LMFDB - Embedded newform 574.2.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [574,2,Mod(1,574)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(574, 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("574.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 574 = 2 \cdot 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	574.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:	$4.58341307602$
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	$\chi$	$=$	574.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

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

\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} -2.00000 q^{9} -1.00000 q^{10} -1.00000 q^{12} +2.00000 q^{13} +1.00000 q^{14} -1.00000 q^{15} +1.00000 q^{16} -5.00000 q^{17} +2.00000 q^{18} -4.00000 q^{19} +1.00000 q^{20} +1.00000 q^{21} +6.00000 q^{23} +1.00000 q^{24} -4.00000 q^{25} -2.00000 q^{26} +5.00000 q^{27} -1.00000 q^{28} -9.00000 q^{29} +1.00000 q^{30} +3.00000 q^{31} -1.00000 q^{32} +5.00000 q^{34} -1.00000 q^{35} -2.00000 q^{36} -8.00000 q^{37} +4.00000 q^{38} -2.00000 q^{39} -1.00000 q^{40} -1.00000 q^{41} -1.00000 q^{42} +7.00000 q^{43} -2.00000 q^{45} -6.00000 q^{46} -10.0000 q^{47} -1.00000 q^{48} +1.00000 q^{49} +4.00000 q^{50} +5.00000 q^{51} +2.00000 q^{52} -13.0000 q^{53} -5.00000 q^{54} +1.00000 q^{56} +4.00000 q^{57} +9.00000 q^{58} -14.0000 q^{59} -1.00000 q^{60} -5.00000 q^{61} -3.00000 q^{62} +2.00000 q^{63} +1.00000 q^{64} +2.00000 q^{65} +4.00000 q^{67} -5.00000 q^{68} -6.00000 q^{69} +1.00000 q^{70} -15.0000 q^{71} +2.00000 q^{72} -6.00000 q^{73} +8.00000 q^{74} +4.00000 q^{75} -4.00000 q^{76} +2.00000 q^{78} -3.00000 q^{79} +1.00000 q^{80} +1.00000 q^{81} +1.00000 q^{82} +16.0000 q^{83} +1.00000 q^{84} -5.00000 q^{85} -7.00000 q^{86} +9.00000 q^{87} +13.0000 q^{89} +2.00000 q^{90} -2.00000 q^{91} +6.00000 q^{92} -3.00000 q^{93} +10.0000 q^{94} -4.00000 q^{95} +1.00000 q^{96} +17.0000 q^{97} -1.00000 q^{98} +O(q^{100})\)

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−1.00000	−0.577350	−0.288675	−	0.957427i	$-0.593215\pi$
$3$	−1.00000	−0.577350	−0.288675	+	0.957427i	$0.593215\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214	0.223607	−	0.974679i	$-0.428217\pi$
$5$	1.00000	0.447214	0.223607	+	0.974679i	$0.428217\pi$
$6$	1.00000	0.408248
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−1.00000	−0.353553
$9$	−2.00000	−0.666667
$10$	−1.00000	−0.316228
$11$	0	0		−	1.00000i	$-0.5\pi$
$11$	0	0			1.00000i	$0.5\pi$
$12$	−1.00000	−0.288675
$13$	2.00000	0.554700	0.277350	−	0.960769i	$-0.410544\pi$
$13$	2.00000	0.554700	0.277350	+	0.960769i	$0.410544\pi$
$14$	1.00000	0.267261
$15$	−1.00000	−0.258199
$16$	1.00000	0.250000
$17$	−5.00000	−1.21268	−0.606339	−	0.795206i	$-0.707363\pi$
$17$	−5.00000	−1.21268	−0.606339	+	0.795206i	$0.707363\pi$
$18$	2.00000	0.471405
$19$	−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
$21$	1.00000	0.218218
$22$	0	0
$23$	6.00000	1.25109	0.625543	−	0.780189i	$-0.284877\pi$
$23$	6.00000	1.25109	0.625543	+	0.780189i	$0.284877\pi$
$24$	1.00000	0.204124
$25$	−4.00000	−0.800000
$26$	−2.00000	−0.392232
$27$	5.00000	0.962250
$28$	−1.00000	−0.188982
$29$	−9.00000	−1.67126	−0.835629	−	0.549294i	$-0.814897\pi$
$29$	−9.00000	−1.67126	−0.835629	+	0.549294i	$0.814897\pi$
$30$	1.00000	0.182574
$31$	3.00000	0.538816	0.269408	−	0.963026i	$-0.413172\pi$
$31$	3.00000	0.538816	0.269408	+	0.963026i	$0.413172\pi$
$32$	−1.00000	−0.176777
$33$	0	0
$34$	5.00000	0.857493
$35$	−1.00000	−0.169031
$36$	−2.00000	−0.333333
$37$	−8.00000	−1.31519	−0.657596	−	0.753371i	$-0.728427\pi$
$37$	−8.00000	−1.31519	−0.657596	+	0.753371i	$0.728427\pi$
$38$	4.00000	0.648886
$39$	−2.00000	−0.320256
$40$	−1.00000	−0.158114
$41$	−1.00000	−0.156174
$41$	−1.00000	−0.156174
$42$	−1.00000	−0.154303
$43$	7.00000	1.06749	0.533745	−	0.845645i	$-0.320784\pi$
$43$	7.00000	1.06749	0.533745	+	0.845645i	$0.320784\pi$
$44$	0	0
$45$	−2.00000	−0.298142
$46$	−6.00000	−0.884652
$47$	−10.0000	−1.45865	−0.729325	−	0.684167i	$-0.760166\pi$
$47$	−10.0000	−1.45865	−0.729325	+	0.684167i	$0.760166\pi$
$48$	−1.00000	−0.144338
$49$	1.00000	0.142857
$50$	4.00000	0.565685
$51$	5.00000	0.700140
$52$	2.00000	0.277350
$53$	−13.0000	−1.78569	−0.892844	−	0.450367i	$-0.851293\pi$
$53$	−13.0000	−1.78569	−0.892844	+	0.450367i	$0.851293\pi$
$54$	−5.00000	−0.680414
$55$	0	0
$56$	1.00000	0.133631
$57$	4.00000	0.529813
$58$	9.00000	1.18176
$59$	−14.0000	−1.82264	−0.911322	−	0.411693i	$-0.864937\pi$
$59$	−14.0000	−1.82264	−0.911322	+	0.411693i	$0.864937\pi$
$60$	−1.00000	−0.129099
$61$	−5.00000	−0.640184	−0.320092	−	0.947386i	$-0.603714\pi$
$61$	−5.00000	−0.640184	−0.320092	+	0.947386i	$0.603714\pi$
$62$	−3.00000	−0.381000
$63$	2.00000	0.251976
$64$	1.00000	0.125000
$65$	2.00000	0.248069
$66$	0	0
$67$	4.00000	0.488678	0.244339	−	0.969690i	$-0.421429\pi$
$67$	4.00000	0.488678	0.244339	+	0.969690i	$0.421429\pi$
$68$	−5.00000	−0.606339
$69$	−6.00000	−0.722315
$70$	1.00000	0.119523
$71$	−15.0000	−1.78017	−0.890086	−	0.455792i	$-0.849356\pi$
$71$	−15.0000	−1.78017	−0.890086	+	0.455792i	$0.849356\pi$
$72$	2.00000	0.235702
$73$	−6.00000	−0.702247	−0.351123	−	0.936329i	$-0.614200\pi$
$73$	−6.00000	−0.702247	−0.351123	+	0.936329i	$0.614200\pi$
$74$	8.00000	0.929981
$75$	4.00000	0.461880
$76$	−4.00000	−0.458831
$77$	0	0
$78$	2.00000	0.226455
$79$	−3.00000	−0.337526	−0.168763	−	0.985657i	$-0.553977\pi$
$79$	−3.00000	−0.337526	−0.168763	+	0.985657i	$0.553977\pi$
$80$	1.00000	0.111803
$81$	1.00000	0.111111
$82$	1.00000	0.110432
$83$	16.0000	1.75623	0.878114	−	0.478451i	$-0.158802\pi$
$83$	16.0000	1.75623	0.878114	+	0.478451i	$0.158802\pi$
$84$	1.00000	0.109109
$85$	−5.00000	−0.542326
$86$	−7.00000	−0.754829
$87$	9.00000	0.964901
$88$	0	0
$89$	13.0000	1.37800	0.688999	−	0.724763i	$-0.258051\pi$
$89$	13.0000	1.37800	0.688999	+	0.724763i	$0.258051\pi$
$90$	2.00000	0.210819
$91$	−2.00000	−0.209657
$92$	6.00000	0.625543
$93$	−3.00000	−0.311086
$94$	10.0000	1.03142
$95$	−4.00000	−0.410391
$96$	1.00000	0.102062
$97$	17.0000	1.72609	0.863044	−	0.505128i	$-0.168555\pi$
$97$	17.0000	1.72609	0.863044	+	0.505128i	$0.168555\pi$
$98$	−1.00000	−0.101015
$99$	0	0
$100$	−4.00000	−0.400000
$101$	18.0000	1.79107	0.895533	−	0.444994i	$-0.146794\pi$
$101$	18.0000	1.79107	0.895533	+	0.444994i	$0.146794\pi$
$102$	−5.00000	−0.495074
$103$	7.00000	0.689730	0.344865	−	0.938652i	$-0.387925\pi$
$103$	7.00000	0.689730	0.344865	+	0.938652i	$0.387925\pi$
$104$	−2.00000	−0.196116
$105$	1.00000	0.0975900
$106$	13.0000	1.26267
$107$	3.00000	0.290021	0.145010	−	0.989430i	$-0.453678\pi$
$107$	3.00000	0.290021	0.145010	+	0.989430i	$0.453678\pi$
$108$	5.00000	0.481125
$109$	−2.00000	−0.191565	−0.0957826	−	0.995402i	$-0.530535\pi$
$109$	−2.00000	−0.191565	−0.0957826	+	0.995402i	$0.530535\pi$
$110$	0	0
$111$	8.00000	0.759326
$112$	−1.00000	−0.0944911
$113$	1.00000	0.0940721	0.0470360	−	0.998893i	$-0.485022\pi$
$113$	1.00000	0.0940721	0.0470360	+	0.998893i	$0.485022\pi$
$114$	−4.00000	−0.374634
$115$	6.00000	0.559503
$116$	−9.00000	−0.835629
$117$	−4.00000	−0.369800
$118$	14.0000	1.28880
$119$	5.00000	0.458349
$120$	1.00000	0.0912871
$121$	−11.0000	−1.00000
$122$	5.00000	0.452679
$123$	1.00000	0.0901670
$124$	3.00000	0.269408
$125$	−9.00000	−0.804984
$126$	−2.00000	−0.178174
$127$	18.0000	1.59724	0.798621	−	0.601834i	$-0.205563\pi$
$127$	18.0000	1.59724	0.798621	+	0.601834i	$0.205563\pi$
$128$	−1.00000	−0.0883883
$129$	−7.00000	−0.616316
$130$	−2.00000	−0.175412
$131$	−18.0000	−1.57267	−0.786334	−	0.617802i	$-0.788023\pi$
$131$	−18.0000	−1.57267	−0.786334	+	0.617802i	$0.788023\pi$
$132$	0	0
$133$	4.00000	0.346844
$134$	−4.00000	−0.345547
$135$	5.00000	0.430331
$136$	5.00000	0.428746
$137$	−18.0000	−1.53784	−0.768922	−	0.639343i	$-0.779207\pi$
$137$	−18.0000	−1.53784	−0.768922	+	0.639343i	$0.779207\pi$
$138$	6.00000	0.510754
$139$	14.0000	1.18746	0.593732	−	0.804663i	$-0.297654\pi$
$139$	14.0000	1.18746	0.593732	+	0.804663i	$0.297654\pi$
$140$	−1.00000	−0.0845154
$141$	10.0000	0.842152
$142$	15.0000	1.25877
$143$	0	0
$144$	−2.00000	−0.166667
$145$	−9.00000	−0.747409
$146$	6.00000	0.496564
$147$	−1.00000	−0.0824786
$148$	−8.00000	−0.657596
$149$	7.00000	0.573462	0.286731	−	0.958011i	$-0.407431\pi$
$149$	7.00000	0.573462	0.286731	+	0.958011i	$0.407431\pi$
$150$	−4.00000	−0.326599
$151$	−5.00000	−0.406894	−0.203447	−	0.979086i	$-0.565214\pi$
$151$	−5.00000	−0.406894	−0.203447	+	0.979086i	$0.565214\pi$
$152$	4.00000	0.324443
$153$	10.0000	0.808452
$154$	0	0
$155$	3.00000	0.240966
$156$	−2.00000	−0.160128
$157$	0	0		−	1.00000i	$-0.5\pi$
$157$	0	0			1.00000i	$0.5\pi$
$158$	3.00000	0.238667
$159$	13.0000	1.03097
$160$	−1.00000	−0.0790569
$161$	−6.00000	−0.472866
$162$	−1.00000	−0.0785674
$163$	12.0000	0.939913	0.469956	−	0.882690i	$-0.344270\pi$
$163$	12.0000	0.939913	0.469956	+	0.882690i	$0.344270\pi$
$164$	−1.00000	−0.0780869
$165$	0	0
$166$	−16.0000	−1.24184
$167$	12.0000	0.928588	0.464294	−	0.885681i	$-0.346308\pi$
$167$	12.0000	0.928588	0.464294	+	0.885681i	$0.346308\pi$
$168$	−1.00000	−0.0771517
$169$	−9.00000	−0.692308
$170$	5.00000	0.383482
$171$	8.00000	0.611775
$172$	7.00000	0.533745
$173$	9.00000	0.684257	0.342129	−	0.939653i	$-0.388852\pi$
$173$	9.00000	0.684257	0.342129	+	0.939653i	$0.388852\pi$
$174$	−9.00000	−0.682288
$175$	4.00000	0.302372
$176$	0	0
$177$	14.0000	1.05230
$178$	−13.0000	−0.974391
$179$	−24.0000	−1.79384	−0.896922	−	0.442189i	$-0.854202\pi$
$179$	−24.0000	−1.79384	−0.896922	+	0.442189i	$0.854202\pi$
$180$	−2.00000	−0.149071
$181$	0	0		−	1.00000i	$-0.5\pi$
$181$	0	0			1.00000i	$0.5\pi$
$182$	2.00000	0.148250
$183$	5.00000	0.369611
$184$	−6.00000	−0.442326
$185$	−8.00000	−0.588172
$186$	3.00000	0.219971
$187$	0	0
$188$	−10.0000	−0.729325
$189$	−5.00000	−0.363696
$190$	4.00000	0.290191
$191$	−15.0000	−1.08536	−0.542681	−	0.839939i	$-0.682591\pi$
$191$	−15.0000	−1.08536	−0.542681	+	0.839939i	$0.682591\pi$
$192$	−1.00000	−0.0721688
$193$	16.0000	1.15171	0.575853	−	0.817554i	$-0.304670\pi$
$193$	16.0000	1.15171	0.575853	+	0.817554i	$0.304670\pi$
$194$	−17.0000	−1.22053
$195$	−2.00000	−0.143223
$196$	1.00000	0.0714286
$197$	0	0		−	1.00000i	$-0.5\pi$
$197$	0	0			1.00000i	$0.5\pi$
$198$	0	0
$199$	4.00000	0.283552	0.141776	−	0.989899i	$-0.454719\pi$
$199$	4.00000	0.283552	0.141776	+	0.989899i	$0.454719\pi$
$200$	4.00000	0.282843
$201$	−4.00000	−0.282138
$202$	−18.0000	−1.26648
$203$	9.00000	0.631676
$204$	5.00000	0.350070
$205$	−1.00000	−0.0698430
$206$	−7.00000	−0.487713
$207$	−12.0000	−0.834058
$208$	2.00000	0.138675
$209$	0	0
$210$	−1.00000	−0.0690066
$211$	20.0000	1.37686	0.688428	−	0.725304i	$-0.258301\pi$
$211$	20.0000	1.37686	0.688428	+	0.725304i	$0.258301\pi$
$212$	−13.0000	−0.892844
$213$	15.0000	1.02778
$214$	−3.00000	−0.205076
$215$	7.00000	0.477396
$216$	−5.00000	−0.340207
$217$	−3.00000	−0.203653
$218$	2.00000	0.135457
$219$	6.00000	0.405442
$220$	0	0
$221$	−10.0000	−0.672673
$222$	−8.00000	−0.536925
$223$	3.00000	0.200895	0.100447	−	0.994942i	$-0.467973\pi$
$223$	3.00000	0.200895	0.100447	+	0.994942i	$0.467973\pi$
$224$	1.00000	0.0668153
$225$	8.00000	0.533333
$226$	−1.00000	−0.0665190
$227$	7.00000	0.464606	0.232303	−	0.972643i	$-0.425374\pi$
$227$	7.00000	0.464606	0.232303	+	0.972643i	$0.425374\pi$
$228$	4.00000	0.264906
$229$	8.00000	0.528655	0.264327	−	0.964433i	$-0.414850\pi$
$229$	8.00000	0.528655	0.264327	+	0.964433i	$0.414850\pi$
$230$	−6.00000	−0.395628
$231$	0	0
$232$	9.00000	0.590879
$233$	−12.0000	−0.786146	−0.393073	−	0.919507i	$-0.628588\pi$
$233$	−12.0000	−0.786146	−0.393073	+	0.919507i	$0.628588\pi$
$234$	4.00000	0.261488
$235$	−10.0000	−0.652328
$236$	−14.0000	−0.911322
$237$	3.00000	0.194871
$238$	−5.00000	−0.324102
$239$	0	0		−	1.00000i	$-0.5\pi$
$239$	0	0			1.00000i	$0.5\pi$
$240$	−1.00000	−0.0645497
$241$	−20.0000	−1.28831	−0.644157	−	0.764894i	$-0.722792\pi$
$241$	−20.0000	−1.28831	−0.644157	+	0.764894i	$0.722792\pi$
$242$	11.0000	0.707107
$243$	−16.0000	−1.02640
$244$	−5.00000	−0.320092
$245$	1.00000	0.0638877
$246$	−1.00000	−0.0637577
$247$	−8.00000	−0.509028
$248$	−3.00000	−0.190500
$249$	−16.0000	−1.01396
$250$	9.00000	0.569210
$251$	−8.00000	−0.504956	−0.252478	−	0.967603i	$-0.581245\pi$
$251$	−8.00000	−0.504956	−0.252478	+	0.967603i	$0.581245\pi$
$252$	2.00000	0.125988
$253$	0	0
$254$	−18.0000	−1.12942
$255$	5.00000	0.313112
$256$	1.00000	0.0625000
$257$	3.00000	0.187135	0.0935674	−	0.995613i	$-0.470173\pi$
$257$	3.00000	0.187135	0.0935674	+	0.995613i	$0.470173\pi$
$258$	7.00000	0.435801
$259$	8.00000	0.497096
$260$	2.00000	0.124035
$261$	18.0000	1.11417
$262$	18.0000	1.11204
$263$	−24.0000	−1.47990	−0.739952	−	0.672660i	$-0.765152\pi$
$263$	−24.0000	−1.47990	−0.739952	+	0.672660i	$0.765152\pi$
$264$	0	0
$265$	−13.0000	−0.798584
$266$	−4.00000	−0.245256
$267$	−13.0000	−0.795587
$268$	4.00000	0.244339
$269$	10.0000	0.609711	0.304855	−	0.952399i	$-0.401392\pi$
$269$	10.0000	0.609711	0.304855	+	0.952399i	$0.401392\pi$
$270$	−5.00000	−0.304290
$271$	16.0000	0.971931	0.485965	−	0.873978i	$-0.338468\pi$
$271$	16.0000	0.971931	0.485965	+	0.873978i	$0.338468\pi$
$272$	−5.00000	−0.303170
$273$	2.00000	0.121046
$274$	18.0000	1.08742
$275$	0	0
$276$	−6.00000	−0.361158
$277$	20.0000	1.20168	0.600842	−	0.799368i	$-0.294832\pi$
$277$	20.0000	1.20168	0.600842	+	0.799368i	$0.294832\pi$
$278$	−14.0000	−0.839664
$279$	−6.00000	−0.359211
$280$	1.00000	0.0597614
$281$	−22.0000	−1.31241	−0.656205	−	0.754583i	$-0.727839\pi$
$281$	−22.0000	−1.31241	−0.656205	+	0.754583i	$0.727839\pi$
$282$	−10.0000	−0.595491
$283$	−12.0000	−0.713326	−0.356663	−	0.934233i	$-0.616086\pi$
$283$	−12.0000	−0.713326	−0.356663	+	0.934233i	$0.616086\pi$
$284$	−15.0000	−0.890086
$285$	4.00000	0.236940
$286$	0	0
$287$	1.00000	0.0590281
$288$	2.00000	0.117851
$289$	8.00000	0.470588
$290$	9.00000	0.528498
$291$	−17.0000	−0.996558
$292$	−6.00000	−0.351123
$293$	24.0000	1.40209	0.701047	−	0.713115i	$-0.252716\pi$
$293$	24.0000	1.40209	0.701047	+	0.713115i	$0.252716\pi$
$294$	1.00000	0.0583212
$295$	−14.0000	−0.815112
$296$	8.00000	0.464991
$297$	0	0
$298$	−7.00000	−0.405499
$299$	12.0000	0.693978
$300$	4.00000	0.230940
$301$	−7.00000	−0.403473
$302$	5.00000	0.287718
$303$	−18.0000	−1.03407
$304$	−4.00000	−0.229416
$305$	−5.00000	−0.286299
$306$	−10.0000	−0.571662
$307$	−16.0000	−0.913168	−0.456584	−	0.889680i	$-0.650927\pi$
$307$	−16.0000	−0.913168	−0.456584	+	0.889680i	$0.650927\pi$
$308$	0	0
$309$	−7.00000	−0.398216
$310$	−3.00000	−0.170389
$311$	18.0000	1.02069	0.510343	−	0.859971i	$-0.329518\pi$
$311$	18.0000	1.02069	0.510343	+	0.859971i	$0.329518\pi$
$312$	2.00000	0.113228
$313$	−6.00000	−0.339140	−0.169570	−	0.985518i	$-0.554238\pi$
$313$	−6.00000	−0.339140	−0.169570	+	0.985518i	$0.554238\pi$
$314$	0	0
$315$	2.00000	0.112687
$316$	−3.00000	−0.168763
$317$	−22.0000	−1.23564	−0.617822	−	0.786318i	$-0.711985\pi$
$317$	−22.0000	−1.23564	−0.617822	+	0.786318i	$0.711985\pi$
$318$	−13.0000	−0.729004
$319$	0	0
$320$	1.00000	0.0559017
$321$	−3.00000	−0.167444
$322$	6.00000	0.334367
$323$	20.0000	1.11283
$324$	1.00000	0.0555556
$325$	−8.00000	−0.443760
$326$	−12.0000	−0.664619
$327$	2.00000	0.110600
$328$	1.00000	0.0552158
$329$	10.0000	0.551318
$330$	0	0
$331$	26.0000	1.42909	0.714545	−	0.699590i	$-0.246634\pi$
$331$	26.0000	1.42909	0.714545	+	0.699590i	$0.246634\pi$
$332$	16.0000	0.878114
$333$	16.0000	0.876795
$334$	−12.0000	−0.656611
$335$	4.00000	0.218543
$336$	1.00000	0.0545545
$337$	−35.0000	−1.90657	−0.953286	−	0.302070i	$-0.902322\pi$
$337$	−35.0000	−1.90657	−0.953286	+	0.302070i	$0.902322\pi$
$338$	9.00000	0.489535
$339$	−1.00000	−0.0543125
$340$	−5.00000	−0.271163
$341$	0	0
$342$	−8.00000	−0.432590
$343$	−1.00000	−0.0539949
$344$	−7.00000	−0.377415
$345$	−6.00000	−0.323029
$346$	−9.00000	−0.483843
$347$	24.0000	1.28839	0.644194	−	0.764862i	$-0.277193\pi$
$347$	24.0000	1.28839	0.644194	+	0.764862i	$0.277193\pi$
$348$	9.00000	0.482451
$349$	2.00000	0.107058	0.0535288	−	0.998566i	$-0.482953\pi$
$349$	2.00000	0.107058	0.0535288	+	0.998566i	$0.482953\pi$
$350$	−4.00000	−0.213809
$351$	10.0000	0.533761
$352$	0	0
$353$	−2.00000	−0.106449	−0.0532246	−	0.998583i	$-0.516950\pi$
$353$	−2.00000	−0.106449	−0.0532246	+	0.998583i	$0.516950\pi$
$354$	−14.0000	−0.744092
$355$	−15.0000	−0.796117
$356$	13.0000	0.688999
$357$	−5.00000	−0.264628
$358$	24.0000	1.26844
$359$	0	0		−	1.00000i	$-0.5\pi$
$359$	0	0			1.00000i	$0.5\pi$
$360$	2.00000	0.105409
$361$	−3.00000	−0.157895
$362$	0	0
$363$	11.0000	0.577350
$364$	−2.00000	−0.104828
$365$	−6.00000	−0.314054
$366$	−5.00000	−0.261354
$367$	−19.0000	−0.991792	−0.495896	−	0.868382i	$-0.665160\pi$
$367$	−19.0000	−0.991792	−0.495896	+	0.868382i	$0.665160\pi$
$368$	6.00000	0.312772
$369$	2.00000	0.104116
$370$	8.00000	0.415900
$371$	13.0000	0.674926
$372$	−3.00000	−0.155543
$373$	−16.0000	−0.828449	−0.414224	−	0.910175i	$-0.635947\pi$
$373$	−16.0000	−0.828449	−0.414224	+	0.910175i	$0.635947\pi$
$374$	0	0
$375$	9.00000	0.464758
$376$	10.0000	0.515711
$377$	−18.0000	−0.927047
$378$	5.00000	0.257172
$379$	−15.0000	−0.770498	−0.385249	−	0.922813i	$-0.625884\pi$
$379$	−15.0000	−0.770498	−0.385249	+	0.922813i	$0.625884\pi$
$380$	−4.00000	−0.205196
$381$	−18.0000	−0.922168
$382$	15.0000	0.767467
$383$	−8.00000	−0.408781	−0.204390	−	0.978889i	$-0.565521\pi$
$383$	−8.00000	−0.408781	−0.204390	+	0.978889i	$0.565521\pi$
$384$	1.00000	0.0510310
$385$	0	0
$386$	−16.0000	−0.814379
$387$	−14.0000	−0.711660
$388$	17.0000	0.863044
$389$	20.0000	1.01404	0.507020	−	0.861934i	$-0.330747\pi$
$389$	20.0000	1.01404	0.507020	+	0.861934i	$0.330747\pi$
$390$	2.00000	0.101274
$391$	−30.0000	−1.51717
$392$	−1.00000	−0.0505076
$393$	18.0000	0.907980
$394$	0	0
$395$	−3.00000	−0.150946
$396$	0	0
$397$	−2.00000	−0.100377	−0.0501886	−	0.998740i	$-0.515982\pi$
$397$	−2.00000	−0.100377	−0.0501886	+	0.998740i	$0.515982\pi$
$398$	−4.00000	−0.200502
$399$	−4.00000	−0.200250
$400$	−4.00000	−0.200000
$401$	−5.00000	−0.249688	−0.124844	−	0.992176i	$-0.539843\pi$
$401$	−5.00000	−0.249688	−0.124844	+	0.992176i	$0.539843\pi$
$402$	4.00000	0.199502
$403$	6.00000	0.298881
$404$	18.0000	0.895533
$405$	1.00000	0.0496904
$406$	−9.00000	−0.446663
$407$	0	0
$408$	−5.00000	−0.247537
$409$	32.0000	1.58230	0.791149	−	0.611623i	$-0.209483\pi$
$409$	32.0000	1.58230	0.791149	+	0.611623i	$0.209483\pi$
$410$	1.00000	0.0493865
$411$	18.0000	0.887875
$412$	7.00000	0.344865
$413$	14.0000	0.688895
$414$	12.0000	0.589768
$415$	16.0000	0.785409
$416$	−2.00000	−0.0980581
$417$	−14.0000	−0.685583
$418$	0	0
$419$	−14.0000	−0.683945	−0.341972	−	0.939710i	$-0.611095\pi$
$419$	−14.0000	−0.683945	−0.341972	+	0.939710i	$0.611095\pi$
$420$	1.00000	0.0487950
$421$	−7.00000	−0.341159	−0.170580	−	0.985344i	$-0.554564\pi$
$421$	−7.00000	−0.341159	−0.170580	+	0.985344i	$0.554564\pi$
$422$	−20.0000	−0.973585
$423$	20.0000	0.972433
$424$	13.0000	0.631336
$425$	20.0000	0.970143
$426$	−15.0000	−0.726752
$427$	5.00000	0.241967
$428$	3.00000	0.145010
$429$	0	0
$430$	−7.00000	−0.337570
$431$	8.00000	0.385346	0.192673	−	0.981263i	$-0.438284\pi$
$431$	8.00000	0.385346	0.192673	+	0.981263i	$0.438284\pi$
$432$	5.00000	0.240563
$433$	6.00000	0.288342	0.144171	−	0.989553i	$-0.453949\pi$
$433$	6.00000	0.288342	0.144171	+	0.989553i	$0.453949\pi$
$434$	3.00000	0.144005
$435$	9.00000	0.431517
$436$	−2.00000	−0.0957826
$437$	−24.0000	−1.14808
$438$	−6.00000	−0.286691
$439$	−28.0000	−1.33637	−0.668184	−	0.743996i	$-0.732928\pi$
$439$	−28.0000	−1.33637	−0.668184	+	0.743996i	$0.732928\pi$
$440$	0	0
$441$	−2.00000	−0.0952381
$442$	10.0000	0.475651
$443$	39.0000	1.85295	0.926473	−	0.376361i	$-0.122825\pi$
$443$	39.0000	1.85295	0.926473	+	0.376361i	$0.122825\pi$
$444$	8.00000	0.379663
$445$	13.0000	0.616259
$446$	−3.00000	−0.142054
$447$	−7.00000	−0.331089
$448$	−1.00000	−0.0472456
$449$	−33.0000	−1.55737	−0.778683	−	0.627417i	$-0.784112\pi$
$449$	−33.0000	−1.55737	−0.778683	+	0.627417i	$0.784112\pi$
$450$	−8.00000	−0.377124
$451$	0	0
$452$	1.00000	0.0470360
$453$	5.00000	0.234920
$454$	−7.00000	−0.328526
$455$	−2.00000	−0.0937614
$456$	−4.00000	−0.187317
$457$	−18.0000	−0.842004	−0.421002	−	0.907060i	$-0.638322\pi$
$457$	−18.0000	−0.842004	−0.421002	+	0.907060i	$0.638322\pi$
$458$	−8.00000	−0.373815
$459$	−25.0000	−1.16690
$460$	6.00000	0.279751
$461$	21.0000	0.978068	0.489034	−	0.872265i	$-0.337349\pi$
$461$	21.0000	0.978068	0.489034	+	0.872265i	$0.337349\pi$
$462$	0	0
$463$	−24.0000	−1.11537	−0.557687	−	0.830051i	$-0.688311\pi$
$463$	−24.0000	−1.11537	−0.557687	+	0.830051i	$0.688311\pi$
$464$	−9.00000	−0.417815
$465$	−3.00000	−0.139122
$466$	12.0000	0.555889
$467$	32.0000	1.48078	0.740392	−	0.672176i	$-0.234640\pi$
$467$	32.0000	1.48078	0.740392	+	0.672176i	$0.234640\pi$
$468$	−4.00000	−0.184900
$469$	−4.00000	−0.184703
$470$	10.0000	0.461266
$471$	0	0
$472$	14.0000	0.644402
$473$	0	0
$474$	−3.00000	−0.137795
$475$	16.0000	0.734130
$476$	5.00000	0.229175
$477$	26.0000	1.19046
$478$	0	0
$479$	−26.0000	−1.18797	−0.593985	−	0.804476i	$-0.702446\pi$
$479$	−26.0000	−1.18797	−0.593985	+	0.804476i	$0.702446\pi$
$480$	1.00000	0.0456435
$481$	−16.0000	−0.729537
$482$	20.0000	0.910975
$483$	6.00000	0.273009
$484$	−11.0000	−0.500000
$485$	17.0000	0.771930
$486$	16.0000	0.725775
$487$	26.0000	1.17817	0.589086	−	0.808070i	$-0.299488\pi$
$487$	26.0000	1.17817	0.589086	+	0.808070i	$0.299488\pi$
$488$	5.00000	0.226339
$489$	−12.0000	−0.542659
$490$	−1.00000	−0.0451754
$491$	5.00000	0.225647	0.112823	−	0.993615i	$-0.464011\pi$
$491$	5.00000	0.225647	0.112823	+	0.993615i	$0.464011\pi$
$492$	1.00000	0.0450835
$493$	45.0000	2.02670
$494$	8.00000	0.359937
$495$	0	0
$496$	3.00000	0.134704
$497$	15.0000	0.672842
$498$	16.0000	0.716977
$499$	−2.00000	−0.0895323	−0.0447661	−	0.998997i	$-0.514254\pi$
$499$	−2.00000	−0.0895323	−0.0447661	+	0.998997i	$0.514254\pi$
$500$	−9.00000	−0.402492
$501$	−12.0000	−0.536120
$502$	8.00000	0.357057
$503$	−10.0000	−0.445878	−0.222939	−	0.974832i	$-0.571565\pi$
$503$	−10.0000	−0.445878	−0.222939	+	0.974832i	$0.571565\pi$
$504$	−2.00000	−0.0890871
$505$	18.0000	0.800989
$506$	0	0
$507$	9.00000	0.399704
$508$	18.0000	0.798621
$509$	−42.0000	−1.86162	−0.930809	−	0.365507i	$-0.880896\pi$
$509$	−42.0000	−1.86162	−0.930809	+	0.365507i	$0.880896\pi$
$510$	−5.00000	−0.221404
$511$	6.00000	0.265424
$512$	−1.00000	−0.0441942
$513$	−20.0000	−0.883022
$514$	−3.00000	−0.132324
$515$	7.00000	0.308457
$516$	−7.00000	−0.308158
$517$	0	0
$518$	−8.00000	−0.351500
$519$	−9.00000	−0.395056
$520$	−2.00000	−0.0877058
$521$	14.0000	0.613351	0.306676	−	0.951814i	$-0.400783\pi$
$521$	14.0000	0.613351	0.306676	+	0.951814i	$0.400783\pi$
$522$	−18.0000	−0.787839
$523$	6.00000	0.262362	0.131181	−	0.991358i	$-0.458123\pi$
$523$	6.00000	0.262362	0.131181	+	0.991358i	$0.458123\pi$
$524$	−18.0000	−0.786334
$525$	−4.00000	−0.174574
$526$	24.0000	1.04645
$527$	−15.0000	−0.653410
$528$	0	0
$529$	13.0000	0.565217
$530$	13.0000	0.564684
$531$	28.0000	1.21510
$532$	4.00000	0.173422
$533$	−2.00000	−0.0866296
$534$	13.0000	0.562565
$535$	3.00000	0.129701
$536$	−4.00000	−0.172774
$537$	24.0000	1.03568
$538$	−10.0000	−0.431131
$539$	0	0
$540$	5.00000	0.215166
$541$	12.0000	0.515920	0.257960	−	0.966156i	$-0.416950\pi$
$541$	12.0000	0.515920	0.257960	+	0.966156i	$0.416950\pi$
$542$	−16.0000	−0.687259
$543$	0	0
$544$	5.00000	0.214373
$545$	−2.00000	−0.0856706
$546$	−2.00000	−0.0855921
$547$	−36.0000	−1.53925	−0.769624	−	0.638497i	$-0.779557\pi$
$547$	−36.0000	−1.53925	−0.769624	+	0.638497i	$0.779557\pi$
$548$	−18.0000	−0.768922
$549$	10.0000	0.426790
$550$	0	0
$551$	36.0000	1.53365
$552$	6.00000	0.255377
$553$	3.00000	0.127573
$554$	−20.0000	−0.849719
$555$	8.00000	0.339581
$556$	14.0000	0.593732
$557$	13.0000	0.550828	0.275414	−	0.961326i	$-0.411185\pi$
$557$	13.0000	0.550828	0.275414	+	0.961326i	$0.411185\pi$
$558$	6.00000	0.254000
$559$	14.0000	0.592137
$560$	−1.00000	−0.0422577
$561$	0	0
$562$	22.0000	0.928014
$563$	20.0000	0.842900	0.421450	−	0.906852i	$-0.361521\pi$
$563$	20.0000	0.842900	0.421450	+	0.906852i	$0.361521\pi$
$564$	10.0000	0.421076
$565$	1.00000	0.0420703
$566$	12.0000	0.504398
$567$	−1.00000	−0.0419961
$568$	15.0000	0.629386
$569$	27.0000	1.13190	0.565949	−	0.824440i	$-0.308510\pi$
$569$	27.0000	1.13190	0.565949	+	0.824440i	$0.308510\pi$
$570$	−4.00000	−0.167542
$571$	−26.0000	−1.08807	−0.544033	−	0.839064i	$-0.683103\pi$
$571$	−26.0000	−1.08807	−0.544033	+	0.839064i	$0.683103\pi$
$572$	0	0
$573$	15.0000	0.626634
$574$	−1.00000	−0.0417392
$575$	−24.0000	−1.00087
$576$	−2.00000	−0.0833333
$577$	−42.0000	−1.74848	−0.874241	−	0.485491i	$-0.838641\pi$
$577$	−42.0000	−1.74848	−0.874241	+	0.485491i	$0.838641\pi$
$578$	−8.00000	−0.332756
$579$	−16.0000	−0.664937
$580$	−9.00000	−0.373705
$581$	−16.0000	−0.663792
$582$	17.0000	0.704673
$583$	0	0
$584$	6.00000	0.248282
$585$	−4.00000	−0.165380
$586$	−24.0000	−0.991431
$587$	−15.0000	−0.619116	−0.309558	−	0.950881i	$-0.600181\pi$
$587$	−15.0000	−0.619116	−0.309558	+	0.950881i	$0.600181\pi$
$588$	−1.00000	−0.0412393
$589$	−12.0000	−0.494451
$590$	14.0000	0.576371
$591$	0	0
$592$	−8.00000	−0.328798
$593$	15.0000	0.615976	0.307988	−	0.951390i	$-0.400344\pi$
$593$	15.0000	0.615976	0.307988	+	0.951390i	$0.400344\pi$
$594$	0	0
$595$	5.00000	0.204980
$596$	7.00000	0.286731
$597$	−4.00000	−0.163709
$598$	−12.0000	−0.490716
$599$	6.00000	0.245153	0.122577	−	0.992459i	$-0.460884\pi$
$599$	6.00000	0.245153	0.122577	+	0.992459i	$0.460884\pi$
$600$	−4.00000	−0.163299
$601$	−37.0000	−1.50926	−0.754631	−	0.656150i	$-0.772184\pi$
$601$	−37.0000	−1.50926	−0.754631	+	0.656150i	$0.772184\pi$
$602$	7.00000	0.285299
$603$	−8.00000	−0.325785
$604$	−5.00000	−0.203447
$605$	−11.0000	−0.447214
$606$	18.0000	0.731200
$607$	3.00000	0.121766	0.0608831	−	0.998145i	$-0.480608\pi$
$607$	3.00000	0.121766	0.0608831	+	0.998145i	$0.480608\pi$
$608$	4.00000	0.162221
$609$	−9.00000	−0.364698
$610$	5.00000	0.202444
$611$	−20.0000	−0.809113
$612$	10.0000	0.404226
$613$	28.0000	1.13091	0.565455	−	0.824779i	$-0.308701\pi$
$613$	28.0000	1.13091	0.565455	+	0.824779i	$0.308701\pi$
$614$	16.0000	0.645707
$615$	1.00000	0.0403239
$616$	0	0
$617$	−26.0000	−1.04672	−0.523360	−	0.852111i	$-0.675322\pi$
$617$	−26.0000	−1.04672	−0.523360	+	0.852111i	$0.675322\pi$
$618$	7.00000	0.281581
$619$	−4.00000	−0.160774	−0.0803868	−	0.996764i	$-0.525616\pi$
$619$	−4.00000	−0.160774	−0.0803868	+	0.996764i	$0.525616\pi$
$620$	3.00000	0.120483
$621$	30.0000	1.20386
$622$	−18.0000	−0.721734
$623$	−13.0000	−0.520834
$624$	−2.00000	−0.0800641
$625$	11.0000	0.440000
$626$	6.00000	0.239808
$627$	0	0
$628$	0	0
$629$	40.0000	1.59490
$630$	−2.00000	−0.0796819
$631$	14.0000	0.557331	0.278666	−	0.960388i	$-0.410108\pi$
$631$	14.0000	0.557331	0.278666	+	0.960388i	$0.410108\pi$
$632$	3.00000	0.119334
$633$	−20.0000	−0.794929
$634$	22.0000	0.873732
$635$	18.0000	0.714308
$636$	13.0000	0.515484
$637$	2.00000	0.0792429
$638$	0	0
$639$	30.0000	1.18678
$640$	−1.00000	−0.0395285
$641$	38.0000	1.50091	0.750455	−	0.660922i	$-0.229834\pi$
$641$	38.0000	1.50091	0.750455	+	0.660922i	$0.229834\pi$
$642$	3.00000	0.118401
$643$	19.0000	0.749287	0.374643	−	0.927169i	$-0.377765\pi$
$643$	19.0000	0.749287	0.374643	+	0.927169i	$0.377765\pi$
$644$	−6.00000	−0.236433
$645$	−7.00000	−0.275625
$646$	−20.0000	−0.786889
$647$	39.0000	1.53325	0.766624	−	0.642096i	$-0.221935\pi$
$647$	39.0000	1.53325	0.766624	+	0.642096i	$0.221935\pi$
$648$	−1.00000	−0.0392837
$649$	0	0
$650$	8.00000	0.313786
$651$	3.00000	0.117579
$652$	12.0000	0.469956
$653$	−9.00000	−0.352197	−0.176099	−	0.984373i	$-0.556348\pi$
$653$	−9.00000	−0.352197	−0.176099	+	0.984373i	$0.556348\pi$
$654$	−2.00000	−0.0782062
$655$	−18.0000	−0.703318
$656$	−1.00000	−0.0390434
$657$	12.0000	0.468165
$658$	−10.0000	−0.389841
$659$	−18.0000	−0.701180	−0.350590	−	0.936529i	$-0.614019\pi$
$659$	−18.0000	−0.701180	−0.350590	+	0.936529i	$0.614019\pi$
$660$	0	0
$661$	−50.0000	−1.94477	−0.972387	−	0.233373i	$-0.925024\pi$
$661$	−50.0000	−1.94477	−0.972387	+	0.233373i	$0.925024\pi$
$662$	−26.0000	−1.01052
$663$	10.0000	0.388368
$664$	−16.0000	−0.620920
$665$	4.00000	0.155113
$666$	−16.0000	−0.619987
$667$	−54.0000	−2.09089
$668$	12.0000	0.464294
$669$	−3.00000	−0.115987
$670$	−4.00000	−0.154533
$671$	0	0
$672$	−1.00000	−0.0385758
$673$	−32.0000	−1.23351	−0.616755	−	0.787155i	$-0.711553\pi$
$673$	−32.0000	−1.23351	−0.616755	+	0.787155i	$0.711553\pi$
$674$	35.0000	1.34815
$675$	−20.0000	−0.769800
$676$	−9.00000	−0.346154
$677$	−6.00000	−0.230599	−0.115299	−	0.993331i	$-0.536783\pi$
$677$	−6.00000	−0.230599	−0.115299	+	0.993331i	$0.536783\pi$
$678$	1.00000	0.0384048
$679$	−17.0000	−0.652400
$680$	5.00000	0.191741
$681$	−7.00000	−0.268241
$682$	0	0
$683$	−12.0000	−0.459167	−0.229584	−	0.973289i	$-0.573736\pi$
$683$	−12.0000	−0.459167	−0.229584	+	0.973289i	$0.573736\pi$
$684$	8.00000	0.305888
$685$	−18.0000	−0.687745
$686$	1.00000	0.0381802
$687$	−8.00000	−0.305219
$688$	7.00000	0.266872
$689$	−26.0000	−0.990521
$690$	6.00000	0.228416
$691$	−13.0000	−0.494543	−0.247272	−	0.968946i	$-0.579534\pi$
$691$	−13.0000	−0.494543	−0.247272	+	0.968946i	$0.579534\pi$
$692$	9.00000	0.342129
$693$	0	0
$694$	−24.0000	−0.911028
$695$	14.0000	0.531050
$696$	−9.00000	−0.341144
$697$	5.00000	0.189389
$698$	−2.00000	−0.0757011
$699$	12.0000	0.453882
$700$	4.00000	0.151186
$701$	−42.0000	−1.58632	−0.793159	−	0.609015i	$-0.791565\pi$
$701$	−42.0000	−1.58632	−0.793159	+	0.609015i	$0.791565\pi$
$702$	−10.0000	−0.377426
$703$	32.0000	1.20690
$704$	0	0
$705$	10.0000	0.376622
$706$	2.00000	0.0752710
$707$	−18.0000	−0.676960
$708$	14.0000	0.526152
$709$	−1.00000	−0.0375558	−0.0187779	−	0.999824i	$-0.505978\pi$
$709$	−1.00000	−0.0375558	−0.0187779	+	0.999824i	$0.505978\pi$
$710$	15.0000	0.562940
$711$	6.00000	0.225018
$712$	−13.0000	−0.487196
$713$	18.0000	0.674105
$714$	5.00000	0.187120
$715$	0	0
$716$	−24.0000	−0.896922
$717$	0	0
$718$	0	0
$719$	−30.0000	−1.11881	−0.559406	−	0.828894i	$-0.688971\pi$
$719$	−30.0000	−1.11881	−0.559406	+	0.828894i	$0.688971\pi$
$720$	−2.00000	−0.0745356
$721$	−7.00000	−0.260694
$722$	3.00000	0.111648
$723$	20.0000	0.743808
$724$	0	0
$725$	36.0000	1.33701
$726$	−11.0000	−0.408248
$727$	−32.0000	−1.18681	−0.593407	−	0.804902i	$-0.702218\pi$
$727$	−32.0000	−1.18681	−0.593407	+	0.804902i	$0.702218\pi$
$728$	2.00000	0.0741249
$729$	13.0000	0.481481
$730$	6.00000	0.222070
$731$	−35.0000	−1.29452
$732$	5.00000	0.184805
$733$	19.0000	0.701781	0.350891	−	0.936416i	$-0.385879\pi$
$733$	19.0000	0.701781	0.350891	+	0.936416i	$0.385879\pi$
$734$	19.0000	0.701303
$735$	−1.00000	−0.0368856
$736$	−6.00000	−0.221163
$737$	0	0
$738$	−2.00000	−0.0736210
$739$	19.0000	0.698926	0.349463	−	0.936950i	$-0.386364\pi$
$739$	19.0000	0.698926	0.349463	+	0.936950i	$0.386364\pi$
$740$	−8.00000	−0.294086
$741$	8.00000	0.293887
$742$	−13.0000	−0.477245
$743$	2.00000	0.0733729	0.0366864	−	0.999327i	$-0.488320\pi$
$743$	2.00000	0.0733729	0.0366864	+	0.999327i	$0.488320\pi$
$744$	3.00000	0.109985
$745$	7.00000	0.256460
$746$	16.0000	0.585802
$747$	−32.0000	−1.17082
$748$	0	0
$749$	−3.00000	−0.109618
$750$	−9.00000	−0.328634
$751$	−32.0000	−1.16770	−0.583848	−	0.811863i	$-0.698454\pi$
$751$	−32.0000	−1.16770	−0.583848	+	0.811863i	$0.698454\pi$
$752$	−10.0000	−0.364662
$753$	8.00000	0.291536
$754$	18.0000	0.655521
$755$	−5.00000	−0.181969
$756$	−5.00000	−0.181848
$757$	15.0000	0.545184	0.272592	−	0.962130i	$-0.412119\pi$
$757$	15.0000	0.545184	0.272592	+	0.962130i	$0.412119\pi$
$758$	15.0000	0.544825
$759$	0	0
$760$	4.00000	0.145095
$761$	−14.0000	−0.507500	−0.253750	−	0.967270i	$-0.581664\pi$
$761$	−14.0000	−0.507500	−0.253750	+	0.967270i	$0.581664\pi$
$762$	18.0000	0.652071
$763$	2.00000	0.0724049
$764$	−15.0000	−0.542681
$765$	10.0000	0.361551
$766$	8.00000	0.289052
$767$	−28.0000	−1.01102
$768$	−1.00000	−0.0360844
$769$	−42.0000	−1.51456	−0.757279	−	0.653091i	$-0.773472\pi$
$769$	−42.0000	−1.51456	−0.757279	+	0.653091i	$0.773472\pi$
$770$	0	0
$771$	−3.00000	−0.108042
$772$	16.0000	0.575853
$773$	−2.00000	−0.0719350	−0.0359675	−	0.999353i	$-0.511451\pi$
$773$	−2.00000	−0.0719350	−0.0359675	+	0.999353i	$0.511451\pi$
$774$	14.0000	0.503220
$775$	−12.0000	−0.431053
$776$	−17.0000	−0.610264
$777$	−8.00000	−0.286998
$778$	−20.0000	−0.717035
$779$	4.00000	0.143315
$780$	−2.00000	−0.0716115
$781$	0	0
$782$	30.0000	1.07280
$783$	−45.0000	−1.60817
$784$	1.00000	0.0357143
$785$	0	0
$786$	−18.0000	−0.642039
$787$	−40.0000	−1.42585	−0.712923	−	0.701242i	$-0.752629\pi$
$787$	−40.0000	−1.42585	−0.712923	+	0.701242i	$0.752629\pi$
$788$	0	0
$789$	24.0000	0.854423
$790$	3.00000	0.106735
$791$	−1.00000	−0.0355559
$792$	0	0
$793$	−10.0000	−0.355110
$794$	2.00000	0.0709773
$795$	13.0000	0.461062
$796$	4.00000	0.141776
$797$	−17.0000	−0.602171	−0.301085	−	0.953597i	$-0.597349\pi$
$797$	−17.0000	−0.602171	−0.301085	+	0.953597i	$0.597349\pi$
$798$	4.00000	0.141598
$799$	50.0000	1.76887
$800$	4.00000	0.141421
$801$	−26.0000	−0.918665
$802$	5.00000	0.176556
$803$	0	0
$804$	−4.00000	−0.141069
$805$	−6.00000	−0.211472
$806$	−6.00000	−0.211341
$807$	−10.0000	−0.352017
$808$	−18.0000	−0.633238
$809$	32.0000	1.12506	0.562530	−	0.826777i	$-0.309828\pi$
$809$	32.0000	1.12506	0.562530	+	0.826777i	$0.309828\pi$
$810$	−1.00000	−0.0351364
$811$	−6.00000	−0.210688	−0.105344	−	0.994436i	$-0.533594\pi$
$811$	−6.00000	−0.210688	−0.105344	+	0.994436i	$0.533594\pi$
$812$	9.00000	0.315838
$813$	−16.0000	−0.561144
$814$	0	0
$815$	12.0000	0.420342
$816$	5.00000	0.175035
$817$	−28.0000	−0.979596
$818$	−32.0000	−1.11885
$819$	4.00000	0.139771
$820$	−1.00000	−0.0349215
$821$	52.0000	1.81481	0.907406	−	0.420255i	$-0.138059\pi$
$821$	52.0000	1.81481	0.907406	+	0.420255i	$0.138059\pi$
$822$	−18.0000	−0.627822
$823$	5.00000	0.174289	0.0871445	−	0.996196i	$-0.472226\pi$
$823$	5.00000	0.174289	0.0871445	+	0.996196i	$0.472226\pi$
$824$	−7.00000	−0.243857
$825$	0	0
$826$	−14.0000	−0.487122
$827$	6.00000	0.208640	0.104320	−	0.994544i	$-0.466733\pi$
$827$	6.00000	0.208640	0.104320	+	0.994544i	$0.466733\pi$
$828$	−12.0000	−0.417029
$829$	37.0000	1.28506	0.642532	−	0.766259i	$-0.277884\pi$
$829$	37.0000	1.28506	0.642532	+	0.766259i	$0.277884\pi$
$830$	−16.0000	−0.555368
$831$	−20.0000	−0.693792
$832$	2.00000	0.0693375
$833$	−5.00000	−0.173240
$834$	14.0000	0.484780
$835$	12.0000	0.415277
$836$	0	0
$837$	15.0000	0.518476
$838$	14.0000	0.483622
$839$	20.0000	0.690477	0.345238	−	0.938515i	$-0.387798\pi$
$839$	20.0000	0.690477	0.345238	+	0.938515i	$0.387798\pi$
$840$	−1.00000	−0.0345033
$841$	52.0000	1.79310
$842$	7.00000	0.241236
$843$	22.0000	0.757720
$844$	20.0000	0.688428
$845$	−9.00000	−0.309609
$846$	−20.0000	−0.687614
$847$	11.0000	0.377964
$848$	−13.0000	−0.446422
$849$	12.0000	0.411839
$850$	−20.0000	−0.685994
$851$	−48.0000	−1.64542
$852$	15.0000	0.513892
$853$	−7.00000	−0.239675	−0.119838	−	0.992793i	$-0.538237\pi$
$853$	−7.00000	−0.239675	−0.119838	+	0.992793i	$0.538237\pi$
$854$	−5.00000	−0.171096
$855$	8.00000	0.273594
$856$	−3.00000	−0.102538
$857$	−30.0000	−1.02478	−0.512390	−	0.858753i	$-0.671240\pi$
$857$	−30.0000	−1.02478	−0.512390	+	0.858753i	$0.671240\pi$
$858$	0	0
$859$	22.0000	0.750630	0.375315	−	0.926897i	$-0.377534\pi$
$859$	22.0000	0.750630	0.375315	+	0.926897i	$0.377534\pi$
$860$	7.00000	0.238698
$861$	−1.00000	−0.0340799
$862$	−8.00000	−0.272481
$863$	−34.0000	−1.15737	−0.578687	−	0.815550i	$-0.696435\pi$
$863$	−34.0000	−1.15737	−0.578687	+	0.815550i	$0.696435\pi$
$864$	−5.00000	−0.170103
$865$	9.00000	0.306009
$866$	−6.00000	−0.203888
$867$	−8.00000	−0.271694
$868$	−3.00000	−0.101827
$869$	0	0
$870$	−9.00000	−0.305129
$871$	8.00000	0.271070
$872$	2.00000	0.0677285
$873$	−34.0000	−1.15073
$874$	24.0000	0.811812
$875$	9.00000	0.304256
$876$	6.00000	0.202721
$877$	12.0000	0.405211	0.202606	−	0.979260i	$-0.435059\pi$
$877$	12.0000	0.405211	0.202606	+	0.979260i	$0.435059\pi$
$878$	28.0000	0.944954
$879$	−24.0000	−0.809500
$880$	0	0
$881$	40.0000	1.34763	0.673817	−	0.738898i	$-0.264654\pi$
$881$	40.0000	1.34763	0.673817	+	0.738898i	$0.264654\pi$
$882$	2.00000	0.0673435
$883$	0	0		−	1.00000i	$-0.5\pi$
$883$	0	0			1.00000i	$0.5\pi$
$884$	−10.0000	−0.336336
$885$	14.0000	0.470605
$886$	−39.0000	−1.31023
$887$	−10.0000	−0.335767	−0.167884	−	0.985807i	$-0.553693\pi$
$887$	−10.0000	−0.335767	−0.167884	+	0.985807i	$0.553693\pi$
$888$	−8.00000	−0.268462
$889$	−18.0000	−0.603701
$890$	−13.0000	−0.435761
$891$	0	0
$892$	3.00000	0.100447
$893$	40.0000	1.33855
$894$	7.00000	0.234115
$895$	−24.0000	−0.802232
$896$	1.00000	0.0334077
$897$	−12.0000	−0.400668
$898$	33.0000	1.10122
$899$	−27.0000	−0.900500
$900$	8.00000	0.266667
$901$	65.0000	2.16546
$902$	0	0
$903$	7.00000	0.232945
$904$	−1.00000	−0.0332595
$905$	0	0
$906$	−5.00000	−0.166114
$907$	35.0000	1.16216	0.581078	−	0.813848i	$-0.302631\pi$
$907$	35.0000	1.16216	0.581078	+	0.813848i	$0.302631\pi$
$908$	7.00000	0.232303
$909$	−36.0000	−1.19404
$910$	2.00000	0.0662994
$911$	36.0000	1.19273	0.596367	−	0.802712i	$-0.296610\pi$
$911$	36.0000	1.19273	0.596367	+	0.802712i	$0.296610\pi$
$912$	4.00000	0.132453
$913$	0	0
$914$	18.0000	0.595387
$915$	5.00000	0.165295
$916$	8.00000	0.264327
$917$	18.0000	0.594412
$918$	25.0000	0.825123
$919$	−9.00000	−0.296883	−0.148441	−	0.988921i	$-0.547426\pi$
$919$	−9.00000	−0.296883	−0.148441	+	0.988921i	$0.547426\pi$
$920$	−6.00000	−0.197814
$921$	16.0000	0.527218
$922$	−21.0000	−0.691598
$923$	−30.0000	−0.987462
$924$	0	0
$925$	32.0000	1.05215
$926$	24.0000	0.788689
$927$	−14.0000	−0.459820
$928$	9.00000	0.295439
$929$	34.0000	1.11550	0.557752	−	0.830008i	$-0.311664\pi$
$929$	34.0000	1.11550	0.557752	+	0.830008i	$0.311664\pi$
$930$	3.00000	0.0983739
$931$	−4.00000	−0.131095
$932$	−12.0000	−0.393073
$933$	−18.0000	−0.589294
$934$	−32.0000	−1.04707
$935$	0	0
$936$	4.00000	0.130744
$937$	9.00000	0.294017	0.147009	−	0.989135i	$-0.453036\pi$
$937$	9.00000	0.294017	0.147009	+	0.989135i	$0.453036\pi$
$938$	4.00000	0.130605
$939$	6.00000	0.195803
$940$	−10.0000	−0.326164
$941$	10.0000	0.325991	0.162995	−	0.986627i	$-0.447884\pi$
$941$	10.0000	0.325991	0.162995	+	0.986627i	$0.447884\pi$
$942$	0	0
$943$	−6.00000	−0.195387
$944$	−14.0000	−0.455661
$945$	−5.00000	−0.162650
$946$	0	0
$947$	−36.0000	−1.16984	−0.584921	−	0.811090i	$-0.698875\pi$
$947$	−36.0000	−1.16984	−0.584921	+	0.811090i	$0.698875\pi$
$948$	3.00000	0.0974355
$949$	−12.0000	−0.389536
$950$	−16.0000	−0.519109
$951$	22.0000	0.713399
$952$	−5.00000	−0.162051
$953$	−26.0000	−0.842223	−0.421111	−	0.907009i	$-0.638360\pi$
$953$	−26.0000	−0.842223	−0.421111	+	0.907009i	$0.638360\pi$
$954$	−26.0000	−0.841781
$955$	−15.0000	−0.485389
$956$	0	0
$957$	0	0
$958$	26.0000	0.840022
$959$	18.0000	0.581250
$960$	−1.00000	−0.0322749
$961$	−22.0000	−0.709677
$962$	16.0000	0.515861
$963$	−6.00000	−0.193347
$964$	−20.0000	−0.644157
$965$	16.0000	0.515058
$966$	−6.00000	−0.193047
$967$	−27.0000	−0.868261	−0.434131	−	0.900850i	$-0.642944\pi$
$967$	−27.0000	−0.868261	−0.434131	+	0.900850i	$0.642944\pi$
$968$	11.0000	0.353553
$969$	−20.0000	−0.642493
$970$	−17.0000	−0.545837
$971$	−21.0000	−0.673922	−0.336961	−	0.941519i	$-0.609399\pi$
$971$	−21.0000	−0.673922	−0.336961	+	0.941519i	$0.609399\pi$
$972$	−16.0000	−0.513200
$973$	−14.0000	−0.448819
$974$	−26.0000	−0.833094
$975$	8.00000	0.256205
$976$	−5.00000	−0.160046
$977$	−6.00000	−0.191957	−0.0959785	−	0.995383i	$-0.530598\pi$
$977$	−6.00000	−0.191957	−0.0959785	+	0.995383i	$0.530598\pi$
$978$	12.0000	0.383718
$979$	0	0
$980$	1.00000	0.0319438
$981$	4.00000	0.127710
$982$	−5.00000	−0.159556
$983$	−21.0000	−0.669796	−0.334898	−	0.942254i	$-0.608702\pi$
$983$	−21.0000	−0.669796	−0.334898	+	0.942254i	$0.608702\pi$
$984$	−1.00000	−0.0318788
$985$	0	0
$986$	−45.0000	−1.43309
$987$	−10.0000	−0.318304
$988$	−8.00000	−0.254514
$989$	42.0000	1.33552
$990$	0	0
$991$	8.00000	0.254128	0.127064	−	0.991894i	$-0.459445\pi$
$991$	8.00000	0.254128	0.127064	+	0.991894i	$0.459445\pi$
$992$	−3.00000	−0.0952501
$993$	−26.0000	−0.825085
$994$	−15.0000	−0.475771
$995$	4.00000	0.126809
$996$	−16.0000	−0.506979
$997$	−14.0000	−0.443384	−0.221692	−	0.975117i	$-0.571158\pi$
$997$	−14.0000	−0.443384	−0.221692	+	0.975117i	$0.571158\pi$
$998$	2.00000	0.0633089
$999$	−40.0000	−1.26554

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	574.2.a.b.1.1	✓	1
3.2	odd	2		5166.2.a.bc.1.1		1
4.3	odd	2		4592.2.a.j.1.1		1
7.6	odd	2		4018.2.a.g.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
574.2.a.b.1.1	✓	1	1.1	even	1	trivial
4018.2.a.g.1.1		1	7.6	odd	2
4592.2.a.j.1.1		1	4.3	odd	2
5166.2.a.bc.1.1		1	3.2	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:	\( N \)	\(=\)	\( 574 = 2 \cdot 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	574.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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