LMFDB - Embedded newform 9800.2.a.cp.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9800,2,Mod(1,9800)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9800, 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("9800.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 9800 = 2^{3} \cdot 5^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	9800.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:	$78.2533939809$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.4.13448.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 7x^{2} + 2 $ x^4 - 7*x^2 + 2
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 1960)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-2.58874$ of defining polynomial
Character	$\chi$	$=$	9800.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.58874 q^{3} +3.70156 q^{9} +O(q^{10})$	$q-2.58874 q^{3} +3.70156 q^{9} +4.70156 q^{11} +2.58874 q^{13} +1.81616 q^{17} -5.95005 q^{19} +7.40312 q^{23} -1.81616 q^{27} -6.70156 q^{29} +1.54515 q^{31} -12.1711 q^{33} +7.40312 q^{37} -6.70156 q^{39} -1.54515 q^{41} +4.00000 q^{43} +10.6260 q^{47} -4.70156 q^{51} +11.4031 q^{53} +15.4031 q^{57} +13.2147 q^{59} -2.85974 q^{61} +8.00000 q^{67} -19.1647 q^{69} +7.40312 q^{71} -12.4421 q^{73} -8.10469 q^{79} -6.40312 q^{81} +2.85974 q^{83} +17.3486 q^{87} -13.4453 q^{89} -4.00000 q^{93} -8.53879 q^{97} +17.4031 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{9}+O(q^{10}) $ 4 * q + 2 * q^9	$ 4 q + 2 q^{9} + 6 q^{11} + 4 q^{23} - 14 q^{29} + 4 q^{37} - 14 q^{39} + 16 q^{43} - 6 q^{51} + 20 q^{53} + 36 q^{57} + 32 q^{67} + 4 q^{71} + 6 q^{79} - 16 q^{93} + 44 q^{99}+O(q^{100}) $ 4 * q + 2 * q^9 + 6 * q^11 + 4 * q^23 - 14 * q^29 + 4 * q^37 - 14 * q^39 + 16 * q^43 - 6 * q^51 + 20 * q^53 + 36 * q^57 + 32 * q^67 + 4 * q^71 + 6 * q^79 - 16 * q^93 + 44 * q^99

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 $

$2$	0	0
$2$	0	0
$3$	−2.58874	−1.49461	−0.747304	−	0.664482i	$-0.768652\pi$
$3$	−2.58874	−1.49461	−0.747304	+	0.664482i	$0.768652\pi$
$4$	0	0
$5$	0	0
$5$	0	0
$6$	0	0
$7$	0	0
$7$	0	0
$8$	0	0
$9$	3.70156	1.23385
$10$	0	0
$11$	4.70156	1.41757	0.708787	−	0.705422i	$-0.249243\pi$
$11$	4.70156	1.41757	0.708787	+	0.705422i	$0.249243\pi$
$12$	0	0
$13$	2.58874	0.717987	0.358993	−	0.933340i	$-0.383120\pi$
$13$	2.58874	0.717987	0.358993	+	0.933340i	$0.383120\pi$
$14$	0	0
$15$	0	0
$16$	0	0
$17$	1.81616	0.440484	0.220242	−	0.975445i	$-0.429315\pi$
$17$	1.81616	0.440484	0.220242	+	0.975445i	$0.429315\pi$
$18$	0	0
$19$	−5.95005	−1.36504	−0.682518	−	0.730869i	$-0.739115\pi$
$19$	−5.95005	−1.36504	−0.682518	+	0.730869i	$0.739115\pi$
$20$	0	0
$21$	0	0
$22$	0	0
$23$	7.40312	1.54366	0.771829	−	0.635830i	$-0.219342\pi$
$23$	7.40312	1.54366	0.771829	+	0.635830i	$0.219342\pi$
$24$	0	0
$25$	0	0
$26$	0	0
$27$	−1.81616	−0.349520
$28$	0	0
$29$	−6.70156	−1.24445	−0.622224	−	0.782839i	$-0.713771\pi$
$29$	−6.70156	−1.24445	−0.622224	+	0.782839i	$0.713771\pi$
$30$	0	0
$31$	1.54515	0.277518	0.138759	−	0.990326i	$-0.455689\pi$
$31$	1.54515	0.277518	0.138759	+	0.990326i	$0.455689\pi$
$32$	0	0
$33$	−12.1711	−2.11872
$34$	0	0
$35$	0	0
$36$	0	0
$37$	7.40312	1.21707	0.608533	−	0.793529i	$-0.291758\pi$
$37$	7.40312	1.21707	0.608533	+	0.793529i	$0.291758\pi$
$38$	0	0
$39$	−6.70156	−1.07311
$40$	0	0
$41$	−1.54515	−0.241313	−0.120656	−	0.992694i	$-0.538500\pi$
$41$	−1.54515	−0.241313	−0.120656	+	0.992694i	$0.538500\pi$
$42$	0	0
$43$	4.00000	0.609994	0.304997	−	0.952353i	$-0.401344\pi$
$43$	4.00000	0.609994	0.304997	+	0.952353i	$0.401344\pi$
$44$	0	0
$45$	0	0
$46$	0	0
$47$	10.6260	1.54995	0.774977	−	0.631989i	$-0.217761\pi$
$47$	10.6260	1.54995	0.774977	+	0.631989i	$0.217761\pi$
$48$	0	0
$49$	0	0
$50$	0	0
$51$	−4.70156	−0.658350
$52$	0	0
$53$	11.4031	1.56634	0.783170	−	0.621808i	$-0.213602\pi$
$53$	11.4031	1.56634	0.783170	+	0.621808i	$0.213602\pi$
$54$	0	0
$55$	0	0
$56$	0	0
$57$	15.4031	2.04019
$58$	0	0
$59$	13.2147	1.72041	0.860203	−	0.509951i	$-0.170337\pi$
$59$	13.2147	1.72041	0.860203	+	0.509951i	$0.170337\pi$
$60$	0	0
$61$	−2.85974	−0.366153	−0.183076	−	0.983099i	$-0.558606\pi$
$61$	−2.85974	−0.366153	−0.183076	+	0.983099i	$0.558606\pi$
$62$	0	0
$63$	0	0
$64$	0	0
$65$	0	0
$66$	0	0
$67$	8.00000	0.977356	0.488678	−	0.872464i	$-0.337479\pi$
$67$	8.00000	0.977356	0.488678	+	0.872464i	$0.337479\pi$
$68$	0	0
$69$	−19.1647	−2.30716
$70$	0	0
$71$	7.40312	0.878589	0.439295	−	0.898343i	$-0.355228\pi$
$71$	7.40312	0.878589	0.439295	+	0.898343i	$0.355228\pi$
$72$	0	0
$73$	−12.4421	−1.45624	−0.728120	−	0.685450i	$-0.759606\pi$
$73$	−12.4421	−1.45624	−0.728120	+	0.685450i	$0.759606\pi$
$74$	0	0
$75$	0	0
$76$	0	0
$77$	0	0
$78$	0	0
$79$	−8.10469	−0.911848	−0.455924	−	0.890019i	$-0.650691\pi$
$79$	−8.10469	−0.911848	−0.455924	+	0.890019i	$0.650691\pi$
$80$	0	0
$81$	−6.40312	−0.711458
$82$	0	0
$83$	2.85974	0.313898	0.156949	−	0.987607i	$-0.449834\pi$
$83$	2.85974	0.313898	0.156949	+	0.987607i	$0.449834\pi$
$84$	0	0
$85$	0	0
$86$	0	0
$87$	17.3486	1.85996
$88$	0	0
$89$	−13.4453	−1.42519	−0.712597	−	0.701573i	$-0.752481\pi$
$89$	−13.4453	−1.42519	−0.712597	+	0.701573i	$0.752481\pi$
$90$	0	0
$91$	0	0
$92$	0	0
$93$	−4.00000	−0.414781
$94$	0	0
$95$	0	0
$96$	0	0
$97$	−8.53879	−0.866983	−0.433491	−	0.901158i	$-0.642719\pi$
$97$	−8.53879	−0.866983	−0.433491	+	0.901158i	$0.642719\pi$
$98$	0	0
$99$	17.4031	1.74908
$100$	0	0
$101$	14.7598	1.46866	0.734330	−	0.678793i	$-0.237497\pi$
$101$	14.7598	1.46866	0.734330	+	0.678793i	$0.237497\pi$
$102$	0	0
$103$	6.45162	0.635697	0.317849	−	0.948141i	$-0.397040\pi$
$103$	6.45162	0.635697	0.317849	+	0.948141i	$0.397040\pi$
$104$	0	0
$105$	0	0
$106$	0	0
$107$	−8.00000	−0.773389	−0.386695	−	0.922208i	$-0.626383\pi$
$107$	−8.00000	−0.773389	−0.386695	+	0.922208i	$0.626383\pi$
$108$	0	0
$109$	10.7016	1.02502	0.512512	−	0.858680i	$-0.328715\pi$
$109$	10.7016	1.02502	0.512512	+	0.858680i	$0.328715\pi$
$110$	0	0
$111$	−19.1647	−1.81904
$112$	0	0
$113$	−7.40312	−0.696427	−0.348214	−	0.937415i	$-0.613212\pi$
$113$	−7.40312	−0.696427	−0.348214	+	0.937415i	$0.613212\pi$
$114$	0	0
$115$	0	0
$116$	0	0
$117$	9.58237	0.885891
$118$	0	0
$119$	0	0
$120$	0	0
$121$	11.1047	1.00952
$122$	0	0
$123$	4.00000	0.360668
$124$	0	0
$125$	0	0
$126$	0	0
$127$	4.59688	0.407907	0.203953	−	0.978981i	$-0.434621\pi$
$127$	4.59688	0.407907	0.203953	+	0.978981i	$0.434621\pi$
$128$	0	0
$129$	−10.3550	−0.911703
$130$	0	0
$131$	−2.85974	−0.249857	−0.124928	−	0.992166i	$-0.539870\pi$
$131$	−2.85974	−0.249857	−0.124928	+	0.992166i	$0.539870\pi$
$132$	0	0
$133$	0	0
$134$	0	0
$135$	0	0
$136$	0	0
$137$	20.0000	1.70872	0.854358	−	0.519685i	$-0.173951\pi$
$137$	20.0000	1.70872	0.854358	+	0.519685i	$0.173951\pi$
$138$	0	0
$139$	−16.3050	−1.38297	−0.691486	−	0.722390i	$-0.743044\pi$
$139$	−16.3050	−1.38297	−0.691486	+	0.722390i	$0.743044\pi$
$140$	0	0
$141$	−27.5078	−2.31658
$142$	0	0
$143$	12.1711	1.01780
$144$	0	0
$145$	0	0
$146$	0	0
$147$	0	0
$148$	0	0
$149$	−10.0000	−0.819232	−0.409616	−	0.912258i	$-0.634337\pi$
$149$	−10.0000	−0.819232	−0.409616	+	0.912258i	$0.634337\pi$
$150$	0	0
$151$	−12.7016	−1.03364	−0.516819	−	0.856095i	$-0.672884\pi$
$151$	−12.7016	−1.03364	−0.516819	+	0.856095i	$0.672884\pi$
$152$	0	0
$153$	6.72263	0.543492
$154$	0	0
$155$	0	0
$156$	0	0
$157$	−3.86289	−0.308292	−0.154146	−	0.988048i	$-0.549263\pi$
$157$	−3.86289	−0.308292	−0.154146	+	0.988048i	$0.549263\pi$
$158$	0	0
$159$	−29.5197	−2.34106
$160$	0	0
$161$	0	0
$162$	0	0
$163$	−14.8062	−1.15971	−0.579857	−	0.814718i	$-0.696892\pi$
$163$	−14.8062	−1.15971	−0.579857	+	0.814718i	$0.696892\pi$
$164$	0	0
$165$	0	0
$166$	0	0
$167$	−3.90333	−0.302048	−0.151024	−	0.988530i	$-0.548257\pi$
$167$	−3.90333	−0.302048	−0.151024	+	0.988530i	$0.548257\pi$
$168$	0	0
$169$	−6.29844	−0.484495
$170$	0	0
$171$	−22.0245	−1.68425
$172$	0	0
$173$	−23.2986	−1.77136	−0.885681	−	0.464294i	$-0.846308\pi$
$173$	−23.2986	−1.77136	−0.885681	+	0.464294i	$0.846308\pi$
$174$	0	0
$175$	0	0
$176$	0	0
$177$	−34.2094	−2.57133
$178$	0	0
$179$	14.8062	1.10667	0.553335	−	0.832958i	$-0.313355\pi$
$179$	14.8062	1.10667	0.553335	+	0.832958i	$0.313355\pi$
$180$	0	0
$181$	4.40490	0.327413	0.163707	−	0.986509i	$-0.447655\pi$
$181$	4.40490	0.327413	0.163707	+	0.986509i	$0.447655\pi$
$182$	0	0
$183$	7.40312	0.547255
$184$	0	0
$185$	0	0
$186$	0	0
$187$	8.53879	0.624418
$188$	0	0
$189$	0	0
$190$	0	0
$191$	5.29844	0.383382	0.191691	−	0.981455i	$-0.438603\pi$
$191$	5.29844	0.383382	0.191691	+	0.981455i	$0.438603\pi$
$192$	0	0
$193$	−22.2094	−1.59867	−0.799333	−	0.600889i	$-0.794814\pi$
$193$	−22.2094	−1.59867	−0.799333	+	0.600889i	$0.794814\pi$
$194$	0	0
$195$	0	0
$196$	0	0
$197$	−14.2094	−1.01238	−0.506188	−	0.862423i	$-0.668946\pi$
$197$	−14.2094	−1.01238	−0.506188	+	0.862423i	$0.668946\pi$
$198$	0	0
$199$	8.80980	0.624510	0.312255	−	0.949998i	$-0.398916\pi$
$199$	8.80980	0.624510	0.312255	+	0.949998i	$0.398916\pi$
$200$	0	0
$201$	−20.7099	−1.46076
$202$	0	0
$203$	0	0
$204$	0	0
$205$	0	0
$206$	0	0
$207$	27.4031	1.90465
$208$	0	0
$209$	−27.9745	−1.93504
$210$	0	0
$211$	7.29844	0.502445	0.251223	−	0.967929i	$-0.419167\pi$
$211$	7.29844	0.502445	0.251223	+	0.967929i	$0.419167\pi$
$212$	0	0
$213$	−19.1647	−1.31315
$214$	0	0
$215$	0	0
$216$	0	0
$217$	0	0
$218$	0	0
$219$	32.2094	2.17651
$220$	0	0
$221$	4.70156	0.316261
$222$	0	0
$223$	−18.8937	−1.26522	−0.632609	−	0.774471i	$-0.718016\pi$
$223$	−18.8937	−1.26522	−0.632609	+	0.774471i	$0.718016\pi$
$224$	0	0
$225$	0	0
$226$	0	0
$227$	−6.76307	−0.448881	−0.224440	−	0.974488i	$-0.572055\pi$
$227$	−6.76307	−0.448881	−0.224440	+	0.974488i	$0.572055\pi$
$228$	0	0
$229$	5.95005	0.393191	0.196595	−	0.980485i	$-0.437012\pi$
$229$	5.95005	0.393191	0.196595	+	0.980485i	$0.437012\pi$
$230$	0	0
$231$	0	0
$232$	0	0
$233$	0	0		−	1.00000i	$-0.5\pi$
$233$	0	0			1.00000i	$0.5\pi$
$234$	0	0
$235$	0	0
$236$	0	0
$237$	20.9809	1.36286
$238$	0	0
$239$	3.29844	0.213358	0.106679	−	0.994294i	$-0.465978\pi$
$239$	3.29844	0.213358	0.106679	+	0.994294i	$0.465978\pi$
$240$	0	0
$241$	19.1647	1.23451	0.617255	−	0.786763i	$-0.288245\pi$
$241$	19.1647	1.23451	0.617255	+	0.786763i	$0.288245\pi$
$242$	0	0
$243$	22.0245	1.41287
$244$	0	0
$245$	0	0
$246$	0	0
$247$	−15.4031	−0.980077
$248$	0	0
$249$	−7.40312	−0.469154
$250$	0	0
$251$	−16.3050	−1.02916	−0.514581	−	0.857442i	$-0.672053\pi$
$251$	−16.3050	−1.02916	−0.514581	+	0.857442i	$0.672053\pi$
$252$	0	0
$253$	34.8062	2.18825
$254$	0	0
$255$	0	0
$256$	0	0
$257$	−25.8874	−1.61481	−0.807405	−	0.589998i	$-0.799129\pi$
$257$	−25.8874	−1.61481	−0.807405	+	0.589998i	$0.799129\pi$
$258$	0	0
$259$	0	0
$260$	0	0
$261$	−24.8062	−1.53547
$262$	0	0
$263$	16.0000	0.986602	0.493301	−	0.869859i	$-0.335790\pi$
$263$	16.0000	0.986602	0.493301	+	0.869859i	$0.335790\pi$
$264$	0	0
$265$	0	0
$266$	0	0
$267$	34.8062	2.13011
$268$	0	0
$269$	10.5855	0.645410	0.322705	−	0.946500i	$-0.395408\pi$
$269$	10.5855	0.645410	0.322705	+	0.946500i	$0.395408\pi$
$270$	0	0
$271$	24.8842	1.51161	0.755805	−	0.654797i	$-0.227246\pi$
$271$	24.8842	1.51161	0.755805	+	0.654797i	$0.227246\pi$
$272$	0	0
$273$	0	0
$274$	0	0
$275$	0	0
$276$	0	0
$277$	12.5969	0.756873	0.378436	−	0.925627i	$-0.376462\pi$
$277$	12.5969	0.756873	0.378436	+	0.925627i	$0.376462\pi$
$278$	0	0
$279$	5.71949	0.342417
$280$	0	0
$281$	26.9109	1.60537	0.802686	−	0.596402i	$-0.203404\pi$
$281$	26.9109	1.60537	0.802686	+	0.596402i	$0.203404\pi$
$282$	0	0
$283$	8.30822	0.493873	0.246936	−	0.969032i	$-0.420576\pi$
$283$	8.30822	0.493873	0.246936	+	0.969032i	$0.420576\pi$
$284$	0	0
$285$	0	0
$286$	0	0
$287$	0	0
$288$	0	0
$289$	−13.7016	−0.805974
$290$	0	0
$291$	22.1047	1.29580
$292$	0	0
$293$	30.0213	1.75386	0.876931	−	0.480617i	$-0.159587\pi$
$293$	30.0213	1.75386	0.876931	+	0.480617i	$0.159587\pi$
$294$	0	0
$295$	0	0
$296$	0	0
$297$	−8.53879	−0.495471
$298$	0	0
$299$	19.1647	1.10833
$300$	0	0
$301$	0	0
$302$	0	0
$303$	−38.2094	−2.19507
$304$	0	0
$305$	0	0
$306$	0	0
$307$	−2.04673	−0.116813	−0.0584064	−	0.998293i	$-0.518602\pi$
$307$	−2.04673	−0.116813	−0.0584064	+	0.998293i	$0.518602\pi$
$308$	0	0
$309$	−16.7016	−0.950119
$310$	0	0
$311$	4.17433	0.236705	0.118352	−	0.992972i	$-0.462239\pi$
$311$	4.17433	0.236705	0.118352	+	0.992972i	$0.462239\pi$
$312$	0	0
$313$	−7.99678	−0.452005	−0.226002	−	0.974127i	$-0.572566\pi$
$313$	−7.99678	−0.452005	−0.226002	+	0.974127i	$0.572566\pi$
$314$	0	0
$315$	0	0
$316$	0	0
$317$	−4.59688	−0.258186	−0.129093	−	0.991632i	$-0.541207\pi$
$317$	−4.59688	−0.258186	−0.129093	+	0.991632i	$0.541207\pi$
$318$	0	0
$319$	−31.5078	−1.76410
$320$	0	0
$321$	20.7099	1.15591
$322$	0	0
$323$	−10.8062	−0.601276
$324$	0	0
$325$	0	0
$326$	0	0
$327$	−27.7035	−1.53201
$328$	0	0
$329$	0	0
$330$	0	0
$331$	14.8062	0.813825	0.406913	−	0.913467i	$-0.366605\pi$
$331$	14.8062	0.813825	0.406913	+	0.913467i	$0.366605\pi$
$332$	0	0
$333$	27.4031	1.50168
$334$	0	0
$335$	0	0
$336$	0	0
$337$	27.4031	1.49274	0.746372	−	0.665529i	$-0.231794\pi$
$337$	27.4031	1.49274	0.746372	+	0.665529i	$0.231794\pi$
$338$	0	0
$339$	19.1647	1.04089
$340$	0	0
$341$	7.26464	0.393402
$342$	0	0
$343$	0	0
$344$	0	0
$345$	0	0
$346$	0	0
$347$	5.19375	0.278815	0.139408	−	0.990235i	$-0.455480\pi$
$347$	5.19375	0.278815	0.139408	+	0.990235i	$0.455480\pi$
$348$	0	0
$349$	11.6695	0.624656	0.312328	−	0.949974i	$-0.398891\pi$
$349$	11.6695	0.624656	0.312328	+	0.949974i	$0.398891\pi$
$350$	0	0
$351$	−4.70156	−0.250951
$352$	0	0
$353$	17.8906	0.952220	0.476110	−	0.879386i	$-0.342046\pi$
$353$	17.8906	0.952220	0.476110	+	0.879386i	$0.342046\pi$
$354$	0	0
$355$	0	0
$356$	0	0
$357$	0	0
$358$	0	0
$359$	5.19375	0.274116	0.137058	−	0.990563i	$-0.456235\pi$
$359$	5.19375	0.274116	0.137058	+	0.990563i	$0.456235\pi$
$360$	0	0
$361$	16.4031	0.863322
$362$	0	0
$363$	−28.7471	−1.50883
$364$	0	0
$365$	0	0
$366$	0	0
$367$	−8.53879	−0.445721	−0.222861	−	0.974850i	$-0.571539\pi$
$367$	−8.53879	−0.445721	−0.222861	+	0.974850i	$0.571539\pi$
$368$	0	0
$369$	−5.71949	−0.297745
$370$	0	0
$371$	0	0
$372$	0	0
$373$	−7.40312	−0.383319	−0.191660	−	0.981461i	$-0.561387\pi$
$373$	−7.40312	−0.383319	−0.191660	+	0.981461i	$0.561387\pi$
$374$	0	0
$375$	0	0
$376$	0	0
$377$	−17.3486	−0.893498
$378$	0	0
$379$	−13.6125	−0.699227	−0.349614	−	0.936894i	$-0.613687\pi$
$379$	−13.6125	−0.699227	−0.349614	+	0.936894i	$0.613687\pi$
$380$	0	0
$381$	−11.9001	−0.609661
$382$	0	0
$383$	32.6100	1.66629	0.833147	−	0.553052i	$-0.186537\pi$
$383$	32.6100	1.66629	0.833147	+	0.553052i	$0.186537\pi$
$384$	0	0
$385$	0	0
$386$	0	0
$387$	14.8062	0.752644
$388$	0	0
$389$	−8.10469	−0.410924	−0.205462	−	0.978665i	$-0.565870\pi$
$389$	−8.10469	−0.410924	−0.205462	+	0.978665i	$0.565870\pi$
$390$	0	0
$391$	13.4453	0.679956
$392$	0	0
$393$	7.40312	0.373438
$394$	0	0
$395$	0	0
$396$	0	0
$397$	−6.76307	−0.339429	−0.169714	−	0.985493i	$-0.554285\pi$
$397$	−6.76307	−0.339429	−0.169714	+	0.985493i	$0.554285\pi$
$398$	0	0
$399$	0	0
$400$	0	0
$401$	−12.7016	−0.634286	−0.317143	−	0.948378i	$-0.602723\pi$
$401$	−12.7016	−0.634286	−0.317143	+	0.948378i	$0.602723\pi$
$402$	0	0
$403$	4.00000	0.199254
$404$	0	0
$405$	0	0
$406$	0	0
$407$	34.8062	1.72528
$408$	0	0
$409$	−8.80980	−0.435616	−0.217808	−	0.975992i	$-0.569891\pi$
$409$	−8.80980	−0.435616	−0.217808	+	0.975992i	$0.569891\pi$
$410$	0	0
$411$	−51.7748	−2.55386
$412$	0	0
$413$	0	0
$414$	0	0
$415$	0	0
$416$	0	0
$417$	42.2094	2.06700
$418$	0	0
$419$	19.3953	0.947523	0.473761	−	0.880653i	$-0.342896\pi$
$419$	19.3953	0.947523	0.473761	+	0.880653i	$0.342896\pi$
$420$	0	0
$421$	9.50781	0.463382	0.231691	−	0.972789i	$-0.425574\pi$
$421$	9.50781	0.463382	0.231691	+	0.972789i	$0.425574\pi$
$422$	0	0
$423$	39.3326	1.91242
$424$	0	0
$425$	0	0
$426$	0	0
$427$	0	0
$428$	0	0
$429$	−31.5078	−1.52121
$430$	0	0
$431$	−22.1047	−1.06475	−0.532373	−	0.846510i	$-0.678699\pi$
$431$	−22.1047	−1.06475	−0.532373	+	0.846510i	$0.678699\pi$
$432$	0	0
$433$	−24.3422	−1.16981	−0.584906	−	0.811101i	$-0.698869\pi$
$433$	−24.3422	−1.16981	−0.584906	+	0.811101i	$0.698869\pi$
$434$	0	0
$435$	0	0
$436$	0	0
$437$	−44.0490	−2.10715
$438$	0	0
$439$	−11.4390	−0.545952	−0.272976	−	0.962021i	$-0.588008\pi$
$439$	−11.4390	−0.545952	−0.272976	+	0.962021i	$0.588008\pi$
$440$	0	0
$441$	0	0
$442$	0	0
$443$	40.4187	1.92035	0.960176	−	0.279395i	$-0.0901339\pi$
$443$	40.4187	1.92035	0.960176	+	0.279395i	$0.0901339\pi$
$444$	0	0
$445$	0	0
$446$	0	0
$447$	25.8874	1.22443
$448$	0	0
$449$	−11.8953	−0.561375	−0.280687	−	0.959799i	$-0.590562\pi$
$449$	−11.8953	−0.561375	−0.280687	+	0.959799i	$0.590562\pi$
$450$	0	0
$451$	−7.26464	−0.342079
$452$	0	0
$453$	32.8810	1.54488
$454$	0	0
$455$	0	0
$456$	0	0
$457$	14.2094	0.664686	0.332343	−	0.943159i	$-0.392161\pi$
$457$	14.2094	0.664686	0.332343	+	0.943159i	$0.392161\pi$
$458$	0	0
$459$	−3.29844	−0.153958
$460$	0	0
$461$	−16.3050	−0.759400	−0.379700	−	0.925110i	$-0.623973\pi$
$461$	−16.3050	−0.759400	−0.379700	+	0.925110i	$0.623973\pi$
$462$	0	0
$463$	5.19375	0.241374	0.120687	−	0.992691i	$-0.461490\pi$
$463$	5.19375	0.241374	0.120687	+	0.992691i	$0.461490\pi$
$464$	0	0
$465$	0	0
$466$	0	0
$467$	19.1243	0.884967	0.442484	−	0.896777i	$-0.354097\pi$
$467$	19.1243	0.884967	0.442484	+	0.896777i	$0.354097\pi$
$468$	0	0
$469$	0	0
$470$	0	0
$471$	10.0000	0.460776
$472$	0	0
$473$	18.8062	0.864712
$474$	0	0
$475$	0	0
$476$	0	0
$477$	42.2094	1.93263
$478$	0	0
$479$	−30.6037	−1.39832	−0.699160	−	0.714965i	$-0.746442\pi$
$479$	−30.6037	−1.39832	−0.699160	+	0.714965i	$0.746442\pi$
$480$	0	0
$481$	19.1647	0.873837
$482$	0	0
$483$	0	0
$484$	0	0
$485$	0	0
$486$	0	0
$487$	−2.20937	−0.100116	−0.0500581	−	0.998746i	$-0.515941\pi$
$487$	−2.20937	−0.100116	−0.0500581	+	0.998746i	$0.515941\pi$
$488$	0	0
$489$	38.3295	1.73332
$490$	0	0
$491$	0.492189	0.0222122	0.0111061	−	0.999938i	$-0.496465\pi$
$491$	0.492189	0.0222122	0.0111061	+	0.999938i	$0.496465\pi$
$492$	0	0
$493$	−12.1711	−0.548159
$494$	0	0
$495$	0	0
$496$	0	0
$497$	0	0
$498$	0	0
$499$	31.5078	1.41048	0.705242	−	0.708967i	$-0.250838\pi$
$499$	31.5078	1.41048	0.705242	+	0.708967i	$0.250838\pi$
$500$	0	0
$501$	10.1047	0.451444
$502$	0	0
$503$	5.44848	0.242936	0.121468	−	0.992595i	$-0.461240\pi$
$503$	5.44848	0.242936	0.121468	+	0.992595i	$0.461240\pi$
$504$	0	0
$505$	0	0
$506$	0	0
$507$	16.3050	0.724131
$508$	0	0
$509$	16.3050	0.722707	0.361353	−	0.932429i	$-0.382315\pi$
$509$	16.3050	0.722707	0.361353	+	0.932429i	$0.382315\pi$
$510$	0	0
$511$	0	0
$512$	0	0
$513$	10.8062	0.477108
$514$	0	0
$515$	0	0
$516$	0	0
$517$	49.9586	2.19718
$518$	0	0
$519$	60.3141	2.64749
$520$	0	0
$521$	−25.3454	−1.11040	−0.555200	−	0.831717i	$-0.687358\pi$
$521$	−25.3454	−1.11040	−0.555200	+	0.831717i	$0.687358\pi$
$522$	0	0
$523$	29.2891	1.28072	0.640362	−	0.768073i	$-0.278784\pi$
$523$	29.2891	1.28072	0.640362	+	0.768073i	$0.278784\pi$
$524$	0	0
$525$	0	0
$526$	0	0
$527$	2.80625	0.122242
$528$	0	0
$529$	31.8062	1.38288
$530$	0	0
$531$	48.9150	2.12273
$532$	0	0
$533$	−4.00000	−0.173259
$534$	0	0
$535$	0	0
$536$	0	0
$537$	−38.3295	−1.65404
$538$	0	0
$539$	0	0
$540$	0	0
$541$	−17.5078	−0.752720	−0.376360	−	0.926474i	$-0.622824\pi$
$541$	−17.5078	−0.752720	−0.376360	+	0.926474i	$0.622824\pi$
$542$	0	0
$543$	−11.4031	−0.489355
$544$	0	0
$545$	0	0
$546$	0	0
$547$	−9.61250	−0.411001	−0.205500	−	0.978657i	$-0.565882\pi$
$547$	−9.61250	−0.411001	−0.205500	+	0.978657i	$0.565882\pi$
$548$	0	0
$549$	−10.5855	−0.451779
$550$	0	0
$551$	39.8746	1.69872
$552$	0	0
$553$	0	0
$554$	0	0
$555$	0	0
$556$	0	0
$557$	12.5969	0.533747	0.266873	−	0.963732i	$-0.414009\pi$
$557$	12.5969	0.533747	0.266873	+	0.963732i	$0.414009\pi$
$558$	0	0
$559$	10.3550	0.437968
$560$	0	0
$561$	−22.1047	−0.933261
$562$	0	0
$563$	41.1892	1.73592	0.867960	−	0.496635i	$-0.165431\pi$
$563$	41.1892	1.73592	0.867960	+	0.496635i	$0.165431\pi$
$564$	0	0
$565$	0	0
$566$	0	0
$567$	0	0
$568$	0	0
$569$	−22.5969	−0.947310	−0.473655	−	0.880710i	$-0.657066\pi$
$569$	−22.5969	−0.947310	−0.473655	+	0.880710i	$0.657066\pi$
$570$	0	0
$571$	−29.6125	−1.23924	−0.619622	−	0.784900i	$-0.712714\pi$
$571$	−29.6125	−1.23924	−0.619622	+	0.784900i	$0.712714\pi$
$572$	0	0
$573$	−13.7163	−0.573005
$574$	0	0
$575$	0	0
$576$	0	0
$577$	30.7938	1.28196	0.640982	−	0.767556i	$-0.278527\pi$
$577$	30.7938	1.28196	0.640982	+	0.767556i	$0.278527\pi$
$578$	0	0
$579$	57.4942	2.38938
$580$	0	0
$581$	0	0
$582$	0	0
$583$	53.6125	2.22040
$584$	0	0
$585$	0	0
$586$	0	0
$587$	−35.4697	−1.46399	−0.731997	−	0.681308i	$-0.761411\pi$
$587$	−35.4697	−1.46399	−0.731997	+	0.681308i	$0.761411\pi$
$588$	0	0
$589$	−9.19375	−0.378822
$590$	0	0
$591$	36.7843	1.51311
$592$	0	0
$593$	−17.8906	−0.734679	−0.367339	−	0.930087i	$-0.619731\pi$
$593$	−17.8906	−0.734679	−0.367339	+	0.930087i	$0.619731\pi$
$594$	0	0
$595$	0	0
$596$	0	0
$597$	−22.8062	−0.933398
$598$	0	0
$599$	8.10469	0.331149	0.165574	−	0.986197i	$-0.447052\pi$
$599$	8.10469	0.331149	0.165574	+	0.986197i	$0.447052\pi$
$600$	0	0
$601$	−32.1489	−1.31138	−0.655690	−	0.755030i	$-0.727622\pi$
$601$	−32.1489	−1.31138	−0.655690	+	0.755030i	$0.727622\pi$
$602$	0	0
$603$	29.6125	1.20591
$604$	0	0
$605$	0	0
$606$	0	0
$607$	−18.3517	−0.744874	−0.372437	−	0.928058i	$-0.621478\pi$
$607$	−18.3517	−0.744874	−0.372437	+	0.928058i	$0.621478\pi$
$608$	0	0
$609$	0	0
$610$	0	0
$611$	27.5078	1.11285
$612$	0	0
$613$	3.40312	0.137451	0.0687254	−	0.997636i	$-0.478107\pi$
$613$	3.40312	0.137451	0.0687254	+	0.997636i	$0.478107\pi$
$614$	0	0
$615$	0	0
$616$	0	0
$617$	12.5969	0.507131	0.253566	−	0.967318i	$-0.418397\pi$
$617$	12.5969	0.507131	0.253566	+	0.967318i	$0.418397\pi$
$618$	0	0
$619$	2.85974	0.114943	0.0574714	−	0.998347i	$-0.481696\pi$
$619$	2.85974	0.114943	0.0574714	+	0.998347i	$0.481696\pi$
$620$	0	0
$621$	−13.4453	−0.539540
$622$	0	0
$623$	0	0
$624$	0	0
$625$	0	0
$626$	0	0
$627$	72.4187	2.89213
$628$	0	0
$629$	13.4453	0.536098
$630$	0	0
$631$	−29.5078	−1.17469	−0.587344	−	0.809338i	$-0.699826\pi$
$631$	−29.5078	−1.17469	−0.587344	+	0.809338i	$0.699826\pi$
$632$	0	0
$633$	−18.8937	−0.750959
$634$	0	0
$635$	0	0
$636$	0	0
$637$	0	0
$638$	0	0
$639$	27.4031	1.08405
$640$	0	0
$641$	−17.4031	−0.687382	−0.343691	−	0.939083i	$-0.611677\pi$
$641$	−17.4031	−0.687382	−0.343691	+	0.939083i	$0.611677\pi$
$642$	0	0
$643$	17.0371	0.671879	0.335940	−	0.941884i	$-0.390946\pi$
$643$	17.0371	0.671879	0.335940	+	0.941884i	$0.390946\pi$
$644$	0	0
$645$	0	0
$646$	0	0
$647$	−35.7003	−1.40352	−0.701762	−	0.712411i	$-0.747603\pi$
$647$	−35.7003	−1.40352	−0.701762	+	0.712411i	$0.747603\pi$
$648$	0	0
$649$	62.1297	2.43880
$650$	0	0
$651$	0	0
$652$	0	0
$653$	−8.59688	−0.336422	−0.168211	−	0.985751i	$-0.553799\pi$
$653$	−8.59688	−0.336422	−0.168211	+	0.985751i	$0.553799\pi$
$654$	0	0
$655$	0	0
$656$	0	0
$657$	−46.0553	−1.79679
$658$	0	0
$659$	21.8953	0.852920	0.426460	−	0.904506i	$-0.359760\pi$
$659$	21.8953	0.852920	0.426460	+	0.904506i	$0.359760\pi$
$660$	0	0
$661$	−22.0245	−0.856653	−0.428327	−	0.903624i	$-0.640897\pi$
$661$	−22.0245	−0.856653	−0.428327	+	0.903624i	$0.640897\pi$
$662$	0	0
$663$	−12.1711	−0.472687
$664$	0	0
$665$	0	0
$666$	0	0
$667$	−49.6125	−1.92100
$668$	0	0
$669$	48.9109	1.89101
$670$	0	0
$671$	−13.4453	−0.519048
$672$	0	0
$673$	−9.61250	−0.370535	−0.185267	−	0.982688i	$-0.559315\pi$
$673$	−9.61250	−0.370535	−0.185267	+	0.982688i	$0.559315\pi$
$674$	0	0
$675$	0	0
$676$	0	0
$677$	36.2828	1.39446	0.697230	−	0.716848i	$-0.254416\pi$
$677$	36.2828	1.39446	0.697230	+	0.716848i	$0.254416\pi$
$678$	0	0
$679$	0	0
$680$	0	0
$681$	17.5078	0.670901
$682$	0	0
$683$	34.8062	1.33182	0.665912	−	0.746030i	$-0.268043\pi$
$683$	34.8062	1.33182	0.665912	+	0.746030i	$0.268043\pi$
$684$	0	0
$685$	0	0
$686$	0	0
$687$	−15.4031	−0.587666
$688$	0	0
$689$	29.5197	1.12461
$690$	0	0
$691$	10.5855	0.402692	0.201346	−	0.979520i	$-0.435468\pi$
$691$	10.5855	0.402692	0.201346	+	0.979520i	$0.435468\pi$
$692$	0	0
$693$	0	0
$694$	0	0
$695$	0	0
$696$	0	0
$697$	−2.80625	−0.106294
$698$	0	0
$699$	0	0
$700$	0	0
$701$	−44.3141	−1.67372	−0.836859	−	0.547418i	$-0.815611\pi$
$701$	−44.3141	−1.67372	−0.836859	+	0.547418i	$0.815611\pi$
$702$	0	0
$703$	−44.0490	−1.66134
$704$	0	0
$705$	0	0
$706$	0	0
$707$	0	0
$708$	0	0
$709$	−15.8953	−0.596961	−0.298481	−	0.954416i	$-0.596480\pi$
$709$	−15.8953	−0.596961	−0.298481	+	0.954416i	$0.596480\pi$
$710$	0	0
$711$	−30.0000	−1.12509
$712$	0	0
$713$	11.4390	0.428393
$714$	0	0
$715$	0	0
$716$	0	0
$717$	−8.53879	−0.318887
$718$	0	0
$719$	19.1647	0.714724	0.357362	−	0.933966i	$-0.383676\pi$
$719$	19.1647	0.714724	0.357362	+	0.933966i	$0.383676\pi$
$720$	0	0
$721$	0	0
$722$	0	0
$723$	−49.6125	−1.84511
$724$	0	0
$725$	0	0
$726$	0	0
$727$	5.71949	0.212124	0.106062	−	0.994360i	$-0.466176\pi$
$727$	5.71949	0.212124	0.106062	+	0.994360i	$0.466176\pi$
$728$	0	0
$729$	−37.8062	−1.40023
$730$	0	0
$731$	7.26464	0.268692
$732$	0	0
$733$	−10.8565	−0.400995	−0.200497	−	0.979694i	$-0.564256\pi$
$733$	−10.8565	−0.400995	−0.200497	+	0.979694i	$0.564256\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	37.6125	1.38547
$738$	0	0
$739$	11.5078	0.423322	0.211661	−	0.977343i	$-0.432113\pi$
$739$	11.5078	0.423322	0.211661	+	0.977343i	$0.432113\pi$
$740$	0	0
$741$	39.8746	1.46483
$742$	0	0
$743$	3.40312	0.124849	0.0624243	−	0.998050i	$-0.480117\pi$
$743$	3.40312	0.124849	0.0624243	+	0.998050i	$0.480117\pi$
$744$	0	0
$745$	0	0
$746$	0	0
$747$	10.5855	0.387304
$748$	0	0
$749$	0	0
$750$	0	0
$751$	−7.50781	−0.273964	−0.136982	−	0.990574i	$-0.543740\pi$
$751$	−7.50781	−0.273964	−0.136982	+	0.990574i	$0.543740\pi$
$752$	0	0
$753$	42.2094	1.53820
$754$	0	0
$755$	0	0
$756$	0	0
$757$	27.4031	0.995983	0.497992	−	0.867182i	$-0.334071\pi$
$757$	27.4031	0.995983	0.497992	+	0.867182i	$0.334071\pi$
$758$	0	0
$759$	−90.1042	−3.27058
$760$	0	0
$761$	46.0553	1.66950	0.834751	−	0.550628i	$-0.185612\pi$
$761$	46.0553	1.66950	0.834751	+	0.550628i	$0.185612\pi$
$762$	0	0
$763$	0	0
$764$	0	0
$765$	0	0
$766$	0	0
$767$	34.2094	1.23523
$768$	0	0
$769$	47.1393	1.69989	0.849943	−	0.526875i	$-0.176636\pi$
$769$	47.1393	1.69989	0.849943	+	0.526875i	$0.176636\pi$
$770$	0	0
$771$	67.0156	2.41351
$772$	0	0
$773$	15.5729	0.560117	0.280059	−	0.959983i	$-0.409646\pi$
$773$	15.5729	0.560117	0.280059	+	0.959983i	$0.409646\pi$
$774$	0	0
$775$	0	0
$776$	0	0
$777$	0	0
$778$	0	0
$779$	9.19375	0.329400
$780$	0	0
$781$	34.8062	1.24547
$782$	0	0
$783$	12.1711	0.434960
$784$	0	0
$785$	0	0
$786$	0	0
$787$	23.8406	0.849827	0.424914	−	0.905234i	$-0.360304\pi$
$787$	23.8406	0.849827	0.424914	+	0.905234i	$0.360304\pi$
$788$	0	0
$789$	−41.4198	−1.47458
$790$	0	0
$791$	0	0
$792$	0	0
$793$	−7.40312	−0.262893
$794$	0	0
$795$	0	0
$796$	0	0
$797$	25.8469	0.915545	0.457773	−	0.889069i	$-0.348647\pi$
$797$	25.8469	0.915545	0.457773	+	0.889069i	$0.348647\pi$
$798$	0	0
$799$	19.2984	0.682730
$800$	0	0
$801$	−49.7685	−1.75848
$802$	0	0
$803$	−58.4974	−2.06433
$804$	0	0
$805$	0	0
$806$	0	0
$807$	−27.4031	−0.964636
$808$	0	0
$809$	−15.5078	−0.545226	−0.272613	−	0.962124i	$-0.587888\pi$
$809$	−15.5078	−0.545226	−0.272613	+	0.962124i	$0.587888\pi$
$810$	0	0
$811$	33.4635	1.17506	0.587531	−	0.809202i	$-0.300100\pi$
$811$	33.4635	1.17506	0.587531	+	0.809202i	$0.300100\pi$
$812$	0	0
$813$	−64.4187	−2.25926
$814$	0	0
$815$	0	0
$816$	0	0
$817$	−23.8002	−0.832664
$818$	0	0
$819$	0	0
$820$	0	0
$821$	12.3141	0.429764	0.214882	−	0.976640i	$-0.431063\pi$
$821$	12.3141	0.429764	0.214882	+	0.976640i	$0.431063\pi$
$822$	0	0
$823$	10.8062	0.376682	0.188341	−	0.982104i	$-0.439689\pi$
$823$	10.8062	0.376682	0.188341	+	0.982104i	$0.439689\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	−14.8062	−0.514864	−0.257432	−	0.966296i	$-0.582876\pi$
$827$	−14.8062	−0.514864	−0.257432	+	0.966296i	$0.582876\pi$
$828$	0	0
$829$	−32.8406	−1.14060	−0.570300	−	0.821436i	$-0.693173\pi$
$829$	−32.8406	−1.14060	−0.570300	+	0.821436i	$0.693173\pi$
$830$	0	0
$831$	−32.6100	−1.13123
$832$	0	0
$833$	0	0
$834$	0	0
$835$	0	0
$836$	0	0
$837$	−2.80625	−0.0969981
$838$	0	0
$839$	46.0553	1.59000	0.795002	−	0.606607i	$-0.207470\pi$
$839$	46.0553	1.59000	0.795002	+	0.606607i	$0.207470\pi$
$840$	0	0
$841$	15.9109	0.548653
$842$	0	0
$843$	−69.6653	−2.39940
$844$	0	0
$845$	0	0
$846$	0	0
$847$	0	0
$848$	0	0
$849$	−21.5078	−0.738146
$850$	0	0
$851$	54.8062	1.87873
$852$	0	0
$853$	9.58237	0.328094	0.164047	−	0.986453i	$-0.447545\pi$
$853$	9.58237	0.328094	0.164047	+	0.986453i	$0.447545\pi$
$854$	0	0
$855$	0	0
$856$	0	0
$857$	20.1679	0.688922	0.344461	−	0.938801i	$-0.388062\pi$
$857$	20.1679	0.688922	0.344461	+	0.938801i	$0.388062\pi$
$858$	0	0
$859$	27.7440	0.946612	0.473306	−	0.880898i	$-0.343060\pi$
$859$	27.7440	0.946612	0.473306	+	0.880898i	$0.343060\pi$
$860$	0	0
$861$	0	0
$862$	0	0
$863$	−48.4187	−1.64819	−0.824097	−	0.566449i	$-0.808317\pi$
$863$	−48.4187	−1.64819	−0.824097	+	0.566449i	$0.808317\pi$
$864$	0	0
$865$	0	0
$866$	0	0
$867$	35.4697	1.20462
$868$	0	0
$869$	−38.1047	−1.29261
$870$	0	0
$871$	20.7099	0.701728
$872$	0	0
$873$	−31.6069	−1.06973
$874$	0	0
$875$	0	0
$876$	0	0
$877$	−29.0156	−0.979788	−0.489894	−	0.871782i	$-0.662965\pi$
$877$	−29.0156	−0.979788	−0.489894	+	0.871782i	$0.662965\pi$
$878$	0	0
$879$	−77.7172	−2.62134
$880$	0	0
$881$	11.4390	0.385389	0.192694	−	0.981259i	$-0.438277\pi$
$881$	11.4390	0.385389	0.192694	+	0.981259i	$0.438277\pi$
$882$	0	0
$883$	34.8062	1.17132	0.585662	−	0.810556i	$-0.300835\pi$
$883$	34.8062	1.17132	0.585662	+	0.810556i	$0.300835\pi$
$884$	0	0
$885$	0	0
$886$	0	0
$887$	44.0490	1.47902	0.739510	−	0.673146i	$-0.235057\pi$
$887$	44.0490	1.47902	0.739510	+	0.673146i	$0.235057\pi$
$888$	0	0
$889$	0	0
$890$	0	0
$891$	−30.1047	−1.00854
$892$	0	0
$893$	−63.2250	−2.11574
$894$	0	0
$895$	0	0
$896$	0	0
$897$	−49.6125	−1.65651
$898$	0	0
$899$	−10.3550	−0.345357
$900$	0	0
$901$	20.7099	0.689947
$902$	0	0
$903$	0	0
$904$	0	0
$905$	0	0
$906$	0	0
$907$	−34.8062	−1.15572	−0.577861	−	0.816135i	$-0.696113\pi$
$907$	−34.8062	−1.15572	−0.577861	+	0.816135i	$0.696113\pi$
$908$	0	0
$909$	54.6345	1.81211
$910$	0	0
$911$	−5.19375	−0.172077	−0.0860383	−	0.996292i	$-0.527421\pi$
$911$	−5.19375	−0.172077	−0.0860383	+	0.996292i	$0.527421\pi$
$912$	0	0
$913$	13.4453	0.444973
$914$	0	0
$915$	0	0
$916$	0	0
$917$	0	0
$918$	0	0
$919$	−2.91093	−0.0960229	−0.0480114	−	0.998847i	$-0.515288\pi$
$919$	−2.91093	−0.0960229	−0.0480114	+	0.998847i	$0.515288\pi$
$920$	0	0
$921$	5.29844	0.174589
$922$	0	0
$923$	19.1647	0.630815
$924$	0	0
$925$	0	0
$926$	0	0
$927$	23.8811	0.784358
$928$	0	0
$929$	−8.80980	−0.289040	−0.144520	−	0.989502i	$-0.546164\pi$
$929$	−8.80980	−0.289040	−0.144520	+	0.989502i	$0.546164\pi$
$930$	0	0
$931$	0	0
$932$	0	0
$933$	−10.8062	−0.353781
$934$	0	0
$935$	0	0
$936$	0	0
$937$	−25.6972	−0.839493	−0.419746	−	0.907641i	$-0.637881\pi$
$937$	−25.6972	−0.839493	−0.419746	+	0.907641i	$0.637881\pi$
$938$	0	0
$939$	20.7016	0.675570
$940$	0	0
$941$	29.7503	0.969831	0.484915	−	0.874561i	$-0.338850\pi$
$941$	29.7503	0.969831	0.484915	+	0.874561i	$0.338850\pi$
$942$	0	0
$943$	−11.4390	−0.372504
$944$	0	0
$945$	0	0
$946$	0	0
$947$	−2.80625	−0.0911908	−0.0455954	−	0.998960i	$-0.514519\pi$
$947$	−2.80625	−0.0911908	−0.0455954	+	0.998960i	$0.514519\pi$
$948$	0	0
$949$	−32.2094	−1.04556
$950$	0	0
$951$	11.9001	0.385887
$952$	0	0
$953$	25.6125	0.829670	0.414835	−	0.909897i	$-0.363839\pi$
$953$	25.6125	0.829670	0.414835	+	0.909897i	$0.363839\pi$
$954$	0	0
$955$	0	0
$956$	0	0
$957$	81.5655	2.63664
$958$	0	0
$959$	0	0
$960$	0	0
$961$	−28.6125	−0.922984
$962$	0	0
$963$	−29.6125	−0.954249
$964$	0	0
$965$	0	0
$966$	0	0
$967$	34.2094	1.10010	0.550050	−	0.835132i	$-0.314609\pi$
$967$	34.2094	1.10010	0.550050	+	0.835132i	$0.314609\pi$
$968$	0	0
$969$	27.9745	0.898672
$970$	0	0
$971$	−2.39861	−0.0769751	−0.0384875	−	0.999259i	$-0.512254\pi$
$971$	−2.39861	−0.0769751	−0.0384875	+	0.999259i	$0.512254\pi$
$972$	0	0
$973$	0	0
$974$	0	0
$975$	0	0
$976$	0	0
$977$	−12.0000	−0.383914	−0.191957	−	0.981403i	$-0.561483\pi$
$977$	−12.0000	−0.383914	−0.191957	+	0.981403i	$0.561483\pi$
$978$	0	0
$979$	−63.2137	−2.02032
$980$	0	0
$981$	39.6125	1.26473
$982$	0	0
$983$	−4.44534	−0.141784	−0.0708921	−	0.997484i	$-0.522585\pi$
$983$	−4.44534	−0.141784	−0.0708921	+	0.997484i	$0.522585\pi$
$984$	0	0
$985$	0	0
$986$	0	0
$987$	0	0
$988$	0	0
$989$	29.6125	0.941623
$990$	0	0
$991$	−9.79063	−0.311010	−0.155505	−	0.987835i	$-0.549700\pi$
$991$	−9.79063	−0.311010	−0.155505	+	0.987835i	$0.549700\pi$
$992$	0	0
$993$	−38.3295	−1.21635
$994$	0	0
$995$	0	0
$996$	0	0
$997$	56.4507	1.78781	0.893905	−	0.448256i	$-0.147955\pi$
$997$	56.4507	1.78781	0.893905	+	0.448256i	$0.147955\pi$
$998$	0	0
$999$	−13.4453	−0.425389

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9800.2.a.cp.1.1		4
5.2	odd	4		1960.2.g.d.1569.7	yes	8
5.3	odd	4		1960.2.g.d.1569.1	✓	8
5.4	even	2		9800.2.a.co.1.4		4
7.6	odd	2	inner	9800.2.a.cp.1.4		4
35.13	even	4		1960.2.g.d.1569.8	yes	8
35.27	even	4		1960.2.g.d.1569.2	yes	8
35.34	odd	2		9800.2.a.co.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1960.2.g.d.1569.1	✓	8	5.3	odd	4
1960.2.g.d.1569.2	yes	8	35.27	even	4
1960.2.g.d.1569.7	yes	8	5.2	odd	4
1960.2.g.d.1569.8	yes	8	35.13	even	4
9800.2.a.co.1.1		4	35.34	odd	2
9800.2.a.co.1.4		4	5.4	even	2
9800.2.a.cp.1.1		4	1.1	even	1	trivial
9800.2.a.cp.1.4		4	7.6	odd	2	inner

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:	\( N \)	\(=\)	\( 9800 = 2^{3} \cdot 5^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9800.a (trivial)

\(f(q)\)	\(=\)	\(q-2.58874 q^{3} +3.70156 q^{9} +O(q^{10})\)	\(q-2.58874 q^{3} +3.70156 q^{9} +4.70156 q^{11} +2.58874 q^{13} +1.81616 q^{17} -5.95005 q^{19} +7.40312 q^{23} -1.81616 q^{27} -6.70156 q^{29} +1.54515 q^{31} -12.1711 q^{33} +7.40312 q^{37} -6.70156 q^{39} -1.54515 q^{41} +4.00000 q^{43} +10.6260 q^{47} -4.70156 q^{51} +11.4031 q^{53} +15.4031 q^{57} +13.2147 q^{59} -2.85974 q^{61} +8.00000 q^{67} -19.1647 q^{69} +7.40312 q^{71} -12.4421 q^{73} -8.10469 q^{79} -6.40312 q^{81} +2.85974 q^{83} +17.3486 q^{87} -13.4453 q^{89} -4.00000 q^{93} -8.53879 q^{97} +17.4031 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{9}+O(q^{10}) \) 4 * q + 2 * q^9	\( 4 q + 2 q^{9} + 6 q^{11} + 4 q^{23} - 14 q^{29} + 4 q^{37} - 14 q^{39} + 16 q^{43} - 6 q^{51} + 20 q^{53} + 36 q^{57} + 32 q^{67} + 4 q^{71} + 6 q^{79} - 16 q^{93} + 44 q^{99}+O(q^{100}) \) 4 * q + 2 * q^9 + 6 * q^11 + 4 * q^23 - 14 * q^29 + 4 * q^37 - 14 * q^39 + 16 * q^43 - 6 * q^51 + 20 * q^53 + 36 * q^57 + 32 * q^67 + 4 * q^71 + 6 * q^79 - 16 * q^93 + 44 * q^99

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