LMFDB - Embedded newform 2646.2.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2646,2,Mod(1,2646)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2646, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("2646.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2646 = 2 \cdot 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2646.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:	$21.1284163748$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 378)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	2646.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-1.00000 q^{2} +1.00000 q^{4} -2.00000 q^{5} -1.00000 q^{8} +O(q^{10})$

$q-1.00000 q^{2} +1.00000 q^{4} -2.00000 q^{5} -1.00000 q^{8} +2.00000 q^{10} -5.00000 q^{11} -6.00000 q^{13} +1.00000 q^{16} -4.00000 q^{17} +4.00000 q^{19} -2.00000 q^{20} +5.00000 q^{22} +4.00000 q^{23} -1.00000 q^{25} +6.00000 q^{26} -7.00000 q^{29} -3.00000 q^{31} -1.00000 q^{32} +4.00000 q^{34} +8.00000 q^{37} -4.00000 q^{38} +2.00000 q^{40} -6.00000 q^{41} +8.00000 q^{43} -5.00000 q^{44} -4.00000 q^{46} +6.00000 q^{47} +1.00000 q^{50} -6.00000 q^{52} +6.00000 q^{53} +10.0000 q^{55} +7.00000 q^{58} +7.00000 q^{59} +3.00000 q^{62} +1.00000 q^{64} +12.0000 q^{65} +10.0000 q^{67} -4.00000 q^{68} +4.00000 q^{71} -13.0000 q^{73} -8.00000 q^{74} +4.00000 q^{76} -3.00000 q^{79} -2.00000 q^{80} +6.00000 q^{82} -7.00000 q^{83} +8.00000 q^{85} -8.00000 q^{86} +5.00000 q^{88} +6.00000 q^{89} +4.00000 q^{92} -6.00000 q^{94} -8.00000 q^{95} +5.00000 q^{97} +O(q^{100})$

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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	0	0
$3$	0	0
$4$	1.00000	0.500000
$5$	−2.00000	−0.894427	−0.447214	−	0.894427i	$-0.647584\pi$
$5$	−2.00000	−0.894427	−0.447214	+	0.894427i	$0.647584\pi$
$6$	0	0
$7$	0	0
$7$	0	0
$8$	−1.00000	−0.353553
$9$	0	0
$10$	2.00000	0.632456
$11$	−5.00000	−1.50756	−0.753778	−	0.657129i	$-0.771771\pi$
$11$	−5.00000	−1.50756	−0.753778	+	0.657129i	$0.771771\pi$
$12$	0	0
$13$	−6.00000	−1.66410	−0.832050	−	0.554700i	$-0.812833\pi$
$13$	−6.00000	−1.66410	−0.832050	+	0.554700i	$0.812833\pi$
$14$	0	0
$15$	0	0
$16$	1.00000	0.250000
$17$	−4.00000	−0.970143	−0.485071	−	0.874475i	$-0.661206\pi$
$17$	−4.00000	−0.970143	−0.485071	+	0.874475i	$0.661206\pi$
$18$	0	0
$19$	4.00000	0.917663	0.458831	−	0.888523i	$-0.348268\pi$
$19$	4.00000	0.917663	0.458831	+	0.888523i	$0.348268\pi$
$20$	−2.00000	−0.447214
$21$	0	0
$22$	5.00000	1.06600
$23$	4.00000	0.834058	0.417029	−	0.908893i	$-0.363071\pi$
$23$	4.00000	0.834058	0.417029	+	0.908893i	$0.363071\pi$
$24$	0	0
$25$	−1.00000	−0.200000
$26$	6.00000	1.17670
$27$	0	0
$28$	0	0
$29$	−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
$31$	−3.00000	−0.538816	−0.269408	−	0.963026i	$-0.586828\pi$
$31$	−3.00000	−0.538816	−0.269408	+	0.963026i	$0.586828\pi$
$32$	−1.00000	−0.176777
$33$	0	0
$34$	4.00000	0.685994
$35$	0	0
$36$	0	0
$37$	8.00000	1.31519	0.657596	−	0.753371i	$-0.271573\pi$
$37$	8.00000	1.31519	0.657596	+	0.753371i	$0.271573\pi$
$38$	−4.00000	−0.648886
$39$	0	0
$40$	2.00000	0.316228
$41$	−6.00000	−0.937043	−0.468521	−	0.883452i	$-0.655213\pi$
$41$	−6.00000	−0.937043	−0.468521	+	0.883452i	$0.655213\pi$
$42$	0	0
$43$	8.00000	1.21999	0.609994	−	0.792406i	$-0.291172\pi$
$43$	8.00000	1.21999	0.609994	+	0.792406i	$0.291172\pi$
$44$	−5.00000	−0.753778
$45$	0	0
$46$	−4.00000	−0.589768
$47$	6.00000	0.875190	0.437595	−	0.899172i	$-0.355830\pi$
$47$	6.00000	0.875190	0.437595	+	0.899172i	$0.355830\pi$
$48$	0	0
$49$	0	0
$50$	1.00000	0.141421
$51$	0	0
$52$	−6.00000	−0.832050
$53$	6.00000	0.824163	0.412082	−	0.911147i	$-0.364802\pi$
$53$	6.00000	0.824163	0.412082	+	0.911147i	$0.364802\pi$
$54$	0	0
$55$	10.0000	1.34840
$56$	0	0
$57$	0	0
$58$	7.00000	0.919145
$59$	7.00000	0.911322	0.455661	−	0.890153i	$-0.349403\pi$
$59$	7.00000	0.911322	0.455661	+	0.890153i	$0.349403\pi$
$60$	0	0
$61$	0	0		−	1.00000i	$-0.5\pi$
$61$	0	0			1.00000i	$0.5\pi$
$62$	3.00000	0.381000
$63$	0	0
$64$	1.00000	0.125000
$65$	12.0000	1.48842
$66$	0	0
$67$	10.0000	1.22169	0.610847	−	0.791748i	$-0.290829\pi$
$67$	10.0000	1.22169	0.610847	+	0.791748i	$0.290829\pi$
$68$	−4.00000	−0.485071
$69$	0	0
$70$	0	0
$71$	4.00000	0.474713	0.237356	−	0.971423i	$-0.423719\pi$
$71$	4.00000	0.474713	0.237356	+	0.971423i	$0.423719\pi$
$72$	0	0
$73$	−13.0000	−1.52153	−0.760767	−	0.649025i	$-0.775177\pi$
$73$	−13.0000	−1.52153	−0.760767	+	0.649025i	$0.775177\pi$
$74$	−8.00000	−0.929981
$75$	0	0
$76$	4.00000	0.458831
$77$	0	0
$78$	0	0
$79$	−3.00000	−0.337526	−0.168763	−	0.985657i	$-0.553977\pi$
$79$	−3.00000	−0.337526	−0.168763	+	0.985657i	$0.553977\pi$
$80$	−2.00000	−0.223607
$81$	0	0
$82$	6.00000	0.662589
$83$	−7.00000	−0.768350	−0.384175	−	0.923260i	$-0.625514\pi$
$83$	−7.00000	−0.768350	−0.384175	+	0.923260i	$0.625514\pi$
$84$	0	0
$85$	8.00000	0.867722
$86$	−8.00000	−0.862662
$87$	0	0
$88$	5.00000	0.533002
$89$	6.00000	0.635999	0.317999	−	0.948091i	$-0.396989\pi$
$89$	6.00000	0.635999	0.317999	+	0.948091i	$0.396989\pi$
$90$	0	0
$91$	0	0
$92$	4.00000	0.417029
$93$	0	0
$94$	−6.00000	−0.618853
$95$	−8.00000	−0.820783
$96$	0	0
$97$	5.00000	0.507673	0.253837	−	0.967247i	$-0.418307\pi$
$97$	5.00000	0.507673	0.253837	+	0.967247i	$0.418307\pi$
$98$	0	0
$99$	0	0
$100$	−1.00000	−0.100000
$101$	−5.00000	−0.497519	−0.248759	−	0.968565i	$-0.580023\pi$
$101$	−5.00000	−0.497519	−0.248759	+	0.968565i	$0.580023\pi$
$102$	0	0
$103$	−8.00000	−0.788263	−0.394132	−	0.919054i	$-0.628955\pi$
$103$	−8.00000	−0.788263	−0.394132	+	0.919054i	$0.628955\pi$
$104$	6.00000	0.588348
$105$	0	0
$106$	−6.00000	−0.582772
$107$	−12.0000	−1.16008	−0.580042	−	0.814587i	$-0.696964\pi$
$107$	−12.0000	−1.16008	−0.580042	+	0.814587i	$0.696964\pi$
$108$	0	0
$109$	16.0000	1.53252	0.766261	−	0.642529i	$-0.222115\pi$
$109$	16.0000	1.53252	0.766261	+	0.642529i	$0.222115\pi$
$110$	−10.0000	−0.953463
$111$	0	0
$112$	0	0
$113$	−4.00000	−0.376288	−0.188144	−	0.982141i	$-0.560247\pi$
$113$	−4.00000	−0.376288	−0.188144	+	0.982141i	$0.560247\pi$
$114$	0	0
$115$	−8.00000	−0.746004
$116$	−7.00000	−0.649934
$117$	0	0
$118$	−7.00000	−0.644402
$119$	0	0
$120$	0	0
$121$	14.0000	1.27273
$122$	0	0
$123$	0	0
$124$	−3.00000	−0.269408
$125$	12.0000	1.07331
$126$	0	0
$127$	0	0		−	1.00000i	$-0.5\pi$
$127$	0	0			1.00000i	$0.5\pi$
$128$	−1.00000	−0.0883883
$129$	0	0
$130$	−12.0000	−1.05247
$131$	13.0000	1.13582	0.567908	−	0.823092i	$-0.307753\pi$
$131$	13.0000	1.13582	0.567908	+	0.823092i	$0.307753\pi$
$132$	0	0
$133$	0	0
$134$	−10.0000	−0.863868
$135$	0	0
$136$	4.00000	0.342997
$137$	8.00000	0.683486	0.341743	−	0.939793i	$-0.388983\pi$
$137$	8.00000	0.683486	0.341743	+	0.939793i	$0.388983\pi$
$138$	0	0
$139$	8.00000	0.678551	0.339276	−	0.940687i	$-0.389818\pi$
$139$	8.00000	0.678551	0.339276	+	0.940687i	$0.389818\pi$
$140$	0	0
$141$	0	0
$142$	−4.00000	−0.335673
$143$	30.0000	2.50873
$144$	0	0
$145$	14.0000	1.16264
$146$	13.0000	1.07589
$147$	0	0
$148$	8.00000	0.657596
$149$	−9.00000	−0.737309	−0.368654	−	0.929567i	$-0.620181\pi$
$149$	−9.00000	−0.737309	−0.368654	+	0.929567i	$0.620181\pi$
$150$	0	0
$151$	−17.0000	−1.38344	−0.691720	−	0.722166i	$-0.743147\pi$
$151$	−17.0000	−1.38344	−0.691720	+	0.722166i	$0.743147\pi$
$152$	−4.00000	−0.324443
$153$	0	0
$154$	0	0
$155$	6.00000	0.481932
$156$	0	0
$157$	−14.0000	−1.11732	−0.558661	−	0.829396i	$-0.688685\pi$
$157$	−14.0000	−1.11732	−0.558661	+	0.829396i	$0.688685\pi$
$158$	3.00000	0.238667
$159$	0	0
$160$	2.00000	0.158114
$161$	0	0
$162$	0	0
$163$	2.00000	0.156652	0.0783260	−	0.996928i	$-0.475042\pi$
$163$	2.00000	0.156652	0.0783260	+	0.996928i	$0.475042\pi$
$164$	−6.00000	−0.468521
$165$	0	0
$166$	7.00000	0.543305
$167$	−14.0000	−1.08335	−0.541676	−	0.840587i	$-0.682210\pi$
$167$	−14.0000	−1.08335	−0.541676	+	0.840587i	$0.682210\pi$
$168$	0	0
$169$	23.0000	1.76923
$170$	−8.00000	−0.613572
$171$	0	0
$172$	8.00000	0.609994
$173$	1.00000	0.0760286	0.0380143	−	0.999277i	$-0.487897\pi$
$173$	1.00000	0.0760286	0.0380143	+	0.999277i	$0.487897\pi$
$174$	0	0
$175$	0	0
$176$	−5.00000	−0.376889
$177$	0	0
$178$	−6.00000	−0.449719
$179$	15.0000	1.12115	0.560576	−	0.828103i	$-0.310580\pi$
$179$	15.0000	1.12115	0.560576	+	0.828103i	$0.310580\pi$
$180$	0	0
$181$	0	0		−	1.00000i	$-0.5\pi$
$181$	0	0			1.00000i	$0.5\pi$
$182$	0	0
$183$	0	0
$184$	−4.00000	−0.294884
$185$	−16.0000	−1.17634
$186$	0	0
$187$	20.0000	1.46254
$188$	6.00000	0.437595
$189$	0	0
$190$	8.00000	0.580381
$191$	18.0000	1.30243	0.651217	−	0.758891i	$-0.274259\pi$
$191$	18.0000	1.30243	0.651217	+	0.758891i	$0.274259\pi$
$192$	0	0
$193$	−19.0000	−1.36765	−0.683825	−	0.729646i	$-0.739685\pi$
$193$	−19.0000	−1.36765	−0.683825	+	0.729646i	$0.739685\pi$
$194$	−5.00000	−0.358979
$195$	0	0
$196$	0	0
$197$	25.0000	1.78118	0.890588	−	0.454811i	$-0.150293\pi$
$197$	25.0000	1.78118	0.890588	+	0.454811i	$0.150293\pi$
$198$	0	0
$199$	19.0000	1.34687	0.673437	−	0.739244i	$-0.264817\pi$
$199$	19.0000	1.34687	0.673437	+	0.739244i	$0.264817\pi$
$200$	1.00000	0.0707107
$201$	0	0
$202$	5.00000	0.351799
$203$	0	0
$204$	0	0
$205$	12.0000	0.838116
$206$	8.00000	0.557386
$207$	0	0
$208$	−6.00000	−0.416025
$209$	−20.0000	−1.38343
$210$	0	0
$211$	26.0000	1.78991	0.894957	−	0.446153i	$-0.147206\pi$
$211$	26.0000	1.78991	0.894957	+	0.446153i	$0.147206\pi$
$212$	6.00000	0.412082
$213$	0	0
$214$	12.0000	0.820303
$215$	−16.0000	−1.09119
$216$	0	0
$217$	0	0
$218$	−16.0000	−1.08366
$219$	0	0
$220$	10.0000	0.674200
$221$	24.0000	1.61441
$222$	0	0
$223$	1.00000	0.0669650	0.0334825	−	0.999439i	$-0.489340\pi$
$223$	1.00000	0.0669650	0.0334825	+	0.999439i	$0.489340\pi$
$224$	0	0
$225$	0	0
$226$	4.00000	0.266076
$227$	−27.0000	−1.79205	−0.896026	−	0.444001i	$-0.853559\pi$
$227$	−27.0000	−1.79205	−0.896026	+	0.444001i	$0.853559\pi$
$228$	0	0
$229$	−4.00000	−0.264327	−0.132164	−	0.991228i	$-0.542192\pi$
$229$	−4.00000	−0.264327	−0.132164	+	0.991228i	$0.542192\pi$
$230$	8.00000	0.527504
$231$	0	0
$232$	7.00000	0.459573
$233$	22.0000	1.44127	0.720634	−	0.693316i	$-0.243851\pi$
$233$	22.0000	1.44127	0.720634	+	0.693316i	$0.243851\pi$
$234$	0	0
$235$	−12.0000	−0.782794
$236$	7.00000	0.455661
$237$	0	0
$238$	0	0
$239$	0	0		−	1.00000i	$-0.5\pi$
$239$	0	0			1.00000i	$0.5\pi$
$240$	0	0
$241$	1.00000	0.0644157	0.0322078	−	0.999481i	$-0.489746\pi$
$241$	1.00000	0.0644157	0.0322078	+	0.999481i	$0.489746\pi$
$242$	−14.0000	−0.899954
$243$	0	0
$244$	0	0
$245$	0	0
$246$	0	0
$247$	−24.0000	−1.52708
$248$	3.00000	0.190500
$249$	0	0
$250$	−12.0000	−0.758947
$251$	−21.0000	−1.32551	−0.662754	−	0.748837i	$-0.730613\pi$
$251$	−21.0000	−1.32551	−0.662754	+	0.748837i	$0.730613\pi$
$252$	0	0
$253$	−20.0000	−1.25739
$254$	0	0
$255$	0	0
$256$	1.00000	0.0625000
$257$	0	0		−	1.00000i	$-0.5\pi$
$257$	0	0			1.00000i	$0.5\pi$
$258$	0	0
$259$	0	0
$260$	12.0000	0.744208
$261$	0	0
$262$	−13.0000	−0.803143
$263$	−12.0000	−0.739952	−0.369976	−	0.929041i	$-0.620634\pi$
$263$	−12.0000	−0.739952	−0.369976	+	0.929041i	$0.620634\pi$
$264$	0	0
$265$	−12.0000	−0.737154
$266$	0	0
$267$	0	0
$268$	10.0000	0.610847
$269$	31.0000	1.89010	0.945052	−	0.326921i	$-0.106011\pi$
$269$	31.0000	1.89010	0.945052	+	0.326921i	$0.106011\pi$
$270$	0	0
$271$	0	0		−	1.00000i	$-0.5\pi$
$271$	0	0			1.00000i	$0.5\pi$
$272$	−4.00000	−0.242536
$273$	0	0
$274$	−8.00000	−0.483298
$275$	5.00000	0.301511
$276$	0	0
$277$	2.00000	0.120168	0.0600842	−	0.998193i	$-0.480863\pi$
$277$	2.00000	0.120168	0.0600842	+	0.998193i	$0.480863\pi$
$278$	−8.00000	−0.479808
$279$	0	0
$280$	0	0
$281$	−2.00000	−0.119310	−0.0596550	−	0.998219i	$-0.519000\pi$
$281$	−2.00000	−0.119310	−0.0596550	+	0.998219i	$0.519000\pi$
$282$	0	0
$283$	−16.0000	−0.951101	−0.475551	−	0.879688i	$-0.657751\pi$
$283$	−16.0000	−0.951101	−0.475551	+	0.879688i	$0.657751\pi$
$284$	4.00000	0.237356
$285$	0	0
$286$	−30.0000	−1.77394
$287$	0	0
$288$	0	0
$289$	−1.00000	−0.0588235
$290$	−14.0000	−0.822108
$291$	0	0
$292$	−13.0000	−0.760767
$293$	27.0000	1.57736	0.788678	−	0.614806i	$-0.210766\pi$
$293$	27.0000	1.57736	0.788678	+	0.614806i	$0.210766\pi$
$294$	0	0
$295$	−14.0000	−0.815112
$296$	−8.00000	−0.464991
$297$	0	0
$298$	9.00000	0.521356
$299$	−24.0000	−1.38796
$300$	0	0
$301$	0	0
$302$	17.0000	0.978240
$303$	0	0
$304$	4.00000	0.229416
$305$	0	0
$306$	0	0
$307$	2.00000	0.114146	0.0570730	−	0.998370i	$-0.481823\pi$
$307$	2.00000	0.114146	0.0570730	+	0.998370i	$0.481823\pi$
$308$	0	0
$309$	0	0
$310$	−6.00000	−0.340777
$311$	22.0000	1.24751	0.623753	−	0.781622i	$-0.285607\pi$
$311$	22.0000	1.24751	0.623753	+	0.781622i	$0.285607\pi$
$312$	0	0
$313$	−10.0000	−0.565233	−0.282617	−	0.959233i	$-0.591202\pi$
$313$	−10.0000	−0.565233	−0.282617	+	0.959233i	$0.591202\pi$
$314$	14.0000	0.790066
$315$	0	0
$316$	−3.00000	−0.168763
$317$	33.0000	1.85346	0.926732	−	0.375722i	$-0.122605\pi$
$317$	33.0000	1.85346	0.926732	+	0.375722i	$0.122605\pi$
$318$	0	0
$319$	35.0000	1.95962
$320$	−2.00000	−0.111803
$321$	0	0
$322$	0	0
$323$	−16.0000	−0.890264
$324$	0	0
$325$	6.00000	0.332820
$326$	−2.00000	−0.110770
$327$	0	0
$328$	6.00000	0.331295
$329$	0	0
$330$	0	0
$331$	32.0000	1.75888	0.879440	−	0.476011i	$-0.157918\pi$
$331$	32.0000	1.75888	0.879440	+	0.476011i	$0.157918\pi$
$332$	−7.00000	−0.384175
$333$	0	0
$334$	14.0000	0.766046
$335$	−20.0000	−1.09272
$336$	0	0
$337$	−27.0000	−1.47078	−0.735392	−	0.677642i	$-0.763002\pi$
$337$	−27.0000	−1.47078	−0.735392	+	0.677642i	$0.763002\pi$
$338$	−23.0000	−1.25104
$339$	0	0
$340$	8.00000	0.433861
$341$	15.0000	0.812296
$342$	0	0
$343$	0	0
$344$	−8.00000	−0.431331
$345$	0	0
$346$	−1.00000	−0.0537603
$347$	27.0000	1.44944	0.724718	−	0.689046i	$-0.241970\pi$
$347$	27.0000	1.44944	0.724718	+	0.689046i	$0.241970\pi$
$348$	0	0
$349$	20.0000	1.07058	0.535288	−	0.844670i	$-0.320203\pi$
$349$	20.0000	1.07058	0.535288	+	0.844670i	$0.320203\pi$
$350$	0	0
$351$	0	0
$352$	5.00000	0.266501
$353$	−30.0000	−1.59674	−0.798369	−	0.602168i	$-0.794304\pi$
$353$	−30.0000	−1.59674	−0.798369	+	0.602168i	$0.794304\pi$
$354$	0	0
$355$	−8.00000	−0.424596
$356$	6.00000	0.317999
$357$	0	0
$358$	−15.0000	−0.792775
$359$	−16.0000	−0.844448	−0.422224	−	0.906492i	$-0.638750\pi$
$359$	−16.0000	−0.844448	−0.422224	+	0.906492i	$0.638750\pi$
$360$	0	0
$361$	−3.00000	−0.157895
$362$	0	0
$363$	0	0
$364$	0	0
$365$	26.0000	1.36090
$366$	0	0
$367$	4.00000	0.208798	0.104399	−	0.994535i	$-0.466708\pi$
$367$	4.00000	0.208798	0.104399	+	0.994535i	$0.466708\pi$
$368$	4.00000	0.208514
$369$	0	0
$370$	16.0000	0.831800
$371$	0	0
$372$	0	0
$373$	−20.0000	−1.03556	−0.517780	−	0.855514i	$-0.673242\pi$
$373$	−20.0000	−1.03556	−0.517780	+	0.855514i	$0.673242\pi$
$374$	−20.0000	−1.03418
$375$	0	0
$376$	−6.00000	−0.309426
$377$	42.0000	2.16311
$378$	0	0
$379$	10.0000	0.513665	0.256833	−	0.966456i	$-0.417321\pi$
$379$	10.0000	0.513665	0.256833	+	0.966456i	$0.417321\pi$
$380$	−8.00000	−0.410391
$381$	0	0
$382$	−18.0000	−0.920960
$383$	−4.00000	−0.204390	−0.102195	−	0.994764i	$-0.532587\pi$
$383$	−4.00000	−0.204390	−0.102195	+	0.994764i	$0.532587\pi$
$384$	0	0
$385$	0	0
$386$	19.0000	0.967075
$387$	0	0
$388$	5.00000	0.253837
$389$	−1.00000	−0.0507020	−0.0253510	−	0.999679i	$-0.508070\pi$
$389$	−1.00000	−0.0507020	−0.0253510	+	0.999679i	$0.508070\pi$
$390$	0	0
$391$	−16.0000	−0.809155
$392$	0	0
$393$	0	0
$394$	−25.0000	−1.25948
$395$	6.00000	0.301893
$396$	0	0
$397$	18.0000	0.903394	0.451697	−	0.892171i	$-0.350819\pi$
$397$	18.0000	0.903394	0.451697	+	0.892171i	$0.350819\pi$
$398$	−19.0000	−0.952384
$399$	0	0
$400$	−1.00000	−0.0500000
$401$	18.0000	0.898877	0.449439	−	0.893311i	$-0.351624\pi$
$401$	18.0000	0.898877	0.449439	+	0.893311i	$0.351624\pi$
$402$	0	0
$403$	18.0000	0.896644
$404$	−5.00000	−0.248759
$405$	0	0
$406$	0	0
$407$	−40.0000	−1.98273
$408$	0	0
$409$	10.0000	0.494468	0.247234	−	0.968956i	$-0.420478\pi$
$409$	10.0000	0.494468	0.247234	+	0.968956i	$0.420478\pi$
$410$	−12.0000	−0.592638
$411$	0	0
$412$	−8.00000	−0.394132
$413$	0	0
$414$	0	0
$415$	14.0000	0.687233
$416$	6.00000	0.294174
$417$	0	0
$418$	20.0000	0.978232
$419$	12.0000	0.586238	0.293119	−	0.956076i	$-0.405307\pi$
$419$	12.0000	0.586238	0.293119	+	0.956076i	$0.405307\pi$
$420$	0	0
$421$	−18.0000	−0.877266	−0.438633	−	0.898666i	$-0.644537\pi$
$421$	−18.0000	−0.877266	−0.438633	+	0.898666i	$0.644537\pi$
$422$	−26.0000	−1.26566
$423$	0	0
$424$	−6.00000	−0.291386
$425$	4.00000	0.194029
$426$	0	0
$427$	0	0
$428$	−12.0000	−0.580042
$429$	0	0
$430$	16.0000	0.771589
$431$	18.0000	0.867029	0.433515	−	0.901146i	$-0.357273\pi$
$431$	18.0000	0.867029	0.433515	+	0.901146i	$0.357273\pi$
$432$	0	0
$433$	7.00000	0.336399	0.168199	−	0.985753i	$-0.446205\pi$
$433$	7.00000	0.336399	0.168199	+	0.985753i	$0.446205\pi$
$434$	0	0
$435$	0	0
$436$	16.0000	0.766261
$437$	16.0000	0.765384
$438$	0	0
$439$	−3.00000	−0.143182	−0.0715911	−	0.997434i	$-0.522808\pi$
$439$	−3.00000	−0.143182	−0.0715911	+	0.997434i	$0.522808\pi$
$440$	−10.0000	−0.476731
$441$	0	0
$442$	−24.0000	−1.14156
$443$	−11.0000	−0.522626	−0.261313	−	0.965254i	$-0.584155\pi$
$443$	−11.0000	−0.522626	−0.261313	+	0.965254i	$0.584155\pi$
$444$	0	0
$445$	−12.0000	−0.568855
$446$	−1.00000	−0.0473514
$447$	0	0
$448$	0	0
$449$	14.0000	0.660701	0.330350	−	0.943858i	$-0.392833\pi$
$449$	14.0000	0.660701	0.330350	+	0.943858i	$0.392833\pi$
$450$	0	0
$451$	30.0000	1.41264
$452$	−4.00000	−0.188144
$453$	0	0
$454$	27.0000	1.26717
$455$	0	0
$456$	0	0
$457$	−26.0000	−1.21623	−0.608114	−	0.793849i	$-0.708074\pi$
$457$	−26.0000	−1.21623	−0.608114	+	0.793849i	$0.708074\pi$
$458$	4.00000	0.186908
$459$	0	0
$460$	−8.00000	−0.373002
$461$	−23.0000	−1.07122	−0.535608	−	0.844466i	$-0.679918\pi$
$461$	−23.0000	−1.07122	−0.535608	+	0.844466i	$0.679918\pi$
$462$	0	0
$463$	−29.0000	−1.34774	−0.673872	−	0.738848i	$-0.735370\pi$
$463$	−29.0000	−1.34774	−0.673872	+	0.738848i	$0.735370\pi$
$464$	−7.00000	−0.324967
$465$	0	0
$466$	−22.0000	−1.01913
$467$	7.00000	0.323921	0.161961	−	0.986797i	$-0.448218\pi$
$467$	7.00000	0.323921	0.161961	+	0.986797i	$0.448218\pi$
$468$	0	0
$469$	0	0
$470$	12.0000	0.553519
$471$	0	0
$472$	−7.00000	−0.322201
$473$	−40.0000	−1.83920
$474$	0	0
$475$	−4.00000	−0.183533
$476$	0	0
$477$	0	0
$478$	0	0
$479$	26.0000	1.18797	0.593985	−	0.804476i	$-0.297554\pi$
$479$	26.0000	1.18797	0.593985	+	0.804476i	$0.297554\pi$
$480$	0	0
$481$	−48.0000	−2.18861
$482$	−1.00000	−0.0455488
$483$	0	0
$484$	14.0000	0.636364
$485$	−10.0000	−0.454077
$486$	0	0
$487$	−13.0000	−0.589086	−0.294543	−	0.955638i	$-0.595167\pi$
$487$	−13.0000	−0.589086	−0.294543	+	0.955638i	$0.595167\pi$
$488$	0	0
$489$	0	0
$490$	0	0
$491$	−12.0000	−0.541552	−0.270776	−	0.962642i	$-0.587280\pi$
$491$	−12.0000	−0.541552	−0.270776	+	0.962642i	$0.587280\pi$
$492$	0	0
$493$	28.0000	1.26106
$494$	24.0000	1.07981
$495$	0	0
$496$	−3.00000	−0.134704
$497$	0	0
$498$	0	0
$499$	−8.00000	−0.358129	−0.179065	−	0.983837i	$-0.557307\pi$
$499$	−8.00000	−0.358129	−0.179065	+	0.983837i	$0.557307\pi$
$500$	12.0000	0.536656
$501$	0	0
$502$	21.0000	0.937276
$503$	6.00000	0.267527	0.133763	−	0.991013i	$-0.457294\pi$
$503$	6.00000	0.267527	0.133763	+	0.991013i	$0.457294\pi$
$504$	0	0
$505$	10.0000	0.444994
$506$	20.0000	0.889108
$507$	0	0
$508$	0	0
$509$	3.00000	0.132973	0.0664863	−	0.997787i	$-0.478821\pi$
$509$	3.00000	0.132973	0.0664863	+	0.997787i	$0.478821\pi$
$510$	0	0
$511$	0	0
$512$	−1.00000	−0.0441942
$513$	0	0
$514$	0	0
$515$	16.0000	0.705044
$516$	0	0
$517$	−30.0000	−1.31940
$518$	0	0
$519$	0	0
$520$	−12.0000	−0.526235
$521$	0	0		−	1.00000i	$-0.5\pi$
$521$	0	0			1.00000i	$0.5\pi$
$522$	0	0
$523$	−26.0000	−1.13690	−0.568450	−	0.822718i	$-0.692457\pi$
$523$	−26.0000	−1.13690	−0.568450	+	0.822718i	$0.692457\pi$
$524$	13.0000	0.567908
$525$	0	0
$526$	12.0000	0.523225
$527$	12.0000	0.522728
$528$	0	0
$529$	−7.00000	−0.304348
$530$	12.0000	0.521247
$531$	0	0
$532$	0	0
$533$	36.0000	1.55933
$534$	0	0
$535$	24.0000	1.03761
$536$	−10.0000	−0.431934
$537$	0	0
$538$	−31.0000	−1.33650
$539$	0	0
$540$	0	0
$541$	−30.0000	−1.28980	−0.644900	−	0.764267i	$-0.723101\pi$
$541$	−30.0000	−1.28980	−0.644900	+	0.764267i	$0.723101\pi$
$542$	0	0
$543$	0	0
$544$	4.00000	0.171499
$545$	−32.0000	−1.37073
$546$	0	0
$547$	−18.0000	−0.769624	−0.384812	−	0.922995i	$-0.625734\pi$
$547$	−18.0000	−0.769624	−0.384812	+	0.922995i	$0.625734\pi$
$548$	8.00000	0.341743
$549$	0	0
$550$	−5.00000	−0.213201
$551$	−28.0000	−1.19284
$552$	0	0
$553$	0	0
$554$	−2.00000	−0.0849719
$555$	0	0
$556$	8.00000	0.339276
$557$	11.0000	0.466085	0.233042	−	0.972467i	$-0.425132\pi$
$557$	11.0000	0.466085	0.233042	+	0.972467i	$0.425132\pi$
$558$	0	0
$559$	−48.0000	−2.03018
$560$	0	0
$561$	0	0
$562$	2.00000	0.0843649
$563$	20.0000	0.842900	0.421450	−	0.906852i	$-0.361521\pi$
$563$	20.0000	0.842900	0.421450	+	0.906852i	$0.361521\pi$
$564$	0	0
$565$	8.00000	0.336563
$566$	16.0000	0.672530
$567$	0	0
$568$	−4.00000	−0.167836
$569$	12.0000	0.503066	0.251533	−	0.967849i	$-0.419065\pi$
$569$	12.0000	0.503066	0.251533	+	0.967849i	$0.419065\pi$
$570$	0	0
$571$	0	0		−	1.00000i	$-0.5\pi$
$571$	0	0			1.00000i	$0.5\pi$
$572$	30.0000	1.25436
$573$	0	0
$574$	0	0
$575$	−4.00000	−0.166812
$576$	0	0
$577$	−43.0000	−1.79011	−0.895057	−	0.445952i	$-0.852865\pi$
$577$	−43.0000	−1.79011	−0.895057	+	0.445952i	$0.852865\pi$
$578$	1.00000	0.0415945
$579$	0	0
$580$	14.0000	0.581318
$581$	0	0
$582$	0	0
$583$	−30.0000	−1.24247
$584$	13.0000	0.537944
$585$	0	0
$586$	−27.0000	−1.11536
$587$	20.0000	0.825488	0.412744	−	0.910847i	$-0.364570\pi$
$587$	20.0000	0.825488	0.412744	+	0.910847i	$0.364570\pi$
$588$	0	0
$589$	−12.0000	−0.494451
$590$	14.0000	0.576371
$591$	0	0
$592$	8.00000	0.328798
$593$	36.0000	1.47834	0.739171	−	0.673517i	$-0.235217\pi$
$593$	36.0000	1.47834	0.739171	+	0.673517i	$0.235217\pi$
$594$	0	0
$595$	0	0
$596$	−9.00000	−0.368654
$597$	0	0
$598$	24.0000	0.981433
$599$	−30.0000	−1.22577	−0.612883	−	0.790173i	$-0.709990\pi$
$599$	−30.0000	−1.22577	−0.612883	+	0.790173i	$0.709990\pi$
$600$	0	0
$601$	10.0000	0.407909	0.203954	−	0.978980i	$-0.434621\pi$
$601$	10.0000	0.407909	0.203954	+	0.978980i	$0.434621\pi$
$602$	0	0
$603$	0	0
$604$	−17.0000	−0.691720
$605$	−28.0000	−1.13836
$606$	0	0
$607$	9.00000	0.365299	0.182649	−	0.983178i	$-0.441533\pi$
$607$	9.00000	0.365299	0.182649	+	0.983178i	$0.441533\pi$
$608$	−4.00000	−0.162221
$609$	0	0
$610$	0	0
$611$	−36.0000	−1.45640
$612$	0	0
$613$	−6.00000	−0.242338	−0.121169	−	0.992632i	$-0.538664\pi$
$613$	−6.00000	−0.242338	−0.121169	+	0.992632i	$0.538664\pi$
$614$	−2.00000	−0.0807134
$615$	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
$619$	−4.00000	−0.160774	−0.0803868	−	0.996764i	$-0.525616\pi$
$619$	−4.00000	−0.160774	−0.0803868	+	0.996764i	$0.525616\pi$
$620$	6.00000	0.240966
$621$	0	0
$622$	−22.0000	−0.882120
$623$	0	0
$624$	0	0
$625$	−19.0000	−0.760000
$626$	10.0000	0.399680
$627$	0	0
$628$	−14.0000	−0.558661
$629$	−32.0000	−1.27592
$630$	0	0
$631$	5.00000	0.199047	0.0995234	−	0.995035i	$-0.468268\pi$
$631$	5.00000	0.199047	0.0995234	+	0.995035i	$0.468268\pi$
$632$	3.00000	0.119334
$633$	0	0
$634$	−33.0000	−1.31060
$635$	0	0
$636$	0	0
$637$	0	0
$638$	−35.0000	−1.38566
$639$	0	0
$640$	2.00000	0.0790569
$641$	−14.0000	−0.552967	−0.276483	−	0.961019i	$-0.589169\pi$
$641$	−14.0000	−0.552967	−0.276483	+	0.961019i	$0.589169\pi$
$642$	0	0
$643$	−14.0000	−0.552106	−0.276053	−	0.961142i	$-0.589027\pi$
$643$	−14.0000	−0.552106	−0.276053	+	0.961142i	$0.589027\pi$
$644$	0	0
$645$	0	0
$646$	16.0000	0.629512
$647$	−18.0000	−0.707653	−0.353827	−	0.935311i	$-0.615120\pi$
$647$	−18.0000	−0.707653	−0.353827	+	0.935311i	$0.615120\pi$
$648$	0	0
$649$	−35.0000	−1.37387
$650$	−6.00000	−0.235339
$651$	0	0
$652$	2.00000	0.0783260
$653$	−18.0000	−0.704394	−0.352197	−	0.935926i	$-0.614565\pi$
$653$	−18.0000	−0.704394	−0.352197	+	0.935926i	$0.614565\pi$
$654$	0	0
$655$	−26.0000	−1.01590
$656$	−6.00000	−0.234261
$657$	0	0
$658$	0	0
$659$	−41.0000	−1.59713	−0.798567	−	0.601906i	$-0.794408\pi$
$659$	−41.0000	−1.59713	−0.798567	+	0.601906i	$0.794408\pi$
$660$	0	0
$661$	38.0000	1.47803	0.739014	−	0.673690i	$-0.235292\pi$
$661$	38.0000	1.47803	0.739014	+	0.673690i	$0.235292\pi$
$662$	−32.0000	−1.24372
$663$	0	0
$664$	7.00000	0.271653
$665$	0	0
$666$	0	0
$667$	−28.0000	−1.08416
$668$	−14.0000	−0.541676
$669$	0	0
$670$	20.0000	0.772667
$671$	0	0
$672$	0	0
$673$	2.00000	0.0770943	0.0385472	−	0.999257i	$-0.487727\pi$
$673$	2.00000	0.0770943	0.0385472	+	0.999257i	$0.487727\pi$
$674$	27.0000	1.04000
$675$	0	0
$676$	23.0000	0.884615
$677$	9.00000	0.345898	0.172949	−	0.984931i	$-0.444670\pi$
$677$	9.00000	0.345898	0.172949	+	0.984931i	$0.444670\pi$
$678$	0	0
$679$	0	0
$680$	−8.00000	−0.306786
$681$	0	0
$682$	−15.0000	−0.574380
$683$	−21.0000	−0.803543	−0.401771	−	0.915740i	$-0.631605\pi$
$683$	−21.0000	−0.803543	−0.401771	+	0.915740i	$0.631605\pi$
$684$	0	0
$685$	−16.0000	−0.611329
$686$	0	0
$687$	0	0
$688$	8.00000	0.304997
$689$	−36.0000	−1.37149
$690$	0	0
$691$	−8.00000	−0.304334	−0.152167	−	0.988355i	$-0.548625\pi$
$691$	−8.00000	−0.304334	−0.152167	+	0.988355i	$0.548625\pi$
$692$	1.00000	0.0380143
$693$	0	0
$694$	−27.0000	−1.02491
$695$	−16.0000	−0.606915
$696$	0	0
$697$	24.0000	0.909065
$698$	−20.0000	−0.757011
$699$	0	0
$700$	0	0
$701$	14.0000	0.528773	0.264386	−	0.964417i	$-0.414831\pi$
$701$	14.0000	0.528773	0.264386	+	0.964417i	$0.414831\pi$
$702$	0	0
$703$	32.0000	1.20690
$704$	−5.00000	−0.188445
$705$	0	0
$706$	30.0000	1.12906
$707$	0	0
$708$	0	0
$709$	8.00000	0.300446	0.150223	−	0.988652i	$-0.452001\pi$
$709$	8.00000	0.300446	0.150223	+	0.988652i	$0.452001\pi$
$710$	8.00000	0.300235
$711$	0	0
$712$	−6.00000	−0.224860
$713$	−12.0000	−0.449404
$714$	0	0
$715$	−60.0000	−2.24387
$716$	15.0000	0.560576
$717$	0	0
$718$	16.0000	0.597115
$719$	6.00000	0.223762	0.111881	−	0.993722i	$-0.464312\pi$
$719$	6.00000	0.223762	0.111881	+	0.993722i	$0.464312\pi$
$720$	0	0
$721$	0	0
$722$	3.00000	0.111648
$723$	0	0
$724$	0	0
$725$	7.00000	0.259973
$726$	0	0
$727$	32.0000	1.18681	0.593407	−	0.804902i	$-0.297782\pi$
$727$	32.0000	1.18681	0.593407	+	0.804902i	$0.297782\pi$
$728$	0	0
$729$	0	0
$730$	−26.0000	−0.962303
$731$	−32.0000	−1.18356
$732$	0	0
$733$	36.0000	1.32969	0.664845	−	0.746981i	$-0.268498\pi$
$733$	36.0000	1.32969	0.664845	+	0.746981i	$0.268498\pi$
$734$	−4.00000	−0.147643
$735$	0	0
$736$	−4.00000	−0.147442
$737$	−50.0000	−1.84177
$738$	0	0
$739$	−6.00000	−0.220714	−0.110357	−	0.993892i	$-0.535199\pi$
$739$	−6.00000	−0.220714	−0.110357	+	0.993892i	$0.535199\pi$
$740$	−16.0000	−0.588172
$741$	0	0
$742$	0	0
$743$	6.00000	0.220119	0.110059	−	0.993925i	$-0.464896\pi$
$743$	6.00000	0.220119	0.110059	+	0.993925i	$0.464896\pi$
$744$	0	0
$745$	18.0000	0.659469
$746$	20.0000	0.732252
$747$	0	0
$748$	20.0000	0.731272
$749$	0	0
$750$	0	0
$751$	12.0000	0.437886	0.218943	−	0.975738i	$-0.429739\pi$
$751$	12.0000	0.437886	0.218943	+	0.975738i	$0.429739\pi$
$752$	6.00000	0.218797
$753$	0	0
$754$	−42.0000	−1.52955
$755$	34.0000	1.23739
$756$	0	0
$757$	−18.0000	−0.654221	−0.327111	−	0.944986i	$-0.606075\pi$
$757$	−18.0000	−0.654221	−0.327111	+	0.944986i	$0.606075\pi$
$758$	−10.0000	−0.363216
$759$	0	0
$760$	8.00000	0.290191
$761$	8.00000	0.290000	0.145000	−	0.989432i	$-0.453682\pi$
$761$	8.00000	0.290000	0.145000	+	0.989432i	$0.453682\pi$
$762$	0	0
$763$	0	0
$764$	18.0000	0.651217
$765$	0	0
$766$	4.00000	0.144526
$767$	−42.0000	−1.51653
$768$	0	0
$769$	−1.00000	−0.0360609	−0.0180305	−	0.999837i	$-0.505740\pi$
$769$	−1.00000	−0.0360609	−0.0180305	+	0.999837i	$0.505740\pi$
$770$	0	0
$771$	0	0
$772$	−19.0000	−0.683825
$773$	−38.0000	−1.36677	−0.683383	−	0.730061i	$-0.739492\pi$
$773$	−38.0000	−1.36677	−0.683383	+	0.730061i	$0.739492\pi$
$774$	0	0
$775$	3.00000	0.107763
$776$	−5.00000	−0.179490
$777$	0	0
$778$	1.00000	0.0358517
$779$	−24.0000	−0.859889
$780$	0	0
$781$	−20.0000	−0.715656
$782$	16.0000	0.572159
$783$	0	0
$784$	0	0
$785$	28.0000	0.999363
$786$	0	0
$787$	−18.0000	−0.641631	−0.320815	−	0.947142i	$-0.603957\pi$
$787$	−18.0000	−0.641631	−0.320815	+	0.947142i	$0.603957\pi$
$788$	25.0000	0.890588
$789$	0	0
$790$	−6.00000	−0.213470
$791$	0	0
$792$	0	0
$793$	0	0
$794$	−18.0000	−0.638796
$795$	0	0
$796$	19.0000	0.673437
$797$	33.0000	1.16892	0.584460	−	0.811423i	$-0.301306\pi$
$797$	33.0000	1.16892	0.584460	+	0.811423i	$0.301306\pi$
$798$	0	0
$799$	−24.0000	−0.849059
$800$	1.00000	0.0353553
$801$	0	0
$802$	−18.0000	−0.635602
$803$	65.0000	2.29380
$804$	0	0
$805$	0	0
$806$	−18.0000	−0.634023
$807$	0	0
$808$	5.00000	0.175899
$809$	−34.0000	−1.19538	−0.597688	−	0.801729i	$-0.703914\pi$
$809$	−34.0000	−1.19538	−0.597688	+	0.801729i	$0.703914\pi$
$810$	0	0
$811$	50.0000	1.75574	0.877869	−	0.478901i	$-0.158965\pi$
$811$	50.0000	1.75574	0.877869	+	0.478901i	$0.158965\pi$
$812$	0	0
$813$	0	0
$814$	40.0000	1.40200
$815$	−4.00000	−0.140114
$816$	0	0
$817$	32.0000	1.11954
$818$	−10.0000	−0.349642
$819$	0	0
$820$	12.0000	0.419058
$821$	49.0000	1.71011	0.855056	−	0.518536i	$-0.173523\pi$
$821$	49.0000	1.71011	0.855056	+	0.518536i	$0.173523\pi$
$822$	0	0
$823$	13.0000	0.453152	0.226576	−	0.973994i	$-0.427247\pi$
$823$	13.0000	0.453152	0.226576	+	0.973994i	$0.427247\pi$
$824$	8.00000	0.278693
$825$	0	0
$826$	0	0
$827$	−51.0000	−1.77344	−0.886722	−	0.462303i	$-0.847023\pi$
$827$	−51.0000	−1.77344	−0.886722	+	0.462303i	$0.847023\pi$
$828$	0	0
$829$	−22.0000	−0.764092	−0.382046	−	0.924143i	$-0.624780\pi$
$829$	−22.0000	−0.764092	−0.382046	+	0.924143i	$0.624780\pi$
$830$	−14.0000	−0.485947
$831$	0	0
$832$	−6.00000	−0.208013
$833$	0	0
$834$	0	0
$835$	28.0000	0.968980
$836$	−20.0000	−0.691714
$837$	0	0
$838$	−12.0000	−0.414533
$839$	−4.00000	−0.138095	−0.0690477	−	0.997613i	$-0.521996\pi$
$839$	−4.00000	−0.138095	−0.0690477	+	0.997613i	$0.521996\pi$
$840$	0	0
$841$	20.0000	0.689655
$842$	18.0000	0.620321
$843$	0	0
$844$	26.0000	0.894957
$845$	−46.0000	−1.58245
$846$	0	0
$847$	0	0
$848$	6.00000	0.206041
$849$	0	0
$850$	−4.00000	−0.137199
$851$	32.0000	1.09695
$852$	0	0
$853$	46.0000	1.57501	0.787505	−	0.616308i	$-0.211372\pi$
$853$	46.0000	1.57501	0.787505	+	0.616308i	$0.211372\pi$
$854$	0	0
$855$	0	0
$856$	12.0000	0.410152
$857$	30.0000	1.02478	0.512390	−	0.858753i	$-0.328760\pi$
$857$	30.0000	1.02478	0.512390	+	0.858753i	$0.328760\pi$
$858$	0	0
$859$	16.0000	0.545913	0.272956	−	0.962026i	$-0.411998\pi$
$859$	16.0000	0.545913	0.272956	+	0.962026i	$0.411998\pi$
$860$	−16.0000	−0.545595
$861$	0	0
$862$	−18.0000	−0.613082
$863$	38.0000	1.29354	0.646768	−	0.762687i	$-0.276120\pi$
$863$	38.0000	1.29354	0.646768	+	0.762687i	$0.276120\pi$
$864$	0	0
$865$	−2.00000	−0.0680020
$866$	−7.00000	−0.237870
$867$	0	0
$868$	0	0
$869$	15.0000	0.508840
$870$	0	0
$871$	−60.0000	−2.03302
$872$	−16.0000	−0.541828
$873$	0	0
$874$	−16.0000	−0.541208
$875$	0	0
$876$	0	0
$877$	34.0000	1.14810	0.574049	−	0.818821i	$-0.305372\pi$
$877$	34.0000	1.14810	0.574049	+	0.818821i	$0.305372\pi$
$878$	3.00000	0.101245
$879$	0	0
$880$	10.0000	0.337100
$881$	−54.0000	−1.81931	−0.909653	−	0.415369i	$-0.863653\pi$
$881$	−54.0000	−1.81931	−0.909653	+	0.415369i	$0.863653\pi$
$882$	0	0
$883$	2.00000	0.0673054	0.0336527	−	0.999434i	$-0.489286\pi$
$883$	2.00000	0.0673054	0.0336527	+	0.999434i	$0.489286\pi$
$884$	24.0000	0.807207
$885$	0	0
$886$	11.0000	0.369552
$887$	−42.0000	−1.41022	−0.705111	−	0.709097i	$-0.749103\pi$
$887$	−42.0000	−1.41022	−0.705111	+	0.709097i	$0.749103\pi$
$888$	0	0
$889$	0	0
$890$	12.0000	0.402241
$891$	0	0
$892$	1.00000	0.0334825
$893$	24.0000	0.803129
$894$	0	0
$895$	−30.0000	−1.00279
$896$	0	0
$897$	0	0
$898$	−14.0000	−0.467186
$899$	21.0000	0.700389
$900$	0	0
$901$	−24.0000	−0.799556
$902$	−30.0000	−0.998891
$903$	0	0
$904$	4.00000	0.133038
$905$	0	0
$906$	0	0
$907$	−42.0000	−1.39459	−0.697294	−	0.716786i	$-0.745613\pi$
$907$	−42.0000	−1.39459	−0.697294	+	0.716786i	$0.745613\pi$
$908$	−27.0000	−0.896026
$909$	0	0
$910$	0	0
$911$	−36.0000	−1.19273	−0.596367	−	0.802712i	$-0.703390\pi$
$911$	−36.0000	−1.19273	−0.596367	+	0.802712i	$0.703390\pi$
$912$	0	0
$913$	35.0000	1.15833
$914$	26.0000	0.860004
$915$	0	0
$916$	−4.00000	−0.132164
$917$	0	0
$918$	0	0
$919$	13.0000	0.428830	0.214415	−	0.976743i	$-0.431215\pi$
$919$	13.0000	0.428830	0.214415	+	0.976743i	$0.431215\pi$
$920$	8.00000	0.263752
$921$	0	0
$922$	23.0000	0.757465
$923$	−24.0000	−0.789970
$924$	0	0
$925$	−8.00000	−0.263038
$926$	29.0000	0.952999
$927$	0	0
$928$	7.00000	0.229786
$929$	36.0000	1.18112	0.590561	−	0.806993i	$-0.298907\pi$
$929$	36.0000	1.18112	0.590561	+	0.806993i	$0.298907\pi$
$930$	0	0
$931$	0	0
$932$	22.0000	0.720634
$933$	0	0
$934$	−7.00000	−0.229047
$935$	−40.0000	−1.30814
$936$	0	0
$937$	−14.0000	−0.457360	−0.228680	−	0.973502i	$-0.573441\pi$
$937$	−14.0000	−0.457360	−0.228680	+	0.973502i	$0.573441\pi$
$938$	0	0
$939$	0	0
$940$	−12.0000	−0.391397
$941$	13.0000	0.423788	0.211894	−	0.977293i	$-0.432037\pi$
$941$	13.0000	0.423788	0.211894	+	0.977293i	$0.432037\pi$
$942$	0	0
$943$	−24.0000	−0.781548
$944$	7.00000	0.227831
$945$	0	0
$946$	40.0000	1.30051
$947$	−25.0000	−0.812391	−0.406195	−	0.913786i	$-0.633145\pi$
$947$	−25.0000	−0.812391	−0.406195	+	0.913786i	$0.633145\pi$
$948$	0	0
$949$	78.0000	2.53199
$950$	4.00000	0.129777
$951$	0	0
$952$	0	0
$953$	−2.00000	−0.0647864	−0.0323932	−	0.999475i	$-0.510313\pi$
$953$	−2.00000	−0.0647864	−0.0323932	+	0.999475i	$0.510313\pi$
$954$	0	0
$955$	−36.0000	−1.16493
$956$	0	0
$957$	0	0
$958$	−26.0000	−0.840022
$959$	0	0
$960$	0	0
$961$	−22.0000	−0.709677
$962$	48.0000	1.54758
$963$	0	0
$964$	1.00000	0.0322078
$965$	38.0000	1.22326
$966$	0	0
$967$	8.00000	0.257263	0.128631	−	0.991692i	$-0.458942\pi$
$967$	8.00000	0.257263	0.128631	+	0.991692i	$0.458942\pi$
$968$	−14.0000	−0.449977
$969$	0	0
$970$	10.0000	0.321081
$971$	12.0000	0.385098	0.192549	−	0.981287i	$-0.438325\pi$
$971$	12.0000	0.385098	0.192549	+	0.981287i	$0.438325\pi$
$972$	0	0
$973$	0	0
$974$	13.0000	0.416547
$975$	0	0
$976$	0	0
$977$	18.0000	0.575871	0.287936	−	0.957650i	$-0.407031\pi$
$977$	18.0000	0.575871	0.287936	+	0.957650i	$0.407031\pi$
$978$	0	0
$979$	−30.0000	−0.958804
$980$	0	0
$981$	0	0
$982$	12.0000	0.382935
$983$	36.0000	1.14822	0.574111	−	0.818778i	$-0.305348\pi$
$983$	36.0000	1.14822	0.574111	+	0.818778i	$0.305348\pi$
$984$	0	0
$985$	−50.0000	−1.59313
$986$	−28.0000	−0.891702
$987$	0	0
$988$	−24.0000	−0.763542
$989$	32.0000	1.01754
$990$	0	0
$991$	8.00000	0.254128	0.127064	−	0.991894i	$-0.459445\pi$
$991$	8.00000	0.254128	0.127064	+	0.991894i	$0.459445\pi$
$992$	3.00000	0.0952501
$993$	0	0
$994$	0	0
$995$	−38.0000	−1.20468
$996$	0	0
$997$	58.0000	1.83688	0.918439	−	0.395562i	$-0.129450\pi$
$997$	58.0000	1.83688	0.918439	+	0.395562i	$0.129450\pi$
$998$	8.00000	0.253236
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2646.2.a.c.1.1		1
3.2	odd	2		2646.2.a.bb.1.1		1
7.3	odd	6		378.2.g.d.163.1	yes	2
7.5	odd	6		378.2.g.d.109.1	yes	2
7.6	odd	2		2646.2.a.k.1.1		1
21.5	even	6		378.2.g.c.109.1	✓	2
21.17	even	6		378.2.g.c.163.1	yes	2
21.20	even	2		2646.2.a.t.1.1		1
63.5	even	6		1134.2.e.o.865.1		2
63.31	odd	6		1134.2.h.o.541.1		2
63.38	even	6		1134.2.e.o.919.1		2
63.40	odd	6		1134.2.e.b.865.1		2
63.47	even	6		1134.2.h.b.109.1		2
63.52	odd	6		1134.2.e.b.919.1		2
63.59	even	6		1134.2.h.b.541.1		2
63.61	odd	6		1134.2.h.o.109.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.g.c.109.1	✓	2	21.5	even	6
378.2.g.c.163.1	yes	2	21.17	even	6
378.2.g.d.109.1	yes	2	7.5	odd	6
378.2.g.d.163.1	yes	2	7.3	odd	6
1134.2.e.b.865.1		2	63.40	odd	6
1134.2.e.b.919.1		2	63.52	odd	6
1134.2.e.o.865.1		2	63.5	even	6
1134.2.e.o.919.1		2	63.38	even	6
1134.2.h.b.109.1		2	63.47	even	6
1134.2.h.b.541.1		2	63.59	even	6
1134.2.h.o.109.1		2	63.61	odd	6
1134.2.h.o.541.1		2	63.31	odd	6
2646.2.a.c.1.1		1	1.1	even	1	trivial
2646.2.a.k.1.1		1	7.6	odd	2
2646.2.a.t.1.1		1	21.20	even	2
2646.2.a.bb.1.1		1	3.2	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:	\( N \)	\(=\)	\( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2646.a (trivial)

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