LMFDB - Embedded newform 9196.2.a.t.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9196,2,Mod(1,9196)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9196, 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("9196.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 9196 = 2^{2} \cdot 11^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	9196.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:	$73.4304296988$
Analytic rank:	$1$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 16x^{8} - 3x^{7} + 84x^{6} + 16x^{5} - 174x^{4} - 16x^{3} + 122x^{2} - 9 $ x^10 - 16x^8 - 3x^7 + 84x^6 + 16x^5 - 174x^4 - 16x^3 + 122*x^2 - 9
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 836)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$3.05348$ of defining polynomial
Character	$\chi$	$=$	9196.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.05348 q^{3} +2.08326 q^{5} +3.50519 q^{7} +6.32373 q^{9} -2.38232 q^{13} -6.36119 q^{15} +1.39662 q^{17} -1.00000 q^{19} -10.7030 q^{21} -0.551290 q^{23} -0.660029 q^{25} -10.1490 q^{27} +8.08217 q^{29} +0.0680194 q^{31} +7.30222 q^{35} +10.0355 q^{37} +7.27436 q^{39} -10.9265 q^{41} -7.50111 q^{43} +13.1740 q^{45} -7.59871 q^{47} +5.28634 q^{49} -4.26456 q^{51} -8.04102 q^{53} +3.05348 q^{57} -0.812498 q^{59} +1.73955 q^{61} +22.1659 q^{63} -4.96299 q^{65} -10.9218 q^{67} +1.68335 q^{69} -16.1169 q^{71} -11.9028 q^{73} +2.01538 q^{75} -3.11141 q^{79} +12.0184 q^{81} -0.715131 q^{83} +2.90953 q^{85} -24.6787 q^{87} -13.9144 q^{89} -8.35047 q^{91} -0.207696 q^{93} -2.08326 q^{95} +3.53255 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 8 q^{5} + 5 q^{7} + 2 q^{9} - 2 q^{13} - 10 q^{15} + 4 q^{17} - 10 q^{19} + 6 q^{21} - 8 q^{23} - 10 q^{25} - 9 q^{27} - 3 q^{29} - 12 q^{31} + 9 q^{35} - 23 q^{37} - 18 q^{39} - 5 q^{41} - 14 q^{43}+ \cdots + 22 q^{97}+O(q^{100}) $ 10 * q + 8 * q^5 + 5 * q^7 + 2 * q^9 - 2 * q^13 - 10 * q^15 + 4 * q^17 - 10 * q^19 + 6 * q^21 - 8 * q^23 - 10 * q^25 - 9 * q^27 - 3 * q^29 - 12 * q^31 + 9 * q^35 - 23 * q^37 - 18 * q^39 - 5 * q^41 - 14 * q^43 - 27 * q^47 - 17 * q^49 - 12 * q^51 - 10 * q^53 - 9 * q^59 + 4 * q^61 + 14 * q^63 + 7 * q^65 - 17 * q^67 - 3 * q^69 - 34 * q^71 - 9 * q^73 - 26 * q^75 - 16 * q^79 - 22 * q^81 + 6 * q^83 + 24 * q^85 + q^87 - 35 * q^89 - 35 * q^91 - 44 * q^93 - 8 * q^95 + 22 * q^97

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
$3$	−3.05348	−1.76293	−0.881463	−	0.472252i	$-0.843441\pi$
$3$	−3.05348	−1.76293	−0.881463	+	0.472252i	$0.843441\pi$
$4$	0	0
$5$	2.08326	0.931662	0.465831	−	0.884874i	$-0.345755\pi$
$5$	2.08326	0.931662	0.465831	+	0.884874i	$0.345755\pi$
$6$	0	0
$7$	3.50519	1.32484	0.662418	−	0.749134i	$-0.269530\pi$
$7$	3.50519	1.32484	0.662418	+	0.749134i	$0.269530\pi$
$8$	0	0
$9$	6.32373	2.10791
$10$	0	0
$11$	0	0
$11$	0	0
$12$	0	0
$13$	−2.38232	−0.660736	−0.330368	−	0.943852i	$-0.607173\pi$
$13$	−2.38232	−0.660736	−0.330368	+	0.943852i	$0.607173\pi$
$14$	0	0
$15$	−6.36119	−1.64245
$16$	0	0
$17$	1.39662	0.338731	0.169366	−	0.985553i	$-0.445828\pi$
$17$	1.39662	0.338731	0.169366	+	0.985553i	$0.445828\pi$
$18$	0	0
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	0	0
$21$	−10.7030	−2.33559
$22$	0	0
$23$	−0.551290	−0.114952	−0.0574759	−	0.998347i	$-0.518305\pi$
$23$	−0.551290	−0.114952	−0.0574759	+	0.998347i	$0.518305\pi$
$24$	0	0
$25$	−0.660029	−0.132006
$26$	0	0
$27$	−10.1490	−1.95317
$28$	0	0
$29$	8.08217	1.50082	0.750411	−	0.660972i	$-0.229856\pi$
$29$	8.08217	1.50082	0.750411	+	0.660972i	$0.229856\pi$
$30$	0	0
$31$	0.0680194	0.0122166	0.00610832	−	0.999981i	$-0.498056\pi$
$31$	0.0680194	0.0122166	0.00610832	+	0.999981i	$0.498056\pi$
$32$	0	0
$33$	0	0
$34$	0	0
$35$	7.30222	1.23430
$36$	0	0
$37$	10.0355	1.64982	0.824910	−	0.565265i	$-0.191226\pi$
$37$	10.0355	1.64982	0.824910	+	0.565265i	$0.191226\pi$
$38$	0	0
$39$	7.27436	1.16483
$40$	0	0
$41$	−10.9265	−1.70643	−0.853215	−	0.521560i	$-0.825350\pi$
$41$	−10.9265	−1.70643	−0.853215	+	0.521560i	$0.825350\pi$
$42$	0	0
$43$	−7.50111	−1.14391	−0.571955	−	0.820285i	$-0.693815\pi$
$43$	−7.50111	−1.14391	−0.571955	+	0.820285i	$0.693815\pi$
$44$	0	0
$45$	13.1740	1.96386
$46$	0	0
$47$	−7.59871	−1.10839	−0.554193	−	0.832388i	$-0.686973\pi$
$47$	−7.59871	−1.10839	−0.554193	+	0.832388i	$0.686973\pi$
$48$	0	0
$49$	5.28634	0.755192
$50$	0	0
$51$	−4.26456	−0.597158
$52$	0	0
$53$	−8.04102	−1.10452	−0.552259	−	0.833672i	$-0.686234\pi$
$53$	−8.04102	−1.10452	−0.552259	+	0.833672i	$0.686234\pi$
$54$	0	0
$55$	0	0
$56$	0	0
$57$	3.05348	0.404443
$58$	0	0
$59$	−0.812498	−0.105778	−0.0528891	−	0.998600i	$-0.516843\pi$
$59$	−0.812498	−0.105778	−0.0528891	+	0.998600i	$0.516843\pi$
$60$	0	0
$61$	1.73955	0.222726	0.111363	−	0.993780i	$-0.464478\pi$
$61$	1.73955	0.222726	0.111363	+	0.993780i	$0.464478\pi$
$62$	0	0
$63$	22.1659	2.79264
$64$	0	0
$65$	−4.96299	−0.615583
$66$	0	0
$67$	−10.9218	−1.33431	−0.667153	−	0.744921i	$-0.732487\pi$
$67$	−10.9218	−1.33431	−0.667153	+	0.744921i	$0.732487\pi$
$68$	0	0
$69$	1.68335	0.202652
$70$	0	0
$71$	−16.1169	−1.91273	−0.956365	−	0.292175i	$-0.905621\pi$
$71$	−16.1169	−1.91273	−0.956365	+	0.292175i	$0.905621\pi$
$72$	0	0
$73$	−11.9028	−1.39312	−0.696560	−	0.717498i	$-0.745287\pi$
$73$	−11.9028	−1.39312	−0.696560	+	0.717498i	$0.745287\pi$
$74$	0	0
$75$	2.01538	0.232716
$76$	0	0
$77$	0	0
$78$	0	0
$79$	−3.11141	−0.350061	−0.175031	−	0.984563i	$-0.556002\pi$
$79$	−3.11141	−0.350061	−0.175031	+	0.984563i	$0.556002\pi$
$80$	0	0
$81$	12.0184	1.33538
$82$	0	0
$83$	−0.715131	−0.0784959	−0.0392479	−	0.999230i	$-0.512496\pi$
$83$	−0.715131	−0.0784959	−0.0392479	+	0.999230i	$0.512496\pi$
$84$	0	0
$85$	2.90953	0.315583
$86$	0	0
$87$	−24.6787	−2.64584
$88$	0	0
$89$	−13.9144	−1.47492	−0.737462	−	0.675389i	$-0.763976\pi$
$89$	−13.9144	−1.47492	−0.737462	+	0.675389i	$0.763976\pi$
$90$	0	0
$91$	−8.35047	−0.875367
$92$	0	0
$93$	−0.207696	−0.0215370
$94$	0	0
$95$	−2.08326	−0.213738
$96$	0	0
$97$	3.53255	0.358676	0.179338	−	0.983788i	$-0.442604\pi$
$97$	3.53255	0.358676	0.179338	+	0.983788i	$0.442604\pi$
$98$	0	0
$99$	0	0
$100$	0	0
$101$	−0.473952	−0.0471600	−0.0235800	−	0.999722i	$-0.507506\pi$
$101$	−0.473952	−0.0471600	−0.0235800	+	0.999722i	$0.507506\pi$
$102$	0	0
$103$	11.2007	1.10364	0.551818	−	0.833965i	$-0.313934\pi$
$103$	11.2007	1.10364	0.551818	+	0.833965i	$0.313934\pi$
$104$	0	0
$105$	−22.2972	−2.17598
$106$	0	0
$107$	−7.87157	−0.760973	−0.380487	−	0.924786i	$-0.624243\pi$
$107$	−7.87157	−0.760973	−0.380487	+	0.924786i	$0.624243\pi$
$108$	0	0
$109$	−7.26224	−0.695596	−0.347798	−	0.937569i	$-0.613070\pi$
$109$	−7.26224	−0.695596	−0.347798	+	0.937569i	$0.613070\pi$
$110$	0	0
$111$	−30.6431	−2.90851
$112$	0	0
$113$	4.83686	0.455013	0.227507	−	0.973777i	$-0.426943\pi$
$113$	4.83686	0.455013	0.227507	+	0.973777i	$0.426943\pi$
$114$	0	0
$115$	−1.14848	−0.107096
$116$	0	0
$117$	−15.0651	−1.39277
$118$	0	0
$119$	4.89543	0.448763
$120$	0	0
$121$	0	0
$122$	0	0
$123$	33.3638	3.00831
$124$	0	0
$125$	−11.7913	−1.05465
$126$	0	0
$127$	−17.4610	−1.54941	−0.774706	−	0.632322i	$-0.782102\pi$
$127$	−17.4610	−1.54941	−0.774706	+	0.632322i	$0.782102\pi$
$128$	0	0
$129$	22.9045	2.01663
$130$	0	0
$131$	0.966995	0.0844868	0.0422434	−	0.999107i	$-0.486550\pi$
$131$	0.966995	0.0844868	0.0422434	+	0.999107i	$0.486550\pi$
$132$	0	0
$133$	−3.50519	−0.303938
$134$	0	0
$135$	−21.1429	−1.81969
$136$	0	0
$137$	12.6932	1.08445	0.542226	−	0.840233i	$-0.317582\pi$
$137$	12.6932	1.08445	0.542226	+	0.840233i	$0.317582\pi$
$138$	0	0
$139$	16.9312	1.43609	0.718044	−	0.695998i	$-0.245038\pi$
$139$	16.9312	1.43609	0.718044	+	0.695998i	$0.245038\pi$
$140$	0	0
$141$	23.2025	1.95400
$142$	0	0
$143$	0	0
$144$	0	0
$145$	16.8373	1.39826
$146$	0	0
$147$	−16.1417	−1.33135
$148$	0	0
$149$	−2.11599	−0.173349	−0.0866743	−	0.996237i	$-0.527624\pi$
$149$	−2.11599	−0.173349	−0.0866743	+	0.996237i	$0.527624\pi$
$150$	0	0
$151$	−11.8277	−0.962528	−0.481264	−	0.876576i	$-0.659822\pi$
$151$	−11.8277	−0.962528	−0.481264	+	0.876576i	$0.659822\pi$
$152$	0	0
$153$	8.83188	0.714015
$154$	0	0
$155$	0.141702	0.0113818
$156$	0	0
$157$	19.7632	1.57728	0.788639	−	0.614857i	$-0.210786\pi$
$157$	19.7632	1.57728	0.788639	+	0.614857i	$0.210786\pi$
$158$	0	0
$159$	24.5531	1.94719
$160$	0	0
$161$	−1.93237	−0.152292
$162$	0	0
$163$	5.75390	0.450680	0.225340	−	0.974280i	$-0.427651\pi$
$163$	5.75390	0.450680	0.225340	+	0.974280i	$0.427651\pi$
$164$	0	0
$165$	0	0
$166$	0	0
$167$	2.23982	0.173322	0.0866611	−	0.996238i	$-0.472380\pi$
$167$	2.23982	0.173322	0.0866611	+	0.996238i	$0.472380\pi$
$168$	0	0
$169$	−7.32456	−0.563428
$170$	0	0
$171$	−6.32373	−0.483588
$172$	0	0
$173$	3.93251	0.298983	0.149492	−	0.988763i	$-0.452236\pi$
$173$	3.93251	0.298983	0.149492	+	0.988763i	$0.452236\pi$
$174$	0	0
$175$	−2.31352	−0.174886
$176$	0	0
$177$	2.48095	0.186479
$178$	0	0
$179$	−20.9513	−1.56598	−0.782988	−	0.622036i	$-0.786306\pi$
$179$	−20.9513	−1.56598	−0.782988	+	0.622036i	$0.786306\pi$
$180$	0	0
$181$	−20.4731	−1.52175	−0.760876	−	0.648897i	$-0.775231\pi$
$181$	−20.4731	−1.52175	−0.760876	+	0.648897i	$0.775231\pi$
$182$	0	0
$183$	−5.31167	−0.392650
$184$	0	0
$185$	20.9065	1.53707
$186$	0	0
$187$	0	0
$188$	0	0
$189$	−35.5740	−2.58763
$190$	0	0
$191$	15.5073	1.12207	0.561034	−	0.827792i	$-0.310404\pi$
$191$	15.5073	1.12207	0.561034	+	0.827792i	$0.310404\pi$
$192$	0	0
$193$	−12.3196	−0.886787	−0.443394	−	0.896327i	$-0.646226\pi$
$193$	−12.3196	−0.886787	−0.443394	+	0.896327i	$0.646226\pi$
$194$	0	0
$195$	15.1544	1.08523
$196$	0	0
$197$	9.59230	0.683423	0.341712	−	0.939805i	$-0.388993\pi$
$197$	9.59230	0.683423	0.341712	+	0.939805i	$0.388993\pi$
$198$	0	0
$199$	5.07345	0.359648	0.179824	−	0.983699i	$-0.442447\pi$
$199$	5.07345	0.359648	0.179824	+	0.983699i	$0.442447\pi$
$200$	0	0
$201$	33.3494	2.35228
$202$	0	0
$203$	28.3295	1.98834
$204$	0	0
$205$	−22.7627	−1.58982
$206$	0	0
$207$	−3.48621	−0.242308
$208$	0	0
$209$	0	0
$210$	0	0
$211$	−16.8848	−1.16240	−0.581198	−	0.813762i	$-0.697416\pi$
$211$	−16.8848	−1.16240	−0.581198	+	0.813762i	$0.697416\pi$
$212$	0	0
$213$	49.2128	3.37200
$214$	0	0
$215$	−15.6268	−1.06574
$216$	0	0
$217$	0.238421	0.0161851
$218$	0	0
$219$	36.3450	2.45597
$220$	0	0
$221$	−3.32720	−0.223812
$222$	0	0
$223$	4.10825	0.275109	0.137554	−	0.990494i	$-0.456076\pi$
$223$	4.10825	0.275109	0.137554	+	0.990494i	$0.456076\pi$
$224$	0	0
$225$	−4.17385	−0.278256
$226$	0	0
$227$	1.41894	0.0941786	0.0470893	−	0.998891i	$-0.485005\pi$
$227$	1.41894	0.0941786	0.0470893	+	0.998891i	$0.485005\pi$
$228$	0	0
$229$	−10.4598	−0.691200	−0.345600	−	0.938382i	$-0.612325\pi$
$229$	−10.4598	−0.691200	−0.345600	+	0.938382i	$0.612325\pi$
$230$	0	0
$231$	0	0
$232$	0	0
$233$	27.4052	1.79537	0.897686	−	0.440637i	$-0.145247\pi$
$233$	27.4052	1.79537	0.897686	+	0.440637i	$0.145247\pi$
$234$	0	0
$235$	−15.8301	−1.03264
$236$	0	0
$237$	9.50063	0.617132
$238$	0	0
$239$	10.5793	0.684321	0.342160	−	0.939642i	$-0.388841\pi$
$239$	10.5793	0.684321	0.342160	+	0.939642i	$0.388841\pi$
$240$	0	0
$241$	26.2304	1.68965	0.844824	−	0.535045i	$-0.179705\pi$
$241$	26.2304	1.68965	0.844824	+	0.535045i	$0.179705\pi$
$242$	0	0
$243$	−6.25110	−0.401008
$244$	0	0
$245$	11.0128	0.703583
$246$	0	0
$247$	2.38232	0.151583
$248$	0	0
$249$	2.18364	0.138382
$250$	0	0
$251$	−14.7375	−0.930225	−0.465113	−	0.885252i	$-0.653986\pi$
$251$	−14.7375	−0.930225	−0.465113	+	0.885252i	$0.653986\pi$
$252$	0	0
$253$	0	0
$254$	0	0
$255$	−8.88419	−0.556350
$256$	0	0
$257$	25.5264	1.59229	0.796146	−	0.605104i	$-0.206869\pi$
$257$	25.5264	1.59229	0.796146	+	0.605104i	$0.206869\pi$
$258$	0	0
$259$	35.1762	2.18574
$260$	0	0
$261$	51.1095	3.16360
$262$	0	0
$263$	−11.7944	−0.727276	−0.363638	−	0.931540i	$-0.618465\pi$
$263$	−11.7944	−0.727276	−0.363638	+	0.931540i	$0.618465\pi$
$264$	0	0
$265$	−16.7515	−1.02904
$266$	0	0
$267$	42.4873	2.60018
$268$	0	0
$269$	19.2620	1.17443	0.587214	−	0.809432i	$-0.300225\pi$
$269$	19.2620	1.17443	0.587214	+	0.809432i	$0.300225\pi$
$270$	0	0
$271$	14.1232	0.857925	0.428962	−	0.903322i	$-0.358879\pi$
$271$	14.1232	0.857925	0.428962	+	0.903322i	$0.358879\pi$
$272$	0	0
$273$	25.4980	1.54321
$274$	0	0
$275$	0	0
$276$	0	0
$277$	−28.8578	−1.73390	−0.866948	−	0.498399i	$-0.833921\pi$
$277$	−28.8578	−1.73390	−0.866948	+	0.498399i	$0.833921\pi$
$278$	0	0
$279$	0.430137	0.0257516
$280$	0	0
$281$	−22.0345	−1.31447	−0.657235	−	0.753686i	$-0.728274\pi$
$281$	−22.0345	−1.31447	−0.657235	+	0.753686i	$0.728274\pi$
$282$	0	0
$283$	12.8574	0.764291	0.382145	−	0.924102i	$-0.375185\pi$
$283$	12.8574	0.764291	0.382145	+	0.924102i	$0.375185\pi$
$284$	0	0
$285$	6.36119	0.376804
$286$	0	0
$287$	−38.2994	−2.26074
$288$	0	0
$289$	−15.0494	−0.885261
$290$	0	0
$291$	−10.7866	−0.632319
$292$	0	0
$293$	24.9253	1.45615	0.728077	−	0.685496i	$-0.240414\pi$
$293$	24.9253	1.45615	0.728077	+	0.685496i	$0.240414\pi$
$294$	0	0
$295$	−1.69265	−0.0985496
$296$	0	0
$297$	0	0
$298$	0	0
$299$	1.31335	0.0759528
$300$	0	0
$301$	−26.2928	−1.51549
$302$	0	0
$303$	1.44720	0.0831396
$304$	0	0
$305$	3.62393	0.207505
$306$	0	0
$307$	−18.7523	−1.07025	−0.535125	−	0.844773i	$-0.679736\pi$
$307$	−18.7523	−1.07025	−0.535125	+	0.844773i	$0.679736\pi$
$308$	0	0
$309$	−34.2010	−1.94563
$310$	0	0
$311$	−33.7192	−1.91204	−0.956020	−	0.293301i	$-0.905246\pi$
$311$	−33.7192	−1.91204	−0.956020	+	0.293301i	$0.905246\pi$
$312$	0	0
$313$	0.808485	0.0456983	0.0228491	−	0.999739i	$-0.492726\pi$
$313$	0.808485	0.0456983	0.0228491	+	0.999739i	$0.492726\pi$
$314$	0	0
$315$	46.1773	2.60179
$316$	0	0
$317$	8.10995	0.455500	0.227750	−	0.973720i	$-0.426863\pi$
$317$	8.10995	0.455500	0.227750	+	0.973720i	$0.426863\pi$
$318$	0	0
$319$	0	0
$320$	0	0
$321$	24.0357	1.34154
$322$	0	0
$323$	−1.39662	−0.0777103
$324$	0	0
$325$	1.57240	0.0872209
$326$	0	0
$327$	22.1751	1.22628
$328$	0	0
$329$	−26.6349	−1.46843
$330$	0	0
$331$	8.07134	0.443641	0.221820	−	0.975088i	$-0.428800\pi$
$331$	8.07134	0.443641	0.221820	+	0.975088i	$0.428800\pi$
$332$	0	0
$333$	63.4616	3.47767
$334$	0	0
$335$	−22.7529	−1.24312
$336$	0	0
$337$	−15.2995	−0.833419	−0.416710	−	0.909040i	$-0.636817\pi$
$337$	−15.2995	−0.833419	−0.416710	+	0.909040i	$0.636817\pi$
$338$	0	0
$339$	−14.7692	−0.802155
$340$	0	0
$341$	0	0
$342$	0	0
$343$	−6.00670	−0.324331
$344$	0	0
$345$	3.50686	0.188803
$346$	0	0
$347$	14.1828	0.761374	0.380687	−	0.924704i	$-0.375687\pi$
$347$	14.1828	0.761374	0.380687	+	0.924704i	$0.375687\pi$
$348$	0	0
$349$	28.9302	1.54860	0.774299	−	0.632820i	$-0.218103\pi$
$349$	28.9302	1.54860	0.774299	+	0.632820i	$0.218103\pi$
$350$	0	0
$351$	24.1780	1.29053
$352$	0	0
$353$	−24.1841	−1.28719	−0.643594	−	0.765367i	$-0.722558\pi$
$353$	−24.1841	−1.28719	−0.643594	+	0.765367i	$0.722558\pi$
$354$	0	0
$355$	−33.5758	−1.78202
$356$	0	0
$357$	−14.9481	−0.791137
$358$	0	0
$359$	−12.9054	−0.681122	−0.340561	−	0.940222i	$-0.610617\pi$
$359$	−12.9054	−0.681122	−0.340561	+	0.940222i	$0.610617\pi$
$360$	0	0
$361$	1.00000	0.0526316
$362$	0	0
$363$	0	0
$364$	0	0
$365$	−24.7967	−1.29792
$366$	0	0
$367$	−20.0813	−1.04824	−0.524118	−	0.851646i	$-0.675605\pi$
$367$	−20.0813	−1.04824	−0.524118	+	0.851646i	$0.675605\pi$
$368$	0	0
$369$	−69.0961	−3.59700
$370$	0	0
$371$	−28.1853	−1.46331
$372$	0	0
$373$	18.9551	0.981459	0.490730	−	0.871312i	$-0.336730\pi$
$373$	18.9551	0.981459	0.490730	+	0.871312i	$0.336730\pi$
$374$	0	0
$375$	36.0045	1.85927
$376$	0	0
$377$	−19.2543	−0.991647
$378$	0	0
$379$	−17.2133	−0.884186	−0.442093	−	0.896969i	$-0.645764\pi$
$379$	−17.2133	−0.884186	−0.442093	+	0.896969i	$0.645764\pi$
$380$	0	0
$381$	53.3168	2.73150
$382$	0	0
$383$	−21.0603	−1.07613	−0.538064	−	0.842904i	$-0.680844\pi$
$383$	−21.0603	−1.07613	−0.538064	+	0.842904i	$0.680844\pi$
$384$	0	0
$385$	0	0
$386$	0	0
$387$	−47.4350	−2.41126
$388$	0	0
$389$	8.89827	0.451160	0.225580	−	0.974225i	$-0.427572\pi$
$389$	8.89827	0.451160	0.225580	+	0.974225i	$0.427572\pi$
$390$	0	0
$391$	−0.769945	−0.0389378
$392$	0	0
$393$	−2.95270	−0.148944
$394$	0	0
$395$	−6.48188	−0.326139
$396$	0	0
$397$	26.3146	1.32069	0.660345	−	0.750963i	$-0.270410\pi$
$397$	26.3146	1.32069	0.660345	+	0.750963i	$0.270410\pi$
$398$	0	0
$399$	10.7030	0.535821
$400$	0	0
$401$	11.0752	0.553070	0.276535	−	0.961004i	$-0.410814\pi$
$401$	11.0752	0.553070	0.276535	+	0.961004i	$0.410814\pi$
$402$	0	0
$403$	−0.162044	−0.00807198
$404$	0	0
$405$	25.0375	1.24412
$406$	0	0
$407$	0	0
$408$	0	0
$409$	3.20897	0.158673	0.0793367	−	0.996848i	$-0.474720\pi$
$409$	3.20897	0.158673	0.0793367	+	0.996848i	$0.474720\pi$
$410$	0	0
$411$	−38.7584	−1.91181
$412$	0	0
$413$	−2.84796	−0.140139
$414$	0	0
$415$	−1.48980	−0.0731316
$416$	0	0
$417$	−51.6991	−2.53172
$418$	0	0
$419$	36.2166	1.76930	0.884648	−	0.466260i	$-0.154399\pi$
$419$	36.2166	1.76930	0.884648	+	0.466260i	$0.154399\pi$
$420$	0	0
$421$	13.3904	0.652607	0.326304	−	0.945265i	$-0.394197\pi$
$421$	13.3904	0.652607	0.326304	+	0.945265i	$0.394197\pi$
$422$	0	0
$423$	−48.0522	−2.33638
$424$	0	0
$425$	−0.921812	−0.0447145
$426$	0	0
$427$	6.09743	0.295076
$428$	0	0
$429$	0	0
$430$	0	0
$431$	−1.73872	−0.0837513	−0.0418757	−	0.999123i	$-0.513333\pi$
$431$	−1.73872	−0.0837513	−0.0418757	+	0.999123i	$0.513333\pi$
$432$	0	0
$433$	−11.2285	−0.539605	−0.269803	−	0.962916i	$-0.586958\pi$
$433$	−11.2285	−0.539605	−0.269803	+	0.962916i	$0.586958\pi$
$434$	0	0
$435$	−51.4122	−2.46503
$436$	0	0
$437$	0.551290	0.0263718
$438$	0	0
$439$	8.47555	0.404516	0.202258	−	0.979332i	$-0.435172\pi$
$439$	8.47555	0.404516	0.202258	+	0.979332i	$0.435172\pi$
$440$	0	0
$441$	33.4294	1.59188
$442$	0	0
$443$	−8.64275	−0.410630	−0.205315	−	0.978696i	$-0.565822\pi$
$443$	−8.64275	−0.410630	−0.205315	+	0.978696i	$0.565822\pi$
$444$	0	0
$445$	−28.9873	−1.37413
$446$	0	0
$447$	6.46113	0.305601
$448$	0	0
$449$	−24.9761	−1.17870	−0.589348	−	0.807880i	$-0.700615\pi$
$449$	−24.9761	−1.17870	−0.589348	+	0.807880i	$0.700615\pi$
$450$	0	0
$451$	0	0
$452$	0	0
$453$	36.1158	1.69687
$454$	0	0
$455$	−17.3962	−0.815546
$456$	0	0
$457$	19.0076	0.889139	0.444570	−	0.895744i	$-0.353357\pi$
$457$	19.0076	0.889139	0.444570	+	0.895744i	$0.353357\pi$
$458$	0	0
$459$	−14.1743	−0.661598
$460$	0	0
$461$	3.03082	0.141159	0.0705796	−	0.997506i	$-0.477515\pi$
$461$	3.03082	0.141159	0.0705796	+	0.997506i	$0.477515\pi$
$462$	0	0
$463$	−3.52642	−0.163887	−0.0819433	−	0.996637i	$-0.526113\pi$
$463$	−3.52642	−0.163887	−0.0819433	+	0.996637i	$0.526113\pi$
$464$	0	0
$465$	−0.432684	−0.0200653
$466$	0	0
$467$	1.37161	0.0634707	0.0317353	−	0.999496i	$-0.489897\pi$
$467$	1.37161	0.0634707	0.0317353	+	0.999496i	$0.489897\pi$
$468$	0	0
$469$	−38.2828	−1.76774
$470$	0	0
$471$	−60.3466	−2.78062
$472$	0	0
$473$	0	0
$474$	0	0
$475$	0.660029	0.0302842
$476$	0	0
$477$	−50.8492	−2.32823
$478$	0	0
$479$	−22.7631	−1.04007	−0.520037	−	0.854143i	$-0.674082\pi$
$479$	−22.7631	−1.04007	−0.520037	+	0.854143i	$0.674082\pi$
$480$	0	0
$481$	−23.9076	−1.09009
$482$	0	0
$483$	5.90046	0.268480
$484$	0	0
$485$	7.35921	0.334165
$486$	0	0
$487$	−27.6490	−1.25290	−0.626448	−	0.779463i	$-0.715492\pi$
$487$	−27.6490	−1.25290	−0.626448	+	0.779463i	$0.715492\pi$
$488$	0	0
$489$	−17.5694	−0.794517
$490$	0	0
$491$	19.6440	0.886520	0.443260	−	0.896393i	$-0.353822\pi$
$491$	19.6440	0.886520	0.443260	+	0.896393i	$0.353822\pi$
$492$	0	0
$493$	11.2878	0.508375
$494$	0	0
$495$	0	0
$496$	0	0
$497$	−56.4929	−2.53405
$498$	0	0
$499$	−33.9361	−1.51919	−0.759595	−	0.650396i	$-0.774603\pi$
$499$	−33.9361	−1.51919	−0.759595	+	0.650396i	$0.774603\pi$
$500$	0	0
$501$	−6.83923	−0.305554
$502$	0	0
$503$	1.83967	0.0820269	0.0410134	−	0.999159i	$-0.486941\pi$
$503$	1.83967	0.0820269	0.0410134	+	0.999159i	$0.486941\pi$
$504$	0	0
$505$	−0.987365	−0.0439372
$506$	0	0
$507$	22.3654	0.993282
$508$	0	0
$509$	5.25743	0.233031	0.116516	−	0.993189i	$-0.462827\pi$
$509$	5.25743	0.233031	0.116516	+	0.993189i	$0.462827\pi$
$510$	0	0
$511$	−41.7216	−1.84566
$512$	0	0
$513$	10.1490	0.448087
$514$	0	0
$515$	23.3339	1.02822
$516$	0	0
$517$	0	0
$518$	0	0
$519$	−12.0078	−0.527086
$520$	0	0
$521$	−6.37350	−0.279228	−0.139614	−	0.990206i	$-0.544586\pi$
$521$	−6.37350	−0.279228	−0.139614	+	0.990206i	$0.544586\pi$
$522$	0	0
$523$	4.61267	0.201698	0.100849	−	0.994902i	$-0.467844\pi$
$523$	4.61267	0.201698	0.100849	+	0.994902i	$0.467844\pi$
$524$	0	0
$525$	7.06430	0.308311
$526$	0	0
$527$	0.0949976	0.00413816
$528$	0	0
$529$	−22.6961	−0.986786
$530$	0	0
$531$	−5.13802	−0.222971
$532$	0	0
$533$	26.0303	1.12750
$534$	0	0
$535$	−16.3985	−0.708970
$536$	0	0
$537$	63.9745	2.76070
$538$	0	0
$539$	0	0
$540$	0	0
$541$	16.2770	0.699801	0.349901	−	0.936787i	$-0.386215\pi$
$541$	16.2770	0.699801	0.349901	+	0.936787i	$0.386215\pi$
$542$	0	0
$543$	62.5141	2.68274
$544$	0	0
$545$	−15.1291	−0.648060
$546$	0	0
$547$	−23.0109	−0.983874	−0.491937	−	0.870631i	$-0.663711\pi$
$547$	−23.0109	−0.983874	−0.491937	+	0.870631i	$0.663711\pi$
$548$	0	0
$549$	11.0004	0.469487
$550$	0	0
$551$	−8.08217	−0.344312
$552$	0	0
$553$	−10.9061	−0.463774
$554$	0	0
$555$	−63.8375	−2.70975
$556$	0	0
$557$	−16.1595	−0.684701	−0.342351	−	0.939572i	$-0.611223\pi$
$557$	−16.1595	−0.684701	−0.342351	+	0.939572i	$0.611223\pi$
$558$	0	0
$559$	17.8700	0.755822
$560$	0	0
$561$	0	0
$562$	0	0
$563$	17.0059	0.716712	0.358356	−	0.933585i	$-0.383337\pi$
$563$	17.0059	0.716712	0.358356	+	0.933585i	$0.383337\pi$
$564$	0	0
$565$	10.0764	0.423919
$566$	0	0
$567$	42.1268	1.76916
$568$	0	0
$569$	28.0037	1.17398	0.586989	−	0.809595i	$-0.300313\pi$
$569$	28.0037	1.17398	0.586989	+	0.809595i	$0.300313\pi$
$570$	0	0
$571$	43.2441	1.80971	0.904855	−	0.425721i	$-0.139979\pi$
$571$	43.2441	1.80971	0.904855	+	0.425721i	$0.139979\pi$
$572$	0	0
$573$	−47.3512	−1.97813
$574$	0	0
$575$	0.363867	0.0151743
$576$	0	0
$577$	−30.5136	−1.27030	−0.635149	−	0.772390i	$-0.719061\pi$
$577$	−30.5136	−1.27030	−0.635149	+	0.772390i	$0.719061\pi$
$578$	0	0
$579$	37.6178	1.56334
$580$	0	0
$581$	−2.50667	−0.103994
$582$	0	0
$583$	0	0
$584$	0	0
$585$	−31.3846	−1.29759
$586$	0	0
$587$	−26.0375	−1.07468	−0.537341	−	0.843365i	$-0.680571\pi$
$587$	−26.0375	−1.07468	−0.537341	+	0.843365i	$0.680571\pi$
$588$	0	0
$589$	−0.0680194	−0.00280269
$590$	0	0
$591$	−29.2899	−1.20483
$592$	0	0
$593$	31.5922	1.29734	0.648668	−	0.761072i	$-0.275327\pi$
$593$	31.5922	1.29734	0.648668	+	0.761072i	$0.275327\pi$
$594$	0	0
$595$	10.1985	0.418096
$596$	0	0
$597$	−15.4917	−0.634032
$598$	0	0
$599$	−27.6041	−1.12787	−0.563936	−	0.825818i	$-0.690714\pi$
$599$	−27.6041	−1.12787	−0.563936	+	0.825818i	$0.690714\pi$
$600$	0	0
$601$	34.0255	1.38793	0.693964	−	0.720009i	$-0.255863\pi$
$601$	34.0255	1.38793	0.693964	+	0.720009i	$0.255863\pi$
$602$	0	0
$603$	−69.0663	−2.81260
$604$	0	0
$605$	0	0
$606$	0	0
$607$	−13.0663	−0.530346	−0.265173	−	0.964201i	$-0.585429\pi$
$607$	−13.0663	−0.530346	−0.265173	+	0.964201i	$0.585429\pi$
$608$	0	0
$609$	−86.5036	−3.50530
$610$	0	0
$611$	18.1025	0.732350
$612$	0	0
$613$	30.6984	1.23990	0.619948	−	0.784643i	$-0.287154\pi$
$613$	30.6984	1.23990	0.619948	+	0.784643i	$0.287154\pi$
$614$	0	0
$615$	69.5054	2.80273
$616$	0	0
$617$	−28.3062	−1.13956	−0.569782	−	0.821796i	$-0.692972\pi$
$617$	−28.3062	−1.13956	−0.569782	+	0.821796i	$0.692972\pi$
$618$	0	0
$619$	11.0167	0.442799	0.221399	−	0.975183i	$-0.428938\pi$
$619$	11.0167	0.442799	0.221399	+	0.975183i	$0.428938\pi$
$620$	0	0
$621$	5.59501	0.224520
$622$	0	0
$623$	−48.7726	−1.95403
$624$	0	0
$625$	−21.2642	−0.850569
$626$	0	0
$627$	0	0
$628$	0	0
$629$	14.0158	0.558845
$630$	0	0
$631$	−23.7546	−0.945657	−0.472828	−	0.881155i	$-0.656767\pi$
$631$	−23.7546	−0.945657	−0.472828	+	0.881155i	$0.656767\pi$
$632$	0	0
$633$	51.5573	2.04922
$634$	0	0
$635$	−36.3758	−1.44353
$636$	0	0
$637$	−12.5937	−0.498982
$638$	0	0
$639$	−101.919	−4.03186
$640$	0	0
$641$	−36.4978	−1.44158	−0.720789	−	0.693154i	$-0.756220\pi$
$641$	−36.4978	−1.44158	−0.720789	+	0.693154i	$0.756220\pi$
$642$	0	0
$643$	−5.89653	−0.232536	−0.116268	−	0.993218i	$-0.537093\pi$
$643$	−5.89653	−0.232536	−0.116268	+	0.993218i	$0.537093\pi$
$644$	0	0
$645$	47.7160	1.87882
$646$	0	0
$647$	16.8028	0.660586	0.330293	−	0.943879i	$-0.392852\pi$
$647$	16.8028	0.660586	0.330293	+	0.943879i	$0.392852\pi$
$648$	0	0
$649$	0	0
$650$	0	0
$651$	−0.728013	−0.0285331
$652$	0	0
$653$	−22.1959	−0.868591	−0.434295	−	0.900771i	$-0.643003\pi$
$653$	−22.1959	−0.868591	−0.434295	+	0.900771i	$0.643003\pi$
$654$	0	0
$655$	2.01450	0.0787131
$656$	0	0
$657$	−75.2703	−2.93657
$658$	0	0
$659$	−1.41754	−0.0552197	−0.0276098	−	0.999619i	$-0.508790\pi$
$659$	−1.41754	−0.0552197	−0.0276098	+	0.999619i	$0.508790\pi$
$660$	0	0
$661$	36.4936	1.41943	0.709717	−	0.704486i	$-0.248823\pi$
$661$	36.4936	1.41943	0.709717	+	0.704486i	$0.248823\pi$
$662$	0	0
$663$	10.1595	0.394564
$664$	0	0
$665$	−7.30222	−0.283168
$666$	0	0
$667$	−4.45562	−0.172522
$668$	0	0
$669$	−12.5444	−0.484996
$670$	0	0
$671$	0	0
$672$	0	0
$673$	27.2994	1.05231	0.526157	−	0.850388i	$-0.323633\pi$
$673$	27.2994	1.05231	0.526157	+	0.850388i	$0.323633\pi$
$674$	0	0
$675$	6.69860	0.257829
$676$	0	0
$677$	−19.8920	−0.764512	−0.382256	−	0.924056i	$-0.624853\pi$
$677$	−19.8920	−0.764512	−0.382256	+	0.924056i	$0.624853\pi$
$678$	0	0
$679$	12.3822	0.475187
$680$	0	0
$681$	−4.33271	−0.166030
$682$	0	0
$683$	−6.64803	−0.254380	−0.127190	−	0.991878i	$-0.540596\pi$
$683$	−6.64803	−0.254380	−0.127190	+	0.991878i	$0.540596\pi$
$684$	0	0
$685$	26.4432	1.01034
$686$	0	0
$687$	31.9386	1.21854
$688$	0	0
$689$	19.1563	0.729795
$690$	0	0
$691$	3.48030	0.132397	0.0661985	−	0.997806i	$-0.478913\pi$
$691$	3.48030	0.132397	0.0661985	+	0.997806i	$0.478913\pi$
$692$	0	0
$693$	0	0
$694$	0	0
$695$	35.2721	1.33795
$696$	0	0
$697$	−15.2602	−0.578021
$698$	0	0
$699$	−83.6810	−3.16511
$700$	0	0
$701$	24.0929	0.909977	0.454988	−	0.890497i	$-0.349643\pi$
$701$	24.0929	0.909977	0.454988	+	0.890497i	$0.349643\pi$
$702$	0	0
$703$	−10.0355	−0.378494
$704$	0	0
$705$	48.3368	1.82047
$706$	0	0
$707$	−1.66129	−0.0624792
$708$	0	0
$709$	17.0675	0.640985	0.320492	−	0.947251i	$-0.396152\pi$
$709$	17.0675	0.640985	0.320492	+	0.947251i	$0.396152\pi$
$710$	0	0
$711$	−19.6757	−0.737898
$712$	0	0
$713$	−0.0374984	−0.00140433
$714$	0	0
$715$	0	0
$716$	0	0
$717$	−32.3038	−1.20641
$718$	0	0
$719$	4.55560	0.169895	0.0849477	−	0.996385i	$-0.472928\pi$
$719$	4.55560	0.169895	0.0849477	+	0.996385i	$0.472928\pi$
$720$	0	0
$721$	39.2605	1.46214
$722$	0	0
$723$	−80.0939	−2.97872
$724$	0	0
$725$	−5.33446	−0.198117
$726$	0	0
$727$	−2.54229	−0.0942882	−0.0471441	−	0.998888i	$-0.515012\pi$
$727$	−2.54229	−0.0942882	−0.0471441	+	0.998888i	$0.515012\pi$
$728$	0	0
$729$	−16.9676	−0.628430
$730$	0	0
$731$	−10.4762	−0.387478
$732$	0	0
$733$	17.2073	0.635566	0.317783	−	0.948164i	$-0.397062\pi$
$733$	17.2073	0.635566	0.317783	+	0.948164i	$0.397062\pi$
$734$	0	0
$735$	−33.6274	−1.24037
$736$	0	0
$737$	0	0
$738$	0	0
$739$	−24.8269	−0.913271	−0.456635	−	0.889654i	$-0.650946\pi$
$739$	−24.8269	−0.913271	−0.456635	+	0.889654i	$0.650946\pi$
$740$	0	0
$741$	−7.27436	−0.267230
$742$	0	0
$743$	10.6452	0.390536	0.195268	−	0.980750i	$-0.437442\pi$
$743$	10.6452	0.390536	0.195268	+	0.980750i	$0.437442\pi$
$744$	0	0
$745$	−4.40816	−0.161502
$746$	0	0
$747$	−4.52230	−0.165462
$748$	0	0
$749$	−27.5913	−1.00817
$750$	0	0
$751$	−43.9781	−1.60478	−0.802392	−	0.596797i	$-0.796440\pi$
$751$	−43.9781	−1.60478	−0.802392	+	0.596797i	$0.796440\pi$
$752$	0	0
$753$	45.0008	1.63992
$754$	0	0
$755$	−24.6403	−0.896751
$756$	0	0
$757$	−27.6806	−1.00607	−0.503034	−	0.864266i	$-0.667783\pi$
$757$	−27.6806	−1.00607	−0.503034	+	0.864266i	$0.667783\pi$
$758$	0	0
$759$	0	0
$760$	0	0
$761$	−43.6445	−1.58211	−0.791057	−	0.611743i	$-0.790469\pi$
$761$	−43.6445	−1.58211	−0.791057	+	0.611743i	$0.790469\pi$
$762$	0	0
$763$	−25.4555	−0.921551
$764$	0	0
$765$	18.3991	0.665221
$766$	0	0
$767$	1.93563	0.0698915
$768$	0	0
$769$	49.5413	1.78650	0.893252	−	0.449556i	$-0.148418\pi$
$769$	49.5413	1.78650	0.893252	+	0.449556i	$0.148418\pi$
$770$	0	0
$771$	−77.9443	−2.80710
$772$	0	0
$773$	−37.6221	−1.35317	−0.676587	−	0.736362i	$-0.736542\pi$
$773$	−37.6221	−1.35317	−0.676587	+	0.736362i	$0.736542\pi$
$774$	0	0
$775$	−0.0448947	−0.00161267
$776$	0	0
$777$	−107.410	−3.85330
$778$	0	0
$779$	10.9265	0.391482
$780$	0	0
$781$	0	0
$782$	0	0
$783$	−82.0255	−2.93135
$784$	0	0
$785$	41.1719	1.46949
$786$	0	0
$787$	24.8221	0.884814	0.442407	−	0.896814i	$-0.354125\pi$
$787$	24.8221	0.884814	0.442407	+	0.896814i	$0.354125\pi$
$788$	0	0
$789$	36.0140	1.28213
$790$	0	0
$791$	16.9541	0.602818
$792$	0	0
$793$	−4.14415	−0.147163
$794$	0	0
$795$	51.1504	1.81412
$796$	0	0
$797$	−6.60415	−0.233931	−0.116966	−	0.993136i	$-0.537317\pi$
$797$	−6.60415	−0.233931	−0.116966	+	0.993136i	$0.537317\pi$
$798$	0	0
$799$	−10.6125	−0.375445
$800$	0	0
$801$	−87.9910	−3.10901
$802$	0	0
$803$	0	0
$804$	0	0
$805$	−4.02564	−0.141885
$806$	0	0
$807$	−58.8162	−2.07043
$808$	0	0
$809$	−10.1926	−0.358353	−0.179177	−	0.983817i	$-0.557343\pi$
$809$	−10.1926	−0.358353	−0.179177	+	0.983817i	$0.557343\pi$
$810$	0	0
$811$	−25.3847	−0.891378	−0.445689	−	0.895188i	$-0.647041\pi$
$811$	−25.3847	−0.891378	−0.445689	+	0.895188i	$0.647041\pi$
$812$	0	0
$813$	−43.1250	−1.51246
$814$	0	0
$815$	11.9869	0.419882
$816$	0	0
$817$	7.50111	0.262431
$818$	0	0
$819$	−52.8062	−1.84520
$820$	0	0
$821$	−42.6490	−1.48846	−0.744231	−	0.667922i	$-0.767184\pi$
$821$	−42.6490	−1.48846	−0.744231	+	0.667922i	$0.767184\pi$
$822$	0	0
$823$	49.9772	1.74210	0.871048	−	0.491199i	$-0.163441\pi$
$823$	49.9772	1.74210	0.871048	+	0.491199i	$0.163441\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	38.1252	1.32574	0.662872	−	0.748733i	$-0.269337\pi$
$827$	38.1252	1.32574	0.662872	+	0.748733i	$0.269337\pi$
$828$	0	0
$829$	50.6945	1.76069	0.880347	−	0.474330i	$-0.157310\pi$
$829$	50.6945	1.76069	0.880347	+	0.474330i	$0.157310\pi$
$830$	0	0
$831$	88.1166	3.05673
$832$	0	0
$833$	7.38303	0.255807
$834$	0	0
$835$	4.66612	0.161478
$836$	0	0
$837$	−0.690325	−0.0238611
$838$	0	0
$839$	1.66069	0.0573334	0.0286667	−	0.999589i	$-0.490874\pi$
$839$	1.66069	0.0573334	0.0286667	+	0.999589i	$0.490874\pi$
$840$	0	0
$841$	36.3215	1.25246
$842$	0	0
$843$	67.2820	2.31731
$844$	0	0
$845$	−15.2590	−0.524924
$846$	0	0
$847$	0	0
$848$	0	0
$849$	−39.2597	−1.34739
$850$	0	0
$851$	−5.53244	−0.189650
$852$	0	0
$853$	−41.4654	−1.41975	−0.709875	−	0.704328i	$-0.751249\pi$
$853$	−41.4654	−1.41975	−0.709875	+	0.704328i	$0.751249\pi$
$854$	0	0
$855$	−13.1740	−0.450541
$856$	0	0
$857$	15.9836	0.545990	0.272995	−	0.962015i	$-0.411986\pi$
$857$	15.9836	0.545990	0.272995	+	0.962015i	$0.411986\pi$
$858$	0	0
$859$	16.5496	0.564665	0.282332	−	0.959317i	$-0.408892\pi$
$859$	16.5496	0.564665	0.282332	+	0.959317i	$0.408892\pi$
$860$	0	0
$861$	116.946	3.98552
$862$	0	0
$863$	9.96667	0.339269	0.169635	−	0.985507i	$-0.445741\pi$
$863$	9.96667	0.339269	0.169635	+	0.985507i	$0.445741\pi$
$864$	0	0
$865$	8.19245	0.278552
$866$	0	0
$867$	45.9531	1.56065
$868$	0	0
$869$	0	0
$870$	0	0
$871$	26.0191	0.881624
$872$	0	0
$873$	22.3389	0.756057
$874$	0	0
$875$	−41.3308	−1.39723
$876$	0	0
$877$	49.8742	1.68413	0.842065	−	0.539376i	$-0.181340\pi$
$877$	49.8742	1.68413	0.842065	+	0.539376i	$0.181340\pi$
$878$	0	0
$879$	−76.1090	−2.56709
$880$	0	0
$881$	−8.44750	−0.284604	−0.142302	−	0.989823i	$-0.545450\pi$
$881$	−8.44750	−0.284604	−0.142302	+	0.989823i	$0.545450\pi$
$882$	0	0
$883$	12.2373	0.411817	0.205909	−	0.978571i	$-0.433985\pi$
$883$	12.2373	0.411817	0.205909	+	0.978571i	$0.433985\pi$
$884$	0	0
$885$	5.16846	0.173736
$886$	0	0
$887$	−2.60472	−0.0874580	−0.0437290	−	0.999043i	$-0.513924\pi$
$887$	−2.60472	−0.0874580	−0.0437290	+	0.999043i	$0.513924\pi$
$888$	0	0
$889$	−61.2040	−2.05272
$890$	0	0
$891$	0	0
$892$	0	0
$893$	7.59871	0.254281
$894$	0	0
$895$	−43.6471	−1.45896
$896$	0	0
$897$	−4.01028	−0.133899
$898$	0	0
$899$	0.549744	0.0183350
$900$	0	0
$901$	−11.2303	−0.374135
$902$	0	0
$903$	80.2845	2.67170
$904$	0	0
$905$	−42.6507	−1.41776
$906$	0	0
$907$	−43.0986	−1.43106	−0.715532	−	0.698580i	$-0.753816\pi$
$907$	−43.0986	−1.43106	−0.715532	+	0.698580i	$0.753816\pi$
$908$	0	0
$909$	−2.99714	−0.0994090
$910$	0	0
$911$	−24.0874	−0.798050	−0.399025	−	0.916940i	$-0.630651\pi$
$911$	−24.0874	−0.798050	−0.399025	+	0.916940i	$0.630651\pi$
$912$	0	0
$913$	0	0
$914$	0	0
$915$	−11.0656	−0.365817
$916$	0	0
$917$	3.38950	0.111931
$918$	0	0
$919$	27.4929	0.906907	0.453453	−	0.891280i	$-0.350192\pi$
$919$	27.4929	0.906907	0.453453	+	0.891280i	$0.350192\pi$
$920$	0	0
$921$	57.2598	1.88677
$922$	0	0
$923$	38.3957	1.26381
$924$	0	0
$925$	−6.62369	−0.217786
$926$	0	0
$927$	70.8301	2.32637
$928$	0	0
$929$	−43.6254	−1.43130	−0.715652	−	0.698457i	$-0.753870\pi$
$929$	−43.6254	−1.43130	−0.715652	+	0.698457i	$0.753870\pi$
$930$	0	0
$931$	−5.28634	−0.173253
$932$	0	0
$933$	102.961	3.37079
$934$	0	0
$935$	0	0
$936$	0	0
$937$	29.0810	0.950034	0.475017	−	0.879977i	$-0.342442\pi$
$937$	29.0810	0.950034	0.475017	+	0.879977i	$0.342442\pi$
$938$	0	0
$939$	−2.46869	−0.0805627
$940$	0	0
$941$	−34.6526	−1.12964	−0.564822	−	0.825213i	$-0.691055\pi$
$941$	−34.6526	−1.12964	−0.564822	+	0.825213i	$0.691055\pi$
$942$	0	0
$943$	6.02365	0.196157
$944$	0	0
$945$	−74.1098	−2.41079
$946$	0	0
$947$	−10.7999	−0.350949	−0.175475	−	0.984484i	$-0.556146\pi$
$947$	−10.7999	−0.350949	−0.175475	+	0.984484i	$0.556146\pi$
$948$	0	0
$949$	28.3563	0.920485
$950$	0	0
$951$	−24.7636	−0.803014
$952$	0	0
$953$	−52.3488	−1.69574	−0.847872	−	0.530201i	$-0.822117\pi$
$953$	−52.3488	−1.69574	−0.847872	+	0.530201i	$0.822117\pi$
$954$	0	0
$955$	32.3057	1.04539
$956$	0	0
$957$	0	0
$958$	0	0
$959$	44.4920	1.43672
$960$	0	0
$961$	−30.9954	−0.999851
$962$	0	0
$963$	−49.7777	−1.60406
$964$	0	0
$965$	−25.6650	−0.826186
$966$	0	0
$967$	11.1964	0.360053	0.180026	−	0.983662i	$-0.442382\pi$
$967$	11.1964	0.360053	0.180026	+	0.983662i	$0.442382\pi$
$968$	0	0
$969$	4.26456	0.136998
$970$	0	0
$971$	44.6433	1.43267	0.716336	−	0.697756i	$-0.245818\pi$
$971$	44.6433	1.43267	0.716336	+	0.697756i	$0.245818\pi$
$972$	0	0
$973$	59.3471	1.90258
$974$	0	0
$975$	−4.80128	−0.153764
$976$	0	0
$977$	6.05033	0.193567	0.0967836	−	0.995305i	$-0.469145\pi$
$977$	6.05033	0.193567	0.0967836	+	0.995305i	$0.469145\pi$
$978$	0	0
$979$	0	0
$980$	0	0
$981$	−45.9244	−1.46625
$982$	0	0
$983$	44.3592	1.41484	0.707420	−	0.706794i	$-0.249859\pi$
$983$	44.3592	1.41484	0.707420	+	0.706794i	$0.249859\pi$
$984$	0	0
$985$	19.9833	0.636720
$986$	0	0
$987$	81.3291	2.58873
$988$	0	0
$989$	4.13529	0.131494
$990$	0	0
$991$	54.2098	1.72203	0.861016	−	0.508578i	$-0.169829\pi$
$991$	54.2098	1.72203	0.861016	+	0.508578i	$0.169829\pi$
$992$	0	0
$993$	−24.6457	−0.782107
$994$	0	0
$995$	10.5693	0.335070
$996$	0	0
$997$	22.7327	0.719952	0.359976	−	0.932962i	$-0.382785\pi$
$997$	22.7327	0.719952	0.359976	+	0.932962i	$0.382785\pi$
$998$	0	0
$999$	−101.849	−3.22237

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9196.2.a.t.1.1		10
11.7	odd	10		836.2.j.b.533.5	yes	20
11.8	odd	10		836.2.j.b.229.5	✓	20
11.10	odd	2		9196.2.a.s.1.1		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
836.2.j.b.229.5	✓	20	11.8	odd	10
836.2.j.b.533.5	yes	20	11.7	odd	10
9196.2.a.s.1.1		10	11.10	odd	2
9196.2.a.t.1.1		10	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:	\( N \)	\(=\)	\( 9196 = 2^{2} \cdot 11^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9196.a (trivial)

\(f(q)\)	\(=\)	\(q-3.05348 q^{3} +2.08326 q^{5} +3.50519 q^{7} +6.32373 q^{9} -2.38232 q^{13} -6.36119 q^{15} +1.39662 q^{17} -1.00000 q^{19} -10.7030 q^{21} -0.551290 q^{23} -0.660029 q^{25} -10.1490 q^{27} +8.08217 q^{29} +0.0680194 q^{31} +7.30222 q^{35} +10.0355 q^{37} +7.27436 q^{39} -10.9265 q^{41} -7.50111 q^{43} +13.1740 q^{45} -7.59871 q^{47} +5.28634 q^{49} -4.26456 q^{51} -8.04102 q^{53} +3.05348 q^{57} -0.812498 q^{59} +1.73955 q^{61} +22.1659 q^{63} -4.96299 q^{65} -10.9218 q^{67} +1.68335 q^{69} -16.1169 q^{71} -11.9028 q^{73} +2.01538 q^{75} -3.11141 q^{79} +12.0184 q^{81} -0.715131 q^{83} +2.90953 q^{85} -24.6787 q^{87} -13.9144 q^{89} -8.35047 q^{91} -0.207696 q^{93} -2.08326 q^{95} +3.53255 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 8 q^{5} + 5 q^{7} + 2 q^{9} - 2 q^{13} - 10 q^{15} + 4 q^{17} - 10 q^{19} + 6 q^{21} - 8 q^{23} - 10 q^{25} - 9 q^{27} - 3 q^{29} - 12 q^{31} + 9 q^{35} - 23 q^{37} - 18 q^{39} - 5 q^{41} - 14 q^{43}+ \cdots + 22 q^{97}+O(q^{100}) \) 10 * q + 8 * q^5 + 5 * q^7 + 2 * q^9 - 2 * q^13 - 10 * q^15 + 4 * q^17 - 10 * q^19 + 6 * q^21 - 8 * q^23 - 10 * q^25 - 9 * q^27 - 3 * q^29 - 12 * q^31 + 9 * q^35 - 23 * q^37 - 18 * q^39 - 5 * q^41 - 14 * q^43 - 27 * q^47 - 17 * q^49 - 12 * q^51 - 10 * q^53 - 9 * q^59 + 4 * q^61 + 14 * q^63 + 7 * q^65 - 17 * q^67 - 3 * q^69 - 34 * q^71 - 9 * q^73 - 26 * q^75 - 16 * q^79 - 22 * q^81 + 6 * q^83 + 24 * q^85 + q^87 - 35 * q^89 - 35 * q^91 - 44 * q^93 - 8 * q^95 + 22 * q^97

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