LMFDB - Embedded newform 2100.2.bo.g.1949.1

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:	$\Z[a_1, \ldots, a_{13}]$
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			1949.1
Root			$0.268793 + 1.71107i$ of defining polynomial
Character	$\chi$	$=$	2100.1949
Dual form			2100.2.bo.g.1349.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.61622 + 0.622752i) q^{3} +(-0.615143 - 2.57325i) q^{7} +(2.22436 - 2.01301i) q^{9} +O(q^{10})$	\(q+(-1.61622 + 0.622752i) q^{3} +(-0.615143 - 2.57325i) q^{7} +(2.22436 - 2.01301i) q^{9} +(1.80606 + 1.04273i) q^{11} -0.245770 q^{13} +(-0.816904 - 0.471640i) q^{17} +(0.465563 - 0.268793i) q^{19} +(2.59670 + 3.77586i) q^{21} +(-1.38570 - 2.40010i) q^{23} +(-2.34145 + 4.63871i) q^{27} -0.267475i q^{29} +(0.981097 + 0.566436i) q^{31} +(-3.56836 - 0.560556i) q^{33} +(5.33755 - 3.08164i) q^{37} +(0.397219 - 0.153054i) q^{39} +2.38340 q^{41} -11.4354i q^{43} +(-10.7944 + 6.23215i) q^{47} +(-6.24320 + 3.16583i) q^{49} +(1.61401 + 0.253547i) q^{51} +(-6.26660 + 10.8541i) q^{53} +(-0.585062 + 0.724359i) q^{57} +(-6.25478 + 10.8336i) q^{59} +(4.96556 - 2.86687i) q^{61} +(-6.54828 - 4.48553i) q^{63} +(-4.81512 - 2.78001i) q^{67} +(3.73427 + 3.01616i) q^{69} -10.1375i q^{71} +(6.56784 - 11.3758i) q^{73} +(1.57221 - 5.28887i) q^{77} +(-3.17314 - 5.49605i) q^{79} +(0.895549 - 8.95533i) q^{81} -1.06674i q^{83} +(0.166571 + 0.432299i) q^{87} +(-0.463787 - 0.803302i) q^{89} +(0.151184 + 0.632426i) q^{91} +(-1.93842 - 0.304508i) q^{93} -3.01245 q^{97} +(6.11636 - 1.31622i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 6 q^{9}+O(q^{10}) $ 20 * q - 6 * q^9	$ 20 q - 6 q^{9} + 12 q^{11} - 6 q^{19} + 24 q^{21} + 30 q^{31} + 42 q^{39} + 16 q^{41} + 26 q^{49} + 80 q^{51} + 84 q^{61} - 28 q^{69} - 2 q^{79} - 26 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 + 24 * q^21 + 30 * q^31 + 42 * q^39 + 16 * q^41 + 26 * q^49 + 80 * q^51 + 84 * q^61 - 28 * q^69 - 2 * q^79 - 26 * 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
$3$	−1.61622	+	0.622752i	−0.933127	+	0.359546i
$3$	−1.61622	+	0.622752i	−0.933127	+	0.359546i
$4$		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
$9$	2.22436	−	2.01301i	0.741453	−	0.671005i
$10$		0			0
$11$	1.80606	+	1.04273i	0.544548	+	0.314395i	0.746920	−	0.664914i	$-0.231532\pi$
$11$	1.80606	+	1.04273i	0.544548	+	0.314395i	−0.202372	+	0.979309i	$0.564865\pi$
$12$		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	0.397654	−	0.917536i	$-0.369824\pi$
$17$	−0.816904	−	0.471640i	−0.198128	−	0.114389i	−0.595782	+	0.803146i	$0.703158\pi$
$18$		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
$21$	2.59670	+	3.77586i	0.566647	+	0.823960i
$22$		0			0
$23$	−1.38570	−	2.40010i	−0.288938	−	0.500456i	0.684618	−	0.728902i	$-0.259969\pi$
$23$	−1.38570	−	2.40010i	−0.288938	−	0.500456i	−0.973557	+	0.228446i	$0.926636\pi$
$24$		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	$-0.992094\pi$
$29$		−	0.267475i		−	0.0496688i	0.999692	−	0.0248344i	$-0.00790585\pi$
$30$		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
$33$	−3.56836	−	0.560556i	−0.621172	−	0.0975803i
$34$		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
$39$	0.397219	−	0.153054i	0.0636059	−	0.0245082i
$40$		0			0
$41$	2.38340			0.372224			0.186112	−	0.982529i	$-0.440411\pi$
$41$	2.38340			0.372224			0.186112	+	0.982529i	$0.440411\pi$
$42$		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	$0.696526\pi$
$47$	−10.7944	+	6.23215i	−1.57452	+	0.909052i	−0.995603	+	0.0936683i	$0.970141\pi$
$48$		0			0
$49$	−6.24320	+	3.16583i	−0.891885	+	0.452261i
$50$		0			0
$51$	1.61401	+	0.253547i	0.226007	+	0.0355036i
$52$		0			0
$53$	−6.26660	+	10.8541i	−0.860784	+	1.49092i	0.0103892	+	0.999946i	$0.496693\pi$
$53$	−6.26660	+	10.8541i	−0.860784	+	1.49092i	−0.871173	+	0.490976i	$0.836640\pi$
$54$		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	$0.469547\pi$
$59$	−6.25478	+	10.8336i	−0.814303	+	1.41041i	−0.909827	+	0.414987i	$0.863786\pi$
$60$		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
$63$	−6.54828	−	4.48553i	−0.825006	−	0.565124i
$64$		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	$-0.794550\pi$
$71$		−	10.1375i		−	1.20310i	0.798835	−	0.601551i	$-0.205450\pi$
$72$		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
$81$	0.895549	−	8.95533i	0.0995055	−	0.995037i
$82$		0			0
$83$		−	1.06674i		−	0.117090i	−0.998285	−	0.0585449i	$-0.981354\pi$
$83$		−	1.06674i		−	0.117090i	0.998285	−	0.0585449i	$-0.0186461\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	0.166571	+	0.432299i	0.0178582	+	0.0463473i
$88$		0			0
$89$	−0.463787	−	0.803302i	−0.0491613	−	0.0851499i	0.840398	−	0.541970i	$-0.182322\pi$
$89$	−0.463787	−	0.803302i	−0.0491613	−	0.0851499i	−0.889559	+	0.456820i	$0.848988\pi$
$90$		0			0
$91$	0.151184	+	0.632426i	0.0158483	+	0.0662963i
$92$		0			0
$93$	−1.93842	−	0.304508i	−0.201005	−	0.0315760i
$94$		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	$-0.622095\pi$
$101$	6.19049	−	10.7223i	0.615977	−	1.06690i	0.990212	−	0.139570i	$-0.0445720\pi$
$102$		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	$-0.953916\pi$
$107$	−6.41036	−	11.1031i	−0.619713	−	1.07337i	0.369825	−	0.929101i	$-0.379418\pi$
$108$		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	$-0.515030\pi$
$113$	−1.00353			−0.0944041			−0.0472020	+	0.998885i	$0.515030\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−0.546680	+	0.494738i	−0.0505406	+	0.0457385i
$118$		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
$123$	−3.85210	+	1.48426i	−0.347332	+	0.133832i
$124$		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
$129$	7.12140	+	18.4821i	0.627004	+	1.62726i
$130$		0			0
$131$	−8.58199	−	14.8644i	−0.749812	−	1.29871i	−0.947913	−	0.318530i	$-0.896811\pi$
$131$	−8.58199	−	14.8644i	−0.749812	−	1.29871i	0.198101	−	0.980182i	$-0.436523\pi$
$132$		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	$-0.611472\pi$
$137$	7.51345	−	13.0137i	0.641918	−	1.11183i	0.985004	−	0.172530i	$-0.0551942\pi$
$138$		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
$147$	8.11888	−	9.00466i	0.669634	−	0.742692i
$148$		0			0
$149$	19.9895	−	11.5409i	1.63760	−	0.945469i	0.655943	−	0.754810i	$-0.272271\pi$
$149$	19.9895	−	11.5409i	1.63760	−	0.945469i	0.981656	−	0.190658i	$-0.0610623\pi$
$150$		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
$159$	3.36883	−	21.4452i	0.267166	−	1.70071i
$160$		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	$0.344825\pi$
$167$			22.8349i			1.76702i	−0.468415	+	0.883509i	$0.655175\pi$
$168$		0			0
$169$	−12.9396			−0.995354
$170$		0			0
$171$	0.494495	−	1.53508i	0.0378150	−	0.117390i
$172$		0			0
$173$	−8.43656	+	4.87085i	−0.641420	+	0.370324i	−0.785161	−	0.619291i	$-0.787420\pi$
$173$	−8.43656	+	4.87085i	−0.641420	+	0.370324i	0.143741	+	0.989615i	$0.454087\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	3.36248	−	21.4047i	0.252739	−	1.60888i
$178$		0			0
$179$	−15.6543	−	9.03800i	−1.17006	−	0.675532i	−0.216363	−	0.976313i	$-0.569419\pi$
$179$	−15.6543	−	9.03800i	−1.17006	−	0.675532i	−0.953693	+	0.300781i	$0.902753\pi$
$180$		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
$189$	13.3769	+	3.17167i	0.973024	+	0.230705i
$190$		0			0
$191$	−19.0353	+	10.9901i	−1.37735	+	0.795212i	−0.991840	−	0.127492i	$-0.959307\pi$
$191$	−19.0353	+	10.9901i	−1.37735	+	0.795212i	−0.385508	+	0.922704i	$0.625974\pi$
$192$		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	$-0.207780\pi$
$197$	22.3002			1.58882			0.794410	+	0.607382i	$0.207780\pi$
$198$		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
$201$	9.51358	+	1.49449i	0.671036	+	0.105414i
$202$		0			0
$203$	−0.688279	+	0.164535i	−0.0483077	+	0.0115481i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−7.91374	−	2.54926i	−0.550043	−	0.177186i
$208$		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
$213$	6.31316	+	16.3845i	0.432571	+	1.12265i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	0.854066	−	2.87304i	0.0579778	−	0.195035i
$218$		0			0
$219$	−3.53077	+	22.4760i	−0.238588	+	1.51879i
$220$		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	0.760556	−	0.649272i	$-0.224926\pi$
$227$	8.71671	+	5.03260i	0.578549	+	0.334025i	−0.182008	+	0.983297i	$0.558260\pi$
$228$		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
$231$	0.752603	+	9.52709i	0.0495176	+	0.626837i
$232$		0			0
$233$	−10.3759	−	17.9716i	−0.679750	−	1.17736i	−0.975056	−	0.221958i	$-0.928755\pi$
$233$	−10.3759	−	17.9716i	−0.679750	−	1.17736i	0.295306	−	0.955403i	$-0.404578\pi$
$234$		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	$-0.949715\pi$
$239$		−	4.86422i		−	0.314640i	0.987548	−	0.157320i	$-0.0502854\pi$
$240$		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
$243$	4.12954	+	15.0315i	0.264910	+	0.964273i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−0.114421	+	0.0660611i	−0.00728045	+	0.00420337i
$248$		0			0
$249$	0.664314	+	1.72409i	0.0420992	+	0.109260i
$250$		0			0
$251$	15.8276			0.999031			0.499516	−	0.866305i	$-0.333511\pi$
$251$	15.8276			0.999031			0.499516	+	0.866305i	$0.333511\pi$
$252$		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	−0.903490	−	0.428609i	$-0.859004\pi$
$257$	−15.7755	+	9.10800i	−0.984050	+	0.568141i	−0.0805593	+	0.996750i	$0.525671\pi$
$258$		0			0
$259$	−11.2132	−	11.8392i	−0.696752	−	0.735651i
$260$		0			0
$261$	−0.538431	−	0.594960i	−0.0333280	−	0.0368271i
$262$		0			0
$263$	−2.63255	+	4.55971i	−0.162330	+	0.281164i	−0.935704	−	0.352786i	$-0.885234\pi$
$263$	−2.63255	+	4.55971i	−0.162330	+	0.281164i	0.773374	+	0.633950i	$0.218568\pi$
$264$		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	−0.841418	−	0.540385i	$-0.818279\pi$
$269$	0.775418	−	1.34306i	0.0472780	−	0.0818880i	0.888696	+	0.458497i	$0.151612\pi$
$270$		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
$273$	−0.638191	−	0.927992i	−0.0386251	−	0.0561647i
$274$		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	$0.149982\pi$
$281$			15.2188i			0.907880i	−0.891032	+	0.453940i	$0.850018\pi$
$282$		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
$291$	4.86879	−	1.87601i	0.285414	−	0.109974i
$292$		0			0
$293$		−	18.1748i		−	1.06179i	−0.847439	−	0.530893i	$-0.821857\pi$
$293$		−	18.1748i		−	1.06179i	0.847439	−	0.530893i	$-0.178143\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−9.06572	+	5.93628i	−0.526047	+	0.344458i
$298$		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
$303$	−3.32792	+	21.1847i	−0.191184	+	1.21703i
$304$		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	$0.392925\pi$
$311$	−11.5061	+	19.9291i	−0.652448	+	1.13007i	−0.982527	+	0.186120i	$0.940409\pi$
$312$		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	0.817295	−	0.576220i	$-0.195473\pi$
$317$	−1.60905	−	2.78696i	−0.0903734	−	0.156531i	−0.907668	+	0.419688i	$0.862139\pi$
$318$		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
$327$	0.964686	−	6.14095i	0.0533472	−	0.339595i
$328$		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
$333$	5.66925	−	17.5992i	0.310673	−	0.964432i
$334$		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
$339$	1.62193	−	0.624950i	0.0880910	−	0.0339426i
$340$		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	−0.995254	−	0.0973081i	$-0.968977\pi$
$347$	−7.69997	+	13.3367i	−0.413356	+	0.715953i	0.581898	+	0.813261i	$0.302310\pi$
$348$		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	0.843055	−	0.537827i	$-0.180755\pi$
$353$	15.0083	+	8.66505i	0.798811	+	0.461194i	−0.0442440	+	0.999021i	$0.514088\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−0.340412	−	4.30922i	−0.0180165	−	0.228068i
$358$		0			0
$359$	0.270990	−	0.156456i	0.0143023	−	0.00825745i	−0.492832	−	0.870125i	$-0.664038\pi$
$359$	0.270990	−	0.156456i	0.0143023	−	0.00825745i	0.507134	+	0.861867i	$0.330705\pi$
$360$		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
$369$	5.30153	−	4.79781i	0.275987	−	0.249764i
$370$		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
$381$	−4.83316	−	12.5435i	−0.247610	−	0.642621i
$382$		0			0
$383$	25.5519	−	14.7524i	1.30564	−	0.753813i	0.324276	−	0.945963i	$-0.394879\pi$
$383$	25.5519	−	14.7524i	1.30564	−	0.753813i	0.981366	+	0.192150i	$0.0615460\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−23.0195	−	25.4364i	−1.17015	−	1.29300i
$388$		0			0
$389$	−11.5224	−	6.65245i	−0.584208	−	0.337293i	0.178596	−	0.983923i	$-0.442845\pi$
$389$	−11.5224	−	6.65245i	−0.584208	−	0.337293i	−0.762804	+	0.646630i	$0.776178\pi$
$390$		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
$399$	2.22385	+	1.05992i	0.111332	+	0.0530626i
$400$		0			0
$401$	−25.4507	+	14.6940i	−1.27095	+	0.733781i	−0.975166	−	0.221475i	$-0.928913\pi$
$401$	−25.4507	+	14.6940i	−1.27095	+	0.733781i	−0.295780	+	0.955256i	$0.595580\pi$
$402$		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
$411$	−4.03912	+	25.7120i	−0.199235	+	1.26828i
$412$		0			0
$413$	31.7251	+	9.43088i	1.56109	+	0.464063i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	6.12253	+	15.8898i	0.299822	+	0.778125i
$418$		0			0
$419$	−1.40692			−0.0687327			−0.0343663	−	0.999409i	$-0.510941\pi$
$419$	−1.40692			−0.0687327			−0.0343663	+	0.999409i	$0.510941\pi$
$420$		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
$423$	−11.4652	+	35.5918i	−0.557458	+	1.73053i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−10.4317	−	11.0141i	−0.504825	−	0.533009i
$428$		0			0
$429$	0.876995	+	0.137768i	0.0423417	+	0.00665149i
$430$		0			0
$431$	9.16199	+	5.28968i	0.441317	+	0.254795i	0.704156	−	0.710045i	$-0.251325\pi$
$431$	9.16199	+	5.28968i	0.441317	+	0.254795i	−0.262839	+	0.964840i	$0.584659\pi$
$432$		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
$441$	−7.51425	+	19.6096i	−0.357822	+	0.933790i
$442$		0			0
$443$	0.274720	+	0.475830i	0.0130524	+	0.0226074i	0.872478	−	0.488654i	$-0.162512\pi$
$443$	0.274720	+	0.475830i	0.0130524	+	0.0226074i	−0.859425	+	0.511261i	$0.829179\pi$
$444$		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	$-0.991552\pi$
$449$		−	1.12469i		−	0.0530772i	0.999648	−	0.0265386i	$-0.00844850\pi$
$450$		0			0
$451$	4.30456	+	2.48524i	0.202694	+	0.117025i
$452$		0			0
$453$	−3.87345	+	24.6574i	−0.181991	+	1.15851i
$454$		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
$459$	4.10054	−	2.68505i	0.191397	−	0.125328i
$460$		0			0
$461$	29.9734			1.39600			0.697999	−	0.716098i	$-0.254074\pi$
$461$	29.9734			1.39600			0.697999	+	0.716098i	$0.254074\pi$
$462$		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	−0.547949	−	0.836512i	$-0.684591\pi$
$467$	−2.10662	+	1.21626i	−0.0974828	+	0.0562817i	0.450466	+	0.892794i	$0.351258\pi$
$468$		0			0
$469$	−4.19167	+	14.1006i	−0.193553	+	0.651105i
$470$		0			0
$471$	0.591082	−	3.76268i	0.0272356	−	0.173375i
$472$		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	−0.712881	−	0.701285i	$-0.752610\pi$
$479$	5.49101	−	9.51071i	0.250891	−	0.434555i	0.963771	+	0.266730i	$0.0859432\pi$
$480$		0			0
$481$	−1.31181	+	0.757373i	−0.0598133	+	0.0345332i
$482$		0			0
$483$	5.46420	−	11.4646i	0.248630	−	0.521656i
$484$		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	$-0.808089\pi$
$491$		−	25.1295i		−	1.13408i	0.823692	−	0.567038i	$-0.191911\pi$
$492$		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
$501$	−14.2205	−	36.9063i	−0.635324	−	1.64885i
$502$		0			0
$503$			42.2496i			1.88382i	0.335872	+	0.941908i	$0.390969\pi$
$503$			42.2496i			1.88382i	−0.335872	+	0.941908i	$0.609031\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	20.9133	−	8.05816i	0.928792	−	0.357876i
$508$		0			0
$509$	−3.76320	−	6.51806i	−0.166801	−	0.288908i	0.770492	−	0.637449i	$-0.220010\pi$
$509$	−3.76320	−	6.51806i	−0.166801	−	0.288908i	−0.937293	+	0.348541i	$0.886677\pi$
$510$		0			0
$511$	−33.3130	−	9.90290i	−1.47368	−	0.438079i
$512$		0			0
$513$	0.156757	+	2.78897i	0.00692099	+	0.123136i
$514$		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	−0.998081	−	0.0619196i	$-0.980278\pi$
$521$	−10.1668	+	17.6095i	−0.445417	+	0.771484i	0.552665	+	0.833404i	$0.313611\pi$
$522$		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
$537$	30.9293	+	4.85870i	1.33470	+	0.209668i
$538$		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
$543$	−11.0370	−	28.6443i	−0.473644	−	1.22924i
$544$		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
$549$	5.27415	−	16.3727i	0.225095	−	0.698770i
$550$		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	$-0.521693\pi$
$557$	19.5879	−	33.9272i	0.829965	−	1.43754i	0.898065	−	0.439863i	$-0.144973\pi$
$558$		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	0.431915	−	0.901914i	$-0.357838\pi$
$563$	−3.16069	−	1.82483i	−0.133207	−	0.0769073i	−0.565123	+	0.825007i	$0.691171\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−23.5952	+	3.20434i	−0.990904	+	0.134570i
$568$		0			0
$569$	−17.1456	+	9.89902i	−0.718781	+	0.414988i	−0.814304	−	0.580439i	$-0.802881\pi$
$569$	−17.1456	+	9.89902i	−0.718781	+	0.414988i	0.0955229	+	0.995427i	$0.469548\pi$
$570$		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
$579$	−15.3592	−	2.41279i	−0.638307	−	0.100272i
$580$		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	$-0.950054\pi$
$587$		−	7.57204i		−	0.312531i	0.987715	−	0.156266i	$-0.0499456\pi$
$588$		0			0
$589$	0.609016			0.0250941
$590$		0			0
$591$	−36.0420	+	13.8875i	−1.48257	+	0.571254i
$592$		0			0
$593$	−2.75258	+	1.58920i	−0.113035	+	0.0652606i	−0.555452	−	0.831549i	$-0.687455\pi$
$593$	−2.75258	+	1.58920i	−0.113035	+	0.0652606i	0.442417	+	0.896810i	$0.354121\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	32.3645	+	5.08416i	1.32459	+	0.208081i
$598$		0			0
$599$	23.5750	+	13.6110i	0.963247	+	0.556131i	0.897171	−	0.441684i	$-0.145619\pi$
$599$	23.5750	+	13.6110i	0.963247	+	0.556131i	0.0660761	+	0.997815i	$0.478952\pi$
$600$		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
$609$	1.00995	−	0.694553i	0.0409252	−	0.0281447i
$610$		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	$-0.281157\pi$
$617$	31.5272			1.26924			0.634619	+	0.772825i	$0.281157\pi$
$618$		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
$621$	14.3779	−	0.808125i	0.576966	−	0.0324289i
$622$		0			0
$623$	−1.78180	+	1.68758i	−0.0713863	+	0.0676116i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−1.81197	+	0.698175i	−0.0723631	+	0.0278824i
$628$		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
$633$	−32.9956	+	12.7136i	−1.31146	+	0.505322i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	1.53439	−	0.778065i	0.0607947	−	0.0308281i
$638$		0			0
$639$	−20.4070	−	22.5495i	−0.807287	−	0.892044i
$640$		0			0
$641$	−27.8245	−	16.0645i	−1.09900	−	0.634510i	−0.163044	−	0.986619i	$-0.552131\pi$
$641$	−27.8245	−	16.0645i	−1.09900	−	0.634510i	−0.935959	+	0.352109i	$0.885465\pi$
$642$		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	0.800004	−	0.599994i	$-0.204830\pi$
$647$	17.3067	+	9.99202i	0.680396	+	0.392827i	−0.119608	+	0.992821i	$0.538164\pi$
$648$		0			0
$649$	−22.5930	+	13.0441i	−0.886854	+	0.512025i
$650$		0			0
$651$	0.408832	+	5.17535i	0.0160234	+	0.202838i
$652$		0			0
$653$	1.26856	+	2.19720i	0.0496424	+	0.0859832i	0.889779	−	0.456392i	$-0.150858\pi$
$653$	1.26856	+	2.19720i	0.0496424	+	0.0859832i	−0.840136	+	0.542375i	$0.817525\pi$
$654$		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	$-0.811960\pi$
$659$		−	28.5964i		−	1.11396i	0.830526	−	0.556979i	$-0.188040\pi$
$660$		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
$663$	−0.396676	−	0.0623141i	−0.0154056	−	0.00242008i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−0.641967	+	0.370640i	−0.0248571	+	0.0143512i
$668$		0			0
$669$	21.9723	−	8.46623i	0.849499	−	0.327323i
$670$		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	0.304987	−	0.952356i	$-0.401348\pi$
$677$	33.3630	−	19.2622i	1.28225	−	0.740305i	0.977259	+	0.212051i	$0.0680144\pi$
$678$		0			0
$679$	1.85309	+	7.75178i	0.0711150	+	0.297486i
$680$		0			0
$681$	−17.2222	−	2.70545i	−0.659957	−	0.103673i
$682$		0			0
$683$	−4.75897	+	8.24278i	−0.182097	+	0.315401i	−0.942594	−	0.333940i	$-0.891622\pi$
$683$	−4.75897	+	8.24278i	−0.182097	+	0.315401i	0.760497	+	0.649341i	$0.224955\pi$
$684$		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
$693$	−7.14939	−	14.9292i	−0.271583	−	0.567115i
$694$		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	$-0.876001\pi$
$701$		−	20.1103i		−	0.759555i	0.925078	−	0.379778i	$-0.123999\pi$
$702$		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
$711$	−18.1218	−	5.83760i	−0.679622	−	0.218927i
$712$		0			0
$713$		−	3.13964i		−	0.117581i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	3.02920	+	7.86166i	0.113128	+	0.293599i
$718$		0			0
$719$	7.70568	+	13.3466i	0.287373	+	0.497745i	0.973182	−	0.230037i	$-0.0738846\pi$
$719$	7.70568	+	13.3466i	0.287373	+	0.497745i	−0.685809	+	0.727782i	$0.740551\pi$
$720$		0			0
$721$	−32.3370	+	30.6271i	−1.20429	+	1.14061i
$722$		0			0
$723$	29.4863	+	4.63202i	1.09661	+	0.172267i
$724$		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	$-0.533631\pi$
$743$	−5.74923			−0.210919			−0.105459	+	0.994424i	$0.533631\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−2.14736	−	2.37281i	−0.0785678	−	0.0868167i
$748$		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
$753$	−25.5810	+	9.85669i	−0.932223	+	0.359198i
$754$		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
$759$	3.59929	+	9.34120i	0.130646	+	0.339064i
$760$		0			0
$761$	−9.03998	−	15.6577i	−0.327699	−	0.567591i	0.654356	−	0.756187i	$-0.272940\pi$
$761$	−9.03998	−	15.6577i	−0.327699	−	0.567591i	−0.982055	+	0.188595i	$0.939607\pi$
$762$		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	−0.103031	−	0.994678i	$-0.532854\pi$
$773$	−28.2467	−	16.3082i	−1.01596	−	0.586567i	−0.912932	+	0.408112i	$0.866187\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	25.4959	+	12.1518i	0.914659	+	0.435942i
$778$		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
$789$	1.41522	−	9.00894i	0.0503832	−	0.320727i
$790$		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	$0.0761094\pi$
$797$			13.3722i			0.473666i	−0.971550	+	0.236833i	$0.923891\pi$
$798$		0			0
$799$	11.7573			0.415944
$800$		0			0
$801$	−2.64869	−	0.853224i	−0.0935868	−	0.0301472i
$802$		0			0
$803$	23.7238	−	13.6970i	0.837196	−	0.483355i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−0.416853	+	2.65358i	−0.0146739	+	0.0934105i
$808$		0			0
$809$	−20.3694	−	11.7603i	−0.716152	−	0.413470i	0.0971830	−	0.995267i	$-0.469017\pi$
$809$	−20.3694	−	11.7603i	−0.716152	−	0.413470i	−0.813335	+	0.581796i	$0.802350\pi$
$810$		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
$819$	1.60937	+	1.10241i	0.0562359	+	0.0385213i
$820$		0			0
$821$	1.50477	−	0.868778i	0.0525167	−	0.0303205i	−0.473512	−	0.880788i	$-0.657014\pi$
$821$	1.50477	−	0.868778i	0.0525167	−	0.0303205i	0.526028	+	0.850467i	$0.323681\pi$
$822$		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	$-0.623252\pi$
$827$	−21.7179			−0.755207			−0.377603	+	0.925967i	$0.623252\pi$
$828$		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
$831$	−29.2377	−	4.59298i	−1.01425	−	0.159329i
$832$		0			0
$833$	6.59322	+	0.358360i	0.228442	+	0.0124165i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−4.92472	+	3.22473i	−0.170223	+	0.111463i
$838$		0			0
$839$	2.46944			0.0852546			0.0426273	−	0.999091i	$-0.486427\pi$
$839$	2.46944			0.0852546			0.0426273	+	0.999091i	$0.486427\pi$
$840$		0			0
$841$	28.9285			0.997533
$842$		0			0
$843$	−9.47757	−	24.5971i	−0.326425	−	0.847168i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−12.7758	+	12.1003i	−0.438982	+	0.415770i
$848$		0			0
$849$	−4.42702	+	28.1813i	−0.151935	+	0.967179i
$850$		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	$-0.989020\pi$
$857$	−44.7601	−	25.8422i	−1.52898	−	0.882754i	−0.529570	−	0.848266i	$-0.677647\pi$
$858$		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
$861$	6.18897	+	8.99937i	0.210920	+	0.306698i
$862$		0			0
$863$	22.7263	+	39.3631i	0.773611	+	1.33993i	0.935572	+	0.353137i	$0.114885\pi$
$863$	22.7263	+	39.3631i	0.773611	+	1.33993i	−0.161960	+	0.986797i	$0.551782\pi$
$864$		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
$873$	−6.70077	+	6.06410i	−0.226787	+	0.205239i
$874$		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
$879$	11.3184	+	29.3746i	0.381761	+	0.990782i
$880$		0			0
$881$	42.5616			1.43394			0.716969	−	0.697105i	$-0.245529\pi$
$881$	42.5616			1.43394			0.716969	+	0.697105i	$0.245529\pi$
$882$		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	−0.383096	−	0.923708i	$-0.625142\pi$
$887$	6.71032	−	3.87420i	0.225310	−	0.130083i	0.608407	+	0.793625i	$0.291809\pi$
$888$		0			0
$889$	19.9709	−	4.77410i	0.669802	−	0.160118i
$890$		0			0
$891$	10.9554	−	15.2401i	0.367020	−	0.510561i
$892$		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
$903$	43.1783	−	29.6943i	1.43689	−	0.988163i
$904$		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	$-0.798076\pi$
$911$		−	35.7765i		−	1.18533i	0.805449	−	0.592665i	$-0.201924\pi$
$912$		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
$921$	39.9143	−	15.3795i	1.31522	−	0.506772i
$922$		0			0
$923$			2.49149i			0.0820085i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−48.0697	−	15.4847i	−1.57882	−	0.508585i
$928$		0			0
$929$	15.9490	+	27.6244i	0.523269	+	0.906329i	0.999633	+	0.0270805i	$0.00862104\pi$
$929$	15.9490	+	27.6244i	0.523269	+	0.906329i	−0.476364	+	0.879248i	$0.658046\pi$
$930$		0			0
$931$	−2.05565	+	3.15202i	−0.0673711	+	0.103303i
$932$		0			0
$933$	6.18549	−	39.3753i	0.202504	−	1.28909i
$934$		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	−0.613547	−	0.789658i	$-0.710258\pi$
$941$	11.5675	−	20.0355i	0.377091	−	0.653140i	0.990638	+	0.136518i	$0.0435912\pi$
$942$		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	$0.0199377\pi$
$947$	17.0247	+	29.4876i	0.553228	+	0.958220i	−0.444811	+	0.895625i	$0.646729\pi$
$948$		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	$-0.521071\pi$
$953$	−4.08410			−0.132297			−0.0661485	+	0.997810i	$0.521071\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−0.149935	+	0.954447i	−0.00484670	+	0.0308529i
$958$		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
$963$	−36.6096	−	11.7931i	−1.17973	−	0.380026i
$964$		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
$969$	0.819576	−	0.315793i	0.0263286	−	0.0101447i
$970$		0			0
$971$	9.79452	+	16.9646i	0.314321	+	0.544420i	0.979293	−	0.202448i	$-0.0648898\pi$
$971$	9.79452	+	16.9646i	0.314321	+	0.544420i	−0.664972	+	0.746868i	$0.731556\pi$
$972$		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	−0.999928	−	0.0120141i	$-0.996176\pi$
$977$	−15.3022	+	26.5041i	−0.489559	+	0.847942i	0.510368	+	0.859956i	$0.329509\pi$
$978$		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	0.0567327	−	0.998389i	$-0.481932\pi$
$983$	−24.4405	−	14.1107i	−0.779532	−	0.450063i	−0.836264	+	0.548327i	$0.815265\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−51.5616	−	24.5751i	−1.64122	−	0.782234i
$988$		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
$999$	1.79718	+	31.9748i	0.0568601	+	1.01164i

Twists

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

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

\(f(q)\)	\(=\)	\(q+(-1.61622 + 0.622752i) q^{3} +(-0.615143 - 2.57325i) q^{7} +(2.22436 - 2.01301i) q^{9} +O(q^{10})\)	\(q+(-1.61622 + 0.622752i) q^{3} +(-0.615143 - 2.57325i) q^{7} +(2.22436 - 2.01301i) q^{9} +(1.80606 + 1.04273i) q^{11} -0.245770 q^{13} +(-0.816904 - 0.471640i) q^{17} +(0.465563 - 0.268793i) q^{19} +(2.59670 + 3.77586i) q^{21} +(-1.38570 - 2.40010i) q^{23} +(-2.34145 + 4.63871i) q^{27} -0.267475i q^{29} +(0.981097 + 0.566436i) q^{31} +(-3.56836 - 0.560556i) q^{33} +(5.33755 - 3.08164i) q^{37} +(0.397219 - 0.153054i) q^{39} +2.38340 q^{41} -11.4354i q^{43} +(-10.7944 + 6.23215i) q^{47} +(-6.24320 + 3.16583i) q^{49} +(1.61401 + 0.253547i) q^{51} +(-6.26660 + 10.8541i) q^{53} +(-0.585062 + 0.724359i) q^{57} +(-6.25478 + 10.8336i) q^{59} +(4.96556 - 2.86687i) q^{61} +(-6.54828 - 4.48553i) q^{63} +(-4.81512 - 2.78001i) q^{67} +(3.73427 + 3.01616i) q^{69} -10.1375i q^{71} +(6.56784 - 11.3758i) q^{73} +(1.57221 - 5.28887i) q^{77} +(-3.17314 - 5.49605i) q^{79} +(0.895549 - 8.95533i) q^{81} -1.06674i q^{83} +(0.166571 + 0.432299i) q^{87} +(-0.463787 - 0.803302i) q^{89} +(0.151184 + 0.632426i) q^{91} +(-1.93842 - 0.304508i) q^{93} -3.01245 q^{97} +(6.11636 - 1.31622i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 6 q^{9}+O(q^{10}) \) 20 * q - 6 * q^9	\( 20 q - 6 q^{9} + 12 q^{11} - 6 q^{19} + 24 q^{21} + 30 q^{31} + 42 q^{39} + 16 q^{41} + 26 q^{49} + 80 q^{51} + 84 q^{61} - 28 q^{69} - 2 q^{79} - 26 q^{81} + 56 q^{89} - 22 q^{91} - 72 q^{99}+O(q^{100}) \) 20 * q - 6 * q^9 + 12 * q^11 - 6 * q^19 + 24 * q^21 + 30 * q^31 + 42 * q^39 + 16 * q^41 + 26 * q^49 + 80 * q^51 + 84 * q^61 - 28 * q^69 - 2 * q^79 - 26 * q^81 + 56 * q^89 - 22 * q^91 - 72 * q^99

Introduction

L-functions

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