LMFDB - Embedded newform 1664.2.n.b.417.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1664,2,Mod(417,1664)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1664, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("1664.417");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1664 = 2^{7} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1664.n (of order $4$, 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:	$13.2871068963$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 208)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			417.8
Character	$\chi$	$=$	1664.417
Dual form			1664.2.n.b.1249.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.902776 - 0.902776i) q^{3} +(1.29480 - 1.29480i) q^{5} -3.20594i q^{7} -1.36999i q^{9} +O(q^{10})$	\(q+(-0.902776 - 0.902776i) q^{3} +(1.29480 - 1.29480i) q^{5} -3.20594i q^{7} -1.36999i q^{9} +(2.72143 - 2.72143i) q^{11} +(-0.707107 - 0.707107i) q^{13} -2.33784 q^{15} -6.03671 q^{17} +(-1.89947 - 1.89947i) q^{19} +(-2.89424 + 2.89424i) q^{21} -8.67448i q^{23} +1.64697i q^{25} +(-3.94512 + 3.94512i) q^{27} +(6.82640 + 6.82640i) q^{29} +5.23082 q^{31} -4.91369 q^{33} +(-4.15106 - 4.15106i) q^{35} +(0.208536 - 0.208536i) q^{37} +1.27672i q^{39} +9.29774i q^{41} +(-0.0416722 + 0.0416722i) q^{43} +(-1.77387 - 1.77387i) q^{45} +2.16694 q^{47} -3.27803 q^{49} +(5.44980 + 5.44980i) q^{51} +(6.38002 - 6.38002i) q^{53} -7.04745i q^{55} +3.42959i q^{57} +(-3.38796 + 3.38796i) q^{59} +(-1.72743 - 1.72743i) q^{61} -4.39210 q^{63} -1.83113 q^{65} +(1.56033 + 1.56033i) q^{67} +(-7.83111 + 7.83111i) q^{69} +9.73843i q^{71} +6.08728i q^{73} +(1.48684 - 1.48684i) q^{75} +(-8.72475 - 8.72475i) q^{77} -5.31445 q^{79} +3.01316 q^{81} +(-9.71028 - 9.71028i) q^{83} +(-7.81635 + 7.81635i) q^{85} -12.3254i q^{87} -5.94615i q^{89} +(-2.26694 + 2.26694i) q^{91} +(-4.72226 - 4.72226i) q^{93} -4.91887 q^{95} -9.79055 q^{97} +(-3.72834 - 3.72834i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q+O(q^{10}) $ 48 * q	$ 48 q + 8 q^{11} - 16 q^{15} + 16 q^{19} + 16 q^{29} + 24 q^{31} - 24 q^{35} + 16 q^{37} + 8 q^{43} - 40 q^{47} - 48 q^{49} + 24 q^{51} - 16 q^{53} - 32 q^{61} + 40 q^{63} - 16 q^{67} - 32 q^{69} + 40 q^{75} - 16 q^{77} + 32 q^{79} - 48 q^{81} - 40 q^{83} + 32 q^{85} - 48 q^{95} + 40 q^{99}+O(q^{100}) $ 48 * q + 8 * q^11 - 16 * q^15 + 16 * q^19 + 16 * q^29 + 24 * q^31 - 24 * q^35 + 16 * q^37 + 8 * q^43 - 40 * q^47 - 48 * q^49 + 24 * q^51 - 16 * q^53 - 32 * q^61 + 40 * q^63 - 16 * q^67 - 32 * q^69 + 40 * q^75 - 16 * q^77 + 32 * q^79 - 48 * q^81 - 40 * q^83 + 32 * q^85 - 48 * q^95 + 40 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1664\mathbb{Z}\right)^\times$.

$n$	$261$	$769$	$1535$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$1$

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
$3$	−0.902776	−	0.902776i	−0.521218	−	0.521218i	0.396721	−	0.917939i	$-0.370148\pi$
$3$	−0.902776	−	0.902776i	−0.521218	−	0.521218i	−0.917939	+	0.396721i	$0.870148\pi$
$4$		0			0
$5$	1.29480	−	1.29480i	0.579054	−	0.579054i	−0.355589	−	0.934643i	$-0.615720\pi$
$5$	1.29480	−	1.29480i	0.579054	−	0.579054i	0.934643	+	0.355589i	$0.115720\pi$
$6$		0			0
$7$		−	3.20594i		−	1.21173i	−0.795567	−	0.605865i	$-0.792827\pi$
$7$		−	3.20594i		−	1.21173i	0.795567	−	0.605865i	$-0.207173\pi$
$8$		0			0
$9$		−	1.36999i		−	0.456663i
$10$		0			0
$11$	2.72143	−	2.72143i	0.820543	−	0.820543i	−0.165642	−	0.986186i	$-0.552970\pi$
$11$	2.72143	−	2.72143i	0.820543	−	0.820543i	0.986186	+	0.165642i	$0.0529698\pi$
$12$		0			0
$13$	−0.707107	−	0.707107i	−0.196116	−	0.196116i
$13$	−0.707107	−	0.707107i	−0.196116	−	0.196116i
$14$		0			0
$15$	−2.33784			−0.603627
$16$		0			0
$17$	−6.03671			−1.46412			−0.732058	−	0.681242i	$-0.761440\pi$
$17$	−6.03671			−1.46412			−0.732058	+	0.681242i	$0.761440\pi$
$18$		0			0
$19$	−1.89947	−	1.89947i	−0.435768	−	0.435768i	0.454817	−	0.890585i	$-0.349705\pi$
$19$	−1.89947	−	1.89947i	−0.435768	−	0.435768i	−0.890585	+	0.454817i	$0.849705\pi$
$20$		0			0
$21$	−2.89424	+	2.89424i	−0.631576	+	0.631576i
$22$		0			0
$23$		−	8.67448i		−	1.80875i	−0.426734	−	0.904377i	$-0.640336\pi$
$23$		−	8.67448i		−	1.80875i	0.426734	−	0.904377i	$-0.359664\pi$
$24$		0			0
$25$			1.64697i			0.329393i
$26$		0			0
$27$	−3.94512	+	3.94512i	−0.759239	+	0.759239i
$28$		0			0
$29$	6.82640	+	6.82640i	1.26763	+	1.26763i	0.947309	+	0.320321i	$0.103791\pi$
$29$	6.82640	+	6.82640i	1.26763	+	1.26763i	0.320321	+	0.947309i	$0.396209\pi$
$30$		0			0
$31$	5.23082			0.939484			0.469742	−	0.882804i	$-0.344347\pi$
$31$	5.23082			0.939484			0.469742	+	0.882804i	$0.344347\pi$
$32$		0			0
$33$	−4.91369			−0.855364
$34$		0			0
$35$	−4.15106	−	4.15106i	−0.701657	−	0.701657i
$36$		0			0
$37$	0.208536	−	0.208536i	0.0342830	−	0.0342830i	−0.689757	−	0.724041i	$-0.742283\pi$
$37$	0.208536	−	0.208536i	0.0342830	−	0.0342830i	0.724041	+	0.689757i	$0.242283\pi$
$38$		0			0
$39$			1.27672i			0.204439i
$40$		0			0
$41$			9.29774i			1.45206i	0.687662	+	0.726031i	$0.258637\pi$
$41$			9.29774i			1.45206i	−0.687662	+	0.726031i	$0.741363\pi$
$42$		0			0
$43$	−0.0416722	+	0.0416722i	−0.00635495	+	0.00635495i	−0.710277	−	0.703922i	$-0.751430\pi$
$43$	−0.0416722	+	0.0416722i	−0.00635495	+	0.00635495i	0.703922	+	0.710277i	$0.251430\pi$
$44$		0			0
$45$	−1.77387	−	1.77387i	−0.264433	−	0.264433i
$46$		0			0
$47$	2.16694			0.316081			0.158040	−	0.987433i	$-0.449482\pi$
$47$	2.16694			0.316081			0.158040	+	0.987433i	$0.449482\pi$
$48$		0			0
$49$	−3.27803			−0.468290
$50$		0			0
$51$	5.44980	+	5.44980i	0.763124	+	0.763124i
$52$		0			0
$53$	6.38002	−	6.38002i	0.876363	−	0.876363i	−0.116793	−	0.993156i	$-0.537261\pi$
$53$	6.38002	−	6.38002i	0.876363	−	0.876363i	0.993156	+	0.116793i	$0.0372614\pi$
$54$		0			0
$55$		−	7.04745i		−	0.950278i
$56$		0			0
$57$			3.42959i			0.454260i
$58$		0			0
$59$	−3.38796	+	3.38796i	−0.441075	+	0.441075i	−0.892373	−	0.451298i	$-0.850961\pi$
$59$	−3.38796	+	3.38796i	−0.441075	+	0.441075i	0.451298	+	0.892373i	$0.350961\pi$
$60$		0			0
$61$	−1.72743	−	1.72743i	−0.221175	−	0.221175i	0.587818	−	0.808993i	$-0.299987\pi$
$61$	−1.72743	−	1.72743i	−0.221175	−	0.221175i	−0.808993	+	0.587818i	$0.799987\pi$
$62$		0			0
$63$	−4.39210			−0.553353
$64$		0			0
$65$	−1.83113			−0.227124
$66$		0			0
$67$	1.56033	+	1.56033i	0.190624	+	0.190624i	0.795966	−	0.605342i	$-0.206963\pi$
$67$	1.56033	+	1.56033i	0.190624	+	0.190624i	−0.605342	+	0.795966i	$0.706963\pi$
$68$		0			0
$69$	−7.83111	+	7.83111i	−0.942755	+	0.942755i
$70$		0			0
$71$			9.73843i			1.15574i	0.816129	+	0.577869i	$0.196116\pi$
$71$			9.73843i			1.15574i	−0.816129	+	0.577869i	$0.803884\pi$
$72$		0			0
$73$			6.08728i			0.712462i	0.934398	+	0.356231i	$0.115938\pi$
$73$			6.08728i			0.712462i	−0.934398	+	0.356231i	$0.884062\pi$
$74$		0			0
$75$	1.48684	−	1.48684i	0.171686	−	0.171686i
$76$		0			0
$77$	−8.72475	−	8.72475i	−0.994277	−	0.994277i
$78$		0			0
$79$	−5.31445			−0.597922			−0.298961	−	0.954265i	$-0.596640\pi$
$79$	−5.31445			−0.597922			−0.298961	+	0.954265i	$0.596640\pi$
$80$		0			0
$81$	3.01316			0.334795
$82$		0			0
$83$	−9.71028	−	9.71028i	−1.06584	−	1.06584i	−0.997674	−	0.0681682i	$-0.978285\pi$
$83$	−9.71028	−	9.71028i	−1.06584	−	1.06584i	−0.0681682	−	0.997674i	$-0.521715\pi$
$84$		0			0
$85$	−7.81635	+	7.81635i	−0.847802	+	0.847802i
$86$		0			0
$87$		−	12.3254i		−	1.32142i
$88$		0			0
$89$		−	5.94615i		−	0.630291i	−0.949043	−	0.315145i	$-0.897947\pi$
$89$		−	5.94615i		−	0.630291i	0.949043	−	0.315145i	$-0.102053\pi$
$90$		0			0
$91$	−2.26694	+	2.26694i	−0.237640	+	0.237640i
$92$		0			0
$93$	−4.72226	−	4.72226i	−0.489676	−	0.489676i
$94$		0			0
$95$	−4.91887			−0.504666
$96$		0			0
$97$	−9.79055			−0.994080			−0.497040	−	0.867728i	$-0.665580\pi$
$97$	−9.79055			−0.994080			−0.497040	+	0.867728i	$0.665580\pi$
$98$		0			0
$99$	−3.72834	−	3.72834i	−0.374712	−	0.374712i
$100$		0			0
$101$	4.75506	−	4.75506i	0.473146	−	0.473146i	−0.429785	−	0.902931i	$-0.641411\pi$
$101$	4.75506	−	4.75506i	0.473146	−	0.473146i	0.902931	+	0.429785i	$0.141411\pi$
$102$		0			0
$103$		−	2.88844i		−	0.284607i	−0.989823	−	0.142303i	$-0.954549\pi$
$103$		−	2.88844i		−	0.284607i	0.989823	−	0.142303i	$-0.0454509\pi$
$104$		0			0
$105$			7.49496i			0.731433i
$106$		0			0
$107$	−3.70795	+	3.70795i	−0.358461	+	0.358461i	−0.863245	−	0.504785i	$-0.831572\pi$
$107$	−3.70795	+	3.70795i	−0.358461	+	0.358461i	0.504785	+	0.863245i	$0.331572\pi$
$108$		0			0
$109$	−2.76524	−	2.76524i	−0.264862	−	0.264862i	0.562164	−	0.827026i	$-0.309969\pi$
$109$	−2.76524	−	2.76524i	−0.264862	−	0.264862i	−0.827026	+	0.562164i	$0.809969\pi$
$110$		0			0
$111$	−0.376522			−0.0357379
$112$		0			0
$113$	9.12934			0.858816			0.429408	−	0.903111i	$-0.358722\pi$
$113$	9.12934			0.858816			0.429408	+	0.903111i	$0.358722\pi$
$114$		0			0
$115$	−11.2317	−	11.2317i	−1.04737	−	1.04737i
$116$		0			0
$117$	−0.968729	+	0.968729i	−0.0895591	+	0.0895591i
$118$		0			0
$119$			19.3533i			1.77411i
$120$		0			0
$121$		−	3.81241i		−	0.346583i
$122$		0			0
$123$	8.39378	−	8.39378i	0.756841	−	0.756841i
$124$		0			0
$125$	8.60652	+	8.60652i	0.769790	+	0.769790i
$126$		0			0
$127$	12.7097			1.12780			0.563901	−	0.825842i	$-0.309300\pi$
$127$	12.7097			1.12780			0.563901	+	0.825842i	$0.309300\pi$
$128$		0			0
$129$	0.0752414			0.00662464
$130$		0			0
$131$	−6.39425	−	6.39425i	−0.558668	−	0.558668i	0.370260	−	0.928928i	$-0.379269\pi$
$131$	−6.39425	−	6.39425i	−0.558668	−	0.558668i	−0.928928	+	0.370260i	$0.879269\pi$
$132$		0			0
$133$	−6.08957	+	6.08957i	−0.528033	+	0.528033i
$134$		0			0
$135$			10.2163i			0.879281i
$136$		0			0
$137$		−	19.8173i		−	1.69310i	−0.532306	−	0.846552i	$-0.678674\pi$
$137$		−	19.8173i		−	1.69310i	0.532306	−	0.846552i	$-0.321326\pi$
$138$		0			0
$139$	7.81457	−	7.81457i	0.662823	−	0.662823i	−0.293221	−	0.956045i	$-0.594727\pi$
$139$	7.81457	−	7.81457i	0.662823	−	0.662823i	0.956045	+	0.293221i	$0.0947273\pi$
$140$		0			0
$141$	−1.95626	−	1.95626i	−0.164747	−	0.164747i
$142$		0			0
$143$	−3.84869			−0.321844
$144$		0			0
$145$	17.6777			1.46805
$146$		0			0
$147$	2.95933	+	2.95933i	0.244081	+	0.244081i
$148$		0			0
$149$	−6.86136	+	6.86136i	−0.562104	+	0.562104i	−0.929905	−	0.367800i	$-0.880111\pi$
$149$	−6.86136	+	6.86136i	−0.562104	+	0.562104i	0.367800	+	0.929905i	$0.380111\pi$
$150$		0			0
$151$		−	12.0002i		−	0.976560i	−0.872687	−	0.488280i	$-0.837624\pi$
$151$		−	12.0002i		−	0.976560i	0.872687	−	0.488280i	$-0.162376\pi$
$152$		0			0
$153$			8.27023i			0.668608i
$154$		0			0
$155$	6.77289	−	6.77289i	0.544012	−	0.544012i
$156$		0			0
$157$	−1.81214	−	1.81214i	−0.144625	−	0.144625i	0.631087	−	0.775712i	$-0.282609\pi$
$157$	−1.81214	−	1.81214i	−0.144625	−	0.144625i	−0.775712	+	0.631087i	$0.782609\pi$
$158$		0			0
$159$	−11.5195			−0.913553
$160$		0			0
$161$	−27.8098			−2.19172
$162$		0			0
$163$	13.8786	+	13.8786i	1.08706	+	1.08706i	0.995830	+	0.0912264i	$0.0290787\pi$
$163$	13.8786	+	13.8786i	1.08706	+	1.08706i	0.0912264	+	0.995830i	$0.470921\pi$
$164$		0			0
$165$	−6.36227	+	6.36227i	−0.495302	+	0.495302i
$166$		0			0
$167$			3.99276i			0.308969i	0.987995	+	0.154485i	$0.0493717\pi$
$167$			3.99276i			0.308969i	−0.987995	+	0.154485i	$0.950628\pi$
$168$		0			0
$169$			1.00000i			0.0769231i
$170$		0			0
$171$	−2.60225	+	2.60225i	−0.198999	+	0.198999i
$172$		0			0
$173$	−12.5447	−	12.5447i	−0.953756	−	0.953756i	0.0452212	−	0.998977i	$-0.485601\pi$
$173$	−12.5447	−	12.5447i	−0.953756	−	0.953756i	−0.998977	+	0.0452212i	$0.985601\pi$
$174$		0			0
$175$	5.28007			0.399136
$176$		0			0
$177$	6.11715			0.459793
$178$		0			0
$179$	6.56516	+	6.56516i	0.490703	+	0.490703i	0.908528	−	0.417825i	$-0.137207\pi$
$179$	6.56516	+	6.56516i	0.490703	+	0.490703i	−0.417825	+	0.908528i	$0.637207\pi$
$180$		0			0
$181$	−6.91102	+	6.91102i	−0.513692	+	0.513692i	−0.915656	−	0.401964i	$-0.868328\pi$
$181$	−6.91102	+	6.91102i	−0.513692	+	0.513692i	0.401964	+	0.915656i	$0.368328\pi$
$182$		0			0
$183$			3.11897i			0.230561i
$184$		0			0
$185$		−	0.540025i		−	0.0397035i
$186$		0			0
$187$	−16.4285	+	16.4285i	−1.20137	+	1.20137i
$188$		0			0
$189$	12.6478	+	12.6478i	0.919993	+	0.919993i
$190$		0			0
$191$	−11.2566			−0.814502			−0.407251	−	0.913316i	$-0.633513\pi$
$191$	−11.2566			−0.814502			−0.407251	+	0.913316i	$0.633513\pi$
$192$		0			0
$193$	−2.54609			−0.183272			−0.0916358	−	0.995793i	$-0.529210\pi$
$193$	−2.54609			−0.183272			−0.0916358	+	0.995793i	$0.529210\pi$
$194$		0			0
$195$	1.65310	+	1.65310i	0.118381	+	0.118381i
$196$		0			0
$197$	−4.30038	+	4.30038i	−0.306389	+	0.306389i	−0.843507	−	0.537118i	$-0.819513\pi$
$197$	−4.30038	+	4.30038i	−0.306389	+	0.306389i	0.537118	+	0.843507i	$0.319513\pi$
$198$		0			0
$199$		−	26.2885i		−	1.86354i	−0.363048	−	0.931771i	$-0.618264\pi$
$199$		−	26.2885i		−	1.86354i	0.363048	−	0.931771i	$-0.381736\pi$
$200$		0			0
$201$		−	2.81725i		−	0.198714i
$202$		0			0
$203$	21.8850	−	21.8850i	1.53603	−	1.53603i
$204$		0			0
$205$	12.0387	+	12.0387i	0.840823	+	0.840823i
$206$		0			0
$207$	−11.8840			−0.825992
$208$		0			0
$209$	−10.3385			−0.715132
$210$		0			0
$211$	7.51991	+	7.51991i	0.517692	+	0.517692i	0.916872	−	0.399180i	$-0.130705\pi$
$211$	7.51991	+	7.51991i	0.517692	+	0.517692i	−0.399180	+	0.916872i	$0.630705\pi$
$212$		0			0
$213$	8.79162	−	8.79162i	0.602392	−	0.602392i
$214$		0			0
$215$			0.107915i			0.00735972i
$216$		0			0
$217$		−	16.7697i		−	1.13840i
$218$		0			0
$219$	5.49545	−	5.49545i	0.371348	−	0.371348i
$220$		0			0
$221$	4.26860	+	4.26860i	0.287137	+	0.287137i
$222$		0			0
$223$	−18.7318			−1.25438			−0.627188	−	0.778868i	$-0.715794\pi$
$223$	−18.7318			−1.25438			−0.627188	+	0.778868i	$0.715794\pi$
$224$		0			0
$225$	2.25633			0.150422
$226$		0			0
$227$	−0.552713	−	0.552713i	−0.0366849	−	0.0366849i	0.688526	−	0.725211i	$-0.258258\pi$
$227$	−0.552713	−	0.552713i	−0.0366849	−	0.0366849i	−0.725211	+	0.688526i	$0.758258\pi$
$228$		0			0
$229$	14.9481	−	14.9481i	0.987798	−	0.987798i	−0.0121281	−	0.999926i	$-0.503861\pi$
$229$	14.9481	−	14.9481i	0.987798	−	0.987798i	0.999926	+	0.0121281i	$0.00386060\pi$
$230$		0			0
$231$			15.7530i			1.03647i
$232$		0			0
$233$		−	23.9526i		−	1.56919i	−0.620009	−	0.784595i	$-0.712871\pi$
$233$		−	23.9526i		−	1.56919i	0.620009	−	0.784595i	$-0.287129\pi$
$234$		0			0
$235$	2.80576	−	2.80576i	0.183028	−	0.183028i
$236$		0			0
$237$	4.79776	+	4.79776i	0.311648	+	0.311648i
$238$		0			0
$239$	1.49140			0.0964709			0.0482354	−	0.998836i	$-0.484640\pi$
$239$	1.49140			0.0964709			0.0482354	+	0.998836i	$0.484640\pi$
$240$		0			0
$241$	−0.0970048			−0.00624863			−0.00312431	−	0.999995i	$-0.500995\pi$
$241$	−0.0970048			−0.00624863			−0.00312431	+	0.999995i	$0.500995\pi$
$242$		0			0
$243$	9.11516	+	9.11516i	0.584738	+	0.584738i
$244$		0			0
$245$	−4.24441	+	4.24441i	−0.271165	+	0.271165i
$246$		0			0
$247$			2.68625i			0.170922i
$248$		0			0
$249$			17.5324i			1.11107i
$250$		0			0
$251$	−7.32996	+	7.32996i	−0.462663	+	0.462663i	−0.899527	−	0.436864i	$-0.856089\pi$
$251$	−7.32996	+	7.32996i	−0.462663	+	0.462663i	0.436864	+	0.899527i	$0.356089\pi$
$252$		0			0
$253$	−23.6070	−	23.6070i	−1.48416	−	1.48416i
$254$		0			0
$255$	14.1128			0.883780
$256$		0			0
$257$	28.9029			1.80291			0.901457	−	0.432869i	$-0.142499\pi$
$257$	28.9029			1.80291			0.901457	+	0.432869i	$0.142499\pi$
$258$		0			0
$259$	−0.668552	−	0.668552i	−0.0415418	−	0.0415418i
$260$		0			0
$261$	9.35210	−	9.35210i	0.578880	−	0.578880i
$262$		0			0
$263$			17.4287i			1.07470i	0.843360	+	0.537349i	$0.180574\pi$
$263$			17.4287i			1.07470i	−0.843360	+	0.537349i	$0.819426\pi$
$264$		0			0
$265$		−	16.5217i		−	1.01492i
$266$		0			0
$267$	−5.36804	+	5.36804i	−0.328519	+	0.328519i
$268$		0			0
$269$	12.0262	+	12.0262i	0.733248	+	0.733248i	0.971262	−	0.238013i	$-0.0764962\pi$
$269$	12.0262	+	12.0262i	0.733248	+	0.733248i	−0.238013	+	0.971262i	$0.576496\pi$
$270$		0			0
$271$	1.79480			0.109026			0.0545131	−	0.998513i	$-0.482639\pi$
$271$	1.79480			0.109026			0.0545131	+	0.998513i	$0.482639\pi$
$272$		0			0
$273$	4.09308			0.247724
$274$		0			0
$275$	4.48211	+	4.48211i	0.270282	+	0.270282i
$276$		0			0
$277$	1.31019	−	1.31019i	0.0787215	−	0.0787215i	−0.666650	−	0.745371i	$-0.732272\pi$
$277$	1.31019	−	1.31019i	0.0787215	−	0.0787215i	0.745371	+	0.666650i	$0.232272\pi$
$278$		0			0
$279$		−	7.16618i		−	0.429028i
$280$		0			0
$281$			26.8404i			1.60116i	0.599225	+	0.800581i	$0.295475\pi$
$281$			26.8404i			1.60116i	−0.599225	+	0.800581i	$0.704525\pi$
$282$		0			0
$283$	−1.50326	+	1.50326i	−0.0893595	+	0.0893595i	−0.750374	−	0.661014i	$-0.770126\pi$
$283$	−1.50326	+	1.50326i	−0.0893595	+	0.0893595i	0.661014	+	0.750374i	$0.270126\pi$
$284$		0			0
$285$	4.44064	+	4.44064i	0.263041	+	0.263041i
$286$		0			0
$287$	29.8080			1.75951
$288$		0			0
$289$	19.4418			1.14364
$290$		0			0
$291$	8.83868	+	8.83868i	0.518133	+	0.518133i
$292$		0			0
$293$	4.58243	−	4.58243i	0.267709	−	0.267709i	−0.560468	−	0.828176i	$-0.689379\pi$
$293$	4.58243	−	4.58243i	0.267709	−	0.267709i	0.828176	+	0.560468i	$0.189379\pi$
$294$		0			0
$295$			8.77350i			0.510813i
$296$		0			0
$297$			21.4728i			1.24598i
$298$		0			0
$299$	−6.13378	+	6.13378i	−0.354726	+	0.354726i
$300$		0			0
$301$	0.133599	+	0.133599i	0.00770049	+	0.00770049i
$302$		0			0
$303$	−8.58551			−0.493224
$304$		0			0
$305$	−4.47337			−0.256144
$306$		0			0
$307$	−13.7315	−	13.7315i	−0.783699	−	0.783699i	0.196754	−	0.980453i	$-0.436960\pi$
$307$	−13.7315	−	13.7315i	−0.783699	−	0.783699i	−0.980453	+	0.196754i	$0.936960\pi$
$308$		0			0
$309$	−2.60762	+	2.60762i	−0.148342	+	0.148342i
$310$		0			0
$311$			1.60913i			0.0912455i	0.998959	+	0.0456228i	$0.0145272\pi$
$311$			1.60913i			0.0912455i	−0.998959	+	0.0456228i	$0.985473\pi$
$312$		0			0
$313$		−	14.3857i		−	0.813126i	−0.913623	−	0.406563i	$-0.866727\pi$
$313$		−	14.3857i		−	0.813126i	0.913623	−	0.406563i	$-0.133273\pi$
$314$		0			0
$315$	−5.68691	+	5.68691i	−0.320421	+	0.320421i
$316$		0			0
$317$	12.4126	+	12.4126i	0.697160	+	0.697160i	0.963797	−	0.266637i	$-0.0859124\pi$
$317$	12.4126	+	12.4126i	0.697160	+	0.697160i	−0.266637	+	0.963797i	$0.585912\pi$
$318$		0			0
$319$	37.1552			2.08029
$320$		0			0
$321$	6.69489			0.373673
$322$		0			0
$323$	11.4665	+	11.4665i	0.638015	+	0.638015i
$324$		0			0
$325$	1.16458	−	1.16458i	0.0645994	−	0.0645994i
$326$		0			0
$327$			4.99279i			0.276102i
$328$		0			0
$329$		−	6.94708i		−	0.383005i
$330$		0			0
$331$	17.1517	−	17.1517i	0.942742	−	0.942742i	−0.0557049	−	0.998447i	$-0.517741\pi$
$331$	17.1517	−	17.1517i	0.942742	−	0.942742i	0.998447	+	0.0557049i	$0.0177406\pi$
$332$		0			0
$333$	−0.285692	−	0.285692i	−0.0156558	−	0.0156558i
$334$		0			0
$335$	4.04064			0.220764
$336$		0			0
$337$	30.8004			1.67781			0.838903	−	0.544281i	$-0.183198\pi$
$337$	30.8004			1.67781			0.838903	+	0.544281i	$0.183198\pi$
$338$		0			0
$339$	−8.24175	−	8.24175i	−0.447631	−	0.447631i
$340$		0			0
$341$	14.2353	−	14.2353i	0.770887	−	0.770887i
$342$		0			0
$343$		−	11.9324i		−	0.644289i
$344$		0			0
$345$			20.2795i			1.09181i
$346$		0			0
$347$	−22.1815	+	22.1815i	−1.19076	+	1.19076i	−0.213910	+	0.976853i	$0.568620\pi$
$347$	−22.1815	+	22.1815i	−1.19076	+	1.19076i	−0.976853	+	0.213910i	$0.931380\pi$
$348$		0			0
$349$	−15.7484	−	15.7484i	−0.842990	−	0.842990i	0.146256	−	0.989247i	$-0.453278\pi$
$349$	−15.7484	−	15.7484i	−0.842990	−	0.842990i	−0.989247	+	0.146256i	$0.953278\pi$
$350$		0			0
$351$	5.57925			0.297798
$352$		0			0
$353$	28.1232			1.49685			0.748424	−	0.663220i	$-0.230811\pi$
$353$	28.1232			1.49685			0.748424	+	0.663220i	$0.230811\pi$
$354$		0			0
$355$	12.6094	+	12.6094i	0.669235	+	0.669235i
$356$		0			0
$357$	17.4717	−	17.4717i	0.924701	−	0.924701i
$358$		0			0
$359$		−	2.91495i		−	0.153845i	−0.997037	−	0.0769225i	$-0.975491\pi$
$359$		−	2.91495i		−	0.153845i	0.997037	−	0.0769225i	$-0.0245094\pi$
$360$		0			0
$361$		−	11.7841i		−	0.620213i
$362$		0			0
$363$	−3.44176	+	3.44176i	−0.180645	+	0.180645i
$364$		0			0
$365$	7.88183	+	7.88183i	0.412554	+	0.412554i
$366$		0			0
$367$	−6.29896			−0.328803			−0.164402	−	0.986394i	$-0.552569\pi$
$367$	−6.29896			−0.328803			−0.164402	+	0.986394i	$0.552569\pi$
$368$		0			0
$369$	12.7378			0.663104
$370$		0			0
$371$	−20.4539	−	20.4539i	−1.06192	−	1.06192i
$372$		0			0
$373$	12.7757	−	12.7757i	0.661498	−	0.661498i	−0.294235	−	0.955733i	$-0.595065\pi$
$373$	12.7757	−	12.7757i	0.661498	−	0.661498i	0.955733	+	0.294235i	$0.0950648\pi$
$374$		0			0
$375$		−	15.5395i		−	0.802457i
$376$		0			0
$377$		−	9.65398i		−	0.497205i
$378$		0			0
$379$	17.8540	−	17.8540i	0.917097	−	0.917097i	−0.0797198	−	0.996817i	$-0.525403\pi$
$379$	17.8540	−	17.8540i	0.917097	−	0.917097i	0.996817	+	0.0797198i	$0.0254026\pi$
$380$		0			0
$381$	−11.4740	−	11.4740i	−0.587831	−	0.587831i
$382$		0			0
$383$	9.20840			0.470527			0.235264	−	0.971932i	$-0.424405\pi$
$383$	9.20840			0.470527			0.235264	+	0.971932i	$0.424405\pi$
$384$		0			0
$385$	−22.5937			−1.15148
$386$		0			0
$387$	0.0570905	+	0.0570905i	0.00290208	+	0.00290208i
$388$		0			0
$389$	19.1892	−	19.1892i	0.972930	−	0.972930i	−0.0267131	−	0.999643i	$-0.508504\pi$
$389$	19.1892	−	19.1892i	0.972930	−	0.972930i	0.999643	+	0.0267131i	$0.00850406\pi$
$390$		0			0
$391$			52.3653i			2.64823i
$392$		0			0
$393$			11.5452i			0.582376i
$394$		0			0
$395$	−6.88117	+	6.88117i	−0.346229	+	0.346229i
$396$		0			0
$397$	15.2018	+	15.2018i	0.762956	+	0.762956i	0.976856	−	0.213900i	$-0.0686165\pi$
$397$	15.2018	+	15.2018i	0.762956	+	0.762956i	−0.213900	+	0.976856i	$0.568617\pi$
$398$		0			0
$399$	10.9950			0.550441
$400$		0			0
$401$	−18.1785			−0.907793			−0.453897	−	0.891054i	$-0.649966\pi$
$401$	−18.1785			−0.907793			−0.453897	+	0.891054i	$0.649966\pi$
$402$		0			0
$403$	−3.69875	−	3.69875i	−0.184248	−	0.184248i
$404$		0			0
$405$	3.90145	−	3.90145i	0.193864	−	0.193864i
$406$		0			0
$407$		−	1.13503i		−	0.0562615i
$408$		0			0
$409$			5.29435i			0.261789i	0.991396	+	0.130894i	$0.0417849\pi$
$409$			5.29435i			0.261789i	−0.991396	+	0.130894i	$0.958215\pi$
$410$		0			0
$411$	−17.8906	+	17.8906i	−0.882477	+	0.882477i
$412$		0			0
$413$	10.8616	+	10.8616i	0.534464	+	0.534464i
$414$		0			0
$415$	−25.1458			−1.23436
$416$		0			0
$417$	−14.1096			−0.690951
$418$		0			0
$419$	1.93469	+	1.93469i	0.0945158	+	0.0945158i	0.752784	−	0.658268i	$-0.228711\pi$
$419$	1.93469	+	1.93469i	0.0945158	+	0.0945158i	−0.658268	+	0.752784i	$0.728711\pi$
$420$		0			0
$421$	7.75321	−	7.75321i	0.377868	−	0.377868i	−0.492464	−	0.870333i	$-0.663904\pi$
$421$	7.75321	−	7.75321i	0.377868	−	0.377868i	0.870333	+	0.492464i	$0.163904\pi$
$422$		0			0
$423$		−	2.96869i		−	0.144343i
$424$		0			0
$425$		−	9.94226i		−	0.482270i
$426$		0			0
$427$	−5.53804	+	5.53804i	−0.268004	+	0.268004i
$428$		0			0
$429$	3.47451	+	3.47451i	0.167751	+	0.167751i
$430$		0			0
$431$	−28.1933			−1.35802			−0.679011	−	0.734128i	$-0.737591\pi$
$431$	−28.1933			−1.35802			−0.679011	+	0.734128i	$0.737591\pi$
$432$		0			0
$433$	−28.5535			−1.37219			−0.686097	−	0.727511i	$-0.740677\pi$
$433$	−28.5535			−1.37219			−0.686097	+	0.727511i	$0.740677\pi$
$434$		0			0
$435$	−15.9590	−	15.9590i	−0.765175	−	0.765175i
$436$		0			0
$437$	−16.4769	+	16.4769i	−0.788196	+	0.788196i
$438$		0			0
$439$		−	0.436290i		−	0.0208230i	−0.999946	−	0.0104115i	$-0.996686\pi$
$439$		−	0.436290i		−	0.0208230i	0.999946	−	0.0104115i	$-0.00331414\pi$
$440$		0			0
$441$			4.49087i			0.213851i
$442$		0			0
$443$	−22.4448	+	22.4448i	−1.06638	+	1.06638i	−0.0687507	+	0.997634i	$0.521901\pi$
$443$	−22.4448	+	22.4448i	−1.06638	+	1.06638i	−0.997634	+	0.0687507i	$0.978099\pi$
$444$		0			0
$445$	−7.69910	−	7.69910i	−0.364972	−	0.364972i
$446$		0			0
$447$	12.3885			0.585958
$448$		0			0
$449$	1.83048			0.0863856			0.0431928	−	0.999067i	$-0.486247\pi$
$449$	1.83048			0.0863856			0.0431928	+	0.999067i	$0.486247\pi$
$450$		0			0
$451$	25.3032	+	25.3032i	1.19148	+	1.19148i
$452$		0			0
$453$	−10.8335	+	10.8335i	−0.509001	+	0.509001i
$454$		0			0
$455$			5.87048i			0.275213i
$456$		0			0
$457$		−	18.3262i		−	0.857264i	−0.903479	−	0.428632i	$-0.858996\pi$
$457$		−	18.3262i		−	0.857264i	0.903479	−	0.428632i	$-0.141004\pi$
$458$		0			0
$459$	23.8156	−	23.8156i	1.11161	−	1.11161i
$460$		0			0
$461$	10.1809	+	10.1809i	0.474171	+	0.474171i	0.903262	−	0.429090i	$-0.141166\pi$
$461$	10.1809	+	10.1809i	0.474171	+	0.474171i	−0.429090	+	0.903262i	$0.641166\pi$
$462$		0			0
$463$	28.8403			1.34032			0.670162	−	0.742215i	$-0.266225\pi$
$463$	28.8403			1.34032			0.670162	+	0.742215i	$0.266225\pi$
$464$		0			0
$465$	−12.2288			−0.567097
$466$		0			0
$467$	11.4431	+	11.4431i	0.529526	+	0.529526i	0.920431	−	0.390905i	$-0.127838\pi$
$467$	11.4431	+	11.4431i	0.529526	+	0.529526i	−0.390905	+	0.920431i	$0.627838\pi$
$468$		0			0
$469$	5.00231	−	5.00231i	0.230985	−	0.230985i
$470$		0			0
$471$			3.27192i			0.150762i
$472$		0			0
$473$			0.226816i			0.0104290i
$474$		0			0
$475$	3.12836	−	3.12836i	0.143539	−	0.143539i
$476$		0			0
$477$	−8.74057	−	8.74057i	−0.400203	−	0.400203i
$478$		0			0
$479$	26.9400			1.23092			0.615459	−	0.788169i	$-0.288971\pi$
$479$	26.9400			1.23092			0.615459	+	0.788169i	$0.288971\pi$
$480$		0			0
$481$	−0.294914			−0.0134469
$482$		0			0
$483$	25.1061	+	25.1061i	1.14237	+	1.14237i
$484$		0			0
$485$	−12.6768	+	12.6768i	−0.575626	+	0.575626i
$486$		0			0
$487$		−	10.4127i		−	0.471844i	−0.971772	−	0.235922i	$-0.924189\pi$
$487$		−	10.4127i		−	0.471844i	0.971772	−	0.235922i	$-0.0758110\pi$
$488$		0			0
$489$		−	25.0586i		−	1.13319i
$490$		0			0
$491$	−3.32818	+	3.32818i	−0.150199	+	0.150199i	−0.778207	−	0.628008i	$-0.783870\pi$
$491$	−3.32818	+	3.32818i	−0.150199	+	0.150199i	0.628008	+	0.778207i	$0.283870\pi$
$492$		0			0
$493$	−41.2090	−	41.2090i	−1.85596	−	1.85596i
$494$		0			0
$495$	−9.65493			−0.433957
$496$		0			0
$497$	31.2208			1.40044
$498$		0			0
$499$	−12.7043	−	12.7043i	−0.568720	−	0.568720i	0.363049	−	0.931770i	$-0.381736\pi$
$499$	−12.7043	−	12.7043i	−0.568720	−	0.568720i	−0.931770	+	0.363049i	$0.881736\pi$
$500$		0			0
$501$	3.60457	−	3.60457i	0.161040	−	0.161040i
$502$		0			0
$503$			4.37422i			0.195037i	0.995234	+	0.0975184i	$0.0310905\pi$
$503$			4.37422i			0.195037i	−0.995234	+	0.0975184i	$0.968910\pi$
$504$		0			0
$505$		−	12.3137i		−	0.547954i
$506$		0			0
$507$	0.902776	−	0.902776i	0.0400937	−	0.0400937i
$508$		0			0
$509$	19.4429	+	19.4429i	0.861791	+	0.861791i	0.991546	−	0.129755i	$-0.0414192\pi$
$509$	19.4429	+	19.4429i	0.861791	+	0.861791i	−0.129755	+	0.991546i	$0.541419\pi$
$510$		0			0
$511$	19.5154			0.863312
$512$		0			0
$513$	14.9873			0.661704
$514$		0			0
$515$	−3.73997	−	3.73997i	−0.164803	−	0.164803i
$516$		0			0
$517$	5.89719	−	5.89719i	0.259358	−	0.259358i
$518$		0			0
$519$			22.6501i			0.994230i
$520$		0			0
$521$			36.9872i			1.62044i	0.586127	+	0.810219i	$0.300652\pi$
$521$			36.9872i			1.62044i	−0.586127	+	0.810219i	$0.699348\pi$
$522$		0			0
$523$	1.80040	−	1.80040i	0.0787260	−	0.0787260i	−0.666647	−	0.745373i	$-0.732271\pi$
$523$	1.80040	−	1.80040i	0.0787260	−	0.0787260i	0.745373	+	0.666647i	$0.232271\pi$
$524$		0			0
$525$	−4.76672	−	4.76672i	−0.208037	−	0.208037i
$526$		0			0
$527$	−31.5770			−1.37551
$528$		0			0
$529$	−52.2466			−2.27159
$530$		0			0
$531$	4.64148	+	4.64148i	0.201423	+	0.201423i
$532$		0			0
$533$	6.57449	−	6.57449i	0.284773	−	0.284773i
$534$		0			0
$535$			9.60213i			0.415136i
$536$		0			0
$537$		−	11.8537i		−	0.511527i
$538$		0			0
$539$	−8.92095	+	8.92095i	−0.384253	+	0.384253i
$540$		0			0
$541$	−13.6616	−	13.6616i	−0.587357	−	0.587357i	0.349558	−	0.936915i	$-0.386332\pi$
$541$	−13.6616	−	13.6616i	−0.587357	−	0.587357i	−0.936915	+	0.349558i	$0.886332\pi$
$542$		0			0
$543$	12.4782			0.535491
$544$		0			0
$545$	−7.16089			−0.306739
$546$		0			0
$547$	5.89436	+	5.89436i	0.252025	+	0.252025i	0.821800	−	0.569776i	$-0.192970\pi$
$547$	5.89436	+	5.89436i	0.252025	+	0.252025i	−0.569776	+	0.821800i	$0.692970\pi$
$548$		0			0
$549$	−2.36656	+	2.36656i	−0.101003	+	0.101003i
$550$		0			0
$551$		−	25.9330i		−	1.10478i
$552$		0			0
$553$			17.0378i			0.724520i
$554$		0			0
$555$	−0.487522	+	0.487522i	−0.0206942	+	0.0206942i
$556$		0			0
$557$	−9.07239	−	9.07239i	−0.384409	−	0.384409i	0.488278	−	0.872688i	$-0.337625\pi$
$557$	−9.07239	−	9.07239i	−0.384409	−	0.384409i	−0.872688	+	0.488278i	$0.837625\pi$
$558$		0			0
$559$	0.0589334			0.00249262
$560$		0			0
$561$	29.6625			1.25235
$562$		0			0
$563$	−17.9168	−	17.9168i	−0.755104	−	0.755104i	0.220323	−	0.975427i	$-0.429289\pi$
$563$	−17.9168	−	17.9168i	−0.755104	−	0.755104i	−0.975427	+	0.220323i	$0.929289\pi$
$564$		0			0
$565$	11.8207	−	11.8207i	0.497301	−	0.497301i
$566$		0			0
$567$		−	9.65999i		−	0.405681i
$568$		0			0
$569$			15.4121i			0.646109i	0.946380	+	0.323054i	$0.104710\pi$
$569$			15.4121i			0.646109i	−0.946380	+	0.323054i	$0.895290\pi$
$570$		0			0
$571$	−15.6916	+	15.6916i	−0.656673	+	0.656673i	−0.954591	−	0.297919i	$-0.903708\pi$
$571$	−15.6916	+	15.6916i	−0.656673	+	0.656673i	0.297919	+	0.954591i	$0.403708\pi$
$572$		0			0
$573$	10.1622	+	10.1622i	0.424533	+	0.424533i
$574$		0			0
$575$	14.2866			0.595792
$576$		0			0
$577$	−17.3626			−0.722815			−0.361407	−	0.932408i	$-0.617704\pi$
$577$	−17.3626			−0.722815			−0.361407	+	0.932408i	$0.617704\pi$
$578$		0			0
$579$	2.29855	+	2.29855i	0.0955244	+	0.0955244i
$580$		0			0
$581$	−31.1306	+	31.1306i	−1.29151	+	1.29151i
$582$		0			0
$583$		−	34.7256i		−	1.43819i
$584$		0			0
$585$			2.50863i			0.103719i
$586$		0			0
$587$	−15.0345	+	15.0345i	−0.620541	+	0.620541i	−0.945670	−	0.325129i	$-0.894592\pi$
$587$	−15.0345	+	15.0345i	−0.620541	+	0.620541i	0.325129	+	0.945670i	$0.394592\pi$
$588$		0			0
$589$	−9.93577	−	9.93577i	−0.409396	−	0.409396i
$590$		0			0
$591$	7.76456			0.319391
$592$		0			0
$593$	−42.6498			−1.75142			−0.875709	−	0.482840i	$-0.839605\pi$
$593$	−42.6498			−1.75142			−0.875709	+	0.482840i	$0.839605\pi$
$594$		0			0
$595$	25.0587	+	25.0587i	1.02731	+	1.02731i
$596$		0			0
$597$	−23.7326	+	23.7326i	−0.971311	+	0.971311i
$598$		0			0
$599$			26.7066i			1.09120i	0.838045	+	0.545602i	$0.183699\pi$
$599$			26.7066i			1.09120i	−0.838045	+	0.545602i	$0.816301\pi$
$600$		0			0
$601$			8.30933i			0.338944i	0.985535	+	0.169472i	$0.0542063\pi$
$601$			8.30933i			0.338944i	−0.985535	+	0.169472i	$0.945794\pi$
$602$		0			0
$603$	2.13763	−	2.13763i	0.0870512	−	0.0870512i
$604$		0			0
$605$	−4.93633	−	4.93633i	−0.200690	−	0.200690i
$606$		0			0
$607$	−22.9913			−0.933190			−0.466595	−	0.884471i	$-0.654519\pi$
$607$	−22.9913			−0.933190			−0.466595	+	0.884471i	$0.654519\pi$
$608$		0			0
$609$	−39.5145			−1.60121
$610$		0			0
$611$	−1.53226	−	1.53226i	−0.0619886	−	0.0619886i
$612$		0			0
$613$	6.71226	−	6.71226i	0.271106	−	0.271106i	−0.558440	−	0.829545i	$-0.688600\pi$
$613$	6.71226	−	6.71226i	0.271106	−	0.271106i	0.829545	+	0.558440i	$0.188600\pi$
$614$		0			0
$615$		−	21.7366i		−	0.876504i
$616$		0			0
$617$			10.3150i			0.415266i	0.978207	+	0.207633i	$0.0665760\pi$
$617$			10.3150i			0.415266i	−0.978207	+	0.207633i	$0.933424\pi$
$618$		0			0
$619$	6.94177	−	6.94177i	0.279013	−	0.279013i	−0.553702	−	0.832715i	$-0.686785\pi$
$619$	6.94177	−	6.94177i	0.279013	−	0.279013i	0.832715	+	0.553702i	$0.186785\pi$
$620$		0			0
$621$	34.2219	+	34.2219i	1.37328	+	1.37328i
$622$		0			0
$623$	−19.0630			−0.763743
$624$		0			0
$625$	14.0527			0.562107
$626$		0			0
$627$	9.33340	+	9.33340i	0.372740	+	0.372740i
$628$		0			0
$629$	−1.25887	+	1.25887i	−0.0501944	+	0.0501944i
$630$		0			0
$631$		−	11.6081i		−	0.462113i	−0.972940	−	0.231056i	$-0.925782\pi$
$631$		−	11.6081i		−	0.462113i	0.972940	−	0.231056i	$-0.0742182\pi$
$632$		0			0
$633$		−	13.5776i		−	0.539661i
$634$		0			0
$635$	16.4565	−	16.4565i	0.653058	−	0.653058i
$636$		0			0
$637$	2.31792	+	2.31792i	0.0918393	+	0.0918393i
$638$		0			0
$639$	13.3416			0.527784
$640$		0			0
$641$	27.0384			1.06795			0.533977	−	0.845499i	$-0.320697\pi$
$641$	27.0384			1.06795			0.533977	+	0.845499i	$0.320697\pi$
$642$		0			0
$643$	12.7661	+	12.7661i	0.503444	+	0.503444i	0.912507	−	0.409062i	$-0.134144\pi$
$643$	12.7661	+	12.7661i	0.503444	+	0.503444i	−0.409062	+	0.912507i	$0.634144\pi$
$644$		0			0
$645$	0.0974228	−	0.0974228i	0.00383602	−	0.00383602i
$646$		0			0
$647$			10.0134i			0.393667i	0.980437	+	0.196833i	$0.0630658\pi$
$647$			10.0134i			0.393667i	−0.980437	+	0.196833i	$0.936934\pi$
$648$		0			0
$649$			18.4402i			0.723843i
$650$		0			0
$651$	−15.1393	+	15.1393i	−0.593355	+	0.593355i
$652$		0			0
$653$	−9.13213	−	9.13213i	−0.357368	−	0.357368i	0.505474	−	0.862842i	$-0.331318\pi$
$653$	−9.13213	−	9.13213i	−0.357368	−	0.357368i	−0.862842	+	0.505474i	$0.831318\pi$
$654$		0			0
$655$	−16.5586			−0.646998
$656$		0			0
$657$	8.33951			0.325355
$658$		0			0
$659$	−26.5843	−	26.5843i	−1.03558	−	1.03558i	−0.999343	−	0.0362320i	$-0.988464\pi$
$659$	−26.5843	−	26.5843i	−1.03558	−	1.03558i	−0.0362320	−	0.999343i	$-0.511536\pi$
$660$		0			0
$661$	−1.76639	+	1.76639i	−0.0687044	+	0.0687044i	−0.740624	−	0.671920i	$-0.765470\pi$
$661$	−1.76639	+	1.76639i	−0.0687044	+	0.0687044i	0.671920	+	0.740624i	$0.265470\pi$
$662$		0			0
$663$		−	7.70718i		−	0.299322i
$664$		0			0
$665$			15.7696i			0.611519i
$666$		0			0
$667$	59.2154	−	59.2154i	2.29283	−	2.29283i
$668$		0			0
$669$	16.9107	+	16.9107i	0.653804	+	0.653804i
$670$		0			0
$671$	−9.40218			−0.362967
$672$		0			0
$673$	39.1888			1.51062			0.755308	−	0.655370i	$-0.227487\pi$
$673$	39.1888			1.51062			0.755308	+	0.655370i	$0.227487\pi$
$674$		0			0
$675$	−6.49749	−	6.49749i	−0.250088	−	0.250088i
$676$		0			0
$677$	13.8583	−	13.8583i	0.532616	−	0.532616i	−0.388734	−	0.921350i	$-0.627087\pi$
$677$	13.8583	−	13.8583i	0.532616	−	0.532616i	0.921350	+	0.388734i	$0.127087\pi$
$678$		0			0
$679$			31.3879i			1.20456i
$680$		0			0
$681$			0.997953i			0.0382416i
$682$		0			0
$683$	8.54143	−	8.54143i	0.326829	−	0.326829i	−0.524550	−	0.851379i	$-0.675767\pi$
$683$	8.54143	−	8.54143i	0.326829	−	0.326829i	0.851379	+	0.524550i	$0.175767\pi$
$684$		0			0
$685$	−25.6595	−	25.6595i	−0.980399	−	0.980399i
$686$		0			0
$687$	−26.9896			−1.02972
$688$		0			0
$689$	−9.02271			−0.343738
$690$		0			0
$691$	5.55830	+	5.55830i	0.211448	+	0.211448i	0.804882	−	0.593435i	$-0.202228\pi$
$691$	5.55830	+	5.55830i	0.211448	+	0.211448i	−0.593435	+	0.804882i	$0.702228\pi$
$692$		0			0
$693$	−11.9528	+	11.9528i	−0.454050	+	0.454050i
$694$		0			0
$695$		−	20.2367i		−	0.767621i
$696$		0			0
$697$		−	56.1277i		−	2.12599i
$698$		0			0
$699$	−21.6239	+	21.6239i	−0.817890	+	0.817890i
$700$		0			0
$701$	30.3550	+	30.3550i	1.14649	+	1.14649i	0.987238	+	0.159253i	$0.0509086\pi$
$701$	30.3550	+	30.3550i	1.14649	+	1.14649i	0.159253	+	0.987238i	$0.449091\pi$
$702$		0			0
$703$	−0.792213			−0.0298789
$704$		0			0
$705$	−5.06595			−0.190795
$706$		0			0
$707$	−15.2444	−	15.2444i	−0.573325	−	0.573325i
$708$		0			0
$709$	33.0689	−	33.0689i	1.24193	−	1.24193i	0.282730	−	0.959199i	$-0.408760\pi$
$709$	33.0689	−	33.0689i	1.24193	−	1.24193i	0.959199	−	0.282730i	$-0.0912401\pi$
$710$		0			0
$711$			7.28074i			0.273049i
$712$		0			0
$713$		−	45.3747i		−	1.69929i
$714$		0			0
$715$	−4.98330	+	4.98330i	−0.186365	+	0.186365i
$716$		0			0
$717$	−1.34640	−	1.34640i	−0.0502824	−	0.0502824i
$718$		0			0
$719$	−24.1360			−0.900121			−0.450060	−	0.892998i	$-0.648598\pi$
$719$	−24.1360			−0.900121			−0.450060	+	0.892998i	$0.648598\pi$
$720$		0			0
$721$	−9.26017			−0.344867
$722$		0			0
$723$	0.0875736	+	0.0875736i	0.00325690	+	0.00325690i
$724$		0			0
$725$	−11.2428	+	11.2428i	−0.417549	+	0.417549i
$726$		0			0
$727$		−	25.4413i		−	0.943564i	−0.881715	−	0.471782i	$-0.843611\pi$
$727$		−	25.4413i		−	0.943564i	0.881715	−	0.471782i	$-0.156389\pi$
$728$		0			0
$729$		−	25.4974i		−	0.944347i
$730$		0			0
$731$	0.251563	−	0.251563i	0.00930440	−	0.00930440i
$732$		0			0
$733$	−1.11861	−	1.11861i	−0.0413170	−	0.0413170i	0.686146	−	0.727463i	$-0.259301\pi$
$733$	−1.11861	−	1.11861i	−0.0413170	−	0.0413170i	−0.727463	+	0.686146i	$0.759301\pi$
$734$		0			0
$735$	7.66350			0.282673
$736$		0			0
$737$	8.49266			0.312831
$738$		0			0
$739$	−27.9487	−	27.9487i	−1.02811	−	1.02811i	−0.999593	−	0.0285153i	$-0.990922\pi$
$739$	−27.9487	−	27.9487i	−1.02811	−	1.02811i	−0.0285153	−	0.999593i	$-0.509078\pi$
$740$		0			0
$741$	2.42508	−	2.42508i	0.0890877	−	0.0890877i
$742$		0			0
$743$		−	6.84243i		−	0.251024i	−0.992092	−	0.125512i	$-0.959943\pi$
$743$		−	6.84243i		−	0.251024i	0.992092	−	0.125512i	$-0.0400574\pi$
$744$		0			0
$745$			17.7682i			0.650977i
$746$		0			0
$747$	−13.3030	+	13.3030i	−0.486731	+	0.486731i
$748$		0			0
$749$	11.8874	+	11.8874i	0.434358	+	0.434358i
$750$		0			0
$751$	−23.3074			−0.850500			−0.425250	−	0.905076i	$-0.639814\pi$
$751$	−23.3074			−0.850500			−0.425250	+	0.905076i	$0.639814\pi$
$752$		0			0
$753$	13.2346			0.482297
$754$		0			0
$755$	−15.5379	−	15.5379i	−0.565481	−	0.565481i
$756$		0			0
$757$	−10.0617	+	10.0617i	−0.365700	+	0.365700i	−0.865906	−	0.500206i	$-0.833258\pi$
$757$	−10.0617	+	10.0617i	−0.365700	+	0.365700i	0.500206	+	0.865906i	$0.333258\pi$
$758$		0			0
$759$			42.6237i			1.54714i
$760$		0			0
$761$			10.4743i			0.379695i	0.981814	+	0.189847i	$0.0607993\pi$
$761$			10.4743i			0.379695i	−0.981814	+	0.189847i	$0.939201\pi$
$762$		0			0
$763$	−8.86519	+	8.86519i	−0.320941	+	0.320941i
$764$		0			0
$765$	10.7083	+	10.7083i	0.387160	+	0.387160i
$766$		0			0
$767$	4.79131			0.173004
$768$		0			0
$769$	39.4816			1.42374			0.711871	−	0.702310i	$-0.247848\pi$
$769$	39.4816			1.42374			0.711871	+	0.702310i	$0.247848\pi$
$770$		0			0
$771$	−26.0928	−	26.0928i	−0.939711	−	0.939711i
$772$		0			0
$773$	−22.4954	+	22.4954i	−0.809104	+	0.809104i	−0.984498	−	0.175394i	$-0.943880\pi$
$773$	−22.4954	+	22.4954i	−0.809104	+	0.809104i	0.175394	+	0.984498i	$0.443880\pi$
$774$		0			0
$775$			8.61499i			0.309460i
$776$		0			0
$777$			1.20711i			0.0433047i
$778$		0			0
$779$	17.6607	−	17.6607i	0.632762	−	0.632762i
$780$		0			0
$781$	26.5025	+	26.5025i	0.948334	+	0.948334i
$782$		0			0
$783$	−53.8619			−1.92487
$784$		0			0
$785$	−4.69274			−0.167491
$786$		0			0
$787$	−16.2640	−	16.2640i	−0.579750	−	0.579750i	0.355085	−	0.934834i	$-0.384452\pi$
$787$	−16.2640	−	16.2640i	−0.579750	−	0.579750i	−0.934834	+	0.355085i	$0.884452\pi$
$788$		0			0
$789$	15.7342	−	15.7342i	0.560152	−	0.560152i
$790$		0			0
$791$		−	29.2681i		−	1.04065i
$792$		0			0
$793$			2.44296i			0.0867520i
$794$		0			0
$795$	−14.9154	+	14.9154i	−0.528996	+	0.528996i
$796$		0			0
$797$	−27.5649	−	27.5649i	−0.976398	−	0.976398i	0.0233299	−	0.999728i	$-0.492573\pi$
$797$	−27.5649	−	27.5649i	−0.976398	−	0.976398i	−0.999728	+	0.0233299i	$0.992573\pi$
$798$		0			0
$799$	−13.0812			−0.462779
$800$		0			0
$801$	−8.14617			−0.287831
$802$		0			0
$803$	16.5661	+	16.5661i	0.584606	+	0.584606i
$804$		0			0
$805$	−36.0083	+	36.0083i	−1.26913	+	1.26913i
$806$		0			0
$807$		−	21.7139i		−	0.764365i
$808$		0			0
$809$		−	5.17865i		−	0.182072i	−0.995848	−	0.0910358i	$-0.970982\pi$
$809$		−	5.17865i		−	0.182072i	0.995848	−	0.0910358i	$-0.0290178\pi$
$810$		0			0
$811$	32.6428	−	32.6428i	1.14625	−	1.14625i	0.158960	−	0.987285i	$-0.449186\pi$
$811$	32.6428	−	32.6428i	1.14625	−	1.14625i	0.987285	−	0.158960i	$-0.0508141\pi$
$812$		0			0
$813$	−1.62030	−	1.62030i	−0.0568264	−	0.0568264i
$814$		0			0
$815$	35.9401			1.25893
$816$		0			0
$817$	0.158310			0.00553857
$818$		0			0
$819$	3.10569	+	3.10569i	0.108521	+	0.108521i
$820$		0			0
$821$	−12.1496	+	12.1496i	−0.424025	+	0.424025i	−0.886587	−	0.462562i	$-0.846930\pi$
$821$	−12.1496	+	12.1496i	−0.424025	+	0.424025i	0.462562	+	0.886587i	$0.346930\pi$
$822$		0			0
$823$		−	27.6976i		−	0.965476i	−0.875765	−	0.482738i	$-0.839642\pi$
$823$		−	27.6976i		−	0.965476i	0.875765	−	0.482738i	$-0.160358\pi$
$824$		0			0
$825$		−	8.09269i		−	0.281751i
$826$		0			0
$827$	21.8635	−	21.8635i	0.760269	−	0.760269i	−0.216102	−	0.976371i	$-0.569334\pi$
$827$	21.8635	−	21.8635i	0.760269	−	0.760269i	0.976371	+	0.216102i	$0.0693343\pi$
$828$		0			0
$829$	−14.7756	−	14.7756i	−0.513178	−	0.513178i	0.402320	−	0.915499i	$-0.368204\pi$
$829$	−14.7756	−	14.7756i	−0.513178	−	0.513178i	−0.915499	+	0.402320i	$0.868204\pi$
$830$		0			0
$831$	−2.36561			−0.0820622
$832$		0			0
$833$	19.7885			0.685632
$834$		0			0
$835$	5.16984	+	5.16984i	0.178910	+	0.178910i
$836$		0			0
$837$	−20.6362	+	20.6362i	−0.713293	+	0.713293i
$838$		0			0
$839$		−	0.625398i		−	0.0215912i	−0.999942	−	0.0107956i	$-0.996564\pi$
$839$		−	0.625398i		−	0.0215912i	0.999942	−	0.0107956i	$-0.00343641\pi$
$840$		0			0
$841$			64.1994i			2.21377i
$842$		0			0
$843$	24.2308	−	24.2308i	0.834554	−	0.834554i
$844$		0			0
$845$	1.29480	+	1.29480i	0.0445426	+	0.0445426i
$846$		0			0
$847$	−12.2224			−0.419965
$848$		0			0
$849$	2.71421			0.0931516
$850$		0			0
$851$	−1.80894	−	1.80894i	−0.0620096	−	0.0620096i
$852$		0			0
$853$	−14.2267	+	14.2267i	−0.487114	+	0.487114i	−0.907394	−	0.420280i	$-0.861932\pi$
$853$	−14.2267	+	14.2267i	−0.487114	+	0.487114i	0.420280	+	0.907394i	$0.361932\pi$
$854$		0			0
$855$			6.73881i			0.230462i
$856$		0			0
$857$			36.8671i			1.25936i	0.776857	+	0.629678i	$0.216813\pi$
$857$			36.8671i			1.25936i	−0.776857	+	0.629678i	$0.783187\pi$
$858$		0			0
$859$	11.0958	−	11.0958i	0.378584	−	0.378584i	−0.492007	−	0.870591i	$-0.663737\pi$
$859$	11.0958	−	11.0958i	0.378584	−	0.378584i	0.870591	+	0.492007i	$0.163737\pi$
$860$		0			0
$861$	−26.9099	−	26.9099i	−0.917088	−	0.917088i
$862$		0			0
$863$	5.79818			0.197372			0.0986862	−	0.995119i	$-0.468536\pi$
$863$	5.79818			0.197372			0.0986862	+	0.995119i	$0.468536\pi$
$864$		0			0
$865$	−32.4858			−1.10455
$866$		0			0
$867$	−17.5516	−	17.5516i	−0.596085	−	0.596085i
$868$		0			0
$869$	−14.4629	+	14.4629i	−0.490621	+	0.490621i
$870$		0			0
$871$		−	2.20664i		−	0.0747690i
$872$		0			0
$873$			13.4130i			0.453960i
$874$		0			0
$875$	27.5920	−	27.5920i	0.932778	−	0.932778i
$876$		0			0
$877$	11.4174	+	11.4174i	0.385537	+	0.385537i	0.873092	−	0.487555i	$-0.162111\pi$
$877$	11.4174	+	11.4174i	0.385537	+	0.385537i	−0.487555	+	0.873092i	$0.662111\pi$
$878$		0			0
$879$	−8.27382			−0.279069
$880$		0			0
$881$	21.6667			0.729971			0.364985	−	0.931013i	$-0.381074\pi$
$881$	21.6667			0.729971			0.364985	+	0.931013i	$0.381074\pi$
$882$		0			0
$883$	−3.37331	−	3.37331i	−0.113521	−	0.113521i	0.648064	−	0.761585i	$-0.275579\pi$
$883$	−3.37331	−	3.37331i	−0.113521	−	0.113521i	−0.761585	+	0.648064i	$0.775579\pi$
$884$		0			0
$885$	7.92050	−	7.92050i	0.266245	−	0.266245i
$886$		0			0
$887$			10.0852i			0.338628i	0.985562	+	0.169314i	$0.0541552\pi$
$887$			10.0852i			0.338628i	−0.985562	+	0.169314i	$0.945845\pi$
$888$		0			0
$889$		−	40.7465i		−	1.36659i
$890$		0			0
$891$	8.20011	−	8.20011i	0.274714	−	0.274714i
$892$		0			0
$893$	−4.11603	−	4.11603i	−0.137738	−	0.137738i
$894$		0			0
$895$	17.0012			0.568287
$896$		0			0
$897$	11.0749			0.369779
$898$		0			0
$899$	35.7077	+	35.7077i	1.19092	+	1.19092i
$900$		0			0
$901$	−38.5143	+	38.5143i	−1.28310	+	1.28310i
$902$		0			0
$903$		−	0.241219i		−	0.00802727i
$904$		0			0
$905$			17.8968i			0.594910i
$906$		0			0
$907$	−14.1727	+	14.1727i	−0.470597	+	0.470597i	−0.902108	−	0.431511i	$-0.857981\pi$
$907$	−14.1727	+	14.1727i	−0.470597	+	0.470597i	0.431511	+	0.902108i	$0.357981\pi$
$908$		0			0
$909$	−6.51438	−	6.51438i	−0.216068	−	0.216068i
$910$		0			0
$911$	5.12861			0.169919			0.0849593	−	0.996384i	$-0.472924\pi$
$911$	5.12861			0.169919			0.0849593	+	0.996384i	$0.472924\pi$
$912$		0			0
$913$	−52.8518			−1.74914
$914$		0			0
$915$	4.03845	+	4.03845i	0.133507	+	0.133507i
$916$		0			0
$917$	−20.4996	+	20.4996i	−0.676955	+	0.676955i
$918$		0			0
$919$			1.74928i			0.0577034i	0.999584	+	0.0288517i	$0.00918506\pi$
$919$			1.74928i			0.0577034i	−0.999584	+	0.0288517i	$0.990815\pi$
$920$		0			0
$921$			24.7930i			0.816956i
$922$		0			0
$923$	6.88611	−	6.88611i	0.226659	−	0.226659i
$924$		0			0
$925$	0.343451	+	0.343451i	0.0112926	+	0.0112926i
$926$		0			0
$927$	−3.95714			−0.129969
$928$		0			0
$929$	−28.8593			−0.946844			−0.473422	−	0.880836i	$-0.656981\pi$
$929$	−28.8593			−0.946844			−0.473422	+	0.880836i	$0.656981\pi$
$930$		0			0
$931$	6.22652	+	6.22652i	0.204066	+	0.204066i
$932$		0			0
$933$	1.45269	−	1.45269i	0.0475588	−	0.0475588i
$934$		0			0
$935$			42.5434i			1.39132i
$936$		0			0
$937$			12.4959i			0.408223i	0.978948	+	0.204111i	$0.0654304\pi$
$937$			12.4959i			0.408223i	−0.978948	+	0.204111i	$0.934570\pi$
$938$		0			0
$939$	−12.9870	+	12.9870i	−0.423816	+	0.423816i
$940$		0			0
$941$	3.93712	+	3.93712i	0.128347	+	0.128347i	0.768362	−	0.640015i	$-0.221072\pi$
$941$	3.93712	+	3.93712i	0.128347	+	0.128347i	−0.640015	+	0.768362i	$0.721072\pi$
$942$		0			0
$943$	80.6530			2.62642
$944$		0			0
$945$	32.7529			1.06545
$946$		0			0
$947$	−31.9342	−	31.9342i	−1.03772	−	1.03772i	−0.999260	−	0.0384618i	$-0.987754\pi$
$947$	−31.9342	−	31.9342i	−1.03772	−	1.03772i	−0.0384618	−	0.999260i	$-0.512246\pi$
$948$		0			0
$949$	4.30436	−	4.30436i	0.139725	−	0.139725i
$950$		0			0
$951$		−	22.4116i		−	0.726745i
$952$		0			0
$953$		−	28.7558i		−	0.931492i	−0.884918	−	0.465746i	$-0.845786\pi$
$953$		−	28.7558i		−	0.931492i	0.884918	−	0.465746i	$-0.154214\pi$
$954$		0			0
$955$	−14.5751	+	14.5751i	−0.471640	+	0.471640i
$956$		0			0
$957$	−33.5428	−	33.5428i	−1.08429	−	1.08429i
$958$		0			0
$959$	−63.5329			−2.05159
$960$		0			0
$961$	−3.63849			−0.117371
$962$		0			0
$963$	5.07985	+	5.07985i	0.163696	+	0.163696i
$964$		0			0
$965$	−3.29669	+	3.29669i	−0.106124	+	0.106124i
$966$		0			0
$967$			5.77351i			0.185664i	0.995682	+	0.0928318i	$0.0295919\pi$
$967$			5.77351i			0.185664i	−0.995682	+	0.0928318i	$0.970408\pi$
$968$		0			0
$969$		−	20.7034i		−	0.665090i
$970$		0			0
$971$	17.9091	−	17.9091i	0.574729	−	0.574729i	−0.358717	−	0.933446i	$-0.616786\pi$
$971$	17.9091	−	17.9091i	0.574729	−	0.574729i	0.933446	+	0.358717i	$0.116786\pi$
$972$		0			0
$973$	−25.0530	−	25.0530i	−0.803163	−	0.803163i
$974$		0			0
$975$	−2.10271			−0.0673407
$976$		0			0
$977$	−3.82926			−0.122509			−0.0612544	−	0.998122i	$-0.519510\pi$
$977$	−3.82926			−0.122509			−0.0612544	+	0.998122i	$0.519510\pi$
$978$		0			0
$979$	−16.1821	−	16.1821i	−0.517181	−	0.517181i
$980$		0			0
$981$	−3.78835	+	3.78835i	−0.120953	+	0.120953i
$982$		0			0
$983$		−	42.4136i		−	1.35279i	−0.736541	−	0.676393i	$-0.763542\pi$
$983$		−	42.4136i		−	1.35279i	0.736541	−	0.676393i	$-0.236458\pi$
$984$		0			0
$985$			11.1363i			0.354832i
$986$		0			0
$987$	−6.27166	+	6.27166i	−0.199629	+	0.199629i
$988$		0			0
$989$	0.361485	+	0.361485i	0.0114946	+	0.0114946i
$990$		0			0
$991$	59.1239			1.87813			0.939066	−	0.343736i	$-0.111693\pi$
$991$	59.1239			1.87813			0.939066	+	0.343736i	$0.111693\pi$
$992$		0			0
$993$	−30.9683			−0.982749
$994$		0			0
$995$	−34.0384	−	34.0384i	−1.07909	−	1.07909i
$996$		0			0
$997$	35.9832	−	35.9832i	1.13960	−	1.13960i	0.151079	−	0.988522i	$-0.451725\pi$
$997$	35.9832	−	35.9832i	1.13960	−	1.13960i	0.988522	−	0.151079i	$-0.0482748\pi$
$998$		0			0
$999$			1.64540i			0.0520581i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1664.2.n.b.417.8		48
4.3	odd	2		1664.2.n.a.417.17		48
8.3	odd	2		832.2.n.a.209.8		48
8.5	even	2		208.2.n.a.157.24	yes	48
16.3	odd	4		832.2.n.a.625.8		48
16.5	even	4	inner	1664.2.n.b.1249.8		48
16.11	odd	4		1664.2.n.a.1249.17		48
16.13	even	4		208.2.n.a.53.24	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
208.2.n.a.53.24	✓	48	16.13	even	4
208.2.n.a.157.24	yes	48	8.5	even	2
832.2.n.a.209.8		48	8.3	odd	2
832.2.n.a.625.8		48	16.3	odd	4
1664.2.n.a.417.17		48	4.3	odd	2
1664.2.n.a.1249.17		48	16.11	odd	4
1664.2.n.b.417.8		48	1.1	even	1	trivial
1664.2.n.b.1249.8		48	16.5	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1664 = 2^{7} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1664.n (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.902776 - 0.902776i) q^{3} +(1.29480 - 1.29480i) q^{5} -3.20594i q^{7} -1.36999i q^{9} +O(q^{10})\)	\(q+(-0.902776 - 0.902776i) q^{3} +(1.29480 - 1.29480i) q^{5} -3.20594i q^{7} -1.36999i q^{9} +(2.72143 - 2.72143i) q^{11} +(-0.707107 - 0.707107i) q^{13} -2.33784 q^{15} -6.03671 q^{17} +(-1.89947 - 1.89947i) q^{19} +(-2.89424 + 2.89424i) q^{21} -8.67448i q^{23} +1.64697i q^{25} +(-3.94512 + 3.94512i) q^{27} +(6.82640 + 6.82640i) q^{29} +5.23082 q^{31} -4.91369 q^{33} +(-4.15106 - 4.15106i) q^{35} +(0.208536 - 0.208536i) q^{37} +1.27672i q^{39} +9.29774i q^{41} +(-0.0416722 + 0.0416722i) q^{43} +(-1.77387 - 1.77387i) q^{45} +2.16694 q^{47} -3.27803 q^{49} +(5.44980 + 5.44980i) q^{51} +(6.38002 - 6.38002i) q^{53} -7.04745i q^{55} +3.42959i q^{57} +(-3.38796 + 3.38796i) q^{59} +(-1.72743 - 1.72743i) q^{61} -4.39210 q^{63} -1.83113 q^{65} +(1.56033 + 1.56033i) q^{67} +(-7.83111 + 7.83111i) q^{69} +9.73843i q^{71} +6.08728i q^{73} +(1.48684 - 1.48684i) q^{75} +(-8.72475 - 8.72475i) q^{77} -5.31445 q^{79} +3.01316 q^{81} +(-9.71028 - 9.71028i) q^{83} +(-7.81635 + 7.81635i) q^{85} -12.3254i q^{87} -5.94615i q^{89} +(-2.26694 + 2.26694i) q^{91} +(-4.72226 - 4.72226i) q^{93} -4.91887 q^{95} -9.79055 q^{97} +(-3.72834 - 3.72834i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q+O(q^{10}) \) 48 * q	\( 48 q + 8 q^{11} - 16 q^{15} + 16 q^{19} + 16 q^{29} + 24 q^{31} - 24 q^{35} + 16 q^{37} + 8 q^{43} - 40 q^{47} - 48 q^{49} + 24 q^{51} - 16 q^{53} - 32 q^{61} + 40 q^{63} - 16 q^{67} - 32 q^{69} + 40 q^{75} - 16 q^{77} + 32 q^{79} - 48 q^{81} - 40 q^{83} + 32 q^{85} - 48 q^{95} + 40 q^{99}+O(q^{100}) \) 48 * q + 8 * q^11 - 16 * q^15 + 16 * q^19 + 16 * q^29 + 24 * q^31 - 24 * q^35 + 16 * q^37 + 8 * q^43 - 40 * q^47 - 48 * q^49 + 24 * q^51 - 16 * q^53 - 32 * q^61 + 40 * q^63 - 16 * q^67 - 32 * q^69 + 40 * q^75 - 16 * q^77 + 32 * q^79 - 48 * q^81 - 40 * q^83 + 32 * q^85 - 48 * q^95 + 40 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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