LMFDB - Embedded newform 190.2.a.a.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)

$f(q)$

$=$

$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} -2.00000 q^{9} +O(q^{10})$

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

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−1.00000	−0.577350	−0.288675	−	0.957427i	$-0.593215\pi$
$3$	−1.00000	−0.577350	−0.288675	+	0.957427i	$0.593215\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	1.00000	0.408248
$7$	−1.00000	−0.377964	−0.188982	−	0.981981i	$-0.560519\pi$
$7$	−1.00000	−0.377964	−0.188982	+	0.981981i	$0.560519\pi$
$8$	−1.00000	−0.353553
$9$	−2.00000	−0.666667
$10$	1.00000	0.316228
$11$	0	0		−	1.00000i	$-0.5\pi$
$11$	0	0			1.00000i	$0.5\pi$
$12$	−1.00000	−0.288675
$13$	−3.00000	−0.832050	−0.416025	−	0.909353i	$-0.636577\pi$
$13$	−3.00000	−0.832050	−0.416025	+	0.909353i	$0.636577\pi$
$14$	1.00000	0.267261
$15$	1.00000	0.258199
$16$	1.00000	0.250000
$17$	−7.00000	−1.69775	−0.848875	−	0.528594i	$-0.822719\pi$
$17$	−7.00000	−1.69775	−0.848875	+	0.528594i	$0.822719\pi$
$18$	2.00000	0.471405
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	−1.00000	−0.223607
$21$	1.00000	0.218218
$22$	0	0
$23$	−5.00000	−1.04257	−0.521286	−	0.853382i	$-0.674548\pi$
$23$	−5.00000	−1.04257	−0.521286	+	0.853382i	$0.674548\pi$
$24$	1.00000	0.204124
$25$	1.00000	0.200000
$26$	3.00000	0.588348
$27$	5.00000	0.962250
$28$	−1.00000	−0.188982
$29$	−5.00000	−0.928477	−0.464238	−	0.885710i	$-0.653672\pi$
$29$	−5.00000	−0.928477	−0.464238	+	0.885710i	$0.653672\pi$
$30$	−1.00000	−0.182574
$31$	10.0000	1.79605	0.898027	−	0.439941i	$-0.145001\pi$
$31$	10.0000	1.79605	0.898027	+	0.439941i	$0.145001\pi$
$32$	−1.00000	−0.176777
$33$	0	0
$34$	7.00000	1.20049
$35$	1.00000	0.169031
$36$	−2.00000	−0.333333
$37$	2.00000	0.328798	0.164399	−	0.986394i	$-0.447432\pi$
$37$	2.00000	0.328798	0.164399	+	0.986394i	$0.447432\pi$
$38$	1.00000	0.162221
$39$	3.00000	0.480384
$40$	1.00000	0.158114
$41$	2.00000	0.312348	0.156174	−	0.987730i	$-0.450084\pi$
$41$	2.00000	0.312348	0.156174	+	0.987730i	$0.450084\pi$
$42$	−1.00000	−0.154303
$43$	6.00000	0.914991	0.457496	−	0.889212i	$-0.348747\pi$
$43$	6.00000	0.914991	0.457496	+	0.889212i	$0.348747\pi$
$44$	0	0
$45$	2.00000	0.298142
$46$	5.00000	0.737210
$47$	0	0		−	1.00000i	$-0.5\pi$
$47$	0	0			1.00000i	$0.5\pi$
$48$	−1.00000	−0.144338
$49$	−6.00000	−0.857143
$50$	−1.00000	−0.141421
$51$	7.00000	0.980196
$52$	−3.00000	−0.416025
$53$	9.00000	1.23625	0.618123	−	0.786082i	$-0.287894\pi$
$53$	9.00000	1.23625	0.618123	+	0.786082i	$0.287894\pi$
$54$	−5.00000	−0.680414
$55$	0	0
$56$	1.00000	0.133631
$57$	1.00000	0.132453
$58$	5.00000	0.656532
$59$	−7.00000	−0.911322	−0.455661	−	0.890153i	$-0.650597\pi$
$59$	−7.00000	−0.911322	−0.455661	+	0.890153i	$0.650597\pi$
$60$	1.00000	0.129099
$61$	−4.00000	−0.512148	−0.256074	−	0.966657i	$-0.582429\pi$
$61$	−4.00000	−0.512148	−0.256074	+	0.966657i	$0.582429\pi$
$62$	−10.0000	−1.27000
$63$	2.00000	0.251976
$64$	1.00000	0.125000
$65$	3.00000	0.372104
$66$	0	0
$67$	7.00000	0.855186	0.427593	−	0.903971i	$-0.359362\pi$
$67$	7.00000	0.855186	0.427593	+	0.903971i	$0.359362\pi$
$68$	−7.00000	−0.848875
$69$	5.00000	0.601929
$70$	−1.00000	−0.119523
$71$	0	0		−	1.00000i	$-0.5\pi$
$71$	0	0			1.00000i	$0.5\pi$
$72$	2.00000	0.235702
$73$	−9.00000	−1.05337	−0.526685	−	0.850060i	$-0.676565\pi$
$73$	−9.00000	−1.05337	−0.526685	+	0.850060i	$0.676565\pi$
$74$	−2.00000	−0.232495
$75$	−1.00000	−0.115470
$76$	−1.00000	−0.114708
$77$	0	0
$78$	−3.00000	−0.339683
$79$	−10.0000	−1.12509	−0.562544	−	0.826767i	$-0.690177\pi$
$79$	−10.0000	−1.12509	−0.562544	+	0.826767i	$0.690177\pi$
$80$	−1.00000	−0.111803
$81$	1.00000	0.111111
$82$	−2.00000	−0.220863
$83$	−2.00000	−0.219529	−0.109764	−	0.993958i	$-0.535010\pi$
$83$	−2.00000	−0.219529	−0.109764	+	0.993958i	$0.535010\pi$
$84$	1.00000	0.109109
$85$	7.00000	0.759257
$86$	−6.00000	−0.646997
$87$	5.00000	0.536056
$88$	0	0
$89$	−10.0000	−1.06000	−0.529999	−	0.847998i	$-0.677808\pi$
$89$	−10.0000	−1.06000	−0.529999	+	0.847998i	$0.677808\pi$
$90$	−2.00000	−0.210819
$91$	3.00000	0.314485
$92$	−5.00000	−0.521286
$93$	−10.0000	−1.03695
$94$	0	0
$95$	1.00000	0.102598
$96$	1.00000	0.102062
$97$	−18.0000	−1.82762	−0.913812	−	0.406138i	$-0.866875\pi$
$97$	−18.0000	−1.82762	−0.913812	+	0.406138i	$0.866875\pi$
$98$	6.00000	0.606092
$99$	0	0
$100$	1.00000	0.100000
$101$	−4.00000	−0.398015	−0.199007	−	0.979998i	$-0.563772\pi$
$101$	−4.00000	−0.398015	−0.199007	+	0.979998i	$0.563772\pi$
$102$	−7.00000	−0.693103
$103$	0	0		−	1.00000i	$-0.5\pi$
$103$	0	0			1.00000i	$0.5\pi$
$104$	3.00000	0.294174
$105$	−1.00000	−0.0975900
$106$	−9.00000	−0.874157
$107$	9.00000	0.870063	0.435031	−	0.900415i	$-0.356737\pi$
$107$	9.00000	0.870063	0.435031	+	0.900415i	$0.356737\pi$
$108$	5.00000	0.481125
$109$	13.0000	1.24517	0.622587	−	0.782551i	$-0.286082\pi$
$109$	13.0000	1.24517	0.622587	+	0.782551i	$0.286082\pi$
$110$	0	0
$111$	−2.00000	−0.189832
$112$	−1.00000	−0.0944911
$113$	8.00000	0.752577	0.376288	−	0.926503i	$-0.377200\pi$
$113$	8.00000	0.752577	0.376288	+	0.926503i	$0.377200\pi$
$114$	−1.00000	−0.0936586
$115$	5.00000	0.466252
$116$	−5.00000	−0.464238
$117$	6.00000	0.554700
$118$	7.00000	0.644402
$119$	7.00000	0.641689
$120$	−1.00000	−0.0912871
$121$	−11.0000	−1.00000
$122$	4.00000	0.362143
$123$	−2.00000	−0.180334
$124$	10.0000	0.898027
$125$	−1.00000	−0.0894427
$126$	−2.00000	−0.178174
$127$	−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
$129$	−6.00000	−0.528271
$130$	−3.00000	−0.263117
$131$	−20.0000	−1.74741	−0.873704	−	0.486458i	$-0.838289\pi$
$131$	−20.0000	−1.74741	−0.873704	+	0.486458i	$0.838289\pi$
$132$	0	0
$133$	1.00000	0.0867110
$134$	−7.00000	−0.604708
$135$	−5.00000	−0.430331
$136$	7.00000	0.600245
$137$	−3.00000	−0.256307	−0.128154	−	0.991754i	$-0.540905\pi$
$137$	−3.00000	−0.256307	−0.128154	+	0.991754i	$0.540905\pi$
$138$	−5.00000	−0.425628
$139$	12.0000	1.01783	0.508913	−	0.860818i	$-0.330047\pi$
$139$	12.0000	1.01783	0.508913	+	0.860818i	$0.330047\pi$
$140$	1.00000	0.0845154
$141$	0	0
$142$	0	0
$143$	0	0
$144$	−2.00000	−0.166667
$145$	5.00000	0.415227
$146$	9.00000	0.744845
$147$	6.00000	0.494872
$148$	2.00000	0.164399
$149$	4.00000	0.327693	0.163846	−	0.986486i	$-0.447610\pi$
$149$	4.00000	0.327693	0.163846	+	0.986486i	$0.447610\pi$
$150$	1.00000	0.0816497
$151$	−6.00000	−0.488273	−0.244137	−	0.969741i	$-0.578505\pi$
$151$	−6.00000	−0.488273	−0.244137	+	0.969741i	$0.578505\pi$
$152$	1.00000	0.0811107
$153$	14.0000	1.13183
$154$	0	0
$155$	−10.0000	−0.803219
$156$	3.00000	0.240192
$157$	18.0000	1.43656	0.718278	−	0.695756i	$-0.244931\pi$
$157$	18.0000	1.43656	0.718278	+	0.695756i	$0.244931\pi$
$158$	10.0000	0.795557
$159$	−9.00000	−0.713746
$160$	1.00000	0.0790569
$161$	5.00000	0.394055
$162$	−1.00000	−0.0785674
$163$	−18.0000	−1.40987	−0.704934	−	0.709273i	$-0.749024\pi$
$163$	−18.0000	−1.40987	−0.704934	+	0.709273i	$0.749024\pi$
$164$	2.00000	0.156174
$165$	0	0
$166$	2.00000	0.155230
$167$	14.0000	1.08335	0.541676	−	0.840587i	$-0.317790\pi$
$167$	14.0000	1.08335	0.541676	+	0.840587i	$0.317790\pi$
$168$	−1.00000	−0.0771517
$169$	−4.00000	−0.307692
$170$	−7.00000	−0.536875
$171$	2.00000	0.152944
$172$	6.00000	0.457496
$173$	6.00000	0.456172	0.228086	−	0.973641i	$-0.426753\pi$
$173$	6.00000	0.456172	0.228086	+	0.973641i	$0.426753\pi$
$174$	−5.00000	−0.379049
$175$	−1.00000	−0.0755929
$176$	0	0
$177$	7.00000	0.526152
$178$	10.0000	0.749532
$179$	24.0000	1.79384	0.896922	−	0.442189i	$-0.145798\pi$
$179$	24.0000	1.79384	0.896922	+	0.442189i	$0.145798\pi$
$180$	2.00000	0.149071
$181$	−10.0000	−0.743294	−0.371647	−	0.928374i	$-0.621207\pi$
$181$	−10.0000	−0.743294	−0.371647	+	0.928374i	$0.621207\pi$
$182$	−3.00000	−0.222375
$183$	4.00000	0.295689
$184$	5.00000	0.368605
$185$	−2.00000	−0.147043
$186$	10.0000	0.733236
$187$	0	0
$188$	0	0
$189$	−5.00000	−0.363696
$190$	−1.00000	−0.0725476
$191$	−7.00000	−0.506502	−0.253251	−	0.967401i	$-0.581500\pi$
$191$	−7.00000	−0.506502	−0.253251	+	0.967401i	$0.581500\pi$
$192$	−1.00000	−0.0721688
$193$	−2.00000	−0.143963	−0.0719816	−	0.997406i	$-0.522932\pi$
$193$	−2.00000	−0.143963	−0.0719816	+	0.997406i	$0.522932\pi$
$194$	18.0000	1.29232
$195$	−3.00000	−0.214834
$196$	−6.00000	−0.428571
$197$	−10.0000	−0.712470	−0.356235	−	0.934396i	$-0.615940\pi$
$197$	−10.0000	−0.712470	−0.356235	+	0.934396i	$0.615940\pi$
$198$	0	0
$199$	17.0000	1.20510	0.602549	−	0.798082i	$-0.294152\pi$
$199$	17.0000	1.20510	0.602549	+	0.798082i	$0.294152\pi$
$200$	−1.00000	−0.0707107
$201$	−7.00000	−0.493742
$202$	4.00000	0.281439
$203$	5.00000	0.350931
$204$	7.00000	0.490098
$205$	−2.00000	−0.139686
$206$	0	0
$207$	10.0000	0.695048
$208$	−3.00000	−0.208013
$209$	0	0
$210$	1.00000	0.0690066
$211$	5.00000	0.344214	0.172107	−	0.985078i	$-0.444942\pi$
$211$	5.00000	0.344214	0.172107	+	0.985078i	$0.444942\pi$
$212$	9.00000	0.618123
$213$	0	0
$214$	−9.00000	−0.615227
$215$	−6.00000	−0.409197
$216$	−5.00000	−0.340207
$217$	−10.0000	−0.678844
$218$	−13.0000	−0.880471
$219$	9.00000	0.608164
$220$	0	0
$221$	21.0000	1.41261
$222$	2.00000	0.134231
$223$	−22.0000	−1.47323	−0.736614	−	0.676313i	$-0.763577\pi$
$223$	−22.0000	−1.47323	−0.736614	+	0.676313i	$0.763577\pi$
$224$	1.00000	0.0668153
$225$	−2.00000	−0.133333
$226$	−8.00000	−0.532152
$227$	−25.0000	−1.65931	−0.829654	−	0.558278i	$-0.811462\pi$
$227$	−25.0000	−1.65931	−0.829654	+	0.558278i	$0.811462\pi$
$228$	1.00000	0.0662266
$229$	−18.0000	−1.18947	−0.594737	−	0.803921i	$-0.702744\pi$
$229$	−18.0000	−1.18947	−0.594737	+	0.803921i	$0.702744\pi$
$230$	−5.00000	−0.329690
$231$	0	0
$232$	5.00000	0.328266
$233$	26.0000	1.70332	0.851658	−	0.524097i	$-0.175597\pi$
$233$	26.0000	1.70332	0.851658	+	0.524097i	$0.175597\pi$
$234$	−6.00000	−0.392232
$235$	0	0
$236$	−7.00000	−0.455661
$237$	10.0000	0.649570
$238$	−7.00000	−0.453743
$239$	−27.0000	−1.74648	−0.873242	−	0.487286i	$-0.837987\pi$
$239$	−27.0000	−1.74648	−0.873242	+	0.487286i	$0.837987\pi$
$240$	1.00000	0.0645497
$241$	−28.0000	−1.80364	−0.901819	−	0.432113i	$-0.857768\pi$
$241$	−28.0000	−1.80364	−0.901819	+	0.432113i	$0.857768\pi$
$242$	11.0000	0.707107
$243$	−16.0000	−1.02640
$244$	−4.00000	−0.256074
$245$	6.00000	0.383326
$246$	2.00000	0.127515
$247$	3.00000	0.190885
$248$	−10.0000	−0.635001
$249$	2.00000	0.126745
$250$	1.00000	0.0632456
$251$	4.00000	0.252478	0.126239	−	0.992000i	$-0.459709\pi$
$251$	4.00000	0.252478	0.126239	+	0.992000i	$0.459709\pi$
$252$	2.00000	0.125988
$253$	0	0
$254$	6.00000	0.376473
$255$	−7.00000	−0.438357
$256$	1.00000	0.0625000
$257$	−6.00000	−0.374270	−0.187135	−	0.982334i	$-0.559920\pi$
$257$	−6.00000	−0.374270	−0.187135	+	0.982334i	$0.559920\pi$
$258$	6.00000	0.373544
$259$	−2.00000	−0.124274
$260$	3.00000	0.186052
$261$	10.0000	0.618984
$262$	20.0000	1.23560
$263$	−8.00000	−0.493301	−0.246651	−	0.969104i	$-0.579330\pi$
$263$	−8.00000	−0.493301	−0.246651	+	0.969104i	$0.579330\pi$
$264$	0	0
$265$	−9.00000	−0.552866
$266$	−1.00000	−0.0613139
$267$	10.0000	0.611990
$268$	7.00000	0.427593
$269$	−10.0000	−0.609711	−0.304855	−	0.952399i	$-0.598608\pi$
$269$	−10.0000	−0.609711	−0.304855	+	0.952399i	$0.598608\pi$
$270$	5.00000	0.304290
$271$	5.00000	0.303728	0.151864	−	0.988401i	$-0.451472\pi$
$271$	5.00000	0.303728	0.151864	+	0.988401i	$0.451472\pi$
$272$	−7.00000	−0.424437
$273$	−3.00000	−0.181568
$274$	3.00000	0.181237
$275$	0	0
$276$	5.00000	0.300965
$277$	28.0000	1.68236	0.841178	−	0.540758i	$-0.181862\pi$
$277$	28.0000	1.68236	0.841178	+	0.540758i	$0.181862\pi$
$278$	−12.0000	−0.719712
$279$	−20.0000	−1.19737
$280$	−1.00000	−0.0597614
$281$	−26.0000	−1.55103	−0.775515	−	0.631329i	$-0.782510\pi$
$281$	−26.0000	−1.55103	−0.775515	+	0.631329i	$0.782510\pi$
$282$	0	0
$283$	−26.0000	−1.54554	−0.772770	−	0.634686i	$-0.781129\pi$
$283$	−26.0000	−1.54554	−0.772770	+	0.634686i	$0.781129\pi$
$284$	0	0
$285$	−1.00000	−0.0592349
$286$	0	0
$287$	−2.00000	−0.118056
$288$	2.00000	0.117851
$289$	32.0000	1.88235
$290$	−5.00000	−0.293610
$291$	18.0000	1.05518
$292$	−9.00000	−0.526685
$293$	31.0000	1.81104	0.905520	−	0.424304i	$-0.139481\pi$
$293$	31.0000	1.81104	0.905520	+	0.424304i	$0.139481\pi$
$294$	−6.00000	−0.349927
$295$	7.00000	0.407556
$296$	−2.00000	−0.116248
$297$	0	0
$298$	−4.00000	−0.231714
$299$	15.0000	0.867472
$300$	−1.00000	−0.0577350
$301$	−6.00000	−0.345834
$302$	6.00000	0.345261
$303$	4.00000	0.229794
$304$	−1.00000	−0.0573539
$305$	4.00000	0.229039
$306$	−14.0000	−0.800327
$307$	4.00000	0.228292	0.114146	−	0.993464i	$-0.463587\pi$
$307$	4.00000	0.228292	0.114146	+	0.993464i	$0.463587\pi$
$308$	0	0
$309$	0	0
$310$	10.0000	0.567962
$311$	33.0000	1.87126	0.935629	−	0.352985i	$-0.114833\pi$
$311$	33.0000	1.87126	0.935629	+	0.352985i	$0.114833\pi$
$312$	−3.00000	−0.169842
$313$	−29.0000	−1.63918	−0.819588	−	0.572953i	$-0.805798\pi$
$313$	−29.0000	−1.63918	−0.819588	+	0.572953i	$0.805798\pi$
$314$	−18.0000	−1.01580
$315$	−2.00000	−0.112687
$316$	−10.0000	−0.562544
$317$	3.00000	0.168497	0.0842484	−	0.996445i	$-0.473151\pi$
$317$	3.00000	0.168497	0.0842484	+	0.996445i	$0.473151\pi$
$318$	9.00000	0.504695
$319$	0	0
$320$	−1.00000	−0.0559017
$321$	−9.00000	−0.502331
$322$	−5.00000	−0.278639
$323$	7.00000	0.389490
$324$	1.00000	0.0555556
$325$	−3.00000	−0.166410
$326$	18.0000	0.996928
$327$	−13.0000	−0.718902
$328$	−2.00000	−0.110432
$329$	0	0
$330$	0	0
$331$	−17.0000	−0.934405	−0.467202	−	0.884150i	$-0.654738\pi$
$331$	−17.0000	−0.934405	−0.467202	+	0.884150i	$0.654738\pi$
$332$	−2.00000	−0.109764
$333$	−4.00000	−0.219199
$334$	−14.0000	−0.766046
$335$	−7.00000	−0.382451
$336$	1.00000	0.0545545
$337$	−14.0000	−0.762629	−0.381314	−	0.924445i	$-0.624528\pi$
$337$	−14.0000	−0.762629	−0.381314	+	0.924445i	$0.624528\pi$
$338$	4.00000	0.217571
$339$	−8.00000	−0.434500
$340$	7.00000	0.379628
$341$	0	0
$342$	−2.00000	−0.108148
$343$	13.0000	0.701934
$344$	−6.00000	−0.323498
$345$	−5.00000	−0.269191
$346$	−6.00000	−0.322562
$347$	−18.0000	−0.966291	−0.483145	−	0.875540i	$-0.660506\pi$
$347$	−18.0000	−0.966291	−0.483145	+	0.875540i	$0.660506\pi$
$348$	5.00000	0.268028
$349$	10.0000	0.535288	0.267644	−	0.963518i	$-0.413755\pi$
$349$	10.0000	0.535288	0.267644	+	0.963518i	$0.413755\pi$
$350$	1.00000	0.0534522
$351$	−15.0000	−0.800641
$352$	0	0
$353$	27.0000	1.43706	0.718532	−	0.695493i	$-0.244814\pi$
$353$	27.0000	1.43706	0.718532	+	0.695493i	$0.244814\pi$
$354$	−7.00000	−0.372046
$355$	0	0
$356$	−10.0000	−0.529999
$357$	−7.00000	−0.370479
$358$	−24.0000	−1.26844
$359$	27.0000	1.42501	0.712503	−	0.701669i	$-0.247562\pi$
$359$	27.0000	1.42501	0.712503	+	0.701669i	$0.247562\pi$
$360$	−2.00000	−0.105409
$361$	1.00000	0.0526316
$362$	10.0000	0.525588
$363$	11.0000	0.577350
$364$	3.00000	0.157243
$365$	9.00000	0.471082
$366$	−4.00000	−0.209083
$367$	8.00000	0.417597	0.208798	−	0.977959i	$-0.433045\pi$
$367$	8.00000	0.417597	0.208798	+	0.977959i	$0.433045\pi$
$368$	−5.00000	−0.260643
$369$	−4.00000	−0.208232
$370$	2.00000	0.103975
$371$	−9.00000	−0.467257
$372$	−10.0000	−0.518476
$373$	3.00000	0.155334	0.0776671	−	0.996979i	$-0.475253\pi$
$373$	3.00000	0.155334	0.0776671	+	0.996979i	$0.475253\pi$
$374$	0	0
$375$	1.00000	0.0516398
$376$	0	0
$377$	15.0000	0.772539
$378$	5.00000	0.257172
$379$	−7.00000	−0.359566	−0.179783	−	0.983706i	$-0.557540\pi$
$379$	−7.00000	−0.359566	−0.179783	+	0.983706i	$0.557540\pi$
$380$	1.00000	0.0512989
$381$	6.00000	0.307389
$382$	7.00000	0.358151
$383$	0	0		−	1.00000i	$-0.5\pi$
$383$	0	0			1.00000i	$0.5\pi$
$384$	1.00000	0.0510310
$385$	0	0
$386$	2.00000	0.101797
$387$	−12.0000	−0.609994
$388$	−18.0000	−0.913812
$389$	24.0000	1.21685	0.608424	−	0.793612i	$-0.291802\pi$
$389$	24.0000	1.21685	0.608424	+	0.793612i	$0.291802\pi$
$390$	3.00000	0.151911
$391$	35.0000	1.77003
$392$	6.00000	0.303046
$393$	20.0000	1.00887
$394$	10.0000	0.503793
$395$	10.0000	0.503155
$396$	0	0
$397$	−20.0000	−1.00377	−0.501886	−	0.864934i	$-0.667360\pi$
$397$	−20.0000	−1.00377	−0.501886	+	0.864934i	$0.667360\pi$
$398$	−17.0000	−0.852133
$399$	−1.00000	−0.0500626
$400$	1.00000	0.0500000
$401$	18.0000	0.898877	0.449439	−	0.893311i	$-0.351624\pi$
$401$	18.0000	0.898877	0.449439	+	0.893311i	$0.351624\pi$
$402$	7.00000	0.349128
$403$	−30.0000	−1.49441
$404$	−4.00000	−0.199007
$405$	−1.00000	−0.0496904
$406$	−5.00000	−0.248146
$407$	0	0
$408$	−7.00000	−0.346552
$409$	26.0000	1.28562	0.642809	−	0.766027i	$-0.277769\pi$
$409$	26.0000	1.28562	0.642809	+	0.766027i	$0.277769\pi$
$410$	2.00000	0.0987730
$411$	3.00000	0.147979
$412$	0	0
$413$	7.00000	0.344447
$414$	−10.0000	−0.491473
$415$	2.00000	0.0981761
$416$	3.00000	0.147087
$417$	−12.0000	−0.587643
$418$	0	0
$419$	−26.0000	−1.27018	−0.635092	−	0.772437i	$-0.719038\pi$
$419$	−26.0000	−1.27018	−0.635092	+	0.772437i	$0.719038\pi$
$420$	−1.00000	−0.0487950
$421$	31.0000	1.51085	0.755424	−	0.655237i	$-0.227431\pi$
$421$	31.0000	1.51085	0.755424	+	0.655237i	$0.227431\pi$
$422$	−5.00000	−0.243396
$423$	0	0
$424$	−9.00000	−0.437079
$425$	−7.00000	−0.339550
$426$	0	0
$427$	4.00000	0.193574
$428$	9.00000	0.435031
$429$	0	0
$430$	6.00000	0.289346
$431$	12.0000	0.578020	0.289010	−	0.957326i	$-0.406674\pi$
$431$	12.0000	0.578020	0.289010	+	0.957326i	$0.406674\pi$
$432$	5.00000	0.240563
$433$	12.0000	0.576683	0.288342	−	0.957528i	$-0.406896\pi$
$433$	12.0000	0.576683	0.288342	+	0.957528i	$0.406896\pi$
$434$	10.0000	0.480015
$435$	−5.00000	−0.239732
$436$	13.0000	0.622587
$437$	5.00000	0.239182
$438$	−9.00000	−0.430037
$439$	10.0000	0.477274	0.238637	−	0.971109i	$-0.423299\pi$
$439$	10.0000	0.477274	0.238637	+	0.971109i	$0.423299\pi$
$440$	0	0
$441$	12.0000	0.571429
$442$	−21.0000	−0.998868
$443$	24.0000	1.14027	0.570137	−	0.821549i	$-0.306890\pi$
$443$	24.0000	1.14027	0.570137	+	0.821549i	$0.306890\pi$
$444$	−2.00000	−0.0949158
$445$	10.0000	0.474045
$446$	22.0000	1.04173
$447$	−4.00000	−0.189194
$448$	−1.00000	−0.0472456
$449$	14.0000	0.660701	0.330350	−	0.943858i	$-0.392833\pi$
$449$	14.0000	0.660701	0.330350	+	0.943858i	$0.392833\pi$
$450$	2.00000	0.0942809
$451$	0	0
$452$	8.00000	0.376288
$453$	6.00000	0.281905
$454$	25.0000	1.17331
$455$	−3.00000	−0.140642
$456$	−1.00000	−0.0468293
$457$	−41.0000	−1.91790	−0.958950	−	0.283577i	$-0.908479\pi$
$457$	−41.0000	−1.91790	−0.958950	+	0.283577i	$0.908479\pi$
$458$	18.0000	0.841085
$459$	−35.0000	−1.63366
$460$	5.00000	0.233126
$461$	−10.0000	−0.465746	−0.232873	−	0.972507i	$-0.574813\pi$
$461$	−10.0000	−0.465746	−0.232873	+	0.972507i	$0.574813\pi$
$462$	0	0
$463$	16.0000	0.743583	0.371792	−	0.928316i	$-0.378744\pi$
$463$	16.0000	0.743583	0.371792	+	0.928316i	$0.378744\pi$
$464$	−5.00000	−0.232119
$465$	10.0000	0.463739
$466$	−26.0000	−1.20443
$467$	−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
$469$	−7.00000	−0.323230
$470$	0	0
$471$	−18.0000	−0.829396
$472$	7.00000	0.322201
$473$	0	0
$474$	−10.0000	−0.459315
$475$	−1.00000	−0.0458831
$476$	7.00000	0.320844
$477$	−18.0000	−0.824163
$478$	27.0000	1.23495
$479$	−24.0000	−1.09659	−0.548294	−	0.836286i	$-0.684723\pi$
$479$	−24.0000	−1.09659	−0.548294	+	0.836286i	$0.684723\pi$
$480$	−1.00000	−0.0456435
$481$	−6.00000	−0.273576
$482$	28.0000	1.27537
$483$	−5.00000	−0.227508
$484$	−11.0000	−0.500000
$485$	18.0000	0.817338
$486$	16.0000	0.725775
$487$	−2.00000	−0.0906287	−0.0453143	−	0.998973i	$-0.514429\pi$
$487$	−2.00000	−0.0906287	−0.0453143	+	0.998973i	$0.514429\pi$
$488$	4.00000	0.181071
$489$	18.0000	0.813988
$490$	−6.00000	−0.271052
$491$	14.0000	0.631811	0.315906	−	0.948791i	$-0.397692\pi$
$491$	14.0000	0.631811	0.315906	+	0.948791i	$0.397692\pi$
$492$	−2.00000	−0.0901670
$493$	35.0000	1.57632
$494$	−3.00000	−0.134976
$495$	0	0
$496$	10.0000	0.449013
$497$	0	0
$498$	−2.00000	−0.0896221
$499$	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
$501$	−14.0000	−0.625474
$502$	−4.00000	−0.178529
$503$	−17.0000	−0.757993	−0.378996	−	0.925398i	$-0.623731\pi$
$503$	−17.0000	−0.757993	−0.378996	+	0.925398i	$0.623731\pi$
$504$	−2.00000	−0.0890871
$505$	4.00000	0.177998
$506$	0	0
$507$	4.00000	0.177646
$508$	−6.00000	−0.266207
$509$	−42.0000	−1.86162	−0.930809	−	0.365507i	$-0.880896\pi$
$509$	−42.0000	−1.86162	−0.930809	+	0.365507i	$0.880896\pi$
$510$	7.00000	0.309965
$511$	9.00000	0.398137
$512$	−1.00000	−0.0441942
$513$	−5.00000	−0.220755
$514$	6.00000	0.264649
$515$	0	0
$516$	−6.00000	−0.264135
$517$	0	0
$518$	2.00000	0.0878750
$519$	−6.00000	−0.263371
$520$	−3.00000	−0.131559
$521$	0	0		−	1.00000i	$-0.5\pi$
$521$	0	0			1.00000i	$0.5\pi$
$522$	−10.0000	−0.437688
$523$	−19.0000	−0.830812	−0.415406	−	0.909636i	$-0.636360\pi$
$523$	−19.0000	−0.830812	−0.415406	+	0.909636i	$0.636360\pi$
$524$	−20.0000	−0.873704
$525$	1.00000	0.0436436
$526$	8.00000	0.348817
$527$	−70.0000	−3.04925
$528$	0	0
$529$	2.00000	0.0869565
$530$	9.00000	0.390935
$531$	14.0000	0.607548
$532$	1.00000	0.0433555
$533$	−6.00000	−0.259889
$534$	−10.0000	−0.432742
$535$	−9.00000	−0.389104
$536$	−7.00000	−0.302354
$537$	−24.0000	−1.03568
$538$	10.0000	0.431131
$539$	0	0
$540$	−5.00000	−0.215166
$541$	−28.0000	−1.20381	−0.601907	−	0.798566i	$-0.705592\pi$
$541$	−28.0000	−1.20381	−0.601907	+	0.798566i	$0.705592\pi$
$542$	−5.00000	−0.214768
$543$	10.0000	0.429141
$544$	7.00000	0.300123
$545$	−13.0000	−0.556859
$546$	3.00000	0.128388
$547$	−20.0000	−0.855138	−0.427569	−	0.903983i	$-0.640630\pi$
$547$	−20.0000	−0.855138	−0.427569	+	0.903983i	$0.640630\pi$
$548$	−3.00000	−0.128154
$549$	8.00000	0.341432
$550$	0	0
$551$	5.00000	0.213007
$552$	−5.00000	−0.212814
$553$	10.0000	0.425243
$554$	−28.0000	−1.18961
$555$	2.00000	0.0848953
$556$	12.0000	0.508913
$557$	8.00000	0.338971	0.169485	−	0.985533i	$-0.445789\pi$
$557$	8.00000	0.338971	0.169485	+	0.985533i	$0.445789\pi$
$558$	20.0000	0.846668
$559$	−18.0000	−0.761319
$560$	1.00000	0.0422577
$561$	0	0
$562$	26.0000	1.09674
$563$	−44.0000	−1.85438	−0.927189	−	0.374593i	$-0.877783\pi$
$563$	−44.0000	−1.85438	−0.927189	+	0.374593i	$0.877783\pi$
$564$	0	0
$565$	−8.00000	−0.336563
$566$	26.0000	1.09286
$567$	−1.00000	−0.0419961
$568$	0	0
$569$	−8.00000	−0.335377	−0.167689	−	0.985840i	$-0.553630\pi$
$569$	−8.00000	−0.335377	−0.167689	+	0.985840i	$0.553630\pi$
$570$	1.00000	0.0418854
$571$	10.0000	0.418487	0.209243	−	0.977864i	$-0.432900\pi$
$571$	10.0000	0.418487	0.209243	+	0.977864i	$0.432900\pi$
$572$	0	0
$573$	7.00000	0.292429
$574$	2.00000	0.0834784
$575$	−5.00000	−0.208514
$576$	−2.00000	−0.0833333
$577$	−11.0000	−0.457936	−0.228968	−	0.973434i	$-0.573535\pi$
$577$	−11.0000	−0.457936	−0.228968	+	0.973434i	$0.573535\pi$
$578$	−32.0000	−1.33102
$579$	2.00000	0.0831172
$580$	5.00000	0.207614
$581$	2.00000	0.0829740
$582$	−18.0000	−0.746124
$583$	0	0
$584$	9.00000	0.372423
$585$	−6.00000	−0.248069
$586$	−31.0000	−1.28060
$587$	30.0000	1.23823	0.619116	−	0.785299i	$-0.287491\pi$
$587$	30.0000	1.23823	0.619116	+	0.785299i	$0.287491\pi$
$588$	6.00000	0.247436
$589$	−10.0000	−0.412043
$590$	−7.00000	−0.288185
$591$	10.0000	0.411345
$592$	2.00000	0.0821995
$593$	−34.0000	−1.39621	−0.698106	−	0.715994i	$-0.745974\pi$
$593$	−34.0000	−1.39621	−0.698106	+	0.715994i	$0.745974\pi$
$594$	0	0
$595$	−7.00000	−0.286972
$596$	4.00000	0.163846
$597$	−17.0000	−0.695764
$598$	−15.0000	−0.613396
$599$	30.0000	1.22577	0.612883	−	0.790173i	$-0.290010\pi$
$599$	30.0000	1.22577	0.612883	+	0.790173i	$0.290010\pi$
$600$	1.00000	0.0408248
$601$	−10.0000	−0.407909	−0.203954	−	0.978980i	$-0.565379\pi$
$601$	−10.0000	−0.407909	−0.203954	+	0.978980i	$0.565379\pi$
$602$	6.00000	0.244542
$603$	−14.0000	−0.570124
$604$	−6.00000	−0.244137
$605$	11.0000	0.447214
$606$	−4.00000	−0.162489
$607$	22.0000	0.892952	0.446476	−	0.894795i	$-0.352679\pi$
$607$	22.0000	0.892952	0.446476	+	0.894795i	$0.352679\pi$
$608$	1.00000	0.0405554
$609$	−5.00000	−0.202610
$610$	−4.00000	−0.161955
$611$	0	0
$612$	14.0000	0.565916
$613$	−16.0000	−0.646234	−0.323117	−	0.946359i	$-0.604731\pi$
$613$	−16.0000	−0.646234	−0.323117	+	0.946359i	$0.604731\pi$
$614$	−4.00000	−0.161427
$615$	2.00000	0.0806478
$616$	0	0
$617$	−2.00000	−0.0805170	−0.0402585	−	0.999189i	$-0.512818\pi$
$617$	−2.00000	−0.0805170	−0.0402585	+	0.999189i	$0.512818\pi$
$618$	0	0
$619$	−8.00000	−0.321547	−0.160774	−	0.986991i	$-0.551399\pi$
$619$	−8.00000	−0.321547	−0.160774	+	0.986991i	$0.551399\pi$
$620$	−10.0000	−0.401610
$621$	−25.0000	−1.00322
$622$	−33.0000	−1.32318
$623$	10.0000	0.400642
$624$	3.00000	0.120096
$625$	1.00000	0.0400000
$626$	29.0000	1.15907
$627$	0	0
$628$	18.0000	0.718278
$629$	−14.0000	−0.558217
$630$	2.00000	0.0796819
$631$	0	0		−	1.00000i	$-0.5\pi$
$631$	0	0			1.00000i	$0.5\pi$
$632$	10.0000	0.397779
$633$	−5.00000	−0.198732
$634$	−3.00000	−0.119145
$635$	6.00000	0.238103
$636$	−9.00000	−0.356873
$637$	18.0000	0.713186
$638$	0	0
$639$	0	0
$640$	1.00000	0.0395285
$641$	−12.0000	−0.473972	−0.236986	−	0.971513i	$-0.576159\pi$
$641$	−12.0000	−0.473972	−0.236986	+	0.971513i	$0.576159\pi$
$642$	9.00000	0.355202
$643$	−2.00000	−0.0788723	−0.0394362	−	0.999222i	$-0.512556\pi$
$643$	−2.00000	−0.0788723	−0.0394362	+	0.999222i	$0.512556\pi$
$644$	5.00000	0.197028
$645$	6.00000	0.236250
$646$	−7.00000	−0.275411
$647$	−9.00000	−0.353827	−0.176913	−	0.984226i	$-0.556611\pi$
$647$	−9.00000	−0.353827	−0.176913	+	0.984226i	$0.556611\pi$
$648$	−1.00000	−0.0392837
$649$	0	0
$650$	3.00000	0.117670
$651$	10.0000	0.391931
$652$	−18.0000	−0.704934
$653$	−12.0000	−0.469596	−0.234798	−	0.972044i	$-0.575443\pi$
$653$	−12.0000	−0.469596	−0.234798	+	0.972044i	$0.575443\pi$
$654$	13.0000	0.508340
$655$	20.0000	0.781465
$656$	2.00000	0.0780869
$657$	18.0000	0.702247
$658$	0	0
$659$	15.0000	0.584317	0.292159	−	0.956370i	$-0.405627\pi$
$659$	15.0000	0.584317	0.292159	+	0.956370i	$0.405627\pi$
$660$	0	0
$661$	17.0000	0.661223	0.330612	−	0.943767i	$-0.392745\pi$
$661$	17.0000	0.661223	0.330612	+	0.943767i	$0.392745\pi$
$662$	17.0000	0.660724
$663$	−21.0000	−0.815572
$664$	2.00000	0.0776151
$665$	−1.00000	−0.0387783
$666$	4.00000	0.154997
$667$	25.0000	0.968004
$668$	14.0000	0.541676
$669$	22.0000	0.850569
$670$	7.00000	0.270434
$671$	0	0
$672$	−1.00000	−0.0385758
$673$	−28.0000	−1.07932	−0.539660	−	0.841883i	$-0.681447\pi$
$673$	−28.0000	−1.07932	−0.539660	+	0.841883i	$0.681447\pi$
$674$	14.0000	0.539260
$675$	5.00000	0.192450
$676$	−4.00000	−0.153846
$677$	19.0000	0.730229	0.365115	−	0.930963i	$-0.381030\pi$
$677$	19.0000	0.730229	0.365115	+	0.930963i	$0.381030\pi$
$678$	8.00000	0.307238
$679$	18.0000	0.690777
$680$	−7.00000	−0.268438
$681$	25.0000	0.958002
$682$	0	0
$683$	36.0000	1.37750	0.688751	−	0.724998i	$-0.258159\pi$
$683$	36.0000	1.37750	0.688751	+	0.724998i	$0.258159\pi$
$684$	2.00000	0.0764719
$685$	3.00000	0.114624
$686$	−13.0000	−0.496342
$687$	18.0000	0.686743
$688$	6.00000	0.228748
$689$	−27.0000	−1.02862
$690$	5.00000	0.190347
$691$	10.0000	0.380418	0.190209	−	0.981744i	$-0.439083\pi$
$691$	10.0000	0.380418	0.190209	+	0.981744i	$0.439083\pi$
$692$	6.00000	0.228086
$693$	0	0
$694$	18.0000	0.683271
$695$	−12.0000	−0.455186
$696$	−5.00000	−0.189525
$697$	−14.0000	−0.530288
$698$	−10.0000	−0.378506
$699$	−26.0000	−0.983410
$700$	−1.00000	−0.0377964
$701$	24.0000	0.906467	0.453234	−	0.891392i	$-0.350270\pi$
$701$	24.0000	0.906467	0.453234	+	0.891392i	$0.350270\pi$
$702$	15.0000	0.566139
$703$	−2.00000	−0.0754314
$704$	0	0
$705$	0	0
$706$	−27.0000	−1.01616
$707$	4.00000	0.150435
$708$	7.00000	0.263076
$709$	−34.0000	−1.27690	−0.638448	−	0.769665i	$-0.720423\pi$
$709$	−34.0000	−1.27690	−0.638448	+	0.769665i	$0.720423\pi$
$710$	0	0
$711$	20.0000	0.750059
$712$	10.0000	0.374766
$713$	−50.0000	−1.87251
$714$	7.00000	0.261968
$715$	0	0
$716$	24.0000	0.896922
$717$	27.0000	1.00833
$718$	−27.0000	−1.00763
$719$	29.0000	1.08152	0.540759	−	0.841178i	$-0.318137\pi$
$719$	29.0000	1.08152	0.540759	+	0.841178i	$0.318137\pi$
$720$	2.00000	0.0745356
$721$	0	0
$722$	−1.00000	−0.0372161
$723$	28.0000	1.04133
$724$	−10.0000	−0.371647
$725$	−5.00000	−0.185695
$726$	−11.0000	−0.408248
$727$	11.0000	0.407967	0.203984	−	0.978974i	$-0.434611\pi$
$727$	11.0000	0.407967	0.203984	+	0.978974i	$0.434611\pi$
$728$	−3.00000	−0.111187
$729$	13.0000	0.481481
$730$	−9.00000	−0.333105
$731$	−42.0000	−1.55343
$732$	4.00000	0.147844
$733$	24.0000	0.886460	0.443230	−	0.896408i	$-0.353832\pi$
$733$	24.0000	0.886460	0.443230	+	0.896408i	$0.353832\pi$
$734$	−8.00000	−0.295285
$735$	−6.00000	−0.221313
$736$	5.00000	0.184302
$737$	0	0
$738$	4.00000	0.147242
$739$	50.0000	1.83928	0.919640	−	0.392763i	$-0.128481\pi$
$739$	50.0000	1.83928	0.919640	+	0.392763i	$0.128481\pi$
$740$	−2.00000	−0.0735215
$741$	−3.00000	−0.110208
$742$	9.00000	0.330400
$743$	34.0000	1.24734	0.623670	−	0.781688i	$-0.285641\pi$
$743$	34.0000	1.24734	0.623670	+	0.781688i	$0.285641\pi$
$744$	10.0000	0.366618
$745$	−4.00000	−0.146549
$746$	−3.00000	−0.109838
$747$	4.00000	0.146352
$748$	0	0
$749$	−9.00000	−0.328853
$750$	−1.00000	−0.0365148
$751$	46.0000	1.67856	0.839282	−	0.543696i	$-0.182976\pi$
$751$	46.0000	1.67856	0.839282	+	0.543696i	$0.182976\pi$
$752$	0	0
$753$	−4.00000	−0.145768
$754$	−15.0000	−0.546268
$755$	6.00000	0.218362
$756$	−5.00000	−0.181848
$757$	22.0000	0.799604	0.399802	−	0.916602i	$-0.369079\pi$
$757$	22.0000	0.799604	0.399802	+	0.916602i	$0.369079\pi$
$758$	7.00000	0.254251
$759$	0	0
$760$	−1.00000	−0.0362738
$761$	−45.0000	−1.63125	−0.815624	−	0.578582i	$-0.803606\pi$
$761$	−45.0000	−1.63125	−0.815624	+	0.578582i	$0.803606\pi$
$762$	−6.00000	−0.217357
$763$	−13.0000	−0.470632
$764$	−7.00000	−0.253251
$765$	−14.0000	−0.506171
$766$	0	0
$767$	21.0000	0.758266
$768$	−1.00000	−0.0360844
$769$	49.0000	1.76699	0.883493	−	0.468445i	$-0.155186\pi$
$769$	49.0000	1.76699	0.883493	+	0.468445i	$0.155186\pi$
$770$	0	0
$771$	6.00000	0.216085
$772$	−2.00000	−0.0719816
$773$	15.0000	0.539513	0.269756	−	0.962929i	$-0.413057\pi$
$773$	15.0000	0.539513	0.269756	+	0.962929i	$0.413057\pi$
$774$	12.0000	0.431331
$775$	10.0000	0.359211
$776$	18.0000	0.646162
$777$	2.00000	0.0717496
$778$	−24.0000	−0.860442
$779$	−2.00000	−0.0716574
$780$	−3.00000	−0.107417
$781$	0	0
$782$	−35.0000	−1.25160
$783$	−25.0000	−0.893427
$784$	−6.00000	−0.214286
$785$	−18.0000	−0.642448
$786$	−20.0000	−0.713376
$787$	11.0000	0.392108	0.196054	−	0.980593i	$-0.437187\pi$
$787$	11.0000	0.392108	0.196054	+	0.980593i	$0.437187\pi$
$788$	−10.0000	−0.356235
$789$	8.00000	0.284808
$790$	−10.0000	−0.355784
$791$	−8.00000	−0.284447
$792$	0	0
$793$	12.0000	0.426132
$794$	20.0000	0.709773
$795$	9.00000	0.319197
$796$	17.0000	0.602549
$797$	5.00000	0.177109	0.0885545	−	0.996071i	$-0.471775\pi$
$797$	5.00000	0.177109	0.0885545	+	0.996071i	$0.471775\pi$
$798$	1.00000	0.0353996
$799$	0	0
$800$	−1.00000	−0.0353553
$801$	20.0000	0.706665
$802$	−18.0000	−0.635602
$803$	0	0
$804$	−7.00000	−0.246871
$805$	−5.00000	−0.176227
$806$	30.0000	1.05670
$807$	10.0000	0.352017
$808$	4.00000	0.140720
$809$	−39.0000	−1.37117	−0.685583	−	0.727994i	$-0.740453\pi$
$809$	−39.0000	−1.37117	−0.685583	+	0.727994i	$0.740453\pi$
$810$	1.00000	0.0351364
$811$	11.0000	0.386262	0.193131	−	0.981173i	$-0.438136\pi$
$811$	11.0000	0.386262	0.193131	+	0.981173i	$0.438136\pi$
$812$	5.00000	0.175466
$813$	−5.00000	−0.175358
$814$	0	0
$815$	18.0000	0.630512
$816$	7.00000	0.245049
$817$	−6.00000	−0.209913
$818$	−26.0000	−0.909069
$819$	−6.00000	−0.209657
$820$	−2.00000	−0.0698430
$821$	−56.0000	−1.95441	−0.977207	−	0.212290i	$-0.931908\pi$
$821$	−56.0000	−1.95441	−0.977207	+	0.212290i	$0.931908\pi$
$822$	−3.00000	−0.104637
$823$	−31.0000	−1.08059	−0.540296	−	0.841475i	$-0.681688\pi$
$823$	−31.0000	−1.08059	−0.540296	+	0.841475i	$0.681688\pi$
$824$	0	0
$825$	0	0
$826$	−7.00000	−0.243561
$827$	−9.00000	−0.312961	−0.156480	−	0.987681i	$-0.550015\pi$
$827$	−9.00000	−0.312961	−0.156480	+	0.987681i	$0.550015\pi$
$828$	10.0000	0.347524
$829$	−51.0000	−1.77130	−0.885652	−	0.464350i	$-0.846288\pi$
$829$	−51.0000	−1.77130	−0.885652	+	0.464350i	$0.846288\pi$
$830$	−2.00000	−0.0694210
$831$	−28.0000	−0.971309
$832$	−3.00000	−0.104006
$833$	42.0000	1.45521
$834$	12.0000	0.415526
$835$	−14.0000	−0.484490
$836$	0	0
$837$	50.0000	1.72825
$838$	26.0000	0.898155
$839$	−48.0000	−1.65714	−0.828572	−	0.559883i	$-0.810846\pi$
$839$	−48.0000	−1.65714	−0.828572	+	0.559883i	$0.810846\pi$
$840$	1.00000	0.0345033
$841$	−4.00000	−0.137931
$842$	−31.0000	−1.06833
$843$	26.0000	0.895488
$844$	5.00000	0.172107
$845$	4.00000	0.137604
$846$	0	0
$847$	11.0000	0.377964
$848$	9.00000	0.309061
$849$	26.0000	0.892318
$850$	7.00000	0.240098
$851$	−10.0000	−0.342796
$852$	0	0
$853$	−46.0000	−1.57501	−0.787505	−	0.616308i	$-0.788628\pi$
$853$	−46.0000	−1.57501	−0.787505	+	0.616308i	$0.788628\pi$
$854$	−4.00000	−0.136877
$855$	−2.00000	−0.0683986
$856$	−9.00000	−0.307614
$857$	24.0000	0.819824	0.409912	−	0.912125i	$-0.365559\pi$
$857$	24.0000	0.819824	0.409912	+	0.912125i	$0.365559\pi$
$858$	0	0
$859$	56.0000	1.91070	0.955348	−	0.295484i	$-0.0954809\pi$
$859$	56.0000	1.91070	0.955348	+	0.295484i	$0.0954809\pi$
$860$	−6.00000	−0.204598
$861$	2.00000	0.0681598
$862$	−12.0000	−0.408722
$863$	24.0000	0.816970	0.408485	−	0.912765i	$-0.366057\pi$
$863$	24.0000	0.816970	0.408485	+	0.912765i	$0.366057\pi$
$864$	−5.00000	−0.170103
$865$	−6.00000	−0.204006
$866$	−12.0000	−0.407777
$867$	−32.0000	−1.08678
$868$	−10.0000	−0.339422
$869$	0	0
$870$	5.00000	0.169516
$871$	−21.0000	−0.711558
$872$	−13.0000	−0.440236
$873$	36.0000	1.21842
$874$	−5.00000	−0.169128
$875$	1.00000	0.0338062
$876$	9.00000	0.304082
$877$	−5.00000	−0.168838	−0.0844190	−	0.996430i	$-0.526903\pi$
$877$	−5.00000	−0.168838	−0.0844190	+	0.996430i	$0.526903\pi$
$878$	−10.0000	−0.337484
$879$	−31.0000	−1.04560
$880$	0	0
$881$	2.00000	0.0673817	0.0336909	−	0.999432i	$-0.489274\pi$
$881$	2.00000	0.0673817	0.0336909	+	0.999432i	$0.489274\pi$
$882$	−12.0000	−0.404061
$883$	26.0000	0.874970	0.437485	−	0.899226i	$-0.355869\pi$
$883$	26.0000	0.874970	0.437485	+	0.899226i	$0.355869\pi$
$884$	21.0000	0.706306
$885$	−7.00000	−0.235302
$886$	−24.0000	−0.806296
$887$	52.0000	1.74599	0.872995	−	0.487730i	$-0.162175\pi$
$887$	52.0000	1.74599	0.872995	+	0.487730i	$0.162175\pi$
$888$	2.00000	0.0671156
$889$	6.00000	0.201234
$890$	−10.0000	−0.335201
$891$	0	0
$892$	−22.0000	−0.736614
$893$	0	0
$894$	4.00000	0.133780
$895$	−24.0000	−0.802232
$896$	1.00000	0.0334077
$897$	−15.0000	−0.500835
$898$	−14.0000	−0.467186
$899$	−50.0000	−1.66759
$900$	−2.00000	−0.0666667
$901$	−63.0000	−2.09883
$902$	0	0
$903$	6.00000	0.199667
$904$	−8.00000	−0.266076
$905$	10.0000	0.332411
$906$	−6.00000	−0.199337
$907$	5.00000	0.166022	0.0830111	−	0.996549i	$-0.473546\pi$
$907$	5.00000	0.166022	0.0830111	+	0.996549i	$0.473546\pi$
$908$	−25.0000	−0.829654
$909$	8.00000	0.265343
$910$	3.00000	0.0994490
$911$	−32.0000	−1.06021	−0.530104	−	0.847933i	$-0.677847\pi$
$911$	−32.0000	−1.06021	−0.530104	+	0.847933i	$0.677847\pi$
$912$	1.00000	0.0331133
$913$	0	0
$914$	41.0000	1.35616
$915$	−4.00000	−0.132236
$916$	−18.0000	−0.594737
$917$	20.0000	0.660458
$918$	35.0000	1.15517
$919$	11.0000	0.362857	0.181428	−	0.983404i	$-0.441928\pi$
$919$	11.0000	0.362857	0.181428	+	0.983404i	$0.441928\pi$
$920$	−5.00000	−0.164845
$921$	−4.00000	−0.131804
$922$	10.0000	0.329332
$923$	0	0
$924$	0	0
$925$	2.00000	0.0657596
$926$	−16.0000	−0.525793
$927$	0	0
$928$	5.00000	0.164133
$929$	21.0000	0.688988	0.344494	−	0.938789i	$-0.388051\pi$
$929$	21.0000	0.688988	0.344494	+	0.938789i	$0.388051\pi$
$930$	−10.0000	−0.327913
$931$	6.00000	0.196642
$932$	26.0000	0.851658
$933$	−33.0000	−1.08037
$934$	8.00000	0.261768
$935$	0	0
$936$	−6.00000	−0.196116
$937$	−13.0000	−0.424691	−0.212346	−	0.977195i	$-0.568110\pi$
$937$	−13.0000	−0.424691	−0.212346	+	0.977195i	$0.568110\pi$
$938$	7.00000	0.228558
$939$	29.0000	0.946379
$940$	0	0
$941$	−37.0000	−1.20617	−0.603083	−	0.797679i	$-0.706061\pi$
$941$	−37.0000	−1.20617	−0.603083	+	0.797679i	$0.706061\pi$
$942$	18.0000	0.586472
$943$	−10.0000	−0.325645
$944$	−7.00000	−0.227831
$945$	5.00000	0.162650
$946$	0	0
$947$	−28.0000	−0.909878	−0.454939	−	0.890523i	$-0.650339\pi$
$947$	−28.0000	−0.909878	−0.454939	+	0.890523i	$0.650339\pi$
$948$	10.0000	0.324785
$949$	27.0000	0.876457
$950$	1.00000	0.0324443
$951$	−3.00000	−0.0972817
$952$	−7.00000	−0.226871
$953$	44.0000	1.42530	0.712650	−	0.701520i	$-0.247495\pi$
$953$	44.0000	1.42530	0.712650	+	0.701520i	$0.247495\pi$
$954$	18.0000	0.582772
$955$	7.00000	0.226515
$956$	−27.0000	−0.873242
$957$	0	0
$958$	24.0000	0.775405
$959$	3.00000	0.0968751
$960$	1.00000	0.0322749
$961$	69.0000	2.22581
$962$	6.00000	0.193448
$963$	−18.0000	−0.580042
$964$	−28.0000	−0.901819
$965$	2.00000	0.0643823
$966$	5.00000	0.160872
$967$	12.0000	0.385894	0.192947	−	0.981209i	$-0.438195\pi$
$967$	12.0000	0.385894	0.192947	+	0.981209i	$0.438195\pi$
$968$	11.0000	0.353553
$969$	−7.00000	−0.224872
$970$	−18.0000	−0.577945
$971$	36.0000	1.15529	0.577647	−	0.816286i	$-0.303971\pi$
$971$	36.0000	1.15529	0.577647	+	0.816286i	$0.303971\pi$
$972$	−16.0000	−0.513200
$973$	−12.0000	−0.384702
$974$	2.00000	0.0640841
$975$	3.00000	0.0960769
$976$	−4.00000	−0.128037
$977$	−18.0000	−0.575871	−0.287936	−	0.957650i	$-0.592969\pi$
$977$	−18.0000	−0.575871	−0.287936	+	0.957650i	$0.592969\pi$
$978$	−18.0000	−0.575577
$979$	0	0
$980$	6.00000	0.191663
$981$	−26.0000	−0.830116
$982$	−14.0000	−0.446758
$983$	−18.0000	−0.574111	−0.287055	−	0.957914i	$-0.592676\pi$
$983$	−18.0000	−0.574111	−0.287055	+	0.957914i	$0.592676\pi$
$984$	2.00000	0.0637577
$985$	10.0000	0.318626
$986$	−35.0000	−1.11463
$987$	0	0
$988$	3.00000	0.0954427
$989$	−30.0000	−0.953945
$990$	0	0
$991$	−46.0000	−1.46124	−0.730619	−	0.682785i	$-0.760768\pi$
$991$	−46.0000	−1.46124	−0.730619	+	0.682785i	$0.760768\pi$
$992$	−10.0000	−0.317500
$993$	17.0000	0.539479
$994$	0	0
$995$	−17.0000	−0.538936
$996$	2.00000	0.0633724
$997$	14.0000	0.443384	0.221692	−	0.975117i	$-0.428842\pi$
$997$	14.0000	0.443384	0.221692	+	0.975117i	$0.428842\pi$
$998$	−42.0000	−1.32949
$999$	10.0000	0.316386

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.2.a.a.1.1	✓	1	1.1	even	1	trivial
950.2.a.e.1.1		1	5.4	even	2
950.2.b.d.799.1		2	5.2	odd	4
950.2.b.d.799.2		2	5.3	odd	4
1520.2.a.g.1.1		1	4.3	odd	2
1710.2.a.r.1.1		1	3.2	odd	2
3610.2.a.h.1.1		1	19.18	odd	2
6080.2.a.i.1.1		1	8.3	odd	2
6080.2.a.r.1.1		1	8.5	even	2
7600.2.a.g.1.1		1	20.19	odd	2
8550.2.a.l.1.1		1	15.14	odd	2
9310.2.a.i.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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