LMFDB - Embedded newform 2100.2.ce.c.1657.6

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			1657.6
Character	$\chi$	$=$	2100.1657
Dual form			2100.2.ce.c.493.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.258819 - 0.965926i) q^{3} +(0.920762 - 2.48036i) q^{7} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})$	\(q+(0.258819 - 0.965926i) q^{3} +(0.920762 - 2.48036i) q^{7} +(-0.866025 - 0.500000i) q^{9} +(1.65754 + 2.87094i) q^{11} +(-1.05702 - 1.05702i) q^{13} +(3.20211 + 0.858003i) q^{17} +(1.10280 - 1.91011i) q^{19} +(-2.15754 - 1.53135i) q^{21} +(-1.83050 - 6.83153i) q^{23} +(-0.707107 + 0.707107i) q^{27} +(1.56249 - 0.902106i) q^{31} +(3.20211 - 0.858003i) q^{33} +(1.67303 - 0.448288i) q^{37} +(-1.29457 + 0.747423i) q^{39} +1.33066i q^{41} +(6.84446 - 6.84446i) q^{43} +(1.11949 + 4.17799i) q^{47} +(-5.30439 - 4.56765i) q^{49} +(1.65754 - 2.87094i) q^{51} +(2.97559 + 0.797308i) q^{53} +(-1.55960 - 1.55960i) q^{57} +(-0.665328 - 1.15238i) q^{59} +(-4.62499 - 2.67024i) q^{61} +(-2.03758 + 1.68768i) q^{63} +(-0.570853 + 2.13045i) q^{67} -7.07253 q^{69} +4.98969 q^{71} +(2.74861 - 10.2580i) q^{73} +(8.64716 - 1.46784i) q^{77} +(-13.8000 - 7.96745i) q^{79} +(0.500000 + 0.866025i) q^{81} +(-10.1150 - 10.1150i) q^{83} +(2.87094 - 4.97261i) q^{89} +(-3.59504 + 1.64852i) q^{91} +(-0.466964 - 1.74273i) q^{93} +(-3.53553 + 3.53553i) q^{97} -3.31507i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/2100\mathbb{Z}\right)^\times$.

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	0.258819	−	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
$7$	0.920762	−	2.48036i	0.348015	−	0.937489i
$7$	0.920762	−	2.48036i	0.348015	−	0.937489i
$8$		0			0
$9$	−0.866025	−	0.500000i	−0.288675	−	0.166667i
$10$		0			0
$11$	1.65754	+	2.87094i	0.499766	+	0.865620i	1.00000		0.000270562i	$-8.61226e-5\pi$
$11$	1.65754	+	2.87094i	0.499766	+	0.865620i	−0.500234	+	0.865890i	$0.666753\pi$
$12$		0			0
$13$	−1.05702	−	1.05702i	−0.293163	−	0.293163i	0.545165	−	0.838329i	$-0.316467\pi$
$13$	−1.05702	−	1.05702i	−0.293163	−	0.293163i	−0.838329	+	0.545165i	$0.816467\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	3.20211	+	0.858003i	0.776626	+	0.208096i	0.625297	−	0.780387i	$-0.284978\pi$
$17$	3.20211	+	0.858003i	0.776626	+	0.208096i	0.151329	+	0.988483i	$0.451645\pi$
$18$		0			0
$19$	1.10280	−	1.91011i	0.253001	−	0.438210i	−0.711350	−	0.702838i	$-0.751916\pi$
$19$	1.10280	−	1.91011i	0.253001	−	0.438210i	0.964351	+	0.264628i	$0.0852492\pi$
$20$		0			0
$21$	−2.15754	−	1.53135i	−0.470813	−	0.334169i
$22$		0			0
$23$	−1.83050	−	6.83153i	−0.381687	−	1.42447i	−0.843324	−	0.537405i	$-0.819405\pi$
$23$	−1.83050	−	6.83153i	−0.381687	−	1.42447i	0.461638	−	0.887069i	$-0.347262\pi$
$24$		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
$31$	1.56249	−	0.902106i	0.280632	−	0.162023i	−0.353077	−	0.935594i	$-0.614865\pi$
$31$	1.56249	−	0.902106i	0.280632	−	0.162023i	0.633710	+	0.773571i	$0.281531\pi$
$32$		0			0
$33$	3.20211	−	0.858003i	0.557416	−	0.149359i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	1.67303	−	0.448288i	0.275045	−	0.0736980i	−0.118660	−	0.992935i	$-0.537860\pi$
$37$	1.67303	−	0.448288i	0.275045	−	0.0736980i	0.393705	+	0.919237i	$0.371193\pi$
$38$		0			0
$39$	−1.29457	+	0.747423i	−0.207298	+	0.119683i
$40$		0			0
$41$			1.33066i			0.207813i	0.994587	+	0.103907i	$0.0331343\pi$
$41$			1.33066i			0.207813i	−0.994587	+	0.103907i	$0.966866\pi$
$42$		0			0
$43$	6.84446	−	6.84446i	1.04377	−	1.04377i	0.0447733	−	0.998997i	$-0.485743\pi$
$43$	6.84446	−	6.84446i	1.04377	−	1.04377i	0.998997	−	0.0447733i	$-0.0142565\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	1.11949	+	4.17799i	0.163294	+	0.609423i	0.998252	+	0.0591082i	$0.0188257\pi$
$47$	1.11949	+	4.17799i	0.163294	+	0.609423i	−0.834957	+	0.550315i	$0.814508\pi$
$48$		0			0
$49$	−5.30439	−	4.56765i	−0.757771	−	0.652521i
$50$		0			0
$51$	1.65754	−	2.87094i	0.232101	−	0.402011i
$52$		0			0
$53$	2.97559	+	0.797308i	0.408729	+	0.109519i	0.457324	−	0.889300i	$-0.348808\pi$
$53$	2.97559	+	0.797308i	0.408729	+	0.109519i	−0.0485954	+	0.998819i	$0.515474\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−1.55960	−	1.55960i	−0.206574	−	0.206574i
$58$		0			0
$59$	−0.665328	−	1.15238i	−0.0866183	−	0.150027i	0.819461	−	0.573134i	$-0.194273\pi$
$59$	−0.665328	−	1.15238i	−0.0866183	−	0.150027i	−0.906080	+	0.423107i	$0.860939\pi$
$60$		0			0
$61$	−4.62499	−	2.67024i	−0.592169	−	0.341889i	0.173786	−	0.984783i	$-0.444400\pi$
$61$	−4.62499	−	2.67024i	−0.592169	−	0.341889i	−0.765955	+	0.642895i	$0.777733\pi$
$62$		0			0
$63$	−2.03758	+	1.68768i	−0.256712	+	0.212627i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−0.570853	+	2.13045i	−0.0697408	+	0.260276i	−0.991989	−	0.126321i	$-0.959683\pi$
$67$	−0.570853	+	2.13045i	−0.0697408	+	0.260276i	0.922249	+	0.386597i	$0.126350\pi$
$68$		0			0
$69$	−7.07253			−0.851432
$70$		0			0
$71$	4.98969			0.592167			0.296084	−	0.955162i	$-0.404319\pi$
$71$	4.98969			0.592167			0.296084	+	0.955162i	$0.404319\pi$
$72$		0			0
$73$	2.74861	−	10.2580i	0.321701	−	1.20060i	−0.595886	−	0.803069i	$-0.703199\pi$
$73$	2.74861	−	10.2580i	0.321701	−	1.20060i	0.917587	−	0.397535i	$-0.130134\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	8.64716	−	1.46784i	0.985435	−	0.167276i
$78$		0			0
$79$	−13.8000	−	7.96745i	−1.55262	−	0.896408i	−0.997927	−	0.0643564i	$-0.979501\pi$
$79$	−13.8000	−	7.96745i	−1.55262	−	0.896408i	−0.554698	−	0.832052i	$-0.687166\pi$
$80$		0			0
$81$	0.500000	+	0.866025i	0.0555556	+	0.0962250i
$82$		0			0
$83$	−10.1150	−	10.1150i	−1.11026	−	1.11026i	−0.993114	−	0.117151i	$-0.962624\pi$
$83$	−10.1150	−	10.1150i	−1.11026	−	1.11026i	−0.117151	−	0.993114i	$-0.537376\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$		0			0
$88$		0			0
$89$	2.87094	−	4.97261i	0.304319	−	0.527095i	−0.672791	−	0.739833i	$-0.734905\pi$
$89$	2.87094	−	4.97261i	0.304319	−	0.527095i	0.977109	+	0.212738i	$0.0682379\pi$
$90$		0			0
$91$	−3.59504	+	1.64852i	−0.376863	+	0.172812i
$92$		0			0
$93$	−0.466964	−	1.74273i	−0.0484220	−	0.180713i
$94$		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
$99$		−	3.31507i		−	0.333177i
$100$		0			0
$101$	−16.2774	+	9.39774i	−1.61966	+	0.935110i	−0.632651	+	0.774437i	$0.718033\pi$
$101$	−16.2774	+	9.39774i	−1.61966	+	0.935110i	−0.987008	+	0.160673i	$0.948633\pi$
$102$		0			0
$103$	−9.59638	+	2.57134i	−0.945559	+	0.253362i	−0.698477	−	0.715633i	$-0.746139\pi$
$103$	−9.59638	+	2.57134i	−0.945559	+	0.253362i	−0.247082	+	0.968994i	$0.579472\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	18.1550	−	4.86463i	1.75511	−	0.470281i	0.769409	−	0.638757i	$-0.220551\pi$
$107$	18.1550	−	4.86463i	1.75511	−	0.470281i	0.985706	+	0.168475i	$0.0538844\pi$
$108$		0			0
$109$	−13.0897	+	7.55734i	−1.25377	+	0.723862i	−0.971855	−	0.235579i	$-0.924301\pi$
$109$	−13.0897	+	7.55734i	−1.25377	+	0.723862i	−0.281910	+	0.959441i	$0.590968\pi$
$110$		0			0
$111$		−	1.73205i		−	0.164399i
$112$		0			0
$113$	7.34847	−	7.34847i	0.691286	−	0.691286i	−0.271229	−	0.962515i	$-0.587430\pi$
$113$	7.34847	−	7.34847i	0.691286	−	0.691286i	0.962515	+	0.271229i	$0.0874301\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	0.386895	+	1.44391i	0.0357684	+	0.133490i
$118$		0			0
$119$	5.07654	−	7.15238i	0.465366	−	0.655658i
$120$		0			0
$121$	0.00515410	−	0.00892716i	0.000468554	−	0.000811560i
$122$		0			0
$123$	1.28531	+	0.344399i	0.115893	+	0.0310534i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	7.83640	+	7.83640i	0.695368	+	0.695368i	0.963408	−	0.268040i	$-0.0863758\pi$
$127$	7.83640	+	7.83640i	0.695368	+	0.695368i	−0.268040	+	0.963408i	$0.586376\pi$
$128$		0			0
$129$	−4.83976	−	8.38272i	−0.426117	−	0.738057i
$130$		0			0
$131$	11.3048	+	6.52681i	0.987702	+	0.570250i	0.904586	−	0.426290i	$-0.140180\pi$
$131$	11.3048	+	6.52681i	0.987702	+	0.570250i	0.0831152	+	0.996540i	$0.473513\pi$
$132$		0			0
$133$	−3.72235	−	4.49411i	−0.322769	−	0.389689i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	2.51930	−	9.40216i	0.215238	−	0.803281i	−0.770844	−	0.637024i	$-0.780165\pi$
$137$	2.51930	−	9.40216i	0.215238	−	0.803281i	0.986082	−	0.166257i	$-0.0531681\pi$
$138$		0			0
$139$	9.22383			0.782355			0.391177	−	0.920315i	$-0.372068\pi$
$139$	9.22383			0.782355			0.391177	+	0.920315i	$0.372068\pi$
$140$		0			0
$141$	4.32538			0.364263
$142$		0			0
$143$	1.28258	−	4.78666i	0.107255	−	0.400281i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−5.78489	+	3.94146i	−0.477129	+	0.325086i
$148$		0			0
$149$	3.41665	+	1.97261i	0.279903	+	0.161602i	0.633380	−	0.773841i	$-0.281667\pi$
$149$	3.41665	+	1.97261i	0.279903	+	0.161602i	−0.353476	+	0.935443i	$0.615001\pi$
$150$		0			0
$151$	1.84246	+	3.19124i	0.149938	+	0.259700i	0.931204	−	0.364498i	$-0.118759\pi$
$151$	1.84246	+	3.19124i	0.149938	+	0.259700i	−0.781267	+	0.624198i	$0.785426\pi$
$152$		0			0
$153$	−2.34411	−	2.34411i	−0.189510	−	0.189510i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−7.37015	−	1.97483i	−0.588202	−	0.157608i	−0.0475707	−	0.998868i	$-0.515148\pi$
$157$	−7.37015	−	1.97483i	−0.588202	−	0.157608i	−0.540631	+	0.841260i	$0.681815\pi$
$158$		0			0
$159$	1.54028	−	2.66784i	0.122152	−	0.211574i
$160$		0			0
$161$	−18.6301	−	1.74991i	−1.46826	−	0.137912i
$162$		0			0
$163$	4.62412	+	17.2574i	0.362189	+	1.35171i	0.871192	+	0.490943i	$0.163348\pi$
$163$	4.62412	+	17.2574i	0.362189	+	1.35171i	−0.509003	+	0.860765i	$0.669986\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	14.5344	−	14.5344i	1.12471	−	1.12471i	0.133681	−	0.991024i	$-0.457320\pi$
$167$	14.5344	−	14.5344i	1.12471	−	1.12471i	0.991024	−	0.133681i	$-0.0426796\pi$
$168$		0			0
$169$		−	10.7654i		−	0.828110i
$170$		0			0
$171$	−1.91011	+	1.10280i	−0.146070	+	0.0843335i
$172$		0			0
$173$	0.608669	−	0.163092i	0.0462763	−	0.0123997i	−0.235607	−	0.971849i	$-0.575708\pi$
$173$	0.608669	−	0.163092i	0.0462763	−	0.0123997i	0.281883	+	0.959449i	$0.409041\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−1.28531	+	0.344399i	−0.0966101	+	0.0258866i
$178$		0			0
$179$	14.3843	−	8.30476i	1.07513	−	0.620727i	0.145552	−	0.989351i	$-0.453504\pi$
$179$	14.3843	−	8.30476i	1.07513	−	0.620727i	0.929579	+	0.368624i	$0.120171\pi$
$180$		0			0
$181$		−	15.6606i		−	1.16404i	−0.813173	−	0.582022i	$-0.802262\pi$
$181$		−	15.6606i		−	1.16404i	0.813173	−	0.582022i	$-0.197738\pi$
$182$		0			0
$183$	−3.77629	+	3.77629i	−0.279151	+	0.279151i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	2.84434	+	10.6152i	0.207999	+	0.776262i
$188$		0			0
$189$	1.10280	+	2.40496i	0.0802172	+	0.174935i
$190$		0			0
$191$	−8.47776	+	14.6839i	−0.613429	+	1.06249i	0.377229	+	0.926120i	$0.376877\pi$
$191$	−8.47776	+	14.6839i	−0.613429	+	1.06249i	−0.990658	+	0.136370i	$0.956456\pi$
$192$		0			0
$193$	−1.74273	−	0.466964i	−0.125445	−	0.0336128i	0.195550	−	0.980694i	$-0.437351\pi$
$193$	−1.74273	−	0.466964i	−0.125445	−	0.0336128i	−0.320995	+	0.947081i	$0.604017\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−6.11110	−	6.11110i	−0.435398	−	0.435398i	0.455062	−	0.890460i	$-0.349617\pi$
$197$	−6.11110	−	6.11110i	−0.435398	−	0.435398i	−0.890460	+	0.455062i	$0.849617\pi$
$198$		0			0
$199$	−9.40667	−	16.2928i	−0.666821	−	1.15497i	−0.978788	−	0.204875i	$-0.934321\pi$
$199$	−9.40667	−	16.2928i	−0.666821	−	1.15497i	0.311967	−	0.950093i	$-0.399012\pi$
$200$		0			0
$201$	1.91011	+	1.10280i	0.134729	+	0.0777858i
$202$		0			0
$203$		0			0
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−1.83050	+	6.83153i	−0.127229	+	0.474825i
$208$		0			0
$209$	7.31174			0.505764
$210$		0			0
$211$	4.69524			0.323233			0.161617	−	0.986854i	$-0.448329\pi$
$211$	4.69524			0.323233			0.161617	+	0.986854i	$0.448329\pi$
$212$		0			0
$213$	1.29143	−	4.81967i	0.0884871	−	0.330238i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−0.798865	−	4.70617i	−0.0542305	−	0.319476i
$218$		0			0
$219$	−9.19704	−	5.30992i	−0.621479	−	0.358811i
$220$		0			0
$221$	−2.47776	−	4.29161i	−0.166672	−	0.288685i
$222$		0			0
$223$	−7.56268	−	7.56268i	−0.506434	−	0.506434i	0.406996	−	0.913430i	$-0.366576\pi$
$223$	−7.56268	−	7.56268i	−0.506434	−	0.506434i	−0.913430	+	0.406996i	$0.866576\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	6.03701	+	1.61761i	0.400690	+	0.107365i	0.453536	−	0.891238i	$-0.350162\pi$
$227$	6.03701	+	1.61761i	0.400690	+	0.107365i	−0.0528454	+	0.998603i	$0.516829\pi$
$228$		0			0
$229$	−7.51000	+	13.0077i	−0.496275	+	0.859573i	−0.999991	−	0.00429607i	$-0.998633\pi$
$229$	−7.51000	+	13.0077i	−0.496275	+	0.859573i	0.503716	+	0.863869i	$0.331966\pi$
$230$		0			0
$231$	0.820225	−	8.73242i	0.0539668	−	0.574551i
$232$		0			0
$233$	4.17583	+	15.5844i	0.273568	+	1.02097i	0.956795	+	0.290763i	$0.0939092\pi$
$233$	4.17583	+	15.5844i	0.273568	+	1.02097i	−0.683227	+	0.730206i	$0.739424\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−11.2677	+	11.2677i	−0.731914	+	0.731914i
$238$		0			0
$239$			25.6404i			1.65854i	0.558846	+	0.829271i	$0.311244\pi$
$239$			25.6404i			1.65854i	−0.558846	+	0.829271i	$0.688756\pi$
$240$		0			0
$241$	−7.50000	+	4.33013i	−0.483117	+	0.278928i	−0.721715	−	0.692191i	$-0.756646\pi$
$241$	−7.50000	+	4.33013i	−0.483117	+	0.278928i	0.238597	+	0.971119i	$0.423312\pi$
$242$		0			0
$243$	0.965926	−	0.258819i	0.0619642	−	0.0166032i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−3.18470	+	0.853338i	−0.202638	+	0.0542966i
$248$		0			0
$249$	−12.3883	+	7.15238i	−0.785076	+	0.453264i
$250$		0			0
$251$		−	0.239219i		−	0.0150994i	−0.999972	−	0.00754969i	$-0.997597\pi$
$251$		−	0.239219i		−	0.0150994i	0.999972	−	0.00754969i	$-0.00240316\pi$
$252$		0			0
$253$	16.5788	−	16.5788i	1.04230	−	1.04230i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−2.31252	−	8.63045i	−0.144251	−	0.538353i	−0.999788	−	0.0206102i	$-0.993439\pi$
$257$	−2.31252	−	8.63045i	−0.144251	−	0.538353i	0.855536	−	0.517743i	$-0.173228\pi$
$258$		0			0
$259$	0.428549	−	4.56249i	0.0266287	−	0.283500i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	3.20666	+	0.859222i	0.197731	+	0.0529819i	0.356325	−	0.934362i	$-0.384029\pi$
$263$	3.20666	+	0.859222i	0.197731	+	0.0529819i	−0.158594	+	0.987344i	$0.550696\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−4.06012	−	4.06012i	−0.248475	−	0.248475i
$268$		0			0
$269$	12.4783	+	21.6131i	0.760816	+	1.31777i	0.942431	+	0.334402i	$0.108534\pi$
$269$	12.4783	+	21.6131i	0.760816	+	1.31777i	−0.181615	+	0.983370i	$0.558133\pi$
$270$		0			0
$271$	25.0702	+	14.4743i	1.52291	+	0.879250i	0.999633	+	0.0270851i	$0.00862250\pi$
$271$	25.0702	+	14.4743i	1.52291	+	0.879250i	0.523273	+	0.852165i	$0.324711\pi$
$272$		0			0
$273$	0.661884	+	3.89921i	0.0400591	+	0.235991i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−0.462343	+	1.72549i	−0.0277795	+	0.103675i	−0.978424	−	0.206609i	$-0.933757\pi$
$277$	−0.462343	+	1.72549i	−0.0277795	+	0.103675i	0.950644	+	0.310283i	$0.100424\pi$
$278$		0			0
$279$	−1.80421			−0.108015
$280$		0			0
$281$	2.05479			0.122578			0.0612892	−	0.998120i	$-0.480479\pi$
$281$	2.05479			0.122578			0.0612892	+	0.998120i	$0.480479\pi$
$282$		0			0
$283$	−6.13143	+	22.8828i	−0.364476	+	1.36024i	0.503654	+	0.863905i	$0.331989\pi$
$283$	−6.13143	+	22.8828i	−0.364476	+	1.36024i	−0.868130	+	0.496337i	$0.834678\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	3.30051	+	1.22522i	0.194823	+	0.0723223i
$288$		0			0
$289$	−5.20508	−	3.00515i	−0.306181	−	0.176774i
$290$		0			0
$291$	2.50000	+	4.33013i	0.146553	+	0.253837i
$292$		0			0
$293$	−18.1305	−	18.1305i	−1.05920	−	1.05920i	−0.998134	−	0.0610633i	$-0.980551\pi$
$293$	−18.1305	−	18.1305i	−1.05920	−	1.05920i	−0.0610633	−	0.998134i	$-0.519449\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−3.20211	−	0.858003i	−0.185805	−	0.0497864i
$298$		0			0
$299$	−5.28617	+	9.15591i	−0.305707	+	0.529500i
$300$		0			0
$301$	−10.6746	−	23.2789i	−0.615275	−	1.34177i
$302$		0			0
$303$	4.86463	+	18.1550i	0.279466	+	1.04298i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−18.6572	+	18.6572i	−1.06482	+	1.06482i	−0.0670748	+	0.997748i	$0.521367\pi$
$307$	−18.6572	+	18.6572i	−1.06482	+	1.06482i	−0.997748	+	0.0670748i	$0.978633\pi$
$308$		0			0
$309$			9.93490i			0.565177i
$310$		0			0
$311$	8.42975	−	4.86692i	0.478007	−	0.275978i	−0.241578	−	0.970381i	$-0.577665\pi$
$311$	8.42975	−	4.86692i	0.478007	−	0.275978i	0.719586	+	0.694404i	$0.244332\pi$
$312$		0			0
$313$	12.3106	−	3.29860i	0.695833	−	0.186448i	0.106470	−	0.994316i	$-0.466045\pi$
$313$	12.3106	−	3.29860i	0.695833	−	0.186448i	0.589364	+	0.807868i	$0.299379\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	18.5600	−	4.97314i	1.04243	−	0.279319i	0.303312	−	0.952891i	$-0.401907\pi$
$317$	18.5600	−	4.97314i	1.04243	−	0.279319i	0.739122	+	0.673572i	$0.235241\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$		−	18.7955i		−	1.04906i
$322$		0			0
$323$	5.17018	−	5.17018i	0.287677	−	0.287677i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	3.91197	+	14.5997i	0.216332	+	0.807363i
$328$		0			0
$329$	11.3937	+	1.07020i	0.628156	+	0.0590019i
$330$		0			0
$331$	0.462297	−	0.800723i	0.0254102	−	0.0440117i	−0.853041	−	0.521844i	$-0.825244\pi$
$331$	0.462297	−	0.800723i	0.0254102	−	0.0440117i	0.878451	+	0.477833i	$0.158577\pi$
$332$		0			0
$333$	−1.67303	−	0.448288i	−0.0916816	−	0.0245660i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−21.7455	−	21.7455i	−1.18455	−	1.18455i	−0.978552	−	0.206001i	$-0.933955\pi$
$337$	−21.7455	−	21.7455i	−1.18455	−	1.18455i	−0.206001	−	0.978552i	$-0.566045\pi$
$338$		0			0
$339$	−5.19615	−	9.00000i	−0.282216	−	0.488813i
$340$		0			0
$341$	5.17978	+	2.99054i	0.280501	+	0.161947i
$342$		0			0
$343$	−16.2135	+	8.95110i	−0.875447	+	0.483314i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−3.31661	+	12.3778i	−0.178045	+	0.664473i	0.817968	+	0.575264i	$0.195101\pi$
$347$	−3.31661	+	12.3778i	−0.178045	+	0.664473i	−0.996013	+	0.0892090i	$0.971566\pi$
$348$		0			0
$349$	19.0347			1.01890			0.509452	−	0.860499i	$-0.329848\pi$
$349$	19.0347			1.01890			0.509452	+	0.860499i	$0.329848\pi$
$350$		0			0
$351$	1.49485			0.0797890
$352$		0			0
$353$	−7.23275	+	26.9930i	−0.384961	+	1.43669i	0.453268	+	0.891374i	$0.350258\pi$
$353$	−7.23275	+	26.9930i	−0.384961	+	1.43669i	−0.838229	+	0.545318i	$0.816409\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−5.59476	−	6.75474i	−0.296106	−	0.357499i
$358$		0			0
$359$	5.98795	+	3.45714i	0.316032	+	0.182461i	0.649622	−	0.760257i	$-0.274927\pi$
$359$	5.98795	+	3.45714i	0.316032	+	0.182461i	−0.333591	+	0.942718i	$0.608260\pi$
$360$		0			0
$361$	7.06765	+	12.2415i	0.371981	+	0.644291i
$362$		0			0
$363$	−0.00728899	−	0.00728899i	−0.000382573	−	0.000382573i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−7.24942	−	1.94248i	−0.378417	−	0.101396i	0.0645966	−	0.997911i	$-0.479424\pi$
$367$	−7.24942	−	1.94248i	−0.378417	−	0.101396i	−0.443013	+	0.896515i	$0.646091\pi$
$368$		0			0
$369$	0.665328	−	1.15238i	0.0346356	−	0.0599906i
$370$		0			0
$371$	4.71742	−	6.64642i	0.244917	−	0.345065i
$372$		0			0
$373$	4.46420	+	16.6606i	0.231148	+	0.862654i	0.979848	+	0.199746i	$0.0640116\pi$
$373$	4.46420	+	16.6606i	0.231148	+	0.862654i	−0.748700	+	0.662909i	$0.769322\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$			31.4401i			1.61497i	0.589890	+	0.807484i	$0.299171\pi$
$379$			31.4401i			1.61497i	−0.589890	+	0.807484i	$0.700829\pi$
$380$		0			0
$381$	9.59759	−	5.54117i	0.491700	−	0.283883i
$382$		0			0
$383$	0.975883	−	0.261487i	0.0498653	−	0.0133614i	−0.233800	−	0.972285i	$-0.575116\pi$
$383$	0.975883	−	0.261487i	0.0498653	−	0.0133614i	0.283665	+	0.958923i	$0.408449\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−9.34971	+	2.50525i	−0.475272	+	0.127349i
$388$		0			0
$389$	27.8640	−	16.0873i	1.41276	−	0.815658i	0.417113	−	0.908855i	$-0.363042\pi$
$389$	27.8640	−	16.0873i	1.41276	−	0.815658i	0.995648	+	0.0931970i	$0.0297086\pi$
$390$		0			0
$391$		−	23.4459i		−	1.18571i
$392$		0			0
$393$	9.23030	−	9.23030i	0.465607	−	0.465607i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−3.82158	−	14.2623i	−0.191799	−	0.715805i	−0.993072	−	0.117506i	$-0.962510\pi$
$397$	−3.82158	−	14.2623i	−0.191799	−	0.715805i	0.801273	−	0.598299i	$-0.204157\pi$
$398$		0			0
$399$	−5.30439	+	2.43235i	−0.265552	+	0.121770i
$400$		0			0
$401$	−12.7722	+	22.1221i	−0.637814	+	1.10473i	0.348098	+	0.937458i	$0.386828\pi$
$401$	−12.7722	+	22.1221i	−0.637814	+	1.10473i	−0.985911	+	0.167268i	$0.946506\pi$
$402$		0			0
$403$	−2.60512	−	0.698040i	−0.129770	−	0.0347718i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	4.06012	+	4.06012i	0.201252	+	0.201252i
$408$		0			0
$409$	7.51000	+	13.0077i	0.371346	+	0.643190i	0.989773	−	0.142653i	$-0.0455631\pi$
$409$	7.51000	+	13.0077i	0.371346	+	0.643190i	−0.618427	+	0.785842i	$0.712230\pi$
$410$		0			0
$411$	−8.42975	−	4.86692i	−0.415809	−	0.240067i
$412$		0			0
$413$	−3.47093	+	0.589184i	−0.170793	+	0.0289919i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	2.38730	−	8.90953i	0.116907	−	0.436302i
$418$		0			0
$419$	40.0131			1.95477			0.977383	−	0.211477i	$-0.0678273\pi$
$419$	40.0131			1.95477			0.977383	+	0.211477i	$0.0678273\pi$
$420$		0			0
$421$	20.0103			0.975243			0.487621	−	0.873055i	$-0.337865\pi$
$421$	20.0103			0.975243			0.487621	+	0.873055i	$0.337865\pi$
$422$		0			0
$423$	1.11949	−	4.17799i	0.0544315	−	0.203141i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−10.8817	+	9.01299i	−0.526601	+	0.436169i
$428$		0			0
$429$	−4.29161	−	2.47776i	−0.207201	−	0.119627i
$430$		0			0
$431$	19.7654	+	34.2347i	0.952068	+	1.64903i	0.740940	+	0.671571i	$0.234380\pi$
$431$	19.7654	+	34.2347i	0.952068	+	1.64903i	0.211127	+	0.977459i	$0.432287\pi$
$432$		0			0
$433$	17.6886	+	17.6886i	0.850058	+	0.850058i	0.990140	−	0.140082i	$-0.0447365\pi$
$433$	17.6886	+	17.6886i	0.850058	+	0.850058i	−0.140082	+	0.990140i	$0.544737\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−15.0677	−	4.03737i	−0.720785	−	0.193134i
$438$		0			0
$439$	0.674255	−	1.16784i	0.0321804	−	0.0557381i	−0.849487	−	0.527610i	$-0.823088\pi$
$439$	0.674255	−	1.16784i	0.0321804	−	0.0557381i	0.881667	+	0.471872i	$0.156422\pi$
$440$		0			0
$441$	2.30992	+	6.60790i	0.109996	+	0.314662i
$442$		0			0
$443$	6.35073	+	23.7013i	0.301733	+	1.12608i	0.935722	+	0.352739i	$0.114750\pi$
$443$	6.35073	+	23.7013i	0.301733	+	1.12608i	−0.633989	+	0.773342i	$0.718584\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	2.78969	−	2.78969i	0.131948	−	0.131948i
$448$		0			0
$449$			16.9555i			0.800180i	0.916476	+	0.400090i	$0.131021\pi$
$449$			16.9555i			0.800180i	−0.916476	+	0.400090i	$0.868979\pi$
$450$		0			0
$451$	−3.82022	+	2.20561i	−0.179887	+	0.103858i
$452$		0			0
$453$	3.55937	−	0.953730i	0.167234	−	0.0448101i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−5.76004	+	1.54340i	−0.269443	+	0.0721972i	−0.391011	−	0.920386i	$-0.627875\pi$
$457$	−5.76004	+	1.54340i	−0.269443	+	0.0721972i	0.121568	+	0.992583i	$0.461208\pi$
$458$		0			0
$459$	−2.87094	+	1.65754i	−0.134004	+	0.0773671i
$460$		0			0
$461$		−	16.5534i		−	0.770970i	−0.922714	−	0.385485i	$-0.874034\pi$
$461$		−	16.5534i		−	0.770970i	0.922714	−	0.385485i	$-0.125966\pi$
$462$		0			0
$463$	−9.82028	+	9.82028i	−0.456387	+	0.456387i	−0.897468	−	0.441080i	$-0.854595\pi$
$463$	−9.82028	+	9.82028i	−0.456387	+	0.456387i	0.441080	+	0.897468i	$0.354595\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	1.87910	+	7.01289i	0.0869543	+	0.324518i	0.995677	−	0.0928822i	$-0.0296080\pi$
$467$	1.87910	+	7.01289i	0.0869543	+	0.324518i	−0.908723	+	0.417400i	$0.862941\pi$
$468$		0			0
$469$	4.75868	+	3.37756i	0.219735	+	0.155961i
$470$		0			0
$471$	−3.81507	+	6.60790i	−0.175789	+	0.304476i
$472$		0			0
$473$	30.9949	+	8.30507i	1.42515	+	0.381867i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−2.17829	−	2.17829i	−0.0997368	−	0.0997368i
$478$		0			0
$479$	17.8009	+	30.8321i	0.813345	+	1.40875i	0.910510	+	0.413487i	$0.135689\pi$
$479$	17.8009	+	30.8321i	0.813345	+	1.40875i	−0.0971653	+	0.995268i	$0.530978\pi$
$480$		0			0
$481$	−2.24227	−	1.29457i	−0.102239	−	0.0590275i
$482$		0			0
$483$	−6.51211	+	17.5424i	−0.296311	+	0.798208i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	4.29840	−	16.0418i	0.194779	−	0.726925i	−0.797545	−	0.603259i	$-0.793868\pi$
$487$	4.29840	−	16.0418i	0.194779	−	0.726925i	0.992324	−	0.123666i	$-0.0394650\pi$
$488$		0			0
$489$	17.8662			0.807939
$490$		0			0
$491$	42.8801			1.93515			0.967576	−	0.252579i	$-0.0812788\pi$
$491$	42.8801			1.93515			0.967576	+	0.252579i	$0.0812788\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$	4.59432	−	12.3762i	0.206083	−	0.555150i
$498$		0			0
$499$	17.9270	+	10.3502i	0.802524	+	0.463337i	0.844353	−	0.535788i	$-0.179985\pi$
$499$	17.9270	+	10.3502i	0.802524	+	0.463337i	−0.0418292	+	0.999125i	$0.513319\pi$
$500$		0			0
$501$	−10.2774	−	17.8009i	−0.459159	−	0.795287i
$502$		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
$507$	−10.3986	−	2.78630i	−0.461819	−	0.123744i
$508$		0			0
$509$	−0.329235	+	0.570251i	−0.0145931	+	0.0252759i	−0.873230	−	0.487309i	$-0.837979\pi$
$509$	−0.329235	+	0.570251i	−0.0145931	+	0.0252759i	0.858637	+	0.512585i	$0.171312\pi$
$510$		0			0
$511$	−22.9127	−	16.2627i	−1.01360	−	0.719420i
$512$		0			0
$513$	0.570853	+	2.13045i	0.0252038	+	0.0940618i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−10.1392	+	10.1392i	−0.445920	+	0.445920i
$518$		0			0
$519$		−	0.630141i		−	0.0276601i
$520$		0			0
$521$	−21.2500	+	12.2687i	−0.930978	+	0.537501i	−0.887121	−	0.461537i	$-0.847298\pi$
$521$	−21.2500	+	12.2687i	−0.930978	+	0.537501i	−0.0438574	+	0.999038i	$0.513965\pi$
$522$		0			0
$523$	19.4094	−	5.20073i	0.848713	−	0.227412i	0.191852	−	0.981424i	$-0.438551\pi$
$523$	19.4094	−	5.20073i	0.848713	−	0.227412i	0.656861	+	0.754012i	$0.271884\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	5.77729	−	1.54802i	0.251663	−	0.0674328i
$528$		0			0
$529$	−23.4005	+	13.5103i	−1.01741	+	0.587405i
$530$		0			0
$531$			1.33066i			0.0577455i
$532$		0			0
$533$	1.40652	−	1.40652i	0.0609233	−	0.0609233i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−4.29886	−	16.0436i	−0.185510	−	0.692331i
$538$		0			0
$539$	4.32120	−	22.7996i	0.186127	−	0.982049i
$540$		0			0
$541$	−4.94781	+	8.56987i	−0.212723	+	0.368447i	−0.952566	−	0.304333i	$-0.901567\pi$
$541$	−4.94781	+	8.56987i	−0.212723	+	0.368447i	0.739843	+	0.672780i	$0.234900\pi$
$542$		0			0
$543$	−15.1270	−	4.05327i	−0.649162	−	0.173942i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	7.99293	+	7.99293i	0.341753	+	0.341753i	0.857026	−	0.515273i	$-0.172309\pi$
$547$	7.99293	+	7.99293i	0.341753	+	0.341753i	−0.515273	+	0.857026i	$0.672309\pi$
$548$		0			0
$549$	2.67024	+	4.62499i	0.113963	+	0.197390i
$550$		0			0
$551$		0			0
$552$		0			0
$553$	−32.4687	+	26.8929i	−1.38071	+	1.14360i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−0.170424	+	0.636032i	−0.00722111	+	0.0269496i	−0.969442	−	0.245319i	$-0.921107\pi$
$557$	−0.170424	+	0.636032i	−0.00722111	+	0.0269496i	0.962221	+	0.272269i	$0.0877739\pi$
$558$		0			0
$559$	−14.4694			−0.611991
$560$		0			0
$561$	10.9897			0.463985
$562$		0			0
$563$	−9.30864	+	34.7403i	−0.392312	+	1.46413i	0.433997	+	0.900914i	$0.357103\pi$
$563$	−9.30864	+	34.7403i	−0.392312	+	1.46413i	−0.826310	+	0.563216i	$0.809564\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	2.60844	−	0.442778i	0.109544	−	0.0185949i
$568$		0			0
$569$	−16.7095	−	9.64723i	−0.700498	−	0.404433i	0.107035	−	0.994255i	$-0.465864\pi$
$569$	−16.7095	−	9.64723i	−0.700498	−	0.404433i	−0.807533	+	0.589822i	$0.799198\pi$
$570$		0			0
$571$	−6.35017	−	10.9988i	−0.265746	−	0.460286i	0.702013	−	0.712165i	$-0.252285\pi$
$571$	−6.35017	−	10.9988i	−0.265746	−	0.460286i	−0.967759	+	0.251878i	$0.918952\pi$
$572$		0			0
$573$	11.9894	+	11.9894i	0.500863	+	0.500863i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	1.21241	+	0.324865i	0.0504733	+	0.0135243i	0.283967	−	0.958834i	$-0.408349\pi$
$577$	1.21241	+	0.324865i	0.0504733	+	0.0135243i	−0.233494	+	0.972358i	$0.575016\pi$
$578$		0			0
$579$	−0.902106	+	1.56249i	−0.0374902	+	0.0649350i
$580$		0			0
$581$	−34.4024	+	15.7753i	−1.42725	+	0.654472i
$582$		0			0
$583$	2.64313	+	9.86430i	0.109467	+	0.408538i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−3.70500	+	3.70500i	−0.152922	+	0.152922i	−0.779422	−	0.626500i	$-0.784487\pi$
$587$	−3.70500	+	3.70500i	−0.152922	+	0.152922i	0.626500	+	0.779422i	$0.284487\pi$
$588$		0			0
$589$		−	3.97938i		−	0.163968i
$590$		0			0
$591$	−7.48454	+	4.32120i	−0.307873	+	0.177750i
$592$		0			0
$593$	−44.5881	+	11.9473i	−1.83101	+	0.490619i	−0.998033	−	0.0626829i	$-0.980034\pi$
$593$	−44.5881	+	11.9473i	−1.83101	+	0.490619i	−0.832981	+	0.553302i	$0.813368\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−18.1723	+	4.86925i	−0.743742	+	0.199285i
$598$		0			0
$599$	−8.50005	+	4.90751i	−0.347303	+	0.200515i	−0.663497	−	0.748179i	$-0.730928\pi$
$599$	−8.50005	+	4.90751i	−0.347303	+	0.200515i	0.316194	+	0.948695i	$0.397595\pi$
$600$		0			0
$601$		−	26.0708i		−	1.06345i	−0.846917	−	0.531725i	$-0.821544\pi$
$601$		−	26.0708i		−	1.06345i	0.846917	−	0.531725i	$-0.178456\pi$
$602$		0			0
$603$	1.55960	−	1.55960i	0.0635118	−	0.0635118i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	5.58411	+	20.8402i	0.226652	+	0.845877i	0.981736	+	0.190249i	$0.0609295\pi$
$607$	5.58411	+	20.8402i	0.226652	+	0.845877i	−0.755084	+	0.655628i	$0.772404\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	3.23289	−	5.59952i	0.130789	−	0.226533i
$612$		0			0
$613$	29.0164	+	7.77493i	1.17196	+	0.314026i	0.791734	−	0.610866i	$-0.209179\pi$
$613$	29.0164	+	7.77493i	1.17196	+	0.314026i	0.380228	+	0.924893i	$0.375845\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−2.34744	−	2.34744i	−0.0945043	−	0.0945043i	0.658274	−	0.752778i	$-0.271287\pi$
$617$	−2.34744	−	2.34744i	−0.0945043	−	0.0945043i	−0.752778	+	0.658274i	$0.771287\pi$
$618$		0			0
$619$	−16.9463	−	29.3518i	−0.681128	−	1.17975i	−0.974637	−	0.223792i	$-0.928156\pi$
$619$	−16.9463	−	29.3518i	−0.681128	−	1.17975i	0.293509	−	0.955956i	$-0.405177\pi$
$620$		0			0
$621$	6.12499	+	3.53626i	0.245787	+	0.141905i
$622$		0			0
$623$	−9.69041	−	11.6995i	−0.388238	−	0.468732i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	1.89242	−	7.06260i	0.0755759	−	0.282053i
$628$		0			0
$629$	5.74187			0.228943
$630$		0			0
$631$	35.5341			1.41459			0.707295	−	0.706918i	$-0.249915\pi$
$631$	35.5341			1.41459			0.707295	+	0.706918i	$0.249915\pi$
$632$		0			0
$633$	1.21522	−	4.53525i	0.0483005	−	0.180260i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	0.778753	+	10.4349i	0.0308553	+	0.413446i
$638$		0			0
$639$	−4.32120	−	2.49485i	−0.170944	−	0.0986946i
$640$		0			0
$641$	−1.83053	−	3.17058i	−0.0723017	−	0.125230i	0.827608	−	0.561307i	$-0.189701\pi$
$641$	−1.83053	−	3.17058i	−0.0723017	−	0.125230i	−0.899910	+	0.436076i	$0.856368\pi$
$642$		0			0
$643$	−22.3417	−	22.3417i	−0.881072	−	0.881072i	0.112572	−	0.993644i	$-0.464091\pi$
$643$	−22.3417	−	22.3417i	−0.881072	−	0.881072i	−0.993644	+	0.112572i	$0.964091\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−27.6017	−	7.39585i	−1.08513	−	0.290761i	−0.328436	−	0.944526i	$-0.606522\pi$
$647$	−27.6017	−	7.39585i	−1.08513	−	0.290761i	−0.756697	+	0.653765i	$0.773188\pi$
$648$		0			0
$649$	2.20561	−	3.82022i	0.0865777	−	0.149957i
$650$		0			0
$651$	−4.75258	−	0.446403i	−0.186268	−	0.0174959i
$652$		0			0
$653$	3.44044	+	12.8399i	0.134635	+	0.502464i	0.999999	+	0.00132058i	$0.000420353\pi$
$653$	3.44044	+	12.8399i	0.134635	+	0.502464i	−0.865364	+	0.501143i	$0.832913\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−7.50936	+	7.50936i	−0.292968	+	0.292968i
$658$		0			0
$659$			33.9452i			1.32232i	0.750246	+	0.661159i	$0.229935\pi$
$659$			33.9452i			1.32232i	−0.750246	+	0.661159i	$0.770065\pi$
$660$		0			0
$661$	−19.5941	+	11.3126i	−0.762121	+	0.440011i	−0.830057	−	0.557679i	$-0.811692\pi$
$661$	−19.5941	+	11.3126i	−0.762121	+	0.440011i	0.0679359	+	0.997690i	$0.478359\pi$
$662$		0			0
$663$	−4.78666	+	1.28258i	−0.185899	+	0.0498114i
$664$		0			0
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$	−9.26235	+	5.34762i	−0.358103	+	0.206751i
$670$		0			0
$671$		−	17.7040i		−	0.683457i
$672$		0			0
$673$	12.8025	−	12.8025i	0.493499	−	0.493499i	−0.415907	−	0.909407i	$-0.636536\pi$
$673$	12.8025	−	12.8025i	0.493499	−	0.493499i	0.909407	+	0.415907i	$0.136536\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−5.08332	−	18.9712i	−0.195368	−	0.729123i	−0.992171	−	0.124884i	$-0.960144\pi$
$677$	−5.08332	−	18.9712i	−0.195368	−	0.729123i	0.796803	−	0.604239i	$-0.206523\pi$
$678$		0			0
$679$	5.51402	+	12.0248i	0.211609	+	0.461469i
$680$		0			0
$681$	3.12499	−	5.41264i	0.119750	−	0.207413i
$682$		0			0
$683$	48.2696	+	12.9338i	1.84699	+	0.494898i	0.999363	−	0.0356996i	$-0.0113660\pi$
$683$	48.2696	+	12.9338i	1.84699	+	0.494898i	0.847624	+	0.530598i	$0.178033\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	10.6207	+	10.6207i	0.405207	+	0.405207i
$688$		0			0
$689$	−2.30248	−	3.98801i	−0.0877176	−	0.151931i
$690$		0			0
$691$	−14.7774	−	8.53172i	−0.562158	−	0.324562i	0.191853	−	0.981424i	$-0.438550\pi$
$691$	−14.7774	−	8.53172i	−0.562158	−	0.324562i	−0.754011	+	0.656862i	$0.771884\pi$
$692$		0			0
$693$	−8.22258	−	3.05239i	−0.312350	−	0.115951i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−1.14171	+	4.26091i	−0.0432452	+	0.161393i
$698$		0			0
$699$	16.1342			0.610251
$700$		0			0
$701$	−2.55474			−0.0964910			−0.0482455	−	0.998836i	$-0.515363\pi$
$701$	−2.55474			−0.0964910			−0.0482455	+	0.998836i	$0.515363\pi$
$702$		0			0
$703$	0.988747	−	3.69005i	0.0372913	−	0.139173i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	8.32222	+	49.0269i	0.312989	+	1.84384i
$708$		0			0
$709$	−1.19526	−	0.690084i	−0.0448889	−	0.0259166i	0.477388	−	0.878693i	$-0.341584\pi$
$709$	−1.19526	−	0.690084i	−0.0448889	−	0.0259166i	−0.522277	+	0.852776i	$0.674917\pi$
$710$		0			0
$711$	7.96745	+	13.8000i	0.298803	+	0.517542i
$712$		0			0
$713$	−9.02292	−	9.02292i	−0.337911	−	0.337911i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	24.7668	+	6.63624i	0.924932	+	0.247835i
$718$		0			0
$719$	−5.86148	+	10.1524i	−0.218596	+	0.378620i	−0.954379	−	0.298598i	$-0.903481\pi$
$719$	−5.86148	+	10.1524i	−0.218596	+	0.378620i	0.735783	+	0.677218i	$0.236814\pi$
$720$		0			0
$721$	−2.45812	+	26.1701i	−0.0915453	+	0.974625i
$722$		0			0
$723$	2.24144	+	8.36516i	0.0833600	+	0.311104i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−2.00149	+	2.00149i	−0.0742311	+	0.0742311i	−0.743248	−	0.669016i	$-0.766716\pi$
$727$	−2.00149	+	2.00149i	−0.0742311	+	0.0742311i	0.669016	+	0.743248i	$0.266716\pi$
$728$		0			0
$729$		−	1.00000i		−	0.0370370i
$730$		0			0
$731$	27.7893	−	16.0442i	1.02782	−	0.593415i
$732$		0			0
$733$	−9.52354	+	2.55183i	−0.351760	+	0.0942538i	−0.430372	−	0.902651i	$-0.641618\pi$
$733$	−9.52354	+	2.55183i	−0.351760	+	0.0942538i	0.0786123	+	0.996905i	$0.474951\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−7.06260	+	1.89242i	−0.260154	+	0.0697081i
$738$		0			0
$739$	7.74678	−	4.47261i	0.284970	−	0.164527i	−0.350701	−	0.936487i	$-0.614057\pi$
$739$	7.74678	−	4.47261i	0.284970	−	0.164527i	0.635671	+	0.771960i	$0.280723\pi$
$740$		0			0
$741$			3.29704i			0.121120i
$742$		0			0
$743$	7.47577	−	7.47577i	0.274259	−	0.274259i	−0.556553	−	0.830812i	$-0.687876\pi$
$743$	7.47577	−	7.47577i	0.274259	−	0.274259i	0.830812	+	0.556553i	$0.187876\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	3.70234	+	13.8173i	0.135462	+	0.505550i
$748$		0			0
$749$	4.65043	−	49.5103i	0.169923	−	1.80907i
$750$		0			0
$751$	−14.4520	+	25.0316i	−0.527361	+	0.913415i	0.472131	+	0.881528i	$0.343485\pi$
$751$	−14.4520	+	25.0316i	−0.527361	+	0.913415i	−0.999491	+	0.0318869i	$0.989848\pi$
$752$		0			0
$753$	−0.231068	−	0.0619145i	−0.00842059	−	0.00225629i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−21.6945	−	21.6945i	−0.788499	−	0.788499i	0.192749	−	0.981248i	$-0.438260\pi$
$757$	−21.6945	−	21.6945i	−0.788499	−	0.788499i	−0.981248	+	0.192749i	$0.938260\pi$
$758$		0			0
$759$	−11.7230	−	20.3048i	−0.425516	−	0.737016i
$760$		0			0
$761$	−32.3476	−	18.6759i	−1.17260	−	0.677000i	−0.218308	−	0.975880i	$-0.570054\pi$
$761$	−32.3476	−	18.6759i	−1.17260	−	0.677000i	−0.954291	+	0.298880i	$0.903387\pi$
$762$		0			0
$763$	6.69244	+	39.4257i	0.242283	+	1.42731i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−0.514823	+	1.92135i	−0.0185892	+	0.0693758i
$768$		0			0
$769$	26.0886			0.940780			0.470390	−	0.882459i	$-0.344113\pi$
$769$	26.0886			0.940780			0.470390	+	0.882459i	$0.344113\pi$
$770$		0			0
$771$	−8.93490			−0.321783
$772$		0			0
$773$	−6.21166	+	23.1822i	−0.223418	+	0.833806i	0.759614	+	0.650374i	$0.225388\pi$
$773$	−6.21166	+	23.1822i	−0.223418	+	0.833806i	−0.983032	+	0.183433i	$0.941279\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−4.29611	−	1.59481i	−0.154122	−	0.0572134i
$778$		0			0
$779$	2.54170	+	1.46745i	0.0910659	+	0.0525769i
$780$		0			0
$781$	8.27059	+	14.3251i	0.295945	+	0.512592i
$782$		0			0
$783$		0			0
$784$		0			0
$785$		0			0
$786$		0			0
$787$	38.8156	+	10.4006i	1.38363	+	0.370742i	0.872437	−	0.488726i	$-0.162538\pi$
$787$	38.8156	+	10.4006i	1.38363	+	0.370742i	0.511190	+	0.859468i	$0.329205\pi$
$788$		0			0
$789$	1.65989	−	2.87501i	0.0590936	−	0.102353i
$790$		0			0
$791$	−11.4607	−	24.9931i	−0.407495	−	0.888651i
$792$		0			0
$793$	2.06620	+	7.71117i	0.0733729	+	0.273832i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	13.3503	−	13.3503i	0.472890	−	0.472890i	−0.429958	−	0.902849i	$-0.641472\pi$
$797$	13.3503	−	13.3503i	0.472890	−	0.472890i	0.902849	+	0.429958i	$0.141472\pi$
$798$		0			0
$799$			14.3389i			0.507275i
$800$		0			0
$801$	−4.97261	+	2.87094i	−0.175698	+	0.101440i
$802$		0			0
$803$	34.0059	−	9.11185i	1.20004	−	0.321550i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	24.1062	−	6.45924i	0.848579	−	0.227376i
$808$		0			0
$809$	−24.9931	+	14.4297i	−0.878709	+	0.507323i	−0.870233	−	0.492641i	$-0.836032\pi$
$809$	−24.9931	+	14.4297i	−0.878709	+	0.507323i	−0.00847656	+	0.999964i	$0.502698\pi$
$810$		0			0
$811$			7.76257i			0.272581i	0.990669	+	0.136290i	$0.0435180\pi$
$811$			7.76257i			0.272581i	−0.990669	+	0.136290i	$0.956482\pi$
$812$		0			0
$813$	20.4697	−	20.4697i	0.717905	−	0.717905i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−5.52559	−	20.6218i	−0.193316	−	0.721465i
$818$		0			0
$819$	3.93766	+	0.369859i	0.137593	+	0.0129239i
$820$		0			0
$821$	−10.6575	+	18.4594i	−0.371951	+	0.644237i	−0.989866	−	0.142008i	$-0.954644\pi$
$821$	−10.6575	+	18.4594i	−0.371951	+	0.644237i	0.617915	+	0.786245i	$0.287978\pi$
$822$		0			0
$823$	−30.7466	−	8.23853i	−1.07176	−	0.287177i	−0.320544	−	0.947234i	$-0.603866\pi$
$823$	−30.7466	−	8.23853i	−1.07176	−	0.287177i	−0.751216	+	0.660056i	$0.770532\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−2.00913	−	2.00913i	−0.0698643	−	0.0698643i	0.671311	−	0.741176i	$-0.265731\pi$
$827$	−2.00913	−	2.00913i	−0.0698643	−	0.0698643i	−0.741176	+	0.671311i	$0.765731\pi$
$828$		0			0
$829$	0.374614	+	0.648851i	0.0130109	+	0.0225355i	0.872458	−	0.488690i	$-0.162525\pi$
$829$	0.374614	+	0.648851i	0.0130109	+	0.0225355i	−0.859447	+	0.511225i	$0.829192\pi$
$830$		0			0
$831$	1.54703	+	0.893179i	0.0536659	+	0.0309840i
$832$		0			0
$833$	−13.0662	−	19.1773i	−0.452717	−	0.664454i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−0.466964	+	1.74273i	−0.0161407	+	0.0602377i
$838$		0			0
$839$	−50.6446			−1.74845			−0.874223	−	0.485525i	$-0.838628\pi$
$839$	−50.6446			−1.74845			−0.874223	+	0.485525i	$0.838628\pi$
$840$		0			0
$841$	29.0000			1.00000
$842$		0			0
$843$	0.531818	−	1.98477i	0.0183168	−	0.0683592i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−0.0173969	−	0.0210038i	−0.000597764	−	0.000721700i
$848$		0			0
$849$	20.5162	+	11.8450i	0.704113	+	0.406520i
$850$		0			0
$851$	−6.12499	−	10.6088i	−0.209962	−	0.363665i
$852$		0			0
$853$	−33.4071	−	33.4071i	−1.14384	−	1.14384i	−0.987742	−	0.156095i	$-0.950109\pi$
$853$	−33.4071	−	33.4071i	−1.14384	−	1.14384i	−0.156095	−	0.987742i	$-0.549891\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	22.6892	+	6.07957i	0.775050	+	0.207674i	0.624601	−	0.780944i	$-0.285262\pi$
$857$	22.6892	+	6.07957i	0.775050	+	0.207674i	0.150449	+	0.988618i	$0.451928\pi$
$858$		0			0
$859$	20.6719	−	35.8047i	0.705315	−	1.22164i	−0.261263	−	0.965268i	$-0.584139\pi$
$859$	20.6719	−	35.8047i	0.705315	−	1.22164i	0.966578	−	0.256373i	$-0.0825276\pi$
$860$		0			0
$861$	2.03770	−	2.87094i	0.0694447	−	0.0978412i
$862$		0			0
$863$	−10.0737	−	37.5954i	−0.342911	−	1.27976i	−0.895033	−	0.445999i	$-0.852848\pi$
$863$	−10.0737	−	37.5954i	−0.342911	−	1.27976i	0.552122	−	0.833763i	$-0.313818\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−4.24993	+	4.24993i	−0.144335	+	0.144335i
$868$		0			0
$869$		−	52.8253i		−	1.79198i
$870$		0			0
$871$	2.85532	−	1.64852i	0.0967489	−	0.0558580i
$872$		0			0
$873$	4.82963	−	1.29410i	0.163458	−	0.0437985i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−5.05359	+	1.35411i	−0.170648	+	0.0457249i	−0.343131	−	0.939288i	$-0.611488\pi$
$877$	−5.05359	+	1.35411i	−0.170648	+	0.0457249i	0.172484	+	0.985012i	$0.444821\pi$
$878$		0			0
$879$	−22.2053	+	12.8202i	−0.748966	+	0.432415i
$880$		0			0
$881$		−	3.31978i		−	0.111846i	−0.998435	−	0.0559231i	$-0.982190\pi$
$881$		−	3.31978i		−	0.111846i	0.998435	−	0.0559231i	$-0.0178102\pi$
$882$		0			0
$883$	17.5455	−	17.5455i	0.590452	−	0.590452i	−0.347302	−	0.937753i	$-0.612902\pi$
$883$	17.5455	−	17.5455i	0.590452	−	0.590452i	0.937753	+	0.347302i	$0.112902\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−14.9548	−	55.8120i	−0.502132	−	1.87398i	−0.485712	−	0.874119i	$-0.661440\pi$
$887$	−14.9548	−	55.8120i	−0.502132	−	1.87398i	−0.0164202	−	0.999865i	$-0.505227\pi$
$888$		0			0
$889$	26.6526	−	12.2217i	0.893899	−	0.409901i
$890$		0			0
$891$	−1.65754	+	2.87094i	−0.0555295	+	0.0961799i
$892$		0			0
$893$	9.21502	+	2.46916i	0.308369	+	0.0826272i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	7.47577	+	7.47577i	0.249609	+	0.249609i
$898$		0			0
$899$		0			0
$900$		0			0
$901$	8.84409	+	5.10614i	0.294639	+	0.170110i
$902$		0			0
$903$	−25.2484	+	4.28588i	−0.840216	+	0.142625i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	7.27649	−	27.1562i	0.241612	−	0.901708i	−0.733444	−	0.679750i	$-0.762088\pi$
$907$	7.27649	−	27.1562i	0.241612	−	0.901708i	0.975056	−	0.221958i	$-0.0712449\pi$
$908$		0			0
$909$	18.7955			0.623407
$910$		0			0
$911$	15.0309			0.497997			0.248998	−	0.968504i	$-0.419899\pi$
$911$	15.0309			0.497997			0.248998	+	0.968504i	$0.419899\pi$
$912$		0			0
$913$	12.2735	−	45.8055i	0.406195	−	1.51594i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	26.5978	−	22.0303i	0.878338	−	0.727504i
$918$		0			0
$919$	−26.8423	−	15.4974i	−0.885445	−	0.511212i	−0.0129952	−	0.999916i	$-0.504137\pi$
$919$	−26.8423	−	15.4974i	−0.885445	−	0.511212i	−0.872450	+	0.488704i	$0.837470\pi$
$920$		0			0
$921$	13.1926	+	22.8503i	0.434712	+	0.752943i
$922$		0			0
$923$	−5.27418	−	5.27418i	−0.173602	−	0.173602i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	9.59638	+	2.57134i	0.315186	+	0.0844540i
$928$		0			0
$929$	−23.4528	+	40.6214i	−0.769461	+	1.33275i	0.168395	+	0.985720i	$0.446142\pi$
$929$	−23.4528	+	40.6214i	−0.769461	+	1.33275i	−0.937856	+	0.347025i	$0.887192\pi$
$930$		0			0
$931$	−14.5744	+	5.09477i	−0.477658	+	0.166974i
$932$		0			0
$933$	−2.51930	−	9.40216i	−0.0824782	−	0.307813i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	30.1331	−	30.1331i	0.984405	−	0.984405i	−0.0154751	−	0.999880i	$-0.504926\pi$
$937$	30.1331	−	30.1331i	0.984405	−	0.984405i	0.999880	+	0.0154751i	$0.00492607\pi$
$938$		0			0
$939$		−	12.7448i		−	0.415911i
$940$		0			0
$941$	13.1952	−	7.61824i	0.430151	−	0.248348i	−0.269260	−	0.963067i	$-0.586779\pi$
$941$	13.1952	−	7.61824i	0.430151	−	0.248348i	0.699411	+	0.714720i	$0.253446\pi$
$942$		0			0
$943$	9.09042	−	2.43577i	0.296025	−	0.0793196i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−29.6525	+	7.94535i	−0.963575	+	0.258189i	−0.706113	−	0.708099i	$-0.749553\pi$
$947$	−29.6525	+	7.94535i	−0.963575	+	0.258189i	−0.257462	+	0.966288i	$0.582886\pi$
$948$		0			0
$949$	−13.7482	+	7.93751i	−0.446284	+	0.257662i
$950$		0			0
$951$		−	19.2147i		−	0.623080i
$952$		0			0
$953$	25.7672	−	25.7672i	0.834682	−	0.834682i	−0.153471	−	0.988153i	$-0.549045\pi$
$953$	25.7672	−	25.7672i	0.834682	−	0.834682i	0.988153	+	0.153471i	$0.0490452\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−21.0011	−	14.9059i	−0.678161	−	0.481338i
$960$		0			0
$961$	−13.8724	+	24.0277i	−0.447497	+	0.775088i
$962$		0			0
$963$	−18.1550	−	4.86463i	−0.585038	−	0.156760i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−1.47070	−	1.47070i	−0.0472945	−	0.0472945i	0.683064	−	0.730359i	$-0.260647\pi$
$967$	−1.47070	−	1.47070i	−0.0472945	−	0.0472945i	−0.730359	+	0.683064i	$0.760647\pi$
$968$		0			0
$969$	−3.65587	−	6.33216i	−0.117444	−	0.203418i
$970$		0			0
$971$	19.6833	+	11.3641i	0.631666	+	0.364692i	0.781397	−	0.624034i	$-0.214508\pi$
$971$	19.6833	+	11.3641i	0.631666	+	0.364692i	−0.149731	+	0.988727i	$0.547841\pi$
$972$		0			0
$973$	8.49295	−	22.8784i	0.272271	−	0.733449i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−14.5939	+	54.4651i	−0.466900	+	1.74249i	0.183613	+	0.982999i	$0.441221\pi$
$977$	−14.5939	+	54.4651i	−0.466900	+	1.74249i	−0.650513	+	0.759495i	$0.725446\pi$
$978$		0			0
$979$	19.0347			0.608352
$980$		0			0
$981$	15.1147			0.482575
$982$		0			0
$983$	5.54775	−	20.7045i	0.176946	−	0.660370i	−0.819266	−	0.573413i	$-0.805619\pi$
$983$	5.54775	−	20.7045i	0.176946	−	0.660370i	0.996212	−	0.0869571i	$-0.0277143\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	3.98264	−	10.7285i	0.126769	−	0.341492i
$988$		0			0
$989$	−59.2870	−	34.2294i	−1.88522	−	1.08843i
$990$		0			0
$991$	28.9922	+	50.2160i	0.920969	+	1.59516i	0.797919	+	0.602764i	$0.205934\pi$
$991$	28.9922	+	50.2160i	0.920969	+	1.59516i	0.123050	+	0.992401i	$0.460733\pi$
$992$		0			0
$993$	−0.653787	−	0.653787i	−0.0207473	−	0.0207473i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	40.2116	+	10.7747i	1.27352	+	0.341237i	0.831377	−	0.555709i	$-0.187553\pi$
$997$	40.2116	+	10.7747i	1.27352	+	0.341237i	0.442138	+	0.896947i	$0.354220\pi$
$998$		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.1657.6	yes	24
5.2	odd	4	inner	2100.2.ce.c.1993.2	yes	24
5.3	odd	4	inner	2100.2.ce.c.1993.5	yes	24
5.4	even	2	inner	2100.2.ce.c.1657.1	yes	24
7.3	odd	6	inner	2100.2.ce.c.157.5	yes	24
35.3	even	12	inner	2100.2.ce.c.493.6	yes	24
35.17	even	12	inner	2100.2.ce.c.493.1	yes	24
35.24	odd	6	inner	2100.2.ce.c.157.2	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2100.2.ce.c.157.2	✓	24	35.24	odd	6	inner
2100.2.ce.c.157.5	yes	24	7.3	odd	6	inner
2100.2.ce.c.493.1	yes	24	35.17	even	12	inner
2100.2.ce.c.493.6	yes	24	35.3	even	12	inner
2100.2.ce.c.1657.1	yes	24	5.4	even	2	inner
2100.2.ce.c.1657.6	yes	24	1.1	even	1	trivial
2100.2.ce.c.1993.2	yes	24	5.2	odd	4	inner
2100.2.ce.c.1993.5	yes	24	5.3	odd	4	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)

\(f(q)\)	\(=\)	\(q+(0.258819 - 0.965926i) q^{3} +(0.920762 - 2.48036i) q^{7} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})\)	\(q+(0.258819 - 0.965926i) q^{3} +(0.920762 - 2.48036i) q^{7} +(-0.866025 - 0.500000i) q^{9} +(1.65754 + 2.87094i) q^{11} +(-1.05702 - 1.05702i) q^{13} +(3.20211 + 0.858003i) q^{17} +(1.10280 - 1.91011i) q^{19} +(-2.15754 - 1.53135i) q^{21} +(-1.83050 - 6.83153i) q^{23} +(-0.707107 + 0.707107i) q^{27} +(1.56249 - 0.902106i) q^{31} +(3.20211 - 0.858003i) q^{33} +(1.67303 - 0.448288i) q^{37} +(-1.29457 + 0.747423i) q^{39} +1.33066i q^{41} +(6.84446 - 6.84446i) q^{43} +(1.11949 + 4.17799i) q^{47} +(-5.30439 - 4.56765i) q^{49} +(1.65754 - 2.87094i) q^{51} +(2.97559 + 0.797308i) q^{53} +(-1.55960 - 1.55960i) q^{57} +(-0.665328 - 1.15238i) q^{59} +(-4.62499 - 2.67024i) q^{61} +(-2.03758 + 1.68768i) q^{63} +(-0.570853 + 2.13045i) q^{67} -7.07253 q^{69} +4.98969 q^{71} +(2.74861 - 10.2580i) q^{73} +(8.64716 - 1.46784i) q^{77} +(-13.8000 - 7.96745i) q^{79} +(0.500000 + 0.866025i) q^{81} +(-10.1150 - 10.1150i) q^{83} +(2.87094 - 4.97261i) q^{89} +(-3.59504 + 1.64852i) q^{91} +(-0.466964 - 1.74273i) q^{93} +(-3.53553 + 3.53553i) q^{97} -3.31507i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q+O(q^{10}) \) 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

Related objects

Downloads

Learn more