LMFDB - Embedded newform 5550.2.a.l.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5550,2,Mod(1,5550)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5550, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("5550.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5550 = 2 \cdot 3 \cdot 5^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5550.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:	$44.3169731218$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 1110)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	5550.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} +5.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$

\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} +5.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{11} -1.00000 q^{12} -5.00000 q^{14} +1.00000 q^{16} +3.00000 q^{17} -1.00000 q^{18} +8.00000 q^{19} -5.00000 q^{21} -1.00000 q^{22} +8.00000 q^{23} +1.00000 q^{24} -1.00000 q^{27} +5.00000 q^{28} -5.00000 q^{29} +3.00000 q^{31} -1.00000 q^{32} -1.00000 q^{33} -3.00000 q^{34} +1.00000 q^{36} -1.00000 q^{37} -8.00000 q^{38} -5.00000 q^{41} +5.00000 q^{42} +9.00000 q^{43} +1.00000 q^{44} -8.00000 q^{46} +12.0000 q^{47} -1.00000 q^{48} +18.0000 q^{49} -3.00000 q^{51} -5.00000 q^{53} +1.00000 q^{54} -5.00000 q^{56} -8.00000 q^{57} +5.00000 q^{58} -4.00000 q^{59} -9.00000 q^{61} -3.00000 q^{62} +5.00000 q^{63} +1.00000 q^{64} +1.00000 q^{66} +8.00000 q^{67} +3.00000 q^{68} -8.00000 q^{69} +6.00000 q^{71} -1.00000 q^{72} -2.00000 q^{73} +1.00000 q^{74} +8.00000 q^{76} +5.00000 q^{77} -8.00000 q^{79} +1.00000 q^{81} +5.00000 q^{82} +4.00000 q^{83} -5.00000 q^{84} -9.00000 q^{86} +5.00000 q^{87} -1.00000 q^{88} -4.00000 q^{89} +8.00000 q^{92} -3.00000 q^{93} -12.0000 q^{94} +1.00000 q^{96} +9.00000 q^{97} -18.0000 q^{98} +1.00000 q^{99} +O(q^{100})\)

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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	0	0
$5$	0	0
$6$	1.00000	0.408248
$7$	5.00000	1.88982	0.944911	−	0.327327i	$-0.106148\pi$
$7$	5.00000	1.88982	0.944911	+	0.327327i	$0.106148\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	0	0
$11$	1.00000	0.301511	0.150756	−	0.988571i	$-0.451829\pi$
$11$	1.00000	0.301511	0.150756	+	0.988571i	$0.451829\pi$
$12$	−1.00000	−0.288675
$13$	0	0		−	1.00000i	$-0.5\pi$
$13$	0	0			1.00000i	$0.5\pi$
$14$	−5.00000	−1.33631
$15$	0	0
$16$	1.00000	0.250000
$17$	3.00000	0.727607	0.363803	−	0.931476i	$-0.381478\pi$
$17$	3.00000	0.727607	0.363803	+	0.931476i	$0.381478\pi$
$18$	−1.00000	−0.235702
$19$	8.00000	1.83533	0.917663	−	0.397360i	$-0.130073\pi$
$19$	8.00000	1.83533	0.917663	+	0.397360i	$0.130073\pi$
$20$	0	0
$21$	−5.00000	−1.09109
$22$	−1.00000	−0.213201
$23$	8.00000	1.66812	0.834058	−	0.551677i	$-0.186012\pi$
$23$	8.00000	1.66812	0.834058	+	0.551677i	$0.186012\pi$
$24$	1.00000	0.204124
$25$	0	0
$26$	0	0
$27$	−1.00000	−0.192450
$28$	5.00000	0.944911
$29$	−5.00000	−0.928477	−0.464238	−	0.885710i	$-0.653672\pi$
$29$	−5.00000	−0.928477	−0.464238	+	0.885710i	$0.653672\pi$
$30$	0	0
$31$	3.00000	0.538816	0.269408	−	0.963026i	$-0.413172\pi$
$31$	3.00000	0.538816	0.269408	+	0.963026i	$0.413172\pi$
$32$	−1.00000	−0.176777
$33$	−1.00000	−0.174078
$34$	−3.00000	−0.514496
$35$	0	0
$36$	1.00000	0.166667
$37$	−1.00000	−0.164399
$37$	−1.00000	−0.164399
$38$	−8.00000	−1.29777
$39$	0	0
$40$	0	0
$41$	−5.00000	−0.780869	−0.390434	−	0.920631i	$-0.627675\pi$
$41$	−5.00000	−0.780869	−0.390434	+	0.920631i	$0.627675\pi$
$42$	5.00000	0.771517
$43$	9.00000	1.37249	0.686244	−	0.727372i	$-0.259258\pi$
$43$	9.00000	1.37249	0.686244	+	0.727372i	$0.259258\pi$
$44$	1.00000	0.150756
$45$	0	0
$46$	−8.00000	−1.17954
$47$	12.0000	1.75038	0.875190	−	0.483779i	$-0.160736\pi$
$47$	12.0000	1.75038	0.875190	+	0.483779i	$0.160736\pi$
$48$	−1.00000	−0.144338
$49$	18.0000	2.57143
$50$	0	0
$51$	−3.00000	−0.420084
$52$	0	0
$53$	−5.00000	−0.686803	−0.343401	−	0.939189i	$-0.611579\pi$
$53$	−5.00000	−0.686803	−0.343401	+	0.939189i	$0.611579\pi$
$54$	1.00000	0.136083
$55$	0	0
$56$	−5.00000	−0.668153
$57$	−8.00000	−1.05963
$58$	5.00000	0.656532
$59$	−4.00000	−0.520756	−0.260378	−	0.965507i	$-0.583847\pi$
$59$	−4.00000	−0.520756	−0.260378	+	0.965507i	$0.583847\pi$
$60$	0	0
$61$	−9.00000	−1.15233	−0.576166	−	0.817333i	$-0.695452\pi$
$61$	−9.00000	−1.15233	−0.576166	+	0.817333i	$0.695452\pi$
$62$	−3.00000	−0.381000
$63$	5.00000	0.629941
$64$	1.00000	0.125000
$65$	0	0
$66$	1.00000	0.123091
$67$	8.00000	0.977356	0.488678	−	0.872464i	$-0.337479\pi$
$67$	8.00000	0.977356	0.488678	+	0.872464i	$0.337479\pi$
$68$	3.00000	0.363803
$69$	−8.00000	−0.963087
$70$	0	0
$71$	6.00000	0.712069	0.356034	−	0.934473i	$-0.384129\pi$
$71$	6.00000	0.712069	0.356034	+	0.934473i	$0.384129\pi$
$72$	−1.00000	−0.117851
$73$	−2.00000	−0.234082	−0.117041	−	0.993127i	$-0.537341\pi$
$73$	−2.00000	−0.234082	−0.117041	+	0.993127i	$0.537341\pi$
$74$	1.00000	0.116248
$75$	0	0
$76$	8.00000	0.917663
$77$	5.00000	0.569803
$78$	0	0
$79$	−8.00000	−0.900070	−0.450035	−	0.893011i	$-0.648589\pi$
$79$	−8.00000	−0.900070	−0.450035	+	0.893011i	$0.648589\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	5.00000	0.552158
$83$	4.00000	0.439057	0.219529	−	0.975606i	$-0.429548\pi$
$83$	4.00000	0.439057	0.219529	+	0.975606i	$0.429548\pi$
$84$	−5.00000	−0.545545
$85$	0	0
$86$	−9.00000	−0.970495
$87$	5.00000	0.536056
$88$	−1.00000	−0.106600
$89$	−4.00000	−0.423999	−0.212000	−	0.977270i	$-0.567998\pi$
$89$	−4.00000	−0.423999	−0.212000	+	0.977270i	$0.567998\pi$
$90$	0	0
$91$	0	0
$92$	8.00000	0.834058
$93$	−3.00000	−0.311086
$94$	−12.0000	−1.23771
$95$	0	0
$96$	1.00000	0.102062
$97$	9.00000	0.913812	0.456906	−	0.889515i	$-0.348958\pi$
$97$	9.00000	0.913812	0.456906	+	0.889515i	$0.348958\pi$
$98$	−18.0000	−1.81827
$99$	1.00000	0.100504
$100$	0	0
$101$	−6.00000	−0.597022	−0.298511	−	0.954406i	$-0.596490\pi$
$101$	−6.00000	−0.597022	−0.298511	+	0.954406i	$0.596490\pi$
$102$	3.00000	0.297044
$103$	−4.00000	−0.394132	−0.197066	−	0.980390i	$-0.563141\pi$
$103$	−4.00000	−0.394132	−0.197066	+	0.980390i	$0.563141\pi$
$104$	0	0
$105$	0	0
$106$	5.00000	0.485643
$107$	−2.00000	−0.193347	−0.0966736	−	0.995316i	$-0.530820\pi$
$107$	−2.00000	−0.193347	−0.0966736	+	0.995316i	$0.530820\pi$
$108$	−1.00000	−0.0962250
$109$	11.0000	1.05361	0.526804	−	0.849987i	$-0.323390\pi$
$109$	11.0000	1.05361	0.526804	+	0.849987i	$0.323390\pi$
$110$	0	0
$111$	1.00000	0.0949158
$112$	5.00000	0.472456
$113$	−15.0000	−1.41108	−0.705541	−	0.708669i	$-0.749296\pi$
$113$	−15.0000	−1.41108	−0.705541	+	0.708669i	$0.749296\pi$
$114$	8.00000	0.749269
$115$	0	0
$116$	−5.00000	−0.464238
$117$	0	0
$118$	4.00000	0.368230
$119$	15.0000	1.37505
$120$	0	0
$121$	−10.0000	−0.909091
$122$	9.00000	0.814822
$123$	5.00000	0.450835
$124$	3.00000	0.269408
$125$	0	0
$126$	−5.00000	−0.445435
$127$	−8.00000	−0.709885	−0.354943	−	0.934888i	$-0.615500\pi$
$127$	−8.00000	−0.709885	−0.354943	+	0.934888i	$0.615500\pi$
$128$	−1.00000	−0.0883883
$129$	−9.00000	−0.792406
$130$	0	0
$131$	−6.00000	−0.524222	−0.262111	−	0.965038i	$-0.584419\pi$
$131$	−6.00000	−0.524222	−0.262111	+	0.965038i	$0.584419\pi$
$132$	−1.00000	−0.0870388
$133$	40.0000	3.46844
$134$	−8.00000	−0.691095
$135$	0	0
$136$	−3.00000	−0.257248
$137$	6.00000	0.512615	0.256307	−	0.966595i	$-0.417494\pi$
$137$	6.00000	0.512615	0.256307	+	0.966595i	$0.417494\pi$
$138$	8.00000	0.681005
$139$	5.00000	0.424094	0.212047	−	0.977259i	$-0.431987\pi$
$139$	5.00000	0.424094	0.212047	+	0.977259i	$0.431987\pi$
$140$	0	0
$141$	−12.0000	−1.01058
$142$	−6.00000	−0.503509
$143$	0	0
$144$	1.00000	0.0833333
$145$	0	0
$146$	2.00000	0.165521
$147$	−18.0000	−1.48461
$148$	−1.00000	−0.0821995
$149$	−20.0000	−1.63846	−0.819232	−	0.573462i	$-0.805600\pi$
$149$	−20.0000	−1.63846	−0.819232	+	0.573462i	$0.805600\pi$
$150$	0	0
$151$	−10.0000	−0.813788	−0.406894	−	0.913475i	$-0.633388\pi$
$151$	−10.0000	−0.813788	−0.406894	+	0.913475i	$0.633388\pi$
$152$	−8.00000	−0.648886
$153$	3.00000	0.242536
$154$	−5.00000	−0.402911
$155$	0	0
$156$	0	0
$157$	11.0000	0.877896	0.438948	−	0.898513i	$-0.355351\pi$
$157$	11.0000	0.877896	0.438948	+	0.898513i	$0.355351\pi$
$158$	8.00000	0.636446
$159$	5.00000	0.396526
$160$	0	0
$161$	40.0000	3.15244
$162$	−1.00000	−0.0785674
$163$	1.00000	0.0783260	0.0391630	−	0.999233i	$-0.487531\pi$
$163$	1.00000	0.0783260	0.0391630	+	0.999233i	$0.487531\pi$
$164$	−5.00000	−0.390434
$165$	0	0
$166$	−4.00000	−0.310460
$167$	2.00000	0.154765	0.0773823	−	0.997001i	$-0.475344\pi$
$167$	2.00000	0.154765	0.0773823	+	0.997001i	$0.475344\pi$
$168$	5.00000	0.385758
$169$	−13.0000	−1.00000
$170$	0	0
$171$	8.00000	0.611775
$172$	9.00000	0.686244
$173$	−21.0000	−1.59660	−0.798300	−	0.602260i	$-0.794267\pi$
$173$	−21.0000	−1.59660	−0.798300	+	0.602260i	$0.794267\pi$
$174$	−5.00000	−0.379049
$175$	0	0
$176$	1.00000	0.0753778
$177$	4.00000	0.300658
$178$	4.00000	0.299813
$179$	−6.00000	−0.448461	−0.224231	−	0.974536i	$-0.571987\pi$
$179$	−6.00000	−0.448461	−0.224231	+	0.974536i	$0.571987\pi$
$180$	0	0
$181$	−12.0000	−0.891953	−0.445976	−	0.895045i	$-0.647144\pi$
$181$	−12.0000	−0.891953	−0.445976	+	0.895045i	$0.647144\pi$
$182$	0	0
$183$	9.00000	0.665299
$184$	−8.00000	−0.589768
$185$	0	0
$186$	3.00000	0.219971
$187$	3.00000	0.219382
$188$	12.0000	0.875190
$189$	−5.00000	−0.363696
$190$	0	0
$191$	−27.0000	−1.95365	−0.976826	−	0.214036i	$-0.931339\pi$
$191$	−27.0000	−1.95365	−0.976826	+	0.214036i	$0.931339\pi$
$192$	−1.00000	−0.0721688
$193$	−10.0000	−0.719816	−0.359908	−	0.932988i	$-0.617192\pi$
$193$	−10.0000	−0.719816	−0.359908	+	0.932988i	$0.617192\pi$
$194$	−9.00000	−0.646162
$195$	0	0
$196$	18.0000	1.28571
$197$	−6.00000	−0.427482	−0.213741	−	0.976890i	$-0.568565\pi$
$197$	−6.00000	−0.427482	−0.213741	+	0.976890i	$0.568565\pi$
$198$	−1.00000	−0.0710669
$199$	16.0000	1.13421	0.567105	−	0.823646i	$-0.308063\pi$
$199$	16.0000	1.13421	0.567105	+	0.823646i	$0.308063\pi$
$200$	0	0
$201$	−8.00000	−0.564276
$202$	6.00000	0.422159
$203$	−25.0000	−1.75466
$204$	−3.00000	−0.210042
$205$	0	0
$206$	4.00000	0.278693
$207$	8.00000	0.556038
$208$	0	0
$209$	8.00000	0.553372
$210$	0	0
$211$	3.00000	0.206529	0.103264	−	0.994654i	$-0.467071\pi$
$211$	3.00000	0.206529	0.103264	+	0.994654i	$0.467071\pi$
$212$	−5.00000	−0.343401
$213$	−6.00000	−0.411113
$214$	2.00000	0.136717
$215$	0	0
$216$	1.00000	0.0680414
$217$	15.0000	1.01827
$218$	−11.0000	−0.745014
$219$	2.00000	0.135147
$220$	0	0
$221$	0	0
$222$	−1.00000	−0.0671156
$223$	23.0000	1.54019	0.770097	−	0.637927i	$-0.220208\pi$
$223$	23.0000	1.54019	0.770097	+	0.637927i	$0.220208\pi$
$224$	−5.00000	−0.334077
$225$	0	0
$226$	15.0000	0.997785
$227$	−21.0000	−1.39382	−0.696909	−	0.717159i	$-0.745442\pi$
$227$	−21.0000	−1.39382	−0.696909	+	0.717159i	$0.745442\pi$
$228$	−8.00000	−0.529813
$229$	−4.00000	−0.264327	−0.132164	−	0.991228i	$-0.542192\pi$
$229$	−4.00000	−0.264327	−0.132164	+	0.991228i	$0.542192\pi$
$230$	0	0
$231$	−5.00000	−0.328976
$232$	5.00000	0.328266
$233$	6.00000	0.393073	0.196537	−	0.980497i	$-0.437031\pi$
$233$	6.00000	0.393073	0.196537	+	0.980497i	$0.437031\pi$
$234$	0	0
$235$	0	0
$236$	−4.00000	−0.260378
$237$	8.00000	0.519656
$238$	−15.0000	−0.972306
$239$	−19.0000	−1.22901	−0.614504	−	0.788914i	$-0.710644\pi$
$239$	−19.0000	−1.22901	−0.614504	+	0.788914i	$0.710644\pi$
$240$	0	0
$241$	−10.0000	−0.644157	−0.322078	−	0.946713i	$-0.604381\pi$
$241$	−10.0000	−0.644157	−0.322078	+	0.946713i	$0.604381\pi$
$242$	10.0000	0.642824
$243$	−1.00000	−0.0641500
$244$	−9.00000	−0.576166
$245$	0	0
$246$	−5.00000	−0.318788
$247$	0	0
$248$	−3.00000	−0.190500
$249$	−4.00000	−0.253490
$250$	0	0
$251$	0	0		−	1.00000i	$-0.5\pi$
$251$	0	0			1.00000i	$0.5\pi$
$252$	5.00000	0.314970
$253$	8.00000	0.502956
$254$	8.00000	0.501965
$255$	0	0
$256$	1.00000	0.0625000
$257$	26.0000	1.62184	0.810918	−	0.585160i	$-0.198968\pi$
$257$	26.0000	1.62184	0.810918	+	0.585160i	$0.198968\pi$
$258$	9.00000	0.560316
$259$	−5.00000	−0.310685
$260$	0	0
$261$	−5.00000	−0.309492
$262$	6.00000	0.370681
$263$	−5.00000	−0.308313	−0.154157	−	0.988046i	$-0.549266\pi$
$263$	−5.00000	−0.308313	−0.154157	+	0.988046i	$0.549266\pi$
$264$	1.00000	0.0615457
$265$	0	0
$266$	−40.0000	−2.45256
$267$	4.00000	0.244796
$268$	8.00000	0.488678
$269$	−4.00000	−0.243884	−0.121942	−	0.992537i	$-0.538912\pi$
$269$	−4.00000	−0.243884	−0.121942	+	0.992537i	$0.538912\pi$
$270$	0	0
$271$	−14.0000	−0.850439	−0.425220	−	0.905090i	$-0.639803\pi$
$271$	−14.0000	−0.850439	−0.425220	+	0.905090i	$0.639803\pi$
$272$	3.00000	0.181902
$273$	0	0
$274$	−6.00000	−0.362473
$275$	0	0
$276$	−8.00000	−0.481543
$277$	−32.0000	−1.92269	−0.961347	−	0.275340i	$-0.911209\pi$
$277$	−32.0000	−1.92269	−0.961347	+	0.275340i	$0.911209\pi$
$278$	−5.00000	−0.299880
$279$	3.00000	0.179605
$280$	0	0
$281$	30.0000	1.78965	0.894825	−	0.446417i	$-0.147300\pi$
$281$	30.0000	1.78965	0.894825	+	0.446417i	$0.147300\pi$
$282$	12.0000	0.714590
$283$	−16.0000	−0.951101	−0.475551	−	0.879688i	$-0.657751\pi$
$283$	−16.0000	−0.951101	−0.475551	+	0.879688i	$0.657751\pi$
$284$	6.00000	0.356034
$285$	0	0
$286$	0	0
$287$	−25.0000	−1.47570
$288$	−1.00000	−0.0589256
$289$	−8.00000	−0.470588
$290$	0	0
$291$	−9.00000	−0.527589
$292$	−2.00000	−0.117041
$293$	−23.0000	−1.34367	−0.671837	−	0.740699i	$-0.734495\pi$
$293$	−23.0000	−1.34367	−0.671837	+	0.740699i	$0.734495\pi$
$294$	18.0000	1.04978
$295$	0	0
$296$	1.00000	0.0581238
$297$	−1.00000	−0.0580259
$298$	20.0000	1.15857
$299$	0	0
$300$	0	0
$301$	45.0000	2.59376
$302$	10.0000	0.575435
$303$	6.00000	0.344691
$304$	8.00000	0.458831
$305$	0	0
$306$	−3.00000	−0.171499
$307$	−4.00000	−0.228292	−0.114146	−	0.993464i	$-0.536413\pi$
$307$	−4.00000	−0.228292	−0.114146	+	0.993464i	$0.536413\pi$
$308$	5.00000	0.284901
$309$	4.00000	0.227552
$310$	0	0
$311$	17.0000	0.963982	0.481991	−	0.876176i	$-0.339914\pi$
$311$	17.0000	0.963982	0.481991	+	0.876176i	$0.339914\pi$
$312$	0	0
$313$	−26.0000	−1.46961	−0.734803	−	0.678280i	$-0.762726\pi$
$313$	−26.0000	−1.46961	−0.734803	+	0.678280i	$0.762726\pi$
$314$	−11.0000	−0.620766
$315$	0	0
$316$	−8.00000	−0.450035
$317$	11.0000	0.617822	0.308911	−	0.951091i	$-0.400036\pi$
$317$	11.0000	0.617822	0.308911	+	0.951091i	$0.400036\pi$
$318$	−5.00000	−0.280386
$319$	−5.00000	−0.279946
$320$	0	0
$321$	2.00000	0.111629
$322$	−40.0000	−2.22911
$323$	24.0000	1.33540
$324$	1.00000	0.0555556
$325$	0	0
$326$	−1.00000	−0.0553849
$327$	−11.0000	−0.608301
$328$	5.00000	0.276079
$329$	60.0000	3.30791
$330$	0	0
$331$	22.0000	1.20923	0.604615	−	0.796518i	$-0.293327\pi$
$331$	22.0000	1.20923	0.604615	+	0.796518i	$0.293327\pi$
$332$	4.00000	0.219529
$333$	−1.00000	−0.0547997
$334$	−2.00000	−0.109435
$335$	0	0
$336$	−5.00000	−0.272772
$337$	20.0000	1.08947	0.544735	−	0.838608i	$-0.316630\pi$
$337$	20.0000	1.08947	0.544735	+	0.838608i	$0.316630\pi$
$338$	13.0000	0.707107
$339$	15.0000	0.814688
$340$	0	0
$341$	3.00000	0.162459
$342$	−8.00000	−0.432590
$343$	55.0000	2.96972
$344$	−9.00000	−0.485247
$345$	0	0
$346$	21.0000	1.12897
$347$	28.0000	1.50312	0.751559	−	0.659665i	$-0.229302\pi$
$347$	28.0000	1.50312	0.751559	+	0.659665i	$0.229302\pi$
$348$	5.00000	0.268028
$349$	2.00000	0.107058	0.0535288	−	0.998566i	$-0.482953\pi$
$349$	2.00000	0.107058	0.0535288	+	0.998566i	$0.482953\pi$
$350$	0	0
$351$	0	0
$352$	−1.00000	−0.0533002
$353$	19.0000	1.01127	0.505634	−	0.862748i	$-0.331259\pi$
$353$	19.0000	1.01127	0.505634	+	0.862748i	$0.331259\pi$
$354$	−4.00000	−0.212598
$355$	0	0
$356$	−4.00000	−0.212000
$357$	−15.0000	−0.793884
$358$	6.00000	0.317110
$359$	18.0000	0.950004	0.475002	−	0.879985i	$-0.342447\pi$
$359$	18.0000	0.950004	0.475002	+	0.879985i	$0.342447\pi$
$360$	0	0
$361$	45.0000	2.36842
$362$	12.0000	0.630706
$363$	10.0000	0.524864
$364$	0	0
$365$	0	0
$366$	−9.00000	−0.470438
$367$	17.0000	0.887393	0.443696	−	0.896177i	$-0.353667\pi$
$367$	17.0000	0.887393	0.443696	+	0.896177i	$0.353667\pi$
$368$	8.00000	0.417029
$369$	−5.00000	−0.260290
$370$	0	0
$371$	−25.0000	−1.29794
$372$	−3.00000	−0.155543
$373$	−26.0000	−1.34623	−0.673114	−	0.739538i	$-0.735044\pi$
$373$	−26.0000	−1.34623	−0.673114	+	0.739538i	$0.735044\pi$
$374$	−3.00000	−0.155126
$375$	0	0
$376$	−12.0000	−0.618853
$377$	0	0
$378$	5.00000	0.257172
$379$	28.0000	1.43826	0.719132	−	0.694874i	$-0.244540\pi$
$379$	28.0000	1.43826	0.719132	+	0.694874i	$0.244540\pi$
$380$	0	0
$381$	8.00000	0.409852
$382$	27.0000	1.38144
$383$	36.0000	1.83951	0.919757	−	0.392488i	$-0.128386\pi$
$383$	36.0000	1.83951	0.919757	+	0.392488i	$0.128386\pi$
$384$	1.00000	0.0510310
$385$	0	0
$386$	10.0000	0.508987
$387$	9.00000	0.457496
$388$	9.00000	0.456906
$389$	9.00000	0.456318	0.228159	−	0.973624i	$-0.426729\pi$
$389$	9.00000	0.456318	0.228159	+	0.973624i	$0.426729\pi$
$390$	0	0
$391$	24.0000	1.21373
$392$	−18.0000	−0.909137
$393$	6.00000	0.302660
$394$	6.00000	0.302276
$395$	0	0
$396$	1.00000	0.0502519
$397$	−18.0000	−0.903394	−0.451697	−	0.892171i	$-0.649181\pi$
$397$	−18.0000	−0.903394	−0.451697	+	0.892171i	$0.649181\pi$
$398$	−16.0000	−0.802008
$399$	−40.0000	−2.00250
$400$	0	0
$401$	14.0000	0.699127	0.349563	−	0.936913i	$-0.386330\pi$
$401$	14.0000	0.699127	0.349563	+	0.936913i	$0.386330\pi$
$402$	8.00000	0.399004
$403$	0	0
$404$	−6.00000	−0.298511
$405$	0	0
$406$	25.0000	1.24073
$407$	−1.00000	−0.0495682
$408$	3.00000	0.148522
$409$	20.0000	0.988936	0.494468	−	0.869196i	$-0.335363\pi$
$409$	20.0000	0.988936	0.494468	+	0.869196i	$0.335363\pi$
$410$	0	0
$411$	−6.00000	−0.295958
$412$	−4.00000	−0.197066
$413$	−20.0000	−0.984136
$414$	−8.00000	−0.393179
$415$	0	0
$416$	0	0
$417$	−5.00000	−0.244851
$418$	−8.00000	−0.391293
$419$	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
$421$	22.0000	1.07221	0.536107	−	0.844150i	$-0.319894\pi$
$421$	22.0000	1.07221	0.536107	+	0.844150i	$0.319894\pi$
$422$	−3.00000	−0.146038
$423$	12.0000	0.583460
$424$	5.00000	0.242821
$425$	0	0
$426$	6.00000	0.290701
$427$	−45.0000	−2.17770
$428$	−2.00000	−0.0966736
$429$	0	0
$430$	0	0
$431$	−3.00000	−0.144505	−0.0722525	−	0.997386i	$-0.523019\pi$
$431$	−3.00000	−0.144505	−0.0722525	+	0.997386i	$0.523019\pi$
$432$	−1.00000	−0.0481125
$433$	−32.0000	−1.53782	−0.768911	−	0.639356i	$-0.779201\pi$
$433$	−32.0000	−1.53782	−0.768911	+	0.639356i	$0.779201\pi$
$434$	−15.0000	−0.720023
$435$	0	0
$436$	11.0000	0.526804
$437$	64.0000	3.06154
$438$	−2.00000	−0.0955637
$439$	−11.0000	−0.525001	−0.262501	−	0.964932i	$-0.584547\pi$
$439$	−11.0000	−0.525001	−0.262501	+	0.964932i	$0.584547\pi$
$440$	0	0
$441$	18.0000	0.857143
$442$	0	0
$443$	−10.0000	−0.475114	−0.237557	−	0.971374i	$-0.576347\pi$
$443$	−10.0000	−0.475114	−0.237557	+	0.971374i	$0.576347\pi$
$444$	1.00000	0.0474579
$445$	0	0
$446$	−23.0000	−1.08908
$447$	20.0000	0.945968
$448$	5.00000	0.236228
$449$	12.0000	0.566315	0.283158	−	0.959073i	$-0.408618\pi$
$449$	12.0000	0.566315	0.283158	+	0.959073i	$0.408618\pi$
$450$	0	0
$451$	−5.00000	−0.235441
$452$	−15.0000	−0.705541
$453$	10.0000	0.469841
$454$	21.0000	0.985579
$455$	0	0
$456$	8.00000	0.374634
$457$	13.0000	0.608114	0.304057	−	0.952654i	$-0.401659\pi$
$457$	13.0000	0.608114	0.304057	+	0.952654i	$0.401659\pi$
$458$	4.00000	0.186908
$459$	−3.00000	−0.140028
$460$	0	0
$461$	−3.00000	−0.139724	−0.0698620	−	0.997557i	$-0.522256\pi$
$461$	−3.00000	−0.139724	−0.0698620	+	0.997557i	$0.522256\pi$
$462$	5.00000	0.232621
$463$	−20.0000	−0.929479	−0.464739	−	0.885448i	$-0.653852\pi$
$463$	−20.0000	−0.929479	−0.464739	+	0.885448i	$0.653852\pi$
$464$	−5.00000	−0.232119
$465$	0	0
$466$	−6.00000	−0.277945
$467$	−31.0000	−1.43451	−0.717254	−	0.696811i	$-0.754601\pi$
$467$	−31.0000	−1.43451	−0.717254	+	0.696811i	$0.754601\pi$
$468$	0	0
$469$	40.0000	1.84703
$470$	0	0
$471$	−11.0000	−0.506853
$472$	4.00000	0.184115
$473$	9.00000	0.413820
$474$	−8.00000	−0.367452
$475$	0	0
$476$	15.0000	0.687524
$477$	−5.00000	−0.228934
$478$	19.0000	0.869040
$479$	−36.0000	−1.64488	−0.822441	−	0.568850i	$-0.807388\pi$
$479$	−36.0000	−1.64488	−0.822441	+	0.568850i	$0.807388\pi$
$480$	0	0
$481$	0	0
$482$	10.0000	0.455488
$483$	−40.0000	−1.82006
$484$	−10.0000	−0.454545
$485$	0	0
$486$	1.00000	0.0453609
$487$	32.0000	1.45006	0.725029	−	0.688718i	$-0.241826\pi$
$487$	32.0000	1.45006	0.725029	+	0.688718i	$0.241826\pi$
$488$	9.00000	0.407411
$489$	−1.00000	−0.0452216
$490$	0	0
$491$	20.0000	0.902587	0.451294	−	0.892375i	$-0.350963\pi$
$491$	20.0000	0.902587	0.451294	+	0.892375i	$0.350963\pi$
$492$	5.00000	0.225417
$493$	−15.0000	−0.675566
$494$	0	0
$495$	0	0
$496$	3.00000	0.134704
$497$	30.0000	1.34568
$498$	4.00000	0.179244
$499$	−6.00000	−0.268597	−0.134298	−	0.990941i	$-0.542878\pi$
$499$	−6.00000	−0.268597	−0.134298	+	0.990941i	$0.542878\pi$
$500$	0	0
$501$	−2.00000	−0.0893534
$502$	0	0
$503$	10.0000	0.445878	0.222939	−	0.974832i	$-0.428435\pi$
$503$	10.0000	0.445878	0.222939	+	0.974832i	$0.428435\pi$
$504$	−5.00000	−0.222718
$505$	0	0
$506$	−8.00000	−0.355643
$507$	13.0000	0.577350
$508$	−8.00000	−0.354943
$509$	6.00000	0.265945	0.132973	−	0.991120i	$-0.457548\pi$
$509$	6.00000	0.265945	0.132973	+	0.991120i	$0.457548\pi$
$510$	0	0
$511$	−10.0000	−0.442374
$512$	−1.00000	−0.0441942
$513$	−8.00000	−0.353209
$514$	−26.0000	−1.14681
$515$	0	0
$516$	−9.00000	−0.396203
$517$	12.0000	0.527759
$518$	5.00000	0.219687
$519$	21.0000	0.921798
$520$	0	0
$521$	−39.0000	−1.70862	−0.854311	−	0.519763i	$-0.826020\pi$
$521$	−39.0000	−1.70862	−0.854311	+	0.519763i	$0.826020\pi$
$522$	5.00000	0.218844
$523$	−44.0000	−1.92399	−0.961993	−	0.273075i	$-0.911959\pi$
$523$	−44.0000	−1.92399	−0.961993	+	0.273075i	$0.911959\pi$
$524$	−6.00000	−0.262111
$525$	0	0
$526$	5.00000	0.218010
$527$	9.00000	0.392046
$528$	−1.00000	−0.0435194
$529$	41.0000	1.78261
$530$	0	0
$531$	−4.00000	−0.173585
$532$	40.0000	1.73422
$533$	0	0
$534$	−4.00000	−0.173097
$535$	0	0
$536$	−8.00000	−0.345547
$537$	6.00000	0.258919
$538$	4.00000	0.172452
$539$	18.0000	0.775315
$540$	0	0
$541$	−2.00000	−0.0859867	−0.0429934	−	0.999075i	$-0.513689\pi$
$541$	−2.00000	−0.0859867	−0.0429934	+	0.999075i	$0.513689\pi$
$542$	14.0000	0.601351
$543$	12.0000	0.514969
$544$	−3.00000	−0.128624
$545$	0	0
$546$	0	0
$547$	−31.0000	−1.32546	−0.662732	−	0.748857i	$-0.730603\pi$
$547$	−31.0000	−1.32546	−0.662732	+	0.748857i	$0.730603\pi$
$548$	6.00000	0.256307
$549$	−9.00000	−0.384111
$550$	0	0
$551$	−40.0000	−1.70406
$552$	8.00000	0.340503
$553$	−40.0000	−1.70097
$554$	32.0000	1.35955
$555$	0	0
$556$	5.00000	0.212047
$557$	−26.0000	−1.10166	−0.550828	−	0.834619i	$-0.685688\pi$
$557$	−26.0000	−1.10166	−0.550828	+	0.834619i	$0.685688\pi$
$558$	−3.00000	−0.127000
$559$	0	0
$560$	0	0
$561$	−3.00000	−0.126660
$562$	−30.0000	−1.26547
$563$	23.0000	0.969334	0.484667	−	0.874699i	$-0.338941\pi$
$563$	23.0000	0.969334	0.484667	+	0.874699i	$0.338941\pi$
$564$	−12.0000	−0.505291
$565$	0	0
$566$	16.0000	0.672530
$567$	5.00000	0.209980
$568$	−6.00000	−0.251754
$569$	14.0000	0.586911	0.293455	−	0.955973i	$-0.405195\pi$
$569$	14.0000	0.586911	0.293455	+	0.955973i	$0.405195\pi$
$570$	0	0
$571$	35.0000	1.46470	0.732352	−	0.680926i	$-0.238422\pi$
$571$	35.0000	1.46470	0.732352	+	0.680926i	$0.238422\pi$
$572$	0	0
$573$	27.0000	1.12794
$574$	25.0000	1.04348
$575$	0	0
$576$	1.00000	0.0416667
$577$	34.0000	1.41544	0.707719	−	0.706494i	$-0.249724\pi$
$577$	34.0000	1.41544	0.707719	+	0.706494i	$0.249724\pi$
$578$	8.00000	0.332756
$579$	10.0000	0.415586
$580$	0	0
$581$	20.0000	0.829740
$582$	9.00000	0.373062
$583$	−5.00000	−0.207079
$584$	2.00000	0.0827606
$585$	0	0
$586$	23.0000	0.950121
$587$	21.0000	0.866763	0.433381	−	0.901211i	$-0.357320\pi$
$587$	21.0000	0.866763	0.433381	+	0.901211i	$0.357320\pi$
$588$	−18.0000	−0.742307
$589$	24.0000	0.988903
$590$	0	0
$591$	6.00000	0.246807
$592$	−1.00000	−0.0410997
$593$	−36.0000	−1.47834	−0.739171	−	0.673517i	$-0.764783\pi$
$593$	−36.0000	−1.47834	−0.739171	+	0.673517i	$0.764783\pi$
$594$	1.00000	0.0410305
$595$	0	0
$596$	−20.0000	−0.819232
$597$	−16.0000	−0.654836
$598$	0	0
$599$	−28.0000	−1.14405	−0.572024	−	0.820237i	$-0.693842\pi$
$599$	−28.0000	−1.14405	−0.572024	+	0.820237i	$0.693842\pi$
$600$	0	0
$601$	25.0000	1.01977	0.509886	−	0.860242i	$-0.329688\pi$
$601$	25.0000	1.01977	0.509886	+	0.860242i	$0.329688\pi$
$602$	−45.0000	−1.83406
$603$	8.00000	0.325785
$604$	−10.0000	−0.406894
$605$	0	0
$606$	−6.00000	−0.243733
$607$	46.0000	1.86708	0.933541	−	0.358470i	$-0.116702\pi$
$607$	46.0000	1.86708	0.933541	+	0.358470i	$0.116702\pi$
$608$	−8.00000	−0.324443
$609$	25.0000	1.01305
$610$	0	0
$611$	0	0
$612$	3.00000	0.121268
$613$	9.00000	0.363507	0.181753	−	0.983344i	$-0.441823\pi$
$613$	9.00000	0.363507	0.181753	+	0.983344i	$0.441823\pi$
$614$	4.00000	0.161427
$615$	0	0
$616$	−5.00000	−0.201456
$617$	−2.00000	−0.0805170	−0.0402585	−	0.999189i	$-0.512818\pi$
$617$	−2.00000	−0.0805170	−0.0402585	+	0.999189i	$0.512818\pi$
$618$	−4.00000	−0.160904
$619$	17.0000	0.683288	0.341644	−	0.939829i	$-0.389016\pi$
$619$	17.0000	0.683288	0.341644	+	0.939829i	$0.389016\pi$
$620$	0	0
$621$	−8.00000	−0.321029
$622$	−17.0000	−0.681638
$623$	−20.0000	−0.801283
$624$	0	0
$625$	0	0
$626$	26.0000	1.03917
$627$	−8.00000	−0.319489
$628$	11.0000	0.438948
$629$	−3.00000	−0.119618
$630$	0	0
$631$	15.0000	0.597141	0.298570	−	0.954388i	$-0.403490\pi$
$631$	15.0000	0.597141	0.298570	+	0.954388i	$0.403490\pi$
$632$	8.00000	0.318223
$633$	−3.00000	−0.119239
$634$	−11.0000	−0.436866
$635$	0	0
$636$	5.00000	0.198263
$637$	0	0
$638$	5.00000	0.197952
$639$	6.00000	0.237356
$640$	0	0
$641$	−17.0000	−0.671460	−0.335730	−	0.941958i	$-0.608983\pi$
$641$	−17.0000	−0.671460	−0.335730	+	0.941958i	$0.608983\pi$
$642$	−2.00000	−0.0789337
$643$	−19.0000	−0.749287	−0.374643	−	0.927169i	$-0.622235\pi$
$643$	−19.0000	−0.749287	−0.374643	+	0.927169i	$0.622235\pi$
$644$	40.0000	1.57622
$645$	0	0
$646$	−24.0000	−0.944267
$647$	−6.00000	−0.235884	−0.117942	−	0.993020i	$-0.537630\pi$
$647$	−6.00000	−0.235884	−0.117942	+	0.993020i	$0.537630\pi$
$648$	−1.00000	−0.0392837
$649$	−4.00000	−0.157014
$650$	0	0
$651$	−15.0000	−0.587896
$652$	1.00000	0.0391630
$653$	−6.00000	−0.234798	−0.117399	−	0.993085i	$-0.537456\pi$
$653$	−6.00000	−0.234798	−0.117399	+	0.993085i	$0.537456\pi$
$654$	11.0000	0.430134
$655$	0	0
$656$	−5.00000	−0.195217
$657$	−2.00000	−0.0780274
$658$	−60.0000	−2.33904
$659$	−8.00000	−0.311636	−0.155818	−	0.987786i	$-0.549801\pi$
$659$	−8.00000	−0.311636	−0.155818	+	0.987786i	$0.549801\pi$
$660$	0	0
$661$	1.00000	0.0388955	0.0194477	−	0.999811i	$-0.493809\pi$
$661$	1.00000	0.0388955	0.0194477	+	0.999811i	$0.493809\pi$
$662$	−22.0000	−0.855054
$663$	0	0
$664$	−4.00000	−0.155230
$665$	0	0
$666$	1.00000	0.0387492
$667$	−40.0000	−1.54881
$668$	2.00000	0.0773823
$669$	−23.0000	−0.889231
$670$	0	0
$671$	−9.00000	−0.347441
$672$	5.00000	0.192879
$673$	−32.0000	−1.23351	−0.616755	−	0.787155i	$-0.711553\pi$
$673$	−32.0000	−1.23351	−0.616755	+	0.787155i	$0.711553\pi$
$674$	−20.0000	−0.770371
$675$	0	0
$676$	−13.0000	−0.500000
$677$	−18.0000	−0.691796	−0.345898	−	0.938272i	$-0.612426\pi$
$677$	−18.0000	−0.691796	−0.345898	+	0.938272i	$0.612426\pi$
$678$	−15.0000	−0.576072
$679$	45.0000	1.72694
$680$	0	0
$681$	21.0000	0.804722
$682$	−3.00000	−0.114876
$683$	47.0000	1.79841	0.899203	−	0.437533i	$-0.144148\pi$
$683$	47.0000	1.79841	0.899203	+	0.437533i	$0.144148\pi$
$684$	8.00000	0.305888
$685$	0	0
$686$	−55.0000	−2.09991
$687$	4.00000	0.152610
$688$	9.00000	0.343122
$689$	0	0
$690$	0	0
$691$	−21.0000	−0.798878	−0.399439	−	0.916760i	$-0.630795\pi$
$691$	−21.0000	−0.798878	−0.399439	+	0.916760i	$0.630795\pi$
$692$	−21.0000	−0.798300
$693$	5.00000	0.189934
$694$	−28.0000	−1.06287
$695$	0	0
$696$	−5.00000	−0.189525
$697$	−15.0000	−0.568166
$698$	−2.00000	−0.0757011
$699$	−6.00000	−0.226941
$700$	0	0
$701$	30.0000	1.13308	0.566542	−	0.824033i	$-0.308281\pi$
$701$	30.0000	1.13308	0.566542	+	0.824033i	$0.308281\pi$
$702$	0	0
$703$	−8.00000	−0.301726
$704$	1.00000	0.0376889
$705$	0	0
$706$	−19.0000	−0.715074
$707$	−30.0000	−1.12827
$708$	4.00000	0.150329
$709$	3.00000	0.112667	0.0563337	−	0.998412i	$-0.482059\pi$
$709$	3.00000	0.112667	0.0563337	+	0.998412i	$0.482059\pi$
$710$	0	0
$711$	−8.00000	−0.300023
$712$	4.00000	0.149906
$713$	24.0000	0.898807
$714$	15.0000	0.561361
$715$	0	0
$716$	−6.00000	−0.224231
$717$	19.0000	0.709568
$718$	−18.0000	−0.671754
$719$	24.0000	0.895049	0.447524	−	0.894272i	$-0.352306\pi$
$719$	24.0000	0.895049	0.447524	+	0.894272i	$0.352306\pi$
$720$	0	0
$721$	−20.0000	−0.744839
$722$	−45.0000	−1.67473
$723$	10.0000	0.371904
$724$	−12.0000	−0.445976
$725$	0	0
$726$	−10.0000	−0.371135
$727$	26.0000	0.964287	0.482143	−	0.876092i	$-0.339858\pi$
$727$	26.0000	0.964287	0.482143	+	0.876092i	$0.339858\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	0	0
$731$	27.0000	0.998631
$732$	9.00000	0.332650
$733$	49.0000	1.80986	0.904928	−	0.425564i	$-0.139924\pi$
$733$	49.0000	1.80986	0.904928	+	0.425564i	$0.139924\pi$
$734$	−17.0000	−0.627481
$735$	0	0
$736$	−8.00000	−0.294884
$737$	8.00000	0.294684
$738$	5.00000	0.184053
$739$	−43.0000	−1.58178	−0.790890	−	0.611958i	$-0.790382\pi$
$739$	−43.0000	−1.58178	−0.790890	+	0.611958i	$0.790382\pi$
$740$	0	0
$741$	0	0
$742$	25.0000	0.917779
$743$	−17.0000	−0.623670	−0.311835	−	0.950136i	$-0.600944\pi$
$743$	−17.0000	−0.623670	−0.311835	+	0.950136i	$0.600944\pi$
$744$	3.00000	0.109985
$745$	0	0
$746$	26.0000	0.951928
$747$	4.00000	0.146352
$748$	3.00000	0.109691
$749$	−10.0000	−0.365392
$750$	0	0
$751$	−32.0000	−1.16770	−0.583848	−	0.811863i	$-0.698454\pi$
$751$	−32.0000	−1.16770	−0.583848	+	0.811863i	$0.698454\pi$
$752$	12.0000	0.437595
$753$	0	0
$754$	0	0
$755$	0	0
$756$	−5.00000	−0.181848
$757$	32.0000	1.16306	0.581530	−	0.813525i	$-0.302454\pi$
$757$	32.0000	1.16306	0.581530	+	0.813525i	$0.302454\pi$
$758$	−28.0000	−1.01701
$759$	−8.00000	−0.290382
$760$	0	0
$761$	47.0000	1.70375	0.851874	−	0.523746i	$-0.175466\pi$
$761$	47.0000	1.70375	0.851874	+	0.523746i	$0.175466\pi$
$762$	−8.00000	−0.289809
$763$	55.0000	1.99113
$764$	−27.0000	−0.976826
$765$	0	0
$766$	−36.0000	−1.30073
$767$	0	0
$768$	−1.00000	−0.0360844
$769$	−52.0000	−1.87517	−0.937584	−	0.347759i	$-0.886943\pi$
$769$	−52.0000	−1.87517	−0.937584	+	0.347759i	$0.886943\pi$
$770$	0	0
$771$	−26.0000	−0.936367
$772$	−10.0000	−0.359908
$773$	−11.0000	−0.395643	−0.197821	−	0.980238i	$-0.563387\pi$
$773$	−11.0000	−0.395643	−0.197821	+	0.980238i	$0.563387\pi$
$774$	−9.00000	−0.323498
$775$	0	0
$776$	−9.00000	−0.323081
$777$	5.00000	0.179374
$778$	−9.00000	−0.322666
$779$	−40.0000	−1.43315
$780$	0	0
$781$	6.00000	0.214697
$782$	−24.0000	−0.858238
$783$	5.00000	0.178685
$784$	18.0000	0.642857
$785$	0	0
$786$	−6.00000	−0.214013
$787$	−26.0000	−0.926800	−0.463400	−	0.886149i	$-0.653371\pi$
$787$	−26.0000	−0.926800	−0.463400	+	0.886149i	$0.653371\pi$
$788$	−6.00000	−0.213741
$789$	5.00000	0.178005
$790$	0	0
$791$	−75.0000	−2.66669
$792$	−1.00000	−0.0355335
$793$	0	0
$794$	18.0000	0.638796
$795$	0	0
$796$	16.0000	0.567105
$797$	−24.0000	−0.850124	−0.425062	−	0.905164i	$-0.639748\pi$
$797$	−24.0000	−0.850124	−0.425062	+	0.905164i	$0.639748\pi$
$798$	40.0000	1.41598
$799$	36.0000	1.27359
$800$	0	0
$801$	−4.00000	−0.141333
$802$	−14.0000	−0.494357
$803$	−2.00000	−0.0705785
$804$	−8.00000	−0.282138
$805$	0	0
$806$	0	0
$807$	4.00000	0.140807
$808$	6.00000	0.211079
$809$	−36.0000	−1.26569	−0.632846	−	0.774277i	$-0.718114\pi$
$809$	−36.0000	−1.26569	−0.632846	+	0.774277i	$0.718114\pi$
$810$	0	0
$811$	8.00000	0.280918	0.140459	−	0.990086i	$-0.455142\pi$
$811$	8.00000	0.280918	0.140459	+	0.990086i	$0.455142\pi$
$812$	−25.0000	−0.877328
$813$	14.0000	0.491001
$814$	1.00000	0.0350500
$815$	0	0
$816$	−3.00000	−0.105021
$817$	72.0000	2.51896
$818$	−20.0000	−0.699284
$819$	0	0
$820$	0	0
$821$	−30.0000	−1.04701	−0.523504	−	0.852023i	$-0.675375\pi$
$821$	−30.0000	−1.04701	−0.523504	+	0.852023i	$0.675375\pi$
$822$	6.00000	0.209274
$823$	24.0000	0.836587	0.418294	−	0.908312i	$-0.362628\pi$
$823$	24.0000	0.836587	0.418294	+	0.908312i	$0.362628\pi$
$824$	4.00000	0.139347
$825$	0	0
$826$	20.0000	0.695889
$827$	31.0000	1.07798	0.538988	−	0.842314i	$-0.318807\pi$
$827$	31.0000	1.07798	0.538988	+	0.842314i	$0.318807\pi$
$828$	8.00000	0.278019
$829$	−25.0000	−0.868286	−0.434143	−	0.900844i	$-0.642949\pi$
$829$	−25.0000	−0.868286	−0.434143	+	0.900844i	$0.642949\pi$
$830$	0	0
$831$	32.0000	1.11007
$832$	0	0
$833$	54.0000	1.87099
$834$	5.00000	0.173136
$835$	0	0
$836$	8.00000	0.276686
$837$	−3.00000	−0.103695
$838$	−12.0000	−0.414533
$839$	0	0		−	1.00000i	$-0.5\pi$
$839$	0	0			1.00000i	$0.5\pi$
$840$	0	0
$841$	−4.00000	−0.137931
$842$	−22.0000	−0.758170
$843$	−30.0000	−1.03325
$844$	3.00000	0.103264
$845$	0	0
$846$	−12.0000	−0.412568
$847$	−50.0000	−1.71802
$848$	−5.00000	−0.171701
$849$	16.0000	0.549119
$850$	0	0
$851$	−8.00000	−0.274236
$852$	−6.00000	−0.205557
$853$	30.0000	1.02718	0.513590	−	0.858036i	$-0.328315\pi$
$853$	30.0000	1.02718	0.513590	+	0.858036i	$0.328315\pi$
$854$	45.0000	1.53987
$855$	0	0
$856$	2.00000	0.0683586
$857$	−39.0000	−1.33221	−0.666107	−	0.745856i	$-0.732041\pi$
$857$	−39.0000	−1.33221	−0.666107	+	0.745856i	$0.732041\pi$
$858$	0	0
$859$	24.0000	0.818869	0.409435	−	0.912339i	$-0.365726\pi$
$859$	24.0000	0.818869	0.409435	+	0.912339i	$0.365726\pi$
$860$	0	0
$861$	25.0000	0.851998
$862$	3.00000	0.102180
$863$	37.0000	1.25949	0.629747	−	0.776800i	$-0.283158\pi$
$863$	37.0000	1.25949	0.629747	+	0.776800i	$0.283158\pi$
$864$	1.00000	0.0340207
$865$	0	0
$866$	32.0000	1.08740
$867$	8.00000	0.271694
$868$	15.0000	0.509133
$869$	−8.00000	−0.271381
$870$	0	0
$871$	0	0
$872$	−11.0000	−0.372507
$873$	9.00000	0.304604
$874$	−64.0000	−2.16483
$875$	0	0
$876$	2.00000	0.0675737
$877$	−17.0000	−0.574049	−0.287025	−	0.957923i	$-0.592666\pi$
$877$	−17.0000	−0.574049	−0.287025	+	0.957923i	$0.592666\pi$
$878$	11.0000	0.371232
$879$	23.0000	0.775771
$880$	0	0
$881$	−25.0000	−0.842271	−0.421136	−	0.906998i	$-0.638368\pi$
$881$	−25.0000	−0.842271	−0.421136	+	0.906998i	$0.638368\pi$
$882$	−18.0000	−0.606092
$883$	47.0000	1.58168	0.790838	−	0.612026i	$-0.209645\pi$
$883$	47.0000	1.58168	0.790838	+	0.612026i	$0.209645\pi$
$884$	0	0
$885$	0	0
$886$	10.0000	0.335957
$887$	3.00000	0.100730	0.0503651	−	0.998731i	$-0.483962\pi$
$887$	3.00000	0.100730	0.0503651	+	0.998731i	$0.483962\pi$
$888$	−1.00000	−0.0335578
$889$	−40.0000	−1.34156
$890$	0	0
$891$	1.00000	0.0335013
$892$	23.0000	0.770097
$893$	96.0000	3.21252
$894$	−20.0000	−0.668900
$895$	0	0
$896$	−5.00000	−0.167038
$897$	0	0
$898$	−12.0000	−0.400445
$899$	−15.0000	−0.500278
$900$	0	0
$901$	−15.0000	−0.499722
$902$	5.00000	0.166482
$903$	−45.0000	−1.49751
$904$	15.0000	0.498893
$905$	0	0
$906$	−10.0000	−0.332228
$907$	−52.0000	−1.72663	−0.863316	−	0.504664i	$-0.831616\pi$
$907$	−52.0000	−1.72663	−0.863316	+	0.504664i	$0.831616\pi$
$908$	−21.0000	−0.696909
$909$	−6.00000	−0.199007
$910$	0	0
$911$	−60.0000	−1.98789	−0.993944	−	0.109885i	$-0.964952\pi$
$911$	−60.0000	−1.98789	−0.993944	+	0.109885i	$0.964952\pi$
$912$	−8.00000	−0.264906
$913$	4.00000	0.132381
$914$	−13.0000	−0.430002
$915$	0	0
$916$	−4.00000	−0.132164
$917$	−30.0000	−0.990687
$918$	3.00000	0.0990148
$919$	40.0000	1.31948	0.659739	−	0.751495i	$-0.270667\pi$
$919$	40.0000	1.31948	0.659739	+	0.751495i	$0.270667\pi$
$920$	0	0
$921$	4.00000	0.131804
$922$	3.00000	0.0987997
$923$	0	0
$924$	−5.00000	−0.164488
$925$	0	0
$926$	20.0000	0.657241
$927$	−4.00000	−0.131377
$928$	5.00000	0.164133
$929$	25.0000	0.820223	0.410112	−	0.912035i	$-0.365490\pi$
$929$	25.0000	0.820223	0.410112	+	0.912035i	$0.365490\pi$
$930$	0	0
$931$	144.000	4.71941
$932$	6.00000	0.196537
$933$	−17.0000	−0.556555
$934$	31.0000	1.01435
$935$	0	0
$936$	0	0
$937$	0	0		−	1.00000i	$-0.5\pi$
$937$	0	0			1.00000i	$0.5\pi$
$938$	−40.0000	−1.30605
$939$	26.0000	0.848478
$940$	0	0
$941$	30.0000	0.977972	0.488986	−	0.872292i	$-0.337367\pi$
$941$	30.0000	0.977972	0.488986	+	0.872292i	$0.337367\pi$
$942$	11.0000	0.358399
$943$	−40.0000	−1.30258
$944$	−4.00000	−0.130189
$945$	0	0
$946$	−9.00000	−0.292615
$947$	15.0000	0.487435	0.243717	−	0.969846i	$-0.421633\pi$
$947$	15.0000	0.487435	0.243717	+	0.969846i	$0.421633\pi$
$948$	8.00000	0.259828
$949$	0	0
$950$	0	0
$951$	−11.0000	−0.356699
$952$	−15.0000	−0.486153
$953$	−22.0000	−0.712650	−0.356325	−	0.934362i	$-0.615970\pi$
$953$	−22.0000	−0.712650	−0.356325	+	0.934362i	$0.615970\pi$
$954$	5.00000	0.161881
$955$	0	0
$956$	−19.0000	−0.614504
$957$	5.00000	0.161627
$958$	36.0000	1.16311
$959$	30.0000	0.968751
$960$	0	0
$961$	−22.0000	−0.709677
$962$	0	0
$963$	−2.00000	−0.0644491
$964$	−10.0000	−0.322078
$965$	0	0
$966$	40.0000	1.28698
$967$	−34.0000	−1.09337	−0.546683	−	0.837340i	$-0.684110\pi$
$967$	−34.0000	−1.09337	−0.546683	+	0.837340i	$0.684110\pi$
$968$	10.0000	0.321412
$969$	−24.0000	−0.770991
$970$	0	0
$971$	−5.00000	−0.160458	−0.0802288	−	0.996776i	$-0.525565\pi$
$971$	−5.00000	−0.160458	−0.0802288	+	0.996776i	$0.525565\pi$
$972$	−1.00000	−0.0320750
$973$	25.0000	0.801463
$974$	−32.0000	−1.02535
$975$	0	0
$976$	−9.00000	−0.288083
$977$	47.0000	1.50366	0.751832	−	0.659355i	$-0.229171\pi$
$977$	47.0000	1.50366	0.751832	+	0.659355i	$0.229171\pi$
$978$	1.00000	0.0319765
$979$	−4.00000	−0.127841
$980$	0	0
$981$	11.0000	0.351203
$982$	−20.0000	−0.638226
$983$	−15.0000	−0.478426	−0.239213	−	0.970967i	$-0.576889\pi$
$983$	−15.0000	−0.478426	−0.239213	+	0.970967i	$0.576889\pi$
$984$	−5.00000	−0.159394
$985$	0	0
$986$	15.0000	0.477697
$987$	−60.0000	−1.90982
$988$	0	0
$989$	72.0000	2.28947
$990$	0	0
$991$	25.0000	0.794151	0.397076	−	0.917786i	$-0.370025\pi$
$991$	25.0000	0.794151	0.397076	+	0.917786i	$0.370025\pi$
$992$	−3.00000	−0.0952501
$993$	−22.0000	−0.698149
$994$	−30.0000	−0.951542
$995$	0	0
$996$	−4.00000	−0.126745
$997$	−60.0000	−1.90022	−0.950110	−	0.311916i	$-0.899029\pi$
$997$	−60.0000	−1.90022	−0.950110	+	0.311916i	$0.899029\pi$
$998$	6.00000	0.189927
$999$	1.00000	0.0316386

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5550.2.a.l.1.1		1
5.2	odd	4		1110.2.d.b.889.1	✓	2
5.3	odd	4		1110.2.d.b.889.2	yes	2
5.4	even	2		5550.2.a.be.1.1		1
15.2	even	4		3330.2.d.e.1999.2		2
15.8	even	4		3330.2.d.e.1999.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.d.b.889.1	✓	2	5.2	odd	4
1110.2.d.b.889.2	yes	2	5.3	odd	4
3330.2.d.e.1999.1		2	15.8	even	4
3330.2.d.e.1999.2		2	15.2	even	4
5550.2.a.l.1.1		1	1.1	even	1	trivial
5550.2.a.be.1.1		1	5.4	even	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:	\( N \)	\(=\)	\( 5550 = 2 \cdot 3 \cdot 5^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5550.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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