LMFDB - Embedded newform 5610.2.a.y.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:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	5610.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

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

\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} -1.00000 q^{11} -1.00000 q^{12} -3.00000 q^{13} -1.00000 q^{14} +1.00000 q^{15} +1.00000 q^{16} -1.00000 q^{17} +1.00000 q^{18} -1.00000 q^{19} -1.00000 q^{20} +1.00000 q^{21} -1.00000 q^{22} +1.00000 q^{23} -1.00000 q^{24} +1.00000 q^{25} -3.00000 q^{26} -1.00000 q^{27} -1.00000 q^{28} +6.00000 q^{29} +1.00000 q^{30} -5.00000 q^{31} +1.00000 q^{32} +1.00000 q^{33} -1.00000 q^{34} +1.00000 q^{35} +1.00000 q^{36} +5.00000 q^{37} -1.00000 q^{38} +3.00000 q^{39} -1.00000 q^{40} -6.00000 q^{41} +1.00000 q^{42} +8.00000 q^{43} -1.00000 q^{44} -1.00000 q^{45} +1.00000 q^{46} +6.00000 q^{47} -1.00000 q^{48} -6.00000 q^{49} +1.00000 q^{50} +1.00000 q^{51} -3.00000 q^{52} -6.00000 q^{53} -1.00000 q^{54} +1.00000 q^{55} -1.00000 q^{56} +1.00000 q^{57} +6.00000 q^{58} -4.00000 q^{59} +1.00000 q^{60} +5.00000 q^{61} -5.00000 q^{62} -1.00000 q^{63} +1.00000 q^{64} +3.00000 q^{65} +1.00000 q^{66} +3.00000 q^{67} -1.00000 q^{68} -1.00000 q^{69} +1.00000 q^{70} +6.00000 q^{71} +1.00000 q^{72} +5.00000 q^{74} -1.00000 q^{75} -1.00000 q^{76} +1.00000 q^{77} +3.00000 q^{78} +14.0000 q^{79} -1.00000 q^{80} +1.00000 q^{81} -6.00000 q^{82} -11.0000 q^{83} +1.00000 q^{84} +1.00000 q^{85} +8.00000 q^{86} -6.00000 q^{87} -1.00000 q^{88} +10.0000 q^{89} -1.00000 q^{90} +3.00000 q^{91} +1.00000 q^{92} +5.00000 q^{93} +6.00000 q^{94} +1.00000 q^{95} -1.00000 q^{96} +13.0000 q^{97} -6.00000 q^{98} -1.00000 q^{99} +O(q^{100})\)

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
$7$	−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
$9$	1.00000	0.333333
$10$	−1.00000	−0.316228
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−1.00000	−0.288675
$13$	−3.00000	−0.832050	−0.416025	−	0.909353i	$-0.636577\pi$
$13$	−3.00000	−0.832050	−0.416025	+	0.909353i	$0.636577\pi$
$14$	−1.00000	−0.267261
$15$	1.00000	0.258199
$16$	1.00000	0.250000
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	1.00000	0.235702
$19$	−1.00000	−0.229416	−0.114708	−	0.993399i	$-0.536593\pi$
$19$	−1.00000	−0.229416	−0.114708	+	0.993399i	$0.536593\pi$
$20$	−1.00000	−0.223607
$21$	1.00000	0.218218
$22$	−1.00000	−0.213201
$23$	1.00000	0.208514	0.104257	−	0.994550i	$-0.466753\pi$
$23$	1.00000	0.208514	0.104257	+	0.994550i	$0.466753\pi$
$24$	−1.00000	−0.204124
$25$	1.00000	0.200000
$26$	−3.00000	−0.588348
$27$	−1.00000	−0.192450
$28$	−1.00000	−0.188982
$29$	6.00000	1.11417	0.557086	−	0.830455i	$-0.311919\pi$
$29$	6.00000	1.11417	0.557086	+	0.830455i	$0.311919\pi$
$30$	1.00000	0.182574
$31$	−5.00000	−0.898027	−0.449013	−	0.893525i	$-0.648224\pi$
$31$	−5.00000	−0.898027	−0.449013	+	0.893525i	$0.648224\pi$
$32$	1.00000	0.176777
$33$	1.00000	0.174078
$34$	−1.00000	−0.171499
$35$	1.00000	0.169031
$36$	1.00000	0.166667
$37$	5.00000	0.821995	0.410997	−	0.911636i	$-0.365181\pi$
$37$	5.00000	0.821995	0.410997	+	0.911636i	$0.365181\pi$
$38$	−1.00000	−0.162221
$39$	3.00000	0.480384
$40$	−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	$0.655213\pi$
$42$	1.00000	0.154303
$43$	8.00000	1.21999	0.609994	−	0.792406i	$-0.291172\pi$
$43$	8.00000	1.21999	0.609994	+	0.792406i	$0.291172\pi$
$44$	−1.00000	−0.150756
$45$	−1.00000	−0.149071
$46$	1.00000	0.147442
$47$	6.00000	0.875190	0.437595	−	0.899172i	$-0.355830\pi$
$47$	6.00000	0.875190	0.437595	+	0.899172i	$0.355830\pi$
$48$	−1.00000	−0.144338
$49$	−6.00000	−0.857143
$50$	1.00000	0.141421
$51$	1.00000	0.140028
$52$	−3.00000	−0.416025
$53$	−6.00000	−0.824163	−0.412082	−	0.911147i	$-0.635198\pi$
$53$	−6.00000	−0.824163	−0.412082	+	0.911147i	$0.635198\pi$
$54$	−1.00000	−0.136083
$55$	1.00000	0.134840
$56$	−1.00000	−0.133631
$57$	1.00000	0.132453
$58$	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
$61$	5.00000	0.640184	0.320092	−	0.947386i	$-0.396286\pi$
$61$	5.00000	0.640184	0.320092	+	0.947386i	$0.396286\pi$
$62$	−5.00000	−0.635001
$63$	−1.00000	−0.125988
$64$	1.00000	0.125000
$65$	3.00000	0.372104
$66$	1.00000	0.123091
$67$	3.00000	0.366508	0.183254	−	0.983066i	$-0.441337\pi$
$67$	3.00000	0.366508	0.183254	+	0.983066i	$0.441337\pi$
$68$	−1.00000	−0.121268
$69$	−1.00000	−0.120386
$70$	1.00000	0.119523
$71$	6.00000	0.712069	0.356034	−	0.934473i	$-0.384129\pi$
$71$	6.00000	0.712069	0.356034	+	0.934473i	$0.384129\pi$
$72$	1.00000	0.117851
$73$	0	0		−	1.00000i	$-0.5\pi$
$73$	0	0			1.00000i	$0.5\pi$
$74$	5.00000	0.581238
$75$	−1.00000	−0.115470
$76$	−1.00000	−0.114708
$77$	1.00000	0.113961
$78$	3.00000	0.339683
$79$	14.0000	1.57512	0.787562	−	0.616236i	$-0.211343\pi$
$79$	14.0000	1.57512	0.787562	+	0.616236i	$0.211343\pi$
$80$	−1.00000	−0.111803
$81$	1.00000	0.111111
$82$	−6.00000	−0.662589
$83$	−11.0000	−1.20741	−0.603703	−	0.797209i	$-0.706309\pi$
$83$	−11.0000	−1.20741	−0.603703	+	0.797209i	$0.706309\pi$
$84$	1.00000	0.109109
$85$	1.00000	0.108465
$86$	8.00000	0.862662
$87$	−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
$91$	3.00000	0.314485
$92$	1.00000	0.104257
$93$	5.00000	0.518476
$94$	6.00000	0.618853
$95$	1.00000	0.102598
$96$	−1.00000	−0.102062
$97$	13.0000	1.31995	0.659975	−	0.751288i	$-0.270567\pi$
$97$	13.0000	1.31995	0.659975	+	0.751288i	$0.270567\pi$
$98$	−6.00000	−0.606092
$99$	−1.00000	−0.100504
$100$	1.00000	0.100000
$101$	2.00000	0.199007	0.0995037	−	0.995037i	$-0.468274\pi$
$101$	2.00000	0.199007	0.0995037	+	0.995037i	$0.468274\pi$
$102$	1.00000	0.0990148
$103$	−1.00000	−0.0985329	−0.0492665	−	0.998786i	$-0.515688\pi$
$103$	−1.00000	−0.0985329	−0.0492665	+	0.998786i	$0.515688\pi$
$104$	−3.00000	−0.294174
$105$	−1.00000	−0.0975900
$106$	−6.00000	−0.582772
$107$	18.0000	1.74013	0.870063	−	0.492941i	$-0.164078\pi$
$107$	18.0000	1.74013	0.870063	+	0.492941i	$0.164078\pi$
$108$	−1.00000	−0.0962250
$109$	7.00000	0.670478	0.335239	−	0.942133i	$-0.391183\pi$
$109$	7.00000	0.670478	0.335239	+	0.942133i	$0.391183\pi$
$110$	1.00000	0.0953463
$111$	−5.00000	−0.474579
$112$	−1.00000	−0.0944911
$113$	18.0000	1.69330	0.846649	−	0.532152i	$-0.178617\pi$
$113$	18.0000	1.69330	0.846649	+	0.532152i	$0.178617\pi$
$114$	1.00000	0.0936586
$115$	−1.00000	−0.0932505
$116$	6.00000	0.557086
$117$	−3.00000	−0.277350
$118$	−4.00000	−0.368230
$119$	1.00000	0.0916698
$120$	1.00000	0.0912871
$121$	1.00000	0.0909091
$122$	5.00000	0.452679
$123$	6.00000	0.541002
$124$	−5.00000	−0.449013
$125$	−1.00000	−0.0894427
$126$	−1.00000	−0.0890871
$127$	−16.0000	−1.41977	−0.709885	−	0.704317i	$-0.751253\pi$
$127$	−16.0000	−1.41977	−0.709885	+	0.704317i	$0.751253\pi$
$128$	1.00000	0.0883883
$129$	−8.00000	−0.704361
$130$	3.00000	0.263117
$131$	−7.00000	−0.611593	−0.305796	−	0.952097i	$-0.598923\pi$
$131$	−7.00000	−0.611593	−0.305796	+	0.952097i	$0.598923\pi$
$132$	1.00000	0.0870388
$133$	1.00000	0.0867110
$134$	3.00000	0.259161
$135$	1.00000	0.0860663
$136$	−1.00000	−0.0857493
$137$	7.00000	0.598050	0.299025	−	0.954245i	$-0.403339\pi$
$137$	7.00000	0.598050	0.299025	+	0.954245i	$0.403339\pi$
$138$	−1.00000	−0.0851257
$139$	−14.0000	−1.18746	−0.593732	−	0.804663i	$-0.702346\pi$
$139$	−14.0000	−1.18746	−0.593732	+	0.804663i	$0.702346\pi$
$140$	1.00000	0.0845154
$141$	−6.00000	−0.505291
$142$	6.00000	0.503509
$143$	3.00000	0.250873
$144$	1.00000	0.0833333
$145$	−6.00000	−0.498273
$146$	0	0
$147$	6.00000	0.494872
$148$	5.00000	0.410997
$149$	−9.00000	−0.737309	−0.368654	−	0.929567i	$-0.620181\pi$
$149$	−9.00000	−0.737309	−0.368654	+	0.929567i	$0.620181\pi$
$150$	−1.00000	−0.0816497
$151$	17.0000	1.38344	0.691720	−	0.722166i	$-0.256853\pi$
$151$	17.0000	1.38344	0.691720	+	0.722166i	$0.256853\pi$
$152$	−1.00000	−0.0811107
$153$	−1.00000	−0.0808452
$154$	1.00000	0.0805823
$155$	5.00000	0.401610
$156$	3.00000	0.240192
$157$	0	0		−	1.00000i	$-0.5\pi$
$157$	0	0			1.00000i	$0.5\pi$
$158$	14.0000	1.11378
$159$	6.00000	0.475831
$160$	−1.00000	−0.0790569
$161$	−1.00000	−0.0788110
$162$	1.00000	0.0785674
$163$	20.0000	1.56652	0.783260	−	0.621694i	$-0.213555\pi$
$163$	20.0000	1.56652	0.783260	+	0.621694i	$0.213555\pi$
$164$	−6.00000	−0.468521
$165$	−1.00000	−0.0778499
$166$	−11.0000	−0.853766
$167$	−4.00000	−0.309529	−0.154765	−	0.987951i	$-0.549462\pi$
$167$	−4.00000	−0.309529	−0.154765	+	0.987951i	$0.549462\pi$
$168$	1.00000	0.0771517
$169$	−4.00000	−0.307692
$170$	1.00000	0.0766965
$171$	−1.00000	−0.0764719
$172$	8.00000	0.609994
$173$	21.0000	1.59660	0.798300	−	0.602260i	$-0.205733\pi$
$173$	21.0000	1.59660	0.798300	+	0.602260i	$0.205733\pi$
$174$	−6.00000	−0.454859
$175$	−1.00000	−0.0755929
$176$	−1.00000	−0.0753778
$177$	4.00000	0.300658
$178$	10.0000	0.749532
$179$	−1.00000	−0.0747435	−0.0373718	−	0.999301i	$-0.511899\pi$
$179$	−1.00000	−0.0747435	−0.0373718	+	0.999301i	$0.511899\pi$
$180$	−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	$0.702704\pi$
$182$	3.00000	0.222375
$183$	−5.00000	−0.369611
$184$	1.00000	0.0737210
$185$	−5.00000	−0.367607
$186$	5.00000	0.366618
$187$	1.00000	0.0731272
$188$	6.00000	0.437595
$189$	1.00000	0.0727393
$190$	1.00000	0.0725476
$191$	−8.00000	−0.578860	−0.289430	−	0.957199i	$-0.593466\pi$
$191$	−8.00000	−0.578860	−0.289430	+	0.957199i	$0.593466\pi$
$192$	−1.00000	−0.0721688
$193$	8.00000	0.575853	0.287926	−	0.957653i	$-0.407034\pi$
$193$	8.00000	0.575853	0.287926	+	0.957653i	$0.407034\pi$
$194$	13.0000	0.933346
$195$	−3.00000	−0.214834
$196$	−6.00000	−0.428571
$197$	17.0000	1.21120	0.605600	−	0.795769i	$-0.292933\pi$
$197$	17.0000	1.21120	0.605600	+	0.795769i	$0.292933\pi$
$198$	−1.00000	−0.0710669
$199$	−5.00000	−0.354441	−0.177220	−	0.984171i	$-0.556711\pi$
$199$	−5.00000	−0.354441	−0.177220	+	0.984171i	$0.556711\pi$
$200$	1.00000	0.0707107
$201$	−3.00000	−0.211604
$202$	2.00000	0.140720
$203$	−6.00000	−0.421117
$204$	1.00000	0.0700140
$205$	6.00000	0.419058
$206$	−1.00000	−0.0696733
$207$	1.00000	0.0695048
$208$	−3.00000	−0.208013
$209$	1.00000	0.0691714
$210$	−1.00000	−0.0690066
$211$	−18.0000	−1.23917	−0.619586	−	0.784929i	$-0.712699\pi$
$211$	−18.0000	−1.23917	−0.619586	+	0.784929i	$0.712699\pi$
$212$	−6.00000	−0.412082
$213$	−6.00000	−0.411113
$214$	18.0000	1.23045
$215$	−8.00000	−0.545595
$216$	−1.00000	−0.0680414
$217$	5.00000	0.339422
$218$	7.00000	0.474100
$219$	0	0
$220$	1.00000	0.0674200
$221$	3.00000	0.201802
$222$	−5.00000	−0.335578
$223$	−15.0000	−1.00447	−0.502237	−	0.864730i	$-0.667490\pi$
$223$	−15.0000	−1.00447	−0.502237	+	0.864730i	$0.667490\pi$
$224$	−1.00000	−0.0668153
$225$	1.00000	0.0666667
$226$	18.0000	1.19734
$227$	18.0000	1.19470	0.597351	−	0.801980i	$-0.296220\pi$
$227$	18.0000	1.19470	0.597351	+	0.801980i	$0.296220\pi$
$228$	1.00000	0.0662266
$229$	23.0000	1.51988	0.759941	−	0.649992i	$-0.225228\pi$
$229$	23.0000	1.51988	0.759941	+	0.649992i	$0.225228\pi$
$230$	−1.00000	−0.0659380
$231$	−1.00000	−0.0657952
$232$	6.00000	0.393919
$233$	18.0000	1.17922	0.589610	−	0.807688i	$-0.299282\pi$
$233$	18.0000	1.17922	0.589610	+	0.807688i	$0.299282\pi$
$234$	−3.00000	−0.196116
$235$	−6.00000	−0.391397
$236$	−4.00000	−0.260378
$237$	−14.0000	−0.909398
$238$	1.00000	0.0648204
$239$	−26.0000	−1.68180	−0.840900	−	0.541190i	$-0.817974\pi$
$239$	−26.0000	−1.68180	−0.840900	+	0.541190i	$0.817974\pi$
$240$	1.00000	0.0645497
$241$	19.0000	1.22390	0.611949	−	0.790897i	$-0.290386\pi$
$241$	19.0000	1.22390	0.611949	+	0.790897i	$0.290386\pi$
$242$	1.00000	0.0642824
$243$	−1.00000	−0.0641500
$244$	5.00000	0.320092
$245$	6.00000	0.383326
$246$	6.00000	0.382546
$247$	3.00000	0.190885
$248$	−5.00000	−0.317500
$249$	11.0000	0.697097
$250$	−1.00000	−0.0632456
$251$	27.0000	1.70422	0.852112	−	0.523359i	$-0.175321\pi$
$251$	27.0000	1.70422	0.852112	+	0.523359i	$0.175321\pi$
$252$	−1.00000	−0.0629941
$253$	−1.00000	−0.0628695
$254$	−16.0000	−1.00393
$255$	−1.00000	−0.0626224
$256$	1.00000	0.0625000
$257$	−2.00000	−0.124757	−0.0623783	−	0.998053i	$-0.519869\pi$
$257$	−2.00000	−0.124757	−0.0623783	+	0.998053i	$0.519869\pi$
$258$	−8.00000	−0.498058
$259$	−5.00000	−0.310685
$260$	3.00000	0.186052
$261$	6.00000	0.371391
$262$	−7.00000	−0.432461
$263$	21.0000	1.29492	0.647458	−	0.762101i	$-0.275832\pi$
$263$	21.0000	1.29492	0.647458	+	0.762101i	$0.275832\pi$
$264$	1.00000	0.0615457
$265$	6.00000	0.368577
$266$	1.00000	0.0613139
$267$	−10.0000	−0.611990
$268$	3.00000	0.183254
$269$	3.00000	0.182913	0.0914566	−	0.995809i	$-0.470848\pi$
$269$	3.00000	0.182913	0.0914566	+	0.995809i	$0.470848\pi$
$270$	1.00000	0.0608581
$271$	20.0000	1.21491	0.607457	−	0.794353i	$-0.292190\pi$
$271$	20.0000	1.21491	0.607457	+	0.794353i	$0.292190\pi$
$272$	−1.00000	−0.0606339
$273$	−3.00000	−0.181568
$274$	7.00000	0.422885
$275$	−1.00000	−0.0603023
$276$	−1.00000	−0.0601929
$277$	−32.0000	−1.92269	−0.961347	−	0.275340i	$-0.911209\pi$
$277$	−32.0000	−1.92269	−0.961347	+	0.275340i	$0.911209\pi$
$278$	−14.0000	−0.839664
$279$	−5.00000	−0.299342
$280$	1.00000	0.0597614
$281$	18.0000	1.07379	0.536895	−	0.843649i	$-0.319597\pi$
$281$	18.0000	1.07379	0.536895	+	0.843649i	$0.319597\pi$
$282$	−6.00000	−0.357295
$283$	28.0000	1.66443	0.832214	−	0.554455i	$-0.187073\pi$
$283$	28.0000	1.66443	0.832214	+	0.554455i	$0.187073\pi$
$284$	6.00000	0.356034
$285$	−1.00000	−0.0592349
$286$	3.00000	0.177394
$287$	6.00000	0.354169
$288$	1.00000	0.0589256
$289$	1.00000	0.0588235
$290$	−6.00000	−0.352332
$291$	−13.0000	−0.762073
$292$	0	0
$293$	0	0		−	1.00000i	$-0.5\pi$
$293$	0	0			1.00000i	$0.5\pi$
$294$	6.00000	0.349927
$295$	4.00000	0.232889
$296$	5.00000	0.290619
$297$	1.00000	0.0580259
$298$	−9.00000	−0.521356
$299$	−3.00000	−0.173494
$300$	−1.00000	−0.0577350
$301$	−8.00000	−0.461112
$302$	17.0000	0.978240
$303$	−2.00000	−0.114897
$304$	−1.00000	−0.0573539
$305$	−5.00000	−0.286299
$306$	−1.00000	−0.0571662
$307$	−28.0000	−1.59804	−0.799022	−	0.601302i	$-0.794649\pi$
$307$	−28.0000	−1.59804	−0.799022	+	0.601302i	$0.794649\pi$
$308$	1.00000	0.0569803
$309$	1.00000	0.0568880
$310$	5.00000	0.283981
$311$	−18.0000	−1.02069	−0.510343	−	0.859971i	$-0.670482\pi$
$311$	−18.0000	−1.02069	−0.510343	+	0.859971i	$0.670482\pi$
$312$	3.00000	0.169842
$313$	−21.0000	−1.18699	−0.593495	−	0.804838i	$-0.702252\pi$
$313$	−21.0000	−1.18699	−0.593495	+	0.804838i	$0.702252\pi$
$314$	0	0
$315$	1.00000	0.0563436
$316$	14.0000	0.787562
$317$	6.00000	0.336994	0.168497	−	0.985702i	$-0.446109\pi$
$317$	6.00000	0.336994	0.168497	+	0.985702i	$0.446109\pi$
$318$	6.00000	0.336463
$319$	−6.00000	−0.335936
$320$	−1.00000	−0.0559017
$321$	−18.0000	−1.00466
$322$	−1.00000	−0.0557278
$323$	1.00000	0.0556415
$324$	1.00000	0.0555556
$325$	−3.00000	−0.166410
$326$	20.0000	1.10770
$327$	−7.00000	−0.387101
$328$	−6.00000	−0.331295
$329$	−6.00000	−0.330791
$330$	−1.00000	−0.0550482
$331$	−28.0000	−1.53902	−0.769510	−	0.638635i	$-0.779499\pi$
$331$	−28.0000	−1.53902	−0.769510	+	0.638635i	$0.779499\pi$
$332$	−11.0000	−0.603703
$333$	5.00000	0.273998
$334$	−4.00000	−0.218870
$335$	−3.00000	−0.163908
$336$	1.00000	0.0545545
$337$	32.0000	1.74315	0.871576	−	0.490261i	$-0.163099\pi$
$337$	32.0000	1.74315	0.871576	+	0.490261i	$0.163099\pi$
$338$	−4.00000	−0.217571
$339$	−18.0000	−0.977626
$340$	1.00000	0.0542326
$341$	5.00000	0.270765
$342$	−1.00000	−0.0540738
$343$	13.0000	0.701934
$344$	8.00000	0.431331
$345$	1.00000	0.0538382
$346$	21.0000	1.12897
$347$	18.0000	0.966291	0.483145	−	0.875540i	$-0.339494\pi$
$347$	18.0000	0.966291	0.483145	+	0.875540i	$0.339494\pi$
$348$	−6.00000	−0.321634
$349$	22.0000	1.17763	0.588817	−	0.808267i	$-0.299594\pi$
$349$	22.0000	1.17763	0.588817	+	0.808267i	$0.299594\pi$
$350$	−1.00000	−0.0534522
$351$	3.00000	0.160128
$352$	−1.00000	−0.0533002
$353$	25.0000	1.33062	0.665308	−	0.746569i	$-0.268300\pi$
$353$	25.0000	1.33062	0.665308	+	0.746569i	$0.268300\pi$
$354$	4.00000	0.212598
$355$	−6.00000	−0.318447
$356$	10.0000	0.529999
$357$	−1.00000	−0.0529256
$358$	−1.00000	−0.0528516
$359$	−6.00000	−0.316668	−0.158334	−	0.987386i	$-0.550612\pi$
$359$	−6.00000	−0.316668	−0.158334	+	0.987386i	$0.550612\pi$
$360$	−1.00000	−0.0527046
$361$	−18.0000	−0.947368
$362$	−16.0000	−0.840941
$363$	−1.00000	−0.0524864
$364$	3.00000	0.157243
$365$	0	0
$366$	−5.00000	−0.261354
$367$	16.0000	0.835193	0.417597	−	0.908633i	$-0.362873\pi$
$367$	16.0000	0.835193	0.417597	+	0.908633i	$0.362873\pi$
$368$	1.00000	0.0521286
$369$	−6.00000	−0.312348
$370$	−5.00000	−0.259938
$371$	6.00000	0.311504
$372$	5.00000	0.259238
$373$	−26.0000	−1.34623	−0.673114	−	0.739538i	$-0.735044\pi$
$373$	−26.0000	−1.34623	−0.673114	+	0.739538i	$0.735044\pi$
$374$	1.00000	0.0517088
$375$	1.00000	0.0516398
$376$	6.00000	0.309426
$377$	−18.0000	−0.927047
$378$	1.00000	0.0514344
$379$	15.0000	0.770498	0.385249	−	0.922813i	$-0.374116\pi$
$379$	15.0000	0.770498	0.385249	+	0.922813i	$0.374116\pi$
$380$	1.00000	0.0512989
$381$	16.0000	0.819705
$382$	−8.00000	−0.409316
$383$	30.0000	1.53293	0.766464	−	0.642287i	$-0.222014\pi$
$383$	30.0000	1.53293	0.766464	+	0.642287i	$0.222014\pi$
$384$	−1.00000	−0.0510310
$385$	−1.00000	−0.0509647
$386$	8.00000	0.407189
$387$	8.00000	0.406663
$388$	13.0000	0.659975
$389$	36.0000	1.82527	0.912636	−	0.408773i	$-0.134043\pi$
$389$	36.0000	1.82527	0.912636	+	0.408773i	$0.134043\pi$
$390$	−3.00000	−0.151911
$391$	−1.00000	−0.0505722
$392$	−6.00000	−0.303046
$393$	7.00000	0.353103
$394$	17.0000	0.856448
$395$	−14.0000	−0.704416
$396$	−1.00000	−0.0502519
$397$	−38.0000	−1.90717	−0.953583	−	0.301131i	$-0.902636\pi$
$397$	−38.0000	−1.90717	−0.953583	+	0.301131i	$0.902636\pi$
$398$	−5.00000	−0.250627
$399$	−1.00000	−0.0500626
$400$	1.00000	0.0500000
$401$	−27.0000	−1.34832	−0.674158	−	0.738587i	$-0.735493\pi$
$401$	−27.0000	−1.34832	−0.674158	+	0.738587i	$0.735493\pi$
$402$	−3.00000	−0.149626
$403$	15.0000	0.747203
$404$	2.00000	0.0995037
$405$	−1.00000	−0.0496904
$406$	−6.00000	−0.297775
$407$	−5.00000	−0.247841
$408$	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	$0.316941\pi$
$410$	6.00000	0.296319
$411$	−7.00000	−0.345285
$412$	−1.00000	−0.0492665
$413$	4.00000	0.196827
$414$	1.00000	0.0491473
$415$	11.0000	0.539969
$416$	−3.00000	−0.147087
$417$	14.0000	0.685583
$418$	1.00000	0.0489116
$419$	32.0000	1.56330	0.781651	−	0.623716i	$-0.214378\pi$
$419$	32.0000	1.56330	0.781651	+	0.623716i	$0.214378\pi$
$420$	−1.00000	−0.0487950
$421$	7.00000	0.341159	0.170580	−	0.985344i	$-0.445436\pi$
$421$	7.00000	0.341159	0.170580	+	0.985344i	$0.445436\pi$
$422$	−18.0000	−0.876226
$423$	6.00000	0.291730
$424$	−6.00000	−0.291386
$425$	−1.00000	−0.0485071
$426$	−6.00000	−0.290701
$427$	−5.00000	−0.241967
$428$	18.0000	0.870063
$429$	−3.00000	−0.144841
$430$	−8.00000	−0.385794
$431$	−40.0000	−1.92673	−0.963366	−	0.268190i	$-0.913575\pi$
$431$	−40.0000	−1.92673	−0.963366	+	0.268190i	$0.913575\pi$
$432$	−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	$0.546051\pi$
$434$	5.00000	0.240008
$435$	6.00000	0.287678
$436$	7.00000	0.335239
$437$	−1.00000	−0.0478365
$438$	0	0
$439$	22.0000	1.05000	0.525001	−	0.851101i	$-0.324065\pi$
$439$	22.0000	1.05000	0.525001	+	0.851101i	$0.324065\pi$
$440$	1.00000	0.0476731
$441$	−6.00000	−0.285714
$442$	3.00000	0.142695
$443$	2.00000	0.0950229	0.0475114	−	0.998871i	$-0.484871\pi$
$443$	2.00000	0.0950229	0.0475114	+	0.998871i	$0.484871\pi$
$444$	−5.00000	−0.237289
$445$	−10.0000	−0.474045
$446$	−15.0000	−0.710271
$447$	9.00000	0.425685
$448$	−1.00000	−0.0472456
$449$	−1.00000	−0.0471929	−0.0235965	−	0.999722i	$-0.507512\pi$
$449$	−1.00000	−0.0471929	−0.0235965	+	0.999722i	$0.507512\pi$
$450$	1.00000	0.0471405
$451$	6.00000	0.282529
$452$	18.0000	0.846649
$453$	−17.0000	−0.798730
$454$	18.0000	0.844782
$455$	−3.00000	−0.140642
$456$	1.00000	0.0468293
$457$	−1.00000	−0.0467780	−0.0233890	−	0.999726i	$-0.507446\pi$
$457$	−1.00000	−0.0467780	−0.0233890	+	0.999726i	$0.507446\pi$
$458$	23.0000	1.07472
$459$	1.00000	0.0466760
$460$	−1.00000	−0.0466252
$461$	−30.0000	−1.39724	−0.698620	−	0.715493i	$-0.746202\pi$
$461$	−30.0000	−1.39724	−0.698620	+	0.715493i	$0.746202\pi$
$462$	−1.00000	−0.0465242
$463$	−11.0000	−0.511213	−0.255607	−	0.966781i	$-0.582275\pi$
$463$	−11.0000	−0.511213	−0.255607	+	0.966781i	$0.582275\pi$
$464$	6.00000	0.278543
$465$	−5.00000	−0.231869
$466$	18.0000	0.833834
$467$	20.0000	0.925490	0.462745	−	0.886492i	$-0.346865\pi$
$467$	20.0000	0.925490	0.462745	+	0.886492i	$0.346865\pi$
$468$	−3.00000	−0.138675
$469$	−3.00000	−0.138527
$470$	−6.00000	−0.276759
$471$	0	0
$472$	−4.00000	−0.184115
$473$	−8.00000	−0.367840
$474$	−14.0000	−0.643041
$475$	−1.00000	−0.0458831
$476$	1.00000	0.0458349
$477$	−6.00000	−0.274721
$478$	−26.0000	−1.18921
$479$	15.0000	0.685367	0.342684	−	0.939451i	$-0.388664\pi$
$479$	15.0000	0.685367	0.342684	+	0.939451i	$0.388664\pi$
$480$	1.00000	0.0456435
$481$	−15.0000	−0.683941
$482$	19.0000	0.865426
$483$	1.00000	0.0455016
$484$	1.00000	0.0454545
$485$	−13.0000	−0.590300
$486$	−1.00000	−0.0453609
$487$	−12.0000	−0.543772	−0.271886	−	0.962329i	$-0.587647\pi$
$487$	−12.0000	−0.543772	−0.271886	+	0.962329i	$0.587647\pi$
$488$	5.00000	0.226339
$489$	−20.0000	−0.904431
$490$	6.00000	0.271052
$491$	6.00000	0.270776	0.135388	−	0.990793i	$-0.456772\pi$
$491$	6.00000	0.270776	0.135388	+	0.990793i	$0.456772\pi$
$492$	6.00000	0.270501
$493$	−6.00000	−0.270226
$494$	3.00000	0.134976
$495$	1.00000	0.0449467
$496$	−5.00000	−0.224507
$497$	−6.00000	−0.269137
$498$	11.0000	0.492922
$499$	−28.0000	−1.25345	−0.626726	−	0.779240i	$-0.715605\pi$
$499$	−28.0000	−1.25345	−0.626726	+	0.779240i	$0.715605\pi$
$500$	−1.00000	−0.0447214
$501$	4.00000	0.178707
$502$	27.0000	1.20507
$503$	16.0000	0.713405	0.356702	−	0.934218i	$-0.383901\pi$
$503$	16.0000	0.713405	0.356702	+	0.934218i	$0.383901\pi$
$504$	−1.00000	−0.0445435
$505$	−2.00000	−0.0889988
$506$	−1.00000	−0.0444554
$507$	4.00000	0.177646
$508$	−16.0000	−0.709885
$509$	14.0000	0.620539	0.310270	−	0.950649i	$-0.399581\pi$
$509$	14.0000	0.620539	0.310270	+	0.950649i	$0.399581\pi$
$510$	−1.00000	−0.0442807
$511$	0	0
$512$	1.00000	0.0441942
$513$	1.00000	0.0441511
$514$	−2.00000	−0.0882162
$515$	1.00000	0.0440653
$516$	−8.00000	−0.352180
$517$	−6.00000	−0.263880
$518$	−5.00000	−0.219687
$519$	−21.0000	−0.921798
$520$	3.00000	0.131559
$521$	5.00000	0.219054	0.109527	−	0.993984i	$-0.465066\pi$
$521$	5.00000	0.219054	0.109527	+	0.993984i	$0.465066\pi$
$522$	6.00000	0.262613
$523$	12.0000	0.524723	0.262362	−	0.964970i	$-0.415499\pi$
$523$	12.0000	0.524723	0.262362	+	0.964970i	$0.415499\pi$
$524$	−7.00000	−0.305796
$525$	1.00000	0.0436436
$526$	21.0000	0.915644
$527$	5.00000	0.217803
$528$	1.00000	0.0435194
$529$	−22.0000	−0.956522
$530$	6.00000	0.260623
$531$	−4.00000	−0.173585
$532$	1.00000	0.0433555
$533$	18.0000	0.779667
$534$	−10.0000	−0.432742
$535$	−18.0000	−0.778208
$536$	3.00000	0.129580
$537$	1.00000	0.0431532
$538$	3.00000	0.129339
$539$	6.00000	0.258438
$540$	1.00000	0.0430331
$541$	22.0000	0.945854	0.472927	−	0.881102i	$-0.343197\pi$
$541$	22.0000	0.945854	0.472927	+	0.881102i	$0.343197\pi$
$542$	20.0000	0.859074
$543$	16.0000	0.686626
$544$	−1.00000	−0.0428746
$545$	−7.00000	−0.299847
$546$	−3.00000	−0.128388
$547$	−31.0000	−1.32546	−0.662732	−	0.748857i	$-0.730603\pi$
$547$	−31.0000	−1.32546	−0.662732	+	0.748857i	$0.730603\pi$
$548$	7.00000	0.299025
$549$	5.00000	0.213395
$550$	−1.00000	−0.0426401
$551$	−6.00000	−0.255609
$552$	−1.00000	−0.0425628
$553$	−14.0000	−0.595341
$554$	−32.0000	−1.35955
$555$	5.00000	0.212238
$556$	−14.0000	−0.593732
$557$	20.0000	0.847427	0.423714	−	0.905796i	$-0.360726\pi$
$557$	20.0000	0.847427	0.423714	+	0.905796i	$0.360726\pi$
$558$	−5.00000	−0.211667
$559$	−24.0000	−1.01509
$560$	1.00000	0.0422577
$561$	−1.00000	−0.0422200
$562$	18.0000	0.759284
$563$	−9.00000	−0.379305	−0.189652	−	0.981851i	$-0.560736\pi$
$563$	−9.00000	−0.379305	−0.189652	+	0.981851i	$0.560736\pi$
$564$	−6.00000	−0.252646
$565$	−18.0000	−0.757266
$566$	28.0000	1.17693
$567$	−1.00000	−0.0419961
$568$	6.00000	0.251754
$569$	−27.0000	−1.13190	−0.565949	−	0.824440i	$-0.691490\pi$
$569$	−27.0000	−1.13190	−0.565949	+	0.824440i	$0.691490\pi$
$570$	−1.00000	−0.0418854
$571$	−26.0000	−1.08807	−0.544033	−	0.839064i	$-0.683103\pi$
$571$	−26.0000	−1.08807	−0.544033	+	0.839064i	$0.683103\pi$
$572$	3.00000	0.125436
$573$	8.00000	0.334205
$574$	6.00000	0.250435
$575$	1.00000	0.0417029
$576$	1.00000	0.0416667
$577$	−14.0000	−0.582828	−0.291414	−	0.956597i	$-0.594126\pi$
$577$	−14.0000	−0.582828	−0.291414	+	0.956597i	$0.594126\pi$
$578$	1.00000	0.0415945
$579$	−8.00000	−0.332469
$580$	−6.00000	−0.249136
$581$	11.0000	0.456357
$582$	−13.0000	−0.538867
$583$	6.00000	0.248495
$584$	0	0
$585$	3.00000	0.124035
$586$	0	0
$587$	−38.0000	−1.56843	−0.784214	−	0.620491i	$-0.786934\pi$
$587$	−38.0000	−1.56843	−0.784214	+	0.620491i	$0.786934\pi$
$588$	6.00000	0.247436
$589$	5.00000	0.206021
$590$	4.00000	0.164677
$591$	−17.0000	−0.699287
$592$	5.00000	0.205499
$593$	42.0000	1.72473	0.862367	−	0.506284i	$-0.168981\pi$
$593$	42.0000	1.72473	0.862367	+	0.506284i	$0.168981\pi$
$594$	1.00000	0.0410305
$595$	−1.00000	−0.0409960
$596$	−9.00000	−0.368654
$597$	5.00000	0.204636
$598$	−3.00000	−0.122679
$599$	−23.0000	−0.939755	−0.469877	−	0.882732i	$-0.655702\pi$
$599$	−23.0000	−0.939755	−0.469877	+	0.882732i	$0.655702\pi$
$600$	−1.00000	−0.0408248
$601$	−5.00000	−0.203954	−0.101977	−	0.994787i	$-0.532517\pi$
$601$	−5.00000	−0.203954	−0.101977	+	0.994787i	$0.532517\pi$
$602$	−8.00000	−0.326056
$603$	3.00000	0.122169
$604$	17.0000	0.691720
$605$	−1.00000	−0.0406558
$606$	−2.00000	−0.0812444
$607$	−25.0000	−1.01472	−0.507359	−	0.861735i	$-0.669378\pi$
$607$	−25.0000	−1.01472	−0.507359	+	0.861735i	$0.669378\pi$
$608$	−1.00000	−0.0405554
$609$	6.00000	0.243132
$610$	−5.00000	−0.202444
$611$	−18.0000	−0.728202
$612$	−1.00000	−0.0404226
$613$	26.0000	1.05013	0.525065	−	0.851062i	$-0.324041\pi$
$613$	26.0000	1.05013	0.525065	+	0.851062i	$0.324041\pi$
$614$	−28.0000	−1.12999
$615$	−6.00000	−0.241943
$616$	1.00000	0.0402911
$617$	−6.00000	−0.241551	−0.120775	−	0.992680i	$-0.538538\pi$
$617$	−6.00000	−0.241551	−0.120775	+	0.992680i	$0.538538\pi$
$618$	1.00000	0.0402259
$619$	−31.0000	−1.24600	−0.622998	−	0.782224i	$-0.714085\pi$
$619$	−31.0000	−1.24600	−0.622998	+	0.782224i	$0.714085\pi$
$620$	5.00000	0.200805
$621$	−1.00000	−0.0401286
$622$	−18.0000	−0.721734
$623$	−10.0000	−0.400642
$624$	3.00000	0.120096
$625$	1.00000	0.0400000
$626$	−21.0000	−0.839329
$627$	−1.00000	−0.0399362
$628$	0	0
$629$	−5.00000	−0.199363
$630$	1.00000	0.0398410
$631$	34.0000	1.35352	0.676759	−	0.736204i	$-0.263384\pi$
$631$	34.0000	1.35352	0.676759	+	0.736204i	$0.263384\pi$
$632$	14.0000	0.556890
$633$	18.0000	0.715436
$634$	6.00000	0.238290
$635$	16.0000	0.634941
$636$	6.00000	0.237915
$637$	18.0000	0.713186
$638$	−6.00000	−0.237542
$639$	6.00000	0.237356
$640$	−1.00000	−0.0395285
$641$	46.0000	1.81689	0.908445	−	0.418004i	$-0.137270\pi$
$641$	46.0000	1.81689	0.908445	+	0.418004i	$0.137270\pi$
$642$	−18.0000	−0.710403
$643$	0	0		−	1.00000i	$-0.5\pi$
$643$	0	0			1.00000i	$0.5\pi$
$644$	−1.00000	−0.0394055
$645$	8.00000	0.315000
$646$	1.00000	0.0393445
$647$	−6.00000	−0.235884	−0.117942	−	0.993020i	$-0.537630\pi$
$647$	−6.00000	−0.235884	−0.117942	+	0.993020i	$0.537630\pi$
$648$	1.00000	0.0392837
$649$	4.00000	0.157014
$650$	−3.00000	−0.117670
$651$	−5.00000	−0.195965
$652$	20.0000	0.783260
$653$	16.0000	0.626128	0.313064	−	0.949732i	$-0.398644\pi$
$653$	16.0000	0.626128	0.313064	+	0.949732i	$0.398644\pi$
$654$	−7.00000	−0.273722
$655$	7.00000	0.273513
$656$	−6.00000	−0.234261
$657$	0	0
$658$	−6.00000	−0.233904
$659$	−2.00000	−0.0779089	−0.0389545	−	0.999241i	$-0.512403\pi$
$659$	−2.00000	−0.0779089	−0.0389545	+	0.999241i	$0.512403\pi$
$660$	−1.00000	−0.0389249
$661$	1.00000	0.0388955	0.0194477	−	0.999811i	$-0.493809\pi$
$661$	1.00000	0.0388955	0.0194477	+	0.999811i	$0.493809\pi$
$662$	−28.0000	−1.08825
$663$	−3.00000	−0.116510
$664$	−11.0000	−0.426883
$665$	−1.00000	−0.0387783
$666$	5.00000	0.193746
$667$	6.00000	0.232321
$668$	−4.00000	−0.154765
$669$	15.0000	0.579934
$670$	−3.00000	−0.115900
$671$	−5.00000	−0.193023
$672$	1.00000	0.0385758
$673$	−4.00000	−0.154189	−0.0770943	−	0.997024i	$-0.524564\pi$
$673$	−4.00000	−0.154189	−0.0770943	+	0.997024i	$0.524564\pi$
$674$	32.0000	1.23259
$675$	−1.00000	−0.0384900
$676$	−4.00000	−0.153846
$677$	−50.0000	−1.92166	−0.960828	−	0.277145i	$-0.910612\pi$
$677$	−50.0000	−1.92166	−0.960828	+	0.277145i	$0.910612\pi$
$678$	−18.0000	−0.691286
$679$	−13.0000	−0.498894
$680$	1.00000	0.0383482
$681$	−18.0000	−0.689761
$682$	5.00000	0.191460
$683$	−39.0000	−1.49229	−0.746147	−	0.665782i	$-0.768098\pi$
$683$	−39.0000	−1.49229	−0.746147	+	0.665782i	$0.768098\pi$
$684$	−1.00000	−0.0382360
$685$	−7.00000	−0.267456
$686$	13.0000	0.496342
$687$	−23.0000	−0.877505
$688$	8.00000	0.304997
$689$	18.0000	0.685745
$690$	1.00000	0.0380693
$691$	−35.0000	−1.33146	−0.665731	−	0.746191i	$-0.731880\pi$
$691$	−35.0000	−1.33146	−0.665731	+	0.746191i	$0.731880\pi$
$692$	21.0000	0.798300
$693$	1.00000	0.0379869
$694$	18.0000	0.683271
$695$	14.0000	0.531050
$696$	−6.00000	−0.227429
$697$	6.00000	0.227266
$698$	22.0000	0.832712
$699$	−18.0000	−0.680823
$700$	−1.00000	−0.0377964
$701$	−38.0000	−1.43524	−0.717620	−	0.696435i	$-0.754769\pi$
$701$	−38.0000	−1.43524	−0.717620	+	0.696435i	$0.754769\pi$
$702$	3.00000	0.113228
$703$	−5.00000	−0.188579
$704$	−1.00000	−0.0376889
$705$	6.00000	0.225973
$706$	25.0000	0.940887
$707$	−2.00000	−0.0752177
$708$	4.00000	0.150329
$709$	−14.0000	−0.525781	−0.262891	−	0.964826i	$-0.584676\pi$
$709$	−14.0000	−0.525781	−0.262891	+	0.964826i	$0.584676\pi$
$710$	−6.00000	−0.225176
$711$	14.0000	0.525041
$712$	10.0000	0.374766
$713$	−5.00000	−0.187251
$714$	−1.00000	−0.0374241
$715$	−3.00000	−0.112194
$716$	−1.00000	−0.0373718
$717$	26.0000	0.970988
$718$	−6.00000	−0.223918
$719$	−30.0000	−1.11881	−0.559406	−	0.828894i	$-0.688971\pi$
$719$	−30.0000	−1.11881	−0.559406	+	0.828894i	$0.688971\pi$
$720$	−1.00000	−0.0372678
$721$	1.00000	0.0372419
$722$	−18.0000	−0.669891
$723$	−19.0000	−0.706618
$724$	−16.0000	−0.594635
$725$	6.00000	0.222834
$726$	−1.00000	−0.0371135
$727$	−24.0000	−0.890111	−0.445055	−	0.895503i	$-0.646816\pi$
$727$	−24.0000	−0.890111	−0.445055	+	0.895503i	$0.646816\pi$
$728$	3.00000	0.111187
$729$	1.00000	0.0370370
$730$	0	0
$731$	−8.00000	−0.295891
$732$	−5.00000	−0.184805
$733$	31.0000	1.14501	0.572506	−	0.819901i	$-0.305971\pi$
$733$	31.0000	1.14501	0.572506	+	0.819901i	$0.305971\pi$
$734$	16.0000	0.590571
$735$	−6.00000	−0.221313
$736$	1.00000	0.0368605
$737$	−3.00000	−0.110506
$738$	−6.00000	−0.220863
$739$	−31.0000	−1.14035	−0.570177	−	0.821522i	$-0.693125\pi$
$739$	−31.0000	−1.14035	−0.570177	+	0.821522i	$0.693125\pi$
$740$	−5.00000	−0.183804
$741$	−3.00000	−0.110208
$742$	6.00000	0.220267
$743$	−4.00000	−0.146746	−0.0733729	−	0.997305i	$-0.523376\pi$
$743$	−4.00000	−0.146746	−0.0733729	+	0.997305i	$0.523376\pi$
$744$	5.00000	0.183309
$745$	9.00000	0.329734
$746$	−26.0000	−0.951928
$747$	−11.0000	−0.402469
$748$	1.00000	0.0365636
$749$	−18.0000	−0.657706
$750$	1.00000	0.0365148
$751$	48.0000	1.75154	0.875772	−	0.482724i	$-0.160353\pi$
$751$	48.0000	1.75154	0.875772	+	0.482724i	$0.160353\pi$
$752$	6.00000	0.218797
$753$	−27.0000	−0.983935
$754$	−18.0000	−0.655521
$755$	−17.0000	−0.618693
$756$	1.00000	0.0363696
$757$	−38.0000	−1.38113	−0.690567	−	0.723269i	$-0.742639\pi$
$757$	−38.0000	−1.38113	−0.690567	+	0.723269i	$0.742639\pi$
$758$	15.0000	0.544825
$759$	1.00000	0.0362977
$760$	1.00000	0.0362738
$761$	45.0000	1.63125	0.815624	−	0.578582i	$-0.196394\pi$
$761$	45.0000	1.63125	0.815624	+	0.578582i	$0.196394\pi$
$762$	16.0000	0.579619
$763$	−7.00000	−0.253417
$764$	−8.00000	−0.289430
$765$	1.00000	0.0361551
$766$	30.0000	1.08394
$767$	12.0000	0.433295
$768$	−1.00000	−0.0360844
$769$	−24.0000	−0.865462	−0.432731	−	0.901523i	$-0.642450\pi$
$769$	−24.0000	−0.865462	−0.432731	+	0.901523i	$0.642450\pi$
$770$	−1.00000	−0.0360375
$771$	2.00000	0.0720282
$772$	8.00000	0.287926
$773$	−15.0000	−0.539513	−0.269756	−	0.962929i	$-0.586943\pi$
$773$	−15.0000	−0.539513	−0.269756	+	0.962929i	$0.586943\pi$
$774$	8.00000	0.287554
$775$	−5.00000	−0.179605
$776$	13.0000	0.466673
$777$	5.00000	0.179374
$778$	36.0000	1.29066
$779$	6.00000	0.214972
$780$	−3.00000	−0.107417
$781$	−6.00000	−0.214697
$782$	−1.00000	−0.0357599
$783$	−6.00000	−0.214423
$784$	−6.00000	−0.214286
$785$	0	0
$786$	7.00000	0.249682
$787$	−21.0000	−0.748569	−0.374285	−	0.927314i	$-0.622112\pi$
$787$	−21.0000	−0.748569	−0.374285	+	0.927314i	$0.622112\pi$
$788$	17.0000	0.605600
$789$	−21.0000	−0.747620
$790$	−14.0000	−0.498098
$791$	−18.0000	−0.640006
$792$	−1.00000	−0.0355335
$793$	−15.0000	−0.532666
$794$	−38.0000	−1.34857
$795$	−6.00000	−0.212798
$796$	−5.00000	−0.177220
$797$	−5.00000	−0.177109	−0.0885545	−	0.996071i	$-0.528225\pi$
$797$	−5.00000	−0.177109	−0.0885545	+	0.996071i	$0.528225\pi$
$798$	−1.00000	−0.0353996
$799$	−6.00000	−0.212265
$800$	1.00000	0.0353553
$801$	10.0000	0.353333
$802$	−27.0000	−0.953403
$803$	0	0
$804$	−3.00000	−0.105802
$805$	1.00000	0.0352454
$806$	15.0000	0.528352
$807$	−3.00000	−0.105605
$808$	2.00000	0.0703598
$809$	−2.00000	−0.0703163	−0.0351581	−	0.999382i	$-0.511193\pi$
$809$	−2.00000	−0.0703163	−0.0351581	+	0.999382i	$0.511193\pi$
$810$	−1.00000	−0.0351364
$811$	2.00000	0.0702295	0.0351147	−	0.999383i	$-0.488820\pi$
$811$	2.00000	0.0702295	0.0351147	+	0.999383i	$0.488820\pi$
$812$	−6.00000	−0.210559
$813$	−20.0000	−0.701431
$814$	−5.00000	−0.175250
$815$	−20.0000	−0.700569
$816$	1.00000	0.0350070
$817$	−8.00000	−0.279885
$818$	22.0000	0.769212
$819$	3.00000	0.104828
$820$	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	$0.398297\pi$
$822$	−7.00000	−0.244153
$823$	50.0000	1.74289	0.871445	−	0.490493i	$-0.163183\pi$
$823$	50.0000	1.74289	0.871445	+	0.490493i	$0.163183\pi$
$824$	−1.00000	−0.0348367
$825$	1.00000	0.0348155
$826$	4.00000	0.139178
$827$	−18.0000	−0.625921	−0.312961	−	0.949766i	$-0.601321\pi$
$827$	−18.0000	−0.625921	−0.312961	+	0.949766i	$0.601321\pi$
$828$	1.00000	0.0347524
$829$	31.0000	1.07667	0.538337	−	0.842729i	$-0.319053\pi$
$829$	31.0000	1.07667	0.538337	+	0.842729i	$0.319053\pi$
$830$	11.0000	0.381816
$831$	32.0000	1.11007
$832$	−3.00000	−0.104006
$833$	6.00000	0.207888
$834$	14.0000	0.484780
$835$	4.00000	0.138426
$836$	1.00000	0.0345857
$837$	5.00000	0.172825
$838$	32.0000	1.10542
$839$	36.0000	1.24286	0.621429	−	0.783470i	$-0.286552\pi$
$839$	36.0000	1.24286	0.621429	+	0.783470i	$0.286552\pi$
$840$	−1.00000	−0.0345033
$841$	7.00000	0.241379
$842$	7.00000	0.241236
$843$	−18.0000	−0.619953
$844$	−18.0000	−0.619586
$845$	4.00000	0.137604
$846$	6.00000	0.206284
$847$	−1.00000	−0.0343604
$848$	−6.00000	−0.206041
$849$	−28.0000	−0.960958
$850$	−1.00000	−0.0342997
$851$	5.00000	0.171398
$852$	−6.00000	−0.205557
$853$	28.0000	0.958702	0.479351	−	0.877623i	$-0.340872\pi$
$853$	28.0000	0.958702	0.479351	+	0.877623i	$0.340872\pi$
$854$	−5.00000	−0.171096
$855$	1.00000	0.0341993
$856$	18.0000	0.615227
$857$	17.0000	0.580709	0.290354	−	0.956919i	$-0.406227\pi$
$857$	17.0000	0.580709	0.290354	+	0.956919i	$0.406227\pi$
$858$	−3.00000	−0.102418
$859$	−24.0000	−0.818869	−0.409435	−	0.912339i	$-0.634274\pi$
$859$	−24.0000	−0.818869	−0.409435	+	0.912339i	$0.634274\pi$
$860$	−8.00000	−0.272798
$861$	−6.00000	−0.204479
$862$	−40.0000	−1.36241
$863$	−36.0000	−1.22545	−0.612727	−	0.790295i	$-0.709928\pi$
$863$	−36.0000	−1.22545	−0.612727	+	0.790295i	$0.709928\pi$
$864$	−1.00000	−0.0340207
$865$	−21.0000	−0.714021
$866$	−6.00000	−0.203888
$867$	−1.00000	−0.0339618
$868$	5.00000	0.169711
$869$	−14.0000	−0.474917
$870$	6.00000	0.203419
$871$	−9.00000	−0.304953
$872$	7.00000	0.237050
$873$	13.0000	0.439983
$874$	−1.00000	−0.0338255
$875$	1.00000	0.0338062
$876$	0	0
$877$	−44.0000	−1.48577	−0.742887	−	0.669417i	$-0.766544\pi$
$877$	−44.0000	−1.48577	−0.742887	+	0.669417i	$0.766544\pi$
$878$	22.0000	0.742464
$879$	0	0
$880$	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	$0.401939\pi$
$882$	−6.00000	−0.202031
$883$	20.0000	0.673054	0.336527	−	0.941674i	$-0.390748\pi$
$883$	20.0000	0.673054	0.336527	+	0.941674i	$0.390748\pi$
$884$	3.00000	0.100901
$885$	−4.00000	−0.134459
$886$	2.00000	0.0671913
$887$	8.00000	0.268614	0.134307	−	0.990940i	$-0.457119\pi$
$887$	8.00000	0.268614	0.134307	+	0.990940i	$0.457119\pi$
$888$	−5.00000	−0.167789
$889$	16.0000	0.536623
$890$	−10.0000	−0.335201
$891$	−1.00000	−0.0335013
$892$	−15.0000	−0.502237
$893$	−6.00000	−0.200782
$894$	9.00000	0.301005
$895$	1.00000	0.0334263
$896$	−1.00000	−0.0334077
$897$	3.00000	0.100167
$898$	−1.00000	−0.0333704
$899$	−30.0000	−1.00056
$900$	1.00000	0.0333333
$901$	6.00000	0.199889
$902$	6.00000	0.199778
$903$	8.00000	0.266223
$904$	18.0000	0.598671
$905$	16.0000	0.531858
$906$	−17.0000	−0.564787
$907$	−32.0000	−1.06254	−0.531271	−	0.847202i	$-0.678286\pi$
$907$	−32.0000	−1.06254	−0.531271	+	0.847202i	$0.678286\pi$
$908$	18.0000	0.597351
$909$	2.00000	0.0663358
$910$	−3.00000	−0.0994490
$911$	8.00000	0.265052	0.132526	−	0.991180i	$-0.457691\pi$
$911$	8.00000	0.265052	0.132526	+	0.991180i	$0.457691\pi$
$912$	1.00000	0.0331133
$913$	11.0000	0.364047
$914$	−1.00000	−0.0330771
$915$	5.00000	0.165295
$916$	23.0000	0.759941
$917$	7.00000	0.231160
$918$	1.00000	0.0330049
$919$	−27.0000	−0.890648	−0.445324	−	0.895370i	$-0.646911\pi$
$919$	−27.0000	−0.890648	−0.445324	+	0.895370i	$0.646911\pi$
$920$	−1.00000	−0.0329690
$921$	28.0000	0.922631
$922$	−30.0000	−0.987997
$923$	−18.0000	−0.592477
$924$	−1.00000	−0.0328976
$925$	5.00000	0.164399
$926$	−11.0000	−0.361482
$927$	−1.00000	−0.0328443
$928$	6.00000	0.196960
$929$	−21.0000	−0.688988	−0.344494	−	0.938789i	$-0.611949\pi$
$929$	−21.0000	−0.688988	−0.344494	+	0.938789i	$0.611949\pi$
$930$	−5.00000	−0.163956
$931$	6.00000	0.196642
$932$	18.0000	0.589610
$933$	18.0000	0.589294
$934$	20.0000	0.654420
$935$	−1.00000	−0.0327035
$936$	−3.00000	−0.0980581
$937$	23.0000	0.751377	0.375689	−	0.926746i	$-0.377406\pi$
$937$	23.0000	0.751377	0.375689	+	0.926746i	$0.377406\pi$
$938$	−3.00000	−0.0979535
$939$	21.0000	0.685309
$940$	−6.00000	−0.195698
$941$	−48.0000	−1.56476	−0.782378	−	0.622804i	$-0.785993\pi$
$941$	−48.0000	−1.56476	−0.782378	+	0.622804i	$0.785993\pi$
$942$	0	0
$943$	−6.00000	−0.195387
$944$	−4.00000	−0.130189
$945$	−1.00000	−0.0325300
$946$	−8.00000	−0.260102
$947$	28.0000	0.909878	0.454939	−	0.890523i	$-0.349661\pi$
$947$	28.0000	0.909878	0.454939	+	0.890523i	$0.349661\pi$
$948$	−14.0000	−0.454699
$949$	0	0
$950$	−1.00000	−0.0324443
$951$	−6.00000	−0.194563
$952$	1.00000	0.0324102
$953$	24.0000	0.777436	0.388718	−	0.921357i	$-0.372918\pi$
$953$	24.0000	0.777436	0.388718	+	0.921357i	$0.372918\pi$
$954$	−6.00000	−0.194257
$955$	8.00000	0.258874
$956$	−26.0000	−0.840900
$957$	6.00000	0.193952
$958$	15.0000	0.484628
$959$	−7.00000	−0.226042
$960$	1.00000	0.0322749
$961$	−6.00000	−0.193548
$962$	−15.0000	−0.483619
$963$	18.0000	0.580042
$964$	19.0000	0.611949
$965$	−8.00000	−0.257529
$966$	1.00000	0.0321745
$967$	2.00000	0.0643157	0.0321578	−	0.999483i	$-0.489762\pi$
$967$	2.00000	0.0643157	0.0321578	+	0.999483i	$0.489762\pi$
$968$	1.00000	0.0321412
$969$	−1.00000	−0.0321246
$970$	−13.0000	−0.417405
$971$	−59.0000	−1.89340	−0.946700	−	0.322116i	$-0.895606\pi$
$971$	−59.0000	−1.89340	−0.946700	+	0.322116i	$0.895606\pi$
$972$	−1.00000	−0.0320750
$973$	14.0000	0.448819
$974$	−12.0000	−0.384505
$975$	3.00000	0.0960769
$976$	5.00000	0.160046
$977$	−3.00000	−0.0959785	−0.0479893	−	0.998848i	$-0.515281\pi$
$977$	−3.00000	−0.0959785	−0.0479893	+	0.998848i	$0.515281\pi$
$978$	−20.0000	−0.639529
$979$	−10.0000	−0.319601
$980$	6.00000	0.191663
$981$	7.00000	0.223493
$982$	6.00000	0.191468
$983$	28.0000	0.893061	0.446531	−	0.894768i	$-0.352659\pi$
$983$	28.0000	0.893061	0.446531	+	0.894768i	$0.352659\pi$
$984$	6.00000	0.191273
$985$	−17.0000	−0.541665
$986$	−6.00000	−0.191079
$987$	6.00000	0.190982
$988$	3.00000	0.0954427
$989$	8.00000	0.254385
$990$	1.00000	0.0317821
$991$	25.0000	0.794151	0.397076	−	0.917786i	$-0.370025\pi$
$991$	25.0000	0.794151	0.397076	+	0.917786i	$0.370025\pi$
$992$	−5.00000	−0.158750
$993$	28.0000	0.888553
$994$	−6.00000	−0.190308
$995$	5.00000	0.158511
$996$	11.0000	0.348548
$997$	22.0000	0.696747	0.348373	−	0.937356i	$-0.386734\pi$
$997$	22.0000	0.696747	0.348373	+	0.937356i	$0.386734\pi$
$998$	−28.0000	−0.886325
$999$	−5.00000	−0.158193

Twists

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

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