LMFDB - Embedded newform 1666.2.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1666,2,Mod(1,1666)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1666, 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("1666.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1666 = 2 \cdot 7^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1666.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:	$13.3030769767$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 238)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	1666.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-1.00000 q^{2} -3.00000 q^{3} +1.00000 q^{4} +2.00000 q^{5} +3.00000 q^{6} -1.00000 q^{8} +6.00000 q^{9} +O(q^{10})$

\(q-1.00000 q^{2} -3.00000 q^{3} +1.00000 q^{4} +2.00000 q^{5} +3.00000 q^{6} -1.00000 q^{8} +6.00000 q^{9} -2.00000 q^{10} -5.00000 q^{11} -3.00000 q^{12} +3.00000 q^{13} -6.00000 q^{15} +1.00000 q^{16} +1.00000 q^{17} -6.00000 q^{18} +2.00000 q^{19} +2.00000 q^{20} +5.00000 q^{22} -8.00000 q^{23} +3.00000 q^{24} -1.00000 q^{25} -3.00000 q^{26} -9.00000 q^{27} -6.00000 q^{29} +6.00000 q^{30} +4.00000 q^{31} -1.00000 q^{32} +15.0000 q^{33} -1.00000 q^{34} +6.00000 q^{36} +8.00000 q^{37} -2.00000 q^{38} -9.00000 q^{39} -2.00000 q^{40} -6.00000 q^{41} +4.00000 q^{43} -5.00000 q^{44} +12.0000 q^{45} +8.00000 q^{46} +10.0000 q^{47} -3.00000 q^{48} +1.00000 q^{50} -3.00000 q^{51} +3.00000 q^{52} +9.00000 q^{53} +9.00000 q^{54} -10.0000 q^{55} -6.00000 q^{57} +6.00000 q^{58} -4.00000 q^{59} -6.00000 q^{60} -4.00000 q^{61} -4.00000 q^{62} +1.00000 q^{64} +6.00000 q^{65} -15.0000 q^{66} -10.0000 q^{67} +1.00000 q^{68} +24.0000 q^{69} -5.00000 q^{71} -6.00000 q^{72} -2.00000 q^{73} -8.00000 q^{74} +3.00000 q^{75} +2.00000 q^{76} +9.00000 q^{78} -1.00000 q^{79} +2.00000 q^{80} +9.00000 q^{81} +6.00000 q^{82} +12.0000 q^{83} +2.00000 q^{85} -4.00000 q^{86} +18.0000 q^{87} +5.00000 q^{88} -9.00000 q^{89} -12.0000 q^{90} -8.00000 q^{92} -12.0000 q^{93} -10.0000 q^{94} +4.00000 q^{95} +3.00000 q^{96} -4.00000 q^{97} -30.0000 q^{99} +O(q^{100})\)

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−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
$5$	2.00000	0.894427	0.447214	−	0.894427i	$-0.352416\pi$
$5$	2.00000	0.894427	0.447214	+	0.894427i	$0.352416\pi$
$6$	3.00000	1.22474
$7$	0	0
$7$	0	0
$8$	−1.00000	−0.353553
$9$	6.00000	2.00000
$10$	−2.00000	−0.632456
$11$	−5.00000	−1.50756	−0.753778	−	0.657129i	$-0.771771\pi$
$11$	−5.00000	−1.50756	−0.753778	+	0.657129i	$0.771771\pi$
$12$	−3.00000	−0.866025
$13$	3.00000	0.832050	0.416025	−	0.909353i	$-0.363423\pi$
$13$	3.00000	0.832050	0.416025	+	0.909353i	$0.363423\pi$
$14$	0	0
$15$	−6.00000	−1.54919
$16$	1.00000	0.250000
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−6.00000	−1.41421
$19$	2.00000	0.458831	0.229416	−	0.973329i	$-0.426318\pi$
$19$	2.00000	0.458831	0.229416	+	0.973329i	$0.426318\pi$
$20$	2.00000	0.447214
$21$	0	0
$22$	5.00000	1.06600
$23$	−8.00000	−1.66812	−0.834058	−	0.551677i	$-0.813988\pi$
$23$	−8.00000	−1.66812	−0.834058	+	0.551677i	$0.813988\pi$
$24$	3.00000	0.612372
$25$	−1.00000	−0.200000
$26$	−3.00000	−0.588348
$27$	−9.00000	−1.73205
$28$	0	0
$29$	−6.00000	−1.11417	−0.557086	−	0.830455i	$-0.688081\pi$
$29$	−6.00000	−1.11417	−0.557086	+	0.830455i	$0.688081\pi$
$30$	6.00000	1.09545
$31$	4.00000	0.718421	0.359211	−	0.933257i	$-0.383046\pi$
$31$	4.00000	0.718421	0.359211	+	0.933257i	$0.383046\pi$
$32$	−1.00000	−0.176777
$33$	15.0000	2.61116
$34$	−1.00000	−0.171499
$35$	0	0
$36$	6.00000	1.00000
$37$	8.00000	1.31519	0.657596	−	0.753371i	$-0.271573\pi$
$37$	8.00000	1.31519	0.657596	+	0.753371i	$0.271573\pi$
$38$	−2.00000	−0.324443
$39$	−9.00000	−1.44115
$40$	−2.00000	−0.316228
$41$	−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	$-0.401344\pi$
$43$	4.00000	0.609994	0.304997	+	0.952353i	$0.401344\pi$
$44$	−5.00000	−0.753778
$45$	12.0000	1.78885
$46$	8.00000	1.17954
$47$	10.0000	1.45865	0.729325	−	0.684167i	$-0.239834\pi$
$47$	10.0000	1.45865	0.729325	+	0.684167i	$0.239834\pi$
$48$	−3.00000	−0.433013
$49$	0	0
$50$	1.00000	0.141421
$51$	−3.00000	−0.420084
$52$	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	$0.287894\pi$
$54$	9.00000	1.22474
$55$	−10.0000	−1.34840
$56$	0	0
$57$	−6.00000	−0.794719
$58$	6.00000	0.787839
$59$	−4.00000	−0.520756	−0.260378	−	0.965507i	$-0.583847\pi$
$59$	−4.00000	−0.520756	−0.260378	+	0.965507i	$0.583847\pi$
$60$	−6.00000	−0.774597
$61$	−4.00000	−0.512148	−0.256074	−	0.966657i	$-0.582429\pi$
$61$	−4.00000	−0.512148	−0.256074	+	0.966657i	$0.582429\pi$
$62$	−4.00000	−0.508001
$63$	0	0
$64$	1.00000	0.125000
$65$	6.00000	0.744208
$66$	−15.0000	−1.84637
$67$	−10.0000	−1.22169	−0.610847	−	0.791748i	$-0.709171\pi$
$67$	−10.0000	−1.22169	−0.610847	+	0.791748i	$0.709171\pi$
$68$	1.00000	0.121268
$69$	24.0000	2.88926
$70$	0	0
$71$	−5.00000	−0.593391	−0.296695	−	0.954972i	$-0.595885\pi$
$71$	−5.00000	−0.593391	−0.296695	+	0.954972i	$0.595885\pi$
$72$	−6.00000	−0.707107
$73$	−2.00000	−0.234082	−0.117041	−	0.993127i	$-0.537341\pi$
$73$	−2.00000	−0.234082	−0.117041	+	0.993127i	$0.537341\pi$
$74$	−8.00000	−0.929981
$75$	3.00000	0.346410
$76$	2.00000	0.229416
$77$	0	0
$78$	9.00000	1.01905
$79$	−1.00000	−0.112509	−0.0562544	−	0.998416i	$-0.517916\pi$
$79$	−1.00000	−0.112509	−0.0562544	+	0.998416i	$0.517916\pi$
$80$	2.00000	0.223607
$81$	9.00000	1.00000
$82$	6.00000	0.662589
$83$	12.0000	1.31717	0.658586	−	0.752506i	$-0.271155\pi$
$83$	12.0000	1.31717	0.658586	+	0.752506i	$0.271155\pi$
$84$	0	0
$85$	2.00000	0.216930
$86$	−4.00000	−0.431331
$87$	18.0000	1.92980
$88$	5.00000	0.533002
$89$	−9.00000	−0.953998	−0.476999	−	0.878904i	$-0.658275\pi$
$89$	−9.00000	−0.953998	−0.476999	+	0.878904i	$0.658275\pi$
$90$	−12.0000	−1.26491
$91$	0	0
$92$	−8.00000	−0.834058
$93$	−12.0000	−1.24434
$94$	−10.0000	−1.03142
$95$	4.00000	0.410391
$96$	3.00000	0.306186
$97$	−4.00000	−0.406138	−0.203069	−	0.979164i	$-0.565092\pi$
$97$	−4.00000	−0.406138	−0.203069	+	0.979164i	$0.565092\pi$
$98$	0	0
$99$	−30.0000	−3.01511
$100$	−1.00000	−0.100000
$101$	2.00000	0.199007	0.0995037	−	0.995037i	$-0.468274\pi$
$101$	2.00000	0.199007	0.0995037	+	0.995037i	$0.468274\pi$
$102$	3.00000	0.297044
$103$	−14.0000	−1.37946	−0.689730	−	0.724066i	$-0.742271\pi$
$103$	−14.0000	−1.37946	−0.689730	+	0.724066i	$0.742271\pi$
$104$	−3.00000	−0.294174
$105$	0	0
$106$	−9.00000	−0.874157
$107$	−9.00000	−0.870063	−0.435031	−	0.900415i	$-0.643263\pi$
$107$	−9.00000	−0.870063	−0.435031	+	0.900415i	$0.643263\pi$
$108$	−9.00000	−0.866025
$109$	−16.0000	−1.53252	−0.766261	−	0.642529i	$-0.777885\pi$
$109$	−16.0000	−1.53252	−0.766261	+	0.642529i	$0.777885\pi$
$110$	10.0000	0.953463
$111$	−24.0000	−2.27798
$112$	0	0
$113$	16.0000	1.50515	0.752577	−	0.658505i	$-0.228811\pi$
$113$	16.0000	1.50515	0.752577	+	0.658505i	$0.228811\pi$
$114$	6.00000	0.561951
$115$	−16.0000	−1.49201
$116$	−6.00000	−0.557086
$117$	18.0000	1.66410
$118$	4.00000	0.368230
$119$	0	0
$120$	6.00000	0.547723
$121$	14.0000	1.27273
$122$	4.00000	0.362143
$123$	18.0000	1.62301
$124$	4.00000	0.359211
$125$	−12.0000	−1.07331
$126$	0	0
$127$	−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
$129$	−12.0000	−1.05654
$130$	−6.00000	−0.526235
$131$	−12.0000	−1.04844	−0.524222	−	0.851581i	$-0.675644\pi$
$131$	−12.0000	−1.04844	−0.524222	+	0.851581i	$0.675644\pi$
$132$	15.0000	1.30558
$133$	0	0
$134$	10.0000	0.863868
$135$	−18.0000	−1.54919
$136$	−1.00000	−0.0857493
$137$	−19.0000	−1.62328	−0.811640	−	0.584158i	$-0.801425\pi$
$137$	−19.0000	−1.62328	−0.811640	+	0.584158i	$0.801425\pi$
$138$	−24.0000	−2.04302
$139$	−9.00000	−0.763370	−0.381685	−	0.924292i	$-0.624656\pi$
$139$	−9.00000	−0.763370	−0.381685	+	0.924292i	$0.624656\pi$
$140$	0	0
$141$	−30.0000	−2.52646
$142$	5.00000	0.419591
$143$	−15.0000	−1.25436
$144$	6.00000	0.500000
$145$	−12.0000	−0.996546
$146$	2.00000	0.165521
$147$	0	0
$148$	8.00000	0.657596
$149$	−17.0000	−1.39269	−0.696347	−	0.717705i	$-0.745193\pi$
$149$	−17.0000	−1.39269	−0.696347	+	0.717705i	$0.745193\pi$
$150$	−3.00000	−0.244949
$151$	2.00000	0.162758	0.0813788	−	0.996683i	$-0.474068\pi$
$151$	2.00000	0.162758	0.0813788	+	0.996683i	$0.474068\pi$
$152$	−2.00000	−0.162221
$153$	6.00000	0.485071
$154$	0	0
$155$	8.00000	0.642575
$156$	−9.00000	−0.720577
$157$	−11.0000	−0.877896	−0.438948	−	0.898513i	$-0.644649\pi$
$157$	−11.0000	−0.877896	−0.438948	+	0.898513i	$0.644649\pi$
$158$	1.00000	0.0795557
$159$	−27.0000	−2.14124
$160$	−2.00000	−0.158114
$161$	0	0
$162$	−9.00000	−0.707107
$163$	12.0000	0.939913	0.469956	−	0.882690i	$-0.344270\pi$
$163$	12.0000	0.939913	0.469956	+	0.882690i	$0.344270\pi$
$164$	−6.00000	−0.468521
$165$	30.0000	2.33550
$166$	−12.0000	−0.931381
$167$	−5.00000	−0.386912	−0.193456	−	0.981109i	$-0.561970\pi$
$167$	−5.00000	−0.386912	−0.193456	+	0.981109i	$0.561970\pi$
$168$	0	0
$169$	−4.00000	−0.307692
$170$	−2.00000	−0.153393
$171$	12.0000	0.917663
$172$	4.00000	0.304997
$173$	0	0		−	1.00000i	$-0.5\pi$
$173$	0	0			1.00000i	$0.5\pi$
$174$	−18.0000	−1.36458
$175$	0	0
$176$	−5.00000	−0.376889
$177$	12.0000	0.901975
$178$	9.00000	0.674579
$179$	4.00000	0.298974	0.149487	−	0.988764i	$-0.452238\pi$
$179$	4.00000	0.298974	0.149487	+	0.988764i	$0.452238\pi$
$180$	12.0000	0.894427
$181$	12.0000	0.891953	0.445976	−	0.895045i	$-0.352856\pi$
$181$	12.0000	0.891953	0.445976	+	0.895045i	$0.352856\pi$
$182$	0	0
$183$	12.0000	0.887066
$184$	8.00000	0.589768
$185$	16.0000	1.17634
$186$	12.0000	0.879883
$187$	−5.00000	−0.365636
$188$	10.0000	0.729325
$189$	0	0
$190$	−4.00000	−0.290191
$191$	−24.0000	−1.73658	−0.868290	−	0.496058i	$-0.834780\pi$
$191$	−24.0000	−1.73658	−0.868290	+	0.496058i	$0.834780\pi$
$192$	−3.00000	−0.216506
$193$	−16.0000	−1.15171	−0.575853	−	0.817554i	$-0.695330\pi$
$193$	−16.0000	−1.15171	−0.575853	+	0.817554i	$0.695330\pi$
$194$	4.00000	0.287183
$195$	−18.0000	−1.28901
$196$	0	0
$197$	−2.00000	−0.142494	−0.0712470	−	0.997459i	$-0.522698\pi$
$197$	−2.00000	−0.142494	−0.0712470	+	0.997459i	$0.522698\pi$
$198$	30.0000	2.13201
$199$	15.0000	1.06332	0.531661	−	0.846957i	$-0.321568\pi$
$199$	15.0000	1.06332	0.531661	+	0.846957i	$0.321568\pi$
$200$	1.00000	0.0707107
$201$	30.0000	2.11604
$202$	−2.00000	−0.140720
$203$	0	0
$204$	−3.00000	−0.210042
$205$	−12.0000	−0.838116
$206$	14.0000	0.975426
$207$	−48.0000	−3.33623
$208$	3.00000	0.208013
$209$	−10.0000	−0.691714
$210$	0	0
$211$	20.0000	1.37686	0.688428	−	0.725304i	$-0.258301\pi$
$211$	20.0000	1.37686	0.688428	+	0.725304i	$0.258301\pi$
$212$	9.00000	0.618123
$213$	15.0000	1.02778
$214$	9.00000	0.615227
$215$	8.00000	0.545595
$216$	9.00000	0.612372
$217$	0	0
$218$	16.0000	1.08366
$219$	6.00000	0.405442
$220$	−10.0000	−0.674200
$221$	3.00000	0.201802
$222$	24.0000	1.61077
$223$	12.0000	0.803579	0.401790	−	0.915732i	$-0.368388\pi$
$223$	12.0000	0.803579	0.401790	+	0.915732i	$0.368388\pi$
$224$	0	0
$225$	−6.00000	−0.400000
$226$	−16.0000	−1.06430
$227$	−3.00000	−0.199117	−0.0995585	−	0.995032i	$-0.531743\pi$
$227$	−3.00000	−0.199117	−0.0995585	+	0.995032i	$0.531743\pi$
$228$	−6.00000	−0.397360
$229$	−2.00000	−0.132164	−0.0660819	−	0.997814i	$-0.521050\pi$
$229$	−2.00000	−0.132164	−0.0660819	+	0.997814i	$0.521050\pi$
$230$	16.0000	1.05501
$231$	0	0
$232$	6.00000	0.393919
$233$	−8.00000	−0.524097	−0.262049	−	0.965055i	$-0.584398\pi$
$233$	−8.00000	−0.524097	−0.262049	+	0.965055i	$0.584398\pi$
$234$	−18.0000	−1.17670
$235$	20.0000	1.30466
$236$	−4.00000	−0.260378
$237$	3.00000	0.194871
$238$	0	0
$239$	−4.00000	−0.258738	−0.129369	−	0.991596i	$-0.541295\pi$
$239$	−4.00000	−0.258738	−0.129369	+	0.991596i	$0.541295\pi$
$240$	−6.00000	−0.387298
$241$	−18.0000	−1.15948	−0.579741	−	0.814801i	$-0.696846\pi$
$241$	−18.0000	−1.15948	−0.579741	+	0.814801i	$0.696846\pi$
$242$	−14.0000	−0.899954
$243$	0	0
$244$	−4.00000	−0.256074
$245$	0	0
$246$	−18.0000	−1.14764
$247$	6.00000	0.381771
$248$	−4.00000	−0.254000
$249$	−36.0000	−2.28141
$250$	12.0000	0.758947
$251$	−2.00000	−0.126239	−0.0631194	−	0.998006i	$-0.520105\pi$
$251$	−2.00000	−0.126239	−0.0631194	+	0.998006i	$0.520105\pi$
$252$	0	0
$253$	40.0000	2.51478
$254$	6.00000	0.376473
$255$	−6.00000	−0.375735
$256$	1.00000	0.0625000
$257$	−23.0000	−1.43470	−0.717350	−	0.696713i	$-0.754645\pi$
$257$	−23.0000	−1.43470	−0.717350	+	0.696713i	$0.754645\pi$
$258$	12.0000	0.747087
$259$	0	0
$260$	6.00000	0.372104
$261$	−36.0000	−2.22834
$262$	12.0000	0.741362
$263$	−18.0000	−1.10993	−0.554964	−	0.831875i	$-0.687268\pi$
$263$	−18.0000	−1.10993	−0.554964	+	0.831875i	$0.687268\pi$
$264$	−15.0000	−0.923186
$265$	18.0000	1.10573
$266$	0	0
$267$	27.0000	1.65237
$268$	−10.0000	−0.610847
$269$	14.0000	0.853595	0.426798	−	0.904347i	$-0.359642\pi$
$269$	14.0000	0.853595	0.426798	+	0.904347i	$0.359642\pi$
$270$	18.0000	1.09545
$271$	4.00000	0.242983	0.121491	−	0.992592i	$-0.461232\pi$
$271$	4.00000	0.242983	0.121491	+	0.992592i	$0.461232\pi$
$272$	1.00000	0.0606339
$273$	0	0
$274$	19.0000	1.14783
$275$	5.00000	0.301511
$276$	24.0000	1.44463
$277$	−4.00000	−0.240337	−0.120168	−	0.992754i	$-0.538343\pi$
$277$	−4.00000	−0.240337	−0.120168	+	0.992754i	$0.538343\pi$
$278$	9.00000	0.539784
$279$	24.0000	1.43684
$280$	0	0
$281$	−27.0000	−1.61068	−0.805342	−	0.592810i	$-0.798019\pi$
$281$	−27.0000	−1.61068	−0.805342	+	0.592810i	$0.798019\pi$
$282$	30.0000	1.78647
$283$	−1.00000	−0.0594438	−0.0297219	−	0.999558i	$-0.509462\pi$
$283$	−1.00000	−0.0594438	−0.0297219	+	0.999558i	$0.509462\pi$
$284$	−5.00000	−0.296695
$285$	−12.0000	−0.710819
$286$	15.0000	0.886969
$287$	0	0
$288$	−6.00000	−0.353553
$289$	1.00000	0.0588235
$290$	12.0000	0.704664
$291$	12.0000	0.703452
$292$	−2.00000	−0.117041
$293$	29.0000	1.69420	0.847099	−	0.531435i	$-0.178347\pi$
$293$	29.0000	1.69420	0.847099	+	0.531435i	$0.178347\pi$
$294$	0	0
$295$	−8.00000	−0.465778
$296$	−8.00000	−0.464991
$297$	45.0000	2.61116
$298$	17.0000	0.984784
$299$	−24.0000	−1.38796
$300$	3.00000	0.173205
$301$	0	0
$302$	−2.00000	−0.115087
$303$	−6.00000	−0.344691
$304$	2.00000	0.114708
$305$	−8.00000	−0.458079
$306$	−6.00000	−0.342997
$307$	26.0000	1.48390	0.741949	−	0.670456i	$-0.233902\pi$
$307$	26.0000	1.48390	0.741949	+	0.670456i	$0.233902\pi$
$308$	0	0
$309$	42.0000	2.38930
$310$	−8.00000	−0.454369
$311$	−15.0000	−0.850572	−0.425286	−	0.905059i	$-0.639826\pi$
$311$	−15.0000	−0.850572	−0.425286	+	0.905059i	$0.639826\pi$
$312$	9.00000	0.509525
$313$	−6.00000	−0.339140	−0.169570	−	0.985518i	$-0.554238\pi$
$313$	−6.00000	−0.339140	−0.169570	+	0.985518i	$0.554238\pi$
$314$	11.0000	0.620766
$315$	0	0
$316$	−1.00000	−0.0562544
$317$	12.0000	0.673987	0.336994	−	0.941507i	$-0.390590\pi$
$317$	12.0000	0.673987	0.336994	+	0.941507i	$0.390590\pi$
$318$	27.0000	1.51408
$319$	30.0000	1.67968
$320$	2.00000	0.111803
$321$	27.0000	1.50699
$322$	0	0
$323$	2.00000	0.111283
$324$	9.00000	0.500000
$325$	−3.00000	−0.166410
$326$	−12.0000	−0.664619
$327$	48.0000	2.65441
$328$	6.00000	0.331295
$329$	0	0
$330$	−30.0000	−1.65145
$331$	−8.00000	−0.439720	−0.219860	−	0.975531i	$-0.570560\pi$
$331$	−8.00000	−0.439720	−0.219860	+	0.975531i	$0.570560\pi$
$332$	12.0000	0.658586
$333$	48.0000	2.63038
$334$	5.00000	0.273588
$335$	−20.0000	−1.09272
$336$	0	0
$337$	−8.00000	−0.435788	−0.217894	−	0.975972i	$-0.569919\pi$
$337$	−8.00000	−0.435788	−0.217894	+	0.975972i	$0.569919\pi$
$338$	4.00000	0.217571
$339$	−48.0000	−2.60700
$340$	2.00000	0.108465
$341$	−20.0000	−1.08306
$342$	−12.0000	−0.648886
$343$	0	0
$344$	−4.00000	−0.215666
$345$	48.0000	2.58423
$346$	0	0
$347$	20.0000	1.07366	0.536828	−	0.843692i	$-0.319622\pi$
$347$	20.0000	1.07366	0.536828	+	0.843692i	$0.319622\pi$
$348$	18.0000	0.964901
$349$	18.0000	0.963518	0.481759	−	0.876304i	$-0.339998\pi$
$349$	18.0000	0.963518	0.481759	+	0.876304i	$0.339998\pi$
$350$	0	0
$351$	−27.0000	−1.44115
$352$	5.00000	0.266501
$353$	1.00000	0.0532246	0.0266123	−	0.999646i	$-0.491528\pi$
$353$	1.00000	0.0532246	0.0266123	+	0.999646i	$0.491528\pi$
$354$	−12.0000	−0.637793
$355$	−10.0000	−0.530745
$356$	−9.00000	−0.476999
$357$	0	0
$358$	−4.00000	−0.211407
$359$	20.0000	1.05556	0.527780	−	0.849381i	$-0.323025\pi$
$359$	20.0000	1.05556	0.527780	+	0.849381i	$0.323025\pi$
$360$	−12.0000	−0.632456
$361$	−15.0000	−0.789474
$362$	−12.0000	−0.630706
$363$	−42.0000	−2.20443
$364$	0	0
$365$	−4.00000	−0.209370
$366$	−12.0000	−0.627250
$367$	−15.0000	−0.782994	−0.391497	−	0.920179i	$-0.628043\pi$
$367$	−15.0000	−0.782994	−0.391497	+	0.920179i	$0.628043\pi$
$368$	−8.00000	−0.417029
$369$	−36.0000	−1.87409
$370$	−16.0000	−0.831800
$371$	0	0
$372$	−12.0000	−0.622171
$373$	−11.0000	−0.569558	−0.284779	−	0.958593i	$-0.591920\pi$
$373$	−11.0000	−0.569558	−0.284779	+	0.958593i	$0.591920\pi$
$374$	5.00000	0.258544
$375$	36.0000	1.85903
$376$	−10.0000	−0.515711
$377$	−18.0000	−0.927047
$378$	0	0
$379$	−5.00000	−0.256833	−0.128416	−	0.991720i	$-0.540989\pi$
$379$	−5.00000	−0.256833	−0.128416	+	0.991720i	$0.540989\pi$
$380$	4.00000	0.205196
$381$	18.0000	0.922168
$382$	24.0000	1.22795
$383$	20.0000	1.02195	0.510976	−	0.859595i	$-0.329284\pi$
$383$	20.0000	1.02195	0.510976	+	0.859595i	$0.329284\pi$
$384$	3.00000	0.153093
$385$	0	0
$386$	16.0000	0.814379
$387$	24.0000	1.21999
$388$	−4.00000	−0.203069
$389$	15.0000	0.760530	0.380265	−	0.924878i	$-0.375833\pi$
$389$	15.0000	0.760530	0.380265	+	0.924878i	$0.375833\pi$
$390$	18.0000	0.911465
$391$	−8.00000	−0.404577
$392$	0	0
$393$	36.0000	1.81596
$394$	2.00000	0.100759
$395$	−2.00000	−0.100631
$396$	−30.0000	−1.50756
$397$	−32.0000	−1.60603	−0.803017	−	0.595956i	$-0.796773\pi$
$397$	−32.0000	−1.60603	−0.803017	+	0.595956i	$0.796773\pi$
$398$	−15.0000	−0.751882
$399$	0	0
$400$	−1.00000	−0.0500000
$401$	16.0000	0.799002	0.399501	−	0.916733i	$-0.369183\pi$
$401$	16.0000	0.799002	0.399501	+	0.916733i	$0.369183\pi$
$402$	−30.0000	−1.49626
$403$	12.0000	0.597763
$404$	2.00000	0.0995037
$405$	18.0000	0.894427
$406$	0	0
$407$	−40.0000	−1.98273
$408$	3.00000	0.148522
$409$	−23.0000	−1.13728	−0.568638	−	0.822588i	$-0.692530\pi$
$409$	−23.0000	−1.13728	−0.568638	+	0.822588i	$0.692530\pi$
$410$	12.0000	0.592638
$411$	57.0000	2.81160
$412$	−14.0000	−0.689730
$413$	0	0
$414$	48.0000	2.35907
$415$	24.0000	1.17811
$416$	−3.00000	−0.147087
$417$	27.0000	1.32220
$418$	10.0000	0.489116
$419$	−39.0000	−1.90527	−0.952637	−	0.304109i	$-0.901641\pi$
$419$	−39.0000	−1.90527	−0.952637	+	0.304109i	$0.901641\pi$
$420$	0	0
$421$	30.0000	1.46211	0.731055	−	0.682318i	$-0.239028\pi$
$421$	30.0000	1.46211	0.731055	+	0.682318i	$0.239028\pi$
$422$	−20.0000	−0.973585
$423$	60.0000	2.91730
$424$	−9.00000	−0.437079
$425$	−1.00000	−0.0485071
$426$	−15.0000	−0.726752
$427$	0	0
$428$	−9.00000	−0.435031
$429$	45.0000	2.17262
$430$	−8.00000	−0.385794
$431$	5.00000	0.240842	0.120421	−	0.992723i	$-0.461576\pi$
$431$	5.00000	0.240842	0.120421	+	0.992723i	$0.461576\pi$
$432$	−9.00000	−0.433013
$433$	−30.0000	−1.44171	−0.720854	−	0.693087i	$-0.756250\pi$
$433$	−30.0000	−1.44171	−0.720854	+	0.693087i	$0.756250\pi$
$434$	0	0
$435$	36.0000	1.72607
$436$	−16.0000	−0.766261
$437$	−16.0000	−0.765384
$438$	−6.00000	−0.286691
$439$	−7.00000	−0.334092	−0.167046	−	0.985949i	$-0.553423\pi$
$439$	−7.00000	−0.334092	−0.167046	+	0.985949i	$0.553423\pi$
$440$	10.0000	0.476731
$441$	0	0
$442$	−3.00000	−0.142695
$443$	0	0		−	1.00000i	$-0.5\pi$
$443$	0	0			1.00000i	$0.5\pi$
$444$	−24.0000	−1.13899
$445$	−18.0000	−0.853282
$446$	−12.0000	−0.568216
$447$	51.0000	2.41222
$448$	0	0
$449$	−6.00000	−0.283158	−0.141579	−	0.989927i	$-0.545218\pi$
$449$	−6.00000	−0.283158	−0.141579	+	0.989927i	$0.545218\pi$
$450$	6.00000	0.282843
$451$	30.0000	1.41264
$452$	16.0000	0.752577
$453$	−6.00000	−0.281905
$454$	3.00000	0.140797
$455$	0	0
$456$	6.00000	0.280976
$457$	−10.0000	−0.467780	−0.233890	−	0.972263i	$-0.575146\pi$
$457$	−10.0000	−0.467780	−0.233890	+	0.972263i	$0.575146\pi$
$458$	2.00000	0.0934539
$459$	−9.00000	−0.420084
$460$	−16.0000	−0.746004
$461$	11.0000	0.512321	0.256161	−	0.966634i	$-0.417542\pi$
$461$	11.0000	0.512321	0.256161	+	0.966634i	$0.417542\pi$
$462$	0	0
$463$	−34.0000	−1.58011	−0.790057	−	0.613033i	$-0.789949\pi$
$463$	−34.0000	−1.58011	−0.790057	+	0.613033i	$0.789949\pi$
$464$	−6.00000	−0.278543
$465$	−24.0000	−1.11297
$466$	8.00000	0.370593
$467$	6.00000	0.277647	0.138823	−	0.990317i	$-0.455668\pi$
$467$	6.00000	0.277647	0.138823	+	0.990317i	$0.455668\pi$
$468$	18.0000	0.832050
$469$	0	0
$470$	−20.0000	−0.922531
$471$	33.0000	1.52056
$472$	4.00000	0.184115
$473$	−20.0000	−0.919601
$474$	−3.00000	−0.137795
$475$	−2.00000	−0.0917663
$476$	0	0
$477$	54.0000	2.47249
$478$	4.00000	0.182956
$479$	0	0		−	1.00000i	$-0.5\pi$
$479$	0	0			1.00000i	$0.5\pi$
$480$	6.00000	0.273861
$481$	24.0000	1.09431
$482$	18.0000	0.819878
$483$	0	0
$484$	14.0000	0.636364
$485$	−8.00000	−0.363261
$486$	0	0
$487$	11.0000	0.498458	0.249229	−	0.968445i	$-0.419823\pi$
$487$	11.0000	0.498458	0.249229	+	0.968445i	$0.419823\pi$
$488$	4.00000	0.181071
$489$	−36.0000	−1.62798
$490$	0	0
$491$	−38.0000	−1.71492	−0.857458	−	0.514554i	$-0.827958\pi$
$491$	−38.0000	−1.71492	−0.857458	+	0.514554i	$0.827958\pi$
$492$	18.0000	0.811503
$493$	−6.00000	−0.270226
$494$	−6.00000	−0.269953
$495$	−60.0000	−2.69680
$496$	4.00000	0.179605
$497$	0	0
$498$	36.0000	1.61320
$499$	−11.0000	−0.492428	−0.246214	−	0.969216i	$-0.579187\pi$
$499$	−11.0000	−0.492428	−0.246214	+	0.969216i	$0.579187\pi$
$500$	−12.0000	−0.536656
$501$	15.0000	0.670151
$502$	2.00000	0.0892644
$503$	−9.00000	−0.401290	−0.200645	−	0.979664i	$-0.564304\pi$
$503$	−9.00000	−0.401290	−0.200645	+	0.979664i	$0.564304\pi$
$504$	0	0
$505$	4.00000	0.177998
$506$	−40.0000	−1.77822
$507$	12.0000	0.532939
$508$	−6.00000	−0.266207
$509$	−26.0000	−1.15243	−0.576215	−	0.817298i	$-0.695471\pi$
$509$	−26.0000	−1.15243	−0.576215	+	0.817298i	$0.695471\pi$
$510$	6.00000	0.265684
$511$	0	0
$512$	−1.00000	−0.0441942
$513$	−18.0000	−0.794719
$514$	23.0000	1.01449
$515$	−28.0000	−1.23383
$516$	−12.0000	−0.528271
$517$	−50.0000	−2.19900
$518$	0	0
$519$	0	0
$520$	−6.00000	−0.263117
$521$	30.0000	1.31432	0.657162	−	0.753749i	$-0.271757\pi$
$521$	30.0000	1.31432	0.657162	+	0.753749i	$0.271757\pi$
$522$	36.0000	1.57568
$523$	−16.0000	−0.699631	−0.349816	−	0.936819i	$-0.613756\pi$
$523$	−16.0000	−0.699631	−0.349816	+	0.936819i	$0.613756\pi$
$524$	−12.0000	−0.524222
$525$	0	0
$526$	18.0000	0.784837
$527$	4.00000	0.174243
$528$	15.0000	0.652791
$529$	41.0000	1.78261
$530$	−18.0000	−0.781870
$531$	−24.0000	−1.04151
$532$	0	0
$533$	−18.0000	−0.779667
$534$	−27.0000	−1.16840
$535$	−18.0000	−0.778208
$536$	10.0000	0.431934
$537$	−12.0000	−0.517838
$538$	−14.0000	−0.603583
$539$	0	0
$540$	−18.0000	−0.774597
$541$	−8.00000	−0.343947	−0.171973	−	0.985102i	$-0.555014\pi$
$541$	−8.00000	−0.343947	−0.171973	+	0.985102i	$0.555014\pi$
$542$	−4.00000	−0.171815
$543$	−36.0000	−1.54491
$544$	−1.00000	−0.0428746
$545$	−32.0000	−1.37073
$546$	0	0
$547$	5.00000	0.213785	0.106892	−	0.994271i	$-0.465910\pi$
$547$	5.00000	0.213785	0.106892	+	0.994271i	$0.465910\pi$
$548$	−19.0000	−0.811640
$549$	−24.0000	−1.02430
$550$	−5.00000	−0.213201
$551$	−12.0000	−0.511217
$552$	−24.0000	−1.02151
$553$	0	0
$554$	4.00000	0.169944
$555$	−48.0000	−2.03749
$556$	−9.00000	−0.381685
$557$	21.0000	0.889799	0.444899	−	0.895581i	$-0.353239\pi$
$557$	21.0000	0.889799	0.444899	+	0.895581i	$0.353239\pi$
$558$	−24.0000	−1.01600
$559$	12.0000	0.507546
$560$	0	0
$561$	15.0000	0.633300
$562$	27.0000	1.13893
$563$	−16.0000	−0.674320	−0.337160	−	0.941447i	$-0.609466\pi$
$563$	−16.0000	−0.674320	−0.337160	+	0.941447i	$0.609466\pi$
$564$	−30.0000	−1.26323
$565$	32.0000	1.34625
$566$	1.00000	0.0420331
$567$	0	0
$568$	5.00000	0.209795
$569$	−3.00000	−0.125767	−0.0628833	−	0.998021i	$-0.520030\pi$
$569$	−3.00000	−0.125767	−0.0628833	+	0.998021i	$0.520030\pi$
$570$	12.0000	0.502625
$571$	−40.0000	−1.67395	−0.836974	−	0.547243i	$-0.815677\pi$
$571$	−40.0000	−1.67395	−0.836974	+	0.547243i	$0.815677\pi$
$572$	−15.0000	−0.627182
$573$	72.0000	3.00784
$574$	0	0
$575$	8.00000	0.333623
$576$	6.00000	0.250000
$577$	43.0000	1.79011	0.895057	−	0.445952i	$-0.147135\pi$
$577$	43.0000	1.79011	0.895057	+	0.445952i	$0.147135\pi$
$578$	−1.00000	−0.0415945
$579$	48.0000	1.99481
$580$	−12.0000	−0.498273
$581$	0	0
$582$	−12.0000	−0.497416
$583$	−45.0000	−1.86371
$584$	2.00000	0.0827606
$585$	36.0000	1.48842
$586$	−29.0000	−1.19798
$587$	−2.00000	−0.0825488	−0.0412744	−	0.999148i	$-0.513142\pi$
$587$	−2.00000	−0.0825488	−0.0412744	+	0.999148i	$0.513142\pi$
$588$	0	0
$589$	8.00000	0.329634
$590$	8.00000	0.329355
$591$	6.00000	0.246807
$592$	8.00000	0.328798
$593$	−9.00000	−0.369586	−0.184793	−	0.982777i	$-0.559161\pi$
$593$	−9.00000	−0.369586	−0.184793	+	0.982777i	$0.559161\pi$
$594$	−45.0000	−1.84637
$595$	0	0
$596$	−17.0000	−0.696347
$597$	−45.0000	−1.84173
$598$	24.0000	0.981433
$599$	−36.0000	−1.47092	−0.735460	−	0.677568i	$-0.763034\pi$
$599$	−36.0000	−1.47092	−0.735460	+	0.677568i	$0.763034\pi$
$600$	−3.00000	−0.122474
$601$	46.0000	1.87638	0.938190	−	0.346122i	$-0.112502\pi$
$601$	46.0000	1.87638	0.938190	+	0.346122i	$0.112502\pi$
$602$	0	0
$603$	−60.0000	−2.44339
$604$	2.00000	0.0813788
$605$	28.0000	1.13836
$606$	6.00000	0.243733
$607$	43.0000	1.74532	0.872658	−	0.488332i	$-0.162394\pi$
$607$	43.0000	1.74532	0.872658	+	0.488332i	$0.162394\pi$
$608$	−2.00000	−0.0811107
$609$	0	0
$610$	8.00000	0.323911
$611$	30.0000	1.21367
$612$	6.00000	0.242536
$613$	35.0000	1.41364	0.706818	−	0.707395i	$-0.250130\pi$
$613$	35.0000	1.41364	0.706818	+	0.707395i	$0.250130\pi$
$614$	−26.0000	−1.04927
$615$	36.0000	1.45166
$616$	0	0
$617$	−14.0000	−0.563619	−0.281809	−	0.959470i	$-0.590935\pi$
$617$	−14.0000	−0.563619	−0.281809	+	0.959470i	$0.590935\pi$
$618$	−42.0000	−1.68949
$619$	−25.0000	−1.00483	−0.502417	−	0.864625i	$-0.667556\pi$
$619$	−25.0000	−1.00483	−0.502417	+	0.864625i	$0.667556\pi$
$620$	8.00000	0.321288
$621$	72.0000	2.88926
$622$	15.0000	0.601445
$623$	0	0
$624$	−9.00000	−0.360288
$625$	−19.0000	−0.760000
$626$	6.00000	0.239808
$627$	30.0000	1.19808
$628$	−11.0000	−0.438948
$629$	8.00000	0.318981
$630$	0	0
$631$	32.0000	1.27390	0.636950	−	0.770905i	$-0.280196\pi$
$631$	32.0000	1.27390	0.636950	+	0.770905i	$0.280196\pi$
$632$	1.00000	0.0397779
$633$	−60.0000	−2.38479
$634$	−12.0000	−0.476581
$635$	−12.0000	−0.476205
$636$	−27.0000	−1.07062
$637$	0	0
$638$	−30.0000	−1.18771
$639$	−30.0000	−1.18678
$640$	−2.00000	−0.0790569
$641$	34.0000	1.34292	0.671460	−	0.741041i	$-0.265668\pi$
$641$	34.0000	1.34292	0.671460	+	0.741041i	$0.265668\pi$
$642$	−27.0000	−1.06561
$643$	−21.0000	−0.828159	−0.414080	−	0.910241i	$-0.635896\pi$
$643$	−21.0000	−0.828159	−0.414080	+	0.910241i	$0.635896\pi$
$644$	0	0
$645$	−24.0000	−0.944999
$646$	−2.00000	−0.0786889
$647$	−4.00000	−0.157256	−0.0786281	−	0.996904i	$-0.525054\pi$
$647$	−4.00000	−0.157256	−0.0786281	+	0.996904i	$0.525054\pi$
$648$	−9.00000	−0.353553
$649$	20.0000	0.785069
$650$	3.00000	0.117670
$651$	0	0
$652$	12.0000	0.469956
$653$	−8.00000	−0.313064	−0.156532	−	0.987673i	$-0.550031\pi$
$653$	−8.00000	−0.313064	−0.156532	+	0.987673i	$0.550031\pi$
$654$	−48.0000	−1.87695
$655$	−24.0000	−0.937758
$656$	−6.00000	−0.234261
$657$	−12.0000	−0.468165
$658$	0	0
$659$	−16.0000	−0.623272	−0.311636	−	0.950202i	$-0.600877\pi$
$659$	−16.0000	−0.623272	−0.311636	+	0.950202i	$0.600877\pi$
$660$	30.0000	1.16775
$661$	18.0000	0.700119	0.350059	−	0.936727i	$-0.386161\pi$
$661$	18.0000	0.700119	0.350059	+	0.936727i	$0.386161\pi$
$662$	8.00000	0.310929
$663$	−9.00000	−0.349531
$664$	−12.0000	−0.465690
$665$	0	0
$666$	−48.0000	−1.85996
$667$	48.0000	1.85857
$668$	−5.00000	−0.193456
$669$	−36.0000	−1.39184
$670$	20.0000	0.772667
$671$	20.0000	0.772091
$672$	0	0
$673$	10.0000	0.385472	0.192736	−	0.981251i	$-0.438264\pi$
$673$	10.0000	0.385472	0.192736	+	0.981251i	$0.438264\pi$
$674$	8.00000	0.308148
$675$	9.00000	0.346410
$676$	−4.00000	−0.153846
$677$	42.0000	1.61419	0.807096	−	0.590421i	$-0.201038\pi$
$677$	42.0000	1.61419	0.807096	+	0.590421i	$0.201038\pi$
$678$	48.0000	1.84343
$679$	0	0
$680$	−2.00000	−0.0766965
$681$	9.00000	0.344881
$682$	20.0000	0.765840
$683$	21.0000	0.803543	0.401771	−	0.915740i	$-0.368395\pi$
$683$	21.0000	0.803543	0.401771	+	0.915740i	$0.368395\pi$
$684$	12.0000	0.458831
$685$	−38.0000	−1.45191
$686$	0	0
$687$	6.00000	0.228914
$688$	4.00000	0.152499
$689$	27.0000	1.02862
$690$	−48.0000	−1.82733
$691$	−4.00000	−0.152167	−0.0760836	−	0.997101i	$-0.524242\pi$
$691$	−4.00000	−0.152167	−0.0760836	+	0.997101i	$0.524242\pi$
$692$	0	0
$693$	0	0
$694$	−20.0000	−0.759190
$695$	−18.0000	−0.682779
$696$	−18.0000	−0.682288
$697$	−6.00000	−0.227266
$698$	−18.0000	−0.681310
$699$	24.0000	0.907763
$700$	0	0
$701$	33.0000	1.24639	0.623196	−	0.782065i	$-0.285834\pi$
$701$	33.0000	1.24639	0.623196	+	0.782065i	$0.285834\pi$
$702$	27.0000	1.01905
$703$	16.0000	0.603451
$704$	−5.00000	−0.188445
$705$	−60.0000	−2.25973
$706$	−1.00000	−0.0376355
$707$	0	0
$708$	12.0000	0.450988
$709$	22.0000	0.826227	0.413114	−	0.910679i	$-0.364441\pi$
$709$	22.0000	0.826227	0.413114	+	0.910679i	$0.364441\pi$
$710$	10.0000	0.375293
$711$	−6.00000	−0.225018
$712$	9.00000	0.337289
$713$	−32.0000	−1.19841
$714$	0	0
$715$	−30.0000	−1.12194
$716$	4.00000	0.149487
$717$	12.0000	0.448148
$718$	−20.0000	−0.746393
$719$	39.0000	1.45445	0.727227	−	0.686397i	$-0.240809\pi$
$719$	39.0000	1.45445	0.727227	+	0.686397i	$0.240809\pi$
$720$	12.0000	0.447214
$721$	0	0
$722$	15.0000	0.558242
$723$	54.0000	2.00828
$724$	12.0000	0.445976
$725$	6.00000	0.222834
$726$	42.0000	1.55877
$727$	32.0000	1.18681	0.593407	−	0.804902i	$-0.297782\pi$
$727$	32.0000	1.18681	0.593407	+	0.804902i	$0.297782\pi$
$728$	0	0
$729$	−27.0000	−1.00000
$730$	4.00000	0.148047
$731$	4.00000	0.147945
$732$	12.0000	0.443533
$733$	−17.0000	−0.627909	−0.313955	−	0.949438i	$-0.601654\pi$
$733$	−17.0000	−0.627909	−0.313955	+	0.949438i	$0.601654\pi$
$734$	15.0000	0.553660
$735$	0	0
$736$	8.00000	0.294884
$737$	50.0000	1.84177
$738$	36.0000	1.32518
$739$	−16.0000	−0.588570	−0.294285	−	0.955718i	$-0.595081\pi$
$739$	−16.0000	−0.588570	−0.294285	+	0.955718i	$0.595081\pi$
$740$	16.0000	0.588172
$741$	−18.0000	−0.661247
$742$	0	0
$743$	−15.0000	−0.550297	−0.275148	−	0.961402i	$-0.588727\pi$
$743$	−15.0000	−0.550297	−0.275148	+	0.961402i	$0.588727\pi$
$744$	12.0000	0.439941
$745$	−34.0000	−1.24566
$746$	11.0000	0.402739
$747$	72.0000	2.63434
$748$	−5.00000	−0.182818
$749$	0	0
$750$	−36.0000	−1.31453
$751$	23.0000	0.839282	0.419641	−	0.907690i	$-0.362156\pi$
$751$	23.0000	0.839282	0.419641	+	0.907690i	$0.362156\pi$
$752$	10.0000	0.364662
$753$	6.00000	0.218652
$754$	18.0000	0.655521
$755$	4.00000	0.145575
$756$	0	0
$757$	23.0000	0.835949	0.417975	−	0.908459i	$-0.362740\pi$
$757$	23.0000	0.835949	0.417975	+	0.908459i	$0.362740\pi$
$758$	5.00000	0.181608
$759$	−120.000	−4.35572
$760$	−4.00000	−0.145095
$761$	−45.0000	−1.63125	−0.815624	−	0.578582i	$-0.803606\pi$
$761$	−45.0000	−1.63125	−0.815624	+	0.578582i	$0.803606\pi$
$762$	−18.0000	−0.652071
$763$	0	0
$764$	−24.0000	−0.868290
$765$	12.0000	0.433861
$766$	−20.0000	−0.722629
$767$	−12.0000	−0.433295
$768$	−3.00000	−0.108253
$769$	23.0000	0.829401	0.414701	−	0.909958i	$-0.363886\pi$
$769$	23.0000	0.829401	0.414701	+	0.909958i	$0.363886\pi$
$770$	0	0
$771$	69.0000	2.48497
$772$	−16.0000	−0.575853
$773$	−3.00000	−0.107903	−0.0539513	−	0.998544i	$-0.517182\pi$
$773$	−3.00000	−0.107903	−0.0539513	+	0.998544i	$0.517182\pi$
$774$	−24.0000	−0.862662
$775$	−4.00000	−0.143684
$776$	4.00000	0.143592
$777$	0	0
$778$	−15.0000	−0.537776
$779$	−12.0000	−0.429945
$780$	−18.0000	−0.644503
$781$	25.0000	0.894570
$782$	8.00000	0.286079
$783$	54.0000	1.92980
$784$	0	0
$785$	−22.0000	−0.785214
$786$	−36.0000	−1.28408
$787$	52.0000	1.85360	0.926800	−	0.375555i	$-0.122548\pi$
$787$	52.0000	1.85360	0.926800	+	0.375555i	$0.122548\pi$
$788$	−2.00000	−0.0712470
$789$	54.0000	1.92245
$790$	2.00000	0.0711568
$791$	0	0
$792$	30.0000	1.06600
$793$	−12.0000	−0.426132
$794$	32.0000	1.13564
$795$	−54.0000	−1.91518
$796$	15.0000	0.531661
$797$	−17.0000	−0.602171	−0.301085	−	0.953597i	$-0.597349\pi$
$797$	−17.0000	−0.602171	−0.301085	+	0.953597i	$0.597349\pi$
$798$	0	0
$799$	10.0000	0.353775
$800$	1.00000	0.0353553
$801$	−54.0000	−1.90800
$802$	−16.0000	−0.564980
$803$	10.0000	0.352892
$804$	30.0000	1.05802
$805$	0	0
$806$	−12.0000	−0.422682
$807$	−42.0000	−1.47847
$808$	−2.00000	−0.0703598
$809$	−30.0000	−1.05474	−0.527372	−	0.849635i	$-0.676823\pi$
$809$	−30.0000	−1.05474	−0.527372	+	0.849635i	$0.676823\pi$
$810$	−18.0000	−0.632456
$811$	37.0000	1.29925	0.649623	−	0.760257i	$-0.274927\pi$
$811$	37.0000	1.29925	0.649623	+	0.760257i	$0.274927\pi$
$812$	0	0
$813$	−12.0000	−0.420858
$814$	40.0000	1.40200
$815$	24.0000	0.840683
$816$	−3.00000	−0.105021
$817$	8.00000	0.279885
$818$	23.0000	0.804176
$819$	0	0
$820$	−12.0000	−0.419058
$821$	0	0		−	1.00000i	$-0.5\pi$
$821$	0	0			1.00000i	$0.5\pi$
$822$	−57.0000	−1.98810
$823$	29.0000	1.01088	0.505438	−	0.862863i	$-0.331331\pi$
$823$	29.0000	1.01088	0.505438	+	0.862863i	$0.331331\pi$
$824$	14.0000	0.487713
$825$	−15.0000	−0.522233
$826$	0	0
$827$	3.00000	0.104320	0.0521601	−	0.998639i	$-0.483389\pi$
$827$	3.00000	0.104320	0.0521601	+	0.998639i	$0.483389\pi$
$828$	−48.0000	−1.66812
$829$	5.00000	0.173657	0.0868286	−	0.996223i	$-0.472327\pi$
$829$	5.00000	0.173657	0.0868286	+	0.996223i	$0.472327\pi$
$830$	−24.0000	−0.833052
$831$	12.0000	0.416275
$832$	3.00000	0.104006
$833$	0	0
$834$	−27.0000	−0.934934
$835$	−10.0000	−0.346064
$836$	−10.0000	−0.345857
$837$	−36.0000	−1.24434
$838$	39.0000	1.34723
$839$	−36.0000	−1.24286	−0.621429	−	0.783470i	$-0.713448\pi$
$839$	−36.0000	−1.24286	−0.621429	+	0.783470i	$0.713448\pi$
$840$	0	0
$841$	7.00000	0.241379
$842$	−30.0000	−1.03387
$843$	81.0000	2.78979
$844$	20.0000	0.688428
$845$	−8.00000	−0.275208
$846$	−60.0000	−2.06284
$847$	0	0
$848$	9.00000	0.309061
$849$	3.00000	0.102960
$850$	1.00000	0.0342997
$851$	−64.0000	−2.19389
$852$	15.0000	0.513892
$853$	10.0000	0.342393	0.171197	−	0.985237i	$-0.445237\pi$
$853$	10.0000	0.342393	0.171197	+	0.985237i	$0.445237\pi$
$854$	0	0
$855$	24.0000	0.820783
$856$	9.00000	0.307614
$857$	−28.0000	−0.956462	−0.478231	−	0.878234i	$-0.658722\pi$
$857$	−28.0000	−0.956462	−0.478231	+	0.878234i	$0.658722\pi$
$858$	−45.0000	−1.53627
$859$	−34.0000	−1.16007	−0.580033	−	0.814593i	$-0.696960\pi$
$859$	−34.0000	−1.16007	−0.580033	+	0.814593i	$0.696960\pi$
$860$	8.00000	0.272798
$861$	0	0
$862$	−5.00000	−0.170301
$863$	−16.0000	−0.544646	−0.272323	−	0.962206i	$-0.587792\pi$
$863$	−16.0000	−0.544646	−0.272323	+	0.962206i	$0.587792\pi$
$864$	9.00000	0.306186
$865$	0	0
$866$	30.0000	1.01944
$867$	−3.00000	−0.101885
$868$	0	0
$869$	5.00000	0.169613
$870$	−36.0000	−1.22051
$871$	−30.0000	−1.01651
$872$	16.0000	0.541828
$873$	−24.0000	−0.812277
$874$	16.0000	0.541208
$875$	0	0
$876$	6.00000	0.202721
$877$	−6.00000	−0.202606	−0.101303	−	0.994856i	$-0.532301\pi$
$877$	−6.00000	−0.202606	−0.101303	+	0.994856i	$0.532301\pi$
$878$	7.00000	0.236239
$879$	−87.0000	−2.93444
$880$	−10.0000	−0.337100
$881$	36.0000	1.21287	0.606435	−	0.795133i	$-0.292599\pi$
$881$	36.0000	1.21287	0.606435	+	0.795133i	$0.292599\pi$
$882$	0	0
$883$	−20.0000	−0.673054	−0.336527	−	0.941674i	$-0.609252\pi$
$883$	−20.0000	−0.673054	−0.336527	+	0.941674i	$0.609252\pi$
$884$	3.00000	0.100901
$885$	24.0000	0.806751
$886$	0	0
$887$	35.0000	1.17518	0.587592	−	0.809157i	$-0.300076\pi$
$887$	35.0000	1.17518	0.587592	+	0.809157i	$0.300076\pi$
$888$	24.0000	0.805387
$889$	0	0
$890$	18.0000	0.603361
$891$	−45.0000	−1.50756
$892$	12.0000	0.401790
$893$	20.0000	0.669274
$894$	−51.0000	−1.70570
$895$	8.00000	0.267411
$896$	0	0
$897$	72.0000	2.40401
$898$	6.00000	0.200223
$899$	−24.0000	−0.800445
$900$	−6.00000	−0.200000
$901$	9.00000	0.299833
$902$	−30.0000	−0.998891
$903$	0	0
$904$	−16.0000	−0.532152
$905$	24.0000	0.797787
$906$	6.00000	0.199337
$907$	48.0000	1.59381	0.796907	−	0.604102i	$-0.206468\pi$
$907$	48.0000	1.59381	0.796907	+	0.604102i	$0.206468\pi$
$908$	−3.00000	−0.0995585
$909$	12.0000	0.398015
$910$	0	0
$911$	−20.0000	−0.662630	−0.331315	−	0.943520i	$-0.607492\pi$
$911$	−20.0000	−0.662630	−0.331315	+	0.943520i	$0.607492\pi$
$912$	−6.00000	−0.198680
$913$	−60.0000	−1.98571
$914$	10.0000	0.330771
$915$	24.0000	0.793416
$916$	−2.00000	−0.0660819
$917$	0	0
$918$	9.00000	0.297044
$919$	14.0000	0.461817	0.230909	−	0.972975i	$-0.425830\pi$
$919$	14.0000	0.461817	0.230909	+	0.972975i	$0.425830\pi$
$920$	16.0000	0.527504
$921$	−78.0000	−2.57019
$922$	−11.0000	−0.362266
$923$	−15.0000	−0.493731
$924$	0	0
$925$	−8.00000	−0.263038
$926$	34.0000	1.11731
$927$	−84.0000	−2.75892
$928$	6.00000	0.196960
$929$	2.00000	0.0656179	0.0328089	−	0.999462i	$-0.489555\pi$
$929$	2.00000	0.0656179	0.0328089	+	0.999462i	$0.489555\pi$
$930$	24.0000	0.786991
$931$	0	0
$932$	−8.00000	−0.262049
$933$	45.0000	1.47323
$934$	−6.00000	−0.196326
$935$	−10.0000	−0.327035
$936$	−18.0000	−0.588348
$937$	−2.00000	−0.0653372	−0.0326686	−	0.999466i	$-0.510401\pi$
$937$	−2.00000	−0.0653372	−0.0326686	+	0.999466i	$0.510401\pi$
$938$	0	0
$939$	18.0000	0.587408
$940$	20.0000	0.652328
$941$	30.0000	0.977972	0.488986	−	0.872292i	$-0.337367\pi$
$941$	30.0000	0.977972	0.488986	+	0.872292i	$0.337367\pi$
$942$	−33.0000	−1.07520
$943$	48.0000	1.56310
$944$	−4.00000	−0.130189
$945$	0	0
$946$	20.0000	0.650256
$947$	3.00000	0.0974869	0.0487435	−	0.998811i	$-0.484478\pi$
$947$	3.00000	0.0974869	0.0487435	+	0.998811i	$0.484478\pi$
$948$	3.00000	0.0974355
$949$	−6.00000	−0.194768
$950$	2.00000	0.0648886
$951$	−36.0000	−1.16738
$952$	0	0
$953$	−15.0000	−0.485898	−0.242949	−	0.970039i	$-0.578115\pi$
$953$	−15.0000	−0.485898	−0.242949	+	0.970039i	$0.578115\pi$
$954$	−54.0000	−1.74831
$955$	−48.0000	−1.55324
$956$	−4.00000	−0.129369
$957$	−90.0000	−2.90929
$958$	0	0
$959$	0	0
$960$	−6.00000	−0.193649
$961$	−15.0000	−0.483871
$962$	−24.0000	−0.773791
$963$	−54.0000	−1.74013
$964$	−18.0000	−0.579741
$965$	−32.0000	−1.03012
$966$	0	0
$967$	14.0000	0.450210	0.225105	−	0.974335i	$-0.427728\pi$
$967$	14.0000	0.450210	0.225105	+	0.974335i	$0.427728\pi$
$968$	−14.0000	−0.449977
$969$	−6.00000	−0.192748
$970$	8.00000	0.256865
$971$	30.0000	0.962746	0.481373	−	0.876516i	$-0.340138\pi$
$971$	30.0000	0.962746	0.481373	+	0.876516i	$0.340138\pi$
$972$	0	0
$973$	0	0
$974$	−11.0000	−0.352463
$975$	9.00000	0.288231
$976$	−4.00000	−0.128037
$977$	10.0000	0.319928	0.159964	−	0.987123i	$-0.448862\pi$
$977$	10.0000	0.319928	0.159964	+	0.987123i	$0.448862\pi$
$978$	36.0000	1.15115
$979$	45.0000	1.43821
$980$	0	0
$981$	−96.0000	−3.06504
$982$	38.0000	1.21263
$983$	37.0000	1.18012	0.590058	−	0.807361i	$-0.299105\pi$
$983$	37.0000	1.18012	0.590058	+	0.807361i	$0.299105\pi$
$984$	−18.0000	−0.573819
$985$	−4.00000	−0.127451
$986$	6.00000	0.191079
$987$	0	0
$988$	6.00000	0.190885
$989$	−32.0000	−1.01754
$990$	60.0000	1.90693
$991$	−47.0000	−1.49300	−0.746502	−	0.665383i	$-0.768268\pi$
$991$	−47.0000	−1.49300	−0.746502	+	0.665383i	$0.768268\pi$
$992$	−4.00000	−0.127000
$993$	24.0000	0.761617
$994$	0	0
$995$	30.0000	0.951064
$996$	−36.0000	−1.14070
$997$	−18.0000	−0.570066	−0.285033	−	0.958518i	$-0.592005\pi$
$997$	−18.0000	−0.570066	−0.285033	+	0.958518i	$0.592005\pi$
$998$	11.0000	0.348199
$999$	−72.0000	−2.27798

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1666.2.a.a.1.1		1
7.3	odd	6		238.2.e.b.205.1	yes	2
7.5	odd	6		238.2.e.b.137.1	✓	2
7.6	odd	2		1666.2.a.h.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
238.2.e.b.137.1	✓	2	7.5	odd	6
238.2.e.b.205.1	yes	2	7.3	odd	6
1666.2.a.a.1.1		1	1.1	even	1	trivial
1666.2.a.h.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:	\( N \)	\(=\)	\( 1666 = 2 \cdot 7^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1666.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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