LMFDB - Embedded newform 966.4.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,4,Mod(1,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("966.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	966.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:	$56.9958450655$
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	$\chi$	$=$	966.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} -6.00000 q^{5} -6.00000 q^{6} +7.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} +O(q^{10})$

\(q-2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} -6.00000 q^{5} -6.00000 q^{6} +7.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} +12.0000 q^{10} +48.0000 q^{11} +12.0000 q^{12} +38.0000 q^{13} -14.0000 q^{14} -18.0000 q^{15} +16.0000 q^{16} +114.000 q^{17} -18.0000 q^{18} +56.0000 q^{19} -24.0000 q^{20} +21.0000 q^{21} -96.0000 q^{22} -23.0000 q^{23} -24.0000 q^{24} -89.0000 q^{25} -76.0000 q^{26} +27.0000 q^{27} +28.0000 q^{28} -162.000 q^{29} +36.0000 q^{30} -16.0000 q^{31} -32.0000 q^{32} +144.000 q^{33} -228.000 q^{34} -42.0000 q^{35} +36.0000 q^{36} -46.0000 q^{37} -112.000 q^{38} +114.000 q^{39} +48.0000 q^{40} -342.000 q^{41} -42.0000 q^{42} +248.000 q^{43} +192.000 q^{44} -54.0000 q^{45} +46.0000 q^{46} -24.0000 q^{47} +48.0000 q^{48} +49.0000 q^{49} +178.000 q^{50} +342.000 q^{51} +152.000 q^{52} +426.000 q^{53} -54.0000 q^{54} -288.000 q^{55} -56.0000 q^{56} +168.000 q^{57} +324.000 q^{58} -852.000 q^{59} -72.0000 q^{60} +338.000 q^{61} +32.0000 q^{62} +63.0000 q^{63} +64.0000 q^{64} -228.000 q^{65} -288.000 q^{66} +488.000 q^{67} +456.000 q^{68} -69.0000 q^{69} +84.0000 q^{70} +336.000 q^{71} -72.0000 q^{72} +362.000 q^{73} +92.0000 q^{74} -267.000 q^{75} +224.000 q^{76} +336.000 q^{77} -228.000 q^{78} +1184.00 q^{79} -96.0000 q^{80} +81.0000 q^{81} +684.000 q^{82} -336.000 q^{83} +84.0000 q^{84} -684.000 q^{85} -496.000 q^{86} -486.000 q^{87} -384.000 q^{88} -78.0000 q^{89} +108.000 q^{90} +266.000 q^{91} -92.0000 q^{92} -48.0000 q^{93} +48.0000 q^{94} -336.000 q^{95} -96.0000 q^{96} +746.000 q^{97} -98.0000 q^{98} +432.000 q^{99} +O(q^{100})\)

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 $

$2$	−2.00000	−0.707107
$2$	−2.00000	−0.707107
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	4.00000	0.500000
$5$	−6.00000	−0.536656	−0.268328	−	0.963328i	$-0.586471\pi$
$5$	−6.00000	−0.536656	−0.268328	+	0.963328i	$0.586471\pi$
$6$	−6.00000	−0.408248
$7$	7.00000	0.377964
$7$	7.00000	0.377964
$8$	−8.00000	−0.353553
$9$	9.00000	0.333333
$10$	12.0000	0.379473
$11$	48.0000	1.31569	0.657843	−	0.753155i	$-0.271469\pi$
$11$	48.0000	1.31569	0.657843	+	0.753155i	$0.271469\pi$
$12$	12.0000	0.288675
$13$	38.0000	0.810716	0.405358	−	0.914158i	$-0.367147\pi$
$13$	38.0000	0.810716	0.405358	+	0.914158i	$0.367147\pi$
$14$	−14.0000	−0.267261
$15$	−18.0000	−0.309839
$16$	16.0000	0.250000
$17$	114.000	1.62642	0.813208	−	0.581974i	$-0.197719\pi$
$17$	114.000	1.62642	0.813208	+	0.581974i	$0.197719\pi$
$18$	−18.0000	−0.235702
$19$	56.0000	0.676173	0.338086	−	0.941115i	$-0.390220\pi$
$19$	56.0000	0.676173	0.338086	+	0.941115i	$0.390220\pi$
$20$	−24.0000	−0.268328
$21$	21.0000	0.218218
$22$	−96.0000	−0.930330
$23$	−23.0000	−0.208514
$23$	−23.0000	−0.208514
$24$	−24.0000	−0.204124
$25$	−89.0000	−0.712000
$26$	−76.0000	−0.573263
$27$	27.0000	0.192450
$28$	28.0000	0.188982
$29$	−162.000	−1.03733	−0.518666	−	0.854977i	$-0.673571\pi$
$29$	−162.000	−1.03733	−0.518666	+	0.854977i	$0.673571\pi$
$30$	36.0000	0.219089
$31$	−16.0000	−0.0926995	−0.0463498	−	0.998925i	$-0.514759\pi$
$31$	−16.0000	−0.0926995	−0.0463498	+	0.998925i	$0.514759\pi$
$32$	−32.0000	−0.176777
$33$	144.000	0.759612
$34$	−228.000	−1.15005
$35$	−42.0000	−0.202837
$36$	36.0000	0.166667
$37$	−46.0000	−0.204388	−0.102194	−	0.994764i	$-0.532586\pi$
$37$	−46.0000	−0.204388	−0.102194	+	0.994764i	$0.532586\pi$
$38$	−112.000	−0.478126
$39$	114.000	0.468067
$40$	48.0000	0.189737
$41$	−342.000	−1.30272	−0.651359	−	0.758770i	$-0.725801\pi$
$41$	−342.000	−1.30272	−0.651359	+	0.758770i	$0.725801\pi$
$42$	−42.0000	−0.154303
$43$	248.000	0.879527	0.439763	−	0.898114i	$-0.355062\pi$
$43$	248.000	0.879527	0.439763	+	0.898114i	$0.355062\pi$
$44$	192.000	0.657843
$45$	−54.0000	−0.178885
$46$	46.0000	0.147442
$47$	−24.0000	−0.0744843	−0.0372421	−	0.999306i	$-0.511857\pi$
$47$	−24.0000	−0.0744843	−0.0372421	+	0.999306i	$0.511857\pi$
$48$	48.0000	0.144338
$49$	49.0000	0.142857
$50$	178.000	0.503460
$51$	342.000	0.939011
$52$	152.000	0.405358
$53$	426.000	1.10407	0.552034	−	0.833822i	$-0.313852\pi$
$53$	426.000	1.10407	0.552034	+	0.833822i	$0.313852\pi$
$54$	−54.0000	−0.136083
$55$	−288.000	−0.706071
$56$	−56.0000	−0.133631
$57$	168.000	0.390388
$58$	324.000	0.733505
$59$	−852.000	−1.88002	−0.940008	−	0.341152i	$-0.889183\pi$
$59$	−852.000	−1.88002	−0.940008	+	0.341152i	$0.889183\pi$
$60$	−72.0000	−0.154919
$61$	338.000	0.709450	0.354725	−	0.934971i	$-0.384574\pi$
$61$	338.000	0.709450	0.354725	+	0.934971i	$0.384574\pi$
$62$	32.0000	0.0655485
$63$	63.0000	0.125988
$64$	64.0000	0.125000
$65$	−228.000	−0.435076
$66$	−288.000	−0.537127
$67$	488.000	0.889831	0.444916	−	0.895573i	$-0.353234\pi$
$67$	488.000	0.889831	0.444916	+	0.895573i	$0.353234\pi$
$68$	456.000	0.813208
$69$	−69.0000	−0.120386
$70$	84.0000	0.143427
$71$	336.000	0.561632	0.280816	−	0.959762i	$-0.409395\pi$
$71$	336.000	0.561632	0.280816	+	0.959762i	$0.409395\pi$
$72$	−72.0000	−0.117851
$73$	362.000	0.580396	0.290198	−	0.956967i	$-0.406279\pi$
$73$	362.000	0.580396	0.290198	+	0.956967i	$0.406279\pi$
$74$	92.0000	0.144524
$75$	−267.000	−0.411073
$76$	224.000	0.338086
$77$	336.000	0.497283
$78$	−228.000	−0.330973
$79$	1184.00	1.68621	0.843104	−	0.537751i	$-0.180726\pi$
$79$	1184.00	1.68621	0.843104	+	0.537751i	$0.180726\pi$
$80$	−96.0000	−0.134164
$81$	81.0000	0.111111
$82$	684.000	0.921161
$83$	−336.000	−0.444347	−0.222173	−	0.975007i	$-0.571315\pi$
$83$	−336.000	−0.444347	−0.222173	+	0.975007i	$0.571315\pi$
$84$	84.0000	0.109109
$85$	−684.000	−0.872826
$86$	−496.000	−0.621919
$87$	−486.000	−0.598904
$88$	−384.000	−0.465165
$89$	−78.0000	−0.0928987	−0.0464493	−	0.998921i	$-0.514791\pi$
$89$	−78.0000	−0.0928987	−0.0464493	+	0.998921i	$0.514791\pi$
$90$	108.000	0.126491
$91$	266.000	0.306422
$92$	−92.0000	−0.104257
$93$	−48.0000	−0.0535201
$94$	48.0000	0.0526683
$95$	−336.000	−0.362872
$96$	−96.0000	−0.102062
$97$	746.000	0.780874	0.390437	−	0.920630i	$-0.372324\pi$
$97$	746.000	0.780874	0.390437	+	0.920630i	$0.372324\pi$
$98$	−98.0000	−0.101015
$99$	432.000	0.438562
$100$	−356.000	−0.356000
$101$	30.0000	0.0295556	0.0147778	−	0.999891i	$-0.495296\pi$
$101$	30.0000	0.0295556	0.0147778	+	0.999891i	$0.495296\pi$
$102$	−684.000	−0.663981
$103$	944.000	0.903059	0.451530	−	0.892256i	$-0.350879\pi$
$103$	944.000	0.903059	0.451530	+	0.892256i	$0.350879\pi$
$104$	−304.000	−0.286631
$105$	−126.000	−0.117108
$106$	−852.000	−0.780694
$107$	264.000	0.238522	0.119261	−	0.992863i	$-0.461947\pi$
$107$	264.000	0.238522	0.119261	+	0.992863i	$0.461947\pi$
$108$	108.000	0.0962250
$109$	578.000	0.507912	0.253956	−	0.967216i	$-0.418268\pi$
$109$	578.000	0.507912	0.253956	+	0.967216i	$0.418268\pi$
$110$	576.000	0.499268
$111$	−138.000	−0.118003
$112$	112.000	0.0944911
$113$	282.000	0.234764	0.117382	−	0.993087i	$-0.462550\pi$
$113$	282.000	0.234764	0.117382	+	0.993087i	$0.462550\pi$
$114$	−336.000	−0.276046
$115$	138.000	0.111901
$116$	−648.000	−0.518666
$117$	342.000	0.270239
$118$	1704.00	1.32937
$119$	798.000	0.614727
$120$	144.000	0.109545
$121$	973.000	0.731029
$122$	−676.000	−0.501657
$123$	−1026.00	−0.752124
$124$	−64.0000	−0.0463498
$125$	1284.00	0.918756
$126$	−126.000	−0.0890871
$127$	−856.000	−0.598092	−0.299046	−	0.954239i	$-0.596668\pi$
$127$	−856.000	−0.598092	−0.299046	+	0.954239i	$0.596668\pi$
$128$	−128.000	−0.0883883
$129$	744.000	0.507795
$130$	456.000	0.307645
$131$	−348.000	−0.232098	−0.116049	−	0.993243i	$-0.537023\pi$
$131$	−348.000	−0.232098	−0.116049	+	0.993243i	$0.537023\pi$
$132$	576.000	0.379806
$133$	392.000	0.255569
$134$	−976.000	−0.629206
$135$	−162.000	−0.103280
$136$	−912.000	−0.575025
$137$	−2598.00	−1.62016	−0.810081	−	0.586318i	$-0.800577\pi$
$137$	−2598.00	−1.62016	−0.810081	+	0.586318i	$0.800577\pi$
$138$	138.000	0.0851257
$139$	−2692.00	−1.64268	−0.821340	−	0.570439i	$-0.806773\pi$
$139$	−2692.00	−1.64268	−0.821340	+	0.570439i	$0.806773\pi$
$140$	−168.000	−0.101419
$141$	−72.0000	−0.0430035
$142$	−672.000	−0.397134
$143$	1824.00	1.06665
$144$	144.000	0.0833333
$145$	972.000	0.556691
$146$	−724.000	−0.410402
$147$	147.000	0.0824786
$148$	−184.000	−0.102194
$149$	−966.000	−0.531126	−0.265563	−	0.964093i	$-0.585558\pi$
$149$	−966.000	−0.531126	−0.265563	+	0.964093i	$0.585558\pi$
$150$	534.000	0.290673
$151$	1208.00	0.651031	0.325515	−	0.945537i	$-0.394462\pi$
$151$	1208.00	0.651031	0.325515	+	0.945537i	$0.394462\pi$
$152$	−448.000	−0.239063
$153$	1026.00	0.542138
$154$	−672.000	−0.351632
$155$	96.0000	0.0497478
$156$	456.000	0.234033
$157$	362.000	0.184017	0.0920087	−	0.995758i	$-0.470671\pi$
$157$	362.000	0.184017	0.0920087	+	0.995758i	$0.470671\pi$
$158$	−2368.00	−1.19233
$159$	1278.00	0.637434
$160$	192.000	0.0948683
$161$	−161.000	−0.0788110
$162$	−162.000	−0.0785674
$163$	3164.00	1.52039	0.760195	−	0.649695i	$-0.225103\pi$
$163$	3164.00	1.52039	0.760195	+	0.649695i	$0.225103\pi$
$164$	−1368.00	−0.651359
$165$	−864.000	−0.407650
$166$	672.000	0.314201
$167$	2352.00	1.08984	0.544920	−	0.838488i	$-0.316560\pi$
$167$	2352.00	1.08984	0.544920	+	0.838488i	$0.316560\pi$
$168$	−168.000	−0.0771517
$169$	−753.000	−0.342740
$170$	1368.00	0.617181
$171$	504.000	0.225391
$172$	992.000	0.439763
$173$	−1458.00	−0.640750	−0.320375	−	0.947291i	$-0.603809\pi$
$173$	−1458.00	−0.640750	−0.320375	+	0.947291i	$0.603809\pi$
$174$	972.000	0.423489
$175$	−623.000	−0.269111
$176$	768.000	0.328921
$177$	−2556.00	−1.08543
$178$	156.000	0.0656893
$179$	2076.00	0.866858	0.433429	−	0.901188i	$-0.357304\pi$
$179$	2076.00	0.866858	0.433429	+	0.901188i	$0.357304\pi$
$180$	−216.000	−0.0894427
$181$	−358.000	−0.147016	−0.0735081	−	0.997295i	$-0.523419\pi$
$181$	−358.000	−0.147016	−0.0735081	+	0.997295i	$0.523419\pi$
$182$	−532.000	−0.216673
$183$	1014.00	0.409601
$184$	184.000	0.0737210
$185$	276.000	0.109686
$186$	96.0000	0.0378444
$187$	5472.00	2.13985
$188$	−96.0000	−0.0372421
$189$	189.000	0.0727393
$190$	672.000	0.256589
$191$	3960.00	1.50019	0.750093	−	0.661332i	$-0.230009\pi$
$191$	3960.00	1.50019	0.750093	+	0.661332i	$0.230009\pi$
$192$	192.000	0.0721688
$193$	−1198.00	−0.446808	−0.223404	−	0.974726i	$-0.571717\pi$
$193$	−1198.00	−0.446808	−0.223404	+	0.974726i	$0.571717\pi$
$194$	−1492.00	−0.552162
$195$	−684.000	−0.251191
$196$	196.000	0.0714286
$197$	1446.00	0.522961	0.261480	−	0.965209i	$-0.415789\pi$
$197$	1446.00	0.522961	0.261480	+	0.965209i	$0.415789\pi$
$198$	−864.000	−0.310110
$199$	4952.00	1.76401	0.882005	−	0.471240i	$-0.156193\pi$
$199$	4952.00	1.76401	0.882005	+	0.471240i	$0.156193\pi$
$200$	712.000	0.251730
$201$	1464.00	0.513744
$202$	−60.0000	−0.0208989
$203$	−1134.00	−0.392075
$204$	1368.00	0.469506
$205$	2052.00	0.699112
$206$	−1888.00	−0.638559
$207$	−207.000	−0.0695048
$208$	608.000	0.202679
$209$	2688.00	0.889631
$210$	252.000	0.0828079
$211$	−1084.00	−0.353676	−0.176838	−	0.984240i	$-0.556587\pi$
$211$	−1084.00	−0.353676	−0.176838	+	0.984240i	$0.556587\pi$
$212$	1704.00	0.552034
$213$	1008.00	0.324258
$214$	−528.000	−0.168660
$215$	−1488.00	−0.472004
$216$	−216.000	−0.0680414
$217$	−112.000	−0.0350371
$218$	−1156.00	−0.359148
$219$	1086.00	0.335092
$220$	−1152.00	−0.353036
$221$	4332.00	1.31856
$222$	276.000	0.0834410
$223$	1856.00	0.557341	0.278670	−	0.960387i	$-0.410106\pi$
$223$	1856.00	0.557341	0.278670	+	0.960387i	$0.410106\pi$
$224$	−224.000	−0.0668153
$225$	−801.000	−0.237333
$226$	−564.000	−0.166003
$227$	−168.000	−0.0491214	−0.0245607	−	0.999698i	$-0.507819\pi$
$227$	−168.000	−0.0491214	−0.0245607	+	0.999698i	$0.507819\pi$
$228$	672.000	0.195194
$229$	2858.00	0.824725	0.412362	−	0.911020i	$-0.364704\pi$
$229$	2858.00	0.824725	0.412362	+	0.911020i	$0.364704\pi$
$230$	−276.000	−0.0791257
$231$	1008.00	0.287106
$232$	1296.00	0.366752
$233$	−3942.00	−1.10836	−0.554182	−	0.832395i	$-0.686969\pi$
$233$	−3942.00	−1.10836	−0.554182	+	0.832395i	$0.686969\pi$
$234$	−684.000	−0.191088
$235$	144.000	0.0399724
$236$	−3408.00	−0.940008
$237$	3552.00	0.973532
$238$	−1596.00	−0.434678
$239$	6048.00	1.63687	0.818436	−	0.574597i	$-0.194841\pi$
$239$	6048.00	1.63687	0.818436	+	0.574597i	$0.194841\pi$
$240$	−288.000	−0.0774597
$241$	−598.000	−0.159836	−0.0799182	−	0.996801i	$-0.525466\pi$
$241$	−598.000	−0.159836	−0.0799182	+	0.996801i	$0.525466\pi$
$242$	−1946.00	−0.516916
$243$	243.000	0.0641500
$244$	1352.00	0.354725
$245$	−294.000	−0.0766652
$246$	2052.00	0.531832
$247$	2128.00	0.548184
$248$	128.000	0.0327742
$249$	−1008.00	−0.256544
$250$	−2568.00	−0.649658
$251$	−600.000	−0.150883	−0.0754416	−	0.997150i	$-0.524037\pi$
$251$	−600.000	−0.150883	−0.0754416	+	0.997150i	$0.524037\pi$
$252$	252.000	0.0629941
$253$	−1104.00	−0.274339
$254$	1712.00	0.422915
$255$	−2052.00	−0.503926
$256$	256.000	0.0625000
$257$	882.000	0.214076	0.107038	−	0.994255i	$-0.465863\pi$
$257$	882.000	0.214076	0.107038	+	0.994255i	$0.465863\pi$
$258$	−1488.00	−0.359065
$259$	−322.000	−0.0772514
$260$	−912.000	−0.217538
$261$	−1458.00	−0.345778
$262$	696.000	0.164118
$263$	−4920.00	−1.15354	−0.576768	−	0.816908i	$-0.695687\pi$
$263$	−4920.00	−1.15354	−0.576768	+	0.816908i	$0.695687\pi$
$264$	−1152.00	−0.268563
$265$	−2556.00	−0.592505
$266$	−784.000	−0.180715
$267$	−234.000	−0.0536351
$268$	1952.00	0.444916
$269$	942.000	0.213512	0.106756	−	0.994285i	$-0.465954\pi$
$269$	942.000	0.213512	0.106756	+	0.994285i	$0.465954\pi$
$270$	324.000	0.0730297
$271$	824.000	0.184703	0.0923514	−	0.995726i	$-0.470562\pi$
$271$	824.000	0.184703	0.0923514	+	0.995726i	$0.470562\pi$
$272$	1824.00	0.406604
$273$	798.000	0.176913
$274$	5196.00	1.14563
$275$	−4272.00	−0.936768
$276$	−276.000	−0.0601929
$277$	−4906.00	−1.06416	−0.532081	−	0.846693i	$-0.678590\pi$
$277$	−4906.00	−1.06416	−0.532081	+	0.846693i	$0.678590\pi$
$278$	5384.00	1.16155
$279$	−144.000	−0.0308998
$280$	336.000	0.0717137
$281$	−3822.00	−0.811393	−0.405696	−	0.914008i	$-0.632971\pi$
$281$	−3822.00	−0.811393	−0.405696	+	0.914008i	$0.632971\pi$
$282$	144.000	0.0304081
$283$	2408.00	0.505798	0.252899	−	0.967493i	$-0.418616\pi$
$283$	2408.00	0.505798	0.252899	+	0.967493i	$0.418616\pi$
$284$	1344.00	0.280816
$285$	−1008.00	−0.209504
$286$	−3648.00	−0.754233
$287$	−2394.00	−0.492381
$288$	−288.000	−0.0589256
$289$	8083.00	1.64523
$290$	−1944.00	−0.393640
$291$	2238.00	0.450838
$292$	1448.00	0.290198
$293$	−1014.00	−0.202179	−0.101090	−	0.994877i	$-0.532233\pi$
$293$	−1014.00	−0.202179	−0.101090	+	0.994877i	$0.532233\pi$
$294$	−294.000	−0.0583212
$295$	5112.00	1.00892
$296$	368.000	0.0722620
$297$	1296.00	0.253204
$298$	1932.00	0.375563
$299$	−874.000	−0.169046
$300$	−1068.00	−0.205537
$301$	1736.00	0.332430
$302$	−2416.00	−0.460348
$303$	90.0000	0.0170639
$304$	896.000	0.169043
$305$	−2028.00	−0.380731
$306$	−2052.00	−0.383350
$307$	−3988.00	−0.741391	−0.370696	−	0.928754i	$-0.620881\pi$
$307$	−3988.00	−0.741391	−0.370696	+	0.928754i	$0.620881\pi$
$308$	1344.00	0.248641
$309$	2832.00	0.521381
$310$	−192.000	−0.0351770
$311$	4680.00	0.853307	0.426653	−	0.904415i	$-0.359692\pi$
$311$	4680.00	0.853307	0.426653	+	0.904415i	$0.359692\pi$
$312$	−912.000	−0.165487
$313$	2450.00	0.442435	0.221218	−	0.975224i	$-0.428997\pi$
$313$	2450.00	0.442435	0.221218	+	0.975224i	$0.428997\pi$
$314$	−724.000	−0.130120
$315$	−378.000	−0.0676123
$316$	4736.00	0.843104
$317$	6414.00	1.13642	0.568212	−	0.822883i	$-0.307636\pi$
$317$	6414.00	1.13642	0.568212	+	0.822883i	$0.307636\pi$
$318$	−2556.00	−0.450734
$319$	−7776.00	−1.36480
$320$	−384.000	−0.0670820
$321$	792.000	0.137711
$322$	322.000	0.0557278
$323$	6384.00	1.09974
$324$	324.000	0.0555556
$325$	−3382.00	−0.577230
$326$	−6328.00	−1.07508
$327$	1734.00	0.293243
$328$	2736.00	0.460580
$329$	−168.000	−0.0281524
$330$	1728.00	0.288252
$331$	−7540.00	−1.25207	−0.626036	−	0.779794i	$-0.715324\pi$
$331$	−7540.00	−1.25207	−0.626036	+	0.779794i	$0.715324\pi$
$332$	−1344.00	−0.222173
$333$	−414.000	−0.0681293
$334$	−4704.00	−0.770633
$335$	−2928.00	−0.477534
$336$	336.000	0.0545545
$337$	−2014.00	−0.325548	−0.162774	−	0.986663i	$-0.552044\pi$
$337$	−2014.00	−0.325548	−0.162774	+	0.986663i	$0.552044\pi$
$338$	1506.00	0.242354
$339$	846.000	0.135541
$340$	−2736.00	−0.436413
$341$	−768.000	−0.121963
$342$	−1008.00	−0.159375
$343$	343.000	0.0539949
$344$	−1984.00	−0.310960
$345$	414.000	0.0646058
$346$	2916.00	0.453078
$347$	−4428.00	−0.685036	−0.342518	−	0.939511i	$-0.611280\pi$
$347$	−4428.00	−0.685036	−0.342518	+	0.939511i	$0.611280\pi$
$348$	−1944.00	−0.299452
$349$	5582.00	0.856154	0.428077	−	0.903742i	$-0.359191\pi$
$349$	5582.00	0.856154	0.428077	+	0.903742i	$0.359191\pi$
$350$	1246.00	0.190290
$351$	1026.00	0.156022
$352$	−1536.00	−0.232583
$353$	−5934.00	−0.894717	−0.447358	−	0.894355i	$-0.647635\pi$
$353$	−5934.00	−0.894717	−0.447358	+	0.894355i	$0.647635\pi$
$354$	5112.00	0.767513
$355$	−2016.00	−0.301403
$356$	−312.000	−0.0464493
$357$	2394.00	0.354913
$358$	−4152.00	−0.612961
$359$	2256.00	0.331663	0.165832	−	0.986154i	$-0.446969\pi$
$359$	2256.00	0.331663	0.165832	+	0.986154i	$0.446969\pi$
$360$	432.000	0.0632456
$361$	−3723.00	−0.542790
$362$	716.000	0.103956
$363$	2919.00	0.422060
$364$	1064.00	0.153211
$365$	−2172.00	−0.311473
$366$	−2028.00	−0.289632
$367$	3296.00	0.468801	0.234400	−	0.972140i	$-0.424687\pi$
$367$	3296.00	0.468801	0.234400	+	0.972140i	$0.424687\pi$
$368$	−368.000	−0.0521286
$369$	−3078.00	−0.434239
$370$	−552.000	−0.0775598
$371$	2982.00	0.417298
$372$	−192.000	−0.0267600
$373$	13250.0	1.83930	0.919650	−	0.392739i	$-0.128472\pi$
$373$	13250.0	1.83930	0.919650	+	0.392739i	$0.128472\pi$
$374$	−10944.0	−1.51310
$375$	3852.00	0.530444
$376$	192.000	0.0263342
$377$	−6156.00	−0.840982
$378$	−378.000	−0.0514344
$379$	−8128.00	−1.10160	−0.550801	−	0.834636i	$-0.685678\pi$
$379$	−8128.00	−1.10160	−0.550801	+	0.834636i	$0.685678\pi$
$380$	−1344.00	−0.181436
$381$	−2568.00	−0.345309
$382$	−7920.00	−1.06079
$383$	−8976.00	−1.19753	−0.598763	−	0.800927i	$-0.704341\pi$
$383$	−8976.00	−1.19753	−0.598763	+	0.800927i	$0.704341\pi$
$384$	−384.000	−0.0510310
$385$	−2016.00	−0.266870
$386$	2396.00	0.315941
$387$	2232.00	0.293176
$388$	2984.00	0.390437
$389$	−14478.0	−1.88705	−0.943527	−	0.331297i	$-0.892514\pi$
$389$	−14478.0	−1.88705	−0.943527	+	0.331297i	$0.892514\pi$
$390$	1368.00	0.177619
$391$	−2622.00	−0.339131
$392$	−392.000	−0.0505076
$393$	−1044.00	−0.134002
$394$	−2892.00	−0.369789
$395$	−7104.00	−0.904914
$396$	1728.00	0.219281
$397$	−14122.0	−1.78530	−0.892648	−	0.450754i	$-0.851155\pi$
$397$	−14122.0	−1.78530	−0.892648	+	0.450754i	$0.851155\pi$
$398$	−9904.00	−1.24734
$399$	1176.00	0.147553
$400$	−1424.00	−0.178000
$401$	1266.00	0.157658	0.0788292	−	0.996888i	$-0.474882\pi$
$401$	1266.00	0.157658	0.0788292	+	0.996888i	$0.474882\pi$
$402$	−2928.00	−0.363272
$403$	−608.000	−0.0751529
$404$	120.000	0.0147778
$405$	−486.000	−0.0596285
$406$	2268.00	0.277239
$407$	−2208.00	−0.268910
$408$	−2736.00	−0.331991
$409$	6554.00	0.792358	0.396179	−	0.918173i	$-0.370336\pi$
$409$	6554.00	0.792358	0.396179	+	0.918173i	$0.370336\pi$
$410$	−4104.00	−0.494347
$411$	−7794.00	−0.935401
$412$	3776.00	0.451530
$413$	−5964.00	−0.710579
$414$	414.000	0.0491473
$415$	2016.00	0.238462
$416$	−1216.00	−0.143316
$417$	−8076.00	−0.948401
$418$	−5376.00	−0.629064
$419$	−2016.00	−0.235055	−0.117527	−	0.993070i	$-0.537497\pi$
$419$	−2016.00	−0.235055	−0.117527	+	0.993070i	$0.537497\pi$
$420$	−504.000	−0.0585540
$421$	4322.00	0.500336	0.250168	−	0.968202i	$-0.419514\pi$
$421$	4322.00	0.500336	0.250168	+	0.968202i	$0.419514\pi$
$422$	2168.00	0.250087
$423$	−216.000	−0.0248281
$424$	−3408.00	−0.390347
$425$	−10146.0	−1.15801
$426$	−2016.00	−0.229285
$427$	2366.00	0.268147
$428$	1056.00	0.119261
$429$	5472.00	0.615829
$430$	2976.00	0.333757
$431$	−11112.0	−1.24187	−0.620935	−	0.783862i	$-0.713247\pi$
$431$	−11112.0	−1.24187	−0.620935	+	0.783862i	$0.713247\pi$
$432$	432.000	0.0481125
$433$	12554.0	1.39332	0.696659	−	0.717402i	$-0.254669\pi$
$433$	12554.0	1.39332	0.696659	+	0.717402i	$0.254669\pi$
$434$	224.000	0.0247750
$435$	2916.00	0.321406
$436$	2312.00	0.253956
$437$	−1288.00	−0.140992
$438$	−2172.00	−0.236946
$439$	416.000	0.0452269	0.0226134	−	0.999744i	$-0.492801\pi$
$439$	416.000	0.0452269	0.0226134	+	0.999744i	$0.492801\pi$
$440$	2304.00	0.249634
$441$	441.000	0.0476190
$442$	−8664.00	−0.932363
$443$	−10044.0	−1.07721	−0.538606	−	0.842558i	$-0.681049\pi$
$443$	−10044.0	−1.07721	−0.538606	+	0.842558i	$0.681049\pi$
$444$	−552.000	−0.0590017
$445$	468.000	0.0498547
$446$	−3712.00	−0.394099
$447$	−2898.00	−0.306646
$448$	448.000	0.0472456
$449$	−14190.0	−1.49146	−0.745732	−	0.666246i	$-0.767900\pi$
$449$	−14190.0	−1.49146	−0.745732	+	0.666246i	$0.767900\pi$
$450$	1602.00	0.167820
$451$	−16416.0	−1.71397
$452$	1128.00	0.117382
$453$	3624.00	0.375873
$454$	336.000	0.0347341
$455$	−1596.00	−0.164443
$456$	−1344.00	−0.138023
$457$	3794.00	0.388350	0.194175	−	0.980967i	$-0.437797\pi$
$457$	3794.00	0.388350	0.194175	+	0.980967i	$0.437797\pi$
$458$	−5716.00	−0.583168
$459$	3078.00	0.313004
$460$	552.000	0.0559503
$461$	6366.00	0.643154	0.321577	−	0.946883i	$-0.395787\pi$
$461$	6366.00	0.643154	0.321577	+	0.946883i	$0.395787\pi$
$462$	−2016.00	−0.203015
$463$	2936.00	0.294703	0.147352	−	0.989084i	$-0.452925\pi$
$463$	2936.00	0.294703	0.147352	+	0.989084i	$0.452925\pi$
$464$	−2592.00	−0.259333
$465$	288.000	0.0287219
$466$	7884.00	0.783732
$467$	11904.0	1.17955	0.589777	−	0.807566i	$-0.299216\pi$
$467$	11904.0	1.17955	0.589777	+	0.807566i	$0.299216\pi$
$468$	1368.00	0.135119
$469$	3416.00	0.336325
$470$	−288.000	−0.0282648
$471$	1086.00	0.106243
$472$	6816.00	0.664686
$473$	11904.0	1.15718
$474$	−7104.00	−0.688391
$475$	−4984.00	−0.481435
$476$	3192.00	0.307364
$477$	3834.00	0.368023
$478$	−12096.0	−1.15744
$479$	−15120.0	−1.44228	−0.721138	−	0.692791i	$-0.756381\pi$
$479$	−15120.0	−1.44228	−0.721138	+	0.692791i	$0.756381\pi$
$480$	576.000	0.0547723
$481$	−1748.00	−0.165700
$482$	1196.00	0.113021
$483$	−483.000	−0.0455016
$484$	3892.00	0.365515
$485$	−4476.00	−0.419061
$486$	−486.000	−0.0453609
$487$	−5344.00	−0.497248	−0.248624	−	0.968600i	$-0.579978\pi$
$487$	−5344.00	−0.497248	−0.248624	+	0.968600i	$0.579978\pi$
$488$	−2704.00	−0.250829
$489$	9492.00	0.877798
$490$	588.000	0.0542105
$491$	13908.0	1.27833	0.639164	−	0.769070i	$-0.279280\pi$
$491$	13908.0	1.27833	0.639164	+	0.769070i	$0.279280\pi$
$492$	−4104.00	−0.376062
$493$	−18468.0	−1.68713
$494$	−4256.00	−0.387624
$495$	−2592.00	−0.235357
$496$	−256.000	−0.0231749
$497$	2352.00	0.212277
$498$	2016.00	0.181404
$499$	−7780.00	−0.697957	−0.348979	−	0.937131i	$-0.613471\pi$
$499$	−7780.00	−0.697957	−0.348979	+	0.937131i	$0.613471\pi$
$500$	5136.00	0.459378
$501$	7056.00	0.629219
$502$	1200.00	0.106690
$503$	5808.00	0.514843	0.257421	−	0.966299i	$-0.417127\pi$
$503$	5808.00	0.514843	0.257421	+	0.966299i	$0.417127\pi$
$504$	−504.000	−0.0445435
$505$	−180.000	−0.0158612
$506$	2208.00	0.193987
$507$	−2259.00	−0.197881
$508$	−3424.00	−0.299046
$509$	8910.00	0.775892	0.387946	−	0.921682i	$-0.373185\pi$
$509$	8910.00	0.775892	0.387946	+	0.921682i	$0.373185\pi$
$510$	4104.00	0.356330
$511$	2534.00	0.219369
$512$	−512.000	−0.0441942
$513$	1512.00	0.130129
$514$	−1764.00	−0.151375
$515$	−5664.00	−0.484632
$516$	2976.00	0.253897
$517$	−1152.00	−0.0979979
$518$	644.000	0.0546250
$519$	−4374.00	−0.369937
$520$	1824.00	0.153822
$521$	19002.0	1.59787	0.798937	−	0.601414i	$-0.205396\pi$
$521$	19002.0	1.59787	0.798937	+	0.601414i	$0.205396\pi$
$522$	2916.00	0.244502
$523$	−4000.00	−0.334432	−0.167216	−	0.985920i	$-0.553478\pi$
$523$	−4000.00	−0.334432	−0.167216	+	0.985920i	$0.553478\pi$
$524$	−1392.00	−0.116049
$525$	−1869.00	−0.155371
$526$	9840.00	0.815674
$527$	−1824.00	−0.150768
$528$	2304.00	0.189903
$529$	529.000	0.0434783
$530$	5112.00	0.418964
$531$	−7668.00	−0.626672
$532$	1568.00	0.127785
$533$	−12996.0	−1.05613
$534$	468.000	0.0379257
$535$	−1584.00	−0.128004
$536$	−3904.00	−0.314603
$537$	6228.00	0.500481
$538$	−1884.00	−0.150976
$539$	2352.00	0.187955
$540$	−648.000	−0.0516398
$541$	5150.00	0.409271	0.204636	−	0.978838i	$-0.434399\pi$
$541$	5150.00	0.409271	0.204636	+	0.978838i	$0.434399\pi$
$542$	−1648.00	−0.130605
$543$	−1074.00	−0.0848798
$544$	−3648.00	−0.287512
$545$	−3468.00	−0.272574
$546$	−1596.00	−0.125096
$547$	−2476.00	−0.193540	−0.0967698	−	0.995307i	$-0.530851\pi$
$547$	−2476.00	−0.193540	−0.0967698	+	0.995307i	$0.530851\pi$
$548$	−10392.0	−0.810081
$549$	3042.00	0.236483
$550$	8544.00	0.662395
$551$	−9072.00	−0.701416
$552$	552.000	0.0425628
$553$	8288.00	0.637327
$554$	9812.00	0.752476
$555$	828.000	0.0633273
$556$	−10768.0	−0.821340
$557$	−9798.00	−0.745340	−0.372670	−	0.927964i	$-0.621558\pi$
$557$	−9798.00	−0.745340	−0.372670	+	0.927964i	$0.621558\pi$
$558$	288.000	0.0218495
$559$	9424.00	0.713046
$560$	−672.000	−0.0507093
$561$	16416.0	1.23544
$562$	7644.00	0.573741
$563$	−1464.00	−0.109592	−0.0547960	−	0.998498i	$-0.517451\pi$
$563$	−1464.00	−0.109592	−0.0547960	+	0.998498i	$0.517451\pi$
$564$	−288.000	−0.0215018
$565$	−1692.00	−0.125988
$566$	−4816.00	−0.357653
$567$	567.000	0.0419961
$568$	−2688.00	−0.198567
$569$	9306.00	0.685638	0.342819	−	0.939402i	$-0.388618\pi$
$569$	9306.00	0.685638	0.342819	+	0.939402i	$0.388618\pi$
$570$	2016.00	0.148142
$571$	−23056.0	−1.68978	−0.844889	−	0.534941i	$-0.820334\pi$
$571$	−23056.0	−1.68978	−0.844889	+	0.534941i	$0.820334\pi$
$572$	7296.00	0.533324
$573$	11880.0	0.866133
$574$	4788.00	0.348166
$575$	2047.00	0.148462
$576$	576.000	0.0416667
$577$	−526.000	−0.0379509	−0.0189754	−	0.999820i	$-0.506040\pi$
$577$	−526.000	−0.0379509	−0.0189754	+	0.999820i	$0.506040\pi$
$578$	−16166.0	−1.16335
$579$	−3594.00	−0.257965
$580$	3888.00	0.278346
$581$	−2352.00	−0.167947
$582$	−4476.00	−0.318791
$583$	20448.0	1.45261
$584$	−2896.00	−0.205201
$585$	−2052.00	−0.145025
$586$	2028.00	0.142962
$587$	18876.0	1.32725	0.663625	−	0.748065i	$-0.269017\pi$
$587$	18876.0	1.32725	0.663625	+	0.748065i	$0.269017\pi$
$588$	588.000	0.0412393
$589$	−896.000	−0.0626809
$590$	−10224.0	−0.713416
$591$	4338.00	0.301931
$592$	−736.000	−0.0510970
$593$	−17214.0	−1.19206	−0.596032	−	0.802960i	$-0.703257\pi$
$593$	−17214.0	−1.19206	−0.596032	+	0.802960i	$0.703257\pi$
$594$	−2592.00	−0.179042
$595$	−4788.00	−0.329897
$596$	−3864.00	−0.265563
$597$	14856.0	1.01845
$598$	1748.00	0.119534
$599$	2808.00	0.191539	0.0957694	−	0.995404i	$-0.469469\pi$
$599$	2808.00	0.191539	0.0957694	+	0.995404i	$0.469469\pi$
$600$	2136.00	0.145336
$601$	19898.0	1.35051	0.675255	−	0.737584i	$-0.264034\pi$
$601$	19898.0	1.35051	0.675255	+	0.737584i	$0.264034\pi$
$602$	−3472.00	−0.235063
$603$	4392.00	0.296610
$604$	4832.00	0.325515
$605$	−5838.00	−0.392311
$606$	−180.000	−0.0120660
$607$	−23344.0	−1.56096	−0.780481	−	0.625180i	$-0.785026\pi$
$607$	−23344.0	−1.56096	−0.780481	+	0.625180i	$0.785026\pi$
$608$	−1792.00	−0.119532
$609$	−3402.00	−0.226365
$610$	4056.00	0.269217
$611$	−912.000	−0.0603855
$612$	4104.00	0.271069
$613$	2282.00	0.150357	0.0751787	−	0.997170i	$-0.476047\pi$
$613$	2282.00	0.150357	0.0751787	+	0.997170i	$0.476047\pi$
$614$	7976.00	0.524243
$615$	6156.00	0.403632
$616$	−2688.00	−0.175816
$617$	−28926.0	−1.88739	−0.943693	−	0.330823i	$-0.892674\pi$
$617$	−28926.0	−1.88739	−0.943693	+	0.330823i	$0.892674\pi$
$618$	−5664.00	−0.368672
$619$	−7288.00	−0.473230	−0.236615	−	0.971603i	$-0.576038\pi$
$619$	−7288.00	−0.473230	−0.236615	+	0.971603i	$0.576038\pi$
$620$	384.000	0.0248739
$621$	−621.000	−0.0401286
$622$	−9360.00	−0.603379
$623$	−546.000	−0.0351124
$624$	1824.00	0.117017
$625$	3421.00	0.218944
$626$	−4900.00	−0.312849
$627$	8064.00	0.513629
$628$	1448.00	0.0920087
$629$	−5244.00	−0.332420
$630$	756.000	0.0478091
$631$	18128.0	1.14368	0.571842	−	0.820364i	$-0.306229\pi$
$631$	18128.0	1.14368	0.571842	+	0.820364i	$0.306229\pi$
$632$	−9472.00	−0.596164
$633$	−3252.00	−0.204195
$634$	−12828.0	−0.803572
$635$	5136.00	0.320970
$636$	5112.00	0.318717
$637$	1862.00	0.115817
$638$	15552.0	0.965062
$639$	3024.00	0.187211
$640$	768.000	0.0474342
$641$	16626.0	1.02447	0.512237	−	0.858844i	$-0.328817\pi$
$641$	16626.0	1.02447	0.512237	+	0.858844i	$0.328817\pi$
$642$	−1584.00	−0.0973762
$643$	14288.0	0.876304	0.438152	−	0.898901i	$-0.355633\pi$
$643$	14288.0	0.876304	0.438152	+	0.898901i	$0.355633\pi$
$644$	−644.000	−0.0394055
$645$	−4464.00	−0.272511
$646$	−12768.0	−0.777632
$647$	27192.0	1.65228	0.826142	−	0.563462i	$-0.190531\pi$
$647$	27192.0	1.65228	0.826142	+	0.563462i	$0.190531\pi$
$648$	−648.000	−0.0392837
$649$	−40896.0	−2.47351
$650$	6764.00	0.408163
$651$	−336.000	−0.0202287
$652$	12656.0	0.760195
$653$	−9066.00	−0.543308	−0.271654	−	0.962395i	$-0.587571\pi$
$653$	−9066.00	−0.543308	−0.271654	+	0.962395i	$0.587571\pi$
$654$	−3468.00	−0.207354
$655$	2088.00	0.124557
$656$	−5472.00	−0.325679
$657$	3258.00	0.193465
$658$	336.000	0.0199068
$659$	9504.00	0.561796	0.280898	−	0.959738i	$-0.409368\pi$
$659$	9504.00	0.561796	0.280898	+	0.959738i	$0.409368\pi$
$660$	−3456.00	−0.203825
$661$	16778.0	0.987275	0.493637	−	0.869668i	$-0.335667\pi$
$661$	16778.0	0.987275	0.493637	+	0.869668i	$0.335667\pi$
$662$	15080.0	0.885349
$663$	12996.0	0.761271
$664$	2688.00	0.157100
$665$	−2352.00	−0.137153
$666$	828.000	0.0481747
$667$	3726.00	0.216299
$668$	9408.00	0.544920
$669$	5568.00	0.321781
$670$	5856.00	0.337667
$671$	16224.0	0.933414
$672$	−672.000	−0.0385758
$673$	−15982.0	−0.915395	−0.457697	−	0.889108i	$-0.651326\pi$
$673$	−15982.0	−0.915395	−0.457697	+	0.889108i	$0.651326\pi$
$674$	4028.00	0.230197
$675$	−2403.00	−0.137024
$676$	−3012.00	−0.171370
$677$	7674.00	0.435651	0.217826	−	0.975988i	$-0.430104\pi$
$677$	7674.00	0.435651	0.217826	+	0.975988i	$0.430104\pi$
$678$	−1692.00	−0.0958420
$679$	5222.00	0.295143
$680$	5472.00	0.308591
$681$	−504.000	−0.0283602
$682$	1536.00	0.0862412
$683$	−12804.0	−0.717323	−0.358661	−	0.933468i	$-0.616767\pi$
$683$	−12804.0	−0.717323	−0.358661	+	0.933468i	$0.616767\pi$
$684$	2016.00	0.112695
$685$	15588.0	0.869470
$686$	−686.000	−0.0381802
$687$	8574.00	0.476155
$688$	3968.00	0.219882
$689$	16188.0	0.895085
$690$	−828.000	−0.0456832
$691$	−6508.00	−0.358287	−0.179143	−	0.983823i	$-0.557333\pi$
$691$	−6508.00	−0.358287	−0.179143	+	0.983823i	$0.557333\pi$
$692$	−5832.00	−0.320375
$693$	3024.00	0.165761
$694$	8856.00	0.484394
$695$	16152.0	0.881554
$696$	3888.00	0.211745
$697$	−38988.0	−2.11876
$698$	−11164.0	−0.605392
$699$	−11826.0	−0.639915
$700$	−2492.00	−0.134555
$701$	−29094.0	−1.56757	−0.783784	−	0.621033i	$-0.786713\pi$
$701$	−29094.0	−1.56757	−0.783784	+	0.621033i	$0.786713\pi$
$702$	−2052.00	−0.110324
$703$	−2576.00	−0.138202
$704$	3072.00	0.164461
$705$	432.000	0.0230781
$706$	11868.0	0.632660
$707$	210.000	0.0111710
$708$	−10224.0	−0.542714
$709$	14834.0	0.785758	0.392879	−	0.919590i	$-0.371479\pi$
$709$	14834.0	0.785758	0.392879	+	0.919590i	$0.371479\pi$
$710$	4032.00	0.213124
$711$	10656.0	0.562069
$712$	624.000	0.0328446
$713$	368.000	0.0193292
$714$	−4788.00	−0.250961
$715$	−10944.0	−0.572423
$716$	8304.00	0.433429
$717$	18144.0	0.945049
$718$	−4512.00	−0.234521
$719$	−37200.0	−1.92952	−0.964761	−	0.263129i	$-0.915246\pi$
$719$	−37200.0	−1.92952	−0.964761	+	0.263129i	$0.915246\pi$
$720$	−864.000	−0.0447214
$721$	6608.00	0.341324
$722$	7446.00	0.383811
$723$	−1794.00	−0.0922816
$724$	−1432.00	−0.0735081
$725$	14418.0	0.738581
$726$	−5838.00	−0.298441
$727$	−29608.0	−1.51045	−0.755227	−	0.655463i	$-0.772473\pi$
$727$	−29608.0	−1.51045	−0.755227	+	0.655463i	$0.772473\pi$
$728$	−2128.00	−0.108336
$729$	729.000	0.0370370
$730$	4344.00	0.220245
$731$	28272.0	1.43048
$732$	4056.00	0.204801
$733$	5930.00	0.298812	0.149406	−	0.988776i	$-0.452264\pi$
$733$	5930.00	0.298812	0.149406	+	0.988776i	$0.452264\pi$
$734$	−6592.00	−0.331492
$735$	−882.000	−0.0442627
$736$	736.000	0.0368605
$737$	23424.0	1.17074
$738$	6156.00	0.307054
$739$	19196.0	0.955529	0.477765	−	0.878488i	$-0.341447\pi$
$739$	19196.0	0.955529	0.477765	+	0.878488i	$0.341447\pi$
$740$	1104.00	0.0548430
$741$	6384.00	0.316494
$742$	−5964.00	−0.295075
$743$	1512.00	0.0746567	0.0373283	−	0.999303i	$-0.488115\pi$
$743$	1512.00	0.0746567	0.0373283	+	0.999303i	$0.488115\pi$
$744$	384.000	0.0189222
$745$	5796.00	0.285032
$746$	−26500.0	−1.30058
$747$	−3024.00	−0.148116
$748$	21888.0	1.06993
$749$	1848.00	0.0901528
$750$	−7704.00	−0.375080
$751$	7400.00	0.359560	0.179780	−	0.983707i	$-0.442461\pi$
$751$	7400.00	0.359560	0.179780	+	0.983707i	$0.442461\pi$
$752$	−384.000	−0.0186211
$753$	−1800.00	−0.0871124
$754$	12312.0	0.594664
$755$	−7248.00	−0.349380
$756$	756.000	0.0363696
$757$	−7894.00	−0.379012	−0.189506	−	0.981880i	$-0.560689\pi$
$757$	−7894.00	−0.379012	−0.189506	+	0.981880i	$0.560689\pi$
$758$	16256.0	0.778951
$759$	−3312.00	−0.158390
$760$	2688.00	0.128295
$761$	7818.00	0.372408	0.186204	−	0.982511i	$-0.440382\pi$
$761$	7818.00	0.372408	0.186204	+	0.982511i	$0.440382\pi$
$762$	5136.00	0.244170
$763$	4046.00	0.191973
$764$	15840.0	0.750093
$765$	−6156.00	−0.290942
$766$	17952.0	0.846778
$767$	−32376.0	−1.52416
$768$	768.000	0.0360844
$769$	−25990.0	−1.21876	−0.609378	−	0.792880i	$-0.708581\pi$
$769$	−25990.0	−1.21876	−0.609378	+	0.792880i	$0.708581\pi$
$770$	4032.00	0.188705
$771$	2646.00	0.123597
$772$	−4792.00	−0.223404
$773$	20466.0	0.952278	0.476139	−	0.879370i	$-0.342036\pi$
$773$	20466.0	0.952278	0.476139	+	0.879370i	$0.342036\pi$
$774$	−4464.00	−0.207306
$775$	1424.00	0.0660021
$776$	−5968.00	−0.276081
$777$	−966.000	−0.0446011
$778$	28956.0	1.33435
$779$	−19152.0	−0.880862
$780$	−2736.00	−0.125596
$781$	16128.0	0.738931
$782$	5244.00	0.239802
$783$	−4374.00	−0.199635
$784$	784.000	0.0357143
$785$	−2172.00	−0.0987541
$786$	2088.00	0.0947538
$787$	−5248.00	−0.237701	−0.118851	−	0.992912i	$-0.537921\pi$
$787$	−5248.00	−0.237701	−0.118851	+	0.992912i	$0.537921\pi$
$788$	5784.00	0.261480
$789$	−14760.0	−0.665995
$790$	14208.0	0.639871
$791$	1974.00	0.0887324
$792$	−3456.00	−0.155055
$793$	12844.0	0.575162
$794$	28244.0	1.26240
$795$	−7668.00	−0.342083
$796$	19808.0	0.882005
$797$	6234.00	0.277063	0.138532	−	0.990358i	$-0.455762\pi$
$797$	6234.00	0.277063	0.138532	+	0.990358i	$0.455762\pi$
$798$	−2352.00	−0.104336
$799$	−2736.00	−0.121142
$800$	2848.00	0.125865
$801$	−702.000	−0.0309662
$802$	−2532.00	−0.111481
$803$	17376.0	0.763619
$804$	5856.00	0.256872
$805$	966.000	0.0422944
$806$	1216.00	0.0531412
$807$	2826.00	0.123271
$808$	−240.000	−0.0104495
$809$	14970.0	0.650577	0.325289	−	0.945615i	$-0.394539\pi$
$809$	14970.0	0.650577	0.325289	+	0.945615i	$0.394539\pi$
$810$	972.000	0.0421637
$811$	−35620.0	−1.54228	−0.771139	−	0.636667i	$-0.780313\pi$
$811$	−35620.0	−1.54228	−0.771139	+	0.636667i	$0.780313\pi$
$812$	−4536.00	−0.196037
$813$	2472.00	0.106638
$814$	4416.00	0.190148
$815$	−18984.0	−0.815927
$816$	5472.00	0.234753
$817$	13888.0	0.594712
$818$	−13108.0	−0.560282
$819$	2394.00	0.102141
$820$	8208.00	0.349556
$821$	−25458.0	−1.08221	−0.541103	−	0.840957i	$-0.681993\pi$
$821$	−25458.0	−1.08221	−0.541103	+	0.840957i	$0.681993\pi$
$822$	15588.0	0.661428
$823$	−32248.0	−1.36585	−0.682925	−	0.730488i	$-0.739292\pi$
$823$	−32248.0	−1.36585	−0.682925	+	0.730488i	$0.739292\pi$
$824$	−7552.00	−0.319280
$825$	−12816.0	−0.540843
$826$	11928.0	0.502455
$827$	31704.0	1.33308	0.666539	−	0.745470i	$-0.267775\pi$
$827$	31704.0	1.33308	0.666539	+	0.745470i	$0.267775\pi$
$828$	−828.000	−0.0347524
$829$	−33010.0	−1.38297	−0.691487	−	0.722389i	$-0.743044\pi$
$829$	−33010.0	−1.38297	−0.691487	+	0.722389i	$0.743044\pi$
$830$	−4032.00	−0.168618
$831$	−14718.0	−0.614394
$832$	2432.00	0.101339
$833$	5586.00	0.232345
$834$	16152.0	0.670621
$835$	−14112.0	−0.584869
$836$	10752.0	0.444815
$837$	−432.000	−0.0178400
$838$	4032.00	0.166209
$839$	−264.000	−0.0108633	−0.00543164	−	0.999985i	$-0.501729\pi$
$839$	−264.000	−0.0108633	−0.00543164	+	0.999985i	$0.501729\pi$
$840$	1008.00	0.0414039
$841$	1855.00	0.0760589
$842$	−8644.00	−0.353791
$843$	−11466.0	−0.468458
$844$	−4336.00	−0.176838
$845$	4518.00	0.183934
$846$	432.000	0.0175561
$847$	6811.00	0.276303
$848$	6816.00	0.276017
$849$	7224.00	0.292022
$850$	20292.0	0.818835
$851$	1058.00	0.0426178
$852$	4032.00	0.162129
$853$	21710.0	0.871438	0.435719	−	0.900083i	$-0.356494\pi$
$853$	21710.0	0.871438	0.435719	+	0.900083i	$0.356494\pi$
$854$	−4732.00	−0.189609
$855$	−3024.00	−0.120957
$856$	−2112.00	−0.0843302
$857$	9546.00	0.380496	0.190248	−	0.981736i	$-0.439071\pi$
$857$	9546.00	0.380496	0.190248	+	0.981736i	$0.439071\pi$
$858$	−10944.0	−0.435457
$859$	−40156.0	−1.59500	−0.797500	−	0.603319i	$-0.793845\pi$
$859$	−40156.0	−1.59500	−0.797500	+	0.603319i	$0.793845\pi$
$860$	−5952.00	−0.236002
$861$	−7182.00	−0.284276
$862$	22224.0	0.878135
$863$	−36096.0	−1.42378	−0.711890	−	0.702291i	$-0.752161\pi$
$863$	−36096.0	−1.42378	−0.711890	+	0.702291i	$0.752161\pi$
$864$	−864.000	−0.0340207
$865$	8748.00	0.343862
$866$	−25108.0	−0.985225
$867$	24249.0	0.949872
$868$	−448.000	−0.0175186
$869$	56832.0	2.21852
$870$	−5832.00	−0.227268
$871$	18544.0	0.721400
$872$	−4624.00	−0.179574
$873$	6714.00	0.260291
$874$	2576.00	0.0996962
$875$	8988.00	0.347257
$876$	4344.00	0.167546
$877$	22094.0	0.850697	0.425349	−	0.905030i	$-0.360152\pi$
$877$	22094.0	0.850697	0.425349	+	0.905030i	$0.360152\pi$
$878$	−832.000	−0.0319802
$879$	−3042.00	−0.116728
$880$	−4608.00	−0.176518
$881$	19866.0	0.759708	0.379854	−	0.925046i	$-0.375974\pi$
$881$	19866.0	0.759708	0.379854	+	0.925046i	$0.375974\pi$
$882$	−882.000	−0.0336718
$883$	41348.0	1.57584	0.787922	−	0.615775i	$-0.211157\pi$
$883$	41348.0	1.57584	0.787922	+	0.615775i	$0.211157\pi$
$884$	17328.0	0.659280
$885$	15336.0	0.582502
$886$	20088.0	0.761704
$887$	−44448.0	−1.68255	−0.841273	−	0.540611i	$-0.818193\pi$
$887$	−44448.0	−1.68255	−0.841273	+	0.540611i	$0.818193\pi$
$888$	1104.00	0.0417205
$889$	−5992.00	−0.226058
$890$	−936.000	−0.0352526
$891$	3888.00	0.146187
$892$	7424.00	0.278670
$893$	−1344.00	−0.0503642
$894$	5796.00	0.216831
$895$	−12456.0	−0.465205
$896$	−896.000	−0.0334077
$897$	−2622.00	−0.0975987
$898$	28380.0	1.05462
$899$	2592.00	0.0961602
$900$	−3204.00	−0.118667
$901$	48564.0	1.79567
$902$	32832.0	1.21196
$903$	5208.00	0.191928
$904$	−2256.00	−0.0830016
$905$	2148.00	0.0788972
$906$	−7248.00	−0.265782
$907$	−1144.00	−0.0418808	−0.0209404	−	0.999781i	$-0.506666\pi$
$907$	−1144.00	−0.0418808	−0.0209404	+	0.999781i	$0.506666\pi$
$908$	−672.000	−0.0245607
$909$	270.000	0.00985185
$910$	3192.00	0.116279
$911$	−25848.0	−0.940047	−0.470023	−	0.882654i	$-0.655754\pi$
$911$	−25848.0	−0.940047	−0.470023	+	0.882654i	$0.655754\pi$
$912$	2688.00	0.0975971
$913$	−16128.0	−0.584621
$914$	−7588.00	−0.274605
$915$	−6084.00	−0.219815
$916$	11432.0	0.412362
$917$	−2436.00	−0.0877250
$918$	−6156.00	−0.221327
$919$	−30808.0	−1.10583	−0.552917	−	0.833236i	$-0.686485\pi$
$919$	−30808.0	−1.10583	−0.552917	+	0.833236i	$0.686485\pi$
$920$	−1104.00	−0.0395628
$921$	−11964.0	−0.428043
$922$	−12732.0	−0.454779
$923$	12768.0	0.455324
$924$	4032.00	0.143553
$925$	4094.00	0.145524
$926$	−5872.00	−0.208386
$927$	8496.00	0.301020
$928$	5184.00	0.183376
$929$	21810.0	0.770251	0.385125	−	0.922864i	$-0.374158\pi$
$929$	21810.0	0.770251	0.385125	+	0.922864i	$0.374158\pi$
$930$	−576.000	−0.0203094
$931$	2744.00	0.0965961
$932$	−15768.0	−0.554182
$933$	14040.0	0.492657
$934$	−23808.0	−0.834070
$935$	−32832.0	−1.14836
$936$	−2736.00	−0.0955438
$937$	−23734.0	−0.827488	−0.413744	−	0.910393i	$-0.635779\pi$
$937$	−23734.0	−0.827488	−0.413744	+	0.910393i	$0.635779\pi$
$938$	−6832.00	−0.237817
$939$	7350.00	0.255440
$940$	576.000	0.0199862
$941$	34050.0	1.17959	0.589797	−	0.807551i	$-0.299208\pi$
$941$	34050.0	1.17959	0.589797	+	0.807551i	$0.299208\pi$
$942$	−2172.00	−0.0751248
$943$	7866.00	0.271635
$944$	−13632.0	−0.470004
$945$	−1134.00	−0.0390360
$946$	−23808.0	−0.818250
$947$	20700.0	0.710306	0.355153	−	0.934808i	$-0.384429\pi$
$947$	20700.0	0.710306	0.355153	+	0.934808i	$0.384429\pi$
$948$	14208.0	0.486766
$949$	13756.0	0.470536
$950$	9968.00	0.340426
$951$	19242.0	0.656114
$952$	−6384.00	−0.217339
$953$	52314.0	1.77819	0.889096	−	0.457721i	$-0.151334\pi$
$953$	52314.0	1.77819	0.889096	+	0.457721i	$0.151334\pi$
$954$	−7668.00	−0.260231
$955$	−23760.0	−0.805084
$956$	24192.0	0.818436
$957$	−23328.0	−0.787970
$958$	30240.0	1.01984
$959$	−18186.0	−0.612363
$960$	−1152.00	−0.0387298
$961$	−29535.0	−0.991407
$962$	3496.00	0.117168
$963$	2376.00	0.0795073
$964$	−2392.00	−0.0799182
$965$	7188.00	0.239782
$966$	966.000	0.0321745
$967$	−32968.0	−1.09636	−0.548180	−	0.836361i	$-0.684679\pi$
$967$	−32968.0	−1.09636	−0.548180	+	0.836361i	$0.684679\pi$
$968$	−7784.00	−0.258458
$969$	19152.0	0.634934
$970$	8952.00	0.296321
$971$	2160.00	0.0713879	0.0356940	−	0.999363i	$-0.488636\pi$
$971$	2160.00	0.0713879	0.0356940	+	0.999363i	$0.488636\pi$
$972$	972.000	0.0320750
$973$	−18844.0	−0.620875
$974$	10688.0	0.351607
$975$	−10146.0	−0.333264
$976$	5408.00	0.177363
$977$	−46446.0	−1.52092	−0.760460	−	0.649385i	$-0.775027\pi$
$977$	−46446.0	−1.52092	−0.760460	+	0.649385i	$0.775027\pi$
$978$	−18984.0	−0.620697
$979$	−3744.00	−0.122225
$980$	−1176.00	−0.0383326
$981$	5202.00	0.169304
$982$	−27816.0	−0.903915
$983$	24432.0	0.792736	0.396368	−	0.918092i	$-0.370270\pi$
$983$	24432.0	0.792736	0.396368	+	0.918092i	$0.370270\pi$
$984$	8208.00	0.265916
$985$	−8676.00	−0.280650
$986$	36936.0	1.19298
$987$	−504.000	−0.0162538
$988$	8512.00	0.274092
$989$	−5704.00	−0.183394
$990$	5184.00	0.166423
$991$	3920.00	0.125654	0.0628269	−	0.998024i	$-0.479988\pi$
$991$	3920.00	0.125654	0.0628269	+	0.998024i	$0.479988\pi$
$992$	512.000	0.0163871
$993$	−22620.0	−0.722884
$994$	−4704.00	−0.150102
$995$	−29712.0	−0.946667
$996$	−4032.00	−0.128272
$997$	5126.00	0.162831	0.0814153	−	0.996680i	$-0.474056\pi$
$997$	5126.00	0.162831	0.0814153	+	0.996680i	$0.474056\pi$
$998$	15560.0	0.493530
$999$	−1242.00	−0.0393345

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.4.a.a.1.1	✓	1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.4.a.a.1.1	✓	1	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	966.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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