LMFDB - Embedded newform 5610.2.a.n.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5610,2,Mod(1,5610)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5610, 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("5610.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5610 = 2 \cdot 3 \cdot 5 \cdot 11 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5610.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:	$44.7960755339$
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	$\chi$	$=$	5610.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

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

\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} +1.00000 q^{11} +1.00000 q^{12} -2.00000 q^{13} -1.00000 q^{15} +1.00000 q^{16} -1.00000 q^{17} -1.00000 q^{18} -1.00000 q^{20} -1.00000 q^{22} +8.00000 q^{23} -1.00000 q^{24} +1.00000 q^{25} +2.00000 q^{26} +1.00000 q^{27} -6.00000 q^{29} +1.00000 q^{30} -8.00000 q^{31} -1.00000 q^{32} +1.00000 q^{33} +1.00000 q^{34} +1.00000 q^{36} -10.0000 q^{37} -2.00000 q^{39} +1.00000 q^{40} -6.00000 q^{41} +12.0000 q^{43} +1.00000 q^{44} -1.00000 q^{45} -8.00000 q^{46} +8.00000 q^{47} +1.00000 q^{48} -7.00000 q^{49} -1.00000 q^{50} -1.00000 q^{51} -2.00000 q^{52} -10.0000 q^{53} -1.00000 q^{54} -1.00000 q^{55} +6.00000 q^{58} -4.00000 q^{59} -1.00000 q^{60} +14.0000 q^{61} +8.00000 q^{62} +1.00000 q^{64} +2.00000 q^{65} -1.00000 q^{66} -4.00000 q^{67} -1.00000 q^{68} +8.00000 q^{69} -1.00000 q^{72} -14.0000 q^{73} +10.0000 q^{74} +1.00000 q^{75} +2.00000 q^{78} +8.00000 q^{79} -1.00000 q^{80} +1.00000 q^{81} +6.00000 q^{82} +12.0000 q^{83} +1.00000 q^{85} -12.0000 q^{86} -6.00000 q^{87} -1.00000 q^{88} +10.0000 q^{89} +1.00000 q^{90} +8.00000 q^{92} -8.00000 q^{93} -8.00000 q^{94} -1.00000 q^{96} -18.0000 q^{97} +7.00000 q^{98} +1.00000 q^{99} +O(q^{100})\)

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
$2$	−1.00000	−0.707107
$3$	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
$7$	0	0		−	1.00000i	$-0.5\pi$
$7$	0	0			1.00000i	$0.5\pi$
$8$	−1.00000	−0.353553
$9$	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	$0.589456\pi$
$14$	0	0
$15$	−1.00000	−0.258199
$16$	1.00000	0.250000
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−1.00000	−0.235702
$19$	0	0		−	1.00000i	$-0.5\pi$
$19$	0	0			1.00000i	$0.5\pi$
$20$	−1.00000	−0.223607
$21$	0	0
$22$	−1.00000	−0.213201
$23$	8.00000	1.66812	0.834058	−	0.551677i	$-0.186012\pi$
$23$	8.00000	1.66812	0.834058	+	0.551677i	$0.186012\pi$
$24$	−1.00000	−0.204124
$25$	1.00000	0.200000
$26$	2.00000	0.392232
$27$	1.00000	0.192450
$28$	0	0
$29$	−6.00000	−1.11417	−0.557086	−	0.830455i	$-0.688081\pi$
$29$	−6.00000	−1.11417	−0.557086	+	0.830455i	$0.688081\pi$
$30$	1.00000	0.182574
$31$	−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
$33$	1.00000	0.174078
$34$	1.00000	0.171499
$35$	0	0
$36$	1.00000	0.166667
$37$	−10.0000	−1.64399	−0.821995	−	0.569495i	$-0.807139\pi$
$37$	−10.0000	−1.64399	−0.821995	+	0.569495i	$0.807139\pi$
$38$	0	0
$39$	−2.00000	−0.320256
$40$	1.00000	0.158114
$41$	−6.00000	−0.937043	−0.468521	−	0.883452i	$-0.655213\pi$
$41$	−6.00000	−0.937043	−0.468521	+	0.883452i	$0.655213\pi$
$42$	0	0
$43$	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
$46$	−8.00000	−1.17954
$47$	8.00000	1.16692	0.583460	−	0.812142i	$-0.301699\pi$
$47$	8.00000	1.16692	0.583460	+	0.812142i	$0.301699\pi$
$48$	1.00000	0.144338
$49$	−7.00000	−1.00000
$50$	−1.00000	−0.141421
$51$	−1.00000	−0.140028
$52$	−2.00000	−0.277350
$53$	−10.0000	−1.37361	−0.686803	−	0.726844i	$-0.740986\pi$
$53$	−10.0000	−1.37361	−0.686803	+	0.726844i	$0.740986\pi$
$54$	−1.00000	−0.136083
$55$	−1.00000	−0.134840
$56$	0	0
$57$	0	0
$58$	6.00000	0.787839
$59$	−4.00000	−0.520756	−0.260378	−	0.965507i	$-0.583847\pi$
$59$	−4.00000	−0.520756	−0.260378	+	0.965507i	$0.583847\pi$
$60$	−1.00000	−0.129099
$61$	14.0000	1.79252	0.896258	−	0.443533i	$-0.146275\pi$
$61$	14.0000	1.79252	0.896258	+	0.443533i	$0.146275\pi$
$62$	8.00000	1.01600
$63$	0	0
$64$	1.00000	0.125000
$65$	2.00000	0.248069
$66$	−1.00000	−0.123091
$67$	−4.00000	−0.488678	−0.244339	−	0.969690i	$-0.578571\pi$
$67$	−4.00000	−0.488678	−0.244339	+	0.969690i	$0.578571\pi$
$68$	−1.00000	−0.121268
$69$	8.00000	0.963087
$70$	0	0
$71$	0	0		−	1.00000i	$-0.5\pi$
$71$	0	0			1.00000i	$0.5\pi$
$72$	−1.00000	−0.117851
$73$	−14.0000	−1.63858	−0.819288	−	0.573382i	$-0.805631\pi$
$73$	−14.0000	−1.63858	−0.819288	+	0.573382i	$0.805631\pi$
$74$	10.0000	1.16248
$75$	1.00000	0.115470
$76$	0	0
$77$	0	0
$78$	2.00000	0.226455
$79$	8.00000	0.900070	0.450035	−	0.893011i	$-0.351411\pi$
$79$	8.00000	0.900070	0.450035	+	0.893011i	$0.351411\pi$
$80$	−1.00000	−0.111803
$81$	1.00000	0.111111
$82$	6.00000	0.662589
$83$	12.0000	1.31717	0.658586	−	0.752506i	$-0.271155\pi$
$83$	12.0000	1.31717	0.658586	+	0.752506i	$0.271155\pi$
$84$	0	0
$85$	1.00000	0.108465
$86$	−12.0000	−1.29399
$87$	−6.00000	−0.643268
$88$	−1.00000	−0.106600
$89$	10.0000	1.06000	0.529999	−	0.847998i	$-0.322192\pi$
$89$	10.0000	1.06000	0.529999	+	0.847998i	$0.322192\pi$
$90$	1.00000	0.105409
$91$	0	0
$92$	8.00000	0.834058
$93$	−8.00000	−0.829561
$94$	−8.00000	−0.825137
$95$	0	0
$96$	−1.00000	−0.102062
$97$	−18.0000	−1.82762	−0.913812	−	0.406138i	$-0.866875\pi$
$97$	−18.0000	−1.82762	−0.913812	+	0.406138i	$0.866875\pi$
$98$	7.00000	0.707107
$99$	1.00000	0.100504
$100$	1.00000	0.100000
$101$	−6.00000	−0.597022	−0.298511	−	0.954406i	$-0.596490\pi$
$101$	−6.00000	−0.597022	−0.298511	+	0.954406i	$0.596490\pi$
$102$	1.00000	0.0990148
$103$	−16.0000	−1.57653	−0.788263	−	0.615338i	$-0.789020\pi$
$103$	−16.0000	−1.57653	−0.788263	+	0.615338i	$0.789020\pi$
$104$	2.00000	0.196116
$105$	0	0
$106$	10.0000	0.971286
$107$	0	0		−	1.00000i	$-0.5\pi$
$107$	0	0			1.00000i	$0.5\pi$
$108$	1.00000	0.0962250
$109$	−2.00000	−0.191565	−0.0957826	−	0.995402i	$-0.530535\pi$
$109$	−2.00000	−0.191565	−0.0957826	+	0.995402i	$0.530535\pi$
$110$	1.00000	0.0953463
$111$	−10.0000	−0.949158
$112$	0	0
$113$	−2.00000	−0.188144	−0.0940721	−	0.995565i	$-0.529988\pi$
$113$	−2.00000	−0.188144	−0.0940721	+	0.995565i	$0.529988\pi$
$114$	0	0
$115$	−8.00000	−0.746004
$116$	−6.00000	−0.557086
$117$	−2.00000	−0.184900
$118$	4.00000	0.368230
$119$	0	0
$120$	1.00000	0.0912871
$121$	1.00000	0.0909091
$122$	−14.0000	−1.26750
$123$	−6.00000	−0.541002
$124$	−8.00000	−0.718421
$125$	−1.00000	−0.0894427
$126$	0	0
$127$	4.00000	0.354943	0.177471	−	0.984126i	$-0.443208\pi$
$127$	4.00000	0.354943	0.177471	+	0.984126i	$0.443208\pi$
$128$	−1.00000	−0.0883883
$129$	12.0000	1.05654
$130$	−2.00000	−0.175412
$131$	12.0000	1.04844	0.524222	−	0.851581i	$-0.324356\pi$
$131$	12.0000	1.04844	0.524222	+	0.851581i	$0.324356\pi$
$132$	1.00000	0.0870388
$133$	0	0
$134$	4.00000	0.345547
$135$	−1.00000	−0.0860663
$136$	1.00000	0.0857493
$137$	−18.0000	−1.53784	−0.768922	−	0.639343i	$-0.779207\pi$
$137$	−18.0000	−1.53784	−0.768922	+	0.639343i	$0.779207\pi$
$138$	−8.00000	−0.681005
$139$	−12.0000	−1.01783	−0.508913	−	0.860818i	$-0.669953\pi$
$139$	−12.0000	−1.01783	−0.508913	+	0.860818i	$0.669953\pi$
$140$	0	0
$141$	8.00000	0.673722
$142$	0	0
$143$	−2.00000	−0.167248
$144$	1.00000	0.0833333
$145$	6.00000	0.498273
$146$	14.0000	1.15865
$147$	−7.00000	−0.577350
$148$	−10.0000	−0.821995
$149$	10.0000	0.819232	0.409616	−	0.912258i	$-0.365663\pi$
$149$	10.0000	0.819232	0.409616	+	0.912258i	$0.365663\pi$
$150$	−1.00000	−0.0816497
$151$	16.0000	1.30206	0.651031	−	0.759051i	$-0.274337\pi$
$151$	16.0000	1.30206	0.651031	+	0.759051i	$0.274337\pi$
$152$	0	0
$153$	−1.00000	−0.0808452
$154$	0	0
$155$	8.00000	0.642575
$156$	−2.00000	−0.160128
$157$	−18.0000	−1.43656	−0.718278	−	0.695756i	$-0.755069\pi$
$157$	−18.0000	−1.43656	−0.718278	+	0.695756i	$0.755069\pi$
$158$	−8.00000	−0.636446
$159$	−10.0000	−0.793052
$160$	1.00000	0.0790569
$161$	0	0
$162$	−1.00000	−0.0785674
$163$	−12.0000	−0.939913	−0.469956	−	0.882690i	$-0.655730\pi$
$163$	−12.0000	−0.939913	−0.469956	+	0.882690i	$0.655730\pi$
$164$	−6.00000	−0.468521
$165$	−1.00000	−0.0778499
$166$	−12.0000	−0.931381
$167$	16.0000	1.23812	0.619059	−	0.785345i	$-0.287514\pi$
$167$	16.0000	1.23812	0.619059	+	0.785345i	$0.287514\pi$
$168$	0	0
$169$	−9.00000	−0.692308
$170$	−1.00000	−0.0766965
$171$	0	0
$172$	12.0000	0.914991
$173$	14.0000	1.06440	0.532200	−	0.846619i	$-0.321365\pi$
$173$	14.0000	1.06440	0.532200	+	0.846619i	$0.321365\pi$
$174$	6.00000	0.454859
$175$	0	0
$176$	1.00000	0.0753778
$177$	−4.00000	−0.300658
$178$	−10.0000	−0.749532
$179$	−12.0000	−0.896922	−0.448461	−	0.893802i	$-0.648028\pi$
$179$	−12.0000	−0.896922	−0.448461	+	0.893802i	$0.648028\pi$
$180$	−1.00000	−0.0745356
$181$	10.0000	0.743294	0.371647	−	0.928374i	$-0.378793\pi$
$181$	10.0000	0.743294	0.371647	+	0.928374i	$0.378793\pi$
$182$	0	0
$183$	14.0000	1.03491
$184$	−8.00000	−0.589768
$185$	10.0000	0.735215
$186$	8.00000	0.586588
$187$	−1.00000	−0.0731272
$188$	8.00000	0.583460
$189$	0	0
$190$	0	0
$191$	20.0000	1.44715	0.723575	−	0.690246i	$-0.242498\pi$
$191$	20.0000	1.44715	0.723575	+	0.690246i	$0.242498\pi$
$192$	1.00000	0.0721688
$193$	−22.0000	−1.58359	−0.791797	−	0.610784i	$-0.790854\pi$
$193$	−22.0000	−1.58359	−0.791797	+	0.610784i	$0.790854\pi$
$194$	18.0000	1.29232
$195$	2.00000	0.143223
$196$	−7.00000	−0.500000
$197$	−18.0000	−1.28245	−0.641223	−	0.767354i	$-0.721573\pi$
$197$	−18.0000	−1.28245	−0.641223	+	0.767354i	$0.721573\pi$
$198$	−1.00000	−0.0710669
$199$	−8.00000	−0.567105	−0.283552	−	0.958957i	$-0.591513\pi$
$199$	−8.00000	−0.567105	−0.283552	+	0.958957i	$0.591513\pi$
$200$	−1.00000	−0.0707107
$201$	−4.00000	−0.282138
$202$	6.00000	0.422159
$203$	0	0
$204$	−1.00000	−0.0700140
$205$	6.00000	0.419058
$206$	16.0000	1.11477
$207$	8.00000	0.556038
$208$	−2.00000	−0.138675
$209$	0	0
$210$	0	0
$211$	−28.0000	−1.92760	−0.963800	−	0.266627i	$-0.914091\pi$
$211$	−28.0000	−1.92760	−0.963800	+	0.266627i	$0.914091\pi$
$212$	−10.0000	−0.686803
$213$	0	0
$214$	0	0
$215$	−12.0000	−0.818393
$216$	−1.00000	−0.0680414
$217$	0	0
$218$	2.00000	0.135457
$219$	−14.0000	−0.946032
$220$	−1.00000	−0.0674200
$221$	2.00000	0.134535
$222$	10.0000	0.671156
$223$	−16.0000	−1.07144	−0.535720	−	0.844396i	$-0.679960\pi$
$223$	−16.0000	−1.07144	−0.535720	+	0.844396i	$0.679960\pi$
$224$	0	0
$225$	1.00000	0.0666667
$226$	2.00000	0.133038
$227$	−24.0000	−1.59294	−0.796468	−	0.604681i	$-0.793301\pi$
$227$	−24.0000	−1.59294	−0.796468	+	0.604681i	$0.793301\pi$
$228$	0	0
$229$	14.0000	0.925146	0.462573	−	0.886581i	$-0.346926\pi$
$229$	14.0000	0.925146	0.462573	+	0.886581i	$0.346926\pi$
$230$	8.00000	0.527504
$231$	0	0
$232$	6.00000	0.393919
$233$	−18.0000	−1.17922	−0.589610	−	0.807688i	$-0.700718\pi$
$233$	−18.0000	−1.17922	−0.589610	+	0.807688i	$0.700718\pi$
$234$	2.00000	0.130744
$235$	−8.00000	−0.521862
$236$	−4.00000	−0.260378
$237$	8.00000	0.519656
$238$	0	0
$239$	−8.00000	−0.517477	−0.258738	−	0.965947i	$-0.583307\pi$
$239$	−8.00000	−0.517477	−0.258738	+	0.965947i	$0.583307\pi$
$240$	−1.00000	−0.0645497
$241$	−14.0000	−0.901819	−0.450910	−	0.892570i	$-0.648900\pi$
$241$	−14.0000	−0.901819	−0.450910	+	0.892570i	$0.648900\pi$
$242$	−1.00000	−0.0642824
$243$	1.00000	0.0641500
$244$	14.0000	0.896258
$245$	7.00000	0.447214
$246$	6.00000	0.382546
$247$	0	0
$248$	8.00000	0.508001
$249$	12.0000	0.760469
$250$	1.00000	0.0632456
$251$	4.00000	0.252478	0.126239	−	0.992000i	$-0.459709\pi$
$251$	4.00000	0.252478	0.126239	+	0.992000i	$0.459709\pi$
$252$	0	0
$253$	8.00000	0.502956
$254$	−4.00000	−0.250982
$255$	1.00000	0.0626224
$256$	1.00000	0.0625000
$257$	14.0000	0.873296	0.436648	−	0.899632i	$-0.356166\pi$
$257$	14.0000	0.873296	0.436648	+	0.899632i	$0.356166\pi$
$258$	−12.0000	−0.747087
$259$	0	0
$260$	2.00000	0.124035
$261$	−6.00000	−0.371391
$262$	−12.0000	−0.741362
$263$	0	0		−	1.00000i	$-0.5\pi$
$263$	0	0			1.00000i	$0.5\pi$
$264$	−1.00000	−0.0615457
$265$	10.0000	0.614295
$266$	0	0
$267$	10.0000	0.611990
$268$	−4.00000	−0.244339
$269$	18.0000	1.09748	0.548740	−	0.835993i	$-0.315108\pi$
$269$	18.0000	1.09748	0.548740	+	0.835993i	$0.315108\pi$
$270$	1.00000	0.0608581
$271$	0	0		−	1.00000i	$-0.5\pi$
$271$	0	0			1.00000i	$0.5\pi$
$272$	−1.00000	−0.0606339
$273$	0	0
$274$	18.0000	1.08742
$275$	1.00000	0.0603023
$276$	8.00000	0.481543
$277$	6.00000	0.360505	0.180253	−	0.983620i	$-0.442309\pi$
$277$	6.00000	0.360505	0.180253	+	0.983620i	$0.442309\pi$
$278$	12.0000	0.719712
$279$	−8.00000	−0.478947
$280$	0	0
$281$	−26.0000	−1.55103	−0.775515	−	0.631329i	$-0.782510\pi$
$281$	−26.0000	−1.55103	−0.775515	+	0.631329i	$0.782510\pi$
$282$	−8.00000	−0.476393
$283$	−4.00000	−0.237775	−0.118888	−	0.992908i	$-0.537933\pi$
$283$	−4.00000	−0.237775	−0.118888	+	0.992908i	$0.537933\pi$
$284$	0	0
$285$	0	0
$286$	2.00000	0.118262
$287$	0	0
$288$	−1.00000	−0.0589256
$289$	1.00000	0.0588235
$290$	−6.00000	−0.352332
$291$	−18.0000	−1.05518
$292$	−14.0000	−0.819288
$293$	−6.00000	−0.350524	−0.175262	−	0.984522i	$-0.556077\pi$
$293$	−6.00000	−0.350524	−0.175262	+	0.984522i	$0.556077\pi$
$294$	7.00000	0.408248
$295$	4.00000	0.232889
$296$	10.0000	0.581238
$297$	1.00000	0.0580259
$298$	−10.0000	−0.579284
$299$	−16.0000	−0.925304
$300$	1.00000	0.0577350
$301$	0	0
$302$	−16.0000	−0.920697
$303$	−6.00000	−0.344691
$304$	0	0
$305$	−14.0000	−0.801638
$306$	1.00000	0.0571662
$307$	4.00000	0.228292	0.114146	−	0.993464i	$-0.463587\pi$
$307$	4.00000	0.228292	0.114146	+	0.993464i	$0.463587\pi$
$308$	0	0
$309$	−16.0000	−0.910208
$310$	−8.00000	−0.454369
$311$	8.00000	0.453638	0.226819	−	0.973937i	$-0.427167\pi$
$311$	8.00000	0.453638	0.226819	+	0.973937i	$0.427167\pi$
$312$	2.00000	0.113228
$313$	6.00000	0.339140	0.169570	−	0.985518i	$-0.445762\pi$
$313$	6.00000	0.339140	0.169570	+	0.985518i	$0.445762\pi$
$314$	18.0000	1.01580
$315$	0	0
$316$	8.00000	0.450035
$317$	−30.0000	−1.68497	−0.842484	−	0.538721i	$-0.818908\pi$
$317$	−30.0000	−1.68497	−0.842484	+	0.538721i	$0.818908\pi$
$318$	10.0000	0.560772
$319$	−6.00000	−0.335936
$320$	−1.00000	−0.0559017
$321$	0	0
$322$	0	0
$323$	0	0
$324$	1.00000	0.0555556
$325$	−2.00000	−0.110940
$326$	12.0000	0.664619
$327$	−2.00000	−0.110600
$328$	6.00000	0.331295
$329$	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	$0.606978\pi$
$332$	12.0000	0.658586
$333$	−10.0000	−0.547997
$334$	−16.0000	−0.875481
$335$	4.00000	0.218543
$336$	0	0
$337$	10.0000	0.544735	0.272367	−	0.962193i	$-0.412193\pi$
$337$	10.0000	0.544735	0.272367	+	0.962193i	$0.412193\pi$
$338$	9.00000	0.489535
$339$	−2.00000	−0.108625
$340$	1.00000	0.0542326
$341$	−8.00000	−0.433224
$342$	0	0
$343$	0	0
$344$	−12.0000	−0.646997
$345$	−8.00000	−0.430706
$346$	−14.0000	−0.752645
$347$	0	0		−	1.00000i	$-0.5\pi$
$347$	0	0			1.00000i	$0.5\pi$
$348$	−6.00000	−0.321634
$349$	18.0000	0.963518	0.481759	−	0.876304i	$-0.339998\pi$
$349$	18.0000	0.963518	0.481759	+	0.876304i	$0.339998\pi$
$350$	0	0
$351$	−2.00000	−0.106752
$352$	−1.00000	−0.0533002
$353$	22.0000	1.17094	0.585471	−	0.810693i	$-0.300910\pi$
$353$	22.0000	1.17094	0.585471	+	0.810693i	$0.300910\pi$
$354$	4.00000	0.212598
$355$	0	0
$356$	10.0000	0.529999
$357$	0	0
$358$	12.0000	0.634220
$359$	8.00000	0.422224	0.211112	−	0.977462i	$-0.432292\pi$
$359$	8.00000	0.422224	0.211112	+	0.977462i	$0.432292\pi$
$360$	1.00000	0.0527046
$361$	−19.0000	−1.00000
$362$	−10.0000	−0.525588
$363$	1.00000	0.0524864
$364$	0	0
$365$	14.0000	0.732793
$366$	−14.0000	−0.731792
$367$	−28.0000	−1.46159	−0.730794	−	0.682598i	$-0.760850\pi$
$367$	−28.0000	−1.46159	−0.730794	+	0.682598i	$0.760850\pi$
$368$	8.00000	0.417029
$369$	−6.00000	−0.312348
$370$	−10.0000	−0.519875
$371$	0	0
$372$	−8.00000	−0.414781
$373$	14.0000	0.724893	0.362446	−	0.932005i	$-0.381942\pi$
$373$	14.0000	0.724893	0.362446	+	0.932005i	$0.381942\pi$
$374$	1.00000	0.0517088
$375$	−1.00000	−0.0516398
$376$	−8.00000	−0.412568
$377$	12.0000	0.618031
$378$	0	0
$379$	0	0		−	1.00000i	$-0.5\pi$
$379$	0	0			1.00000i	$0.5\pi$
$380$	0	0
$381$	4.00000	0.204926
$382$	−20.0000	−1.02329
$383$	8.00000	0.408781	0.204390	−	0.978889i	$-0.434479\pi$
$383$	8.00000	0.408781	0.204390	+	0.978889i	$0.434479\pi$
$384$	−1.00000	−0.0510310
$385$	0	0
$386$	22.0000	1.11977
$387$	12.0000	0.609994
$388$	−18.0000	−0.913812
$389$	−30.0000	−1.52106	−0.760530	−	0.649303i	$-0.775061\pi$
$389$	−30.0000	−1.52106	−0.760530	+	0.649303i	$0.775061\pi$
$390$	−2.00000	−0.101274
$391$	−8.00000	−0.404577
$392$	7.00000	0.353553
$393$	12.0000	0.605320
$394$	18.0000	0.906827
$395$	−8.00000	−0.402524
$396$	1.00000	0.0502519
$397$	−18.0000	−0.903394	−0.451697	−	0.892171i	$-0.649181\pi$
$397$	−18.0000	−0.903394	−0.451697	+	0.892171i	$0.649181\pi$
$398$	8.00000	0.401004
$399$	0	0
$400$	1.00000	0.0500000
$401$	−10.0000	−0.499376	−0.249688	−	0.968326i	$-0.580328\pi$
$401$	−10.0000	−0.499376	−0.249688	+	0.968326i	$0.580328\pi$
$402$	4.00000	0.199502
$403$	16.0000	0.797017
$404$	−6.00000	−0.298511
$405$	−1.00000	−0.0496904
$406$	0	0
$407$	−10.0000	−0.495682
$408$	1.00000	0.0495074
$409$	10.0000	0.494468	0.247234	−	0.968956i	$-0.420478\pi$
$409$	10.0000	0.494468	0.247234	+	0.968956i	$0.420478\pi$
$410$	−6.00000	−0.296319
$411$	−18.0000	−0.887875
$412$	−16.0000	−0.788263
$413$	0	0
$414$	−8.00000	−0.393179
$415$	−12.0000	−0.589057
$416$	2.00000	0.0980581
$417$	−12.0000	−0.587643
$418$	0	0
$419$	−28.0000	−1.36789	−0.683945	−	0.729534i	$-0.739737\pi$
$419$	−28.0000	−1.36789	−0.683945	+	0.729534i	$0.739737\pi$
$420$	0	0
$421$	−34.0000	−1.65706	−0.828529	−	0.559946i	$-0.810822\pi$
$421$	−34.0000	−1.65706	−0.828529	+	0.559946i	$0.810822\pi$
$422$	28.0000	1.36302
$423$	8.00000	0.388973
$424$	10.0000	0.485643
$425$	−1.00000	−0.0485071
$426$	0	0
$427$	0	0
$428$	0	0
$429$	−2.00000	−0.0965609
$430$	12.0000	0.578691
$431$	28.0000	1.34871	0.674356	−	0.738406i	$-0.264421\pi$
$431$	28.0000	1.34871	0.674356	+	0.738406i	$0.264421\pi$
$432$	1.00000	0.0481125
$433$	−6.00000	−0.288342	−0.144171	−	0.989553i	$-0.546051\pi$
$433$	−6.00000	−0.288342	−0.144171	+	0.989553i	$0.546051\pi$
$434$	0	0
$435$	6.00000	0.287678
$436$	−2.00000	−0.0957826
$437$	0	0
$438$	14.0000	0.668946
$439$	8.00000	0.381819	0.190910	−	0.981608i	$-0.438856\pi$
$439$	8.00000	0.381819	0.190910	+	0.981608i	$0.438856\pi$
$440$	1.00000	0.0476731
$441$	−7.00000	−0.333333
$442$	−2.00000	−0.0951303
$443$	16.0000	0.760183	0.380091	−	0.924949i	$-0.375893\pi$
$443$	16.0000	0.760183	0.380091	+	0.924949i	$0.375893\pi$
$444$	−10.0000	−0.474579
$445$	−10.0000	−0.474045
$446$	16.0000	0.757622
$447$	10.0000	0.472984
$448$	0	0
$449$	30.0000	1.41579	0.707894	−	0.706319i	$-0.249646\pi$
$449$	30.0000	1.41579	0.707894	+	0.706319i	$0.249646\pi$
$450$	−1.00000	−0.0471405
$451$	−6.00000	−0.282529
$452$	−2.00000	−0.0940721
$453$	16.0000	0.751746
$454$	24.0000	1.12638
$455$	0	0
$456$	0	0
$457$	−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
$459$	−1.00000	−0.0466760
$460$	−8.00000	−0.373002
$461$	−30.0000	−1.39724	−0.698620	−	0.715493i	$-0.746202\pi$
$461$	−30.0000	−1.39724	−0.698620	+	0.715493i	$0.746202\pi$
$462$	0	0
$463$	24.0000	1.11537	0.557687	−	0.830051i	$-0.311689\pi$
$463$	24.0000	1.11537	0.557687	+	0.830051i	$0.311689\pi$
$464$	−6.00000	−0.278543
$465$	8.00000	0.370991
$466$	18.0000	0.833834
$467$	−8.00000	−0.370196	−0.185098	−	0.982720i	$-0.559260\pi$
$467$	−8.00000	−0.370196	−0.185098	+	0.982720i	$0.559260\pi$
$468$	−2.00000	−0.0924500
$469$	0	0
$470$	8.00000	0.369012
$471$	−18.0000	−0.829396
$472$	4.00000	0.184115
$473$	12.0000	0.551761
$474$	−8.00000	−0.367452
$475$	0	0
$476$	0	0
$477$	−10.0000	−0.457869
$478$	8.00000	0.365911
$479$	12.0000	0.548294	0.274147	−	0.961688i	$-0.411605\pi$
$479$	12.0000	0.548294	0.274147	+	0.961688i	$0.411605\pi$
$480$	1.00000	0.0456435
$481$	20.0000	0.911922
$482$	14.0000	0.637683
$483$	0	0
$484$	1.00000	0.0454545
$485$	18.0000	0.817338
$486$	−1.00000	−0.0453609
$487$	−4.00000	−0.181257	−0.0906287	−	0.995885i	$-0.528888\pi$
$487$	−4.00000	−0.181257	−0.0906287	+	0.995885i	$0.528888\pi$
$488$	−14.0000	−0.633750
$489$	−12.0000	−0.542659
$490$	−7.00000	−0.316228
$491$	4.00000	0.180517	0.0902587	−	0.995918i	$-0.471231\pi$
$491$	4.00000	0.180517	0.0902587	+	0.995918i	$0.471231\pi$
$492$	−6.00000	−0.270501
$493$	6.00000	0.270226
$494$	0	0
$495$	−1.00000	−0.0449467
$496$	−8.00000	−0.359211
$497$	0	0
$498$	−12.0000	−0.537733
$499$	32.0000	1.43252	0.716258	−	0.697835i	$-0.245853\pi$
$499$	32.0000	1.43252	0.716258	+	0.697835i	$0.245853\pi$
$500$	−1.00000	−0.0447214
$501$	16.0000	0.714827
$502$	−4.00000	−0.178529
$503$	16.0000	0.713405	0.356702	−	0.934218i	$-0.383901\pi$
$503$	16.0000	0.713405	0.356702	+	0.934218i	$0.383901\pi$
$504$	0	0
$505$	6.00000	0.266996
$506$	−8.00000	−0.355643
$507$	−9.00000	−0.399704
$508$	4.00000	0.177471
$509$	−6.00000	−0.265945	−0.132973	−	0.991120i	$-0.542452\pi$
$509$	−6.00000	−0.265945	−0.132973	+	0.991120i	$0.542452\pi$
$510$	−1.00000	−0.0442807
$511$	0	0
$512$	−1.00000	−0.0441942
$513$	0	0
$514$	−14.0000	−0.617514
$515$	16.0000	0.705044
$516$	12.0000	0.528271
$517$	8.00000	0.351840
$518$	0	0
$519$	14.0000	0.614532
$520$	−2.00000	−0.0877058
$521$	14.0000	0.613351	0.306676	−	0.951814i	$-0.400783\pi$
$521$	14.0000	0.613351	0.306676	+	0.951814i	$0.400783\pi$
$522$	6.00000	0.262613
$523$	4.00000	0.174908	0.0874539	−	0.996169i	$-0.472127\pi$
$523$	4.00000	0.174908	0.0874539	+	0.996169i	$0.472127\pi$
$524$	12.0000	0.524222
$525$	0	0
$526$	0	0
$527$	8.00000	0.348485
$528$	1.00000	0.0435194
$529$	41.0000	1.78261
$530$	−10.0000	−0.434372
$531$	−4.00000	−0.173585
$532$	0	0
$533$	12.0000	0.519778
$534$	−10.0000	−0.432742
$535$	0	0
$536$	4.00000	0.172774
$537$	−12.0000	−0.517838
$538$	−18.0000	−0.776035
$539$	−7.00000	−0.301511
$540$	−1.00000	−0.0430331
$541$	6.00000	0.257960	0.128980	−	0.991647i	$-0.458830\pi$
$541$	6.00000	0.257960	0.128980	+	0.991647i	$0.458830\pi$
$542$	0	0
$543$	10.0000	0.429141
$544$	1.00000	0.0428746
$545$	2.00000	0.0856706
$546$	0	0
$547$	−20.0000	−0.855138	−0.427569	−	0.903983i	$-0.640630\pi$
$547$	−20.0000	−0.855138	−0.427569	+	0.903983i	$0.640630\pi$
$548$	−18.0000	−0.768922
$549$	14.0000	0.597505
$550$	−1.00000	−0.0426401
$551$	0	0
$552$	−8.00000	−0.340503
$553$	0	0
$554$	−6.00000	−0.254916
$555$	10.0000	0.424476
$556$	−12.0000	−0.508913
$557$	−6.00000	−0.254228	−0.127114	−	0.991888i	$-0.540571\pi$
$557$	−6.00000	−0.254228	−0.127114	+	0.991888i	$0.540571\pi$
$558$	8.00000	0.338667
$559$	−24.0000	−1.01509
$560$	0	0
$561$	−1.00000	−0.0422200
$562$	26.0000	1.09674
$563$	12.0000	0.505740	0.252870	−	0.967500i	$-0.418626\pi$
$563$	12.0000	0.505740	0.252870	+	0.967500i	$0.418626\pi$
$564$	8.00000	0.336861
$565$	2.00000	0.0841406
$566$	4.00000	0.168133
$567$	0	0
$568$	0	0
$569$	30.0000	1.25767	0.628833	−	0.777541i	$-0.283533\pi$
$569$	30.0000	1.25767	0.628833	+	0.777541i	$0.283533\pi$
$570$	0	0
$571$	−4.00000	−0.167395	−0.0836974	−	0.996491i	$-0.526673\pi$
$571$	−4.00000	−0.167395	−0.0836974	+	0.996491i	$0.526673\pi$
$572$	−2.00000	−0.0836242
$573$	20.0000	0.835512
$574$	0	0
$575$	8.00000	0.333623
$576$	1.00000	0.0416667
$577$	−30.0000	−1.24892	−0.624458	−	0.781058i	$-0.714680\pi$
$577$	−30.0000	−1.24892	−0.624458	+	0.781058i	$0.714680\pi$
$578$	−1.00000	−0.0415945
$579$	−22.0000	−0.914289
$580$	6.00000	0.249136
$581$	0	0
$582$	18.0000	0.746124
$583$	−10.0000	−0.414158
$584$	14.0000	0.579324
$585$	2.00000	0.0826898
$586$	6.00000	0.247858
$587$	−16.0000	−0.660391	−0.330195	−	0.943913i	$-0.607115\pi$
$587$	−16.0000	−0.660391	−0.330195	+	0.943913i	$0.607115\pi$
$588$	−7.00000	−0.288675
$589$	0	0
$590$	−4.00000	−0.164677
$591$	−18.0000	−0.740421
$592$	−10.0000	−0.410997
$593$	−34.0000	−1.39621	−0.698106	−	0.715994i	$-0.745974\pi$
$593$	−34.0000	−1.39621	−0.698106	+	0.715994i	$0.745974\pi$
$594$	−1.00000	−0.0410305
$595$	0	0
$596$	10.0000	0.409616
$597$	−8.00000	−0.327418
$598$	16.0000	0.654289
$599$	36.0000	1.47092	0.735460	−	0.677568i	$-0.236966\pi$
$599$	36.0000	1.47092	0.735460	+	0.677568i	$0.236966\pi$
$600$	−1.00000	−0.0408248
$601$	10.0000	0.407909	0.203954	−	0.978980i	$-0.434621\pi$
$601$	10.0000	0.407909	0.203954	+	0.978980i	$0.434621\pi$
$602$	0	0
$603$	−4.00000	−0.162893
$604$	16.0000	0.651031
$605$	−1.00000	−0.0406558
$606$	6.00000	0.243733
$607$	0	0		−	1.00000i	$-0.5\pi$
$607$	0	0			1.00000i	$0.5\pi$
$608$	0	0
$609$	0	0
$610$	14.0000	0.566843
$611$	−16.0000	−0.647291
$612$	−1.00000	−0.0404226
$613$	−42.0000	−1.69636	−0.848182	−	0.529705i	$-0.822303\pi$
$613$	−42.0000	−1.69636	−0.848182	+	0.529705i	$0.822303\pi$
$614$	−4.00000	−0.161427
$615$	6.00000	0.241943
$616$	0	0
$617$	22.0000	0.885687	0.442843	−	0.896599i	$-0.353970\pi$
$617$	22.0000	0.885687	0.442843	+	0.896599i	$0.353970\pi$
$618$	16.0000	0.643614
$619$	48.0000	1.92928	0.964641	−	0.263566i	$-0.0848986\pi$
$619$	48.0000	1.92928	0.964641	+	0.263566i	$0.0848986\pi$
$620$	8.00000	0.321288
$621$	8.00000	0.321029
$622$	−8.00000	−0.320771
$623$	0	0
$624$	−2.00000	−0.0800641
$625$	1.00000	0.0400000
$626$	−6.00000	−0.239808
$627$	0	0
$628$	−18.0000	−0.718278
$629$	10.0000	0.398726
$630$	0	0
$631$	−8.00000	−0.318475	−0.159237	−	0.987240i	$-0.550904\pi$
$631$	−8.00000	−0.318475	−0.159237	+	0.987240i	$0.550904\pi$
$632$	−8.00000	−0.318223
$633$	−28.0000	−1.11290
$634$	30.0000	1.19145
$635$	−4.00000	−0.158735
$636$	−10.0000	−0.396526
$637$	14.0000	0.554700
$638$	6.00000	0.237542
$639$	0	0
$640$	1.00000	0.0395285
$641$	−26.0000	−1.02694	−0.513469	−	0.858108i	$-0.671640\pi$
$641$	−26.0000	−1.02694	−0.513469	+	0.858108i	$0.671640\pi$
$642$	0	0
$643$	−44.0000	−1.73519	−0.867595	−	0.497271i	$-0.834335\pi$
$643$	−44.0000	−1.73519	−0.867595	+	0.497271i	$0.834335\pi$
$644$	0	0
$645$	−12.0000	−0.472500
$646$	0	0
$647$	−32.0000	−1.25805	−0.629025	−	0.777385i	$-0.716546\pi$
$647$	−32.0000	−1.25805	−0.629025	+	0.777385i	$0.716546\pi$
$648$	−1.00000	−0.0392837
$649$	−4.00000	−0.157014
$650$	2.00000	0.0784465
$651$	0	0
$652$	−12.0000	−0.469956
$653$	−6.00000	−0.234798	−0.117399	−	0.993085i	$-0.537456\pi$
$653$	−6.00000	−0.234798	−0.117399	+	0.993085i	$0.537456\pi$
$654$	2.00000	0.0782062
$655$	−12.0000	−0.468879
$656$	−6.00000	−0.234261
$657$	−14.0000	−0.546192
$658$	0	0
$659$	−20.0000	−0.779089	−0.389545	−	0.921008i	$-0.627368\pi$
$659$	−20.0000	−0.779089	−0.389545	+	0.921008i	$0.627368\pi$
$660$	−1.00000	−0.0389249
$661$	6.00000	0.233373	0.116686	−	0.993169i	$-0.462773\pi$
$661$	6.00000	0.233373	0.116686	+	0.993169i	$0.462773\pi$
$662$	12.0000	0.466393
$663$	2.00000	0.0776736
$664$	−12.0000	−0.465690
$665$	0	0
$666$	10.0000	0.387492
$667$	−48.0000	−1.85857
$668$	16.0000	0.619059
$669$	−16.0000	−0.618596
$670$	−4.00000	−0.154533
$671$	14.0000	0.540464
$672$	0	0
$673$	−6.00000	−0.231283	−0.115642	−	0.993291i	$-0.536892\pi$
$673$	−6.00000	−0.231283	−0.115642	+	0.993291i	$0.536892\pi$
$674$	−10.0000	−0.385186
$675$	1.00000	0.0384900
$676$	−9.00000	−0.346154
$677$	−42.0000	−1.61419	−0.807096	−	0.590421i	$-0.798962\pi$
$677$	−42.0000	−1.61419	−0.807096	+	0.590421i	$0.798962\pi$
$678$	2.00000	0.0768095
$679$	0	0
$680$	−1.00000	−0.0383482
$681$	−24.0000	−0.919682
$682$	8.00000	0.306336
$683$	−12.0000	−0.459167	−0.229584	−	0.973289i	$-0.573736\pi$
$683$	−12.0000	−0.459167	−0.229584	+	0.973289i	$0.573736\pi$
$684$	0	0
$685$	18.0000	0.687745
$686$	0	0
$687$	14.0000	0.534133
$688$	12.0000	0.457496
$689$	20.0000	0.761939
$690$	8.00000	0.304555
$691$	−40.0000	−1.52167	−0.760836	−	0.648944i	$-0.775211\pi$
$691$	−40.0000	−1.52167	−0.760836	+	0.648944i	$0.775211\pi$
$692$	14.0000	0.532200
$693$	0	0
$694$	0	0
$695$	12.0000	0.455186
$696$	6.00000	0.227429
$697$	6.00000	0.227266
$698$	−18.0000	−0.681310
$699$	−18.0000	−0.680823
$700$	0	0
$701$	−46.0000	−1.73740	−0.868698	−	0.495342i	$-0.835043\pi$
$701$	−46.0000	−1.73740	−0.868698	+	0.495342i	$0.835043\pi$
$702$	2.00000	0.0754851
$703$	0	0
$704$	1.00000	0.0376889
$705$	−8.00000	−0.301297
$706$	−22.0000	−0.827981
$707$	0	0
$708$	−4.00000	−0.150329
$709$	−38.0000	−1.42712	−0.713560	−	0.700594i	$-0.752918\pi$
$709$	−38.0000	−1.42712	−0.713560	+	0.700594i	$0.752918\pi$
$710$	0	0
$711$	8.00000	0.300023
$712$	−10.0000	−0.374766
$713$	−64.0000	−2.39682
$714$	0	0
$715$	2.00000	0.0747958
$716$	−12.0000	−0.448461
$717$	−8.00000	−0.298765
$718$	−8.00000	−0.298557
$719$	48.0000	1.79010	0.895049	−	0.445968i	$-0.147140\pi$
$719$	48.0000	1.79010	0.895049	+	0.445968i	$0.147140\pi$
$720$	−1.00000	−0.0372678
$721$	0	0
$722$	19.0000	0.707107
$723$	−14.0000	−0.520666
$724$	10.0000	0.371647
$725$	−6.00000	−0.222834
$726$	−1.00000	−0.0371135
$727$	32.0000	1.18681	0.593407	−	0.804902i	$-0.297782\pi$
$727$	32.0000	1.18681	0.593407	+	0.804902i	$0.297782\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−14.0000	−0.518163
$731$	−12.0000	−0.443836
$732$	14.0000	0.517455
$733$	22.0000	0.812589	0.406294	−	0.913742i	$-0.366821\pi$
$733$	22.0000	0.812589	0.406294	+	0.913742i	$0.366821\pi$
$734$	28.0000	1.03350
$735$	7.00000	0.258199
$736$	−8.00000	−0.294884
$737$	−4.00000	−0.147342
$738$	6.00000	0.220863
$739$	32.0000	1.17714	0.588570	−	0.808447i	$-0.299691\pi$
$739$	32.0000	1.17714	0.588570	+	0.808447i	$0.299691\pi$
$740$	10.0000	0.367607
$741$	0	0
$742$	0	0
$743$	−16.0000	−0.586983	−0.293492	−	0.955962i	$-0.594817\pi$
$743$	−16.0000	−0.586983	−0.293492	+	0.955962i	$0.594817\pi$
$744$	8.00000	0.293294
$745$	−10.0000	−0.366372
$746$	−14.0000	−0.512576
$747$	12.0000	0.439057
$748$	−1.00000	−0.0365636
$749$	0	0
$750$	1.00000	0.0365148
$751$	−48.0000	−1.75154	−0.875772	−	0.482724i	$-0.839647\pi$
$751$	−48.0000	−1.75154	−0.875772	+	0.482724i	$0.839647\pi$
$752$	8.00000	0.291730
$753$	4.00000	0.145768
$754$	−12.0000	−0.437014
$755$	−16.0000	−0.582300
$756$	0	0
$757$	−42.0000	−1.52652	−0.763258	−	0.646094i	$-0.776401\pi$
$757$	−42.0000	−1.52652	−0.763258	+	0.646094i	$0.776401\pi$
$758$	0	0
$759$	8.00000	0.290382
$760$	0	0
$761$	14.0000	0.507500	0.253750	−	0.967270i	$-0.418336\pi$
$761$	14.0000	0.507500	0.253750	+	0.967270i	$0.418336\pi$
$762$	−4.00000	−0.144905
$763$	0	0
$764$	20.0000	0.723575
$765$	1.00000	0.0361551
$766$	−8.00000	−0.289052
$767$	8.00000	0.288863
$768$	1.00000	0.0360844
$769$	−14.0000	−0.504853	−0.252426	−	0.967616i	$-0.581229\pi$
$769$	−14.0000	−0.504853	−0.252426	+	0.967616i	$0.581229\pi$
$770$	0	0
$771$	14.0000	0.504198
$772$	−22.0000	−0.791797
$773$	46.0000	1.65451	0.827253	−	0.561830i	$-0.189903\pi$
$773$	46.0000	1.65451	0.827253	+	0.561830i	$0.189903\pi$
$774$	−12.0000	−0.431331
$775$	−8.00000	−0.287368
$776$	18.0000	0.646162
$777$	0	0
$778$	30.0000	1.07555
$779$	0	0
$780$	2.00000	0.0716115
$781$	0	0
$782$	8.00000	0.286079
$783$	−6.00000	−0.214423
$784$	−7.00000	−0.250000
$785$	18.0000	0.642448
$786$	−12.0000	−0.428026
$787$	28.0000	0.998092	0.499046	−	0.866575i	$-0.333684\pi$
$787$	28.0000	0.998092	0.499046	+	0.866575i	$0.333684\pi$
$788$	−18.0000	−0.641223
$789$	0	0
$790$	8.00000	0.284627
$791$	0	0
$792$	−1.00000	−0.0355335
$793$	−28.0000	−0.994309
$794$	18.0000	0.638796
$795$	10.0000	0.354663
$796$	−8.00000	−0.283552
$797$	6.00000	0.212531	0.106265	−	0.994338i	$-0.466111\pi$
$797$	6.00000	0.212531	0.106265	+	0.994338i	$0.466111\pi$
$798$	0	0
$799$	−8.00000	−0.283020
$800$	−1.00000	−0.0353553
$801$	10.0000	0.353333
$802$	10.0000	0.353112
$803$	−14.0000	−0.494049
$804$	−4.00000	−0.141069
$805$	0	0
$806$	−16.0000	−0.563576
$807$	18.0000	0.633630
$808$	6.00000	0.211079
$809$	−30.0000	−1.05474	−0.527372	−	0.849635i	$-0.676823\pi$
$809$	−30.0000	−1.05474	−0.527372	+	0.849635i	$0.676823\pi$
$810$	1.00000	0.0351364
$811$	44.0000	1.54505	0.772524	−	0.634985i	$-0.218994\pi$
$811$	44.0000	1.54505	0.772524	+	0.634985i	$0.218994\pi$
$812$	0	0
$813$	0	0
$814$	10.0000	0.350500
$815$	12.0000	0.420342
$816$	−1.00000	−0.0350070
$817$	0	0
$818$	−10.0000	−0.349642
$819$	0	0
$820$	6.00000	0.209529
$821$	18.0000	0.628204	0.314102	−	0.949389i	$-0.398297\pi$
$821$	18.0000	0.628204	0.314102	+	0.949389i	$0.398297\pi$
$822$	18.0000	0.627822
$823$	36.0000	1.25488	0.627441	−	0.778664i	$-0.284103\pi$
$823$	36.0000	1.25488	0.627441	+	0.778664i	$0.284103\pi$
$824$	16.0000	0.557386
$825$	1.00000	0.0348155
$826$	0	0
$827$	−48.0000	−1.66912	−0.834562	−	0.550914i	$-0.814279\pi$
$827$	−48.0000	−1.66912	−0.834562	+	0.550914i	$0.814279\pi$
$828$	8.00000	0.278019
$829$	14.0000	0.486240	0.243120	−	0.969996i	$-0.421829\pi$
$829$	14.0000	0.486240	0.243120	+	0.969996i	$0.421829\pi$
$830$	12.0000	0.416526
$831$	6.00000	0.208138
$832$	−2.00000	−0.0693375
$833$	7.00000	0.242536
$834$	12.0000	0.415526
$835$	−16.0000	−0.553703
$836$	0	0
$837$	−8.00000	−0.276520
$838$	28.0000	0.967244
$839$	0	0		−	1.00000i	$-0.5\pi$
$839$	0	0			1.00000i	$0.5\pi$
$840$	0	0
$841$	7.00000	0.241379
$842$	34.0000	1.17172
$843$	−26.0000	−0.895488
$844$	−28.0000	−0.963800
$845$	9.00000	0.309609
$846$	−8.00000	−0.275046
$847$	0	0
$848$	−10.0000	−0.343401
$849$	−4.00000	−0.137280
$850$	1.00000	0.0342997
$851$	−80.0000	−2.74236
$852$	0	0
$853$	22.0000	0.753266	0.376633	−	0.926363i	$-0.377082\pi$
$853$	22.0000	0.753266	0.376633	+	0.926363i	$0.377082\pi$
$854$	0	0
$855$	0	0
$856$	0	0
$857$	54.0000	1.84460	0.922302	−	0.386469i	$-0.126305\pi$
$857$	54.0000	1.84460	0.922302	+	0.386469i	$0.126305\pi$
$858$	2.00000	0.0682789
$859$	20.0000	0.682391	0.341196	−	0.939992i	$-0.389168\pi$
$859$	20.0000	0.682391	0.341196	+	0.939992i	$0.389168\pi$
$860$	−12.0000	−0.409197
$861$	0	0
$862$	−28.0000	−0.953684
$863$	−48.0000	−1.63394	−0.816970	−	0.576681i	$-0.804348\pi$
$863$	−48.0000	−1.63394	−0.816970	+	0.576681i	$0.804348\pi$
$864$	−1.00000	−0.0340207
$865$	−14.0000	−0.476014
$866$	6.00000	0.203888
$867$	1.00000	0.0339618
$868$	0	0
$869$	8.00000	0.271381
$870$	−6.00000	−0.203419
$871$	8.00000	0.271070
$872$	2.00000	0.0677285
$873$	−18.0000	−0.609208
$874$	0	0
$875$	0	0
$876$	−14.0000	−0.473016
$877$	46.0000	1.55331	0.776655	−	0.629926i	$-0.216915\pi$
$877$	46.0000	1.55331	0.776655	+	0.629926i	$0.216915\pi$
$878$	−8.00000	−0.269987
$879$	−6.00000	−0.202375
$880$	−1.00000	−0.0337100
$881$	6.00000	0.202145	0.101073	−	0.994879i	$-0.467773\pi$
$881$	6.00000	0.202145	0.101073	+	0.994879i	$0.467773\pi$
$882$	7.00000	0.235702
$883$	52.0000	1.74994	0.874970	−	0.484178i	$-0.160881\pi$
$883$	52.0000	1.74994	0.874970	+	0.484178i	$0.160881\pi$
$884$	2.00000	0.0672673
$885$	4.00000	0.134459
$886$	−16.0000	−0.537531
$887$	−8.00000	−0.268614	−0.134307	−	0.990940i	$-0.542881\pi$
$887$	−8.00000	−0.268614	−0.134307	+	0.990940i	$0.542881\pi$
$888$	10.0000	0.335578
$889$	0	0
$890$	10.0000	0.335201
$891$	1.00000	0.0335013
$892$	−16.0000	−0.535720
$893$	0	0
$894$	−10.0000	−0.334450
$895$	12.0000	0.401116
$896$	0	0
$897$	−16.0000	−0.534224
$898$	−30.0000	−1.00111
$899$	48.0000	1.60089
$900$	1.00000	0.0333333
$901$	10.0000	0.333148
$902$	6.00000	0.199778
$903$	0	0
$904$	2.00000	0.0665190
$905$	−10.0000	−0.332411
$906$	−16.0000	−0.531564
$907$	−44.0000	−1.46100	−0.730498	−	0.682915i	$-0.760712\pi$
$907$	−44.0000	−1.46100	−0.730498	+	0.682915i	$0.760712\pi$
$908$	−24.0000	−0.796468
$909$	−6.00000	−0.199007
$910$	0	0
$911$	48.0000	1.59031	0.795155	−	0.606406i	$-0.207389\pi$
$911$	48.0000	1.59031	0.795155	+	0.606406i	$0.207389\pi$
$912$	0	0
$913$	12.0000	0.397142
$914$	18.0000	0.595387
$915$	−14.0000	−0.462826
$916$	14.0000	0.462573
$917$	0	0
$918$	1.00000	0.0330049
$919$	−48.0000	−1.58337	−0.791687	−	0.610927i	$-0.790797\pi$
$919$	−48.0000	−1.58337	−0.791687	+	0.610927i	$0.790797\pi$
$920$	8.00000	0.263752
$921$	4.00000	0.131804
$922$	30.0000	0.987997
$923$	0	0
$924$	0	0
$925$	−10.0000	−0.328798
$926$	−24.0000	−0.788689
$927$	−16.0000	−0.525509
$928$	6.00000	0.196960
$929$	−18.0000	−0.590561	−0.295280	−	0.955411i	$-0.595413\pi$
$929$	−18.0000	−0.590561	−0.295280	+	0.955411i	$0.595413\pi$
$930$	−8.00000	−0.262330
$931$	0	0
$932$	−18.0000	−0.589610
$933$	8.00000	0.261908
$934$	8.00000	0.261768
$935$	1.00000	0.0327035
$936$	2.00000	0.0653720
$937$	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
$939$	6.00000	0.195803
$940$	−8.00000	−0.260931
$941$	10.0000	0.325991	0.162995	−	0.986627i	$-0.447884\pi$
$941$	10.0000	0.325991	0.162995	+	0.986627i	$0.447884\pi$
$942$	18.0000	0.586472
$943$	−48.0000	−1.56310
$944$	−4.00000	−0.130189
$945$	0	0
$946$	−12.0000	−0.390154
$947$	−12.0000	−0.389948	−0.194974	−	0.980808i	$-0.562462\pi$
$947$	−12.0000	−0.389948	−0.194974	+	0.980808i	$0.562462\pi$
$948$	8.00000	0.259828
$949$	28.0000	0.908918
$950$	0	0
$951$	−30.0000	−0.972817
$952$	0	0
$953$	6.00000	0.194359	0.0971795	−	0.995267i	$-0.469018\pi$
$953$	6.00000	0.194359	0.0971795	+	0.995267i	$0.469018\pi$
$954$	10.0000	0.323762
$955$	−20.0000	−0.647185
$956$	−8.00000	−0.258738
$957$	−6.00000	−0.193952
$958$	−12.0000	−0.387702
$959$	0	0
$960$	−1.00000	−0.0322749
$961$	33.0000	1.06452
$962$	−20.0000	−0.644826
$963$	0	0
$964$	−14.0000	−0.450910
$965$	22.0000	0.708205
$966$	0	0
$967$	−36.0000	−1.15768	−0.578841	−	0.815440i	$-0.696495\pi$
$967$	−36.0000	−1.15768	−0.578841	+	0.815440i	$0.696495\pi$
$968$	−1.00000	−0.0321412
$969$	0	0
$970$	−18.0000	−0.577945
$971$	−52.0000	−1.66876	−0.834380	−	0.551190i	$-0.814174\pi$
$971$	−52.0000	−1.66876	−0.834380	+	0.551190i	$0.814174\pi$
$972$	1.00000	0.0320750
$973$	0	0
$974$	4.00000	0.128168
$975$	−2.00000	−0.0640513
$976$	14.0000	0.448129
$977$	−18.0000	−0.575871	−0.287936	−	0.957650i	$-0.592969\pi$
$977$	−18.0000	−0.575871	−0.287936	+	0.957650i	$0.592969\pi$
$978$	12.0000	0.383718
$979$	10.0000	0.319601
$980$	7.00000	0.223607
$981$	−2.00000	−0.0638551
$982$	−4.00000	−0.127645
$983$	−16.0000	−0.510321	−0.255160	−	0.966899i	$-0.582128\pi$
$983$	−16.0000	−0.510321	−0.255160	+	0.966899i	$0.582128\pi$
$984$	6.00000	0.191273
$985$	18.0000	0.573528
$986$	−6.00000	−0.191079
$987$	0	0
$988$	0	0
$989$	96.0000	3.05262
$990$	1.00000	0.0317821
$991$	24.0000	0.762385	0.381193	−	0.924496i	$-0.375513\pi$
$991$	24.0000	0.762385	0.381193	+	0.924496i	$0.375513\pi$
$992$	8.00000	0.254000
$993$	−12.0000	−0.380808
$994$	0	0
$995$	8.00000	0.253617
$996$	12.0000	0.380235
$997$	−10.0000	−0.316703	−0.158352	−	0.987383i	$-0.550618\pi$
$997$	−10.0000	−0.316703	−0.158352	+	0.987383i	$0.550618\pi$
$998$	−32.0000	−1.01294
$999$	−10.0000	−0.316386

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5610.2.a.n.1.1	✓	1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5610.2.a.n.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:	\( N \)	\(=\)	\( 5610 = 2 \cdot 3 \cdot 5 \cdot 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5610.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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