LMFDB - Embedded newform 9801.2.a.co.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9801,2,Mod(1,9801)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9801, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("9801.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 9801 = 3^{4} \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	9801.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:	$78.2613790211$
Analytic rank:	$0$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 2 x^{17} - 22 x^{16} + 42 x^{15} + 198 x^{14} - 357 x^{13} - 944 x^{12} + 1579 x^{11} + \cdots - 55 $ x^18 - 2x^17 - 22x^16 + 42x^15 + 198x^14 - 357x^13 - 944x^12 + 1579x^11 + 2594x^10 - 3897x^9 - 4219x^8 + 5363x^7 + 4035x^6 - 3886x^5 - 2173x^4 + 1303x^3 + 576x^2 - 155*x - 55
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 99)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-2.32900$ of defining polynomial
Character	$\chi$	$=$	9801.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.32900 q^{2} +3.42425 q^{4} -0.317020 q^{5} +1.41849 q^{7} -3.31708 q^{8} +0.738340 q^{10} -4.19704 q^{13} -3.30367 q^{14} +0.876991 q^{16} +6.24422 q^{17} -3.09786 q^{19} -1.08556 q^{20} -4.52050 q^{23} -4.89950 q^{25} +9.77491 q^{26} +4.85727 q^{28} -2.92845 q^{29} -9.54176 q^{31} +4.59165 q^{32} -14.5428 q^{34} -0.449690 q^{35} +0.847494 q^{37} +7.21491 q^{38} +1.05158 q^{40} +3.86961 q^{41} -3.55302 q^{43} +10.5282 q^{46} -7.45100 q^{47} -4.98788 q^{49} +11.4109 q^{50} -14.3717 q^{52} +6.68304 q^{53} -4.70526 q^{56} +6.82035 q^{58} -12.0748 q^{59} -4.62032 q^{61} +22.2228 q^{62} -12.4479 q^{64} +1.33054 q^{65} +9.96771 q^{67} +21.3818 q^{68} +1.04733 q^{70} +2.93068 q^{71} -4.24167 q^{73} -1.97382 q^{74} -10.6078 q^{76} +3.38199 q^{79} -0.278024 q^{80} -9.01233 q^{82} +13.4875 q^{83} -1.97954 q^{85} +8.27498 q^{86} +2.69745 q^{89} -5.95347 q^{91} -15.4793 q^{92} +17.3534 q^{94} +0.982082 q^{95} -5.25744 q^{97} +11.6168 q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 2 q^{2} + 12 q^{4} - q^{5} - q^{7} + 6 q^{8} + 2 q^{10} - 3 q^{13} - 8 q^{16} + 20 q^{17} + 3 q^{19} - 5 q^{20} - 10 q^{23} + 7 q^{25} + 2 q^{26} - 19 q^{28} + 21 q^{29} + 6 q^{31} + 9 q^{32} - 4 q^{34}+ \cdots + 82 q^{98}+O(q^{100}) $ 18 * q + 2 * q^2 + 12 * q^4 - q^5 - q^7 + 6 * q^8 + 2 * q^10 - 3 * q^13 - 8 * q^16 + 20 * q^17 + 3 * q^19 - 5 * q^20 - 10 * q^23 + 7 * q^25 + 2 * q^26 - 19 * q^28 + 21 * q^29 + 6 * q^31 + 9 * q^32 - 4 * q^34 + 38 * q^35 + 7 * q^37 + 13 * q^38 + 20 * q^41 - 4 * q^43 - 8 * q^46 + 7 * q^47 + 7 * q^49 + 25 * q^50 + 19 * q^52 + 31 * q^53 - 57 * q^56 + 12 * q^58 - 12 * q^59 + 16 * q^61 + 19 * q^62 - 16 * q^64 + 42 * q^65 - 5 * q^67 + 51 * q^68 + 8 * q^70 + 13 * q^71 + 9 * q^74 + 8 * q^76 + 2 * q^79 + 46 * q^80 - 34 * q^82 + 36 * q^83 - 25 * q^85 + 26 * q^86 - 14 * q^89 - 15 * q^91 - 15 * q^92 - 4 * q^94 + 64 * q^95 - 16 * q^97 + 82 * q^98

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 $

$2$	−2.32900	−1.64685	−0.823427	−	0.567423i	$-0.807941\pi$
$2$	−2.32900	−1.64685	−0.823427	+	0.567423i	$0.807941\pi$
$3$	0	0
$3$	0	0
$4$	3.42425	1.71213
$5$	−0.317020	−0.141776	−0.0708878	−	0.997484i	$-0.522583\pi$
$5$	−0.317020	−0.141776	−0.0708878	+	0.997484i	$0.522583\pi$
$6$	0	0
$7$	1.41849	0.536140	0.268070	−	0.963399i	$-0.413614\pi$
$7$	1.41849	0.536140	0.268070	+	0.963399i	$0.413614\pi$
$8$	−3.31708	−1.17277
$9$	0	0
$10$	0.738340	0.233484
$11$	0	0
$11$	0	0
$12$	0	0
$13$	−4.19704	−1.16405	−0.582024	−	0.813171i	$-0.697739\pi$
$13$	−4.19704	−1.16405	−0.582024	+	0.813171i	$0.697739\pi$
$14$	−3.30367	−0.882944
$15$	0	0
$16$	0.876991	0.219248
$17$	6.24422	1.51445	0.757223	−	0.653157i	$-0.226556\pi$
$17$	6.24422	1.51445	0.757223	+	0.653157i	$0.226556\pi$
$18$	0	0
$19$	−3.09786	−0.710697	−0.355348	−	0.934734i	$-0.615638\pi$
$19$	−3.09786	−0.710697	−0.355348	+	0.934734i	$0.615638\pi$
$20$	−1.08556	−0.242738
$21$	0	0
$22$	0	0
$23$	−4.52050	−0.942589	−0.471295	−	0.881976i	$-0.656213\pi$
$23$	−4.52050	−0.942589	−0.471295	+	0.881976i	$0.656213\pi$
$24$	0	0
$25$	−4.89950	−0.979900
$26$	9.77491	1.91702
$27$	0	0
$28$	4.85727	0.917939
$29$	−2.92845	−0.543799	−0.271899	−	0.962326i	$-0.587652\pi$
$29$	−2.92845	−0.543799	−0.271899	+	0.962326i	$0.587652\pi$
$30$	0	0
$31$	−9.54176	−1.71375	−0.856876	−	0.515523i	$-0.827598\pi$
$31$	−9.54176	−1.71375	−0.856876	+	0.515523i	$0.827598\pi$
$32$	4.59165	0.811697
$33$	0	0
$34$	−14.5428	−2.49407
$35$	−0.449690	−0.0760116
$36$	0	0
$37$	0.847494	0.139327	0.0696636	−	0.997571i	$-0.477807\pi$
$37$	0.847494	0.139327	0.0696636	+	0.997571i	$0.477807\pi$
$38$	7.21491	1.17041
$39$	0	0
$40$	1.05158	0.166270
$41$	3.86961	0.604331	0.302166	−	0.953255i	$-0.402290\pi$
$41$	3.86961	0.604331	0.302166	+	0.953255i	$0.402290\pi$
$42$	0	0
$43$	−3.55302	−0.541830	−0.270915	−	0.962603i	$-0.587326\pi$
$43$	−3.55302	−0.541830	−0.270915	+	0.962603i	$0.587326\pi$
$44$	0	0
$45$	0	0
$46$	10.5282	1.55231
$47$	−7.45100	−1.08684	−0.543420	−	0.839461i	$-0.682871\pi$
$47$	−7.45100	−1.08684	−0.543420	+	0.839461i	$0.682871\pi$
$48$	0	0
$49$	−4.98788	−0.712554
$50$	11.4109	1.61375
$51$	0	0
$52$	−14.3717	−1.99300
$53$	6.68304	0.917986	0.458993	−	0.888440i	$-0.348210\pi$
$53$	6.68304	0.917986	0.458993	+	0.888440i	$0.348210\pi$
$54$	0	0
$55$	0	0
$56$	−4.70526	−0.628766
$57$	0	0
$58$	6.82035	0.895556
$59$	−12.0748	−1.57200	−0.786001	−	0.618226i	$-0.787852\pi$
$59$	−12.0748	−1.57200	−0.786001	+	0.618226i	$0.787852\pi$
$60$	0	0
$61$	−4.62032	−0.591571	−0.295786	−	0.955254i	$-0.595581\pi$
$61$	−4.62032	−0.591571	−0.295786	+	0.955254i	$0.595581\pi$
$62$	22.2228	2.82230
$63$	0	0
$64$	−12.4479	−1.55599
$65$	1.33054	0.165034
$66$	0	0
$67$	9.96771	1.21775	0.608875	−	0.793266i	$-0.291621\pi$
$67$	9.96771	1.21775	0.608875	+	0.793266i	$0.291621\pi$
$68$	21.3818	2.59292
$69$	0	0
$70$	1.04733	0.125180
$71$	2.93068	0.347808	0.173904	−	0.984763i	$-0.444362\pi$
$71$	2.93068	0.347808	0.173904	+	0.984763i	$0.444362\pi$
$72$	0	0
$73$	−4.24167	−0.496450	−0.248225	−	0.968702i	$-0.579847\pi$
$73$	−4.24167	−0.496450	−0.248225	+	0.968702i	$0.579847\pi$
$74$	−1.97382	−0.229451
$75$	0	0
$76$	−10.6078	−1.21680
$77$	0	0
$78$	0	0
$79$	3.38199	0.380503	0.190252	−	0.981735i	$-0.439070\pi$
$79$	3.38199	0.380503	0.190252	+	0.981735i	$0.439070\pi$
$80$	−0.278024	−0.0310840
$81$	0	0
$82$	−9.01233	−0.995245
$83$	13.4875	1.48044	0.740221	−	0.672363i	$-0.234721\pi$
$83$	13.4875	1.48044	0.740221	+	0.672363i	$0.234721\pi$
$84$	0	0
$85$	−1.97954	−0.214711
$86$	8.27498	0.892315
$87$	0	0
$88$	0	0
$89$	2.69745	0.285929	0.142965	−	0.989728i	$-0.454336\pi$
$89$	2.69745	0.285929	0.142965	+	0.989728i	$0.454336\pi$
$90$	0	0
$91$	−5.95347	−0.624093
$92$	−15.4793	−1.61383
$93$	0	0
$94$	17.3534	1.78987
$95$	0.982082	0.100759
$96$	0	0
$97$	−5.25744	−0.533813	−0.266906	−	0.963722i	$-0.586001\pi$
$97$	−5.25744	−0.533813	−0.266906	+	0.963722i	$0.586001\pi$
$98$	11.6168	1.17347
$99$	0	0
$100$	−16.7771	−1.67771
$101$	9.52974	0.948245	0.474123	−	0.880459i	$-0.342765\pi$
$101$	9.52974	0.948245	0.474123	+	0.880459i	$0.342765\pi$
$102$	0	0
$103$	9.53563	0.939574	0.469787	−	0.882780i	$-0.344331\pi$
$103$	9.53563	0.939574	0.469787	+	0.882780i	$0.344331\pi$
$104$	13.9219	1.36516
$105$	0	0
$106$	−15.5648	−1.51179
$107$	−5.17260	−0.500054	−0.250027	−	0.968239i	$-0.580440\pi$
$107$	−5.17260	−0.500054	−0.250027	+	0.968239i	$0.580440\pi$
$108$	0	0
$109$	−14.4767	−1.38661	−0.693307	−	0.720643i	$-0.743847\pi$
$109$	−14.4767	−1.38661	−0.693307	+	0.720643i	$0.743847\pi$
$110$	0	0
$111$	0	0
$112$	1.24401	0.117547
$113$	−7.43161	−0.699107	−0.349553	−	0.936916i	$-0.613667\pi$
$113$	−7.43161	−0.699107	−0.349553	+	0.936916i	$0.613667\pi$
$114$	0	0
$115$	1.43309	0.133636
$116$	−10.0277	−0.931051
$117$	0	0
$118$	28.1222	2.58886
$119$	8.85738	0.811954
$120$	0	0
$121$	0	0
$122$	10.7607	0.974231
$123$	0	0
$124$	−32.6734	−2.93416
$125$	3.13834	0.280702
$126$	0	0
$127$	13.2044	1.17171	0.585853	−	0.810418i	$-0.300760\pi$
$127$	13.2044	1.17171	0.585853	+	0.810418i	$0.300760\pi$
$128$	19.8080	1.75080
$129$	0	0
$130$	−3.09884	−0.271786
$131$	7.30043	0.637841	0.318921	−	0.947781i	$-0.396680\pi$
$131$	7.30043	0.637841	0.318921	+	0.947781i	$0.396680\pi$
$132$	0	0
$133$	−4.39429	−0.381033
$134$	−23.2148	−2.00545
$135$	0	0
$136$	−20.7126	−1.77609
$137$	9.80733	0.837897	0.418948	−	0.908010i	$-0.362399\pi$
$137$	9.80733	0.837897	0.418948	+	0.908010i	$0.362399\pi$
$138$	0	0
$139$	9.47690	0.803820	0.401910	−	0.915679i	$-0.368347\pi$
$139$	9.47690	0.803820	0.401910	+	0.915679i	$0.368347\pi$
$140$	−1.53985	−0.130141
$141$	0	0
$142$	−6.82556	−0.572789
$143$	0	0
$144$	0	0
$145$	0.928375	0.0770974
$146$	9.87886	0.817580
$147$	0	0
$148$	2.90203	0.238546
$149$	4.12745	0.338134	0.169067	−	0.985605i	$-0.445925\pi$
$149$	4.12745	0.338134	0.169067	+	0.985605i	$0.445925\pi$
$150$	0	0
$151$	17.7753	1.44653	0.723265	−	0.690570i	$-0.242640\pi$
$151$	17.7753	1.44653	0.723265	+	0.690570i	$0.242640\pi$
$152$	10.2758	0.833481
$153$	0	0
$154$	0	0
$155$	3.02493	0.242968
$156$	0	0
$157$	−2.01726	−0.160995	−0.0804974	−	0.996755i	$-0.525651\pi$
$157$	−2.01726	−0.160995	−0.0804974	+	0.996755i	$0.525651\pi$
$158$	−7.87666	−0.626633
$159$	0	0
$160$	−1.45564	−0.115079
$161$	−6.41229	−0.505359
$162$	0	0
$163$	−1.58042	−0.123788	−0.0618940	−	0.998083i	$-0.519714\pi$
$163$	−1.58042	−0.123788	−0.0618940	+	0.998083i	$0.519714\pi$
$164$	13.2505	1.03469
$165$	0	0
$166$	−31.4124	−2.43807
$167$	−15.3216	−1.18562	−0.592812	−	0.805341i	$-0.701982\pi$
$167$	−15.3216	−1.18562	−0.592812	+	0.805341i	$0.701982\pi$
$168$	0	0
$169$	4.61512	0.355009
$170$	4.61036	0.353598
$171$	0	0
$172$	−12.1664	−0.927681
$173$	0.986039	0.0749672	0.0374836	−	0.999297i	$-0.488066\pi$
$173$	0.986039	0.0749672	0.0374836	+	0.999297i	$0.488066\pi$
$174$	0	0
$175$	−6.94990	−0.525363
$176$	0	0
$177$	0	0
$178$	−6.28237	−0.470884
$179$	−11.2258	−0.839056	−0.419528	−	0.907742i	$-0.637804\pi$
$179$	−11.2258	−0.839056	−0.419528	+	0.907742i	$0.637804\pi$
$180$	0	0
$181$	17.9256	1.33240	0.666201	−	0.745773i	$-0.267919\pi$
$181$	17.9256	1.33240	0.666201	+	0.745773i	$0.267919\pi$
$182$	13.8656	1.02779
$183$	0	0
$184$	14.9949	1.10544
$185$	−0.268673	−0.0197532
$186$	0	0
$187$	0	0
$188$	−25.5141	−1.86081
$189$	0	0
$190$	−2.28727	−0.165936
$191$	12.8879	0.932539	0.466269	−	0.884643i	$-0.345598\pi$
$191$	12.8879	0.932539	0.466269	+	0.884643i	$0.345598\pi$
$192$	0	0
$193$	23.1510	1.66645	0.833224	−	0.552936i	$-0.186493\pi$
$193$	23.1510	1.66645	0.833224	+	0.552936i	$0.186493\pi$
$194$	12.2446	0.879111
$195$	0	0
$196$	−17.0797	−1.21998
$197$	−1.07766	−0.0767801	−0.0383900	−	0.999263i	$-0.512223\pi$
$197$	−1.07766	−0.0767801	−0.0383900	+	0.999263i	$0.512223\pi$
$198$	0	0
$199$	16.4307	1.16474	0.582371	−	0.812923i	$-0.302125\pi$
$199$	16.4307	1.16474	0.582371	+	0.812923i	$0.302125\pi$
$200$	16.2520	1.14919
$201$	0	0
$202$	−22.1948	−1.56162
$203$	−4.15398	−0.291552
$204$	0	0
$205$	−1.22674	−0.0856795
$206$	−22.2085	−1.54734
$207$	0	0
$208$	−3.68076	−0.255215
$209$	0	0
$210$	0	0
$211$	14.9498	1.02919	0.514593	−	0.857435i	$-0.327943\pi$
$211$	14.9498	1.02919	0.514593	+	0.857435i	$0.327943\pi$
$212$	22.8844	1.57171
$213$	0	0
$214$	12.0470	0.823516
$215$	1.12638	0.0768183
$216$	0	0
$217$	−13.5349	−0.918810
$218$	33.7162	2.28355
$219$	0	0
$220$	0	0
$221$	−26.2072	−1.76289
$222$	0	0
$223$	1.92628	0.128993	0.0644966	−	0.997918i	$-0.479456\pi$
$223$	1.92628	0.128993	0.0644966	+	0.997918i	$0.479456\pi$
$224$	6.51322	0.435183
$225$	0	0
$226$	17.3082	1.15133
$227$	16.0111	1.06269	0.531347	−	0.847154i	$-0.321686\pi$
$227$	16.0111	1.06269	0.531347	+	0.847154i	$0.321686\pi$
$228$	0	0
$229$	−0.522925	−0.0345559	−0.0172779	−	0.999851i	$-0.505500\pi$
$229$	−0.522925	−0.0345559	−0.0172779	+	0.999851i	$0.505500\pi$
$230$	−3.33766	−0.220079
$231$	0	0
$232$	9.71389	0.637748
$233$	10.2525	0.671665	0.335833	−	0.941922i	$-0.390982\pi$
$233$	10.2525	0.671665	0.335833	+	0.941922i	$0.390982\pi$
$234$	0	0
$235$	2.36212	0.154087
$236$	−41.3470	−2.69146
$237$	0	0
$238$	−20.6288	−1.33717
$239$	9.64104	0.623627	0.311814	−	0.950143i	$-0.399064\pi$
$239$	9.64104	0.623627	0.311814	+	0.950143i	$0.399064\pi$
$240$	0	0
$241$	0.278731	0.0179547	0.00897733	−	0.999960i	$-0.497142\pi$
$241$	0.278731	0.0179547	0.00897733	+	0.999960i	$0.497142\pi$
$242$	0	0
$243$	0	0
$244$	−15.8211	−1.01284
$245$	1.58126	0.101023
$246$	0	0
$247$	13.0018	0.827286
$248$	31.6508	2.00983
$249$	0	0
$250$	−7.30920	−0.462274
$251$	4.42541	0.279329	0.139665	−	0.990199i	$-0.455398\pi$
$251$	4.42541	0.279329	0.139665	+	0.990199i	$0.455398\pi$
$252$	0	0
$253$	0	0
$254$	−30.7532	−1.92963
$255$	0	0
$256$	−21.2370	−1.32731
$257$	3.65452	0.227963	0.113981	−	0.993483i	$-0.463640\pi$
$257$	3.65452	0.227963	0.113981	+	0.993483i	$0.463640\pi$
$258$	0	0
$259$	1.20216	0.0746989
$260$	4.55612	0.282558
$261$	0	0
$262$	−17.0027	−1.05043
$263$	14.4524	0.891174	0.445587	−	0.895239i	$-0.352995\pi$
$263$	14.4524	0.891174	0.445587	+	0.895239i	$0.352995\pi$
$264$	0	0
$265$	−2.11866	−0.130148
$266$	10.2343	0.627505
$267$	0	0
$268$	34.1319	2.08494
$269$	0.917748	0.0559561	0.0279780	−	0.999609i	$-0.491093\pi$
$269$	0.917748	0.0559561	0.0279780	+	0.999609i	$0.491093\pi$
$270$	0	0
$271$	2.64421	0.160624	0.0803120	−	0.996770i	$-0.474408\pi$
$271$	2.64421	0.160624	0.0803120	+	0.996770i	$0.474408\pi$
$272$	5.47612	0.332039
$273$	0	0
$274$	−22.8413	−1.37989
$275$	0	0
$276$	0	0
$277$	−28.9045	−1.73670	−0.868351	−	0.495949i	$-0.834820\pi$
$277$	−28.9045	−1.73670	−0.868351	+	0.495949i	$0.834820\pi$
$278$	−22.0717	−1.32377
$279$	0	0
$280$	1.49166	0.0891437
$281$	−8.74257	−0.521538	−0.260769	−	0.965401i	$-0.583976\pi$
$281$	−8.74257	−0.521538	−0.260769	+	0.965401i	$0.583976\pi$
$282$	0	0
$283$	23.2173	1.38012	0.690061	−	0.723751i	$-0.257583\pi$
$283$	23.2173	1.38012	0.690061	+	0.723751i	$0.257583\pi$
$284$	10.0354	0.595491
$285$	0	0
$286$	0	0
$287$	5.48901	0.324006
$288$	0	0
$289$	21.9902	1.29354
$290$	−2.16219	−0.126968
$291$	0	0
$292$	−14.5245	−0.849984
$293$	20.9754	1.22540	0.612698	−	0.790317i	$-0.290084\pi$
$293$	20.9754	1.22540	0.612698	+	0.790317i	$0.290084\pi$
$294$	0	0
$295$	3.82794	0.222871
$296$	−2.81121	−0.163398
$297$	0	0
$298$	−9.61284	−0.556857
$299$	18.9727	1.09722
$300$	0	0
$301$	−5.03993	−0.290497
$302$	−41.3986	−2.38222
$303$	0	0
$304$	−2.71679	−0.155819
$305$	1.46473	0.0838704
$306$	0	0
$307$	−23.1324	−1.32024	−0.660118	−	0.751162i	$-0.729494\pi$
$307$	−23.1324	−1.32024	−0.660118	+	0.751162i	$0.729494\pi$
$308$	0	0
$309$	0	0
$310$	−7.04507	−0.400133
$311$	20.4148	1.15762	0.578809	−	0.815463i	$-0.303518\pi$
$311$	20.4148	1.15762	0.578809	+	0.815463i	$0.303518\pi$
$312$	0	0
$313$	−34.0393	−1.92402	−0.962008	−	0.273020i	$-0.911978\pi$
$313$	−34.0393	−1.92402	−0.962008	+	0.273020i	$0.911978\pi$
$314$	4.69820	0.265135
$315$	0	0
$316$	11.5808	0.651469
$317$	−27.4204	−1.54008	−0.770042	−	0.637993i	$-0.779765\pi$
$317$	−27.4204	−1.54008	−0.770042	+	0.637993i	$0.779765\pi$
$318$	0	0
$319$	0	0
$320$	3.94625	0.220602
$321$	0	0
$322$	14.9342	0.832253
$323$	−19.3437	−1.07631
$324$	0	0
$325$	20.5634	1.14065
$326$	3.68080	0.203861
$327$	0	0
$328$	−12.8358	−0.708739
$329$	−10.5692	−0.582698
$330$	0	0
$331$	−17.9724	−0.987854	−0.493927	−	0.869503i	$-0.664439\pi$
$331$	−17.9724	−0.987854	−0.493927	+	0.869503i	$0.664439\pi$
$332$	46.1845	2.53470
$333$	0	0
$334$	35.6841	1.95255
$335$	−3.15996	−0.172647
$336$	0	0
$337$	−10.9721	−0.597691	−0.298845	−	0.954302i	$-0.596601\pi$
$337$	−10.9721	−0.597691	−0.298845	+	0.954302i	$0.596601\pi$
$338$	−10.7486	−0.584648
$339$	0	0
$340$	−6.77845	−0.367613
$341$	0	0
$342$	0	0
$343$	−17.0047	−0.918168
$344$	11.7857	0.635440
$345$	0	0
$346$	−2.29649	−0.123460
$347$	−22.0988	−1.18633	−0.593163	−	0.805082i	$-0.702121\pi$
$347$	−22.0988	−1.18633	−0.593163	+	0.805082i	$0.702121\pi$
$348$	0	0
$349$	18.4037	0.985129	0.492564	−	0.870276i	$-0.336060\pi$
$349$	18.4037	0.985129	0.492564	+	0.870276i	$0.336060\pi$
$350$	16.1863	0.865196
$351$	0	0
$352$	0	0
$353$	33.0708	1.76018	0.880089	−	0.474808i	$-0.157483\pi$
$353$	33.0708	1.76018	0.880089	+	0.474808i	$0.157483\pi$
$354$	0	0
$355$	−0.929084	−0.0493107
$356$	9.23676	0.489547
$357$	0	0
$358$	26.1449	1.38180
$359$	−2.99864	−0.158262	−0.0791311	−	0.996864i	$-0.525215\pi$
$359$	−2.99864	−0.158262	−0.0791311	+	0.996864i	$0.525215\pi$
$360$	0	0
$361$	−9.40329	−0.494910
$362$	−41.7488	−2.19427
$363$	0	0
$364$	−20.3862	−1.06852
$365$	1.34469	0.0703845
$366$	0	0
$367$	1.66246	0.0867797	0.0433899	−	0.999058i	$-0.486184\pi$
$367$	1.66246	0.0867797	0.0433899	+	0.999058i	$0.486184\pi$
$368$	−3.96444	−0.206661
$369$	0	0
$370$	0.625739	0.0325306
$371$	9.47985	0.492169
$372$	0	0
$373$	21.5087	1.11368	0.556839	−	0.830621i	$-0.312014\pi$
$373$	21.5087	1.11368	0.556839	+	0.830621i	$0.312014\pi$
$374$	0	0
$375$	0	0
$376$	24.7156	1.27461
$377$	12.2908	0.633008
$378$	0	0
$379$	12.4193	0.637938	0.318969	−	0.947765i	$-0.396663\pi$
$379$	12.4193	0.637938	0.318969	+	0.947765i	$0.396663\pi$
$380$	3.36290	0.172513
$381$	0	0
$382$	−30.0160	−1.53575
$383$	0.799677	0.0408616	0.0204308	−	0.999791i	$-0.493496\pi$
$383$	0.799677	0.0408616	0.0204308	+	0.999791i	$0.493496\pi$
$384$	0	0
$385$	0	0
$386$	−53.9188	−2.74439
$387$	0	0
$388$	−18.0028	−0.913954
$389$	−1.73669	−0.0880534	−0.0440267	−	0.999030i	$-0.514019\pi$
$389$	−1.73669	−0.0880534	−0.0440267	+	0.999030i	$0.514019\pi$
$390$	0	0
$391$	−28.2270	−1.42750
$392$	16.5452	0.835659
$393$	0	0
$394$	2.50987	0.126446
$395$	−1.07216	−0.0539461
$396$	0	0
$397$	−24.7599	−1.24267	−0.621333	−	0.783547i	$-0.713409\pi$
$397$	−24.7599	−1.24267	−0.621333	+	0.783547i	$0.713409\pi$
$398$	−38.2672	−1.91816
$399$	0	0
$400$	−4.29682	−0.214841
$401$	21.8523	1.09125	0.545627	−	0.838028i	$-0.316292\pi$
$401$	21.8523	1.09125	0.545627	+	0.838028i	$0.316292\pi$
$402$	0	0
$403$	40.0471	1.99489
$404$	32.6322	1.62351
$405$	0	0
$406$	9.67462	0.480143
$407$	0	0
$408$	0	0
$409$	−8.03477	−0.397294	−0.198647	−	0.980071i	$-0.563655\pi$
$409$	−8.03477	−0.397294	−0.198647	+	0.980071i	$0.563655\pi$
$410$	2.85709	0.141101
$411$	0	0
$412$	32.6524	1.60867
$413$	−17.1280	−0.842812
$414$	0	0
$415$	−4.27580	−0.209891
$416$	−19.2713	−0.944855
$417$	0	0
$418$	0	0
$419$	−5.59681	−0.273422	−0.136711	−	0.990611i	$-0.543653\pi$
$419$	−5.59681	−0.273422	−0.136711	+	0.990611i	$0.543653\pi$
$420$	0	0
$421$	37.8544	1.84491	0.922455	−	0.386105i	$-0.126180\pi$
$421$	37.8544	1.84491	0.922455	+	0.386105i	$0.126180\pi$
$422$	−34.8181	−1.69492
$423$	0	0
$424$	−22.1682	−1.07658
$425$	−30.5935	−1.48400
$426$	0	0
$427$	−6.55389	−0.317165
$428$	−17.7123	−0.856155
$429$	0	0
$430$	−2.62333	−0.126508
$431$	29.7844	1.43466	0.717332	−	0.696731i	$-0.245363\pi$
$431$	29.7844	1.43466	0.717332	+	0.696731i	$0.245363\pi$
$432$	0	0
$433$	−0.279271	−0.0134209	−0.00671046	−	0.999977i	$-0.502136\pi$
$433$	−0.279271	−0.0134209	−0.00671046	+	0.999977i	$0.502136\pi$
$434$	31.5229	1.51315
$435$	0	0
$436$	−49.5717	−2.37406
$437$	14.0039	0.669895
$438$	0	0
$439$	−14.9965	−0.715746	−0.357873	−	0.933770i	$-0.616498\pi$
$439$	−14.9965	−0.715746	−0.357873	+	0.933770i	$0.616498\pi$
$440$	0	0
$441$	0	0
$442$	61.0366	2.90322
$443$	14.4998	0.688907	0.344453	−	0.938803i	$-0.388064\pi$
$443$	14.4998	0.688907	0.344453	+	0.938803i	$0.388064\pi$
$444$	0	0
$445$	−0.855146	−0.0405378
$446$	−4.48631	−0.212433
$447$	0	0
$448$	−17.6573	−0.834230
$449$	−21.2217	−1.00151	−0.500757	−	0.865588i	$-0.666945\pi$
$449$	−21.2217	−1.00151	−0.500757	+	0.865588i	$0.666945\pi$
$450$	0	0
$451$	0	0
$452$	−25.4477	−1.19696
$453$	0	0
$454$	−37.2899	−1.75010
$455$	1.88737	0.0884811
$456$	0	0
$457$	3.20950	0.150134	0.0750671	−	0.997178i	$-0.476083\pi$
$457$	3.20950	0.150134	0.0750671	+	0.997178i	$0.476083\pi$
$458$	1.21789	0.0569085
$459$	0	0
$460$	4.90725	0.228802
$461$	−26.3256	−1.22610	−0.613052	−	0.790042i	$-0.710058\pi$
$461$	−26.3256	−1.22610	−0.613052	+	0.790042i	$0.710058\pi$
$462$	0	0
$463$	3.62824	0.168619	0.0843093	−	0.996440i	$-0.473132\pi$
$463$	3.62824	0.168619	0.0843093	+	0.996440i	$0.473132\pi$
$464$	−2.56822	−0.119227
$465$	0	0
$466$	−23.8782	−1.10613
$467$	−18.4952	−0.855854	−0.427927	−	0.903813i	$-0.640756\pi$
$467$	−18.4952	−0.855854	−0.427927	+	0.903813i	$0.640756\pi$
$468$	0	0
$469$	14.1391	0.652884
$470$	−5.50137	−0.253759
$471$	0	0
$472$	40.0530	1.84359
$473$	0	0
$474$	0	0
$475$	15.1779	0.696412
$476$	30.3299	1.39017
$477$	0	0
$478$	−22.4540	−1.02702
$479$	0.156998	0.00717343	0.00358672	−	0.999994i	$-0.498858\pi$
$479$	0.156998	0.00717343	0.00358672	+	0.999994i	$0.498858\pi$
$480$	0	0
$481$	−3.55697	−0.162184
$482$	−0.649165	−0.0295687
$483$	0	0
$484$	0	0
$485$	1.66671	0.0756816
$486$	0	0
$487$	17.9265	0.812327	0.406164	−	0.913800i	$-0.366866\pi$
$487$	17.9265	0.812327	0.406164	+	0.913800i	$0.366866\pi$
$488$	15.3260	0.693775
$489$	0	0
$490$	−3.68275	−0.166370
$491$	6.64797	0.300019	0.150009	−	0.988685i	$-0.452070\pi$
$491$	6.64797	0.300019	0.150009	+	0.988685i	$0.452070\pi$
$492$	0	0
$493$	−18.2858	−0.823553
$494$	−30.2813	−1.36242
$495$	0	0
$496$	−8.36804	−0.375736
$497$	4.15715	0.186474
$498$	0	0
$499$	33.9473	1.51969	0.759846	−	0.650103i	$-0.225274\pi$
$499$	33.9473	1.51969	0.759846	+	0.650103i	$0.225274\pi$
$500$	10.7465	0.480596
$501$	0	0
$502$	−10.3068	−0.460014
$503$	−3.13729	−0.139885	−0.0699423	−	0.997551i	$-0.522282\pi$
$503$	−3.13729	−0.139885	−0.0699423	+	0.997551i	$0.522282\pi$
$504$	0	0
$505$	−3.02112	−0.134438
$506$	0	0
$507$	0	0
$508$	45.2153	2.00611
$509$	22.8035	1.01075	0.505374	−	0.862901i	$-0.331355\pi$
$509$	22.8035	1.01075	0.505374	+	0.862901i	$0.331355\pi$
$510$	0	0
$511$	−6.01678	−0.266167
$512$	9.84494	0.435089
$513$	0	0
$514$	−8.51139	−0.375421
$515$	−3.02298	−0.133209
$516$	0	0
$517$	0	0
$518$	−2.79984	−0.123018
$519$	0	0
$520$	−4.41353	−0.193546
$521$	5.26812	0.230801	0.115400	−	0.993319i	$-0.463185\pi$
$521$	5.26812	0.230801	0.115400	+	0.993319i	$0.463185\pi$
$522$	0	0
$523$	−11.8956	−0.520159	−0.260080	−	0.965587i	$-0.583749\pi$
$523$	−11.8956	−0.520159	−0.260080	+	0.965587i	$0.583749\pi$
$524$	24.9985	1.09206
$525$	0	0
$526$	−33.6597	−1.46763
$527$	−59.5808	−2.59538
$528$	0	0
$529$	−2.56510	−0.111526
$530$	4.93436	0.214335
$531$	0	0
$532$	−15.0471	−0.652376
$533$	−16.2409	−0.703471
$534$	0	0
$535$	1.63982	0.0708955
$536$	−33.0637	−1.42813
$537$	0	0
$538$	−2.13744	−0.0921515
$539$	0	0
$540$	0	0
$541$	−40.5807	−1.74470	−0.872350	−	0.488882i	$-0.837405\pi$
$541$	−40.5807	−1.74470	−0.872350	+	0.488882i	$0.837405\pi$
$542$	−6.15836	−0.264524
$543$	0	0
$544$	28.6713	1.22927
$545$	4.58939	0.196588
$546$	0	0
$547$	−23.5343	−1.00625	−0.503127	−	0.864212i	$-0.667817\pi$
$547$	−23.5343	−1.00625	−0.503127	+	0.864212i	$0.667817\pi$
$548$	33.5828	1.43458
$549$	0	0
$550$	0	0
$551$	9.07190	0.386476
$552$	0	0
$553$	4.79732	0.204003
$554$	67.3186	2.86009
$555$	0	0
$556$	32.4513	1.37624
$557$	6.28652	0.266369	0.133184	−	0.991091i	$-0.457480\pi$
$557$	6.28652	0.266369	0.133184	+	0.991091i	$0.457480\pi$
$558$	0	0
$559$	14.9121	0.630716
$560$	−0.394374	−0.0166654
$561$	0	0
$562$	20.3615	0.858896
$563$	16.9664	0.715049	0.357524	−	0.933904i	$-0.383621\pi$
$563$	16.9664	0.715049	0.357524	+	0.933904i	$0.383621\pi$
$564$	0	0
$565$	2.35597	0.0991163
$566$	−54.0731	−2.27286
$567$	0	0
$568$	−9.72131	−0.407897
$569$	−22.2505	−0.932790	−0.466395	−	0.884577i	$-0.654447\pi$
$569$	−22.2505	−0.932790	−0.466395	+	0.884577i	$0.654447\pi$
$570$	0	0
$571$	−35.3152	−1.47789	−0.738947	−	0.673763i	$-0.764677\pi$
$571$	−35.3152	−1.47789	−0.738947	+	0.673763i	$0.764677\pi$
$572$	0	0
$573$	0	0
$574$	−12.7839	−0.533591
$575$	22.1482	0.923643
$576$	0	0
$577$	−38.2361	−1.59179	−0.795894	−	0.605436i	$-0.792999\pi$
$577$	−38.2361	−1.59179	−0.795894	+	0.605436i	$0.792999\pi$
$578$	−51.2153	−2.13028
$579$	0	0
$580$	3.17899	0.132000
$581$	19.1319	0.793724
$582$	0	0
$583$	0	0
$584$	14.0700	0.582219
$585$	0	0
$586$	−48.8517	−2.01805
$587$	−12.3896	−0.511375	−0.255688	−	0.966759i	$-0.582302\pi$
$587$	−12.3896	−0.511375	−0.255688	+	0.966759i	$0.582302\pi$
$588$	0	0
$589$	29.5590	1.21796
$590$	−8.91529	−0.367037
$591$	0	0
$592$	0.743245	0.0305472
$593$	−4.18039	−0.171668	−0.0858340	−	0.996309i	$-0.527355\pi$
$593$	−4.18039	−0.171668	−0.0858340	+	0.996309i	$0.527355\pi$
$594$	0	0
$595$	−2.80796	−0.115115
$596$	14.1334	0.578927
$597$	0	0
$598$	−44.1875	−1.80696
$599$	−44.0788	−1.80101	−0.900505	−	0.434847i	$-0.856803\pi$
$599$	−44.0788	−1.80101	−0.900505	+	0.434847i	$0.856803\pi$
$600$	0	0
$601$	1.75132	0.0714377	0.0357188	−	0.999362i	$-0.488628\pi$
$601$	1.75132	0.0714377	0.0357188	+	0.999362i	$0.488628\pi$
$602$	11.7380	0.478405
$603$	0	0
$604$	60.8670	2.47664
$605$	0	0
$606$	0	0
$607$	10.8691	0.441165	0.220583	−	0.975368i	$-0.429204\pi$
$607$	10.8691	0.441165	0.220583	+	0.975368i	$0.429204\pi$
$608$	−14.2243	−0.576870
$609$	0	0
$610$	−3.41137	−0.138122
$611$	31.2721	1.26513
$612$	0	0
$613$	−17.7933	−0.718665	−0.359333	−	0.933210i	$-0.616996\pi$
$613$	−17.7933	−0.718665	−0.359333	+	0.933210i	$0.616996\pi$
$614$	53.8754	2.17423
$615$	0	0
$616$	0	0
$617$	3.99611	0.160877	0.0804386	−	0.996760i	$-0.474368\pi$
$617$	3.99611	0.160877	0.0804386	+	0.996760i	$0.474368\pi$
$618$	0	0
$619$	−10.9754	−0.441138	−0.220569	−	0.975371i	$-0.570791\pi$
$619$	−10.9754	−0.441138	−0.220569	+	0.975371i	$0.570791\pi$
$620$	10.3581	0.415992
$621$	0	0
$622$	−47.5462	−1.90643
$623$	3.82632	0.153298
$624$	0	0
$625$	23.5026	0.940103
$626$	79.2777	3.16857
$627$	0	0
$628$	−6.90760	−0.275643
$629$	5.29194	0.211003
$630$	0	0
$631$	8.64921	0.344319	0.172160	−	0.985069i	$-0.444925\pi$
$631$	8.64921	0.344319	0.172160	+	0.985069i	$0.444925\pi$
$632$	−11.2183	−0.446241
$633$	0	0
$634$	63.8622	2.53629
$635$	−4.18607	−0.166119
$636$	0	0
$637$	20.9343	0.829448
$638$	0	0
$639$	0	0
$640$	−6.27953	−0.248220
$641$	37.0876	1.46487	0.732436	−	0.680836i	$-0.238383\pi$
$641$	37.0876	1.46487	0.732436	+	0.680836i	$0.238383\pi$
$642$	0	0
$643$	−40.7326	−1.60634	−0.803168	−	0.595752i	$-0.796854\pi$
$643$	−40.7326	−1.60634	−0.803168	+	0.595752i	$0.796854\pi$
$644$	−21.9573	−0.865239
$645$	0	0
$646$	45.0515	1.77253
$647$	−0.568944	−0.0223675	−0.0111837	−	0.999937i	$-0.503560\pi$
$647$	−0.568944	−0.0223675	−0.0111837	+	0.999937i	$0.503560\pi$
$648$	0	0
$649$	0	0
$650$	−47.8921	−1.87848
$651$	0	0
$652$	−5.41175	−0.211941
$653$	−36.5276	−1.42944	−0.714718	−	0.699413i	$-0.753445\pi$
$653$	−36.5276	−1.42944	−0.714718	+	0.699413i	$0.753445\pi$
$654$	0	0
$655$	−2.31438	−0.0904304
$656$	3.39361	0.132498
$657$	0	0
$658$	24.6157	0.959618
$659$	24.0070	0.935179	0.467590	−	0.883946i	$-0.345123\pi$
$659$	24.0070	0.935179	0.467590	+	0.883946i	$0.345123\pi$
$660$	0	0
$661$	12.9833	0.504992	0.252496	−	0.967598i	$-0.418749\pi$
$661$	12.9833	0.504992	0.252496	+	0.967598i	$0.418749\pi$
$662$	41.8578	1.62685
$663$	0	0
$664$	−44.7391	−1.73621
$665$	1.39308	0.0540212
$666$	0	0
$667$	13.2380	0.512579
$668$	−52.4651	−2.02994
$669$	0	0
$670$	7.35956	0.284325
$671$	0	0
$672$	0	0
$673$	−17.0257	−0.656291	−0.328145	−	0.944627i	$-0.606424\pi$
$673$	−17.0257	−0.656291	−0.328145	+	0.944627i	$0.606424\pi$
$674$	25.5541	0.984309
$675$	0	0
$676$	15.8033	0.607820
$677$	35.4316	1.36175	0.680874	−	0.732400i	$-0.261600\pi$
$677$	35.4316	1.36175	0.680874	+	0.732400i	$0.261600\pi$
$678$	0	0
$679$	−7.45764	−0.286198
$680$	6.56630	0.251806
$681$	0	0
$682$	0	0
$683$	23.8967	0.914381	0.457191	−	0.889369i	$-0.348856\pi$
$683$	23.8967	0.914381	0.457191	+	0.889369i	$0.348856\pi$
$684$	0	0
$685$	−3.10912	−0.118793
$686$	39.6040	1.51209
$687$	0	0
$688$	−3.11596	−0.118795
$689$	−28.0490	−1.06858
$690$	0	0
$691$	−0.592615	−0.0225441	−0.0112721	−	0.999936i	$-0.503588\pi$
$691$	−0.592615	−0.0225441	−0.0112721	+	0.999936i	$0.503588\pi$
$692$	3.37645	0.128353
$693$	0	0
$694$	51.4682	1.95371
$695$	−3.00436	−0.113962
$696$	0	0
$697$	24.1627	0.915227
$698$	−42.8623	−1.62236
$699$	0	0
$700$	−23.7982	−0.899488
$701$	25.4261	0.960329	0.480164	−	0.877179i	$-0.340577\pi$
$701$	25.4261	0.960329	0.480164	+	0.877179i	$0.340577\pi$
$702$	0	0
$703$	−2.62542	−0.0990194
$704$	0	0
$705$	0	0
$706$	−77.0219	−2.89876
$707$	13.5179	0.508392
$708$	0	0
$709$	15.1047	0.567268	0.283634	−	0.958933i	$-0.408460\pi$
$709$	15.1047	0.567268	0.283634	+	0.958933i	$0.408460\pi$
$710$	2.16384	0.0812074
$711$	0	0
$712$	−8.94768	−0.335328
$713$	43.1335	1.61536
$714$	0	0
$715$	0	0
$716$	−38.4399	−1.43657
$717$	0	0
$718$	6.98384	0.260635
$719$	12.0428	0.449120	0.224560	−	0.974460i	$-0.427906\pi$
$719$	12.0428	0.449120	0.224560	+	0.974460i	$0.427906\pi$
$720$	0	0
$721$	13.5262	0.503743
$722$	21.9003	0.815044
$723$	0	0
$724$	61.3818	2.28124
$725$	14.3479	0.532868
$726$	0	0
$727$	49.5932	1.83931	0.919654	−	0.392729i	$-0.128469\pi$
$727$	49.5932	1.83931	0.919654	+	0.392729i	$0.128469\pi$
$728$	19.7481	0.731915
$729$	0	0
$730$	−3.13179	−0.115913
$731$	−22.1858	−0.820572
$732$	0	0
$733$	32.2654	1.19175	0.595875	−	0.803078i	$-0.296806\pi$
$733$	32.2654	1.19175	0.595875	+	0.803078i	$0.296806\pi$
$734$	−3.87187	−0.142913
$735$	0	0
$736$	−20.7566	−0.765097
$737$	0	0
$738$	0	0
$739$	3.13253	0.115232	0.0576160	−	0.998339i	$-0.481650\pi$
$739$	3.13253	0.115232	0.0576160	+	0.998339i	$0.481650\pi$
$740$	−0.920002	−0.0338200
$741$	0	0
$742$	−22.0786	−0.810530
$743$	−7.78877	−0.285742	−0.142871	−	0.989741i	$-0.545633\pi$
$743$	−7.78877	−0.285742	−0.142871	+	0.989741i	$0.545633\pi$
$744$	0	0
$745$	−1.30848	−0.0479391
$746$	−50.0938	−1.83406
$747$	0	0
$748$	0	0
$749$	−7.33730	−0.268099
$750$	0	0
$751$	49.6890	1.81318	0.906589	−	0.422015i	$-0.138677\pi$
$751$	49.6890	1.81318	0.906589	+	0.422015i	$0.138677\pi$
$752$	−6.53446	−0.238287
$753$	0	0
$754$	−28.6253	−1.04247
$755$	−5.63511	−0.205083
$756$	0	0
$757$	−27.0307	−0.982449	−0.491225	−	0.871033i	$-0.663451\pi$
$757$	−27.0307	−0.982449	−0.491225	+	0.871033i	$0.663451\pi$
$758$	−28.9247	−1.05059
$759$	0	0
$760$	−3.25765	−0.118167
$761$	−44.5105	−1.61351	−0.806753	−	0.590889i	$-0.798777\pi$
$761$	−44.5105	−1.61351	−0.806753	+	0.590889i	$0.798777\pi$
$762$	0	0
$763$	−20.5350	−0.743419
$764$	44.1315	1.59662
$765$	0	0
$766$	−1.86245	−0.0672930
$767$	50.6783	1.82989
$768$	0	0
$769$	3.31905	0.119688	0.0598440	−	0.998208i	$-0.480940\pi$
$769$	3.31905	0.119688	0.0598440	+	0.998208i	$0.480940\pi$
$770$	0	0
$771$	0	0
$772$	79.2749	2.85317
$773$	28.4878	1.02463	0.512317	−	0.858797i	$-0.328787\pi$
$773$	28.4878	1.02463	0.512317	+	0.858797i	$0.328787\pi$
$774$	0	0
$775$	46.7498	1.67930
$776$	17.4394	0.626037
$777$	0	0
$778$	4.04474	0.145011
$779$	−11.9875	−0.429496
$780$	0	0
$781$	0	0
$782$	65.7407	2.35088
$783$	0	0
$784$	−4.37433	−0.156226
$785$	0.639511	0.0228251
$786$	0	0
$787$	−13.0487	−0.465136	−0.232568	−	0.972580i	$-0.574713\pi$
$787$	−13.0487	−0.465136	−0.232568	+	0.972580i	$0.574713\pi$
$788$	−3.69018	−0.131457
$789$	0	0
$790$	2.49706	0.0888413
$791$	−10.5417	−0.374819
$792$	0	0
$793$	19.3917	0.688618
$794$	57.6660	2.04649
$795$	0	0
$796$	56.2629	1.99418
$797$	50.1733	1.77723	0.888616	−	0.458653i	$-0.151668\pi$
$797$	50.1733	1.77723	0.888616	+	0.458653i	$0.151668\pi$
$798$	0	0
$799$	−46.5257	−1.64596
$800$	−22.4968	−0.795382
$801$	0	0
$802$	−50.8941	−1.79713
$803$	0	0
$804$	0	0
$805$	2.03282	0.0716477
$806$	−93.2698	−3.28529
$807$	0	0
$808$	−31.6110	−1.11207
$809$	35.1505	1.23583	0.617914	−	0.786246i	$-0.287978\pi$
$809$	35.1505	1.23583	0.617914	+	0.786246i	$0.287978\pi$
$810$	0	0
$811$	−22.1055	−0.776228	−0.388114	−	0.921611i	$-0.626873\pi$
$811$	−22.1055	−0.776228	−0.388114	+	0.921611i	$0.626873\pi$
$812$	−14.2243	−0.499174
$813$	0	0
$814$	0	0
$815$	0.501025	0.0175501
$816$	0	0
$817$	11.0067	0.385077
$818$	18.7130	0.654285
$819$	0	0
$820$	−4.20068	−0.146694
$821$	−2.53720	−0.0885488	−0.0442744	−	0.999019i	$-0.514098\pi$
$821$	−2.53720	−0.0885488	−0.0442744	+	0.999019i	$0.514098\pi$
$822$	0	0
$823$	−10.3727	−0.361569	−0.180785	−	0.983523i	$-0.557864\pi$
$823$	−10.3727	−0.361569	−0.180785	+	0.983523i	$0.557864\pi$
$824$	−31.6305	−1.10190
$825$	0	0
$826$	39.8911	1.38799
$827$	−52.7236	−1.83338	−0.916690	−	0.399599i	$-0.869149\pi$
$827$	−52.7236	−1.83338	−0.916690	+	0.399599i	$0.869149\pi$
$828$	0	0
$829$	37.8438	1.31437	0.657184	−	0.753730i	$-0.271747\pi$
$829$	37.8438	1.31437	0.657184	+	0.753730i	$0.271747\pi$
$830$	9.95834	0.345659
$831$	0	0
$832$	52.2445	1.81125
$833$	−31.1454	−1.07912
$834$	0	0
$835$	4.85726	0.168092
$836$	0	0
$837$	0	0
$838$	13.0350	0.450286
$839$	−20.1156	−0.694466	−0.347233	−	0.937779i	$-0.612879\pi$
$839$	−20.1156	−0.694466	−0.347233	+	0.937779i	$0.612879\pi$
$840$	0	0
$841$	−20.4242	−0.704283
$842$	−88.1629	−3.03830
$843$	0	0
$844$	51.1918	1.76209
$845$	−1.46308	−0.0503316
$846$	0	0
$847$	0	0
$848$	5.86097	0.201266
$849$	0	0
$850$	71.2524	2.44394
$851$	−3.83110	−0.131328
$852$	0	0
$853$	−9.12019	−0.312269	−0.156135	−	0.987736i	$-0.549903\pi$
$853$	−9.12019	−0.312269	−0.156135	+	0.987736i	$0.549903\pi$
$854$	15.2640	0.522324
$855$	0	0
$856$	17.1579	0.586446
$857$	1.84536	0.0630362	0.0315181	−	0.999503i	$-0.489966\pi$
$857$	1.84536	0.0630362	0.0315181	+	0.999503i	$0.489966\pi$
$858$	0	0
$859$	28.5111	0.972785	0.486392	−	0.873741i	$-0.338313\pi$
$859$	28.5111	0.972785	0.486392	+	0.873741i	$0.338313\pi$
$860$	3.85700	0.131523
$861$	0	0
$862$	−69.3680	−2.36268
$863$	−10.6994	−0.364210	−0.182105	−	0.983279i	$-0.558291\pi$
$863$	−10.6994	−0.364210	−0.182105	+	0.983279i	$0.558291\pi$
$864$	0	0
$865$	−0.312594	−0.0106285
$866$	0.650424	0.0221023
$867$	0	0
$868$	−46.3470	−1.57312
$869$	0	0
$870$	0	0
$871$	−41.8348	−1.41752
$872$	48.0203	1.62617
$873$	0	0
$874$	−32.6150	−1.10322
$875$	4.45171	0.150495
$876$	0	0
$877$	−40.8322	−1.37881	−0.689404	−	0.724377i	$-0.742127\pi$
$877$	−40.8322	−1.37881	−0.689404	+	0.724377i	$0.742127\pi$
$878$	34.9270	1.17873
$879$	0	0
$880$	0	0
$881$	21.0458	0.709050	0.354525	−	0.935047i	$-0.384643\pi$
$881$	21.0458	0.709050	0.354525	+	0.935047i	$0.384643\pi$
$882$	0	0
$883$	12.7282	0.428338	0.214169	−	0.976797i	$-0.431296\pi$
$883$	12.7282	0.428338	0.214169	+	0.976797i	$0.431296\pi$
$884$	−89.7401	−3.01828
$885$	0	0
$886$	−33.7701	−1.13453
$887$	−10.7250	−0.360110	−0.180055	−	0.983657i	$-0.557628\pi$
$887$	−10.7250	−0.360110	−0.180055	+	0.983657i	$0.557628\pi$
$888$	0	0
$889$	18.7304	0.628198
$890$	1.99164	0.0667599
$891$	0	0
$892$	6.59606	0.220852
$893$	23.0821	0.772414
$894$	0	0
$895$	3.55880	0.118958
$896$	28.0975	0.938671
$897$	0	0
$898$	49.4254	1.64935
$899$	27.9425	0.931935
$900$	0	0
$901$	41.7304	1.39024
$902$	0	0
$903$	0	0
$904$	24.6513	0.819889
$905$	−5.68278	−0.188902
$906$	0	0
$907$	−13.2456	−0.439812	−0.219906	−	0.975521i	$-0.570575\pi$
$907$	−13.2456	−0.439812	−0.219906	+	0.975521i	$0.570575\pi$
$908$	54.8260	1.81946
$909$	0	0
$910$	−4.39568	−0.145715
$911$	−57.1245	−1.89262	−0.946309	−	0.323264i	$-0.895220\pi$
$911$	−57.1245	−1.89262	−0.946309	+	0.323264i	$0.895220\pi$
$912$	0	0
$913$	0	0
$914$	−7.47494	−0.247249
$915$	0	0
$916$	−1.79063	−0.0591640
$917$	10.3556	0.341972
$918$	0	0
$919$	−16.5780	−0.546856	−0.273428	−	0.961892i	$-0.588158\pi$
$919$	−16.5780	−0.546856	−0.273428	+	0.961892i	$0.588158\pi$
$920$	−4.75367	−0.156724
$921$	0	0
$922$	61.3123	2.01921
$923$	−12.3002	−0.404865
$924$	0	0
$925$	−4.15230	−0.136527
$926$	−8.45018	−0.277690
$927$	0	0
$928$	−13.4464	−0.441400
$929$	−7.36379	−0.241598	−0.120799	−	0.992677i	$-0.538546\pi$
$929$	−7.36379	−0.241598	−0.120799	+	0.992677i	$0.538546\pi$
$930$	0	0
$931$	15.4517	0.506410
$932$	35.1072	1.14997
$933$	0	0
$934$	43.0753	1.40947
$935$	0	0
$936$	0	0
$937$	−47.2573	−1.54383	−0.771914	−	0.635727i	$-0.780701\pi$
$937$	−47.2573	−1.54383	−0.771914	+	0.635727i	$0.780701\pi$
$938$	−32.9300	−1.07520
$939$	0	0
$940$	8.08847	0.263817
$941$	56.1287	1.82974	0.914872	−	0.403744i	$-0.132291\pi$
$941$	56.1287	1.82974	0.914872	+	0.403744i	$0.132291\pi$
$942$	0	0
$943$	−17.4926	−0.569636
$944$	−10.5895	−0.344658
$945$	0	0
$946$	0	0
$947$	−12.7865	−0.415504	−0.207752	−	0.978182i	$-0.566615\pi$
$947$	−12.7865	−0.415504	−0.207752	+	0.978182i	$0.566615\pi$
$948$	0	0
$949$	17.8024	0.577892
$950$	−35.3495	−1.14689
$951$	0	0
$952$	−29.3806	−0.952232
$953$	23.2974	0.754677	0.377338	−	0.926075i	$-0.376839\pi$
$953$	23.2974	0.754677	0.377338	+	0.926075i	$0.376839\pi$
$954$	0	0
$955$	−4.08573	−0.132211
$956$	33.0133	1.06773
$957$	0	0
$958$	−0.365649	−0.0118136
$959$	13.9116	0.449230
$960$	0	0
$961$	60.0452	1.93694
$962$	8.28418	0.267093
$963$	0	0
$964$	0.954445	0.0307406
$965$	−7.33934	−0.236262
$966$	0	0
$967$	55.5173	1.78531	0.892657	−	0.450736i	$-0.148838\pi$
$967$	55.5173	1.78531	0.892657	+	0.450736i	$0.148838\pi$
$968$	0	0
$969$	0	0
$970$	−3.88178	−0.124636
$971$	−4.52027	−0.145063	−0.0725313	−	0.997366i	$-0.523108\pi$
$971$	−4.52027	−0.145063	−0.0725313	+	0.997366i	$0.523108\pi$
$972$	0	0
$973$	13.4429	0.430960
$974$	−41.7509	−1.33778
$975$	0	0
$976$	−4.05198	−0.129701
$977$	−27.0393	−0.865063	−0.432532	−	0.901619i	$-0.642380\pi$
$977$	−27.0393	−0.865063	−0.432532	+	0.901619i	$0.642380\pi$
$978$	0	0
$979$	0	0
$980$	5.41462	0.172964
$981$	0	0
$982$	−15.4831	−0.494087
$983$	10.6376	0.339287	0.169643	−	0.985506i	$-0.445738\pi$
$983$	10.6376	0.339287	0.169643	+	0.985506i	$0.445738\pi$
$984$	0	0
$985$	0.341640	0.0108855
$986$	42.5878	1.35627
$987$	0	0
$988$	44.5215	1.41642
$989$	16.0614	0.510723
$990$	0	0
$991$	−18.7938	−0.597005	−0.298502	−	0.954409i	$-0.596487\pi$
$991$	−18.7938	−0.597005	−0.298502	+	0.954409i	$0.596487\pi$
$992$	−43.8124	−1.39105
$993$	0	0
$994$	−9.68201	−0.307095
$995$	−5.20886	−0.165132
$996$	0	0
$997$	26.1274	0.827464	0.413732	−	0.910399i	$-0.364225\pi$
$997$	26.1274	0.827464	0.413732	+	0.910399i	$0.364225\pi$
$998$	−79.0634	−2.50271
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9801.2.a.co.1.1		18
3.2	odd	2		9801.2.a.cn.1.18		18
9.4	even	3		1089.2.e.o.727.18		36
9.7	even	3		1089.2.e.o.364.18		36
11.7	odd	10		891.2.f.f.82.9		36
11.8	odd	10		891.2.f.f.163.9		36
11.10	odd	2		9801.2.a.cm.1.18		18
33.8	even	10		891.2.f.e.163.1		36
33.29	even	10		891.2.f.e.82.1		36
33.32	even	2		9801.2.a.cp.1.1		18
99.7	odd	30		99.2.m.b.49.9	yes	72
99.29	even	30		297.2.n.b.280.1		72
99.40	odd	30		99.2.m.b.16.1	✓	72
99.41	even	30		297.2.n.b.262.1		72
99.43	odd	6		1089.2.e.p.364.1		36
99.52	odd	30		99.2.m.b.31.1	yes	72
99.74	even	30		297.2.n.b.64.9		72
99.76	odd	6		1089.2.e.p.727.1		36
99.85	odd	30		99.2.m.b.97.9	yes	72
99.95	even	30		297.2.n.b.181.9		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.m.b.16.1	✓	72	99.40	odd	30
99.2.m.b.31.1	yes	72	99.52	odd	30
99.2.m.b.49.9	yes	72	99.7	odd	30
99.2.m.b.97.9	yes	72	99.85	odd	30
297.2.n.b.64.9		72	99.74	even	30
297.2.n.b.181.9		72	99.95	even	30
297.2.n.b.262.1		72	99.41	even	30
297.2.n.b.280.1		72	99.29	even	30
891.2.f.e.82.1		36	33.29	even	10
891.2.f.e.163.1		36	33.8	even	10
891.2.f.f.82.9		36	11.7	odd	10
891.2.f.f.163.9		36	11.8	odd	10
1089.2.e.o.364.18		36	9.7	even	3
1089.2.e.o.727.18		36	9.4	even	3
1089.2.e.p.364.1		36	99.43	odd	6
1089.2.e.p.727.1		36	99.76	odd	6
9801.2.a.cm.1.18		18	11.10	odd	2
9801.2.a.cn.1.18		18	3.2	odd	2
9801.2.a.co.1.1		18	1.1	even	1	trivial
9801.2.a.cp.1.1		18	33.32	even	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:	\( N \)	\(=\)	\( 9801 = 3^{4} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9801.a (trivial)

\(f(q)\)	\(=\)	\(q-2.32900 q^{2} +3.42425 q^{4} -0.317020 q^{5} +1.41849 q^{7} -3.31708 q^{8} +0.738340 q^{10} -4.19704 q^{13} -3.30367 q^{14} +0.876991 q^{16} +6.24422 q^{17} -3.09786 q^{19} -1.08556 q^{20} -4.52050 q^{23} -4.89950 q^{25} +9.77491 q^{26} +4.85727 q^{28} -2.92845 q^{29} -9.54176 q^{31} +4.59165 q^{32} -14.5428 q^{34} -0.449690 q^{35} +0.847494 q^{37} +7.21491 q^{38} +1.05158 q^{40} +3.86961 q^{41} -3.55302 q^{43} +10.5282 q^{46} -7.45100 q^{47} -4.98788 q^{49} +11.4109 q^{50} -14.3717 q^{52} +6.68304 q^{53} -4.70526 q^{56} +6.82035 q^{58} -12.0748 q^{59} -4.62032 q^{61} +22.2228 q^{62} -12.4479 q^{64} +1.33054 q^{65} +9.96771 q^{67} +21.3818 q^{68} +1.04733 q^{70} +2.93068 q^{71} -4.24167 q^{73} -1.97382 q^{74} -10.6078 q^{76} +3.38199 q^{79} -0.278024 q^{80} -9.01233 q^{82} +13.4875 q^{83} -1.97954 q^{85} +8.27498 q^{86} +2.69745 q^{89} -5.95347 q^{91} -15.4793 q^{92} +17.3534 q^{94} +0.982082 q^{95} -5.25744 q^{97} +11.6168 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 2 q^{2} + 12 q^{4} - q^{5} - q^{7} + 6 q^{8} + 2 q^{10} - 3 q^{13} - 8 q^{16} + 20 q^{17} + 3 q^{19} - 5 q^{20} - 10 q^{23} + 7 q^{25} + 2 q^{26} - 19 q^{28} + 21 q^{29} + 6 q^{31} + 9 q^{32} - 4 q^{34}+ \cdots + 82 q^{98}+O(q^{100}) \) 18 * q + 2 * q^2 + 12 * q^4 - q^5 - q^7 + 6 * q^8 + 2 * q^10 - 3 * q^13 - 8 * q^16 + 20 * q^17 + 3 * q^19 - 5 * q^20 - 10 * q^23 + 7 * q^25 + 2 * q^26 - 19 * q^28 + 21 * q^29 + 6 * q^31 + 9 * q^32 - 4 * q^34 + 38 * q^35 + 7 * q^37 + 13 * q^38 + 20 * q^41 - 4 * q^43 - 8 * q^46 + 7 * q^47 + 7 * q^49 + 25 * q^50 + 19 * q^52 + 31 * q^53 - 57 * q^56 + 12 * q^58 - 12 * q^59 + 16 * q^61 + 19 * q^62 - 16 * q^64 + 42 * q^65 - 5 * q^67 + 51 * q^68 + 8 * q^70 + 13 * q^71 + 9 * q^74 + 8 * q^76 + 2 * q^79 + 46 * q^80 - 34 * q^82 + 36 * q^83 - 25 * q^85 + 26 * q^86 - 14 * q^89 - 15 * q^91 - 15 * q^92 - 4 * q^94 + 64 * q^95 - 16 * q^97 + 82 * q^98

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