LMFDB - Embedded newform 190.2.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [190,2,Mod(1,190)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(190, 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("190.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 190 = 2 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	190.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:	$1.51715763840$
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	$\chi$	$=$	190.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

\(q+1.00000 q^{2} -3.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -3.00000 q^{6} -5.00000 q^{7} +1.00000 q^{8} +6.00000 q^{9} -1.00000 q^{10} -4.00000 q^{11} -3.00000 q^{12} -1.00000 q^{13} -5.00000 q^{14} +3.00000 q^{15} +1.00000 q^{16} -3.00000 q^{17} +6.00000 q^{18} +1.00000 q^{19} -1.00000 q^{20} +15.0000 q^{21} -4.00000 q^{22} +7.00000 q^{23} -3.00000 q^{24} +1.00000 q^{25} -1.00000 q^{26} -9.00000 q^{27} -5.00000 q^{28} -3.00000 q^{29} +3.00000 q^{30} -2.00000 q^{31} +1.00000 q^{32} +12.0000 q^{33} -3.00000 q^{34} +5.00000 q^{35} +6.00000 q^{36} -2.00000 q^{37} +1.00000 q^{38} +3.00000 q^{39} -1.00000 q^{40} -6.00000 q^{41} +15.0000 q^{42} +6.00000 q^{43} -4.00000 q^{44} -6.00000 q^{45} +7.00000 q^{46} -3.00000 q^{48} +18.0000 q^{49} +1.00000 q^{50} +9.00000 q^{51} -1.00000 q^{52} -13.0000 q^{53} -9.00000 q^{54} +4.00000 q^{55} -5.00000 q^{56} -3.00000 q^{57} -3.00000 q^{58} -9.00000 q^{59} +3.00000 q^{60} -12.0000 q^{61} -2.00000 q^{62} -30.0000 q^{63} +1.00000 q^{64} +1.00000 q^{65} +12.0000 q^{66} -3.00000 q^{67} -3.00000 q^{68} -21.0000 q^{69} +5.00000 q^{70} +6.00000 q^{72} +11.0000 q^{73} -2.00000 q^{74} -3.00000 q^{75} +1.00000 q^{76} +20.0000 q^{77} +3.00000 q^{78} -2.00000 q^{79} -1.00000 q^{80} +9.00000 q^{81} -6.00000 q^{82} -10.0000 q^{83} +15.0000 q^{84} +3.00000 q^{85} +6.00000 q^{86} +9.00000 q^{87} -4.00000 q^{88} +2.00000 q^{89} -6.00000 q^{90} +5.00000 q^{91} +7.00000 q^{92} +6.00000 q^{93} -1.00000 q^{95} -3.00000 q^{96} -2.00000 q^{97} +18.0000 q^{98} -24.0000 q^{99} +O(q^{100})\)

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
$3$	−3.00000	−1.73205	−0.866025	−	0.500000i	$-0.833333\pi$
$3$	−3.00000	−1.73205	−0.866025	+	0.500000i	$0.833333\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−3.00000	−1.22474
$7$	−5.00000	−1.88982	−0.944911	−	0.327327i	$-0.893852\pi$
$7$	−5.00000	−1.88982	−0.944911	+	0.327327i	$0.893852\pi$
$8$	1.00000	0.353553
$9$	6.00000	2.00000
$10$	−1.00000	−0.316228
$11$	−4.00000	−1.20605	−0.603023	−	0.797724i	$-0.706037\pi$
$11$	−4.00000	−1.20605	−0.603023	+	0.797724i	$0.706037\pi$
$12$	−3.00000	−0.866025
$13$	−1.00000	−0.277350	−0.138675	−	0.990338i	$-0.544284\pi$
$13$	−1.00000	−0.277350	−0.138675	+	0.990338i	$0.544284\pi$
$14$	−5.00000	−1.33631
$15$	3.00000	0.774597
$16$	1.00000	0.250000
$17$	−3.00000	−0.727607	−0.363803	−	0.931476i	$-0.618522\pi$
$17$	−3.00000	−0.727607	−0.363803	+	0.931476i	$0.618522\pi$
$18$	6.00000	1.41421
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	−1.00000	−0.223607
$21$	15.0000	3.27327
$22$	−4.00000	−0.852803
$23$	7.00000	1.45960	0.729800	−	0.683660i	$-0.239613\pi$
$23$	7.00000	1.45960	0.729800	+	0.683660i	$0.239613\pi$
$24$	−3.00000	−0.612372
$25$	1.00000	0.200000
$26$	−1.00000	−0.196116
$27$	−9.00000	−1.73205
$28$	−5.00000	−0.944911
$29$	−3.00000	−0.557086	−0.278543	−	0.960424i	$-0.589851\pi$
$29$	−3.00000	−0.557086	−0.278543	+	0.960424i	$0.589851\pi$
$30$	3.00000	0.547723
$31$	−2.00000	−0.359211	−0.179605	−	0.983739i	$-0.557482\pi$
$31$	−2.00000	−0.359211	−0.179605	+	0.983739i	$0.557482\pi$
$32$	1.00000	0.176777
$33$	12.0000	2.08893
$34$	−3.00000	−0.514496
$35$	5.00000	0.845154
$36$	6.00000	1.00000
$37$	−2.00000	−0.328798	−0.164399	−	0.986394i	$-0.552568\pi$
$37$	−2.00000	−0.328798	−0.164399	+	0.986394i	$0.552568\pi$
$38$	1.00000	0.162221
$39$	3.00000	0.480384
$40$	−1.00000	−0.158114
$41$	−6.00000	−0.937043	−0.468521	−	0.883452i	$-0.655213\pi$
$41$	−6.00000	−0.937043	−0.468521	+	0.883452i	$0.655213\pi$
$42$	15.0000	2.31455
$43$	6.00000	0.914991	0.457496	−	0.889212i	$-0.348747\pi$
$43$	6.00000	0.914991	0.457496	+	0.889212i	$0.348747\pi$
$44$	−4.00000	−0.603023
$45$	−6.00000	−0.894427
$46$	7.00000	1.03209
$47$	0	0		−	1.00000i	$-0.5\pi$
$47$	0	0			1.00000i	$0.5\pi$
$48$	−3.00000	−0.433013
$49$	18.0000	2.57143
$50$	1.00000	0.141421
$51$	9.00000	1.26025
$52$	−1.00000	−0.138675
$53$	−13.0000	−1.78569	−0.892844	−	0.450367i	$-0.851293\pi$
$53$	−13.0000	−1.78569	−0.892844	+	0.450367i	$0.851293\pi$
$54$	−9.00000	−1.22474
$55$	4.00000	0.539360
$56$	−5.00000	−0.668153
$57$	−3.00000	−0.397360
$58$	−3.00000	−0.393919
$59$	−9.00000	−1.17170	−0.585850	−	0.810419i	$-0.699239\pi$
$59$	−9.00000	−1.17170	−0.585850	+	0.810419i	$0.699239\pi$
$60$	3.00000	0.387298
$61$	−12.0000	−1.53644	−0.768221	−	0.640184i	$-0.778858\pi$
$61$	−12.0000	−1.53644	−0.768221	+	0.640184i	$0.778858\pi$
$62$	−2.00000	−0.254000
$63$	−30.0000	−3.77964
$64$	1.00000	0.125000
$65$	1.00000	0.124035
$66$	12.0000	1.47710
$67$	−3.00000	−0.366508	−0.183254	−	0.983066i	$-0.558663\pi$
$67$	−3.00000	−0.366508	−0.183254	+	0.983066i	$0.558663\pi$
$68$	−3.00000	−0.363803
$69$	−21.0000	−2.52810
$70$	5.00000	0.597614
$71$	0	0		−	1.00000i	$-0.5\pi$
$71$	0	0			1.00000i	$0.5\pi$
$72$	6.00000	0.707107
$73$	11.0000	1.28745	0.643726	−	0.765256i	$-0.277388\pi$
$73$	11.0000	1.28745	0.643726	+	0.765256i	$0.277388\pi$
$74$	−2.00000	−0.232495
$75$	−3.00000	−0.346410
$76$	1.00000	0.114708
$77$	20.0000	2.27921
$78$	3.00000	0.339683
$79$	−2.00000	−0.225018	−0.112509	−	0.993651i	$-0.535889\pi$
$79$	−2.00000	−0.225018	−0.112509	+	0.993651i	$0.535889\pi$
$80$	−1.00000	−0.111803
$81$	9.00000	1.00000
$82$	−6.00000	−0.662589
$83$	−10.0000	−1.09764	−0.548821	−	0.835940i	$-0.684923\pi$
$83$	−10.0000	−1.09764	−0.548821	+	0.835940i	$0.684923\pi$
$84$	15.0000	1.63663
$85$	3.00000	0.325396
$86$	6.00000	0.646997
$87$	9.00000	0.964901
$88$	−4.00000	−0.426401
$89$	2.00000	0.212000	0.106000	−	0.994366i	$-0.466196\pi$
$89$	2.00000	0.212000	0.106000	+	0.994366i	$0.466196\pi$
$90$	−6.00000	−0.632456
$91$	5.00000	0.524142
$92$	7.00000	0.729800
$93$	6.00000	0.622171
$94$	0	0
$95$	−1.00000	−0.102598
$96$	−3.00000	−0.306186
$97$	−2.00000	−0.203069	−0.101535	−	0.994832i	$-0.532375\pi$
$97$	−2.00000	−0.203069	−0.101535	+	0.994832i	$0.532375\pi$
$98$	18.0000	1.81827
$99$	−24.0000	−2.41209
$100$	1.00000	0.100000
$101$	−8.00000	−0.796030	−0.398015	−	0.917379i	$-0.630301\pi$
$101$	−8.00000	−0.796030	−0.398015	+	0.917379i	$0.630301\pi$
$102$	9.00000	0.891133
$103$	4.00000	0.394132	0.197066	−	0.980390i	$-0.436859\pi$
$103$	4.00000	0.394132	0.197066	+	0.980390i	$0.436859\pi$
$104$	−1.00000	−0.0980581
$105$	−15.0000	−1.46385
$106$	−13.0000	−1.26267
$107$	−13.0000	−1.25676	−0.628379	−	0.777908i	$-0.716281\pi$
$107$	−13.0000	−1.25676	−0.628379	+	0.777908i	$0.716281\pi$
$108$	−9.00000	−0.866025
$109$	19.0000	1.81987	0.909935	−	0.414751i	$-0.136131\pi$
$109$	19.0000	1.81987	0.909935	+	0.414751i	$0.136131\pi$
$110$	4.00000	0.381385
$111$	6.00000	0.569495
$112$	−5.00000	−0.472456
$113$	0	0		−	1.00000i	$-0.5\pi$
$113$	0	0			1.00000i	$0.5\pi$
$114$	−3.00000	−0.280976
$115$	−7.00000	−0.652753
$116$	−3.00000	−0.278543
$117$	−6.00000	−0.554700
$118$	−9.00000	−0.828517
$119$	15.0000	1.37505
$120$	3.00000	0.273861
$121$	5.00000	0.454545
$122$	−12.0000	−1.08643
$123$	18.0000	1.62301
$124$	−2.00000	−0.179605
$125$	−1.00000	−0.0894427
$126$	−30.0000	−2.67261
$127$	−6.00000	−0.532414	−0.266207	−	0.963916i	$-0.585770\pi$
$127$	−6.00000	−0.532414	−0.266207	+	0.963916i	$0.585770\pi$
$128$	1.00000	0.0883883
$129$	−18.0000	−1.58481
$130$	1.00000	0.0877058
$131$	16.0000	1.39793	0.698963	−	0.715158i	$-0.253645\pi$
$131$	16.0000	1.39793	0.698963	+	0.715158i	$0.253645\pi$
$132$	12.0000	1.04447
$133$	−5.00000	−0.433555
$134$	−3.00000	−0.259161
$135$	9.00000	0.774597
$136$	−3.00000	−0.257248
$137$	9.00000	0.768922	0.384461	−	0.923141i	$-0.374387\pi$
$137$	9.00000	0.768922	0.384461	+	0.923141i	$0.374387\pi$
$138$	−21.0000	−1.78764
$139$	16.0000	1.35710	0.678551	−	0.734553i	$-0.262608\pi$
$139$	16.0000	1.35710	0.678551	+	0.734553i	$0.262608\pi$
$140$	5.00000	0.422577
$141$	0	0
$142$	0	0
$143$	4.00000	0.334497
$144$	6.00000	0.500000
$145$	3.00000	0.249136
$146$	11.0000	0.910366
$147$	−54.0000	−4.45384
$148$	−2.00000	−0.164399
$149$	−4.00000	−0.327693	−0.163846	−	0.986486i	$-0.552390\pi$
$149$	−4.00000	−0.327693	−0.163846	+	0.986486i	$0.552390\pi$
$150$	−3.00000	−0.244949
$151$	−10.0000	−0.813788	−0.406894	−	0.913475i	$-0.633388\pi$
$151$	−10.0000	−0.813788	−0.406894	+	0.913475i	$0.633388\pi$
$152$	1.00000	0.0811107
$153$	−18.0000	−1.45521
$154$	20.0000	1.61165
$155$	2.00000	0.160644
$156$	3.00000	0.240192
$157$	6.00000	0.478852	0.239426	−	0.970915i	$-0.423041\pi$
$157$	6.00000	0.478852	0.239426	+	0.970915i	$0.423041\pi$
$158$	−2.00000	−0.159111
$159$	39.0000	3.09290
$160$	−1.00000	−0.0790569
$161$	−35.0000	−2.75839
$162$	9.00000	0.707107
$163$	22.0000	1.72317	0.861586	−	0.507611i	$-0.169471\pi$
$163$	22.0000	1.72317	0.861586	+	0.507611i	$0.169471\pi$
$164$	−6.00000	−0.468521
$165$	−12.0000	−0.934199
$166$	−10.0000	−0.776151
$167$	−2.00000	−0.154765	−0.0773823	−	0.997001i	$-0.524656\pi$
$167$	−2.00000	−0.154765	−0.0773823	+	0.997001i	$0.524656\pi$
$168$	15.0000	1.15728
$169$	−12.0000	−0.923077
$170$	3.00000	0.230089
$171$	6.00000	0.458831
$172$	6.00000	0.457496
$173$	−14.0000	−1.06440	−0.532200	−	0.846619i	$-0.678635\pi$
$173$	−14.0000	−1.06440	−0.532200	+	0.846619i	$0.678635\pi$
$174$	9.00000	0.682288
$175$	−5.00000	−0.377964
$176$	−4.00000	−0.301511
$177$	27.0000	2.02944
$178$	2.00000	0.149906
$179$	−8.00000	−0.597948	−0.298974	−	0.954261i	$-0.596644\pi$
$179$	−8.00000	−0.597948	−0.298974	+	0.954261i	$0.596644\pi$
$180$	−6.00000	−0.447214
$181$	26.0000	1.93256	0.966282	−	0.257485i	$-0.0828937\pi$
$181$	26.0000	1.93256	0.966282	+	0.257485i	$0.0828937\pi$
$182$	5.00000	0.370625
$183$	36.0000	2.66120
$184$	7.00000	0.516047
$185$	2.00000	0.147043
$186$	6.00000	0.439941
$187$	12.0000	0.877527
$188$	0	0
$189$	45.0000	3.27327
$190$	−1.00000	−0.0725476
$191$	9.00000	0.651217	0.325609	−	0.945505i	$-0.394431\pi$
$191$	9.00000	0.651217	0.325609	+	0.945505i	$0.394431\pi$
$192$	−3.00000	−0.216506
$193$	10.0000	0.719816	0.359908	−	0.932988i	$-0.382808\pi$
$193$	10.0000	0.719816	0.359908	+	0.932988i	$0.382808\pi$
$194$	−2.00000	−0.143592
$195$	−3.00000	−0.214834
$196$	18.0000	1.28571
$197$	−22.0000	−1.56744	−0.783718	−	0.621117i	$-0.786679\pi$
$197$	−22.0000	−1.56744	−0.783718	+	0.621117i	$0.786679\pi$
$198$	−24.0000	−1.70561
$199$	−15.0000	−1.06332	−0.531661	−	0.846957i	$-0.678432\pi$
$199$	−15.0000	−1.06332	−0.531661	+	0.846957i	$0.678432\pi$
$200$	1.00000	0.0707107
$201$	9.00000	0.634811
$202$	−8.00000	−0.562878
$203$	15.0000	1.05279
$204$	9.00000	0.630126
$205$	6.00000	0.419058
$206$	4.00000	0.278693
$207$	42.0000	2.91920
$208$	−1.00000	−0.0693375
$209$	−4.00000	−0.276686
$210$	−15.0000	−1.03510
$211$	−5.00000	−0.344214	−0.172107	−	0.985078i	$-0.555058\pi$
$211$	−5.00000	−0.344214	−0.172107	+	0.985078i	$0.555058\pi$
$212$	−13.0000	−0.892844
$213$	0	0
$214$	−13.0000	−0.888662
$215$	−6.00000	−0.409197
$216$	−9.00000	−0.612372
$217$	10.0000	0.678844
$218$	19.0000	1.28684
$219$	−33.0000	−2.22993
$220$	4.00000	0.269680
$221$	3.00000	0.201802
$222$	6.00000	0.402694
$223$	−2.00000	−0.133930	−0.0669650	−	0.997755i	$-0.521332\pi$
$223$	−2.00000	−0.133930	−0.0669650	+	0.997755i	$0.521332\pi$
$224$	−5.00000	−0.334077
$225$	6.00000	0.400000
$226$	0	0
$227$	5.00000	0.331862	0.165931	−	0.986137i	$-0.446937\pi$
$227$	5.00000	0.331862	0.165931	+	0.986137i	$0.446937\pi$
$228$	−3.00000	−0.198680
$229$	−6.00000	−0.396491	−0.198246	−	0.980152i	$-0.563524\pi$
$229$	−6.00000	−0.396491	−0.198246	+	0.980152i	$0.563524\pi$
$230$	−7.00000	−0.461566
$231$	−60.0000	−3.94771
$232$	−3.00000	−0.196960
$233$	10.0000	0.655122	0.327561	−	0.944830i	$-0.393773\pi$
$233$	10.0000	0.655122	0.327561	+	0.944830i	$0.393773\pi$
$234$	−6.00000	−0.392232
$235$	0	0
$236$	−9.00000	−0.585850
$237$	6.00000	0.389742
$238$	15.0000	0.972306
$239$	−11.0000	−0.711531	−0.355765	−	0.934575i	$-0.615780\pi$
$239$	−11.0000	−0.711531	−0.355765	+	0.934575i	$0.615780\pi$
$240$	3.00000	0.193649
$241$	−12.0000	−0.772988	−0.386494	−	0.922292i	$-0.626314\pi$
$241$	−12.0000	−0.772988	−0.386494	+	0.922292i	$0.626314\pi$
$242$	5.00000	0.321412
$243$	0	0
$244$	−12.0000	−0.768221
$245$	−18.0000	−1.14998
$246$	18.0000	1.14764
$247$	−1.00000	−0.0636285
$248$	−2.00000	−0.127000
$249$	30.0000	1.90117
$250$	−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	$0.623635\pi$
$252$	−30.0000	−1.88982
$253$	−28.0000	−1.76034
$254$	−6.00000	−0.376473
$255$	−9.00000	−0.563602
$256$	1.00000	0.0625000
$257$	22.0000	1.37232	0.686161	−	0.727450i	$-0.259294\pi$
$257$	22.0000	1.37232	0.686161	+	0.727450i	$0.259294\pi$
$258$	−18.0000	−1.12063
$259$	10.0000	0.621370
$260$	1.00000	0.0620174
$261$	−18.0000	−1.11417
$262$	16.0000	0.988483
$263$	8.00000	0.493301	0.246651	−	0.969104i	$-0.420670\pi$
$263$	8.00000	0.493301	0.246651	+	0.969104i	$0.420670\pi$
$264$	12.0000	0.738549
$265$	13.0000	0.798584
$266$	−5.00000	−0.306570
$267$	−6.00000	−0.367194
$268$	−3.00000	−0.183254
$269$	2.00000	0.121942	0.0609711	−	0.998140i	$-0.480580\pi$
$269$	2.00000	0.121942	0.0609711	+	0.998140i	$0.480580\pi$
$270$	9.00000	0.547723
$271$	−27.0000	−1.64013	−0.820067	−	0.572268i	$-0.806064\pi$
$271$	−27.0000	−1.64013	−0.820067	+	0.572268i	$0.806064\pi$
$272$	−3.00000	−0.181902
$273$	−15.0000	−0.907841
$274$	9.00000	0.543710
$275$	−4.00000	−0.241209
$276$	−21.0000	−1.26405
$277$	−8.00000	−0.480673	−0.240337	−	0.970690i	$-0.577258\pi$
$277$	−8.00000	−0.480673	−0.240337	+	0.970690i	$0.577258\pi$
$278$	16.0000	0.959616
$279$	−12.0000	−0.718421
$280$	5.00000	0.298807
$281$	−18.0000	−1.07379	−0.536895	−	0.843649i	$-0.680403\pi$
$281$	−18.0000	−1.07379	−0.536895	+	0.843649i	$0.680403\pi$
$282$	0	0
$283$	−2.00000	−0.118888	−0.0594438	−	0.998232i	$-0.518933\pi$
$283$	−2.00000	−0.118888	−0.0594438	+	0.998232i	$0.518933\pi$
$284$	0	0
$285$	3.00000	0.177705
$286$	4.00000	0.236525
$287$	30.0000	1.77084
$288$	6.00000	0.353553
$289$	−8.00000	−0.470588
$290$	3.00000	0.176166
$291$	6.00000	0.351726
$292$	11.0000	0.643726
$293$	−27.0000	−1.57736	−0.788678	−	0.614806i	$-0.789234\pi$
$293$	−27.0000	−1.57736	−0.788678	+	0.614806i	$0.789234\pi$
$294$	−54.0000	−3.14934
$295$	9.00000	0.524000
$296$	−2.00000	−0.116248
$297$	36.0000	2.08893
$298$	−4.00000	−0.231714
$299$	−7.00000	−0.404820
$300$	−3.00000	−0.173205
$301$	−30.0000	−1.72917
$302$	−10.0000	−0.575435
$303$	24.0000	1.37876
$304$	1.00000	0.0573539
$305$	12.0000	0.687118
$306$	−18.0000	−1.02899
$307$	4.00000	0.228292	0.114146	−	0.993464i	$-0.463587\pi$
$307$	4.00000	0.228292	0.114146	+	0.993464i	$0.463587\pi$
$308$	20.0000	1.13961
$309$	−12.0000	−0.682656
$310$	2.00000	0.113592
$311$	25.0000	1.41762	0.708810	−	0.705399i	$-0.249232\pi$
$311$	25.0000	1.41762	0.708810	+	0.705399i	$0.249232\pi$
$312$	3.00000	0.169842
$313$	−1.00000	−0.0565233	−0.0282617	−	0.999601i	$-0.508997\pi$
$313$	−1.00000	−0.0565233	−0.0282617	+	0.999601i	$0.508997\pi$
$314$	6.00000	0.338600
$315$	30.0000	1.69031
$316$	−2.00000	−0.112509
$317$	9.00000	0.505490	0.252745	−	0.967533i	$-0.418667\pi$
$317$	9.00000	0.505490	0.252745	+	0.967533i	$0.418667\pi$
$318$	39.0000	2.18701
$319$	12.0000	0.671871
$320$	−1.00000	−0.0559017
$321$	39.0000	2.17677
$322$	−35.0000	−1.95047
$323$	−3.00000	−0.166924
$324$	9.00000	0.500000
$325$	−1.00000	−0.0554700
$326$	22.0000	1.21847
$327$	−57.0000	−3.15211
$328$	−6.00000	−0.331295
$329$	0	0
$330$	−12.0000	−0.660578
$331$	−7.00000	−0.384755	−0.192377	−	0.981321i	$-0.561620\pi$
$331$	−7.00000	−0.384755	−0.192377	+	0.981321i	$0.561620\pi$
$332$	−10.0000	−0.548821
$333$	−12.0000	−0.657596
$334$	−2.00000	−0.109435
$335$	3.00000	0.163908
$336$	15.0000	0.818317
$337$	6.00000	0.326841	0.163420	−	0.986557i	$-0.447747\pi$
$337$	6.00000	0.326841	0.163420	+	0.986557i	$0.447747\pi$
$338$	−12.0000	−0.652714
$339$	0	0
$340$	3.00000	0.162698
$341$	8.00000	0.433224
$342$	6.00000	0.324443
$343$	−55.0000	−2.96972
$344$	6.00000	0.323498
$345$	21.0000	1.13060
$346$	−14.0000	−0.752645
$347$	−6.00000	−0.322097	−0.161048	−	0.986947i	$-0.551488\pi$
$347$	−6.00000	−0.322097	−0.161048	+	0.986947i	$0.551488\pi$
$348$	9.00000	0.482451
$349$	14.0000	0.749403	0.374701	−	0.927146i	$-0.377745\pi$
$349$	14.0000	0.749403	0.374701	+	0.927146i	$0.377745\pi$
$350$	−5.00000	−0.267261
$351$	9.00000	0.480384
$352$	−4.00000	−0.213201
$353$	7.00000	0.372572	0.186286	−	0.982496i	$-0.440355\pi$
$353$	7.00000	0.372572	0.186286	+	0.982496i	$0.440355\pi$
$354$	27.0000	1.43503
$355$	0	0
$356$	2.00000	0.106000
$357$	−45.0000	−2.38165
$358$	−8.00000	−0.422813
$359$	−5.00000	−0.263890	−0.131945	−	0.991257i	$-0.542122\pi$
$359$	−5.00000	−0.263890	−0.131945	+	0.991257i	$0.542122\pi$
$360$	−6.00000	−0.316228
$361$	1.00000	0.0526316
$362$	26.0000	1.36653
$363$	−15.0000	−0.787296
$364$	5.00000	0.262071
$365$	−11.0000	−0.575766
$366$	36.0000	1.88175
$367$	8.00000	0.417597	0.208798	−	0.977959i	$-0.433045\pi$
$367$	8.00000	0.417597	0.208798	+	0.977959i	$0.433045\pi$
$368$	7.00000	0.364900
$369$	−36.0000	−1.87409
$370$	2.00000	0.103975
$371$	65.0000	3.37463
$372$	6.00000	0.311086
$373$	−23.0000	−1.19089	−0.595447	−	0.803394i	$-0.703025\pi$
$373$	−23.0000	−1.19089	−0.595447	+	0.803394i	$0.703025\pi$
$374$	12.0000	0.620505
$375$	3.00000	0.154919
$376$	0	0
$377$	3.00000	0.154508
$378$	45.0000	2.31455
$379$	−33.0000	−1.69510	−0.847548	−	0.530719i	$-0.821922\pi$
$379$	−33.0000	−1.69510	−0.847548	+	0.530719i	$0.821922\pi$
$380$	−1.00000	−0.0512989
$381$	18.0000	0.922168
$382$	9.00000	0.460480
$383$	−4.00000	−0.204390	−0.102195	−	0.994764i	$-0.532587\pi$
$383$	−4.00000	−0.204390	−0.102195	+	0.994764i	$0.532587\pi$
$384$	−3.00000	−0.153093
$385$	−20.0000	−1.01929
$386$	10.0000	0.508987
$387$	36.0000	1.82998
$388$	−2.00000	−0.101535
$389$	−4.00000	−0.202808	−0.101404	−	0.994845i	$-0.532333\pi$
$389$	−4.00000	−0.202808	−0.101404	+	0.994845i	$0.532333\pi$
$390$	−3.00000	−0.151911
$391$	−21.0000	−1.06202
$392$	18.0000	0.909137
$393$	−48.0000	−2.42128
$394$	−22.0000	−1.10834
$395$	2.00000	0.100631
$396$	−24.0000	−1.20605
$397$	−16.0000	−0.803017	−0.401508	−	0.915855i	$-0.631514\pi$
$397$	−16.0000	−0.803017	−0.401508	+	0.915855i	$0.631514\pi$
$398$	−15.0000	−0.751882
$399$	15.0000	0.750939
$400$	1.00000	0.0500000
$401$	−6.00000	−0.299626	−0.149813	−	0.988714i	$-0.547867\pi$
$401$	−6.00000	−0.299626	−0.149813	+	0.988714i	$0.547867\pi$
$402$	9.00000	0.448879
$403$	2.00000	0.0996271
$404$	−8.00000	−0.398015
$405$	−9.00000	−0.447214
$406$	15.0000	0.744438
$407$	8.00000	0.396545
$408$	9.00000	0.445566
$409$	22.0000	1.08783	0.543915	−	0.839140i	$-0.316941\pi$
$409$	22.0000	1.08783	0.543915	+	0.839140i	$0.316941\pi$
$410$	6.00000	0.296319
$411$	−27.0000	−1.33181
$412$	4.00000	0.197066
$413$	45.0000	2.21431
$414$	42.0000	2.06419
$415$	10.0000	0.490881
$416$	−1.00000	−0.0490290
$417$	−48.0000	−2.35057
$418$	−4.00000	−0.195646
$419$	14.0000	0.683945	0.341972	−	0.939710i	$-0.388905\pi$
$419$	14.0000	0.683945	0.341972	+	0.939710i	$0.388905\pi$
$420$	−15.0000	−0.731925
$421$	1.00000	0.0487370	0.0243685	−	0.999703i	$-0.492242\pi$
$421$	1.00000	0.0487370	0.0243685	+	0.999703i	$0.492242\pi$
$422$	−5.00000	−0.243396
$423$	0	0
$424$	−13.0000	−0.631336
$425$	−3.00000	−0.145521
$426$	0	0
$427$	60.0000	2.90360
$428$	−13.0000	−0.628379
$429$	−12.0000	−0.579365
$430$	−6.00000	−0.289346
$431$	−36.0000	−1.73406	−0.867029	−	0.498257i	$-0.833974\pi$
$431$	−36.0000	−1.73406	−0.867029	+	0.498257i	$0.833974\pi$
$432$	−9.00000	−0.433013
$433$	−16.0000	−0.768911	−0.384455	−	0.923144i	$-0.625611\pi$
$433$	−16.0000	−0.768911	−0.384455	+	0.923144i	$0.625611\pi$
$434$	10.0000	0.480015
$435$	−9.00000	−0.431517
$436$	19.0000	0.909935
$437$	7.00000	0.334855
$438$	−33.0000	−1.57680
$439$	26.0000	1.24091	0.620456	−	0.784241i	$-0.286947\pi$
$439$	26.0000	1.24091	0.620456	+	0.784241i	$0.286947\pi$
$440$	4.00000	0.190693
$441$	108.000	5.14286
$442$	3.00000	0.142695
$443$	36.0000	1.71041	0.855206	−	0.518289i	$-0.173431\pi$
$443$	36.0000	1.71041	0.855206	+	0.518289i	$0.173431\pi$
$444$	6.00000	0.284747
$445$	−2.00000	−0.0948091
$446$	−2.00000	−0.0947027
$447$	12.0000	0.567581
$448$	−5.00000	−0.236228
$449$	−22.0000	−1.03824	−0.519122	−	0.854700i	$-0.673741\pi$
$449$	−22.0000	−1.03824	−0.519122	+	0.854700i	$0.673741\pi$
$450$	6.00000	0.282843
$451$	24.0000	1.13012
$452$	0	0
$453$	30.0000	1.40952
$454$	5.00000	0.234662
$455$	−5.00000	−0.234404
$456$	−3.00000	−0.140488
$457$	−29.0000	−1.35656	−0.678281	−	0.734802i	$-0.737275\pi$
$457$	−29.0000	−1.35656	−0.678281	+	0.734802i	$0.737275\pi$
$458$	−6.00000	−0.280362
$459$	27.0000	1.26025
$460$	−7.00000	−0.326377
$461$	18.0000	0.838344	0.419172	−	0.907907i	$-0.362320\pi$
$461$	18.0000	0.838344	0.419172	+	0.907907i	$0.362320\pi$
$462$	−60.0000	−2.79145
$463$	−8.00000	−0.371792	−0.185896	−	0.982569i	$-0.559519\pi$
$463$	−8.00000	−0.371792	−0.185896	+	0.982569i	$0.559519\pi$
$464$	−3.00000	−0.139272
$465$	−6.00000	−0.278243
$466$	10.0000	0.463241
$467$	−8.00000	−0.370196	−0.185098	−	0.982720i	$-0.559260\pi$
$467$	−8.00000	−0.370196	−0.185098	+	0.982720i	$0.559260\pi$
$468$	−6.00000	−0.277350
$469$	15.0000	0.692636
$470$	0	0
$471$	−18.0000	−0.829396
$472$	−9.00000	−0.414259
$473$	−24.0000	−1.10352
$474$	6.00000	0.275589
$475$	1.00000	0.0458831
$476$	15.0000	0.687524
$477$	−78.0000	−3.57137
$478$	−11.0000	−0.503128
$479$	0	0		−	1.00000i	$-0.5\pi$
$479$	0	0			1.00000i	$0.5\pi$
$480$	3.00000	0.136931
$481$	2.00000	0.0911922
$482$	−12.0000	−0.546585
$483$	105.000	4.77767
$484$	5.00000	0.227273
$485$	2.00000	0.0908153
$486$	0	0
$487$	−38.0000	−1.72194	−0.860972	−	0.508652i	$-0.830144\pi$
$487$	−38.0000	−1.72194	−0.860972	+	0.508652i	$0.830144\pi$
$488$	−12.0000	−0.543214
$489$	−66.0000	−2.98462
$490$	−18.0000	−0.813157
$491$	18.0000	0.812329	0.406164	−	0.913800i	$-0.366866\pi$
$491$	18.0000	0.812329	0.406164	+	0.913800i	$0.366866\pi$
$492$	18.0000	0.811503
$493$	9.00000	0.405340
$494$	−1.00000	−0.0449921
$495$	24.0000	1.07872
$496$	−2.00000	−0.0898027
$497$	0	0
$498$	30.0000	1.34433
$499$	42.0000	1.88018	0.940089	−	0.340929i	$-0.110742\pi$
$499$	42.0000	1.88018	0.940089	+	0.340929i	$0.110742\pi$
$500$	−1.00000	−0.0447214
$501$	6.00000	0.268060
$502$	−12.0000	−0.535586
$503$	−21.0000	−0.936344	−0.468172	−	0.883637i	$-0.655087\pi$
$503$	−21.0000	−0.936344	−0.468172	+	0.883637i	$0.655087\pi$
$504$	−30.0000	−1.33631
$505$	8.00000	0.355995
$506$	−28.0000	−1.24475
$507$	36.0000	1.59882
$508$	−6.00000	−0.266207
$509$	2.00000	0.0886484	0.0443242	−	0.999017i	$-0.485887\pi$
$509$	2.00000	0.0886484	0.0443242	+	0.999017i	$0.485887\pi$
$510$	−9.00000	−0.398527
$511$	−55.0000	−2.43306
$512$	1.00000	0.0441942
$513$	−9.00000	−0.397360
$514$	22.0000	0.970378
$515$	−4.00000	−0.176261
$516$	−18.0000	−0.792406
$517$	0	0
$518$	10.0000	0.439375
$519$	42.0000	1.84360
$520$	1.00000	0.0438529
$521$	24.0000	1.05146	0.525730	−	0.850652i	$-0.323792\pi$
$521$	24.0000	1.05146	0.525730	+	0.850652i	$0.323792\pi$
$522$	−18.0000	−0.787839
$523$	−9.00000	−0.393543	−0.196771	−	0.980449i	$-0.563046\pi$
$523$	−9.00000	−0.393543	−0.196771	+	0.980449i	$0.563046\pi$
$524$	16.0000	0.698963
$525$	15.0000	0.654654
$526$	8.00000	0.348817
$527$	6.00000	0.261364
$528$	12.0000	0.522233
$529$	26.0000	1.13043
$530$	13.0000	0.564684
$531$	−54.0000	−2.34340
$532$	−5.00000	−0.216777
$533$	6.00000	0.259889
$534$	−6.00000	−0.259645
$535$	13.0000	0.562039
$536$	−3.00000	−0.129580
$537$	24.0000	1.03568
$538$	2.00000	0.0862261
$539$	−72.0000	−3.10126
$540$	9.00000	0.387298
$541$	16.0000	0.687894	0.343947	−	0.938989i	$-0.388236\pi$
$541$	16.0000	0.687894	0.343947	+	0.938989i	$0.388236\pi$
$542$	−27.0000	−1.15975
$543$	−78.0000	−3.34730
$544$	−3.00000	−0.128624
$545$	−19.0000	−0.813871
$546$	−15.0000	−0.641941
$547$	20.0000	0.855138	0.427569	−	0.903983i	$-0.359370\pi$
$547$	20.0000	0.855138	0.427569	+	0.903983i	$0.359370\pi$
$548$	9.00000	0.384461
$549$	−72.0000	−3.07289
$550$	−4.00000	−0.170561
$551$	−3.00000	−0.127804
$552$	−21.0000	−0.893819
$553$	10.0000	0.425243
$554$	−8.00000	−0.339887
$555$	−6.00000	−0.254686
$556$	16.0000	0.678551
$557$	12.0000	0.508456	0.254228	−	0.967144i	$-0.418179\pi$
$557$	12.0000	0.508456	0.254228	+	0.967144i	$0.418179\pi$
$558$	−12.0000	−0.508001
$559$	−6.00000	−0.253773
$560$	5.00000	0.211289
$561$	−36.0000	−1.51992
$562$	−18.0000	−0.759284
$563$	20.0000	0.842900	0.421450	−	0.906852i	$-0.361521\pi$
$563$	20.0000	0.842900	0.421450	+	0.906852i	$0.361521\pi$
$564$	0	0
$565$	0	0
$566$	−2.00000	−0.0840663
$567$	−45.0000	−1.88982
$568$	0	0
$569$	24.0000	1.00613	0.503066	−	0.864248i	$-0.332205\pi$
$569$	24.0000	1.00613	0.503066	+	0.864248i	$0.332205\pi$
$570$	3.00000	0.125656
$571$	6.00000	0.251092	0.125546	−	0.992088i	$-0.459932\pi$
$571$	6.00000	0.251092	0.125546	+	0.992088i	$0.459932\pi$
$572$	4.00000	0.167248
$573$	−27.0000	−1.12794
$574$	30.0000	1.25218
$575$	7.00000	0.291920
$576$	6.00000	0.250000
$577$	−7.00000	−0.291414	−0.145707	−	0.989328i	$-0.546546\pi$
$577$	−7.00000	−0.291414	−0.145707	+	0.989328i	$0.546546\pi$
$578$	−8.00000	−0.332756
$579$	−30.0000	−1.24676
$580$	3.00000	0.124568
$581$	50.0000	2.07435
$582$	6.00000	0.248708
$583$	52.0000	2.15362
$584$	11.0000	0.455183
$585$	6.00000	0.248069
$586$	−27.0000	−1.11536
$587$	18.0000	0.742940	0.371470	−	0.928445i	$-0.378854\pi$
$587$	18.0000	0.742940	0.371470	+	0.928445i	$0.378854\pi$
$588$	−54.0000	−2.22692
$589$	−2.00000	−0.0824086
$590$	9.00000	0.370524
$591$	66.0000	2.71488
$592$	−2.00000	−0.0821995
$593$	30.0000	1.23195	0.615976	−	0.787765i	$-0.288762\pi$
$593$	30.0000	1.23195	0.615976	+	0.787765i	$0.288762\pi$
$594$	36.0000	1.47710
$595$	−15.0000	−0.614940
$596$	−4.00000	−0.163846
$597$	45.0000	1.84173
$598$	−7.00000	−0.286251
$599$	−26.0000	−1.06233	−0.531166	−	0.847268i	$-0.678246\pi$
$599$	−26.0000	−1.06233	−0.531166	+	0.847268i	$0.678246\pi$
$600$	−3.00000	−0.122474
$601$	42.0000	1.71322	0.856608	−	0.515968i	$-0.172568\pi$
$601$	42.0000	1.71322	0.856608	+	0.515968i	$0.172568\pi$
$602$	−30.0000	−1.22271
$603$	−18.0000	−0.733017
$604$	−10.0000	−0.406894
$605$	−5.00000	−0.203279
$606$	24.0000	0.974933
$607$	−26.0000	−1.05531	−0.527654	−	0.849460i	$-0.676928\pi$
$607$	−26.0000	−1.05531	−0.527654	+	0.849460i	$0.676928\pi$
$608$	1.00000	0.0405554
$609$	−45.0000	−1.82349
$610$	12.0000	0.485866
$611$	0	0
$612$	−18.0000	−0.727607
$613$	−20.0000	−0.807792	−0.403896	−	0.914805i	$-0.632344\pi$
$613$	−20.0000	−0.807792	−0.403896	+	0.914805i	$0.632344\pi$
$614$	4.00000	0.161427
$615$	−18.0000	−0.725830
$616$	20.0000	0.805823
$617$	14.0000	0.563619	0.281809	−	0.959470i	$-0.409065\pi$
$617$	14.0000	0.563619	0.281809	+	0.959470i	$0.409065\pi$
$618$	−12.0000	−0.482711
$619$	−24.0000	−0.964641	−0.482321	−	0.875995i	$-0.660206\pi$
$619$	−24.0000	−0.964641	−0.482321	+	0.875995i	$0.660206\pi$
$620$	2.00000	0.0803219
$621$	−63.0000	−2.52810
$622$	25.0000	1.00241
$623$	−10.0000	−0.400642
$624$	3.00000	0.120096
$625$	1.00000	0.0400000
$626$	−1.00000	−0.0399680
$627$	12.0000	0.479234
$628$	6.00000	0.239426
$629$	6.00000	0.239236
$630$	30.0000	1.19523
$631$	8.00000	0.318475	0.159237	−	0.987240i	$-0.449096\pi$
$631$	8.00000	0.318475	0.159237	+	0.987240i	$0.449096\pi$
$632$	−2.00000	−0.0795557
$633$	15.0000	0.596196
$634$	9.00000	0.357436
$635$	6.00000	0.238103
$636$	39.0000	1.54645
$637$	−18.0000	−0.713186
$638$	12.0000	0.475085
$639$	0	0
$640$	−1.00000	−0.0395285
$641$	8.00000	0.315981	0.157991	−	0.987441i	$-0.449498\pi$
$641$	8.00000	0.315981	0.157991	+	0.987441i	$0.449498\pi$
$642$	39.0000	1.53921
$643$	26.0000	1.02534	0.512670	−	0.858586i	$-0.328656\pi$
$643$	26.0000	1.02534	0.512670	+	0.858586i	$0.328656\pi$
$644$	−35.0000	−1.37919
$645$	18.0000	0.708749
$646$	−3.00000	−0.118033
$647$	−21.0000	−0.825595	−0.412798	−	0.910823i	$-0.635448\pi$
$647$	−21.0000	−0.825595	−0.412798	+	0.910823i	$0.635448\pi$
$648$	9.00000	0.353553
$649$	36.0000	1.41312
$650$	−1.00000	−0.0392232
$651$	−30.0000	−1.17579
$652$	22.0000	0.861586
$653$	−16.0000	−0.626128	−0.313064	−	0.949732i	$-0.601356\pi$
$653$	−16.0000	−0.626128	−0.313064	+	0.949732i	$0.601356\pi$
$654$	−57.0000	−2.22888
$655$	−16.0000	−0.625172
$656$	−6.00000	−0.234261
$657$	66.0000	2.57491
$658$	0	0
$659$	33.0000	1.28550	0.642749	−	0.766077i	$-0.277794\pi$
$659$	33.0000	1.28550	0.642749	+	0.766077i	$0.277794\pi$
$660$	−12.0000	−0.467099
$661$	15.0000	0.583432	0.291716	−	0.956505i	$-0.405774\pi$
$661$	15.0000	0.583432	0.291716	+	0.956505i	$0.405774\pi$
$662$	−7.00000	−0.272063
$663$	−9.00000	−0.349531
$664$	−10.0000	−0.388075
$665$	5.00000	0.193892
$666$	−12.0000	−0.464991
$667$	−21.0000	−0.813123
$668$	−2.00000	−0.0773823
$669$	6.00000	0.231973
$670$	3.00000	0.115900
$671$	48.0000	1.85302
$672$	15.0000	0.578638
$673$	−44.0000	−1.69608	−0.848038	−	0.529936i	$-0.822216\pi$
$673$	−44.0000	−1.69608	−0.848038	+	0.529936i	$0.822216\pi$
$674$	6.00000	0.231111
$675$	−9.00000	−0.346410
$676$	−12.0000	−0.461538
$677$	−39.0000	−1.49889	−0.749446	−	0.662066i	$-0.769680\pi$
$677$	−39.0000	−1.49889	−0.749446	+	0.662066i	$0.769680\pi$
$678$	0	0
$679$	10.0000	0.383765
$680$	3.00000	0.115045
$681$	−15.0000	−0.574801
$682$	8.00000	0.306336
$683$	−44.0000	−1.68361	−0.841807	−	0.539779i	$-0.818508\pi$
$683$	−44.0000	−1.68361	−0.841807	+	0.539779i	$0.818508\pi$
$684$	6.00000	0.229416
$685$	−9.00000	−0.343872
$686$	−55.0000	−2.09991
$687$	18.0000	0.686743
$688$	6.00000	0.228748
$689$	13.0000	0.495261
$690$	21.0000	0.799456
$691$	−42.0000	−1.59776	−0.798878	−	0.601494i	$-0.794573\pi$
$691$	−42.0000	−1.59776	−0.798878	+	0.601494i	$0.794573\pi$
$692$	−14.0000	−0.532200
$693$	120.000	4.55842
$694$	−6.00000	−0.227757
$695$	−16.0000	−0.606915
$696$	9.00000	0.341144
$697$	18.0000	0.681799
$698$	14.0000	0.529908
$699$	−30.0000	−1.13470
$700$	−5.00000	−0.188982
$701$	24.0000	0.906467	0.453234	−	0.891392i	$-0.350270\pi$
$701$	24.0000	0.906467	0.453234	+	0.891392i	$0.350270\pi$
$702$	9.00000	0.339683
$703$	−2.00000	−0.0754314
$704$	−4.00000	−0.150756
$705$	0	0
$706$	7.00000	0.263448
$707$	40.0000	1.50435
$708$	27.0000	1.01472
$709$	2.00000	0.0751116	0.0375558	−	0.999295i	$-0.488043\pi$
$709$	2.00000	0.0751116	0.0375558	+	0.999295i	$0.488043\pi$
$710$	0	0
$711$	−12.0000	−0.450035
$712$	2.00000	0.0749532
$713$	−14.0000	−0.524304
$714$	−45.0000	−1.68408
$715$	−4.00000	−0.149592
$716$	−8.00000	−0.298974
$717$	33.0000	1.23241
$718$	−5.00000	−0.186598
$719$	−27.0000	−1.00693	−0.503465	−	0.864016i	$-0.667942\pi$
$719$	−27.0000	−1.00693	−0.503465	+	0.864016i	$0.667942\pi$
$720$	−6.00000	−0.223607
$721$	−20.0000	−0.744839
$722$	1.00000	0.0372161
$723$	36.0000	1.33885
$724$	26.0000	0.966282
$725$	−3.00000	−0.111417
$726$	−15.0000	−0.556702
$727$	23.0000	0.853023	0.426511	−	0.904482i	$-0.359742\pi$
$727$	23.0000	0.853023	0.426511	+	0.904482i	$0.359742\pi$
$728$	5.00000	0.185312
$729$	−27.0000	−1.00000
$730$	−11.0000	−0.407128
$731$	−18.0000	−0.665754
$732$	36.0000	1.33060
$733$	36.0000	1.32969	0.664845	−	0.746981i	$-0.268498\pi$
$733$	36.0000	1.32969	0.664845	+	0.746981i	$0.268498\pi$
$734$	8.00000	0.295285
$735$	54.0000	1.99182
$736$	7.00000	0.258023
$737$	12.0000	0.442026
$738$	−36.0000	−1.32518
$739$	−10.0000	−0.367856	−0.183928	−	0.982940i	$-0.558881\pi$
$739$	−10.0000	−0.367856	−0.183928	+	0.982940i	$0.558881\pi$
$740$	2.00000	0.0735215
$741$	3.00000	0.110208
$742$	65.0000	2.38623
$743$	−18.0000	−0.660356	−0.330178	−	0.943919i	$-0.607109\pi$
$743$	−18.0000	−0.660356	−0.330178	+	0.943919i	$0.607109\pi$
$744$	6.00000	0.219971
$745$	4.00000	0.146549
$746$	−23.0000	−0.842090
$747$	−60.0000	−2.19529
$748$	12.0000	0.438763
$749$	65.0000	2.37505
$750$	3.00000	0.109545
$751$	−26.0000	−0.948753	−0.474377	−	0.880322i	$-0.657327\pi$
$751$	−26.0000	−0.948753	−0.474377	+	0.880322i	$0.657327\pi$
$752$	0	0
$753$	36.0000	1.31191
$754$	3.00000	0.109254
$755$	10.0000	0.363937
$756$	45.0000	1.63663
$757$	−6.00000	−0.218074	−0.109037	−	0.994038i	$-0.534777\pi$
$757$	−6.00000	−0.218074	−0.109037	+	0.994038i	$0.534777\pi$
$758$	−33.0000	−1.19861
$759$	84.0000	3.04901
$760$	−1.00000	−0.0362738
$761$	11.0000	0.398750	0.199375	−	0.979923i	$-0.436109\pi$
$761$	11.0000	0.398750	0.199375	+	0.979923i	$0.436109\pi$
$762$	18.0000	0.652071
$763$	−95.0000	−3.43923
$764$	9.00000	0.325609
$765$	18.0000	0.650791
$766$	−4.00000	−0.144526
$767$	9.00000	0.324971
$768$	−3.00000	−0.108253
$769$	−47.0000	−1.69486	−0.847432	−	0.530904i	$-0.821852\pi$
$769$	−47.0000	−1.69486	−0.847432	+	0.530904i	$0.821852\pi$
$770$	−20.0000	−0.720750
$771$	−66.0000	−2.37693
$772$	10.0000	0.359908
$773$	−51.0000	−1.83434	−0.917171	−	0.398493i	$-0.869533\pi$
$773$	−51.0000	−1.83434	−0.917171	+	0.398493i	$0.869533\pi$
$774$	36.0000	1.29399
$775$	−2.00000	−0.0718421
$776$	−2.00000	−0.0717958
$777$	−30.0000	−1.07624
$778$	−4.00000	−0.143407
$779$	−6.00000	−0.214972
$780$	−3.00000	−0.107417
$781$	0	0
$782$	−21.0000	−0.750958
$783$	27.0000	0.964901
$784$	18.0000	0.642857
$785$	−6.00000	−0.214149
$786$	−48.0000	−1.71210
$787$	−39.0000	−1.39020	−0.695100	−	0.718913i	$-0.744640\pi$
$787$	−39.0000	−1.39020	−0.695100	+	0.718913i	$0.744640\pi$
$788$	−22.0000	−0.783718
$789$	−24.0000	−0.854423
$790$	2.00000	0.0711568
$791$	0	0
$792$	−24.0000	−0.852803
$793$	12.0000	0.426132
$794$	−16.0000	−0.567819
$795$	−39.0000	−1.38319
$796$	−15.0000	−0.531661
$797$	31.0000	1.09808	0.549038	−	0.835797i	$-0.314994\pi$
$797$	31.0000	1.09808	0.549038	+	0.835797i	$0.314994\pi$
$798$	15.0000	0.530994
$799$	0	0
$800$	1.00000	0.0353553
$801$	12.0000	0.423999
$802$	−6.00000	−0.211867
$803$	−44.0000	−1.55273
$804$	9.00000	0.317406
$805$	35.0000	1.23359
$806$	2.00000	0.0704470
$807$	−6.00000	−0.211210
$808$	−8.00000	−0.281439
$809$	25.0000	0.878953	0.439477	−	0.898254i	$-0.355164\pi$
$809$	25.0000	0.878953	0.439477	+	0.898254i	$0.355164\pi$
$810$	−9.00000	−0.316228
$811$	37.0000	1.29925	0.649623	−	0.760257i	$-0.274927\pi$
$811$	37.0000	1.29925	0.649623	+	0.760257i	$0.274927\pi$
$812$	15.0000	0.526397
$813$	81.0000	2.84079
$814$	8.00000	0.280400
$815$	−22.0000	−0.770626
$816$	9.00000	0.315063
$817$	6.00000	0.209913
$818$	22.0000	0.769212
$819$	30.0000	1.04828
$820$	6.00000	0.209529
$821$	−52.0000	−1.81481	−0.907406	−	0.420255i	$-0.861941\pi$
$821$	−52.0000	−1.81481	−0.907406	+	0.420255i	$0.861941\pi$
$822$	−27.0000	−0.941733
$823$	−43.0000	−1.49889	−0.749443	−	0.662069i	$-0.769679\pi$
$823$	−43.0000	−1.49889	−0.749443	+	0.662069i	$0.769679\pi$
$824$	4.00000	0.139347
$825$	12.0000	0.417786
$826$	45.0000	1.56575
$827$	−3.00000	−0.104320	−0.0521601	−	0.998639i	$-0.516611\pi$
$827$	−3.00000	−0.104320	−0.0521601	+	0.998639i	$0.516611\pi$
$828$	42.0000	1.45960
$829$	35.0000	1.21560	0.607800	−	0.794090i	$-0.292052\pi$
$829$	35.0000	1.21560	0.607800	+	0.794090i	$0.292052\pi$
$830$	10.0000	0.347105
$831$	24.0000	0.832551
$832$	−1.00000	−0.0346688
$833$	−54.0000	−1.87099
$834$	−48.0000	−1.66210
$835$	2.00000	0.0692129
$836$	−4.00000	−0.138343
$837$	18.0000	0.622171
$838$	14.0000	0.483622
$839$	−4.00000	−0.138095	−0.0690477	−	0.997613i	$-0.521996\pi$
$839$	−4.00000	−0.138095	−0.0690477	+	0.997613i	$0.521996\pi$
$840$	−15.0000	−0.517549
$841$	−20.0000	−0.689655
$842$	1.00000	0.0344623
$843$	54.0000	1.85986
$844$	−5.00000	−0.172107
$845$	12.0000	0.412813
$846$	0	0
$847$	−25.0000	−0.859010
$848$	−13.0000	−0.446422
$849$	6.00000	0.205919
$850$	−3.00000	−0.102899
$851$	−14.0000	−0.479914
$852$	0	0
$853$	42.0000	1.43805	0.719026	−	0.694983i	$-0.244588\pi$
$853$	42.0000	1.43805	0.719026	+	0.694983i	$0.244588\pi$
$854$	60.0000	2.05316
$855$	−6.00000	−0.205196
$856$	−13.0000	−0.444331
$857$	−40.0000	−1.36637	−0.683187	−	0.730243i	$-0.739407\pi$
$857$	−40.0000	−1.36637	−0.683187	+	0.730243i	$0.739407\pi$
$858$	−12.0000	−0.409673
$859$	−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
$861$	−90.0000	−3.06719
$862$	−36.0000	−1.22616
$863$	56.0000	1.90626	0.953131	−	0.302558i	$-0.0978405\pi$
$863$	56.0000	1.90626	0.953131	+	0.302558i	$0.0978405\pi$
$864$	−9.00000	−0.306186
$865$	14.0000	0.476014
$866$	−16.0000	−0.543702
$867$	24.0000	0.815083
$868$	10.0000	0.339422
$869$	8.00000	0.271381
$870$	−9.00000	−0.305129
$871$	3.00000	0.101651
$872$	19.0000	0.643421
$873$	−12.0000	−0.406138
$874$	7.00000	0.236779
$875$	5.00000	0.169031
$876$	−33.0000	−1.11497
$877$	33.0000	1.11433	0.557165	−	0.830402i	$-0.311889\pi$
$877$	33.0000	1.11433	0.557165	+	0.830402i	$0.311889\pi$
$878$	26.0000	0.877457
$879$	81.0000	2.73206
$880$	4.00000	0.134840
$881$	10.0000	0.336909	0.168454	−	0.985709i	$-0.446122\pi$
$881$	10.0000	0.336909	0.168454	+	0.985709i	$0.446122\pi$
$882$	108.000	3.63655
$883$	30.0000	1.00958	0.504790	−	0.863242i	$-0.331570\pi$
$883$	30.0000	1.00958	0.504790	+	0.863242i	$0.331570\pi$
$884$	3.00000	0.100901
$885$	−27.0000	−0.907595
$886$	36.0000	1.20944
$887$	−28.0000	−0.940148	−0.470074	−	0.882627i	$-0.655773\pi$
$887$	−28.0000	−0.940148	−0.470074	+	0.882627i	$0.655773\pi$
$888$	6.00000	0.201347
$889$	30.0000	1.00617
$890$	−2.00000	−0.0670402
$891$	−36.0000	−1.20605
$892$	−2.00000	−0.0669650
$893$	0	0
$894$	12.0000	0.401340
$895$	8.00000	0.267411
$896$	−5.00000	−0.167038
$897$	21.0000	0.701170
$898$	−22.0000	−0.734150
$899$	6.00000	0.200111
$900$	6.00000	0.200000
$901$	39.0000	1.29928
$902$	24.0000	0.799113
$903$	90.0000	2.99501
$904$	0	0
$905$	−26.0000	−0.864269
$906$	30.0000	0.996683
$907$	−1.00000	−0.0332045	−0.0166022	−	0.999862i	$-0.505285\pi$
$907$	−1.00000	−0.0332045	−0.0166022	+	0.999862i	$0.505285\pi$
$908$	5.00000	0.165931
$909$	−48.0000	−1.59206
$910$	−5.00000	−0.165748
$911$	−12.0000	−0.397578	−0.198789	−	0.980042i	$-0.563701\pi$
$911$	−12.0000	−0.397578	−0.198789	+	0.980042i	$0.563701\pi$
$912$	−3.00000	−0.0993399
$913$	40.0000	1.32381
$914$	−29.0000	−0.959235
$915$	−36.0000	−1.19012
$916$	−6.00000	−0.198246
$917$	−80.0000	−2.64183
$918$	27.0000	0.891133
$919$	−5.00000	−0.164935	−0.0824674	−	0.996594i	$-0.526280\pi$
$919$	−5.00000	−0.164935	−0.0824674	+	0.996594i	$0.526280\pi$
$920$	−7.00000	−0.230783
$921$	−12.0000	−0.395413
$922$	18.0000	0.592798
$923$	0	0
$924$	−60.0000	−1.97386
$925$	−2.00000	−0.0657596
$926$	−8.00000	−0.262896
$927$	24.0000	0.788263
$928$	−3.00000	−0.0984798
$929$	−3.00000	−0.0984268	−0.0492134	−	0.998788i	$-0.515671\pi$
$929$	−3.00000	−0.0984268	−0.0492134	+	0.998788i	$0.515671\pi$
$930$	−6.00000	−0.196748
$931$	18.0000	0.589926
$932$	10.0000	0.327561
$933$	−75.0000	−2.45539
$934$	−8.00000	−0.261768
$935$	−12.0000	−0.392442
$936$	−6.00000	−0.196116
$937$	47.0000	1.53542	0.767712	−	0.640796i	$-0.221395\pi$
$937$	47.0000	1.53542	0.767712	+	0.640796i	$0.221395\pi$
$938$	15.0000	0.489767
$939$	3.00000	0.0979013
$940$	0	0
$941$	−51.0000	−1.66255	−0.831276	−	0.555860i	$-0.812389\pi$
$941$	−51.0000	−1.66255	−0.831276	+	0.555860i	$0.812389\pi$
$942$	−18.0000	−0.586472
$943$	−42.0000	−1.36771
$944$	−9.00000	−0.292925
$945$	−45.0000	−1.46385
$946$	−24.0000	−0.780307
$947$	−24.0000	−0.779895	−0.389948	−	0.920837i	$-0.627507\pi$
$947$	−24.0000	−0.779895	−0.389948	+	0.920837i	$0.627507\pi$
$948$	6.00000	0.194871
$949$	−11.0000	−0.357075
$950$	1.00000	0.0324443
$951$	−27.0000	−0.875535
$952$	15.0000	0.486153
$953$	−24.0000	−0.777436	−0.388718	−	0.921357i	$-0.627082\pi$
$953$	−24.0000	−0.777436	−0.388718	+	0.921357i	$0.627082\pi$
$954$	−78.0000	−2.52534
$955$	−9.00000	−0.291233
$956$	−11.0000	−0.355765
$957$	−36.0000	−1.16371
$958$	0	0
$959$	−45.0000	−1.45313
$960$	3.00000	0.0968246
$961$	−27.0000	−0.870968
$962$	2.00000	0.0644826
$963$	−78.0000	−2.51351
$964$	−12.0000	−0.386494
$965$	−10.0000	−0.321911
$966$	105.000	3.37832
$967$	−44.0000	−1.41494	−0.707472	−	0.706741i	$-0.750165\pi$
$967$	−44.0000	−1.41494	−0.707472	+	0.706741i	$0.750165\pi$
$968$	5.00000	0.160706
$969$	9.00000	0.289122
$970$	2.00000	0.0642161
$971$	28.0000	0.898563	0.449281	−	0.893390i	$-0.351680\pi$
$971$	28.0000	0.898563	0.449281	+	0.893390i	$0.351680\pi$
$972$	0	0
$973$	−80.0000	−2.56468
$974$	−38.0000	−1.21760
$975$	3.00000	0.0960769
$976$	−12.0000	−0.384111
$977$	−62.0000	−1.98356	−0.991778	−	0.127971i	$-0.959153\pi$
$977$	−62.0000	−1.98356	−0.991778	+	0.127971i	$0.959153\pi$
$978$	−66.0000	−2.11045
$979$	−8.00000	−0.255681
$980$	−18.0000	−0.574989
$981$	114.000	3.63974
$982$	18.0000	0.574403
$983$	−42.0000	−1.33959	−0.669796	−	0.742545i	$-0.733618\pi$
$983$	−42.0000	−1.33959	−0.669796	+	0.742545i	$0.733618\pi$
$984$	18.0000	0.573819
$985$	22.0000	0.700978
$986$	9.00000	0.286618
$987$	0	0
$988$	−1.00000	−0.0318142
$989$	42.0000	1.33552
$990$	24.0000	0.762770
$991$	30.0000	0.952981	0.476491	−	0.879180i	$-0.341909\pi$
$991$	30.0000	0.952981	0.476491	+	0.879180i	$0.341909\pi$
$992$	−2.00000	−0.0635001
$993$	21.0000	0.666415
$994$	0	0
$995$	15.0000	0.475532
$996$	30.0000	0.950586
$997$	−50.0000	−1.58352	−0.791758	−	0.610835i	$-0.790834\pi$
$997$	−50.0000	−1.58352	−0.791758	+	0.610835i	$0.790834\pi$
$998$	42.0000	1.32949
$999$	18.0000	0.569495

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	190.2.a.b.1.1	✓	1
3.2	odd	2		1710.2.a.g.1.1		1
4.3	odd	2		1520.2.a.j.1.1		1
5.2	odd	4		950.2.b.a.799.2		2
5.3	odd	4		950.2.b.a.799.1		2
5.4	even	2		950.2.a.c.1.1		1
7.6	odd	2		9310.2.a.u.1.1		1
8.3	odd	2		6080.2.a.b.1.1		1
8.5	even	2		6080.2.a.x.1.1		1
15.14	odd	2		8550.2.a.bm.1.1		1
19.18	odd	2		3610.2.a.e.1.1		1
20.19	odd	2		7600.2.a.a.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.2.a.b.1.1	✓	1	1.1	even	1	trivial
950.2.a.c.1.1		1	5.4	even	2
950.2.b.a.799.1		2	5.3	odd	4
950.2.b.a.799.2		2	5.2	odd	4
1520.2.a.j.1.1		1	4.3	odd	2
1710.2.a.g.1.1		1	3.2	odd	2
3610.2.a.e.1.1		1	19.18	odd	2
6080.2.a.b.1.1		1	8.3	odd	2
6080.2.a.x.1.1		1	8.5	even	2
7600.2.a.a.1.1		1	20.19	odd	2
8550.2.a.bm.1.1		1	15.14	odd	2
9310.2.a.u.1.1		1	7.6	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:	\( N \)	\(=\)	\( 190 = 2 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	190.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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