LMFDB - Embedded newform 1441.2.a.d.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1441,2,Mod(1,1441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1441, 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("1441.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1441 = 11 \cdot 131 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1441.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:	$11.5064429313$
Analytic rank:	$1$
Dimension:	$23$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	1441.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.16219 q^{2} -2.96733 q^{3} +2.67508 q^{4} +2.79492 q^{5} +6.41593 q^{6} +0.0561777 q^{7} -1.45964 q^{8} +5.80503 q^{9} +O(q^{10})$	\(q-2.16219 q^{2} -2.96733 q^{3} +2.67508 q^{4} +2.79492 q^{5} +6.41593 q^{6} +0.0561777 q^{7} -1.45964 q^{8} +5.80503 q^{9} -6.04316 q^{10} -1.00000 q^{11} -7.93783 q^{12} +1.45141 q^{13} -0.121467 q^{14} -8.29345 q^{15} -2.19412 q^{16} +4.50639 q^{17} -12.5516 q^{18} -6.25998 q^{19} +7.47663 q^{20} -0.166698 q^{21} +2.16219 q^{22} -7.69425 q^{23} +4.33124 q^{24} +2.81159 q^{25} -3.13823 q^{26} -8.32344 q^{27} +0.150280 q^{28} -4.54941 q^{29} +17.9320 q^{30} +0.500936 q^{31} +7.66340 q^{32} +2.96733 q^{33} -9.74368 q^{34} +0.157012 q^{35} +15.5289 q^{36} +3.93101 q^{37} +13.5353 q^{38} -4.30681 q^{39} -4.07959 q^{40} -2.22808 q^{41} +0.360432 q^{42} +0.495076 q^{43} -2.67508 q^{44} +16.2246 q^{45} +16.6365 q^{46} +9.84279 q^{47} +6.51067 q^{48} -6.99684 q^{49} -6.07919 q^{50} -13.3719 q^{51} +3.88263 q^{52} -0.774613 q^{53} +17.9969 q^{54} -2.79492 q^{55} -0.0819995 q^{56} +18.5754 q^{57} +9.83671 q^{58} -13.5296 q^{59} -22.1856 q^{60} +6.76911 q^{61} -1.08312 q^{62} +0.326113 q^{63} -12.1815 q^{64} +4.05658 q^{65} -6.41593 q^{66} +13.2605 q^{67} +12.0549 q^{68} +22.8314 q^{69} -0.339491 q^{70} -3.44587 q^{71} -8.47328 q^{72} -5.47993 q^{73} -8.49960 q^{74} -8.34290 q^{75} -16.7459 q^{76} -0.0561777 q^{77} +9.31215 q^{78} -0.0836399 q^{79} -6.13239 q^{80} +7.28329 q^{81} +4.81754 q^{82} +11.0874 q^{83} -0.445929 q^{84} +12.5950 q^{85} -1.07045 q^{86} +13.4996 q^{87} +1.45964 q^{88} -15.1504 q^{89} -35.0807 q^{90} +0.0815368 q^{91} -20.5827 q^{92} -1.48644 q^{93} -21.2820 q^{94} -17.4962 q^{95} -22.7398 q^{96} -8.17789 q^{97} +15.1285 q^{98} -5.80503 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 23 q - 7 q^{2} - 3 q^{3} + 19 q^{4} - 9 q^{5} - 5 q^{6} - 8 q^{7} - 15 q^{8} + 12 q^{9}+O(q^{10}) $ 23 * q - 7 * q^2 - 3 * q^3 + 19 * q^4 - 9 * q^5 - 5 * q^6 - 8 * q^7 - 15 * q^8 + 12 * q^9	\( 23 q - 7 q^{2} - 3 q^{3} + 19 q^{4} - 9 q^{5} - 5 q^{6} - 8 q^{7} - 15 q^{8} + 12 q^{9} - 2 q^{10} - 23 q^{11} - 12 q^{12} + 6 q^{13} - 13 q^{14} - 27 q^{15} - q^{16} - 11 q^{17} - 16 q^{19} - 24 q^{20} - 7 q^{21} + 7 q^{22} - 30 q^{23} - 20 q^{24} + 10 q^{25} - 22 q^{26} - 15 q^{27} + 11 q^{28} - 15 q^{29} + 17 q^{30} - 31 q^{31} - 22 q^{32} + 3 q^{33} - 18 q^{34} - 34 q^{35} - 18 q^{36} - 26 q^{37} - 32 q^{39} + 16 q^{40} - 21 q^{41} - 37 q^{42} - 2 q^{43} - 19 q^{44} - 18 q^{45} - 6 q^{46} - 25 q^{47} + 14 q^{48} + 7 q^{49} - 27 q^{50} - 7 q^{51} + 23 q^{52} - 34 q^{53} + 26 q^{54} + 9 q^{55} - 42 q^{56} + 6 q^{57} - 5 q^{58} - 31 q^{59} - 7 q^{60} + 19 q^{61} + 24 q^{62} - 34 q^{63} - 17 q^{64} - 13 q^{65} + 5 q^{66} - 39 q^{67} - 59 q^{68} - 12 q^{69} + 17 q^{70} - 103 q^{71} + 19 q^{72} + q^{73} - 9 q^{74} - 19 q^{75} + 10 q^{76} + 8 q^{77} - 43 q^{78} - 14 q^{79} - q^{80} - 29 q^{81} + 20 q^{82} - 14 q^{83} + 57 q^{84} + 20 q^{85} - 54 q^{86} - 23 q^{87} + 15 q^{88} - 71 q^{89} - 52 q^{90} - 18 q^{91} - 24 q^{92} - q^{93} + q^{94} - 38 q^{95} - 31 q^{96} - 26 q^{97} + 19 q^{98} - 12 q^{99}+O(q^{100}) \) 23 * q - 7 * q^2 - 3 * q^3 + 19 * q^4 - 9 * q^5 - 5 * q^6 - 8 * q^7 - 15 * q^8 + 12 * q^9 - 2 * q^10 - 23 * q^11 - 12 * q^12 + 6 * q^13 - 13 * q^14 - 27 * q^15 - q^16 - 11 * q^17 - 16 * q^19 - 24 * q^20 - 7 * q^21 + 7 * q^22 - 30 * q^23 - 20 * q^24 + 10 * q^25 - 22 * q^26 - 15 * q^27 + 11 * q^28 - 15 * q^29 + 17 * q^30 - 31 * q^31 - 22 * q^32 + 3 * q^33 - 18 * q^34 - 34 * q^35 - 18 * q^36 - 26 * q^37 - 32 * q^39 + 16 * q^40 - 21 * q^41 - 37 * q^42 - 2 * q^43 - 19 * q^44 - 18 * q^45 - 6 * q^46 - 25 * q^47 + 14 * q^48 + 7 * q^49 - 27 * q^50 - 7 * q^51 + 23 * q^52 - 34 * q^53 + 26 * q^54 + 9 * q^55 - 42 * q^56 + 6 * q^57 - 5 * q^58 - 31 * q^59 - 7 * q^60 + 19 * q^61 + 24 * q^62 - 34 * q^63 - 17 * q^64 - 13 * q^65 + 5 * q^66 - 39 * q^67 - 59 * q^68 - 12 * q^69 + 17 * q^70 - 103 * q^71 + 19 * q^72 + q^73 - 9 * q^74 - 19 * q^75 + 10 * q^76 + 8 * q^77 - 43 * q^78 - 14 * q^79 - q^80 - 29 * q^81 + 20 * q^82 - 14 * q^83 + 57 * q^84 + 20 * q^85 - 54 * q^86 - 23 * q^87 + 15 * q^88 - 71 * q^89 - 52 * q^90 - 18 * q^91 - 24 * q^92 - q^93 + q^94 - 38 * q^95 - 31 * q^96 - 26 * q^97 + 19 * q^98 - 12 * 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 $

$2$	−2.16219	−1.52890	−0.764450	−	0.644682i	$-0.776990\pi$
$2$	−2.16219	−1.52890	−0.764450	+	0.644682i	$0.776990\pi$
$3$	−2.96733	−1.71319	−0.856594	−	0.515992i	$-0.827424\pi$
$3$	−2.96733	−1.71319	−0.856594	+	0.515992i	$0.827424\pi$
$4$	2.67508	1.33754
$5$	2.79492	1.24993	0.624963	−	0.780654i	$-0.285114\pi$
$5$	2.79492	1.24993	0.624963	+	0.780654i	$0.285114\pi$
$6$	6.41593	2.61929
$7$	0.0561777	0.0212332	0.0106166	−	0.999944i	$-0.496621\pi$
$7$	0.0561777	0.0212332	0.0106166	+	0.999944i	$0.496621\pi$
$8$	−1.45964	−0.516062
$9$	5.80503	1.93501
$10$	−6.04316	−1.91101
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−7.93783	−2.29145
$13$	1.45141	0.402549	0.201274	−	0.979535i	$-0.435492\pi$
$13$	1.45141	0.402549	0.201274	+	0.979535i	$0.435492\pi$
$14$	−0.121467	−0.0324634
$15$	−8.29345	−2.14136
$16$	−2.19412	−0.548530
$17$	4.50639	1.09296	0.546480	−	0.837472i	$-0.315967\pi$
$17$	4.50639	1.09296	0.546480	+	0.837472i	$0.315967\pi$
$18$	−12.5516	−2.95844
$19$	−6.25998	−1.43614	−0.718069	−	0.695972i	$-0.754974\pi$
$19$	−6.25998	−1.43614	−0.718069	+	0.695972i	$0.754974\pi$
$20$	7.47663	1.67182
$21$	−0.166698	−0.0363764
$22$	2.16219	0.460981
$23$	−7.69425	−1.60436	−0.802181	−	0.597081i	$-0.796327\pi$
$23$	−7.69425	−1.60436	−0.802181	+	0.597081i	$0.796327\pi$
$24$	4.33124	0.884111
$25$	2.81159	0.562317
$26$	−3.13823	−0.615457
$27$	−8.32344	−1.60185
$28$	0.150280	0.0284002
$29$	−4.54941	−0.844805	−0.422402	−	0.906408i	$-0.638813\pi$
$29$	−4.54941	−0.844805	−0.422402	+	0.906408i	$0.638813\pi$
$30$	17.9320	3.27393
$31$	0.500936	0.0899707	0.0449854	−	0.998988i	$-0.485676\pi$
$31$	0.500936	0.0899707	0.0449854	+	0.998988i	$0.485676\pi$
$32$	7.66340	1.35471
$33$	2.96733	0.516545
$34$	−9.74368	−1.67103
$35$	0.157012	0.0265399
$36$	15.5289	2.58815
$37$	3.93101	0.646254	0.323127	−	0.946356i	$-0.395266\pi$
$37$	3.93101	0.646254	0.323127	+	0.946356i	$0.395266\pi$
$38$	13.5353	2.19571
$39$	−4.30681	−0.689641
$40$	−4.07959	−0.645040
$41$	−2.22808	−0.347967	−0.173984	−	0.984749i	$-0.555664\pi$
$41$	−2.22808	−0.347967	−0.173984	+	0.984749i	$0.555664\pi$
$42$	0.360432	0.0556159
$43$	0.495076	0.0754984	0.0377492	−	0.999287i	$-0.487981\pi$
$43$	0.495076	0.0754984	0.0377492	+	0.999287i	$0.487981\pi$
$44$	−2.67508	−0.403283
$45$	16.2246	2.41862
$46$	16.6365	2.45291
$47$	9.84279	1.43572	0.717859	−	0.696189i	$-0.245122\pi$
$47$	9.84279	1.43572	0.717859	+	0.696189i	$0.245122\pi$
$48$	6.51067	0.939734
$49$	−6.99684	−0.999549
$50$	−6.07919	−0.859727
$51$	−13.3719	−1.87244
$52$	3.88263	0.538424
$53$	−0.774613	−0.106401	−0.0532007	−	0.998584i	$-0.516942\pi$
$53$	−0.774613	−0.106401	−0.0532007	+	0.998584i	$0.516942\pi$
$54$	17.9969	2.44907
$55$	−2.79492	−0.376867
$56$	−0.0819995	−0.0109576
$57$	18.5754	2.46037
$58$	9.83671	1.29162
$59$	−13.5296	−1.76141	−0.880705	−	0.473665i	$-0.842931\pi$
$59$	−13.5296	−1.76141	−0.880705	+	0.473665i	$0.842931\pi$
$60$	−22.1856	−2.86415
$61$	6.76911	0.866696	0.433348	−	0.901227i	$-0.357332\pi$
$61$	6.76911	0.866696	0.433348	+	0.901227i	$0.357332\pi$
$62$	−1.08312	−0.137556
$63$	0.326113	0.0410864
$64$	−12.1815	−1.52269
$65$	4.05658	0.503156
$66$	−6.41593	−0.789747
$67$	13.2605	1.62003	0.810013	−	0.586412i	$-0.199460\pi$
$67$	13.2605	1.62003	0.810013	+	0.586412i	$0.199460\pi$
$68$	12.0549	1.46188
$69$	22.8314	2.74857
$70$	−0.339491	−0.0405769
$71$	−3.44587	−0.408949	−0.204475	−	0.978872i	$-0.565549\pi$
$71$	−3.44587	−0.408949	−0.204475	+	0.978872i	$0.565549\pi$
$72$	−8.47328	−0.998586
$73$	−5.47993	−0.641378	−0.320689	−	0.947185i	$-0.603914\pi$
$73$	−5.47993	−0.641378	−0.320689	+	0.947185i	$0.603914\pi$
$74$	−8.49960	−0.988058
$75$	−8.34290	−0.963355
$76$	−16.7459	−1.92089
$77$	−0.0561777	−0.00640204
$78$	9.31215	1.05439
$79$	−0.0836399	−0.00941022	−0.00470511	−	0.999989i	$-0.501498\pi$
$79$	−0.0836399	−0.00941022	−0.00470511	+	0.999989i	$0.501498\pi$
$80$	−6.13239	−0.685622
$81$	7.28329	0.809254
$82$	4.81754	0.532008
$83$	11.0874	1.21700	0.608502	−	0.793552i	$-0.291771\pi$
$83$	11.0874	1.21700	0.608502	+	0.793552i	$0.291771\pi$
$84$	−0.445929	−0.0486548
$85$	12.5950	1.36612
$86$	−1.07045	−0.115430
$87$	13.4996	1.44731
$88$	1.45964	0.155599
$89$	−15.1504	−1.60594	−0.802972	−	0.596017i	$-0.796749\pi$
$89$	−15.1504	−1.60594	−0.802972	+	0.596017i	$0.796749\pi$
$90$	−35.0807	−3.69783
$91$	0.0815368	0.00854738
$92$	−20.5827	−2.14590
$93$	−1.48644	−0.154137
$94$	−21.2820	−2.19507
$95$	−17.4962	−1.79507
$96$	−22.7398	−2.32087
$97$	−8.17789	−0.830339	−0.415169	−	0.909744i	$-0.636278\pi$
$97$	−8.17789	−0.830339	−0.415169	+	0.909744i	$0.636278\pi$
$98$	15.1285	1.52821
$99$	−5.80503	−0.583428
$100$	7.52121	0.752121
$101$	−1.52296	−0.151540	−0.0757701	−	0.997125i	$-0.524142\pi$
$101$	−1.52296	−0.151540	−0.0757701	+	0.997125i	$0.524142\pi$
$102$	28.9127	2.86278
$103$	1.10397	0.108777	0.0543886	−	0.998520i	$-0.482679\pi$
$103$	1.10397	0.108777	0.0543886	+	0.998520i	$0.482679\pi$
$104$	−2.11854	−0.207740
$105$	−0.465907	−0.0454678
$106$	1.67486	0.162677
$107$	−13.2966	−1.28543	−0.642715	−	0.766105i	$-0.722192\pi$
$107$	−13.2966	−1.28543	−0.642715	+	0.766105i	$0.722192\pi$
$108$	−22.2658	−2.14253
$109$	10.7733	1.03189	0.515946	−	0.856621i	$-0.327441\pi$
$109$	10.7733	1.03189	0.515946	+	0.856621i	$0.327441\pi$
$110$	6.04316	0.576193
$111$	−11.6646	−1.10715
$112$	−0.123261	−0.0116470
$113$	−7.52938	−0.708304	−0.354152	−	0.935188i	$-0.615231\pi$
$113$	−7.52938	−0.708304	−0.354152	+	0.935188i	$0.615231\pi$
$114$	−40.1636	−3.76167
$115$	−21.5048	−2.00534
$116$	−12.1700	−1.12996
$117$	8.42548	0.778936
$118$	29.2537	2.69302
$119$	0.253159	0.0232070
$120$	12.1055	1.10507
$121$	1.00000	0.0909091
$122$	−14.6361	−1.32509
$123$	6.61144	0.596133
$124$	1.34004	0.120339
$125$	−6.11644	−0.547071
$126$	−0.705120	−0.0628170
$127$	−10.7400	−0.953019	−0.476510	−	0.879169i	$-0.658098\pi$
$127$	−10.7400	−0.953019	−0.476510	+	0.879169i	$0.658098\pi$
$128$	11.0120	0.973329
$129$	−1.46905	−0.129343
$130$	−8.77110	−0.769276
$131$	−1.00000	−0.0873704
$131$	−1.00000	−0.0873704
$132$	7.93783	0.690899
$133$	−0.351671	−0.0304938
$134$	−28.6717	−2.47686
$135$	−23.2634	−2.00219
$136$	−6.57773	−0.564035
$137$	−6.26875	−0.535576	−0.267788	−	0.963478i	$-0.586293\pi$
$137$	−6.26875	−0.535576	−0.267788	+	0.963478i	$0.586293\pi$
$138$	−49.3658	−4.20230
$139$	−5.54200	−0.470067	−0.235033	−	0.971987i	$-0.575520\pi$
$139$	−5.54200	−0.470067	−0.235033	+	0.971987i	$0.575520\pi$
$140$	0.420020	0.0354981
$141$	−29.2068	−2.45965
$142$	7.45063	0.625243
$143$	−1.45141	−0.121373
$144$	−12.7369	−1.06141
$145$	−12.7153	−1.05594
$146$	11.8487	0.980603
$147$	20.7619	1.71241
$148$	10.5157	0.864389
$149$	18.7825	1.53872	0.769362	−	0.638814i	$-0.220574\pi$
$149$	18.7825	1.53872	0.769362	+	0.638814i	$0.220574\pi$
$150$	18.0389	1.47287
$151$	18.2350	1.48394	0.741970	−	0.670433i	$-0.233892\pi$
$151$	18.2350	1.48394	0.741970	+	0.670433i	$0.233892\pi$
$152$	9.13735	0.741137
$153$	26.1597	2.11489
$154$	0.121467	0.00978809
$155$	1.40008	0.112457
$156$	−11.5210	−0.922421
$157$	−7.74422	−0.618056	−0.309028	−	0.951053i	$-0.600004\pi$
$157$	−7.74422	−0.618056	−0.309028	+	0.951053i	$0.600004\pi$
$158$	0.180846	0.0143873
$159$	2.29853	0.182285
$160$	21.4186	1.69329
$161$	−0.432245	−0.0340657
$162$	−15.7479	−1.23727
$163$	12.3113	0.964293	0.482147	−	0.876091i	$-0.339857\pi$
$163$	12.3113	0.964293	0.482147	+	0.876091i	$0.339857\pi$
$164$	−5.96028	−0.465420
$165$	8.29345	0.645644
$166$	−23.9732	−1.86068
$167$	−16.3916	−1.26842	−0.634211	−	0.773160i	$-0.718675\pi$
$167$	−16.3916	−1.26842	−0.634211	+	0.773160i	$0.718675\pi$
$168$	0.243319	0.0187725
$169$	−10.8934	−0.837955
$170$	−27.2328	−2.08866
$171$	−36.3394	−2.77894
$172$	1.32437	0.100982
$173$	−25.5950	−1.94595	−0.972977	−	0.230901i	$-0.925833\pi$
$173$	−25.5950	−1.94595	−0.972977	+	0.230901i	$0.925833\pi$
$174$	−29.1887	−2.21279
$175$	0.157948	0.0119398
$176$	2.19412	0.165388
$177$	40.1469	3.01763
$178$	32.7582	2.45533
$179$	−14.9066	−1.11417	−0.557084	−	0.830456i	$-0.688080\pi$
$179$	−14.9066	−1.11417	−0.557084	+	0.830456i	$0.688080\pi$
$180$	43.4021	3.23500
$181$	2.62416	0.195053	0.0975263	−	0.995233i	$-0.468907\pi$
$181$	2.62416	0.195053	0.0975263	+	0.995233i	$0.468907\pi$
$182$	−0.176298	−0.0130681
$183$	−20.0862	−1.48481
$184$	11.2309	0.827951
$185$	10.9869	0.807770
$186$	3.21397	0.235660
$187$	−4.50639	−0.329540
$188$	26.3302	1.92033
$189$	−0.467592	−0.0340123
$190$	37.8301	2.74448
$191$	−0.749920	−0.0542623	−0.0271312	−	0.999632i	$-0.508637\pi$
$191$	−0.749920	−0.0542623	−0.0271312	+	0.999632i	$0.508637\pi$
$192$	36.1465	2.60865
$193$	16.4809	1.18632	0.593162	−	0.805083i	$-0.297879\pi$
$193$	16.4809	1.18632	0.593162	+	0.805083i	$0.297879\pi$
$194$	17.6822	1.26951
$195$	−12.0372	−0.862001
$196$	−18.7171	−1.33694
$197$	−3.90697	−0.278360	−0.139180	−	0.990267i	$-0.544447\pi$
$197$	−3.90697	−0.278360	−0.139180	+	0.990267i	$0.544447\pi$
$198$	12.5516	0.892003
$199$	0.748231	0.0530407	0.0265203	−	0.999648i	$-0.491557\pi$
$199$	0.748231	0.0530407	0.0265203	+	0.999648i	$0.491557\pi$
$200$	−4.10392	−0.290191
$201$	−39.3482	−2.77541
$202$	3.29293	0.231690
$203$	−0.255576	−0.0179379
$204$	−35.7709	−2.50447
$205$	−6.22731	−0.434934
$206$	−2.38699	−0.166310
$207$	−44.6654	−3.10446
$208$	−3.18457	−0.220810
$209$	6.25998	0.433012
$210$	1.00738	0.0695158
$211$	−1.54124	−0.106103	−0.0530517	−	0.998592i	$-0.516895\pi$
$211$	−1.54124	−0.106103	−0.0530517	+	0.998592i	$0.516895\pi$
$212$	−2.07215	−0.142316
$213$	10.2250	0.700607
$214$	28.7498	1.96530
$215$	1.38370	0.0943675
$216$	12.1493	0.826653
$217$	0.0281414	0.00191036
$218$	−23.2939	−1.57766
$219$	16.2608	1.09880
$220$	−7.47663	−0.504074
$221$	6.54062	0.439969
$222$	25.2211	1.69273
$223$	−18.1014	−1.21216	−0.606078	−	0.795405i	$-0.707258\pi$
$223$	−18.1014	−1.21216	−0.606078	+	0.795405i	$0.707258\pi$
$224$	0.430512	0.0287648
$225$	16.3213	1.08809
$226$	16.2800	1.08293
$227$	11.1222	0.738206	0.369103	−	0.929389i	$-0.379665\pi$
$227$	11.1222	0.738206	0.369103	+	0.929389i	$0.379665\pi$
$228$	49.6906	3.29084
$229$	−3.03508	−0.200564	−0.100282	−	0.994959i	$-0.531974\pi$
$229$	−3.03508	−0.200564	−0.100282	+	0.994959i	$0.531974\pi$
$230$	46.4976	3.06596
$231$	0.166698	0.0109679
$232$	6.64053	0.435972
$233$	0.701972	0.0459877	0.0229938	−	0.999736i	$-0.492680\pi$
$233$	0.701972	0.0459877	0.0229938	+	0.999736i	$0.492680\pi$
$234$	−18.2175	−1.19092
$235$	27.5098	1.79454
$236$	−36.1928	−2.35595
$237$	0.248187	0.0161215
$238$	−0.547377	−0.0354812
$239$	4.08822	0.264445	0.132223	−	0.991220i	$-0.457789\pi$
$239$	4.08822	0.264445	0.132223	+	0.991220i	$0.457789\pi$
$240$	18.1968	1.17460
$241$	20.7251	1.33502	0.667512	−	0.744599i	$-0.267359\pi$
$241$	20.7251	1.33502	0.667512	+	0.744599i	$0.267359\pi$
$242$	−2.16219	−0.138991
$243$	3.35843	0.215443
$244$	18.1079	1.15924
$245$	−19.5556	−1.24936
$246$	−14.2952	−0.911429
$247$	−9.08580	−0.578115
$248$	−0.731188	−0.0464305
$249$	−32.9000	−2.08496
$250$	13.2249	0.836418
$251$	−2.04668	−0.129185	−0.0645927	−	0.997912i	$-0.520575\pi$
$251$	−2.04668	−0.129185	−0.0645927	+	0.997912i	$0.520575\pi$
$252$	0.872378	0.0549546
$253$	7.69425	0.483733
$254$	23.2219	1.45707
$255$	−37.3735	−2.34042
$256$	0.553036	0.0345648
$257$	−19.5032	−1.21658	−0.608288	−	0.793717i	$-0.708143\pi$
$257$	−19.5032	−1.21658	−0.608288	+	0.793717i	$0.708143\pi$
$258$	3.17638	0.197753
$259$	0.220835	0.0137220
$260$	10.8516	0.672991
$261$	−26.4095	−1.63471
$262$	2.16219	0.133581
$263$	21.4603	1.32330	0.661649	−	0.749813i	$-0.269857\pi$
$263$	21.4603	1.32330	0.661649	+	0.749813i	$0.269857\pi$
$264$	−4.33124	−0.266570
$265$	−2.16498	−0.132994
$266$	0.760381	0.0466220
$267$	44.9563	2.75128
$268$	35.4728	2.16685
$269$	22.1669	1.35154	0.675771	−	0.737112i	$-0.263811\pi$
$269$	22.1669	1.35154	0.675771	+	0.737112i	$0.263811\pi$
$270$	50.2999	3.06115
$271$	0.485779	0.0295090	0.0147545	−	0.999891i	$-0.495303\pi$
$271$	0.485779	0.0295090	0.0147545	+	0.999891i	$0.495303\pi$
$272$	−9.88756	−0.599521
$273$	−0.241946	−0.0146433
$274$	13.5543	0.818842
$275$	−2.81159	−0.169545
$276$	61.0756	3.67632
$277$	−2.81914	−0.169386	−0.0846930	−	0.996407i	$-0.526991\pi$
$277$	−2.81914	−0.169386	−0.0846930	+	0.996407i	$0.526991\pi$
$278$	11.9829	0.718685
$279$	2.90795	0.174094
$280$	−0.229182	−0.0136962
$281$	−32.8912	−1.96213	−0.981063	−	0.193686i	$-0.937956\pi$
$281$	−32.8912	−1.96213	−0.981063	+	0.193686i	$0.937956\pi$
$282$	63.1507	3.76057
$283$	21.0162	1.24928	0.624642	−	0.780911i	$-0.285245\pi$
$283$	21.0162	1.24928	0.624642	+	0.780911i	$0.285245\pi$
$284$	−9.21796	−0.546985
$285$	51.9168	3.07529
$286$	3.13823	0.185567
$287$	−0.125168	−0.00738845
$288$	44.4863	2.62138
$289$	3.30754	0.194561
$290$	27.4928	1.61443
$291$	24.2665	1.42253
$292$	−14.6592	−0.857867
$293$	−23.6436	−1.38127	−0.690636	−	0.723203i	$-0.742669\pi$
$293$	−23.6436	−1.38127	−0.690636	+	0.723203i	$0.742669\pi$
$294$	−44.8913	−2.61811
$295$	−37.8143	−2.20163
$296$	−5.73788	−0.333507
$297$	8.32344	0.482975
$298$	−40.6114	−2.35256
$299$	−11.1675	−0.645834
$300$	−22.3179	−1.28852
$301$	0.0278122	0.00160307
$302$	−39.4275	−2.26880
$303$	4.51912	0.259617
$304$	13.7351	0.787765
$305$	18.9191	1.08331
$306$	−56.5624	−3.23346
$307$	16.0183	0.914215	0.457108	−	0.889411i	$-0.348885\pi$
$307$	16.0183	0.914215	0.457108	+	0.889411i	$0.348885\pi$
$308$	−0.150280	−0.00856297
$309$	−3.27583	−0.186356
$310$	−3.02723	−0.171935
$311$	−12.6615	−0.717967	−0.358983	−	0.933344i	$-0.616877\pi$
$311$	−12.6615	−0.717967	−0.358983	+	0.933344i	$0.616877\pi$
$312$	6.28641	0.355898
$313$	−28.8545	−1.63095	−0.815475	−	0.578792i	$-0.803524\pi$
$313$	−28.8545	−1.63095	−0.815475	+	0.578792i	$0.803524\pi$
$314$	16.7445	0.944946
$315$	0.911461	0.0513550
$316$	−0.223743	−0.0125865
$317$	−9.34754	−0.525010	−0.262505	−	0.964931i	$-0.584549\pi$
$317$	−9.34754	−0.525010	−0.262505	+	0.964931i	$0.584549\pi$
$318$	−4.96987	−0.278696
$319$	4.54941	0.254718
$320$	−34.0463	−1.90325
$321$	39.4553	2.20218
$322$	0.934598	0.0520831
$323$	−28.2099	−1.56964
$324$	19.4834	1.08241
$325$	4.08076	0.226360
$326$	−26.6193	−1.47431
$327$	−31.9678	−1.76782
$328$	3.25220	0.179573
$329$	0.552945	0.0304848
$330$	−17.9320	−0.987126
$331$	−18.6524	−1.02523	−0.512614	−	0.858619i	$-0.671323\pi$
$331$	−18.6524	−1.02523	−0.512614	+	0.858619i	$0.671323\pi$
$332$	29.6597	1.62779
$333$	22.8196	1.25051
$334$	35.4419	1.93929
$335$	37.0620	2.02491
$336$	0.365754	0.0199535
$337$	−21.2427	−1.15717	−0.578583	−	0.815624i	$-0.696394\pi$
$337$	−21.2427	−1.15717	−0.578583	+	0.815624i	$0.696394\pi$
$338$	23.5536	1.28115
$339$	22.3421	1.21346
$340$	33.6926	1.82724
$341$	−0.500936	−0.0271272
$342$	78.5727	4.24873
$343$	−0.786310	−0.0424568
$344$	−0.722636	−0.0389619
$345$	63.8119	3.43552
$346$	55.3414	2.97517
$347$	−25.9382	−1.39243	−0.696217	−	0.717831i	$-0.745135\pi$
$347$	−25.9382	−1.39243	−0.696217	+	0.717831i	$0.745135\pi$
$348$	36.1125	1.93583
$349$	−15.5932	−0.834683	−0.417342	−	0.908750i	$-0.637038\pi$
$349$	−15.5932	−0.834683	−0.417342	+	0.908750i	$0.637038\pi$
$350$	−0.341515	−0.0182547
$351$	−12.0807	−0.644821
$352$	−7.66340	−0.408461
$353$	−23.6013	−1.25617	−0.628085	−	0.778145i	$-0.716161\pi$
$353$	−23.6013	−1.25617	−0.628085	+	0.778145i	$0.716161\pi$
$354$	−86.8053	−4.61365
$355$	−9.63093	−0.511157
$356$	−40.5286	−2.14801
$357$	−0.751204	−0.0397579
$358$	32.2308	1.70345
$359$	−17.3662	−0.916554	−0.458277	−	0.888809i	$-0.651533\pi$
$359$	−17.3662	−0.916554	−0.458277	+	0.888809i	$0.651533\pi$
$360$	−23.6822	−1.24816
$361$	20.1874	1.06249
$362$	−5.67395	−0.298216
$363$	−2.96733	−0.155744
$364$	0.218117	0.0114324
$365$	−15.3160	−0.801675
$366$	43.4301	2.27013
$367$	35.6521	1.86103	0.930513	−	0.366260i	$-0.119362\pi$
$367$	35.6521	1.86103	0.930513	+	0.366260i	$0.119362\pi$
$368$	16.8821	0.880041
$369$	−12.9341	−0.673321
$370$	−23.7557	−1.23500
$371$	−0.0435160	−0.00225924
$372$	−3.97634	−0.206164
$373$	−23.9338	−1.23924	−0.619621	−	0.784901i	$-0.712714\pi$
$373$	−23.9338	−1.23924	−0.619621	+	0.784901i	$0.712714\pi$
$374$	9.74368	0.503834
$375$	18.1495	0.937236
$376$	−14.3670	−0.740920
$377$	−6.60306	−0.340075
$378$	1.01102	0.0520014
$379$	20.6880	1.06267	0.531336	−	0.847161i	$-0.321690\pi$
$379$	20.6880	1.06267	0.531336	+	0.847161i	$0.321690\pi$
$380$	−46.8036	−2.40097
$381$	31.8690	1.63270
$382$	1.62147	0.0829617
$383$	−3.53819	−0.180793	−0.0903965	−	0.995906i	$-0.528813\pi$
$383$	−3.53819	−0.180793	−0.0903965	+	0.995906i	$0.528813\pi$
$384$	−32.6761	−1.66749
$385$	−0.157012	−0.00800208
$386$	−35.6350	−1.81377
$387$	2.87393	0.146090
$388$	−21.8765	−1.11061
$389$	−7.98629	−0.404921	−0.202460	−	0.979290i	$-0.564894\pi$
$389$	−7.98629	−0.404921	−0.202460	+	0.979290i	$0.564894\pi$
$390$	26.0267	1.31791
$391$	−34.6733	−1.75350
$392$	10.2129	0.515830
$393$	2.96733	0.149682
$394$	8.44762	0.425585
$395$	−0.233767	−0.0117621
$396$	−15.5289	−0.780357
$397$	−0.0268118	−0.00134565	−0.000672823	−	1.00000i	$-0.500214\pi$
$397$	−0.0268118	−0.00134565	−0.000672823		1.00000i	$0.500214\pi$
$398$	−1.61782	−0.0810940
$399$	1.04352	0.0522415
$400$	−6.16896	−0.308448
$401$	−14.4103	−0.719615	−0.359807	−	0.933027i	$-0.617158\pi$
$401$	−14.4103	−0.719615	−0.359807	+	0.933027i	$0.617158\pi$
$402$	85.0784	4.24332
$403$	0.727063	0.0362176
$404$	−4.07404	−0.202691
$405$	20.3562	1.01151
$406$	0.552604	0.0274253
$407$	−3.93101	−0.194853
$408$	19.5183	0.966298
$409$	−25.4018	−1.25604	−0.628020	−	0.778197i	$-0.716134\pi$
$409$	−25.4018	−1.25604	−0.628020	+	0.778197i	$0.716134\pi$
$410$	13.4646	0.664971
$411$	18.6014	0.917542
$412$	2.95320	0.145494
$413$	−0.760064	−0.0374003
$414$	96.5751	4.74641
$415$	30.9885	1.52117
$416$	11.1227	0.545337
$417$	16.4449	0.805312
$418$	−13.5353	−0.662032
$419$	−19.5877	−0.956920	−0.478460	−	0.878109i	$-0.658805\pi$
$419$	−19.5877	−0.956920	−0.478460	+	0.878109i	$0.658805\pi$
$420$	−1.24634	−0.0608150
$421$	0.191310	0.00932388	0.00466194	−	0.999989i	$-0.498516\pi$
$421$	0.191310	0.00932388	0.00466194	+	0.999989i	$0.498516\pi$
$422$	3.33246	0.162222
$423$	57.1377	2.77813
$424$	1.13066	0.0549097
$425$	12.6701	0.614590
$426$	−22.1085	−1.07116
$427$	0.380273	0.0184027
$428$	−35.5694	−1.71931
$429$	4.30681	0.207935
$430$	−2.99182	−0.144279
$431$	−9.63860	−0.464275	−0.232138	−	0.972683i	$-0.574572\pi$
$431$	−9.63860	−0.464275	−0.232138	+	0.972683i	$0.574572\pi$
$432$	18.2626	0.878661
$433$	−20.8056	−0.999852	−0.499926	−	0.866068i	$-0.666639\pi$
$433$	−20.8056	−0.999852	−0.499926	+	0.866068i	$0.666639\pi$
$434$	−0.0608471	−0.00292076
$435$	37.7303	1.80903
$436$	28.8193	1.38019
$437$	48.1659	2.30409
$438$	−35.1589	−1.67996
$439$	−22.4786	−1.07284	−0.536422	−	0.843950i	$-0.680225\pi$
$439$	−22.4786	−1.07284	−0.536422	+	0.843950i	$0.680225\pi$
$440$	4.07959	0.194487
$441$	−40.6169	−1.93414
$442$	−14.1421	−0.672670
$443$	0.755870	0.0359124	0.0179562	−	0.999839i	$-0.494284\pi$
$443$	0.755870	0.0359124	0.0179562	+	0.999839i	$0.494284\pi$
$444$	−31.2037	−1.48086
$445$	−42.3443	−2.00731
$446$	39.1386	1.85327
$447$	−55.7339	−2.63612
$448$	−0.684329	−0.0323315
$449$	−17.0643	−0.805312	−0.402656	−	0.915351i	$-0.631913\pi$
$449$	−17.0643	−0.805312	−0.402656	+	0.915351i	$0.631913\pi$
$450$	−35.2899	−1.66358
$451$	2.22808	0.104916
$452$	−20.1417	−0.947384
$453$	−54.1091	−2.54227
$454$	−24.0483	−1.12864
$455$	0.227889	0.0106836
$456$	−27.1135	−1.26971
$457$	29.5134	1.38058	0.690289	−	0.723534i	$-0.257484\pi$
$457$	29.5134	1.38058	0.690289	+	0.723534i	$0.257484\pi$
$458$	6.56243	0.306642
$459$	−37.5087	−1.75076
$460$	−57.5271	−2.68221
$461$	21.2056	0.987644	0.493822	−	0.869563i	$-0.335599\pi$
$461$	21.2056	0.987644	0.493822	+	0.869563i	$0.335599\pi$
$462$	−0.360432	−0.0167688
$463$	−42.5228	−1.97620	−0.988101	−	0.153804i	$-0.950848\pi$
$463$	−42.5228	−1.97620	−0.988101	+	0.153804i	$0.950848\pi$
$464$	9.98196	0.463401
$465$	−4.15448	−0.192660
$466$	−1.51780	−0.0703106
$467$	40.9470	1.89480	0.947401	−	0.320050i	$-0.103700\pi$
$467$	40.9470	1.89480	0.947401	+	0.320050i	$0.103700\pi$
$468$	22.5388	1.04186
$469$	0.744943	0.0343983
$470$	−59.4815	−2.74368
$471$	22.9796	1.05885
$472$	19.7485	0.908998
$473$	−0.495076	−0.0227636
$474$	−0.536628	−0.0246481
$475$	−17.6005	−0.807565
$476$	0.677218	0.0310403
$477$	−4.49665	−0.205888
$478$	−8.83952	−0.404310
$479$	5.82294	0.266057	0.133028	−	0.991112i	$-0.457530\pi$
$479$	5.82294	0.266057	0.133028	+	0.991112i	$0.457530\pi$
$480$	−63.5560	−2.90092
$481$	5.70550	0.260149
$482$	−44.8118	−2.04112
$483$	1.28261	0.0583609
$484$	2.67508	0.121594
$485$	−22.8566	−1.03786
$486$	−7.26158	−0.329392
$487$	−0.612476	−0.0277539	−0.0138770	−	0.999904i	$-0.504417\pi$
$487$	−0.612476	−0.0277539	−0.0138770	+	0.999904i	$0.504417\pi$
$488$	−9.88049	−0.447269
$489$	−36.5316	−1.65201
$490$	42.2830	1.91015
$491$	−9.93175	−0.448213	−0.224107	−	0.974565i	$-0.571946\pi$
$491$	−9.93175	−0.448213	−0.224107	+	0.974565i	$0.571946\pi$
$492$	17.6861	0.797351
$493$	−20.5014	−0.923338
$494$	19.6452	0.883881
$495$	−16.2246	−0.729242
$496$	−1.09911	−0.0493516
$497$	−0.193581	−0.00868329
$498$	71.1362	3.18769
$499$	−31.0604	−1.39045	−0.695227	−	0.718790i	$-0.744696\pi$
$499$	−31.0604	−1.39045	−0.695227	+	0.718790i	$0.744696\pi$
$500$	−16.3620	−0.731729
$501$	48.6393	2.17305
$502$	4.42532	0.197512
$503$	32.5247	1.45020	0.725102	−	0.688641i	$-0.241792\pi$
$503$	32.5247	1.45020	0.725102	+	0.688641i	$0.241792\pi$
$504$	−0.476009	−0.0212031
$505$	−4.25656	−0.189414
$506$	−16.6365	−0.739581
$507$	32.3243	1.43557
$508$	−28.7303	−1.27470
$509$	−2.92936	−0.129842	−0.0649209	−	0.997890i	$-0.520680\pi$
$509$	−2.92936	−0.129842	−0.0649209	+	0.997890i	$0.520680\pi$
$510$	80.8087	3.57827
$511$	−0.307850	−0.0136185
$512$	−23.2197	−1.02617
$513$	52.1046	2.30047
$514$	42.1697	1.86002
$515$	3.08550	0.135964
$516$	−3.92983	−0.173001
$517$	−9.84279	−0.432885
$518$	−0.477488	−0.0209796
$519$	75.9488	3.33378
$520$	−5.92116	−0.259660
$521$	−8.41672	−0.368743	−0.184372	−	0.982857i	$-0.559025\pi$
$521$	−8.41672	−0.368743	−0.184372	+	0.982857i	$0.559025\pi$
$522$	57.1024	2.49930
$523$	−39.4401	−1.72459	−0.862297	−	0.506404i	$-0.830975\pi$
$523$	−39.4401	−1.72459	−0.862297	+	0.506404i	$0.830975\pi$
$524$	−2.67508	−0.116861
$525$	−0.468685	−0.0204551
$526$	−46.4013	−2.02319
$527$	2.25741	0.0983344
$528$	−6.51067	−0.283341
$529$	36.2015	1.57398
$530$	4.68111	0.203334
$531$	−78.5400	−3.40835
$532$	−0.940748	−0.0407866
$533$	−3.23385	−0.140074
$534$	−97.2042	−4.20644
$535$	−37.1629	−1.60669
$536$	−19.3556	−0.836034
$537$	44.2326	1.90878
$538$	−47.9292	−2.06637
$539$	6.99684	0.301375
$540$	−62.2313	−2.67801
$541$	45.6421	1.96231	0.981153	−	0.193232i	$-0.0618969\pi$
$541$	45.6421	1.96231	0.981153	+	0.193232i	$0.0618969\pi$
$542$	−1.05035	−0.0451163
$543$	−7.78675	−0.334162
$544$	34.5343	1.48064
$545$	30.1104	1.28979
$546$	0.523135	0.0223881
$547$	12.4206	0.531066	0.265533	−	0.964102i	$-0.414452\pi$
$547$	12.4206	0.531066	0.265533	+	0.964102i	$0.414452\pi$
$548$	−16.7694	−0.716353
$549$	39.2949	1.67706
$550$	6.07919	0.259218
$551$	28.4792	1.21326
$552$	−33.3257	−1.41844
$553$	−0.00469870	−0.000199809 0
$554$	6.09553	0.258974
$555$	−32.6016	−1.38386
$556$	−14.8253	−0.628732
$557$	19.2631	0.816205	0.408103	−	0.912936i	$-0.366191\pi$
$557$	19.2631	0.816205	0.408103	+	0.912936i	$0.366191\pi$
$558$	−6.28754	−0.266173
$559$	0.718559	0.0303918
$560$	−0.344504	−0.0145579
$561$	13.3719	0.564563
$562$	71.1172	2.99990
$563$	−21.1235	−0.890249	−0.445125	−	0.895469i	$-0.646841\pi$
$563$	−21.1235	−0.890249	−0.445125	+	0.895469i	$0.646841\pi$
$564$	−78.1303	−3.28988
$565$	−21.0440	−0.885329
$566$	−45.4411	−1.91003
$567$	0.409158	0.0171830
$568$	5.02974	0.211043
$569$	29.8526	1.25148	0.625742	−	0.780030i	$-0.284796\pi$
$569$	29.8526	1.25148	0.625742	+	0.780030i	$0.284796\pi$
$570$	−112.254	−4.70181
$571$	24.5862	1.02890	0.514449	−	0.857521i	$-0.327996\pi$
$571$	24.5862	1.02890	0.514449	+	0.857521i	$0.327996\pi$
$572$	−3.88263	−0.162341
$573$	2.22526	0.0929615
$574$	0.270638	0.0112962
$575$	−21.6331	−0.902161
$576$	−70.7140	−2.94642
$577$	−8.08354	−0.336522	−0.168261	−	0.985742i	$-0.553815\pi$
$577$	−8.08354	−0.336522	−0.168261	+	0.985742i	$0.553815\pi$
$578$	−7.15155	−0.297465
$579$	−48.9044	−2.03240
$580$	−34.0143	−1.41237
$581$	0.622866	0.0258409
$582$	−52.4688	−2.17490
$583$	0.774613	0.0320812
$584$	7.99875	0.330991
$585$	23.5485	0.973613
$586$	51.1219	2.11183
$587$	3.16334	0.130565	0.0652825	−	0.997867i	$-0.479205\pi$
$587$	3.16334	0.130565	0.0652825	+	0.997867i	$0.479205\pi$
$588$	55.5397	2.29042
$589$	−3.13585	−0.129210
$590$	81.7618	3.36608
$591$	11.5933	0.476883
$592$	−8.62510	−0.354490
$593$	6.32482	0.259729	0.129865	−	0.991532i	$-0.458546\pi$
$593$	6.32482	0.259729	0.129865	+	0.991532i	$0.458546\pi$
$594$	−17.9969	−0.738421
$595$	0.707558	0.0290071
$596$	50.2446	2.05810
$597$	−2.22025	−0.0908686
$598$	24.1463	0.987416
$599$	−30.1028	−1.22997	−0.614983	−	0.788541i	$-0.710837\pi$
$599$	−30.1028	−1.22997	−0.614983	+	0.788541i	$0.710837\pi$
$600$	12.1777	0.497151
$601$	36.2001	1.47663	0.738317	−	0.674454i	$-0.235621\pi$
$601$	36.2001	1.47663	0.738317	+	0.674454i	$0.235621\pi$
$602$	−0.0601354	−0.00245094
$603$	76.9775	3.13477
$604$	48.7799	1.98483
$605$	2.79492	0.113630
$606$	−9.77121	−0.396928
$607$	24.3242	0.987289	0.493644	−	0.869664i	$-0.335664\pi$
$607$	24.3242	0.987289	0.493644	+	0.869664i	$0.335664\pi$
$608$	−47.9727	−1.94555
$609$	0.758376	0.0307310
$610$	−40.9068	−1.65627
$611$	14.2859	0.577946
$612$	69.9793	2.82874
$613$	23.8262	0.962333	0.481167	−	0.876629i	$-0.340213\pi$
$613$	23.8262	0.962333	0.481167	+	0.876629i	$0.340213\pi$
$614$	−34.6348	−1.39774
$615$	18.4785	0.745123
$616$	0.0819995	0.00330385
$617$	40.2716	1.62127	0.810636	−	0.585550i	$-0.199121\pi$
$617$	40.2716	1.62127	0.810636	+	0.585550i	$0.199121\pi$
$618$	7.08298	0.284919
$619$	−0.627713	−0.0252299	−0.0126150	−	0.999920i	$-0.504016\pi$
$619$	−0.627713	−0.0252299	−0.0126150	+	0.999920i	$0.504016\pi$
$620$	3.74531	0.150415
$621$	64.0427	2.56994
$622$	27.3766	1.09770
$623$	−0.851117	−0.0340993
$624$	9.44965	0.378289
$625$	−31.1529	−1.24612
$626$	62.3889	2.49356
$627$	−18.5754	−0.741831
$628$	−20.7164	−0.826673
$629$	17.7147	0.706330
$630$	−1.97075	−0.0785167
$631$	−43.8947	−1.74742	−0.873711	−	0.486446i	$-0.838293\pi$
$631$	−43.8947	−1.74742	−0.873711	+	0.486446i	$0.838293\pi$
$632$	0.122085	0.00485626
$633$	4.57337	0.181775
$634$	20.2112	0.802689
$635$	−30.0174	−1.19120
$636$	6.14875	0.243814
$637$	−10.1553	−0.402367
$638$	−9.83671	−0.389439
$639$	−20.0034	−0.791321
$640$	30.7776	1.21659
$641$	−30.8221	−1.21740	−0.608700	−	0.793401i	$-0.708309\pi$
$641$	−30.8221	−1.21740	−0.608700	+	0.793401i	$0.708309\pi$
$642$	−85.3100	−3.36692
$643$	−27.9947	−1.10400	−0.552001	−	0.833843i	$-0.686136\pi$
$643$	−27.9947	−1.10400	−0.552001	+	0.833843i	$0.686136\pi$
$644$	−1.15629	−0.0455642
$645$	−4.10589	−0.161669
$646$	60.9953	2.39983
$647$	28.7955	1.13207	0.566034	−	0.824382i	$-0.308477\pi$
$647$	28.7955	1.13207	0.566034	+	0.824382i	$0.308477\pi$
$648$	−10.6310	−0.417626
$649$	13.5296	0.531085
$650$	−8.82340	−0.346082
$651$	−0.0835048	−0.00327281
$652$	32.9336	1.28978
$653$	22.9473	0.897999	0.449000	−	0.893532i	$-0.351780\pi$
$653$	22.9473	0.897999	0.449000	+	0.893532i	$0.351780\pi$
$654$	69.1205	2.70283
$655$	−2.79492	−0.109207
$656$	4.88867	0.190871
$657$	−31.8112	−1.24107
$658$	−1.19557	−0.0466083
$659$	−39.1144	−1.52368	−0.761841	−	0.647764i	$-0.775704\pi$
$659$	−39.1144	−1.52368	−0.761841	+	0.647764i	$0.775704\pi$
$660$	22.1856	0.863573
$661$	−37.3043	−1.45097	−0.725484	−	0.688239i	$-0.758384\pi$
$661$	−37.3043	−1.45097	−0.725484	+	0.688239i	$0.758384\pi$
$662$	40.3301	1.56747
$663$	−19.4081	−0.753750
$664$	−16.1837	−0.628050
$665$	−0.982894	−0.0381150
$666$	−49.3404	−1.91190
$667$	35.0043	1.35537
$668$	−43.8489	−1.69656
$669$	53.7126	2.07665
$670$	−80.1352	−3.09589
$671$	−6.76911	−0.261319
$672$	−1.27747	−0.0492795
$673$	32.8427	1.26599	0.632997	−	0.774154i	$-0.281825\pi$
$673$	32.8427	1.26599	0.632997	+	0.774154i	$0.281825\pi$
$674$	45.9309	1.76919
$675$	−23.4021	−0.900747
$676$	−29.1407	−1.12080
$677$	−19.9601	−0.767128	−0.383564	−	0.923514i	$-0.625303\pi$
$677$	−19.9601	−0.767128	−0.383564	+	0.923514i	$0.625303\pi$
$678$	−48.3080	−1.85526
$679$	−0.459415	−0.0176307
$680$	−18.3842	−0.705003
$681$	−33.0032	−1.26468
$682$	1.08312	0.0414748
$683$	−3.12260	−0.119483	−0.0597416	−	0.998214i	$-0.519028\pi$
$683$	−3.12260	−0.119483	−0.0597416	+	0.998214i	$0.519028\pi$
$684$	−97.2106	−3.71694
$685$	−17.5207	−0.669431
$686$	1.70015	0.0649122
$687$	9.00608	0.343603
$688$	−1.08626	−0.0414132
$689$	−1.12428	−0.0428317
$690$	−137.974	−5.25256
$691$	16.1600	0.614755	0.307378	−	0.951588i	$-0.400549\pi$
$691$	16.1600	0.614755	0.307378	+	0.951588i	$0.400549\pi$
$692$	−68.4687	−2.60279
$693$	−0.326113	−0.0123880
$694$	56.0833	2.12889
$695$	−15.4895	−0.587549
$696$	−19.7046	−0.746902
$697$	−10.0406	−0.380314
$698$	33.7154	1.27615
$699$	−2.08298	−0.0787855
$700$	0.422524	0.0159699
$701$	0.535823	0.0202377	0.0101189	−	0.999949i	$-0.496779\pi$
$701$	0.535823	0.0202377	0.0101189	+	0.999949i	$0.496779\pi$
$702$	26.1209	0.985868
$703$	−24.6080	−0.928110
$704$	12.1815	0.459108
$705$	−81.6306	−3.07439
$706$	51.0305	1.92056
$707$	−0.0855564	−0.00321768
$708$	107.396	4.03619
$709$	−16.2456	−0.610118	−0.305059	−	0.952333i	$-0.598676\pi$
$709$	−16.2456	−0.610118	−0.305059	+	0.952333i	$0.598676\pi$
$710$	20.8239	0.781508
$711$	−0.485532	−0.0182089
$712$	22.1143	0.828767
$713$	−3.85433	−0.144346
$714$	1.62425	0.0607860
$715$	−4.05658	−0.151707
$716$	−39.8762	−1.49024
$717$	−12.1311	−0.453044
$718$	37.5491	1.40132
$719$	−21.3655	−0.796800	−0.398400	−	0.917212i	$-0.630434\pi$
$719$	−21.3655	−0.796800	−0.398400	+	0.917212i	$0.630434\pi$
$720$	−35.5987	−1.32669
$721$	0.0620184	0.00230968
$722$	−43.6490	−1.62445
$723$	−61.4983	−2.28715
$724$	7.01984	0.260890
$725$	−12.7911	−0.475048
$726$	6.41593	0.238118
$727$	44.6469	1.65586	0.827930	−	0.560831i	$-0.189518\pi$
$727$	44.6469	1.65586	0.827930	+	0.560831i	$0.189518\pi$
$728$	−0.119015	−0.00441098
$729$	−31.8154	−1.17835
$730$	33.1161	1.22568
$731$	2.23101	0.0825168
$732$	−53.7320	−1.98599
$733$	21.6784	0.800710	0.400355	−	0.916360i	$-0.368887\pi$
$733$	21.6784	0.800710	0.400355	+	0.916360i	$0.368887\pi$
$734$	−77.0867	−2.84532
$735$	58.0280	2.14039
$736$	−58.9641	−2.17345
$737$	−13.2605	−0.488456
$738$	27.9659	1.02944
$739$	−40.1210	−1.47587	−0.737937	−	0.674870i	$-0.764200\pi$
$739$	−40.1210	−1.47587	−0.737937	+	0.674870i	$0.764200\pi$
$740$	29.3907	1.08042
$741$	26.9605	0.990420
$742$	0.0940899	0.00345415
$743$	−1.43491	−0.0526416	−0.0263208	−	0.999654i	$-0.508379\pi$
$743$	−1.43491	−0.0526416	−0.0263208	+	0.999654i	$0.508379\pi$
$744$	2.16967	0.0795441
$745$	52.4956	1.92329
$746$	51.7494	1.89468
$747$	64.3629	2.35492
$748$	−12.0549	−0.440772
$749$	−0.746972	−0.0272938
$750$	−39.2427	−1.43294
$751$	−37.4618	−1.36700	−0.683500	−	0.729951i	$-0.739543\pi$
$751$	−37.4618	−1.36700	−0.683500	+	0.729951i	$0.739543\pi$
$752$	−21.5963	−0.787534
$753$	6.07317	0.221319
$754$	14.2771	0.519941
$755$	50.9653	1.85482
$756$	−1.25084	−0.0454927
$757$	8.32324	0.302513	0.151257	−	0.988495i	$-0.451668\pi$
$757$	8.32324	0.302513	0.151257	+	0.988495i	$0.451668\pi$
$758$	−44.7315	−1.62472
$759$	−22.8314	−0.828726
$760$	25.5382	0.926367
$761$	−0.885586	−0.0321025	−0.0160512	−	0.999871i	$-0.505109\pi$
$761$	−0.885586	−0.0321025	−0.0160512	+	0.999871i	$0.505109\pi$
$762$	−68.9070	−2.49624
$763$	0.605217	0.0219103
$764$	−2.00609	−0.0725779
$765$	73.1144	2.64346
$766$	7.65024	0.276415
$767$	−19.6371	−0.709053
$768$	−1.64104	−0.0592159
$769$	43.3453	1.56307	0.781535	−	0.623862i	$-0.214437\pi$
$769$	43.3453	1.56307	0.781535	+	0.623862i	$0.214437\pi$
$770$	0.339491	0.0122344
$771$	57.8723	2.08422
$772$	44.0878	1.58675
$773$	41.1911	1.48154	0.740770	−	0.671759i	$-0.234461\pi$
$773$	41.1911	1.48154	0.740770	+	0.671759i	$0.234461\pi$
$774$	−6.21400	−0.223358
$775$	1.40842	0.0505921
$776$	11.9368	0.428506
$777$	−0.655290	−0.0235084
$778$	17.2679	0.619084
$779$	13.9477	0.499729
$780$	−32.2004	−1.15296
$781$	3.44587	0.123303
$782$	74.9703	2.68093
$783$	37.8668	1.35325
$784$	15.3519	0.548283
$785$	−21.6445	−0.772525
$786$	−6.41593	−0.228849
$787$	32.8443	1.17077	0.585387	−	0.810754i	$-0.300943\pi$
$787$	32.8443	1.17077	0.585387	+	0.810754i	$0.300943\pi$
$788$	−10.4514	−0.372317
$789$	−63.6797	−2.26706
$790$	0.505449	0.0179831
$791$	−0.422983	−0.0150395
$792$	8.47328	0.301085
$793$	9.82475	0.348887
$794$	0.0579723	0.00205736
$795$	6.42421	0.227843
$796$	2.00158	0.0709440
$797$	10.9191	0.386774	0.193387	−	0.981123i	$-0.438053\pi$
$797$	10.9191	0.386774	0.193387	+	0.981123i	$0.438053\pi$
$798$	−2.25630	−0.0798721
$799$	44.3554	1.56918
$800$	21.5463	0.761777
$801$	−87.9488	−3.10752
$802$	31.1578	1.10022
$803$	5.47993	0.193383
$804$	−105.259	−3.71221
$805$	−1.20809	−0.0425796
$806$	−1.57205	−0.0553731
$807$	−65.7765	−2.31544
$808$	2.22298	0.0782042
$809$	−1.83537	−0.0645280	−0.0322640	−	0.999479i	$-0.510272\pi$
$809$	−1.83537	−0.0645280	−0.0322640	+	0.999479i	$0.510272\pi$
$810$	−44.0141	−1.54650
$811$	−0.00294230	−0.000103318 0	−5.16590e−5	−	1.00000i	$-0.500016\pi$
$811$	−0.00294230	−0.000103318 0	−5.16590e−5		1.00000i	$0.500016\pi$
$812$	−0.683684	−0.0239926
$813$	−1.44147	−0.0505544
$814$	8.49960	0.297911
$815$	34.4090	1.20530
$816$	29.3396	1.02709
$817$	−3.09917	−0.108426
$818$	54.9236	1.92036
$819$	0.473324	0.0165393
$820$	−16.6585	−0.581741
$821$	−35.5408	−1.24038	−0.620190	−	0.784451i	$-0.712945\pi$
$821$	−35.5408	−1.24038	−0.620190	+	0.784451i	$0.712945\pi$
$822$	−40.2199	−1.40283
$823$	−12.3570	−0.430739	−0.215369	−	0.976533i	$-0.569096\pi$
$823$	−12.3570	−0.430739	−0.215369	+	0.976533i	$0.569096\pi$
$824$	−1.61140	−0.0561358
$825$	8.34290	0.290462
$826$	1.64341	0.0571814
$827$	−6.74481	−0.234540	−0.117270	−	0.993100i	$-0.537414\pi$
$827$	−6.74481	−0.234540	−0.117270	+	0.993100i	$0.537414\pi$
$828$	−119.483	−4.15233
$829$	46.3345	1.60926	0.804632	−	0.593773i	$-0.202362\pi$
$829$	46.3345	1.60926	0.804632	+	0.593773i	$0.202362\pi$
$830$	−67.0031	−2.32571
$831$	8.36532	0.290190
$832$	−17.6803	−0.612956
$833$	−31.5305	−1.09247
$834$	−35.5571	−1.23124
$835$	−45.8133	−1.58544
$836$	16.7459	0.579170
$837$	−4.16951	−0.144119
$838$	42.3523	1.46304
$839$	19.8349	0.684777	0.342389	−	0.939558i	$-0.388764\pi$
$839$	19.8349	0.684777	0.342389	+	0.939558i	$0.388764\pi$
$840$	0.680058	0.0234642
$841$	−8.30283	−0.286305
$842$	−0.413649	−0.0142553
$843$	97.5991	3.36149
$844$	−4.12294	−0.141917
$845$	−30.4462	−1.04738
$846$	−123.543	−4.24748
$847$	0.0561777	0.00193029
$848$	1.69959	0.0583643
$849$	−62.3620	−2.14026
$850$	−27.3952	−0.939648
$851$	−30.2462	−1.03683
$852$	27.3527	0.937088
$853$	13.5718	0.464689	0.232345	−	0.972634i	$-0.425360\pi$
$853$	13.5718	0.464689	0.232345	+	0.972634i	$0.425360\pi$
$854$	−0.822223	−0.0281359
$855$	−101.566	−3.47347
$856$	19.4083	0.663362
$857$	2.68727	0.0917954	0.0458977	−	0.998946i	$-0.485385\pi$
$857$	2.68727	0.0917954	0.0458977	+	0.998946i	$0.485385\pi$
$858$	−9.31215	−0.317911
$859$	−22.5118	−0.768092	−0.384046	−	0.923314i	$-0.625470\pi$
$859$	−22.5118	−0.768092	−0.384046	+	0.923314i	$0.625470\pi$
$860$	3.70150	0.126220
$861$	0.371415	0.0126578
$862$	20.8405	0.709831
$863$	20.8869	0.710998	0.355499	−	0.934677i	$-0.384311\pi$
$863$	20.8869	0.710998	0.355499	+	0.934677i	$0.384311\pi$
$864$	−63.7859	−2.17004
$865$	−71.5361	−2.43230
$866$	44.9856	1.52867
$867$	−9.81456	−0.333320
$868$	0.0752804	0.00255518
$869$	0.0836399	0.00283729
$870$	−81.5802	−2.76583
$871$	19.2464	0.652139
$872$	−15.7251	−0.532520
$873$	−47.4729	−1.60671
$874$	−104.144	−3.52272
$875$	−0.343608	−0.0116161
$876$	43.4988	1.46969
$877$	26.8416	0.906377	0.453189	−	0.891415i	$-0.350286\pi$
$877$	26.8416	0.906377	0.453189	+	0.891415i	$0.350286\pi$
$878$	48.6030	1.64027
$879$	70.1582	2.36638
$880$	6.13239	0.206723
$881$	7.03756	0.237102	0.118551	−	0.992948i	$-0.462175\pi$
$881$	7.03756	0.237102	0.118551	+	0.992948i	$0.462175\pi$
$882$	87.8215	2.95711
$883$	49.0850	1.65184	0.825921	−	0.563786i	$-0.190656\pi$
$883$	49.0850	1.65184	0.825921	+	0.563786i	$0.190656\pi$
$884$	17.4966	0.588476
$885$	112.207	3.77181
$886$	−1.63434	−0.0549066
$887$	−28.7051	−0.963823	−0.481911	−	0.876220i	$-0.660057\pi$
$887$	−28.7051	−0.963823	−0.481911	+	0.876220i	$0.660057\pi$
$888$	17.0262	0.571360
$889$	−0.603348	−0.0202356
$890$	91.5566	3.06898
$891$	−7.28329	−0.243999
$892$	−48.4225	−1.62131
$893$	−61.6157	−2.06189
$894$	120.507	4.03037
$895$	−41.6627	−1.39263
$896$	0.618626	0.0206669
$897$	33.1377	1.10643
$898$	36.8962	1.23124
$899$	−2.27896	−0.0760077
$900$	43.6608	1.45536
$901$	−3.49071	−0.116292
$902$	−4.81754	−0.160406
$903$	−0.0825280	−0.00274636
$904$	10.9902	0.365529
$905$	7.33433	0.243801
$906$	116.994	3.88687
$907$	−35.3780	−1.17471	−0.587354	−	0.809330i	$-0.699830\pi$
$907$	−35.3780	−1.17471	−0.587354	+	0.809330i	$0.699830\pi$
$908$	29.7527	0.987378
$909$	−8.84083	−0.293232
$910$	−0.492740	−0.0163342
$911$	5.35583	0.177447	0.0887233	−	0.996056i	$-0.471721\pi$
$911$	5.35583	0.177447	0.0887233	+	0.996056i	$0.471721\pi$
$912$	−40.7567	−1.34959
$913$	−11.0874	−0.366940
$914$	−63.8136	−2.11077
$915$	−56.1392	−1.85591
$916$	−8.11907	−0.268262
$917$	−0.0561777	−0.00185515
$918$	81.1010	2.67673
$919$	−17.6063	−0.580778	−0.290389	−	0.956909i	$-0.593785\pi$
$919$	−17.6063	−0.580778	−0.290389	+	0.956909i	$0.593785\pi$
$920$	31.3894	1.03488
$921$	−47.5317	−1.56622
$922$	−45.8506	−1.51001
$923$	−5.00137	−0.164622
$924$	0.445929	0.0146700
$925$	11.0524	0.363400
$926$	91.9425	3.02142
$927$	6.40857	0.210485
$928$	−34.8640	−1.14447
$929$	1.93698	0.0635502	0.0317751	−	0.999495i	$-0.489884\pi$
$929$	1.93698	0.0635502	0.0317751	+	0.999495i	$0.489884\pi$
$930$	8.98279	0.294557
$931$	43.8001	1.43549
$932$	1.87783	0.0615103
$933$	37.5708	1.23001
$934$	−88.5353	−2.89696
$935$	−12.5950	−0.411901
$936$	−12.2982	−0.401979
$937$	−3.29221	−0.107552	−0.0537760	−	0.998553i	$-0.517126\pi$
$937$	−3.29221	−0.107552	−0.0537760	+	0.998553i	$0.517126\pi$
$938$	−1.61071	−0.0525916
$939$	85.6206	2.79412
$940$	73.5909	2.40027
$941$	24.3868	0.794988	0.397494	−	0.917605i	$-0.369880\pi$
$941$	24.3868	0.794988	0.397494	+	0.917605i	$0.369880\pi$
$942$	−49.6864	−1.61887
$943$	17.1434	0.558266
$944$	29.6857	0.966186
$945$	−1.30688	−0.0425129
$946$	1.07045	0.0348033
$947$	−11.7974	−0.383363	−0.191681	−	0.981457i	$-0.561394\pi$
$947$	−11.7974	−0.383363	−0.191681	+	0.981457i	$0.561394\pi$
$948$	0.663919	0.0215631
$949$	−7.95363	−0.258186
$950$	38.0556	1.23469
$951$	27.7372	0.899441
$952$	−0.369522	−0.0119763
$953$	12.4842	0.404403	0.202201	−	0.979344i	$-0.435190\pi$
$953$	12.4842	0.404403	0.202201	+	0.979344i	$0.435190\pi$
$954$	9.72263	0.314782
$955$	−2.09597	−0.0678239
$956$	10.9363	0.353705
$957$	−13.4996	−0.436380
$958$	−12.5903	−0.406775
$959$	−0.352164	−0.0113720
$960$	101.027	3.26062
$961$	−30.7491	−0.991905
$962$	−12.3364	−0.397741
$963$	−77.1871	−2.48732
$964$	55.4414	1.78565
$965$	46.0630	1.48282
$966$	−2.77326	−0.0892281
$967$	−52.5201	−1.68893	−0.844466	−	0.535610i	$-0.820082\pi$
$967$	−52.5201	−1.68893	−0.844466	+	0.535610i	$0.820082\pi$
$968$	−1.45964	−0.0469148
$969$	83.7080	2.68909
$970$	49.4203	1.58679
$971$	−24.1754	−0.775825	−0.387913	−	0.921696i	$-0.626804\pi$
$971$	−24.1754	−0.775825	−0.387913	+	0.921696i	$0.626804\pi$
$972$	8.98406	0.288164
$973$	−0.311337	−0.00998100
$974$	1.32429	0.0424330
$975$	−12.1090	−0.387797
$976$	−14.8522	−0.475408
$977$	39.0744	1.25010	0.625051	−	0.780584i	$-0.285078\pi$
$977$	39.0744	1.25010	0.625051	+	0.780584i	$0.285078\pi$
$978$	78.9883	2.52577
$979$	15.1504	0.484210
$980$	−52.3128	−1.67107
$981$	62.5391	1.99672
$982$	21.4743	0.685274
$983$	30.1232	0.960781	0.480390	−	0.877055i	$-0.340495\pi$
$983$	30.1232	0.960781	0.480390	+	0.877055i	$0.340495\pi$
$984$	−9.65035	−0.307642
$985$	−10.9197	−0.347930
$986$	44.3280	1.41169
$987$	−1.64077	−0.0522262
$988$	−24.3052	−0.773251
$989$	−3.80924	−0.121127
$990$	35.0807	1.11494
$991$	20.2104	0.642005	0.321003	−	0.947078i	$-0.395980\pi$
$991$	20.2104	0.642005	0.321003	+	0.947078i	$0.395980\pi$
$992$	3.83887	0.121884
$993$	55.3478	1.75641
$994$	0.418559	0.0132759
$995$	2.09125	0.0662970
$996$	−88.0101	−2.78871
$997$	−4.81372	−0.152452	−0.0762260	−	0.997091i	$-0.524287\pi$
$997$	−4.81372	−0.152452	−0.0762260	+	0.997091i	$0.524287\pi$
$998$	67.1585	2.12587
$999$	−32.7195	−1.03520

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1441.2.a.d.1.4	✓	23

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1441.2.a.d.1.4	✓	23	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:	\( N \)	\(=\)	\( 1441 = 11 \cdot 131 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1441.a (trivial)

\(f(q)\)	\(=\)	\(q-2.16219 q^{2} -2.96733 q^{3} +2.67508 q^{4} +2.79492 q^{5} +6.41593 q^{6} +0.0561777 q^{7} -1.45964 q^{8} +5.80503 q^{9} +O(q^{10})\)	\(q-2.16219 q^{2} -2.96733 q^{3} +2.67508 q^{4} +2.79492 q^{5} +6.41593 q^{6} +0.0561777 q^{7} -1.45964 q^{8} +5.80503 q^{9} -6.04316 q^{10} -1.00000 q^{11} -7.93783 q^{12} +1.45141 q^{13} -0.121467 q^{14} -8.29345 q^{15} -2.19412 q^{16} +4.50639 q^{17} -12.5516 q^{18} -6.25998 q^{19} +7.47663 q^{20} -0.166698 q^{21} +2.16219 q^{22} -7.69425 q^{23} +4.33124 q^{24} +2.81159 q^{25} -3.13823 q^{26} -8.32344 q^{27} +0.150280 q^{28} -4.54941 q^{29} +17.9320 q^{30} +0.500936 q^{31} +7.66340 q^{32} +2.96733 q^{33} -9.74368 q^{34} +0.157012 q^{35} +15.5289 q^{36} +3.93101 q^{37} +13.5353 q^{38} -4.30681 q^{39} -4.07959 q^{40} -2.22808 q^{41} +0.360432 q^{42} +0.495076 q^{43} -2.67508 q^{44} +16.2246 q^{45} +16.6365 q^{46} +9.84279 q^{47} +6.51067 q^{48} -6.99684 q^{49} -6.07919 q^{50} -13.3719 q^{51} +3.88263 q^{52} -0.774613 q^{53} +17.9969 q^{54} -2.79492 q^{55} -0.0819995 q^{56} +18.5754 q^{57} +9.83671 q^{58} -13.5296 q^{59} -22.1856 q^{60} +6.76911 q^{61} -1.08312 q^{62} +0.326113 q^{63} -12.1815 q^{64} +4.05658 q^{65} -6.41593 q^{66} +13.2605 q^{67} +12.0549 q^{68} +22.8314 q^{69} -0.339491 q^{70} -3.44587 q^{71} -8.47328 q^{72} -5.47993 q^{73} -8.49960 q^{74} -8.34290 q^{75} -16.7459 q^{76} -0.0561777 q^{77} +9.31215 q^{78} -0.0836399 q^{79} -6.13239 q^{80} +7.28329 q^{81} +4.81754 q^{82} +11.0874 q^{83} -0.445929 q^{84} +12.5950 q^{85} -1.07045 q^{86} +13.4996 q^{87} +1.45964 q^{88} -15.1504 q^{89} -35.0807 q^{90} +0.0815368 q^{91} -20.5827 q^{92} -1.48644 q^{93} -21.2820 q^{94} -17.4962 q^{95} -22.7398 q^{96} -8.17789 q^{97} +15.1285 q^{98} -5.80503 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 23 q - 7 q^{2} - 3 q^{3} + 19 q^{4} - 9 q^{5} - 5 q^{6} - 8 q^{7} - 15 q^{8} + 12 q^{9}+O(q^{10}) \) 23 * q - 7 * q^2 - 3 * q^3 + 19 * q^4 - 9 * q^5 - 5 * q^6 - 8 * q^7 - 15 * q^8 + 12 * q^9	\( 23 q - 7 q^{2} - 3 q^{3} + 19 q^{4} - 9 q^{5} - 5 q^{6} - 8 q^{7} - 15 q^{8} + 12 q^{9} - 2 q^{10} - 23 q^{11} - 12 q^{12} + 6 q^{13} - 13 q^{14} - 27 q^{15} - q^{16} - 11 q^{17} - 16 q^{19} - 24 q^{20} - 7 q^{21} + 7 q^{22} - 30 q^{23} - 20 q^{24} + 10 q^{25} - 22 q^{26} - 15 q^{27} + 11 q^{28} - 15 q^{29} + 17 q^{30} - 31 q^{31} - 22 q^{32} + 3 q^{33} - 18 q^{34} - 34 q^{35} - 18 q^{36} - 26 q^{37} - 32 q^{39} + 16 q^{40} - 21 q^{41} - 37 q^{42} - 2 q^{43} - 19 q^{44} - 18 q^{45} - 6 q^{46} - 25 q^{47} + 14 q^{48} + 7 q^{49} - 27 q^{50} - 7 q^{51} + 23 q^{52} - 34 q^{53} + 26 q^{54} + 9 q^{55} - 42 q^{56} + 6 q^{57} - 5 q^{58} - 31 q^{59} - 7 q^{60} + 19 q^{61} + 24 q^{62} - 34 q^{63} - 17 q^{64} - 13 q^{65} + 5 q^{66} - 39 q^{67} - 59 q^{68} - 12 q^{69} + 17 q^{70} - 103 q^{71} + 19 q^{72} + q^{73} - 9 q^{74} - 19 q^{75} + 10 q^{76} + 8 q^{77} - 43 q^{78} - 14 q^{79} - q^{80} - 29 q^{81} + 20 q^{82} - 14 q^{83} + 57 q^{84} + 20 q^{85} - 54 q^{86} - 23 q^{87} + 15 q^{88} - 71 q^{89} - 52 q^{90} - 18 q^{91} - 24 q^{92} - q^{93} + q^{94} - 38 q^{95} - 31 q^{96} - 26 q^{97} + 19 q^{98} - 12 q^{99}+O(q^{100}) \) 23 * q - 7 * q^2 - 3 * q^3 + 19 * q^4 - 9 * q^5 - 5 * q^6 - 8 * q^7 - 15 * q^8 + 12 * q^9 - 2 * q^10 - 23 * q^11 - 12 * q^12 + 6 * q^13 - 13 * q^14 - 27 * q^15 - q^16 - 11 * q^17 - 16 * q^19 - 24 * q^20 - 7 * q^21 + 7 * q^22 - 30 * q^23 - 20 * q^24 + 10 * q^25 - 22 * q^26 - 15 * q^27 + 11 * q^28 - 15 * q^29 + 17 * q^30 - 31 * q^31 - 22 * q^32 + 3 * q^33 - 18 * q^34 - 34 * q^35 - 18 * q^36 - 26 * q^37 - 32 * q^39 + 16 * q^40 - 21 * q^41 - 37 * q^42 - 2 * q^43 - 19 * q^44 - 18 * q^45 - 6 * q^46 - 25 * q^47 + 14 * q^48 + 7 * q^49 - 27 * q^50 - 7 * q^51 + 23 * q^52 - 34 * q^53 + 26 * q^54 + 9 * q^55 - 42 * q^56 + 6 * q^57 - 5 * q^58 - 31 * q^59 - 7 * q^60 + 19 * q^61 + 24 * q^62 - 34 * q^63 - 17 * q^64 - 13 * q^65 + 5 * q^66 - 39 * q^67 - 59 * q^68 - 12 * q^69 + 17 * q^70 - 103 * q^71 + 19 * q^72 + q^73 - 9 * q^74 - 19 * q^75 + 10 * q^76 + 8 * q^77 - 43 * q^78 - 14 * q^79 - q^80 - 29 * q^81 + 20 * q^82 - 14 * q^83 + 57 * q^84 + 20 * q^85 - 54 * q^86 - 23 * q^87 + 15 * q^88 - 71 * q^89 - 52 * q^90 - 18 * q^91 - 24 * q^92 - q^93 + q^94 - 38 * q^95 - 31 * q^96 - 26 * q^97 + 19 * q^98 - 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more