LMFDB - Embedded newform 2100.2.ce.c.493.5

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			493.5
Character	$\chi$	$=$	2100.493
Dual form			2100.2.ce.c.1657.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.258819 + 0.965926i) q^{3} +(-2.57942 - 0.588711i) q^{7} +(-0.866025 + 0.500000i) q^{9} +O(q^{10})$	\(q+(0.258819 + 0.965926i) q^{3} +(-2.57942 - 0.588711i) q^{7} +(-0.866025 + 0.500000i) q^{9} +(-0.401047 + 0.694634i) q^{11} +(2.60097 - 2.60097i) q^{13} +(-0.774764 + 0.207597i) q^{17} +(1.40765 + 2.43811i) q^{19} +(-0.0989528 - 2.64390i) q^{21} +(2.17644 - 8.12259i) q^{23} +(-0.707107 - 0.707107i) q^{27} +(-5.14126 - 2.96831i) q^{31} +(-0.774764 - 0.207597i) q^{33} +(1.67303 + 0.448288i) q^{37} +(3.18552 + 1.83916i) q^{39} +7.01985i q^{41} +(2.23310 + 2.23310i) q^{43} +(2.73172 - 10.1949i) q^{47} +(6.30684 + 3.03707i) q^{49} +(-0.401047 - 0.694634i) q^{51} +(12.2194 - 3.27417i) q^{53} +(-1.99071 + 1.99071i) q^{57} +(3.50993 - 6.07937i) q^{59} +(8.78251 - 5.07059i) q^{61} +(2.52820 - 0.779873i) q^{63} +(-0.728651 - 2.71936i) q^{67} +8.40912 q^{69} -5.35664 q^{71} +(-2.06042 - 7.68957i) q^{73} +(1.44341 - 1.55565i) q^{77} +(5.85687 - 3.38146i) q^{79} +(0.500000 - 0.866025i) q^{81} +(0.112245 - 0.112245i) q^{83} +(-0.694634 - 1.20314i) q^{89} +(-8.24021 + 5.17777i) q^{91} +(1.53651 - 5.73433i) q^{93} +(-3.53553 - 3.53553i) q^{97} -0.802094i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/2100\mathbb{Z}\right)^\times$.

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

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
$3$	0.258819	+	0.965926i	0.149429	+	0.557678i
$3$	0.258819	+	0.965926i	0.149429	+	0.557678i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−2.57942	−	0.588711i	−0.974930	−	0.222512i
$7$	−2.57942	−	0.588711i	−0.974930	−	0.222512i
$8$		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	−0.247508	−	0.968886i	$-0.579612\pi$
$13$	2.60097	−	2.60097i	0.721378	−	0.721378i	0.968886	+	0.247508i	$0.0796115\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−0.774764	+	0.207597i	−0.187908	+	0.0503497i	−0.351546	−	0.936171i	$-0.614344\pi$
$17$	−0.774764	+	0.207597i	−0.187908	+	0.0503497i	0.163638	+	0.986520i	$0.447677\pi$
$18$		0			0
$19$	1.40765	+	2.43811i	0.322936	+	0.559342i	0.981092	−	0.193540i	$-0.0619968\pi$
$19$	1.40765	+	2.43811i	0.322936	+	0.559342i	−0.658156	+	0.752881i	$0.728663\pi$
$20$		0			0
$21$	−0.0989528	−	2.64390i	−0.0215933	−	0.576946i
$22$		0			0
$23$	2.17644	−	8.12259i	0.453819	−	1.69368i	−0.237717	−	0.971334i	$-0.576399\pi$
$23$	2.17644	−	8.12259i	0.453819	−	1.69368i	0.691536	−	0.722342i	$-0.256934\pi$
$24$		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
$33$	−0.774764	−	0.207597i	−0.134869	−	0.0361381i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	1.67303	+	0.448288i	0.275045	+	0.0736980i	0.393705	−	0.919237i	$-0.371193\pi$
$37$	1.67303	+	0.448288i	0.275045	+	0.0736980i	−0.118660	+	0.992935i	$0.537860\pi$
$38$		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	$-0.172590\pi$
$43$	2.23310	+	2.23310i	0.340544	+	0.340544i	−0.516028	+	0.856572i	$0.672590\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	2.73172	−	10.1949i	0.398462	−	1.48708i	−0.417340	−	0.908750i	$-0.637038\pi$
$47$	2.73172	−	10.1949i	0.398462	−	1.48708i	0.815802	−	0.578331i	$-0.196296\pi$
$48$		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
$53$	12.2194	−	3.27417i	1.67846	−	0.449742i	0.711089	−	0.703102i	$-0.248202\pi$
$53$	12.2194	−	3.27417i	1.67846	−	0.449742i	0.967372	+	0.253360i	$0.0815356\pi$
$54$		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	−0.541845	−	0.840479i	$-0.682274\pi$
$59$	3.50993	−	6.07937i	0.456953	−	0.791466i	0.998798	+	0.0490121i	$0.0156073\pi$
$60$		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
$63$	2.52820	−	0.779873i	0.318523	−	0.0982547i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−0.728651	−	2.71936i	−0.0890189	−	0.332223i	0.907026	−	0.421075i	$-0.138347\pi$
$67$	−0.728651	−	2.71936i	−0.0890189	−	0.332223i	−0.996045	+	0.0888516i	$0.971680\pi$
$68$		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
$73$	−2.06042	−	7.68957i	−0.241153	−	0.899997i	−0.975278	−	0.220982i	$-0.929074\pi$
$73$	−2.06042	−	7.68957i	−0.241153	−	0.899997i	0.734125	−	0.679015i	$-0.237593\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	1.44341	−	1.55565i	0.164492	−	0.177283i
$78$		0			0
$79$	5.85687	−	3.38146i	0.658949	−	0.380444i	−0.132927	−	0.991126i	$-0.542438\pi$
$79$	5.85687	−	3.38146i	0.658949	−	0.380444i	0.791876	+	0.610681i	$0.209104\pi$
$80$		0			0
$81$	0.500000	−	0.866025i	0.0555556	−	0.0962250i
$82$		0			0
$83$	0.112245	−	0.112245i	0.0123205	−	0.0123205i	−0.700920	−	0.713240i	$-0.747227\pi$
$83$	0.112245	−	0.112245i	0.0123205	−	0.0123205i	0.713240	+	0.700920i	$0.247227\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−0.694634	−	1.20314i	−0.0736311	−	0.127533i	0.826859	−	0.562409i	$-0.190125\pi$
$89$	−0.694634	−	1.20314i	−0.0736311	−	0.127533i	−0.900490	+	0.434876i	$0.856792\pi$
$90$		0			0
$91$	−8.24021	+	5.17777i	−0.863809	+	0.542778i
$92$		0			0
$93$	1.53651	−	5.73433i	0.159328	−	0.594622i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−3.53553	−	3.53553i	−0.358979	−	0.358979i	0.504457	−	0.863437i	$-0.331693\pi$
$97$	−3.53553	−	3.53553i	−0.358979	−	0.358979i	−0.863437	+	0.504457i	$0.831693\pi$
$98$		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
$103$	12.3280	+	3.30329i	1.21472	+	0.325483i	0.808611	−	0.588343i	$-0.200220\pi$
$103$	12.3280	+	3.30329i	1.21472	+	0.325483i	0.406107	+	0.913826i	$0.366886\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−4.86505	−	1.30359i	−0.470322	−	0.126022i	0.0158708	−	0.999874i	$-0.494948\pi$
$107$	−4.86505	−	1.30359i	−0.470322	−	0.126022i	−0.486193	+	0.873852i	$0.661615\pi$
$108$		0			0
$109$	7.48173	+	4.31958i	0.716620	+	0.413741i	0.813507	−	0.581555i	$-0.197555\pi$
$109$	7.48173	+	4.31958i	0.716620	+	0.413741i	−0.0968876	+	0.995295i	$0.530889\pi$
$110$		0			0
$111$			1.73205i			0.164399i
$112$		0			0
$113$	7.34847	+	7.34847i	0.691286	+	0.691286i	0.962515	−	0.271229i	$-0.0874301\pi$
$113$	7.34847	+	7.34847i	0.691286	+	0.691286i	−0.271229	+	0.962515i	$0.587430\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−0.952020	+	3.55299i	−0.0880143	+	0.328474i
$118$		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
$123$	−6.78066	+	1.81687i	−0.611391	+	0.163822i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−8.15325	+	8.15325i	−0.723484	+	0.723484i	−0.969313	−	0.245829i	$-0.920940\pi$
$127$	−8.15325	+	8.15325i	−0.723484	+	0.723484i	0.245829	+	0.969313i	$0.420940\pi$
$128$		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
$133$	−2.19557	−	7.11762i	−0.190380	−	0.617176i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−5.81018	−	21.6839i	−0.496397	−	1.85258i	−0.522059	−	0.852910i	$-0.674836\pi$
$137$	−5.81018	−	21.6839i	−0.496397	−	1.85258i	0.0256612	−	0.999671i	$-0.491831\pi$
$138$		0			0
$139$	20.0131			1.69749			0.848743	−	0.528805i	$-0.177360\pi$
$139$	20.0131			1.69749			0.848743	+	0.528805i	$0.177360\pi$
$140$		0			0
$141$	10.5546			0.888853
$142$		0			0
$143$	0.763610	+	2.84983i	0.0638563	+	0.238315i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−1.30125	+	6.87799i	−0.107325	+	0.567287i
$148$		0			0
$149$	−7.28005	+	4.20314i	−0.596405	+	0.344335i	−0.767626	−	0.640898i	$-0.778562\pi$
$149$	−7.28005	+	4.20314i	−0.596405	+	0.344335i	0.171221	+	0.985233i	$0.445229\pi$
$150$		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
$157$	0.583601	−	0.156376i	0.0465765	−	0.0124801i	−0.235456	−	0.971885i	$-0.575658\pi$
$157$	0.583601	−	0.156376i	0.0465765	−	0.0124801i	0.282032	+	0.959405i	$0.408992\pi$
$158$		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
$163$	2.77845	−	10.3693i	0.217625	−	0.812186i	−0.767601	−	0.640927i	$-0.778550\pi$
$163$	2.77845	−	10.3693i	0.217625	−	0.812186i	0.985226	−	0.171259i	$-0.0547834\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−14.6539	−	14.6539i	−1.13395	−	1.13395i	−0.989514	−	0.144440i	$-0.953862\pi$
$167$	−14.6539	−	14.6539i	−1.13395	−	1.13395i	−0.144440	−	0.989514i	$-0.546138\pi$
$168$		0			0
$169$		−	0.530055i		−	0.0407735i
$170$		0			0
$171$	−2.43811	−	1.40765i	−0.186447	−	0.107645i
$172$		0			0
$173$	−7.34508	−	1.96811i	−0.558436	−	0.149633i	−0.0314484	−	0.999505i	$-0.510012\pi$
$173$	−7.34508	−	1.96811i	−0.558436	−	0.149633i	−0.526988	+	0.849873i	$0.676679\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	6.78066	+	1.81687i	0.509665	+	0.136564i
$178$		0			0
$179$	−10.6672	−	6.15874i	−0.797308	−	0.460326i	0.0452212	−	0.998977i	$-0.485601\pi$
$179$	−10.6672	−	6.15874i	−0.797308	−	0.460326i	−0.842529	+	0.538651i	$0.818934\pi$
$180$		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
$187$	0.166513	−	0.621434i	0.0121766	−	0.0454437i
$188$		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
$193$	5.73433	−	1.53651i	0.412766	−	0.110600i	−0.0464593	−	0.998920i	$-0.514794\pi$
$193$	5.73433	−	1.53651i	0.412766	−	0.110600i	0.459225	+	0.888320i	$0.348127\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	6.56052	−	6.56052i	0.467418	−	0.467418i	−0.433659	−	0.901077i	$-0.642778\pi$
$197$	6.56052	−	6.56052i	0.467418	−	0.467418i	0.901077	+	0.433659i	$0.142778\pi$
$198$		0			0
$199$	−6.45078	+	11.1731i	−0.457284	+	0.792039i	−0.998816	−	0.0486408i	$-0.984511\pi$
$199$	−6.45078	+	11.1731i	−0.457284	+	0.792039i	0.541532	+	0.840680i	$0.317844\pi$
$200$		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
$207$	2.17644	+	8.12259i	0.151273	+	0.564559i
$208$		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
$213$	−1.38640	−	5.17412i	−0.0949947	−	0.354525i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	11.5140	+	10.6832i	0.781621	+	0.725225i
$218$		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	−0.214598	+	0.976702i	$0.568844\pi$
$223$	−17.7899	+	17.7899i	−1.19130	+	1.19130i	−0.976702	+	0.214598i	$0.931156\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−19.8643	+	5.32262i	−1.31844	+	0.353275i	−0.848393	−	0.529367i	$-0.822429\pi$
$227$	−19.8643	+	5.32262i	−1.31844	+	0.353275i	−0.470046	+	0.882642i	$0.655763\pi$
$228$		0			0
$229$	3.49155	+	6.04754i	0.230728	+	0.399633i	0.958023	−	0.286693i	$-0.0925559\pi$
$229$	3.49155	+	6.04754i	0.230728	+	0.399633i	−0.727295	+	0.686325i	$0.759223\pi$
$230$		0			0
$231$	1.87623	+	0.991593i	0.123447	+	0.0652420i
$232$		0			0
$233$	2.33016	−	8.69627i	0.152654	−	0.569711i	−0.846641	−	0.532164i	$-0.821379\pi$
$233$	2.33016	−	8.69627i	0.152654	−	0.569711i	0.999295	−	0.0375471i	$-0.0119544\pi$
$234$		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	$-0.645325\pi$
$239$		−	27.7525i		−	1.79516i	0.440855	−	0.897579i	$-0.354675\pi$
$240$		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
$243$	0.965926	+	0.258819i	0.0619642	+	0.0166032i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	10.0027	+	2.68021i	0.636456	+	0.170538i
$248$		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
$257$	3.56211	−	13.2940i	0.222198	−	0.829255i	−0.761310	−	0.648389i	$-0.775443\pi$
$257$	3.56211	−	13.2940i	0.222198	−	0.829255i	0.983508	−	0.180866i	$-0.0578901\pi$
$258$		0			0
$259$	−4.05155	−	2.14126i	−0.251751	−	0.133051i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	18.1608	−	4.86617i	1.11984	−	0.300061i	0.349022	−	0.937114i	$-0.386514\pi$
$263$	18.1608	−	4.86617i	1.11984	−	0.300061i	0.770819	+	0.637054i	$0.219847\pi$
$264$		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	$-0.621372\pi$
$269$	10.1321	−	17.5493i	0.617765	−	1.07000i	0.989893	−	0.141819i	$-0.0452951\pi$
$270$		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
$273$	−7.13407	−	6.61932i	−0.431774	−	0.400620i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	6.17926	+	23.0613i	0.371276	+	1.38562i	0.858710	+	0.512461i	$0.171266\pi$
$277$	6.17926	+	23.0613i	0.371276	+	1.38562i	−0.487434	+	0.873160i	$0.662067\pi$
$278$		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
$283$	5.34452	+	19.9460i	0.317699	+	1.18567i	0.921451	+	0.388495i	$0.127005\pi$
$283$	5.34452	+	19.9460i	0.317699	+	1.18567i	−0.603752	+	0.797172i	$0.706328\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	4.13266	−	18.1072i	0.243943	−	1.06883i
$288$		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	−0.159196	+	0.987247i	$0.550890\pi$
$293$	−19.6239	+	19.6239i	−1.14644	+	1.14644i	−0.987247	+	0.159196i	$0.949110\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	0.774764	−	0.207597i	0.0449563	−	0.0120460i
$298$		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
$303$	−1.30359	+	4.86505i	−0.0748890	+	0.279490i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	2.46843	+	2.46843i	0.140881	+	0.140881i	0.774030	−	0.633149i	$-0.218238\pi$
$307$	2.46843	+	2.46843i	0.140881	+	0.140881i	−0.633149	+	0.774030i	$0.718238\pi$
$308$		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
$313$	−18.5876	−	4.98054i	−1.05064	−	0.281517i	−0.308121	−	0.951347i	$-0.599700\pi$
$313$	−18.5876	−	4.98054i	−1.05064	−	0.281517i	−0.742514	+	0.669830i	$0.766367\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	20.9156	+	5.60433i	1.17474	+	0.314771i	0.792838	−	0.609432i	$-0.208603\pi$
$317$	20.9156	+	5.60433i	1.17474	+	0.314771i	0.381902	+	0.924203i	$0.375269\pi$
$318$		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
$327$	−2.23598	+	8.34478i	−0.123650	+	0.461468i
$328$		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
$333$	−1.67303	+	0.448288i	−0.0916816	+	0.0245660i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	4.76022	−	4.76022i	0.259305	−	0.259305i	−0.565466	−	0.824772i	$-0.691304\pi$
$337$	4.76022	−	4.76022i	0.259305	−	0.259305i	0.824772	+	0.565466i	$0.191304\pi$
$338$		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
$343$	−14.4800	−	11.5468i	−0.781849	−	0.623468i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	2.53601	+	9.46452i	0.136140	+	0.508082i	0.999991	+	0.00433355i	$0.00137942\pi$
$347$	2.53601	+	9.46452i	0.136140	+	0.508082i	−0.863850	+	0.503748i	$0.831954\pi$
$348$		0			0
$349$	1.11432			0.0596484			0.0298242	−	0.999555i	$-0.490505\pi$
$349$	1.11432			0.0596484			0.0298242	+	0.999555i	$0.490505\pi$
$350$		0			0
$351$	−3.67832			−0.196334
$352$		0			0
$353$	−4.03595	−	15.0624i	−0.214812	−	0.801689i	−0.986233	−	0.165364i	$-0.947120\pi$
$353$	−4.03595	−	15.0624i	−0.214812	−	0.801689i	0.771421	−	0.636326i	$-0.219546\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	0.625532	+	2.02786i	0.0331066	+	0.107325i
$358$		0			0
$359$	−31.5893	+	18.2381i	−1.66722	+	0.962571i	−0.698095	+	0.716005i	$0.745969\pi$
$359$	−31.5893	+	18.2381i	−1.66722	+	0.962571i	−0.969126	+	0.246565i	$0.920698\pi$
$360$		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
$367$	−12.2463	+	3.28139i	−0.639253	+	0.171287i	−0.563865	−	0.825867i	$-0.690686\pi$
$367$	−12.2463	+	3.28139i	−0.639253	+	0.171287i	−0.0753878	+	0.997154i	$0.524019\pi$
$368$		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
$373$	6.46767	−	24.1377i	0.334883	−	1.24980i	−0.569112	−	0.822260i	$-0.692713\pi$
$373$	6.46767	−	24.1377i	0.334883	−	1.24980i	0.903996	−	0.427542i	$-0.140620\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$		−	13.9154i		−	0.714786i	−0.933954	−	0.357393i	$-0.883666\pi$
$379$		−	13.9154i		−	0.714786i	0.933954	−	0.357393i	$-0.116334\pi$
$380$		0			0
$381$	−9.98565	−	5.76522i	−0.511580	−	0.295361i
$382$		0			0
$383$	10.9697	+	2.93932i	0.560524	+	0.150192i	0.527947	−	0.849277i	$-0.322962\pi$
$383$	10.9697	+	2.93932i	0.560524	+	0.150192i	0.0325771	+	0.999469i	$0.489629\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−3.05047	−	0.817370i	−0.155064	−	0.0415492i
$388$		0			0
$389$	−23.9756	−	13.8423i	−1.21561	−	0.701832i	−0.251634	−	0.967823i	$-0.580968\pi$
$389$	−23.9756	−	13.8423i	−1.21561	−	0.701832i	−0.963976	+	0.265990i	$0.914301\pi$
$390$		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
$397$	−0.898088	+	3.35171i	−0.0450737	+	0.168217i	−0.984794	−	0.173727i	$-0.944419\pi$
$397$	−0.898088	+	3.35171i	−0.0450737	+	0.168217i	0.939720	+	0.341945i	$0.111086\pi$
$398$		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
$403$	−21.0927	+	5.65177i	−1.05070	+	0.281535i
$404$		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	−0.939344	−	0.342976i	$-0.888565\pi$
$409$	−3.49155	+	6.04754i	−0.172646	+	0.299032i	0.766698	+	0.642008i	$0.221898\pi$
$410$		0			0
$411$	19.4413	−	11.2244i	0.958966	−	0.553659i
$412$		0			0
$413$	−12.6326	+	13.6149i	−0.621608	+	0.669947i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	5.17976	+	19.3311i	0.253654	+	0.946650i
$418$		0			0
$419$	−30.2640			−1.47849			−0.739247	−	0.673434i	$-0.764818\pi$
$419$	−30.2640			−1.47849			−0.739247	+	0.673434i	$0.764818\pi$
$420$		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
$423$	2.73172	+	10.1949i	0.132821	+	0.495694i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−25.6389	+	7.90882i	−1.24075	+	0.382735i
$428$		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	−0.893685	−	0.448696i	$-0.851889\pi$
$433$	−9.25962	+	9.25962i	−0.444989	+	0.444989i	0.448696	+	0.893685i	$0.351889\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	22.8674	−	6.12731i	1.09390	−	0.293109i
$438$		0			0
$439$	5.45919	+	9.45560i	0.260553	+	0.451291i	0.966389	−	0.257084i	$-0.0827618\pi$
$439$	5.45919	+	9.45560i	0.260553	+	0.451291i	−0.705836	+	0.708375i	$0.749428\pi$
$440$		0			0
$441$	−6.98042	+	0.523243i	−0.332401	+	0.0249163i
$442$		0			0
$443$	−1.66315	+	6.20698i	−0.0790188	+	0.294902i	−0.994114	−	0.108335i	$-0.965448\pi$
$443$	−1.66315	+	6.20698i	−0.0790188	+	0.294902i	0.915096	+	0.403237i	$0.132115\pi$
$444$		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	$-0.885238\pi$
$449$		−	14.9504i		−	0.705551i	0.935708	−	0.352776i	$-0.114762\pi$
$450$		0			0
$451$	−4.87623	−	2.81529i	−0.229613	−	0.132567i
$452$		0			0
$453$	7.53624	+	2.01933i	0.354084	+	0.0948764i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	12.7275	+	3.41033i	0.595369	+	0.159529i	0.543906	−	0.839146i	$-0.316945\pi$
$457$	12.7275	+	3.41033i	0.595369	+	0.159529i	0.0514631	+	0.998675i	$0.483612\pi$
$458$		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	0.891725	+	0.452578i	$0.149495\pi$
$463$	28.9259	+	28.9259i	1.34430	+	1.34430i	0.452578	+	0.891725i	$0.350505\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−2.38330	+	8.89461i	−0.110286	+	0.411593i	−0.998891	−	0.0470798i	$-0.985008\pi$
$467$	−2.38330	+	8.89461i	−0.110286	+	0.411593i	0.888605	+	0.458673i	$0.151675\pi$
$468$		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
$473$	−2.44676	+	0.655608i	−0.112502	+	0.0301449i
$474$		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	$0.472712\pi$
$479$	−17.9473	+	31.0856i	−0.820033	+	1.42034i	−0.905657	+	0.424012i	$0.860622\pi$
$480$		0			0
$481$	5.51748	−	3.18552i	0.251576	−	0.145247i
$482$		0			0
$483$	−21.6907	−	4.95054i	−0.986960	−	0.225257i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	2.61052	+	9.74260i	0.118294	+	0.441479i	0.999512	−	0.0312305i	$-0.00994260\pi$
$487$	2.61052	+	9.74260i	0.118294	+	0.441479i	−0.881218	+	0.472710i	$0.843276\pi$
$488$		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
$497$	13.8170	+	3.15351i	0.619779	+	0.141454i
$498$		0			0
$499$	−11.5121	+	6.64649i	−0.515351	+	0.297538i	−0.735030	−	0.678034i	$-0.762832\pi$
$499$	−11.5121	+	6.64649i	−0.515351	+	0.297538i	0.219680	+	0.975572i	$0.429499\pi$
$500$		0			0
$501$	10.3619	−	17.9473i	0.462935	−	0.801826i
$502$		0			0
$503$	−25.4558	+	25.4558i	−1.13502	+	1.13502i	−0.145690	+	0.989330i	$0.546540\pi$
$503$	−25.4558	+	25.4558i	−1.13502	+	1.13502i	−0.989330	+	0.145690i	$0.953460\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	0.511994	−	0.137188i	0.0227384	−	0.00609275i
$508$		0			0
$509$	−16.4206	−	28.4413i	−0.727829	−	1.26064i	−0.957799	−	0.287439i	$-0.907196\pi$
$509$	−16.4206	−	28.4413i	−0.727829	−	1.26064i	0.229970	−	0.973198i	$-0.426137\pi$
$510$		0			0
$511$	0.787747	+	21.0476i	0.0348479	+	0.931093i
$512$		0			0
$513$	0.728651	−	2.71936i	0.0321707	−	0.120063i
$514$		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
$523$	−23.5227	−	6.30288i	−1.02857	−	0.275606i	−0.295203	−	0.955434i	$-0.595387\pi$
$523$	−23.5227	−	6.30288i	−1.02857	−	0.275606i	−0.733371	+	0.679829i	$0.762054\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	4.59947	+	1.23242i	0.200356	+	0.0536852i
$528$		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
$537$	3.18800	−	11.8978i	0.137572	−	0.513427i
$538$		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
$543$	−7.64994	+	2.04979i	−0.328290	+	0.0879651i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−16.4881	+	16.4881i	−0.704980	+	0.704980i	−0.965475	−	0.260495i	$-0.916114\pi$
$547$	−16.4881	+	16.4881i	−0.704980	+	0.704980i	0.260495	+	0.965475i	$0.416114\pi$
$548$		0			0
$549$	−5.07059	+	8.78251i	−0.216407	+	0.374828i
$550$		0			0
$551$		0			0
$552$		0			0
$553$	−17.0980	+	5.27422i	−0.727083	+	0.224283i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−8.49991	−	31.7221i	−0.360153	−	1.34411i	−0.873875	−	0.486151i	$-0.838400\pi$
$557$	−8.49991	−	31.7221i	−0.360153	−	1.34411i	0.513722	−	0.857957i	$-0.328266\pi$
$558$		0			0
$559$	11.6164			0.491322
$560$		0			0
$561$	0.643355			0.0271625
$562$		0			0
$563$	−11.4675	−	42.7973i	−0.483297	−	1.80369i	−0.587608	−	0.809146i	$-0.699930\pi$
$563$	−11.4675	−	42.7973i	−0.483297	−	1.80369i	0.104311	−	0.994545i	$-0.466736\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−1.79955	+	1.93949i	−0.0755740	+	0.0814509i
$568$		0			0
$569$	4.77646	−	2.75769i	0.200240	−	0.115608i	−0.396528	−	0.918023i	$-0.629785\pi$
$569$	4.77646	−	2.75769i	0.200240	−	0.115608i	0.596767	+	0.802414i	$0.296452\pi$
$570$		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
$577$	32.1106	−	8.60401i	1.33678	−	0.358190i	0.481543	−	0.876423i	$-0.340077\pi$
$577$	32.1106	−	8.60401i	1.33678	−	0.358190i	0.855239	+	0.518233i	$0.173410\pi$
$578$		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
$583$	−2.62620	+	9.80110i	−0.108766	+	0.405920i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	22.5720	+	22.5720i	0.931647	+	0.931647i	0.997809	−	0.0661617i	$-0.0210753\pi$
$587$	22.5720	+	22.5720i	0.931647	+	0.931647i	−0.0661617	+	0.997809i	$0.521075\pi$
$588$		0			0
$589$		−	16.7133i		−	0.688659i
$590$		0			0
$591$	8.03497	+	4.63899i	0.330514	+	0.190823i
$592$		0			0
$593$	−14.8131	−	3.96917i	−0.608303	−	0.162994i	−0.0584983	−	0.998288i	$-0.518631\pi$
$593$	−14.8131	−	3.96917i	−0.608303	−	0.162994i	−0.549805	+	0.835293i	$0.685298\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−12.4620	−	3.33917i	−0.510034	−	0.136663i
$598$		0			0
$599$	41.5104	+	23.9661i	1.69607	+	0.979227i	0.949419	+	0.314012i	$0.101673\pi$
$599$	41.5104	+	23.9661i	1.69607	+	0.979227i	0.746652	+	0.665215i	$0.231660\pi$
$600$		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
$607$	0.256109	−	0.955811i	0.0103951	−	0.0387952i	−0.960533	−	0.278164i	$-0.910274\pi$
$607$	0.256109	−	0.955811i	0.0103951	−	0.0387952i	0.970929	+	0.239369i	$0.0769407\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−19.4115	−	33.6217i	−0.785306	−	1.36019i
$612$		0			0
$613$	−13.4903	+	3.61472i	−0.544868	+	0.145997i	−0.520745	−	0.853712i	$-0.674346\pi$
$613$	−13.4903	+	3.61472i	−0.544868	+	0.145997i	−0.0241228	+	0.999709i	$0.507679\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−13.2946	+	13.2946i	−0.535221	+	0.535221i	−0.922121	−	0.386900i	$-0.873546\pi$
$617$	−13.2946	+	13.2946i	−0.535221	+	0.535221i	0.386900	+	0.922121i	$0.373546\pi$
$618$		0			0
$619$	4.23484	−	7.33496i	0.170213	−	0.294817i	−0.768281	−	0.640112i	$-0.778888\pi$
$619$	4.23484	−	7.33496i	0.170213	−	0.294817i	0.938494	+	0.345295i	$0.112221\pi$
$620$		0			0
$621$	−7.28251	+	4.20456i	−0.292237	+	0.168723i
$622$		0			0
$623$	1.08345	+	3.51235i	0.0434076	+	0.140719i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−0.584447	−	2.18119i	−0.0233406	−	0.0871082i
$628$		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
$633$	4.95865	+	18.5059i	0.197089	+	0.735544i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	24.3032	−	8.50457i	0.962927	−	0.336963i
$638$		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	−0.993943	−	0.109892i	$-0.964949\pi$
$643$	−22.4173	+	22.4173i	−0.884051	+	0.884051i	0.109892	+	0.993943i	$0.464949\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−7.71729	+	2.06784i	−0.303398	+	0.0812953i	−0.407306	−	0.913292i	$-0.633532\pi$
$647$	−7.71729	+	2.06784i	−0.303398	+	0.0812953i	0.103908	+	0.994587i	$0.466865\pi$
$648$		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
$653$	0.647977	−	2.41828i	0.0253573	−	0.0946348i	−0.952088	−	0.305826i	$-0.901068\pi$
$653$	0.647977	−	2.41828i	0.0253573	−	0.0946348i	0.977445	+	0.211191i	$0.0677342\pi$
$654$		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	$-0.861825\pi$
$659$		−	21.5937i		−	0.841172i	0.907253	−	0.420586i	$-0.138175\pi$
$660$		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
$663$	−2.84983	−	0.763610i	−0.110678	−	0.0296561i
$664$		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	$-0.144482\pi$
$673$	11.9403	+	11.9403i	0.460263	+	0.460263i	−0.438478	+	0.898742i	$0.644482\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−5.62995	+	21.0113i	−0.216377	+	0.807528i	0.769301	+	0.638887i	$0.220605\pi$
$677$	−5.62995	+	21.0113i	−0.216377	+	0.807528i	−0.985677	+	0.168642i	$0.946062\pi$
$678$		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
$683$	25.2495	−	6.76559i	0.966147	−	0.258878i	0.258947	−	0.965892i	$-0.416625\pi$
$683$	25.2495	−	6.76559i	0.966147	−	0.258878i	0.707200	+	0.707013i	$0.249958\pi$
$684$		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
$693$	−0.472201	+	2.06894i	−0.0179375	+	0.0785925i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−1.45730	−	5.43873i	−0.0551993	−	0.206006i
$698$		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
$703$	1.26206	+	4.71007i	0.0475995	+	0.177644i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−9.76856	−	9.06373i	−0.367385	−	0.340877i
$708$		0			0
$709$	−17.2866	+	9.98042i	−0.649211	+	0.374822i	−0.788154	−	0.615478i	$-0.788963\pi$
$709$	−17.2866	+	9.98042i	−0.649211	+	0.374822i	0.138943	+	0.990300i	$0.455630\pi$
$710$		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
$717$	26.8068	−	7.18286i	1.00112	−	0.268249i
$718$		0			0
$719$	−1.68623	−	2.92063i	−0.0628856	−	0.108921i	0.832868	−	0.553471i	$-0.186697\pi$
$719$	−1.68623	−	2.92063i	−0.0628856	−	0.108921i	−0.895754	+	0.444550i	$0.853364\pi$
$720$		0			0
$721$	−29.8545	−	15.7782i	−1.11184	−	0.587612i
$722$		0			0
$723$	2.24144	−	8.36516i	0.0833600	−	0.311104i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−10.0642	−	10.0642i	−0.373259	−	0.373259i	0.495404	−	0.868663i	$-0.335020\pi$
$727$	−10.0642	−	10.0642i	−0.373259	−	0.373259i	−0.868663	+	0.495404i	$0.835020\pi$
$728$		0			0
$729$			1.00000i			0.0370370i
$730$		0			0
$731$	−2.19371	−	1.26654i	−0.0811371	−	0.0468446i
$732$		0			0
$733$	44.3191	+	11.8753i	1.63696	+	0.438623i	0.955922	−	0.293622i	$-0.0948607\pi$
$733$	44.3191	+	11.8753i	1.63696	+	0.438623i	0.681041	+	0.732245i	$0.261527\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	2.18119	+	0.584447i	0.0803450	+	0.0215284i
$738$		0			0
$739$	−2.94993	−	1.70314i	−0.108515	−	0.0626511i	0.444760	−	0.895650i	$-0.353289\pi$
$739$	−2.94993	−	1.70314i	−0.108515	−	0.0626511i	−0.553275	+	0.832999i	$0.686622\pi$
$740$		0			0
$741$			10.3555i			0.380421i
$742$		0			0
$743$	21.8718	+	21.8718i	0.802400	+	0.802400i	0.983470	−	0.181070i	$-0.0579561\pi$
$743$	21.8718	+	21.8718i	0.802400	+	0.802400i	−0.181070	+	0.983470i	$0.557956\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−0.0410847	+	0.153330i	−0.00150321	+	0.00561005i
$748$		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
$753$	−5.94140	+	1.59199i	−0.216517	+	0.0580155i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−0.662347	+	0.662347i	−0.0240734	+	0.0240734i	−0.719041	−	0.694968i	$-0.755419\pi$
$757$	−0.662347	+	0.662347i	−0.0240734	+	0.0240734i	0.694968	+	0.719041i	$0.255419\pi$
$758$		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
$763$	−16.7556	−	15.5466i	−0.606592	−	0.562824i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−6.68304	−	24.9414i	−0.241311	−	0.900583i
$768$		0			0
$769$	54.1886			1.95409			0.977045	−	0.213033i	$-0.0683343\pi$
$769$	54.1886			1.95409			0.977045	+	0.213033i	$0.0683343\pi$
$770$		0			0
$771$	13.7629			0.495660
$772$		0			0
$773$	−6.21166	−	23.1822i	−0.223418	−	0.833806i	−0.983032	−	0.183433i	$-0.941279\pi$
$773$	−6.21166	−	23.1822i	−0.223418	−	0.833806i	0.759614	−	0.650374i	$-0.225388\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	1.01968	−	4.46769i	0.0365807	−	0.160278i
$778$		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
$787$	−9.01011	+	2.41425i	−0.321176	+	0.0860588i	−0.415805	−	0.909454i	$-0.636500\pi$
$787$	−9.01011	+	2.41425i	−0.321176	+	0.0860588i	0.0946293	+	0.995513i	$0.469833\pi$
$788$		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
$793$	9.65460	−	36.0314i	0.342845	−	1.27951i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−11.4334	−	11.4334i	−0.404990	−	0.404990i	0.474997	−	0.879987i	$-0.342449\pi$
$797$	−11.4334	−	11.4334i	−0.404990	−	0.404990i	−0.879987	+	0.474997i	$0.842449\pi$
$798$		0			0
$799$			8.46575i			0.299497i
$800$		0			0
$801$	1.20314	+	0.694634i	0.0425109	+	0.0245437i
$802$		0			0
$803$	6.16776	+	1.65265i	0.217656	+	0.0583207i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	19.5737	+	5.24476i	0.689027	+	0.184624i
$808$		0			0
$809$	23.2809	+	13.4413i	0.818514	+	0.472569i	0.849904	−	0.526938i	$-0.176660\pi$
$809$	23.2809	+	13.4413i	0.818514	+	0.472569i	−0.0313899	+	0.999507i	$0.509993\pi$
$810$		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
$817$	−2.30113	+	8.58795i	−0.0805065	+	0.300454i
$818$		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
$823$	25.7152	−	6.89036i	0.896374	−	0.240183i	0.218916	−	0.975744i	$-0.429748\pi$
$823$	25.7152	−	6.89036i	0.896374	−	0.240183i	0.677459	+	0.735561i	$0.263081\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−4.59580	+	4.59580i	−0.159812	+	0.159812i	−0.782483	−	0.622672i	$-0.786047\pi$
$827$	−4.59580	+	4.59580i	−0.159812	+	0.159812i	0.622672	+	0.782483i	$0.286047\pi$
$828$		0			0
$829$	−18.1555	+	31.4462i	−0.630565	+	1.09217i	0.356872	+	0.934153i	$0.383843\pi$
$829$	−18.1555	+	31.4462i	−0.630565	+	1.09217i	−0.987436	+	0.158017i	$0.949490\pi$
$830$		0			0
$831$	−20.6762	+	11.9374i	−0.717250	+	0.414105i
$832$		0			0
$833$	−5.51680	−	1.04373i	−0.191146	−	0.0361630i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	1.53651	+	5.73433i	0.0531095	+	0.198207i
$838$		0			0
$839$	13.7207			0.473692			0.236846	−	0.971547i	$-0.423886\pi$
$839$	13.7207			0.473692			0.236846	+	0.971547i	$0.423886\pi$
$840$		0			0
$841$	29.0000			1.00000
$842$		0			0
$843$	3.72862	+	13.9154i	0.128421	+	0.479272i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−8.07687	−	26.1837i	−0.277524	−	0.899682i
$848$		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	−0.0685915	−	0.997645i	$-0.521851\pi$
$853$	27.1341	−	27.1341i	0.929053	−	0.929053i	0.997645	+	0.0685915i	$0.0218505\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−39.1071	+	10.4787i	−1.33587	+	0.357946i	−0.854902	−	0.518789i	$-0.826383\pi$
$857$	−39.1071	+	10.4787i	−1.33587	+	0.357946i	−0.480972	+	0.876736i	$0.659716\pi$
$858$		0			0
$859$	−18.6419	−	32.2888i	−0.636055	−	1.10168i	−0.986291	−	0.165018i	$-0.947232\pi$
$859$	−18.6419	−	32.2888i	−0.636055	−	1.10168i	0.350236	−	0.936662i	$-0.386101\pi$
$860$		0			0
$861$	18.5598	−	0.694634i	0.632516	−	0.0236731i
$862$		0			0
$863$	4.42404	−	16.5107i	0.150596	−	0.562032i	−0.848846	−	0.528640i	$-0.822702\pi$
$863$	4.42404	−	16.5107i	0.150596	−	0.562032i	0.999442	−	0.0333925i	$-0.0106311\pi$
$864$		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
$873$	4.82963	+	1.29410i	0.163458	+	0.0437985i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−39.6731	−	10.6304i	−1.33967	−	0.358962i	−0.483355	−	0.875424i	$-0.660582\pi$
$877$	−39.6731	−	10.6304i	−1.33967	−	0.358962i	−0.856310	+	0.516462i	$0.827249\pi$
$878$		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	−0.999045	−	0.0436994i	$-0.986086\pi$
$883$	−30.9855	−	30.9855i	−1.04274	−	1.04274i	−0.0436994	−	0.999045i	$-0.513914\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−2.16758	+	8.08950i	−0.0727801	+	0.271619i	−0.992721	−	0.120439i	$-0.961570\pi$
$887$	−2.16758	+	8.08950i	−0.0727801	+	0.271619i	0.919941	+	0.392057i	$0.128237\pi$
$888$		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
$893$	28.7017	−	7.69058i	0.960464	−	0.257356i
$894$		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
$903$	5.68311	−	6.12505i	0.189122	−	0.203829i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	9.43776	+	35.2222i	0.313376	+	1.16953i	0.925492	+	0.378767i	$0.123652\pi$
$907$	9.43776	+	35.2222i	0.313376	+	1.16953i	−0.612116	+	0.790768i	$0.709682\pi$
$908$		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
$913$	0.0329538	+	0.122985i	0.00109061	+	0.00407022i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	9.22135	−	2.84451i	0.304516	−	0.0939339i
$918$		0			0
$919$	24.0828	−	13.9042i	0.794417	−	0.458657i	−0.0470984	−	0.998890i	$-0.514997\pi$
$919$	24.0828	−	13.9042i	0.794417	−	0.458657i	0.841515	+	0.540234i	$0.181664\pi$
$920$		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
$927$	−12.3280	+	3.30329i	−0.404906	+	0.108494i
$928$		0			0
$929$	29.6061	+	51.2793i	0.971346	+	1.68242i	0.691501	+	0.722376i	$0.256950\pi$
$929$	29.6061	+	51.2793i	0.971346	+	1.68242i	0.279845	+	0.960045i	$0.409717\pi$
$930$		0			0
$931$	1.47308	+	19.6519i	0.0482783	+	0.644065i
$932$		0			0
$933$	5.81018	−	21.6839i	0.190217	−	0.709899i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−24.5855	−	24.5855i	−0.803174	−	0.803174i	0.180416	−	0.983590i	$-0.442256\pi$
$937$	−24.5855	−	24.5855i	−0.803174	−	0.803174i	−0.983590	+	0.180416i	$0.942256\pi$
$938$		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
$943$	57.0193	+	15.2783i	1.85681	+	0.497529i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−18.2318	−	4.88519i	−0.592453	−	0.158747i	−0.0498792	−	0.998755i	$-0.515884\pi$
$947$	−18.2318	−	4.88519i	−0.592453	−	0.158747i	−0.542574	+	0.840008i	$0.682550\pi$
$948$		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	$-0.158601\pi$
$953$	12.3642	+	12.3642i	0.400517	+	0.400517i	−0.477898	+	0.878415i	$0.658601\pi$
$954$		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
$963$	4.86505	−	1.30359i	0.156774	−	0.0420074i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	30.6395	−	30.6395i	0.985299	−	0.985299i	−0.0145946	−	0.999893i	$-0.504646\pi$
$967$	30.6395	−	30.6395i	0.985299	−	0.985299i	0.999893	+	0.0145946i	$0.00464578\pi$
$968$		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
$973$	−51.6222	−	11.7819i	−1.65493	−	0.377711i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	3.91076	+	14.5951i	0.125116	+	0.466940i	0.999844	−	0.0176751i	$-0.00562644\pi$
$977$	3.91076	+	14.5951i	0.125116	+	0.466940i	−0.874728	+	0.484615i	$0.838960\pi$
$978$		0			0
$979$	1.11432			0.0356140
$980$		0			0
$981$	−8.63916			−0.275827
$982$		0			0
$983$	−14.2073	−	53.0225i	−0.453144	−	1.69116i	−0.693488	−	0.720469i	$-0.743927\pi$
$983$	−14.2073	−	53.0225i	−0.453144	−	1.69116i	0.240344	−	0.970688i	$-0.422740\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−27.2246	−	6.21358i	−0.866570	−	0.197780i
$988$		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
$997$	32.2579	−	8.64347i	1.02162	−	0.273742i	0.291141	−	0.956680i	$-0.405965\pi$
$997$	32.2579	−	8.64347i	1.02162	−	0.273742i	0.730476	+	0.682939i	$0.239298\pi$
$998$		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.493.5	yes	24
5.2	odd	4	inner	2100.2.ce.c.157.6	yes	24
5.3	odd	4	inner	2100.2.ce.c.157.1	✓	24
5.4	even	2	inner	2100.2.ce.c.493.3	yes	24
7.5	odd	6	inner	2100.2.ce.c.1993.6	yes	24
35.12	even	12	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.1657.3	yes	24

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

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