LMFDB - Embedded newform 5610.2.a.w.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)

$f(q)$

$=$

$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} -4.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$

\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} -4.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} +1.00000 q^{11} -1.00000 q^{12} +4.00000 q^{13} -4.00000 q^{14} +1.00000 q^{15} +1.00000 q^{16} -1.00000 q^{17} +1.00000 q^{18} +4.00000 q^{19} -1.00000 q^{20} +4.00000 q^{21} +1.00000 q^{22} -8.00000 q^{23} -1.00000 q^{24} +1.00000 q^{25} +4.00000 q^{26} -1.00000 q^{27} -4.00000 q^{28} -4.00000 q^{29} +1.00000 q^{30} +6.00000 q^{31} +1.00000 q^{32} -1.00000 q^{33} -1.00000 q^{34} +4.00000 q^{35} +1.00000 q^{36} +4.00000 q^{37} +4.00000 q^{38} -4.00000 q^{39} -1.00000 q^{40} -10.0000 q^{41} +4.00000 q^{42} +4.00000 q^{43} +1.00000 q^{44} -1.00000 q^{45} -8.00000 q^{46} -2.00000 q^{47} -1.00000 q^{48} +9.00000 q^{49} +1.00000 q^{50} +1.00000 q^{51} +4.00000 q^{52} -4.00000 q^{53} -1.00000 q^{54} -1.00000 q^{55} -4.00000 q^{56} -4.00000 q^{57} -4.00000 q^{58} +4.00000 q^{59} +1.00000 q^{60} -14.0000 q^{61} +6.00000 q^{62} -4.00000 q^{63} +1.00000 q^{64} -4.00000 q^{65} -1.00000 q^{66} -4.00000 q^{67} -1.00000 q^{68} +8.00000 q^{69} +4.00000 q^{70} +12.0000 q^{71} +1.00000 q^{72} +14.0000 q^{73} +4.00000 q^{74} -1.00000 q^{75} +4.00000 q^{76} -4.00000 q^{77} -4.00000 q^{78} +12.0000 q^{79} -1.00000 q^{80} +1.00000 q^{81} -10.0000 q^{82} -4.00000 q^{83} +4.00000 q^{84} +1.00000 q^{85} +4.00000 q^{86} +4.00000 q^{87} +1.00000 q^{88} +2.00000 q^{89} -1.00000 q^{90} -16.0000 q^{91} -8.00000 q^{92} -6.00000 q^{93} -2.00000 q^{94} -4.00000 q^{95} -1.00000 q^{96} -10.0000 q^{97} +9.00000 q^{98} +1.00000 q^{99} +O(q^{100})\)

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
$7$	−4.00000	−1.51186	−0.755929	−	0.654654i	$-0.772814\pi$
$7$	−4.00000	−1.51186	−0.755929	+	0.654654i	$0.772814\pi$
$8$	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
$13$	4.00000	1.10940	0.554700	−	0.832050i	$-0.312833\pi$
$13$	4.00000	1.10940	0.554700	+	0.832050i	$0.312833\pi$
$14$	−4.00000	−1.06904
$15$	1.00000	0.258199
$16$	1.00000	0.250000
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	1.00000	0.235702
$19$	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
$21$	4.00000	0.872872
$22$	1.00000	0.213201
$23$	−8.00000	−1.66812	−0.834058	−	0.551677i	$-0.813988\pi$
$23$	−8.00000	−1.66812	−0.834058	+	0.551677i	$0.813988\pi$
$24$	−1.00000	−0.204124
$25$	1.00000	0.200000
$26$	4.00000	0.784465
$27$	−1.00000	−0.192450
$28$	−4.00000	−0.755929
$29$	−4.00000	−0.742781	−0.371391	−	0.928477i	$-0.621119\pi$
$29$	−4.00000	−0.742781	−0.371391	+	0.928477i	$0.621119\pi$
$30$	1.00000	0.182574
$31$	6.00000	1.07763	0.538816	−	0.842424i	$-0.318872\pi$
$31$	6.00000	1.07763	0.538816	+	0.842424i	$0.318872\pi$
$32$	1.00000	0.176777
$33$	−1.00000	−0.174078
$34$	−1.00000	−0.171499
$35$	4.00000	0.676123
$36$	1.00000	0.166667
$37$	4.00000	0.657596	0.328798	−	0.944400i	$-0.393356\pi$
$37$	4.00000	0.657596	0.328798	+	0.944400i	$0.393356\pi$
$38$	4.00000	0.648886
$39$	−4.00000	−0.640513
$40$	−1.00000	−0.158114
$41$	−10.0000	−1.56174	−0.780869	−	0.624695i	$-0.785223\pi$
$41$	−10.0000	−1.56174	−0.780869	+	0.624695i	$0.785223\pi$
$42$	4.00000	0.617213
$43$	4.00000	0.609994	0.304997	−	0.952353i	$-0.401344\pi$
$43$	4.00000	0.609994	0.304997	+	0.952353i	$0.401344\pi$
$44$	1.00000	0.150756
$45$	−1.00000	−0.149071
$46$	−8.00000	−1.17954
$47$	−2.00000	−0.291730	−0.145865	−	0.989305i	$-0.546597\pi$
$47$	−2.00000	−0.291730	−0.145865	+	0.989305i	$0.546597\pi$
$48$	−1.00000	−0.144338
$49$	9.00000	1.28571
$50$	1.00000	0.141421
$51$	1.00000	0.140028
$52$	4.00000	0.554700
$53$	−4.00000	−0.549442	−0.274721	−	0.961524i	$-0.588586\pi$
$53$	−4.00000	−0.549442	−0.274721	+	0.961524i	$0.588586\pi$
$54$	−1.00000	−0.136083
$55$	−1.00000	−0.134840
$56$	−4.00000	−0.534522
$57$	−4.00000	−0.529813
$58$	−4.00000	−0.525226
$59$	4.00000	0.520756	0.260378	−	0.965507i	$-0.416153\pi$
$59$	4.00000	0.520756	0.260378	+	0.965507i	$0.416153\pi$
$60$	1.00000	0.129099
$61$	−14.0000	−1.79252	−0.896258	−	0.443533i	$-0.853725\pi$
$61$	−14.0000	−1.79252	−0.896258	+	0.443533i	$0.853725\pi$
$62$	6.00000	0.762001
$63$	−4.00000	−0.503953
$64$	1.00000	0.125000
$65$	−4.00000	−0.496139
$66$	−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
$70$	4.00000	0.478091
$71$	12.0000	1.42414	0.712069	−	0.702109i	$-0.247758\pi$
$71$	12.0000	1.42414	0.712069	+	0.702109i	$0.247758\pi$
$72$	1.00000	0.117851
$73$	14.0000	1.63858	0.819288	−	0.573382i	$-0.194369\pi$
$73$	14.0000	1.63858	0.819288	+	0.573382i	$0.194369\pi$
$74$	4.00000	0.464991
$75$	−1.00000	−0.115470
$76$	4.00000	0.458831
$77$	−4.00000	−0.455842
$78$	−4.00000	−0.452911
$79$	12.0000	1.35011	0.675053	−	0.737769i	$-0.264121\pi$
$79$	12.0000	1.35011	0.675053	+	0.737769i	$0.264121\pi$
$80$	−1.00000	−0.111803
$81$	1.00000	0.111111
$82$	−10.0000	−1.10432
$83$	−4.00000	−0.439057	−0.219529	−	0.975606i	$-0.570452\pi$
$83$	−4.00000	−0.439057	−0.219529	+	0.975606i	$0.570452\pi$
$84$	4.00000	0.436436
$85$	1.00000	0.108465
$86$	4.00000	0.431331
$87$	4.00000	0.428845
$88$	1.00000	0.106600
$89$	2.00000	0.212000	0.106000	−	0.994366i	$-0.466196\pi$
$89$	2.00000	0.212000	0.106000	+	0.994366i	$0.466196\pi$
$90$	−1.00000	−0.105409
$91$	−16.0000	−1.67726
$92$	−8.00000	−0.834058
$93$	−6.00000	−0.622171
$94$	−2.00000	−0.206284
$95$	−4.00000	−0.410391
$96$	−1.00000	−0.102062
$97$	−10.0000	−1.01535	−0.507673	−	0.861550i	$-0.669494\pi$
$97$	−10.0000	−1.01535	−0.507673	+	0.861550i	$0.669494\pi$
$98$	9.00000	0.909137
$99$	1.00000	0.100504
$100$	1.00000	0.100000
$101$	−10.0000	−0.995037	−0.497519	−	0.867453i	$-0.665755\pi$
$101$	−10.0000	−0.995037	−0.497519	+	0.867453i	$0.665755\pi$
$102$	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	$0.789020\pi$
$104$	4.00000	0.392232
$105$	−4.00000	−0.390360
$106$	−4.00000	−0.388514
$107$	12.0000	1.16008	0.580042	−	0.814587i	$-0.303036\pi$
$107$	12.0000	1.16008	0.580042	+	0.814587i	$0.303036\pi$
$108$	−1.00000	−0.0962250
$109$	−6.00000	−0.574696	−0.287348	−	0.957826i	$-0.592774\pi$
$109$	−6.00000	−0.574696	−0.287348	+	0.957826i	$0.592774\pi$
$110$	−1.00000	−0.0953463
$111$	−4.00000	−0.379663
$112$	−4.00000	−0.377964
$113$	−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
$115$	8.00000	0.746004
$116$	−4.00000	−0.371391
$117$	4.00000	0.369800
$118$	4.00000	0.368230
$119$	4.00000	0.366679
$120$	1.00000	0.0912871
$121$	1.00000	0.0909091
$122$	−14.0000	−1.26750
$123$	10.0000	0.901670
$124$	6.00000	0.538816
$125$	−1.00000	−0.0894427
$126$	−4.00000	−0.356348
$127$	−2.00000	−0.177471	−0.0887357	−	0.996055i	$-0.528283\pi$
$127$	−2.00000	−0.177471	−0.0887357	+	0.996055i	$0.528283\pi$
$128$	1.00000	0.0883883
$129$	−4.00000	−0.352180
$130$	−4.00000	−0.350823
$131$	0	0		−	1.00000i	$-0.5\pi$
$131$	0	0			1.00000i	$0.5\pi$
$132$	−1.00000	−0.0870388
$133$	−16.0000	−1.38738
$134$	−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	$0.669953\pi$
$140$	4.00000	0.338062
$141$	2.00000	0.168430
$142$	12.0000	1.00702
$143$	4.00000	0.334497
$144$	1.00000	0.0833333
$145$	4.00000	0.332182
$146$	14.0000	1.15865
$147$	−9.00000	−0.742307
$148$	4.00000	0.328798
$149$	6.00000	0.491539	0.245770	−	0.969328i	$-0.420959\pi$
$149$	6.00000	0.491539	0.245770	+	0.969328i	$0.420959\pi$
$150$	−1.00000	−0.0816497
$151$	−10.0000	−0.813788	−0.406894	−	0.913475i	$-0.633388\pi$
$151$	−10.0000	−0.813788	−0.406894	+	0.913475i	$0.633388\pi$
$152$	4.00000	0.324443
$153$	−1.00000	−0.0808452
$154$	−4.00000	−0.322329
$155$	−6.00000	−0.481932
$156$	−4.00000	−0.320256
$157$	−14.0000	−1.11732	−0.558661	−	0.829396i	$-0.688685\pi$
$157$	−14.0000	−1.11732	−0.558661	+	0.829396i	$0.688685\pi$
$158$	12.0000	0.954669
$159$	4.00000	0.317221
$160$	−1.00000	−0.0790569
$161$	32.0000	2.52195
$162$	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	$0.655730\pi$
$164$	−10.0000	−0.780869
$165$	1.00000	0.0778499
$166$	−4.00000	−0.310460
$167$	−2.00000	−0.154765	−0.0773823	−	0.997001i	$-0.524656\pi$
$167$	−2.00000	−0.154765	−0.0773823	+	0.997001i	$0.524656\pi$
$168$	4.00000	0.308607
$169$	3.00000	0.230769
$170$	1.00000	0.0766965
$171$	4.00000	0.305888
$172$	4.00000	0.304997
$173$	−20.0000	−1.52057	−0.760286	−	0.649589i	$-0.774941\pi$
$173$	−20.0000	−1.52057	−0.760286	+	0.649589i	$0.774941\pi$
$174$	4.00000	0.303239
$175$	−4.00000	−0.302372
$176$	1.00000	0.0753778
$177$	−4.00000	−0.300658
$178$	2.00000	0.149906
$179$	0	0		−	1.00000i	$-0.5\pi$
$179$	0	0			1.00000i	$0.5\pi$
$180$	−1.00000	−0.0745356
$181$	−16.0000	−1.18927	−0.594635	−	0.803996i	$-0.702704\pi$
$181$	−16.0000	−1.18927	−0.594635	+	0.803996i	$0.702704\pi$
$182$	−16.0000	−1.18600
$183$	14.0000	1.03491
$184$	−8.00000	−0.589768
$185$	−4.00000	−0.294086
$186$	−6.00000	−0.439941
$187$	−1.00000	−0.0731272
$188$	−2.00000	−0.145865
$189$	4.00000	0.290957
$190$	−4.00000	−0.290191
$191$	6.00000	0.434145	0.217072	−	0.976156i	$-0.430349\pi$
$191$	6.00000	0.434145	0.217072	+	0.976156i	$0.430349\pi$
$192$	−1.00000	−0.0721688
$193$	−14.0000	−1.00774	−0.503871	−	0.863779i	$-0.668091\pi$
$193$	−14.0000	−1.00774	−0.503871	+	0.863779i	$0.668091\pi$
$194$	−10.0000	−0.717958
$195$	4.00000	0.286446
$196$	9.00000	0.642857
$197$	−24.0000	−1.70993	−0.854965	−	0.518686i	$-0.826421\pi$
$197$	−24.0000	−1.70993	−0.854965	+	0.518686i	$0.826421\pi$
$198$	1.00000	0.0710669
$199$	−2.00000	−0.141776	−0.0708881	−	0.997484i	$-0.522583\pi$
$199$	−2.00000	−0.141776	−0.0708881	+	0.997484i	$0.522583\pi$
$200$	1.00000	0.0707107
$201$	4.00000	0.282138
$202$	−10.0000	−0.703598
$203$	16.0000	1.12298
$204$	1.00000	0.0700140
$205$	10.0000	0.698430
$206$	−16.0000	−1.11477
$207$	−8.00000	−0.556038
$208$	4.00000	0.277350
$209$	4.00000	0.276686
$210$	−4.00000	−0.276026
$211$	−12.0000	−0.826114	−0.413057	−	0.910705i	$-0.635539\pi$
$211$	−12.0000	−0.826114	−0.413057	+	0.910705i	$0.635539\pi$
$212$	−4.00000	−0.274721
$213$	−12.0000	−0.822226
$214$	12.0000	0.820303
$215$	−4.00000	−0.272798
$216$	−1.00000	−0.0680414
$217$	−24.0000	−1.62923
$218$	−6.00000	−0.406371
$219$	−14.0000	−0.946032
$220$	−1.00000	−0.0674200
$221$	−4.00000	−0.269069
$222$	−4.00000	−0.268462
$223$	20.0000	1.33930	0.669650	−	0.742677i	$-0.266444\pi$
$223$	20.0000	1.33930	0.669650	+	0.742677i	$0.266444\pi$
$224$	−4.00000	−0.267261
$225$	1.00000	0.0666667
$226$	−18.0000	−1.19734
$227$	0	0		−	1.00000i	$-0.5\pi$
$227$	0	0			1.00000i	$0.5\pi$
$228$	−4.00000	−0.264906
$229$	−14.0000	−0.925146	−0.462573	−	0.886581i	$-0.653074\pi$
$229$	−14.0000	−0.925146	−0.462573	+	0.886581i	$0.653074\pi$
$230$	8.00000	0.527504
$231$	4.00000	0.263181
$232$	−4.00000	−0.262613
$233$	−22.0000	−1.44127	−0.720634	−	0.693316i	$-0.756149\pi$
$233$	−22.0000	−1.44127	−0.720634	+	0.693316i	$0.756149\pi$
$234$	4.00000	0.261488
$235$	2.00000	0.130466
$236$	4.00000	0.260378
$237$	−12.0000	−0.779484
$238$	4.00000	0.259281
$239$	−24.0000	−1.55243	−0.776215	−	0.630468i	$-0.782863\pi$
$239$	−24.0000	−1.55243	−0.776215	+	0.630468i	$0.782863\pi$
$240$	1.00000	0.0645497
$241$	18.0000	1.15948	0.579741	−	0.814801i	$-0.303154\pi$
$241$	18.0000	1.15948	0.579741	+	0.814801i	$0.303154\pi$
$242$	1.00000	0.0642824
$243$	−1.00000	−0.0641500
$244$	−14.0000	−0.896258
$245$	−9.00000	−0.574989
$246$	10.0000	0.637577
$247$	16.0000	1.01806
$248$	6.00000	0.381000
$249$	4.00000	0.253490
$250$	−1.00000	−0.0632456
$251$	16.0000	1.00991	0.504956	−	0.863145i	$-0.331509\pi$
$251$	16.0000	1.00991	0.504956	+	0.863145i	$0.331509\pi$
$252$	−4.00000	−0.251976
$253$	−8.00000	−0.502956
$254$	−2.00000	−0.125491
$255$	−1.00000	−0.0626224
$256$	1.00000	0.0625000
$257$	10.0000	0.623783	0.311891	−	0.950118i	$-0.399037\pi$
$257$	10.0000	0.623783	0.311891	+	0.950118i	$0.399037\pi$
$258$	−4.00000	−0.249029
$259$	−16.0000	−0.994192
$260$	−4.00000	−0.248069
$261$	−4.00000	−0.247594
$262$	0	0
$263$	−12.0000	−0.739952	−0.369976	−	0.929041i	$-0.620634\pi$
$263$	−12.0000	−0.739952	−0.369976	+	0.929041i	$0.620634\pi$
$264$	−1.00000	−0.0615457
$265$	4.00000	0.245718
$266$	−16.0000	−0.981023
$267$	−2.00000	−0.122398
$268$	−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
$271$	10.0000	0.607457	0.303728	−	0.952759i	$-0.401768\pi$
$271$	10.0000	0.607457	0.303728	+	0.952759i	$0.401768\pi$
$272$	−1.00000	−0.0606339
$273$	16.0000	0.968364
$274$	−18.0000	−1.08742
$275$	1.00000	0.0603023
$276$	8.00000	0.481543
$277$	−26.0000	−1.56219	−0.781094	−	0.624413i	$-0.785338\pi$
$277$	−26.0000	−1.56219	−0.781094	+	0.624413i	$0.785338\pi$
$278$	−12.0000	−0.719712
$279$	6.00000	0.359211
$280$	4.00000	0.239046
$281$	−2.00000	−0.119310	−0.0596550	−	0.998219i	$-0.519000\pi$
$281$	−2.00000	−0.119310	−0.0596550	+	0.998219i	$0.519000\pi$
$282$	2.00000	0.119098
$283$	20.0000	1.18888	0.594438	−	0.804141i	$-0.297374\pi$
$283$	20.0000	1.18888	0.594438	+	0.804141i	$0.297374\pi$
$284$	12.0000	0.712069
$285$	4.00000	0.236940
$286$	4.00000	0.236525
$287$	40.0000	2.36113
$288$	1.00000	0.0589256
$289$	1.00000	0.0588235
$290$	4.00000	0.234888
$291$	10.0000	0.586210
$292$	14.0000	0.819288
$293$	22.0000	1.28525	0.642627	−	0.766179i	$-0.277845\pi$
$293$	22.0000	1.28525	0.642627	+	0.766179i	$0.277845\pi$
$294$	−9.00000	−0.524891
$295$	−4.00000	−0.232889
$296$	4.00000	0.232495
$297$	−1.00000	−0.0580259
$298$	6.00000	0.347571
$299$	−32.0000	−1.85061
$300$	−1.00000	−0.0577350
$301$	−16.0000	−0.922225
$302$	−10.0000	−0.575435
$303$	10.0000	0.574485
$304$	4.00000	0.229416
$305$	14.0000	0.801638
$306$	−1.00000	−0.0571662
$307$	−8.00000	−0.456584	−0.228292	−	0.973593i	$-0.573314\pi$
$307$	−8.00000	−0.456584	−0.228292	+	0.973593i	$0.573314\pi$
$308$	−4.00000	−0.227921
$309$	16.0000	0.910208
$310$	−6.00000	−0.340777
$311$	−16.0000	−0.907277	−0.453638	−	0.891186i	$-0.649874\pi$
$311$	−16.0000	−0.907277	−0.453638	+	0.891186i	$0.649874\pi$
$312$	−4.00000	−0.226455
$313$	−10.0000	−0.565233	−0.282617	−	0.959233i	$-0.591202\pi$
$313$	−10.0000	−0.565233	−0.282617	+	0.959233i	$0.591202\pi$
$314$	−14.0000	−0.790066
$315$	4.00000	0.225374
$316$	12.0000	0.675053
$317$	18.0000	1.01098	0.505490	−	0.862832i	$-0.331312\pi$
$317$	18.0000	1.01098	0.505490	+	0.862832i	$0.331312\pi$
$318$	4.00000	0.224309
$319$	−4.00000	−0.223957
$320$	−1.00000	−0.0559017
$321$	−12.0000	−0.669775
$322$	32.0000	1.78329
$323$	−4.00000	−0.222566
$324$	1.00000	0.0555556
$325$	4.00000	0.221880
$326$	−12.0000	−0.664619
$327$	6.00000	0.331801
$328$	−10.0000	−0.552158
$329$	8.00000	0.441054
$330$	1.00000	0.0550482
$331$	−4.00000	−0.219860	−0.109930	−	0.993939i	$-0.535063\pi$
$331$	−4.00000	−0.219860	−0.109930	+	0.993939i	$0.535063\pi$
$332$	−4.00000	−0.219529
$333$	4.00000	0.219199
$334$	−2.00000	−0.109435
$335$	4.00000	0.218543
$336$	4.00000	0.218218
$337$	18.0000	0.980522	0.490261	−	0.871576i	$-0.336901\pi$
$337$	18.0000	0.980522	0.490261	+	0.871576i	$0.336901\pi$
$338$	3.00000	0.163178
$339$	18.0000	0.977626
$340$	1.00000	0.0542326
$341$	6.00000	0.324918
$342$	4.00000	0.216295
$343$	−8.00000	−0.431959
$344$	4.00000	0.215666
$345$	−8.00000	−0.430706
$346$	−20.0000	−1.07521
$347$	4.00000	0.214731	0.107366	−	0.994220i	$-0.465758\pi$
$347$	4.00000	0.214731	0.107366	+	0.994220i	$0.465758\pi$
$348$	4.00000	0.214423
$349$	20.0000	1.07058	0.535288	−	0.844670i	$-0.320203\pi$
$349$	20.0000	1.07058	0.535288	+	0.844670i	$0.320203\pi$
$350$	−4.00000	−0.213809
$351$	−4.00000	−0.213504
$352$	1.00000	0.0533002
$353$	−30.0000	−1.59674	−0.798369	−	0.602168i	$-0.794304\pi$
$353$	−30.0000	−1.59674	−0.798369	+	0.602168i	$0.794304\pi$
$354$	−4.00000	−0.212598
$355$	−12.0000	−0.636894
$356$	2.00000	0.106000
$357$	−4.00000	−0.211702
$358$	0	0
$359$	−4.00000	−0.211112	−0.105556	−	0.994413i	$-0.533662\pi$
$359$	−4.00000	−0.211112	−0.105556	+	0.994413i	$0.533662\pi$
$360$	−1.00000	−0.0527046
$361$	−3.00000	−0.157895
$362$	−16.0000	−0.840941
$363$	−1.00000	−0.0524864
$364$	−16.0000	−0.838628
$365$	−14.0000	−0.732793
$366$	14.0000	0.731792
$367$	22.0000	1.14839	0.574195	−	0.818718i	$-0.305315\pi$
$367$	22.0000	1.14839	0.574195	+	0.818718i	$0.305315\pi$
$368$	−8.00000	−0.417029
$369$	−10.0000	−0.520579
$370$	−4.00000	−0.207950
$371$	16.0000	0.830679
$372$	−6.00000	−0.311086
$373$	−4.00000	−0.207112	−0.103556	−	0.994624i	$-0.533022\pi$
$373$	−4.00000	−0.207112	−0.103556	+	0.994624i	$0.533022\pi$
$374$	−1.00000	−0.0517088
$375$	1.00000	0.0516398
$376$	−2.00000	−0.103142
$377$	−16.0000	−0.824042
$378$	4.00000	0.205738
$379$	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
$381$	2.00000	0.102463
$382$	6.00000	0.306987
$383$	−14.0000	−0.715367	−0.357683	−	0.933843i	$-0.616433\pi$
$383$	−14.0000	−0.715367	−0.357683	+	0.933843i	$0.616433\pi$
$384$	−1.00000	−0.0510310
$385$	4.00000	0.203859
$386$	−14.0000	−0.712581
$387$	4.00000	0.203331
$388$	−10.0000	−0.507673
$389$	−24.0000	−1.21685	−0.608424	−	0.793612i	$-0.708198\pi$
$389$	−24.0000	−1.21685	−0.608424	+	0.793612i	$0.708198\pi$
$390$	4.00000	0.202548
$391$	8.00000	0.404577
$392$	9.00000	0.454569
$393$	0	0
$394$	−24.0000	−1.20910
$395$	−12.0000	−0.603786
$396$	1.00000	0.0502519
$397$	8.00000	0.401508	0.200754	−	0.979642i	$-0.435661\pi$
$397$	8.00000	0.401508	0.200754	+	0.979642i	$0.435661\pi$
$398$	−2.00000	−0.100251
$399$	16.0000	0.801002
$400$	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
$403$	24.0000	1.19553
$404$	−10.0000	−0.497519
$405$	−1.00000	−0.0496904
$406$	16.0000	0.794067
$407$	4.00000	0.198273
$408$	1.00000	0.0495074
$409$	22.0000	1.08783	0.543915	−	0.839140i	$-0.316941\pi$
$409$	22.0000	1.08783	0.543915	+	0.839140i	$0.316941\pi$
$410$	10.0000	0.493865
$411$	18.0000	0.887875
$412$	−16.0000	−0.788263
$413$	−16.0000	−0.787309
$414$	−8.00000	−0.393179
$415$	4.00000	0.196352
$416$	4.00000	0.196116
$417$	12.0000	0.587643
$418$	4.00000	0.195646
$419$	−4.00000	−0.195413	−0.0977064	−	0.995215i	$-0.531151\pi$
$419$	−4.00000	−0.195413	−0.0977064	+	0.995215i	$0.531151\pi$
$420$	−4.00000	−0.195180
$421$	2.00000	0.0974740	0.0487370	−	0.998812i	$-0.484480\pi$
$421$	2.00000	0.0974740	0.0487370	+	0.998812i	$0.484480\pi$
$422$	−12.0000	−0.584151
$423$	−2.00000	−0.0972433
$424$	−4.00000	−0.194257
$425$	−1.00000	−0.0485071
$426$	−12.0000	−0.581402
$427$	56.0000	2.71003
$428$	12.0000	0.580042
$429$	−4.00000	−0.193122
$430$	−4.00000	−0.192897
$431$	26.0000	1.25238	0.626188	−	0.779672i	$-0.284614\pi$
$431$	26.0000	1.25238	0.626188	+	0.779672i	$0.284614\pi$
$432$	−1.00000	−0.0481125
$433$	14.0000	0.672797	0.336399	−	0.941720i	$-0.390791\pi$
$433$	14.0000	0.672797	0.336399	+	0.941720i	$0.390791\pi$
$434$	−24.0000	−1.15204
$435$	−4.00000	−0.191785
$436$	−6.00000	−0.287348
$437$	−32.0000	−1.53077
$438$	−14.0000	−0.668946
$439$	24.0000	1.14546	0.572729	−	0.819745i	$-0.305885\pi$
$439$	24.0000	1.14546	0.572729	+	0.819745i	$0.305885\pi$
$440$	−1.00000	−0.0476731
$441$	9.00000	0.428571
$442$	−4.00000	−0.190261
$443$	16.0000	0.760183	0.380091	−	0.924949i	$-0.375893\pi$
$443$	16.0000	0.760183	0.380091	+	0.924949i	$0.375893\pi$
$444$	−4.00000	−0.189832
$445$	−2.00000	−0.0948091
$446$	20.0000	0.947027
$447$	−6.00000	−0.283790
$448$	−4.00000	−0.188982
$449$	10.0000	0.471929	0.235965	−	0.971762i	$-0.424175\pi$
$449$	10.0000	0.471929	0.235965	+	0.971762i	$0.424175\pi$
$450$	1.00000	0.0471405
$451$	−10.0000	−0.470882
$452$	−18.0000	−0.846649
$453$	10.0000	0.469841
$454$	0	0
$455$	16.0000	0.750092
$456$	−4.00000	−0.187317
$457$	38.0000	1.77757	0.888783	−	0.458329i	$-0.151552\pi$
$457$	38.0000	1.77757	0.888783	+	0.458329i	$0.151552\pi$
$458$	−14.0000	−0.654177
$459$	1.00000	0.0466760
$460$	8.00000	0.373002
$461$	−6.00000	−0.279448	−0.139724	−	0.990190i	$-0.544622\pi$
$461$	−6.00000	−0.279448	−0.139724	+	0.990190i	$0.544622\pi$
$462$	4.00000	0.186097
$463$	−32.0000	−1.48717	−0.743583	−	0.668644i	$-0.766875\pi$
$463$	−32.0000	−1.48717	−0.743583	+	0.668644i	$0.766875\pi$
$464$	−4.00000	−0.185695
$465$	6.00000	0.278243
$466$	−22.0000	−1.01913
$467$	12.0000	0.555294	0.277647	−	0.960683i	$-0.410445\pi$
$467$	12.0000	0.555294	0.277647	+	0.960683i	$0.410445\pi$
$468$	4.00000	0.184900
$469$	16.0000	0.738811
$470$	2.00000	0.0922531
$471$	14.0000	0.645086
$472$	4.00000	0.184115
$473$	4.00000	0.183920
$474$	−12.0000	−0.551178
$475$	4.00000	0.183533
$476$	4.00000	0.183340
$477$	−4.00000	−0.183147
$478$	−24.0000	−1.09773
$479$	38.0000	1.73626	0.868132	−	0.496333i	$-0.165321\pi$
$479$	38.0000	1.73626	0.868132	+	0.496333i	$0.165321\pi$
$480$	1.00000	0.0456435
$481$	16.0000	0.729537
$482$	18.0000	0.819878
$483$	−32.0000	−1.45605
$484$	1.00000	0.0454545
$485$	10.0000	0.454077
$486$	−1.00000	−0.0453609
$487$	26.0000	1.17817	0.589086	−	0.808070i	$-0.299488\pi$
$487$	26.0000	1.17817	0.589086	+	0.808070i	$0.299488\pi$
$488$	−14.0000	−0.633750
$489$	12.0000	0.542659
$490$	−9.00000	−0.406579
$491$	−20.0000	−0.902587	−0.451294	−	0.892375i	$-0.649037\pi$
$491$	−20.0000	−0.902587	−0.451294	+	0.892375i	$0.649037\pi$
$492$	10.0000	0.450835
$493$	4.00000	0.180151
$494$	16.0000	0.719874
$495$	−1.00000	−0.0449467
$496$	6.00000	0.269408
$497$	−48.0000	−2.15309
$498$	4.00000	0.179244
$499$	24.0000	1.07439	0.537194	−	0.843459i	$-0.319484\pi$
$499$	24.0000	1.07439	0.537194	+	0.843459i	$0.319484\pi$
$500$	−1.00000	−0.0447214
$501$	2.00000	0.0893534
$502$	16.0000	0.714115
$503$	−26.0000	−1.15928	−0.579641	−	0.814872i	$-0.696807\pi$
$503$	−26.0000	−1.15928	−0.579641	+	0.814872i	$0.696807\pi$
$504$	−4.00000	−0.178174
$505$	10.0000	0.444994
$506$	−8.00000	−0.355643
$507$	−3.00000	−0.133235
$508$	−2.00000	−0.0887357
$509$	−8.00000	−0.354594	−0.177297	−	0.984157i	$-0.556735\pi$
$509$	−8.00000	−0.354594	−0.177297	+	0.984157i	$0.556735\pi$
$510$	−1.00000	−0.0442807
$511$	−56.0000	−2.47729
$512$	1.00000	0.0441942
$513$	−4.00000	−0.176604
$514$	10.0000	0.441081
$515$	16.0000	0.705044
$516$	−4.00000	−0.176090
$517$	−2.00000	−0.0879599
$518$	−16.0000	−0.703000
$519$	20.0000	0.877903
$520$	−4.00000	−0.175412
$521$	10.0000	0.438108	0.219054	−	0.975713i	$-0.429703\pi$
$521$	10.0000	0.438108	0.219054	+	0.975713i	$0.429703\pi$
$522$	−4.00000	−0.175075
$523$	−24.0000	−1.04945	−0.524723	−	0.851273i	$-0.675831\pi$
$523$	−24.0000	−1.04945	−0.524723	+	0.851273i	$0.675831\pi$
$524$	0	0
$525$	4.00000	0.174574
$526$	−12.0000	−0.523225
$527$	−6.00000	−0.261364
$528$	−1.00000	−0.0435194
$529$	41.0000	1.78261
$530$	4.00000	0.173749
$531$	4.00000	0.173585
$532$	−16.0000	−0.693688
$533$	−40.0000	−1.73259
$534$	−2.00000	−0.0865485
$535$	−12.0000	−0.518805
$536$	−4.00000	−0.172774
$537$	0	0
$538$	10.0000	0.431131
$539$	9.00000	0.387657
$540$	1.00000	0.0430331
$541$	−10.0000	−0.429934	−0.214967	−	0.976621i	$-0.568964\pi$
$541$	−10.0000	−0.429934	−0.214967	+	0.976621i	$0.568964\pi$
$542$	10.0000	0.429537
$543$	16.0000	0.686626
$544$	−1.00000	−0.0428746
$545$	6.00000	0.257012
$546$	16.0000	0.684737
$547$	−12.0000	−0.513083	−0.256541	−	0.966533i	$-0.582583\pi$
$547$	−12.0000	−0.513083	−0.256541	+	0.966533i	$0.582583\pi$
$548$	−18.0000	−0.768922
$549$	−14.0000	−0.597505
$550$	1.00000	0.0426401
$551$	−16.0000	−0.681623
$552$	8.00000	0.340503
$553$	−48.0000	−2.04117
$554$	−26.0000	−1.10463
$555$	4.00000	0.169791
$556$	−12.0000	−0.508913
$557$	26.0000	1.10166	0.550828	−	0.834619i	$-0.314312\pi$
$557$	26.0000	1.10166	0.550828	+	0.834619i	$0.314312\pi$
$558$	6.00000	0.254000
$559$	16.0000	0.676728
$560$	4.00000	0.169031
$561$	1.00000	0.0422200
$562$	−2.00000	−0.0843649
$563$	−20.0000	−0.842900	−0.421450	−	0.906852i	$-0.638479\pi$
$563$	−20.0000	−0.842900	−0.421450	+	0.906852i	$0.638479\pi$
$564$	2.00000	0.0842152
$565$	18.0000	0.757266
$566$	20.0000	0.840663
$567$	−4.00000	−0.167984
$568$	12.0000	0.503509
$569$	18.0000	0.754599	0.377300	−	0.926091i	$-0.376853\pi$
$569$	18.0000	0.754599	0.377300	+	0.926091i	$0.376853\pi$
$570$	4.00000	0.167542
$571$	12.0000	0.502184	0.251092	−	0.967963i	$-0.419210\pi$
$571$	12.0000	0.502184	0.251092	+	0.967963i	$0.419210\pi$
$572$	4.00000	0.167248
$573$	−6.00000	−0.250654
$574$	40.0000	1.66957
$575$	−8.00000	−0.333623
$576$	1.00000	0.0416667
$577$	22.0000	0.915872	0.457936	−	0.888985i	$-0.348589\pi$
$577$	22.0000	0.915872	0.457936	+	0.888985i	$0.348589\pi$
$578$	1.00000	0.0415945
$579$	14.0000	0.581820
$580$	4.00000	0.166091
$581$	16.0000	0.663792
$582$	10.0000	0.414513
$583$	−4.00000	−0.165663
$584$	14.0000	0.579324
$585$	−4.00000	−0.165380
$586$	22.0000	0.908812
$587$	−16.0000	−0.660391	−0.330195	−	0.943913i	$-0.607115\pi$
$587$	−16.0000	−0.660391	−0.330195	+	0.943913i	$0.607115\pi$
$588$	−9.00000	−0.371154
$589$	24.0000	0.988903
$590$	−4.00000	−0.164677
$591$	24.0000	0.987228
$592$	4.00000	0.164399
$593$	−30.0000	−1.23195	−0.615976	−	0.787765i	$-0.711238\pi$
$593$	−30.0000	−1.23195	−0.615976	+	0.787765i	$0.711238\pi$
$594$	−1.00000	−0.0410305
$595$	−4.00000	−0.163984
$596$	6.00000	0.245770
$597$	2.00000	0.0818546
$598$	−32.0000	−1.30858
$599$	−42.0000	−1.71607	−0.858037	−	0.513588i	$-0.828316\pi$
$599$	−42.0000	−1.71607	−0.858037	+	0.513588i	$0.828316\pi$
$600$	−1.00000	−0.0408248
$601$	14.0000	0.571072	0.285536	−	0.958368i	$-0.407828\pi$
$601$	14.0000	0.571072	0.285536	+	0.958368i	$0.407828\pi$
$602$	−16.0000	−0.652111
$603$	−4.00000	−0.162893
$604$	−10.0000	−0.406894
$605$	−1.00000	−0.0406558
$606$	10.0000	0.406222
$607$	4.00000	0.162355	0.0811775	−	0.996700i	$-0.474132\pi$
$607$	4.00000	0.162355	0.0811775	+	0.996700i	$0.474132\pi$
$608$	4.00000	0.162221
$609$	−16.0000	−0.648353
$610$	14.0000	0.566843
$611$	−8.00000	−0.323645
$612$	−1.00000	−0.0404226
$613$	12.0000	0.484675	0.242338	−	0.970192i	$-0.422086\pi$
$613$	12.0000	0.484675	0.242338	+	0.970192i	$0.422086\pi$
$614$	−8.00000	−0.322854
$615$	−10.0000	−0.403239
$616$	−4.00000	−0.161165
$617$	42.0000	1.69086	0.845428	−	0.534089i	$-0.179345\pi$
$617$	42.0000	1.69086	0.845428	+	0.534089i	$0.179345\pi$
$618$	16.0000	0.643614
$619$	8.00000	0.321547	0.160774	−	0.986991i	$-0.448601\pi$
$619$	8.00000	0.321547	0.160774	+	0.986991i	$0.448601\pi$
$620$	−6.00000	−0.240966
$621$	8.00000	0.321029
$622$	−16.0000	−0.641542
$623$	−8.00000	−0.320513
$624$	−4.00000	−0.160128
$625$	1.00000	0.0400000
$626$	−10.0000	−0.399680
$627$	−4.00000	−0.159745
$628$	−14.0000	−0.558661
$629$	−4.00000	−0.159490
$630$	4.00000	0.159364
$631$	20.0000	0.796187	0.398094	−	0.917345i	$-0.369672\pi$
$631$	20.0000	0.796187	0.398094	+	0.917345i	$0.369672\pi$
$632$	12.0000	0.477334
$633$	12.0000	0.476957
$634$	18.0000	0.714871
$635$	2.00000	0.0793676
$636$	4.00000	0.158610
$637$	36.0000	1.42637
$638$	−4.00000	−0.158362
$639$	12.0000	0.474713
$640$	−1.00000	−0.0395285
$641$	−2.00000	−0.0789953	−0.0394976	−	0.999220i	$-0.512576\pi$
$641$	−2.00000	−0.0789953	−0.0394976	+	0.999220i	$0.512576\pi$
$642$	−12.0000	−0.473602
$643$	−8.00000	−0.315489	−0.157745	−	0.987480i	$-0.550422\pi$
$643$	−8.00000	−0.315489	−0.157745	+	0.987480i	$0.550422\pi$
$644$	32.0000	1.26098
$645$	4.00000	0.157500
$646$	−4.00000	−0.157378
$647$	−38.0000	−1.49393	−0.746967	−	0.664861i	$-0.768491\pi$
$647$	−38.0000	−1.49393	−0.746967	+	0.664861i	$0.768491\pi$
$648$	1.00000	0.0392837
$649$	4.00000	0.157014
$650$	4.00000	0.156893
$651$	24.0000	0.940634
$652$	−12.0000	−0.469956
$653$	−26.0000	−1.01746	−0.508729	−	0.860927i	$-0.669885\pi$
$653$	−26.0000	−1.01746	−0.508729	+	0.860927i	$0.669885\pi$
$654$	6.00000	0.234619
$655$	0	0
$656$	−10.0000	−0.390434
$657$	14.0000	0.546192
$658$	8.00000	0.311872
$659$	−12.0000	−0.467454	−0.233727	−	0.972302i	$-0.575092\pi$
$659$	−12.0000	−0.467454	−0.233727	+	0.972302i	$0.575092\pi$
$660$	1.00000	0.0389249
$661$	−42.0000	−1.63361	−0.816805	−	0.576913i	$-0.804257\pi$
$661$	−42.0000	−1.63361	−0.816805	+	0.576913i	$0.804257\pi$
$662$	−4.00000	−0.155464
$663$	4.00000	0.155347
$664$	−4.00000	−0.155230
$665$	16.0000	0.620453
$666$	4.00000	0.154997
$667$	32.0000	1.23904
$668$	−2.00000	−0.0773823
$669$	−20.0000	−0.773245
$670$	4.00000	0.154533
$671$	−14.0000	−0.540464
$672$	4.00000	0.154303
$673$	2.00000	0.0770943	0.0385472	−	0.999257i	$-0.487727\pi$
$673$	2.00000	0.0770943	0.0385472	+	0.999257i	$0.487727\pi$
$674$	18.0000	0.693334
$675$	−1.00000	−0.0384900
$676$	3.00000	0.115385
$677$	8.00000	0.307465	0.153732	−	0.988113i	$-0.450871\pi$
$677$	8.00000	0.307465	0.153732	+	0.988113i	$0.450871\pi$
$678$	18.0000	0.691286
$679$	40.0000	1.53506
$680$	1.00000	0.0383482
$681$	0	0
$682$	6.00000	0.229752
$683$	12.0000	0.459167	0.229584	−	0.973289i	$-0.426264\pi$
$683$	12.0000	0.459167	0.229584	+	0.973289i	$0.426264\pi$
$684$	4.00000	0.152944
$685$	18.0000	0.687745
$686$	−8.00000	−0.305441
$687$	14.0000	0.534133
$688$	4.00000	0.152499
$689$	−16.0000	−0.609551
$690$	−8.00000	−0.304555
$691$	36.0000	1.36950	0.684752	−	0.728776i	$-0.259910\pi$
$691$	36.0000	1.36950	0.684752	+	0.728776i	$0.259910\pi$
$692$	−20.0000	−0.760286
$693$	−4.00000	−0.151947
$694$	4.00000	0.151838
$695$	12.0000	0.455186
$696$	4.00000	0.151620
$697$	10.0000	0.378777
$698$	20.0000	0.757011
$699$	22.0000	0.832116
$700$	−4.00000	−0.151186
$701$	42.0000	1.58632	0.793159	−	0.609015i	$-0.208435\pi$
$701$	42.0000	1.58632	0.793159	+	0.609015i	$0.208435\pi$
$702$	−4.00000	−0.150970
$703$	16.0000	0.603451
$704$	1.00000	0.0376889
$705$	−2.00000	−0.0753244
$706$	−30.0000	−1.12906
$707$	40.0000	1.50435
$708$	−4.00000	−0.150329
$709$	−28.0000	−1.05156	−0.525781	−	0.850620i	$-0.676227\pi$
$709$	−28.0000	−1.05156	−0.525781	+	0.850620i	$0.676227\pi$
$710$	−12.0000	−0.450352
$711$	12.0000	0.450035
$712$	2.00000	0.0749532
$713$	−48.0000	−1.79761
$714$	−4.00000	−0.149696
$715$	−4.00000	−0.149592
$716$	0	0
$717$	24.0000	0.896296
$718$	−4.00000	−0.149279
$719$	20.0000	0.745874	0.372937	−	0.927857i	$-0.378351\pi$
$719$	20.0000	0.745874	0.372937	+	0.927857i	$0.378351\pi$
$720$	−1.00000	−0.0372678
$721$	64.0000	2.38348
$722$	−3.00000	−0.111648
$723$	−18.0000	−0.669427
$724$	−16.0000	−0.594635
$725$	−4.00000	−0.148556
$726$	−1.00000	−0.0371135
$727$	−12.0000	−0.445055	−0.222528	−	0.974926i	$-0.571431\pi$
$727$	−12.0000	−0.445055	−0.222528	+	0.974926i	$0.571431\pi$
$728$	−16.0000	−0.592999
$729$	1.00000	0.0370370
$730$	−14.0000	−0.518163
$731$	−4.00000	−0.147945
$732$	14.0000	0.517455
$733$	44.0000	1.62518	0.812589	−	0.582838i	$-0.198058\pi$
$733$	44.0000	1.62518	0.812589	+	0.582838i	$0.198058\pi$
$734$	22.0000	0.812035
$735$	9.00000	0.331970
$736$	−8.00000	−0.294884
$737$	−4.00000	−0.147342
$738$	−10.0000	−0.368105
$739$	−40.0000	−1.47142	−0.735712	−	0.677295i	$-0.763152\pi$
$739$	−40.0000	−1.47142	−0.735712	+	0.677295i	$0.763152\pi$
$740$	−4.00000	−0.147043
$741$	−16.0000	−0.587775
$742$	16.0000	0.587378
$743$	−18.0000	−0.660356	−0.330178	−	0.943919i	$-0.607109\pi$
$743$	−18.0000	−0.660356	−0.330178	+	0.943919i	$0.607109\pi$
$744$	−6.00000	−0.219971
$745$	−6.00000	−0.219823
$746$	−4.00000	−0.146450
$747$	−4.00000	−0.146352
$748$	−1.00000	−0.0365636
$749$	−48.0000	−1.75388
$750$	1.00000	0.0365148
$751$	−46.0000	−1.67856	−0.839282	−	0.543696i	$-0.817024\pi$
$751$	−46.0000	−1.67856	−0.839282	+	0.543696i	$0.817024\pi$
$752$	−2.00000	−0.0729325
$753$	−16.0000	−0.583072
$754$	−16.0000	−0.582686
$755$	10.0000	0.363937
$756$	4.00000	0.145479
$757$	−26.0000	−0.944986	−0.472493	−	0.881334i	$-0.656646\pi$
$757$	−26.0000	−0.944986	−0.472493	+	0.881334i	$0.656646\pi$
$758$	4.00000	0.145287
$759$	8.00000	0.290382
$760$	−4.00000	−0.145095
$761$	18.0000	0.652499	0.326250	−	0.945284i	$-0.394215\pi$
$761$	18.0000	0.652499	0.326250	+	0.945284i	$0.394215\pi$
$762$	2.00000	0.0724524
$763$	24.0000	0.868858
$764$	6.00000	0.217072
$765$	1.00000	0.0361551
$766$	−14.0000	−0.505841
$767$	16.0000	0.577727
$768$	−1.00000	−0.0360844
$769$	−10.0000	−0.360609	−0.180305	−	0.983611i	$-0.557708\pi$
$769$	−10.0000	−0.360609	−0.180305	+	0.983611i	$0.557708\pi$
$770$	4.00000	0.144150
$771$	−10.0000	−0.360141
$772$	−14.0000	−0.503871
$773$	−24.0000	−0.863220	−0.431610	−	0.902060i	$-0.642054\pi$
$773$	−24.0000	−0.863220	−0.431610	+	0.902060i	$0.642054\pi$
$774$	4.00000	0.143777
$775$	6.00000	0.215526
$776$	−10.0000	−0.358979
$777$	16.0000	0.573997
$778$	−24.0000	−0.860442
$779$	−40.0000	−1.43315
$780$	4.00000	0.143223
$781$	12.0000	0.429394
$782$	8.00000	0.286079
$783$	4.00000	0.142948
$784$	9.00000	0.321429
$785$	14.0000	0.499681
$786$	0	0
$787$	−52.0000	−1.85360	−0.926800	−	0.375555i	$-0.877452\pi$
$787$	−52.0000	−1.85360	−0.926800	+	0.375555i	$0.877452\pi$
$788$	−24.0000	−0.854965
$789$	12.0000	0.427211
$790$	−12.0000	−0.426941
$791$	72.0000	2.56003
$792$	1.00000	0.0355335
$793$	−56.0000	−1.98862
$794$	8.00000	0.283909
$795$	−4.00000	−0.141865
$796$	−2.00000	−0.0708881
$797$	12.0000	0.425062	0.212531	−	0.977154i	$-0.431829\pi$
$797$	12.0000	0.425062	0.212531	+	0.977154i	$0.431829\pi$
$798$	16.0000	0.566394
$799$	2.00000	0.0707549
$800$	1.00000	0.0353553
$801$	2.00000	0.0706665
$802$	18.0000	0.635602
$803$	14.0000	0.494049
$804$	4.00000	0.141069
$805$	−32.0000	−1.12785
$806$	24.0000	0.845364
$807$	−10.0000	−0.352017
$808$	−10.0000	−0.351799
$809$	−34.0000	−1.19538	−0.597688	−	0.801729i	$-0.703914\pi$
$809$	−34.0000	−1.19538	−0.597688	+	0.801729i	$0.703914\pi$
$810$	−1.00000	−0.0351364
$811$	−20.0000	−0.702295	−0.351147	−	0.936320i	$-0.614208\pi$
$811$	−20.0000	−0.702295	−0.351147	+	0.936320i	$0.614208\pi$
$812$	16.0000	0.561490
$813$	−10.0000	−0.350715
$814$	4.00000	0.140200
$815$	12.0000	0.420342
$816$	1.00000	0.0350070
$817$	16.0000	0.559769
$818$	22.0000	0.769212
$819$	−16.0000	−0.559085
$820$	10.0000	0.349215
$821$	−48.0000	−1.67521	−0.837606	−	0.546275i	$-0.816045\pi$
$821$	−48.0000	−1.67521	−0.837606	+	0.546275i	$0.816045\pi$
$822$	18.0000	0.627822
$823$	−26.0000	−0.906303	−0.453152	−	0.891434i	$-0.649700\pi$
$823$	−26.0000	−0.906303	−0.453152	+	0.891434i	$0.649700\pi$
$824$	−16.0000	−0.557386
$825$	−1.00000	−0.0348155
$826$	−16.0000	−0.556711
$827$	16.0000	0.556375	0.278187	−	0.960527i	$-0.410266\pi$
$827$	16.0000	0.556375	0.278187	+	0.960527i	$0.410266\pi$
$828$	−8.00000	−0.278019
$829$	−34.0000	−1.18087	−0.590434	−	0.807086i	$-0.701044\pi$
$829$	−34.0000	−1.18087	−0.590434	+	0.807086i	$0.701044\pi$
$830$	4.00000	0.138842
$831$	26.0000	0.901930
$832$	4.00000	0.138675
$833$	−9.00000	−0.311832
$834$	12.0000	0.415526
$835$	2.00000	0.0692129
$836$	4.00000	0.138343
$837$	−6.00000	−0.207390
$838$	−4.00000	−0.138178
$839$	56.0000	1.93333	0.966667	−	0.256036i	$-0.0824164\pi$
$839$	56.0000	1.93333	0.966667	+	0.256036i	$0.0824164\pi$
$840$	−4.00000	−0.138013
$841$	−13.0000	−0.448276
$842$	2.00000	0.0689246
$843$	2.00000	0.0688837
$844$	−12.0000	−0.413057
$845$	−3.00000	−0.103203
$846$	−2.00000	−0.0687614
$847$	−4.00000	−0.137442
$848$	−4.00000	−0.137361
$849$	−20.0000	−0.686398
$850$	−1.00000	−0.0342997
$851$	−32.0000	−1.09695
$852$	−12.0000	−0.411113
$853$	−42.0000	−1.43805	−0.719026	−	0.694983i	$-0.755412\pi$
$853$	−42.0000	−1.43805	−0.719026	+	0.694983i	$0.755412\pi$
$854$	56.0000	1.91628
$855$	−4.00000	−0.136797
$856$	12.0000	0.410152
$857$	−2.00000	−0.0683187	−0.0341593	−	0.999416i	$-0.510875\pi$
$857$	−2.00000	−0.0683187	−0.0341593	+	0.999416i	$0.510875\pi$
$858$	−4.00000	−0.136558
$859$	−36.0000	−1.22830	−0.614152	−	0.789188i	$-0.710502\pi$
$859$	−36.0000	−1.22830	−0.614152	+	0.789188i	$0.710502\pi$
$860$	−4.00000	−0.136399
$861$	−40.0000	−1.36320
$862$	26.0000	0.885564
$863$	26.0000	0.885050	0.442525	−	0.896756i	$-0.354083\pi$
$863$	26.0000	0.885050	0.442525	+	0.896756i	$0.354083\pi$
$864$	−1.00000	−0.0340207
$865$	20.0000	0.680020
$866$	14.0000	0.475739
$867$	−1.00000	−0.0339618
$868$	−24.0000	−0.814613
$869$	12.0000	0.407072
$870$	−4.00000	−0.135613
$871$	−16.0000	−0.542139
$872$	−6.00000	−0.203186
$873$	−10.0000	−0.338449
$874$	−32.0000	−1.08242
$875$	4.00000	0.135225
$876$	−14.0000	−0.473016
$877$	10.0000	0.337676	0.168838	−	0.985644i	$-0.445999\pi$
$877$	10.0000	0.337676	0.168838	+	0.985644i	$0.445999\pi$
$878$	24.0000	0.809961
$879$	−22.0000	−0.742042
$880$	−1.00000	−0.0337100
$881$	18.0000	0.606435	0.303218	−	0.952921i	$-0.401939\pi$
$881$	18.0000	0.606435	0.303218	+	0.952921i	$0.401939\pi$
$882$	9.00000	0.303046
$883$	−20.0000	−0.673054	−0.336527	−	0.941674i	$-0.609252\pi$
$883$	−20.0000	−0.673054	−0.336527	+	0.941674i	$0.609252\pi$
$884$	−4.00000	−0.134535
$885$	4.00000	0.134459
$886$	16.0000	0.537531
$887$	−22.0000	−0.738688	−0.369344	−	0.929293i	$-0.620418\pi$
$887$	−22.0000	−0.738688	−0.369344	+	0.929293i	$0.620418\pi$
$888$	−4.00000	−0.134231
$889$	8.00000	0.268311
$890$	−2.00000	−0.0670402
$891$	1.00000	0.0335013
$892$	20.0000	0.669650
$893$	−8.00000	−0.267710
$894$	−6.00000	−0.200670
$895$	0	0
$896$	−4.00000	−0.133631
$897$	32.0000	1.06845
$898$	10.0000	0.333704
$899$	−24.0000	−0.800445
$900$	1.00000	0.0333333
$901$	4.00000	0.133259
$902$	−10.0000	−0.332964
$903$	16.0000	0.532447
$904$	−18.0000	−0.598671
$905$	16.0000	0.531858
$906$	10.0000	0.332228
$907$	28.0000	0.929725	0.464862	−	0.885383i	$-0.346104\pi$
$907$	28.0000	0.929725	0.464862	+	0.885383i	$0.346104\pi$
$908$	0	0
$909$	−10.0000	−0.331679
$910$	16.0000	0.530395
$911$	−36.0000	−1.19273	−0.596367	−	0.802712i	$-0.703390\pi$
$911$	−36.0000	−1.19273	−0.596367	+	0.802712i	$0.703390\pi$
$912$	−4.00000	−0.132453
$913$	−4.00000	−0.132381
$914$	38.0000	1.25693
$915$	−14.0000	−0.462826
$916$	−14.0000	−0.462573
$917$	0	0
$918$	1.00000	0.0330049
$919$	−22.0000	−0.725713	−0.362857	−	0.931845i	$-0.618198\pi$
$919$	−22.0000	−0.725713	−0.362857	+	0.931845i	$0.618198\pi$
$920$	8.00000	0.263752
$921$	8.00000	0.263609
$922$	−6.00000	−0.197599
$923$	48.0000	1.57994
$924$	4.00000	0.131590
$925$	4.00000	0.131519
$926$	−32.0000	−1.05159
$927$	−16.0000	−0.525509
$928$	−4.00000	−0.131306
$929$	−50.0000	−1.64045	−0.820223	−	0.572043i	$-0.806151\pi$
$929$	−50.0000	−1.64045	−0.820223	+	0.572043i	$0.806151\pi$
$930$	6.00000	0.196748
$931$	36.0000	1.17985
$932$	−22.0000	−0.720634
$933$	16.0000	0.523816
$934$	12.0000	0.392652
$935$	1.00000	0.0327035
$936$	4.00000	0.130744
$937$	−30.0000	−0.980057	−0.490029	−	0.871706i	$-0.663014\pi$
$937$	−30.0000	−0.980057	−0.490029	+	0.871706i	$0.663014\pi$
$938$	16.0000	0.522419
$939$	10.0000	0.326338
$940$	2.00000	0.0652328
$941$	8.00000	0.260793	0.130396	−	0.991462i	$-0.458375\pi$
$941$	8.00000	0.260793	0.130396	+	0.991462i	$0.458375\pi$
$942$	14.0000	0.456145
$943$	80.0000	2.60516
$944$	4.00000	0.130189
$945$	−4.00000	−0.130120
$946$	4.00000	0.130051
$947$	20.0000	0.649913	0.324956	−	0.945729i	$-0.394650\pi$
$947$	20.0000	0.649913	0.324956	+	0.945729i	$0.394650\pi$
$948$	−12.0000	−0.389742
$949$	56.0000	1.81784
$950$	4.00000	0.129777
$951$	−18.0000	−0.583690
$952$	4.00000	0.129641
$953$	2.00000	0.0647864	0.0323932	−	0.999475i	$-0.489687\pi$
$953$	2.00000	0.0647864	0.0323932	+	0.999475i	$0.489687\pi$
$954$	−4.00000	−0.129505
$955$	−6.00000	−0.194155
$956$	−24.0000	−0.776215
$957$	4.00000	0.129302
$958$	38.0000	1.22772
$959$	72.0000	2.32500
$960$	1.00000	0.0322749
$961$	5.00000	0.161290
$962$	16.0000	0.515861
$963$	12.0000	0.386695
$964$	18.0000	0.579741
$965$	14.0000	0.450676
$966$	−32.0000	−1.02958
$967$	26.0000	0.836104	0.418052	−	0.908423i	$-0.362713\pi$
$967$	26.0000	0.836104	0.418052	+	0.908423i	$0.362713\pi$
$968$	1.00000	0.0321412
$969$	4.00000	0.128499
$970$	10.0000	0.321081
$971$	36.0000	1.15529	0.577647	−	0.816286i	$-0.303971\pi$
$971$	36.0000	1.15529	0.577647	+	0.816286i	$0.303971\pi$
$972$	−1.00000	−0.0320750
$973$	48.0000	1.53881
$974$	26.0000	0.833094
$975$	−4.00000	−0.128103
$976$	−14.0000	−0.448129
$977$	−42.0000	−1.34370	−0.671850	−	0.740688i	$-0.734500\pi$
$977$	−42.0000	−1.34370	−0.671850	+	0.740688i	$0.734500\pi$
$978$	12.0000	0.383718
$979$	2.00000	0.0639203
$980$	−9.00000	−0.287494
$981$	−6.00000	−0.191565
$982$	−20.0000	−0.638226
$983$	20.0000	0.637901	0.318950	−	0.947771i	$-0.396670\pi$
$983$	20.0000	0.637901	0.318950	+	0.947771i	$0.396670\pi$
$984$	10.0000	0.318788
$985$	24.0000	0.764704
$986$	4.00000	0.127386
$987$	−8.00000	−0.254643
$988$	16.0000	0.509028
$989$	−32.0000	−1.01754
$990$	−1.00000	−0.0317821
$991$	−6.00000	−0.190596	−0.0952981	−	0.995449i	$-0.530380\pi$
$991$	−6.00000	−0.190596	−0.0952981	+	0.995449i	$0.530380\pi$
$992$	6.00000	0.190500
$993$	4.00000	0.126936
$994$	−48.0000	−1.52247
$995$	2.00000	0.0634043
$996$	4.00000	0.126745
$997$	38.0000	1.20347	0.601736	−	0.798695i	$-0.294476\pi$
$997$	38.0000	1.20347	0.601736	+	0.798695i	$0.294476\pi$
$998$	24.0000	0.759707
$999$	−4.00000	−0.126554

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5610.2.a.w.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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