LMFDB - Embedded newform 9800.2.a.cv.1.6

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:	$1$
Dimension:	$6$
Coefficient field:	6.6.239575536.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 12x^{4} + 8x^{3} + 35x^{2} - 15x - 8 $ x^6 - x^5 - 12x^4 + 8x^3 + 35x^2 - 15x - 8
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 280)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$-2.54431$ 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)

$f(q)$	$=$	$q+2.54431 q^{3} +3.47349 q^{9} +O(q^{10})$	$q+2.54431 q^{3} +3.47349 q^{9} -3.91228 q^{11} -3.47349 q^{13} +5.08262 q^{17} -5.25188 q^{19} +6.01780 q^{23} +1.20471 q^{27} -10.2660 q^{29} +2.04350 q^{31} -9.95405 q^{33} -0.405001 q^{37} -8.83763 q^{39} -2.57534 q^{41} +6.15769 q^{43} +0.480556 q^{47} +12.9317 q^{51} -0.466428 q^{53} -13.3624 q^{57} -10.3113 q^{59} +8.08088 q^{61} -4.15169 q^{67} +15.3111 q^{69} -4.28658 q^{71} -4.81483 q^{73} -12.6639 q^{79} -7.35533 q^{81} -8.42280 q^{83} -26.1199 q^{87} +2.38595 q^{89} +5.19930 q^{93} -1.32080 q^{97} -13.5893 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - q^{3} + 7 q^{9}+O(q^{10}) $ 6 * q - q^3 + 7 * q^9	$ 6 q - q^{3} + 7 q^{9} + q^{11} - 7 q^{13} - 4 q^{17} - 5 q^{19} + 6 q^{23} - 7 q^{27} - 3 q^{29} - 2 q^{31} - 16 q^{33} + 9 q^{37} + 10 q^{39} + 6 q^{41} - 3 q^{43} - 27 q^{47} - 5 q^{53} - 26 q^{57} - 24 q^{59} + 9 q^{61} + 17 q^{67} + 15 q^{69} + 4 q^{71} - 18 q^{73} - 22 q^{79} - 6 q^{81} - 9 q^{83} - 39 q^{87} + 15 q^{89} + 10 q^{93} - 12 q^{97} + 11 q^{99}+O(q^{100}) $ 6 * q - q^3 + 7 * q^9 + q^11 - 7 * q^13 - 4 * q^17 - 5 * q^19 + 6 * q^23 - 7 * q^27 - 3 * q^29 - 2 * q^31 - 16 * q^33 + 9 * q^37 + 10 * q^39 + 6 * q^41 - 3 * q^43 - 27 * q^47 - 5 * q^53 - 26 * q^57 - 24 * q^59 + 9 * q^61 + 17 * q^67 + 15 * q^69 + 4 * q^71 - 18 * q^73 - 22 * q^79 - 6 * q^81 - 9 * q^83 - 39 * q^87 + 15 * q^89 + 10 * q^93 - 12 * q^97 + 11 * 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
$3$	2.54431	1.46896	0.734478	−	0.678633i	$-0.237427\pi$
$3$	2.54431	1.46896	0.734478	+	0.678633i	$0.237427\pi$
$4$	0	0
$5$	0	0
$5$	0	0
$6$	0	0
$7$	0	0
$7$	0	0
$8$	0	0
$9$	3.47349	1.15783
$10$	0	0
$11$	−3.91228	−1.17960	−0.589799	−	0.807550i	$-0.700793\pi$
$11$	−3.91228	−1.17960	−0.589799	+	0.807550i	$0.700793\pi$
$12$	0	0
$13$	−3.47349	−0.963373	−0.481687	−	0.876344i	$-0.659976\pi$
$13$	−3.47349	−0.963373	−0.481687	+	0.876344i	$0.659976\pi$
$14$	0	0
$15$	0	0
$16$	0	0
$17$	5.08262	1.23272	0.616358	−	0.787466i	$-0.288607\pi$
$17$	5.08262	1.23272	0.616358	+	0.787466i	$0.288607\pi$
$18$	0	0
$19$	−5.25188	−1.20486	−0.602432	−	0.798170i	$-0.705802\pi$
$19$	−5.25188	−1.20486	−0.602432	+	0.798170i	$0.705802\pi$
$20$	0	0
$21$	0	0
$22$	0	0
$23$	6.01780	1.25480	0.627399	−	0.778698i	$-0.284120\pi$
$23$	6.01780	1.25480	0.627399	+	0.778698i	$0.284120\pi$
$24$	0	0
$25$	0	0
$26$	0	0
$27$	1.20471	0.231846
$28$	0	0
$29$	−10.2660	−1.90635	−0.953175	−	0.302419i	$-0.902206\pi$
$29$	−10.2660	−1.90635	−0.953175	+	0.302419i	$0.902206\pi$
$30$	0	0
$31$	2.04350	0.367024	0.183512	−	0.983017i	$-0.441253\pi$
$31$	2.04350	0.367024	0.183512	+	0.983017i	$0.441253\pi$
$32$	0	0
$33$	−9.95405	−1.73278
$34$	0	0
$35$	0	0
$36$	0	0
$37$	−0.405001	−0.0665818	−0.0332909	−	0.999446i	$-0.510599\pi$
$37$	−0.405001	−0.0665818	−0.0332909	+	0.999446i	$0.510599\pi$
$38$	0	0
$39$	−8.83763	−1.41515
$40$	0	0
$41$	−2.57534	−0.402200	−0.201100	−	0.979571i	$-0.564452\pi$
$41$	−2.57534	−0.402200	−0.201100	+	0.979571i	$0.564452\pi$
$42$	0	0
$43$	6.15769	0.939038	0.469519	−	0.882922i	$-0.344427\pi$
$43$	6.15769	0.939038	0.469519	+	0.882922i	$0.344427\pi$
$44$	0	0
$45$	0	0
$46$	0	0
$47$	0.480556	0.0700963	0.0350481	−	0.999386i	$-0.488842\pi$
$47$	0.480556	0.0700963	0.0350481	+	0.999386i	$0.488842\pi$
$48$	0	0
$49$	0	0
$50$	0	0
$51$	12.9317	1.81081
$52$	0	0
$53$	−0.466428	−0.0640688	−0.0320344	−	0.999487i	$-0.510199\pi$
$53$	−0.466428	−0.0640688	−0.0320344	+	0.999487i	$0.510199\pi$
$54$	0	0
$55$	0	0
$56$	0	0
$57$	−13.3624	−1.76989
$58$	0	0
$59$	−10.3113	−1.34242	−0.671208	−	0.741269i	$-0.734224\pi$
$59$	−10.3113	−1.34242	−0.671208	+	0.741269i	$0.734224\pi$
$60$	0	0
$61$	8.08088	1.03465	0.517325	−	0.855789i	$-0.326928\pi$
$61$	8.08088	1.03465	0.517325	+	0.855789i	$0.326928\pi$
$62$	0	0
$63$	0	0
$64$	0	0
$65$	0	0
$66$	0	0
$67$	−4.15169	−0.507210	−0.253605	−	0.967308i	$-0.581616\pi$
$67$	−4.15169	−0.507210	−0.253605	+	0.967308i	$0.581616\pi$
$68$	0	0
$69$	15.3111	1.84324
$70$	0	0
$71$	−4.28658	−0.508724	−0.254362	−	0.967109i	$-0.581865\pi$
$71$	−4.28658	−0.508724	−0.254362	+	0.967109i	$0.581865\pi$
$72$	0	0
$73$	−4.81483	−0.563533	−0.281767	−	0.959483i	$-0.590920\pi$
$73$	−4.81483	−0.563533	−0.281767	+	0.959483i	$0.590920\pi$
$74$	0	0
$75$	0	0
$76$	0	0
$77$	0	0
$78$	0	0
$79$	−12.6639	−1.42481	−0.712403	−	0.701771i	$-0.752393\pi$
$79$	−12.6639	−1.42481	−0.712403	+	0.701771i	$0.752393\pi$
$80$	0	0
$81$	−7.35533	−0.817259
$82$	0	0
$83$	−8.42280	−0.924522	−0.462261	−	0.886744i	$-0.652962\pi$
$83$	−8.42280	−0.924522	−0.462261	+	0.886744i	$0.652962\pi$
$84$	0	0
$85$	0	0
$86$	0	0
$87$	−26.1199	−2.80034
$88$	0	0
$89$	2.38595	0.252910	0.126455	−	0.991972i	$-0.459640\pi$
$89$	2.38595	0.252910	0.126455	+	0.991972i	$0.459640\pi$
$90$	0	0
$91$	0	0
$92$	0	0
$93$	5.19930	0.539142
$94$	0	0
$95$	0	0
$96$	0	0
$97$	−1.32080	−0.134107	−0.0670537	−	0.997749i	$-0.521360\pi$
$97$	−1.32080	−0.134107	−0.0670537	+	0.997749i	$0.521360\pi$
$98$	0	0
$99$	−13.5893	−1.36577
$100$	0	0
$101$	7.75166	0.771319	0.385660	−	0.922641i	$-0.373974\pi$
$101$	7.75166	0.771319	0.385660	+	0.922641i	$0.373974\pi$
$102$	0	0
$103$	−2.20364	−0.217131	−0.108565	−	0.994089i	$-0.534626\pi$
$103$	−2.20364	−0.217131	−0.108565	+	0.994089i	$0.534626\pi$
$104$	0	0
$105$	0	0
$106$	0	0
$107$	10.8235	1.04635	0.523176	−	0.852225i	$-0.324747\pi$
$107$	10.8235	1.04635	0.523176	+	0.852225i	$0.324747\pi$
$108$	0	0
$109$	−11.0433	−1.05776	−0.528880	−	0.848697i	$-0.677388\pi$
$109$	−11.0433	−1.05776	−0.528880	+	0.848697i	$0.677388\pi$
$110$	0	0
$111$	−1.03045	−0.0978057
$112$	0	0
$113$	−7.29167	−0.685942	−0.342971	−	0.939346i	$-0.611433\pi$
$113$	−7.29167	−0.685942	−0.342971	+	0.939346i	$0.611433\pi$
$114$	0	0
$115$	0	0
$116$	0	0
$117$	−12.0651	−1.11542
$118$	0	0
$119$	0	0
$120$	0	0
$121$	4.30597	0.391452
$122$	0	0
$123$	−6.55244	−0.590814
$124$	0	0
$125$	0	0
$126$	0	0
$127$	−7.66305	−0.679986	−0.339993	−	0.940428i	$-0.610425\pi$
$127$	−7.66305	−0.679986	−0.339993	+	0.940428i	$0.610425\pi$
$128$	0	0
$129$	15.6670	1.37941
$130$	0	0
$131$	−17.2119	−1.50381	−0.751906	−	0.659270i	$-0.770865\pi$
$131$	−17.2119	−1.50381	−0.751906	+	0.659270i	$0.770865\pi$
$132$	0	0
$133$	0	0
$134$	0	0
$135$	0	0
$136$	0	0
$137$	5.26072	0.449454	0.224727	−	0.974422i	$-0.427851\pi$
$137$	5.26072	0.449454	0.224727	+	0.974422i	$0.427851\pi$
$138$	0	0
$139$	−15.2148	−1.29050	−0.645250	−	0.763971i	$-0.723247\pi$
$139$	−15.2148	−1.29050	−0.645250	+	0.763971i	$0.723247\pi$
$140$	0	0
$141$	1.22268	0.102968
$142$	0	0
$143$	13.5893	1.13639
$144$	0	0
$145$	0	0
$146$	0	0
$147$	0	0
$148$	0	0
$149$	−1.01721	−0.0833335	−0.0416667	−	0.999132i	$-0.513267\pi$
$149$	−1.01721	−0.0833335	−0.0416667	+	0.999132i	$0.513267\pi$
$150$	0	0
$151$	13.2583	1.07894	0.539472	−	0.842004i	$-0.318624\pi$
$151$	13.2583	1.07894	0.539472	+	0.842004i	$0.318624\pi$
$152$	0	0
$153$	17.6544	1.42728
$154$	0	0
$155$	0	0
$156$	0	0
$157$	−17.7722	−1.41838	−0.709189	−	0.705019i	$-0.750939\pi$
$157$	−17.7722	−1.41838	−0.709189	+	0.705019i	$0.750939\pi$
$158$	0	0
$159$	−1.18674	−0.0941143
$160$	0	0
$161$	0	0
$162$	0	0
$163$	−2.91952	−0.228675	−0.114337	−	0.993442i	$-0.536474\pi$
$163$	−2.91952	−0.228675	−0.114337	+	0.993442i	$0.536474\pi$
$164$	0	0
$165$	0	0
$166$	0	0
$167$	9.21710	0.713240	0.356620	−	0.934249i	$-0.383929\pi$
$167$	9.21710	0.713240	0.356620	+	0.934249i	$0.383929\pi$
$168$	0	0
$169$	−0.934854	−0.0719118
$170$	0	0
$171$	−18.2424	−1.39503
$172$	0	0
$173$	21.6803	1.64832	0.824162	−	0.566354i	$-0.191647\pi$
$173$	21.6803	1.64832	0.824162	+	0.566354i	$0.191647\pi$
$174$	0	0
$175$	0	0
$176$	0	0
$177$	−26.2351	−1.97195
$178$	0	0
$179$	−24.9965	−1.86833	−0.934164	−	0.356843i	$-0.883853\pi$
$179$	−24.9965	−1.86833	−0.934164	+	0.356843i	$0.883853\pi$
$180$	0	0
$181$	−4.17900	−0.310623	−0.155311	−	0.987866i	$-0.549638\pi$
$181$	−4.17900	−0.310623	−0.155311	+	0.987866i	$0.549638\pi$
$182$	0	0
$183$	20.5602	1.51986
$184$	0	0
$185$	0	0
$186$	0	0
$187$	−19.8846	−1.45411
$188$	0	0
$189$	0	0
$190$	0	0
$191$	−8.97169	−0.649169	−0.324585	−	0.945857i	$-0.605224\pi$
$191$	−8.97169	−0.649169	−0.324585	+	0.945857i	$0.605224\pi$
$192$	0	0
$193$	18.2218	1.31164	0.655818	−	0.754919i	$-0.272324\pi$
$193$	18.2218	1.31164	0.655818	+	0.754919i	$0.272324\pi$
$194$	0	0
$195$	0	0
$196$	0	0
$197$	−23.5632	−1.67881	−0.839403	−	0.543509i	$-0.817095\pi$
$197$	−23.5632	−1.67881	−0.839403	+	0.543509i	$0.817095\pi$
$198$	0	0
$199$	20.7163	1.46854	0.734271	−	0.678856i	$-0.237524\pi$
$199$	20.7163	1.46854	0.734271	+	0.678856i	$0.237524\pi$
$200$	0	0
$201$	−10.5632	−0.745069
$202$	0	0
$203$	0	0
$204$	0	0
$205$	0	0
$206$	0	0
$207$	20.9028	1.45284
$208$	0	0
$209$	20.5469	1.42126
$210$	0	0
$211$	7.69865	0.529997	0.264998	−	0.964249i	$-0.414629\pi$
$211$	7.69865	0.529997	0.264998	+	0.964249i	$0.414629\pi$
$212$	0	0
$213$	−10.9064	−0.747292
$214$	0	0
$215$	0	0
$216$	0	0
$217$	0	0
$218$	0	0
$219$	−12.2504	−0.827805
$220$	0	0
$221$	−17.6544	−1.18757
$222$	0	0
$223$	−12.7136	−0.851366	−0.425683	−	0.904872i	$-0.639966\pi$
$223$	−12.7136	−0.851366	−0.425683	+	0.904872i	$0.639966\pi$
$224$	0	0
$225$	0	0
$226$	0	0
$227$	10.7229	0.711706	0.355853	−	0.934542i	$-0.384190\pi$
$227$	10.7229	0.711706	0.355853	+	0.934542i	$0.384190\pi$
$228$	0	0
$229$	−24.7892	−1.63812	−0.819059	−	0.573709i	$-0.805504\pi$
$229$	−24.7892	−1.63812	−0.819059	+	0.573709i	$0.805504\pi$
$230$	0	0
$231$	0	0
$232$	0	0
$233$	−22.7544	−1.49069	−0.745345	−	0.666679i	$-0.767715\pi$
$233$	−22.7544	−1.49069	−0.745345	+	0.666679i	$0.767715\pi$
$234$	0	0
$235$	0	0
$236$	0	0
$237$	−32.2210	−2.09298
$238$	0	0
$239$	−1.49071	−0.0964258	−0.0482129	−	0.998837i	$-0.515353\pi$
$239$	−1.49071	−0.0964258	−0.0482129	+	0.998837i	$0.515353\pi$
$240$	0	0
$241$	26.1677	1.68561	0.842806	−	0.538217i	$-0.180902\pi$
$241$	26.1677	1.68561	0.842806	+	0.538217i	$0.180902\pi$
$242$	0	0
$243$	−22.3283	−1.43236
$244$	0	0
$245$	0	0
$246$	0	0
$247$	18.2424	1.16073
$248$	0	0
$249$	−21.4302	−1.35808
$250$	0	0
$251$	4.90277	0.309460	0.154730	−	0.987957i	$-0.450549\pi$
$251$	4.90277	0.309460	0.154730	+	0.987957i	$0.450549\pi$
$252$	0	0
$253$	−23.5433	−1.48016
$254$	0	0
$255$	0	0
$256$	0	0
$257$	−12.3399	−0.769739	−0.384870	−	0.922971i	$-0.625754\pi$
$257$	−12.3399	−0.769739	−0.384870	+	0.922971i	$0.625754\pi$
$258$	0	0
$259$	0	0
$260$	0	0
$261$	−35.6589	−2.20723
$262$	0	0
$263$	20.1247	1.24094	0.620471	−	0.784229i	$-0.286941\pi$
$263$	20.1247	1.24094	0.620471	+	0.784229i	$0.286941\pi$
$264$	0	0
$265$	0	0
$266$	0	0
$267$	6.07059	0.371514
$268$	0	0
$269$	−14.9394	−0.910874	−0.455437	−	0.890268i	$-0.650517\pi$
$269$	−14.9394	−0.910874	−0.455437	+	0.890268i	$0.650517\pi$
$270$	0	0
$271$	−5.80932	−0.352891	−0.176446	−	0.984310i	$-0.556460\pi$
$271$	−5.80932	−0.352891	−0.176446	+	0.984310i	$0.556460\pi$
$272$	0	0
$273$	0	0
$274$	0	0
$275$	0	0
$276$	0	0
$277$	25.9390	1.55853	0.779263	−	0.626697i	$-0.215594\pi$
$277$	25.9390	1.55853	0.779263	+	0.626697i	$0.215594\pi$
$278$	0	0
$279$	7.09809	0.424952
$280$	0	0
$281$	−14.8840	−0.887904	−0.443952	−	0.896051i	$-0.646424\pi$
$281$	−14.8840	−0.887904	−0.443952	+	0.896051i	$0.646424\pi$
$282$	0	0
$283$	−9.71540	−0.577520	−0.288760	−	0.957401i	$-0.593243\pi$
$283$	−9.71540	−0.577520	−0.288760	+	0.957401i	$0.593243\pi$
$284$	0	0
$285$	0	0
$286$	0	0
$287$	0	0
$288$	0	0
$289$	8.83301	0.519589
$290$	0	0
$291$	−3.36053	−0.196998
$292$	0	0
$293$	8.08596	0.472387	0.236194	−	0.971706i	$-0.424100\pi$
$293$	8.08596	0.472387	0.236194	+	0.971706i	$0.424100\pi$
$294$	0	0
$295$	0	0
$296$	0	0
$297$	−4.71316	−0.273485
$298$	0	0
$299$	−20.9028	−1.20884
$300$	0	0
$301$	0	0
$302$	0	0
$303$	19.7226	1.13303
$304$	0	0
$305$	0	0
$306$	0	0
$307$	−8.81809	−0.503275	−0.251637	−	0.967822i	$-0.580969\pi$
$307$	−8.81809	−0.503275	−0.251637	+	0.967822i	$0.580969\pi$
$308$	0	0
$309$	−5.60673	−0.318956
$310$	0	0
$311$	9.66439	0.548017	0.274009	−	0.961727i	$-0.411650\pi$
$311$	9.66439	0.548017	0.274009	+	0.961727i	$0.411650\pi$
$312$	0	0
$313$	−27.1864	−1.53667	−0.768334	−	0.640049i	$-0.778914\pi$
$313$	−27.1864	−1.53667	−0.768334	+	0.640049i	$0.778914\pi$
$314$	0	0
$315$	0	0
$316$	0	0
$317$	12.1583	0.682876	0.341438	−	0.939904i	$-0.389086\pi$
$317$	12.1583	0.682876	0.341438	+	0.939904i	$0.389086\pi$
$318$	0	0
$319$	40.1635	2.24873
$320$	0	0
$321$	27.5384	1.53704
$322$	0	0
$323$	−26.6933	−1.48526
$324$	0	0
$325$	0	0
$326$	0	0
$327$	−28.0976	−1.55380
$328$	0	0
$329$	0	0
$330$	0	0
$331$	−3.42945	−0.188500	−0.0942499	−	0.995549i	$-0.530045\pi$
$331$	−3.42945	−0.188500	−0.0942499	+	0.995549i	$0.530045\pi$
$332$	0	0
$333$	−1.40677	−0.0770904
$334$	0	0
$335$	0	0
$336$	0	0
$337$	−1.39770	−0.0761375	−0.0380687	−	0.999275i	$-0.512121\pi$
$337$	−1.39770	−0.0761375	−0.0380687	+	0.999275i	$0.512121\pi$
$338$	0	0
$339$	−18.5522	−1.00762
$340$	0	0
$341$	−7.99477	−0.432941
$342$	0	0
$343$	0	0
$344$	0	0
$345$	0	0
$346$	0	0
$347$	3.46302	0.185904	0.0929522	−	0.995671i	$-0.470370\pi$
$347$	3.46302	0.185904	0.0929522	+	0.995671i	$0.470370\pi$
$348$	0	0
$349$	−19.2360	−1.02968	−0.514838	−	0.857287i	$-0.672148\pi$
$349$	−19.2360	−1.02968	−0.514838	+	0.857287i	$0.672148\pi$
$350$	0	0
$351$	−4.18454	−0.223354
$352$	0	0
$353$	−17.2651	−0.918931	−0.459465	−	0.888196i	$-0.651959\pi$
$353$	−17.2651	−0.918931	−0.459465	+	0.888196i	$0.651959\pi$
$354$	0	0
$355$	0	0
$356$	0	0
$357$	0	0
$358$	0	0
$359$	0.867633	0.0457919	0.0228960	−	0.999738i	$-0.492711\pi$
$359$	0.867633	0.0457919	0.0228960	+	0.999738i	$0.492711\pi$
$360$	0	0
$361$	8.58226	0.451698
$362$	0	0
$363$	10.9557	0.575025
$364$	0	0
$365$	0	0
$366$	0	0
$367$	16.4984	0.861210	0.430605	−	0.902541i	$-0.358300\pi$
$367$	16.4984	0.861210	0.430605	+	0.902541i	$0.358300\pi$
$368$	0	0
$369$	−8.94541	−0.465679
$370$	0	0
$371$	0	0
$372$	0	0
$373$	20.3871	1.05560	0.527801	−	0.849368i	$-0.323017\pi$
$373$	20.3871	1.05560	0.527801	+	0.849368i	$0.323017\pi$
$374$	0	0
$375$	0	0
$376$	0	0
$377$	35.6589	1.83653
$378$	0	0
$379$	13.1652	0.676251	0.338126	−	0.941101i	$-0.390207\pi$
$379$	13.1652	0.676251	0.338126	+	0.941101i	$0.390207\pi$
$380$	0	0
$381$	−19.4971	−0.998869
$382$	0	0
$383$	−5.19162	−0.265280	−0.132640	−	0.991164i	$-0.542345\pi$
$383$	−5.19162	−0.265280	−0.132640	+	0.991164i	$0.542345\pi$
$384$	0	0
$385$	0	0
$386$	0	0
$387$	21.3887	1.08725
$388$	0	0
$389$	31.1419	1.57896	0.789478	−	0.613779i	$-0.210351\pi$
$389$	31.1419	1.57896	0.789478	+	0.613779i	$0.210351\pi$
$390$	0	0
$391$	30.5862	1.54681
$392$	0	0
$393$	−43.7924	−2.20903
$394$	0	0
$395$	0	0
$396$	0	0
$397$	15.1065	0.758174	0.379087	−	0.925361i	$-0.376238\pi$
$397$	15.1065	0.758174	0.379087	+	0.925361i	$0.376238\pi$
$398$	0	0
$399$	0	0
$400$	0	0
$401$	16.2471	0.811340	0.405670	−	0.914020i	$-0.367038\pi$
$401$	16.2471	0.811340	0.405670	+	0.914020i	$0.367038\pi$
$402$	0	0
$403$	−7.09809	−0.353581
$404$	0	0
$405$	0	0
$406$	0	0
$407$	1.58448	0.0785397
$408$	0	0
$409$	33.3206	1.64760	0.823798	−	0.566883i	$-0.191851\pi$
$409$	33.3206	1.64760	0.823798	+	0.566883i	$0.191851\pi$
$410$	0	0
$411$	13.3849	0.660228
$412$	0	0
$413$	0	0
$414$	0	0
$415$	0	0
$416$	0	0
$417$	−38.7110	−1.89569
$418$	0	0
$419$	11.3290	0.553457	0.276729	−	0.960948i	$-0.410750\pi$
$419$	11.3290	0.553457	0.276729	+	0.960948i	$0.410750\pi$
$420$	0	0
$421$	12.5047	0.609440	0.304720	−	0.952442i	$-0.401437\pi$
$421$	12.5047	0.609440	0.304720	+	0.952442i	$0.401437\pi$
$422$	0	0
$423$	1.66921	0.0811596
$424$	0	0
$425$	0	0
$426$	0	0
$427$	0	0
$428$	0	0
$429$	34.5753	1.66931
$430$	0	0
$431$	−5.14713	−0.247928	−0.123964	−	0.992287i	$-0.539561\pi$
$431$	−5.14713	−0.247928	−0.123964	+	0.992287i	$0.539561\pi$
$432$	0	0
$433$	−1.88420	−0.0905491	−0.0452745	−	0.998975i	$-0.514416\pi$
$433$	−1.88420	−0.0905491	−0.0452745	+	0.998975i	$0.514416\pi$
$434$	0	0
$435$	0	0
$436$	0	0
$437$	−31.6048	−1.51186
$438$	0	0
$439$	10.5904	0.505454	0.252727	−	0.967538i	$-0.418673\pi$
$439$	10.5904	0.505454	0.252727	+	0.967538i	$0.418673\pi$
$440$	0	0
$441$	0	0
$442$	0	0
$443$	−24.3510	−1.15695	−0.578476	−	0.815700i	$-0.696352\pi$
$443$	−24.3510	−1.15695	−0.578476	+	0.815700i	$0.696352\pi$
$444$	0	0
$445$	0	0
$446$	0	0
$447$	−2.58811	−0.122413
$448$	0	0
$449$	20.2506	0.955684	0.477842	−	0.878446i	$-0.341419\pi$
$449$	20.2506	0.955684	0.477842	+	0.878446i	$0.341419\pi$
$450$	0	0
$451$	10.0754	0.474434
$452$	0	0
$453$	33.7331	1.58492
$454$	0	0
$455$	0	0
$456$	0	0
$457$	19.1864	0.897503	0.448752	−	0.893657i	$-0.351869\pi$
$457$	19.1864	0.897503	0.448752	+	0.893657i	$0.351869\pi$
$458$	0	0
$459$	6.12307	0.285801
$460$	0	0
$461$	−13.4096	−0.624548	−0.312274	−	0.949992i	$-0.601091\pi$
$461$	−13.4096	−0.624548	−0.312274	+	0.949992i	$0.601091\pi$
$462$	0	0
$463$	17.7864	0.826604	0.413302	−	0.910594i	$-0.364375\pi$
$463$	17.7864	0.826604	0.413302	+	0.910594i	$0.364375\pi$
$464$	0	0
$465$	0	0
$466$	0	0
$467$	−15.2100	−0.703835	−0.351918	−	0.936031i	$-0.614470\pi$
$467$	−15.2100	−0.703835	−0.351918	+	0.936031i	$0.614470\pi$
$468$	0	0
$469$	0	0
$470$	0	0
$471$	−45.2180	−2.08353
$472$	0	0
$473$	−24.0906	−1.10769
$474$	0	0
$475$	0	0
$476$	0	0
$477$	−1.62013	−0.0741809
$478$	0	0
$479$	−12.5684	−0.574266	−0.287133	−	0.957891i	$-0.592702\pi$
$479$	−12.5684	−0.574266	−0.287133	+	0.957891i	$0.592702\pi$
$480$	0	0
$481$	1.40677	0.0641431
$482$	0	0
$483$	0	0
$484$	0	0
$485$	0	0
$486$	0	0
$487$	−13.7901	−0.624888	−0.312444	−	0.949936i	$-0.601148\pi$
$487$	−13.7901	−0.624888	−0.312444	+	0.949936i	$0.601148\pi$
$488$	0	0
$489$	−7.42816	−0.335913
$490$	0	0
$491$	27.4423	1.23845	0.619226	−	0.785213i	$-0.287447\pi$
$491$	27.4423	1.23845	0.619226	+	0.785213i	$0.287447\pi$
$492$	0	0
$493$	−52.1782	−2.34999
$494$	0	0
$495$	0	0
$496$	0	0
$497$	0	0
$498$	0	0
$499$	−19.7379	−0.883590	−0.441795	−	0.897116i	$-0.645658\pi$
$499$	−19.7379	−0.883590	−0.441795	+	0.897116i	$0.645658\pi$
$500$	0	0
$501$	23.4511	1.04772
$502$	0	0
$503$	−5.00417	−0.223125	−0.111562	−	0.993757i	$-0.535585\pi$
$503$	−5.00417	−0.223125	−0.111562	+	0.993757i	$0.535585\pi$
$504$	0	0
$505$	0	0
$506$	0	0
$507$	−2.37855	−0.105635
$508$	0	0
$509$	22.7592	1.00878	0.504392	−	0.863475i	$-0.331717\pi$
$509$	22.7592	1.00878	0.504392	+	0.863475i	$0.331717\pi$
$510$	0	0
$511$	0	0
$512$	0	0
$513$	−6.32699	−0.279343
$514$	0	0
$515$	0	0
$516$	0	0
$517$	−1.88007	−0.0826854
$518$	0	0
$519$	55.1614	2.42131
$520$	0	0
$521$	−17.5371	−0.768315	−0.384158	−	0.923267i	$-0.625508\pi$
$521$	−17.5371	−0.768315	−0.384158	+	0.923267i	$0.625508\pi$
$522$	0	0
$523$	13.7901	0.602998	0.301499	−	0.953467i	$-0.402513\pi$
$523$	13.7901	0.602998	0.301499	+	0.953467i	$0.402513\pi$
$524$	0	0
$525$	0	0
$526$	0	0
$527$	10.3863	0.452436
$528$	0	0
$529$	13.2139	0.574517
$530$	0	0
$531$	−35.8162	−1.55429
$532$	0	0
$533$	8.94541	0.387469
$534$	0	0
$535$	0	0
$536$	0	0
$537$	−63.5988	−2.74449
$538$	0	0
$539$	0	0
$540$	0	0
$541$	46.0001	1.97770	0.988849	−	0.148922i	$-0.0475805\pi$
$541$	46.0001	1.97770	0.988849	+	0.148922i	$0.0475805\pi$
$542$	0	0
$543$	−10.6327	−0.456291
$544$	0	0
$545$	0	0
$546$	0	0
$547$	−26.4411	−1.13054	−0.565270	−	0.824906i	$-0.691228\pi$
$547$	−26.4411	−1.13054	−0.565270	+	0.824906i	$0.691228\pi$
$548$	0	0
$549$	28.0689	1.19795
$550$	0	0
$551$	53.9159	2.29689
$552$	0	0
$553$	0	0
$554$	0	0
$555$	0	0
$556$	0	0
$557$	31.7219	1.34410	0.672050	−	0.740506i	$-0.265414\pi$
$557$	31.7219	1.34410	0.672050	+	0.740506i	$0.265414\pi$
$558$	0	0
$559$	−21.3887	−0.904644
$560$	0	0
$561$	−50.5926	−2.13602
$562$	0	0
$563$	20.7249	0.873448	0.436724	−	0.899595i	$-0.356139\pi$
$563$	20.7249	0.873448	0.436724	+	0.899595i	$0.356139\pi$
$564$	0	0
$565$	0	0
$566$	0	0
$567$	0	0
$568$	0	0
$569$	42.5454	1.78360	0.891799	−	0.452432i	$-0.149444\pi$
$569$	42.5454	1.78360	0.891799	+	0.452432i	$0.149444\pi$
$570$	0	0
$571$	30.1062	1.25990	0.629952	−	0.776634i	$-0.283074\pi$
$571$	30.1062	1.25990	0.629952	+	0.776634i	$0.283074\pi$
$572$	0	0
$573$	−22.8267	−0.953601
$574$	0	0
$575$	0	0
$576$	0	0
$577$	10.2683	0.427473	0.213736	−	0.976891i	$-0.431437\pi$
$577$	10.2683	0.427473	0.213736	+	0.976891i	$0.431437\pi$
$578$	0	0
$579$	46.3619	1.92674
$580$	0	0
$581$	0	0
$582$	0	0
$583$	1.82480	0.0755755
$584$	0	0
$585$	0	0
$586$	0	0
$587$	−41.5546	−1.71514	−0.857570	−	0.514367i	$-0.828027\pi$
$587$	−41.5546	−1.71514	−0.857570	+	0.514367i	$0.828027\pi$
$588$	0	0
$589$	−10.7322	−0.442214
$590$	0	0
$591$	−59.9519	−2.46609
$592$	0	0
$593$	−23.9303	−0.982698	−0.491349	−	0.870963i	$-0.663496\pi$
$593$	−23.9303	−0.982698	−0.491349	+	0.870963i	$0.663496\pi$
$594$	0	0
$595$	0	0
$596$	0	0
$597$	52.7087	2.15722
$598$	0	0
$599$	9.08267	0.371108	0.185554	−	0.982634i	$-0.440592\pi$
$599$	9.08267	0.371108	0.185554	+	0.982634i	$0.440592\pi$
$600$	0	0
$601$	−29.8162	−1.21623	−0.608114	−	0.793850i	$-0.708074\pi$
$601$	−29.8162	−1.21623	−0.608114	+	0.793850i	$0.708074\pi$
$602$	0	0
$603$	−14.4209	−0.587263
$604$	0	0
$605$	0	0
$606$	0	0
$607$	−14.5480	−0.590486	−0.295243	−	0.955422i	$-0.595401\pi$
$607$	−14.5480	−0.590486	−0.295243	+	0.955422i	$0.595401\pi$
$608$	0	0
$609$	0	0
$610$	0	0
$611$	−1.66921	−0.0675289
$612$	0	0
$613$	−10.3228	−0.416934	−0.208467	−	0.978029i	$-0.566847\pi$
$613$	−10.3228	−0.416934	−0.208467	+	0.978029i	$0.566847\pi$
$614$	0	0
$615$	0	0
$616$	0	0
$617$	−13.0906	−0.527008	−0.263504	−	0.964658i	$-0.584878\pi$
$617$	−13.0906	−0.527008	−0.263504	+	0.964658i	$0.584878\pi$
$618$	0	0
$619$	−32.5588	−1.30865	−0.654325	−	0.756213i	$-0.727047\pi$
$619$	−32.5588	−1.30865	−0.654325	+	0.756213i	$0.727047\pi$
$620$	0	0
$621$	7.24969	0.290920
$622$	0	0
$623$	0	0
$624$	0	0
$625$	0	0
$626$	0	0
$627$	52.2775	2.08776
$628$	0	0
$629$	−2.05847	−0.0820764
$630$	0	0
$631$	−13.2537	−0.527620	−0.263810	−	0.964575i	$-0.584979\pi$
$631$	−13.2537	−0.527620	−0.263810	+	0.964575i	$0.584979\pi$
$632$	0	0
$633$	19.5877	0.778542
$634$	0	0
$635$	0	0
$636$	0	0
$637$	0	0
$638$	0	0
$639$	−14.8894	−0.589016
$640$	0	0
$641$	0.703073	0.0277697	0.0138848	−	0.999904i	$-0.495580\pi$
$641$	0.703073	0.0277697	0.0138848	+	0.999904i	$0.495580\pi$
$642$	0	0
$643$	−4.64163	−0.183048	−0.0915240	−	0.995803i	$-0.529174\pi$
$643$	−4.64163	−0.183048	−0.0915240	+	0.995803i	$0.529174\pi$
$644$	0	0
$645$	0	0
$646$	0	0
$647$	−12.0354	−0.473161	−0.236580	−	0.971612i	$-0.576027\pi$
$647$	−12.0354	−0.473161	−0.236580	+	0.971612i	$0.576027\pi$
$648$	0	0
$649$	40.3407	1.58351
$650$	0	0
$651$	0	0
$652$	0	0
$653$	−18.2464	−0.714036	−0.357018	−	0.934098i	$-0.616206\pi$
$653$	−18.2464	−0.714036	−0.357018	+	0.934098i	$0.616206\pi$
$654$	0	0
$655$	0	0
$656$	0	0
$657$	−16.7243	−0.652476
$658$	0	0
$659$	29.4231	1.14616	0.573081	−	0.819499i	$-0.305748\pi$
$659$	29.4231	1.14616	0.573081	+	0.819499i	$0.305748\pi$
$660$	0	0
$661$	−17.2957	−0.672723	−0.336361	−	0.941733i	$-0.609196\pi$
$661$	−17.2957	−0.672723	−0.336361	+	0.941733i	$0.609196\pi$
$662$	0	0
$663$	−44.9183	−1.74448
$664$	0	0
$665$	0	0
$666$	0	0
$667$	−61.7788	−2.39208
$668$	0	0
$669$	−32.3473	−1.25062
$670$	0	0
$671$	−31.6147	−1.22047
$672$	0	0
$673$	28.7525	1.10833	0.554164	−	0.832407i	$-0.313038\pi$
$673$	28.7525	1.10833	0.554164	+	0.832407i	$0.313038\pi$
$674$	0	0
$675$	0	0
$676$	0	0
$677$	5.48594	0.210842	0.105421	−	0.994428i	$-0.466381\pi$
$677$	5.48594	0.210842	0.105421	+	0.994428i	$0.466381\pi$
$678$	0	0
$679$	0	0
$680$	0	0
$681$	27.2824	1.04546
$682$	0	0
$683$	11.3768	0.435319	0.217660	−	0.976025i	$-0.430158\pi$
$683$	11.3768	0.435319	0.217660	+	0.976025i	$0.430158\pi$
$684$	0	0
$685$	0	0
$686$	0	0
$687$	−63.0714	−2.40632
$688$	0	0
$689$	1.62013	0.0617222
$690$	0	0
$691$	−45.3261	−1.72429	−0.862144	−	0.506664i	$-0.830879\pi$
$691$	−45.3261	−1.72429	−0.862144	+	0.506664i	$0.830879\pi$
$692$	0	0
$693$	0	0
$694$	0	0
$695$	0	0
$696$	0	0
$697$	−13.0894	−0.495798
$698$	0	0
$699$	−57.8941	−2.18976
$700$	0	0
$701$	4.87634	0.184177	0.0920884	−	0.995751i	$-0.470646\pi$
$701$	4.87634	0.184177	0.0920884	+	0.995751i	$0.470646\pi$
$702$	0	0
$703$	2.12702	0.0802220
$704$	0	0
$705$	0	0
$706$	0	0
$707$	0	0
$708$	0	0
$709$	−24.8887	−0.934713	−0.467357	−	0.884069i	$-0.654794\pi$
$709$	−24.8887	−0.934713	−0.467357	+	0.884069i	$0.654794\pi$
$710$	0	0
$711$	−43.9881	−1.64968
$712$	0	0
$713$	12.2974	0.460541
$714$	0	0
$715$	0	0
$716$	0	0
$717$	−3.79281	−0.141645
$718$	0	0
$719$	−5.43573	−0.202719	−0.101359	−	0.994850i	$-0.532319\pi$
$719$	−5.43573	−0.202719	−0.101359	+	0.994850i	$0.532319\pi$
$720$	0	0
$721$	0	0
$722$	0	0
$723$	66.5787	2.47609
$724$	0	0
$725$	0	0
$726$	0	0
$727$	−17.1112	−0.634621	−0.317310	−	0.948322i	$-0.602780\pi$
$727$	−17.1112	−0.634621	−0.317310	+	0.948322i	$0.602780\pi$
$728$	0	0
$729$	−34.7441	−1.28682
$730$	0	0
$731$	31.2972	1.15757
$732$	0	0
$733$	−7.85744	−0.290221	−0.145111	−	0.989415i	$-0.546354\pi$
$733$	−7.85744	−0.290221	−0.145111	+	0.989415i	$0.546354\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	16.2426	0.598304
$738$	0	0
$739$	51.0109	1.87647	0.938234	−	0.346002i	$-0.112461\pi$
$739$	51.0109	1.87647	0.938234	+	0.346002i	$0.112461\pi$
$740$	0	0
$741$	46.4142	1.70507
$742$	0	0
$743$	−6.82733	−0.250470	−0.125235	−	0.992127i	$-0.539969\pi$
$743$	−6.82733	−0.250470	−0.125235	+	0.992127i	$0.539969\pi$
$744$	0	0
$745$	0	0
$746$	0	0
$747$	−29.2565	−1.07044
$748$	0	0
$749$	0	0
$750$	0	0
$751$	32.3570	1.18072	0.590361	−	0.807139i	$-0.298985\pi$
$751$	32.3570	1.18072	0.590361	+	0.807139i	$0.298985\pi$
$752$	0	0
$753$	12.4742	0.454583
$754$	0	0
$755$	0	0
$756$	0	0
$757$	29.1180	1.05831	0.529156	−	0.848524i	$-0.322509\pi$
$757$	29.1180	1.05831	0.529156	+	0.848524i	$0.322509\pi$
$758$	0	0
$759$	−59.9014	−2.17428
$760$	0	0
$761$	28.1730	1.02127	0.510636	−	0.859797i	$-0.329410\pi$
$761$	28.1730	1.02127	0.510636	+	0.859797i	$0.329410\pi$
$762$	0	0
$763$	0	0
$764$	0	0
$765$	0	0
$766$	0	0
$767$	35.8162	1.29325
$768$	0	0
$769$	16.5017	0.595065	0.297532	−	0.954712i	$-0.403836\pi$
$769$	16.5017	0.595065	0.297532	+	0.954712i	$0.403836\pi$
$770$	0	0
$771$	−31.3964	−1.13071
$772$	0	0
$773$	18.4891	0.665005	0.332503	−	0.943102i	$-0.392107\pi$
$773$	18.4891	0.665005	0.332503	+	0.943102i	$0.392107\pi$
$774$	0	0
$775$	0	0
$776$	0	0
$777$	0	0
$778$	0	0
$779$	13.5254	0.484596
$780$	0	0
$781$	16.7703	0.600089
$782$	0	0
$783$	−12.3675	−0.441980
$784$	0	0
$785$	0	0
$786$	0	0
$787$	−15.7443	−0.561224	−0.280612	−	0.959821i	$-0.590537\pi$
$787$	−15.7443	−0.561224	−0.280612	+	0.959821i	$0.590537\pi$
$788$	0	0
$789$	51.2034	1.82289
$790$	0	0
$791$	0	0
$792$	0	0
$793$	−28.0689	−0.996755
$794$	0	0
$795$	0	0
$796$	0	0
$797$	29.9307	1.06020	0.530100	−	0.847935i	$-0.322154\pi$
$797$	29.9307	1.06020	0.530100	+	0.847935i	$0.322154\pi$
$798$	0	0
$799$	2.44248	0.0864088
$800$	0	0
$801$	8.28758	0.292827
$802$	0	0
$803$	18.8370	0.664743
$804$	0	0
$805$	0	0
$806$	0	0
$807$	−38.0105	−1.33803
$808$	0	0
$809$	5.16658	0.181647	0.0908236	−	0.995867i	$-0.471050\pi$
$809$	5.16658	0.181647	0.0908236	+	0.995867i	$0.471050\pi$
$810$	0	0
$811$	−38.4698	−1.35086	−0.675430	−	0.737425i	$-0.736042\pi$
$811$	−38.4698	−1.35086	−0.675430	+	0.737425i	$0.736042\pi$
$812$	0	0
$813$	−14.7807	−0.518381
$814$	0	0
$815$	0	0
$816$	0	0
$817$	−32.3394	−1.13141
$818$	0	0
$819$	0	0
$820$	0	0
$821$	−3.69551	−0.128974	−0.0644872	−	0.997919i	$-0.520541\pi$
$821$	−3.69551	−0.128974	−0.0644872	+	0.997919i	$0.520541\pi$
$822$	0	0
$823$	42.4030	1.47807	0.739037	−	0.673665i	$-0.235281\pi$
$823$	42.4030	1.47807	0.739037	+	0.673665i	$0.235281\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	40.0950	1.39424	0.697120	−	0.716954i	$-0.254464\pi$
$827$	40.0950	1.39424	0.697120	+	0.716954i	$0.254464\pi$
$828$	0	0
$829$	53.8264	1.86947	0.934734	−	0.355347i	$-0.115637\pi$
$829$	53.8264	1.86947	0.934734	+	0.355347i	$0.115637\pi$
$830$	0	0
$831$	65.9968	2.28941
$832$	0	0
$833$	0	0
$834$	0	0
$835$	0	0
$836$	0	0
$837$	2.46183	0.0850931
$838$	0	0
$839$	−25.1002	−0.866556	−0.433278	−	0.901260i	$-0.642643\pi$
$839$	−25.1002	−0.866556	−0.433278	+	0.901260i	$0.642643\pi$
$840$	0	0
$841$	76.3910	2.63417
$842$	0	0
$843$	−37.8694	−1.30429
$844$	0	0
$845$	0	0
$846$	0	0
$847$	0	0
$848$	0	0
$849$	−24.7189	−0.848352
$850$	0	0
$851$	−2.43721	−0.0835466
$852$	0	0
$853$	−26.7320	−0.915286	−0.457643	−	0.889136i	$-0.651306\pi$
$853$	−26.7320	−0.915286	−0.457643	+	0.889136i	$0.651306\pi$
$854$	0	0
$855$	0	0
$856$	0	0
$857$	−46.5891	−1.59145	−0.795726	−	0.605657i	$-0.792911\pi$
$857$	−46.5891	−1.59145	−0.795726	+	0.605657i	$0.792911\pi$
$858$	0	0
$859$	−18.6535	−0.636448	−0.318224	−	0.948016i	$-0.603086\pi$
$859$	−18.6535	−0.636448	−0.318224	+	0.948016i	$0.603086\pi$
$860$	0	0
$861$	0	0
$862$	0	0
$863$	17.8239	0.606733	0.303367	−	0.952874i	$-0.401889\pi$
$863$	17.8239	0.606733	0.303367	+	0.952874i	$0.401889\pi$
$864$	0	0
$865$	0	0
$866$	0	0
$867$	22.4739	0.763253
$868$	0	0
$869$	49.5450	1.68070
$870$	0	0
$871$	14.4209	0.488633
$872$	0	0
$873$	−4.58781	−0.155274
$874$	0	0
$875$	0	0
$876$	0	0
$877$	−26.7793	−0.904273	−0.452136	−	0.891949i	$-0.649338\pi$
$877$	−26.7793	−0.904273	−0.452136	+	0.891949i	$0.649338\pi$
$878$	0	0
$879$	20.5732	0.693916
$880$	0	0
$881$	17.5843	0.592429	0.296215	−	0.955121i	$-0.404276\pi$
$881$	17.5843	0.592429	0.296215	+	0.955121i	$0.404276\pi$
$882$	0	0
$883$	18.9638	0.638182	0.319091	−	0.947724i	$-0.396622\pi$
$883$	18.9638	0.638182	0.319091	+	0.947724i	$0.396622\pi$
$884$	0	0
$885$	0	0
$886$	0	0
$887$	11.1654	0.374897	0.187448	−	0.982274i	$-0.439978\pi$
$887$	11.1654	0.374897	0.187448	+	0.982274i	$0.439978\pi$
$888$	0	0
$889$	0	0
$890$	0	0
$891$	28.7761	0.964037
$892$	0	0
$893$	−2.52382	−0.0844565
$894$	0	0
$895$	0	0
$896$	0	0
$897$	−53.1830	−1.77573
$898$	0	0
$899$	−20.9786	−0.699676
$900$	0	0
$901$	−2.37068	−0.0789787
$902$	0	0
$903$	0	0
$904$	0	0
$905$	0	0
$906$	0	0
$907$	−38.1647	−1.26724	−0.633619	−	0.773645i	$-0.718431\pi$
$907$	−38.1647	−1.26724	−0.633619	+	0.773645i	$0.718431\pi$
$908$	0	0
$909$	26.9253	0.893057
$910$	0	0
$911$	47.0251	1.55801	0.779006	−	0.627016i	$-0.215724\pi$
$911$	47.0251	1.55801	0.779006	+	0.627016i	$0.215724\pi$
$912$	0	0
$913$	32.9524	1.09056
$914$	0	0
$915$	0	0
$916$	0	0
$917$	0	0
$918$	0	0
$919$	25.3879	0.837469	0.418734	−	0.908109i	$-0.362474\pi$
$919$	25.3879	0.837469	0.418734	+	0.908109i	$0.362474\pi$
$920$	0	0
$921$	−22.4359	−0.739288
$922$	0	0
$923$	14.8894	0.490091
$924$	0	0
$925$	0	0
$926$	0	0
$927$	−7.65432	−0.251401
$928$	0	0
$929$	7.64709	0.250893	0.125446	−	0.992100i	$-0.459964\pi$
$929$	7.64709	0.250893	0.125446	+	0.992100i	$0.459964\pi$
$930$	0	0
$931$	0	0
$932$	0	0
$933$	24.5892	0.805013
$934$	0	0
$935$	0	0
$936$	0	0
$937$	−1.40923	−0.0460375	−0.0230188	−	0.999735i	$-0.507328\pi$
$937$	−1.40923	−0.0460375	−0.0230188	+	0.999735i	$0.507328\pi$
$938$	0	0
$939$	−69.1706	−2.25730
$940$	0	0
$941$	52.4101	1.70852	0.854260	−	0.519845i	$-0.174010\pi$
$941$	52.4101	1.70852	0.854260	+	0.519845i	$0.174010\pi$
$942$	0	0
$943$	−15.4978	−0.504679
$944$	0	0
$945$	0	0
$946$	0	0
$947$	32.7229	1.06335	0.531675	−	0.846948i	$-0.321563\pi$
$947$	32.7229	1.06335	0.531675	+	0.846948i	$0.321563\pi$
$948$	0	0
$949$	16.7243	0.542893
$950$	0	0
$951$	30.9344	1.00312
$952$	0	0
$953$	41.7747	1.35322	0.676608	−	0.736344i	$-0.263449\pi$
$953$	41.7747	1.35322	0.676608	+	0.736344i	$0.263449\pi$
$954$	0	0
$955$	0	0
$956$	0	0
$957$	102.188	3.30328
$958$	0	0
$959$	0	0
$960$	0	0
$961$	−26.8241	−0.865293
$962$	0	0
$963$	37.5955	1.21150
$964$	0	0
$965$	0	0
$966$	0	0
$967$	6.47375	0.208182	0.104091	−	0.994568i	$-0.466807\pi$
$967$	6.47375	0.208182	0.104091	+	0.994568i	$0.466807\pi$
$968$	0	0
$969$	−67.9159	−2.18177
$970$	0	0
$971$	−33.1743	−1.06462	−0.532308	−	0.846551i	$-0.678675\pi$
$971$	−33.1743	−1.06462	−0.532308	+	0.846551i	$0.678675\pi$
$972$	0	0
$973$	0	0
$974$	0	0
$975$	0	0
$976$	0	0
$977$	−40.0711	−1.28199	−0.640994	−	0.767546i	$-0.721478\pi$
$977$	−40.0711	−1.28199	−0.640994	+	0.767546i	$0.721478\pi$
$978$	0	0
$979$	−9.33452	−0.298333
$980$	0	0
$981$	−38.3589	−1.22471
$982$	0	0
$983$	−0.852116	−0.0271783	−0.0135891	−	0.999908i	$-0.504326\pi$
$983$	−0.852116	−0.0271783	−0.0135891	+	0.999908i	$0.504326\pi$
$984$	0	0
$985$	0	0
$986$	0	0
$987$	0	0
$988$	0	0
$989$	37.0557	1.17830
$990$	0	0
$991$	−5.02760	−0.159707	−0.0798535	−	0.996807i	$-0.525445\pi$
$991$	−5.02760	−0.159707	−0.0798535	+	0.996807i	$0.525445\pi$
$992$	0	0
$993$	−8.72558	−0.276898
$994$	0	0
$995$	0	0
$996$	0	0
$997$	−27.0291	−0.856021	−0.428011	−	0.903774i	$-0.640785\pi$
$997$	−27.0291	−0.856021	−0.428011	+	0.903774i	$0.640785\pi$
$998$	0	0
$999$	−0.487908	−0.0154367

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9800.2.a.cv.1.6		6
5.2	odd	4		1960.2.g.f.1569.2		12
5.3	odd	4		1960.2.g.f.1569.11		12
5.4	even	2		9800.2.a.cx.1.1		6
7.2	even	3		1400.2.q.o.1201.1		12
7.4	even	3		1400.2.q.o.401.1		12
7.6	odd	2		9800.2.a.cy.1.1		6
35.2	odd	12		280.2.bg.a.249.11	yes	24
35.4	even	6		1400.2.q.n.401.6		12
35.9	even	6		1400.2.q.n.1201.6		12
35.13	even	4		1960.2.g.e.1569.2		12
35.18	odd	12		280.2.bg.a.9.11	yes	24
35.23	odd	12		280.2.bg.a.249.2	yes	24
35.27	even	4		1960.2.g.e.1569.11		12
35.32	odd	12		280.2.bg.a.9.2	✓	24
35.34	odd	2		9800.2.a.cw.1.6		6
140.23	even	12		560.2.bw.f.529.11		24
140.67	even	12		560.2.bw.f.289.11		24
140.107	even	12		560.2.bw.f.529.2		24
140.123	even	12		560.2.bw.f.289.2		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.bg.a.9.2	✓	24	35.32	odd	12
280.2.bg.a.9.11	yes	24	35.18	odd	12
280.2.bg.a.249.2	yes	24	35.23	odd	12
280.2.bg.a.249.11	yes	24	35.2	odd	12
560.2.bw.f.289.2		24	140.123	even	12
560.2.bw.f.289.11		24	140.67	even	12
560.2.bw.f.529.2		24	140.107	even	12
560.2.bw.f.529.11		24	140.23	even	12
1400.2.q.n.401.6		12	35.4	even	6
1400.2.q.n.1201.6		12	35.9	even	6
1400.2.q.o.401.1		12	7.4	even	3
1400.2.q.o.1201.1		12	7.2	even	3
1960.2.g.e.1569.2		12	35.13	even	4
1960.2.g.e.1569.11		12	35.27	even	4
1960.2.g.f.1569.2		12	5.2	odd	4
1960.2.g.f.1569.11		12	5.3	odd	4
9800.2.a.cv.1.6		6	1.1	even	1	trivial
9800.2.a.cw.1.6		6	35.34	odd	2
9800.2.a.cx.1.1		6	5.4	even	2
9800.2.a.cy.1.1		6	7.6	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+2.54431 q^{3} +3.47349 q^{9} +O(q^{10})\)	\(q+2.54431 q^{3} +3.47349 q^{9} -3.91228 q^{11} -3.47349 q^{13} +5.08262 q^{17} -5.25188 q^{19} +6.01780 q^{23} +1.20471 q^{27} -10.2660 q^{29} +2.04350 q^{31} -9.95405 q^{33} -0.405001 q^{37} -8.83763 q^{39} -2.57534 q^{41} +6.15769 q^{43} +0.480556 q^{47} +12.9317 q^{51} -0.466428 q^{53} -13.3624 q^{57} -10.3113 q^{59} +8.08088 q^{61} -4.15169 q^{67} +15.3111 q^{69} -4.28658 q^{71} -4.81483 q^{73} -12.6639 q^{79} -7.35533 q^{81} -8.42280 q^{83} -26.1199 q^{87} +2.38595 q^{89} +5.19930 q^{93} -1.32080 q^{97} -13.5893 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - q^{3} + 7 q^{9}+O(q^{10}) \) 6 * q - q^3 + 7 * q^9	\( 6 q - q^{3} + 7 q^{9} + q^{11} - 7 q^{13} - 4 q^{17} - 5 q^{19} + 6 q^{23} - 7 q^{27} - 3 q^{29} - 2 q^{31} - 16 q^{33} + 9 q^{37} + 10 q^{39} + 6 q^{41} - 3 q^{43} - 27 q^{47} - 5 q^{53} - 26 q^{57} - 24 q^{59} + 9 q^{61} + 17 q^{67} + 15 q^{69} + 4 q^{71} - 18 q^{73} - 22 q^{79} - 6 q^{81} - 9 q^{83} - 39 q^{87} + 15 q^{89} + 10 q^{93} - 12 q^{97} + 11 q^{99}+O(q^{100}) \) 6 * q - q^3 + 7 * q^9 + q^11 - 7 * q^13 - 4 * q^17 - 5 * q^19 + 6 * q^23 - 7 * q^27 - 3 * q^29 - 2 * q^31 - 16 * q^33 + 9 * q^37 + 10 * q^39 + 6 * q^41 - 3 * q^43 - 27 * q^47 - 5 * q^53 - 26 * q^57 - 24 * q^59 + 9 * q^61 + 17 * q^67 + 15 * q^69 + 4 * q^71 - 18 * q^73 - 22 * q^79 - 6 * q^81 - 9 * q^83 - 39 * q^87 + 15 * q^89 + 10 * q^93 - 12 * q^97 + 11 * q^99

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