16.0920	−	9.08421i	1.04528	−	0.590083i
$238$	−6.79957	+	9.35881i	−0.440751	+	0.606641i
$239$	15.2628	−	11.0891i	0.987270	−	0.717294i	0.0279488	−	0.999609i	$-0.491102\pi$
$239$	15.2628	−	11.0891i	0.987270	−	0.717294i	0.959322	+	0.282315i	$0.0911025\pi$
$240$		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
$246$	7.61599	+	3.47955i	0.485577	+	0.221848i
$247$	−3.61327	−	11.1205i	−0.229907	−	0.707580i
$248$	4.28658	+	13.1927i	0.272198	+	0.837739i
$249$	24.1611	+	11.0386i	1.53115	+	0.699542i
$250$		0			0
$251$	−2.22750	−	0.723758i	−0.140598	−	0.0456832i	0.237872	−	0.971296i	$-0.423550\pi$
$251$	−2.22750	−	0.723758i	−0.140598	−	0.0456832i	−0.378471	+	0.925613i	$0.623550\pi$
$252$	−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	−0.577729	−	0.816229i	$-0.696061\pi$
$257$	6.04504	−	8.32028i	0.377079	−	0.519005i	0.954808	+	0.297224i	$0.0960609\pi$
$258$	−2.48502	+	1.40284i	−0.154711	+	0.0873372i
$259$	−3.86673	+	1.25638i	−0.240267	+	0.0780675i
$260$		0			0
$261$	1.52449	−	2.52629i	0.0943636	−	0.156374i
$262$	2.69634	−	8.29848i	0.166580	−	0.512682i
$263$	−12.1665			−0.750219			−0.375110	−	0.926980i	$-0.622395\pi$
$263$	−12.1665			−0.750219			−0.375110	+	0.926980i	$0.622395\pi$
$264$	5.43108	−	15.3189i	0.334260	−	0.942816i
$265$		0			0
$266$	−5.17286	+	15.9204i	−0.317168	+	0.976144i
$267$	−3.66943	−	3.36884i	−0.224566	−	0.206169i
$268$	13.1972	+	9.58830i	0.806145	+	0.585698i
$269$	−2.56774	+	0.834310i	−0.156558	+	0.0508688i	−0.386248	−	0.922395i	$-0.626229\pi$
$269$	−2.56774	+	0.834310i	−0.156558	+	0.0508688i	0.229689	+	0.973264i	$0.426229\pi$
$270$		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
$273$	1.29956	−	11.3105i	0.0786530	−	0.684545i
$274$			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
$279$	−14.3252	−	3.33592i	−0.857627	−	0.199716i
$280$		0			0
$281$	5.06988	+	15.6035i	0.302444	+	0.930827i	0.980619	+	0.195926i	$0.0627713\pi$
$281$	5.06988	+	15.6035i	0.302444	+	0.930827i	−0.678175	+	0.734901i	$0.737229\pi$
$282$	−2.36937	+	5.18605i	−0.141094	+	0.308825i
$283$	−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
$288$	1.44649	+	16.9034i	0.0852355	+	0.996043i
$289$	0.598172	−	0.434598i	0.0351866	−	0.0255646i
$290$		0			0
$291$	−2.58588	−	4.58068i	−0.151587	−	0.268524i
$292$	−4.94932	+	1.60813i	−0.289637	+	0.0941088i
$293$	−2.58332	−	1.87689i	−0.150919	−	0.109649i	0.509763	−	0.860315i	$-0.329733\pi$
$293$	−2.58332	−	1.87689i	−0.150919	−	0.109649i	−0.660682	+	0.750665i	$0.729733\pi$
$294$	−3.85190	+	4.19560i	−0.224647	+	0.244692i
$295$		0			0
$296$	3.50681			0.203829
$297$	10.9318	+	13.3228i	0.634326	+	0.773066i
$298$	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
$303$	10.1579	+	17.9938i	0.583554	+	1.03372i
$304$	0.0140202	−	0.0192971i	0.000804112	−	0.00110677i
$305$		0			0
$306$	0.902059	+	10.5413i	0.0515673	+	0.602604i
$307$			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	$-0.996971\pi$
$311$	−12.3446	−	16.9909i	−0.700001	−	0.963468i	0.299954	−	0.953954i	$-0.403029\pi$
$312$	−4.08073	+	8.93184i	−0.231026	+	0.505666i
$313$	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	0.843070	−	0.537804i	$-0.180746\pi$
$317$	21.5259	+	6.99418i	1.20901	+	0.392832i	0.365944	+	0.930637i	$0.380746\pi$
$318$	−2.42181	−	11.9617i	−0.135808	−	0.670780i
$319$	2.14153	+	2.46065i	0.119902	+	0.137770i
$320$		0			0
$321$	−1.11891	+	9.73825i	−0.0624514	+	0.543536i
$322$	−15.2648	+	11.0905i	−0.850672	+	0.618049i
$323$	−13.8306	+	19.0362i	−0.769555	+	1.05920i
$324$	−9.97275	−	4.91104i	−0.554041	−	0.272836i
$325$		0			0
$326$	9.74816	+	7.08246i	0.539901	+	0.392261i
$327$	−6.96141	−	6.39114i	−0.384967	−	0.353431i
$328$	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
$333$	−1.92115	+	3.18362i	−0.105279	+	0.174461i
$334$	0.110836	+	0.0805268i	0.00606466	+	0.00440623i
$335$		0			0
$336$	0.0202245	−	0.0114171i	0.00110334	−	0.000622856i
$337$	−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
$339$	−12.6156	−	1.44951i	−0.685183	−	0.0787263i
$340$		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	0.884401	−	0.466729i	$-0.154568\pi$
$347$	−1.96396	−	6.04444i	−0.105431	−	0.324482i	−0.989831	+	0.142246i	$0.954568\pi$
$348$	−1.91386	−	0.874393i	−0.102594	−	0.0468724i
$349$	−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	$0.157014\pi$
$353$			17.7930i			0.947024i	−0.880787	+	0.473512i	$0.842986\pi$
$354$	18.2241	+	2.09392i	0.968600	+	0.111290i
$355$		0			0
$356$	−2.08798	+	2.87385i	−0.110663	+	0.152314i
$357$	−19.9511	+	11.2628i	−1.05592	+	0.596089i
$358$	1.87706	−	0.609892i	0.0992055	−	0.0322338i
$359$	−8.01407	−	5.82257i	−0.422967	−	0.307303i	0.355864	−	0.934538i	$-0.384187\pi$
$359$	−8.01407	−	5.82257i	−0.422967	−	0.307303i	−0.778830	+	0.627235i	$0.784187\pi$
$360$		0			0
$361$	−4.65048	+	14.3127i	−0.244762	+	0.753300i
$362$	7.43515			0.390783
$363$	−17.7253	+	6.98656i	−0.930340	+	0.366699i
$364$	−8.11880			−0.425541
$365$		0			0
$366$	−4.68112	−	4.29765i	−0.244686	−	0.224642i
$367$	−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
$369$	10.8557	+	12.5361i	0.565124	+	0.652601i
$370$		0			0
$371$	21.3813	−	15.5344i	1.11006	−	0.806508i
$372$	−1.19727	+	10.4203i	−0.0620758	+	0.540267i
$373$		−	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
$378$	−0.432682	+	14.9002i	−0.0222548	+	0.766385i
$379$	−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
$381$	4.53414	−	9.92427i	0.232291	−	0.508436i
$382$	4.70485	+	6.47567i	0.240721	+	0.331324i
$383$	−27.0846	−	8.80032i	−1.38396	−	0.449675i	−0.479990	−	0.877274i	$-0.659360\pi$
$383$	−27.0846	−	8.80032i	−1.38396	−	0.449675i	−0.903969	+	0.427598i	$0.859360\pi$
$384$	11.8454	−	2.39826i	0.604485	−	0.122386i
$385$		0			0
$386$			8.46406i			0.430810i
$387$	−5.63105	+	0.481872i	−0.286242	+	0.0244949i
$388$	−3.03472	+	2.20485i	−0.154064	+	0.111934i
$389$	7.85595	−	10.8128i	0.398312	−	0.548230i	−0.562007	−	0.827132i	$-0.689971\pi$
$389$	7.85595	−	10.8128i	0.398312	−	0.548230i	0.960319	+	0.278903i	$0.0899707\pi$
$390$		0			0
$391$	−25.2239	+	8.19576i	−1.27563	+	0.414477i
$392$	8.60664	+	6.25309i	0.434701	+	0.315829i
$393$	11.6869	−	12.7297i	0.589526	−	0.642128i
$394$	−3.23333	+	9.95117i	−0.162893	+	0.501333i
$395$		0			0
$396$	8.54874	−	8.82915i	0.429590	−	0.443681i
$397$	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
$399$	−22.4210	+	24.4216i	−1.12245	+	1.22261i
$400$		0			0
$401$	−14.0903	+	4.57823i	−0.703637	+	0.228626i	−0.638915	−	0.769278i	$-0.720616\pi$
$401$	−14.0903	+	4.57823i	−0.703637	+	0.228626i	−0.0647228	+	0.997903i	$0.520616\pi$
$402$	−9.83463	−	17.4213i	−0.490507	−	0.868893i
$403$	−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
$411$	−5.70541	+	12.4879i	−0.281427	+	0.615984i
$412$	3.07816	+	9.47359i	0.151650	+	0.466730i
$413$	12.2754	+	37.7798i	0.604033	+	1.85902i
$414$	−3.91376	+	16.8066i	−0.192351	+	0.825998i
$415$		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	$-0.971453\pi$
$419$		−	3.66657i		−	0.179123i	0.995981	−	0.0895617i	$-0.0285466\pi$
$420$		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
$423$	−8.53633	+	7.39208i	−0.415051	+	0.359415i
$424$	−21.6799	+	7.04424i	−1.05287	+	0.342098i
$425$		0			0
$426$	1.85090	+	1.69927i	0.0896763	+	0.0823301i
$427$	4.25245	−	13.0877i	0.205791	−	0.633359i
$428$	6.99020			0.337884
$429$	11.0384	−	3.26529i	0.532938	−	0.157650i
$430$		0			0
$431$	7.04575	−	21.6846i	0.339382	−	1.04451i	−0.625141	−	0.780512i	$-0.714959\pi$
$431$	7.04575	−	21.6846i	0.339382	−	1.04451i	0.964523	−	0.263999i	$-0.0850414\pi$
$432$	0.00714723	−	0.0200018i	0.000343871	−	0.000962336i
$433$	−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
$438$	6.34042	+	0.728503i	0.302957	+	0.0348092i
$439$		−	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	0.812672	−	0.582721i	$-0.198012\pi$
$443$	0.154522	+	0.212682i	0.00734157	+	0.0101048i	−0.805330	+	0.592826i	$0.798012\pi$
$444$	2.41183	+	1.10190i	0.114460	+	0.0522940i
$445$		0			0
$446$	−6.88187	−	21.1802i	−0.325866	−	1.00291i
$447$	8.26565	+	3.77636i	0.390952	+	0.178616i
$448$	−9.55142	−	13.1464i	−0.451262	−	0.621109i
$449$	7.95876	+	2.58596i	0.375597	+	0.122039i	0.490731	−	0.871311i	$-0.336730\pi$
$449$	7.95876	+	2.58596i	0.375597	+	0.122039i	−0.115134	+	0.993350i	$0.536730\pi$
$450$		0			0
$451$	−16.8717	+	7.17320i	−0.794457	+	0.337773i
$452$			9.05555i			0.425937i
$453$	−16.1004	−	1.84990i	−0.756461	−	0.0869160i
$454$	15.7107	−	11.4145i	0.737340	−	0.535709i
$455$		0			0
$456$	24.9016	−	14.0574i	1.16612	−	0.658298i
$457$	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
$459$	−7.05060	+	19.7313i	−0.329094	+	0.920980i
$460$		0			0
$461$	18.8046			0.875819			0.437909	−	0.899019i	$-0.355719\pi$
$461$	18.8046			0.875819			0.437909	+	0.899019i	$0.355719\pi$
$462$	−15.5325	−	5.50679i	−0.722637	−	0.256199i
$463$	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	−0.861713	−	0.507396i	$-0.830608\pi$
$467$	−27.2421	+	8.85149i	−1.26061	+	0.409598i	−0.398900	+	0.916994i	$0.630608\pi$
$468$	−5.61309	+	4.86069i	−0.259465	+	0.224685i
$469$	25.4641	−	35.0483i	1.17582	−	1.61838i
$470$		0			0
$471$	1.02642	−	8.93327i	0.0472948	−	0.411623i
$472$		−	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
$477$	5.48199	−	23.5409i	0.251003	−	1.07786i
$478$	5.09855	+	15.6917i	0.233202	+	0.717723i
$479$	−12.8091	−	39.4224i	−0.585264	−	1.80126i	−0.598210	−	0.801340i	$-0.704121\pi$
$479$	−12.8091	−	39.4224i	−0.585264	−	1.80126i	0.0129461	−	0.999916i	$-0.495879\pi$
$480$		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
$486$	8.62156	+	10.5606i	0.391082	+	0.479039i
$487$	−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
$489$	11.7313	+	20.7811i	0.530509	+	0.939754i
$490$		0			0
$491$	−17.6468	−	12.8212i	−0.796390	−	0.578611i	0.113463	−	0.993542i	$-0.463806\pi$
$491$	−17.6468	−	12.8212i	−0.796390	−	0.578611i	−0.909853	+	0.414931i	$0.863806\pi$
$492$	7.99758	−	8.71120i	0.360559	−	0.392731i
$493$	−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
$498$	−15.7110	+	17.1128i	−0.704025	+	0.766844i
$499$	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
$501$	0.133384	+	0.236279i	0.00595916	+	0.0105562i
$502$	1.20397	−	1.65713i	0.0537359	−	0.0739612i
$503$	−18.2609	+	13.2673i	−0.814215	+	0.591562i	−0.915050	−	0.403342i	$-0.867849\pi$
$503$	−18.2609	+	13.2673i	−0.814215	+	0.591562i	0.100835	+	0.994903i	$0.467849\pi$
$504$	27.7413	−	2.37393i	1.23569	−	0.105743i
$505$		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	0.453470	−	0.891272i	$-0.350186\pi$
$509$	−12.0546	−	16.5917i	−0.534310	−	0.735414i	−0.987780	+	0.155857i	$0.950186\pi$
$510$		0			0
$511$	4.27079	+	13.1441i	0.188928	+	0.581462i
$512$	0.0142912	+	0.0439837i	0.000631587	+	0.00194382i
$513$	−0.880093	+	30.3077i	−0.0388571	+	1.33812i
$514$	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
$519$	−3.78872	+	32.9746i	−0.166306	+	1.44742i
$520$		0			0
$521$	−2.41526	+	3.32432i	−0.105814	+	0.145641i	−0.858640	−	0.512579i	$-0.828690\pi$
$521$	−2.41526	+	3.32432i	−0.105814	+	0.145641i	0.752826	+	0.658220i	$0.228690\pi$
$522$	1.68925	+	1.95073i	0.0739364	+	0.0853813i
$523$	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
$528$	0.0186244	+	0.0143019i	0.000810521	+	0.000622410i
$529$	−20.2590			−0.880826
$530$		0			0
$531$	31.1054	+	18.7706i	1.34986	+	0.814573i
$532$	19.1267	+	13.8964i	0.829247	+	0.602483i
$533$	10.5345	−	3.42287i	0.456300	−	0.148261i
$534$	3.79371	−	2.14162i	0.164170	−	0.0926769i
$535$		0			0
$536$	−30.2302	+	21.9635i	−1.30575	+	0.948681i
$537$	3.88326	+	0.446180i	0.167575	+	0.0192541i
$538$		−	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
$543$	13.3936	+	6.11920i	0.574775	+	0.262600i
$544$	−7.04674	−	21.6876i	−0.302127	−	0.929850i
$545$		0			0
$546$	9.05635	+	4.13761i	0.387576	+	0.177074i
$547$	−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
$552$	32.0209	+	3.67914i	1.36290	+	0.156595i
$553$	−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	0.368950	−	0.929449i	$-0.379717\pi$
$557$	−9.46385	−	6.87589i	−0.400996	−	0.291341i	−0.769947	+	0.638108i	$0.779717\pi$
$558$	6.64607	−	11.0135i	0.281350	−	0.466237i
$559$	−1.16654	+	3.59023i	−0.0493393	+	0.151851i
$560$		0			0
$561$	−18.3725	−	14.1085i	−0.775689	−	0.595662i
$562$	−14.3484			−0.605250
$563$	−2.06731	+	6.36251i	−0.0871266	+	0.268148i	−0.985122	−	0.171857i	$-0.945023\pi$
$563$	−2.06731	+	6.36251i	−0.0871266	+	0.268148i	0.897995	+	0.440005i	$0.145023\pi$
$564$	5.93182	+	5.44589i	0.249775	+	0.229313i
$565$		0			0
$566$	26.2926	−	8.54298i	1.10516	−	0.359088i
$567$	−13.0425	+	26.4851i	−0.547732	+	1.11227i
$568$	2.75856	−	3.79684i	0.115747	−	0.159312i
$569$	−30.8612	+	22.4220i	−1.29377	+	0.939978i	−0.999874	−	0.0158600i	$-0.994951\pi$
$569$	−30.8612	+	22.4220i	−1.29377	+	0.939978i	−0.293894	+	0.955838i	$0.594951\pi$
$570$		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
$576$	−14.4742	−	3.37063i	−0.603093	−	0.140443i
$577$	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
$579$	−6.96601	+	15.2471i	−0.289497	+	0.633648i
$580$		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	−0.999871	−	0.0160773i	$-0.994882\pi$
$587$	−16.3686	+	22.5294i	−0.675603	+	0.929888i	0.324267	+	0.945965i	$0.394882\pi$
$588$	3.95444	+	7.00496i	0.163078	+	0.288880i
$589$	27.2086	−	8.84062i	1.12111	−	0.364271i
$590$		0			0
$591$	−14.0144	+	15.2649i	−0.576475	+	0.627914i
$592$	−0.00156565	+	0.00481857i	−6.43477e−5	+	0.000198042i
$593$	23.0788			0.947731			0.473865	−	0.880597i	$-0.342858\pi$
$593$	23.0788			0.947731			0.473865	+	0.880597i	$0.342858\pi$
$594$	−14.0356	+	5.49200i	−0.575886	+	0.225340i
$595$		0			0
$596$	2.00256	−	6.16324i	0.0820280	−	0.252456i
$597$	−31.1268	+	33.9042i	−1.27393	+	1.38760i
$598$	9.32495	+	6.77497i	0.381326	+	0.277049i
$599$	−14.7956	+	4.80738i	−0.604532	+	0.196424i	−0.595261	−	0.803533i	$-0.702951\pi$
$599$	−14.7956	+	4.80738i	−0.604532	+	0.196424i	−0.00927118	+	0.999957i	$0.502951\pi$
$600$		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
$603$	−3.37817	−	39.4765i	−0.137570	−	1.60761i
$604$			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
$609$	−2.32216	+	5.08272i	−0.0940988	+	0.205962i
$610$		0			0
$611$	2.33077	+	7.17338i	0.0942930	+	0.290204i
$612$	14.5527	+	3.38890i	0.588258	+	0.136988i
$613$	−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	$0.127541\pi$
$617$			19.3771i			0.780095i	−0.920795	+	0.390047i	$0.872459\pi$
$618$	1.39444	−	12.1363i	0.0560927	−	0.488194i
$619$	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
$621$	−20.8822	+	27.0542i	−0.837973	+	1.08565i
$622$	17.4684	−	5.67583i	0.700419	−	0.227580i
$623$	7.63222	+	5.54513i	0.305778	+	0.222161i
$624$	−0.0104510	−	0.00959485i	−0.000418374	−	0.000384101i
$625$		0			0
$626$	−16.2566			−0.649746
$627$	−31.5937	−	11.2010i	−1.26173	−	0.447326i
$628$	−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
$633$	23.2613	−	13.1315i	0.924554	−	0.521929i
$634$	−11.6348	+	16.0140i	−0.462079	+	0.635996i
$635$		0			0
$636$	−17.1239	−	1.96751i	−0.679008	−	0.0780168i
$637$			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	0.777923	−	0.628360i	$-0.216274\pi$
$641$	−1.52097	−	2.09343i	−0.0600746	−	0.0826856i	−0.837997	+	0.545674i	$0.816274\pi$
$642$	−7.79742	−	3.56244i	−0.307739	−	0.140598i
$643$	−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	−0.106519	−	0.994311i	$-0.533970\pi$
$647$	−19.7674	−	6.42281i	−0.777136	−	0.252507i	−0.670617	+	0.741804i	$0.733970\pi$
$648$	17.7582	−	18.2498i	0.697607	−	0.716921i
$649$	−30.2972	+	26.3679i	−1.18927	+	1.03503i
$650$		0			0
$651$	27.6736	+	3.17965i	1.08462	+	0.124620i
$652$	13.7676	−	10.0027i	0.539179	−	0.391736i
$653$	6.19152	−	8.52190i	0.242293	−	0.333488i	−0.670501	−	0.741909i	$-0.733921\pi$
$653$	6.19152	−	8.52190i	0.242293	−	0.333488i	0.912793	+	0.408421i	$0.133921\pi$
$654$	7.19718	−	4.06294i	0.281432	−	0.158874i
$655$		0			0
$656$	0.0182803	+	0.0132814i	0.000713724	+	0.000518551i
$657$	10.8220	+	6.53054i	0.422207	+	0.254781i
$658$	3.33680	−	10.2696i	0.130082	−	0.400352i
$659$	37.3557			1.45517			0.727586	−	0.686016i	$-0.240642\pi$
$659$	37.3557			1.45517			0.727586	+	0.686016i	$0.240642\pi$
$660$		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
$663$	10.3097	+	9.46512i	0.400395	+	0.367595i
$664$	35.1044	+	25.5048i	1.36231	+	0.989779i
$665$		0			0
$666$	−2.12878	−	2.45830i	−0.0824885	−	0.0952572i
$667$	−3.80234	+	5.23347i	−0.147227	+	0.202641i
$668$	0.156536	−	0.113730i	0.00605655	−	0.00440034i
$669$	5.03457	−	43.8177i	0.194648	−	1.69409i
$670$		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	$-0.985245\pi$
$677$	−5.67258	−	17.4584i	−0.218015	−	0.670981i	0.780911	−	0.624643i	$-0.214755\pi$
$678$	4.61501	−	10.1013i	0.177239	−	0.387937i
$679$	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	$-0.902995\pi$
$683$		−	15.6834i		−	0.600109i	0.953922	−	0.300055i	$-0.0970049\pi$
$684$	21.5433	−	1.84355i	0.823728	−	0.0704898i
$685$		0			0
$686$	−5.46325	+	7.51951i	−0.208588	+	0.287096i
$687$	−16.2576	−	28.7990i	−0.620265	−	1.09875i
$688$	−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
$693$	−23.4480	−	22.7033i	−0.890714	−	0.862426i
$694$	5.55823			0.210988
$695$		0			0
$696$	3.25964	−	3.55049i	0.123556	−	0.134581i
$697$	−18.0331	−	13.1018i	−0.683052	−	0.496266i
$698$	1.27350	−	0.413785i	0.0482027	−	0.0156620i
$699$	16.1221	+	28.5591i	0.609795	+	1.08020i
$700$		0			0
$701$	18.1727	−	13.2032i	0.686373	−	0.498679i	−0.189093	−	0.981959i	$-0.560555\pi$
$701$	18.1727	−	13.2032i	0.686373	−	0.498679i	0.875466	+	0.483280i	$0.160555\pi$
$702$	8.73845	−	2.56137i	0.329812	−	0.0966729i
$703$		−	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
$708$	10.7661	−	23.5647i	0.404615	−	0.885617i
$709$	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
$711$	−7.25917	+	31.1725i	−0.272240	+	1.16906i
$712$	−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
$717$	−3.72995	+	32.4631i	−0.139298	+	1.21236i
$718$	7.00875	−	5.09215i	0.261564	−	0.190037i
$719$	20.8046	−	28.6351i	0.775880	−	1.06791i	−0.219844	−	0.975535i	$-0.570555\pi$
$719$	20.8046	−	28.6351i	0.775880	−	1.06791i	0.995724	−	0.0923728i	$-0.0294451\pi$
$720$		0			0
$721$	25.1594	−	8.17479i	0.936986	−	0.304445i
$722$	−10.6478	−	7.73608i	−0.396270	−	0.287907i
$723$	−2.74946	−	2.52423i	−0.102254	−	0.0938771i
$724$	3.24493	−	9.98688i	0.120597	−	0.371159i
$725$		0			0
$726$	−1.02076	−	16.6312i	−0.0378841	−	0.617242i
$727$	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
$729$	6.83932	+	26.1194i	0.253308	+	0.967386i
$730$		0			0
$731$	7.22483	−	2.34749i	0.267220	−	0.0868250i
$732$	−7.81559	+	4.41205i	−0.288872	+	0.163074i
$733$	−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
$741$	18.4210	+	8.41607i	0.676712	+	0.309172i
$742$	7.14243	+	21.9822i	0.262207	+	0.806990i
$743$	−15.5121	−	47.7414i	−0.569084	−	1.75146i	−0.655493	−	0.755201i	$-0.727539\pi$
$743$	−15.5121	−	47.7414i	−0.569084	−	1.75146i	0.0864090	−	0.996260i	$-0.472461\pi$
$744$	−21.8536	−	9.98436i	−0.801193	−	0.366045i
$745$		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
$753$	3.53266	−	1.99425i	0.128737	−	0.0726746i
$754$	1.63927	−	0.532632i	0.0596987	−	0.0193973i
$755$		0			0
$756$	19.8251	+	7.08411i	0.721033	+	0.257647i
$757$	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
$759$	−21.3890	−	31.1458i	−0.776371	−	1.13052i
$760$		0			0
$761$	−4.81075	+	14.8060i	−0.174390	+	0.536716i	−0.999605	−	0.0281019i	$-0.991054\pi$
$761$	−4.81075	+	14.8060i	−0.174390	+	0.536716i	0.825215	+	0.564818i	$0.191054\pi$
$762$	7.02916	+	6.45334i	0.254640	+	0.233780i
$763$	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
$768$	−3.16533	+	27.5490i	−0.114219	+	0.994090i
$769$			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	$-0.923186\pi$
$773$	−24.9738	−	34.3735i	−0.898247	−	1.23633i	0.0727775	−	0.997348i	$-0.476814\pi$
$774$	1.12101	−	4.81386i	0.0402938	−	0.173031i
$775$		0			0
$776$	−2.65524	−	8.17199i	−0.0953176	−	0.293357i
$777$	2.92637	−	6.40521i	0.104983	−	0.229786i
$778$	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
$783$	1.43753	+	4.90430i	0.0513730	+	0.175266i
$784$	−0.0124346	+	0.00903428i	−0.000444094	+	0.000322653i
$785$		0			0
$786$	7.42953	+	13.1608i	0.265003	+	0.469431i
$787$	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
$789$	14.2515	−	15.5231i	0.507366	−	0.552638i
$790$		0			0
$791$	24.0492			0.855092
$792$	13.1835	+	24.8736i	0.468454	+	0.883845i
$793$	−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	0.507529	−	0.861634i	$-0.330559\pi$
$797$	40.2177	−	13.0675i	1.42459	−	0.462876i	0.917056	+	0.398759i	$0.130559\pi$
$798$	−14.2534	−	25.2487i	−0.504564	−	0.893794i
$799$	8.92157	−	12.2795i	0.315622	−	0.434417i
$800$		0			0
$801$	8.59652	−	0.735640i	0.303743	−	0.0259925i
$802$		−	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
$807$	1.94329	−	4.25344i	0.0684070	−	0.149728i
$808$	10.4303	+	32.1012i	0.366938	+	1.12932i
$809$	10.5925	+	32.6003i	0.372412	+	1.14617i	0.945208	+	0.326468i	$0.105859\pi$
$809$	10.5925	+	32.6003i	0.372412	+	1.14617i	−0.572796	+	0.819698i	$0.694141\pi$
$810$		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
$816$	−0.00325893	+	0.0283636i	−0.000114085	+	0.000992926i
$817$	8.89333	−	6.46138i	0.311138	−	0.226055i
$818$	12.5827	−	17.3185i	0.439942	−	0.605528i
$819$	12.9087	+	14.9069i	0.451068	+	0.520890i
$820$		0			0
$821$	−23.8031	−	17.2940i	−0.830733	−	0.603563i	0.0890334	−	0.996029i	$-0.471622\pi$
$821$	−23.8031	−	17.2940i	−0.830733	−	0.603563i	−0.919767	+	0.392466i	$0.871622\pi$
$822$	−8.84495	−	8.12037i	−0.308503	−	0.283231i
$823$	−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	−0.828195	−	0.560441i	$-0.810632\pi$
$827$	4.92467	−	15.1566i	0.171248	−	0.527046i	0.999442	+	0.0333946i	$0.0106318\pi$
$828$	20.8665	+	12.5919i	0.725160	+	0.437598i
$829$	−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
$831$	−21.3040	+	12.0265i	−0.739029	+	0.417196i
$832$	−5.83478	+	8.03088i	−0.202284	+	0.278421i
$833$	12.2665	−	8.91213i	0.425009	−	0.308787i
$834$	0.525205	+	0.0603451i	0.0181864	+	0.00208958i
$835$		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	$0.204513\pi$
$839$	32.5303	+	44.7742i	1.12307	+	1.54578i	0.322470	+	0.946580i	$0.395487\pi$
$840$		0			0
$841$	−8.66256	−	26.6606i	−0.298709	−	0.919332i
$842$	3.39463	+	10.4476i	0.116987	+	0.360048i
$843$	−25.8470	−	11.8089i	−0.890220	−	0.406718i
$844$	−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
$849$	54.3942	+	6.24980i	1.86680	+	0.214493i
$850$		0			0
$851$	4.79168	−	6.59518i	0.164257	−	0.226080i
$852$	3.09025	−	1.74451i	0.105870	−	0.0597658i
$853$	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	$-0.768870\pi$
$857$	−43.7806			−1.49552			−0.747759	+	0.663970i	$0.768870\pi$
$858$	−0.267238	+	10.0636i	−0.00912334	+	0.343567i
$859$	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
$861$	−23.1347	−	21.2395i	−0.788429	−	0.723841i
$862$	16.1321	+	11.7206i	0.549460	+	0.399206i
$863$	2.81745	−	0.915446i	0.0959072	−	0.0311621i	−0.260670	−	0.965428i	$-0.583944\pi$
$863$	2.81745	−	0.915446i	0.0959072	−	0.0311621i	0.356578	+	0.934266i	$0.383944\pi$
$864$	−23.2613	−	17.9546i	−0.791364	−	0.610827i
$865$		0			0
$866$	20.1318	−	14.6266i	0.684106	−	0.497032i
$867$	−0.146182	+	1.27228i	−0.00496461	+	0.0432088i
$868$		−	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
$873$	8.87347	+	2.06637i	0.300321	+	0.0699360i
$874$	−10.3720	−	31.9217i	−0.350837	−	1.07977i
$875$		0			0
$876$	3.74568	−	8.19850i	0.126555	−	0.277002i
$877$	−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	$-0.736139\pi$
$881$		−	43.7637i		−	1.47444i	0.675655	−	0.737218i	$-0.263861\pi$
$882$	−0.841125	−	9.82920i	−0.0283221	−	0.330966i
$883$	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	0.636212	−	0.771515i	$-0.280501\pi$
$887$	2.95019	+	2.14344i	0.0990577	+	0.0719696i	−0.537154	+	0.843484i	$0.680501\pi$
$888$	−4.10777	+	4.47431i	−0.137848	+	0.150148i
$889$	−6.38547	+	19.6525i	−0.214162	+	0.659122i
$890$		0			0
$891$	−29.8035	−	1.65816i	−0.998456	−	0.0555504i
$892$	−31.4527			−1.05311
$893$	6.78719	−	20.8888i	0.227125	−	0.699018i
$894$	−5.37480	+	5.85439i	−0.179760	+	0.195800i
$895$		0			0
$896$	−21.7684	+	7.07300i	−0.727233	+	0.236292i
$897$	11.2220	+	19.8789i	0.374692	+	0.663737i
$898$	−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
$906$	5.88982	−	12.8916i	0.195676	−	0.428293i
$907$	−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
$909$	−34.8568	−	8.11712i	−1.15613	−	0.269228i
$910$		0			0
$911$	37.3651	+	12.1406i	1.23796	+	0.402237i	0.853592	−	0.520943i	$-0.174419\pi$
$911$	37.3651	+	12.1406i	1.23796	+	0.402237i	0.384368	+	0.923180i	$0.374419\pi$
$912$	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
$918$	−14.5061	−	11.1968i	−0.478773	−	0.369549i
$919$	−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
$921$	−19.4136	−	17.8233i	−0.639700	−	0.587296i
$922$	−5.08199	+	15.6408i	−0.167367	+	0.515101i
$923$	3.32389			0.109407
$924$	−14.1756	+	18.4599i	−0.466342	+	0.607286i
$925$		0			0
$926$	−9.01070	+	27.7321i	−0.296110	+	0.911333i
$927$	12.5002	−	20.7146i	0.410562	−	0.680358i
$928$	−4.49976	−	3.26926i	−0.147712	−	0.107319i
$929$	−19.7724	+	6.42444i	−0.648712	+	0.210779i	−0.614846	−	0.788647i	$-0.710782\pi$
$929$	−19.7724	+	6.42444i	−0.648712	+	0.210779i	−0.0338656	+	0.999426i	$0.510782\pi$
$930$		0			0
$931$	12.8963	−	17.7503i	0.422661	−	0.581743i
$932$	18.9205	−	13.7465i	0.619761	−	0.450283i
$933$	36.1387	+	4.15227i	1.18313	+	0.135939i
$934$		−	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
$939$	−29.2846	−	13.3794i	−0.955665	−	0.436619i
$940$		0			0
$941$	1.83270	+	5.64048i	0.0597444	+	0.183874i	0.976475	−	0.215633i	$-0.0691813\pi$
$941$	1.83270	+	5.64048i	0.0597444	+	0.183874i	−0.916730	+	0.399507i	$0.869181\pi$
$942$	7.15287	+	3.26796i	0.233053	+	0.106476i
$943$	−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	$0.139569\pi$
$947$			26.1300i			0.849110i	−0.905402	+	0.424555i	$0.860431\pi$
$948$	22.6752	+	2.60534i	0.736457	+	0.0846176i
$949$	6.83030	−	4.96250i	0.221721	−	0.161090i
$950$		0			0
$951$	−34.1386	+	19.2719i	−1.10702	+	0.624933i
$952$	−35.5930	+	11.5649i	−1.15357	+	0.374819i
$953$	−3.28163	−	2.38424i	−0.106302	−	0.0772331i	0.533364	−	0.845886i	$-0.320928\pi$
$953$	−3.28163	−	2.38424i	−0.106302	−	0.0772331i	−0.639666	+	0.768653i	$0.720928\pi$
$954$	18.0987	+	10.9216i	0.585966	+	0.353601i
$955$		0			0
$956$	23.3023			0.753650
$957$	−5.64804	−	0.149983i	−0.182575	−	0.00484825i
$958$	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
$963$	−11.1143	−	12.8347i	−0.358153	−	0.413592i
$964$	−1.56450	+	2.15334i	−0.0503890	+	0.0693545i
$965$		0			0
$966$	3.73043	−	32.4672i	0.120025	−	1.04462i
$967$			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	$0.103417\pi$
$971$	29.8652	+	41.1059i	0.958419	+	1.31915i	0.0107342	+	0.999942i	$0.496583\pi$
$972$	17.9477	−	6.97148i	0.575673	−	0.223610i
$973$	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	−0.475388	−	0.879776i	$-0.657692\pi$
$977$	−43.0442	−	13.9859i	−1.37711	−	0.447449i	−0.901717	+	0.432327i	$0.857692\pi$
$978$	−20.4551	+	4.14141i	−0.654083	+	0.132428i
$979$	−2.14030	+	9.29532i	−0.0684043	+	0.297080i
$980$		0			0
$981$	16.3088	−	1.39561i	0.520699	−	0.0445583i
$982$	15.4331	−	11.2128i	0.492491	−	0.357815i
$983$	−3.51639	+	4.83989i	−0.112155	+	0.154369i	−0.861404	−	0.507920i	$-0.830415\pi$
$983$	−3.51639	+	4.83989i	−0.112155	+	0.154369i	0.749249	+	0.662288i	$0.230415\pi$
$984$	13.3167	+	23.5894i	0.424519	+	0.752002i
$985$		0			0
$986$	−2.80612	−	2.03877i	−0.0893652	−	0.0649276i
$987$	14.4629	−	15.7534i	0.460359	−	0.501436i
$988$	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
$993$	−0.766680	+	0.835090i	−0.0243298	+	0.0265008i
$994$	−3.84977	−	2.79702i	−0.122107	−	0.0887160i
$995$		0			0
$996$	16.1292	+	28.5715i	0.511072	+	0.905323i
$997$	−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
$999$	−1.81156	−	6.18037i	−0.0573153	−	0.195538i

Twists

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

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

\(f(q)\)	\(=\)	\(q+(-0.270252 + 0.831751i) q^{2} +(-1.17137 + 1.27589i) q^{3} +(0.999260 + 0.726005i) q^{4} +(-0.744657 - 1.31910i) q^{6} +(1.92808 - 2.65378i) q^{7} +(-2.28897 + 1.66303i) q^{8} +(-0.255787 - 2.98908i) q^{9} +O(q^{10})\)	\(q+(-0.270252 + 0.831751i) q^{2} +(-1.17137 + 1.27589i) q^{3} +(0.999260 + 0.726005i) q^{4} +(-0.744657 - 1.31910i) q^{6} +(1.92808 - 2.65378i) q^{7} +(-2.28897 + 1.66303i) q^{8} +(-0.255787 - 2.98908i) 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} +(2.55529 + 0.595053i) q^{18} +(3.42983 + 4.72076i) q^{19} +(1.12743 + 5.56858i) q^{21} +(-1.49246 + 2.48714i) q^{22} +6.57716i q^{23} +(0.559381 - 4.86849i) q^{24} +(1.03008 - 1.41778i) q^{26} +(4.11335 + 3.17496i) q^{27} +(3.85332 - 1.25202i) q^{28} +(0.795704 + 0.578113i) q^{29} +(1.51506 - 4.66286i) q^{31} -5.65506 q^{32} +(-4.73544 + 3.25201i) q^{33} -3.52660 q^{34} +(1.91449 - 3.17257i) q^{36} +(-1.00274 - 0.728533i) q^{37} +(-4.85341 + 1.57697i) q^{38} +(3.02242 - 1.70621i) q^{39} +(-4.47200 + 3.24910i) q^{41} +(-4.93636 - 0.567179i) q^{42} -1.88388i q^{43} +(2.68937 + 3.09014i) q^{44} +(-5.47056 - 1.77749i) q^{46} +(-2.21245 - 3.04517i) q^{47} +(0.00643985 + 0.00294220i) q^{48} +(-1.16192 - 3.57602i) q^{49} +(-6.35278 - 2.90242i) q^{51} +(-1.45480 - 2.00236i) q^{52} +(7.66260 + 2.48973i) q^{53} +(-3.75242 + 2.56325i) q^{54} +9.28088i q^{56} +(-10.0408 - 1.15367i) 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} +(-8.42553 - 5.08438i) q^{63} +(1.53082 - 4.71138i) q^{64} +(-1.42510 - 4.81757i) q^{66} +13.2069 q^{67} +(-1.53912 + 4.73692i) q^{68} +(-8.39172 - 7.70428i) q^{69} +(-1.57757 + 0.512584i) q^{71} +(5.55642 + 6.41651i) 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} +(-8.86915 + 1.52914i) q^{81} +(-1.49387 - 4.59766i) q^{82} +(-4.73919 - 14.5857i) q^{83} +(-2.91622 + 6.38298i) 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} +(4.17461 + 7.39498i) q^{93} +(3.13074 - 1.01724i) q^{94} +(6.62417 - 7.21524i) q^{96} +(-0.938473 + 2.88832i) q^{97} +3.28837 q^{98} +(1.39775 - 9.85121i) 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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