LMFDB - Embedded newform 2100.2.bo.h.1949.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2100,2,Mod(1349,2100)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2100, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 3, 5]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("2100.1349");

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.bo (of order $6$, degree $2$, not 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:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 3 x^{18} - 16 x^{16} + 87 x^{14} + 91 x^{12} - 1104 x^{10} + 819 x^{8} + 7047 x^{6} + \cdots + 59049 $ x^20 - 3x^18 - 16x^16 + 87x^14 + 91x^12 - 1104x^10 + 819x^8 + 7047x^6 - 11664x^4 - 19683*x^2 + 59049
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	no (minimal twist has level 420)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1949.6
Root			$-0.268793 - 1.71107i$ of defining polynomial
Character	$\chi$	$=$	2100.1949
Dual form			2100.2.bo.h.1349.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.268793 + 1.71107i) q^{3} +(-0.615143 - 2.57325i) q^{7} +(-2.85550 + 0.919845i) q^{9} +O(q^{10})$	\(q+(0.268793 + 1.71107i) q^{3} +(-0.615143 - 2.57325i) q^{7} +(-2.85550 + 0.919845i) q^{9} +(-1.80606 - 1.04273i) q^{11} -0.245770 q^{13} +(0.816904 + 0.471640i) q^{17} +(0.465563 - 0.268793i) q^{19} +(4.23765 - 1.74422i) q^{21} +(1.38570 + 2.40010i) q^{23} +(-2.34145 - 4.63871i) q^{27} +0.267475i q^{29} +(0.981097 + 0.566436i) q^{31} +(1.29872 - 3.37057i) q^{33} +(5.33755 - 3.08164i) q^{37} +(-0.0660611 - 0.420528i) q^{39} -2.38340 q^{41} -11.4354i q^{43} +(10.7944 - 6.23215i) q^{47} +(-6.24320 + 3.16583i) q^{49} +(-0.587429 + 1.52455i) q^{51} +(6.26660 - 10.8541i) q^{53} +(0.585062 + 0.724359i) q^{57} +(6.25478 - 10.8336i) q^{59} +(4.96556 - 2.86687i) q^{61} +(4.12353 + 6.78207i) q^{63} +(-4.81512 - 2.78001i) q^{67} +(-3.73427 + 3.01616i) q^{69} +10.1375i q^{71} +(6.56784 - 11.3758i) q^{73} +(-1.57221 + 5.28887i) q^{77} +(-3.17314 - 5.49605i) q^{79} +(7.30777 - 5.25324i) q^{81} +1.06674i q^{83} +(-0.457667 + 0.0718953i) q^{87} +(0.463787 + 0.803302i) q^{89} +(0.151184 + 0.632426i) q^{91} +(-0.705499 + 1.83098i) q^{93} -3.01245 q^{97} +(6.11636 + 1.31622i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 6 q^{9}+O(q^{10}) $ 20 * q + 6 * q^9	$ 20 q + 6 q^{9} - 12 q^{11} - 6 q^{19} + 20 q^{21} + 30 q^{31} - 30 q^{39} - 16 q^{41} + 26 q^{49} - 88 q^{51} + 84 q^{61} + 28 q^{69} - 2 q^{79} + 82 q^{81} - 56 q^{89} - 22 q^{91} - 72 q^{99}+O(q^{100}) $ 20 * q + 6 * q^9 - 12 * q^11 - 6 * q^19 + 20 * q^21 + 30 * q^31 - 30 * q^39 - 16 * q^41 + 26 * q^49 - 88 * q^51 + 84 * q^61 + 28 * q^69 - 2 * q^79 + 82 * q^81 - 56 * q^89 - 22 * q^91 - 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2100\mathbb{Z}\right)^\times$.

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

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
$3$	0.268793	+	1.71107i	0.155188	+	0.987885i
$3$	0.268793	+	1.71107i	0.155188	+	0.987885i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−0.615143	−	2.57325i	−0.232502	−	0.972596i
$7$	−0.615143	−	2.57325i	−0.232502	−	0.972596i
$8$		0			0
$9$	−2.85550	+	0.919845i	−0.951834	+	0.306615i
$10$		0			0
$11$	−1.80606	−	1.04273i	−0.544548	−	0.314395i	0.202372	−	0.979309i	$-0.435135\pi$
$11$	−1.80606	−	1.04273i	−0.544548	−	0.314395i	−0.746920	+	0.664914i	$0.768468\pi$
$12$		0			0
$13$	−0.245770			−0.0681643			−0.0340821	−	0.999419i	$-0.510851\pi$
$13$	−0.245770			−0.0681643			−0.0340821	+	0.999419i	$0.510851\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	0.816904	+	0.471640i	0.198128	+	0.114389i	0.595782	−	0.803146i	$-0.296842\pi$
$17$	0.816904	+	0.471640i	0.198128	+	0.114389i	−0.397654	+	0.917536i	$0.630176\pi$
$18$		0			0
$19$	0.465563	−	0.268793i	0.106807	−	0.0616653i	−0.445645	−	0.895210i	$-0.647026\pi$
$19$	0.465563	−	0.268793i	0.106807	−	0.0616653i	0.552452	+	0.833545i	$0.313692\pi$
$20$		0			0
$21$	4.23765	−	1.74422i	0.924731	−	0.380620i
$22$		0			0
$23$	1.38570	+	2.40010i	0.288938	+	0.500456i	0.973557	−	0.228446i	$-0.0733644\pi$
$23$	1.38570	+	2.40010i	0.288938	+	0.500456i	−0.684618	+	0.728902i	$0.740031\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−2.34145	−	4.63871i	−0.450613	−	0.892719i
$28$		0			0
$29$			0.267475i			0.0496688i	0.999692	+	0.0248344i	$0.00790585\pi$
$29$			0.267475i			0.0496688i	−0.999692	+	0.0248344i	$0.992094\pi$
$30$		0			0
$31$	0.981097	+	0.566436i	0.176210	+	0.101735i	0.585511	−	0.810665i	$-0.300894\pi$
$31$	0.981097	+	0.566436i	0.176210	+	0.101735i	−0.409301	+	0.912400i	$0.634227\pi$
$32$		0			0
$33$	1.29872	−	3.37057i	0.226079	−	0.586741i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	5.33755	−	3.08164i	0.877488	−	0.506618i	0.00765857	−	0.999971i	$-0.497562\pi$
$37$	5.33755	−	3.08164i	0.877488	−	0.506618i	0.869829	+	0.493353i	$0.164229\pi$
$38$		0			0
$39$	−0.0660611	−	0.420528i	−0.0105782	−	0.0673384i
$40$		0			0
$41$	−2.38340			−0.372224			−0.186112	−	0.982529i	$-0.559589\pi$
$41$	−2.38340			−0.372224			−0.186112	+	0.982529i	$0.559589\pi$
$42$		0			0
$43$		−	11.4354i		−	1.74388i	−0.489616	−	0.871938i	$-0.662863\pi$
$43$		−	11.4354i		−	1.74388i	0.489616	−	0.871938i	$-0.337137\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	10.7944	−	6.23215i	1.57452	−	0.909052i	0.578921	−	0.815384i	$-0.303474\pi$
$47$	10.7944	−	6.23215i	1.57452	−	0.909052i	0.995603	−	0.0936683i	$-0.0298593\pi$
$48$		0			0
$49$	−6.24320	+	3.16583i	−0.891885	+	0.452261i
$50$		0			0
$51$	−0.587429	+	1.52455i	−0.0822565	+	0.213480i
$52$		0			0
$53$	6.26660	−	10.8541i	0.860784	−	1.49092i	−0.0103892	−	0.999946i	$-0.503307\pi$
$53$	6.26660	−	10.8541i	0.860784	−	1.49092i	0.871173	−	0.490976i	$-0.163360\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	0.585062	+	0.724359i	0.0774934	+	0.0959437i
$58$		0			0
$59$	6.25478	−	10.8336i	0.814303	−	1.41041i	−0.0955244	−	0.995427i	$-0.530453\pi$
$59$	6.25478	−	10.8336i	0.814303	−	1.41041i	0.909827	−	0.414987i	$-0.136214\pi$
$60$		0			0
$61$	4.96556	−	2.86687i	0.635775	−	0.367065i	−0.147210	−	0.989105i	$-0.547029\pi$
$61$	4.96556	−	2.86687i	0.635775	−	0.367065i	0.782985	+	0.622040i	$0.213696\pi$
$62$		0			0
$63$	4.12353	+	6.78207i	0.519516	+	0.854461i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−4.81512	−	2.78001i	−0.588261	−	0.339633i	0.176149	−	0.984364i	$-0.443636\pi$
$67$	−4.81512	−	2.78001i	−0.588261	−	0.339633i	−0.764410	+	0.644731i	$0.776969\pi$
$68$		0			0
$69$	−3.73427	+	3.01616i	−0.449553	+	0.363103i
$70$		0			0
$71$			10.1375i			1.20310i	0.798835	+	0.601551i	$0.205450\pi$
$71$			10.1375i			1.20310i	−0.798835	+	0.601551i	$0.794550\pi$
$72$		0			0
$73$	6.56784	−	11.3758i	0.768707	−	1.33144i	−0.169557	−	0.985520i	$-0.554234\pi$
$73$	6.56784	−	11.3758i	0.768707	−	1.33144i	0.938264	−	0.345919i	$-0.112433\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−1.57221	+	5.28887i	−0.179170	+	0.602722i
$78$		0			0
$79$	−3.17314	−	5.49605i	−0.357007	−	0.618353i	0.630453	−	0.776228i	$-0.282869\pi$
$79$	−3.17314	−	5.49605i	−0.357007	−	0.618353i	−0.987459	+	0.157874i	$0.949536\pi$
$80$		0			0
$81$	7.30777	−	5.25324i	0.811975	−	0.583693i
$82$		0			0
$83$			1.06674i			0.117090i	0.998285	+	0.0585449i	$0.0186461\pi$
$83$			1.06674i			0.117090i	−0.998285	+	0.0585449i	$0.981354\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−0.457667	+	0.0718953i	−0.0490671	+	0.00770798i
$88$		0			0
$89$	0.463787	+	0.803302i	0.0491613	+	0.0851499i	0.889559	−	0.456820i	$-0.151012\pi$
$89$	0.463787	+	0.803302i	0.0491613	+	0.0851499i	−0.840398	+	0.541970i	$0.817678\pi$
$90$		0			0
$91$	0.151184	+	0.632426i	0.0158483	+	0.0662963i
$92$		0			0
$93$	−0.705499	+	1.83098i	−0.0731568	+	0.189863i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−3.01245			−0.305868			−0.152934	−	0.988236i	$-0.548872\pi$
$97$	−3.01245			−0.305868			−0.152934	+	0.988236i	$0.548872\pi$
$98$		0			0
$99$	6.11636	+	1.31622i	0.614717	+	0.132285i
$100$		0			0
$101$	−6.19049	+	10.7223i	−0.615977	+	1.06690i	0.374235	+	0.927334i	$0.377905\pi$
$101$	−6.19049	+	10.7223i	−0.615977	+	1.06690i	−0.990212	+	0.139570i	$0.955428\pi$
$102$		0			0
$103$	−8.41703	−	14.5787i	−0.829355	−	1.43648i	−0.898545	−	0.438881i	$-0.855375\pi$
$103$	−8.41703	−	14.5787i	−0.829355	−	1.43648i	0.0691903	−	0.997603i	$-0.477958\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	6.41036	+	11.1031i	0.619713	+	1.07337i	0.989538	+	0.144273i	$0.0460843\pi$
$107$	6.41036	+	11.1031i	0.619713	+	1.07337i	−0.369825	+	0.929101i	$0.620582\pi$
$108$		0			0
$109$	−1.79448	+	3.10813i	−0.171880	+	0.297705i	−0.939077	−	0.343707i	$-0.888317\pi$
$109$	−1.79448	+	3.10813i	−0.171880	+	0.297705i	0.767197	+	0.641411i	$0.221651\pi$
$110$		0			0
$111$	6.70758	+	8.30459i	0.636655	+	0.788236i
$112$		0			0
$113$	1.00353			0.0944041			0.0472020	−	0.998885i	$-0.484970\pi$
$113$	1.00353			0.0944041			0.0472020	+	0.998885i	$0.484970\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	0.701796	−	0.226070i	0.0648810	−	0.0209002i
$118$		0			0
$119$	0.711132	−	2.39222i	0.0651894	−	0.219295i
$120$		0			0
$121$	−3.32543	−	5.75981i	−0.302312	−	0.523619i
$122$		0			0
$123$	−0.640639	−	4.07815i	−0.0577645	−	0.367714i
$124$		0			0
$125$		0			0
$126$		0			0
$127$			7.76096i			0.688674i	0.938846	+	0.344337i	$0.111896\pi$
$127$			7.76096i			0.688674i	−0.938846	+	0.344337i	$0.888104\pi$
$128$		0			0
$129$	19.5667	−	3.07374i	1.72275	−	0.270628i
$130$		0			0
$131$	8.58199	+	14.8644i	0.749812	+	1.29871i	0.947913	+	0.318530i	$0.103189\pi$
$131$	8.58199	+	14.8644i	0.749812	+	1.29871i	−0.198101	+	0.980182i	$0.563477\pi$
$132$		0			0
$133$	−0.978058	−	1.03266i	−0.0848084	−	0.0895431i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−7.51345	+	13.0137i	−0.641918	+	1.11183i	0.343087	+	0.939304i	$0.388528\pi$
$137$	−7.51345	+	13.0137i	−0.641918	+	1.11183i	−0.985004	+	0.172530i	$0.944806\pi$
$138$		0			0
$139$		−	9.83141i		−	0.833889i	−0.908932	−	0.416945i	$-0.863101\pi$
$139$		−	9.83141i		−	0.833889i	0.908932	−	0.416945i	$-0.136899\pi$
$140$		0			0
$141$	13.5651	+	16.7948i	1.14239	+	1.41438i
$142$		0			0
$143$	0.443875	+	0.256271i	0.0371187	+	0.0214305i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−7.09507	−	9.83158i	−0.585192	−	0.810895i
$148$		0			0
$149$	−19.9895	+	11.5409i	−1.63760	+	0.945469i	−0.655943	+	0.754810i	$0.727729\pi$
$149$	−19.9895	+	11.5409i	−1.63760	+	0.945469i	−0.981656	+	0.190658i	$0.938938\pi$
$150$		0			0
$151$	7.20527	−	12.4799i	0.586357	−	1.01560i	−0.408348	−	0.912826i	$-0.633895\pi$
$151$	7.20527	−	12.4799i	0.586357	−	1.01560i	0.994705	−	0.102774i	$-0.0327717\pi$
$152$		0			0
$153$	−2.76650	−	0.595343i	−0.223659	−	0.0481306i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−1.09951	+	1.90441i	−0.0877506	+	0.151988i	−0.906560	−	0.422077i	$-0.861301\pi$
$157$	−1.09951	+	1.90441i	−0.0877506	+	0.151988i	0.818809	+	0.574065i	$0.194635\pi$
$158$		0			0
$159$	20.2565	+	7.80508i	1.60644	+	0.618983i
$160$		0			0
$161$	5.32365	−	5.04216i	0.419563	−	0.397378i
$162$		0			0
$163$	8.53481	−	4.92757i	0.668498	−	0.385957i	−0.127009	−	0.991902i	$-0.540538\pi$
$163$	8.53481	−	4.92757i	0.668498	−	0.385957i	0.795507	+	0.605944i	$0.207205\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$		−	22.8349i		−	1.76702i	−0.468415	−	0.883509i	$-0.655175\pi$
$167$		−	22.8349i		−	1.76702i	0.468415	−	0.883509i	$-0.344825\pi$
$168$		0			0
$169$	−12.9396			−0.995354
$170$		0			0
$171$	−1.08217	+	1.19578i	−0.0827554	+	0.0914438i
$172$		0			0
$173$	8.43656	−	4.87085i	0.641420	−	0.370324i	−0.143741	−	0.989615i	$-0.545913\pi$
$173$	8.43656	−	4.87085i	0.641420	−	0.370324i	0.785161	+	0.619291i	$0.212580\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	20.2182	+	7.79036i	1.51970	+	0.585559i
$178$		0			0
$179$	15.6543	+	9.03800i	1.17006	+	0.675532i	0.953693	−	0.300781i	$-0.0972473\pi$
$179$	15.6543	+	9.03800i	1.17006	+	0.675532i	0.216363	+	0.976313i	$0.430581\pi$
$180$		0			0
$181$			17.7230i			1.31734i	0.752433	+	0.658669i	$0.228880\pi$
$181$			17.7230i			1.31734i	−0.752433	+	0.658669i	$0.771120\pi$
$182$		0			0
$183$	6.24011	+	7.72582i	0.461282	+	0.571109i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−0.983585	−	1.70362i	−0.0719269	−	0.124581i
$188$		0			0
$189$	−10.4962	+	8.87861i	−0.763487	+	0.645824i
$190$		0			0
$191$	19.0353	−	10.9901i	1.37735	−	0.795212i	0.385508	−	0.922704i	$-0.374026\pi$
$191$	19.0353	−	10.9901i	1.37735	−	0.795212i	0.991840	+	0.127492i	$0.0406927\pi$
$192$		0			0
$193$	7.77378	+	4.48820i	0.559569	+	0.323067i	0.752973	−	0.658052i	$-0.228619\pi$
$193$	7.77378	+	4.48820i	0.559569	+	0.323067i	−0.193403	+	0.981119i	$0.561953\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−22.3002			−1.58882			−0.794410	−	0.607382i	$-0.792220\pi$
$197$	−22.3002			−1.58882			−0.794410	+	0.607382i	$0.792220\pi$
$198$		0			0
$199$	−16.3807	−	9.45740i	−1.16120	−	0.670417i	−0.209606	−	0.977786i	$-0.567218\pi$
$199$	−16.3807	−	9.45740i	−1.16120	−	0.670417i	−0.951591	+	0.307368i	$0.900552\pi$
$200$		0			0
$201$	3.46252	−	8.98625i	0.244227	−	0.633841i
$202$		0			0
$203$	0.688279	−	0.164535i	0.0483077	−	0.0115481i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−6.16459	−	5.57887i	−0.428469	−	0.387758i
$208$		0			0
$209$	−1.12111			−0.0775490
$210$		0			0
$211$	20.4152			1.40544			0.702722	−	0.711465i	$-0.251968\pi$
$211$	20.4152			1.40544			0.702722	+	0.711465i	$0.251968\pi$
$212$		0			0
$213$	−17.3460	+	2.72489i	−1.18853	+	0.186706i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	0.854066	−	2.87304i	0.0579778	−	0.195035i
$218$		0			0
$219$	21.2302	+	8.18027i	1.43460	+	0.552771i
$220$		0			0
$221$	−0.200770	−	0.115915i	−0.0135053	−	0.00779727i
$222$		0			0
$223$	−13.5949			−0.910379			−0.455189	−	0.890395i	$-0.650428\pi$
$223$	−13.5949			−0.910379			−0.455189	+	0.890395i	$0.650428\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−8.71671	−	5.03260i	−0.578549	−	0.334025i	0.182008	−	0.983297i	$-0.441740\pi$
$227$	−8.71671	−	5.03260i	−0.578549	−	0.334025i	−0.760556	+	0.649272i	$0.775074\pi$
$228$		0			0
$229$	−12.3651	+	7.13897i	−0.817106	+	0.471756i	−0.849418	−	0.527721i	$-0.823047\pi$
$229$	−12.3651	+	7.13897i	−0.817106	+	0.471756i	0.0323114	+	0.999478i	$0.489713\pi$
$230$		0			0
$231$	−9.47221	−	1.26856i	−0.623225	−	0.0834648i
$232$		0			0
$233$	10.3759	+	17.9716i	0.679750	+	1.17736i	0.975056	+	0.221958i	$0.0712449\pi$
$233$	10.3759	+	17.9716i	0.679750	+	1.17736i	−0.295306	+	0.955403i	$0.595422\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	8.55118	−	6.90676i	0.555459	−	0.448642i
$238$		0			0
$239$			4.86422i			0.314640i	0.987548	+	0.157320i	$0.0502854\pi$
$239$			4.86422i			0.314640i	−0.987548	+	0.157320i	$0.949715\pi$
$240$		0			0
$241$	−14.9239	−	8.61634i	−0.961336	−	0.555028i	−0.0647520	−	0.997901i	$-0.520626\pi$
$241$	−14.9239	−	8.61634i	−0.961336	−	0.555028i	−0.896584	+	0.442874i	$0.853959\pi$
$242$		0			0
$243$	10.9529	+	11.0921i	0.702630	+	0.711556i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−0.114421	+	0.0660611i	−0.00728045	+	0.00420337i
$248$		0			0
$249$	−1.82526	+	0.286732i	−0.115671	+	0.0181709i
$250$		0			0
$251$	−15.8276			−0.999031			−0.499516	−	0.866305i	$-0.666489\pi$
$251$	−15.8276			−0.999031			−0.499516	+	0.866305i	$0.666489\pi$
$252$		0			0
$253$		−	5.77964i		−	0.363363i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	15.7755	−	9.10800i	0.984050	−	0.568141i	0.0805593	−	0.996750i	$-0.474329\pi$
$257$	15.7755	−	9.10800i	0.984050	−	0.568141i	0.903490	+	0.428609i	$0.140996\pi$
$258$		0			0
$259$	−11.2132	−	11.8392i	−0.696752	−	0.735651i
$260$		0			0
$261$	−0.246035	−	0.763775i	−0.0152292	−	0.0472765i
$262$		0			0
$263$	2.63255	−	4.55971i	0.162330	−	0.281164i	−0.773374	−	0.633950i	$-0.781432\pi$
$263$	2.63255	−	4.55971i	0.162330	−	0.281164i	0.935704	+	0.352786i	$0.114766\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−1.24984	+	1.00949i	−0.0764891	+	0.0617799i
$268$		0			0
$269$	−0.775418	+	1.34306i	−0.0472780	+	0.0818880i	−0.888696	−	0.458497i	$-0.848388\pi$
$269$	−0.775418	+	1.34306i	−0.0472780	+	0.0818880i	0.841418	+	0.540385i	$0.181721\pi$
$270$		0			0
$271$	−9.77676	+	5.64461i	−0.593896	+	0.342886i	−0.766636	−	0.642082i	$-0.778071\pi$
$271$	−9.77676	+	5.64461i	−0.593896	+	0.342886i	0.172741	+	0.984967i	$0.444738\pi$
$272$		0			0
$273$	−1.04149	+	0.428677i	−0.0630336	+	0.0259447i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	14.7981	+	8.54371i	0.889134	+	0.513342i	0.873659	−	0.486538i	$-0.161741\pi$
$277$	14.7981	+	8.54371i	0.889134	+	0.513342i	0.0154751	+	0.999880i	$0.495074\pi$
$278$		0			0
$279$	−3.32256	−	0.715003i	−0.198916	−	0.0428061i
$280$		0			0
$281$		−	15.2188i		−	0.907880i	−0.891032	−	0.453940i	$-0.850018\pi$
$281$		−	15.2188i		−	0.907880i	0.891032	−	0.453940i	$-0.149982\pi$
$282$		0			0
$283$	8.23500	−	14.2634i	0.489520	−	0.847874i	−0.510407	−	0.859933i	$-0.670505\pi$
$283$	8.23500	−	14.2634i	0.489520	−	0.847874i	0.999927	+	0.0120590i	$0.00383860\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	1.46613	+	6.13307i	0.0865429	+	0.362023i
$288$		0			0
$289$	−8.05511	−	13.9519i	−0.473830	−	0.820698i
$290$		0			0
$291$	−0.809725	−	5.15450i	−0.0474669	−	0.302162i
$292$		0			0
$293$			18.1748i			1.06179i	0.847439	+	0.530893i	$0.178143\pi$
$293$			18.1748i			1.06179i	−0.847439	+	0.530893i	$0.821857\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−0.608108	+	10.8193i	−0.0352860	+	0.627799i
$298$		0			0
$299$	−0.340563	−	0.589873i	−0.0196953	−	0.0341132i
$300$		0			0
$301$	−29.4260	+	7.03438i	−1.69609	+	0.405455i
$302$		0			0
$303$	−20.0104	−	7.71029i	−1.14957	−	0.442944i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−24.6960			−1.40948			−0.704738	−	0.709468i	$-0.748935\pi$
$307$	−24.6960			−1.40948			−0.704738	+	0.709468i	$0.748935\pi$
$308$		0			0
$309$	22.6827	−	18.3208i	1.29038	−	1.04223i
$310$		0			0
$311$	11.5061	−	19.9291i	0.652448	−	1.13007i	−0.330079	−	0.943953i	$-0.607075\pi$
$311$	11.5061	−	19.9291i	0.652448	−	1.13007i	0.982527	−	0.186120i	$-0.0595914\pi$
$312$		0			0
$313$	1.57900	+	2.73490i	0.0892502	+	0.154586i	0.907194	−	0.420712i	$-0.138220\pi$
$313$	1.57900	+	2.73490i	0.0892502	+	0.154586i	−0.817944	+	0.575298i	$0.804886\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	1.60905	+	2.78696i	0.0903734	+	0.156531i	0.907668	−	0.419688i	$-0.137861\pi$
$317$	1.60905	+	2.78696i	0.0903734	+	0.156531i	−0.817295	+	0.576220i	$0.804527\pi$
$318$		0			0
$319$	0.278904	−	0.483076i	0.0156156	−	0.0270471i
$320$		0			0
$321$	−17.2750	+	13.9530i	−0.964199	+	0.778780i
$322$		0			0
$323$	0.507093			0.0282154
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−5.80056	−	2.23503i	−0.320772	−	0.123598i
$328$		0			0
$329$	−22.6770	−	23.9430i	−1.25022	−	1.32002i
$330$		0			0
$331$	−14.0918	−	24.4077i	−0.774554	−	1.34157i	−0.935045	−	0.354529i	$-0.884641\pi$
$331$	−14.0918	−	24.4077i	−0.774554	−	1.34157i	0.160491	−	0.987037i	$-0.448692\pi$
$332$		0			0
$333$	−12.4068	+	13.7093i	−0.679886	+	0.751267i
$334$		0			0
$335$		0			0
$336$		0			0
$337$			18.4497i			1.00502i	0.864571	+	0.502510i	$0.167590\pi$
$337$			18.4497i			1.00502i	−0.864571	+	0.502510i	$0.832410\pi$
$338$		0			0
$339$	0.269741	+	1.71711i	0.0146503	+	0.0932604i
$340$		0			0
$341$	−1.18128	−	2.04604i	−0.0639699	−	0.110799i
$342$		0			0
$343$	11.9869	+	14.1178i	0.647233	+	0.762292i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	7.69997	−	13.3367i	0.413356	−	0.715953i	−0.581898	−	0.813261i	$-0.697690\pi$
$347$	7.69997	−	13.3367i	0.413356	−	0.715953i	0.995254	+	0.0973081i	$0.0310232\pi$
$348$		0			0
$349$			21.9727i			1.17617i	0.808799	+	0.588086i	$0.200118\pi$
$349$			21.9727i			1.17617i	−0.808799	+	0.588086i	$0.799882\pi$
$350$		0			0
$351$	0.575458	+	1.14005i	0.0307157	+	0.0608516i
$352$		0			0
$353$	−15.0083	−	8.66505i	−0.798811	−	0.461194i	0.0442440	−	0.999021i	$-0.485912\pi$
$353$	−15.0083	−	8.66505i	−0.798811	−	0.461194i	−0.843055	+	0.537827i	$0.819245\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	4.28440	+	0.573783i	0.226754	+	0.0303678i
$358$		0			0
$359$	−0.270990	+	0.156456i	−0.0143023	+	0.00825745i	−0.507134	−	0.861867i	$-0.669295\pi$
$359$	−0.270990	+	0.156456i	−0.0143023	+	0.00825745i	0.492832	+	0.870125i	$0.335962\pi$
$360$		0			0
$361$	−9.35550	+	16.2042i	−0.492395	+	0.852853i
$362$		0			0
$363$	8.96158	−	7.23823i	0.470361	−	0.379909i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	1.84807	−	3.20094i	0.0964682	−	0.167088i	−0.813752	−	0.581212i	$-0.802579\pi$
$367$	1.84807	−	3.20094i	0.0964682	−	0.167088i	0.910220	+	0.414124i	$0.135912\pi$
$368$		0			0
$369$	6.80579	−	2.19235i	0.354295	−	0.114129i
$370$		0			0
$371$	−31.7851	−	9.44871i	−1.65020	−	0.490552i
$372$		0			0
$373$	−0.609103	+	0.351666i	−0.0315381	+	0.0182086i	−0.515686	−	0.856778i	$-0.672463\pi$
$373$	−0.609103	+	0.351666i	−0.0315381	+	0.0182086i	0.484148	+	0.874986i	$0.339130\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		−	0.0657372i		−	0.00338564i
$378$		0			0
$379$	10.3929			0.533849			0.266924	−	0.963717i	$-0.413993\pi$
$379$	10.3929			0.533849			0.266924	+	0.963717i	$0.413993\pi$
$380$		0			0
$381$	−13.2795	+	2.08609i	−0.680331	+	0.106874i
$382$		0			0
$383$	−25.5519	+	14.7524i	−1.30564	+	0.753813i	−0.981366	−	0.192150i	$-0.938454\pi$
$383$	−25.5519	+	14.7524i	−1.30564	+	0.753813i	−0.324276	+	0.945963i	$0.605121\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	10.5188	+	32.6537i	0.534698	+	1.65988i
$388$		0			0
$389$	11.5224	+	6.65245i	0.584208	+	0.337293i	0.762804	−	0.646630i	$-0.223822\pi$
$389$	11.5224	+	6.65245i	0.584208	+	0.337293i	−0.178596	+	0.983923i	$0.557155\pi$
$390$		0			0
$391$			2.61420i			0.132206i
$392$		0			0
$393$	−23.1273	+	18.6798i	−1.16662	+	0.942271i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	2.21028	+	3.82832i	0.110931	+	0.192138i	0.916146	−	0.400845i	$-0.131283\pi$
$397$	2.21028	+	3.82832i	0.110931	+	0.192138i	−0.805215	+	0.592983i	$0.797950\pi$
$398$		0			0
$399$	1.50406	−	1.95109i	0.0752971	−	0.0976769i
$400$		0			0
$401$	25.4507	−	14.6940i	1.27095	−	0.733781i	0.295780	−	0.955256i	$-0.404420\pi$
$401$	25.4507	−	14.6940i	1.27095	−	0.733781i	0.975166	+	0.221475i	$0.0710871\pi$
$402$		0			0
$403$	−0.241124	−	0.139213i	−0.0120112	−	0.00693469i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−12.8533			−0.637112
$408$		0			0
$409$	−6.67308	−	3.85270i	−0.329962	−	0.190504i	0.325862	−	0.945417i	$-0.394346\pi$
$409$	−6.67308	−	3.85270i	−0.329962	−	0.190504i	−0.655824	+	0.754913i	$0.727679\pi$
$410$		0			0
$411$	−24.2868	−	9.35804i	−1.19798	−	0.461598i
$412$		0			0
$413$	−31.7251	−	9.43088i	−1.56109	−	0.464063i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	16.8222	−	2.64261i	0.823787	−	0.129409i
$418$		0			0
$419$	1.40692			0.0687327			0.0343663	−	0.999409i	$-0.489059\pi$
$419$	1.40692			0.0687327			0.0343663	+	0.999409i	$0.489059\pi$
$420$		0			0
$421$	−7.23785			−0.352751			−0.176375	−	0.984323i	$-0.556437\pi$
$421$	−7.23785			−0.352751			−0.176375	+	0.984323i	$0.556437\pi$
$422$		0			0
$423$	−25.0908	+	27.7251i	−1.21996	+	1.34804i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−10.4317	−	11.0141i	−0.504825	−	0.533009i
$428$		0			0
$429$	−0.319187	+	0.828384i	−0.0154105	+	0.0399947i
$430$		0			0
$431$	−9.16199	−	5.28968i	−0.441317	−	0.254795i	0.262839	−	0.964840i	$-0.415341\pi$
$431$	−9.16199	−	5.28968i	−0.441317	−	0.254795i	−0.704156	+	0.710045i	$0.748675\pi$
$432$		0			0
$433$	23.7164			1.13974			0.569869	−	0.821735i	$-0.306994\pi$
$433$	23.7164			1.13974			0.569869	+	0.821735i	$0.306994\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	1.29026	+	0.744932i	0.0617215	+	0.0356349i
$438$		0			0
$439$	17.6684	−	10.2009i	0.843268	−	0.486861i	−0.0151058	−	0.999886i	$-0.504809\pi$
$439$	17.6684	−	10.2009i	0.843268	−	0.486861i	0.858374	+	0.513025i	$0.171475\pi$
$440$		0			0
$441$	14.9154	−	14.7828i	0.710256	−	0.703943i
$442$		0			0
$443$	−0.274720	−	0.475830i	−0.0130524	−	0.0226074i	0.859425	−	0.511261i	$-0.170821\pi$
$443$	−0.274720	−	0.475830i	−0.0130524	−	0.0226074i	−0.872478	+	0.488654i	$0.837488\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−25.1203	−	31.1012i	−1.18815	−	1.47104i
$448$		0			0
$449$			1.12469i			0.0530772i	0.999648	+	0.0265386i	$0.00844850\pi$
$449$			1.12469i			0.0530772i	−0.999648	+	0.0265386i	$0.991552\pi$
$450$		0			0
$451$	4.30456	+	2.48524i	0.202694	+	0.117025i
$452$		0			0
$453$	23.2907	+	8.97420i	1.09429	+	0.421645i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	25.4518	−	14.6946i	1.19059	−	0.687385i	0.232146	−	0.972681i	$-0.425425\pi$
$457$	25.4518	−	14.6946i	1.19059	−	0.687385i	0.958439	+	0.285296i	$0.0920919\pi$
$458$		0			0
$459$	0.275055	−	4.89370i	0.0128385	−	0.228418i
$460$		0			0
$461$	−29.9734			−1.39600			−0.697999	−	0.716098i	$-0.745926\pi$
$461$	−29.9734			−1.39600			−0.697999	+	0.716098i	$0.745926\pi$
$462$		0			0
$463$			13.0355i			0.605809i	0.953021	+	0.302905i	$0.0979563\pi$
$463$			13.0355i			0.605809i	−0.953021	+	0.302905i	$0.902044\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	2.10662	−	1.21626i	0.0974828	−	0.0562817i	−0.450466	−	0.892794i	$-0.648742\pi$
$467$	2.10662	−	1.21626i	0.0974828	−	0.0562817i	0.547949	+	0.836512i	$0.315409\pi$
$468$		0			0
$469$	−4.19167	+	14.1006i	−0.193553	+	0.651105i
$470$		0			0
$471$	−3.55411	−	1.36945i	−0.163765	−	0.0631008i
$472$		0			0
$473$	−11.9240	+	20.6530i	−0.548266	+	0.949624i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−7.91023	+	36.7581i	−0.362184	+	1.68304i
$478$		0			0
$479$	−5.49101	+	9.51071i	−0.250891	+	0.434555i	−0.963771	−	0.266730i	$-0.914057\pi$
$479$	−5.49101	+	9.51071i	−0.250891	+	0.434555i	0.712881	+	0.701285i	$0.247390\pi$
$480$		0			0
$481$	−1.31181	+	0.757373i	−0.0598133	+	0.0345332i
$482$		0			0
$483$	10.0584	+	7.75383i	0.457674	+	0.352812i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	23.2776	+	13.4393i	1.05481	+	0.608993i	0.923991	−	0.382414i	$-0.124907\pi$
$487$	23.2776	+	13.4393i	1.05481	+	0.608993i	0.130816	+	0.991407i	$0.458240\pi$
$488$		0			0
$489$	10.7255	+	13.2791i	0.485024	+	0.600503i
$490$		0			0
$491$			25.1295i			1.13408i	0.823692	+	0.567038i	$0.191911\pi$
$491$			25.1295i			1.13408i	−0.823692	+	0.567038i	$0.808089\pi$
$492$		0			0
$493$	−0.126152	+	0.218501i	−0.00568159	+	0.00984080i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	26.0863	−	6.23602i	1.17013	−	0.279724i
$498$		0			0
$499$	2.58341	+	4.47460i	0.115649	+	0.200311i	0.918039	−	0.396490i	$-0.129772\pi$
$499$	2.58341	+	4.47460i	0.115649	+	0.200311i	−0.802390	+	0.596800i	$0.796438\pi$
$500$		0			0
$501$	39.0720	−	6.13785i	1.74561	−	0.274219i
$502$		0			0
$503$		−	42.2496i		−	1.88382i	−0.335872	−	0.941908i	$-0.609031\pi$
$503$		−	42.2496i		−	1.88382i	0.335872	−	0.941908i	$-0.390969\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−3.47807	−	22.1405i	−0.154466	−	0.983295i
$508$		0			0
$509$	3.76320	+	6.51806i	0.166801	+	0.288908i	0.937293	−	0.348541i	$-0.113323\pi$
$509$	3.76320	+	6.51806i	0.166801	+	0.288908i	−0.770492	+	0.637449i	$0.779990\pi$
$510$		0			0
$511$	−33.3130	−	9.90290i	−1.47368	−	0.438079i
$512$		0			0
$513$	−2.33694	−	1.53024i	−0.103179	−	0.0675619i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−25.9938			−1.14320
$518$		0			0
$519$	10.6020	+	13.1263i	0.465378	+	0.576180i
$520$		0			0
$521$	10.1668	−	17.6095i	0.445417	−	0.771484i	−0.552665	−	0.833404i	$-0.686389\pi$
$521$	10.1668	−	17.6095i	0.445417	−	0.771484i	0.998081	+	0.0619196i	$0.0197222\pi$
$522$		0			0
$523$	1.81768	+	3.14832i	0.0794818	+	0.137666i	0.903026	−	0.429585i	$-0.141340\pi$
$523$	1.81768	+	3.14832i	0.0794818	+	0.137666i	−0.823545	+	0.567251i	$0.808007\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	0.534308	+	0.925448i	0.0232748	+	0.0403131i
$528$		0			0
$529$	7.65967	−	13.2669i	0.333029	−	0.576823i
$530$		0			0
$531$	−7.89530	+	36.6888i	−0.342627	+	1.59216i
$532$		0			0
$533$	0.585766			0.0253724
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−11.2569	+	29.2149i	−0.485770	+	1.26071i
$538$		0			0
$539$	14.5767	+	0.792285i	0.627863	+	0.0341261i
$540$		0			0
$541$	−9.20758	−	15.9480i	−0.395865	−	0.685658i	0.597346	−	0.801983i	$-0.296222\pi$
$541$	−9.20758	−	15.9480i	−0.395865	−	0.685658i	−0.993211	+	0.116325i	$0.962888\pi$
$542$		0			0
$543$	−30.3252	+	4.76381i	−1.30138	+	0.204434i
$544$		0			0
$545$		0			0
$546$		0			0
$547$			22.6376i			0.967915i	0.875092	+	0.483957i	$0.160801\pi$
$547$			22.6376i			0.967915i	−0.875092	+	0.483957i	$0.839199\pi$
$548$		0			0
$549$	−11.5421	+	12.7539i	−0.492605	+	0.544323i
$550$		0			0
$551$	0.0718953	+	0.124526i	0.00306284	+	0.00530500i
$552$		0			0
$553$	−12.1907	+	11.5461i	−0.518403	+	0.490992i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−19.5879	+	33.9272i	−0.829965	+	1.43754i	0.0680994	+	0.997679i	$0.478307\pi$
$557$	−19.5879	+	33.9272i	−0.829965	+	1.43754i	−0.898065	+	0.439863i	$0.855027\pi$
$558$		0			0
$559$			2.81047i			0.118870i
$560$		0			0
$561$	2.65063	−	2.14090i	0.111910	−	0.0903889i
$562$		0			0
$563$	3.16069	+	1.82483i	0.133207	+	0.0769073i	0.565123	−	0.825007i	$-0.308829\pi$
$563$	3.16069	+	1.82483i	0.133207	+	0.0769073i	−0.431915	+	0.901914i	$0.642162\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−18.0132	−	15.5732i	−0.756483	−	0.654013i
$568$		0			0
$569$	17.1456	−	9.89902i	0.718781	−	0.414988i	−0.0955229	−	0.995427i	$-0.530452\pi$
$569$	17.1456	−	9.89902i	0.718781	−	0.414988i	0.814304	+	0.580439i	$0.197119\pi$
$570$		0			0
$571$	−18.7342	+	32.4487i	−0.784004	+	1.35793i	0.145589	+	0.989345i	$0.453492\pi$
$571$	−18.7342	+	32.4487i	−0.784004	+	1.35793i	−0.929592	+	0.368589i	$0.879841\pi$
$572$		0			0
$573$	23.9213	+	29.6167i	0.999326	+	1.23725i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	12.7684	−	22.1156i	0.531558	−	0.920685i	−0.467764	−	0.883853i	$-0.654940\pi$
$577$	12.7684	−	22.1156i	0.531558	−	0.920685i	0.999322	−	0.0368312i	$-0.0117264\pi$
$578$		0			0
$579$	−5.59007	+	14.5079i	−0.232315	+	0.602926i
$580$		0			0
$581$	2.74498	−	0.656198i	0.113881	−	0.0272237i
$582$		0			0
$583$	−22.6357	+	13.0687i	−0.937476	+	0.541252i
$584$		0			0
$585$		0			0
$586$		0			0
$587$			7.57204i			0.312531i	0.987715	+	0.156266i	$0.0499456\pi$
$587$			7.57204i			0.312531i	−0.987715	+	0.156266i	$0.950054\pi$
$588$		0			0
$589$	0.609016			0.0250941
$590$		0			0
$591$	−5.99412	−	38.1571i	−0.246565	−	1.56957i
$592$		0			0
$593$	2.75258	−	1.58920i	0.113035	−	0.0652606i	−0.442417	−	0.896810i	$-0.645879\pi$
$593$	2.75258	−	1.58920i	0.113035	−	0.0652606i	0.555452	+	0.831549i	$0.312545\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	11.7792	−	30.5706i	0.482092	−	1.25117i
$598$		0			0
$599$	−23.5750	−	13.6110i	−0.963247	−	0.556131i	−0.0660761	−	0.997815i	$-0.521048\pi$
$599$	−23.5750	−	13.6110i	−0.963247	−	0.556131i	−0.897171	+	0.441684i	$0.854381\pi$
$600$		0			0
$601$		−	13.1953i		−	0.538247i	−0.963106	−	0.269123i	$-0.913266\pi$
$601$		−	13.1953i		−	0.538247i	0.963106	−	0.269123i	$-0.0867340\pi$
$602$		0			0
$603$	16.3068	+	3.50916i	0.664063	+	0.142904i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	3.85023	+	6.66879i	0.156276	+	0.270678i	0.933523	−	0.358518i	$-0.116718\pi$
$607$	3.85023	+	6.66879i	0.156276	+	0.270678i	−0.777247	+	0.629196i	$0.783384\pi$
$608$		0			0
$609$	0.466535	+	1.13347i	0.0189050	+	0.0459303i
$610$		0			0
$611$	−2.65294	+	1.53167i	−0.107326	+	0.0619649i
$612$		0			0
$613$	24.9912	+	14.4287i	1.00939	+	0.582769i	0.911012	−	0.412381i	$-0.135303\pi$
$613$	24.9912	+	14.4287i	1.00939	+	0.582769i	0.0983735	+	0.995150i	$0.468636\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−31.5272			−1.26924			−0.634619	−	0.772825i	$-0.718843\pi$
$617$	−31.5272			−1.26924			−0.634619	+	0.772825i	$0.718843\pi$
$618$		0			0
$619$	−25.4695	−	14.7048i	−1.02370	−	0.591036i	−0.108530	−	0.994093i	$-0.534614\pi$
$619$	−25.4695	−	14.7048i	−1.02370	−	0.591036i	−0.915175	+	0.403057i	$0.867948\pi$
$620$		0			0
$621$	7.88882	−	12.0476i	0.316567	−	0.483453i
$622$		0			0
$623$	1.78180	−	1.68758i	0.0713863	−	0.0676116i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−0.301347	−	1.91830i	−0.0120346	−	0.0766095i
$628$		0			0
$629$	5.81369			0.231807
$630$		0			0
$631$	29.9987			1.19423			0.597115	−	0.802155i	$-0.296313\pi$
$631$	29.9987			1.19423			0.597115	+	0.802155i	$0.296313\pi$
$632$		0			0
$633$	5.48747	+	34.9319i	0.218107	+	1.38842i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	1.53439	−	0.778065i	0.0607947	−	0.0308281i
$638$		0			0
$639$	−9.32494	−	28.9477i	−0.368889	−	1.14515i
$640$		0			0
$641$	27.8245	+	16.0645i	1.09900	+	0.634510i	0.935959	−	0.352109i	$-0.114535\pi$
$641$	27.8245	+	16.0645i	1.09900	+	0.634510i	0.163044	+	0.986619i	$0.447869\pi$
$642$		0			0
$643$	−5.88352			−0.232024			−0.116012	−	0.993248i	$-0.537011\pi$
$643$	−5.88352			−0.232024			−0.116012	+	0.993248i	$0.537011\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−17.3067	−	9.99202i	−0.680396	−	0.392827i	0.119608	−	0.992821i	$-0.461836\pi$
$647$	−17.3067	−	9.99202i	−0.680396	−	0.392827i	−0.800004	+	0.599994i	$0.795170\pi$
$648$		0			0
$649$	−22.5930	+	13.0441i	−0.886854	+	0.512025i
$650$		0			0
$651$	5.14554	+	0.689111i	0.201669	+	0.0270084i
$652$		0			0
$653$	−1.26856	−	2.19720i	−0.0496424	−	0.0859832i	0.840136	−	0.542375i	$-0.182475\pi$
$653$	−1.26856	−	2.19720i	−0.0496424	−	0.0859832i	−0.889779	+	0.456392i	$0.849142\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−8.29047	+	38.5251i	−0.323442	+	1.50301i
$658$		0			0
$659$			28.5964i			1.11396i	0.830526	+	0.556979i	$0.188040\pi$
$659$			28.5964i			1.11396i	−0.830526	+	0.556979i	$0.811960\pi$
$660$		0			0
$661$	25.4569	+	14.6975i	0.990158	+	0.571668i	0.905321	−	0.424727i	$-0.139630\pi$
$661$	25.4569	+	14.6975i	0.990158	+	0.571668i	0.0848363	+	0.996395i	$0.472963\pi$
$662$		0			0
$663$	0.144372	−	0.374688i	0.00560696	−	0.0145517i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−0.641967	+	0.370640i	−0.0248571	+	0.0143512i
$668$		0			0
$669$	−3.65420	−	23.2617i	−0.141279	−	0.899350i
$670$		0			0
$671$	−11.9575			−0.461613
$672$		0			0
$673$		−	18.1428i		−	0.699354i	−0.936870	−	0.349677i	$-0.886291\pi$
$673$		−	18.1428i		−	0.699354i	0.936870	−	0.349677i	$-0.113709\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−33.3630	+	19.2622i	−1.28225	+	0.740305i	−0.977259	−	0.212051i	$-0.931986\pi$
$677$	−33.3630	+	19.2622i	−1.28225	+	0.740305i	−0.304987	+	0.952356i	$0.598652\pi$
$678$		0			0
$679$	1.85309	+	7.75178i	0.0711150	+	0.297486i
$680$		0			0
$681$	6.26812	−	16.2676i	0.240195	−	0.623376i
$682$		0			0
$683$	4.75897	−	8.24278i	0.182097	−	0.315401i	−0.760497	−	0.649341i	$-0.775045\pi$
$683$	4.75897	−	8.24278i	0.182097	−	0.315401i	0.942594	+	0.333940i	$0.108378\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−15.5389	−	19.2385i	−0.592846	−	0.733996i
$688$		0			0
$689$	−1.54014	+	2.66760i	−0.0586747	+	0.101628i
$690$		0			0
$691$	36.4810	−	21.0623i	1.38780	−	0.801248i	0.394734	−	0.918795i	$-0.370837\pi$
$691$	36.4810	−	21.0623i	1.38780	−	0.801248i	0.993067	+	0.117548i	$0.0375033\pi$
$692$		0			0
$693$	−0.375477	−	16.5486i	−0.0142632	−	0.628628i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−1.94700	−	1.12410i	−0.0737481	−	0.0425785i
$698$		0			0
$699$	−27.9617	+	22.5846i	−1.05761	+	0.854226i
$700$		0			0
$701$			20.1103i			0.759555i	0.925078	+	0.379778i	$0.123999\pi$
$701$			20.1103i			0.759555i	−0.925078	+	0.379778i	$0.876001\pi$
$702$		0			0
$703$	1.65664	−	2.86939i	0.0624815	−	0.108221i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	31.3990	+	9.33395i	1.18088	+	0.351039i
$708$		0			0
$709$	−12.6523	−	21.9145i	−0.475168	−	0.823015i	0.524427	−	0.851455i	$-0.324279\pi$
$709$	−12.6523	−	21.9145i	−0.475168	−	0.823015i	−0.999596	+	0.0284398i	$0.990946\pi$
$710$		0			0
$711$	14.1164	+	12.7752i	0.529407	+	0.479106i
$712$		0			0
$713$			3.13964i			0.117581i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−8.32300	+	1.30747i	−0.310828	+	0.0488282i
$718$		0			0
$719$	−7.70568	−	13.3466i	−0.287373	−	0.497745i	0.685809	−	0.727782i	$-0.259449\pi$
$719$	−7.70568	−	13.3466i	−0.287373	−	0.497745i	−0.973182	+	0.230037i	$0.926115\pi$
$720$		0			0
$721$	−32.3370	+	30.6271i	−1.20429	+	1.14061i
$722$		0			0
$723$	10.7317	−	27.8519i	0.399116	−	1.03582i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−17.2053			−0.638109			−0.319054	−	0.947736i	$-0.603365\pi$
$727$	−17.2053			−0.638109			−0.319054	+	0.947736i	$0.603365\pi$
$728$		0			0
$729$	−16.0352	+	21.7226i	−0.593896	+	0.804542i
$730$		0			0
$731$	5.39337	−	9.34159i	0.199481	−	0.345511i
$732$		0			0
$733$	−2.43611	−	4.21946i	−0.0899797	−	0.155849i	0.817523	−	0.575896i	$-0.195347\pi$
$733$	−2.43611	−	4.21946i	−0.0899797	−	0.155849i	−0.907502	+	0.420047i	$0.862014\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	5.79760	+	10.0417i	0.213557	+	0.369892i
$738$		0			0
$739$	11.2489	−	19.4836i	0.413796	−	0.716716i	−0.581505	−	0.813543i	$-0.697536\pi$
$739$	11.2489	−	19.4836i	0.413796	−	0.716716i	0.995301	+	0.0968269i	$0.0308693\pi$
$740$		0			0
$741$	−0.143791	−	0.178026i	−0.00528228	−	0.00653993i
$742$		0			0
$743$	5.74923			0.210919			0.105459	−	0.994424i	$-0.466369\pi$
$743$	5.74923			0.210919			0.105459	+	0.994424i	$0.466369\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−0.981235	−	3.04608i	−0.0359015	−	0.111450i
$748$		0			0
$749$	24.6277	−	23.3254i	0.899875	−	0.852292i
$750$		0			0
$751$	−13.4867	−	23.3597i	−0.492138	−	0.852409i	0.507821	−	0.861463i	$-0.330451\pi$
$751$	−13.4867	−	23.3597i	−0.492138	−	0.852409i	−0.999959	+	0.00905407i	$0.997118\pi$
$752$		0			0
$753$	−4.25435	−	27.0821i	−0.155037	−	0.986928i
$754$		0			0
$755$		0			0
$756$		0			0
$757$			3.74640i			0.136165i	0.997680	+	0.0680826i	$0.0216882\pi$
$757$			3.74640i			0.136165i	−0.997680	+	0.0680826i	$0.978312\pi$
$758$		0			0
$759$	9.88936	−	1.55353i	0.358961	−	0.0563894i
$760$		0			0
$761$	9.03998	+	15.6577i	0.327699	+	0.567591i	0.982055	−	0.188595i	$-0.0603935\pi$
$761$	9.03998	+	15.6577i	0.327699	+	0.567591i	−0.654356	+	0.756187i	$0.727060\pi$
$762$		0			0
$763$	9.10184	+	2.70569i	0.329509	+	0.0979527i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−1.53724	+	2.66257i	−0.0555064	+	0.0961398i
$768$		0			0
$769$			25.1297i			0.906199i	0.891460	+	0.453100i	$0.149682\pi$
$769$			25.1297i			0.906199i	−0.891460	+	0.453100i	$0.850318\pi$
$770$		0			0
$771$	19.8247	+	24.5448i	0.713971	+	0.883959i
$772$		0			0
$773$	28.2467	+	16.3082i	1.01596	+	0.586567i	0.912932	−	0.408112i	$-0.133813\pi$
$773$	28.2467	+	16.3082i	1.01596	+	0.586567i	0.103031	+	0.994678i	$0.467146\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	17.2436	−	22.3688i	0.618612	−	0.802475i
$778$		0			0
$779$	−1.10962	+	0.640639i	−0.0397563	+	0.0229533i
$780$		0			0
$781$	10.5707	−	18.3090i	0.378249	−	0.655146i
$782$		0			0
$783$	1.24074	−	0.626280i	0.0443403	−	0.0223814i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	2.30085	−	3.98518i	0.0820164	−	0.142056i	−0.822100	−	0.569344i	$-0.807197\pi$
$787$	2.30085	−	3.98518i	0.0820164	−	0.142056i	0.904116	+	0.427287i	$0.140531\pi$
$788$		0			0
$789$	8.50958	+	3.27885i	0.302949	+	0.116730i
$790$		0			0
$791$	−0.617314	−	2.58233i	−0.0219492	−	0.0918170i
$792$		0			0
$793$	−1.22038	+	0.704590i	−0.0433371	+	0.0250207i
$794$		0			0
$795$		0			0
$796$		0			0
$797$		−	13.3722i		−	0.473666i	−0.971550	−	0.236833i	$-0.923891\pi$
$797$		−	13.3722i		−	0.473666i	0.971550	−	0.236833i	$-0.0761094\pi$
$798$		0			0
$799$	11.7573			0.415944
$800$		0			0
$801$	−2.06326	−	1.86722i	−0.0729016	−	0.0659749i
$802$		0			0
$803$	−23.7238	+	13.6970i	−0.837196	+	0.483355i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−2.50650	−	0.965786i	−0.0882329	−	0.0339973i
$808$		0			0
$809$	20.3694	+	11.7603i	0.716152	+	0.413470i	0.813335	−	0.581796i	$-0.197650\pi$
$809$	20.3694	+	11.7603i	0.716152	+	0.413470i	−0.0971830	+	0.995267i	$0.530983\pi$
$810$		0			0
$811$			25.5058i			0.895628i	0.894127	+	0.447814i	$0.147797\pi$
$811$			25.5058i			0.895628i	−0.894127	+	0.447814i	$0.852203\pi$
$812$		0			0
$813$	−12.2862	−	15.2115i	−0.430897	−	0.533489i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−3.07374	−	5.32388i	−0.107537	−	0.186259i
$818$		0			0
$819$	−1.01344	−	1.66683i	−0.0354124	−	0.0582437i
$820$		0			0
$821$	−1.50477	+	0.868778i	−0.0525167	+	0.0303205i	−0.526028	−	0.850467i	$-0.676319\pi$
$821$	−1.50477	+	0.868778i	−0.0525167	+	0.0303205i	0.473512	+	0.880788i	$0.342986\pi$
$822$		0			0
$823$	−0.173518	−	0.100180i	−0.00604844	−	0.00349207i	0.496973	−	0.867766i	$-0.334445\pi$
$823$	−0.173518	−	0.100180i	−0.00604844	−	0.00349207i	−0.503021	+	0.864274i	$0.667778\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	21.7179			0.755207			0.377603	−	0.925967i	$-0.376748\pi$
$827$	21.7179			0.755207			0.377603	+	0.925967i	$0.376748\pi$
$828$		0			0
$829$	22.5419	+	13.0146i	0.782913	+	0.452015i	0.837462	−	0.546496i	$-0.184039\pi$
$829$	22.5419	+	13.0146i	0.782913	+	0.452015i	−0.0545485	+	0.998511i	$0.517372\pi$
$830$		0			0
$831$	−10.6412	+	27.6171i	−0.369140	+	0.958027i
$832$		0			0
$833$	−6.59322	−	0.358360i	−0.228442	−	0.0124165i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	0.330339	−	5.87730i	0.0114182	−	0.203149i
$838$		0			0
$839$	−2.46944			−0.0852546			−0.0426273	−	0.999091i	$-0.513573\pi$
$839$	−2.46944			−0.0852546			−0.0426273	+	0.999091i	$0.513573\pi$
$840$		0			0
$841$	28.9285			0.997533
$842$		0			0
$843$	26.0405	−	4.09072i	0.896881	−	0.140892i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−12.7758	+	12.1003i	−0.438982	+	0.415770i
$848$		0			0
$849$	26.6192	+	10.2567i	0.913569	+	0.352010i
$850$		0			0
$851$	14.7925	+	8.54045i	0.507080	+	0.292763i
$852$		0			0
$853$	−30.3776			−1.04011			−0.520055	−	0.854133i	$-0.674088\pi$
$853$	−30.3776			−1.04011			−0.520055	+	0.854133i	$0.674088\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	44.7601	+	25.8422i	1.52898	+	0.882754i	0.999405	+	0.0344882i	$0.0109801\pi$
$857$	44.7601	+	25.8422i	1.52898	+	0.882754i	0.529570	+	0.848266i	$0.322353\pi$
$858$		0			0
$859$	21.0239	−	12.1381i	0.717326	−	0.414148i	−0.0964418	−	0.995339i	$-0.530746\pi$
$859$	21.0239	−	12.1381i	0.717326	−	0.414148i	0.813768	+	0.581190i	$0.197413\pi$
$860$		0			0
$861$	−10.1000	+	4.15717i	−0.344207	+	0.141676i
$862$		0			0
$863$	−22.7263	−	39.3631i	−0.773611	−	1.33993i	−0.935572	−	0.353137i	$-0.885115\pi$
$863$	−22.7263	−	39.3631i	−0.773611	−	1.33993i	0.161960	−	0.986797i	$-0.448218\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	21.7074	−	17.5330i	0.737223	−	0.595452i
$868$		0			0
$869$			13.2349i			0.448964i
$870$		0			0
$871$	1.18341	+	0.683243i	0.0400984	+	0.0231508i
$872$		0			0
$873$	8.60205	−	2.77099i	0.291135	−	0.0937837i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−21.9817	+	12.6911i	−0.742268	+	0.428549i	−0.822893	−	0.568196i	$-0.807642\pi$
$877$	−21.9817	+	12.6911i	−0.742268	+	0.428549i	0.0806254	+	0.996744i	$0.474308\pi$
$878$		0			0
$879$	−31.0984	+	4.88527i	−1.04892	+	0.164776i
$880$		0			0
$881$	−42.5616			−1.43394			−0.716969	−	0.697105i	$-0.754471\pi$
$881$	−42.5616			−1.43394			−0.716969	+	0.697105i	$0.754471\pi$
$882$		0			0
$883$		−	6.16214i		−	0.207372i	−0.994610	−	0.103686i	$-0.966936\pi$
$883$		−	6.16214i		−	0.207372i	0.994610	−	0.103686i	$-0.0330638\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−6.71032	+	3.87420i	−0.225310	+	0.130083i	−0.608407	−	0.793625i	$-0.708191\pi$
$887$	−6.71032	+	3.87420i	−0.225310	+	0.130083i	0.383096	+	0.923708i	$0.374858\pi$
$888$		0			0
$889$	19.9709	−	4.77410i	0.669802	−	0.160118i
$890$		0			0
$891$	−18.6760	+	1.86763i	−0.625669	+	0.0625680i
$892$		0			0
$893$	3.35031	−	5.80291i	0.112114	−	0.194187i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	0.917771	−	0.741280i	0.0306435	−	0.0247506i
$898$		0			0
$899$	−0.151507	+	0.262419i	−0.00505306	+	0.00875215i
$900$		0			0
$901$	10.2384	−	5.91116i	0.341091	−	0.196929i
$902$		0			0
$903$	−19.9458	−	48.4591i	−0.663755	−	1.61262i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	39.3584	+	22.7236i	1.30687	+	0.754524i	0.981573	−	0.191087i	$-0.0612012\pi$
$907$	39.3584	+	22.7236i	1.30687	+	0.754524i	0.325300	+	0.945611i	$0.394535\pi$
$908$		0			0
$909$	7.81416	−	36.3117i	0.259179	−	1.20438i
$910$		0			0
$911$			35.7765i			1.18533i	0.805449	+	0.592665i	$0.201924\pi$
$911$			35.7765i			1.18533i	−0.805449	+	0.592665i	$0.798076\pi$
$912$		0			0
$913$	1.11232	−	1.92660i	0.0368124	−	0.0637610i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	32.9707	−	31.2273i	1.08879	−	1.03122i
$918$		0			0
$919$	14.4006	+	24.9427i	0.475034	+	0.822782i	0.999591	−	0.0285927i	$-0.00910257\pi$
$919$	14.4006	+	24.9427i	0.475034	+	0.822782i	−0.524558	+	0.851375i	$0.675769\pi$
$920$		0			0
$921$	−6.63811	−	42.2565i	−0.218733	−	1.39240i
$922$		0			0
$923$		−	2.49149i		−	0.0820085i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	37.4450	+	33.8872i	1.22986	+	1.11300i
$928$		0			0
$929$	−15.9490	−	27.6244i	−0.523269	−	0.906329i	−0.999633	−	0.0270805i	$-0.991379\pi$
$929$	−15.9490	−	27.6244i	−0.523269	−	0.906329i	0.476364	−	0.879248i	$-0.341954\pi$
$930$		0			0
$931$	−2.05565	+	3.15202i	−0.0673711	+	0.103303i
$932$		0			0
$933$	37.1927	+	14.3308i	1.21763	+	0.469171i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−36.5715			−1.19474			−0.597370	−	0.801966i	$-0.703787\pi$
$937$	−36.5715			−1.19474			−0.597370	+	0.801966i	$0.703787\pi$
$938$		0			0
$939$	−4.25518	+	3.43689i	−0.138863	+	0.112159i
$940$		0			0
$941$	−11.5675	+	20.0355i	−0.377091	+	0.653140i	−0.990638	−	0.136518i	$-0.956409\pi$
$941$	−11.5675	+	20.0355i	−0.377091	+	0.653140i	0.613547	+	0.789658i	$0.289742\pi$
$942$		0			0
$943$	−3.30267	−	5.72040i	−0.107550	−	0.186282i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−17.0247	−	29.4876i	−0.553228	−	0.958220i	−0.998039	−	0.0625952i	$-0.980062\pi$
$947$	−17.0247	−	29.4876i	−0.553228	−	0.958220i	0.444811	−	0.895625i	$-0.353271\pi$
$948$		0			0
$949$	−1.61418	+	2.79583i	−0.0523984	+	0.0907566i
$950$		0			0
$951$	−4.33618	+	3.50231i	−0.140610	+	0.113570i
$952$		0			0
$953$	4.08410			0.132297			0.0661485	−	0.997810i	$-0.478929\pi$
$953$	4.08410			0.132297			0.0661485	+	0.997810i	$0.478929\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	0.901542	+	0.347376i	0.0291427	+	0.0112291i
$958$		0			0
$959$	38.1093	+	11.3287i	1.23061	+	0.365822i
$960$		0			0
$961$	−14.8583	−	25.7353i	−0.479300	−	0.830172i
$962$		0			0
$963$	−28.5179	−	25.8083i	−0.918976	−	0.831661i
$964$		0			0
$965$		0			0
$966$		0			0
$967$			8.66642i			0.278693i	0.990244	+	0.139347i	$0.0445002\pi$
$967$			8.66642i			0.278693i	−0.990244	+	0.139347i	$0.955500\pi$
$968$		0			0
$969$	0.136303	+	0.867670i	0.00437868	+	0.0278736i
$970$		0			0
$971$	−9.79452	−	16.9646i	−0.314321	−	0.544420i	0.664972	−	0.746868i	$-0.268444\pi$
$971$	−9.79452	−	16.9646i	−0.314321	−	0.544420i	−0.979293	+	0.202448i	$0.935110\pi$
$972$		0			0
$973$	−25.2986	+	6.04772i	−0.811037	+	0.193881i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	15.3022	−	26.5041i	0.489559	−	0.847942i	−0.510368	−	0.859956i	$-0.670491\pi$
$977$	15.3022	−	26.5041i	0.489559	−	0.847942i	0.999928	+	0.0120141i	$0.00382430\pi$
$978$		0			0
$979$		−	1.93442i		−	0.0618242i
$980$		0			0
$981$	2.26514	−	10.5259i	0.0723204	−	0.336066i
$982$		0			0
$983$	24.4405	+	14.1107i	0.779532	+	0.450063i	0.836264	−	0.548327i	$-0.184735\pi$
$983$	24.4405	+	14.1107i	0.779532	+	0.450063i	−0.0567327	+	0.998389i	$0.518068\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	34.8726	−	45.2375i	1.11001	−	1.43992i
$988$		0			0
$989$	27.4460	−	15.8460i	0.872734	−	0.503873i
$990$		0			0
$991$	12.2999	−	21.3040i	0.390719	−	0.676745i	−0.601826	−	0.798628i	$-0.705560\pi$
$991$	12.2999	−	21.3040i	0.390719	−	0.676745i	0.992545	+	0.121882i	$0.0388931\pi$
$992$		0			0
$993$	37.9754	−	30.6726i	1.20511	−	0.973364i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	27.8892	−	48.3054i	0.883258	−	1.52985i	0.0355613	−	0.999367i	$-0.488678\pi$
$997$	27.8892	−	48.3054i	0.883258	−	1.52985i	0.847697	−	0.530481i	$-0.177989\pi$
$998$		0			0
$999$	−26.7924	−	17.5438i	−0.847675	−	0.555062i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2100.2.bo.h.1949.6		20
3.2	odd	2		2100.2.bo.g.1949.1		20
5.2	odd	4		420.2.bh.a.101.5	✓	10
5.3	odd	4		2100.2.bi.k.101.1		10
5.4	even	2	inner	2100.2.bo.h.1949.5		20
7.5	odd	6		2100.2.bo.g.1349.10		20
15.2	even	4		420.2.bh.b.101.3	yes	10
15.8	even	4		2100.2.bi.j.101.3		10
15.14	odd	2		2100.2.bo.g.1949.10		20
21.5	even	6	inner	2100.2.bo.h.1349.5		20
35.12	even	12		420.2.bh.b.341.3	yes	10
35.17	even	12		2940.2.d.a.881.8		10
35.19	odd	6		2100.2.bo.g.1349.1		20
35.32	odd	12		2940.2.d.b.881.3		10
35.33	even	12		2100.2.bi.j.1601.3		10
105.17	odd	12		2940.2.d.b.881.4		10
105.32	even	12		2940.2.d.a.881.7		10
105.47	odd	12		420.2.bh.a.341.5	yes	10
105.68	odd	12		2100.2.bi.k.1601.1		10
105.89	even	6	inner	2100.2.bo.h.1349.6		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
420.2.bh.a.101.5	✓	10	5.2	odd	4
420.2.bh.a.341.5	yes	10	105.47	odd	12
420.2.bh.b.101.3	yes	10	15.2	even	4
420.2.bh.b.341.3	yes	10	35.12	even	12
2100.2.bi.j.101.3		10	15.8	even	4
2100.2.bi.j.1601.3		10	35.33	even	12
2100.2.bi.k.101.1		10	5.3	odd	4
2100.2.bi.k.1601.1		10	105.68	odd	12
2100.2.bo.g.1349.1		20	35.19	odd	6
2100.2.bo.g.1349.10		20	7.5	odd	6
2100.2.bo.g.1949.1		20	3.2	odd	2
2100.2.bo.g.1949.10		20	15.14	odd	2
2100.2.bo.h.1349.5		20	21.5	even	6	inner
2100.2.bo.h.1349.6		20	105.89	even	6	inner
2100.2.bo.h.1949.5		20	5.4	even	2	inner
2100.2.bo.h.1949.6		20	1.1	even	1	trivial
2940.2.d.a.881.7		10	105.32	even	12
2940.2.d.a.881.8		10	35.17	even	12
2940.2.d.b.881.3		10	35.32	odd	12
2940.2.d.b.881.4		10	105.17	odd	12

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.bo (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.268793 + 1.71107i) q^{3} +(-0.615143 - 2.57325i) q^{7} +(-2.85550 + 0.919845i) q^{9} +O(q^{10})\)	\(q+(0.268793 + 1.71107i) q^{3} +(-0.615143 - 2.57325i) q^{7} +(-2.85550 + 0.919845i) q^{9} +(-1.80606 - 1.04273i) q^{11} -0.245770 q^{13} +(0.816904 + 0.471640i) q^{17} +(0.465563 - 0.268793i) q^{19} +(4.23765 - 1.74422i) q^{21} +(1.38570 + 2.40010i) q^{23} +(-2.34145 - 4.63871i) q^{27} +0.267475i q^{29} +(0.981097 + 0.566436i) q^{31} +(1.29872 - 3.37057i) q^{33} +(5.33755 - 3.08164i) q^{37} +(-0.0660611 - 0.420528i) q^{39} -2.38340 q^{41} -11.4354i q^{43} +(10.7944 - 6.23215i) q^{47} +(-6.24320 + 3.16583i) q^{49} +(-0.587429 + 1.52455i) q^{51} +(6.26660 - 10.8541i) q^{53} +(0.585062 + 0.724359i) q^{57} +(6.25478 - 10.8336i) q^{59} +(4.96556 - 2.86687i) q^{61} +(4.12353 + 6.78207i) q^{63} +(-4.81512 - 2.78001i) q^{67} +(-3.73427 + 3.01616i) q^{69} +10.1375i q^{71} +(6.56784 - 11.3758i) q^{73} +(-1.57221 + 5.28887i) q^{77} +(-3.17314 - 5.49605i) q^{79} +(7.30777 - 5.25324i) q^{81} +1.06674i q^{83} +(-0.457667 + 0.0718953i) q^{87} +(0.463787 + 0.803302i) q^{89} +(0.151184 + 0.632426i) q^{91} +(-0.705499 + 1.83098i) q^{93} -3.01245 q^{97} +(6.11636 + 1.31622i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 6 q^{9}+O(q^{10}) \) 20 * q + 6 * q^9	\( 20 q + 6 q^{9} - 12 q^{11} - 6 q^{19} + 20 q^{21} + 30 q^{31} - 30 q^{39} - 16 q^{41} + 26 q^{49} - 88 q^{51} + 84 q^{61} + 28 q^{69} - 2 q^{79} + 82 q^{81} - 56 q^{89} - 22 q^{91} - 72 q^{99}+O(q^{100}) \) 20 * q + 6 * q^9 - 12 * q^11 - 6 * q^19 + 20 * q^21 + 30 * q^31 - 30 * q^39 - 16 * q^41 + 26 * q^49 - 88 * q^51 + 84 * q^61 + 28 * q^69 - 2 * q^79 + 82 * q^81 - 56 * q^89 - 22 * q^91 - 72 * q^99

Introduction

L-functions

Modular forms

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