LMFDB - Embedded newform 3630.2.a.l.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3630,2,Mod(1,3630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3630, 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("3630.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3630 = 2 \cdot 3 \cdot 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3630.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:	$28.9856959337$
Analytic rank:	$0$
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	$\chi$	$=$	3630.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

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

\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} +3.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} +1.00000 q^{12} +5.00000 q^{13} -3.00000 q^{14} +1.00000 q^{15} +1.00000 q^{16} +7.00000 q^{17} -1.00000 q^{18} +7.00000 q^{19} +1.00000 q^{20} +3.00000 q^{21} -1.00000 q^{24} +1.00000 q^{25} -5.00000 q^{26} +1.00000 q^{27} +3.00000 q^{28} -7.00000 q^{29} -1.00000 q^{30} +6.00000 q^{31} -1.00000 q^{32} -7.00000 q^{34} +3.00000 q^{35} +1.00000 q^{36} -5.00000 q^{37} -7.00000 q^{38} +5.00000 q^{39} -1.00000 q^{40} +10.0000 q^{41} -3.00000 q^{42} -6.00000 q^{43} +1.00000 q^{45} -10.0000 q^{47} +1.00000 q^{48} +2.00000 q^{49} -1.00000 q^{50} +7.00000 q^{51} +5.00000 q^{52} -12.0000 q^{53} -1.00000 q^{54} -3.00000 q^{56} +7.00000 q^{57} +7.00000 q^{58} +1.00000 q^{60} -12.0000 q^{61} -6.00000 q^{62} +3.00000 q^{63} +1.00000 q^{64} +5.00000 q^{65} -2.00000 q^{67} +7.00000 q^{68} -3.00000 q^{70} -9.00000 q^{71} -1.00000 q^{72} +6.00000 q^{73} +5.00000 q^{74} +1.00000 q^{75} +7.00000 q^{76} -5.00000 q^{78} +10.0000 q^{79} +1.00000 q^{80} +1.00000 q^{81} -10.0000 q^{82} -13.0000 q^{83} +3.00000 q^{84} +7.00000 q^{85} +6.00000 q^{86} -7.00000 q^{87} +4.00000 q^{89} -1.00000 q^{90} +15.0000 q^{91} +6.00000 q^{93} +10.0000 q^{94} +7.00000 q^{95} -1.00000 q^{96} +2.00000 q^{97} -2.00000 q^{98} +O(q^{100})\)

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
$11$	0	0
$11$	0	0
$12$	1.00000	0.288675
$13$	5.00000	1.38675	0.693375	−	0.720577i	$-0.256123\pi$
$13$	5.00000	1.38675	0.693375	+	0.720577i	$0.256123\pi$
$14$	−3.00000	−0.801784
$15$	1.00000	0.258199
$16$	1.00000	0.250000
$17$	7.00000	1.69775	0.848875	−	0.528594i	$-0.177281\pi$
$17$	7.00000	1.69775	0.848875	+	0.528594i	$0.177281\pi$
$18$	−1.00000	−0.235702
$19$	7.00000	1.60591	0.802955	−	0.596040i	$-0.203260\pi$
$19$	7.00000	1.60591	0.802955	+	0.596040i	$0.203260\pi$
$20$	1.00000	0.223607
$21$	3.00000	0.654654
$22$	0	0
$23$	0	0		−	1.00000i	$-0.5\pi$
$23$	0	0			1.00000i	$0.5\pi$
$24$	−1.00000	−0.204124
$25$	1.00000	0.200000
$26$	−5.00000	−0.980581
$27$	1.00000	0.192450
$28$	3.00000	0.566947
$29$	−7.00000	−1.29987	−0.649934	−	0.759991i	$-0.725203\pi$
$29$	−7.00000	−1.29987	−0.649934	+	0.759991i	$0.725203\pi$
$30$	−1.00000	−0.182574
$31$	6.00000	1.07763	0.538816	−	0.842424i	$-0.318872\pi$
$31$	6.00000	1.07763	0.538816	+	0.842424i	$0.318872\pi$
$32$	−1.00000	−0.176777
$33$	0	0
$34$	−7.00000	−1.20049
$35$	3.00000	0.507093
$36$	1.00000	0.166667
$37$	−5.00000	−0.821995	−0.410997	−	0.911636i	$-0.634819\pi$
$37$	−5.00000	−0.821995	−0.410997	+	0.911636i	$0.634819\pi$
$38$	−7.00000	−1.13555
$39$	5.00000	0.800641
$40$	−1.00000	−0.158114
$41$	10.0000	1.56174	0.780869	−	0.624695i	$-0.214777\pi$
$41$	10.0000	1.56174	0.780869	+	0.624695i	$0.214777\pi$
$42$	−3.00000	−0.462910
$43$	−6.00000	−0.914991	−0.457496	−	0.889212i	$-0.651253\pi$
$43$	−6.00000	−0.914991	−0.457496	+	0.889212i	$0.651253\pi$
$44$	0	0
$45$	1.00000	0.149071
$46$	0	0
$47$	−10.0000	−1.45865	−0.729325	−	0.684167i	$-0.760166\pi$
$47$	−10.0000	−1.45865	−0.729325	+	0.684167i	$0.760166\pi$
$48$	1.00000	0.144338
$49$	2.00000	0.285714
$50$	−1.00000	−0.141421
$51$	7.00000	0.980196
$52$	5.00000	0.693375
$53$	−12.0000	−1.64833	−0.824163	−	0.566352i	$-0.808354\pi$
$53$	−12.0000	−1.64833	−0.824163	+	0.566352i	$0.808354\pi$
$54$	−1.00000	−0.136083
$55$	0	0
$56$	−3.00000	−0.400892
$57$	7.00000	0.927173
$58$	7.00000	0.919145
$59$	0	0		−	1.00000i	$-0.5\pi$
$59$	0	0			1.00000i	$0.5\pi$
$60$	1.00000	0.129099
$61$	−12.0000	−1.53644	−0.768221	−	0.640184i	$-0.778858\pi$
$61$	−12.0000	−1.53644	−0.768221	+	0.640184i	$0.778858\pi$
$62$	−6.00000	−0.762001
$63$	3.00000	0.377964
$64$	1.00000	0.125000
$65$	5.00000	0.620174
$66$	0	0
$67$	−2.00000	−0.244339	−0.122169	−	0.992509i	$-0.538985\pi$
$67$	−2.00000	−0.244339	−0.122169	+	0.992509i	$0.538985\pi$
$68$	7.00000	0.848875
$69$	0	0
$70$	−3.00000	−0.358569
$71$	−9.00000	−1.06810	−0.534052	−	0.845452i	$-0.679331\pi$
$71$	−9.00000	−1.06810	−0.534052	+	0.845452i	$0.679331\pi$
$72$	−1.00000	−0.117851
$73$	6.00000	0.702247	0.351123	−	0.936329i	$-0.385800\pi$
$73$	6.00000	0.702247	0.351123	+	0.936329i	$0.385800\pi$
$74$	5.00000	0.581238
$75$	1.00000	0.115470
$76$	7.00000	0.802955
$77$	0	0
$78$	−5.00000	−0.566139
$79$	10.0000	1.12509	0.562544	−	0.826767i	$-0.309823\pi$
$79$	10.0000	1.12509	0.562544	+	0.826767i	$0.309823\pi$
$80$	1.00000	0.111803
$81$	1.00000	0.111111
$82$	−10.0000	−1.10432
$83$	−13.0000	−1.42694	−0.713468	−	0.700688i	$-0.752876\pi$
$83$	−13.0000	−1.42694	−0.713468	+	0.700688i	$0.752876\pi$
$84$	3.00000	0.327327
$85$	7.00000	0.759257
$86$	6.00000	0.646997
$87$	−7.00000	−0.750479
$88$	0	0
$89$	4.00000	0.423999	0.212000	−	0.977270i	$-0.432002\pi$
$89$	4.00000	0.423999	0.212000	+	0.977270i	$0.432002\pi$
$90$	−1.00000	−0.105409
$91$	15.0000	1.57243
$92$	0	0
$93$	6.00000	0.622171
$94$	10.0000	1.03142
$95$	7.00000	0.718185
$96$	−1.00000	−0.102062
$97$	2.00000	0.203069	0.101535	−	0.994832i	$-0.467625\pi$
$97$	2.00000	0.203069	0.101535	+	0.994832i	$0.467625\pi$
$98$	−2.00000	−0.202031
$99$	0	0
$100$	1.00000	0.100000
$101$	3.00000	0.298511	0.149256	−	0.988799i	$-0.452312\pi$
$101$	3.00000	0.298511	0.149256	+	0.988799i	$0.452312\pi$
$102$	−7.00000	−0.693103
$103$	−3.00000	−0.295599	−0.147799	−	0.989017i	$-0.547219\pi$
$103$	−3.00000	−0.295599	−0.147799	+	0.989017i	$0.547219\pi$
$104$	−5.00000	−0.490290
$105$	3.00000	0.292770
$106$	12.0000	1.16554
$107$	0	0		−	1.00000i	$-0.5\pi$
$107$	0	0			1.00000i	$0.5\pi$
$108$	1.00000	0.0962250
$109$	−20.0000	−1.91565	−0.957826	−	0.287348i	$-0.907226\pi$
$109$	−20.0000	−1.91565	−0.957826	+	0.287348i	$0.907226\pi$
$110$	0	0
$111$	−5.00000	−0.474579
$112$	3.00000	0.283473
$113$	10.0000	0.940721	0.470360	−	0.882474i	$-0.344124\pi$
$113$	10.0000	0.940721	0.470360	+	0.882474i	$0.344124\pi$
$114$	−7.00000	−0.655610
$115$	0	0
$116$	−7.00000	−0.649934
$117$	5.00000	0.462250
$118$	0	0
$119$	21.0000	1.92507
$120$	−1.00000	−0.0912871
$121$	0	0
$122$	12.0000	1.08643
$123$	10.0000	0.901670
$124$	6.00000	0.538816
$125$	1.00000	0.0894427
$126$	−3.00000	−0.267261
$127$	4.00000	0.354943	0.177471	−	0.984126i	$-0.443208\pi$
$127$	4.00000	0.354943	0.177471	+	0.984126i	$0.443208\pi$
$128$	−1.00000	−0.0883883
$129$	−6.00000	−0.528271
$130$	−5.00000	−0.438529
$131$	−16.0000	−1.39793	−0.698963	−	0.715158i	$-0.746355\pi$
$131$	−16.0000	−1.39793	−0.698963	+	0.715158i	$0.746355\pi$
$132$	0	0
$133$	21.0000	1.82093
$134$	2.00000	0.172774
$135$	1.00000	0.0860663
$136$	−7.00000	−0.600245
$137$	3.00000	0.256307	0.128154	−	0.991754i	$-0.459095\pi$
$137$	3.00000	0.256307	0.128154	+	0.991754i	$0.459095\pi$
$138$	0	0
$139$	5.00000	0.424094	0.212047	−	0.977259i	$-0.431987\pi$
$139$	5.00000	0.424094	0.212047	+	0.977259i	$0.431987\pi$
$140$	3.00000	0.253546
$141$	−10.0000	−0.842152
$142$	9.00000	0.755263
$143$	0	0
$144$	1.00000	0.0833333
$145$	−7.00000	−0.581318
$146$	−6.00000	−0.496564
$147$	2.00000	0.164957
$148$	−5.00000	−0.410997
$149$	−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
$151$	−20.0000	−1.62758	−0.813788	−	0.581161i	$-0.802599\pi$
$151$	−20.0000	−1.62758	−0.813788	+	0.581161i	$0.802599\pi$
$152$	−7.00000	−0.567775
$153$	7.00000	0.565916
$154$	0	0
$155$	6.00000	0.481932
$156$	5.00000	0.400320
$157$	−11.0000	−0.877896	−0.438948	−	0.898513i	$-0.644649\pi$
$157$	−11.0000	−0.877896	−0.438948	+	0.898513i	$0.644649\pi$
$158$	−10.0000	−0.795557
$159$	−12.0000	−0.951662
$160$	−1.00000	−0.0790569
$161$	0	0
$162$	−1.00000	−0.0785674
$163$	4.00000	0.313304	0.156652	−	0.987654i	$-0.449930\pi$
$163$	4.00000	0.313304	0.156652	+	0.987654i	$0.449930\pi$
$164$	10.0000	0.780869
$165$	0	0
$166$	13.0000	1.00900
$167$	16.0000	1.23812	0.619059	−	0.785345i	$-0.287514\pi$
$167$	16.0000	1.23812	0.619059	+	0.785345i	$0.287514\pi$
$168$	−3.00000	−0.231455
$169$	12.0000	0.923077
$170$	−7.00000	−0.536875
$171$	7.00000	0.535303
$172$	−6.00000	−0.457496
$173$	4.00000	0.304114	0.152057	−	0.988372i	$-0.451410\pi$
$173$	4.00000	0.304114	0.152057	+	0.988372i	$0.451410\pi$
$174$	7.00000	0.530669
$175$	3.00000	0.226779
$176$	0	0
$177$	0	0
$178$	−4.00000	−0.299813
$179$	−16.0000	−1.19590	−0.597948	−	0.801535i	$-0.704017\pi$
$179$	−16.0000	−1.19590	−0.597948	+	0.801535i	$0.704017\pi$
$180$	1.00000	0.0745356
$181$	−8.00000	−0.594635	−0.297318	−	0.954779i	$-0.596092\pi$
$181$	−8.00000	−0.594635	−0.297318	+	0.954779i	$0.596092\pi$
$182$	−15.0000	−1.11187
$183$	−12.0000	−0.887066
$184$	0	0
$185$	−5.00000	−0.367607
$186$	−6.00000	−0.439941
$187$	0	0
$188$	−10.0000	−0.729325
$189$	3.00000	0.218218
$190$	−7.00000	−0.507833
$191$	−3.00000	−0.217072	−0.108536	−	0.994092i	$-0.534616\pi$
$191$	−3.00000	−0.217072	−0.108536	+	0.994092i	$0.534616\pi$
$192$	1.00000	0.0721688
$193$	24.0000	1.72756	0.863779	−	0.503871i	$-0.168091\pi$
$193$	24.0000	1.72756	0.863779	+	0.503871i	$0.168091\pi$
$194$	−2.00000	−0.143592
$195$	5.00000	0.358057
$196$	2.00000	0.142857
$197$	−12.0000	−0.854965	−0.427482	−	0.904024i	$-0.640599\pi$
$197$	−12.0000	−0.854965	−0.427482	+	0.904024i	$0.640599\pi$
$198$	0	0
$199$	−16.0000	−1.13421	−0.567105	−	0.823646i	$-0.691937\pi$
$199$	−16.0000	−1.13421	−0.567105	+	0.823646i	$0.691937\pi$
$200$	−1.00000	−0.0707107
$201$	−2.00000	−0.141069
$202$	−3.00000	−0.211079
$203$	−21.0000	−1.47391
$204$	7.00000	0.490098
$205$	10.0000	0.698430
$206$	3.00000	0.209020
$207$	0	0
$208$	5.00000	0.346688
$209$	0	0
$210$	−3.00000	−0.207020
$211$	7.00000	0.481900	0.240950	−	0.970538i	$-0.422541\pi$
$211$	7.00000	0.481900	0.240950	+	0.970538i	$0.422541\pi$
$212$	−12.0000	−0.824163
$213$	−9.00000	−0.616670
$214$	0	0
$215$	−6.00000	−0.409197
$216$	−1.00000	−0.0680414
$217$	18.0000	1.22192
$218$	20.0000	1.35457
$219$	6.00000	0.405442
$220$	0	0
$221$	35.0000	2.35435
$222$	5.00000	0.335578
$223$	−1.00000	−0.0669650	−0.0334825	−	0.999439i	$-0.510660\pi$
$223$	−1.00000	−0.0669650	−0.0334825	+	0.999439i	$0.510660\pi$
$224$	−3.00000	−0.200446
$225$	1.00000	0.0666667
$226$	−10.0000	−0.665190
$227$	0	0		−	1.00000i	$-0.5\pi$
$227$	0	0			1.00000i	$0.5\pi$
$228$	7.00000	0.463586
$229$	16.0000	1.05731	0.528655	−	0.848837i	$-0.322697\pi$
$229$	16.0000	1.05731	0.528655	+	0.848837i	$0.322697\pi$
$230$	0	0
$231$	0	0
$232$	7.00000	0.459573
$233$	2.00000	0.131024	0.0655122	−	0.997852i	$-0.479132\pi$
$233$	2.00000	0.131024	0.0655122	+	0.997852i	$0.479132\pi$
$234$	−5.00000	−0.326860
$235$	−10.0000	−0.652328
$236$	0	0
$237$	10.0000	0.649570
$238$	−21.0000	−1.36123
$239$	3.00000	0.194054	0.0970269	−	0.995282i	$-0.469067\pi$
$239$	3.00000	0.194054	0.0970269	+	0.995282i	$0.469067\pi$
$240$	1.00000	0.0645497
$241$	−25.0000	−1.61039	−0.805196	−	0.593009i	$-0.797940\pi$
$241$	−25.0000	−1.61039	−0.805196	+	0.593009i	$0.797940\pi$
$242$	0	0
$243$	1.00000	0.0641500
$244$	−12.0000	−0.768221
$245$	2.00000	0.127775
$246$	−10.0000	−0.637577
$247$	35.0000	2.22700
$248$	−6.00000	−0.381000
$249$	−13.0000	−0.823842
$250$	−1.00000	−0.0632456
$251$	−12.0000	−0.757433	−0.378717	−	0.925513i	$-0.623635\pi$
$251$	−12.0000	−0.757433	−0.378717	+	0.925513i	$0.623635\pi$
$252$	3.00000	0.188982
$253$	0	0
$254$	−4.00000	−0.250982
$255$	7.00000	0.438357
$256$	1.00000	0.0625000
$257$	17.0000	1.06043	0.530215	−	0.847863i	$-0.322111\pi$
$257$	17.0000	1.06043	0.530215	+	0.847863i	$0.322111\pi$
$258$	6.00000	0.373544
$259$	−15.0000	−0.932055
$260$	5.00000	0.310087
$261$	−7.00000	−0.433289
$262$	16.0000	0.988483
$263$	−22.0000	−1.35658	−0.678289	−	0.734795i	$-0.737278\pi$
$263$	−22.0000	−1.35658	−0.678289	+	0.734795i	$0.737278\pi$
$264$	0	0
$265$	−12.0000	−0.737154
$266$	−21.0000	−1.28759
$267$	4.00000	0.244796
$268$	−2.00000	−0.122169
$269$	−19.0000	−1.15845	−0.579225	−	0.815168i	$-0.696645\pi$
$269$	−19.0000	−1.15845	−0.579225	+	0.815168i	$0.696645\pi$
$270$	−1.00000	−0.0608581
$271$	22.0000	1.33640	0.668202	−	0.743980i	$-0.267064\pi$
$271$	22.0000	1.33640	0.668202	+	0.743980i	$0.267064\pi$
$272$	7.00000	0.424437
$273$	15.0000	0.907841
$274$	−3.00000	−0.181237
$275$	0	0
$276$	0	0
$277$	26.0000	1.56219	0.781094	−	0.624413i	$-0.214662\pi$
$277$	26.0000	1.56219	0.781094	+	0.624413i	$0.214662\pi$
$278$	−5.00000	−0.299880
$279$	6.00000	0.359211
$280$	−3.00000	−0.179284
$281$	4.00000	0.238620	0.119310	−	0.992857i	$-0.461932\pi$
$281$	4.00000	0.238620	0.119310	+	0.992857i	$0.461932\pi$
$282$	10.0000	0.595491
$283$	24.0000	1.42665	0.713326	−	0.700832i	$-0.247188\pi$
$283$	24.0000	1.42665	0.713326	+	0.700832i	$0.247188\pi$
$284$	−9.00000	−0.534052
$285$	7.00000	0.414644
$286$	0	0
$287$	30.0000	1.77084
$288$	−1.00000	−0.0589256
$289$	32.0000	1.88235
$290$	7.00000	0.411054
$291$	2.00000	0.117242
$292$	6.00000	0.351123
$293$	−16.0000	−0.934730	−0.467365	−	0.884064i	$-0.654797\pi$
$293$	−16.0000	−0.934730	−0.467365	+	0.884064i	$0.654797\pi$
$294$	−2.00000	−0.116642
$295$	0	0
$296$	5.00000	0.290619
$297$	0	0
$298$	6.00000	0.347571
$299$	0	0
$300$	1.00000	0.0577350
$301$	−18.0000	−1.03750
$302$	20.0000	1.15087
$303$	3.00000	0.172345
$304$	7.00000	0.401478
$305$	−12.0000	−0.687118
$306$	−7.00000	−0.400163
$307$	34.0000	1.94048	0.970241	−	0.242140i	$-0.0778494\pi$
$307$	34.0000	1.94048	0.970241	+	0.242140i	$0.0778494\pi$
$308$	0	0
$309$	−3.00000	−0.170664
$310$	−6.00000	−0.340777
$311$	−8.00000	−0.453638	−0.226819	−	0.973937i	$-0.572833\pi$
$311$	−8.00000	−0.453638	−0.226819	+	0.973937i	$0.572833\pi$
$312$	−5.00000	−0.283069
$313$	−2.00000	−0.113047	−0.0565233	−	0.998401i	$-0.518002\pi$
$313$	−2.00000	−0.113047	−0.0565233	+	0.998401i	$0.518002\pi$
$314$	11.0000	0.620766
$315$	3.00000	0.169031
$316$	10.0000	0.562544
$317$	12.0000	0.673987	0.336994	−	0.941507i	$-0.390590\pi$
$317$	12.0000	0.673987	0.336994	+	0.941507i	$0.390590\pi$
$318$	12.0000	0.672927
$319$	0	0
$320$	1.00000	0.0559017
$321$	0	0
$322$	0	0
$323$	49.0000	2.72643
$324$	1.00000	0.0555556
$325$	5.00000	0.277350
$326$	−4.00000	−0.221540
$327$	−20.0000	−1.10600
$328$	−10.0000	−0.552158
$329$	−30.0000	−1.65395
$330$	0	0
$331$	−17.0000	−0.934405	−0.467202	−	0.884150i	$-0.654738\pi$
$331$	−17.0000	−0.934405	−0.467202	+	0.884150i	$0.654738\pi$
$332$	−13.0000	−0.713468
$333$	−5.00000	−0.273998
$334$	−16.0000	−0.875481
$335$	−2.00000	−0.109272
$336$	3.00000	0.163663
$337$	−6.00000	−0.326841	−0.163420	−	0.986557i	$-0.552253\pi$
$337$	−6.00000	−0.326841	−0.163420	+	0.986557i	$0.552253\pi$
$338$	−12.0000	−0.652714
$339$	10.0000	0.543125
$340$	7.00000	0.379628
$341$	0	0
$342$	−7.00000	−0.378517
$343$	−15.0000	−0.809924
$344$	6.00000	0.323498
$345$	0	0
$346$	−4.00000	−0.215041
$347$	−3.00000	−0.161048	−0.0805242	−	0.996753i	$-0.525659\pi$
$347$	−3.00000	−0.161048	−0.0805242	+	0.996753i	$0.525659\pi$
$348$	−7.00000	−0.375239
$349$	−14.0000	−0.749403	−0.374701	−	0.927146i	$-0.622255\pi$
$349$	−14.0000	−0.749403	−0.374701	+	0.927146i	$0.622255\pi$
$350$	−3.00000	−0.160357
$351$	5.00000	0.266880
$352$	0	0
$353$	6.00000	0.319348	0.159674	−	0.987170i	$-0.448956\pi$
$353$	6.00000	0.319348	0.159674	+	0.987170i	$0.448956\pi$
$354$	0	0
$355$	−9.00000	−0.477670
$356$	4.00000	0.212000
$357$	21.0000	1.11144
$358$	16.0000	0.845626
$359$	24.0000	1.26667	0.633336	−	0.773877i	$-0.281685\pi$
$359$	24.0000	1.26667	0.633336	+	0.773877i	$0.281685\pi$
$360$	−1.00000	−0.0527046
$361$	30.0000	1.57895
$362$	8.00000	0.420471
$363$	0	0
$364$	15.0000	0.786214
$365$	6.00000	0.314054
$366$	12.0000	0.627250
$367$	−27.0000	−1.40939	−0.704694	−	0.709511i	$-0.748916\pi$
$367$	−27.0000	−1.40939	−0.704694	+	0.709511i	$0.748916\pi$
$368$	0	0
$369$	10.0000	0.520579
$370$	5.00000	0.259938
$371$	−36.0000	−1.86903
$372$	6.00000	0.311086
$373$	−29.0000	−1.50156	−0.750782	−	0.660551i	$-0.770323\pi$
$373$	−29.0000	−1.50156	−0.750782	+	0.660551i	$0.770323\pi$
$374$	0	0
$375$	1.00000	0.0516398
$376$	10.0000	0.515711
$377$	−35.0000	−1.80259
$378$	−3.00000	−0.154303
$379$	1.00000	0.0513665	0.0256833	−	0.999670i	$-0.491824\pi$
$379$	1.00000	0.0513665	0.0256833	+	0.999670i	$0.491824\pi$
$380$	7.00000	0.359092
$381$	4.00000	0.204926
$382$	3.00000	0.153493
$383$	6.00000	0.306586	0.153293	−	0.988181i	$-0.451012\pi$
$383$	6.00000	0.306586	0.153293	+	0.988181i	$0.451012\pi$
$384$	−1.00000	−0.0510310
$385$	0	0
$386$	−24.0000	−1.22157
$387$	−6.00000	−0.304997
$388$	2.00000	0.101535
$389$	34.0000	1.72387	0.861934	−	0.507020i	$-0.169253\pi$
$389$	34.0000	1.72387	0.861934	+	0.507020i	$0.169253\pi$
$390$	−5.00000	−0.253185
$391$	0	0
$392$	−2.00000	−0.101015
$393$	−16.0000	−0.807093
$394$	12.0000	0.604551
$395$	10.0000	0.503155
$396$	0	0
$397$	35.0000	1.75660	0.878300	−	0.478110i	$-0.158678\pi$
$397$	35.0000	1.75660	0.878300	+	0.478110i	$0.158678\pi$
$398$	16.0000	0.802008
$399$	21.0000	1.05131
$400$	1.00000	0.0500000
$401$	−34.0000	−1.69788	−0.848939	−	0.528490i	$-0.822758\pi$
$401$	−34.0000	−1.69788	−0.848939	+	0.528490i	$0.822758\pi$
$402$	2.00000	0.0997509
$403$	30.0000	1.49441
$404$	3.00000	0.149256
$405$	1.00000	0.0496904
$406$	21.0000	1.04221
$407$	0	0
$408$	−7.00000	−0.346552
$409$	−6.00000	−0.296681	−0.148340	−	0.988936i	$-0.547393\pi$
$409$	−6.00000	−0.296681	−0.148340	+	0.988936i	$0.547393\pi$
$410$	−10.0000	−0.493865
$411$	3.00000	0.147979
$412$	−3.00000	−0.147799
$413$	0	0
$414$	0	0
$415$	−13.0000	−0.638145
$416$	−5.00000	−0.245145
$417$	5.00000	0.244851
$418$	0	0
$419$	−14.0000	−0.683945	−0.341972	−	0.939710i	$-0.611095\pi$
$419$	−14.0000	−0.683945	−0.341972	+	0.939710i	$0.611095\pi$
$420$	3.00000	0.146385
$421$	−6.00000	−0.292422	−0.146211	−	0.989253i	$-0.546708\pi$
$421$	−6.00000	−0.292422	−0.146211	+	0.989253i	$0.546708\pi$
$422$	−7.00000	−0.340755
$423$	−10.0000	−0.486217
$424$	12.0000	0.582772
$425$	7.00000	0.339550
$426$	9.00000	0.436051
$427$	−36.0000	−1.74216
$428$	0	0
$429$	0	0
$430$	6.00000	0.289346
$431$	1.00000	0.0481683	0.0240842	−	0.999710i	$-0.492333\pi$
$431$	1.00000	0.0481683	0.0240842	+	0.999710i	$0.492333\pi$
$432$	1.00000	0.0481125
$433$	−28.0000	−1.34559	−0.672797	−	0.739827i	$-0.734907\pi$
$433$	−28.0000	−1.34559	−0.672797	+	0.739827i	$0.734907\pi$
$434$	−18.0000	−0.864028
$435$	−7.00000	−0.335624
$436$	−20.0000	−0.957826
$437$	0	0
$438$	−6.00000	−0.286691
$439$	26.0000	1.24091	0.620456	−	0.784241i	$-0.286947\pi$
$439$	26.0000	1.24091	0.620456	+	0.784241i	$0.286947\pi$
$440$	0	0
$441$	2.00000	0.0952381
$442$	−35.0000	−1.66478
$443$	15.0000	0.712672	0.356336	−	0.934358i	$-0.384026\pi$
$443$	15.0000	0.712672	0.356336	+	0.934358i	$0.384026\pi$
$444$	−5.00000	−0.237289
$445$	4.00000	0.189618
$446$	1.00000	0.0473514
$447$	−6.00000	−0.283790
$448$	3.00000	0.141737
$449$	22.0000	1.03824	0.519122	−	0.854700i	$-0.326259\pi$
$449$	22.0000	1.03824	0.519122	+	0.854700i	$0.326259\pi$
$450$	−1.00000	−0.0471405
$451$	0	0
$452$	10.0000	0.470360
$453$	−20.0000	−0.939682
$454$	0	0
$455$	15.0000	0.703211
$456$	−7.00000	−0.327805
$457$	−4.00000	−0.187112	−0.0935561	−	0.995614i	$-0.529823\pi$
$457$	−4.00000	−0.187112	−0.0935561	+	0.995614i	$0.529823\pi$
$458$	−16.0000	−0.747631
$459$	7.00000	0.326732
$460$	0	0
$461$	33.0000	1.53696	0.768482	−	0.639872i	$-0.221013\pi$
$461$	33.0000	1.53696	0.768482	+	0.639872i	$0.221013\pi$
$462$	0	0
$463$	−8.00000	−0.371792	−0.185896	−	0.982569i	$-0.559519\pi$
$463$	−8.00000	−0.371792	−0.185896	+	0.982569i	$0.559519\pi$
$464$	−7.00000	−0.324967
$465$	6.00000	0.278243
$466$	−2.00000	−0.0926482
$467$	−7.00000	−0.323921	−0.161961	−	0.986797i	$-0.551782\pi$
$467$	−7.00000	−0.323921	−0.161961	+	0.986797i	$0.551782\pi$
$468$	5.00000	0.231125
$469$	−6.00000	−0.277054
$470$	10.0000	0.461266
$471$	−11.0000	−0.506853
$472$	0	0
$473$	0	0
$474$	−10.0000	−0.459315
$475$	7.00000	0.321182
$476$	21.0000	0.962533
$477$	−12.0000	−0.549442
$478$	−3.00000	−0.137217
$479$	3.00000	0.137073	0.0685367	−	0.997649i	$-0.478167\pi$
$479$	3.00000	0.137073	0.0685367	+	0.997649i	$0.478167\pi$
$480$	−1.00000	−0.0456435
$481$	−25.0000	−1.13990
$482$	25.0000	1.13872
$483$	0	0
$484$	0	0
$485$	2.00000	0.0908153
$486$	−1.00000	−0.0453609
$487$	29.0000	1.31412	0.657058	−	0.753840i	$-0.271801\pi$
$487$	29.0000	1.31412	0.657058	+	0.753840i	$0.271801\pi$
$488$	12.0000	0.543214
$489$	4.00000	0.180886
$490$	−2.00000	−0.0903508
$491$	−30.0000	−1.35388	−0.676941	−	0.736038i	$-0.736695\pi$
$491$	−30.0000	−1.35388	−0.676941	+	0.736038i	$0.736695\pi$
$492$	10.0000	0.450835
$493$	−49.0000	−2.20685
$494$	−35.0000	−1.57472
$495$	0	0
$496$	6.00000	0.269408
$497$	−27.0000	−1.21112
$498$	13.0000	0.582544
$499$	33.0000	1.47728	0.738641	−	0.674099i	$-0.235468\pi$
$499$	33.0000	1.47728	0.738641	+	0.674099i	$0.235468\pi$
$500$	1.00000	0.0447214
$501$	16.0000	0.714827
$502$	12.0000	0.535586
$503$	−16.0000	−0.713405	−0.356702	−	0.934218i	$-0.616099\pi$
$503$	−16.0000	−0.713405	−0.356702	+	0.934218i	$0.616099\pi$
$504$	−3.00000	−0.133631
$505$	3.00000	0.133498
$506$	0	0
$507$	12.0000	0.532939
$508$	4.00000	0.177471
$509$	−2.00000	−0.0886484	−0.0443242	−	0.999017i	$-0.514113\pi$
$509$	−2.00000	−0.0886484	−0.0443242	+	0.999017i	$0.514113\pi$
$510$	−7.00000	−0.309965
$511$	18.0000	0.796273
$512$	−1.00000	−0.0441942
$513$	7.00000	0.309058
$514$	−17.0000	−0.749838
$515$	−3.00000	−0.132196
$516$	−6.00000	−0.264135
$517$	0	0
$518$	15.0000	0.659062
$519$	4.00000	0.175581
$520$	−5.00000	−0.219265
$521$	8.00000	0.350486	0.175243	−	0.984525i	$-0.443929\pi$
$521$	8.00000	0.350486	0.175243	+	0.984525i	$0.443929\pi$
$522$	7.00000	0.306382
$523$	−12.0000	−0.524723	−0.262362	−	0.964970i	$-0.584501\pi$
$523$	−12.0000	−0.524723	−0.262362	+	0.964970i	$0.584501\pi$
$524$	−16.0000	−0.698963
$525$	3.00000	0.130931
$526$	22.0000	0.959246
$527$	42.0000	1.82955
$528$	0	0
$529$	−23.0000	−1.00000
$530$	12.0000	0.521247
$531$	0	0
$532$	21.0000	0.910465
$533$	50.0000	2.16574
$534$	−4.00000	−0.173097
$535$	0	0
$536$	2.00000	0.0863868
$537$	−16.0000	−0.690451
$538$	19.0000	0.819148
$539$	0	0
$540$	1.00000	0.0430331
$541$	26.0000	1.11783	0.558914	−	0.829226i	$-0.311218\pi$
$541$	26.0000	1.11783	0.558914	+	0.829226i	$0.311218\pi$
$542$	−22.0000	−0.944981
$543$	−8.00000	−0.343313
$544$	−7.00000	−0.300123
$545$	−20.0000	−0.856706
$546$	−15.0000	−0.641941
$547$	38.0000	1.62476	0.812381	−	0.583127i	$-0.198171\pi$
$547$	38.0000	1.62476	0.812381	+	0.583127i	$0.198171\pi$
$548$	3.00000	0.128154
$549$	−12.0000	−0.512148
$550$	0	0
$551$	−49.0000	−2.08747
$552$	0	0
$553$	30.0000	1.27573
$554$	−26.0000	−1.10463
$555$	−5.00000	−0.212238
$556$	5.00000	0.212047
$557$	42.0000	1.77960	0.889799	−	0.456354i	$-0.150845\pi$
$557$	42.0000	1.77960	0.889799	+	0.456354i	$0.150845\pi$
$558$	−6.00000	−0.254000
$559$	−30.0000	−1.26886
$560$	3.00000	0.126773
$561$	0	0
$562$	−4.00000	−0.168730
$563$	−15.0000	−0.632175	−0.316087	−	0.948730i	$-0.602369\pi$
$563$	−15.0000	−0.632175	−0.316087	+	0.948730i	$0.602369\pi$
$564$	−10.0000	−0.421076
$565$	10.0000	0.420703
$566$	−24.0000	−1.00880
$567$	3.00000	0.125988
$568$	9.00000	0.377632
$569$	2.00000	0.0838444	0.0419222	−	0.999121i	$-0.486652\pi$
$569$	2.00000	0.0838444	0.0419222	+	0.999121i	$0.486652\pi$
$570$	−7.00000	−0.293198
$571$	24.0000	1.00437	0.502184	−	0.864761i	$-0.332530\pi$
$571$	24.0000	1.00437	0.502184	+	0.864761i	$0.332530\pi$
$572$	0	0
$573$	−3.00000	−0.125327
$574$	−30.0000	−1.25218
$575$	0	0
$576$	1.00000	0.0416667
$577$	42.0000	1.74848	0.874241	−	0.485491i	$-0.161359\pi$
$577$	42.0000	1.74848	0.874241	+	0.485491i	$0.161359\pi$
$578$	−32.0000	−1.33102
$579$	24.0000	0.997406
$580$	−7.00000	−0.290659
$581$	−39.0000	−1.61799
$582$	−2.00000	−0.0829027
$583$	0	0
$584$	−6.00000	−0.248282
$585$	5.00000	0.206725
$586$	16.0000	0.660954
$587$	7.00000	0.288921	0.144460	−	0.989511i	$-0.453855\pi$
$587$	7.00000	0.288921	0.144460	+	0.989511i	$0.453855\pi$
$588$	2.00000	0.0824786
$589$	42.0000	1.73058
$590$	0	0
$591$	−12.0000	−0.493614
$592$	−5.00000	−0.205499
$593$	−14.0000	−0.574911	−0.287456	−	0.957794i	$-0.592809\pi$
$593$	−14.0000	−0.574911	−0.287456	+	0.957794i	$0.592809\pi$
$594$	0	0
$595$	21.0000	0.860916
$596$	−6.00000	−0.245770
$597$	−16.0000	−0.654836
$598$	0	0
$599$	8.00000	0.326871	0.163436	−	0.986554i	$-0.447742\pi$
$599$	8.00000	0.326871	0.163436	+	0.986554i	$0.447742\pi$
$600$	−1.00000	−0.0408248
$601$	10.0000	0.407909	0.203954	−	0.978980i	$-0.434621\pi$
$601$	10.0000	0.407909	0.203954	+	0.978980i	$0.434621\pi$
$602$	18.0000	0.733625
$603$	−2.00000	−0.0814463
$604$	−20.0000	−0.813788
$605$	0	0
$606$	−3.00000	−0.121867
$607$	33.0000	1.33943	0.669714	−	0.742619i	$-0.266417\pi$
$607$	33.0000	1.33943	0.669714	+	0.742619i	$0.266417\pi$
$608$	−7.00000	−0.283887
$609$	−21.0000	−0.850963
$610$	12.0000	0.485866
$611$	−50.0000	−2.02278
$612$	7.00000	0.282958
$613$	−3.00000	−0.121169	−0.0605844	−	0.998163i	$-0.519296\pi$
$613$	−3.00000	−0.121169	−0.0605844	+	0.998163i	$0.519296\pi$
$614$	−34.0000	−1.37213
$615$	10.0000	0.403239
$616$	0	0
$617$	3.00000	0.120775	0.0603877	−	0.998175i	$-0.480766\pi$
$617$	3.00000	0.120775	0.0603877	+	0.998175i	$0.480766\pi$
$618$	3.00000	0.120678
$619$	25.0000	1.00483	0.502417	−	0.864625i	$-0.332444\pi$
$619$	25.0000	1.00483	0.502417	+	0.864625i	$0.332444\pi$
$620$	6.00000	0.240966
$621$	0	0
$622$	8.00000	0.320771
$623$	12.0000	0.480770
$624$	5.00000	0.200160
$625$	1.00000	0.0400000
$626$	2.00000	0.0799361
$627$	0	0
$628$	−11.0000	−0.438948
$629$	−35.0000	−1.39554
$630$	−3.00000	−0.119523
$631$	4.00000	0.159237	0.0796187	−	0.996825i	$-0.474630\pi$
$631$	4.00000	0.159237	0.0796187	+	0.996825i	$0.474630\pi$
$632$	−10.0000	−0.397779
$633$	7.00000	0.278225
$634$	−12.0000	−0.476581
$635$	4.00000	0.158735
$636$	−12.0000	−0.475831
$637$	10.0000	0.396214
$638$	0	0
$639$	−9.00000	−0.356034
$640$	−1.00000	−0.0395285
$641$	−26.0000	−1.02694	−0.513469	−	0.858108i	$-0.671640\pi$
$641$	−26.0000	−1.02694	−0.513469	+	0.858108i	$0.671640\pi$
$642$	0	0
$643$	−44.0000	−1.73519	−0.867595	−	0.497271i	$-0.834335\pi$
$643$	−44.0000	−1.73519	−0.867595	+	0.497271i	$0.834335\pi$
$644$	0	0
$645$	−6.00000	−0.236250
$646$	−49.0000	−1.92788
$647$	−32.0000	−1.25805	−0.629025	−	0.777385i	$-0.716546\pi$
$647$	−32.0000	−1.25805	−0.629025	+	0.777385i	$0.716546\pi$
$648$	−1.00000	−0.0392837
$649$	0	0
$650$	−5.00000	−0.196116
$651$	18.0000	0.705476
$652$	4.00000	0.156652
$653$	30.0000	1.17399	0.586995	−	0.809590i	$-0.300311\pi$
$653$	30.0000	1.17399	0.586995	+	0.809590i	$0.300311\pi$
$654$	20.0000	0.782062
$655$	−16.0000	−0.625172
$656$	10.0000	0.390434
$657$	6.00000	0.234082
$658$	30.0000	1.16952
$659$	−42.0000	−1.63609	−0.818044	−	0.575156i	$-0.804941\pi$
$659$	−42.0000	−1.63609	−0.818044	+	0.575156i	$0.804941\pi$
$660$	0	0
$661$	−30.0000	−1.16686	−0.583432	−	0.812162i	$-0.698291\pi$
$661$	−30.0000	−1.16686	−0.583432	+	0.812162i	$0.698291\pi$
$662$	17.0000	0.660724
$663$	35.0000	1.35929
$664$	13.0000	0.504498
$665$	21.0000	0.814345
$666$	5.00000	0.193746
$667$	0	0
$668$	16.0000	0.619059
$669$	−1.00000	−0.0386622
$670$	2.00000	0.0772667
$671$	0	0
$672$	−3.00000	−0.115728
$673$	−16.0000	−0.616755	−0.308377	−	0.951264i	$-0.599786\pi$
$673$	−16.0000	−0.616755	−0.308377	+	0.951264i	$0.599786\pi$
$674$	6.00000	0.231111
$675$	1.00000	0.0384900
$676$	12.0000	0.461538
$677$	−10.0000	−0.384331	−0.192166	−	0.981363i	$-0.561551\pi$
$677$	−10.0000	−0.384331	−0.192166	+	0.981363i	$0.561551\pi$
$678$	−10.0000	−0.384048
$679$	6.00000	0.230259
$680$	−7.00000	−0.268438
$681$	0	0
$682$	0	0
$683$	25.0000	0.956598	0.478299	−	0.878197i	$-0.341253\pi$
$683$	25.0000	0.956598	0.478299	+	0.878197i	$0.341253\pi$
$684$	7.00000	0.267652
$685$	3.00000	0.114624
$686$	15.0000	0.572703
$687$	16.0000	0.610438
$688$	−6.00000	−0.228748
$689$	−60.0000	−2.28582
$690$	0	0
$691$	−31.0000	−1.17930	−0.589648	−	0.807661i	$-0.700733\pi$
$691$	−31.0000	−1.17930	−0.589648	+	0.807661i	$0.700733\pi$
$692$	4.00000	0.152057
$693$	0	0
$694$	3.00000	0.113878
$695$	5.00000	0.189661
$696$	7.00000	0.265334
$697$	70.0000	2.65144
$698$	14.0000	0.529908
$699$	2.00000	0.0756469
$700$	3.00000	0.113389
$701$	33.0000	1.24639	0.623196	−	0.782065i	$-0.285834\pi$
$701$	33.0000	1.24639	0.623196	+	0.782065i	$0.285834\pi$
$702$	−5.00000	−0.188713
$703$	−35.0000	−1.32005
$704$	0	0
$705$	−10.0000	−0.376622
$706$	−6.00000	−0.225813
$707$	9.00000	0.338480
$708$	0	0
$709$	30.0000	1.12667	0.563337	−	0.826227i	$-0.309517\pi$
$709$	30.0000	1.12667	0.563337	+	0.826227i	$0.309517\pi$
$710$	9.00000	0.337764
$711$	10.0000	0.375029
$712$	−4.00000	−0.149906
$713$	0	0
$714$	−21.0000	−0.785905
$715$	0	0
$716$	−16.0000	−0.597948
$717$	3.00000	0.112037
$718$	−24.0000	−0.895672
$719$	4.00000	0.149175	0.0745874	−	0.997214i	$-0.476236\pi$
$719$	4.00000	0.149175	0.0745874	+	0.997214i	$0.476236\pi$
$720$	1.00000	0.0372678
$721$	−9.00000	−0.335178
$722$	−30.0000	−1.11648
$723$	−25.0000	−0.929760
$724$	−8.00000	−0.297318
$725$	−7.00000	−0.259973
$726$	0	0
$727$	7.00000	0.259616	0.129808	−	0.991539i	$-0.458564\pi$
$727$	7.00000	0.259616	0.129808	+	0.991539i	$0.458564\pi$
$728$	−15.0000	−0.555937
$729$	1.00000	0.0370370
$730$	−6.00000	−0.222070
$731$	−42.0000	−1.55343
$732$	−12.0000	−0.443533
$733$	−46.0000	−1.69905	−0.849524	−	0.527549i	$-0.823111\pi$
$733$	−46.0000	−1.69905	−0.849524	+	0.527549i	$0.823111\pi$
$734$	27.0000	0.996588
$735$	2.00000	0.0737711
$736$	0	0
$737$	0	0
$738$	−10.0000	−0.368105
$739$	−27.0000	−0.993211	−0.496606	−	0.867976i	$-0.665420\pi$
$739$	−27.0000	−0.993211	−0.496606	+	0.867976i	$0.665420\pi$
$740$	−5.00000	−0.183804
$741$	35.0000	1.28576
$742$	36.0000	1.32160
$743$	16.0000	0.586983	0.293492	−	0.955962i	$-0.405183\pi$
$743$	16.0000	0.586983	0.293492	+	0.955962i	$0.405183\pi$
$744$	−6.00000	−0.219971
$745$	−6.00000	−0.219823
$746$	29.0000	1.06177
$747$	−13.0000	−0.475645
$748$	0	0
$749$	0	0
$750$	−1.00000	−0.0365148
$751$	−46.0000	−1.67856	−0.839282	−	0.543696i	$-0.817024\pi$
$751$	−46.0000	−1.67856	−0.839282	+	0.543696i	$0.817024\pi$
$752$	−10.0000	−0.364662
$753$	−12.0000	−0.437304
$754$	35.0000	1.27462
$755$	−20.0000	−0.727875
$756$	3.00000	0.109109
$757$	−26.0000	−0.944986	−0.472493	−	0.881334i	$-0.656646\pi$
$757$	−26.0000	−0.944986	−0.472493	+	0.881334i	$0.656646\pi$
$758$	−1.00000	−0.0363216
$759$	0	0
$760$	−7.00000	−0.253917
$761$	−36.0000	−1.30500	−0.652499	−	0.757789i	$-0.726280\pi$
$761$	−36.0000	−1.30500	−0.652499	+	0.757789i	$0.726280\pi$
$762$	−4.00000	−0.144905
$763$	−60.0000	−2.17215
$764$	−3.00000	−0.108536
$765$	7.00000	0.253086
$766$	−6.00000	−0.216789
$767$	0	0
$768$	1.00000	0.0360844
$769$	9.00000	0.324548	0.162274	−	0.986746i	$-0.448117\pi$
$769$	9.00000	0.324548	0.162274	+	0.986746i	$0.448117\pi$
$770$	0	0
$771$	17.0000	0.612240
$772$	24.0000	0.863779
$773$	−12.0000	−0.431610	−0.215805	−	0.976436i	$-0.569238\pi$
$773$	−12.0000	−0.431610	−0.215805	+	0.976436i	$0.569238\pi$
$774$	6.00000	0.215666
$775$	6.00000	0.215526
$776$	−2.00000	−0.0717958
$777$	−15.0000	−0.538122
$778$	−34.0000	−1.21896
$779$	70.0000	2.50801
$780$	5.00000	0.179029
$781$	0	0
$782$	0	0
$783$	−7.00000	−0.250160
$784$	2.00000	0.0714286
$785$	−11.0000	−0.392607
$786$	16.0000	0.570701
$787$	−28.0000	−0.998092	−0.499046	−	0.866575i	$-0.666316\pi$
$787$	−28.0000	−0.998092	−0.499046	+	0.866575i	$0.666316\pi$
$788$	−12.0000	−0.427482
$789$	−22.0000	−0.783221
$790$	−10.0000	−0.355784
$791$	30.0000	1.06668
$792$	0	0
$793$	−60.0000	−2.13066
$794$	−35.0000	−1.24210
$795$	−12.0000	−0.425596
$796$	−16.0000	−0.567105
$797$	40.0000	1.41687	0.708436	−	0.705775i	$-0.249401\pi$
$797$	40.0000	1.41687	0.708436	+	0.705775i	$0.249401\pi$
$798$	−21.0000	−0.743392
$799$	−70.0000	−2.47642
$800$	−1.00000	−0.0353553
$801$	4.00000	0.141333
$802$	34.0000	1.20058
$803$	0	0
$804$	−2.00000	−0.0705346
$805$	0	0
$806$	−30.0000	−1.05670
$807$	−19.0000	−0.668832
$808$	−3.00000	−0.105540
$809$	−18.0000	−0.632846	−0.316423	−	0.948618i	$-0.602482\pi$
$809$	−18.0000	−0.632846	−0.316423	+	0.948618i	$0.602482\pi$
$810$	−1.00000	−0.0351364
$811$	−17.0000	−0.596951	−0.298475	−	0.954417i	$-0.596478\pi$
$811$	−17.0000	−0.596951	−0.298475	+	0.954417i	$0.596478\pi$
$812$	−21.0000	−0.736956
$813$	22.0000	0.771574
$814$	0	0
$815$	4.00000	0.140114
$816$	7.00000	0.245049
$817$	−42.0000	−1.46939
$818$	6.00000	0.209785
$819$	15.0000	0.524142
$820$	10.0000	0.349215
$821$	6.00000	0.209401	0.104701	−	0.994504i	$-0.466612\pi$
$821$	6.00000	0.209401	0.104701	+	0.994504i	$0.466612\pi$
$822$	−3.00000	−0.104637
$823$	11.0000	0.383436	0.191718	−	0.981450i	$-0.438594\pi$
$823$	11.0000	0.383436	0.191718	+	0.981450i	$0.438594\pi$
$824$	3.00000	0.104510
$825$	0	0
$826$	0	0
$827$	−47.0000	−1.63435	−0.817175	−	0.576390i	$-0.804461\pi$
$827$	−47.0000	−1.63435	−0.817175	+	0.576390i	$0.804461\pi$
$828$	0	0
$829$	0	0		−	1.00000i	$-0.5\pi$
$829$	0	0			1.00000i	$0.5\pi$
$830$	13.0000	0.451237
$831$	26.0000	0.901930
$832$	5.00000	0.173344
$833$	14.0000	0.485071
$834$	−5.00000	−0.173136
$835$	16.0000	0.553703
$836$	0	0
$837$	6.00000	0.207390
$838$	14.0000	0.483622
$839$	35.0000	1.20833	0.604167	−	0.796858i	$-0.293506\pi$
$839$	35.0000	1.20833	0.604167	+	0.796858i	$0.293506\pi$
$840$	−3.00000	−0.103510
$841$	20.0000	0.689655
$842$	6.00000	0.206774
$843$	4.00000	0.137767
$844$	7.00000	0.240950
$845$	12.0000	0.412813
$846$	10.0000	0.343807
$847$	0	0
$848$	−12.0000	−0.412082
$849$	24.0000	0.823678
$850$	−7.00000	−0.240098
$851$	0	0
$852$	−9.00000	−0.308335
$853$	−7.00000	−0.239675	−0.119838	−	0.992793i	$-0.538237\pi$
$853$	−7.00000	−0.239675	−0.119838	+	0.992793i	$0.538237\pi$
$854$	36.0000	1.23189
$855$	7.00000	0.239395
$856$	0	0
$857$	51.0000	1.74213	0.871063	−	0.491171i	$-0.163431\pi$
$857$	51.0000	1.74213	0.871063	+	0.491171i	$0.163431\pi$
$858$	0	0
$859$	−28.0000	−0.955348	−0.477674	−	0.878537i	$-0.658520\pi$
$859$	−28.0000	−0.955348	−0.477674	+	0.878537i	$0.658520\pi$
$860$	−6.00000	−0.204598
$861$	30.0000	1.02240
$862$	−1.00000	−0.0340601
$863$	−30.0000	−1.02121	−0.510606	−	0.859815i	$-0.670579\pi$
$863$	−30.0000	−1.02121	−0.510606	+	0.859815i	$0.670579\pi$
$864$	−1.00000	−0.0340207
$865$	4.00000	0.136004
$866$	28.0000	0.951479
$867$	32.0000	1.08678
$868$	18.0000	0.610960
$869$	0	0
$870$	7.00000	0.237322
$871$	−10.0000	−0.338837
$872$	20.0000	0.677285
$873$	2.00000	0.0676897
$874$	0	0
$875$	3.00000	0.101419
$876$	6.00000	0.202721
$877$	47.0000	1.58708	0.793539	−	0.608520i	$-0.208236\pi$
$877$	47.0000	1.58708	0.793539	+	0.608520i	$0.208236\pi$
$878$	−26.0000	−0.877457
$879$	−16.0000	−0.539667
$880$	0	0
$881$	26.0000	0.875962	0.437981	−	0.898984i	$-0.355694\pi$
$881$	26.0000	0.875962	0.437981	+	0.898984i	$0.355694\pi$
$882$	−2.00000	−0.0673435
$883$	−14.0000	−0.471138	−0.235569	−	0.971858i	$-0.575695\pi$
$883$	−14.0000	−0.471138	−0.235569	+	0.971858i	$0.575695\pi$
$884$	35.0000	1.17718
$885$	0	0
$886$	−15.0000	−0.503935
$887$	16.0000	0.537227	0.268614	−	0.963248i	$-0.413434\pi$
$887$	16.0000	0.537227	0.268614	+	0.963248i	$0.413434\pi$
$888$	5.00000	0.167789
$889$	12.0000	0.402467
$890$	−4.00000	−0.134080
$891$	0	0
$892$	−1.00000	−0.0334825
$893$	−70.0000	−2.34246
$894$	6.00000	0.200670
$895$	−16.0000	−0.534821
$896$	−3.00000	−0.100223
$897$	0	0
$898$	−22.0000	−0.734150
$899$	−42.0000	−1.40078
$900$	1.00000	0.0333333
$901$	−84.0000	−2.79845
$902$	0	0
$903$	−18.0000	−0.599002
$904$	−10.0000	−0.332595
$905$	−8.00000	−0.265929
$906$	20.0000	0.664455
$907$	6.00000	0.199227	0.0996134	−	0.995026i	$-0.468239\pi$
$907$	6.00000	0.199227	0.0996134	+	0.995026i	$0.468239\pi$
$908$	0	0
$909$	3.00000	0.0995037
$910$	−15.0000	−0.497245
$911$	−57.0000	−1.88849	−0.944247	−	0.329238i	$-0.893208\pi$
$911$	−57.0000	−1.88849	−0.944247	+	0.329238i	$0.893208\pi$
$912$	7.00000	0.231793
$913$	0	0
$914$	4.00000	0.132308
$915$	−12.0000	−0.396708
$916$	16.0000	0.528655
$917$	−48.0000	−1.58510
$918$	−7.00000	−0.231034
$919$	−48.0000	−1.58337	−0.791687	−	0.610927i	$-0.790797\pi$
$919$	−48.0000	−1.58337	−0.791687	+	0.610927i	$0.790797\pi$
$920$	0	0
$921$	34.0000	1.12034
$922$	−33.0000	−1.08680
$923$	−45.0000	−1.48119
$924$	0	0
$925$	−5.00000	−0.164399
$926$	8.00000	0.262896
$927$	−3.00000	−0.0985329
$928$	7.00000	0.229786
$929$	−16.0000	−0.524943	−0.262471	−	0.964940i	$-0.584538\pi$
$929$	−16.0000	−0.524943	−0.262471	+	0.964940i	$0.584538\pi$
$930$	−6.00000	−0.196748
$931$	14.0000	0.458831
$932$	2.00000	0.0655122
$933$	−8.00000	−0.261908
$934$	7.00000	0.229047
$935$	0	0
$936$	−5.00000	−0.163430
$937$	18.0000	0.588034	0.294017	−	0.955800i	$-0.405008\pi$
$937$	18.0000	0.588034	0.294017	+	0.955800i	$0.405008\pi$
$938$	6.00000	0.195907
$939$	−2.00000	−0.0652675
$940$	−10.0000	−0.326164
$941$	33.0000	1.07577	0.537885	−	0.843018i	$-0.319224\pi$
$941$	33.0000	1.07577	0.537885	+	0.843018i	$0.319224\pi$
$942$	11.0000	0.358399
$943$	0	0
$944$	0	0
$945$	3.00000	0.0975900
$946$	0	0
$947$	3.00000	0.0974869	0.0487435	−	0.998811i	$-0.484478\pi$
$947$	3.00000	0.0974869	0.0487435	+	0.998811i	$0.484478\pi$
$948$	10.0000	0.324785
$949$	30.0000	0.973841
$950$	−7.00000	−0.227110
$951$	12.0000	0.389127
$952$	−21.0000	−0.680614
$953$	18.0000	0.583077	0.291539	−	0.956559i	$-0.405833\pi$
$953$	18.0000	0.583077	0.291539	+	0.956559i	$0.405833\pi$
$954$	12.0000	0.388514
$955$	−3.00000	−0.0970777
$956$	3.00000	0.0970269
$957$	0	0
$958$	−3.00000	−0.0969256
$959$	9.00000	0.290625
$960$	1.00000	0.0322749
$961$	5.00000	0.161290
$962$	25.0000	0.806032
$963$	0	0
$964$	−25.0000	−0.805196
$965$	24.0000	0.772587
$966$	0	0
$967$	−16.0000	−0.514525	−0.257263	−	0.966342i	$-0.582821\pi$
$967$	−16.0000	−0.514525	−0.257263	+	0.966342i	$0.582821\pi$
$968$	0	0
$969$	49.0000	1.57411
$970$	−2.00000	−0.0642161
$971$	48.0000	1.54039	0.770197	−	0.637806i	$-0.220158\pi$
$971$	48.0000	1.54039	0.770197	+	0.637806i	$0.220158\pi$
$972$	1.00000	0.0320750
$973$	15.0000	0.480878
$974$	−29.0000	−0.929220
$975$	5.00000	0.160128
$976$	−12.0000	−0.384111
$977$	42.0000	1.34370	0.671850	−	0.740688i	$-0.265500\pi$
$977$	42.0000	1.34370	0.671850	+	0.740688i	$0.265500\pi$
$978$	−4.00000	−0.127906
$979$	0	0
$980$	2.00000	0.0638877
$981$	−20.0000	−0.638551
$982$	30.0000	0.957338
$983$	−14.0000	−0.446531	−0.223265	−	0.974758i	$-0.571672\pi$
$983$	−14.0000	−0.446531	−0.223265	+	0.974758i	$0.571672\pi$
$984$	−10.0000	−0.318788
$985$	−12.0000	−0.382352
$986$	49.0000	1.56048
$987$	−30.0000	−0.954911
$988$	35.0000	1.11350
$989$	0	0
$990$	0	0
$991$	−34.0000	−1.08005	−0.540023	−	0.841650i	$-0.681584\pi$
$991$	−34.0000	−1.08005	−0.540023	+	0.841650i	$0.681584\pi$
$992$	−6.00000	−0.190500
$993$	−17.0000	−0.539479
$994$	27.0000	0.856388
$995$	−16.0000	−0.507234
$996$	−13.0000	−0.411921
$997$	23.0000	0.728417	0.364209	−	0.931317i	$-0.381339\pi$
$997$	23.0000	0.728417	0.364209	+	0.931317i	$0.381339\pi$
$998$	−33.0000	−1.04460
$999$	−5.00000	−0.158193

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3630.2.a.l.1.1	✓	1
11.10	odd	2		3630.2.a.y.1.1	yes	1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3630.2.a.l.1.1	✓	1	1.1	even	1	trivial
3630.2.a.y.1.1	yes	1	11.10	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:	\( N \)	\(=\)	\( 3630 = 2 \cdot 3 \cdot 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3630.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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