LMFDB - Embedded newform 2100.2.bi.n.101.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2100,2,Mod(101,2100)]

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, 0, 1]))

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

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

chi := DirichletCharacter("2100.101");

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.bi (of order $6$, degree $2$, 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:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 420)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.10
Character	$\chi$	$=$	2100.101
Dual form			2100.2.bi.n.1601.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.772078 - 1.55045i) q^{3} +(-2.60236 + 0.477214i) q^{7} +(-1.80779 - 2.39414i) q^{9} +O(q^{10})$	\(q+(0.772078 - 1.55045i) q^{3} +(-2.60236 + 0.477214i) q^{7} +(-1.80779 - 2.39414i) q^{9} +(-1.34052 - 0.773950i) q^{11} +4.18432i q^{13} +(2.55387 - 4.42344i) q^{17} +(-4.62984 + 2.67304i) q^{19} +(-1.26933 + 4.40327i) q^{21} +(-3.15990 + 1.82437i) q^{23} +(-5.10775 + 0.954427i) q^{27} +9.79665i q^{29} +(6.79882 + 3.92530i) q^{31} +(-2.23496 + 1.48086i) q^{33} +(-1.71446 - 2.96953i) q^{37} +(6.48759 + 3.23063i) q^{39} +8.82093 q^{41} -3.79814 q^{43} +(1.24989 + 2.16487i) q^{47} +(6.54453 - 2.48376i) q^{49} +(-4.88653 - 7.37489i) q^{51} +(0.684586 + 0.395246i) q^{53} +(0.569815 + 9.24212i) q^{57} +(-2.73316 + 4.73397i) q^{59} +(-6.76285 + 3.90454i) q^{61} +(5.84703 + 5.36770i) q^{63} +(-5.58414 + 9.67202i) q^{67} +(0.388903 + 6.30782i) q^{69} +7.97077i q^{71} +(-10.7377 - 6.19943i) q^{73} +(3.85786 + 1.37438i) q^{77} +(1.12127 + 1.94209i) q^{79} +(-2.46379 + 8.65620i) q^{81} -5.26486 q^{83} +(15.1892 + 7.56378i) q^{87} +(7.65723 + 13.2627i) q^{89} +(-1.99682 - 10.8891i) q^{91} +(11.3352 - 7.51059i) q^{93} -15.9016i q^{97} +(0.570438 + 4.60853i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q+O(q^{10}) $ 32 * q	$ 32 q - 12 q^{19} - 8 q^{21} - 12 q^{31} - 24 q^{39} + 44 q^{49} - 10 q^{51} - 24 q^{61} + 28 q^{79} - 20 q^{81} + 16 q^{91} + 28 q^{99}+O(q^{100}) $ 32 * q - 12 * q^19 - 8 * q^21 - 12 * q^31 - 24 * q^39 + 44 * q^49 - 10 * q^51 - 24 * q^61 + 28 * q^79 - 20 * q^81 + 16 * q^91 + 28 * 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
$3$	0.772078	−	1.55045i	0.445760	−	0.895153i
$3$	0.772078	−	1.55045i	0.445760	−	0.895153i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−2.60236	+	0.477214i	−0.983599	+	0.180370i
$7$	−2.60236	+	0.477214i	−0.983599	+	0.180370i
$8$		0			0
$9$	−1.80779	−	2.39414i	−0.602597	−	0.798046i
$10$		0			0
$11$	−1.34052	−	0.773950i	−0.404182	−	0.233355i	0.284105	−	0.958793i	$-0.408304\pi$
$11$	−1.34052	−	0.773950i	−0.404182	−	0.233355i	−0.688287	+	0.725438i	$0.741637\pi$
$12$		0			0
$13$			4.18432i			1.16052i	0.814430	+	0.580261i	$0.197050\pi$
$13$			4.18432i			1.16052i	−0.814430	+	0.580261i	$0.802950\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	2.55387	−	4.42344i	0.619405	−	1.07284i	−0.370189	−	0.928956i	$-0.620707\pi$
$17$	2.55387	−	4.42344i	0.619405	−	1.07284i	0.989594	−	0.143885i	$-0.0459595\pi$
$18$		0			0
$19$	−4.62984	+	2.67304i	−1.06216	+	0.613237i	−0.926028	−	0.377454i	$-0.876799\pi$
$19$	−4.62984	+	2.67304i	−1.06216	+	0.613237i	−0.136129	+	0.990691i	$0.543466\pi$
$20$		0			0
$21$	−1.26933	+	4.40327i	−0.276990	+	0.960873i
$22$		0			0
$23$	−3.15990	+	1.82437i	−0.658885	+	0.380407i	−0.791852	−	0.610713i	$-0.790883\pi$
$23$	−3.15990	+	1.82437i	−0.658885	+	0.380407i	0.132967	+	0.991120i	$0.457550\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−5.10775	+	0.954427i	−0.982986	+	0.183680i
$28$		0			0
$29$			9.79665i			1.81919i	0.415494	+	0.909596i	$0.363609\pi$
$29$			9.79665i			1.81919i	−0.415494	+	0.909596i	$0.636391\pi$
$30$		0			0
$31$	6.79882	+	3.92530i	1.22110	+	0.705005i	0.965153	−	0.261685i	$-0.0842782\pi$
$31$	6.79882	+	3.92530i	1.22110	+	0.705005i	0.255951	+	0.966690i	$0.417612\pi$
$32$		0			0
$33$	−2.23496	+	1.48086i	−0.389056	+	0.257785i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−1.71446	−	2.96953i	−0.281855	−	0.488188i	0.689987	−	0.723822i	$-0.257616\pi$
$37$	−1.71446	−	2.96953i	−0.281855	−	0.488188i	−0.971842	+	0.235635i	$0.924283\pi$
$38$		0			0
$39$	6.48759	+	3.23063i	1.03885	+	0.517314i
$40$		0			0
$41$	8.82093			1.37760			0.688799	−	0.724952i	$-0.258138\pi$
$41$	8.82093			1.37760			0.688799	+	0.724952i	$0.258138\pi$
$42$		0			0
$43$	−3.79814			−0.579211			−0.289605	−	0.957146i	$-0.593524\pi$
$43$	−3.79814			−0.579211			−0.289605	+	0.957146i	$0.593524\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	1.24989	+	2.16487i	0.182315	+	0.315779i	0.942669	−	0.333731i	$-0.108308\pi$
$47$	1.24989	+	2.16487i	0.182315	+	0.315779i	−0.760353	+	0.649510i	$0.774974\pi$
$48$		0			0
$49$	6.54453	−	2.48376i	0.934933	−	0.354823i
$50$		0			0
$51$	−4.88653	−	7.37489i	−0.684251	−	1.03269i
$52$		0			0
$53$	0.684586	+	0.395246i	0.0940351	+	0.0542912i	0.546280	−	0.837603i	$-0.316043\pi$
$53$	0.684586	+	0.395246i	0.0940351	+	0.0542912i	−0.452245	+	0.891894i	$0.649377\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	0.569815	+	9.24212i	0.0754738	+	1.22415i
$58$		0			0
$59$	−2.73316	+	4.73397i	−0.355827	+	0.616310i	−0.987259	−	0.159121i	$-0.949134\pi$
$59$	−2.73316	+	4.73397i	−0.355827	+	0.616310i	0.631432	+	0.775431i	$0.282467\pi$
$60$		0			0
$61$	−6.76285	+	3.90454i	−0.865895	+	0.499925i	−0.865982	−	0.500075i	$-0.833306\pi$
$61$	−6.76285	+	3.90454i	−0.865895	+	0.499925i	8.71528e−5		1.00000i	$0.499972\pi$
$62$		0			0
$63$	5.84703	+	5.36770i	0.736657	+	0.676267i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−5.58414	+	9.67202i	−0.682212	+	1.18163i	0.292093	+	0.956390i	$0.405648\pi$
$67$	−5.58414	+	9.67202i	−0.682212	+	1.18163i	−0.974304	+	0.225235i	$0.927685\pi$
$68$		0			0
$69$	0.388903	+	6.30782i	0.0468184	+	0.759373i
$70$		0			0
$71$			7.97077i			0.945957i	0.881074	+	0.472978i	$0.156821\pi$
$71$			7.97077i			0.945957i	−0.881074	+	0.472978i	$0.843179\pi$
$72$		0			0
$73$	−10.7377	−	6.19943i	−1.25676	−	0.725588i	−0.284313	−	0.958732i	$-0.591765\pi$
$73$	−10.7377	−	6.19943i	−1.25676	−	0.725588i	−0.972442	+	0.233144i	$0.925099\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	3.85786	+	1.37438i	0.439644	+	0.156625i
$78$		0			0
$79$	1.12127	+	1.94209i	0.126152	+	0.218502i	0.922183	−	0.386754i	$-0.126404\pi$
$79$	1.12127	+	1.94209i	0.126152	+	0.218502i	−0.796030	+	0.605257i	$0.793071\pi$
$80$		0			0
$81$	−2.46379	+	8.65620i	−0.273754	+	0.961800i
$82$		0			0
$83$	−5.26486			−0.577894			−0.288947	−	0.957345i	$-0.593305\pi$
$83$	−5.26486			−0.577894			−0.288947	+	0.957345i	$0.593305\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	15.1892	+	7.56378i	1.62845	+	0.810922i
$88$		0			0
$89$	7.65723	+	13.2627i	0.811664	+	1.40584i	0.911698	+	0.410860i	$0.134771\pi$
$89$	7.65723	+	13.2627i	0.811664	+	1.40584i	−0.100034	+	0.994984i	$0.531895\pi$
$90$		0			0
$91$	−1.99682	−	10.8891i	−0.209323	−	1.14149i
$92$		0			0
$93$	11.3352	−	7.51059i	1.17541	−	0.778812i
$94$		0			0
$95$		0			0
$96$		0			0
$97$		−	15.9016i		−	1.61457i	−0.590163	−	0.807284i	$-0.700937\pi$
$97$		−	15.9016i		−	1.61457i	0.590163	−	0.807284i	$-0.299063\pi$
$98$		0			0
$99$	0.570438	+	4.60853i	0.0573312	+	0.463175i
$100$		0			0
$101$	−3.83295	+	6.63886i	−0.381392	+	0.660591i	−0.991262	−	0.131911i	$-0.957889\pi$
$101$	−3.83295	+	6.63886i	−0.381392	+	0.660591i	0.609869	+	0.792502i	$0.291222\pi$
$102$		0			0
$103$	0.960032	−	0.554275i	0.0945947	−	0.0546143i	−0.451956	−	0.892040i	$-0.649274\pi$
$103$	0.960032	−	0.554275i	0.0945947	−	0.0546143i	0.546551	+	0.837426i	$0.315940\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	1.27436	−	0.735749i	0.123197	−	0.0711276i	−0.437135	−	0.899396i	$-0.644007\pi$
$107$	1.27436	−	0.735749i	0.123197	−	0.0711276i	0.560332	+	0.828268i	$0.310674\pi$
$108$		0			0
$109$	4.66898	−	8.08692i	0.447208	−	0.774586i	−0.550996	−	0.834508i	$-0.685752\pi$
$109$	4.66898	−	8.08692i	0.447208	−	0.774586i	0.998203	+	0.0599221i	$0.0190852\pi$
$110$		0			0
$111$	−5.92780	+	0.365473i	−0.562642	+	0.0346892i
$112$		0			0
$113$			11.9773i			1.12673i	0.826210	+	0.563363i	$0.190493\pi$
$113$			11.9773i			1.12673i	−0.826210	+	0.563363i	$0.809507\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	10.0178	−	7.56438i	0.926150	−	0.699327i
$118$		0			0
$119$	−4.53517	+	12.7301i	−0.415738	+	1.16697i
$120$		0			0
$121$	−4.30200	−	7.45129i	−0.391091	−	0.677390i
$122$		0			0
$123$	6.81045	−	13.6764i	0.614078	−	1.23316i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−3.16197			−0.280579			−0.140290	−	0.990110i	$-0.544803\pi$
$127$	−3.16197			−0.280579			−0.140290	+	0.990110i	$0.544803\pi$
$128$		0			0
$129$	−2.93246	+	5.88883i	−0.258189	+	0.518482i
$130$		0			0
$131$	−3.13073	−	5.42258i	−0.273533	−	0.473773i	0.696231	−	0.717818i	$-0.254859\pi$
$131$	−3.13073	−	5.42258i	−0.273533	−	0.473773i	−0.969764	+	0.244045i	$0.921526\pi$
$132$		0			0
$133$	10.7729	−	9.16562i	0.934127	−	0.794760i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−12.0959	−	6.98356i	−1.03342	−	0.596645i	−0.115458	−	0.993312i	$-0.536833\pi$
$137$	−12.0959	−	6.98356i	−1.03342	−	0.596645i	−0.917963	+	0.396667i	$0.870167\pi$
$138$		0			0
$139$			8.07923i			0.685271i	0.939468	+	0.342636i	$0.111320\pi$
$139$			8.07923i			0.685271i	−0.939468	+	0.342636i	$0.888680\pi$
$140$		0			0
$141$	4.32154	−	0.266441i	0.363939	−	0.0224384i
$142$		0			0
$143$	3.23846	−	5.60918i	0.270814	−	0.469063i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	1.20194	−	12.0646i	0.0991346	−	0.995074i
$148$		0			0
$149$	3.98112	−	2.29850i	0.326146	−	0.188301i	−0.327983	−	0.944684i	$-0.606369\pi$
$149$	3.98112	−	2.29850i	0.326146	−	0.188301i	0.654129	+	0.756383i	$0.273035\pi$
$150$		0			0
$151$	−4.04453	+	7.00534i	−0.329140	+	0.570086i	−0.982341	−	0.187097i	$-0.940092\pi$
$151$	−4.04453	+	7.00534i	−0.329140	+	0.570086i	0.653202	+	0.757184i	$0.273425\pi$
$152$		0			0
$153$	−15.2072	+	1.88233i	−1.22943	+	0.152177i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−3.62951	−	2.09550i	−0.289666	−	0.167239i	0.348125	−	0.937448i	$-0.386818\pi$
$157$	−3.62951	−	2.09550i	−0.289666	−	0.167239i	−0.637791	+	0.770209i	$0.720152\pi$
$158$		0			0
$159$	1.14136	−	0.756256i	0.0905160	−	0.0599750i
$160$		0			0
$161$	7.35258	−	6.25561i	0.579464	−	0.493011i
$162$		0			0
$163$	3.35101	+	5.80412i	0.262471	+	0.454613i	0.966898	−	0.255163i	$-0.0821292\pi$
$163$	3.35101	+	5.80412i	0.262471	+	0.454613i	−0.704427	+	0.709777i	$0.748796\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	3.82002			0.295602			0.147801	−	0.989017i	$-0.452780\pi$
$167$	3.82002			0.295602			0.147801	+	0.989017i	$0.452780\pi$
$168$		0			0
$169$	−4.50857			−0.346813
$170$		0			0
$171$	14.7694	+	6.25217i	1.12944	+	0.478115i
$172$		0			0
$173$	1.35808	+	2.35226i	0.103253	+	0.178839i	0.913023	−	0.407908i	$-0.133742\pi$
$173$	1.35808	+	2.35226i	0.103253	+	0.178839i	−0.809770	+	0.586747i	$0.800408\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	5.22957	+	7.89261i	0.393078	+	0.593245i
$178$		0			0
$179$	−0.815115	−	0.470607i	−0.0609246	−	0.0351748i	0.469228	−	0.883077i	$-0.344532\pi$
$179$	−0.815115	−	0.470607i	−0.0609246	−	0.0351748i	−0.530153	+	0.847902i	$0.677865\pi$
$180$		0			0
$181$		−	0.0415289i		−	0.00308682i	−0.999999	−	0.00154341i	$-0.999509\pi$
$181$		−	0.0415289i		−	0.00308682i	0.999999	−	0.00154341i	$-0.000491283\pi$
$182$		0			0
$183$	0.832335	+	13.5001i	0.0615280	+	0.997954i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−6.84704	+	3.95314i	−0.500705	+	0.289082i
$188$		0			0
$189$	12.8367	−	4.92125i	0.933734	−	0.357968i
$190$		0			0
$191$	−8.11005	+	4.68234i	−0.586822	+	0.338802i	−0.763840	−	0.645406i	$-0.776688\pi$
$191$	−8.11005	+	4.68234i	−0.586822	+	0.338802i	0.177018	+	0.984208i	$0.443355\pi$
$192$		0			0
$193$	5.14337	−	8.90859i	0.370228	−	0.641254i	−0.619372	−	0.785097i	$-0.712613\pi$
$193$	5.14337	−	8.90859i	0.370228	−	0.641254i	0.989600	+	0.143843i	$0.0459462\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	1.19936i		−	0.0854511i	−0.999087	−	0.0427256i	$-0.986396\pi$
$197$		−	1.19936i		−	0.0854511i	0.999087	−	0.0427256i	$-0.0136041\pi$
$198$		0			0
$199$	−16.7956	−	9.69696i	−1.19061	−	0.687400i	−0.232166	−	0.972676i	$-0.574581\pi$
$199$	−16.7956	−	9.69696i	−1.19061	−	0.687400i	−0.958445	+	0.285277i	$0.907915\pi$
$200$		0			0
$201$	10.6846	+	16.1255i	0.753633	+	1.13740i
$202$		0			0
$203$	−4.67509	−	25.4944i	−0.328127	−	1.78935i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	10.0802	+	4.26716i	0.700624	+	0.296588i
$208$		0			0
$209$	8.27519			0.572407
$210$		0			0
$211$	9.35510			0.644032			0.322016	−	0.946734i	$-0.395640\pi$
$211$	9.35510			0.644032			0.322016	+	0.946734i	$0.395640\pi$
$212$		0			0
$213$	12.3583	+	6.15406i	0.846776	+	0.421669i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−19.5662	−	6.97055i	−1.32824	−	0.473191i
$218$		0			0
$219$	−17.9023	+	11.8619i	−1.20972	+	0.801550i
$220$		0			0
$221$	18.5091	+	10.6862i	1.24506	+	0.718834i
$222$		0			0
$223$			6.78138i			0.454115i	0.973881	+	0.227057i	$0.0729105\pi$
$223$			6.78138i			0.454115i	−0.973881	+	0.227057i	$0.927090\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−7.09632	+	12.2912i	−0.470999	+	0.815794i	−0.999450	−	0.0331698i	$-0.989440\pi$
$227$	−7.09632	+	12.2912i	−0.470999	+	0.815794i	0.528451	+	0.848964i	$0.322773\pi$
$228$		0			0
$229$	−9.79882	+	5.65735i	−0.647524	+	0.373848i	−0.787507	−	0.616306i	$-0.788629\pi$
$229$	−9.79882	+	5.65735i	−0.647524	+	0.373848i	0.139983	+	0.990154i	$0.455295\pi$
$230$		0			0
$231$	5.10948	−	4.92028i	0.336179	−	0.323731i
$232$		0			0
$233$	15.8160	−	9.13138i	1.03614	−	0.598216i	0.117403	−	0.993084i	$-0.462543\pi$
$233$	15.8160	−	9.13138i	1.03614	−	0.598216i	0.918738	+	0.394868i	$0.129210\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	3.87682	−	0.239022i	0.251826	−	0.0155261i
$238$		0			0
$239$		−	18.8834i		−	1.22146i	−0.791838	−	0.610731i	$-0.790876\pi$
$239$		−	18.8834i		−	1.22146i	0.791838	−	0.610731i	$-0.209124\pi$
$240$		0			0
$241$	12.0617	+	6.96381i	0.776961	+	0.448578i	0.835352	−	0.549715i	$-0.185264\pi$
$241$	12.0617	+	6.96381i	0.776961	+	0.448578i	−0.0583914	+	0.998294i	$0.518597\pi$
$242$		0			0
$243$	11.5188	+	10.5032i	0.738929	+	0.673783i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−11.1849	−	19.3727i	−0.711675	−	1.23266i
$248$		0			0
$249$	−4.06489	+	8.16291i	−0.257602	+	0.517303i
$250$		0			0
$251$	−26.8164			−1.69264			−0.846319	−	0.532676i	$-0.821186\pi$
$251$	−26.8164			−1.69264			−0.846319	+	0.532676i	$0.821186\pi$
$252$		0			0
$253$	5.64789			0.355079
$254$		0			0
$255$		0			0
$256$		0			0
$257$	6.98813	+	12.1038i	0.435907	+	0.755014i	0.997369	−	0.0724888i	$-0.0230941\pi$
$257$	6.98813	+	12.1038i	0.435907	+	0.755014i	−0.561462	+	0.827503i	$0.689761\pi$
$258$		0			0
$259$	5.87873	+	6.90961i	0.365287	+	0.429343i
$260$		0			0
$261$	23.4545	−	17.7103i	1.45180	−	1.09624i
$262$		0			0
$263$	26.1233	+	15.0823i	1.61083	+	0.930015i	0.989177	+	0.146726i	$0.0468734\pi$
$263$	26.1233	+	15.0823i	1.61083	+	0.930015i	0.621657	+	0.783290i	$0.286460\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	26.4751	−	1.63230i	1.62025	−	0.0998952i
$268$		0			0
$269$	3.43538	−	5.95025i	0.209459	−	0.362793i	−0.742086	−	0.670305i	$-0.766163\pi$
$269$	3.43538	−	5.95025i	0.209459	−	0.362793i	0.951544	+	0.307512i	$0.0994965\pi$
$270$		0			0
$271$	−19.3996	+	11.2004i	−1.17844	+	0.680375i	−0.955654	−	0.294491i	$-0.904850\pi$
$271$	−19.3996	+	11.2004i	−1.17844	+	0.680375i	−0.222790	+	0.974866i	$0.571516\pi$
$272$		0			0
$273$	−18.4247	−	5.31128i	−1.11511	−	0.321453i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−3.49026	+	6.04530i	−0.209709	+	0.363227i	−0.951623	−	0.307268i	$-0.900585\pi$
$277$	−3.49026	+	6.04530i	−0.209709	+	0.363227i	0.741914	+	0.670495i	$0.233918\pi$
$278$		0			0
$279$	−2.89313	−	23.3734i	−0.173207	−	1.39933i
$280$		0			0
$281$		−	2.38586i		−	0.142328i	−0.997465	−	0.0711642i	$-0.977329\pi$
$281$		−	2.38586i		−	0.142328i	0.997465	−	0.0711642i	$-0.0226714\pi$
$282$		0			0
$283$	−21.0245	−	12.1385i	−1.24977	−	0.721558i	−0.278710	−	0.960375i	$-0.589907\pi$
$283$	−21.0245	−	12.1385i	−1.24977	−	0.721558i	−0.971065	+	0.238817i	$0.923240\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−22.9552	+	4.20947i	−1.35500	+	0.248477i
$288$		0			0
$289$	−4.54453	−	7.87136i	−0.267326	−	0.463021i
$290$		0			0
$291$	−24.6547	−	12.2773i	−1.44528	−	0.719709i
$292$		0			0
$293$	−24.8305			−1.45062			−0.725308	−	0.688425i	$-0.758303\pi$
$293$	−24.8305			−1.45062			−0.725308	+	0.688425i	$0.758303\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	7.58572	+	2.67371i	0.440168	+	0.155144i
$298$		0			0
$299$	−7.63375	−	13.2220i	−0.441471	−	0.764651i
$300$		0			0
$301$	9.88412	−	1.81252i	0.569711	−	0.104472i
$302$		0			0
$303$	7.33388	+	11.0685i	0.421321	+	0.635869i
$304$		0			0
$305$		0			0
$306$		0			0
$307$			15.7829i			0.900776i	0.892833	+	0.450388i	$0.148714\pi$
$307$			15.7829i			0.900776i	−0.892833	+	0.450388i	$0.851286\pi$
$308$		0			0
$309$	−0.118155	−	1.91642i	−0.00672163	−	0.109022i
$310$		0			0
$311$	1.70595	−	2.95479i	0.0967356	−	0.167551i	−0.813596	−	0.581431i	$-0.802493\pi$
$311$	1.70595	−	2.95479i	0.0967356	−	0.167551i	0.910332	+	0.413880i	$0.135827\pi$
$312$		0			0
$313$	−22.3991	+	12.9321i	−1.26607	+	0.730967i	−0.974242	−	0.225504i	$-0.927597\pi$
$313$	−22.3991	+	12.9321i	−1.26607	+	0.730967i	−0.291829	+	0.956471i	$0.594264\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	15.1610	−	8.75318i	0.851524	−	0.491628i	−0.00964062	−	0.999954i	$-0.503069\pi$
$317$	15.1610	−	8.75318i	0.851524	−	0.491628i	0.861165	+	0.508326i	$0.169735\pi$
$318$		0			0
$319$	7.58212	−	13.1326i	0.424517	−	0.735285i
$320$		0			0
$321$	−0.156841	−	2.54388i	−0.00875399	−	0.141986i
$322$		0			0
$323$			27.3064i			1.51937i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−8.93354	−	13.4828i	−0.494026	−	0.745598i
$328$		0			0
$329$	−4.28577	−	5.03731i	−0.236282	−	0.277716i
$330$		0			0
$331$	−14.0585	−	24.3500i	−0.772724	−	1.33840i	−0.936065	−	0.351828i	$-0.885560\pi$
$331$	−14.0585	−	24.3500i	−0.772724	−	1.33840i	0.163340	−	0.986570i	$-0.447773\pi$
$332$		0			0
$333$	−4.01008	+	9.47293i	−0.219751	+	0.519114i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−22.6854			−1.23575			−0.617876	−	0.786276i	$-0.712007\pi$
$337$	−22.6854			−1.23575			−0.617876	+	0.786276i	$0.712007\pi$
$338$		0			0
$339$	18.5701	+	9.24738i	1.00859	+	0.502249i
$340$		0			0
$341$	−6.07597	−	10.5239i	−0.329032	−	0.569901i
$342$		0			0
$343$	−15.8459	+	9.58678i	−0.855600	+	0.517637i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	23.3828	+	13.5001i	1.25526	+	0.724722i	0.972148	−	0.234366i	$-0.0753016\pi$
$347$	23.3828	+	13.5001i	1.25526	+	0.724722i	0.283107	+	0.959088i	$0.408635\pi$
$348$		0			0
$349$			26.4459i			1.41562i	0.706405	+	0.707808i	$0.250316\pi$
$349$			26.4459i			1.41562i	−0.706405	+	0.707808i	$0.749684\pi$
$350$		0			0
$351$	−3.99363	−	21.3725i	−0.213164	−	1.14078i
$352$		0			0
$353$	3.38448	−	5.86209i	0.180138	−	0.312008i	−0.761790	−	0.647825i	$-0.775679\pi$
$353$	3.38448	−	5.86209i	0.180138	−	0.312008i	0.941927	+	0.335817i	$0.109012\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	16.2359	+	16.8602i	0.859295	+	0.892336i
$358$		0			0
$359$	22.0053	−	12.7047i	1.16139	−	0.670531i	0.209756	−	0.977754i	$-0.432733\pi$
$359$	22.0053	−	12.7047i	1.16139	−	0.670531i	0.951637	+	0.307223i	$0.0993999\pi$
$360$		0			0
$361$	4.79025	−	8.29696i	0.252118	−	0.436682i
$362$		0			0
$363$	−14.8743	+	0.917063i	−0.780700	+	0.0481333i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−16.1174	−	9.30540i	−0.841323	−	0.485738i	0.0163906	−	0.999866i	$-0.494782\pi$
$367$	−16.1174	−	9.30540i	−0.841323	−	0.485738i	−0.857714	+	0.514128i	$0.828116\pi$
$368$		0			0
$369$	−15.9464	−	21.1185i	−0.830136	−	1.09939i
$370$		0			0
$371$	−1.97016	−	0.701878i	−0.102285	−	0.0364397i
$372$		0			0
$373$	−5.60012	−	9.69970i	−0.289963	−	0.502231i	0.683837	−	0.729634i	$-0.260310\pi$
$373$	−5.60012	−	9.69970i	−0.289963	−	0.502231i	−0.973801	+	0.227403i	$0.926976\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−40.9923			−2.11121
$378$		0			0
$379$	21.8808			1.12394			0.561971	−	0.827157i	$-0.310043\pi$
$379$	21.8808			1.12394			0.561971	+	0.827157i	$0.310043\pi$
$380$		0			0
$381$	−2.44129	+	4.90248i	−0.125071	+	0.251161i
$382$		0			0
$383$	−15.1365	−	26.2172i	−0.773439	−	1.33964i	−0.935668	−	0.352882i	$-0.885202\pi$
$383$	−15.1365	−	26.2172i	−0.773439	−	1.33964i	0.162229	−	0.986753i	$-0.448132\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	6.86624	+	9.09327i	0.349031	+	0.462237i
$388$		0			0
$389$	−17.2125	−	9.93765i	−0.872709	−	0.503859i	−0.00446179	−	0.999990i	$-0.501420\pi$
$389$	−17.2125	−	9.93765i	−0.872709	−	0.503859i	−0.868248	+	0.496131i	$0.834754\pi$
$390$		0			0
$391$			18.6368i			0.942505i
$392$		0			0
$393$	−10.8246	+	0.667381i	−0.546029	+	0.0336649i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−1.83714	+	1.06067i	−0.0922035	+	0.0532337i	−0.545393	−	0.838181i	$-0.683619\pi$
$397$	−1.83714	+	1.06067i	−0.0922035	+	0.0532337i	0.453189	+	0.891414i	$0.350286\pi$
$398$		0			0
$399$	−5.89333	−	23.7794i	−0.295035	−	1.19046i
$400$		0			0
$401$	−11.4094	+	6.58723i	−0.569759	+	0.328951i	−0.757053	−	0.653353i	$-0.773362\pi$
$401$	−11.4094	+	6.58723i	−0.569759	+	0.328951i	0.187294	+	0.982304i	$0.440028\pi$
$402$		0			0
$403$	−16.4247	+	28.4485i	−0.818174	+	1.41712i
$404$		0			0
$405$		0			0
$406$		0			0
$407$			5.30762i			0.263089i
$408$		0			0
$409$	21.6170	+	12.4806i	1.06889	+	0.617124i	0.927878	−	0.372883i	$-0.121631\pi$
$409$	21.6170	+	12.4806i	1.06889	+	0.617124i	0.141013	+	0.990008i	$0.454964\pi$
$410$		0			0
$411$	−20.1666	+	13.3622i	−0.994746	+	0.659109i
$412$		0			0
$413$	4.85354	−	13.6238i	0.238827	−	0.670382i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	12.5264	+	6.23780i	0.613422	+	0.305466i
$418$		0			0
$419$	−26.0213			−1.27122			−0.635612	−	0.772009i	$-0.719252\pi$
$419$	−26.0213			−1.27122			−0.635612	+	0.772009i	$0.719252\pi$
$420$		0			0
$421$	−6.60400			−0.321859			−0.160930	−	0.986966i	$-0.551449\pi$
$421$	−6.60400			−0.321859			−0.160930	+	0.986966i	$0.551449\pi$
$422$		0			0
$423$	2.92346	−	6.90604i	0.142144	−	0.335783i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	15.7361	−	13.3883i	0.761522	−	0.647906i
$428$		0			0
$429$	−6.19640	−	9.35179i	−0.299165	−	0.451509i
$430$		0			0
$431$	−3.36279	−	1.94151i	−0.161980	−	0.0935191i	0.416819	−	0.908990i	$-0.363145\pi$
$431$	−3.36279	−	1.94151i	−0.161980	−	0.0935191i	−0.578799	+	0.815470i	$0.696478\pi$
$432$		0			0
$433$		−	26.6809i		−	1.28220i	−0.767456	−	0.641101i	$-0.778478\pi$
$433$		−	26.6809i		−	1.28220i	0.767456	−	0.641101i	$-0.221522\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	9.75321	−	16.8931i	0.466559	−	0.808105i
$438$		0			0
$439$	2.45130	−	1.41526i	0.116994	−	0.0675467i	−0.440361	−	0.897821i	$-0.645150\pi$
$439$	2.45130	−	1.41526i	0.116994	−	0.0675467i	0.557355	+	0.830274i	$0.311816\pi$
$440$		0			0
$441$	−17.7776	−	11.1784i	−0.846553	−	0.532304i
$442$		0			0
$443$	27.8171	−	16.0602i	1.32163	−	0.763043i	0.337640	−	0.941275i	$-0.390371\pi$
$443$	27.8171	−	16.0602i	1.32163	−	0.763043i	0.983988	+	0.178232i	$0.0570379\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−0.489974	−	7.94715i	−0.0231750	−	0.375887i
$448$		0			0
$449$		−	19.6498i		−	0.927334i	−0.886010	−	0.463667i	$-0.846533\pi$
$449$		−	19.6498i		−	0.927334i	0.886010	−	0.463667i	$-0.153467\pi$
$450$		0			0
$451$	−11.8247	−	6.82697i	−0.556801	−	0.321469i
$452$		0			0
$453$	7.73873	+	11.6795i	0.363597	+	0.548752i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	15.8753	+	27.4969i	0.742616	+	1.28625i	0.951300	+	0.308266i	$0.0997486\pi$
$457$	15.8753	+	27.4969i	0.742616	+	1.28625i	−0.208684	+	0.977983i	$0.566918\pi$
$458$		0			0
$459$	−8.82268	+	25.0313i	−0.411808	+	1.16836i
$460$		0			0
$461$	34.2329			1.59439			0.797193	−	0.603724i	$-0.206317\pi$
$461$	34.2329			1.59439			0.797193	+	0.603724i	$0.206317\pi$
$462$		0			0
$463$	−17.0910			−0.794288			−0.397144	−	0.917756i	$-0.629999\pi$
$463$	−17.0910			−0.794288			−0.397144	+	0.917756i	$0.629999\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−3.89858	−	6.75254i	−0.180405	−	0.312470i	0.761614	−	0.648031i	$-0.224407\pi$
$467$	−3.89858	−	6.75254i	−0.180405	−	0.312470i	−0.942018	+	0.335561i	$0.891074\pi$
$468$		0			0
$469$	9.91632	−	27.8349i	0.457893	−	1.28530i
$470$		0			0
$471$	−6.05123	+	4.00948i	−0.278826	+	0.184747i
$472$		0			0
$473$	5.09149	+	2.93957i	0.234107	+	0.135162i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−0.291315	−	2.35352i	−0.0133384	−	0.107760i
$478$		0			0
$479$	17.4180	−	30.1688i	0.795848	−	1.37845i	−0.126452	−	0.991973i	$-0.540359\pi$
$479$	17.4180	−	30.1688i	0.795848	−	1.37845i	0.922300	−	0.386476i	$-0.126308\pi$
$480$		0			0
$481$	12.4255	−	7.17385i	0.566553	−	0.327099i
$482$		0			0
$483$	−4.02225	−	16.2296i	−0.183018	−	0.738474i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	7.88941	−	13.6649i	0.357503	−	0.619214i	−0.630040	−	0.776563i	$-0.716961\pi$
$487$	7.88941	−	13.6649i	0.357503	−	0.619214i	0.987543	+	0.157349i	$0.0502948\pi$
$488$		0			0
$489$	11.5862	−	0.714339i	0.523948	−	0.0323035i
$490$		0			0
$491$		−	4.36169i		−	0.196840i	−0.995145	−	0.0984201i	$-0.968621\pi$
$491$		−	4.36169i		−	0.196840i	0.995145	−	0.0984201i	$-0.0313789\pi$
$492$		0			0
$493$	43.3349	+	25.0194i	1.95170	+	1.12682i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−3.80376	−	20.7428i	−0.170622	−	0.930442i
$498$		0			0
$499$	−3.21195	−	5.56327i	−0.143787	−	0.249046i	0.785133	−	0.619327i	$-0.212595\pi$
$499$	−3.21195	−	5.56327i	−0.143787	−	0.249046i	−0.928920	+	0.370281i	$0.879261\pi$
$500$		0			0
$501$	2.94936	−	5.92275i	0.131767	−	0.264609i
$502$		0			0
$503$	−34.7482			−1.54935			−0.774673	−	0.632362i	$-0.782086\pi$
$503$	−34.7482			−1.54935			−0.774673	+	0.632362i	$0.782086\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−3.48097	+	6.99031i	−0.154595	+	0.310451i
$508$		0			0
$509$	4.59595	+	7.96042i	0.203712	+	0.352839i	0.949722	−	0.313096i	$-0.101366\pi$
$509$	4.59595	+	7.96042i	0.203712	+	0.352839i	−0.746010	+	0.665935i	$0.768033\pi$
$510$		0			0
$511$	30.9018	+	11.0089i	1.36702	+	0.487007i
$512$		0			0
$513$	21.0968	−	18.0720i	0.931447	−	0.797900i
$514$		0			0
$515$		0			0
$516$		0			0
$517$		−	3.86941i		−	0.170176i
$518$		0			0
$519$	4.69560	−	0.289503i	0.206114	−	0.0127078i
$520$		0			0
$521$	10.3096	−	17.8568i	0.451673	−	0.782321i	−0.546817	−	0.837252i	$-0.684161\pi$
$521$	10.3096	−	17.8568i	0.451673	−	0.782321i	0.998490	+	0.0549315i	$0.0174940\pi$
$522$		0			0
$523$	17.5284	−	10.1200i	0.766465	−	0.442519i	−0.0651472	−	0.997876i	$-0.520752\pi$
$523$	17.5284	−	10.1200i	0.766465	−	0.442519i	0.831612	+	0.555357i	$0.187418\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	34.7266	−	20.0494i	1.51272	−	0.873367i
$528$		0			0
$529$	−4.84335	+	8.38893i	−0.210581	+	0.364736i
$530$		0			0
$531$	16.2747	−	2.01447i	0.706263	−	0.0874204i
$532$		0			0
$533$			36.9096i			1.59873i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−1.35899	+	0.900450i	−0.0586445	+	0.0388573i
$538$		0			0
$539$	−10.6954	−	1.73561i	−0.460683	−	0.0747580i
$540$		0			0
$541$	11.0976	+	19.2217i	0.477125	+	0.826404i	0.999656	−	0.0262157i	$-0.00834567\pi$
$541$	11.0976	+	19.2217i	0.477125	+	0.826404i	−0.522532	+	0.852620i	$0.675012\pi$
$542$		0			0
$543$	−0.0643885	−	0.0320636i	−0.00276317	−	0.00137598i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−23.3955			−1.00032			−0.500160	−	0.865933i	$-0.666725\pi$
$547$	−23.3955			−1.00032			−0.500160	+	0.865933i	$0.666725\pi$
$548$		0			0
$549$	21.5738	+	9.13262i	0.920748	+	0.389771i
$550$		0			0
$551$	−26.1868	−	45.3569i	−1.11559	−	1.93227i
$552$		0			0
$553$	−3.84473	−	4.51893i	−0.163494	−	0.192164i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	1.06603	+	0.615475i	0.0451693	+	0.0260785i	0.522415	−	0.852692i	$-0.325031\pi$
$557$	1.06603	+	0.615475i	0.0451693	+	0.0260785i	−0.477245	+	0.878770i	$0.658365\pi$
$558$		0			0
$559$		−	15.8926i		−	0.672187i
$560$		0			0
$561$	0.842696	+	13.6681i	0.0355787	+	0.577069i
$562$		0			0
$563$	−9.00633	+	15.5994i	−0.379571	+	0.657437i	−0.991000	−	0.133863i	$-0.957262\pi$
$563$	−9.00633	+	15.5994i	−0.379571	+	0.657437i	0.611429	+	0.791300i	$0.290595\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	2.28080	−	23.7023i	0.0957846	−	0.995402i
$568$		0			0
$569$	17.8273	−	10.2926i	0.747361	−	0.431489i	−0.0773783	−	0.997002i	$-0.524655\pi$
$569$	17.8273	−	10.2926i	0.747361	−	0.431489i	0.824740	+	0.565513i	$0.191322\pi$
$570$		0			0
$571$	5.12127	−	8.87029i	0.214318	−	0.371210i	−0.738743	−	0.673987i	$-0.764580\pi$
$571$	5.12127	−	8.87029i	0.214318	−	0.371210i	0.953061	+	0.302777i	$0.0979137\pi$
$572$		0			0
$573$	0.998140	+	16.1894i	0.0416979	+	0.676320i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−19.8281	−	11.4478i	−0.825455	−	0.476576i	0.0268392	−	0.999640i	$-0.491456\pi$
$577$	−19.8281	−	11.4478i	−0.825455	−	0.476576i	−0.852294	+	0.523063i	$0.824789\pi$
$578$		0			0
$579$	−9.84123	−	14.8527i	−0.408988	−	0.617256i
$580$		0			0
$581$	13.7011	−	2.51247i	0.568416	−	0.104235i
$582$		0			0
$583$	−0.611802	−	1.05967i	−0.0253382	−	0.0438871i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−13.1377			−0.542251			−0.271125	−	0.962544i	$-0.587396\pi$
$587$	−13.1377			−0.542251			−0.271125	+	0.962544i	$0.587396\pi$
$588$		0			0
$589$	−41.9699			−1.72934
$590$		0			0
$591$	−1.85955	−	0.926002i	−0.0764918	−	0.0380906i
$592$		0			0
$593$	16.0998	+	27.8856i	0.661138	+	1.14512i	0.980317	+	0.197430i	$0.0632594\pi$
$593$	16.0998	+	27.8856i	0.661138	+	1.14512i	−0.319179	+	0.947694i	$0.603407\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−28.0022	+	18.5540i	−1.14605	+	0.759364i
$598$		0			0
$599$	−37.7878	−	21.8168i	−1.54397	−	0.891411i	−0.998582	−	0.0532262i	$-0.983050\pi$
$599$	−37.7878	−	21.8168i	−1.54397	−	0.891411i	−0.545387	−	0.838185i	$-0.683617\pi$
$600$		0			0
$601$			23.7804i			0.970024i	0.874508	+	0.485012i	$0.161185\pi$
$601$			23.7804i			0.970024i	−0.874508	+	0.485012i	$0.838815\pi$
$602$		0			0
$603$	33.2511	−	4.11578i	1.35409	−	0.167607i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−18.4055	+	10.6264i	−0.747058	+	0.431314i	−0.824630	−	0.565673i	$-0.808617\pi$
$607$	−18.4055	+	10.6264i	−0.747058	+	0.431314i	0.0775719	+	0.996987i	$0.475283\pi$
$608$		0			0
$609$	−43.1373	−	12.4352i	−1.74801	−	0.503898i
$610$		0			0
$611$	−9.05853	+	5.22994i	−0.366469	+	0.211581i
$612$		0			0
$613$	4.59974	−	7.96699i	0.185782	−	0.321784i	−0.758058	−	0.652187i	$-0.773852\pi$
$613$	4.59974	−	7.96699i	0.185782	−	0.321784i	0.943840	+	0.330404i	$0.107185\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$			48.7268i			1.96167i	0.194850	+	0.980833i	$0.437578\pi$
$617$			48.7268i			1.96167i	−0.194850	+	0.980833i	$0.562422\pi$
$618$		0			0
$619$	−26.7205	−	15.4271i	−1.07399	−	0.620068i	−0.144720	−	0.989473i	$-0.546228\pi$
$619$	−26.7205	−	15.4271i	−1.07399	−	0.620068i	−0.929268	+	0.369405i	$0.879561\pi$
$620$		0			0
$621$	14.3987	−	12.3343i	0.577802	−	0.494959i
$622$		0			0
$623$	−26.2560	−	30.8602i	−1.05192	−	1.23639i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	6.38909	−	12.8303i	0.255156	−	0.512392i
$628$		0			0
$629$	−17.5140			−0.698330
$630$		0			0
$631$	11.0171			0.438585			0.219293	−	0.975659i	$-0.429625\pi$
$631$	11.0171			0.438585			0.219293	+	0.975659i	$0.429625\pi$
$632$		0			0
$633$	7.22287	−	14.5046i	0.287083	−	0.576507i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	10.3929	+	27.3845i	0.411780	+	1.08501i
$638$		0			0
$639$	19.0831	−	14.4095i	0.754917	−	0.570031i
$640$		0			0
$641$	−6.08428	−	3.51276i	−0.240314	−	0.138746i	0.375007	−	0.927022i	$-0.377640\pi$
$641$	−6.08428	−	3.51276i	−0.240314	−	0.138746i	−0.615321	+	0.788276i	$0.710974\pi$
$642$		0			0
$643$		−	35.3578i		−	1.39438i	−0.716889	−	0.697188i	$-0.754434\pi$
$643$		−	35.3578i		−	1.39438i	0.716889	−	0.697188i	$-0.245566\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−0.0623003	+	0.107907i	−0.00244928	+	0.00424227i	−0.867247	−	0.497877i	$-0.834113\pi$
$647$	−0.0623003	+	0.107907i	−0.00244928	+	0.00424227i	0.864798	+	0.502120i	$0.167446\pi$
$648$		0			0
$649$	7.32771	−	4.23065i	0.287638	−	0.166068i
$650$		0			0
$651$	−25.9141	+	24.9546i	−1.01565	+	0.978046i
$652$		0			0
$653$	−18.9320	+	10.9304i	−0.740868	+	0.427741i	−0.822385	−	0.568931i	$-0.807357\pi$
$653$	−18.9320	+	10.9304i	−0.740868	+	0.427741i	0.0815166	+	0.996672i	$0.474024\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	4.56927	+	36.9148i	0.178264	+	1.44019i
$658$		0			0
$659$			16.4975i			0.642651i	0.946969	+	0.321326i	$0.104128\pi$
$659$			16.4975i			0.642651i	−0.946969	+	0.321326i	$0.895872\pi$
$660$		0			0
$661$	−30.8643	−	17.8195i	−1.20048	−	0.693098i	−0.239818	−	0.970818i	$-0.577088\pi$
$661$	−30.8643	−	17.8195i	−1.20048	−	0.693098i	−0.960662	+	0.277720i	$0.910421\pi$
$662$		0			0
$663$	30.8589	−	20.4468i	1.19846	−	0.794089i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−17.8727	−	30.9564i	−0.692034	−	1.19864i
$668$		0			0
$669$	10.5142	+	5.23575i	0.406502	+	0.202426i
$670$		0			0
$671$	12.0877			0.466639
$672$		0			0
$673$	15.6461			0.603113			0.301557	−	0.953448i	$-0.402494\pi$
$673$	15.6461			0.603113			0.301557	+	0.953448i	$0.402494\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	12.6612	+	21.9298i	0.486609	+	0.842831i	0.999881	−	0.0153946i	$-0.00490046\pi$
$677$	12.6612	+	21.9298i	0.486609	+	0.842831i	−0.513273	+	0.858225i	$0.671567\pi$
$678$		0			0
$679$	7.58848	+	41.3818i	0.291219	+	1.58809i
$680$		0			0
$681$	13.5779	+	20.4922i	0.520308	+	0.785264i
$682$		0			0
$683$	18.2913	+	10.5605i	0.699898	+	0.404086i	0.807309	−	0.590128i	$-0.200923\pi$
$683$	18.2913	+	10.5605i	0.699898	+	0.404086i	−0.107411	+	0.994215i	$0.534256\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	1.20598	+	19.5605i	0.0460112	+	0.746279i
$688$		0			0
$689$	−1.65384	+	2.86453i	−0.0630062	+	0.109130i
$690$		0			0
$691$	12.3309	−	7.11924i	0.469089	−	0.270829i	−0.246769	−	0.969074i	$-0.579369\pi$
$691$	12.3309	−	7.11924i	0.469089	−	0.270829i	0.715858	+	0.698245i	$0.246036\pi$
$692$		0			0
$693$	−3.68374	−	11.7208i	−0.139934	−	0.445237i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	22.5275	−	39.0189i	0.853292	−	1.47794i
$698$		0			0
$699$	−1.94655	−	31.5721i	−0.0736252	−	1.19417i
$700$		0			0
$701$			12.1825i			0.460127i	0.973176	+	0.230063i	$0.0738934\pi$
$701$			12.1825i			0.460127i	−0.973176	+	0.230063i	$0.926107\pi$
$702$		0			0
$703$	15.8753	+	9.16562i	0.598749	+	0.345688i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	6.80655	−	19.1058i	0.255987	−	0.718548i
$708$		0			0
$709$	12.5140	+	21.6748i	0.469971	+	0.814014i	0.999410	−	0.0343336i	$-0.0109309\pi$
$709$	12.5140	+	21.6748i	0.469971	+	0.814014i	−0.529439	+	0.848348i	$0.677598\pi$
$710$		0			0
$711$	2.62262	−	6.19536i	0.0983558	−	0.232344i
$712$		0			0
$713$	−28.6448			−1.07276
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−29.2777	−	14.5794i	−1.09340	−	0.544479i
$718$		0			0
$719$	5.93961	+	10.2877i	0.221510	+	0.383666i	0.955267	−	0.295746i	$-0.0955682\pi$
$719$	5.93961	+	10.2877i	0.221510	+	0.383666i	−0.733757	+	0.679412i	$0.762235\pi$
$720$		0			0
$721$	−2.23384	+	1.90056i	−0.0831925	+	0.0707806i
$722$		0			0
$723$	20.1096	−	13.3244i	0.747884	−	0.495540i
$724$		0			0
$725$		0			0
$726$		0			0
$727$			11.1429i			0.413265i	0.978419	+	0.206633i	$0.0662505\pi$
$727$			11.1429i			0.413265i	−0.978419	+	0.206633i	$0.933749\pi$
$728$		0			0
$729$	25.1781	−	9.74995i	0.932524	−	0.361109i
$730$		0			0
$731$	−9.69997	+	16.8008i	−0.358766	+	0.621401i
$732$		0			0
$733$	29.2014	−	16.8594i	1.07858	−	0.622717i	0.148065	−	0.988978i	$-0.452696\pi$
$733$	29.2014	−	16.8594i	1.07858	−	0.622717i	0.930512	+	0.366261i	$0.119362\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	14.9713	−	8.64370i	0.551476	−	0.318395i
$738$		0			0
$739$	0.619063	−	1.07225i	0.0227726	−	0.0394433i	−0.854415	−	0.519592i	$-0.826084\pi$
$739$	0.619063	−	1.07225i	0.0227726	−	0.0394433i	0.877187	+	0.480149i	$0.159417\pi$
$740$		0			0
$741$	−38.6720	+	2.38429i	−1.42065	+	0.0875891i
$742$		0			0
$743$			42.5482i			1.56094i	0.625191	+	0.780472i	$0.285021\pi$
$743$			42.5482i			1.56094i	−0.625191	+	0.780472i	$0.714979\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	9.51777	+	12.6048i	0.348237	+	0.461186i
$748$		0			0
$749$	−2.96522	+	2.52282i	−0.108347	+	0.0921819i
$750$		0			0
$751$	11.5563	+	20.0161i	0.421695	+	0.730397i	0.996105	−	0.0881704i	$-0.0281020\pi$
$751$	11.5563	+	20.0161i	0.421695	+	0.730397i	−0.574411	+	0.818567i	$0.694769\pi$
$752$		0			0
$753$	−20.7044	+	41.5775i	−0.754510	+	1.51517i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	37.9224			1.37831			0.689156	−	0.724613i	$-0.257981\pi$
$757$	37.9224			1.37831			0.689156	+	0.724613i	$0.257981\pi$
$758$		0			0
$759$	4.36061	−	8.75676i	0.158280	−	0.317850i
$760$		0			0
$761$	18.1928	+	31.5108i	0.659488	+	1.14227i	0.980748	+	0.195275i	$0.0625601\pi$
$761$	18.1928	+	31.5108i	0.659488	+	1.14227i	−0.321261	+	0.946991i	$0.604107\pi$
$762$		0			0
$763$	−8.29118	+	23.2732i	−0.300161	+	0.842545i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−19.8084	−	11.4364i	−0.715242	−	0.412945i
$768$		0			0
$769$			3.93239i			0.141805i	0.997483	+	0.0709027i	$0.0225880\pi$
$769$			3.93239i			0.141805i	−0.997483	+	0.0709027i	$0.977412\pi$
$770$		0			0
$771$	24.1617	−	1.48967i	0.870163	−	0.0536491i
$772$		0			0
$773$	22.8767	−	39.6236i	0.822817	−	1.42516i	−0.0807599	−	0.996734i	$-0.525735\pi$
$773$	22.8767	−	39.6236i	0.822817	−	1.42516i	0.903577	−	0.428427i	$-0.140932\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	15.2519	−	3.77992i	0.547157	−	0.135604i
$778$		0			0
$779$	−40.8395	+	23.5787i	−1.46323	+	0.844794i
$780$		0			0
$781$	6.16898	−	10.6850i	0.220744	−	0.382339i
$782$		0			0
$783$	−9.35019	−	50.0388i	−0.334148	−	1.78824i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	9.99986	+	5.77342i	0.356457	+	0.205800i	0.667525	−	0.744587i	$-0.267354\pi$
$787$	9.99986	+	5.77342i	0.356457	+	0.205800i	−0.311069	+	0.950387i	$0.600687\pi$
$788$		0			0
$789$	43.5536	−	28.8582i	1.55055	−	1.02738i
$790$		0			0
$791$	−5.71571	−	31.1691i	−0.203227	−	1.10825i
$792$		0			0
$793$	−16.3378	−	28.2980i	−0.580174	−	1.00489i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	5.24845			0.185910			0.0929548	−	0.995670i	$-0.470369\pi$
$797$	5.24845			0.185910			0.0929548	+	0.995670i	$0.470369\pi$
$798$		0			0
$799$	12.7682			0.451708
$800$		0			0
$801$	17.9101	−	42.3086i	0.632821	−	1.49490i
$802$		0			0
$803$	9.59609	+	16.6209i	0.338639	+	0.586540i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−6.57318	−	9.92043i	−0.231387	−	0.349216i
$808$		0			0
$809$	40.9993	+	23.6710i	1.44146	+	0.832227i	0.997947	−	0.0640417i	$-0.0203991\pi$
$809$	40.9993	+	23.6710i	1.44146	+	0.832227i	0.443512	+	0.896268i	$0.353732\pi$
$810$		0			0
$811$		−	31.5218i		−	1.10688i	−0.832889	−	0.553440i	$-0.813315\pi$
$811$		−	31.5218i		−	1.10688i	0.832889	−	0.553440i	$-0.186685\pi$
$812$		0			0
$813$	2.38760	+	38.7257i	0.0837368	+	1.35817i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	17.5848	−	10.1526i	0.615213	−	0.355193i
$818$		0			0
$819$	−22.4602	+	24.4659i	−0.784823	+	0.854907i
$820$		0			0
$821$	17.1600	−	9.90735i	0.598890	−	0.345769i	−0.169715	−	0.985493i	$-0.554285\pi$
$821$	17.1600	−	9.90735i	0.598890	−	0.345769i	0.768605	+	0.639724i	$0.220951\pi$
$822$		0			0
$823$	3.45569	−	5.98542i	0.120458	−	0.208639i	−0.799491	−	0.600679i	$-0.794897\pi$
$823$	3.45569	−	5.98542i	0.120458	−	0.208639i	0.919948	+	0.392040i	$0.128230\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	27.6374i		−	0.961045i	−0.876982	−	0.480523i	$-0.840447\pi$
$827$		−	27.6374i		−	0.961045i	0.876982	−	0.480523i	$-0.159553\pi$
$828$		0			0
$829$	−22.5579	−	13.0238i	−0.783468	−	0.452336i	0.0541897	−	0.998531i	$-0.482742\pi$
$829$	−22.5579	−	13.0238i	−0.783468	−	0.452336i	−0.837658	+	0.546195i	$0.816076\pi$
$830$		0			0
$831$	6.67819	+	10.0789i	0.231664	+	0.349634i
$832$		0			0
$833$	5.72714	−	35.2926i	0.198434	−	1.22281i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−38.4731	−	13.5605i	−1.32982	−	0.468718i
$838$		0			0
$839$	57.2133			1.97522			0.987611	−	0.156924i	$-0.0501577\pi$
$839$	57.2133			1.97522			0.987611	+	0.156924i	$0.0501577\pi$
$840$		0			0
$841$	−66.9743			−2.30946
$842$		0			0
$843$	−3.69915	−	1.84207i	−0.127406	−	0.0634442i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	14.7512	+	17.3379i	0.506857	+	0.595739i
$848$		0			0
$849$	−35.0526	+	23.2255i	−1.20300	+	0.797098i
$850$		0			0
$851$	10.8350	+	6.25561i	0.371420	+	0.214440i
$852$		0			0
$853$			36.1034i			1.23616i	0.786117	+	0.618078i	$0.212088\pi$
$853$			36.1034i			1.23616i	−0.786117	+	0.618078i	$0.787912\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	23.7562	−	41.1470i	0.811497	−	1.40555i	−0.100320	−	0.994955i	$-0.531987\pi$
$857$	23.7562	−	41.1470i	0.811497	−	1.40555i	0.911816	−	0.410598i	$-0.134680\pi$
$858$		0			0
$859$	−5.37937	+	3.10578i	−0.183542	+	0.105968i	−0.588956	−	0.808165i	$-0.700461\pi$
$859$	−5.37937	+	3.10578i	−0.183542	+	0.105968i	0.405414	+	0.914133i	$0.367127\pi$
$860$		0			0
$861$	−11.1967	+	38.8410i	−0.381581	+	1.32370i
$862$		0			0
$863$	38.0000	−	21.9393i	1.29354	−	0.746824i	0.314257	−	0.949338i	$-0.398245\pi$
$863$	38.0000	−	21.9393i	1.29354	−	0.746824i	0.979279	+	0.202514i	$0.0649112\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−15.7129	+	0.968764i	−0.533638	+	0.0329010i
$868$		0			0
$869$		−	3.47122i		−	0.117753i
$870$		0			0
$871$	−40.4709	−	23.3659i	−1.37130	−	0.791722i
$872$		0			0
$873$	−38.0707	+	28.7468i	−1.28850	+	0.972933i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	11.2462	+	19.4790i	0.379757	+	0.657758i	0.991027	−	0.133664i	$-0.0426743\pi$
$877$	11.2462	+	19.4790i	0.379757	+	0.657758i	−0.611270	+	0.791422i	$0.709341\pi$
$878$		0			0
$879$	−19.1711	+	38.4985i	−0.646626	+	1.29852i
$880$		0			0
$881$	−5.24052			−0.176558			−0.0882788	−	0.996096i	$-0.528137\pi$
$881$	−5.24052			−0.176558			−0.0882788	+	0.996096i	$0.528137\pi$
$882$		0			0
$883$	−35.5284			−1.19562			−0.597812	−	0.801636i	$-0.703963\pi$
$883$	−35.5284			−1.19562			−0.597812	+	0.801636i	$0.703963\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	3.72520	+	6.45224i	0.125080	+	0.216645i	0.921764	−	0.387751i	$-0.126748\pi$
$887$	3.72520	+	6.45224i	0.125080	+	0.216645i	−0.796684	+	0.604396i	$0.793415\pi$
$888$		0			0
$889$	8.22858	−	1.50894i	0.275978	−	0.0506081i
$890$		0			0
$891$	10.0022	−	9.69697i	0.335087	−	0.324861i
$892$		0			0
$893$	−11.5736	−	6.68200i	−0.387295	−	0.223605i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−26.3940	+	1.62730i	−0.881269	+	0.0543339i
$898$		0			0
$899$	−38.4548	+	66.6056i	−1.28254	+	2.22142i
$900$		0			0
$901$	3.49669	−	2.01882i	0.116492	−	0.0672565i
$902$		0			0
$903$	4.82108	−	16.7242i	0.160436	−	0.556548i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−10.3321	+	17.8957i	−0.343072	+	0.594218i	−0.985002	−	0.172545i	$-0.944801\pi$
$907$	−10.3321	+	17.8957i	−0.343072	+	0.594218i	0.641929	+	0.766764i	$0.278134\pi$
$908$		0			0
$909$	22.8235	−	2.82506i	0.757008	−	0.0937015i
$910$		0			0
$911$			9.23666i			0.306024i	0.988224	+	0.153012i	$0.0488974\pi$
$911$			9.23666i			0.306024i	−0.988224	+	0.153012i	$0.951103\pi$
$912$		0			0
$913$	7.05766	+	4.07474i	0.233575	+	0.134854i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	10.7350	+	12.6175i	0.354501	+	0.416665i
$918$		0			0
$919$	20.0585	+	34.7423i	0.661669	+	1.14604i	0.980177	+	0.198123i	$0.0634847\pi$
$919$	20.0585	+	34.7423i	0.661669	+	1.14604i	−0.318509	+	0.947920i	$0.603182\pi$
$920$		0			0
$921$	24.4705	+	12.1856i	0.806332	+	0.401529i
$922$		0			0
$923$	−33.3523			−1.09780
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−3.06255	−	1.29644i	−0.100587	−	0.0425805i
$928$		0			0
$929$	6.25279	+	10.8301i	0.205147	+	0.355326i	0.950180	−	0.311703i	$-0.100899\pi$
$929$	6.25279	+	10.8301i	0.205147	+	0.355326i	−0.745032	+	0.667028i	$0.767566\pi$
$930$		0			0
$931$	−23.6609	+	28.9932i	−0.775456	+	0.950213i
$932$		0			0
$933$	−3.26413	−	4.92632i	−0.106863	−	0.161281i
$934$		0			0
$935$		0			0
$936$		0			0
$937$			15.6057i			0.509817i	0.966965	+	0.254908i	$0.0820453\pi$
$937$			15.6057i			0.509817i	−0.966965	+	0.254908i	$0.917955\pi$
$938$		0			0
$939$	2.75676	+	44.7133i	0.0899634	+	1.45916i
$940$		0			0
$941$	−15.0129	+	26.0032i	−0.489408	+	0.847679i	−0.999926	−	0.0121879i	$-0.996120\pi$
$941$	−15.0129	+	26.0032i	−0.489408	+	0.847679i	0.510518	+	0.859867i	$0.329454\pi$
$942$		0			0
$943$	−27.8733	+	16.0926i	−0.907679	+	0.524049i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−18.6750	+	10.7820i	−0.606854	+	0.350368i	−0.771733	−	0.635946i	$-0.780610\pi$
$947$	−18.6750	+	10.7820i	−0.606854	+	0.350368i	0.164879	+	0.986314i	$0.447277\pi$
$948$		0			0
$949$	25.9404	−	44.9301i	0.842061	−	1.45849i
$950$		0			0
$951$	−1.86593	−	30.2644i	−0.0605068	−	0.981392i
$952$		0			0
$953$			32.6140i			1.05647i	0.849098	+	0.528236i	$0.177146\pi$
$953$			32.6140i			1.05647i	−0.849098	+	0.528236i	$0.822854\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−14.5075	−	21.8951i	−0.468960	−	0.707768i
$958$		0			0
$959$	34.8104	+	12.4014i	1.12409	+	0.400462i
$960$		0			0
$961$	15.3160	+	26.5280i	0.494063	+	0.855742i
$962$		0			0
$963$	−4.06525	−	1.72090i	−0.131001	−	0.0554553i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	8.08819			0.260099			0.130049	−	0.991508i	$-0.458486\pi$
$967$	8.08819			0.260099			0.130049	+	0.991508i	$0.458486\pi$
$968$		0			0
$969$	42.3372	+	21.0827i	1.36007	+	0.677273i
$970$		0			0
$971$	28.7921	+	49.8694i	0.923983	+	1.60039i	0.793189	+	0.608976i	$0.208419\pi$
$971$	28.7921	+	49.8694i	0.923983	+	1.60039i	0.130794	+	0.991410i	$0.458247\pi$
$972$		0			0
$973$	−3.85552	−	21.0250i	−0.123602	−	0.674032i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−18.0342	−	10.4121i	−0.576966	−	0.333112i	0.182961	−	0.983120i	$-0.441432\pi$
$977$	−18.0342	−	10.4121i	−0.576966	−	0.333112i	−0.759927	+	0.650009i	$0.774765\pi$
$978$		0			0
$979$		−	23.7053i		−	0.757623i
$980$		0			0
$981$	−27.8017	+	3.44126i	−0.887641	+	0.109871i
$982$		0			0
$983$	−4.90474	+	8.49526i	−0.156437	+	0.270957i	−0.933581	−	0.358366i	$-0.883334\pi$
$983$	−4.90474	+	8.49526i	−0.156437	+	0.270957i	0.777144	+	0.629322i	$0.216667\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−11.1190	+	2.75567i	−0.353923	+	0.0877140i
$988$		0			0
$989$	12.0017	−	6.92921i	0.381633	−	0.220336i
$990$		0			0
$991$	19.9849	−	34.6149i	0.634843	−	1.09958i	−0.351706	−	0.936111i	$-0.614398\pi$
$991$	19.9849	−	34.6149i	0.634843	−	1.09958i	0.986548	−	0.163469i	$-0.0522684\pi$
$992$		0			0
$993$	−48.6077	+	2.99687i	−1.54252	+	0.0951027i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	20.2236	+	11.6761i	0.640489	+	0.369786i	0.784803	−	0.619746i	$-0.212764\pi$
$997$	20.2236	+	11.6761i	0.640489	+	0.369786i	−0.144314	+	0.989532i	$0.546098\pi$
$998$		0			0
$999$	11.5912	+	13.5313i	0.366730	+	0.428111i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2100.2.bi.n.101.10		32
3.2	odd	2	inner	2100.2.bi.n.101.5		32
5.2	odd	4		420.2.bn.a.269.2	yes	32
5.3	odd	4		420.2.bn.a.269.15	yes	32
5.4	even	2	inner	2100.2.bi.n.101.7		32
7.5	odd	6	inner	2100.2.bi.n.1601.5		32
15.2	even	4		420.2.bn.a.269.13	yes	32
15.8	even	4		420.2.bn.a.269.4	yes	32
15.14	odd	2	inner	2100.2.bi.n.101.12		32
21.5	even	6	inner	2100.2.bi.n.1601.10		32
35.3	even	12		2940.2.f.a.1469.20		32
35.12	even	12		420.2.bn.a.89.4	yes	32
35.17	even	12		2940.2.f.a.1469.14		32
35.18	odd	12		2940.2.f.a.1469.13		32
35.19	odd	6	inner	2100.2.bi.n.1601.12		32
35.32	odd	12		2940.2.f.a.1469.19		32
35.33	even	12		420.2.bn.a.89.13	yes	32
105.17	odd	12		2940.2.f.a.1469.15		32
105.32	even	12		2940.2.f.a.1469.18		32
105.38	odd	12		2940.2.f.a.1469.17		32
105.47	odd	12		420.2.bn.a.89.15	yes	32
105.53	even	12		2940.2.f.a.1469.16		32
105.68	odd	12		420.2.bn.a.89.2	✓	32
105.89	even	6	inner	2100.2.bi.n.1601.7		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
420.2.bn.a.89.2	✓	32	105.68	odd	12
420.2.bn.a.89.4	yes	32	35.12	even	12
420.2.bn.a.89.13	yes	32	35.33	even	12
420.2.bn.a.89.15	yes	32	105.47	odd	12
420.2.bn.a.269.2	yes	32	5.2	odd	4
420.2.bn.a.269.4	yes	32	15.8	even	4
420.2.bn.a.269.13	yes	32	15.2	even	4
420.2.bn.a.269.15	yes	32	5.3	odd	4
2100.2.bi.n.101.5		32	3.2	odd	2	inner
2100.2.bi.n.101.7		32	5.4	even	2	inner
2100.2.bi.n.101.10		32	1.1	even	1	trivial
2100.2.bi.n.101.12		32	15.14	odd	2	inner
2100.2.bi.n.1601.5		32	7.5	odd	6	inner
2100.2.bi.n.1601.7		32	105.89	even	6	inner
2100.2.bi.n.1601.10		32	21.5	even	6	inner
2100.2.bi.n.1601.12		32	35.19	odd	6	inner
2940.2.f.a.1469.13		32	35.18	odd	12
2940.2.f.a.1469.14		32	35.17	even	12
2940.2.f.a.1469.15		32	105.17	odd	12
2940.2.f.a.1469.16		32	105.53	even	12
2940.2.f.a.1469.17		32	105.38	odd	12
2940.2.f.a.1469.18		32	105.32	even	12
2940.2.f.a.1469.19		32	35.32	odd	12
2940.2.f.a.1469.20		32	35.3	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.bi (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.772078 - 1.55045i) q^{3} +(-2.60236 + 0.477214i) q^{7} +(-1.80779 - 2.39414i) q^{9} +O(q^{10})\)	\(q+(0.772078 - 1.55045i) q^{3} +(-2.60236 + 0.477214i) q^{7} +(-1.80779 - 2.39414i) q^{9} +(-1.34052 - 0.773950i) q^{11} +4.18432i q^{13} +(2.55387 - 4.42344i) q^{17} +(-4.62984 + 2.67304i) q^{19} +(-1.26933 + 4.40327i) q^{21} +(-3.15990 + 1.82437i) q^{23} +(-5.10775 + 0.954427i) q^{27} +9.79665i q^{29} +(6.79882 + 3.92530i) q^{31} +(-2.23496 + 1.48086i) q^{33} +(-1.71446 - 2.96953i) q^{37} +(6.48759 + 3.23063i) q^{39} +8.82093 q^{41} -3.79814 q^{43} +(1.24989 + 2.16487i) q^{47} +(6.54453 - 2.48376i) q^{49} +(-4.88653 - 7.37489i) q^{51} +(0.684586 + 0.395246i) q^{53} +(0.569815 + 9.24212i) q^{57} +(-2.73316 + 4.73397i) q^{59} +(-6.76285 + 3.90454i) q^{61} +(5.84703 + 5.36770i) q^{63} +(-5.58414 + 9.67202i) q^{67} +(0.388903 + 6.30782i) q^{69} +7.97077i q^{71} +(-10.7377 - 6.19943i) q^{73} +(3.85786 + 1.37438i) q^{77} +(1.12127 + 1.94209i) q^{79} +(-2.46379 + 8.65620i) q^{81} -5.26486 q^{83} +(15.1892 + 7.56378i) q^{87} +(7.65723 + 13.2627i) q^{89} +(-1.99682 - 10.8891i) q^{91} +(11.3352 - 7.51059i) q^{93} -15.9016i q^{97} +(0.570438 + 4.60853i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 32 * q	\( 32 q - 12 q^{19} - 8 q^{21} - 12 q^{31} - 24 q^{39} + 44 q^{49} - 10 q^{51} - 24 q^{61} + 28 q^{79} - 20 q^{81} + 16 q^{91} + 28 q^{99}+O(q^{100}) \) 32 * q - 12 * q^19 - 8 * q^21 - 12 * q^31 - 24 * q^39 + 44 * q^49 - 10 * q^51 - 24 * q^61 + 28 * q^79 - 20 * q^81 + 16 * q^91 + 28 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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