LMFDB - Embedded newform 2100.2.ce.c.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:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			157.1
Character	$\chi$	$=$	2100.157
Dual form			2100.2.ce.c.1993.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.965926 + 0.258819i) q^{3} +(-0.588711 + 2.57942i) q^{7} +(0.866025 - 0.500000i) q^{9} +O(q^{10})$	\(q+(-0.965926 + 0.258819i) q^{3} +(-0.588711 + 2.57942i) q^{7} +(0.866025 - 0.500000i) q^{9} +(-0.401047 + 0.694634i) q^{11} +(2.60097 + 2.60097i) q^{13} +(0.207597 + 0.774764i) q^{17} +(-1.40765 - 2.43811i) q^{19} +(-0.0989528 - 2.64390i) q^{21} +(8.12259 + 2.17644i) q^{23} +(-0.707107 + 0.707107i) q^{27} +(-5.14126 - 2.96831i) q^{31} +(0.207597 - 0.774764i) q^{33} +(0.448288 - 1.67303i) q^{37} +(-3.18552 - 1.83916i) q^{39} +7.01985i q^{41} +(-2.23310 + 2.23310i) q^{43} +(-10.1949 - 2.73172i) q^{47} +(-6.30684 - 3.03707i) q^{49} +(-0.401047 - 0.694634i) q^{51} +(3.27417 + 12.2194i) q^{53} +(1.99071 + 1.99071i) q^{57} +(-3.50993 + 6.07937i) q^{59} +(8.78251 - 5.07059i) q^{61} +(0.779873 + 2.52820i) q^{63} +(-2.71936 + 0.728651i) q^{67} -8.40912 q^{69} -5.35664 q^{71} +(7.68957 - 2.06042i) q^{73} +(-1.55565 - 1.44341i) q^{77} +(-5.85687 + 3.38146i) q^{79} +(0.500000 - 0.866025i) q^{81} +(0.112245 + 0.112245i) q^{83} +(0.694634 + 1.20314i) q^{89} +(-8.24021 + 5.17777i) q^{91} +(5.73433 + 1.53651i) q^{93} +(-3.53553 + 3.53553i) q^{97} +0.802094i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q+O(q^{10}) $ 24 * q	$ 24 q - 8 q^{11} - 4 q^{21} - 60 q^{31} - 8 q^{51} + 84 q^{61} + 112 q^{71} + 12 q^{81} - 136 q^{91}+O(q^{100}) $ 24 * q - 8 * q^11 - 4 * q^21 - 60 * q^31 - 8 * q^51 + 84 * q^61 + 112 * q^71 + 12 * q^81 - 136 * q^91

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
$7$	−0.588711	+	2.57942i	−0.222512	+	0.974930i
$7$	−0.588711	+	2.57942i	−0.222512	+	0.974930i
$8$		0			0
$9$	0.866025	−	0.500000i	0.288675	−	0.166667i
$10$		0			0
$11$	−0.401047	+	0.694634i	−0.120920	+	0.209440i	−0.920131	−	0.391611i	$-0.871918\pi$
$11$	−0.401047	+	0.694634i	−0.120920	+	0.209440i	0.799211	+	0.601051i	$0.205251\pi$
$12$		0			0
$13$	2.60097	+	2.60097i	0.721378	+	0.721378i	0.968886	−	0.247508i	$-0.0796115\pi$
$13$	2.60097	+	2.60097i	0.721378	+	0.721378i	−0.247508	+	0.968886i	$0.579612\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	0.207597	+	0.774764i	0.0503497	+	0.187908i	0.986520	−	0.163638i	$-0.0523229\pi$
$17$	0.207597	+	0.774764i	0.0503497	+	0.187908i	−0.936171	+	0.351546i	$0.885656\pi$
$18$		0			0
$19$	−1.40765	−	2.43811i	−0.322936	−	0.559342i	0.658156	−	0.752881i	$-0.271337\pi$
$19$	−1.40765	−	2.43811i	−0.322936	−	0.559342i	−0.981092	+	0.193540i	$0.938003\pi$
$20$		0			0
$21$	−0.0989528	−	2.64390i	−0.0215933	−	0.576946i
$22$		0			0
$23$	8.12259	+	2.17644i	1.69368	+	0.453819i	0.971334	−	0.237717i	$-0.0763991\pi$
$23$	8.12259	+	2.17644i	1.69368	+	0.453819i	0.722342	+	0.691536i	$0.243066\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$		0			0
$29$		0			0		1.00000			$0$
$29$		0			0		−1.00000			$\pi$
$30$		0			0
$31$	−5.14126	−	2.96831i	−0.923397	−	0.533123i	−0.0386796	−	0.999252i	$-0.512315\pi$
$31$	−5.14126	−	2.96831i	−0.923397	−	0.533123i	−0.884717	+	0.466128i	$0.845649\pi$
$32$		0			0
$33$	0.207597	−	0.774764i	0.0361381	−	0.134869i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	0.448288	−	1.67303i	0.0736980	−	0.275045i	−0.919237	−	0.393705i	$-0.871193\pi$
$37$	0.448288	−	1.67303i	0.0736980	−	0.275045i	0.992935	+	0.118660i	$0.0378599\pi$
$38$		0			0
$39$	−3.18552	−	1.83916i	−0.510092	−	0.294501i
$40$		0			0
$41$			7.01985i			1.09632i	0.836375	+	0.548158i	$0.184671\pi$
$41$			7.01985i			1.09632i	−0.836375	+	0.548158i	$0.815329\pi$
$42$		0			0
$43$	−2.23310	+	2.23310i	−0.340544	+	0.340544i	−0.856572	−	0.516028i	$-0.827410\pi$
$43$	−2.23310	+	2.23310i	−0.340544	+	0.340544i	0.516028	+	0.856572i	$0.327410\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−10.1949	−	2.73172i	−1.48708	−	0.398462i	−0.578331	−	0.815802i	$-0.696296\pi$
$47$	−10.1949	−	2.73172i	−1.48708	−	0.398462i	−0.908750	+	0.417340i	$0.862962\pi$
$48$		0			0
$49$	−6.30684	−	3.03707i	−0.900977	−	0.433867i
$50$		0			0
$51$	−0.401047	−	0.694634i	−0.0561578	−	0.0972682i
$52$		0			0
$53$	3.27417	+	12.2194i	0.449742	+	1.67846i	0.703102	+	0.711089i	$0.251798\pi$
$53$	3.27417	+	12.2194i	0.449742	+	1.67846i	−0.253360	+	0.967372i	$0.581536\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	1.99071	+	1.99071i	0.263676	+	0.263676i
$58$		0			0
$59$	−3.50993	+	6.07937i	−0.456953	+	0.791466i	−0.998798	−	0.0490121i	$-0.984393\pi$
$59$	−3.50993	+	6.07937i	−0.456953	+	0.791466i	0.541845	+	0.840479i	$0.317726\pi$
$60$		0			0
$61$	8.78251	−	5.07059i	1.12449	−	0.649222i	0.181943	−	0.983309i	$-0.441761\pi$
$61$	8.78251	−	5.07059i	1.12449	−	0.649222i	0.942542	+	0.334087i	$0.108428\pi$
$62$		0			0
$63$	0.779873	+	2.52820i	0.0982547	+	0.318523i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−2.71936	+	0.728651i	−0.332223	+	0.0890189i	−0.421075	−	0.907026i	$-0.638347\pi$
$67$	−2.71936	+	0.728651i	−0.332223	+	0.0890189i	0.0888516	+	0.996045i	$0.471680\pi$
$68$		0			0
$69$	−8.40912			−1.01234
$70$		0			0
$71$	−5.35664			−0.635717			−0.317858	−	0.948138i	$-0.602964\pi$
$71$	−5.35664			−0.635717			−0.317858	+	0.948138i	$0.602964\pi$
$72$		0			0
$73$	7.68957	−	2.06042i	0.899997	−	0.241153i	0.220982	−	0.975278i	$-0.429074\pi$
$73$	7.68957	−	2.06042i	0.899997	−	0.241153i	0.679015	+	0.734125i	$0.262407\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−1.55565	−	1.44341i	−0.177283	−	0.164492i
$78$		0			0
$79$	−5.85687	+	3.38146i	−0.658949	+	0.380444i	−0.791876	−	0.610681i	$-0.790896\pi$
$79$	−5.85687	+	3.38146i	−0.658949	+	0.380444i	0.132927	+	0.991126i	$0.457562\pi$
$80$		0			0
$81$	0.500000	−	0.866025i	0.0555556	−	0.0962250i
$82$		0			0
$83$	0.112245	+	0.112245i	0.0123205	+	0.0123205i	0.713240	−	0.700920i	$-0.247227\pi$
$83$	0.112245	+	0.112245i	0.0123205	+	0.0123205i	−0.700920	+	0.713240i	$0.747227\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$		0			0
$88$		0			0
$89$	0.694634	+	1.20314i	0.0736311	+	0.127533i	0.900490	−	0.434876i	$-0.143208\pi$
$89$	0.694634	+	1.20314i	0.0736311	+	0.127533i	−0.826859	+	0.562409i	$0.809875\pi$
$90$		0			0
$91$	−8.24021	+	5.17777i	−0.863809	+	0.542778i
$92$		0			0
$93$	5.73433	+	1.53651i	0.594622	+	0.159328i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−3.53553	+	3.53553i	−0.358979	+	0.358979i	−0.863437	−	0.504457i	$-0.831693\pi$
$97$	−3.53553	+	3.53553i	−0.358979	+	0.358979i	0.504457	+	0.863437i	$0.331693\pi$
$98$		0			0
$99$			0.802094i			0.0806135i
$100$		0			0
$101$	4.36188	+	2.51833i	0.434023	+	0.250583i	0.701059	−	0.713103i	$-0.252711\pi$
$101$	4.36188	+	2.51833i	0.434023	+	0.250583i	−0.267036	+	0.963687i	$0.586044\pi$
$102$		0			0
$103$	−3.30329	+	12.3280i	−0.325483	+	1.21472i	0.588343	+	0.808611i	$0.299780\pi$
$103$	−3.30329	+	12.3280i	−0.325483	+	1.21472i	−0.913826	+	0.406107i	$0.866886\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−1.30359	+	4.86505i	−0.126022	+	0.470322i	−0.999874	−	0.0158708i	$-0.994948\pi$
$107$	−1.30359	+	4.86505i	−0.126022	+	0.470322i	0.873852	+	0.486193i	$0.161615\pi$
$108$		0			0
$109$	−7.48173	−	4.31958i	−0.716620	−	0.413741i	0.0968876	−	0.995295i	$-0.469111\pi$
$109$	−7.48173	−	4.31958i	−0.716620	−	0.413741i	−0.813507	+	0.581555i	$0.802445\pi$
$110$		0			0
$111$			1.73205i			0.164399i
$112$		0			0
$113$	−7.34847	+	7.34847i	−0.691286	+	0.691286i	−0.962515	−	0.271229i	$-0.912570\pi$
$113$	−7.34847	+	7.34847i	−0.691286	+	0.691286i	0.271229	+	0.962515i	$0.412570\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	3.55299	+	0.952020i	0.328474	+	0.0880143i
$118$		0			0
$119$	−2.12066	+	0.0793695i	−0.194400	+	0.00727579i
$120$		0			0
$121$	5.17832	+	8.96912i	0.470757	+	0.815374i
$122$		0			0
$123$	−1.81687	−	6.78066i	−0.163822	−	0.611391i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	8.15325	+	8.15325i	0.723484	+	0.723484i	0.969313	−	0.245829i	$-0.0790602\pi$
$127$	8.15325	+	8.15325i	0.723484	+	0.723484i	−0.245829	+	0.969313i	$0.579060\pi$
$128$		0			0
$129$	1.57904	−	2.73497i	0.139026	−	0.240801i
$130$		0			0
$131$	−3.15874	+	1.82370i	−0.275980	+	0.159337i	−0.631602	−	0.775293i	$-0.717602\pi$
$131$	−3.15874	+	1.82370i	−0.275980	+	0.159337i	0.355622	+	0.934630i	$0.384269\pi$
$132$		0			0
$133$	7.11762	−	2.19557i	0.617176	−	0.190380i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−21.6839	+	5.81018i	−1.85258	+	0.496397i	−0.999671	−	0.0256612i	$-0.991831\pi$
$137$	−21.6839	+	5.81018i	−1.85258	+	0.496397i	−0.852910	+	0.522059i	$0.825164\pi$
$138$		0			0
$139$	−20.0131			−1.69749			−0.848743	−	0.528805i	$-0.822640\pi$
$139$	−20.0131			−1.69749			−0.848743	+	0.528805i	$0.822640\pi$
$140$		0			0
$141$	10.5546			0.888853
$142$		0			0
$143$	−2.84983	+	0.763610i	−0.238315	+	0.0638563i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	6.87799	+	1.30125i	0.567287	+	0.107325i
$148$		0			0
$149$	7.28005	−	4.20314i	0.596405	−	0.344335i	−0.171221	−	0.985233i	$-0.554771\pi$
$149$	7.28005	−	4.20314i	0.596405	−	0.344335i	0.767626	+	0.640898i	$0.221438\pi$
$150$		0			0
$151$	3.90105	−	6.75681i	0.317463	−	0.549862i	−0.662495	−	0.749066i	$-0.730503\pi$
$151$	3.90105	−	6.75681i	0.317463	−	0.549862i	0.979958	+	0.199205i	$0.0638358\pi$
$152$		0			0
$153$	0.567166	+	0.567166i	0.0458527	+	0.0458527i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−0.156376	−	0.583601i	−0.0124801	−	0.0465765i	0.959405	−	0.282032i	$-0.0910085\pi$
$157$	−0.156376	−	0.583601i	−0.0124801	−	0.0465765i	−0.971885	+	0.235456i	$0.924342\pi$
$158$		0			0
$159$	−6.32522	−	10.9556i	−0.501622	−	0.868835i
$160$		0			0
$161$	−10.3958	+	19.6703i	−0.819305	+	1.55024i
$162$		0			0
$163$	10.3693	+	2.77845i	0.812186	+	0.217625i	0.640927	−	0.767601i	$-0.278550\pi$
$163$	10.3693	+	2.77845i	0.812186	+	0.217625i	0.171259	+	0.985226i	$0.445217\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−14.6539	+	14.6539i	−1.13395	+	1.13395i	−0.144440	+	0.989514i	$0.546138\pi$
$167$	−14.6539	+	14.6539i	−1.13395	+	1.13395i	−0.989514	+	0.144440i	$0.953862\pi$
$168$		0			0
$169$			0.530055i			0.0407735i
$170$		0			0
$171$	−2.43811	−	1.40765i	−0.186447	−	0.107645i
$172$		0			0
$173$	1.96811	−	7.34508i	0.149633	−	0.558436i	−0.849873	−	0.526988i	$-0.823321\pi$
$173$	1.96811	−	7.34508i	0.149633	−	0.558436i	0.999505	−	0.0314484i	$-0.0100120\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	1.81687	−	6.78066i	0.136564	−	0.509665i
$178$		0			0
$179$	10.6672	+	6.15874i	0.797308	+	0.460326i	0.842529	−	0.538651i	$-0.181066\pi$
$179$	10.6672	+	6.15874i	0.797308	+	0.460326i	−0.0452212	+	0.998977i	$0.514399\pi$
$180$		0			0
$181$			7.91980i			0.588674i	0.955702	+	0.294337i	$0.0950988\pi$
$181$			7.91980i			0.588674i	−0.955702	+	0.294337i	$0.904901\pi$
$182$		0			0
$183$	−7.17089	+	7.17089i	−0.530087	+	0.530087i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−0.621434	−	0.166513i	−0.0454437	−	0.0121766i
$188$		0			0
$189$	−1.40765	−	2.24021i	−0.102391	−	0.162951i
$190$		0			0
$191$	−7.47518	−	12.9474i	−0.540885	−	0.936840i	−0.998853	−	0.0478720i	$-0.984756\pi$
$191$	−7.47518	−	12.9474i	−0.540885	−	0.936840i	0.457968	−	0.888968i	$-0.348577\pi$
$192$		0			0
$193$	1.53651	+	5.73433i	0.110600	+	0.412766i	0.998920	−	0.0464593i	$-0.0147938\pi$
$193$	1.53651	+	5.73433i	0.110600	+	0.412766i	−0.888320	+	0.459225i	$0.848127\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−6.56052	−	6.56052i	−0.467418	−	0.467418i	0.433659	−	0.901077i	$-0.357222\pi$
$197$	−6.56052	−	6.56052i	−0.467418	−	0.467418i	−0.901077	+	0.433659i	$0.857222\pi$
$198$		0			0
$199$	6.45078	−	11.1731i	0.457284	−	0.792039i	−0.541532	−	0.840680i	$-0.682156\pi$
$199$	6.45078	−	11.1731i	0.457284	−	0.792039i	0.998816	+	0.0486408i	$0.0154890\pi$
$200$		0			0
$201$	2.43811	−	1.40765i	0.171971	−	0.0992877i
$202$		0			0
$203$		0			0
$204$		0			0
$205$		0			0
$206$		0			0
$207$	8.12259	−	2.17644i	0.564559	−	0.151273i
$208$		0			0
$209$	2.25813			0.156198
$210$		0			0
$211$	19.1587			1.31894			0.659471	−	0.751730i	$-0.270780\pi$
$211$	19.1587			1.31894			0.659471	+	0.751730i	$0.270780\pi$
$212$		0			0
$213$	5.17412	−	1.38640i	0.354525	−	0.0949947i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	10.6832	−	11.5140i	0.725225	−	0.781621i
$218$		0			0
$219$	−6.89428	+	3.98042i	−0.465873	+	0.268972i
$220$		0			0
$221$	−1.47518	+	2.55509i	−0.0992314	+	0.171874i
$222$		0			0
$223$	−17.7899	−	17.7899i	−1.19130	−	1.19130i	−0.976702	−	0.214598i	$-0.931156\pi$
$223$	−17.7899	−	17.7899i	−1.19130	−	1.19130i	−0.214598	−	0.976702i	$-0.568844\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	5.32262	+	19.8643i	0.353275	+	1.31844i	0.882642	+	0.470046i	$0.155763\pi$
$227$	5.32262	+	19.8643i	0.353275	+	1.31844i	−0.529367	+	0.848393i	$0.677571\pi$
$228$		0			0
$229$	−3.49155	−	6.04754i	−0.230728	−	0.399633i	0.727295	−	0.686325i	$-0.240777\pi$
$229$	−3.49155	−	6.04754i	−0.230728	−	0.399633i	−0.958023	+	0.286693i	$0.907444\pi$
$230$		0			0
$231$	1.87623	+	0.991593i	0.123447	+	0.0652420i
$232$		0			0
$233$	8.69627	+	2.33016i	0.569711	+	0.152654i	0.532164	−	0.846641i	$-0.321379\pi$
$233$	8.69627	+	2.33016i	0.569711	+	0.152654i	0.0375471	+	0.999295i	$0.488046\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	4.78211	−	4.78211i	0.310632	−	0.310632i
$238$		0			0
$239$			27.7525i			1.79516i	0.440855	+	0.897579i	$0.354675\pi$
$239$			27.7525i			1.79516i	−0.440855	+	0.897579i	$0.645325\pi$
$240$		0			0
$241$	−7.50000	−	4.33013i	−0.483117	−	0.278928i	0.238597	−	0.971119i	$-0.423312\pi$
$241$	−7.50000	−	4.33013i	−0.483117	−	0.278928i	−0.721715	+	0.692191i	$0.756646\pi$
$242$		0			0
$243$	−0.258819	+	0.965926i	−0.0166032	+	0.0619642i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	2.68021	−	10.0027i	0.170538	−	0.636456i
$248$		0			0
$249$	−0.137472	−	0.0793695i	−0.00871193	−	0.00502984i
$250$		0			0
$251$			6.15099i			0.388247i	0.980977	+	0.194124i	$0.0621863\pi$
$251$			6.15099i			0.388247i	−0.980977	+	0.194124i	$0.937814\pi$
$252$		0			0
$253$	−4.76937	+	4.76937i	−0.299848	+	0.299848i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−13.2940	−	3.56211i	−0.829255	−	0.222198i	−0.180866	−	0.983508i	$-0.557890\pi$
$257$	−13.2940	−	3.56211i	−0.829255	−	0.222198i	−0.648389	+	0.761310i	$0.724557\pi$
$258$		0			0
$259$	4.05155	+	2.14126i	0.251751	+	0.133051i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	4.86617	+	18.1608i	0.300061	+	1.11984i	0.937114	+	0.349022i	$0.113486\pi$
$263$	4.86617	+	18.1608i	0.300061	+	1.11984i	−0.637054	+	0.770819i	$0.719847\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−0.982361	−	0.982361i	−0.0601195	−	0.0601195i
$268$		0			0
$269$	−10.1321	+	17.5493i	−0.617765	+	1.07000i	0.372127	+	0.928182i	$0.378628\pi$
$269$	−10.1321	+	17.5493i	−0.617765	+	1.07000i	−0.989893	+	0.141819i	$0.954705\pi$
$270$		0			0
$271$	−0.688794	+	0.397675i	−0.0418413	+	0.0241571i	−0.520775	−	0.853694i	$-0.674357\pi$
$271$	−0.688794	+	0.397675i	−0.0418413	+	0.0241571i	0.478933	+	0.877851i	$0.341024\pi$
$272$		0			0
$273$	6.61932	−	7.13407i	0.400620	−	0.431774i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	23.0613	−	6.17926i	1.38562	−	0.371276i	0.512461	−	0.858710i	$-0.328734\pi$
$277$	23.0613	−	6.17926i	1.38562	−	0.371276i	0.873160	+	0.487434i	$0.162067\pi$
$278$		0			0
$279$	−5.93661			−0.355416
$280$		0			0
$281$	14.4063			0.859407			0.429703	−	0.902970i	$-0.358618\pi$
$281$	14.4063			0.859407			0.429703	+	0.902970i	$0.358618\pi$
$282$		0			0
$283$	−19.9460	+	5.34452i	−1.18567	+	0.317699i	−0.797172	−	0.603752i	$-0.793672\pi$
$283$	−19.9460	+	5.34452i	−1.18567	+	0.317699i	−0.388495	+	0.921451i	$0.627005\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−18.1072	−	4.13266i	−1.06883	−	0.243943i
$288$		0			0
$289$	14.1653	−	8.17832i	0.833251	−	0.481078i
$290$		0			0
$291$	2.50000	−	4.33013i	0.146553	−	0.253837i
$292$		0			0
$293$	−19.6239	−	19.6239i	−1.14644	−	1.14644i	−0.987247	−	0.159196i	$-0.949110\pi$
$293$	−19.6239	−	19.6239i	−1.14644	−	1.14644i	−0.159196	−	0.987247i	$-0.550890\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−0.207597	−	0.774764i	−0.0120460	−	0.0449563i
$298$		0			0
$299$	15.4657	+	26.7874i	0.894406	+	1.54916i
$300$		0			0
$301$	−4.44545	−	7.07474i	−0.256231	−	0.407781i
$302$		0			0
$303$	−4.86505	−	1.30359i	−0.279490	−	0.0748890i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	2.46843	−	2.46843i	0.140881	−	0.140881i	−0.633149	−	0.774030i	$-0.718238\pi$
$307$	2.46843	−	2.46843i	0.140881	−	0.140881i	0.774030	+	0.633149i	$0.218238\pi$
$308$		0			0
$309$		−	12.7629i		−	0.726058i
$310$		0			0
$311$	−19.4413	−	11.2244i	−1.10241	−	0.636478i	−0.165559	−	0.986200i	$-0.552943\pi$
$311$	−19.4413	−	11.2244i	−1.10241	−	0.636478i	−0.936854	+	0.349722i	$0.886276\pi$
$312$		0			0
$313$	4.98054	−	18.5876i	0.281517	−	1.05064i	−0.669830	−	0.742514i	$-0.733633\pi$
$313$	4.98054	−	18.5876i	0.281517	−	1.05064i	0.951347	−	0.308121i	$-0.0997003\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	5.60433	−	20.9156i	0.314771	−	1.17474i	−0.609432	−	0.792838i	$-0.708603\pi$
$317$	5.60433	−	20.9156i	0.314771	−	1.17474i	0.924203	−	0.381902i	$-0.124731\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$		−	5.03667i		−	0.281119i
$322$		0			0
$323$	1.59674	−	1.59674i	0.0888449	−	0.0888449i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	8.34478	+	2.23598i	0.461468	+	0.123650i
$328$		0			0
$329$	13.0481	−	24.6888i	0.719366	−	1.36114i
$330$		0			0
$331$	−16.0598	−	27.8164i	−0.882726	−	1.52893i	−0.848298	−	0.529519i	$-0.822373\pi$
$331$	−16.0598	−	27.8164i	−0.882726	−	1.52893i	−0.0344273	−	0.999407i	$-0.510961\pi$
$332$		0			0
$333$	−0.448288	−	1.67303i	−0.0245660	−	0.0916816i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−4.76022	−	4.76022i	−0.259305	−	0.259305i	0.565466	−	0.824772i	$-0.308696\pi$
$337$	−4.76022	−	4.76022i	−0.259305	−	0.259305i	−0.824772	+	0.565466i	$0.808696\pi$
$338$		0			0
$339$	5.19615	−	9.00000i	0.282216	−	0.488813i
$340$		0			0
$341$	4.12377	−	2.38086i	0.223315	−	0.128931i
$342$		0			0
$343$	11.5468	−	14.4800i	0.623468	−	0.781849i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	9.46452	−	2.53601i	0.508082	−	0.136140i	0.00433355	−	0.999991i	$-0.498621\pi$
$347$	9.46452	−	2.53601i	0.508082	−	0.136140i	0.503748	+	0.863850i	$0.331954\pi$
$348$		0			0
$349$	−1.11432			−0.0596484			−0.0298242	−	0.999555i	$-0.509495\pi$
$349$	−1.11432			−0.0596484			−0.0298242	+	0.999555i	$0.509495\pi$
$350$		0			0
$351$	−3.67832			−0.196334
$352$		0			0
$353$	15.0624	−	4.03595i	0.801689	−	0.214812i	0.165364	−	0.986233i	$-0.447120\pi$
$353$	15.0624	−	4.03595i	0.801689	−	0.214812i	0.636326	+	0.771421i	$0.280454\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	2.02786	−	0.625532i	0.107325	−	0.0331066i
$358$		0			0
$359$	31.5893	−	18.2381i	1.66722	−	0.962571i	0.698095	−	0.716005i	$-0.254031\pi$
$359$	31.5893	−	18.2381i	1.66722	−	0.962571i	0.969126	−	0.246565i	$-0.0793020\pi$
$360$		0			0
$361$	5.53707	−	9.59048i	0.291425	−	0.504762i
$362$		0			0
$363$	−7.32325	−	7.32325i	−0.384371	−	0.384371i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	3.28139	+	12.2463i	0.171287	+	0.639253i	0.997154	+	0.0753878i	$0.0240195\pi$
$367$	3.28139	+	12.2463i	0.171287	+	0.639253i	−0.825867	+	0.563865i	$0.809314\pi$
$368$		0			0
$369$	3.50993	+	6.07937i	0.182719	+	0.316479i
$370$		0			0
$371$	−33.4465	+	1.25180i	−1.73646	+	0.0649900i
$372$		0			0
$373$	24.1377	+	6.46767i	1.24980	+	0.334883i	0.822260	−	0.569112i	$-0.192713\pi$
$373$	24.1377	+	6.46767i	1.24980	+	0.334883i	0.427542	+	0.903996i	$0.359380\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$			13.9154i			0.714786i	0.933954	+	0.357393i	$0.116334\pi$
$379$			13.9154i			0.714786i	−0.933954	+	0.357393i	$0.883666\pi$
$380$		0			0
$381$	−9.98565	−	5.76522i	−0.511580	−	0.295361i
$382$		0			0
$383$	−2.93932	+	10.9697i	−0.150192	+	0.560524i	0.849277	+	0.527947i	$0.177038\pi$
$383$	−2.93932	+	10.9697i	−0.150192	+	0.560524i	−0.999469	+	0.0325771i	$0.989629\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−0.817370	+	3.05047i	−0.0415492	+	0.155064i
$388$		0			0
$389$	23.9756	+	13.8423i	1.21561	+	0.701832i	0.963976	−	0.265990i	$-0.0856989\pi$
$389$	23.9756	+	13.8423i	1.21561	+	0.701832i	0.251634	+	0.967823i	$0.419032\pi$
$390$		0			0
$391$			6.74491i			0.341105i
$392$		0			0
$393$	2.57910	−	2.57910i	0.130098	−	0.130098i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	3.35171	+	0.898088i	0.168217	+	0.0450737i	0.341945	−	0.939720i	$-0.388914\pi$
$397$	3.35171	+	0.898088i	0.168217	+	0.0450737i	−0.173727	+	0.984794i	$0.555581\pi$
$398$		0			0
$399$	−6.30684	+	3.96293i	−0.315737	+	0.198395i
$400$		0			0
$401$	13.0402	+	22.5863i	0.651197	+	1.12791i	0.982833	+	0.184498i	$0.0590660\pi$
$401$	13.0402	+	22.5863i	0.651197	+	1.12791i	−0.331636	+	0.943407i	$0.607601\pi$
$402$		0			0
$403$	−5.65177	−	21.0927i	−0.281535	−	1.05070i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	0.982361	+	0.982361i	0.0486938	+	0.0486938i
$408$		0			0
$409$	3.49155	−	6.04754i	0.172646	−	0.299032i	−0.766698	−	0.642008i	$-0.778102\pi$
$409$	3.49155	−	6.04754i	0.172646	−	0.299032i	0.939344	+	0.342976i	$0.111435\pi$
$410$		0			0
$411$	19.4413	−	11.2244i	0.958966	−	0.553659i
$412$		0			0
$413$	−13.6149	−	12.6326i	−0.669947	−	0.621608i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	19.3311	−	5.17976i	0.946650	−	0.253654i
$418$		0			0
$419$	30.2640			1.47849			0.739247	−	0.673434i	$-0.235182\pi$
$419$	30.2640			1.47849			0.739247	+	0.673434i	$0.235182\pi$
$420$		0			0
$421$	30.3566			1.47949			0.739746	−	0.672886i	$-0.234946\pi$
$421$	30.3566			1.47949			0.739746	+	0.672886i	$0.234946\pi$
$422$		0			0
$423$	−10.1949	+	2.73172i	−0.495694	+	0.132821i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	7.90882	+	25.6389i	0.382735	+	1.24075i
$428$		0			0
$429$	2.55509	−	1.47518i	0.123361	−	0.0712224i
$430$		0			0
$431$	8.46994	−	14.6704i	0.407983	−	0.706647i	−0.586681	−	0.809818i	$-0.699566\pi$
$431$	8.46994	−	14.6704i	0.407983	−	0.706647i	0.994664	+	0.103171i	$0.0328990\pi$
$432$		0			0
$433$	−9.25962	−	9.25962i	−0.444989	−	0.444989i	0.448696	−	0.893685i	$-0.351889\pi$
$433$	−9.25962	−	9.25962i	−0.444989	−	0.444989i	−0.893685	+	0.448696i	$0.851889\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−6.12731	−	22.8674i	−0.293109	−	1.09390i
$438$		0			0
$439$	−5.45919	−	9.45560i	−0.260553	−	0.451291i	0.705836	−	0.708375i	$-0.250572\pi$
$439$	−5.45919	−	9.45560i	−0.260553	−	0.451291i	−0.966389	+	0.257084i	$0.917238\pi$
$440$		0			0
$441$	−6.98042	+	0.523243i	−0.332401	+	0.0249163i
$442$		0			0
$443$	−6.20698	−	1.66315i	−0.294902	−	0.0790188i	0.108335	−	0.994114i	$-0.465448\pi$
$443$	−6.20698	−	1.66315i	−0.294902	−	0.0790188i	−0.403237	+	0.915096i	$0.632115\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−5.94414	+	5.94414i	−0.281148	+	0.281148i
$448$		0			0
$449$			14.9504i			0.705551i	0.935708	+	0.352776i	$0.114762\pi$
$449$			14.9504i			0.705551i	−0.935708	+	0.352776i	$0.885238\pi$
$450$		0			0
$451$	−4.87623	−	2.81529i	−0.229613	−	0.132567i
$452$		0			0
$453$	−2.01933	+	7.53624i	−0.0948764	+	0.354084i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	3.41033	−	12.7275i	0.159529	−	0.595369i	−0.839146	−	0.543906i	$-0.816945\pi$
$457$	3.41033	−	12.7275i	0.159529	−	0.595369i	0.998675	−	0.0514631i	$-0.0163885\pi$
$458$		0			0
$459$	−0.694634	−	0.401047i	−0.0324227	−	0.0187193i
$460$		0			0
$461$			35.6932i			1.66240i	0.555976	+	0.831198i	$0.312345\pi$
$461$			35.6932i			1.66240i	−0.555976	+	0.831198i	$0.687655\pi$
$462$		0			0
$463$	−28.9259	+	28.9259i	−1.34430	+	1.34430i	−0.452578	+	0.891725i	$0.649495\pi$
$463$	−28.9259	+	28.9259i	−1.34430	+	1.34430i	−0.891725	+	0.452578i	$0.850505\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	8.89461	+	2.38330i	0.411593	+	0.110286i	0.458673	−	0.888605i	$-0.348325\pi$
$467$	8.89461	+	2.38330i	0.411593	+	0.110286i	−0.0470798	+	0.998891i	$0.514992\pi$
$468$		0			0
$469$	−0.278581	−	7.44335i	−0.0128637	−	0.343702i
$470$		0			0
$471$	0.302094	+	0.523243i	0.0139198	+	0.0241098i
$472$		0			0
$473$	−0.655608	−	2.44676i	−0.0301449	−	0.112502i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	8.94521	+	8.94521i	0.409573	+	0.409573i
$478$		0			0
$479$	17.9473	−	31.0856i	0.820033	−	1.42034i	−0.0856235	−	0.996328i	$-0.527288\pi$
$479$	17.9473	−	31.0856i	0.820033	−	1.42034i	0.905657	−	0.424012i	$-0.139378\pi$
$480$		0			0
$481$	5.51748	−	3.18552i	0.251576	−	0.145247i
$482$		0			0
$483$	4.95054	−	21.6907i	0.225257	−	0.986960i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	9.74260	−	2.61052i	0.441479	−	0.118294i	−0.0312305	−	0.999512i	$-0.509943\pi$
$487$	9.74260	−	2.61052i	0.441479	−	0.118294i	0.472710	+	0.881218i	$0.343276\pi$
$488$		0			0
$489$	−10.7351			−0.485457
$490$		0			0
$491$	7.83079			0.353399			0.176699	−	0.984265i	$-0.443458\pi$
$491$	7.83079			0.353399			0.176699	+	0.984265i	$0.443458\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$	3.15351	−	13.8170i	0.141454	−	0.619779i
$498$		0			0
$499$	11.5121	−	6.64649i	0.515351	−	0.297538i	−0.219680	−	0.975572i	$-0.570501\pi$
$499$	11.5121	−	6.64649i	0.515351	−	0.297538i	0.735030	+	0.678034i	$0.237168\pi$
$500$		0			0
$501$	10.3619	−	17.9473i	0.462935	−	0.801826i
$502$		0			0
$503$	−25.4558	−	25.4558i	−1.13502	−	1.13502i	−0.989330	−	0.145690i	$-0.953460\pi$
$503$	−25.4558	−	25.4558i	−1.13502	−	1.13502i	−0.145690	−	0.989330i	$-0.546540\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−0.137188	−	0.511994i	−0.00609275	−	0.0227384i
$508$		0			0
$509$	16.4206	+	28.4413i	0.727829	+	1.26064i	0.957799	+	0.287439i	$0.0928037\pi$
$509$	16.4206	+	28.4413i	0.727829	+	1.26064i	−0.229970	+	0.973198i	$0.573863\pi$
$510$		0			0
$511$	0.787747	+	21.0476i	0.0348479	+	0.931093i
$512$		0			0
$513$	2.71936	+	0.728651i	0.120063	+	0.0321707i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	5.98619	−	5.98619i	0.263272	−	0.263272i
$518$		0			0
$519$			7.60419i			0.333787i
$520$		0			0
$521$	5.56502	+	3.21297i	0.243808	+	0.140763i	0.616926	−	0.787021i	$-0.288378\pi$
$521$	5.56502	+	3.21297i	0.243808	+	0.140763i	−0.373118	+	0.927784i	$0.621711\pi$
$522$		0			0
$523$	6.30288	−	23.5227i	0.275606	−	1.02857i	−0.679829	−	0.733371i	$-0.737946\pi$
$523$	6.30288	−	23.5227i	0.275606	−	1.02857i	0.955434	−	0.295203i	$-0.0953873\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	1.23242	−	4.59947i	0.0536852	−	0.200356i
$528$		0			0
$529$	41.3209	+	23.8566i	1.79656	+	1.03725i
$530$		0			0
$531$			7.01985i			0.304636i
$532$		0			0
$533$	−18.2584	+	18.2584i	−0.790859	+	0.790859i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−11.8978	−	3.18800i	−0.513427	−	0.137572i
$538$		0			0
$539$	4.63899	−	3.16294i	0.199815	−	0.136237i
$540$		0			0
$541$	−21.9979	−	38.1015i	−0.945764	−	1.63811i	−0.754215	−	0.656627i	$-0.771982\pi$
$541$	−21.9979	−	38.1015i	−0.945764	−	1.63811i	−0.191549	−	0.981483i	$-0.561351\pi$
$542$		0			0
$543$	−2.04979	−	7.64994i	−0.0879651	−	0.328290i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	16.4881	+	16.4881i	0.704980	+	0.704980i	0.965475	−	0.260495i	$-0.0838858\pi$
$547$	16.4881	+	16.4881i	0.704980	+	0.704980i	−0.260495	+	0.965475i	$0.583886\pi$
$548$		0			0
$549$	5.07059	−	8.78251i	0.216407	−	0.374828i
$550$		0			0
$551$		0			0
$552$		0			0
$553$	−5.27422	−	17.0980i	−0.224283	−	0.727083i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−31.7221	+	8.49991i	−1.34411	+	0.360153i	−0.857957	−	0.513722i	$-0.828266\pi$
$557$	−31.7221	+	8.49991i	−1.34411	+	0.360153i	−0.486151	+	0.873875i	$0.661600\pi$
$558$		0			0
$559$	−11.6164			−0.491322
$560$		0			0
$561$	0.643355			0.0271625
$562$		0			0
$563$	42.7973	−	11.4675i	1.80369	−	0.483297i	0.809146	−	0.587608i	$-0.199930\pi$
$563$	42.7973	−	11.4675i	1.80369	−	0.483297i	0.994545	+	0.104311i	$0.0332637\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	1.93949	+	1.79955i	0.0814509	+	0.0755740i
$568$		0			0
$569$	−4.77646	+	2.75769i	−0.200240	+	0.115608i	−0.596767	−	0.802414i	$-0.703548\pi$
$569$	−4.77646	+	2.75769i	−0.200240	+	0.115608i	0.396528	+	0.918023i	$0.370215\pi$
$570$		0			0
$571$	10.6465	−	18.4403i	0.445542	−	0.771701i	−0.552548	−	0.833481i	$-0.686344\pi$
$571$	10.6465	−	18.4403i	0.445542	−	0.771701i	0.998090	+	0.0617801i	$0.0196777\pi$
$572$		0			0
$573$	10.5715	+	10.5715i	0.441631	+	0.441631i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−8.60401	−	32.1106i	−0.358190	−	1.33678i	−0.876423	−	0.481543i	$-0.840077\pi$
$577$	−8.60401	−	32.1106i	−0.358190	−	1.33678i	0.518233	−	0.855239i	$-0.326590\pi$
$578$		0			0
$579$	−2.96831	−	5.14126i	−0.123359	−	0.213663i
$580$		0			0
$581$	−0.355608	+	0.223448i	−0.0147531	+	0.00927020i
$582$		0			0
$583$	−9.80110	−	2.62620i	−0.405920	−	0.108766i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	22.5720	−	22.5720i	0.931647	−	0.931647i	−0.0661617	−	0.997809i	$-0.521075\pi$
$587$	22.5720	−	22.5720i	0.931647	−	0.931647i	0.997809	+	0.0661617i	$0.0210753\pi$
$588$		0			0
$589$			16.7133i			0.688659i
$590$		0			0
$591$	8.03497	+	4.63899i	0.330514	+	0.190823i
$592$		0			0
$593$	3.96917	−	14.8131i	0.162994	−	0.608303i	−0.835293	−	0.549805i	$-0.814702\pi$
$593$	3.96917	−	14.8131i	0.162994	−	0.608303i	0.998288	−	0.0584983i	$-0.0186312\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−3.33917	+	12.4620i	−0.136663	+	0.510034i
$598$		0			0
$599$	−41.5104	−	23.9661i	−1.69607	−	0.979227i	−0.949419	−	0.314012i	$-0.898327\pi$
$599$	−41.5104	−	23.9661i	−1.69607	−	0.979227i	−0.746652	−	0.665215i	$-0.768340\pi$
$600$		0			0
$601$			36.2503i			1.47868i	0.673331	+	0.739341i	$0.264863\pi$
$601$			36.2503i			1.47868i	−0.673331	+	0.739341i	$0.735137\pi$
$602$		0			0
$603$	−1.99071	+	1.99071i	−0.0810680	+	0.0810680i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−0.955811	−	0.256109i	−0.0387952	−	0.0103951i	0.239369	−	0.970929i	$-0.423059\pi$
$607$	−0.955811	−	0.256109i	−0.0387952	−	0.0103951i	−0.278164	+	0.960533i	$0.589726\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−19.4115	−	33.6217i	−0.785306	−	1.36019i
$612$		0			0
$613$	−3.61472	−	13.4903i	−0.145997	−	0.544868i	−0.999709	−	0.0241228i	$-0.992321\pi$
$613$	−3.61472	−	13.4903i	−0.145997	−	0.544868i	0.853712	−	0.520745i	$-0.174346\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	13.2946	+	13.2946i	0.535221	+	0.535221i	0.922121	−	0.386900i	$-0.126454\pi$
$617$	13.2946	+	13.2946i	0.535221	+	0.535221i	−0.386900	+	0.922121i	$0.626454\pi$
$618$		0			0
$619$	−4.23484	+	7.33496i	−0.170213	+	0.294817i	−0.938494	−	0.345295i	$-0.887779\pi$
$619$	−4.23484	+	7.33496i	−0.170213	+	0.294817i	0.768281	+	0.640112i	$0.221112\pi$
$620$		0			0
$621$	−7.28251	+	4.20456i	−0.292237	+	0.168723i
$622$		0			0
$623$	−3.51235	+	1.08345i	−0.140719	+	0.0434076i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−2.18119	+	0.584447i	−0.0871082	+	0.0233406i
$628$		0			0
$629$	1.38927			0.0553937
$630$		0			0
$631$	−26.4371			−1.05244			−0.526221	−	0.850348i	$-0.676392\pi$
$631$	−26.4371			−1.05244			−0.526221	+	0.850348i	$0.676392\pi$
$632$		0			0
$633$	−18.5059	+	4.95865i	−0.735544	+	0.197089i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−8.50457	−	24.3032i	−0.336963	−	0.962927i
$638$		0			0
$639$	−4.63899	+	2.67832i	−0.183516	+	0.105953i
$640$		0			0
$641$	−13.2329	+	22.9200i	−0.522667	+	0.905286i	0.476985	+	0.878911i	$0.341730\pi$
$641$	−13.2329	+	22.9200i	−0.522667	+	0.905286i	−0.999652	+	0.0263745i	$0.991604\pi$
$642$		0			0
$643$	−22.4173	−	22.4173i	−0.884051	−	0.884051i	0.109892	−	0.993943i	$-0.464949\pi$
$643$	−22.4173	−	22.4173i	−0.884051	−	0.884051i	−0.993943	+	0.109892i	$0.964949\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	2.06784	+	7.71729i	0.0812953	+	0.303398i	0.994587	−	0.103908i	$-0.0331348\pi$
$647$	2.06784	+	7.71729i	0.0812953	+	0.303398i	−0.913292	+	0.407306i	$0.866468\pi$
$648$		0			0
$649$	−2.81529	−	4.87623i	−0.110510	−	0.191409i
$650$		0			0
$651$	−7.33916	+	13.8867i	−0.287644	+	0.544262i
$652$		0			0
$653$	2.41828	+	0.647977i	0.0946348	+	0.0253573i	0.305826	−	0.952088i	$-0.401068\pi$
$653$	2.41828	+	0.647977i	0.0946348	+	0.0253573i	−0.211191	+	0.977445i	$0.567734\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	5.62916	−	5.62916i	0.219614	−	0.219614i
$658$		0			0
$659$			21.5937i			0.841172i	0.907253	+	0.420586i	$0.138175\pi$
$659$			21.5937i			0.841172i	−0.907253	+	0.420586i	$0.861825\pi$
$660$		0			0
$661$	24.8524	+	14.3486i	0.966648	+	0.558095i	0.898213	−	0.439561i	$-0.144866\pi$
$661$	24.8524	+	14.3486i	0.966648	+	0.558095i	0.0684353	+	0.997656i	$0.478199\pi$
$662$		0			0
$663$	0.763610	−	2.84983i	0.0296561	−	0.110678i
$664$		0			0
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$	21.7881	+	12.5794i	0.842377	+	0.486347i
$670$		0			0
$671$			8.13418i			0.314016i
$672$		0			0
$673$	−11.9403	+	11.9403i	−0.460263	+	0.460263i	−0.898742	−	0.438478i	$-0.855518\pi$
$673$	−11.9403	+	11.9403i	−0.460263	+	0.460263i	0.438478	+	0.898742i	$0.355518\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	21.0113	+	5.62995i	0.807528	+	0.216377i	0.638887	−	0.769301i	$-0.279395\pi$
$677$	21.0113	+	5.62995i	0.807528	+	0.216377i	0.168642	+	0.985677i	$0.446062\pi$
$678$		0			0
$679$	−7.03823	−	11.2010i	−0.270102	−	0.429857i
$680$		0			0
$681$	−10.2825	−	17.8098i	−0.394027	−	0.682474i
$682$		0			0
$683$	6.76559	+	25.2495i	0.258878	+	0.966147i	0.965892	+	0.258947i	$0.0833754\pi$
$683$	6.76559	+	25.2495i	0.258878	+	0.966147i	−0.707013	+	0.707200i	$0.749958\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	4.93779	+	4.93779i	0.188389	+	0.188389i
$688$		0			0
$689$	−23.2662	+	40.2982i	−0.886371	+	1.53524i
$690$		0			0
$691$	5.86188	−	3.38436i	0.222996	−	0.128747i	−0.384341	−	0.923191i	$-0.625571\pi$
$691$	5.86188	−	3.38436i	0.222996	−	0.128747i	0.607337	+	0.794444i	$0.292238\pi$
$692$		0			0
$693$	−2.06894	−	0.472201i	−0.0785925	−	0.0179375i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−5.43873	+	1.45730i	−0.206006	+	0.0551993i
$698$		0			0
$699$	−9.00304			−0.340526
$700$		0			0
$701$	38.7238			1.46258			0.731288	−	0.682069i	$-0.238919\pi$
$701$	38.7238			1.46258			0.731288	+	0.682069i	$0.238919\pi$
$702$		0			0
$703$	−4.71007	+	1.26206i	−0.177644	+	0.0475995i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−9.06373	+	9.76856i	−0.340877	+	0.367385i
$708$		0			0
$709$	17.2866	−	9.98042i	0.649211	−	0.374822i	−0.138943	−	0.990300i	$-0.544370\pi$
$709$	17.2866	−	9.98042i	0.649211	−	0.374822i	0.788154	+	0.615478i	$0.211037\pi$
$710$		0			0
$711$	−3.38146	+	5.85687i	−0.126815	+	0.219650i
$712$		0			0
$713$	−35.2999	−	35.2999i	−1.32199	−	1.32199i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−7.18286	−	26.8068i	−0.268249	−	1.00112i
$718$		0			0
$719$	1.68623	+	2.92063i	0.0628856	+	0.108921i	0.895754	−	0.444550i	$-0.146636\pi$
$719$	1.68623	+	2.92063i	0.0628856	+	0.108921i	−0.832868	+	0.553471i	$0.813303\pi$
$720$		0			0
$721$	−29.8545	−	15.7782i	−1.11184	−	0.587612i
$722$		0			0
$723$	8.36516	+	2.24144i	0.311104	+	0.0833600i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−10.0642	+	10.0642i	−0.373259	+	0.373259i	−0.868663	−	0.495404i	$-0.835020\pi$
$727$	−10.0642	+	10.0642i	−0.373259	+	0.373259i	0.495404	+	0.868663i	$0.335020\pi$
$728$		0			0
$729$		−	1.00000i		−	0.0370370i
$730$		0			0
$731$	−2.19371	−	1.26654i	−0.0811371	−	0.0468446i
$732$		0			0
$733$	−11.8753	+	44.3191i	−0.438623	+	1.63696i	0.293622	+	0.955922i	$0.405139\pi$
$733$	−11.8753	+	44.3191i	−0.438623	+	1.63696i	−0.732245	+	0.681041i	$0.761527\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	0.584447	−	2.18119i	0.0215284	−	0.0803450i
$738$		0			0
$739$	2.94993	+	1.70314i	0.108515	+	0.0626511i	0.553275	−	0.832999i	$-0.313378\pi$
$739$	2.94993	+	1.70314i	0.108515	+	0.0626511i	−0.444760	+	0.895650i	$0.646711\pi$
$740$		0			0
$741$			10.3555i			0.380421i
$742$		0			0
$743$	−21.8718	+	21.8718i	−0.802400	+	0.802400i	−0.983470	−	0.181070i	$-0.942044\pi$
$743$	−21.8718	+	21.8718i	−0.802400	+	0.802400i	0.181070	+	0.983470i	$0.442044\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	0.153330	+	0.0410847i	0.00561005	+	0.00150321i
$748$		0			0
$749$	−11.7816	−	6.22660i	−0.430489	−	0.227515i
$750$		0			0
$751$	12.4164	+	21.5059i	0.453082	+	0.784761i	0.998576	−	0.0533539i	$-0.0169911\pi$
$751$	12.4164	+	21.5059i	0.453082	+	0.784761i	−0.545494	+	0.838115i	$0.683658\pi$
$752$		0			0
$753$	−1.59199	−	5.94140i	−0.0580155	−	0.216517i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	0.662347	+	0.662347i	0.0240734	+	0.0240734i	0.719041	−	0.694968i	$-0.244581\pi$
$757$	0.662347	+	0.662347i	0.0240734	+	0.0240734i	−0.694968	+	0.719041i	$0.744581\pi$
$758$		0			0
$759$	3.37245	−	5.84126i	0.122412	−	0.212024i
$760$		0			0
$761$	14.0507	−	8.11216i	0.509337	−	0.294066i	−0.223224	−	0.974767i	$-0.571658\pi$
$761$	14.0507	−	8.11216i	0.509337	−	0.294066i	0.732561	+	0.680701i	$0.238325\pi$
$762$		0			0
$763$	15.5466	−	16.7556i	0.562824	−	0.606592i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−24.9414	+	6.68304i	−0.900583	+	0.241311i
$768$		0			0
$769$	−54.1886			−1.95409			−0.977045	−	0.213033i	$-0.931666\pi$
$769$	−54.1886			−1.95409			−0.977045	+	0.213033i	$0.931666\pi$
$770$		0			0
$771$	13.7629			0.495660
$772$		0			0
$773$	23.1822	−	6.21166i	0.833806	−	0.223418i	0.183433	−	0.983032i	$-0.441279\pi$
$773$	23.1822	−	6.21166i	0.833806	−	0.223418i	0.650374	+	0.759614i	$0.274612\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−4.46769	−	1.01968i	−0.160278	−	0.0365807i
$778$		0			0
$779$	17.1152	−	9.88146i	0.613216	−	0.354040i
$780$		0			0
$781$	2.14827	−	3.72091i	0.0768710	−	0.133145i
$782$		0			0
$783$		0			0
$784$		0			0
$785$		0			0
$786$		0			0
$787$	2.41425	+	9.01011i	0.0860588	+	0.321176i	0.995513	−	0.0946293i	$-0.0301666\pi$
$787$	2.41425	+	9.01011i	0.0860588	+	0.321176i	−0.909454	+	0.415805i	$0.863500\pi$
$788$		0			0
$789$	−9.40071	−	16.2825i	−0.334674	−	0.579673i
$790$		0			0
$791$	−14.6287	−	23.2809i	−0.520136	−	0.827775i
$792$		0			0
$793$	36.0314	+	9.65460i	1.27951	+	0.342845i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−11.4334	+	11.4334i	−0.404990	+	0.404990i	−0.879987	−	0.474997i	$-0.842449\pi$
$797$	−11.4334	+	11.4334i	−0.404990	+	0.404990i	0.474997	+	0.879987i	$0.342449\pi$
$798$		0			0
$799$		−	8.46575i		−	0.299497i
$800$		0			0
$801$	1.20314	+	0.694634i	0.0425109	+	0.0245437i
$802$		0			0
$803$	−1.65265	+	6.16776i	−0.0583207	+	0.217656i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	5.24476	−	19.5737i	0.184624	−	0.689027i
$808$		0			0
$809$	−23.2809	−	13.4413i	−0.818514	−	0.472569i	0.0313899	−	0.999507i	$-0.490007\pi$
$809$	−23.2809	−	13.4413i	−0.818514	−	0.472569i	−0.849904	+	0.526938i	$0.823340\pi$
$810$		0			0
$811$			30.3319i			1.06510i	0.846400	+	0.532548i	$0.178765\pi$
$811$			30.3319i			1.06510i	−0.846400	+	0.532548i	$0.821235\pi$
$812$		0			0
$813$	0.562398	−	0.562398i	0.0197242	−	0.0197242i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	8.58795	+	2.30113i	0.300454	+	0.0805065i
$818$		0			0
$819$	−4.54734	+	8.60419i	−0.158897	+	0.300655i
$820$		0			0
$821$	−8.59895	−	14.8938i	−0.300106	−	0.519798i	0.676054	−	0.736852i	$-0.263689\pi$
$821$	−8.59895	−	14.8938i	−0.300106	−	0.519798i	−0.976160	+	0.217054i	$0.930355\pi$
$822$		0			0
$823$	6.89036	+	25.7152i	0.240183	+	0.896374i	0.975744	+	0.218916i	$0.0702520\pi$
$823$	6.89036	+	25.7152i	0.240183	+	0.896374i	−0.735561	+	0.677459i	$0.763081\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	4.59580	+	4.59580i	0.159812	+	0.159812i	0.782483	−	0.622672i	$-0.213953\pi$
$827$	4.59580	+	4.59580i	0.159812	+	0.159812i	−0.622672	+	0.782483i	$0.713953\pi$
$828$		0			0
$829$	18.1555	−	31.4462i	0.630565	−	1.09217i	−0.356872	−	0.934153i	$-0.616157\pi$
$829$	18.1555	−	31.4462i	0.630565	−	1.09217i	0.987436	−	0.158017i	$-0.0505100\pi$
$830$		0			0
$831$	−20.6762	+	11.9374i	−0.717250	+	0.414105i
$832$		0			0
$833$	1.04373	−	5.51680i	0.0361630	−	0.191146i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	5.73433	−	1.53651i	0.198207	−	0.0531095i
$838$		0			0
$839$	−13.7207			−0.473692			−0.236846	−	0.971547i	$-0.576114\pi$
$839$	−13.7207			−0.473692			−0.236846	+	0.971547i	$0.576114\pi$
$840$		0			0
$841$	29.0000			1.00000
$842$		0			0
$843$	−13.9154	+	3.72862i	−0.479272	+	0.128421i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−26.1837	+	8.07687i	−0.899682	+	0.277524i
$848$		0			0
$849$	17.8831	−	10.3248i	0.613746	−	0.354347i
$850$		0			0
$851$	7.28251	−	12.6137i	0.249641	−	0.432391i
$852$		0			0
$853$	27.1341	+	27.1341i	0.929053	+	0.929053i	0.997645	−	0.0685915i	$-0.0218505\pi$
$853$	27.1341	+	27.1341i	0.929053	+	0.929053i	−0.0685915	+	0.997645i	$0.521851\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	10.4787	+	39.1071i	0.357946	+	1.33587i	0.876736	+	0.480972i	$0.159716\pi$
$857$	10.4787	+	39.1071i	0.357946	+	1.33587i	−0.518789	+	0.854902i	$0.673617\pi$
$858$		0			0
$859$	18.6419	+	32.2888i	0.636055	+	1.10168i	0.986291	+	0.165018i	$0.0527681\pi$
$859$	18.6419	+	32.2888i	0.636055	+	1.10168i	−0.350236	+	0.936662i	$0.613899\pi$
$860$		0			0
$861$	18.5598	−	0.694634i	0.632516	−	0.0236731i
$862$		0			0
$863$	16.5107	+	4.42404i	0.562032	+	0.150596i	0.528640	−	0.848846i	$-0.322702\pi$
$863$	16.5107	+	4.42404i	0.562032	+	0.150596i	0.0333925	+	0.999442i	$0.489369\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−11.5659	+	11.5659i	−0.392798	+	0.392798i
$868$		0			0
$869$		−	5.42451i		−	0.184014i
$870$		0			0
$871$	−8.96817	−	5.17777i	−0.303875	−	0.175442i
$872$		0			0
$873$	−1.29410	+	4.82963i	−0.0437985	+	0.163458i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−10.6304	+	39.6731i	−0.358962	+	1.33967i	0.516462	+	0.856310i	$0.327249\pi$
$877$	−10.6304	+	39.6731i	−0.358962	+	1.33967i	−0.875424	+	0.483355i	$0.839418\pi$
$878$		0			0
$879$	24.0343	+	13.8762i	0.810658	+	0.468034i
$880$		0			0
$881$			18.8014i			0.633436i	0.948520	+	0.316718i	$0.102581\pi$
$881$			18.8014i			0.633436i	−0.948520	+	0.316718i	$0.897419\pi$
$882$		0			0
$883$	30.9855	−	30.9855i	1.04274	−	1.04274i	0.0436994	−	0.999045i	$-0.486086\pi$
$883$	30.9855	−	30.9855i	1.04274	−	1.04274i	0.999045	−	0.0436994i	$-0.0139144\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	8.08950	+	2.16758i	0.271619	+	0.0727801i	0.392057	−	0.919941i	$-0.371763\pi$
$887$	8.08950	+	2.16758i	0.271619	+	0.0727801i	−0.120439	+	0.992721i	$0.538430\pi$
$888$		0			0
$889$	−25.8306	+	16.2308i	−0.866330	+	0.544363i
$890$		0			0
$891$	0.401047	+	0.694634i	0.0134356	+	0.0232711i
$892$		0			0
$893$	7.69058	+	28.7017i	0.257356	+	0.960464i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−21.8718	−	21.8718i	−0.730279	−	0.730279i
$898$		0			0
$899$		0			0
$900$		0			0
$901$	−8.78742	+	5.07342i	−0.292752	+	0.169020i
$902$		0			0
$903$	6.12505	+	5.68311i	0.203829	+	0.189122i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	35.2222	−	9.43776i	1.16953	−	0.313376i	0.378767	−	0.925492i	$-0.376348\pi$
$907$	35.2222	−	9.43776i	1.16953	−	0.313376i	0.790768	+	0.612116i	$0.209682\pi$
$908$		0			0
$909$	5.03667			0.167056
$910$		0			0
$911$	46.0699			1.52637			0.763183	−	0.646183i	$-0.223636\pi$
$911$	46.0699			1.52637			0.763183	+	0.646183i	$0.223636\pi$
$912$		0			0
$913$	−0.122985	+	0.0329538i	−0.00407022	+	0.00109061i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−2.84451	−	9.22135i	−0.0939339	−	0.304516i
$918$		0			0
$919$	−24.0828	+	13.9042i	−0.794417	+	0.458657i	−0.841515	−	0.540234i	$-0.818336\pi$
$919$	−24.0828	+	13.9042i	−0.794417	+	0.458657i	0.0470984	+	0.998890i	$0.485003\pi$
$920$		0			0
$921$	−1.74544	+	3.02320i	−0.0575143	+	0.0996178i
$922$		0			0
$923$	−13.9325	−	13.9325i	−0.458592	−	0.458592i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	3.30329	+	12.3280i	0.108494	+	0.404906i
$928$		0			0
$929$	−29.6061	−	51.2793i	−0.971346	−	1.68242i	−0.691501	−	0.722376i	$-0.743050\pi$
$929$	−29.6061	−	51.2793i	−0.971346	−	1.68242i	−0.279845	−	0.960045i	$-0.590283\pi$
$930$		0			0
$931$	1.47308	+	19.6519i	0.0482783	+	0.644065i
$932$		0			0
$933$	21.6839	+	5.81018i	0.709899	+	0.190217i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−24.5855	+	24.5855i	−0.803174	+	0.803174i	−0.983590	−	0.180416i	$-0.942256\pi$
$937$	−24.5855	+	24.5855i	−0.803174	+	0.803174i	0.180416	+	0.983590i	$0.442256\pi$
$938$		0			0
$939$			19.2433i			0.627983i
$940$		0			0
$941$	−25.9713	−	14.9945i	−0.846640	−	0.488808i	0.0128755	−	0.999917i	$-0.495901\pi$
$941$	−25.9713	−	14.9945i	−0.846640	−	0.488808i	−0.859516	+	0.511109i	$0.829235\pi$
$942$		0			0
$943$	−15.2783	+	57.0193i	−0.497529	+	1.85681i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−4.88519	+	18.2318i	−0.158747	+	0.592453i	0.840008	+	0.542574i	$0.182550\pi$
$947$	−4.88519	+	18.2318i	−0.158747	+	0.592453i	−0.998755	+	0.0498792i	$0.984116\pi$
$948$		0			0
$949$	25.3594	+	14.6413i	0.823201	+	0.475275i
$950$		0			0
$951$			21.6535i			0.702162i
$952$		0			0
$953$	−12.3642	+	12.3642i	−0.400517	+	0.400517i	−0.878415	−	0.477898i	$-0.841399\pi$
$953$	−12.3642	+	12.3642i	−0.400517	+	0.400517i	0.477898	+	0.878415i	$0.341399\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−2.22137	−	59.3524i	−0.0717319	−	1.91659i
$960$		0			0
$961$	2.12167	+	3.67484i	0.0684410	+	0.118543i
$962$		0			0
$963$	1.30359	+	4.86505i	0.0420074	+	0.156774i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−30.6395	−	30.6395i	−0.985299	−	0.985299i	0.0145946	−	0.999893i	$-0.495354\pi$
$967$	−30.6395	−	30.6395i	−0.985299	−	0.985299i	−0.999893	+	0.0145946i	$0.995354\pi$
$968$		0			0
$969$	−1.12906	+	1.95560i	−0.0362708	+	0.0628228i
$970$		0			0
$971$	−10.1395	+	5.85403i	−0.325391	+	0.187865i	−0.653793	−	0.756673i	$-0.726823\pi$
$971$	−10.1395	+	5.85403i	−0.325391	+	0.187865i	0.328402	+	0.944538i	$0.393490\pi$
$972$		0			0
$973$	11.7819	−	51.6222i	0.377711	−	1.65493i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	14.5951	−	3.91076i	0.466940	−	0.125116i	−0.0176751	−	0.999844i	$-0.505626\pi$
$977$	14.5951	−	3.91076i	0.466940	−	0.125116i	0.484615	+	0.874728i	$0.338960\pi$
$978$		0			0
$979$	−1.11432			−0.0356140
$980$		0			0
$981$	−8.63916			−0.275827
$982$		0			0
$983$	53.0225	−	14.2073i	1.69116	−	0.453144i	0.720469	−	0.693488i	$-0.243927\pi$
$983$	53.0225	−	14.2073i	1.69116	−	0.453144i	0.970688	+	0.240344i	$0.0772601\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−6.21358	+	27.2246i	−0.197780	+	0.866570i
$988$		0			0
$989$	−22.9987	+	13.2783i	−0.731316	+	0.422226i
$990$		0			0
$991$	−5.58251	+	9.66918i	−0.177334	+	0.307152i	−0.940967	−	0.338499i	$-0.890081\pi$
$991$	−5.58251	+	9.66918i	−0.177334	+	0.307152i	0.763632	+	0.645651i	$0.223414\pi$
$992$		0			0
$993$	22.7120	+	22.7120i	0.720743	+	0.720743i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−8.64347	−	32.2579i	−0.273742	−	1.02162i	−0.956680	−	0.291141i	$-0.905965\pi$
$997$	−8.64347	−	32.2579i	−0.273742	−	1.02162i	0.682939	−	0.730476i	$-0.260702\pi$
$998$		0			0
$999$	0.866025	+	1.50000i	0.0273998	+	0.0474579i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2100.2.ce.c.157.1	✓	24
5.2	odd	4	inner	2100.2.ce.c.493.5	yes	24
5.3	odd	4	inner	2100.2.ce.c.493.3	yes	24
5.4	even	2	inner	2100.2.ce.c.157.6	yes	24
7.5	odd	6	inner	2100.2.ce.c.1657.3	yes	24
35.12	even	12	inner	2100.2.ce.c.1993.6	yes	24
35.19	odd	6	inner	2100.2.ce.c.1657.5	yes	24
35.33	even	12	inner	2100.2.ce.c.1993.1	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2100.2.ce.c.157.1	✓	24	1.1	even	1	trivial
2100.2.ce.c.157.6	yes	24	5.4	even	2	inner
2100.2.ce.c.493.3	yes	24	5.3	odd	4	inner
2100.2.ce.c.493.5	yes	24	5.2	odd	4	inner
2100.2.ce.c.1657.3	yes	24	7.5	odd	6	inner
2100.2.ce.c.1657.5	yes	24	35.19	odd	6	inner
2100.2.ce.c.1993.1	yes	24	35.33	even	12	inner
2100.2.ce.c.1993.6	yes	24	35.12	even	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.965926 + 0.258819i) q^{3} +(-0.588711 + 2.57942i) q^{7} +(0.866025 - 0.500000i) q^{9} +O(q^{10})\)	\(q+(-0.965926 + 0.258819i) q^{3} +(-0.588711 + 2.57942i) q^{7} +(0.866025 - 0.500000i) q^{9} +(-0.401047 + 0.694634i) q^{11} +(2.60097 + 2.60097i) q^{13} +(0.207597 + 0.774764i) q^{17} +(-1.40765 - 2.43811i) q^{19} +(-0.0989528 - 2.64390i) q^{21} +(8.12259 + 2.17644i) q^{23} +(-0.707107 + 0.707107i) q^{27} +(-5.14126 - 2.96831i) q^{31} +(0.207597 - 0.774764i) q^{33} +(0.448288 - 1.67303i) q^{37} +(-3.18552 - 1.83916i) q^{39} +7.01985i q^{41} +(-2.23310 + 2.23310i) q^{43} +(-10.1949 - 2.73172i) q^{47} +(-6.30684 - 3.03707i) q^{49} +(-0.401047 - 0.694634i) q^{51} +(3.27417 + 12.2194i) q^{53} +(1.99071 + 1.99071i) q^{57} +(-3.50993 + 6.07937i) q^{59} +(8.78251 - 5.07059i) q^{61} +(0.779873 + 2.52820i) q^{63} +(-2.71936 + 0.728651i) q^{67} -8.40912 q^{69} -5.35664 q^{71} +(7.68957 - 2.06042i) q^{73} +(-1.55565 - 1.44341i) q^{77} +(-5.85687 + 3.38146i) q^{79} +(0.500000 - 0.866025i) q^{81} +(0.112245 + 0.112245i) q^{83} +(0.694634 + 1.20314i) q^{89} +(-8.24021 + 5.17777i) q^{91} +(5.73433 + 1.53651i) q^{93} +(-3.53553 + 3.53553i) q^{97} +0.802094i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q+O(q^{10}) \) 24 * q	\( 24 q - 8 q^{11} - 4 q^{21} - 60 q^{31} - 8 q^{51} + 84 q^{61} + 112 q^{71} + 12 q^{81} - 136 q^{91}+O(q^{100}) \) 24 * q - 8 * q^11 - 4 * q^21 - 60 * q^31 - 8 * q^51 + 84 * q^61 + 112 * q^71 + 12 * q^81 - 136 * q^91

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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