LMFDB - Embedded newform 4598.2.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4598,2,Mod(1,4598)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4598, 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("4598.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4598 = 2 \cdot 11^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4598.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:	$36.7152148494$
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	$\chi$	$=$	4598.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.00000 q^{5} +1.00000 q^{6} +3.00000 q^{7} -1.00000 q^{8} -2.00000 q^{9} +O(q^{10})$

\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.00000 q^{5} +1.00000 q^{6} +3.00000 q^{7} -1.00000 q^{8} -2.00000 q^{9} -2.00000 q^{10} -1.00000 q^{12} -2.00000 q^{13} -3.00000 q^{14} -2.00000 q^{15} +1.00000 q^{16} -2.00000 q^{17} +2.00000 q^{18} +1.00000 q^{19} +2.00000 q^{20} -3.00000 q^{21} -1.00000 q^{23} +1.00000 q^{24} -1.00000 q^{25} +2.00000 q^{26} +5.00000 q^{27} +3.00000 q^{28} +5.00000 q^{29} +2.00000 q^{30} -8.00000 q^{31} -1.00000 q^{32} +2.00000 q^{34} +6.00000 q^{35} -2.00000 q^{36} +3.00000 q^{37} -1.00000 q^{38} +2.00000 q^{39} -2.00000 q^{40} -6.00000 q^{41} +3.00000 q^{42} +2.00000 q^{43} -4.00000 q^{45} +1.00000 q^{46} -3.00000 q^{47} -1.00000 q^{48} +2.00000 q^{49} +1.00000 q^{50} +2.00000 q^{51} -2.00000 q^{52} +1.00000 q^{53} -5.00000 q^{54} -3.00000 q^{56} -1.00000 q^{57} -5.00000 q^{58} -3.00000 q^{59} -2.00000 q^{60} -6.00000 q^{61} +8.00000 q^{62} -6.00000 q^{63} +1.00000 q^{64} -4.00000 q^{65} -12.0000 q^{67} -2.00000 q^{68} +1.00000 q^{69} -6.00000 q^{70} -14.0000 q^{71} +2.00000 q^{72} +6.00000 q^{73} -3.00000 q^{74} +1.00000 q^{75} +1.00000 q^{76} -2.00000 q^{78} -4.00000 q^{79} +2.00000 q^{80} +1.00000 q^{81} +6.00000 q^{82} -2.00000 q^{83} -3.00000 q^{84} -4.00000 q^{85} -2.00000 q^{86} -5.00000 q^{87} -4.00000 q^{89} +4.00000 q^{90} -6.00000 q^{91} -1.00000 q^{92} +8.00000 q^{93} +3.00000 q^{94} +2.00000 q^{95} +1.00000 q^{96} -4.00000 q^{97} -2.00000 q^{98} +O(q^{100})\)

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
$5$	2.00000	0.894427	0.447214	−	0.894427i	$-0.352416\pi$
$5$	2.00000	0.894427	0.447214	+	0.894427i	$0.352416\pi$
$6$	1.00000	0.408248
$7$	3.00000	1.13389	0.566947	−	0.823754i	$-0.308125\pi$
$7$	3.00000	1.13389	0.566947	+	0.823754i	$0.308125\pi$
$8$	−1.00000	−0.353553
$9$	−2.00000	−0.666667
$10$	−2.00000	−0.632456
$11$	0	0
$11$	0	0
$12$	−1.00000	−0.288675
$13$	−2.00000	−0.554700	−0.277350	−	0.960769i	$-0.589456\pi$
$13$	−2.00000	−0.554700	−0.277350	+	0.960769i	$0.589456\pi$
$14$	−3.00000	−0.801784
$15$	−2.00000	−0.516398
$16$	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	$0.577979\pi$
$18$	2.00000	0.471405
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	2.00000	0.447214
$21$	−3.00000	−0.654654
$22$	0	0
$23$	−1.00000	−0.208514	−0.104257	−	0.994550i	$-0.533247\pi$
$23$	−1.00000	−0.208514	−0.104257	+	0.994550i	$0.533247\pi$
$24$	1.00000	0.204124
$25$	−1.00000	−0.200000
$26$	2.00000	0.392232
$27$	5.00000	0.962250
$28$	3.00000	0.566947
$29$	5.00000	0.928477	0.464238	−	0.885710i	$-0.346328\pi$
$29$	5.00000	0.928477	0.464238	+	0.885710i	$0.346328\pi$
$30$	2.00000	0.365148
$31$	−8.00000	−1.43684	−0.718421	−	0.695608i	$-0.755135\pi$
$31$	−8.00000	−1.43684	−0.718421	+	0.695608i	$0.755135\pi$
$32$	−1.00000	−0.176777
$33$	0	0
$34$	2.00000	0.342997
$35$	6.00000	1.01419
$36$	−2.00000	−0.333333
$37$	3.00000	0.493197	0.246598	−	0.969118i	$-0.420687\pi$
$37$	3.00000	0.493197	0.246598	+	0.969118i	$0.420687\pi$
$38$	−1.00000	−0.162221
$39$	2.00000	0.320256
$40$	−2.00000	−0.316228
$41$	−6.00000	−0.937043	−0.468521	−	0.883452i	$-0.655213\pi$
$41$	−6.00000	−0.937043	−0.468521	+	0.883452i	$0.655213\pi$
$42$	3.00000	0.462910
$43$	2.00000	0.304997	0.152499	−	0.988304i	$-0.451268\pi$
$43$	2.00000	0.304997	0.152499	+	0.988304i	$0.451268\pi$
$44$	0	0
$45$	−4.00000	−0.596285
$46$	1.00000	0.147442
$47$	−3.00000	−0.437595	−0.218797	−	0.975770i	$-0.570213\pi$
$47$	−3.00000	−0.437595	−0.218797	+	0.975770i	$0.570213\pi$
$48$	−1.00000	−0.144338
$49$	2.00000	0.285714
$50$	1.00000	0.141421
$51$	2.00000	0.280056
$52$	−2.00000	−0.277350
$53$	1.00000	0.137361	0.0686803	−	0.997639i	$-0.478121\pi$
$53$	1.00000	0.137361	0.0686803	+	0.997639i	$0.478121\pi$
$54$	−5.00000	−0.680414
$55$	0	0
$56$	−3.00000	−0.400892
$57$	−1.00000	−0.132453
$58$	−5.00000	−0.656532
$59$	−3.00000	−0.390567	−0.195283	−	0.980747i	$-0.562563\pi$
$59$	−3.00000	−0.390567	−0.195283	+	0.980747i	$0.562563\pi$
$60$	−2.00000	−0.258199
$61$	−6.00000	−0.768221	−0.384111	−	0.923287i	$-0.625492\pi$
$61$	−6.00000	−0.768221	−0.384111	+	0.923287i	$0.625492\pi$
$62$	8.00000	1.01600
$63$	−6.00000	−0.755929
$64$	1.00000	0.125000
$65$	−4.00000	−0.496139
$66$	0	0
$67$	−12.0000	−1.46603	−0.733017	−	0.680211i	$-0.761888\pi$
$67$	−12.0000	−1.46603	−0.733017	+	0.680211i	$0.761888\pi$
$68$	−2.00000	−0.242536
$69$	1.00000	0.120386
$70$	−6.00000	−0.717137
$71$	−14.0000	−1.66149	−0.830747	−	0.556650i	$-0.812086\pi$
$71$	−14.0000	−1.66149	−0.830747	+	0.556650i	$0.812086\pi$
$72$	2.00000	0.235702
$73$	6.00000	0.702247	0.351123	−	0.936329i	$-0.385800\pi$
$73$	6.00000	0.702247	0.351123	+	0.936329i	$0.385800\pi$
$74$	−3.00000	−0.348743
$75$	1.00000	0.115470
$76$	1.00000	0.114708
$77$	0	0
$78$	−2.00000	−0.226455
$79$	−4.00000	−0.450035	−0.225018	−	0.974355i	$-0.572244\pi$
$79$	−4.00000	−0.450035	−0.225018	+	0.974355i	$0.572244\pi$
$80$	2.00000	0.223607
$81$	1.00000	0.111111
$82$	6.00000	0.662589
$83$	−2.00000	−0.219529	−0.109764	−	0.993958i	$-0.535010\pi$
$83$	−2.00000	−0.219529	−0.109764	+	0.993958i	$0.535010\pi$
$84$	−3.00000	−0.327327
$85$	−4.00000	−0.433861
$86$	−2.00000	−0.215666
$87$	−5.00000	−0.536056
$88$	0	0
$89$	−4.00000	−0.423999	−0.212000	−	0.977270i	$-0.567998\pi$
$89$	−4.00000	−0.423999	−0.212000	+	0.977270i	$0.567998\pi$
$90$	4.00000	0.421637
$91$	−6.00000	−0.628971
$92$	−1.00000	−0.104257
$93$	8.00000	0.829561
$94$	3.00000	0.309426
$95$	2.00000	0.205196
$96$	1.00000	0.102062
$97$	−4.00000	−0.406138	−0.203069	−	0.979164i	$-0.565092\pi$
$97$	−4.00000	−0.406138	−0.203069	+	0.979164i	$0.565092\pi$
$98$	−2.00000	−0.202031
$99$	0	0
$100$	−1.00000	−0.100000
$101$	18.0000	1.79107	0.895533	−	0.444994i	$-0.146794\pi$
$101$	18.0000	1.79107	0.895533	+	0.444994i	$0.146794\pi$
$102$	−2.00000	−0.198030
$103$	−12.0000	−1.18240	−0.591198	−	0.806527i	$-0.701345\pi$
$103$	−12.0000	−1.18240	−0.591198	+	0.806527i	$0.701345\pi$
$104$	2.00000	0.196116
$105$	−6.00000	−0.585540
$106$	−1.00000	−0.0971286
$107$	7.00000	0.676716	0.338358	−	0.941018i	$-0.390129\pi$
$107$	7.00000	0.676716	0.338358	+	0.941018i	$0.390129\pi$
$108$	5.00000	0.481125
$109$	−1.00000	−0.0957826	−0.0478913	−	0.998853i	$-0.515250\pi$
$109$	−1.00000	−0.0957826	−0.0478913	+	0.998853i	$0.515250\pi$
$110$	0	0
$111$	−3.00000	−0.284747
$112$	3.00000	0.283473
$113$	6.00000	0.564433	0.282216	−	0.959351i	$-0.408930\pi$
$113$	6.00000	0.564433	0.282216	+	0.959351i	$0.408930\pi$
$114$	1.00000	0.0936586
$115$	−2.00000	−0.186501
$116$	5.00000	0.464238
$117$	4.00000	0.369800
$118$	3.00000	0.276172
$119$	−6.00000	−0.550019
$120$	2.00000	0.182574
$121$	0	0
$122$	6.00000	0.543214
$123$	6.00000	0.541002
$124$	−8.00000	−0.718421
$125$	−12.0000	−1.07331
$126$	6.00000	0.534522
$127$	−20.0000	−1.77471	−0.887357	−	0.461084i	$-0.847461\pi$
$127$	−20.0000	−1.77471	−0.887357	+	0.461084i	$0.847461\pi$
$128$	−1.00000	−0.0883883
$129$	−2.00000	−0.176090
$130$	4.00000	0.350823
$131$	−2.00000	−0.174741	−0.0873704	−	0.996176i	$-0.527846\pi$
$131$	−2.00000	−0.174741	−0.0873704	+	0.996176i	$0.527846\pi$
$132$	0	0
$133$	3.00000	0.260133
$134$	12.0000	1.03664
$135$	10.0000	0.860663
$136$	2.00000	0.171499
$137$	−10.0000	−0.854358	−0.427179	−	0.904167i	$-0.640493\pi$
$137$	−10.0000	−0.854358	−0.427179	+	0.904167i	$0.640493\pi$
$138$	−1.00000	−0.0851257
$139$	16.0000	1.35710	0.678551	−	0.734553i	$-0.262608\pi$
$139$	16.0000	1.35710	0.678551	+	0.734553i	$0.262608\pi$
$140$	6.00000	0.507093
$141$	3.00000	0.252646
$142$	14.0000	1.17485
$143$	0	0
$144$	−2.00000	−0.166667
$145$	10.0000	0.830455
$146$	−6.00000	−0.496564
$147$	−2.00000	−0.164957
$148$	3.00000	0.246598
$149$	0	0		−	1.00000i	$-0.5\pi$
$149$	0	0			1.00000i	$0.5\pi$
$150$	−1.00000	−0.0816497
$151$	0	0		−	1.00000i	$-0.5\pi$
$151$	0	0			1.00000i	$0.5\pi$
$152$	−1.00000	−0.0811107
$153$	4.00000	0.323381
$154$	0	0
$155$	−16.0000	−1.28515
$156$	2.00000	0.160128
$157$	−4.00000	−0.319235	−0.159617	−	0.987179i	$-0.551026\pi$
$157$	−4.00000	−0.319235	−0.159617	+	0.987179i	$0.551026\pi$
$158$	4.00000	0.318223
$159$	−1.00000	−0.0793052
$160$	−2.00000	−0.158114
$161$	−3.00000	−0.236433
$162$	−1.00000	−0.0785674
$163$	10.0000	0.783260	0.391630	−	0.920123i	$-0.371911\pi$
$163$	10.0000	0.783260	0.391630	+	0.920123i	$0.371911\pi$
$164$	−6.00000	−0.468521
$165$	0	0
$166$	2.00000	0.155230
$167$	22.0000	1.70241	0.851206	−	0.524832i	$-0.175872\pi$
$167$	22.0000	1.70241	0.851206	+	0.524832i	$0.175872\pi$
$168$	3.00000	0.231455
$169$	−9.00000	−0.692308
$170$	4.00000	0.306786
$171$	−2.00000	−0.152944
$172$	2.00000	0.152499
$173$	−11.0000	−0.836315	−0.418157	−	0.908375i	$-0.637324\pi$
$173$	−11.0000	−0.836315	−0.418157	+	0.908375i	$0.637324\pi$
$174$	5.00000	0.379049
$175$	−3.00000	−0.226779
$176$	0	0
$177$	3.00000	0.225494
$178$	4.00000	0.299813
$179$	17.0000	1.27064	0.635320	−	0.772249i	$-0.280868\pi$
$179$	17.0000	1.27064	0.635320	+	0.772249i	$0.280868\pi$
$180$	−4.00000	−0.298142
$181$	−14.0000	−1.04061	−0.520306	−	0.853980i	$-0.674182\pi$
$181$	−14.0000	−1.04061	−0.520306	+	0.853980i	$0.674182\pi$
$182$	6.00000	0.444750
$183$	6.00000	0.443533
$184$	1.00000	0.0737210
$185$	6.00000	0.441129
$186$	−8.00000	−0.586588
$187$	0	0
$188$	−3.00000	−0.218797
$189$	15.0000	1.09109
$190$	−2.00000	−0.145095
$191$	3.00000	0.217072	0.108536	−	0.994092i	$-0.465384\pi$
$191$	3.00000	0.217072	0.108536	+	0.994092i	$0.465384\pi$
$192$	−1.00000	−0.0721688
$193$	14.0000	1.00774	0.503871	−	0.863779i	$-0.331909\pi$
$193$	14.0000	1.00774	0.503871	+	0.863779i	$0.331909\pi$
$194$	4.00000	0.287183
$195$	4.00000	0.286446
$196$	2.00000	0.142857
$197$	−12.0000	−0.854965	−0.427482	−	0.904024i	$-0.640599\pi$
$197$	−12.0000	−0.854965	−0.427482	+	0.904024i	$0.640599\pi$
$198$	0	0
$199$	8.00000	0.567105	0.283552	−	0.958957i	$-0.408487\pi$
$199$	8.00000	0.567105	0.283552	+	0.958957i	$0.408487\pi$
$200$	1.00000	0.0707107
$201$	12.0000	0.846415
$202$	−18.0000	−1.26648
$203$	15.0000	1.05279
$204$	2.00000	0.140028
$205$	−12.0000	−0.838116
$206$	12.0000	0.836080
$207$	2.00000	0.139010
$208$	−2.00000	−0.138675
$209$	0	0
$210$	6.00000	0.414039
$211$	−5.00000	−0.344214	−0.172107	−	0.985078i	$-0.555058\pi$
$211$	−5.00000	−0.344214	−0.172107	+	0.985078i	$0.555058\pi$
$212$	1.00000	0.0686803
$213$	14.0000	0.959264
$214$	−7.00000	−0.478510
$215$	4.00000	0.272798
$216$	−5.00000	−0.340207
$217$	−24.0000	−1.62923
$218$	1.00000	0.0677285
$219$	−6.00000	−0.405442
$220$	0	0
$221$	4.00000	0.269069
$222$	3.00000	0.201347
$223$	−2.00000	−0.133930	−0.0669650	−	0.997755i	$-0.521332\pi$
$223$	−2.00000	−0.133930	−0.0669650	+	0.997755i	$0.521332\pi$
$224$	−3.00000	−0.200446
$225$	2.00000	0.133333
$226$	−6.00000	−0.399114
$227$	24.0000	1.59294	0.796468	−	0.604681i	$-0.206699\pi$
$227$	24.0000	1.59294	0.796468	+	0.604681i	$0.206699\pi$
$228$	−1.00000	−0.0662266
$229$	20.0000	1.32164	0.660819	−	0.750546i	$-0.270209\pi$
$229$	20.0000	1.32164	0.660819	+	0.750546i	$0.270209\pi$
$230$	2.00000	0.131876
$231$	0	0
$232$	−5.00000	−0.328266
$233$	−17.0000	−1.11371	−0.556854	−	0.830611i	$-0.687992\pi$
$233$	−17.0000	−1.11371	−0.556854	+	0.830611i	$0.687992\pi$
$234$	−4.00000	−0.261488
$235$	−6.00000	−0.391397
$236$	−3.00000	−0.195283
$237$	4.00000	0.259828
$238$	6.00000	0.388922
$239$	5.00000	0.323423	0.161712	−	0.986838i	$-0.448299\pi$
$239$	5.00000	0.323423	0.161712	+	0.986838i	$0.448299\pi$
$240$	−2.00000	−0.129099
$241$	−28.0000	−1.80364	−0.901819	−	0.432113i	$-0.857768\pi$
$241$	−28.0000	−1.80364	−0.901819	+	0.432113i	$0.857768\pi$
$242$	0	0
$243$	−16.0000	−1.02640
$244$	−6.00000	−0.384111
$245$	4.00000	0.255551
$246$	−6.00000	−0.382546
$247$	−2.00000	−0.127257
$248$	8.00000	0.508001
$249$	2.00000	0.126745
$250$	12.0000	0.758947
$251$	−18.0000	−1.13615	−0.568075	−	0.822977i	$-0.692312\pi$
$251$	−18.0000	−1.13615	−0.568075	+	0.822977i	$0.692312\pi$
$252$	−6.00000	−0.377964
$253$	0	0
$254$	20.0000	1.25491
$255$	4.00000	0.250490
$256$	1.00000	0.0625000
$257$	−8.00000	−0.499026	−0.249513	−	0.968371i	$-0.580271\pi$
$257$	−8.00000	−0.499026	−0.249513	+	0.968371i	$0.580271\pi$
$258$	2.00000	0.124515
$259$	9.00000	0.559233
$260$	−4.00000	−0.248069
$261$	−10.0000	−0.618984
$262$	2.00000	0.123560
$263$	−16.0000	−0.986602	−0.493301	−	0.869859i	$-0.664210\pi$
$263$	−16.0000	−0.986602	−0.493301	+	0.869859i	$0.664210\pi$
$264$	0	0
$265$	2.00000	0.122859
$266$	−3.00000	−0.183942
$267$	4.00000	0.244796
$268$	−12.0000	−0.733017
$269$	−21.0000	−1.28039	−0.640196	−	0.768211i	$-0.721147\pi$
$269$	−21.0000	−1.28039	−0.640196	+	0.768211i	$0.721147\pi$
$270$	−10.0000	−0.608581
$271$	12.0000	0.728948	0.364474	−	0.931214i	$-0.381249\pi$
$271$	12.0000	0.728948	0.364474	+	0.931214i	$0.381249\pi$
$272$	−2.00000	−0.121268
$273$	6.00000	0.363137
$274$	10.0000	0.604122
$275$	0	0
$276$	1.00000	0.0601929
$277$	2.00000	0.120168	0.0600842	−	0.998193i	$-0.480863\pi$
$277$	2.00000	0.120168	0.0600842	+	0.998193i	$0.480863\pi$
$278$	−16.0000	−0.959616
$279$	16.0000	0.957895
$280$	−6.00000	−0.358569
$281$	20.0000	1.19310	0.596550	−	0.802576i	$-0.296538\pi$
$281$	20.0000	1.19310	0.596550	+	0.802576i	$0.296538\pi$
$282$	−3.00000	−0.178647
$283$	4.00000	0.237775	0.118888	−	0.992908i	$-0.462067\pi$
$283$	4.00000	0.237775	0.118888	+	0.992908i	$0.462067\pi$
$284$	−14.0000	−0.830747
$285$	−2.00000	−0.118470
$286$	0	0
$287$	−18.0000	−1.06251
$288$	2.00000	0.117851
$289$	−13.0000	−0.764706
$290$	−10.0000	−0.587220
$291$	4.00000	0.234484
$292$	6.00000	0.351123
$293$	−9.00000	−0.525786	−0.262893	−	0.964825i	$-0.584677\pi$
$293$	−9.00000	−0.525786	−0.262893	+	0.964825i	$0.584677\pi$
$294$	2.00000	0.116642
$295$	−6.00000	−0.349334
$296$	−3.00000	−0.174371
$297$	0	0
$298$	0	0
$299$	2.00000	0.115663
$300$	1.00000	0.0577350
$301$	6.00000	0.345834
$302$	0	0
$303$	−18.0000	−1.03407
$304$	1.00000	0.0573539
$305$	−12.0000	−0.687118
$306$	−4.00000	−0.228665
$307$	−1.00000	−0.0570730	−0.0285365	−	0.999593i	$-0.509085\pi$
$307$	−1.00000	−0.0570730	−0.0285365	+	0.999593i	$0.509085\pi$
$308$	0	0
$309$	12.0000	0.682656
$310$	16.0000	0.908739
$311$	24.0000	1.36092	0.680458	−	0.732787i	$-0.261781\pi$
$311$	24.0000	1.36092	0.680458	+	0.732787i	$0.261781\pi$
$312$	−2.00000	−0.113228
$313$	−27.0000	−1.52613	−0.763065	−	0.646322i	$-0.776306\pi$
$313$	−27.0000	−1.52613	−0.763065	+	0.646322i	$0.776306\pi$
$314$	4.00000	0.225733
$315$	−12.0000	−0.676123
$316$	−4.00000	−0.225018
$317$	−6.00000	−0.336994	−0.168497	−	0.985702i	$-0.553891\pi$
$317$	−6.00000	−0.336994	−0.168497	+	0.985702i	$0.553891\pi$
$318$	1.00000	0.0560772
$319$	0	0
$320$	2.00000	0.111803
$321$	−7.00000	−0.390702
$322$	3.00000	0.167183
$323$	−2.00000	−0.111283
$324$	1.00000	0.0555556
$325$	2.00000	0.110940
$326$	−10.0000	−0.553849
$327$	1.00000	0.0553001
$328$	6.00000	0.331295
$329$	−9.00000	−0.496186
$330$	0	0
$331$	11.0000	0.604615	0.302307	−	0.953211i	$-0.402243\pi$
$331$	11.0000	0.604615	0.302307	+	0.953211i	$0.402243\pi$
$332$	−2.00000	−0.109764
$333$	−6.00000	−0.328798
$334$	−22.0000	−1.20379
$335$	−24.0000	−1.31126
$336$	−3.00000	−0.163663
$337$	−26.0000	−1.41631	−0.708155	−	0.706057i	$-0.750472\pi$
$337$	−26.0000	−1.41631	−0.708155	+	0.706057i	$0.750472\pi$
$338$	9.00000	0.489535
$339$	−6.00000	−0.325875
$340$	−4.00000	−0.216930
$341$	0	0
$342$	2.00000	0.108148
$343$	−15.0000	−0.809924
$344$	−2.00000	−0.107833
$345$	2.00000	0.107676
$346$	11.0000	0.591364
$347$	14.0000	0.751559	0.375780	−	0.926709i	$-0.377375\pi$
$347$	14.0000	0.751559	0.375780	+	0.926709i	$0.377375\pi$
$348$	−5.00000	−0.268028
$349$	−26.0000	−1.39175	−0.695874	−	0.718164i	$-0.744983\pi$
$349$	−26.0000	−1.39175	−0.695874	+	0.718164i	$0.744983\pi$
$350$	3.00000	0.160357
$351$	−10.0000	−0.533761
$352$	0	0
$353$	29.0000	1.54351	0.771757	−	0.635917i	$-0.219378\pi$
$353$	29.0000	1.54351	0.771757	+	0.635917i	$0.219378\pi$
$354$	−3.00000	−0.159448
$355$	−28.0000	−1.48609
$356$	−4.00000	−0.212000
$357$	6.00000	0.317554
$358$	−17.0000	−0.898478
$359$	8.00000	0.422224	0.211112	−	0.977462i	$-0.432292\pi$
$359$	8.00000	0.422224	0.211112	+	0.977462i	$0.432292\pi$
$360$	4.00000	0.210819
$361$	1.00000	0.0526316
$362$	14.0000	0.735824
$363$	0	0
$364$	−6.00000	−0.314485
$365$	12.0000	0.628109
$366$	−6.00000	−0.313625
$367$	7.00000	0.365397	0.182699	−	0.983169i	$-0.441517\pi$
$367$	7.00000	0.365397	0.182699	+	0.983169i	$0.441517\pi$
$368$	−1.00000	−0.0521286
$369$	12.0000	0.624695
$370$	−6.00000	−0.311925
$371$	3.00000	0.155752
$372$	8.00000	0.414781
$373$	−1.00000	−0.0517780	−0.0258890	−	0.999665i	$-0.508242\pi$
$373$	−1.00000	−0.0517780	−0.0258890	+	0.999665i	$0.508242\pi$
$374$	0	0
$375$	12.0000	0.619677
$376$	3.00000	0.154713
$377$	−10.0000	−0.515026
$378$	−15.0000	−0.771517
$379$	−35.0000	−1.79783	−0.898915	−	0.438124i	$-0.855643\pi$
$379$	−35.0000	−1.79783	−0.898915	+	0.438124i	$0.855643\pi$
$380$	2.00000	0.102598
$381$	20.0000	1.02463
$382$	−3.00000	−0.153493
$383$	4.00000	0.204390	0.102195	−	0.994764i	$-0.467413\pi$
$383$	4.00000	0.204390	0.102195	+	0.994764i	$0.467413\pi$
$384$	1.00000	0.0510310
$385$	0	0
$386$	−14.0000	−0.712581
$387$	−4.00000	−0.203331
$388$	−4.00000	−0.203069
$389$	−24.0000	−1.21685	−0.608424	−	0.793612i	$-0.708198\pi$
$389$	−24.0000	−1.21685	−0.608424	+	0.793612i	$0.708198\pi$
$390$	−4.00000	−0.202548
$391$	2.00000	0.101144
$392$	−2.00000	−0.101015
$393$	2.00000	0.100887
$394$	12.0000	0.604551
$395$	−8.00000	−0.402524
$396$	0	0
$397$	−2.00000	−0.100377	−0.0501886	−	0.998740i	$-0.515982\pi$
$397$	−2.00000	−0.100377	−0.0501886	+	0.998740i	$0.515982\pi$
$398$	−8.00000	−0.401004
$399$	−3.00000	−0.150188
$400$	−1.00000	−0.0500000
$401$	14.0000	0.699127	0.349563	−	0.936913i	$-0.386330\pi$
$401$	14.0000	0.699127	0.349563	+	0.936913i	$0.386330\pi$
$402$	−12.0000	−0.598506
$403$	16.0000	0.797017
$404$	18.0000	0.895533
$405$	2.00000	0.0993808
$406$	−15.0000	−0.744438
$407$	0	0
$408$	−2.00000	−0.0990148
$409$	−20.0000	−0.988936	−0.494468	−	0.869196i	$-0.664637\pi$
$409$	−20.0000	−0.988936	−0.494468	+	0.869196i	$0.664637\pi$
$410$	12.0000	0.592638
$411$	10.0000	0.493264
$412$	−12.0000	−0.591198
$413$	−9.00000	−0.442861
$414$	−2.00000	−0.0982946
$415$	−4.00000	−0.196352
$416$	2.00000	0.0980581
$417$	−16.0000	−0.783523
$418$	0	0
$419$	−22.0000	−1.07477	−0.537385	−	0.843337i	$-0.680588\pi$
$419$	−22.0000	−1.07477	−0.537385	+	0.843337i	$0.680588\pi$
$420$	−6.00000	−0.292770
$421$	−27.0000	−1.31590	−0.657950	−	0.753062i	$-0.728576\pi$
$421$	−27.0000	−1.31590	−0.657950	+	0.753062i	$0.728576\pi$
$422$	5.00000	0.243396
$423$	6.00000	0.291730
$424$	−1.00000	−0.0485643
$425$	2.00000	0.0970143
$426$	−14.0000	−0.678302
$427$	−18.0000	−0.871081
$428$	7.00000	0.338358
$429$	0	0
$430$	−4.00000	−0.192897
$431$	−16.0000	−0.770693	−0.385346	−	0.922772i	$-0.625918\pi$
$431$	−16.0000	−0.770693	−0.385346	+	0.922772i	$0.625918\pi$
$432$	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	$0.453949\pi$
$434$	24.0000	1.15204
$435$	−10.0000	−0.479463
$436$	−1.00000	−0.0478913
$437$	−1.00000	−0.0478365
$438$	6.00000	0.286691
$439$	−8.00000	−0.381819	−0.190910	−	0.981608i	$-0.561144\pi$
$439$	−8.00000	−0.381819	−0.190910	+	0.981608i	$0.561144\pi$
$440$	0	0
$441$	−4.00000	−0.190476
$442$	−4.00000	−0.190261
$443$	18.0000	0.855206	0.427603	−	0.903967i	$-0.359358\pi$
$443$	18.0000	0.855206	0.427603	+	0.903967i	$0.359358\pi$
$444$	−3.00000	−0.142374
$445$	−8.00000	−0.379236
$446$	2.00000	0.0947027
$447$	0	0
$448$	3.00000	0.141737
$449$	−6.00000	−0.283158	−0.141579	−	0.989927i	$-0.545218\pi$
$449$	−6.00000	−0.283158	−0.141579	+	0.989927i	$0.545218\pi$
$450$	−2.00000	−0.0942809
$451$	0	0
$452$	6.00000	0.282216
$453$	0	0
$454$	−24.0000	−1.12638
$455$	−12.0000	−0.562569
$456$	1.00000	0.0468293
$457$	−31.0000	−1.45012	−0.725059	−	0.688686i	$-0.758188\pi$
$457$	−31.0000	−1.45012	−0.725059	+	0.688686i	$0.758188\pi$
$458$	−20.0000	−0.934539
$459$	−10.0000	−0.466760
$460$	−2.00000	−0.0932505
$461$	−22.0000	−1.02464	−0.512321	−	0.858794i	$-0.671214\pi$
$461$	−22.0000	−1.02464	−0.512321	+	0.858794i	$0.671214\pi$
$462$	0	0
$463$	16.0000	0.743583	0.371792	−	0.928316i	$-0.378744\pi$
$463$	16.0000	0.743583	0.371792	+	0.928316i	$0.378744\pi$
$464$	5.00000	0.232119
$465$	16.0000	0.741982
$466$	17.0000	0.787510
$467$	−14.0000	−0.647843	−0.323921	−	0.946084i	$-0.605001\pi$
$467$	−14.0000	−0.647843	−0.323921	+	0.946084i	$0.605001\pi$
$468$	4.00000	0.184900
$469$	−36.0000	−1.66233
$470$	6.00000	0.276759
$471$	4.00000	0.184310
$472$	3.00000	0.138086
$473$	0	0
$474$	−4.00000	−0.183726
$475$	−1.00000	−0.0458831
$476$	−6.00000	−0.275010
$477$	−2.00000	−0.0915737
$478$	−5.00000	−0.228695
$479$	15.0000	0.685367	0.342684	−	0.939451i	$-0.388664\pi$
$479$	15.0000	0.685367	0.342684	+	0.939451i	$0.388664\pi$
$480$	2.00000	0.0912871
$481$	−6.00000	−0.273576
$482$	28.0000	1.27537
$483$	3.00000	0.136505
$484$	0	0
$485$	−8.00000	−0.363261
$486$	16.0000	0.725775
$487$	−30.0000	−1.35943	−0.679715	−	0.733476i	$-0.737896\pi$
$487$	−30.0000	−1.35943	−0.679715	+	0.733476i	$0.737896\pi$
$488$	6.00000	0.271607
$489$	−10.0000	−0.452216
$490$	−4.00000	−0.180702
$491$	32.0000	1.44414	0.722070	−	0.691820i	$-0.243191\pi$
$491$	32.0000	1.44414	0.722070	+	0.691820i	$0.243191\pi$
$492$	6.00000	0.270501
$493$	−10.0000	−0.450377
$494$	2.00000	0.0899843
$495$	0	0
$496$	−8.00000	−0.359211
$497$	−42.0000	−1.88396
$498$	−2.00000	−0.0896221
$499$	8.00000	0.358129	0.179065	−	0.983837i	$-0.442693\pi$
$499$	8.00000	0.358129	0.179065	+	0.983837i	$0.442693\pi$
$500$	−12.0000	−0.536656
$501$	−22.0000	−0.982888
$502$	18.0000	0.803379
$503$	7.00000	0.312115	0.156057	−	0.987748i	$-0.450122\pi$
$503$	7.00000	0.312115	0.156057	+	0.987748i	$0.450122\pi$
$504$	6.00000	0.267261
$505$	36.0000	1.60198
$506$	0	0
$507$	9.00000	0.399704
$508$	−20.0000	−0.887357
$509$	19.0000	0.842160	0.421080	−	0.907023i	$-0.361651\pi$
$509$	19.0000	0.842160	0.421080	+	0.907023i	$0.361651\pi$
$510$	−4.00000	−0.177123
$511$	18.0000	0.796273
$512$	−1.00000	−0.0441942
$513$	5.00000	0.220755
$514$	8.00000	0.352865
$515$	−24.0000	−1.05757
$516$	−2.00000	−0.0880451
$517$	0	0
$518$	−9.00000	−0.395437
$519$	11.0000	0.482846
$520$	4.00000	0.175412
$521$	38.0000	1.66481	0.832405	−	0.554168i	$-0.186963\pi$
$521$	38.0000	1.66481	0.832405	+	0.554168i	$0.186963\pi$
$522$	10.0000	0.437688
$523$	−21.0000	−0.918266	−0.459133	−	0.888368i	$-0.651840\pi$
$523$	−21.0000	−0.918266	−0.459133	+	0.888368i	$0.651840\pi$
$524$	−2.00000	−0.0873704
$525$	3.00000	0.130931
$526$	16.0000	0.697633
$527$	16.0000	0.696971
$528$	0	0
$529$	−22.0000	−0.956522
$530$	−2.00000	−0.0868744
$531$	6.00000	0.260378
$532$	3.00000	0.130066
$533$	12.0000	0.519778
$534$	−4.00000	−0.173097
$535$	14.0000	0.605273
$536$	12.0000	0.518321
$537$	−17.0000	−0.733604
$538$	21.0000	0.905374
$539$	0	0
$540$	10.0000	0.430331
$541$	2.00000	0.0859867	0.0429934	−	0.999075i	$-0.486311\pi$
$541$	2.00000	0.0859867	0.0429934	+	0.999075i	$0.486311\pi$
$542$	−12.0000	−0.515444
$543$	14.0000	0.600798
$544$	2.00000	0.0857493
$545$	−2.00000	−0.0856706
$546$	−6.00000	−0.256776
$547$	−19.0000	−0.812381	−0.406191	−	0.913788i	$-0.633143\pi$
$547$	−19.0000	−0.812381	−0.406191	+	0.913788i	$0.633143\pi$
$548$	−10.0000	−0.427179
$549$	12.0000	0.512148
$550$	0	0
$551$	5.00000	0.213007
$552$	−1.00000	−0.0425628
$553$	−12.0000	−0.510292
$554$	−2.00000	−0.0849719
$555$	−6.00000	−0.254686
$556$	16.0000	0.678551
$557$	−30.0000	−1.27114	−0.635570	−	0.772043i	$-0.719235\pi$
$557$	−30.0000	−1.27114	−0.635570	+	0.772043i	$0.719235\pi$
$558$	−16.0000	−0.677334
$559$	−4.00000	−0.169182
$560$	6.00000	0.253546
$561$	0	0
$562$	−20.0000	−0.843649
$563$	−9.00000	−0.379305	−0.189652	−	0.981851i	$-0.560736\pi$
$563$	−9.00000	−0.379305	−0.189652	+	0.981851i	$0.560736\pi$
$564$	3.00000	0.126323
$565$	12.0000	0.504844
$566$	−4.00000	−0.168133
$567$	3.00000	0.125988
$568$	14.0000	0.587427
$569$	−24.0000	−1.00613	−0.503066	−	0.864248i	$-0.667795\pi$
$569$	−24.0000	−1.00613	−0.503066	+	0.864248i	$0.667795\pi$
$570$	2.00000	0.0837708
$571$	40.0000	1.67395	0.836974	−	0.547243i	$-0.184323\pi$
$571$	40.0000	1.67395	0.836974	+	0.547243i	$0.184323\pi$
$572$	0	0
$573$	−3.00000	−0.125327
$574$	18.0000	0.751305
$575$	1.00000	0.0417029
$576$	−2.00000	−0.0833333
$577$	−10.0000	−0.416305	−0.208153	−	0.978096i	$-0.566745\pi$
$577$	−10.0000	−0.416305	−0.208153	+	0.978096i	$0.566745\pi$
$578$	13.0000	0.540729
$579$	−14.0000	−0.581820
$580$	10.0000	0.415227
$581$	−6.00000	−0.248922
$582$	−4.00000	−0.165805
$583$	0	0
$584$	−6.00000	−0.248282
$585$	8.00000	0.330759
$586$	9.00000	0.371787
$587$	−42.0000	−1.73353	−0.866763	−	0.498721i	$-0.833803\pi$
$587$	−42.0000	−1.73353	−0.866763	+	0.498721i	$0.833803\pi$
$588$	−2.00000	−0.0824786
$589$	−8.00000	−0.329634
$590$	6.00000	0.247016
$591$	12.0000	0.493614
$592$	3.00000	0.123299
$593$	27.0000	1.10876	0.554379	−	0.832265i	$-0.312956\pi$
$593$	27.0000	1.10876	0.554379	+	0.832265i	$0.312956\pi$
$594$	0	0
$595$	−12.0000	−0.491952
$596$	0	0
$597$	−8.00000	−0.327418
$598$	−2.00000	−0.0817861
$599$	−44.0000	−1.79779	−0.898896	−	0.438163i	$-0.855629\pi$
$599$	−44.0000	−1.79779	−0.898896	+	0.438163i	$0.855629\pi$
$600$	−1.00000	−0.0408248
$601$	26.0000	1.06056	0.530281	−	0.847822i	$-0.322086\pi$
$601$	26.0000	1.06056	0.530281	+	0.847822i	$0.322086\pi$
$602$	−6.00000	−0.244542
$603$	24.0000	0.977356
$604$	0	0
$605$	0	0
$606$	18.0000	0.731200
$607$	−16.0000	−0.649420	−0.324710	−	0.945814i	$-0.605267\pi$
$607$	−16.0000	−0.649420	−0.324710	+	0.945814i	$0.605267\pi$
$608$	−1.00000	−0.0405554
$609$	−15.0000	−0.607831
$610$	12.0000	0.485866
$611$	6.00000	0.242734
$612$	4.00000	0.161690
$613$	44.0000	1.77714	0.888572	−	0.458738i	$-0.151698\pi$
$613$	44.0000	1.77714	0.888572	+	0.458738i	$0.151698\pi$
$614$	1.00000	0.0403567
$615$	12.0000	0.483887
$616$	0	0
$617$	−3.00000	−0.120775	−0.0603877	−	0.998175i	$-0.519234\pi$
$617$	−3.00000	−0.120775	−0.0603877	+	0.998175i	$0.519234\pi$
$618$	−12.0000	−0.482711
$619$	46.0000	1.84890	0.924448	−	0.381308i	$-0.124526\pi$
$619$	46.0000	1.84890	0.924448	+	0.381308i	$0.124526\pi$
$620$	−16.0000	−0.642575
$621$	−5.00000	−0.200643
$622$	−24.0000	−0.962312
$623$	−12.0000	−0.480770
$624$	2.00000	0.0800641
$625$	−19.0000	−0.760000
$626$	27.0000	1.07914
$627$	0	0
$628$	−4.00000	−0.159617
$629$	−6.00000	−0.239236
$630$	12.0000	0.478091
$631$	31.0000	1.23409	0.617045	−	0.786928i	$-0.288330\pi$
$631$	31.0000	1.23409	0.617045	+	0.786928i	$0.288330\pi$
$632$	4.00000	0.159111
$633$	5.00000	0.198732
$634$	6.00000	0.238290
$635$	−40.0000	−1.58735
$636$	−1.00000	−0.0396526
$637$	−4.00000	−0.158486
$638$	0	0
$639$	28.0000	1.10766
$640$	−2.00000	−0.0790569
$641$	2.00000	0.0789953	0.0394976	−	0.999220i	$-0.487424\pi$
$641$	2.00000	0.0789953	0.0394976	+	0.999220i	$0.487424\pi$
$642$	7.00000	0.276268
$643$	34.0000	1.34083	0.670415	−	0.741987i	$-0.266116\pi$
$643$	34.0000	1.34083	0.670415	+	0.741987i	$0.266116\pi$
$644$	−3.00000	−0.118217
$645$	−4.00000	−0.157500
$646$	2.00000	0.0786889
$647$	21.0000	0.825595	0.412798	−	0.910823i	$-0.364552\pi$
$647$	21.0000	0.825595	0.412798	+	0.910823i	$0.364552\pi$
$648$	−1.00000	−0.0392837
$649$	0	0
$650$	−2.00000	−0.0784465
$651$	24.0000	0.940634
$652$	10.0000	0.391630
$653$	−46.0000	−1.80012	−0.900060	−	0.435767i	$-0.856477\pi$
$653$	−46.0000	−1.80012	−0.900060	+	0.435767i	$0.856477\pi$
$654$	−1.00000	−0.0391031
$655$	−4.00000	−0.156293
$656$	−6.00000	−0.234261
$657$	−12.0000	−0.468165
$658$	9.00000	0.350857
$659$	28.0000	1.09073	0.545363	−	0.838200i	$-0.316392\pi$
$659$	28.0000	1.09073	0.545363	+	0.838200i	$0.316392\pi$
$660$	0	0
$661$	23.0000	0.894596	0.447298	−	0.894385i	$-0.352386\pi$
$661$	23.0000	0.894596	0.447298	+	0.894385i	$0.352386\pi$
$662$	−11.0000	−0.427527
$663$	−4.00000	−0.155347
$664$	2.00000	0.0776151
$665$	6.00000	0.232670
$666$	6.00000	0.232495
$667$	−5.00000	−0.193601
$668$	22.0000	0.851206
$669$	2.00000	0.0773245
$670$	24.0000	0.927201
$671$	0	0
$672$	3.00000	0.115728
$673$	−48.0000	−1.85026	−0.925132	−	0.379646i	$-0.876046\pi$
$673$	−48.0000	−1.85026	−0.925132	+	0.379646i	$0.876046\pi$
$674$	26.0000	1.00148
$675$	−5.00000	−0.192450
$676$	−9.00000	−0.346154
$677$	35.0000	1.34516	0.672580	−	0.740025i	$-0.265186\pi$
$677$	35.0000	1.34516	0.672580	+	0.740025i	$0.265186\pi$
$678$	6.00000	0.230429
$679$	−12.0000	−0.460518
$680$	4.00000	0.153393
$681$	−24.0000	−0.919682
$682$	0	0
$683$	−4.00000	−0.153056	−0.0765279	−	0.997067i	$-0.524383\pi$
$683$	−4.00000	−0.153056	−0.0765279	+	0.997067i	$0.524383\pi$
$684$	−2.00000	−0.0764719
$685$	−20.0000	−0.764161
$686$	15.0000	0.572703
$687$	−20.0000	−0.763048
$688$	2.00000	0.0762493
$689$	−2.00000	−0.0761939
$690$	−2.00000	−0.0761387
$691$	−2.00000	−0.0760836	−0.0380418	−	0.999276i	$-0.512112\pi$
$691$	−2.00000	−0.0760836	−0.0380418	+	0.999276i	$0.512112\pi$
$692$	−11.0000	−0.418157
$693$	0	0
$694$	−14.0000	−0.531433
$695$	32.0000	1.21383
$696$	5.00000	0.189525
$697$	12.0000	0.454532
$698$	26.0000	0.984115
$699$	17.0000	0.642999
$700$	−3.00000	−0.113389
$701$	−12.0000	−0.453234	−0.226617	−	0.973984i	$-0.572767\pi$
$701$	−12.0000	−0.453234	−0.226617	+	0.973984i	$0.572767\pi$
$702$	10.0000	0.377426
$703$	3.00000	0.113147
$704$	0	0
$705$	6.00000	0.225973
$706$	−29.0000	−1.09143
$707$	54.0000	2.03088
$708$	3.00000	0.112747
$709$	40.0000	1.50223	0.751116	−	0.660171i	$-0.229516\pi$
$709$	40.0000	1.50223	0.751116	+	0.660171i	$0.229516\pi$
$710$	28.0000	1.05082
$711$	8.00000	0.300023
$712$	4.00000	0.149906
$713$	8.00000	0.299602
$714$	−6.00000	−0.224544
$715$	0	0
$716$	17.0000	0.635320
$717$	−5.00000	−0.186728
$718$	−8.00000	−0.298557
$719$	24.0000	0.895049	0.447524	−	0.894272i	$-0.352306\pi$
$719$	24.0000	0.895049	0.447524	+	0.894272i	$0.352306\pi$
$720$	−4.00000	−0.149071
$721$	−36.0000	−1.34071
$722$	−1.00000	−0.0372161
$723$	28.0000	1.04133
$724$	−14.0000	−0.520306
$725$	−5.00000	−0.185695
$726$	0	0
$727$	−7.00000	−0.259616	−0.129808	−	0.991539i	$-0.541436\pi$
$727$	−7.00000	−0.259616	−0.129808	+	0.991539i	$0.541436\pi$
$728$	6.00000	0.222375
$729$	13.0000	0.481481
$730$	−12.0000	−0.444140
$731$	−4.00000	−0.147945
$732$	6.00000	0.221766
$733$	−32.0000	−1.18195	−0.590973	−	0.806691i	$-0.701256\pi$
$733$	−32.0000	−1.18195	−0.590973	+	0.806691i	$0.701256\pi$
$734$	−7.00000	−0.258375
$735$	−4.00000	−0.147542
$736$	1.00000	0.0368605
$737$	0	0
$738$	−12.0000	−0.441726
$739$	−40.0000	−1.47142	−0.735712	−	0.677295i	$-0.763152\pi$
$739$	−40.0000	−1.47142	−0.735712	+	0.677295i	$0.763152\pi$
$740$	6.00000	0.220564
$741$	2.00000	0.0734718
$742$	−3.00000	−0.110133
$743$	6.00000	0.220119	0.110059	−	0.993925i	$-0.464896\pi$
$743$	6.00000	0.220119	0.110059	+	0.993925i	$0.464896\pi$
$744$	−8.00000	−0.293294
$745$	0	0
$746$	1.00000	0.0366126
$747$	4.00000	0.146352
$748$	0	0
$749$	21.0000	0.767323
$750$	−12.0000	−0.438178
$751$	4.00000	0.145962	0.0729810	−	0.997333i	$-0.476749\pi$
$751$	4.00000	0.145962	0.0729810	+	0.997333i	$0.476749\pi$
$752$	−3.00000	−0.109399
$753$	18.0000	0.655956
$754$	10.0000	0.364179
$755$	0	0
$756$	15.0000	0.545545
$757$	8.00000	0.290765	0.145382	−	0.989376i	$-0.453559\pi$
$757$	8.00000	0.290765	0.145382	+	0.989376i	$0.453559\pi$
$758$	35.0000	1.27126
$759$	0	0
$760$	−2.00000	−0.0725476
$761$	−1.00000	−0.0362500	−0.0181250	−	0.999836i	$-0.505770\pi$
$761$	−1.00000	−0.0362500	−0.0181250	+	0.999836i	$0.505770\pi$
$762$	−20.0000	−0.724524
$763$	−3.00000	−0.108607
$764$	3.00000	0.108536
$765$	8.00000	0.289241
$766$	−4.00000	−0.144526
$767$	6.00000	0.216647
$768$	−1.00000	−0.0360844
$769$	−31.0000	−1.11789	−0.558944	−	0.829205i	$-0.688793\pi$
$769$	−31.0000	−1.11789	−0.558944	+	0.829205i	$0.688793\pi$
$770$	0	0
$771$	8.00000	0.288113
$772$	14.0000	0.503871
$773$	−49.0000	−1.76241	−0.881204	−	0.472737i	$-0.843266\pi$
$773$	−49.0000	−1.76241	−0.881204	+	0.472737i	$0.843266\pi$
$774$	4.00000	0.143777
$775$	8.00000	0.287368
$776$	4.00000	0.143592
$777$	−9.00000	−0.322873
$778$	24.0000	0.860442
$779$	−6.00000	−0.214972
$780$	4.00000	0.143223
$781$	0	0
$782$	−2.00000	−0.0715199
$783$	25.0000	0.893427
$784$	2.00000	0.0714286
$785$	−8.00000	−0.285532
$786$	−2.00000	−0.0713376
$787$	19.0000	0.677277	0.338638	−	0.940917i	$-0.390034\pi$
$787$	19.0000	0.677277	0.338638	+	0.940917i	$0.390034\pi$
$788$	−12.0000	−0.427482
$789$	16.0000	0.569615
$790$	8.00000	0.284627
$791$	18.0000	0.640006
$792$	0	0
$793$	12.0000	0.426132
$794$	2.00000	0.0709773
$795$	−2.00000	−0.0709327
$796$	8.00000	0.283552
$797$	38.0000	1.34603	0.673015	−	0.739629i	$-0.264999\pi$
$797$	38.0000	1.34603	0.673015	+	0.739629i	$0.264999\pi$
$798$	3.00000	0.106199
$799$	6.00000	0.212265
$800$	1.00000	0.0353553
$801$	8.00000	0.282666
$802$	−14.0000	−0.494357
$803$	0	0
$804$	12.0000	0.423207
$805$	−6.00000	−0.211472
$806$	−16.0000	−0.563576
$807$	21.0000	0.739235
$808$	−18.0000	−0.633238
$809$	−23.0000	−0.808637	−0.404318	−	0.914618i	$-0.632491\pi$
$809$	−23.0000	−0.808637	−0.404318	+	0.914618i	$0.632491\pi$
$810$	−2.00000	−0.0702728
$811$	−19.0000	−0.667180	−0.333590	−	0.942718i	$-0.608260\pi$
$811$	−19.0000	−0.667180	−0.333590	+	0.942718i	$0.608260\pi$
$812$	15.0000	0.526397
$813$	−12.0000	−0.420858
$814$	0	0
$815$	20.0000	0.700569
$816$	2.00000	0.0700140
$817$	2.00000	0.0699711
$818$	20.0000	0.699284
$819$	12.0000	0.419314
$820$	−12.0000	−0.419058
$821$	22.0000	0.767805	0.383903	−	0.923374i	$-0.374580\pi$
$821$	22.0000	0.767805	0.383903	+	0.923374i	$0.374580\pi$
$822$	−10.0000	−0.348790
$823$	11.0000	0.383436	0.191718	−	0.981450i	$-0.438594\pi$
$823$	11.0000	0.383436	0.191718	+	0.981450i	$0.438594\pi$
$824$	12.0000	0.418040
$825$	0	0
$826$	9.00000	0.313150
$827$	−28.0000	−0.973655	−0.486828	−	0.873498i	$-0.661846\pi$
$827$	−28.0000	−0.973655	−0.486828	+	0.873498i	$0.661846\pi$
$828$	2.00000	0.0695048
$829$	34.0000	1.18087	0.590434	−	0.807086i	$-0.298956\pi$
$829$	34.0000	1.18087	0.590434	+	0.807086i	$0.298956\pi$
$830$	4.00000	0.138842
$831$	−2.00000	−0.0693792
$832$	−2.00000	−0.0693375
$833$	−4.00000	−0.138592
$834$	16.0000	0.554035
$835$	44.0000	1.52268
$836$	0	0
$837$	−40.0000	−1.38260
$838$	22.0000	0.759977
$839$	14.0000	0.483334	0.241667	−	0.970359i	$-0.422306\pi$
$839$	14.0000	0.483334	0.241667	+	0.970359i	$0.422306\pi$
$840$	6.00000	0.207020
$841$	−4.00000	−0.137931
$842$	27.0000	0.930481
$843$	−20.0000	−0.688837
$844$	−5.00000	−0.172107
$845$	−18.0000	−0.619219
$846$	−6.00000	−0.206284
$847$	0	0
$848$	1.00000	0.0343401
$849$	−4.00000	−0.137280
$850$	−2.00000	−0.0685994
$851$	−3.00000	−0.102839
$852$	14.0000	0.479632
$853$	18.0000	0.616308	0.308154	−	0.951336i	$-0.400289\pi$
$853$	18.0000	0.616308	0.308154	+	0.951336i	$0.400289\pi$
$854$	18.0000	0.615947
$855$	−4.00000	−0.136797
$856$	−7.00000	−0.239255
$857$	−42.0000	−1.43469	−0.717346	−	0.696717i	$-0.754643\pi$
$857$	−42.0000	−1.43469	−0.717346	+	0.696717i	$0.754643\pi$
$858$	0	0
$859$	−30.0000	−1.02359	−0.511793	−	0.859109i	$-0.671019\pi$
$859$	−30.0000	−1.02359	−0.511793	+	0.859109i	$0.671019\pi$
$860$	4.00000	0.136399
$861$	18.0000	0.613438
$862$	16.0000	0.544962
$863$	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
$865$	−22.0000	−0.748022
$866$	−6.00000	−0.203888
$867$	13.0000	0.441503
$868$	−24.0000	−0.814613
$869$	0	0
$870$	10.0000	0.339032
$871$	24.0000	0.813209
$872$	1.00000	0.0338643
$873$	8.00000	0.270759
$874$	1.00000	0.0338255
$875$	−36.0000	−1.21702
$876$	−6.00000	−0.202721
$877$	−6.00000	−0.202606	−0.101303	−	0.994856i	$-0.532301\pi$
$877$	−6.00000	−0.202606	−0.101303	+	0.994856i	$0.532301\pi$
$878$	8.00000	0.269987
$879$	9.00000	0.303562
$880$	0	0
$881$	57.0000	1.92038	0.960189	−	0.279350i	$-0.0901189\pi$
$881$	57.0000	1.92038	0.960189	+	0.279350i	$0.0901189\pi$
$882$	4.00000	0.134687
$883$	−20.0000	−0.673054	−0.336527	−	0.941674i	$-0.609252\pi$
$883$	−20.0000	−0.673054	−0.336527	+	0.941674i	$0.609252\pi$
$884$	4.00000	0.134535
$885$	6.00000	0.201688
$886$	−18.0000	−0.604722
$887$	−14.0000	−0.470074	−0.235037	−	0.971986i	$-0.575521\pi$
$887$	−14.0000	−0.470074	−0.235037	+	0.971986i	$0.575521\pi$
$888$	3.00000	0.100673
$889$	−60.0000	−2.01234
$890$	8.00000	0.268161
$891$	0	0
$892$	−2.00000	−0.0669650
$893$	−3.00000	−0.100391
$894$	0	0
$895$	34.0000	1.13649
$896$	−3.00000	−0.100223
$897$	−2.00000	−0.0667781
$898$	6.00000	0.200223
$899$	−40.0000	−1.33407
$900$	2.00000	0.0666667
$901$	−2.00000	−0.0666297
$902$	0	0
$903$	−6.00000	−0.199667
$904$	−6.00000	−0.199557
$905$	−28.0000	−0.930751
$906$	0	0
$907$	−17.0000	−0.564476	−0.282238	−	0.959344i	$-0.591077\pi$
$907$	−17.0000	−0.564476	−0.282238	+	0.959344i	$0.591077\pi$
$908$	24.0000	0.796468
$909$	−36.0000	−1.19404
$910$	12.0000	0.397796
$911$	−12.0000	−0.397578	−0.198789	−	0.980042i	$-0.563701\pi$
$911$	−12.0000	−0.397578	−0.198789	+	0.980042i	$0.563701\pi$
$912$	−1.00000	−0.0331133
$913$	0	0
$914$	31.0000	1.02539
$915$	12.0000	0.396708
$916$	20.0000	0.660819
$917$	−6.00000	−0.198137
$918$	10.0000	0.330049
$919$	24.0000	0.791687	0.395843	−	0.918318i	$-0.370452\pi$
$919$	24.0000	0.791687	0.395843	+	0.918318i	$0.370452\pi$
$920$	2.00000	0.0659380
$921$	1.00000	0.0329511
$922$	22.0000	0.724531
$923$	28.0000	0.921631
$924$	0	0
$925$	−3.00000	−0.0986394
$926$	−16.0000	−0.525793
$927$	24.0000	0.788263
$928$	−5.00000	−0.164133
$929$	25.0000	0.820223	0.410112	−	0.912035i	$-0.365490\pi$
$929$	25.0000	0.820223	0.410112	+	0.912035i	$0.365490\pi$
$930$	−16.0000	−0.524661
$931$	2.00000	0.0655474
$932$	−17.0000	−0.556854
$933$	−24.0000	−0.785725
$934$	14.0000	0.458094
$935$	0	0
$936$	−4.00000	−0.130744
$937$	25.0000	0.816714	0.408357	−	0.912822i	$-0.366102\pi$
$937$	25.0000	0.816714	0.408357	+	0.912822i	$0.366102\pi$
$938$	36.0000	1.17544
$939$	27.0000	0.881112
$940$	−6.00000	−0.195698
$941$	−18.0000	−0.586783	−0.293392	−	0.955992i	$-0.594784\pi$
$941$	−18.0000	−0.586783	−0.293392	+	0.955992i	$0.594784\pi$
$942$	−4.00000	−0.130327
$943$	6.00000	0.195387
$944$	−3.00000	−0.0976417
$945$	30.0000	0.975900
$946$	0	0
$947$	24.0000	0.779895	0.389948	−	0.920837i	$-0.372493\pi$
$947$	24.0000	0.779895	0.389948	+	0.920837i	$0.372493\pi$
$948$	4.00000	0.129914
$949$	−12.0000	−0.389536
$950$	1.00000	0.0324443
$951$	6.00000	0.194563
$952$	6.00000	0.194461
$953$	24.0000	0.777436	0.388718	−	0.921357i	$-0.372918\pi$
$953$	24.0000	0.777436	0.388718	+	0.921357i	$0.372918\pi$
$954$	2.00000	0.0647524
$955$	6.00000	0.194155
$956$	5.00000	0.161712
$957$	0	0
$958$	−15.0000	−0.484628
$959$	−30.0000	−0.968751
$960$	−2.00000	−0.0645497
$961$	33.0000	1.06452
$962$	6.00000	0.193448
$963$	−14.0000	−0.451144
$964$	−28.0000	−0.901819
$965$	28.0000	0.901352
$966$	−3.00000	−0.0965234
$967$	−1.00000	−0.0321578	−0.0160789	−	0.999871i	$-0.505118\pi$
$967$	−1.00000	−0.0321578	−0.0160789	+	0.999871i	$0.505118\pi$
$968$	0	0
$969$	2.00000	0.0642493
$970$	8.00000	0.256865
$971$	29.0000	0.930654	0.465327	−	0.885139i	$-0.345937\pi$
$971$	29.0000	0.930654	0.465327	+	0.885139i	$0.345937\pi$
$972$	−16.0000	−0.513200
$973$	48.0000	1.53881
$974$	30.0000	0.961262
$975$	−2.00000	−0.0640513
$976$	−6.00000	−0.192055
$977$	18.0000	0.575871	0.287936	−	0.957650i	$-0.407031\pi$
$977$	18.0000	0.575871	0.287936	+	0.957650i	$0.407031\pi$
$978$	10.0000	0.319765
$979$	0	0
$980$	4.00000	0.127775
$981$	2.00000	0.0638551
$982$	−32.0000	−1.02116
$983$	−26.0000	−0.829271	−0.414636	−	0.909988i	$-0.636091\pi$
$983$	−26.0000	−0.829271	−0.414636	+	0.909988i	$0.636091\pi$
$984$	−6.00000	−0.191273
$985$	−24.0000	−0.764704
$986$	10.0000	0.318465
$987$	9.00000	0.286473
$988$	−2.00000	−0.0636285
$989$	−2.00000	−0.0635963
$990$	0	0
$991$	14.0000	0.444725	0.222362	−	0.974964i	$-0.428623\pi$
$991$	14.0000	0.444725	0.222362	+	0.974964i	$0.428623\pi$
$992$	8.00000	0.254000
$993$	−11.0000	−0.349074
$994$	42.0000	1.33216
$995$	16.0000	0.507234
$996$	2.00000	0.0633724
$997$	2.00000	0.0633406	0.0316703	−	0.999498i	$-0.489917\pi$
$997$	2.00000	0.0633406	0.0316703	+	0.999498i	$0.489917\pi$
$998$	−8.00000	−0.253236
$999$	15.0000	0.474579

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4598.2.a.c.1.1	✓	1
11.10	odd	2		4598.2.a.l.1.1	yes	1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4598.2.a.c.1.1	✓	1	1.1	even	1	trivial
4598.2.a.l.1.1	yes	1	11.10	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:	\( N \)	\(=\)	\( 4598 = 2 \cdot 11^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4598.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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