LMFDB - Embedded newform 667.2.a.a.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [667,2,Mod(1,667)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(667, 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("667.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 667 = 23 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	667.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:	$5.32602181482$
Analytic rank:	$1$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 3x^{9} - 10x^{8} + 32x^{7} + 32x^{6} - 118x^{5} - 29x^{4} + 182x^{3} - 28x^{2} - 101x + 43 $ x^10 - 3x^9 - 10x^8 + 32x^7 + 32x^6 - 118x^5 - 29x^4 + 182x^3 - 28x^2 - 101*x + 43
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$1.68137$ of defining polynomial
Character	$\chi$	$=$	667.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.68137 q^{2} -2.54941 q^{3} +0.827018 q^{4} -1.60084 q^{5} +4.28651 q^{6} -4.81497 q^{7} +1.97222 q^{8} +3.49949 q^{9} +O(q^{10})$	\(q-1.68137 q^{2} -2.54941 q^{3} +0.827018 q^{4} -1.60084 q^{5} +4.28651 q^{6} -4.81497 q^{7} +1.97222 q^{8} +3.49949 q^{9} +2.69161 q^{10} +6.43743 q^{11} -2.10841 q^{12} +3.23728 q^{13} +8.09577 q^{14} +4.08119 q^{15} -4.97008 q^{16} -4.60504 q^{17} -5.88395 q^{18} +4.55028 q^{19} -1.32392 q^{20} +12.2753 q^{21} -10.8237 q^{22} +1.00000 q^{23} -5.02800 q^{24} -2.43731 q^{25} -5.44308 q^{26} -1.27340 q^{27} -3.98207 q^{28} +1.00000 q^{29} -6.86201 q^{30} -1.11371 q^{31} +4.41211 q^{32} -16.4117 q^{33} +7.74280 q^{34} +7.70800 q^{35} +2.89414 q^{36} +4.51518 q^{37} -7.65072 q^{38} -8.25315 q^{39} -3.15721 q^{40} -10.0963 q^{41} -20.6394 q^{42} +8.83757 q^{43} +5.32387 q^{44} -5.60212 q^{45} -1.68137 q^{46} -5.22064 q^{47} +12.6708 q^{48} +16.1840 q^{49} +4.09804 q^{50} +11.7401 q^{51} +2.67729 q^{52} -7.18320 q^{53} +2.14107 q^{54} -10.3053 q^{55} -9.49620 q^{56} -11.6005 q^{57} -1.68137 q^{58} +4.45792 q^{59} +3.37522 q^{60} -3.88029 q^{61} +1.87257 q^{62} -16.8500 q^{63} +2.52174 q^{64} -5.18236 q^{65} +27.5941 q^{66} -12.5392 q^{67} -3.80845 q^{68} -2.54941 q^{69} -12.9600 q^{70} +10.9516 q^{71} +6.90177 q^{72} -0.460744 q^{73} -7.59170 q^{74} +6.21371 q^{75} +3.76316 q^{76} -30.9961 q^{77} +13.8766 q^{78} -0.482984 q^{79} +7.95629 q^{80} -7.25204 q^{81} +16.9757 q^{82} -4.96905 q^{83} +10.1519 q^{84} +7.37193 q^{85} -14.8593 q^{86} -2.54941 q^{87} +12.6960 q^{88} -17.2218 q^{89} +9.41926 q^{90} -15.5874 q^{91} +0.827018 q^{92} +2.83931 q^{93} +8.77784 q^{94} -7.28426 q^{95} -11.2483 q^{96} +1.06047 q^{97} -27.2113 q^{98} +22.5277 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 3 q^{2} - 9 q^{3} + 9 q^{4} - 10 q^{5} + 4 q^{6} + q^{7} - 9 q^{8} + 7 q^{9}+O(q^{10}) $ 10 * q - 3 * q^2 - 9 * q^3 + 9 * q^4 - 10 * q^5 + 4 * q^6 + q^7 - 9 * q^8 + 7 * q^9	\( 10 q - 3 q^{2} - 9 q^{3} + 9 q^{4} - 10 q^{5} + 4 q^{6} + q^{7} - 9 q^{8} + 7 q^{9} - 6 q^{10} - 17 q^{12} - 13 q^{13} - 12 q^{14} + 2 q^{15} - 5 q^{16} - 22 q^{17} + 12 q^{18} - 2 q^{19} + 3 q^{20} - 7 q^{21} + 3 q^{22} + 10 q^{23} - 6 q^{24} + 10 q^{25} - 25 q^{26} - 24 q^{27} + 19 q^{28} + 10 q^{29} - 3 q^{30} - 22 q^{31} - 31 q^{32} - 9 q^{33} + 13 q^{34} - 15 q^{35} + 19 q^{36} - 9 q^{37} - 10 q^{38} + 4 q^{39} - 6 q^{40} - 25 q^{41} - 34 q^{42} + 3 q^{43} - 27 q^{44} - 28 q^{45} - 3 q^{46} - 17 q^{47} - 3 q^{48} + 17 q^{49} + 2 q^{50} + 38 q^{51} - 18 q^{52} - 43 q^{53} - 47 q^{54} - 11 q^{55} - 7 q^{56} + 18 q^{57} - 3 q^{58} - 7 q^{59} - 21 q^{60} - 6 q^{61} + 3 q^{62} + 11 q^{63} + 33 q^{64} + 11 q^{65} + 55 q^{66} + 11 q^{67} - 51 q^{68} - 9 q^{69} + 34 q^{70} - 17 q^{71} + 34 q^{72} - 44 q^{73} + 9 q^{74} + q^{75} + 24 q^{76} - 71 q^{77} + 38 q^{78} + 5 q^{79} + 38 q^{80} + 18 q^{81} + 33 q^{82} - 32 q^{83} + 14 q^{84} + 16 q^{85} - 9 q^{86} - 9 q^{87} + 18 q^{88} - 10 q^{89} - 9 q^{90} - 3 q^{91} + 9 q^{92} - 8 q^{93} + 47 q^{94} - 8 q^{95} + 60 q^{96} + 6 q^{97} - 73 q^{98} + 26 q^{99}+O(q^{100}) \) 10 * q - 3 * q^2 - 9 * q^3 + 9 * q^4 - 10 * q^5 + 4 * q^6 + q^7 - 9 * q^8 + 7 * q^9 - 6 * q^10 - 17 * q^12 - 13 * q^13 - 12 * q^14 + 2 * q^15 - 5 * q^16 - 22 * q^17 + 12 * q^18 - 2 * q^19 + 3 * q^20 - 7 * q^21 + 3 * q^22 + 10 * q^23 - 6 * q^24 + 10 * q^25 - 25 * q^26 - 24 * q^27 + 19 * q^28 + 10 * q^29 - 3 * q^30 - 22 * q^31 - 31 * q^32 - 9 * q^33 + 13 * q^34 - 15 * q^35 + 19 * q^36 - 9 * q^37 - 10 * q^38 + 4 * q^39 - 6 * q^40 - 25 * q^41 - 34 * q^42 + 3 * q^43 - 27 * q^44 - 28 * q^45 - 3 * q^46 - 17 * q^47 - 3 * q^48 + 17 * q^49 + 2 * q^50 + 38 * q^51 - 18 * q^52 - 43 * q^53 - 47 * q^54 - 11 * q^55 - 7 * q^56 + 18 * q^57 - 3 * q^58 - 7 * q^59 - 21 * q^60 - 6 * q^61 + 3 * q^62 + 11 * q^63 + 33 * q^64 + 11 * q^65 + 55 * q^66 + 11 * q^67 - 51 * q^68 - 9 * q^69 + 34 * q^70 - 17 * q^71 + 34 * q^72 - 44 * q^73 + 9 * q^74 + q^75 + 24 * q^76 - 71 * q^77 + 38 * q^78 + 5 * q^79 + 38 * q^80 + 18 * q^81 + 33 * q^82 - 32 * q^83 + 14 * q^84 + 16 * q^85 - 9 * q^86 - 9 * q^87 + 18 * q^88 - 10 * q^89 - 9 * q^90 - 3 * q^91 + 9 * q^92 - 8 * q^93 + 47 * q^94 - 8 * q^95 + 60 * q^96 + 6 * q^97 - 73 * q^98 + 26 * 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 $

$2$	−1.68137	−1.18891	−0.594455	−	0.804129i	$-0.702632\pi$
$2$	−1.68137	−1.18891	−0.594455	+	0.804129i	$0.702632\pi$
$3$	−2.54941	−1.47190	−0.735951	−	0.677035i	$-0.763265\pi$
$3$	−2.54941	−1.47190	−0.735951	+	0.677035i	$0.763265\pi$
$4$	0.827018	0.413509
$5$	−1.60084	−0.715917	−0.357958	−	0.933738i	$-0.616527\pi$
$5$	−1.60084	−0.715917	−0.357958	+	0.933738i	$0.616527\pi$
$6$	4.28651	1.74996
$7$	−4.81497	−1.81989	−0.909945	−	0.414730i	$-0.863876\pi$
$7$	−4.81497	−1.81989	−0.909945	+	0.414730i	$0.863876\pi$
$8$	1.97222	0.697286
$9$	3.49949	1.16650
$10$	2.69161	0.851161
$11$	6.43743	1.94096	0.970480	−	0.241184i	$-0.0775356\pi$
$11$	6.43743	1.94096	0.970480	+	0.241184i	$0.0775356\pi$
$12$	−2.10841	−0.608645
$13$	3.23728	0.897860	0.448930	−	0.893567i	$-0.351805\pi$
$13$	3.23728	0.897860	0.448930	+	0.893567i	$0.351805\pi$
$14$	8.09577	2.16369
$15$	4.08119	1.05376
$16$	−4.97008	−1.24252
$17$	−4.60504	−1.11689	−0.558444	−	0.829543i	$-0.688601\pi$
$17$	−4.60504	−1.11689	−0.558444	+	0.829543i	$0.688601\pi$
$18$	−5.88395	−1.38686
$19$	4.55028	1.04391	0.521953	−	0.852974i	$-0.325204\pi$
$19$	4.55028	1.04391	0.521953	+	0.852974i	$0.325204\pi$
$20$	−1.32392	−0.296038
$21$	12.2753	2.67870
$22$	−10.8237	−2.30763
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	−5.02800	−1.02634
$25$	−2.43731	−0.487463
$26$	−5.44308	−1.06747
$27$	−1.27340	−0.245067
$28$	−3.98207	−0.752540
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	−6.86201	−1.25283
$31$	−1.11371	−0.200029	−0.100014	−	0.994986i	$-0.531889\pi$
$31$	−1.11371	−0.200029	−0.100014	+	0.994986i	$0.531889\pi$
$32$	4.41211	0.779959
$33$	−16.4117	−2.85690
$34$	7.74280	1.32788
$35$	7.70800	1.30289
$36$	2.89414	0.482357
$37$	4.51518	0.742291	0.371145	−	0.928575i	$-0.378965\pi$
$37$	4.51518	0.742291	0.371145	+	0.928575i	$0.378965\pi$
$38$	−7.65072	−1.24111
$39$	−8.25315	−1.32156
$40$	−3.15721	−0.499199
$41$	−10.0963	−1.57678	−0.788389	−	0.615177i	$-0.789085\pi$
$41$	−10.0963	−1.57678	−0.788389	+	0.615177i	$0.789085\pi$
$42$	−20.6394	−3.18473
$43$	8.83757	1.34772	0.673858	−	0.738860i	$-0.264636\pi$
$43$	8.83757	1.34772	0.673858	+	0.738860i	$0.264636\pi$
$44$	5.32387	0.802604
$45$	−5.60212	−0.835115
$46$	−1.68137	−0.247905
$47$	−5.22064	−0.761508	−0.380754	−	0.924676i	$-0.624336\pi$
$47$	−5.22064	−0.761508	−0.380754	+	0.924676i	$0.624336\pi$
$48$	12.6708	1.82887
$49$	16.1840	2.31200
$50$	4.09804	0.579550
$51$	11.7401	1.64395
$52$	2.67729	0.371273
$53$	−7.18320	−0.986688	−0.493344	−	0.869834i	$-0.664226\pi$
$53$	−7.18320	−0.986688	−0.493344	+	0.869834i	$0.664226\pi$
$54$	2.14107	0.291362
$55$	−10.3053	−1.38957
$56$	−9.49620	−1.26898
$57$	−11.6005	−1.53653
$58$	−1.68137	−0.220775
$59$	4.45792	0.580372	0.290186	−	0.956970i	$-0.406283\pi$
$59$	4.45792	0.580372	0.290186	+	0.956970i	$0.406283\pi$
$60$	3.37522	0.435739
$61$	−3.88029	−0.496820	−0.248410	−	0.968655i	$-0.579908\pi$
$61$	−3.88029	−0.496820	−0.248410	+	0.968655i	$0.579908\pi$
$62$	1.87257	0.237817
$63$	−16.8500	−2.12289
$64$	2.52174	0.315218
$65$	−5.18236	−0.642793
$66$	27.5941	3.39660
$67$	−12.5392	−1.53190	−0.765951	−	0.642899i	$-0.777731\pi$
$67$	−12.5392	−1.53190	−0.765951	+	0.642899i	$0.777731\pi$
$68$	−3.80845	−0.461843
$69$	−2.54941	−0.306913
$70$	−12.9600	−1.54902
$71$	10.9516	1.29972	0.649860	−	0.760054i	$-0.274828\pi$
$71$	10.9516	1.29972	0.649860	+	0.760054i	$0.274828\pi$
$72$	6.90177	0.813381
$73$	−0.460744	−0.0539260	−0.0269630	−	0.999636i	$-0.508584\pi$
$73$	−0.460744	−0.0539260	−0.0269630	+	0.999636i	$0.508584\pi$
$74$	−7.59170	−0.882518
$75$	6.21371	0.717498
$76$	3.76316	0.431664
$77$	−30.9961	−3.53233
$78$	13.8766	1.57122
$79$	−0.482984	−0.0543400	−0.0271700	−	0.999631i	$-0.508650\pi$
$79$	−0.482984	−0.0543400	−0.0271700	+	0.999631i	$0.508650\pi$
$80$	7.95629	0.889541
$81$	−7.25204	−0.805782
$82$	16.9757	1.87465
$83$	−4.96905	−0.545424	−0.272712	−	0.962096i	$-0.587921\pi$
$83$	−4.96905	−0.545424	−0.272712	+	0.962096i	$0.587921\pi$
$84$	10.1519	1.10767
$85$	7.37193	0.799598
$86$	−14.8593	−1.60232
$87$	−2.54941	−0.273325
$88$	12.6960	1.35340
$89$	−17.2218	−1.82550	−0.912752	−	0.408513i	$-0.866047\pi$
$89$	−17.2218	−1.82550	−0.912752	+	0.408513i	$0.866047\pi$
$90$	9.41926	0.992877
$91$	−15.5874	−1.63400
$92$	0.827018	0.0862226
$93$	2.83931	0.294423
$94$	8.77784	0.905365
$95$	−7.28426	−0.747350
$96$	−11.2483	−1.14802
$97$	1.06047	0.107675	0.0538373	−	0.998550i	$-0.482855\pi$
$97$	1.06047	0.107675	0.0538373	+	0.998550i	$0.482855\pi$
$98$	−27.2113	−2.74876
$99$	22.5277	2.26412
$100$	−2.01570	−0.201570
$101$	−5.50199	−0.547469	−0.273734	−	0.961805i	$-0.588259\pi$
$101$	−5.50199	−0.547469	−0.273734	+	0.961805i	$0.588259\pi$
$102$	−19.7396	−1.95451
$103$	11.3403	1.11739	0.558695	−	0.829373i	$-0.311302\pi$
$103$	11.3403	1.11739	0.558695	+	0.829373i	$0.311302\pi$
$104$	6.38463	0.626065
$105$	−19.6508	−1.91773
$106$	12.0776	1.17308
$107$	3.06127	0.295944	0.147972	−	0.988992i	$-0.452725\pi$
$107$	3.06127	0.295944	0.147972	+	0.988992i	$0.452725\pi$
$108$	−1.05313	−0.101337
$109$	6.89736	0.660647	0.330324	−	0.943868i	$-0.392842\pi$
$109$	6.89736	0.660647	0.330324	+	0.943868i	$0.392842\pi$
$110$	17.3270	1.65207
$111$	−11.5110	−1.09258
$112$	23.9308	2.26125
$113$	−1.58895	−0.149475	−0.0747377	−	0.997203i	$-0.523812\pi$
$113$	−1.58895	−0.149475	−0.0747377	+	0.997203i	$0.523812\pi$
$114$	19.5048	1.82679
$115$	−1.60084	−0.149279
$116$	0.827018	0.0767867
$117$	11.3288	1.04735
$118$	−7.49544	−0.690011
$119$	22.1732	2.03261
$120$	8.04902	0.734772
$121$	30.4405	2.76732
$122$	6.52422	0.590675
$123$	25.7396	2.32086
$124$	−0.921061	−0.0827138
$125$	11.9059	1.06490
$126$	28.3311	2.52393
$127$	−3.05960	−0.271496	−0.135748	−	0.990743i	$-0.543344\pi$
$127$	−3.05960	−0.271496	−0.135748	+	0.990743i	$0.543344\pi$
$128$	−13.0642	−1.15472
$129$	−22.5306	−1.98371
$130$	8.71349	0.764223
$131$	−6.01078	−0.525164	−0.262582	−	0.964910i	$-0.584574\pi$
$131$	−6.01078	−0.525164	−0.262582	+	0.964910i	$0.584574\pi$
$132$	−13.5727	−1.18135
$133$	−21.9095	−1.89979
$134$	21.0830	1.82129
$135$	2.03851	0.175447
$136$	−9.08217	−0.778789
$137$	3.47329	0.296743	0.148372	−	0.988932i	$-0.452597\pi$
$137$	3.47329	0.296743	0.148372	+	0.988932i	$0.452597\pi$
$138$	4.28651	0.364892
$139$	3.17264	0.269100	0.134550	−	0.990907i	$-0.457041\pi$
$139$	3.17264	0.269100	0.134550	+	0.990907i	$0.457041\pi$
$140$	6.37465	0.538756
$141$	13.3095	1.12087
$142$	−18.4138	−1.54525
$143$	20.8398	1.74271
$144$	−17.3927	−1.44939
$145$	−1.60084	−0.132942
$146$	0.774682	0.0641131
$147$	−41.2596	−3.40303
$148$	3.73413	0.306944
$149$	−6.52252	−0.534346	−0.267173	−	0.963649i	$-0.586090\pi$
$149$	−6.52252	−0.534346	−0.267173	+	0.963649i	$0.586090\pi$
$150$	−10.4476	−0.853041
$151$	−8.50988	−0.692524	−0.346262	−	0.938138i	$-0.612549\pi$
$151$	−8.50988	−0.692524	−0.346262	+	0.938138i	$0.612549\pi$
$152$	8.97416	0.727900
$153$	−16.1153	−1.30284
$154$	52.1160	4.19963
$155$	1.78288	0.143204
$156$	−6.82550	−0.546477
$157$	0.655927	0.0523487	0.0261744	−	0.999657i	$-0.491667\pi$
$157$	0.655927	0.0523487	0.0261744	+	0.999657i	$0.491667\pi$
$158$	0.812077	0.0646054
$159$	18.3129	1.45231
$160$	−7.06308	−0.558386
$161$	−4.81497	−0.379473
$162$	12.1934	0.958003
$163$	16.1610	1.26583	0.632914	−	0.774222i	$-0.281859\pi$
$163$	16.1610	1.26583	0.632914	+	0.774222i	$0.281859\pi$
$164$	−8.34982	−0.652012
$165$	26.2724	2.04530
$166$	8.35482	0.648460
$167$	−0.0420128	−0.00325105	−0.00162553	−	0.999999i	$-0.500517\pi$
$167$	−0.0420128	−0.00325105	−0.00162553	+	0.999999i	$0.500517\pi$
$168$	24.2097	1.86782
$169$	−2.52003	−0.193848
$170$	−12.3950	−0.950651
$171$	15.9237	1.21771
$172$	7.30883	0.557293
$173$	−21.8701	−1.66276	−0.831378	−	0.555708i	$-0.812447\pi$
$173$	−21.8701	−1.66276	−0.831378	+	0.555708i	$0.812447\pi$
$174$	4.28651	0.324960
$175$	11.7356	0.887129
$176$	−31.9945	−2.41168
$177$	−11.3651	−0.854251
$178$	28.9562	2.17036
$179$	−19.9950	−1.49450	−0.747249	−	0.664544i	$-0.768626\pi$
$179$	−19.9950	−1.49450	−0.747249	+	0.664544i	$0.768626\pi$
$180$	−4.63305	−0.345327
$181$	−3.65534	−0.271700	−0.135850	−	0.990729i	$-0.543376\pi$
$181$	−3.65534	−0.271700	−0.135850	+	0.990729i	$0.543376\pi$
$182$	26.2083	1.94269
$183$	9.89245	0.731271
$184$	1.97222	0.145394
$185$	−7.22807	−0.531419
$186$	−4.77395	−0.350043
$187$	−29.6447	−2.16783
$188$	−4.31756	−0.314890
$189$	6.13141	0.445994
$190$	12.2476	0.888532
$191$	−22.6912	−1.64188	−0.820938	−	0.571018i	$-0.806549\pi$
$191$	−22.6912	−1.64188	−0.820938	+	0.571018i	$0.806549\pi$
$192$	−6.42895	−0.463970
$193$	−19.2052	−1.38242	−0.691212	−	0.722652i	$-0.742923\pi$
$193$	−19.2052	−1.38242	−0.691212	+	0.722652i	$0.742923\pi$
$194$	−1.78305	−0.128015
$195$	13.2120	0.946128
$196$	13.3844	0.956031
$197$	1.26964	0.0904580	0.0452290	−	0.998977i	$-0.485598\pi$
$197$	1.26964	0.0904580	0.0452290	+	0.998977i	$0.485598\pi$
$198$	−37.8775	−2.69184
$199$	12.0877	0.856872	0.428436	−	0.903572i	$-0.359065\pi$
$199$	12.0877	0.856872	0.428436	+	0.903572i	$0.359065\pi$
$200$	−4.80692	−0.339901
$201$	31.9674	2.25481
$202$	9.25090	0.650891
$203$	−4.81497	−0.337945
$204$	9.70931	0.679787
$205$	16.1626	1.12884
$206$	−19.0672	−1.32848
$207$	3.49949	0.243231
$208$	−16.0895	−1.11561
$209$	29.2921	2.02618
$210$	33.0404	2.28001
$211$	2.59871	0.178903	0.0894515	−	0.995991i	$-0.471489\pi$
$211$	2.59871	0.178903	0.0894515	+	0.995991i	$0.471489\pi$
$212$	−5.94063	−0.408004
$213$	−27.9202	−1.91306
$214$	−5.14714	−0.351852
$215$	−14.1475	−0.964853
$216$	−2.51143	−0.170881
$217$	5.36251	0.364031
$218$	−11.5970	−0.785451
$219$	1.17462	0.0793737
$220$	−8.52266	−0.574598
$221$	−14.9078	−1.00281
$222$	19.3544	1.29898
$223$	−21.3712	−1.43112	−0.715561	−	0.698550i	$-0.753829\pi$
$223$	−21.3712	−1.43112	−0.715561	+	0.698550i	$0.753829\pi$
$224$	−21.2442	−1.41944
$225$	−8.52936	−0.568624
$226$	2.67161	0.177713
$227$	21.5679	1.43151	0.715757	−	0.698349i	$-0.246082\pi$
$227$	21.5679	1.43151	0.715757	+	0.698349i	$0.246082\pi$
$228$	−9.59384	−0.635367
$229$	−20.6885	−1.36713	−0.683566	−	0.729888i	$-0.739572\pi$
$229$	−20.6885	−1.36713	−0.683566	+	0.729888i	$0.739572\pi$
$230$	2.69161	0.177479
$231$	79.0217	5.19925
$232$	1.97222	0.129483
$233$	24.1369	1.58126	0.790630	−	0.612295i	$-0.209753\pi$
$233$	24.1369	1.58126	0.790630	+	0.612295i	$0.209753\pi$
$234$	−19.0480	−1.24521
$235$	8.35740	0.545177
$236$	3.68678	0.239989
$237$	1.23132	0.0799831
$238$	−37.2814	−2.41659
$239$	−22.5135	−1.45628	−0.728140	−	0.685429i	$-0.759615\pi$
$239$	−22.5135	−1.45628	−0.728140	+	0.685429i	$0.759615\pi$
$240$	−20.2839	−1.30932
$241$	−21.1023	−1.35932	−0.679659	−	0.733528i	$-0.737872\pi$
$241$	−21.1023	−1.35932	−0.679659	+	0.733528i	$0.737872\pi$
$242$	−51.1819	−3.29010
$243$	22.3086	1.43110
$244$	−3.20907	−0.205440
$245$	−25.9079	−1.65520
$246$	−43.2779	−2.75930
$247$	14.7305	0.937280
$248$	−2.19649	−0.139477
$249$	12.6681	0.802810
$250$	−20.0183	−1.26607
$251$	5.52800	0.348924	0.174462	−	0.984664i	$-0.444181\pi$
$251$	5.52800	0.348924	0.174462	+	0.984664i	$0.444181\pi$
$252$	−13.9352	−0.877836
$253$	6.43743	0.404718
$254$	5.14433	0.322784
$255$	−18.7941	−1.17693
$256$	16.9223	1.05765
$257$	10.2732	0.640823	0.320412	−	0.947278i	$-0.396179\pi$
$257$	10.2732	0.640823	0.320412	+	0.947278i	$0.396179\pi$
$258$	37.8823	2.35845
$259$	−21.7405	−1.35089
$260$	−4.28590	−0.265801
$261$	3.49949	0.216613
$262$	10.1064	0.624373
$263$	−16.0225	−0.987993	−0.493996	−	0.869464i	$-0.664464\pi$
$263$	−16.0225	−0.987993	−0.493996	+	0.869464i	$0.664464\pi$
$264$	−32.3674	−1.99208
$265$	11.4991	0.706387
$266$	36.8380	2.25868
$267$	43.9054	2.68696
$268$	−10.3701	−0.633455
$269$	−9.31782	−0.568118	−0.284059	−	0.958807i	$-0.591681\pi$
$269$	−9.31782	−0.568118	−0.284059	+	0.958807i	$0.591681\pi$
$270$	−3.42750	−0.208591
$271$	7.27051	0.441652	0.220826	−	0.975313i	$-0.429125\pi$
$271$	7.27051	0.441652	0.220826	+	0.975313i	$0.429125\pi$
$272$	22.8874	1.38775
$273$	39.7387	2.40510
$274$	−5.83990	−0.352801
$275$	−15.6900	−0.946146
$276$	−2.10841	−0.126911
$277$	−11.2055	−0.673272	−0.336636	−	0.941635i	$-0.609289\pi$
$277$	−11.2055	−0.673272	−0.336636	+	0.941635i	$0.609289\pi$
$278$	−5.33440	−0.319936
$279$	−3.89743	−0.233333
$280$	15.2019	0.908486
$281$	3.15279	0.188079	0.0940397	−	0.995568i	$-0.470022\pi$
$281$	3.15279	0.188079	0.0940397	+	0.995568i	$0.470022\pi$
$282$	−22.3783	−1.33261
$283$	−1.81112	−0.107660	−0.0538299	−	0.998550i	$-0.517143\pi$
$283$	−1.81112	−0.107660	−0.0538299	+	0.998550i	$0.517143\pi$
$284$	9.05719	0.537445
$285$	18.5706	1.10003
$286$	−35.0394	−2.07192
$287$	48.6135	2.86956
$288$	15.4401	0.909819
$289$	4.20643	0.247437
$290$	2.69161	0.158057
$291$	−2.70358	−0.158486
$292$	−0.381043	−0.0222989
$293$	−23.6297	−1.38046	−0.690232	−	0.723588i	$-0.742492\pi$
$293$	−23.6297	−1.38046	−0.690232	+	0.723588i	$0.742492\pi$
$294$	69.3728	4.04590
$295$	−7.13642	−0.415498
$296$	8.90493	0.517589
$297$	−8.19745	−0.475664
$298$	10.9668	0.635290
$299$	3.23728	0.187217
$300$	5.13885	0.296692
$301$	−42.5527	−2.45270
$302$	14.3083	0.823349
$303$	14.0268	0.805820
$304$	−22.6152	−1.29707
$305$	6.21172	0.355682
$306$	27.0958	1.54897
$307$	−1.18611	−0.0676947	−0.0338474	−	0.999427i	$-0.510776\pi$
$307$	−1.18611	−0.0676947	−0.0338474	+	0.999427i	$0.510776\pi$
$308$	−25.6343	−1.46065
$309$	−28.9110	−1.64469
$310$	−2.99768	−0.170257
$311$	−13.3026	−0.754324	−0.377162	−	0.926147i	$-0.623100\pi$
$311$	−13.3026	−0.754324	−0.377162	+	0.926147i	$0.623100\pi$
$312$	−16.2770	−0.921506
$313$	0.504365	0.0285084	0.0142542	−	0.999898i	$-0.495463\pi$
$313$	0.504365	0.0285084	0.0142542	+	0.999898i	$0.495463\pi$
$314$	−1.10286	−0.0622379
$315$	26.9741	1.51982
$316$	−0.399437	−0.0224701
$317$	0.455841	0.0256026	0.0128013	−	0.999918i	$-0.495925\pi$
$317$	0.455841	0.0256026	0.0128013	+	0.999918i	$0.495925\pi$
$318$	−30.7909	−1.72667
$319$	6.43743	0.360427
$320$	−4.03690	−0.225670
$321$	−7.80444	−0.435601
$322$	8.09577	0.451160
$323$	−20.9542	−1.16592
$324$	−5.99757	−0.333198
$325$	−7.89027	−0.437673
$326$	−27.1727	−1.50496
$327$	−17.5842	−0.972408
$328$	−19.9122	−1.09946
$329$	25.1372	1.38586
$330$	−44.1737	−2.43168
$331$	−26.8153	−1.47390	−0.736951	−	0.675946i	$-0.763735\pi$
$331$	−26.8153	−1.47390	−0.736951	+	0.675946i	$0.763735\pi$
$332$	−4.10949	−0.225537
$333$	15.8008	0.865880
$334$	0.0706393	0.00386521
$335$	20.0732	1.09671
$336$	−61.0094	−3.32834
$337$	18.8374	1.02614	0.513069	−	0.858347i	$-0.328508\pi$
$337$	18.8374	1.02614	0.513069	+	0.858347i	$0.328508\pi$
$338$	4.23711	0.230468
$339$	4.05087	0.220013
$340$	6.09672	0.330641
$341$	−7.16946	−0.388248
$342$	−26.7736	−1.44775
$343$	−44.2206	−2.38769
$344$	17.4296	0.939744
$345$	4.08119	0.219724
$346$	36.7719	1.97687
$347$	−13.1589	−0.706408	−0.353204	−	0.935546i	$-0.614908\pi$
$347$	−13.1589	−0.706408	−0.353204	+	0.935546i	$0.614908\pi$
$348$	−2.10841	−0.113022
$349$	2.97143	0.159057	0.0795285	−	0.996833i	$-0.474659\pi$
$349$	2.97143	0.159057	0.0795285	+	0.996833i	$0.474659\pi$
$350$	−19.7319	−1.05472
$351$	−4.12236	−0.220035
$352$	28.4027	1.51387
$353$	0.498800	0.0265484	0.0132742	−	0.999912i	$-0.495775\pi$
$353$	0.498800	0.0265484	0.0132742	+	0.999912i	$0.495775\pi$
$354$	19.1089	1.01563
$355$	−17.5318	−0.930491
$356$	−14.2427	−0.754862
$357$	−56.5285	−2.99180
$358$	33.6191	1.77683
$359$	−9.16521	−0.483721	−0.241861	−	0.970311i	$-0.577758\pi$
$359$	−9.16521	−0.483721	−0.241861	+	0.970311i	$0.577758\pi$
$360$	−11.0486	−0.582313
$361$	1.70503	0.0897383
$362$	6.14600	0.323026
$363$	−77.6054	−4.07323
$364$	−12.8911	−0.675675
$365$	0.737576	0.0386065
$366$	−16.6329	−0.869416
$367$	−14.6305	−0.763706	−0.381853	−	0.924223i	$-0.624714\pi$
$367$	−14.6305	−0.763706	−0.381853	+	0.924223i	$0.624714\pi$
$368$	−4.97008	−0.259083
$369$	−35.3319	−1.83931
$370$	12.1531	0.631809
$371$	34.5869	1.79566
$372$	2.34816	0.121747
$373$	2.29578	0.118871	0.0594356	−	0.998232i	$-0.481070\pi$
$373$	2.29578	0.118871	0.0594356	+	0.998232i	$0.481070\pi$
$374$	49.8437	2.57736
$375$	−30.3531	−1.56743
$376$	−10.2963	−0.530989
$377$	3.23728	0.166728
$378$	−10.3092	−0.530247
$379$	37.1473	1.90813	0.954064	−	0.299604i	$-0.0968545\pi$
$379$	37.1473	1.90813	0.954064	+	0.299604i	$0.0968545\pi$
$380$	−6.02421	−0.309036
$381$	7.80018	0.399615
$382$	38.1523	1.95204
$383$	−33.8199	−1.72812	−0.864059	−	0.503390i	$-0.832086\pi$
$383$	−33.8199	−1.72812	−0.864059	+	0.503390i	$0.832086\pi$
$384$	33.3060	1.69964
$385$	49.6197	2.52886
$386$	32.2912	1.64358
$387$	30.9270	1.57211
$388$	0.877028	0.0445244
$389$	12.9460	0.656390	0.328195	−	0.944610i	$-0.393560\pi$
$389$	12.9460	0.656390	0.328195	+	0.944610i	$0.393560\pi$
$390$	−22.2142	−1.12486
$391$	−4.60504	−0.232887
$392$	31.9184	1.61212
$393$	15.3239	0.772990
$394$	−2.13474	−0.107546
$395$	0.773180	0.0389029
$396$	18.6308	0.936234
$397$	−22.8143	−1.14502	−0.572508	−	0.819899i	$-0.694029\pi$
$397$	−22.8143	−1.14502	−0.572508	+	0.819899i	$0.694029\pi$
$398$	−20.3239	−1.01874
$399$	55.8562	2.79631
$400$	12.1136	0.605682
$401$	−3.51519	−0.175540	−0.0877702	−	0.996141i	$-0.527974\pi$
$401$	−3.51519	−0.175540	−0.0877702	+	0.996141i	$0.527974\pi$
$402$	−53.7492	−2.68077
$403$	−3.60540	−0.179598
$404$	−4.55024	−0.226383
$405$	11.6093	0.576873
$406$	8.09577	0.401786
$407$	29.0662	1.44076
$408$	23.1542	1.14630
$409$	23.9897	1.18621	0.593107	−	0.805124i	$-0.297901\pi$
$409$	23.9897	1.18621	0.593107	+	0.805124i	$0.297901\pi$
$410$	−27.1753	−1.34209
$411$	−8.85484	−0.436777
$412$	9.37860	0.462051
$413$	−21.4648	−1.05621
$414$	−5.88395	−0.289180
$415$	7.95464	0.390478
$416$	14.2832	0.700293
$417$	−8.08837	−0.396089
$418$	−49.2510	−2.40894
$419$	27.2826	1.33284	0.666421	−	0.745575i	$-0.267825\pi$
$419$	27.2826	1.33284	0.666421	+	0.745575i	$0.267825\pi$
$420$	−16.2516	−0.792997
$421$	−1.37060	−0.0667992	−0.0333996	−	0.999442i	$-0.510633\pi$
$421$	−1.37060	−0.0667992	−0.0333996	+	0.999442i	$0.510633\pi$
$422$	−4.36941	−0.212700
$423$	−18.2696	−0.888297
$424$	−14.1669	−0.688004
$425$	11.2239	0.544441
$426$	46.9443	2.27446
$427$	18.6835	0.904158
$428$	2.53173	0.122376
$429$	−53.1291	−2.56510
$430$	23.7873	1.14712
$431$	12.0532	0.580581	0.290291	−	0.956939i	$-0.406248\pi$
$431$	12.0532	0.580581	0.290291	+	0.956939i	$0.406248\pi$
$432$	6.32892	0.304500
$433$	−13.8279	−0.664528	−0.332264	−	0.943186i	$-0.607813\pi$
$433$	−13.8279	−0.664528	−0.332264	+	0.943186i	$0.607813\pi$
$434$	−9.01638	−0.432800
$435$	4.08119	0.195678
$436$	5.70424	0.273183
$437$	4.55028	0.217669
$438$	−1.97498	−0.0943683
$439$	−27.8167	−1.32762	−0.663809	−	0.747902i	$-0.731061\pi$
$439$	−27.8167	−1.32762	−0.663809	+	0.747902i	$0.731061\pi$
$440$	−20.3243	−0.968924
$441$	56.6357	2.69694
$442$	25.0656	1.19225
$443$	−8.80616	−0.418393	−0.209197	−	0.977874i	$-0.567085\pi$
$443$	−8.80616	−0.418393	−0.209197	+	0.977874i	$0.567085\pi$
$444$	−9.51983	−0.451791
$445$	27.5693	1.30691
$446$	35.9330	1.70148
$447$	16.6286	0.786505
$448$	−12.1421	−0.573661
$449$	24.5577	1.15895	0.579475	−	0.814990i	$-0.303258\pi$
$449$	24.5577	1.15895	0.579475	+	0.814990i	$0.303258\pi$
$450$	14.3410	0.676043
$451$	−64.9943	−3.06046
$452$	−1.31409	−0.0618094
$453$	21.6952	1.01933
$454$	−36.2638	−1.70194
$455$	24.9529	1.16981
$456$	−22.8788	−1.07140
$457$	10.1612	0.475320	0.237660	−	0.971348i	$-0.423620\pi$
$457$	10.1612	0.475320	0.237660	+	0.971348i	$0.423620\pi$
$458$	34.7851	1.62540
$459$	5.86408	0.273712
$460$	−1.32392	−0.0617282
$461$	0.775304	0.0361095	0.0180548	−	0.999837i	$-0.494253\pi$
$461$	0.775304	0.0361095	0.0180548	+	0.999837i	$0.494253\pi$
$462$	−132.865	−6.18144
$463$	26.1512	1.21535	0.607676	−	0.794185i	$-0.292102\pi$
$463$	26.1512	1.21535	0.607676	+	0.794185i	$0.292102\pi$
$464$	−4.97008	−0.230730
$465$	−4.54528	−0.210783
$466$	−40.5831	−1.87998
$467$	−10.9205	−0.505340	−0.252670	−	0.967553i	$-0.581309\pi$
$467$	−10.9205	−0.505340	−0.252670	+	0.967553i	$0.581309\pi$
$468$	9.36914	0.433088
$469$	60.3757	2.78789
$470$	−14.0519	−0.648166
$471$	−1.67223	−0.0770522
$472$	8.79201	0.404685
$473$	56.8913	2.61586
$474$	−2.07032	−0.0950928
$475$	−11.0905	−0.508865
$476$	18.3376	0.840503
$477$	−25.1375	−1.15097
$478$	37.8537	1.73139
$479$	−32.2575	−1.47388	−0.736940	−	0.675958i	$-0.763730\pi$
$479$	−32.2575	−1.47388	−0.736940	+	0.675958i	$0.763730\pi$
$480$	18.0067	0.821889
$481$	14.6169	0.666473
$482$	35.4808	1.61611
$483$	12.2753	0.558547
$484$	25.1749	1.14431
$485$	−1.69764	−0.0770860
$486$	−37.5092	−1.70145
$487$	−33.7336	−1.52862	−0.764308	−	0.644852i	$-0.776919\pi$
$487$	−33.7336	−1.52862	−0.764308	+	0.644852i	$0.776919\pi$
$488$	−7.65279	−0.346426
$489$	−41.2011	−1.86318
$490$	43.5609	1.96788
$491$	6.13372	0.276811	0.138406	−	0.990376i	$-0.455802\pi$
$491$	6.13372	0.276811	0.138406	+	0.990376i	$0.455802\pi$
$492$	21.2871	0.959697
$493$	−4.60504	−0.207401
$494$	−24.7675	−1.11434
$495$	−36.0633	−1.62092
$496$	5.53525	0.248540
$497$	−52.7318	−2.36535
$498$	−21.2999	−0.954470
$499$	−20.6952	−0.926443	−0.463222	−	0.886242i	$-0.653307\pi$
$499$	−20.6952	−0.926443	−0.463222	+	0.886242i	$0.653307\pi$
$500$	9.84643	0.440346
$501$	0.107108	0.00478523
$502$	−9.29463	−0.414840
$503$	−26.7545	−1.19293	−0.596463	−	0.802641i	$-0.703428\pi$
$503$	−26.7545	−1.19293	−0.596463	+	0.802641i	$0.703428\pi$
$504$	−33.2318	−1.48026
$505$	8.80780	0.391942
$506$	−10.8237	−0.481174
$507$	6.42458	0.285326
$508$	−2.53034	−0.112266
$509$	−12.8632	−0.570149	−0.285075	−	0.958505i	$-0.592018\pi$
$509$	−12.8632	−0.570149	−0.285075	+	0.958505i	$0.592018\pi$
$510$	31.5999	1.39927
$511$	2.21847	0.0981393
$512$	−2.32436	−0.102723
$513$	−5.79434	−0.255826
$514$	−17.2730	−0.761882
$515$	−18.1539	−0.799958
$516$	−18.6332	−0.820281
$517$	−33.6075	−1.47806
$518$	36.5539	1.60608
$519$	55.7559	2.44741
$520$	−10.2208	−0.448210
$521$	29.9380	1.31161	0.655805	−	0.754931i	$-0.272329\pi$
$521$	29.9380	1.31161	0.655805	+	0.754931i	$0.272329\pi$
$522$	−5.88395	−0.257534
$523$	43.3872	1.89719	0.948596	−	0.316490i	$-0.102504\pi$
$523$	43.3872	1.89719	0.948596	+	0.316490i	$0.102504\pi$
$524$	−4.97102	−0.217160
$525$	−29.9189	−1.30577
$526$	26.9399	1.17464
$527$	5.12870	0.223410
$528$	81.5672	3.54976
$529$	1.00000	0.0434783
$530$	−19.3344	−0.839831
$531$	15.6005	0.677002
$532$	−18.1195	−0.785581
$533$	−32.6846	−1.41573
$534$	−73.8213	−3.19456
$535$	−4.90061	−0.211872
$536$	−24.7300	−1.06817
$537$	50.9755	2.19976
$538$	15.6667	0.675441
$539$	104.183	4.48749
$540$	1.68589	0.0725490
$541$	21.9289	0.942798	0.471399	−	0.881920i	$-0.343749\pi$
$541$	21.9289	0.942798	0.471399	+	0.881920i	$0.343749\pi$
$542$	−12.2244	−0.525085
$543$	9.31897	0.399915
$544$	−20.3180	−0.871126
$545$	−11.0416	−0.472968
$546$	−66.8156	−2.85944
$547$	8.25534	0.352973	0.176486	−	0.984303i	$-0.443527\pi$
$547$	8.25534	0.352973	0.176486	+	0.984303i	$0.443527\pi$
$548$	2.87247	0.122706
$549$	−13.5790	−0.579539
$550$	26.3808	1.12488
$551$	4.55028	0.193848
$552$	−5.02800	−0.214006
$553$	2.32556	0.0988927
$554$	18.8406	0.800460
$555$	18.4273	0.782196
$556$	2.62383	0.111275
$557$	−6.92176	−0.293284	−0.146642	−	0.989190i	$-0.546847\pi$
$557$	−6.92176	−0.293284	−0.146642	+	0.989190i	$0.546847\pi$
$558$	6.55304	0.277412
$559$	28.6097	1.21006
$560$	−38.3093	−1.61887
$561$	75.5764	3.19084
$562$	−5.30101	−0.223610
$563$	8.22790	0.346765	0.173382	−	0.984855i	$-0.444530\pi$
$563$	8.22790	0.346765	0.173382	+	0.984855i	$0.444530\pi$
$564$	11.0072	0.463488
$565$	2.54365	0.107012
$566$	3.04516	0.127998
$567$	34.9184	1.46643
$568$	21.5990	0.906276
$569$	−46.5493	−1.95145	−0.975723	−	0.219006i	$-0.929719\pi$
$569$	−46.5493	−1.95145	−0.975723	+	0.219006i	$0.929719\pi$
$570$	−31.2241	−1.30783
$571$	26.8952	1.12553	0.562765	−	0.826617i	$-0.309738\pi$
$571$	26.8952	1.12553	0.562765	+	0.826617i	$0.309738\pi$
$572$	17.2349	0.720625
$573$	57.8491	2.41668
$574$	−81.7374	−3.41165
$575$	−2.43731	−0.101643
$576$	8.82481	0.367700
$577$	−41.4087	−1.72387	−0.861933	−	0.507022i	$-0.830746\pi$
$577$	−41.4087	−1.72387	−0.861933	+	0.507022i	$0.830746\pi$
$578$	−7.07257	−0.294180
$579$	48.9620	2.03479
$580$	−1.32392	−0.0549729
$581$	23.9258	0.992611
$582$	4.54572	0.188426
$583$	−46.2414	−1.91512
$584$	−0.908688	−0.0376018
$585$	−18.1356	−0.749816
$586$	39.7304	1.64125
$587$	19.8813	0.820588	0.410294	−	0.911953i	$-0.365426\pi$
$587$	19.8813	0.820588	0.410294	+	0.911953i	$0.365426\pi$
$588$	−34.1224	−1.40718
$589$	−5.06771	−0.208811
$590$	11.9990	0.493990
$591$	−3.23683	−0.133145
$592$	−22.4408	−0.922311
$593$	−19.4211	−0.797527	−0.398764	−	0.917054i	$-0.630561\pi$
$593$	−19.4211	−0.797527	−0.398764	+	0.917054i	$0.630561\pi$
$594$	13.7830	0.565523
$595$	−35.4957	−1.45518
$596$	−5.39424	−0.220957
$597$	−30.8164	−1.26123
$598$	−5.44308	−0.222584
$599$	10.4692	0.427758	0.213879	−	0.976860i	$-0.431390\pi$
$599$	10.4692	0.427758	0.213879	+	0.976860i	$0.431390\pi$
$600$	12.2548	0.500301
$601$	22.2282	0.906707	0.453354	−	0.891331i	$-0.350228\pi$
$601$	22.2282	0.906707	0.453354	+	0.891331i	$0.350228\pi$
$602$	71.5470	2.91604
$603$	−43.8806	−1.78696
$604$	−7.03782	−0.286365
$605$	−48.7304	−1.98117
$606$	−23.5843	−0.958048
$607$	−16.8715	−0.684793	−0.342396	−	0.939556i	$-0.611239\pi$
$607$	−16.8715	−0.684793	−0.342396	+	0.939556i	$0.611239\pi$
$608$	20.0763	0.814203
$609$	12.2753	0.497422
$610$	−10.4442	−0.422874
$611$	−16.9007	−0.683727
$612$	−13.3276	−0.538738
$613$	10.0024	0.403995	0.201997	−	0.979386i	$-0.435257\pi$
$613$	10.0024	0.403995	0.201997	+	0.979386i	$0.435257\pi$
$614$	1.99429	0.0804830
$615$	−41.2050	−1.66155
$616$	−61.1311	−2.46304
$617$	−21.5133	−0.866091	−0.433046	−	0.901372i	$-0.642561\pi$
$617$	−21.5133	−0.866091	−0.433046	+	0.901372i	$0.642561\pi$
$618$	48.6102	1.95539
$619$	38.6298	1.55266	0.776330	−	0.630326i	$-0.217079\pi$
$619$	38.6298	1.55266	0.776330	+	0.630326i	$0.217079\pi$
$620$	1.47447	0.0592162
$621$	−1.27340	−0.0510999
$622$	22.3667	0.896824
$623$	82.9224	3.32222
$624$	41.0188	1.64207
$625$	−6.87292	−0.274917
$626$	−0.848026	−0.0338939
$627$	−74.6776	−2.98234
$628$	0.542464	0.0216467
$629$	−20.7926	−0.829055
$630$	−45.3535	−1.80693
$631$	23.0317	0.916877	0.458439	−	0.888726i	$-0.348409\pi$
$631$	23.0317	0.916877	0.458439	+	0.888726i	$0.348409\pi$
$632$	−0.952552	−0.0378905
$633$	−6.62519	−0.263328
$634$	−0.766439	−0.0304392
$635$	4.89793	0.194368
$636$	15.1451	0.600543
$637$	52.3920	2.07585
$638$	−10.8237	−0.428516
$639$	38.3251	1.51612
$640$	20.9137	0.826687
$641$	−20.0523	−0.792019	−0.396010	−	0.918246i	$-0.629605\pi$
$641$	−20.0523	−0.792019	−0.396010	+	0.918246i	$0.629605\pi$
$642$	13.1222	0.517891
$643$	44.7864	1.76620	0.883101	−	0.469182i	$-0.155451\pi$
$643$	44.7864	1.76620	0.883101	+	0.469182i	$0.155451\pi$
$644$	−3.98207	−0.156915
$645$	36.0678	1.42017
$646$	35.2319	1.38618
$647$	−27.4834	−1.08049	−0.540243	−	0.841509i	$-0.681668\pi$
$647$	−27.4834	−1.08049	−0.540243	+	0.841509i	$0.681668\pi$
$648$	−14.3026	−0.561860
$649$	28.6976	1.12648
$650$	13.2665	0.520354
$651$	−13.6712	−0.535818
$652$	13.3654	0.523431
$653$	15.3774	0.601764	0.300882	−	0.953661i	$-0.402719\pi$
$653$	15.3774	0.601764	0.300882	+	0.953661i	$0.402719\pi$
$654$	29.5656	1.15611
$655$	9.62228	0.375974
$656$	50.1794	1.95918
$657$	−1.61237	−0.0629044
$658$	−42.2651	−1.64766
$659$	−37.7949	−1.47228	−0.736141	−	0.676829i	$-0.763354\pi$
$659$	−37.7949	−1.47228	−0.736141	+	0.676829i	$0.763354\pi$
$660$	21.7278	0.845752
$661$	−26.1249	−1.01614	−0.508070	−	0.861316i	$-0.669641\pi$
$661$	−26.1249	−1.01614	−0.508070	+	0.861316i	$0.669641\pi$
$662$	45.0865	1.75234
$663$	38.0061	1.47604
$664$	−9.80006	−0.380316
$665$	35.0735	1.36009
$666$	−26.5671	−1.02945
$667$	1.00000	0.0387202
$668$	−0.0347454	−0.00134434
$669$	54.4840	2.10647
$670$	−33.7505	−1.30390
$671$	−24.9791	−0.964308
$672$	54.1602	2.08928
$673$	−3.68363	−0.141994	−0.0709968	−	0.997477i	$-0.522618\pi$
$673$	−3.68363	−0.141994	−0.0709968	+	0.997477i	$0.522618\pi$
$674$	−31.6727	−1.21999
$675$	3.10369	0.119461
$676$	−2.08411	−0.0801580
$677$	32.9920	1.26798	0.633992	−	0.773340i	$-0.281415\pi$
$677$	32.9920	1.26798	0.633992	+	0.773340i	$0.281415\pi$
$678$	−6.81103	−0.261576
$679$	−5.10614	−0.195956
$680$	14.5391	0.557549
$681$	−54.9855	−2.10705
$682$	12.0545	0.461592
$683$	38.3314	1.46671	0.733355	−	0.679846i	$-0.237953\pi$
$683$	38.3314	1.46671	0.733355	+	0.679846i	$0.237953\pi$
$684$	13.1691	0.503535
$685$	−5.56018	−0.212444
$686$	74.3514	2.83875
$687$	52.7434	2.01229
$688$	−43.9234	−1.67456
$689$	−23.2540	−0.885907
$690$	−6.86201	−0.261232
$691$	−17.5734	−0.668524	−0.334262	−	0.942480i	$-0.608487\pi$
$691$	−17.5734	−0.668524	−0.334262	+	0.942480i	$0.608487\pi$
$692$	−18.0870	−0.687564
$693$	−108.470	−4.12045
$694$	22.1251	0.839856
$695$	−5.07889	−0.192653
$696$	−5.02800	−0.190586
$697$	46.4939	1.76108
$698$	−4.99608	−0.189105
$699$	−61.5348	−2.32746
$700$	9.70555	0.366835
$701$	−33.7148	−1.27339	−0.636696	−	0.771115i	$-0.719699\pi$
$701$	−33.7148	−1.27339	−0.636696	+	0.771115i	$0.719699\pi$
$702$	6.93123	0.261603
$703$	20.5453	0.774881
$704$	16.2335	0.611825
$705$	−21.3064	−0.802447
$706$	−0.838669	−0.0315637
$707$	26.4919	0.996332
$708$	−9.39912	−0.353240
$709$	28.8835	1.08474	0.542371	−	0.840139i	$-0.317527\pi$
$709$	28.8835	1.08474	0.542371	+	0.840139i	$0.317527\pi$
$710$	29.4775	1.10627
$711$	−1.69020	−0.0633874
$712$	−33.9652	−1.27290
$713$	−1.11371	−0.0417089
$714$	95.0455	3.55699
$715$	−33.3611	−1.24763
$716$	−16.5362	−0.617988
$717$	57.3962	2.14350
$718$	15.4101	0.575102
$719$	12.8825	0.480434	0.240217	−	0.970719i	$-0.422781\pi$
$719$	12.8825	0.480434	0.240217	+	0.970719i	$0.422781\pi$
$720$	27.8430	1.03765
$721$	−54.6031	−2.03353
$722$	−2.86679	−0.106691
$723$	53.7984	2.00078
$724$	−3.02303	−0.112350
$725$	−2.43731	−0.0905196
$726$	130.484	4.84270
$727$	23.3004	0.864165	0.432083	−	0.901834i	$-0.357779\pi$
$727$	23.3004	0.864165	0.432083	+	0.901834i	$0.357779\pi$
$728$	−30.7418	−1.13937
$729$	−35.1177	−1.30066
$730$	−1.24014	−0.0458997
$731$	−40.6974	−1.50525
$732$	8.18123	0.302387
$733$	−21.1360	−0.780676	−0.390338	−	0.920672i	$-0.627642\pi$
$733$	−21.1360	−0.780676	−0.390338	+	0.920672i	$0.627642\pi$
$734$	24.5993	0.907978
$735$	66.0500	2.43629
$736$	4.41211	0.162633
$737$	−80.7200	−2.97336
$738$	59.4062	2.18677
$739$	10.7981	0.397214	0.198607	−	0.980079i	$-0.436358\pi$
$739$	10.7981	0.397214	0.198607	+	0.980079i	$0.436358\pi$
$740$	−5.97775	−0.219746
$741$	−37.5541	−1.37959
$742$	−58.1535	−2.13488
$743$	14.3921	0.527996	0.263998	−	0.964523i	$-0.414959\pi$
$743$	14.3921	0.527996	0.263998	+	0.964523i	$0.414959\pi$
$744$	5.59976	0.205297
$745$	10.4415	0.382547
$746$	−3.86007	−0.141327
$747$	−17.3891	−0.636235
$748$	−24.5167	−0.896418
$749$	−14.7400	−0.538586
$750$	51.0349	1.86353
$751$	33.1386	1.20924	0.604622	−	0.796512i	$-0.293324\pi$
$751$	33.1386	1.20924	0.604622	+	0.796512i	$0.293324\pi$
$752$	25.9470	0.946189
$753$	−14.0931	−0.513582
$754$	−5.44308	−0.198225
$755$	13.6229	0.495790
$756$	5.07078	0.184423
$757$	−40.6036	−1.47576	−0.737881	−	0.674930i	$-0.764174\pi$
$757$	−40.6036	−1.47576	−0.737881	+	0.674930i	$0.764174\pi$
$758$	−62.4585	−2.26859
$759$	−16.4117	−0.595705
$760$	−14.3662	−0.521116
$761$	34.5658	1.25301	0.626505	−	0.779417i	$-0.284485\pi$
$761$	34.5658	1.25301	0.626505	+	0.779417i	$0.284485\pi$
$762$	−13.1150	−0.475107
$763$	−33.2106	−1.20230
$764$	−18.7660	−0.678930
$765$	25.7980	0.932729
$766$	56.8640	2.05458
$767$	14.4315	0.521093
$768$	−43.1420	−1.55675
$769$	−1.16752	−0.0421018	−0.0210509	−	0.999778i	$-0.506701\pi$
$769$	−1.16752	−0.0421018	−0.0210509	+	0.999778i	$0.506701\pi$
$770$	−83.4293	−3.00658
$771$	−26.1905	−0.943229
$772$	−15.8831	−0.571645
$773$	46.0245	1.65539	0.827693	−	0.561182i	$-0.189653\pi$
$773$	46.0245	1.65539	0.827693	+	0.561182i	$0.189653\pi$
$774$	−51.9998	−1.86910
$775$	2.71447	0.0975067
$776$	2.09148	0.0750799
$777$	55.4254	1.98837
$778$	−21.7671	−0.780389
$779$	−45.9410	−1.64601
$780$	10.9265	0.391232
$781$	70.5004	2.52270
$782$	7.74280	0.276882
$783$	−1.27340	−0.0455077
$784$	−80.4356	−2.87270
$785$	−1.05003	−0.0374773
$786$	−25.7653	−0.919016
$787$	−10.7137	−0.381901	−0.190950	−	0.981600i	$-0.561157\pi$
$787$	−10.7137	−0.381901	−0.190950	+	0.981600i	$0.561157\pi$
$788$	1.05001	0.0374052
$789$	40.8480	1.45423
$790$	−1.30000	−0.0462521
$791$	7.65073	0.272029
$792$	44.4297	1.57874
$793$	−12.5616	−0.446075
$794$	38.3593	1.36132
$795$	−29.3160	−1.03973
$796$	9.99671	0.354324
$797$	−50.3132	−1.78219	−0.891093	−	0.453821i	$-0.850061\pi$
$797$	−50.3132	−1.78219	−0.891093	+	0.453821i	$0.850061\pi$
$798$	−93.9152	−3.32456
$799$	24.0413	0.850519
$800$	−10.7537	−0.380201
$801$	−60.2674	−2.12944
$802$	5.91035	0.208702
$803$	−2.96601	−0.104668
$804$	26.4376	0.932384
$805$	7.70800	0.271671
$806$	6.06203	0.213526
$807$	23.7549	0.836214
$808$	−10.8511	−0.381742
$809$	−36.1726	−1.27176	−0.635880	−	0.771788i	$-0.719363\pi$
$809$	−36.1726	−1.27176	−0.635880	+	0.771788i	$0.719363\pi$
$810$	−19.5197	−0.685851
$811$	−15.5935	−0.547561	−0.273781	−	0.961792i	$-0.588274\pi$
$811$	−15.5935	−0.547561	−0.273781	+	0.961792i	$0.588274\pi$
$812$	−3.98207	−0.139743
$813$	−18.5355	−0.650069
$814$	−48.8711	−1.71293
$815$	−25.8712	−0.906228
$816$	−58.3494	−2.04264
$817$	40.2134	1.40689
$818$	−40.3357	−1.41030
$819$	−54.5480	−1.90606
$820$	13.3667	0.466786
$821$	−17.0501	−0.595054	−0.297527	−	0.954713i	$-0.596162\pi$
$821$	−17.0501	−0.595054	−0.297527	+	0.954713i	$0.596162\pi$
$822$	14.8883	0.519289
$823$	−2.67938	−0.0933974	−0.0466987	−	0.998909i	$-0.514870\pi$
$823$	−2.67938	−0.0933974	−0.0466987	+	0.998909i	$0.514870\pi$
$824$	22.3655	0.779140
$825$	40.0004	1.39263
$826$	36.0903	1.25574
$827$	6.85300	0.238302	0.119151	−	0.992876i	$-0.461983\pi$
$827$	6.85300	0.238302	0.119151	+	0.992876i	$0.461983\pi$
$828$	2.89414	0.100578
$829$	−16.0498	−0.557433	−0.278717	−	0.960373i	$-0.589909\pi$
$829$	−16.0498	−0.557433	−0.278717	+	0.960373i	$0.589909\pi$
$830$	−13.3747	−0.464243
$831$	28.5674	0.990990
$832$	8.16358	0.283021
$833$	−74.5279	−2.58224
$834$	13.5996	0.470915
$835$	0.0672558	0.00232748
$836$	24.2251	0.837842
$837$	1.41821	0.0490204
$838$	−45.8723	−1.58463
$839$	−16.0979	−0.555761	−0.277880	−	0.960616i	$-0.589632\pi$
$839$	−16.0979	−0.555761	−0.277880	+	0.960616i	$0.589632\pi$
$840$	−38.7558	−1.33720
$841$	1.00000	0.0344828
$842$	2.30450	0.0794183
$843$	−8.03774	−0.276835
$844$	2.14918	0.0739779
$845$	4.03416	0.138779
$846$	30.7180	1.05611
$847$	−146.570	−5.03622
$848$	35.7011	1.22598
$849$	4.61728	0.158465
$850$	−18.8716	−0.647292
$851$	4.51518	0.154778
$852$	−23.0905	−0.791067
$853$	−24.2573	−0.830552	−0.415276	−	0.909695i	$-0.636315\pi$
$853$	−24.2573	−0.830552	−0.415276	+	0.909695i	$0.636315\pi$
$854$	−31.4139	−1.07496
$855$	−25.4912	−0.871781
$856$	6.03751	0.206358
$857$	−50.4923	−1.72478	−0.862391	−	0.506242i	$-0.831034\pi$
$857$	−50.4923	−1.72478	−0.862391	+	0.506242i	$0.831034\pi$
$858$	89.3299	3.04967
$859$	−15.5299	−0.529873	−0.264937	−	0.964266i	$-0.585351\pi$
$859$	−15.5299	−0.529873	−0.264937	+	0.964266i	$0.585351\pi$
$860$	−11.7003	−0.398975
$861$	−123.936	−4.22371
$862$	−20.2659	−0.690259
$863$	13.8161	0.470306	0.235153	−	0.971958i	$-0.424441\pi$
$863$	13.8161	0.470306	0.235153	+	0.971958i	$0.424441\pi$
$864$	−5.61840	−0.191142
$865$	35.0106	1.19039
$866$	23.2499	0.790065
$867$	−10.7239	−0.364203
$868$	4.43489	0.150530
$869$	−3.10918	−0.105472
$870$	−6.86201	−0.232644
$871$	−40.5927	−1.37543
$872$	13.6031	0.460660
$873$	3.71111	0.125602
$874$	−7.65072	−0.258789
$875$	−57.3268	−1.93800
$876$	0.971435	0.0328217
$877$	23.5097	0.793866	0.396933	−	0.917848i	$-0.370075\pi$
$877$	23.5097	0.793866	0.396933	+	0.917848i	$0.370075\pi$
$878$	46.7703	1.57842
$879$	60.2419	2.03191
$880$	51.2181	1.72656
$881$	−34.4420	−1.16038	−0.580191	−	0.814481i	$-0.697022\pi$
$881$	−34.4420	−1.16038	−0.580191	+	0.814481i	$0.697022\pi$
$882$	−95.2257	−3.20642
$883$	15.0881	0.507755	0.253878	−	0.967236i	$-0.418294\pi$
$883$	15.0881	0.507755	0.253878	+	0.967236i	$0.418294\pi$
$884$	−12.3290	−0.414670
$885$	18.1937	0.611573
$886$	14.8064	0.497432
$887$	−27.1965	−0.913169	−0.456584	−	0.889680i	$-0.650927\pi$
$887$	−27.1965	−0.913169	−0.456584	+	0.889680i	$0.650927\pi$
$888$	−22.7023	−0.761840
$889$	14.7319	0.494092
$890$	−46.3543	−1.55380
$891$	−46.6845	−1.56399
$892$	−17.6744	−0.591782
$893$	−23.7554	−0.794943
$894$	−27.9589	−0.935085
$895$	32.0088	1.06994
$896$	62.9039	2.10147
$897$	−8.25315	−0.275565
$898$	−41.2907	−1.37789
$899$	−1.11371	−0.0371445
$900$	−7.05393	−0.235131
$901$	33.0789	1.10202
$902$	109.280	3.63862
$903$	108.484	3.61013
$904$	−3.13375	−0.104227
$905$	5.85162	0.194514
$906$	−36.4777	−1.21189
$907$	−32.7246	−1.08660	−0.543301	−	0.839538i	$-0.682826\pi$
$907$	−32.7246	−1.08660	−0.543301	+	0.839538i	$0.682826\pi$
$908$	17.8371	0.591944
$909$	−19.2542	−0.638620
$910$	−41.9552	−1.39080
$911$	−6.31180	−0.209119	−0.104560	−	0.994519i	$-0.533343\pi$
$911$	−6.31180	−0.209119	−0.104560	+	0.994519i	$0.533343\pi$
$912$	57.6555	1.90916
$913$	−31.9879	−1.05864
$914$	−17.0848	−0.565114
$915$	−15.8362	−0.523529
$916$	−17.1097	−0.565321
$917$	28.9417	0.955740
$918$	−9.85971	−0.325419
$919$	27.6020	0.910507	0.455254	−	0.890362i	$-0.349549\pi$
$919$	27.6020	0.910507	0.455254	+	0.890362i	$0.349549\pi$
$920$	−3.15721	−0.104090
$921$	3.02387	0.0996400
$922$	−1.30358	−0.0429310
$923$	35.4535	1.16697
$924$	65.3523	2.14993
$925$	−11.0049	−0.361839
$926$	−43.9700	−1.44494
$927$	39.6852	1.30343
$928$	4.41211	0.144835
$929$	12.6957	0.416533	0.208266	−	0.978072i	$-0.433218\pi$
$929$	12.6957	0.416533	0.208266	+	0.978072i	$0.433218\pi$
$930$	7.64232	0.250602
$931$	73.6416	2.41351
$932$	19.9616	0.653865
$933$	33.9139	1.11029
$934$	18.3614	0.600804
$935$	47.4563	1.55199
$936$	22.3430	0.730302
$937$	19.3527	0.632225	0.316112	−	0.948722i	$-0.397622\pi$
$937$	19.3527	0.632225	0.316112	+	0.948722i	$0.397622\pi$
$938$	−101.514	−3.31455
$939$	−1.28583	−0.0419616
$940$	6.91172	0.225435
$941$	2.26837	0.0739467	0.0369733	−	0.999316i	$-0.488228\pi$
$941$	2.26837	0.0739467	0.0369733	+	0.999316i	$0.488228\pi$
$942$	2.81164	0.0916082
$943$	−10.0963	−0.328781
$944$	−22.1562	−0.721124
$945$	−9.81540	−0.319295
$946$	−95.6555	−3.11003
$947$	−59.7576	−1.94186	−0.970930	−	0.239364i	$-0.923061\pi$
$947$	−59.7576	−1.94186	−0.970930	+	0.239364i	$0.923061\pi$
$948$	1.01833	0.0330737
$949$	−1.49156	−0.0484179
$950$	18.6472	0.604995
$951$	−1.16213	−0.0376845
$952$	43.7304	1.41731
$953$	57.0944	1.84947	0.924734	−	0.380615i	$-0.124288\pi$
$953$	57.0944	1.84947	0.924734	+	0.380615i	$0.124288\pi$
$954$	42.2656	1.36840
$955$	36.3249	1.17545
$956$	−18.6191	−0.602184
$957$	−16.4117	−0.530513
$958$	54.2368	1.75231
$959$	−16.7238	−0.540040
$960$	10.2917	0.332164
$961$	−29.7596	−0.959988
$962$	−24.5765	−0.792377
$963$	10.7129	0.345218
$964$	−17.4520	−0.562090
$965$	30.7445	0.989701
$966$	−20.6394	−0.664063
$967$	8.21507	0.264179	0.132089	−	0.991238i	$-0.457831\pi$
$967$	8.21507	0.264179	0.132089	+	0.991238i	$0.457831\pi$
$968$	60.0355	1.92961
$969$	53.4209	1.71613
$970$	2.85437	0.0916484
$971$	−27.4049	−0.879464	−0.439732	−	0.898129i	$-0.644927\pi$
$971$	−27.4049	−0.879464	−0.439732	+	0.898129i	$0.644927\pi$
$972$	18.4496	0.591772
$973$	−15.2762	−0.489733
$974$	56.7188	1.81739
$975$	20.1155	0.644212
$976$	19.2853	0.617309
$977$	55.7031	1.78210	0.891050	−	0.453905i	$-0.149969\pi$
$977$	55.7031	1.78210	0.891050	+	0.453905i	$0.149969\pi$
$978$	69.2744	2.21515
$979$	−110.864	−3.54323
$980$	−21.4263	−0.684439
$981$	24.1372	0.770643
$982$	−10.3131	−0.329104
$983$	32.4589	1.03528	0.517639	−	0.855599i	$-0.326811\pi$
$983$	32.4589	1.03528	0.517639	+	0.855599i	$0.326811\pi$
$984$	50.7642	1.61830
$985$	−2.03249	−0.0647604
$986$	7.74280	0.246581
$987$	−64.0851	−2.03985
$988$	12.1824	0.387574
$989$	8.83757	0.281018
$990$	60.6358	1.92713
$991$	−22.4212	−0.712234	−0.356117	−	0.934441i	$-0.615900\pi$
$991$	−22.4212	−0.712234	−0.356117	+	0.934441i	$0.615900\pi$
$992$	−4.91383	−0.156014
$993$	68.3632	2.16944
$994$	88.6619	2.81218
$995$	−19.3504	−0.613449
$996$	10.4768	0.331969
$997$	57.9261	1.83454	0.917269	−	0.398268i	$-0.130389\pi$
$997$	57.9261	1.83454	0.917269	+	0.398268i	$0.130389\pi$
$998$	34.7963	1.10146
$999$	−5.74965	−0.181911

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	667.2.a.a.1.3	✓	10
3.2	odd	2		6003.2.a.l.1.8		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
667.2.a.a.1.3	✓	10	1.1	even	1	trivial
6003.2.a.l.1.8		10	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 667 = 23 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	667.a (trivial)

\(f(q)\)	\(=\)	\(q-1.68137 q^{2} -2.54941 q^{3} +0.827018 q^{4} -1.60084 q^{5} +4.28651 q^{6} -4.81497 q^{7} +1.97222 q^{8} +3.49949 q^{9} +O(q^{10})\)	\(q-1.68137 q^{2} -2.54941 q^{3} +0.827018 q^{4} -1.60084 q^{5} +4.28651 q^{6} -4.81497 q^{7} +1.97222 q^{8} +3.49949 q^{9} +2.69161 q^{10} +6.43743 q^{11} -2.10841 q^{12} +3.23728 q^{13} +8.09577 q^{14} +4.08119 q^{15} -4.97008 q^{16} -4.60504 q^{17} -5.88395 q^{18} +4.55028 q^{19} -1.32392 q^{20} +12.2753 q^{21} -10.8237 q^{22} +1.00000 q^{23} -5.02800 q^{24} -2.43731 q^{25} -5.44308 q^{26} -1.27340 q^{27} -3.98207 q^{28} +1.00000 q^{29} -6.86201 q^{30} -1.11371 q^{31} +4.41211 q^{32} -16.4117 q^{33} +7.74280 q^{34} +7.70800 q^{35} +2.89414 q^{36} +4.51518 q^{37} -7.65072 q^{38} -8.25315 q^{39} -3.15721 q^{40} -10.0963 q^{41} -20.6394 q^{42} +8.83757 q^{43} +5.32387 q^{44} -5.60212 q^{45} -1.68137 q^{46} -5.22064 q^{47} +12.6708 q^{48} +16.1840 q^{49} +4.09804 q^{50} +11.7401 q^{51} +2.67729 q^{52} -7.18320 q^{53} +2.14107 q^{54} -10.3053 q^{55} -9.49620 q^{56} -11.6005 q^{57} -1.68137 q^{58} +4.45792 q^{59} +3.37522 q^{60} -3.88029 q^{61} +1.87257 q^{62} -16.8500 q^{63} +2.52174 q^{64} -5.18236 q^{65} +27.5941 q^{66} -12.5392 q^{67} -3.80845 q^{68} -2.54941 q^{69} -12.9600 q^{70} +10.9516 q^{71} +6.90177 q^{72} -0.460744 q^{73} -7.59170 q^{74} +6.21371 q^{75} +3.76316 q^{76} -30.9961 q^{77} +13.8766 q^{78} -0.482984 q^{79} +7.95629 q^{80} -7.25204 q^{81} +16.9757 q^{82} -4.96905 q^{83} +10.1519 q^{84} +7.37193 q^{85} -14.8593 q^{86} -2.54941 q^{87} +12.6960 q^{88} -17.2218 q^{89} +9.41926 q^{90} -15.5874 q^{91} +0.827018 q^{92} +2.83931 q^{93} +8.77784 q^{94} -7.28426 q^{95} -11.2483 q^{96} +1.06047 q^{97} -27.2113 q^{98} +22.5277 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 3 q^{2} - 9 q^{3} + 9 q^{4} - 10 q^{5} + 4 q^{6} + q^{7} - 9 q^{8} + 7 q^{9}+O(q^{10}) \) 10 * q - 3 * q^2 - 9 * q^3 + 9 * q^4 - 10 * q^5 + 4 * q^6 + q^7 - 9 * q^8 + 7 * q^9	\( 10 q - 3 q^{2} - 9 q^{3} + 9 q^{4} - 10 q^{5} + 4 q^{6} + q^{7} - 9 q^{8} + 7 q^{9} - 6 q^{10} - 17 q^{12} - 13 q^{13} - 12 q^{14} + 2 q^{15} - 5 q^{16} - 22 q^{17} + 12 q^{18} - 2 q^{19} + 3 q^{20} - 7 q^{21} + 3 q^{22} + 10 q^{23} - 6 q^{24} + 10 q^{25} - 25 q^{26} - 24 q^{27} + 19 q^{28} + 10 q^{29} - 3 q^{30} - 22 q^{31} - 31 q^{32} - 9 q^{33} + 13 q^{34} - 15 q^{35} + 19 q^{36} - 9 q^{37} - 10 q^{38} + 4 q^{39} - 6 q^{40} - 25 q^{41} - 34 q^{42} + 3 q^{43} - 27 q^{44} - 28 q^{45} - 3 q^{46} - 17 q^{47} - 3 q^{48} + 17 q^{49} + 2 q^{50} + 38 q^{51} - 18 q^{52} - 43 q^{53} - 47 q^{54} - 11 q^{55} - 7 q^{56} + 18 q^{57} - 3 q^{58} - 7 q^{59} - 21 q^{60} - 6 q^{61} + 3 q^{62} + 11 q^{63} + 33 q^{64} + 11 q^{65} + 55 q^{66} + 11 q^{67} - 51 q^{68} - 9 q^{69} + 34 q^{70} - 17 q^{71} + 34 q^{72} - 44 q^{73} + 9 q^{74} + q^{75} + 24 q^{76} - 71 q^{77} + 38 q^{78} + 5 q^{79} + 38 q^{80} + 18 q^{81} + 33 q^{82} - 32 q^{83} + 14 q^{84} + 16 q^{85} - 9 q^{86} - 9 q^{87} + 18 q^{88} - 10 q^{89} - 9 q^{90} - 3 q^{91} + 9 q^{92} - 8 q^{93} + 47 q^{94} - 8 q^{95} + 60 q^{96} + 6 q^{97} - 73 q^{98} + 26 q^{99}+O(q^{100}) \) 10 * q - 3 * q^2 - 9 * q^3 + 9 * q^4 - 10 * q^5 + 4 * q^6 + q^7 - 9 * q^8 + 7 * q^9 - 6 * q^10 - 17 * q^12 - 13 * q^13 - 12 * q^14 + 2 * q^15 - 5 * q^16 - 22 * q^17 + 12 * q^18 - 2 * q^19 + 3 * q^20 - 7 * q^21 + 3 * q^22 + 10 * q^23 - 6 * q^24 + 10 * q^25 - 25 * q^26 - 24 * q^27 + 19 * q^28 + 10 * q^29 - 3 * q^30 - 22 * q^31 - 31 * q^32 - 9 * q^33 + 13 * q^34 - 15 * q^35 + 19 * q^36 - 9 * q^37 - 10 * q^38 + 4 * q^39 - 6 * q^40 - 25 * q^41 - 34 * q^42 + 3 * q^43 - 27 * q^44 - 28 * q^45 - 3 * q^46 - 17 * q^47 - 3 * q^48 + 17 * q^49 + 2 * q^50 + 38 * q^51 - 18 * q^52 - 43 * q^53 - 47 * q^54 - 11 * q^55 - 7 * q^56 + 18 * q^57 - 3 * q^58 - 7 * q^59 - 21 * q^60 - 6 * q^61 + 3 * q^62 + 11 * q^63 + 33 * q^64 + 11 * q^65 + 55 * q^66 + 11 * q^67 - 51 * q^68 - 9 * q^69 + 34 * q^70 - 17 * q^71 + 34 * q^72 - 44 * q^73 + 9 * q^74 + q^75 + 24 * q^76 - 71 * q^77 + 38 * q^78 + 5 * q^79 + 38 * q^80 + 18 * q^81 + 33 * q^82 - 32 * q^83 + 14 * q^84 + 16 * q^85 - 9 * q^86 - 9 * q^87 + 18 * q^88 - 10 * q^89 - 9 * q^90 - 3 * q^91 + 9 * q^92 - 8 * q^93 + 47 * q^94 - 8 * q^95 + 60 * q^96 + 6 * q^97 - 73 * q^98 + 26 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more