LMFDB - Embedded newform 170.2.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [170,2,Mod(1,170)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(170, 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("170.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 170 = 2 \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	170.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:	$1.35745683436$
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	$\chi$	$=$	170.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

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

\(q-1.00000 q^{2} -2.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.00000 q^{6} -2.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} -2.00000 q^{11} -2.00000 q^{12} -6.00000 q^{13} +2.00000 q^{14} -2.00000 q^{15} +1.00000 q^{16} +1.00000 q^{17} -1.00000 q^{18} -8.00000 q^{19} +1.00000 q^{20} +4.00000 q^{21} +2.00000 q^{22} -2.00000 q^{23} +2.00000 q^{24} +1.00000 q^{25} +6.00000 q^{26} +4.00000 q^{27} -2.00000 q^{28} +6.00000 q^{29} +2.00000 q^{30} -2.00000 q^{31} -1.00000 q^{32} +4.00000 q^{33} -1.00000 q^{34} -2.00000 q^{35} +1.00000 q^{36} +6.00000 q^{37} +8.00000 q^{38} +12.0000 q^{39} -1.00000 q^{40} +2.00000 q^{41} -4.00000 q^{42} -4.00000 q^{43} -2.00000 q^{44} +1.00000 q^{45} +2.00000 q^{46} +4.00000 q^{47} -2.00000 q^{48} -3.00000 q^{49} -1.00000 q^{50} -2.00000 q^{51} -6.00000 q^{52} -10.0000 q^{53} -4.00000 q^{54} -2.00000 q^{55} +2.00000 q^{56} +16.0000 q^{57} -6.00000 q^{58} -2.00000 q^{60} -10.0000 q^{61} +2.00000 q^{62} -2.00000 q^{63} +1.00000 q^{64} -6.00000 q^{65} -4.00000 q^{66} +8.00000 q^{67} +1.00000 q^{68} +4.00000 q^{69} +2.00000 q^{70} +14.0000 q^{71} -1.00000 q^{72} +10.0000 q^{73} -6.00000 q^{74} -2.00000 q^{75} -8.00000 q^{76} +4.00000 q^{77} -12.0000 q^{78} -14.0000 q^{79} +1.00000 q^{80} -11.0000 q^{81} -2.00000 q^{82} -4.00000 q^{83} +4.00000 q^{84} +1.00000 q^{85} +4.00000 q^{86} -12.0000 q^{87} +2.00000 q^{88} +6.00000 q^{89} -1.00000 q^{90} +12.0000 q^{91} -2.00000 q^{92} +4.00000 q^{93} -4.00000 q^{94} -8.00000 q^{95} +2.00000 q^{96} -14.0000 q^{97} +3.00000 q^{98} -2.00000 q^{99} +O(q^{100})\)

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
$2$	−1.00000	−0.707107
$3$	−2.00000	−1.15470	−0.577350	−	0.816497i	$-0.695913\pi$
$3$	−2.00000	−1.15470	−0.577350	+	0.816497i	$0.695913\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	2.00000	0.816497
$7$	−2.00000	−0.755929	−0.377964	−	0.925820i	$-0.623376\pi$
$7$	−2.00000	−0.755929	−0.377964	+	0.925820i	$0.623376\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−1.00000	−0.316228
$11$	−2.00000	−0.603023	−0.301511	−	0.953463i	$-0.597491\pi$
$11$	−2.00000	−0.603023	−0.301511	+	0.953463i	$0.597491\pi$
$12$	−2.00000	−0.577350
$13$	−6.00000	−1.66410	−0.832050	−	0.554700i	$-0.812833\pi$
$13$	−6.00000	−1.66410	−0.832050	+	0.554700i	$0.812833\pi$
$14$	2.00000	0.534522
$15$	−2.00000	−0.516398
$16$	1.00000	0.250000
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−1.00000	−0.235702
$19$	−8.00000	−1.83533	−0.917663	−	0.397360i	$-0.869927\pi$
$19$	−8.00000	−1.83533	−0.917663	+	0.397360i	$0.869927\pi$
$20$	1.00000	0.223607
$21$	4.00000	0.872872
$22$	2.00000	0.426401
$23$	−2.00000	−0.417029	−0.208514	−	0.978019i	$-0.566863\pi$
$23$	−2.00000	−0.417029	−0.208514	+	0.978019i	$0.566863\pi$
$24$	2.00000	0.408248
$25$	1.00000	0.200000
$26$	6.00000	1.17670
$27$	4.00000	0.769800
$28$	−2.00000	−0.377964
$29$	6.00000	1.11417	0.557086	−	0.830455i	$-0.311919\pi$
$29$	6.00000	1.11417	0.557086	+	0.830455i	$0.311919\pi$
$30$	2.00000	0.365148
$31$	−2.00000	−0.359211	−0.179605	−	0.983739i	$-0.557482\pi$
$31$	−2.00000	−0.359211	−0.179605	+	0.983739i	$0.557482\pi$
$32$	−1.00000	−0.176777
$33$	4.00000	0.696311
$34$	−1.00000	−0.171499
$35$	−2.00000	−0.338062
$36$	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	$0.335828\pi$
$38$	8.00000	1.29777
$39$	12.0000	1.92154
$40$	−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	$0.450084\pi$
$42$	−4.00000	−0.617213
$43$	−4.00000	−0.609994	−0.304997	−	0.952353i	$-0.598656\pi$
$43$	−4.00000	−0.609994	−0.304997	+	0.952353i	$0.598656\pi$
$44$	−2.00000	−0.301511
$45$	1.00000	0.149071
$46$	2.00000	0.294884
$47$	4.00000	0.583460	0.291730	−	0.956501i	$-0.405769\pi$
$47$	4.00000	0.583460	0.291730	+	0.956501i	$0.405769\pi$
$48$	−2.00000	−0.288675
$49$	−3.00000	−0.428571
$50$	−1.00000	−0.141421
$51$	−2.00000	−0.280056
$52$	−6.00000	−0.832050
$53$	−10.0000	−1.37361	−0.686803	−	0.726844i	$-0.740986\pi$
$53$	−10.0000	−1.37361	−0.686803	+	0.726844i	$0.740986\pi$
$54$	−4.00000	−0.544331
$55$	−2.00000	−0.269680
$56$	2.00000	0.267261
$57$	16.0000	2.11925
$58$	−6.00000	−0.787839
$59$	0	0		−	1.00000i	$-0.5\pi$
$59$	0	0			1.00000i	$0.5\pi$
$60$	−2.00000	−0.258199
$61$	−10.0000	−1.28037	−0.640184	−	0.768221i	$-0.721142\pi$
$61$	−10.0000	−1.28037	−0.640184	+	0.768221i	$0.721142\pi$
$62$	2.00000	0.254000
$63$	−2.00000	−0.251976
$64$	1.00000	0.125000
$65$	−6.00000	−0.744208
$66$	−4.00000	−0.492366
$67$	8.00000	0.977356	0.488678	−	0.872464i	$-0.337479\pi$
$67$	8.00000	0.977356	0.488678	+	0.872464i	$0.337479\pi$
$68$	1.00000	0.121268
$69$	4.00000	0.481543
$70$	2.00000	0.239046
$71$	14.0000	1.66149	0.830747	−	0.556650i	$-0.187914\pi$
$71$	14.0000	1.66149	0.830747	+	0.556650i	$0.187914\pi$
$72$	−1.00000	−0.117851
$73$	10.0000	1.17041	0.585206	−	0.810885i	$-0.301014\pi$
$73$	10.0000	1.17041	0.585206	+	0.810885i	$0.301014\pi$
$74$	−6.00000	−0.697486
$75$	−2.00000	−0.230940
$76$	−8.00000	−0.917663
$77$	4.00000	0.455842
$78$	−12.0000	−1.35873
$79$	−14.0000	−1.57512	−0.787562	−	0.616236i	$-0.788657\pi$
$79$	−14.0000	−1.57512	−0.787562	+	0.616236i	$0.788657\pi$
$80$	1.00000	0.111803
$81$	−11.0000	−1.22222
$82$	−2.00000	−0.220863
$83$	−4.00000	−0.439057	−0.219529	−	0.975606i	$-0.570452\pi$
$83$	−4.00000	−0.439057	−0.219529	+	0.975606i	$0.570452\pi$
$84$	4.00000	0.436436
$85$	1.00000	0.108465
$86$	4.00000	0.431331
$87$	−12.0000	−1.28654
$88$	2.00000	0.213201
$89$	6.00000	0.635999	0.317999	−	0.948091i	$-0.396989\pi$
$89$	6.00000	0.635999	0.317999	+	0.948091i	$0.396989\pi$
$90$	−1.00000	−0.105409
$91$	12.0000	1.25794
$92$	−2.00000	−0.208514
$93$	4.00000	0.414781
$94$	−4.00000	−0.412568
$95$	−8.00000	−0.820783
$96$	2.00000	0.204124
$97$	−14.0000	−1.42148	−0.710742	−	0.703452i	$-0.751641\pi$
$97$	−14.0000	−1.42148	−0.710742	+	0.703452i	$0.751641\pi$
$98$	3.00000	0.303046
$99$	−2.00000	−0.201008
$100$	1.00000	0.100000
$101$	−6.00000	−0.597022	−0.298511	−	0.954406i	$-0.596490\pi$
$101$	−6.00000	−0.597022	−0.298511	+	0.954406i	$0.596490\pi$
$102$	2.00000	0.198030
$103$	4.00000	0.394132	0.197066	−	0.980390i	$-0.436859\pi$
$103$	4.00000	0.394132	0.197066	+	0.980390i	$0.436859\pi$
$104$	6.00000	0.588348
$105$	4.00000	0.390360
$106$	10.0000	0.971286
$107$	−10.0000	−0.966736	−0.483368	−	0.875417i	$-0.660587\pi$
$107$	−10.0000	−0.966736	−0.483368	+	0.875417i	$0.660587\pi$
$108$	4.00000	0.384900
$109$	−2.00000	−0.191565	−0.0957826	−	0.995402i	$-0.530535\pi$
$109$	−2.00000	−0.191565	−0.0957826	+	0.995402i	$0.530535\pi$
$110$	2.00000	0.190693
$111$	−12.0000	−1.13899
$112$	−2.00000	−0.188982
$113$	18.0000	1.69330	0.846649	−	0.532152i	$-0.178617\pi$
$113$	18.0000	1.69330	0.846649	+	0.532152i	$0.178617\pi$
$114$	−16.0000	−1.49854
$115$	−2.00000	−0.186501
$116$	6.00000	0.557086
$117$	−6.00000	−0.554700
$118$	0	0
$119$	−2.00000	−0.183340
$120$	2.00000	0.182574
$121$	−7.00000	−0.636364
$122$	10.0000	0.905357
$123$	−4.00000	−0.360668
$124$	−2.00000	−0.179605
$125$	1.00000	0.0894427
$126$	2.00000	0.178174
$127$	16.0000	1.41977	0.709885	−	0.704317i	$-0.248747\pi$
$127$	16.0000	1.41977	0.709885	+	0.704317i	$0.248747\pi$
$128$	−1.00000	−0.0883883
$129$	8.00000	0.704361
$130$	6.00000	0.526235
$131$	−6.00000	−0.524222	−0.262111	−	0.965038i	$-0.584419\pi$
$131$	−6.00000	−0.524222	−0.262111	+	0.965038i	$0.584419\pi$
$132$	4.00000	0.348155
$133$	16.0000	1.38738
$134$	−8.00000	−0.691095
$135$	4.00000	0.344265
$136$	−1.00000	−0.0857493
$137$	−18.0000	−1.53784	−0.768922	−	0.639343i	$-0.779207\pi$
$137$	−18.0000	−1.53784	−0.768922	+	0.639343i	$0.779207\pi$
$138$	−4.00000	−0.340503
$139$	2.00000	0.169638	0.0848189	−	0.996396i	$-0.472969\pi$
$139$	2.00000	0.169638	0.0848189	+	0.996396i	$0.472969\pi$
$140$	−2.00000	−0.169031
$141$	−8.00000	−0.673722
$142$	−14.0000	−1.17485
$143$	12.0000	1.00349
$144$	1.00000	0.0833333
$145$	6.00000	0.498273
$146$	−10.0000	−0.827606
$147$	6.00000	0.494872
$148$	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	$0.634337\pi$
$150$	2.00000	0.163299
$151$	20.0000	1.62758	0.813788	−	0.581161i	$-0.197401\pi$
$151$	20.0000	1.62758	0.813788	+	0.581161i	$0.197401\pi$
$152$	8.00000	0.648886
$153$	1.00000	0.0808452
$154$	−4.00000	−0.322329
$155$	−2.00000	−0.160644
$156$	12.0000	0.960769
$157$	−18.0000	−1.43656	−0.718278	−	0.695756i	$-0.755069\pi$
$157$	−18.0000	−1.43656	−0.718278	+	0.695756i	$0.755069\pi$
$158$	14.0000	1.11378
$159$	20.0000	1.58610
$160$	−1.00000	−0.0790569
$161$	4.00000	0.315244
$162$	11.0000	0.864242
$163$	2.00000	0.156652	0.0783260	−	0.996928i	$-0.475042\pi$
$163$	2.00000	0.156652	0.0783260	+	0.996928i	$0.475042\pi$
$164$	2.00000	0.156174
$165$	4.00000	0.311400
$166$	4.00000	0.310460
$167$	2.00000	0.154765	0.0773823	−	0.997001i	$-0.475344\pi$
$167$	2.00000	0.154765	0.0773823	+	0.997001i	$0.475344\pi$
$168$	−4.00000	−0.308607
$169$	23.0000	1.76923
$170$	−1.00000	−0.0766965
$171$	−8.00000	−0.611775
$172$	−4.00000	−0.304997
$173$	−10.0000	−0.760286	−0.380143	−	0.924928i	$-0.624125\pi$
$173$	−10.0000	−0.760286	−0.380143	+	0.924928i	$0.624125\pi$
$174$	12.0000	0.909718
$175$	−2.00000	−0.151186
$176$	−2.00000	−0.150756
$177$	0	0
$178$	−6.00000	−0.449719
$179$	−16.0000	−1.19590	−0.597948	−	0.801535i	$-0.704017\pi$
$179$	−16.0000	−1.19590	−0.597948	+	0.801535i	$0.704017\pi$
$180$	1.00000	0.0745356
$181$	14.0000	1.04061	0.520306	−	0.853980i	$-0.325818\pi$
$181$	14.0000	1.04061	0.520306	+	0.853980i	$0.325818\pi$
$182$	−12.0000	−0.889499
$183$	20.0000	1.47844
$184$	2.00000	0.147442
$185$	6.00000	0.441129
$186$	−4.00000	−0.293294
$187$	−2.00000	−0.146254
$188$	4.00000	0.291730
$189$	−8.00000	−0.581914
$190$	8.00000	0.580381
$191$	−8.00000	−0.578860	−0.289430	−	0.957199i	$-0.593466\pi$
$191$	−8.00000	−0.578860	−0.289430	+	0.957199i	$0.593466\pi$
$192$	−2.00000	−0.144338
$193$	−14.0000	−1.00774	−0.503871	−	0.863779i	$-0.668091\pi$
$193$	−14.0000	−1.00774	−0.503871	+	0.863779i	$0.668091\pi$
$194$	14.0000	1.00514
$195$	12.0000	0.859338
$196$	−3.00000	−0.214286
$197$	6.00000	0.427482	0.213741	−	0.976890i	$-0.431435\pi$
$197$	6.00000	0.427482	0.213741	+	0.976890i	$0.431435\pi$
$198$	2.00000	0.142134
$199$	−26.0000	−1.84309	−0.921546	−	0.388270i	$-0.873073\pi$
$199$	−26.0000	−1.84309	−0.921546	+	0.388270i	$0.873073\pi$
$200$	−1.00000	−0.0707107
$201$	−16.0000	−1.12855
$202$	6.00000	0.422159
$203$	−12.0000	−0.842235
$204$	−2.00000	−0.140028
$205$	2.00000	0.139686
$206$	−4.00000	−0.278693
$207$	−2.00000	−0.139010
$208$	−6.00000	−0.416025
$209$	16.0000	1.10674
$210$	−4.00000	−0.276026
$211$	−2.00000	−0.137686	−0.0688428	−	0.997628i	$-0.521931\pi$
$211$	−2.00000	−0.137686	−0.0688428	+	0.997628i	$0.521931\pi$
$212$	−10.0000	−0.686803
$213$	−28.0000	−1.91853
$214$	10.0000	0.683586
$215$	−4.00000	−0.272798
$216$	−4.00000	−0.272166
$217$	4.00000	0.271538
$218$	2.00000	0.135457
$219$	−20.0000	−1.35147
$220$	−2.00000	−0.134840
$221$	−6.00000	−0.403604
$222$	12.0000	0.805387
$223$	−8.00000	−0.535720	−0.267860	−	0.963458i	$-0.586316\pi$
$223$	−8.00000	−0.535720	−0.267860	+	0.963458i	$0.586316\pi$
$224$	2.00000	0.133631
$225$	1.00000	0.0666667
$226$	−18.0000	−1.19734
$227$	−30.0000	−1.99117	−0.995585	−	0.0938647i	$-0.970078\pi$
$227$	−30.0000	−1.99117	−0.995585	+	0.0938647i	$0.970078\pi$
$228$	16.0000	1.05963
$229$	−14.0000	−0.925146	−0.462573	−	0.886581i	$-0.653074\pi$
$229$	−14.0000	−0.925146	−0.462573	+	0.886581i	$0.653074\pi$
$230$	2.00000	0.131876
$231$	−8.00000	−0.526361
$232$	−6.00000	−0.393919
$233$	10.0000	0.655122	0.327561	−	0.944830i	$-0.393773\pi$
$233$	10.0000	0.655122	0.327561	+	0.944830i	$0.393773\pi$
$234$	6.00000	0.392232
$235$	4.00000	0.260931
$236$	0	0
$237$	28.0000	1.81880
$238$	2.00000	0.129641
$239$	24.0000	1.55243	0.776215	−	0.630468i	$-0.217137\pi$
$239$	24.0000	1.55243	0.776215	+	0.630468i	$0.217137\pi$
$240$	−2.00000	−0.129099
$241$	−14.0000	−0.901819	−0.450910	−	0.892570i	$-0.648900\pi$
$241$	−14.0000	−0.901819	−0.450910	+	0.892570i	$0.648900\pi$
$242$	7.00000	0.449977
$243$	10.0000	0.641500
$244$	−10.0000	−0.640184
$245$	−3.00000	−0.191663
$246$	4.00000	0.255031
$247$	48.0000	3.05417
$248$	2.00000	0.127000
$249$	8.00000	0.506979
$250$	−1.00000	−0.0632456
$251$	−20.0000	−1.26239	−0.631194	−	0.775625i	$-0.717435\pi$
$251$	−20.0000	−1.26239	−0.631194	+	0.775625i	$0.717435\pi$
$252$	−2.00000	−0.125988
$253$	4.00000	0.251478
$254$	−16.0000	−1.00393
$255$	−2.00000	−0.125245
$256$	1.00000	0.0625000
$257$	−18.0000	−1.12281	−0.561405	−	0.827541i	$-0.689739\pi$
$257$	−18.0000	−1.12281	−0.561405	+	0.827541i	$0.689739\pi$
$258$	−8.00000	−0.498058
$259$	−12.0000	−0.745644
$260$	−6.00000	−0.372104
$261$	6.00000	0.371391
$262$	6.00000	0.370681
$263$	16.0000	0.986602	0.493301	−	0.869859i	$-0.335790\pi$
$263$	16.0000	0.986602	0.493301	+	0.869859i	$0.335790\pi$
$264$	−4.00000	−0.246183
$265$	−10.0000	−0.614295
$266$	−16.0000	−0.981023
$267$	−12.0000	−0.734388
$268$	8.00000	0.488678
$269$	22.0000	1.34136	0.670682	−	0.741745i	$-0.266002\pi$
$269$	22.0000	1.34136	0.670682	+	0.741745i	$0.266002\pi$
$270$	−4.00000	−0.243432
$271$	16.0000	0.971931	0.485965	−	0.873978i	$-0.338468\pi$
$271$	16.0000	0.971931	0.485965	+	0.873978i	$0.338468\pi$
$272$	1.00000	0.0606339
$273$	−24.0000	−1.45255
$274$	18.0000	1.08742
$275$	−2.00000	−0.120605
$276$	4.00000	0.240772
$277$	−18.0000	−1.08152	−0.540758	−	0.841178i	$-0.681862\pi$
$277$	−18.0000	−1.08152	−0.540758	+	0.841178i	$0.681862\pi$
$278$	−2.00000	−0.119952
$279$	−2.00000	−0.119737
$280$	2.00000	0.119523
$281$	−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
$283$	18.0000	1.06999	0.534994	−	0.844856i	$-0.320314\pi$
$283$	18.0000	1.06999	0.534994	+	0.844856i	$0.320314\pi$
$284$	14.0000	0.830747
$285$	16.0000	0.947758
$286$	−12.0000	−0.709575
$287$	−4.00000	−0.236113
$288$	−1.00000	−0.0589256
$289$	1.00000	0.0588235
$290$	−6.00000	−0.352332
$291$	28.0000	1.64139
$292$	10.0000	0.585206
$293$	6.00000	0.350524	0.175262	−	0.984522i	$-0.443923\pi$
$293$	6.00000	0.350524	0.175262	+	0.984522i	$0.443923\pi$
$294$	−6.00000	−0.349927
$295$	0	0
$296$	−6.00000	−0.348743
$297$	−8.00000	−0.464207
$298$	10.0000	0.579284
$299$	12.0000	0.693978
$300$	−2.00000	−0.115470
$301$	8.00000	0.461112
$302$	−20.0000	−1.15087
$303$	12.0000	0.689382
$304$	−8.00000	−0.458831
$305$	−10.0000	−0.572598
$306$	−1.00000	−0.0571662
$307$	−16.0000	−0.913168	−0.456584	−	0.889680i	$-0.650927\pi$
$307$	−16.0000	−0.913168	−0.456584	+	0.889680i	$0.650927\pi$
$308$	4.00000	0.227921
$309$	−8.00000	−0.455104
$310$	2.00000	0.113592
$311$	−2.00000	−0.113410	−0.0567048	−	0.998391i	$-0.518059\pi$
$311$	−2.00000	−0.113410	−0.0567048	+	0.998391i	$0.518059\pi$
$312$	−12.0000	−0.679366
$313$	−14.0000	−0.791327	−0.395663	−	0.918396i	$-0.629485\pi$
$313$	−14.0000	−0.791327	−0.395663	+	0.918396i	$0.629485\pi$
$314$	18.0000	1.01580
$315$	−2.00000	−0.112687
$316$	−14.0000	−0.787562
$317$	30.0000	1.68497	0.842484	−	0.538721i	$-0.181092\pi$
$317$	30.0000	1.68497	0.842484	+	0.538721i	$0.181092\pi$
$318$	−20.0000	−1.12154
$319$	−12.0000	−0.671871
$320$	1.00000	0.0559017
$321$	20.0000	1.11629
$322$	−4.00000	−0.222911
$323$	−8.00000	−0.445132
$324$	−11.0000	−0.611111
$325$	−6.00000	−0.332820
$326$	−2.00000	−0.110770
$327$	4.00000	0.221201
$328$	−2.00000	−0.110432
$329$	−8.00000	−0.441054
$330$	−4.00000	−0.220193
$331$	24.0000	1.31916	0.659580	−	0.751635i	$-0.270734\pi$
$331$	24.0000	1.31916	0.659580	+	0.751635i	$0.270734\pi$
$332$	−4.00000	−0.219529
$333$	6.00000	0.328798
$334$	−2.00000	−0.109435
$335$	8.00000	0.437087
$336$	4.00000	0.218218
$337$	2.00000	0.108947	0.0544735	−	0.998515i	$-0.482652\pi$
$337$	2.00000	0.108947	0.0544735	+	0.998515i	$0.482652\pi$
$338$	−23.0000	−1.25104
$339$	−36.0000	−1.95525
$340$	1.00000	0.0542326
$341$	4.00000	0.216612
$342$	8.00000	0.432590
$343$	20.0000	1.07990
$344$	4.00000	0.215666
$345$	4.00000	0.215353
$346$	10.0000	0.537603
$347$	10.0000	0.536828	0.268414	−	0.963304i	$-0.413500\pi$
$347$	10.0000	0.536828	0.268414	+	0.963304i	$0.413500\pi$
$348$	−12.0000	−0.643268
$349$	−2.00000	−0.107058	−0.0535288	−	0.998566i	$-0.517047\pi$
$349$	−2.00000	−0.107058	−0.0535288	+	0.998566i	$0.517047\pi$
$350$	2.00000	0.106904
$351$	−24.0000	−1.28103
$352$	2.00000	0.106600
$353$	−30.0000	−1.59674	−0.798369	−	0.602168i	$-0.794304\pi$
$353$	−30.0000	−1.59674	−0.798369	+	0.602168i	$0.794304\pi$
$354$	0	0
$355$	14.0000	0.743043
$356$	6.00000	0.317999
$357$	4.00000	0.211702
$358$	16.0000	0.845626
$359$	20.0000	1.05556	0.527780	−	0.849381i	$-0.323025\pi$
$359$	20.0000	1.05556	0.527780	+	0.849381i	$0.323025\pi$
$360$	−1.00000	−0.0527046
$361$	45.0000	2.36842
$362$	−14.0000	−0.735824
$363$	14.0000	0.734809
$364$	12.0000	0.628971
$365$	10.0000	0.523424
$366$	−20.0000	−1.04542
$367$	22.0000	1.14839	0.574195	−	0.818718i	$-0.305315\pi$
$367$	22.0000	1.14839	0.574195	+	0.818718i	$0.305315\pi$
$368$	−2.00000	−0.104257
$369$	2.00000	0.104116
$370$	−6.00000	−0.311925
$371$	20.0000	1.03835
$372$	4.00000	0.207390
$373$	−30.0000	−1.55334	−0.776671	−	0.629907i	$-0.783093\pi$
$373$	−30.0000	−1.55334	−0.776671	+	0.629907i	$0.783093\pi$
$374$	2.00000	0.103418
$375$	−2.00000	−0.103280
$376$	−4.00000	−0.206284
$377$	−36.0000	−1.85409
$378$	8.00000	0.411476
$379$	26.0000	1.33553	0.667765	−	0.744372i	$-0.267251\pi$
$379$	26.0000	1.33553	0.667765	+	0.744372i	$0.267251\pi$
$380$	−8.00000	−0.410391
$381$	−32.0000	−1.63941
$382$	8.00000	0.409316
$383$	8.00000	0.408781	0.204390	−	0.978889i	$-0.434479\pi$
$383$	8.00000	0.408781	0.204390	+	0.978889i	$0.434479\pi$
$384$	2.00000	0.102062
$385$	4.00000	0.203859
$386$	14.0000	0.712581
$387$	−4.00000	−0.203331
$388$	−14.0000	−0.710742
$389$	18.0000	0.912636	0.456318	−	0.889817i	$-0.349168\pi$
$389$	18.0000	0.912636	0.456318	+	0.889817i	$0.349168\pi$
$390$	−12.0000	−0.607644
$391$	−2.00000	−0.101144
$392$	3.00000	0.151523
$393$	12.0000	0.605320
$394$	−6.00000	−0.302276
$395$	−14.0000	−0.704416
$396$	−2.00000	−0.100504
$397$	22.0000	1.10415	0.552074	−	0.833795i	$-0.313837\pi$
$397$	22.0000	1.10415	0.552074	+	0.833795i	$0.313837\pi$
$398$	26.0000	1.30326
$399$	−32.0000	−1.60200
$400$	1.00000	0.0500000
$401$	26.0000	1.29838	0.649189	−	0.760627i	$-0.275108\pi$
$401$	26.0000	1.29838	0.649189	+	0.760627i	$0.275108\pi$
$402$	16.0000	0.798007
$403$	12.0000	0.597763
$404$	−6.00000	−0.298511
$405$	−11.0000	−0.546594
$406$	12.0000	0.595550
$407$	−12.0000	−0.594818
$408$	2.00000	0.0990148
$409$	10.0000	0.494468	0.247234	−	0.968956i	$-0.420478\pi$
$409$	10.0000	0.494468	0.247234	+	0.968956i	$0.420478\pi$
$410$	−2.00000	−0.0987730
$411$	36.0000	1.77575
$412$	4.00000	0.197066
$413$	0	0
$414$	2.00000	0.0982946
$415$	−4.00000	−0.196352
$416$	6.00000	0.294174
$417$	−4.00000	−0.195881
$418$	−16.0000	−0.782586
$419$	−10.0000	−0.488532	−0.244266	−	0.969708i	$-0.578547\pi$
$419$	−10.0000	−0.488532	−0.244266	+	0.969708i	$0.578547\pi$
$420$	4.00000	0.195180
$421$	26.0000	1.26716	0.633581	−	0.773676i	$-0.281584\pi$
$421$	26.0000	1.26716	0.633581	+	0.773676i	$0.281584\pi$
$422$	2.00000	0.0973585
$423$	4.00000	0.194487
$424$	10.0000	0.485643
$425$	1.00000	0.0485071
$426$	28.0000	1.35660
$427$	20.0000	0.967868
$428$	−10.0000	−0.483368
$429$	−24.0000	−1.15873
$430$	4.00000	0.192897
$431$	10.0000	0.481683	0.240842	−	0.970564i	$-0.422577\pi$
$431$	10.0000	0.481683	0.240842	+	0.970564i	$0.422577\pi$
$432$	4.00000	0.192450
$433$	−18.0000	−0.865025	−0.432512	−	0.901628i	$-0.642373\pi$
$433$	−18.0000	−0.865025	−0.432512	+	0.901628i	$0.642373\pi$
$434$	−4.00000	−0.192006
$435$	−12.0000	−0.575356
$436$	−2.00000	−0.0957826
$437$	16.0000	0.765384
$438$	20.0000	0.955637
$439$	−10.0000	−0.477274	−0.238637	−	0.971109i	$-0.576701\pi$
$439$	−10.0000	−0.477274	−0.238637	+	0.971109i	$0.576701\pi$
$440$	2.00000	0.0953463
$441$	−3.00000	−0.142857
$442$	6.00000	0.285391
$443$	−24.0000	−1.14027	−0.570137	−	0.821549i	$-0.693110\pi$
$443$	−24.0000	−1.14027	−0.570137	+	0.821549i	$0.693110\pi$
$444$	−12.0000	−0.569495
$445$	6.00000	0.284427
$446$	8.00000	0.378811
$447$	20.0000	0.945968
$448$	−2.00000	−0.0944911
$449$	−6.00000	−0.283158	−0.141579	−	0.989927i	$-0.545218\pi$
$449$	−6.00000	−0.283158	−0.141579	+	0.989927i	$0.545218\pi$
$450$	−1.00000	−0.0471405
$451$	−4.00000	−0.188353
$452$	18.0000	0.846649
$453$	−40.0000	−1.87936
$454$	30.0000	1.40797
$455$	12.0000	0.562569
$456$	−16.0000	−0.749269
$457$	−42.0000	−1.96468	−0.982339	−	0.187112i	$-0.940087\pi$
$457$	−42.0000	−1.96468	−0.982339	+	0.187112i	$0.940087\pi$
$458$	14.0000	0.654177
$459$	4.00000	0.186704
$460$	−2.00000	−0.0932505
$461$	30.0000	1.39724	0.698620	−	0.715493i	$-0.253798\pi$
$461$	30.0000	1.39724	0.698620	+	0.715493i	$0.253798\pi$
$462$	8.00000	0.372194
$463$	−28.0000	−1.30127	−0.650635	−	0.759390i	$-0.725497\pi$
$463$	−28.0000	−1.30127	−0.650635	+	0.759390i	$0.725497\pi$
$464$	6.00000	0.278543
$465$	4.00000	0.185496
$466$	−10.0000	−0.463241
$467$	−28.0000	−1.29569	−0.647843	−	0.761774i	$-0.724329\pi$
$467$	−28.0000	−1.29569	−0.647843	+	0.761774i	$0.724329\pi$
$468$	−6.00000	−0.277350
$469$	−16.0000	−0.738811
$470$	−4.00000	−0.184506
$471$	36.0000	1.65879
$472$	0	0
$473$	8.00000	0.367840
$474$	−28.0000	−1.28608
$475$	−8.00000	−0.367065
$476$	−2.00000	−0.0916698
$477$	−10.0000	−0.457869
$478$	−24.0000	−1.09773
$479$	−18.0000	−0.822441	−0.411220	−	0.911536i	$-0.634897\pi$
$479$	−18.0000	−0.822441	−0.411220	+	0.911536i	$0.634897\pi$
$480$	2.00000	0.0912871
$481$	−36.0000	−1.64146
$482$	14.0000	0.637683
$483$	−8.00000	−0.364013
$484$	−7.00000	−0.318182
$485$	−14.0000	−0.635707
$486$	−10.0000	−0.453609
$487$	−18.0000	−0.815658	−0.407829	−	0.913058i	$-0.633714\pi$
$487$	−18.0000	−0.815658	−0.407829	+	0.913058i	$0.633714\pi$
$488$	10.0000	0.452679
$489$	−4.00000	−0.180886
$490$	3.00000	0.135526
$491$	24.0000	1.08310	0.541552	−	0.840667i	$-0.317837\pi$
$491$	24.0000	1.08310	0.541552	+	0.840667i	$0.317837\pi$
$492$	−4.00000	−0.180334
$493$	6.00000	0.270226
$494$	−48.0000	−2.15962
$495$	−2.00000	−0.0898933
$496$	−2.00000	−0.0898027
$497$	−28.0000	−1.25597
$498$	−8.00000	−0.358489
$499$	−18.0000	−0.805791	−0.402895	−	0.915246i	$-0.631996\pi$
$499$	−18.0000	−0.805791	−0.402895	+	0.915246i	$0.631996\pi$
$500$	1.00000	0.0447214
$501$	−4.00000	−0.178707
$502$	20.0000	0.892644
$503$	14.0000	0.624229	0.312115	−	0.950044i	$-0.398963\pi$
$503$	14.0000	0.624229	0.312115	+	0.950044i	$0.398963\pi$
$504$	2.00000	0.0890871
$505$	−6.00000	−0.266996
$506$	−4.00000	−0.177822
$507$	−46.0000	−2.04293
$508$	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
$511$	−20.0000	−0.884748
$512$	−1.00000	−0.0441942
$513$	−32.0000	−1.41283
$514$	18.0000	0.793946
$515$	4.00000	0.176261
$516$	8.00000	0.352180
$517$	−8.00000	−0.351840
$518$	12.0000	0.527250
$519$	20.0000	0.877903
$520$	6.00000	0.263117
$521$	−6.00000	−0.262865	−0.131432	−	0.991325i	$-0.541958\pi$
$521$	−6.00000	−0.262865	−0.131432	+	0.991325i	$0.541958\pi$
$522$	−6.00000	−0.262613
$523$	0	0		−	1.00000i	$-0.5\pi$
$523$	0	0			1.00000i	$0.5\pi$
$524$	−6.00000	−0.262111
$525$	4.00000	0.174574
$526$	−16.0000	−0.697633
$527$	−2.00000	−0.0871214
$528$	4.00000	0.174078
$529$	−19.0000	−0.826087
$530$	10.0000	0.434372
$531$	0	0
$532$	16.0000	0.693688
$533$	−12.0000	−0.519778
$534$	12.0000	0.519291
$535$	−10.0000	−0.432338
$536$	−8.00000	−0.345547
$537$	32.0000	1.38090
$538$	−22.0000	−0.948487
$539$	6.00000	0.258438
$540$	4.00000	0.172133
$541$	6.00000	0.257960	0.128980	−	0.991647i	$-0.458830\pi$
$541$	6.00000	0.257960	0.128980	+	0.991647i	$0.458830\pi$
$542$	−16.0000	−0.687259
$543$	−28.0000	−1.20160
$544$	−1.00000	−0.0428746
$545$	−2.00000	−0.0856706
$546$	24.0000	1.02711
$547$	−18.0000	−0.769624	−0.384812	−	0.922995i	$-0.625734\pi$
$547$	−18.0000	−0.769624	−0.384812	+	0.922995i	$0.625734\pi$
$548$	−18.0000	−0.768922
$549$	−10.0000	−0.426790
$550$	2.00000	0.0852803
$551$	−48.0000	−2.04487
$552$	−4.00000	−0.170251
$553$	28.0000	1.19068
$554$	18.0000	0.764747
$555$	−12.0000	−0.509372
$556$	2.00000	0.0848189
$557$	−6.00000	−0.254228	−0.127114	−	0.991888i	$-0.540571\pi$
$557$	−6.00000	−0.254228	−0.127114	+	0.991888i	$0.540571\pi$
$558$	2.00000	0.0846668
$559$	24.0000	1.01509
$560$	−2.00000	−0.0845154
$561$	4.00000	0.168880
$562$	22.0000	0.928014
$563$	28.0000	1.18006	0.590030	−	0.807382i	$-0.299116\pi$
$563$	28.0000	1.18006	0.590030	+	0.807382i	$0.299116\pi$
$564$	−8.00000	−0.336861
$565$	18.0000	0.757266
$566$	−18.0000	−0.756596
$567$	22.0000	0.923913
$568$	−14.0000	−0.587427
$569$	10.0000	0.419222	0.209611	−	0.977785i	$-0.432780\pi$
$569$	10.0000	0.419222	0.209611	+	0.977785i	$0.432780\pi$
$570$	−16.0000	−0.670166
$571$	−10.0000	−0.418487	−0.209243	−	0.977864i	$-0.567100\pi$
$571$	−10.0000	−0.418487	−0.209243	+	0.977864i	$0.567100\pi$
$572$	12.0000	0.501745
$573$	16.0000	0.668410
$574$	4.00000	0.166957
$575$	−2.00000	−0.0834058
$576$	1.00000	0.0416667
$577$	38.0000	1.58196	0.790980	−	0.611842i	$-0.209571\pi$
$577$	38.0000	1.58196	0.790980	+	0.611842i	$0.209571\pi$
$578$	−1.00000	−0.0415945
$579$	28.0000	1.16364
$580$	6.00000	0.249136
$581$	8.00000	0.331896
$582$	−28.0000	−1.16064
$583$	20.0000	0.828315
$584$	−10.0000	−0.413803
$585$	−6.00000	−0.248069
$586$	−6.00000	−0.247858
$587$	28.0000	1.15568	0.577842	−	0.816149i	$-0.303895\pi$
$587$	28.0000	1.15568	0.577842	+	0.816149i	$0.303895\pi$
$588$	6.00000	0.247436
$589$	16.0000	0.659269
$590$	0	0
$591$	−12.0000	−0.493614
$592$	6.00000	0.246598
$593$	−14.0000	−0.574911	−0.287456	−	0.957794i	$-0.592809\pi$
$593$	−14.0000	−0.574911	−0.287456	+	0.957794i	$0.592809\pi$
$594$	8.00000	0.328244
$595$	−2.00000	−0.0819920
$596$	−10.0000	−0.409616
$597$	52.0000	2.12822
$598$	−12.0000	−0.490716
$599$	0	0		−	1.00000i	$-0.5\pi$
$599$	0	0			1.00000i	$0.5\pi$
$600$	2.00000	0.0816497
$601$	−22.0000	−0.897399	−0.448699	−	0.893683i	$-0.648113\pi$
$601$	−22.0000	−0.897399	−0.448699	+	0.893683i	$0.648113\pi$
$602$	−8.00000	−0.326056
$603$	8.00000	0.325785
$604$	20.0000	0.813788
$605$	−7.00000	−0.284590
$606$	−12.0000	−0.487467
$607$	−14.0000	−0.568242	−0.284121	−	0.958788i	$-0.591702\pi$
$607$	−14.0000	−0.568242	−0.284121	+	0.958788i	$0.591702\pi$
$608$	8.00000	0.324443
$609$	24.0000	0.972529
$610$	10.0000	0.404888
$611$	−24.0000	−0.970936
$612$	1.00000	0.0404226
$613$	6.00000	0.242338	0.121169	−	0.992632i	$-0.461336\pi$
$613$	6.00000	0.242338	0.121169	+	0.992632i	$0.461336\pi$
$614$	16.0000	0.645707
$615$	−4.00000	−0.161296
$616$	−4.00000	−0.161165
$617$	2.00000	0.0805170	0.0402585	−	0.999189i	$-0.487182\pi$
$617$	2.00000	0.0805170	0.0402585	+	0.999189i	$0.487182\pi$
$618$	8.00000	0.321807
$619$	6.00000	0.241160	0.120580	−	0.992704i	$-0.461525\pi$
$619$	6.00000	0.241160	0.120580	+	0.992704i	$0.461525\pi$
$620$	−2.00000	−0.0803219
$621$	−8.00000	−0.321029
$622$	2.00000	0.0801927
$623$	−12.0000	−0.480770
$624$	12.0000	0.480384
$625$	1.00000	0.0400000
$626$	14.0000	0.559553
$627$	−32.0000	−1.27796
$628$	−18.0000	−0.718278
$629$	6.00000	0.239236
$630$	2.00000	0.0796819
$631$	−36.0000	−1.43314	−0.716569	−	0.697517i	$-0.754288\pi$
$631$	−36.0000	−1.43314	−0.716569	+	0.697517i	$0.754288\pi$
$632$	14.0000	0.556890
$633$	4.00000	0.158986
$634$	−30.0000	−1.19145
$635$	16.0000	0.634941
$636$	20.0000	0.793052
$637$	18.0000	0.713186
$638$	12.0000	0.475085
$639$	14.0000	0.553831
$640$	−1.00000	−0.0395285
$641$	10.0000	0.394976	0.197488	−	0.980305i	$-0.436722\pi$
$641$	10.0000	0.394976	0.197488	+	0.980305i	$0.436722\pi$
$642$	−20.0000	−0.789337
$643$	−2.00000	−0.0788723	−0.0394362	−	0.999222i	$-0.512556\pi$
$643$	−2.00000	−0.0788723	−0.0394362	+	0.999222i	$0.512556\pi$
$644$	4.00000	0.157622
$645$	8.00000	0.315000
$646$	8.00000	0.314756
$647$	−12.0000	−0.471769	−0.235884	−	0.971781i	$-0.575799\pi$
$647$	−12.0000	−0.471769	−0.235884	+	0.971781i	$0.575799\pi$
$648$	11.0000	0.432121
$649$	0	0
$650$	6.00000	0.235339
$651$	−8.00000	−0.313545
$652$	2.00000	0.0783260
$653$	14.0000	0.547862	0.273931	−	0.961749i	$-0.411676\pi$
$653$	14.0000	0.547862	0.273931	+	0.961749i	$0.411676\pi$
$654$	−4.00000	−0.156412
$655$	−6.00000	−0.234439
$656$	2.00000	0.0780869
$657$	10.0000	0.390137
$658$	8.00000	0.311872
$659$	−12.0000	−0.467454	−0.233727	−	0.972302i	$-0.575092\pi$
$659$	−12.0000	−0.467454	−0.233727	+	0.972302i	$0.575092\pi$
$660$	4.00000	0.155700
$661$	6.00000	0.233373	0.116686	−	0.993169i	$-0.462773\pi$
$661$	6.00000	0.233373	0.116686	+	0.993169i	$0.462773\pi$
$662$	−24.0000	−0.932786
$663$	12.0000	0.466041
$664$	4.00000	0.155230
$665$	16.0000	0.620453
$666$	−6.00000	−0.232495
$667$	−12.0000	−0.464642
$668$	2.00000	0.0773823
$669$	16.0000	0.618596
$670$	−8.00000	−0.309067
$671$	20.0000	0.772091
$672$	−4.00000	−0.154303
$673$	−6.00000	−0.231283	−0.115642	−	0.993291i	$-0.536892\pi$
$673$	−6.00000	−0.231283	−0.115642	+	0.993291i	$0.536892\pi$
$674$	−2.00000	−0.0770371
$675$	4.00000	0.153960
$676$	23.0000	0.884615
$677$	6.00000	0.230599	0.115299	−	0.993331i	$-0.463217\pi$
$677$	6.00000	0.230599	0.115299	+	0.993331i	$0.463217\pi$
$678$	36.0000	1.38257
$679$	28.0000	1.07454
$680$	−1.00000	−0.0383482
$681$	60.0000	2.29920
$682$	−4.00000	−0.153168
$683$	14.0000	0.535695	0.267848	−	0.963461i	$-0.413688\pi$
$683$	14.0000	0.535695	0.267848	+	0.963461i	$0.413688\pi$
$684$	−8.00000	−0.305888
$685$	−18.0000	−0.687745
$686$	−20.0000	−0.763604
$687$	28.0000	1.06827
$688$	−4.00000	−0.152499
$689$	60.0000	2.28582
$690$	−4.00000	−0.152277
$691$	−50.0000	−1.90209	−0.951045	−	0.309053i	$-0.899988\pi$
$691$	−50.0000	−1.90209	−0.951045	+	0.309053i	$0.899988\pi$
$692$	−10.0000	−0.380143
$693$	4.00000	0.151947
$694$	−10.0000	−0.379595
$695$	2.00000	0.0758643
$696$	12.0000	0.454859
$697$	2.00000	0.0757554
$698$	2.00000	0.0757011
$699$	−20.0000	−0.756469
$700$	−2.00000	−0.0755929
$701$	34.0000	1.28416	0.642081	−	0.766637i	$-0.278071\pi$
$701$	34.0000	1.28416	0.642081	+	0.766637i	$0.278071\pi$
$702$	24.0000	0.905822
$703$	−48.0000	−1.81035
$704$	−2.00000	−0.0753778
$705$	−8.00000	−0.301297
$706$	30.0000	1.12906
$707$	12.0000	0.451306
$708$	0	0
$709$	−10.0000	−0.375558	−0.187779	−	0.982211i	$-0.560129\pi$
$709$	−10.0000	−0.375558	−0.187779	+	0.982211i	$0.560129\pi$
$710$	−14.0000	−0.525411
$711$	−14.0000	−0.525041
$712$	−6.00000	−0.224860
$713$	4.00000	0.149801
$714$	−4.00000	−0.149696
$715$	12.0000	0.448775
$716$	−16.0000	−0.597948
$717$	−48.0000	−1.79259
$718$	−20.0000	−0.746393
$719$	−34.0000	−1.26799	−0.633993	−	0.773339i	$-0.718585\pi$
$719$	−34.0000	−1.26799	−0.633993	+	0.773339i	$0.718585\pi$
$720$	1.00000	0.0372678
$721$	−8.00000	−0.297936
$722$	−45.0000	−1.67473
$723$	28.0000	1.04133
$724$	14.0000	0.520306
$725$	6.00000	0.222834
$726$	−14.0000	−0.519589
$727$	28.0000	1.03846	0.519231	−	0.854634i	$-0.326218\pi$
$727$	28.0000	1.03846	0.519231	+	0.854634i	$0.326218\pi$
$728$	−12.0000	−0.444750
$729$	13.0000	0.481481
$730$	−10.0000	−0.370117
$731$	−4.00000	−0.147945
$732$	20.0000	0.739221
$733$	−2.00000	−0.0738717	−0.0369358	−	0.999318i	$-0.511760\pi$
$733$	−2.00000	−0.0738717	−0.0369358	+	0.999318i	$0.511760\pi$
$734$	−22.0000	−0.812035
$735$	6.00000	0.221313
$736$	2.00000	0.0737210
$737$	−16.0000	−0.589368
$738$	−2.00000	−0.0736210
$739$	−32.0000	−1.17714	−0.588570	−	0.808447i	$-0.700309\pi$
$739$	−32.0000	−1.17714	−0.588570	+	0.808447i	$0.700309\pi$
$740$	6.00000	0.220564
$741$	−96.0000	−3.52665
$742$	−20.0000	−0.734223
$743$	−22.0000	−0.807102	−0.403551	−	0.914957i	$-0.632224\pi$
$743$	−22.0000	−0.807102	−0.403551	+	0.914957i	$0.632224\pi$
$744$	−4.00000	−0.146647
$745$	−10.0000	−0.366372
$746$	30.0000	1.09838
$747$	−4.00000	−0.146352
$748$	−2.00000	−0.0731272
$749$	20.0000	0.730784
$750$	2.00000	0.0730297
$751$	−18.0000	−0.656829	−0.328415	−	0.944534i	$-0.606514\pi$
$751$	−18.0000	−0.656829	−0.328415	+	0.944534i	$0.606514\pi$
$752$	4.00000	0.145865
$753$	40.0000	1.45768
$754$	36.0000	1.31104
$755$	20.0000	0.727875
$756$	−8.00000	−0.290957
$757$	−22.0000	−0.799604	−0.399802	−	0.916602i	$-0.630921\pi$
$757$	−22.0000	−0.799604	−0.399802	+	0.916602i	$0.630921\pi$
$758$	−26.0000	−0.944363
$759$	−8.00000	−0.290382
$760$	8.00000	0.290191
$761$	38.0000	1.37750	0.688749	−	0.724999i	$-0.258160\pi$
$761$	38.0000	1.37750	0.688749	+	0.724999i	$0.258160\pi$
$762$	32.0000	1.15924
$763$	4.00000	0.144810
$764$	−8.00000	−0.289430
$765$	1.00000	0.0361551
$766$	−8.00000	−0.289052
$767$	0	0
$768$	−2.00000	−0.0721688
$769$	−50.0000	−1.80305	−0.901523	−	0.432731i	$-0.857550\pi$
$769$	−50.0000	−1.80305	−0.901523	+	0.432731i	$0.857550\pi$
$770$	−4.00000	−0.144150
$771$	36.0000	1.29651
$772$	−14.0000	−0.503871
$773$	26.0000	0.935155	0.467578	−	0.883952i	$-0.345127\pi$
$773$	26.0000	0.935155	0.467578	+	0.883952i	$0.345127\pi$
$774$	4.00000	0.143777
$775$	−2.00000	−0.0718421
$776$	14.0000	0.502571
$777$	24.0000	0.860995
$778$	−18.0000	−0.645331
$779$	−16.0000	−0.573259
$780$	12.0000	0.429669
$781$	−28.0000	−1.00192
$782$	2.00000	0.0715199
$783$	24.0000	0.857690
$784$	−3.00000	−0.107143
$785$	−18.0000	−0.642448
$786$	−12.0000	−0.428026
$787$	14.0000	0.499046	0.249523	−	0.968369i	$-0.419726\pi$
$787$	14.0000	0.499046	0.249523	+	0.968369i	$0.419726\pi$
$788$	6.00000	0.213741
$789$	−32.0000	−1.13923
$790$	14.0000	0.498098
$791$	−36.0000	−1.28001
$792$	2.00000	0.0710669
$793$	60.0000	2.13066
$794$	−22.0000	−0.780751
$795$	20.0000	0.709327
$796$	−26.0000	−0.921546
$797$	30.0000	1.06265	0.531327	−	0.847167i	$-0.321693\pi$
$797$	30.0000	1.06265	0.531327	+	0.847167i	$0.321693\pi$
$798$	32.0000	1.13279
$799$	4.00000	0.141510
$800$	−1.00000	−0.0353553
$801$	6.00000	0.212000
$802$	−26.0000	−0.918092
$803$	−20.0000	−0.705785
$804$	−16.0000	−0.564276
$805$	4.00000	0.140981
$806$	−12.0000	−0.422682
$807$	−44.0000	−1.54887
$808$	6.00000	0.211079
$809$	18.0000	0.632846	0.316423	−	0.948618i	$-0.397518\pi$
$809$	18.0000	0.632846	0.316423	+	0.948618i	$0.397518\pi$
$810$	11.0000	0.386501
$811$	26.0000	0.912983	0.456492	−	0.889728i	$-0.349106\pi$
$811$	26.0000	0.912983	0.456492	+	0.889728i	$0.349106\pi$
$812$	−12.0000	−0.421117
$813$	−32.0000	−1.12229
$814$	12.0000	0.420600
$815$	2.00000	0.0700569
$816$	−2.00000	−0.0700140
$817$	32.0000	1.11954
$818$	−10.0000	−0.349642
$819$	12.0000	0.419314
$820$	2.00000	0.0698430
$821$	−42.0000	−1.46581	−0.732905	−	0.680331i	$-0.761836\pi$
$821$	−42.0000	−1.46581	−0.732905	+	0.680331i	$0.761836\pi$
$822$	−36.0000	−1.25564
$823$	22.0000	0.766872	0.383436	−	0.923567i	$-0.374741\pi$
$823$	22.0000	0.766872	0.383436	+	0.923567i	$0.374741\pi$
$824$	−4.00000	−0.139347
$825$	4.00000	0.139262
$826$	0	0
$827$	−30.0000	−1.04320	−0.521601	−	0.853189i	$-0.674665\pi$
$827$	−30.0000	−1.04320	−0.521601	+	0.853189i	$0.674665\pi$
$828$	−2.00000	−0.0695048
$829$	−2.00000	−0.0694629	−0.0347314	−	0.999397i	$-0.511058\pi$
$829$	−2.00000	−0.0694629	−0.0347314	+	0.999397i	$0.511058\pi$
$830$	4.00000	0.138842
$831$	36.0000	1.24883
$832$	−6.00000	−0.208013
$833$	−3.00000	−0.103944
$834$	4.00000	0.138509
$835$	2.00000	0.0692129
$836$	16.0000	0.553372
$837$	−8.00000	−0.276520
$838$	10.0000	0.345444
$839$	−30.0000	−1.03572	−0.517858	−	0.855467i	$-0.673270\pi$
$839$	−30.0000	−1.03572	−0.517858	+	0.855467i	$0.673270\pi$
$840$	−4.00000	−0.138013
$841$	7.00000	0.241379
$842$	−26.0000	−0.896019
$843$	44.0000	1.51544
$844$	−2.00000	−0.0688428
$845$	23.0000	0.791224
$846$	−4.00000	−0.137523
$847$	14.0000	0.481046
$848$	−10.0000	−0.343401
$849$	−36.0000	−1.23552
$850$	−1.00000	−0.0342997
$851$	−12.0000	−0.411355
$852$	−28.0000	−0.959264
$853$	30.0000	1.02718	0.513590	−	0.858036i	$-0.328315\pi$
$853$	30.0000	1.02718	0.513590	+	0.858036i	$0.328315\pi$
$854$	−20.0000	−0.684386
$855$	−8.00000	−0.273594
$856$	10.0000	0.341793
$857$	50.0000	1.70797	0.853984	−	0.520300i	$-0.174180\pi$
$857$	50.0000	1.70797	0.853984	+	0.520300i	$0.174180\pi$
$858$	24.0000	0.819346
$859$	16.0000	0.545913	0.272956	−	0.962026i	$-0.411998\pi$
$859$	16.0000	0.545913	0.272956	+	0.962026i	$0.411998\pi$
$860$	−4.00000	−0.136399
$861$	8.00000	0.272639
$862$	−10.0000	−0.340601
$863$	20.0000	0.680808	0.340404	−	0.940279i	$-0.389436\pi$
$863$	20.0000	0.680808	0.340404	+	0.940279i	$0.389436\pi$
$864$	−4.00000	−0.136083
$865$	−10.0000	−0.340010
$866$	18.0000	0.611665
$867$	−2.00000	−0.0679236
$868$	4.00000	0.135769
$869$	28.0000	0.949835
$870$	12.0000	0.406838
$871$	−48.0000	−1.62642
$872$	2.00000	0.0677285
$873$	−14.0000	−0.473828
$874$	−16.0000	−0.541208
$875$	−2.00000	−0.0676123
$876$	−20.0000	−0.675737
$877$	−18.0000	−0.607817	−0.303908	−	0.952701i	$-0.598292\pi$
$877$	−18.0000	−0.607817	−0.303908	+	0.952701i	$0.598292\pi$
$878$	10.0000	0.337484
$879$	−12.0000	−0.404750
$880$	−2.00000	−0.0674200
$881$	−22.0000	−0.741199	−0.370599	−	0.928793i	$-0.620848\pi$
$881$	−22.0000	−0.741199	−0.370599	+	0.928793i	$0.620848\pi$
$882$	3.00000	0.101015
$883$	16.0000	0.538443	0.269221	−	0.963078i	$-0.413234\pi$
$883$	16.0000	0.538443	0.269221	+	0.963078i	$0.413234\pi$
$884$	−6.00000	−0.201802
$885$	0	0
$886$	24.0000	0.806296
$887$	−30.0000	−1.00730	−0.503651	−	0.863907i	$-0.668010\pi$
$887$	−30.0000	−1.00730	−0.503651	+	0.863907i	$0.668010\pi$
$888$	12.0000	0.402694
$889$	−32.0000	−1.07325
$890$	−6.00000	−0.201120
$891$	22.0000	0.737028
$892$	−8.00000	−0.267860
$893$	−32.0000	−1.07084
$894$	−20.0000	−0.668900
$895$	−16.0000	−0.534821
$896$	2.00000	0.0668153
$897$	−24.0000	−0.801337
$898$	6.00000	0.200223
$899$	−12.0000	−0.400222
$900$	1.00000	0.0333333
$901$	−10.0000	−0.333148
$902$	4.00000	0.133185
$903$	−16.0000	−0.532447
$904$	−18.0000	−0.598671
$905$	14.0000	0.465376
$906$	40.0000	1.32891
$907$	26.0000	0.863316	0.431658	−	0.902037i	$-0.357929\pi$
$907$	26.0000	0.863316	0.431658	+	0.902037i	$0.357929\pi$
$908$	−30.0000	−0.995585
$909$	−6.00000	−0.199007
$910$	−12.0000	−0.397796
$911$	2.00000	0.0662630	0.0331315	−	0.999451i	$-0.489452\pi$
$911$	2.00000	0.0662630	0.0331315	+	0.999451i	$0.489452\pi$
$912$	16.0000	0.529813
$913$	8.00000	0.264761
$914$	42.0000	1.38924
$915$	20.0000	0.661180
$916$	−14.0000	−0.462573
$917$	12.0000	0.396275
$918$	−4.00000	−0.132020
$919$	−32.0000	−1.05558	−0.527791	−	0.849374i	$-0.676980\pi$
$919$	−32.0000	−1.05558	−0.527791	+	0.849374i	$0.676980\pi$
$920$	2.00000	0.0659380
$921$	32.0000	1.05444
$922$	−30.0000	−0.987997
$923$	−84.0000	−2.76489
$924$	−8.00000	−0.263181
$925$	6.00000	0.197279
$926$	28.0000	0.920137
$927$	4.00000	0.131377
$928$	−6.00000	−0.196960
$929$	34.0000	1.11550	0.557752	−	0.830008i	$-0.311664\pi$
$929$	34.0000	1.11550	0.557752	+	0.830008i	$0.311664\pi$
$930$	−4.00000	−0.131165
$931$	24.0000	0.786568
$932$	10.0000	0.327561
$933$	4.00000	0.130954
$934$	28.0000	0.916188
$935$	−2.00000	−0.0654070
$936$	6.00000	0.196116
$937$	−38.0000	−1.24141	−0.620703	−	0.784046i	$-0.713153\pi$
$937$	−38.0000	−1.24141	−0.620703	+	0.784046i	$0.713153\pi$
$938$	16.0000	0.522419
$939$	28.0000	0.913745
$940$	4.00000	0.130466
$941$	−42.0000	−1.36916	−0.684580	−	0.728937i	$-0.740015\pi$
$941$	−42.0000	−1.36916	−0.684580	+	0.728937i	$0.740015\pi$
$942$	−36.0000	−1.17294
$943$	−4.00000	−0.130258
$944$	0	0
$945$	−8.00000	−0.260240
$946$	−8.00000	−0.260102
$947$	−18.0000	−0.584921	−0.292461	−	0.956278i	$-0.594474\pi$
$947$	−18.0000	−0.584921	−0.292461	+	0.956278i	$0.594474\pi$
$948$	28.0000	0.909398
$949$	−60.0000	−1.94768
$950$	8.00000	0.259554
$951$	−60.0000	−1.94563
$952$	2.00000	0.0648204
$953$	30.0000	0.971795	0.485898	−	0.874016i	$-0.338493\pi$
$953$	30.0000	0.971795	0.485898	+	0.874016i	$0.338493\pi$
$954$	10.0000	0.323762
$955$	−8.00000	−0.258874
$956$	24.0000	0.776215
$957$	24.0000	0.775810
$958$	18.0000	0.581554
$959$	36.0000	1.16250
$960$	−2.00000	−0.0645497
$961$	−27.0000	−0.870968
$962$	36.0000	1.16069
$963$	−10.0000	−0.322245
$964$	−14.0000	−0.450910
$965$	−14.0000	−0.450676
$966$	8.00000	0.257396
$967$	−8.00000	−0.257263	−0.128631	−	0.991692i	$-0.541058\pi$
$967$	−8.00000	−0.257263	−0.128631	+	0.991692i	$0.541058\pi$
$968$	7.00000	0.224989
$969$	16.0000	0.513994
$970$	14.0000	0.449513
$971$	32.0000	1.02693	0.513464	−	0.858111i	$-0.328362\pi$
$971$	32.0000	1.02693	0.513464	+	0.858111i	$0.328362\pi$
$972$	10.0000	0.320750
$973$	−4.00000	−0.128234
$974$	18.0000	0.576757
$975$	12.0000	0.384308
$976$	−10.0000	−0.320092
$977$	18.0000	0.575871	0.287936	−	0.957650i	$-0.407031\pi$
$977$	18.0000	0.575871	0.287936	+	0.957650i	$0.407031\pi$
$978$	4.00000	0.127906
$979$	−12.0000	−0.383522
$980$	−3.00000	−0.0958315
$981$	−2.00000	−0.0638551
$982$	−24.0000	−0.765871
$983$	18.0000	0.574111	0.287055	−	0.957914i	$-0.407324\pi$
$983$	18.0000	0.574111	0.287055	+	0.957914i	$0.407324\pi$
$984$	4.00000	0.127515
$985$	6.00000	0.191176
$986$	−6.00000	−0.191079
$987$	16.0000	0.509286
$988$	48.0000	1.52708
$989$	8.00000	0.254385
$990$	2.00000	0.0635642
$991$	6.00000	0.190596	0.0952981	−	0.995449i	$-0.469620\pi$
$991$	6.00000	0.190596	0.0952981	+	0.995449i	$0.469620\pi$
$992$	2.00000	0.0635001
$993$	−48.0000	−1.52323
$994$	28.0000	0.888106
$995$	−26.0000	−0.824255
$996$	8.00000	0.253490
$997$	−26.0000	−0.823428	−0.411714	−	0.911313i	$-0.635070\pi$
$997$	−26.0000	−0.823428	−0.411714	+	0.911313i	$0.635070\pi$
$998$	18.0000	0.569780
$999$	24.0000	0.759326

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	170.2.a.b.1.1	✓	1
3.2	odd	2		1530.2.a.j.1.1		1
4.3	odd	2		1360.2.a.j.1.1		1
5.2	odd	4		850.2.c.f.749.1		2
5.3	odd	4		850.2.c.f.749.2		2
5.4	even	2		850.2.a.k.1.1		1
7.6	odd	2		8330.2.a.l.1.1		1
8.3	odd	2		5440.2.a.c.1.1		1
8.5	even	2		5440.2.a.u.1.1		1
15.14	odd	2		7650.2.a.bc.1.1		1
17.4	even	4		2890.2.b.e.2311.2		2
17.13	even	4		2890.2.b.e.2311.1		2
17.16	even	2		2890.2.a.h.1.1		1
20.19	odd	2		6800.2.a.c.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
170.2.a.b.1.1	✓	1	1.1	even	1	trivial
850.2.a.k.1.1		1	5.4	even	2
850.2.c.f.749.1		2	5.2	odd	4
850.2.c.f.749.2		2	5.3	odd	4
1360.2.a.j.1.1		1	4.3	odd	2
1530.2.a.j.1.1		1	3.2	odd	2
2890.2.a.h.1.1		1	17.16	even	2
2890.2.b.e.2311.1		2	17.13	even	4
2890.2.b.e.2311.2		2	17.4	even	4
5440.2.a.c.1.1		1	8.3	odd	2
5440.2.a.u.1.1		1	8.5	even	2
6800.2.a.c.1.1		1	20.19	odd	2
7650.2.a.bc.1.1		1	15.14	odd	2
8330.2.a.l.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:	\( N \)	\(=\)	\( 170 = 2 \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	170.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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