LMFDB - Embedded newform 574.2.a.h.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)

$f(q)$

$=$

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

\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} -2.00000 q^{9} -1.00000 q^{10} -6.00000 q^{11} -1.00000 q^{12} -4.00000 q^{13} -1.00000 q^{14} +1.00000 q^{15} +1.00000 q^{16} +7.00000 q^{17} -2.00000 q^{18} -1.00000 q^{20} +1.00000 q^{21} -6.00000 q^{22} -8.00000 q^{23} -1.00000 q^{24} -4.00000 q^{25} -4.00000 q^{26} +5.00000 q^{27} -1.00000 q^{28} +1.00000 q^{29} +1.00000 q^{30} +5.00000 q^{31} +1.00000 q^{32} +6.00000 q^{33} +7.00000 q^{34} +1.00000 q^{35} -2.00000 q^{36} -2.00000 q^{37} +4.00000 q^{39} -1.00000 q^{40} +1.00000 q^{41} +1.00000 q^{42} -5.00000 q^{43} -6.00000 q^{44} +2.00000 q^{45} -8.00000 q^{46} -6.00000 q^{47} -1.00000 q^{48} +1.00000 q^{49} -4.00000 q^{50} -7.00000 q^{51} -4.00000 q^{52} -3.00000 q^{53} +5.00000 q^{54} +6.00000 q^{55} -1.00000 q^{56} +1.00000 q^{58} -10.0000 q^{59} +1.00000 q^{60} -3.00000 q^{61} +5.00000 q^{62} +2.00000 q^{63} +1.00000 q^{64} +4.00000 q^{65} +6.00000 q^{66} +14.0000 q^{67} +7.00000 q^{68} +8.00000 q^{69} +1.00000 q^{70} +3.00000 q^{71} -2.00000 q^{72} +8.00000 q^{73} -2.00000 q^{74} +4.00000 q^{75} +6.00000 q^{77} +4.00000 q^{78} +7.00000 q^{79} -1.00000 q^{80} +1.00000 q^{81} +1.00000 q^{82} -2.00000 q^{83} +1.00000 q^{84} -7.00000 q^{85} -5.00000 q^{86} -1.00000 q^{87} -6.00000 q^{88} +5.00000 q^{89} +2.00000 q^{90} +4.00000 q^{91} -8.00000 q^{92} -5.00000 q^{93} -6.00000 q^{94} -1.00000 q^{96} +5.00000 q^{97} +1.00000 q^{98} +12.0000 q^{99} +O(q^{100})\)

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−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	$-0.571783\pi$
$5$	−1.00000	−0.447214	−0.223607	+	0.974679i	$0.571783\pi$
$6$	−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
$11$	−6.00000	−1.80907	−0.904534	−	0.426401i	$-0.859781\pi$
$11$	−6.00000	−1.80907	−0.904534	+	0.426401i	$0.859781\pi$
$12$	−1.00000	−0.288675
$13$	−4.00000	−1.10940	−0.554700	−	0.832050i	$-0.687167\pi$
$13$	−4.00000	−1.10940	−0.554700	+	0.832050i	$0.687167\pi$
$14$	−1.00000	−0.267261
$15$	1.00000	0.258199
$16$	1.00000	0.250000
$17$	7.00000	1.69775	0.848875	−	0.528594i	$-0.177281\pi$
$17$	7.00000	1.69775	0.848875	+	0.528594i	$0.177281\pi$
$18$	−2.00000	−0.471405
$19$	0	0		−	1.00000i	$-0.5\pi$
$19$	0	0			1.00000i	$0.5\pi$
$20$	−1.00000	−0.223607
$21$	1.00000	0.218218
$22$	−6.00000	−1.27920
$23$	−8.00000	−1.66812	−0.834058	−	0.551677i	$-0.813988\pi$
$23$	−8.00000	−1.66812	−0.834058	+	0.551677i	$0.813988\pi$
$24$	−1.00000	−0.204124
$25$	−4.00000	−0.800000
$26$	−4.00000	−0.784465
$27$	5.00000	0.962250
$28$	−1.00000	−0.188982
$29$	1.00000	0.185695	0.0928477	−	0.995680i	$-0.470403\pi$
$29$	1.00000	0.185695	0.0928477	+	0.995680i	$0.470403\pi$
$30$	1.00000	0.182574
$31$	5.00000	0.898027	0.449013	−	0.893525i	$-0.351776\pi$
$31$	5.00000	0.898027	0.449013	+	0.893525i	$0.351776\pi$
$32$	1.00000	0.176777
$33$	6.00000	1.04447
$34$	7.00000	1.20049
$35$	1.00000	0.169031
$36$	−2.00000	−0.333333
$37$	−2.00000	−0.328798	−0.164399	−	0.986394i	$-0.552568\pi$
$37$	−2.00000	−0.328798	−0.164399	+	0.986394i	$0.552568\pi$
$38$	0	0
$39$	4.00000	0.640513
$40$	−1.00000	−0.158114
$41$	1.00000	0.156174
$41$	1.00000	0.156174
$42$	1.00000	0.154303
$43$	−5.00000	−0.762493	−0.381246	−	0.924473i	$-0.624505\pi$
$43$	−5.00000	−0.762493	−0.381246	+	0.924473i	$0.624505\pi$
$44$	−6.00000	−0.904534
$45$	2.00000	0.298142
$46$	−8.00000	−1.17954
$47$	−6.00000	−0.875190	−0.437595	−	0.899172i	$-0.644170\pi$
$47$	−6.00000	−0.875190	−0.437595	+	0.899172i	$0.644170\pi$
$48$	−1.00000	−0.144338
$49$	1.00000	0.142857
$50$	−4.00000	−0.565685
$51$	−7.00000	−0.980196
$52$	−4.00000	−0.554700
$53$	−3.00000	−0.412082	−0.206041	−	0.978543i	$-0.566058\pi$
$53$	−3.00000	−0.412082	−0.206041	+	0.978543i	$0.566058\pi$
$54$	5.00000	0.680414
$55$	6.00000	0.809040
$56$	−1.00000	−0.133631
$57$	0	0
$58$	1.00000	0.131306
$59$	−10.0000	−1.30189	−0.650945	−	0.759125i	$-0.725627\pi$
$59$	−10.0000	−1.30189	−0.650945	+	0.759125i	$0.725627\pi$
$60$	1.00000	0.129099
$61$	−3.00000	−0.384111	−0.192055	−	0.981384i	$-0.561515\pi$
$61$	−3.00000	−0.384111	−0.192055	+	0.981384i	$0.561515\pi$
$62$	5.00000	0.635001
$63$	2.00000	0.251976
$64$	1.00000	0.125000
$65$	4.00000	0.496139
$66$	6.00000	0.738549
$67$	14.0000	1.71037	0.855186	−	0.518321i	$-0.173443\pi$
$67$	14.0000	1.71037	0.855186	+	0.518321i	$0.173443\pi$
$68$	7.00000	0.848875
$69$	8.00000	0.963087
$70$	1.00000	0.119523
$71$	3.00000	0.356034	0.178017	−	0.984027i	$-0.443032\pi$
$71$	3.00000	0.356034	0.178017	+	0.984027i	$0.443032\pi$
$72$	−2.00000	−0.235702
$73$	8.00000	0.936329	0.468165	−	0.883641i	$-0.344915\pi$
$73$	8.00000	0.936329	0.468165	+	0.883641i	$0.344915\pi$
$74$	−2.00000	−0.232495
$75$	4.00000	0.461880
$76$	0	0
$77$	6.00000	0.683763
$78$	4.00000	0.452911
$79$	7.00000	0.787562	0.393781	−	0.919204i	$-0.371167\pi$
$79$	7.00000	0.787562	0.393781	+	0.919204i	$0.371167\pi$
$80$	−1.00000	−0.111803
$81$	1.00000	0.111111
$82$	1.00000	0.110432
$83$	−2.00000	−0.219529	−0.109764	−	0.993958i	$-0.535010\pi$
$83$	−2.00000	−0.219529	−0.109764	+	0.993958i	$0.535010\pi$
$84$	1.00000	0.109109
$85$	−7.00000	−0.759257
$86$	−5.00000	−0.539164
$87$	−1.00000	−0.107211
$88$	−6.00000	−0.639602
$89$	5.00000	0.529999	0.264999	−	0.964249i	$-0.414628\pi$
$89$	5.00000	0.529999	0.264999	+	0.964249i	$0.414628\pi$
$90$	2.00000	0.210819
$91$	4.00000	0.419314
$92$	−8.00000	−0.834058
$93$	−5.00000	−0.518476
$94$	−6.00000	−0.618853
$95$	0	0
$96$	−1.00000	−0.102062
$97$	5.00000	0.507673	0.253837	−	0.967247i	$-0.418307\pi$
$97$	5.00000	0.507673	0.253837	+	0.967247i	$0.418307\pi$
$98$	1.00000	0.101015
$99$	12.0000	1.20605
$100$	−4.00000	−0.400000
$101$	6.00000	0.597022	0.298511	−	0.954406i	$-0.403510\pi$
$101$	6.00000	0.597022	0.298511	+	0.954406i	$0.403510\pi$
$102$	−7.00000	−0.693103
$103$	−11.0000	−1.08386	−0.541931	−	0.840423i	$-0.682307\pi$
$103$	−11.0000	−1.08386	−0.541931	+	0.840423i	$0.682307\pi$
$104$	−4.00000	−0.392232
$105$	−1.00000	−0.0975900
$106$	−3.00000	−0.291386
$107$	−13.0000	−1.25676	−0.628379	−	0.777908i	$-0.716281\pi$
$107$	−13.0000	−1.25676	−0.628379	+	0.777908i	$0.716281\pi$
$108$	5.00000	0.481125
$109$	2.00000	0.191565	0.0957826	−	0.995402i	$-0.469465\pi$
$109$	2.00000	0.191565	0.0957826	+	0.995402i	$0.469465\pi$
$110$	6.00000	0.572078
$111$	2.00000	0.189832
$112$	−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	$0.485022\pi$
$114$	0	0
$115$	8.00000	0.746004
$116$	1.00000	0.0928477
$117$	8.00000	0.739600
$118$	−10.0000	−0.920575
$119$	−7.00000	−0.641689
$120$	1.00000	0.0912871
$121$	25.0000	2.27273
$122$	−3.00000	−0.271607
$123$	−1.00000	−0.0901670
$124$	5.00000	0.449013
$125$	9.00000	0.804984
$126$	2.00000	0.178174
$127$	6.00000	0.532414	0.266207	−	0.963916i	$-0.414230\pi$
$127$	6.00000	0.532414	0.266207	+	0.963916i	$0.414230\pi$
$128$	1.00000	0.0883883
$129$	5.00000	0.440225
$130$	4.00000	0.350823
$131$	−20.0000	−1.74741	−0.873704	−	0.486458i	$-0.838289\pi$
$131$	−20.0000	−1.74741	−0.873704	+	0.486458i	$0.838289\pi$
$132$	6.00000	0.522233
$133$	0	0
$134$	14.0000	1.20942
$135$	−5.00000	−0.430331
$136$	7.00000	0.600245
$137$	−4.00000	−0.341743	−0.170872	−	0.985293i	$-0.554658\pi$
$137$	−4.00000	−0.341743	−0.170872	+	0.985293i	$0.554658\pi$
$138$	8.00000	0.681005
$139$	−18.0000	−1.52674	−0.763370	−	0.645961i	$-0.776457\pi$
$139$	−18.0000	−1.52674	−0.763370	+	0.645961i	$0.776457\pi$
$140$	1.00000	0.0845154
$141$	6.00000	0.505291
$142$	3.00000	0.251754
$143$	24.0000	2.00698
$144$	−2.00000	−0.166667
$145$	−1.00000	−0.0830455
$146$	8.00000	0.662085
$147$	−1.00000	−0.0824786
$148$	−2.00000	−0.164399
$149$	−15.0000	−1.22885	−0.614424	−	0.788976i	$-0.710612\pi$
$149$	−15.0000	−1.22885	−0.614424	+	0.788976i	$0.710612\pi$
$150$	4.00000	0.326599
$151$	−15.0000	−1.22068	−0.610341	−	0.792139i	$-0.708968\pi$
$151$	−15.0000	−1.22068	−0.610341	+	0.792139i	$0.708968\pi$
$152$	0	0
$153$	−14.0000	−1.13183
$154$	6.00000	0.483494
$155$	−5.00000	−0.401610
$156$	4.00000	0.320256
$157$	0	0		−	1.00000i	$-0.5\pi$
$157$	0	0			1.00000i	$0.5\pi$
$158$	7.00000	0.556890
$159$	3.00000	0.237915
$160$	−1.00000	−0.0790569
$161$	8.00000	0.630488
$162$	1.00000	0.0785674
$163$	−4.00000	−0.313304	−0.156652	−	0.987654i	$-0.550070\pi$
$163$	−4.00000	−0.313304	−0.156652	+	0.987654i	$0.550070\pi$
$164$	1.00000	0.0780869
$165$	−6.00000	−0.467099
$166$	−2.00000	−0.155230
$167$	4.00000	0.309529	0.154765	−	0.987951i	$-0.450538\pi$
$167$	4.00000	0.309529	0.154765	+	0.987951i	$0.450538\pi$
$168$	1.00000	0.0771517
$169$	3.00000	0.230769
$170$	−7.00000	−0.536875
$171$	0	0
$172$	−5.00000	−0.381246
$173$	−1.00000	−0.0760286	−0.0380143	−	0.999277i	$-0.512103\pi$
$173$	−1.00000	−0.0760286	−0.0380143	+	0.999277i	$0.512103\pi$
$174$	−1.00000	−0.0758098
$175$	4.00000	0.302372
$176$	−6.00000	−0.452267
$177$	10.0000	0.751646
$178$	5.00000	0.374766
$179$	0	0		−	1.00000i	$-0.5\pi$
$179$	0	0			1.00000i	$0.5\pi$
$180$	2.00000	0.149071
$181$	14.0000	1.04061	0.520306	−	0.853980i	$-0.325818\pi$
$181$	14.0000	1.04061	0.520306	+	0.853980i	$0.325818\pi$
$182$	4.00000	0.296500
$183$	3.00000	0.221766
$184$	−8.00000	−0.589768
$185$	2.00000	0.147043
$186$	−5.00000	−0.366618
$187$	−42.0000	−3.07134
$188$	−6.00000	−0.437595
$189$	−5.00000	−0.363696
$190$	0	0
$191$	−25.0000	−1.80894	−0.904468	−	0.426541i	$-0.859732\pi$
$191$	−25.0000	−1.80894	−0.904468	+	0.426541i	$0.859732\pi$
$192$	−1.00000	−0.0721688
$193$	−4.00000	−0.287926	−0.143963	−	0.989583i	$-0.545985\pi$
$193$	−4.00000	−0.287926	−0.143963	+	0.989583i	$0.545985\pi$
$194$	5.00000	0.358979
$195$	−4.00000	−0.286446
$196$	1.00000	0.0714286
$197$	12.0000	0.854965	0.427482	−	0.904024i	$-0.359401\pi$
$197$	12.0000	0.854965	0.427482	+	0.904024i	$0.359401\pi$
$198$	12.0000	0.852803
$199$	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
$201$	−14.0000	−0.987484
$202$	6.00000	0.422159
$203$	−1.00000	−0.0701862
$204$	−7.00000	−0.490098
$205$	−1.00000	−0.0698430
$206$	−11.0000	−0.766406
$207$	16.0000	1.11208
$208$	−4.00000	−0.277350
$209$	0	0
$210$	−1.00000	−0.0690066
$211$	28.0000	1.92760	0.963800	−	0.266627i	$-0.0859092\pi$
$211$	28.0000	1.92760	0.963800	+	0.266627i	$0.0859092\pi$
$212$	−3.00000	−0.206041
$213$	−3.00000	−0.205557
$214$	−13.0000	−0.888662
$215$	5.00000	0.340997
$216$	5.00000	0.340207
$217$	−5.00000	−0.339422
$218$	2.00000	0.135457
$219$	−8.00000	−0.540590
$220$	6.00000	0.404520
$221$	−28.0000	−1.88348
$222$	2.00000	0.134231
$223$	21.0000	1.40626	0.703132	−	0.711059i	$-0.251784\pi$
$223$	21.0000	1.40626	0.703132	+	0.711059i	$0.251784\pi$
$224$	−1.00000	−0.0668153
$225$	8.00000	0.533333
$226$	1.00000	0.0665190
$227$	3.00000	0.199117	0.0995585	−	0.995032i	$-0.468257\pi$
$227$	3.00000	0.199117	0.0995585	+	0.995032i	$0.468257\pi$
$228$	0	0
$229$	−20.0000	−1.32164	−0.660819	−	0.750546i	$-0.729791\pi$
$229$	−20.0000	−1.32164	−0.660819	+	0.750546i	$0.729791\pi$
$230$	8.00000	0.527504
$231$	−6.00000	−0.394771
$232$	1.00000	0.0656532
$233$	−6.00000	−0.393073	−0.196537	−	0.980497i	$-0.562969\pi$
$233$	−6.00000	−0.393073	−0.196537	+	0.980497i	$0.562969\pi$
$234$	8.00000	0.522976
$235$	6.00000	0.391397
$236$	−10.0000	−0.650945
$237$	−7.00000	−0.454699
$238$	−7.00000	−0.453743
$239$	−28.0000	−1.81117	−0.905585	−	0.424165i	$-0.860568\pi$
$239$	−28.0000	−1.81117	−0.905585	+	0.424165i	$0.860568\pi$
$240$	1.00000	0.0645497
$241$	−18.0000	−1.15948	−0.579741	−	0.814801i	$-0.696846\pi$
$241$	−18.0000	−1.15948	−0.579741	+	0.814801i	$0.696846\pi$
$242$	25.0000	1.60706
$243$	−16.0000	−1.02640
$244$	−3.00000	−0.192055
$245$	−1.00000	−0.0638877
$246$	−1.00000	−0.0637577
$247$	0	0
$248$	5.00000	0.317500
$249$	2.00000	0.126745
$250$	9.00000	0.569210
$251$	−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
$253$	48.0000	3.01773
$254$	6.00000	0.376473
$255$	7.00000	0.438357
$256$	1.00000	0.0625000
$257$	19.0000	1.18519	0.592594	−	0.805502i	$-0.298104\pi$
$257$	19.0000	1.18519	0.592594	+	0.805502i	$0.298104\pi$
$258$	5.00000	0.311286
$259$	2.00000	0.124274
$260$	4.00000	0.248069
$261$	−2.00000	−0.123797
$262$	−20.0000	−1.23560
$263$	−16.0000	−0.986602	−0.493301	−	0.869859i	$-0.664210\pi$
$263$	−16.0000	−0.986602	−0.493301	+	0.869859i	$0.664210\pi$
$264$	6.00000	0.369274
$265$	3.00000	0.184289
$266$	0	0
$267$	−5.00000	−0.305995
$268$	14.0000	0.855186
$269$	6.00000	0.365826	0.182913	−	0.983129i	$-0.441447\pi$
$269$	6.00000	0.365826	0.182913	+	0.983129i	$0.441447\pi$
$270$	−5.00000	−0.304290
$271$	−12.0000	−0.728948	−0.364474	−	0.931214i	$-0.618751\pi$
$271$	−12.0000	−0.728948	−0.364474	+	0.931214i	$0.618751\pi$
$272$	7.00000	0.424437
$273$	−4.00000	−0.242091
$274$	−4.00000	−0.241649
$275$	24.0000	1.44725
$276$	8.00000	0.481543
$277$	−26.0000	−1.56219	−0.781094	−	0.624413i	$-0.785338\pi$
$277$	−26.0000	−1.56219	−0.781094	+	0.624413i	$0.785338\pi$
$278$	−18.0000	−1.07957
$279$	−10.0000	−0.598684
$280$	1.00000	0.0597614
$281$	−10.0000	−0.596550	−0.298275	−	0.954480i	$-0.596411\pi$
$281$	−10.0000	−0.596550	−0.298275	+	0.954480i	$0.596411\pi$
$282$	6.00000	0.357295
$283$	6.00000	0.356663	0.178331	−	0.983970i	$-0.442930\pi$
$283$	6.00000	0.356663	0.178331	+	0.983970i	$0.442930\pi$
$284$	3.00000	0.178017
$285$	0	0
$286$	24.0000	1.41915
$287$	−1.00000	−0.0590281
$288$	−2.00000	−0.117851
$289$	32.0000	1.88235
$290$	−1.00000	−0.0587220
$291$	−5.00000	−0.293105
$292$	8.00000	0.468165
$293$	−14.0000	−0.817889	−0.408944	−	0.912559i	$-0.634103\pi$
$293$	−14.0000	−0.817889	−0.408944	+	0.912559i	$0.634103\pi$
$294$	−1.00000	−0.0583212
$295$	10.0000	0.582223
$296$	−2.00000	−0.116248
$297$	−30.0000	−1.74078
$298$	−15.0000	−0.868927
$299$	32.0000	1.85061
$300$	4.00000	0.230940
$301$	5.00000	0.288195
$302$	−15.0000	−0.863153
$303$	−6.00000	−0.344691
$304$	0	0
$305$	3.00000	0.171780
$306$	−14.0000	−0.800327
$307$	−4.00000	−0.228292	−0.114146	−	0.993464i	$-0.536413\pi$
$307$	−4.00000	−0.228292	−0.114146	+	0.993464i	$0.536413\pi$
$308$	6.00000	0.341882
$309$	11.0000	0.625768
$310$	−5.00000	−0.283981
$311$	−34.0000	−1.92796	−0.963982	−	0.265969i	$-0.914308\pi$
$311$	−34.0000	−1.92796	−0.963982	+	0.265969i	$0.914308\pi$
$312$	4.00000	0.226455
$313$	22.0000	1.24351	0.621757	−	0.783210i	$-0.286419\pi$
$313$	22.0000	1.24351	0.621757	+	0.783210i	$0.286419\pi$
$314$	0	0
$315$	−2.00000	−0.112687
$316$	7.00000	0.393781
$317$	2.00000	0.112331	0.0561656	−	0.998421i	$-0.482113\pi$
$317$	2.00000	0.112331	0.0561656	+	0.998421i	$0.482113\pi$
$318$	3.00000	0.168232
$319$	−6.00000	−0.335936
$320$	−1.00000	−0.0559017
$321$	13.0000	0.725589
$322$	8.00000	0.445823
$323$	0	0
$324$	1.00000	0.0555556
$325$	16.0000	0.887520
$326$	−4.00000	−0.221540
$327$	−2.00000	−0.110600
$328$	1.00000	0.0552158
$329$	6.00000	0.330791
$330$	−6.00000	−0.330289
$331$	−12.0000	−0.659580	−0.329790	−	0.944054i	$-0.606978\pi$
$331$	−12.0000	−0.659580	−0.329790	+	0.944054i	$0.606978\pi$
$332$	−2.00000	−0.109764
$333$	4.00000	0.219199
$334$	4.00000	0.218870
$335$	−14.0000	−0.764902
$336$	1.00000	0.0545545
$337$	−27.0000	−1.47078	−0.735392	−	0.677642i	$-0.763002\pi$
$337$	−27.0000	−1.47078	−0.735392	+	0.677642i	$0.763002\pi$
$338$	3.00000	0.163178
$339$	−1.00000	−0.0543125
$340$	−7.00000	−0.379628
$341$	−30.0000	−1.62459
$342$	0	0
$343$	−1.00000	−0.0539949
$344$	−5.00000	−0.269582
$345$	−8.00000	−0.430706
$346$	−1.00000	−0.0537603
$347$	28.0000	1.50312	0.751559	−	0.659665i	$-0.229302\pi$
$347$	28.0000	1.50312	0.751559	+	0.659665i	$0.229302\pi$
$348$	−1.00000	−0.0536056
$349$	6.00000	0.321173	0.160586	−	0.987022i	$-0.448662\pi$
$349$	6.00000	0.321173	0.160586	+	0.987022i	$0.448662\pi$
$350$	4.00000	0.213809
$351$	−20.0000	−1.06752
$352$	−6.00000	−0.319801
$353$	32.0000	1.70319	0.851594	−	0.524202i	$-0.175636\pi$
$353$	32.0000	1.70319	0.851594	+	0.524202i	$0.175636\pi$
$354$	10.0000	0.531494
$355$	−3.00000	−0.159223
$356$	5.00000	0.264999
$357$	7.00000	0.370479
$358$	0	0
$359$	20.0000	1.05556	0.527780	−	0.849381i	$-0.323025\pi$
$359$	20.0000	1.05556	0.527780	+	0.849381i	$0.323025\pi$
$360$	2.00000	0.105409
$361$	−19.0000	−1.00000
$362$	14.0000	0.735824
$363$	−25.0000	−1.31216
$364$	4.00000	0.209657
$365$	−8.00000	−0.418739
$366$	3.00000	0.156813
$367$	15.0000	0.782994	0.391497	−	0.920179i	$-0.371957\pi$
$367$	15.0000	0.782994	0.391497	+	0.920179i	$0.371957\pi$
$368$	−8.00000	−0.417029
$369$	−2.00000	−0.104116
$370$	2.00000	0.103975
$371$	3.00000	0.155752
$372$	−5.00000	−0.259238
$373$	−2.00000	−0.103556	−0.0517780	−	0.998659i	$-0.516489\pi$
$373$	−2.00000	−0.103556	−0.0517780	+	0.998659i	$0.516489\pi$
$374$	−42.0000	−2.17177
$375$	−9.00000	−0.464758
$376$	−6.00000	−0.309426
$377$	−4.00000	−0.206010
$378$	−5.00000	−0.257172
$379$	5.00000	0.256833	0.128416	−	0.991720i	$-0.459011\pi$
$379$	5.00000	0.256833	0.128416	+	0.991720i	$0.459011\pi$
$380$	0	0
$381$	−6.00000	−0.307389
$382$	−25.0000	−1.27911
$383$	30.0000	1.53293	0.766464	−	0.642287i	$-0.222014\pi$
$383$	30.0000	1.53293	0.766464	+	0.642287i	$0.222014\pi$
$384$	−1.00000	−0.0510310
$385$	−6.00000	−0.305788
$386$	−4.00000	−0.203595
$387$	10.0000	0.508329
$388$	5.00000	0.253837
$389$	−34.0000	−1.72387	−0.861934	−	0.507020i	$-0.830747\pi$
$389$	−34.0000	−1.72387	−0.861934	+	0.507020i	$0.830747\pi$
$390$	−4.00000	−0.202548
$391$	−56.0000	−2.83204
$392$	1.00000	0.0505076
$393$	20.0000	1.00887
$394$	12.0000	0.604551
$395$	−7.00000	−0.352208
$396$	12.0000	0.603023
$397$	−12.0000	−0.602263	−0.301131	−	0.953583i	$-0.597364\pi$
$397$	−12.0000	−0.602263	−0.301131	+	0.953583i	$0.597364\pi$
$398$	4.00000	0.200502
$399$	0	0
$400$	−4.00000	−0.200000
$401$	−25.0000	−1.24844	−0.624220	−	0.781248i	$-0.714583\pi$
$401$	−25.0000	−1.24844	−0.624220	+	0.781248i	$0.714583\pi$
$402$	−14.0000	−0.698257
$403$	−20.0000	−0.996271
$404$	6.00000	0.298511
$405$	−1.00000	−0.0496904
$406$	−1.00000	−0.0496292
$407$	12.0000	0.594818
$408$	−7.00000	−0.346552
$409$	18.0000	0.890043	0.445021	−	0.895520i	$-0.353196\pi$
$409$	18.0000	0.890043	0.445021	+	0.895520i	$0.353196\pi$
$410$	−1.00000	−0.0493865
$411$	4.00000	0.197305
$412$	−11.0000	−0.541931
$413$	10.0000	0.492068
$414$	16.0000	0.786357
$415$	2.00000	0.0981761
$416$	−4.00000	−0.196116
$417$	18.0000	0.881464
$418$	0	0
$419$	36.0000	1.75872	0.879358	−	0.476162i	$-0.157972\pi$
$419$	36.0000	1.75872	0.879358	+	0.476162i	$0.157972\pi$
$420$	−1.00000	−0.0487950
$421$	39.0000	1.90074	0.950372	−	0.311116i	$-0.100703\pi$
$421$	39.0000	1.90074	0.950372	+	0.311116i	$0.100703\pi$
$422$	28.0000	1.36302
$423$	12.0000	0.583460
$424$	−3.00000	−0.145693
$425$	−28.0000	−1.35820
$426$	−3.00000	−0.145350
$427$	3.00000	0.145180
$428$	−13.0000	−0.628379
$429$	−24.0000	−1.15873
$430$	5.00000	0.241121
$431$	−28.0000	−1.34871	−0.674356	−	0.738406i	$-0.735579\pi$
$431$	−28.0000	−1.34871	−0.674356	+	0.738406i	$0.735579\pi$
$432$	5.00000	0.240563
$433$	24.0000	1.15337	0.576683	−	0.816968i	$-0.304347\pi$
$433$	24.0000	1.15337	0.576683	+	0.816968i	$0.304347\pi$
$434$	−5.00000	−0.240008
$435$	1.00000	0.0479463
$436$	2.00000	0.0957826
$437$	0	0
$438$	−8.00000	−0.382255
$439$	22.0000	1.05000	0.525001	−	0.851101i	$-0.324065\pi$
$439$	22.0000	1.05000	0.525001	+	0.851101i	$0.324065\pi$
$440$	6.00000	0.286039
$441$	−2.00000	−0.0952381
$442$	−28.0000	−1.33182
$443$	−9.00000	−0.427603	−0.213801	−	0.976877i	$-0.568585\pi$
$443$	−9.00000	−0.427603	−0.213801	+	0.976877i	$0.568585\pi$
$444$	2.00000	0.0949158
$445$	−5.00000	−0.237023
$446$	21.0000	0.994379
$447$	15.0000	0.709476
$448$	−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
$451$	−6.00000	−0.282529
$452$	1.00000	0.0470360
$453$	15.0000	0.704761
$454$	3.00000	0.140797
$455$	−4.00000	−0.187523
$456$	0	0
$457$	6.00000	0.280668	0.140334	−	0.990104i	$-0.455182\pi$
$457$	6.00000	0.280668	0.140334	+	0.990104i	$0.455182\pi$
$458$	−20.0000	−0.934539
$459$	35.0000	1.63366
$460$	8.00000	0.373002
$461$	−37.0000	−1.72326	−0.861631	−	0.507535i	$-0.830557\pi$
$461$	−37.0000	−1.72326	−0.861631	+	0.507535i	$0.830557\pi$
$462$	−6.00000	−0.279145
$463$	−16.0000	−0.743583	−0.371792	−	0.928316i	$-0.621256\pi$
$463$	−16.0000	−0.743583	−0.371792	+	0.928316i	$0.621256\pi$
$464$	1.00000	0.0464238
$465$	5.00000	0.231869
$466$	−6.00000	−0.277945
$467$	6.00000	0.277647	0.138823	−	0.990317i	$-0.455668\pi$
$467$	6.00000	0.277647	0.138823	+	0.990317i	$0.455668\pi$
$468$	8.00000	0.369800
$469$	−14.0000	−0.646460
$470$	6.00000	0.276759
$471$	0	0
$472$	−10.0000	−0.460287
$473$	30.0000	1.37940
$474$	−7.00000	−0.321521
$475$	0	0
$476$	−7.00000	−0.320844
$477$	6.00000	0.274721
$478$	−28.0000	−1.28069
$479$	−2.00000	−0.0913823	−0.0456912	−	0.998956i	$-0.514549\pi$
$479$	−2.00000	−0.0913823	−0.0456912	+	0.998956i	$0.514549\pi$
$480$	1.00000	0.0456435
$481$	8.00000	0.364769
$482$	−18.0000	−0.819878
$483$	−8.00000	−0.364013
$484$	25.0000	1.13636
$485$	−5.00000	−0.227038
$486$	−16.0000	−0.725775
$487$	4.00000	0.181257	0.0906287	−	0.995885i	$-0.471112\pi$
$487$	4.00000	0.181257	0.0906287	+	0.995885i	$0.471112\pi$
$488$	−3.00000	−0.135804
$489$	4.00000	0.180886
$490$	−1.00000	−0.0451754
$491$	−3.00000	−0.135388	−0.0676941	−	0.997706i	$-0.521564\pi$
$491$	−3.00000	−0.135388	−0.0676941	+	0.997706i	$0.521564\pi$
$492$	−1.00000	−0.0450835
$493$	7.00000	0.315264
$494$	0	0
$495$	−12.0000	−0.539360
$496$	5.00000	0.224507
$497$	−3.00000	−0.134568
$498$	2.00000	0.0896221
$499$	2.00000	0.0895323	0.0447661	−	0.998997i	$-0.485746\pi$
$499$	2.00000	0.0895323	0.0447661	+	0.998997i	$0.485746\pi$
$500$	9.00000	0.402492
$501$	−4.00000	−0.178707
$502$	−20.0000	−0.892644
$503$	36.0000	1.60516	0.802580	−	0.596544i	$-0.203460\pi$
$503$	36.0000	1.60516	0.802580	+	0.596544i	$0.203460\pi$
$504$	2.00000	0.0890871
$505$	−6.00000	−0.266996
$506$	48.0000	2.13386
$507$	−3.00000	−0.133235
$508$	6.00000	0.266207
$509$	−20.0000	−0.886484	−0.443242	−	0.896402i	$-0.646172\pi$
$509$	−20.0000	−0.886484	−0.443242	+	0.896402i	$0.646172\pi$
$510$	7.00000	0.309965
$511$	−8.00000	−0.353899
$512$	1.00000	0.0441942
$513$	0	0
$514$	19.0000	0.838054
$515$	11.0000	0.484718
$516$	5.00000	0.220113
$517$	36.0000	1.58328
$518$	2.00000	0.0878750
$519$	1.00000	0.0438951
$520$	4.00000	0.175412
$521$	−2.00000	−0.0876216	−0.0438108	−	0.999040i	$-0.513950\pi$
$521$	−2.00000	−0.0876216	−0.0438108	+	0.999040i	$0.513950\pi$
$522$	−2.00000	−0.0875376
$523$	20.0000	0.874539	0.437269	−	0.899331i	$-0.355946\pi$
$523$	20.0000	0.874539	0.437269	+	0.899331i	$0.355946\pi$
$524$	−20.0000	−0.873704
$525$	−4.00000	−0.174574
$526$	−16.0000	−0.697633
$527$	35.0000	1.52462
$528$	6.00000	0.261116
$529$	41.0000	1.78261
$530$	3.00000	0.130312
$531$	20.0000	0.867926
$532$	0	0
$533$	−4.00000	−0.173259
$534$	−5.00000	−0.216371
$535$	13.0000	0.562039
$536$	14.0000	0.604708
$537$	0	0
$538$	6.00000	0.258678
$539$	−6.00000	−0.258438
$540$	−5.00000	−0.215166
$541$	−22.0000	−0.945854	−0.472927	−	0.881102i	$-0.656803\pi$
$541$	−22.0000	−0.945854	−0.472927	+	0.881102i	$0.656803\pi$
$542$	−12.0000	−0.515444
$543$	−14.0000	−0.600798
$544$	7.00000	0.300123
$545$	−2.00000	−0.0856706
$546$	−4.00000	−0.171184
$547$	22.0000	0.940652	0.470326	−	0.882493i	$-0.344136\pi$
$547$	22.0000	0.940652	0.470326	+	0.882493i	$0.344136\pi$
$548$	−4.00000	−0.170872
$549$	6.00000	0.256074
$550$	24.0000	1.02336
$551$	0	0
$552$	8.00000	0.340503
$553$	−7.00000	−0.297670
$554$	−26.0000	−1.10463
$555$	−2.00000	−0.0848953
$556$	−18.0000	−0.763370
$557$	−21.0000	−0.889799	−0.444899	−	0.895581i	$-0.646761\pi$
$557$	−21.0000	−0.889799	−0.444899	+	0.895581i	$0.646761\pi$
$558$	−10.0000	−0.423334
$559$	20.0000	0.845910
$560$	1.00000	0.0422577
$561$	42.0000	1.77324
$562$	−10.0000	−0.421825
$563$	−12.0000	−0.505740	−0.252870	−	0.967500i	$-0.581374\pi$
$563$	−12.0000	−0.505740	−0.252870	+	0.967500i	$0.581374\pi$
$564$	6.00000	0.252646
$565$	−1.00000	−0.0420703
$566$	6.00000	0.252199
$567$	−1.00000	−0.0419961
$568$	3.00000	0.125877
$569$	39.0000	1.63497	0.817483	−	0.575953i	$-0.195369\pi$
$569$	39.0000	1.63497	0.817483	+	0.575953i	$0.195369\pi$
$570$	0	0
$571$	40.0000	1.67395	0.836974	−	0.547243i	$-0.184323\pi$
$571$	40.0000	1.67395	0.836974	+	0.547243i	$0.184323\pi$
$572$	24.0000	1.00349
$573$	25.0000	1.04439
$574$	−1.00000	−0.0417392
$575$	32.0000	1.33449
$576$	−2.00000	−0.0833333
$577$	2.00000	0.0832611	0.0416305	−	0.999133i	$-0.486745\pi$
$577$	2.00000	0.0832611	0.0416305	+	0.999133i	$0.486745\pi$
$578$	32.0000	1.33102
$579$	4.00000	0.166234
$580$	−1.00000	−0.0415227
$581$	2.00000	0.0829740
$582$	−5.00000	−0.207257
$583$	18.0000	0.745484
$584$	8.00000	0.331042
$585$	−8.00000	−0.330759
$586$	−14.0000	−0.578335
$587$	−39.0000	−1.60970	−0.804851	−	0.593477i	$-0.797755\pi$
$587$	−39.0000	−1.60970	−0.804851	+	0.593477i	$0.797755\pi$
$588$	−1.00000	−0.0412393
$589$	0	0
$590$	10.0000	0.411693
$591$	−12.0000	−0.493614
$592$	−2.00000	−0.0821995
$593$	−33.0000	−1.35515	−0.677574	−	0.735455i	$-0.736969\pi$
$593$	−33.0000	−1.35515	−0.677574	+	0.735455i	$0.736969\pi$
$594$	−30.0000	−1.23091
$595$	7.00000	0.286972
$596$	−15.0000	−0.614424
$597$	−4.00000	−0.163709
$598$	32.0000	1.30858
$599$	44.0000	1.79779	0.898896	−	0.438163i	$-0.144371\pi$
$599$	44.0000	1.79779	0.898896	+	0.438163i	$0.144371\pi$
$600$	4.00000	0.163299
$601$	39.0000	1.59084	0.795422	−	0.606057i	$-0.207249\pi$
$601$	39.0000	1.59084	0.795422	+	0.606057i	$0.207249\pi$
$602$	5.00000	0.203785
$603$	−28.0000	−1.14025
$604$	−15.0000	−0.610341
$605$	−25.0000	−1.01639
$606$	−6.00000	−0.243733
$607$	5.00000	0.202944	0.101472	−	0.994838i	$-0.467645\pi$
$607$	5.00000	0.202944	0.101472	+	0.994838i	$0.467645\pi$
$608$	0	0
$609$	1.00000	0.0405220
$610$	3.00000	0.121466
$611$	24.0000	0.970936
$612$	−14.0000	−0.565916
$613$	28.0000	1.13091	0.565455	−	0.824779i	$-0.308701\pi$
$613$	28.0000	1.13091	0.565455	+	0.824779i	$0.308701\pi$
$614$	−4.00000	−0.161427
$615$	1.00000	0.0403239
$616$	6.00000	0.241747
$617$	46.0000	1.85189	0.925945	−	0.377658i	$-0.123271\pi$
$617$	46.0000	1.85189	0.925945	+	0.377658i	$0.123271\pi$
$618$	11.0000	0.442485
$619$	16.0000	0.643094	0.321547	−	0.946894i	$-0.395797\pi$
$619$	16.0000	0.643094	0.321547	+	0.946894i	$0.395797\pi$
$620$	−5.00000	−0.200805
$621$	−40.0000	−1.60514
$622$	−34.0000	−1.36328
$623$	−5.00000	−0.200321
$624$	4.00000	0.160128
$625$	11.0000	0.440000
$626$	22.0000	0.879297
$627$	0	0
$628$	0	0
$629$	−14.0000	−0.558217
$630$	−2.00000	−0.0796819
$631$	−26.0000	−1.03504	−0.517522	−	0.855670i	$-0.673145\pi$
$631$	−26.0000	−1.03504	−0.517522	+	0.855670i	$0.673145\pi$
$632$	7.00000	0.278445
$633$	−28.0000	−1.11290
$634$	2.00000	0.0794301
$635$	−6.00000	−0.238103
$636$	3.00000	0.118958
$637$	−4.00000	−0.158486
$638$	−6.00000	−0.237542
$639$	−6.00000	−0.237356
$640$	−1.00000	−0.0395285
$641$	−2.00000	−0.0789953	−0.0394976	−	0.999220i	$-0.512576\pi$
$641$	−2.00000	−0.0789953	−0.0394976	+	0.999220i	$0.512576\pi$
$642$	13.0000	0.513069
$643$	−29.0000	−1.14365	−0.571824	−	0.820376i	$-0.693764\pi$
$643$	−29.0000	−1.14365	−0.571824	+	0.820376i	$0.693764\pi$
$644$	8.00000	0.315244
$645$	−5.00000	−0.196875
$646$	0	0
$647$	−27.0000	−1.06148	−0.530740	−	0.847535i	$-0.678086\pi$
$647$	−27.0000	−1.06148	−0.530740	+	0.847535i	$0.678086\pi$
$648$	1.00000	0.0392837
$649$	60.0000	2.35521
$650$	16.0000	0.627572
$651$	5.00000	0.195965
$652$	−4.00000	−0.156652
$653$	17.0000	0.665261	0.332631	−	0.943057i	$-0.392064\pi$
$653$	17.0000	0.665261	0.332631	+	0.943057i	$0.392064\pi$
$654$	−2.00000	−0.0782062
$655$	20.0000	0.781465
$656$	1.00000	0.0390434
$657$	−16.0000	−0.624219
$658$	6.00000	0.233904
$659$	−36.0000	−1.40236	−0.701180	−	0.712984i	$-0.747343\pi$
$659$	−36.0000	−1.40236	−0.701180	+	0.712984i	$0.747343\pi$
$660$	−6.00000	−0.233550
$661$	18.0000	0.700119	0.350059	−	0.936727i	$-0.386161\pi$
$661$	18.0000	0.700119	0.350059	+	0.936727i	$0.386161\pi$
$662$	−12.0000	−0.466393
$663$	28.0000	1.08743
$664$	−2.00000	−0.0776151
$665$	0	0
$666$	4.00000	0.154997
$667$	−8.00000	−0.309761
$668$	4.00000	0.154765
$669$	−21.0000	−0.811907
$670$	−14.0000	−0.540867
$671$	18.0000	0.694882
$672$	1.00000	0.0385758
$673$	50.0000	1.92736	0.963679	−	0.267063i	$-0.0860531\pi$
$673$	50.0000	1.92736	0.963679	+	0.267063i	$0.0860531\pi$
$674$	−27.0000	−1.04000
$675$	−20.0000	−0.769800
$676$	3.00000	0.115385
$677$	6.00000	0.230599	0.115299	−	0.993331i	$-0.463217\pi$
$677$	6.00000	0.230599	0.115299	+	0.993331i	$0.463217\pi$
$678$	−1.00000	−0.0384048
$679$	−5.00000	−0.191882
$680$	−7.00000	−0.268438
$681$	−3.00000	−0.114960
$682$	−30.0000	−1.14876
$683$	4.00000	0.153056	0.0765279	−	0.997067i	$-0.475617\pi$
$683$	4.00000	0.153056	0.0765279	+	0.997067i	$0.475617\pi$
$684$	0	0
$685$	4.00000	0.152832
$686$	−1.00000	−0.0381802
$687$	20.0000	0.763048
$688$	−5.00000	−0.190623
$689$	12.0000	0.457164
$690$	−8.00000	−0.304555
$691$	−17.0000	−0.646710	−0.323355	−	0.946278i	$-0.604811\pi$
$691$	−17.0000	−0.646710	−0.323355	+	0.946278i	$0.604811\pi$
$692$	−1.00000	−0.0380143
$693$	−12.0000	−0.455842
$694$	28.0000	1.06287
$695$	18.0000	0.682779
$696$	−1.00000	−0.0379049
$697$	7.00000	0.265144
$698$	6.00000	0.227103
$699$	6.00000	0.226941
$700$	4.00000	0.151186
$701$	−20.0000	−0.755390	−0.377695	−	0.925930i	$-0.623283\pi$
$701$	−20.0000	−0.755390	−0.377695	+	0.925930i	$0.623283\pi$
$702$	−20.0000	−0.754851
$703$	0	0
$704$	−6.00000	−0.226134
$705$	−6.00000	−0.225973
$706$	32.0000	1.20434
$707$	−6.00000	−0.225653
$708$	10.0000	0.375823
$709$	−31.0000	−1.16423	−0.582115	−	0.813107i	$-0.697775\pi$
$709$	−31.0000	−1.16423	−0.582115	+	0.813107i	$0.697775\pi$
$710$	−3.00000	−0.112588
$711$	−14.0000	−0.525041
$712$	5.00000	0.187383
$713$	−40.0000	−1.49801
$714$	7.00000	0.261968
$715$	−24.0000	−0.897549
$716$	0	0
$717$	28.0000	1.04568
$718$	20.0000	0.746393
$719$	12.0000	0.447524	0.223762	−	0.974644i	$-0.428166\pi$
$719$	12.0000	0.447524	0.223762	+	0.974644i	$0.428166\pi$
$720$	2.00000	0.0745356
$721$	11.0000	0.409661
$722$	−19.0000	−0.707107
$723$	18.0000	0.669427
$724$	14.0000	0.520306
$725$	−4.00000	−0.148556
$726$	−25.0000	−0.927837
$727$	8.00000	0.296704	0.148352	−	0.988935i	$-0.452603\pi$
$727$	8.00000	0.296704	0.148352	+	0.988935i	$0.452603\pi$
$728$	4.00000	0.148250
$729$	13.0000	0.481481
$730$	−8.00000	−0.296093
$731$	−35.0000	−1.29452
$732$	3.00000	0.110883
$733$	−11.0000	−0.406294	−0.203147	−	0.979148i	$-0.565117\pi$
$733$	−11.0000	−0.406294	−0.203147	+	0.979148i	$0.565117\pi$
$734$	15.0000	0.553660
$735$	1.00000	0.0368856
$736$	−8.00000	−0.294884
$737$	−84.0000	−3.09418
$738$	−2.00000	−0.0736210
$739$	−29.0000	−1.06678	−0.533391	−	0.845869i	$-0.679083\pi$
$739$	−29.0000	−1.06678	−0.533391	+	0.845869i	$0.679083\pi$
$740$	2.00000	0.0735215
$741$	0	0
$742$	3.00000	0.110133
$743$	−12.0000	−0.440237	−0.220119	−	0.975473i	$-0.570644\pi$
$743$	−12.0000	−0.440237	−0.220119	+	0.975473i	$0.570644\pi$
$744$	−5.00000	−0.183309
$745$	15.0000	0.549557
$746$	−2.00000	−0.0732252
$747$	4.00000	0.146352
$748$	−42.0000	−1.53567
$749$	13.0000	0.475010
$750$	−9.00000	−0.328634
$751$	16.0000	0.583848	0.291924	−	0.956441i	$-0.405705\pi$
$751$	16.0000	0.583848	0.291924	+	0.956441i	$0.405705\pi$
$752$	−6.00000	−0.218797
$753$	20.0000	0.728841
$754$	−4.00000	−0.145671
$755$	15.0000	0.545906
$756$	−5.00000	−0.181848
$757$	−7.00000	−0.254419	−0.127210	−	0.991876i	$-0.540602\pi$
$757$	−7.00000	−0.254419	−0.127210	+	0.991876i	$0.540602\pi$
$758$	5.00000	0.181608
$759$	−48.0000	−1.74229
$760$	0	0
$761$	50.0000	1.81250	0.906249	−	0.422744i	$-0.138933\pi$
$761$	50.0000	1.81250	0.906249	+	0.422744i	$0.138933\pi$
$762$	−6.00000	−0.217357
$763$	−2.00000	−0.0724049
$764$	−25.0000	−0.904468
$765$	14.0000	0.506171
$766$	30.0000	1.08394
$767$	40.0000	1.44432
$768$	−1.00000	−0.0360844
$769$	−34.0000	−1.22607	−0.613036	−	0.790055i	$-0.710052\pi$
$769$	−34.0000	−1.22607	−0.613036	+	0.790055i	$0.710052\pi$
$770$	−6.00000	−0.216225
$771$	−19.0000	−0.684268
$772$	−4.00000	−0.143963
$773$	−42.0000	−1.51064	−0.755318	−	0.655359i	$-0.772517\pi$
$773$	−42.0000	−1.51064	−0.755318	+	0.655359i	$0.772517\pi$
$774$	10.0000	0.359443
$775$	−20.0000	−0.718421
$776$	5.00000	0.179490
$777$	−2.00000	−0.0717496
$778$	−34.0000	−1.21896
$779$	0	0
$780$	−4.00000	−0.143223
$781$	−18.0000	−0.644091
$782$	−56.0000	−2.00256
$783$	5.00000	0.178685
$784$	1.00000	0.0357143
$785$	0	0
$786$	20.0000	0.713376
$787$	−8.00000	−0.285169	−0.142585	−	0.989783i	$-0.545541\pi$
$787$	−8.00000	−0.285169	−0.142585	+	0.989783i	$0.545541\pi$
$788$	12.0000	0.427482
$789$	16.0000	0.569615
$790$	−7.00000	−0.249049
$791$	−1.00000	−0.0355559
$792$	12.0000	0.426401
$793$	12.0000	0.426132
$794$	−12.0000	−0.425864
$795$	−3.00000	−0.106399
$796$	4.00000	0.141776
$797$	−19.0000	−0.673015	−0.336507	−	0.941681i	$-0.609246\pi$
$797$	−19.0000	−0.673015	−0.336507	+	0.941681i	$0.609246\pi$
$798$	0	0
$799$	−42.0000	−1.48585
$800$	−4.00000	−0.141421
$801$	−10.0000	−0.353333
$802$	−25.0000	−0.882781
$803$	−48.0000	−1.69388
$804$	−14.0000	−0.493742
$805$	−8.00000	−0.281963
$806$	−20.0000	−0.704470
$807$	−6.00000	−0.211210
$808$	6.00000	0.211079
$809$	2.00000	0.0703163	0.0351581	−	0.999382i	$-0.488807\pi$
$809$	2.00000	0.0703163	0.0351581	+	0.999382i	$0.488807\pi$
$810$	−1.00000	−0.0351364
$811$	48.0000	1.68551	0.842754	−	0.538299i	$-0.180933\pi$
$811$	48.0000	1.68551	0.842754	+	0.538299i	$0.180933\pi$
$812$	−1.00000	−0.0350931
$813$	12.0000	0.420858
$814$	12.0000	0.420600
$815$	4.00000	0.140114
$816$	−7.00000	−0.245049
$817$	0	0
$818$	18.0000	0.629355
$819$	−8.00000	−0.279543
$820$	−1.00000	−0.0349215
$821$	−8.00000	−0.279202	−0.139601	−	0.990208i	$-0.544582\pi$
$821$	−8.00000	−0.279202	−0.139601	+	0.990208i	$0.544582\pi$
$822$	4.00000	0.139516
$823$	−1.00000	−0.0348578	−0.0174289	−	0.999848i	$-0.505548\pi$
$823$	−1.00000	−0.0348578	−0.0174289	+	0.999848i	$0.505548\pi$
$824$	−11.0000	−0.383203
$825$	−24.0000	−0.835573
$826$	10.0000	0.347945
$827$	22.0000	0.765015	0.382507	−	0.923952i	$-0.375061\pi$
$827$	22.0000	0.765015	0.382507	+	0.923952i	$0.375061\pi$
$828$	16.0000	0.556038
$829$	−29.0000	−1.00721	−0.503606	−	0.863934i	$-0.667994\pi$
$829$	−29.0000	−1.00721	−0.503606	+	0.863934i	$0.667994\pi$
$830$	2.00000	0.0694210
$831$	26.0000	0.901930
$832$	−4.00000	−0.138675
$833$	7.00000	0.242536
$834$	18.0000	0.623289
$835$	−4.00000	−0.138426
$836$	0	0
$837$	25.0000	0.864126
$838$	36.0000	1.24360
$839$	26.0000	0.897620	0.448810	−	0.893627i	$-0.351848\pi$
$839$	26.0000	0.897620	0.448810	+	0.893627i	$0.351848\pi$
$840$	−1.00000	−0.0345033
$841$	−28.0000	−0.965517
$842$	39.0000	1.34403
$843$	10.0000	0.344418
$844$	28.0000	0.963800
$845$	−3.00000	−0.103203
$846$	12.0000	0.412568
$847$	−25.0000	−0.859010
$848$	−3.00000	−0.103020
$849$	−6.00000	−0.205919
$850$	−28.0000	−0.960392
$851$	16.0000	0.548473
$852$	−3.00000	−0.102778
$853$	−37.0000	−1.26686	−0.633428	−	0.773802i	$-0.718353\pi$
$853$	−37.0000	−1.26686	−0.633428	+	0.773802i	$0.718353\pi$
$854$	3.00000	0.102658
$855$	0	0
$856$	−13.0000	−0.444331
$857$	42.0000	1.43469	0.717346	−	0.696717i	$-0.245357\pi$
$857$	42.0000	1.43469	0.717346	+	0.696717i	$0.245357\pi$
$858$	−24.0000	−0.819346
$859$	8.00000	0.272956	0.136478	−	0.990643i	$-0.456422\pi$
$859$	8.00000	0.272956	0.136478	+	0.990643i	$0.456422\pi$
$860$	5.00000	0.170499
$861$	1.00000	0.0340799
$862$	−28.0000	−0.953684
$863$	36.0000	1.22545	0.612727	−	0.790295i	$-0.290072\pi$
$863$	36.0000	1.22545	0.612727	+	0.790295i	$0.290072\pi$
$864$	5.00000	0.170103
$865$	1.00000	0.0340010
$866$	24.0000	0.815553
$867$	−32.0000	−1.08678
$868$	−5.00000	−0.169711
$869$	−42.0000	−1.42475
$870$	1.00000	0.0339032
$871$	−56.0000	−1.89749
$872$	2.00000	0.0677285
$873$	−10.0000	−0.338449
$874$	0	0
$875$	−9.00000	−0.304256
$876$	−8.00000	−0.270295
$877$	−44.0000	−1.48577	−0.742887	−	0.669417i	$-0.766544\pi$
$877$	−44.0000	−1.48577	−0.742887	+	0.669417i	$0.766544\pi$
$878$	22.0000	0.742464
$879$	14.0000	0.472208
$880$	6.00000	0.202260
$881$	−4.00000	−0.134763	−0.0673817	−	0.997727i	$-0.521465\pi$
$881$	−4.00000	−0.134763	−0.0673817	+	0.997727i	$0.521465\pi$
$882$	−2.00000	−0.0673435
$883$	34.0000	1.14419	0.572096	−	0.820187i	$-0.306131\pi$
$883$	34.0000	1.14419	0.572096	+	0.820187i	$0.306131\pi$
$884$	−28.0000	−0.941742
$885$	−10.0000	−0.336146
$886$	−9.00000	−0.302361
$887$	48.0000	1.61168	0.805841	−	0.592132i	$-0.201714\pi$
$887$	48.0000	1.61168	0.805841	+	0.592132i	$0.201714\pi$
$888$	2.00000	0.0671156
$889$	−6.00000	−0.201234
$890$	−5.00000	−0.167600
$891$	−6.00000	−0.201008
$892$	21.0000	0.703132
$893$	0	0
$894$	15.0000	0.501675
$895$	0	0
$896$	−1.00000	−0.0334077
$897$	−32.0000	−1.06845
$898$	−33.0000	−1.10122
$899$	5.00000	0.166759
$900$	8.00000	0.266667
$901$	−21.0000	−0.699611
$902$	−6.00000	−0.199778
$903$	−5.00000	−0.166390
$904$	1.00000	0.0332595
$905$	−14.0000	−0.465376
$906$	15.0000	0.498342
$907$	43.0000	1.42779	0.713896	−	0.700252i	$-0.246929\pi$
$907$	43.0000	1.42779	0.713896	+	0.700252i	$0.246929\pi$
$908$	3.00000	0.0995585
$909$	−12.0000	−0.398015
$910$	−4.00000	−0.132599
$911$	−42.0000	−1.39152	−0.695761	−	0.718273i	$-0.744933\pi$
$911$	−42.0000	−1.39152	−0.695761	+	0.718273i	$0.744933\pi$
$912$	0	0
$913$	12.0000	0.397142
$914$	6.00000	0.198462
$915$	−3.00000	−0.0991769
$916$	−20.0000	−0.660819
$917$	20.0000	0.660458
$918$	35.0000	1.15517
$919$	25.0000	0.824674	0.412337	−	0.911031i	$-0.364713\pi$
$919$	25.0000	0.824674	0.412337	+	0.911031i	$0.364713\pi$
$920$	8.00000	0.263752
$921$	4.00000	0.131804
$922$	−37.0000	−1.21853
$923$	−12.0000	−0.394985
$924$	−6.00000	−0.197386
$925$	8.00000	0.263038
$926$	−16.0000	−0.525793
$927$	22.0000	0.722575
$928$	1.00000	0.0328266
$929$	−6.00000	−0.196854	−0.0984268	−	0.995144i	$-0.531381\pi$
$929$	−6.00000	−0.196854	−0.0984268	+	0.995144i	$0.531381\pi$
$930$	5.00000	0.163956
$931$	0	0
$932$	−6.00000	−0.196537
$933$	34.0000	1.11311
$934$	6.00000	0.196326
$935$	42.0000	1.37355
$936$	8.00000	0.261488
$937$	−43.0000	−1.40475	−0.702374	−	0.711808i	$-0.747877\pi$
$937$	−43.0000	−1.40475	−0.702374	+	0.711808i	$0.747877\pi$
$938$	−14.0000	−0.457116
$939$	−22.0000	−0.717943
$940$	6.00000	0.195698
$941$	50.0000	1.62995	0.814977	−	0.579494i	$-0.196750\pi$
$941$	50.0000	1.62995	0.814977	+	0.579494i	$0.196750\pi$
$942$	0	0
$943$	−8.00000	−0.260516
$944$	−10.0000	−0.325472
$945$	5.00000	0.162650
$946$	30.0000	0.975384
$947$	−28.0000	−0.909878	−0.454939	−	0.890523i	$-0.650339\pi$
$947$	−28.0000	−0.909878	−0.454939	+	0.890523i	$0.650339\pi$
$948$	−7.00000	−0.227349
$949$	−32.0000	−1.03876
$950$	0	0
$951$	−2.00000	−0.0648544
$952$	−7.00000	−0.226871
$953$	22.0000	0.712650	0.356325	−	0.934362i	$-0.384030\pi$
$953$	22.0000	0.712650	0.356325	+	0.934362i	$0.384030\pi$
$954$	6.00000	0.194257
$955$	25.0000	0.808981
$956$	−28.0000	−0.905585
$957$	6.00000	0.193952
$958$	−2.00000	−0.0646171
$959$	4.00000	0.129167
$960$	1.00000	0.0322749
$961$	−6.00000	−0.193548
$962$	8.00000	0.257930
$963$	26.0000	0.837838
$964$	−18.0000	−0.579741
$965$	4.00000	0.128765
$966$	−8.00000	−0.257396
$967$	−29.0000	−0.932577	−0.466289	−	0.884633i	$-0.654409\pi$
$967$	−29.0000	−0.932577	−0.466289	+	0.884633i	$0.654409\pi$
$968$	25.0000	0.803530
$969$	0	0
$970$	−5.00000	−0.160540
$971$	39.0000	1.25157	0.625785	−	0.779996i	$-0.284779\pi$
$971$	39.0000	1.25157	0.625785	+	0.779996i	$0.284779\pi$
$972$	−16.0000	−0.513200
$973$	18.0000	0.577054
$974$	4.00000	0.128168
$975$	−16.0000	−0.512410
$976$	−3.00000	−0.0960277
$977$	−6.00000	−0.191957	−0.0959785	−	0.995383i	$-0.530598\pi$
$977$	−6.00000	−0.191957	−0.0959785	+	0.995383i	$0.530598\pi$
$978$	4.00000	0.127906
$979$	−30.0000	−0.958804
$980$	−1.00000	−0.0319438
$981$	−4.00000	−0.127710
$982$	−3.00000	−0.0957338
$983$	−3.00000	−0.0956851	−0.0478426	−	0.998855i	$-0.515235\pi$
$983$	−3.00000	−0.0956851	−0.0478426	+	0.998855i	$0.515235\pi$
$984$	−1.00000	−0.0318788
$985$	−12.0000	−0.382352
$986$	7.00000	0.222925
$987$	−6.00000	−0.190982
$988$	0	0
$989$	40.0000	1.27193
$990$	−12.0000	−0.381385
$991$	24.0000	0.762385	0.381193	−	0.924496i	$-0.375513\pi$
$991$	24.0000	0.762385	0.381193	+	0.924496i	$0.375513\pi$
$992$	5.00000	0.158750
$993$	12.0000	0.380808
$994$	−3.00000	−0.0951542
$995$	−4.00000	−0.126809
$996$	2.00000	0.0633724
$997$	−20.0000	−0.633406	−0.316703	−	0.948525i	$-0.602576\pi$
$997$	−20.0000	−0.633406	−0.316703	+	0.948525i	$0.602576\pi$
$998$	2.00000	0.0633089
$999$	−10.0000	−0.316386

Twists

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

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