LMFDB - Embedded newform 8027.2.a.c.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8027,2,Mod(1,8027)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8027, 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("8027.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8027 = 23 \cdot 349 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8027.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:	$64.0959177025$
Analytic rank:	$1$
Dimension:	$143$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	8027.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.62887 q^{2} +1.58844 q^{3} +4.91095 q^{4} +0.705653 q^{5} -4.17581 q^{6} -0.559393 q^{7} -7.65249 q^{8} -0.476845 q^{9} +O(q^{10})$	\(q-2.62887 q^{2} +1.58844 q^{3} +4.91095 q^{4} +0.705653 q^{5} -4.17581 q^{6} -0.559393 q^{7} -7.65249 q^{8} -0.476845 q^{9} -1.85507 q^{10} +4.06095 q^{11} +7.80076 q^{12} +1.29090 q^{13} +1.47057 q^{14} +1.12089 q^{15} +10.2955 q^{16} -6.54776 q^{17} +1.25356 q^{18} +5.89958 q^{19} +3.46542 q^{20} -0.888565 q^{21} -10.6757 q^{22} +1.00000 q^{23} -12.1556 q^{24} -4.50205 q^{25} -3.39359 q^{26} -5.52277 q^{27} -2.74715 q^{28} +7.49666 q^{29} -2.94667 q^{30} -1.56182 q^{31} -11.7605 q^{32} +6.45059 q^{33} +17.2132 q^{34} -0.394737 q^{35} -2.34176 q^{36} +0.00417881 q^{37} -15.5092 q^{38} +2.05052 q^{39} -5.40000 q^{40} -5.01119 q^{41} +2.33592 q^{42} -7.68858 q^{43} +19.9431 q^{44} -0.336487 q^{45} -2.62887 q^{46} +7.15567 q^{47} +16.3538 q^{48} -6.68708 q^{49} +11.8353 q^{50} -10.4008 q^{51} +6.33952 q^{52} -10.9556 q^{53} +14.5186 q^{54} +2.86562 q^{55} +4.28075 q^{56} +9.37115 q^{57} -19.7077 q^{58} +2.34420 q^{59} +5.50463 q^{60} -7.10970 q^{61} +4.10582 q^{62} +0.266744 q^{63} +10.3258 q^{64} +0.910924 q^{65} -16.9578 q^{66} -10.7564 q^{67} -32.1557 q^{68} +1.58844 q^{69} +1.03771 q^{70} -2.08612 q^{71} +3.64905 q^{72} -16.4105 q^{73} -0.0109855 q^{74} -7.15126 q^{75} +28.9725 q^{76} -2.27167 q^{77} -5.39053 q^{78} +3.05742 q^{79} +7.26504 q^{80} -7.34208 q^{81} +13.1738 q^{82} -14.2123 q^{83} -4.36369 q^{84} -4.62044 q^{85} +20.2122 q^{86} +11.9080 q^{87} -31.0764 q^{88} +15.0061 q^{89} +0.884579 q^{90} -0.722118 q^{91} +4.91095 q^{92} -2.48087 q^{93} -18.8113 q^{94} +4.16305 q^{95} -18.6809 q^{96} +7.87392 q^{97} +17.5794 q^{98} -1.93644 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 143 q - 17 q^{2} - 17 q^{3} + 121 q^{4} - 22 q^{5} - 11 q^{6} - 33 q^{7} - 45 q^{8} + 104 q^{9}+O(q^{10}) $ 143 * q - 17 * q^2 - 17 * q^3 + 121 * q^4 - 22 * q^5 - 11 * q^6 - 33 * q^7 - 45 * q^8 + 104 * q^9	\( 143 q - 17 q^{2} - 17 q^{3} + 121 q^{4} - 22 q^{5} - 11 q^{6} - 33 q^{7} - 45 q^{8} + 104 q^{9} - 22 q^{10} - 14 q^{11} - 36 q^{12} - 87 q^{13} - 18 q^{14} - 19 q^{15} + 81 q^{16} - 14 q^{17} - 60 q^{18} - 18 q^{19} - 25 q^{20} - 26 q^{21} - 62 q^{22} + 143 q^{23} - 21 q^{24} + 67 q^{25} - 5 q^{26} - 47 q^{27} - 76 q^{28} - 54 q^{29} - 22 q^{30} - 62 q^{31} - 117 q^{32} - 59 q^{33} - 35 q^{34} - 52 q^{35} + 52 q^{36} - 190 q^{37} - 19 q^{38} - 43 q^{39} - 41 q^{40} - 50 q^{41} + 8 q^{42} - 50 q^{43} - 18 q^{44} - 75 q^{45} - 17 q^{46} - 63 q^{47} - 35 q^{48} + 74 q^{49} - 53 q^{50} - 33 q^{51} - 124 q^{52} - 100 q^{53} - 46 q^{54} - 61 q^{55} - 3 q^{56} - 80 q^{57} - 112 q^{58} - 109 q^{59} - 55 q^{60} - 76 q^{61} - 6 q^{62} - 93 q^{63} + 57 q^{64} - 17 q^{65} + 50 q^{66} - 120 q^{67} + 26 q^{68} - 17 q^{69} - 109 q^{71} - 153 q^{72} - 94 q^{73} + 35 q^{74} - 105 q^{75} - 16 q^{76} - 52 q^{77} - 59 q^{78} - 29 q^{79} - 30 q^{80} + 39 q^{81} - 65 q^{82} + 8 q^{83} + 11 q^{84} - 155 q^{85} - 15 q^{86} - 25 q^{87} - 139 q^{88} + 6 q^{89} + 82 q^{90} - 34 q^{91} + 121 q^{92} - 151 q^{93} - 3 q^{94} - 70 q^{95} - 23 q^{96} - 203 q^{97} - 18 q^{98} - 49 q^{99}+O(q^{100}) \) 143 * q - 17 * q^2 - 17 * q^3 + 121 * q^4 - 22 * q^5 - 11 * q^6 - 33 * q^7 - 45 * q^8 + 104 * q^9 - 22 * q^10 - 14 * q^11 - 36 * q^12 - 87 * q^13 - 18 * q^14 - 19 * q^15 + 81 * q^16 - 14 * q^17 - 60 * q^18 - 18 * q^19 - 25 * q^20 - 26 * q^21 - 62 * q^22 + 143 * q^23 - 21 * q^24 + 67 * q^25 - 5 * q^26 - 47 * q^27 - 76 * q^28 - 54 * q^29 - 22 * q^30 - 62 * q^31 - 117 * q^32 - 59 * q^33 - 35 * q^34 - 52 * q^35 + 52 * q^36 - 190 * q^37 - 19 * q^38 - 43 * q^39 - 41 * q^40 - 50 * q^41 + 8 * q^42 - 50 * q^43 - 18 * q^44 - 75 * q^45 - 17 * q^46 - 63 * q^47 - 35 * q^48 + 74 * q^49 - 53 * q^50 - 33 * q^51 - 124 * q^52 - 100 * q^53 - 46 * q^54 - 61 * q^55 - 3 * q^56 - 80 * q^57 - 112 * q^58 - 109 * q^59 - 55 * q^60 - 76 * q^61 - 6 * q^62 - 93 * q^63 + 57 * q^64 - 17 * q^65 + 50 * q^66 - 120 * q^67 + 26 * q^68 - 17 * q^69 - 109 * q^71 - 153 * q^72 - 94 * q^73 + 35 * q^74 - 105 * q^75 - 16 * q^76 - 52 * q^77 - 59 * q^78 - 29 * q^79 - 30 * q^80 + 39 * q^81 - 65 * q^82 + 8 * q^83 + 11 * q^84 - 155 * q^85 - 15 * q^86 - 25 * q^87 - 139 * q^88 + 6 * q^89 + 82 * q^90 - 34 * q^91 + 121 * q^92 - 151 * q^93 - 3 * q^94 - 70 * q^95 - 23 * q^96 - 203 * q^97 - 18 * q^98 - 49 * 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 $

$2$	−2.62887	−1.85889	−0.929445	−	0.368960i	$-0.879714\pi$
$2$	−2.62887	−1.85889	−0.929445	+	0.368960i	$0.879714\pi$
$3$	1.58844	0.917089	0.458544	−	0.888672i	$-0.348371\pi$
$3$	1.58844	0.917089	0.458544	+	0.888672i	$0.348371\pi$
$4$	4.91095	2.45547
$5$	0.705653	0.315577	0.157789	−	0.987473i	$-0.449564\pi$
$5$	0.705653	0.315577	0.157789	+	0.987473i	$0.449564\pi$
$6$	−4.17581	−1.70477
$7$	−0.559393	−0.211431	−0.105715	−	0.994396i	$-0.533713\pi$
$7$	−0.559393	−0.211431	−0.105715	+	0.994396i	$0.533713\pi$
$8$	−7.65249	−2.70556
$9$	−0.476845	−0.158948
$10$	−1.85507	−0.586624
$11$	4.06095	1.22442	0.612211	−	0.790694i	$-0.290280\pi$
$11$	4.06095	1.22442	0.612211	+	0.790694i	$0.290280\pi$
$12$	7.80076	2.25189
$13$	1.29090	0.358030	0.179015	−	0.983846i	$-0.442709\pi$
$13$	1.29090	0.358030	0.179015	+	0.983846i	$0.442709\pi$
$14$	1.47057	0.393027
$15$	1.12089	0.289413
$16$	10.2955	2.57387
$17$	−6.54776	−1.58806	−0.794032	−	0.607875i	$-0.792022\pi$
$17$	−6.54776	−1.58806	−0.794032	+	0.607875i	$0.792022\pi$
$18$	1.25356	0.295467
$19$	5.89958	1.35346	0.676728	−	0.736233i	$-0.263397\pi$
$19$	5.89958	1.35346	0.676728	+	0.736233i	$0.263397\pi$
$20$	3.46542	0.774892
$21$	−0.888565	−0.193901
$22$	−10.6757	−2.27607
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	−12.1556	−2.48124
$25$	−4.50205	−0.900411
$26$	−3.39359	−0.665538
$27$	−5.52277	−1.06286
$28$	−2.74715	−0.519163
$29$	7.49666	1.39210	0.696048	−	0.717996i	$-0.254940\pi$
$29$	7.49666	1.39210	0.696048	+	0.717996i	$0.254940\pi$
$30$	−2.94667	−0.537986
$31$	−1.56182	−0.280511	−0.140256	−	0.990115i	$-0.544792\pi$
$31$	−1.56182	−0.280511	−0.140256	+	0.990115i	$0.544792\pi$
$32$	−11.7605	−2.07898
$33$	6.45059	1.12290
$34$	17.2132	2.95204
$35$	−0.394737	−0.0667228
$36$	−2.34176	−0.390293
$37$	0.00417881	0.000686993 0	0.000343496	−	1.00000i	$-0.499891\pi$
$37$	0.00417881	0.000686993 0	0.000343496		1.00000i	$0.499891\pi$
$38$	−15.5092	−2.51593
$39$	2.05052	0.328345
$40$	−5.40000	−0.853815
$41$	−5.01119	−0.782616	−0.391308	−	0.920260i	$-0.627977\pi$
$41$	−5.01119	−0.782616	−0.391308	+	0.920260i	$0.627977\pi$
$42$	2.33592	0.360440
$43$	−7.68858	−1.17250	−0.586248	−	0.810131i	$-0.699396\pi$
$43$	−7.68858	−1.17250	−0.586248	+	0.810131i	$0.699396\pi$
$44$	19.9431	3.00654
$45$	−0.336487	−0.0501605
$46$	−2.62887	−0.387605
$47$	7.15567	1.04376	0.521881	−	0.853018i	$-0.325231\pi$
$47$	7.15567	1.04376	0.521881	+	0.853018i	$0.325231\pi$
$48$	16.3538	2.36047
$49$	−6.68708	−0.955297
$50$	11.8353	1.67376
$51$	−10.4008	−1.45640
$52$	6.33952	0.879133
$53$	−10.9556	−1.50487	−0.752433	−	0.658668i	$-0.771120\pi$
$53$	−10.9556	−1.50487	−0.752433	+	0.658668i	$0.771120\pi$
$54$	14.5186	1.97574
$55$	2.86562	0.386400
$56$	4.28075	0.572040
$57$	9.37115	1.24124
$58$	−19.7077	−2.58775
$59$	2.34420	0.305189	0.152594	−	0.988289i	$-0.451237\pi$
$59$	2.34420	0.305189	0.152594	+	0.988289i	$0.451237\pi$
$60$	5.50463	0.710645
$61$	−7.10970	−0.910304	−0.455152	−	0.890414i	$-0.650415\pi$
$61$	−7.10970	−0.910304	−0.455152	+	0.890414i	$0.650415\pi$
$62$	4.10582	0.521440
$63$	0.266744	0.0336066
$64$	10.3258	1.29073
$65$	0.910924	0.112986
$66$	−16.9578	−2.08735
$67$	−10.7564	−1.31410	−0.657051	−	0.753846i	$-0.728196\pi$
$67$	−10.7564	−1.31410	−0.657051	+	0.753846i	$0.728196\pi$
$68$	−32.1557	−3.89945
$69$	1.58844	0.191226
$70$	1.03771	0.124030
$71$	−2.08612	−0.247577	−0.123788	−	0.992309i	$-0.539504\pi$
$71$	−2.08612	−0.247577	−0.123788	+	0.992309i	$0.539504\pi$
$72$	3.64905	0.430045
$73$	−16.4105	−1.92070	−0.960349	−	0.278800i	$-0.910063\pi$
$73$	−16.4105	−1.92070	−0.960349	+	0.278800i	$0.910063\pi$
$74$	−0.0109855	−0.00127704
$75$	−7.15126	−0.825757
$76$	28.9725	3.32337
$77$	−2.27167	−0.258881
$78$	−5.39053	−0.610358
$79$	3.05742	0.343987	0.171993	−	0.985098i	$-0.444979\pi$
$79$	3.05742	0.343987	0.171993	+	0.985098i	$0.444979\pi$
$80$	7.26504	0.812256
$81$	−7.34208	−0.815787
$82$	13.1738	1.45480
$83$	−14.2123	−1.56000	−0.780002	−	0.625777i	$-0.784782\pi$
$83$	−14.2123	−1.56000	−0.780002	+	0.625777i	$0.784782\pi$
$84$	−4.36369	−0.476118
$85$	−4.62044	−0.501157
$86$	20.2122	2.17954
$87$	11.9080	1.27668
$88$	−31.0764	−3.31275
$89$	15.0061	1.59065	0.795324	−	0.606185i	$-0.207301\pi$
$89$	15.0061	1.59065	0.795324	+	0.606185i	$0.207301\pi$
$90$	0.884579	0.0932428
$91$	−0.722118	−0.0756985
$92$	4.91095	0.512001
$93$	−2.48087	−0.257254
$94$	−18.8113	−1.94024
$95$	4.16305	0.427120
$96$	−18.6809	−1.90661
$97$	7.87392	0.799475	0.399738	−	0.916630i	$-0.369101\pi$
$97$	7.87392	0.799475	0.399738	+	0.916630i	$0.369101\pi$
$98$	17.5794	1.77579
$99$	−1.93644	−0.194620
$100$	−22.1093	−2.21093
$101$	−11.9921	−1.19326	−0.596632	−	0.802515i	$-0.703495\pi$
$101$	−11.9921	−1.19326	−0.596632	+	0.802515i	$0.703495\pi$
$102$	27.3422	2.70728
$103$	−13.2882	−1.30932	−0.654662	−	0.755922i	$-0.727189\pi$
$103$	−13.2882	−1.30932	−0.654662	+	0.755922i	$0.727189\pi$
$104$	−9.87856	−0.968673
$105$	−0.627018	−0.0611907
$106$	28.8008	2.79738
$107$	−5.93272	−0.573538	−0.286769	−	0.958000i	$-0.592581\pi$
$107$	−5.93272	−0.573538	−0.286769	+	0.958000i	$0.592581\pi$
$108$	−27.1220	−2.60982
$109$	14.1590	1.35618	0.678092	−	0.734977i	$-0.262807\pi$
$109$	14.1590	1.35618	0.678092	+	0.734977i	$0.262807\pi$
$110$	−7.53333	−0.718275
$111$	0.00663781	0.000630033 0
$112$	−5.75923	−0.544196
$113$	18.8064	1.76915	0.884577	−	0.466393i	$-0.154447\pi$
$113$	18.8064	1.76915	0.884577	+	0.466393i	$0.154447\pi$
$114$	−24.6355	−2.30733
$115$	0.705653	0.0658025
$116$	36.8157	3.41825
$117$	−0.615557	−0.0569082
$118$	−6.16259	−0.567312
$119$	3.66277	0.335766
$120$	−8.57760	−0.783024
$121$	5.49131	0.499210
$122$	18.6905	1.69216
$123$	−7.96000	−0.717729
$124$	−7.67002	−0.688788
$125$	−6.70515	−0.599727
$126$	−0.701234	−0.0624709
$127$	9.23194	0.819202	0.409601	−	0.912265i	$-0.365668\pi$
$127$	9.23194	0.819202	0.409601	+	0.912265i	$0.365668\pi$
$128$	−3.62424	−0.320341
$129$	−12.2129	−1.07528
$130$	−2.39470	−0.210029
$131$	9.11406	0.796300	0.398150	−	0.917320i	$-0.369652\pi$
$131$	9.11406	0.796300	0.398150	+	0.917320i	$0.369652\pi$
$132$	31.6785	2.75726
$133$	−3.30018	−0.286162
$134$	28.2771	2.44277
$135$	−3.89716	−0.335414
$136$	50.1067	4.29661
$137$	−6.43932	−0.550148	−0.275074	−	0.961423i	$-0.588702\pi$
$137$	−6.43932	−0.550148	−0.275074	+	0.961423i	$0.588702\pi$
$138$	−4.17581	−0.355469
$139$	−12.6388	−1.07201	−0.536006	−	0.844214i	$-0.680068\pi$
$139$	−12.6388	−1.07201	−0.536006	+	0.844214i	$0.680068\pi$
$140$	−1.93853	−0.163836
$141$	11.3664	0.957222
$142$	5.48413	0.460218
$143$	5.24226	0.438380
$144$	−4.90935	−0.409113
$145$	5.29004	0.439314
$146$	43.1409	3.57037
$147$	−10.6221	−0.876092
$148$	0.0205219	0.00168689
$149$	9.58131	0.784932	0.392466	−	0.919767i	$-0.371622\pi$
$149$	9.58131	0.784932	0.392466	+	0.919767i	$0.371622\pi$
$150$	18.7997	1.53499
$151$	11.5850	0.942774	0.471387	−	0.881926i	$-0.343753\pi$
$151$	11.5850	0.942774	0.471387	+	0.881926i	$0.343753\pi$
$152$	−45.1464	−3.66186
$153$	3.12226	0.252420
$154$	5.97191	0.481231
$155$	−1.10210	−0.0885231
$156$	10.0700	0.806243
$157$	2.73027	0.217899	0.108950	−	0.994047i	$-0.465251\pi$
$157$	2.73027	0.217899	0.108950	+	0.994047i	$0.465251\pi$
$158$	−8.03756	−0.639434
$159$	−17.4024	−1.38010
$160$	−8.29884	−0.656081
$161$	−0.559393	−0.0440864
$162$	19.3014	1.51646
$163$	−20.8611	−1.63397	−0.816985	−	0.576659i	$-0.804356\pi$
$163$	−20.8611	−1.63397	−0.816985	+	0.576659i	$0.804356\pi$
$164$	−24.6097	−1.92169
$165$	4.55188	0.354363
$166$	37.3623	2.89987
$167$	12.4693	0.964900	0.482450	−	0.875924i	$-0.339747\pi$
$167$	12.4693	0.964900	0.482450	+	0.875924i	$0.339747\pi$
$168$	6.79974	0.524611
$169$	−11.3336	−0.871815
$170$	12.1465	0.931597
$171$	−2.81318	−0.215129
$172$	−37.7582	−2.87903
$173$	−3.14439	−0.239064	−0.119532	−	0.992830i	$-0.538139\pi$
$173$	−3.14439	−0.239064	−0.119532	+	0.992830i	$0.538139\pi$
$174$	−31.3046	−2.37320
$175$	2.51842	0.190375
$176$	41.8095	3.15151
$177$	3.72363	0.279885
$178$	−39.4492	−2.95684
$179$	−2.17424	−0.162511	−0.0812553	−	0.996693i	$-0.525893\pi$
$179$	−2.17424	−0.162511	−0.0812553	+	0.996693i	$0.525893\pi$
$180$	−1.65247	−0.123168
$181$	−9.30907	−0.691938	−0.345969	−	0.938246i	$-0.612450\pi$
$181$	−9.30907	−0.691938	−0.345969	+	0.938246i	$0.612450\pi$
$182$	1.89835	0.140715
$183$	−11.2934	−0.834830
$184$	−7.65249	−0.564149
$185$	0.00294879	0.000216799 0
$186$	6.52187	0.478207
$187$	−26.5901	−1.94446
$188$	35.1411	2.56293
$189$	3.08940	0.224721
$190$	−10.9441	−0.793969
$191$	15.1846	1.09872	0.549360	−	0.835586i	$-0.314872\pi$
$191$	15.1846	1.09872	0.549360	+	0.835586i	$0.314872\pi$
$192$	16.4020	1.18371
$193$	8.11667	0.584251	0.292125	−	0.956380i	$-0.405638\pi$
$193$	8.11667	0.584251	0.292125	+	0.956380i	$0.405638\pi$
$194$	−20.6995	−1.48614
$195$	1.44695	0.103618
$196$	−32.8399	−2.34571
$197$	0.104118	0.00741809	0.00370905	−	0.999993i	$-0.498819\pi$
$197$	0.104118	0.00741809	0.00370905	+	0.999993i	$0.498819\pi$
$198$	5.09065	0.361777
$199$	−20.8288	−1.47651	−0.738257	−	0.674520i	$-0.764351\pi$
$199$	−20.8288	−1.47651	−0.738257	+	0.674520i	$0.764351\pi$
$200$	34.4519	2.43612
$201$	−17.0859	−1.20515
$202$	31.5258	2.21815
$203$	−4.19358	−0.294332
$204$	−51.0775	−3.57614
$205$	−3.53616	−0.246976
$206$	34.9329	2.43389
$207$	−0.476845	−0.0331430
$208$	13.2904	0.921524
$209$	23.9579	1.65720
$210$	1.64835	0.113747
$211$	22.5214	1.55043	0.775217	−	0.631695i	$-0.217640\pi$
$211$	22.5214	1.55043	0.775217	+	0.631695i	$0.217640\pi$
$212$	−53.8023	−3.69516
$213$	−3.31368	−0.227050
$214$	15.5963	1.06614
$215$	−5.42546	−0.370014
$216$	42.2630	2.87563
$217$	0.873672	0.0593088
$218$	−37.2221	−2.52100
$219$	−26.0671	−1.76145
$220$	14.0729	0.948795
$221$	−8.45247	−0.568575
$222$	−0.0174499	−0.00117116
$223$	10.6791	0.715124	0.357562	−	0.933889i	$-0.383608\pi$
$223$	10.6791	0.715124	0.357562	+	0.933889i	$0.383608\pi$
$224$	6.57875	0.439561
$225$	2.14678	0.143119
$226$	−49.4395	−3.28866
$227$	−4.40584	−0.292426	−0.146213	−	0.989253i	$-0.546709\pi$
$227$	−4.40584	−0.292426	−0.146213	+	0.989253i	$0.546709\pi$
$228$	46.0212	3.04783
$229$	0.133514	0.00882283	0.00441142	−	0.999990i	$-0.498596\pi$
$229$	0.133514	0.00882283	0.00441142	+	0.999990i	$0.498596\pi$
$230$	−1.85507	−0.122320
$231$	−3.60842	−0.237416
$232$	−57.3681	−3.76640
$233$	−17.4686	−1.14441	−0.572203	−	0.820112i	$-0.693911\pi$
$233$	−17.4686	−1.14441	−0.572203	+	0.820112i	$0.693911\pi$
$234$	1.61822	0.105786
$235$	5.04942	0.329388
$236$	11.5122	0.749382
$237$	4.85654	0.315466
$238$	−9.62894	−0.624152
$239$	−6.47519	−0.418845	−0.209423	−	0.977825i	$-0.567158\pi$
$239$	−6.47519	−0.418845	−0.209423	+	0.977825i	$0.567158\pi$
$240$	11.5401	0.744911
$241$	−1.40620	−0.0905811	−0.0452905	−	0.998974i	$-0.514421\pi$
$241$	−1.40620	−0.0905811	−0.0452905	+	0.998974i	$0.514421\pi$
$242$	−14.4359	−0.927976
$243$	4.90583	0.314709
$244$	−34.9154	−2.23523
$245$	−4.71876	−0.301470
$246$	20.9258	1.33418
$247$	7.61573	0.484578
$248$	11.9518	0.758942
$249$	−22.5755	−1.43066
$250$	17.6270	1.11483
$251$	−29.5457	−1.86491	−0.932455	−	0.361287i	$-0.882337\pi$
$251$	−29.5457	−1.86491	−0.932455	+	0.361287i	$0.882337\pi$
$252$	1.30996	0.0825200
$253$	4.06095	0.255310
$254$	−24.2695	−1.52281
$255$	−7.33932	−0.459606
$256$	−11.1240	−0.695251
$257$	6.81643	0.425197	0.212598	−	0.977140i	$-0.431807\pi$
$257$	6.81643	0.425197	0.212598	+	0.977140i	$0.431807\pi$
$258$	32.1060	1.99883
$259$	−0.00233760	−0.000145251 0
$260$	4.47350	0.277434
$261$	−3.57475	−0.221271
$262$	−23.9597	−1.48023
$263$	−28.9508	−1.78518	−0.892590	−	0.450869i	$-0.851114\pi$
$263$	−28.9508	−1.78518	−0.892590	+	0.450869i	$0.851114\pi$
$264$	−49.3631	−3.03809
$265$	−7.73085	−0.474902
$266$	8.67575	0.531944
$267$	23.8364	1.45877
$268$	−52.8240	−3.22674
$269$	−11.1901	−0.682273	−0.341137	−	0.940014i	$-0.610812\pi$
$269$	−11.1901	−0.682273	−0.341137	+	0.940014i	$0.610812\pi$
$270$	10.2451	0.623498
$271$	−5.64286	−0.342779	−0.171390	−	0.985203i	$-0.554826\pi$
$271$	−5.64286	−0.342779	−0.171390	+	0.985203i	$0.554826\pi$
$272$	−67.4124	−4.08748
$273$	−1.14704	−0.0694223
$274$	16.9281	1.02266
$275$	−18.2826	−1.10248
$276$	7.80076	0.469551
$277$	−24.0694	−1.44619	−0.723095	−	0.690749i	$-0.757281\pi$
$277$	−24.0694	−1.44619	−0.723095	+	0.690749i	$0.757281\pi$
$278$	33.2258	1.99275
$279$	0.744746	0.0445868
$280$	3.02072	0.180523
$281$	5.82586	0.347542	0.173771	−	0.984786i	$-0.444405\pi$
$281$	5.82586	0.347542	0.173771	+	0.984786i	$0.444405\pi$
$282$	−29.8807	−1.77937
$283$	3.46808	0.206156	0.103078	−	0.994673i	$-0.467131\pi$
$283$	3.46808	0.206156	0.103078	+	0.994673i	$0.467131\pi$
$284$	−10.2448	−0.607918
$285$	6.61278	0.391707
$286$	−13.7812	−0.814900
$287$	2.80323	0.165469
$288$	5.60794	0.330451
$289$	25.8731	1.52195
$290$	−13.9068	−0.816636
$291$	12.5073	0.733190
$292$	−80.5909	−4.71622
$293$	21.4612	1.25378	0.626888	−	0.779109i	$-0.284328\pi$
$293$	21.4612	1.25378	0.626888	+	0.779109i	$0.284328\pi$
$294$	27.9240	1.62856
$295$	1.65419	0.0963106
$296$	−0.0319783	−0.00185870
$297$	−22.4277	−1.30139
$298$	−25.1880	−1.45910
$299$	1.29090	0.0746544
$300$	−35.1195	−2.02762
$301$	4.30094	0.247902
$302$	−30.4554	−1.75251
$303$	−19.0489	−1.09433
$304$	60.7390	3.48362
$305$	−5.01698	−0.287271
$306$	−8.20802	−0.469221
$307$	3.39122	0.193547	0.0967736	−	0.995306i	$-0.469148\pi$
$307$	3.39122	0.193547	0.0967736	+	0.995306i	$0.469148\pi$
$308$	−11.1560	−0.635674
$309$	−21.1075	−1.20077
$310$	2.89728	0.164555
$311$	−14.5230	−0.823525	−0.411763	−	0.911291i	$-0.635087\pi$
$311$	−14.5230	−0.823525	−0.411763	+	0.911291i	$0.635087\pi$
$312$	−15.6915	−0.888359
$313$	29.8540	1.68745	0.843724	−	0.536778i	$-0.180359\pi$
$313$	29.8540	1.68745	0.843724	+	0.536778i	$0.180359\pi$
$314$	−7.17752	−0.405051
$315$	0.188228	0.0106055
$316$	15.0148	0.844650
$317$	11.8672	0.666528	0.333264	−	0.942834i	$-0.391850\pi$
$317$	11.8672	0.666528	0.333264	+	0.942834i	$0.391850\pi$
$318$	45.7485	2.56545
$319$	30.4436	1.70451
$320$	7.28646	0.407325
$321$	−9.42380	−0.525985
$322$	1.47057	0.0819517
$323$	−38.6290	−2.14938
$324$	−36.0566	−2.00314
$325$	−5.81168	−0.322374
$326$	54.8412	3.03737
$327$	22.4908	1.24374
$328$	38.3481	2.11742
$329$	−4.00283	−0.220683
$330$	−11.9663	−0.658722
$331$	−33.0139	−1.81461	−0.907304	−	0.420476i	$-0.861863\pi$
$331$	−33.0139	−1.81461	−0.907304	+	0.420476i	$0.861863\pi$
$332$	−69.7959	−3.83055
$333$	−0.00199265	−0.000109196 0
$334$	−32.7800	−1.79364
$335$	−7.59027	−0.414701
$336$	−9.14822	−0.499076
$337$	−16.3592	−0.891142	−0.445571	−	0.895247i	$-0.646999\pi$
$337$	−16.3592	−0.891142	−0.445571	+	0.895247i	$0.646999\pi$
$338$	29.7945	1.62061
$339$	29.8729	1.62247
$340$	−22.6907	−1.23058
$341$	−6.34248	−0.343464
$342$	7.39548	0.399902
$343$	7.65646	0.413410
$344$	58.8368	3.17227
$345$	1.12089	0.0603467
$346$	8.26620	0.444394
$347$	9.69139	0.520261	0.260131	−	0.965573i	$-0.416234\pi$
$347$	9.69139	0.520261	0.260131	+	0.965573i	$0.416234\pi$
$348$	58.4797	3.13484
$349$	1.00000	0.0535288
$349$	1.00000	0.0535288
$350$	−6.62059	−0.353885
$351$	−7.12932	−0.380535
$352$	−47.7588	−2.54555
$353$	30.9804	1.64892	0.824460	−	0.565921i	$-0.191479\pi$
$353$	30.9804	1.64892	0.824460	+	0.565921i	$0.191479\pi$
$354$	−9.78892	−0.520275
$355$	−1.47207	−0.0781296
$356$	73.6944	3.90579
$357$	5.81811	0.307927
$358$	5.71580	0.302089
$359$	2.69579	0.142278	0.0711392	−	0.997466i	$-0.477337\pi$
$359$	2.69579	0.142278	0.0711392	+	0.997466i	$0.477337\pi$
$360$	2.57496	0.135712
$361$	15.8050	0.831842
$362$	24.4723	1.28624
$363$	8.72264	0.457820
$364$	−3.54628	−0.185876
$365$	−11.5801	−0.606129
$366$	29.6888	1.55186
$367$	−12.6665	−0.661187	−0.330593	−	0.943773i	$-0.607249\pi$
$367$	−12.6665	−0.661187	−0.330593	+	0.943773i	$0.607249\pi$
$368$	10.2955	0.536690
$369$	2.38956	0.124396
$370$	−0.00775198	−0.000403006 0
$371$	6.12849	0.318175
$372$	−12.1834	−0.631680
$373$	18.1796	0.941303	0.470651	−	0.882319i	$-0.344019\pi$
$373$	18.1796	0.941303	0.470651	+	0.882319i	$0.344019\pi$
$374$	69.9019	3.61454
$375$	−10.6508	−0.550003
$376$	−54.7587	−2.82396
$377$	9.67741	0.498412
$378$	−8.12163	−0.417732
$379$	−36.2973	−1.86447	−0.932233	−	0.361859i	$-0.882142\pi$
$379$	−36.2973	−1.86447	−0.932233	+	0.361859i	$0.882142\pi$
$380$	20.4445	1.04878
$381$	14.6644	0.751281
$382$	−39.9183	−2.04240
$383$	14.6799	0.750107	0.375054	−	0.927003i	$-0.377624\pi$
$383$	14.6799	0.750107	0.375054	+	0.927003i	$0.377624\pi$
$384$	−5.75691	−0.293781
$385$	−1.60301	−0.0816969
$386$	−21.3377	−1.08606
$387$	3.66626	0.186366
$388$	38.6684	1.96309
$389$	−20.1071	−1.01947	−0.509734	−	0.860332i	$-0.670256\pi$
$389$	−20.1071	−1.01947	−0.509734	+	0.860332i	$0.670256\pi$
$390$	−3.80384	−0.192615
$391$	−6.54776	−0.331134
$392$	51.1728	2.58462
$393$	14.4772	0.730277
$394$	−0.273712	−0.0137894
$395$	2.15748	0.108554
$396$	−9.50976	−0.477884
$397$	−20.2198	−1.01480	−0.507402	−	0.861709i	$-0.669394\pi$
$397$	−20.2198	−1.01480	−0.507402	+	0.861709i	$0.669394\pi$
$398$	54.7561	2.74468
$399$	−5.24216	−0.262436
$400$	−46.3509	−2.31754
$401$	7.41761	0.370418	0.185209	−	0.982699i	$-0.440704\pi$
$401$	7.41761	0.370418	0.185209	+	0.982699i	$0.440704\pi$
$402$	44.9166	2.24024
$403$	−2.01615	−0.100431
$404$	−58.8928	−2.93003
$405$	−5.18096	−0.257444
$406$	11.0244	0.547131
$407$	0.0169699	0.000841169 0
$408$	79.5916	3.94037
$409$	9.03258	0.446632	0.223316	−	0.974746i	$-0.428312\pi$
$409$	9.03258	0.446632	0.223316	+	0.974746i	$0.428312\pi$
$410$	9.29609	0.459101
$411$	−10.2285	−0.504534
$412$	−65.2575	−3.21501
$413$	−1.31133	−0.0645263
$414$	1.25356	0.0616092
$415$	−10.0290	−0.492302
$416$	−15.1816	−0.744339
$417$	−20.0761	−0.983130
$418$	−62.9821	−3.08055
$419$	19.1362	0.934866	0.467433	−	0.884028i	$-0.345179\pi$
$419$	19.1362	0.934866	0.467433	+	0.884028i	$0.345179\pi$
$420$	−3.07925	−0.150252
$421$	−16.2928	−0.794064	−0.397032	−	0.917805i	$-0.629960\pi$
$421$	−16.2928	−0.794064	−0.397032	+	0.917805i	$0.629960\pi$
$422$	−59.2057	−2.88209
$423$	−3.41214	−0.165904
$424$	83.8376	4.07151
$425$	29.4784	1.42991
$426$	8.71123	0.422061
$427$	3.97712	0.192466
$428$	−29.1353	−1.40831
$429$	8.32704	0.402033
$430$	14.2628	0.687815
$431$	29.6581	1.42858	0.714290	−	0.699850i	$-0.246750\pi$
$431$	29.6581	1.42858	0.714290	+	0.699850i	$0.246750\pi$
$432$	−56.8597	−2.73566
$433$	−17.5834	−0.845005	−0.422502	−	0.906362i	$-0.638848\pi$
$433$	−17.5834	−0.845005	−0.422502	+	0.906362i	$0.638848\pi$
$434$	−2.29677	−0.110248
$435$	8.40293	0.402890
$436$	69.5340	3.33007
$437$	5.89958	0.282215
$438$	68.5269	3.27434
$439$	31.7161	1.51373	0.756863	−	0.653573i	$-0.226731\pi$
$439$	31.7161	1.51373	0.756863	+	0.653573i	$0.226731\pi$
$440$	−21.9291	−1.04543
$441$	3.18870	0.151843
$442$	22.2204	1.05692
$443$	−30.7549	−1.46121	−0.730606	−	0.682800i	$-0.760762\pi$
$443$	−30.7549	−1.46121	−0.730606	+	0.682800i	$0.760762\pi$
$444$	0.0325979	0.00154703
$445$	10.5891	0.501973
$446$	−28.0739	−1.32934
$447$	15.2194	0.719852
$448$	−5.77621	−0.272900
$449$	−24.6626	−1.16390	−0.581950	−	0.813225i	$-0.697710\pi$
$449$	−24.6626	−1.16390	−0.581950	+	0.813225i	$0.697710\pi$
$450$	−5.64360	−0.266042
$451$	−20.3502	−0.958253
$452$	92.3571	4.34411
$453$	18.4021	0.864608
$454$	11.5824	0.543588
$455$	−0.509565	−0.0238888
$456$	−71.7126	−3.35825
$457$	−17.6293	−0.824665	−0.412332	−	0.911033i	$-0.635286\pi$
$457$	−17.6293	−0.824665	−0.412332	+	0.911033i	$0.635286\pi$
$458$	−0.350990	−0.0164007
$459$	36.1618	1.68789
$460$	3.46542	0.161576
$461$	30.2650	1.40958	0.704791	−	0.709415i	$-0.251041\pi$
$461$	30.2650	1.40958	0.704791	+	0.709415i	$0.251041\pi$
$462$	9.48605	0.441331
$463$	−31.6497	−1.47089	−0.735443	−	0.677586i	$-0.763026\pi$
$463$	−31.6497	−1.47089	−0.735443	+	0.677586i	$0.763026\pi$
$464$	77.1819	3.58308
$465$	−1.75063	−0.0811835
$466$	45.9227	2.12733
$467$	−11.8737	−0.549451	−0.274725	−	0.961523i	$-0.588587\pi$
$467$	−11.8737	−0.549451	−0.274725	+	0.961523i	$0.588587\pi$
$468$	−3.02297	−0.139737
$469$	6.01705	0.277842
$470$	−13.2743	−0.612296
$471$	4.33688	0.199833
$472$	−17.9390	−0.825707
$473$	−31.2229	−1.43563
$474$	−12.7672	−0.586417
$475$	−26.5602	−1.21867
$476$	17.9877	0.824464
$477$	5.22412	0.239196
$478$	17.0224	0.778587
$479$	−6.98756	−0.319270	−0.159635	−	0.987176i	$-0.551032\pi$
$479$	−6.98756	−0.319270	−0.159635	+	0.987176i	$0.551032\pi$
$480$	−13.1822	−0.601684
$481$	0.00539441	0.000245964 0
$482$	3.69670	0.168380
$483$	−0.888565	−0.0404311
$484$	26.9675	1.22580
$485$	5.55625	0.252296
$486$	−12.8968	−0.585010
$487$	17.7633	0.804932	0.402466	−	0.915435i	$-0.368153\pi$
$487$	17.7633	0.804932	0.402466	+	0.915435i	$0.368153\pi$
$488$	54.4069	2.46289
$489$	−33.1368	−1.49850
$490$	12.4050	0.560400
$491$	−29.5335	−1.33283	−0.666414	−	0.745582i	$-0.732172\pi$
$491$	−29.5335	−1.33283	−0.666414	+	0.745582i	$0.732172\pi$
$492$	−39.0911	−1.76236
$493$	−49.0863	−2.21074
$494$	−20.0208	−0.900776
$495$	−1.36646	−0.0614176
$496$	−16.0797	−0.722001
$497$	1.16696	0.0523453
$498$	59.3479	2.65944
$499$	16.9806	0.760154	0.380077	−	0.924955i	$-0.375897\pi$
$499$	16.9806	0.760154	0.380077	+	0.924955i	$0.375897\pi$
$500$	−32.9286	−1.47261
$501$	19.8067	0.884899
$502$	77.6718	3.46666
$503$	33.2870	1.48420	0.742098	−	0.670291i	$-0.233831\pi$
$503$	33.2870	1.48420	0.742098	+	0.670291i	$0.233831\pi$
$504$	−2.04125	−0.0909247
$505$	−8.46229	−0.376567
$506$	−10.6757	−0.474593
$507$	−18.0028	−0.799531
$508$	45.3375	2.01153
$509$	35.6307	1.57930	0.789652	−	0.613555i	$-0.210261\pi$
$509$	35.6307	1.57930	0.789652	+	0.613555i	$0.210261\pi$
$510$	19.2941	0.854357
$511$	9.17990	0.406095
$512$	36.4921	1.61274
$513$	−32.5820	−1.43853
$514$	−17.9195	−0.790394
$515$	−9.37684	−0.413193
$516$	−59.9768	−2.64033
$517$	29.0588	1.27801
$518$	0.00614524	0.000270006 0
$519$	−4.99470	−0.219243
$520$	−6.97083	−0.305691
$521$	−17.3546	−0.760321	−0.380160	−	0.924921i	$-0.624131\pi$
$521$	−17.3546	−0.760321	−0.380160	+	0.924921i	$0.624131\pi$
$522$	9.39753	0.411319
$523$	−7.18895	−0.314351	−0.157175	−	0.987571i	$-0.550239\pi$
$523$	−7.18895	−0.314351	−0.157175	+	0.987571i	$0.550239\pi$
$524$	44.7587	1.95529
$525$	4.00037	0.174590
$526$	76.1077	3.31845
$527$	10.2264	0.445470
$528$	66.4120	2.89021
$529$	1.00000	0.0434783
$530$	20.3234	0.882791
$531$	−1.11782	−0.0485092
$532$	−16.2070	−0.702663
$533$	−6.46892	−0.280200
$534$	−62.6628	−2.71168
$535$	−4.18644	−0.180996
$536$	82.3132	3.55539
$537$	−3.45367	−0.149037
$538$	29.4173	1.26827
$539$	−27.1559	−1.16969
$540$	−19.1387	−0.823600
$541$	21.0467	0.904868	0.452434	−	0.891798i	$-0.350556\pi$
$541$	21.0467	0.904868	0.452434	+	0.891798i	$0.350556\pi$
$542$	14.8343	0.637189
$543$	−14.7869	−0.634568
$544$	77.0050	3.30156
$545$	9.99132	0.427981
$546$	3.01543	0.129048
$547$	6.02179	0.257473	0.128737	−	0.991679i	$-0.458908\pi$
$547$	6.02179	0.257473	0.128737	+	0.991679i	$0.458908\pi$
$548$	−31.6231	−1.35087
$549$	3.39022	0.144691
$550$	48.0626	2.04939
$551$	44.2271	1.88414
$552$	−12.1556	−0.517375
$553$	−1.71030	−0.0727294
$554$	63.2752	2.68831
$555$	0.00468399	0.000198824 0
$556$	−62.0686	−2.63230
$557$	34.1294	1.44611	0.723056	−	0.690790i	$-0.242737\pi$
$557$	34.1294	1.44611	0.723056	+	0.690790i	$0.242737\pi$
$558$	−1.95784	−0.0828820
$559$	−9.92515	−0.419789
$560$	−4.06402	−0.171736
$561$	−42.2369	−1.78324
$562$	−15.3154	−0.646042
$563$	22.1230	0.932375	0.466187	−	0.884686i	$-0.345627\pi$
$563$	22.1230	0.932375	0.466187	+	0.884686i	$0.345627\pi$
$564$	55.8197	2.35043
$565$	13.2708	0.558305
$566$	−9.11713	−0.383221
$567$	4.10711	0.172483
$568$	15.9640	0.669834
$569$	−23.4567	−0.983355	−0.491678	−	0.870777i	$-0.663616\pi$
$569$	−23.4567	−0.983355	−0.491678	+	0.870777i	$0.663616\pi$
$570$	−17.3841	−0.728140
$571$	2.49720	0.104505	0.0522523	−	0.998634i	$-0.483360\pi$
$571$	2.49720	0.104505	0.0522523	+	0.998634i	$0.483360\pi$
$572$	25.7445	1.07643
$573$	24.1199	1.00762
$574$	−7.36931	−0.307589
$575$	−4.50205	−0.187749
$576$	−4.92382	−0.205159
$577$	−10.4954	−0.436931	−0.218465	−	0.975845i	$-0.570105\pi$
$577$	−10.4954	−0.436931	−0.218465	+	0.975845i	$0.570105\pi$
$578$	−68.0171	−2.82914
$579$	12.8929	0.535810
$580$	25.9791	1.07872
$581$	7.95027	0.329833
$582$	−32.8800	−1.36292
$583$	−44.4901	−1.84259
$584$	125.581	5.19657
$585$	−0.434369	−0.0179590
$586$	−56.4186	−2.33063
$587$	5.90031	0.243532	0.121766	−	0.992559i	$-0.461144\pi$
$587$	5.90031	0.243532	0.121766	+	0.992559i	$0.461144\pi$
$588$	−52.1643	−2.15122
$589$	−9.21408	−0.379660
$590$	−4.34865	−0.179031
$591$	0.165386	0.00680305
$592$	0.0430229	0.00176823
$593$	−34.7892	−1.42862	−0.714311	−	0.699829i	$-0.753260\pi$
$593$	−34.7892	−1.42862	−0.714311	+	0.699829i	$0.753260\pi$
$594$	58.9595	2.41914
$595$	2.58465	0.105960
$596$	47.0533	1.92738
$597$	−33.0854	−1.35409
$598$	−3.39359	−0.138774
$599$	19.4030	0.792784	0.396392	−	0.918081i	$-0.370262\pi$
$599$	19.4030	0.792784	0.396392	+	0.918081i	$0.370262\pi$
$600$	54.7250	2.23414
$601$	−25.4419	−1.03780	−0.518898	−	0.854836i	$-0.673657\pi$
$601$	−25.4419	−1.03780	−0.518898	+	0.854836i	$0.673657\pi$
$602$	−11.3066	−0.460822
$603$	5.12913	0.208874
$604$	56.8933	2.31496
$605$	3.87496	0.157539
$606$	50.0769	2.03424
$607$	−13.8456	−0.561976	−0.280988	−	0.959711i	$-0.590662\pi$
$607$	−13.8456	−0.561976	−0.280988	+	0.959711i	$0.590662\pi$
$608$	−69.3820	−2.81381
$609$	−6.66127	−0.269928
$610$	13.1890	0.534006
$611$	9.23722	0.373698
$612$	15.3333	0.619811
$613$	32.0439	1.29424	0.647121	−	0.762387i	$-0.275973\pi$
$613$	32.0439	1.29424	0.647121	+	0.762387i	$0.275973\pi$
$614$	−8.91507	−0.359783
$615$	−5.61699	−0.226499
$616$	17.3839	0.700418
$617$	39.9487	1.60827	0.804137	−	0.594443i	$-0.202628\pi$
$617$	39.9487	1.60827	0.804137	+	0.594443i	$0.202628\pi$
$618$	55.4889	2.23209
$619$	−10.4946	−0.421815	−0.210908	−	0.977506i	$-0.567642\pi$
$619$	−10.4946	−0.421815	−0.210908	+	0.977506i	$0.567642\pi$
$620$	−5.41237	−0.217366
$621$	−5.52277	−0.221621
$622$	38.1791	1.53084
$623$	−8.39434	−0.336312
$624$	21.1111	0.845119
$625$	17.7788	0.711151
$626$	−78.4822	−3.13678
$627$	38.0558	1.51980
$628$	13.4082	0.535046
$629$	−0.0273619	−0.00109099
$630$	−0.494828	−0.0197144
$631$	−1.12761	−0.0448896	−0.0224448	−	0.999748i	$-0.507145\pi$
$631$	−1.12761	−0.0448896	−0.0224448	+	0.999748i	$0.507145\pi$
$632$	−23.3969	−0.930678
$633$	35.7739	1.42189
$634$	−31.1973	−1.23900
$635$	6.51454	0.258522
$636$	−85.4620	−3.38879
$637$	−8.63232	−0.342025
$638$	−80.0321	−3.16850
$639$	0.994754	0.0393519
$640$	−2.55746	−0.101092
$641$	30.5940	1.20839	0.604195	−	0.796837i	$-0.293495\pi$
$641$	30.5940	1.20839	0.604195	+	0.796837i	$0.293495\pi$
$642$	24.7739	0.977749
$643$	−30.7772	−1.21373	−0.606867	−	0.794803i	$-0.707574\pi$
$643$	−30.7772	−1.21373	−0.606867	+	0.794803i	$0.707574\pi$
$644$	−2.74715	−0.108253
$645$	−8.61805	−0.339335
$646$	101.551	3.99545
$647$	−2.04003	−0.0802017	−0.0401008	−	0.999196i	$-0.512768\pi$
$647$	−2.04003	−0.0802017	−0.0401008	+	0.999196i	$0.512768\pi$
$648$	56.1852	2.20716
$649$	9.51967	0.373680
$650$	15.2781	0.599258
$651$	1.38778	0.0543914
$652$	−102.448	−4.01217
$653$	−1.42418	−0.0557325	−0.0278663	−	0.999612i	$-0.508871\pi$
$653$	−1.42418	−0.0557325	−0.0278663	+	0.999612i	$0.508871\pi$
$654$	−59.1252	−2.31198
$655$	6.43136	0.251294
$656$	−51.5927	−2.01436
$657$	7.82524	0.305292
$658$	10.5229	0.410226
$659$	−46.3308	−1.80479	−0.902395	−	0.430909i	$-0.858193\pi$
$659$	−46.3308	−1.80479	−0.902395	+	0.430909i	$0.858193\pi$
$660$	22.3540	0.870129
$661$	−21.6999	−0.844029	−0.422014	−	0.906589i	$-0.638677\pi$
$661$	−21.6999	−0.844029	−0.422014	+	0.906589i	$0.638677\pi$
$662$	86.7891	3.37316
$663$	−13.4263	−0.521433
$664$	108.760	4.22069
$665$	−2.32878	−0.0903063
$666$	0.00523840	0.000202984 0
$667$	7.49666	0.290272
$668$	61.2358	2.36929
$669$	16.9631	0.655832
$670$	19.9538	0.770884
$671$	−28.8721	−1.11460
$672$	10.4500	0.403117
$673$	23.1544	0.892535	0.446268	−	0.894900i	$-0.352753\pi$
$673$	23.1544	0.892535	0.446268	+	0.894900i	$0.352753\pi$
$674$	43.0061	1.65653
$675$	24.8638	0.957009
$676$	−55.6586	−2.14072
$677$	−23.3699	−0.898177	−0.449088	−	0.893487i	$-0.648251\pi$
$677$	−23.3699	−0.898177	−0.449088	+	0.893487i	$0.648251\pi$
$678$	−78.5318	−3.01600
$679$	−4.40462	−0.169034
$680$	35.3579	1.35591
$681$	−6.99844	−0.268181
$682$	16.6735	0.638463
$683$	−36.0542	−1.37958	−0.689789	−	0.724011i	$-0.742297\pi$
$683$	−36.0542	−1.37958	−0.689789	+	0.724011i	$0.742297\pi$
$684$	−13.8154	−0.528244
$685$	−4.54392	−0.173614
$686$	−20.1278	−0.768484
$687$	0.212079	0.00809132
$688$	−79.1577	−3.01786
$689$	−14.1425	−0.538787
$690$	−2.94667	−0.112178
$691$	36.0848	1.37273	0.686366	−	0.727256i	$-0.259205\pi$
$691$	36.0848	1.37273	0.686366	+	0.727256i	$0.259205\pi$
$692$	−15.4420	−0.587015
$693$	1.08323	0.0411486
$694$	−25.4774	−0.967108
$695$	−8.91863	−0.338303
$696$	−91.1261	−3.45413
$697$	32.8121	1.24285
$698$	−2.62887	−0.0995041
$699$	−27.7479	−1.04952
$700$	12.3678	0.467460
$701$	0.203916	0.00770179	0.00385089	−	0.999993i	$-0.498774\pi$
$701$	0.203916	0.00770179	0.00385089	+	0.999993i	$0.498774\pi$
$702$	18.7420	0.707373
$703$	0.0246532	0.000929814 0
$704$	41.9327	1.58040
$705$	8.02072	0.302078
$706$	−81.4433	−3.06516
$707$	6.70833	0.252293
$708$	18.2865	0.687250
$709$	−34.7528	−1.30517	−0.652584	−	0.757716i	$-0.726315\pi$
$709$	−34.7528	−1.30517	−0.652584	+	0.757716i	$0.726315\pi$
$710$	3.86989	0.145234
$711$	−1.45792	−0.0546761
$712$	−114.834	−4.30360
$713$	−1.56182	−0.0584907
$714$	−15.2950	−0.572403
$715$	3.69921	0.138343
$716$	−10.6776	−0.399040
$717$	−10.2855	−0.384118
$718$	−7.08688	−0.264480
$719$	−6.77690	−0.252736	−0.126368	−	0.991983i	$-0.540332\pi$
$719$	−6.77690	−0.252736	−0.126368	+	0.991983i	$0.540332\pi$
$720$	−3.46430	−0.129107
$721$	7.43332	0.276831
$722$	−41.5492	−1.54630
$723$	−2.23366	−0.0830709
$724$	−45.7163	−1.69903
$725$	−33.7504	−1.25346
$726$	−22.9307	−0.851037
$727$	−39.5631	−1.46731	−0.733657	−	0.679520i	$-0.762188\pi$
$727$	−39.5631	−1.46731	−0.733657	+	0.679520i	$0.762188\pi$
$728$	5.52600	0.204807
$729$	29.8189	1.10440
$730$	30.4425	1.12673
$731$	50.3429	1.86200
$732$	−55.4611	−2.04990
$733$	9.91817	0.366336	0.183168	−	0.983082i	$-0.441365\pi$
$733$	9.91817	0.366336	0.183168	+	0.983082i	$0.441365\pi$
$734$	33.2986	1.22907
$735$	−7.49548	−0.276475
$736$	−11.7605	−0.433498
$737$	−43.6811	−1.60902
$738$	−6.28184	−0.231238
$739$	−4.56217	−0.167822	−0.0839111	−	0.996473i	$-0.526741\pi$
$739$	−4.56217	−0.167822	−0.0839111	+	0.996473i	$0.526741\pi$
$740$	0.0144813	0.000532345 0
$741$	12.0972	0.444401
$742$	−16.1110	−0.591453
$743$	−3.13016	−0.114835	−0.0574173	−	0.998350i	$-0.518287\pi$
$743$	−3.13016	−0.114835	−0.0574173	+	0.998350i	$0.518287\pi$
$744$	18.9848	0.696017
$745$	6.76108	0.247707
$746$	−47.7917	−1.74978
$747$	6.77706	0.247960
$748$	−130.583	−4.77457
$749$	3.31873	0.121264
$750$	27.9994	1.02239
$751$	−20.3041	−0.740908	−0.370454	−	0.928851i	$-0.620798\pi$
$751$	−20.3041	−0.740908	−0.370454	+	0.928851i	$0.620798\pi$
$752$	73.6712	2.68651
$753$	−46.9317	−1.71029
$754$	−25.4406	−0.926493
$755$	8.17499	0.297518
$756$	15.1719	0.551796
$757$	−24.7020	−0.897809	−0.448905	−	0.893580i	$-0.648186\pi$
$757$	−24.7020	−0.897809	−0.448905	+	0.893580i	$0.648186\pi$
$758$	95.4207	3.46584
$759$	6.45059	0.234142
$760$	−31.8577	−1.15560
$761$	−37.5081	−1.35967	−0.679834	−	0.733366i	$-0.737948\pi$
$761$	−37.5081	−1.35967	−0.679834	+	0.733366i	$0.737948\pi$
$762$	−38.5508	−1.39655
$763$	−7.92044	−0.286739
$764$	74.5708	2.69788
$765$	2.20323	0.0796581
$766$	−38.5915	−1.39437
$767$	3.02611	0.109267
$768$	−17.6699	−0.637607
$769$	10.2647	0.370153	0.185076	−	0.982724i	$-0.440747\pi$
$769$	10.2647	0.370153	0.185076	+	0.982724i	$0.440747\pi$
$770$	4.21410	0.151866
$771$	10.8275	0.389943
$772$	39.8605	1.43461
$773$	40.9096	1.47142	0.735708	−	0.677298i	$-0.236849\pi$
$773$	40.9096	1.47142	0.735708	+	0.677298i	$0.236849\pi$
$774$	−9.63811	−0.346435
$775$	7.03140	0.252576
$776$	−60.2551	−2.16303
$777$	−0.00371315	−0.000133208 0
$778$	52.8588	1.89508
$779$	−29.5639	−1.05924
$780$	7.10590	0.254432
$781$	−8.47162	−0.303138
$782$	17.2132	0.615542
$783$	−41.4024	−1.47960
$784$	−68.8468	−2.45881
$785$	1.92662	0.0687641
$786$	−38.0586	−1.35751
$787$	−9.54453	−0.340226	−0.170113	−	0.985425i	$-0.554413\pi$
$787$	−9.54453	−0.340226	−0.170113	+	0.985425i	$0.554413\pi$
$788$	0.511317	0.0182149
$789$	−45.9867	−1.63717
$790$	−5.67172	−0.201791
$791$	−10.5202	−0.374054
$792$	14.8186	0.526556
$793$	−9.17788	−0.325916
$794$	53.1553	1.88641
$795$	−12.2800	−0.435527
$796$	−102.289	−3.62554
$797$	−46.1206	−1.63368	−0.816838	−	0.576867i	$-0.804275\pi$
$797$	−46.1206	−1.63368	−0.816838	+	0.576867i	$0.804275\pi$
$798$	13.7809	0.487840
$799$	−46.8536	−1.65756
$800$	52.9465	1.87194
$801$	−7.15560	−0.252831
$802$	−19.4999	−0.688566
$803$	−66.6420	−2.35175
$804$	−83.9080	−2.95921
$805$	−0.394737	−0.0139127
$806$	5.30019	0.186691
$807$	−17.7749	−0.625705
$808$	91.7698	3.22845
$809$	16.1390	0.567416	0.283708	−	0.958911i	$-0.408435\pi$
$809$	16.1390	0.567416	0.283708	+	0.958911i	$0.408435\pi$
$810$	13.6201	0.478560
$811$	−3.54315	−0.124417	−0.0622084	−	0.998063i	$-0.519814\pi$
$811$	−3.54315	−0.124417	−0.0622084	+	0.998063i	$0.519814\pi$
$812$	−20.5945	−0.722724
$813$	−8.96337	−0.314359
$814$	−0.0446117	−0.00156364
$815$	−14.7207	−0.515644
$816$	−107.081	−3.74858
$817$	−45.3593	−1.58692
$818$	−23.7455	−0.830240
$819$	0.344338	0.0120322
$820$	−17.3659	−0.606443
$821$	−3.11557	−0.108734	−0.0543671	−	0.998521i	$-0.517314\pi$
$821$	−3.11557	−0.108734	−0.0543671	+	0.998521i	$0.517314\pi$
$822$	26.8894	0.937874
$823$	10.0119	0.348992	0.174496	−	0.984658i	$-0.444170\pi$
$823$	10.0119	0.348992	0.174496	+	0.984658i	$0.444170\pi$
$824$	101.688	3.54246
$825$	−29.0409	−1.01107
$826$	3.44731	0.119947
$827$	−36.5539	−1.27111	−0.635553	−	0.772058i	$-0.719228\pi$
$827$	−36.5539	−1.27111	−0.635553	+	0.772058i	$0.719228\pi$
$828$	−2.34176	−0.0813817
$829$	−14.6350	−0.508295	−0.254147	−	0.967166i	$-0.581795\pi$
$829$	−14.6350	−0.508295	−0.254147	+	0.967166i	$0.581795\pi$
$830$	26.3648	0.915135
$831$	−38.2329	−1.32628
$832$	13.3296	0.462120
$833$	43.7854	1.51707
$834$	52.7774	1.82753
$835$	8.79896	0.304501
$836$	117.656	4.06921
$837$	8.62559	0.298144
$838$	−50.3066	−1.73781
$839$	−46.4749	−1.60449	−0.802245	−	0.596995i	$-0.796361\pi$
$839$	−46.4749	−1.60449	−0.802245	+	0.596995i	$0.796361\pi$
$840$	4.79825	0.165555
$841$	27.2000	0.937930
$842$	42.8317	1.47608
$843$	9.25406	0.318727
$844$	110.601	3.80705
$845$	−7.99758	−0.275125
$846$	8.97008	0.308398
$847$	−3.07180	−0.105548
$848$	−112.793	−3.87334
$849$	5.50885	0.189063
$850$	−77.4947	−2.65805
$851$	0.00417881	0.000143248 0
$852$	−16.2733	−0.557514
$853$	33.2537	1.13859	0.569293	−	0.822135i	$-0.307217\pi$
$853$	33.2537	1.13859	0.569293	+	0.822135i	$0.307217\pi$
$854$	−10.4553	−0.357774
$855$	−1.98513	−0.0678900
$856$	45.4001	1.55174
$857$	17.6468	0.602802	0.301401	−	0.953498i	$-0.402546\pi$
$857$	17.6468	0.602802	0.301401	+	0.953498i	$0.402546\pi$
$858$	−21.8907	−0.747335
$859$	−5.80130	−0.197938	−0.0989689	−	0.995091i	$-0.531554\pi$
$859$	−5.80130	−0.197938	−0.0989689	+	0.995091i	$0.531554\pi$
$860$	−26.6442	−0.908558
$861$	4.45277	0.151750
$862$	−77.9672	−2.65557
$863$	−13.6497	−0.464640	−0.232320	−	0.972639i	$-0.574632\pi$
$863$	−13.6497	−0.464640	−0.232320	+	0.972639i	$0.574632\pi$
$864$	64.9506	2.20967
$865$	−2.21885	−0.0754432
$866$	46.2245	1.57077
$867$	41.0981	1.39576
$868$	4.29056	0.145631
$869$	12.4160	0.421185
$870$	−22.0902	−0.748928
$871$	−13.8854	−0.470488
$872$	−108.351	−3.66924
$873$	−3.75464	−0.127075
$874$	−15.5092	−0.524607
$875$	3.75082	0.126801
$876$	−128.014	−4.32519
$877$	−52.4405	−1.77079	−0.885395	−	0.464840i	$-0.846112\pi$
$877$	−52.4405	−1.77079	−0.885395	+	0.464840i	$0.846112\pi$
$878$	−83.3774	−2.81385
$879$	34.0899	1.14982
$880$	29.5030	0.994545
$881$	21.1652	0.713074	0.356537	−	0.934281i	$-0.383957\pi$
$881$	21.1652	0.713074	0.356537	+	0.934281i	$0.383957\pi$
$882$	−8.38267	−0.282259
$883$	29.3176	0.986615	0.493308	−	0.869855i	$-0.335788\pi$
$883$	29.3176	0.986615	0.493308	+	0.869855i	$0.335788\pi$
$884$	−41.5096	−1.39612
$885$	2.62759	0.0883254
$886$	80.8507	2.71623
$887$	14.3010	0.480182	0.240091	−	0.970750i	$-0.422823\pi$
$887$	14.3010	0.480182	0.240091	+	0.970750i	$0.422823\pi$
$888$	−0.0507958	−0.00170459
$889$	−5.16428	−0.173205
$890$	−27.8374	−0.933112
$891$	−29.8158	−0.998868
$892$	52.4444	1.75597
$893$	42.2154	1.41269
$894$	−40.0097	−1.33813
$895$	−1.53426	−0.0512847
$896$	2.02738	0.0677300
$897$	2.05052	0.0684647
$898$	64.8347	2.16356
$899$	−11.7084	−0.390499
$900$	10.5427	0.351424
$901$	71.7346	2.38983
$902$	53.4979	1.78129
$903$	6.83180	0.227348
$904$	−143.916	−4.78656
$905$	−6.56897	−0.218360
$906$	−48.3768	−1.60721
$907$	20.6850	0.686833	0.343417	−	0.939183i	$-0.388416\pi$
$907$	20.6850	0.686833	0.343417	+	0.939183i	$0.388416\pi$
$908$	−21.6369	−0.718044
$909$	5.71839	0.189667
$910$	1.33958	0.0444066
$911$	48.4817	1.60627	0.803135	−	0.595797i	$-0.203164\pi$
$911$	48.4817	1.60627	0.803135	+	0.595797i	$0.203164\pi$
$912$	96.4806	3.19479
$913$	−57.7155	−1.91010
$914$	46.3452	1.53296
$915$	−7.96919	−0.263453
$916$	0.655678	0.0216642
$917$	−5.09835	−0.168362
$918$	−95.0646	−3.13760
$919$	57.8405	1.90798	0.953990	−	0.299837i	$-0.0969324\pi$
$919$	57.8405	1.90798	0.953990	+	0.299837i	$0.0969324\pi$
$920$	−5.40000	−0.178033
$921$	5.38676	0.177500
$922$	−79.5627	−2.62026
$923$	−2.69296	−0.0886398
$924$	−17.7207	−0.582970
$925$	−0.0188132	−0.000618576 0
$926$	83.2029	2.73422
$927$	6.33640	0.208115
$928$	−88.1646	−2.89414
$929$	4.48504	0.147149	0.0735747	−	0.997290i	$-0.476559\pi$
$929$	4.48504	0.147149	0.0735747	+	0.997290i	$0.476559\pi$
$930$	4.60217	0.150911
$931$	−39.4509	−1.29295
$932$	−85.7874	−2.81006
$933$	−23.0690	−0.755246
$934$	31.2145	1.02137
$935$	−18.7634	−0.613628
$936$	4.71054	0.153969
$937$	12.5447	0.409819	0.204909	−	0.978781i	$-0.434310\pi$
$937$	12.5447	0.409819	0.204909	+	0.978781i	$0.434310\pi$
$938$	−15.8180	−0.516477
$939$	47.4214	1.54754
$940$	24.7974	0.808803
$941$	−12.8876	−0.420123	−0.210061	−	0.977688i	$-0.567366\pi$
$941$	−12.8876	−0.420123	−0.210061	+	0.977688i	$0.567366\pi$
$942$	−11.4011	−0.371468
$943$	−5.01119	−0.163187
$944$	24.1347	0.785517
$945$	2.18005	0.0709169
$946$	82.0809	2.66868
$947$	−35.3057	−1.14728	−0.573641	−	0.819107i	$-0.694469\pi$
$947$	−35.3057	−1.14728	−0.573641	+	0.819107i	$0.694469\pi$
$948$	23.8502	0.774619
$949$	−21.1842	−0.687667
$950$	69.8233	2.26537
$951$	18.8504	0.611265
$952$	−28.0293	−0.908436
$953$	12.5015	0.404964	0.202482	−	0.979286i	$-0.435099\pi$
$953$	12.5015	0.404964	0.202482	+	0.979286i	$0.435099\pi$
$954$	−13.7335	−0.444639
$955$	10.7151	0.346731
$956$	−31.7993	−1.02846
$957$	48.3579	1.56319
$958$	18.3694	0.593488
$959$	3.60211	0.116318
$960$	11.5741	0.373553
$961$	−28.5607	−0.921313
$962$	−0.0141812	−0.000457220 0
$963$	2.82899	0.0911629
$964$	−6.90575	−0.222419
$965$	5.72755	0.184376
$966$	2.33592	0.0751570
$967$	−33.2556	−1.06943	−0.534715	−	0.845033i	$-0.679581\pi$
$967$	−33.2556	−1.06943	−0.534715	+	0.845033i	$0.679581\pi$
$968$	−42.0222	−1.35064
$969$	−61.3600	−1.97117
$970$	−14.6067	−0.468991
$971$	26.4195	0.847842	0.423921	−	0.905699i	$-0.360653\pi$
$971$	26.4195	0.847842	0.423921	+	0.905699i	$0.360653\pi$
$972$	24.0923	0.772760
$973$	7.07008	0.226656
$974$	−46.6974	−1.49628
$975$	−9.23153	−0.295646
$976$	−73.1979	−2.34301
$977$	26.4657	0.846714	0.423357	−	0.905963i	$-0.360852\pi$
$977$	26.4657	0.846714	0.423357	+	0.905963i	$0.360852\pi$
$978$	87.1121	2.78554
$979$	60.9392	1.94762
$980$	−23.1735	−0.740252
$981$	−6.75164	−0.215563
$982$	77.6396	2.47758
$983$	−27.3717	−0.873022	−0.436511	−	0.899699i	$-0.643786\pi$
$983$	−27.3717	−0.873022	−0.436511	+	0.899699i	$0.643786\pi$
$984$	60.9138	1.94186
$985$	0.0734711	0.00234098
$986$	129.042	4.10952
$987$	−6.35828	−0.202386
$988$	37.4005	1.18987
$989$	−7.68858	−0.244482
$990$	3.59223	0.114169
$991$	39.8449	1.26572	0.632858	−	0.774268i	$-0.281882\pi$
$991$	39.8449	1.26572	0.632858	+	0.774268i	$0.281882\pi$
$992$	18.3678	0.583179
$993$	−52.4407	−1.66416
$994$	−3.06778	−0.0973042
$995$	−14.6979	−0.465955
$996$	−110.867	−3.51295
$997$	0.972154	0.0307884	0.0153942	−	0.999882i	$-0.495100\pi$
$997$	0.972154	0.0307884	0.0153942	+	0.999882i	$0.495100\pi$
$998$	−44.6397	−1.41304
$999$	−0.0230786	−0.000730176 0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8027.2.a.c.1.7	✓	143

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8027.2.a.c.1.7	✓	143	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:	\( N \)	\(=\)	\( 8027 = 23 \cdot 349 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8027.a (trivial)

\(f(q)\)	\(=\)	\(q-2.62887 q^{2} +1.58844 q^{3} +4.91095 q^{4} +0.705653 q^{5} -4.17581 q^{6} -0.559393 q^{7} -7.65249 q^{8} -0.476845 q^{9} +O(q^{10})\)	\(q-2.62887 q^{2} +1.58844 q^{3} +4.91095 q^{4} +0.705653 q^{5} -4.17581 q^{6} -0.559393 q^{7} -7.65249 q^{8} -0.476845 q^{9} -1.85507 q^{10} +4.06095 q^{11} +7.80076 q^{12} +1.29090 q^{13} +1.47057 q^{14} +1.12089 q^{15} +10.2955 q^{16} -6.54776 q^{17} +1.25356 q^{18} +5.89958 q^{19} +3.46542 q^{20} -0.888565 q^{21} -10.6757 q^{22} +1.00000 q^{23} -12.1556 q^{24} -4.50205 q^{25} -3.39359 q^{26} -5.52277 q^{27} -2.74715 q^{28} +7.49666 q^{29} -2.94667 q^{30} -1.56182 q^{31} -11.7605 q^{32} +6.45059 q^{33} +17.2132 q^{34} -0.394737 q^{35} -2.34176 q^{36} +0.00417881 q^{37} -15.5092 q^{38} +2.05052 q^{39} -5.40000 q^{40} -5.01119 q^{41} +2.33592 q^{42} -7.68858 q^{43} +19.9431 q^{44} -0.336487 q^{45} -2.62887 q^{46} +7.15567 q^{47} +16.3538 q^{48} -6.68708 q^{49} +11.8353 q^{50} -10.4008 q^{51} +6.33952 q^{52} -10.9556 q^{53} +14.5186 q^{54} +2.86562 q^{55} +4.28075 q^{56} +9.37115 q^{57} -19.7077 q^{58} +2.34420 q^{59} +5.50463 q^{60} -7.10970 q^{61} +4.10582 q^{62} +0.266744 q^{63} +10.3258 q^{64} +0.910924 q^{65} -16.9578 q^{66} -10.7564 q^{67} -32.1557 q^{68} +1.58844 q^{69} +1.03771 q^{70} -2.08612 q^{71} +3.64905 q^{72} -16.4105 q^{73} -0.0109855 q^{74} -7.15126 q^{75} +28.9725 q^{76} -2.27167 q^{77} -5.39053 q^{78} +3.05742 q^{79} +7.26504 q^{80} -7.34208 q^{81} +13.1738 q^{82} -14.2123 q^{83} -4.36369 q^{84} -4.62044 q^{85} +20.2122 q^{86} +11.9080 q^{87} -31.0764 q^{88} +15.0061 q^{89} +0.884579 q^{90} -0.722118 q^{91} +4.91095 q^{92} -2.48087 q^{93} -18.8113 q^{94} +4.16305 q^{95} -18.6809 q^{96} +7.87392 q^{97} +17.5794 q^{98} -1.93644 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 143 q - 17 q^{2} - 17 q^{3} + 121 q^{4} - 22 q^{5} - 11 q^{6} - 33 q^{7} - 45 q^{8} + 104 q^{9}+O(q^{10}) \) 143 * q - 17 * q^2 - 17 * q^3 + 121 * q^4 - 22 * q^5 - 11 * q^6 - 33 * q^7 - 45 * q^8 + 104 * q^9	\( 143 q - 17 q^{2} - 17 q^{3} + 121 q^{4} - 22 q^{5} - 11 q^{6} - 33 q^{7} - 45 q^{8} + 104 q^{9} - 22 q^{10} - 14 q^{11} - 36 q^{12} - 87 q^{13} - 18 q^{14} - 19 q^{15} + 81 q^{16} - 14 q^{17} - 60 q^{18} - 18 q^{19} - 25 q^{20} - 26 q^{21} - 62 q^{22} + 143 q^{23} - 21 q^{24} + 67 q^{25} - 5 q^{26} - 47 q^{27} - 76 q^{28} - 54 q^{29} - 22 q^{30} - 62 q^{31} - 117 q^{32} - 59 q^{33} - 35 q^{34} - 52 q^{35} + 52 q^{36} - 190 q^{37} - 19 q^{38} - 43 q^{39} - 41 q^{40} - 50 q^{41} + 8 q^{42} - 50 q^{43} - 18 q^{44} - 75 q^{45} - 17 q^{46} - 63 q^{47} - 35 q^{48} + 74 q^{49} - 53 q^{50} - 33 q^{51} - 124 q^{52} - 100 q^{53} - 46 q^{54} - 61 q^{55} - 3 q^{56} - 80 q^{57} - 112 q^{58} - 109 q^{59} - 55 q^{60} - 76 q^{61} - 6 q^{62} - 93 q^{63} + 57 q^{64} - 17 q^{65} + 50 q^{66} - 120 q^{67} + 26 q^{68} - 17 q^{69} - 109 q^{71} - 153 q^{72} - 94 q^{73} + 35 q^{74} - 105 q^{75} - 16 q^{76} - 52 q^{77} - 59 q^{78} - 29 q^{79} - 30 q^{80} + 39 q^{81} - 65 q^{82} + 8 q^{83} + 11 q^{84} - 155 q^{85} - 15 q^{86} - 25 q^{87} - 139 q^{88} + 6 q^{89} + 82 q^{90} - 34 q^{91} + 121 q^{92} - 151 q^{93} - 3 q^{94} - 70 q^{95} - 23 q^{96} - 203 q^{97} - 18 q^{98} - 49 q^{99}+O(q^{100}) \) 143 * q - 17 * q^2 - 17 * q^3 + 121 * q^4 - 22 * q^5 - 11 * q^6 - 33 * q^7 - 45 * q^8 + 104 * q^9 - 22 * q^10 - 14 * q^11 - 36 * q^12 - 87 * q^13 - 18 * q^14 - 19 * q^15 + 81 * q^16 - 14 * q^17 - 60 * q^18 - 18 * q^19 - 25 * q^20 - 26 * q^21 - 62 * q^22 + 143 * q^23 - 21 * q^24 + 67 * q^25 - 5 * q^26 - 47 * q^27 - 76 * q^28 - 54 * q^29 - 22 * q^30 - 62 * q^31 - 117 * q^32 - 59 * q^33 - 35 * q^34 - 52 * q^35 + 52 * q^36 - 190 * q^37 - 19 * q^38 - 43 * q^39 - 41 * q^40 - 50 * q^41 + 8 * q^42 - 50 * q^43 - 18 * q^44 - 75 * q^45 - 17 * q^46 - 63 * q^47 - 35 * q^48 + 74 * q^49 - 53 * q^50 - 33 * q^51 - 124 * q^52 - 100 * q^53 - 46 * q^54 - 61 * q^55 - 3 * q^56 - 80 * q^57 - 112 * q^58 - 109 * q^59 - 55 * q^60 - 76 * q^61 - 6 * q^62 - 93 * q^63 + 57 * q^64 - 17 * q^65 + 50 * q^66 - 120 * q^67 + 26 * q^68 - 17 * q^69 - 109 * q^71 - 153 * q^72 - 94 * q^73 + 35 * q^74 - 105 * q^75 - 16 * q^76 - 52 * q^77 - 59 * q^78 - 29 * q^79 - 30 * q^80 + 39 * q^81 - 65 * q^82 + 8 * q^83 + 11 * q^84 - 155 * q^85 - 15 * q^86 - 25 * q^87 - 139 * q^88 + 6 * q^89 + 82 * q^90 - 34 * q^91 + 121 * q^92 - 151 * q^93 - 3 * q^94 - 70 * q^95 - 23 * q^96 - 203 * q^97 - 18 * q^98 - 49 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more