LMFDB - Embedded newform 1859.2.a.t.1.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1859,2,Mod(1,1859)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1859, 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("1859.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1859 = 11 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1859.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:	$14.8441897358$
Analytic rank:	$0$
Dimension:	$21$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
Character	$\chi$	$=$	1859.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.26490 q^{2} +3.17598 q^{3} +3.12978 q^{4} +2.32745 q^{5} +7.19329 q^{6} -4.39568 q^{7} +2.55884 q^{8} +7.08687 q^{9} +O(q^{10})$	\(q+2.26490 q^{2} +3.17598 q^{3} +3.12978 q^{4} +2.32745 q^{5} +7.19329 q^{6} -4.39568 q^{7} +2.55884 q^{8} +7.08687 q^{9} +5.27144 q^{10} +1.00000 q^{11} +9.94013 q^{12} -9.95579 q^{14} +7.39194 q^{15} -0.464040 q^{16} -3.60615 q^{17} +16.0511 q^{18} -2.34411 q^{19} +7.28440 q^{20} -13.9606 q^{21} +2.26490 q^{22} +2.46089 q^{23} +8.12683 q^{24} +0.417018 q^{25} +12.9798 q^{27} -13.7575 q^{28} +6.42191 q^{29} +16.7420 q^{30} -4.49503 q^{31} -6.16868 q^{32} +3.17598 q^{33} -8.16757 q^{34} -10.2307 q^{35} +22.1803 q^{36} +3.91017 q^{37} -5.30917 q^{38} +5.95557 q^{40} -9.00689 q^{41} -31.6194 q^{42} -0.179144 q^{43} +3.12978 q^{44} +16.4943 q^{45} +5.57368 q^{46} +0.0336641 q^{47} -1.47378 q^{48} +12.3220 q^{49} +0.944504 q^{50} -11.4531 q^{51} -7.80795 q^{53} +29.3980 q^{54} +2.32745 q^{55} -11.2478 q^{56} -7.44484 q^{57} +14.5450 q^{58} +7.69487 q^{59} +23.1351 q^{60} +3.02228 q^{61} -10.1808 q^{62} -31.1516 q^{63} -13.0434 q^{64} +7.19329 q^{66} -12.9678 q^{67} -11.2864 q^{68} +7.81575 q^{69} -23.1716 q^{70} +7.10607 q^{71} +18.1342 q^{72} -11.7832 q^{73} +8.85615 q^{74} +1.32444 q^{75} -7.33654 q^{76} -4.39568 q^{77} +2.77099 q^{79} -1.08003 q^{80} +19.9631 q^{81} -20.3997 q^{82} +9.48182 q^{83} -43.6936 q^{84} -8.39312 q^{85} -0.405744 q^{86} +20.3959 q^{87} +2.55884 q^{88} +11.5018 q^{89} +37.3580 q^{90} +7.70205 q^{92} -14.2761 q^{93} +0.0762459 q^{94} -5.45579 q^{95} -19.5916 q^{96} +5.83595 q^{97} +27.9082 q^{98} +7.08687 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 21 q + 6 q^{3} + 32 q^{4} + 7 q^{5} - 19 q^{6} + q^{7} - 3 q^{8} + 33 q^{9}+O(q^{10}) $ 21 * q + 6 * q^3 + 32 * q^4 + 7 * q^5 - 19 * q^6 + q^7 - 3 * q^8 + 33 * q^9	\( 21 q + 6 q^{3} + 32 q^{4} + 7 q^{5} - 19 q^{6} + q^{7} - 3 q^{8} + 33 q^{9} + 18 q^{10} + 21 q^{11} + 23 q^{12} + 20 q^{14} + 16 q^{15} + 50 q^{16} + 16 q^{17} + 3 q^{18} - 11 q^{19} + 24 q^{20} - 5 q^{21} - 9 q^{23} - 54 q^{24} + 36 q^{25} - 11 q^{28} + 28 q^{29} + 21 q^{30} + 15 q^{31} - 61 q^{32} + 6 q^{33} - 6 q^{34} - 3 q^{35} + 45 q^{36} - 12 q^{37} + q^{38} + 55 q^{40} - 4 q^{41} - 34 q^{42} + 17 q^{43} + 32 q^{44} + 9 q^{45} + 11 q^{46} + 36 q^{47} + 24 q^{48} + 72 q^{49} - 9 q^{50} + 2 q^{51} + 19 q^{53} + q^{54} + 7 q^{55} + 44 q^{56} - 4 q^{57} - 33 q^{58} + 54 q^{59} + 64 q^{60} + 98 q^{61} - 29 q^{62} - 81 q^{63} + 63 q^{64} - 19 q^{66} + 25 q^{67} + 4 q^{68} + 89 q^{69} + 65 q^{70} + 37 q^{71} + 55 q^{72} + 8 q^{73} - 11 q^{74} + 24 q^{75} + 13 q^{76} + q^{77} + 24 q^{79} + 26 q^{80} + 81 q^{81} + 26 q^{82} - 34 q^{83} - 103 q^{84} - 11 q^{85} + 30 q^{86} + 32 q^{87} - 3 q^{88} + 6 q^{89} + 47 q^{90} - 80 q^{92} + 41 q^{93} + 40 q^{94} + 20 q^{95} - 98 q^{96} - 5 q^{98} + 33 q^{99}+O(q^{100}) \) 21 * q + 6 * q^3 + 32 * q^4 + 7 * q^5 - 19 * q^6 + q^7 - 3 * q^8 + 33 * q^9 + 18 * q^10 + 21 * q^11 + 23 * q^12 + 20 * q^14 + 16 * q^15 + 50 * q^16 + 16 * q^17 + 3 * q^18 - 11 * q^19 + 24 * q^20 - 5 * q^21 - 9 * q^23 - 54 * q^24 + 36 * q^25 - 11 * q^28 + 28 * q^29 + 21 * q^30 + 15 * q^31 - 61 * q^32 + 6 * q^33 - 6 * q^34 - 3 * q^35 + 45 * q^36 - 12 * q^37 + q^38 + 55 * q^40 - 4 * q^41 - 34 * q^42 + 17 * q^43 + 32 * q^44 + 9 * q^45 + 11 * q^46 + 36 * q^47 + 24 * q^48 + 72 * q^49 - 9 * q^50 + 2 * q^51 + 19 * q^53 + q^54 + 7 * q^55 + 44 * q^56 - 4 * q^57 - 33 * q^58 + 54 * q^59 + 64 * q^60 + 98 * q^61 - 29 * q^62 - 81 * q^63 + 63 * q^64 - 19 * q^66 + 25 * q^67 + 4 * q^68 + 89 * q^69 + 65 * q^70 + 37 * q^71 + 55 * q^72 + 8 * q^73 - 11 * q^74 + 24 * q^75 + 13 * q^76 + q^77 + 24 * q^79 + 26 * q^80 + 81 * q^81 + 26 * q^82 - 34 * q^83 - 103 * q^84 - 11 * q^85 + 30 * q^86 + 32 * q^87 - 3 * q^88 + 6 * q^89 + 47 * q^90 - 80 * q^92 + 41 * q^93 + 40 * q^94 + 20 * q^95 - 98 * q^96 - 5 * q^98 + 33 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	2.26490	1.60153	0.800764	−	0.598980i	$-0.204427\pi$
$2$	2.26490	1.60153	0.800764	+	0.598980i	$0.204427\pi$
$3$	3.17598	1.83365	0.916827	−	0.399284i	$-0.130741\pi$
$3$	3.17598	1.83365	0.916827	+	0.399284i	$0.130741\pi$
$4$	3.12978	1.56489
$5$	2.32745	1.04087	0.520433	−	0.853902i	$-0.325770\pi$
$5$	2.32745	1.04087	0.520433	+	0.853902i	$0.325770\pi$
$6$	7.19329	2.93665
$7$	−4.39568	−1.66141	−0.830706	−	0.556711i	$-0.812063\pi$
$7$	−4.39568	−1.66141	−0.830706	+	0.556711i	$0.812063\pi$
$8$	2.55884	0.904686
$9$	7.08687	2.36229
$10$	5.27144	1.66698
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	9.94013	2.86947
$13$	0	0
$13$	0	0
$14$	−9.95579	−2.66080
$15$	7.39194	1.90859
$16$	−0.464040	−0.116010
$17$	−3.60615	−0.874619	−0.437309	−	0.899311i	$-0.644069\pi$
$17$	−3.60615	−0.874619	−0.437309	+	0.899311i	$0.644069\pi$
$18$	16.0511	3.78327
$19$	−2.34411	−0.537775	−0.268887	−	0.963172i	$-0.586656\pi$
$19$	−2.34411	−0.537775	−0.268887	+	0.963172i	$0.586656\pi$
$20$	7.28440	1.62884
$21$	−13.9606	−3.04646
$22$	2.26490	0.482879
$23$	2.46089	0.513131	0.256566	−	0.966527i	$-0.417409\pi$
$23$	2.46089	0.513131	0.256566	+	0.966527i	$0.417409\pi$
$24$	8.12683	1.65888
$25$	0.417018	0.0834036
$26$	0	0
$27$	12.9798	2.49797
$28$	−13.7575	−2.59993
$29$	6.42191	1.19252	0.596259	−	0.802792i	$-0.296653\pi$
$29$	6.42191	1.19252	0.596259	+	0.802792i	$0.296653\pi$
$30$	16.7420	3.05666
$31$	−4.49503	−0.807332	−0.403666	−	0.914906i	$-0.632264\pi$
$31$	−4.49503	−0.807332	−0.403666	+	0.914906i	$0.632264\pi$
$32$	−6.16868	−1.09048
$33$	3.17598	0.552868
$34$	−8.16757	−1.40073
$35$	−10.2307	−1.72931
$36$	22.1803	3.69672
$37$	3.91017	0.642828	0.321414	−	0.946939i	$-0.395842\pi$
$37$	3.91017	0.642828	0.321414	+	0.946939i	$0.395842\pi$
$38$	−5.30917	−0.861261
$39$	0	0
$40$	5.95557	0.941658
$41$	−9.00689	−1.40664	−0.703320	−	0.710873i	$-0.748300\pi$
$41$	−9.00689	−1.40664	−0.703320	+	0.710873i	$0.748300\pi$
$42$	−31.6194	−4.87898
$43$	−0.179144	−0.0273192	−0.0136596	−	0.999907i	$-0.504348\pi$
$43$	−0.179144	−0.0273192	−0.0136596	+	0.999907i	$0.504348\pi$
$44$	3.12978	0.471832
$45$	16.4943	2.45883
$46$	5.57368	0.821794
$47$	0.0336641	0.00491042	0.00245521	−	0.999997i	$-0.499218\pi$
$47$	0.0336641	0.00491042	0.00245521	+	0.999997i	$0.499218\pi$
$48$	−1.47378	−0.212722
$49$	12.3220	1.76029
$50$	0.944504	0.133573
$51$	−11.4531	−1.60375
$52$	0	0
$53$	−7.80795	−1.07250	−0.536252	−	0.844058i	$-0.680160\pi$
$53$	−7.80795	−1.07250	−0.536252	+	0.844058i	$0.680160\pi$
$54$	29.3980	4.00056
$55$	2.32745	0.313833
$56$	−11.2478	−1.50306
$57$	−7.44484	−0.986094
$58$	14.5450	1.90985
$59$	7.69487	1.00179	0.500893	−	0.865509i	$-0.333005\pi$
$59$	7.69487	1.00179	0.500893	+	0.865509i	$0.333005\pi$
$60$	23.1351	2.98673
$61$	3.02228	0.386963	0.193482	−	0.981104i	$-0.438022\pi$
$61$	3.02228	0.386963	0.193482	+	0.981104i	$0.438022\pi$
$62$	−10.1808	−1.29296
$63$	−31.1516	−3.92474
$64$	−13.0434	−1.63042
$65$	0	0
$66$	7.19329	0.885433
$67$	−12.9678	−1.58427	−0.792135	−	0.610346i	$-0.791031\pi$
$67$	−12.9678	−1.58427	−0.792135	+	0.610346i	$0.791031\pi$
$68$	−11.2864	−1.36868
$69$	7.81575	0.940906
$70$	−23.1716	−2.76954
$71$	7.10607	0.843335	0.421668	−	0.906750i	$-0.361445\pi$
$71$	7.10607	0.843335	0.421668	+	0.906750i	$0.361445\pi$
$72$	18.1342	2.13713
$73$	−11.7832	−1.37912	−0.689561	−	0.724228i	$-0.742196\pi$
$73$	−11.7832	−1.37912	−0.689561	+	0.724228i	$0.742196\pi$
$74$	8.85615	1.02951
$75$	1.32444	0.152933
$76$	−7.33654	−0.841559
$77$	−4.39568	−0.500935
$78$	0	0
$79$	2.77099	0.311761	0.155881	−	0.987776i	$-0.450179\pi$
$79$	2.77099	0.311761	0.155881	+	0.987776i	$0.450179\pi$
$80$	−1.08003	−0.120751
$81$	19.9631	2.21812
$82$	−20.3997	−2.25277
$83$	9.48182	1.04077	0.520383	−	0.853933i	$-0.325789\pi$
$83$	9.48182	1.04077	0.520383	+	0.853933i	$0.325789\pi$
$84$	−43.6936	−4.76737
$85$	−8.39312	−0.910362
$86$	−0.405744	−0.0437525
$87$	20.3959	2.18667
$88$	2.55884	0.272773
$89$	11.5018	1.21919	0.609595	−	0.792713i	$-0.291332\pi$
$89$	11.5018	1.21919	0.609595	+	0.792713i	$0.291332\pi$
$90$	37.3580	3.93788
$91$	0	0
$92$	7.70205	0.802994
$93$	−14.2761	−1.48037
$94$	0.0762459	0.00786417
$95$	−5.45579	−0.559752
$96$	−19.5916	−1.99956
$97$	5.83595	0.592551	0.296275	−	0.955103i	$-0.404255\pi$
$97$	5.83595	0.592551	0.296275	+	0.955103i	$0.404255\pi$
$98$	27.9082	2.81915
$99$	7.08687	0.712257
$100$	1.30517	0.130517
$101$	9.65478	0.960686	0.480343	−	0.877081i	$-0.340512\pi$
$101$	9.65478	0.960686	0.480343	+	0.877081i	$0.340512\pi$
$102$	−25.9400	−2.56845
$103$	8.58581	0.845985	0.422993	−	0.906133i	$-0.360980\pi$
$103$	8.58581	0.845985	0.422993	+	0.906133i	$0.360980\pi$
$104$	0	0
$105$	−32.4926	−3.17095
$106$	−17.6842	−1.71765
$107$	10.4959	1.01468	0.507340	−	0.861746i	$-0.330629\pi$
$107$	10.4959	1.01468	0.507340	+	0.861746i	$0.330629\pi$
$108$	40.6240	3.90904
$109$	4.20186	0.402465	0.201232	−	0.979544i	$-0.435505\pi$
$109$	4.20186	0.402465	0.201232	+	0.979544i	$0.435505\pi$
$110$	5.27144	0.502612
$111$	12.4186	1.17872
$112$	2.03977	0.192740
$113$	−16.4640	−1.54880	−0.774401	−	0.632695i	$-0.781949\pi$
$113$	−16.4640	−1.54880	−0.774401	+	0.632695i	$0.781949\pi$
$114$	−16.8618	−1.57926
$115$	5.72760	0.534101
$116$	20.0992	1.86616
$117$	0	0
$118$	17.4281	1.60439
$119$	15.8515	1.45310
$120$	18.9148	1.72668
$121$	1.00000	0.0909091
$122$	6.84516	0.619732
$123$	−28.6057	−2.57929
$124$	−14.0685	−1.26339
$125$	−10.6667	−0.954055
$126$	−70.5554	−6.28557
$127$	−16.6381	−1.47639	−0.738197	−	0.674585i	$-0.764323\pi$
$127$	−16.6381	−1.47639	−0.738197	+	0.674585i	$0.764323\pi$
$128$	−17.2046	−1.52069
$129$	−0.568958	−0.0500940
$130$	0	0
$131$	6.56292	0.573405	0.286702	−	0.958020i	$-0.407441\pi$
$131$	6.56292	0.573405	0.286702	+	0.958020i	$0.407441\pi$
$132$	9.94013	0.865177
$133$	10.3040	0.893466
$134$	−29.3708	−2.53725
$135$	30.2099	2.60005
$136$	−9.22755	−0.791256
$137$	1.55770	0.133084	0.0665418	−	0.997784i	$-0.478803\pi$
$137$	1.55770	0.133084	0.0665418	+	0.997784i	$0.478803\pi$
$138$	17.7019	1.50689
$139$	−8.10863	−0.687765	−0.343882	−	0.939013i	$-0.611742\pi$
$139$	−8.10863	−0.687765	−0.343882	+	0.939013i	$0.611742\pi$
$140$	−32.0199	−2.70618
$141$	0.106917	0.00900401
$142$	16.0945	1.35062
$143$	0	0
$144$	−3.28859	−0.274049
$145$	14.9467	1.24125
$146$	−26.6878	−2.20870
$147$	39.1346	3.22776
$148$	12.2380	1.00595
$149$	−5.48659	−0.449479	−0.224739	−	0.974419i	$-0.572153\pi$
$149$	−5.48659	−0.449479	−0.224739	+	0.974419i	$0.572153\pi$
$150$	2.99973	0.244927
$151$	−6.97757	−0.567826	−0.283913	−	0.958850i	$-0.591633\pi$
$151$	−6.97757	−0.567826	−0.283913	+	0.958850i	$0.591633\pi$
$152$	−5.99819	−0.486518
$153$	−25.5563	−2.06610
$154$	−9.95579	−0.802260
$155$	−10.4620	−0.840325
$156$	0	0
$157$	−5.03843	−0.402111	−0.201055	−	0.979580i	$-0.564437\pi$
$157$	−5.03843	−0.402111	−0.201055	+	0.979580i	$0.564437\pi$
$158$	6.27603	0.499294
$159$	−24.7979	−1.96660
$160$	−14.3573	−1.13504
$161$	−10.8173	−0.852523
$162$	45.2144	3.55238
$163$	−17.8890	−1.40118	−0.700589	−	0.713565i	$-0.747079\pi$
$163$	−17.8890	−1.40118	−0.700589	+	0.713565i	$0.747079\pi$
$164$	−28.1896	−2.20124
$165$	7.39194	0.575462
$166$	21.4754	1.66681
$167$	1.60051	0.123851	0.0619256	−	0.998081i	$-0.480276\pi$
$167$	1.60051	0.123851	0.0619256	+	0.998081i	$0.480276\pi$
$168$	−35.7230	−2.75609
$169$	0	0
$170$	−19.0096	−1.45797
$171$	−16.6124	−1.27038
$172$	−0.560681	−0.0427515
$173$	16.3925	1.24630	0.623148	−	0.782104i	$-0.285854\pi$
$173$	16.3925	1.24630	0.623148	+	0.782104i	$0.285854\pi$
$174$	46.1947	3.50201
$175$	−1.83308	−0.138568
$176$	−0.464040	−0.0349783
$177$	24.4388	1.83693
$178$	26.0505	1.95257
$179$	13.0693	0.976848	0.488424	−	0.872606i	$-0.337572\pi$
$179$	13.0693	0.976848	0.488424	+	0.872606i	$0.337572\pi$
$180$	51.6236	3.84779
$181$	7.53850	0.560332	0.280166	−	0.959952i	$-0.409610\pi$
$181$	7.53850	0.560332	0.280166	+	0.959952i	$0.409610\pi$
$182$	0	0
$183$	9.59870	0.709557
$184$	6.29703	0.464223
$185$	9.10072	0.669098
$186$	−32.3341	−2.37085
$187$	−3.60615	−0.263708
$188$	0.105361	0.00768426
$189$	−57.0552	−4.15015
$190$	−12.3568	−0.896458
$191$	−8.09206	−0.585521	−0.292760	−	0.956186i	$-0.594574\pi$
$191$	−8.09206	−0.585521	−0.292760	+	0.956186i	$0.594574\pi$
$192$	−41.4256	−2.98963
$193$	6.87618	0.494958	0.247479	−	0.968893i	$-0.420398\pi$
$193$	6.87618	0.494958	0.247479	+	0.968893i	$0.420398\pi$
$194$	13.2178	0.948986
$195$	0	0
$196$	38.5652	2.75466
$197$	7.03820	0.501451	0.250725	−	0.968058i	$-0.419331\pi$
$197$	7.03820	0.501451	0.250725	+	0.968058i	$0.419331\pi$
$198$	16.0511	1.14070
$199$	−21.2915	−1.50932	−0.754658	−	0.656119i	$-0.772197\pi$
$199$	−21.2915	−1.50932	−0.754658	+	0.656119i	$0.772197\pi$
$200$	1.06708	0.0754541
$201$	−41.1856	−2.90500
$202$	21.8671	1.53857
$203$	−28.2287	−1.98127
$204$	−35.8455	−2.50969
$205$	−20.9631	−1.46412
$206$	19.4460	1.35487
$207$	17.4400	1.21216
$208$	0	0
$209$	−2.34411	−0.162145
$210$	−73.5926	−5.07837
$211$	2.17049	0.149423	0.0747113	−	0.997205i	$-0.476196\pi$
$211$	2.17049	0.149423	0.0747113	+	0.997205i	$0.476196\pi$
$212$	−24.4372	−1.67835
$213$	22.5688	1.54639
$214$	23.7722	1.62504
$215$	−0.416949	−0.0284357
$216$	33.2133	2.25988
$217$	19.7587	1.34131
$218$	9.51679	0.644559
$219$	−37.4233	−2.52883
$220$	7.28440	0.491114
$221$	0	0
$222$	28.1270	1.88776
$223$	−20.0941	−1.34560	−0.672802	−	0.739823i	$-0.734909\pi$
$223$	−20.0941	−1.34560	−0.672802	+	0.739823i	$0.734909\pi$
$224$	27.1156	1.81174
$225$	2.95535	0.197023
$226$	−37.2893	−2.48045
$227$	−2.03771	−0.135248	−0.0676239	−	0.997711i	$-0.521542\pi$
$227$	−2.03771	−0.135248	−0.0676239	+	0.997711i	$0.521542\pi$
$228$	−23.3007	−1.54313
$229$	26.4780	1.74972	0.874858	−	0.484379i	$-0.160954\pi$
$229$	26.4780	1.74972	0.874858	+	0.484379i	$0.160954\pi$
$230$	12.9724	0.855378
$231$	−13.9606	−0.918541
$232$	16.4326	1.07886
$233$	13.2446	0.867684	0.433842	−	0.900989i	$-0.357158\pi$
$233$	13.2446	0.867684	0.433842	+	0.900989i	$0.357158\pi$
$234$	0	0
$235$	0.0783515	0.00511109
$236$	24.0832	1.56769
$237$	8.80063	0.571662
$238$	35.9020	2.32718
$239$	14.9348	0.966049	0.483024	−	0.875607i	$-0.339538\pi$
$239$	14.9348	0.966049	0.483024	+	0.875607i	$0.339538\pi$
$240$	−3.43015	−0.221415
$241$	21.9593	1.41452	0.707262	−	0.706952i	$-0.249930\pi$
$241$	21.9593	1.41452	0.707262	+	0.706952i	$0.249930\pi$
$242$	2.26490	0.145593
$243$	24.4629	1.56930
$244$	9.45906	0.605555
$245$	28.6789	1.83223
$246$	−64.7892	−4.13081
$247$	0	0
$248$	−11.5021	−0.730382
$249$	30.1141	1.90840
$250$	−24.1589	−1.52794
$251$	−6.67219	−0.421145	−0.210572	−	0.977578i	$-0.567533\pi$
$251$	−6.67219	−0.421145	−0.210572	+	0.977578i	$0.567533\pi$
$252$	−97.4977	−6.14178
$253$	2.46089	0.154715
$254$	−37.6837	−2.36449
$255$	−26.6564	−1.66929
$256$	−12.8800	−0.804999
$257$	14.5884	0.909997	0.454998	−	0.890492i	$-0.349640\pi$
$257$	14.5884	0.909997	0.454998	+	0.890492i	$0.349640\pi$
$258$	−1.28863	−0.0802269
$259$	−17.1879	−1.06800
$260$	0	0
$261$	45.5112	2.81707
$262$	14.8644	0.918323
$263$	22.5923	1.39310	0.696550	−	0.717508i	$-0.254717\pi$
$263$	22.5923	1.39310	0.696550	+	0.717508i	$0.254717\pi$
$264$	8.12683	0.500172
$265$	−18.1726	−1.11633
$266$	23.3374	1.43091
$267$	36.5296	2.23557
$268$	−40.5864	−2.47921
$269$	27.6973	1.68873	0.844367	−	0.535765i	$-0.179977\pi$
$269$	27.6973	1.68873	0.844367	+	0.535765i	$0.179977\pi$
$270$	68.4224	4.16405
$271$	−8.51223	−0.517081	−0.258541	−	0.966000i	$-0.583242\pi$
$271$	−8.51223	−0.517081	−0.258541	+	0.966000i	$0.583242\pi$
$272$	1.67340	0.101464
$273$	0	0
$274$	3.52804	0.213137
$275$	0.417018	0.0251471
$276$	24.4616	1.47241
$277$	22.0263	1.32343	0.661716	−	0.749754i	$-0.269828\pi$
$277$	22.0263	1.32343	0.661716	+	0.749754i	$0.269828\pi$
$278$	−18.3652	−1.10147
$279$	−31.8557	−1.90715
$280$	−26.1788	−1.56448
$281$	18.6880	1.11483	0.557415	−	0.830234i	$-0.311793\pi$
$281$	18.6880	1.11483	0.557415	+	0.830234i	$0.311793\pi$
$282$	0.242156	0.0144202
$283$	−12.2498	−0.728173	−0.364087	−	0.931365i	$-0.618619\pi$
$283$	−12.2498	−0.728173	−0.364087	+	0.931365i	$0.618619\pi$
$284$	22.2404	1.31973
$285$	−17.3275	−1.02639
$286$	0	0
$287$	39.5914	2.33701
$288$	−43.7166	−2.57603
$289$	−3.99571	−0.235042
$290$	33.8527	1.98790
$291$	18.5349	1.08653
$292$	−36.8789	−2.15817
$293$	−17.7766	−1.03852	−0.519259	−	0.854617i	$-0.673792\pi$
$293$	−17.7766	−1.03852	−0.519259	+	0.854617i	$0.673792\pi$
$294$	88.6359	5.16935
$295$	17.9094	1.04273
$296$	10.0055	0.581558
$297$	12.9798	0.753165
$298$	−12.4266	−0.719853
$299$	0	0
$300$	4.14521	0.239324
$301$	0.787460	0.0453885
$302$	−15.8035	−0.909389
$303$	30.6634	1.76157
$304$	1.08776	0.0623873
$305$	7.03420	0.402777
$306$	−57.8825	−3.30892
$307$	2.57203	0.146793	0.0733967	−	0.997303i	$-0.476616\pi$
$307$	2.57203	0.146793	0.0733967	+	0.997303i	$0.476616\pi$
$308$	−13.7575	−0.783907
$309$	27.2684	1.55124
$310$	−23.6953	−1.34580
$311$	9.54000	0.540964	0.270482	−	0.962725i	$-0.412817\pi$
$311$	9.54000	0.540964	0.270482	+	0.962725i	$0.412817\pi$
$312$	0	0
$313$	−31.8648	−1.80110	−0.900552	−	0.434748i	$-0.856837\pi$
$313$	−31.8648	−1.80110	−0.900552	+	0.434748i	$0.856837\pi$
$314$	−11.4116	−0.643991
$315$	−72.5038	−4.08513
$316$	8.67260	0.487872
$317$	32.1914	1.80805	0.904024	−	0.427482i	$-0.140599\pi$
$317$	32.1914	1.80805	0.904024	+	0.427482i	$0.140599\pi$
$318$	−56.1649	−3.14957
$319$	6.42191	0.359558
$320$	−30.3578	−1.69705
$321$	33.3349	1.86057
$322$	−24.5001	−1.36534
$323$	8.45319	0.470348
$324$	62.4800	3.47111
$325$	0	0
$326$	−40.5169	−2.24402
$327$	13.3450	0.737982
$328$	−23.0472	−1.27257
$329$	−0.147977	−0.00815823
$330$	16.7420	0.921617
$331$	−2.42102	−0.133072	−0.0665358	−	0.997784i	$-0.521195\pi$
$331$	−2.42102	−0.133072	−0.0665358	+	0.997784i	$0.521195\pi$
$332$	29.6760	1.62868
$333$	27.7109	1.51855
$334$	3.62500	0.198351
$335$	−30.1819	−1.64901
$336$	6.47828	0.353419
$337$	−31.1343	−1.69599	−0.847996	−	0.530003i	$-0.822191\pi$
$337$	−31.1343	−1.69599	−0.847996	+	0.530003i	$0.822191\pi$
$338$	0	0
$339$	−52.2894	−2.83997
$340$	−26.2686	−1.42462
$341$	−4.49503	−0.243420
$342$	−37.6254	−2.03455
$343$	−23.3940	−1.26316
$344$	−0.458401	−0.0247153
$345$	18.1908	0.979357
$346$	37.1273	1.99598
$347$	−21.5915	−1.15909	−0.579546	−	0.814939i	$-0.696770\pi$
$347$	−21.5915	−1.15909	−0.579546	+	0.814939i	$0.696770\pi$
$348$	63.8346	3.42189
$349$	7.51782	0.402420	0.201210	−	0.979548i	$-0.435513\pi$
$349$	7.51782	0.402420	0.201210	+	0.979548i	$0.435513\pi$
$350$	−4.15174	−0.221920
$351$	0	0
$352$	−6.16868	−0.328792
$353$	32.6049	1.73538	0.867692	−	0.497102i	$-0.165603\pi$
$353$	32.6049	1.73538	0.867692	+	0.497102i	$0.165603\pi$
$354$	55.3514	2.94190
$355$	16.5390	0.877800
$356$	35.9982	1.90790
$357$	50.3440	2.66449
$358$	29.6008	1.56445
$359$	−36.7060	−1.93727	−0.968633	−	0.248495i	$-0.920064\pi$
$359$	−36.7060	−1.93727	−0.968633	+	0.248495i	$0.920064\pi$
$360$	42.2063	2.22447
$361$	−13.5052	−0.710798
$362$	17.0740	0.897388
$363$	3.17598	0.166696
$364$	0	0
$365$	−27.4248	−1.43548
$366$	21.7401	1.13637
$367$	10.5024	0.548219	0.274109	−	0.961699i	$-0.411617\pi$
$367$	10.5024	0.548219	0.274109	+	0.961699i	$0.411617\pi$
$368$	−1.14195	−0.0595283
$369$	−63.8306	−3.32289
$370$	20.6122	1.07158
$371$	34.3213	1.78187
$372$	−44.6812	−2.31661
$373$	11.2568	0.582853	0.291427	−	0.956593i	$-0.405870\pi$
$373$	11.2568	0.582853	0.291427	+	0.956593i	$0.405870\pi$
$374$	−8.16757	−0.422335
$375$	−33.8771	−1.74941
$376$	0.0861411	0.00444239
$377$	0	0
$378$	−129.224	−6.64658
$379$	−30.9736	−1.59101	−0.795505	−	0.605948i	$-0.792794\pi$
$379$	−30.9736	−1.59101	−0.795505	+	0.605948i	$0.792794\pi$
$380$	−17.0754	−0.875950
$381$	−52.8424	−2.70720
$382$	−18.3277	−0.937727
$383$	−1.64383	−0.0839956	−0.0419978	−	0.999118i	$-0.513372\pi$
$383$	−1.64383	−0.0839956	−0.0419978	+	0.999118i	$0.513372\pi$
$384$	−54.6415	−2.78841
$385$	−10.2307	−0.521406
$386$	15.5739	0.792689
$387$	−1.26957	−0.0645359
$388$	18.2652	0.927277
$389$	−10.5028	−0.532513	−0.266257	−	0.963902i	$-0.585787\pi$
$389$	−10.5028	−0.532513	−0.266257	+	0.963902i	$0.585787\pi$
$390$	0	0
$391$	−8.87434	−0.448794
$392$	31.5301	1.59251
$393$	20.8437	1.05143
$394$	15.9408	0.803087
$395$	6.44934	0.324502
$396$	22.1803	1.11460
$397$	2.37693	0.119295	0.0596474	−	0.998220i	$-0.481002\pi$
$397$	2.37693	0.119295	0.0596474	+	0.998220i	$0.481002\pi$
$398$	−48.2232	−2.41721
$399$	32.7252	1.63831
$400$	−0.193513	−0.00967564
$401$	−10.5726	−0.527971	−0.263985	−	0.964527i	$-0.585037\pi$
$401$	−10.5726	−0.527971	−0.263985	+	0.964527i	$0.585037\pi$
$402$	−93.2812	−4.65244
$403$	0	0
$404$	30.2173	1.50337
$405$	46.4630	2.30877
$406$	−63.9352	−3.17305
$407$	3.91017	0.193820
$408$	−29.3065	−1.45089
$409$	32.7342	1.61860	0.809301	−	0.587395i	$-0.199846\pi$
$409$	32.7342	1.61860	0.809301	+	0.587395i	$0.199846\pi$
$410$	−47.4793	−2.34484
$411$	4.94724	0.244029
$412$	26.8717	1.32387
$413$	−33.8242	−1.66438
$414$	39.4999	1.94131
$415$	22.0685	1.08330
$416$	0	0
$417$	−25.7529	−1.26112
$418$	−5.30917	−0.259680
$419$	10.3533	0.505793	0.252896	−	0.967493i	$-0.418617\pi$
$419$	10.3533	0.505793	0.252896	+	0.967493i	$0.418617\pi$
$420$	−101.695	−4.96219
$421$	−9.96868	−0.485844	−0.242922	−	0.970046i	$-0.578106\pi$
$421$	−9.96868	−0.485844	−0.242922	+	0.970046i	$0.578106\pi$
$422$	4.91594	0.239304
$423$	0.238573	0.0115998
$424$	−19.9793	−0.970280
$425$	−1.50383	−0.0729463
$426$	51.1160	2.47658
$427$	−13.2850	−0.642905
$428$	32.8499	1.58786
$429$	0	0
$430$	−0.944347	−0.0455405
$431$	−7.20363	−0.346987	−0.173493	−	0.984835i	$-0.555506\pi$
$431$	−7.20363	−0.346987	−0.173493	+	0.984835i	$0.555506\pi$
$432$	−6.02315	−0.289789
$433$	−38.2837	−1.83980	−0.919899	−	0.392156i	$-0.871729\pi$
$433$	−38.2837	−1.83980	−0.919899	+	0.392156i	$0.871729\pi$
$434$	44.7516	2.14815
$435$	47.4704	2.27603
$436$	13.1509	0.629813
$437$	−5.76859	−0.275949
$438$	−84.7601	−4.04999
$439$	5.38316	0.256924	0.128462	−	0.991714i	$-0.458996\pi$
$439$	5.38316	0.256924	0.128462	+	0.991714i	$0.458996\pi$
$440$	5.95557	0.283921
$441$	87.3246	4.15831
$442$	0	0
$443$	20.3401	0.966389	0.483194	−	0.875513i	$-0.339476\pi$
$443$	20.3401	0.966389	0.483194	+	0.875513i	$0.339476\pi$
$444$	38.8676	1.84457
$445$	26.7699	1.26902
$446$	−45.5113	−2.15502
$447$	−17.4253	−0.824189
$448$	57.3346	2.70880
$449$	−4.25666	−0.200884	−0.100442	−	0.994943i	$-0.532026\pi$
$449$	−4.25666	−0.200884	−0.100442	+	0.994943i	$0.532026\pi$
$450$	6.69358	0.315538
$451$	−9.00689	−0.424118
$452$	−51.5287	−2.42371
$453$	−22.1606	−1.04120
$454$	−4.61522	−0.216603
$455$	0	0
$456$	−19.0502	−0.892105
$457$	−6.00959	−0.281117	−0.140558	−	0.990072i	$-0.544890\pi$
$457$	−6.00959	−0.281117	−0.140558	+	0.990072i	$0.544890\pi$
$458$	59.9701	2.80222
$459$	−46.8071	−2.18477
$460$	17.9261	0.835810
$461$	9.81702	0.457224	0.228612	−	0.973518i	$-0.426581\pi$
$461$	9.81702	0.457224	0.228612	+	0.973518i	$0.426581\pi$
$462$	−31.6194	−1.47107
$463$	24.9919	1.16147	0.580736	−	0.814092i	$-0.302765\pi$
$463$	24.9919	1.16147	0.580736	+	0.814092i	$0.302765\pi$
$464$	−2.98002	−0.138344
$465$	−33.2270	−1.54087
$466$	29.9978	1.38962
$467$	−13.4570	−0.622716	−0.311358	−	0.950293i	$-0.600784\pi$
$467$	−13.4570	−0.622716	−0.311358	+	0.950293i	$0.600784\pi$
$468$	0	0
$469$	57.0024	2.63213
$470$	0.177459	0.00818555
$471$	−16.0020	−0.737332
$472$	19.6899	0.906303
$473$	−0.179144	−0.00823705
$474$	19.9326	0.915532
$475$	−0.977534	−0.0448524
$476$	49.6116	2.27395
$477$	−55.3339	−2.53357
$478$	33.8257	1.54715
$479$	−9.57851	−0.437653	−0.218827	−	0.975764i	$-0.570223\pi$
$479$	−9.57851	−0.437653	−0.218827	+	0.975764i	$0.570223\pi$
$480$	−45.5985	−2.08128
$481$	0	0
$482$	49.7357	2.26540
$483$	−34.3556	−1.56323
$484$	3.12978	0.142263
$485$	13.5829	0.616766
$486$	55.4061	2.51327
$487$	2.21089	0.100185	0.0500925	−	0.998745i	$-0.484048\pi$
$487$	2.21089	0.100185	0.0500925	+	0.998745i	$0.484048\pi$
$488$	7.73352	0.350080
$489$	−56.8153	−2.56928
$490$	64.9549	2.93436
$491$	20.7032	0.934323	0.467162	−	0.884172i	$-0.345277\pi$
$491$	20.7032	0.934323	0.467162	+	0.884172i	$0.345277\pi$
$492$	−89.5296	−4.03631
$493$	−23.1584	−1.04300
$494$	0	0
$495$	16.4943	0.741365
$496$	2.08587	0.0936585
$497$	−31.2360	−1.40113
$498$	68.2055	3.05636
$499$	−15.0934	−0.675672	−0.337836	−	0.941205i	$-0.609695\pi$
$499$	−15.0934	−0.675672	−0.337836	+	0.941205i	$0.609695\pi$
$500$	−33.3843	−1.49299
$501$	5.08319	0.227100
$502$	−15.1119	−0.674475
$503$	−21.4709	−0.957338	−0.478669	−	0.877995i	$-0.658881\pi$
$503$	−21.4709	−0.957338	−0.478669	+	0.877995i	$0.658881\pi$
$504$	−79.7120	−3.55065
$505$	22.4710	0.999946
$506$	5.57368	0.247780
$507$	0	0
$508$	−52.0737	−2.31039
$509$	20.2395	0.897100	0.448550	−	0.893758i	$-0.351941\pi$
$509$	20.2395	0.897100	0.448550	+	0.893758i	$0.351941\pi$
$510$	−60.3741	−2.67341
$511$	51.7953	2.29129
$512$	5.23732	0.231459
$513$	−30.4261	−1.34334
$514$	33.0412	1.45738
$515$	19.9830	0.880558
$516$	−1.78071	−0.0783916
$517$	0.0336641	0.00148055
$518$	−38.9288	−1.71043
$519$	52.0621	2.28527
$520$	0	0
$521$	−21.9430	−0.961341	−0.480670	−	0.876901i	$-0.659607\pi$
$521$	−21.9430	−0.961341	−0.480670	+	0.876901i	$0.659607\pi$
$522$	103.078	4.51162
$523$	3.87346	0.169374	0.0846872	−	0.996408i	$-0.473011\pi$
$523$	3.87346	0.169374	0.0846872	+	0.996408i	$0.473011\pi$
$524$	20.5405	0.897315
$525$	−5.82183	−0.254085
$526$	51.1693	2.23109
$527$	16.2097	0.706108
$528$	−1.47378	−0.0641381
$529$	−16.9440	−0.736696
$530$	−41.1592	−1.78784
$531$	54.5325	2.36651
$532$	32.2491	1.39818
$533$	0	0
$534$	82.7359	3.58033
$535$	24.4287	1.05615
$536$	−33.1825	−1.43327
$537$	41.5080	1.79120
$538$	62.7317	2.70455
$539$	12.3220	0.530748
$540$	94.5502	4.06879
$541$	39.4975	1.69813	0.849066	−	0.528288i	$-0.177166\pi$
$541$	39.4975	1.69813	0.849066	+	0.528288i	$0.177166\pi$
$542$	−19.2794	−0.828120
$543$	23.9422	1.02746
$544$	22.2452	0.953754
$545$	9.77961	0.418912
$546$	0	0
$547$	−11.9320	−0.510176	−0.255088	−	0.966918i	$-0.582104\pi$
$547$	−11.9320	−0.510176	−0.255088	+	0.966918i	$0.582104\pi$
$548$	4.87527	0.208261
$549$	21.4185	0.914119
$550$	0.944504	0.0402738
$551$	−15.0536	−0.641307
$552$	19.9992	0.851224
$553$	−12.1804	−0.517964
$554$	49.8874	2.11951
$555$	28.9037	1.22690
$556$	−25.3782	−1.07628
$557$	−16.2002	−0.686423	−0.343212	−	0.939258i	$-0.611515\pi$
$557$	−16.2002	−0.686423	−0.343212	+	0.939258i	$0.611515\pi$
$558$	−72.1500	−3.05435
$559$	0	0
$560$	4.74747	0.200617
$561$	−11.4531	−0.483548
$562$	42.3264	1.78543
$563$	−34.2081	−1.44170	−0.720850	−	0.693091i	$-0.756248\pi$
$563$	−34.2081	−1.44170	−0.720850	+	0.693091i	$0.756248\pi$
$564$	0.334626	0.0140903
$565$	−38.3191	−1.61210
$566$	−27.7445	−1.16619
$567$	−87.7514	−3.68521
$568$	18.1833	0.762954
$569$	4.35080	0.182395	0.0911975	−	0.995833i	$-0.470931\pi$
$569$	4.35080	0.182395	0.0911975	+	0.995833i	$0.470931\pi$
$570$	−39.2451	−1.64379
$571$	−8.32394	−0.348346	−0.174173	−	0.984715i	$-0.555725\pi$
$571$	−8.32394	−0.348346	−0.174173	+	0.984715i	$0.555725\pi$
$572$	0	0
$573$	−25.7002	−1.07364
$574$	89.6707	3.74278
$575$	1.02624	0.0427970
$576$	−92.4367	−3.85153
$577$	18.6210	0.775202	0.387601	−	0.921827i	$-0.373304\pi$
$577$	18.6210	0.775202	0.387601	+	0.921827i	$0.373304\pi$
$578$	−9.04989	−0.376426
$579$	21.8386	0.907583
$580$	46.7798	1.94242
$581$	−41.6791	−1.72914
$582$	41.9797	1.74011
$583$	−7.80795	−0.323372
$584$	−30.1514	−1.24767
$585$	0	0
$586$	−40.2622	−1.66321
$587$	7.39069	0.305046	0.152523	−	0.988300i	$-0.451260\pi$
$587$	7.39069	0.305046	0.152523	+	0.988300i	$0.451260\pi$
$588$	122.483	5.05110
$589$	10.5368	0.434163
$590$	40.5631	1.66996
$591$	22.3532	0.919488
$592$	−1.81447	−0.0745744
$593$	38.9506	1.59951	0.799754	−	0.600328i	$-0.204963\pi$
$593$	38.9506	1.59951	0.799754	+	0.600328i	$0.204963\pi$
$594$	29.3980	1.20621
$595$	36.8935	1.51249
$596$	−17.1718	−0.703385
$597$	−67.6215	−2.76756
$598$	0	0
$599$	13.6775	0.558847	0.279423	−	0.960168i	$-0.409857\pi$
$599$	13.6775	0.558847	0.279423	+	0.960168i	$0.409857\pi$
$600$	3.38903	0.138357
$601$	−39.2674	−1.60175	−0.800876	−	0.598831i	$-0.795632\pi$
$601$	−39.2674	−1.60175	−0.800876	+	0.598831i	$0.795632\pi$
$602$	1.78352	0.0726909
$603$	−91.9012	−3.74250
$604$	−21.8382	−0.888585
$605$	2.32745	0.0946242
$606$	69.4496	2.82120
$607$	−22.8474	−0.927345	−0.463673	−	0.886007i	$-0.653469\pi$
$607$	−22.8474	−0.927345	−0.463673	+	0.886007i	$0.653469\pi$
$608$	14.4601	0.586433
$609$	−89.6538	−3.63296
$610$	15.9318	0.645058
$611$	0	0
$612$	−79.9855	−3.23322
$613$	−15.2795	−0.617132	−0.308566	−	0.951203i	$-0.599849\pi$
$613$	−15.2795	−0.617132	−0.308566	+	0.951203i	$0.599849\pi$
$614$	5.82539	0.235094
$615$	−66.5784	−2.68470
$616$	−11.2478	−0.453189
$617$	27.1029	1.09112	0.545561	−	0.838071i	$-0.316316\pi$
$617$	27.1029	1.09112	0.545561	+	0.838071i	$0.316316\pi$
$618$	61.7602	2.48436
$619$	−21.4251	−0.861146	−0.430573	−	0.902556i	$-0.641688\pi$
$619$	−21.4251	−0.861146	−0.430573	+	0.902556i	$0.641688\pi$
$620$	−32.7436	−1.31502
$621$	31.9419	1.28179
$622$	21.6072	0.866369
$623$	−50.5584	−2.02558
$624$	0	0
$625$	−26.9112	−1.07645
$626$	−72.1706	−2.88452
$627$	−7.44484	−0.297318
$628$	−15.7692	−0.629259
$629$	−14.1006	−0.562229
$630$	−164.214	−6.54244
$631$	−26.5023	−1.05504	−0.527521	−	0.849542i	$-0.676878\pi$
$631$	−26.5023	−1.05504	−0.527521	+	0.849542i	$0.676878\pi$
$632$	7.09052	0.282046
$633$	6.89344	0.273989
$634$	72.9103	2.89564
$635$	−38.7244	−1.53673
$636$	−77.6120	−3.07752
$637$	0	0
$638$	14.5450	0.575842
$639$	50.3598	1.99220
$640$	−40.0428	−1.58283
$641$	−1.18681	−0.0468761	−0.0234380	−	0.999725i	$-0.507461\pi$
$641$	−1.18681	−0.0468761	−0.0234380	+	0.999725i	$0.507461\pi$
$642$	75.5002	2.97976
$643$	−35.0462	−1.38209	−0.691043	−	0.722813i	$-0.742849\pi$
$643$	−35.0462	−1.38209	−0.691043	+	0.722813i	$0.742849\pi$
$644$	−33.8558	−1.33410
$645$	−1.32422	−0.0521412
$646$	19.1456	0.753275
$647$	24.5856	0.966559	0.483280	−	0.875466i	$-0.339445\pi$
$647$	24.5856	0.966559	0.483280	+	0.875466i	$0.339445\pi$
$648$	51.0823	2.00670
$649$	7.69487	0.302050
$650$	0	0
$651$	62.7534	2.45950
$652$	−55.9888	−2.19269
$653$	5.01763	0.196355	0.0981774	−	0.995169i	$-0.468699\pi$
$653$	5.01763	0.196355	0.0981774	+	0.995169i	$0.468699\pi$
$654$	30.2252	1.18190
$655$	15.2749	0.596838
$656$	4.17956	0.163184
$657$	−83.5061	−3.25788
$658$	−0.335153	−0.0130656
$659$	−44.2947	−1.72547	−0.862737	−	0.505652i	$-0.831252\pi$
$659$	−44.2947	−1.72547	−0.862737	+	0.505652i	$0.831252\pi$
$660$	23.1351	0.900534
$661$	39.2602	1.52704	0.763522	−	0.645782i	$-0.223468\pi$
$661$	39.2602	1.52704	0.763522	+	0.645782i	$0.223468\pi$
$662$	−5.48338	−0.213118
$663$	0	0
$664$	24.2625	0.941566
$665$	23.9819	0.929979
$666$	62.7624	2.43199
$667$	15.8036	0.611919
$668$	5.00924	0.193813
$669$	−63.8187	−2.46737
$670$	−68.3591	−2.64094
$671$	3.02228	0.116674
$672$	86.1186	3.32210
$673$	−30.5790	−1.17873	−0.589367	−	0.807865i	$-0.700623\pi$
$673$	−30.5790	−1.17873	−0.589367	+	0.807865i	$0.700623\pi$
$674$	−70.5160	−2.71618
$675$	5.41282	0.208339
$676$	0	0
$677$	6.59361	0.253413	0.126706	−	0.991940i	$-0.459559\pi$
$677$	6.59361	0.253413	0.126706	+	0.991940i	$0.459559\pi$
$678$	−118.430	−4.54829
$679$	−25.6530	−0.984471
$680$	−21.4766	−0.823592
$681$	−6.47174	−0.247998
$682$	−10.1808	−0.389843
$683$	−15.4414	−0.590850	−0.295425	−	0.955366i	$-0.595461\pi$
$683$	−15.4414	−0.590850	−0.295425	+	0.955366i	$0.595461\pi$
$684$	−51.9931	−1.98800
$685$	3.62547	0.138522
$686$	−52.9850	−2.02298
$687$	84.0937	3.20838
$688$	0.0831300	0.00316930
$689$	0	0
$690$	41.2003	1.56847
$691$	−10.8955	−0.414484	−0.207242	−	0.978290i	$-0.566449\pi$
$691$	−10.8955	−0.414484	−0.207242	+	0.978290i	$0.566449\pi$
$692$	51.3048	1.95031
$693$	−31.1516	−1.18335
$694$	−48.9026	−1.85632
$695$	−18.8724	−0.715872
$696$	52.1898	1.97825
$697$	32.4802	1.23027
$698$	17.0271	0.644486
$699$	42.0647	1.59103
$700$	−5.73713	−0.216843
$701$	6.30826	0.238260	0.119130	−	0.992879i	$-0.461990\pi$
$701$	6.30826	0.238260	0.119130	+	0.992879i	$0.461990\pi$
$702$	0	0
$703$	−9.16586	−0.345697
$704$	−13.0434	−0.491591
$705$	0.248843	0.00937197
$706$	73.8469	2.77926
$707$	−42.4393	−1.59610
$708$	76.4880	2.87459
$709$	26.2553	0.986038	0.493019	−	0.870019i	$-0.335893\pi$
$709$	26.2553	0.986038	0.493019	+	0.870019i	$0.335893\pi$
$710$	37.4592	1.40582
$711$	19.6377	0.736470
$712$	29.4313	1.10299
$713$	−11.0618	−0.414267
$714$	114.024	4.26725
$715$	0	0
$716$	40.9041	1.52866
$717$	47.4325	1.77140
$718$	−83.1354	−3.10259
$719$	37.9637	1.41581	0.707903	−	0.706309i	$-0.249641\pi$
$719$	37.9637	1.41581	0.707903	+	0.706309i	$0.249641\pi$
$720$	−7.65402	−0.285249
$721$	−37.7405	−1.40553
$722$	−30.5879	−1.13836
$723$	69.7424	2.59375
$724$	23.5938	0.876858
$725$	2.67805	0.0994603
$726$	7.19329	0.266968
$727$	−42.4503	−1.57439	−0.787197	−	0.616701i	$-0.788469\pi$
$727$	−42.4503	−1.57439	−0.787197	+	0.616701i	$0.788469\pi$
$728$	0	0
$729$	17.8046	0.659431
$730$	−62.1146	−2.29896
$731$	0.646019	0.0238939
$732$	30.0418	1.11038
$733$	28.7508	1.06193	0.530967	−	0.847393i	$-0.321829\pi$
$733$	28.7508	1.06193	0.530967	+	0.847393i	$0.321829\pi$
$734$	23.7868	0.877987
$735$	91.0837	3.35967
$736$	−15.1805	−0.559559
$737$	−12.9678	−0.477676
$738$	−144.570	−5.32170
$739$	15.4432	0.568086	0.284043	−	0.958812i	$-0.408324\pi$
$739$	15.4432	0.568086	0.284043	+	0.958812i	$0.408324\pi$
$740$	28.4832	1.04706
$741$	0	0
$742$	77.7343	2.85372
$743$	36.2998	1.33171	0.665855	−	0.746081i	$-0.268067\pi$
$743$	36.2998	1.33171	0.665855	+	0.746081i	$0.268067\pi$
$744$	−36.5304	−1.33927
$745$	−12.7698	−0.467848
$746$	25.4955	0.933455
$747$	67.1964	2.45859
$748$	−11.2864	−0.412673
$749$	−46.1368	−1.68580
$750$	−76.7283	−2.80172
$751$	−2.15250	−0.0785458	−0.0392729	−	0.999229i	$-0.512504\pi$
$751$	−2.15250	−0.0785458	−0.0392729	+	0.999229i	$0.512504\pi$
$752$	−0.0156215	−0.000569657 0
$753$	−21.1908	−0.772234
$754$	0	0
$755$	−16.2399	−0.591031
$756$	−178.570	−6.49453
$757$	14.7876	0.537465	0.268733	−	0.963215i	$-0.413395\pi$
$757$	14.7876	0.537465	0.268733	+	0.963215i	$0.413395\pi$
$758$	−70.1522	−2.54804
$759$	7.81575	0.283694
$760$	−13.9605	−0.506400
$761$	−11.4983	−0.416813	−0.208406	−	0.978042i	$-0.566828\pi$
$761$	−11.4983	−0.416813	−0.208406	+	0.978042i	$0.566828\pi$
$762$	−119.683	−4.33565
$763$	−18.4700	−0.668660
$764$	−25.3264	−0.916275
$765$	−59.4809	−2.15054
$766$	−3.72310	−0.134521
$767$	0	0
$768$	−40.9066	−1.47609
$769$	0.165953	0.00598443	0.00299221	−	0.999996i	$-0.499048\pi$
$769$	0.165953	0.00598443	0.00299221	+	0.999996i	$0.499048\pi$
$770$	−23.1716	−0.835046
$771$	46.3324	1.66862
$772$	21.5209	0.774555
$773$	29.7127	1.06869	0.534346	−	0.845266i	$-0.320558\pi$
$773$	29.7127	1.06869	0.534346	+	0.845266i	$0.320558\pi$
$774$	−2.87545	−0.103356
$775$	−1.87451	−0.0673343
$776$	14.9333	0.536073
$777$	−54.5884	−1.95835
$778$	−23.7878	−0.852834
$779$	21.1131	0.756456
$780$	0	0
$781$	7.10607	0.254275
$782$	−20.0995	−0.718757
$783$	83.3552	2.97887
$784$	−5.71791	−0.204211
$785$	−11.7267	−0.418544
$786$	47.2090	1.68389
$787$	21.6909	0.773198	0.386599	−	0.922248i	$-0.373650\pi$
$787$	21.6909	0.773198	0.386599	+	0.922248i	$0.373650\pi$
$788$	22.0280	0.784715
$789$	71.7527	2.55446
$790$	14.6071	0.519698
$791$	72.3705	2.57320
$792$	18.1342	0.644369
$793$	0	0
$794$	5.38352	0.191054
$795$	−57.7159	−2.04697
$796$	−66.6377	−2.36191
$797$	−34.8232	−1.23350	−0.616750	−	0.787159i	$-0.711551\pi$
$797$	−34.8232	−1.23350	−0.616750	+	0.787159i	$0.711551\pi$
$798$	74.1193	2.62379
$799$	−0.121398	−0.00429474
$800$	−2.57245	−0.0909499
$801$	81.5119	2.88008
$802$	−23.9459	−0.845560
$803$	−11.7832	−0.415821
$804$	−128.902	−4.54601
$805$	−25.1767	−0.887363
$806$	0	0
$807$	87.9662	3.09656
$808$	24.7050	0.869120
$809$	−30.2774	−1.06450	−0.532248	−	0.846588i	$-0.678653\pi$
$809$	−30.2774	−1.06450	−0.532248	+	0.846588i	$0.678653\pi$
$810$	105.234	3.69755
$811$	29.7788	1.04567	0.522837	−	0.852433i	$-0.324874\pi$
$811$	29.7788	1.04567	0.522837	+	0.852433i	$0.324874\pi$
$812$	−88.3496	−3.10046
$813$	−27.0347	−0.948148
$814$	8.85615	0.310408
$815$	−41.6358	−1.45844
$816$	5.31467	0.186051
$817$	0.419933	0.0146916
$818$	74.1397	2.59223
$819$	0	0
$820$	−65.6098	−2.29119
$821$	−7.67232	−0.267766	−0.133883	−	0.990997i	$-0.542745\pi$
$821$	−7.67232	−0.267766	−0.133883	+	0.990997i	$0.542745\pi$
$822$	11.2050	0.390819
$823$	41.5169	1.44719	0.723595	−	0.690225i	$-0.242489\pi$
$823$	41.5169	1.44719	0.723595	+	0.690225i	$0.242489\pi$
$824$	21.9697	0.765351
$825$	1.32444	0.0461111
$826$	−76.6085	−2.66555
$827$	7.05778	0.245423	0.122711	−	0.992442i	$-0.460841\pi$
$827$	7.05778	0.245423	0.122711	+	0.992442i	$0.460841\pi$
$828$	54.5834	1.89690
$829$	43.2766	1.50306	0.751529	−	0.659701i	$-0.229317\pi$
$829$	43.2766	1.50306	0.751529	+	0.659701i	$0.229317\pi$
$830$	49.9829	1.73493
$831$	69.9552	2.42672
$832$	0	0
$833$	−44.4351	−1.53958
$834$	−58.3277	−2.01972
$835$	3.72510	0.128913
$836$	−7.33654	−0.253739
$837$	−58.3447	−2.01669
$838$	23.4492	0.810041
$839$	34.4289	1.18862	0.594308	−	0.804238i	$-0.297426\pi$
$839$	34.4289	1.18862	0.594308	+	0.804238i	$0.297426\pi$
$840$	−83.1434	−2.86872
$841$	12.2409	0.422102
$842$	−22.5781	−0.778092
$843$	59.3526	2.04421
$844$	6.79315	0.233830
$845$	0	0
$846$	0.540345	0.0185774
$847$	−4.39568	−0.151037
$848$	3.62320	0.124421
$849$	−38.9051	−1.33522
$850$	−3.40602	−0.116826
$851$	9.62250	0.329855
$852$	70.6352	2.41992
$853$	−41.3342	−1.41526	−0.707628	−	0.706585i	$-0.750235\pi$
$853$	−41.3342	−1.41526	−0.707628	+	0.706585i	$0.750235\pi$
$854$	−30.0892	−1.02963
$855$	−38.6644	−1.32230
$856$	26.8574	0.917966
$857$	−40.7028	−1.39038	−0.695191	−	0.718825i	$-0.744680\pi$
$857$	−40.7028	−1.39038	−0.695191	+	0.718825i	$0.744680\pi$
$858$	0	0
$859$	6.36084	0.217029	0.108515	−	0.994095i	$-0.465391\pi$
$859$	6.36084	0.217029	0.108515	+	0.994095i	$0.465391\pi$
$860$	−1.30496	−0.0444987
$861$	125.742	4.28527
$862$	−16.3155	−0.555709
$863$	−40.9662	−1.39451	−0.697253	−	0.716825i	$-0.745595\pi$
$863$	−40.9662	−1.39451	−0.697253	+	0.716825i	$0.745595\pi$
$864$	−80.0684	−2.72398
$865$	38.1526	1.29723
$866$	−86.7088	−2.94649
$867$	−12.6903	−0.430985
$868$	61.8405	2.09900
$869$	2.77099	0.0939995
$870$	107.516	3.64512
$871$	0	0
$872$	10.7519	0.364104
$873$	41.3586	1.39978
$874$	−13.0653	−0.441940
$875$	46.8872	1.58508
$876$	−117.127	−3.95734
$877$	−48.1858	−1.62712	−0.813560	−	0.581481i	$-0.802473\pi$
$877$	−48.1858	−1.62712	−0.813560	+	0.581481i	$0.802473\pi$
$878$	12.1923	0.411471
$879$	−56.4581	−1.90428
$880$	−1.08003	−0.0364078
$881$	41.1749	1.38722	0.693609	−	0.720351i	$-0.256019\pi$
$881$	41.1749	1.38722	0.693609	+	0.720351i	$0.256019\pi$
$882$	197.782	6.65965
$883$	−34.8551	−1.17297	−0.586484	−	0.809961i	$-0.699488\pi$
$883$	−34.8551	−1.17297	−0.586484	+	0.809961i	$0.699488\pi$
$884$	0	0
$885$	56.8800	1.91200
$886$	46.0684	1.54770
$887$	−23.7296	−0.796763	−0.398382	−	0.917220i	$-0.630428\pi$
$887$	−23.7296	−0.796763	−0.398382	+	0.917220i	$0.630428\pi$
$888$	31.7773	1.06638
$889$	73.1359	2.45290
$890$	60.6312	2.03236
$891$	19.9631	0.668788
$892$	−62.8903	−2.10572
$893$	−0.0789123	−0.00264070
$894$	−39.4666	−1.31996
$895$	30.4182	1.01677
$896$	75.6260	2.52649
$897$	0	0
$898$	−9.64090	−0.321721
$899$	−28.8667	−0.962758
$900$	9.24959	0.308320
$901$	28.1566	0.938033
$902$	−20.3997	−0.679236
$903$	2.50096	0.0832268
$904$	−42.1287	−1.40118
$905$	17.5455	0.583231
$906$	−50.1916	−1.66751
$907$	−41.3010	−1.37138	−0.685689	−	0.727895i	$-0.740499\pi$
$907$	−41.3010	−1.37138	−0.685689	+	0.727895i	$0.740499\pi$
$908$	−6.37759	−0.211648
$909$	68.4221	2.26942
$910$	0	0
$911$	−30.7960	−1.02032	−0.510159	−	0.860080i	$-0.670413\pi$
$911$	−30.7960	−1.02032	−0.510159	+	0.860080i	$0.670413\pi$
$912$	3.45470	0.114397
$913$	9.48182	0.313803
$914$	−13.6111	−0.450216
$915$	22.3405	0.738554
$916$	82.8704	2.73811
$917$	−28.8485	−0.952662
$918$	−106.014	−3.49897
$919$	19.7956	0.652998	0.326499	−	0.945198i	$-0.394131\pi$
$919$	19.7956	0.652998	0.326499	+	0.945198i	$0.394131\pi$
$920$	14.6560	0.483194
$921$	8.16871	0.269168
$922$	22.2346	0.732257
$923$	0	0
$924$	−43.6936	−1.43742
$925$	1.63061	0.0536141
$926$	56.6042	1.86013
$927$	60.8465	1.99846
$928$	−39.6147	−1.30042
$929$	−39.9249	−1.30989	−0.654947	−	0.755675i	$-0.727309\pi$
$929$	−39.9249	−1.30989	−0.654947	+	0.755675i	$0.727309\pi$
$930$	−75.2559	−2.46774
$931$	−28.8842	−0.946640
$932$	41.4527	1.35783
$933$	30.2989	0.991941
$934$	−30.4788	−0.997297
$935$	−8.39312	−0.274484
$936$	0	0
$937$	−6.42120	−0.209771	−0.104886	−	0.994484i	$-0.533448\pi$
$937$	−6.42120	−0.209771	−0.104886	+	0.994484i	$0.533448\pi$
$938$	129.105	4.21542
$939$	−101.202	−3.30260
$940$	0.245223	0.00799829
$941$	−33.8003	−1.10186	−0.550928	−	0.834553i	$-0.685726\pi$
$941$	−33.8003	−1.10186	−0.550928	+	0.834553i	$0.685726\pi$
$942$	−36.2429	−1.18086
$943$	−22.1650	−0.721791
$944$	−3.57073	−0.116217
$945$	−132.793	−4.31976
$946$	−0.405744	−0.0131919
$947$	21.7598	0.707100	0.353550	−	0.935416i	$-0.384974\pi$
$947$	21.7598	0.707100	0.353550	+	0.935416i	$0.384974\pi$
$948$	27.5440	0.894588
$949$	0	0
$950$	−2.21402	−0.0718323
$951$	102.239	3.31533
$952$	40.5614	1.31460
$953$	46.8789	1.51856	0.759278	−	0.650766i	$-0.225552\pi$
$953$	46.8789	1.51856	0.759278	+	0.650766i	$0.225552\pi$
$954$	−125.326	−4.05757
$955$	−18.8338	−0.609449
$956$	46.7425	1.51176
$957$	20.3959	0.659305
$958$	−21.6944	−0.700914
$959$	−6.84717	−0.221107
$960$	−96.4158	−3.11181
$961$	−10.7947	−0.348215
$962$	0	0
$963$	74.3832	2.39697
$964$	68.7278	2.21357
$965$	16.0040	0.515186
$966$	−77.8120	−2.50356
$967$	60.6688	1.95098	0.975489	−	0.220048i	$-0.0706213\pi$
$967$	60.6688	1.95098	0.975489	+	0.220048i	$0.0706213\pi$
$968$	2.55884	0.0822442
$969$	26.8472	0.862456
$970$	30.7639	0.987768
$971$	−21.4566	−0.688575	−0.344287	−	0.938864i	$-0.611879\pi$
$971$	−21.4566	−0.688575	−0.344287	+	0.938864i	$0.611879\pi$
$972$	76.5636	2.45578
$973$	35.6430	1.14266
$974$	5.00745	0.160449
$975$	0	0
$976$	−1.40246	−0.0448916
$977$	−44.1140	−1.41133	−0.705667	−	0.708544i	$-0.749352\pi$
$977$	−44.1140	−1.41133	−0.705667	+	0.708544i	$0.749352\pi$
$978$	−128.681	−4.11477
$979$	11.5018	0.367600
$980$	89.7586	2.86723
$981$	29.7780	0.950738
$982$	46.8907	1.49634
$983$	−3.52430	−0.112408	−0.0562038	−	0.998419i	$-0.517900\pi$
$983$	−3.52430	−0.112408	−0.0562038	+	0.998419i	$0.517900\pi$
$984$	−73.1975	−2.33345
$985$	16.3810	0.521944
$986$	−52.4514	−1.67039
$987$	−0.469972	−0.0149594
$988$	0	0
$989$	−0.440854	−0.0140183
$990$	37.3580	1.18732
$991$	25.9551	0.824491	0.412246	−	0.911073i	$-0.364745\pi$
$991$	25.9551	0.824491	0.412246	+	0.911073i	$0.364745\pi$
$992$	27.7284	0.880379
$993$	−7.68913	−0.244007
$994$	−70.7465	−2.24394
$995$	−49.5549	−1.57100
$996$	94.2505	2.98644
$997$	−9.76069	−0.309124	−0.154562	−	0.987983i	$-0.549397\pi$
$997$	−9.76069	−0.309124	−0.154562	+	0.987983i	$0.549397\pi$
$998$	−34.1850	−1.08211
$999$	50.7533	1.60576

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1859.2.a.t.1.19	yes	21
13.12	even	2		1859.2.a.s.1.3	✓	21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1859.2.a.s.1.3	✓	21	13.12	even	2
1859.2.a.t.1.19	yes	21	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:	\( N \)	\(=\)	\( 1859 = 11 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1859.a (trivial)

\(f(q)\)	\(=\)	\(q+2.26490 q^{2} +3.17598 q^{3} +3.12978 q^{4} +2.32745 q^{5} +7.19329 q^{6} -4.39568 q^{7} +2.55884 q^{8} +7.08687 q^{9} +O(q^{10})\)	\(q+2.26490 q^{2} +3.17598 q^{3} +3.12978 q^{4} +2.32745 q^{5} +7.19329 q^{6} -4.39568 q^{7} +2.55884 q^{8} +7.08687 q^{9} +5.27144 q^{10} +1.00000 q^{11} +9.94013 q^{12} -9.95579 q^{14} +7.39194 q^{15} -0.464040 q^{16} -3.60615 q^{17} +16.0511 q^{18} -2.34411 q^{19} +7.28440 q^{20} -13.9606 q^{21} +2.26490 q^{22} +2.46089 q^{23} +8.12683 q^{24} +0.417018 q^{25} +12.9798 q^{27} -13.7575 q^{28} +6.42191 q^{29} +16.7420 q^{30} -4.49503 q^{31} -6.16868 q^{32} +3.17598 q^{33} -8.16757 q^{34} -10.2307 q^{35} +22.1803 q^{36} +3.91017 q^{37} -5.30917 q^{38} +5.95557 q^{40} -9.00689 q^{41} -31.6194 q^{42} -0.179144 q^{43} +3.12978 q^{44} +16.4943 q^{45} +5.57368 q^{46} +0.0336641 q^{47} -1.47378 q^{48} +12.3220 q^{49} +0.944504 q^{50} -11.4531 q^{51} -7.80795 q^{53} +29.3980 q^{54} +2.32745 q^{55} -11.2478 q^{56} -7.44484 q^{57} +14.5450 q^{58} +7.69487 q^{59} +23.1351 q^{60} +3.02228 q^{61} -10.1808 q^{62} -31.1516 q^{63} -13.0434 q^{64} +7.19329 q^{66} -12.9678 q^{67} -11.2864 q^{68} +7.81575 q^{69} -23.1716 q^{70} +7.10607 q^{71} +18.1342 q^{72} -11.7832 q^{73} +8.85615 q^{74} +1.32444 q^{75} -7.33654 q^{76} -4.39568 q^{77} +2.77099 q^{79} -1.08003 q^{80} +19.9631 q^{81} -20.3997 q^{82} +9.48182 q^{83} -43.6936 q^{84} -8.39312 q^{85} -0.405744 q^{86} +20.3959 q^{87} +2.55884 q^{88} +11.5018 q^{89} +37.3580 q^{90} +7.70205 q^{92} -14.2761 q^{93} +0.0762459 q^{94} -5.45579 q^{95} -19.5916 q^{96} +5.83595 q^{97} +27.9082 q^{98} +7.08687 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q + 6 q^{3} + 32 q^{4} + 7 q^{5} - 19 q^{6} + q^{7} - 3 q^{8} + 33 q^{9}+O(q^{10}) \) 21 * q + 6 * q^3 + 32 * q^4 + 7 * q^5 - 19 * q^6 + q^7 - 3 * q^8 + 33 * q^9	\( 21 q + 6 q^{3} + 32 q^{4} + 7 q^{5} - 19 q^{6} + q^{7} - 3 q^{8} + 33 q^{9} + 18 q^{10} + 21 q^{11} + 23 q^{12} + 20 q^{14} + 16 q^{15} + 50 q^{16} + 16 q^{17} + 3 q^{18} - 11 q^{19} + 24 q^{20} - 5 q^{21} - 9 q^{23} - 54 q^{24} + 36 q^{25} - 11 q^{28} + 28 q^{29} + 21 q^{30} + 15 q^{31} - 61 q^{32} + 6 q^{33} - 6 q^{34} - 3 q^{35} + 45 q^{36} - 12 q^{37} + q^{38} + 55 q^{40} - 4 q^{41} - 34 q^{42} + 17 q^{43} + 32 q^{44} + 9 q^{45} + 11 q^{46} + 36 q^{47} + 24 q^{48} + 72 q^{49} - 9 q^{50} + 2 q^{51} + 19 q^{53} + q^{54} + 7 q^{55} + 44 q^{56} - 4 q^{57} - 33 q^{58} + 54 q^{59} + 64 q^{60} + 98 q^{61} - 29 q^{62} - 81 q^{63} + 63 q^{64} - 19 q^{66} + 25 q^{67} + 4 q^{68} + 89 q^{69} + 65 q^{70} + 37 q^{71} + 55 q^{72} + 8 q^{73} - 11 q^{74} + 24 q^{75} + 13 q^{76} + q^{77} + 24 q^{79} + 26 q^{80} + 81 q^{81} + 26 q^{82} - 34 q^{83} - 103 q^{84} - 11 q^{85} + 30 q^{86} + 32 q^{87} - 3 q^{88} + 6 q^{89} + 47 q^{90} - 80 q^{92} + 41 q^{93} + 40 q^{94} + 20 q^{95} - 98 q^{96} - 5 q^{98} + 33 q^{99}+O(q^{100}) \) 21 * q + 6 * q^3 + 32 * q^4 + 7 * q^5 - 19 * q^6 + q^7 - 3 * q^8 + 33 * q^9 + 18 * q^10 + 21 * q^11 + 23 * q^12 + 20 * q^14 + 16 * q^15 + 50 * q^16 + 16 * q^17 + 3 * q^18 - 11 * q^19 + 24 * q^20 - 5 * q^21 - 9 * q^23 - 54 * q^24 + 36 * q^25 - 11 * q^28 + 28 * q^29 + 21 * q^30 + 15 * q^31 - 61 * q^32 + 6 * q^33 - 6 * q^34 - 3 * q^35 + 45 * q^36 - 12 * q^37 + q^38 + 55 * q^40 - 4 * q^41 - 34 * q^42 + 17 * q^43 + 32 * q^44 + 9 * q^45 + 11 * q^46 + 36 * q^47 + 24 * q^48 + 72 * q^49 - 9 * q^50 + 2 * q^51 + 19 * q^53 + q^54 + 7 * q^55 + 44 * q^56 - 4 * q^57 - 33 * q^58 + 54 * q^59 + 64 * q^60 + 98 * q^61 - 29 * q^62 - 81 * q^63 + 63 * q^64 - 19 * q^66 + 25 * q^67 + 4 * q^68 + 89 * q^69 + 65 * q^70 + 37 * q^71 + 55 * q^72 + 8 * q^73 - 11 * q^74 + 24 * q^75 + 13 * q^76 + q^77 + 24 * q^79 + 26 * q^80 + 81 * q^81 + 26 * q^82 - 34 * q^83 - 103 * q^84 - 11 * q^85 + 30 * q^86 + 32 * q^87 - 3 * q^88 + 6 * q^89 + 47 * q^90 - 80 * q^92 + 41 * q^93 + 40 * q^94 + 20 * q^95 - 98 * q^96 - 5 * q^98 + 33 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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