LMFDB - Embedded newform 7406.2.a.d.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7406,2,Mod(1,7406)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7406, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("7406.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7406 = 2 \cdot 7 \cdot 23^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7406.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:	$59.1372077370$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 322)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	7406.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-1.00000 q^{2} +1.00000 q^{4} +2.00000 q^{5} -1.00000 q^{7} -1.00000 q^{8} -3.00000 q^{9} +O(q^{10})$

\(q-1.00000 q^{2} +1.00000 q^{4} +2.00000 q^{5} -1.00000 q^{7} -1.00000 q^{8} -3.00000 q^{9} -2.00000 q^{10} +4.00000 q^{11} +4.00000 q^{13} +1.00000 q^{14} +1.00000 q^{16} +8.00000 q^{17} +3.00000 q^{18} +2.00000 q^{19} +2.00000 q^{20} -4.00000 q^{22} -1.00000 q^{25} -4.00000 q^{26} -1.00000 q^{28} +2.00000 q^{29} -6.00000 q^{31} -1.00000 q^{32} -8.00000 q^{34} -2.00000 q^{35} -3.00000 q^{36} +10.0000 q^{37} -2.00000 q^{38} -2.00000 q^{40} +6.00000 q^{41} +8.00000 q^{43} +4.00000 q^{44} -6.00000 q^{45} +6.00000 q^{47} +1.00000 q^{49} +1.00000 q^{50} +4.00000 q^{52} -2.00000 q^{53} +8.00000 q^{55} +1.00000 q^{56} -2.00000 q^{58} -10.0000 q^{61} +6.00000 q^{62} +3.00000 q^{63} +1.00000 q^{64} +8.00000 q^{65} -8.00000 q^{67} +8.00000 q^{68} +2.00000 q^{70} -12.0000 q^{71} +3.00000 q^{72} +6.00000 q^{73} -10.0000 q^{74} +2.00000 q^{76} -4.00000 q^{77} +2.00000 q^{80} +9.00000 q^{81} -6.00000 q^{82} -2.00000 q^{83} +16.0000 q^{85} -8.00000 q^{86} -4.00000 q^{88} -12.0000 q^{89} +6.00000 q^{90} -4.00000 q^{91} -6.00000 q^{94} +4.00000 q^{95} -12.0000 q^{97} -1.00000 q^{98} -12.0000 q^{99} +O(q^{100})\)

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
$3$	0	0		−	1.00000i	$-0.5\pi$
$3$	0	0			1.00000i	$0.5\pi$
$4$	1.00000	0.500000
$5$	2.00000	0.894427	0.447214	−	0.894427i	$-0.352416\pi$
$5$	2.00000	0.894427	0.447214	+	0.894427i	$0.352416\pi$
$6$	0	0
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−1.00000	−0.353553
$9$	−3.00000	−1.00000
$10$	−2.00000	−0.632456
$11$	4.00000	1.20605	0.603023	−	0.797724i	$-0.293963\pi$
$11$	4.00000	1.20605	0.603023	+	0.797724i	$0.293963\pi$
$12$	0	0
$13$	4.00000	1.10940	0.554700	−	0.832050i	$-0.312833\pi$
$13$	4.00000	1.10940	0.554700	+	0.832050i	$0.312833\pi$
$14$	1.00000	0.267261
$15$	0	0
$16$	1.00000	0.250000
$17$	8.00000	1.94029	0.970143	−	0.242536i	$-0.0779791\pi$
$17$	8.00000	1.94029	0.970143	+	0.242536i	$0.0779791\pi$
$18$	3.00000	0.707107
$19$	2.00000	0.458831	0.229416	−	0.973329i	$-0.426318\pi$
$19$	2.00000	0.458831	0.229416	+	0.973329i	$0.426318\pi$
$20$	2.00000	0.447214
$21$	0	0
$22$	−4.00000	−0.852803
$23$	0	0
$23$	0	0
$24$	0	0
$25$	−1.00000	−0.200000
$26$	−4.00000	−0.784465
$27$	0	0
$28$	−1.00000	−0.188982
$29$	2.00000	0.371391	0.185695	−	0.982607i	$-0.440546\pi$
$29$	2.00000	0.371391	0.185695	+	0.982607i	$0.440546\pi$
$30$	0	0
$31$	−6.00000	−1.07763	−0.538816	−	0.842424i	$-0.681128\pi$
$31$	−6.00000	−1.07763	−0.538816	+	0.842424i	$0.681128\pi$
$32$	−1.00000	−0.176777
$33$	0	0
$34$	−8.00000	−1.37199
$35$	−2.00000	−0.338062
$36$	−3.00000	−0.500000
$37$	10.0000	1.64399	0.821995	−	0.569495i	$-0.192861\pi$
$37$	10.0000	1.64399	0.821995	+	0.569495i	$0.192861\pi$
$38$	−2.00000	−0.324443
$39$	0	0
$40$	−2.00000	−0.316228
$41$	6.00000	0.937043	0.468521	−	0.883452i	$-0.344787\pi$
$41$	6.00000	0.937043	0.468521	+	0.883452i	$0.344787\pi$
$42$	0	0
$43$	8.00000	1.21999	0.609994	−	0.792406i	$-0.291172\pi$
$43$	8.00000	1.21999	0.609994	+	0.792406i	$0.291172\pi$
$44$	4.00000	0.603023
$45$	−6.00000	−0.894427
$46$	0	0
$47$	6.00000	0.875190	0.437595	−	0.899172i	$-0.355830\pi$
$47$	6.00000	0.875190	0.437595	+	0.899172i	$0.355830\pi$
$48$	0	0
$49$	1.00000	0.142857
$50$	1.00000	0.141421
$51$	0	0
$52$	4.00000	0.554700
$53$	−2.00000	−0.274721	−0.137361	−	0.990521i	$-0.543862\pi$
$53$	−2.00000	−0.274721	−0.137361	+	0.990521i	$0.543862\pi$
$54$	0	0
$55$	8.00000	1.07872
$56$	1.00000	0.133631
$57$	0	0
$58$	−2.00000	−0.262613
$59$	0	0		−	1.00000i	$-0.5\pi$
$59$	0	0			1.00000i	$0.5\pi$
$60$	0	0
$61$	−10.0000	−1.28037	−0.640184	−	0.768221i	$-0.721142\pi$
$61$	−10.0000	−1.28037	−0.640184	+	0.768221i	$0.721142\pi$
$62$	6.00000	0.762001
$63$	3.00000	0.377964
$64$	1.00000	0.125000
$65$	8.00000	0.992278
$66$	0	0
$67$	−8.00000	−0.977356	−0.488678	−	0.872464i	$-0.662521\pi$
$67$	−8.00000	−0.977356	−0.488678	+	0.872464i	$0.662521\pi$
$68$	8.00000	0.970143
$69$	0	0
$70$	2.00000	0.239046
$71$	−12.0000	−1.42414	−0.712069	−	0.702109i	$-0.752242\pi$
$71$	−12.0000	−1.42414	−0.712069	+	0.702109i	$0.752242\pi$
$72$	3.00000	0.353553
$73$	6.00000	0.702247	0.351123	−	0.936329i	$-0.385800\pi$
$73$	6.00000	0.702247	0.351123	+	0.936329i	$0.385800\pi$
$74$	−10.0000	−1.16248
$75$	0	0
$76$	2.00000	0.229416
$77$	−4.00000	−0.455842
$78$	0	0
$79$	0	0		−	1.00000i	$-0.5\pi$
$79$	0	0			1.00000i	$0.5\pi$
$80$	2.00000	0.223607
$81$	9.00000	1.00000
$82$	−6.00000	−0.662589
$83$	−2.00000	−0.219529	−0.109764	−	0.993958i	$-0.535010\pi$
$83$	−2.00000	−0.219529	−0.109764	+	0.993958i	$0.535010\pi$
$84$	0	0
$85$	16.0000	1.73544
$86$	−8.00000	−0.862662
$87$	0	0
$88$	−4.00000	−0.426401
$89$	−12.0000	−1.27200	−0.635999	−	0.771690i	$-0.719412\pi$
$89$	−12.0000	−1.27200	−0.635999	+	0.771690i	$0.719412\pi$
$90$	6.00000	0.632456
$91$	−4.00000	−0.419314
$92$	0	0
$93$	0	0
$94$	−6.00000	−0.618853
$95$	4.00000	0.410391
$96$	0	0
$97$	−12.0000	−1.21842	−0.609208	−	0.793011i	$-0.708512\pi$
$97$	−12.0000	−1.21842	−0.609208	+	0.793011i	$0.708512\pi$
$98$	−1.00000	−0.101015
$99$	−12.0000	−1.20605
$100$	−1.00000	−0.100000
$101$	8.00000	0.796030	0.398015	−	0.917379i	$-0.369699\pi$
$101$	8.00000	0.796030	0.398015	+	0.917379i	$0.369699\pi$
$102$	0	0
$103$	20.0000	1.97066	0.985329	−	0.170664i	$-0.0545913\pi$
$103$	20.0000	1.97066	0.985329	+	0.170664i	$0.0545913\pi$
$104$	−4.00000	−0.392232
$105$	0	0
$106$	2.00000	0.194257
$107$	4.00000	0.386695	0.193347	−	0.981130i	$-0.438066\pi$
$107$	4.00000	0.386695	0.193347	+	0.981130i	$0.438066\pi$
$108$	0	0
$109$	−18.0000	−1.72409	−0.862044	−	0.506834i	$-0.830816\pi$
$109$	−18.0000	−1.72409	−0.862044	+	0.506834i	$0.830816\pi$
$110$	−8.00000	−0.762770
$111$	0	0
$112$	−1.00000	−0.0944911
$113$	14.0000	1.31701	0.658505	−	0.752577i	$-0.271189\pi$
$113$	14.0000	1.31701	0.658505	+	0.752577i	$0.271189\pi$
$114$	0	0
$115$	0	0
$116$	2.00000	0.185695
$117$	−12.0000	−1.10940
$118$	0	0
$119$	−8.00000	−0.733359
$120$	0	0
$121$	5.00000	0.454545
$122$	10.0000	0.905357
$123$	0	0
$124$	−6.00000	−0.538816
$125$	−12.0000	−1.07331
$126$	−3.00000	−0.267261
$127$	−20.0000	−1.77471	−0.887357	−	0.461084i	$-0.847461\pi$
$127$	−20.0000	−1.77471	−0.887357	+	0.461084i	$0.847461\pi$
$128$	−1.00000	−0.0883883
$129$	0	0
$130$	−8.00000	−0.701646
$131$	0	0		−	1.00000i	$-0.5\pi$
$131$	0	0			1.00000i	$0.5\pi$
$132$	0	0
$133$	−2.00000	−0.173422
$134$	8.00000	0.691095
$135$	0	0
$136$	−8.00000	−0.685994
$137$	18.0000	1.53784	0.768922	−	0.639343i	$-0.220793\pi$
$137$	18.0000	1.53784	0.768922	+	0.639343i	$0.220793\pi$
$138$	0	0
$139$	−4.00000	−0.339276	−0.169638	−	0.985506i	$-0.554260\pi$
$139$	−4.00000	−0.339276	−0.169638	+	0.985506i	$0.554260\pi$
$140$	−2.00000	−0.169031
$141$	0	0
$142$	12.0000	1.00702
$143$	16.0000	1.33799
$144$	−3.00000	−0.250000
$145$	4.00000	0.332182
$146$	−6.00000	−0.496564
$147$	0	0
$148$	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	$0.365663\pi$
$150$	0	0
$151$	−20.0000	−1.62758	−0.813788	−	0.581161i	$-0.802599\pi$
$151$	−20.0000	−1.62758	−0.813788	+	0.581161i	$0.802599\pi$
$152$	−2.00000	−0.162221
$153$	−24.0000	−1.94029
$154$	4.00000	0.322329
$155$	−12.0000	−0.963863
$156$	0	0
$157$	18.0000	1.43656	0.718278	−	0.695756i	$-0.244931\pi$
$157$	18.0000	1.43656	0.718278	+	0.695756i	$0.244931\pi$
$158$	0	0
$159$	0	0
$160$	−2.00000	−0.158114
$161$	0	0
$162$	−9.00000	−0.707107
$163$	4.00000	0.313304	0.156652	−	0.987654i	$-0.449930\pi$
$163$	4.00000	0.313304	0.156652	+	0.987654i	$0.449930\pi$
$164$	6.00000	0.468521
$165$	0	0
$166$	2.00000	0.155230
$167$	−14.0000	−1.08335	−0.541676	−	0.840587i	$-0.682210\pi$
$167$	−14.0000	−1.08335	−0.541676	+	0.840587i	$0.682210\pi$
$168$	0	0
$169$	3.00000	0.230769
$170$	−16.0000	−1.22714
$171$	−6.00000	−0.458831
$172$	8.00000	0.609994
$173$	0	0		−	1.00000i	$-0.5\pi$
$173$	0	0			1.00000i	$0.5\pi$
$174$	0	0
$175$	1.00000	0.0755929
$176$	4.00000	0.301511
$177$	0	0
$178$	12.0000	0.899438
$179$	20.0000	1.49487	0.747435	−	0.664335i	$-0.231285\pi$
$179$	20.0000	1.49487	0.747435	+	0.664335i	$0.231285\pi$
$180$	−6.00000	−0.447214
$181$	6.00000	0.445976	0.222988	−	0.974821i	$-0.428419\pi$
$181$	6.00000	0.445976	0.222988	+	0.974821i	$0.428419\pi$
$182$	4.00000	0.296500
$183$	0	0
$184$	0	0
$185$	20.0000	1.47043
$186$	0	0
$187$	32.0000	2.34007
$188$	6.00000	0.437595
$189$	0	0
$190$	−4.00000	−0.290191
$191$	16.0000	1.15772	0.578860	−	0.815427i	$-0.303498\pi$
$191$	16.0000	1.15772	0.578860	+	0.815427i	$0.303498\pi$
$192$	0	0
$193$	−10.0000	−0.719816	−0.359908	−	0.932988i	$-0.617192\pi$
$193$	−10.0000	−0.719816	−0.359908	+	0.932988i	$0.617192\pi$
$194$	12.0000	0.861550
$195$	0	0
$196$	1.00000	0.0714286
$197$	6.00000	0.427482	0.213741	−	0.976890i	$-0.431435\pi$
$197$	6.00000	0.427482	0.213741	+	0.976890i	$0.431435\pi$
$198$	12.0000	0.852803
$199$	−20.0000	−1.41776	−0.708881	−	0.705328i	$-0.750800\pi$
$199$	−20.0000	−1.41776	−0.708881	+	0.705328i	$0.750800\pi$
$200$	1.00000	0.0707107
$201$	0	0
$202$	−8.00000	−0.562878
$203$	−2.00000	−0.140372
$204$	0	0
$205$	12.0000	0.838116
$206$	−20.0000	−1.39347
$207$	0	0
$208$	4.00000	0.277350
$209$	8.00000	0.553372
$210$	0	0
$211$	4.00000	0.275371	0.137686	−	0.990476i	$-0.456034\pi$
$211$	4.00000	0.275371	0.137686	+	0.990476i	$0.456034\pi$
$212$	−2.00000	−0.137361
$213$	0	0
$214$	−4.00000	−0.273434
$215$	16.0000	1.09119
$216$	0	0
$217$	6.00000	0.407307
$218$	18.0000	1.21911
$219$	0	0
$220$	8.00000	0.539360
$221$	32.0000	2.15255
$222$	0	0
$223$	−10.0000	−0.669650	−0.334825	−	0.942280i	$-0.608677\pi$
$223$	−10.0000	−0.669650	−0.334825	+	0.942280i	$0.608677\pi$
$224$	1.00000	0.0668153
$225$	3.00000	0.200000
$226$	−14.0000	−0.931266
$227$	−6.00000	−0.398234	−0.199117	−	0.979976i	$-0.563807\pi$
$227$	−6.00000	−0.398234	−0.199117	+	0.979976i	$0.563807\pi$
$228$	0	0
$229$	−2.00000	−0.132164	−0.0660819	−	0.997814i	$-0.521050\pi$
$229$	−2.00000	−0.132164	−0.0660819	+	0.997814i	$0.521050\pi$
$230$	0	0
$231$	0	0
$232$	−2.00000	−0.131306
$233$	6.00000	0.393073	0.196537	−	0.980497i	$-0.437031\pi$
$233$	6.00000	0.393073	0.196537	+	0.980497i	$0.437031\pi$
$234$	12.0000	0.784465
$235$	12.0000	0.782794
$236$	0	0
$237$	0	0
$238$	8.00000	0.518563
$239$	12.0000	0.776215	0.388108	−	0.921614i	$-0.373129\pi$
$239$	12.0000	0.776215	0.388108	+	0.921614i	$0.373129\pi$
$240$	0	0
$241$	8.00000	0.515325	0.257663	−	0.966235i	$-0.417048\pi$
$241$	8.00000	0.515325	0.257663	+	0.966235i	$0.417048\pi$
$242$	−5.00000	−0.321412
$243$	0	0
$244$	−10.0000	−0.640184
$245$	2.00000	0.127775
$246$	0	0
$247$	8.00000	0.509028
$248$	6.00000	0.381000
$249$	0	0
$250$	12.0000	0.758947
$251$	22.0000	1.38863	0.694314	−	0.719672i	$-0.255708\pi$
$251$	22.0000	1.38863	0.694314	+	0.719672i	$0.255708\pi$
$252$	3.00000	0.188982
$253$	0	0
$254$	20.0000	1.25491
$255$	0	0
$256$	1.00000	0.0625000
$257$	−14.0000	−0.873296	−0.436648	−	0.899632i	$-0.643834\pi$
$257$	−14.0000	−0.873296	−0.436648	+	0.899632i	$0.643834\pi$
$258$	0	0
$259$	−10.0000	−0.621370
$260$	8.00000	0.496139
$261$	−6.00000	−0.371391
$262$	0	0
$263$	−8.00000	−0.493301	−0.246651	−	0.969104i	$-0.579330\pi$
$263$	−8.00000	−0.493301	−0.246651	+	0.969104i	$0.579330\pi$
$264$	0	0
$265$	−4.00000	−0.245718
$266$	2.00000	0.122628
$267$	0	0
$268$	−8.00000	−0.488678
$269$	16.0000	0.975537	0.487769	−	0.872973i	$-0.337811\pi$
$269$	16.0000	0.975537	0.487769	+	0.872973i	$0.337811\pi$
$270$	0	0
$271$	2.00000	0.121491	0.0607457	−	0.998153i	$-0.480652\pi$
$271$	2.00000	0.121491	0.0607457	+	0.998153i	$0.480652\pi$
$272$	8.00000	0.485071
$273$	0	0
$274$	−18.0000	−1.08742
$275$	−4.00000	−0.241209
$276$	0	0
$277$	22.0000	1.32185	0.660926	−	0.750451i	$-0.270164\pi$
$277$	22.0000	1.32185	0.660926	+	0.750451i	$0.270164\pi$
$278$	4.00000	0.239904
$279$	18.0000	1.07763
$280$	2.00000	0.119523
$281$	−6.00000	−0.357930	−0.178965	−	0.983855i	$-0.557275\pi$
$281$	−6.00000	−0.357930	−0.178965	+	0.983855i	$0.557275\pi$
$282$	0	0
$283$	2.00000	0.118888	0.0594438	−	0.998232i	$-0.481067\pi$
$283$	2.00000	0.118888	0.0594438	+	0.998232i	$0.481067\pi$
$284$	−12.0000	−0.712069
$285$	0	0
$286$	−16.0000	−0.946100
$287$	−6.00000	−0.354169
$288$	3.00000	0.176777
$289$	47.0000	2.76471
$290$	−4.00000	−0.234888
$291$	0	0
$292$	6.00000	0.351123
$293$	−22.0000	−1.28525	−0.642627	−	0.766179i	$-0.722155\pi$
$293$	−22.0000	−1.28525	−0.642627	+	0.766179i	$0.722155\pi$
$294$	0	0
$295$	0	0
$296$	−10.0000	−0.581238
$297$	0	0
$298$	−10.0000	−0.579284
$299$	0	0
$300$	0	0
$301$	−8.00000	−0.461112
$302$	20.0000	1.15087
$303$	0	0
$304$	2.00000	0.114708
$305$	−20.0000	−1.14520
$306$	24.0000	1.37199
$307$	−28.0000	−1.59804	−0.799022	−	0.601302i	$-0.794649\pi$
$307$	−28.0000	−1.59804	−0.799022	+	0.601302i	$0.794649\pi$
$308$	−4.00000	−0.227921
$309$	0	0
$310$	12.0000	0.681554
$311$	−10.0000	−0.567048	−0.283524	−	0.958965i	$-0.591504\pi$
$311$	−10.0000	−0.567048	−0.283524	+	0.958965i	$0.591504\pi$
$312$	0	0
$313$	8.00000	0.452187	0.226093	−	0.974106i	$-0.427405\pi$
$313$	8.00000	0.452187	0.226093	+	0.974106i	$0.427405\pi$
$314$	−18.0000	−1.01580
$315$	6.00000	0.338062
$316$	0	0
$317$	−10.0000	−0.561656	−0.280828	−	0.959758i	$-0.590609\pi$
$317$	−10.0000	−0.561656	−0.280828	+	0.959758i	$0.590609\pi$
$318$	0	0
$319$	8.00000	0.447914
$320$	2.00000	0.111803
$321$	0	0
$322$	0	0
$323$	16.0000	0.890264
$324$	9.00000	0.500000
$325$	−4.00000	−0.221880
$326$	−4.00000	−0.221540
$327$	0	0
$328$	−6.00000	−0.331295
$329$	−6.00000	−0.330791
$330$	0	0
$331$	20.0000	1.09930	0.549650	−	0.835395i	$-0.314761\pi$
$331$	20.0000	1.09930	0.549650	+	0.835395i	$0.314761\pi$
$332$	−2.00000	−0.109764
$333$	−30.0000	−1.64399
$334$	14.0000	0.766046
$335$	−16.0000	−0.874173
$336$	0	0
$337$	26.0000	1.41631	0.708155	−	0.706057i	$-0.249528\pi$
$337$	26.0000	1.41631	0.708155	+	0.706057i	$0.249528\pi$
$338$	−3.00000	−0.163178
$339$	0	0
$340$	16.0000	0.867722
$341$	−24.0000	−1.29967
$342$	6.00000	0.324443
$343$	−1.00000	−0.0539949
$344$	−8.00000	−0.431331
$345$	0	0
$346$	0	0
$347$	−28.0000	−1.50312	−0.751559	−	0.659665i	$-0.770698\pi$
$347$	−28.0000	−1.50312	−0.751559	+	0.659665i	$0.770698\pi$
$348$	0	0
$349$	−16.0000	−0.856460	−0.428230	−	0.903670i	$-0.640863\pi$
$349$	−16.0000	−0.856460	−0.428230	+	0.903670i	$0.640863\pi$
$350$	−1.00000	−0.0534522
$351$	0	0
$352$	−4.00000	−0.213201
$353$	−10.0000	−0.532246	−0.266123	−	0.963939i	$-0.585743\pi$
$353$	−10.0000	−0.532246	−0.266123	+	0.963939i	$0.585743\pi$
$354$	0	0
$355$	−24.0000	−1.27379
$356$	−12.0000	−0.635999
$357$	0	0
$358$	−20.0000	−1.05703
$359$	24.0000	1.26667	0.633336	−	0.773877i	$-0.281685\pi$
$359$	24.0000	1.26667	0.633336	+	0.773877i	$0.281685\pi$
$360$	6.00000	0.316228
$361$	−15.0000	−0.789474
$362$	−6.00000	−0.315353
$363$	0	0
$364$	−4.00000	−0.209657
$365$	12.0000	0.628109
$366$	0	0
$367$	12.0000	0.626395	0.313197	−	0.949688i	$-0.398600\pi$
$367$	12.0000	0.626395	0.313197	+	0.949688i	$0.398600\pi$
$368$	0	0
$369$	−18.0000	−0.937043
$370$	−20.0000	−1.03975
$371$	2.00000	0.103835
$372$	0	0
$373$	10.0000	0.517780	0.258890	−	0.965907i	$-0.416643\pi$
$373$	10.0000	0.517780	0.258890	+	0.965907i	$0.416643\pi$
$374$	−32.0000	−1.65468
$375$	0	0
$376$	−6.00000	−0.309426
$377$	8.00000	0.412021
$378$	0	0
$379$	−4.00000	−0.205466	−0.102733	−	0.994709i	$-0.532759\pi$
$379$	−4.00000	−0.205466	−0.102733	+	0.994709i	$0.532759\pi$
$380$	4.00000	0.205196
$381$	0	0
$382$	−16.0000	−0.818631
$383$	−24.0000	−1.22634	−0.613171	−	0.789950i	$-0.710106\pi$
$383$	−24.0000	−1.22634	−0.613171	+	0.789950i	$0.710106\pi$
$384$	0	0
$385$	−8.00000	−0.407718
$386$	10.0000	0.508987
$387$	−24.0000	−1.21999
$388$	−12.0000	−0.609208
$389$	6.00000	0.304212	0.152106	−	0.988364i	$-0.451394\pi$
$389$	6.00000	0.304212	0.152106	+	0.988364i	$0.451394\pi$
$390$	0	0
$391$	0	0
$392$	−1.00000	−0.0505076
$393$	0	0
$394$	−6.00000	−0.302276
$395$	0	0
$396$	−12.0000	−0.603023
$397$	20.0000	1.00377	0.501886	−	0.864934i	$-0.332640\pi$
$397$	20.0000	1.00377	0.501886	+	0.864934i	$0.332640\pi$
$398$	20.0000	1.00251
$399$	0	0
$400$	−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	$0.351624\pi$
$402$	0	0
$403$	−24.0000	−1.19553
$404$	8.00000	0.398015
$405$	18.0000	0.894427
$406$	2.00000	0.0992583
$407$	40.0000	1.98273
$408$	0	0
$409$	10.0000	0.494468	0.247234	−	0.968956i	$-0.420478\pi$
$409$	10.0000	0.494468	0.247234	+	0.968956i	$0.420478\pi$
$410$	−12.0000	−0.592638
$411$	0	0
$412$	20.0000	0.985329
$413$	0	0
$414$	0	0
$415$	−4.00000	−0.196352
$416$	−4.00000	−0.196116
$417$	0	0
$418$	−8.00000	−0.391293
$419$	6.00000	0.293119	0.146560	−	0.989202i	$-0.453180\pi$
$419$	6.00000	0.293119	0.146560	+	0.989202i	$0.453180\pi$
$420$	0	0
$421$	14.0000	0.682318	0.341159	−	0.940006i	$-0.389181\pi$
$421$	14.0000	0.682318	0.341159	+	0.940006i	$0.389181\pi$
$422$	−4.00000	−0.194717
$423$	−18.0000	−0.875190
$424$	2.00000	0.0971286
$425$	−8.00000	−0.388057
$426$	0	0
$427$	10.0000	0.483934
$428$	4.00000	0.193347
$429$	0	0
$430$	−16.0000	−0.771589
$431$	0	0		−	1.00000i	$-0.5\pi$
$431$	0	0			1.00000i	$0.5\pi$
$432$	0	0
$433$	−4.00000	−0.192228	−0.0961139	−	0.995370i	$-0.530641\pi$
$433$	−4.00000	−0.192228	−0.0961139	+	0.995370i	$0.530641\pi$
$434$	−6.00000	−0.288009
$435$	0	0
$436$	−18.0000	−0.862044
$437$	0	0
$438$	0	0
$439$	−10.0000	−0.477274	−0.238637	−	0.971109i	$-0.576701\pi$
$439$	−10.0000	−0.477274	−0.238637	+	0.971109i	$0.576701\pi$
$440$	−8.00000	−0.381385
$441$	−3.00000	−0.142857
$442$	−32.0000	−1.52208
$443$	−4.00000	−0.190046	−0.0950229	−	0.995475i	$-0.530292\pi$
$443$	−4.00000	−0.190046	−0.0950229	+	0.995475i	$0.530292\pi$
$444$	0	0
$445$	−24.0000	−1.13771
$446$	10.0000	0.473514
$447$	0	0
$448$	−1.00000	−0.0472456
$449$	−34.0000	−1.60456	−0.802280	−	0.596948i	$-0.796380\pi$
$449$	−34.0000	−1.60456	−0.802280	+	0.596948i	$0.796380\pi$
$450$	−3.00000	−0.141421
$451$	24.0000	1.13012
$452$	14.0000	0.658505
$453$	0	0
$454$	6.00000	0.281594
$455$	−8.00000	−0.375046
$456$	0	0
$457$	−26.0000	−1.21623	−0.608114	−	0.793849i	$-0.708074\pi$
$457$	−26.0000	−1.21623	−0.608114	+	0.793849i	$0.708074\pi$
$458$	2.00000	0.0934539
$459$	0	0
$460$	0	0
$461$	−24.0000	−1.11779	−0.558896	−	0.829238i	$-0.688775\pi$
$461$	−24.0000	−1.11779	−0.558896	+	0.829238i	$0.688775\pi$
$462$	0	0
$463$	16.0000	0.743583	0.371792	−	0.928316i	$-0.378744\pi$
$463$	16.0000	0.743583	0.371792	+	0.928316i	$0.378744\pi$
$464$	2.00000	0.0928477
$465$	0	0
$466$	−6.00000	−0.277945
$467$	−22.0000	−1.01804	−0.509019	−	0.860755i	$-0.669992\pi$
$467$	−22.0000	−1.01804	−0.509019	+	0.860755i	$0.669992\pi$
$468$	−12.0000	−0.554700
$469$	8.00000	0.369406
$470$	−12.0000	−0.553519
$471$	0	0
$472$	0	0
$473$	32.0000	1.47136
$474$	0	0
$475$	−2.00000	−0.0917663
$476$	−8.00000	−0.366679
$477$	6.00000	0.274721
$478$	−12.0000	−0.548867
$479$	−4.00000	−0.182765	−0.0913823	−	0.995816i	$-0.529129\pi$
$479$	−4.00000	−0.182765	−0.0913823	+	0.995816i	$0.529129\pi$
$480$	0	0
$481$	40.0000	1.82384
$482$	−8.00000	−0.364390
$483$	0	0
$484$	5.00000	0.227273
$485$	−24.0000	−1.08978
$486$	0	0
$487$	16.0000	0.725029	0.362515	−	0.931978i	$-0.381918\pi$
$487$	16.0000	0.725029	0.362515	+	0.931978i	$0.381918\pi$
$488$	10.0000	0.452679
$489$	0	0
$490$	−2.00000	−0.0903508
$491$	36.0000	1.62466	0.812329	−	0.583200i	$-0.198200\pi$
$491$	36.0000	1.62466	0.812329	+	0.583200i	$0.198200\pi$
$492$	0	0
$493$	16.0000	0.720604
$494$	−8.00000	−0.359937
$495$	−24.0000	−1.07872
$496$	−6.00000	−0.269408
$497$	12.0000	0.538274
$498$	0	0
$499$	28.0000	1.25345	0.626726	−	0.779240i	$-0.284395\pi$
$499$	28.0000	1.25345	0.626726	+	0.779240i	$0.284395\pi$
$500$	−12.0000	−0.536656
$501$	0	0
$502$	−22.0000	−0.981908
$503$	−24.0000	−1.07011	−0.535054	−	0.844818i	$-0.679709\pi$
$503$	−24.0000	−1.07011	−0.535054	+	0.844818i	$0.679709\pi$
$504$	−3.00000	−0.133631
$505$	16.0000	0.711991
$506$	0	0
$507$	0	0
$508$	−20.0000	−0.887357
$509$	24.0000	1.06378	0.531891	−	0.846813i	$-0.321482\pi$
$509$	24.0000	1.06378	0.531891	+	0.846813i	$0.321482\pi$
$510$	0	0
$511$	−6.00000	−0.265424
$512$	−1.00000	−0.0441942
$513$	0	0
$514$	14.0000	0.617514
$515$	40.0000	1.76261
$516$	0	0
$517$	24.0000	1.05552
$518$	10.0000	0.439375
$519$	0	0
$520$	−8.00000	−0.350823
$521$	−20.0000	−0.876216	−0.438108	−	0.898922i	$-0.644351\pi$
$521$	−20.0000	−0.876216	−0.438108	+	0.898922i	$0.644351\pi$
$522$	6.00000	0.262613
$523$	34.0000	1.48672	0.743358	−	0.668894i	$-0.233232\pi$
$523$	34.0000	1.48672	0.743358	+	0.668894i	$0.233232\pi$
$524$	0	0
$525$	0	0
$526$	8.00000	0.348817
$527$	−48.0000	−2.09091
$528$	0	0
$529$	0	0
$530$	4.00000	0.173749
$531$	0	0
$532$	−2.00000	−0.0867110
$533$	24.0000	1.03956
$534$	0	0
$535$	8.00000	0.345870
$536$	8.00000	0.345547
$537$	0	0
$538$	−16.0000	−0.689809
$539$	4.00000	0.172292
$540$	0	0
$541$	6.00000	0.257960	0.128980	−	0.991647i	$-0.458830\pi$
$541$	6.00000	0.257960	0.128980	+	0.991647i	$0.458830\pi$
$542$	−2.00000	−0.0859074
$543$	0	0
$544$	−8.00000	−0.342997
$545$	−36.0000	−1.54207
$546$	0	0
$547$	−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
$549$	30.0000	1.28037
$550$	4.00000	0.170561
$551$	4.00000	0.170406
$552$	0	0
$553$	0	0
$554$	−22.0000	−0.934690
$555$	0	0
$556$	−4.00000	−0.169638
$557$	2.00000	0.0847427	0.0423714	−	0.999102i	$-0.486509\pi$
$557$	2.00000	0.0847427	0.0423714	+	0.999102i	$0.486509\pi$
$558$	−18.0000	−0.762001
$559$	32.0000	1.35346
$560$	−2.00000	−0.0845154
$561$	0	0
$562$	6.00000	0.253095
$563$	38.0000	1.60151	0.800755	−	0.598993i	$-0.204432\pi$
$563$	38.0000	1.60151	0.800755	+	0.598993i	$0.204432\pi$
$564$	0	0
$565$	28.0000	1.17797
$566$	−2.00000	−0.0840663
$567$	−9.00000	−0.377964
$568$	12.0000	0.503509
$569$	10.0000	0.419222	0.209611	−	0.977785i	$-0.432780\pi$
$569$	10.0000	0.419222	0.209611	+	0.977785i	$0.432780\pi$
$570$	0	0
$571$	40.0000	1.67395	0.836974	−	0.547243i	$-0.184323\pi$
$571$	40.0000	1.67395	0.836974	+	0.547243i	$0.184323\pi$
$572$	16.0000	0.668994
$573$	0	0
$574$	6.00000	0.250435
$575$	0	0
$576$	−3.00000	−0.125000
$577$	30.0000	1.24892	0.624458	−	0.781058i	$-0.285320\pi$
$577$	30.0000	1.24892	0.624458	+	0.781058i	$0.285320\pi$
$578$	−47.0000	−1.95494
$579$	0	0
$580$	4.00000	0.166091
$581$	2.00000	0.0829740
$582$	0	0
$583$	−8.00000	−0.331326
$584$	−6.00000	−0.248282
$585$	−24.0000	−0.992278
$586$	22.0000	0.908812
$587$	44.0000	1.81607	0.908037	−	0.418890i	$-0.137581\pi$
$587$	44.0000	1.81607	0.908037	+	0.418890i	$0.137581\pi$
$588$	0	0
$589$	−12.0000	−0.494451
$590$	0	0
$591$	0	0
$592$	10.0000	0.410997
$593$	−30.0000	−1.23195	−0.615976	−	0.787765i	$-0.711238\pi$
$593$	−30.0000	−1.23195	−0.615976	+	0.787765i	$0.711238\pi$
$594$	0	0
$595$	−16.0000	−0.655936
$596$	10.0000	0.409616
$597$	0	0
$598$	0	0
$599$	−32.0000	−1.30748	−0.653742	−	0.756717i	$-0.726802\pi$
$599$	−32.0000	−1.30748	−0.653742	+	0.756717i	$0.726802\pi$
$600$	0	0
$601$	−2.00000	−0.0815817	−0.0407909	−	0.999168i	$-0.512988\pi$
$601$	−2.00000	−0.0815817	−0.0407909	+	0.999168i	$0.512988\pi$
$602$	8.00000	0.326056
$603$	24.0000	0.977356
$604$	−20.0000	−0.813788
$605$	10.0000	0.406558
$606$	0	0
$607$	−22.0000	−0.892952	−0.446476	−	0.894795i	$-0.647321\pi$
$607$	−22.0000	−0.892952	−0.446476	+	0.894795i	$0.647321\pi$
$608$	−2.00000	−0.0811107
$609$	0	0
$610$	20.0000	0.809776
$611$	24.0000	0.970936
$612$	−24.0000	−0.970143
$613$	−26.0000	−1.05013	−0.525065	−	0.851062i	$-0.675959\pi$
$613$	−26.0000	−1.05013	−0.525065	+	0.851062i	$0.675959\pi$
$614$	28.0000	1.12999
$615$	0	0
$616$	4.00000	0.161165
$617$	−6.00000	−0.241551	−0.120775	−	0.992680i	$-0.538538\pi$
$617$	−6.00000	−0.241551	−0.120775	+	0.992680i	$0.538538\pi$
$618$	0	0
$619$	−10.0000	−0.401934	−0.200967	−	0.979598i	$-0.564408\pi$
$619$	−10.0000	−0.401934	−0.200967	+	0.979598i	$0.564408\pi$
$620$	−12.0000	−0.481932
$621$	0	0
$622$	10.0000	0.400963
$623$	12.0000	0.480770
$624$	0	0
$625$	−19.0000	−0.760000
$626$	−8.00000	−0.319744
$627$	0	0
$628$	18.0000	0.718278
$629$	80.0000	3.18981
$630$	−6.00000	−0.239046
$631$	−8.00000	−0.318475	−0.159237	−	0.987240i	$-0.550904\pi$
$631$	−8.00000	−0.318475	−0.159237	+	0.987240i	$0.550904\pi$
$632$	0	0
$633$	0	0
$634$	10.0000	0.397151
$635$	−40.0000	−1.58735
$636$	0	0
$637$	4.00000	0.158486
$638$	−8.00000	−0.316723
$639$	36.0000	1.42414
$640$	−2.00000	−0.0790569
$641$	−38.0000	−1.50091	−0.750455	−	0.660922i	$-0.770166\pi$
$641$	−38.0000	−1.50091	−0.750455	+	0.660922i	$0.770166\pi$
$642$	0	0
$643$	38.0000	1.49857	0.749287	−	0.662246i	$-0.230396\pi$
$643$	38.0000	1.49857	0.749287	+	0.662246i	$0.230396\pi$
$644$	0	0
$645$	0	0
$646$	−16.0000	−0.629512
$647$	−46.0000	−1.80845	−0.904223	−	0.427060i	$-0.859549\pi$
$647$	−46.0000	−1.80845	−0.904223	+	0.427060i	$0.859549\pi$
$648$	−9.00000	−0.353553
$649$	0	0
$650$	4.00000	0.156893
$651$	0	0
$652$	4.00000	0.156652
$653$	−6.00000	−0.234798	−0.117399	−	0.993085i	$-0.537456\pi$
$653$	−6.00000	−0.234798	−0.117399	+	0.993085i	$0.537456\pi$
$654$	0	0
$655$	0	0
$656$	6.00000	0.234261
$657$	−18.0000	−0.702247
$658$	6.00000	0.233904
$659$	−24.0000	−0.934907	−0.467454	−	0.884018i	$-0.654829\pi$
$659$	−24.0000	−0.934907	−0.467454	+	0.884018i	$0.654829\pi$
$660$	0	0
$661$	−18.0000	−0.700119	−0.350059	−	0.936727i	$-0.613839\pi$
$661$	−18.0000	−0.700119	−0.350059	+	0.936727i	$0.613839\pi$
$662$	−20.0000	−0.777322
$663$	0	0
$664$	2.00000	0.0776151
$665$	−4.00000	−0.155113
$666$	30.0000	1.16248
$667$	0	0
$668$	−14.0000	−0.541676
$669$	0	0
$670$	16.0000	0.618134
$671$	−40.0000	−1.54418
$672$	0	0
$673$	46.0000	1.77317	0.886585	−	0.462566i	$-0.153071\pi$
$673$	46.0000	1.77317	0.886585	+	0.462566i	$0.153071\pi$
$674$	−26.0000	−1.00148
$675$	0	0
$676$	3.00000	0.115385
$677$	18.0000	0.691796	0.345898	−	0.938272i	$-0.387574\pi$
$677$	18.0000	0.691796	0.345898	+	0.938272i	$0.387574\pi$
$678$	0	0
$679$	12.0000	0.460518
$680$	−16.0000	−0.613572
$681$	0	0
$682$	24.0000	0.919007
$683$	36.0000	1.37750	0.688751	−	0.724998i	$-0.258159\pi$
$683$	36.0000	1.37750	0.688751	+	0.724998i	$0.258159\pi$
$684$	−6.00000	−0.229416
$685$	36.0000	1.37549
$686$	1.00000	0.0381802
$687$	0	0
$688$	8.00000	0.304997
$689$	−8.00000	−0.304776
$690$	0	0
$691$	−4.00000	−0.152167	−0.0760836	−	0.997101i	$-0.524242\pi$
$691$	−4.00000	−0.152167	−0.0760836	+	0.997101i	$0.524242\pi$
$692$	0	0
$693$	12.0000	0.455842
$694$	28.0000	1.06287
$695$	−8.00000	−0.303457
$696$	0	0
$697$	48.0000	1.81813
$698$	16.0000	0.605609
$699$	0	0
$700$	1.00000	0.0377964
$701$	42.0000	1.58632	0.793159	−	0.609015i	$-0.208435\pi$
$701$	42.0000	1.58632	0.793159	+	0.609015i	$0.208435\pi$
$702$	0	0
$703$	20.0000	0.754314
$704$	4.00000	0.150756
$705$	0	0
$706$	10.0000	0.376355
$707$	−8.00000	−0.300871
$708$	0	0
$709$	10.0000	0.375558	0.187779	−	0.982211i	$-0.439871\pi$
$709$	10.0000	0.375558	0.187779	+	0.982211i	$0.439871\pi$
$710$	24.0000	0.900704
$711$	0	0
$712$	12.0000	0.449719
$713$	0	0
$714$	0	0
$715$	32.0000	1.19673
$716$	20.0000	0.747435
$717$	0	0
$718$	−24.0000	−0.895672
$719$	42.0000	1.56634	0.783168	−	0.621810i	$-0.213603\pi$
$719$	42.0000	1.56634	0.783168	+	0.621810i	$0.213603\pi$
$720$	−6.00000	−0.223607
$721$	−20.0000	−0.744839
$722$	15.0000	0.558242
$723$	0	0
$724$	6.00000	0.222988
$725$	−2.00000	−0.0742781
$726$	0	0
$727$	12.0000	0.445055	0.222528	−	0.974926i	$-0.428569\pi$
$727$	12.0000	0.445055	0.222528	+	0.974926i	$0.428569\pi$
$728$	4.00000	0.148250
$729$	−27.0000	−1.00000
$730$	−12.0000	−0.444140
$731$	64.0000	2.36713
$732$	0	0
$733$	50.0000	1.84679	0.923396	−	0.383849i	$-0.125402\pi$
$733$	50.0000	1.84679	0.923396	+	0.383849i	$0.125402\pi$
$734$	−12.0000	−0.442928
$735$	0	0
$736$	0	0
$737$	−32.0000	−1.17874
$738$	18.0000	0.662589
$739$	−20.0000	−0.735712	−0.367856	−	0.929883i	$-0.619908\pi$
$739$	−20.0000	−0.735712	−0.367856	+	0.929883i	$0.619908\pi$
$740$	20.0000	0.735215
$741$	0	0
$742$	−2.00000	−0.0734223
$743$	−24.0000	−0.880475	−0.440237	−	0.897881i	$-0.645106\pi$
$743$	−24.0000	−0.880475	−0.440237	+	0.897881i	$0.645106\pi$
$744$	0	0
$745$	20.0000	0.732743
$746$	−10.0000	−0.366126
$747$	6.00000	0.219529
$748$	32.0000	1.17004
$749$	−4.00000	−0.146157
$750$	0	0
$751$	−24.0000	−0.875772	−0.437886	−	0.899030i	$-0.644273\pi$
$751$	−24.0000	−0.875772	−0.437886	+	0.899030i	$0.644273\pi$
$752$	6.00000	0.218797
$753$	0	0
$754$	−8.00000	−0.291343
$755$	−40.0000	−1.45575
$756$	0	0
$757$	−42.0000	−1.52652	−0.763258	−	0.646094i	$-0.776401\pi$
$757$	−42.0000	−1.52652	−0.763258	+	0.646094i	$0.776401\pi$
$758$	4.00000	0.145287
$759$	0	0
$760$	−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	$0.394215\pi$
$762$	0	0
$763$	18.0000	0.651644
$764$	16.0000	0.578860
$765$	−48.0000	−1.73544
$766$	24.0000	0.867155
$767$	0	0
$768$	0	0
$769$	−16.0000	−0.576975	−0.288487	−	0.957484i	$-0.593152\pi$
$769$	−16.0000	−0.576975	−0.288487	+	0.957484i	$0.593152\pi$
$770$	8.00000	0.288300
$771$	0	0
$772$	−10.0000	−0.359908
$773$	46.0000	1.65451	0.827253	−	0.561830i	$-0.189903\pi$
$773$	46.0000	1.65451	0.827253	+	0.561830i	$0.189903\pi$
$774$	24.0000	0.862662
$775$	6.00000	0.215526
$776$	12.0000	0.430775
$777$	0	0
$778$	−6.00000	−0.215110
$779$	12.0000	0.429945
$780$	0	0
$781$	−48.0000	−1.71758
$782$	0	0
$783$	0	0
$784$	1.00000	0.0357143
$785$	36.0000	1.28490
$786$	0	0
$787$	−18.0000	−0.641631	−0.320815	−	0.947142i	$-0.603957\pi$
$787$	−18.0000	−0.641631	−0.320815	+	0.947142i	$0.603957\pi$
$788$	6.00000	0.213741
$789$	0	0
$790$	0	0
$791$	−14.0000	−0.497783
$792$	12.0000	0.426401
$793$	−40.0000	−1.42044
$794$	−20.0000	−0.709773
$795$	0	0
$796$	−20.0000	−0.708881
$797$	22.0000	0.779280	0.389640	−	0.920967i	$-0.372599\pi$
$797$	22.0000	0.779280	0.389640	+	0.920967i	$0.372599\pi$
$798$	0	0
$799$	48.0000	1.69812
$800$	1.00000	0.0353553
$801$	36.0000	1.27200
$802$	−18.0000	−0.635602
$803$	24.0000	0.846942
$804$	0	0
$805$	0	0
$806$	24.0000	0.845364
$807$	0	0
$808$	−8.00000	−0.281439
$809$	−18.0000	−0.632846	−0.316423	−	0.948618i	$-0.602482\pi$
$809$	−18.0000	−0.632846	−0.316423	+	0.948618i	$0.602482\pi$
$810$	−18.0000	−0.632456
$811$	8.00000	0.280918	0.140459	−	0.990086i	$-0.455142\pi$
$811$	8.00000	0.280918	0.140459	+	0.990086i	$0.455142\pi$
$812$	−2.00000	−0.0701862
$813$	0	0
$814$	−40.0000	−1.40200
$815$	8.00000	0.280228
$816$	0	0
$817$	16.0000	0.559769
$818$	−10.0000	−0.349642
$819$	12.0000	0.419314
$820$	12.0000	0.419058
$821$	6.00000	0.209401	0.104701	−	0.994504i	$-0.466612\pi$
$821$	6.00000	0.209401	0.104701	+	0.994504i	$0.466612\pi$
$822$	0	0
$823$	−12.0000	−0.418294	−0.209147	−	0.977884i	$-0.567069\pi$
$823$	−12.0000	−0.418294	−0.209147	+	0.977884i	$0.567069\pi$
$824$	−20.0000	−0.696733
$825$	0	0
$826$	0	0
$827$	12.0000	0.417281	0.208640	−	0.977992i	$-0.433096\pi$
$827$	12.0000	0.417281	0.208640	+	0.977992i	$0.433096\pi$
$828$	0	0
$829$	−12.0000	−0.416777	−0.208389	−	0.978046i	$-0.566822\pi$
$829$	−12.0000	−0.416777	−0.208389	+	0.978046i	$0.566822\pi$
$830$	4.00000	0.138842
$831$	0	0
$832$	4.00000	0.138675
$833$	8.00000	0.277184
$834$	0	0
$835$	−28.0000	−0.968980
$836$	8.00000	0.276686
$837$	0	0
$838$	−6.00000	−0.207267
$839$	−24.0000	−0.828572	−0.414286	−	0.910147i	$-0.635969\pi$
$839$	−24.0000	−0.828572	−0.414286	+	0.910147i	$0.635969\pi$
$840$	0	0
$841$	−25.0000	−0.862069
$842$	−14.0000	−0.482472
$843$	0	0
$844$	4.00000	0.137686
$845$	6.00000	0.206406
$846$	18.0000	0.618853
$847$	−5.00000	−0.171802
$848$	−2.00000	−0.0686803
$849$	0	0
$850$	8.00000	0.274398
$851$	0	0
$852$	0	0
$853$	4.00000	0.136957	0.0684787	−	0.997653i	$-0.478185\pi$
$853$	4.00000	0.136957	0.0684787	+	0.997653i	$0.478185\pi$
$854$	−10.0000	−0.342193
$855$	−12.0000	−0.410391
$856$	−4.00000	−0.136717
$857$	6.00000	0.204956	0.102478	−	0.994735i	$-0.467323\pi$
$857$	6.00000	0.204956	0.102478	+	0.994735i	$0.467323\pi$
$858$	0	0
$859$	4.00000	0.136478	0.0682391	−	0.997669i	$-0.478262\pi$
$859$	4.00000	0.136478	0.0682391	+	0.997669i	$0.478262\pi$
$860$	16.0000	0.545595
$861$	0	0
$862$	0	0
$863$	4.00000	0.136162	0.0680808	−	0.997680i	$-0.478312\pi$
$863$	4.00000	0.136162	0.0680808	+	0.997680i	$0.478312\pi$
$864$	0	0
$865$	0	0
$866$	4.00000	0.135926
$867$	0	0
$868$	6.00000	0.203653
$869$	0	0
$870$	0	0
$871$	−32.0000	−1.08428
$872$	18.0000	0.609557
$873$	36.0000	1.21842
$874$	0	0
$875$	12.0000	0.405674
$876$	0	0
$877$	−6.00000	−0.202606	−0.101303	−	0.994856i	$-0.532301\pi$
$877$	−6.00000	−0.202606	−0.101303	+	0.994856i	$0.532301\pi$
$878$	10.0000	0.337484
$879$	0	0
$880$	8.00000	0.269680
$881$	24.0000	0.808581	0.404290	−	0.914631i	$-0.367519\pi$
$881$	24.0000	0.808581	0.404290	+	0.914631i	$0.367519\pi$
$882$	3.00000	0.101015
$883$	36.0000	1.21150	0.605748	−	0.795656i	$-0.292874\pi$
$883$	36.0000	1.21150	0.605748	+	0.795656i	$0.292874\pi$
$884$	32.0000	1.07628
$885$	0	0
$886$	4.00000	0.134383
$887$	−54.0000	−1.81314	−0.906571	−	0.422053i	$-0.861310\pi$
$887$	−54.0000	−1.81314	−0.906571	+	0.422053i	$0.861310\pi$
$888$	0	0
$889$	20.0000	0.670778
$890$	24.0000	0.804482
$891$	36.0000	1.20605
$892$	−10.0000	−0.334825
$893$	12.0000	0.401565
$894$	0	0
$895$	40.0000	1.33705
$896$	1.00000	0.0334077
$897$	0	0
$898$	34.0000	1.13459
$899$	−12.0000	−0.400222
$900$	3.00000	0.100000
$901$	−16.0000	−0.533037
$902$	−24.0000	−0.799113
$903$	0	0
$904$	−14.0000	−0.465633
$905$	12.0000	0.398893
$906$	0	0
$907$	−4.00000	−0.132818	−0.0664089	−	0.997792i	$-0.521154\pi$
$907$	−4.00000	−0.132818	−0.0664089	+	0.997792i	$0.521154\pi$
$908$	−6.00000	−0.199117
$909$	−24.0000	−0.796030
$910$	8.00000	0.265197
$911$	16.0000	0.530104	0.265052	−	0.964234i	$-0.414611\pi$
$911$	16.0000	0.530104	0.265052	+	0.964234i	$0.414611\pi$
$912$	0	0
$913$	−8.00000	−0.264761
$914$	26.0000	0.860004
$915$	0	0
$916$	−2.00000	−0.0660819
$917$	0	0
$918$	0	0
$919$	40.0000	1.31948	0.659739	−	0.751495i	$-0.270667\pi$
$919$	40.0000	1.31948	0.659739	+	0.751495i	$0.270667\pi$
$920$	0	0
$921$	0	0
$922$	24.0000	0.790398
$923$	−48.0000	−1.57994
$924$	0	0
$925$	−10.0000	−0.328798
$926$	−16.0000	−0.525793
$927$	−60.0000	−1.97066
$928$	−2.00000	−0.0656532
$929$	54.0000	1.77168	0.885841	−	0.463988i	$-0.153582\pi$
$929$	54.0000	1.77168	0.885841	+	0.463988i	$0.153582\pi$
$930$	0	0
$931$	2.00000	0.0655474
$932$	6.00000	0.196537
$933$	0	0
$934$	22.0000	0.719862
$935$	64.0000	2.09302
$936$	12.0000	0.392232
$937$	8.00000	0.261349	0.130674	−	0.991425i	$-0.458286\pi$
$937$	8.00000	0.261349	0.130674	+	0.991425i	$0.458286\pi$
$938$	−8.00000	−0.261209
$939$	0	0
$940$	12.0000	0.391397
$941$	−6.00000	−0.195594	−0.0977972	−	0.995206i	$-0.531180\pi$
$941$	−6.00000	−0.195594	−0.0977972	+	0.995206i	$0.531180\pi$
$942$	0	0
$943$	0	0
$944$	0	0
$945$	0	0
$946$	−32.0000	−1.04041
$947$	−12.0000	−0.389948	−0.194974	−	0.980808i	$-0.562462\pi$
$947$	−12.0000	−0.389948	−0.194974	+	0.980808i	$0.562462\pi$
$948$	0	0
$949$	24.0000	0.779073
$950$	2.00000	0.0648886
$951$	0	0
$952$	8.00000	0.259281
$953$	14.0000	0.453504	0.226752	−	0.973952i	$-0.427189\pi$
$953$	14.0000	0.453504	0.226752	+	0.973952i	$0.427189\pi$
$954$	−6.00000	−0.194257
$955$	32.0000	1.03550
$956$	12.0000	0.388108
$957$	0	0
$958$	4.00000	0.129234
$959$	−18.0000	−0.581250
$960$	0	0
$961$	5.00000	0.161290
$962$	−40.0000	−1.28965
$963$	−12.0000	−0.386695
$964$	8.00000	0.257663
$965$	−20.0000	−0.643823
$966$	0	0
$967$	−40.0000	−1.28631	−0.643157	−	0.765735i	$-0.722376\pi$
$967$	−40.0000	−1.28631	−0.643157	+	0.765735i	$0.722376\pi$
$968$	−5.00000	−0.160706
$969$	0	0
$970$	24.0000	0.770594
$971$	14.0000	0.449281	0.224641	−	0.974442i	$-0.427879\pi$
$971$	14.0000	0.449281	0.224641	+	0.974442i	$0.427879\pi$
$972$	0	0
$973$	4.00000	0.128234
$974$	−16.0000	−0.512673
$975$	0	0
$976$	−10.0000	−0.320092
$977$	−30.0000	−0.959785	−0.479893	−	0.877327i	$-0.659324\pi$
$977$	−30.0000	−0.959785	−0.479893	+	0.877327i	$0.659324\pi$
$978$	0	0
$979$	−48.0000	−1.53409
$980$	2.00000	0.0638877
$981$	54.0000	1.72409
$982$	−36.0000	−1.14881
$983$	−24.0000	−0.765481	−0.382741	−	0.923856i	$-0.625020\pi$
$983$	−24.0000	−0.765481	−0.382741	+	0.923856i	$0.625020\pi$
$984$	0	0
$985$	12.0000	0.382352
$986$	−16.0000	−0.509544
$987$	0	0
$988$	8.00000	0.254514
$989$	0	0
$990$	24.0000	0.762770
$991$	52.0000	1.65183	0.825917	−	0.563791i	$-0.190658\pi$
$991$	52.0000	1.65183	0.825917	+	0.563791i	$0.190658\pi$
$992$	6.00000	0.190500
$993$	0	0
$994$	−12.0000	−0.380617
$995$	−40.0000	−1.26809
$996$	0	0
$997$	28.0000	0.886769	0.443384	−	0.896332i	$-0.353778\pi$
$997$	28.0000	0.886769	0.443384	+	0.896332i	$0.353778\pi$
$998$	−28.0000	−0.886325
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7406.2.a.d.1.1		1
23.22	odd	2		322.2.a.a.1.1	✓	1
69.68	even	2		2898.2.a.s.1.1		1
92.91	even	2		2576.2.a.i.1.1		1
115.114	odd	2		8050.2.a.o.1.1		1
161.160	even	2		2254.2.a.d.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
322.2.a.a.1.1	✓	1	23.22	odd	2
2254.2.a.d.1.1		1	161.160	even	2
2576.2.a.i.1.1		1	92.91	even	2
2898.2.a.s.1.1		1	69.68	even	2
7406.2.a.d.1.1		1	1.1	even	1	trivial
8050.2.a.o.1.1		1	115.114	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 7406 = 2 \cdot 7 \cdot 23^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7406.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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