LMFDB - Embedded newform 9680.2.a.cn.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9680,2,Mod(1,9680)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9680, 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("9680.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 9680 = 2^{4} \cdot 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	9680.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:	$77.2951891566$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.4.725.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 3x^{2} + x + 1 $ x^4 - x^3 - 3*x^2 + x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 55)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$0.737640$ of defining polynomial
Character	$\chi$	$=$	9680.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.575493 q^{3} -1.00000 q^{5} +3.64941 q^{7} -2.66881 q^{9} +O(q^{10})$	$q-0.575493 q^{3} -1.00000 q^{5} +3.64941 q^{7} -2.66881 q^{9} -2.83095 q^{13} +0.575493 q^{15} +3.69195 q^{17} +0.0951243 q^{19} -2.10021 q^{21} -1.16215 q^{23} +1.00000 q^{25} +3.26236 q^{27} -6.75389 q^{29} -6.77837 q^{31} -3.64941 q^{35} +9.83980 q^{37} +1.62920 q^{39} -8.31822 q^{41} +2.96862 q^{43} +2.66881 q^{45} +2.22491 q^{47} +6.31822 q^{49} -2.12469 q^{51} +2.99393 q^{53} -0.0547434 q^{57} +8.50860 q^{59} -8.48037 q^{61} -9.73958 q^{63} +2.83095 q^{65} +13.4153 q^{67} +0.668808 q^{69} -8.30309 q^{71} -1.32003 q^{73} -0.575493 q^{75} +13.8661 q^{79} +6.12896 q^{81} +10.6445 q^{83} -3.69195 q^{85} +3.88682 q^{87} -12.1612 q^{89} -10.3313 q^{91} +3.90091 q^{93} -0.0951243 q^{95} -4.33133 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{5} + 3 q^{7}+O(q^{10}) $ 4 * q - 4 * q^5 + 3 * q^7	$ 4 q - 4 q^{5} + 3 q^{7} - q^{13} + q^{17} + 20 q^{19} - 10 q^{21} - 5 q^{23} + 4 q^{25} + 15 q^{27} - 12 q^{29} + 5 q^{31} - 3 q^{35} + 7 q^{37} + 7 q^{39} - 11 q^{41} + 19 q^{43} - 5 q^{47} + 3 q^{49} + 7 q^{51} - 11 q^{53} + 5 q^{57} - 9 q^{59} - 12 q^{61} - 5 q^{63} + q^{65} + 19 q^{67} - 8 q^{69} - 5 q^{71} - 11 q^{73} + 34 q^{79} + 4 q^{81} - 11 q^{83} - q^{85} - 19 q^{87} - 8 q^{89} + 8 q^{91} - 5 q^{93} - 20 q^{95} + 32 q^{97}+O(q^{100}) $ 4 * q - 4 * q^5 + 3 * q^7 - q^13 + q^17 + 20 * q^19 - 10 * q^21 - 5 * q^23 + 4 * q^25 + 15 * q^27 - 12 * q^29 + 5 * q^31 - 3 * q^35 + 7 * q^37 + 7 * q^39 - 11 * q^41 + 19 * q^43 - 5 * q^47 + 3 * q^49 + 7 * q^51 - 11 * q^53 + 5 * q^57 - 9 * q^59 - 12 * q^61 - 5 * q^63 + q^65 + 19 * q^67 - 8 * q^69 - 5 * q^71 - 11 * q^73 + 34 * q^79 + 4 * q^81 - 11 * q^83 - q^85 - 19 * q^87 - 8 * q^89 + 8 * q^91 - 5 * q^93 - 20 * q^95 + 32 * q^97

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
$3$	−0.575493	−0.332261	−0.166131	−	0.986104i	$-0.553127\pi$
$3$	−0.575493	−0.332261	−0.166131	+	0.986104i	$0.553127\pi$
$4$	0	0
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	0	0
$7$	3.64941	1.37935	0.689674	−	0.724120i	$-0.257754\pi$
$7$	3.64941	1.37935	0.689674	+	0.724120i	$0.257754\pi$
$8$	0	0
$9$	−2.66881	−0.889603
$10$	0	0
$11$	0	0
$11$	0	0
$12$	0	0
$13$	−2.83095	−0.785166	−0.392583	−	0.919717i	$-0.628418\pi$
$13$	−2.83095	−0.785166	−0.392583	+	0.919717i	$0.628418\pi$
$14$	0	0
$15$	0.575493	0.148592
$16$	0	0
$17$	3.69195	0.895431	0.447715	−	0.894176i	$-0.352238\pi$
$17$	3.69195	0.895431	0.447715	+	0.894176i	$0.352238\pi$
$18$	0	0
$19$	0.0951243	0.0218230	0.0109115	−	0.999940i	$-0.496527\pi$
$19$	0.0951243	0.0218230	0.0109115	+	0.999940i	$0.496527\pi$
$20$	0	0
$21$	−2.10021	−0.458304
$22$	0	0
$23$	−1.16215	−0.242324	−0.121162	−	0.992633i	$-0.538662\pi$
$23$	−1.16215	−0.242324	−0.121162	+	0.992633i	$0.538662\pi$
$24$	0	0
$25$	1.00000	0.200000
$26$	0	0
$27$	3.26236	0.627841
$28$	0	0
$29$	−6.75389	−1.25417	−0.627083	−	0.778953i	$-0.715751\pi$
$29$	−6.75389	−1.25417	−0.627083	+	0.778953i	$0.715751\pi$
$30$	0	0
$31$	−6.77837	−1.21743	−0.608716	−	0.793388i	$-0.708315\pi$
$31$	−6.77837	−1.21743	−0.608716	+	0.793388i	$0.708315\pi$
$32$	0	0
$33$	0	0
$34$	0	0
$35$	−3.64941	−0.616864
$36$	0	0
$37$	9.83980	1.61765	0.808826	−	0.588048i	$-0.200103\pi$
$37$	9.83980	1.61765	0.808826	+	0.588048i	$0.200103\pi$
$38$	0	0
$39$	1.62920	0.260880
$40$	0	0
$41$	−8.31822	−1.29909	−0.649544	−	0.760324i	$-0.725040\pi$
$41$	−8.31822	−1.29909	−0.649544	+	0.760324i	$0.725040\pi$
$42$	0	0
$43$	2.96862	0.452710	0.226355	−	0.974045i	$-0.427319\pi$
$43$	2.96862	0.452710	0.226355	+	0.974045i	$0.427319\pi$
$44$	0	0
$45$	2.66881	0.397842
$46$	0	0
$47$	2.22491	0.324536	0.162268	−	0.986747i	$-0.448119\pi$
$47$	2.22491	0.324536	0.162268	+	0.986747i	$0.448119\pi$
$48$	0	0
$49$	6.31822	0.902603
$50$	0	0
$51$	−2.12469	−0.297517
$52$	0	0
$53$	2.99393	0.411248	0.205624	−	0.978631i	$-0.434078\pi$
$53$	2.99393	0.411248	0.205624	+	0.978631i	$0.434078\pi$
$54$	0	0
$55$	0	0
$56$	0	0
$57$	−0.0547434	−0.00725094
$58$	0	0
$59$	8.50860	1.10773	0.553863	−	0.832608i	$-0.313153\pi$
$59$	8.50860	1.10773	0.553863	+	0.832608i	$0.313153\pi$
$60$	0	0
$61$	−8.48037	−1.08580	−0.542900	−	0.839797i	$-0.682674\pi$
$61$	−8.48037	−1.08580	−0.542900	+	0.839797i	$0.682674\pi$
$62$	0	0
$63$	−9.73958	−1.22707
$64$	0	0
$65$	2.83095	0.351137
$66$	0	0
$67$	13.4153	1.63894	0.819469	−	0.573123i	$-0.194268\pi$
$67$	13.4153	1.63894	0.819469	+	0.573123i	$0.194268\pi$
$68$	0	0
$69$	0.668808	0.0805150
$70$	0	0
$71$	−8.30309	−0.985396	−0.492698	−	0.870200i	$-0.663989\pi$
$71$	−8.30309	−0.985396	−0.492698	+	0.870200i	$0.663989\pi$
$72$	0	0
$73$	−1.32003	−0.154498	−0.0772490	−	0.997012i	$-0.524614\pi$
$73$	−1.32003	−0.154498	−0.0772490	+	0.997012i	$0.524614\pi$
$74$	0	0
$75$	−0.575493	−0.0664522
$76$	0	0
$77$	0	0
$78$	0	0
$79$	13.8661	1.56006	0.780028	−	0.625744i	$-0.215205\pi$
$79$	13.8661	1.56006	0.780028	+	0.625744i	$0.215205\pi$
$80$	0	0
$81$	6.12896	0.680995
$82$	0	0
$83$	10.6445	1.16838	0.584191	−	0.811616i	$-0.301412\pi$
$83$	10.6445	1.16838	0.584191	+	0.811616i	$0.301412\pi$
$84$	0	0
$85$	−3.69195	−0.400449
$86$	0	0
$87$	3.88682	0.416710
$88$	0	0
$89$	−12.1612	−1.28908	−0.644540	−	0.764570i	$-0.722951\pi$
$89$	−12.1612	−1.28908	−0.644540	+	0.764570i	$0.722951\pi$
$90$	0	0
$91$	−10.3313	−1.08302
$92$	0	0
$93$	3.90091	0.404505
$94$	0	0
$95$	−0.0951243	−0.00975955
$96$	0	0
$97$	−4.33133	−0.439780	−0.219890	−	0.975525i	$-0.570570\pi$
$97$	−4.33133	−0.439780	−0.219890	+	0.975525i	$0.570570\pi$
$98$	0	0
$99$	0	0
$100$	0	0
$101$	9.90570	0.985654	0.492827	−	0.870127i	$-0.335964\pi$
$101$	9.90570	0.985654	0.492827	+	0.870127i	$0.335964\pi$
$102$	0	0
$103$	−4.06590	−0.400625	−0.200313	−	0.979732i	$-0.564196\pi$
$103$	−4.06590	−0.400625	−0.200313	+	0.979732i	$0.564196\pi$
$104$	0	0
$105$	2.10021	0.204960
$106$	0	0
$107$	−1.93858	−0.187409	−0.0937046	−	0.995600i	$-0.529871\pi$
$107$	−1.93858	−0.187409	−0.0937046	+	0.995600i	$0.529871\pi$
$108$	0	0
$109$	6.12664	0.586825	0.293413	−	0.955986i	$-0.405209\pi$
$109$	6.12664	0.586825	0.293413	+	0.955986i	$0.405209\pi$
$110$	0	0
$111$	−5.66273	−0.537483
$112$	0	0
$113$	5.78527	0.544232	0.272116	−	0.962264i	$-0.412276\pi$
$113$	5.78527	0.544232	0.272116	+	0.962264i	$0.412276\pi$
$114$	0	0
$115$	1.16215	0.108371
$116$	0	0
$117$	7.55527	0.698485
$118$	0	0
$119$	13.4735	1.23511
$120$	0	0
$121$	0	0
$122$	0	0
$123$	4.78708	0.431636
$124$	0	0
$125$	−1.00000	−0.0894427
$126$	0	0
$127$	−2.43783	−0.216322	−0.108161	−	0.994133i	$-0.534496\pi$
$127$	−2.43783	−0.216322	−0.108161	+	0.994133i	$0.534496\pi$
$128$	0	0
$129$	−1.70842	−0.150418
$130$	0	0
$131$	−7.04156	−0.615224	−0.307612	−	0.951512i	$-0.599530\pi$
$131$	−7.04156	−0.615224	−0.307612	+	0.951512i	$0.599530\pi$
$132$	0	0
$133$	0.347148	0.0301016
$134$	0	0
$135$	−3.26236	−0.280779
$136$	0	0
$137$	−9.57286	−0.817864	−0.408932	−	0.912565i	$-0.634099\pi$
$137$	−9.57286	−0.817864	−0.408932	+	0.912565i	$0.634099\pi$
$138$	0	0
$139$	−0.515502	−0.0437243	−0.0218621	−	0.999761i	$-0.506959\pi$
$139$	−0.515502	−0.0437243	−0.0218621	+	0.999761i	$0.506959\pi$
$140$	0	0
$141$	−1.28042	−0.107831
$142$	0	0
$143$	0	0
$144$	0	0
$145$	6.75389	0.560880
$146$	0	0
$147$	−3.63609	−0.299900
$148$	0	0
$149$	−8.15983	−0.668479	−0.334240	−	0.942488i	$-0.608479\pi$
$149$	−8.15983	−0.668479	−0.334240	+	0.942488i	$0.608479\pi$
$150$	0	0
$151$	−1.94023	−0.157893	−0.0789466	−	0.996879i	$-0.525156\pi$
$151$	−1.94023	−0.157893	−0.0789466	+	0.996879i	$0.525156\pi$
$152$	0	0
$153$	−9.85312	−0.796577
$154$	0	0
$155$	6.77837	0.544452
$156$	0	0
$157$	21.2745	1.69789	0.848944	−	0.528483i	$-0.177239\pi$
$157$	21.2745	1.69789	0.848944	+	0.528483i	$0.177239\pi$
$158$	0	0
$159$	−1.72298	−0.136642
$160$	0	0
$161$	−4.24116	−0.334250
$162$	0	0
$163$	15.9810	1.25173	0.625863	−	0.779933i	$-0.284747\pi$
$163$	15.9810	1.25173	0.625863	+	0.779933i	$0.284747\pi$
$164$	0	0
$165$	0	0
$166$	0	0
$167$	−17.7090	−1.37037	−0.685183	−	0.728371i	$-0.740278\pi$
$167$	−17.7090	−1.37037	−0.685183	+	0.728371i	$0.740278\pi$
$168$	0	0
$169$	−4.98569	−0.383515
$170$	0	0
$171$	−0.253869	−0.0194138
$172$	0	0
$173$	15.8855	1.20775	0.603875	−	0.797079i	$-0.293622\pi$
$173$	15.8855	1.20775	0.603875	+	0.797079i	$0.293622\pi$
$174$	0	0
$175$	3.64941	0.275870
$176$	0	0
$177$	−4.89664	−0.368054
$178$	0	0
$179$	16.8810	1.26175	0.630874	−	0.775885i	$-0.282696\pi$
$179$	16.8810	1.26175	0.630874	+	0.775885i	$0.282696\pi$
$180$	0	0
$181$	−24.0874	−1.79040	−0.895200	−	0.445664i	$-0.852968\pi$
$181$	−24.0874	−1.79040	−0.895200	+	0.445664i	$0.852968\pi$
$182$	0	0
$183$	4.88039	0.360769
$184$	0	0
$185$	−9.83980	−0.723436
$186$	0	0
$187$	0	0
$188$	0	0
$189$	11.9057	0.866012
$190$	0	0
$191$	−5.38279	−0.389485	−0.194743	−	0.980854i	$-0.562387\pi$
$191$	−5.38279	−0.389485	−0.194743	+	0.980854i	$0.562387\pi$
$192$	0	0
$193$	18.2840	1.31611	0.658057	−	0.752968i	$-0.271378\pi$
$193$	18.2840	1.31611	0.658057	+	0.752968i	$0.271378\pi$
$194$	0	0
$195$	−1.62920	−0.116669
$196$	0	0
$197$	2.64566	0.188496	0.0942478	−	0.995549i	$-0.469955\pi$
$197$	2.64566	0.188496	0.0942478	+	0.995549i	$0.469955\pi$
$198$	0	0
$199$	−6.52800	−0.462757	−0.231379	−	0.972864i	$-0.574324\pi$
$199$	−6.52800	−0.462757	−0.231379	+	0.972864i	$0.574324\pi$
$200$	0	0
$201$	−7.72041	−0.544555
$202$	0	0
$203$	−24.6477	−1.72993
$204$	0	0
$205$	8.31822	0.580970
$206$	0	0
$207$	3.10155	0.215572
$208$	0	0
$209$	0	0
$210$	0	0
$211$	27.4478	1.88958	0.944792	−	0.327671i	$-0.106264\pi$
$211$	27.4478	1.88958	0.944792	+	0.327671i	$0.106264\pi$
$212$	0	0
$213$	4.77837	0.327409
$214$	0	0
$215$	−2.96862	−0.202458
$216$	0	0
$217$	−24.7371	−1.67926
$218$	0	0
$219$	0.759669	0.0513337
$220$	0	0
$221$	−10.4518	−0.703061
$222$	0	0
$223$	5.08194	0.340312	0.170156	−	0.985417i	$-0.445573\pi$
$223$	5.08194	0.340312	0.170156	+	0.985417i	$0.445573\pi$
$224$	0	0
$225$	−2.66881	−0.177921
$226$	0	0
$227$	−3.73980	−0.248219	−0.124110	−	0.992269i	$-0.539607\pi$
$227$	−3.73980	−0.248219	−0.124110	+	0.992269i	$0.539607\pi$
$228$	0	0
$229$	26.9241	1.77920	0.889598	−	0.456745i	$-0.150985\pi$
$229$	26.9241	1.77920	0.889598	+	0.456745i	$0.150985\pi$
$230$	0	0
$231$	0	0
$232$	0	0
$233$	18.3167	1.19997	0.599984	−	0.800012i	$-0.295174\pi$
$233$	18.3167	1.19997	0.599984	+	0.800012i	$0.295174\pi$
$234$	0	0
$235$	−2.22491	−0.145137
$236$	0	0
$237$	−7.97984	−0.518346
$238$	0	0
$239$	10.9559	0.708676	0.354338	−	0.935117i	$-0.384706\pi$
$239$	10.9559	0.708676	0.354338	+	0.935117i	$0.384706\pi$
$240$	0	0
$241$	−9.99444	−0.643798	−0.321899	−	0.946774i	$-0.604321\pi$
$241$	−9.99444	−0.643798	−0.321899	+	0.946774i	$0.604321\pi$
$242$	0	0
$243$	−13.3143	−0.854110
$244$	0	0
$245$	−6.31822	−0.403656
$246$	0	0
$247$	−0.269293	−0.0171347
$248$	0	0
$249$	−6.12581	−0.388208
$250$	0	0
$251$	−9.65743	−0.609572	−0.304786	−	0.952421i	$-0.598585\pi$
$251$	−9.65743	−0.609572	−0.304786	+	0.952421i	$0.598585\pi$
$252$	0	0
$253$	0	0
$254$	0	0
$255$	2.12469	0.133054
$256$	0	0
$257$	10.4276	0.650454	0.325227	−	0.945636i	$-0.394559\pi$
$257$	10.4276	0.650454	0.325227	+	0.945636i	$0.394559\pi$
$258$	0	0
$259$	35.9095	2.23131
$260$	0	0
$261$	18.0248	1.11571
$262$	0	0
$263$	10.9619	0.675937	0.337968	−	0.941157i	$-0.390260\pi$
$263$	10.9619	0.675937	0.337968	+	0.941157i	$0.390260\pi$
$264$	0	0
$265$	−2.99393	−0.183915
$266$	0	0
$267$	6.99867	0.428311
$268$	0	0
$269$	−0.0893449	−0.00544746	−0.00272373	−	0.999996i	$-0.500867\pi$
$269$	−0.0893449	−0.00544746	−0.00272373	+	0.999996i	$0.500867\pi$
$270$	0	0
$271$	13.3996	0.813965	0.406982	−	0.913436i	$-0.366581\pi$
$271$	13.3996	0.813965	0.406982	+	0.913436i	$0.366581\pi$
$272$	0	0
$273$	5.94561	0.359844
$274$	0	0
$275$	0	0
$276$	0	0
$277$	−3.90669	−0.234730	−0.117365	−	0.993089i	$-0.537445\pi$
$277$	−3.90669	−0.234730	−0.117365	+	0.993089i	$0.537445\pi$
$278$	0	0
$279$	18.0902	1.08303
$280$	0	0
$281$	−1.53743	−0.0917155	−0.0458577	−	0.998948i	$-0.514602\pi$
$281$	−1.53743	−0.0917155	−0.0458577	+	0.998948i	$0.514602\pi$
$282$	0	0
$283$	5.41170	0.321692	0.160846	−	0.986980i	$-0.448578\pi$
$283$	5.41170	0.321692	0.160846	+	0.986980i	$0.448578\pi$
$284$	0	0
$285$	0.0547434	0.00324272
$286$	0	0
$287$	−30.3566	−1.79190
$288$	0	0
$289$	−3.36947	−0.198204
$290$	0	0
$291$	2.49265	0.146122
$292$	0	0
$293$	11.4165	0.666958	0.333479	−	0.942757i	$-0.391777\pi$
$293$	11.4165	0.666958	0.333479	+	0.942757i	$0.391777\pi$
$294$	0	0
$295$	−8.50860	−0.495390
$296$	0	0
$297$	0	0
$298$	0	0
$299$	3.28999	0.190265
$300$	0	0
$301$	10.8337	0.624445
$302$	0	0
$303$	−5.70066	−0.327494
$304$	0	0
$305$	8.48037	0.485585
$306$	0	0
$307$	4.25008	0.242565	0.121282	−	0.992618i	$-0.461299\pi$
$307$	4.25008	0.242565	0.121282	+	0.992618i	$0.461299\pi$
$308$	0	0
$309$	2.33990	0.133112
$310$	0	0
$311$	16.6195	0.942404	0.471202	−	0.882025i	$-0.343820\pi$
$311$	16.6195	0.942404	0.471202	+	0.882025i	$0.343820\pi$
$312$	0	0
$313$	−26.5770	−1.50222	−0.751109	−	0.660178i	$-0.770481\pi$
$313$	−26.5770	−1.50222	−0.751109	+	0.660178i	$0.770481\pi$
$314$	0	0
$315$	9.73958	0.548763
$316$	0	0
$317$	5.79694	0.325589	0.162794	−	0.986660i	$-0.447949\pi$
$317$	5.79694	0.325589	0.162794	+	0.986660i	$0.447949\pi$
$318$	0	0
$319$	0	0
$320$	0	0
$321$	1.11564	0.0622688
$322$	0	0
$323$	0.351195	0.0195410
$324$	0	0
$325$	−2.83095	−0.157033
$326$	0	0
$327$	−3.52584	−0.194979
$328$	0	0
$329$	8.11961	0.447648
$330$	0	0
$331$	12.9230	0.710311	0.355155	−	0.934807i	$-0.384428\pi$
$331$	12.9230	0.710311	0.355155	+	0.934807i	$0.384428\pi$
$332$	0	0
$333$	−26.2605	−1.43907
$334$	0	0
$335$	−13.4153	−0.732956
$336$	0	0
$337$	13.3854	0.729148	0.364574	−	0.931174i	$-0.381215\pi$
$337$	13.3854	0.729148	0.364574	+	0.931174i	$0.381215\pi$
$338$	0	0
$339$	−3.32938	−0.180827
$340$	0	0
$341$	0	0
$342$	0	0
$343$	−2.48809	−0.134344
$344$	0	0
$345$	−0.668808	−0.0360074
$346$	0	0
$347$	8.44899	0.453565	0.226783	−	0.973945i	$-0.427179\pi$
$347$	8.44899	0.453565	0.226783	+	0.973945i	$0.427179\pi$
$348$	0	0
$349$	−10.3988	−0.556636	−0.278318	−	0.960489i	$-0.589777\pi$
$349$	−10.3988	−0.556636	−0.278318	+	0.960489i	$0.589777\pi$
$350$	0	0
$351$	−9.23559	−0.492959
$352$	0	0
$353$	19.1073	1.01698	0.508489	−	0.861069i	$-0.330204\pi$
$353$	19.1073	1.01698	0.508489	+	0.861069i	$0.330204\pi$
$354$	0	0
$355$	8.30309	0.440682
$356$	0	0
$357$	−7.75389	−0.410379
$358$	0	0
$359$	4.41417	0.232971	0.116486	−	0.993192i	$-0.462837\pi$
$359$	4.41417	0.232971	0.116486	+	0.993192i	$0.462837\pi$
$360$	0	0
$361$	−18.9910	−0.999524
$362$	0	0
$363$	0	0
$364$	0	0
$365$	1.32003	0.0690936
$366$	0	0
$367$	29.3617	1.53267	0.766335	−	0.642442i	$-0.222078\pi$
$367$	29.3617	1.53267	0.766335	+	0.642442i	$0.222078\pi$
$368$	0	0
$369$	22.1997	1.15567
$370$	0	0
$371$	10.9261	0.567254
$372$	0	0
$373$	−4.96478	−0.257067	−0.128533	−	0.991705i	$-0.541027\pi$
$373$	−4.96478	−0.257067	−0.128533	+	0.991705i	$0.541027\pi$
$374$	0	0
$375$	0.575493	0.0297183
$376$	0	0
$377$	19.1200	0.984728
$378$	0	0
$379$	−7.92315	−0.406985	−0.203492	−	0.979077i	$-0.565229\pi$
$379$	−7.92315	−0.406985	−0.203492	+	0.979077i	$0.565229\pi$
$380$	0	0
$381$	1.40295	0.0718755
$382$	0	0
$383$	24.5155	1.25268	0.626342	−	0.779549i	$-0.284551\pi$
$383$	24.5155	1.25268	0.626342	+	0.779549i	$0.284551\pi$
$384$	0	0
$385$	0	0
$386$	0	0
$387$	−7.92268	−0.402732
$388$	0	0
$389$	5.46094	0.276881	0.138440	−	0.990371i	$-0.455791\pi$
$389$	5.46094	0.276881	0.138440	+	0.990371i	$0.455791\pi$
$390$	0	0
$391$	−4.29059	−0.216985
$392$	0	0
$393$	4.05237	0.204415
$394$	0	0
$395$	−13.8661	−0.697679
$396$	0	0
$397$	−6.43455	−0.322941	−0.161470	−	0.986878i	$-0.551624\pi$
$397$	−6.43455	−0.322941	−0.161470	+	0.986878i	$0.551624\pi$
$398$	0	0
$399$	−0.199781	−0.0100016
$400$	0	0
$401$	−14.7026	−0.734213	−0.367107	−	0.930179i	$-0.619652\pi$
$401$	−14.7026	−0.734213	−0.367107	+	0.930179i	$0.619652\pi$
$402$	0	0
$403$	19.1893	0.955885
$404$	0	0
$405$	−6.12896	−0.304550
$406$	0	0
$407$	0	0
$408$	0	0
$409$	4.39576	0.217356	0.108678	−	0.994077i	$-0.465338\pi$
$409$	4.39576	0.217356	0.108678	+	0.994077i	$0.465338\pi$
$410$	0	0
$411$	5.50911	0.271745
$412$	0	0
$413$	31.0514	1.52794
$414$	0	0
$415$	−10.6445	−0.522516
$416$	0	0
$417$	0.296668	0.0145279
$418$	0	0
$419$	−17.8526	−0.872159	−0.436079	−	0.899908i	$-0.643633\pi$
$419$	−17.8526	−0.872159	−0.436079	+	0.899908i	$0.643633\pi$
$420$	0	0
$421$	−4.82854	−0.235328	−0.117664	−	0.993053i	$-0.537541\pi$
$421$	−4.82854	−0.235328	−0.117664	+	0.993053i	$0.537541\pi$
$422$	0	0
$423$	−5.93785	−0.288708
$424$	0	0
$425$	3.69195	0.179086
$426$	0	0
$427$	−30.9484	−1.49770
$428$	0	0
$429$	0	0
$430$	0	0
$431$	24.8739	1.19814	0.599068	−	0.800698i	$-0.295538\pi$
$431$	24.8739	1.19814	0.599068	+	0.800698i	$0.295538\pi$
$432$	0	0
$433$	−21.2502	−1.02122	−0.510611	−	0.859812i	$-0.670581\pi$
$433$	−21.2502	−1.02122	−0.510611	+	0.859812i	$0.670581\pi$
$434$	0	0
$435$	−3.88682	−0.186359
$436$	0	0
$437$	−0.110548	−0.00528825
$438$	0	0
$439$	15.9119	0.759434	0.379717	−	0.925103i	$-0.376021\pi$
$439$	15.9119	0.759434	0.379717	+	0.925103i	$0.376021\pi$
$440$	0	0
$441$	−16.8621	−0.802958
$442$	0	0
$443$	−26.2876	−1.24896	−0.624481	−	0.781040i	$-0.714690\pi$
$443$	−26.2876	−1.24896	−0.624481	+	0.781040i	$0.714690\pi$
$444$	0	0
$445$	12.1612	0.576494
$446$	0	0
$447$	4.69592	0.222110
$448$	0	0
$449$	−8.18961	−0.386492	−0.193246	−	0.981150i	$-0.561902\pi$
$449$	−8.18961	−0.386492	−0.193246	+	0.981150i	$0.561902\pi$
$450$	0	0
$451$	0	0
$452$	0	0
$453$	1.11659	0.0524618
$454$	0	0
$455$	10.3313	0.484340
$456$	0	0
$457$	11.9164	0.557425	0.278713	−	0.960375i	$-0.410092\pi$
$457$	11.9164	0.557425	0.278713	+	0.960375i	$0.410092\pi$
$458$	0	0
$459$	12.0445	0.562188
$460$	0	0
$461$	6.96172	0.324240	0.162120	−	0.986771i	$-0.448167\pi$
$461$	6.96172	0.324240	0.162120	+	0.986771i	$0.448167\pi$
$462$	0	0
$463$	−12.4762	−0.579817	−0.289909	−	0.957054i	$-0.593625\pi$
$463$	−12.4762	−0.579817	−0.289909	+	0.957054i	$0.593625\pi$
$464$	0	0
$465$	−3.90091	−0.180900
$466$	0	0
$467$	6.14617	0.284411	0.142205	−	0.989837i	$-0.454581\pi$
$467$	6.14617	0.284411	0.142205	+	0.989837i	$0.454581\pi$
$468$	0	0
$469$	48.9579	2.26067
$470$	0	0
$471$	−12.2433	−0.564142
$472$	0	0
$473$	0	0
$474$	0	0
$475$	0.0951243	0.00436460
$476$	0	0
$477$	−7.99022	−0.365847
$478$	0	0
$479$	−22.1942	−1.01408	−0.507039	−	0.861923i	$-0.669260\pi$
$479$	−22.1942	−1.01408	−0.507039	+	0.861923i	$0.669260\pi$
$480$	0	0
$481$	−27.8560	−1.27013
$482$	0	0
$483$	2.44076	0.111058
$484$	0	0
$485$	4.33133	0.196675
$486$	0	0
$487$	34.2306	1.55114	0.775569	−	0.631263i	$-0.217463\pi$
$487$	34.2306	1.55114	0.775569	+	0.631263i	$0.217463\pi$
$488$	0	0
$489$	−9.19693	−0.415900
$490$	0	0
$491$	16.9957	0.767007	0.383503	−	0.923539i	$-0.374717\pi$
$491$	16.9957	0.767007	0.383503	+	0.923539i	$0.374717\pi$
$492$	0	0
$493$	−24.9351	−1.12302
$494$	0	0
$495$	0	0
$496$	0	0
$497$	−30.3014	−1.35920
$498$	0	0
$499$	−5.22946	−0.234103	−0.117051	−	0.993126i	$-0.537344\pi$
$499$	−5.22946	−0.234103	−0.117051	+	0.993126i	$0.537344\pi$
$500$	0	0
$501$	10.1914	0.455319
$502$	0	0
$503$	−41.9448	−1.87023	−0.935113	−	0.354350i	$-0.884702\pi$
$503$	−41.9448	−1.87023	−0.935113	+	0.354350i	$0.884702\pi$
$504$	0	0
$505$	−9.90570	−0.440798
$506$	0	0
$507$	2.86923	0.127427
$508$	0	0
$509$	20.3678	0.902787	0.451393	−	0.892325i	$-0.350927\pi$
$509$	20.3678	0.902787	0.451393	+	0.892325i	$0.350927\pi$
$510$	0	0
$511$	−4.81734	−0.213107
$512$	0	0
$513$	0.310330	0.0137014
$514$	0	0
$515$	4.06590	0.179165
$516$	0	0
$517$	0	0
$518$	0	0
$519$	−9.14199	−0.401289
$520$	0	0
$521$	14.4779	0.634287	0.317143	−	0.948378i	$-0.397276\pi$
$521$	14.4779	0.634287	0.317143	+	0.948378i	$0.397276\pi$
$522$	0	0
$523$	−11.1601	−0.487998	−0.243999	−	0.969775i	$-0.578459\pi$
$523$	−11.1601	−0.487998	−0.243999	+	0.969775i	$0.578459\pi$
$524$	0	0
$525$	−2.10021	−0.0916608
$526$	0	0
$527$	−25.0254	−1.09013
$528$	0	0
$529$	−21.6494	−0.941279
$530$	0	0
$531$	−22.7078	−0.985436
$532$	0	0
$533$	23.5485	1.02000
$534$	0	0
$535$	1.93858	0.0838119
$536$	0	0
$537$	−9.71492	−0.419230
$538$	0	0
$539$	0	0
$540$	0	0
$541$	10.6808	0.459203	0.229602	−	0.973285i	$-0.426258\pi$
$541$	10.6808	0.459203	0.229602	+	0.973285i	$0.426258\pi$
$542$	0	0
$543$	13.8621	0.594880
$544$	0	0
$545$	−6.12664	−0.262436
$546$	0	0
$547$	−1.74760	−0.0747220	−0.0373610	−	0.999302i	$-0.511895\pi$
$547$	−1.74760	−0.0747220	−0.0373610	+	0.999302i	$0.511895\pi$
$548$	0	0
$549$	22.6325	0.965930
$550$	0	0
$551$	−0.642459	−0.0273697
$552$	0	0
$553$	50.6031	2.15186
$554$	0	0
$555$	5.66273	0.240370
$556$	0	0
$557$	−19.4844	−0.825579	−0.412790	−	0.910826i	$-0.635446\pi$
$557$	−19.4844	−0.825579	−0.412790	+	0.910826i	$0.635446\pi$
$558$	0	0
$559$	−8.40403	−0.355453
$560$	0	0
$561$	0	0
$562$	0	0
$563$	14.6892	0.619074	0.309537	−	0.950887i	$-0.399826\pi$
$563$	14.6892	0.619074	0.309537	+	0.950887i	$0.399826\pi$
$564$	0	0
$565$	−5.78527	−0.243388
$566$	0	0
$567$	22.3671	0.939330
$568$	0	0
$569$	19.9335	0.835658	0.417829	−	0.908526i	$-0.362791\pi$
$569$	19.9335	0.835658	0.417829	+	0.908526i	$0.362791\pi$
$570$	0	0
$571$	−5.24422	−0.219464	−0.109732	−	0.993961i	$-0.534999\pi$
$571$	−5.24422	−0.219464	−0.109732	+	0.993961i	$0.534999\pi$
$572$	0	0
$573$	3.09776	0.129411
$574$	0	0
$575$	−1.16215	−0.0484649
$576$	0	0
$577$	37.6004	1.56533	0.782663	−	0.622446i	$-0.213861\pi$
$577$	37.6004	1.56533	0.782663	+	0.622446i	$0.213861\pi$
$578$	0	0
$579$	−10.5223	−0.437294
$580$	0	0
$581$	38.8460	1.61161
$582$	0	0
$583$	0	0
$584$	0	0
$585$	−7.55527	−0.312372
$586$	0	0
$587$	−25.5711	−1.05543	−0.527716	−	0.849421i	$-0.676952\pi$
$587$	−25.5711	−1.05543	−0.527716	+	0.849421i	$0.676952\pi$
$588$	0	0
$589$	−0.644788	−0.0265680
$590$	0	0
$591$	−1.52256	−0.0626297
$592$	0	0
$593$	40.2260	1.65188	0.825942	−	0.563754i	$-0.190644\pi$
$593$	40.2260	1.65188	0.825942	+	0.563754i	$0.190644\pi$
$594$	0	0
$595$	−13.4735	−0.552358
$596$	0	0
$597$	3.75682	0.153756
$598$	0	0
$599$	−4.92997	−0.201433	−0.100716	−	0.994915i	$-0.532114\pi$
$599$	−4.92997	−0.201433	−0.100716	+	0.994915i	$0.532114\pi$
$600$	0	0
$601$	46.0896	1.88003	0.940017	−	0.341127i	$-0.110809\pi$
$601$	46.0896	1.88003	0.940017	+	0.341127i	$0.110809\pi$
$602$	0	0
$603$	−35.8028	−1.45800
$604$	0	0
$605$	0	0
$606$	0	0
$607$	45.1365	1.83203	0.916016	−	0.401141i	$-0.131386\pi$
$607$	45.1365	1.83203	0.916016	+	0.401141i	$0.131386\pi$
$608$	0	0
$609$	14.1846	0.574789
$610$	0	0
$611$	−6.29861	−0.254815
$612$	0	0
$613$	4.73418	0.191212	0.0956059	−	0.995419i	$-0.469521\pi$
$613$	4.73418	0.191212	0.0956059	+	0.995419i	$0.469521\pi$
$614$	0	0
$615$	−4.78708	−0.193034
$616$	0	0
$617$	17.8468	0.718486	0.359243	−	0.933244i	$-0.383035\pi$
$617$	17.8468	0.718486	0.359243	+	0.933244i	$0.383035\pi$
$618$	0	0
$619$	−0.356952	−0.0143471	−0.00717356	−	0.999974i	$-0.502283\pi$
$619$	−0.356952	−0.0143471	−0.00717356	+	0.999974i	$0.502283\pi$
$620$	0	0
$621$	−3.79134	−0.152141
$622$	0	0
$623$	−44.3811	−1.77809
$624$	0	0
$625$	1.00000	0.0400000
$626$	0	0
$627$	0	0
$628$	0	0
$629$	36.3281	1.44850
$630$	0	0
$631$	31.9922	1.27359	0.636795	−	0.771033i	$-0.280260\pi$
$631$	31.9922	1.27359	0.636795	+	0.771033i	$0.280260\pi$
$632$	0	0
$633$	−15.7960	−0.627835
$634$	0	0
$635$	2.43783	0.0967422
$636$	0	0
$637$	−17.8866	−0.708693
$638$	0	0
$639$	22.1594	0.876610
$640$	0	0
$641$	1.01285	0.0400050	0.0200025	−	0.999800i	$-0.493633\pi$
$641$	1.01285	0.0400050	0.0200025	+	0.999800i	$0.493633\pi$
$642$	0	0
$643$	14.9724	0.590455	0.295228	−	0.955427i	$-0.404605\pi$
$643$	14.9724	0.590455	0.295228	+	0.955427i	$0.404605\pi$
$644$	0	0
$645$	1.70842	0.0672690
$646$	0	0
$647$	−17.8873	−0.703224	−0.351612	−	0.936146i	$-0.614366\pi$
$647$	−17.8873	−0.703224	−0.351612	+	0.936146i	$0.614366\pi$
$648$	0	0
$649$	0	0
$650$	0	0
$651$	14.2360	0.557954
$652$	0	0
$653$	45.7642	1.79089	0.895446	−	0.445169i	$-0.146856\pi$
$653$	45.7642	1.79089	0.895446	+	0.445169i	$0.146856\pi$
$654$	0	0
$655$	7.04156	0.275136
$656$	0	0
$657$	3.52291	0.137442
$658$	0	0
$659$	9.54036	0.371640	0.185820	−	0.982584i	$-0.440506\pi$
$659$	9.54036	0.371640	0.185820	+	0.982584i	$0.440506\pi$
$660$	0	0
$661$	15.7769	0.613651	0.306825	−	0.951766i	$-0.400733\pi$
$661$	15.7769	0.613651	0.306825	+	0.951766i	$0.400733\pi$
$662$	0	0
$663$	6.01491	0.233600
$664$	0	0
$665$	−0.347148	−0.0134618
$666$	0	0
$667$	7.84901	0.303915
$668$	0	0
$669$	−2.92462	−0.113072
$670$	0	0
$671$	0	0
$672$	0	0
$673$	47.3031	1.82340	0.911700	−	0.410856i	$-0.134770\pi$
$673$	47.3031	1.82340	0.911700	+	0.410856i	$0.134770\pi$
$674$	0	0
$675$	3.26236	0.125568
$676$	0	0
$677$	27.5431	1.05857	0.529284	−	0.848445i	$-0.322461\pi$
$677$	27.5431	1.05857	0.529284	+	0.848445i	$0.322461\pi$
$678$	0	0
$679$	−15.8068	−0.606609
$680$	0	0
$681$	2.15223	0.0824736
$682$	0	0
$683$	27.1617	1.03931	0.519656	−	0.854375i	$-0.326060\pi$
$683$	27.1617	1.03931	0.519656	+	0.854375i	$0.326060\pi$
$684$	0	0
$685$	9.57286	0.365760
$686$	0	0
$687$	−15.4946	−0.591157
$688$	0	0
$689$	−8.47567	−0.322897
$690$	0	0
$691$	7.52680	0.286333	0.143166	−	0.989699i	$-0.454272\pi$
$691$	7.52680	0.286333	0.143166	+	0.989699i	$0.454272\pi$
$692$	0	0
$693$	0	0
$694$	0	0
$695$	0.515502	0.0195541
$696$	0	0
$697$	−30.7105	−1.16324
$698$	0	0
$699$	−10.5411	−0.398702
$700$	0	0
$701$	−31.8207	−1.20185	−0.600926	−	0.799305i	$-0.705201\pi$
$701$	−31.8207	−1.20185	−0.600926	+	0.799305i	$0.705201\pi$
$702$	0	0
$703$	0.936004	0.0353021
$704$	0	0
$705$	1.28042	0.0482234
$706$	0	0
$707$	36.1500	1.35956
$708$	0	0
$709$	−14.4381	−0.542235	−0.271118	−	0.962546i	$-0.587393\pi$
$709$	−14.4381	−0.542235	−0.271118	+	0.962546i	$0.587393\pi$
$710$	0	0
$711$	−37.0059	−1.38783
$712$	0	0
$713$	7.87747	0.295013
$714$	0	0
$715$	0	0
$716$	0	0
$717$	−6.30503	−0.235465
$718$	0	0
$719$	−5.41004	−0.201761	−0.100880	−	0.994899i	$-0.532166\pi$
$719$	−5.41004	−0.201761	−0.100880	+	0.994899i	$0.532166\pi$
$720$	0	0
$721$	−14.8382	−0.552602
$722$	0	0
$723$	5.75173	0.213909
$724$	0	0
$725$	−6.75389	−0.250833
$726$	0	0
$727$	16.7753	0.622161	0.311080	−	0.950384i	$-0.399309\pi$
$727$	16.7753	0.622161	0.311080	+	0.950384i	$0.399309\pi$
$728$	0	0
$729$	−10.7246	−0.397208
$730$	0	0
$731$	10.9600	0.405371
$732$	0	0
$733$	−14.0851	−0.520243	−0.260122	−	0.965576i	$-0.583763\pi$
$733$	−14.0851	−0.520243	−0.260122	+	0.965576i	$0.583763\pi$
$734$	0	0
$735$	3.63609	0.134119
$736$	0	0
$737$	0	0
$738$	0	0
$739$	36.3457	1.33700	0.668499	−	0.743713i	$-0.266937\pi$
$739$	36.3457	1.33700	0.668499	+	0.743713i	$0.266937\pi$
$740$	0	0
$741$	0.154976	0.00569319
$742$	0	0
$743$	1.95716	0.0718012	0.0359006	−	0.999355i	$-0.488570\pi$
$743$	1.95716	0.0718012	0.0359006	+	0.999355i	$0.488570\pi$
$744$	0	0
$745$	8.15983	0.298953
$746$	0	0
$747$	−28.4080	−1.03939
$748$	0	0
$749$	−7.07466	−0.258503
$750$	0	0
$751$	−18.7106	−0.682759	−0.341379	−	0.939926i	$-0.610894\pi$
$751$	−18.7106	−0.682759	−0.341379	+	0.939926i	$0.610894\pi$
$752$	0	0
$753$	5.55778	0.202537
$754$	0	0
$755$	1.94023	0.0706120
$756$	0	0
$757$	−14.5470	−0.528721	−0.264361	−	0.964424i	$-0.585161\pi$
$757$	−14.5470	−0.528721	−0.264361	+	0.964424i	$0.585161\pi$
$758$	0	0
$759$	0	0
$760$	0	0
$761$	13.1406	0.476345	0.238173	−	0.971223i	$-0.423452\pi$
$761$	13.1406	0.476345	0.238173	+	0.971223i	$0.423452\pi$
$762$	0	0
$763$	22.3586	0.809437
$764$	0	0
$765$	9.85312	0.356240
$766$	0	0
$767$	−24.0875	−0.869748
$768$	0	0
$769$	38.9767	1.40554	0.702768	−	0.711419i	$-0.251947\pi$
$769$	38.9767	1.40554	0.702768	+	0.711419i	$0.251947\pi$
$770$	0	0
$771$	−6.00099	−0.216121
$772$	0	0
$773$	−38.7539	−1.39388	−0.696940	−	0.717129i	$-0.745456\pi$
$773$	−38.7539	−1.39388	−0.696940	+	0.717129i	$0.745456\pi$
$774$	0	0
$775$	−6.77837	−0.243486
$776$	0	0
$777$	−20.6657	−0.741377
$778$	0	0
$779$	−0.791265	−0.0283500
$780$	0	0
$781$	0	0
$782$	0	0
$783$	−22.0336	−0.787417
$784$	0	0
$785$	−21.2745	−0.759319
$786$	0	0
$787$	21.3842	0.762265	0.381132	−	0.924521i	$-0.375534\pi$
$787$	21.3842	0.762265	0.381132	+	0.924521i	$0.375534\pi$
$788$	0	0
$789$	−6.30847	−0.224588
$790$	0	0
$791$	21.1128	0.750686
$792$	0	0
$793$	24.0075	0.852533
$794$	0	0
$795$	1.72298	0.0611080
$796$	0	0
$797$	−2.22456	−0.0787978	−0.0393989	−	0.999224i	$-0.512544\pi$
$797$	−2.22456	−0.0787978	−0.0393989	+	0.999224i	$0.512544\pi$
$798$	0	0
$799$	8.21426	0.290599
$800$	0	0
$801$	32.4558	1.14677
$802$	0	0
$803$	0	0
$804$	0	0
$805$	4.24116	0.149481
$806$	0	0
$807$	0.0514174	0.00180998
$808$	0	0
$809$	21.1682	0.744234	0.372117	−	0.928186i	$-0.378632\pi$
$809$	21.1682	0.744234	0.372117	+	0.928186i	$0.378632\pi$
$810$	0	0
$811$	36.7172	1.28932	0.644658	−	0.764471i	$-0.277000\pi$
$811$	36.7172	1.28932	0.644658	+	0.764471i	$0.277000\pi$
$812$	0	0
$813$	−7.71135	−0.270449
$814$	0	0
$815$	−15.9810	−0.559788
$816$	0	0
$817$	0.282388	0.00987951
$818$	0	0
$819$	27.5723	0.963455
$820$	0	0
$821$	−39.6693	−1.38447	−0.692235	−	0.721673i	$-0.743374\pi$
$821$	−39.6693	−1.38447	−0.692235	+	0.721673i	$0.743374\pi$
$822$	0	0
$823$	45.9283	1.60096	0.800480	−	0.599359i	$-0.204578\pi$
$823$	45.9283	1.60096	0.800480	+	0.599359i	$0.204578\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	39.6949	1.38033	0.690164	−	0.723653i	$-0.257538\pi$
$827$	39.6949	1.38033	0.690164	+	0.723653i	$0.257538\pi$
$828$	0	0
$829$	7.65584	0.265898	0.132949	−	0.991123i	$-0.457555\pi$
$829$	7.65584	0.265898	0.132949	+	0.991123i	$0.457555\pi$
$830$	0	0
$831$	2.24827	0.0779916
$832$	0	0
$833$	23.3266	0.808218
$834$	0	0
$835$	17.7090	0.612846
$836$	0	0
$837$	−22.1135	−0.764354
$838$	0	0
$839$	−27.5886	−0.952465	−0.476233	−	0.879319i	$-0.657998\pi$
$839$	−27.5886	−0.952465	−0.476233	+	0.879319i	$0.657998\pi$
$840$	0	0
$841$	16.6150	0.572932
$842$	0	0
$843$	0.884781	0.0304735
$844$	0	0
$845$	4.98569	0.171513
$846$	0	0
$847$	0	0
$848$	0	0
$849$	−3.11439	−0.106886
$850$	0	0
$851$	−11.4353	−0.391997
$852$	0	0
$853$	42.1496	1.44318	0.721588	−	0.692323i	$-0.243413\pi$
$853$	42.1496	1.44318	0.721588	+	0.692323i	$0.243413\pi$
$854$	0	0
$855$	0.253869	0.00868212
$856$	0	0
$857$	−45.0850	−1.54008	−0.770038	−	0.637998i	$-0.779763\pi$
$857$	−45.0850	−1.54008	−0.770038	+	0.637998i	$0.779763\pi$
$858$	0	0
$859$	11.8257	0.403488	0.201744	−	0.979438i	$-0.435339\pi$
$859$	11.8257	0.403488	0.201744	+	0.979438i	$0.435339\pi$
$860$	0	0
$861$	17.4700	0.595377
$862$	0	0
$863$	−27.8713	−0.948750	−0.474375	−	0.880323i	$-0.657326\pi$
$863$	−27.8713	−0.948750	−0.474375	+	0.880323i	$0.657326\pi$
$864$	0	0
$865$	−15.8855	−0.540123
$866$	0	0
$867$	1.93911	0.0658555
$868$	0	0
$869$	0	0
$870$	0	0
$871$	−37.9781	−1.28684
$872$	0	0
$873$	11.5595	0.391229
$874$	0	0
$875$	−3.64941	−0.123373
$876$	0	0
$877$	−11.4471	−0.386543	−0.193271	−	0.981145i	$-0.561910\pi$
$877$	−11.4471	−0.386543	−0.193271	+	0.981145i	$0.561910\pi$
$878$	0	0
$879$	−6.57011	−0.221604
$880$	0	0
$881$	47.0037	1.58360	0.791798	−	0.610783i	$-0.209145\pi$
$881$	47.0037	1.58360	0.791798	+	0.610783i	$0.209145\pi$
$882$	0	0
$883$	46.9146	1.57880	0.789401	−	0.613877i	$-0.210391\pi$
$883$	46.9146	1.57880	0.789401	+	0.613877i	$0.210391\pi$
$884$	0	0
$885$	4.89664	0.164599
$886$	0	0
$887$	27.8427	0.934866	0.467433	−	0.884029i	$-0.345179\pi$
$887$	27.8427	0.934866	0.467433	+	0.884029i	$0.345179\pi$
$888$	0	0
$889$	−8.89664	−0.298384
$890$	0	0
$891$	0	0
$892$	0	0
$893$	0.211643	0.00708236
$894$	0	0
$895$	−16.8810	−0.564271
$896$	0	0
$897$	−1.89336	−0.0632176
$898$	0	0
$899$	45.7804	1.52686
$900$	0	0
$901$	11.0534	0.368244
$902$	0	0
$903$	−6.23473	−0.207479
$904$	0	0
$905$	24.0874	0.800691
$906$	0	0
$907$	28.6233	0.950421	0.475210	−	0.879872i	$-0.342372\pi$
$907$	28.6233	0.950421	0.475210	+	0.879872i	$0.342372\pi$
$908$	0	0
$909$	−26.4364	−0.876840
$910$	0	0
$911$	−5.12823	−0.169906	−0.0849529	−	0.996385i	$-0.527074\pi$
$911$	−5.12823	−0.169906	−0.0849529	+	0.996385i	$0.527074\pi$
$912$	0	0
$913$	0	0
$914$	0	0
$915$	−4.88039	−0.161341
$916$	0	0
$917$	−25.6976	−0.848608
$918$	0	0
$919$	−35.2810	−1.16381	−0.581906	−	0.813256i	$-0.697693\pi$
$919$	−35.2810	−1.16381	−0.581906	+	0.813256i	$0.697693\pi$
$920$	0	0
$921$	−2.44589	−0.0805949
$922$	0	0
$923$	23.5057	0.773699
$924$	0	0
$925$	9.83980	0.323531
$926$	0	0
$927$	10.8511	0.356397
$928$	0	0
$929$	−59.1427	−1.94041	−0.970204	−	0.242289i	$-0.922102\pi$
$929$	−59.1427	−1.94041	−0.970204	+	0.242289i	$0.922102\pi$
$930$	0	0
$931$	0.601017	0.0196975
$932$	0	0
$933$	−9.56439	−0.313124
$934$	0	0
$935$	0	0
$936$	0	0
$937$	14.4425	0.471817	0.235909	−	0.971775i	$-0.424193\pi$
$937$	14.4425	0.471817	0.235909	+	0.971775i	$0.424193\pi$
$938$	0	0
$939$	15.2949	0.499129
$940$	0	0
$941$	−18.6591	−0.608269	−0.304135	−	0.952629i	$-0.598367\pi$
$941$	−18.6591	−0.608269	−0.304135	+	0.952629i	$0.598367\pi$
$942$	0	0
$943$	9.66700	0.314801
$944$	0	0
$945$	−11.9057	−0.387292
$946$	0	0
$947$	0.991391	0.0322159	0.0161079	−	0.999870i	$-0.494872\pi$
$947$	0.991391	0.0322159	0.0161079	+	0.999870i	$0.494872\pi$
$948$	0	0
$949$	3.73695	0.121306
$950$	0	0
$951$	−3.33610	−0.108180
$952$	0	0
$953$	−8.26404	−0.267699	−0.133849	−	0.991002i	$-0.542734\pi$
$953$	−8.26404	−0.267699	−0.133849	+	0.991002i	$0.542734\pi$
$954$	0	0
$955$	5.38279	0.174183
$956$	0	0
$957$	0	0
$958$	0	0
$959$	−34.9353	−1.12812
$960$	0	0
$961$	14.9463	0.482139
$962$	0	0
$963$	5.17368	0.166720
$964$	0	0
$965$	−18.2840	−0.588584
$966$	0	0
$967$	−7.36029	−0.236691	−0.118345	−	0.992972i	$-0.537759\pi$
$967$	−7.36029	−0.236691	−0.118345	+	0.992972i	$0.537759\pi$
$968$	0	0
$969$	−0.202110	−0.00649271
$970$	0	0
$971$	4.97733	0.159730	0.0798650	−	0.996806i	$-0.474551\pi$
$971$	4.97733	0.159730	0.0798650	+	0.996806i	$0.474551\pi$
$972$	0	0
$973$	−1.88128	−0.0603111
$974$	0	0
$975$	1.62920	0.0521760
$976$	0	0
$977$	10.3368	0.330704	0.165352	−	0.986235i	$-0.447124\pi$
$977$	10.3368	0.330704	0.165352	+	0.986235i	$0.447124\pi$
$978$	0	0
$979$	0	0
$980$	0	0
$981$	−16.3508	−0.522041
$982$	0	0
$983$	29.0614	0.926913	0.463457	−	0.886120i	$-0.346609\pi$
$983$	29.0614	0.926913	0.463457	+	0.886120i	$0.346609\pi$
$984$	0	0
$985$	−2.64566	−0.0842978
$986$	0	0
$987$	−4.67278	−0.148736
$988$	0	0
$989$	−3.44997	−0.109703
$990$	0	0
$991$	−7.70381	−0.244719	−0.122360	−	0.992486i	$-0.539046\pi$
$991$	−7.70381	−0.244719	−0.122360	+	0.992486i	$0.539046\pi$
$992$	0	0
$993$	−7.43708	−0.236009
$994$	0	0
$995$	6.52800	0.206951
$996$	0	0
$997$	−2.86418	−0.0907095	−0.0453547	−	0.998971i	$-0.514442\pi$
$997$	−2.86418	−0.0907095	−0.0453547	+	0.998971i	$0.514442\pi$
$998$	0	0
$999$	32.1010	1.01563

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9680.2.a.cn.1.2		4
4.3	odd	2		605.2.a.j.1.4		4
11.5	even	5		880.2.bo.h.641.1		8
11.9	even	5		880.2.bo.h.81.1		8
11.10	odd	2		9680.2.a.cm.1.2		4
12.11	even	2		5445.2.a.bp.1.1		4
20.19	odd	2		3025.2.a.bd.1.1		4
44.3	odd	10		605.2.g.m.251.2		8
44.7	even	10		605.2.g.e.511.1		8
44.15	odd	10		605.2.g.m.511.2		8
44.19	even	10		605.2.g.e.251.1		8
44.27	odd	10		55.2.g.b.36.1	yes	8
44.31	odd	10		55.2.g.b.26.1	✓	8
44.35	even	10		605.2.g.k.81.2		8
44.39	even	10		605.2.g.k.366.2		8
44.43	even	2		605.2.a.k.1.1		4
132.71	even	10		495.2.n.e.91.2		8
132.119	even	10		495.2.n.e.136.2		8
132.131	odd	2		5445.2.a.bi.1.4		4
220.27	even	20		275.2.z.a.124.1		16
220.119	odd	10		275.2.h.a.26.2		8
220.159	odd	10		275.2.h.a.201.2		8
220.163	even	20		275.2.z.a.224.1		16
220.203	even	20		275.2.z.a.124.4		16
220.207	even	20		275.2.z.a.224.4		16
220.219	even	2		3025.2.a.w.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.g.b.26.1	✓	8	44.31	odd	10
55.2.g.b.36.1	yes	8	44.27	odd	10
275.2.h.a.26.2		8	220.119	odd	10
275.2.h.a.201.2		8	220.159	odd	10
275.2.z.a.124.1		16	220.27	even	20
275.2.z.a.124.4		16	220.203	even	20
275.2.z.a.224.1		16	220.163	even	20
275.2.z.a.224.4		16	220.207	even	20
495.2.n.e.91.2		8	132.71	even	10
495.2.n.e.136.2		8	132.119	even	10
605.2.a.j.1.4		4	4.3	odd	2
605.2.a.k.1.1		4	44.43	even	2
605.2.g.e.251.1		8	44.19	even	10
605.2.g.e.511.1		8	44.7	even	10
605.2.g.k.81.2		8	44.35	even	10
605.2.g.k.366.2		8	44.39	even	10
605.2.g.m.251.2		8	44.3	odd	10
605.2.g.m.511.2		8	44.15	odd	10
880.2.bo.h.81.1		8	11.9	even	5
880.2.bo.h.641.1		8	11.5	even	5
3025.2.a.w.1.4		4	220.219	even	2
3025.2.a.bd.1.1		4	20.19	odd	2
5445.2.a.bi.1.4		4	132.131	odd	2
5445.2.a.bp.1.1		4	12.11	even	2
9680.2.a.cm.1.2		4	11.10	odd	2
9680.2.a.cn.1.2		4	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:	\( N \)	\(=\)	\( 9680 = 2^{4} \cdot 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9680.a (trivial)

\(f(q)\)	\(=\)	\(q-0.575493 q^{3} -1.00000 q^{5} +3.64941 q^{7} -2.66881 q^{9} +O(q^{10})\)	\(q-0.575493 q^{3} -1.00000 q^{5} +3.64941 q^{7} -2.66881 q^{9} -2.83095 q^{13} +0.575493 q^{15} +3.69195 q^{17} +0.0951243 q^{19} -2.10021 q^{21} -1.16215 q^{23} +1.00000 q^{25} +3.26236 q^{27} -6.75389 q^{29} -6.77837 q^{31} -3.64941 q^{35} +9.83980 q^{37} +1.62920 q^{39} -8.31822 q^{41} +2.96862 q^{43} +2.66881 q^{45} +2.22491 q^{47} +6.31822 q^{49} -2.12469 q^{51} +2.99393 q^{53} -0.0547434 q^{57} +8.50860 q^{59} -8.48037 q^{61} -9.73958 q^{63} +2.83095 q^{65} +13.4153 q^{67} +0.668808 q^{69} -8.30309 q^{71} -1.32003 q^{73} -0.575493 q^{75} +13.8661 q^{79} +6.12896 q^{81} +10.6445 q^{83} -3.69195 q^{85} +3.88682 q^{87} -12.1612 q^{89} -10.3313 q^{91} +3.90091 q^{93} -0.0951243 q^{95} -4.33133 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{5} + 3 q^{7}+O(q^{10}) \) 4 * q - 4 * q^5 + 3 * q^7	\( 4 q - 4 q^{5} + 3 q^{7} - q^{13} + q^{17} + 20 q^{19} - 10 q^{21} - 5 q^{23} + 4 q^{25} + 15 q^{27} - 12 q^{29} + 5 q^{31} - 3 q^{35} + 7 q^{37} + 7 q^{39} - 11 q^{41} + 19 q^{43} - 5 q^{47} + 3 q^{49} + 7 q^{51} - 11 q^{53} + 5 q^{57} - 9 q^{59} - 12 q^{61} - 5 q^{63} + q^{65} + 19 q^{67} - 8 q^{69} - 5 q^{71} - 11 q^{73} + 34 q^{79} + 4 q^{81} - 11 q^{83} - q^{85} - 19 q^{87} - 8 q^{89} + 8 q^{91} - 5 q^{93} - 20 q^{95} + 32 q^{97}+O(q^{100}) \) 4 * q - 4 * q^5 + 3 * q^7 - q^13 + q^17 + 20 * q^19 - 10 * q^21 - 5 * q^23 + 4 * q^25 + 15 * q^27 - 12 * q^29 + 5 * q^31 - 3 * q^35 + 7 * q^37 + 7 * q^39 - 11 * q^41 + 19 * q^43 - 5 * q^47 + 3 * q^49 + 7 * q^51 - 11 * q^53 + 5 * q^57 - 9 * q^59 - 12 * q^61 - 5 * q^63 + q^65 + 19 * q^67 - 8 * q^69 - 5 * q^71 - 11 * q^73 + 34 * q^79 + 4 * q^81 - 11 * q^83 - q^85 - 19 * q^87 - 8 * q^89 + 8 * q^91 - 5 * q^93 - 20 * q^95 + 32 * q^97

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