LMFDB - Embedded newform 5775.2.a.o.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5775,2,Mod(1,5775)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5775, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("5775.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5775 = 3 \cdot 5^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5775.a (trivial)

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:	yes
Analytic conductor:	$46.1136071673$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 1155)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	5775.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+1.00000 q^{3} -2.00000 q^{4} -1.00000 q^{7} +1.00000 q^{9} +O(q^{10})$

$q+1.00000 q^{3} -2.00000 q^{4} -1.00000 q^{7} +1.00000 q^{9} +1.00000 q^{11} -2.00000 q^{12} +4.00000 q^{16} -3.00000 q^{17} -3.00000 q^{19} -1.00000 q^{21} +1.00000 q^{23} +1.00000 q^{27} +2.00000 q^{28} -7.00000 q^{29} +6.00000 q^{31} +1.00000 q^{33} -2.00000 q^{36} +8.00000 q^{37} -2.00000 q^{41} +5.00000 q^{43} -2.00000 q^{44} +6.00000 q^{47} +4.00000 q^{48} +1.00000 q^{49} -3.00000 q^{51} +3.00000 q^{53} -3.00000 q^{57} -5.00000 q^{59} -7.00000 q^{61} -1.00000 q^{63} -8.00000 q^{64} -6.00000 q^{67} +6.00000 q^{68} +1.00000 q^{69} -10.0000 q^{71} -12.0000 q^{73} +6.00000 q^{76} -1.00000 q^{77} -16.0000 q^{79} +1.00000 q^{81} +3.00000 q^{83} +2.00000 q^{84} -7.00000 q^{87} +3.00000 q^{89} -2.00000 q^{92} +6.00000 q^{93} +1.00000 q^{97} +1.00000 q^{99} +O(q^{100})$

Display 100 coefficients 10 coefficients

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		−	1.00000i	$-0.5\pi$
$2$	0	0			1.00000i	$0.5\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−2.00000	−1.00000
$5$	0	0
$5$	0	0
$6$	0	0
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	0	0
$9$	1.00000	0.333333
$10$	0	0
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−2.00000	−0.577350
$13$	0	0		−	1.00000i	$-0.5\pi$
$13$	0	0			1.00000i	$0.5\pi$
$14$	0	0
$15$	0	0
$16$	4.00000	1.00000
$17$	−3.00000	−0.727607	−0.363803	−	0.931476i	$-0.618522\pi$
$17$	−3.00000	−0.727607	−0.363803	+	0.931476i	$0.618522\pi$
$18$	0	0
$19$	−3.00000	−0.688247	−0.344124	−	0.938924i	$-0.611824\pi$
$19$	−3.00000	−0.688247	−0.344124	+	0.938924i	$0.611824\pi$
$20$	0	0
$21$	−1.00000	−0.218218
$22$	0	0
$23$	1.00000	0.208514	0.104257	−	0.994550i	$-0.466753\pi$
$23$	1.00000	0.208514	0.104257	+	0.994550i	$0.466753\pi$
$24$	0	0
$25$	0	0
$26$	0	0
$27$	1.00000	0.192450
$28$	2.00000	0.377964
$29$	−7.00000	−1.29987	−0.649934	−	0.759991i	$-0.725203\pi$
$29$	−7.00000	−1.29987	−0.649934	+	0.759991i	$0.725203\pi$
$30$	0	0
$31$	6.00000	1.07763	0.538816	−	0.842424i	$-0.318872\pi$
$31$	6.00000	1.07763	0.538816	+	0.842424i	$0.318872\pi$
$32$	0	0
$33$	1.00000	0.174078
$34$	0	0
$35$	0	0
$36$	−2.00000	−0.333333
$37$	8.00000	1.31519	0.657596	−	0.753371i	$-0.271573\pi$
$37$	8.00000	1.31519	0.657596	+	0.753371i	$0.271573\pi$
$38$	0	0
$39$	0	0
$40$	0	0
$41$	−2.00000	−0.312348	−0.156174	−	0.987730i	$-0.549916\pi$
$41$	−2.00000	−0.312348	−0.156174	+	0.987730i	$0.549916\pi$
$42$	0	0
$43$	5.00000	0.762493	0.381246	−	0.924473i	$-0.375495\pi$
$43$	5.00000	0.762493	0.381246	+	0.924473i	$0.375495\pi$
$44$	−2.00000	−0.301511
$45$	0	0
$46$	0	0
$47$	6.00000	0.875190	0.437595	−	0.899172i	$-0.355830\pi$
$47$	6.00000	0.875190	0.437595	+	0.899172i	$0.355830\pi$
$48$	4.00000	0.577350
$49$	1.00000	0.142857
$50$	0	0
$51$	−3.00000	−0.420084
$52$	0	0
$53$	3.00000	0.412082	0.206041	−	0.978543i	$-0.433942\pi$
$53$	3.00000	0.412082	0.206041	+	0.978543i	$0.433942\pi$
$54$	0	0
$55$	0	0
$56$	0	0
$57$	−3.00000	−0.397360
$58$	0	0
$59$	−5.00000	−0.650945	−0.325472	−	0.945552i	$-0.605523\pi$
$59$	−5.00000	−0.650945	−0.325472	+	0.945552i	$0.605523\pi$
$60$	0	0
$61$	−7.00000	−0.896258	−0.448129	−	0.893969i	$-0.647910\pi$
$61$	−7.00000	−0.896258	−0.448129	+	0.893969i	$0.647910\pi$
$62$	0	0
$63$	−1.00000	−0.125988
$64$	−8.00000	−1.00000
$65$	0	0
$66$	0	0
$67$	−6.00000	−0.733017	−0.366508	−	0.930415i	$-0.619447\pi$
$67$	−6.00000	−0.733017	−0.366508	+	0.930415i	$0.619447\pi$
$68$	6.00000	0.727607
$69$	1.00000	0.120386
$70$	0	0
$71$	−10.0000	−1.18678	−0.593391	−	0.804914i	$-0.702211\pi$
$71$	−10.0000	−1.18678	−0.593391	+	0.804914i	$0.702211\pi$
$72$	0	0
$73$	−12.0000	−1.40449	−0.702247	−	0.711934i	$-0.747820\pi$
$73$	−12.0000	−1.40449	−0.702247	+	0.711934i	$0.747820\pi$
$74$	0	0
$75$	0	0
$76$	6.00000	0.688247
$77$	−1.00000	−0.113961
$78$	0	0
$79$	−16.0000	−1.80014	−0.900070	−	0.435745i	$-0.856485\pi$
$79$	−16.0000	−1.80014	−0.900070	+	0.435745i	$0.856485\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	0	0
$83$	3.00000	0.329293	0.164646	−	0.986353i	$-0.447352\pi$
$83$	3.00000	0.329293	0.164646	+	0.986353i	$0.447352\pi$
$84$	2.00000	0.218218
$85$	0	0
$86$	0	0
$87$	−7.00000	−0.750479
$88$	0	0
$89$	3.00000	0.317999	0.159000	−	0.987279i	$-0.449173\pi$
$89$	3.00000	0.317999	0.159000	+	0.987279i	$0.449173\pi$
$90$	0	0
$91$	0	0
$92$	−2.00000	−0.208514
$93$	6.00000	0.622171
$94$	0	0
$95$	0	0
$96$	0	0
$97$	1.00000	0.101535	0.0507673	−	0.998711i	$-0.483833\pi$
$97$	1.00000	0.101535	0.0507673	+	0.998711i	$0.483833\pi$
$98$	0	0
$99$	1.00000	0.100504
$100$	0	0
$101$	−14.0000	−1.39305	−0.696526	−	0.717532i	$-0.745272\pi$
$101$	−14.0000	−1.39305	−0.696526	+	0.717532i	$0.745272\pi$
$102$	0	0
$103$	5.00000	0.492665	0.246332	−	0.969185i	$-0.420775\pi$
$103$	5.00000	0.492665	0.246332	+	0.969185i	$0.420775\pi$
$104$	0	0
$105$	0	0
$106$	0	0
$107$	−6.00000	−0.580042	−0.290021	−	0.957020i	$-0.593662\pi$
$107$	−6.00000	−0.580042	−0.290021	+	0.957020i	$0.593662\pi$
$108$	−2.00000	−0.192450
$109$	−2.00000	−0.191565	−0.0957826	−	0.995402i	$-0.530535\pi$
$109$	−2.00000	−0.191565	−0.0957826	+	0.995402i	$0.530535\pi$
$110$	0	0
$111$	8.00000	0.759326
$112$	−4.00000	−0.377964
$113$	19.0000	1.78737	0.893685	−	0.448695i	$-0.148111\pi$
$113$	19.0000	1.78737	0.893685	+	0.448695i	$0.148111\pi$
$114$	0	0
$115$	0	0
$116$	14.0000	1.29987
$117$	0	0
$118$	0	0
$119$	3.00000	0.275010
$120$	0	0
$121$	1.00000	0.0909091
$122$	0	0
$123$	−2.00000	−0.180334
$124$	−12.0000	−1.07763
$125$	0	0
$126$	0	0
$127$	−19.0000	−1.68598	−0.842989	−	0.537931i	$-0.819206\pi$
$127$	−19.0000	−1.68598	−0.842989	+	0.537931i	$0.819206\pi$
$128$	0	0
$129$	5.00000	0.440225
$130$	0	0
$131$	4.00000	0.349482	0.174741	−	0.984614i	$-0.444091\pi$
$131$	4.00000	0.349482	0.174741	+	0.984614i	$0.444091\pi$
$132$	−2.00000	−0.174078
$133$	3.00000	0.260133
$134$	0	0
$135$	0	0
$136$	0	0
$137$	2.00000	0.170872	0.0854358	−	0.996344i	$-0.472772\pi$
$137$	2.00000	0.170872	0.0854358	+	0.996344i	$0.472772\pi$
$138$	0	0
$139$	4.00000	0.339276	0.169638	−	0.985506i	$-0.445740\pi$
$139$	4.00000	0.339276	0.169638	+	0.985506i	$0.445740\pi$
$140$	0	0
$141$	6.00000	0.505291
$142$	0	0
$143$	0	0
$144$	4.00000	0.333333
$145$	0	0
$146$	0	0
$147$	1.00000	0.0824786
$148$	−16.0000	−1.31519
$149$	−6.00000	−0.491539	−0.245770	−	0.969328i	$-0.579041\pi$
$149$	−6.00000	−0.491539	−0.245770	+	0.969328i	$0.579041\pi$
$150$	0	0
$151$	14.0000	1.13930	0.569652	−	0.821886i	$-0.307078\pi$
$151$	14.0000	1.13930	0.569652	+	0.821886i	$0.307078\pi$
$152$	0	0
$153$	−3.00000	−0.242536
$154$	0	0
$155$	0	0
$156$	0	0
$157$	1.00000	0.0798087	0.0399043	−	0.999204i	$-0.487295\pi$
$157$	1.00000	0.0798087	0.0399043	+	0.999204i	$0.487295\pi$
$158$	0	0
$159$	3.00000	0.237915
$160$	0	0
$161$	−1.00000	−0.0788110
$162$	0	0
$163$	−12.0000	−0.939913	−0.469956	−	0.882690i	$-0.655730\pi$
$163$	−12.0000	−0.939913	−0.469956	+	0.882690i	$0.655730\pi$
$164$	4.00000	0.312348
$165$	0	0
$166$	0	0
$167$	−12.0000	−0.928588	−0.464294	−	0.885681i	$-0.653692\pi$
$167$	−12.0000	−0.928588	−0.464294	+	0.885681i	$0.653692\pi$
$168$	0	0
$169$	−13.0000	−1.00000
$170$	0	0
$171$	−3.00000	−0.229416
$172$	−10.0000	−0.762493
$173$	14.0000	1.06440	0.532200	−	0.846619i	$-0.321365\pi$
$173$	14.0000	1.06440	0.532200	+	0.846619i	$0.321365\pi$
$174$	0	0
$175$	0	0
$176$	4.00000	0.301511
$177$	−5.00000	−0.375823
$178$	0	0
$179$	−18.0000	−1.34538	−0.672692	−	0.739923i	$-0.734862\pi$
$179$	−18.0000	−1.34538	−0.672692	+	0.739923i	$0.734862\pi$
$180$	0	0
$181$	10.0000	0.743294	0.371647	−	0.928374i	$-0.378793\pi$
$181$	10.0000	0.743294	0.371647	+	0.928374i	$0.378793\pi$
$182$	0	0
$183$	−7.00000	−0.517455
$184$	0	0
$185$	0	0
$186$	0	0
$187$	−3.00000	−0.219382
$188$	−12.0000	−0.875190
$189$	−1.00000	−0.0727393
$190$	0	0
$191$	−16.0000	−1.15772	−0.578860	−	0.815427i	$-0.696502\pi$
$191$	−16.0000	−1.15772	−0.578860	+	0.815427i	$0.696502\pi$
$192$	−8.00000	−0.577350
$193$	−6.00000	−0.431889	−0.215945	−	0.976406i	$-0.569283\pi$
$193$	−6.00000	−0.431889	−0.215945	+	0.976406i	$0.569283\pi$
$194$	0	0
$195$	0	0
$196$	−2.00000	−0.142857
$197$	0	0		−	1.00000i	$-0.5\pi$
$197$	0	0			1.00000i	$0.5\pi$
$198$	0	0
$199$	24.0000	1.70131	0.850657	−	0.525720i	$-0.176204\pi$
$199$	24.0000	1.70131	0.850657	+	0.525720i	$0.176204\pi$
$200$	0	0
$201$	−6.00000	−0.423207
$202$	0	0
$203$	7.00000	0.491304
$204$	6.00000	0.420084
$205$	0	0
$206$	0	0
$207$	1.00000	0.0695048
$208$	0	0
$209$	−3.00000	−0.207514
$210$	0	0
$211$	−18.0000	−1.23917	−0.619586	−	0.784929i	$-0.712699\pi$
$211$	−18.0000	−1.23917	−0.619586	+	0.784929i	$0.712699\pi$
$212$	−6.00000	−0.412082
$213$	−10.0000	−0.685189
$214$	0	0
$215$	0	0
$216$	0	0
$217$	−6.00000	−0.407307
$218$	0	0
$219$	−12.0000	−0.810885
$220$	0	0
$221$	0	0
$222$	0	0
$223$	−1.00000	−0.0669650	−0.0334825	−	0.999439i	$-0.510660\pi$
$223$	−1.00000	−0.0669650	−0.0334825	+	0.999439i	$0.510660\pi$
$224$	0	0
$225$	0	0
$226$	0	0
$227$	3.00000	0.199117	0.0995585	−	0.995032i	$-0.468257\pi$
$227$	3.00000	0.199117	0.0995585	+	0.995032i	$0.468257\pi$
$228$	6.00000	0.397360
$229$	−14.0000	−0.925146	−0.462573	−	0.886581i	$-0.653074\pi$
$229$	−14.0000	−0.925146	−0.462573	+	0.886581i	$0.653074\pi$
$230$	0	0
$231$	−1.00000	−0.0657952
$232$	0	0
$233$	16.0000	1.04819	0.524097	−	0.851658i	$-0.324403\pi$
$233$	16.0000	1.04819	0.524097	+	0.851658i	$0.324403\pi$
$234$	0	0
$235$	0	0
$236$	10.0000	0.650945
$237$	−16.0000	−1.03931
$238$	0	0
$239$	−21.0000	−1.35838	−0.679189	−	0.733964i	$-0.737668\pi$
$239$	−21.0000	−1.35838	−0.679189	+	0.733964i	$0.737668\pi$
$240$	0	0
$241$	10.0000	0.644157	0.322078	−	0.946713i	$-0.395619\pi$
$241$	10.0000	0.644157	0.322078	+	0.946713i	$0.395619\pi$
$242$	0	0
$243$	1.00000	0.0641500
$244$	14.0000	0.896258
$245$	0	0
$246$	0	0
$247$	0	0
$248$	0	0
$249$	3.00000	0.190117
$250$	0	0
$251$	−12.0000	−0.757433	−0.378717	−	0.925513i	$-0.623635\pi$
$251$	−12.0000	−0.757433	−0.378717	+	0.925513i	$0.623635\pi$
$252$	2.00000	0.125988
$253$	1.00000	0.0628695
$254$	0	0
$255$	0	0
$256$	16.0000	1.00000
$257$	−20.0000	−1.24757	−0.623783	−	0.781598i	$-0.714405\pi$
$257$	−20.0000	−1.24757	−0.623783	+	0.781598i	$0.714405\pi$
$258$	0	0
$259$	−8.00000	−0.497096
$260$	0	0
$261$	−7.00000	−0.433289
$262$	0	0
$263$	−16.0000	−0.986602	−0.493301	−	0.869859i	$-0.664210\pi$
$263$	−16.0000	−0.986602	−0.493301	+	0.869859i	$0.664210\pi$
$264$	0	0
$265$	0	0
$266$	0	0
$267$	3.00000	0.183597
$268$	12.0000	0.733017
$269$	−1.00000	−0.0609711	−0.0304855	−	0.999535i	$-0.509705\pi$
$269$	−1.00000	−0.0609711	−0.0304855	+	0.999535i	$0.509705\pi$
$270$	0	0
$271$	−1.00000	−0.0607457	−0.0303728	−	0.999539i	$-0.509669\pi$
$271$	−1.00000	−0.0607457	−0.0303728	+	0.999539i	$0.509669\pi$
$272$	−12.0000	−0.727607
$273$	0	0
$274$	0	0
$275$	0	0
$276$	−2.00000	−0.120386
$277$	10.0000	0.600842	0.300421	−	0.953807i	$-0.402873\pi$
$277$	10.0000	0.600842	0.300421	+	0.953807i	$0.402873\pi$
$278$	0	0
$279$	6.00000	0.359211
$280$	0	0
$281$	−22.0000	−1.31241	−0.656205	−	0.754583i	$-0.727839\pi$
$281$	−22.0000	−1.31241	−0.656205	+	0.754583i	$0.727839\pi$
$282$	0	0
$283$	8.00000	0.475551	0.237775	−	0.971320i	$-0.423582\pi$
$283$	8.00000	0.475551	0.237775	+	0.971320i	$0.423582\pi$
$284$	20.0000	1.18678
$285$	0	0
$286$	0	0
$287$	2.00000	0.118056
$288$	0	0
$289$	−8.00000	−0.470588
$290$	0	0
$291$	1.00000	0.0586210
$292$	24.0000	1.40449
$293$	−19.0000	−1.10999	−0.554996	−	0.831853i	$-0.687280\pi$
$293$	−19.0000	−1.10999	−0.554996	+	0.831853i	$0.687280\pi$
$294$	0	0
$295$	0	0
$296$	0	0
$297$	1.00000	0.0580259
$298$	0	0
$299$	0	0
$300$	0	0
$301$	−5.00000	−0.288195
$302$	0	0
$303$	−14.0000	−0.804279
$304$	−12.0000	−0.688247
$305$	0	0
$306$	0	0
$307$	−26.0000	−1.48390	−0.741949	−	0.670456i	$-0.766098\pi$
$307$	−26.0000	−1.48390	−0.741949	+	0.670456i	$0.766098\pi$
$308$	2.00000	0.113961
$309$	5.00000	0.284440
$310$	0	0
$311$	−32.0000	−1.81455	−0.907277	−	0.420534i	$-0.861843\pi$
$311$	−32.0000	−1.81455	−0.907277	+	0.420534i	$0.861843\pi$
$312$	0	0
$313$	−21.0000	−1.18699	−0.593495	−	0.804838i	$-0.702252\pi$
$313$	−21.0000	−1.18699	−0.593495	+	0.804838i	$0.702252\pi$
$314$	0	0
$315$	0	0
$316$	32.0000	1.80014
$317$	−2.00000	−0.112331	−0.0561656	−	0.998421i	$-0.517887\pi$
$317$	−2.00000	−0.112331	−0.0561656	+	0.998421i	$0.517887\pi$
$318$	0	0
$319$	−7.00000	−0.391925
$320$	0	0
$321$	−6.00000	−0.334887
$322$	0	0
$323$	9.00000	0.500773
$324$	−2.00000	−0.111111
$325$	0	0
$326$	0	0
$327$	−2.00000	−0.110600
$328$	0	0
$329$	−6.00000	−0.330791
$330$	0	0
$331$	17.0000	0.934405	0.467202	−	0.884150i	$-0.345262\pi$
$331$	17.0000	0.934405	0.467202	+	0.884150i	$0.345262\pi$
$332$	−6.00000	−0.329293
$333$	8.00000	0.438397
$334$	0	0
$335$	0	0
$336$	−4.00000	−0.218218
$337$	1.00000	0.0544735	0.0272367	−	0.999629i	$-0.491329\pi$
$337$	1.00000	0.0544735	0.0272367	+	0.999629i	$0.491329\pi$
$338$	0	0
$339$	19.0000	1.03194
$340$	0	0
$341$	6.00000	0.324918
$342$	0	0
$343$	−1.00000	−0.0539949
$344$	0	0
$345$	0	0
$346$	0	0
$347$	8.00000	0.429463	0.214731	−	0.976673i	$-0.431112\pi$
$347$	8.00000	0.429463	0.214731	+	0.976673i	$0.431112\pi$
$348$	14.0000	0.750479
$349$	−19.0000	−1.01705	−0.508523	−	0.861048i	$-0.669808\pi$
$349$	−19.0000	−1.01705	−0.508523	+	0.861048i	$0.669808\pi$
$350$	0	0
$351$	0	0
$352$	0	0
$353$	10.0000	0.532246	0.266123	−	0.963939i	$-0.414257\pi$
$353$	10.0000	0.532246	0.266123	+	0.963939i	$0.414257\pi$
$354$	0	0
$355$	0	0
$356$	−6.00000	−0.317999
$357$	3.00000	0.158777
$358$	0	0
$359$	−21.0000	−1.10834	−0.554169	−	0.832404i	$-0.686964\pi$
$359$	−21.0000	−1.10834	−0.554169	+	0.832404i	$0.686964\pi$
$360$	0	0
$361$	−10.0000	−0.526316
$362$	0	0
$363$	1.00000	0.0524864
$364$	0	0
$365$	0	0
$366$	0	0
$367$	−7.00000	−0.365397	−0.182699	−	0.983169i	$-0.558483\pi$
$367$	−7.00000	−0.365397	−0.182699	+	0.983169i	$0.558483\pi$
$368$	4.00000	0.208514
$369$	−2.00000	−0.104116
$370$	0	0
$371$	−3.00000	−0.155752
$372$	−12.0000	−0.622171
$373$	−11.0000	−0.569558	−0.284779	−	0.958593i	$-0.591920\pi$
$373$	−11.0000	−0.569558	−0.284779	+	0.958593i	$0.591920\pi$
$374$	0	0
$375$	0	0
$376$	0	0
$377$	0	0
$378$	0	0
$379$	5.00000	0.256833	0.128416	−	0.991720i	$-0.459011\pi$
$379$	5.00000	0.256833	0.128416	+	0.991720i	$0.459011\pi$
$380$	0	0
$381$	−19.0000	−0.973399
$382$	0	0
$383$	−32.0000	−1.63512	−0.817562	−	0.575841i	$-0.804675\pi$
$383$	−32.0000	−1.63512	−0.817562	+	0.575841i	$0.804675\pi$
$384$	0	0
$385$	0	0
$386$	0	0
$387$	5.00000	0.254164
$388$	−2.00000	−0.101535
$389$	12.0000	0.608424	0.304212	−	0.952604i	$-0.401607\pi$
$389$	12.0000	0.608424	0.304212	+	0.952604i	$0.401607\pi$
$390$	0	0
$391$	−3.00000	−0.151717
$392$	0	0
$393$	4.00000	0.201773
$394$	0	0
$395$	0	0
$396$	−2.00000	−0.100504
$397$	10.0000	0.501886	0.250943	−	0.968002i	$-0.419259\pi$
$397$	10.0000	0.501886	0.250943	+	0.968002i	$0.419259\pi$
$398$	0	0
$399$	3.00000	0.150188
$400$	0	0
$401$	−10.0000	−0.499376	−0.249688	−	0.968326i	$-0.580328\pi$
$401$	−10.0000	−0.499376	−0.249688	+	0.968326i	$0.580328\pi$
$402$	0	0
$403$	0	0
$404$	28.0000	1.39305
$405$	0	0
$406$	0	0
$407$	8.00000	0.396545
$408$	0	0
$409$	−6.00000	−0.296681	−0.148340	−	0.988936i	$-0.547393\pi$
$409$	−6.00000	−0.296681	−0.148340	+	0.988936i	$0.547393\pi$
$410$	0	0
$411$	2.00000	0.0986527
$412$	−10.0000	−0.492665
$413$	5.00000	0.246034
$414$	0	0
$415$	0	0
$416$	0	0
$417$	4.00000	0.195881
$418$	0	0
$419$	33.0000	1.61216	0.806078	−	0.591810i	$-0.201586\pi$
$419$	33.0000	1.61216	0.806078	+	0.591810i	$0.201586\pi$
$420$	0	0
$421$	−23.0000	−1.12095	−0.560476	−	0.828171i	$-0.689382\pi$
$421$	−23.0000	−1.12095	−0.560476	+	0.828171i	$0.689382\pi$
$422$	0	0
$423$	6.00000	0.291730
$424$	0	0
$425$	0	0
$426$	0	0
$427$	7.00000	0.338754
$428$	12.0000	0.580042
$429$	0	0
$430$	0	0
$431$	36.0000	1.73406	0.867029	−	0.498257i	$-0.166026\pi$
$431$	36.0000	1.73406	0.867029	+	0.498257i	$0.166026\pi$
$432$	4.00000	0.192450
$433$	−22.0000	−1.05725	−0.528626	−	0.848855i	$-0.677293\pi$
$433$	−22.0000	−1.05725	−0.528626	+	0.848855i	$0.677293\pi$
$434$	0	0
$435$	0	0
$436$	4.00000	0.191565
$437$	−3.00000	−0.143509
$438$	0	0
$439$	1.00000	0.0477274	0.0238637	−	0.999715i	$-0.492403\pi$
$439$	1.00000	0.0477274	0.0238637	+	0.999715i	$0.492403\pi$
$440$	0	0
$441$	1.00000	0.0476190
$442$	0	0
$443$	−32.0000	−1.52037	−0.760183	−	0.649709i	$-0.774891\pi$
$443$	−32.0000	−1.52037	−0.760183	+	0.649709i	$0.774891\pi$
$444$	−16.0000	−0.759326
$445$	0	0
$446$	0	0
$447$	−6.00000	−0.283790
$448$	8.00000	0.377964
$449$	26.0000	1.22702	0.613508	−	0.789689i	$-0.289758\pi$
$449$	26.0000	1.22702	0.613508	+	0.789689i	$0.289758\pi$
$450$	0	0
$451$	−2.00000	−0.0941763
$452$	−38.0000	−1.78737
$453$	14.0000	0.657777
$454$	0	0
$455$	0	0
$456$	0	0
$457$	37.0000	1.73079	0.865393	−	0.501093i	$-0.167069\pi$
$457$	37.0000	1.73079	0.865393	+	0.501093i	$0.167069\pi$
$458$	0	0
$459$	−3.00000	−0.140028
$460$	0	0
$461$	6.00000	0.279448	0.139724	−	0.990190i	$-0.455378\pi$
$461$	6.00000	0.279448	0.139724	+	0.990190i	$0.455378\pi$
$462$	0	0
$463$	18.0000	0.836531	0.418265	−	0.908325i	$-0.362638\pi$
$463$	18.0000	0.836531	0.418265	+	0.908325i	$0.362638\pi$
$464$	−28.0000	−1.29987
$465$	0	0
$466$	0	0
$467$	0	0		−	1.00000i	$-0.5\pi$
$467$	0	0			1.00000i	$0.5\pi$
$468$	0	0
$469$	6.00000	0.277054
$470$	0	0
$471$	1.00000	0.0460776
$472$	0	0
$473$	5.00000	0.229900
$474$	0	0
$475$	0	0
$476$	−6.00000	−0.275010
$477$	3.00000	0.137361
$478$	0	0
$479$	0	0		−	1.00000i	$-0.5\pi$
$479$	0	0			1.00000i	$0.5\pi$
$480$	0	0
$481$	0	0
$482$	0	0
$483$	−1.00000	−0.0455016
$484$	−2.00000	−0.0909091
$485$	0	0
$486$	0	0
$487$	22.0000	0.996915	0.498458	−	0.866914i	$-0.333900\pi$
$487$	22.0000	0.996915	0.498458	+	0.866914i	$0.333900\pi$
$488$	0	0
$489$	−12.0000	−0.542659
$490$	0	0
$491$	−15.0000	−0.676941	−0.338470	−	0.940977i	$-0.609909\pi$
$491$	−15.0000	−0.676941	−0.338470	+	0.940977i	$0.609909\pi$
$492$	4.00000	0.180334
$493$	21.0000	0.945792
$494$	0	0
$495$	0	0
$496$	24.0000	1.07763
$497$	10.0000	0.448561
$498$	0	0
$499$	−21.0000	−0.940089	−0.470045	−	0.882643i	$-0.655762\pi$
$499$	−21.0000	−0.940089	−0.470045	+	0.882643i	$0.655762\pi$
$500$	0	0
$501$	−12.0000	−0.536120
$502$	0	0
$503$	13.0000	0.579641	0.289821	−	0.957081i	$-0.406404\pi$
$503$	13.0000	0.579641	0.289821	+	0.957081i	$0.406404\pi$
$504$	0	0
$505$	0	0
$506$	0	0
$507$	−13.0000	−0.577350
$508$	38.0000	1.68598
$509$	−11.0000	−0.487566	−0.243783	−	0.969830i	$-0.578389\pi$
$509$	−11.0000	−0.487566	−0.243783	+	0.969830i	$0.578389\pi$
$510$	0	0
$511$	12.0000	0.530849
$512$	0	0
$513$	−3.00000	−0.132453
$514$	0	0
$515$	0	0
$516$	−10.0000	−0.440225
$517$	6.00000	0.263880
$518$	0	0
$519$	14.0000	0.614532
$520$	0	0
$521$	−27.0000	−1.18289	−0.591446	−	0.806345i	$-0.701443\pi$
$521$	−27.0000	−1.18289	−0.591446	+	0.806345i	$0.701443\pi$
$522$	0	0
$523$	20.0000	0.874539	0.437269	−	0.899331i	$-0.355946\pi$
$523$	20.0000	0.874539	0.437269	+	0.899331i	$0.355946\pi$
$524$	−8.00000	−0.349482
$525$	0	0
$526$	0	0
$527$	−18.0000	−0.784092
$528$	4.00000	0.174078
$529$	−22.0000	−0.956522
$530$	0	0
$531$	−5.00000	−0.216982
$532$	−6.00000	−0.260133
$533$	0	0
$534$	0	0
$535$	0	0
$536$	0	0
$537$	−18.0000	−0.776757
$538$	0	0
$539$	1.00000	0.0430730
$540$	0	0
$541$	−14.0000	−0.601907	−0.300954	−	0.953639i	$-0.597305\pi$
$541$	−14.0000	−0.601907	−0.300954	+	0.953639i	$0.597305\pi$
$542$	0	0
$543$	10.0000	0.429141
$544$	0	0
$545$	0	0
$546$	0	0
$547$	−13.0000	−0.555840	−0.277920	−	0.960604i	$-0.589645\pi$
$547$	−13.0000	−0.555840	−0.277920	+	0.960604i	$0.589645\pi$
$548$	−4.00000	−0.170872
$549$	−7.00000	−0.298753
$550$	0	0
$551$	21.0000	0.894630
$552$	0	0
$553$	16.0000	0.680389
$554$	0	0
$555$	0	0
$556$	−8.00000	−0.339276
$557$	−6.00000	−0.254228	−0.127114	−	0.991888i	$-0.540571\pi$
$557$	−6.00000	−0.254228	−0.127114	+	0.991888i	$0.540571\pi$
$558$	0	0
$559$	0	0
$560$	0	0
$561$	−3.00000	−0.126660
$562$	0	0
$563$	4.00000	0.168580	0.0842900	−	0.996441i	$-0.473138\pi$
$563$	4.00000	0.168580	0.0842900	+	0.996441i	$0.473138\pi$
$564$	−12.0000	−0.505291
$565$	0	0
$566$	0	0
$567$	−1.00000	−0.0419961
$568$	0	0
$569$	13.0000	0.544988	0.272494	−	0.962157i	$-0.412151\pi$
$569$	13.0000	0.544988	0.272494	+	0.962157i	$0.412151\pi$
$570$	0	0
$571$	36.0000	1.50655	0.753277	−	0.657704i	$-0.228472\pi$
$571$	36.0000	1.50655	0.753277	+	0.657704i	$0.228472\pi$
$572$	0	0
$573$	−16.0000	−0.668410
$574$	0	0
$575$	0	0
$576$	−8.00000	−0.333333
$577$	−18.0000	−0.749350	−0.374675	−	0.927156i	$-0.622246\pi$
$577$	−18.0000	−0.749350	−0.374675	+	0.927156i	$0.622246\pi$
$578$	0	0
$579$	−6.00000	−0.249351
$580$	0	0
$581$	−3.00000	−0.124461
$582$	0	0
$583$	3.00000	0.124247
$584$	0	0
$585$	0	0
$586$	0	0
$587$	−36.0000	−1.48588	−0.742940	−	0.669359i	$-0.766569\pi$
$587$	−36.0000	−1.48588	−0.742940	+	0.669359i	$0.766569\pi$
$588$	−2.00000	−0.0824786
$589$	−18.0000	−0.741677
$590$	0	0
$591$	0	0
$592$	32.0000	1.31519
$593$	34.0000	1.39621	0.698106	−	0.715994i	$-0.254026\pi$
$593$	34.0000	1.39621	0.698106	+	0.715994i	$0.254026\pi$
$594$	0	0
$595$	0	0
$596$	12.0000	0.491539
$597$	24.0000	0.982255
$598$	0	0
$599$	30.0000	1.22577	0.612883	−	0.790173i	$-0.290010\pi$
$599$	30.0000	1.22577	0.612883	+	0.790173i	$0.290010\pi$
$600$	0	0
$601$	15.0000	0.611863	0.305931	−	0.952054i	$-0.401032\pi$
$601$	15.0000	0.611863	0.305931	+	0.952054i	$0.401032\pi$
$602$	0	0
$603$	−6.00000	−0.244339
$604$	−28.0000	−1.13930
$605$	0	0
$606$	0	0
$607$	38.0000	1.54237	0.771186	−	0.636610i	$-0.219664\pi$
$607$	38.0000	1.54237	0.771186	+	0.636610i	$0.219664\pi$
$608$	0	0
$609$	7.00000	0.283654
$610$	0	0
$611$	0	0
$612$	6.00000	0.242536
$613$	38.0000	1.53481	0.767403	−	0.641165i	$-0.221549\pi$
$613$	38.0000	1.53481	0.767403	+	0.641165i	$0.221549\pi$
$614$	0	0
$615$	0	0
$616$	0	0
$617$	−2.00000	−0.0805170	−0.0402585	−	0.999189i	$-0.512818\pi$
$617$	−2.00000	−0.0805170	−0.0402585	+	0.999189i	$0.512818\pi$
$618$	0	0
$619$	46.0000	1.84890	0.924448	−	0.381308i	$-0.124526\pi$
$619$	46.0000	1.84890	0.924448	+	0.381308i	$0.124526\pi$
$620$	0	0
$621$	1.00000	0.0401286
$622$	0	0
$623$	−3.00000	−0.120192
$624$	0	0
$625$	0	0
$626$	0	0
$627$	−3.00000	−0.119808
$628$	−2.00000	−0.0798087
$629$	−24.0000	−0.956943
$630$	0	0
$631$	29.0000	1.15447	0.577236	−	0.816577i	$-0.304131\pi$
$631$	29.0000	1.15447	0.577236	+	0.816577i	$0.304131\pi$
$632$	0	0
$633$	−18.0000	−0.715436
$634$	0	0
$635$	0	0
$636$	−6.00000	−0.237915
$637$	0	0
$638$	0	0
$639$	−10.0000	−0.395594
$640$	0	0
$641$	−30.0000	−1.18493	−0.592464	−	0.805597i	$-0.701845\pi$
$641$	−30.0000	−1.18493	−0.592464	+	0.805597i	$0.701845\pi$
$642$	0	0
$643$	−31.0000	−1.22252	−0.611260	−	0.791430i	$-0.709337\pi$
$643$	−31.0000	−1.22252	−0.611260	+	0.791430i	$0.709337\pi$
$644$	2.00000	0.0788110
$645$	0	0
$646$	0	0
$647$	4.00000	0.157256	0.0786281	−	0.996904i	$-0.474946\pi$
$647$	4.00000	0.157256	0.0786281	+	0.996904i	$0.474946\pi$
$648$	0	0
$649$	−5.00000	−0.196267
$650$	0	0
$651$	−6.00000	−0.235159
$652$	24.0000	0.939913
$653$	−39.0000	−1.52619	−0.763094	−	0.646288i	$-0.776321\pi$
$653$	−39.0000	−1.52619	−0.763094	+	0.646288i	$0.776321\pi$
$654$	0	0
$655$	0	0
$656$	−8.00000	−0.312348
$657$	−12.0000	−0.468165
$658$	0	0
$659$	−15.0000	−0.584317	−0.292159	−	0.956370i	$-0.594373\pi$
$659$	−15.0000	−0.584317	−0.292159	+	0.956370i	$0.594373\pi$
$660$	0	0
$661$	−18.0000	−0.700119	−0.350059	−	0.936727i	$-0.613839\pi$
$661$	−18.0000	−0.700119	−0.350059	+	0.936727i	$0.613839\pi$
$662$	0	0
$663$	0	0
$664$	0	0
$665$	0	0
$666$	0	0
$667$	−7.00000	−0.271041
$668$	24.0000	0.928588
$669$	−1.00000	−0.0386622
$670$	0	0
$671$	−7.00000	−0.270232
$672$	0	0
$673$	43.0000	1.65753	0.828764	−	0.559598i	$-0.189045\pi$
$673$	43.0000	1.65753	0.828764	+	0.559598i	$0.189045\pi$
$674$	0	0
$675$	0	0
$676$	26.0000	1.00000
$677$	25.0000	0.960828	0.480414	−	0.877042i	$-0.340486\pi$
$677$	25.0000	0.960828	0.480414	+	0.877042i	$0.340486\pi$
$678$	0	0
$679$	−1.00000	−0.0383765
$680$	0	0
$681$	3.00000	0.114960
$682$	0	0
$683$	4.00000	0.153056	0.0765279	−	0.997067i	$-0.475617\pi$
$683$	4.00000	0.153056	0.0765279	+	0.997067i	$0.475617\pi$
$684$	6.00000	0.229416
$685$	0	0
$686$	0	0
$687$	−14.0000	−0.534133
$688$	20.0000	0.762493
$689$	0	0
$690$	0	0
$691$	2.00000	0.0760836	0.0380418	−	0.999276i	$-0.487888\pi$
$691$	2.00000	0.0760836	0.0380418	+	0.999276i	$0.487888\pi$
$692$	−28.0000	−1.06440
$693$	−1.00000	−0.0379869
$694$	0	0
$695$	0	0
$696$	0	0
$697$	6.00000	0.227266
$698$	0	0
$699$	16.0000	0.605176
$700$	0	0
$701$	11.0000	0.415464	0.207732	−	0.978186i	$-0.433392\pi$
$701$	11.0000	0.415464	0.207732	+	0.978186i	$0.433392\pi$
$702$	0	0
$703$	−24.0000	−0.905177
$704$	−8.00000	−0.301511
$705$	0	0
$706$	0	0
$707$	14.0000	0.526524
$708$	10.0000	0.375823
$709$	−15.0000	−0.563337	−0.281668	−	0.959512i	$-0.590888\pi$
$709$	−15.0000	−0.563337	−0.281668	+	0.959512i	$0.590888\pi$
$710$	0	0
$711$	−16.0000	−0.600047
$712$	0	0
$713$	6.00000	0.224702
$714$	0	0
$715$	0	0
$716$	36.0000	1.34538
$717$	−21.0000	−0.784259
$718$	0	0
$719$	15.0000	0.559406	0.279703	−	0.960087i	$-0.409764\pi$
$719$	15.0000	0.559406	0.279703	+	0.960087i	$0.409764\pi$
$720$	0	0
$721$	−5.00000	−0.186210
$722$	0	0
$723$	10.0000	0.371904
$724$	−20.0000	−0.743294
$725$	0	0
$726$	0	0
$727$	7.00000	0.259616	0.129808	−	0.991539i	$-0.458564\pi$
$727$	7.00000	0.259616	0.129808	+	0.991539i	$0.458564\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	0	0
$731$	−15.0000	−0.554795
$732$	14.0000	0.517455
$733$	6.00000	0.221615	0.110808	−	0.993842i	$-0.464656\pi$
$733$	6.00000	0.221615	0.110808	+	0.993842i	$0.464656\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	−6.00000	−0.221013
$738$	0	0
$739$	22.0000	0.809283	0.404642	−	0.914475i	$-0.367396\pi$
$739$	22.0000	0.809283	0.404642	+	0.914475i	$0.367396\pi$
$740$	0	0
$741$	0	0
$742$	0	0
$743$	−18.0000	−0.660356	−0.330178	−	0.943919i	$-0.607109\pi$
$743$	−18.0000	−0.660356	−0.330178	+	0.943919i	$0.607109\pi$
$744$	0	0
$745$	0	0
$746$	0	0
$747$	3.00000	0.109764
$748$	6.00000	0.219382
$749$	6.00000	0.219235
$750$	0	0
$751$	53.0000	1.93400	0.966999	−	0.254781i	$-0.0820034\pi$
$751$	53.0000	1.93400	0.966999	+	0.254781i	$0.0820034\pi$
$752$	24.0000	0.875190
$753$	−12.0000	−0.437304
$754$	0	0
$755$	0	0
$756$	2.00000	0.0727393
$757$	6.00000	0.218074	0.109037	−	0.994038i	$-0.465223\pi$
$757$	6.00000	0.218074	0.109037	+	0.994038i	$0.465223\pi$
$758$	0	0
$759$	1.00000	0.0362977
$760$	0	0
$761$	−30.0000	−1.08750	−0.543750	−	0.839248i	$-0.682996\pi$
$761$	−30.0000	−1.08750	−0.543750	+	0.839248i	$0.682996\pi$
$762$	0	0
$763$	2.00000	0.0724049
$764$	32.0000	1.15772
$765$	0	0
$766$	0	0
$767$	0	0
$768$	16.0000	0.577350
$769$	9.00000	0.324548	0.162274	−	0.986746i	$-0.448117\pi$
$769$	9.00000	0.324548	0.162274	+	0.986746i	$0.448117\pi$
$770$	0	0
$771$	−20.0000	−0.720282
$772$	12.0000	0.431889
$773$	−26.0000	−0.935155	−0.467578	−	0.883952i	$-0.654873\pi$
$773$	−26.0000	−0.935155	−0.467578	+	0.883952i	$0.654873\pi$
$774$	0	0
$775$	0	0
$776$	0	0
$777$	−8.00000	−0.286998
$778$	0	0
$779$	6.00000	0.214972
$780$	0	0
$781$	−10.0000	−0.357828
$782$	0	0
$783$	−7.00000	−0.250160
$784$	4.00000	0.142857
$785$	0	0
$786$	0	0
$787$	40.0000	1.42585	0.712923	−	0.701242i	$-0.247371\pi$
$787$	40.0000	1.42585	0.712923	+	0.701242i	$0.247371\pi$
$788$	0	0
$789$	−16.0000	−0.569615
$790$	0	0
$791$	−19.0000	−0.675562
$792$	0	0
$793$	0	0
$794$	0	0
$795$	0	0
$796$	−48.0000	−1.70131
$797$	30.0000	1.06265	0.531327	−	0.847167i	$-0.321693\pi$
$797$	30.0000	1.06265	0.531327	+	0.847167i	$0.321693\pi$
$798$	0	0
$799$	−18.0000	−0.636794
$800$	0	0
$801$	3.00000	0.106000
$802$	0	0
$803$	−12.0000	−0.423471
$804$	12.0000	0.423207
$805$	0	0
$806$	0	0
$807$	−1.00000	−0.0352017
$808$	0	0
$809$	10.0000	0.351581	0.175791	−	0.984428i	$-0.443752\pi$
$809$	10.0000	0.351581	0.175791	+	0.984428i	$0.443752\pi$
$810$	0	0
$811$	12.0000	0.421377	0.210688	−	0.977553i	$-0.432429\pi$
$811$	12.0000	0.421377	0.210688	+	0.977553i	$0.432429\pi$
$812$	−14.0000	−0.491304
$813$	−1.00000	−0.0350715
$814$	0	0
$815$	0	0
$816$	−12.0000	−0.420084
$817$	−15.0000	−0.524784
$818$	0	0
$819$	0	0
$820$	0	0
$821$	23.0000	0.802706	0.401353	−	0.915924i	$-0.368540\pi$
$821$	23.0000	0.802706	0.401353	+	0.915924i	$0.368540\pi$
$822$	0	0
$823$	24.0000	0.836587	0.418294	−	0.908312i	$-0.362628\pi$
$823$	24.0000	0.836587	0.418294	+	0.908312i	$0.362628\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	36.0000	1.25184	0.625921	−	0.779886i	$-0.284723\pi$
$827$	36.0000	1.25184	0.625921	+	0.779886i	$0.284723\pi$
$828$	−2.00000	−0.0695048
$829$	38.0000	1.31979	0.659897	−	0.751356i	$-0.270600\pi$
$829$	38.0000	1.31979	0.659897	+	0.751356i	$0.270600\pi$
$830$	0	0
$831$	10.0000	0.346896
$832$	0	0
$833$	−3.00000	−0.103944
$834$	0	0
$835$	0	0
$836$	6.00000	0.207514
$837$	6.00000	0.207390
$838$	0	0
$839$	−17.0000	−0.586905	−0.293453	−	0.955974i	$-0.594804\pi$
$839$	−17.0000	−0.586905	−0.293453	+	0.955974i	$0.594804\pi$
$840$	0	0
$841$	20.0000	0.689655
$842$	0	0
$843$	−22.0000	−0.757720
$844$	36.0000	1.23917
$845$	0	0
$846$	0	0
$847$	−1.00000	−0.0343604
$848$	12.0000	0.412082
$849$	8.00000	0.274559
$850$	0	0
$851$	8.00000	0.274236
$852$	20.0000	0.685189
$853$	10.0000	0.342393	0.171197	−	0.985237i	$-0.445237\pi$
$853$	10.0000	0.342393	0.171197	+	0.985237i	$0.445237\pi$
$854$	0	0
$855$	0	0
$856$	0	0
$857$	−50.0000	−1.70797	−0.853984	−	0.520300i	$-0.825820\pi$
$857$	−50.0000	−1.70797	−0.853984	+	0.520300i	$0.825820\pi$
$858$	0	0
$859$	46.0000	1.56950	0.784750	−	0.619813i	$-0.212791\pi$
$859$	46.0000	1.56950	0.784750	+	0.619813i	$0.212791\pi$
$860$	0	0
$861$	2.00000	0.0681598
$862$	0	0
$863$	−39.0000	−1.32758	−0.663788	−	0.747921i	$-0.731052\pi$
$863$	−39.0000	−1.32758	−0.663788	+	0.747921i	$0.731052\pi$
$864$	0	0
$865$	0	0
$866$	0	0
$867$	−8.00000	−0.271694
$868$	12.0000	0.407307
$869$	−16.0000	−0.542763
$870$	0	0
$871$	0	0
$872$	0	0
$873$	1.00000	0.0338449
$874$	0	0
$875$	0	0
$876$	24.0000	0.810885
$877$	−45.0000	−1.51954	−0.759771	−	0.650191i	$-0.774689\pi$
$877$	−45.0000	−1.51954	−0.759771	+	0.650191i	$0.774689\pi$
$878$	0	0
$879$	−19.0000	−0.640854
$880$	0	0
$881$	15.0000	0.505363	0.252681	−	0.967550i	$-0.418688\pi$
$881$	15.0000	0.505363	0.252681	+	0.967550i	$0.418688\pi$
$882$	0	0
$883$	−20.0000	−0.673054	−0.336527	−	0.941674i	$-0.609252\pi$
$883$	−20.0000	−0.673054	−0.336527	+	0.941674i	$0.609252\pi$
$884$	0	0
$885$	0	0
$886$	0	0
$887$	−41.0000	−1.37665	−0.688323	−	0.725405i	$-0.741653\pi$
$887$	−41.0000	−1.37665	−0.688323	+	0.725405i	$0.741653\pi$
$888$	0	0
$889$	19.0000	0.637240
$890$	0	0
$891$	1.00000	0.0335013
$892$	2.00000	0.0669650
$893$	−18.0000	−0.602347
$894$	0	0
$895$	0	0
$896$	0	0
$897$	0	0
$898$	0	0
$899$	−42.0000	−1.40078
$900$	0	0
$901$	−9.00000	−0.299833
$902$	0	0
$903$	−5.00000	−0.166390
$904$	0	0
$905$	0	0
$906$	0	0
$907$	44.0000	1.46100	0.730498	−	0.682915i	$-0.239288\pi$
$907$	44.0000	1.46100	0.730498	+	0.682915i	$0.239288\pi$
$908$	−6.00000	−0.199117
$909$	−14.0000	−0.464351
$910$	0	0
$911$	−4.00000	−0.132526	−0.0662630	−	0.997802i	$-0.521108\pi$
$911$	−4.00000	−0.132526	−0.0662630	+	0.997802i	$0.521108\pi$
$912$	−12.0000	−0.397360
$913$	3.00000	0.0992855
$914$	0	0
$915$	0	0
$916$	28.0000	0.925146
$917$	−4.00000	−0.132092
$918$	0	0
$919$	−14.0000	−0.461817	−0.230909	−	0.972975i	$-0.574170\pi$
$919$	−14.0000	−0.461817	−0.230909	+	0.972975i	$0.574170\pi$
$920$	0	0
$921$	−26.0000	−0.856729
$922$	0	0
$923$	0	0
$924$	2.00000	0.0657952
$925$	0	0
$926$	0	0
$927$	5.00000	0.164222
$928$	0	0
$929$	6.00000	0.196854	0.0984268	−	0.995144i	$-0.468619\pi$
$929$	6.00000	0.196854	0.0984268	+	0.995144i	$0.468619\pi$
$930$	0	0
$931$	−3.00000	−0.0983210
$932$	−32.0000	−1.04819
$933$	−32.0000	−1.04763
$934$	0	0
$935$	0	0
$936$	0	0
$937$	38.0000	1.24141	0.620703	−	0.784046i	$-0.286847\pi$
$937$	38.0000	1.24141	0.620703	+	0.784046i	$0.286847\pi$
$938$	0	0
$939$	−21.0000	−0.685309
$940$	0	0
$941$	40.0000	1.30396	0.651981	−	0.758235i	$-0.273938\pi$
$941$	40.0000	1.30396	0.651981	+	0.758235i	$0.273938\pi$
$942$	0	0
$943$	−2.00000	−0.0651290
$944$	−20.0000	−0.650945
$945$	0	0
$946$	0	0
$947$	45.0000	1.46230	0.731152	−	0.682215i	$-0.238983\pi$
$947$	45.0000	1.46230	0.731152	+	0.682215i	$0.238983\pi$
$948$	32.0000	1.03931
$949$	0	0
$950$	0	0
$951$	−2.00000	−0.0648544
$952$	0	0
$953$	−30.0000	−0.971795	−0.485898	−	0.874016i	$-0.661507\pi$
$953$	−30.0000	−0.971795	−0.485898	+	0.874016i	$0.661507\pi$
$954$	0	0
$955$	0	0
$956$	42.0000	1.35838
$957$	−7.00000	−0.226278
$958$	0	0
$959$	−2.00000	−0.0645834
$960$	0	0
$961$	5.00000	0.161290
$962$	0	0
$963$	−6.00000	−0.193347
$964$	−20.0000	−0.644157
$965$	0	0
$966$	0	0
$967$	17.0000	0.546683	0.273342	−	0.961917i	$-0.411871\pi$
$967$	17.0000	0.546683	0.273342	+	0.961917i	$0.411871\pi$
$968$	0	0
$969$	9.00000	0.289122
$970$	0	0
$971$	47.0000	1.50830	0.754151	−	0.656701i	$-0.228049\pi$
$971$	47.0000	1.50830	0.754151	+	0.656701i	$0.228049\pi$
$972$	−2.00000	−0.0641500
$973$	−4.00000	−0.128234
$974$	0	0
$975$	0	0
$976$	−28.0000	−0.896258
$977$	−49.0000	−1.56765	−0.783824	−	0.620982i	$-0.786734\pi$
$977$	−49.0000	−1.56765	−0.783824	+	0.620982i	$0.786734\pi$
$978$	0	0
$979$	3.00000	0.0958804
$980$	0	0
$981$	−2.00000	−0.0638551
$982$	0	0
$983$	6.00000	0.191370	0.0956851	−	0.995412i	$-0.469496\pi$
$983$	6.00000	0.191370	0.0956851	+	0.995412i	$0.469496\pi$
$984$	0	0
$985$	0	0
$986$	0	0
$987$	−6.00000	−0.190982
$988$	0	0
$989$	5.00000	0.158991
$990$	0	0
$991$	31.0000	0.984747	0.492374	−	0.870384i	$-0.336129\pi$
$991$	31.0000	0.984747	0.492374	+	0.870384i	$0.336129\pi$
$992$	0	0
$993$	17.0000	0.539479
$994$	0	0
$995$	0	0
$996$	−6.00000	−0.190117
$997$	42.0000	1.33015	0.665077	−	0.746775i	$-0.268399\pi$
$997$	42.0000	1.33015	0.665077	+	0.746775i	$0.268399\pi$
$998$	0	0
$999$	8.00000	0.253109

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5775.2.a.o.1.1		1
5.4	even	2		1155.2.a.g.1.1	✓	1
15.14	odd	2		3465.2.a.i.1.1		1
35.34	odd	2		8085.2.a.q.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1155.2.a.g.1.1	✓	1	5.4	even	2
3465.2.a.i.1.1		1	15.14	odd	2
5775.2.a.o.1.1		1	1.1	even	1	trivial
8085.2.a.q.1.1		1	35.34	odd	2

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:	\( N \)	\(=\)	\( 5775 = 3 \cdot 5^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5775.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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