LMFDB - Embedded newform 195.2.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [195,2,Mod(1,195)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(195, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("195.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 195 = 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	195.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:	$1.55708283941$
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	$\chi$	$=$	195.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

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

\(q-1.00000 q^{2} +1.00000 q^{3} -1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} +3.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} +4.00000 q^{11} -1.00000 q^{12} +1.00000 q^{13} +1.00000 q^{15} -1.00000 q^{16} +2.00000 q^{17} -1.00000 q^{18} -4.00000 q^{19} -1.00000 q^{20} -4.00000 q^{22} +8.00000 q^{23} +3.00000 q^{24} +1.00000 q^{25} -1.00000 q^{26} +1.00000 q^{27} -2.00000 q^{29} -1.00000 q^{30} -8.00000 q^{31} -5.00000 q^{32} +4.00000 q^{33} -2.00000 q^{34} -1.00000 q^{36} +6.00000 q^{37} +4.00000 q^{38} +1.00000 q^{39} +3.00000 q^{40} -6.00000 q^{41} -4.00000 q^{43} -4.00000 q^{44} +1.00000 q^{45} -8.00000 q^{46} -8.00000 q^{47} -1.00000 q^{48} -7.00000 q^{49} -1.00000 q^{50} +2.00000 q^{51} -1.00000 q^{52} +6.00000 q^{53} -1.00000 q^{54} +4.00000 q^{55} -4.00000 q^{57} +2.00000 q^{58} -12.0000 q^{59} -1.00000 q^{60} -2.00000 q^{61} +8.00000 q^{62} +7.00000 q^{64} +1.00000 q^{65} -4.00000 q^{66} -4.00000 q^{67} -2.00000 q^{68} +8.00000 q^{69} +3.00000 q^{72} -6.00000 q^{73} -6.00000 q^{74} +1.00000 q^{75} +4.00000 q^{76} -1.00000 q^{78} +16.0000 q^{79} -1.00000 q^{80} +1.00000 q^{81} +6.00000 q^{82} -4.00000 q^{83} +2.00000 q^{85} +4.00000 q^{86} -2.00000 q^{87} +12.0000 q^{88} +10.0000 q^{89} -1.00000 q^{90} -8.00000 q^{92} -8.00000 q^{93} +8.00000 q^{94} -4.00000 q^{95} -5.00000 q^{96} +18.0000 q^{97} +7.00000 q^{98} +4.00000 q^{99} +O(q^{100})\)

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107	−0.353553	−	0.935414i	$-0.615027\pi$
$2$	−1.00000	−0.707107	−0.353553	+	0.935414i	$0.615027\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.00000	−0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−1.00000	−0.408248
$7$	0	0		−	1.00000i	$-0.5\pi$
$7$	0	0			1.00000i	$0.5\pi$
$8$	3.00000	1.06066
$9$	1.00000	0.333333
$10$	−1.00000	−0.316228
$11$	4.00000	1.20605	0.603023	−	0.797724i	$-0.293963\pi$
$11$	4.00000	1.20605	0.603023	+	0.797724i	$0.293963\pi$
$12$	−1.00000	−0.288675
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	0	0
$15$	1.00000	0.258199
$16$	−1.00000	−0.250000
$17$	2.00000	0.485071	0.242536	−	0.970143i	$-0.422021\pi$
$17$	2.00000	0.485071	0.242536	+	0.970143i	$0.422021\pi$
$18$	−1.00000	−0.235702
$19$	−4.00000	−0.917663	−0.458831	−	0.888523i	$-0.651732\pi$
$19$	−4.00000	−0.917663	−0.458831	+	0.888523i	$0.651732\pi$
$20$	−1.00000	−0.223607
$21$	0	0
$22$	−4.00000	−0.852803
$23$	8.00000	1.66812	0.834058	−	0.551677i	$-0.186012\pi$
$23$	8.00000	1.66812	0.834058	+	0.551677i	$0.186012\pi$
$24$	3.00000	0.612372
$25$	1.00000	0.200000
$26$	−1.00000	−0.196116
$27$	1.00000	0.192450
$28$	0	0
$29$	−2.00000	−0.371391	−0.185695	−	0.982607i	$-0.559454\pi$
$29$	−2.00000	−0.371391	−0.185695	+	0.982607i	$0.559454\pi$
$30$	−1.00000	−0.182574
$31$	−8.00000	−1.43684	−0.718421	−	0.695608i	$-0.755135\pi$
$31$	−8.00000	−1.43684	−0.718421	+	0.695608i	$0.755135\pi$
$32$	−5.00000	−0.883883
$33$	4.00000	0.696311
$34$	−2.00000	−0.342997
$35$	0	0
$36$	−1.00000	−0.166667
$37$	6.00000	0.986394	0.493197	−	0.869918i	$-0.335828\pi$
$37$	6.00000	0.986394	0.493197	+	0.869918i	$0.335828\pi$
$38$	4.00000	0.648886
$39$	1.00000	0.160128
$40$	3.00000	0.474342
$41$	−6.00000	−0.937043	−0.468521	−	0.883452i	$-0.655213\pi$
$41$	−6.00000	−0.937043	−0.468521	+	0.883452i	$0.655213\pi$
$42$	0	0
$43$	−4.00000	−0.609994	−0.304997	−	0.952353i	$-0.598656\pi$
$43$	−4.00000	−0.609994	−0.304997	+	0.952353i	$0.598656\pi$
$44$	−4.00000	−0.603023
$45$	1.00000	0.149071
$46$	−8.00000	−1.17954
$47$	−8.00000	−1.16692	−0.583460	−	0.812142i	$-0.698301\pi$
$47$	−8.00000	−1.16692	−0.583460	+	0.812142i	$0.698301\pi$
$48$	−1.00000	−0.144338
$49$	−7.00000	−1.00000
$50$	−1.00000	−0.141421
$51$	2.00000	0.280056
$52$	−1.00000	−0.138675
$53$	6.00000	0.824163	0.412082	−	0.911147i	$-0.364802\pi$
$53$	6.00000	0.824163	0.412082	+	0.911147i	$0.364802\pi$
$54$	−1.00000	−0.136083
$55$	4.00000	0.539360
$56$	0	0
$57$	−4.00000	−0.529813
$58$	2.00000	0.262613
$59$	−12.0000	−1.56227	−0.781133	−	0.624364i	$-0.785358\pi$
$59$	−12.0000	−1.56227	−0.781133	+	0.624364i	$0.785358\pi$
$60$	−1.00000	−0.129099
$61$	−2.00000	−0.256074	−0.128037	−	0.991769i	$-0.540868\pi$
$61$	−2.00000	−0.256074	−0.128037	+	0.991769i	$0.540868\pi$
$62$	8.00000	1.01600
$63$	0	0
$64$	7.00000	0.875000
$65$	1.00000	0.124035
$66$	−4.00000	−0.492366
$67$	−4.00000	−0.488678	−0.244339	−	0.969690i	$-0.578571\pi$
$67$	−4.00000	−0.488678	−0.244339	+	0.969690i	$0.578571\pi$
$68$	−2.00000	−0.242536
$69$	8.00000	0.963087
$70$	0	0
$71$	0	0		−	1.00000i	$-0.5\pi$
$71$	0	0			1.00000i	$0.5\pi$
$72$	3.00000	0.353553
$73$	−6.00000	−0.702247	−0.351123	−	0.936329i	$-0.614200\pi$
$73$	−6.00000	−0.702247	−0.351123	+	0.936329i	$0.614200\pi$
$74$	−6.00000	−0.697486
$75$	1.00000	0.115470
$76$	4.00000	0.458831
$77$	0	0
$78$	−1.00000	−0.113228
$79$	16.0000	1.80014	0.900070	−	0.435745i	$-0.143515\pi$
$79$	16.0000	1.80014	0.900070	+	0.435745i	$0.143515\pi$
$80$	−1.00000	−0.111803
$81$	1.00000	0.111111
$82$	6.00000	0.662589
$83$	−4.00000	−0.439057	−0.219529	−	0.975606i	$-0.570452\pi$
$83$	−4.00000	−0.439057	−0.219529	+	0.975606i	$0.570452\pi$
$84$	0	0
$85$	2.00000	0.216930
$86$	4.00000	0.431331
$87$	−2.00000	−0.214423
$88$	12.0000	1.27920
$89$	10.0000	1.06000	0.529999	−	0.847998i	$-0.322192\pi$
$89$	10.0000	1.06000	0.529999	+	0.847998i	$0.322192\pi$
$90$	−1.00000	−0.105409
$91$	0	0
$92$	−8.00000	−0.834058
$93$	−8.00000	−0.829561
$94$	8.00000	0.825137
$95$	−4.00000	−0.410391
$96$	−5.00000	−0.510310
$97$	18.0000	1.82762	0.913812	−	0.406138i	$-0.133125\pi$
$97$	18.0000	1.82762	0.913812	+	0.406138i	$0.133125\pi$
$98$	7.00000	0.707107
$99$	4.00000	0.402015
$100$	−1.00000	−0.100000
$101$	6.00000	0.597022	0.298511	−	0.954406i	$-0.403510\pi$
$101$	6.00000	0.597022	0.298511	+	0.954406i	$0.403510\pi$
$102$	−2.00000	−0.198030
$103$	−8.00000	−0.788263	−0.394132	−	0.919054i	$-0.628955\pi$
$103$	−8.00000	−0.788263	−0.394132	+	0.919054i	$0.628955\pi$
$104$	3.00000	0.294174
$105$	0	0
$106$	−6.00000	−0.582772
$107$	12.0000	1.16008	0.580042	−	0.814587i	$-0.303036\pi$
$107$	12.0000	1.16008	0.580042	+	0.814587i	$0.303036\pi$
$108$	−1.00000	−0.0962250
$109$	−2.00000	−0.191565	−0.0957826	−	0.995402i	$-0.530535\pi$
$109$	−2.00000	−0.191565	−0.0957826	+	0.995402i	$0.530535\pi$
$110$	−4.00000	−0.381385
$111$	6.00000	0.569495
$112$	0	0
$113$	2.00000	0.188144	0.0940721	−	0.995565i	$-0.470012\pi$
$113$	2.00000	0.188144	0.0940721	+	0.995565i	$0.470012\pi$
$114$	4.00000	0.374634
$115$	8.00000	0.746004
$116$	2.00000	0.185695
$117$	1.00000	0.0924500
$118$	12.0000	1.10469
$119$	0	0
$120$	3.00000	0.273861
$121$	5.00000	0.454545
$122$	2.00000	0.181071
$123$	−6.00000	−0.541002
$124$	8.00000	0.718421
$125$	1.00000	0.0894427
$126$	0	0
$127$	−16.0000	−1.41977	−0.709885	−	0.704317i	$-0.751253\pi$
$127$	−16.0000	−1.41977	−0.709885	+	0.704317i	$0.751253\pi$
$128$	3.00000	0.265165
$129$	−4.00000	−0.352180
$130$	−1.00000	−0.0877058
$131$	−12.0000	−1.04844	−0.524222	−	0.851581i	$-0.675644\pi$
$131$	−12.0000	−1.04844	−0.524222	+	0.851581i	$0.675644\pi$
$132$	−4.00000	−0.348155
$133$	0	0
$134$	4.00000	0.345547
$135$	1.00000	0.0860663
$136$	6.00000	0.514496
$137$	−6.00000	−0.512615	−0.256307	−	0.966595i	$-0.582506\pi$
$137$	−6.00000	−0.512615	−0.256307	+	0.966595i	$0.582506\pi$
$138$	−8.00000	−0.681005
$139$	−20.0000	−1.69638	−0.848189	−	0.529694i	$-0.822307\pi$
$139$	−20.0000	−1.69638	−0.848189	+	0.529694i	$0.822307\pi$
$140$	0	0
$141$	−8.00000	−0.673722
$142$	0	0
$143$	4.00000	0.334497
$144$	−1.00000	−0.0833333
$145$	−2.00000	−0.166091
$146$	6.00000	0.496564
$147$	−7.00000	−0.577350
$148$	−6.00000	−0.493197
$149$	−10.0000	−0.819232	−0.409616	−	0.912258i	$-0.634337\pi$
$149$	−10.0000	−0.819232	−0.409616	+	0.912258i	$0.634337\pi$
$150$	−1.00000	−0.0816497
$151$	0	0		−	1.00000i	$-0.5\pi$
$151$	0	0			1.00000i	$0.5\pi$
$152$	−12.0000	−0.973329
$153$	2.00000	0.161690
$154$	0	0
$155$	−8.00000	−0.642575
$156$	−1.00000	−0.0800641
$157$	−2.00000	−0.159617	−0.0798087	−	0.996810i	$-0.525431\pi$
$157$	−2.00000	−0.159617	−0.0798087	+	0.996810i	$0.525431\pi$
$158$	−16.0000	−1.27289
$159$	6.00000	0.475831
$160$	−5.00000	−0.395285
$161$	0	0
$162$	−1.00000	−0.0785674
$163$	−20.0000	−1.56652	−0.783260	−	0.621694i	$-0.786445\pi$
$163$	−20.0000	−1.56652	−0.783260	+	0.621694i	$0.786445\pi$
$164$	6.00000	0.468521
$165$	4.00000	0.311400
$166$	4.00000	0.310460
$167$	16.0000	1.23812	0.619059	−	0.785345i	$-0.287514\pi$
$167$	16.0000	1.23812	0.619059	+	0.785345i	$0.287514\pi$
$168$	0	0
$169$	1.00000	0.0769231
$170$	−2.00000	−0.153393
$171$	−4.00000	−0.305888
$172$	4.00000	0.304997
$173$	−2.00000	−0.152057	−0.0760286	−	0.997106i	$-0.524224\pi$
$173$	−2.00000	−0.152057	−0.0760286	+	0.997106i	$0.524224\pi$
$174$	2.00000	0.151620
$175$	0	0
$176$	−4.00000	−0.301511
$177$	−12.0000	−0.901975
$178$	−10.0000	−0.749532
$179$	−12.0000	−0.896922	−0.448461	−	0.893802i	$-0.648028\pi$
$179$	−12.0000	−0.896922	−0.448461	+	0.893802i	$0.648028\pi$
$180$	−1.00000	−0.0745356
$181$	22.0000	1.63525	0.817624	−	0.575753i	$-0.195291\pi$
$181$	22.0000	1.63525	0.817624	+	0.575753i	$0.195291\pi$
$182$	0	0
$183$	−2.00000	−0.147844
$184$	24.0000	1.76930
$185$	6.00000	0.441129
$186$	8.00000	0.586588
$187$	8.00000	0.585018
$188$	8.00000	0.583460
$189$	0	0
$190$	4.00000	0.290191
$191$	16.0000	1.15772	0.578860	−	0.815427i	$-0.303498\pi$
$191$	16.0000	1.15772	0.578860	+	0.815427i	$0.303498\pi$
$192$	7.00000	0.505181
$193$	−14.0000	−1.00774	−0.503871	−	0.863779i	$-0.668091\pi$
$193$	−14.0000	−1.00774	−0.503871	+	0.863779i	$0.668091\pi$
$194$	−18.0000	−1.29232
$195$	1.00000	0.0716115
$196$	7.00000	0.500000
$197$	6.00000	0.427482	0.213741	−	0.976890i	$-0.431435\pi$
$197$	6.00000	0.427482	0.213741	+	0.976890i	$0.431435\pi$
$198$	−4.00000	−0.284268
$199$	−8.00000	−0.567105	−0.283552	−	0.958957i	$-0.591513\pi$
$199$	−8.00000	−0.567105	−0.283552	+	0.958957i	$0.591513\pi$
$200$	3.00000	0.212132
$201$	−4.00000	−0.282138
$202$	−6.00000	−0.422159
$203$	0	0
$204$	−2.00000	−0.140028
$205$	−6.00000	−0.419058
$206$	8.00000	0.557386
$207$	8.00000	0.556038
$208$	−1.00000	−0.0693375
$209$	−16.0000	−1.10674
$210$	0	0
$211$	20.0000	1.37686	0.688428	−	0.725304i	$-0.258301\pi$
$211$	20.0000	1.37686	0.688428	+	0.725304i	$0.258301\pi$
$212$	−6.00000	−0.412082
$213$	0	0
$214$	−12.0000	−0.820303
$215$	−4.00000	−0.272798
$216$	3.00000	0.204124
$217$	0	0
$218$	2.00000	0.135457
$219$	−6.00000	−0.405442
$220$	−4.00000	−0.269680
$221$	2.00000	0.134535
$222$	−6.00000	−0.402694
$223$	−24.0000	−1.60716	−0.803579	−	0.595198i	$-0.797074\pi$
$223$	−24.0000	−1.60716	−0.803579	+	0.595198i	$0.797074\pi$
$224$	0	0
$225$	1.00000	0.0666667
$226$	−2.00000	−0.133038
$227$	12.0000	0.796468	0.398234	−	0.917284i	$-0.369623\pi$
$227$	12.0000	0.796468	0.398234	+	0.917284i	$0.369623\pi$
$228$	4.00000	0.264906
$229$	22.0000	1.45380	0.726900	−	0.686743i	$-0.240960\pi$
$229$	22.0000	1.45380	0.726900	+	0.686743i	$0.240960\pi$
$230$	−8.00000	−0.527504
$231$	0	0
$232$	−6.00000	−0.393919
$233$	26.0000	1.70332	0.851658	−	0.524097i	$-0.175597\pi$
$233$	26.0000	1.70332	0.851658	+	0.524097i	$0.175597\pi$
$234$	−1.00000	−0.0653720
$235$	−8.00000	−0.521862
$236$	12.0000	0.781133
$237$	16.0000	1.03931
$238$	0	0
$239$	−24.0000	−1.55243	−0.776215	−	0.630468i	$-0.782863\pi$
$239$	−24.0000	−1.55243	−0.776215	+	0.630468i	$0.782863\pi$
$240$	−1.00000	−0.0645497
$241$	−14.0000	−0.901819	−0.450910	−	0.892570i	$-0.648900\pi$
$241$	−14.0000	−0.901819	−0.450910	+	0.892570i	$0.648900\pi$
$242$	−5.00000	−0.321412
$243$	1.00000	0.0641500
$244$	2.00000	0.128037
$245$	−7.00000	−0.447214
$246$	6.00000	0.382546
$247$	−4.00000	−0.254514
$248$	−24.0000	−1.52400
$249$	−4.00000	−0.253490
$250$	−1.00000	−0.0632456
$251$	−4.00000	−0.252478	−0.126239	−	0.992000i	$-0.540291\pi$
$251$	−4.00000	−0.252478	−0.126239	+	0.992000i	$0.540291\pi$
$252$	0	0
$253$	32.0000	2.01182
$254$	16.0000	1.00393
$255$	2.00000	0.125245
$256$	−17.0000	−1.06250
$257$	18.0000	1.12281	0.561405	−	0.827541i	$-0.310261\pi$
$257$	18.0000	1.12281	0.561405	+	0.827541i	$0.310261\pi$
$258$	4.00000	0.249029
$259$	0	0
$260$	−1.00000	−0.0620174
$261$	−2.00000	−0.123797
$262$	12.0000	0.741362
$263$	−24.0000	−1.47990	−0.739952	−	0.672660i	$-0.765152\pi$
$263$	−24.0000	−1.47990	−0.739952	+	0.672660i	$0.765152\pi$
$264$	12.0000	0.738549
$265$	6.00000	0.368577
$266$	0	0
$267$	10.0000	0.611990
$268$	4.00000	0.244339
$269$	14.0000	0.853595	0.426798	−	0.904347i	$-0.359642\pi$
$269$	14.0000	0.853595	0.426798	+	0.904347i	$0.359642\pi$
$270$	−1.00000	−0.0608581
$271$	−8.00000	−0.485965	−0.242983	−	0.970031i	$-0.578126\pi$
$271$	−8.00000	−0.485965	−0.242983	+	0.970031i	$0.578126\pi$
$272$	−2.00000	−0.121268
$273$	0	0
$274$	6.00000	0.362473
$275$	4.00000	0.241209
$276$	−8.00000	−0.481543
$277$	−10.0000	−0.600842	−0.300421	−	0.953807i	$-0.597127\pi$
$277$	−10.0000	−0.600842	−0.300421	+	0.953807i	$0.597127\pi$
$278$	20.0000	1.19952
$279$	−8.00000	−0.478947
$280$	0	0
$281$	−22.0000	−1.31241	−0.656205	−	0.754583i	$-0.727839\pi$
$281$	−22.0000	−1.31241	−0.656205	+	0.754583i	$0.727839\pi$
$282$	8.00000	0.476393
$283$	−20.0000	−1.18888	−0.594438	−	0.804141i	$-0.702626\pi$
$283$	−20.0000	−1.18888	−0.594438	+	0.804141i	$0.702626\pi$
$284$	0	0
$285$	−4.00000	−0.236940
$286$	−4.00000	−0.236525
$287$	0	0
$288$	−5.00000	−0.294628
$289$	−13.0000	−0.764706
$290$	2.00000	0.117444
$291$	18.0000	1.05518
$292$	6.00000	0.351123
$293$	6.00000	0.350524	0.175262	−	0.984522i	$-0.443923\pi$
$293$	6.00000	0.350524	0.175262	+	0.984522i	$0.443923\pi$
$294$	7.00000	0.408248
$295$	−12.0000	−0.698667
$296$	18.0000	1.04623
$297$	4.00000	0.232104
$298$	10.0000	0.579284
$299$	8.00000	0.462652
$300$	−1.00000	−0.0577350
$301$	0	0
$302$	0	0
$303$	6.00000	0.344691
$304$	4.00000	0.229416
$305$	−2.00000	−0.114520
$306$	−2.00000	−0.114332
$307$	−4.00000	−0.228292	−0.114146	−	0.993464i	$-0.536413\pi$
$307$	−4.00000	−0.228292	−0.114146	+	0.993464i	$0.536413\pi$
$308$	0	0
$309$	−8.00000	−0.455104
$310$	8.00000	0.454369
$311$	24.0000	1.36092	0.680458	−	0.732787i	$-0.261781\pi$
$311$	24.0000	1.36092	0.680458	+	0.732787i	$0.261781\pi$
$312$	3.00000	0.169842
$313$	26.0000	1.46961	0.734803	−	0.678280i	$-0.237274\pi$
$313$	26.0000	1.46961	0.734803	+	0.678280i	$0.237274\pi$
$314$	2.00000	0.112867
$315$	0	0
$316$	−16.0000	−0.900070
$317$	30.0000	1.68497	0.842484	−	0.538721i	$-0.181092\pi$
$317$	30.0000	1.68497	0.842484	+	0.538721i	$0.181092\pi$
$318$	−6.00000	−0.336463
$319$	−8.00000	−0.447914
$320$	7.00000	0.391312
$321$	12.0000	0.669775
$322$	0	0
$323$	−8.00000	−0.445132
$324$	−1.00000	−0.0555556
$325$	1.00000	0.0554700
$326$	20.0000	1.10770
$327$	−2.00000	−0.110600
$328$	−18.0000	−0.993884
$329$	0	0
$330$	−4.00000	−0.220193
$331$	20.0000	1.09930	0.549650	−	0.835395i	$-0.314761\pi$
$331$	20.0000	1.09930	0.549650	+	0.835395i	$0.314761\pi$
$332$	4.00000	0.219529
$333$	6.00000	0.328798
$334$	−16.0000	−0.875481
$335$	−4.00000	−0.218543
$336$	0	0
$337$	−14.0000	−0.762629	−0.381314	−	0.924445i	$-0.624528\pi$
$337$	−14.0000	−0.762629	−0.381314	+	0.924445i	$0.624528\pi$
$338$	−1.00000	−0.0543928
$339$	2.00000	0.108625
$340$	−2.00000	−0.108465
$341$	−32.0000	−1.73290
$342$	4.00000	0.216295
$343$	0	0
$344$	−12.0000	−0.646997
$345$	8.00000	0.430706
$346$	2.00000	0.107521
$347$	−4.00000	−0.214731	−0.107366	−	0.994220i	$-0.534242\pi$
$347$	−4.00000	−0.214731	−0.107366	+	0.994220i	$0.534242\pi$
$348$	2.00000	0.107211
$349$	14.0000	0.749403	0.374701	−	0.927146i	$-0.377745\pi$
$349$	14.0000	0.749403	0.374701	+	0.927146i	$0.377745\pi$
$350$	0	0
$351$	1.00000	0.0533761
$352$	−20.0000	−1.06600
$353$	−14.0000	−0.745145	−0.372572	−	0.928003i	$-0.621524\pi$
$353$	−14.0000	−0.745145	−0.372572	+	0.928003i	$0.621524\pi$
$354$	12.0000	0.637793
$355$	0	0
$356$	−10.0000	−0.529999
$357$	0	0
$358$	12.0000	0.634220
$359$	16.0000	0.844448	0.422224	−	0.906492i	$-0.361250\pi$
$359$	16.0000	0.844448	0.422224	+	0.906492i	$0.361250\pi$
$360$	3.00000	0.158114
$361$	−3.00000	−0.157895
$362$	−22.0000	−1.15629
$363$	5.00000	0.262432
$364$	0	0
$365$	−6.00000	−0.314054
$366$	2.00000	0.104542
$367$	−16.0000	−0.835193	−0.417597	−	0.908633i	$-0.637127\pi$
$367$	−16.0000	−0.835193	−0.417597	+	0.908633i	$0.637127\pi$
$368$	−8.00000	−0.417029
$369$	−6.00000	−0.312348
$370$	−6.00000	−0.311925
$371$	0	0
$372$	8.00000	0.414781
$373$	22.0000	1.13912	0.569558	−	0.821951i	$-0.307114\pi$
$373$	22.0000	1.13912	0.569558	+	0.821951i	$0.307114\pi$
$374$	−8.00000	−0.413670
$375$	1.00000	0.0516398
$376$	−24.0000	−1.23771
$377$	−2.00000	−0.103005
$378$	0	0
$379$	36.0000	1.84920	0.924598	−	0.380945i	$-0.124401\pi$
$379$	36.0000	1.84920	0.924598	+	0.380945i	$0.124401\pi$
$380$	4.00000	0.205196
$381$	−16.0000	−0.819705
$382$	−16.0000	−0.818631
$383$	24.0000	1.22634	0.613171	−	0.789950i	$-0.289894\pi$
$383$	24.0000	1.22634	0.613171	+	0.789950i	$0.289894\pi$
$384$	3.00000	0.153093
$385$	0	0
$386$	14.0000	0.712581
$387$	−4.00000	−0.203331
$388$	−18.0000	−0.913812
$389$	6.00000	0.304212	0.152106	−	0.988364i	$-0.451394\pi$
$389$	6.00000	0.304212	0.152106	+	0.988364i	$0.451394\pi$
$390$	−1.00000	−0.0506370
$391$	16.0000	0.809155
$392$	−21.0000	−1.06066
$393$	−12.0000	−0.605320
$394$	−6.00000	−0.302276
$395$	16.0000	0.805047
$396$	−4.00000	−0.201008
$397$	14.0000	0.702640	0.351320	−	0.936255i	$-0.385733\pi$
$397$	14.0000	0.702640	0.351320	+	0.936255i	$0.385733\pi$
$398$	8.00000	0.401004
$399$	0	0
$400$	−1.00000	−0.0500000
$401$	−30.0000	−1.49813	−0.749064	−	0.662497i	$-0.769497\pi$
$401$	−30.0000	−1.49813	−0.749064	+	0.662497i	$0.769497\pi$
$402$	4.00000	0.199502
$403$	−8.00000	−0.398508
$404$	−6.00000	−0.298511
$405$	1.00000	0.0496904
$406$	0	0
$407$	24.0000	1.18964
$408$	6.00000	0.297044
$409$	−38.0000	−1.87898	−0.939490	−	0.342578i	$-0.888700\pi$
$409$	−38.0000	−1.87898	−0.939490	+	0.342578i	$0.888700\pi$
$410$	6.00000	0.296319
$411$	−6.00000	−0.295958
$412$	8.00000	0.394132
$413$	0	0
$414$	−8.00000	−0.393179
$415$	−4.00000	−0.196352
$416$	−5.00000	−0.245145
$417$	−20.0000	−0.979404
$418$	16.0000	0.782586
$419$	20.0000	0.977064	0.488532	−	0.872546i	$-0.337533\pi$
$419$	20.0000	0.977064	0.488532	+	0.872546i	$0.337533\pi$
$420$	0	0
$421$	−10.0000	−0.487370	−0.243685	−	0.969854i	$-0.578356\pi$
$421$	−10.0000	−0.487370	−0.243685	+	0.969854i	$0.578356\pi$
$422$	−20.0000	−0.973585
$423$	−8.00000	−0.388973
$424$	18.0000	0.874157
$425$	2.00000	0.0970143
$426$	0	0
$427$	0	0
$428$	−12.0000	−0.580042
$429$	4.00000	0.193122
$430$	4.00000	0.192897
$431$	8.00000	0.385346	0.192673	−	0.981263i	$-0.438284\pi$
$431$	8.00000	0.385346	0.192673	+	0.981263i	$0.438284\pi$
$432$	−1.00000	−0.0481125
$433$	18.0000	0.865025	0.432512	−	0.901628i	$-0.357627\pi$
$433$	18.0000	0.865025	0.432512	+	0.901628i	$0.357627\pi$
$434$	0	0
$435$	−2.00000	−0.0958927
$436$	2.00000	0.0957826
$437$	−32.0000	−1.53077
$438$	6.00000	0.286691
$439$	−24.0000	−1.14546	−0.572729	−	0.819745i	$-0.694115\pi$
$439$	−24.0000	−1.14546	−0.572729	+	0.819745i	$0.694115\pi$
$440$	12.0000	0.572078
$441$	−7.00000	−0.333333
$442$	−2.00000	−0.0951303
$443$	−4.00000	−0.190046	−0.0950229	−	0.995475i	$-0.530292\pi$
$443$	−4.00000	−0.190046	−0.0950229	+	0.995475i	$0.530292\pi$
$444$	−6.00000	−0.284747
$445$	10.0000	0.474045
$446$	24.0000	1.13643
$447$	−10.0000	−0.472984
$448$	0	0
$449$	18.0000	0.849473	0.424736	−	0.905317i	$-0.360367\pi$
$449$	18.0000	0.849473	0.424736	+	0.905317i	$0.360367\pi$
$450$	−1.00000	−0.0471405
$451$	−24.0000	−1.13012
$452$	−2.00000	−0.0940721
$453$	0	0
$454$	−12.0000	−0.563188
$455$	0	0
$456$	−12.0000	−0.561951
$457$	26.0000	1.21623	0.608114	−	0.793849i	$-0.291926\pi$
$457$	26.0000	1.21623	0.608114	+	0.793849i	$0.291926\pi$
$458$	−22.0000	−1.02799
$459$	2.00000	0.0933520
$460$	−8.00000	−0.373002
$461$	−18.0000	−0.838344	−0.419172	−	0.907907i	$-0.637680\pi$
$461$	−18.0000	−0.838344	−0.419172	+	0.907907i	$0.637680\pi$
$462$	0	0
$463$	8.00000	0.371792	0.185896	−	0.982569i	$-0.440481\pi$
$463$	8.00000	0.371792	0.185896	+	0.982569i	$0.440481\pi$
$464$	2.00000	0.0928477
$465$	−8.00000	−0.370991
$466$	−26.0000	−1.20443
$467$	4.00000	0.185098	0.0925490	−	0.995708i	$-0.470499\pi$
$467$	4.00000	0.185098	0.0925490	+	0.995708i	$0.470499\pi$
$468$	−1.00000	−0.0462250
$469$	0	0
$470$	8.00000	0.369012
$471$	−2.00000	−0.0921551
$472$	−36.0000	−1.65703
$473$	−16.0000	−0.735681
$474$	−16.0000	−0.734904
$475$	−4.00000	−0.183533
$476$	0	0
$477$	6.00000	0.274721
$478$	24.0000	1.09773
$479$	8.00000	0.365529	0.182765	−	0.983157i	$-0.441495\pi$
$479$	8.00000	0.365529	0.182765	+	0.983157i	$0.441495\pi$
$480$	−5.00000	−0.228218
$481$	6.00000	0.273576
$482$	14.0000	0.637683
$483$	0	0
$484$	−5.00000	−0.227273
$485$	18.0000	0.817338
$486$	−1.00000	−0.0453609
$487$	16.0000	0.725029	0.362515	−	0.931978i	$-0.381918\pi$
$487$	16.0000	0.725029	0.362515	+	0.931978i	$0.381918\pi$
$488$	−6.00000	−0.271607
$489$	−20.0000	−0.904431
$490$	7.00000	0.316228
$491$	−20.0000	−0.902587	−0.451294	−	0.892375i	$-0.649037\pi$
$491$	−20.0000	−0.902587	−0.451294	+	0.892375i	$0.649037\pi$
$492$	6.00000	0.270501
$493$	−4.00000	−0.180151
$494$	4.00000	0.179969
$495$	4.00000	0.179787
$496$	8.00000	0.359211
$497$	0	0
$498$	4.00000	0.179244
$499$	28.0000	1.25345	0.626726	−	0.779240i	$-0.284395\pi$
$499$	28.0000	1.25345	0.626726	+	0.779240i	$0.284395\pi$
$500$	−1.00000	−0.0447214
$501$	16.0000	0.714827
$502$	4.00000	0.178529
$503$	24.0000	1.07011	0.535054	−	0.844818i	$-0.320291\pi$
$503$	24.0000	1.07011	0.535054	+	0.844818i	$0.320291\pi$
$504$	0	0
$505$	6.00000	0.266996
$506$	−32.0000	−1.42257
$507$	1.00000	0.0444116
$508$	16.0000	0.709885
$509$	30.0000	1.32973	0.664863	−	0.746965i	$-0.268490\pi$
$509$	30.0000	1.32973	0.664863	+	0.746965i	$0.268490\pi$
$510$	−2.00000	−0.0885615
$511$	0	0
$512$	11.0000	0.486136
$513$	−4.00000	−0.176604
$514$	−18.0000	−0.793946
$515$	−8.00000	−0.352522
$516$	4.00000	0.176090
$517$	−32.0000	−1.40736
$518$	0	0
$519$	−2.00000	−0.0877903
$520$	3.00000	0.131559
$521$	−22.0000	−0.963837	−0.481919	−	0.876216i	$-0.660060\pi$
$521$	−22.0000	−0.963837	−0.481919	+	0.876216i	$0.660060\pi$
$522$	2.00000	0.0875376
$523$	−20.0000	−0.874539	−0.437269	−	0.899331i	$-0.644054\pi$
$523$	−20.0000	−0.874539	−0.437269	+	0.899331i	$0.644054\pi$
$524$	12.0000	0.524222
$525$	0	0
$526$	24.0000	1.04645
$527$	−16.0000	−0.696971
$528$	−4.00000	−0.174078
$529$	41.0000	1.78261
$530$	−6.00000	−0.260623
$531$	−12.0000	−0.520756
$532$	0	0
$533$	−6.00000	−0.259889
$534$	−10.0000	−0.432742
$535$	12.0000	0.518805
$536$	−12.0000	−0.518321
$537$	−12.0000	−0.517838
$538$	−14.0000	−0.603583
$539$	−28.0000	−1.20605
$540$	−1.00000	−0.0430331
$541$	14.0000	0.601907	0.300954	−	0.953639i	$-0.402695\pi$
$541$	14.0000	0.601907	0.300954	+	0.953639i	$0.402695\pi$
$542$	8.00000	0.343629
$543$	22.0000	0.944110
$544$	−10.0000	−0.428746
$545$	−2.00000	−0.0856706
$546$	0	0
$547$	36.0000	1.53925	0.769624	−	0.638497i	$-0.220443\pi$
$547$	36.0000	1.53925	0.769624	+	0.638497i	$0.220443\pi$
$548$	6.00000	0.256307
$549$	−2.00000	−0.0853579
$550$	−4.00000	−0.170561
$551$	8.00000	0.340811
$552$	24.0000	1.02151
$553$	0	0
$554$	10.0000	0.424859
$555$	6.00000	0.254686
$556$	20.0000	0.848189
$557$	−18.0000	−0.762684	−0.381342	−	0.924434i	$-0.624538\pi$
$557$	−18.0000	−0.762684	−0.381342	+	0.924434i	$0.624538\pi$
$558$	8.00000	0.338667
$559$	−4.00000	−0.169182
$560$	0	0
$561$	8.00000	0.337760
$562$	22.0000	0.928014
$563$	4.00000	0.168580	0.0842900	−	0.996441i	$-0.473138\pi$
$563$	4.00000	0.168580	0.0842900	+	0.996441i	$0.473138\pi$
$564$	8.00000	0.336861
$565$	2.00000	0.0841406
$566$	20.0000	0.840663
$567$	0	0
$568$	0	0
$569$	−38.0000	−1.59304	−0.796521	−	0.604610i	$-0.793329\pi$
$569$	−38.0000	−1.59304	−0.796521	+	0.604610i	$0.793329\pi$
$570$	4.00000	0.167542
$571$	44.0000	1.84134	0.920671	−	0.390339i	$-0.127642\pi$
$571$	44.0000	1.84134	0.920671	+	0.390339i	$0.127642\pi$
$572$	−4.00000	−0.167248
$573$	16.0000	0.668410
$574$	0	0
$575$	8.00000	0.333623
$576$	7.00000	0.291667
$577$	18.0000	0.749350	0.374675	−	0.927156i	$-0.377754\pi$
$577$	18.0000	0.749350	0.374675	+	0.927156i	$0.377754\pi$
$578$	13.0000	0.540729
$579$	−14.0000	−0.581820
$580$	2.00000	0.0830455
$581$	0	0
$582$	−18.0000	−0.746124
$583$	24.0000	0.993978
$584$	−18.0000	−0.744845
$585$	1.00000	0.0413449
$586$	−6.00000	−0.247858
$587$	−12.0000	−0.495293	−0.247647	−	0.968850i	$-0.579657\pi$
$587$	−12.0000	−0.495293	−0.247647	+	0.968850i	$0.579657\pi$
$588$	7.00000	0.288675
$589$	32.0000	1.31854
$590$	12.0000	0.494032
$591$	6.00000	0.246807
$592$	−6.00000	−0.246598
$593$	−30.0000	−1.23195	−0.615976	−	0.787765i	$-0.711238\pi$
$593$	−30.0000	−1.23195	−0.615976	+	0.787765i	$0.711238\pi$
$594$	−4.00000	−0.164122
$595$	0	0
$596$	10.0000	0.409616
$597$	−8.00000	−0.327418
$598$	−8.00000	−0.327144
$599$	40.0000	1.63436	0.817178	−	0.576386i	$-0.195537\pi$
$599$	40.0000	1.63436	0.817178	+	0.576386i	$0.195537\pi$
$600$	3.00000	0.122474
$601$	−38.0000	−1.55005	−0.775026	−	0.631929i	$-0.782263\pi$
$601$	−38.0000	−1.55005	−0.775026	+	0.631929i	$0.782263\pi$
$602$	0	0
$603$	−4.00000	−0.162893
$604$	0	0
$605$	5.00000	0.203279
$606$	−6.00000	−0.243733
$607$	32.0000	1.29884	0.649420	−	0.760430i	$-0.275012\pi$
$607$	32.0000	1.29884	0.649420	+	0.760430i	$0.275012\pi$
$608$	20.0000	0.811107
$609$	0	0
$610$	2.00000	0.0809776
$611$	−8.00000	−0.323645
$612$	−2.00000	−0.0808452
$613$	6.00000	0.242338	0.121169	−	0.992632i	$-0.461336\pi$
$613$	6.00000	0.242338	0.121169	+	0.992632i	$0.461336\pi$
$614$	4.00000	0.161427
$615$	−6.00000	−0.241943
$616$	0	0
$617$	−38.0000	−1.52982	−0.764911	−	0.644136i	$-0.777217\pi$
$617$	−38.0000	−1.52982	−0.764911	+	0.644136i	$0.777217\pi$
$618$	8.00000	0.321807
$619$	4.00000	0.160774	0.0803868	−	0.996764i	$-0.474384\pi$
$619$	4.00000	0.160774	0.0803868	+	0.996764i	$0.474384\pi$
$620$	8.00000	0.321288
$621$	8.00000	0.321029
$622$	−24.0000	−0.962312
$623$	0	0
$624$	−1.00000	−0.0400320
$625$	1.00000	0.0400000
$626$	−26.0000	−1.03917
$627$	−16.0000	−0.638978
$628$	2.00000	0.0798087
$629$	12.0000	0.478471
$630$	0	0
$631$	0	0		−	1.00000i	$-0.5\pi$
$631$	0	0			1.00000i	$0.5\pi$
$632$	48.0000	1.90934
$633$	20.0000	0.794929
$634$	−30.0000	−1.19145
$635$	−16.0000	−0.634941
$636$	−6.00000	−0.237915
$637$	−7.00000	−0.277350
$638$	8.00000	0.316723
$639$	0	0
$640$	3.00000	0.118585
$641$	−30.0000	−1.18493	−0.592464	−	0.805597i	$-0.701845\pi$
$641$	−30.0000	−1.18493	−0.592464	+	0.805597i	$0.701845\pi$
$642$	−12.0000	−0.473602
$643$	28.0000	1.10421	0.552106	−	0.833774i	$-0.313824\pi$
$643$	28.0000	1.10421	0.552106	+	0.833774i	$0.313824\pi$
$644$	0	0
$645$	−4.00000	−0.157500
$646$	8.00000	0.314756
$647$	24.0000	0.943537	0.471769	−	0.881722i	$-0.343616\pi$
$647$	24.0000	0.943537	0.471769	+	0.881722i	$0.343616\pi$
$648$	3.00000	0.117851
$649$	−48.0000	−1.88416
$650$	−1.00000	−0.0392232
$651$	0	0
$652$	20.0000	0.783260
$653$	30.0000	1.17399	0.586995	−	0.809590i	$-0.300311\pi$
$653$	30.0000	1.17399	0.586995	+	0.809590i	$0.300311\pi$
$654$	2.00000	0.0782062
$655$	−12.0000	−0.468879
$656$	6.00000	0.234261
$657$	−6.00000	−0.234082
$658$	0	0
$659$	36.0000	1.40236	0.701180	−	0.712984i	$-0.252657\pi$
$659$	36.0000	1.40236	0.701180	+	0.712984i	$0.252657\pi$
$660$	−4.00000	−0.155700
$661$	38.0000	1.47803	0.739014	−	0.673690i	$-0.235292\pi$
$661$	38.0000	1.47803	0.739014	+	0.673690i	$0.235292\pi$
$662$	−20.0000	−0.777322
$663$	2.00000	0.0776736
$664$	−12.0000	−0.465690
$665$	0	0
$666$	−6.00000	−0.232495
$667$	−16.0000	−0.619522
$668$	−16.0000	−0.619059
$669$	−24.0000	−0.927894
$670$	4.00000	0.154533
$671$	−8.00000	−0.308837
$672$	0	0
$673$	34.0000	1.31060	0.655302	−	0.755367i	$-0.272541\pi$
$673$	34.0000	1.31060	0.655302	+	0.755367i	$0.272541\pi$
$674$	14.0000	0.539260
$675$	1.00000	0.0384900
$676$	−1.00000	−0.0384615
$677$	−10.0000	−0.384331	−0.192166	−	0.981363i	$-0.561551\pi$
$677$	−10.0000	−0.384331	−0.192166	+	0.981363i	$0.561551\pi$
$678$	−2.00000	−0.0768095
$679$	0	0
$680$	6.00000	0.230089
$681$	12.0000	0.459841
$682$	32.0000	1.22534
$683$	4.00000	0.153056	0.0765279	−	0.997067i	$-0.475617\pi$
$683$	4.00000	0.153056	0.0765279	+	0.997067i	$0.475617\pi$
$684$	4.00000	0.152944
$685$	−6.00000	−0.229248
$686$	0	0
$687$	22.0000	0.839352
$688$	4.00000	0.152499
$689$	6.00000	0.228582
$690$	−8.00000	−0.304555
$691$	−36.0000	−1.36950	−0.684752	−	0.728776i	$-0.740090\pi$
$691$	−36.0000	−1.36950	−0.684752	+	0.728776i	$0.740090\pi$
$692$	2.00000	0.0760286
$693$	0	0
$694$	4.00000	0.151838
$695$	−20.0000	−0.758643
$696$	−6.00000	−0.227429
$697$	−12.0000	−0.454532
$698$	−14.0000	−0.529908
$699$	26.0000	0.983410
$700$	0	0
$701$	−34.0000	−1.28416	−0.642081	−	0.766637i	$-0.721929\pi$
$701$	−34.0000	−1.28416	−0.642081	+	0.766637i	$0.721929\pi$
$702$	−1.00000	−0.0377426
$703$	−24.0000	−0.905177
$704$	28.0000	1.05529
$705$	−8.00000	−0.301297
$706$	14.0000	0.526897
$707$	0	0
$708$	12.0000	0.450988
$709$	−10.0000	−0.375558	−0.187779	−	0.982211i	$-0.560129\pi$
$709$	−10.0000	−0.375558	−0.187779	+	0.982211i	$0.560129\pi$
$710$	0	0
$711$	16.0000	0.600047
$712$	30.0000	1.12430
$713$	−64.0000	−2.39682
$714$	0	0
$715$	4.00000	0.149592
$716$	12.0000	0.448461
$717$	−24.0000	−0.896296
$718$	−16.0000	−0.597115
$719$	−48.0000	−1.79010	−0.895049	−	0.445968i	$-0.852860\pi$
$719$	−48.0000	−1.79010	−0.895049	+	0.445968i	$0.852860\pi$
$720$	−1.00000	−0.0372678
$721$	0	0
$722$	3.00000	0.111648
$723$	−14.0000	−0.520666
$724$	−22.0000	−0.817624
$725$	−2.00000	−0.0742781
$726$	−5.00000	−0.185567
$727$	−24.0000	−0.890111	−0.445055	−	0.895503i	$-0.646816\pi$
$727$	−24.0000	−0.890111	−0.445055	+	0.895503i	$0.646816\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	6.00000	0.222070
$731$	−8.00000	−0.295891
$732$	2.00000	0.0739221
$733$	30.0000	1.10808	0.554038	−	0.832492i	$-0.313086\pi$
$733$	30.0000	1.10808	0.554038	+	0.832492i	$0.313086\pi$
$734$	16.0000	0.590571
$735$	−7.00000	−0.258199
$736$	−40.0000	−1.47442
$737$	−16.0000	−0.589368
$738$	6.00000	0.220863
$739$	−4.00000	−0.147142	−0.0735712	−	0.997290i	$-0.523440\pi$
$739$	−4.00000	−0.147142	−0.0735712	+	0.997290i	$0.523440\pi$
$740$	−6.00000	−0.220564
$741$	−4.00000	−0.146944
$742$	0	0
$743$	0	0		−	1.00000i	$-0.5\pi$
$743$	0	0			1.00000i	$0.5\pi$
$744$	−24.0000	−0.879883
$745$	−10.0000	−0.366372
$746$	−22.0000	−0.805477
$747$	−4.00000	−0.146352
$748$	−8.00000	−0.292509
$749$	0	0
$750$	−1.00000	−0.0365148
$751$	0	0		−	1.00000i	$-0.5\pi$
$751$	0	0			1.00000i	$0.5\pi$
$752$	8.00000	0.291730
$753$	−4.00000	−0.145768
$754$	2.00000	0.0728357
$755$	0	0
$756$	0	0
$757$	−42.0000	−1.52652	−0.763258	−	0.646094i	$-0.776401\pi$
$757$	−42.0000	−1.52652	−0.763258	+	0.646094i	$0.776401\pi$
$758$	−36.0000	−1.30758
$759$	32.0000	1.16153
$760$	−12.0000	−0.435286
$761$	10.0000	0.362500	0.181250	−	0.983437i	$-0.441986\pi$
$761$	10.0000	0.362500	0.181250	+	0.983437i	$0.441986\pi$
$762$	16.0000	0.579619
$763$	0	0
$764$	−16.0000	−0.578860
$765$	2.00000	0.0723102
$766$	−24.0000	−0.867155
$767$	−12.0000	−0.433295
$768$	−17.0000	−0.613435
$769$	−30.0000	−1.08183	−0.540914	−	0.841078i	$-0.681921\pi$
$769$	−30.0000	−1.08183	−0.540914	+	0.841078i	$0.681921\pi$
$770$	0	0
$771$	18.0000	0.648254
$772$	14.0000	0.503871
$773$	6.00000	0.215805	0.107903	−	0.994161i	$-0.465587\pi$
$773$	6.00000	0.215805	0.107903	+	0.994161i	$0.465587\pi$
$774$	4.00000	0.143777
$775$	−8.00000	−0.287368
$776$	54.0000	1.93849
$777$	0	0
$778$	−6.00000	−0.215110
$779$	24.0000	0.859889
$780$	−1.00000	−0.0358057
$781$	0	0
$782$	−16.0000	−0.572159
$783$	−2.00000	−0.0714742
$784$	7.00000	0.250000
$785$	−2.00000	−0.0713831
$786$	12.0000	0.428026
$787$	−4.00000	−0.142585	−0.0712923	−	0.997455i	$-0.522712\pi$
$787$	−4.00000	−0.142585	−0.0712923	+	0.997455i	$0.522712\pi$
$788$	−6.00000	−0.213741
$789$	−24.0000	−0.854423
$790$	−16.0000	−0.569254
$791$	0	0
$792$	12.0000	0.426401
$793$	−2.00000	−0.0710221
$794$	−14.0000	−0.496841
$795$	6.00000	0.212798
$796$	8.00000	0.283552
$797$	46.0000	1.62940	0.814702	−	0.579880i	$-0.196901\pi$
$797$	46.0000	1.62940	0.814702	+	0.579880i	$0.196901\pi$
$798$	0	0
$799$	−16.0000	−0.566039
$800$	−5.00000	−0.176777
$801$	10.0000	0.353333
$802$	30.0000	1.05934
$803$	−24.0000	−0.846942
$804$	4.00000	0.141069
$805$	0	0
$806$	8.00000	0.281788
$807$	14.0000	0.492823
$808$	18.0000	0.633238
$809$	42.0000	1.47664	0.738321	−	0.674450i	$-0.235619\pi$
$809$	42.0000	1.47664	0.738321	+	0.674450i	$0.235619\pi$
$810$	−1.00000	−0.0351364
$811$	20.0000	0.702295	0.351147	−	0.936320i	$-0.385792\pi$
$811$	20.0000	0.702295	0.351147	+	0.936320i	$0.385792\pi$
$812$	0	0
$813$	−8.00000	−0.280572
$814$	−24.0000	−0.841200
$815$	−20.0000	−0.700569
$816$	−2.00000	−0.0700140
$817$	16.0000	0.559769
$818$	38.0000	1.32864
$819$	0	0
$820$	6.00000	0.209529
$821$	22.0000	0.767805	0.383903	−	0.923374i	$-0.374580\pi$
$821$	22.0000	0.767805	0.383903	+	0.923374i	$0.374580\pi$
$822$	6.00000	0.209274
$823$	−24.0000	−0.836587	−0.418294	−	0.908312i	$-0.637372\pi$
$823$	−24.0000	−0.836587	−0.418294	+	0.908312i	$0.637372\pi$
$824$	−24.0000	−0.836080
$825$	4.00000	0.139262
$826$	0	0
$827$	−12.0000	−0.417281	−0.208640	−	0.977992i	$-0.566904\pi$
$827$	−12.0000	−0.417281	−0.208640	+	0.977992i	$0.566904\pi$
$828$	−8.00000	−0.278019
$829$	−34.0000	−1.18087	−0.590434	−	0.807086i	$-0.701044\pi$
$829$	−34.0000	−1.18087	−0.590434	+	0.807086i	$0.701044\pi$
$830$	4.00000	0.138842
$831$	−10.0000	−0.346896
$832$	7.00000	0.242681
$833$	−14.0000	−0.485071
$834$	20.0000	0.692543
$835$	16.0000	0.553703
$836$	16.0000	0.553372
$837$	−8.00000	−0.276520
$838$	−20.0000	−0.690889
$839$	16.0000	0.552381	0.276191	−	0.961103i	$-0.410928\pi$
$839$	16.0000	0.552381	0.276191	+	0.961103i	$0.410928\pi$
$840$	0	0
$841$	−25.0000	−0.862069
$842$	10.0000	0.344623
$843$	−22.0000	−0.757720
$844$	−20.0000	−0.688428
$845$	1.00000	0.0344010
$846$	8.00000	0.275046
$847$	0	0
$848$	−6.00000	−0.206041
$849$	−20.0000	−0.686398
$850$	−2.00000	−0.0685994
$851$	48.0000	1.64542
$852$	0	0
$853$	−42.0000	−1.43805	−0.719026	−	0.694983i	$-0.755412\pi$
$853$	−42.0000	−1.43805	−0.719026	+	0.694983i	$0.755412\pi$
$854$	0	0
$855$	−4.00000	−0.136797
$856$	36.0000	1.23045
$857$	10.0000	0.341593	0.170797	−	0.985306i	$-0.445366\pi$
$857$	10.0000	0.341593	0.170797	+	0.985306i	$0.445366\pi$
$858$	−4.00000	−0.136558
$859$	−4.00000	−0.136478	−0.0682391	−	0.997669i	$-0.521738\pi$
$859$	−4.00000	−0.136478	−0.0682391	+	0.997669i	$0.521738\pi$
$860$	4.00000	0.136399
$861$	0	0
$862$	−8.00000	−0.272481
$863$	−40.0000	−1.36162	−0.680808	−	0.732462i	$-0.738371\pi$
$863$	−40.0000	−1.36162	−0.680808	+	0.732462i	$0.738371\pi$
$864$	−5.00000	−0.170103
$865$	−2.00000	−0.0680020
$866$	−18.0000	−0.611665
$867$	−13.0000	−0.441503
$868$	0	0
$869$	64.0000	2.17105
$870$	2.00000	0.0678064
$871$	−4.00000	−0.135535
$872$	−6.00000	−0.203186
$873$	18.0000	0.609208
$874$	32.0000	1.08242
$875$	0	0
$876$	6.00000	0.202721
$877$	−50.0000	−1.68838	−0.844190	−	0.536044i	$-0.819918\pi$
$877$	−50.0000	−1.68838	−0.844190	+	0.536044i	$0.819918\pi$
$878$	24.0000	0.809961
$879$	6.00000	0.202375
$880$	−4.00000	−0.134840
$881$	−14.0000	−0.471672	−0.235836	−	0.971793i	$-0.575783\pi$
$881$	−14.0000	−0.471672	−0.235836	+	0.971793i	$0.575783\pi$
$882$	7.00000	0.235702
$883$	36.0000	1.21150	0.605748	−	0.795656i	$-0.292874\pi$
$883$	36.0000	1.21150	0.605748	+	0.795656i	$0.292874\pi$
$884$	−2.00000	−0.0672673
$885$	−12.0000	−0.403376
$886$	4.00000	0.134383
$887$	24.0000	0.805841	0.402921	−	0.915235i	$-0.367995\pi$
$887$	24.0000	0.805841	0.402921	+	0.915235i	$0.367995\pi$
$888$	18.0000	0.604040
$889$	0	0
$890$	−10.0000	−0.335201
$891$	4.00000	0.134005
$892$	24.0000	0.803579
$893$	32.0000	1.07084
$894$	10.0000	0.334450
$895$	−12.0000	−0.401116
$896$	0	0
$897$	8.00000	0.267112
$898$	−18.0000	−0.600668
$899$	16.0000	0.533630
$900$	−1.00000	−0.0333333
$901$	12.0000	0.399778
$902$	24.0000	0.799113
$903$	0	0
$904$	6.00000	0.199557
$905$	22.0000	0.731305
$906$	0	0
$907$	−4.00000	−0.132818	−0.0664089	−	0.997792i	$-0.521154\pi$
$907$	−4.00000	−0.132818	−0.0664089	+	0.997792i	$0.521154\pi$
$908$	−12.0000	−0.398234
$909$	6.00000	0.199007
$910$	0	0
$911$	32.0000	1.06021	0.530104	−	0.847933i	$-0.322153\pi$
$911$	32.0000	1.06021	0.530104	+	0.847933i	$0.322153\pi$
$912$	4.00000	0.132453
$913$	−16.0000	−0.529523
$914$	−26.0000	−0.860004
$915$	−2.00000	−0.0661180
$916$	−22.0000	−0.726900
$917$	0	0
$918$	−2.00000	−0.0660098
$919$	−40.0000	−1.31948	−0.659739	−	0.751495i	$-0.729333\pi$
$919$	−40.0000	−1.31948	−0.659739	+	0.751495i	$0.729333\pi$
$920$	24.0000	0.791257
$921$	−4.00000	−0.131804
$922$	18.0000	0.592798
$923$	0	0
$924$	0	0
$925$	6.00000	0.197279
$926$	−8.00000	−0.262896
$927$	−8.00000	−0.262754
$928$	10.0000	0.328266
$929$	18.0000	0.590561	0.295280	−	0.955411i	$-0.404587\pi$
$929$	18.0000	0.590561	0.295280	+	0.955411i	$0.404587\pi$
$930$	8.00000	0.262330
$931$	28.0000	0.917663
$932$	−26.0000	−0.851658
$933$	24.0000	0.785725
$934$	−4.00000	−0.130884
$935$	8.00000	0.261628
$936$	3.00000	0.0980581
$937$	−22.0000	−0.718709	−0.359354	−	0.933201i	$-0.617003\pi$
$937$	−22.0000	−0.718709	−0.359354	+	0.933201i	$0.617003\pi$
$938$	0	0
$939$	26.0000	0.848478
$940$	8.00000	0.260931
$941$	46.0000	1.49956	0.749779	−	0.661689i	$-0.230160\pi$
$941$	46.0000	1.49956	0.749779	+	0.661689i	$0.230160\pi$
$942$	2.00000	0.0651635
$943$	−48.0000	−1.56310
$944$	12.0000	0.390567
$945$	0	0
$946$	16.0000	0.520205
$947$	12.0000	0.389948	0.194974	−	0.980808i	$-0.437538\pi$
$947$	12.0000	0.389948	0.194974	+	0.980808i	$0.437538\pi$
$948$	−16.0000	−0.519656
$949$	−6.00000	−0.194768
$950$	4.00000	0.129777
$951$	30.0000	0.972817
$952$	0	0
$953$	10.0000	0.323932	0.161966	−	0.986796i	$-0.448217\pi$
$953$	10.0000	0.323932	0.161966	+	0.986796i	$0.448217\pi$
$954$	−6.00000	−0.194257
$955$	16.0000	0.517748
$956$	24.0000	0.776215
$957$	−8.00000	−0.258603
$958$	−8.00000	−0.258468
$959$	0	0
$960$	7.00000	0.225924
$961$	33.0000	1.06452
$962$	−6.00000	−0.193448
$963$	12.0000	0.386695
$964$	14.0000	0.450910
$965$	−14.0000	−0.450676
$966$	0	0
$967$	−16.0000	−0.514525	−0.257263	−	0.966342i	$-0.582821\pi$
$967$	−16.0000	−0.514525	−0.257263	+	0.966342i	$0.582821\pi$
$968$	15.0000	0.482118
$969$	−8.00000	−0.256997
$970$	−18.0000	−0.577945
$971$	−36.0000	−1.15529	−0.577647	−	0.816286i	$-0.696029\pi$
$971$	−36.0000	−1.15529	−0.577647	+	0.816286i	$0.696029\pi$
$972$	−1.00000	−0.0320750
$973$	0	0
$974$	−16.0000	−0.512673
$975$	1.00000	0.0320256
$976$	2.00000	0.0640184
$977$	−30.0000	−0.959785	−0.479893	−	0.877327i	$-0.659324\pi$
$977$	−30.0000	−0.959785	−0.479893	+	0.877327i	$0.659324\pi$
$978$	20.0000	0.639529
$979$	40.0000	1.27841
$980$	7.00000	0.223607
$981$	−2.00000	−0.0638551
$982$	20.0000	0.638226
$983$	0	0		−	1.00000i	$-0.5\pi$
$983$	0	0			1.00000i	$0.5\pi$
$984$	−18.0000	−0.573819
$985$	6.00000	0.191176
$986$	4.00000	0.127386
$987$	0	0
$988$	4.00000	0.127257
$989$	−32.0000	−1.01754
$990$	−4.00000	−0.127128
$991$	0	0		−	1.00000i	$-0.5\pi$
$991$	0	0			1.00000i	$0.5\pi$
$992$	40.0000	1.27000
$993$	20.0000	0.634681
$994$	0	0
$995$	−8.00000	−0.253617
$996$	4.00000	0.126745
$997$	38.0000	1.20347	0.601736	−	0.798695i	$-0.294476\pi$
$997$	38.0000	1.20347	0.601736	+	0.798695i	$0.294476\pi$
$998$	−28.0000	−0.886325
$999$	6.00000	0.189832

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	195.2.a.a.1.1	✓	1
3.2	odd	2		585.2.a.g.1.1		1
4.3	odd	2		3120.2.a.k.1.1		1
5.2	odd	4		975.2.c.e.274.1		2
5.3	odd	4		975.2.c.e.274.2		2
5.4	even	2		975.2.a.i.1.1		1
7.6	odd	2		9555.2.a.b.1.1		1
12.11	even	2		9360.2.a.o.1.1		1
13.12	even	2		2535.2.a.k.1.1		1
15.2	even	4		2925.2.c.f.2224.2		2
15.8	even	4		2925.2.c.f.2224.1		2
15.14	odd	2		2925.2.a.d.1.1		1
39.38	odd	2		7605.2.a.h.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.a.a.1.1	✓	1	1.1	even	1	trivial
585.2.a.g.1.1		1	3.2	odd	2
975.2.a.i.1.1		1	5.4	even	2
975.2.c.e.274.1		2	5.2	odd	4
975.2.c.e.274.2		2	5.3	odd	4
2535.2.a.k.1.1		1	13.12	even	2
2925.2.a.d.1.1		1	15.14	odd	2
2925.2.c.f.2224.1		2	15.8	even	4
2925.2.c.f.2224.2		2	15.2	even	4
3120.2.a.k.1.1		1	4.3	odd	2
7605.2.a.h.1.1		1	39.38	odd	2
9360.2.a.o.1.1		1	12.11	even	2
9555.2.a.b.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:	\( N \)	\(=\)	\( 195 = 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	195.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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