LMFDB - Embedded newform 825.2.cw.b.382.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [825,2,Mod(7,825)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(825, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([0, 5, 14]))

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

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

chi := DirichletCharacter("825.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 825 = 3 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	825.cw (of order $20$, degree $8$, 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:	$96$
Relative dimension:	$12$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 165)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			382.5
Character	$\chi$	$=$	825.382
Dual form			825.2.cw.b.568.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.178502 + 1.12702i) q^{2} +(0.891007 + 0.453990i) q^{3} +(0.663811 + 0.215685i) q^{4} +(-0.670701 + 0.923140i) q^{6} +(-0.694338 - 1.36271i) q^{7} +(-1.39764 + 2.74302i) q^{8} +(0.587785 + 0.809017i) q^{9} +O(q^{10})$	\(q+(-0.178502 + 1.12702i) q^{2} +(0.891007 + 0.453990i) q^{3} +(0.663811 + 0.215685i) q^{4} +(-0.670701 + 0.923140i) q^{6} +(-0.694338 - 1.36271i) q^{7} +(-1.39764 + 2.74302i) q^{8} +(0.587785 + 0.809017i) q^{9} +(1.00122 - 3.16189i) q^{11} +(0.493541 + 0.493541i) q^{12} +(5.09369 + 0.806762i) q^{13} +(1.65974 - 0.539283i) q^{14} +(-1.71260 - 1.24428i) q^{16} +(4.76995 - 0.755485i) q^{17} +(-1.01670 + 0.518032i) q^{18} +(1.65150 + 5.08279i) q^{19} -1.52941i q^{21} +(3.38478 + 1.69280i) q^{22} +(-4.97973 + 4.97973i) q^{23} +(-2.49061 + 1.80953i) q^{24} +(-1.81847 + 5.59667i) q^{26} +(0.156434 + 0.987688i) q^{27} +(-0.166992 - 1.05434i) q^{28} +(-0.562510 + 1.73123i) q^{29} +(-2.07975 + 1.51103i) q^{31} +(-2.64572 + 2.64572i) q^{32} +(2.32756 - 2.36272i) q^{33} +5.51066i q^{34} +(0.215685 + 0.663811i) q^{36} +(8.27261 - 4.21510i) q^{37} +(-6.02318 + 0.953978i) q^{38} +(4.17225 + 3.03132i) q^{39} +(-10.1057 + 3.28353i) q^{41} +(1.72367 + 0.273002i) q^{42} +(0.373613 + 0.373613i) q^{43} +(1.34660 - 1.88295i) q^{44} +(-4.72334 - 6.50112i) q^{46} +(-0.702519 + 1.37877i) q^{47} +(-0.961048 - 1.88616i) q^{48} +(2.73961 - 3.77075i) q^{49} +(4.59304 + 1.49237i) q^{51} +(3.20725 + 1.63417i) q^{52} +(1.75355 - 11.0715i) q^{53} -1.14106 q^{54} +4.70838 q^{56} +(-0.836043 + 5.27857i) q^{57} +(-1.85071 - 0.942986i) q^{58} +(-1.41843 - 0.460877i) q^{59} +(2.06914 - 2.84793i) q^{61} +(-1.33171 - 2.61364i) q^{62} +(0.694338 - 1.36271i) q^{63} +(-4.99806 - 6.87923i) q^{64} +(2.24735 + 3.04495i) q^{66} +(-0.161671 - 0.161671i) q^{67} +(3.32929 + 0.527308i) q^{68} +(-6.69772 + 2.17622i) q^{69} +(-1.37579 - 0.999573i) q^{71} +(-3.04066 + 0.481593i) q^{72} +(-2.78166 + 1.41733i) q^{73} +(3.27381 + 10.0758i) q^{74} +3.73022i q^{76} +(-5.00394 + 0.831042i) q^{77} +(-4.16110 + 4.16110i) q^{78} +(-1.71158 + 1.24354i) q^{79} +(-0.309017 + 0.951057i) q^{81} +(-1.89671 - 11.9753i) q^{82} +(1.10640 + 6.98551i) q^{83} +(0.329871 - 1.01524i) q^{84} +(-0.487759 + 0.354378i) q^{86} +(-1.28716 + 1.28716i) q^{87} +(7.27378 + 7.16554i) q^{88} -11.0867i q^{89} +(-2.43736 - 7.50142i) q^{91} +(-4.37965 + 2.23155i) q^{92} +(-2.53907 + 0.402149i) q^{93} +(-1.42850 - 1.03786i) q^{94} +(-3.55849 + 1.15622i) q^{96} +(-18.0446 - 2.85798i) q^{97} +(3.76067 + 3.76067i) q^{98} +(3.14653 - 1.04851i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 20 q^{7}+O(q^{10}) $ 96 * q + 20 * q^7	$ 96 q + 20 q^{7} + 8 q^{11} + 16 q^{12} + 8 q^{16} + 20 q^{17} + 32 q^{22} - 32 q^{23} + 60 q^{28} + 16 q^{31} + 16 q^{33} + 24 q^{36} - 8 q^{37} - 56 q^{38} - 120 q^{41} - 12 q^{42} - 200 q^{46} - 60 q^{47} - 48 q^{48} + 40 q^{51} - 40 q^{52} - 36 q^{53} - 80 q^{56} - 40 q^{57} - 44 q^{58} + 40 q^{61} - 80 q^{62} - 20 q^{63} + 56 q^{66} + 48 q^{67} - 80 q^{68} + 32 q^{71} + 60 q^{73} + 24 q^{77} + 96 q^{78} + 24 q^{81} - 32 q^{82} + 200 q^{83} - 80 q^{86} + 144 q^{88} + 56 q^{91} - 20 q^{92} + 72 q^{93} - 32 q^{97}+O(q^{100}) $ 96 * q + 20 * q^7 + 8 * q^11 + 16 * q^12 + 8 * q^16 + 20 * q^17 + 32 * q^22 - 32 * q^23 + 60 * q^28 + 16 * q^31 + 16 * q^33 + 24 * q^36 - 8 * q^37 - 56 * q^38 - 120 * q^41 - 12 * q^42 - 200 * q^46 - 60 * q^47 - 48 * q^48 + 40 * q^51 - 40 * q^52 - 36 * q^53 - 80 * q^56 - 40 * q^57 - 44 * q^58 + 40 * q^61 - 80 * q^62 - 20 * q^63 + 56 * q^66 + 48 * q^67 - 80 * q^68 + 32 * q^71 + 60 * q^73 + 24 * q^77 + 96 * q^78 + 24 * q^81 - 32 * q^82 + 200 * q^83 - 80 * q^86 + 144 * q^88 + 56 * q^91 - 20 * q^92 + 72 * q^93 - 32 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$376$	$551$	$727$
$\chi(n)$	$e\left(\frac{3}{10}\right)$	$1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−0.178502	+	1.12702i	−0.126220	+	0.796920i	0.840637	+	0.541600i	$0.182181\pi$
$2$	−0.178502	+	1.12702i	−0.126220	+	0.796920i	−0.966856	+	0.255321i	$0.917819\pi$
$3$	0.891007	+	0.453990i	0.514423	+	0.262112i
$3$	0.891007	+	0.453990i	0.514423	+	0.262112i
$4$	0.663811	+	0.215685i	0.331906	+	0.107843i
$5$		0			0
$5$		0			0
$6$	−0.670701	+	0.923140i	−0.273812	+	0.376870i
$7$	−0.694338	−	1.36271i	−0.262435	−	0.515058i	0.721761	−	0.692143i	$-0.243333\pi$
$7$	−0.694338	−	1.36271i	−0.262435	−	0.515058i	−0.984196	+	0.177085i	$0.943333\pi$
$8$	−1.39764	+	2.74302i	−0.494139	+	0.969803i
$9$	0.587785	+	0.809017i	0.195928	+	0.269672i
$10$		0			0
$11$	1.00122	−	3.16189i	0.301880	−	0.953346i
$11$	1.00122	−	3.16189i	0.301880	−	0.953346i
$12$	0.493541	+	0.493541i	0.142473	+	0.142473i
$13$	5.09369	+	0.806762i	1.41274	+	0.223756i	0.815708	−	0.578464i	$-0.196348\pi$
$13$	5.09369	+	0.806762i	1.41274	+	0.223756i	0.597029	+	0.802220i	$0.296348\pi$
$14$	1.65974	−	0.539283i	0.443585	−	0.144129i
$15$		0			0
$16$	−1.71260	−	1.24428i	−0.428150	−	0.311069i
$17$	4.76995	−	0.755485i	1.15688	−	0.183232i	0.451641	−	0.892200i	$-0.350839\pi$
$17$	4.76995	−	0.755485i	1.15688	−	0.183232i	0.705241	+	0.708968i	$0.250839\pi$
$18$	−1.01670	+	0.518032i	−0.239637	+	0.122101i
$19$	1.65150	+	5.08279i	0.378880	+	1.16607i	0.940823	+	0.338897i	$0.110054\pi$
$19$	1.65150	+	5.08279i	0.378880	+	1.16607i	−0.561944	+	0.827176i	$0.689946\pi$
$20$		0			0
$21$		−	1.52941i		−	0.333745i
$22$	3.38478	+	1.69280i	0.721638	+	0.360905i
$23$	−4.97973	+	4.97973i	−1.03834	+	1.03834i	−0.0391100	+	0.999235i	$0.512452\pi$
$23$	−4.97973	+	4.97973i	−1.03834	+	1.03834i	−0.999235	+	0.0391100i	$0.987548\pi$
$24$	−2.49061	+	1.80953i	−0.508393	+	0.369369i
$25$		0			0
$26$	−1.81847	+	5.59667i	−0.356631	+	1.09760i
$27$	0.156434	+	0.987688i	0.0301058	+	0.190081i
$28$	−0.166992	−	1.05434i	−0.0315585	−	0.199252i
$29$	−0.562510	+	1.73123i	−0.104456	+	0.321481i	−0.989602	−	0.143831i	$-0.954058\pi$
$29$	−0.562510	+	1.73123i	−0.104456	+	0.321481i	0.885147	+	0.465312i	$0.154058\pi$
$30$		0			0
$31$	−2.07975	+	1.51103i	−0.373535	+	0.271389i	−0.758675	−	0.651469i	$-0.774153\pi$
$31$	−2.07975	+	1.51103i	−0.373535	+	0.271389i	0.385140	+	0.922858i	$0.374153\pi$
$32$	−2.64572	+	2.64572i	−0.467702	+	0.467702i
$33$	2.32756	−	2.36272i	0.405177	−	0.411297i
$34$			5.51066i			0.945071i
$35$		0			0
$36$	0.215685	+	0.663811i	0.0359476	+	0.110635i
$37$	8.27261	−	4.21510i	1.36001	−	0.692959i	0.386645	−	0.922229i	$-0.373634\pi$
$37$	8.27261	−	4.21510i	1.36001	−	0.692959i	0.973363	+	0.229270i	$0.0736339\pi$
$38$	−6.02318	+	0.953978i	−0.977089	+	0.154756i
$39$	4.17225	+	3.03132i	0.668095	+	0.485400i
$40$		0			0
$41$	−10.1057	+	3.28353i	−1.57824	+	0.512801i	−0.961602	−	0.274448i	$-0.911505\pi$
$41$	−10.1057	+	3.28353i	−1.57824	+	0.512801i	−0.616636	+	0.787248i	$0.711505\pi$
$42$	1.72367	+	0.273002i	0.265968	+	0.0421252i
$43$	0.373613	+	0.373613i	0.0569755	+	0.0569755i	0.735020	−	0.678045i	$-0.237173\pi$
$43$	0.373613	+	0.373613i	0.0569755	+	0.0569755i	−0.678045	+	0.735020i	$0.737173\pi$
$44$	1.34660	−	1.88295i	0.203007	−	0.283865i
$45$		0			0
$46$	−4.72334	−	6.50112i	−0.696419	−	0.958538i
$47$	−0.702519	+	1.37877i	−0.102473	+	0.201115i	−0.936550	−	0.350533i	$-0.886001\pi$
$47$	−0.702519	+	1.37877i	−0.102473	+	0.201115i	0.834077	+	0.551647i	$0.186001\pi$
$48$	−0.961048	−	1.88616i	−0.138715	−	0.272244i
$49$	2.73961	−	3.77075i	0.391373	−	0.538679i
$50$		0			0
$51$	4.59304	+	1.49237i	0.643154	+	0.208973i
$52$	3.20725	+	1.63417i	0.444765	+	0.226619i
$53$	1.75355	−	11.0715i	0.240869	−	1.52079i	−0.509907	−	0.860230i	$-0.670320\pi$
$53$	1.75355	−	11.0715i	0.240869	−	1.52079i	0.750776	−	0.660557i	$-0.229680\pi$
$54$	−1.14106			−0.155279
$55$		0			0
$56$	4.70838			0.629184
$57$	−0.836043	+	5.27857i	−0.110737	+	0.699163i
$58$	−1.85071	−	0.942986i	−0.243011	−	0.123820i
$59$	−1.41843	−	0.460877i	−0.184664	−	0.0600011i	0.215225	−	0.976564i	$-0.430951\pi$
$59$	−1.41843	−	0.460877i	−0.184664	−	0.0600011i	−0.399889	+	0.916563i	$0.630951\pi$
$60$		0			0
$61$	2.06914	−	2.84793i	0.264926	−	0.364640i	−0.655742	−	0.754985i	$-0.727644\pi$
$61$	2.06914	−	2.84793i	0.264926	−	0.364640i	0.920669	+	0.390345i	$0.127644\pi$
$62$	−1.33171	−	2.61364i	−0.169128	−	0.331932i
$63$	0.694338	−	1.36271i	0.0874783	−	0.171686i
$64$	−4.99806	−	6.87923i	−0.624757	−	0.859904i
$65$		0			0
$66$	2.24735	+	3.04495i	0.276630	+	0.374807i
$67$	−0.161671	−	0.161671i	−0.0197513	−	0.0197513i	0.697162	−	0.716913i	$-0.254446\pi$
$67$	−0.161671	−	0.161671i	−0.0197513	−	0.0197513i	−0.716913	+	0.697162i	$0.754446\pi$
$68$	3.32929	+	0.527308i	0.403736	+	0.0639455i
$69$	−6.69772	+	2.17622i	−0.806311	+	0.261986i
$70$		0			0
$71$	−1.37579	−	0.999573i	−0.163277	−	0.118627i	0.503147	−	0.864201i	$-0.332176\pi$
$71$	−1.37579	−	0.999573i	−0.163277	−	0.118627i	−0.666423	+	0.745574i	$0.732176\pi$
$72$	−3.04066	+	0.481593i	−0.358345	+	0.0567563i
$73$	−2.78166	+	1.41733i	−0.325569	+	0.165886i	−0.609134	−	0.793067i	$-0.708483\pi$
$73$	−2.78166	+	1.41733i	−0.325569	+	0.165886i	0.283565	+	0.958953i	$0.408483\pi$
$74$	3.27381	+	10.0758i	0.380573	+	1.17128i
$75$		0			0
$76$			3.73022i			0.427886i
$77$	−5.00394	+	0.831042i	−0.570252	+	0.0947060i
$78$	−4.16110	+	4.16110i	−0.471152	+	0.471152i
$79$	−1.71158	+	1.24354i	−0.192568	+	0.139909i	−0.679892	−	0.733312i	$-0.737973\pi$
$79$	−1.71158	+	1.24354i	−0.192568	+	0.139909i	0.487323	+	0.873222i	$0.337973\pi$
$80$		0			0
$81$	−0.309017	+	0.951057i	−0.0343352	+	0.105673i
$82$	−1.89671	−	11.9753i	−0.209456	−	1.32246i
$83$	1.10640	+	6.98551i	0.121443	+	0.766759i	0.970968	+	0.239211i	$0.0768887\pi$
$83$	1.10640	+	6.98551i	0.121443	+	0.766759i	−0.849525	+	0.527548i	$0.823111\pi$
$84$	0.329871	−	1.01524i	0.0359919	−	0.110772i
$85$		0			0
$86$	−0.487759	+	0.354378i	−0.0525964	+	0.0382135i
$87$	−1.28716	+	1.28716i	−0.137998	+	0.137998i
$88$	7.27378	+	7.16554i	0.775387	+	0.763849i
$89$		−	11.0867i		−	1.17518i	−0.809158	−	0.587591i	$-0.800076\pi$
$89$		−	11.0867i		−	1.17518i	0.809158	−	0.587591i	$-0.199924\pi$
$90$		0			0
$91$	−2.43736	−	7.50142i	−0.255505	−	0.786362i
$92$	−4.37965	+	2.23155i	−0.456610	+	0.232655i
$93$	−2.53907	+	0.402149i	−0.263289	+	0.0417009i
$94$	−1.42850	−	1.03786i	−0.147338	−	0.107047i
$95$		0			0
$96$	−3.55849	+	1.15622i	−0.363186	+	0.118006i
$97$	−18.0446	−	2.85798i	−1.83215	−	0.290184i	−0.857594	−	0.514327i	$-0.828042\pi$
$97$	−18.0446	−	2.85798i	−1.83215	−	0.290184i	−0.974556	+	0.224143i	$0.928042\pi$
$98$	3.76067	+	3.76067i	0.379885	+	0.379885i
$99$	3.14653	−	1.04851i	0.316238	−	0.105379i
$100$		0			0
$101$	−1.50802	−	2.07561i	−0.150053	−	0.206531i	0.727373	−	0.686243i	$-0.240741\pi$
$101$	−1.50802	−	2.07561i	−0.150053	−	0.206531i	−0.877426	+	0.479712i	$0.840741\pi$
$102$	−2.50179	+	4.91003i	−0.247714	+	0.486166i
$103$	−1.94230	−	3.81197i	−0.191380	−	0.375605i	0.775300	−	0.631594i	$-0.217599\pi$
$103$	−1.94230	−	3.81197i	−0.191380	−	0.375605i	−0.966680	+	0.255989i	$0.917599\pi$
$104$	−9.33210	+	12.8445i	−0.915087	+	1.25951i
$105$		0			0
$106$	12.1647	+	3.95256i	1.18154	+	0.383907i
$107$	8.99672	+	4.58406i	0.869746	+	0.443157i	0.831118	−	0.556096i	$-0.187701\pi$
$107$	8.99672	+	4.58406i	0.869746	+	0.443157i	0.0386276	+	0.999254i	$0.487701\pi$
$108$	−0.109187	+	0.689379i	−0.0105065	+	0.0663356i
$109$	15.9895			1.53152			0.765758	−	0.643129i	$-0.222364\pi$
$109$	15.9895			1.53152			0.765758	+	0.643129i	$0.222364\pi$
$110$		0			0
$111$	9.28456			0.881252
$112$	−0.506471	+	3.19773i	−0.0478570	+	0.302157i
$113$	−6.36008	−	3.24062i	−0.598306	−	0.304852i	0.128484	−	0.991712i	$-0.458989\pi$
$113$	−6.36008	−	3.24062i	−0.598306	−	0.304852i	−0.726790	+	0.686859i	$0.758989\pi$
$114$	−5.79979	−	1.88447i	−0.543200	−	0.176496i
$115$		0			0
$116$	−0.746802	+	1.02788i	−0.0693388	+	0.0954367i
$117$	2.34131	+	4.59509i	0.216455	+	0.424816i
$118$	0.772609	−	1.51633i	0.0711244	−	0.139589i
$119$	−4.34147	−	5.97551i	−0.397981	−	0.547775i
$120$		0			0
$121$	−8.99511	−	6.33151i	−0.817737	−	0.575591i
$122$	2.84031	+	2.84031i	0.257150	+	0.257150i
$123$	−10.4949	−	1.66223i	−0.946293	−	0.149878i
$124$	−1.70647	+	0.554466i	−0.153246	+	0.0497925i
$125$		0			0
$126$	1.41186	+	1.02578i	0.125779	+	0.0913834i
$127$	−0.950634	+	0.150566i	−0.0843551	+	0.0133605i	−0.198469	−	0.980107i	$-0.563597\pi$
$127$	−0.950634	+	0.150566i	−0.0843551	+	0.0133605i	0.114114	+	0.993468i	$0.463597\pi$
$128$	1.97756	−	1.00762i	0.174793	−	0.0890617i
$129$	0.163275	+	0.502509i	0.0143756	+	0.0442435i
$130$		0			0
$131$			6.91325i			0.604013i	0.953306	+	0.302007i	$0.0976565\pi$
$131$			6.91325i			0.604013i	−0.953306	+	0.302007i	$0.902344\pi$
$132$	2.05467	−	1.06638i	0.178836	−	0.0928164i
$133$	5.77970	−	5.77970i	0.501163	−	0.501163i
$134$	0.211065	−	0.153348i	0.0182332	−	0.0132472i
$135$		0			0
$136$	−4.59434	+	14.1399i	−0.393962	+	1.21249i
$137$	−0.110994	−	0.700789i	−0.00948286	−	0.0598724i	0.982493	−	0.186299i	$-0.0596493\pi$
$137$	−0.110994	−	0.700789i	−0.00948286	−	0.0598724i	−0.991976	+	0.126426i	$0.959649\pi$
$138$	−1.25708	−	7.93689i	−0.107010	−	0.675633i
$139$	3.23794	−	9.96534i	0.274638	−	0.845249i	−0.714677	−	0.699455i	$-0.753426\pi$
$139$	3.23794	−	9.96534i	0.274638	−	0.845249i	0.989315	−	0.145794i	$-0.0465738\pi$
$140$		0			0
$141$	−1.25190	+	0.909558i	−0.105429	+	0.0765986i
$142$	1.37212	−	1.37212i	0.115145	−	0.115145i
$143$	7.65081	−	15.2980i	0.639793	−	1.27928i
$144$		−	2.11689i		−	0.176407i
$145$		0			0
$146$	−1.10082	−	3.38797i	−0.0911045	−	0.280391i
$147$	4.15290	−	2.11601i	0.342525	−	0.174525i
$148$	6.40059	−	1.01375i	0.526125	−	0.0833300i
$149$	−3.78796	−	2.75211i	−0.310322	−	0.225462i	0.421713	−	0.906729i	$-0.361429\pi$
$149$	−3.78796	−	2.75211i	−0.310322	−	0.225462i	−0.732035	+	0.681267i	$0.761429\pi$
$150$		0			0
$151$	17.1709	−	5.57917i	1.39735	−	0.454027i	0.489017	−	0.872274i	$-0.337355\pi$
$151$	17.1709	−	5.57917i	1.39735	−	0.454027i	0.908333	+	0.418247i	$0.137355\pi$
$152$	−16.2504	−	2.57381i	−1.31808	−	0.208763i
$153$	3.41490	+	3.41490i	0.276079	+	0.276079i
$154$	−0.0433847	−	5.78786i	−0.00349604	−	0.466399i
$155$		0			0
$156$	2.11578	+	2.91212i	0.169398	+	0.233156i
$157$	7.23471	−	14.1989i	0.577393	−	1.13320i	−0.398951	−	0.916972i	$-0.630625\pi$
$157$	7.23471	−	14.1989i	0.577393	−	1.13320i	0.976344	−	0.216225i	$-0.0693745\pi$
$158$	−1.09597	−	2.15096i	−0.0871905	−	0.171121i
$159$	6.58878	−	9.06868i	0.522524	−	0.719193i
$160$		0			0
$161$	10.2436	+	3.32833i	0.807306	+	0.262309i
$162$	−1.01670	−	0.518032i	−0.0798792	−	0.0407005i
$163$	−0.725442	+	4.58026i	−0.0568210	+	0.358754i	0.942853	+	0.333210i	$0.108132\pi$
$163$	−0.725442	+	4.58026i	−0.0568210	+	0.358754i	−0.999674	+	0.0255440i	$0.991868\pi$
$164$	−7.41646			−0.579128
$165$		0			0
$166$	−8.07027			−0.626374
$167$	−1.00552	+	6.34862i	−0.0778097	+	0.491271i	0.917751	+	0.397155i	$0.130003\pi$
$167$	−1.00552	+	6.34862i	−0.0778097	+	0.491271i	−0.995561	+	0.0941162i	$0.969997\pi$
$168$	4.19520	+	2.13756i	0.323667	+	0.164916i
$169$	12.9311	+	4.20158i	0.994702	+	0.323198i
$170$		0			0
$171$	−3.14134	+	4.32368i	−0.240224	+	0.330640i
$172$	0.167426	+	0.328592i	0.0127661	+	0.0250549i
$173$	0.868748	−	1.70501i	0.0660497	−	0.129630i	−0.855621	−	0.517603i	$-0.826825\pi$
$173$	0.868748	−	1.70501i	0.0660497	−	0.129630i	0.921671	+	0.387973i	$0.126825\pi$
$174$	−1.22089	−	1.68041i	−0.0925555	−	0.127392i
$175$		0			0
$176$	−5.64896	+	4.16926i	−0.425806	+	0.314270i
$177$	−1.05460	−	1.05460i	−0.0792686	−	0.0792686i
$178$	12.4948	+	1.97899i	0.936527	+	0.148331i
$179$	−7.59792	+	2.46871i	−0.567895	+	0.184520i	−0.578871	−	0.815419i	$-0.696506\pi$
$179$	−7.59792	+	2.46871i	−0.567895	+	0.184520i	0.0109754	+	0.999940i	$0.496506\pi$
$180$		0			0
$181$	−8.76400	−	6.36742i	−0.651423	−	0.473287i	0.212332	−	0.977197i	$-0.431894\pi$
$181$	−8.76400	−	6.36742i	−0.651423	−	0.473287i	−0.863756	+	0.503911i	$0.831894\pi$
$182$	8.88929	−	1.40793i	0.658918	−	0.104362i
$183$	3.13655	−	1.59815i	0.231860	−	0.118139i
$184$	−6.69963	−	20.6193i	−0.493903	−	1.52008i
$185$		0			0
$186$		−	2.93335i		−	0.215084i
$187$	2.38701	−	15.8385i	0.174555	−	1.15822i
$188$	−0.763721	+	0.763721i	−0.0557001	+	0.0557001i
$189$	1.23732	−	0.898965i	0.0900017	−	0.0653901i
$190$		0			0
$191$	4.71158	−	14.5007i	0.340918	−	1.04924i	−0.622815	−	0.782369i	$-0.714011\pi$
$191$	4.71158	−	14.5007i	0.340918	−	1.04924i	0.963733	−	0.266868i	$-0.0859889\pi$
$192$	−1.33019	−	8.39851i	−0.0959984	−	0.606110i
$193$	1.87221	+	11.8207i	0.134765	+	0.850872i	0.958748	+	0.284258i	$0.0917472\pi$
$193$	1.87221	+	11.8207i	0.134765	+	0.850872i	−0.823983	+	0.566615i	$0.808253\pi$
$194$	6.44198	−	19.8264i	0.462507	−	1.42345i
$195$		0			0
$196$	2.63188	−	1.91217i	0.187991	−	0.136584i
$197$	−11.1163	+	11.1163i	−0.792004	+	0.792004i	−0.981820	−	0.189816i	$-0.939211\pi$
$197$	−11.1163	+	11.1163i	−0.792004	+	0.792004i	0.189816	+	0.981820i	$0.439211\pi$
$198$	0.620024	+	3.73335i	0.0440632	+	0.265317i
$199$			21.5416i			1.52704i	0.645783	+	0.763521i	$0.276531\pi$
$199$			21.5416i			1.52704i	−0.645783	+	0.763521i	$0.723469\pi$
$200$		0			0
$201$	−0.0706530	−	0.217448i	−0.00498348	−	0.0153376i
$202$	2.60843	−	1.32906i	0.183528	−	0.0935124i
$203$	2.74974	−	0.435517i	0.192994	−	0.0305673i
$204$	2.72703	+	1.98130i	0.190930	+	0.138719i
$205$		0			0
$206$	4.64285	−	1.50855i	0.323483	−	0.105106i
$207$	−6.95569	−	1.10167i	−0.483454	−	0.0765716i
$208$	−7.71962	−	7.71962i	−0.535260	−	0.535260i
$209$	17.7248	−	0.132861i	1.22605	−	0.00919022i
$210$		0			0
$211$	−4.13145	−	5.68646i	−0.284421	−	0.391472i	0.642771	−	0.766058i	$-0.277785\pi$
$211$	−4.13145	−	5.68646i	−0.284421	−	0.391472i	−0.927192	+	0.374587i	$0.877785\pi$
$212$	3.55199	−	6.97117i	0.243952	−	0.478782i
$213$	−0.772045	−	1.51522i	−0.0528996	−	0.103821i
$214$	−6.77223	+	9.32118i	−0.462940	+	0.637183i
$215$		0			0
$216$	−2.92788	−	0.951327i	−0.199217	−	0.0647296i
$217$	3.50315	+	1.78495i	0.237810	+	0.121170i
$218$	−2.85415	+	18.0204i	−0.193308	+	1.22050i
$219$	−3.12193			−0.210961
$220$		0			0
$221$	24.9062			1.67537
$222$	−1.65731	+	10.4638i	−0.111231	+	0.702287i
$223$	−15.1020	−	7.69484i	−1.01130	−	0.515285i	−0.131850	−	0.991270i	$-0.542092\pi$
$223$	−15.1020	−	7.69484i	−1.01130	−	0.515285i	−0.879454	+	0.475985i	$0.842092\pi$
$224$	5.44239	+	1.76834i	0.363635	+	0.118152i
$225$		0			0
$226$	4.78752	−	6.58946i	0.318461	−	0.438324i
$227$	−6.23734	−	12.2415i	−0.413987	−	0.812495i	−0.999998	−	0.00219156i	$-0.999302\pi$
$227$	−6.23734	−	12.2415i	−0.413987	−	0.812495i	0.586011	−	0.810303i	$-0.300698\pi$
$228$	−1.69348	+	3.32365i	−0.112154	+	0.220114i
$229$	−12.1652	−	16.7439i	−0.803897	−	1.10647i	−0.992236	−	0.124365i	$-0.960310\pi$
$229$	−12.1652	−	16.7439i	−0.803897	−	1.10647i	0.188339	−	0.982104i	$-0.439690\pi$
$230$		0			0
$231$	−4.83583	−	1.53128i	−0.318174	−	0.100751i
$232$	−3.96261	−	3.96261i	−0.260158	−	0.260158i
$233$	−16.4801	−	2.61019i	−1.07965	−	0.170999i	−0.408821	−	0.912615i	$-0.634060\pi$
$233$	−16.4801	−	2.61019i	−1.07965	−	0.170999i	−0.670825	+	0.741615i	$0.734060\pi$
$234$	−5.59667	+	1.81847i	−0.365866	+	0.118877i
$235$		0			0
$236$	−0.842168	−	0.611871i	−0.0548205	−	0.0398294i
$237$	−2.08959	+	0.330958i	−0.135733	+	0.0214980i
$238$	7.50946	−	3.82626i	0.486766	−	0.248020i
$239$	0.433057	+	1.33281i	0.0280121	+	0.0862124i	0.964085	−	0.265593i	$-0.0855678\pi$
$239$	0.433057	+	1.33281i	0.0280121	+	0.0862124i	−0.936073	+	0.351806i	$0.885568\pi$
$240$		0			0
$241$			1.19156i			0.0767551i	0.999263	+	0.0383775i	$0.0122190\pi$
$241$			1.19156i			0.0767551i	−0.999263	+	0.0383775i	$0.987781\pi$
$242$	8.74135	−	9.00745i	0.561915	−	0.579021i
$243$	−0.707107	+	0.707107i	−0.0453609	+	0.0453609i
$244$	1.98777	−	1.44420i	0.127254	−	0.0924556i
$245$		0			0
$246$	3.74671	−	11.5312i	0.238882	−	0.735202i
$247$	4.31163	+	27.2226i	0.274342	+	1.73213i
$248$	−1.23804	−	7.81667i	−0.0786155	−	0.496359i
$249$	−2.18555	+	6.72643i	−0.138503	+	0.426270i
$250$		0			0
$251$	22.6893	−	16.4847i	1.43213	−	1.04051i	0.442521	−	0.896758i	$-0.354084\pi$
$251$	22.6893	−	16.4847i	1.43213	−	1.04051i	0.989614	−	0.143749i	$-0.0459157\pi$
$252$	0.754827	−	0.754827i	0.0475496	−	0.0475496i
$253$	10.7595	+	20.7312i	0.676447	+	1.30336i
$254$		−	1.09826i		−	0.0689107i
$255$		0			0
$256$	−4.47266	−	13.7654i	−0.279541	−	0.860340i
$257$	7.36549	−	3.75290i	0.459446	−	0.234100i	−0.208919	−	0.977933i	$-0.566994\pi$
$257$	7.36549	−	3.75290i	0.459446	−	0.234100i	0.668365	+	0.743833i	$0.266994\pi$
$258$	−0.595480	+	0.0943148i	−0.0370730	+	0.00587179i
$259$	−11.4880	−	8.34650i	−0.713827	−	0.518626i
$260$		0			0
$261$	−1.73123	+	0.562510i	−0.107160	+	0.0348185i
$262$	−7.79134	−	1.23403i	−0.481351	−	0.0762385i
$263$	−11.5967	−	11.5967i	−0.715083	−	0.715083i	0.252511	−	0.967594i	$-0.418744\pi$
$263$	−11.5967	−	11.5967i	−0.715083	−	0.715083i	−0.967594	+	0.252511i	$0.918744\pi$
$264$	3.22789	+	9.68677i	0.198663	+	0.596180i
$265$		0			0
$266$	5.48212	+	7.54550i	0.336131	+	0.462644i
$267$	5.03323	−	9.87828i	0.308029	−	0.604541i
$268$	−0.0724491	−	0.142189i	−0.00442554	−	0.00868560i
$269$	7.41230	−	10.2022i	0.451936	−	0.622036i	−0.520876	−	0.853632i	$-0.674395\pi$
$269$	7.41230	−	10.2022i	0.451936	−	0.622036i	0.972812	+	0.231596i	$0.0743947\pi$
$270$		0			0
$271$	5.44539	+	1.76932i	0.330784	+	0.107478i	0.469700	−	0.882826i	$-0.344362\pi$
$271$	5.44539	+	1.76932i	0.330784	+	0.107478i	−0.138916	+	0.990304i	$0.544362\pi$
$272$	−9.10904	−	4.64129i	−0.552317	−	0.281419i
$273$	1.23387	−	7.79035i	0.0746772	−	0.471493i
$274$	0.809613			0.0489105
$275$		0			0
$276$	−4.91540			−0.295872
$277$	2.75443	−	17.3908i	0.165498	−	1.04491i	−0.755444	−	0.655213i	$-0.772579\pi$
$277$	2.75443	−	17.3908i	0.165498	−	1.04491i	0.920942	−	0.389699i	$-0.127421\pi$
$278$	10.6531	+	5.42804i	0.638932	+	0.325552i
$279$	−2.44490	−	0.794395i	−0.146372	−	0.0475592i
$280$		0			0
$281$	−7.90740	+	10.8836i	−0.471716	+	0.649261i	−0.976887	−	0.213758i	$-0.931430\pi$
$281$	−7.90740	+	10.8836i	−0.471716	+	0.649261i	0.505171	+	0.863020i	$0.331430\pi$
$282$	−0.801620	−	1.57327i	−0.0477358	−	0.0936867i
$283$	−5.64529	+	11.0795i	−0.335578	+	0.658608i	−0.995709	−	0.0925422i	$-0.970501\pi$
$283$	−5.64529	+	11.0795i	−0.335578	+	0.658608i	0.660131	+	0.751150i	$0.270501\pi$
$284$	−0.697674	−	0.960266i	−0.0413994	−	0.0569813i
$285$		0			0
$286$	15.8754	+	11.3533i	0.938730	+	0.671334i
$287$	11.4912	+	11.4912i	0.678307	+	0.678307i
$288$	−3.69555	−	0.585317i	−0.217762	−	0.0344902i
$289$	6.01367	−	1.95396i	0.353746	−	0.114939i
$290$		0			0
$291$	−14.7803	−	10.7386i	−0.866439	−	0.629505i
$292$	−2.15220	+	0.340874i	−0.125948	+	0.0199482i
$293$	15.1593	−	7.72404i	0.885615	−	0.451243i	0.0488501	−	0.998806i	$-0.484444\pi$
$293$	15.1593	−	7.72404i	0.885615	−	0.451243i	0.836764	+	0.547563i	$0.184444\pi$
$294$	1.64347	+	5.05809i	0.0958493	+	0.294994i
$295$		0			0
$296$			28.5831i			1.66136i
$297$	3.27959	+	0.494266i	0.190301	+	0.0286802i
$298$	3.77783	−	3.77783i	0.218844	−	0.218844i
$299$	−29.3827	+	21.3478i	−1.69924	+	1.23457i
$300$		0			0
$301$	0.249715	−	0.768543i	0.0143933	−	0.0442981i
$302$	3.22278	+	20.3478i	0.185450	+	1.17088i
$303$	−0.401347	−	2.53401i	−0.0230568	−	0.145575i
$304$	3.49604	−	10.7597i	0.200512	−	0.617112i
$305$		0			0
$306$	−4.45822	+	3.23909i	−0.254859	+	0.185166i
$307$	3.41893	−	3.41893i	0.195128	−	0.195128i	−0.602779	−	0.797908i	$-0.705940\pi$
$307$	3.41893	−	3.41893i	0.195128	−	0.195128i	0.797908	+	0.602779i	$0.205940\pi$
$308$	−3.50092	−	0.527622i	−0.199483	−	0.0300641i
$309$		−	4.27827i		−	0.243382i
$310$		0			0
$311$	−4.08382	−	12.5687i	−0.231572	−	0.712706i	−0.997558	−	0.0698483i	$-0.977748\pi$
$311$	−4.08382	−	12.5687i	−0.231572	−	0.712706i	0.765985	−	0.642858i	$-0.222252\pi$
$312$	−14.1463	+	7.20788i	−0.800874	+	0.408066i
$313$	2.66537	−	0.422154i	0.150656	−	0.0238615i	−0.0806510	−	0.996742i	$-0.525700\pi$
$313$	2.66537	−	0.422154i	0.150656	−	0.0238615i	0.231307	+	0.972881i	$0.425700\pi$
$314$	14.7110	+	10.6882i	0.830190	+	0.603168i
$315$		0			0
$316$	−1.40438	+	0.456311i	−0.0790027	+	0.0256695i
$317$	4.11199	+	0.651276i	0.230953	+	0.0365793i	0.270838	−	0.962625i	$-0.412699\pi$
$317$	4.11199	+	0.651276i	0.230953	+	0.0365793i	−0.0398853	+	0.999204i	$0.512699\pi$
$318$	9.04443	+	9.04443i	0.507187	+	0.507187i
$319$	4.91076	+	3.51194i	0.274950	+	0.196631i
$320$		0			0
$321$	5.93502	+	8.16885i	0.331260	+	0.455941i
$322$	−5.57958	+	10.9505i	−0.310938	+	0.610250i
$323$	11.7175	+	22.9970i	0.651981	+	1.27959i
$324$	−0.410258	+	0.564672i	−0.0227921	+	0.0313706i
$325$		0			0
$326$	−5.03254	−	1.63517i	−0.278726	−	0.0905637i
$327$	14.2467	+	7.25908i	0.787847	+	0.401428i
$328$	5.11727	−	32.3092i	0.282554	−	1.78397i
$329$	2.36666			0.130478
$330$		0			0
$331$	−34.3521			−1.88816			−0.944082	−	0.329710i	$-0.893049\pi$
$331$	−34.3521			−1.88816			−0.944082	+	0.329710i	$0.893049\pi$
$332$	−0.772234	+	4.87569i	−0.0423818	+	0.267588i
$333$	8.27261	+	4.21510i	0.453336	+	0.230986i
$334$	−6.97551	−	2.26648i	−0.381683	−	0.124016i
$335$		0			0
$336$	−1.90301	+	2.61927i	−0.103818	+	0.142893i
$337$	−5.05306	−	9.91719i	−0.275258	−	0.540224i	0.711448	−	0.702738i	$-0.248040\pi$
$337$	−5.05306	−	9.91719i	−0.275258	−	0.540224i	−0.986706	+	0.162514i	$0.948040\pi$
$338$	−7.04347	+	13.8236i	−0.383114	+	0.751904i
$339$	−4.19566	−	5.77483i	−0.227877	−	0.313646i
$340$		0			0
$341$	2.69542	+	8.08883i	0.145965	+	0.438035i
$342$	−4.31212	−	4.31212i	−0.233173	−	0.233173i
$343$	−17.6147	−	2.78990i	−0.951106	−	0.150640i
$344$	−1.54700	+	0.502652i	−0.0834089	+	0.0271012i
$345$		0			0
$346$	1.76651	+	1.28344i	0.0949679	+	0.0689982i
$347$	8.37634	−	1.32668i	0.449665	−	0.0712200i	0.0725052	−	0.997368i	$-0.476901\pi$
$347$	8.37634	−	1.32668i	0.449665	−	0.0712200i	0.377160	+	0.926148i	$0.376901\pi$
$348$	−1.13205	+	0.576811i	−0.0606845	+	0.0309203i
$349$	10.7385	+	33.0498i	0.574820	+	1.76911i	0.636793	+	0.771035i	$0.280261\pi$
$349$	10.7385	+	33.0498i	0.574820	+	1.76911i	−0.0619732	+	0.998078i	$0.519739\pi$
$350$		0			0
$351$			5.15719i			0.275270i
$352$	5.71653	+	11.0144i	0.304692	+	0.587071i
$353$	−1.39846	+	1.39846i	−0.0744324	+	0.0744324i	−0.743343	−	0.668911i	$-0.766761\pi$
$353$	−1.39846	+	1.39846i	−0.0744324	+	0.0744324i	0.668911	+	0.743343i	$0.266761\pi$
$354$	1.37680	−	1.00030i	0.0731760	−	0.0531655i
$355$		0			0
$356$	2.39123	−	7.35945i	0.126735	−	0.390050i
$357$	−1.15545	−	7.29521i	−0.0611527	−	0.386103i
$358$	−1.42604	−	9.00364i	−0.0753684	−	0.475857i
$359$	1.56703	−	4.82281i	0.0827045	−	0.254538i	−0.901150	−	0.433507i	$-0.857276\pi$
$359$	1.56703	−	4.82281i	0.0827045	−	0.254538i	0.983855	+	0.178969i	$0.0572760\pi$
$360$		0			0
$361$	−7.73601	+	5.62054i	−0.407158	+	0.295818i
$362$	8.74057	−	8.74057i	0.459394	−	0.459394i
$363$	−5.14026	−	9.72511i	−0.269794	−	0.510436i
$364$		−	5.50523i		−	0.288552i
$365$		0			0
$366$	1.24126	+	3.82021i	0.0648818	+	0.199686i
$367$	−29.2526	+	14.9050i	−1.52697	+	0.778033i	−0.997525	−	0.0703089i	$-0.977602\pi$
$367$	−29.2526	+	14.9050i	−1.52697	+	0.778033i	−0.529450	+	0.848341i	$0.677602\pi$
$368$	14.7244	−	2.33212i	0.767564	−	0.121570i
$369$	−8.59638	−	6.24564i	−0.447510	−	0.325135i
$370$		0			0
$371$	−16.3048	+	5.29777i	−0.846505	+	0.275046i
$372$	−1.77220	−	0.280689i	−0.0918842	−	0.0145530i
$373$	−21.3362	−	21.3362i	−1.10475	−	1.10475i	−0.993830	−	0.110918i	$-0.964621\pi$
$373$	−21.3362	−	21.3362i	−1.10475	−	1.10475i	−0.110918	−	0.993830i	$-0.535379\pi$
$374$	17.4241	+	5.51739i	0.900979	+	0.285297i
$375$		0			0
$376$	−2.80013	−	3.85405i	−0.144406	−	0.198757i
$377$	−4.26195	+	8.36454i	−0.219501	+	0.430796i
$378$	0.792284	+	1.55494i	0.0407507	+	0.0799777i
$379$	−17.2174	+	23.6978i	−0.884400	+	1.21727i	0.0907827	+	0.995871i	$0.471063\pi$
$379$	−17.2174	+	23.6978i	−0.884400	+	1.21727i	−0.975183	+	0.221401i	$0.928937\pi$
$380$		0			0
$381$	−0.915376	−	0.297424i	−0.0468961	−	0.0152375i
$382$	15.5015	+	7.89843i	0.793128	+	0.404119i
$383$	3.46880	−	21.9012i	0.177248	−	1.11910i	−0.725276	−	0.688458i	$-0.758288\pi$
$383$	3.46880	−	21.9012i	0.177248	−	1.11910i	0.902524	−	0.430639i	$-0.141712\pi$
$384$	2.21947			0.113262
$385$		0			0
$386$	−13.6563			−0.695088
$387$	−0.0826552	+	0.521864i	−0.00420160	+	0.0265278i
$388$	−11.3618	−	5.78911i	−0.576807	−	0.293898i
$389$	−3.18340	−	1.03435i	−0.161405	−	0.0524437i	0.227200	−	0.973848i	$-0.427043\pi$
$389$	−3.18340	−	1.03435i	−0.161405	−	0.0524437i	−0.388605	+	0.921404i	$0.627043\pi$
$390$		0			0
$391$	−19.9909	+	27.5151i	−1.01098	+	1.39150i
$392$	6.51425	+	12.7849i	0.329019	+	0.645737i
$393$	−3.13855	+	6.15975i	−0.158319	+	0.310718i
$394$	−10.5440	−	14.5125i	−0.531197	−	0.731131i
$395$		0			0
$396$	2.31485	−	0.0173517i	0.116325	−	0.000871954i
$397$	13.1144	+	13.1144i	0.658193	+	0.658193i	0.954952	−	0.296759i	$-0.0959059\pi$
$397$	13.1144	+	13.1144i	0.658193	+	0.658193i	−0.296759	+	0.954952i	$0.595906\pi$
$398$	−24.2777	−	3.84521i	−1.21693	−	0.192743i
$399$	7.77368	−	2.52582i	0.389171	−	0.126449i
$400$		0			0
$401$	11.5293	+	8.37654i	0.575747	+	0.418305i	0.837188	−	0.546915i	$-0.184198\pi$
$401$	11.5293	+	8.37654i	0.575747	+	0.418305i	−0.261441	+	0.965219i	$0.584198\pi$
$402$	0.257678	−	0.0408123i	0.0128518	−	0.00203553i
$403$	−11.8127	+	6.01886i	−0.588431	+	0.299821i
$404$	−0.553361	−	1.70307i	−0.0275307	−	0.0847309i
$405$		0			0
$406$			3.17675i			0.157659i
$407$	−5.04499	−	30.3773i	−0.250071	−	1.50575i
$408$	−10.5130	+	10.5130i	−0.520471	+	0.520471i
$409$	−23.5669	+	17.1224i	−1.16531	+	0.846646i	−0.990440	−	0.137946i	$-0.955950\pi$
$409$	−23.5669	+	17.1224i	−1.16531	+	0.846646i	−0.174869	+	0.984592i	$0.555950\pi$
$410$		0			0
$411$	0.219255	−	0.674798i	0.0108151	−	0.0332853i
$412$	−0.467132	−	2.94935i	−0.0230139	−	0.145304i
$413$	0.356828	+	2.25293i	0.0175584	+	0.110859i
$414$	2.48321	−	7.64253i	0.122043	−	0.375610i
$415$		0			0
$416$	−15.6110	+	11.3420i	−0.765390	+	0.556088i
$417$	7.40919	−	7.40919i	0.362830	−	0.362830i
$418$	−3.01416	+	19.9998i	−0.147428	+	0.978222i
$419$			24.0358i			1.17423i	0.809505	+	0.587113i	$0.199735\pi$
$419$			24.0358i			1.17423i	−0.809505	+	0.587113i	$0.800265\pi$
$420$		0			0
$421$	5.17693	+	15.9330i	0.252308	+	0.776525i	0.994348	+	0.106169i	$0.0338584\pi$
$421$	5.17693	+	15.9330i	0.252308	+	0.776525i	−0.742040	+	0.670356i	$0.766142\pi$
$422$	7.14620	−	3.64117i	0.347871	−	0.177249i
$423$	−1.52838	+	0.242072i	−0.0743124	+	0.0117699i
$424$	27.9185	+	20.2840i	1.35584	+	0.985076i
$425$		0			0
$426$	1.84549	−	0.599637i	0.0894144	−	0.0290525i
$427$	−5.31759	−	0.842224i	−0.257336	−	0.0407581i
$428$	4.98341	+	4.98341i	0.240882	+	0.240882i
$429$	13.7621	−	10.1572i	0.664438	−	0.490394i
$430$		0			0
$431$	−16.3046	−	22.4413i	−0.785363	−	1.08096i	−0.994670	−	0.103110i	$-0.967121\pi$
$431$	−16.3046	−	22.4413i	−0.785363	−	1.08096i	0.209307	−	0.977850i	$-0.432879\pi$
$432$	0.961048	−	1.88616i	0.0462384	−	0.0907480i
$433$	12.9918	+	25.4978i	0.624344	+	1.22534i	0.959108	+	0.283042i	$0.0913435\pi$
$433$	12.9918	+	25.4978i	0.624344	+	1.22534i	−0.334764	+	0.942302i	$0.608656\pi$
$434$	−2.63698	+	3.62949i	−0.126579	+	0.174221i
$435$		0			0
$436$	10.6140	+	3.44870i	0.508319	+	0.165163i
$437$	−33.5349	−	17.0869i	−1.60419	−	0.817377i
$438$	0.557271	−	3.51847i	0.0266274	−	0.168119i
$439$	25.4805			1.21612			0.608059	−	0.793892i	$-0.291949\pi$
$439$	25.4805			1.21612			0.608059	+	0.793892i	$0.291949\pi$
$440$		0			0
$441$	4.66090			0.221948
$442$	−4.44579	+	28.0696i	−0.211465	+	1.33514i
$443$	15.9292	+	8.11633i	0.756819	+	0.385619i	0.789423	−	0.613850i	$-0.210380\pi$
$443$	15.9292	+	8.11633i	0.756819	+	0.385619i	−0.0326037	+	0.999468i	$0.510380\pi$
$444$	6.16320	+	2.00254i	0.292492	+	0.0950365i
$445$		0			0
$446$	11.3679	−	15.6466i	0.538288	−	0.740889i
$447$	−2.12566	−	4.17185i	−0.100540	−	0.197322i
$448$	−5.90409	+	11.5874i	−0.278942	+	0.547455i
$449$	−2.89649	−	3.98668i	−0.136694	−	0.188143i	0.735182	−	0.677870i	$-0.237097\pi$
$449$	−2.89649	−	3.98668i	−0.136694	−	0.188143i	−0.871876	+	0.489726i	$0.837097\pi$
$450$		0			0
$451$	0.264156	+	35.2405i	0.0124386	+	1.65941i
$452$	−3.52294	−	3.52294i	−0.165705	−	0.165705i
$453$	17.8323	+	2.82436i	0.837835	+	0.132700i
$454$	14.9097	−	4.84446i	0.699747	−	0.227362i
$455$		0			0
$456$	−13.3107	−	9.67080i	−0.623331	−	0.452877i
$457$	3.53972	−	0.560637i	0.165581	−	0.0262255i	−0.0730934	−	0.997325i	$-0.523287\pi$
$457$	3.53972	−	0.560637i	0.165581	−	0.0262255i	0.238674	+	0.971100i	$0.423287\pi$
$458$	21.0422	−	10.7215i	0.983236	−	0.500984i
$459$	1.49237	+	4.59304i	0.0696578	+	0.214385i
$460$		0			0
$461$		−	6.46205i		−	0.300968i	−0.988612	−	0.150484i	$-0.951917\pi$
$461$		−	6.46205i		−	0.300968i	0.988612	−	0.150484i	$-0.0480832\pi$
$462$	2.58898	−	5.17672i	0.120450	−	0.240843i
$463$	−8.69314	+	8.69314i	−0.404005	+	0.404005i	−0.879642	−	0.475637i	$-0.842218\pi$
$463$	−8.69314	+	8.69314i	−0.404005	+	0.404005i	0.475637	+	0.879642i	$0.342218\pi$
$464$	3.11748	−	2.26498i	0.144725	−	0.105149i
$465$		0			0
$466$	5.88345	−	18.1074i	0.272546	−	0.838809i
$467$	4.87697	+	30.7920i	0.225679	+	1.42488i	0.796912	+	0.604096i	$0.206466\pi$
$467$	4.87697	+	30.7920i	0.225679	+	1.42488i	−0.571232	+	0.820788i	$0.693534\pi$
$468$	0.563098	+	3.55526i	0.0260292	+	0.164342i
$469$	−0.108057	+	0.332566i	−0.00498963	+	0.0153565i
$470$		0			0
$471$	12.8924	−	9.36684i	0.594048	−	0.431601i
$472$	3.24665	−	3.24665i	0.149439	−	0.149439i
$473$	1.55539	−	0.807255i	0.0715171	−	0.0371176i
$474$		−	2.41407i		−	0.110882i
$475$		0			0
$476$	−1.59308	−	4.90300i	−0.0730188	−	0.224729i
$477$	9.98774	−	5.08901i	0.457307	−	0.233010i
$478$	−1.57940	+	0.250152i	−0.0722401	+	0.0114417i
$479$	28.8664	+	20.9727i	1.31894	+	0.958265i	0.999945	+	0.0105085i	$0.00334504\pi$
$479$	28.8664	+	20.9727i	1.31894	+	0.958265i	0.318994	+	0.947757i	$0.396655\pi$
$480$		0			0
$481$	45.5387	−	14.7964i	2.07639	−	0.674659i
$482$	−1.34291	−	0.212695i	−0.0611677	−	0.00968801i
$483$	7.61605	+	7.61605i	0.346542	+	0.346542i
$484$	−4.60544	−	6.14304i	−0.209338	−	0.279229i
$485$		0			0
$486$	−0.670701	−	0.923140i	−0.0304236	−	0.0418745i
$487$	−6.70725	+	13.1637i	−0.303934	+	0.596505i	−0.991573	−	0.129548i	$-0.958647\pi$
$487$	−6.70725	+	13.1637i	−0.303934	+	0.596505i	0.687639	+	0.726053i	$0.258647\pi$
$488$	4.92000	+	9.65605i	0.222718	+	0.437109i
$489$	−2.72577	+	3.75170i	−0.123264	+	0.169658i
$490$		0			0
$491$	−30.7738	−	9.99901i	−1.38880	−	0.451249i	−0.483249	−	0.875483i	$-0.660543\pi$
$491$	−30.7738	−	9.99901i	−1.38880	−	0.451249i	−0.905553	+	0.424234i	$0.860543\pi$
$492$	−6.60811	−	3.36700i	−0.297917	−	0.151796i
$493$	−1.37523	+	8.68284i	−0.0619371	+	0.391055i
$494$	−31.4499			−1.41500
$495$		0			0
$496$	5.44192			0.244350
$497$	−0.406867	+	2.56886i	−0.0182505	+	0.115229i
$498$	−7.19066	−	3.66383i	−0.322221	−	0.164180i
$499$	−22.6752	−	7.36761i	−1.01508	−	0.329819i	−0.246204	−	0.969218i	$-0.579183\pi$
$499$	−22.6752	−	7.36761i	−1.01508	−	0.329819i	−0.768875	+	0.639399i	$0.779183\pi$
$500$		0			0
$501$	−3.77814	+	5.20017i	−0.168795	+	0.232326i
$502$	14.5285	+	28.5137i	0.648438	+	1.27263i
$503$	6.56640	−	12.8873i	0.292781	−	0.574615i	−0.697023	−	0.717048i	$-0.745493\pi$
$503$	6.56640	−	12.8873i	0.292781	−	0.574615i	0.989804	+	0.142433i	$0.0454926\pi$
$504$	2.76752	+	3.80916i	0.123275	+	0.169674i
$505$		0			0
$506$	−25.2849	+	8.42563i	−1.12405	+	0.374565i
$507$	9.61424	+	9.61424i	0.426984	+	0.426984i
$508$	−0.663516	−	0.105091i	−0.0294388	−	0.00466264i
$509$	−27.4102	+	8.90613i	−1.21494	+	0.394757i	−0.845236	−	0.534394i	$-0.820540\pi$
$509$	−27.4102	+	8.90613i	−1.21494	+	0.394757i	−0.369702	+	0.929151i	$0.620540\pi$
$510$		0			0
$511$	3.86283	+	2.80651i	0.170881	+	0.124153i
$512$	20.6965	−	3.27801i	0.914666	−	0.144869i
$513$	−4.76186	+	2.42629i	−0.210241	+	0.107123i
$514$	2.91483	+	8.97092i	0.128568	+	0.395690i
$515$		0			0
$516$			0.368787i			0.0162350i
$517$	3.65615	+	3.60175i	0.160797	+	0.158405i
$518$	11.4573	−	11.4573i	0.503403	−	0.503403i
$519$	1.54812	−	1.12478i	0.0679550	−	0.0493722i
$520$		0			0
$521$	6.78813	−	20.8917i	0.297394	−	0.915283i	−0.685013	−	0.728531i	$-0.740204\pi$
$521$	6.78813	−	20.8917i	0.297394	−	0.915283i	0.982407	−	0.186753i	$-0.0597963\pi$
$522$	−0.324931	−	2.05153i	−0.0142218	−	0.0897931i
$523$	1.34203	+	8.47327i	0.0586831	+	0.370510i	0.999501	+	0.0315970i	$0.0100593\pi$
$523$	1.34203	+	8.47327i	0.0586831	+	0.370510i	−0.940818	+	0.338913i	$0.889941\pi$
$524$	−1.49109	+	4.58909i	−0.0651384	+	0.200475i
$525$		0			0
$526$	15.1397	−	10.9996i	0.660122	−	0.479607i
$527$	−8.77875	+	8.77875i	−0.382408	+	0.382408i
$528$	−6.92606	+	1.15026i	−0.301418	+	0.0500587i
$529$		−	26.5954i		−	1.15632i
$530$		0			0
$531$	−0.460877	−	1.41843i	−0.0200004	−	0.0615548i
$532$	5.08323	−	2.59003i	0.220386	−	0.112292i
$533$	−54.1241	+	8.57242i	−2.34438	+	0.371313i
$534$	10.2345	+	7.43582i	0.442892	+	0.321780i
$535$		0			0
$536$	0.669425	−	0.217509i	0.0289148	−	0.00939498i
$537$	−7.89057	−	1.24974i	−0.340503	−	0.0539304i
$538$	10.1749	+	10.1749i	0.438670	+	0.438670i
$539$	−9.17975	−	12.4377i	−0.395400	−	0.535730i
$540$		0			0
$541$	−11.0577	−	15.2196i	−0.475406	−	0.654340i	0.502208	−	0.864747i	$-0.332521\pi$
$541$	−11.0577	−	15.2196i	−0.475406	−	0.654340i	−0.977614	+	0.210407i	$0.932521\pi$
$542$	−2.96606	+	5.82122i	−0.127403	+	0.250043i
$543$	−4.91804	−	9.65219i	−0.211053	−	0.414215i
$544$	−10.6211	+	14.6187i	−0.455378	+	0.626774i
$545$		0			0
$546$	8.55960	+	2.78118i	0.366317	+	0.119024i
$547$	14.5409	+	7.40894i	0.621723	+	0.316783i	0.736325	−	0.676628i	$-0.236559\pi$
$547$	14.5409	+	7.40894i	0.621723	+	0.316783i	−0.114602	+	0.993411i	$0.536559\pi$
$548$	0.0774708	−	0.489131i	0.00330939	−	0.0208947i
$549$	3.52023			0.150240
$550$		0			0
$551$	−9.72846			−0.414447
$552$	3.39157	−	21.4135i	0.144355	−	0.911420i
$553$	2.88301	+	1.46897i	0.122598	+	0.0624667i
$554$	19.1080	+	6.20858i	0.811823	+	0.263777i
$555$		0			0
$556$	4.29876	−	5.91673i	0.182308	−	0.250925i
$557$	−17.7910	−	34.9168i	−0.753828	−	1.47947i	−0.873587	−	0.486668i	$-0.838212\pi$
$557$	−17.7910	−	34.9168i	−0.753828	−	1.47947i	0.119758	−	0.992803i	$-0.461788\pi$
$558$	1.33171	−	2.61364i	0.0563760	−	0.110644i
$559$	1.60166	+	2.20449i	0.0677428	+	0.0932400i
$560$		0			0
$561$	9.31735	−	13.0285i	0.393379	−	0.550063i
$562$	−10.8545	−	10.8545i	−0.457870	−	0.457870i
$563$	24.9534	+	3.95223i	1.05166	+	0.166567i	0.658253	−	0.752797i	$-0.271296\pi$
$563$	24.9534	+	3.95223i	1.05166	+	0.166567i	0.393408	+	0.919364i	$0.371296\pi$
$564$	−1.02720	+	0.333758i	−0.0432530	+	0.0140538i
$565$		0			0
$566$	−11.4791	−	8.34004i	−0.482502	−	0.350558i
$567$	1.51058	−	0.239253i	0.0634384	−	0.0100477i
$568$	4.66471	−	2.37679i	0.195727	−	0.0997277i
$569$	−6.03151	−	18.5631i	−0.252854	−	0.778205i	−0.994245	−	0.107131i	$-0.965833\pi$
$569$	−6.03151	−	18.5631i	−0.252854	−	0.778205i	0.741391	−	0.671074i	$-0.234167\pi$
$570$		0			0
$571$			36.8794i			1.54335i	0.636015	+	0.771677i	$0.280582\pi$
$571$			36.8794i			1.54335i	−0.636015	+	0.771677i	$0.719418\pi$
$572$	8.37824	−	8.50479i	0.350312	−	0.355603i
$573$	10.7812	−	10.7812i	0.450393	−	0.450393i
$574$	−15.0020	+	10.8996i	−0.626172	+	0.454941i
$575$		0			0
$576$	2.62763	−	8.08702i	0.109485	−	0.336959i
$577$	−1.59230	−	10.0534i	−0.0662884	−	0.418528i	−0.998409	−	0.0563813i	$-0.982044\pi$
$577$	−1.59230	−	10.0534i	−0.0662884	−	0.418528i	0.932121	−	0.362147i	$-0.117956\pi$
$578$	1.12869	+	7.12629i	0.0469475	+	0.296415i
$579$	−3.69833	+	11.3823i	−0.153697	+	0.473032i
$580$		0			0
$581$	8.75104	−	6.35800i	0.363054	−	0.263774i
$582$	14.7408	−	14.7408i	0.611027	−	0.611027i
$583$	−33.2512	−	16.6296i	−1.37712	−	0.688726i
$584$		−	9.61106i		−	0.397708i
$585$		0			0
$586$	5.99916	+	18.4635i	0.247823	+	0.762720i
$587$	27.6148	−	14.0705i	1.13979	−	0.580750i	0.220910	−	0.975294i	$-0.429097\pi$
$587$	27.6148	−	14.0705i	1.13979	−	0.580750i	0.918877	+	0.394544i	$0.129097\pi$
$588$	3.21313	−	0.508910i	0.132507	−	0.0209871i
$589$	−11.1150	−	8.07549i	−0.457984	−	0.332745i
$590$		0			0
$591$	−14.9514	+	4.85800i	−0.615018	+	0.199831i
$592$	−19.4124	−	3.07462i	−0.797845	−	0.126366i
$593$	14.3239	+	14.3239i	0.588212	+	0.588212i	0.937147	−	0.348935i	$-0.113457\pi$
$593$	14.3239	+	14.3239i	0.588212	+	0.588212i	−0.348935	+	0.937147i	$0.613457\pi$
$594$	−1.14246	+	3.60792i	−0.0468756	+	0.148035i
$595$		0			0
$596$	−1.92090	−	2.64389i	−0.0786832	−	0.108298i
$597$	−9.77967	+	19.1937i	−0.400255	+	0.785545i
$598$	−18.8144	−	36.9253i	−0.769378	−	1.50999i
$599$	−5.02516	+	6.91653i	−0.205322	+	0.282602i	−0.899243	−	0.437450i	$-0.855882\pi$
$599$	−5.02516	+	6.91653i	−0.205322	+	0.282602i	0.693921	+	0.720052i	$0.255882\pi$
$600$		0			0
$601$	−19.5570	−	6.35445i	−0.797746	−	0.259204i	−0.118347	−	0.992972i	$-0.537760\pi$
$601$	−19.5570	−	6.35445i	−0.797746	−	0.259204i	−0.679399	+	0.733769i	$0.737760\pi$
$602$	0.821585	+	0.418618i	0.0334853	+	0.0170616i
$603$	0.0357668	−	0.225823i	0.00145654	−	0.00919622i
$604$	12.6016			0.512752
$605$		0			0
$606$	2.92751			0.118922
$607$	−3.71230	+	23.4385i	−0.150678	+	0.951341i	0.790263	+	0.612768i	$0.209944\pi$
$607$	−3.71230	+	23.4385i	−0.150678	+	0.951341i	−0.940940	+	0.338572i	$0.890056\pi$
$608$	−17.8171	−	9.07824i	−0.722577	−	0.368171i
$609$	2.64776	+	0.860309i	0.107293	+	0.0348615i
$610$		0			0
$611$	−4.69076	+	6.45628i	−0.189768	+	0.261193i
$612$	1.53031	+	3.00340i	0.0618590	+	0.121405i
$613$	7.16345	−	14.0591i	0.289329	−	0.567840i	−0.699896	−	0.714245i	$-0.746770\pi$
$613$	7.16345	−	14.0591i	0.289329	−	0.567840i	0.989225	+	0.146405i	$0.0467702\pi$
$614$	3.24290	+	4.46347i	0.130873	+	0.180131i
$615$		0			0
$616$	4.71413	−	14.8874i	0.189938	−	0.599830i
$617$	3.71959	+	3.71959i	0.149745	+	0.149745i	0.778004	−	0.628259i	$-0.216232\pi$
$617$	3.71959	+	3.71959i	0.149745	+	0.149745i	−0.628259	+	0.778004i	$0.716232\pi$
$618$	4.82168	+	0.763679i	0.193956	+	0.0307197i
$619$	3.25418	−	1.05735i	0.130796	−	0.0424983i	−0.242887	−	0.970055i	$-0.578095\pi$
$619$	3.25418	−	1.05735i	0.130796	−	0.0424983i	0.373684	+	0.927556i	$0.378095\pi$
$620$		0			0
$621$	−5.69742	−	4.13942i	−0.228630	−	0.166109i
$622$	14.8941	−	2.35900i	0.597199	−	0.0945871i
$623$	−15.1079	+	7.69788i	−0.605287	+	0.308409i
$624$	−3.37360	−	10.3829i	−0.135052	−	0.415647i
$625$		0			0
$626$			3.07927i			0.123072i
$627$	15.8532	+	7.92849i	0.633115	+	0.316633i
$628$	7.86499	−	7.86499i	0.313847	−	0.313847i
$629$	36.2754	−	26.3556i	1.44640	−	1.05087i
$630$		0			0
$631$	−7.93923	+	24.4344i	−0.316056	+	0.972720i	0.659262	+	0.751913i	$0.270869\pi$
$631$	−7.93923	+	24.4344i	−0.316056	+	0.972720i	−0.975318	+	0.220806i	$0.929131\pi$
$632$	−1.01887	−	6.43292i	−0.0405287	−	0.255888i
$633$	−1.09955	−	6.94231i	−0.0437033	−	0.275932i
$634$	−1.46800	+	4.51803i	−0.0583016	+	0.179434i
$635$		0			0
$636$	6.32969	−	4.59879i	0.250988	−	0.182354i
$637$	16.9968	−	16.9968i	0.673439	−	0.673439i
$638$	−4.83459	+	4.90762i	−0.191403	+	0.194294i
$639$		−	1.70057i		−	0.0672737i
$640$		0			0
$641$	13.0377	+	40.1258i	0.514956	+	1.58487i	0.783362	+	0.621566i	$0.213503\pi$
$641$	13.0377	+	40.1258i	0.514956	+	1.58487i	−0.268405	+	0.963306i	$0.586497\pi$
$642$	−10.2658	+	5.23070i	−0.405160	+	0.206439i
$643$	30.6900	−	4.86082i	1.21030	−	0.191692i	0.481514	−	0.876438i	$-0.340087\pi$
$643$	30.6900	−	4.86082i	1.21030	−	0.191692i	0.728782	+	0.684746i	$0.240087\pi$
$644$	6.08192	+	4.41877i	0.239661	+	0.174124i
$645$		0			0
$646$	−28.0095	+	9.10085i	−1.10202	+	0.358068i
$647$	14.2373	+	2.25497i	0.559727	+	0.0886521i	0.429887	−	0.902883i	$-0.358553\pi$
$647$	14.2373	+	2.25497i	0.559727	+	0.0886521i	0.129840	+	0.991535i	$0.458553\pi$
$648$	−2.17687	−	2.17687i	−0.0855156	−	0.0855156i
$649$	−2.87741	+	4.02349i	−0.112948	+	0.157936i
$650$		0			0
$651$	2.31098	+	3.18080i	0.0905746	+	0.124665i
$652$	−1.46945	+	2.88396i	−0.0575482	+	0.112945i
$653$	7.46123	+	14.6435i	0.291980	+	0.573044i	0.989671	−	0.143355i	$-0.0457891\pi$
$653$	7.46123	+	14.6435i	0.291980	+	0.573044i	−0.697691	+	0.716399i	$0.745789\pi$
$654$	−10.7242	+	14.7606i	−0.419348	+	0.577183i
$655$		0			0
$656$	21.3925	+	6.95086i	0.835239	+	0.271385i
$657$	−2.78166	−	1.41733i	−0.108523	−	0.0552952i
$658$	−0.422453	+	2.66726i	−0.0164689	+	0.103981i
$659$	27.5121			1.07172			0.535860	−	0.844307i	$-0.319988\pi$
$659$	27.5121			1.07172			0.535860	+	0.844307i	$0.319988\pi$
$660$		0			0
$661$	47.5374			1.84899			0.924496	−	0.381193i	$-0.124487\pi$
$661$	47.5374			1.84899			0.924496	+	0.381193i	$0.124487\pi$
$662$	6.13192	−	38.7154i	0.238324	−	1.50472i
$663$	22.1915	+	11.3072i	0.861848	+	0.439134i
$664$	−20.7077	−	6.72834i	−0.803615	−	0.261110i
$665$		0			0
$666$	−6.22716	+	8.57095i	−0.241298	+	0.332118i
$667$	−5.81990	−	11.4222i	−0.225347	−	0.442269i
$668$	−2.03678	+	3.99741i	−0.0788055	+	0.154665i
$669$	−9.96258	−	13.7123i	−0.385176	−	0.530149i
$670$		0			0
$671$	−6.93317	−	9.39380i	−0.267652	−	0.362644i
$672$	4.04639	+	4.04639i	0.156093	+	0.156093i
$673$	−36.5676	−	5.79174i	−1.40958	−	0.223255i	−0.595194	−	0.803582i	$-0.702925\pi$
$673$	−36.5676	−	5.79174i	−1.40958	−	0.223255i	−0.814384	+	0.580327i	$0.802925\pi$
$674$	12.0788	−	3.92464i	0.465259	−	0.151172i
$675$		0			0
$676$	7.67761	+	5.57811i	0.295293	+	0.214543i
$677$	2.16419	−	0.342773i	0.0831764	−	0.0131739i	−0.114708	−	0.993399i	$-0.536593\pi$
$677$	2.16419	−	0.342773i	0.0831764	−	0.0131739i	0.197884	+	0.980225i	$0.436593\pi$
$678$	7.25726	−	3.69776i	0.278713	−	0.142012i
$679$	8.63443	+	26.5740i	0.331359	+	1.01982i
$680$		0			0
$681$		−	13.7389i		−	0.526477i
$682$	−9.59737	+	1.59391i	−0.367502	+	0.0610339i
$683$	8.84087	−	8.84087i	0.338286	−	0.338286i	−0.517436	−	0.855722i	$-0.673113\pi$
$683$	8.84087	−	8.84087i	0.338286	−	0.338286i	0.855722	+	0.517436i	$0.173113\pi$
$684$	−3.01781	+	2.19257i	−0.115389	+	0.0838349i
$685$		0			0
$686$	6.28852	−	19.3541i	0.240097	−	0.738942i
$687$	−3.23767	−	20.4418i	−0.123525	−	0.779904i
$688$	−0.174972	−	1.10473i	−0.00667074	−	0.0421174i
$689$	17.8641	−	54.9801i	0.680569	−	2.09458i
$690$		0			0
$691$	10.3561	−	7.52417i	0.393966	−	0.286233i	−0.373113	−	0.927786i	$-0.621710\pi$
$691$	10.3561	−	7.52417i	0.393966	−	0.286233i	0.767079	+	0.641553i	$0.221710\pi$
$692$	0.944432	−	0.944432i	0.0359019	−	0.0359019i
$693$	−3.61357	−	3.55980i	−0.137268	−	0.135226i
$694$			9.67708i			0.367337i
$695$		0			0
$696$	−1.73172	−	5.32969i	−0.0656408	−	0.202021i
$697$	−45.7228	+	23.2969i	−1.73187	+	0.882434i
$698$	−39.1644	+	6.20304i	−1.48240	+	0.234788i
$699$	−13.4989	−	9.80750i	−0.510574	−	0.370954i
$700$		0			0
$701$	−15.0984	+	4.90578i	−0.570260	+	0.185289i	−0.579932	−	0.814665i	$-0.696921\pi$
$701$	−15.0984	+	4.90578i	−0.570260	+	0.185289i	0.00967259	+	0.999953i	$0.496921\pi$
$702$	−5.81223	−	0.920567i	−0.219369	−	0.0347446i
$703$	35.0867	+	35.0867i	1.32332	+	1.32332i
$704$	−26.7555	+	8.91567i	−1.00839	+	0.336022i
$705$		0			0
$706$	−1.32646	−	1.82571i	−0.0499219	−	0.0687116i
$707$	−1.78139	+	3.49617i	−0.0669960	+	0.131487i
$708$	−0.472594	−	0.927517i	−0.0177612	−	0.0348582i
$709$	9.51797	−	13.1004i	0.357455	−	0.491995i	−0.591982	−	0.805951i	$-0.701655\pi$
$709$	9.51797	−	13.1004i	0.357455	−	0.491995i	0.949437	+	0.313956i	$0.101655\pi$
$710$		0			0
$711$	−2.01209	−	0.653767i	−0.0754592	−	0.0245182i
$712$	30.4109	+	15.4951i	1.13970	+	0.580704i
$713$	2.83209	−	17.8811i	0.106063	−	0.669653i
$714$	8.42806			0.315412
$715$		0			0
$716$	−5.57605			−0.208387
$717$	−0.219227	+	1.38415i	−0.00818720	+	0.0516919i
$718$	5.15567	+	2.62694i	0.192408	+	0.0980366i
$719$	11.5085	+	3.73935i	0.429196	+	0.139454i	0.515646	−	0.856802i	$-0.327552\pi$
$719$	11.5085	+	3.73935i	0.429196	+	0.139454i	−0.0864496	+	0.996256i	$0.527552\pi$
$720$		0			0
$721$	−3.84602	+	5.29359i	−0.143233	+	0.197144i
$722$	−4.95354	−	9.72188i	−0.184352	−	0.361811i
$723$	−0.540957	+	1.06169i	−0.0201184	+	0.0394846i
$724$	−4.44429	−	6.11703i	−0.165171	−	0.227338i
$725$		0			0
$726$	11.8779	−	4.05721i	0.440830	−	0.150577i
$727$	7.08408	+	7.08408i	0.262734	+	0.262734i	0.826164	−	0.563430i	$-0.190519\pi$
$727$	7.08408	+	7.08408i	0.262734	+	0.262734i	−0.563430	+	0.826164i	$0.690519\pi$
$728$	23.9831	+	3.79854i	0.888871	+	0.140783i
$729$	−0.951057	+	0.309017i	−0.0352243	+	0.0114451i
$730$		0			0
$731$	2.06438	+	1.49986i	0.0763537	+	0.0554742i
$732$	2.42677	−	0.384363i	0.0896962	−	0.0142065i
$733$	4.50478	−	2.29530i	0.166388	−	0.0847788i	−0.368813	−	0.929504i	$-0.620236\pi$
$733$	4.50478	−	2.29530i	0.166388	−	0.0847788i	0.535201	+	0.844725i	$0.320236\pi$
$734$	−11.5765	−	35.6287i	−0.427296	−	1.31508i
$735$		0			0
$736$		−	26.3499i		−	0.971271i
$737$	−0.673056	+	0.349318i	−0.0247923	+	0.0128673i
$738$	8.57340	−	8.57340i	0.315591	−	0.315591i
$739$	−15.2930	+	11.1110i	−0.562562	+	0.408725i	−0.832396	−	0.554182i	$-0.813031\pi$
$739$	−15.2930	+	11.1110i	−0.562562	+	0.408725i	0.269834	+	0.962907i	$0.413031\pi$
$740$		0			0
$741$	−8.51709	+	26.2129i	−0.312883	+	0.962956i
$742$	−3.06022	−	19.3215i	−0.112344	−	0.709314i
$743$	6.00526	+	37.9157i	0.220312	+	1.39099i	0.811450	+	0.584422i	$0.198679\pi$
$743$	6.00526	+	37.9157i	0.220312	+	1.39099i	−0.591138	+	0.806570i	$0.701321\pi$
$744$	2.44559	−	7.52676i	0.0896598	−	0.275944i
$745$		0			0
$746$	27.8548	−	20.2377i	1.01984	−	0.740955i
$747$	−5.00107	+	5.00107i	−0.182980	+	0.182980i
$748$	5.00065	−	9.99891i	0.182842	−	0.365596i
$749$		−	15.4428i		−	0.564269i
$750$		0			0
$751$	−15.8889	−	48.9010i	−0.579794	−	1.78442i	−0.619240	−	0.785202i	$-0.712559\pi$
$751$	−15.8889	−	48.9010i	−0.579794	−	1.78442i	0.0394461	−	0.999222i	$-0.487441\pi$
$752$	2.91871	−	1.48716i	0.106434	−	0.0542310i
$753$	27.7002	−	4.38728i	1.00945	−	0.159881i
$754$	−8.66621	−	6.29637i	−0.315605	−	0.229300i
$755$		0			0
$756$	1.01524	−	0.329871i	0.0369239	−	0.0119973i
$757$	11.4556	+	1.81438i	0.416360	+	0.0659449i	0.361100	−	0.932527i	$-0.382401\pi$
$757$	11.4556	+	1.81438i	0.416360	+	0.0659449i	0.0552598	+	0.998472i	$0.482401\pi$
$758$	−23.6344	−	23.6344i	−0.858440	−	0.858440i
$759$	0.175075	+	23.3563i	0.00635481	+	0.847781i
$760$		0			0
$761$	14.5038	+	19.9627i	0.525761	+	0.723648i	0.986477	−	0.163900i	$-0.0524073\pi$
$761$	14.5038	+	19.9627i	0.525761	+	0.723648i	−0.460716	+	0.887548i	$0.652407\pi$
$762$	0.498597	−	0.978553i	0.0180623	−	0.0354492i
$763$	−11.1021	−	21.7891i	−0.401924	−	0.788819i
$764$	6.25520	−	8.60954i	0.226305	−	0.311482i
$765$		0			0
$766$	24.0638	+	7.81879i	0.869459	+	0.282504i
$767$	−6.85325	−	3.49191i	−0.247457	−	0.126085i
$768$	2.26421	−	14.2956i	0.0817026	−	0.515850i
$769$	1.44960			0.0522737			0.0261369	−	0.999658i	$-0.491679\pi$
$769$	1.44960			0.0522737			0.0261369	+	0.999658i	$0.491679\pi$
$770$		0			0
$771$	8.26648			0.297710
$772$	−1.30675	+	8.25052i	−0.0470311	+	0.296943i
$773$	16.6690	+	8.49326i	0.599541	+	0.305481i	0.727296	−	0.686324i	$-0.240777\pi$
$773$	16.6690	+	8.49326i	0.599541	+	0.305481i	−0.127754	+	0.991806i	$0.540777\pi$
$774$	−0.573395	−	0.186307i	−0.0206103	−	0.00669668i
$775$		0			0
$776$	33.0593	−	45.5022i	1.18676	−	1.63343i
$777$	−6.44662	−	12.6522i	−0.231271	−	0.453895i
$778$	1.73397	−	3.40311i	0.0621660	−	0.122008i
$779$	−33.3790	−	45.9422i	−1.19593	−	1.64605i
$780$		0			0
$781$	−4.53801	+	3.34932i	−0.162383	+	0.119848i
$782$	−27.4416	−	27.4416i	−0.981309	−	0.981309i
$783$	−1.79791	−	0.284761i	−0.0642521	−	0.0101765i
$784$	−9.38371	+	3.04895i	−0.335133	+	0.108891i
$785$		0			0
$786$	−6.38190	−	4.63672i	−0.227635	−	0.165386i
$787$	−47.3293	+	7.49622i	−1.68711	+	0.267211i	−0.924925	−	0.380151i	$-0.875872\pi$
$787$	−47.3293	+	7.49622i	−1.68711	+	0.267211i	−0.762182	+	0.647362i	$0.775872\pi$
$788$	−9.77675	+	4.98150i	−0.348282	+	0.177459i
$789$	−5.06794	−	15.5975i	−0.180424	−	0.555287i
$790$		0			0
$791$			10.9171i			0.388166i
$792$	−1.52163	+	10.0964i	−0.0540687	+	0.358760i
$793$	12.8372	−	12.8372i	0.455861	−	0.455861i
$794$	−17.1211	+	12.4392i	−0.607604	+	0.441450i
$795$		0			0
$796$	−4.64620	+	14.2995i	−0.164680	+	0.506834i
$797$	1.01261	+	6.39340i	0.0358686	+	0.226466i	0.999110	−	0.0421702i	$-0.0134272\pi$
$797$	1.01261	+	6.39340i	0.0358686	+	0.226466i	−0.963242	+	0.268636i	$0.913427\pi$
$798$	1.45902	+	9.21192i	0.0516489	+	0.326098i
$799$	−2.30934	+	7.10741i	−0.0816985	+	0.251442i
$800$		0			0
$801$	8.96929	−	6.51657i	0.316914	−	0.230252i
$802$	−11.4985	+	11.4985i	−0.406026	+	0.406026i
$803$	1.69638	+	10.2144i	0.0598639	+	0.360458i
$804$		−	0.159583i		−	0.00562806i
$805$		0			0
$806$	−4.67476	−	14.3874i	−0.164662	−	0.506776i
$807$	11.2361	−	5.72507i	0.395529	−	0.201532i
$808$	7.80109	−	1.23557i	0.274442	−	0.0434673i
$809$	6.35210	+	4.61507i	0.223328	+	0.162257i	0.693823	−	0.720145i	$-0.255925\pi$
$809$	6.35210	+	4.61507i	0.223328	+	0.162257i	−0.470496	+	0.882402i	$0.655925\pi$
$810$		0			0
$811$	10.7006	−	3.47684i	0.375749	−	0.122088i	−0.115053	−	0.993359i	$-0.536704\pi$
$811$	10.7006	−	3.47684i	0.375749	−	0.122088i	0.490802	+	0.871271i	$0.336704\pi$
$812$	1.91925	+	0.303979i	0.0673523	+	0.0106676i
$813$	4.04863	+	4.04863i	0.141992	+	0.141992i
$814$	35.1363	−	0.263375i	1.23153	−	0.00923129i
$815$		0			0
$816$	−6.00911	−	8.27084i	−0.210361	−	0.289537i
$817$	−1.28198	+	2.51602i	−0.0448507	+	0.0880245i
$818$	−15.0904	−	29.6166i	−0.527625	−	1.03552i
$819$	4.63613	−	6.38109i	0.162000	−	0.222973i
$820$		0			0
$821$	−0.129033	−	0.0419254i	−0.00450329	−	0.00146321i	0.306764	−	0.951785i	$-0.400754\pi$
$821$	−0.129033	−	0.0419254i	−0.00450329	−	0.00146321i	−0.311268	+	0.950322i	$0.600754\pi$
$822$	0.721370	+	0.367557i	0.0251607	+	0.0128200i
$823$	−1.96582	+	12.4117i	−0.0685243	+	0.432646i	0.929446	+	0.368959i	$0.120286\pi$
$823$	−1.96582	+	12.4117i	−0.0685243	+	0.432646i	−0.997970	+	0.0636865i	$0.979714\pi$
$824$	13.1709			0.458831
$825$		0			0
$826$	−2.60278			−0.0905622
$827$	−6.55948	+	41.4149i	−0.228096	+	1.44014i	0.561991	+	0.827143i	$0.310036\pi$
$827$	−6.55948	+	41.4149i	−0.228096	+	1.44014i	−0.790086	+	0.612995i	$0.789964\pi$
$828$	−4.37965	−	2.23155i	−0.152203	−	0.0775516i
$829$	−0.734919	−	0.238790i	−0.0255248	−	0.00829351i	0.296227	−	0.955118i	$-0.404272\pi$
$829$	−0.734919	−	0.238790i	−0.0255248	−	0.00829351i	−0.321752	+	0.946824i	$0.604272\pi$
$830$		0			0
$831$	10.3495	−	14.2448i	0.359019	−	0.494148i
$832$	−19.9087	−	39.0730i	−0.690209	−	1.35461i
$833$	10.2190	−	20.0560i	0.354069	−	0.694900i
$834$	7.02772	+	9.67283i	0.243350	+	0.334943i
$835$		0			0
$836$	11.7945	+	3.73478i	0.407923	+	0.129170i
$837$	−1.81777	−	1.81777i	−0.0628314	−	0.0628314i
$838$	−27.0887	−	4.29043i	−0.935764	−	0.148210i
$839$	−30.3509	+	9.86162i	−1.04783	+	0.340461i	−0.781817	−	0.623508i	$-0.785707\pi$
$839$	−30.3509	+	9.86162i	−1.04783	+	0.340461i	−0.266014	+	0.963969i	$0.585707\pi$
$840$		0			0
$841$	20.7808	+	15.0981i	0.716578	+	0.520624i
$842$	−18.8808	+	2.99042i	−0.650675	+	0.103057i
$843$	−11.9866	+	6.10748i	−0.412840	+	0.210353i
$844$	−1.51602	−	4.66583i	−0.0521835	−	0.160604i
$845$		0			0
$846$		−	1.76572i		−	0.0607067i
$847$	−2.38239	+	16.6540i	−0.0818599	+	0.572237i
$848$	−16.7791	+	16.7791i	−0.576198	+	0.576198i
$849$	−10.0600	+	7.30900i	−0.345258	+	0.250844i
$850$		0			0
$851$	−20.2053	+	62.1854i	−0.692627	+	2.13169i
$852$	−0.185681	−	1.17234i	−0.00636131	−	0.0401637i
$853$	3.38848	+	21.3940i	0.116019	+	0.732517i	0.975279	+	0.220977i	$0.0709247\pi$
$853$	3.38848	+	21.3940i	0.116019	+	0.732517i	−0.859260	+	0.511540i	$0.829075\pi$
$854$	1.89840	−	5.84267i	0.0649619	−	0.199932i
$855$		0			0
$856$	−25.1483	+	18.2713i	−0.859551	+	0.624500i
$857$	−20.0724	+	20.0724i	−0.685660	+	0.685660i	−0.961270	−	0.275610i	$-0.911120\pi$
$857$	−20.0724	+	20.0724i	−0.685660	+	0.685660i	0.275610	+	0.961270i	$0.411120\pi$
$858$	8.99076	+	17.3231i	0.306940	+	0.591402i
$859$		−	42.2029i		−	1.43994i	−0.694003	−	0.719972i	$-0.744154\pi$
$859$		−	42.2029i		−	1.43994i	0.694003	−	0.719972i	$-0.255846\pi$
$860$		0			0
$861$	5.02186	+	15.4557i	0.171144	+	0.526729i
$862$	28.2021	−	14.3697i	0.960568	−	0.489434i
$863$	−4.31065	+	0.682739i	−0.146736	+	0.0232407i	−0.229370	−	0.973339i	$-0.573667\pi$
$863$	−4.31065	+	0.682739i	−0.146736	+	0.0232407i	0.0826342	+	0.996580i	$0.473667\pi$
$864$	−3.02703	−	2.19927i	−0.102982	−	0.0748205i
$865$		0			0
$866$	−31.0554	+	10.0905i	−1.05531	+	0.342890i
$867$	6.24530	+	0.989159i	0.212102	+	0.0335936i
$868$	1.94045	+	1.94045i	0.0658630	+	0.0658630i
$869$	2.21826	+	6.65690i	0.0752493	+	0.225820i
$870$		0			0
$871$	−0.693074	−	0.953935i	−0.0234839	−	0.0323229i
$872$	−22.3475	+	43.8595i	−0.756782	+	1.48527i
$873$	−8.29419	−	16.2783i	−0.280716	−	0.550936i
$874$	25.2433	−	34.7444i	0.853866	−	1.17525i
$875$		0			0
$876$	−2.07238	−	0.673355i	−0.0700191	−	0.0227506i
$877$	−40.6149	−	20.6943i	−1.37147	−	0.698797i	−0.395858	−	0.918312i	$-0.629553\pi$
$877$	−40.6149	−	20.6943i	−1.37147	−	0.698797i	−0.975609	+	0.219514i	$0.929553\pi$
$878$	−4.54831	+	28.7169i	−0.153498	+	0.969149i
$879$	17.0137			0.573856
$880$		0			0
$881$	−4.08780			−0.137721			−0.0688607	−	0.997626i	$-0.521936\pi$
$881$	−4.08780			−0.137721			−0.0688607	+	0.997626i	$0.521936\pi$
$882$	−0.831980	+	5.25291i	−0.0280142	+	0.176875i
$883$	−0.352882	−	0.179803i	−0.0118754	−	0.00605084i	0.448043	−	0.894012i	$-0.352121\pi$
$883$	−0.352882	−	0.179803i	−0.0118754	−	0.00605084i	−0.459918	+	0.887961i	$0.652121\pi$
$884$	16.5330	+	5.37189i	0.556064	+	0.180676i
$885$		0			0
$886$	−11.9906	+	16.5037i	−0.402833	+	0.554452i
$887$	−10.7322	−	21.0632i	−0.360353	−	0.707233i	0.637655	−	0.770322i	$-0.279905\pi$
$887$	−10.7322	−	21.0632i	−0.360353	−	0.707233i	−0.998008	+	0.0630894i	$0.979905\pi$
$888$	−12.9764	+	25.4677i	−0.435461	+	0.854640i
$889$	0.865239	+	1.19090i	0.0290192	+	0.0399415i
$890$		0			0
$891$	2.69774	+	1.92930i	0.0903778	+	0.0646339i
$892$	−8.36520	−	8.36520i	−0.280088	−	0.280088i
$893$	−8.16822	−	1.29372i	−0.273339	−	0.0432927i
$894$	5.08118	−	1.65097i	0.169940	−	0.0552168i
$895$		0			0
$896$	−2.74619	−	1.99523i	−0.0917438	−	0.0666558i
$897$	−35.8718	+	5.68154i	−1.19773	+	0.189701i
$898$	5.01008	−	2.55277i	0.167189	−	0.0851869i
$899$	−1.44606	−	4.45050i	−0.0482286	−	0.148432i
$900$		0			0
$901$		−	54.1352i		−	1.80351i
$902$	−39.7638	−	5.99279i	−1.32399	−	0.199538i
$903$	0.571408	−	0.571408i	0.0190153	−	0.0190153i
$904$	17.7782	−	12.9166i	0.591293	−	0.429600i
$905$		0			0
$906$	−6.36620	+	19.5931i	−0.211503	+	0.650938i
$907$	3.25040	+	20.5222i	0.107928	+	0.681429i	0.981025	+	0.193883i	$0.0621081\pi$
$907$	3.25040	+	20.5222i	0.107928	+	0.681429i	−0.873097	+	0.487547i	$0.837892\pi$
$908$	−1.50011	−	9.47133i	−0.0497829	−	0.314317i
$909$	0.792812	−	2.44003i	0.0262959	−	0.0809305i
$910$		0			0
$911$	31.2914	−	22.7346i	1.03673	−	0.753229i	0.0670864	−	0.997747i	$-0.478630\pi$
$911$	31.2914	−	22.7346i	1.03673	−	0.753229i	0.969645	+	0.244518i	$0.0786297\pi$
$912$	7.99980	−	7.99980i	0.264900	−	0.264900i
$913$	23.1952	+	3.49574i	0.767648	+	0.115692i
$914$			4.08940i			0.135265i
$915$		0			0
$916$	−4.46396	−	13.7387i	−0.147493	−	0.453938i
$917$	9.42079	−	4.80013i	0.311102	−	0.158514i
$918$	−5.44282	+	0.862057i	−0.179640	+	0.0284521i
$919$	12.4240	+	9.02653i	0.409828	+	0.297758i	0.773532	−	0.633757i	$-0.218488\pi$
$919$	12.4240	+	9.02653i	0.409828	+	0.297758i	−0.363704	+	0.931515i	$0.618488\pi$
$920$		0			0
$921$	4.59845	−	1.49413i	0.151524	−	0.0492331i
$922$	7.28284	+	1.15349i	0.239847	+	0.0379881i
$923$	−6.20146	−	6.20146i	−0.204123	−	0.204123i
$924$	−2.87980	−	2.05950i	−0.0947386	−	0.0677525i
$925$		0			0
$926$	−8.24557	−	11.3490i	−0.270966	−	0.372953i
$927$	1.94230	−	3.81197i	0.0637934	−	0.125202i
$928$	−3.09210	−	6.06859i	−0.101503	−	0.199211i
$929$	−30.4150	+	41.8626i	−0.997882	+	1.37347i	−0.0712667	+	0.997457i	$0.522704\pi$
$929$	−30.4150	+	41.8626i	−0.997882	+	1.37347i	−0.926616	+	0.376010i	$0.877296\pi$
$930$		0			0
$931$	23.6904	+	7.69748i	0.776422	+	0.252275i
$932$	−10.3767	−	5.28719i	−0.339900	−	0.173188i
$933$	2.06736	−	13.0528i	0.0676825	−	0.427330i
$934$	−35.5736			−1.16400
$935$		0			0
$936$	−15.8767			−0.518947
$937$	2.22128	−	14.0246i	0.0725659	−	0.458163i	−0.924472	−	0.381250i	$-0.875494\pi$
$937$	2.22128	−	14.0246i	0.0725659	−	0.458163i	0.997038	−	0.0769129i	$-0.0245063\pi$
$938$	−0.355519	−	0.181146i	−0.0116081	−	0.00591463i
$939$	2.56652	+	0.833912i	0.0837552	+	0.0272137i
$940$		0			0
$941$	−1.00940	+	1.38932i	−0.0329054	+	0.0452904i	−0.825153	−	0.564910i	$-0.808911\pi$
$941$	−1.00940	+	1.38932i	−0.0329054	+	0.0452904i	0.792247	+	0.610200i	$0.208911\pi$
$942$	8.25527	+	16.2019i	0.268971	+	0.527886i
$943$	33.9723	−	66.6745i	1.10629	−	2.17122i
$944$	1.85575	+	2.55422i	0.0603995	+	0.0831328i
$945$		0			0
$946$	0.632149	+	1.89705i	0.0205529	+	0.0616785i
$947$	−36.4494	−	36.4494i	−1.18444	−	1.18444i	−0.978581	−	0.205864i	$-0.933999\pi$
$947$	−36.4494	−	36.4494i	−1.18444	−	1.18444i	−0.205864	−	0.978581i	$-0.566001\pi$
$948$	−1.45847	−	0.231000i	−0.0473691	−	0.00750252i
$949$	−15.3124	+	4.97530i	−0.497061	+	0.161505i
$950$		0			0
$951$	3.36814	+	2.44710i	0.109219	+	0.0793525i
$952$	22.4587	−	3.55711i	0.727892	−	0.115287i
$953$	28.7053	−	14.6261i	0.929856	−	0.473785i	0.0776436	−	0.996981i	$-0.475260\pi$
$953$	28.7053	−	14.6261i	0.929856	−	0.473785i	0.852213	+	0.523196i	$0.175260\pi$
$954$	3.95256	+	12.1647i	0.127969	+	0.393848i
$955$		0			0
$956$			0.978139i			0.0316353i
$957$	2.78113	+	5.35860i	0.0899012	+	0.173219i
$958$	−28.7892	+	28.7892i	−0.930137	+	0.930137i
$959$	−0.877908	+	0.637837i	−0.0283491	+	0.0205968i
$960$		0			0
$961$	−7.53736	+	23.1976i	−0.243141	+	0.748310i
$962$	8.54706	+	53.9640i	0.275568	+	1.73987i
$963$	1.57956	+	9.97294i	0.0509006	+	0.321373i
$964$	−0.257002	+	0.790971i	−0.00827748	+	0.0254755i
$965$		0			0
$966$	−9.94288	+	7.22393i	−0.319907	+	0.232426i
$967$	42.0426	−	42.0426i	1.35200	−	1.35200i	0.468574	−	0.883424i	$-0.344768\pi$
$967$	42.0426	−	42.0426i	1.35200	−	1.35200i	0.883424	−	0.468574i	$-0.155232\pi$
$968$	29.9393	−	15.8246i	0.962286	−	0.508622i
$969$			25.8101i			0.829140i
$970$		0			0
$971$	11.6094	+	35.7301i	0.372564	+	1.14664i	0.945107	+	0.326760i	$0.105957\pi$
$971$	11.6094	+	35.7301i	0.372564	+	1.14664i	−0.572543	+	0.819875i	$0.694043\pi$
$972$	−0.621898	+	0.316873i	−0.0199474	+	0.0101637i
$973$	−15.8281	+	2.50693i	−0.507427	+	0.0803685i
$974$	−13.6385	−	9.90892i	−0.437004	−	0.317502i
$975$		0			0
$976$	−7.08722	+	2.30278i	−0.226856	+	0.0737101i
$977$	56.0810	+	8.88236i	1.79419	+	0.284172i	0.962542	−	0.271132i	$-0.0873979\pi$
$977$	56.0810	+	8.88236i	1.79419	+	0.284172i	0.831648	+	0.555303i	$0.187398\pi$
$978$	−3.74167	−	3.74167i	−0.119645	−	0.119645i
$979$	−35.0548	−	11.1002i	−1.12036	−	0.354764i
$980$		0			0
$981$	9.39839	+	12.9358i	0.300068	+	0.413008i
$982$	16.7622	−	32.8977i	0.534904	−	1.04981i
$983$	−11.8357	−	23.2288i	−0.377500	−	0.740885i	0.621599	−	0.783336i	$-0.286483\pi$
$983$	−11.8357	−	23.2288i	−0.377500	−	0.740885i	−0.999099	+	0.0424509i	$0.986483\pi$
$984$	19.2276	−	26.4645i	0.612952	−	0.843657i
$985$		0			0
$986$	−9.54022	−	3.09980i	−0.303822	−	0.0987179i
$987$	2.10871	+	1.07444i	0.0671209	+	0.0341998i
$988$	−3.00940	+	19.0006i	−0.0957418	+	0.604490i
$989$	−3.72099			−0.118320
$990$		0			0
$991$	20.4321			0.649046			0.324523	−	0.945878i	$-0.394796\pi$
$991$	20.4321			0.649046			0.324523	+	0.945878i	$0.394796\pi$
$992$	1.50468	−	9.50021i	0.0477738	−	0.301632i
$993$	−30.6080	−	15.5955i	−0.971315	−	0.494910i
$994$	−2.82251	−	0.917091i	−0.0895247	−	0.0290883i
$995$		0			0
$996$	−2.90158	+	3.99369i	−0.0919402	+	0.126545i
$997$	9.76731	+	19.1694i	0.309334	+	0.607102i	0.992372	−	0.123281i	$-0.0393417\pi$
$997$	9.76731	+	19.1694i	0.309334	+	0.607102i	−0.683038	+	0.730383i	$0.739342\pi$
$998$	12.3510	−	24.2401i	0.390963	−	0.767308i
$999$	5.45733	+	7.51137i	0.172662	+	0.237649i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	825.2.cw.b.382.5		96
5.2	odd	4		165.2.w.a.118.5	yes	96
5.3	odd	4	inner	825.2.cw.b.118.8		96
5.4	even	2		165.2.w.a.52.8	yes	96
11.7	odd	10	inner	825.2.cw.b.7.8		96
15.2	even	4		495.2.bj.c.118.8		96
15.14	odd	2		495.2.bj.c.217.5		96
55.7	even	20		165.2.w.a.73.8	yes	96
55.18	even	20	inner	825.2.cw.b.568.5		96
55.29	odd	10		165.2.w.a.7.5	✓	96
165.29	even	10		495.2.bj.c.172.8		96
165.62	odd	20		495.2.bj.c.73.5		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.2.w.a.7.5	✓	96	55.29	odd	10
165.2.w.a.52.8	yes	96	5.4	even	2
165.2.w.a.73.8	yes	96	55.7	even	20
165.2.w.a.118.5	yes	96	5.2	odd	4
495.2.bj.c.73.5		96	165.62	odd	20
495.2.bj.c.118.8		96	15.2	even	4
495.2.bj.c.172.8		96	165.29	even	10
495.2.bj.c.217.5		96	15.14	odd	2
825.2.cw.b.7.8		96	11.7	odd	10	inner
825.2.cw.b.118.8		96	5.3	odd	4	inner
825.2.cw.b.382.5		96	1.1	even	1	trivial
825.2.cw.b.568.5		96	55.18	even	20	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.cw (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.178502 + 1.12702i) q^{2} +(0.891007 + 0.453990i) q^{3} +(0.663811 + 0.215685i) q^{4} +(-0.670701 + 0.923140i) q^{6} +(-0.694338 - 1.36271i) q^{7} +(-1.39764 + 2.74302i) q^{8} +(0.587785 + 0.809017i) q^{9} +O(q^{10})\)	\(q+(-0.178502 + 1.12702i) q^{2} +(0.891007 + 0.453990i) q^{3} +(0.663811 + 0.215685i) q^{4} +(-0.670701 + 0.923140i) q^{6} +(-0.694338 - 1.36271i) q^{7} +(-1.39764 + 2.74302i) q^{8} +(0.587785 + 0.809017i) q^{9} +(1.00122 - 3.16189i) q^{11} +(0.493541 + 0.493541i) q^{12} +(5.09369 + 0.806762i) q^{13} +(1.65974 - 0.539283i) q^{14} +(-1.71260 - 1.24428i) q^{16} +(4.76995 - 0.755485i) q^{17} +(-1.01670 + 0.518032i) q^{18} +(1.65150 + 5.08279i) q^{19} -1.52941i q^{21} +(3.38478 + 1.69280i) q^{22} +(-4.97973 + 4.97973i) q^{23} +(-2.49061 + 1.80953i) q^{24} +(-1.81847 + 5.59667i) q^{26} +(0.156434 + 0.987688i) q^{27} +(-0.166992 - 1.05434i) q^{28} +(-0.562510 + 1.73123i) q^{29} +(-2.07975 + 1.51103i) q^{31} +(-2.64572 + 2.64572i) q^{32} +(2.32756 - 2.36272i) q^{33} +5.51066i q^{34} +(0.215685 + 0.663811i) q^{36} +(8.27261 - 4.21510i) q^{37} +(-6.02318 + 0.953978i) q^{38} +(4.17225 + 3.03132i) q^{39} +(-10.1057 + 3.28353i) q^{41} +(1.72367 + 0.273002i) q^{42} +(0.373613 + 0.373613i) q^{43} +(1.34660 - 1.88295i) q^{44} +(-4.72334 - 6.50112i) q^{46} +(-0.702519 + 1.37877i) q^{47} +(-0.961048 - 1.88616i) q^{48} +(2.73961 - 3.77075i) q^{49} +(4.59304 + 1.49237i) q^{51} +(3.20725 + 1.63417i) q^{52} +(1.75355 - 11.0715i) q^{53} -1.14106 q^{54} +4.70838 q^{56} +(-0.836043 + 5.27857i) q^{57} +(-1.85071 - 0.942986i) q^{58} +(-1.41843 - 0.460877i) q^{59} +(2.06914 - 2.84793i) q^{61} +(-1.33171 - 2.61364i) q^{62} +(0.694338 - 1.36271i) q^{63} +(-4.99806 - 6.87923i) q^{64} +(2.24735 + 3.04495i) q^{66} +(-0.161671 - 0.161671i) q^{67} +(3.32929 + 0.527308i) q^{68} +(-6.69772 + 2.17622i) q^{69} +(-1.37579 - 0.999573i) q^{71} +(-3.04066 + 0.481593i) q^{72} +(-2.78166 + 1.41733i) q^{73} +(3.27381 + 10.0758i) q^{74} +3.73022i q^{76} +(-5.00394 + 0.831042i) q^{77} +(-4.16110 + 4.16110i) q^{78} +(-1.71158 + 1.24354i) q^{79} +(-0.309017 + 0.951057i) q^{81} +(-1.89671 - 11.9753i) q^{82} +(1.10640 + 6.98551i) q^{83} +(0.329871 - 1.01524i) q^{84} +(-0.487759 + 0.354378i) q^{86} +(-1.28716 + 1.28716i) q^{87} +(7.27378 + 7.16554i) q^{88} -11.0867i q^{89} +(-2.43736 - 7.50142i) q^{91} +(-4.37965 + 2.23155i) q^{92} +(-2.53907 + 0.402149i) q^{93} +(-1.42850 - 1.03786i) q^{94} +(-3.55849 + 1.15622i) q^{96} +(-18.0446 - 2.85798i) q^{97} +(3.76067 + 3.76067i) q^{98} +(3.14653 - 1.04851i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 20 q^{7}+O(q^{10}) \) 96 * q + 20 * q^7	\( 96 q + 20 q^{7} + 8 q^{11} + 16 q^{12} + 8 q^{16} + 20 q^{17} + 32 q^{22} - 32 q^{23} + 60 q^{28} + 16 q^{31} + 16 q^{33} + 24 q^{36} - 8 q^{37} - 56 q^{38} - 120 q^{41} - 12 q^{42} - 200 q^{46} - 60 q^{47} - 48 q^{48} + 40 q^{51} - 40 q^{52} - 36 q^{53} - 80 q^{56} - 40 q^{57} - 44 q^{58} + 40 q^{61} - 80 q^{62} - 20 q^{63} + 56 q^{66} + 48 q^{67} - 80 q^{68} + 32 q^{71} + 60 q^{73} + 24 q^{77} + 96 q^{78} + 24 q^{81} - 32 q^{82} + 200 q^{83} - 80 q^{86} + 144 q^{88} + 56 q^{91} - 20 q^{92} + 72 q^{93} - 32 q^{97}+O(q^{100}) \) 96 * q + 20 * q^7 + 8 * q^11 + 16 * q^12 + 8 * q^16 + 20 * q^17 + 32 * q^22 - 32 * q^23 + 60 * q^28 + 16 * q^31 + 16 * q^33 + 24 * q^36 - 8 * q^37 - 56 * q^38 - 120 * q^41 - 12 * q^42 - 200 * q^46 - 60 * q^47 - 48 * q^48 + 40 * q^51 - 40 * q^52 - 36 * q^53 - 80 * q^56 - 40 * q^57 - 44 * q^58 + 40 * q^61 - 80 * q^62 - 20 * q^63 + 56 * q^66 + 48 * q^67 - 80 * q^68 + 32 * q^71 + 60 * q^73 + 24 * q^77 + 96 * q^78 + 24 * q^81 - 32 * q^82 + 200 * q^83 - 80 * q^86 + 144 * q^88 + 56 * q^91 - 20 * q^92 + 72 * q^93 - 32 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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