LMFDB - Embedded newform 2100.2.ce.c.157.5

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			157.5
Character	$\chi$	$=$	2100.157
Dual form			2100.2.ce.c.1993.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.965926	−	0.258819i	0.557678	−	0.149429i
$3$	0.965926	−	0.258819i	0.557678	−	0.149429i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−2.48036	+	0.920762i	−0.937489	+	0.348015i
$7$	−2.48036	+	0.920762i	−0.937489	+	0.348015i
$8$		0			0
$9$	0.866025	−	0.500000i	0.288675	−	0.166667i
$10$		0			0
$11$	1.65754	−	2.87094i	0.499766	−	0.865620i	−0.500234	−	0.865890i	$-0.666753\pi$
$11$	1.65754	−	2.87094i	0.499766	−	0.865620i	1.00000		0.000270562i	$8.61226e-5\pi$
$12$		0			0
$13$	1.05702	+	1.05702i	0.293163	+	0.293163i	0.838329	−	0.545165i	$-0.183533\pi$
$13$	1.05702	+	1.05702i	0.293163	+	0.293163i	−0.545165	+	0.838329i	$0.683533\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	0.858003	+	3.20211i	0.208096	+	0.776626i	0.988483	+	0.151329i	$0.0483554\pi$
$17$	0.858003	+	3.20211i	0.208096	+	0.776626i	−0.780387	+	0.625297i	$0.784978\pi$
$18$		0			0
$19$	−1.10280	−	1.91011i	−0.253001	−	0.438210i	0.711350	−	0.702838i	$-0.248084\pi$
$19$	−1.10280	−	1.91011i	−0.253001	−	0.438210i	−0.964351	+	0.264628i	$0.914751\pi$
$20$		0			0
$21$	−2.15754	+	1.53135i	−0.470813	+	0.334169i
$22$		0			0
$23$	6.83153	+	1.83050i	1.42447	+	0.381687i	0.887069	−	0.461638i	$-0.152738\pi$
$23$	6.83153	+	1.83050i	1.42447	+	0.381687i	0.537405	+	0.843324i	$0.319405\pi$
$24$		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	0.633710	−	0.773571i	$-0.281531\pi$
$31$	1.56249	+	0.902106i	0.280632	+	0.162023i	−0.353077	+	0.935594i	$0.614865\pi$
$32$		0			0
$33$	0.858003	−	3.20211i	0.149359	−	0.557416i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−0.448288	+	1.67303i	−0.0736980	+	0.275045i	−0.992935	−	0.118660i	$-0.962140\pi$
$37$	−0.448288	+	1.67303i	−0.0736980	+	0.275045i	0.919237	+	0.393705i	$0.128807\pi$
$38$		0			0
$39$	1.29457	+	0.747423i	0.207298	+	0.119683i
$40$		0			0
$41$		−	1.33066i		−	0.207813i	−0.994587	−	0.103907i	$-0.966866\pi$
$41$		−	1.33066i		−	0.207813i	0.994587	−	0.103907i	$-0.0331343\pi$
$42$		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
$47$	4.17799	+	1.11949i	0.609423	+	0.163294i	0.550315	−	0.834957i	$-0.314508\pi$
$47$	4.17799	+	1.11949i	0.609423	+	0.163294i	0.0591082	+	0.998252i	$0.481174\pi$
$48$		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
$53$	−0.797308	−	2.97559i	−0.109519	−	0.408729i	0.889300	−	0.457324i	$-0.151192\pi$
$53$	−0.797308	−	2.97559i	−0.109519	−	0.408729i	−0.998819	+	0.0485954i	$0.984526\pi$
$54$		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	$-0.805727\pi$
$59$	0.665328	−	1.15238i	0.0866183	−	0.150027i	0.906080	+	0.423107i	$0.139061\pi$
$60$		0			0
$61$	−4.62499	+	2.67024i	−0.592169	+	0.341889i	−0.765955	−	0.642895i	$-0.777733\pi$
$61$	−4.62499	+	2.67024i	−0.592169	+	0.341889i	0.173786	+	0.984783i	$0.444400\pi$
$62$		0			0
$63$	−1.68768	+	2.03758i	−0.212627	+	0.256712i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	2.13045	−	0.570853i	0.260276	−	0.0697408i	−0.126321	−	0.991989i	$-0.540317\pi$
$67$	2.13045	−	0.570853i	0.260276	−	0.0697408i	0.386597	+	0.922249i	$0.373650\pi$
$68$		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
$73$	10.2580	−	2.74861i	1.20060	−	0.321701i	0.397535	−	0.917587i	$-0.369866\pi$
$73$	10.2580	−	2.74861i	1.20060	−	0.321701i	0.803069	+	0.595886i	$0.203199\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−1.46784	+	8.64716i	−0.167276	+	0.985435i
$78$		0			0
$79$	13.8000	−	7.96745i	1.55262	−	0.896408i	0.554698	−	0.832052i	$-0.312834\pi$
$79$	13.8000	−	7.96745i	1.55262	−	0.896408i	0.997927	−	0.0643564i	$-0.0204995\pi$
$80$		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	$0.0373761\pi$
$83$	10.1150	+	10.1150i	1.11026	+	1.11026i	0.117151	+	0.993114i	$0.462624\pi$
$84$		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	$-0.265095\pi$
$89$	−2.87094	−	4.97261i	−0.304319	−	0.527095i	−0.977109	+	0.212738i	$0.931762\pi$
$90$		0			0
$91$	−3.59504	−	1.64852i	−0.376863	−	0.172812i
$92$		0			0
$93$	1.74273	+	0.466964i	0.180713	+	0.0484220i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	3.53553	−	3.53553i	0.358979	−	0.358979i	−0.504457	−	0.863437i	$-0.668307\pi$
$97$	3.53553	−	3.53553i	0.358979	−	0.358979i	0.863437	+	0.504457i	$0.168307\pi$
$98$		0			0
$99$		−	3.31507i		−	0.333177i
$100$		0			0
$101$	−16.2774	−	9.39774i	−1.61966	−	0.935110i	−0.987008	−	0.160673i	$-0.948633\pi$
$101$	−16.2774	−	9.39774i	−1.61966	−	0.935110i	−0.632651	−	0.774437i	$-0.718033\pi$
$102$		0			0
$103$	−2.57134	+	9.59638i	−0.253362	+	0.945559i	0.715633	+	0.698477i	$0.246139\pi$
$103$	−2.57134	+	9.59638i	−0.253362	+	0.945559i	−0.968994	+	0.247082i	$0.920528\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−4.86463	+	18.1550i	−0.470281	+	1.75511i	0.168475	+	0.985706i	$0.446116\pi$
$107$	−4.86463	+	18.1550i	−0.470281	+	1.75511i	−0.638757	+	0.769409i	$0.720551\pi$
$108$		0			0
$109$	13.0897	+	7.55734i	1.25377	+	0.723862i	0.971855	−	0.235579i	$-0.0756986\pi$
$109$	13.0897	+	7.55734i	1.25377	+	0.723862i	0.281910	+	0.959441i	$0.409032\pi$
$110$		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
$117$	1.44391	+	0.386895i	0.133490	+	0.0357684i
$118$		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
$123$	−0.344399	−	1.28531i	−0.0310534	−	0.115893i
$124$		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	0.0831152	−	0.996540i	$-0.473513\pi$
$131$	11.3048	−	6.52681i	0.987702	−	0.570250i	0.904586	+	0.426290i	$0.140180\pi$
$132$		0			0
$133$	4.49411	+	3.72235i	0.389689	+	0.322769i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−9.40216	+	2.51930i	−0.803281	+	0.215238i	−0.637024	−	0.770844i	$-0.719835\pi$
$137$	−9.40216	+	2.51930i	−0.803281	+	0.215238i	−0.166257	+	0.986082i	$0.553168\pi$
$138$		0			0
$139$	−9.22383			−0.782355			−0.391177	−	0.920315i	$-0.627932\pi$
$139$	−9.22383			−0.782355			−0.391177	+	0.920315i	$0.627932\pi$
$140$		0			0
$141$	4.32538			0.364263
$142$		0			0
$143$	4.78666	−	1.28258i	0.400281	−	0.107255i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	3.94146	−	5.78489i	0.325086	−	0.477129i
$148$		0			0
$149$	−3.41665	+	1.97261i	−0.279903	+	0.161602i	−0.633380	−	0.773841i	$-0.718333\pi$
$149$	−3.41665	+	1.97261i	−0.279903	+	0.161602i	0.353476	+	0.935443i	$0.384999\pi$
$150$		0			0
$151$	1.84246	−	3.19124i	0.149938	−	0.259700i	−0.781267	−	0.624198i	$-0.785426\pi$
$151$	1.84246	−	3.19124i	0.149938	−	0.259700i	0.931204	+	0.364498i	$0.118759\pi$
$152$		0			0
$153$	2.34411	+	2.34411i	0.189510	+	0.189510i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−1.97483	−	7.37015i	−0.157608	−	0.588202i	−0.998868	−	0.0475707i	$-0.984852\pi$
$157$	−1.97483	−	7.37015i	−0.157608	−	0.588202i	0.841260	−	0.540631i	$-0.181815\pi$
$158$		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
$163$	−17.2574	−	4.62412i	−1.35171	−	0.362189i	−0.490943	−	0.871192i	$-0.663348\pi$
$163$	−17.2574	−	4.62412i	−1.35171	−	0.362189i	−0.860765	+	0.509003i	$0.830014\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−14.5344	+	14.5344i	−1.12471	+	1.12471i	−0.133681	+	0.991024i	$0.542680\pi$
$167$	−14.5344	+	14.5344i	−1.12471	+	1.12471i	−0.991024	+	0.133681i	$0.957320\pi$
$168$		0			0
$169$		−	10.7654i		−	0.828110i
$170$		0			0
$171$	−1.91011	−	1.10280i	−0.146070	−	0.0843335i
$172$		0			0
$173$	0.163092	−	0.608669i	0.0123997	−	0.0462763i	−0.959449	−	0.281883i	$-0.909041\pi$
$173$	0.163092	−	0.608669i	0.0123997	−	0.0462763i	0.971849	+	0.235607i	$0.0757077\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	0.344399	−	1.28531i	0.0258866	−	0.0966101i
$178$		0			0
$179$	−14.3843	−	8.30476i	−1.07513	−	0.620727i	−0.145552	−	0.989351i	$-0.546496\pi$
$179$	−14.3843	−	8.30476i	−1.07513	−	0.620727i	−0.929579	+	0.368624i	$0.879829\pi$
$180$		0			0
$181$			15.6606i			1.16404i	0.813173	+	0.582022i	$0.197738\pi$
$181$			15.6606i			1.16404i	−0.813173	+	0.582022i	$0.802262\pi$
$182$		0			0
$183$	−3.77629	+	3.77629i	−0.279151	+	0.279151i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	10.6152	+	2.84434i	0.776262	+	0.207999i
$188$		0			0
$189$	−1.10280	+	2.40496i	−0.0802172	+	0.174935i
$190$		0			0
$191$	−8.47776	−	14.6839i	−0.613429	−	1.06249i	−0.990658	−	0.136370i	$-0.956456\pi$
$191$	−8.47776	−	14.6839i	−0.613429	−	1.06249i	0.377229	−	0.926120i	$-0.376877\pi$
$192$		0			0
$193$	0.466964	+	1.74273i	0.0336128	+	0.125445i	0.980694	−	0.195550i	$-0.0626493\pi$
$193$	0.466964	+	1.74273i	0.0336128	+	0.125445i	−0.947081	+	0.320995i	$0.895983\pi$
$194$		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	−0.311967	−	0.950093i	$-0.600988\pi$
$199$	9.40667	−	16.2928i	0.666821	−	1.15497i	0.978788	−	0.204875i	$-0.0656788\pi$
$200$		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
$207$	6.83153	−	1.83050i	0.474825	−	0.127229i
$208$		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
$213$	4.81967	−	1.29143i	0.330238	−	0.0884871i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−4.70617	−	0.798865i	−0.319476	−	0.0542305i
$218$		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	0.913430	−	0.406996i	$-0.133424\pi$
$223$	7.56268	+	7.56268i	0.506434	+	0.506434i	−0.406996	+	0.913430i	$0.633424\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	1.61761	+	6.03701i	0.107365	+	0.400690i	0.998603	−	0.0528454i	$-0.0168291\pi$
$227$	1.61761	+	6.03701i	0.107365	+	0.400690i	−0.891238	+	0.453536i	$0.850162\pi$
$228$		0			0
$229$	7.51000	+	13.0077i	0.496275	+	0.859573i	0.999991	−	0.00429607i	$-0.00136748\pi$
$229$	7.51000	+	13.0077i	0.496275	+	0.859573i	−0.503716	+	0.863869i	$0.668034\pi$
$230$		0			0
$231$	0.820225	+	8.73242i	0.0539668	+	0.574551i
$232$		0			0
$233$	−15.5844	−	4.17583i	−1.02097	−	0.273568i	−0.290763	−	0.956795i	$-0.593909\pi$
$233$	−15.5844	−	4.17583i	−1.02097	−	0.273568i	−0.730206	+	0.683227i	$0.760576\pi$
$234$		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	0.238597	−	0.971119i	$-0.423312\pi$
$241$	−7.50000	−	4.33013i	−0.483117	−	0.278928i	−0.721715	+	0.692191i	$0.756646\pi$
$242$		0			0
$243$	0.258819	−	0.965926i	0.0166032	−	0.0619642i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	0.853338	−	3.18470i	0.0542966	−	0.202638i
$248$		0			0
$249$	12.3883	+	7.15238i	0.785076	+	0.453264i
$250$		0			0
$251$			0.239219i			0.0150994i	0.999972	+	0.00754969i	$0.00240316\pi$
$251$			0.239219i			0.0150994i	−0.999972	+	0.00754969i	$0.997597\pi$
$252$		0			0
$253$	16.5788	−	16.5788i	1.04230	−	1.04230i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−8.63045	−	2.31252i	−0.538353	−	0.144251i	−0.0206102	−	0.999788i	$-0.506561\pi$
$257$	−8.63045	−	2.31252i	−0.538353	−	0.144251i	−0.517743	+	0.855536i	$0.673228\pi$
$258$		0			0
$259$	−0.428549	−	4.56249i	−0.0266287	−	0.283500i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−0.859222	−	3.20666i	−0.0529819	−	0.197731i	0.934362	−	0.356325i	$-0.115971\pi$
$263$	−0.859222	−	3.20666i	−0.0529819	−	0.197731i	−0.987344	+	0.158594i	$0.949304\pi$
$264$		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	0.181615	+	0.983370i	$0.441867\pi$
$269$	−12.4783	+	21.6131i	−0.760816	+	1.31777i	−0.942431	+	0.334402i	$0.891466\pi$
$270$		0			0
$271$	25.0702	−	14.4743i	1.52291	−	0.879250i	0.523273	−	0.852165i	$-0.324711\pi$
$271$	25.0702	−	14.4743i	1.52291	−	0.879250i	0.999633	−	0.0270851i	$-0.00862250\pi$
$272$		0			0
$273$	−3.89921	−	0.661884i	−0.235991	−	0.0400591i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	1.72549	−	0.462343i	0.103675	−	0.0277795i	−0.206609	−	0.978424i	$-0.566243\pi$
$277$	1.72549	−	0.462343i	0.103675	−	0.0277795i	0.310283	+	0.950644i	$0.399576\pi$
$278$		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
$283$	−22.8828	+	6.13143i	−1.36024	+	0.364476i	−0.863905	−	0.503654i	$-0.831989\pi$
$283$	−22.8828	+	6.13143i	−1.36024	+	0.364476i	−0.496337	+	0.868130i	$0.665322\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	1.22522	+	3.30051i	0.0723223	+	0.194823i
$288$		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	$0.0194491\pi$
$293$	18.1305	+	18.1305i	1.05920	+	1.05920i	0.0610633	+	0.998134i	$0.480551\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−0.858003	−	3.20211i	−0.0497864	−	0.185805i
$298$		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
$303$	−18.1550	−	4.86463i	−1.04298	−	0.279466i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	18.6572	−	18.6572i	1.06482	−	1.06482i	0.0670748	−	0.997748i	$-0.478633\pi$
$307$	18.6572	−	18.6572i	1.06482	−	1.06482i	0.997748	−	0.0670748i	$-0.0213666\pi$
$308$		0			0
$309$			9.93490i			0.565177i
$310$		0			0
$311$	8.42975	+	4.86692i	0.478007	+	0.275978i	0.719586	−	0.694404i	$-0.244332\pi$
$311$	8.42975	+	4.86692i	0.478007	+	0.275978i	−0.241578	+	0.970381i	$0.577665\pi$
$312$		0			0
$313$	3.29860	−	12.3106i	0.186448	−	0.695833i	−0.807868	−	0.589364i	$-0.799379\pi$
$313$	3.29860	−	12.3106i	0.186448	−	0.695833i	0.994316	−	0.106470i	$-0.0339548\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−4.97314	+	18.5600i	−0.279319	+	1.04243i	0.673572	+	0.739122i	$0.264759\pi$
$317$	−4.97314	+	18.5600i	−0.279319	+	1.04243i	−0.952891	+	0.303312i	$0.901907\pi$
$318$		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
$327$	14.5997	+	3.91197i	0.807363	+	0.216332i
$328$		0			0
$329$	−11.3937	+	1.07020i	−0.628156	+	0.0590019i
$330$		0			0
$331$	0.462297	+	0.800723i	0.0254102	+	0.0440117i	0.878451	−	0.477833i	$-0.158577\pi$
$331$	0.462297	+	0.800723i	0.0254102	+	0.0440117i	−0.853041	+	0.521844i	$0.825244\pi$
$332$		0			0
$333$	0.448288	+	1.67303i	0.0245660	+	0.0916816i
$334$		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
$343$	−8.95110	+	16.2135i	−0.483314	+	0.875447i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	12.3778	−	3.31661i	0.664473	−	0.178045i	0.0892090	−	0.996013i	$-0.471566\pi$
$347$	12.3778	−	3.31661i	0.664473	−	0.178045i	0.575264	+	0.817968i	$0.304899\pi$
$348$		0			0
$349$	−19.0347			−1.01890			−0.509452	−	0.860499i	$-0.670152\pi$
$349$	−19.0347			−1.01890			−0.509452	+	0.860499i	$0.670152\pi$
$350$		0			0
$351$	1.49485			0.0797890
$352$		0			0
$353$	−26.9930	+	7.23275i	−1.43669	+	0.384961i	−0.891374	−	0.453268i	$-0.850258\pi$
$353$	−26.9930	+	7.23275i	−1.43669	+	0.384961i	−0.545318	+	0.838229i	$0.683591\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−6.75474	−	5.59476i	−0.357499	−	0.296106i
$358$		0			0
$359$	−5.98795	+	3.45714i	−0.316032	+	0.182461i	−0.649622	−	0.760257i	$-0.725073\pi$
$359$	−5.98795	+	3.45714i	−0.316032	+	0.182461i	0.333591	+	0.942718i	$0.391740\pi$
$360$		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
$367$	−1.94248	−	7.24942i	−0.101396	−	0.378417i	0.896515	−	0.443013i	$-0.146091\pi$
$367$	−1.94248	−	7.24942i	−0.101396	−	0.378417i	−0.997911	+	0.0645966i	$0.979424\pi$
$368$		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
$373$	−16.6606	−	4.46420i	−0.862654	−	0.231148i	−0.199746	−	0.979848i	$-0.564012\pi$
$373$	−16.6606	−	4.46420i	−0.862654	−	0.231148i	−0.662909	+	0.748700i	$0.730678\pi$
$374$		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
$383$	0.261487	−	0.975883i	0.0133614	−	0.0498653i	−0.958923	−	0.283665i	$-0.908449\pi$
$383$	0.261487	−	0.975883i	0.0133614	−	0.0498653i	0.972285	+	0.233800i	$0.0751162\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	2.50525	−	9.34971i	0.127349	−	0.475272i
$388$		0			0
$389$	−27.8640	−	16.0873i	−1.41276	−	0.815658i	−0.417113	−	0.908855i	$-0.636958\pi$
$389$	−27.8640	−	16.0873i	−1.41276	−	0.815658i	−0.995648	+	0.0931970i	$0.970291\pi$
$390$		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
$397$	−14.2623	−	3.82158i	−0.715805	−	0.191799i	−0.117506	−	0.993072i	$-0.537490\pi$
$397$	−14.2623	−	3.82158i	−0.715805	−	0.191799i	−0.598299	+	0.801273i	$0.704157\pi$
$398$		0			0
$399$	5.30439	+	2.43235i	0.265552	+	0.121770i
$400$		0			0
$401$	−12.7722	−	22.1221i	−0.637814	−	1.10473i	−0.985911	−	0.167268i	$-0.946506\pi$
$401$	−12.7722	−	22.1221i	−0.637814	−	1.10473i	0.348098	−	0.937458i	$-0.386828\pi$
$402$		0			0
$403$	0.698040	+	2.60512i	0.0347718	+	0.129770i
$404$		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	$-0.954437\pi$
$409$	−7.51000	+	13.0077i	−0.371346	+	0.643190i	0.618427	+	0.785842i	$0.287770\pi$
$410$		0			0
$411$	−8.42975	+	4.86692i	−0.415809	+	0.240067i
$412$		0			0
$413$	−0.589184	+	3.47093i	−0.0289919	+	0.170793i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−8.90953	+	2.38730i	−0.436302	+	0.116907i
$418$		0			0
$419$	−40.0131			−1.95477			−0.977383	−	0.211477i	$-0.932173\pi$
$419$	−40.0131			−1.95477			−0.977383	+	0.211477i	$0.932173\pi$
$420$		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
$423$	4.17799	−	1.11949i	0.203141	−	0.0544315i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	9.01299	−	10.8817i	0.436169	−	0.526601i
$428$		0			0
$429$	4.29161	−	2.47776i	0.207201	−	0.119627i
$430$		0			0
$431$	19.7654	−	34.2347i	0.952068	−	1.64903i	0.211127	−	0.977459i	$-0.432287\pi$
$431$	19.7654	−	34.2347i	0.952068	−	1.64903i	0.740940	−	0.671571i	$-0.234380\pi$
$432$		0			0
$433$	−17.6886	−	17.6886i	−0.850058	−	0.850058i	0.140082	−	0.990140i	$-0.455263\pi$
$433$	−17.6886	−	17.6886i	−0.850058	−	0.850058i	−0.990140	+	0.140082i	$0.955263\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−4.03737	−	15.0677i	−0.193134	−	0.720785i
$438$		0			0
$439$	−0.674255	−	1.16784i	−0.0321804	−	0.0557381i	0.849487	−	0.527610i	$-0.176912\pi$
$439$	−0.674255	−	1.16784i	−0.0321804	−	0.0557381i	−0.881667	+	0.471872i	$0.843578\pi$
$440$		0			0
$441$	2.30992	−	6.60790i	0.109996	−	0.314662i
$442$		0			0
$443$	−23.7013	−	6.35073i	−1.12608	−	0.301733i	−0.352739	−	0.935722i	$-0.614750\pi$
$443$	−23.7013	−	6.35073i	−1.12608	−	0.301733i	−0.773342	+	0.633989i	$0.781416\pi$
$444$		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
$453$	0.953730	−	3.55937i	0.0448101	−	0.167234i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	1.54340	−	5.76004i	0.0721972	−	0.269443i	−0.920386	−	0.391011i	$-0.872125\pi$
$457$	1.54340	−	5.76004i	0.0721972	−	0.269443i	0.992583	+	0.121568i	$0.0387921\pi$
$458$		0			0
$459$	2.87094	+	1.65754i	0.134004	+	0.0773671i
$460$		0			0
$461$			16.5534i			0.770970i	0.922714	+	0.385485i	$0.125966\pi$
$461$			16.5534i			0.770970i	−0.922714	+	0.385485i	$0.874034\pi$
$462$		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
$467$	7.01289	+	1.87910i	0.324518	+	0.0869543i	0.417400	−	0.908723i	$-0.362941\pi$
$467$	7.01289	+	1.87910i	0.324518	+	0.0869543i	−0.0928822	+	0.995677i	$0.529608\pi$
$468$		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
$473$	−8.30507	−	30.9949i	−0.381867	−	1.42515i
$474$		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	0.0971653	+	0.995268i	$0.469022\pi$
$479$	−17.8009	+	30.8321i	−0.813345	+	1.40875i	−0.910510	+	0.413487i	$0.864311\pi$
$480$		0			0
$481$	−2.24227	+	1.29457i	−0.102239	+	0.0590275i
$482$		0			0
$483$	−17.5424	+	6.51211i	−0.798208	+	0.296311i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−16.0418	+	4.29840i	−0.726925	+	0.194779i	−0.603259	−	0.797545i	$-0.706132\pi$
$487$	−16.0418	+	4.29840i	−0.726925	+	0.194779i	−0.123666	+	0.992324i	$0.539465\pi$
$488$		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
$497$	−12.3762	+	4.59432i	−0.555150	+	0.206083i
$498$		0			0
$499$	−17.9270	+	10.3502i	−0.802524	+	0.463337i	−0.844353	−	0.535788i	$-0.820015\pi$
$499$	−17.9270	+	10.3502i	−0.802524	+	0.463337i	0.0418292	+	0.999125i	$0.486681\pi$
$500$		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	$0.0465401\pi$
$503$	25.4558	+	25.4558i	1.13502	+	1.13502i	0.145690	+	0.989330i	$0.453460\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−2.78630	−	10.3986i	−0.123744	−	0.461819i
$508$		0			0
$509$	0.329235	+	0.570251i	0.0145931	+	0.0252759i	0.873230	−	0.487309i	$-0.162021\pi$
$509$	0.329235	+	0.570251i	0.0145931	+	0.0252759i	−0.858637	+	0.512585i	$0.828688\pi$
$510$		0			0
$511$	−22.9127	+	16.2627i	−1.01360	+	0.719420i
$512$		0			0
$513$	−2.13045	−	0.570853i	−0.0940618	−	0.0252038i
$514$		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	−0.0438574	−	0.999038i	$-0.513965\pi$
$521$	−21.2500	−	12.2687i	−0.930978	−	0.537501i	−0.887121	+	0.461537i	$0.847298\pi$
$522$		0			0
$523$	5.20073	−	19.4094i	0.227412	−	0.848713i	−0.754012	−	0.656861i	$-0.771884\pi$
$523$	5.20073	−	19.4094i	0.227412	−	0.848713i	0.981424	−	0.191852i	$-0.0614494\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−1.54802	+	5.77729i	−0.0674328	+	0.251663i
$528$		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
$537$	−16.0436	−	4.29886i	−0.692331	−	0.185510i
$538$		0			0
$539$	−4.32120	−	22.7996i	−0.186127	−	0.982049i
$540$		0			0
$541$	−4.94781	−	8.56987i	−0.212723	−	0.368447i	0.739843	−	0.672780i	$-0.234900\pi$
$541$	−4.94781	−	8.56987i	−0.212723	−	0.368447i	−0.952566	+	0.304333i	$0.901567\pi$
$542$		0			0
$543$	4.05327	+	15.1270i	0.173942	+	0.649162i
$544$		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
$553$	−26.8929	+	32.4687i	−1.14360	+	1.38071i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	0.636032	−	0.170424i	0.0269496	−	0.00722111i	−0.245319	−	0.969442i	$-0.578893\pi$
$557$	0.636032	−	0.170424i	0.0269496	−	0.00722111i	0.272269	+	0.962221i	$0.412226\pi$
$558$		0			0
$559$	14.4694			0.611991
$560$		0			0
$561$	10.9897			0.463985
$562$		0			0
$563$	−34.7403	+	9.30864i	−1.46413	+	0.392312i	−0.900914	−	0.433997i	$-0.857103\pi$
$563$	−34.7403	+	9.30864i	−1.46413	+	0.392312i	−0.563216	+	0.826310i	$0.690436\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−0.442778	+	2.60844i	−0.0185949	+	0.109544i
$568$		0			0
$569$	16.7095	−	9.64723i	0.700498	−	0.404433i	−0.107035	−	0.994255i	$-0.534136\pi$
$569$	16.7095	−	9.64723i	0.700498	−	0.404433i	0.807533	+	0.589822i	$0.200802\pi$
$570$		0			0
$571$	−6.35017	+	10.9988i	−0.265746	+	0.460286i	−0.967759	−	0.251878i	$-0.918952\pi$
$571$	−6.35017	+	10.9988i	−0.265746	+	0.460286i	0.702013	+	0.712165i	$0.252285\pi$
$572$		0			0
$573$	−11.9894	−	11.9894i	−0.500863	−	0.500863i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	0.324865	+	1.21241i	0.0135243	+	0.0504733i	0.972358	−	0.233494i	$-0.0750159\pi$
$577$	0.324865	+	1.21241i	0.0135243	+	0.0504733i	−0.958834	+	0.283967i	$0.908349\pi$
$578$		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
$583$	−9.86430	−	2.64313i	−0.408538	−	0.109467i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	3.70500	−	3.70500i	0.152922	−	0.152922i	−0.626500	−	0.779422i	$-0.715513\pi$
$587$	3.70500	−	3.70500i	0.152922	−	0.152922i	0.779422	+	0.626500i	$0.215513\pi$
$588$		0			0
$589$		−	3.97938i		−	0.163968i
$590$		0			0
$591$	−7.48454	−	4.32120i	−0.307873	−	0.177750i
$592$		0			0
$593$	−11.9473	+	44.5881i	−0.490619	+	1.83101i	0.0626829	+	0.998033i	$0.480034\pi$
$593$	−11.9473	+	44.5881i	−0.490619	+	1.83101i	−0.553302	+	0.832981i	$0.686632\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	4.86925	−	18.1723i	0.199285	−	0.743742i
$598$		0			0
$599$	8.50005	+	4.90751i	0.347303	+	0.200515i	0.663497	−	0.748179i	$-0.269072\pi$
$599$	8.50005	+	4.90751i	0.347303	+	0.200515i	−0.316194	+	0.948695i	$0.602405\pi$
$600$		0			0
$601$			26.0708i			1.06345i	0.846917	+	0.531725i	$0.178456\pi$
$601$			26.0708i			1.06345i	−0.846917	+	0.531725i	$0.821544\pi$
$602$		0			0
$603$	1.55960	−	1.55960i	0.0635118	−	0.0635118i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	20.8402	+	5.58411i	0.845877	+	0.226652i	0.655628	−	0.755084i	$-0.272404\pi$
$607$	20.8402	+	5.58411i	0.845877	+	0.226652i	0.190249	+	0.981736i	$0.439071\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	3.23289	+	5.59952i	0.130789	+	0.226533i
$612$		0			0
$613$	−7.77493	−	29.0164i	−0.314026	−	1.17196i	−0.924893	−	0.380228i	$-0.875845\pi$
$613$	−7.77493	−	29.0164i	−0.314026	−	1.17196i	0.610866	−	0.791734i	$-0.290821\pi$
$614$		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	−0.293509	−	0.955956i	$-0.594823\pi$
$619$	16.9463	−	29.3518i	0.681128	−	1.17975i	0.974637	−	0.223792i	$-0.0718436\pi$
$620$		0			0
$621$	6.12499	−	3.53626i	0.245787	−	0.141905i
$622$		0			0
$623$	11.6995	+	9.69041i	0.468732	+	0.388238i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−7.06260	+	1.89242i	−0.282053	+	0.0755759i
$628$		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
$633$	4.53525	−	1.21522i	0.180260	−	0.0483005i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	10.4349	+	0.778753i	0.413446	+	0.0308553i
$638$		0			0
$639$	4.32120	−	2.49485i	0.170944	−	0.0986946i
$640$		0			0
$641$	−1.83053	+	3.17058i	−0.0723017	+	0.125230i	−0.899910	−	0.436076i	$-0.856368\pi$
$641$	−1.83053	+	3.17058i	−0.0723017	+	0.125230i	0.827608	+	0.561307i	$0.189701\pi$
$642$		0			0
$643$	22.3417	+	22.3417i	0.881072	+	0.881072i	0.993644	−	0.112572i	$-0.0359089\pi$
$643$	22.3417	+	22.3417i	0.881072	+	0.881072i	−0.112572	+	0.993644i	$0.535909\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−7.39585	−	27.6017i	−0.290761	−	1.08513i	−0.944526	−	0.328436i	$-0.893478\pi$
$647$	−7.39585	−	27.6017i	−0.290761	−	1.08513i	0.653765	−	0.756697i	$-0.273188\pi$
$648$		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
$653$	−12.8399	−	3.44044i	−0.502464	−	0.134635i	−0.00132058	−	0.999999i	$-0.500420\pi$
$653$	−12.8399	−	3.44044i	−0.502464	−	0.134635i	−0.501143	+	0.865364i	$0.667087\pi$
$654$		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	0.0679359	−	0.997690i	$-0.478359\pi$
$661$	−19.5941	−	11.3126i	−0.762121	−	0.440011i	−0.830057	+	0.557679i	$0.811692\pi$
$662$		0			0
$663$	−1.28258	+	4.78666i	−0.0498114	+	0.185899i
$664$		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
$677$	−18.9712	−	5.08332i	−0.729123	−	0.195368i	−0.124884	−	0.992171i	$-0.539856\pi$
$677$	−18.9712	−	5.08332i	−0.729123	−	0.195368i	−0.604239	+	0.796803i	$0.706523\pi$
$678$		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
$683$	−12.9338	−	48.2696i	−0.494898	−	1.84699i	−0.530598	−	0.847624i	$-0.678033\pi$
$683$	−12.9338	−	48.2696i	−0.494898	−	1.84699i	0.0356996	−	0.999363i	$-0.488634\pi$
$684$		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	−0.754011	−	0.656862i	$-0.771884\pi$
$691$	−14.7774	+	8.53172i	−0.562158	+	0.324562i	0.191853	+	0.981424i	$0.438550\pi$
$692$		0			0
$693$	3.05239	+	8.22258i	0.115951	+	0.312350i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	4.26091	−	1.14171i	0.161393	−	0.0432452i
$698$		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
$703$	3.69005	−	0.988747i	0.139173	−	0.0372913i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	49.0269	+	8.32222i	1.84384	+	0.312989i
$708$		0			0
$709$	1.19526	−	0.690084i	0.0448889	−	0.0259166i	−0.477388	−	0.878693i	$-0.658416\pi$
$709$	1.19526	−	0.690084i	0.0448889	−	0.0259166i	0.522277	+	0.852776i	$0.325083\pi$
$710$		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
$717$	6.63624	+	24.7668i	0.247835	+	0.924932i
$718$		0			0
$719$	5.86148	+	10.1524i	0.218596	+	0.378620i	0.954379	−	0.298598i	$-0.0965189\pi$
$719$	5.86148	+	10.1524i	0.218596	+	0.378620i	−0.735783	+	0.677218i	$0.763186\pi$
$720$		0			0
$721$	−2.45812	−	26.1701i	−0.0915453	−	0.974625i
$722$		0			0
$723$	−8.36516	−	2.24144i	−0.311104	−	0.0833600i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	2.00149	−	2.00149i	0.0742311	−	0.0742311i	−0.669016	−	0.743248i	$-0.733284\pi$
$727$	2.00149	−	2.00149i	0.0742311	−	0.0742311i	0.743248	+	0.669016i	$0.233284\pi$
$728$		0			0
$729$		−	1.00000i		−	0.0370370i
$730$		0			0
$731$	27.7893	+	16.0442i	1.02782	+	0.593415i
$732$		0			0
$733$	−2.55183	+	9.52354i	−0.0942538	+	0.351760i	−0.996905	−	0.0786123i	$-0.974951\pi$
$733$	−2.55183	+	9.52354i	−0.0942538	+	0.351760i	0.902651	+	0.430372i	$0.141618\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	1.89242	−	7.06260i	0.0697081	−	0.260154i
$738$		0			0
$739$	−7.74678	−	4.47261i	−0.284970	−	0.164527i	0.350701	−	0.936487i	$-0.385943\pi$
$739$	−7.74678	−	4.47261i	−0.284970	−	0.164527i	−0.635671	+	0.771960i	$0.719277\pi$
$740$		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
$747$	13.8173	+	3.70234i	0.505550	+	0.135462i
$748$		0			0
$749$	−4.65043	−	49.5103i	−0.169923	−	1.80907i
$750$		0			0
$751$	−14.4520	−	25.0316i	−0.527361	−	0.913415i	−0.999491	−	0.0318869i	$-0.989848\pi$
$751$	−14.4520	−	25.0316i	−0.527361	−	0.913415i	0.472131	−	0.881528i	$-0.343485\pi$
$752$		0			0
$753$	0.0619145	+	0.231068i	0.00225629	+	0.00842059i
$754$		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	−0.954291	−	0.298880i	$-0.903387\pi$
$761$	−32.3476	+	18.6759i	−1.17260	+	0.677000i	−0.218308	+	0.975880i	$0.570054\pi$
$762$		0			0
$763$	−39.4257	−	6.69244i	−1.42731	−	0.242283i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	1.92135	−	0.514823i	0.0693758	−	0.0185892i
$768$		0			0
$769$	−26.0886			−0.940780			−0.470390	−	0.882459i	$-0.655887\pi$
$769$	−26.0886			−0.940780			−0.470390	+	0.882459i	$0.655887\pi$
$770$		0			0
$771$	−8.93490			−0.321783
$772$		0			0
$773$	−23.1822	+	6.21166i	−0.833806	+	0.223418i	−0.650374	−	0.759614i	$-0.725388\pi$
$773$	−23.1822	+	6.21166i	−0.833806	+	0.223418i	−0.183433	+	0.983032i	$0.558721\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−1.59481	−	4.29611i	−0.0572134	−	0.154122i
$778$		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
$787$	10.4006	+	38.8156i	0.370742	+	1.38363i	0.859468	+	0.511190i	$0.170795\pi$
$787$	10.4006	+	38.8156i	0.370742	+	1.38363i	−0.488726	+	0.872437i	$0.662538\pi$
$788$		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
$793$	−7.71117	−	2.06620i	−0.273832	−	0.0733729i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−13.3503	+	13.3503i	−0.472890	+	0.472890i	−0.902849	−	0.429958i	$-0.858528\pi$
$797$	−13.3503	+	13.3503i	−0.472890	+	0.472890i	0.429958	+	0.902849i	$0.358528\pi$
$798$		0			0
$799$			14.3389i			0.507275i
$800$		0			0
$801$	−4.97261	−	2.87094i	−0.175698	−	0.101440i
$802$		0			0
$803$	9.11185	−	34.0059i	0.321550	−	1.20004i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−6.45924	+	24.1062i	−0.227376	+	0.848579i
$808$		0			0
$809$	24.9931	+	14.4297i	0.878709	+	0.507323i	0.870233	−	0.492641i	$-0.163968\pi$
$809$	24.9931	+	14.4297i	0.878709	+	0.507323i	0.00847656	+	0.999964i	$0.497302\pi$
$810$		0			0
$811$		−	7.76257i		−	0.272581i	−0.990669	−	0.136290i	$-0.956482\pi$
$811$		−	7.76257i		−	0.272581i	0.990669	−	0.136290i	$-0.0435180\pi$
$812$		0			0
$813$	20.4697	−	20.4697i	0.717905	−	0.717905i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−20.6218	−	5.52559i	−0.721465	−	0.193316i
$818$		0			0
$819$	−3.93766	+	0.369859i	−0.137593	+	0.0129239i
$820$		0			0
$821$	−10.6575	−	18.4594i	−0.371951	−	0.644237i	0.617915	−	0.786245i	$-0.287978\pi$
$821$	−10.6575	−	18.4594i	−0.371951	−	0.644237i	−0.989866	+	0.142008i	$0.954644\pi$
$822$		0			0
$823$	8.23853	+	30.7466i	0.287177	+	1.07176i	0.947234	+	0.320544i	$0.103866\pi$
$823$	8.23853	+	30.7466i	0.287177	+	1.07176i	−0.660056	+	0.751216i	$0.729468\pi$
$824$		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	$-0.837475\pi$
$829$	−0.374614	+	0.648851i	−0.0130109	+	0.0225355i	0.859447	+	0.511225i	$0.170808\pi$
$830$		0			0
$831$	1.54703	−	0.893179i	0.0536659	−	0.0309840i
$832$		0			0
$833$	19.1773	+	13.0662i	0.664454	+	0.452717i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	1.74273	−	0.466964i	0.0602377	−	0.0161407i
$838$		0			0
$839$	50.6446			1.74845			0.874223	−	0.485525i	$-0.161372\pi$
$839$	50.6446			1.74845			0.874223	+	0.485525i	$0.161372\pi$
$840$		0			0
$841$	29.0000			1.00000
$842$		0			0
$843$	1.98477	−	0.531818i	0.0683592	−	0.0183168i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−0.0210038	−	0.0173969i	−0.000721700	−	0.000597764i
$848$		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	$0.0498906\pi$
$853$	33.4071	+	33.4071i	1.14384	+	1.14384i	0.156095	+	0.987742i	$0.450109\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	6.07957	+	22.6892i	0.207674	+	0.775050i	0.988618	+	0.150449i	$0.0480718\pi$
$857$	6.07957	+	22.6892i	0.207674	+	0.775050i	−0.780944	+	0.624601i	$0.785262\pi$
$858$		0			0
$859$	−20.6719	−	35.8047i	−0.705315	−	1.22164i	−0.966578	−	0.256373i	$-0.917472\pi$
$859$	−20.6719	−	35.8047i	−0.705315	−	1.22164i	0.261263	−	0.965268i	$-0.415861\pi$
$860$		0			0
$861$	2.03770	+	2.87094i	0.0694447	+	0.0978412i
$862$		0			0
$863$	37.5954	+	10.0737i	1.27976	+	0.342911i	0.833763	−	0.552122i	$-0.186182\pi$
$863$	37.5954	+	10.0737i	1.27976	+	0.342911i	0.445999	+	0.895033i	$0.352848\pi$
$864$		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
$873$	1.29410	−	4.82963i	0.0437985	−	0.163458i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	1.35411	−	5.05359i	0.0457249	−	0.170648i	−0.939288	−	0.343131i	$-0.888512\pi$
$877$	1.35411	−	5.05359i	0.0457249	−	0.170648i	0.985012	+	0.172484i	$0.0551791\pi$
$878$		0			0
$879$	22.2053	+	12.8202i	0.748966	+	0.432415i
$880$		0			0
$881$			3.31978i			0.111846i	0.998435	+	0.0559231i	$0.0178102\pi$
$881$			3.31978i			0.111846i	−0.998435	+	0.0559231i	$0.982190\pi$
$882$		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
$887$	−55.8120	−	14.9548i	−1.87398	−	0.502132i	−0.999865	−	0.0164202i	$-0.994773\pi$
$887$	−55.8120	−	14.9548i	−1.87398	−	0.502132i	−0.874119	−	0.485712i	$-0.838560\pi$
$888$		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
$893$	−2.46916	−	9.21502i	−0.0826272	−	0.308369i
$894$		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
$903$	−4.28588	+	25.2484i	−0.142625	+	0.840216i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−27.1562	+	7.27649i	−0.901708	+	0.241612i	−0.679750	−	0.733444i	$-0.737912\pi$
$907$	−27.1562	+	7.27649i	−0.901708	+	0.241612i	−0.221958	+	0.975056i	$0.571245\pi$
$908$		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
$913$	45.8055	−	12.2735i	1.51594	−	0.406195i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−22.0303	+	26.5978i	−0.727504	+	0.878338i
$918$		0			0
$919$	26.8423	−	15.4974i	0.885445	−	0.511212i	0.0129952	−	0.999916i	$-0.495863\pi$
$919$	26.8423	−	15.4974i	0.885445	−	0.511212i	0.872450	+	0.488704i	$0.162530\pi$
$920$		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
$927$	2.57134	+	9.59638i	0.0844540	+	0.315186i
$928$		0			0
$929$	23.4528	+	40.6214i	0.769461	+	1.33275i	0.937856	+	0.347025i	$0.112808\pi$
$929$	23.4528	+	40.6214i	0.769461	+	1.33275i	−0.168395	+	0.985720i	$0.553858\pi$
$930$		0			0
$931$	−14.5744	−	5.09477i	−0.477658	−	0.166974i
$932$		0			0
$933$	9.40216	+	2.51930i	0.307813	+	0.0824782i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−30.1331	+	30.1331i	−0.984405	+	0.984405i	−0.999880	−	0.0154751i	$-0.995074\pi$
$937$	−30.1331	+	30.1331i	−0.984405	+	0.984405i	0.0154751	+	0.999880i	$0.495074\pi$
$938$		0			0
$939$		−	12.7448i		−	0.415911i
$940$		0			0
$941$	13.1952	+	7.61824i	0.430151	+	0.248348i	0.699411	−	0.714720i	$-0.253446\pi$
$941$	13.1952	+	7.61824i	0.430151	+	0.248348i	−0.269260	+	0.963067i	$0.586779\pi$
$942$		0			0
$943$	2.43577	−	9.09042i	0.0793196	−	0.296025i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	7.94535	−	29.6525i	0.258189	−	0.963575i	−0.708099	−	0.706113i	$-0.750447\pi$
$947$	7.94535	−	29.6525i	0.258189	−	0.963575i	0.966288	−	0.257462i	$-0.0828863\pi$
$948$		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
$963$	4.86463	+	18.1550i	0.156760	+	0.585038i
$964$		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	−0.149731	−	0.988727i	$-0.547841\pi$
$971$	19.6833	−	11.3641i	0.631666	−	0.364692i	0.781397	+	0.624034i	$0.214508\pi$
$972$		0			0
$973$	22.8784	−	8.49295i	0.733449	−	0.272271i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	54.4651	−	14.5939i	1.74249	−	0.466900i	0.759495	−	0.650513i	$-0.225446\pi$
$977$	54.4651	−	14.5939i	1.74249	−	0.466900i	0.982999	+	0.183613i	$0.0587793\pi$
$978$		0			0
$979$	−19.0347			−0.608352
$980$		0			0
$981$	15.1147			0.482575
$982$		0			0
$983$	20.7045	−	5.54775i	0.660370	−	0.176946i	0.0869571	−	0.996212i	$-0.472286\pi$
$983$	20.7045	−	5.54775i	0.660370	−	0.176946i	0.573413	+	0.819266i	$0.305619\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−10.7285	+	3.98264i	−0.341492	+	0.126769i
$988$		0			0
$989$	59.2870	−	34.2294i	1.88522	−	1.08843i
$990$		0			0
$991$	28.9922	−	50.2160i	0.920969	−	1.59516i	0.123050	−	0.992401i	$-0.460733\pi$
$991$	28.9922	−	50.2160i	0.920969	−	1.59516i	0.797919	−	0.602764i	$-0.205934\pi$
$992$		0			0
$993$	0.653787	+	0.653787i	0.0207473	+	0.0207473i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	10.7747	+	40.2116i	0.341237	+	1.27352i	0.896947	+	0.442138i	$0.145780\pi$
$997$	10.7747	+	40.2116i	0.341237	+	1.27352i	−0.555709	+	0.831377i	$0.687553\pi$
$998$		0			0
$999$	0.866025	+	1.50000i	0.0273998	+	0.0474579i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2100.2.ce.c.157.5	yes	24
5.2	odd	4	inner	2100.2.ce.c.493.1	yes	24
5.3	odd	4	inner	2100.2.ce.c.493.6	yes	24
5.4	even	2	inner	2100.2.ce.c.157.2	✓	24
7.5	odd	6	inner	2100.2.ce.c.1657.6	yes	24
35.12	even	12	inner	2100.2.ce.c.1993.2	yes	24
35.19	odd	6	inner	2100.2.ce.c.1657.1	yes	24
35.33	even	12	inner	2100.2.ce.c.1993.5	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2100.2.ce.c.157.2	✓	24	5.4	even	2	inner
2100.2.ce.c.157.5	yes	24	1.1	even	1	trivial
2100.2.ce.c.493.1	yes	24	5.2	odd	4	inner
2100.2.ce.c.493.6	yes	24	5.3	odd	4	inner
2100.2.ce.c.1657.1	yes	24	35.19	odd	6	inner
2100.2.ce.c.1657.6	yes	24	7.5	odd	6	inner
2100.2.ce.c.1993.2	yes	24	35.12	even	12	inner
2100.2.ce.c.1993.5	yes	24	35.33	even	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

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

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