LMFDB - Embedded newform 9702.2.a.ea.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9702,2,Mod(1,9702)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9702, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("9702.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 9702 = 2 \cdot 3^{2} \cdot 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	9702.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:	$77.4708600410$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.4.4352.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 6x^{2} - 4x + 2 $ x^4 - 6x^2 - 4x + 2
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 3234)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$0.334904$ of defining polynomial
Character	$\chi$	$=$	9702.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{4} -0.473626 q^{5} -1.00000 q^{8} +O(q^{10})$	$q-1.00000 q^{2} +1.00000 q^{4} -0.473626 q^{5} -1.00000 q^{8} +0.473626 q^{10} -1.00000 q^{11} -7.03127 q^{13} +1.00000 q^{16} -4.64167 q^{17} -6.55765 q^{19} -0.473626 q^{20} +1.00000 q^{22} -1.49824 q^{23} -4.77568 q^{25} +7.03127 q^{26} +2.11882 q^{29} -6.83509 q^{31} -1.00000 q^{32} +4.64167 q^{34} -4.32666 q^{37} +6.55765 q^{38} +0.473626 q^{40} -11.2458 q^{41} +0.158619 q^{43} -1.00000 q^{44} +1.49824 q^{46} +0.270780 q^{47} +4.77568 q^{50} -7.03127 q^{52} +9.66628 q^{53} +0.473626 q^{55} -2.11882 q^{58} +9.82490 q^{59} -15.1993 q^{61} +6.83509 q^{62} +1.00000 q^{64} +3.33019 q^{65} -1.21137 q^{67} -4.64167 q^{68} -15.0098 q^{71} +6.13048 q^{73} +4.32666 q^{74} -6.55765 q^{76} +11.4420 q^{79} -0.473626 q^{80} +11.2458 q^{82} -7.54469 q^{83} +2.19841 q^{85} -0.158619 q^{86} +1.00000 q^{88} +16.6881 q^{89} -1.49824 q^{92} -0.270780 q^{94} +3.10587 q^{95} -12.9656 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} + 4 q^{4} + 4 q^{5} - 4 q^{8}+O(q^{10}) $ 4 * q - 4 * q^2 + 4 * q^4 + 4 * q^5 - 4 * q^8	$ 4 q - 4 q^{2} + 4 q^{4} + 4 q^{5} - 4 q^{8} - 4 q^{10} - 4 q^{11} - 8 q^{13} + 4 q^{16} + 4 q^{17} - 12 q^{19} + 4 q^{20} + 4 q^{22} + 8 q^{23} + 4 q^{25} + 8 q^{26} + 8 q^{29} - 4 q^{31} - 4 q^{32} - 4 q^{34} + 8 q^{37} + 12 q^{38} - 4 q^{40} + 12 q^{41} - 8 q^{43} - 4 q^{44} - 8 q^{46} + 4 q^{47} - 4 q^{50} - 8 q^{52} + 8 q^{53} - 4 q^{55} - 8 q^{58} - 24 q^{61} + 4 q^{62} + 4 q^{64} + 16 q^{65} - 8 q^{67} + 4 q^{68} - 8 q^{71} - 4 q^{73} - 8 q^{74} - 12 q^{76} - 8 q^{79} + 4 q^{80} - 12 q^{82} + 4 q^{83} - 8 q^{85} + 8 q^{86} + 4 q^{88} + 24 q^{89} + 8 q^{92} - 4 q^{94} - 8 q^{95}+O(q^{100}) $ 4 * q - 4 * q^2 + 4 * q^4 + 4 * q^5 - 4 * q^8 - 4 * q^10 - 4 * q^11 - 8 * q^13 + 4 * q^16 + 4 * q^17 - 12 * q^19 + 4 * q^20 + 4 * q^22 + 8 * q^23 + 4 * q^25 + 8 * q^26 + 8 * q^29 - 4 * q^31 - 4 * q^32 - 4 * q^34 + 8 * q^37 + 12 * q^38 - 4 * q^40 + 12 * q^41 - 8 * q^43 - 4 * q^44 - 8 * q^46 + 4 * q^47 - 4 * q^50 - 8 * q^52 + 8 * q^53 - 4 * q^55 - 8 * q^58 - 24 * q^61 + 4 * q^62 + 4 * q^64 + 16 * q^65 - 8 * q^67 + 4 * q^68 - 8 * q^71 - 4 * q^73 - 8 * q^74 - 12 * q^76 - 8 * q^79 + 4 * q^80 - 12 * q^82 + 4 * q^83 - 8 * q^85 + 8 * q^86 + 4 * q^88 + 24 * q^89 + 8 * q^92 - 4 * q^94 - 8 * q^95

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	0	0
$3$	0	0
$4$	1.00000	0.500000
$5$	−0.473626	−0.211812	−0.105906	−	0.994376i	$-0.533774\pi$
$5$	−0.473626	−0.211812	−0.105906	+	0.994376i	$0.533774\pi$
$6$	0	0
$7$	0	0
$7$	0	0
$8$	−1.00000	−0.353553
$9$	0	0
$10$	0.473626	0.149774
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	0	0
$13$	−7.03127	−1.95012	−0.975062	−	0.221932i	$-0.928764\pi$
$13$	−7.03127	−1.95012	−0.975062	+	0.221932i	$0.928764\pi$
$14$	0	0
$15$	0	0
$16$	1.00000	0.250000
$17$	−4.64167	−1.12577	−0.562885	−	0.826535i	$-0.690309\pi$
$17$	−4.64167	−1.12577	−0.562885	+	0.826535i	$0.690309\pi$
$18$	0	0
$19$	−6.55765	−1.50443	−0.752214	−	0.658919i	$-0.771014\pi$
$19$	−6.55765	−1.50443	−0.752214	+	0.658919i	$0.771014\pi$
$20$	−0.473626	−0.105906
$21$	0	0
$22$	1.00000	0.213201
$23$	−1.49824	−0.312404	−0.156202	−	0.987725i	$-0.549925\pi$
$23$	−1.49824	−0.312404	−0.156202	+	0.987725i	$0.549925\pi$
$24$	0	0
$25$	−4.77568	−0.955136
$26$	7.03127	1.37895
$27$	0	0
$28$	0	0
$29$	2.11882	0.393456	0.196728	−	0.980458i	$-0.436968\pi$
$29$	2.11882	0.393456	0.196728	+	0.980458i	$0.436968\pi$
$30$	0	0
$31$	−6.83509	−1.22762	−0.613809	−	0.789454i	$-0.710364\pi$
$31$	−6.83509	−1.22762	−0.613809	+	0.789454i	$0.710364\pi$
$32$	−1.00000	−0.176777
$33$	0	0
$34$	4.64167	0.796040
$35$	0	0
$36$	0	0
$37$	−4.32666	−0.711299	−0.355649	−	0.934619i	$-0.615740\pi$
$37$	−4.32666	−0.711299	−0.355649	+	0.934619i	$0.615740\pi$
$38$	6.55765	1.06379
$39$	0	0
$40$	0.473626	0.0748868
$41$	−11.2458	−1.75629	−0.878147	−	0.478390i	$-0.841221\pi$
$41$	−11.2458	−1.75629	−0.878147	+	0.478390i	$0.841221\pi$
$42$	0	0
$43$	0.158619	0.0241892	0.0120946	−	0.999927i	$-0.496150\pi$
$43$	0.158619	0.0241892	0.0120946	+	0.999927i	$0.496150\pi$
$44$	−1.00000	−0.150756
$45$	0	0
$46$	1.49824	0.220903
$47$	0.270780	0.0394973	0.0197486	−	0.999805i	$-0.493713\pi$
$47$	0.270780	0.0394973	0.0197486	+	0.999805i	$0.493713\pi$
$48$	0	0
$49$	0	0
$50$	4.77568	0.675383
$51$	0	0
$52$	−7.03127	−0.975062
$53$	9.66628	1.32777	0.663883	−	0.747837i	$-0.268907\pi$
$53$	9.66628	1.32777	0.663883	+	0.747837i	$0.268907\pi$
$54$	0	0
$55$	0.473626	0.0638637
$56$	0	0
$57$	0	0
$58$	−2.11882	−0.278215
$59$	9.82490	1.27909	0.639546	−	0.768753i	$-0.279122\pi$
$59$	9.82490	1.27909	0.639546	+	0.768753i	$0.279122\pi$
$60$	0	0
$61$	−15.1993	−1.94607	−0.973037	−	0.230651i	$-0.925914\pi$
$61$	−15.1993	−1.94607	−0.973037	+	0.230651i	$0.925914\pi$
$62$	6.83509	0.868057
$63$	0	0
$64$	1.00000	0.125000
$65$	3.33019	0.413059
$66$	0	0
$67$	−1.21137	−0.147992	−0.0739961	−	0.997259i	$-0.523575\pi$
$67$	−1.21137	−0.147992	−0.0739961	+	0.997259i	$0.523575\pi$
$68$	−4.64167	−0.562885
$69$	0	0
$70$	0	0
$71$	−15.0098	−1.78134	−0.890668	−	0.454655i	$-0.849763\pi$
$71$	−15.0098	−1.78134	−0.890668	+	0.454655i	$0.849763\pi$
$72$	0	0
$73$	6.13048	0.717518	0.358759	−	0.933430i	$-0.383200\pi$
$73$	6.13048	0.717518	0.358759	+	0.933430i	$0.383200\pi$
$74$	4.32666	0.502964
$75$	0	0
$76$	−6.55765	−0.752214
$77$	0	0
$78$	0	0
$79$	11.4420	1.28732	0.643660	−	0.765311i	$-0.277415\pi$
$79$	11.4420	1.28732	0.643660	+	0.765311i	$0.277415\pi$
$80$	−0.473626	−0.0529530
$81$	0	0
$82$	11.2458	1.24189
$83$	−7.54469	−0.828138	−0.414069	−	0.910246i	$-0.635893\pi$
$83$	−7.54469	−0.828138	−0.414069	+	0.910246i	$0.635893\pi$
$84$	0	0
$85$	2.19841	0.238451
$86$	−0.158619	−0.0171043
$87$	0	0
$88$	1.00000	0.106600
$89$	16.6881	1.76894	0.884469	−	0.466599i	$-0.154521\pi$
$89$	16.6881	1.76894	0.884469	+	0.466599i	$0.154521\pi$
$90$	0	0
$91$	0	0
$92$	−1.49824	−0.156202
$93$	0	0
$94$	−0.270780	−0.0279288
$95$	3.10587	0.318656
$96$	0	0
$97$	−12.9656	−1.31645	−0.658227	−	0.752819i	$-0.728693\pi$
$97$	−12.9656	−1.31645	−0.658227	+	0.752819i	$0.728693\pi$
$98$	0	0
$99$	0	0
$100$	−4.77568	−0.477568
$101$	0.298919	0.0297436	0.0148718	−	0.999889i	$-0.495266\pi$
$101$	0.298919	0.0297436	0.0148718	+	0.999889i	$0.495266\pi$
$102$	0	0
$103$	7.39550	0.728700	0.364350	−	0.931262i	$-0.381291\pi$
$103$	7.39550	0.728700	0.364350	+	0.931262i	$0.381291\pi$
$104$	7.03127	0.689473
$105$	0	0
$106$	−9.66628	−0.938872
$107$	15.3231	1.48134	0.740672	−	0.671867i	$-0.234507\pi$
$107$	15.3231	1.48134	0.740672	+	0.671867i	$0.234507\pi$
$108$	0	0
$109$	−0.422735	−0.0404907	−0.0202453	−	0.999795i	$-0.506445\pi$
$109$	−0.422735	−0.0404907	−0.0202453	+	0.999795i	$0.506445\pi$
$110$	−0.473626	−0.0451584
$111$	0	0
$112$	0	0
$113$	8.40569	0.790741	0.395370	−	0.918522i	$-0.370616\pi$
$113$	8.40569	0.790741	0.395370	+	0.918522i	$0.370616\pi$
$114$	0	0
$115$	0.709603	0.0661708
$116$	2.11882	0.196728
$117$	0	0
$118$	−9.82490	−0.904455
$119$	0	0
$120$	0	0
$121$	1.00000	0.0909091
$122$	15.1993	1.37608
$123$	0	0
$124$	−6.83509	−0.613809
$125$	4.63001	0.414121
$126$	0	0
$127$	10.1023	0.896438	0.448219	−	0.893924i	$-0.352059\pi$
$127$	10.1023	0.896438	0.448219	+	0.893924i	$0.352059\pi$
$128$	−1.00000	−0.0883883
$129$	0	0
$130$	−3.33019	−0.292077
$131$	20.8843	1.82467	0.912335	−	0.409444i	$-0.134277\pi$
$131$	20.8843	1.82467	0.912335	+	0.409444i	$0.134277\pi$
$132$	0	0
$133$	0	0
$134$	1.21137	0.104646
$135$	0	0
$136$	4.64167	0.398020
$137$	−7.35294	−0.628204	−0.314102	−	0.949389i	$-0.601703\pi$
$137$	−7.35294	−0.628204	−0.314102	+	0.949389i	$0.601703\pi$
$138$	0	0
$139$	4.67647	0.396653	0.198327	−	0.980136i	$-0.436449\pi$
$139$	4.67647	0.396653	0.198327	+	0.980136i	$0.436449\pi$
$140$	0	0
$141$	0	0
$142$	15.0098	1.25959
$143$	7.03127	0.587985
$144$	0	0
$145$	−1.00353	−0.0833386
$146$	−6.13048	−0.507362
$147$	0	0
$148$	−4.32666	−0.355649
$149$	−4.89097	−0.400684	−0.200342	−	0.979726i	$-0.564205\pi$
$149$	−4.89097	−0.400684	−0.200342	+	0.979726i	$0.564205\pi$
$150$	0	0
$151$	−16.6533	−1.35523	−0.677614	−	0.735418i	$-0.736986\pi$
$151$	−16.6533	−1.35523	−0.677614	+	0.735418i	$0.736986\pi$
$152$	6.55765	0.531895
$153$	0	0
$154$	0	0
$155$	3.23728	0.260024
$156$	0	0
$157$	14.5228	1.15905	0.579525	−	0.814955i	$-0.303238\pi$
$157$	14.5228	1.15905	0.579525	+	0.814955i	$0.303238\pi$
$158$	−11.4420	−0.910273
$159$	0	0
$160$	0.473626	0.0374434
$161$	0	0
$162$	0	0
$163$	−8.33609	−0.652933	−0.326466	−	0.945209i	$-0.605858\pi$
$163$	−8.33609	−0.652933	−0.326466	+	0.945209i	$0.605858\pi$
$164$	−11.2458	−0.878147
$165$	0	0
$166$	7.54469	0.585582
$167$	2.84727	0.220329	0.110164	−	0.993913i	$-0.464862\pi$
$167$	2.84727	0.220329	0.110164	+	0.993913i	$0.464862\pi$
$168$	0	0
$169$	36.4388	2.80298
$170$	−2.19841	−0.168611
$171$	0	0
$172$	0.158619	0.0120946
$173$	9.17656	0.697681	0.348841	−	0.937182i	$-0.386575\pi$
$173$	9.17656	0.697681	0.348841	+	0.937182i	$0.386575\pi$
$174$	0	0
$175$	0	0
$176$	−1.00000	−0.0753778
$177$	0	0
$178$	−16.6881	−1.25083
$179$	5.76625	0.430990	0.215495	−	0.976505i	$-0.430863\pi$
$179$	5.76625	0.430990	0.215495	+	0.976505i	$0.430863\pi$
$180$	0	0
$181$	−3.38164	−0.251356	−0.125678	−	0.992071i	$-0.540111\pi$
$181$	−3.38164	−0.251356	−0.125678	+	0.992071i	$0.540111\pi$
$182$	0	0
$183$	0	0
$184$	1.49824	0.110451
$185$	2.04922	0.150662
$186$	0	0
$187$	4.64167	0.339432
$188$	0.270780	0.0197486
$189$	0	0
$190$	−3.10587	−0.225324
$191$	16.1586	1.16920	0.584598	−	0.811323i	$-0.301252\pi$
$191$	16.1586	1.16920	0.584598	+	0.811323i	$0.301252\pi$
$192$	0	0
$193$	−24.8651	−1.78983	−0.894913	−	0.446240i	$-0.852763\pi$
$193$	−24.8651	−1.78983	−0.894913	+	0.446240i	$0.852763\pi$
$194$	12.9656	0.930874
$195$	0	0
$196$	0	0
$197$	−10.4290	−0.743036	−0.371518	−	0.928426i	$-0.621163\pi$
$197$	−10.4290	−0.743036	−0.371518	+	0.928426i	$0.621163\pi$
$198$	0	0
$199$	13.2712	0.940767	0.470384	−	0.882462i	$-0.344116\pi$
$199$	13.2712	0.940767	0.470384	+	0.882462i	$0.344116\pi$
$200$	4.77568	0.337691
$201$	0	0
$202$	−0.298919	−0.0210319
$203$	0	0
$204$	0	0
$205$	5.32629	0.372004
$206$	−7.39550	−0.515269
$207$	0	0
$208$	−7.03127	−0.487531
$209$	6.55765	0.453602
$210$	0	0
$211$	−24.2837	−1.67176	−0.835880	−	0.548912i	$-0.815042\pi$
$211$	−24.2837	−1.67176	−0.835880	+	0.548912i	$0.815042\pi$
$212$	9.66628	0.663883
$213$	0	0
$214$	−15.3231	−1.04747
$215$	−0.0751261	−0.00512356
$216$	0	0
$217$	0	0
$218$	0.422735	0.0286312
$219$	0	0
$220$	0.473626	0.0319318
$221$	32.6368	2.19539
$222$	0	0
$223$	3.82529	0.256161	0.128080	−	0.991764i	$-0.459118\pi$
$223$	3.82529	0.256161	0.128080	+	0.991764i	$0.459118\pi$
$224$	0	0
$225$	0	0
$226$	−8.40569	−0.559138
$227$	−12.3106	−0.817082	−0.408541	−	0.912740i	$-0.633962\pi$
$227$	−12.3106	−0.817082	−0.408541	+	0.912740i	$0.633962\pi$
$228$	0	0
$229$	20.2726	1.33965	0.669826	−	0.742518i	$-0.266369\pi$
$229$	20.2726	1.33965	0.669826	+	0.742518i	$0.266369\pi$
$230$	−0.709603	−0.0467898
$231$	0	0
$232$	−2.11882	−0.139108
$233$	10.8114	0.708277	0.354139	−	0.935193i	$-0.384774\pi$
$233$	10.8114	0.708277	0.354139	+	0.935193i	$0.384774\pi$
$234$	0	0
$235$	−0.128248	−0.00836600
$236$	9.82490	0.639546
$237$	0	0
$238$	0	0
$239$	−4.07959	−0.263887	−0.131943	−	0.991257i	$-0.542122\pi$
$239$	−4.07959	−0.263887	−0.131943	+	0.991257i	$0.542122\pi$
$240$	0	0
$241$	−21.9946	−1.41680	−0.708399	−	0.705812i	$-0.750582\pi$
$241$	−21.9946	−1.41680	−0.708399	+	0.705812i	$0.750582\pi$
$242$	−1.00000	−0.0642824
$243$	0	0
$244$	−15.1993	−0.973037
$245$	0	0
$246$	0	0
$247$	46.1086	2.93382
$248$	6.83509	0.434029
$249$	0	0
$250$	−4.63001	−0.292828
$251$	−23.1082	−1.45858	−0.729289	−	0.684205i	$-0.760149\pi$
$251$	−23.1082	−1.45858	−0.729289	+	0.684205i	$0.760149\pi$
$252$	0	0
$253$	1.49824	0.0941932
$254$	−10.1023	−0.633877
$255$	0	0
$256$	1.00000	0.0625000
$257$	−7.75420	−0.483694	−0.241847	−	0.970314i	$-0.577753\pi$
$257$	−7.75420	−0.483694	−0.241847	+	0.970314i	$0.577753\pi$
$258$	0	0
$259$	0	0
$260$	3.33019	0.206530
$261$	0	0
$262$	−20.8843	−1.29024
$263$	13.7851	0.850026	0.425013	−	0.905187i	$-0.360270\pi$
$263$	13.7851	0.850026	0.425013	+	0.905187i	$0.360270\pi$
$264$	0	0
$265$	−4.57820	−0.281236
$266$	0	0
$267$	0	0
$268$	−1.21137	−0.0739961
$269$	−6.13048	−0.373782	−0.186891	−	0.982381i	$-0.559841\pi$
$269$	−6.13048	−0.373782	−0.186891	+	0.982381i	$0.559841\pi$
$270$	0	0
$271$	11.0661	0.672216	0.336108	−	0.941823i	$-0.390889\pi$
$271$	11.0661	0.672216	0.336108	+	0.941823i	$0.390889\pi$
$272$	−4.64167	−0.281443
$273$	0	0
$274$	7.35294	0.444208
$275$	4.77568	0.287984
$276$	0	0
$277$	−16.4986	−0.991305	−0.495653	−	0.868521i	$-0.665071\pi$
$277$	−16.4986	−0.991305	−0.495653	+	0.868521i	$0.665071\pi$
$278$	−4.67647	−0.280476
$279$	0	0
$280$	0	0
$281$	17.2341	1.02810	0.514051	−	0.857760i	$-0.328144\pi$
$281$	17.2341	1.02810	0.514051	+	0.857760i	$0.328144\pi$
$282$	0	0
$283$	18.3333	1.08980	0.544902	−	0.838500i	$-0.316567\pi$
$283$	18.3333	1.08980	0.544902	+	0.838500i	$0.316567\pi$
$284$	−15.0098	−0.890668
$285$	0	0
$286$	−7.03127	−0.415768
$287$	0	0
$288$	0	0
$289$	4.54509	0.267358
$290$	1.00353	0.0589293
$291$	0	0
$292$	6.13048	0.358759
$293$	−26.1560	−1.52805	−0.764025	−	0.645187i	$-0.776779\pi$
$293$	−26.1560	−1.52805	−0.764025	+	0.645187i	$0.776779\pi$
$294$	0	0
$295$	−4.65332	−0.270927
$296$	4.32666	0.251482
$297$	0	0
$298$	4.89097	0.283326
$299$	10.5345	0.609226
$300$	0	0
$301$	0	0
$302$	16.6533	0.958291
$303$	0	0
$304$	−6.55765	−0.376107
$305$	7.19879	0.412201
$306$	0	0
$307$	−25.3109	−1.44457	−0.722286	−	0.691594i	$-0.756909\pi$
$307$	−25.3109	−1.44457	−0.722286	+	0.691594i	$0.756909\pi$
$308$	0	0
$309$	0	0
$310$	−3.23728	−0.183865
$311$	−24.6202	−1.39608	−0.698042	−	0.716057i	$-0.745945\pi$
$311$	−24.6202	−1.39608	−0.698042	+	0.716057i	$0.745945\pi$
$312$	0	0
$313$	−19.2713	−1.08928	−0.544639	−	0.838671i	$-0.683333\pi$
$313$	−19.2713	−1.08928	−0.544639	+	0.838671i	$0.683333\pi$
$314$	−14.5228	−0.819572
$315$	0	0
$316$	11.4420	0.643660
$317$	−4.34551	−0.244068	−0.122034	−	0.992526i	$-0.538942\pi$
$317$	−4.34551	−0.244068	−0.122034	+	0.992526i	$0.538942\pi$
$318$	0	0
$319$	−2.11882	−0.118631
$320$	−0.473626	−0.0264765
$321$	0	0
$322$	0	0
$323$	30.4384	1.69364
$324$	0	0
$325$	33.5791	1.86263
$326$	8.33609	0.461693
$327$	0	0
$328$	11.2458	0.620944
$329$	0	0
$330$	0	0
$331$	−5.46786	−0.300541	−0.150270	−	0.988645i	$-0.548014\pi$
$331$	−5.46786	−0.300541	−0.150270	+	0.988645i	$0.548014\pi$
$332$	−7.54469	−0.414069
$333$	0	0
$334$	−2.84727	−0.155796
$335$	0.573735	0.0313465
$336$	0	0
$337$	7.43569	0.405048	0.202524	−	0.979277i	$-0.435086\pi$
$337$	7.43569	0.405048	0.202524	+	0.979277i	$0.435086\pi$
$338$	−36.4388	−1.98201
$339$	0	0
$340$	2.19841	0.119226
$341$	6.83509	0.370141
$342$	0	0
$343$	0	0
$344$	−0.158619	−0.00855217
$345$	0	0
$346$	−9.17656	−0.493335
$347$	−5.88508	−0.315928	−0.157964	−	0.987445i	$-0.550493\pi$
$347$	−5.88508	−0.315928	−0.157964	+	0.987445i	$0.550493\pi$
$348$	0	0
$349$	−17.5658	−0.940274	−0.470137	−	0.882593i	$-0.655796\pi$
$349$	−17.5658	−0.940274	−0.470137	+	0.882593i	$0.655796\pi$
$350$	0	0
$351$	0	0
$352$	1.00000	0.0533002
$353$	−1.45401	−0.0773891	−0.0386945	−	0.999251i	$-0.512320\pi$
$353$	−1.45401	−0.0773891	−0.0386945	+	0.999251i	$0.512320\pi$
$354$	0	0
$355$	7.10903	0.377308
$356$	16.6881	0.884469
$357$	0	0
$358$	−5.76625	−0.304756
$359$	−19.6796	−1.03865	−0.519325	−	0.854577i	$-0.673817\pi$
$359$	−19.6796	−1.03865	−0.519325	+	0.854577i	$0.673817\pi$
$360$	0	0
$361$	24.0027	1.26330
$362$	3.38164	0.177735
$363$	0	0
$364$	0	0
$365$	−2.90355	−0.151979
$366$	0	0
$367$	18.0692	0.943205	0.471603	−	0.881811i	$-0.343676\pi$
$367$	18.0692	0.943205	0.471603	+	0.881811i	$0.343676\pi$
$368$	−1.49824	−0.0781009
$369$	0	0
$370$	−2.04922	−0.106534
$371$	0	0
$372$	0	0
$373$	−21.3459	−1.10525	−0.552624	−	0.833431i	$-0.686373\pi$
$373$	−21.3459	−1.10525	−0.552624	+	0.833431i	$0.686373\pi$
$374$	−4.64167	−0.240015
$375$	0	0
$376$	−0.270780	−0.0139644
$377$	−14.8980	−0.767288
$378$	0	0
$379$	−4.63448	−0.238057	−0.119029	−	0.992891i	$-0.537978\pi$
$379$	−4.63448	−0.238057	−0.119029	+	0.992891i	$0.537978\pi$
$380$	3.10587	0.159328
$381$	0	0
$382$	−16.1586	−0.826747
$383$	−7.37981	−0.377091	−0.188545	−	0.982065i	$-0.560377\pi$
$383$	−7.37981	−0.377091	−0.188545	+	0.982065i	$0.560377\pi$
$384$	0	0
$385$	0	0
$386$	24.8651	1.26560
$387$	0	0
$388$	−12.9656	−0.658227
$389$	1.34668	0.0682792	0.0341396	−	0.999417i	$-0.489131\pi$
$389$	1.34668	0.0682792	0.0341396	+	0.999417i	$0.489131\pi$
$390$	0	0
$391$	6.95431	0.351695
$392$	0	0
$393$	0	0
$394$	10.4290	0.525406
$395$	−5.41921	−0.272670
$396$	0	0
$397$	20.7346	1.04064	0.520320	−	0.853972i	$-0.325813\pi$
$397$	20.7346	1.04064	0.520320	+	0.853972i	$0.325813\pi$
$398$	−13.2712	−0.665223
$399$	0	0
$400$	−4.77568	−0.238784
$401$	−7.96077	−0.397542	−0.198771	−	0.980046i	$-0.563695\pi$
$401$	−7.96077	−0.397542	−0.198771	+	0.980046i	$0.563695\pi$
$402$	0	0
$403$	48.0594	2.39401
$404$	0.298919	0.0148718
$405$	0	0
$406$	0	0
$407$	4.32666	0.214465
$408$	0	0
$409$	−30.1438	−1.49052	−0.745258	−	0.666777i	$-0.767674\pi$
$409$	−30.1438	−1.49052	−0.745258	+	0.666777i	$0.767674\pi$
$410$	−5.32629	−0.263047
$411$	0	0
$412$	7.39550	0.364350
$413$	0	0
$414$	0	0
$415$	3.57336	0.175409
$416$	7.03127	0.344737
$417$	0	0
$418$	−6.55765	−0.320745
$419$	−26.7025	−1.30450	−0.652252	−	0.758002i	$-0.726176\pi$
$419$	−26.7025	−1.30450	−0.652252	+	0.758002i	$0.726176\pi$
$420$	0	0
$421$	8.44158	0.411418	0.205709	−	0.978613i	$-0.434050\pi$
$421$	8.44158	0.411418	0.205709	+	0.978613i	$0.434050\pi$
$422$	24.2837	1.18211
$423$	0	0
$424$	−9.66628	−0.469436
$425$	22.1671	1.07526
$426$	0	0
$427$	0	0
$428$	15.3231	0.740672
$429$	0	0
$430$	0.0751261	0.00362290
$431$	−18.5510	−0.893569	−0.446785	−	0.894642i	$-0.647431\pi$
$431$	−18.5510	−0.893569	−0.446785	+	0.894642i	$0.647431\pi$
$432$	0	0
$433$	4.19969	0.201824	0.100912	−	0.994895i	$-0.467824\pi$
$433$	4.19969	0.201824	0.100912	+	0.994895i	$0.467824\pi$
$434$	0	0
$435$	0	0
$436$	−0.422735	−0.0202453
$437$	9.82490	0.469989
$438$	0	0
$439$	3.48175	0.166175	0.0830875	−	0.996542i	$-0.473522\pi$
$439$	3.48175	0.166175	0.0830875	+	0.996542i	$0.473522\pi$
$440$	−0.473626	−0.0225792
$441$	0	0
$442$	−32.6368	−1.55238
$443$	−24.6690	−1.17206	−0.586030	−	0.810289i	$-0.699310\pi$
$443$	−24.6690	−1.17206	−0.586030	+	0.810289i	$0.699310\pi$
$444$	0	0
$445$	−7.90393	−0.374682
$446$	−3.82529	−0.181133
$447$	0	0
$448$	0	0
$449$	−6.39863	−0.301970	−0.150985	−	0.988536i	$-0.548245\pi$
$449$	−6.39863	−0.301970	−0.150985	+	0.988536i	$0.548245\pi$
$450$	0	0
$451$	11.2458	0.529543
$452$	8.40569	0.395370
$453$	0	0
$454$	12.3106	0.577764
$455$	0	0
$456$	0	0
$457$	14.5549	0.680849	0.340424	−	0.940272i	$-0.389429\pi$
$457$	14.5549	0.680849	0.340424	+	0.940272i	$0.389429\pi$
$458$	−20.2726	−0.947277
$459$	0	0
$460$	0.709603	0.0330854
$461$	−16.3115	−0.759700	−0.379850	−	0.925048i	$-0.624024\pi$
$461$	−16.3115	−0.759700	−0.379850	+	0.925048i	$0.624024\pi$
$462$	0	0
$463$	8.81138	0.409500	0.204750	−	0.978814i	$-0.434362\pi$
$463$	8.81138	0.409500	0.204750	+	0.978814i	$0.434362\pi$
$464$	2.11882	0.0983640
$465$	0	0
$466$	−10.8114	−0.500828
$467$	8.20468	0.379667	0.189834	−	0.981816i	$-0.439205\pi$
$467$	8.20468	0.379667	0.189834	+	0.981816i	$0.439205\pi$
$468$	0	0
$469$	0	0
$470$	0.128248	0.00591565
$471$	0	0
$472$	−9.82490	−0.452228
$473$	−0.158619	−0.00729332
$474$	0	0
$475$	31.3172	1.43693
$476$	0	0
$477$	0	0
$478$	4.07959	0.186596
$479$	6.72920	0.307465	0.153732	−	0.988113i	$-0.450871\pi$
$479$	6.72920	0.307465	0.153732	+	0.988113i	$0.450871\pi$
$480$	0	0
$481$	30.4219	1.38712
$482$	21.9946	1.00183
$483$	0	0
$484$	1.00000	0.0454545
$485$	6.14083	0.278841
$486$	0	0
$487$	18.9870	0.860385	0.430193	−	0.902737i	$-0.358446\pi$
$487$	18.9870	0.860385	0.430193	+	0.902737i	$0.358446\pi$
$488$	15.1993	0.688041
$489$	0	0
$490$	0	0
$491$	−19.1027	−0.862093	−0.431047	−	0.902330i	$-0.641856\pi$
$491$	−19.1027	−0.862093	−0.431047	+	0.902330i	$0.641856\pi$
$492$	0	0
$493$	−9.83488	−0.442941
$494$	−46.1086	−2.07452
$495$	0	0
$496$	−6.83509	−0.306905
$497$	0	0
$498$	0	0
$499$	−38.6243	−1.72906	−0.864530	−	0.502582i	$-0.832384\pi$
$499$	−38.6243	−1.72906	−0.864530	+	0.502582i	$0.832384\pi$
$500$	4.63001	0.207060
$501$	0	0
$502$	23.1082	1.03137
$503$	2.53784	0.113157	0.0565784	−	0.998398i	$-0.481981\pi$
$503$	2.53784	0.113157	0.0565784	+	0.998398i	$0.481981\pi$
$504$	0	0
$505$	−0.141576	−0.00630004
$506$	−1.49824	−0.0666047
$507$	0	0
$508$	10.1023	0.448219
$509$	−28.5987	−1.26762	−0.633808	−	0.773490i	$-0.718509\pi$
$509$	−28.5987	−1.26762	−0.633808	+	0.773490i	$0.718509\pi$
$510$	0	0
$511$	0	0
$512$	−1.00000	−0.0441942
$513$	0	0
$514$	7.75420	0.342023
$515$	−3.50270	−0.154347
$516$	0	0
$517$	−0.270780	−0.0119089
$518$	0	0
$519$	0	0
$520$	−3.33019	−0.146039
$521$	15.2789	0.669381	0.334691	−	0.942328i	$-0.391368\pi$
$521$	15.2789	0.669381	0.334691	+	0.942328i	$0.391368\pi$
$522$	0	0
$523$	34.6031	1.51309	0.756545	−	0.653942i	$-0.226886\pi$
$523$	34.6031	1.51309	0.756545	+	0.653942i	$0.226886\pi$
$524$	20.8843	0.912335
$525$	0	0
$526$	−13.7851	−0.601059
$527$	31.7262	1.38202
$528$	0	0
$529$	−20.7553	−0.902404
$530$	4.57820	0.198864
$531$	0	0
$532$	0	0
$533$	79.0721	3.42499
$534$	0	0
$535$	−7.25743	−0.313766
$536$	1.21137	0.0523231
$537$	0	0
$538$	6.13048	0.264304
$539$	0	0
$540$	0	0
$541$	11.1153	0.477884	0.238942	−	0.971034i	$-0.423199\pi$
$541$	11.1153	0.477884	0.238942	+	0.971034i	$0.423199\pi$
$542$	−11.0661	−0.475329
$543$	0	0
$544$	4.64167	0.199010
$545$	0.200218	0.00857641
$546$	0	0
$547$	41.5576	1.77688	0.888438	−	0.458997i	$-0.151791\pi$
$547$	41.5576	1.77688	0.888438	+	0.458997i	$0.151791\pi$
$548$	−7.35294	−0.314102
$549$	0	0
$550$	−4.77568	−0.203636
$551$	−13.8945	−0.591926
$552$	0	0
$553$	0	0
$554$	16.4986	0.700959
$555$	0	0
$556$	4.67647	0.198327
$557$	−4.19841	−0.177893	−0.0889463	−	0.996036i	$-0.528350\pi$
$557$	−4.19841	−0.177893	−0.0889463	+	0.996036i	$0.528350\pi$
$558$	0	0
$559$	−1.11529	−0.0471719
$560$	0	0
$561$	0	0
$562$	−17.2341	−0.726977
$563$	5.10311	0.215070	0.107535	−	0.994201i	$-0.465704\pi$
$563$	5.10311	0.215070	0.107535	+	0.994201i	$0.465704\pi$
$564$	0	0
$565$	−3.98115	−0.167488
$566$	−18.3333	−0.770607
$567$	0	0
$568$	15.0098	0.629797
$569$	36.9635	1.54959	0.774795	−	0.632212i	$-0.217853\pi$
$569$	36.9635	1.54959	0.774795	+	0.632212i	$0.217853\pi$
$570$	0	0
$571$	16.7462	0.700808	0.350404	−	0.936599i	$-0.386044\pi$
$571$	16.7462	0.700808	0.350404	+	0.936599i	$0.386044\pi$
$572$	7.03127	0.293992
$573$	0	0
$574$	0	0
$575$	7.15509	0.298388
$576$	0	0
$577$	20.9889	0.873779	0.436889	−	0.899515i	$-0.356080\pi$
$577$	20.9889	0.873779	0.436889	+	0.899515i	$0.356080\pi$
$578$	−4.54509	−0.189051
$579$	0	0
$580$	−1.00353	−0.0416693
$581$	0	0
$582$	0	0
$583$	−9.66628	−0.400336
$584$	−6.13048	−0.253681
$585$	0	0
$586$	26.1560	1.08049
$587$	2.56747	0.105971	0.0529854	−	0.998595i	$-0.483126\pi$
$587$	2.56747	0.105971	0.0529854	+	0.998595i	$0.483126\pi$
$588$	0	0
$589$	44.8221	1.84686
$590$	4.65332	0.191574
$591$	0	0
$592$	−4.32666	−0.177825
$593$	27.7177	1.13823	0.569115	−	0.822258i	$-0.307286\pi$
$593$	27.7177	1.13823	0.569115	+	0.822258i	$0.307286\pi$
$594$	0	0
$595$	0	0
$596$	−4.89097	−0.200342
$597$	0	0
$598$	−10.5345	−0.430788
$599$	−26.2173	−1.07121	−0.535604	−	0.844469i	$-0.679916\pi$
$599$	−26.2173	−1.07121	−0.535604	+	0.844469i	$0.679916\pi$
$600$	0	0
$601$	−20.5621	−0.838745	−0.419372	−	0.907814i	$-0.637750\pi$
$601$	−20.5621	−0.838745	−0.419372	+	0.907814i	$0.637750\pi$
$602$	0	0
$603$	0	0
$604$	−16.6533	−0.677614
$605$	−0.473626	−0.0192556
$606$	0	0
$607$	−22.8839	−0.928829	−0.464415	−	0.885618i	$-0.653735\pi$
$607$	−22.8839	−0.928829	−0.464415	+	0.885618i	$0.653735\pi$
$608$	6.55765	0.265948
$609$	0	0
$610$	−7.19879	−0.291470
$611$	−1.90393	−0.0770246
$612$	0	0
$613$	6.82843	0.275798	0.137899	−	0.990446i	$-0.455965\pi$
$613$	6.82843	0.275798	0.137899	+	0.990446i	$0.455965\pi$
$614$	25.3109	1.02147
$615$	0	0
$616$	0	0
$617$	−22.4120	−0.902272	−0.451136	−	0.892455i	$-0.648981\pi$
$617$	−22.4120	−0.902272	−0.451136	+	0.892455i	$0.648981\pi$
$618$	0	0
$619$	15.6076	0.627324	0.313662	−	0.949535i	$-0.398444\pi$
$619$	15.6076	0.627324	0.313662	+	0.949535i	$0.398444\pi$
$620$	3.23728	0.130012
$621$	0	0
$622$	24.6202	0.987180
$623$	0	0
$624$	0	0
$625$	21.6855	0.867420
$626$	19.2713	0.770236
$627$	0	0
$628$	14.5228	0.579525
$629$	20.0829	0.800759
$630$	0	0
$631$	−18.4588	−0.734834	−0.367417	−	0.930056i	$-0.619758\pi$
$631$	−18.4588	−0.734834	−0.367417	+	0.930056i	$0.619758\pi$
$632$	−11.4420	−0.455137
$633$	0	0
$634$	4.34551	0.172582
$635$	−4.78473	−0.189876
$636$	0	0
$637$	0	0
$638$	2.11882	0.0838851
$639$	0	0
$640$	0.473626	0.0187217
$641$	29.6006	1.16915	0.584576	−	0.811339i	$-0.301261\pi$
$641$	29.6006	1.16915	0.584576	+	0.811339i	$0.301261\pi$
$642$	0	0
$643$	7.93039	0.312744	0.156372	−	0.987698i	$-0.450020\pi$
$643$	7.93039	0.312744	0.156372	+	0.987698i	$0.450020\pi$
$644$	0	0
$645$	0	0
$646$	−30.4384	−1.19758
$647$	−40.4810	−1.59147	−0.795736	−	0.605644i	$-0.792916\pi$
$647$	−40.4810	−1.59147	−0.795736	+	0.605644i	$0.792916\pi$
$648$	0	0
$649$	−9.82490	−0.385661
$650$	−33.5791	−1.31708
$651$	0	0
$652$	−8.33609	−0.326466
$653$	22.8643	0.894750	0.447375	−	0.894346i	$-0.352359\pi$
$653$	22.8643	0.894750	0.447375	+	0.894346i	$0.352359\pi$
$654$	0	0
$655$	−9.89135	−0.386487
$656$	−11.2458	−0.439074
$657$	0	0
$658$	0	0
$659$	−8.96114	−0.349076	−0.174538	−	0.984650i	$-0.555843\pi$
$659$	−8.96114	−0.349076	−0.174538	+	0.984650i	$0.555843\pi$
$660$	0	0
$661$	−8.95891	−0.348461	−0.174231	−	0.984705i	$-0.555744\pi$
$661$	−8.95891	−0.348461	−0.174231	+	0.984705i	$0.555744\pi$
$662$	5.46786	0.212515
$663$	0	0
$664$	7.54469	0.292791
$665$	0	0
$666$	0	0
$667$	−3.17450	−0.122917
$668$	2.84727	0.110164
$669$	0	0
$670$	−0.573735	−0.0221653
$671$	15.1993	0.586763
$672$	0	0
$673$	−32.2141	−1.24176	−0.620881	−	0.783905i	$-0.713225\pi$
$673$	−32.2141	−1.24176	−0.620881	+	0.783905i	$0.713225\pi$
$674$	−7.43569	−0.286412
$675$	0	0
$676$	36.4388	1.40149
$677$	−2.96482	−0.113947	−0.0569737	−	0.998376i	$-0.518145\pi$
$677$	−2.96482	−0.113947	−0.0569737	+	0.998376i	$0.518145\pi$
$678$	0	0
$679$	0	0
$680$	−2.19841	−0.0843053
$681$	0	0
$682$	−6.83509	−0.261729
$683$	−25.4616	−0.974259	−0.487130	−	0.873330i	$-0.661956\pi$
$683$	−25.4616	−0.974259	−0.487130	+	0.873330i	$0.661956\pi$
$684$	0	0
$685$	3.48254	0.133061
$686$	0	0
$687$	0	0
$688$	0.158619	0.00604730
$689$	−67.9662	−2.58931
$690$	0	0
$691$	−8.44785	−0.321371	−0.160686	−	0.987006i	$-0.551371\pi$
$691$	−8.44785	−0.321371	−0.160686	+	0.987006i	$0.551371\pi$
$692$	9.17656	0.348841
$693$	0	0
$694$	5.88508	0.223395
$695$	−2.21490	−0.0840158
$696$	0	0
$697$	52.1992	1.97718
$698$	17.5658	0.664874
$699$	0	0
$700$	0	0
$701$	−49.0886	−1.85405	−0.927025	−	0.374999i	$-0.877643\pi$
$701$	−49.0886	−1.85405	−0.927025	+	0.374999i	$0.877643\pi$
$702$	0	0
$703$	28.3727	1.07010
$704$	−1.00000	−0.0376889
$705$	0	0
$706$	1.45401	0.0547223
$707$	0	0
$708$	0	0
$709$	−0.167483	−0.00628996	−0.00314498	−	0.999995i	$-0.501001\pi$
$709$	−0.167483	−0.00628996	−0.00314498	+	0.999995i	$0.501001\pi$
$710$	−7.10903	−0.266797
$711$	0	0
$712$	−16.6881	−0.625414
$713$	10.2406	0.383512
$714$	0	0
$715$	−3.33019	−0.124542
$716$	5.76625	0.215495
$717$	0	0
$718$	19.6796	0.734436
$719$	−1.83472	−0.0684234	−0.0342117	−	0.999415i	$-0.510892\pi$
$719$	−1.83472	−0.0684234	−0.0342117	+	0.999415i	$0.510892\pi$
$720$	0	0
$721$	0	0
$722$	−24.0027	−0.893289
$723$	0	0
$724$	−3.38164	−0.125678
$725$	−10.1188	−0.375804
$726$	0	0
$727$	27.7394	1.02880	0.514399	−	0.857551i	$-0.328015\pi$
$727$	27.7394	1.02880	0.514399	+	0.857551i	$0.328015\pi$
$728$	0	0
$729$	0	0
$730$	2.90355	0.107465
$731$	−0.736258	−0.0272315
$732$	0	0
$733$	−41.5283	−1.53388	−0.766942	−	0.641716i	$-0.778223\pi$
$733$	−41.5283	−1.53388	−0.766942	+	0.641716i	$0.778223\pi$
$734$	−18.0692	−0.666947
$735$	0	0
$736$	1.49824	0.0552257
$737$	1.21137	0.0446213
$738$	0	0
$739$	1.19488	0.0439545	0.0219773	−	0.999758i	$-0.493004\pi$
$739$	1.19488	0.0439545	0.0219773	+	0.999758i	$0.493004\pi$
$740$	2.04922	0.0753308
$741$	0	0
$742$	0	0
$743$	−4.25650	−0.156156	−0.0780779	−	0.996947i	$-0.524878\pi$
$743$	−4.25650	−0.156156	−0.0780779	+	0.996947i	$0.524878\pi$
$744$	0	0
$745$	2.31649	0.0848697
$746$	21.3459	0.781528
$747$	0	0
$748$	4.64167	0.169716
$749$	0	0
$750$	0	0
$751$	−13.0925	−0.477754	−0.238877	−	0.971050i	$-0.576779\pi$
$751$	−13.0925	−0.477754	−0.238877	+	0.971050i	$0.576779\pi$
$752$	0.270780	0.00987432
$753$	0	0
$754$	14.8980	0.542554
$755$	7.88744	0.287053
$756$	0	0
$757$	−4.21411	−0.153164	−0.0765821	−	0.997063i	$-0.524401\pi$
$757$	−4.21411	−0.153164	−0.0765821	+	0.997063i	$0.524401\pi$
$758$	4.63448	0.168332
$759$	0	0
$760$	−3.10587	−0.112662
$761$	45.8587	1.66238	0.831189	−	0.555990i	$-0.187661\pi$
$761$	45.8587	1.66238	0.831189	+	0.555990i	$0.187661\pi$
$762$	0	0
$763$	0	0
$764$	16.1586	0.584598
$765$	0	0
$766$	7.37981	0.266643
$767$	−69.0815	−2.49439
$768$	0	0
$769$	−53.7185	−1.93714	−0.968569	−	0.248745i	$-0.919982\pi$
$769$	−53.7185	−1.93714	−0.968569	+	0.248745i	$0.919982\pi$
$770$	0	0
$771$	0	0
$772$	−24.8651	−0.894913
$773$	6.90523	0.248364	0.124182	−	0.992259i	$-0.460369\pi$
$773$	6.90523	0.248364	0.124182	+	0.992259i	$0.460369\pi$
$774$	0	0
$775$	32.6422	1.17254
$776$	12.9656	0.465437
$777$	0	0
$778$	−1.34668	−0.0482807
$779$	73.7458	2.64222
$780$	0	0
$781$	15.0098	0.537093
$782$	−6.95431	−0.248686
$783$	0	0
$784$	0	0
$785$	−6.87839	−0.245500
$786$	0	0
$787$	3.06703	0.109328	0.0546639	−	0.998505i	$-0.482591\pi$
$787$	3.06703	0.109328	0.0546639	+	0.998505i	$0.482591\pi$
$788$	−10.4290	−0.371518
$789$	0	0
$790$	5.41921	0.192807
$791$	0	0
$792$	0	0
$793$	106.871	3.79508
$794$	−20.7346	−0.735843
$795$	0	0
$796$	13.2712	0.470384
$797$	−41.1028	−1.45594	−0.727969	−	0.685610i	$-0.759535\pi$
$797$	−41.1028	−1.45594	−0.727969	+	0.685610i	$0.759535\pi$
$798$	0	0
$799$	−1.25687	−0.0444649
$800$	4.77568	0.168846
$801$	0	0
$802$	7.96077	0.281104
$803$	−6.13048	−0.216340
$804$	0	0
$805$	0	0
$806$	−48.0594	−1.69282
$807$	0	0
$808$	−0.298919	−0.0105159
$809$	36.2141	1.27322	0.636610	−	0.771186i	$-0.280336\pi$
$809$	36.2141	1.27322	0.636610	+	0.771186i	$0.280336\pi$
$810$	0	0
$811$	−12.2752	−0.431042	−0.215521	−	0.976499i	$-0.569145\pi$
$811$	−12.2752	−0.431042	−0.215521	+	0.976499i	$0.569145\pi$
$812$	0	0
$813$	0	0
$814$	−4.32666	−0.151649
$815$	3.94819	0.138299
$816$	0	0
$817$	−1.04017	−0.0363909
$818$	30.1438	1.05395
$819$	0	0
$820$	5.32629	0.186002
$821$	43.0697	1.50314	0.751572	−	0.659651i	$-0.229296\pi$
$821$	43.0697	1.50314	0.751572	+	0.659651i	$0.229296\pi$
$822$	0	0
$823$	26.9541	0.939560	0.469780	−	0.882783i	$-0.344333\pi$
$823$	26.9541	0.939560	0.469780	+	0.882783i	$0.344333\pi$
$824$	−7.39550	−0.257634
$825$	0	0
$826$	0	0
$827$	34.9902	1.21673	0.608364	−	0.793659i	$-0.291826\pi$
$827$	34.9902	1.21673	0.608364	+	0.793659i	$0.291826\pi$
$828$	0	0
$829$	−20.7246	−0.719795	−0.359898	−	0.932992i	$-0.617188\pi$
$829$	−20.7246	−0.719795	−0.359898	+	0.932992i	$0.617188\pi$
$830$	−3.57336	−0.124033
$831$	0	0
$832$	−7.03127	−0.243766
$833$	0	0
$834$	0	0
$835$	−1.34854	−0.0466682
$836$	6.55765	0.226801
$837$	0	0
$838$	26.7025	0.922424
$839$	−31.3128	−1.08104	−0.540518	−	0.841332i	$-0.681772\pi$
$839$	−31.3128	−1.08104	−0.540518	+	0.841332i	$0.681772\pi$
$840$	0	0
$841$	−24.5106	−0.845193
$842$	−8.44158	−0.290916
$843$	0	0
$844$	−24.2837	−0.835880
$845$	−17.2584	−0.593705
$846$	0	0
$847$	0	0
$848$	9.66628	0.331941
$849$	0	0
$850$	−22.1671	−0.760326
$851$	6.48236	0.222212
$852$	0	0
$853$	29.5524	1.01186	0.505928	−	0.862576i	$-0.331150\pi$
$853$	29.5524	1.01186	0.505928	+	0.862576i	$0.331150\pi$
$854$	0	0
$855$	0	0
$856$	−15.3231	−0.523734
$857$	−36.7050	−1.25382	−0.626909	−	0.779093i	$-0.715680\pi$
$857$	−36.7050	−1.25382	−0.626909	+	0.779093i	$0.715680\pi$
$858$	0	0
$859$	−0.326102	−0.0111265	−0.00556323	−	0.999985i	$-0.501771\pi$
$859$	−0.326102	−0.0111265	−0.00556323	+	0.999985i	$0.501771\pi$
$860$	−0.0751261	−0.00256178
$861$	0	0
$862$	18.5510	0.631849
$863$	−16.8727	−0.574353	−0.287176	−	0.957878i	$-0.592717\pi$
$863$	−16.8727	−0.574353	−0.287176	+	0.957878i	$0.592717\pi$
$864$	0	0
$865$	−4.34626	−0.147777
$866$	−4.19969	−0.142711
$867$	0	0
$868$	0	0
$869$	−11.4420	−0.388142
$870$	0	0
$871$	8.51746	0.288603
$872$	0.422735	0.0143156
$873$	0	0
$874$	−9.82490	−0.332332
$875$	0	0
$876$	0	0
$877$	−9.71054	−0.327902	−0.163951	−	0.986469i	$-0.552424\pi$
$877$	−9.71054	−0.327902	−0.163951	+	0.986469i	$0.552424\pi$
$878$	−3.48175	−0.117503
$879$	0	0
$880$	0.473626	0.0159659
$881$	22.2976	0.751224	0.375612	−	0.926777i	$-0.377433\pi$
$881$	22.2976	0.751224	0.375612	+	0.926777i	$0.377433\pi$
$882$	0	0
$883$	6.70589	0.225671	0.112836	−	0.993614i	$-0.464007\pi$
$883$	6.70589	0.225671	0.112836	+	0.993614i	$0.464007\pi$
$884$	32.6368	1.09770
$885$	0	0
$886$	24.6690	0.828772
$887$	−58.3368	−1.95876	−0.979380	−	0.202029i	$-0.935247\pi$
$887$	−58.3368	−1.95876	−0.979380	+	0.202029i	$0.935247\pi$
$888$	0	0
$889$	0	0
$890$	7.90393	0.264940
$891$	0	0
$892$	3.82529	0.128080
$893$	−1.77568	−0.0594208
$894$	0	0
$895$	−2.73105	−0.0912888
$896$	0	0
$897$	0	0
$898$	6.39863	0.213525
$899$	−14.4824	−0.483014
$900$	0	0
$901$	−44.8677	−1.49476
$902$	−11.2458	−0.374443
$903$	0	0
$904$	−8.40569	−0.279569
$905$	1.60163	0.0532401
$906$	0	0
$907$	46.2804	1.53671	0.768357	−	0.640021i	$-0.221074\pi$
$907$	46.2804	1.53671	0.768357	+	0.640021i	$0.221074\pi$
$908$	−12.3106	−0.408541
$909$	0	0
$910$	0	0
$911$	55.3864	1.83503	0.917517	−	0.397696i	$-0.130190\pi$
$911$	55.3864	1.83503	0.917517	+	0.397696i	$0.130190\pi$
$912$	0	0
$913$	7.54469	0.249693
$914$	−14.5549	−0.481433
$915$	0	0
$916$	20.2726	0.669826
$917$	0	0
$918$	0	0
$919$	14.1851	0.467923	0.233961	−	0.972246i	$-0.424831\pi$
$919$	14.1851	0.467923	0.233961	+	0.972246i	$0.424831\pi$
$920$	−0.709603	−0.0233949
$921$	0	0
$922$	16.3115	0.537189
$923$	105.538	3.47383
$924$	0	0
$925$	20.6627	0.679387
$926$	−8.81138	−0.289560
$927$	0	0
$928$	−2.11882	−0.0695538
$929$	−31.0150	−1.01757	−0.508784	−	0.860894i	$-0.669905\pi$
$929$	−31.0150	−1.01757	−0.508784	+	0.860894i	$0.669905\pi$
$930$	0	0
$931$	0	0
$932$	10.8114	0.354139
$933$	0	0
$934$	−8.20468	−0.268465
$935$	−2.19841	−0.0718958
$936$	0	0
$937$	−33.5238	−1.09517	−0.547587	−	0.836749i	$-0.684454\pi$
$937$	−33.5238	−1.09517	−0.547587	+	0.836749i	$0.684454\pi$
$938$	0	0
$939$	0	0
$940$	−0.128248	−0.00418300
$941$	32.2097	1.05001	0.525003	−	0.851101i	$-0.324064\pi$
$941$	32.2097	1.05001	0.525003	+	0.851101i	$0.324064\pi$
$942$	0	0
$943$	16.8488	0.548673
$944$	9.82490	0.319773
$945$	0	0
$946$	0.158619	0.00515715
$947$	45.4459	1.47679	0.738396	−	0.674367i	$-0.235584\pi$
$947$	45.4459	1.47679	0.738396	+	0.674367i	$0.235584\pi$
$948$	0	0
$949$	−43.1051	−1.39925
$950$	−31.3172	−1.01606
$951$	0	0
$952$	0	0
$953$	38.5651	1.24924	0.624622	−	0.780927i	$-0.285253\pi$
$953$	38.5651	1.24924	0.624622	+	0.780927i	$0.285253\pi$
$954$	0	0
$955$	−7.65314	−0.247650
$956$	−4.07959	−0.131943
$957$	0	0
$958$	−6.72920	−0.217411
$959$	0	0
$960$	0	0
$961$	15.7185	0.507047
$962$	−30.4219	−0.980843
$963$	0	0
$964$	−21.9946	−0.708399
$965$	11.7767	0.379107
$966$	0	0
$967$	30.4086	0.977875	0.488938	−	0.872319i	$-0.337385\pi$
$967$	30.4086	0.977875	0.488938	+	0.872319i	$0.337385\pi$
$968$	−1.00000	−0.0321412
$969$	0	0
$970$	−6.14083	−0.197170
$971$	−18.1366	−0.582032	−0.291016	−	0.956718i	$-0.593993\pi$
$971$	−18.1366	−0.582032	−0.291016	+	0.956718i	$0.593993\pi$
$972$	0	0
$973$	0	0
$974$	−18.9870	−0.608384
$975$	0	0
$976$	−15.1993	−0.486518
$977$	−2.68370	−0.0858590	−0.0429295	−	0.999078i	$-0.513669\pi$
$977$	−2.68370	−0.0858590	−0.0429295	+	0.999078i	$0.513669\pi$
$978$	0	0
$979$	−16.6881	−0.533355
$980$	0	0
$981$	0	0
$982$	19.1027	0.609592
$983$	39.2806	1.25286	0.626428	−	0.779479i	$-0.284516\pi$
$983$	39.2806	1.25286	0.626428	+	0.779479i	$0.284516\pi$
$984$	0	0
$985$	4.93944	0.157384
$986$	9.83488	0.313206
$987$	0	0
$988$	46.1086	1.46691
$989$	−0.237649	−0.00755679
$990$	0	0
$991$	−48.8051	−1.55034	−0.775172	−	0.631750i	$-0.782337\pi$
$991$	−48.8051	−1.55034	−0.775172	+	0.631750i	$0.782337\pi$
$992$	6.83509	0.217014
$993$	0	0
$994$	0	0
$995$	−6.28556	−0.199266
$996$	0	0
$997$	0.552259	0.0174902	0.00874512	−	0.999962i	$-0.497216\pi$
$997$	0.552259	0.0174902	0.00874512	+	0.999962i	$0.497216\pi$
$998$	38.6243	1.22263
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9702.2.a.ea.1.2		4
3.2	odd	2		3234.2.a.bl.1.3	✓	4
7.6	odd	2		9702.2.a.dz.1.3		4
21.20	even	2		3234.2.a.bm.1.2	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3234.2.a.bl.1.3	✓	4	3.2	odd	2
3234.2.a.bm.1.2	yes	4	21.20	even	2
9702.2.a.dz.1.3		4	7.6	odd	2
9702.2.a.ea.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:	\( N \)	\(=\)	\( 9702 = 2 \cdot 3^{2} \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9702.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{4} -0.473626 q^{5} -1.00000 q^{8} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{4} -0.473626 q^{5} -1.00000 q^{8} +0.473626 q^{10} -1.00000 q^{11} -7.03127 q^{13} +1.00000 q^{16} -4.64167 q^{17} -6.55765 q^{19} -0.473626 q^{20} +1.00000 q^{22} -1.49824 q^{23} -4.77568 q^{25} +7.03127 q^{26} +2.11882 q^{29} -6.83509 q^{31} -1.00000 q^{32} +4.64167 q^{34} -4.32666 q^{37} +6.55765 q^{38} +0.473626 q^{40} -11.2458 q^{41} +0.158619 q^{43} -1.00000 q^{44} +1.49824 q^{46} +0.270780 q^{47} +4.77568 q^{50} -7.03127 q^{52} +9.66628 q^{53} +0.473626 q^{55} -2.11882 q^{58} +9.82490 q^{59} -15.1993 q^{61} +6.83509 q^{62} +1.00000 q^{64} +3.33019 q^{65} -1.21137 q^{67} -4.64167 q^{68} -15.0098 q^{71} +6.13048 q^{73} +4.32666 q^{74} -6.55765 q^{76} +11.4420 q^{79} -0.473626 q^{80} +11.2458 q^{82} -7.54469 q^{83} +2.19841 q^{85} -0.158619 q^{86} +1.00000 q^{88} +16.6881 q^{89} -1.49824 q^{92} -0.270780 q^{94} +3.10587 q^{95} -12.9656 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} + 4 q^{4} + 4 q^{5} - 4 q^{8}+O(q^{10}) \) 4 * q - 4 * q^2 + 4 * q^4 + 4 * q^5 - 4 * q^8	\( 4 q - 4 q^{2} + 4 q^{4} + 4 q^{5} - 4 q^{8} - 4 q^{10} - 4 q^{11} - 8 q^{13} + 4 q^{16} + 4 q^{17} - 12 q^{19} + 4 q^{20} + 4 q^{22} + 8 q^{23} + 4 q^{25} + 8 q^{26} + 8 q^{29} - 4 q^{31} - 4 q^{32} - 4 q^{34} + 8 q^{37} + 12 q^{38} - 4 q^{40} + 12 q^{41} - 8 q^{43} - 4 q^{44} - 8 q^{46} + 4 q^{47} - 4 q^{50} - 8 q^{52} + 8 q^{53} - 4 q^{55} - 8 q^{58} - 24 q^{61} + 4 q^{62} + 4 q^{64} + 16 q^{65} - 8 q^{67} + 4 q^{68} - 8 q^{71} - 4 q^{73} - 8 q^{74} - 12 q^{76} - 8 q^{79} + 4 q^{80} - 12 q^{82} + 4 q^{83} - 8 q^{85} + 8 q^{86} + 4 q^{88} + 24 q^{89} + 8 q^{92} - 4 q^{94} - 8 q^{95}+O(q^{100}) \) 4 * q - 4 * q^2 + 4 * q^4 + 4 * q^5 - 4 * q^8 - 4 * q^10 - 4 * q^11 - 8 * q^13 + 4 * q^16 + 4 * q^17 - 12 * q^19 + 4 * q^20 + 4 * q^22 + 8 * q^23 + 4 * q^25 + 8 * q^26 + 8 * q^29 - 4 * q^31 - 4 * q^32 - 4 * q^34 + 8 * q^37 + 12 * q^38 - 4 * q^40 + 12 * q^41 - 8 * q^43 - 4 * q^44 - 8 * q^46 + 4 * q^47 - 4 * q^50 - 8 * q^52 + 8 * q^53 - 4 * q^55 - 8 * q^58 - 24 * q^61 + 4 * q^62 + 4 * q^64 + 16 * q^65 - 8 * q^67 + 4 * q^68 - 8 * q^71 - 4 * q^73 - 8 * q^74 - 12 * q^76 - 8 * q^79 + 4 * q^80 - 12 * q^82 + 4 * q^83 - 8 * q^85 + 8 * q^86 + 4 * q^88 + 24 * q^89 + 8 * q^92 - 4 * q^94 - 8 * q^95

Introduction

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