LMFDB - Embedded newform 1155.2.a.j.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1155,2,Mod(1,1155)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1155, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 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("1155.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1155 = 3 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1155.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:	$9.22272143346$
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	$\chi$	$=$	1155.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

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

\(q+1.00000 q^{2} -1.00000 q^{3} -1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} +1.00000 q^{7} -3.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} -1.00000 q^{11} +1.00000 q^{12} -2.00000 q^{13} +1.00000 q^{14} +1.00000 q^{15} -1.00000 q^{16} +6.00000 q^{17} +1.00000 q^{18} +4.00000 q^{19} +1.00000 q^{20} -1.00000 q^{21} -1.00000 q^{22} -4.00000 q^{23} +3.00000 q^{24} +1.00000 q^{25} -2.00000 q^{26} -1.00000 q^{27} -1.00000 q^{28} +10.0000 q^{29} +1.00000 q^{30} -4.00000 q^{31} +5.00000 q^{32} +1.00000 q^{33} +6.00000 q^{34} -1.00000 q^{35} -1.00000 q^{36} -2.00000 q^{37} +4.00000 q^{38} +2.00000 q^{39} +3.00000 q^{40} +10.0000 q^{41} -1.00000 q^{42} +12.0000 q^{43} +1.00000 q^{44} -1.00000 q^{45} -4.00000 q^{46} +1.00000 q^{48} +1.00000 q^{49} +1.00000 q^{50} -6.00000 q^{51} +2.00000 q^{52} +10.0000 q^{53} -1.00000 q^{54} +1.00000 q^{55} -3.00000 q^{56} -4.00000 q^{57} +10.0000 q^{58} -12.0000 q^{59} -1.00000 q^{60} -2.00000 q^{61} -4.00000 q^{62} +1.00000 q^{63} +7.00000 q^{64} +2.00000 q^{65} +1.00000 q^{66} +4.00000 q^{67} -6.00000 q^{68} +4.00000 q^{69} -1.00000 q^{70} +8.00000 q^{71} -3.00000 q^{72} -14.0000 q^{73} -2.00000 q^{74} -1.00000 q^{75} -4.00000 q^{76} -1.00000 q^{77} +2.00000 q^{78} +4.00000 q^{79} +1.00000 q^{80} +1.00000 q^{81} +10.0000 q^{82} +8.00000 q^{83} +1.00000 q^{84} -6.00000 q^{85} +12.0000 q^{86} -10.0000 q^{87} +3.00000 q^{88} +6.00000 q^{89} -1.00000 q^{90} -2.00000 q^{91} +4.00000 q^{92} +4.00000 q^{93} -4.00000 q^{95} -5.00000 q^{96} -10.0000 q^{97} +1.00000 q^{98} -1.00000 q^{99} +O(q^{100})\)

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	0.353553	−	0.935414i	$-0.384973\pi$
$2$	1.00000	0.707107	0.353553	+	0.935414i	$0.384973\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.00000	−0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−1.00000	−0.408248
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−3.00000	−1.06066
$9$	1.00000	0.333333
$10$	−1.00000	−0.316228
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	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	$0.589456\pi$
$14$	1.00000	0.267261
$15$	1.00000	0.258199
$16$	−1.00000	−0.250000
$17$	6.00000	1.45521	0.727607	−	0.685994i	$-0.240633\pi$
$17$	6.00000	1.45521	0.727607	+	0.685994i	$0.240633\pi$
$18$	1.00000	0.235702
$19$	4.00000	0.917663	0.458831	−	0.888523i	$-0.348268\pi$
$19$	4.00000	0.917663	0.458831	+	0.888523i	$0.348268\pi$
$20$	1.00000	0.223607
$21$	−1.00000	−0.218218
$22$	−1.00000	−0.213201
$23$	−4.00000	−0.834058	−0.417029	−	0.908893i	$-0.636929\pi$
$23$	−4.00000	−0.834058	−0.417029	+	0.908893i	$0.636929\pi$
$24$	3.00000	0.612372
$25$	1.00000	0.200000
$26$	−2.00000	−0.392232
$27$	−1.00000	−0.192450
$28$	−1.00000	−0.188982
$29$	10.0000	1.85695	0.928477	−	0.371391i	$-0.121119\pi$
$29$	10.0000	1.85695	0.928477	+	0.371391i	$0.121119\pi$
$30$	1.00000	0.182574
$31$	−4.00000	−0.718421	−0.359211	−	0.933257i	$-0.616954\pi$
$31$	−4.00000	−0.718421	−0.359211	+	0.933257i	$0.616954\pi$
$32$	5.00000	0.883883
$33$	1.00000	0.174078
$34$	6.00000	1.02899
$35$	−1.00000	−0.169031
$36$	−1.00000	−0.166667
$37$	−2.00000	−0.328798	−0.164399	−	0.986394i	$-0.552568\pi$
$37$	−2.00000	−0.328798	−0.164399	+	0.986394i	$0.552568\pi$
$38$	4.00000	0.648886
$39$	2.00000	0.320256
$40$	3.00000	0.474342
$41$	10.0000	1.56174	0.780869	−	0.624695i	$-0.214777\pi$
$41$	10.0000	1.56174	0.780869	+	0.624695i	$0.214777\pi$
$42$	−1.00000	−0.154303
$43$	12.0000	1.82998	0.914991	−	0.403473i	$-0.132197\pi$
$43$	12.0000	1.82998	0.914991	+	0.403473i	$0.132197\pi$
$44$	1.00000	0.150756
$45$	−1.00000	−0.149071
$46$	−4.00000	−0.589768
$47$	0	0		−	1.00000i	$-0.5\pi$
$47$	0	0			1.00000i	$0.5\pi$
$48$	1.00000	0.144338
$49$	1.00000	0.142857
$50$	1.00000	0.141421
$51$	−6.00000	−0.840168
$52$	2.00000	0.277350
$53$	10.0000	1.37361	0.686803	−	0.726844i	$-0.259014\pi$
$53$	10.0000	1.37361	0.686803	+	0.726844i	$0.259014\pi$
$54$	−1.00000	−0.136083
$55$	1.00000	0.134840
$56$	−3.00000	−0.400892
$57$	−4.00000	−0.529813
$58$	10.0000	1.31306
$59$	−12.0000	−1.56227	−0.781133	−	0.624364i	$-0.785358\pi$
$59$	−12.0000	−1.56227	−0.781133	+	0.624364i	$0.785358\pi$
$60$	−1.00000	−0.129099
$61$	−2.00000	−0.256074	−0.128037	−	0.991769i	$-0.540868\pi$
$61$	−2.00000	−0.256074	−0.128037	+	0.991769i	$0.540868\pi$
$62$	−4.00000	−0.508001
$63$	1.00000	0.125988
$64$	7.00000	0.875000
$65$	2.00000	0.248069
$66$	1.00000	0.123091
$67$	4.00000	0.488678	0.244339	−	0.969690i	$-0.421429\pi$
$67$	4.00000	0.488678	0.244339	+	0.969690i	$0.421429\pi$
$68$	−6.00000	−0.727607
$69$	4.00000	0.481543
$70$	−1.00000	−0.119523
$71$	8.00000	0.949425	0.474713	−	0.880141i	$-0.342552\pi$
$71$	8.00000	0.949425	0.474713	+	0.880141i	$0.342552\pi$
$72$	−3.00000	−0.353553
$73$	−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
$75$	−1.00000	−0.115470
$76$	−4.00000	−0.458831
$77$	−1.00000	−0.113961
$78$	2.00000	0.226455
$79$	4.00000	0.450035	0.225018	−	0.974355i	$-0.427756\pi$
$79$	4.00000	0.450035	0.225018	+	0.974355i	$0.427756\pi$
$80$	1.00000	0.111803
$81$	1.00000	0.111111
$82$	10.0000	1.10432
$83$	8.00000	0.878114	0.439057	−	0.898459i	$-0.355313\pi$
$83$	8.00000	0.878114	0.439057	+	0.898459i	$0.355313\pi$
$84$	1.00000	0.109109
$85$	−6.00000	−0.650791
$86$	12.0000	1.29399
$87$	−10.0000	−1.07211
$88$	3.00000	0.319801
$89$	6.00000	0.635999	0.317999	−	0.948091i	$-0.396989\pi$
$89$	6.00000	0.635999	0.317999	+	0.948091i	$0.396989\pi$
$90$	−1.00000	−0.105409
$91$	−2.00000	−0.209657
$92$	4.00000	0.417029
$93$	4.00000	0.414781
$94$	0	0
$95$	−4.00000	−0.410391
$96$	−5.00000	−0.510310
$97$	−10.0000	−1.01535	−0.507673	−	0.861550i	$-0.669494\pi$
$97$	−10.0000	−1.01535	−0.507673	+	0.861550i	$0.669494\pi$
$98$	1.00000	0.101015
$99$	−1.00000	−0.100504
$100$	−1.00000	−0.100000
$101$	−2.00000	−0.199007	−0.0995037	−	0.995037i	$-0.531726\pi$
$101$	−2.00000	−0.199007	−0.0995037	+	0.995037i	$0.531726\pi$
$102$	−6.00000	−0.594089
$103$	8.00000	0.788263	0.394132	−	0.919054i	$-0.371045\pi$
$103$	8.00000	0.788263	0.394132	+	0.919054i	$0.371045\pi$
$104$	6.00000	0.588348
$105$	1.00000	0.0975900
$106$	10.0000	0.971286
$107$	4.00000	0.386695	0.193347	−	0.981130i	$-0.438066\pi$
$107$	4.00000	0.386695	0.193347	+	0.981130i	$0.438066\pi$
$108$	1.00000	0.0962250
$109$	14.0000	1.34096	0.670478	−	0.741929i	$-0.266089\pi$
$109$	14.0000	1.34096	0.670478	+	0.741929i	$0.266089\pi$
$110$	1.00000	0.0953463
$111$	2.00000	0.189832
$112$	−1.00000	−0.0944911
$113$	−18.0000	−1.69330	−0.846649	−	0.532152i	$-0.821383\pi$
$113$	−18.0000	−1.69330	−0.846649	+	0.532152i	$0.821383\pi$
$114$	−4.00000	−0.374634
$115$	4.00000	0.373002
$116$	−10.0000	−0.928477
$117$	−2.00000	−0.184900
$118$	−12.0000	−1.10469
$119$	6.00000	0.550019
$120$	−3.00000	−0.273861
$121$	1.00000	0.0909091
$122$	−2.00000	−0.181071
$123$	−10.0000	−0.901670
$124$	4.00000	0.359211
$125$	−1.00000	−0.0894427
$126$	1.00000	0.0890871
$127$	8.00000	0.709885	0.354943	−	0.934888i	$-0.384500\pi$
$127$	8.00000	0.709885	0.354943	+	0.934888i	$0.384500\pi$
$128$	−3.00000	−0.265165
$129$	−12.0000	−1.05654
$130$	2.00000	0.175412
$131$	−4.00000	−0.349482	−0.174741	−	0.984614i	$-0.555909\pi$
$131$	−4.00000	−0.349482	−0.174741	+	0.984614i	$0.555909\pi$
$132$	−1.00000	−0.0870388
$133$	4.00000	0.346844
$134$	4.00000	0.345547
$135$	1.00000	0.0860663
$136$	−18.0000	−1.54349
$137$	−10.0000	−0.854358	−0.427179	−	0.904167i	$-0.640493\pi$
$137$	−10.0000	−0.854358	−0.427179	+	0.904167i	$0.640493\pi$
$138$	4.00000	0.340503
$139$	−4.00000	−0.339276	−0.169638	−	0.985506i	$-0.554260\pi$
$139$	−4.00000	−0.339276	−0.169638	+	0.985506i	$0.554260\pi$
$140$	1.00000	0.0845154
$141$	0	0
$142$	8.00000	0.671345
$143$	2.00000	0.167248
$144$	−1.00000	−0.0833333
$145$	−10.0000	−0.830455
$146$	−14.0000	−1.15865
$147$	−1.00000	−0.0824786
$148$	2.00000	0.164399
$149$	18.0000	1.47462	0.737309	−	0.675556i	$-0.236096\pi$
$149$	18.0000	1.47462	0.737309	+	0.675556i	$0.236096\pi$
$150$	−1.00000	−0.0816497
$151$	−4.00000	−0.325515	−0.162758	−	0.986666i	$-0.552039\pi$
$151$	−4.00000	−0.325515	−0.162758	+	0.986666i	$0.552039\pi$
$152$	−12.0000	−0.973329
$153$	6.00000	0.485071
$154$	−1.00000	−0.0805823
$155$	4.00000	0.321288
$156$	−2.00000	−0.160128
$157$	−14.0000	−1.11732	−0.558661	−	0.829396i	$-0.688685\pi$
$157$	−14.0000	−1.11732	−0.558661	+	0.829396i	$0.688685\pi$
$158$	4.00000	0.318223
$159$	−10.0000	−0.793052
$160$	−5.00000	−0.395285
$161$	−4.00000	−0.315244
$162$	1.00000	0.0785674
$163$	−20.0000	−1.56652	−0.783260	−	0.621694i	$-0.786445\pi$
$163$	−20.0000	−1.56652	−0.783260	+	0.621694i	$0.786445\pi$
$164$	−10.0000	−0.780869
$165$	−1.00000	−0.0778499
$166$	8.00000	0.620920
$167$	−12.0000	−0.928588	−0.464294	−	0.885681i	$-0.653692\pi$
$167$	−12.0000	−0.928588	−0.464294	+	0.885681i	$0.653692\pi$
$168$	3.00000	0.231455
$169$	−9.00000	−0.692308
$170$	−6.00000	−0.460179
$171$	4.00000	0.305888
$172$	−12.0000	−0.914991
$173$	26.0000	1.97674	0.988372	−	0.152057i	$-0.0485898\pi$
$173$	26.0000	1.97674	0.988372	+	0.152057i	$0.0485898\pi$
$174$	−10.0000	−0.758098
$175$	1.00000	0.0755929
$176$	1.00000	0.0753778
$177$	12.0000	0.901975
$178$	6.00000	0.449719
$179$	−4.00000	−0.298974	−0.149487	−	0.988764i	$-0.547762\pi$
$179$	−4.00000	−0.298974	−0.149487	+	0.988764i	$0.547762\pi$
$180$	1.00000	0.0745356
$181$	−10.0000	−0.743294	−0.371647	−	0.928374i	$-0.621207\pi$
$181$	−10.0000	−0.743294	−0.371647	+	0.928374i	$0.621207\pi$
$182$	−2.00000	−0.148250
$183$	2.00000	0.147844
$184$	12.0000	0.884652
$185$	2.00000	0.147043
$186$	4.00000	0.293294
$187$	−6.00000	−0.438763
$188$	0	0
$189$	−1.00000	−0.0727393
$190$	−4.00000	−0.290191
$191$	16.0000	1.15772	0.578860	−	0.815427i	$-0.303498\pi$
$191$	16.0000	1.15772	0.578860	+	0.815427i	$0.303498\pi$
$192$	−7.00000	−0.505181
$193$	14.0000	1.00774	0.503871	−	0.863779i	$-0.331909\pi$
$193$	14.0000	1.00774	0.503871	+	0.863779i	$0.331909\pi$
$194$	−10.0000	−0.717958
$195$	−2.00000	−0.143223
$196$	−1.00000	−0.0714286
$197$	26.0000	1.85242	0.926212	−	0.377004i	$-0.123046\pi$
$197$	26.0000	1.85242	0.926212	+	0.377004i	$0.123046\pi$
$198$	−1.00000	−0.0710669
$199$	4.00000	0.283552	0.141776	−	0.989899i	$-0.454719\pi$
$199$	4.00000	0.283552	0.141776	+	0.989899i	$0.454719\pi$
$200$	−3.00000	−0.212132
$201$	−4.00000	−0.282138
$202$	−2.00000	−0.140720
$203$	10.0000	0.701862
$204$	6.00000	0.420084
$205$	−10.0000	−0.698430
$206$	8.00000	0.557386
$207$	−4.00000	−0.278019
$208$	2.00000	0.138675
$209$	−4.00000	−0.276686
$210$	1.00000	0.0690066
$211$	−16.0000	−1.10149	−0.550743	−	0.834675i	$-0.685655\pi$
$211$	−16.0000	−1.10149	−0.550743	+	0.834675i	$0.685655\pi$
$212$	−10.0000	−0.686803
$213$	−8.00000	−0.548151
$214$	4.00000	0.273434
$215$	−12.0000	−0.818393
$216$	3.00000	0.204124
$217$	−4.00000	−0.271538
$218$	14.0000	0.948200
$219$	14.0000	0.946032
$220$	−1.00000	−0.0674200
$221$	−12.0000	−0.807207
$222$	2.00000	0.134231
$223$	−24.0000	−1.60716	−0.803579	−	0.595198i	$-0.797074\pi$
$223$	−24.0000	−1.60716	−0.803579	+	0.595198i	$0.797074\pi$
$224$	5.00000	0.334077
$225$	1.00000	0.0666667
$226$	−18.0000	−1.19734
$227$	8.00000	0.530979	0.265489	−	0.964114i	$-0.414466\pi$
$227$	8.00000	0.530979	0.265489	+	0.964114i	$0.414466\pi$
$228$	4.00000	0.264906
$229$	14.0000	0.925146	0.462573	−	0.886581i	$-0.346926\pi$
$229$	14.0000	0.925146	0.462573	+	0.886581i	$0.346926\pi$
$230$	4.00000	0.263752
$231$	1.00000	0.0657952
$232$	−30.0000	−1.96960
$233$	−26.0000	−1.70332	−0.851658	−	0.524097i	$-0.824403\pi$
$233$	−26.0000	−1.70332	−0.851658	+	0.524097i	$0.824403\pi$
$234$	−2.00000	−0.130744
$235$	0	0
$236$	12.0000	0.781133
$237$	−4.00000	−0.259828
$238$	6.00000	0.388922
$239$	24.0000	1.55243	0.776215	−	0.630468i	$-0.217137\pi$
$239$	24.0000	1.55243	0.776215	+	0.630468i	$0.217137\pi$
$240$	−1.00000	−0.0645497
$241$	2.00000	0.128831	0.0644157	−	0.997923i	$-0.479482\pi$
$241$	2.00000	0.128831	0.0644157	+	0.997923i	$0.479482\pi$
$242$	1.00000	0.0642824
$243$	−1.00000	−0.0641500
$244$	2.00000	0.128037
$245$	−1.00000	−0.0638877
$246$	−10.0000	−0.637577
$247$	−8.00000	−0.509028
$248$	12.0000	0.762001
$249$	−8.00000	−0.506979
$250$	−1.00000	−0.0632456
$251$	12.0000	0.757433	0.378717	−	0.925513i	$-0.376365\pi$
$251$	12.0000	0.757433	0.378717	+	0.925513i	$0.376365\pi$
$252$	−1.00000	−0.0629941
$253$	4.00000	0.251478
$254$	8.00000	0.501965
$255$	6.00000	0.375735
$256$	−17.0000	−1.06250
$257$	−2.00000	−0.124757	−0.0623783	−	0.998053i	$-0.519869\pi$
$257$	−2.00000	−0.124757	−0.0623783	+	0.998053i	$0.519869\pi$
$258$	−12.0000	−0.747087
$259$	−2.00000	−0.124274
$260$	−2.00000	−0.124035
$261$	10.0000	0.618984
$262$	−4.00000	−0.247121
$263$	−24.0000	−1.47990	−0.739952	−	0.672660i	$-0.765152\pi$
$263$	−24.0000	−1.47990	−0.739952	+	0.672660i	$0.765152\pi$
$264$	−3.00000	−0.184637
$265$	−10.0000	−0.614295
$266$	4.00000	0.245256
$267$	−6.00000	−0.367194
$268$	−4.00000	−0.244339
$269$	10.0000	0.609711	0.304855	−	0.952399i	$-0.401392\pi$
$269$	10.0000	0.609711	0.304855	+	0.952399i	$0.401392\pi$
$270$	1.00000	0.0608581
$271$	−8.00000	−0.485965	−0.242983	−	0.970031i	$-0.578126\pi$
$271$	−8.00000	−0.485965	−0.242983	+	0.970031i	$0.578126\pi$
$272$	−6.00000	−0.363803
$273$	2.00000	0.121046
$274$	−10.0000	−0.604122
$275$	−1.00000	−0.0603023
$276$	−4.00000	−0.240772
$277$	2.00000	0.120168	0.0600842	−	0.998193i	$-0.480863\pi$
$277$	2.00000	0.120168	0.0600842	+	0.998193i	$0.480863\pi$
$278$	−4.00000	−0.239904
$279$	−4.00000	−0.239474
$280$	3.00000	0.179284
$281$	30.0000	1.78965	0.894825	−	0.446417i	$-0.147300\pi$
$281$	30.0000	1.78965	0.894825	+	0.446417i	$0.147300\pi$
$282$	0	0
$283$	−28.0000	−1.66443	−0.832214	−	0.554455i	$-0.812927\pi$
$283$	−28.0000	−1.66443	−0.832214	+	0.554455i	$0.812927\pi$
$284$	−8.00000	−0.474713
$285$	4.00000	0.236940
$286$	2.00000	0.118262
$287$	10.0000	0.590281
$288$	5.00000	0.294628
$289$	19.0000	1.11765
$290$	−10.0000	−0.587220
$291$	10.0000	0.586210
$292$	14.0000	0.819288
$293$	18.0000	1.05157	0.525786	−	0.850617i	$-0.323771\pi$
$293$	18.0000	1.05157	0.525786	+	0.850617i	$0.323771\pi$
$294$	−1.00000	−0.0583212
$295$	12.0000	0.698667
$296$	6.00000	0.348743
$297$	1.00000	0.0580259
$298$	18.0000	1.04271
$299$	8.00000	0.462652
$300$	1.00000	0.0577350
$301$	12.0000	0.691669
$302$	−4.00000	−0.230174
$303$	2.00000	0.114897
$304$	−4.00000	−0.229416
$305$	2.00000	0.114520
$306$	6.00000	0.342997
$307$	12.0000	0.684876	0.342438	−	0.939540i	$-0.388747\pi$
$307$	12.0000	0.684876	0.342438	+	0.939540i	$0.388747\pi$
$308$	1.00000	0.0569803
$309$	−8.00000	−0.455104
$310$	4.00000	0.227185
$311$	8.00000	0.453638	0.226819	−	0.973937i	$-0.427167\pi$
$311$	8.00000	0.453638	0.226819	+	0.973937i	$0.427167\pi$
$312$	−6.00000	−0.339683
$313$	30.0000	1.69570	0.847850	−	0.530236i	$-0.177897\pi$
$313$	30.0000	1.69570	0.847850	+	0.530236i	$0.177897\pi$
$314$	−14.0000	−0.790066
$315$	−1.00000	−0.0563436
$316$	−4.00000	−0.225018
$317$	18.0000	1.01098	0.505490	−	0.862832i	$-0.331312\pi$
$317$	18.0000	1.01098	0.505490	+	0.862832i	$0.331312\pi$
$318$	−10.0000	−0.560772
$319$	−10.0000	−0.559893
$320$	−7.00000	−0.391312
$321$	−4.00000	−0.223258
$322$	−4.00000	−0.222911
$323$	24.0000	1.33540
$324$	−1.00000	−0.0555556
$325$	−2.00000	−0.110940
$326$	−20.0000	−1.10770
$327$	−14.0000	−0.774202
$328$	−30.0000	−1.65647
$329$	0	0
$330$	−1.00000	−0.0550482
$331$	−12.0000	−0.659580	−0.329790	−	0.944054i	$-0.606978\pi$
$331$	−12.0000	−0.659580	−0.329790	+	0.944054i	$0.606978\pi$
$332$	−8.00000	−0.439057
$333$	−2.00000	−0.109599
$334$	−12.0000	−0.656611
$335$	−4.00000	−0.218543
$336$	1.00000	0.0545545
$337$	22.0000	1.19842	0.599208	−	0.800593i	$-0.295482\pi$
$337$	22.0000	1.19842	0.599208	+	0.800593i	$0.295482\pi$
$338$	−9.00000	−0.489535
$339$	18.0000	0.977626
$340$	6.00000	0.325396
$341$	4.00000	0.216612
$342$	4.00000	0.216295
$343$	1.00000	0.0539949
$344$	−36.0000	−1.94099
$345$	−4.00000	−0.215353
$346$	26.0000	1.39777
$347$	−28.0000	−1.50312	−0.751559	−	0.659665i	$-0.770698\pi$
$347$	−28.0000	−1.50312	−0.751559	+	0.659665i	$0.770698\pi$
$348$	10.0000	0.536056
$349$	30.0000	1.60586	0.802932	−	0.596071i	$-0.203272\pi$
$349$	30.0000	1.60586	0.802932	+	0.596071i	$0.203272\pi$
$350$	1.00000	0.0534522
$351$	2.00000	0.106752
$352$	−5.00000	−0.266501
$353$	−18.0000	−0.958043	−0.479022	−	0.877803i	$-0.659008\pi$
$353$	−18.0000	−0.958043	−0.479022	+	0.877803i	$0.659008\pi$
$354$	12.0000	0.637793
$355$	−8.00000	−0.424596
$356$	−6.00000	−0.317999
$357$	−6.00000	−0.317554
$358$	−4.00000	−0.211407
$359$	24.0000	1.26667	0.633336	−	0.773877i	$-0.281685\pi$
$359$	24.0000	1.26667	0.633336	+	0.773877i	$0.281685\pi$
$360$	3.00000	0.158114
$361$	−3.00000	−0.157895
$362$	−10.0000	−0.525588
$363$	−1.00000	−0.0524864
$364$	2.00000	0.104828
$365$	14.0000	0.732793
$366$	2.00000	0.104542
$367$	−8.00000	−0.417597	−0.208798	−	0.977959i	$-0.566955\pi$
$367$	−8.00000	−0.417597	−0.208798	+	0.977959i	$0.566955\pi$
$368$	4.00000	0.208514
$369$	10.0000	0.520579
$370$	2.00000	0.103975
$371$	10.0000	0.519174
$372$	−4.00000	−0.207390
$373$	−6.00000	−0.310668	−0.155334	−	0.987862i	$-0.549645\pi$
$373$	−6.00000	−0.310668	−0.155334	+	0.987862i	$0.549645\pi$
$374$	−6.00000	−0.310253
$375$	1.00000	0.0516398
$376$	0	0
$377$	−20.0000	−1.03005
$378$	−1.00000	−0.0514344
$379$	4.00000	0.205466	0.102733	−	0.994709i	$-0.467241\pi$
$379$	4.00000	0.205466	0.102733	+	0.994709i	$0.467241\pi$
$380$	4.00000	0.205196
$381$	−8.00000	−0.409852
$382$	16.0000	0.818631
$383$	−32.0000	−1.63512	−0.817562	−	0.575841i	$-0.804675\pi$
$383$	−32.0000	−1.63512	−0.817562	+	0.575841i	$0.804675\pi$
$384$	3.00000	0.153093
$385$	1.00000	0.0509647
$386$	14.0000	0.712581
$387$	12.0000	0.609994
$388$	10.0000	0.507673
$389$	22.0000	1.11544	0.557722	−	0.830028i	$-0.311675\pi$
$389$	22.0000	1.11544	0.557722	+	0.830028i	$0.311675\pi$
$390$	−2.00000	−0.101274
$391$	−24.0000	−1.21373
$392$	−3.00000	−0.151523
$393$	4.00000	0.201773
$394$	26.0000	1.30986
$395$	−4.00000	−0.201262
$396$	1.00000	0.0502519
$397$	−6.00000	−0.301131	−0.150566	−	0.988600i	$-0.548110\pi$
$397$	−6.00000	−0.301131	−0.150566	+	0.988600i	$0.548110\pi$
$398$	4.00000	0.200502
$399$	−4.00000	−0.200250
$400$	−1.00000	−0.0500000
$401$	18.0000	0.898877	0.449439	−	0.893311i	$-0.351624\pi$
$401$	18.0000	0.898877	0.449439	+	0.893311i	$0.351624\pi$
$402$	−4.00000	−0.199502
$403$	8.00000	0.398508
$404$	2.00000	0.0995037
$405$	−1.00000	−0.0496904
$406$	10.0000	0.496292
$407$	2.00000	0.0991363
$408$	18.0000	0.891133
$409$	−22.0000	−1.08783	−0.543915	−	0.839140i	$-0.683059\pi$
$409$	−22.0000	−1.08783	−0.543915	+	0.839140i	$0.683059\pi$
$410$	−10.0000	−0.493865
$411$	10.0000	0.493264
$412$	−8.00000	−0.394132
$413$	−12.0000	−0.590481
$414$	−4.00000	−0.196589
$415$	−8.00000	−0.392705
$416$	−10.0000	−0.490290
$417$	4.00000	0.195881
$418$	−4.00000	−0.195646
$419$	4.00000	0.195413	0.0977064	−	0.995215i	$-0.468849\pi$
$419$	4.00000	0.195413	0.0977064	+	0.995215i	$0.468849\pi$
$420$	−1.00000	−0.0487950
$421$	6.00000	0.292422	0.146211	−	0.989253i	$-0.453292\pi$
$421$	6.00000	0.292422	0.146211	+	0.989253i	$0.453292\pi$
$422$	−16.0000	−0.778868
$423$	0	0
$424$	−30.0000	−1.45693
$425$	6.00000	0.291043
$426$	−8.00000	−0.387601
$427$	−2.00000	−0.0967868
$428$	−4.00000	−0.193347
$429$	−2.00000	−0.0965609
$430$	−12.0000	−0.578691
$431$	40.0000	1.92673	0.963366	−	0.268190i	$-0.0864254\pi$
$431$	40.0000	1.92673	0.963366	+	0.268190i	$0.0864254\pi$
$432$	1.00000	0.0481125
$433$	−2.00000	−0.0961139	−0.0480569	−	0.998845i	$-0.515303\pi$
$433$	−2.00000	−0.0961139	−0.0480569	+	0.998845i	$0.515303\pi$
$434$	−4.00000	−0.192006
$435$	10.0000	0.479463
$436$	−14.0000	−0.670478
$437$	−16.0000	−0.765384
$438$	14.0000	0.668946
$439$	−8.00000	−0.381819	−0.190910	−	0.981608i	$-0.561144\pi$
$439$	−8.00000	−0.381819	−0.190910	+	0.981608i	$0.561144\pi$
$440$	−3.00000	−0.143019
$441$	1.00000	0.0476190
$442$	−12.0000	−0.570782
$443$	−8.00000	−0.380091	−0.190046	−	0.981775i	$-0.560864\pi$
$443$	−8.00000	−0.380091	−0.190046	+	0.981775i	$0.560864\pi$
$444$	−2.00000	−0.0949158
$445$	−6.00000	−0.284427
$446$	−24.0000	−1.13643
$447$	−18.0000	−0.851371
$448$	7.00000	0.330719
$449$	18.0000	0.849473	0.424736	−	0.905317i	$-0.360367\pi$
$449$	18.0000	0.849473	0.424736	+	0.905317i	$0.360367\pi$
$450$	1.00000	0.0471405
$451$	−10.0000	−0.470882
$452$	18.0000	0.846649
$453$	4.00000	0.187936
$454$	8.00000	0.375459
$455$	2.00000	0.0937614
$456$	12.0000	0.561951
$457$	−18.0000	−0.842004	−0.421002	−	0.907060i	$-0.638322\pi$
$457$	−18.0000	−0.842004	−0.421002	+	0.907060i	$0.638322\pi$
$458$	14.0000	0.654177
$459$	−6.00000	−0.280056
$460$	−4.00000	−0.186501
$461$	30.0000	1.39724	0.698620	−	0.715493i	$-0.253798\pi$
$461$	30.0000	1.39724	0.698620	+	0.715493i	$0.253798\pi$
$462$	1.00000	0.0465242
$463$	16.0000	0.743583	0.371792	−	0.928316i	$-0.378744\pi$
$463$	16.0000	0.743583	0.371792	+	0.928316i	$0.378744\pi$
$464$	−10.0000	−0.464238
$465$	−4.00000	−0.185496
$466$	−26.0000	−1.20443
$467$	−4.00000	−0.185098	−0.0925490	−	0.995708i	$-0.529501\pi$
$467$	−4.00000	−0.185098	−0.0925490	+	0.995708i	$0.529501\pi$
$468$	2.00000	0.0924500
$469$	4.00000	0.184703
$470$	0	0
$471$	14.0000	0.645086
$472$	36.0000	1.65703
$473$	−12.0000	−0.551761
$474$	−4.00000	−0.183726
$475$	4.00000	0.183533
$476$	−6.00000	−0.275010
$477$	10.0000	0.457869
$478$	24.0000	1.09773
$479$	−8.00000	−0.365529	−0.182765	−	0.983157i	$-0.558505\pi$
$479$	−8.00000	−0.365529	−0.182765	+	0.983157i	$0.558505\pi$
$480$	5.00000	0.228218
$481$	4.00000	0.182384
$482$	2.00000	0.0910975
$483$	4.00000	0.182006
$484$	−1.00000	−0.0454545
$485$	10.0000	0.454077
$486$	−1.00000	−0.0453609
$487$	−8.00000	−0.362515	−0.181257	−	0.983436i	$-0.558017\pi$
$487$	−8.00000	−0.362515	−0.181257	+	0.983436i	$0.558017\pi$
$488$	6.00000	0.271607
$489$	20.0000	0.904431
$490$	−1.00000	−0.0451754
$491$	−12.0000	−0.541552	−0.270776	−	0.962642i	$-0.587280\pi$
$491$	−12.0000	−0.541552	−0.270776	+	0.962642i	$0.587280\pi$
$492$	10.0000	0.450835
$493$	60.0000	2.70226
$494$	−8.00000	−0.359937
$495$	1.00000	0.0449467
$496$	4.00000	0.179605
$497$	8.00000	0.358849
$498$	−8.00000	−0.358489
$499$	4.00000	0.179065	0.0895323	−	0.995984i	$-0.471463\pi$
$499$	4.00000	0.179065	0.0895323	+	0.995984i	$0.471463\pi$
$500$	1.00000	0.0447214
$501$	12.0000	0.536120
$502$	12.0000	0.535586
$503$	−20.0000	−0.891756	−0.445878	−	0.895094i	$-0.647108\pi$
$503$	−20.0000	−0.891756	−0.445878	+	0.895094i	$0.647108\pi$
$504$	−3.00000	−0.133631
$505$	2.00000	0.0889988
$506$	4.00000	0.177822
$507$	9.00000	0.399704
$508$	−8.00000	−0.354943
$509$	−6.00000	−0.265945	−0.132973	−	0.991120i	$-0.542452\pi$
$509$	−6.00000	−0.265945	−0.132973	+	0.991120i	$0.542452\pi$
$510$	6.00000	0.265684
$511$	−14.0000	−0.619324
$512$	−11.0000	−0.486136
$513$	−4.00000	−0.176604
$514$	−2.00000	−0.0882162
$515$	−8.00000	−0.352522
$516$	12.0000	0.528271
$517$	0	0
$518$	−2.00000	−0.0878750
$519$	−26.0000	−1.14127
$520$	−6.00000	−0.263117
$521$	22.0000	0.963837	0.481919	−	0.876216i	$-0.339940\pi$
$521$	22.0000	0.963837	0.481919	+	0.876216i	$0.339940\pi$
$522$	10.0000	0.437688
$523$	−4.00000	−0.174908	−0.0874539	−	0.996169i	$-0.527873\pi$
$523$	−4.00000	−0.174908	−0.0874539	+	0.996169i	$0.527873\pi$
$524$	4.00000	0.174741
$525$	−1.00000	−0.0436436
$526$	−24.0000	−1.04645
$527$	−24.0000	−1.04546
$528$	−1.00000	−0.0435194
$529$	−7.00000	−0.304348
$530$	−10.0000	−0.434372
$531$	−12.0000	−0.520756
$532$	−4.00000	−0.173422
$533$	−20.0000	−0.866296
$534$	−6.00000	−0.259645
$535$	−4.00000	−0.172935
$536$	−12.0000	−0.518321
$537$	4.00000	0.172613
$538$	10.0000	0.431131
$539$	−1.00000	−0.0430730
$540$	−1.00000	−0.0430331
$541$	−18.0000	−0.773880	−0.386940	−	0.922105i	$-0.626468\pi$
$541$	−18.0000	−0.773880	−0.386940	+	0.922105i	$0.626468\pi$
$542$	−8.00000	−0.343629
$543$	10.0000	0.429141
$544$	30.0000	1.28624
$545$	−14.0000	−0.599694
$546$	2.00000	0.0855921
$547$	44.0000	1.88130	0.940652	−	0.339372i	$-0.110215\pi$
$547$	44.0000	1.88130	0.940652	+	0.339372i	$0.110215\pi$
$548$	10.0000	0.427179
$549$	−2.00000	−0.0853579
$550$	−1.00000	−0.0426401
$551$	40.0000	1.70406
$552$	−12.0000	−0.510754
$553$	4.00000	0.170097
$554$	2.00000	0.0849719
$555$	−2.00000	−0.0848953
$556$	4.00000	0.169638
$557$	18.0000	0.762684	0.381342	−	0.924434i	$-0.375462\pi$
$557$	18.0000	0.762684	0.381342	+	0.924434i	$0.375462\pi$
$558$	−4.00000	−0.169334
$559$	−24.0000	−1.01509
$560$	1.00000	0.0422577
$561$	6.00000	0.253320
$562$	30.0000	1.26547
$563$	−24.0000	−1.01148	−0.505740	−	0.862686i	$-0.668780\pi$
$563$	−24.0000	−1.01148	−0.505740	+	0.862686i	$0.668780\pi$
$564$	0	0
$565$	18.0000	0.757266
$566$	−28.0000	−1.17693
$567$	1.00000	0.0419961
$568$	−24.0000	−1.00702
$569$	−26.0000	−1.08998	−0.544988	−	0.838444i	$-0.683466\pi$
$569$	−26.0000	−1.08998	−0.544988	+	0.838444i	$0.683466\pi$
$570$	4.00000	0.167542
$571$	8.00000	0.334790	0.167395	−	0.985890i	$-0.446465\pi$
$571$	8.00000	0.334790	0.167395	+	0.985890i	$0.446465\pi$
$572$	−2.00000	−0.0836242
$573$	−16.0000	−0.668410
$574$	10.0000	0.417392
$575$	−4.00000	−0.166812
$576$	7.00000	0.291667
$577$	−2.00000	−0.0832611	−0.0416305	−	0.999133i	$-0.513255\pi$
$577$	−2.00000	−0.0832611	−0.0416305	+	0.999133i	$0.513255\pi$
$578$	19.0000	0.790296
$579$	−14.0000	−0.581820
$580$	10.0000	0.415227
$581$	8.00000	0.331896
$582$	10.0000	0.414513
$583$	−10.0000	−0.414158
$584$	42.0000	1.73797
$585$	2.00000	0.0826898
$586$	18.0000	0.743573
$587$	12.0000	0.495293	0.247647	−	0.968850i	$-0.420343\pi$
$587$	12.0000	0.495293	0.247647	+	0.968850i	$0.420343\pi$
$588$	1.00000	0.0412393
$589$	−16.0000	−0.659269
$590$	12.0000	0.494032
$591$	−26.0000	−1.06950
$592$	2.00000	0.0821995
$593$	−2.00000	−0.0821302	−0.0410651	−	0.999156i	$-0.513075\pi$
$593$	−2.00000	−0.0821302	−0.0410651	+	0.999156i	$0.513075\pi$
$594$	1.00000	0.0410305
$595$	−6.00000	−0.245976
$596$	−18.0000	−0.737309
$597$	−4.00000	−0.163709
$598$	8.00000	0.327144
$599$	−32.0000	−1.30748	−0.653742	−	0.756717i	$-0.726802\pi$
$599$	−32.0000	−1.30748	−0.653742	+	0.756717i	$0.726802\pi$
$600$	3.00000	0.122474
$601$	−6.00000	−0.244745	−0.122373	−	0.992484i	$-0.539050\pi$
$601$	−6.00000	−0.244745	−0.122373	+	0.992484i	$0.539050\pi$
$602$	12.0000	0.489083
$603$	4.00000	0.162893
$604$	4.00000	0.162758
$605$	−1.00000	−0.0406558
$606$	2.00000	0.0812444
$607$	−32.0000	−1.29884	−0.649420	−	0.760430i	$-0.724988\pi$
$607$	−32.0000	−1.29884	−0.649420	+	0.760430i	$0.724988\pi$
$608$	20.0000	0.811107
$609$	−10.0000	−0.405220
$610$	2.00000	0.0809776
$611$	0	0
$612$	−6.00000	−0.242536
$613$	2.00000	0.0807792	0.0403896	−	0.999184i	$-0.487140\pi$
$613$	2.00000	0.0807792	0.0403896	+	0.999184i	$0.487140\pi$
$614$	12.0000	0.484281
$615$	10.0000	0.403239
$616$	3.00000	0.120873
$617$	−18.0000	−0.724653	−0.362326	−	0.932051i	$-0.618017\pi$
$617$	−18.0000	−0.724653	−0.362326	+	0.932051i	$0.618017\pi$
$618$	−8.00000	−0.321807
$619$	0	0		−	1.00000i	$-0.5\pi$
$619$	0	0			1.00000i	$0.5\pi$
$620$	−4.00000	−0.160644
$621$	4.00000	0.160514
$622$	8.00000	0.320771
$623$	6.00000	0.240385
$624$	−2.00000	−0.0800641
$625$	1.00000	0.0400000
$626$	30.0000	1.19904
$627$	4.00000	0.159745
$628$	14.0000	0.558661
$629$	−12.0000	−0.478471
$630$	−1.00000	−0.0398410
$631$	8.00000	0.318475	0.159237	−	0.987240i	$-0.449096\pi$
$631$	8.00000	0.318475	0.159237	+	0.987240i	$0.449096\pi$
$632$	−12.0000	−0.477334
$633$	16.0000	0.635943
$634$	18.0000	0.714871
$635$	−8.00000	−0.317470
$636$	10.0000	0.396526
$637$	−2.00000	−0.0792429
$638$	−10.0000	−0.395904
$639$	8.00000	0.316475
$640$	3.00000	0.118585
$641$	−30.0000	−1.18493	−0.592464	−	0.805597i	$-0.701845\pi$
$641$	−30.0000	−1.18493	−0.592464	+	0.805597i	$0.701845\pi$
$642$	−4.00000	−0.157867
$643$	36.0000	1.41970	0.709851	−	0.704352i	$-0.248762\pi$
$643$	36.0000	1.41970	0.709851	+	0.704352i	$0.248762\pi$
$644$	4.00000	0.157622
$645$	12.0000	0.472500
$646$	24.0000	0.944267
$647$	0	0		−	1.00000i	$-0.5\pi$
$647$	0	0			1.00000i	$0.5\pi$
$648$	−3.00000	−0.117851
$649$	12.0000	0.471041
$650$	−2.00000	−0.0784465
$651$	4.00000	0.156772
$652$	20.0000	0.783260
$653$	−30.0000	−1.17399	−0.586995	−	0.809590i	$-0.699689\pi$
$653$	−30.0000	−1.17399	−0.586995	+	0.809590i	$0.699689\pi$
$654$	−14.0000	−0.547443
$655$	4.00000	0.156293
$656$	−10.0000	−0.390434
$657$	−14.0000	−0.546192
$658$	0	0
$659$	36.0000	1.40236	0.701180	−	0.712984i	$-0.252657\pi$
$659$	36.0000	1.40236	0.701180	+	0.712984i	$0.252657\pi$
$660$	1.00000	0.0389249
$661$	38.0000	1.47803	0.739014	−	0.673690i	$-0.235292\pi$
$661$	38.0000	1.47803	0.739014	+	0.673690i	$0.235292\pi$
$662$	−12.0000	−0.466393
$663$	12.0000	0.466041
$664$	−24.0000	−0.931381
$665$	−4.00000	−0.155113
$666$	−2.00000	−0.0774984
$667$	−40.0000	−1.54881
$668$	12.0000	0.464294
$669$	24.0000	0.927894
$670$	−4.00000	−0.154533
$671$	2.00000	0.0772091
$672$	−5.00000	−0.192879
$673$	−26.0000	−1.00223	−0.501113	−	0.865382i	$-0.667076\pi$
$673$	−26.0000	−1.00223	−0.501113	+	0.865382i	$0.667076\pi$
$674$	22.0000	0.847408
$675$	−1.00000	−0.0384900
$676$	9.00000	0.346154
$677$	−6.00000	−0.230599	−0.115299	−	0.993331i	$-0.536783\pi$
$677$	−6.00000	−0.230599	−0.115299	+	0.993331i	$0.536783\pi$
$678$	18.0000	0.691286
$679$	−10.0000	−0.383765
$680$	18.0000	0.690268
$681$	−8.00000	−0.306561
$682$	4.00000	0.153168
$683$	−40.0000	−1.53056	−0.765279	−	0.643699i	$-0.777399\pi$
$683$	−40.0000	−1.53056	−0.765279	+	0.643699i	$0.777399\pi$
$684$	−4.00000	−0.152944
$685$	10.0000	0.382080
$686$	1.00000	0.0381802
$687$	−14.0000	−0.534133
$688$	−12.0000	−0.457496
$689$	−20.0000	−0.761939
$690$	−4.00000	−0.152277
$691$	−8.00000	−0.304334	−0.152167	−	0.988355i	$-0.548625\pi$
$691$	−8.00000	−0.304334	−0.152167	+	0.988355i	$0.548625\pi$
$692$	−26.0000	−0.988372
$693$	−1.00000	−0.0379869
$694$	−28.0000	−1.06287
$695$	4.00000	0.151729
$696$	30.0000	1.13715
$697$	60.0000	2.27266
$698$	30.0000	1.13552
$699$	26.0000	0.983410
$700$	−1.00000	−0.0377964
$701$	−14.0000	−0.528773	−0.264386	−	0.964417i	$-0.585169\pi$
$701$	−14.0000	−0.528773	−0.264386	+	0.964417i	$0.585169\pi$
$702$	2.00000	0.0754851
$703$	−8.00000	−0.301726
$704$	−7.00000	−0.263822
$705$	0	0
$706$	−18.0000	−0.677439
$707$	−2.00000	−0.0752177
$708$	−12.0000	−0.450988
$709$	6.00000	0.225335	0.112667	−	0.993633i	$-0.464061\pi$
$709$	6.00000	0.225335	0.112667	+	0.993633i	$0.464061\pi$
$710$	−8.00000	−0.300235
$711$	4.00000	0.150012
$712$	−18.0000	−0.674579
$713$	16.0000	0.599205
$714$	−6.00000	−0.224544
$715$	−2.00000	−0.0747958
$716$	4.00000	0.149487
$717$	−24.0000	−0.896296
$718$	24.0000	0.895672
$719$	−48.0000	−1.79010	−0.895049	−	0.445968i	$-0.852860\pi$
$719$	−48.0000	−1.79010	−0.895049	+	0.445968i	$0.852860\pi$
$720$	1.00000	0.0372678
$721$	8.00000	0.297936
$722$	−3.00000	−0.111648
$723$	−2.00000	−0.0743808
$724$	10.0000	0.371647
$725$	10.0000	0.371391
$726$	−1.00000	−0.0371135
$727$	−8.00000	−0.296704	−0.148352	−	0.988935i	$-0.547397\pi$
$727$	−8.00000	−0.296704	−0.148352	+	0.988935i	$0.547397\pi$
$728$	6.00000	0.222375
$729$	1.00000	0.0370370
$730$	14.0000	0.518163
$731$	72.0000	2.66302
$732$	−2.00000	−0.0739221
$733$	38.0000	1.40356	0.701781	−	0.712393i	$-0.252388\pi$
$733$	38.0000	1.40356	0.701781	+	0.712393i	$0.252388\pi$
$734$	−8.00000	−0.295285
$735$	1.00000	0.0368856
$736$	−20.0000	−0.737210
$737$	−4.00000	−0.147342
$738$	10.0000	0.368105
$739$	0	0		−	1.00000i	$-0.5\pi$
$739$	0	0			1.00000i	$0.5\pi$
$740$	−2.00000	−0.0735215
$741$	8.00000	0.293887
$742$	10.0000	0.367112
$743$	24.0000	0.880475	0.440237	−	0.897881i	$-0.354894\pi$
$743$	24.0000	0.880475	0.440237	+	0.897881i	$0.354894\pi$
$744$	−12.0000	−0.439941
$745$	−18.0000	−0.659469
$746$	−6.00000	−0.219676
$747$	8.00000	0.292705
$748$	6.00000	0.219382
$749$	4.00000	0.146157
$750$	1.00000	0.0365148
$751$	8.00000	0.291924	0.145962	−	0.989290i	$-0.453372\pi$
$751$	8.00000	0.291924	0.145962	+	0.989290i	$0.453372\pi$
$752$	0	0
$753$	−12.0000	−0.437304
$754$	−20.0000	−0.728357
$755$	4.00000	0.145575
$756$	1.00000	0.0363696
$757$	−18.0000	−0.654221	−0.327111	−	0.944986i	$-0.606075\pi$
$757$	−18.0000	−0.654221	−0.327111	+	0.944986i	$0.606075\pi$
$758$	4.00000	0.145287
$759$	−4.00000	−0.145191
$760$	12.0000	0.435286
$761$	−6.00000	−0.217500	−0.108750	−	0.994069i	$-0.534685\pi$
$761$	−6.00000	−0.217500	−0.108750	+	0.994069i	$0.534685\pi$
$762$	−8.00000	−0.289809
$763$	14.0000	0.506834
$764$	−16.0000	−0.578860
$765$	−6.00000	−0.216930
$766$	−32.0000	−1.15621
$767$	24.0000	0.866590
$768$	17.0000	0.613435
$769$	−30.0000	−1.08183	−0.540914	−	0.841078i	$-0.681921\pi$
$769$	−30.0000	−1.08183	−0.540914	+	0.841078i	$0.681921\pi$
$770$	1.00000	0.0360375
$771$	2.00000	0.0720282
$772$	−14.0000	−0.503871
$773$	−6.00000	−0.215805	−0.107903	−	0.994161i	$-0.534413\pi$
$773$	−6.00000	−0.215805	−0.107903	+	0.994161i	$0.534413\pi$
$774$	12.0000	0.431331
$775$	−4.00000	−0.143684
$776$	30.0000	1.07694
$777$	2.00000	0.0717496
$778$	22.0000	0.788738
$779$	40.0000	1.43315
$780$	2.00000	0.0716115
$781$	−8.00000	−0.286263
$782$	−24.0000	−0.858238
$783$	−10.0000	−0.357371
$784$	−1.00000	−0.0357143
$785$	14.0000	0.499681
$786$	4.00000	0.142675
$787$	28.0000	0.998092	0.499046	−	0.866575i	$-0.333684\pi$
$787$	28.0000	0.998092	0.499046	+	0.866575i	$0.333684\pi$
$788$	−26.0000	−0.926212
$789$	24.0000	0.854423
$790$	−4.00000	−0.142314
$791$	−18.0000	−0.640006
$792$	3.00000	0.106600
$793$	4.00000	0.142044
$794$	−6.00000	−0.212932
$795$	10.0000	0.354663
$796$	−4.00000	−0.141776
$797$	−46.0000	−1.62940	−0.814702	−	0.579880i	$-0.803099\pi$
$797$	−46.0000	−1.62940	−0.814702	+	0.579880i	$0.803099\pi$
$798$	−4.00000	−0.141598
$799$	0	0
$800$	5.00000	0.176777
$801$	6.00000	0.212000
$802$	18.0000	0.635602
$803$	14.0000	0.494049
$804$	4.00000	0.141069
$805$	4.00000	0.140981
$806$	8.00000	0.281788
$807$	−10.0000	−0.352017
$808$	6.00000	0.211079
$809$	−18.0000	−0.632846	−0.316423	−	0.948618i	$-0.602482\pi$
$809$	−18.0000	−0.632846	−0.316423	+	0.948618i	$0.602482\pi$
$810$	−1.00000	−0.0351364
$811$	−52.0000	−1.82597	−0.912983	−	0.407997i	$-0.866228\pi$
$811$	−52.0000	−1.82597	−0.912983	+	0.407997i	$0.866228\pi$
$812$	−10.0000	−0.350931
$813$	8.00000	0.280572
$814$	2.00000	0.0701000
$815$	20.0000	0.700569
$816$	6.00000	0.210042
$817$	48.0000	1.67931
$818$	−22.0000	−0.769212
$819$	−2.00000	−0.0698857
$820$	10.0000	0.349215
$821$	10.0000	0.349002	0.174501	−	0.984657i	$-0.444169\pi$
$821$	10.0000	0.349002	0.174501	+	0.984657i	$0.444169\pi$
$822$	10.0000	0.348790
$823$	−32.0000	−1.11545	−0.557725	−	0.830026i	$-0.688326\pi$
$823$	−32.0000	−1.11545	−0.557725	+	0.830026i	$0.688326\pi$
$824$	−24.0000	−0.836080
$825$	1.00000	0.0348155
$826$	−12.0000	−0.417533
$827$	4.00000	0.139094	0.0695468	−	0.997579i	$-0.477845\pi$
$827$	4.00000	0.139094	0.0695468	+	0.997579i	$0.477845\pi$
$828$	4.00000	0.139010
$829$	14.0000	0.486240	0.243120	−	0.969996i	$-0.421829\pi$
$829$	14.0000	0.486240	0.243120	+	0.969996i	$0.421829\pi$
$830$	−8.00000	−0.277684
$831$	−2.00000	−0.0693792
$832$	−14.0000	−0.485363
$833$	6.00000	0.207888
$834$	4.00000	0.138509
$835$	12.0000	0.415277
$836$	4.00000	0.138343
$837$	4.00000	0.138260
$838$	4.00000	0.138178
$839$	0	0		−	1.00000i	$-0.5\pi$
$839$	0	0			1.00000i	$0.5\pi$
$840$	−3.00000	−0.103510
$841$	71.0000	2.44828
$842$	6.00000	0.206774
$843$	−30.0000	−1.03325
$844$	16.0000	0.550743
$845$	9.00000	0.309609
$846$	0	0
$847$	1.00000	0.0343604
$848$	−10.0000	−0.343401
$849$	28.0000	0.960958
$850$	6.00000	0.205798
$851$	8.00000	0.274236
$852$	8.00000	0.274075
$853$	−34.0000	−1.16414	−0.582069	−	0.813139i	$-0.697757\pi$
$853$	−34.0000	−1.16414	−0.582069	+	0.813139i	$0.697757\pi$
$854$	−2.00000	−0.0684386
$855$	−4.00000	−0.136797
$856$	−12.0000	−0.410152
$857$	46.0000	1.57133	0.785665	−	0.618652i	$-0.212321\pi$
$857$	46.0000	1.57133	0.785665	+	0.618652i	$0.212321\pi$
$858$	−2.00000	−0.0682789
$859$	48.0000	1.63774	0.818869	−	0.573980i	$-0.194601\pi$
$859$	48.0000	1.63774	0.818869	+	0.573980i	$0.194601\pi$
$860$	12.0000	0.409197
$861$	−10.0000	−0.340799
$862$	40.0000	1.36241
$863$	−20.0000	−0.680808	−0.340404	−	0.940279i	$-0.610564\pi$
$863$	−20.0000	−0.680808	−0.340404	+	0.940279i	$0.610564\pi$
$864$	−5.00000	−0.170103
$865$	−26.0000	−0.884027
$866$	−2.00000	−0.0679628
$867$	−19.0000	−0.645274
$868$	4.00000	0.135769
$869$	−4.00000	−0.135691
$870$	10.0000	0.339032
$871$	−8.00000	−0.271070
$872$	−42.0000	−1.42230
$873$	−10.0000	−0.338449
$874$	−16.0000	−0.541208
$875$	−1.00000	−0.0338062
$876$	−14.0000	−0.473016
$877$	42.0000	1.41824	0.709120	−	0.705088i	$-0.249093\pi$
$877$	42.0000	1.41824	0.709120	+	0.705088i	$0.249093\pi$
$878$	−8.00000	−0.269987
$879$	−18.0000	−0.607125
$880$	−1.00000	−0.0337100
$881$	14.0000	0.471672	0.235836	−	0.971793i	$-0.424217\pi$
$881$	14.0000	0.471672	0.235836	+	0.971793i	$0.424217\pi$
$882$	1.00000	0.0336718
$883$	−12.0000	−0.403832	−0.201916	−	0.979403i	$-0.564717\pi$
$883$	−12.0000	−0.403832	−0.201916	+	0.979403i	$0.564717\pi$
$884$	12.0000	0.403604
$885$	−12.0000	−0.403376
$886$	−8.00000	−0.268765
$887$	52.0000	1.74599	0.872995	−	0.487730i	$-0.162175\pi$
$887$	52.0000	1.74599	0.872995	+	0.487730i	$0.162175\pi$
$888$	−6.00000	−0.201347
$889$	8.00000	0.268311
$890$	−6.00000	−0.201120
$891$	−1.00000	−0.0335013
$892$	24.0000	0.803579
$893$	0	0
$894$	−18.0000	−0.602010
$895$	4.00000	0.133705
$896$	−3.00000	−0.100223
$897$	−8.00000	−0.267112
$898$	18.0000	0.600668
$899$	−40.0000	−1.33407
$900$	−1.00000	−0.0333333
$901$	60.0000	1.99889
$902$	−10.0000	−0.332964
$903$	−12.0000	−0.399335
$904$	54.0000	1.79601
$905$	10.0000	0.332411
$906$	4.00000	0.132891
$907$	12.0000	0.398453	0.199227	−	0.979953i	$-0.436157\pi$
$907$	12.0000	0.398453	0.199227	+	0.979953i	$0.436157\pi$
$908$	−8.00000	−0.265489
$909$	−2.00000	−0.0663358
$910$	2.00000	0.0662994
$911$	−48.0000	−1.59031	−0.795155	−	0.606406i	$-0.792611\pi$
$911$	−48.0000	−1.59031	−0.795155	+	0.606406i	$0.792611\pi$
$912$	4.00000	0.132453
$913$	−8.00000	−0.264761
$914$	−18.0000	−0.595387
$915$	−2.00000	−0.0661180
$916$	−14.0000	−0.462573
$917$	−4.00000	−0.132092
$918$	−6.00000	−0.198030
$919$	20.0000	0.659739	0.329870	−	0.944027i	$-0.392995\pi$
$919$	20.0000	0.659739	0.329870	+	0.944027i	$0.392995\pi$
$920$	−12.0000	−0.395628
$921$	−12.0000	−0.395413
$922$	30.0000	0.987997
$923$	−16.0000	−0.526646
$924$	−1.00000	−0.0328976
$925$	−2.00000	−0.0657596
$926$	16.0000	0.525793
$927$	8.00000	0.262754
$928$	50.0000	1.64133
$929$	6.00000	0.196854	0.0984268	−	0.995144i	$-0.468619\pi$
$929$	6.00000	0.196854	0.0984268	+	0.995144i	$0.468619\pi$
$930$	−4.00000	−0.131165
$931$	4.00000	0.131095
$932$	26.0000	0.851658
$933$	−8.00000	−0.261908
$934$	−4.00000	−0.130884
$935$	6.00000	0.196221
$936$	6.00000	0.196116
$937$	−38.0000	−1.24141	−0.620703	−	0.784046i	$-0.713153\pi$
$937$	−38.0000	−1.24141	−0.620703	+	0.784046i	$0.713153\pi$
$938$	4.00000	0.130605
$939$	−30.0000	−0.979013
$940$	0	0
$941$	14.0000	0.456387	0.228193	−	0.973616i	$-0.426718\pi$
$941$	14.0000	0.456387	0.228193	+	0.973616i	$0.426718\pi$
$942$	14.0000	0.456145
$943$	−40.0000	−1.30258
$944$	12.0000	0.390567
$945$	1.00000	0.0325300
$946$	−12.0000	−0.390154
$947$	−24.0000	−0.779895	−0.389948	−	0.920837i	$-0.627507\pi$
$947$	−24.0000	−0.779895	−0.389948	+	0.920837i	$0.627507\pi$
$948$	4.00000	0.129914
$949$	28.0000	0.908918
$950$	4.00000	0.129777
$951$	−18.0000	−0.583690
$952$	−18.0000	−0.583383
$953$	38.0000	1.23094	0.615470	−	0.788160i	$-0.288966\pi$
$953$	38.0000	1.23094	0.615470	+	0.788160i	$0.288966\pi$
$954$	10.0000	0.323762
$955$	−16.0000	−0.517748
$956$	−24.0000	−0.776215
$957$	10.0000	0.323254
$958$	−8.00000	−0.258468
$959$	−10.0000	−0.322917
$960$	7.00000	0.225924
$961$	−15.0000	−0.483871
$962$	4.00000	0.128965
$963$	4.00000	0.128898
$964$	−2.00000	−0.0644157
$965$	−14.0000	−0.450676
$966$	4.00000	0.128698
$967$	8.00000	0.257263	0.128631	−	0.991692i	$-0.458942\pi$
$967$	8.00000	0.257263	0.128631	+	0.991692i	$0.458942\pi$
$968$	−3.00000	−0.0964237
$969$	−24.0000	−0.770991
$970$	10.0000	0.321081
$971$	−44.0000	−1.41203	−0.706014	−	0.708198i	$-0.749508\pi$
$971$	−44.0000	−1.41203	−0.706014	+	0.708198i	$0.749508\pi$
$972$	1.00000	0.0320750
$973$	−4.00000	−0.128234
$974$	−8.00000	−0.256337
$975$	2.00000	0.0640513
$976$	2.00000	0.0640184
$977$	−26.0000	−0.831814	−0.415907	−	0.909407i	$-0.636536\pi$
$977$	−26.0000	−0.831814	−0.415907	+	0.909407i	$0.636536\pi$
$978$	20.0000	0.639529
$979$	−6.00000	−0.191761
$980$	1.00000	0.0319438
$981$	14.0000	0.446986
$982$	−12.0000	−0.382935
$983$	−32.0000	−1.02064	−0.510321	−	0.859984i	$-0.670473\pi$
$983$	−32.0000	−1.02064	−0.510321	+	0.859984i	$0.670473\pi$
$984$	30.0000	0.956365
$985$	−26.0000	−0.828429
$986$	60.0000	1.91079
$987$	0	0
$988$	8.00000	0.254514
$989$	−48.0000	−1.52631
$990$	1.00000	0.0317821
$991$	−16.0000	−0.508257	−0.254128	−	0.967170i	$-0.581789\pi$
$991$	−16.0000	−0.508257	−0.254128	+	0.967170i	$0.581789\pi$
$992$	−20.0000	−0.635001
$993$	12.0000	0.380808
$994$	8.00000	0.253745
$995$	−4.00000	−0.126809
$996$	8.00000	0.253490
$997$	−2.00000	−0.0633406	−0.0316703	−	0.999498i	$-0.510083\pi$
$997$	−2.00000	−0.0633406	−0.0316703	+	0.999498i	$0.510083\pi$
$998$	4.00000	0.126618
$999$	2.00000	0.0632772

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1155.2.a.j.1.1	✓	1
3.2	odd	2		3465.2.a.g.1.1		1
5.4	even	2		5775.2.a.f.1.1		1
7.6	odd	2		8085.2.a.w.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1155.2.a.j.1.1	✓	1	1.1	even	1	trivial
3465.2.a.g.1.1		1	3.2	odd	2
5775.2.a.f.1.1		1	5.4	even	2
8085.2.a.w.1.1		1	7.6	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1155.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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