LMFDB - Embedded newform 574.2.a.a.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:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	574.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-1.00000 q^{2} -2.00000 q^{3} +1.00000 q^{4} +4.00000 q^{5} +2.00000 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$

\(q-1.00000 q^{2} -2.00000 q^{3} +1.00000 q^{4} +4.00000 q^{5} +2.00000 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} -4.00000 q^{10} +4.00000 q^{11} -2.00000 q^{12} +4.00000 q^{13} -1.00000 q^{14} -8.00000 q^{15} +1.00000 q^{16} -2.00000 q^{17} -1.00000 q^{18} -6.00000 q^{19} +4.00000 q^{20} -2.00000 q^{21} -4.00000 q^{22} -8.00000 q^{23} +2.00000 q^{24} +11.0000 q^{25} -4.00000 q^{26} +4.00000 q^{27} +1.00000 q^{28} +6.00000 q^{29} +8.00000 q^{30} +4.00000 q^{31} -1.00000 q^{32} -8.00000 q^{33} +2.00000 q^{34} +4.00000 q^{35} +1.00000 q^{36} +2.00000 q^{37} +6.00000 q^{38} -8.00000 q^{39} -4.00000 q^{40} -1.00000 q^{41} +2.00000 q^{42} +4.00000 q^{44} +4.00000 q^{45} +8.00000 q^{46} +4.00000 q^{47} -2.00000 q^{48} +1.00000 q^{49} -11.0000 q^{50} +4.00000 q^{51} +4.00000 q^{52} +2.00000 q^{53} -4.00000 q^{54} +16.0000 q^{55} -1.00000 q^{56} +12.0000 q^{57} -6.00000 q^{58} +14.0000 q^{59} -8.00000 q^{60} +4.00000 q^{61} -4.00000 q^{62} +1.00000 q^{63} +1.00000 q^{64} +16.0000 q^{65} +8.00000 q^{66} -8.00000 q^{67} -2.00000 q^{68} +16.0000 q^{69} -4.00000 q^{70} +8.00000 q^{71} -1.00000 q^{72} -14.0000 q^{73} -2.00000 q^{74} -22.0000 q^{75} -6.00000 q^{76} +4.00000 q^{77} +8.00000 q^{78} -8.00000 q^{79} +4.00000 q^{80} -11.0000 q^{81} +1.00000 q^{82} +6.00000 q^{83} -2.00000 q^{84} -8.00000 q^{85} -12.0000 q^{87} -4.00000 q^{88} +10.0000 q^{89} -4.00000 q^{90} +4.00000 q^{91} -8.00000 q^{92} -8.00000 q^{93} -4.00000 q^{94} -24.0000 q^{95} +2.00000 q^{96} +6.00000 q^{97} -1.00000 q^{98} +4.00000 q^{99} +O(q^{100})\)

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−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
$5$	4.00000	1.78885	0.894427	−	0.447214i	$-0.147584\pi$
$5$	4.00000	1.78885	0.894427	+	0.447214i	$0.147584\pi$
$6$	2.00000	0.816497
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−4.00000	−1.26491
$11$	4.00000	1.20605	0.603023	−	0.797724i	$-0.293963\pi$
$11$	4.00000	1.20605	0.603023	+	0.797724i	$0.293963\pi$
$12$	−2.00000	−0.577350
$13$	4.00000	1.10940	0.554700	−	0.832050i	$-0.312833\pi$
$13$	4.00000	1.10940	0.554700	+	0.832050i	$0.312833\pi$
$14$	−1.00000	−0.267261
$15$	−8.00000	−2.06559
$16$	1.00000	0.250000
$17$	−2.00000	−0.485071	−0.242536	−	0.970143i	$-0.577979\pi$
$17$	−2.00000	−0.485071	−0.242536	+	0.970143i	$0.577979\pi$
$18$	−1.00000	−0.235702
$19$	−6.00000	−1.37649	−0.688247	−	0.725476i	$-0.741620\pi$
$19$	−6.00000	−1.37649	−0.688247	+	0.725476i	$0.741620\pi$
$20$	4.00000	0.894427
$21$	−2.00000	−0.436436
$22$	−4.00000	−0.852803
$23$	−8.00000	−1.66812	−0.834058	−	0.551677i	$-0.813988\pi$
$23$	−8.00000	−1.66812	−0.834058	+	0.551677i	$0.813988\pi$
$24$	2.00000	0.408248
$25$	11.0000	2.20000
$26$	−4.00000	−0.784465
$27$	4.00000	0.769800
$28$	1.00000	0.188982
$29$	6.00000	1.11417	0.557086	−	0.830455i	$-0.311919\pi$
$29$	6.00000	1.11417	0.557086	+	0.830455i	$0.311919\pi$
$30$	8.00000	1.46059
$31$	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
$33$	−8.00000	−1.39262
$34$	2.00000	0.342997
$35$	4.00000	0.676123
$36$	1.00000	0.166667
$37$	2.00000	0.328798	0.164399	−	0.986394i	$-0.447432\pi$
$37$	2.00000	0.328798	0.164399	+	0.986394i	$0.447432\pi$
$38$	6.00000	0.973329
$39$	−8.00000	−1.28103
$40$	−4.00000	−0.632456
$41$	−1.00000	−0.156174
$41$	−1.00000	−0.156174
$42$	2.00000	0.308607
$43$	0	0		−	1.00000i	$-0.5\pi$
$43$	0	0			1.00000i	$0.5\pi$
$44$	4.00000	0.603023
$45$	4.00000	0.596285
$46$	8.00000	1.17954
$47$	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
$49$	1.00000	0.142857
$50$	−11.0000	−1.55563
$51$	4.00000	0.560112
$52$	4.00000	0.554700
$53$	2.00000	0.274721	0.137361	−	0.990521i	$-0.456138\pi$
$53$	2.00000	0.274721	0.137361	+	0.990521i	$0.456138\pi$
$54$	−4.00000	−0.544331
$55$	16.0000	2.15744
$56$	−1.00000	−0.133631
$57$	12.0000	1.58944
$58$	−6.00000	−0.787839
$59$	14.0000	1.82264	0.911322	−	0.411693i	$-0.135063\pi$
$59$	14.0000	1.82264	0.911322	+	0.411693i	$0.135063\pi$
$60$	−8.00000	−1.03280
$61$	4.00000	0.512148	0.256074	−	0.966657i	$-0.417571\pi$
$61$	4.00000	0.512148	0.256074	+	0.966657i	$0.417571\pi$
$62$	−4.00000	−0.508001
$63$	1.00000	0.125988
$64$	1.00000	0.125000
$65$	16.0000	1.98456
$66$	8.00000	0.984732
$67$	−8.00000	−0.977356	−0.488678	−	0.872464i	$-0.662521\pi$
$67$	−8.00000	−0.977356	−0.488678	+	0.872464i	$0.662521\pi$
$68$	−2.00000	−0.242536
$69$	16.0000	1.92617
$70$	−4.00000	−0.478091
$71$	8.00000	0.949425	0.474713	−	0.880141i	$-0.342552\pi$
$71$	8.00000	0.949425	0.474713	+	0.880141i	$0.342552\pi$
$72$	−1.00000	−0.117851
$73$	−14.0000	−1.63858	−0.819288	−	0.573382i	$-0.805631\pi$
$73$	−14.0000	−1.63858	−0.819288	+	0.573382i	$0.805631\pi$
$74$	−2.00000	−0.232495
$75$	−22.0000	−2.54034
$76$	−6.00000	−0.688247
$77$	4.00000	0.455842
$78$	8.00000	0.905822
$79$	−8.00000	−0.900070	−0.450035	−	0.893011i	$-0.648589\pi$
$79$	−8.00000	−0.900070	−0.450035	+	0.893011i	$0.648589\pi$
$80$	4.00000	0.447214
$81$	−11.0000	−1.22222
$82$	1.00000	0.110432
$83$	6.00000	0.658586	0.329293	−	0.944228i	$-0.393190\pi$
$83$	6.00000	0.658586	0.329293	+	0.944228i	$0.393190\pi$
$84$	−2.00000	−0.218218
$85$	−8.00000	−0.867722
$86$	0	0
$87$	−12.0000	−1.28654
$88$	−4.00000	−0.426401
$89$	10.0000	1.06000	0.529999	−	0.847998i	$-0.322192\pi$
$89$	10.0000	1.06000	0.529999	+	0.847998i	$0.322192\pi$
$90$	−4.00000	−0.421637
$91$	4.00000	0.419314
$92$	−8.00000	−0.834058
$93$	−8.00000	−0.829561
$94$	−4.00000	−0.412568
$95$	−24.0000	−2.46235
$96$	2.00000	0.204124
$97$	6.00000	0.609208	0.304604	−	0.952479i	$-0.401476\pi$
$97$	6.00000	0.609208	0.304604	+	0.952479i	$0.401476\pi$
$98$	−1.00000	−0.101015
$99$	4.00000	0.402015
$100$	11.0000	1.10000
$101$	0	0		−	1.00000i	$-0.5\pi$
$101$	0	0			1.00000i	$0.5\pi$
$102$	−4.00000	−0.396059
$103$	−12.0000	−1.18240	−0.591198	−	0.806527i	$-0.701345\pi$
$103$	−12.0000	−1.18240	−0.591198	+	0.806527i	$0.701345\pi$
$104$	−4.00000	−0.392232
$105$	−8.00000	−0.780720
$106$	−2.00000	−0.194257
$107$	−4.00000	−0.386695	−0.193347	−	0.981130i	$-0.561934\pi$
$107$	−4.00000	−0.386695	−0.193347	+	0.981130i	$0.561934\pi$
$108$	4.00000	0.384900
$109$	6.00000	0.574696	0.287348	−	0.957826i	$-0.407226\pi$
$109$	6.00000	0.574696	0.287348	+	0.957826i	$0.407226\pi$
$110$	−16.0000	−1.52554
$111$	−4.00000	−0.379663
$112$	1.00000	0.0944911
$113$	−10.0000	−0.940721	−0.470360	−	0.882474i	$-0.655876\pi$
$113$	−10.0000	−0.940721	−0.470360	+	0.882474i	$0.655876\pi$
$114$	−12.0000	−1.12390
$115$	−32.0000	−2.98402
$116$	6.00000	0.557086
$117$	4.00000	0.369800
$118$	−14.0000	−1.28880
$119$	−2.00000	−0.183340
$120$	8.00000	0.730297
$121$	5.00000	0.454545
$122$	−4.00000	−0.362143
$123$	2.00000	0.180334
$124$	4.00000	0.359211
$125$	24.0000	2.14663
$126$	−1.00000	−0.0890871
$127$	−8.00000	−0.709885	−0.354943	−	0.934888i	$-0.615500\pi$
$127$	−8.00000	−0.709885	−0.354943	+	0.934888i	$0.615500\pi$
$128$	−1.00000	−0.0883883
$129$	0	0
$130$	−16.0000	−1.40329
$131$	6.00000	0.524222	0.262111	−	0.965038i	$-0.415581\pi$
$131$	6.00000	0.524222	0.262111	+	0.965038i	$0.415581\pi$
$132$	−8.00000	−0.696311
$133$	−6.00000	−0.520266
$134$	8.00000	0.691095
$135$	16.0000	1.37706
$136$	2.00000	0.171499
$137$	−6.00000	−0.512615	−0.256307	−	0.966595i	$-0.582506\pi$
$137$	−6.00000	−0.512615	−0.256307	+	0.966595i	$0.582506\pi$
$138$	−16.0000	−1.36201
$139$	−22.0000	−1.86602	−0.933008	−	0.359856i	$-0.882826\pi$
$139$	−22.0000	−1.86602	−0.933008	+	0.359856i	$0.882826\pi$
$140$	4.00000	0.338062
$141$	−8.00000	−0.673722
$142$	−8.00000	−0.671345
$143$	16.0000	1.33799
$144$	1.00000	0.0833333
$145$	24.0000	1.99309
$146$	14.0000	1.15865
$147$	−2.00000	−0.164957
$148$	2.00000	0.164399
$149$	−6.00000	−0.491539	−0.245770	−	0.969328i	$-0.579041\pi$
$149$	−6.00000	−0.491539	−0.245770	+	0.969328i	$0.579041\pi$
$150$	22.0000	1.79629
$151$	16.0000	1.30206	0.651031	−	0.759051i	$-0.274337\pi$
$151$	16.0000	1.30206	0.651031	+	0.759051i	$0.274337\pi$
$152$	6.00000	0.486664
$153$	−2.00000	−0.161690
$154$	−4.00000	−0.322329
$155$	16.0000	1.28515
$156$	−8.00000	−0.640513
$157$	4.00000	0.319235	0.159617	−	0.987179i	$-0.448974\pi$
$157$	4.00000	0.319235	0.159617	+	0.987179i	$0.448974\pi$
$158$	8.00000	0.636446
$159$	−4.00000	−0.317221
$160$	−4.00000	−0.316228
$161$	−8.00000	−0.630488
$162$	11.0000	0.864242
$163$	−24.0000	−1.87983	−0.939913	−	0.341415i	$-0.889094\pi$
$163$	−24.0000	−1.87983	−0.939913	+	0.341415i	$0.889094\pi$
$164$	−1.00000	−0.0780869
$165$	−32.0000	−2.49120
$166$	−6.00000	−0.465690
$167$	20.0000	1.54765	0.773823	−	0.633402i	$-0.218342\pi$
$167$	20.0000	1.54765	0.773823	+	0.633402i	$0.218342\pi$
$168$	2.00000	0.154303
$169$	3.00000	0.230769
$170$	8.00000	0.613572
$171$	−6.00000	−0.458831
$172$	0	0
$173$	24.0000	1.82469	0.912343	−	0.409426i	$-0.134271\pi$
$173$	24.0000	1.82469	0.912343	+	0.409426i	$0.134271\pi$
$174$	12.0000	0.909718
$175$	11.0000	0.831522
$176$	4.00000	0.301511
$177$	−28.0000	−2.10461
$178$	−10.0000	−0.749532
$179$	−24.0000	−1.79384	−0.896922	−	0.442189i	$-0.854202\pi$
$179$	−24.0000	−1.79384	−0.896922	+	0.442189i	$0.854202\pi$
$180$	4.00000	0.298142
$181$	20.0000	1.48659	0.743294	−	0.668965i	$-0.233262\pi$
$181$	20.0000	1.48659	0.743294	+	0.668965i	$0.233262\pi$
$182$	−4.00000	−0.296500
$183$	−8.00000	−0.591377
$184$	8.00000	0.589768
$185$	8.00000	0.588172
$186$	8.00000	0.586588
$187$	−8.00000	−0.585018
$188$	4.00000	0.291730
$189$	4.00000	0.290957
$190$	24.0000	1.74114
$191$	0	0		−	1.00000i	$-0.5\pi$
$191$	0	0			1.00000i	$0.5\pi$
$192$	−2.00000	−0.144338
$193$	−18.0000	−1.29567	−0.647834	−	0.761781i	$-0.724325\pi$
$193$	−18.0000	−1.29567	−0.647834	+	0.761781i	$0.724325\pi$
$194$	−6.00000	−0.430775
$195$	−32.0000	−2.29157
$196$	1.00000	0.0714286
$197$	−10.0000	−0.712470	−0.356235	−	0.934396i	$-0.615940\pi$
$197$	−10.0000	−0.712470	−0.356235	+	0.934396i	$0.615940\pi$
$198$	−4.00000	−0.284268
$199$	20.0000	1.41776	0.708881	−	0.705328i	$-0.249200\pi$
$199$	20.0000	1.41776	0.708881	+	0.705328i	$0.249200\pi$
$200$	−11.0000	−0.777817
$201$	16.0000	1.12855
$202$	0	0
$203$	6.00000	0.421117
$204$	4.00000	0.280056
$205$	−4.00000	−0.279372
$206$	12.0000	0.836080
$207$	−8.00000	−0.556038
$208$	4.00000	0.277350
$209$	−24.0000	−1.66011
$210$	8.00000	0.552052
$211$	8.00000	0.550743	0.275371	−	0.961338i	$-0.411199\pi$
$211$	8.00000	0.550743	0.275371	+	0.961338i	$0.411199\pi$
$212$	2.00000	0.137361
$213$	−16.0000	−1.09630
$214$	4.00000	0.273434
$215$	0	0
$216$	−4.00000	−0.272166
$217$	4.00000	0.271538
$218$	−6.00000	−0.406371
$219$	28.0000	1.89206
$220$	16.0000	1.07872
$221$	−8.00000	−0.538138
$222$	4.00000	0.268462
$223$	24.0000	1.60716	0.803579	−	0.595198i	$-0.202926\pi$
$223$	24.0000	1.60716	0.803579	+	0.595198i	$0.202926\pi$
$224$	−1.00000	−0.0668153
$225$	11.0000	0.733333
$226$	10.0000	0.665190
$227$	−6.00000	−0.398234	−0.199117	−	0.979976i	$-0.563807\pi$
$227$	−6.00000	−0.398234	−0.199117	+	0.979976i	$0.563807\pi$
$228$	12.0000	0.794719
$229$	−20.0000	−1.32164	−0.660819	−	0.750546i	$-0.729791\pi$
$229$	−20.0000	−1.32164	−0.660819	+	0.750546i	$0.729791\pi$
$230$	32.0000	2.11002
$231$	−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	$0.393773\pi$
$234$	−4.00000	−0.261488
$235$	16.0000	1.04372
$236$	14.0000	0.911322
$237$	16.0000	1.03931
$238$	2.00000	0.129641
$239$	0	0		−	1.00000i	$-0.5\pi$
$239$	0	0			1.00000i	$0.5\pi$
$240$	−8.00000	−0.516398
$241$	−26.0000	−1.67481	−0.837404	−	0.546585i	$-0.815928\pi$
$241$	−26.0000	−1.67481	−0.837404	+	0.546585i	$0.815928\pi$
$242$	−5.00000	−0.321412
$243$	10.0000	0.641500
$244$	4.00000	0.256074
$245$	4.00000	0.255551
$246$	−2.00000	−0.127515
$247$	−24.0000	−1.52708
$248$	−4.00000	−0.254000
$249$	−12.0000	−0.760469
$250$	−24.0000	−1.51789
$251$	−6.00000	−0.378717	−0.189358	−	0.981908i	$-0.560641\pi$
$251$	−6.00000	−0.378717	−0.189358	+	0.981908i	$0.560641\pi$
$252$	1.00000	0.0629941
$253$	−32.0000	−2.01182
$254$	8.00000	0.501965
$255$	16.0000	1.00196
$256$	1.00000	0.0625000
$257$	2.00000	0.124757	0.0623783	−	0.998053i	$-0.480131\pi$
$257$	2.00000	0.124757	0.0623783	+	0.998053i	$0.480131\pi$
$258$	0	0
$259$	2.00000	0.124274
$260$	16.0000	0.992278
$261$	6.00000	0.371391
$262$	−6.00000	−0.370681
$263$	−16.0000	−0.986602	−0.493301	−	0.869859i	$-0.664210\pi$
$263$	−16.0000	−0.986602	−0.493301	+	0.869859i	$0.664210\pi$
$264$	8.00000	0.492366
$265$	8.00000	0.491436
$266$	6.00000	0.367884
$267$	−20.0000	−1.22398
$268$	−8.00000	−0.488678
$269$	0	0		−	1.00000i	$-0.5\pi$
$269$	0	0			1.00000i	$0.5\pi$
$270$	−16.0000	−0.973729
$271$	−16.0000	−0.971931	−0.485965	−	0.873978i	$-0.661532\pi$
$271$	−16.0000	−0.971931	−0.485965	+	0.873978i	$0.661532\pi$
$272$	−2.00000	−0.121268
$273$	−8.00000	−0.484182
$274$	6.00000	0.362473
$275$	44.0000	2.65330
$276$	16.0000	0.963087
$277$	−18.0000	−1.08152	−0.540758	−	0.841178i	$-0.681862\pi$
$277$	−18.0000	−1.08152	−0.540758	+	0.841178i	$0.681862\pi$
$278$	22.0000	1.31947
$279$	4.00000	0.239474
$280$	−4.00000	−0.239046
$281$	10.0000	0.596550	0.298275	−	0.954480i	$-0.403589\pi$
$281$	10.0000	0.596550	0.298275	+	0.954480i	$0.403589\pi$
$282$	8.00000	0.476393
$283$	14.0000	0.832214	0.416107	−	0.909316i	$-0.363394\pi$
$283$	14.0000	0.832214	0.416107	+	0.909316i	$0.363394\pi$
$284$	8.00000	0.474713
$285$	48.0000	2.84327
$286$	−16.0000	−0.946100
$287$	−1.00000	−0.0590281
$288$	−1.00000	−0.0589256
$289$	−13.0000	−0.764706
$290$	−24.0000	−1.40933
$291$	−12.0000	−0.703452
$292$	−14.0000	−0.819288
$293$	−16.0000	−0.934730	−0.467365	−	0.884064i	$-0.654797\pi$
$293$	−16.0000	−0.934730	−0.467365	+	0.884064i	$0.654797\pi$
$294$	2.00000	0.116642
$295$	56.0000	3.26045
$296$	−2.00000	−0.116248
$297$	16.0000	0.928414
$298$	6.00000	0.347571
$299$	−32.0000	−1.85061
$300$	−22.0000	−1.27017
$301$	0	0
$302$	−16.0000	−0.920697
$303$	0	0
$304$	−6.00000	−0.344124
$305$	16.0000	0.916157
$306$	2.00000	0.114332
$307$	−26.0000	−1.48390	−0.741949	−	0.670456i	$-0.766098\pi$
$307$	−26.0000	−1.48390	−0.741949	+	0.670456i	$0.766098\pi$
$308$	4.00000	0.227921
$309$	24.0000	1.36531
$310$	−16.0000	−0.908739
$311$	8.00000	0.453638	0.226819	−	0.973937i	$-0.427167\pi$
$311$	8.00000	0.453638	0.226819	+	0.973937i	$0.427167\pi$
$312$	8.00000	0.452911
$313$	−34.0000	−1.92179	−0.960897	−	0.276907i	$-0.910691\pi$
$313$	−34.0000	−1.92179	−0.960897	+	0.276907i	$0.910691\pi$
$314$	−4.00000	−0.225733
$315$	4.00000	0.225374
$316$	−8.00000	−0.450035
$317$	−14.0000	−0.786318	−0.393159	−	0.919470i	$-0.628618\pi$
$317$	−14.0000	−0.786318	−0.393159	+	0.919470i	$0.628618\pi$
$318$	4.00000	0.224309
$319$	24.0000	1.34374
$320$	4.00000	0.223607
$321$	8.00000	0.446516
$322$	8.00000	0.445823
$323$	12.0000	0.667698
$324$	−11.0000	−0.611111
$325$	44.0000	2.44068
$326$	24.0000	1.32924
$327$	−12.0000	−0.663602
$328$	1.00000	0.0552158
$329$	4.00000	0.220527
$330$	32.0000	1.76154
$331$	−12.0000	−0.659580	−0.329790	−	0.944054i	$-0.606978\pi$
$331$	−12.0000	−0.659580	−0.329790	+	0.944054i	$0.606978\pi$
$332$	6.00000	0.329293
$333$	2.00000	0.109599
$334$	−20.0000	−1.09435
$335$	−32.0000	−1.74835
$336$	−2.00000	−0.109109
$337$	30.0000	1.63420	0.817102	−	0.576493i	$-0.195579\pi$
$337$	30.0000	1.63420	0.817102	+	0.576493i	$0.195579\pi$
$338$	−3.00000	−0.163178
$339$	20.0000	1.08625
$340$	−8.00000	−0.433861
$341$	16.0000	0.866449
$342$	6.00000	0.324443
$343$	1.00000	0.0539949
$344$	0	0
$345$	64.0000	3.44564
$346$	−24.0000	−1.29025
$347$	−4.00000	−0.214731	−0.107366	−	0.994220i	$-0.534242\pi$
$347$	−4.00000	−0.214731	−0.107366	+	0.994220i	$0.534242\pi$
$348$	−12.0000	−0.643268
$349$	−16.0000	−0.856460	−0.428230	−	0.903670i	$-0.640863\pi$
$349$	−16.0000	−0.856460	−0.428230	+	0.903670i	$0.640863\pi$
$350$	−11.0000	−0.587975
$351$	16.0000	0.854017
$352$	−4.00000	−0.213201
$353$	−22.0000	−1.17094	−0.585471	−	0.810693i	$-0.699090\pi$
$353$	−22.0000	−1.17094	−0.585471	+	0.810693i	$0.699090\pi$
$354$	28.0000	1.48818
$355$	32.0000	1.69838
$356$	10.0000	0.529999
$357$	4.00000	0.211702
$358$	24.0000	1.26844
$359$	24.0000	1.26667	0.633336	−	0.773877i	$-0.281685\pi$
$359$	24.0000	1.26667	0.633336	+	0.773877i	$0.281685\pi$
$360$	−4.00000	−0.210819
$361$	17.0000	0.894737
$362$	−20.0000	−1.05118
$363$	−10.0000	−0.524864
$364$	4.00000	0.209657
$365$	−56.0000	−2.93117
$366$	8.00000	0.418167
$367$	8.00000	0.417597	0.208798	−	0.977959i	$-0.433045\pi$
$367$	8.00000	0.417597	0.208798	+	0.977959i	$0.433045\pi$
$368$	−8.00000	−0.417029
$369$	−1.00000	−0.0520579
$370$	−8.00000	−0.415900
$371$	2.00000	0.103835
$372$	−8.00000	−0.414781
$373$	−34.0000	−1.76045	−0.880227	−	0.474554i	$-0.842610\pi$
$373$	−34.0000	−1.76045	−0.880227	+	0.474554i	$0.842610\pi$
$374$	8.00000	0.413670
$375$	−48.0000	−2.47871
$376$	−4.00000	−0.206284
$377$	24.0000	1.23606
$378$	−4.00000	−0.205738
$379$	−32.0000	−1.64373	−0.821865	−	0.569683i	$-0.807066\pi$
$379$	−32.0000	−1.64373	−0.821865	+	0.569683i	$0.807066\pi$
$380$	−24.0000	−1.23117
$381$	16.0000	0.819705
$382$	0	0
$383$	20.0000	1.02195	0.510976	−	0.859595i	$-0.329284\pi$
$383$	20.0000	1.02195	0.510976	+	0.859595i	$0.329284\pi$
$384$	2.00000	0.102062
$385$	16.0000	0.815436
$386$	18.0000	0.916176
$387$	0	0
$388$	6.00000	0.304604
$389$	18.0000	0.912636	0.456318	−	0.889817i	$-0.349168\pi$
$389$	18.0000	0.912636	0.456318	+	0.889817i	$0.349168\pi$
$390$	32.0000	1.62038
$391$	16.0000	0.809155
$392$	−1.00000	−0.0505076
$393$	−12.0000	−0.605320
$394$	10.0000	0.503793
$395$	−32.0000	−1.61009
$396$	4.00000	0.201008
$397$	−28.0000	−1.40528	−0.702640	−	0.711546i	$-0.747995\pi$
$397$	−28.0000	−1.40528	−0.702640	+	0.711546i	$0.747995\pi$
$398$	−20.0000	−1.00251
$399$	12.0000	0.600751
$400$	11.0000	0.550000
$401$	−34.0000	−1.69788	−0.848939	−	0.528490i	$-0.822758\pi$
$401$	−34.0000	−1.69788	−0.848939	+	0.528490i	$0.822758\pi$
$402$	−16.0000	−0.798007
$403$	16.0000	0.797017
$404$	0	0
$405$	−44.0000	−2.18638
$406$	−6.00000	−0.297775
$407$	8.00000	0.396545
$408$	−4.00000	−0.198030
$409$	−2.00000	−0.0988936	−0.0494468	−	0.998777i	$-0.515746\pi$
$409$	−2.00000	−0.0988936	−0.0494468	+	0.998777i	$0.515746\pi$
$410$	4.00000	0.197546
$411$	12.0000	0.591916
$412$	−12.0000	−0.591198
$413$	14.0000	0.688895
$414$	8.00000	0.393179
$415$	24.0000	1.17811
$416$	−4.00000	−0.196116
$417$	44.0000	2.15469
$418$	24.0000	1.17388
$419$	−6.00000	−0.293119	−0.146560	−	0.989202i	$-0.546820\pi$
$419$	−6.00000	−0.293119	−0.146560	+	0.989202i	$0.546820\pi$
$420$	−8.00000	−0.390360
$421$	−6.00000	−0.292422	−0.146211	−	0.989253i	$-0.546708\pi$
$421$	−6.00000	−0.292422	−0.146211	+	0.989253i	$0.546708\pi$
$422$	−8.00000	−0.389434
$423$	4.00000	0.194487
$424$	−2.00000	−0.0971286
$425$	−22.0000	−1.06716
$426$	16.0000	0.775203
$427$	4.00000	0.193574
$428$	−4.00000	−0.193347
$429$	−32.0000	−1.54497
$430$	0	0
$431$	0	0		−	1.00000i	$-0.5\pi$
$431$	0	0			1.00000i	$0.5\pi$
$432$	4.00000	0.192450
$433$	14.0000	0.672797	0.336399	−	0.941720i	$-0.390791\pi$
$433$	14.0000	0.672797	0.336399	+	0.941720i	$0.390791\pi$
$434$	−4.00000	−0.192006
$435$	−48.0000	−2.30142
$436$	6.00000	0.287348
$437$	48.0000	2.29615
$438$	−28.0000	−1.33789
$439$	8.00000	0.381819	0.190910	−	0.981608i	$-0.438856\pi$
$439$	8.00000	0.381819	0.190910	+	0.981608i	$0.438856\pi$
$440$	−16.0000	−0.762770
$441$	1.00000	0.0476190
$442$	8.00000	0.380521
$443$	12.0000	0.570137	0.285069	−	0.958507i	$-0.407984\pi$
$443$	12.0000	0.570137	0.285069	+	0.958507i	$0.407984\pi$
$444$	−4.00000	−0.189832
$445$	40.0000	1.89618
$446$	−24.0000	−1.13643
$447$	12.0000	0.567581
$448$	1.00000	0.0472456
$449$	−30.0000	−1.41579	−0.707894	−	0.706319i	$-0.750354\pi$
$449$	−30.0000	−1.41579	−0.707894	+	0.706319i	$0.750354\pi$
$450$	−11.0000	−0.518545
$451$	−4.00000	−0.188353
$452$	−10.0000	−0.470360
$453$	−32.0000	−1.50349
$454$	6.00000	0.281594
$455$	16.0000	0.750092
$456$	−12.0000	−0.561951
$457$	38.0000	1.77757	0.888783	−	0.458329i	$-0.151552\pi$
$457$	38.0000	1.77757	0.888783	+	0.458329i	$0.151552\pi$
$458$	20.0000	0.934539
$459$	−8.00000	−0.373408
$460$	−32.0000	−1.49201
$461$	−16.0000	−0.745194	−0.372597	−	0.927993i	$-0.621533\pi$
$461$	−16.0000	−0.745194	−0.372597	+	0.927993i	$0.621533\pi$
$462$	8.00000	0.372194
$463$	−32.0000	−1.48717	−0.743583	−	0.668644i	$-0.766875\pi$
$463$	−32.0000	−1.48717	−0.743583	+	0.668644i	$0.766875\pi$
$464$	6.00000	0.278543
$465$	−32.0000	−1.48396
$466$	−10.0000	−0.463241
$467$	14.0000	0.647843	0.323921	−	0.946084i	$-0.394999\pi$
$467$	14.0000	0.647843	0.323921	+	0.946084i	$0.394999\pi$
$468$	4.00000	0.184900
$469$	−8.00000	−0.369406
$470$	−16.0000	−0.738025
$471$	−8.00000	−0.368621
$472$	−14.0000	−0.644402
$473$	0	0
$474$	−16.0000	−0.734904
$475$	−66.0000	−3.02829
$476$	−2.00000	−0.0916698
$477$	2.00000	0.0915737
$478$	0	0
$479$	−36.0000	−1.64488	−0.822441	−	0.568850i	$-0.807388\pi$
$479$	−36.0000	−1.64488	−0.822441	+	0.568850i	$0.807388\pi$
$480$	8.00000	0.365148
$481$	8.00000	0.364769
$482$	26.0000	1.18427
$483$	16.0000	0.728025
$484$	5.00000	0.227273
$485$	24.0000	1.08978
$486$	−10.0000	−0.453609
$487$	32.0000	1.45006	0.725029	−	0.688718i	$-0.241826\pi$
$487$	32.0000	1.45006	0.725029	+	0.688718i	$0.241826\pi$
$488$	−4.00000	−0.181071
$489$	48.0000	2.17064
$490$	−4.00000	−0.180702
$491$	−20.0000	−0.902587	−0.451294	−	0.892375i	$-0.649037\pi$
$491$	−20.0000	−0.902587	−0.451294	+	0.892375i	$0.649037\pi$
$492$	2.00000	0.0901670
$493$	−12.0000	−0.540453
$494$	24.0000	1.07981
$495$	16.0000	0.719147
$496$	4.00000	0.179605
$497$	8.00000	0.358849
$498$	12.0000	0.537733
$499$	32.0000	1.43252	0.716258	−	0.697835i	$-0.245853\pi$
$499$	32.0000	1.43252	0.716258	+	0.697835i	$0.245853\pi$
$500$	24.0000	1.07331
$501$	−40.0000	−1.78707
$502$	6.00000	0.267793
$503$	0	0		−	1.00000i	$-0.5\pi$
$503$	0	0			1.00000i	$0.5\pi$
$504$	−1.00000	−0.0445435
$505$	0	0
$506$	32.0000	1.42257
$507$	−6.00000	−0.266469
$508$	−8.00000	−0.354943
$509$	20.0000	0.886484	0.443242	−	0.896402i	$-0.353828\pi$
$509$	20.0000	0.886484	0.443242	+	0.896402i	$0.353828\pi$
$510$	−16.0000	−0.708492
$511$	−14.0000	−0.619324
$512$	−1.00000	−0.0441942
$513$	−24.0000	−1.05963
$514$	−2.00000	−0.0882162
$515$	−48.0000	−2.11513
$516$	0	0
$517$	16.0000	0.703679
$518$	−2.00000	−0.0878750
$519$	−48.0000	−2.10697
$520$	−16.0000	−0.701646
$521$	14.0000	0.613351	0.306676	−	0.951814i	$-0.400783\pi$
$521$	14.0000	0.613351	0.306676	+	0.951814i	$0.400783\pi$
$522$	−6.00000	−0.262613
$523$	−34.0000	−1.48672	−0.743358	−	0.668894i	$-0.766768\pi$
$523$	−34.0000	−1.48672	−0.743358	+	0.668894i	$0.766768\pi$
$524$	6.00000	0.262111
$525$	−22.0000	−0.960159
$526$	16.0000	0.697633
$527$	−8.00000	−0.348485
$528$	−8.00000	−0.348155
$529$	41.0000	1.78261
$530$	−8.00000	−0.347498
$531$	14.0000	0.607548
$532$	−6.00000	−0.260133
$533$	−4.00000	−0.173259
$534$	20.0000	0.865485
$535$	−16.0000	−0.691740
$536$	8.00000	0.345547
$537$	48.0000	2.07135
$538$	0	0
$539$	4.00000	0.172292
$540$	16.0000	0.688530
$541$	−10.0000	−0.429934	−0.214967	−	0.976621i	$-0.568964\pi$
$541$	−10.0000	−0.429934	−0.214967	+	0.976621i	$0.568964\pi$
$542$	16.0000	0.687259
$543$	−40.0000	−1.71656
$544$	2.00000	0.0857493
$545$	24.0000	1.02805
$546$	8.00000	0.342368
$547$	36.0000	1.53925	0.769624	−	0.638497i	$-0.220443\pi$
$547$	36.0000	1.53925	0.769624	+	0.638497i	$0.220443\pi$
$548$	−6.00000	−0.256307
$549$	4.00000	0.170716
$550$	−44.0000	−1.87617
$551$	−36.0000	−1.53365
$552$	−16.0000	−0.681005
$553$	−8.00000	−0.340195
$554$	18.0000	0.764747
$555$	−16.0000	−0.679162
$556$	−22.0000	−0.933008
$557$	−6.00000	−0.254228	−0.127114	−	0.991888i	$-0.540571\pi$
$557$	−6.00000	−0.254228	−0.127114	+	0.991888i	$0.540571\pi$
$558$	−4.00000	−0.169334
$559$	0	0
$560$	4.00000	0.169031
$561$	16.0000	0.675521
$562$	−10.0000	−0.421825
$563$	−10.0000	−0.421450	−0.210725	−	0.977545i	$-0.567582\pi$
$563$	−10.0000	−0.421450	−0.210725	+	0.977545i	$0.567582\pi$
$564$	−8.00000	−0.336861
$565$	−40.0000	−1.68281
$566$	−14.0000	−0.588464
$567$	−11.0000	−0.461957
$568$	−8.00000	−0.335673
$569$	−42.0000	−1.76073	−0.880366	−	0.474295i	$-0.842703\pi$
$569$	−42.0000	−1.76073	−0.880366	+	0.474295i	$0.842703\pi$
$570$	−48.0000	−2.01050
$571$	12.0000	0.502184	0.251092	−	0.967963i	$-0.419210\pi$
$571$	12.0000	0.502184	0.251092	+	0.967963i	$0.419210\pi$
$572$	16.0000	0.668994
$573$	0	0
$574$	1.00000	0.0417392
$575$	−88.0000	−3.66985
$576$	1.00000	0.0416667
$577$	−38.0000	−1.58196	−0.790980	−	0.611842i	$-0.790429\pi$
$577$	−38.0000	−1.58196	−0.790980	+	0.611842i	$0.790429\pi$
$578$	13.0000	0.540729
$579$	36.0000	1.49611
$580$	24.0000	0.996546
$581$	6.00000	0.248922
$582$	12.0000	0.497416
$583$	8.00000	0.331326
$584$	14.0000	0.579324
$585$	16.0000	0.661519
$586$	16.0000	0.660954
$587$	38.0000	1.56843	0.784214	−	0.620491i	$-0.213066\pi$
$587$	38.0000	1.56843	0.784214	+	0.620491i	$0.213066\pi$
$588$	−2.00000	−0.0824786
$589$	−24.0000	−0.988903
$590$	−56.0000	−2.30548
$591$	20.0000	0.822690
$592$	2.00000	0.0821995
$593$	−6.00000	−0.246390	−0.123195	−	0.992382i	$-0.539314\pi$
$593$	−6.00000	−0.246390	−0.123195	+	0.992382i	$0.539314\pi$
$594$	−16.0000	−0.656488
$595$	−8.00000	−0.327968
$596$	−6.00000	−0.245770
$597$	−40.0000	−1.63709
$598$	32.0000	1.30858
$599$	24.0000	0.980613	0.490307	−	0.871550i	$-0.336885\pi$
$599$	24.0000	0.980613	0.490307	+	0.871550i	$0.336885\pi$
$600$	22.0000	0.898146
$601$	34.0000	1.38689	0.693444	−	0.720510i	$-0.256092\pi$
$601$	34.0000	1.38689	0.693444	+	0.720510i	$0.256092\pi$
$602$	0	0
$603$	−8.00000	−0.325785
$604$	16.0000	0.651031
$605$	20.0000	0.813116
$606$	0	0
$607$	16.0000	0.649420	0.324710	−	0.945814i	$-0.394733\pi$
$607$	16.0000	0.649420	0.324710	+	0.945814i	$0.394733\pi$
$608$	6.00000	0.243332
$609$	−12.0000	−0.486265
$610$	−16.0000	−0.647821
$611$	16.0000	0.647291
$612$	−2.00000	−0.0808452
$613$	10.0000	0.403896	0.201948	−	0.979396i	$-0.435273\pi$
$613$	10.0000	0.403896	0.201948	+	0.979396i	$0.435273\pi$
$614$	26.0000	1.04927
$615$	8.00000	0.322591
$616$	−4.00000	−0.161165
$617$	22.0000	0.885687	0.442843	−	0.896599i	$-0.353970\pi$
$617$	22.0000	0.885687	0.442843	+	0.896599i	$0.353970\pi$
$618$	−24.0000	−0.965422
$619$	30.0000	1.20580	0.602901	−	0.797816i	$-0.294011\pi$
$619$	30.0000	1.20580	0.602901	+	0.797816i	$0.294011\pi$
$620$	16.0000	0.642575
$621$	−32.0000	−1.28412
$622$	−8.00000	−0.320771
$623$	10.0000	0.400642
$624$	−8.00000	−0.320256
$625$	41.0000	1.64000
$626$	34.0000	1.35891
$627$	48.0000	1.91694
$628$	4.00000	0.159617
$629$	−4.00000	−0.159490
$630$	−4.00000	−0.159364
$631$	−8.00000	−0.318475	−0.159237	−	0.987240i	$-0.550904\pi$
$631$	−8.00000	−0.318475	−0.159237	+	0.987240i	$0.550904\pi$
$632$	8.00000	0.318223
$633$	−16.0000	−0.635943
$634$	14.0000	0.556011
$635$	−32.0000	−1.26988
$636$	−4.00000	−0.158610
$637$	4.00000	0.158486
$638$	−24.0000	−0.950169
$639$	8.00000	0.316475
$640$	−4.00000	−0.158114
$641$	−18.0000	−0.710957	−0.355479	−	0.934684i	$-0.615682\pi$
$641$	−18.0000	−0.710957	−0.355479	+	0.934684i	$0.615682\pi$
$642$	−8.00000	−0.315735
$643$	22.0000	0.867595	0.433798	−	0.901010i	$-0.357173\pi$
$643$	22.0000	0.867595	0.433798	+	0.901010i	$0.357173\pi$
$644$	−8.00000	−0.315244
$645$	0	0
$646$	−12.0000	−0.472134
$647$	28.0000	1.10079	0.550397	−	0.834903i	$-0.314476\pi$
$647$	28.0000	1.10079	0.550397	+	0.834903i	$0.314476\pi$
$648$	11.0000	0.432121
$649$	56.0000	2.19819
$650$	−44.0000	−1.72582
$651$	−8.00000	−0.313545
$652$	−24.0000	−0.939913
$653$	30.0000	1.17399	0.586995	−	0.809590i	$-0.300311\pi$
$653$	30.0000	1.17399	0.586995	+	0.809590i	$0.300311\pi$
$654$	12.0000	0.469237
$655$	24.0000	0.937758
$656$	−1.00000	−0.0390434
$657$	−14.0000	−0.546192
$658$	−4.00000	−0.155936
$659$	−12.0000	−0.467454	−0.233727	−	0.972302i	$-0.575092\pi$
$659$	−12.0000	−0.467454	−0.233727	+	0.972302i	$0.575092\pi$
$660$	−32.0000	−1.24560
$661$	−4.00000	−0.155582	−0.0777910	−	0.996970i	$-0.524787\pi$
$661$	−4.00000	−0.155582	−0.0777910	+	0.996970i	$0.524787\pi$
$662$	12.0000	0.466393
$663$	16.0000	0.621389
$664$	−6.00000	−0.232845
$665$	−24.0000	−0.930680
$666$	−2.00000	−0.0774984
$667$	−48.0000	−1.85857
$668$	20.0000	0.773823
$669$	−48.0000	−1.85579
$670$	32.0000	1.23627
$671$	16.0000	0.617673
$672$	2.00000	0.0771517
$673$	−14.0000	−0.539660	−0.269830	−	0.962908i	$-0.586968\pi$
$673$	−14.0000	−0.539660	−0.269830	+	0.962908i	$0.586968\pi$
$674$	−30.0000	−1.15556
$675$	44.0000	1.69356
$676$	3.00000	0.115385
$677$	0	0		−	1.00000i	$-0.5\pi$
$677$	0	0			1.00000i	$0.5\pi$
$678$	−20.0000	−0.768095
$679$	6.00000	0.230259
$680$	8.00000	0.306786
$681$	12.0000	0.459841
$682$	−16.0000	−0.612672
$683$	−8.00000	−0.306111	−0.153056	−	0.988218i	$-0.548911\pi$
$683$	−8.00000	−0.306111	−0.153056	+	0.988218i	$0.548911\pi$
$684$	−6.00000	−0.229416
$685$	−24.0000	−0.916993
$686$	−1.00000	−0.0381802
$687$	40.0000	1.52610
$688$	0	0
$689$	8.00000	0.304776
$690$	−64.0000	−2.43644
$691$	34.0000	1.29342	0.646710	−	0.762736i	$-0.276144\pi$
$691$	34.0000	1.29342	0.646710	+	0.762736i	$0.276144\pi$
$692$	24.0000	0.912343
$693$	4.00000	0.151947
$694$	4.00000	0.151838
$695$	−88.0000	−3.33803
$696$	12.0000	0.454859
$697$	2.00000	0.0757554
$698$	16.0000	0.605609
$699$	−20.0000	−0.756469
$700$	11.0000	0.415761
$701$	2.00000	0.0755390	0.0377695	−	0.999286i	$-0.487975\pi$
$701$	2.00000	0.0755390	0.0377695	+	0.999286i	$0.487975\pi$
$702$	−16.0000	−0.603881
$703$	−12.0000	−0.452589
$704$	4.00000	0.150756
$705$	−32.0000	−1.20519
$706$	22.0000	0.827981
$707$	0	0
$708$	−28.0000	−1.05230
$709$	46.0000	1.72757	0.863783	−	0.503864i	$-0.168089\pi$
$709$	46.0000	1.72757	0.863783	+	0.503864i	$0.168089\pi$
$710$	−32.0000	−1.20094
$711$	−8.00000	−0.300023
$712$	−10.0000	−0.374766
$713$	−32.0000	−1.19841
$714$	−4.00000	−0.149696
$715$	64.0000	2.39346
$716$	−24.0000	−0.896922
$717$	0	0
$718$	−24.0000	−0.895672
$719$	−4.00000	−0.149175	−0.0745874	−	0.997214i	$-0.523764\pi$
$719$	−4.00000	−0.149175	−0.0745874	+	0.997214i	$0.523764\pi$
$720$	4.00000	0.149071
$721$	−12.0000	−0.446903
$722$	−17.0000	−0.632674
$723$	52.0000	1.93390
$724$	20.0000	0.743294
$725$	66.0000	2.45118
$726$	10.0000	0.371135
$727$	28.0000	1.03846	0.519231	−	0.854634i	$-0.326218\pi$
$727$	28.0000	1.03846	0.519231	+	0.854634i	$0.326218\pi$
$728$	−4.00000	−0.148250
$729$	13.0000	0.481481
$730$	56.0000	2.07265
$731$	0	0
$732$	−8.00000	−0.295689
$733$	20.0000	0.738717	0.369358	−	0.929287i	$-0.379577\pi$
$733$	20.0000	0.738717	0.369358	+	0.929287i	$0.379577\pi$
$734$	−8.00000	−0.295285
$735$	−8.00000	−0.295084
$736$	8.00000	0.294884
$737$	−32.0000	−1.17874
$738$	1.00000	0.0368105
$739$	−8.00000	−0.294285	−0.147142	−	0.989115i	$-0.547008\pi$
$739$	−8.00000	−0.294285	−0.147142	+	0.989115i	$0.547008\pi$
$740$	8.00000	0.294086
$741$	48.0000	1.76332
$742$	−2.00000	−0.0734223
$743$	−8.00000	−0.293492	−0.146746	−	0.989174i	$-0.546880\pi$
$743$	−8.00000	−0.293492	−0.146746	+	0.989174i	$0.546880\pi$
$744$	8.00000	0.293294
$745$	−24.0000	−0.879292
$746$	34.0000	1.24483
$747$	6.00000	0.219529
$748$	−8.00000	−0.292509
$749$	−4.00000	−0.146157
$750$	48.0000	1.75271
$751$	16.0000	0.583848	0.291924	−	0.956441i	$-0.405705\pi$
$751$	16.0000	0.583848	0.291924	+	0.956441i	$0.405705\pi$
$752$	4.00000	0.145865
$753$	12.0000	0.437304
$754$	−24.0000	−0.874028
$755$	64.0000	2.32920
$756$	4.00000	0.145479
$757$	−18.0000	−0.654221	−0.327111	−	0.944986i	$-0.606075\pi$
$757$	−18.0000	−0.654221	−0.327111	+	0.944986i	$0.606075\pi$
$758$	32.0000	1.16229
$759$	64.0000	2.32305
$760$	24.0000	0.870572
$761$	−10.0000	−0.362500	−0.181250	−	0.983437i	$-0.558014\pi$
$761$	−10.0000	−0.362500	−0.181250	+	0.983437i	$0.558014\pi$
$762$	−16.0000	−0.579619
$763$	6.00000	0.217215
$764$	0	0
$765$	−8.00000	−0.289241
$766$	−20.0000	−0.722629
$767$	56.0000	2.02204
$768$	−2.00000	−0.0721688
$769$	−26.0000	−0.937584	−0.468792	−	0.883309i	$-0.655311\pi$
$769$	−26.0000	−0.937584	−0.468792	+	0.883309i	$0.655311\pi$
$770$	−16.0000	−0.576600
$771$	−4.00000	−0.144056
$772$	−18.0000	−0.647834
$773$	−48.0000	−1.72644	−0.863220	−	0.504828i	$-0.831556\pi$
$773$	−48.0000	−1.72644	−0.863220	+	0.504828i	$0.831556\pi$
$774$	0	0
$775$	44.0000	1.58053
$776$	−6.00000	−0.215387
$777$	−4.00000	−0.143499
$778$	−18.0000	−0.645331
$779$	6.00000	0.214972
$780$	−32.0000	−1.14578
$781$	32.0000	1.14505
$782$	−16.0000	−0.572159
$783$	24.0000	0.857690
$784$	1.00000	0.0357143
$785$	16.0000	0.571064
$786$	12.0000	0.428026
$787$	−18.0000	−0.641631	−0.320815	−	0.947142i	$-0.603957\pi$
$787$	−18.0000	−0.641631	−0.320815	+	0.947142i	$0.603957\pi$
$788$	−10.0000	−0.356235
$789$	32.0000	1.13923
$790$	32.0000	1.13851
$791$	−10.0000	−0.355559
$792$	−4.00000	−0.142134
$793$	16.0000	0.568177
$794$	28.0000	0.993683
$795$	−16.0000	−0.567462
$796$	20.0000	0.708881
$797$	−16.0000	−0.566749	−0.283375	−	0.959009i	$-0.591454\pi$
$797$	−16.0000	−0.566749	−0.283375	+	0.959009i	$0.591454\pi$
$798$	−12.0000	−0.424795
$799$	−8.00000	−0.283020
$800$	−11.0000	−0.388909
$801$	10.0000	0.353333
$802$	34.0000	1.20058
$803$	−56.0000	−1.97620
$804$	16.0000	0.564276
$805$	−32.0000	−1.12785
$806$	−16.0000	−0.563576
$807$	0	0
$808$	0	0
$809$	22.0000	0.773479	0.386739	−	0.922189i	$-0.373601\pi$
$809$	22.0000	0.773479	0.386739	+	0.922189i	$0.373601\pi$
$810$	44.0000	1.54600
$811$	−42.0000	−1.47482	−0.737410	−	0.675446i	$-0.763951\pi$
$811$	−42.0000	−1.47482	−0.737410	+	0.675446i	$0.763951\pi$
$812$	6.00000	0.210559
$813$	32.0000	1.12229
$814$	−8.00000	−0.280400
$815$	−96.0000	−3.36273
$816$	4.00000	0.140028
$817$	0	0
$818$	2.00000	0.0699284
$819$	4.00000	0.139771
$820$	−4.00000	−0.139686
$821$	−18.0000	−0.628204	−0.314102	−	0.949389i	$-0.601703\pi$
$821$	−18.0000	−0.628204	−0.314102	+	0.949389i	$0.601703\pi$
$822$	−12.0000	−0.418548
$823$	−16.0000	−0.557725	−0.278862	−	0.960331i	$-0.589957\pi$
$823$	−16.0000	−0.557725	−0.278862	+	0.960331i	$0.589957\pi$
$824$	12.0000	0.418040
$825$	−88.0000	−3.06377
$826$	−14.0000	−0.487122
$827$	16.0000	0.556375	0.278187	−	0.960527i	$-0.410266\pi$
$827$	16.0000	0.556375	0.278187	+	0.960527i	$0.410266\pi$
$828$	−8.00000	−0.278019
$829$	12.0000	0.416777	0.208389	−	0.978046i	$-0.433178\pi$
$829$	12.0000	0.416777	0.208389	+	0.978046i	$0.433178\pi$
$830$	−24.0000	−0.833052
$831$	36.0000	1.24883
$832$	4.00000	0.138675
$833$	−2.00000	−0.0692959
$834$	−44.0000	−1.52360
$835$	80.0000	2.76851
$836$	−24.0000	−0.830057
$837$	16.0000	0.553041
$838$	6.00000	0.207267
$839$	−36.0000	−1.24286	−0.621429	−	0.783470i	$-0.713448\pi$
$839$	−36.0000	−1.24286	−0.621429	+	0.783470i	$0.713448\pi$
$840$	8.00000	0.276026
$841$	7.00000	0.241379
$842$	6.00000	0.206774
$843$	−20.0000	−0.688837
$844$	8.00000	0.275371
$845$	12.0000	0.412813
$846$	−4.00000	−0.137523
$847$	5.00000	0.171802
$848$	2.00000	0.0686803
$849$	−28.0000	−0.960958
$850$	22.0000	0.754594
$851$	−16.0000	−0.548473
$852$	−16.0000	−0.548151
$853$	16.0000	0.547830	0.273915	−	0.961754i	$-0.411681\pi$
$853$	16.0000	0.547830	0.273915	+	0.961754i	$0.411681\pi$
$854$	−4.00000	−0.136877
$855$	−24.0000	−0.820783
$856$	4.00000	0.136717
$857$	−18.0000	−0.614868	−0.307434	−	0.951569i	$-0.599470\pi$
$857$	−18.0000	−0.614868	−0.307434	+	0.951569i	$0.599470\pi$
$858$	32.0000	1.09246
$859$	−6.00000	−0.204717	−0.102359	−	0.994748i	$-0.532639\pi$
$859$	−6.00000	−0.204717	−0.102359	+	0.994748i	$0.532639\pi$
$860$	0	0
$861$	2.00000	0.0681598
$862$	0	0
$863$	56.0000	1.90626	0.953131	−	0.302558i	$-0.0978405\pi$
$863$	56.0000	1.90626	0.953131	+	0.302558i	$0.0978405\pi$
$864$	−4.00000	−0.136083
$865$	96.0000	3.26410
$866$	−14.0000	−0.475739
$867$	26.0000	0.883006
$868$	4.00000	0.135769
$869$	−32.0000	−1.08553
$870$	48.0000	1.62735
$871$	−32.0000	−1.08428
$872$	−6.00000	−0.203186
$873$	6.00000	0.203069
$874$	−48.0000	−1.62362
$875$	24.0000	0.811348
$876$	28.0000	0.946032
$877$	−14.0000	−0.472746	−0.236373	−	0.971662i	$-0.575959\pi$
$877$	−14.0000	−0.472746	−0.236373	+	0.971662i	$0.575959\pi$
$878$	−8.00000	−0.269987
$879$	32.0000	1.07933
$880$	16.0000	0.539360
$881$	18.0000	0.606435	0.303218	−	0.952921i	$-0.401939\pi$
$881$	18.0000	0.606435	0.303218	+	0.952921i	$0.401939\pi$
$882$	−1.00000	−0.0336718
$883$	8.00000	0.269221	0.134611	−	0.990899i	$-0.457022\pi$
$883$	8.00000	0.269221	0.134611	+	0.990899i	$0.457022\pi$
$884$	−8.00000	−0.269069
$885$	−112.000	−3.76484
$886$	−12.0000	−0.403148
$887$	−20.0000	−0.671534	−0.335767	−	0.941945i	$-0.608996\pi$
$887$	−20.0000	−0.671534	−0.335767	+	0.941945i	$0.608996\pi$
$888$	4.00000	0.134231
$889$	−8.00000	−0.268311
$890$	−40.0000	−1.34080
$891$	−44.0000	−1.47406
$892$	24.0000	0.803579
$893$	−24.0000	−0.803129
$894$	−12.0000	−0.401340
$895$	−96.0000	−3.20893
$896$	−1.00000	−0.0334077
$897$	64.0000	2.13690
$898$	30.0000	1.00111
$899$	24.0000	0.800445
$900$	11.0000	0.366667
$901$	−4.00000	−0.133259
$902$	4.00000	0.133185
$903$	0	0
$904$	10.0000	0.332595
$905$	80.0000	2.65929
$906$	32.0000	1.06313
$907$	−12.0000	−0.398453	−0.199227	−	0.979953i	$-0.563843\pi$
$907$	−12.0000	−0.398453	−0.199227	+	0.979953i	$0.563843\pi$
$908$	−6.00000	−0.199117
$909$	0	0
$910$	−16.0000	−0.530395
$911$	40.0000	1.32526	0.662630	−	0.748947i	$-0.269440\pi$
$911$	40.0000	1.32526	0.662630	+	0.748947i	$0.269440\pi$
$912$	12.0000	0.397360
$913$	24.0000	0.794284
$914$	−38.0000	−1.25693
$915$	−32.0000	−1.05789
$916$	−20.0000	−0.660819
$917$	6.00000	0.198137
$918$	8.00000	0.264039
$919$	−32.0000	−1.05558	−0.527791	−	0.849374i	$-0.676980\pi$
$919$	−32.0000	−1.05558	−0.527791	+	0.849374i	$0.676980\pi$
$920$	32.0000	1.05501
$921$	52.0000	1.71346
$922$	16.0000	0.526932
$923$	32.0000	1.05329
$924$	−8.00000	−0.263181
$925$	22.0000	0.723356
$926$	32.0000	1.05159
$927$	−12.0000	−0.394132
$928$	−6.00000	−0.196960
$929$	38.0000	1.24674	0.623370	−	0.781927i	$-0.285763\pi$
$929$	38.0000	1.24674	0.623370	+	0.781927i	$0.285763\pi$
$930$	32.0000	1.04932
$931$	−6.00000	−0.196642
$932$	10.0000	0.327561
$933$	−16.0000	−0.523816
$934$	−14.0000	−0.458094
$935$	−32.0000	−1.04651
$936$	−4.00000	−0.130744
$937$	2.00000	0.0653372	0.0326686	−	0.999466i	$-0.489599\pi$
$937$	2.00000	0.0653372	0.0326686	+	0.999466i	$0.489599\pi$
$938$	8.00000	0.261209
$939$	68.0000	2.21910
$940$	16.0000	0.521862
$941$	−28.0000	−0.912774	−0.456387	−	0.889781i	$-0.650857\pi$
$941$	−28.0000	−0.912774	−0.456387	+	0.889781i	$0.650857\pi$
$942$	8.00000	0.260654
$943$	8.00000	0.260516
$944$	14.0000	0.455661
$945$	16.0000	0.520480
$946$	0	0
$947$	24.0000	0.779895	0.389948	−	0.920837i	$-0.372493\pi$
$947$	24.0000	0.779895	0.389948	+	0.920837i	$0.372493\pi$
$948$	16.0000	0.519656
$949$	−56.0000	−1.81784
$950$	66.0000	2.14132
$951$	28.0000	0.907962
$952$	2.00000	0.0648204
$953$	−22.0000	−0.712650	−0.356325	−	0.934362i	$-0.615970\pi$
$953$	−22.0000	−0.712650	−0.356325	+	0.934362i	$0.615970\pi$
$954$	−2.00000	−0.0647524
$955$	0	0
$956$	0	0
$957$	−48.0000	−1.55162
$958$	36.0000	1.16311
$959$	−6.00000	−0.193750
$960$	−8.00000	−0.258199
$961$	−15.0000	−0.483871
$962$	−8.00000	−0.257930
$963$	−4.00000	−0.128898
$964$	−26.0000	−0.837404
$965$	−72.0000	−2.31776
$966$	−16.0000	−0.514792
$967$	−16.0000	−0.514525	−0.257263	−	0.966342i	$-0.582821\pi$
$967$	−16.0000	−0.514525	−0.257263	+	0.966342i	$0.582821\pi$
$968$	−5.00000	−0.160706
$969$	−24.0000	−0.770991
$970$	−24.0000	−0.770594
$971$	18.0000	0.577647	0.288824	−	0.957382i	$-0.406736\pi$
$971$	18.0000	0.577647	0.288824	+	0.957382i	$0.406736\pi$
$972$	10.0000	0.320750
$973$	−22.0000	−0.705288
$974$	−32.0000	−1.02535
$975$	−88.0000	−2.81826
$976$	4.00000	0.128037
$977$	18.0000	0.575871	0.287936	−	0.957650i	$-0.407031\pi$
$977$	18.0000	0.575871	0.287936	+	0.957650i	$0.407031\pi$
$978$	−48.0000	−1.53487
$979$	40.0000	1.27841
$980$	4.00000	0.127775
$981$	6.00000	0.191565
$982$	20.0000	0.638226
$983$	36.0000	1.14822	0.574111	−	0.818778i	$-0.305348\pi$
$983$	36.0000	1.14822	0.574111	+	0.818778i	$0.305348\pi$
$984$	−2.00000	−0.0637577
$985$	−40.0000	−1.27451
$986$	12.0000	0.382158
$987$	−8.00000	−0.254643
$988$	−24.0000	−0.763542
$989$	0	0
$990$	−16.0000	−0.508513
$991$	−40.0000	−1.27064	−0.635321	−	0.772248i	$-0.719132\pi$
$991$	−40.0000	−1.27064	−0.635321	+	0.772248i	$0.719132\pi$
$992$	−4.00000	−0.127000
$993$	24.0000	0.761617
$994$	−8.00000	−0.253745
$995$	80.0000	2.53617
$996$	−12.0000	−0.380235
$997$	−8.00000	−0.253363	−0.126681	−	0.991943i	$-0.540433\pi$
$997$	−8.00000	−0.253363	−0.126681	+	0.991943i	$0.540433\pi$
$998$	−32.0000	−1.01294
$999$	8.00000	0.253109

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	574.2.a.a.1.1	✓	1
3.2	odd	2		5166.2.a.u.1.1		1
4.3	odd	2		4592.2.a.k.1.1		1
7.6	odd	2		4018.2.a.i.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
574.2.a.a.1.1	✓	1	1.1	even	1	trivial
4018.2.a.i.1.1		1	7.6	odd	2
4592.2.a.k.1.1		1	4.3	odd	2
5166.2.a.u.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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