LMFDB - Embedded newform 7245.2.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7245,2,Mod(1,7245)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7245, 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("7245.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7245 = 3^{2} \cdot 5 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7245.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:	$57.8516162644$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 805)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	7245.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

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

$q-2.00000 q^{2} +2.00000 q^{4} +1.00000 q^{5} -1.00000 q^{7} -2.00000 q^{10} +1.00000 q^{11} +7.00000 q^{13} +2.00000 q^{14} -4.00000 q^{16} -3.00000 q^{17} -8.00000 q^{19} +2.00000 q^{20} -2.00000 q^{22} -1.00000 q^{23} +1.00000 q^{25} -14.0000 q^{26} -2.00000 q^{28} +5.00000 q^{29} -2.00000 q^{31} +8.00000 q^{32} +6.00000 q^{34} -1.00000 q^{35} -4.00000 q^{37} +16.0000 q^{38} +8.00000 q^{41} +6.00000 q^{43} +2.00000 q^{44} +2.00000 q^{46} -3.00000 q^{47} +1.00000 q^{49} -2.00000 q^{50} +14.0000 q^{52} -2.00000 q^{53} +1.00000 q^{55} -10.0000 q^{58} -2.00000 q^{59} -14.0000 q^{61} +4.00000 q^{62} -8.00000 q^{64} +7.00000 q^{65} -4.00000 q^{67} -6.00000 q^{68} +2.00000 q^{70} -8.00000 q^{71} -6.00000 q^{73} +8.00000 q^{74} -16.0000 q^{76} -1.00000 q^{77} -3.00000 q^{79} -4.00000 q^{80} -16.0000 q^{82} -12.0000 q^{83} -3.00000 q^{85} -12.0000 q^{86} +2.00000 q^{89} -7.00000 q^{91} -2.00000 q^{92} +6.00000 q^{94} -8.00000 q^{95} +7.00000 q^{97} -2.00000 q^{98} +O(q^{100})$

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−2.00000	−1.41421	−0.707107	−	0.707107i	$-0.750000\pi$
$2$	−2.00000	−1.41421	−0.707107	+	0.707107i	$0.750000\pi$
$3$	0	0
$3$	0	0
$4$	2.00000	1.00000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	0	0
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	0	0
$9$	0	0
$10$	−2.00000	−0.632456
$11$	1.00000	0.301511	0.150756	−	0.988571i	$-0.451829\pi$
$11$	1.00000	0.301511	0.150756	+	0.988571i	$0.451829\pi$
$12$	0	0
$13$	7.00000	1.94145	0.970725	−	0.240192i	$-0.0772105\pi$
$13$	7.00000	1.94145	0.970725	+	0.240192i	$0.0772105\pi$
$14$	2.00000	0.534522
$15$	0	0
$16$	−4.00000	−1.00000
$17$	−3.00000	−0.727607	−0.363803	−	0.931476i	$-0.618522\pi$
$17$	−3.00000	−0.727607	−0.363803	+	0.931476i	$0.618522\pi$
$18$	0	0
$19$	−8.00000	−1.83533	−0.917663	−	0.397360i	$-0.869927\pi$
$19$	−8.00000	−1.83533	−0.917663	+	0.397360i	$0.869927\pi$
$20$	2.00000	0.447214
$21$	0	0
$22$	−2.00000	−0.426401
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	0	0
$25$	1.00000	0.200000
$26$	−14.0000	−2.74563
$27$	0	0
$28$	−2.00000	−0.377964
$29$	5.00000	0.928477	0.464238	−	0.885710i	$-0.346328\pi$
$29$	5.00000	0.928477	0.464238	+	0.885710i	$0.346328\pi$
$30$	0	0
$31$	−2.00000	−0.359211	−0.179605	−	0.983739i	$-0.557482\pi$
$31$	−2.00000	−0.359211	−0.179605	+	0.983739i	$0.557482\pi$
$32$	8.00000	1.41421
$33$	0	0
$34$	6.00000	1.02899
$35$	−1.00000	−0.169031
$36$	0	0
$37$	−4.00000	−0.657596	−0.328798	−	0.944400i	$-0.606644\pi$
$37$	−4.00000	−0.657596	−0.328798	+	0.944400i	$0.606644\pi$
$38$	16.0000	2.59554
$39$	0	0
$40$	0	0
$41$	8.00000	1.24939	0.624695	−	0.780869i	$-0.285223\pi$
$41$	8.00000	1.24939	0.624695	+	0.780869i	$0.285223\pi$
$42$	0	0
$43$	6.00000	0.914991	0.457496	−	0.889212i	$-0.348747\pi$
$43$	6.00000	0.914991	0.457496	+	0.889212i	$0.348747\pi$
$44$	2.00000	0.301511
$45$	0	0
$46$	2.00000	0.294884
$47$	−3.00000	−0.437595	−0.218797	−	0.975770i	$-0.570213\pi$
$47$	−3.00000	−0.437595	−0.218797	+	0.975770i	$0.570213\pi$
$48$	0	0
$49$	1.00000	0.142857
$50$	−2.00000	−0.282843
$51$	0	0
$52$	14.0000	1.94145
$53$	−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
$55$	1.00000	0.134840
$56$	0	0
$57$	0	0
$58$	−10.0000	−1.31306
$59$	−2.00000	−0.260378	−0.130189	−	0.991489i	$-0.541558\pi$
$59$	−2.00000	−0.260378	−0.130189	+	0.991489i	$0.541558\pi$
$60$	0	0
$61$	−14.0000	−1.79252	−0.896258	−	0.443533i	$-0.853725\pi$
$61$	−14.0000	−1.79252	−0.896258	+	0.443533i	$0.853725\pi$
$62$	4.00000	0.508001
$63$	0	0
$64$	−8.00000	−1.00000
$65$	7.00000	0.868243
$66$	0	0
$67$	−4.00000	−0.488678	−0.244339	−	0.969690i	$-0.578571\pi$
$67$	−4.00000	−0.488678	−0.244339	+	0.969690i	$0.578571\pi$
$68$	−6.00000	−0.727607
$69$	0	0
$70$	2.00000	0.239046
$71$	−8.00000	−0.949425	−0.474713	−	0.880141i	$-0.657448\pi$
$71$	−8.00000	−0.949425	−0.474713	+	0.880141i	$0.657448\pi$
$72$	0	0
$73$	−6.00000	−0.702247	−0.351123	−	0.936329i	$-0.614200\pi$
$73$	−6.00000	−0.702247	−0.351123	+	0.936329i	$0.614200\pi$
$74$	8.00000	0.929981
$75$	0	0
$76$	−16.0000	−1.83533
$77$	−1.00000	−0.113961
$78$	0	0
$79$	−3.00000	−0.337526	−0.168763	−	0.985657i	$-0.553977\pi$
$79$	−3.00000	−0.337526	−0.168763	+	0.985657i	$0.553977\pi$
$80$	−4.00000	−0.447214
$81$	0	0
$82$	−16.0000	−1.76690
$83$	−12.0000	−1.31717	−0.658586	−	0.752506i	$-0.728845\pi$
$83$	−12.0000	−1.31717	−0.658586	+	0.752506i	$0.728845\pi$
$84$	0	0
$85$	−3.00000	−0.325396
$86$	−12.0000	−1.29399
$87$	0	0
$88$	0	0
$89$	2.00000	0.212000	0.106000	−	0.994366i	$-0.466196\pi$
$89$	2.00000	0.212000	0.106000	+	0.994366i	$0.466196\pi$
$90$	0	0
$91$	−7.00000	−0.733799
$92$	−2.00000	−0.208514
$93$	0	0
$94$	6.00000	0.618853
$95$	−8.00000	−0.820783
$96$	0	0
$97$	7.00000	0.710742	0.355371	−	0.934725i	$-0.384354\pi$
$97$	7.00000	0.710742	0.355371	+	0.934725i	$0.384354\pi$
$98$	−2.00000	−0.202031
$99$	0	0
$100$	2.00000	0.200000
$101$	14.0000	1.39305	0.696526	−	0.717532i	$-0.254728\pi$
$101$	14.0000	1.39305	0.696526	+	0.717532i	$0.254728\pi$
$102$	0	0
$103$	1.00000	0.0985329	0.0492665	−	0.998786i	$-0.484312\pi$
$103$	1.00000	0.0985329	0.0492665	+	0.998786i	$0.484312\pi$
$104$	0	0
$105$	0	0
$106$	4.00000	0.388514
$107$	−18.0000	−1.74013	−0.870063	−	0.492941i	$-0.835922\pi$
$107$	−18.0000	−1.74013	−0.870063	+	0.492941i	$0.835922\pi$
$108$	0	0
$109$	11.0000	1.05361	0.526804	−	0.849987i	$-0.323390\pi$
$109$	11.0000	1.05361	0.526804	+	0.849987i	$0.323390\pi$
$110$	−2.00000	−0.190693
$111$	0	0
$112$	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	$0.821383\pi$
$114$	0	0
$115$	−1.00000	−0.0932505
$116$	10.0000	0.928477
$117$	0	0
$118$	4.00000	0.368230
$119$	3.00000	0.275010
$120$	0	0
$121$	−10.0000	−0.909091
$122$	28.0000	2.53500
$123$	0	0
$124$	−4.00000	−0.359211
$125$	1.00000	0.0894427
$126$	0	0
$127$	−4.00000	−0.354943	−0.177471	−	0.984126i	$-0.556792\pi$
$127$	−4.00000	−0.354943	−0.177471	+	0.984126i	$0.556792\pi$
$128$	0	0
$129$	0	0
$130$	−14.0000	−1.22788
$131$	−12.0000	−1.04844	−0.524222	−	0.851581i	$-0.675644\pi$
$131$	−12.0000	−1.04844	−0.524222	+	0.851581i	$0.675644\pi$
$132$	0	0
$133$	8.00000	0.693688
$134$	8.00000	0.691095
$135$	0	0
$136$	0	0
$137$	6.00000	0.512615	0.256307	−	0.966595i	$-0.417494\pi$
$137$	6.00000	0.512615	0.256307	+	0.966595i	$0.417494\pi$
$138$	0	0
$139$	8.00000	0.678551	0.339276	−	0.940687i	$-0.389818\pi$
$139$	8.00000	0.678551	0.339276	+	0.940687i	$0.389818\pi$
$140$	−2.00000	−0.169031
$141$	0	0
$142$	16.0000	1.34269
$143$	7.00000	0.585369
$144$	0	0
$145$	5.00000	0.415227
$146$	12.0000	0.993127
$147$	0	0
$148$	−8.00000	−0.657596
$149$	2.00000	0.163846	0.0819232	−	0.996639i	$-0.473894\pi$
$149$	2.00000	0.163846	0.0819232	+	0.996639i	$0.473894\pi$
$150$	0	0
$151$	−9.00000	−0.732410	−0.366205	−	0.930534i	$-0.619343\pi$
$151$	−9.00000	−0.732410	−0.366205	+	0.930534i	$0.619343\pi$
$152$	0	0
$153$	0	0
$154$	2.00000	0.161165
$155$	−2.00000	−0.160644
$156$	0	0
$157$	2.00000	0.159617	0.0798087	−	0.996810i	$-0.474569\pi$
$157$	2.00000	0.159617	0.0798087	+	0.996810i	$0.474569\pi$
$158$	6.00000	0.477334
$159$	0	0
$160$	8.00000	0.632456
$161$	1.00000	0.0788110
$162$	0	0
$163$	24.0000	1.87983	0.939913	−	0.341415i	$-0.110906\pi$
$163$	24.0000	1.87983	0.939913	+	0.341415i	$0.110906\pi$
$164$	16.0000	1.24939
$165$	0	0
$166$	24.0000	1.86276
$167$	−3.00000	−0.232147	−0.116073	−	0.993241i	$-0.537031\pi$
$167$	−3.00000	−0.232147	−0.116073	+	0.993241i	$0.537031\pi$
$168$	0	0
$169$	36.0000	2.76923
$170$	6.00000	0.460179
$171$	0	0
$172$	12.0000	0.914991
$173$	15.0000	1.14043	0.570214	−	0.821496i	$-0.306860\pi$
$173$	15.0000	1.14043	0.570214	+	0.821496i	$0.306860\pi$
$174$	0	0
$175$	−1.00000	−0.0755929
$176$	−4.00000	−0.301511
$177$	0	0
$178$	−4.00000	−0.299813
$179$	−24.0000	−1.79384	−0.896922	−	0.442189i	$-0.854202\pi$
$179$	−24.0000	−1.79384	−0.896922	+	0.442189i	$0.854202\pi$
$180$	0	0
$181$	−14.0000	−1.04061	−0.520306	−	0.853980i	$-0.674182\pi$
$181$	−14.0000	−1.04061	−0.520306	+	0.853980i	$0.674182\pi$
$182$	14.0000	1.03775
$183$	0	0
$184$	0	0
$185$	−4.00000	−0.294086
$186$	0	0
$187$	−3.00000	−0.219382
$188$	−6.00000	−0.437595
$189$	0	0
$190$	16.0000	1.16076
$191$	9.00000	0.651217	0.325609	−	0.945505i	$-0.394431\pi$
$191$	9.00000	0.651217	0.325609	+	0.945505i	$0.394431\pi$
$192$	0	0
$193$	−2.00000	−0.143963	−0.0719816	−	0.997406i	$-0.522932\pi$
$193$	−2.00000	−0.143963	−0.0719816	+	0.997406i	$0.522932\pi$
$194$	−14.0000	−1.00514
$195$	0	0
$196$	2.00000	0.142857
$197$	−28.0000	−1.99492	−0.997459	−	0.0712470i	$-0.977302\pi$
$197$	−28.0000	−1.99492	−0.997459	+	0.0712470i	$0.977302\pi$
$198$	0	0
$199$	26.0000	1.84309	0.921546	−	0.388270i	$-0.126927\pi$
$199$	26.0000	1.84309	0.921546	+	0.388270i	$0.126927\pi$
$200$	0	0
$201$	0	0
$202$	−28.0000	−1.97007
$203$	−5.00000	−0.350931
$204$	0	0
$205$	8.00000	0.558744
$206$	−2.00000	−0.139347
$207$	0	0
$208$	−28.0000	−1.94145
$209$	−8.00000	−0.553372
$210$	0	0
$211$	15.0000	1.03264	0.516321	−	0.856395i	$-0.327301\pi$
$211$	15.0000	1.03264	0.516321	+	0.856395i	$0.327301\pi$
$212$	−4.00000	−0.274721
$213$	0	0
$214$	36.0000	2.46091
$215$	6.00000	0.409197
$216$	0	0
$217$	2.00000	0.135769
$218$	−22.0000	−1.49003
$219$	0	0
$220$	2.00000	0.134840
$221$	−21.0000	−1.41261
$222$	0	0
$223$	−13.0000	−0.870544	−0.435272	−	0.900299i	$-0.643348\pi$
$223$	−13.0000	−0.870544	−0.435272	+	0.900299i	$0.643348\pi$
$224$	−8.00000	−0.534522
$225$	0	0
$226$	36.0000	2.39468
$227$	−13.0000	−0.862840	−0.431420	−	0.902151i	$-0.641987\pi$
$227$	−13.0000	−0.862840	−0.431420	+	0.902151i	$0.641987\pi$
$228$	0	0
$229$	−16.0000	−1.05731	−0.528655	−	0.848837i	$-0.677303\pi$
$229$	−16.0000	−1.05731	−0.528655	+	0.848837i	$0.677303\pi$
$230$	2.00000	0.131876
$231$	0	0
$232$	0	0
$233$	−10.0000	−0.655122	−0.327561	−	0.944830i	$-0.606227\pi$
$233$	−10.0000	−0.655122	−0.327561	+	0.944830i	$0.606227\pi$
$234$	0	0
$235$	−3.00000	−0.195698
$236$	−4.00000	−0.260378
$237$	0	0
$238$	−6.00000	−0.388922
$239$	17.0000	1.09964	0.549819	−	0.835284i	$-0.314697\pi$
$239$	17.0000	1.09964	0.549819	+	0.835284i	$0.314697\pi$
$240$	0	0
$241$	−6.00000	−0.386494	−0.193247	−	0.981150i	$-0.561902\pi$
$241$	−6.00000	−0.386494	−0.193247	+	0.981150i	$0.561902\pi$
$242$	20.0000	1.28565
$243$	0	0
$244$	−28.0000	−1.79252
$245$	1.00000	0.0638877
$246$	0	0
$247$	−56.0000	−3.56319
$248$	0	0
$249$	0	0
$250$	−2.00000	−0.126491
$251$	20.0000	1.26239	0.631194	−	0.775625i	$-0.282565\pi$
$251$	20.0000	1.26239	0.631194	+	0.775625i	$0.282565\pi$
$252$	0	0
$253$	−1.00000	−0.0628695
$254$	8.00000	0.501965
$255$	0	0
$256$	16.0000	1.00000
$257$	14.0000	0.873296	0.436648	−	0.899632i	$-0.356166\pi$
$257$	14.0000	0.873296	0.436648	+	0.899632i	$0.356166\pi$
$258$	0	0
$259$	4.00000	0.248548
$260$	14.0000	0.868243
$261$	0	0
$262$	24.0000	1.48272
$263$	−28.0000	−1.72655	−0.863277	−	0.504730i	$-0.831592\pi$
$263$	−28.0000	−1.72655	−0.863277	+	0.504730i	$0.831592\pi$
$264$	0	0
$265$	−2.00000	−0.122859
$266$	−16.0000	−0.981023
$267$	0	0
$268$	−8.00000	−0.488678
$269$	30.0000	1.82913	0.914566	−	0.404436i	$-0.132532\pi$
$269$	30.0000	1.82913	0.914566	+	0.404436i	$0.132532\pi$
$270$	0	0
$271$	−2.00000	−0.121491	−0.0607457	−	0.998153i	$-0.519348\pi$
$271$	−2.00000	−0.121491	−0.0607457	+	0.998153i	$0.519348\pi$
$272$	12.0000	0.727607
$273$	0	0
$274$	−12.0000	−0.724947
$275$	1.00000	0.0603023
$276$	0	0
$277$	−24.0000	−1.44202	−0.721010	−	0.692925i	$-0.756322\pi$
$277$	−24.0000	−1.44202	−0.721010	+	0.692925i	$0.756322\pi$
$278$	−16.0000	−0.959616
$279$	0	0
$280$	0	0
$281$	15.0000	0.894825	0.447412	−	0.894328i	$-0.352346\pi$
$281$	15.0000	0.894825	0.447412	+	0.894328i	$0.352346\pi$
$282$	0	0
$283$	−1.00000	−0.0594438	−0.0297219	−	0.999558i	$-0.509462\pi$
$283$	−1.00000	−0.0594438	−0.0297219	+	0.999558i	$0.509462\pi$
$284$	−16.0000	−0.949425
$285$	0	0
$286$	−14.0000	−0.827837
$287$	−8.00000	−0.472225
$288$	0	0
$289$	−8.00000	−0.470588
$290$	−10.0000	−0.587220
$291$	0	0
$292$	−12.0000	−0.702247
$293$	9.00000	0.525786	0.262893	−	0.964825i	$-0.415323\pi$
$293$	9.00000	0.525786	0.262893	+	0.964825i	$0.415323\pi$
$294$	0	0
$295$	−2.00000	−0.116445
$296$	0	0
$297$	0	0
$298$	−4.00000	−0.231714
$299$	−7.00000	−0.404820
$300$	0	0
$301$	−6.00000	−0.345834
$302$	18.0000	1.03578
$303$	0	0
$304$	32.0000	1.83533
$305$	−14.0000	−0.801638
$306$	0	0
$307$	−11.0000	−0.627803	−0.313902	−	0.949456i	$-0.601636\pi$
$307$	−11.0000	−0.627803	−0.313902	+	0.949456i	$0.601636\pi$
$308$	−2.00000	−0.113961
$309$	0	0
$310$	4.00000	0.227185
$311$	−4.00000	−0.226819	−0.113410	−	0.993548i	$-0.536177\pi$
$311$	−4.00000	−0.226819	−0.113410	+	0.993548i	$0.536177\pi$
$312$	0	0
$313$	9.00000	0.508710	0.254355	−	0.967111i	$-0.418137\pi$
$313$	9.00000	0.508710	0.254355	+	0.967111i	$0.418137\pi$
$314$	−4.00000	−0.225733
$315$	0	0
$316$	−6.00000	−0.337526
$317$	12.0000	0.673987	0.336994	−	0.941507i	$-0.390590\pi$
$317$	12.0000	0.673987	0.336994	+	0.941507i	$0.390590\pi$
$318$	0	0
$319$	5.00000	0.279946
$320$	−8.00000	−0.447214
$321$	0	0
$322$	−2.00000	−0.111456
$323$	24.0000	1.33540
$324$	0	0
$325$	7.00000	0.388290
$326$	−48.0000	−2.65847
$327$	0	0
$328$	0	0
$329$	3.00000	0.165395
$330$	0	0
$331$	8.00000	0.439720	0.219860	−	0.975531i	$-0.429440\pi$
$331$	8.00000	0.439720	0.219860	+	0.975531i	$0.429440\pi$
$332$	−24.0000	−1.31717
$333$	0	0
$334$	6.00000	0.328305
$335$	−4.00000	−0.218543
$336$	0	0
$337$	−14.0000	−0.762629	−0.381314	−	0.924445i	$-0.624528\pi$
$337$	−14.0000	−0.762629	−0.381314	+	0.924445i	$0.624528\pi$
$338$	−72.0000	−3.91628
$339$	0	0
$340$	−6.00000	−0.325396
$341$	−2.00000	−0.108306
$342$	0	0
$343$	−1.00000	−0.0539949
$344$	0	0
$345$	0	0
$346$	−30.0000	−1.61281
$347$	−12.0000	−0.644194	−0.322097	−	0.946707i	$-0.604388\pi$
$347$	−12.0000	−0.644194	−0.322097	+	0.946707i	$0.604388\pi$
$348$	0	0
$349$	−28.0000	−1.49881	−0.749403	−	0.662114i	$-0.769659\pi$
$349$	−28.0000	−1.49881	−0.749403	+	0.662114i	$0.769659\pi$
$350$	2.00000	0.106904
$351$	0	0
$352$	8.00000	0.426401
$353$	−25.0000	−1.33062	−0.665308	−	0.746569i	$-0.731700\pi$
$353$	−25.0000	−1.33062	−0.665308	+	0.746569i	$0.731700\pi$
$354$	0	0
$355$	−8.00000	−0.424596
$356$	4.00000	0.212000
$357$	0	0
$358$	48.0000	2.53688
$359$	24.0000	1.26667	0.633336	−	0.773877i	$-0.281685\pi$
$359$	24.0000	1.26667	0.633336	+	0.773877i	$0.281685\pi$
$360$	0	0
$361$	45.0000	2.36842
$362$	28.0000	1.47165
$363$	0	0
$364$	−14.0000	−0.733799
$365$	−6.00000	−0.314054
$366$	0	0
$367$	−7.00000	−0.365397	−0.182699	−	0.983169i	$-0.558483\pi$
$367$	−7.00000	−0.365397	−0.182699	+	0.983169i	$0.558483\pi$
$368$	4.00000	0.208514
$369$	0	0
$370$	8.00000	0.415900
$371$	2.00000	0.103835
$372$	0	0
$373$	26.0000	1.34623	0.673114	−	0.739538i	$-0.264956\pi$
$373$	26.0000	1.34623	0.673114	+	0.739538i	$0.264956\pi$
$374$	6.00000	0.310253
$375$	0	0
$376$	0	0
$377$	35.0000	1.80259
$378$	0	0
$379$	−12.0000	−0.616399	−0.308199	−	0.951322i	$-0.599726\pi$
$379$	−12.0000	−0.616399	−0.308199	+	0.951322i	$0.599726\pi$
$380$	−16.0000	−0.820783
$381$	0	0
$382$	−18.0000	−0.920960
$383$	16.0000	0.817562	0.408781	−	0.912633i	$-0.365954\pi$
$383$	16.0000	0.817562	0.408781	+	0.912633i	$0.365954\pi$
$384$	0	0
$385$	−1.00000	−0.0509647
$386$	4.00000	0.203595
$387$	0	0
$388$	14.0000	0.710742
$389$	−19.0000	−0.963338	−0.481669	−	0.876353i	$-0.659969\pi$
$389$	−19.0000	−0.963338	−0.481669	+	0.876353i	$0.659969\pi$
$390$	0	0
$391$	3.00000	0.151717
$392$	0	0
$393$	0	0
$394$	56.0000	2.82124
$395$	−3.00000	−0.150946
$396$	0	0
$397$	25.0000	1.25471	0.627357	−	0.778732i	$-0.284137\pi$
$397$	25.0000	1.25471	0.627357	+	0.778732i	$0.284137\pi$
$398$	−52.0000	−2.60652
$399$	0	0
$400$	−4.00000	−0.200000
$401$	25.0000	1.24844	0.624220	−	0.781248i	$-0.285417\pi$
$401$	25.0000	1.24844	0.624220	+	0.781248i	$0.285417\pi$
$402$	0	0
$403$	−14.0000	−0.697390
$404$	28.0000	1.39305
$405$	0	0
$406$	10.0000	0.496292
$407$	−4.00000	−0.198273
$408$	0	0
$409$	−14.0000	−0.692255	−0.346128	−	0.938187i	$-0.612504\pi$
$409$	−14.0000	−0.692255	−0.346128	+	0.938187i	$0.612504\pi$
$410$	−16.0000	−0.790184
$411$	0	0
$412$	2.00000	0.0985329
$413$	2.00000	0.0984136
$414$	0	0
$415$	−12.0000	−0.589057
$416$	56.0000	2.74563
$417$	0	0
$418$	16.0000	0.782586
$419$	−30.0000	−1.46560	−0.732798	−	0.680446i	$-0.761786\pi$
$419$	−30.0000	−1.46560	−0.732798	+	0.680446i	$0.761786\pi$
$420$	0	0
$421$	7.00000	0.341159	0.170580	−	0.985344i	$-0.445436\pi$
$421$	7.00000	0.341159	0.170580	+	0.985344i	$0.445436\pi$
$422$	−30.0000	−1.46038
$423$	0	0
$424$	0	0
$425$	−3.00000	−0.145521
$426$	0	0
$427$	14.0000	0.677507
$428$	−36.0000	−1.74013
$429$	0	0
$430$	−12.0000	−0.578691
$431$	−19.0000	−0.915198	−0.457599	−	0.889159i	$-0.651290\pi$
$431$	−19.0000	−0.915198	−0.457599	+	0.889159i	$0.651290\pi$
$432$	0	0
$433$	2.00000	0.0961139	0.0480569	−	0.998845i	$-0.484697\pi$
$433$	2.00000	0.0961139	0.0480569	+	0.998845i	$0.484697\pi$
$434$	−4.00000	−0.192006
$435$	0	0
$436$	22.0000	1.05361
$437$	8.00000	0.382692
$438$	0	0
$439$	26.0000	1.24091	0.620456	−	0.784241i	$-0.286947\pi$
$439$	26.0000	1.24091	0.620456	+	0.784241i	$0.286947\pi$
$440$	0	0
$441$	0	0
$442$	42.0000	1.99774
$443$	−10.0000	−0.475114	−0.237557	−	0.971374i	$-0.576347\pi$
$443$	−10.0000	−0.475114	−0.237557	+	0.971374i	$0.576347\pi$
$444$	0	0
$445$	2.00000	0.0948091
$446$	26.0000	1.23114
$447$	0	0
$448$	8.00000	0.377964
$449$	9.00000	0.424736	0.212368	−	0.977190i	$-0.431882\pi$
$449$	9.00000	0.424736	0.212368	+	0.977190i	$0.431882\pi$
$450$	0	0
$451$	8.00000	0.376705
$452$	−36.0000	−1.69330
$453$	0	0
$454$	26.0000	1.22024
$455$	−7.00000	−0.328165
$456$	0	0
$457$	−8.00000	−0.374224	−0.187112	−	0.982339i	$-0.559913\pi$
$457$	−8.00000	−0.374224	−0.187112	+	0.982339i	$0.559913\pi$
$458$	32.0000	1.49526
$459$	0	0
$460$	−2.00000	−0.0932505
$461$	−16.0000	−0.745194	−0.372597	−	0.927993i	$-0.621533\pi$
$461$	−16.0000	−0.745194	−0.372597	+	0.927993i	$0.621533\pi$
$462$	0	0
$463$	−34.0000	−1.58011	−0.790057	−	0.613033i	$-0.789949\pi$
$463$	−34.0000	−1.58011	−0.790057	+	0.613033i	$0.789949\pi$
$464$	−20.0000	−0.928477
$465$	0	0
$466$	20.0000	0.926482
$467$	21.0000	0.971764	0.485882	−	0.874024i	$-0.338498\pi$
$467$	21.0000	0.971764	0.485882	+	0.874024i	$0.338498\pi$
$468$	0	0
$469$	4.00000	0.184703
$470$	6.00000	0.276759
$471$	0	0
$472$	0	0
$473$	6.00000	0.275880
$474$	0	0
$475$	−8.00000	−0.367065
$476$	6.00000	0.275010
$477$	0	0
$478$	−34.0000	−1.55512
$479$	−6.00000	−0.274147	−0.137073	−	0.990561i	$-0.543770\pi$
$479$	−6.00000	−0.274147	−0.137073	+	0.990561i	$0.543770\pi$
$480$	0	0
$481$	−28.0000	−1.27669
$482$	12.0000	0.546585
$483$	0	0
$484$	−20.0000	−0.909091
$485$	7.00000	0.317854
$486$	0	0
$487$	2.00000	0.0906287	0.0453143	−	0.998973i	$-0.485571\pi$
$487$	2.00000	0.0906287	0.0453143	+	0.998973i	$0.485571\pi$
$488$	0	0
$489$	0	0
$490$	−2.00000	−0.0903508
$491$	9.00000	0.406164	0.203082	−	0.979162i	$-0.434904\pi$
$491$	9.00000	0.406164	0.203082	+	0.979162i	$0.434904\pi$
$492$	0	0
$493$	−15.0000	−0.675566
$494$	112.000	5.03912
$495$	0	0
$496$	8.00000	0.359211
$497$	8.00000	0.358849
$498$	0	0
$499$	25.0000	1.11915	0.559577	−	0.828778i	$-0.310964\pi$
$499$	25.0000	1.11915	0.559577	+	0.828778i	$0.310964\pi$
$500$	2.00000	0.0894427
$501$	0	0
$502$	−40.0000	−1.78529
$503$	−39.0000	−1.73892	−0.869462	−	0.494000i	$-0.835534\pi$
$503$	−39.0000	−1.73892	−0.869462	+	0.494000i	$0.835534\pi$
$504$	0	0
$505$	14.0000	0.622992
$506$	2.00000	0.0889108
$507$	0	0
$508$	−8.00000	−0.354943
$509$	12.0000	0.531891	0.265945	−	0.963988i	$-0.414316\pi$
$509$	12.0000	0.531891	0.265945	+	0.963988i	$0.414316\pi$
$510$	0	0
$511$	6.00000	0.265424
$512$	−32.0000	−1.41421
$513$	0	0
$514$	−28.0000	−1.23503
$515$	1.00000	0.0440653
$516$	0	0
$517$	−3.00000	−0.131940
$518$	−8.00000	−0.351500
$519$	0	0
$520$	0	0
$521$	−30.0000	−1.31432	−0.657162	−	0.753749i	$-0.728243\pi$
$521$	−30.0000	−1.31432	−0.657162	+	0.753749i	$0.728243\pi$
$522$	0	0
$523$	−16.0000	−0.699631	−0.349816	−	0.936819i	$-0.613756\pi$
$523$	−16.0000	−0.699631	−0.349816	+	0.936819i	$0.613756\pi$
$524$	−24.0000	−1.04844
$525$	0	0
$526$	56.0000	2.44172
$527$	6.00000	0.261364
$528$	0	0
$529$	1.00000	0.0434783
$530$	4.00000	0.173749
$531$	0	0
$532$	16.0000	0.693688
$533$	56.0000	2.42563
$534$	0	0
$535$	−18.0000	−0.778208
$536$	0	0
$537$	0	0
$538$	−60.0000	−2.58678
$539$	1.00000	0.0430730
$540$	0	0
$541$	−17.0000	−0.730887	−0.365444	−	0.930834i	$-0.619083\pi$
$541$	−17.0000	−0.730887	−0.365444	+	0.930834i	$0.619083\pi$
$542$	4.00000	0.171815
$543$	0	0
$544$	−24.0000	−1.02899
$545$	11.0000	0.471188
$546$	0	0
$547$	−30.0000	−1.28271	−0.641354	−	0.767245i	$-0.721627\pi$
$547$	−30.0000	−1.28271	−0.641354	+	0.767245i	$0.721627\pi$
$548$	12.0000	0.512615
$549$	0	0
$550$	−2.00000	−0.0852803
$551$	−40.0000	−1.70406
$552$	0	0
$553$	3.00000	0.127573
$554$	48.0000	2.03932
$555$	0	0
$556$	16.0000	0.678551
$557$	−2.00000	−0.0847427	−0.0423714	−	0.999102i	$-0.513491\pi$
$557$	−2.00000	−0.0847427	−0.0423714	+	0.999102i	$0.513491\pi$
$558$	0	0
$559$	42.0000	1.77641
$560$	4.00000	0.169031
$561$	0	0
$562$	−30.0000	−1.26547
$563$	−4.00000	−0.168580	−0.0842900	−	0.996441i	$-0.526862\pi$
$563$	−4.00000	−0.168580	−0.0842900	+	0.996441i	$0.526862\pi$
$564$	0	0
$565$	−18.0000	−0.757266
$566$	2.00000	0.0840663
$567$	0	0
$568$	0	0
$569$	18.0000	0.754599	0.377300	−	0.926091i	$-0.376853\pi$
$569$	18.0000	0.754599	0.377300	+	0.926091i	$0.376853\pi$
$570$	0	0
$571$	−16.0000	−0.669579	−0.334790	−	0.942293i	$-0.608665\pi$
$571$	−16.0000	−0.669579	−0.334790	+	0.942293i	$0.608665\pi$
$572$	14.0000	0.585369
$573$	0	0
$574$	16.0000	0.667827
$575$	−1.00000	−0.0417029
$576$	0	0
$577$	−37.0000	−1.54033	−0.770165	−	0.637845i	$-0.779826\pi$
$577$	−37.0000	−1.54033	−0.770165	+	0.637845i	$0.779826\pi$
$578$	16.0000	0.665512
$579$	0	0
$580$	10.0000	0.415227
$581$	12.0000	0.497844
$582$	0	0
$583$	−2.00000	−0.0828315
$584$	0	0
$585$	0	0
$586$	−18.0000	−0.743573
$587$	−44.0000	−1.81607	−0.908037	−	0.418890i	$-0.862419\pi$
$587$	−44.0000	−1.81607	−0.908037	+	0.418890i	$0.862419\pi$
$588$	0	0
$589$	16.0000	0.659269
$590$	4.00000	0.164677
$591$	0	0
$592$	16.0000	0.657596
$593$	25.0000	1.02663	0.513313	−	0.858201i	$-0.328418\pi$
$593$	25.0000	1.02663	0.513313	+	0.858201i	$0.328418\pi$
$594$	0	0
$595$	3.00000	0.122988
$596$	4.00000	0.163846
$597$	0	0
$598$	14.0000	0.572503
$599$	−21.0000	−0.858037	−0.429018	−	0.903296i	$-0.641140\pi$
$599$	−21.0000	−0.858037	−0.429018	+	0.903296i	$0.641140\pi$
$600$	0	0
$601$	24.0000	0.978980	0.489490	−	0.872009i	$-0.337183\pi$
$601$	24.0000	0.978980	0.489490	+	0.872009i	$0.337183\pi$
$602$	12.0000	0.489083
$603$	0	0
$604$	−18.0000	−0.732410
$605$	−10.0000	−0.406558
$606$	0	0
$607$	−43.0000	−1.74532	−0.872658	−	0.488332i	$-0.837606\pi$
$607$	−43.0000	−1.74532	−0.872658	+	0.488332i	$0.837606\pi$
$608$	−64.0000	−2.59554
$609$	0	0
$610$	28.0000	1.13369
$611$	−21.0000	−0.849569
$612$	0	0
$613$	16.0000	0.646234	0.323117	−	0.946359i	$-0.395269\pi$
$613$	16.0000	0.646234	0.323117	+	0.946359i	$0.395269\pi$
$614$	22.0000	0.887848
$615$	0	0
$616$	0	0
$617$	−4.00000	−0.161034	−0.0805170	−	0.996753i	$-0.525657\pi$
$617$	−4.00000	−0.161034	−0.0805170	+	0.996753i	$0.525657\pi$
$618$	0	0
$619$	−18.0000	−0.723481	−0.361741	−	0.932279i	$-0.617817\pi$
$619$	−18.0000	−0.723481	−0.361741	+	0.932279i	$0.617817\pi$
$620$	−4.00000	−0.160644
$621$	0	0
$622$	8.00000	0.320771
$623$	−2.00000	−0.0801283
$624$	0	0
$625$	1.00000	0.0400000
$626$	−18.0000	−0.719425
$627$	0	0
$628$	4.00000	0.159617
$629$	12.0000	0.478471
$630$	0	0
$631$	−17.0000	−0.676759	−0.338380	−	0.941010i	$-0.609879\pi$
$631$	−17.0000	−0.676759	−0.338380	+	0.941010i	$0.609879\pi$
$632$	0	0
$633$	0	0
$634$	−24.0000	−0.953162
$635$	−4.00000	−0.158735
$636$	0	0
$637$	7.00000	0.277350
$638$	−10.0000	−0.395904
$639$	0	0
$640$	0	0
$641$	−26.0000	−1.02694	−0.513469	−	0.858108i	$-0.671640\pi$
$641$	−26.0000	−1.02694	−0.513469	+	0.858108i	$0.671640\pi$
$642$	0	0
$643$	−23.0000	−0.907031	−0.453516	−	0.891248i	$-0.649830\pi$
$643$	−23.0000	−0.907031	−0.453516	+	0.891248i	$0.649830\pi$
$644$	2.00000	0.0788110
$645$	0	0
$646$	−48.0000	−1.88853
$647$	8.00000	0.314512	0.157256	−	0.987558i	$-0.449735\pi$
$647$	8.00000	0.314512	0.157256	+	0.987558i	$0.449735\pi$
$648$	0	0
$649$	−2.00000	−0.0785069
$650$	−14.0000	−0.549125
$651$	0	0
$652$	48.0000	1.87983
$653$	−36.0000	−1.40879	−0.704394	−	0.709809i	$-0.748781\pi$
$653$	−36.0000	−1.40879	−0.704394	+	0.709809i	$0.748781\pi$
$654$	0	0
$655$	−12.0000	−0.468879
$656$	−32.0000	−1.24939
$657$	0	0
$658$	−6.00000	−0.233904
$659$	33.0000	1.28550	0.642749	−	0.766077i	$-0.277794\pi$
$659$	33.0000	1.28550	0.642749	+	0.766077i	$0.277794\pi$
$660$	0	0
$661$	40.0000	1.55582	0.777910	−	0.628376i	$-0.216280\pi$
$661$	40.0000	1.55582	0.777910	+	0.628376i	$0.216280\pi$
$662$	−16.0000	−0.621858
$663$	0	0
$664$	0	0
$665$	8.00000	0.310227
$666$	0	0
$667$	−5.00000	−0.193601
$668$	−6.00000	−0.232147
$669$	0	0
$670$	8.00000	0.309067
$671$	−14.0000	−0.540464
$672$	0	0
$673$	28.0000	1.07932	0.539660	−	0.841883i	$-0.318553\pi$
$673$	28.0000	1.07932	0.539660	+	0.841883i	$0.318553\pi$
$674$	28.0000	1.07852
$675$	0	0
$676$	72.0000	2.76923
$677$	−33.0000	−1.26829	−0.634147	−	0.773213i	$-0.718648\pi$
$677$	−33.0000	−1.26829	−0.634147	+	0.773213i	$0.718648\pi$
$678$	0	0
$679$	−7.00000	−0.268635
$680$	0	0
$681$	0	0
$682$	4.00000	0.153168
$683$	28.0000	1.07139	0.535695	−	0.844411i	$-0.320050\pi$
$683$	28.0000	1.07139	0.535695	+	0.844411i	$0.320050\pi$
$684$	0	0
$685$	6.00000	0.229248
$686$	2.00000	0.0763604
$687$	0	0
$688$	−24.0000	−0.914991
$689$	−14.0000	−0.533358
$690$	0	0
$691$	10.0000	0.380418	0.190209	−	0.981744i	$-0.439083\pi$
$691$	10.0000	0.380418	0.190209	+	0.981744i	$0.439083\pi$
$692$	30.0000	1.14043
$693$	0	0
$694$	24.0000	0.911028
$695$	8.00000	0.303457
$696$	0	0
$697$	−24.0000	−0.909065
$698$	56.0000	2.11963
$699$	0	0
$700$	−2.00000	−0.0755929
$701$	−9.00000	−0.339925	−0.169963	−	0.985451i	$-0.554365\pi$
$701$	−9.00000	−0.339925	−0.169963	+	0.985451i	$0.554365\pi$
$702$	0	0
$703$	32.0000	1.20690
$704$	−8.00000	−0.301511
$705$	0	0
$706$	50.0000	1.88177
$707$	−14.0000	−0.526524
$708$	0	0
$709$	−39.0000	−1.46468	−0.732338	−	0.680941i	$-0.761571\pi$
$709$	−39.0000	−1.46468	−0.732338	+	0.680941i	$0.761571\pi$
$710$	16.0000	0.600469
$711$	0	0
$712$	0	0
$713$	2.00000	0.0749006
$714$	0	0
$715$	7.00000	0.261785
$716$	−48.0000	−1.79384
$717$	0	0
$718$	−48.0000	−1.79134
$719$	22.0000	0.820462	0.410231	−	0.911982i	$-0.365448\pi$
$719$	22.0000	0.820462	0.410231	+	0.911982i	$0.365448\pi$
$720$	0	0
$721$	−1.00000	−0.0372419
$722$	−90.0000	−3.34945
$723$	0	0
$724$	−28.0000	−1.04061
$725$	5.00000	0.185695
$726$	0	0
$727$	−32.0000	−1.18681	−0.593407	−	0.804902i	$-0.702218\pi$
$727$	−32.0000	−1.18681	−0.593407	+	0.804902i	$0.702218\pi$
$728$	0	0
$729$	0	0
$730$	12.0000	0.444140
$731$	−18.0000	−0.665754
$732$	0	0
$733$	−43.0000	−1.58824	−0.794121	−	0.607760i	$-0.792068\pi$
$733$	−43.0000	−1.58824	−0.794121	+	0.607760i	$0.792068\pi$
$734$	14.0000	0.516749
$735$	0	0
$736$	−8.00000	−0.294884
$737$	−4.00000	−0.147342
$738$	0	0
$739$	−19.0000	−0.698926	−0.349463	−	0.936950i	$-0.613636\pi$
$739$	−19.0000	−0.698926	−0.349463	+	0.936950i	$0.613636\pi$
$740$	−8.00000	−0.294086
$741$	0	0
$742$	−4.00000	−0.146845
$743$	−10.0000	−0.366864	−0.183432	−	0.983032i	$-0.558721\pi$
$743$	−10.0000	−0.366864	−0.183432	+	0.983032i	$0.558721\pi$
$744$	0	0
$745$	2.00000	0.0732743
$746$	−52.0000	−1.90386
$747$	0	0
$748$	−6.00000	−0.219382
$749$	18.0000	0.657706
$750$	0	0
$751$	−31.0000	−1.13121	−0.565603	−	0.824678i	$-0.691357\pi$
$751$	−31.0000	−1.13121	−0.565603	+	0.824678i	$0.691357\pi$
$752$	12.0000	0.437595
$753$	0	0
$754$	−70.0000	−2.54925
$755$	−9.00000	−0.327544
$756$	0	0
$757$	−8.00000	−0.290765	−0.145382	−	0.989376i	$-0.546441\pi$
$757$	−8.00000	−0.290765	−0.145382	+	0.989376i	$0.546441\pi$
$758$	24.0000	0.871719
$759$	0	0
$760$	0	0
$761$	−12.0000	−0.435000	−0.217500	−	0.976060i	$-0.569790\pi$
$761$	−12.0000	−0.435000	−0.217500	+	0.976060i	$0.569790\pi$
$762$	0	0
$763$	−11.0000	−0.398227
$764$	18.0000	0.651217
$765$	0	0
$766$	−32.0000	−1.15621
$767$	−14.0000	−0.505511
$768$	0	0
$769$	−40.0000	−1.44244	−0.721218	−	0.692708i	$-0.756418\pi$
$769$	−40.0000	−1.44244	−0.721218	+	0.692708i	$0.756418\pi$
$770$	2.00000	0.0720750
$771$	0	0
$772$	−4.00000	−0.143963
$773$	31.0000	1.11499	0.557496	−	0.830179i	$-0.311762\pi$
$773$	31.0000	1.11499	0.557496	+	0.830179i	$0.311762\pi$
$774$	0	0
$775$	−2.00000	−0.0718421
$776$	0	0
$777$	0	0
$778$	38.0000	1.36237
$779$	−64.0000	−2.29304
$780$	0	0
$781$	−8.00000	−0.286263
$782$	−6.00000	−0.214560
$783$	0	0
$784$	−4.00000	−0.142857
$785$	2.00000	0.0713831
$786$	0	0
$787$	53.0000	1.88925	0.944623	−	0.328158i	$-0.106428\pi$
$787$	53.0000	1.88925	0.944623	+	0.328158i	$0.106428\pi$
$788$	−56.0000	−1.99492
$789$	0	0
$790$	6.00000	0.213470
$791$	18.0000	0.640006
$792$	0	0
$793$	−98.0000	−3.48008
$794$	−50.0000	−1.77443
$795$	0	0
$796$	52.0000	1.84309
$797$	−35.0000	−1.23976	−0.619882	−	0.784695i	$-0.712819\pi$
$797$	−35.0000	−1.23976	−0.619882	+	0.784695i	$0.712819\pi$
$798$	0	0
$799$	9.00000	0.318397
$800$	8.00000	0.282843
$801$	0	0
$802$	−50.0000	−1.76556
$803$	−6.00000	−0.211735
$804$	0	0
$805$	1.00000	0.0352454
$806$	28.0000	0.986258
$807$	0	0
$808$	0	0
$809$	15.0000	0.527372	0.263686	−	0.964609i	$-0.415062\pi$
$809$	15.0000	0.527372	0.263686	+	0.964609i	$0.415062\pi$
$810$	0	0
$811$	6.00000	0.210688	0.105344	−	0.994436i	$-0.466406\pi$
$811$	6.00000	0.210688	0.105344	+	0.994436i	$0.466406\pi$
$812$	−10.0000	−0.350931
$813$	0	0
$814$	8.00000	0.280400
$815$	24.0000	0.840683
$816$	0	0
$817$	−48.0000	−1.67931
$818$	28.0000	0.978997
$819$	0	0
$820$	16.0000	0.558744
$821$	11.0000	0.383903	0.191951	−	0.981404i	$-0.438518\pi$
$821$	11.0000	0.383903	0.191951	+	0.981404i	$0.438518\pi$
$822$	0	0
$823$	26.0000	0.906303	0.453152	−	0.891434i	$-0.350300\pi$
$823$	26.0000	0.906303	0.453152	+	0.891434i	$0.350300\pi$
$824$	0	0
$825$	0	0
$826$	−4.00000	−0.139178
$827$	20.0000	0.695468	0.347734	−	0.937593i	$-0.386951\pi$
$827$	20.0000	0.695468	0.347734	+	0.937593i	$0.386951\pi$
$828$	0	0
$829$	−24.0000	−0.833554	−0.416777	−	0.909009i	$-0.636840\pi$
$829$	−24.0000	−0.833554	−0.416777	+	0.909009i	$0.636840\pi$
$830$	24.0000	0.833052
$831$	0	0
$832$	−56.0000	−1.94145
$833$	−3.00000	−0.103944
$834$	0	0
$835$	−3.00000	−0.103819
$836$	−16.0000	−0.553372
$837$	0	0
$838$	60.0000	2.07267
$839$	12.0000	0.414286	0.207143	−	0.978311i	$-0.433583\pi$
$839$	12.0000	0.414286	0.207143	+	0.978311i	$0.433583\pi$
$840$	0	0
$841$	−4.00000	−0.137931
$842$	−14.0000	−0.482472
$843$	0	0
$844$	30.0000	1.03264
$845$	36.0000	1.23844
$846$	0	0
$847$	10.0000	0.343604
$848$	8.00000	0.274721
$849$	0	0
$850$	6.00000	0.205798
$851$	4.00000	0.137118
$852$	0	0
$853$	−2.00000	−0.0684787	−0.0342393	−	0.999414i	$-0.510901\pi$
$853$	−2.00000	−0.0684787	−0.0342393	+	0.999414i	$0.510901\pi$
$854$	−28.0000	−0.958140
$855$	0	0
$856$	0	0
$857$	50.0000	1.70797	0.853984	−	0.520300i	$-0.174180\pi$
$857$	50.0000	1.70797	0.853984	+	0.520300i	$0.174180\pi$
$858$	0	0
$859$	40.0000	1.36478	0.682391	−	0.730987i	$-0.260940\pi$
$859$	40.0000	1.36478	0.682391	+	0.730987i	$0.260940\pi$
$860$	12.0000	0.409197
$861$	0	0
$862$	38.0000	1.29429
$863$	−30.0000	−1.02121	−0.510606	−	0.859815i	$-0.670579\pi$
$863$	−30.0000	−1.02121	−0.510606	+	0.859815i	$0.670579\pi$
$864$	0	0
$865$	15.0000	0.510015
$866$	−4.00000	−0.135926
$867$	0	0
$868$	4.00000	0.135769
$869$	−3.00000	−0.101768
$870$	0	0
$871$	−28.0000	−0.948744
$872$	0	0
$873$	0	0
$874$	−16.0000	−0.541208
$875$	−1.00000	−0.0338062
$876$	0	0
$877$	−32.0000	−1.08056	−0.540282	−	0.841484i	$-0.681682\pi$
$877$	−32.0000	−1.08056	−0.540282	+	0.841484i	$0.681682\pi$
$878$	−52.0000	−1.75491
$879$	0	0
$880$	−4.00000	−0.134840
$881$	−22.0000	−0.741199	−0.370599	−	0.928793i	$-0.620848\pi$
$881$	−22.0000	−0.741199	−0.370599	+	0.928793i	$0.620848\pi$
$882$	0	0
$883$	−32.0000	−1.07689	−0.538443	−	0.842662i	$-0.680987\pi$
$883$	−32.0000	−1.07689	−0.538443	+	0.842662i	$0.680987\pi$
$884$	−42.0000	−1.41261
$885$	0	0
$886$	20.0000	0.671913
$887$	8.00000	0.268614	0.134307	−	0.990940i	$-0.457119\pi$
$887$	8.00000	0.268614	0.134307	+	0.990940i	$0.457119\pi$
$888$	0	0
$889$	4.00000	0.134156
$890$	−4.00000	−0.134080
$891$	0	0
$892$	−26.0000	−0.870544
$893$	24.0000	0.803129
$894$	0	0
$895$	−24.0000	−0.802232
$896$	0	0
$897$	0	0
$898$	−18.0000	−0.600668
$899$	−10.0000	−0.333519
$900$	0	0
$901$	6.00000	0.199889
$902$	−16.0000	−0.532742
$903$	0	0
$904$	0	0
$905$	−14.0000	−0.465376
$906$	0	0
$907$	−28.0000	−0.929725	−0.464862	−	0.885383i	$-0.653896\pi$
$907$	−28.0000	−0.929725	−0.464862	+	0.885383i	$0.653896\pi$
$908$	−26.0000	−0.862840
$909$	0	0
$910$	14.0000	0.464095
$911$	−8.00000	−0.265052	−0.132526	−	0.991180i	$-0.542309\pi$
$911$	−8.00000	−0.265052	−0.132526	+	0.991180i	$0.542309\pi$
$912$	0	0
$913$	−12.0000	−0.397142
$914$	16.0000	0.529233
$915$	0	0
$916$	−32.0000	−1.05731
$917$	12.0000	0.396275
$918$	0	0
$919$	−7.00000	−0.230909	−0.115454	−	0.993313i	$-0.536832\pi$
$919$	−7.00000	−0.230909	−0.115454	+	0.993313i	$0.536832\pi$
$920$	0	0
$921$	0	0
$922$	32.0000	1.05386
$923$	−56.0000	−1.84326
$924$	0	0
$925$	−4.00000	−0.131519
$926$	68.0000	2.23462
$927$	0	0
$928$	40.0000	1.31306
$929$	6.00000	0.196854	0.0984268	−	0.995144i	$-0.468619\pi$
$929$	6.00000	0.196854	0.0984268	+	0.995144i	$0.468619\pi$
$930$	0	0
$931$	−8.00000	−0.262189
$932$	−20.0000	−0.655122
$933$	0	0
$934$	−42.0000	−1.37428
$935$	−3.00000	−0.0981105
$936$	0	0
$937$	59.0000	1.92745	0.963723	−	0.266904i	$-0.0860008\pi$
$937$	59.0000	1.92745	0.963723	+	0.266904i	$0.0860008\pi$
$938$	−8.00000	−0.261209
$939$	0	0
$940$	−6.00000	−0.195698
$941$	12.0000	0.391189	0.195594	−	0.980685i	$-0.437336\pi$
$941$	12.0000	0.391189	0.195594	+	0.980685i	$0.437336\pi$
$942$	0	0
$943$	−8.00000	−0.260516
$944$	8.00000	0.260378
$945$	0	0
$946$	−12.0000	−0.390154
$947$	28.0000	0.909878	0.454939	−	0.890523i	$-0.349661\pi$
$947$	28.0000	0.909878	0.454939	+	0.890523i	$0.349661\pi$
$948$	0	0
$949$	−42.0000	−1.36338
$950$	16.0000	0.519109
$951$	0	0
$952$	0	0
$953$	−26.0000	−0.842223	−0.421111	−	0.907009i	$-0.638360\pi$
$953$	−26.0000	−0.842223	−0.421111	+	0.907009i	$0.638360\pi$
$954$	0	0
$955$	9.00000	0.291233
$956$	34.0000	1.09964
$957$	0	0
$958$	12.0000	0.387702
$959$	−6.00000	−0.193750
$960$	0	0
$961$	−27.0000	−0.870968
$962$	56.0000	1.80551
$963$	0	0
$964$	−12.0000	−0.386494
$965$	−2.00000	−0.0643823
$966$	0	0
$967$	−16.0000	−0.514525	−0.257263	−	0.966342i	$-0.582821\pi$
$967$	−16.0000	−0.514525	−0.257263	+	0.966342i	$0.582821\pi$
$968$	0	0
$969$	0	0
$970$	−14.0000	−0.449513
$971$	−36.0000	−1.15529	−0.577647	−	0.816286i	$-0.696029\pi$
$971$	−36.0000	−1.15529	−0.577647	+	0.816286i	$0.696029\pi$
$972$	0	0
$973$	−8.00000	−0.256468
$974$	−4.00000	−0.128168
$975$	0	0
$976$	56.0000	1.79252
$977$	−24.0000	−0.767828	−0.383914	−	0.923369i	$-0.625424\pi$
$977$	−24.0000	−0.767828	−0.383914	+	0.923369i	$0.625424\pi$
$978$	0	0
$979$	2.00000	0.0639203
$980$	2.00000	0.0638877
$981$	0	0
$982$	−18.0000	−0.574403
$983$	21.0000	0.669796	0.334898	−	0.942254i	$-0.391298\pi$
$983$	21.0000	0.669796	0.334898	+	0.942254i	$0.391298\pi$
$984$	0	0
$985$	−28.0000	−0.892154
$986$	30.0000	0.955395
$987$	0	0
$988$	−112.000	−3.56319
$989$	−6.00000	−0.190789
$990$	0	0
$991$	−40.0000	−1.27064	−0.635321	−	0.772248i	$-0.719132\pi$
$991$	−40.0000	−1.27064	−0.635321	+	0.772248i	$0.719132\pi$
$992$	−16.0000	−0.508001
$993$	0	0
$994$	−16.0000	−0.507489
$995$	26.0000	0.824255
$996$	0	0
$997$	−7.00000	−0.221692	−0.110846	−	0.993838i	$-0.535356\pi$
$997$	−7.00000	−0.221692	−0.110846	+	0.993838i	$0.535356\pi$
$998$	−50.0000	−1.58272
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7245.2.a.c.1.1		1
3.2	odd	2		805.2.a.d.1.1	✓	1
15.14	odd	2		4025.2.a.a.1.1		1
21.20	even	2		5635.2.a.g.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
805.2.a.d.1.1	✓	1	3.2	odd	2
4025.2.a.a.1.1		1	15.14	odd	2
5635.2.a.g.1.1		1	21.20	even	2
7245.2.a.c.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:	\( N \)	\(=\)	\( 7245 = 3^{2} \cdot 5 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7245.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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