LMFDB - Embedded newform 2100.2.ce.a.1993.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2100,2,Mod(157,2100)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2100, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 0, 3, 2]))

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

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

chi := DirichletCharacter("2100.157");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2100.ce (of order $12$, 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:	$16.7685844245$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{12})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			1993.2
Root			$0.965926 - 0.258819i$ of defining polynomial
Character	$\chi$	$=$	2100.1993
Dual form			2100.2.ce.a.157.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.965926 + 0.258819i) q^{3} +(-2.38014 + 1.15539i) q^{7} +(0.866025 + 0.500000i) q^{9} +O(q^{10})$	\(q+(0.965926 + 0.258819i) q^{3} +(-2.38014 + 1.15539i) q^{7} +(0.866025 + 0.500000i) q^{9} +(-1.36603 - 2.36603i) q^{11} +(0.707107 - 0.707107i) q^{13} +(1.74238 - 6.50266i) q^{17} +(-4.23205 + 7.33013i) q^{19} +(-2.59808 + 0.500000i) q^{21} +(-7.20977 + 1.93185i) q^{23} +(0.707107 + 0.707107i) q^{27} +6.92820i q^{29} +(-1.73205 + 1.00000i) q^{31} +(-0.707107 - 2.63896i) q^{33} +(2.89778 + 10.8147i) q^{37} +(0.866025 - 0.500000i) q^{39} +4.19615i q^{41} +(-0.378937 - 0.378937i) q^{43} +(-9.84873 + 2.63896i) q^{47} +(4.33013 - 5.50000i) q^{49} +(3.36603 - 5.83013i) q^{51} +(2.26002 - 8.43451i) q^{53} +(-5.98502 + 5.98502i) q^{57} +(4.63397 + 8.02628i) q^{59} +(-8.42820 - 4.86603i) q^{61} +(-2.63896 - 0.189469i) q^{63} +(-6.76148 - 1.81173i) q^{67} -7.46410 q^{69} -8.00000 q^{71} +(-14.8678 - 3.98382i) q^{73} +(5.98502 + 4.05317i) q^{77} +(-1.96410 - 1.13397i) q^{79} +(0.500000 + 0.866025i) q^{81} +(3.34607 - 3.34607i) q^{83} +(-1.79315 + 6.69213i) q^{87} +(-3.63397 + 6.29423i) q^{89} +(-0.866025 + 2.50000i) q^{91} +(-1.93185 + 0.517638i) q^{93} +(-2.50026 - 2.50026i) q^{97} -2.73205i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q+O(q^{10}) $ 8 * q	$ 8 q - 4 q^{11} - 20 q^{19} + 20 q^{51} + 44 q^{59} - 12 q^{61} - 32 q^{69} - 64 q^{71} + 12 q^{79} + 4 q^{81} - 36 q^{89}+O(q^{100}) $ 8 * q - 4 * q^11 - 20 * q^19 + 20 * q^51 + 44 * q^59 - 12 * q^61 - 32 * q^69 - 64 * q^71 + 12 * q^79 + 4 * q^81 - 36 * q^89

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2100\mathbb{Z}\right)^\times$.

$n$	$701$	$1051$	$1177$	$1501$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{5}{6}\right)$

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			0
$2$		0			0
$3$	0.965926	+	0.258819i	0.557678	+	0.149429i
$3$	0.965926	+	0.258819i	0.557678	+	0.149429i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−2.38014	+	1.15539i	−0.899608	+	0.436698i
$7$	−2.38014	+	1.15539i	−0.899608	+	0.436698i
$8$		0			0
$9$	0.866025	+	0.500000i	0.288675	+	0.166667i
$10$		0			0
$11$	−1.36603	−	2.36603i	−0.411872	−	0.713384i	0.583222	−	0.812313i	$-0.301792\pi$
$11$	−1.36603	−	2.36603i	−0.411872	−	0.713384i	−0.995094	+	0.0989291i	$0.968458\pi$
$12$		0			0
$13$	0.707107	−	0.707107i	0.196116	−	0.196116i	−0.602217	−	0.798333i	$-0.705716\pi$
$13$	0.707107	−	0.707107i	0.196116	−	0.196116i	0.798333	+	0.602217i	$0.205716\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	1.74238	−	6.50266i	0.422590	−	1.57713i	−0.346540	−	0.938035i	$-0.612644\pi$
$17$	1.74238	−	6.50266i	0.422590	−	1.57713i	0.769130	−	0.639092i	$-0.220690\pi$
$18$		0			0
$19$	−4.23205	+	7.33013i	−0.970899	+	1.68165i	−0.278046	+	0.960568i	$0.589687\pi$
$19$	−4.23205	+	7.33013i	−0.970899	+	1.68165i	−0.692853	+	0.721079i	$0.743647\pi$
$20$		0			0
$21$	−2.59808	+	0.500000i	−0.566947	+	0.109109i
$22$		0			0
$23$	−7.20977	+	1.93185i	−1.50334	+	0.402819i	−0.914217	−	0.405224i	$-0.867193\pi$
$23$	−7.20977	+	1.93185i	−1.50334	+	0.402819i	−0.589123	+	0.808043i	$0.700527\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$		0			0
$29$			6.92820i			1.28654i	0.765641	+	0.643268i	$0.222422\pi$
$29$			6.92820i			1.28654i	−0.765641	+	0.643268i	$0.777578\pi$
$30$		0			0
$31$	−1.73205	+	1.00000i	−0.311086	+	0.179605i	−0.647412	−	0.762140i	$-0.724149\pi$
$31$	−1.73205	+	1.00000i	−0.311086	+	0.179605i	0.336327	+	0.941745i	$0.390815\pi$
$32$		0			0
$33$	−0.707107	−	2.63896i	−0.123091	−	0.459384i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	2.89778	+	10.8147i	0.476392	+	1.77792i	0.616038	+	0.787717i	$0.288737\pi$
$37$	2.89778	+	10.8147i	0.476392	+	1.77792i	−0.139646	+	0.990201i	$0.544597\pi$
$38$		0			0
$39$	0.866025	−	0.500000i	0.138675	−	0.0800641i
$40$		0			0
$41$			4.19615i			0.655329i	0.944794	+	0.327664i	$0.106262\pi$
$41$			4.19615i			0.655329i	−0.944794	+	0.327664i	$0.893738\pi$
$42$		0			0
$43$	−0.378937	−	0.378937i	−0.0577874	−	0.0577874i	0.677623	−	0.735410i	$-0.263010\pi$
$43$	−0.378937	−	0.378937i	−0.0577874	−	0.0577874i	−0.735410	+	0.677623i	$0.763010\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−9.84873	+	2.63896i	−1.43658	+	0.384932i	−0.891336	−	0.453343i	$-0.850231\pi$
$47$	−9.84873	+	2.63896i	−1.43658	+	0.384932i	−0.545248	+	0.838275i	$0.683565\pi$
$48$		0			0
$49$	4.33013	−	5.50000i	0.618590	−	0.785714i
$50$		0			0
$51$	3.36603	−	5.83013i	0.471338	−	0.816381i
$52$		0			0
$53$	2.26002	−	8.43451i	0.310438	−	1.15857i	−0.617725	−	0.786394i	$-0.711945\pi$
$53$	2.26002	−	8.43451i	0.310438	−	1.15857i	0.928163	−	0.372175i	$-0.121388\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−5.98502	+	5.98502i	−0.792736	+	0.792736i
$58$		0			0
$59$	4.63397	+	8.02628i	0.603292	+	1.04493i	0.992319	+	0.123706i	$0.0394780\pi$
$59$	4.63397	+	8.02628i	0.603292	+	1.04493i	−0.389027	+	0.921226i	$0.627189\pi$
$60$		0			0
$61$	−8.42820	−	4.86603i	−1.07912	−	0.623031i	−0.148462	−	0.988918i	$-0.547432\pi$
$61$	−8.42820	−	4.86603i	−1.07912	−	0.623031i	−0.930659	+	0.365887i	$0.880766\pi$
$62$		0			0
$63$	−2.63896	−	0.189469i	−0.332478	−	0.0238708i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−6.76148	−	1.81173i	−0.826046	−	0.221338i	−0.179058	−	0.983838i	$-0.557305\pi$
$67$	−6.76148	−	1.81173i	−0.826046	−	0.221338i	−0.646988	+	0.762500i	$0.723972\pi$
$68$		0			0
$69$	−7.46410			−0.898572
$70$		0			0
$71$	−8.00000			−0.949425			−0.474713	−	0.880141i	$-0.657448\pi$
$71$	−8.00000			−0.949425			−0.474713	+	0.880141i	$0.657448\pi$
$72$		0			0
$73$	−14.8678	−	3.98382i	−1.74015	−	0.466271i	−0.757668	−	0.652641i	$-0.773661\pi$
$73$	−14.8678	−	3.98382i	−1.74015	−	0.466271i	−0.982480	+	0.186370i	$0.940328\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	5.98502	+	4.05317i	0.682057	+	0.461902i
$78$		0			0
$79$	−1.96410	−	1.13397i	−0.220979	−	0.127582i	0.385425	−	0.922739i	$-0.374055\pi$
$79$	−1.96410	−	1.13397i	−0.220979	−	0.127582i	−0.606403	+	0.795157i	$0.707388\pi$
$80$		0			0
$81$	0.500000	+	0.866025i	0.0555556	+	0.0962250i
$82$		0			0
$83$	3.34607	−	3.34607i	0.367278	−	0.367278i	−0.499205	−	0.866484i	$-0.666375\pi$
$83$	3.34607	−	3.34607i	0.367278	−	0.367278i	0.866484	+	0.499205i	$0.166375\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−1.79315	+	6.69213i	−0.192246	+	0.717472i
$88$		0			0
$89$	−3.63397	+	6.29423i	−0.385201	+	0.667187i	−0.991797	−	0.127823i	$-0.959201\pi$
$89$	−3.63397	+	6.29423i	−0.385201	+	0.667187i	0.606596	+	0.795010i	$0.292534\pi$
$90$		0			0
$91$	−0.866025	+	2.50000i	−0.0907841	+	0.262071i
$92$		0			0
$93$	−1.93185	+	0.517638i	−0.200324	+	0.0536766i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−2.50026	−	2.50026i	−0.253863	−	0.253863i	0.568690	−	0.822552i	$-0.307451\pi$
$97$	−2.50026	−	2.50026i	−0.253863	−	0.253863i	−0.822552	+	0.568690i	$0.807451\pi$
$98$		0			0
$99$		−	2.73205i		−	0.274581i
$100$		0			0
$101$	5.83013	−	3.36603i	0.580119	−	0.334932i	−0.181061	−	0.983472i	$-0.557953\pi$
$101$	5.83013	−	3.36603i	0.580119	−	0.334932i	0.761181	+	0.648540i	$0.224620\pi$
$102$		0			0
$103$	−1.20616	−	4.50146i	−0.118847	−	0.443542i	0.880699	−	0.473676i	$-0.157073\pi$
$103$	−1.20616	−	4.50146i	−0.118847	−	0.443542i	−0.999546	+	0.0301341i	$0.990407\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−3.81294	−	14.2301i	−0.368610	−	1.37567i	−0.862460	−	0.506125i	$-0.831077\pi$
$107$	−3.81294	−	14.2301i	−0.368610	−	1.37567i	0.493850	−	0.869547i	$-0.335589\pi$
$108$		0			0
$109$	−12.0622	+	6.96410i	−1.15535	+	0.667040i	−0.950185	−	0.311688i	$-0.899106\pi$
$109$	−12.0622	+	6.96410i	−1.15535	+	0.667040i	−0.205163	+	0.978728i	$0.565772\pi$
$110$		0			0
$111$			11.1962i			1.06269i
$112$		0			0
$113$	−6.03579	−	6.03579i	−0.567800	−	0.567800i	0.363712	−	0.931511i	$-0.381509\pi$
$113$	−6.03579	−	6.03579i	−0.567800	−	0.567800i	−0.931511	+	0.363712i	$0.881509\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	0.965926	−	0.258819i	0.0892999	−	0.0239278i
$118$		0			0
$119$	3.36603	+	17.4904i	0.308563	+	1.60334i
$120$		0			0
$121$	1.76795	−	3.06218i	0.160723	−	0.278380i
$122$		0			0
$123$	−1.08604	+	4.05317i	−0.0979253	+	0.365462i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−0.0507680	+	0.0507680i	−0.00450493	+	0.00450493i	−0.709356	−	0.704851i	$-0.751014\pi$
$127$	−0.0507680	+	0.0507680i	−0.00450493	+	0.00450493i	0.704851	+	0.709356i	$0.251014\pi$
$128$		0			0
$129$	−0.267949	−	0.464102i	−0.0235916	−	0.0408619i
$130$		0			0
$131$	14.6603	+	8.46410i	1.28087	+	0.739512i	0.977008	−	0.213203i	$-0.0683897\pi$
$131$	14.6603	+	8.46410i	1.28087	+	0.739512i	0.303864	+	0.952715i	$0.401723\pi$
$132$		0			0
$133$	1.60368	−	22.3364i	0.139057	−	1.93681i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	5.79555	+	1.55291i	0.495148	+	0.132674i	0.497747	−	0.867322i	$-0.334161\pi$
$137$	5.79555	+	1.55291i	0.495148	+	0.132674i	−0.00259945	+	0.999997i	$0.500827\pi$
$138$		0			0
$139$	16.8564			1.42974			0.714871	−	0.699256i	$-0.246485\pi$
$139$	16.8564			1.42974			0.714871	+	0.699256i	$0.246485\pi$
$140$		0			0
$141$	−10.1962			−0.858671
$142$		0			0
$143$	−2.63896	−	0.707107i	−0.220681	−	0.0591312i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	5.60609	−	4.19187i	0.462382	−	0.345740i
$148$		0			0
$149$	7.90192	+	4.56218i	0.647351	+	0.373748i	0.787441	−	0.616391i	$-0.211406\pi$
$149$	7.90192	+	4.56218i	0.647351	+	0.373748i	−0.140090	+	0.990139i	$0.544739\pi$
$150$		0			0
$151$	5.33013	+	9.23205i	0.433760	+	0.751294i	0.997193	−	0.0748675i	$-0.0238534\pi$
$151$	5.33013	+	9.23205i	0.433760	+	0.751294i	−0.563434	+	0.826161i	$0.690520\pi$
$152$		0			0
$153$	4.76028	−	4.76028i	0.384846	−	0.384846i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−3.32748	+	12.4183i	−0.265562	+	0.991091i	0.696343	+	0.717709i	$0.254809\pi$
$157$	−3.32748	+	12.4183i	−0.265562	+	0.991091i	−0.961905	+	0.273382i	$0.911858\pi$
$158$		0			0
$159$	4.36603	−	7.56218i	0.346248	−	0.599720i
$160$		0			0
$161$	14.9282	−	12.9282i	1.17651	−	1.01889i
$162$		0			0
$163$	−2.89778	+	0.776457i	−0.226971	+	0.0608168i	−0.370512	−	0.928828i	$-0.620818\pi$
$163$	−2.89778	+	0.776457i	−0.226971	+	0.0608168i	0.143541	+	0.989644i	$0.454151\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	0.240237	+	0.240237i	0.0185901	+	0.0185901i	0.716341	−	0.697751i	$-0.245816\pi$
$167$	0.240237	+	0.240237i	0.0185901	+	0.0185901i	−0.697751	+	0.716341i	$0.745816\pi$
$168$		0			0
$169$			12.0000i			0.923077i
$170$		0			0
$171$	−7.33013	+	4.23205i	−0.560549	+	0.323633i
$172$		0			0
$173$	3.24453	+	12.1087i	0.246677	+	0.920611i	0.972533	+	0.232765i	$0.0747771\pi$
$173$	3.24453	+	12.1087i	0.246677	+	0.920611i	−0.725856	+	0.687847i	$0.758556\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	2.39872	+	8.95215i	0.180299	+	0.672885i
$178$		0			0
$179$	−8.19615	+	4.73205i	−0.612609	+	0.353690i	−0.773986	−	0.633203i	$-0.781740\pi$
$179$	−8.19615	+	4.73205i	−0.612609	+	0.353690i	0.161377	+	0.986893i	$0.448407\pi$
$180$		0			0
$181$			6.39230i			0.475136i	0.971371	+	0.237568i	$0.0763503\pi$
$181$			6.39230i			0.475136i	−0.971371	+	0.237568i	$0.923650\pi$
$182$		0			0
$183$	−6.88160	−	6.88160i	−0.508702	−	0.508702i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−17.7656	+	4.76028i	−1.29915	+	0.348106i
$188$		0			0
$189$	−2.50000	−	0.866025i	−0.181848	−	0.0629941i
$190$		0			0
$191$	12.0981	−	20.9545i	0.875386	−	1.51621i	0.0190352	−	0.999819i	$-0.493941\pi$
$191$	12.0981	−	20.9545i	0.875386	−	1.51621i	0.856351	−	0.516394i	$-0.172726\pi$
$192$		0			0
$193$	−3.44760	+	12.8666i	−0.248164	+	0.926160i	0.723603	+	0.690216i	$0.242485\pi$
$193$	−3.44760	+	12.8666i	−0.248164	+	0.926160i	−0.971767	+	0.235943i	$0.924182\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	3.58630	−	3.58630i	0.255513	−	0.255513i	−0.567713	−	0.823226i	$-0.692172\pi$
$197$	3.58630	−	3.58630i	0.255513	−	0.255513i	0.823226	+	0.567713i	$0.192172\pi$
$198$		0			0
$199$	−4.23205	−	7.33013i	−0.300002	−	0.519619i	0.676134	−	0.736779i	$-0.263654\pi$
$199$	−4.23205	−	7.33013i	−0.300002	−	0.519619i	−0.976136	+	0.217160i	$0.930321\pi$
$200$		0			0
$201$	−6.06218	−	3.50000i	−0.427593	−	0.246871i
$202$		0			0
$203$	−8.00481	−	16.4901i	−0.561827	−	1.15738i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−7.20977	−	1.93185i	−0.501114	−	0.134273i
$208$		0			0
$209$	23.1244			1.59955
$210$		0			0
$211$	−15.7321			−1.08304			−0.541520	−	0.840688i	$-0.682151\pi$
$211$	−15.7321			−1.08304			−0.541520	+	0.840688i	$0.682151\pi$
$212$		0			0
$213$	−7.72741	−	2.07055i	−0.529473	−	0.141872i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	2.96713	−	4.38134i	0.201422	−	0.297425i
$218$		0			0
$219$	−13.3301	−	7.69615i	−0.900767	−	0.520058i
$220$		0			0
$221$	−3.36603	−	5.83013i	−0.226423	−	0.392177i
$222$		0			0
$223$	0.947343	−	0.947343i	0.0634388	−	0.0634388i	−0.674676	−	0.738114i	$-0.735716\pi$
$223$	0.947343	−	0.947343i	0.0634388	−	0.0634388i	0.738114	+	0.674676i	$0.235716\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	3.58630	−	13.3843i	0.238031	−	0.888345i	−0.738728	−	0.674004i	$-0.764573\pi$
$227$	3.58630	−	13.3843i	0.238031	−	0.888345i	0.976759	−	0.214341i	$-0.0687603\pi$
$228$		0			0
$229$	5.86603	−	10.1603i	0.387638	−	0.671408i	−0.604493	−	0.796610i	$-0.706624\pi$
$229$	5.86603	−	10.1603i	0.387638	−	0.671408i	0.992131	+	0.125202i	$0.0399578\pi$
$230$		0			0
$231$	4.73205	+	5.46410i	0.311346	+	0.359511i
$232$		0			0
$233$	10.3664	−	2.77766i	0.679123	−	0.181971i	0.0972622	−	0.995259i	$-0.468991\pi$
$233$	10.3664	−	2.77766i	0.679123	−	0.181971i	0.581861	+	0.813288i	$0.302325\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−1.60368	−	1.60368i	−0.104170	−	0.104170i
$238$		0			0
$239$			23.3205i			1.50848i	0.656600	+	0.754239i	$0.271994\pi$
$239$			23.3205i			1.50848i	−0.656600	+	0.754239i	$0.728006\pi$
$240$		0			0
$241$	−9.69615	+	5.59808i	−0.624584	+	0.360604i	−0.778652	−	0.627457i	$-0.784096\pi$
$241$	−9.69615	+	5.59808i	−0.624584	+	0.360604i	0.154068	+	0.988060i	$0.450763\pi$
$242$		0			0
$243$	0.258819	+	0.965926i	0.0166032	+	0.0619642i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	2.19067	+	8.17569i	0.139389	+	0.520207i
$248$		0			0
$249$	4.09808	−	2.36603i	0.259705	−	0.149941i
$250$		0			0
$251$			10.5885i			0.668337i	0.942513	+	0.334169i	$0.108456\pi$
$251$			10.5885i			0.668337i	−0.942513	+	0.334169i	$0.891544\pi$
$252$		0			0
$253$	14.4195	+	14.4195i	0.906549	+	0.906549i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	20.7835	−	5.56892i	1.29644	−	0.347380i	0.456336	−	0.889807i	$-0.349161\pi$
$257$	20.7835	−	5.56892i	1.29644	−	0.347380i	0.840103	+	0.542428i	$0.182495\pi$
$258$		0			0
$259$	−19.3923	−	22.3923i	−1.20498	−	1.39139i
$260$		0			0
$261$	−3.46410	+	6.00000i	−0.214423	+	0.371391i
$262$		0			0
$263$	−2.34795	+	8.76268i	−0.144781	+	0.540330i	0.854984	+	0.518654i	$0.173567\pi$
$263$	−2.34795	+	8.76268i	−0.144781	+	0.540330i	−0.999765	+	0.0216758i	$0.993100\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−5.13922	+	5.13922i	−0.314515	+	0.314515i
$268$		0			0
$269$	−4.29423	−	7.43782i	−0.261824	−	0.453492i	0.704903	−	0.709304i	$-0.250991\pi$
$269$	−4.29423	−	7.43782i	−0.261824	−	0.453492i	−0.966727	+	0.255812i	$0.917657\pi$
$270$		0			0
$271$	12.9282	+	7.46410i	0.785332	+	0.453412i	0.838317	−	0.545183i	$-0.183540\pi$
$271$	12.9282	+	7.46410i	0.785332	+	0.453412i	−0.0529843	+	0.998595i	$0.516873\pi$
$272$		0			0
$273$	−1.48356	+	2.19067i	−0.0897894	+	0.132585i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	20.4739	+	5.48597i	1.23016	+	0.329620i	0.814641	−	0.579966i	$-0.196934\pi$
$277$	20.4739	+	5.48597i	1.23016	+	0.329620i	0.415517	+	0.909585i	$0.363601\pi$
$278$		0			0
$279$	−2.00000			−0.119737
$280$		0			0
$281$	−8.87564			−0.529477			−0.264738	−	0.964320i	$-0.585286\pi$
$281$	−8.87564			−0.529477			−0.264738	+	0.964320i	$0.585286\pi$
$282$		0			0
$283$	−7.08965	−	1.89967i	−0.421436	−	0.112923i	0.0418674	−	0.999123i	$-0.486669\pi$
$283$	−7.08965	−	1.89967i	−0.421436	−	0.112923i	−0.463303	+	0.886200i	$0.653336\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−4.84821	−	9.98743i	−0.286181	−	0.589539i
$288$		0			0
$289$	−24.5263	−	14.1603i	−1.44272	−	0.832956i
$290$		0			0
$291$	−1.76795	−	3.06218i	−0.103639	−	0.179508i
$292$		0			0
$293$	11.5911	−	11.5911i	0.677160	−	0.677160i	−0.282197	−	0.959357i	$-0.591063\pi$
$293$	11.5911	−	11.5911i	0.677160	−	0.677160i	0.959357	+	0.282197i	$0.0910631\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	0.707107	−	2.63896i	0.0410305	−	0.153128i
$298$		0			0
$299$	−3.73205	+	6.46410i	−0.215830	+	0.373829i
$300$		0			0
$301$	1.33975	+	0.464102i	0.0772217	+	0.0267504i
$302$		0			0
$303$	6.50266	−	1.74238i	0.373568	−	0.100097i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	1.79315	+	1.79315i	0.102341	+	0.102341i	0.756423	−	0.654083i	$-0.226945\pi$
$307$	1.79315	+	1.79315i	0.102341	+	0.102341i	−0.654083	+	0.756423i	$0.726945\pi$
$308$		0			0
$309$		−	4.66025i		−	0.265113i
$310$		0			0
$311$	5.19615	−	3.00000i	0.294647	−	0.170114i	−0.345389	−	0.938460i	$-0.612253\pi$
$311$	5.19615	−	3.00000i	0.294647	−	0.170114i	0.640036	+	0.768345i	$0.278920\pi$
$312$		0			0
$313$	−0.656339	−	2.44949i	−0.0370985	−	0.138453i	0.944893	−	0.327380i	$-0.106166\pi$
$313$	−0.656339	−	2.44949i	−0.0370985	−	0.138453i	−0.981991	+	0.188927i	$0.939499\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	0.619174	+	2.31079i	0.0347763	+	0.129787i	0.981132	−	0.193341i	$-0.0619323\pi$
$317$	0.619174	+	2.31079i	0.0347763	+	0.129787i	−0.946355	+	0.323128i	$0.895266\pi$
$318$		0			0
$319$	16.3923	−	9.46410i	0.917793	−	0.529888i
$320$		0			0
$321$		−	14.7321i		−	0.822263i
$322$		0			0
$323$	40.2915	+	40.2915i	2.24188	+	2.24188i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−13.4536	+	3.60488i	−0.743986	+	0.199351i
$328$		0			0
$329$	20.3923	−	17.6603i	1.12426	−	0.973641i
$330$		0			0
$331$	6.66987	−	11.5526i	0.366609	−	0.634986i	−0.622424	−	0.782681i	$-0.713852\pi$
$331$	6.66987	−	11.5526i	0.366609	−	0.634986i	0.989033	+	0.147694i	$0.0471852\pi$
$332$		0			0
$333$	−2.89778	+	10.8147i	−0.158797	+	0.592639i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−0.656339	+	0.656339i	−0.0357531	+	0.0357531i	−0.724757	−	0.689004i	$-0.758048\pi$
$337$	−0.656339	+	0.656339i	−0.0357531	+	0.0357531i	0.689004	+	0.724757i	$0.258048\pi$
$338$		0			0
$339$	−4.26795	−	7.39230i	−0.231803	−	0.401495i
$340$		0			0
$341$	4.73205	+	2.73205i	0.256255	+	0.147949i
$342$		0			0
$343$	−3.95164	+	18.0938i	−0.213368	+	0.976972i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−34.3065	−	9.19239i	−1.84167	−	0.493473i	−0.842678	−	0.538418i	$-0.819022\pi$
$347$	−34.3065	−	9.19239i	−1.84167	−	0.493473i	−0.998989	+	0.0449449i	$0.985689\pi$
$348$		0			0
$349$	−12.9282			−0.692031			−0.346015	−	0.938229i	$-0.612466\pi$
$349$	−12.9282			−0.692031			−0.346015	+	0.938229i	$0.612466\pi$
$350$		0			0
$351$	1.00000			0.0533761
$352$		0			0
$353$	11.2629	+	3.01790i	0.599466	+	0.160626i	0.545776	−	0.837931i	$-0.316235\pi$
$353$	11.2629	+	3.01790i	0.599466	+	0.160626i	0.0536901	+	0.998558i	$0.482902\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−1.27551	+	17.7656i	−0.0675073	+	0.940255i
$358$		0			0
$359$	24.2942	+	14.0263i	1.28220	+	0.740279i	0.977250	−	0.212090i	$-0.0680269\pi$
$359$	24.2942	+	14.0263i	1.28220	+	0.740279i	0.304950	+	0.952368i	$0.401360\pi$
$360$		0			0
$361$	−26.3205	−	45.5885i	−1.38529	−	2.39939i
$362$		0			0
$363$	2.50026	−	2.50026i	0.131229	−	0.131229i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	1.93185	−	7.20977i	0.100842	−	0.376347i	−0.896998	−	0.442034i	$-0.854257\pi$
$367$	1.93185	−	7.20977i	0.100842	−	0.376347i	0.997840	+	0.0656868i	$0.0209238\pi$
$368$		0			0
$369$	−2.09808	+	3.63397i	−0.109221	+	0.189177i
$370$		0			0
$371$	4.36603	+	22.6865i	0.226673	+	1.17783i
$372$		0			0
$373$	−14.5397	+	3.89589i	−0.752835	+	0.201721i	−0.614775	−	0.788702i	$-0.710753\pi$
$373$	−14.5397	+	3.89589i	−0.752835	+	0.201721i	−0.138060	+	0.990424i	$0.544087\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	4.89898	+	4.89898i	0.252310	+	0.252310i
$378$		0			0
$379$		−	23.4449i		−	1.20428i	−0.798390	−	0.602141i	$-0.794315\pi$
$379$		−	23.4449i		−	1.20428i	0.798390	−	0.602141i	$-0.205685\pi$
$380$		0			0
$381$	−0.0621778	+	0.0358984i	−0.00318547	+	0.00183913i
$382$		0			0
$383$	7.69024	+	28.7004i	0.392953	+	1.46652i	0.825239	+	0.564784i	$0.191040\pi$
$383$	7.69024	+	28.7004i	0.392953	+	1.46652i	−0.432286	+	0.901737i	$0.642293\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−0.138701	−	0.517638i	−0.00705055	−	0.0263130i
$388$		0			0
$389$	−15.4186	+	8.90192i	−0.781753	+	0.451345i	−0.837051	−	0.547124i	$-0.815722\pi$
$389$	−15.4186	+	8.90192i	−0.781753	+	0.451345i	0.0552980	+	0.998470i	$0.482389\pi$
$390$		0			0
$391$			50.2487i			2.54119i
$392$		0			0
$393$	11.9700	+	11.9700i	0.603809	+	0.603809i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−6.31319	+	1.69161i	−0.316850	+	0.0848997i	−0.413739	−	0.910395i	$-0.635777\pi$
$397$	−6.31319	+	1.69161i	−0.316850	+	0.0848997i	0.0968891	+	0.995295i	$0.469111\pi$
$398$		0			0
$399$	7.33013	−	21.1603i	0.366965	−	1.05934i
$400$		0			0
$401$	13.2942	−	23.0263i	0.663882	−	1.14988i	−0.315705	−	0.948857i	$-0.602241\pi$
$401$	13.2942	−	23.0263i	0.663882	−	1.14988i	0.979587	−	0.201020i	$-0.0644257\pi$
$402$		0			0
$403$	−0.517638	+	1.93185i	−0.0257854	+	0.0962324i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	21.6293	−	21.6293i	1.07212	−	1.07212i
$408$		0			0
$409$	5.79423	+	10.0359i	0.286506	+	0.496243i	0.972973	−	0.230918i	$-0.0741728\pi$
$409$	5.79423	+	10.0359i	0.286506	+	0.496243i	−0.686467	+	0.727161i	$0.740839\pi$
$410$		0			0
$411$	5.19615	+	3.00000i	0.256307	+	0.147979i
$412$		0			0
$413$	−20.3030	−	13.7496i	−0.999047	−	0.676573i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	16.2820	+	4.36276i	0.797335	+	0.213645i
$418$		0			0
$419$	0.0525589			0.00256767			0.00128383	−	0.999999i	$-0.499591\pi$
$419$	0.0525589			0.00256767			0.00128383	+	0.999999i	$0.499591\pi$
$420$		0			0
$421$	−31.3923			−1.52997			−0.764984	−	0.644050i	$-0.777253\pi$
$421$	−31.3923			−1.52997			−0.764984	+	0.644050i	$0.777253\pi$
$422$		0			0
$423$	−9.84873	−	2.63896i	−0.478861	−	0.128311i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	25.6825	+	1.84392i	1.24286	+	0.0892335i
$428$		0			0
$429$	−2.36603	−	1.36603i	−0.114233	−	0.0659523i
$430$		0			0
$431$	−5.53590	−	9.58846i	−0.266655	−	0.461860i	0.701341	−	0.712826i	$-0.252585\pi$
$431$	−5.53590	−	9.58846i	−0.266655	−	0.461860i	−0.967996	+	0.250966i	$0.919252\pi$
$432$		0			0
$433$	21.5921	−	21.5921i	1.03765	−	1.03765i	0.0383892	−	0.999263i	$-0.487777\pi$
$433$	21.5921	−	21.5921i	1.03765	−	1.03765i	0.999263	−	0.0383892i	$-0.0122227\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	16.3514	−	61.0242i	0.782193	−	2.91918i
$438$		0			0
$439$	−6.89230	+	11.9378i	−0.328952	+	0.569761i	−0.982304	−	0.187293i	$-0.940029\pi$
$439$	−6.89230	+	11.9378i	−0.328952	+	0.569761i	0.653352	+	0.757054i	$0.273362\pi$
$440$		0			0
$441$	6.50000	−	2.59808i	0.309524	−	0.123718i
$442$		0			0
$443$	−22.3872	+	5.99863i	−1.06365	+	0.285003i	−0.747880	−	0.663834i	$-0.768928\pi$
$443$	−22.3872	+	5.99863i	−1.06365	+	0.285003i	−0.315767	+	0.948837i	$0.602262\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	6.45189	+	6.45189i	0.305164	+	0.305164i
$448$		0			0
$449$			10.3397i			0.487963i	0.969780	+	0.243981i	$0.0784536\pi$
$449$			10.3397i			0.487963i	−0.969780	+	0.243981i	$0.921546\pi$
$450$		0			0
$451$	9.92820	−	5.73205i	0.467501	−	0.269912i
$452$		0			0
$453$	2.75908	+	10.2970i	0.129633	+	0.483796i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−4.17329	−	15.5749i	−0.195218	−	0.728565i	−0.992210	−	0.124575i	$-0.960243\pi$
$457$	−4.17329	−	15.5749i	−0.195218	−	0.728565i	0.796992	−	0.603990i	$-0.206423\pi$
$458$		0			0
$459$	5.83013	−	3.36603i	0.272127	−	0.157113i
$460$		0			0
$461$			17.7128i			0.824968i	0.910965	+	0.412484i	$0.135339\pi$
$461$			17.7128i			0.824968i	−0.910965	+	0.412484i	$0.864661\pi$
$462$		0			0
$463$	22.0962	+	22.0962i	1.02690	+	1.02690i	0.999628	+	0.0272682i	$0.00868082\pi$
$463$	22.0962	+	22.0962i	1.02690	+	1.02690i	0.0272682	+	0.999628i	$0.491319\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	26.9072	−	7.20977i	1.24512	−	0.333628i	0.424669	−	0.905349i	$-0.360390\pi$
$467$	26.9072	−	7.20977i	1.24512	−	0.333628i	0.820449	+	0.571720i	$0.193724\pi$
$468$		0			0
$469$	18.1865	−	3.50000i	0.839776	−	0.161615i
$470$		0			0
$471$	−6.42820	+	11.1340i	−0.296196	+	0.513026i
$472$		0			0
$473$	−0.378937	+	1.41421i	−0.0174236	+	0.0650256i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	6.17449	−	6.17449i	0.282711	−	0.282711i
$478$		0			0
$479$	−13.2224	−	22.9019i	−0.604148	−	1.04642i	−0.992185	−	0.124772i	$-0.960180\pi$
$479$	−13.2224	−	22.9019i	−0.604148	−	1.04642i	0.388037	−	0.921644i	$-0.373153\pi$
$480$		0			0
$481$	9.69615	+	5.59808i	0.442106	+	0.255250i
$482$		0			0
$483$	17.7656	−	8.62398i	0.808363	−	0.392405i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−24.4577	−	6.55343i	−1.10829	−	0.296964i	−0.342151	−	0.939645i	$-0.611156\pi$
$487$	−24.4577	−	6.55343i	−1.10829	−	0.296964i	−0.766134	+	0.642681i	$0.777822\pi$
$488$		0			0
$489$	−3.00000			−0.135665
$490$		0			0
$491$	14.3923			0.649516			0.324758	−	0.945797i	$-0.394717\pi$
$491$	14.3923			0.649516			0.324758	+	0.945797i	$0.394717\pi$
$492$		0			0
$493$	45.0518	+	12.0716i	2.02903	+	0.543677i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	19.0411	−	9.24316i	0.854111	−	0.414612i
$498$		0			0
$499$	−1.03590	−	0.598076i	−0.0463732	−	0.0267736i	0.476634	−	0.879102i	$-0.341857\pi$
$499$	−1.03590	−	0.598076i	−0.0463732	−	0.0267736i	−0.523007	+	0.852328i	$0.675190\pi$
$500$		0			0
$501$	0.169873	+	0.294229i	0.00758937	+	0.0131452i
$502$		0			0
$503$	−14.6969	+	14.6969i	−0.655304	+	0.655304i	−0.954265	−	0.298961i	$-0.903360\pi$
$503$	−14.6969	+	14.6969i	−0.655304	+	0.655304i	0.298961	+	0.954265i	$0.403360\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−3.10583	+	11.5911i	−0.137935	+	0.514779i
$508$		0			0
$509$	10.7321	−	18.5885i	0.475690	−	0.823919i	−0.523922	−	0.851766i	$-0.675532\pi$
$509$	10.7321	−	18.5885i	0.475690	−	0.823919i	0.999612	+	0.0278471i	$0.00886516\pi$
$510$		0			0
$511$	39.9904	−	7.69615i	1.76907	−	0.340458i
$512$		0			0
$513$	−8.17569	+	2.19067i	−0.360966	+	0.0967205i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	19.6975	+	19.6975i	0.866293	+	0.866293i
$518$		0			0
$519$			12.5359i			0.550265i
$520$		0			0
$521$	32.3205	−	18.6603i	1.41599	−	0.817521i	0.420044	−	0.907504i	$-0.362015\pi$
$521$	32.3205	−	18.6603i	1.41599	−	0.817521i	0.995943	+	0.0899832i	$0.0286813\pi$
$522$		0			0
$523$	5.00052	+	18.6622i	0.218657	+	0.816040i	0.984847	+	0.173426i	$0.0554836\pi$
$523$	5.00052	+	18.6622i	0.218657	+	0.816040i	−0.766190	+	0.642614i	$0.777850\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	3.48477	+	13.0053i	0.151799	+	0.566521i
$528$		0			0
$529$	28.3301	−	16.3564i	1.23174	−	0.711148i
$530$		0			0
$531$			9.26795i			0.402195i
$532$		0			0
$533$	2.96713	+	2.96713i	0.128521	+	0.128521i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−9.14162	+	2.44949i	−0.394490	+	0.105703i
$538$		0			0
$539$	−18.9282	−	2.73205i	−0.815295	−	0.117678i
$540$		0			0
$541$	19.1603	−	33.1865i	0.823764	−	1.42680i	−0.0790969	−	0.996867i	$-0.525204\pi$
$541$	19.1603	−	33.1865i	0.823764	−	1.42680i	0.902861	−	0.429934i	$-0.141463\pi$
$542$		0			0
$543$	−1.65445	+	6.17449i	−0.0709993	+	0.264973i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−20.3538	+	20.3538i	−0.870265	+	0.870265i	−0.992501	−	0.122236i	$-0.960994\pi$
$547$	−20.3538	+	20.3538i	−0.870265	+	0.870265i	0.122236	+	0.992501i	$0.460994\pi$
$548$		0			0
$549$	−4.86603	−	8.42820i	−0.207677	−	0.359707i
$550$		0			0
$551$	−50.7846	−	29.3205i	−2.16350	−	1.24910i
$552$		0			0
$553$	5.98502	+	0.429705i	0.254509	+	0.0182729i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−4.24264	−	1.13681i	−0.179766	−	0.0481683i	0.167813	−	0.985819i	$-0.446330\pi$
$557$	−4.24264	−	1.13681i	−0.179766	−	0.0481683i	−0.347579	+	0.937651i	$0.612996\pi$
$558$		0			0
$559$	−0.535898			−0.0226661
$560$		0			0
$561$	−18.3923			−0.776524
$562$		0			0
$563$	38.1702	+	10.2277i	1.60868	+	0.431045i	0.947649	−	0.319314i	$-0.103452\pi$
$563$	38.1702	+	10.2277i	1.60868	+	0.431045i	0.661031	+	0.750358i	$0.270119\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−2.19067	−	1.48356i	−0.0919995	−	0.0623038i
$568$		0			0
$569$	−33.4186	−	19.2942i	−1.40098	−	0.808856i	−0.406487	−	0.913657i	$-0.633246\pi$
$569$	−33.4186	−	19.2942i	−1.40098	−	0.808856i	−0.994493	+	0.104801i	$0.966580\pi$
$570$		0			0
$571$	13.4545	+	23.3038i	0.563053	+	0.975236i	0.997228	+	0.0744073i	$0.0237065\pi$
$571$	13.4545	+	23.3038i	0.563053	+	0.975236i	−0.434175	+	0.900828i	$0.642960\pi$
$572$		0			0
$573$	17.1093	−	17.1093i	0.714750	−	0.714750i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−2.58819	+	9.65926i	−0.107748	+	0.402120i	−0.998642	−	0.0520899i	$-0.983412\pi$
$577$	−2.58819	+	9.65926i	−0.107748	+	0.402120i	0.890895	+	0.454210i	$0.150078\pi$
$578$		0			0
$579$	−6.66025	+	11.5359i	−0.276791	+	0.479416i
$580$		0			0
$581$	−4.09808	+	11.8301i	−0.170017	+	0.490796i
$582$		0			0
$583$	−23.0435	+	6.17449i	−0.954365	+	0.255721i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−21.0101	−	21.0101i	−0.867181	−	0.867181i	0.124979	−	0.992159i	$-0.460114\pi$
$587$	−21.0101	−	21.0101i	−0.867181	−	0.867181i	−0.992159	+	0.124979i	$0.960114\pi$
$588$		0			0
$589$		−	16.9282i		−	0.697514i
$590$		0			0
$591$	4.39230	−	2.53590i	0.180675	−	0.104313i
$592$		0			0
$593$	−9.10446	−	33.9783i	−0.373875	−	1.39532i	−0.854981	−	0.518659i	$-0.826432\pi$
$593$	−9.10446	−	33.9783i	−0.373875	−	1.39532i	0.481106	−	0.876662i	$-0.340235\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−2.19067	−	8.17569i	−0.0896582	−	0.334609i
$598$		0			0
$599$	−11.9545	+	6.90192i	−0.488447	+	0.282005i	−0.723930	−	0.689874i	$-0.757666\pi$
$599$	−11.9545	+	6.90192i	−0.488447	+	0.282005i	0.235483	+	0.971878i	$0.424333\pi$
$600$		0			0
$601$			12.5167i			0.510565i	0.966866	+	0.255283i	$0.0821685\pi$
$601$			12.5167i			0.510565i	−0.966866	+	0.255283i	$0.917831\pi$
$602$		0			0
$603$	−4.94975	−	4.94975i	−0.201569	−	0.201569i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	14.1607	−	3.79435i	0.574766	−	0.154008i	0.0402844	−	0.999188i	$-0.487174\pi$
$607$	14.1607	−	3.79435i	0.574766	−	0.154008i	0.534481	+	0.845180i	$0.320507\pi$
$608$		0			0
$609$	−3.46410	−	18.0000i	−0.140372	−	0.729397i
$610$		0			0
$611$	−5.09808	+	8.83013i	−0.206246	+	0.357229i
$612$		0			0
$613$	−7.20977	+	26.9072i	−0.291200	+	1.08677i	0.652989	+	0.757367i	$0.273515\pi$
$613$	−7.20977	+	26.9072i	−0.291200	+	1.08677i	−0.944189	+	0.329405i	$0.893152\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−4.14110	+	4.14110i	−0.166715	+	0.166715i	−0.785534	−	0.618819i	$-0.787611\pi$
$617$	−4.14110	+	4.14110i	−0.166715	+	0.166715i	0.618819	+	0.785534i	$0.287611\pi$
$618$		0			0
$619$	−19.1962	−	33.2487i	−0.771559	−	1.33638i	−0.936709	−	0.350110i	$-0.886144\pi$
$619$	−19.1962	−	33.2487i	−0.771559	−	1.33638i	0.165150	−	0.986268i	$-0.447189\pi$
$620$		0			0
$621$	−6.46410	−	3.73205i	−0.259395	−	0.149762i
$622$		0			0
$623$	1.37705	−	19.1798i	0.0551703	−	0.768423i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	22.3364	+	5.98502i	0.892030	+	0.239019i
$628$		0			0
$629$	75.3731			3.00532
$630$		0			0
$631$	−26.8038			−1.06704			−0.533522	−	0.845786i	$-0.679132\pi$
$631$	−26.8038			−1.06704			−0.533522	+	0.845786i	$0.679132\pi$
$632$		0			0
$633$	−15.1960	−	4.07175i	−0.603987	−	0.161838i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−0.827225	−	6.95095i	−0.0327759	−	0.275407i
$638$		0			0
$639$	−6.92820	−	4.00000i	−0.274075	−	0.158238i
$640$		0			0
$641$	22.5885	+	39.1244i	0.892190	+	1.54532i	0.837244	+	0.546830i	$0.184166\pi$
$641$	22.5885	+	39.1244i	0.892190	+	1.54532i	0.0549467	+	0.998489i	$0.482501\pi$
$642$		0			0
$643$	33.5486	−	33.5486i	1.32303	−	1.32303i	0.411714	−	0.911313i	$-0.364930\pi$
$643$	33.5486	−	33.5486i	1.32303	−	1.32303i	0.911313	−	0.411714i	$-0.135070\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−9.19239	+	34.3065i	−0.361390	+	1.34873i	0.510859	+	0.859664i	$0.329327\pi$
$647$	−9.19239	+	34.3065i	−0.361390	+	1.34873i	−0.872249	+	0.489062i	$0.837339\pi$
$648$		0			0
$649$	12.6603	−	21.9282i	0.496958	−	0.860757i
$650$		0			0
$651$	4.00000	−	3.46410i	0.156772	−	0.135769i
$652$		0			0
$653$	−0.568406	+	0.152304i	−0.0222434	+	0.00596011i	−0.269924	−	0.962882i	$-0.586998\pi$
$653$	−0.568406	+	0.152304i	−0.0222434	+	0.00596011i	0.247680	+	0.968842i	$0.420332\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−10.8840	−	10.8840i	−0.424625	−	0.424625i
$658$		0			0
$659$		−	5.66025i		−	0.220492i	−0.993904	−	0.110246i	$-0.964836\pi$
$659$		−	5.66025i		−	0.220492i	0.993904	−	0.110246i	$-0.0351639\pi$
$660$		0			0
$661$	1.37564	−	0.794229i	0.0535064	−	0.0308919i	−0.473008	−	0.881058i	$-0.656832\pi$
$661$	1.37564	−	0.794229i	0.0535064	−	0.0308919i	0.526515	+	0.850166i	$0.323499\pi$
$662$		0			0
$663$	−1.74238	−	6.50266i	−0.0676685	−	0.252542i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−13.3843	−	49.9507i	−0.518241	−	1.93410i
$668$		0			0
$669$	1.16025	−	0.669873i	0.0448580	−	0.0258988i
$670$		0			0
$671$			26.5885i			1.02644i
$672$		0			0
$673$	−8.29581	−	8.29581i	−0.319780	−	0.319780i	0.528903	−	0.848683i	$-0.322604\pi$
$673$	−8.29581	−	8.29581i	−0.319780	−	0.319780i	−0.848683	+	0.528903i	$0.822604\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−3.34607	+	0.896575i	−0.128600	+	0.0344582i	−0.322545	−	0.946554i	$-0.604538\pi$
$677$	−3.34607	+	0.896575i	−0.128600	+	0.0344582i	0.193945	+	0.981012i	$0.437872\pi$
$678$		0			0
$679$	8.83975	+	3.06218i	0.339238	+	0.117516i
$680$		0			0
$681$	6.92820	−	12.0000i	0.265489	−	0.459841i
$682$		0			0
$683$	−2.91636	+	10.8840i	−0.111591	+	0.416465i	−0.999009	−	0.0445009i	$-0.985830\pi$
$683$	−2.91636	+	10.8840i	−0.111591	+	0.416465i	0.887418	+	0.460966i	$0.152497\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	8.29581	−	8.29581i	0.316505	−	0.316505i
$688$		0			0
$689$	−4.36603	−	7.56218i	−0.166332	−	0.288096i
$690$		0			0
$691$	−11.4737	−	6.62436i	−0.436481	−	0.252002i	0.265623	−	0.964077i	$-0.414422\pi$
$691$	−11.4737	−	6.62436i	−0.436481	−	0.252002i	−0.702104	+	0.712075i	$0.747756\pi$
$692$		0			0
$693$	3.15660	+	6.50266i	0.119909	+	0.247016i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	27.2862	+	7.31130i	1.03354	+	0.276935i
$698$		0			0
$699$	10.7321			0.405923
$700$		0			0
$701$	−18.3397			−0.692683			−0.346341	−	0.938109i	$-0.612576\pi$
$701$	−18.3397			−0.692683			−0.346341	+	0.938109i	$0.612576\pi$
$702$		0			0
$703$	−91.5363	−	24.5271i	−3.45236	−	0.925056i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−9.98743	+	14.7477i	−0.375616	+	0.554645i
$708$		0			0
$709$	−4.45448	−	2.57180i	−0.167292	−	0.0965859i	0.414017	−	0.910269i	$-0.364126\pi$
$709$	−4.45448	−	2.57180i	−0.167292	−	0.0965859i	−0.581308	+	0.813684i	$0.697459\pi$
$710$		0			0
$711$	−1.13397	−	1.96410i	−0.0425274	−	0.0736596i
$712$		0			0
$713$	10.5558	−	10.5558i	0.395319	−	0.395319i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−6.03579	+	22.5259i	−0.225411	+	0.841244i
$718$		0			0
$719$	4.75833	−	8.24167i	0.177456	−	0.307362i	−0.763553	−	0.645746i	$-0.776547\pi$
$719$	4.75833	−	8.24167i	0.177456	−	0.307362i	0.941008	+	0.338383i	$0.109880\pi$
$720$		0			0
$721$	8.07180	+	9.32051i	0.300609	+	0.347114i
$722$		0			0
$723$	−10.8147	+	2.89778i	−0.402201	+	0.107770i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−0.568406	−	0.568406i	−0.0210810	−	0.0210810i	0.696488	−	0.717569i	$-0.254745\pi$
$727$	−0.568406	−	0.568406i	−0.0210810	−	0.0210810i	−0.717569	+	0.696488i	$0.754745\pi$
$728$		0			0
$729$			1.00000i			0.0370370i
$730$		0			0
$731$	−3.12436	+	1.80385i	−0.115558	+	0.0667177i
$732$		0			0
$733$	4.26122	+	15.9031i	0.157392	+	0.587394i	0.998889	+	0.0471323i	$0.0150082\pi$
$733$	4.26122	+	15.9031i	0.157392	+	0.587394i	−0.841497	+	0.540262i	$0.818325\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	4.94975	+	18.4727i	0.182326	+	0.680451i
$738$		0			0
$739$	−25.0359	+	14.4545i	−0.920960	+	0.531717i	−0.883941	−	0.467598i	$-0.845120\pi$
$739$	−25.0359	+	14.4545i	−0.920960	+	0.531717i	−0.0370191	+	0.999315i	$0.511786\pi$
$740$		0			0
$741$			8.46410i			0.310937i
$742$		0			0
$743$	24.1160	+	24.1160i	0.884729	+	0.884729i	0.994011	−	0.109282i	$-0.0348552\pi$
$743$	24.1160	+	24.1160i	0.884729	+	0.884729i	−0.109282	+	0.994011i	$0.534855\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	4.57081	−	1.22474i	0.167237	−	0.0448111i
$748$		0			0
$749$	25.5167	+	29.4641i	0.932358	+	1.07659i
$750$		0			0
$751$	−0.0621778	+	0.107695i	−0.00226890	+	0.00392985i	−0.867158	−	0.498034i	$-0.834056\pi$
$751$	−0.0621778	+	0.107695i	−0.00226890	+	0.00392985i	0.864889	+	0.501964i	$0.167389\pi$
$752$		0			0
$753$	−2.74049	+	10.2277i	−0.0998692	+	0.372717i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−5.74479	+	5.74479i	−0.208798	+	0.208798i	−0.803756	−	0.594959i	$-0.797168\pi$
$757$	−5.74479	+	5.74479i	−0.208798	+	0.208798i	0.594959	+	0.803756i	$0.297168\pi$
$758$		0			0
$759$	10.1962	+	17.6603i	0.370097	+	0.641027i
$760$		0			0
$761$	20.4904	+	11.8301i	0.742776	+	0.428842i	0.823078	−	0.567929i	$-0.192255\pi$
$761$	20.4904	+	11.8301i	0.742776	+	0.428842i	−0.0803019	+	0.996771i	$0.525588\pi$
$762$		0			0
$763$	20.6634	−	30.5121i	0.748065	−	1.10461i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	8.95215	+	2.39872i	0.323243	+	0.0866128i
$768$		0			0
$769$	−21.3205			−0.768837			−0.384419	−	0.923159i	$-0.625598\pi$
$769$	−21.3205			−0.768837			−0.384419	+	0.923159i	$0.625598\pi$
$770$		0			0
$771$	21.5167			0.774904
$772$		0			0
$773$	3.10583	+	0.832204i	0.111709	+	0.0299323i	0.314240	−	0.949343i	$-0.398250\pi$
$773$	3.10583	+	0.832204i	0.111709	+	0.0299323i	−0.202532	+	0.979276i	$0.564917\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−12.9360	−	26.6484i	−0.464075	−	0.956006i
$778$		0			0
$779$	−30.7583	−	17.7583i	−1.10203	−	0.636258i
$780$		0			0
$781$	10.9282	+	18.9282i	0.391042	+	0.677304i
$782$		0			0
$783$	−4.89898	+	4.89898i	−0.175075	+	0.175075i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−0.106515	+	0.397520i	−0.00379685	+	0.0141700i	−0.967798	−	0.251727i	$-0.919001\pi$
$787$	−0.106515	+	0.397520i	−0.00379685	+	0.0141700i	0.964001	+	0.265897i	$0.0856681\pi$
$788$		0			0
$789$	−4.53590	+	7.85641i	−0.161482	+	0.279695i
$790$		0			0
$791$	21.3397	+	7.39230i	0.758754	+	0.262840i
$792$		0			0
$793$	−9.40044	+	2.51884i	−0.333819	+	0.0894466i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	29.9759	+	29.9759i	1.06180	+	1.06180i	0.997960	+	0.0638402i	$0.0203348\pi$
$797$	29.9759	+	29.9759i	1.06180	+	1.06180i	0.0638402	+	0.997960i	$0.479665\pi$
$798$		0			0
$799$			68.6410i			2.42834i
$800$		0			0
$801$	−6.29423	+	3.63397i	−0.222396	+	0.128400i
$802$		0			0
$803$	10.8840	+	40.6197i	0.384088	+	1.43344i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−2.22286	−	8.29581i	−0.0782482	−	0.292026i
$808$		0			0
$809$	−44.5692	+	25.7321i	−1.56697	+	0.904691i	−0.570451	+	0.821332i	$0.693231\pi$
$809$	−44.5692	+	25.7321i	−1.56697	+	0.904691i	−0.996520	+	0.0833589i	$0.973435\pi$
$810$		0			0
$811$		−	27.1436i		−	0.953140i	−0.879136	−	0.476570i	$-0.841880\pi$
$811$		−	27.1436i		−	0.953140i	0.879136	−	0.476570i	$-0.158120\pi$
$812$		0			0
$813$	10.5558	+	10.5558i	0.370209	+	0.370209i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	4.38134	−	1.17398i	0.153284	−	0.0410723i
$818$		0			0
$819$	−2.00000	+	1.73205i	−0.0698857	+	0.0605228i
$820$		0			0
$821$	25.8301	−	44.7391i	0.901478	−	1.56141i	0.0759008	−	0.997115i	$-0.475817\pi$
$821$	25.8301	−	44.7391i	0.901478	−	1.56141i	0.825577	−	0.564290i	$-0.190850\pi$
$822$		0			0
$823$	−0.0829536	+	0.309587i	−0.00289158	+	0.0107915i	−0.967357	−	0.253419i	$-0.918445\pi$
$823$	−0.0829536	+	0.309587i	−0.00289158	+	0.0107915i	0.964465	+	0.264211i	$0.0851115\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−10.2784	+	10.2784i	−0.357416	+	0.357416i	−0.862860	−	0.505444i	$-0.831329\pi$
$827$	−10.2784	+	10.2784i	−0.357416	+	0.357416i	0.505444	+	0.862860i	$0.331329\pi$
$828$		0			0
$829$	22.7224	+	39.3564i	0.789183	+	1.36690i	0.926468	+	0.376373i	$0.122829\pi$
$829$	22.7224	+	39.3564i	0.789183	+	1.36690i	−0.137286	+	0.990532i	$0.543838\pi$
$830$		0			0
$831$	18.3564	+	10.5981i	0.636777	+	0.367643i
$832$		0			0
$833$	−28.2199	−	37.7405i	−0.977762	−	1.30763i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−1.93185	−	0.517638i	−0.0667746	−	0.0178922i
$838$		0			0
$839$	51.9615			1.79391			0.896956	−	0.442121i	$-0.145774\pi$
$839$	51.9615			1.79391			0.896956	+	0.442121i	$0.145774\pi$
$840$		0			0
$841$	−19.0000			−0.655172
$842$		0			0
$843$	−8.57321	−	2.29719i	−0.295277	−	0.0791193i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−0.669942	+	9.33109i	−0.0230195	+	0.320620i
$848$		0			0
$849$	−6.35641	−	3.66987i	−0.218151	−	0.125950i
$850$		0			0
$851$	−41.7846	−	72.3731i	−1.43236	−	2.48092i
$852$		0			0
$853$	15.5563	−	15.5563i	0.532639	−	0.532639i	−0.388718	−	0.921357i	$-0.627082\pi$
$853$	15.5563	−	15.5563i	0.532639	−	0.532639i	0.921357	+	0.388718i	$0.127082\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−6.37756	+	23.8014i	−0.217853	+	0.813040i	0.767289	+	0.641301i	$0.221605\pi$
$857$	−6.37756	+	23.8014i	−0.217853	+	0.813040i	−0.985143	+	0.171739i	$0.945062\pi$
$858$		0			0
$859$	−0.464102	+	0.803848i	−0.0158349	+	0.0274269i	−0.873834	−	0.486224i	$-0.838374\pi$
$859$	−0.464102	+	0.803848i	−0.0158349	+	0.0274269i	0.857999	+	0.513651i	$0.171707\pi$
$860$		0			0
$861$	−2.09808	−	10.9019i	−0.0715022	−	0.371537i
$862$		0			0
$863$	−43.0691	+	11.5403i	−1.46609	+	0.392838i	−0.901589	−	0.432594i	$-0.857598\pi$
$863$	−43.0691	+	11.5403i	−1.46609	+	0.392838i	−0.564502	+	0.825432i	$0.690932\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−20.0256	−	20.0256i	−0.680106	−	0.680106i
$868$		0			0
$869$			6.19615i			0.210190i
$870$		0			0
$871$	−6.06218	+	3.50000i	−0.205409	+	0.118593i
$872$		0			0
$873$	−0.915158	−	3.41542i	−0.0309734	−	0.115594i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−2.72191	−	10.1583i	−0.0919124	−	0.343022i	0.904621	−	0.426217i	$-0.140154\pi$
$877$	−2.72191	−	10.1583i	−0.0919124	−	0.343022i	−0.996533	+	0.0831954i	$0.973487\pi$
$878$		0			0
$879$	14.1962	−	8.19615i	0.478824	−	0.276449i
$880$		0			0
$881$			20.0000i			0.673817i	0.941537	+	0.336909i	$0.109381\pi$
$881$			20.0000i			0.673817i	−0.941537	+	0.336909i	$0.890619\pi$
$882$		0			0
$883$	0.226633	+	0.226633i	0.00762682	+	0.00762682i	0.710910	−	0.703283i	$-0.248283\pi$
$883$	0.226633	+	0.226633i	0.00762682	+	0.00762682i	−0.703283	+	0.710910i	$0.748283\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−16.0740	+	4.30701i	−0.539712	+	0.144615i	−0.518369	−	0.855157i	$-0.673461\pi$
$887$	−16.0740	+	4.30701i	−0.539712	+	0.144615i	−0.0213425	+	0.999772i	$0.506794\pi$
$888$		0			0
$889$	0.0621778	−	0.179492i	0.00208538	−	0.00601997i
$890$		0			0
$891$	1.36603	−	2.36603i	0.0457636	−	0.0792648i
$892$		0			0
$893$	22.3364	−	83.3606i	0.747460	−	2.78956i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−5.27792	+	5.27792i	−0.176225	+	0.176225i
$898$		0			0
$899$	−6.92820	−	12.0000i	−0.231069	−	0.400222i
$900$		0			0
$901$	−50.9090	−	29.3923i	−1.69602	−	0.979200i
$902$		0			0
$903$	1.17398	+	0.795040i	0.0390675	+	0.0264573i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	15.7644	+	4.22406i	0.523448	+	0.140258i	0.510861	−	0.859663i	$-0.329327\pi$
$907$	15.7644	+	4.22406i	0.523448	+	0.140258i	0.0125871	+	0.999921i	$0.495993\pi$
$908$		0			0
$909$	6.73205			0.223288
$910$		0			0
$911$	−9.71281			−0.321800			−0.160900	−	0.986971i	$-0.551440\pi$
$911$	−9.71281			−0.321800			−0.160900	+	0.986971i	$0.551440\pi$
$912$		0			0
$913$	−12.4877	−	3.34607i	−0.413282	−	0.110739i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−44.6728	−	3.20736i	−1.47523	−	0.105917i
$918$		0			0
$919$	−10.3923	−	6.00000i	−0.342811	−	0.197922i	0.318704	−	0.947854i	$-0.396753\pi$
$919$	−10.3923	−	6.00000i	−0.342811	−	0.197922i	−0.661514	+	0.749933i	$0.730086\pi$
$920$		0			0
$921$	1.26795	+	2.19615i	0.0417803	+	0.0723657i
$922$		0			0
$923$	−5.65685	+	5.65685i	−0.186198	+	0.186198i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	1.20616	−	4.50146i	0.0396156	−	0.147847i
$928$		0			0
$929$	6.09808	−	10.5622i	0.200071	−	0.346534i	−0.748480	−	0.663158i	$-0.769216\pi$
$929$	6.09808	−	10.5622i	0.200071	−	0.346534i	0.948551	+	0.316624i	$0.102549\pi$
$930$		0			0
$931$	21.9904	+	55.0167i	0.720706	+	1.80310i
$932$		0			0
$933$	5.79555	−	1.55291i	0.189738	−	0.0508401i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−11.8685	−	11.8685i	−0.387727	−	0.387727i	0.486149	−	0.873876i	$-0.338401\pi$
$937$	−11.8685	−	11.8685i	−0.387727	−	0.387727i	−0.873876	+	0.486149i	$0.838401\pi$
$938$		0			0
$939$		−	2.53590i		−	0.0827559i
$940$		0			0
$941$	−0.124356	+	0.0717968i	−0.00405388	+	0.00234051i	−0.502026	−	0.864853i	$-0.667412\pi$
$941$	−0.124356	+	0.0717968i	−0.00405388	+	0.00234051i	0.497972	+	0.867193i	$0.334078\pi$
$942$		0			0
$943$	−8.10634	−	30.2533i	−0.263979	−	0.985183i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−8.44812	−	31.5288i	−0.274527	−	1.02455i	−0.956158	−	0.292852i	$-0.905396\pi$
$947$	−8.44812	−	31.5288i	−0.274527	−	1.02455i	0.681631	−	0.731696i	$-0.261271\pi$
$948$		0			0
$949$	−13.3301	+	7.69615i	−0.432714	+	0.249828i
$950$		0			0
$951$			2.39230i			0.0775758i
$952$		0			0
$953$	−2.41233	−	2.41233i	−0.0781429	−	0.0781429i	0.666955	−	0.745098i	$-0.267597\pi$
$953$	−2.41233	−	2.41233i	−0.0781429	−	0.0781429i	−0.745098	+	0.666955i	$0.767597\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	18.2832	−	4.89898i	0.591013	−	0.158362i
$958$		0			0
$959$	−15.5885	+	3.00000i	−0.503378	+	0.0968751i
$960$		0			0
$961$	−13.5000	+	23.3827i	−0.435484	+	0.754280i
$962$		0			0
$963$	3.81294	−	14.2301i	0.122870	−	0.458558i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−2.50026	+	2.50026i	−0.0804029	+	0.0804029i	−0.746164	−	0.665762i	$-0.768107\pi$
$967$	−2.50026	+	2.50026i	−0.0804029	+	0.0804029i	0.665762	+	0.746164i	$0.268107\pi$
$968$		0			0
$969$	28.4904	+	49.3468i	0.915243	+	1.58525i
$970$		0			0
$971$	−1.22243	−	0.705771i	−0.0392297	−	0.0226493i	0.480257	−	0.877128i	$-0.340543\pi$
$971$	−1.22243	−	0.705771i	−0.0392297	−	0.0226493i	−0.519487	+	0.854479i	$0.673877\pi$
$972$		0			0
$973$	−40.1206	+	19.4758i	−1.28621	+	0.624365i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−23.7506	−	6.36396i	−0.759850	−	0.203601i	−0.141967	−	0.989871i	$-0.545343\pi$
$977$	−23.7506	−	6.36396i	−0.759850	−	0.203601i	−0.617883	+	0.786270i	$0.712009\pi$
$978$		0			0
$979$	19.8564			0.634614
$980$		0			0
$981$	−13.9282			−0.444693
$982$		0			0
$983$	2.39872	+	0.642736i	0.0765073	+	0.0205001i	0.296870	−	0.954918i	$-0.404057\pi$
$983$	2.39872	+	0.642736i	0.0765073	+	0.0205001i	−0.220362	+	0.975418i	$0.570724\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	24.2683	−	11.7806i	0.772467	−	0.374980i
$988$		0			0
$989$	3.46410	+	2.00000i	0.110152	+	0.0635963i
$990$		0			0
$991$	−10.6603	−	18.4641i	−0.338634	−	0.586532i	0.645542	−	0.763725i	$-0.276632\pi$
$991$	−10.6603	−	18.4641i	−0.338634	−	0.586532i	−0.984176	+	0.177193i	$0.943298\pi$
$992$		0			0
$993$	9.43262	−	9.43262i	0.299335	−	0.299335i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	9.02150	−	33.6687i	0.285714	−	1.06630i	−0.662602	−	0.748971i	$-0.730548\pi$
$997$	9.02150	−	33.6687i	0.285714	−	1.06630i	0.948316	−	0.317327i	$-0.102785\pi$
$998$		0			0
$999$	−5.59808	+	9.69615i	−0.177115	+	0.306773i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2100.2.ce.a.1993.2	yes	8
5.2	odd	4		2100.2.ce.b.1657.2	yes	8
5.3	odd	4		2100.2.ce.b.1657.1	yes	8
5.4	even	2	inner	2100.2.ce.a.1993.1	yes	8
7.3	odd	6		2100.2.ce.b.493.2	yes	8
35.3	even	12	inner	2100.2.ce.a.157.1	✓	8
35.17	even	12	inner	2100.2.ce.a.157.2	yes	8
35.24	odd	6		2100.2.ce.b.493.1	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2100.2.ce.a.157.1	✓	8	35.3	even	12	inner
2100.2.ce.a.157.2	yes	8	35.17	even	12	inner
2100.2.ce.a.1993.1	yes	8	5.4	even	2	inner
2100.2.ce.a.1993.2	yes	8	1.1	even	1	trivial
2100.2.ce.b.493.1	yes	8	35.24	odd	6
2100.2.ce.b.493.2	yes	8	7.3	odd	6
2100.2.ce.b.1657.1	yes	8	5.3	odd	4
2100.2.ce.b.1657.2	yes	8	5.2	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2100.ce (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.965926 + 0.258819i) q^{3} +(-2.38014 + 1.15539i) q^{7} +(0.866025 + 0.500000i) q^{9} +O(q^{10})\)	\(q+(0.965926 + 0.258819i) q^{3} +(-2.38014 + 1.15539i) q^{7} +(0.866025 + 0.500000i) q^{9} +(-1.36603 - 2.36603i) q^{11} +(0.707107 - 0.707107i) q^{13} +(1.74238 - 6.50266i) q^{17} +(-4.23205 + 7.33013i) q^{19} +(-2.59808 + 0.500000i) q^{21} +(-7.20977 + 1.93185i) q^{23} +(0.707107 + 0.707107i) q^{27} +6.92820i q^{29} +(-1.73205 + 1.00000i) q^{31} +(-0.707107 - 2.63896i) q^{33} +(2.89778 + 10.8147i) q^{37} +(0.866025 - 0.500000i) q^{39} +4.19615i q^{41} +(-0.378937 - 0.378937i) q^{43} +(-9.84873 + 2.63896i) q^{47} +(4.33013 - 5.50000i) q^{49} +(3.36603 - 5.83013i) q^{51} +(2.26002 - 8.43451i) q^{53} +(-5.98502 + 5.98502i) q^{57} +(4.63397 + 8.02628i) q^{59} +(-8.42820 - 4.86603i) q^{61} +(-2.63896 - 0.189469i) q^{63} +(-6.76148 - 1.81173i) q^{67} -7.46410 q^{69} -8.00000 q^{71} +(-14.8678 - 3.98382i) q^{73} +(5.98502 + 4.05317i) q^{77} +(-1.96410 - 1.13397i) q^{79} +(0.500000 + 0.866025i) q^{81} +(3.34607 - 3.34607i) q^{83} +(-1.79315 + 6.69213i) q^{87} +(-3.63397 + 6.29423i) q^{89} +(-0.866025 + 2.50000i) q^{91} +(-1.93185 + 0.517638i) q^{93} +(-2.50026 - 2.50026i) q^{97} -2.73205i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q+O(q^{10}) \) 8 * q	\( 8 q - 4 q^{11} - 20 q^{19} + 20 q^{51} + 44 q^{59} - 12 q^{61} - 32 q^{69} - 64 q^{71} + 12 q^{79} + 4 q^{81} - 36 q^{89}+O(q^{100}) \) 8 * q - 4 * q^11 - 20 * q^19 + 20 * q^51 + 44 * q^59 - 12 * q^61 - 32 * q^69 - 64 * q^71 + 12 * q^79 + 4 * q^81 - 36 * q^89

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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