LMFDB - Embedded newform 1805.2.a.r.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1805,2,Mod(1,1805)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1805, 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("1805.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1805 = 5 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1805.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:	$14.4129975648$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.6.5822000.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 8x^{4} + 5x^{3} + 14x^{2} + x - 1 $ x^6 - x^5 - 8x^4 + 5x^3 + 14*x^2 + x - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$2.03780$ of defining polynomial
Character	$\chi$	$=$	1805.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.65583 q^{2} -2.41205 q^{3} +5.05344 q^{4} -1.00000 q^{5} +6.40599 q^{6} -2.14656 q^{7} -8.10942 q^{8} +2.81796 q^{9} +O(q^{10})$	\(q-2.65583 q^{2} -2.41205 q^{3} +5.05344 q^{4} -1.00000 q^{5} +6.40599 q^{6} -2.14656 q^{7} -8.10942 q^{8} +2.81796 q^{9} +2.65583 q^{10} +4.94842 q^{11} -12.1891 q^{12} +4.54101 q^{13} +5.70089 q^{14} +2.41205 q^{15} +11.4304 q^{16} -0.0358478 q^{17} -7.48403 q^{18} -5.05344 q^{20} +5.17759 q^{21} -13.1422 q^{22} +0.737666 q^{23} +19.5603 q^{24} +1.00000 q^{25} -12.0602 q^{26} +0.439083 q^{27} -10.8475 q^{28} -7.02799 q^{29} -6.40599 q^{30} +7.77708 q^{31} -14.1383 q^{32} -11.9358 q^{33} +0.0952057 q^{34} +2.14656 q^{35} +14.2404 q^{36} +3.53458 q^{37} -10.9531 q^{39} +8.10942 q^{40} +2.88713 q^{41} -13.7508 q^{42} +4.28764 q^{43} +25.0066 q^{44} -2.81796 q^{45} -1.95912 q^{46} -1.66850 q^{47} -27.5706 q^{48} -2.39229 q^{49} -2.65583 q^{50} +0.0864665 q^{51} +22.9477 q^{52} +6.01759 q^{53} -1.16613 q^{54} -4.94842 q^{55} +17.4073 q^{56} +18.6652 q^{58} -8.55188 q^{59} +12.1891 q^{60} -10.6991 q^{61} -20.6546 q^{62} -6.04892 q^{63} +14.6882 q^{64} -4.54101 q^{65} +31.6995 q^{66} +0.166172 q^{67} -0.181155 q^{68} -1.77928 q^{69} -5.70089 q^{70} -11.9307 q^{71} -22.8520 q^{72} +4.62873 q^{73} -9.38726 q^{74} -2.41205 q^{75} -10.6221 q^{77} +29.0896 q^{78} +12.8775 q^{79} -11.4304 q^{80} -9.51297 q^{81} -7.66773 q^{82} -14.4149 q^{83} +26.1647 q^{84} +0.0358478 q^{85} -11.3873 q^{86} +16.9518 q^{87} -40.1288 q^{88} -3.15934 q^{89} +7.48403 q^{90} -9.74754 q^{91} +3.72775 q^{92} -18.7587 q^{93} +4.43125 q^{94} +34.1022 q^{96} +3.28561 q^{97} +6.35352 q^{98} +13.9445 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 2 q^{2} + 4 q^{3} + 8 q^{4} - 6 q^{5} + 8 q^{6} + 7 q^{7} + 10 q^{9}+O(q^{10}) $ 6 * q + 2 * q^2 + 4 * q^3 + 8 * q^4 - 6 * q^5 + 8 * q^6 + 7 * q^7 + 10 * q^9	\( 6 q + 2 q^{2} + 4 q^{3} + 8 q^{4} - 6 q^{5} + 8 q^{6} + 7 q^{7} + 10 q^{9} - 2 q^{10} + 15 q^{11} - 20 q^{12} + 6 q^{13} + 20 q^{14} - 4 q^{15} + 20 q^{16} + 5 q^{17} - 8 q^{18} - 8 q^{20} + 7 q^{21} + 14 q^{22} + 18 q^{24} + 6 q^{25} - 22 q^{26} + 28 q^{27} + 10 q^{28} - 20 q^{29} - 8 q^{30} + 12 q^{31} - 8 q^{32} + q^{33} - 7 q^{35} - 14 q^{36} + 20 q^{37} + 16 q^{39} + 8 q^{41} - 30 q^{42} + 27 q^{43} + 46 q^{44} - 10 q^{45} + 16 q^{46} - 8 q^{47} - 24 q^{48} + 11 q^{49} + 2 q^{50} - 11 q^{51} + 4 q^{52} + 19 q^{53} + 30 q^{54} - 15 q^{55} + 62 q^{56} + 20 q^{58} - 41 q^{59} + 20 q^{60} + 6 q^{61} - 30 q^{62} - 18 q^{63} + 48 q^{64} - 6 q^{65} + 46 q^{66} - 15 q^{67} - 14 q^{68} - 10 q^{69} - 20 q^{70} + 2 q^{71} - 68 q^{72} + 8 q^{73} + 2 q^{74} + 4 q^{75} + 21 q^{77} + 46 q^{78} + 18 q^{79} - 20 q^{80} + 50 q^{81} - 18 q^{82} - 10 q^{83} + 4 q^{84} - 5 q^{85} - 10 q^{86} - 14 q^{87} - 52 q^{88} + 17 q^{89} + 8 q^{90} - 23 q^{91} + 28 q^{92} + 10 q^{93} - 28 q^{94} + 26 q^{96} - 4 q^{97} + 50 q^{98} + 58 q^{99}+O(q^{100}) \) 6 * q + 2 * q^2 + 4 * q^3 + 8 * q^4 - 6 * q^5 + 8 * q^6 + 7 * q^7 + 10 * q^9 - 2 * q^10 + 15 * q^11 - 20 * q^12 + 6 * q^13 + 20 * q^14 - 4 * q^15 + 20 * q^16 + 5 * q^17 - 8 * q^18 - 8 * q^20 + 7 * q^21 + 14 * q^22 + 18 * q^24 + 6 * q^25 - 22 * q^26 + 28 * q^27 + 10 * q^28 - 20 * q^29 - 8 * q^30 + 12 * q^31 - 8 * q^32 + q^33 - 7 * q^35 - 14 * q^36 + 20 * q^37 + 16 * q^39 + 8 * q^41 - 30 * q^42 + 27 * q^43 + 46 * q^44 - 10 * q^45 + 16 * q^46 - 8 * q^47 - 24 * q^48 + 11 * q^49 + 2 * q^50 - 11 * q^51 + 4 * q^52 + 19 * q^53 + 30 * q^54 - 15 * q^55 + 62 * q^56 + 20 * q^58 - 41 * q^59 + 20 * q^60 + 6 * q^61 - 30 * q^62 - 18 * q^63 + 48 * q^64 - 6 * q^65 + 46 * q^66 - 15 * q^67 - 14 * q^68 - 10 * q^69 - 20 * q^70 + 2 * q^71 - 68 * q^72 + 8 * q^73 + 2 * q^74 + 4 * q^75 + 21 * q^77 + 46 * q^78 + 18 * q^79 - 20 * q^80 + 50 * q^81 - 18 * q^82 - 10 * q^83 + 4 * q^84 - 5 * q^85 - 10 * q^86 - 14 * q^87 - 52 * q^88 + 17 * q^89 + 8 * q^90 - 23 * q^91 + 28 * q^92 + 10 * q^93 - 28 * q^94 + 26 * q^96 - 4 * q^97 + 50 * q^98 + 58 * 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 $

$2$	−2.65583	−1.87796	−0.938978	−	0.343977i	$-0.888226\pi$
$2$	−2.65583	−1.87796	−0.938978	+	0.343977i	$0.888226\pi$
$3$	−2.41205	−1.39259	−0.696297	−	0.717753i	$-0.745171\pi$
$3$	−2.41205	−1.39259	−0.696297	+	0.717753i	$0.745171\pi$
$4$	5.05344	2.52672
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	6.40599	2.61523
$7$	−2.14656	−0.811322	−0.405661	−	0.914024i	$-0.632959\pi$
$7$	−2.14656	−0.811322	−0.405661	+	0.914024i	$0.632959\pi$
$8$	−8.10942	−2.86711
$9$	2.81796	0.939321
$10$	2.65583	0.839848
$11$	4.94842	1.49201	0.746003	−	0.665942i	$-0.231970\pi$
$11$	4.94842	1.49201	0.746003	+	0.665942i	$0.231970\pi$
$12$	−12.1891	−3.51870
$13$	4.54101	1.25945	0.629725	−	0.776818i	$-0.283168\pi$
$13$	4.54101	1.25945	0.629725	+	0.776818i	$0.283168\pi$
$14$	5.70089	1.52363
$15$	2.41205	0.622787
$16$	11.4304	2.85759
$17$	−0.0358478	−0.00869436	−0.00434718	−	0.999991i	$-0.501384\pi$
$17$	−0.0358478	−0.00869436	−0.00434718	+	0.999991i	$0.501384\pi$
$18$	−7.48403	−1.76400
$19$	0	0
$19$	0	0
$20$	−5.05344	−1.12998
$21$	5.17759	1.12984
$22$	−13.1422	−2.80192
$23$	0.737666	0.153814	0.0769070	−	0.997038i	$-0.475496\pi$
$23$	0.737666	0.153814	0.0769070	+	0.997038i	$0.475496\pi$
$24$	19.5603	3.99273
$25$	1.00000	0.200000
$26$	−12.0602	−2.36519
$27$	0.439083	0.0845015
$28$	−10.8475	−2.04998
$29$	−7.02799	−1.30507	−0.652533	−	0.757761i	$-0.726293\pi$
$29$	−7.02799	−1.30507	−0.652533	+	0.757761i	$0.726293\pi$
$30$	−6.40599	−1.16957
$31$	7.77708	1.39680	0.698402	−	0.715705i	$-0.253895\pi$
$31$	7.77708	1.39680	0.698402	+	0.715705i	$0.253895\pi$
$32$	−14.1383	−2.49932
$33$	−11.9358	−2.07776
$34$	0.0952057	0.0163276
$35$	2.14656	0.362834
$36$	14.2404	2.37340
$37$	3.53458	0.581082	0.290541	−	0.956863i	$-0.406165\pi$
$37$	3.53458	0.581082	0.290541	+	0.956863i	$0.406165\pi$
$38$	0	0
$39$	−10.9531	−1.75390
$40$	8.10942	1.28221
$41$	2.88713	0.450894	0.225447	−	0.974255i	$-0.427616\pi$
$41$	2.88713	0.450894	0.225447	+	0.974255i	$0.427616\pi$
$42$	−13.7508	−2.12180
$43$	4.28764	0.653859	0.326930	−	0.945049i	$-0.393986\pi$
$43$	4.28764	0.653859	0.326930	+	0.945049i	$0.393986\pi$
$44$	25.0066	3.76988
$45$	−2.81796	−0.420077
$46$	−1.95912	−0.288856
$47$	−1.66850	−0.243376	−0.121688	−	0.992568i	$-0.538831\pi$
$47$	−1.66850	−0.243376	−0.121688	+	0.992568i	$0.538831\pi$
$48$	−27.5706	−3.97947
$49$	−2.39229	−0.341756
$50$	−2.65583	−0.375591
$51$	0.0864665	0.0121077
$52$	22.9477	3.18228
$53$	6.01759	0.826580	0.413290	−	0.910600i	$-0.364380\pi$
$53$	6.01759	0.826580	0.413290	+	0.910600i	$0.364380\pi$
$54$	−1.16613	−0.158690
$55$	−4.94842	−0.667245
$56$	17.4073	2.32615
$57$	0	0
$58$	18.6652	2.45086
$59$	−8.55188	−1.11336	−0.556680	−	0.830727i	$-0.687925\pi$
$59$	−8.55188	−1.11336	−0.556680	+	0.830727i	$0.687925\pi$
$60$	12.1891	1.57361
$61$	−10.6991	−1.36988	−0.684940	−	0.728600i	$-0.740171\pi$
$61$	−10.6991	−1.36988	−0.684940	+	0.728600i	$0.740171\pi$
$62$	−20.6546	−2.62314
$63$	−6.04892	−0.762092
$64$	14.6882	1.83602
$65$	−4.54101	−0.563243
$66$	31.6995	3.90194
$67$	0.166172	0.0203011	0.0101505	−	0.999948i	$-0.496769\pi$
$67$	0.166172	0.0203011	0.0101505	+	0.999948i	$0.496769\pi$
$68$	−0.181155	−0.0219682
$69$	−1.77928	−0.214201
$70$	−5.70089	−0.681387
$71$	−11.9307	−1.41591	−0.707955	−	0.706257i	$-0.750382\pi$
$71$	−11.9307	−1.41591	−0.707955	+	0.706257i	$0.750382\pi$
$72$	−22.8520	−2.69314
$73$	4.62873	0.541751	0.270876	−	0.962614i	$-0.412687\pi$
$73$	4.62873	0.541751	0.270876	+	0.962614i	$0.412687\pi$
$74$	−9.38726	−1.09125
$75$	−2.41205	−0.278519
$76$	0	0
$77$	−10.6221	−1.21050
$78$	29.0896	3.29375
$79$	12.8775	1.44884	0.724418	−	0.689361i	$-0.242109\pi$
$79$	12.8775	1.44884	0.724418	+	0.689361i	$0.242109\pi$
$80$	−11.4304	−1.27795
$81$	−9.51297	−1.05700
$82$	−7.66773	−0.846759
$83$	−14.4149	−1.58224	−0.791122	−	0.611658i	$-0.790503\pi$
$83$	−14.4149	−1.58224	−0.791122	+	0.611658i	$0.790503\pi$
$84$	26.1647	2.85480
$85$	0.0358478	0.00388824
$86$	−11.3873	−1.22792
$87$	16.9518	1.81743
$88$	−40.1288	−4.27775
$89$	−3.15934	−0.334889	−0.167445	−	0.985882i	$-0.553552\pi$
$89$	−3.15934	−0.334889	−0.167445	+	0.985882i	$0.553552\pi$
$90$	7.48403	0.788886
$91$	−9.74754	−1.02182
$92$	3.72775	0.388645
$93$	−18.7587	−1.94518
$94$	4.43125	0.457049
$95$	0	0
$96$	34.1022	3.48054
$97$	3.28561	0.333603	0.166801	−	0.985990i	$-0.446656\pi$
$97$	3.28561	0.333603	0.166801	+	0.985990i	$0.446656\pi$
$98$	6.35352	0.641803
$99$	13.9445	1.40147
$100$	5.05344	0.505344
$101$	8.00275	0.796303	0.398152	−	0.917320i	$-0.369652\pi$
$101$	8.00275	0.796303	0.398152	+	0.917320i	$0.369652\pi$
$102$	−0.229640	−0.0227378
$103$	5.75663	0.567217	0.283609	−	0.958940i	$-0.408468\pi$
$103$	5.75663	0.567217	0.283609	+	0.958940i	$0.408468\pi$
$104$	−36.8250	−3.61098
$105$	−5.17759	−0.505281
$106$	−15.9817	−1.55228
$107$	5.87978	0.568419	0.284210	−	0.958762i	$-0.408269\pi$
$107$	5.87978	0.568419	0.284210	+	0.958762i	$0.408269\pi$
$108$	2.21888	0.213512
$109$	−12.2203	−1.17050	−0.585248	−	0.810854i	$-0.699003\pi$
$109$	−12.2203	−1.17050	−0.585248	+	0.810854i	$0.699003\pi$
$110$	13.1422	1.25306
$111$	−8.52558	−0.809212
$112$	−24.5359	−2.31843
$113$	−12.6081	−1.18607	−0.593037	−	0.805175i	$-0.702071\pi$
$113$	−12.6081	−1.18607	−0.593037	+	0.805175i	$0.702071\pi$
$114$	0	0
$115$	−0.737666	−0.0687877
$116$	−35.5155	−3.29753
$117$	12.7964	1.18303
$118$	22.7124	2.09084
$119$	0.0769493	0.00705393
$120$	−19.5603	−1.78560
$121$	13.4869	1.22608
$122$	28.4150	2.57257
$123$	−6.96389	−0.627912
$124$	39.3010	3.52933
$125$	−1.00000	−0.0894427
$126$	16.0649	1.43118
$127$	−1.60165	−0.142123	−0.0710616	−	0.997472i	$-0.522639\pi$
$127$	−1.60165	−0.142123	−0.0710616	+	0.997472i	$0.522639\pi$
$128$	−10.7327	−0.948649
$129$	−10.3420	−0.910561
$130$	12.0602	1.05775
$131$	7.74112	0.676345	0.338173	−	0.941084i	$-0.390191\pi$
$131$	7.74112	0.676345	0.338173	+	0.941084i	$0.390191\pi$
$132$	−60.3170	−5.24992
$133$	0	0
$134$	−0.441324	−0.0381246
$135$	−0.439083	−0.0377902
$136$	0.290705	0.0249277
$137$	13.4505	1.14915	0.574576	−	0.818451i	$-0.305167\pi$
$137$	13.4505	1.14915	0.574576	+	0.818451i	$0.305167\pi$
$138$	4.72548	0.402259
$139$	15.7045	1.33204	0.666021	−	0.745933i	$-0.267996\pi$
$139$	15.7045	1.33204	0.666021	+	0.745933i	$0.267996\pi$
$140$	10.8475	0.916781
$141$	4.02450	0.338924
$142$	31.6859	2.65902
$143$	22.4709	1.87911
$144$	32.2104	2.68420
$145$	7.02799	0.583643
$146$	−12.2931	−1.01739
$147$	5.77032	0.475928
$148$	17.8618	1.46823
$149$	13.4370	1.10080	0.550401	−	0.834901i	$-0.314475\pi$
$149$	13.4370	1.10080	0.550401	+	0.834901i	$0.314475\pi$
$150$	6.40599	0.523046
$151$	17.6127	1.43330	0.716649	−	0.697434i	$-0.245675\pi$
$151$	17.6127	1.43330	0.716649	+	0.697434i	$0.245675\pi$
$152$	0	0
$153$	−0.101018	−0.00816680
$154$	28.2104	2.27326
$155$	−7.77708	−0.624670
$156$	−55.3509	−4.43162
$157$	−18.1670	−1.44988	−0.724941	−	0.688811i	$-0.758133\pi$
$157$	−18.1670	−1.44988	−0.724941	+	0.688811i	$0.758133\pi$
$158$	−34.2005	−2.72085
$159$	−14.5147	−1.15109
$160$	14.1383	1.11773
$161$	−1.58344	−0.124793
$162$	25.2649	1.98499
$163$	−5.55371	−0.435000	−0.217500	−	0.976060i	$-0.569790\pi$
$163$	−5.55371	−0.435000	−0.217500	+	0.976060i	$0.569790\pi$
$164$	14.5899	1.13928
$165$	11.9358	0.929203
$166$	38.2836	2.97139
$167$	−3.43021	−0.265437	−0.132719	−	0.991154i	$-0.542371\pi$
$167$	−3.43021	−0.265437	−0.132719	+	0.991154i	$0.542371\pi$
$168$	−41.9873	−3.23939
$169$	7.62078	0.586214
$170$	−0.0952057	−0.00730194
$171$	0	0
$172$	21.6673	1.65212
$173$	−16.9297	−1.28714	−0.643571	−	0.765386i	$-0.722548\pi$
$173$	−16.9297	−1.28714	−0.643571	+	0.765386i	$0.722548\pi$
$174$	−45.0212	−3.41305
$175$	−2.14656	−0.162264
$176$	56.5623	4.26355
$177$	20.6275	1.55046
$178$	8.39066	0.628907
$179$	−9.20760	−0.688209	−0.344104	−	0.938931i	$-0.611817\pi$
$179$	−9.20760	−0.688209	−0.344104	+	0.938931i	$0.611817\pi$
$180$	−14.2404	−1.06142
$181$	14.8691	1.10521	0.552607	−	0.833442i	$-0.313633\pi$
$181$	14.8691	1.10521	0.552607	+	0.833442i	$0.313633\pi$
$182$	25.8878	1.91893
$183$	25.8067	1.90769
$184$	−5.98204	−0.441002
$185$	−3.53458	−0.259868
$186$	49.8199	3.65297
$187$	−0.177390	−0.0129720
$188$	−8.43166	−0.614942
$189$	−0.942516	−0.0685580
$190$	0	0
$191$	19.7967	1.43244	0.716220	−	0.697874i	$-0.245871\pi$
$191$	19.7967	1.43244	0.716220	+	0.697874i	$0.245871\pi$
$192$	−35.4286	−2.55684
$193$	21.0884	1.51798	0.758988	−	0.651104i	$-0.225694\pi$
$193$	21.0884	1.51798	0.758988	+	0.651104i	$0.225694\pi$
$194$	−8.72602	−0.626492
$195$	10.9531	0.784370
$196$	−12.0893	−0.863522
$197$	−4.92842	−0.351136	−0.175568	−	0.984467i	$-0.556176\pi$
$197$	−4.92842	−0.351136	−0.175568	+	0.984467i	$0.556176\pi$
$198$	−37.0342	−2.63190
$199$	4.32056	0.306277	0.153138	−	0.988205i	$-0.451062\pi$
$199$	4.32056	0.306277	0.153138	+	0.988205i	$0.451062\pi$
$200$	−8.10942	−0.573423
$201$	−0.400814	−0.0282712
$202$	−21.2539	−1.49542
$203$	15.0860	1.05883
$204$	0.436953	0.0305928
$205$	−2.88713	−0.201646
$206$	−15.2886	−1.06521
$207$	2.07872	0.144481
$208$	51.9054	3.59899
$209$	0	0
$210$	13.7508	0.948896
$211$	22.4372	1.54464	0.772319	−	0.635235i	$-0.219097\pi$
$211$	22.4372	1.54464	0.772319	+	0.635235i	$0.219097\pi$
$212$	30.4095	2.08854
$213$	28.7773	1.97179
$214$	−15.6157	−1.06747
$215$	−4.28764	−0.292415
$216$	−3.56071	−0.242275
$217$	−16.6939	−1.13326
$218$	32.4552	2.19814
$219$	−11.1647	−0.754440
$220$	−25.0066	−1.68594
$221$	−0.162785	−0.0109501
$222$	22.6425	1.51966
$223$	1.97634	0.132346	0.0661729	−	0.997808i	$-0.478921\pi$
$223$	1.97634	0.132346	0.0661729	+	0.997808i	$0.478921\pi$
$224$	30.3487	2.02775
$225$	2.81796	0.187864
$226$	33.4851	2.22740
$227$	29.8951	1.98421	0.992105	−	0.125410i	$-0.0400246\pi$
$227$	29.8951	1.98421	0.992105	+	0.125410i	$0.0400246\pi$
$228$	0	0
$229$	9.50575	0.628158	0.314079	−	0.949397i	$-0.398304\pi$
$229$	9.50575	0.628158	0.314079	+	0.949397i	$0.398304\pi$
$230$	1.95912	0.129180
$231$	25.6209	1.68573
$232$	56.9929	3.74177
$233$	5.21468	0.341625	0.170813	−	0.985304i	$-0.445361\pi$
$233$	5.21468	0.341625	0.170813	+	0.985304i	$0.445361\pi$
$234$	−33.9851	−2.22167
$235$	1.66850	0.108841
$236$	−43.2164	−2.81315
$237$	−31.0612	−2.01764
$238$	−0.204364	−0.0132470
$239$	16.8458	1.08966	0.544832	−	0.838545i	$-0.316593\pi$
$239$	16.8458	1.08966	0.544832	+	0.838545i	$0.316593\pi$
$240$	27.5706	1.77967
$241$	−24.9198	−1.60523	−0.802614	−	0.596499i	$-0.796558\pi$
$241$	−24.9198	−1.60523	−0.802614	+	0.596499i	$0.796558\pi$
$242$	−35.8189	−2.30253
$243$	21.6285	1.38747
$244$	−54.0672	−3.46130
$245$	2.39229	0.152838
$246$	18.4949	1.17919
$247$	0	0
$248$	−63.0676	−4.00480
$249$	34.7695	2.20343
$250$	2.65583	0.167970
$251$	5.01194	0.316351	0.158175	−	0.987411i	$-0.449439\pi$
$251$	5.01194	0.316351	0.158175	+	0.987411i	$0.449439\pi$
$252$	−30.5678	−1.92559
$253$	3.65028	0.229491
$254$	4.25370	0.266901
$255$	−0.0864665	−0.00541474
$256$	−0.872008	−0.0545005
$257$	−7.55536	−0.471290	−0.235645	−	0.971839i	$-0.575720\pi$
$257$	−7.55536	−0.471290	−0.235645	+	0.971839i	$0.575720\pi$
$258$	27.4666	1.70999
$259$	−7.58719	−0.471445
$260$	−22.9477	−1.42316
$261$	−19.8046	−1.22587
$262$	−20.5591	−1.27015
$263$	16.6909	1.02921	0.514604	−	0.857428i	$-0.327939\pi$
$263$	16.6909	1.02921	0.514604	+	0.857428i	$0.327939\pi$
$264$	96.7926	5.95717
$265$	−6.01759	−0.369658
$266$	0	0
$267$	7.62046	0.466365
$268$	0.839738	0.0512952
$269$	−12.7758	−0.778954	−0.389477	−	0.921036i	$-0.627344\pi$
$269$	−12.7758	−0.778954	−0.389477	+	0.921036i	$0.627344\pi$
$270$	1.16613	0.0709684
$271$	7.97952	0.484722	0.242361	−	0.970186i	$-0.422078\pi$
$271$	7.97952	0.484722	0.242361	+	0.970186i	$0.422078\pi$
$272$	−0.409753	−0.0248449
$273$	23.5115	1.42298
$274$	−35.7222	−2.15806
$275$	4.94842	0.298401
$276$	−8.99150	−0.541225
$277$	−14.9823	−0.900198	−0.450099	−	0.892979i	$-0.648611\pi$
$277$	−14.9823	−0.900198	−0.450099	+	0.892979i	$0.648611\pi$
$278$	−41.7086	−2.50152
$279$	21.9155	1.31205
$280$	−17.4073	−1.04029
$281$	−14.8955	−0.888593	−0.444296	−	0.895880i	$-0.646546\pi$
$281$	−14.8955	−0.888593	−0.444296	+	0.895880i	$0.646546\pi$
$282$	−10.6884	−0.636484
$283$	20.4772	1.21724	0.608620	−	0.793462i	$-0.291723\pi$
$283$	20.4772	1.21724	0.608620	+	0.793462i	$0.291723\pi$
$284$	−60.2910	−3.57761
$285$	0	0
$286$	−59.6788	−3.52888
$287$	−6.19739	−0.365820
$288$	−39.8412	−2.34766
$289$	−16.9987	−0.999924
$290$	−18.6652	−1.09606
$291$	−7.92504	−0.464574
$292$	23.3910	1.36885
$293$	−7.29756	−0.426328	−0.213164	−	0.977016i	$-0.568377\pi$
$293$	−7.29756	−0.426328	−0.213164	+	0.977016i	$0.568377\pi$
$294$	−15.3250	−0.893772
$295$	8.55188	0.497910
$296$	−28.6634	−1.66603
$297$	2.17277	0.126077
$298$	−35.6864	−2.06726
$299$	3.34975	0.193721
$300$	−12.1891	−0.703739
$301$	−9.20367	−0.530491
$302$	−46.7762	−2.69167
$303$	−19.3030	−1.10893
$304$	0	0
$305$	10.6991	0.612629
$306$	0.268286	0.0153369
$307$	−19.6155	−1.11952	−0.559759	−	0.828655i	$-0.689106\pi$
$307$	−19.6155	−1.11952	−0.559759	+	0.828655i	$0.689106\pi$
$308$	−53.6780	−3.05859
$309$	−13.8852	−0.789904
$310$	20.6546	1.17310
$311$	−17.4971	−0.992167	−0.496084	−	0.868275i	$-0.665229\pi$
$311$	−17.4971	−0.992167	−0.496084	+	0.868275i	$0.665229\pi$
$312$	88.8235	5.02864
$313$	15.6670	0.885549	0.442774	−	0.896633i	$-0.353994\pi$
$313$	15.6670	0.885549	0.442774	+	0.896633i	$0.353994\pi$
$314$	48.2484	2.72282
$315$	6.04892	0.340818
$316$	65.0758	3.66080
$317$	−23.4580	−1.31753	−0.658767	−	0.752347i	$-0.728922\pi$
$317$	−23.4580	−1.31753	−0.658767	+	0.752347i	$0.728922\pi$
$318$	38.5486	2.16170
$319$	−34.7775	−1.94717
$320$	−14.6882	−0.821094
$321$	−14.1823	−0.791578
$322$	4.20536	0.234355
$323$	0	0
$324$	−48.0732	−2.67074
$325$	4.54101	0.251890
$326$	14.7497	0.816910
$327$	29.4760	1.63003
$328$	−23.4129	−1.29276
$329$	3.58153	0.197456
$330$	−31.6995	−1.74500
$331$	13.1415	0.722321	0.361161	−	0.932504i	$-0.382381\pi$
$331$	13.1415	0.722321	0.361161	+	0.932504i	$0.382381\pi$
$332$	−72.8450	−3.99789
$333$	9.96032	0.545822
$334$	9.11005	0.498480
$335$	−0.166172	−0.00907893
$336$	59.1818	3.22863
$337$	−16.7799	−0.914060	−0.457030	−	0.889451i	$-0.651087\pi$
$337$	−16.7799	−0.914060	−0.457030	+	0.889451i	$0.651087\pi$
$338$	−20.2395	−1.10088
$339$	30.4114	1.65172
$340$	0.181155	0.00982449
$341$	38.4843	2.08404
$342$	0	0
$343$	20.1611	1.08860
$344$	−34.7703	−1.87469
$345$	1.77928	0.0957934
$346$	44.9625	2.41720
$347$	17.6091	0.945307	0.472654	−	0.881248i	$-0.343296\pi$
$347$	17.6091	0.945307	0.472654	+	0.881248i	$0.343296\pi$
$348$	85.6651	4.59213
$349$	21.7793	1.16582	0.582910	−	0.812537i	$-0.301914\pi$
$349$	21.7793	1.16582	0.582910	+	0.812537i	$0.301914\pi$
$350$	5.70089	0.304726
$351$	1.99388	0.106425
$352$	−69.9623	−3.72900
$353$	19.3069	1.02760	0.513802	−	0.857909i	$-0.328237\pi$
$353$	19.3069	1.02760	0.513802	+	0.857909i	$0.328237\pi$
$354$	−54.7832	−2.91170
$355$	11.9307	0.633215
$356$	−15.9655	−0.846171
$357$	−0.185605	−0.00982327
$358$	24.4538	1.29243
$359$	−19.6399	−1.03655	−0.518276	−	0.855213i	$-0.673426\pi$
$359$	−19.6399	−1.03655	−0.518276	+	0.855213i	$0.673426\pi$
$360$	22.8520	1.20441
$361$	0	0
$362$	−39.4899	−2.07554
$363$	−32.5310	−1.70744
$364$	−49.2586	−2.58185
$365$	−4.62873	−0.242279
$366$	−68.5383	−3.58255
$367$	−0.820572	−0.0428335	−0.0214167	−	0.999771i	$-0.506818\pi$
$367$	−0.820572	−0.0428335	−0.0214167	+	0.999771i	$0.506818\pi$
$368$	8.43180	0.439538
$369$	8.13582	0.423534
$370$	9.38726	0.488020
$371$	−12.9171	−0.670623
$372$	−94.7958	−4.91493
$373$	28.0641	1.45310	0.726551	−	0.687113i	$-0.241122\pi$
$373$	28.0641	1.45310	0.726551	+	0.687113i	$0.241122\pi$
$374$	0.471118	0.0243609
$375$	2.41205	0.124557
$376$	13.5306	0.697785
$377$	−31.9142	−1.64366
$378$	2.50316	0.128749
$379$	−10.3311	−0.530674	−0.265337	−	0.964156i	$-0.585483\pi$
$379$	−10.3311	−0.530674	−0.265337	+	0.964156i	$0.585483\pi$
$380$	0	0
$381$	3.86325	0.197920
$382$	−52.5767	−2.69006
$383$	3.65218	0.186618	0.0933089	−	0.995637i	$-0.470256\pi$
$383$	3.65218	0.186618	0.0933089	+	0.995637i	$0.470256\pi$
$384$	25.8879	1.32108
$385$	10.6221	0.541351
$386$	−56.0072	−2.85069
$387$	12.0824	0.614184
$388$	16.6036	0.842921
$389$	20.8481	1.05704	0.528521	−	0.848920i	$-0.322747\pi$
$389$	20.8481	1.05704	0.528521	+	0.848920i	$0.322747\pi$
$390$	−29.0896	−1.47301
$391$	−0.0264437	−0.00133732
$392$	19.4001	0.979853
$393$	−18.6719	−0.941875
$394$	13.0891	0.659417
$395$	−12.8775	−0.647939
$396$	70.4676	3.54113
$397$	11.6561	0.585004	0.292502	−	0.956265i	$-0.405512\pi$
$397$	11.6561	0.585004	0.292502	+	0.956265i	$0.405512\pi$
$398$	−11.4747	−0.575174
$399$	0	0
$400$	11.4304	0.571518
$401$	27.3976	1.36817	0.684085	−	0.729402i	$-0.260202\pi$
$401$	27.3976	1.36817	0.684085	+	0.729402i	$0.260202\pi$
$402$	1.06449	0.0530921
$403$	35.3158	1.75921
$404$	40.4414	2.01203
$405$	9.51297	0.472704
$406$	−40.0658	−1.98843
$407$	17.4906	0.866978
$408$	−0.701193	−0.0347142
$409$	−38.5377	−1.90557	−0.952784	−	0.303648i	$-0.901795\pi$
$409$	−38.5377	−1.90557	−0.952784	+	0.303648i	$0.901795\pi$
$410$	7.66773	0.378682
$411$	−32.4432	−1.60030
$412$	29.0908	1.43320
$413$	18.3571	0.903294
$414$	−5.52072	−0.271328
$415$	14.4149	0.707601
$416$	−64.2021	−3.14777
$417$	−37.8801	−1.85500
$418$	0	0
$419$	−9.06751	−0.442977	−0.221488	−	0.975163i	$-0.571091\pi$
$419$	−9.06751	−0.442977	−0.221488	+	0.975163i	$0.571091\pi$
$420$	−26.1647	−1.27670
$421$	9.60328	0.468035	0.234018	−	0.972232i	$-0.424813\pi$
$421$	9.60328	0.468035	0.234018	+	0.972232i	$0.424813\pi$
$422$	−59.5893	−2.90076
$423$	−4.70177	−0.228608
$424$	−48.7992	−2.36990
$425$	−0.0358478	−0.00173887
$426$	−76.4277	−3.70294
$427$	22.9662	1.11141
$428$	29.7131	1.43624
$429$	−54.2007	−2.61683
$430$	11.3873	0.549142
$431$	40.9474	1.97237	0.986183	−	0.165662i	$-0.0529761\pi$
$431$	40.9474	1.97237	0.986183	+	0.165662i	$0.0529761\pi$
$432$	5.01888	0.241471
$433$	−4.24047	−0.203784	−0.101892	−	0.994795i	$-0.532490\pi$
$433$	−4.24047	−0.203784	−0.101892	+	0.994795i	$0.532490\pi$
$434$	44.3363	2.12821
$435$	−16.9518	−0.812778
$436$	−61.7547	−2.95752
$437$	0	0
$438$	29.6515	1.41681
$439$	−17.9702	−0.857671	−0.428836	−	0.903383i	$-0.641076\pi$
$439$	−17.9702	−0.857671	−0.428836	+	0.903383i	$0.641076\pi$
$440$	40.1288	1.91307
$441$	−6.74139	−0.321019
$442$	0.432330	0.0205638
$443$	−11.8397	−0.562522	−0.281261	−	0.959631i	$-0.590753\pi$
$443$	−11.8397	−0.562522	−0.281261	+	0.959631i	$0.590753\pi$
$444$	−43.0835	−2.04465
$445$	3.15934	0.149767
$446$	−5.24884	−0.248540
$447$	−32.4106	−1.53297
$448$	−31.5290	−1.48961
$449$	3.96479	0.187110	0.0935551	−	0.995614i	$-0.470177\pi$
$449$	3.96479	0.187110	0.0935551	+	0.995614i	$0.470177\pi$
$450$	−7.48403	−0.352801
$451$	14.2867	0.672736
$452$	−63.7145	−2.99688
$453$	−42.4825	−1.99600
$454$	−79.3964	−3.72626
$455$	9.74754	0.456972
$456$	0	0
$457$	12.7072	0.594419	0.297209	−	0.954812i	$-0.403944\pi$
$457$	12.7072	0.594419	0.297209	+	0.954812i	$0.403944\pi$
$458$	−25.2457	−1.17965
$459$	−0.0157401	−0.000734687 0
$460$	−3.72775	−0.173807
$461$	−3.87570	−0.180509	−0.0902546	−	0.995919i	$-0.528768\pi$
$461$	−3.87570	−0.180509	−0.0902546	+	0.995919i	$0.528768\pi$
$462$	−68.0449	−3.16573
$463$	−25.7892	−1.19853	−0.599264	−	0.800552i	$-0.704540\pi$
$463$	−25.7892	−1.19853	−0.599264	+	0.800552i	$0.704540\pi$
$464$	−80.3325	−3.72934
$465$	18.7587	0.869912
$466$	−13.8493	−0.641557
$467$	−5.51576	−0.255239	−0.127620	−	0.991823i	$-0.540734\pi$
$467$	−5.51576	−0.255239	−0.127620	+	0.991823i	$0.540734\pi$
$468$	64.6658	2.98918
$469$	−0.356697	−0.0164707
$470$	−4.43125	−0.204398
$471$	43.8196	2.01910
$472$	69.3508	3.19213
$473$	21.2171	0.975562
$474$	82.4933	3.78904
$475$	0	0
$476$	0.388859	0.0178233
$477$	16.9573	0.776424
$478$	−44.7396	−2.04634
$479$	−4.99328	−0.228149	−0.114074	−	0.993472i	$-0.536390\pi$
$479$	−4.99328	−0.228149	−0.114074	+	0.993472i	$0.536390\pi$
$480$	−34.1022	−1.55655
$481$	16.0506	0.731844
$482$	66.1829	3.01455
$483$	3.81933	0.173786
$484$	68.1553	3.09797
$485$	−3.28561	−0.149192
$486$	−57.4416	−2.60560
$487$	−21.1572	−0.958726	−0.479363	−	0.877617i	$-0.659132\pi$
$487$	−21.1572	−0.958726	−0.479363	+	0.877617i	$0.659132\pi$
$488$	86.7635	3.92760
$489$	13.3958	0.605778
$490$	−6.35352	−0.287023
$491$	−3.94962	−0.178244	−0.0891220	−	0.996021i	$-0.528406\pi$
$491$	−3.94962	−0.178244	−0.0891220	+	0.996021i	$0.528406\pi$
$492$	−35.1916	−1.58656
$493$	0.251938	0.0113467
$494$	0	0
$495$	−13.9445	−0.626758
$496$	88.8949	3.99150
$497$	25.6099	1.14876
$498$	−92.3419	−4.13794
$499$	17.7976	0.796730	0.398365	−	0.917227i	$-0.369578\pi$
$499$	17.7976	0.796730	0.398365	+	0.917227i	$0.369578\pi$
$500$	−5.05344	−0.225997
$501$	8.27381	0.369647
$502$	−13.3109	−0.594092
$503$	−7.16657	−0.319541	−0.159771	−	0.987154i	$-0.551075\pi$
$503$	−7.16657	−0.319541	−0.159771	+	0.987154i	$0.551075\pi$
$504$	49.0532	2.18500
$505$	−8.00275	−0.356118
$506$	−9.69454	−0.430975
$507$	−18.3817	−0.816359
$508$	−8.09383	−0.359106
$509$	24.6399	1.09214	0.546072	−	0.837738i	$-0.316123\pi$
$509$	24.6399	1.09214	0.546072	+	0.837738i	$0.316123\pi$
$510$	0.229640	0.0101686
$511$	−9.93582	−0.439535
$512$	23.7814	1.05100
$513$	0	0
$514$	20.0657	0.885062
$515$	−5.75663	−0.253667
$516$	−52.2626	−2.30073
$517$	−8.25644	−0.363118
$518$	20.1503	0.885353
$519$	40.8353	1.79247
$520$	36.8250	1.61488
$521$	37.2156	1.63044	0.815222	−	0.579148i	$-0.196615\pi$
$521$	37.2156	1.63044	0.815222	+	0.579148i	$0.196615\pi$
$522$	52.5977	2.30214
$523$	13.7304	0.600389	0.300195	−	0.953878i	$-0.402948\pi$
$523$	13.7304	0.600389	0.300195	+	0.953878i	$0.402948\pi$
$524$	39.1193	1.70893
$525$	5.17759	0.225969
$526$	−44.3283	−1.93281
$527$	−0.278791	−0.0121443
$528$	−136.431	−5.93739
$529$	−22.4558	−0.976341
$530$	15.9817	0.694201
$531$	−24.0989	−1.04580
$532$	0	0
$533$	13.1105	0.567878
$534$	−20.2387	−0.875813
$535$	−5.87978	−0.254205
$536$	−1.34756	−0.0582055
$537$	22.2092	0.958396
$538$	33.9304	1.46284
$539$	−11.8381	−0.509902
$540$	−2.21888	−0.0954853
$541$	−20.4831	−0.880636	−0.440318	−	0.897842i	$-0.645134\pi$
$541$	−20.4831	−0.880636	−0.440318	+	0.897842i	$0.645134\pi$
$542$	−21.1923	−0.910286
$543$	−35.8650	−1.53911
$544$	0.506826	0.0217300
$545$	12.2203	0.523462
$546$	−62.4426	−2.67230
$547$	30.1428	1.28881	0.644407	−	0.764683i	$-0.277104\pi$
$547$	30.1428	1.28881	0.644407	+	0.764683i	$0.277104\pi$
$548$	67.9712	2.90359
$549$	−30.1497	−1.28676
$550$	−13.1422	−0.560384
$551$	0	0
$552$	14.4290	0.614137
$553$	−27.6424	−1.17547
$554$	39.7904	1.69053
$555$	8.52558	0.361891
$556$	79.3620	3.36570
$557$	28.1724	1.19370	0.596851	−	0.802352i	$-0.296418\pi$
$557$	28.1724	1.19370	0.596851	+	0.802352i	$0.296418\pi$
$558$	−58.2039	−2.46397
$559$	19.4702	0.823503
$560$	24.5359	1.03683
$561$	0.427873	0.0180648
$562$	39.5600	1.66874
$563$	17.4071	0.733621	0.366810	−	0.930296i	$-0.380450\pi$
$563$	17.4071	0.733621	0.366810	+	0.930296i	$0.380450\pi$
$564$	20.3375	0.856365
$565$	12.6081	0.530429
$566$	−54.3839	−2.28592
$567$	20.4201	0.857565
$568$	96.7509	4.05958
$569$	12.4678	0.522679	0.261339	−	0.965247i	$-0.415836\pi$
$569$	12.4678	0.522679	0.261339	+	0.965247i	$0.415836\pi$
$570$	0	0
$571$	−12.8438	−0.537496	−0.268748	−	0.963210i	$-0.586610\pi$
$571$	−12.8438	−0.537496	−0.268748	+	0.963210i	$0.586610\pi$
$572$	113.555	4.74798
$573$	−47.7506	−1.99481
$574$	16.4592	0.686994
$575$	0.737666	0.0307628
$576$	41.3907	1.72461
$577$	−33.4757	−1.39361	−0.696806	−	0.717260i	$-0.745396\pi$
$577$	−33.4757	−1.39361	−0.696806	+	0.717260i	$0.745396\pi$
$578$	45.1457	1.87781
$579$	−50.8662	−2.11393
$580$	35.5155	1.47470
$581$	30.9425	1.28371
$582$	21.0476	0.872449
$583$	29.7776	1.23326
$584$	−37.5363	−1.55326
$585$	−12.7964	−0.529066
$586$	19.3811	0.800625
$587$	41.5845	1.71637	0.858187	−	0.513337i	$-0.171591\pi$
$587$	41.5845	1.71637	0.858187	+	0.513337i	$0.171591\pi$
$588$	29.1599	1.20254
$589$	0	0
$590$	−22.7124	−0.935053
$591$	11.8876	0.488990
$592$	40.4016	1.66050
$593$	−11.2967	−0.463900	−0.231950	−	0.972728i	$-0.574511\pi$
$593$	−11.2967	−0.463900	−0.231950	+	0.972728i	$0.574511\pi$
$594$	−5.77051	−0.236767
$595$	−0.0769493	−0.00315461
$596$	67.9030	2.78142
$597$	−10.4214	−0.426519
$598$	−8.89637	−0.363800
$599$	−31.7953	−1.29912	−0.649560	−	0.760311i	$-0.725047\pi$
$599$	−31.7953	−1.29912	−0.649560	+	0.760311i	$0.725047\pi$
$600$	19.5603	0.798545
$601$	−5.28529	−0.215591	−0.107796	−	0.994173i	$-0.534379\pi$
$601$	−5.28529	−0.215591	−0.107796	+	0.994173i	$0.534379\pi$
$602$	24.4434	0.996238
$603$	0.468266	0.0190692
$604$	89.0045	3.62154
$605$	−13.4869	−0.548321
$606$	51.2655	2.08252
$607$	−47.3858	−1.92333	−0.961665	−	0.274227i	$-0.911578\pi$
$607$	−47.3858	−1.92333	−0.961665	+	0.274227i	$0.911578\pi$
$608$	0	0
$609$	−36.3881	−1.47452
$610$	−28.4150	−1.15049
$611$	−7.57667	−0.306519
$612$	−0.510487	−0.0206352
$613$	−42.3432	−1.71023	−0.855113	−	0.518441i	$-0.826513\pi$
$613$	−42.3432	−1.71023	−0.855113	+	0.518441i	$0.826513\pi$
$614$	52.0956	2.10241
$615$	6.96389	0.280811
$616$	86.1389	3.47063
$617$	−17.3464	−0.698341	−0.349171	−	0.937059i	$-0.613537\pi$
$617$	−17.3464	−0.698341	−0.349171	+	0.937059i	$0.613537\pi$
$618$	36.8769	1.48340
$619$	0.906866	0.0364500	0.0182250	−	0.999834i	$-0.494198\pi$
$619$	0.906866	0.0364500	0.0182250	+	0.999834i	$0.494198\pi$
$620$	−39.3010	−1.57837
$621$	0.323896	0.0129975
$622$	46.4692	1.86325
$623$	6.78170	0.271703
$624$	−125.198	−5.01194
$625$	1.00000	0.0400000
$626$	−41.6088	−1.66302
$627$	0	0
$628$	−91.8057	−3.66345
$629$	−0.126707	−0.00505214
$630$	−16.0649	−0.640041
$631$	−23.6805	−0.942706	−0.471353	−	0.881945i	$-0.656234\pi$
$631$	−23.6805	−0.942706	−0.471353	+	0.881945i	$0.656234\pi$
$632$	−104.429	−4.15397
$633$	−54.1194	−2.15105
$634$	62.3006	2.47427
$635$	1.60165	0.0635594
$636$	−73.3492	−2.90848
$637$	−10.8634	−0.430425
$638$	92.3631	3.65669
$639$	−33.6202	−1.32999
$640$	10.7327	0.424249
$641$	0.818318	0.0323216	0.0161608	−	0.999869i	$-0.494856\pi$
$641$	0.818318	0.0323216	0.0161608	+	0.999869i	$0.494856\pi$
$642$	37.6658	1.48655
$643$	−27.8740	−1.09924	−0.549622	−	0.835414i	$-0.685228\pi$
$643$	−27.8740	−1.09924	−0.549622	+	0.835414i	$0.685228\pi$
$644$	−8.00183	−0.315316
$645$	10.3420	0.407215
$646$	0	0
$647$	−33.1507	−1.30329	−0.651644	−	0.758525i	$-0.725920\pi$
$647$	−33.1507	−1.30329	−0.651644	+	0.758525i	$0.725920\pi$
$648$	77.1447	3.03053
$649$	−42.3183	−1.66114
$650$	−12.0602	−0.473038
$651$	40.2665	1.57817
$652$	−28.0653	−1.09912
$653$	44.3166	1.73424	0.867121	−	0.498098i	$-0.165968\pi$
$653$	44.3166	1.73424	0.867121	+	0.498098i	$0.165968\pi$
$654$	−78.2833	−3.06112
$655$	−7.74112	−0.302471
$656$	33.0010	1.28847
$657$	13.0436	0.508878
$658$	−9.51194	−0.370814
$659$	12.7418	0.496350	0.248175	−	0.968715i	$-0.420169\pi$
$659$	12.7418	0.496350	0.248175	+	0.968715i	$0.420169\pi$
$660$	60.3170	2.34783
$661$	21.1469	0.822520	0.411260	−	0.911518i	$-0.365089\pi$
$661$	21.1469	0.822520	0.411260	+	0.911518i	$0.365089\pi$
$662$	−34.9016	−1.35649
$663$	0.392645	0.0152491
$664$	116.897	4.53647
$665$	0	0
$666$	−26.4529	−1.02503
$667$	−5.18431	−0.200737
$668$	−17.3343	−0.670686
$669$	−4.76703	−0.184304
$670$	0.441324	0.0170498
$671$	−52.9437	−2.04387
$672$	−73.2023	−2.82384
$673$	−3.75767	−0.144848	−0.0724239	−	0.997374i	$-0.523073\pi$
$673$	−3.75767	−0.144848	−0.0724239	+	0.997374i	$0.523073\pi$
$674$	44.5646	1.71657
$675$	0.439083	0.0169003
$676$	38.5112	1.48120
$677$	−14.4848	−0.556696	−0.278348	−	0.960480i	$-0.589787\pi$
$677$	−14.4848	−0.556696	−0.278348	+	0.960480i	$0.589787\pi$
$678$	−80.7676	−3.10186
$679$	−7.05275	−0.270660
$680$	−0.290705	−0.0111480
$681$	−72.1084	−2.76320
$682$	−102.208	−3.91374
$683$	43.4481	1.66250	0.831248	−	0.555901i	$-0.187627\pi$
$683$	43.4481	1.66250	0.831248	+	0.555901i	$0.187627\pi$
$684$	0	0
$685$	−13.4505	−0.513917
$686$	−53.5445	−2.04434
$687$	−22.9283	−0.874770
$688$	49.0093	1.86846
$689$	27.3259	1.04104
$690$	−4.72548	−0.179896
$691$	46.9489	1.78602	0.893010	−	0.450036i	$-0.148589\pi$
$691$	46.9489	1.78602	0.893010	+	0.450036i	$0.148589\pi$
$692$	−85.5533	−3.25225
$693$	−29.9326	−1.13705
$694$	−46.7669	−1.77525
$695$	−15.7045	−0.595707
$696$	−137.470	−5.21077
$697$	−0.103497	−0.00392024
$698$	−57.8422	−2.18936
$699$	−12.5781	−0.475746
$700$	−10.8475	−0.409997
$701$	−8.32839	−0.314559	−0.157280	−	0.987554i	$-0.550272\pi$
$701$	−8.32839	−0.314559	−0.157280	+	0.987554i	$0.550272\pi$
$702$	−5.29541	−0.199862
$703$	0	0
$704$	72.6834	2.73936
$705$	−4.02450	−0.151571
$706$	−51.2759	−1.92980
$707$	−17.1784	−0.646058
$708$	104.240	3.91758
$709$	39.0150	1.46524	0.732620	−	0.680638i	$-0.238297\pi$
$709$	39.0150	1.46524	0.732620	+	0.680638i	$0.238297\pi$
$710$	−31.6859	−1.18915
$711$	36.2884	1.36092
$712$	25.6204	0.960165
$713$	5.73689	0.214848
$714$	0.492936	0.0184477
$715$	−22.4709	−0.840362
$716$	−46.5301	−1.73891
$717$	−40.6328	−1.51746
$718$	52.1601	1.94660
$719$	40.9931	1.52878	0.764392	−	0.644752i	$-0.223039\pi$
$719$	40.9931	1.52878	0.764392	+	0.644752i	$0.223039\pi$
$720$	−32.2104	−1.20041
$721$	−12.3569	−0.460196
$722$	0	0
$723$	60.1078	2.23543
$724$	75.1402	2.79256
$725$	−7.02799	−0.261013
$726$	86.3969	3.20649
$727$	−7.88884	−0.292581	−0.146290	−	0.989242i	$-0.546733\pi$
$727$	−7.88884	−0.292581	−0.146290	+	0.989242i	$0.546733\pi$
$728$	79.0469	2.92967
$729$	−23.6299	−0.875183
$730$	12.2931	0.454989
$731$	−0.153703	−0.00568489
$732$	130.413	4.82019
$733$	24.1367	0.891510	0.445755	−	0.895155i	$-0.352935\pi$
$733$	24.1367	0.891510	0.445755	+	0.895155i	$0.352935\pi$
$734$	2.17930	0.0804394
$735$	−5.77032	−0.212841
$736$	−10.4293	−0.384431
$737$	0.822288	0.0302894
$738$	−21.6074	−0.795378
$739$	28.0268	1.03098	0.515491	−	0.856895i	$-0.327610\pi$
$739$	28.0268	1.03098	0.515491	+	0.856895i	$0.327610\pi$
$740$	−17.8618	−0.656613
$741$	0	0
$742$	34.3056	1.25940
$743$	−12.9393	−0.474697	−0.237348	−	0.971425i	$-0.576278\pi$
$743$	−12.9393	−0.474697	−0.237348	+	0.971425i	$0.576278\pi$
$744$	152.122	5.57706
$745$	−13.4370	−0.492293
$746$	−74.5334	−2.72886
$747$	−40.6207	−1.48624
$748$	−0.896430	−0.0327767
$749$	−12.6213	−0.461171
$750$	−6.40599	−0.233914
$751$	−4.08509	−0.149067	−0.0745335	−	0.997219i	$-0.523747\pi$
$751$	−4.08509	−0.149067	−0.0745335	+	0.997219i	$0.523747\pi$
$752$	−19.0716	−0.695468
$753$	−12.0890	−0.440548
$754$	84.7587	3.08673
$755$	−17.6127	−0.640990
$756$	−4.76295	−0.173227
$757$	−30.1259	−1.09494	−0.547471	−	0.836824i	$-0.684410\pi$
$757$	−30.1259	−1.09494	−0.547471	+	0.836824i	$0.684410\pi$
$758$	27.4377	0.996582
$759$	−8.80465	−0.319589
$760$	0	0
$761$	36.2632	1.31454	0.657270	−	0.753655i	$-0.271711\pi$
$761$	36.2632	1.31454	0.657270	+	0.753655i	$0.271711\pi$
$762$	−10.2601	−0.371685
$763$	26.2317	0.949650
$764$	100.042	3.61938
$765$	0.101018	0.00365230
$766$	−9.69958	−0.350460
$767$	−38.8342	−1.40222
$768$	2.10332	0.0758971
$769$	23.5588	0.849553	0.424776	−	0.905298i	$-0.360353\pi$
$769$	23.5588	0.849553	0.424776	+	0.905298i	$0.360353\pi$
$770$	−28.2104	−1.01663
$771$	18.2239	0.656316
$772$	106.569	3.83550
$773$	−12.2240	−0.439667	−0.219834	−	0.975537i	$-0.570551\pi$
$773$	−12.2240	−0.439667	−0.219834	+	0.975537i	$0.570551\pi$
$774$	−32.0889	−1.15341
$775$	7.77708	0.279361
$776$	−26.6444	−0.956477
$777$	18.3006	0.656532
$778$	−55.3691	−1.98508
$779$	0	0
$780$	55.3509	1.98188
$781$	−59.0381	−2.11255
$782$	0.0702300	0.00251142
$783$	−3.08587	−0.110280
$784$	−27.3448	−0.976600
$785$	18.1670	0.648407
$786$	49.5895	1.76880
$787$	7.66986	0.273401	0.136700	−	0.990612i	$-0.456350\pi$
$787$	7.66986	0.273401	0.136700	+	0.990612i	$0.456350\pi$
$788$	−24.9055	−0.887221
$789$	−40.2593	−1.43327
$790$	34.2005	1.21680
$791$	27.0641	0.962289
$792$	−113.082	−4.01818
$793$	−48.5847	−1.72529
$794$	−30.9567	−1.09861
$795$	14.5147	0.514783
$796$	21.8337	0.773875
$797$	48.9718	1.73467	0.867336	−	0.497723i	$-0.165831\pi$
$797$	48.9718	1.73467	0.867336	+	0.497723i	$0.165831\pi$
$798$	0	0
$799$	0.0598120	0.00211600
$800$	−14.1383	−0.499864
$801$	−8.90289	−0.314568
$802$	−72.7633	−2.56936
$803$	22.9049	0.808296
$804$	−2.02549	−0.0714334
$805$	1.58344	0.0558090
$806$	−93.7928	−3.30371
$807$	30.8158	1.08477
$808$	−64.8976	−2.28309
$809$	−28.1027	−0.988039	−0.494019	−	0.869451i	$-0.664473\pi$
$809$	−28.1027	−0.988039	−0.494019	+	0.869451i	$0.664473\pi$
$810$	−25.2649	−0.887717
$811$	−5.20539	−0.182786	−0.0913929	−	0.995815i	$-0.529132\pi$
$811$	−5.20539	−0.182786	−0.0913929	+	0.995815i	$0.529132\pi$
$812$	76.2361	2.67536
$813$	−19.2470	−0.675021
$814$	−46.4521	−1.62815
$815$	5.55371	0.194538
$816$	0.988344	0.0345990
$817$	0	0
$818$	102.350	3.57857
$819$	−27.4682	−0.959817
$820$	−14.5899	−0.509503
$821$	−20.8544	−0.727825	−0.363913	−	0.931433i	$-0.618559\pi$
$821$	−20.8544	−0.727825	−0.363913	+	0.931433i	$0.618559\pi$
$822$	86.1636	3.00530
$823$	7.77083	0.270874	0.135437	−	0.990786i	$-0.456756\pi$
$823$	7.77083	0.270874	0.135437	+	0.990786i	$0.456756\pi$
$824$	−46.6829	−1.62628
$825$	−11.9358	−0.415552
$826$	−48.7534	−1.69635
$827$	52.5985	1.82903	0.914514	−	0.404554i	$-0.132573\pi$
$827$	52.5985	1.82903	0.914514	+	0.404554i	$0.132573\pi$
$828$	10.5047	0.365062
$829$	15.8252	0.549633	0.274816	−	0.961497i	$-0.411383\pi$
$829$	15.8252	0.549633	0.274816	+	0.961497i	$0.411383\pi$
$830$	−38.2836	−1.32884
$831$	36.1379	1.25361
$832$	66.6992	2.31238
$833$	0.0857584	0.00297135
$834$	100.603	3.48360
$835$	3.43021	0.118707
$836$	0	0
$837$	3.41478	0.118032
$838$	24.0818	0.831891
$839$	−17.5703	−0.606595	−0.303298	−	0.952896i	$-0.598088\pi$
$839$	−17.5703	−0.606595	−0.303298	+	0.952896i	$0.598088\pi$
$840$	41.9873	1.44870
$841$	20.3927	0.703195
$842$	−25.5047	−0.878950
$843$	35.9287	1.23745
$844$	113.385	3.90287
$845$	−7.62078	−0.262163
$846$	12.4871	0.429315
$847$	−28.9504	−0.994748
$848$	68.7833	2.36203
$849$	−49.3918	−1.69512
$850$	0.0952057	0.00326553
$851$	2.60734	0.0893785
$852$	145.425	4.98216
$853$	12.7245	0.435678	0.217839	−	0.975985i	$-0.430099\pi$
$853$	12.7245	0.435678	0.217839	+	0.975985i	$0.430099\pi$
$854$	−60.9944	−2.08719
$855$	0	0
$856$	−47.6816	−1.62972
$857$	−24.2183	−0.827282	−0.413641	−	0.910440i	$-0.635743\pi$
$857$	−24.2183	−0.827282	−0.413641	+	0.910440i	$0.635743\pi$
$858$	143.948	4.91430
$859$	−20.7054	−0.706458	−0.353229	−	0.935537i	$-0.614916\pi$
$859$	−20.7054	−0.706458	−0.353229	+	0.935537i	$0.614916\pi$
$860$	−21.6673	−0.738850
$861$	14.9484	0.509439
$862$	−108.749	−3.70402
$863$	35.7447	1.21676	0.608382	−	0.793644i	$-0.291819\pi$
$863$	35.7447	1.21676	0.608382	+	0.793644i	$0.291819\pi$
$864$	−6.20788	−0.211196
$865$	16.9297	0.575628
$866$	11.2620	0.382697
$867$	41.0017	1.39249
$868$	−84.3618	−2.86343
$869$	63.7235	2.16167
$870$	45.0212	1.52636
$871$	0.754587	0.0255682
$872$	99.0999	3.35594
$873$	9.25872	0.313360
$874$	0	0
$875$	2.14656	0.0725669
$876$	−56.4201	−1.90626
$877$	−6.98831	−0.235978	−0.117989	−	0.993015i	$-0.537645\pi$
$877$	−6.98831	−0.235978	−0.117989	+	0.993015i	$0.537645\pi$
$878$	47.7258	1.61067
$879$	17.6020	0.593702
$880$	−56.5623	−1.90672
$881$	−9.66834	−0.325735	−0.162867	−	0.986648i	$-0.552074\pi$
$881$	−9.66834	−0.325735	−0.162867	+	0.986648i	$0.552074\pi$
$882$	17.9040	0.602859
$883$	22.5686	0.759493	0.379746	−	0.925091i	$-0.376011\pi$
$883$	22.5686	0.759493	0.379746	+	0.925091i	$0.376011\pi$
$884$	−0.822625	−0.0276679
$885$	−20.6275	−0.693387
$886$	31.4443	1.05639
$887$	−21.1456	−0.710001	−0.355000	−	0.934866i	$-0.615519\pi$
$887$	−21.1456	−0.710001	−0.355000	+	0.934866i	$0.615519\pi$
$888$	69.1375	2.32010
$889$	3.43803	0.115308
$890$	−8.39066	−0.281256
$891$	−47.0742	−1.57705
$892$	9.98733	0.334401
$893$	0	0
$894$	86.0772	2.87885
$895$	9.20760	0.307776
$896$	23.0384	0.769661
$897$	−8.07975	−0.269775
$898$	−10.5298	−0.351385
$899$	−54.6572	−1.82292
$900$	14.2404	0.474680
$901$	−0.215717	−0.00718659
$902$	−37.9432	−1.26337
$903$	22.1997	0.738759
$904$	102.245	3.40061
$905$	−14.8691	−0.494267
$906$	112.826	3.74841
$907$	55.2756	1.83539	0.917697	−	0.397280i	$-0.130046\pi$
$907$	55.2756	1.83539	0.917697	+	0.397280i	$0.130046\pi$
$908$	151.073	5.01354
$909$	22.5514	0.747984
$910$	−25.8878	−0.858173
$911$	−44.4006	−1.47106	−0.735529	−	0.677493i	$-0.763066\pi$
$911$	−44.4006	−1.47106	−0.735529	+	0.677493i	$0.763066\pi$
$912$	0	0
$913$	−71.3312	−2.36072
$914$	−33.7482	−1.11629
$915$	−25.8067	−0.853144
$916$	48.0368	1.58718
$917$	−16.6168	−0.548734
$918$	0.0418032	0.00137971
$919$	−5.70996	−0.188354	−0.0941771	−	0.995555i	$-0.530022\pi$
$919$	−5.70996	−0.188354	−0.0941771	+	0.995555i	$0.530022\pi$
$920$	5.98204	0.197222
$921$	47.3136	1.55904
$922$	10.2932	0.338988
$923$	−54.1773	−1.78327
$924$	129.474	4.25938
$925$	3.53458	0.116216
$926$	68.4918	2.25078
$927$	16.2220	0.532799
$928$	99.3638	3.26178
$929$	46.8663	1.53763	0.768817	−	0.639469i	$-0.220846\pi$
$929$	46.8663	1.53763	0.768817	+	0.639469i	$0.220846\pi$
$930$	−49.8199	−1.63366
$931$	0	0
$932$	26.3521	0.863191
$933$	42.2037	1.38169
$934$	14.6489	0.479328
$935$	0.177390	0.00580128
$936$	−103.771	−3.39187
$937$	−32.2494	−1.05354	−0.526771	−	0.850007i	$-0.676597\pi$
$937$	−32.2494	−1.05354	−0.526771	+	0.850007i	$0.676597\pi$
$938$	0.947327	0.0309313
$939$	−37.7894	−1.23321
$940$	8.43166	0.275010
$941$	22.5519	0.735170	0.367585	−	0.929990i	$-0.380185\pi$
$941$	22.5519	0.735170	0.367585	+	0.929990i	$0.380185\pi$
$942$	−116.377	−3.79178
$943$	2.12974	0.0693538
$944$	−97.7512	−3.18153
$945$	0.942516	0.0306601
$946$	−56.3490	−1.83206
$947$	38.6745	1.25675	0.628377	−	0.777909i	$-0.283720\pi$
$947$	38.6745	1.25675	0.628377	+	0.777909i	$0.283720\pi$
$948$	−156.966	−5.09801
$949$	21.0191	0.682309
$950$	0	0
$951$	56.5818	1.83479
$952$	−0.624014	−0.0202244
$953$	33.0869	1.07179	0.535895	−	0.844284i	$-0.319974\pi$
$953$	33.0869	1.07179	0.535895	+	0.844284i	$0.319974\pi$
$954$	−45.0359	−1.45809
$955$	−19.7967	−0.640607
$956$	85.1292	2.75328
$957$	83.8849	2.71161
$958$	13.2613	0.428454
$959$	−28.8722	−0.932333
$960$	35.4286	1.14345
$961$	29.4830	0.951063
$962$	−42.6276	−1.37437
$963$	16.5690	0.533928
$964$	−125.931	−4.05596
$965$	−21.0884	−0.678860
$966$	−10.1435	−0.326362
$967$	12.4218	0.399457	0.199728	−	0.979851i	$-0.435994\pi$
$967$	12.4218	0.399457	0.199728	+	0.979851i	$0.435994\pi$
$968$	−109.371	−3.51532
$969$	0	0
$970$	8.72602	0.280176
$971$	1.47196	0.0472375	0.0236188	−	0.999721i	$-0.492481\pi$
$971$	1.47196	0.0472375	0.0236188	+	0.999721i	$0.492481\pi$
$972$	109.298	3.50574
$973$	−33.7107	−1.08072
$974$	56.1900	1.80044
$975$	−10.9531	−0.350781
$976$	−122.295	−3.91456
$977$	26.5549	0.849567	0.424784	−	0.905295i	$-0.360350\pi$
$977$	26.5549	0.849567	0.424784	+	0.905295i	$0.360350\pi$
$978$	−35.5770	−1.13763
$979$	−15.6337	−0.499656
$980$	12.0893	0.386179
$981$	−34.4365	−1.09947
$982$	10.4895	0.334734
$983$	33.7295	1.07580	0.537902	−	0.843007i	$-0.319217\pi$
$983$	33.7295	1.07580	0.537902	+	0.843007i	$0.319217\pi$
$984$	56.4731	1.80030
$985$	4.92842	0.157033
$986$	−0.669105	−0.0213086
$987$	−8.63881	−0.274976
$988$	0	0
$989$	3.16285	0.100573
$990$	37.0342	1.17702
$991$	37.8824	1.20338	0.601688	−	0.798732i	$-0.294495\pi$
$991$	37.8824	1.20338	0.601688	+	0.798732i	$0.294495\pi$
$992$	−109.955	−3.49106
$993$	−31.6979	−1.00590
$994$	−68.0155	−2.15732
$995$	−4.32056	−0.136971
$996$	175.705	5.56744
$997$	−29.0155	−0.918930	−0.459465	−	0.888196i	$-0.651959\pi$
$997$	−29.0155	−0.918930	−0.459465	+	0.888196i	$0.651959\pi$
$998$	−47.2674	−1.49622
$999$	1.55197	0.0491023

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1805.2.a.r.1.1	yes	6
5.4	even	2		9025.2.a.bq.1.6		6
19.18	odd	2		1805.2.a.q.1.6	✓	6
95.94	odd	2		9025.2.a.ca.1.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1805.2.a.q.1.6	✓	6	19.18	odd	2
1805.2.a.r.1.1	yes	6	1.1	even	1	trivial
9025.2.a.bq.1.6		6	5.4	even	2
9025.2.a.ca.1.1		6	95.94	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1805 = 5 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1805.a (trivial)

\(f(q)\)	\(=\)	\(q-2.65583 q^{2} -2.41205 q^{3} +5.05344 q^{4} -1.00000 q^{5} +6.40599 q^{6} -2.14656 q^{7} -8.10942 q^{8} +2.81796 q^{9} +O(q^{10})\)	\(q-2.65583 q^{2} -2.41205 q^{3} +5.05344 q^{4} -1.00000 q^{5} +6.40599 q^{6} -2.14656 q^{7} -8.10942 q^{8} +2.81796 q^{9} +2.65583 q^{10} +4.94842 q^{11} -12.1891 q^{12} +4.54101 q^{13} +5.70089 q^{14} +2.41205 q^{15} +11.4304 q^{16} -0.0358478 q^{17} -7.48403 q^{18} -5.05344 q^{20} +5.17759 q^{21} -13.1422 q^{22} +0.737666 q^{23} +19.5603 q^{24} +1.00000 q^{25} -12.0602 q^{26} +0.439083 q^{27} -10.8475 q^{28} -7.02799 q^{29} -6.40599 q^{30} +7.77708 q^{31} -14.1383 q^{32} -11.9358 q^{33} +0.0952057 q^{34} +2.14656 q^{35} +14.2404 q^{36} +3.53458 q^{37} -10.9531 q^{39} +8.10942 q^{40} +2.88713 q^{41} -13.7508 q^{42} +4.28764 q^{43} +25.0066 q^{44} -2.81796 q^{45} -1.95912 q^{46} -1.66850 q^{47} -27.5706 q^{48} -2.39229 q^{49} -2.65583 q^{50} +0.0864665 q^{51} +22.9477 q^{52} +6.01759 q^{53} -1.16613 q^{54} -4.94842 q^{55} +17.4073 q^{56} +18.6652 q^{58} -8.55188 q^{59} +12.1891 q^{60} -10.6991 q^{61} -20.6546 q^{62} -6.04892 q^{63} +14.6882 q^{64} -4.54101 q^{65} +31.6995 q^{66} +0.166172 q^{67} -0.181155 q^{68} -1.77928 q^{69} -5.70089 q^{70} -11.9307 q^{71} -22.8520 q^{72} +4.62873 q^{73} -9.38726 q^{74} -2.41205 q^{75} -10.6221 q^{77} +29.0896 q^{78} +12.8775 q^{79} -11.4304 q^{80} -9.51297 q^{81} -7.66773 q^{82} -14.4149 q^{83} +26.1647 q^{84} +0.0358478 q^{85} -11.3873 q^{86} +16.9518 q^{87} -40.1288 q^{88} -3.15934 q^{89} +7.48403 q^{90} -9.74754 q^{91} +3.72775 q^{92} -18.7587 q^{93} +4.43125 q^{94} +34.1022 q^{96} +3.28561 q^{97} +6.35352 q^{98} +13.9445 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 2 q^{2} + 4 q^{3} + 8 q^{4} - 6 q^{5} + 8 q^{6} + 7 q^{7} + 10 q^{9}+O(q^{10}) \) 6 * q + 2 * q^2 + 4 * q^3 + 8 * q^4 - 6 * q^5 + 8 * q^6 + 7 * q^7 + 10 * q^9	\( 6 q + 2 q^{2} + 4 q^{3} + 8 q^{4} - 6 q^{5} + 8 q^{6} + 7 q^{7} + 10 q^{9} - 2 q^{10} + 15 q^{11} - 20 q^{12} + 6 q^{13} + 20 q^{14} - 4 q^{15} + 20 q^{16} + 5 q^{17} - 8 q^{18} - 8 q^{20} + 7 q^{21} + 14 q^{22} + 18 q^{24} + 6 q^{25} - 22 q^{26} + 28 q^{27} + 10 q^{28} - 20 q^{29} - 8 q^{30} + 12 q^{31} - 8 q^{32} + q^{33} - 7 q^{35} - 14 q^{36} + 20 q^{37} + 16 q^{39} + 8 q^{41} - 30 q^{42} + 27 q^{43} + 46 q^{44} - 10 q^{45} + 16 q^{46} - 8 q^{47} - 24 q^{48} + 11 q^{49} + 2 q^{50} - 11 q^{51} + 4 q^{52} + 19 q^{53} + 30 q^{54} - 15 q^{55} + 62 q^{56} + 20 q^{58} - 41 q^{59} + 20 q^{60} + 6 q^{61} - 30 q^{62} - 18 q^{63} + 48 q^{64} - 6 q^{65} + 46 q^{66} - 15 q^{67} - 14 q^{68} - 10 q^{69} - 20 q^{70} + 2 q^{71} - 68 q^{72} + 8 q^{73} + 2 q^{74} + 4 q^{75} + 21 q^{77} + 46 q^{78} + 18 q^{79} - 20 q^{80} + 50 q^{81} - 18 q^{82} - 10 q^{83} + 4 q^{84} - 5 q^{85} - 10 q^{86} - 14 q^{87} - 52 q^{88} + 17 q^{89} + 8 q^{90} - 23 q^{91} + 28 q^{92} + 10 q^{93} - 28 q^{94} + 26 q^{96} - 4 q^{97} + 50 q^{98} + 58 q^{99}+O(q^{100}) \) 6 * q + 2 * q^2 + 4 * q^3 + 8 * q^4 - 6 * q^5 + 8 * q^6 + 7 * q^7 + 10 * q^9 - 2 * q^10 + 15 * q^11 - 20 * q^12 + 6 * q^13 + 20 * q^14 - 4 * q^15 + 20 * q^16 + 5 * q^17 - 8 * q^18 - 8 * q^20 + 7 * q^21 + 14 * q^22 + 18 * q^24 + 6 * q^25 - 22 * q^26 + 28 * q^27 + 10 * q^28 - 20 * q^29 - 8 * q^30 + 12 * q^31 - 8 * q^32 + q^33 - 7 * q^35 - 14 * q^36 + 20 * q^37 + 16 * q^39 + 8 * q^41 - 30 * q^42 + 27 * q^43 + 46 * q^44 - 10 * q^45 + 16 * q^46 - 8 * q^47 - 24 * q^48 + 11 * q^49 + 2 * q^50 - 11 * q^51 + 4 * q^52 + 19 * q^53 + 30 * q^54 - 15 * q^55 + 62 * q^56 + 20 * q^58 - 41 * q^59 + 20 * q^60 + 6 * q^61 - 30 * q^62 - 18 * q^63 + 48 * q^64 - 6 * q^65 + 46 * q^66 - 15 * q^67 - 14 * q^68 - 10 * q^69 - 20 * q^70 + 2 * q^71 - 68 * q^72 + 8 * q^73 + 2 * q^74 + 4 * q^75 + 21 * q^77 + 46 * q^78 + 18 * q^79 - 20 * q^80 + 50 * q^81 - 18 * q^82 - 10 * q^83 + 4 * q^84 - 5 * q^85 - 10 * q^86 - 14 * q^87 - 52 * q^88 + 17 * q^89 + 8 * q^90 - 23 * q^91 + 28 * q^92 + 10 * q^93 - 28 * q^94 + 26 * q^96 - 4 * q^97 + 50 * q^98 + 58 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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