LMFDB - Embedded newform 209.2.a.c.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [209,2,Mod(1,209)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(209, 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("209.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 209 = 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	209.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:	$1.66887340224$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	5.5.246832.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 2x^{4} - 5x^{3} + 6x^{2} + 7x - 2 $ x^5 - 2x^4 - 5x^3 + 6x^2 + 7x - 2
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$2.71457$ of defining polynomial
Character	$\chi$	$=$	209.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.65432 q^{2} +0.121872 q^{3} +5.04540 q^{4} -1.06025 q^{5} +0.323487 q^{6} -3.36889 q^{7} +8.08346 q^{8} -2.98515 q^{9} -2.81425 q^{10} +1.00000 q^{11} +0.614893 q^{12} -2.15993 q^{13} -8.94209 q^{14} -0.129215 q^{15} +11.3653 q^{16} +3.67288 q^{17} -7.92353 q^{18} -1.00000 q^{19} -5.34940 q^{20} -0.410573 q^{21} +2.65432 q^{22} +3.15468 q^{23} +0.985147 q^{24} -3.87587 q^{25} -5.73313 q^{26} -0.729422 q^{27} -16.9974 q^{28} +7.17849 q^{29} -0.342978 q^{30} +4.65295 q^{31} +14.0001 q^{32} +0.121872 q^{33} +9.74900 q^{34} +3.57187 q^{35} -15.0613 q^{36} +2.27446 q^{37} -2.65432 q^{38} -0.263235 q^{39} -8.57050 q^{40} -11.3852 q^{41} -1.08979 q^{42} +9.38838 q^{43} +5.04540 q^{44} +3.16501 q^{45} +8.37352 q^{46} -5.77094 q^{47} +1.38511 q^{48} +4.34940 q^{49} -10.2878 q^{50} +0.447622 q^{51} -10.8977 q^{52} -5.65820 q^{53} -1.93612 q^{54} -1.06025 q^{55} -27.2322 q^{56} -0.121872 q^{57} +19.0540 q^{58} -13.7944 q^{59} -0.651942 q^{60} +6.98152 q^{61} +12.3504 q^{62} +10.0566 q^{63} +14.4301 q^{64} +2.29007 q^{65} +0.323487 q^{66} -4.81332 q^{67} +18.5312 q^{68} +0.384467 q^{69} +9.48087 q^{70} +15.2629 q^{71} -24.1303 q^{72} -8.08806 q^{73} +6.03713 q^{74} -0.472360 q^{75} -5.04540 q^{76} -3.36889 q^{77} -0.698709 q^{78} +13.4291 q^{79} -12.0500 q^{80} +8.86655 q^{81} -30.2199 q^{82} +9.96666 q^{83} -2.07150 q^{84} -3.89418 q^{85} +24.9197 q^{86} +0.874858 q^{87} +8.08346 q^{88} -4.61626 q^{89} +8.40094 q^{90} +7.27655 q^{91} +15.9166 q^{92} +0.567064 q^{93} -15.3179 q^{94} +1.06025 q^{95} +1.70622 q^{96} -4.09907 q^{97} +11.5447 q^{98} -2.98515 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 2 q^{2} + q^{3} + 6 q^{4} - 5 q^{5} - 2 q^{6} + 6 q^{7} + 6 q^{8} + 4 q^{9} + 12 q^{10} + 5 q^{11} + 6 q^{12} + 4 q^{13} - 14 q^{14} + 3 q^{15} + 8 q^{16} - 4 q^{17} - 20 q^{18} - 5 q^{19} - 8 q^{20}+ \cdots + 4 q^{99}+O(q^{100}) $ 5 * q + 2 * q^2 + q^3 + 6 * q^4 - 5 * q^5 - 2 * q^6 + 6 * q^7 + 6 * q^8 + 4 * q^9 + 12 * q^10 + 5 * q^11 + 6 * q^12 + 4 * q^13 - 14 * q^14 + 3 * q^15 + 8 * q^16 - 4 * q^17 - 20 * q^18 - 5 * q^19 - 8 * q^20 + 10 * q^21 + 2 * q^22 + 3 * q^23 - 14 * q^24 + 6 * q^25 - 6 * q^26 - 11 * q^27 - 10 * q^28 + 10 * q^29 + 6 * q^30 + 11 * q^31 + 14 * q^32 + q^33 - 4 * q^34 - 8 * q^35 - 26 * q^36 + q^37 - 2 * q^38 + 2 * q^39 - 16 * q^40 + 2 * q^41 - 16 * q^42 + 20 * q^43 + 6 * q^44 - 28 * q^45 - 4 * q^46 - 20 * q^47 + 4 * q^48 + 3 * q^49 - 32 * q^50 + 24 * q^51 + 6 * q^52 - 14 * q^53 + 16 * q^54 - 5 * q^55 - 38 * q^56 - q^57 - 6 * q^58 + 3 * q^59 - 40 * q^60 - 10 * q^61 - 6 * q^62 + 24 * q^63 - 2 * q^66 + 9 * q^67 + 24 * q^68 - 5 * q^69 + 50 * q^70 + 23 * q^71 - 12 * q^72 + 8 * q^74 - 18 * q^75 - 6 * q^76 + 6 * q^77 - 22 * q^78 + 44 * q^79 - 18 * q^80 + q^81 - 30 * q^82 - 14 * q^83 + 14 * q^84 - 12 * q^85 + 52 * q^86 + 28 * q^87 + 6 * q^88 - 27 * q^89 + 26 * q^90 + 24 * q^91 + 58 * q^92 - 27 * q^93 - 8 * q^94 + 5 * q^95 + 50 * q^96 + 15 * q^97 - 10 * q^98 + 4 * q^99

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 $

$2$	2.65432	1.87689	0.938443	−	0.345435i	$-0.112268\pi$
$2$	2.65432	1.87689	0.938443	+	0.345435i	$0.112268\pi$
$3$	0.121872	0.0703629	0.0351814	−	0.999381i	$-0.488799\pi$
$3$	0.121872	0.0703629	0.0351814	+	0.999381i	$0.488799\pi$
$4$	5.04540	2.52270
$5$	−1.06025	−0.474159	−0.237080	−	0.971490i	$-0.576190\pi$
$5$	−1.06025	−0.474159	−0.237080	+	0.971490i	$0.576190\pi$
$6$	0.323487	0.132063
$7$	−3.36889	−1.27332	−0.636660	−	0.771145i	$-0.719684\pi$
$7$	−3.36889	−1.27332	−0.636660	+	0.771145i	$0.719684\pi$
$8$	8.08346	2.85793
$9$	−2.98515	−0.995049
$10$	−2.81425	−0.889943
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	0.614893	0.177504
$13$	−2.15993	−0.599056	−0.299528	−	0.954087i	$-0.596829\pi$
$13$	−2.15993	−0.599056	−0.299528	+	0.954087i	$0.596829\pi$
$14$	−8.94209	−2.38987
$15$	−0.129215	−0.0333632
$16$	11.3653	2.84131
$17$	3.67288	0.890805	0.445402	−	0.895330i	$-0.353061\pi$
$17$	3.67288	0.890805	0.445402	+	0.895330i	$0.353061\pi$
$18$	−7.92353	−1.86759
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	−5.34940	−1.19616
$21$	−0.410573	−0.0895944
$22$	2.65432	0.565902
$23$	3.15468	0.657797	0.328898	−	0.944365i	$-0.393323\pi$
$23$	3.15468	0.657797	0.328898	+	0.944365i	$0.393323\pi$
$24$	0.985147	0.201092
$25$	−3.87587	−0.775173
$26$	−5.73313	−1.12436
$27$	−0.729422	−0.140377
$28$	−16.9974	−3.21220
$29$	7.17849	1.33301	0.666506	−	0.745499i	$-0.267789\pi$
$29$	7.17849	1.33301	0.666506	+	0.745499i	$0.267789\pi$
$30$	−0.342978	−0.0626189
$31$	4.65295	0.835694	0.417847	−	0.908517i	$-0.362785\pi$
$31$	4.65295	0.835694	0.417847	+	0.908517i	$0.362785\pi$
$32$	14.0001	2.47489
$33$	0.121872	0.0212152
$34$	9.74900	1.67194
$35$	3.57187	0.603756
$36$	−15.0613	−2.51021
$37$	2.27446	0.373918	0.186959	−	0.982368i	$-0.440137\pi$
$37$	2.27446	0.373918	0.186959	+	0.982368i	$0.440137\pi$
$38$	−2.65432	−0.430587
$39$	−0.263235	−0.0421513
$40$	−8.57050	−1.35512
$41$	−11.3852	−1.77807	−0.889034	−	0.457841i	$-0.848623\pi$
$41$	−11.3852	−1.77807	−0.889034	+	0.457841i	$0.848623\pi$
$42$	−1.08979	−0.168158
$43$	9.38838	1.43171	0.715857	−	0.698247i	$-0.246036\pi$
$43$	9.38838	1.43171	0.715857	+	0.698247i	$0.246036\pi$
$44$	5.04540	0.760623
$45$	3.16501	0.471812
$46$	8.37352	1.23461
$47$	−5.77094	−0.841778	−0.420889	−	0.907112i	$-0.638282\pi$
$47$	−5.77094	−0.841778	−0.420889	+	0.907112i	$0.638282\pi$
$48$	1.38511	0.199923
$49$	4.34940	0.621342
$50$	−10.2878	−1.45491
$51$	0.447622	0.0626796
$52$	−10.8977	−1.51124
$53$	−5.65820	−0.777213	−0.388607	−	0.921404i	$-0.627043\pi$
$53$	−5.65820	−0.777213	−0.388607	+	0.921404i	$0.627043\pi$
$54$	−1.93612	−0.263472
$55$	−1.06025	−0.142964
$56$	−27.2322	−3.63906
$57$	−0.121872	−0.0161423
$58$	19.0540	2.50191
$59$	−13.7944	−1.79588	−0.897939	−	0.440121i	$-0.854936\pi$
$59$	−13.7944	−1.79588	−0.897939	+	0.440121i	$0.854936\pi$
$60$	−0.651942	−0.0841653
$61$	6.98152	0.893892	0.446946	−	0.894561i	$-0.352512\pi$
$61$	6.98152	0.893892	0.446946	+	0.894561i	$0.352512\pi$
$62$	12.3504	1.56850
$63$	10.0566	1.26702
$64$	14.4301	1.80377
$65$	2.29007	0.284048
$66$	0.323487	0.0398185
$67$	−4.81332	−0.588041	−0.294020	−	0.955799i	$-0.594993\pi$
$67$	−4.81332	−0.588041	−0.294020	+	0.955799i	$0.594993\pi$
$68$	18.5312	2.24723
$69$	0.384467	0.0462844
$70$	9.48087	1.13318
$71$	15.2629	1.81137	0.905685	−	0.423951i	$-0.139357\pi$
$71$	15.2629	1.81137	0.905685	+	0.423951i	$0.139357\pi$
$72$	−24.1303	−2.84378
$73$	−8.08806	−0.946636	−0.473318	−	0.880892i	$-0.656944\pi$
$73$	−8.08806	−0.946636	−0.473318	+	0.880892i	$0.656944\pi$
$74$	6.03713	0.701802
$75$	−0.472360	−0.0545434
$76$	−5.04540	−0.578747
$77$	−3.36889	−0.383920
$78$	−0.698709	−0.0791132
$79$	13.4291	1.51090	0.755448	−	0.655209i	$-0.227419\pi$
$79$	13.4291	1.51090	0.755448	+	0.655209i	$0.227419\pi$
$80$	−12.0500	−1.34724
$81$	8.86655	0.985172
$82$	−30.2199	−3.33723
$83$	9.96666	1.09398	0.546992	−	0.837138i	$-0.315773\pi$
$83$	9.96666	1.09398	0.546992	+	0.837138i	$0.315773\pi$
$84$	−2.07150	−0.226020
$85$	−3.89418	−0.422383
$86$	24.9197	2.68716
$87$	0.874858	0.0937946
$88$	8.08346	0.861699
$89$	−4.61626	−0.489323	−0.244661	−	0.969609i	$-0.578677\pi$
$89$	−4.61626	−0.489323	−0.244661	+	0.969609i	$0.578677\pi$
$90$	8.40094	0.885537
$91$	7.27655	0.762790
$92$	15.9166	1.65942
$93$	0.567064	0.0588018
$94$	−15.3179	−1.57992
$95$	1.06025	0.108780
$96$	1.70622	0.174140
$97$	−4.09907	−0.416197	−0.208099	−	0.978108i	$-0.566727\pi$
$97$	−4.09907	−0.416197	−0.208099	+	0.978108i	$0.566727\pi$
$98$	11.5447	1.16619
$99$	−2.98515	−0.300019
$100$	−19.5553	−1.95553
$101$	−10.8730	−1.08190	−0.540950	−	0.841055i	$-0.681935\pi$
$101$	−10.8730	−1.08190	−0.540950	+	0.841055i	$0.681935\pi$
$102$	1.18813	0.117642
$103$	8.85864	0.872867	0.436434	−	0.899736i	$-0.356241\pi$
$103$	8.85864	0.872867	0.436434	+	0.899736i	$0.356241\pi$
$104$	−17.4597	−1.71206
$105$	0.435311	0.0424820
$106$	−15.0186	−1.45874
$107$	−18.1669	−1.75626	−0.878131	−	0.478421i	$-0.841209\pi$
$107$	−18.1669	−1.75626	−0.878131	+	0.478421i	$0.841209\pi$
$108$	−3.68023	−0.354130
$109$	−0.211303	−0.0202392	−0.0101196	−	0.999949i	$-0.503221\pi$
$109$	−0.211303	−0.0202392	−0.0101196	+	0.999949i	$0.503221\pi$
$110$	−2.81425	−0.268328
$111$	0.277193	0.0263100
$112$	−38.2883	−3.61790
$113$	−0.198345	−0.0186587	−0.00932935	−	0.999956i	$-0.502970\pi$
$113$	−0.198345	−0.0186587	−0.00932935	+	0.999956i	$0.502970\pi$
$114$	−0.323487	−0.0302973
$115$	−3.34476	−0.311900
$116$	36.2184	3.36279
$117$	6.44770	0.596090
$118$	−36.6147	−3.37066
$119$	−12.3735	−1.13428
$120$	−1.04450	−0.0953498
$121$	1.00000	0.0909091
$122$	18.5312	1.67773
$123$	−1.38754	−0.125110
$124$	23.4760	2.10821
$125$	9.41066	0.841715
$126$	26.6935	2.37804
$127$	−3.60331	−0.319742	−0.159871	−	0.987138i	$-0.551108\pi$
$127$	−3.60331	−0.319742	−0.159871	+	0.987138i	$0.551108\pi$
$128$	10.3020	0.910578
$129$	1.14418	0.100739
$130$	6.07857	0.533126
$131$	16.8741	1.47430	0.737150	−	0.675729i	$-0.236171\pi$
$131$	16.8741	1.47430	0.737150	+	0.675729i	$0.236171\pi$
$132$	0.614893	0.0535196
$133$	3.36889	0.292119
$134$	−12.7761	−1.10369
$135$	0.773371	0.0665612
$136$	29.6896	2.54586
$137$	−6.10839	−0.521875	−0.260937	−	0.965356i	$-0.584032\pi$
$137$	−6.10839	−0.521875	−0.260937	+	0.965356i	$0.584032\pi$
$138$	1.02050	0.0868706
$139$	11.3347	0.961398	0.480699	−	0.876886i	$-0.340383\pi$
$139$	11.3347	0.961398	0.480699	+	0.876886i	$0.340383\pi$
$140$	18.0215	1.52310
$141$	−0.703316	−0.0592299
$142$	40.5125	3.39973
$143$	−2.15993	−0.180622
$144$	−33.9270	−2.82725
$145$	−7.61101	−0.632060
$146$	−21.4683	−1.77673
$147$	0.530070	0.0437194
$148$	11.4755	0.943284
$149$	6.75698	0.553554	0.276777	−	0.960934i	$-0.410734\pi$
$149$	6.75698	0.553554	0.276777	+	0.960934i	$0.410734\pi$
$150$	−1.25379	−0.102372
$151$	6.46231	0.525895	0.262948	−	0.964810i	$-0.415305\pi$
$151$	6.46231	0.525895	0.262948	+	0.964810i	$0.415305\pi$
$152$	−8.08346	−0.655655
$153$	−10.9641	−0.886395
$154$	−8.94209	−0.720574
$155$	−4.93330	−0.396252
$156$	−1.32813	−0.106335
$157$	0.248382	0.0198230	0.00991152	−	0.999951i	$-0.496845\pi$
$157$	0.248382	0.0198230	0.00991152	+	0.999951i	$0.496845\pi$
$158$	35.6452	2.83578
$159$	−0.689576	−0.0546869
$160$	−14.8436	−1.17349
$161$	−10.6278	−0.837585
$162$	23.5346	1.84905
$163$	−16.9710	−1.32927	−0.664637	−	0.747167i	$-0.731414\pi$
$163$	−16.9710	−1.32927	−0.664637	+	0.747167i	$0.731414\pi$
$164$	−57.4428	−4.48553
$165$	−0.129215	−0.0100594
$166$	26.4547	2.05328
$167$	−0.865538	−0.0669773	−0.0334887	−	0.999439i	$-0.510662\pi$
$167$	−0.865538	−0.0669773	−0.0334887	+	0.999439i	$0.510662\pi$
$168$	−3.31885	−0.256055
$169$	−8.33471	−0.641132
$170$	−10.3364	−0.792765
$171$	2.98515	0.228280
$172$	47.3681	3.61178
$173$	−4.14483	−0.315125	−0.157563	−	0.987509i	$-0.550364\pi$
$173$	−4.14483	−0.315125	−0.157563	+	0.987509i	$0.550364\pi$
$174$	2.32215	0.176042
$175$	13.0574	0.987043
$176$	11.3653	0.856688
$177$	−1.68115	−0.126363
$178$	−12.2530	−0.918403
$179$	2.04584	0.152913	0.0764567	−	0.997073i	$-0.475639\pi$
$179$	2.04584	0.152913	0.0764567	+	0.997073i	$0.475639\pi$
$180$	15.9687	1.19024
$181$	5.27519	0.392101	0.196051	−	0.980594i	$-0.437188\pi$
$181$	5.27519	0.392101	0.196051	+	0.980594i	$0.437188\pi$
$182$	19.3143	1.43167
$183$	0.850852	0.0628968
$184$	25.5007	1.87994
$185$	−2.41150	−0.177297
$186$	1.50517	0.110364
$187$	3.67288	0.268588
$188$	−29.1167	−2.12355
$189$	2.45734	0.178745
$190$	2.81425	0.204167
$191$	−16.1899	−1.17146	−0.585729	−	0.810507i	$-0.699192\pi$
$191$	−16.1899	−1.17146	−0.585729	+	0.810507i	$0.699192\pi$
$192$	1.75863	0.126918
$193$	−20.0620	−1.44409	−0.722045	−	0.691846i	$-0.756798\pi$
$193$	−20.0620	−1.44409	−0.722045	+	0.691846i	$0.756798\pi$
$194$	−10.8802	−0.781155
$195$	0.279095	0.0199864
$196$	21.9444	1.56746
$197$	−23.8398	−1.69851	−0.849257	−	0.527979i	$-0.822950\pi$
$197$	−23.8398	−1.69851	−0.849257	+	0.527979i	$0.822950\pi$
$198$	−7.92353	−0.563101
$199$	−1.90194	−0.134825	−0.0674125	−	0.997725i	$-0.521474\pi$
$199$	−1.90194	−0.134825	−0.0674125	+	0.997725i	$0.521474\pi$
$200$	−31.3304	−2.21539
$201$	−0.586609	−0.0413762
$202$	−28.8603	−2.03060
$203$	−24.1835	−1.69735
$204$	2.25843	0.158122
$205$	12.0712	0.843087
$206$	23.5136	1.63827
$207$	−9.41719	−0.654540
$208$	−24.5481	−1.70211
$209$	−1.00000	−0.0691714
$210$	1.15545	0.0797339
$211$	12.3048	0.847100	0.423550	−	0.905873i	$-0.360784\pi$
$211$	12.3048	0.847100	0.423550	+	0.905873i	$0.360784\pi$
$212$	−28.5479	−1.96068
$213$	1.86012	0.127453
$214$	−48.2207	−3.29630
$215$	−9.95405	−0.678860
$216$	−5.89625	−0.401189
$217$	−15.6753	−1.06411
$218$	−0.560865	−0.0379866
$219$	−0.985709	−0.0666080
$220$	−5.34940	−0.360656
$221$	−7.93316	−0.533642
$222$	0.735757	0.0493808
$223$	22.8473	1.52997	0.764985	−	0.644048i	$-0.222746\pi$
$223$	22.8473	1.52997	0.764985	+	0.644048i	$0.222746\pi$
$224$	−47.1647	−3.15132
$225$	11.5700	0.771335
$226$	−0.526470	−0.0350202
$227$	4.00654	0.265923	0.132962	−	0.991121i	$-0.457551\pi$
$227$	4.00654	0.265923	0.132962	+	0.991121i	$0.457551\pi$
$228$	−0.614893	−0.0407223
$229$	−24.6024	−1.62577	−0.812887	−	0.582422i	$-0.802105\pi$
$229$	−24.6024	−1.62577	−0.812887	+	0.582422i	$0.802105\pi$
$230$	−8.87805	−0.585401
$231$	−0.410573	−0.0270137
$232$	58.0270	3.80966
$233$	16.2994	1.06781	0.533903	−	0.845545i	$-0.320725\pi$
$233$	16.2994	1.06781	0.533903	+	0.845545i	$0.320725\pi$
$234$	17.1143	1.11879
$235$	6.11865	0.399137
$236$	−69.5982	−4.53046
$237$	1.63664	0.106311
$238$	−32.8433	−2.12891
$239$	−15.4182	−0.997324	−0.498662	−	0.866797i	$-0.666175\pi$
$239$	−15.4182	−0.997324	−0.498662	+	0.866797i	$0.666175\pi$
$240$	−1.46856	−0.0947953
$241$	24.1441	1.55526	0.777629	−	0.628723i	$-0.216422\pi$
$241$	24.1441	1.55526	0.777629	+	0.628723i	$0.216422\pi$
$242$	2.65432	0.170626
$243$	3.26885	0.209697
$244$	35.2245	2.25502
$245$	−4.61146	−0.294615
$246$	−3.68296	−0.234817
$247$	2.15993	0.137433
$248$	37.6119	2.38836
$249$	1.21466	0.0769758
$250$	24.9789	1.57980
$251$	−19.9099	−1.25670	−0.628350	−	0.777931i	$-0.716269\pi$
$251$	−19.9099	−1.25670	−0.628350	+	0.777931i	$0.716269\pi$
$252$	50.7397	3.19630
$253$	3.15468	0.198333
$254$	−9.56433	−0.600119
$255$	−0.474592	−0.0297201
$256$	−1.51547	−0.0947166
$257$	−22.3126	−1.39182	−0.695911	−	0.718128i	$-0.744999\pi$
$257$	−22.3126	−1.39182	−0.695911	+	0.718128i	$0.744999\pi$
$258$	3.03702	0.189076
$259$	−7.66239	−0.476118
$260$	11.5543	0.716568
$261$	−21.4289	−1.32641
$262$	44.7893	2.76709
$263$	13.7963	0.850716	0.425358	−	0.905025i	$-0.360148\pi$
$263$	13.7963	0.850716	0.425358	+	0.905025i	$0.360148\pi$
$264$	0.985147	0.0606316
$265$	5.99912	0.368523
$266$	8.94209	0.548275
$267$	−0.562593	−0.0344301
$268$	−24.2851	−1.48345
$269$	−11.2028	−0.683048	−0.341524	−	0.939873i	$-0.610943\pi$
$269$	−11.2028	−0.683048	−0.341524	+	0.939873i	$0.610943\pi$
$270$	2.05277	0.124928
$271$	17.1234	1.04017	0.520085	−	0.854115i	$-0.325900\pi$
$271$	17.1234	1.04017	0.520085	+	0.854115i	$0.325900\pi$
$272$	41.7433	2.53106
$273$	0.886808	0.0536721
$274$	−16.2136	−0.979499
$275$	−3.87587	−0.233723
$276$	1.93979	0.116762
$277$	−13.7127	−0.823919	−0.411960	−	0.911202i	$-0.635156\pi$
$277$	−13.7127	−0.823919	−0.411960	+	0.911202i	$0.635156\pi$
$278$	30.0859	1.80443
$279$	−13.8897	−0.831557
$280$	28.8730	1.72549
$281$	25.8599	1.54267	0.771337	−	0.636427i	$-0.219588\pi$
$281$	25.8599	1.54267	0.771337	+	0.636427i	$0.219588\pi$
$282$	−1.86682	−0.111168
$283$	28.8711	1.71621	0.858103	−	0.513477i	$-0.171643\pi$
$283$	28.8711	1.71621	0.858103	+	0.513477i	$0.171643\pi$
$284$	77.0073	4.56954
$285$	0.129215	0.00765404
$286$	−5.73313	−0.339007
$287$	38.3554	2.26405
$288$	−41.7923	−2.46264
$289$	−3.50993	−0.206467
$290$	−20.2020	−1.18630
$291$	−0.499562	−0.0292848
$292$	−40.8075	−2.38808
$293$	6.37971	0.372707	0.186353	−	0.982483i	$-0.440333\pi$
$293$	6.37971	0.372707	0.186353	+	0.982483i	$0.440333\pi$
$294$	1.40697	0.0820563
$295$	14.6255	0.851532
$296$	18.3855	1.06863
$297$	−0.729422	−0.0423254
$298$	17.9352	1.03896
$299$	−6.81389	−0.394057
$300$	−2.38324	−0.137597
$301$	−31.6284	−1.82303
$302$	17.1530	0.987045
$303$	−1.32511	−0.0761256
$304$	−11.3653	−0.651842
$305$	−7.40217	−0.423847
$306$	−29.1022	−1.66366
$307$	10.4299	0.595264	0.297632	−	0.954681i	$-0.403803\pi$
$307$	10.4299	0.595264	0.297632	+	0.954681i	$0.403803\pi$
$308$	−16.9974	−0.968515
$309$	1.07962	0.0614174
$310$	−13.0945	−0.743720
$311$	−8.26224	−0.468508	−0.234254	−	0.972175i	$-0.575265\pi$
$311$	−8.26224	−0.468508	−0.234254	+	0.972175i	$0.575265\pi$
$312$	−2.12785	−0.120466
$313$	−24.1167	−1.36315	−0.681577	−	0.731746i	$-0.738706\pi$
$313$	−24.1167	−1.36315	−0.681577	+	0.731746i	$0.738706\pi$
$314$	0.659285	0.0372056
$315$	−10.6626	−0.600767
$316$	67.7554	3.81154
$317$	−11.7330	−0.658989	−0.329495	−	0.944157i	$-0.606878\pi$
$317$	−11.7330	−0.658989	−0.329495	+	0.944157i	$0.606878\pi$
$318$	−1.83035	−0.102641
$319$	7.17849	0.401918
$320$	−15.2996	−0.855273
$321$	−2.21404	−0.123576
$322$	−28.2095	−1.57205
$323$	−3.67288	−0.204365
$324$	44.7353	2.48529
$325$	8.37159	0.464372
$326$	−45.0465	−2.49489
$327$	−0.0257519	−0.00142409
$328$	−92.0317	−5.08160
$329$	19.4416	1.07185
$330$	−0.342978	−0.0188803
$331$	−6.95223	−0.382129	−0.191065	−	0.981577i	$-0.561194\pi$
$331$	−6.95223	−0.382129	−0.191065	+	0.981577i	$0.561194\pi$
$332$	50.2858	2.75979
$333$	−6.78959	−0.372067
$334$	−2.29741	−0.125709
$335$	5.10333	0.278825
$336$	−4.66627	−0.254566
$337$	29.4416	1.60379	0.801893	−	0.597468i	$-0.203826\pi$
$337$	29.4416	1.60379	0.801893	+	0.597468i	$0.203826\pi$
$338$	−22.1230	−1.20333
$339$	−0.0241727	−0.00131288
$340$	−19.6477	−1.06555
$341$	4.65295	0.251971
$342$	7.92353	0.428455
$343$	8.92959	0.482152
$344$	75.8905	4.09174
$345$	−0.407632	−0.0219462
$346$	−11.0017	−0.591454
$347$	−17.2180	−0.924311	−0.462155	−	0.886799i	$-0.652924\pi$
$347$	−17.2180	−0.924311	−0.462155	+	0.886799i	$0.652924\pi$
$348$	4.41401	0.236616
$349$	4.32405	0.231461	0.115731	−	0.993281i	$-0.463079\pi$
$349$	4.32405	0.231461	0.115731	+	0.993281i	$0.463079\pi$
$350$	34.6583	1.85257
$351$	1.57550	0.0840939
$352$	14.0001	0.746207
$353$	23.4421	1.24770	0.623848	−	0.781545i	$-0.285568\pi$
$353$	23.4421	1.24770	0.623848	+	0.781545i	$0.285568\pi$
$354$	−4.46231	−0.237169
$355$	−16.1825	−0.858878
$356$	−23.2909	−1.23441
$357$	−1.50799	−0.0798111
$358$	5.43031	0.287001
$359$	8.20544	0.433066	0.216533	−	0.976275i	$-0.430525\pi$
$359$	8.20544	0.433066	0.216533	+	0.976275i	$0.430525\pi$
$360$	25.5842	1.34841
$361$	1.00000	0.0526316
$362$	14.0020	0.735930
$363$	0.121872	0.00639662
$364$	36.7131	1.92429
$365$	8.57539	0.448856
$366$	2.25843	0.118050
$367$	33.1494	1.73039	0.865193	−	0.501439i	$-0.167196\pi$
$367$	33.1494	1.73039	0.865193	+	0.501439i	$0.167196\pi$
$368$	35.8538	1.86901
$369$	33.9865	1.76926
$370$	−6.40088	−0.332766
$371$	19.0618	0.989640
$372$	2.86107	0.148339
$373$	−16.5840	−0.858685	−0.429343	−	0.903142i	$-0.641255\pi$
$373$	−16.5840	−0.858685	−0.429343	+	0.903142i	$0.641255\pi$
$374$	9.74900	0.504109
$375$	1.14690	0.0592254
$376$	−46.6492	−2.40575
$377$	−15.5050	−0.798550
$378$	6.52256	0.335484
$379$	5.79467	0.297652	0.148826	−	0.988863i	$-0.452451\pi$
$379$	5.79467	0.297652	0.148826	+	0.988863i	$0.452451\pi$
$380$	5.34940	0.274418
$381$	−0.439143	−0.0224980
$382$	−42.9730	−2.19869
$383$	5.89016	0.300973	0.150487	−	0.988612i	$-0.451916\pi$
$383$	5.89016	0.300973	0.150487	+	0.988612i	$0.451916\pi$
$384$	1.25553	0.0640709
$385$	3.57187	0.182039
$386$	−53.2508	−2.71039
$387$	−28.0257	−1.42463
$388$	−20.6814	−1.04994
$389$	13.8055	0.699964	0.349982	−	0.936756i	$-0.386188\pi$
$389$	13.8055	0.699964	0.349982	+	0.936756i	$0.386188\pi$
$390$	0.740808	0.0375122
$391$	11.5868	0.585968
$392$	35.1581	1.77575
$393$	2.05649	0.103736
$394$	−63.2784	−3.18792
$395$	−14.2383	−0.716405
$396$	−15.0613	−0.756857
$397$	6.48471	0.325458	0.162729	−	0.986671i	$-0.447970\pi$
$397$	6.48471	0.325458	0.162729	+	0.986671i	$0.447970\pi$
$398$	−5.04835	−0.253051
$399$	0.410573	0.0205544
$400$	−44.0502	−2.20251
$401$	3.70806	0.185172	0.0925858	−	0.995705i	$-0.470487\pi$
$401$	3.70806	0.185172	0.0925858	+	0.995705i	$0.470487\pi$
$402$	−1.55705	−0.0776584
$403$	−10.0500	−0.500628
$404$	−54.8584	−2.72931
$405$	−9.40077	−0.467128
$406$	−64.1908	−3.18573
$407$	2.27446	0.112741
$408$	3.61833	0.179134
$409$	31.0569	1.53567	0.767833	−	0.640650i	$-0.221335\pi$
$409$	31.0569	1.53567	0.767833	+	0.640650i	$0.221335\pi$
$410$	32.0407	1.58238
$411$	−0.744442	−0.0367206
$412$	44.6954	2.20198
$413$	46.4717	2.28673
$414$	−24.9962	−1.22850
$415$	−10.5672	−0.518722
$416$	−30.2392	−1.48260
$417$	1.38138	0.0676467
$418$	−2.65432	−0.129827
$419$	−11.2871	−0.551410	−0.275705	−	0.961242i	$-0.588911\pi$
$419$	−11.2871	−0.551410	−0.275705	+	0.961242i	$0.588911\pi$
$420$	2.19632	0.107169
$421$	34.5194	1.68237	0.841186	−	0.540746i	$-0.181858\pi$
$421$	34.5194	1.68237	0.841186	+	0.540746i	$0.181858\pi$
$422$	32.6609	1.58991
$423$	17.2271	0.837611
$424$	−45.7378	−2.22122
$425$	−14.2356	−0.690528
$426$	4.93734	0.239215
$427$	−23.5199	−1.13821
$428$	−91.6593	−4.43052
$429$	−0.263235	−0.0127091
$430$	−26.4212	−1.27414
$431$	18.1654	0.874996	0.437498	−	0.899219i	$-0.355865\pi$
$431$	18.1654	0.874996	0.437498	+	0.899219i	$0.355865\pi$
$432$	−8.29007	−0.398856
$433$	10.7804	0.518075	0.259037	−	0.965867i	$-0.416595\pi$
$433$	10.7804	0.518075	0.259037	+	0.965867i	$0.416595\pi$
$434$	−41.6071	−1.99720
$435$	−0.927570	−0.0444736
$436$	−1.06611	−0.0510573
$437$	−3.15468	−0.150909
$438$	−2.61638	−0.125016
$439$	−1.38742	−0.0662180	−0.0331090	−	0.999452i	$-0.510541\pi$
$439$	−1.38742	−0.0662180	−0.0331090	+	0.999452i	$0.510541\pi$
$440$	−8.57050	−0.408583
$441$	−12.9836	−0.618266
$442$	−21.0571	−1.00159
$443$	−7.26792	−0.345310	−0.172655	−	0.984982i	$-0.555234\pi$
$443$	−7.26792	−0.345310	−0.172655	+	0.984982i	$0.555234\pi$
$444$	1.39855	0.0663722
$445$	4.89440	0.232017
$446$	60.6441	2.87158
$447$	0.823487	0.0389496
$448$	−48.6135	−2.29677
$449$	21.4298	1.01134	0.505668	−	0.862728i	$-0.331246\pi$
$449$	21.4298	1.01134	0.505668	+	0.862728i	$0.331246\pi$
$450$	30.7105	1.44771
$451$	−11.3852	−0.536108
$452$	−1.00073	−0.0470703
$453$	0.787575	0.0370035
$454$	10.6346	0.499108
$455$	−7.71498	−0.361684
$456$	−0.985147	−0.0461337
$457$	−17.6312	−0.824754	−0.412377	−	0.911013i	$-0.635301\pi$
$457$	−17.6312	−0.824754	−0.412377	+	0.911013i	$0.635301\pi$
$458$	−65.3026	−3.05139
$459$	−2.67908	−0.125049
$460$	−16.8756	−0.786831
$461$	34.2073	1.59320	0.796598	−	0.604510i	$-0.206631\pi$
$461$	34.2073	1.59320	0.796598	+	0.604510i	$0.206631\pi$
$462$	−1.08979	−0.0507017
$463$	−11.0009	−0.511253	−0.255626	−	0.966776i	$-0.582282\pi$
$463$	−11.0009	−0.511253	−0.255626	+	0.966776i	$0.582282\pi$
$464$	81.5854	3.78751
$465$	−0.601231	−0.0278814
$466$	43.2637	2.00415
$467$	4.38453	0.202892	0.101446	−	0.994841i	$-0.467653\pi$
$467$	4.38453	0.202892	0.101446	+	0.994841i	$0.467653\pi$
$468$	32.5312	1.50376
$469$	16.2155	0.748764
$470$	16.2408	0.749134
$471$	0.0302708	0.00139481
$472$	−111.506	−5.13250
$473$	9.38838	0.431678
$474$	4.34415	0.199534
$475$	3.87587	0.177837
$476$	−62.4294	−2.86145
$477$	16.8905	0.773365
$478$	−40.9249	−1.87186
$479$	−14.3683	−0.656505	−0.328253	−	0.944590i	$-0.606460\pi$
$479$	−14.3683	−0.656505	−0.328253	+	0.944590i	$0.606460\pi$
$480$	−1.80902	−0.0825702
$481$	−4.91266	−0.223998
$482$	64.0861	2.91904
$483$	−1.29523	−0.0589349
$484$	5.04540	0.229336
$485$	4.34604	0.197344
$486$	8.67657	0.393577
$487$	1.01712	0.0460899	0.0230449	−	0.999734i	$-0.492664\pi$
$487$	1.01712	0.0460899	0.0230449	+	0.999734i	$0.492664\pi$
$488$	56.4348	2.55468
$489$	−2.06829	−0.0935314
$490$	−12.2403	−0.552959
$491$	−2.41045	−0.108782	−0.0543910	−	0.998520i	$-0.517322\pi$
$491$	−2.41045	−0.108782	−0.0543910	+	0.998520i	$0.517322\pi$
$492$	−7.00067	−0.315615
$493$	26.3658	1.18745
$494$	5.73313	0.257946
$495$	3.16501	0.142257
$496$	52.8820	2.37447
$497$	−51.4189	−2.30645
$498$	3.22409	0.144475
$499$	4.07426	0.182389	0.0911945	−	0.995833i	$-0.470931\pi$
$499$	4.07426	0.182389	0.0911945	+	0.995833i	$0.470931\pi$
$500$	47.4805	2.12339
$501$	−0.105485	−0.00471272
$502$	−52.8471	−2.35868
$503$	−19.9553	−0.889762	−0.444881	−	0.895590i	$-0.646754\pi$
$503$	−19.9553	−0.889762	−0.444881	+	0.895590i	$0.646754\pi$
$504$	81.2923	3.62104
$505$	11.5281	0.512993
$506$	8.37352	0.372249
$507$	−1.01577	−0.0451118
$508$	−18.1801	−0.806613
$509$	−8.79239	−0.389716	−0.194858	−	0.980831i	$-0.562425\pi$
$509$	−8.79239	−0.389716	−0.194858	+	0.980831i	$0.562425\pi$
$510$	−1.25972	−0.0557812
$511$	27.2478	1.20537
$512$	−24.6266	−1.08835
$513$	0.729422	0.0322048
$514$	−59.2247	−2.61229
$515$	−9.39239	−0.413878
$516$	5.77285	0.254135
$517$	−5.77094	−0.253806
$518$	−20.3384	−0.893618
$519$	−0.505138	−0.0221731
$520$	18.5117	0.811790
$521$	27.3483	1.19815	0.599075	−	0.800693i	$-0.295535\pi$
$521$	27.3483	1.19815	0.599075	+	0.800693i	$0.295535\pi$
$522$	−56.8790	−2.48953
$523$	−41.7043	−1.82360	−0.911800	−	0.410634i	$-0.865307\pi$
$523$	−41.7043	−1.82360	−0.911800	+	0.410634i	$0.865307\pi$
$524$	85.1368	3.71922
$525$	1.59133	0.0694512
$526$	36.6197	1.59670
$527$	17.0897	0.744441
$528$	1.38511	0.0602790
$529$	−13.0480	−0.567304
$530$	15.9236	0.691675
$531$	41.1783	1.78699
$532$	16.9974	0.736930
$533$	24.5912	1.06516
$534$	−1.49330	−0.0646214
$535$	19.2615	0.832748
$536$	−38.9083	−1.68058
$537$	0.249331	0.0107594
$538$	−29.7358	−1.28200
$539$	4.34940	0.187342
$540$	3.90197	0.167914
$541$	−20.7584	−0.892472	−0.446236	−	0.894915i	$-0.647236\pi$
$541$	−20.7584	−0.892472	−0.446236	+	0.894915i	$0.647236\pi$
$542$	45.4508	1.95228
$543$	0.642898	0.0275894
$544$	51.4207	2.20464
$545$	0.224035	0.00959659
$546$	2.35387	0.100736
$547$	5.39396	0.230629	0.115315	−	0.993329i	$-0.463212\pi$
$547$	5.39396	0.230629	0.115315	+	0.993329i	$0.463212\pi$
$548$	−30.8193	−1.31653
$549$	−20.8409	−0.889466
$550$	−10.2878	−0.438672
$551$	−7.17849	−0.305814
$552$	3.10783	0.132278
$553$	−45.2412	−1.92385
$554$	−36.3980	−1.54640
$555$	−0.293894	−0.0124751
$556$	57.1881	2.42532
$557$	−38.0076	−1.61043	−0.805217	−	0.592981i	$-0.797951\pi$
$557$	−38.0076	−1.61043	−0.805217	+	0.592981i	$0.797951\pi$
$558$	−36.8678	−1.56074
$559$	−20.2782	−0.857677
$560$	40.5952	1.71546
$561$	0.447622	0.0188986
$562$	68.6404	2.89542
$563$	−26.4313	−1.11395	−0.556973	−	0.830530i	$-0.688037\pi$
$563$	−26.4313	−1.11395	−0.556973	+	0.830530i	$0.688037\pi$
$564$	−3.54851	−0.149419
$565$	0.210295	0.00884719
$566$	76.6330	3.22112
$567$	−29.8704	−1.25444
$568$	123.377	5.17677
$569$	40.6105	1.70248	0.851239	−	0.524778i	$-0.175852\pi$
$569$	40.6105	1.70248	0.851239	+	0.524778i	$0.175852\pi$
$570$	0.342978	0.0143658
$571$	8.44299	0.353328	0.176664	−	0.984271i	$-0.443469\pi$
$571$	8.44299	0.353328	0.176664	+	0.984271i	$0.443469\pi$
$572$	−10.8977	−0.455656
$573$	−1.97309	−0.0824271
$574$	101.807	4.24936
$575$	−12.2271	−0.509906
$576$	−43.0761	−1.79484
$577$	20.9771	0.873288	0.436644	−	0.899634i	$-0.356167\pi$
$577$	20.9771	0.873288	0.436644	+	0.899634i	$0.356167\pi$
$578$	−9.31648	−0.387514
$579$	−2.44499	−0.101610
$580$	−38.4006	−1.59450
$581$	−33.5766	−1.39299
$582$	−1.32600	−0.0549643
$583$	−5.65820	−0.234339
$584$	−65.3795	−2.70542
$585$	−6.83619	−0.282642
$586$	16.9338	0.699528
$587$	−21.1452	−0.872756	−0.436378	−	0.899764i	$-0.643739\pi$
$587$	−21.1452	−0.872756	−0.436378	+	0.899764i	$0.643739\pi$
$588$	2.67441	0.110291
$589$	−4.65295	−0.191721
$590$	38.8208	1.59823
$591$	−2.90540	−0.119512
$592$	25.8498	1.06242
$593$	27.7731	1.14051	0.570253	−	0.821469i	$-0.306845\pi$
$593$	27.7731	1.14051	0.570253	+	0.821469i	$0.306845\pi$
$594$	−1.93612	−0.0794399
$595$	13.1191	0.537829
$596$	34.0917	1.39645
$597$	−0.231793	−0.00948667
$598$	−18.0862	−0.739600
$599$	23.0129	0.940281	0.470140	−	0.882592i	$-0.344203\pi$
$599$	23.0129	0.940281	0.470140	+	0.882592i	$0.344203\pi$
$600$	−3.81830	−0.155881
$601$	23.3322	0.951738	0.475869	−	0.879516i	$-0.342134\pi$
$601$	23.3322	0.951738	0.475869	+	0.879516i	$0.342134\pi$
$602$	−83.9517	−3.42162
$603$	14.3685	0.585129
$604$	32.6049	1.32668
$605$	−1.06025	−0.0431054
$606$	−3.51726	−0.142879
$607$	−3.22857	−0.131044	−0.0655218	−	0.997851i	$-0.520871\pi$
$607$	−3.22857	−0.131044	−0.0655218	+	0.997851i	$0.520871\pi$
$608$	−14.0001	−0.567778
$609$	−2.94730	−0.119430
$610$	−19.6477	−0.795512
$611$	12.4648	0.504273
$612$	−55.3182	−2.23611
$613$	−17.2202	−0.695519	−0.347759	−	0.937584i	$-0.613057\pi$
$613$	−17.2202	−0.695519	−0.347759	+	0.937584i	$0.613057\pi$
$614$	27.6842	1.11724
$615$	1.47114	0.0593220
$616$	−27.2322	−1.09722
$617$	−27.4776	−1.10621	−0.553103	−	0.833113i	$-0.686557\pi$
$617$	−27.4776	−1.10621	−0.553103	+	0.833113i	$0.686557\pi$
$618$	2.86565	0.115274
$619$	−9.53870	−0.383393	−0.191696	−	0.981454i	$-0.561399\pi$
$619$	−9.53870	−0.383393	−0.191696	+	0.981454i	$0.561399\pi$
$620$	−24.8905	−0.999625
$621$	−2.30109	−0.0923397
$622$	−21.9306	−0.879337
$623$	15.5517	0.623064
$624$	−2.99173	−0.119765
$625$	9.40166	0.376066
$626$	−64.0133	−2.55848
$627$	−0.121872	−0.00486710
$628$	1.25319	0.0500076
$629$	8.35381	0.333088
$630$	−28.3018	−1.12757
$631$	1.16647	0.0464363	0.0232182	−	0.999730i	$-0.492609\pi$
$631$	1.16647	0.0464363	0.0232182	+	0.999730i	$0.492609\pi$
$632$	108.554	4.31804
$633$	1.49962	0.0596044
$634$	−31.1430	−1.23685
$635$	3.82042	0.151609
$636$	−3.47919	−0.137959
$637$	−9.39438	−0.372219
$638$	19.0540	0.754355
$639$	−45.5619	−1.80240
$640$	−10.9227	−0.431759
$641$	10.0249	0.395960	0.197980	−	0.980206i	$-0.436562\pi$
$641$	10.0249	0.395960	0.197980	+	0.980206i	$0.436562\pi$
$642$	−5.87676	−0.231937
$643$	−40.7197	−1.60583	−0.802915	−	0.596094i	$-0.796719\pi$
$643$	−40.7197	−1.60583	−0.802915	+	0.596094i	$0.796719\pi$
$644$	−53.6213	−2.11298
$645$	−1.21312	−0.0477666
$646$	−9.74900	−0.383569
$647$	−16.6460	−0.654423	−0.327211	−	0.944951i	$-0.606109\pi$
$647$	−16.6460	−0.654423	−0.327211	+	0.944951i	$0.606109\pi$
$648$	71.6723	2.81555
$649$	−13.7944	−0.541477
$650$	22.2209	0.871574
$651$	−1.91038	−0.0748735
$652$	−85.6256	−3.35336
$653$	−34.7416	−1.35954	−0.679771	−	0.733424i	$-0.737921\pi$
$653$	−34.7416	−1.35954	−0.679771	+	0.733424i	$0.737921\pi$
$654$	−0.0683538	−0.00267285
$655$	−17.8908	−0.699053
$656$	−129.396	−5.05205
$657$	24.1441	0.941949
$658$	51.6043	2.01175
$659$	−22.9537	−0.894148	−0.447074	−	0.894497i	$-0.647534\pi$
$659$	−22.9537	−0.894148	−0.447074	+	0.894497i	$0.647534\pi$
$660$	−0.651942	−0.0253768
$661$	−22.7141	−0.883476	−0.441738	−	0.897144i	$-0.645638\pi$
$661$	−22.7141	−0.883476	−0.441738	+	0.897144i	$0.645638\pi$
$662$	−18.4534	−0.717213
$663$	−0.966831	−0.0375486
$664$	80.5651	3.12653
$665$	−3.57187	−0.138511
$666$	−18.0217	−0.698328
$667$	22.6459	0.876851
$668$	−4.36698	−0.168964
$669$	2.78445	0.107653
$670$	13.5459	0.523322
$671$	6.98152	0.269518
$672$	−5.74806	−0.221736
$673$	20.9448	0.807364	0.403682	−	0.914899i	$-0.367730\pi$
$673$	20.9448	0.807364	0.403682	+	0.914899i	$0.367730\pi$
$674$	78.1473	3.01012
$675$	2.82714	0.108817
$676$	−42.0519	−1.61738
$677$	11.4153	0.438726	0.219363	−	0.975643i	$-0.429602\pi$
$677$	11.4153	0.438726	0.219363	+	0.975643i	$0.429602\pi$
$678$	−0.0641619	−0.00246412
$679$	13.8093	0.529952
$680$	−31.4784	−1.20714
$681$	0.488285	0.0187111
$682$	12.3504	0.472921
$683$	−34.9550	−1.33752	−0.668759	−	0.743479i	$-0.733174\pi$
$683$	−34.9550	−1.33752	−0.668759	+	0.743479i	$0.733174\pi$
$684$	15.0613	0.575882
$685$	6.47643	0.247452
$686$	23.7020	0.904945
$687$	−2.99835	−0.114394
$688$	106.701	4.06795
$689$	12.2213	0.465594
$690$	−1.08199	−0.0411905
$691$	−15.8717	−0.603789	−0.301894	−	0.953341i	$-0.597619\pi$
$691$	−15.8717	−0.603789	−0.301894	+	0.953341i	$0.597619\pi$
$692$	−20.9123	−0.794967
$693$	10.0566	0.382019
$694$	−45.7020	−1.73483
$695$	−12.0177	−0.455855
$696$	7.07187	0.268059
$697$	−41.8165	−1.58391
$698$	11.4774	0.434426
$699$	1.98644	0.0751339
$700$	65.8795	2.49001
$701$	−18.5830	−0.701869	−0.350935	−	0.936400i	$-0.614136\pi$
$701$	−18.5830	−0.701869	−0.350935	+	0.936400i	$0.614136\pi$
$702$	4.18188	0.157835
$703$	−2.27446	−0.0857828
$704$	14.4301	0.543857
$705$	0.745693	0.0280844
$706$	62.2228	2.34178
$707$	36.6298	1.37760
$708$	−8.48208	−0.318776
$709$	23.8063	0.894064	0.447032	−	0.894518i	$-0.352481\pi$
$709$	23.8063	0.894064	0.447032	+	0.894518i	$0.352481\pi$
$710$	−42.9535	−1.61202
$711$	−40.0880	−1.50342
$712$	−37.3153	−1.39845
$713$	14.6786	0.549717
$714$	−4.00267	−0.149796
$715$	2.29007	0.0856437
$716$	10.3221	0.385755
$717$	−1.87905	−0.0701745
$718$	21.7798	0.812816
$719$	37.0144	1.38040	0.690202	−	0.723616i	$-0.257522\pi$
$719$	37.0144	1.38040	0.690202	+	0.723616i	$0.257522\pi$
$720$	35.9711	1.34057
$721$	−29.8437	−1.11144
$722$	2.65432	0.0987835
$723$	2.94249	0.109432
$724$	26.6154	0.989154
$725$	−27.8229	−1.03332
$726$	0.323487	0.0120057
$727$	−22.0744	−0.818694	−0.409347	−	0.912379i	$-0.634243\pi$
$727$	−22.0744	−0.818694	−0.409347	+	0.912379i	$0.634243\pi$
$728$	58.8197	2.18000
$729$	−26.2013	−0.970417
$730$	22.7618	0.842452
$731$	34.4824	1.27538
$732$	4.29289	0.158670
$733$	−18.7090	−0.691031	−0.345515	−	0.938413i	$-0.612296\pi$
$733$	−18.7090	−0.691031	−0.345515	+	0.938413i	$0.612296\pi$
$734$	87.9891	3.24774
$735$	−0.562008	−0.0207300
$736$	44.1658	1.62797
$737$	−4.81332	−0.177301
$738$	90.2109	3.32071
$739$	−5.91630	−0.217635	−0.108817	−	0.994062i	$-0.534706\pi$
$739$	−5.91630	−0.217635	−0.108817	+	0.994062i	$0.534706\pi$
$740$	−12.1670	−0.447267
$741$	0.263235	0.00967017
$742$	50.5961	1.85744
$743$	14.0422	0.515159	0.257579	−	0.966257i	$-0.417075\pi$
$743$	14.0422	0.515159	0.257579	+	0.966257i	$0.417075\pi$
$744$	4.58384	0.168052
$745$	−7.16411	−0.262473
$746$	−44.0191	−1.61165
$747$	−29.7520	−1.08857
$748$	18.5312	0.677566
$749$	61.2023	2.23628
$750$	3.04423	0.111159
$751$	4.91166	0.179229	0.0896145	−	0.995977i	$-0.471437\pi$
$751$	4.91166	0.179229	0.0896145	+	0.995977i	$0.471437\pi$
$752$	−65.5882	−2.39176
$753$	−2.42646	−0.0884250
$754$	−41.1553	−1.49879
$755$	−6.85168	−0.249358
$756$	12.3983	0.450920
$757$	49.2829	1.79122	0.895609	−	0.444843i	$-0.146741\pi$
$757$	49.2829	1.79122	0.895609	+	0.444843i	$0.146741\pi$
$758$	15.3809	0.558659
$759$	0.384467	0.0139553
$760$	8.57050	0.310885
$761$	−7.25922	−0.263146	−0.131573	−	0.991306i	$-0.542003\pi$
$761$	−7.25922	−0.263146	−0.131573	+	0.991306i	$0.542003\pi$
$762$	−1.16562	−0.0422261
$763$	0.711856	0.0257709
$764$	−81.6843	−2.95524
$765$	11.6247	0.420292
$766$	15.6344	0.564892
$767$	29.7949	1.07583
$768$	−0.184693	−0.00666453
$769$	−21.5123	−0.775755	−0.387877	−	0.921711i	$-0.626792\pi$
$769$	−21.5123	−0.775755	−0.387877	+	0.921711i	$0.626792\pi$
$770$	9.48087	0.341667
$771$	−2.71928	−0.0979325
$772$	−101.221	−3.64301
$773$	4.54038	0.163306	0.0816530	−	0.996661i	$-0.473980\pi$
$773$	4.54038	0.163306	0.0816530	+	0.996661i	$0.473980\pi$
$774$	−74.3891	−2.67386
$775$	−18.0342	−0.647808
$776$	−33.1346	−1.18946
$777$	−0.933831	−0.0335010
$778$	36.6440	1.31375
$779$	11.3852	0.407917
$780$	1.40815	0.0504198
$781$	15.2629	0.546149
$782$	30.7550	1.09980
$783$	−5.23615	−0.187125
$784$	49.4320	1.76543
$785$	−0.263348	−0.00939928
$786$	5.45856	0.194701
$787$	−7.25028	−0.258444	−0.129222	−	0.991616i	$-0.541248\pi$
$787$	−7.25028	−0.258444	−0.129222	+	0.991616i	$0.541248\pi$
$788$	−120.281	−4.28484
$789$	1.68138	0.0598588
$790$	−37.7929	−1.34461
$791$	0.668201	0.0237585
$792$	−24.1303	−0.857433
$793$	−15.0796	−0.535491
$794$	17.2125	0.610848
$795$	0.731124	0.0259303
$796$	−9.59605	−0.340123
$797$	18.8674	0.668319	0.334159	−	0.942517i	$-0.391548\pi$
$797$	18.8674	0.668319	0.334159	+	0.942517i	$0.391548\pi$
$798$	1.08979	0.0385782
$799$	−21.1960	−0.749860
$800$	−54.2624	−1.91847
$801$	13.7802	0.486900
$802$	9.84236	0.347546
$803$	−8.08806	−0.285422
$804$	−2.95968	−0.104380
$805$	11.2681	0.397149
$806$	−26.6760	−0.939622
$807$	−1.36531	−0.0480612
$808$	−87.8911	−3.09200
$809$	−19.4948	−0.685399	−0.342700	−	0.939445i	$-0.611341\pi$
$809$	−19.4948	−0.685399	−0.342700	+	0.939445i	$0.611341\pi$
$810$	−24.9526	−0.876746
$811$	4.28635	0.150514	0.0752570	−	0.997164i	$-0.476022\pi$
$811$	4.28635	0.150514	0.0752570	+	0.997164i	$0.476022\pi$
$812$	−122.016	−4.28191
$813$	2.08686	0.0731893
$814$	6.03713	0.211601
$815$	17.9936	0.630287
$816$	5.08734	0.178092
$817$	−9.38838	−0.328458
$818$	82.4350	2.88227
$819$	−21.7216	−0.759014
$820$	60.9039	2.12686
$821$	5.37419	0.187561	0.0937803	−	0.995593i	$-0.470105\pi$
$821$	5.37419	0.187561	0.0937803	+	0.995593i	$0.470105\pi$
$822$	−1.97598	−0.0689204
$823$	26.3196	0.917445	0.458723	−	0.888580i	$-0.348307\pi$
$823$	26.3196	0.917445	0.458723	+	0.888580i	$0.348307\pi$
$824$	71.6084	2.49460
$825$	−0.472360	−0.0164455
$826$	123.351	4.29192
$827$	−8.11186	−0.282077	−0.141039	−	0.990004i	$-0.545044\pi$
$827$	−8.11186	−0.282077	−0.141039	+	0.990004i	$0.545044\pi$
$828$	−47.5135	−1.65121
$829$	−21.5948	−0.750017	−0.375009	−	0.927021i	$-0.622360\pi$
$829$	−21.5948	−0.750017	−0.375009	+	0.927021i	$0.622360\pi$
$830$	−28.0486	−0.973582
$831$	−1.67120	−0.0579733
$832$	−31.1681	−1.08056
$833$	15.9748	0.553495
$834$	3.66663	0.126965
$835$	0.917688	0.0317579
$836$	−5.04540	−0.174499
$837$	−3.39396	−0.117313
$838$	−29.9595	−1.03493
$839$	−4.35109	−0.150216	−0.0751082	−	0.997175i	$-0.523930\pi$
$839$	−4.35109	−0.150216	−0.0751082	+	0.997175i	$0.523930\pi$
$840$	3.51882	0.121411
$841$	22.5308	0.776923
$842$	91.6254	3.15762
$843$	3.15160	0.108547
$844$	62.0828	2.13698
$845$	8.83689	0.303998
$846$	45.7262	1.57210
$847$	−3.36889	−0.115756
$848$	−64.3069	−2.20831
$849$	3.51858	0.120757
$850$	−37.7858	−1.29604
$851$	7.17519	0.245962
$852$	9.38504	0.321526
$853$	19.5022	0.667744	0.333872	−	0.942618i	$-0.391645\pi$
$853$	19.5022	0.667744	0.333872	+	0.942618i	$0.391645\pi$
$854$	−62.4294	−2.13629
$855$	−3.16501	−0.108241
$856$	−146.851	−5.01928
$857$	13.3462	0.455898	0.227949	−	0.973673i	$-0.426798\pi$
$857$	13.3462	0.455898	0.227949	+	0.973673i	$0.426798\pi$
$858$	−0.698709	−0.0238535
$859$	21.6016	0.737036	0.368518	−	0.929621i	$-0.379865\pi$
$859$	21.6016	0.737036	0.368518	+	0.929621i	$0.379865\pi$
$860$	−50.2221	−1.71256
$861$	4.67445	0.159305
$862$	48.2167	1.64227
$863$	−2.72425	−0.0927345	−0.0463673	−	0.998924i	$-0.514764\pi$
$863$	−2.72425	−0.0927345	−0.0463673	+	0.998924i	$0.514764\pi$
$864$	−10.2120	−0.347418
$865$	4.39456	0.149420
$866$	28.6147	0.972367
$867$	−0.427763	−0.0145276
$868$	−79.0879	−2.68442
$869$	13.4291	0.455552
$870$	−2.46206	−0.0834718
$871$	10.3964	0.352269
$872$	−1.70806	−0.0578422
$873$	12.2363	0.414137
$874$	−8.37352	−0.283239
$875$	−31.7034	−1.07177
$876$	−4.97329	−0.168032
$877$	1.29130	0.0436041	0.0218021	−	0.999762i	$-0.493060\pi$
$877$	1.29130	0.0436041	0.0218021	+	0.999762i	$0.493060\pi$
$878$	−3.68266	−0.124284
$879$	0.777508	0.0262247
$880$	−12.0500	−0.406207
$881$	24.9873	0.841844	0.420922	−	0.907097i	$-0.361707\pi$
$881$	24.9873	0.841844	0.420922	+	0.907097i	$0.361707\pi$
$882$	−34.4626	−1.16041
$883$	15.5046	0.521772	0.260886	−	0.965370i	$-0.415985\pi$
$883$	15.5046	0.521772	0.260886	+	0.965370i	$0.415985\pi$
$884$	−40.0260	−1.34622
$885$	1.78244	0.0599162
$886$	−19.2914	−0.648107
$887$	−9.98029	−0.335105	−0.167553	−	0.985863i	$-0.553586\pi$
$887$	−9.98029	−0.335105	−0.167553	+	0.985863i	$0.553586\pi$
$888$	2.24068	0.0751921
$889$	12.1391	0.407134
$890$	12.9913	0.435469
$891$	8.86655	0.297040
$892$	115.274	3.85966
$893$	5.77094	0.193117
$894$	2.18580	0.0731040
$895$	−2.16911	−0.0725053
$896$	−34.7063	−1.15946
$897$	−0.830422	−0.0277270
$898$	56.8815	1.89816
$899$	33.4012	1.11399
$900$	58.3754	1.94585
$901$	−20.7819	−0.692345
$902$	−30.2199	−1.00621
$903$	−3.85461	−0.128274
$904$	−1.60331	−0.0533253
$905$	−5.59303	−0.185919
$906$	2.09047	0.0694513
$907$	11.8887	0.394758	0.197379	−	0.980327i	$-0.436757\pi$
$907$	11.8887	0.394758	0.197379	+	0.980327i	$0.436757\pi$
$908$	20.2146	0.670845
$909$	32.4574	1.07654
$910$	−20.4780	−0.678839
$911$	−23.7166	−0.785767	−0.392883	−	0.919588i	$-0.628522\pi$
$911$	−23.7166	−0.785767	−0.392883	+	0.919588i	$0.628522\pi$
$912$	−1.38511	−0.0458655
$913$	9.96666	0.329848
$914$	−46.7989	−1.54797
$915$	−0.902117	−0.0298231
$916$	−124.129	−4.10134
$917$	−56.8471	−1.87726
$918$	−7.11113	−0.234702
$919$	18.1426	0.598470	0.299235	−	0.954179i	$-0.403269\pi$
$919$	18.1426	0.598470	0.299235	+	0.954179i	$0.403269\pi$
$920$	−27.0372	−0.891390
$921$	1.27111	0.0418845
$922$	90.7972	2.99024
$923$	−32.9667	−1.08511
$924$	−2.07150	−0.0681475
$925$	−8.81549	−0.289852
$926$	−29.1997	−0.959563
$927$	−26.4443	−0.868546
$928$	100.500	3.29906
$929$	−50.5019	−1.65691	−0.828457	−	0.560053i	$-0.810781\pi$
$929$	−50.5019	−1.65691	−0.828457	+	0.560053i	$0.810781\pi$
$930$	−1.59586	−0.0523303
$931$	−4.34940	−0.142546
$932$	82.2368	2.69376
$933$	−1.00694	−0.0329656
$934$	11.6379	0.380805
$935$	−3.89418	−0.127353
$936$	52.1197	1.70359
$937$	−39.6587	−1.29559	−0.647797	−	0.761813i	$-0.724309\pi$
$937$	−39.6587	−1.29559	−0.647797	+	0.761813i	$0.724309\pi$
$938$	43.0412	1.40534
$939$	−2.93915	−0.0959154
$940$	30.8711	1.00690
$941$	−34.8809	−1.13709	−0.568543	−	0.822653i	$-0.692493\pi$
$941$	−34.8809	−1.13709	−0.568543	+	0.822653i	$0.692493\pi$
$942$	0.0803484	0.00261789
$943$	−35.9166	−1.16961
$944$	−156.777	−5.10265
$945$	−2.60540	−0.0847537
$946$	24.9197	0.810210
$947$	−30.3067	−0.984835	−0.492417	−	0.870359i	$-0.663887\pi$
$947$	−30.3067	−0.984835	−0.492417	+	0.870359i	$0.663887\pi$
$948$	8.25748	0.268191
$949$	17.4696	0.567088
$950$	10.2878	0.333780
$951$	−1.42992	−0.0463684
$952$	−100.021	−3.24169
$953$	−6.65804	−0.215675	−0.107838	−	0.994169i	$-0.534393\pi$
$953$	−6.65804	−0.215675	−0.107838	+	0.994169i	$0.534393\pi$
$954$	44.8329	1.45152
$955$	17.1653	0.555457
$956$	−77.7912	−2.51595
$957$	0.874858	0.0282801
$958$	−38.1381	−1.23219
$959$	20.5785	0.664513
$960$	−1.86459	−0.0601795
$961$	−9.35006	−0.301615
$962$	−13.0398	−0.420419
$963$	54.2309	1.74757
$964$	121.817	3.92345
$965$	21.2707	0.684729
$966$	−3.43794	−0.110614
$967$	−20.0020	−0.643221	−0.321611	−	0.946872i	$-0.604224\pi$
$967$	−20.0020	−0.643221	−0.321611	+	0.946872i	$0.604224\pi$
$968$	8.08346	0.259812
$969$	−0.447622	−0.0143797
$970$	11.5358	0.370392
$971$	−0.491941	−0.0157871	−0.00789357	−	0.999969i	$-0.502513\pi$
$971$	−0.491941	−0.0157871	−0.00789357	+	0.999969i	$0.502513\pi$
$972$	16.4927	0.529002
$973$	−38.1853	−1.22417
$974$	2.69975	0.0865055
$975$	1.02026	0.0326746
$976$	79.3467	2.53983
$977$	23.6515	0.756679	0.378339	−	0.925667i	$-0.376495\pi$
$977$	23.6515	0.756679	0.378339	+	0.925667i	$0.376495\pi$
$978$	−5.48991	−0.175548
$979$	−4.61626	−0.147536
$980$	−23.2666	−0.743225
$981$	0.630771	0.0201390
$982$	−6.39809	−0.204171
$983$	39.5609	1.26180	0.630899	−	0.775865i	$-0.282686\pi$
$983$	39.5609	1.26180	0.630899	+	0.775865i	$0.282686\pi$
$984$	−11.2161	−0.357556
$985$	25.2762	0.805366
$986$	69.9831	2.22872
$987$	2.36939	0.0754186
$988$	10.8977	0.346702
$989$	29.6173	0.941777
$990$	8.40094	0.266999
$991$	−13.6096	−0.432322	−0.216161	−	0.976358i	$-0.569354\pi$
$991$	−13.6096	−0.432322	−0.216161	+	0.976358i	$0.569354\pi$
$992$	65.1417	2.06825
$993$	−0.847283	−0.0268877
$994$	−136.482	−4.32895
$995$	2.01654	0.0639285
$996$	6.12843	0.194187
$997$	41.1821	1.30425	0.652125	−	0.758111i	$-0.273878\pi$
$997$	41.1821	1.30425	0.652125	+	0.758111i	$0.273878\pi$
$998$	10.8144	0.342323
$999$	−1.65904	−0.0524897

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	209.2.a.c.1.5	✓	5
3.2	odd	2		1881.2.a.k.1.1		5
4.3	odd	2		3344.2.a.t.1.3		5
5.4	even	2		5225.2.a.h.1.1		5
11.10	odd	2		2299.2.a.n.1.1		5
19.18	odd	2		3971.2.a.h.1.1		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
209.2.a.c.1.5	✓	5	1.1	even	1	trivial
1881.2.a.k.1.1		5	3.2	odd	2
2299.2.a.n.1.1		5	11.10	odd	2
3344.2.a.t.1.3		5	4.3	odd	2
3971.2.a.h.1.1		5	19.18	odd	2
5225.2.a.h.1.1		5	5.4	even	2

Overview	Random
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Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 209 = 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	209.a (trivial)

\(f(q)\)	\(=\)	\(q+2.65432 q^{2} +0.121872 q^{3} +5.04540 q^{4} -1.06025 q^{5} +0.323487 q^{6} -3.36889 q^{7} +8.08346 q^{8} -2.98515 q^{9} -2.81425 q^{10} +1.00000 q^{11} +0.614893 q^{12} -2.15993 q^{13} -8.94209 q^{14} -0.129215 q^{15} +11.3653 q^{16} +3.67288 q^{17} -7.92353 q^{18} -1.00000 q^{19} -5.34940 q^{20} -0.410573 q^{21} +2.65432 q^{22} +3.15468 q^{23} +0.985147 q^{24} -3.87587 q^{25} -5.73313 q^{26} -0.729422 q^{27} -16.9974 q^{28} +7.17849 q^{29} -0.342978 q^{30} +4.65295 q^{31} +14.0001 q^{32} +0.121872 q^{33} +9.74900 q^{34} +3.57187 q^{35} -15.0613 q^{36} +2.27446 q^{37} -2.65432 q^{38} -0.263235 q^{39} -8.57050 q^{40} -11.3852 q^{41} -1.08979 q^{42} +9.38838 q^{43} +5.04540 q^{44} +3.16501 q^{45} +8.37352 q^{46} -5.77094 q^{47} +1.38511 q^{48} +4.34940 q^{49} -10.2878 q^{50} +0.447622 q^{51} -10.8977 q^{52} -5.65820 q^{53} -1.93612 q^{54} -1.06025 q^{55} -27.2322 q^{56} -0.121872 q^{57} +19.0540 q^{58} -13.7944 q^{59} -0.651942 q^{60} +6.98152 q^{61} +12.3504 q^{62} +10.0566 q^{63} +14.4301 q^{64} +2.29007 q^{65} +0.323487 q^{66} -4.81332 q^{67} +18.5312 q^{68} +0.384467 q^{69} +9.48087 q^{70} +15.2629 q^{71} -24.1303 q^{72} -8.08806 q^{73} +6.03713 q^{74} -0.472360 q^{75} -5.04540 q^{76} -3.36889 q^{77} -0.698709 q^{78} +13.4291 q^{79} -12.0500 q^{80} +8.86655 q^{81} -30.2199 q^{82} +9.96666 q^{83} -2.07150 q^{84} -3.89418 q^{85} +24.9197 q^{86} +0.874858 q^{87} +8.08346 q^{88} -4.61626 q^{89} +8.40094 q^{90} +7.27655 q^{91} +15.9166 q^{92} +0.567064 q^{93} -15.3179 q^{94} +1.06025 q^{95} +1.70622 q^{96} -4.09907 q^{97} +11.5447 q^{98} -2.98515 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 2 q^{2} + q^{3} + 6 q^{4} - 5 q^{5} - 2 q^{6} + 6 q^{7} + 6 q^{8} + 4 q^{9} + 12 q^{10} + 5 q^{11} + 6 q^{12} + 4 q^{13} - 14 q^{14} + 3 q^{15} + 8 q^{16} - 4 q^{17} - 20 q^{18} - 5 q^{19} - 8 q^{20}+ \cdots + 4 q^{99}+O(q^{100}) \) 5 * q + 2 * q^2 + q^3 + 6 * q^4 - 5 * q^5 - 2 * q^6 + 6 * q^7 + 6 * q^8 + 4 * q^9 + 12 * q^10 + 5 * q^11 + 6 * q^12 + 4 * q^13 - 14 * q^14 + 3 * q^15 + 8 * q^16 - 4 * q^17 - 20 * q^18 - 5 * q^19 - 8 * q^20 + 10 * q^21 + 2 * q^22 + 3 * q^23 - 14 * q^24 + 6 * q^25 - 6 * q^26 - 11 * q^27 - 10 * q^28 + 10 * q^29 + 6 * q^30 + 11 * q^31 + 14 * q^32 + q^33 - 4 * q^34 - 8 * q^35 - 26 * q^36 + q^37 - 2 * q^38 + 2 * q^39 - 16 * q^40 + 2 * q^41 - 16 * q^42 + 20 * q^43 + 6 * q^44 - 28 * q^45 - 4 * q^46 - 20 * q^47 + 4 * q^48 + 3 * q^49 - 32 * q^50 + 24 * q^51 + 6 * q^52 - 14 * q^53 + 16 * q^54 - 5 * q^55 - 38 * q^56 - q^57 - 6 * q^58 + 3 * q^59 - 40 * q^60 - 10 * q^61 - 6 * q^62 + 24 * q^63 - 2 * q^66 + 9 * q^67 + 24 * q^68 - 5 * q^69 + 50 * q^70 + 23 * q^71 - 12 * q^72 + 8 * q^74 - 18 * q^75 - 6 * q^76 + 6 * q^77 - 22 * q^78 + 44 * q^79 - 18 * q^80 + q^81 - 30 * q^82 - 14 * q^83 + 14 * q^84 - 12 * q^85 + 52 * q^86 + 28 * q^87 + 6 * q^88 - 27 * q^89 + 26 * q^90 + 24 * q^91 + 58 * q^92 - 27 * q^93 - 8 * q^94 + 5 * q^95 + 50 * q^96 + 15 * q^97 - 10 * q^98 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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