LMFDB - Embedded newform 1110.2.a.d.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(1,1110)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1110, 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("1110.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.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:	$8.86339462436$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	1110.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} +3.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$

\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} +3.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} -5.00000 q^{11} -1.00000 q^{12} -2.00000 q^{13} -3.00000 q^{14} -1.00000 q^{15} +1.00000 q^{16} -7.00000 q^{17} -1.00000 q^{18} -2.00000 q^{19} +1.00000 q^{20} -3.00000 q^{21} +5.00000 q^{22} +4.00000 q^{23} +1.00000 q^{24} +1.00000 q^{25} +2.00000 q^{26} -1.00000 q^{27} +3.00000 q^{28} -5.00000 q^{29} +1.00000 q^{30} -7.00000 q^{31} -1.00000 q^{32} +5.00000 q^{33} +7.00000 q^{34} +3.00000 q^{35} +1.00000 q^{36} +1.00000 q^{37} +2.00000 q^{38} +2.00000 q^{39} -1.00000 q^{40} +1.00000 q^{41} +3.00000 q^{42} +9.00000 q^{43} -5.00000 q^{44} +1.00000 q^{45} -4.00000 q^{46} -1.00000 q^{48} +2.00000 q^{49} -1.00000 q^{50} +7.00000 q^{51} -2.00000 q^{52} +3.00000 q^{53} +1.00000 q^{54} -5.00000 q^{55} -3.00000 q^{56} +2.00000 q^{57} +5.00000 q^{58} -14.0000 q^{59} -1.00000 q^{60} -7.00000 q^{61} +7.00000 q^{62} +3.00000 q^{63} +1.00000 q^{64} -2.00000 q^{65} -5.00000 q^{66} -4.00000 q^{67} -7.00000 q^{68} -4.00000 q^{69} -3.00000 q^{70} +8.00000 q^{71} -1.00000 q^{72} -12.0000 q^{73} -1.00000 q^{74} -1.00000 q^{75} -2.00000 q^{76} -15.0000 q^{77} -2.00000 q^{78} +4.00000 q^{79} +1.00000 q^{80} +1.00000 q^{81} -1.00000 q^{82} -10.0000 q^{83} -3.00000 q^{84} -7.00000 q^{85} -9.00000 q^{86} +5.00000 q^{87} +5.00000 q^{88} -14.0000 q^{89} -1.00000 q^{90} -6.00000 q^{91} +4.00000 q^{92} +7.00000 q^{93} -2.00000 q^{95} +1.00000 q^{96} +1.00000 q^{97} -2.00000 q^{98} -5.00000 q^{99} +O(q^{100})\)

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
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	1.00000	0.408248
$7$	3.00000	1.13389	0.566947	−	0.823754i	$-0.308125\pi$
$7$	3.00000	1.13389	0.566947	+	0.823754i	$0.308125\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−1.00000	−0.316228
$11$	−5.00000	−1.50756	−0.753778	−	0.657129i	$-0.771771\pi$
$11$	−5.00000	−1.50756	−0.753778	+	0.657129i	$0.771771\pi$
$12$	−1.00000	−0.288675
$13$	−2.00000	−0.554700	−0.277350	−	0.960769i	$-0.589456\pi$
$13$	−2.00000	−0.554700	−0.277350	+	0.960769i	$0.589456\pi$
$14$	−3.00000	−0.801784
$15$	−1.00000	−0.258199
$16$	1.00000	0.250000
$17$	−7.00000	−1.69775	−0.848875	−	0.528594i	$-0.822719\pi$
$17$	−7.00000	−1.69775	−0.848875	+	0.528594i	$0.822719\pi$
$18$	−1.00000	−0.235702
$19$	−2.00000	−0.458831	−0.229416	−	0.973329i	$-0.573682\pi$
$19$	−2.00000	−0.458831	−0.229416	+	0.973329i	$0.573682\pi$
$20$	1.00000	0.223607
$21$	−3.00000	−0.654654
$22$	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	$0.363071\pi$
$24$	1.00000	0.204124
$25$	1.00000	0.200000
$26$	2.00000	0.392232
$27$	−1.00000	−0.192450
$28$	3.00000	0.566947
$29$	−5.00000	−0.928477	−0.464238	−	0.885710i	$-0.653672\pi$
$29$	−5.00000	−0.928477	−0.464238	+	0.885710i	$0.653672\pi$
$30$	1.00000	0.182574
$31$	−7.00000	−1.25724	−0.628619	−	0.777714i	$-0.716379\pi$
$31$	−7.00000	−1.25724	−0.628619	+	0.777714i	$0.716379\pi$
$32$	−1.00000	−0.176777
$33$	5.00000	0.870388
$34$	7.00000	1.20049
$35$	3.00000	0.507093
$36$	1.00000	0.166667
$37$	1.00000	0.164399
$37$	1.00000	0.164399
$38$	2.00000	0.324443
$39$	2.00000	0.320256
$40$	−1.00000	−0.158114
$41$	1.00000	0.156174	0.0780869	−	0.996947i	$-0.475119\pi$
$41$	1.00000	0.156174	0.0780869	+	0.996947i	$0.475119\pi$
$42$	3.00000	0.462910
$43$	9.00000	1.37249	0.686244	−	0.727372i	$-0.259258\pi$
$43$	9.00000	1.37249	0.686244	+	0.727372i	$0.259258\pi$
$44$	−5.00000	−0.753778
$45$	1.00000	0.149071
$46$	−4.00000	−0.589768
$47$	0	0		−	1.00000i	$-0.5\pi$
$47$	0	0			1.00000i	$0.5\pi$
$48$	−1.00000	−0.144338
$49$	2.00000	0.285714
$50$	−1.00000	−0.141421
$51$	7.00000	0.980196
$52$	−2.00000	−0.277350
$53$	3.00000	0.412082	0.206041	−	0.978543i	$-0.433942\pi$
$53$	3.00000	0.412082	0.206041	+	0.978543i	$0.433942\pi$
$54$	1.00000	0.136083
$55$	−5.00000	−0.674200
$56$	−3.00000	−0.400892
$57$	2.00000	0.264906
$58$	5.00000	0.656532
$59$	−14.0000	−1.82264	−0.911322	−	0.411693i	$-0.864937\pi$
$59$	−14.0000	−1.82264	−0.911322	+	0.411693i	$0.864937\pi$
$60$	−1.00000	−0.129099
$61$	−7.00000	−0.896258	−0.448129	−	0.893969i	$-0.647910\pi$
$61$	−7.00000	−0.896258	−0.448129	+	0.893969i	$0.647910\pi$
$62$	7.00000	0.889001
$63$	3.00000	0.377964
$64$	1.00000	0.125000
$65$	−2.00000	−0.248069
$66$	−5.00000	−0.615457
$67$	−4.00000	−0.488678	−0.244339	−	0.969690i	$-0.578571\pi$
$67$	−4.00000	−0.488678	−0.244339	+	0.969690i	$0.578571\pi$
$68$	−7.00000	−0.848875
$69$	−4.00000	−0.481543
$70$	−3.00000	−0.358569
$71$	8.00000	0.949425	0.474713	−	0.880141i	$-0.342552\pi$
$71$	8.00000	0.949425	0.474713	+	0.880141i	$0.342552\pi$
$72$	−1.00000	−0.117851
$73$	−12.0000	−1.40449	−0.702247	−	0.711934i	$-0.747820\pi$
$73$	−12.0000	−1.40449	−0.702247	+	0.711934i	$0.747820\pi$
$74$	−1.00000	−0.116248
$75$	−1.00000	−0.115470
$76$	−2.00000	−0.229416
$77$	−15.0000	−1.70941
$78$	−2.00000	−0.226455
$79$	4.00000	0.450035	0.225018	−	0.974355i	$-0.427756\pi$
$79$	4.00000	0.450035	0.225018	+	0.974355i	$0.427756\pi$
$80$	1.00000	0.111803
$81$	1.00000	0.111111
$82$	−1.00000	−0.110432
$83$	−10.0000	−1.09764	−0.548821	−	0.835940i	$-0.684923\pi$
$83$	−10.0000	−1.09764	−0.548821	+	0.835940i	$0.684923\pi$
$84$	−3.00000	−0.327327
$85$	−7.00000	−0.759257
$86$	−9.00000	−0.970495
$87$	5.00000	0.536056
$88$	5.00000	0.533002
$89$	−14.0000	−1.48400	−0.741999	−	0.670402i	$-0.766122\pi$
$89$	−14.0000	−1.48400	−0.741999	+	0.670402i	$0.766122\pi$
$90$	−1.00000	−0.105409
$91$	−6.00000	−0.628971
$92$	4.00000	0.417029
$93$	7.00000	0.725866
$94$	0	0
$95$	−2.00000	−0.205196
$96$	1.00000	0.102062
$97$	1.00000	0.101535	0.0507673	−	0.998711i	$-0.483833\pi$
$97$	1.00000	0.101535	0.0507673	+	0.998711i	$0.483833\pi$
$98$	−2.00000	−0.202031
$99$	−5.00000	−0.502519
$100$	1.00000	0.100000
$101$	0	0		−	1.00000i	$-0.5\pi$
$101$	0	0			1.00000i	$0.5\pi$
$102$	−7.00000	−0.693103
$103$	8.00000	0.788263	0.394132	−	0.919054i	$-0.371045\pi$
$103$	8.00000	0.788263	0.394132	+	0.919054i	$0.371045\pi$
$104$	2.00000	0.196116
$105$	−3.00000	−0.292770
$106$	−3.00000	−0.291386
$107$	14.0000	1.35343	0.676716	−	0.736245i	$-0.263403\pi$
$107$	14.0000	1.35343	0.676716	+	0.736245i	$0.263403\pi$
$108$	−1.00000	−0.0962250
$109$	−7.00000	−0.670478	−0.335239	−	0.942133i	$-0.608817\pi$
$109$	−7.00000	−0.670478	−0.335239	+	0.942133i	$0.608817\pi$
$110$	5.00000	0.476731
$111$	−1.00000	−0.0949158
$112$	3.00000	0.283473
$113$	−5.00000	−0.470360	−0.235180	−	0.971952i	$-0.575568\pi$
$113$	−5.00000	−0.470360	−0.235180	+	0.971952i	$0.575568\pi$
$114$	−2.00000	−0.187317
$115$	4.00000	0.373002
$116$	−5.00000	−0.464238
$117$	−2.00000	−0.184900
$118$	14.0000	1.28880
$119$	−21.0000	−1.92507
$120$	1.00000	0.0912871
$121$	14.0000	1.27273
$122$	7.00000	0.633750
$123$	−1.00000	−0.0901670
$124$	−7.00000	−0.628619
$125$	1.00000	0.0894427
$126$	−3.00000	−0.267261
$127$	16.0000	1.41977	0.709885	−	0.704317i	$-0.248747\pi$
$127$	16.0000	1.41977	0.709885	+	0.704317i	$0.248747\pi$
$128$	−1.00000	−0.0883883
$129$	−9.00000	−0.792406
$130$	2.00000	0.175412
$131$	−6.00000	−0.524222	−0.262111	−	0.965038i	$-0.584419\pi$
$131$	−6.00000	−0.524222	−0.262111	+	0.965038i	$0.584419\pi$
$132$	5.00000	0.435194
$133$	−6.00000	−0.520266
$134$	4.00000	0.345547
$135$	−1.00000	−0.0860663
$136$	7.00000	0.600245
$137$	−22.0000	−1.87959	−0.939793	−	0.341743i	$-0.888983\pi$
$137$	−22.0000	−1.87959	−0.939793	+	0.341743i	$0.888983\pi$
$138$	4.00000	0.340503
$139$	−3.00000	−0.254457	−0.127228	−	0.991873i	$-0.540608\pi$
$139$	−3.00000	−0.254457	−0.127228	+	0.991873i	$0.540608\pi$
$140$	3.00000	0.253546
$141$	0	0
$142$	−8.00000	−0.671345
$143$	10.0000	0.836242
$144$	1.00000	0.0833333
$145$	−5.00000	−0.415227
$146$	12.0000	0.993127
$147$	−2.00000	−0.164957
$148$	1.00000	0.0821995
$149$	−6.00000	−0.491539	−0.245770	−	0.969328i	$-0.579041\pi$
$149$	−6.00000	−0.491539	−0.245770	+	0.969328i	$0.579041\pi$
$150$	1.00000	0.0816497
$151$	10.0000	0.813788	0.406894	−	0.913475i	$-0.366612\pi$
$151$	10.0000	0.813788	0.406894	+	0.913475i	$0.366612\pi$
$152$	2.00000	0.162221
$153$	−7.00000	−0.565916
$154$	15.0000	1.20873
$155$	−7.00000	−0.562254
$156$	2.00000	0.160128
$157$	−11.0000	−0.877896	−0.438948	−	0.898513i	$-0.644649\pi$
$157$	−11.0000	−0.877896	−0.438948	+	0.898513i	$0.644649\pi$
$158$	−4.00000	−0.318223
$159$	−3.00000	−0.237915
$160$	−1.00000	−0.0790569
$161$	12.0000	0.945732
$162$	−1.00000	−0.0785674
$163$	−15.0000	−1.17489	−0.587445	−	0.809264i	$-0.699866\pi$
$163$	−15.0000	−1.17489	−0.587445	+	0.809264i	$0.699866\pi$
$164$	1.00000	0.0780869
$165$	5.00000	0.389249
$166$	10.0000	0.776151
$167$	20.0000	1.54765	0.773823	−	0.633402i	$-0.218342\pi$
$167$	20.0000	1.54765	0.773823	+	0.633402i	$0.218342\pi$
$168$	3.00000	0.231455
$169$	−9.00000	−0.692308
$170$	7.00000	0.536875
$171$	−2.00000	−0.152944
$172$	9.00000	0.686244
$173$	19.0000	1.44454	0.722272	−	0.691609i	$-0.243098\pi$
$173$	19.0000	1.44454	0.722272	+	0.691609i	$0.243098\pi$
$174$	−5.00000	−0.379049
$175$	3.00000	0.226779
$176$	−5.00000	−0.376889
$177$	14.0000	1.05230
$178$	14.0000	1.04934
$179$	−24.0000	−1.79384	−0.896922	−	0.442189i	$-0.854202\pi$
$179$	−24.0000	−1.79384	−0.896922	+	0.442189i	$0.854202\pi$
$180$	1.00000	0.0745356
$181$	14.0000	1.04061	0.520306	−	0.853980i	$-0.325818\pi$
$181$	14.0000	1.04061	0.520306	+	0.853980i	$0.325818\pi$
$182$	6.00000	0.444750
$183$	7.00000	0.517455
$184$	−4.00000	−0.294884
$185$	1.00000	0.0735215
$186$	−7.00000	−0.513265
$187$	35.0000	2.55945
$188$	0	0
$189$	−3.00000	−0.218218
$190$	2.00000	0.145095
$191$	−7.00000	−0.506502	−0.253251	−	0.967401i	$-0.581500\pi$
$191$	−7.00000	−0.506502	−0.253251	+	0.967401i	$0.581500\pi$
$192$	−1.00000	−0.0721688
$193$	14.0000	1.00774	0.503871	−	0.863779i	$-0.331909\pi$
$193$	14.0000	1.00774	0.503871	+	0.863779i	$0.331909\pi$
$194$	−1.00000	−0.0717958
$195$	2.00000	0.143223
$196$	2.00000	0.142857
$197$	10.0000	0.712470	0.356235	−	0.934396i	$-0.384060\pi$
$197$	10.0000	0.712470	0.356235	+	0.934396i	$0.384060\pi$
$198$	5.00000	0.355335
$199$	4.00000	0.283552	0.141776	−	0.989899i	$-0.454719\pi$
$199$	4.00000	0.283552	0.141776	+	0.989899i	$0.454719\pi$
$200$	−1.00000	−0.0707107
$201$	4.00000	0.282138
$202$	0	0
$203$	−15.0000	−1.05279
$204$	7.00000	0.490098
$205$	1.00000	0.0698430
$206$	−8.00000	−0.557386
$207$	4.00000	0.278019
$208$	−2.00000	−0.138675
$209$	10.0000	0.691714
$210$	3.00000	0.207020
$211$	−13.0000	−0.894957	−0.447478	−	0.894295i	$-0.647678\pi$
$211$	−13.0000	−0.894957	−0.447478	+	0.894295i	$0.647678\pi$
$212$	3.00000	0.206041
$213$	−8.00000	−0.548151
$214$	−14.0000	−0.957020
$215$	9.00000	0.613795
$216$	1.00000	0.0680414
$217$	−21.0000	−1.42557
$218$	7.00000	0.474100
$219$	12.0000	0.810885
$220$	−5.00000	−0.337100
$221$	14.0000	0.941742
$222$	1.00000	0.0671156
$223$	9.00000	0.602685	0.301342	−	0.953516i	$-0.402565\pi$
$223$	9.00000	0.602685	0.301342	+	0.953516i	$0.402565\pi$
$224$	−3.00000	−0.200446
$225$	1.00000	0.0666667
$226$	5.00000	0.332595
$227$	−7.00000	−0.464606	−0.232303	−	0.972643i	$-0.574626\pi$
$227$	−7.00000	−0.464606	−0.232303	+	0.972643i	$0.574626\pi$
$228$	2.00000	0.132453
$229$	−28.0000	−1.85029	−0.925146	−	0.379611i	$-0.876058\pi$
$229$	−28.0000	−1.85029	−0.925146	+	0.379611i	$0.876058\pi$
$230$	−4.00000	−0.263752
$231$	15.0000	0.986928
$232$	5.00000	0.328266
$233$	−20.0000	−1.31024	−0.655122	−	0.755523i	$-0.727383\pi$
$233$	−20.0000	−1.31024	−0.655122	+	0.755523i	$0.727383\pi$
$234$	2.00000	0.130744
$235$	0	0
$236$	−14.0000	−0.911322
$237$	−4.00000	−0.259828
$238$	21.0000	1.36123
$239$	17.0000	1.09964	0.549819	−	0.835284i	$-0.314697\pi$
$239$	17.0000	1.09964	0.549819	+	0.835284i	$0.314697\pi$
$240$	−1.00000	−0.0645497
$241$	−2.00000	−0.128831	−0.0644157	−	0.997923i	$-0.520518\pi$
$241$	−2.00000	−0.128831	−0.0644157	+	0.997923i	$0.520518\pi$
$242$	−14.0000	−0.899954
$243$	−1.00000	−0.0641500
$244$	−7.00000	−0.448129
$245$	2.00000	0.127775
$246$	1.00000	0.0637577
$247$	4.00000	0.254514
$248$	7.00000	0.444500
$249$	10.0000	0.633724
$250$	−1.00000	−0.0632456
$251$	0	0		−	1.00000i	$-0.5\pi$
$251$	0	0			1.00000i	$0.5\pi$
$252$	3.00000	0.188982
$253$	−20.0000	−1.25739
$254$	−16.0000	−1.00393
$255$	7.00000	0.438357
$256$	1.00000	0.0625000
$257$	14.0000	0.873296	0.436648	−	0.899632i	$-0.356166\pi$
$257$	14.0000	0.873296	0.436648	+	0.899632i	$0.356166\pi$
$258$	9.00000	0.560316
$259$	3.00000	0.186411
$260$	−2.00000	−0.124035
$261$	−5.00000	−0.309492
$262$	6.00000	0.370681
$263$	11.0000	0.678289	0.339145	−	0.940734i	$-0.389862\pi$
$263$	11.0000	0.678289	0.339145	+	0.940734i	$0.389862\pi$
$264$	−5.00000	−0.307729
$265$	3.00000	0.184289
$266$	6.00000	0.367884
$267$	14.0000	0.856786
$268$	−4.00000	−0.244339
$269$	16.0000	0.975537	0.487769	−	0.872973i	$-0.337811\pi$
$269$	16.0000	0.975537	0.487769	+	0.872973i	$0.337811\pi$
$270$	1.00000	0.0608581
$271$	20.0000	1.21491	0.607457	−	0.794353i	$-0.292190\pi$
$271$	20.0000	1.21491	0.607457	+	0.794353i	$0.292190\pi$
$272$	−7.00000	−0.424437
$273$	6.00000	0.363137
$274$	22.0000	1.32907
$275$	−5.00000	−0.301511
$276$	−4.00000	−0.240772
$277$	16.0000	0.961347	0.480673	−	0.876900i	$-0.340392\pi$
$277$	16.0000	0.961347	0.480673	+	0.876900i	$0.340392\pi$
$278$	3.00000	0.179928
$279$	−7.00000	−0.419079
$280$	−3.00000	−0.179284
$281$	10.0000	0.596550	0.298275	−	0.954480i	$-0.403589\pi$
$281$	10.0000	0.596550	0.298275	+	0.954480i	$0.403589\pi$
$282$	0	0
$283$	−12.0000	−0.713326	−0.356663	−	0.934233i	$-0.616086\pi$
$283$	−12.0000	−0.713326	−0.356663	+	0.934233i	$0.616086\pi$
$284$	8.00000	0.474713
$285$	2.00000	0.118470
$286$	−10.0000	−0.591312
$287$	3.00000	0.177084
$288$	−1.00000	−0.0589256
$289$	32.0000	1.88235
$290$	5.00000	0.293610
$291$	−1.00000	−0.0586210
$292$	−12.0000	−0.702247
$293$	9.00000	0.525786	0.262893	−	0.964825i	$-0.415323\pi$
$293$	9.00000	0.525786	0.262893	+	0.964825i	$0.415323\pi$
$294$	2.00000	0.116642
$295$	−14.0000	−0.815112
$296$	−1.00000	−0.0581238
$297$	5.00000	0.290129
$298$	6.00000	0.347571
$299$	−8.00000	−0.462652
$300$	−1.00000	−0.0577350
$301$	27.0000	1.55625
$302$	−10.0000	−0.575435
$303$	0	0
$304$	−2.00000	−0.114708
$305$	−7.00000	−0.400819
$306$	7.00000	0.400163
$307$	6.00000	0.342438	0.171219	−	0.985233i	$-0.445229\pi$
$307$	6.00000	0.342438	0.171219	+	0.985233i	$0.445229\pi$
$308$	−15.0000	−0.854704
$309$	−8.00000	−0.455104
$310$	7.00000	0.397573
$311$	21.0000	1.19080	0.595400	−	0.803429i	$-0.296993\pi$
$311$	21.0000	1.19080	0.595400	+	0.803429i	$0.296993\pi$
$312$	−2.00000	−0.113228
$313$	−10.0000	−0.565233	−0.282617	−	0.959233i	$-0.591202\pi$
$313$	−10.0000	−0.565233	−0.282617	+	0.959233i	$0.591202\pi$
$314$	11.0000	0.620766
$315$	3.00000	0.169031
$316$	4.00000	0.225018
$317$	−21.0000	−1.17948	−0.589739	−	0.807594i	$-0.700769\pi$
$317$	−21.0000	−1.17948	−0.589739	+	0.807594i	$0.700769\pi$
$318$	3.00000	0.168232
$319$	25.0000	1.39973
$320$	1.00000	0.0559017
$321$	−14.0000	−0.781404
$322$	−12.0000	−0.668734
$323$	14.0000	0.778981
$324$	1.00000	0.0555556
$325$	−2.00000	−0.110940
$326$	15.0000	0.830773
$327$	7.00000	0.387101
$328$	−1.00000	−0.0552158
$329$	0	0
$330$	−5.00000	−0.275241
$331$	0	0		−	1.00000i	$-0.5\pi$
$331$	0	0			1.00000i	$0.5\pi$
$332$	−10.0000	−0.548821
$333$	1.00000	0.0547997
$334$	−20.0000	−1.09435
$335$	−4.00000	−0.218543
$336$	−3.00000	−0.163663
$337$	−22.0000	−1.19842	−0.599208	−	0.800593i	$-0.704518\pi$
$337$	−22.0000	−1.19842	−0.599208	+	0.800593i	$0.704518\pi$
$338$	9.00000	0.489535
$339$	5.00000	0.271563
$340$	−7.00000	−0.379628
$341$	35.0000	1.89536
$342$	2.00000	0.108148
$343$	−15.0000	−0.809924
$344$	−9.00000	−0.485247
$345$	−4.00000	−0.215353
$346$	−19.0000	−1.02145
$347$	−12.0000	−0.644194	−0.322097	−	0.946707i	$-0.604388\pi$
$347$	−12.0000	−0.644194	−0.322097	+	0.946707i	$0.604388\pi$
$348$	5.00000	0.268028
$349$	−16.0000	−0.856460	−0.428230	−	0.903670i	$-0.640863\pi$
$349$	−16.0000	−0.856460	−0.428230	+	0.903670i	$0.640863\pi$
$350$	−3.00000	−0.160357
$351$	2.00000	0.106752
$352$	5.00000	0.266501
$353$	17.0000	0.904819	0.452409	−	0.891810i	$-0.350565\pi$
$353$	17.0000	0.904819	0.452409	+	0.891810i	$0.350565\pi$
$354$	−14.0000	−0.744092
$355$	8.00000	0.424596
$356$	−14.0000	−0.741999
$357$	21.0000	1.11144
$358$	24.0000	1.26844
$359$	34.0000	1.79445	0.897226	−	0.441572i	$-0.145579\pi$
$359$	34.0000	1.79445	0.897226	+	0.441572i	$0.145579\pi$
$360$	−1.00000	−0.0527046
$361$	−15.0000	−0.789474
$362$	−14.0000	−0.735824
$363$	−14.0000	−0.734809
$364$	−6.00000	−0.314485
$365$	−12.0000	−0.628109
$366$	−7.00000	−0.365896
$367$	−13.0000	−0.678594	−0.339297	−	0.940679i	$-0.610189\pi$
$367$	−13.0000	−0.678594	−0.339297	+	0.940679i	$0.610189\pi$
$368$	4.00000	0.208514
$369$	1.00000	0.0520579
$370$	−1.00000	−0.0519875
$371$	9.00000	0.467257
$372$	7.00000	0.362933
$373$	22.0000	1.13912	0.569558	−	0.821951i	$-0.307114\pi$
$373$	22.0000	1.13912	0.569558	+	0.821951i	$0.307114\pi$
$374$	−35.0000	−1.80981
$375$	−1.00000	−0.0516398
$376$	0	0
$377$	10.0000	0.515026
$378$	3.00000	0.154303
$379$	16.0000	0.821865	0.410932	−	0.911666i	$-0.365203\pi$
$379$	16.0000	0.821865	0.410932	+	0.911666i	$0.365203\pi$
$380$	−2.00000	−0.102598
$381$	−16.0000	−0.819705
$382$	7.00000	0.358151
$383$	4.00000	0.204390	0.102195	−	0.994764i	$-0.467413\pi$
$383$	4.00000	0.204390	0.102195	+	0.994764i	$0.467413\pi$
$384$	1.00000	0.0510310
$385$	−15.0000	−0.764471
$386$	−14.0000	−0.712581
$387$	9.00000	0.457496
$388$	1.00000	0.0507673
$389$	−31.0000	−1.57176	−0.785881	−	0.618378i	$-0.787790\pi$
$389$	−31.0000	−1.57176	−0.785881	+	0.618378i	$0.787790\pi$
$390$	−2.00000	−0.101274
$391$	−28.0000	−1.41602
$392$	−2.00000	−0.101015
$393$	6.00000	0.302660
$394$	−10.0000	−0.503793
$395$	4.00000	0.201262
$396$	−5.00000	−0.251259
$397$	−34.0000	−1.70641	−0.853206	−	0.521575i	$-0.825345\pi$
$397$	−34.0000	−1.70641	−0.853206	+	0.521575i	$0.825345\pi$
$398$	−4.00000	−0.200502
$399$	6.00000	0.300376
$400$	1.00000	0.0500000
$401$	22.0000	1.09863	0.549314	−	0.835616i	$-0.314889\pi$
$401$	22.0000	1.09863	0.549314	+	0.835616i	$0.314889\pi$
$402$	−4.00000	−0.199502
$403$	14.0000	0.697390
$404$	0	0
$405$	1.00000	0.0496904
$406$	15.0000	0.744438
$407$	−5.00000	−0.247841
$408$	−7.00000	−0.346552
$409$	34.0000	1.68119	0.840596	−	0.541663i	$-0.182205\pi$
$409$	34.0000	1.68119	0.840596	+	0.541663i	$0.182205\pi$
$410$	−1.00000	−0.0493865
$411$	22.0000	1.08518
$412$	8.00000	0.394132
$413$	−42.0000	−2.06668
$414$	−4.00000	−0.196589
$415$	−10.0000	−0.490881
$416$	2.00000	0.0980581
$417$	3.00000	0.146911
$418$	−10.0000	−0.489116
$419$	20.0000	0.977064	0.488532	−	0.872546i	$-0.337533\pi$
$419$	20.0000	0.977064	0.488532	+	0.872546i	$0.337533\pi$
$420$	−3.00000	−0.146385
$421$	10.0000	0.487370	0.243685	−	0.969854i	$-0.421644\pi$
$421$	10.0000	0.487370	0.243685	+	0.969854i	$0.421644\pi$
$422$	13.0000	0.632830
$423$	0	0
$424$	−3.00000	−0.145693
$425$	−7.00000	−0.339550
$426$	8.00000	0.387601
$427$	−21.0000	−1.01626
$428$	14.0000	0.676716
$429$	−10.0000	−0.482805
$430$	−9.00000	−0.434019
$431$	21.0000	1.01153	0.505767	−	0.862670i	$-0.331209\pi$
$431$	21.0000	1.01153	0.505767	+	0.862670i	$0.331209\pi$
$432$	−1.00000	−0.0481125
$433$	−16.0000	−0.768911	−0.384455	−	0.923144i	$-0.625611\pi$
$433$	−16.0000	−0.768911	−0.384455	+	0.923144i	$0.625611\pi$
$434$	21.0000	1.00803
$435$	5.00000	0.239732
$436$	−7.00000	−0.335239
$437$	−8.00000	−0.382692
$438$	−12.0000	−0.573382
$439$	−33.0000	−1.57500	−0.787502	−	0.616312i	$-0.788626\pi$
$439$	−33.0000	−1.57500	−0.787502	+	0.616312i	$0.788626\pi$
$440$	5.00000	0.238366
$441$	2.00000	0.0952381
$442$	−14.0000	−0.665912
$443$	42.0000	1.99548	0.997740	−	0.0671913i	$-0.0214038\pi$
$443$	42.0000	1.99548	0.997740	+	0.0671913i	$0.0214038\pi$
$444$	−1.00000	−0.0474579
$445$	−14.0000	−0.663664
$446$	−9.00000	−0.426162
$447$	6.00000	0.283790
$448$	3.00000	0.141737
$449$	−12.0000	−0.566315	−0.283158	−	0.959073i	$-0.591382\pi$
$449$	−12.0000	−0.566315	−0.283158	+	0.959073i	$0.591382\pi$
$450$	−1.00000	−0.0471405
$451$	−5.00000	−0.235441
$452$	−5.00000	−0.235180
$453$	−10.0000	−0.469841
$454$	7.00000	0.328526
$455$	−6.00000	−0.281284
$456$	−2.00000	−0.0936586
$457$	−39.0000	−1.82434	−0.912172	−	0.409809i	$-0.865595\pi$
$457$	−39.0000	−1.82434	−0.912172	+	0.409809i	$0.865595\pi$
$458$	28.0000	1.30835
$459$	7.00000	0.326732
$460$	4.00000	0.186501
$461$	−15.0000	−0.698620	−0.349310	−	0.937007i	$-0.613584\pi$
$461$	−15.0000	−0.698620	−0.349310	+	0.937007i	$0.613584\pi$
$462$	−15.0000	−0.697863
$463$	−6.00000	−0.278844	−0.139422	−	0.990233i	$-0.544524\pi$
$463$	−6.00000	−0.278844	−0.139422	+	0.990233i	$0.544524\pi$
$464$	−5.00000	−0.232119
$465$	7.00000	0.324617
$466$	20.0000	0.926482
$467$	3.00000	0.138823	0.0694117	−	0.997588i	$-0.477888\pi$
$467$	3.00000	0.138823	0.0694117	+	0.997588i	$0.477888\pi$
$468$	−2.00000	−0.0924500
$469$	−12.0000	−0.554109
$470$	0	0
$471$	11.0000	0.506853
$472$	14.0000	0.644402
$473$	−45.0000	−2.06910
$474$	4.00000	0.183726
$475$	−2.00000	−0.0917663
$476$	−21.0000	−0.962533
$477$	3.00000	0.137361
$478$	−17.0000	−0.777562
$479$	−24.0000	−1.09659	−0.548294	−	0.836286i	$-0.684723\pi$
$479$	−24.0000	−1.09659	−0.548294	+	0.836286i	$0.684723\pi$
$480$	1.00000	0.0456435
$481$	−2.00000	−0.0911922
$482$	2.00000	0.0910975
$483$	−12.0000	−0.546019
$484$	14.0000	0.636364
$485$	1.00000	0.0454077
$486$	1.00000	0.0453609
$487$	−30.0000	−1.35943	−0.679715	−	0.733476i	$-0.737896\pi$
$487$	−30.0000	−1.35943	−0.679715	+	0.733476i	$0.737896\pi$
$488$	7.00000	0.316875
$489$	15.0000	0.678323
$490$	−2.00000	−0.0903508
$491$	28.0000	1.26362	0.631811	−	0.775122i	$-0.282312\pi$
$491$	28.0000	1.26362	0.631811	+	0.775122i	$0.282312\pi$
$492$	−1.00000	−0.0450835
$493$	35.0000	1.57632
$494$	−4.00000	−0.179969
$495$	−5.00000	−0.224733
$496$	−7.00000	−0.314309
$497$	24.0000	1.07655
$498$	−10.0000	−0.448111
$499$	4.00000	0.179065	0.0895323	−	0.995984i	$-0.471463\pi$
$499$	4.00000	0.179065	0.0895323	+	0.995984i	$0.471463\pi$
$500$	1.00000	0.0447214
$501$	−20.0000	−0.893534
$502$	0	0
$503$	24.0000	1.07011	0.535054	−	0.844818i	$-0.320291\pi$
$503$	24.0000	1.07011	0.535054	+	0.844818i	$0.320291\pi$
$504$	−3.00000	−0.133631
$505$	0	0
$506$	20.0000	0.889108
$507$	9.00000	0.399704
$508$	16.0000	0.709885
$509$	−20.0000	−0.886484	−0.443242	−	0.896402i	$-0.646172\pi$
$509$	−20.0000	−0.886484	−0.443242	+	0.896402i	$0.646172\pi$
$510$	−7.00000	−0.309965
$511$	−36.0000	−1.59255
$512$	−1.00000	−0.0441942
$513$	2.00000	0.0883022
$514$	−14.0000	−0.617514
$515$	8.00000	0.352522
$516$	−9.00000	−0.396203
$517$	0	0
$518$	−3.00000	−0.131812
$519$	−19.0000	−0.834007
$520$	2.00000	0.0877058
$521$	3.00000	0.131432	0.0657162	−	0.997838i	$-0.479067\pi$
$521$	3.00000	0.131432	0.0657162	+	0.997838i	$0.479067\pi$
$522$	5.00000	0.218844
$523$	16.0000	0.699631	0.349816	−	0.936819i	$-0.386244\pi$
$523$	16.0000	0.699631	0.349816	+	0.936819i	$0.386244\pi$
$524$	−6.00000	−0.262111
$525$	−3.00000	−0.130931
$526$	−11.0000	−0.479623
$527$	49.0000	2.13447
$528$	5.00000	0.217597
$529$	−7.00000	−0.304348
$530$	−3.00000	−0.130312
$531$	−14.0000	−0.607548
$532$	−6.00000	−0.260133
$533$	−2.00000	−0.0866296
$534$	−14.0000	−0.605839
$535$	14.0000	0.605273
$536$	4.00000	0.172774
$537$	24.0000	1.03568
$538$	−16.0000	−0.689809
$539$	−10.0000	−0.430730
$540$	−1.00000	−0.0430331
$541$	42.0000	1.80572	0.902861	−	0.429934i	$-0.141463\pi$
$541$	42.0000	1.80572	0.902861	+	0.429934i	$0.141463\pi$
$542$	−20.0000	−0.859074
$543$	−14.0000	−0.600798
$544$	7.00000	0.300123
$545$	−7.00000	−0.299847
$546$	−6.00000	−0.256776
$547$	−7.00000	−0.299298	−0.149649	−	0.988739i	$-0.547814\pi$
$547$	−7.00000	−0.299298	−0.149649	+	0.988739i	$0.547814\pi$
$548$	−22.0000	−0.939793
$549$	−7.00000	−0.298753
$550$	5.00000	0.213201
$551$	10.0000	0.426014
$552$	4.00000	0.170251
$553$	12.0000	0.510292
$554$	−16.0000	−0.679775
$555$	−1.00000	−0.0424476
$556$	−3.00000	−0.127228
$557$	−18.0000	−0.762684	−0.381342	−	0.924434i	$-0.624538\pi$
$557$	−18.0000	−0.762684	−0.381342	+	0.924434i	$0.624538\pi$
$558$	7.00000	0.296334
$559$	−18.0000	−0.761319
$560$	3.00000	0.126773
$561$	−35.0000	−1.47770
$562$	−10.0000	−0.421825
$563$	−3.00000	−0.126435	−0.0632175	−	0.998000i	$-0.520136\pi$
$563$	−3.00000	−0.126435	−0.0632175	+	0.998000i	$0.520136\pi$
$564$	0	0
$565$	−5.00000	−0.210352
$566$	12.0000	0.504398
$567$	3.00000	0.125988
$568$	−8.00000	−0.335673
$569$	−10.0000	−0.419222	−0.209611	−	0.977785i	$-0.567220\pi$
$569$	−10.0000	−0.419222	−0.209611	+	0.977785i	$0.567220\pi$
$570$	−2.00000	−0.0837708
$571$	27.0000	1.12991	0.564957	−	0.825120i	$-0.308893\pi$
$571$	27.0000	1.12991	0.564957	+	0.825120i	$0.308893\pi$
$572$	10.0000	0.418121
$573$	7.00000	0.292429
$574$	−3.00000	−0.125218
$575$	4.00000	0.166812
$576$	1.00000	0.0416667
$577$	10.0000	0.416305	0.208153	−	0.978096i	$-0.433255\pi$
$577$	10.0000	0.416305	0.208153	+	0.978096i	$0.433255\pi$
$578$	−32.0000	−1.33102
$579$	−14.0000	−0.581820
$580$	−5.00000	−0.207614
$581$	−30.0000	−1.24461
$582$	1.00000	0.0414513
$583$	−15.0000	−0.621237
$584$	12.0000	0.496564
$585$	−2.00000	−0.0826898
$586$	−9.00000	−0.371787
$587$	−21.0000	−0.866763	−0.433381	−	0.901211i	$-0.642680\pi$
$587$	−21.0000	−0.866763	−0.433381	+	0.901211i	$0.642680\pi$
$588$	−2.00000	−0.0824786
$589$	14.0000	0.576860
$590$	14.0000	0.576371
$591$	−10.0000	−0.411345
$592$	1.00000	0.0410997
$593$	46.0000	1.88899	0.944497	−	0.328521i	$-0.106550\pi$
$593$	46.0000	1.88899	0.944497	+	0.328521i	$0.106550\pi$
$594$	−5.00000	−0.205152
$595$	−21.0000	−0.860916
$596$	−6.00000	−0.245770
$597$	−4.00000	−0.163709
$598$	8.00000	0.327144
$599$	−24.0000	−0.980613	−0.490307	−	0.871550i	$-0.663115\pi$
$599$	−24.0000	−0.980613	−0.490307	+	0.871550i	$0.663115\pi$
$600$	1.00000	0.0408248
$601$	−7.00000	−0.285536	−0.142768	−	0.989756i	$-0.545600\pi$
$601$	−7.00000	−0.285536	−0.142768	+	0.989756i	$0.545600\pi$
$602$	−27.0000	−1.10044
$603$	−4.00000	−0.162893
$604$	10.0000	0.406894
$605$	14.0000	0.569181
$606$	0	0
$607$	−14.0000	−0.568242	−0.284121	−	0.958788i	$-0.591702\pi$
$607$	−14.0000	−0.568242	−0.284121	+	0.958788i	$0.591702\pi$
$608$	2.00000	0.0811107
$609$	15.0000	0.607831
$610$	7.00000	0.283422
$611$	0	0
$612$	−7.00000	−0.282958
$613$	43.0000	1.73675	0.868377	−	0.495905i	$-0.165164\pi$
$613$	43.0000	1.73675	0.868377	+	0.495905i	$0.165164\pi$
$614$	−6.00000	−0.242140
$615$	−1.00000	−0.0403239
$616$	15.0000	0.604367
$617$	6.00000	0.241551	0.120775	−	0.992680i	$-0.461462\pi$
$617$	6.00000	0.241551	0.120775	+	0.992680i	$0.461462\pi$
$618$	8.00000	0.321807
$619$	5.00000	0.200967	0.100483	−	0.994939i	$-0.467961\pi$
$619$	5.00000	0.200967	0.100483	+	0.994939i	$0.467961\pi$
$620$	−7.00000	−0.281127
$621$	−4.00000	−0.160514
$622$	−21.0000	−0.842023
$623$	−42.0000	−1.68269
$624$	2.00000	0.0800641
$625$	1.00000	0.0400000
$626$	10.0000	0.399680
$627$	−10.0000	−0.399362
$628$	−11.0000	−0.438948
$629$	−7.00000	−0.279108
$630$	−3.00000	−0.119523
$631$	−7.00000	−0.278666	−0.139333	−	0.990246i	$-0.544496\pi$
$631$	−7.00000	−0.278666	−0.139333	+	0.990246i	$0.544496\pi$
$632$	−4.00000	−0.159111
$633$	13.0000	0.516704
$634$	21.0000	0.834017
$635$	16.0000	0.634941
$636$	−3.00000	−0.118958
$637$	−4.00000	−0.158486
$638$	−25.0000	−0.989759
$639$	8.00000	0.316475
$640$	−1.00000	−0.0395285
$641$	41.0000	1.61940	0.809701	−	0.586842i	$-0.199629\pi$
$641$	41.0000	1.61940	0.809701	+	0.586842i	$0.199629\pi$
$642$	14.0000	0.552536
$643$	−43.0000	−1.69575	−0.847877	−	0.530193i	$-0.822120\pi$
$643$	−43.0000	−1.69575	−0.847877	+	0.530193i	$0.822120\pi$
$644$	12.0000	0.472866
$645$	−9.00000	−0.354375
$646$	−14.0000	−0.550823
$647$	40.0000	1.57256	0.786281	−	0.617869i	$-0.212004\pi$
$647$	40.0000	1.57256	0.786281	+	0.617869i	$0.212004\pi$
$648$	−1.00000	−0.0392837
$649$	70.0000	2.74774
$650$	2.00000	0.0784465
$651$	21.0000	0.823055
$652$	−15.0000	−0.587445
$653$	36.0000	1.40879	0.704394	−	0.709809i	$-0.251219\pi$
$653$	36.0000	1.40879	0.704394	+	0.709809i	$0.251219\pi$
$654$	−7.00000	−0.273722
$655$	−6.00000	−0.234439
$656$	1.00000	0.0390434
$657$	−12.0000	−0.468165
$658$	0	0
$659$	0	0		−	1.00000i	$-0.5\pi$
$659$	0	0			1.00000i	$0.5\pi$
$660$	5.00000	0.194625
$661$	31.0000	1.20576	0.602880	−	0.797832i	$-0.294020\pi$
$661$	31.0000	1.20576	0.602880	+	0.797832i	$0.294020\pi$
$662$	0	0
$663$	−14.0000	−0.543715
$664$	10.0000	0.388075
$665$	−6.00000	−0.232670
$666$	−1.00000	−0.0387492
$667$	−20.0000	−0.774403
$668$	20.0000	0.773823
$669$	−9.00000	−0.347960
$670$	4.00000	0.154533
$671$	35.0000	1.35116
$672$	3.00000	0.115728
$673$	−8.00000	−0.308377	−0.154189	−	0.988041i	$-0.549276\pi$
$673$	−8.00000	−0.308377	−0.154189	+	0.988041i	$0.549276\pi$
$674$	22.0000	0.847408
$675$	−1.00000	−0.0384900
$676$	−9.00000	−0.346154
$677$	−42.0000	−1.61419	−0.807096	−	0.590421i	$-0.798962\pi$
$677$	−42.0000	−1.61419	−0.807096	+	0.590421i	$0.798962\pi$
$678$	−5.00000	−0.192024
$679$	3.00000	0.115129
$680$	7.00000	0.268438
$681$	7.00000	0.268241
$682$	−35.0000	−1.34022
$683$	−47.0000	−1.79841	−0.899203	−	0.437533i	$-0.855852\pi$
$683$	−47.0000	−1.79841	−0.899203	+	0.437533i	$0.855852\pi$
$684$	−2.00000	−0.0764719
$685$	−22.0000	−0.840577
$686$	15.0000	0.572703
$687$	28.0000	1.06827
$688$	9.00000	0.343122
$689$	−6.00000	−0.228582
$690$	4.00000	0.152277
$691$	−41.0000	−1.55971	−0.779857	−	0.625958i	$-0.784708\pi$
$691$	−41.0000	−1.55971	−0.779857	+	0.625958i	$0.784708\pi$
$692$	19.0000	0.722272
$693$	−15.0000	−0.569803
$694$	12.0000	0.455514
$695$	−3.00000	−0.113796
$696$	−5.00000	−0.189525
$697$	−7.00000	−0.265144
$698$	16.0000	0.605609
$699$	20.0000	0.756469
$700$	3.00000	0.113389
$701$	−34.0000	−1.28416	−0.642081	−	0.766637i	$-0.721929\pi$
$701$	−34.0000	−1.28416	−0.642081	+	0.766637i	$0.721929\pi$
$702$	−2.00000	−0.0754851
$703$	−2.00000	−0.0754314
$704$	−5.00000	−0.188445
$705$	0	0
$706$	−17.0000	−0.639803
$707$	0	0
$708$	14.0000	0.526152
$709$	−27.0000	−1.01401	−0.507003	−	0.861944i	$-0.669247\pi$
$709$	−27.0000	−1.01401	−0.507003	+	0.861944i	$0.669247\pi$
$710$	−8.00000	−0.300235
$711$	4.00000	0.150012
$712$	14.0000	0.524672
$713$	−28.0000	−1.04861
$714$	−21.0000	−0.785905
$715$	10.0000	0.373979
$716$	−24.0000	−0.896922
$717$	−17.0000	−0.634877
$718$	−34.0000	−1.26887
$719$	34.0000	1.26799	0.633993	−	0.773339i	$-0.281415\pi$
$719$	34.0000	1.26799	0.633993	+	0.773339i	$0.281415\pi$
$720$	1.00000	0.0372678
$721$	24.0000	0.893807
$722$	15.0000	0.558242
$723$	2.00000	0.0743808
$724$	14.0000	0.520306
$725$	−5.00000	−0.185695
$726$	14.0000	0.519589
$727$	−18.0000	−0.667583	−0.333792	−	0.942647i	$-0.608328\pi$
$727$	−18.0000	−0.667583	−0.333792	+	0.942647i	$0.608328\pi$
$728$	6.00000	0.222375
$729$	1.00000	0.0370370
$730$	12.0000	0.444140
$731$	−63.0000	−2.33014
$732$	7.00000	0.258727
$733$	−13.0000	−0.480166	−0.240083	−	0.970752i	$-0.577175\pi$
$733$	−13.0000	−0.480166	−0.240083	+	0.970752i	$0.577175\pi$
$734$	13.0000	0.479839
$735$	−2.00000	−0.0737711
$736$	−4.00000	−0.147442
$737$	20.0000	0.736709
$738$	−1.00000	−0.0368105
$739$	33.0000	1.21392	0.606962	−	0.794731i	$-0.292388\pi$
$739$	33.0000	1.21392	0.606962	+	0.794731i	$0.292388\pi$
$740$	1.00000	0.0367607
$741$	−4.00000	−0.146944
$742$	−9.00000	−0.330400
$743$	−13.0000	−0.476924	−0.238462	−	0.971152i	$-0.576643\pi$
$743$	−13.0000	−0.476924	−0.238462	+	0.971152i	$0.576643\pi$
$744$	−7.00000	−0.256632
$745$	−6.00000	−0.219823
$746$	−22.0000	−0.805477
$747$	−10.0000	−0.365881
$748$	35.0000	1.27973
$749$	42.0000	1.53465
$750$	1.00000	0.0365148
$751$	20.0000	0.729810	0.364905	−	0.931045i	$-0.381101\pi$
$751$	20.0000	0.729810	0.364905	+	0.931045i	$0.381101\pi$
$752$	0	0
$753$	0	0
$754$	−10.0000	−0.364179
$755$	10.0000	0.363937
$756$	−3.00000	−0.109109
$757$	22.0000	0.799604	0.399802	−	0.916602i	$-0.369079\pi$
$757$	22.0000	0.799604	0.399802	+	0.916602i	$0.369079\pi$
$758$	−16.0000	−0.581146
$759$	20.0000	0.725954
$760$	2.00000	0.0725476
$761$	−47.0000	−1.70375	−0.851874	−	0.523746i	$-0.824534\pi$
$761$	−47.0000	−1.70375	−0.851874	+	0.523746i	$0.824534\pi$
$762$	16.0000	0.579619
$763$	−21.0000	−0.760251
$764$	−7.00000	−0.253251
$765$	−7.00000	−0.253086
$766$	−4.00000	−0.144526
$767$	28.0000	1.01102
$768$	−1.00000	−0.0360844
$769$	2.00000	0.0721218	0.0360609	−	0.999350i	$-0.488519\pi$
$769$	2.00000	0.0721218	0.0360609	+	0.999350i	$0.488519\pi$
$770$	15.0000	0.540562
$771$	−14.0000	−0.504198
$772$	14.0000	0.503871
$773$	33.0000	1.18693	0.593464	−	0.804861i	$-0.297760\pi$
$773$	33.0000	1.18693	0.593464	+	0.804861i	$0.297760\pi$
$774$	−9.00000	−0.323498
$775$	−7.00000	−0.251447
$776$	−1.00000	−0.0358979
$777$	−3.00000	−0.107624
$778$	31.0000	1.11140
$779$	−2.00000	−0.0716574
$780$	2.00000	0.0716115
$781$	−40.0000	−1.43131
$782$	28.0000	1.00128
$783$	5.00000	0.178685
$784$	2.00000	0.0714286
$785$	−11.0000	−0.392607
$786$	−6.00000	−0.214013
$787$	−4.00000	−0.142585	−0.0712923	−	0.997455i	$-0.522712\pi$
$787$	−4.00000	−0.142585	−0.0712923	+	0.997455i	$0.522712\pi$
$788$	10.0000	0.356235
$789$	−11.0000	−0.391610
$790$	−4.00000	−0.142314
$791$	−15.0000	−0.533339
$792$	5.00000	0.177667
$793$	14.0000	0.497155
$794$	34.0000	1.20661
$795$	−3.00000	−0.106399
$796$	4.00000	0.141776
$797$	32.0000	1.13350	0.566749	−	0.823890i	$-0.308201\pi$
$797$	32.0000	1.13350	0.566749	+	0.823890i	$0.308201\pi$
$798$	−6.00000	−0.212398
$799$	0	0
$800$	−1.00000	−0.0353553
$801$	−14.0000	−0.494666
$802$	−22.0000	−0.776847
$803$	60.0000	2.11735
$804$	4.00000	0.141069
$805$	12.0000	0.422944
$806$	−14.0000	−0.493129
$807$	−16.0000	−0.563227
$808$	0	0
$809$	−4.00000	−0.140633	−0.0703163	−	0.997525i	$-0.522401\pi$
$809$	−4.00000	−0.140633	−0.0703163	+	0.997525i	$0.522401\pi$
$810$	−1.00000	−0.0351364
$811$	20.0000	0.702295	0.351147	−	0.936320i	$-0.385792\pi$
$811$	20.0000	0.702295	0.351147	+	0.936320i	$0.385792\pi$
$812$	−15.0000	−0.526397
$813$	−20.0000	−0.701431
$814$	5.00000	0.175250
$815$	−15.0000	−0.525427
$816$	7.00000	0.245049
$817$	−18.0000	−0.629740
$818$	−34.0000	−1.18878
$819$	−6.00000	−0.209657
$820$	1.00000	0.0349215
$821$	−6.00000	−0.209401	−0.104701	−	0.994504i	$-0.533388\pi$
$821$	−6.00000	−0.209401	−0.104701	+	0.994504i	$0.533388\pi$
$822$	−22.0000	−0.767338
$823$	−32.0000	−1.11545	−0.557725	−	0.830026i	$-0.688326\pi$
$823$	−32.0000	−1.11545	−0.557725	+	0.830026i	$0.688326\pi$
$824$	−8.00000	−0.278693
$825$	5.00000	0.174078
$826$	42.0000	1.46137
$827$	21.0000	0.730242	0.365121	−	0.930960i	$-0.381028\pi$
$827$	21.0000	0.730242	0.365121	+	0.930960i	$0.381028\pi$
$828$	4.00000	0.139010
$829$	29.0000	1.00721	0.503606	−	0.863934i	$-0.332006\pi$
$829$	29.0000	1.00721	0.503606	+	0.863934i	$0.332006\pi$
$830$	10.0000	0.347105
$831$	−16.0000	−0.555034
$832$	−2.00000	−0.0693375
$833$	−14.0000	−0.485071
$834$	−3.00000	−0.103882
$835$	20.0000	0.692129
$836$	10.0000	0.345857
$837$	7.00000	0.241955
$838$	−20.0000	−0.690889
$839$	18.0000	0.621429	0.310715	−	0.950503i	$-0.399432\pi$
$839$	18.0000	0.621429	0.310715	+	0.950503i	$0.399432\pi$
$840$	3.00000	0.103510
$841$	−4.00000	−0.137931
$842$	−10.0000	−0.344623
$843$	−10.0000	−0.344418
$844$	−13.0000	−0.447478
$845$	−9.00000	−0.309609
$846$	0	0
$847$	42.0000	1.44314
$848$	3.00000	0.103020
$849$	12.0000	0.411839
$850$	7.00000	0.240098
$851$	4.00000	0.137118
$852$	−8.00000	−0.274075
$853$	6.00000	0.205436	0.102718	−	0.994711i	$-0.467246\pi$
$853$	6.00000	0.205436	0.102718	+	0.994711i	$0.467246\pi$
$854$	21.0000	0.718605
$855$	−2.00000	−0.0683986
$856$	−14.0000	−0.478510
$857$	39.0000	1.33221	0.666107	−	0.745856i	$-0.267959\pi$
$857$	39.0000	1.33221	0.666107	+	0.745856i	$0.267959\pi$
$858$	10.0000	0.341394
$859$	−6.00000	−0.204717	−0.102359	−	0.994748i	$-0.532639\pi$
$859$	−6.00000	−0.204717	−0.102359	+	0.994748i	$0.532639\pi$
$860$	9.00000	0.306897
$861$	−3.00000	−0.102240
$862$	−21.0000	−0.715263
$863$	−51.0000	−1.73606	−0.868030	−	0.496512i	$-0.834614\pi$
$863$	−51.0000	−1.73606	−0.868030	+	0.496512i	$0.834614\pi$
$864$	1.00000	0.0340207
$865$	19.0000	0.646019
$866$	16.0000	0.543702
$867$	−32.0000	−1.08678
$868$	−21.0000	−0.712786
$869$	−20.0000	−0.678454
$870$	−5.00000	−0.169516
$871$	8.00000	0.271070
$872$	7.00000	0.237050
$873$	1.00000	0.0338449
$874$	8.00000	0.270604
$875$	3.00000	0.101419
$876$	12.0000	0.405442
$877$	−3.00000	−0.101303	−0.0506514	−	0.998716i	$-0.516130\pi$
$877$	−3.00000	−0.101303	−0.0506514	+	0.998716i	$0.516130\pi$
$878$	33.0000	1.11370
$879$	−9.00000	−0.303562
$880$	−5.00000	−0.168550
$881$	−15.0000	−0.505363	−0.252681	−	0.967550i	$-0.581312\pi$
$881$	−15.0000	−0.505363	−0.252681	+	0.967550i	$0.581312\pi$
$882$	−2.00000	−0.0673435
$883$	−49.0000	−1.64898	−0.824491	−	0.565876i	$-0.808538\pi$
$883$	−49.0000	−1.64898	−0.824491	+	0.565876i	$0.808538\pi$
$884$	14.0000	0.470871
$885$	14.0000	0.470605
$886$	−42.0000	−1.41102
$887$	15.0000	0.503651	0.251825	−	0.967773i	$-0.418969\pi$
$887$	15.0000	0.503651	0.251825	+	0.967773i	$0.418969\pi$
$888$	1.00000	0.0335578
$889$	48.0000	1.60987
$890$	14.0000	0.469281
$891$	−5.00000	−0.167506
$892$	9.00000	0.301342
$893$	0	0
$894$	−6.00000	−0.200670
$895$	−24.0000	−0.802232
$896$	−3.00000	−0.100223
$897$	8.00000	0.267112
$898$	12.0000	0.400445
$899$	35.0000	1.16732
$900$	1.00000	0.0333333
$901$	−21.0000	−0.699611
$902$	5.00000	0.166482
$903$	−27.0000	−0.898504
$904$	5.00000	0.166298
$905$	14.0000	0.465376
$906$	10.0000	0.332228
$907$	−36.0000	−1.19536	−0.597680	−	0.801735i	$-0.703911\pi$
$907$	−36.0000	−1.19536	−0.597680	+	0.801735i	$0.703911\pi$
$908$	−7.00000	−0.232303
$909$	0	0
$910$	6.00000	0.198898
$911$	−40.0000	−1.32526	−0.662630	−	0.748947i	$-0.730560\pi$
$911$	−40.0000	−1.32526	−0.662630	+	0.748947i	$0.730560\pi$
$912$	2.00000	0.0662266
$913$	50.0000	1.65476
$914$	39.0000	1.29001
$915$	7.00000	0.231413
$916$	−28.0000	−0.925146
$917$	−18.0000	−0.594412
$918$	−7.00000	−0.231034
$919$	0	0		−	1.00000i	$-0.5\pi$
$919$	0	0			1.00000i	$0.5\pi$
$920$	−4.00000	−0.131876
$921$	−6.00000	−0.197707
$922$	15.0000	0.493999
$923$	−16.0000	−0.526646
$924$	15.0000	0.493464
$925$	1.00000	0.0328798
$926$	6.00000	0.197172
$927$	8.00000	0.262754
$928$	5.00000	0.164133
$929$	−41.0000	−1.34517	−0.672583	−	0.740022i	$-0.734815\pi$
$929$	−41.0000	−1.34517	−0.672583	+	0.740022i	$0.734815\pi$
$930$	−7.00000	−0.229539
$931$	−4.00000	−0.131095
$932$	−20.0000	−0.655122
$933$	−21.0000	−0.687509
$934$	−3.00000	−0.0981630
$935$	35.0000	1.14462
$936$	2.00000	0.0653720
$937$	32.0000	1.04539	0.522697	−	0.852518i	$-0.324926\pi$
$937$	32.0000	1.04539	0.522697	+	0.852518i	$0.324926\pi$
$938$	12.0000	0.391814
$939$	10.0000	0.326338
$940$	0	0
$941$	6.00000	0.195594	0.0977972	−	0.995206i	$-0.468820\pi$
$941$	6.00000	0.195594	0.0977972	+	0.995206i	$0.468820\pi$
$942$	−11.0000	−0.358399
$943$	4.00000	0.130258
$944$	−14.0000	−0.455661
$945$	−3.00000	−0.0975900
$946$	45.0000	1.46308
$947$	49.0000	1.59229	0.796143	−	0.605108i	$-0.206870\pi$
$947$	49.0000	1.59229	0.796143	+	0.605108i	$0.206870\pi$
$948$	−4.00000	−0.129914
$949$	24.0000	0.779073
$950$	2.00000	0.0648886
$951$	21.0000	0.680972
$952$	21.0000	0.680614
$953$	−4.00000	−0.129573	−0.0647864	−	0.997899i	$-0.520637\pi$
$953$	−4.00000	−0.129573	−0.0647864	+	0.997899i	$0.520637\pi$
$954$	−3.00000	−0.0971286
$955$	−7.00000	−0.226515
$956$	17.0000	0.549819
$957$	−25.0000	−0.808135
$958$	24.0000	0.775405
$959$	−66.0000	−2.13125
$960$	−1.00000	−0.0322749
$961$	18.0000	0.580645
$962$	2.00000	0.0644826
$963$	14.0000	0.451144
$964$	−2.00000	−0.0644157
$965$	14.0000	0.450676
$966$	12.0000	0.386094
$967$	−4.00000	−0.128631	−0.0643157	−	0.997930i	$-0.520486\pi$
$967$	−4.00000	−0.128631	−0.0643157	+	0.997930i	$0.520486\pi$
$968$	−14.0000	−0.449977
$969$	−14.0000	−0.449745
$970$	−1.00000	−0.0321081
$971$	53.0000	1.70085	0.850425	−	0.526096i	$-0.176345\pi$
$971$	53.0000	1.70085	0.850425	+	0.526096i	$0.176345\pi$
$972$	−1.00000	−0.0320750
$973$	−9.00000	−0.288527
$974$	30.0000	0.961262
$975$	2.00000	0.0640513
$976$	−7.00000	−0.224065
$977$	5.00000	0.159964	0.0799821	−	0.996796i	$-0.474514\pi$
$977$	5.00000	0.159964	0.0799821	+	0.996796i	$0.474514\pi$
$978$	−15.0000	−0.479647
$979$	70.0000	2.23721
$980$	2.00000	0.0638877
$981$	−7.00000	−0.223493
$982$	−28.0000	−0.893516
$983$	45.0000	1.43528	0.717639	−	0.696416i	$-0.245223\pi$
$983$	45.0000	1.43528	0.717639	+	0.696416i	$0.245223\pi$
$984$	1.00000	0.0318788
$985$	10.0000	0.318626
$986$	−35.0000	−1.11463
$987$	0	0
$988$	4.00000	0.127257
$989$	36.0000	1.14473
$990$	5.00000	0.158910
$991$	19.0000	0.603555	0.301777	−	0.953378i	$-0.402420\pi$
$991$	19.0000	0.603555	0.301777	+	0.953378i	$0.402420\pi$
$992$	7.00000	0.222250
$993$	0	0
$994$	−24.0000	−0.761234
$995$	4.00000	0.126809
$996$	10.0000	0.316862
$997$	6.00000	0.190022	0.0950110	−	0.995476i	$-0.469711\pi$
$997$	6.00000	0.190022	0.0950110	+	0.995476i	$0.469711\pi$
$998$	−4.00000	−0.126618
$999$	−1.00000	−0.0316386

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.a.d.1.1	✓	1
3.2	odd	2		3330.2.a.q.1.1		1
4.3	odd	2		8880.2.a.z.1.1		1
5.4	even	2		5550.2.a.bf.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.a.d.1.1	✓	1	1.1	even	1	trivial
3330.2.a.q.1.1		1	3.2	odd	2
5550.2.a.bf.1.1		1	5.4	even	2
8880.2.a.z.1.1		1	4.3	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:	\( N \)	\(=\)	\( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1110.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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