LMFDB - Embedded newform 2100.2.ce.a.157.1

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			157.1
Root			$-0.965926 - 0.258819i$ of defining polynomial
Character	$\chi$	$=$	2100.157
Dual form			2100.2.ce.a.1993.1

$q$-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 $\left(\mathbb{Z}/2100\mathbb{Z}\right)^\times$.

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

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	−0.995094	−	0.0989291i	$-0.968458\pi$
$11$	−1.36603	+	2.36603i	−0.411872	+	0.713384i	0.583222	+	0.812313i	$0.301792\pi$
$12$		0			0
$13$	−0.707107	−	0.707107i	−0.196116	−	0.196116i	0.602217	−	0.798333i	$-0.294284\pi$
$13$	−0.707107	−	0.707107i	−0.196116	−	0.196116i	−0.798333	+	0.602217i	$0.794284\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−1.74238	−	6.50266i	−0.422590	−	1.57713i	−0.769130	−	0.639092i	$-0.779310\pi$
$17$	−1.74238	−	6.50266i	−0.422590	−	1.57713i	0.346540	−	0.938035i	$-0.387356\pi$
$18$		0			0
$19$	−4.23205	−	7.33013i	−0.970899	−	1.68165i	−0.692853	−	0.721079i	$-0.743647\pi$
$19$	−4.23205	−	7.33013i	−0.970899	−	1.68165i	−0.278046	−	0.960568i	$-0.589687\pi$
$20$		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	$-0.132807\pi$
$23$	7.20977	+	1.93185i	1.50334	+	0.402819i	0.589123	+	0.808043i	$0.299473\pi$
$24$		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	$-0.777578\pi$
$29$		−	6.92820i		−	1.28654i	0.765641	−	0.643268i	$-0.222422\pi$
$30$		0			0
$31$	−1.73205	−	1.00000i	−0.311086	−	0.179605i	0.336327	−	0.941745i	$-0.390815\pi$
$31$	−1.73205	−	1.00000i	−0.311086	−	0.179605i	−0.647412	+	0.762140i	$0.724149\pi$
$32$		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	0.139646	+	0.990201i	$0.455403\pi$
$37$	−2.89778	+	10.8147i	−0.476392	+	1.77792i	−0.616038	+	0.787717i	$0.711263\pi$
$38$		0			0
$39$	0.866025	+	0.500000i	0.138675	+	0.0800641i
$40$		0			0
$41$		−	4.19615i		−	0.655329i	−0.944794	−	0.327664i	$-0.893738\pi$
$41$		−	4.19615i		−	0.655329i	0.944794	−	0.327664i	$-0.106262\pi$
$42$		0			0
$43$	0.378937	−	0.378937i	0.0577874	−	0.0577874i	−0.677623	−	0.735410i	$-0.736990\pi$
$43$	0.378937	−	0.378937i	0.0577874	−	0.0577874i	0.735410	+	0.677623i	$0.236990\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	9.84873	+	2.63896i	1.43658	+	0.384932i	0.891336	−	0.453343i	$-0.149769\pi$
$47$	9.84873	+	2.63896i	1.43658	+	0.384932i	0.545248	+	0.838275i	$0.316435\pi$
$48$		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	−0.928163	−	0.372175i	$-0.878612\pi$
$53$	−2.26002	−	8.43451i	−0.310438	−	1.15857i	0.617725	−	0.786394i	$-0.288055\pi$
$54$		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	−0.389027	−	0.921226i	$-0.627189\pi$
$59$	4.63397	−	8.02628i	0.603292	−	1.04493i	0.992319	−	0.123706i	$-0.0394780\pi$
$60$		0			0
$61$	−8.42820	+	4.86603i	−1.07912	+	0.623031i	−0.930659	−	0.365887i	$-0.880766\pi$
$61$	−8.42820	+	4.86603i	−1.07912	+	0.623031i	−0.148462	+	0.988918i	$0.547432\pi$
$62$		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	$-0.442695\pi$
$67$	6.76148	−	1.81173i	0.826046	−	0.221338i	0.646988	+	0.762500i	$0.276028\pi$
$68$		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	$-0.226339\pi$
$73$	14.8678	−	3.98382i	1.74015	−	0.466271i	0.982480	+	0.186370i	$0.0596722\pi$
$74$		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	−0.606403	−	0.795157i	$-0.707388\pi$
$79$	−1.96410	+	1.13397i	−0.220979	+	0.127582i	0.385425	+	0.922739i	$0.374055\pi$
$80$		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	$-0.333625\pi$
$83$	−3.34607	−	3.34607i	−0.367278	−	0.367278i	−0.866484	+	0.499205i	$0.833625\pi$
$84$		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	0.606596	−	0.795010i	$-0.292534\pi$
$89$	−3.63397	−	6.29423i	−0.385201	−	0.667187i	−0.991797	+	0.127823i	$0.959201\pi$
$90$		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	$-0.692549\pi$
$97$	2.50026	−	2.50026i	0.253863	−	0.253863i	0.822552	+	0.568690i	$0.192549\pi$
$98$		0			0
$99$			2.73205i			0.274581i
$100$		0			0
$101$	5.83013	+	3.36603i	0.580119	+	0.334932i	0.761181	−	0.648540i	$-0.224620\pi$
$101$	5.83013	+	3.36603i	0.580119	+	0.334932i	−0.181061	+	0.983472i	$0.557953\pi$
$102$		0			0
$103$	1.20616	−	4.50146i	0.118847	−	0.443542i	−0.880699	−	0.473676i	$-0.842927\pi$
$103$	1.20616	−	4.50146i	0.118847	−	0.443542i	0.999546	+	0.0301341i	$0.00959342\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	3.81294	−	14.2301i	0.368610	−	1.37567i	−0.493850	−	0.869547i	$-0.664411\pi$
$107$	3.81294	−	14.2301i	0.368610	−	1.37567i	0.862460	−	0.506125i	$-0.168923\pi$
$108$		0			0
$109$	−12.0622	−	6.96410i	−1.15535	−	0.667040i	−0.205163	−	0.978728i	$-0.565772\pi$
$109$	−12.0622	−	6.96410i	−1.15535	−	0.667040i	−0.950185	+	0.311688i	$0.899106\pi$
$110$		0			0
$111$		−	11.1962i		−	1.06269i
$112$		0			0
$113$	6.03579	−	6.03579i	0.567800	−	0.567800i	−0.363712	−	0.931511i	$-0.618491\pi$
$113$	6.03579	−	6.03579i	0.567800	−	0.567800i	0.931511	+	0.363712i	$0.118491\pi$
$114$		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	$-0.248986\pi$
$127$	0.0507680	+	0.0507680i	0.00450493	+	0.00450493i	−0.704851	+	0.709356i	$0.748986\pi$
$128$		0			0
$129$	−0.267949	+	0.464102i	−0.0235916	+	0.0408619i
$130$		0			0
$131$	14.6603	−	8.46410i	1.28087	−	0.739512i	0.303864	−	0.952715i	$-0.401723\pi$
$131$	14.6603	−	8.46410i	1.28087	−	0.739512i	0.977008	+	0.213203i	$0.0683897\pi$
$132$		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	$-0.665839\pi$
$137$	−5.79555	+	1.55291i	−0.495148	+	0.132674i	0.00259945	+	0.999997i	$0.499173\pi$
$138$		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	−0.140090	−	0.990139i	$-0.544739\pi$
$149$	7.90192	−	4.56218i	0.647351	−	0.373748i	0.787441	+	0.616391i	$0.211406\pi$
$150$		0			0
$151$	5.33013	−	9.23205i	0.433760	−	0.751294i	−0.563434	−	0.826161i	$-0.690520\pi$
$151$	5.33013	−	9.23205i	0.433760	−	0.751294i	0.997193	+	0.0748675i	$0.0238534\pi$
$152$		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	0.961905	+	0.273382i	$0.0881424\pi$
$157$	3.32748	+	12.4183i	0.265562	+	0.991091i	−0.696343	+	0.717709i	$0.745191\pi$
$158$		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	$-0.379182\pi$
$163$	2.89778	+	0.776457i	0.226971	+	0.0608168i	−0.143541	+	0.989644i	$0.545849\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−0.240237	+	0.240237i	−0.0185901	+	0.0185901i	−0.716341	−	0.697751i	$-0.754184\pi$
$167$	−0.240237	+	0.240237i	−0.0185901	+	0.0185901i	0.697751	+	0.716341i	$0.254184\pi$
$168$		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	0.725856	+	0.687847i	$0.241444\pi$
$173$	−3.24453	+	12.1087i	−0.246677	+	0.920611i	−0.972533	+	0.232765i	$0.925223\pi$
$174$		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	0.161377	−	0.986893i	$-0.448407\pi$
$179$	−8.19615	−	4.73205i	−0.612609	−	0.353690i	−0.773986	+	0.633203i	$0.781740\pi$
$180$		0			0
$181$		−	6.39230i		−	0.475136i	−0.971371	−	0.237568i	$-0.923650\pi$
$181$		−	6.39230i		−	0.475136i	0.971371	−	0.237568i	$-0.0763503\pi$
$182$		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	0.856351	+	0.516394i	$0.172726\pi$
$191$	12.0981	+	20.9545i	0.875386	+	1.51621i	0.0190352	+	0.999819i	$0.493941\pi$
$192$		0			0
$193$	3.44760	+	12.8666i	0.248164	+	0.926160i	0.971767	+	0.235943i	$0.0758180\pi$
$193$	3.44760	+	12.8666i	0.248164	+	0.926160i	−0.723603	+	0.690216i	$0.757515\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−3.58630	−	3.58630i	−0.255513	−	0.255513i	0.567713	−	0.823226i	$-0.307828\pi$
$197$	−3.58630	−	3.58630i	−0.255513	−	0.255513i	−0.823226	+	0.567713i	$0.807828\pi$
$198$		0			0
$199$	−4.23205	+	7.33013i	−0.300002	+	0.519619i	−0.976136	−	0.217160i	$-0.930321\pi$
$199$	−4.23205	+	7.33013i	−0.300002	+	0.519619i	0.676134	+	0.736779i	$0.263654\pi$
$200$		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	$-0.264284\pi$
$223$	−0.947343	−	0.947343i	−0.0634388	−	0.0634388i	−0.738114	+	0.674676i	$0.764284\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−3.58630	−	13.3843i	−0.238031	−	0.888345i	−0.976759	−	0.214341i	$-0.931240\pi$
$227$	−3.58630	−	13.3843i	−0.238031	−	0.888345i	0.738728	−	0.674004i	$-0.235427\pi$
$228$		0			0
$229$	5.86603	+	10.1603i	0.387638	+	0.671408i	0.992131	−	0.125202i	$-0.0399578\pi$
$229$	5.86603	+	10.1603i	0.387638	+	0.671408i	−0.604493	+	0.796610i	$0.706624\pi$
$230$		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	$-0.531009\pi$
$233$	−10.3664	−	2.77766i	−0.679123	−	0.181971i	−0.581861	+	0.813288i	$0.697675\pi$
$234$		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	$-0.728006\pi$
$239$		−	23.3205i		−	1.50848i	0.656600	−	0.754239i	$-0.271994\pi$
$240$		0			0
$241$	−9.69615	−	5.59808i	−0.624584	−	0.360604i	0.154068	−	0.988060i	$-0.450763\pi$
$241$	−9.69615	−	5.59808i	−0.624584	−	0.360604i	−0.778652	+	0.627457i	$0.784096\pi$
$242$		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	$-0.891544\pi$
$251$		−	10.5885i		−	0.668337i	0.942513	−	0.334169i	$-0.108456\pi$
$252$		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	$-0.650839\pi$
$257$	−20.7835	−	5.56892i	−1.29644	−	0.347380i	−0.840103	+	0.542428i	$0.817505\pi$
$258$		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	0.999765	+	0.0216758i	$0.00690017\pi$
$263$	2.34795	+	8.76268i	0.144781	+	0.540330i	−0.854984	+	0.518654i	$0.826433\pi$
$264$		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	−0.966727	−	0.255812i	$-0.917657\pi$
$269$	−4.29423	+	7.43782i	−0.261824	+	0.453492i	0.704903	+	0.709304i	$0.250991\pi$
$270$		0			0
$271$	12.9282	−	7.46410i	0.785332	−	0.453412i	−0.0529843	−	0.998595i	$-0.516873\pi$
$271$	12.9282	−	7.46410i	0.785332	−	0.453412i	0.838317	+	0.545183i	$0.183540\pi$
$272$		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	$-0.803066\pi$
$277$	−20.4739	+	5.48597i	−1.23016	+	0.329620i	−0.415517	+	0.909585i	$0.636399\pi$
$278$		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	$-0.513331\pi$
$283$	7.08965	−	1.89967i	0.421436	−	0.112923i	0.463303	+	0.886200i	$0.346664\pi$
$284$		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	$-0.408937\pi$
$293$	−11.5911	−	11.5911i	−0.677160	−	0.677160i	−0.959357	+	0.282197i	$0.908937\pi$
$294$		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	$-0.773055\pi$
$307$	−1.79315	+	1.79315i	−0.102341	+	0.102341i	0.654083	+	0.756423i	$0.273055\pi$
$308$		0			0
$309$			4.66025i			0.265113i
$310$		0			0
$311$	5.19615	+	3.00000i	0.294647	+	0.170114i	0.640036	−	0.768345i	$-0.278920\pi$
$311$	5.19615	+	3.00000i	0.294647	+	0.170114i	−0.345389	+	0.938460i	$0.612253\pi$
$312$		0			0
$313$	0.656339	−	2.44949i	0.0370985	−	0.138453i	−0.944893	−	0.327380i	$-0.893834\pi$
$313$	0.656339	−	2.44949i	0.0370985	−	0.138453i	0.981991	+	0.188927i	$0.0605009\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−0.619174	+	2.31079i	−0.0347763	+	0.129787i	−0.981132	−	0.193341i	$-0.938068\pi$
$317$	−0.619174	+	2.31079i	−0.0347763	+	0.129787i	0.946355	+	0.323128i	$0.104734\pi$
$318$		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	0.989033	−	0.147694i	$-0.0471852\pi$
$331$	6.66987	+	11.5526i	0.366609	+	0.634986i	−0.622424	+	0.782681i	$0.713852\pi$
$332$		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	$-0.241952\pi$
$337$	0.656339	+	0.656339i	0.0357531	+	0.0357531i	−0.689004	+	0.724757i	$0.741952\pi$
$338$		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	$-0.180978\pi$
$347$	34.3065	−	9.19239i	1.84167	−	0.493473i	0.998989	+	0.0449449i	$0.0143112\pi$
$348$		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	$-0.683765\pi$
$353$	−11.2629	+	3.01790i	−0.599466	+	0.160626i	−0.0536901	+	0.998558i	$0.517098\pi$
$354$		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	0.304950	−	0.952368i	$-0.401360\pi$
$359$	24.2942	−	14.0263i	1.28220	−	0.740279i	0.977250	+	0.212090i	$0.0680269\pi$
$360$		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	$-0.145743\pi$
$367$	−1.93185	−	7.20977i	−0.100842	−	0.376347i	−0.997840	+	0.0656868i	$0.979076\pi$
$368$		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	$-0.289247\pi$
$373$	14.5397	+	3.89589i	0.752835	+	0.201721i	0.138060	+	0.990424i	$0.455913\pi$
$374$		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	$0.205685\pi$
$379$			23.4449i			1.20428i	−0.798390	+	0.602141i	$0.794315\pi$
$380$		0			0
$381$	−0.0621778	−	0.0358984i	−0.00318547	−	0.00183913i
$382$		0			0
$383$	−7.69024	+	28.7004i	−0.392953	+	1.46652i	0.432286	+	0.901737i	$0.357707\pi$
$383$	−7.69024	+	28.7004i	−0.392953	+	1.46652i	−0.825239	+	0.564784i	$0.808960\pi$
$384$		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	0.0552980	−	0.998470i	$-0.482389\pi$
$389$	−15.4186	−	8.90192i	−0.781753	−	0.451345i	−0.837051	+	0.547124i	$0.815722\pi$
$390$		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	$-0.364223\pi$
$397$	6.31319	+	1.69161i	0.316850	+	0.0848997i	−0.0968891	+	0.995295i	$0.530889\pi$
$398$		0			0
$399$	7.33013	+	21.1603i	0.366965	+	1.05934i
$400$		0			0
$401$	13.2942	+	23.0263i	0.663882	+	1.14988i	0.979587	+	0.201020i	$0.0644257\pi$
$401$	13.2942	+	23.0263i	0.663882	+	1.14988i	−0.315705	+	0.948857i	$0.602241\pi$
$402$		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	−0.686467	−	0.727161i	$-0.740839\pi$
$409$	5.79423	−	10.0359i	0.286506	−	0.496243i	0.972973	+	0.230918i	$0.0741728\pi$
$410$		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	−0.967996	−	0.250966i	$-0.919252\pi$
$431$	−5.53590	+	9.58846i	−0.266655	+	0.461860i	0.701341	+	0.712826i	$0.252585\pi$
$432$		0			0
$433$	−21.5921	−	21.5921i	−1.03765	−	1.03765i	−0.999263	−	0.0383892i	$-0.987777\pi$
$433$	−21.5921	−	21.5921i	−1.03765	−	1.03765i	−0.0383892	−	0.999263i	$-0.512223\pi$
$434$		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	0.653352	−	0.757054i	$-0.273362\pi$
$439$	−6.89230	−	11.9378i	−0.328952	−	0.569761i	−0.982304	+	0.187293i	$0.940029\pi$
$440$		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	$-0.231072\pi$
$443$	22.3872	+	5.99863i	1.06365	+	0.285003i	0.315767	+	0.948837i	$0.397738\pi$
$444$		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	$-0.921546\pi$
$449$		−	10.3397i		−	0.487963i	0.969780	−	0.243981i	$-0.0784536\pi$
$450$		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	−0.796992	−	0.603990i	$-0.793577\pi$
$457$	4.17329	−	15.5749i	0.195218	−	0.728565i	0.992210	−	0.124575i	$-0.0397566\pi$
$458$		0			0
$459$	5.83013	+	3.36603i	0.272127	+	0.157113i
$460$		0			0
$461$		−	17.7128i		−	0.824968i	−0.910965	−	0.412484i	$-0.864661\pi$
$461$		−	17.7128i		−	0.824968i	0.910965	−	0.412484i	$-0.135339\pi$
$462$		0			0
$463$	−22.0962	+	22.0962i	−1.02690	+	1.02690i	−0.0272682	+	0.999628i	$0.508681\pi$
$463$	−22.0962	+	22.0962i	−1.02690	+	1.02690i	−0.999628	+	0.0272682i	$0.991319\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−26.9072	−	7.20977i	−1.24512	−	0.333628i	−0.424669	−	0.905349i	$-0.639610\pi$
$467$	−26.9072	−	7.20977i	−1.24512	−	0.333628i	−0.820449	+	0.571720i	$0.806276\pi$
$468$		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	0.388037	+	0.921644i	$0.373153\pi$
$479$	−13.2224	+	22.9019i	−0.604148	+	1.04642i	−0.992185	+	0.124772i	$0.960180\pi$
$480$		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	$-0.388844\pi$
$487$	24.4577	−	6.55343i	1.10829	−	0.296964i	0.766134	+	0.642681i	$0.222178\pi$
$488$		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	−0.523007	−	0.852328i	$-0.675190\pi$
$499$	−1.03590	+	0.598076i	−0.0463732	+	0.0267736i	0.476634	+	0.879102i	$0.341857\pi$
$500$		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	$-0.0966401\pi$
$503$	14.6969	+	14.6969i	0.655304	+	0.655304i	−0.298961	+	0.954265i	$0.596640\pi$
$504$		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	0.999612	−	0.0278471i	$-0.00886516\pi$
$509$	10.7321	+	18.5885i	0.475690	+	0.823919i	−0.523922	+	0.851766i	$0.675532\pi$
$510$		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	0.995943	−	0.0899832i	$-0.0286813\pi$
$521$	32.3205	+	18.6603i	1.41599	+	0.817521i	0.420044	+	0.907504i	$0.362015\pi$
$522$		0			0
$523$	−5.00052	+	18.6622i	−0.218657	+	0.816040i	0.766190	+	0.642614i	$0.222150\pi$
$523$	−5.00052	+	18.6622i	−0.218657	+	0.816040i	−0.984847	+	0.173426i	$0.944516\pi$
$524$		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	0.902861	+	0.429934i	$0.141463\pi$
$541$	19.1603	+	33.1865i	0.823764	+	1.42680i	−0.0790969	+	0.996867i	$0.525204\pi$
$542$		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	$-0.0390064\pi$
$547$	20.3538	+	20.3538i	0.870265	+	0.870265i	−0.122236	+	0.992501i	$0.539006\pi$
$548$		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	$-0.553670\pi$
$557$	4.24264	−	1.13681i	0.179766	−	0.0481683i	0.347579	+	0.937651i	$0.387004\pi$
$558$		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	$-0.896548\pi$
$563$	−38.1702	+	10.2277i	−1.60868	+	0.431045i	−0.661031	+	0.750358i	$0.729881\pi$
$564$		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	−0.994493	−	0.104801i	$-0.966580\pi$
$569$	−33.4186	+	19.2942i	−1.40098	+	0.808856i	−0.406487	+	0.913657i	$0.633246\pi$
$570$		0			0
$571$	13.4545	−	23.3038i	0.563053	−	0.975236i	−0.434175	−	0.900828i	$-0.642960\pi$
$571$	13.4545	−	23.3038i	0.563053	−	0.975236i	0.997228	−	0.0744073i	$-0.0237065\pi$
$572$		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	$-0.0165882\pi$
$577$	2.58819	+	9.65926i	0.107748	+	0.402120i	−0.890895	+	0.454210i	$0.849922\pi$
$578$		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	$-0.539886\pi$
$587$	21.0101	−	21.0101i	0.867181	−	0.867181i	0.992159	+	0.124979i	$0.0398862\pi$
$588$		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	−0.481106	−	0.876662i	$-0.659765\pi$
$593$	9.10446	−	33.9783i	0.373875	−	1.39532i	0.854981	−	0.518659i	$-0.173568\pi$
$594$		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	0.235483	−	0.971878i	$-0.424333\pi$
$599$	−11.9545	−	6.90192i	−0.488447	−	0.282005i	−0.723930	+	0.689874i	$0.757666\pi$
$600$		0			0
$601$		−	12.5167i		−	0.510565i	−0.966866	−	0.255283i	$-0.917831\pi$
$601$		−	12.5167i		−	0.510565i	0.966866	−	0.255283i	$-0.0821685\pi$
$602$		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	$-0.512826\pi$
$607$	−14.1607	−	3.79435i	−0.574766	−	0.154008i	−0.534481	+	0.845180i	$0.679493\pi$
$608$		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	0.944189	+	0.329405i	$0.106848\pi$
$613$	7.20977	+	26.9072i	0.291200	+	1.08677i	−0.652989	+	0.757367i	$0.726485\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	4.14110	+	4.14110i	0.166715	+	0.166715i	0.785534	−	0.618819i	$-0.212389\pi$
$617$	4.14110	+	4.14110i	0.166715	+	0.166715i	−0.618819	+	0.785534i	$0.712389\pi$
$618$		0			0
$619$	−19.1962	+	33.2487i	−0.771559	+	1.33638i	0.165150	+	0.986268i	$0.447189\pi$
$619$	−19.1962	+	33.2487i	−0.771559	+	1.33638i	−0.936709	+	0.350110i	$0.886144\pi$
$620$		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	0.0549467	−	0.998489i	$-0.482501\pi$
$641$	22.5885	−	39.1244i	0.892190	−	1.54532i	0.837244	−	0.546830i	$-0.184166\pi$
$642$		0			0
$643$	−33.5486	−	33.5486i	−1.32303	−	1.32303i	−0.911313	−	0.411714i	$-0.864930\pi$
$643$	−33.5486	−	33.5486i	−1.32303	−	1.32303i	−0.411714	−	0.911313i	$-0.635070\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	9.19239	+	34.3065i	0.361390	+	1.34873i	0.872249	+	0.489062i	$0.162661\pi$
$647$	9.19239	+	34.3065i	0.361390	+	1.34873i	−0.510859	+	0.859664i	$0.670673\pi$
$648$		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	$-0.413002\pi$
$653$	0.568406	+	0.152304i	0.0222434	+	0.00596011i	−0.247680	+	0.968842i	$0.579668\pi$
$654$		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	$0.0351639\pi$
$659$			5.66025i			0.220492i	−0.993904	+	0.110246i	$0.964836\pi$
$660$		0			0
$661$	1.37564	+	0.794229i	0.0535064	+	0.0308919i	0.526515	−	0.850166i	$-0.323499\pi$
$661$	1.37564	+	0.794229i	0.0535064	+	0.0308919i	−0.473008	+	0.881058i	$0.656832\pi$
$662$		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	$-0.677396\pi$
$673$	8.29581	−	8.29581i	0.319780	−	0.319780i	0.848683	+	0.528903i	$0.177396\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	3.34607	+	0.896575i	0.128600	+	0.0344582i	0.322545	−	0.946554i	$-0.395462\pi$
$677$	3.34607	+	0.896575i	0.128600	+	0.0344582i	−0.193945	+	0.981012i	$0.562128\pi$
$678$		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	$-0.0141698\pi$
$683$	2.91636	+	10.8840i	0.111591	+	0.416465i	−0.887418	+	0.460966i	$0.847503\pi$
$684$		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	−0.702104	−	0.712075i	$-0.747756\pi$
$691$	−11.4737	+	6.62436i	−0.436481	+	0.252002i	0.265623	+	0.964077i	$0.414422\pi$
$692$		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	−0.581308	−	0.813684i	$-0.697459\pi$
$709$	−4.45448	+	2.57180i	−0.167292	+	0.0965859i	0.414017	+	0.910269i	$0.364126\pi$
$710$		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	0.941008	−	0.338383i	$-0.109880\pi$
$719$	4.75833	+	8.24167i	0.177456	+	0.307362i	−0.763553	+	0.645746i	$0.776547\pi$
$720$		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	$-0.745255\pi$
$727$	0.568406	−	0.568406i	0.0210810	−	0.0210810i	0.717569	+	0.696488i	$0.245255\pi$
$728$		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	0.841497	+	0.540262i	$0.181675\pi$
$733$	−4.26122	+	15.9031i	−0.157392	+	0.587394i	−0.998889	+	0.0471323i	$0.984992\pi$
$734$		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	−0.0370191	−	0.999315i	$-0.511786\pi$
$739$	−25.0359	−	14.4545i	−0.920960	−	0.531717i	−0.883941	+	0.467598i	$0.845120\pi$
$740$		0			0
$741$		−	8.46410i		−	0.310937i
$742$		0			0
$743$	−24.1160	+	24.1160i	−0.884729	+	0.884729i	−0.994011	−	0.109282i	$-0.965145\pi$
$743$	−24.1160	+	24.1160i	−0.884729	+	0.884729i	0.109282	+	0.994011i	$0.465145\pi$
$744$		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	0.864889	−	0.501964i	$-0.167389\pi$
$751$	−0.0621778	−	0.107695i	−0.00226890	−	0.00392985i	−0.867158	+	0.498034i	$0.834056\pi$
$752$		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	$-0.202832\pi$
$757$	5.74479	+	5.74479i	0.208798	+	0.208798i	−0.594959	+	0.803756i	$0.702832\pi$
$758$		0			0
$759$	10.1962	−	17.6603i	0.370097	−	0.641027i
$760$		0			0
$761$	20.4904	−	11.8301i	0.742776	−	0.428842i	−0.0803019	−	0.996771i	$-0.525588\pi$
$761$	20.4904	−	11.8301i	0.742776	−	0.428842i	0.823078	+	0.567929i	$0.192255\pi$
$762$		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	$-0.601750\pi$
$773$	−3.10583	+	0.832204i	−0.111709	+	0.0299323i	0.202532	+	0.979276i	$0.435083\pi$
$774$		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	$-0.0809985\pi$
$787$	0.106515	+	0.397520i	0.00379685	+	0.0141700i	−0.964001	+	0.265897i	$0.914332\pi$
$788$		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	−0.0638402	+	0.997960i	$0.520335\pi$
$797$	−29.9759	+	29.9759i	−1.06180	+	1.06180i	−0.997960	+	0.0638402i	$0.979665\pi$
$798$		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	−0.996520	−	0.0833589i	$-0.973435\pi$
$809$	−44.5692	−	25.7321i	−1.56697	−	0.904691i	−0.570451	−	0.821332i	$-0.693231\pi$
$810$		0			0
$811$			27.1436i			0.953140i	0.879136	+	0.476570i	$0.158120\pi$
$811$			27.1436i			0.953140i	−0.879136	+	0.476570i	$0.841880\pi$
$812$		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	0.825577	+	0.564290i	$0.190850\pi$
$821$	25.8301	+	44.7391i	0.901478	+	1.56141i	0.0759008	+	0.997115i	$0.475817\pi$
$822$		0			0
$823$	0.0829536	+	0.309587i	0.00289158	+	0.0107915i	0.967357	−	0.253419i	$-0.0815552\pi$
$823$	0.0829536	+	0.309587i	0.00289158	+	0.0107915i	−0.964465	+	0.264211i	$0.914889\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	10.2784	+	10.2784i	0.357416	+	0.357416i	0.862860	−	0.505444i	$-0.168671\pi$
$827$	10.2784	+	10.2784i	0.357416	+	0.357416i	−0.505444	+	0.862860i	$0.668671\pi$
$828$		0			0
$829$	22.7224	−	39.3564i	0.789183	−	1.36690i	−0.137286	−	0.990532i	$-0.543838\pi$
$829$	22.7224	−	39.3564i	0.789183	−	1.36690i	0.926468	−	0.376373i	$-0.122829\pi$
$830$		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	$-0.372918\pi$
$853$	−15.5563	−	15.5563i	−0.532639	−	0.532639i	−0.921357	+	0.388718i	$0.872918\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	6.37756	+	23.8014i	0.217853	+	0.813040i	0.985143	+	0.171739i	$0.0549385\pi$
$857$	6.37756	+	23.8014i	0.217853	+	0.813040i	−0.767289	+	0.641301i	$0.778395\pi$
$858$		0			0
$859$	−0.464102	−	0.803848i	−0.0158349	−	0.0274269i	0.857999	−	0.513651i	$-0.171707\pi$
$859$	−0.464102	−	0.803848i	−0.0158349	−	0.0274269i	−0.873834	+	0.486224i	$0.838374\pi$
$860$		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	$-0.142402\pi$
$863$	43.0691	+	11.5403i	1.46609	+	0.392838i	0.564502	+	0.825432i	$0.309068\pi$
$864$		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	$-0.859846\pi$
$877$	2.72191	−	10.1583i	0.0919124	−	0.343022i	0.996533	+	0.0831954i	$0.0265126\pi$
$878$		0			0
$879$	14.1962	+	8.19615i	0.478824	+	0.276449i
$880$		0			0
$881$		−	20.0000i		−	0.673817i	−0.941537	−	0.336909i	$-0.890619\pi$
$881$		−	20.0000i		−	0.673817i	0.941537	−	0.336909i	$-0.109381\pi$
$882$		0			0
$883$	−0.226633	+	0.226633i	−0.00762682	+	0.00762682i	−0.710910	−	0.703283i	$-0.751717\pi$
$883$	−0.226633	+	0.226633i	−0.00762682	+	0.00762682i	0.703283	+	0.710910i	$0.251717\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	16.0740	+	4.30701i	0.539712	+	0.144615i	0.518369	−	0.855157i	$-0.326539\pi$
$887$	16.0740	+	4.30701i	0.539712	+	0.144615i	0.0213425	+	0.999772i	$0.493206\pi$
$888$		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	$-0.670673\pi$
$907$	−15.7644	+	4.22406i	−0.523448	+	0.140258i	−0.0125871	+	0.999921i	$0.504007\pi$
$908$		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	−0.661514	−	0.749933i	$-0.730086\pi$
$919$	−10.3923	+	6.00000i	−0.342811	+	0.197922i	0.318704	+	0.947854i	$0.396753\pi$
$920$		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	0.948551	−	0.316624i	$-0.102549\pi$
$929$	6.09808	+	10.5622i	0.200071	+	0.346534i	−0.748480	+	0.663158i	$0.769216\pi$
$930$		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	$-0.661599\pi$
$937$	11.8685	−	11.8685i	0.387727	−	0.387727i	0.873876	+	0.486149i	$0.161599\pi$
$938$		0			0
$939$			2.53590i			0.0827559i
$940$		0			0
$941$	−0.124356	−	0.0717968i	−0.00405388	−	0.00234051i	0.497972	−	0.867193i	$-0.334078\pi$
$941$	−0.124356	−	0.0717968i	−0.00405388	−	0.00234051i	−0.502026	+	0.864853i	$0.667412\pi$
$942$		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	−0.681631	−	0.731696i	$-0.738729\pi$
$947$	8.44812	−	31.5288i	0.274527	−	1.02455i	0.956158	−	0.292852i	$-0.0946044\pi$
$948$		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	$-0.732403\pi$
$953$	2.41233	−	2.41233i	0.0781429	−	0.0781429i	0.745098	+	0.666955i	$0.232403\pi$
$954$		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	$-0.231893\pi$
$967$	2.50026	+	2.50026i	0.0804029	+	0.0804029i	−0.665762	+	0.746164i	$0.731893\pi$
$968$		0			0
$969$	28.4904	−	49.3468i	0.915243	−	1.58525i
$970$		0			0
$971$	−1.22243	+	0.705771i	−0.0392297	+	0.0226493i	−0.519487	−	0.854479i	$-0.673877\pi$
$971$	−1.22243	+	0.705771i	−0.0392297	+	0.0226493i	0.480257	+	0.877128i	$0.340543\pi$
$972$		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	$-0.454657\pi$
$977$	23.7506	−	6.36396i	0.759850	−	0.203601i	0.617883	+	0.786270i	$0.287991\pi$
$978$		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	$-0.595943\pi$
$983$	−2.39872	+	0.642736i	−0.0765073	+	0.0205001i	0.220362	+	0.975418i	$0.429276\pi$
$984$		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	−0.984176	−	0.177193i	$-0.943298\pi$
$991$	−10.6603	+	18.4641i	−0.338634	+	0.586532i	0.645542	+	0.763725i	$0.276632\pi$
$992$		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	−0.948316	−	0.317327i	$-0.897215\pi$
$997$	−9.02150	−	33.6687i	−0.285714	−	1.06630i	0.662602	−	0.748971i	$-0.269452\pi$
$998$		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.157.1	✓	8
5.2	odd	4		2100.2.ce.b.493.2	yes	8
5.3	odd	4		2100.2.ce.b.493.1	yes	8
5.4	even	2	inner	2100.2.ce.a.157.2	yes	8
7.5	odd	6		2100.2.ce.b.1657.1	yes	8
35.12	even	12	inner	2100.2.ce.a.1993.2	yes	8
35.19	odd	6		2100.2.ce.b.1657.2	yes	8
35.33	even	12	inner	2100.2.ce.a.1993.1	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2100.2.ce.a.157.1	✓	8	1.1	even	1	trivial
2100.2.ce.a.157.2	yes	8	5.4	even	2	inner
2100.2.ce.a.1993.1	yes	8	35.33	even	12	inner
2100.2.ce.a.1993.2	yes	8	35.12	even	12	inner
2100.2.ce.b.493.1	yes	8	5.3	odd	4
2100.2.ce.b.493.2	yes	8	5.2	odd	4
2100.2.ce.b.1657.1	yes	8	7.5	odd	6
2100.2.ce.b.1657.2	yes	8	35.19	odd	6

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

Related objects

Downloads

Learn more