LMFDB - Embedded newform 366.2.a.d.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [366,2,Mod(1,366)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(366, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("366.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 366 = 2 \cdot 3 \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	366.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:	$2.92252471398$
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	$\chi$	$=$	366.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

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

\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.00000 q^{5} -1.00000 q^{6} -3.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} -3.00000 q^{10} -1.00000 q^{11} -1.00000 q^{12} -5.00000 q^{13} -3.00000 q^{14} +3.00000 q^{15} +1.00000 q^{16} +2.00000 q^{17} +1.00000 q^{18} -8.00000 q^{19} -3.00000 q^{20} +3.00000 q^{21} -1.00000 q^{22} +5.00000 q^{23} -1.00000 q^{24} +4.00000 q^{25} -5.00000 q^{26} -1.00000 q^{27} -3.00000 q^{28} +3.00000 q^{30} -4.00000 q^{31} +1.00000 q^{32} +1.00000 q^{33} +2.00000 q^{34} +9.00000 q^{35} +1.00000 q^{36} +4.00000 q^{37} -8.00000 q^{38} +5.00000 q^{39} -3.00000 q^{40} +3.00000 q^{41} +3.00000 q^{42} +4.00000 q^{43} -1.00000 q^{44} -3.00000 q^{45} +5.00000 q^{46} +2.00000 q^{47} -1.00000 q^{48} +2.00000 q^{49} +4.00000 q^{50} -2.00000 q^{51} -5.00000 q^{52} -1.00000 q^{54} +3.00000 q^{55} -3.00000 q^{56} +8.00000 q^{57} -7.00000 q^{59} +3.00000 q^{60} +1.00000 q^{61} -4.00000 q^{62} -3.00000 q^{63} +1.00000 q^{64} +15.0000 q^{65} +1.00000 q^{66} -13.0000 q^{67} +2.00000 q^{68} -5.00000 q^{69} +9.00000 q^{70} -16.0000 q^{71} +1.00000 q^{72} +9.00000 q^{73} +4.00000 q^{74} -4.00000 q^{75} -8.00000 q^{76} +3.00000 q^{77} +5.00000 q^{78} -1.00000 q^{79} -3.00000 q^{80} +1.00000 q^{81} +3.00000 q^{82} +14.0000 q^{83} +3.00000 q^{84} -6.00000 q^{85} +4.00000 q^{86} -1.00000 q^{88} -4.00000 q^{89} -3.00000 q^{90} +15.0000 q^{91} +5.00000 q^{92} +4.00000 q^{93} +2.00000 q^{94} +24.0000 q^{95} -1.00000 q^{96} +14.0000 q^{97} +2.00000 q^{98} -1.00000 q^{99} +O(q^{100})\)

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
$5$	−3.00000	−1.34164	−0.670820	−	0.741620i	$-0.734058\pi$
$5$	−3.00000	−1.34164	−0.670820	+	0.741620i	$0.734058\pi$
$6$	−1.00000	−0.408248
$7$	−3.00000	−1.13389	−0.566947	−	0.823754i	$-0.691875\pi$
$7$	−3.00000	−1.13389	−0.566947	+	0.823754i	$0.691875\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−3.00000	−0.948683
$11$	−1.00000	−0.301511	−0.150756	−	0.988571i	$-0.548171\pi$
$11$	−1.00000	−0.301511	−0.150756	+	0.988571i	$0.548171\pi$
$12$	−1.00000	−0.288675
$13$	−5.00000	−1.38675	−0.693375	−	0.720577i	$-0.743877\pi$
$13$	−5.00000	−1.38675	−0.693375	+	0.720577i	$0.743877\pi$
$14$	−3.00000	−0.801784
$15$	3.00000	0.774597
$16$	1.00000	0.250000
$17$	2.00000	0.485071	0.242536	−	0.970143i	$-0.422021\pi$
$17$	2.00000	0.485071	0.242536	+	0.970143i	$0.422021\pi$
$18$	1.00000	0.235702
$19$	−8.00000	−1.83533	−0.917663	−	0.397360i	$-0.869927\pi$
$19$	−8.00000	−1.83533	−0.917663	+	0.397360i	$0.869927\pi$
$20$	−3.00000	−0.670820
$21$	3.00000	0.654654
$22$	−1.00000	−0.213201
$23$	5.00000	1.04257	0.521286	−	0.853382i	$-0.325452\pi$
$23$	5.00000	1.04257	0.521286	+	0.853382i	$0.325452\pi$
$24$	−1.00000	−0.204124
$25$	4.00000	0.800000
$26$	−5.00000	−0.980581
$27$	−1.00000	−0.192450
$28$	−3.00000	−0.566947
$29$	0	0		−	1.00000i	$-0.5\pi$
$29$	0	0			1.00000i	$0.5\pi$
$30$	3.00000	0.547723
$31$	−4.00000	−0.718421	−0.359211	−	0.933257i	$-0.616954\pi$
$31$	−4.00000	−0.718421	−0.359211	+	0.933257i	$0.616954\pi$
$32$	1.00000	0.176777
$33$	1.00000	0.174078
$34$	2.00000	0.342997
$35$	9.00000	1.52128
$36$	1.00000	0.166667
$37$	4.00000	0.657596	0.328798	−	0.944400i	$-0.393356\pi$
$37$	4.00000	0.657596	0.328798	+	0.944400i	$0.393356\pi$
$38$	−8.00000	−1.29777
$39$	5.00000	0.800641
$40$	−3.00000	−0.474342
$41$	3.00000	0.468521	0.234261	−	0.972174i	$-0.424733\pi$
$41$	3.00000	0.468521	0.234261	+	0.972174i	$0.424733\pi$
$42$	3.00000	0.462910
$43$	4.00000	0.609994	0.304997	−	0.952353i	$-0.401344\pi$
$43$	4.00000	0.609994	0.304997	+	0.952353i	$0.401344\pi$
$44$	−1.00000	−0.150756
$45$	−3.00000	−0.447214
$46$	5.00000	0.737210
$47$	2.00000	0.291730	0.145865	−	0.989305i	$-0.453403\pi$
$47$	2.00000	0.291730	0.145865	+	0.989305i	$0.453403\pi$
$48$	−1.00000	−0.144338
$49$	2.00000	0.285714
$50$	4.00000	0.565685
$51$	−2.00000	−0.280056
$52$	−5.00000	−0.693375
$53$	0	0		−	1.00000i	$-0.5\pi$
$53$	0	0			1.00000i	$0.5\pi$
$54$	−1.00000	−0.136083
$55$	3.00000	0.404520
$56$	−3.00000	−0.400892
$57$	8.00000	1.05963
$58$	0	0
$59$	−7.00000	−0.911322	−0.455661	−	0.890153i	$-0.650597\pi$
$59$	−7.00000	−0.911322	−0.455661	+	0.890153i	$0.650597\pi$
$60$	3.00000	0.387298
$61$	1.00000	0.128037
$61$	1.00000	0.128037
$62$	−4.00000	−0.508001
$63$	−3.00000	−0.377964
$64$	1.00000	0.125000
$65$	15.0000	1.86052
$66$	1.00000	0.123091
$67$	−13.0000	−1.58820	−0.794101	−	0.607785i	$-0.792058\pi$
$67$	−13.0000	−1.58820	−0.794101	+	0.607785i	$0.792058\pi$
$68$	2.00000	0.242536
$69$	−5.00000	−0.601929
$70$	9.00000	1.07571
$71$	−16.0000	−1.89885	−0.949425	−	0.313993i	$-0.898333\pi$
$71$	−16.0000	−1.89885	−0.949425	+	0.313993i	$0.898333\pi$
$72$	1.00000	0.117851
$73$	9.00000	1.05337	0.526685	−	0.850060i	$-0.323435\pi$
$73$	9.00000	1.05337	0.526685	+	0.850060i	$0.323435\pi$
$74$	4.00000	0.464991
$75$	−4.00000	−0.461880
$76$	−8.00000	−0.917663
$77$	3.00000	0.341882
$78$	5.00000	0.566139
$79$	−1.00000	−0.112509	−0.0562544	−	0.998416i	$-0.517916\pi$
$79$	−1.00000	−0.112509	−0.0562544	+	0.998416i	$0.517916\pi$
$80$	−3.00000	−0.335410
$81$	1.00000	0.111111
$82$	3.00000	0.331295
$83$	14.0000	1.53670	0.768350	−	0.640030i	$-0.221078\pi$
$83$	14.0000	1.53670	0.768350	+	0.640030i	$0.221078\pi$
$84$	3.00000	0.327327
$85$	−6.00000	−0.650791
$86$	4.00000	0.431331
$87$	0	0
$88$	−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	$0.567998\pi$
$90$	−3.00000	−0.316228
$91$	15.0000	1.57243
$92$	5.00000	0.521286
$93$	4.00000	0.414781
$94$	2.00000	0.206284
$95$	24.0000	2.46235
$96$	−1.00000	−0.102062
$97$	14.0000	1.42148	0.710742	−	0.703452i	$-0.248359\pi$
$97$	14.0000	1.42148	0.710742	+	0.703452i	$0.248359\pi$
$98$	2.00000	0.202031
$99$	−1.00000	−0.100504
$100$	4.00000	0.400000
$101$	−8.00000	−0.796030	−0.398015	−	0.917379i	$-0.630301\pi$
$101$	−8.00000	−0.796030	−0.398015	+	0.917379i	$0.630301\pi$
$102$	−2.00000	−0.198030
$103$	−14.0000	−1.37946	−0.689730	−	0.724066i	$-0.742271\pi$
$103$	−14.0000	−1.37946	−0.689730	+	0.724066i	$0.742271\pi$
$104$	−5.00000	−0.490290
$105$	−9.00000	−0.878310
$106$	0	0
$107$	−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
$109$	−15.0000	−1.43674	−0.718370	−	0.695662i	$-0.755111\pi$
$109$	−15.0000	−1.43674	−0.718370	+	0.695662i	$0.755111\pi$
$110$	3.00000	0.286039
$111$	−4.00000	−0.379663
$112$	−3.00000	−0.283473
$113$	11.0000	1.03479	0.517396	−	0.855746i	$-0.326901\pi$
$113$	11.0000	1.03479	0.517396	+	0.855746i	$0.326901\pi$
$114$	8.00000	0.749269
$115$	−15.0000	−1.39876
$116$	0	0
$117$	−5.00000	−0.462250
$118$	−7.00000	−0.644402
$119$	−6.00000	−0.550019
$120$	3.00000	0.273861
$121$	−10.0000	−0.909091
$122$	1.00000	0.0905357
$123$	−3.00000	−0.270501
$124$	−4.00000	−0.359211
$125$	3.00000	0.268328
$126$	−3.00000	−0.267261
$127$	−22.0000	−1.95218	−0.976092	−	0.217357i	$-0.930256\pi$
$127$	−22.0000	−1.95218	−0.976092	+	0.217357i	$0.930256\pi$
$128$	1.00000	0.0883883
$129$	−4.00000	−0.352180
$130$	15.0000	1.31559
$131$	10.0000	0.873704	0.436852	−	0.899533i	$-0.356093\pi$
$131$	10.0000	0.873704	0.436852	+	0.899533i	$0.356093\pi$
$132$	1.00000	0.0870388
$133$	24.0000	2.08106
$134$	−13.0000	−1.12303
$135$	3.00000	0.258199
$136$	2.00000	0.171499
$137$	15.0000	1.28154	0.640768	−	0.767734i	$-0.278616\pi$
$137$	15.0000	1.28154	0.640768	+	0.767734i	$0.278616\pi$
$138$	−5.00000	−0.425628
$139$	−5.00000	−0.424094	−0.212047	−	0.977259i	$-0.568013\pi$
$139$	−5.00000	−0.424094	−0.212047	+	0.977259i	$0.568013\pi$
$140$	9.00000	0.760639
$141$	−2.00000	−0.168430
$142$	−16.0000	−1.34269
$143$	5.00000	0.418121
$144$	1.00000	0.0833333
$145$	0	0
$146$	9.00000	0.744845
$147$	−2.00000	−0.164957
$148$	4.00000	0.328798
$149$	−21.0000	−1.72039	−0.860194	−	0.509968i	$-0.829657\pi$
$149$	−21.0000	−1.72039	−0.860194	+	0.509968i	$0.829657\pi$
$150$	−4.00000	−0.326599
$151$	−9.00000	−0.732410	−0.366205	−	0.930534i	$-0.619343\pi$
$151$	−9.00000	−0.732410	−0.366205	+	0.930534i	$0.619343\pi$
$152$	−8.00000	−0.648886
$153$	2.00000	0.161690
$154$	3.00000	0.241747
$155$	12.0000	0.963863
$156$	5.00000	0.400320
$157$	6.00000	0.478852	0.239426	−	0.970915i	$-0.423041\pi$
$157$	6.00000	0.478852	0.239426	+	0.970915i	$0.423041\pi$
$158$	−1.00000	−0.0795557
$159$	0	0
$160$	−3.00000	−0.237171
$161$	−15.0000	−1.18217
$162$	1.00000	0.0785674
$163$	−4.00000	−0.313304	−0.156652	−	0.987654i	$-0.550070\pi$
$163$	−4.00000	−0.313304	−0.156652	+	0.987654i	$0.550070\pi$
$164$	3.00000	0.234261
$165$	−3.00000	−0.233550
$166$	14.0000	1.08661
$167$	−18.0000	−1.39288	−0.696441	−	0.717614i	$-0.745234\pi$
$167$	−18.0000	−1.39288	−0.696441	+	0.717614i	$0.745234\pi$
$168$	3.00000	0.231455
$169$	12.0000	0.923077
$170$	−6.00000	−0.460179
$171$	−8.00000	−0.611775
$172$	4.00000	0.304997
$173$	−22.0000	−1.67263	−0.836315	−	0.548250i	$-0.815294\pi$
$173$	−22.0000	−1.67263	−0.836315	+	0.548250i	$0.815294\pi$
$174$	0	0
$175$	−12.0000	−0.907115
$176$	−1.00000	−0.0753778
$177$	7.00000	0.526152
$178$	−4.00000	−0.299813
$179$	0	0		−	1.00000i	$-0.5\pi$
$179$	0	0			1.00000i	$0.5\pi$
$180$	−3.00000	−0.223607
$181$	26.0000	1.93256	0.966282	−	0.257485i	$-0.0828937\pi$
$181$	26.0000	1.93256	0.966282	+	0.257485i	$0.0828937\pi$
$182$	15.0000	1.11187
$183$	−1.00000	−0.0739221
$184$	5.00000	0.368605
$185$	−12.0000	−0.882258
$186$	4.00000	0.293294
$187$	−2.00000	−0.146254
$188$	2.00000	0.145865
$189$	3.00000	0.218218
$190$	24.0000	1.74114
$191$	−15.0000	−1.08536	−0.542681	−	0.839939i	$-0.682591\pi$
$191$	−15.0000	−1.08536	−0.542681	+	0.839939i	$0.682591\pi$
$192$	−1.00000	−0.0721688
$193$	−18.0000	−1.29567	−0.647834	−	0.761781i	$-0.724325\pi$
$193$	−18.0000	−1.29567	−0.647834	+	0.761781i	$0.724325\pi$
$194$	14.0000	1.00514
$195$	−15.0000	−1.07417
$196$	2.00000	0.142857
$197$	21.0000	1.49619	0.748094	−	0.663593i	$-0.230969\pi$
$197$	21.0000	1.49619	0.748094	+	0.663593i	$0.230969\pi$
$198$	−1.00000	−0.0710669
$199$	18.0000	1.27599	0.637993	−	0.770042i	$-0.279765\pi$
$199$	18.0000	1.27599	0.637993	+	0.770042i	$0.279765\pi$
$200$	4.00000	0.282843
$201$	13.0000	0.916949
$202$	−8.00000	−0.562878
$203$	0	0
$204$	−2.00000	−0.140028
$205$	−9.00000	−0.628587
$206$	−14.0000	−0.975426
$207$	5.00000	0.347524
$208$	−5.00000	−0.346688
$209$	8.00000	0.553372
$210$	−9.00000	−0.621059
$211$	20.0000	1.37686	0.688428	−	0.725304i	$-0.258301\pi$
$211$	20.0000	1.37686	0.688428	+	0.725304i	$0.258301\pi$
$212$	0	0
$213$	16.0000	1.09630
$214$	−2.00000	−0.136717
$215$	−12.0000	−0.818393
$216$	−1.00000	−0.0680414
$217$	12.0000	0.814613
$218$	−15.0000	−1.01593
$219$	−9.00000	−0.608164
$220$	3.00000	0.202260
$221$	−10.0000	−0.672673
$222$	−4.00000	−0.268462
$223$	−21.0000	−1.40626	−0.703132	−	0.711059i	$-0.748216\pi$
$223$	−21.0000	−1.40626	−0.703132	+	0.711059i	$0.748216\pi$
$224$	−3.00000	−0.200446
$225$	4.00000	0.266667
$226$	11.0000	0.731709
$227$	−15.0000	−0.995585	−0.497792	−	0.867296i	$-0.665856\pi$
$227$	−15.0000	−0.995585	−0.497792	+	0.867296i	$0.665856\pi$
$228$	8.00000	0.529813
$229$	−17.0000	−1.12339	−0.561696	−	0.827344i	$-0.689851\pi$
$229$	−17.0000	−1.12339	−0.561696	+	0.827344i	$0.689851\pi$
$230$	−15.0000	−0.989071
$231$	−3.00000	−0.197386
$232$	0	0
$233$	0	0		−	1.00000i	$-0.5\pi$
$233$	0	0			1.00000i	$0.5\pi$
$234$	−5.00000	−0.326860
$235$	−6.00000	−0.391397
$236$	−7.00000	−0.455661
$237$	1.00000	0.0649570
$238$	−6.00000	−0.388922
$239$	−12.0000	−0.776215	−0.388108	−	0.921614i	$-0.626871\pi$
$239$	−12.0000	−0.776215	−0.388108	+	0.921614i	$0.626871\pi$
$240$	3.00000	0.193649
$241$	25.0000	1.61039	0.805196	−	0.593009i	$-0.202060\pi$
$241$	25.0000	1.61039	0.805196	+	0.593009i	$0.202060\pi$
$242$	−10.0000	−0.642824
$243$	−1.00000	−0.0641500
$244$	1.00000	0.0640184
$245$	−6.00000	−0.383326
$246$	−3.00000	−0.191273
$247$	40.0000	2.54514
$248$	−4.00000	−0.254000
$249$	−14.0000	−0.887214
$250$	3.00000	0.189737
$251$	8.00000	0.504956	0.252478	−	0.967603i	$-0.418755\pi$
$251$	8.00000	0.504956	0.252478	+	0.967603i	$0.418755\pi$
$252$	−3.00000	−0.188982
$253$	−5.00000	−0.314347
$254$	−22.0000	−1.38040
$255$	6.00000	0.375735
$256$	1.00000	0.0625000
$257$	−18.0000	−1.12281	−0.561405	−	0.827541i	$-0.689739\pi$
$257$	−18.0000	−1.12281	−0.561405	+	0.827541i	$0.689739\pi$
$258$	−4.00000	−0.249029
$259$	−12.0000	−0.745644
$260$	15.0000	0.930261
$261$	0	0
$262$	10.0000	0.617802
$263$	24.0000	1.47990	0.739952	−	0.672660i	$-0.234848\pi$
$263$	24.0000	1.47990	0.739952	+	0.672660i	$0.234848\pi$
$264$	1.00000	0.0615457
$265$	0	0
$266$	24.0000	1.47153
$267$	4.00000	0.244796
$268$	−13.0000	−0.794101
$269$	−18.0000	−1.09748	−0.548740	−	0.835993i	$-0.684892\pi$
$269$	−18.0000	−1.09748	−0.548740	+	0.835993i	$0.684892\pi$
$270$	3.00000	0.182574
$271$	8.00000	0.485965	0.242983	−	0.970031i	$-0.421874\pi$
$271$	8.00000	0.485965	0.242983	+	0.970031i	$0.421874\pi$
$272$	2.00000	0.121268
$273$	−15.0000	−0.907841
$274$	15.0000	0.906183
$275$	−4.00000	−0.241209
$276$	−5.00000	−0.300965
$277$	22.0000	1.32185	0.660926	−	0.750451i	$-0.270164\pi$
$277$	22.0000	1.32185	0.660926	+	0.750451i	$0.270164\pi$
$278$	−5.00000	−0.299880
$279$	−4.00000	−0.239474
$280$	9.00000	0.537853
$281$	24.0000	1.43172	0.715860	−	0.698244i	$-0.246035\pi$
$281$	24.0000	1.43172	0.715860	+	0.698244i	$0.246035\pi$
$282$	−2.00000	−0.119098
$283$	−14.0000	−0.832214	−0.416107	−	0.909316i	$-0.636606\pi$
$283$	−14.0000	−0.832214	−0.416107	+	0.909316i	$0.636606\pi$
$284$	−16.0000	−0.949425
$285$	−24.0000	−1.42164
$286$	5.00000	0.295656
$287$	−9.00000	−0.531253
$288$	1.00000	0.0589256
$289$	−13.0000	−0.764706
$290$	0	0
$291$	−14.0000	−0.820695
$292$	9.00000	0.526685
$293$	−6.00000	−0.350524	−0.175262	−	0.984522i	$-0.556077\pi$
$293$	−6.00000	−0.350524	−0.175262	+	0.984522i	$0.556077\pi$
$294$	−2.00000	−0.116642
$295$	21.0000	1.22267
$296$	4.00000	0.232495
$297$	1.00000	0.0580259
$298$	−21.0000	−1.21650
$299$	−25.0000	−1.44579
$300$	−4.00000	−0.230940
$301$	−12.0000	−0.691669
$302$	−9.00000	−0.517892
$303$	8.00000	0.459588
$304$	−8.00000	−0.458831
$305$	−3.00000	−0.171780
$306$	2.00000	0.114332
$307$	19.0000	1.08439	0.542194	−	0.840254i	$-0.317594\pi$
$307$	19.0000	1.08439	0.542194	+	0.840254i	$0.317594\pi$
$308$	3.00000	0.170941
$309$	14.0000	0.796432
$310$	12.0000	0.681554
$311$	35.0000	1.98467	0.992334	−	0.123585i	$-0.0394392\pi$
$311$	35.0000	1.98467	0.992334	+	0.123585i	$0.0394392\pi$
$312$	5.00000	0.283069
$313$	−8.00000	−0.452187	−0.226093	−	0.974106i	$-0.572595\pi$
$313$	−8.00000	−0.452187	−0.226093	+	0.974106i	$0.572595\pi$
$314$	6.00000	0.338600
$315$	9.00000	0.507093
$316$	−1.00000	−0.0562544
$317$	10.0000	0.561656	0.280828	−	0.959758i	$-0.409391\pi$
$317$	10.0000	0.561656	0.280828	+	0.959758i	$0.409391\pi$
$318$	0	0
$319$	0	0
$320$	−3.00000	−0.167705
$321$	2.00000	0.111629
$322$	−15.0000	−0.835917
$323$	−16.0000	−0.890264
$324$	1.00000	0.0555556
$325$	−20.0000	−1.10940
$326$	−4.00000	−0.221540
$327$	15.0000	0.829502
$328$	3.00000	0.165647
$329$	−6.00000	−0.330791
$330$	−3.00000	−0.165145
$331$	9.00000	0.494685	0.247342	−	0.968928i	$-0.420443\pi$
$331$	9.00000	0.494685	0.247342	+	0.968928i	$0.420443\pi$
$332$	14.0000	0.768350
$333$	4.00000	0.219199
$334$	−18.0000	−0.984916
$335$	39.0000	2.13080
$336$	3.00000	0.163663
$337$	−16.0000	−0.871576	−0.435788	−	0.900049i	$-0.643530\pi$
$337$	−16.0000	−0.871576	−0.435788	+	0.900049i	$0.643530\pi$
$338$	12.0000	0.652714
$339$	−11.0000	−0.597438
$340$	−6.00000	−0.325396
$341$	4.00000	0.216612
$342$	−8.00000	−0.432590
$343$	15.0000	0.809924
$344$	4.00000	0.215666
$345$	15.0000	0.807573
$346$	−22.0000	−1.18273
$347$	−4.00000	−0.214731	−0.107366	−	0.994220i	$-0.534242\pi$
$347$	−4.00000	−0.214731	−0.107366	+	0.994220i	$0.534242\pi$
$348$	0	0
$349$	−22.0000	−1.17763	−0.588817	−	0.808267i	$-0.700406\pi$
$349$	−22.0000	−1.17763	−0.588817	+	0.808267i	$0.700406\pi$
$350$	−12.0000	−0.641427
$351$	5.00000	0.266880
$352$	−1.00000	−0.0533002
$353$	25.0000	1.33062	0.665308	−	0.746569i	$-0.268300\pi$
$353$	25.0000	1.33062	0.665308	+	0.746569i	$0.268300\pi$
$354$	7.00000	0.372046
$355$	48.0000	2.54758
$356$	−4.00000	−0.212000
$357$	6.00000	0.317554
$358$	0	0
$359$	36.0000	1.90001	0.950004	−	0.312239i	$-0.101079\pi$
$359$	36.0000	1.90001	0.950004	+	0.312239i	$0.101079\pi$
$360$	−3.00000	−0.158114
$361$	45.0000	2.36842
$362$	26.0000	1.36653
$363$	10.0000	0.524864
$364$	15.0000	0.786214
$365$	−27.0000	−1.41324
$366$	−1.00000	−0.0522708
$367$	36.0000	1.87918	0.939592	−	0.342296i	$-0.111204\pi$
$367$	36.0000	1.87918	0.939592	+	0.342296i	$0.111204\pi$
$368$	5.00000	0.260643
$369$	3.00000	0.156174
$370$	−12.0000	−0.623850
$371$	0	0
$372$	4.00000	0.207390
$373$	4.00000	0.207112	0.103556	−	0.994624i	$-0.466978\pi$
$373$	4.00000	0.207112	0.103556	+	0.994624i	$0.466978\pi$
$374$	−2.00000	−0.103418
$375$	−3.00000	−0.154919
$376$	2.00000	0.103142
$377$	0	0
$378$	3.00000	0.154303
$379$	0	0		−	1.00000i	$-0.5\pi$
$379$	0	0			1.00000i	$0.5\pi$
$380$	24.0000	1.23117
$381$	22.0000	1.12709
$382$	−15.0000	−0.767467
$383$	7.00000	0.357683	0.178842	−	0.983878i	$-0.442765\pi$
$383$	7.00000	0.357683	0.178842	+	0.983878i	$0.442765\pi$
$384$	−1.00000	−0.0510310
$385$	−9.00000	−0.458682
$386$	−18.0000	−0.916176
$387$	4.00000	0.203331
$388$	14.0000	0.710742
$389$	18.0000	0.912636	0.456318	−	0.889817i	$-0.349168\pi$
$389$	18.0000	0.912636	0.456318	+	0.889817i	$0.349168\pi$
$390$	−15.0000	−0.759555
$391$	10.0000	0.505722
$392$	2.00000	0.101015
$393$	−10.0000	−0.504433
$394$	21.0000	1.05796
$395$	3.00000	0.150946
$396$	−1.00000	−0.0502519
$397$	−2.00000	−0.100377	−0.0501886	−	0.998740i	$-0.515982\pi$
$397$	−2.00000	−0.100377	−0.0501886	+	0.998740i	$0.515982\pi$
$398$	18.0000	0.902258
$399$	−24.0000	−1.20150
$400$	4.00000	0.200000
$401$	6.00000	0.299626	0.149813	−	0.988714i	$-0.452133\pi$
$401$	6.00000	0.299626	0.149813	+	0.988714i	$0.452133\pi$
$402$	13.0000	0.648381
$403$	20.0000	0.996271
$404$	−8.00000	−0.398015
$405$	−3.00000	−0.149071
$406$	0	0
$407$	−4.00000	−0.198273
$408$	−2.00000	−0.0990148
$409$	−20.0000	−0.988936	−0.494468	−	0.869196i	$-0.664637\pi$
$409$	−20.0000	−0.988936	−0.494468	+	0.869196i	$0.664637\pi$
$410$	−9.00000	−0.444478
$411$	−15.0000	−0.739895
$412$	−14.0000	−0.689730
$413$	21.0000	1.03334
$414$	5.00000	0.245737
$415$	−42.0000	−2.06170
$416$	−5.00000	−0.245145
$417$	5.00000	0.244851
$418$	8.00000	0.391293
$419$	4.00000	0.195413	0.0977064	−	0.995215i	$-0.468849\pi$
$419$	4.00000	0.195413	0.0977064	+	0.995215i	$0.468849\pi$
$420$	−9.00000	−0.439155
$421$	2.00000	0.0974740	0.0487370	−	0.998812i	$-0.484480\pi$
$421$	2.00000	0.0974740	0.0487370	+	0.998812i	$0.484480\pi$
$422$	20.0000	0.973585
$423$	2.00000	0.0972433
$424$	0	0
$425$	8.00000	0.388057
$426$	16.0000	0.775203
$427$	−3.00000	−0.145180
$428$	−2.00000	−0.0966736
$429$	−5.00000	−0.241402
$430$	−12.0000	−0.578691
$431$	−2.00000	−0.0963366	−0.0481683	−	0.998839i	$-0.515338\pi$
$431$	−2.00000	−0.0963366	−0.0481683	+	0.998839i	$0.515338\pi$
$432$	−1.00000	−0.0481125
$433$	−2.00000	−0.0961139	−0.0480569	−	0.998845i	$-0.515303\pi$
$433$	−2.00000	−0.0961139	−0.0480569	+	0.998845i	$0.515303\pi$
$434$	12.0000	0.576018
$435$	0	0
$436$	−15.0000	−0.718370
$437$	−40.0000	−1.91346
$438$	−9.00000	−0.430037
$439$	−12.0000	−0.572729	−0.286364	−	0.958121i	$-0.592447\pi$
$439$	−12.0000	−0.572729	−0.286364	+	0.958121i	$0.592447\pi$
$440$	3.00000	0.143019
$441$	2.00000	0.0952381
$442$	−10.0000	−0.475651
$443$	−16.0000	−0.760183	−0.380091	−	0.924949i	$-0.624107\pi$
$443$	−16.0000	−0.760183	−0.380091	+	0.924949i	$0.624107\pi$
$444$	−4.00000	−0.189832
$445$	12.0000	0.568855
$446$	−21.0000	−0.994379
$447$	21.0000	0.993266
$448$	−3.00000	−0.141737
$449$	−17.0000	−0.802280	−0.401140	−	0.916017i	$-0.631386\pi$
$449$	−17.0000	−0.802280	−0.401140	+	0.916017i	$0.631386\pi$
$450$	4.00000	0.188562
$451$	−3.00000	−0.141264
$452$	11.0000	0.517396
$453$	9.00000	0.422857
$454$	−15.0000	−0.703985
$455$	−45.0000	−2.10963
$456$	8.00000	0.374634
$457$	8.00000	0.374224	0.187112	−	0.982339i	$-0.440087\pi$
$457$	8.00000	0.374224	0.187112	+	0.982339i	$0.440087\pi$
$458$	−17.0000	−0.794358
$459$	−2.00000	−0.0933520
$460$	−15.0000	−0.699379
$461$	−6.00000	−0.279448	−0.139724	−	0.990190i	$-0.544622\pi$
$461$	−6.00000	−0.279448	−0.139724	+	0.990190i	$0.544622\pi$
$462$	−3.00000	−0.139573
$463$	8.00000	0.371792	0.185896	−	0.982569i	$-0.440481\pi$
$463$	8.00000	0.371792	0.185896	+	0.982569i	$0.440481\pi$
$464$	0	0
$465$	−12.0000	−0.556487
$466$	0	0
$467$	−25.0000	−1.15686	−0.578431	−	0.815731i	$-0.696335\pi$
$467$	−25.0000	−1.15686	−0.578431	+	0.815731i	$0.696335\pi$
$468$	−5.00000	−0.231125
$469$	39.0000	1.80085
$470$	−6.00000	−0.276759
$471$	−6.00000	−0.276465
$472$	−7.00000	−0.322201
$473$	−4.00000	−0.183920
$474$	1.00000	0.0459315
$475$	−32.0000	−1.46826
$476$	−6.00000	−0.275010
$477$	0	0
$478$	−12.0000	−0.548867
$479$	−36.0000	−1.64488	−0.822441	−	0.568850i	$-0.807388\pi$
$479$	−36.0000	−1.64488	−0.822441	+	0.568850i	$0.807388\pi$
$480$	3.00000	0.136931
$481$	−20.0000	−0.911922
$482$	25.0000	1.13872
$483$	15.0000	0.682524
$484$	−10.0000	−0.454545
$485$	−42.0000	−1.90712
$486$	−1.00000	−0.0453609
$487$	−16.0000	−0.725029	−0.362515	−	0.931978i	$-0.618082\pi$
$487$	−16.0000	−0.725029	−0.362515	+	0.931978i	$0.618082\pi$
$488$	1.00000	0.0452679
$489$	4.00000	0.180886
$490$	−6.00000	−0.271052
$491$	28.0000	1.26362	0.631811	−	0.775122i	$-0.282312\pi$
$491$	28.0000	1.26362	0.631811	+	0.775122i	$0.282312\pi$
$492$	−3.00000	−0.135250
$493$	0	0
$494$	40.0000	1.79969
$495$	3.00000	0.134840
$496$	−4.00000	−0.179605
$497$	48.0000	2.15309
$498$	−14.0000	−0.627355
$499$	−5.00000	−0.223831	−0.111915	−	0.993718i	$-0.535699\pi$
$499$	−5.00000	−0.223831	−0.111915	+	0.993718i	$0.535699\pi$
$500$	3.00000	0.134164
$501$	18.0000	0.804181
$502$	8.00000	0.357057
$503$	−10.0000	−0.445878	−0.222939	−	0.974832i	$-0.571565\pi$
$503$	−10.0000	−0.445878	−0.222939	+	0.974832i	$0.571565\pi$
$504$	−3.00000	−0.133631
$505$	24.0000	1.06799
$506$	−5.00000	−0.222277
$507$	−12.0000	−0.532939
$508$	−22.0000	−0.976092
$509$	−10.0000	−0.443242	−0.221621	−	0.975133i	$-0.571135\pi$
$509$	−10.0000	−0.443242	−0.221621	+	0.975133i	$0.571135\pi$
$510$	6.00000	0.265684
$511$	−27.0000	−1.19441
$512$	1.00000	0.0441942
$513$	8.00000	0.353209
$514$	−18.0000	−0.793946
$515$	42.0000	1.85074
$516$	−4.00000	−0.176090
$517$	−2.00000	−0.0879599
$518$	−12.0000	−0.527250
$519$	22.0000	0.965693
$520$	15.0000	0.657794
$521$	−22.0000	−0.963837	−0.481919	−	0.876216i	$-0.660060\pi$
$521$	−22.0000	−0.963837	−0.481919	+	0.876216i	$0.660060\pi$
$522$	0	0
$523$	5.00000	0.218635	0.109317	−	0.994007i	$-0.465134\pi$
$523$	5.00000	0.218635	0.109317	+	0.994007i	$0.465134\pi$
$524$	10.0000	0.436852
$525$	12.0000	0.523723
$526$	24.0000	1.04645
$527$	−8.00000	−0.348485
$528$	1.00000	0.0435194
$529$	2.00000	0.0869565
$530$	0	0
$531$	−7.00000	−0.303774
$532$	24.0000	1.04053
$533$	−15.0000	−0.649722
$534$	4.00000	0.173097
$535$	6.00000	0.259403
$536$	−13.0000	−0.561514
$537$	0	0
$538$	−18.0000	−0.776035
$539$	−2.00000	−0.0861461
$540$	3.00000	0.129099
$541$	−40.0000	−1.71973	−0.859867	−	0.510518i	$-0.829454\pi$
$541$	−40.0000	−1.71973	−0.859867	+	0.510518i	$0.829454\pi$
$542$	8.00000	0.343629
$543$	−26.0000	−1.11577
$544$	2.00000	0.0857493
$545$	45.0000	1.92759
$546$	−15.0000	−0.641941
$547$	−35.0000	−1.49649	−0.748246	−	0.663421i	$-0.769104\pi$
$547$	−35.0000	−1.49649	−0.748246	+	0.663421i	$0.769104\pi$
$548$	15.0000	0.640768
$549$	1.00000	0.0426790
$550$	−4.00000	−0.170561
$551$	0	0
$552$	−5.00000	−0.212814
$553$	3.00000	0.127573
$554$	22.0000	0.934690
$555$	12.0000	0.509372
$556$	−5.00000	−0.212047
$557$	−12.0000	−0.508456	−0.254228	−	0.967144i	$-0.581821\pi$
$557$	−12.0000	−0.508456	−0.254228	+	0.967144i	$0.581821\pi$
$558$	−4.00000	−0.169334
$559$	−20.0000	−0.845910
$560$	9.00000	0.380319
$561$	2.00000	0.0844401
$562$	24.0000	1.01238
$563$	6.00000	0.252870	0.126435	−	0.991975i	$-0.459647\pi$
$563$	6.00000	0.252870	0.126435	+	0.991975i	$0.459647\pi$
$564$	−2.00000	−0.0842152
$565$	−33.0000	−1.38832
$566$	−14.0000	−0.588464
$567$	−3.00000	−0.125988
$568$	−16.0000	−0.671345
$569$	−17.0000	−0.712677	−0.356339	−	0.934357i	$-0.615975\pi$
$569$	−17.0000	−0.712677	−0.356339	+	0.934357i	$0.615975\pi$
$570$	−24.0000	−1.00525
$571$	−2.00000	−0.0836974	−0.0418487	−	0.999124i	$-0.513325\pi$
$571$	−2.00000	−0.0836974	−0.0418487	+	0.999124i	$0.513325\pi$
$572$	5.00000	0.209061
$573$	15.0000	0.626634
$574$	−9.00000	−0.375653
$575$	20.0000	0.834058
$576$	1.00000	0.0416667
$577$	2.00000	0.0832611	0.0416305	−	0.999133i	$-0.486745\pi$
$577$	2.00000	0.0832611	0.0416305	+	0.999133i	$0.486745\pi$
$578$	−13.0000	−0.540729
$579$	18.0000	0.748054
$580$	0	0
$581$	−42.0000	−1.74245
$582$	−14.0000	−0.580319
$583$	0	0
$584$	9.00000	0.372423
$585$	15.0000	0.620174
$586$	−6.00000	−0.247858
$587$	12.0000	0.495293	0.247647	−	0.968850i	$-0.420343\pi$
$587$	12.0000	0.495293	0.247647	+	0.968850i	$0.420343\pi$
$588$	−2.00000	−0.0824786
$589$	32.0000	1.31854
$590$	21.0000	0.864556
$591$	−21.0000	−0.863825
$592$	4.00000	0.164399
$593$	−6.00000	−0.246390	−0.123195	−	0.992382i	$-0.539314\pi$
$593$	−6.00000	−0.246390	−0.123195	+	0.992382i	$0.539314\pi$
$594$	1.00000	0.0410305
$595$	18.0000	0.737928
$596$	−21.0000	−0.860194
$597$	−18.0000	−0.736691
$598$	−25.0000	−1.02233
$599$	39.0000	1.59350	0.796748	−	0.604311i	$-0.206552\pi$
$599$	39.0000	1.59350	0.796748	+	0.604311i	$0.206552\pi$
$600$	−4.00000	−0.163299
$601$	−3.00000	−0.122373	−0.0611863	−	0.998126i	$-0.519488\pi$
$601$	−3.00000	−0.122373	−0.0611863	+	0.998126i	$0.519488\pi$
$602$	−12.0000	−0.489083
$603$	−13.0000	−0.529401
$604$	−9.00000	−0.366205
$605$	30.0000	1.21967
$606$	8.00000	0.324978
$607$	−4.00000	−0.162355	−0.0811775	−	0.996700i	$-0.525868\pi$
$607$	−4.00000	−0.162355	−0.0811775	+	0.996700i	$0.525868\pi$
$608$	−8.00000	−0.324443
$609$	0	0
$610$	−3.00000	−0.121466
$611$	−10.0000	−0.404557
$612$	2.00000	0.0808452
$613$	−38.0000	−1.53481	−0.767403	−	0.641165i	$-0.778451\pi$
$613$	−38.0000	−1.53481	−0.767403	+	0.641165i	$0.778451\pi$
$614$	19.0000	0.766778
$615$	9.00000	0.362915
$616$	3.00000	0.120873
$617$	10.0000	0.402585	0.201292	−	0.979531i	$-0.435486\pi$
$617$	10.0000	0.402585	0.201292	+	0.979531i	$0.435486\pi$
$618$	14.0000	0.563163
$619$	−14.0000	−0.562708	−0.281354	−	0.959604i	$-0.590783\pi$
$619$	−14.0000	−0.562708	−0.281354	+	0.959604i	$0.590783\pi$
$620$	12.0000	0.481932
$621$	−5.00000	−0.200643
$622$	35.0000	1.40337
$623$	12.0000	0.480770
$624$	5.00000	0.200160
$625$	−29.0000	−1.16000
$626$	−8.00000	−0.319744
$627$	−8.00000	−0.319489
$628$	6.00000	0.239426
$629$	8.00000	0.318981
$630$	9.00000	0.358569
$631$	25.0000	0.995234	0.497617	−	0.867397i	$-0.334208\pi$
$631$	25.0000	0.995234	0.497617	+	0.867397i	$0.334208\pi$
$632$	−1.00000	−0.0397779
$633$	−20.0000	−0.794929
$634$	10.0000	0.397151
$635$	66.0000	2.61913
$636$	0	0
$637$	−10.0000	−0.396214
$638$	0	0
$639$	−16.0000	−0.632950
$640$	−3.00000	−0.118585
$641$	−44.0000	−1.73790	−0.868948	−	0.494904i	$-0.835203\pi$
$641$	−44.0000	−1.73790	−0.868948	+	0.494904i	$0.835203\pi$
$642$	2.00000	0.0789337
$643$	−8.00000	−0.315489	−0.157745	−	0.987480i	$-0.550422\pi$
$643$	−8.00000	−0.315489	−0.157745	+	0.987480i	$0.550422\pi$
$644$	−15.0000	−0.591083
$645$	12.0000	0.472500
$646$	−16.0000	−0.629512
$647$	−3.00000	−0.117942	−0.0589711	−	0.998260i	$-0.518782\pi$
$647$	−3.00000	−0.117942	−0.0589711	+	0.998260i	$0.518782\pi$
$648$	1.00000	0.0392837
$649$	7.00000	0.274774
$650$	−20.0000	−0.784465
$651$	−12.0000	−0.470317
$652$	−4.00000	−0.156652
$653$	−14.0000	−0.547862	−0.273931	−	0.961749i	$-0.588324\pi$
$653$	−14.0000	−0.547862	−0.273931	+	0.961749i	$0.588324\pi$
$654$	15.0000	0.586546
$655$	−30.0000	−1.17220
$656$	3.00000	0.117130
$657$	9.00000	0.351123
$658$	−6.00000	−0.233904
$659$	6.00000	0.233727	0.116863	−	0.993148i	$-0.462716\pi$
$659$	6.00000	0.233727	0.116863	+	0.993148i	$0.462716\pi$
$660$	−3.00000	−0.116775
$661$	32.0000	1.24466	0.622328	−	0.782757i	$-0.286187\pi$
$661$	32.0000	1.24466	0.622328	+	0.782757i	$0.286187\pi$
$662$	9.00000	0.349795
$663$	10.0000	0.388368
$664$	14.0000	0.543305
$665$	−72.0000	−2.79204
$666$	4.00000	0.154997
$667$	0	0
$668$	−18.0000	−0.696441
$669$	21.0000	0.811907
$670$	39.0000	1.50670
$671$	−1.00000	−0.0386046
$672$	3.00000	0.115728
$673$	−14.0000	−0.539660	−0.269830	−	0.962908i	$-0.586968\pi$
$673$	−14.0000	−0.539660	−0.269830	+	0.962908i	$0.586968\pi$
$674$	−16.0000	−0.616297
$675$	−4.00000	−0.153960
$676$	12.0000	0.461538
$677$	30.0000	1.15299	0.576497	−	0.817099i	$-0.304419\pi$
$677$	30.0000	1.15299	0.576497	+	0.817099i	$0.304419\pi$
$678$	−11.0000	−0.422452
$679$	−42.0000	−1.61181
$680$	−6.00000	−0.230089
$681$	15.0000	0.574801
$682$	4.00000	0.153168
$683$	48.0000	1.83667	0.918334	−	0.395805i	$-0.129534\pi$
$683$	48.0000	1.83667	0.918334	+	0.395805i	$0.129534\pi$
$684$	−8.00000	−0.305888
$685$	−45.0000	−1.71936
$686$	15.0000	0.572703
$687$	17.0000	0.648590
$688$	4.00000	0.152499
$689$	0	0
$690$	15.0000	0.571040
$691$	−24.0000	−0.913003	−0.456502	−	0.889723i	$-0.650898\pi$
$691$	−24.0000	−0.913003	−0.456502	+	0.889723i	$0.650898\pi$
$692$	−22.0000	−0.836315
$693$	3.00000	0.113961
$694$	−4.00000	−0.151838
$695$	15.0000	0.568982
$696$	0	0
$697$	6.00000	0.227266
$698$	−22.0000	−0.832712
$699$	0	0
$700$	−12.0000	−0.453557
$701$	−18.0000	−0.679851	−0.339925	−	0.940452i	$-0.610402\pi$
$701$	−18.0000	−0.679851	−0.339925	+	0.940452i	$0.610402\pi$
$702$	5.00000	0.188713
$703$	−32.0000	−1.20690
$704$	−1.00000	−0.0376889
$705$	6.00000	0.225973
$706$	25.0000	0.940887
$707$	24.0000	0.902613
$708$	7.00000	0.263076
$709$	−14.0000	−0.525781	−0.262891	−	0.964826i	$-0.584676\pi$
$709$	−14.0000	−0.525781	−0.262891	+	0.964826i	$0.584676\pi$
$710$	48.0000	1.80141
$711$	−1.00000	−0.0375029
$712$	−4.00000	−0.149906
$713$	−20.0000	−0.749006
$714$	6.00000	0.224544
$715$	−15.0000	−0.560968
$716$	0	0
$717$	12.0000	0.448148
$718$	36.0000	1.34351
$719$	−20.0000	−0.745874	−0.372937	−	0.927857i	$-0.621649\pi$
$719$	−20.0000	−0.745874	−0.372937	+	0.927857i	$0.621649\pi$
$720$	−3.00000	−0.111803
$721$	42.0000	1.56416
$722$	45.0000	1.67473
$723$	−25.0000	−0.929760
$724$	26.0000	0.966282
$725$	0	0
$726$	10.0000	0.371135
$727$	34.0000	1.26099	0.630495	−	0.776193i	$-0.282852\pi$
$727$	34.0000	1.26099	0.630495	+	0.776193i	$0.282852\pi$
$728$	15.0000	0.555937
$729$	1.00000	0.0370370
$730$	−27.0000	−0.999315
$731$	8.00000	0.295891
$732$	−1.00000	−0.0369611
$733$	−1.00000	−0.0369358	−0.0184679	−	0.999829i	$-0.505879\pi$
$733$	−1.00000	−0.0369358	−0.0184679	+	0.999829i	$0.505879\pi$
$734$	36.0000	1.32878
$735$	6.00000	0.221313
$736$	5.00000	0.184302
$737$	13.0000	0.478861
$738$	3.00000	0.110432
$739$	19.0000	0.698926	0.349463	−	0.936950i	$-0.386364\pi$
$739$	19.0000	0.698926	0.349463	+	0.936950i	$0.386364\pi$
$740$	−12.0000	−0.441129
$741$	−40.0000	−1.46944
$742$	0	0
$743$	−31.0000	−1.13728	−0.568640	−	0.822587i	$-0.692530\pi$
$743$	−31.0000	−1.13728	−0.568640	+	0.822587i	$0.692530\pi$
$744$	4.00000	0.146647
$745$	63.0000	2.30814
$746$	4.00000	0.146450
$747$	14.0000	0.512233
$748$	−2.00000	−0.0731272
$749$	6.00000	0.219235
$750$	−3.00000	−0.109545
$751$	−12.0000	−0.437886	−0.218943	−	0.975738i	$-0.570261\pi$
$751$	−12.0000	−0.437886	−0.218943	+	0.975738i	$0.570261\pi$
$752$	2.00000	0.0729325
$753$	−8.00000	−0.291536
$754$	0	0
$755$	27.0000	0.982631
$756$	3.00000	0.109109
$757$	−23.0000	−0.835949	−0.417975	−	0.908459i	$-0.637260\pi$
$757$	−23.0000	−0.835949	−0.417975	+	0.908459i	$0.637260\pi$
$758$	0	0
$759$	5.00000	0.181489
$760$	24.0000	0.870572
$761$	−10.0000	−0.362500	−0.181250	−	0.983437i	$-0.558014\pi$
$761$	−10.0000	−0.362500	−0.181250	+	0.983437i	$0.558014\pi$
$762$	22.0000	0.796976
$763$	45.0000	1.62911
$764$	−15.0000	−0.542681
$765$	−6.00000	−0.216930
$766$	7.00000	0.252920
$767$	35.0000	1.26378
$768$	−1.00000	−0.0360844
$769$	−10.0000	−0.360609	−0.180305	−	0.983611i	$-0.557708\pi$
$769$	−10.0000	−0.360609	−0.180305	+	0.983611i	$0.557708\pi$
$770$	−9.00000	−0.324337
$771$	18.0000	0.648254
$772$	−18.0000	−0.647834
$773$	18.0000	0.647415	0.323708	−	0.946157i	$-0.395071\pi$
$773$	18.0000	0.647415	0.323708	+	0.946157i	$0.395071\pi$
$774$	4.00000	0.143777
$775$	−16.0000	−0.574737
$776$	14.0000	0.502571
$777$	12.0000	0.430498
$778$	18.0000	0.645331
$779$	−24.0000	−0.859889
$780$	−15.0000	−0.537086
$781$	16.0000	0.572525
$782$	10.0000	0.357599
$783$	0	0
$784$	2.00000	0.0714286
$785$	−18.0000	−0.642448
$786$	−10.0000	−0.356688
$787$	−32.0000	−1.14068	−0.570338	−	0.821410i	$-0.693188\pi$
$787$	−32.0000	−1.14068	−0.570338	+	0.821410i	$0.693188\pi$
$788$	21.0000	0.748094
$789$	−24.0000	−0.854423
$790$	3.00000	0.106735
$791$	−33.0000	−1.17334
$792$	−1.00000	−0.0355335
$793$	−5.00000	−0.177555
$794$	−2.00000	−0.0709773
$795$	0	0
$796$	18.0000	0.637993
$797$	29.0000	1.02723	0.513616	−	0.858020i	$-0.328305\pi$
$797$	29.0000	1.02723	0.513616	+	0.858020i	$0.328305\pi$
$798$	−24.0000	−0.849591
$799$	4.00000	0.141510
$800$	4.00000	0.141421
$801$	−4.00000	−0.141333
$802$	6.00000	0.211867
$803$	−9.00000	−0.317603
$804$	13.0000	0.458475
$805$	45.0000	1.58604
$806$	20.0000	0.704470
$807$	18.0000	0.633630
$808$	−8.00000	−0.281439
$809$	23.0000	0.808637	0.404318	−	0.914618i	$-0.367509\pi$
$809$	23.0000	0.808637	0.404318	+	0.914618i	$0.367509\pi$
$810$	−3.00000	−0.105409
$811$	−7.00000	−0.245803	−0.122902	−	0.992419i	$-0.539220\pi$
$811$	−7.00000	−0.245803	−0.122902	+	0.992419i	$0.539220\pi$
$812$	0	0
$813$	−8.00000	−0.280572
$814$	−4.00000	−0.140200
$815$	12.0000	0.420342
$816$	−2.00000	−0.0700140
$817$	−32.0000	−1.11954
$818$	−20.0000	−0.699284
$819$	15.0000	0.524142
$820$	−9.00000	−0.314294
$821$	−30.0000	−1.04701	−0.523504	−	0.852023i	$-0.675375\pi$
$821$	−30.0000	−1.04701	−0.523504	+	0.852023i	$0.675375\pi$
$822$	−15.0000	−0.523185
$823$	40.0000	1.39431	0.697156	−	0.716919i	$-0.254448\pi$
$823$	40.0000	1.39431	0.697156	+	0.716919i	$0.254448\pi$
$824$	−14.0000	−0.487713
$825$	4.00000	0.139262
$826$	21.0000	0.730683
$827$	−48.0000	−1.66912	−0.834562	−	0.550914i	$-0.814279\pi$
$827$	−48.0000	−1.66912	−0.834562	+	0.550914i	$0.814279\pi$
$828$	5.00000	0.173762
$829$	−7.00000	−0.243120	−0.121560	−	0.992584i	$-0.538790\pi$
$829$	−7.00000	−0.243120	−0.121560	+	0.992584i	$0.538790\pi$
$830$	−42.0000	−1.45784
$831$	−22.0000	−0.763172
$832$	−5.00000	−0.173344
$833$	4.00000	0.138592
$834$	5.00000	0.173136
$835$	54.0000	1.86875
$836$	8.00000	0.276686
$837$	4.00000	0.138260
$838$	4.00000	0.138178
$839$	20.0000	0.690477	0.345238	−	0.938515i	$-0.387798\pi$
$839$	20.0000	0.690477	0.345238	+	0.938515i	$0.387798\pi$
$840$	−9.00000	−0.310530
$841$	−29.0000	−1.00000
$842$	2.00000	0.0689246
$843$	−24.0000	−0.826604
$844$	20.0000	0.688428
$845$	−36.0000	−1.23844
$846$	2.00000	0.0687614
$847$	30.0000	1.03081
$848$	0	0
$849$	14.0000	0.480479
$850$	8.00000	0.274398
$851$	20.0000	0.685591
$852$	16.0000	0.548151
$853$	39.0000	1.33533	0.667667	−	0.744460i	$-0.267293\pi$
$853$	39.0000	1.33533	0.667667	+	0.744460i	$0.267293\pi$
$854$	−3.00000	−0.102658
$855$	24.0000	0.820783
$856$	−2.00000	−0.0683586
$857$	−53.0000	−1.81045	−0.905223	−	0.424937i	$-0.860296\pi$
$857$	−53.0000	−1.81045	−0.905223	+	0.424937i	$0.860296\pi$
$858$	−5.00000	−0.170697
$859$	−14.0000	−0.477674	−0.238837	−	0.971060i	$-0.576766\pi$
$859$	−14.0000	−0.477674	−0.238837	+	0.971060i	$0.576766\pi$
$860$	−12.0000	−0.409197
$861$	9.00000	0.306719
$862$	−2.00000	−0.0681203
$863$	−56.0000	−1.90626	−0.953131	−	0.302558i	$-0.902160\pi$
$863$	−56.0000	−1.90626	−0.953131	+	0.302558i	$0.902160\pi$
$864$	−1.00000	−0.0340207
$865$	66.0000	2.24407
$866$	−2.00000	−0.0679628
$867$	13.0000	0.441503
$868$	12.0000	0.407307
$869$	1.00000	0.0339227
$870$	0	0
$871$	65.0000	2.20244
$872$	−15.0000	−0.507964
$873$	14.0000	0.473828
$874$	−40.0000	−1.35302
$875$	−9.00000	−0.304256
$876$	−9.00000	−0.304082
$877$	−40.0000	−1.35070	−0.675352	−	0.737496i	$-0.736008\pi$
$877$	−40.0000	−1.35070	−0.675352	+	0.737496i	$0.736008\pi$
$878$	−12.0000	−0.404980
$879$	6.00000	0.202375
$880$	3.00000	0.101130
$881$	−35.0000	−1.17918	−0.589590	−	0.807703i	$-0.700711\pi$
$881$	−35.0000	−1.17918	−0.589590	+	0.807703i	$0.700711\pi$
$882$	2.00000	0.0673435
$883$	15.0000	0.504790	0.252395	−	0.967624i	$-0.418782\pi$
$883$	15.0000	0.504790	0.252395	+	0.967624i	$0.418782\pi$
$884$	−10.0000	−0.336336
$885$	−21.0000	−0.705907
$886$	−16.0000	−0.537531
$887$	32.0000	1.07445	0.537227	−	0.843437i	$-0.319472\pi$
$887$	32.0000	1.07445	0.537227	+	0.843437i	$0.319472\pi$
$888$	−4.00000	−0.134231
$889$	66.0000	2.21357
$890$	12.0000	0.402241
$891$	−1.00000	−0.0335013
$892$	−21.0000	−0.703132
$893$	−16.0000	−0.535420
$894$	21.0000	0.702345
$895$	0	0
$896$	−3.00000	−0.100223
$897$	25.0000	0.834726
$898$	−17.0000	−0.567297
$899$	0	0
$900$	4.00000	0.133333
$901$	0	0
$902$	−3.00000	−0.0998891
$903$	12.0000	0.399335
$904$	11.0000	0.365855
$905$	−78.0000	−2.59281
$906$	9.00000	0.299005
$907$	28.0000	0.929725	0.464862	−	0.885383i	$-0.346104\pi$
$907$	28.0000	0.929725	0.464862	+	0.885383i	$0.346104\pi$
$908$	−15.0000	−0.497792
$909$	−8.00000	−0.265343
$910$	−45.0000	−1.49174
$911$	12.0000	0.397578	0.198789	−	0.980042i	$-0.436299\pi$
$911$	12.0000	0.397578	0.198789	+	0.980042i	$0.436299\pi$
$912$	8.00000	0.264906
$913$	−14.0000	−0.463332
$914$	8.00000	0.264616
$915$	3.00000	0.0991769
$916$	−17.0000	−0.561696
$917$	−30.0000	−0.990687
$918$	−2.00000	−0.0660098
$919$	−52.0000	−1.71532	−0.857661	−	0.514216i	$-0.828083\pi$
$919$	−52.0000	−1.71532	−0.857661	+	0.514216i	$0.828083\pi$
$920$	−15.0000	−0.494535
$921$	−19.0000	−0.626071
$922$	−6.00000	−0.197599
$923$	80.0000	2.63323
$924$	−3.00000	−0.0986928
$925$	16.0000	0.526077
$926$	8.00000	0.262896
$927$	−14.0000	−0.459820
$928$	0	0
$929$	43.0000	1.41078	0.705392	−	0.708817i	$-0.250771\pi$
$929$	43.0000	1.41078	0.705392	+	0.708817i	$0.250771\pi$
$930$	−12.0000	−0.393496
$931$	−16.0000	−0.524379
$932$	0	0
$933$	−35.0000	−1.14585
$934$	−25.0000	−0.818025
$935$	6.00000	0.196221
$936$	−5.00000	−0.163430
$937$	−41.0000	−1.33941	−0.669706	−	0.742627i	$-0.733580\pi$
$937$	−41.0000	−1.33941	−0.669706	+	0.742627i	$0.733580\pi$
$938$	39.0000	1.27340
$939$	8.00000	0.261070
$940$	−6.00000	−0.195698
$941$	40.0000	1.30396	0.651981	−	0.758235i	$-0.273938\pi$
$941$	40.0000	1.30396	0.651981	+	0.758235i	$0.273938\pi$
$942$	−6.00000	−0.195491
$943$	15.0000	0.488467
$944$	−7.00000	−0.227831
$945$	−9.00000	−0.292770
$946$	−4.00000	−0.130051
$947$	35.0000	1.13735	0.568674	−	0.822563i	$-0.307457\pi$
$947$	35.0000	1.13735	0.568674	+	0.822563i	$0.307457\pi$
$948$	1.00000	0.0324785
$949$	−45.0000	−1.46076
$950$	−32.0000	−1.03822
$951$	−10.0000	−0.324272
$952$	−6.00000	−0.194461
$953$	50.0000	1.61966	0.809829	−	0.586665i	$-0.199560\pi$
$953$	50.0000	1.61966	0.809829	+	0.586665i	$0.199560\pi$
$954$	0	0
$955$	45.0000	1.45617
$956$	−12.0000	−0.388108
$957$	0	0
$958$	−36.0000	−1.16311
$959$	−45.0000	−1.45313
$960$	3.00000	0.0968246
$961$	−15.0000	−0.483871
$962$	−20.0000	−0.644826
$963$	−2.00000	−0.0644491
$964$	25.0000	0.805196
$965$	54.0000	1.73832
$966$	15.0000	0.482617
$967$	18.0000	0.578841	0.289420	−	0.957202i	$-0.406537\pi$
$967$	18.0000	0.578841	0.289420	+	0.957202i	$0.406537\pi$
$968$	−10.0000	−0.321412
$969$	16.0000	0.513994
$970$	−42.0000	−1.34854
$971$	−14.0000	−0.449281	−0.224641	−	0.974442i	$-0.572121\pi$
$971$	−14.0000	−0.449281	−0.224641	+	0.974442i	$0.572121\pi$
$972$	−1.00000	−0.0320750
$973$	15.0000	0.480878
$974$	−16.0000	−0.512673
$975$	20.0000	0.640513
$976$	1.00000	0.0320092
$977$	−30.0000	−0.959785	−0.479893	−	0.877327i	$-0.659324\pi$
$977$	−30.0000	−0.959785	−0.479893	+	0.877327i	$0.659324\pi$
$978$	4.00000	0.127906
$979$	4.00000	0.127841
$980$	−6.00000	−0.191663
$981$	−15.0000	−0.478913
$982$	28.0000	0.893516
$983$	−4.00000	−0.127580	−0.0637901	−	0.997963i	$-0.520319\pi$
$983$	−4.00000	−0.127580	−0.0637901	+	0.997963i	$0.520319\pi$
$984$	−3.00000	−0.0956365
$985$	−63.0000	−2.00735
$986$	0	0
$987$	6.00000	0.190982
$988$	40.0000	1.27257
$989$	20.0000	0.635963
$990$	3.00000	0.0953463
$991$	40.0000	1.27064	0.635321	−	0.772248i	$-0.280868\pi$
$991$	40.0000	1.27064	0.635321	+	0.772248i	$0.280868\pi$
$992$	−4.00000	−0.127000
$993$	−9.00000	−0.285606
$994$	48.0000	1.52247
$995$	−54.0000	−1.71192
$996$	−14.0000	−0.443607
$997$	2.00000	0.0633406	0.0316703	−	0.999498i	$-0.489917\pi$
$997$	2.00000	0.0633406	0.0316703	+	0.999498i	$0.489917\pi$
$998$	−5.00000	−0.158272
$999$	−4.00000	−0.126554

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	366.2.a.d.1.1	✓	1
3.2	odd	2		1098.2.a.e.1.1		1
4.3	odd	2		2928.2.a.h.1.1		1
5.4	even	2		9150.2.a.n.1.1		1
12.11	even	2		8784.2.a.z.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
366.2.a.d.1.1	✓	1	1.1	even	1	trivial
1098.2.a.e.1.1		1	3.2	odd	2
2928.2.a.h.1.1		1	4.3	odd	2
8784.2.a.z.1.1		1	12.11	even	2
9150.2.a.n.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:	\( N \)	\(=\)	\( 366 = 2 \cdot 3 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	366.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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