LMFDB - Embedded newform 2006.2.a.g.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2006,2,Mod(1,2006)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2006, 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("2006.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2006 = 2 \cdot 17 \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2006.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:	$16.0179906455$
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	$\chi$	$=$	2006.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+1.00000 q^{2} -3.00000 q^{3} +1.00000 q^{4} -3.00000 q^{5} -3.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +6.00000 q^{9} +O(q^{10})$

\(q+1.00000 q^{2} -3.00000 q^{3} +1.00000 q^{4} -3.00000 q^{5} -3.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +6.00000 q^{9} -3.00000 q^{10} -3.00000 q^{12} +4.00000 q^{13} -1.00000 q^{14} +9.00000 q^{15} +1.00000 q^{16} +1.00000 q^{17} +6.00000 q^{18} -1.00000 q^{19} -3.00000 q^{20} +3.00000 q^{21} -2.00000 q^{23} -3.00000 q^{24} +4.00000 q^{25} +4.00000 q^{26} -9.00000 q^{27} -1.00000 q^{28} +7.00000 q^{29} +9.00000 q^{30} -4.00000 q^{31} +1.00000 q^{32} +1.00000 q^{34} +3.00000 q^{35} +6.00000 q^{36} +4.00000 q^{37} -1.00000 q^{38} -12.0000 q^{39} -3.00000 q^{40} +1.00000 q^{41} +3.00000 q^{42} -4.00000 q^{43} -18.0000 q^{45} -2.00000 q^{46} +2.00000 q^{47} -3.00000 q^{48} -6.00000 q^{49} +4.00000 q^{50} -3.00000 q^{51} +4.00000 q^{52} -1.00000 q^{53} -9.00000 q^{54} -1.00000 q^{56} +3.00000 q^{57} +7.00000 q^{58} -1.00000 q^{59} +9.00000 q^{60} -6.00000 q^{61} -4.00000 q^{62} -6.00000 q^{63} +1.00000 q^{64} -12.0000 q^{65} +1.00000 q^{68} +6.00000 q^{69} +3.00000 q^{70} -12.0000 q^{71} +6.00000 q^{72} -10.0000 q^{73} +4.00000 q^{74} -12.0000 q^{75} -1.00000 q^{76} -12.0000 q^{78} -7.00000 q^{79} -3.00000 q^{80} +9.00000 q^{81} +1.00000 q^{82} +4.00000 q^{83} +3.00000 q^{84} -3.00000 q^{85} -4.00000 q^{86} -21.0000 q^{87} -12.0000 q^{89} -18.0000 q^{90} -4.00000 q^{91} -2.00000 q^{92} +12.0000 q^{93} +2.00000 q^{94} +3.00000 q^{95} -3.00000 q^{96} -8.00000 q^{97} -6.00000 q^{98} +O(q^{100})\)

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
$3$	−3.00000	−1.73205	−0.866025	−	0.500000i	$-0.833333\pi$
$3$	−3.00000	−1.73205	−0.866025	+	0.500000i	$0.833333\pi$
$4$	1.00000	0.500000
$5$	−3.00000	−1.34164	−0.670820	−	0.741620i	$-0.734058\pi$
$5$	−3.00000	−1.34164	−0.670820	+	0.741620i	$0.734058\pi$
$6$	−3.00000	−1.22474
$7$	−1.00000	−0.377964	−0.188982	−	0.981981i	$-0.560519\pi$
$7$	−1.00000	−0.377964	−0.188982	+	0.981981i	$0.560519\pi$
$8$	1.00000	0.353553
$9$	6.00000	2.00000
$10$	−3.00000	−0.948683
$11$	0	0		−	1.00000i	$-0.5\pi$
$11$	0	0			1.00000i	$0.5\pi$
$12$	−3.00000	−0.866025
$13$	4.00000	1.10940	0.554700	−	0.832050i	$-0.312833\pi$
$13$	4.00000	1.10940	0.554700	+	0.832050i	$0.312833\pi$
$14$	−1.00000	−0.267261
$15$	9.00000	2.32379
$16$	1.00000	0.250000
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	6.00000	1.41421
$19$	−1.00000	−0.229416	−0.114708	−	0.993399i	$-0.536593\pi$
$19$	−1.00000	−0.229416	−0.114708	+	0.993399i	$0.536593\pi$
$20$	−3.00000	−0.670820
$21$	3.00000	0.654654
$22$	0	0
$23$	−2.00000	−0.417029	−0.208514	−	0.978019i	$-0.566863\pi$
$23$	−2.00000	−0.417029	−0.208514	+	0.978019i	$0.566863\pi$
$24$	−3.00000	−0.612372
$25$	4.00000	0.800000
$26$	4.00000	0.784465
$27$	−9.00000	−1.73205
$28$	−1.00000	−0.188982
$29$	7.00000	1.29987	0.649934	−	0.759991i	$-0.274797\pi$
$29$	7.00000	1.29987	0.649934	+	0.759991i	$0.274797\pi$
$30$	9.00000	1.64317
$31$	−4.00000	−0.718421	−0.359211	−	0.933257i	$-0.616954\pi$
$31$	−4.00000	−0.718421	−0.359211	+	0.933257i	$0.616954\pi$
$32$	1.00000	0.176777
$33$	0	0
$34$	1.00000	0.171499
$35$	3.00000	0.507093
$36$	6.00000	1.00000
$37$	4.00000	0.657596	0.328798	−	0.944400i	$-0.393356\pi$
$37$	4.00000	0.657596	0.328798	+	0.944400i	$0.393356\pi$
$38$	−1.00000	−0.162221
$39$	−12.0000	−1.92154
$40$	−3.00000	−0.474342
$41$	1.00000	0.156174	0.0780869	−	0.996947i	$-0.475119\pi$
$41$	1.00000	0.156174	0.0780869	+	0.996947i	$0.475119\pi$
$42$	3.00000	0.462910
$43$	−4.00000	−0.609994	−0.304997	−	0.952353i	$-0.598656\pi$
$43$	−4.00000	−0.609994	−0.304997	+	0.952353i	$0.598656\pi$
$44$	0	0
$45$	−18.0000	−2.68328
$46$	−2.00000	−0.294884
$47$	2.00000	0.291730	0.145865	−	0.989305i	$-0.453403\pi$
$47$	2.00000	0.291730	0.145865	+	0.989305i	$0.453403\pi$
$48$	−3.00000	−0.433013
$49$	−6.00000	−0.857143
$50$	4.00000	0.565685
$51$	−3.00000	−0.420084
$52$	4.00000	0.554700
$53$	−1.00000	−0.137361	−0.0686803	−	0.997639i	$-0.521879\pi$
$53$	−1.00000	−0.137361	−0.0686803	+	0.997639i	$0.521879\pi$
$54$	−9.00000	−1.22474
$55$	0	0
$56$	−1.00000	−0.133631
$57$	3.00000	0.397360
$58$	7.00000	0.919145
$59$	−1.00000	−0.130189
$59$	−1.00000	−0.130189
$60$	9.00000	1.16190
$61$	−6.00000	−0.768221	−0.384111	−	0.923287i	$-0.625492\pi$
$61$	−6.00000	−0.768221	−0.384111	+	0.923287i	$0.625492\pi$
$62$	−4.00000	−0.508001
$63$	−6.00000	−0.755929
$64$	1.00000	0.125000
$65$	−12.0000	−1.48842
$66$	0	0
$67$	0	0		−	1.00000i	$-0.5\pi$
$67$	0	0			1.00000i	$0.5\pi$
$68$	1.00000	0.121268
$69$	6.00000	0.722315
$70$	3.00000	0.358569
$71$	−12.0000	−1.42414	−0.712069	−	0.702109i	$-0.752242\pi$
$71$	−12.0000	−1.42414	−0.712069	+	0.702109i	$0.752242\pi$
$72$	6.00000	0.707107
$73$	−10.0000	−1.17041	−0.585206	−	0.810885i	$-0.698986\pi$
$73$	−10.0000	−1.17041	−0.585206	+	0.810885i	$0.698986\pi$
$74$	4.00000	0.464991
$75$	−12.0000	−1.38564
$76$	−1.00000	−0.114708
$77$	0	0
$78$	−12.0000	−1.35873
$79$	−7.00000	−0.787562	−0.393781	−	0.919204i	$-0.628833\pi$
$79$	−7.00000	−0.787562	−0.393781	+	0.919204i	$0.628833\pi$
$80$	−3.00000	−0.335410
$81$	9.00000	1.00000
$82$	1.00000	0.110432
$83$	4.00000	0.439057	0.219529	−	0.975606i	$-0.429548\pi$
$83$	4.00000	0.439057	0.219529	+	0.975606i	$0.429548\pi$
$84$	3.00000	0.327327
$85$	−3.00000	−0.325396
$86$	−4.00000	−0.431331
$87$	−21.0000	−2.25144
$88$	0	0
$89$	−12.0000	−1.27200	−0.635999	−	0.771690i	$-0.719412\pi$
$89$	−12.0000	−1.27200	−0.635999	+	0.771690i	$0.719412\pi$
$90$	−18.0000	−1.89737
$91$	−4.00000	−0.419314
$92$	−2.00000	−0.208514
$93$	12.0000	1.24434
$94$	2.00000	0.206284
$95$	3.00000	0.307794
$96$	−3.00000	−0.306186
$97$	−8.00000	−0.812277	−0.406138	−	0.913812i	$-0.633125\pi$
$97$	−8.00000	−0.812277	−0.406138	+	0.913812i	$0.633125\pi$
$98$	−6.00000	−0.606092
$99$	0	0
$100$	4.00000	0.400000
$101$	0	0		−	1.00000i	$-0.5\pi$
$101$	0	0			1.00000i	$0.5\pi$
$102$	−3.00000	−0.297044
$103$	−12.0000	−1.18240	−0.591198	−	0.806527i	$-0.701345\pi$
$103$	−12.0000	−1.18240	−0.591198	+	0.806527i	$0.701345\pi$
$104$	4.00000	0.392232
$105$	−9.00000	−0.878310
$106$	−1.00000	−0.0971286
$107$	13.0000	1.25676	0.628379	−	0.777908i	$-0.283719\pi$
$107$	13.0000	1.25676	0.628379	+	0.777908i	$0.283719\pi$
$108$	−9.00000	−0.866025
$109$	−10.0000	−0.957826	−0.478913	−	0.877862i	$-0.658969\pi$
$109$	−10.0000	−0.957826	−0.478913	+	0.877862i	$0.658969\pi$
$110$	0	0
$111$	−12.0000	−1.13899
$112$	−1.00000	−0.0944911
$113$	10.0000	0.940721	0.470360	−	0.882474i	$-0.344124\pi$
$113$	10.0000	0.940721	0.470360	+	0.882474i	$0.344124\pi$
$114$	3.00000	0.280976
$115$	6.00000	0.559503
$116$	7.00000	0.649934
$117$	24.0000	2.21880
$118$	−1.00000	−0.0920575
$119$	−1.00000	−0.0916698
$120$	9.00000	0.821584
$121$	−11.0000	−1.00000
$122$	−6.00000	−0.543214
$123$	−3.00000	−0.270501
$124$	−4.00000	−0.359211
$125$	3.00000	0.268328
$126$	−6.00000	−0.534522
$127$	7.00000	0.621150	0.310575	−	0.950549i	$-0.399478\pi$
$127$	7.00000	0.621150	0.310575	+	0.950549i	$0.399478\pi$
$128$	1.00000	0.0883883
$129$	12.0000	1.05654
$130$	−12.0000	−1.05247
$131$	−6.00000	−0.524222	−0.262111	−	0.965038i	$-0.584419\pi$
$131$	−6.00000	−0.524222	−0.262111	+	0.965038i	$0.584419\pi$
$132$	0	0
$133$	1.00000	0.0867110
$134$	0	0
$135$	27.0000	2.32379
$136$	1.00000	0.0857493
$137$	3.00000	0.256307	0.128154	−	0.991754i	$-0.459095\pi$
$137$	3.00000	0.256307	0.128154	+	0.991754i	$0.459095\pi$
$138$	6.00000	0.510754
$139$	4.00000	0.339276	0.169638	−	0.985506i	$-0.445740\pi$
$139$	4.00000	0.339276	0.169638	+	0.985506i	$0.445740\pi$
$140$	3.00000	0.253546
$141$	−6.00000	−0.505291
$142$	−12.0000	−1.00702
$143$	0	0
$144$	6.00000	0.500000
$145$	−21.0000	−1.74396
$146$	−10.0000	−0.827606
$147$	18.0000	1.48461
$148$	4.00000	0.328798
$149$	18.0000	1.47462	0.737309	−	0.675556i	$-0.236096\pi$
$149$	18.0000	1.47462	0.737309	+	0.675556i	$0.236096\pi$
$150$	−12.0000	−0.979796
$151$	0	0		−	1.00000i	$-0.5\pi$
$151$	0	0			1.00000i	$0.5\pi$
$152$	−1.00000	−0.0811107
$153$	6.00000	0.485071
$154$	0	0
$155$	12.0000	0.963863
$156$	−12.0000	−0.960769
$157$	−14.0000	−1.11732	−0.558661	−	0.829396i	$-0.688685\pi$
$157$	−14.0000	−1.11732	−0.558661	+	0.829396i	$0.688685\pi$
$158$	−7.00000	−0.556890
$159$	3.00000	0.237915
$160$	−3.00000	−0.237171
$161$	2.00000	0.157622
$162$	9.00000	0.707107
$163$	8.00000	0.626608	0.313304	−	0.949653i	$-0.398564\pi$
$163$	8.00000	0.626608	0.313304	+	0.949653i	$0.398564\pi$
$164$	1.00000	0.0780869
$165$	0	0
$166$	4.00000	0.310460
$167$	−21.0000	−1.62503	−0.812514	−	0.582941i	$-0.801902\pi$
$167$	−21.0000	−1.62503	−0.812514	+	0.582941i	$0.801902\pi$
$168$	3.00000	0.231455
$169$	3.00000	0.230769
$170$	−3.00000	−0.230089
$171$	−6.00000	−0.458831
$172$	−4.00000	−0.304997
$173$	8.00000	0.608229	0.304114	−	0.952636i	$-0.401639\pi$
$173$	8.00000	0.608229	0.304114	+	0.952636i	$0.401639\pi$
$174$	−21.0000	−1.59201
$175$	−4.00000	−0.302372
$176$	0	0
$177$	3.00000	0.225494
$178$	−12.0000	−0.899438
$179$	−6.00000	−0.448461	−0.224231	−	0.974536i	$-0.571987\pi$
$179$	−6.00000	−0.448461	−0.224231	+	0.974536i	$0.571987\pi$
$180$	−18.0000	−1.34164
$181$	−9.00000	−0.668965	−0.334482	−	0.942402i	$-0.608561\pi$
$181$	−9.00000	−0.668965	−0.334482	+	0.942402i	$0.608561\pi$
$182$	−4.00000	−0.296500
$183$	18.0000	1.33060
$184$	−2.00000	−0.147442
$185$	−12.0000	−0.882258
$186$	12.0000	0.879883
$187$	0	0
$188$	2.00000	0.145865
$189$	9.00000	0.654654
$190$	3.00000	0.217643
$191$	−14.0000	−1.01300	−0.506502	−	0.862239i	$-0.669062\pi$
$191$	−14.0000	−1.01300	−0.506502	+	0.862239i	$0.669062\pi$
$192$	−3.00000	−0.216506
$193$	13.0000	0.935760	0.467880	−	0.883792i	$-0.345018\pi$
$193$	13.0000	0.935760	0.467880	+	0.883792i	$0.345018\pi$
$194$	−8.00000	−0.574367
$195$	36.0000	2.57801
$196$	−6.00000	−0.428571
$197$	10.0000	0.712470	0.356235	−	0.934396i	$-0.384060\pi$
$197$	10.0000	0.712470	0.356235	+	0.934396i	$0.384060\pi$
$198$	0	0
$199$	−5.00000	−0.354441	−0.177220	−	0.984171i	$-0.556711\pi$
$199$	−5.00000	−0.354441	−0.177220	+	0.984171i	$0.556711\pi$
$200$	4.00000	0.282843
$201$	0	0
$202$	0	0
$203$	−7.00000	−0.491304
$204$	−3.00000	−0.210042
$205$	−3.00000	−0.209529
$206$	−12.0000	−0.836080
$207$	−12.0000	−0.834058
$208$	4.00000	0.277350
$209$	0	0
$210$	−9.00000	−0.621059
$211$	8.00000	0.550743	0.275371	−	0.961338i	$-0.411199\pi$
$211$	8.00000	0.550743	0.275371	+	0.961338i	$0.411199\pi$
$212$	−1.00000	−0.0686803
$213$	36.0000	2.46668
$214$	13.0000	0.888662
$215$	12.0000	0.818393
$216$	−9.00000	−0.612372
$217$	4.00000	0.271538
$218$	−10.0000	−0.677285
$219$	30.0000	2.02721
$220$	0	0
$221$	4.00000	0.269069
$222$	−12.0000	−0.805387
$223$	0	0		−	1.00000i	$-0.5\pi$
$223$	0	0			1.00000i	$0.5\pi$
$224$	−1.00000	−0.0668153
$225$	24.0000	1.60000
$226$	10.0000	0.665190
$227$	−14.0000	−0.929213	−0.464606	−	0.885517i	$-0.653804\pi$
$227$	−14.0000	−0.929213	−0.464606	+	0.885517i	$0.653804\pi$
$228$	3.00000	0.198680
$229$	22.0000	1.45380	0.726900	−	0.686743i	$-0.240960\pi$
$229$	22.0000	1.45380	0.726900	+	0.686743i	$0.240960\pi$
$230$	6.00000	0.395628
$231$	0	0
$232$	7.00000	0.459573
$233$	4.00000	0.262049	0.131024	−	0.991379i	$-0.458173\pi$
$233$	4.00000	0.262049	0.131024	+	0.991379i	$0.458173\pi$
$234$	24.0000	1.56893
$235$	−6.00000	−0.391397
$236$	−1.00000	−0.0650945
$237$	21.0000	1.36410
$238$	−1.00000	−0.0648204
$239$	−19.0000	−1.22901	−0.614504	−	0.788914i	$-0.710644\pi$
$239$	−19.0000	−1.22901	−0.614504	+	0.788914i	$0.710644\pi$
$240$	9.00000	0.580948
$241$	−5.00000	−0.322078	−0.161039	−	0.986948i	$-0.551485\pi$
$241$	−5.00000	−0.322078	−0.161039	+	0.986948i	$0.551485\pi$
$242$	−11.0000	−0.707107
$243$	0	0
$244$	−6.00000	−0.384111
$245$	18.0000	1.14998
$246$	−3.00000	−0.191273
$247$	−4.00000	−0.254514
$248$	−4.00000	−0.254000
$249$	−12.0000	−0.760469
$250$	3.00000	0.189737
$251$	−7.00000	−0.441836	−0.220918	−	0.975292i	$-0.570905\pi$
$251$	−7.00000	−0.441836	−0.220918	+	0.975292i	$0.570905\pi$
$252$	−6.00000	−0.377964
$253$	0	0
$254$	7.00000	0.439219
$255$	9.00000	0.563602
$256$	1.00000	0.0625000
$257$	21.0000	1.30994	0.654972	−	0.755653i	$-0.272680\pi$
$257$	21.0000	1.30994	0.654972	+	0.755653i	$0.272680\pi$
$258$	12.0000	0.747087
$259$	−4.00000	−0.248548
$260$	−12.0000	−0.744208
$261$	42.0000	2.59973
$262$	−6.00000	−0.370681
$263$	13.0000	0.801614	0.400807	−	0.916162i	$-0.368730\pi$
$263$	13.0000	0.801614	0.400807	+	0.916162i	$0.368730\pi$
$264$	0	0
$265$	3.00000	0.184289
$266$	1.00000	0.0613139
$267$	36.0000	2.20316
$268$	0	0
$269$	−18.0000	−1.09748	−0.548740	−	0.835993i	$-0.684892\pi$
$269$	−18.0000	−1.09748	−0.548740	+	0.835993i	$0.684892\pi$
$270$	27.0000	1.64317
$271$	−29.0000	−1.76162	−0.880812	−	0.473466i	$-0.843003\pi$
$271$	−29.0000	−1.76162	−0.880812	+	0.473466i	$0.843003\pi$
$272$	1.00000	0.0606339
$273$	12.0000	0.726273
$274$	3.00000	0.181237
$275$	0	0
$276$	6.00000	0.361158
$277$	−23.0000	−1.38194	−0.690968	−	0.722885i	$-0.742815\pi$
$277$	−23.0000	−1.38194	−0.690968	+	0.722885i	$0.742815\pi$
$278$	4.00000	0.239904
$279$	−24.0000	−1.43684
$280$	3.00000	0.179284
$281$	15.0000	0.894825	0.447412	−	0.894328i	$-0.352346\pi$
$281$	15.0000	0.894825	0.447412	+	0.894328i	$0.352346\pi$
$282$	−6.00000	−0.357295
$283$	−18.0000	−1.06999	−0.534994	−	0.844856i	$-0.679686\pi$
$283$	−18.0000	−1.06999	−0.534994	+	0.844856i	$0.679686\pi$
$284$	−12.0000	−0.712069
$285$	−9.00000	−0.533114
$286$	0	0
$287$	−1.00000	−0.0590281
$288$	6.00000	0.353553
$289$	1.00000	0.0588235
$290$	−21.0000	−1.23316
$291$	24.0000	1.40690
$292$	−10.0000	−0.585206
$293$	−3.00000	−0.175262	−0.0876309	−	0.996153i	$-0.527930\pi$
$293$	−3.00000	−0.175262	−0.0876309	+	0.996153i	$0.527930\pi$
$294$	18.0000	1.04978
$295$	3.00000	0.174667
$296$	4.00000	0.232495
$297$	0	0
$298$	18.0000	1.04271
$299$	−8.00000	−0.462652
$300$	−12.0000	−0.692820
$301$	4.00000	0.230556
$302$	0	0
$303$	0	0
$304$	−1.00000	−0.0573539
$305$	18.0000	1.03068
$306$	6.00000	0.342997
$307$	−23.0000	−1.31268	−0.656340	−	0.754466i	$-0.727896\pi$
$307$	−23.0000	−1.31268	−0.656340	+	0.754466i	$0.727896\pi$
$308$	0	0
$309$	36.0000	2.04797
$310$	12.0000	0.681554
$311$	−29.0000	−1.64444	−0.822220	−	0.569170i	$-0.807264\pi$
$311$	−29.0000	−1.64444	−0.822220	+	0.569170i	$0.807264\pi$
$312$	−12.0000	−0.679366
$313$	10.0000	0.565233	0.282617	−	0.959233i	$-0.408798\pi$
$313$	10.0000	0.565233	0.282617	+	0.959233i	$0.408798\pi$
$314$	−14.0000	−0.790066
$315$	18.0000	1.01419
$316$	−7.00000	−0.393781
$317$	10.0000	0.561656	0.280828	−	0.959758i	$-0.409391\pi$
$317$	10.0000	0.561656	0.280828	+	0.959758i	$0.409391\pi$
$318$	3.00000	0.168232
$319$	0	0
$320$	−3.00000	−0.167705
$321$	−39.0000	−2.17677
$322$	2.00000	0.111456
$323$	−1.00000	−0.0556415
$324$	9.00000	0.500000
$325$	16.0000	0.887520
$326$	8.00000	0.443079
$327$	30.0000	1.65900
$328$	1.00000	0.0552158
$329$	−2.00000	−0.110264
$330$	0	0
$331$	−17.0000	−0.934405	−0.467202	−	0.884150i	$-0.654738\pi$
$331$	−17.0000	−0.934405	−0.467202	+	0.884150i	$0.654738\pi$
$332$	4.00000	0.219529
$333$	24.0000	1.31519
$334$	−21.0000	−1.14907
$335$	0	0
$336$	3.00000	0.163663
$337$	10.0000	0.544735	0.272367	−	0.962193i	$-0.412193\pi$
$337$	10.0000	0.544735	0.272367	+	0.962193i	$0.412193\pi$
$338$	3.00000	0.163178
$339$	−30.0000	−1.62938
$340$	−3.00000	−0.162698
$341$	0	0
$342$	−6.00000	−0.324443
$343$	13.0000	0.701934
$344$	−4.00000	−0.215666
$345$	−18.0000	−0.969087
$346$	8.00000	0.430083
$347$	−24.0000	−1.28839	−0.644194	−	0.764862i	$-0.722807\pi$
$347$	−24.0000	−1.28839	−0.644194	+	0.764862i	$0.722807\pi$
$348$	−21.0000	−1.12572
$349$	−6.00000	−0.321173	−0.160586	−	0.987022i	$-0.551338\pi$
$349$	−6.00000	−0.321173	−0.160586	+	0.987022i	$0.551338\pi$
$350$	−4.00000	−0.213809
$351$	−36.0000	−1.92154
$352$	0	0
$353$	4.00000	0.212899	0.106449	−	0.994318i	$-0.466052\pi$
$353$	4.00000	0.212899	0.106449	+	0.994318i	$0.466052\pi$
$354$	3.00000	0.159448
$355$	36.0000	1.91068
$356$	−12.0000	−0.635999
$357$	3.00000	0.158777
$358$	−6.00000	−0.317110
$359$	11.0000	0.580558	0.290279	−	0.956942i	$-0.406252\pi$
$359$	11.0000	0.580558	0.290279	+	0.956942i	$0.406252\pi$
$360$	−18.0000	−0.948683
$361$	−18.0000	−0.947368
$362$	−9.00000	−0.473029
$363$	33.0000	1.73205
$364$	−4.00000	−0.209657
$365$	30.0000	1.57027
$366$	18.0000	0.940875
$367$	12.0000	0.626395	0.313197	−	0.949688i	$-0.398600\pi$
$367$	12.0000	0.626395	0.313197	+	0.949688i	$0.398600\pi$
$368$	−2.00000	−0.104257
$369$	6.00000	0.312348
$370$	−12.0000	−0.623850
$371$	1.00000	0.0519174
$372$	12.0000	0.622171
$373$	−14.0000	−0.724893	−0.362446	−	0.932005i	$-0.618058\pi$
$373$	−14.0000	−0.724893	−0.362446	+	0.932005i	$0.618058\pi$
$374$	0	0
$375$	−9.00000	−0.464758
$376$	2.00000	0.103142
$377$	28.0000	1.44207
$378$	9.00000	0.462910
$379$	−25.0000	−1.28416	−0.642082	−	0.766636i	$-0.721929\pi$
$379$	−25.0000	−1.28416	−0.642082	+	0.766636i	$0.721929\pi$
$380$	3.00000	0.153897
$381$	−21.0000	−1.07586
$382$	−14.0000	−0.716302
$383$	−16.0000	−0.817562	−0.408781	−	0.912633i	$-0.634046\pi$
$383$	−16.0000	−0.817562	−0.408781	+	0.912633i	$0.634046\pi$
$384$	−3.00000	−0.153093
$385$	0	0
$386$	13.0000	0.661683
$387$	−24.0000	−1.21999
$388$	−8.00000	−0.406138
$389$	−14.0000	−0.709828	−0.354914	−	0.934899i	$-0.615490\pi$
$389$	−14.0000	−0.709828	−0.354914	+	0.934899i	$0.615490\pi$
$390$	36.0000	1.82293
$391$	−2.00000	−0.101144
$392$	−6.00000	−0.303046
$393$	18.0000	0.907980
$394$	10.0000	0.503793
$395$	21.0000	1.05662
$396$	0	0
$397$	−34.0000	−1.70641	−0.853206	−	0.521575i	$-0.825345\pi$
$397$	−34.0000	−1.70641	−0.853206	+	0.521575i	$0.825345\pi$
$398$	−5.00000	−0.250627
$399$	−3.00000	−0.150188
$400$	4.00000	0.200000
$401$	12.0000	0.599251	0.299626	−	0.954057i	$-0.403138\pi$
$401$	12.0000	0.599251	0.299626	+	0.954057i	$0.403138\pi$
$402$	0	0
$403$	−16.0000	−0.797017
$404$	0	0
$405$	−27.0000	−1.34164
$406$	−7.00000	−0.347404
$407$	0	0
$408$	−3.00000	−0.148522
$409$	0	0		−	1.00000i	$-0.5\pi$
$409$	0	0			1.00000i	$0.5\pi$
$410$	−3.00000	−0.148159
$411$	−9.00000	−0.443937
$412$	−12.0000	−0.591198
$413$	1.00000	0.0492068
$414$	−12.0000	−0.589768
$415$	−12.0000	−0.589057
$416$	4.00000	0.196116
$417$	−12.0000	−0.587643
$418$	0	0
$419$	40.0000	1.95413	0.977064	−	0.212946i	$-0.0683059\pi$
$419$	40.0000	1.95413	0.977064	+	0.212946i	$0.0683059\pi$
$420$	−9.00000	−0.439155
$421$	28.0000	1.36464	0.682318	−	0.731055i	$-0.260972\pi$
$421$	28.0000	1.36464	0.682318	+	0.731055i	$0.260972\pi$
$422$	8.00000	0.389434
$423$	12.0000	0.583460
$424$	−1.00000	−0.0485643
$425$	4.00000	0.194029
$426$	36.0000	1.74421
$427$	6.00000	0.290360
$428$	13.0000	0.628379
$429$	0	0
$430$	12.0000	0.578691
$431$	24.0000	1.15604	0.578020	−	0.816023i	$-0.303826\pi$
$431$	24.0000	1.15604	0.578020	+	0.816023i	$0.303826\pi$
$432$	−9.00000	−0.433013
$433$	−1.00000	−0.0480569	−0.0240285	−	0.999711i	$-0.507649\pi$
$433$	−1.00000	−0.0480569	−0.0240285	+	0.999711i	$0.507649\pi$
$434$	4.00000	0.192006
$435$	63.0000	3.02062
$436$	−10.0000	−0.478913
$437$	2.00000	0.0956730
$438$	30.0000	1.43346
$439$	16.0000	0.763638	0.381819	−	0.924237i	$-0.375298\pi$
$439$	16.0000	0.763638	0.381819	+	0.924237i	$0.375298\pi$
$440$	0	0
$441$	−36.0000	−1.71429
$442$	4.00000	0.190261
$443$	−24.0000	−1.14027	−0.570137	−	0.821549i	$-0.693110\pi$
$443$	−24.0000	−1.14027	−0.570137	+	0.821549i	$0.693110\pi$
$444$	−12.0000	−0.569495
$445$	36.0000	1.70656
$446$	0	0
$447$	−54.0000	−2.55411
$448$	−1.00000	−0.0472456
$449$	−9.00000	−0.424736	−0.212368	−	0.977190i	$-0.568118\pi$
$449$	−9.00000	−0.424736	−0.212368	+	0.977190i	$0.568118\pi$
$450$	24.0000	1.13137
$451$	0	0
$452$	10.0000	0.470360
$453$	0	0
$454$	−14.0000	−0.657053
$455$	12.0000	0.562569
$456$	3.00000	0.140488
$457$	−20.0000	−0.935561	−0.467780	−	0.883845i	$-0.654946\pi$
$457$	−20.0000	−0.935561	−0.467780	+	0.883845i	$0.654946\pi$
$458$	22.0000	1.02799
$459$	−9.00000	−0.420084
$460$	6.00000	0.279751
$461$	18.0000	0.838344	0.419172	−	0.907907i	$-0.362320\pi$
$461$	18.0000	0.838344	0.419172	+	0.907907i	$0.362320\pi$
$462$	0	0
$463$	2.00000	0.0929479	0.0464739	−	0.998920i	$-0.485202\pi$
$463$	2.00000	0.0929479	0.0464739	+	0.998920i	$0.485202\pi$
$464$	7.00000	0.324967
$465$	−36.0000	−1.66946
$466$	4.00000	0.185296
$467$	−42.0000	−1.94353	−0.971764	−	0.235954i	$-0.924178\pi$
$467$	−42.0000	−1.94353	−0.971764	+	0.235954i	$0.924178\pi$
$468$	24.0000	1.10940
$469$	0	0
$470$	−6.00000	−0.276759
$471$	42.0000	1.93526
$472$	−1.00000	−0.0460287
$473$	0	0
$474$	21.0000	0.964562
$475$	−4.00000	−0.183533
$476$	−1.00000	−0.0458349
$477$	−6.00000	−0.274721
$478$	−19.0000	−0.869040
$479$	16.0000	0.731059	0.365529	−	0.930800i	$-0.380888\pi$
$479$	16.0000	0.731059	0.365529	+	0.930800i	$0.380888\pi$
$480$	9.00000	0.410792
$481$	16.0000	0.729537
$482$	−5.00000	−0.227744
$483$	−6.00000	−0.273009
$484$	−11.0000	−0.500000
$485$	24.0000	1.08978
$486$	0	0
$487$	27.0000	1.22349	0.611743	−	0.791056i	$-0.290469\pi$
$487$	27.0000	1.22349	0.611743	+	0.791056i	$0.290469\pi$
$488$	−6.00000	−0.271607
$489$	−24.0000	−1.08532
$490$	18.0000	0.813157
$491$	9.00000	0.406164	0.203082	−	0.979162i	$-0.434904\pi$
$491$	9.00000	0.406164	0.203082	+	0.979162i	$0.434904\pi$
$492$	−3.00000	−0.135250
$493$	7.00000	0.315264
$494$	−4.00000	−0.179969
$495$	0	0
$496$	−4.00000	−0.179605
$497$	12.0000	0.538274
$498$	−12.0000	−0.537733
$499$	29.0000	1.29822	0.649109	−	0.760695i	$-0.275142\pi$
$499$	29.0000	1.29822	0.649109	+	0.760695i	$0.275142\pi$
$500$	3.00000	0.134164
$501$	63.0000	2.81463
$502$	−7.00000	−0.312425
$503$	32.0000	1.42681	0.713405	−	0.700752i	$-0.247152\pi$
$503$	32.0000	1.42681	0.713405	+	0.700752i	$0.247152\pi$
$504$	−6.00000	−0.267261
$505$	0	0
$506$	0	0
$507$	−9.00000	−0.399704
$508$	7.00000	0.310575
$509$	−22.0000	−0.975133	−0.487566	−	0.873086i	$-0.662115\pi$
$509$	−22.0000	−0.975133	−0.487566	+	0.873086i	$0.662115\pi$
$510$	9.00000	0.398527
$511$	10.0000	0.442374
$512$	1.00000	0.0441942
$513$	9.00000	0.397360
$514$	21.0000	0.926270
$515$	36.0000	1.58635
$516$	12.0000	0.528271
$517$	0	0
$518$	−4.00000	−0.175750
$519$	−24.0000	−1.05348
$520$	−12.0000	−0.526235
$521$	−38.0000	−1.66481	−0.832405	−	0.554168i	$-0.813037\pi$
$521$	−38.0000	−1.66481	−0.832405	+	0.554168i	$0.813037\pi$
$522$	42.0000	1.83829
$523$	1.00000	0.0437269	0.0218635	−	0.999761i	$-0.493040\pi$
$523$	1.00000	0.0437269	0.0218635	+	0.999761i	$0.493040\pi$
$524$	−6.00000	−0.262111
$525$	12.0000	0.523723
$526$	13.0000	0.566827
$527$	−4.00000	−0.174243
$528$	0	0
$529$	−19.0000	−0.826087
$530$	3.00000	0.130312
$531$	−6.00000	−0.260378
$532$	1.00000	0.0433555
$533$	4.00000	0.173259
$534$	36.0000	1.55787
$535$	−39.0000	−1.68612
$536$	0	0
$537$	18.0000	0.776757
$538$	−18.0000	−0.776035
$539$	0	0
$540$	27.0000	1.16190
$541$	−10.0000	−0.429934	−0.214967	−	0.976621i	$-0.568964\pi$
$541$	−10.0000	−0.429934	−0.214967	+	0.976621i	$0.568964\pi$
$542$	−29.0000	−1.24566
$543$	27.0000	1.15868
$544$	1.00000	0.0428746
$545$	30.0000	1.28506
$546$	12.0000	0.513553
$547$	−4.00000	−0.171028	−0.0855138	−	0.996337i	$-0.527253\pi$
$547$	−4.00000	−0.171028	−0.0855138	+	0.996337i	$0.527253\pi$
$548$	3.00000	0.128154
$549$	−36.0000	−1.53644
$550$	0	0
$551$	−7.00000	−0.298210
$552$	6.00000	0.255377
$553$	7.00000	0.297670
$554$	−23.0000	−0.977176
$555$	36.0000	1.52811
$556$	4.00000	0.169638
$557$	11.0000	0.466085	0.233042	−	0.972467i	$-0.425132\pi$
$557$	11.0000	0.466085	0.233042	+	0.972467i	$0.425132\pi$
$558$	−24.0000	−1.01600
$559$	−16.0000	−0.676728
$560$	3.00000	0.126773
$561$	0	0
$562$	15.0000	0.632737
$563$	14.0000	0.590030	0.295015	−	0.955493i	$-0.404675\pi$
$563$	14.0000	0.590030	0.295015	+	0.955493i	$0.404675\pi$
$564$	−6.00000	−0.252646
$565$	−30.0000	−1.26211
$566$	−18.0000	−0.756596
$567$	−9.00000	−0.377964
$568$	−12.0000	−0.503509
$569$	−18.0000	−0.754599	−0.377300	−	0.926091i	$-0.623147\pi$
$569$	−18.0000	−0.754599	−0.377300	+	0.926091i	$0.623147\pi$
$570$	−9.00000	−0.376969
$571$	12.0000	0.502184	0.251092	−	0.967963i	$-0.419210\pi$
$571$	12.0000	0.502184	0.251092	+	0.967963i	$0.419210\pi$
$572$	0	0
$573$	42.0000	1.75458
$574$	−1.00000	−0.0417392
$575$	−8.00000	−0.333623
$576$	6.00000	0.250000
$577$	−15.0000	−0.624458	−0.312229	−	0.950007i	$-0.601076\pi$
$577$	−15.0000	−0.624458	−0.312229	+	0.950007i	$0.601076\pi$
$578$	1.00000	0.0415945
$579$	−39.0000	−1.62078
$580$	−21.0000	−0.871978
$581$	−4.00000	−0.165948
$582$	24.0000	0.994832
$583$	0	0
$584$	−10.0000	−0.413803
$585$	−72.0000	−2.97683
$586$	−3.00000	−0.123929
$587$	24.0000	0.990586	0.495293	−	0.868726i	$-0.335061\pi$
$587$	24.0000	0.990586	0.495293	+	0.868726i	$0.335061\pi$
$588$	18.0000	0.742307
$589$	4.00000	0.164817
$590$	3.00000	0.123508
$591$	−30.0000	−1.23404
$592$	4.00000	0.164399
$593$	−3.00000	−0.123195	−0.0615976	−	0.998101i	$-0.519620\pi$
$593$	−3.00000	−0.123195	−0.0615976	+	0.998101i	$0.519620\pi$
$594$	0	0
$595$	3.00000	0.122988
$596$	18.0000	0.737309
$597$	15.0000	0.613909
$598$	−8.00000	−0.327144
$599$	−13.0000	−0.531166	−0.265583	−	0.964088i	$-0.585564\pi$
$599$	−13.0000	−0.531166	−0.265583	+	0.964088i	$0.585564\pi$
$600$	−12.0000	−0.489898
$601$	28.0000	1.14214	0.571072	−	0.820900i	$-0.306528\pi$
$601$	28.0000	1.14214	0.571072	+	0.820900i	$0.306528\pi$
$602$	4.00000	0.163028
$603$	0	0
$604$	0	0
$605$	33.0000	1.34164
$606$	0	0
$607$	11.0000	0.446476	0.223238	−	0.974764i	$-0.428337\pi$
$607$	11.0000	0.446476	0.223238	+	0.974764i	$0.428337\pi$
$608$	−1.00000	−0.0405554
$609$	21.0000	0.850963
$610$	18.0000	0.728799
$611$	8.00000	0.323645
$612$	6.00000	0.242536
$613$	20.0000	0.807792	0.403896	−	0.914805i	$-0.367656\pi$
$613$	20.0000	0.807792	0.403896	+	0.914805i	$0.367656\pi$
$614$	−23.0000	−0.928204
$615$	9.00000	0.362915
$616$	0	0
$617$	−41.0000	−1.65060	−0.825299	−	0.564696i	$-0.808993\pi$
$617$	−41.0000	−1.65060	−0.825299	+	0.564696i	$0.808993\pi$
$618$	36.0000	1.44813
$619$	−41.0000	−1.64793	−0.823965	−	0.566641i	$-0.808243\pi$
$619$	−41.0000	−1.64793	−0.823965	+	0.566641i	$0.808243\pi$
$620$	12.0000	0.481932
$621$	18.0000	0.722315
$622$	−29.0000	−1.16279
$623$	12.0000	0.480770
$624$	−12.0000	−0.480384
$625$	−29.0000	−1.16000
$626$	10.0000	0.399680
$627$	0	0
$628$	−14.0000	−0.558661
$629$	4.00000	0.159490
$630$	18.0000	0.717137
$631$	−12.0000	−0.477712	−0.238856	−	0.971055i	$-0.576772\pi$
$631$	−12.0000	−0.477712	−0.238856	+	0.971055i	$0.576772\pi$
$632$	−7.00000	−0.278445
$633$	−24.0000	−0.953914
$634$	10.0000	0.397151
$635$	−21.0000	−0.833360
$636$	3.00000	0.118958
$637$	−24.0000	−0.950915
$638$	0	0
$639$	−72.0000	−2.84828
$640$	−3.00000	−0.118585
$641$	2.00000	0.0789953	0.0394976	−	0.999220i	$-0.487424\pi$
$641$	2.00000	0.0789953	0.0394976	+	0.999220i	$0.487424\pi$
$642$	−39.0000	−1.53921
$643$	1.00000	0.0394362	0.0197181	−	0.999806i	$-0.493723\pi$
$643$	1.00000	0.0394362	0.0197181	+	0.999806i	$0.493723\pi$
$644$	2.00000	0.0788110
$645$	−36.0000	−1.41750
$646$	−1.00000	−0.0393445
$647$	−23.0000	−0.904223	−0.452112	−	0.891961i	$-0.649329\pi$
$647$	−23.0000	−0.904223	−0.452112	+	0.891961i	$0.649329\pi$
$648$	9.00000	0.353553
$649$	0	0
$650$	16.0000	0.627572
$651$	−12.0000	−0.470317
$652$	8.00000	0.313304
$653$	−39.0000	−1.52619	−0.763094	−	0.646288i	$-0.776321\pi$
$653$	−39.0000	−1.52619	−0.763094	+	0.646288i	$0.776321\pi$
$654$	30.0000	1.17309
$655$	18.0000	0.703318
$656$	1.00000	0.0390434
$657$	−60.0000	−2.34082
$658$	−2.00000	−0.0779681
$659$	−40.0000	−1.55818	−0.779089	−	0.626913i	$-0.784318\pi$
$659$	−40.0000	−1.55818	−0.779089	+	0.626913i	$0.784318\pi$
$660$	0	0
$661$	51.0000	1.98367	0.991835	−	0.127527i	$-0.0407041\pi$
$661$	51.0000	1.98367	0.991835	+	0.127527i	$0.0407041\pi$
$662$	−17.0000	−0.660724
$663$	−12.0000	−0.466041
$664$	4.00000	0.155230
$665$	−3.00000	−0.116335
$666$	24.0000	0.929981
$667$	−14.0000	−0.542082
$668$	−21.0000	−0.812514
$669$	0	0
$670$	0	0
$671$	0	0
$672$	3.00000	0.115728
$673$	−16.0000	−0.616755	−0.308377	−	0.951264i	$-0.599786\pi$
$673$	−16.0000	−0.616755	−0.308377	+	0.951264i	$0.599786\pi$
$674$	10.0000	0.385186
$675$	−36.0000	−1.38564
$676$	3.00000	0.115385
$677$	38.0000	1.46046	0.730229	−	0.683202i	$-0.239413\pi$
$677$	38.0000	1.46046	0.730229	+	0.683202i	$0.239413\pi$
$678$	−30.0000	−1.15214
$679$	8.00000	0.307012
$680$	−3.00000	−0.115045
$681$	42.0000	1.60944
$682$	0	0
$683$	−4.00000	−0.153056	−0.0765279	−	0.997067i	$-0.524383\pi$
$683$	−4.00000	−0.153056	−0.0765279	+	0.997067i	$0.524383\pi$
$684$	−6.00000	−0.229416
$685$	−9.00000	−0.343872
$686$	13.0000	0.496342
$687$	−66.0000	−2.51806
$688$	−4.00000	−0.152499
$689$	−4.00000	−0.152388
$690$	−18.0000	−0.685248
$691$	−14.0000	−0.532585	−0.266293	−	0.963892i	$-0.585799\pi$
$691$	−14.0000	−0.532585	−0.266293	+	0.963892i	$0.585799\pi$
$692$	8.00000	0.304114
$693$	0	0
$694$	−24.0000	−0.911028
$695$	−12.0000	−0.455186
$696$	−21.0000	−0.796003
$697$	1.00000	0.0378777
$698$	−6.00000	−0.227103
$699$	−12.0000	−0.453882
$700$	−4.00000	−0.151186
$701$	−24.0000	−0.906467	−0.453234	−	0.891392i	$-0.649730\pi$
$701$	−24.0000	−0.906467	−0.453234	+	0.891392i	$0.649730\pi$
$702$	−36.0000	−1.35873
$703$	−4.00000	−0.150863
$704$	0	0
$705$	18.0000	0.677919
$706$	4.00000	0.150542
$707$	0	0
$708$	3.00000	0.112747
$709$	−33.0000	−1.23934	−0.619671	−	0.784862i	$-0.712734\pi$
$709$	−33.0000	−1.23934	−0.619671	+	0.784862i	$0.712734\pi$
$710$	36.0000	1.35106
$711$	−42.0000	−1.57512
$712$	−12.0000	−0.449719
$713$	8.00000	0.299602
$714$	3.00000	0.112272
$715$	0	0
$716$	−6.00000	−0.224231
$717$	57.0000	2.12870
$718$	11.0000	0.410516
$719$	−8.00000	−0.298350	−0.149175	−	0.988811i	$-0.547662\pi$
$719$	−8.00000	−0.298350	−0.149175	+	0.988811i	$0.547662\pi$
$720$	−18.0000	−0.670820
$721$	12.0000	0.446903
$722$	−18.0000	−0.669891
$723$	15.0000	0.557856
$724$	−9.00000	−0.334482
$725$	28.0000	1.03989
$726$	33.0000	1.22474
$727$	32.0000	1.18681	0.593407	−	0.804902i	$-0.297782\pi$
$727$	32.0000	1.18681	0.593407	+	0.804902i	$0.297782\pi$
$728$	−4.00000	−0.148250
$729$	−27.0000	−1.00000
$730$	30.0000	1.11035
$731$	−4.00000	−0.147945
$732$	18.0000	0.665299
$733$	34.0000	1.25582	0.627909	−	0.778287i	$-0.283911\pi$
$733$	34.0000	1.25582	0.627909	+	0.778287i	$0.283911\pi$
$734$	12.0000	0.442928
$735$	−54.0000	−1.99182
$736$	−2.00000	−0.0737210
$737$	0	0
$738$	6.00000	0.220863
$739$	0	0		−	1.00000i	$-0.5\pi$
$739$	0	0			1.00000i	$0.5\pi$
$740$	−12.0000	−0.441129
$741$	12.0000	0.440831
$742$	1.00000	0.0367112
$743$	−16.0000	−0.586983	−0.293492	−	0.955962i	$-0.594817\pi$
$743$	−16.0000	−0.586983	−0.293492	+	0.955962i	$0.594817\pi$
$744$	12.0000	0.439941
$745$	−54.0000	−1.97841
$746$	−14.0000	−0.512576
$747$	24.0000	0.878114
$748$	0	0
$749$	−13.0000	−0.475010
$750$	−9.00000	−0.328634
$751$	34.0000	1.24068	0.620339	−	0.784334i	$-0.286995\pi$
$751$	34.0000	1.24068	0.620339	+	0.784334i	$0.286995\pi$
$752$	2.00000	0.0729325
$753$	21.0000	0.765283
$754$	28.0000	1.01970
$755$	0	0
$756$	9.00000	0.327327
$757$	−19.0000	−0.690567	−0.345283	−	0.938498i	$-0.612217\pi$
$757$	−19.0000	−0.690567	−0.345283	+	0.938498i	$0.612217\pi$
$758$	−25.0000	−0.908041
$759$	0	0
$760$	3.00000	0.108821
$761$	5.00000	0.181250	0.0906249	−	0.995885i	$-0.471114\pi$
$761$	5.00000	0.181250	0.0906249	+	0.995885i	$0.471114\pi$
$762$	−21.0000	−0.760750
$763$	10.0000	0.362024
$764$	−14.0000	−0.506502
$765$	−18.0000	−0.650791
$766$	−16.0000	−0.578103
$767$	−4.00000	−0.144432
$768$	−3.00000	−0.108253
$769$	−42.0000	−1.51456	−0.757279	−	0.653091i	$-0.773472\pi$
$769$	−42.0000	−1.51456	−0.757279	+	0.653091i	$0.773472\pi$
$770$	0	0
$771$	−63.0000	−2.26889
$772$	13.0000	0.467880
$773$	54.0000	1.94225	0.971123	−	0.238581i	$-0.0766824\pi$
$773$	54.0000	1.94225	0.971123	+	0.238581i	$0.0766824\pi$
$774$	−24.0000	−0.862662
$775$	−16.0000	−0.574737
$776$	−8.00000	−0.287183
$777$	12.0000	0.430498
$778$	−14.0000	−0.501924
$779$	−1.00000	−0.0358287
$780$	36.0000	1.28901
$781$	0	0
$782$	−2.00000	−0.0715199
$783$	−63.0000	−2.25144
$784$	−6.00000	−0.214286
$785$	42.0000	1.49904
$786$	18.0000	0.642039
$787$	4.00000	0.142585	0.0712923	−	0.997455i	$-0.477288\pi$
$787$	4.00000	0.142585	0.0712923	+	0.997455i	$0.477288\pi$
$788$	10.0000	0.356235
$789$	−39.0000	−1.38844
$790$	21.0000	0.747146
$791$	−10.0000	−0.355559
$792$	0	0
$793$	−24.0000	−0.852265
$794$	−34.0000	−1.20661
$795$	−9.00000	−0.319197
$796$	−5.00000	−0.177220
$797$	20.0000	0.708436	0.354218	−	0.935163i	$-0.384747\pi$
$797$	20.0000	0.708436	0.354218	+	0.935163i	$0.384747\pi$
$798$	−3.00000	−0.106199
$799$	2.00000	0.0707549
$800$	4.00000	0.141421
$801$	−72.0000	−2.54399
$802$	12.0000	0.423735
$803$	0	0
$804$	0	0
$805$	−6.00000	−0.211472
$806$	−16.0000	−0.563576
$807$	54.0000	1.90089
$808$	0	0
$809$	6.00000	0.210949	0.105474	−	0.994422i	$-0.466364\pi$
$809$	6.00000	0.210949	0.105474	+	0.994422i	$0.466364\pi$
$810$	−27.0000	−0.948683
$811$	4.00000	0.140459	0.0702295	−	0.997531i	$-0.477627\pi$
$811$	4.00000	0.140459	0.0702295	+	0.997531i	$0.477627\pi$
$812$	−7.00000	−0.245652
$813$	87.0000	3.05122
$814$	0	0
$815$	−24.0000	−0.840683
$816$	−3.00000	−0.105021
$817$	4.00000	0.139942
$818$	0	0
$819$	−24.0000	−0.838628
$820$	−3.00000	−0.104765
$821$	−42.0000	−1.46581	−0.732905	−	0.680331i	$-0.761836\pi$
$821$	−42.0000	−1.46581	−0.732905	+	0.680331i	$0.761836\pi$
$822$	−9.00000	−0.313911
$823$	−26.0000	−0.906303	−0.453152	−	0.891434i	$-0.649700\pi$
$823$	−26.0000	−0.906303	−0.453152	+	0.891434i	$0.649700\pi$
$824$	−12.0000	−0.418040
$825$	0	0
$826$	1.00000	0.0347945
$827$	44.0000	1.53003	0.765015	−	0.644013i	$-0.222732\pi$
$827$	44.0000	1.53003	0.765015	+	0.644013i	$0.222732\pi$
$828$	−12.0000	−0.417029
$829$	−31.0000	−1.07667	−0.538337	−	0.842729i	$-0.680947\pi$
$829$	−31.0000	−1.07667	−0.538337	+	0.842729i	$0.680947\pi$
$830$	−12.0000	−0.416526
$831$	69.0000	2.39358
$832$	4.00000	0.138675
$833$	−6.00000	−0.207888
$834$	−12.0000	−0.415526
$835$	63.0000	2.18020
$836$	0	0
$837$	36.0000	1.24434
$838$	40.0000	1.38178
$839$	50.0000	1.72619	0.863096	−	0.505040i	$-0.168522\pi$
$839$	50.0000	1.72619	0.863096	+	0.505040i	$0.168522\pi$
$840$	−9.00000	−0.310530
$841$	20.0000	0.689655
$842$	28.0000	0.964944
$843$	−45.0000	−1.54988
$844$	8.00000	0.275371
$845$	−9.00000	−0.309609
$846$	12.0000	0.412568
$847$	11.0000	0.377964
$848$	−1.00000	−0.0343401
$849$	54.0000	1.85328
$850$	4.00000	0.137199
$851$	−8.00000	−0.274236
$852$	36.0000	1.23334
$853$	55.0000	1.88316	0.941582	−	0.336784i	$-0.109339\pi$
$853$	55.0000	1.88316	0.941582	+	0.336784i	$0.109339\pi$
$854$	6.00000	0.205316
$855$	18.0000	0.615587
$856$	13.0000	0.444331
$857$	18.0000	0.614868	0.307434	−	0.951569i	$-0.400530\pi$
$857$	18.0000	0.614868	0.307434	+	0.951569i	$0.400530\pi$
$858$	0	0
$859$	−10.0000	−0.341196	−0.170598	−	0.985341i	$-0.554570\pi$
$859$	−10.0000	−0.341196	−0.170598	+	0.985341i	$0.554570\pi$
$860$	12.0000	0.409197
$861$	3.00000	0.102240
$862$	24.0000	0.817443
$863$	−6.00000	−0.204242	−0.102121	−	0.994772i	$-0.532563\pi$
$863$	−6.00000	−0.204242	−0.102121	+	0.994772i	$0.532563\pi$
$864$	−9.00000	−0.306186
$865$	−24.0000	−0.816024
$866$	−1.00000	−0.0339814
$867$	−3.00000	−0.101885
$868$	4.00000	0.135769
$869$	0	0
$870$	63.0000	2.13590
$871$	0	0
$872$	−10.0000	−0.338643
$873$	−48.0000	−1.62455
$874$	2.00000	0.0676510
$875$	−3.00000	−0.101419
$876$	30.0000	1.01361
$877$	−5.00000	−0.168838	−0.0844190	−	0.996430i	$-0.526903\pi$
$877$	−5.00000	−0.168838	−0.0844190	+	0.996430i	$0.526903\pi$
$878$	16.0000	0.539974
$879$	9.00000	0.303562
$880$	0	0
$881$	−12.0000	−0.404290	−0.202145	−	0.979356i	$-0.564791\pi$
$881$	−12.0000	−0.404290	−0.202145	+	0.979356i	$0.564791\pi$
$882$	−36.0000	−1.21218
$883$	−27.0000	−0.908622	−0.454311	−	0.890843i	$-0.650115\pi$
$883$	−27.0000	−0.908622	−0.454311	+	0.890843i	$0.650115\pi$
$884$	4.00000	0.134535
$885$	−9.00000	−0.302532
$886$	−24.0000	−0.806296
$887$	18.0000	0.604381	0.302190	−	0.953248i	$-0.402282\pi$
$887$	18.0000	0.604381	0.302190	+	0.953248i	$0.402282\pi$
$888$	−12.0000	−0.402694
$889$	−7.00000	−0.234772
$890$	36.0000	1.20672
$891$	0	0
$892$	0	0
$893$	−2.00000	−0.0669274
$894$	−54.0000	−1.80603
$895$	18.0000	0.601674
$896$	−1.00000	−0.0334077
$897$	24.0000	0.801337
$898$	−9.00000	−0.300334
$899$	−28.0000	−0.933852
$900$	24.0000	0.800000
$901$	−1.00000	−0.0333148
$902$	0	0
$903$	−12.0000	−0.399335
$904$	10.0000	0.332595
$905$	27.0000	0.897510
$906$	0	0
$907$	9.00000	0.298840	0.149420	−	0.988774i	$-0.452259\pi$
$907$	9.00000	0.298840	0.149420	+	0.988774i	$0.452259\pi$
$908$	−14.0000	−0.464606
$909$	0	0
$910$	12.0000	0.397796
$911$	−17.0000	−0.563235	−0.281618	−	0.959527i	$-0.590871\pi$
$911$	−17.0000	−0.563235	−0.281618	+	0.959527i	$0.590871\pi$
$912$	3.00000	0.0993399
$913$	0	0
$914$	−20.0000	−0.661541
$915$	−54.0000	−1.78518
$916$	22.0000	0.726900
$917$	6.00000	0.198137
$918$	−9.00000	−0.297044
$919$	16.0000	0.527791	0.263896	−	0.964551i	$-0.414993\pi$
$919$	16.0000	0.527791	0.263896	+	0.964551i	$0.414993\pi$
$920$	6.00000	0.197814
$921$	69.0000	2.27363
$922$	18.0000	0.592798
$923$	−48.0000	−1.57994
$924$	0	0
$925$	16.0000	0.526077
$926$	2.00000	0.0657241
$927$	−72.0000	−2.36479
$928$	7.00000	0.229786
$929$	48.0000	1.57483	0.787414	−	0.616424i	$-0.211419\pi$
$929$	48.0000	1.57483	0.787414	+	0.616424i	$0.211419\pi$
$930$	−36.0000	−1.18049
$931$	6.00000	0.196642
$932$	4.00000	0.131024
$933$	87.0000	2.84825
$934$	−42.0000	−1.37428
$935$	0	0
$936$	24.0000	0.784465
$937$	14.0000	0.457360	0.228680	−	0.973502i	$-0.426559\pi$
$937$	14.0000	0.457360	0.228680	+	0.973502i	$0.426559\pi$
$938$	0	0
$939$	−30.0000	−0.979013
$940$	−6.00000	−0.195698
$941$	28.0000	0.912774	0.456387	−	0.889781i	$-0.349143\pi$
$941$	28.0000	0.912774	0.456387	+	0.889781i	$0.349143\pi$
$942$	42.0000	1.36843
$943$	−2.00000	−0.0651290
$944$	−1.00000	−0.0325472
$945$	−27.0000	−0.878310
$946$	0	0
$947$	−39.0000	−1.26733	−0.633665	−	0.773608i	$-0.718450\pi$
$947$	−39.0000	−1.26733	−0.633665	+	0.773608i	$0.718450\pi$
$948$	21.0000	0.682048
$949$	−40.0000	−1.29845
$950$	−4.00000	−0.129777
$951$	−30.0000	−0.972817
$952$	−1.00000	−0.0324102
$953$	6.00000	0.194359	0.0971795	−	0.995267i	$-0.469018\pi$
$953$	6.00000	0.194359	0.0971795	+	0.995267i	$0.469018\pi$
$954$	−6.00000	−0.194257
$955$	42.0000	1.35909
$956$	−19.0000	−0.614504
$957$	0	0
$958$	16.0000	0.516937
$959$	−3.00000	−0.0968751
$960$	9.00000	0.290474
$961$	−15.0000	−0.483871
$962$	16.0000	0.515861
$963$	78.0000	2.51351
$964$	−5.00000	−0.161039
$965$	−39.0000	−1.25545
$966$	−6.00000	−0.193047
$967$	6.00000	0.192947	0.0964735	−	0.995336i	$-0.469244\pi$
$967$	6.00000	0.192947	0.0964735	+	0.995336i	$0.469244\pi$
$968$	−11.0000	−0.353553
$969$	3.00000	0.0963739
$970$	24.0000	0.770594
$971$	21.0000	0.673922	0.336961	−	0.941519i	$-0.390601\pi$
$971$	21.0000	0.673922	0.336961	+	0.941519i	$0.390601\pi$
$972$	0	0
$973$	−4.00000	−0.128234
$974$	27.0000	0.865136
$975$	−48.0000	−1.53723
$976$	−6.00000	−0.192055
$977$	−30.0000	−0.959785	−0.479893	−	0.877327i	$-0.659324\pi$
$977$	−30.0000	−0.959785	−0.479893	+	0.877327i	$0.659324\pi$
$978$	−24.0000	−0.767435
$979$	0	0
$980$	18.0000	0.574989
$981$	−60.0000	−1.91565
$982$	9.00000	0.287202
$983$	38.0000	1.21201	0.606006	−	0.795460i	$-0.292771\pi$
$983$	38.0000	1.21201	0.606006	+	0.795460i	$0.292771\pi$
$984$	−3.00000	−0.0956365
$985$	−30.0000	−0.955879
$986$	7.00000	0.222925
$987$	6.00000	0.190982
$988$	−4.00000	−0.127257
$989$	8.00000	0.254385
$990$	0	0
$991$	−12.0000	−0.381193	−0.190596	−	0.981669i	$-0.561042\pi$
$991$	−12.0000	−0.381193	−0.190596	+	0.981669i	$0.561042\pi$
$992$	−4.00000	−0.127000
$993$	51.0000	1.61844
$994$	12.0000	0.380617
$995$	15.0000	0.475532
$996$	−12.0000	−0.380235
$997$	59.0000	1.86855	0.934274	−	0.356555i	$-0.116049\pi$
$997$	59.0000	1.86855	0.934274	+	0.356555i	$0.116049\pi$
$998$	29.0000	0.917979
$999$	−36.0000	−1.13899

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2006.2.a.g.1.1	✓	1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2006.2.a.g.1.1	✓	1	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 2006 = 2 \cdot 17 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2006.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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