LMFDB - Embedded newform 667.2.a.b.1.4

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:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} - 13 x^{10} + 41 x^{9} + 54 x^{8} - 188 x^{7} - 77 x^{6} + 342 x^{5} + 13 x^{4} + \cdots - 5 $ x^12 - 3x^11 - 13x^10 + 41x^9 + 54x^8 - 188x^7 - 77x^6 + 342x^5 + 13x^4 - 215x^3 + 9x^2 + 37*x - 5
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$1.49364$ 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)

$f(q)$	$=$	$q-1.49364 q^{2} -1.48170 q^{3} +0.230961 q^{4} -1.29771 q^{5} +2.21312 q^{6} +1.16738 q^{7} +2.64231 q^{8} -0.804576 q^{9} +O(q^{10})$	\(q-1.49364 q^{2} -1.48170 q^{3} +0.230961 q^{4} -1.29771 q^{5} +2.21312 q^{6} +1.16738 q^{7} +2.64231 q^{8} -0.804576 q^{9} +1.93831 q^{10} -3.17939 q^{11} -0.342214 q^{12} +5.91984 q^{13} -1.74364 q^{14} +1.92281 q^{15} -4.40858 q^{16} +0.673199 q^{17} +1.20175 q^{18} +4.27963 q^{19} -0.299720 q^{20} -1.72970 q^{21} +4.74887 q^{22} -1.00000 q^{23} -3.91510 q^{24} -3.31595 q^{25} -8.84211 q^{26} +5.63723 q^{27} +0.269618 q^{28} -1.00000 q^{29} -2.87199 q^{30} +4.60616 q^{31} +1.30022 q^{32} +4.71089 q^{33} -1.00552 q^{34} -1.51491 q^{35} -0.185826 q^{36} -6.04113 q^{37} -6.39223 q^{38} -8.77140 q^{39} -3.42894 q^{40} -4.61201 q^{41} +2.58354 q^{42} -7.40960 q^{43} -0.734316 q^{44} +1.04410 q^{45} +1.49364 q^{46} +0.716847 q^{47} +6.53218 q^{48} -5.63724 q^{49} +4.95284 q^{50} -0.997476 q^{51} +1.36725 q^{52} -5.40161 q^{53} -8.41999 q^{54} +4.12592 q^{55} +3.08456 q^{56} -6.34112 q^{57} +1.49364 q^{58} -14.4815 q^{59} +0.444094 q^{60} -1.19231 q^{61} -6.87995 q^{62} -0.939241 q^{63} +6.87510 q^{64} -7.68222 q^{65} -7.03638 q^{66} -6.43036 q^{67} +0.155483 q^{68} +1.48170 q^{69} +2.26273 q^{70} -1.33803 q^{71} -2.12594 q^{72} +1.17657 q^{73} +9.02327 q^{74} +4.91324 q^{75} +0.988429 q^{76} -3.71154 q^{77} +13.1013 q^{78} +8.62001 q^{79} +5.72105 q^{80} -5.93893 q^{81} +6.88869 q^{82} +5.29591 q^{83} -0.399492 q^{84} -0.873615 q^{85} +11.0673 q^{86} +1.48170 q^{87} -8.40093 q^{88} +7.45016 q^{89} -1.55952 q^{90} +6.91067 q^{91} -0.230961 q^{92} -6.82494 q^{93} -1.07071 q^{94} -5.55371 q^{95} -1.92653 q^{96} -12.7317 q^{97} +8.42000 q^{98} +2.55806 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{2} - 3 q^{3} + 11 q^{4} - 16 q^{5} - 2 q^{6} - 7 q^{7} - 9 q^{8} + 3 q^{9}+O(q^{10}) $ 12 * q - 3 * q^2 - 3 * q^3 + 11 * q^4 - 16 * q^5 - 2 * q^6 - 7 * q^7 - 9 * q^8 + 3 * q^9	\( 12 q - 3 q^{2} - 3 q^{3} + 11 q^{4} - 16 q^{5} - 2 q^{6} - 7 q^{7} - 9 q^{8} + 3 q^{9} - 6 q^{11} - 21 q^{12} - 15 q^{13} - 8 q^{14} + 6 q^{15} + 17 q^{16} - 18 q^{17} - 12 q^{18} - 6 q^{19} - 39 q^{20} - q^{21} - 5 q^{22} - 12 q^{23} + 4 q^{24} + 14 q^{25} - 3 q^{26} - 12 q^{27} - 19 q^{28} - 12 q^{29} - 11 q^{30} + 16 q^{31} - 21 q^{32} - 19 q^{33} - 7 q^{34} - 11 q^{35} - 13 q^{36} - q^{37} - 24 q^{38} + 6 q^{39} + 30 q^{40} + 3 q^{41} + 22 q^{42} - 23 q^{43} + 23 q^{44} - 22 q^{45} + 3 q^{46} - 35 q^{47} - 21 q^{48} + 3 q^{49} - 2 q^{50} - 34 q^{51} - 45 q^{53} + 55 q^{54} + 17 q^{55} - 17 q^{56} - 34 q^{57} + 3 q^{58} - 11 q^{59} + 93 q^{60} + 4 q^{61} - 7 q^{62} + q^{63} + 15 q^{64} + 5 q^{65} - 35 q^{66} - 19 q^{67} + q^{68} + 3 q^{69} + 14 q^{70} + 19 q^{71} + 4 q^{72} + 10 q^{73} - 15 q^{74} - 3 q^{75} - 4 q^{76} - 39 q^{77} + 16 q^{78} + 17 q^{79} - 90 q^{80} + 4 q^{81} - 3 q^{82} - 12 q^{83} + 42 q^{84} + 14 q^{85} + 17 q^{86} + 3 q^{87} - 2 q^{88} - 20 q^{89} + 65 q^{90} + 11 q^{91} - 11 q^{92} - 2 q^{93} + 13 q^{94} + 12 q^{95} + 14 q^{96} - 12 q^{97} + 75 q^{98} - 4 q^{99}+O(q^{100}) \) 12 * q - 3 * q^2 - 3 * q^3 + 11 * q^4 - 16 * q^5 - 2 * q^6 - 7 * q^7 - 9 * q^8 + 3 * q^9 - 6 * q^11 - 21 * q^12 - 15 * q^13 - 8 * q^14 + 6 * q^15 + 17 * q^16 - 18 * q^17 - 12 * q^18 - 6 * q^19 - 39 * q^20 - q^21 - 5 * q^22 - 12 * q^23 + 4 * q^24 + 14 * q^25 - 3 * q^26 - 12 * q^27 - 19 * q^28 - 12 * q^29 - 11 * q^30 + 16 * q^31 - 21 * q^32 - 19 * q^33 - 7 * q^34 - 11 * q^35 - 13 * q^36 - q^37 - 24 * q^38 + 6 * q^39 + 30 * q^40 + 3 * q^41 + 22 * q^42 - 23 * q^43 + 23 * q^44 - 22 * q^45 + 3 * q^46 - 35 * q^47 - 21 * q^48 + 3 * q^49 - 2 * q^50 - 34 * q^51 - 45 * q^53 + 55 * q^54 + 17 * q^55 - 17 * q^56 - 34 * q^57 + 3 * q^58 - 11 * q^59 + 93 * q^60 + 4 * q^61 - 7 * q^62 + q^63 + 15 * q^64 + 5 * q^65 - 35 * q^66 - 19 * q^67 + q^68 + 3 * q^69 + 14 * q^70 + 19 * q^71 + 4 * q^72 + 10 * q^73 - 15 * q^74 - 3 * q^75 - 4 * q^76 - 39 * q^77 + 16 * q^78 + 17 * q^79 - 90 * q^80 + 4 * q^81 - 3 * q^82 - 12 * q^83 + 42 * q^84 + 14 * q^85 + 17 * q^86 + 3 * q^87 - 2 * q^88 - 20 * q^89 + 65 * q^90 + 11 * q^91 - 11 * q^92 - 2 * q^93 + 13 * q^94 + 12 * q^95 + 14 * q^96 - 12 * q^97 + 75 * q^98 - 4 * 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 $

$2$	−1.49364	−1.05616	−0.528082	−	0.849194i	$-0.677088\pi$
$2$	−1.49364	−1.05616	−0.528082	+	0.849194i	$0.677088\pi$
$3$	−1.48170	−0.855458	−0.427729	−	0.903907i	$-0.640686\pi$
$3$	−1.48170	−0.855458	−0.427729	+	0.903907i	$0.640686\pi$
$4$	0.230961	0.115481
$5$	−1.29771	−0.580353	−0.290176	−	0.956973i	$-0.593714\pi$
$5$	−1.29771	−0.580353	−0.290176	+	0.956973i	$0.593714\pi$
$6$	2.21312	0.903503
$7$	1.16738	0.441226	0.220613	−	0.975361i	$-0.429194\pi$
$7$	1.16738	0.441226	0.220613	+	0.975361i	$0.429194\pi$
$8$	2.64231	0.934197
$9$	−0.804576	−0.268192
$10$	1.93831	0.612947
$11$	−3.17939	−0.958623	−0.479311	−	0.877645i	$-0.659114\pi$
$11$	−3.17939	−0.958623	−0.479311	+	0.877645i	$0.659114\pi$
$12$	−0.342214	−0.0987887
$13$	5.91984	1.64187	0.820934	−	0.571023i	$-0.193453\pi$
$13$	5.91984	1.64187	0.820934	+	0.571023i	$0.193453\pi$
$14$	−1.74364	−0.466007
$15$	1.92281	0.496467
$16$	−4.40858	−1.10214
$17$	0.673199	0.163275	0.0816373	−	0.996662i	$-0.473985\pi$
$17$	0.673199	0.163275	0.0816373	+	0.996662i	$0.473985\pi$
$18$	1.20175	0.283254
$19$	4.27963	0.981815	0.490908	−	0.871212i	$-0.336665\pi$
$19$	4.27963	0.981815	0.490908	+	0.871212i	$0.336665\pi$
$20$	−0.299720	−0.0670194
$21$	−1.72970	−0.377451
$22$	4.74887	1.01246
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−3.91510	−0.799166
$25$	−3.31595	−0.663191
$26$	−8.84211	−1.73408
$27$	5.63723	1.08488
$28$	0.269618	0.0509531
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	−2.87199	−0.524350
$31$	4.60616	0.827291	0.413646	−	0.910438i	$-0.364255\pi$
$31$	4.60616	0.827291	0.413646	+	0.910438i	$0.364255\pi$
$32$	1.30022	0.229848
$33$	4.71089	0.820061
$34$	−1.00552	−0.172445
$35$	−1.51491	−0.256067
$36$	−0.185826	−0.0309709
$37$	−6.04113	−0.993155	−0.496578	−	0.867992i	$-0.665410\pi$
$37$	−6.04113	−0.993155	−0.496578	+	0.867992i	$0.665410\pi$
$38$	−6.39223	−1.03696
$39$	−8.77140	−1.40455
$40$	−3.42894	−0.542164
$41$	−4.61201	−0.720275	−0.360138	−	0.932899i	$-0.617270\pi$
$41$	−4.61201	−0.720275	−0.360138	+	0.932899i	$0.617270\pi$
$42$	2.58354	0.398649
$43$	−7.40960	−1.12995	−0.564977	−	0.825107i	$-0.691115\pi$
$43$	−7.40960	−1.12995	−0.564977	+	0.825107i	$0.691115\pi$
$44$	−0.734316	−0.110702
$45$	1.04410	0.155646
$46$	1.49364	0.220225
$47$	0.716847	0.104563	0.0522815	−	0.998632i	$-0.483351\pi$
$47$	0.716847	0.104563	0.0522815	+	0.998632i	$0.483351\pi$
$48$	6.53218	0.942838
$49$	−5.63724	−0.805319
$50$	4.95284	0.700438
$51$	−0.997476	−0.139675
$52$	1.36725	0.189604
$53$	−5.40161	−0.741968	−0.370984	−	0.928639i	$-0.620980\pi$
$53$	−5.40161	−0.741968	−0.370984	+	0.928639i	$0.620980\pi$
$54$	−8.41999	−1.14582
$55$	4.12592	0.556339
$56$	3.08456	0.412192
$57$	−6.34112	−0.839902
$58$	1.49364	0.196125
$59$	−14.4815	−1.88533	−0.942665	−	0.333740i	$-0.891689\pi$
$59$	−14.4815	−1.88533	−0.942665	+	0.333740i	$0.891689\pi$
$60$	0.444094	0.0573323
$61$	−1.19231	−0.152659	−0.0763297	−	0.997083i	$-0.524320\pi$
$61$	−1.19231	−0.152659	−0.0763297	+	0.997083i	$0.524320\pi$
$62$	−6.87995	−0.873755
$63$	−0.939241	−0.118333
$64$	6.87510	0.859388
$65$	−7.68222	−0.952862
$66$	−7.03638	−0.866118
$67$	−6.43036	−0.785594	−0.392797	−	0.919625i	$-0.628492\pi$
$67$	−6.43036	−0.785594	−0.392797	+	0.919625i	$0.628492\pi$
$68$	0.155483	0.0188550
$69$	1.48170	0.178375
$70$	2.26273	0.270448
$71$	−1.33803	−0.158795	−0.0793973	−	0.996843i	$-0.525300\pi$
$71$	−1.33803	−0.158795	−0.0793973	+	0.996843i	$0.525300\pi$
$72$	−2.12594	−0.250544
$73$	1.17657	0.137708	0.0688538	−	0.997627i	$-0.478066\pi$
$73$	1.17657	0.137708	0.0688538	+	0.997627i	$0.478066\pi$
$74$	9.02327	1.04893
$75$	4.91324	0.567332
$76$	0.988429	0.113381
$77$	−3.71154	−0.422969
$78$	13.1013	1.48343
$79$	8.62001	0.969827	0.484913	−	0.874562i	$-0.338851\pi$
$79$	8.62001	0.969827	0.484913	+	0.874562i	$0.338851\pi$
$80$	5.72105	0.639633
$81$	−5.93893	−0.659881
$82$	6.88869	0.760728
$83$	5.29591	0.581302	0.290651	−	0.956829i	$-0.406128\pi$
$83$	5.29591	0.581302	0.290651	+	0.956829i	$0.406128\pi$
$84$	−0.399492	−0.0435882
$85$	−0.873615	−0.0947569
$86$	11.0673	1.19342
$87$	1.48170	0.158855
$88$	−8.40093	−0.895542
$89$	7.45016	0.789715	0.394858	−	0.918742i	$-0.370794\pi$
$89$	7.45016	0.789715	0.394858	+	0.918742i	$0.370794\pi$
$90$	−1.55952	−0.164387
$91$	6.91067	0.724435
$92$	−0.230961	−0.0240794
$93$	−6.82494	−0.707713
$94$	−1.07071	−0.110436
$95$	−5.55371	−0.569799
$96$	−1.92653	−0.196625
$97$	−12.7317	−1.29270	−0.646352	−	0.763039i	$-0.723706\pi$
$97$	−12.7317	−1.29270	−0.646352	+	0.763039i	$0.723706\pi$
$98$	8.42000	0.850549
$99$	2.55806	0.257095
$100$	−0.765856	−0.0765856
$101$	−3.82595	−0.380697	−0.190348	−	0.981717i	$-0.560962\pi$
$101$	−3.82595	−0.380697	−0.190348	+	0.981717i	$0.560962\pi$
$102$	1.48987	0.147519
$103$	−0.148474	−0.0146296	−0.00731481	−	0.999973i	$-0.502328\pi$
$103$	−0.148474	−0.0146296	−0.00731481	+	0.999973i	$0.502328\pi$
$104$	15.6420	1.53383
$105$	2.24464	0.219054
$106$	8.06806	0.783640
$107$	−19.5744	−1.89233	−0.946164	−	0.323688i	$-0.895077\pi$
$107$	−19.5744	−1.89233	−0.946164	+	0.323688i	$0.895077\pi$
$108$	1.30198	0.125283
$109$	−1.96837	−0.188535	−0.0942677	−	0.995547i	$-0.530051\pi$
$109$	−1.96837	−0.188535	−0.0942677	+	0.995547i	$0.530051\pi$
$110$	−6.16264	−0.587585
$111$	8.95112	0.849603
$112$	−5.14647	−0.486295
$113$	−6.59256	−0.620176	−0.310088	−	0.950708i	$-0.600359\pi$
$113$	−6.59256	−0.620176	−0.310088	+	0.950708i	$0.600359\pi$
$114$	9.47135	0.887073
$115$	1.29771	0.121012
$116$	−0.230961	−0.0214442
$117$	−4.76296	−0.440336
$118$	21.6301	1.99122
$119$	0.785875	0.0720411
$120$	5.08065	0.463798
$121$	−0.891471	−0.0810428
$122$	1.78088	0.161233
$123$	6.83360	0.616165
$124$	1.06384	0.0955361
$125$	10.7917	0.965237
$126$	1.40289	0.124979
$127$	15.0960	1.33955	0.669775	−	0.742564i	$-0.266391\pi$
$127$	15.0960	1.33955	0.669775	+	0.742564i	$0.266391\pi$
$128$	−12.8694	−1.13750
$129$	10.9788	0.966628
$130$	11.4745	1.00638
$131$	1.82312	0.159286	0.0796432	−	0.996823i	$-0.474622\pi$
$131$	1.82312	0.159286	0.0796432	+	0.996823i	$0.474622\pi$
$132$	1.08803	0.0947011
$133$	4.99594	0.433203
$134$	9.60465	0.829715
$135$	−7.31547	−0.629616
$136$	1.77880	0.152531
$137$	−13.5349	−1.15636	−0.578181	−	0.815908i	$-0.696237\pi$
$137$	−13.5349	−1.15636	−0.578181	+	0.815908i	$0.696237\pi$
$138$	−2.21312	−0.188393
$139$	16.0080	1.35778	0.678890	−	0.734240i	$-0.262461\pi$
$139$	16.0080	1.35778	0.678890	+	0.734240i	$0.262461\pi$
$140$	−0.349886	−0.0295707
$141$	−1.06215	−0.0894492
$142$	1.99853	0.167713
$143$	−18.8215	−1.57393
$144$	3.54703	0.295586
$145$	1.29771	0.107769
$146$	−1.75738	−0.145442
$147$	8.35267	0.688917
$148$	−1.39527	−0.114690
$149$	−17.6397	−1.44510	−0.722550	−	0.691319i	$-0.757030\pi$
$149$	−17.6397	−1.44510	−0.722550	+	0.691319i	$0.757030\pi$
$150$	−7.33861	−0.599195
$151$	−14.4314	−1.17441	−0.587205	−	0.809438i	$-0.699772\pi$
$151$	−14.4314	−1.17441	−0.587205	+	0.809438i	$0.699772\pi$
$152$	11.3081	0.917209
$153$	−0.541639	−0.0437889
$154$	5.54371	0.446725
$155$	−5.97746	−0.480121
$156$	−2.02585	−0.162198
$157$	2.94676	0.235177	0.117588	−	0.993062i	$-0.462484\pi$
$157$	2.94676	0.235177	0.117588	+	0.993062i	$0.462484\pi$
$158$	−12.8752	−1.02430
$159$	8.00355	0.634723
$160$	−1.68730	−0.133393
$161$	−1.16738	−0.0920020
$162$	8.87063	0.696942
$163$	8.18387	0.641010	0.320505	−	0.947247i	$-0.396147\pi$
$163$	8.18387	0.641010	0.320505	+	0.947247i	$0.396147\pi$
$164$	−1.06520	−0.0831778
$165$	−6.11336	−0.475925
$166$	−7.91019	−0.613950
$167$	9.32371	0.721490	0.360745	−	0.932664i	$-0.382522\pi$
$167$	9.32371	0.721490	0.360745	+	0.932664i	$0.382522\pi$
$168$	−4.57039	−0.352613
$169$	22.0445	1.69573
$170$	1.30487	0.100079
$171$	−3.44329	−0.263315
$172$	−1.71133	−0.130488
$173$	4.04893	0.307835	0.153917	−	0.988084i	$-0.450811\pi$
$173$	4.04893	0.307835	0.153917	+	0.988084i	$0.450811\pi$
$174$	−2.21312	−0.167776
$175$	−3.87096	−0.292617
$176$	14.0166	1.05654
$177$	21.4572	1.61282
$178$	−11.1279	−0.834068
$179$	13.4832	1.00778	0.503892	−	0.863767i	$-0.331901\pi$
$179$	13.4832	1.00778	0.503892	+	0.863767i	$0.331901\pi$
$180$	0.241147	0.0179741
$181$	0.702492	0.0522158	0.0261079	−	0.999659i	$-0.491689\pi$
$181$	0.702492	0.0522158	0.0261079	+	0.999659i	$0.491689\pi$
$182$	−10.3221	−0.765122
$183$	1.76664	0.130594
$184$	−2.64231	−0.194794
$185$	7.83962	0.576380
$186$	10.1940	0.747460
$187$	−2.14036	−0.156519
$188$	0.165564	0.0120750
$189$	6.58076	0.478680
$190$	8.29525	0.601801
$191$	7.39338	0.534966	0.267483	−	0.963563i	$-0.413808\pi$
$191$	7.39338	0.534966	0.267483	+	0.963563i	$0.413808\pi$
$192$	−10.1868	−0.735170
$193$	5.36534	0.386206	0.193103	−	0.981179i	$-0.438145\pi$
$193$	5.36534	0.386206	0.193103	+	0.981179i	$0.438145\pi$
$194$	19.0165	1.36531
$195$	11.3827	0.815134
$196$	−1.30198	−0.0929987
$197$	−8.69682	−0.619623	−0.309811	−	0.950798i	$-0.600266\pi$
$197$	−8.69682	−0.619623	−0.309811	+	0.950798i	$0.600266\pi$
$198$	−3.82082	−0.271534
$199$	17.5435	1.24363	0.621813	−	0.783166i	$-0.286396\pi$
$199$	17.5435	1.24363	0.621813	+	0.783166i	$0.286396\pi$
$200$	−8.76177	−0.619551
$201$	9.52785	0.672042
$202$	5.71460	0.402078
$203$	−1.16738	−0.0819337
$204$	−0.230378	−0.0161297
$205$	5.98505	0.418014
$206$	0.221767	0.0154513
$207$	0.804576	0.0559219
$208$	−26.0981	−1.80958
$209$	−13.6066	−0.941190
$210$	−3.35268	−0.231357
$211$	−25.6156	−1.76345	−0.881724	−	0.471765i	$-0.843617\pi$
$211$	−25.6156	−1.76345	−0.881724	+	0.471765i	$0.843617\pi$
$212$	−1.24756	−0.0856829
$213$	1.98255	0.135842
$214$	29.2371	1.99861
$215$	9.61550	0.655772
$216$	14.8953	1.01350
$217$	5.37712	0.365023
$218$	2.94003	0.199124
$219$	−1.74332	−0.117803
$220$	0.952927	0.0642463
$221$	3.98523	0.268075
$222$	−13.3698	−0.897319
$223$	−22.0659	−1.47764	−0.738819	−	0.673904i	$-0.764616\pi$
$223$	−22.0659	−1.47764	−0.738819	+	0.673904i	$0.764616\pi$
$224$	1.51784	0.101415
$225$	2.66794	0.177862
$226$	9.84691	0.655007
$227$	−11.5046	−0.763584	−0.381792	−	0.924248i	$-0.624693\pi$
$227$	−11.5046	−0.763584	−0.381792	+	0.924248i	$0.624693\pi$
$228$	−1.46455	−0.0969923
$229$	10.0787	0.666016	0.333008	−	0.942924i	$-0.391936\pi$
$229$	10.0787	0.666016	0.333008	+	0.942924i	$0.391936\pi$
$230$	−1.93831	−0.127808
$231$	5.49938	0.361833
$232$	−2.64231	−0.173476
$233$	−24.0981	−1.57872	−0.789359	−	0.613933i	$-0.789587\pi$
$233$	−24.0981	−1.57872	−0.789359	+	0.613933i	$0.789587\pi$
$234$	7.11414	0.465066
$235$	−0.930259	−0.0606834
$236$	−3.34466	−0.217719
$237$	−12.7722	−0.829646
$238$	−1.17382	−0.0760871
$239$	10.9768	0.710032	0.355016	−	0.934860i	$-0.384475\pi$
$239$	10.9768	0.710032	0.355016	+	0.934860i	$0.384475\pi$
$240$	−8.47686	−0.547179
$241$	−19.8940	−1.28149	−0.640744	−	0.767755i	$-0.721374\pi$
$241$	−19.8940	−1.28149	−0.640744	+	0.767755i	$0.721374\pi$
$242$	1.33154	0.0855944
$243$	−8.11198	−0.520384
$244$	−0.275377	−0.0176292
$245$	7.31549	0.467369
$246$	−10.2069	−0.650771
$247$	25.3347	1.61201
$248$	12.1709	0.772853
$249$	−7.84694	−0.497279
$250$	−16.1189	−1.01945
$251$	−16.9216	−1.06808	−0.534041	−	0.845459i	$-0.679327\pi$
$251$	−16.9216	−1.06808	−0.534041	+	0.845459i	$0.679327\pi$
$252$	−0.216928	−0.0136652
$253$	3.17939	0.199887
$254$	−22.5479	−1.41478
$255$	1.29443	0.0810605
$256$	5.47199	0.341999
$257$	−22.8305	−1.42413	−0.712063	−	0.702116i	$-0.752239\pi$
$257$	−22.8305	−1.42413	−0.712063	+	0.702116i	$0.752239\pi$
$258$	−16.3983	−1.02092
$259$	−7.05226	−0.438206
$260$	−1.77429	−0.110037
$261$	0.804576	0.0498020
$262$	−2.72308	−0.168232
$263$	−19.7277	−1.21646	−0.608232	−	0.793760i	$-0.708121\pi$
$263$	−19.7277	−1.21646	−0.608232	+	0.793760i	$0.708121\pi$
$264$	12.4476	0.766099
$265$	7.00971	0.430603
$266$	−7.46213	−0.457533
$267$	−11.0389	−0.675568
$268$	−1.48516	−0.0907208
$269$	27.9021	1.70122	0.850610	−	0.525797i	$-0.176233\pi$
$269$	27.9021	1.70122	0.850610	+	0.525797i	$0.176233\pi$
$270$	10.9267	0.664977
$271$	7.23512	0.439502	0.219751	−	0.975556i	$-0.429476\pi$
$271$	7.23512	0.439502	0.219751	+	0.975556i	$0.429476\pi$
$272$	−2.96785	−0.179952
$273$	−10.2395	−0.619724
$274$	20.2162	1.22131
$275$	10.5427	0.635750
$276$	0.342214	0.0205989
$277$	−11.4780	−0.689649	−0.344824	−	0.938667i	$-0.612062\pi$
$277$	−11.4780	−0.689649	−0.344824	+	0.938667i	$0.612062\pi$
$278$	−23.9102	−1.43404
$279$	−3.70601	−0.221873
$280$	−4.00286	−0.239217
$281$	−15.5703	−0.928845	−0.464422	−	0.885614i	$-0.653738\pi$
$281$	−15.5703	−0.928845	−0.464422	+	0.885614i	$0.653738\pi$
$282$	1.58647	0.0944729
$283$	−30.4249	−1.80857	−0.904286	−	0.426928i	$-0.859596\pi$
$283$	−30.4249	−1.80857	−0.904286	+	0.426928i	$0.859596\pi$
$284$	−0.309032	−0.0183377
$285$	8.22892	0.487439
$286$	28.1125	1.66233
$287$	−5.38395	−0.317804
$288$	−1.04612	−0.0616433
$289$	−16.5468	−0.973341
$290$	−1.93831	−0.113821
$291$	18.8645	1.10585
$292$	0.271743	0.0159025
$293$	−18.5211	−1.08201	−0.541007	−	0.841018i	$-0.681957\pi$
$293$	−18.5211	−1.08201	−0.541007	+	0.841018i	$0.681957\pi$
$294$	−12.4759	−0.727608
$295$	18.7928	1.09416
$296$	−15.9625	−0.927803
$297$	−17.9229	−1.03999
$298$	26.3473	1.52626
$299$	−5.91984	−0.342353
$300$	1.13477	0.0655158
$301$	−8.64978	−0.498565
$302$	21.5553	1.24037
$303$	5.66890	0.325670
$304$	−18.8671	−1.08210
$305$	1.54727	0.0885962
$306$	0.809014	0.0462483
$307$	12.0497	0.687714	0.343857	−	0.939022i	$-0.388266\pi$
$307$	12.0497	0.687714	0.343857	+	0.939022i	$0.388266\pi$
$308$	−0.857222	−0.0488447
$309$	0.219994	0.0125150
$310$	8.92817	0.507086
$311$	20.2843	1.15021	0.575107	−	0.818078i	$-0.304960\pi$
$311$	20.2843	1.15021	0.575107	+	0.818078i	$0.304960\pi$
$312$	−23.1767	−1.31213
$313$	10.7243	0.606171	0.303086	−	0.952963i	$-0.401983\pi$
$313$	10.7243	0.606171	0.303086	+	0.952963i	$0.401983\pi$
$314$	−4.40139	−0.248385
$315$	1.21886	0.0686750
$316$	1.99089	0.111996
$317$	−15.7554	−0.884912	−0.442456	−	0.896790i	$-0.645893\pi$
$317$	−15.7554	−0.884912	−0.442456	+	0.896790i	$0.645893\pi$
$318$	−11.9544	−0.670371
$319$	3.17939	0.178012
$320$	−8.92188	−0.498748
$321$	29.0033	1.61881
$322$	1.74364	0.0971692
$323$	2.88104	0.160306
$324$	−1.37166	−0.0762034
$325$	−19.6299	−1.08887
$326$	−12.2238	−0.677011
$327$	2.91652	0.161284
$328$	−12.1864	−0.672879
$329$	0.836830	0.0461359
$330$	9.13117	0.502654
$331$	−7.42952	−0.408363	−0.204182	−	0.978933i	$-0.565453\pi$
$331$	−7.42952	−0.408363	−0.204182	+	0.978933i	$0.565453\pi$
$332$	1.22315	0.0671291
$333$	4.86054	0.266356
$334$	−13.9263	−0.762011
$335$	8.34473	0.455922
$336$	7.62550	0.416005
$337$	25.5652	1.39263	0.696313	−	0.717738i	$-0.254822\pi$
$337$	25.5652	1.39263	0.696313	+	0.717738i	$0.254822\pi$
$338$	−32.9265	−1.79097
$339$	9.76817	0.530534
$340$	−0.201771	−0.0109426
$341$	−14.6448	−0.793060
$342$	5.14303	0.278103
$343$	−14.7524	−0.796554
$344$	−19.5784	−1.05560
$345$	−1.92281	−0.103521
$346$	−6.04765	−0.325124
$347$	−20.1132	−1.07973	−0.539865	−	0.841751i	$-0.681525\pi$
$347$	−20.1132	−1.07973	−0.539865	+	0.841751i	$0.681525\pi$
$348$	0.342214	0.0183446
$349$	−30.8244	−1.64999	−0.824995	−	0.565140i	$-0.808822\pi$
$349$	−30.8244	−1.64999	−0.824995	+	0.565140i	$0.808822\pi$
$350$	5.78182	0.309052
$351$	33.3715	1.78124
$352$	−4.13389	−0.220337
$353$	24.1070	1.28308	0.641542	−	0.767088i	$-0.278295\pi$
$353$	24.1070	1.28308	0.641542	+	0.767088i	$0.278295\pi$
$354$	−32.0493	−1.70340
$355$	1.73637	0.0921569
$356$	1.72070	0.0911967
$357$	−1.16443	−0.0616281
$358$	−20.1391	−1.06438
$359$	25.8722	1.36548	0.682741	−	0.730660i	$-0.260788\pi$
$359$	25.8722	1.36548	0.682741	+	0.730660i	$0.260788\pi$
$360$	2.75884	0.145404
$361$	−0.684739	−0.0360389
$362$	−1.04927	−0.0551484
$363$	1.32089	0.0693287
$364$	1.59610	0.0836582
$365$	−1.52685	−0.0799189
$366$	−2.63872	−0.137928
$367$	13.7202	0.716187	0.358093	−	0.933686i	$-0.383427\pi$
$367$	13.7202	0.716187	0.358093	+	0.933686i	$0.383427\pi$
$368$	4.40858	0.229813
$369$	3.71071	0.193172
$370$	−11.7096	−0.608752
$371$	−6.30571	−0.327376
$372$	−1.57629	−0.0817271
$373$	0.195827	0.0101395	0.00506977	−	0.999987i	$-0.498386\pi$
$373$	0.195827	0.0101395	0.00506977	+	0.999987i	$0.498386\pi$
$374$	3.19693	0.165309
$375$	−15.9900	−0.825720
$376$	1.89413	0.0976824
$377$	−5.91984	−0.304887
$378$	−9.82928	−0.505564
$379$	2.35901	0.121174	0.0605870	−	0.998163i	$-0.480703\pi$
$379$	2.35901	0.121174	0.0605870	+	0.998163i	$0.480703\pi$
$380$	−1.28269	−0.0658007
$381$	−22.3676	−1.14593
$382$	−11.0431	−0.565012
$383$	34.7167	1.77394	0.886970	−	0.461827i	$-0.152806\pi$
$383$	34.7167	1.77394	0.886970	+	0.461827i	$0.152806\pi$
$384$	19.0685	0.973085
$385$	4.81650	0.245471
$386$	−8.01389	−0.407896
$387$	5.96158	0.303044
$388$	−2.94052	−0.149282
$389$	13.7439	0.696844	0.348422	−	0.937338i	$-0.386718\pi$
$389$	13.7439	0.696844	0.348422	+	0.937338i	$0.386718\pi$
$390$	−17.0017	−0.860914
$391$	−0.673199	−0.0340451
$392$	−14.8953	−0.752327
$393$	−2.70131	−0.136263
$394$	12.9899	0.654423
$395$	−11.1863	−0.562842
$396$	0.590812	0.0296894
$397$	−28.5181	−1.43128	−0.715641	−	0.698468i	$-0.753865\pi$
$397$	−28.5181	−1.43128	−0.715641	+	0.698468i	$0.753865\pi$
$398$	−26.2037	−1.31347
$399$	−7.40246	−0.370587
$400$	14.6186	0.730932
$401$	14.4508	0.721641	0.360820	−	0.932635i	$-0.382497\pi$
$401$	14.4508	0.721641	0.360820	+	0.932635i	$0.382497\pi$
$402$	−14.2312	−0.709786
$403$	27.2677	1.35830
$404$	−0.883646	−0.0439630
$405$	7.70700	0.382964
$406$	1.74364	0.0865353
$407$	19.2071	0.952061
$408$	−2.63564	−0.130484
$409$	16.8600	0.833672	0.416836	−	0.908982i	$-0.363139\pi$
$409$	16.8600	0.833672	0.416836	+	0.908982i	$0.363139\pi$
$410$	−8.93951	−0.441491
$411$	20.0546	0.989219
$412$	−0.0342918	−0.00168944
$413$	−16.9053	−0.831857
$414$	−1.20175	−0.0590626
$415$	−6.87255	−0.337360
$416$	7.69707	0.377380
$417$	−23.7190	−1.16152
$418$	20.3234	0.994050
$419$	35.1048	1.71498	0.857490	−	0.514501i	$-0.172023\pi$
$419$	35.1048	1.71498	0.857490	+	0.514501i	$0.172023\pi$
$420$	0.518424	0.0252965
$421$	−3.37724	−0.164597	−0.0822983	−	0.996608i	$-0.526226\pi$
$421$	−3.37724	−0.164597	−0.0822983	+	0.996608i	$0.526226\pi$
$422$	38.2604	1.86249
$423$	−0.576758	−0.0280429
$424$	−14.2727	−0.693144
$425$	−2.23230	−0.108282
$426$	−2.96122	−0.143471
$427$	−1.39187	−0.0673573
$428$	−4.52092	−0.218527
$429$	27.8877	1.34643
$430$	−14.3621	−0.692602
$431$	−13.1118	−0.631571	−0.315786	−	0.948831i	$-0.602268\pi$
$431$	−13.1118	−0.631571	−0.315786	+	0.948831i	$0.602268\pi$
$432$	−24.8522	−1.19570
$433$	−26.4943	−1.27323	−0.636617	−	0.771180i	$-0.719667\pi$
$433$	−26.4943	−1.27323	−0.636617	+	0.771180i	$0.719667\pi$
$434$	−8.03148	−0.385524
$435$	−1.92281	−0.0921917
$436$	−0.454616	−0.0217722
$437$	−4.27963	−0.204723
$438$	2.60390	0.124419
$439$	13.4177	0.640393	0.320197	−	0.947351i	$-0.396251\pi$
$439$	13.4177	0.640393	0.320197	+	0.947351i	$0.396251\pi$
$440$	10.9020	0.519730
$441$	4.53558	0.215980
$442$	−5.95250	−0.283131
$443$	2.22169	0.105556	0.0527778	−	0.998606i	$-0.483193\pi$
$443$	2.22169	0.105556	0.0527778	+	0.998606i	$0.483193\pi$
$444$	2.06736	0.0981126
$445$	−9.66813	−0.458313
$446$	32.9584	1.56063
$447$	26.1367	1.23622
$448$	8.02582	0.379185
$449$	−14.7380	−0.695527	−0.347764	−	0.937582i	$-0.613059\pi$
$449$	−14.7380	−0.695527	−0.347764	+	0.937582i	$0.613059\pi$
$450$	−3.98494	−0.187852
$451$	14.6634	0.690472
$452$	−1.52262	−0.0716183
$453$	21.3829	1.00466
$454$	17.1837	0.806470
$455$	−8.96803	−0.420428
$456$	−16.7552	−0.784633
$457$	−19.7353	−0.923179	−0.461590	−	0.887094i	$-0.652721\pi$
$457$	−19.7353	−0.923179	−0.461590	+	0.887094i	$0.652721\pi$
$458$	−15.0539	−0.703422
$459$	3.79497	0.177134
$460$	0.299720	0.0139745
$461$	−10.5153	−0.489748	−0.244874	−	0.969555i	$-0.578747\pi$
$461$	−10.5153	−0.489748	−0.244874	+	0.969555i	$0.578747\pi$
$462$	−8.21409	−0.382154
$463$	25.9265	1.20491	0.602453	−	0.798154i	$-0.294190\pi$
$463$	25.9265	1.20491	0.602453	+	0.798154i	$0.294190\pi$
$464$	4.40858	0.204663
$465$	8.85677	0.410723
$466$	35.9938	1.66738
$467$	10.2042	0.472195	0.236098	−	0.971729i	$-0.424131\pi$
$467$	10.2042	0.472195	0.236098	+	0.971729i	$0.424131\pi$
$468$	−1.10006	−0.0508502
$469$	−7.50665	−0.346625
$470$	1.38947	0.0640915
$471$	−4.36620	−0.201184
$472$	−38.2646	−1.76127
$473$	23.5580	1.08320
$474$	19.0771	0.876241
$475$	−14.1911	−0.651131
$476$	0.181507	0.00831934
$477$	4.34600	0.198990
$478$	−16.3954	−0.749910
$479$	26.5594	1.21353	0.606765	−	0.794881i	$-0.292467\pi$
$479$	26.5594	1.21353	0.606765	+	0.794881i	$0.292467\pi$
$480$	2.50007	0.114112
$481$	−35.7625	−1.63063
$482$	29.7145	1.35346
$483$	1.72970	0.0787039
$484$	−0.205895	−0.00935886
$485$	16.5220	0.750224
$486$	12.1164	0.549610
$487$	26.9015	1.21902	0.609511	−	0.792778i	$-0.291366\pi$
$487$	26.9015	1.21902	0.609511	+	0.792778i	$0.291366\pi$
$488$	−3.15044	−0.142614
$489$	−12.1260	−0.548357
$490$	−10.9267	−0.493618
$491$	8.26994	0.373217	0.186609	−	0.982434i	$-0.440250\pi$
$491$	8.26994	0.373217	0.186609	+	0.982434i	$0.440250\pi$
$492$	1.57830	0.0711551
$493$	−0.673199	−0.0303193
$494$	−37.8410	−1.70255
$495$	−3.31962	−0.149206
$496$	−20.3066	−0.911795
$497$	−1.56198	−0.0700644
$498$	11.7205	0.525208
$499$	−13.7870	−0.617192	−0.308596	−	0.951193i	$-0.599859\pi$
$499$	−13.7870	−0.617192	−0.308596	+	0.951193i	$0.599859\pi$
$500$	2.49246	0.111466
$501$	−13.8149	−0.617205
$502$	25.2748	1.12807
$503$	−13.2272	−0.589773	−0.294886	−	0.955532i	$-0.595282\pi$
$503$	−13.2272	−0.589773	−0.294886	+	0.955532i	$0.595282\pi$
$504$	−2.48176	−0.110547
$505$	4.96497	0.220938
$506$	−4.74887	−0.211113
$507$	−32.6632	−1.45063
$508$	3.48658	0.154692
$509$	−6.89753	−0.305728	−0.152864	−	0.988247i	$-0.548850\pi$
$509$	−6.89753	−0.305728	−0.152864	+	0.988247i	$0.548850\pi$
$510$	−1.93342	−0.0856131
$511$	1.37350	0.0607602
$512$	17.5655	0.776295
$513$	24.1253	1.06516
$514$	34.1005	1.50411
$515$	0.192676	0.00849034
$516$	2.53567	0.111627
$517$	−2.27914	−0.100236
$518$	10.5335	0.462817
$519$	−5.99929	−0.263340
$520$	−20.2988	−0.890161
$521$	−28.5349	−1.25013	−0.625067	−	0.780571i	$-0.714929\pi$
$521$	−28.5349	−1.25013	−0.625067	+	0.780571i	$0.714929\pi$
$522$	−1.20175	−0.0525990
$523$	−19.5288	−0.853934	−0.426967	−	0.904267i	$-0.640418\pi$
$523$	−19.5288	−0.853934	−0.426967	+	0.904267i	$0.640418\pi$
$524$	0.421069	0.0183945
$525$	5.73559	0.250322
$526$	29.4661	1.28478
$527$	3.10086	0.135076
$528$	−20.7683	−0.903826
$529$	1.00000	0.0434783
$530$	−10.4700	−0.454787
$531$	11.6515	0.505630
$532$	1.15387	0.0500265
$533$	−27.3024	−1.18260
$534$	16.4881	0.713510
$535$	25.4018	1.09822
$536$	−16.9910	−0.733899
$537$	−19.9780	−0.862116
$538$	−41.6757	−1.79677
$539$	17.9230	0.771997
$540$	−1.68959	−0.0727084
$541$	−40.9453	−1.76037	−0.880187	−	0.474627i	$-0.842583\pi$
$541$	−40.9453	−1.76037	−0.880187	+	0.474627i	$0.842583\pi$
$542$	−10.8067	−0.464186
$543$	−1.04088	−0.0446684
$544$	0.875304	0.0375283
$545$	2.55437	0.109417
$546$	15.2942	0.654529
$547$	4.12171	0.176232	0.0881158	−	0.996110i	$-0.471915\pi$
$547$	4.12171	0.176232	0.0881158	+	0.996110i	$0.471915\pi$
$548$	−3.12603	−0.133537
$549$	0.959301	0.0409420
$550$	−15.7470	−0.671455
$551$	−4.27963	−0.182319
$552$	3.91510	0.166638
$553$	10.0628	0.427913
$554$	17.1441	0.728382
$555$	−11.6159	−0.493069
$556$	3.69723	0.156797
$557$	37.4499	1.58680	0.793401	−	0.608699i	$-0.208308\pi$
$557$	37.4499	1.58680	0.793401	+	0.608699i	$0.208308\pi$
$558$	5.53544	0.234334
$559$	−43.8636	−1.85523
$560$	6.67861	0.282223
$561$	3.17137	0.133895
$562$	23.2564	0.981012
$563$	8.66439	0.365161	0.182580	−	0.983191i	$-0.441555\pi$
$563$	8.66439	0.365161	0.182580	+	0.983191i	$0.441555\pi$
$564$	−0.245315	−0.0103296
$565$	8.55522	0.359921
$566$	45.4438	1.91015
$567$	−6.93296	−0.291157
$568$	−3.53548	−0.148345
$569$	11.7203	0.491340	0.245670	−	0.969354i	$-0.420992\pi$
$569$	11.7203	0.491340	0.245670	+	0.969354i	$0.420992\pi$
$570$	−12.2910	−0.514815
$571$	28.1015	1.17601	0.588006	−	0.808856i	$-0.299913\pi$
$571$	28.1015	1.17601	0.588006	+	0.808856i	$0.299913\pi$
$572$	−4.34703	−0.181758
$573$	−10.9547	−0.457641
$574$	8.04168	0.335653
$575$	3.31595	0.138285
$576$	−5.53154	−0.230481
$577$	8.84892	0.368385	0.184193	−	0.982890i	$-0.441033\pi$
$577$	8.84892	0.368385	0.184193	+	0.982890i	$0.441033\pi$
$578$	24.7150	1.02801
$579$	−7.94980	−0.330383
$580$	0.299720	0.0124452
$581$	6.18232	0.256486
$582$	−28.1767	−1.16796
$583$	17.1738	0.711268
$584$	3.10887	0.128646
$585$	6.18093	0.255550
$586$	27.6639	1.14278
$587$	−13.5003	−0.557217	−0.278608	−	0.960405i	$-0.589873\pi$
$587$	−13.5003	−0.557217	−0.278608	+	0.960405i	$0.589873\pi$
$588$	1.92914	0.0795565
$589$	19.7127	0.812247
$590$	−28.0696	−1.15561
$591$	12.8860	0.530061
$592$	26.6328	1.09460
$593$	44.2407	1.81675	0.908374	−	0.418159i	$-0.137325\pi$
$593$	44.2407	1.81675	0.908374	+	0.418159i	$0.137325\pi$
$594$	26.7704	1.09840
$595$	−1.01984	−0.0418092
$596$	−4.07408	−0.166881
$597$	−25.9942	−1.06387
$598$	8.84211	0.361581
$599$	34.5369	1.41114	0.705569	−	0.708641i	$-0.250691\pi$
$599$	34.5369	1.41114	0.705569	+	0.708641i	$0.250691\pi$
$600$	12.9823	0.530000
$601$	33.0691	1.34892	0.674458	−	0.738313i	$-0.264377\pi$
$601$	33.0691	1.34892	0.674458	+	0.738313i	$0.264377\pi$
$602$	12.9197	0.526566
$603$	5.17371	0.210690
$604$	−3.33309	−0.135622
$605$	1.15687	0.0470334
$606$	−8.46730	−0.343961
$607$	2.62492	0.106542	0.0532711	−	0.998580i	$-0.483035\pi$
$607$	2.62492	0.106542	0.0532711	+	0.998580i	$0.483035\pi$
$608$	5.56445	0.225668
$609$	1.72970	0.0700908
$610$	−2.31106	−0.0935721
$611$	4.24362	0.171679
$612$	−0.125098	−0.00505677
$613$	15.3460	0.619818	0.309909	−	0.950766i	$-0.399701\pi$
$613$	15.3460	0.619818	0.309909	+	0.950766i	$0.399701\pi$
$614$	−17.9980	−0.726338
$615$	−8.86802	−0.357593
$616$	−9.80704	−0.395137
$617$	26.6017	1.07094	0.535472	−	0.844553i	$-0.320134\pi$
$617$	26.6017	1.07094	0.535472	+	0.844553i	$0.320134\pi$
$618$	−0.328592	−0.0132179
$619$	−42.2088	−1.69651	−0.848257	−	0.529585i	$-0.822348\pi$
$619$	−42.2088	−1.69651	−0.848257	+	0.529585i	$0.822348\pi$
$620$	−1.38056	−0.0554446
$621$	−5.63723	−0.226214
$622$	−30.2974	−1.21481
$623$	8.69713	0.348443
$624$	38.6694	1.54802
$625$	2.57532	0.103013
$626$	−16.0182	−0.640215
$627$	20.1609	0.805149
$628$	0.680586	0.0271583
$629$	−4.06688	−0.162157
$630$	−1.82054	−0.0725320
$631$	−6.27960	−0.249987	−0.124993	−	0.992158i	$-0.539891\pi$
$631$	−6.27960	−0.249987	−0.124993	+	0.992158i	$0.539891\pi$
$632$	22.7767	0.906009
$633$	37.9545	1.50856
$634$	23.5329	0.934611
$635$	−19.5901	−0.777411
$636$	1.84851	0.0732981
$637$	−33.3715	−1.32223
$638$	−4.74887	−0.188009
$639$	1.07654	0.0425874
$640$	16.7007	0.660152
$641$	13.1279	0.518523	0.259261	−	0.965807i	$-0.416521\pi$
$641$	13.1279	0.518523	0.259261	+	0.965807i	$0.416521\pi$
$642$	−43.3205	−1.70972
$643$	−26.4084	−1.04144	−0.520722	−	0.853726i	$-0.674337\pi$
$643$	−26.4084	−1.04144	−0.520722	+	0.853726i	$0.674337\pi$
$644$	−0.269618	−0.0106244
$645$	−14.2472	−0.560985
$646$	−4.30324	−0.169309
$647$	5.46033	0.214668	0.107334	−	0.994223i	$-0.465769\pi$
$647$	5.46033	0.214668	0.107334	+	0.994223i	$0.465769\pi$
$648$	−15.6925	−0.616459
$649$	46.0423	1.80732
$650$	29.3200	1.15003
$651$	−7.96726	−0.312262
$652$	1.89016	0.0740242
$653$	1.85055	0.0724178	0.0362089	−	0.999344i	$-0.488472\pi$
$653$	1.85055	0.0724178	0.0362089	+	0.999344i	$0.488472\pi$
$654$	−4.35624	−0.170342
$655$	−2.36587	−0.0924423
$656$	20.3324	0.793848
$657$	−0.946642	−0.0369320
$658$	−1.24992	−0.0487271
$659$	1.58855	0.0618811	0.0309406	−	0.999521i	$-0.490150\pi$
$659$	1.58855	0.0618811	0.0309406	+	0.999521i	$0.490150\pi$
$660$	−1.41195	−0.0549600
$661$	−46.2763	−1.79994	−0.899969	−	0.435954i	$-0.856411\pi$
$661$	−46.2763	−1.79994	−0.899969	+	0.435954i	$0.856411\pi$
$662$	11.0970	0.431298
$663$	−5.90490	−0.229327
$664$	13.9934	0.543050
$665$	−6.48327	−0.251410
$666$	−7.25990	−0.281316
$667$	1.00000	0.0387202
$668$	2.15341	0.0833181
$669$	32.6949	1.26406
$670$	−12.4640	−0.481527
$671$	3.79081	0.146343
$672$	−2.24898	−0.0867562
$673$	35.5308	1.36961	0.684806	−	0.728725i	$-0.259887\pi$
$673$	35.5308	1.36961	0.684806	+	0.728725i	$0.259887\pi$
$674$	−38.1852	−1.47084
$675$	−18.6928	−0.719486
$676$	5.09142	0.195824
$677$	−37.5636	−1.44369	−0.721844	−	0.692056i	$-0.756705\pi$
$677$	−37.5636	−1.44369	−0.721844	+	0.692056i	$0.756705\pi$
$678$	−14.5901	−0.560331
$679$	−14.8626	−0.570375
$680$	−2.30836	−0.0885216
$681$	17.0463	0.653214
$682$	21.8741	0.837601
$683$	0.622046	0.0238019	0.0119010	−	0.999929i	$-0.496212\pi$
$683$	0.622046	0.0238019	0.0119010	+	0.999929i	$0.496212\pi$
$684$	−0.795266	−0.0304077
$685$	17.5643	0.671098
$686$	22.0348	0.841291
$687$	−14.9335	−0.569749
$688$	32.6658	1.24537
$689$	−31.9767	−1.21821
$690$	2.87199	0.109335
$691$	32.5967	1.24004	0.620018	−	0.784588i	$-0.287125\pi$
$691$	32.5967	1.24004	0.620018	+	0.784588i	$0.287125\pi$
$692$	0.935146	0.0355489
$693$	2.98622	0.113437
$694$	30.0418	1.14037
$695$	−20.7737	−0.787992
$696$	3.91510	0.148401
$697$	−3.10480	−0.117603
$698$	46.0405	1.74266
$699$	35.7060	1.35053
$700$	−0.894042	−0.0337916
$701$	−24.8747	−0.939503	−0.469752	−	0.882799i	$-0.655657\pi$
$701$	−24.8747	−0.939503	−0.469752	+	0.882799i	$0.655657\pi$
$702$	−49.8450	−1.88128
$703$	−25.8538	−0.975095
$704$	−21.8586	−0.823829
$705$	1.37836	0.0519121
$706$	−36.0071	−1.35515
$707$	−4.46632	−0.167973
$708$	4.95577	0.186249
$709$	−4.90817	−0.184330	−0.0921651	−	0.995744i	$-0.529379\pi$
$709$	−4.90817	−0.184330	−0.0921651	+	0.995744i	$0.529379\pi$
$710$	−2.59351	−0.0973327
$711$	−6.93545	−0.260100
$712$	19.6856	0.737749
$713$	−4.60616	−0.172502
$714$	1.73924	0.0650893
$715$	24.4248	0.913435
$716$	3.11410	0.116379
$717$	−16.2643	−0.607403
$718$	−38.6438	−1.44217
$719$	19.4339	0.724764	0.362382	−	0.932030i	$-0.381964\pi$
$719$	19.4339	0.724764	0.362382	+	0.932030i	$0.381964\pi$
$720$	−4.60302	−0.171544
$721$	−0.173325	−0.00645497
$722$	1.02275	0.0380629
$723$	29.4769	1.09626
$724$	0.162248	0.00602991
$725$	3.31595	0.123151
$726$	−1.97293	−0.0732224
$727$	−20.6999	−0.767716	−0.383858	−	0.923392i	$-0.625405\pi$
$727$	−20.6999	−0.767716	−0.383858	+	0.923392i	$0.625405\pi$
$728$	18.2601	0.676765
$729$	29.8363	1.10505
$730$	2.28056	0.0844074
$731$	−4.98813	−0.184493
$732$	0.408025	0.0150810
$733$	22.3559	0.825733	0.412866	−	0.910792i	$-0.364528\pi$
$733$	22.3559	0.825733	0.412866	+	0.910792i	$0.364528\pi$
$734$	−20.4930	−0.756410
$735$	−10.8393	−0.399815
$736$	−1.30022	−0.0479266
$737$	20.4446	0.753088
$738$	−5.54247	−0.204021
$739$	−12.9550	−0.476557	−0.238279	−	0.971197i	$-0.576583\pi$
$739$	−12.9550	−0.476557	−0.238279	+	0.971197i	$0.576583\pi$
$740$	1.81065	0.0665607
$741$	−37.5384	−1.37901
$742$	9.41846	0.345762
$743$	39.6828	1.45582	0.727911	−	0.685672i	$-0.240492\pi$
$743$	39.6828	1.45582	0.727911	+	0.685672i	$0.240492\pi$
$744$	−18.0336	−0.661143
$745$	22.8912	0.838667
$746$	−0.292495	−0.0107090
$747$	−4.26096	−0.155900
$748$	−0.494340	−0.0180749
$749$	−22.8507	−0.834945
$750$	23.8833	0.872095
$751$	5.79396	0.211425	0.105712	−	0.994397i	$-0.466288\pi$
$751$	5.79396	0.211425	0.105712	+	0.994397i	$0.466288\pi$
$752$	−3.16028	−0.115243
$753$	25.0727	0.913699
$754$	8.84211	0.322011
$755$	18.7277	0.681572
$756$	1.51990	0.0552782
$757$	24.7251	0.898650	0.449325	−	0.893368i	$-0.351664\pi$
$757$	24.7251	0.898650	0.449325	+	0.893368i	$0.351664\pi$
$758$	−3.52351	−0.127979
$759$	−4.71089	−0.170995
$760$	−14.6746	−0.532304
$761$	−42.7364	−1.54919	−0.774597	−	0.632455i	$-0.782047\pi$
$761$	−42.7364	−1.54919	−0.774597	+	0.632455i	$0.782047\pi$
$762$	33.4092	1.21029
$763$	−2.29782	−0.0831868
$764$	1.70758	0.0617782
$765$	0.702890	0.0254130
$766$	−51.8543	−1.87357
$767$	−85.7281	−3.09546
$768$	−8.10783	−0.292566
$769$	33.7548	1.21723	0.608614	−	0.793466i	$-0.291726\pi$
$769$	33.7548	1.21723	0.608614	+	0.793466i	$0.291726\pi$
$770$	−7.19411	−0.259258
$771$	33.8278	1.21828
$772$	1.23918	0.0445992
$773$	24.1705	0.869351	0.434675	−	0.900587i	$-0.356863\pi$
$773$	24.1705	0.869351	0.434675	+	0.900587i	$0.356863\pi$
$774$	−8.90446	−0.320064
$775$	−15.2738	−0.548652
$776$	−33.6410	−1.20764
$777$	10.4493	0.374867
$778$	−20.5285	−0.735981
$779$	−19.7377	−0.707177
$780$	2.62897	0.0941321
$781$	4.25411	0.152224
$782$	1.00552	0.0359572
$783$	−5.63723	−0.201458
$784$	24.8522	0.887579
$785$	−3.82403	−0.136485
$786$	4.03478	0.143916
$787$	8.33952	0.297272	0.148636	−	0.988892i	$-0.452512\pi$
$787$	8.33952	0.297272	0.148636	+	0.988892i	$0.452512\pi$
$788$	−2.00863	−0.0715544
$789$	29.2305	1.04063
$790$	16.7082	0.594452
$791$	−7.69599	−0.273638
$792$	6.75918	0.240177
$793$	−7.05827	−0.250646
$794$	42.5958	1.51167
$795$	−10.3863	−0.368363
$796$	4.05187	0.143615
$797$	−55.2888	−1.95843	−0.979215	−	0.202823i	$-0.934988\pi$
$797$	−55.2888	−1.95843	−0.979215	+	0.202823i	$0.934988\pi$
$798$	11.0566	0.391400
$799$	0.482581	0.0170725
$800$	−4.31146	−0.152433
$801$	−5.99421	−0.211795
$802$	−21.5844	−0.762170
$803$	−3.74079	−0.132010
$804$	2.20056	0.0776078
$805$	1.51491	0.0533936
$806$	−40.7282	−1.43459
$807$	−41.3424	−1.45532
$808$	−10.1093	−0.355646
$809$	−18.5304	−0.651493	−0.325746	−	0.945457i	$-0.605616\pi$
$809$	−18.5304	−0.651493	−0.325746	+	0.945457i	$0.605616\pi$
$810$	−11.5115	−0.404472
$811$	−26.2679	−0.922392	−0.461196	−	0.887298i	$-0.652579\pi$
$811$	−26.2679	−0.922392	−0.461196	+	0.887298i	$0.652579\pi$
$812$	−0.269618	−0.00946174
$813$	−10.7202	−0.375975
$814$	−28.6885	−1.00553
$815$	−10.6203	−0.372012
$816$	4.39745	0.153942
$817$	−31.7104	−1.10941
$818$	−25.1827	−0.880493
$819$	−5.56016	−0.194288
$820$	1.38231	0.0482725
$821$	6.75231	0.235657	0.117829	−	0.993034i	$-0.462407\pi$
$821$	6.75231	0.235657	0.117829	+	0.993034i	$0.462407\pi$
$822$	−29.9543	−1.04478
$823$	1.23489	0.0430456	0.0215228	−	0.999768i	$-0.493149\pi$
$823$	1.23489	0.0430456	0.0215228	+	0.999768i	$0.493149\pi$
$824$	−0.392315	−0.0136669
$825$	−15.6211	−0.543857
$826$	25.2505	0.878577
$827$	52.1426	1.81317	0.906587	−	0.422019i	$-0.138678\pi$
$827$	52.1426	1.81317	0.906587	+	0.422019i	$0.138678\pi$
$828$	0.185826	0.00645789
$829$	−10.7504	−0.373378	−0.186689	−	0.982419i	$-0.559776\pi$
$829$	−10.7504	−0.373378	−0.186689	+	0.982419i	$0.559776\pi$
$830$	10.2651	0.356307
$831$	17.0070	0.589965
$832$	40.6995	1.41100
$833$	−3.79498	−0.131488
$834$	35.4277	1.22676
$835$	−12.0995	−0.418719
$836$	−3.14260	−0.108689
$837$	25.9660	0.897516
$838$	−52.4339	−1.81130
$839$	−18.5402	−0.640080	−0.320040	−	0.947404i	$-0.603696\pi$
$839$	−18.5402	−0.640080	−0.320040	+	0.947404i	$0.603696\pi$
$840$	5.93103	0.204640
$841$	1.00000	0.0344828
$842$	5.04438	0.173841
$843$	23.0704	0.794588
$844$	−5.91620	−0.203644
$845$	−28.6073	−0.984122
$846$	0.861469	0.0296179
$847$	−1.04068	−0.0357582
$848$	23.8134	0.817756
$849$	45.0804	1.54716
$850$	3.33425	0.114364
$851$	6.04113	0.207087
$852$	0.457892	0.0156871
$853$	−35.0039	−1.19851	−0.599255	−	0.800558i	$-0.704536\pi$
$853$	−35.0039	−1.19851	−0.599255	+	0.800558i	$0.704536\pi$
$854$	2.07895	0.0711403
$855$	4.46838	0.152815
$856$	−51.7216	−1.76781
$857$	−2.86356	−0.0978175	−0.0489087	−	0.998803i	$-0.515574\pi$
$857$	−2.86356	−0.0978175	−0.0489087	+	0.998803i	$0.515574\pi$
$858$	−41.6542	−1.42205
$859$	−26.7373	−0.912264	−0.456132	−	0.889912i	$-0.650765\pi$
$859$	−26.7373	−0.912264	−0.456132	+	0.889912i	$0.650765\pi$
$860$	2.22081	0.0757288
$861$	7.97738	0.271868
$862$	19.5843	0.667042
$863$	12.5154	0.426030	0.213015	−	0.977049i	$-0.431672\pi$
$863$	12.5154	0.426030	0.213015	+	0.977049i	$0.431672\pi$
$864$	7.32961	0.249358
$865$	−5.25433	−0.178653
$866$	39.5730	1.34474
$867$	24.5173	0.832653
$868$	1.24191	0.0421530
$869$	−27.4064	−0.929698
$870$	2.87199	0.0973694
$871$	−38.0667	−1.28984
$872$	−5.20103	−0.176129
$873$	10.2436	0.346693
$874$	6.39223	0.216220
$875$	12.5979	0.425888
$876$	−0.402640	−0.0136040
$877$	31.5123	1.06410	0.532048	−	0.846714i	$-0.321423\pi$
$877$	31.5123	1.06410	0.532048	+	0.846714i	$0.321423\pi$
$878$	−20.0413	−0.676360
$879$	27.4427	0.925618
$880$	−18.1895	−0.613166
$881$	−7.76763	−0.261698	−0.130849	−	0.991402i	$-0.541770\pi$
$881$	−7.76763	−0.261698	−0.130849	+	0.991402i	$0.541770\pi$
$882$	−6.77453	−0.228110
$883$	−4.92453	−0.165724	−0.0828618	−	0.996561i	$-0.526406\pi$
$883$	−4.92453	−0.165724	−0.0828618	+	0.996561i	$0.526406\pi$
$884$	0.920433	0.0309575
$885$	−27.8452	−0.936005
$886$	−3.31840	−0.111484
$887$	13.5530	0.455065	0.227533	−	0.973770i	$-0.426934\pi$
$887$	13.5530	0.455065	0.227533	+	0.973770i	$0.426934\pi$
$888$	23.6516	0.793696
$889$	17.6226	0.591045
$890$	14.4407	0.484054
$891$	18.8822	0.632577
$892$	−5.09635	−0.170639
$893$	3.06784	0.102661
$894$	−39.0388	−1.30565
$895$	−17.4973	−0.584870
$896$	−15.0234	−0.501896
$897$	8.77140	0.292869
$898$	22.0132	0.734590
$899$	−4.60616	−0.153624
$900$	0.616189	0.0205396
$901$	−3.63636	−0.121145
$902$	−21.9018	−0.729251
$903$	12.8164	0.426502
$904$	−17.4196	−0.579366
$905$	−0.911629	−0.0303036
$906$	−31.9384	−1.06108
$907$	−42.4399	−1.40919	−0.704596	−	0.709608i	$-0.748872\pi$
$907$	−42.4399	−1.40919	−0.704596	+	0.709608i	$0.748872\pi$
$908$	−2.65710	−0.0881791
$909$	3.07827	0.102100
$910$	13.3950	0.444040
$911$	1.59129	0.0527218	0.0263609	−	0.999652i	$-0.491608\pi$
$911$	1.59129	0.0527218	0.0263609	+	0.999652i	$0.491608\pi$
$912$	27.9553	0.925693
$913$	−16.8378	−0.557249
$914$	29.4775	0.975028
$915$	−2.29258	−0.0757903
$916$	2.32778	0.0769119
$917$	2.12826	0.0702814
$918$	−5.66833	−0.187083
$919$	−43.1546	−1.42354	−0.711769	−	0.702413i	$-0.752106\pi$
$919$	−43.1546	−1.42354	−0.711769	+	0.702413i	$0.752106\pi$
$920$	3.42894	0.113049
$921$	−17.8540	−0.588311
$922$	15.7061	0.517254
$923$	−7.92091	−0.260720
$924$	1.27014	0.0417846
$925$	20.0321	0.658652
$926$	−38.7248	−1.27258
$927$	0.119459	0.00392355
$928$	−1.30022	−0.0426817
$929$	38.4049	1.26002	0.630012	−	0.776586i	$-0.283050\pi$
$929$	38.4049	1.26002	0.630012	+	0.776586i	$0.283050\pi$
$930$	−13.2288	−0.433791
$931$	−24.1253	−0.790675
$932$	−5.56572	−0.182311
$933$	−30.0551	−0.983960
$934$	−15.2414	−0.498715
$935$	2.77757	0.0908361
$936$	−12.5852	−0.411360
$937$	18.1261	0.592152	0.296076	−	0.955164i	$-0.404322\pi$
$937$	18.1261	0.592152	0.296076	+	0.955164i	$0.404322\pi$
$938$	11.2122	0.366092
$939$	−15.8901	−0.518554
$940$	−0.214854	−0.00700775
$941$	3.54619	0.115603	0.0578013	−	0.998328i	$-0.481591\pi$
$941$	3.54619	0.115603	0.0578013	+	0.998328i	$0.481591\pi$
$942$	6.52153	0.212483
$943$	4.61201	0.150188
$944$	63.8428	2.07791
$945$	−8.53990	−0.277803
$946$	−35.1872	−1.14403
$947$	−25.0690	−0.814633	−0.407317	−	0.913287i	$-0.633535\pi$
$947$	−25.0690	−0.814633	−0.407317	+	0.913287i	$0.633535\pi$
$948$	−2.94989	−0.0958080
$949$	6.96513	0.226098
$950$	21.1963	0.687700
$951$	23.3447	0.757005
$952$	2.07652	0.0673006
$953$	15.3654	0.497734	0.248867	−	0.968538i	$-0.419942\pi$
$953$	15.3654	0.497734	0.248867	+	0.968538i	$0.419942\pi$
$954$	−6.49137	−0.210166
$955$	−9.59445	−0.310469
$956$	2.53522	0.0819949
$957$	−4.71089	−0.152282
$958$	−39.6702	−1.28169
$959$	−15.8003	−0.510217
$960$	13.2195	0.426658
$961$	−9.78326	−0.315589
$962$	53.4163	1.72221
$963$	15.7491	0.507507
$964$	−4.59475	−0.147987
$965$	−6.96264	−0.224135
$966$	−2.58354	−0.0831241
$967$	−33.5070	−1.07751	−0.538756	−	0.842462i	$-0.681106\pi$
$967$	−33.5070	−1.07751	−0.538756	+	0.842462i	$0.681106\pi$
$968$	−2.35554	−0.0757099
$969$	−4.26883	−0.137135
$970$	−24.6779	−0.792359
$971$	−41.9681	−1.34682	−0.673410	−	0.739269i	$-0.735171\pi$
$971$	−41.9681	−1.34682	−0.673410	+	0.739269i	$0.735171\pi$
$972$	−1.87355	−0.0600942
$973$	18.6873	0.599089
$974$	−40.1811	−1.28749
$975$	29.0856	0.931484
$976$	5.25638	0.168253
$977$	34.6346	1.10806	0.554029	−	0.832497i	$-0.313090\pi$
$977$	34.6346	1.10806	0.554029	+	0.832497i	$0.313090\pi$
$978$	18.1119	0.579155
$979$	−23.6870	−0.757039
$980$	1.68959	0.0539721
$981$	1.58370	0.0505637
$982$	−12.3523	−0.394178
$983$	−38.4569	−1.22658	−0.613292	−	0.789856i	$-0.710155\pi$
$983$	−38.4569	−1.22658	−0.613292	+	0.789856i	$0.710155\pi$
$984$	18.0565	0.575620
$985$	11.2859	0.359600
$986$	1.00552	0.0320222
$987$	−1.23993	−0.0394673
$988$	5.85134	0.186156
$989$	7.40960	0.235612
$990$	4.95831	0.157585
$991$	40.8327	1.29709	0.648546	−	0.761175i	$-0.275377\pi$
$991$	40.8327	1.29709	0.648546	+	0.761175i	$0.275377\pi$
$992$	5.98901	0.190151
$993$	11.0083	0.349337
$994$	2.33304	0.0739994
$995$	−22.7663	−0.721742
$996$	−1.81234	−0.0574261
$997$	49.1008	1.55504	0.777518	−	0.628860i	$-0.216478\pi$
$997$	49.1008	1.55504	0.777518	+	0.628860i	$0.216478\pi$
$998$	20.5929	0.651856
$999$	−34.0552	−1.07746

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	667.2.a.b.1.4	✓	12
3.2	odd	2		6003.2.a.n.1.9		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
667.2.a.b.1.4	✓	12	1.1	even	1	trivial
6003.2.a.n.1.9		12	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)

\(f(q)\)	\(=\)	\(q-1.49364 q^{2} -1.48170 q^{3} +0.230961 q^{4} -1.29771 q^{5} +2.21312 q^{6} +1.16738 q^{7} +2.64231 q^{8} -0.804576 q^{9} +O(q^{10})\)	\(q-1.49364 q^{2} -1.48170 q^{3} +0.230961 q^{4} -1.29771 q^{5} +2.21312 q^{6} +1.16738 q^{7} +2.64231 q^{8} -0.804576 q^{9} +1.93831 q^{10} -3.17939 q^{11} -0.342214 q^{12} +5.91984 q^{13} -1.74364 q^{14} +1.92281 q^{15} -4.40858 q^{16} +0.673199 q^{17} +1.20175 q^{18} +4.27963 q^{19} -0.299720 q^{20} -1.72970 q^{21} +4.74887 q^{22} -1.00000 q^{23} -3.91510 q^{24} -3.31595 q^{25} -8.84211 q^{26} +5.63723 q^{27} +0.269618 q^{28} -1.00000 q^{29} -2.87199 q^{30} +4.60616 q^{31} +1.30022 q^{32} +4.71089 q^{33} -1.00552 q^{34} -1.51491 q^{35} -0.185826 q^{36} -6.04113 q^{37} -6.39223 q^{38} -8.77140 q^{39} -3.42894 q^{40} -4.61201 q^{41} +2.58354 q^{42} -7.40960 q^{43} -0.734316 q^{44} +1.04410 q^{45} +1.49364 q^{46} +0.716847 q^{47} +6.53218 q^{48} -5.63724 q^{49} +4.95284 q^{50} -0.997476 q^{51} +1.36725 q^{52} -5.40161 q^{53} -8.41999 q^{54} +4.12592 q^{55} +3.08456 q^{56} -6.34112 q^{57} +1.49364 q^{58} -14.4815 q^{59} +0.444094 q^{60} -1.19231 q^{61} -6.87995 q^{62} -0.939241 q^{63} +6.87510 q^{64} -7.68222 q^{65} -7.03638 q^{66} -6.43036 q^{67} +0.155483 q^{68} +1.48170 q^{69} +2.26273 q^{70} -1.33803 q^{71} -2.12594 q^{72} +1.17657 q^{73} +9.02327 q^{74} +4.91324 q^{75} +0.988429 q^{76} -3.71154 q^{77} +13.1013 q^{78} +8.62001 q^{79} +5.72105 q^{80} -5.93893 q^{81} +6.88869 q^{82} +5.29591 q^{83} -0.399492 q^{84} -0.873615 q^{85} +11.0673 q^{86} +1.48170 q^{87} -8.40093 q^{88} +7.45016 q^{89} -1.55952 q^{90} +6.91067 q^{91} -0.230961 q^{92} -6.82494 q^{93} -1.07071 q^{94} -5.55371 q^{95} -1.92653 q^{96} -12.7317 q^{97} +8.42000 q^{98} +2.55806 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{2} - 3 q^{3} + 11 q^{4} - 16 q^{5} - 2 q^{6} - 7 q^{7} - 9 q^{8} + 3 q^{9}+O(q^{10}) \) 12 * q - 3 * q^2 - 3 * q^3 + 11 * q^4 - 16 * q^5 - 2 * q^6 - 7 * q^7 - 9 * q^8 + 3 * q^9	\( 12 q - 3 q^{2} - 3 q^{3} + 11 q^{4} - 16 q^{5} - 2 q^{6} - 7 q^{7} - 9 q^{8} + 3 q^{9} - 6 q^{11} - 21 q^{12} - 15 q^{13} - 8 q^{14} + 6 q^{15} + 17 q^{16} - 18 q^{17} - 12 q^{18} - 6 q^{19} - 39 q^{20} - q^{21} - 5 q^{22} - 12 q^{23} + 4 q^{24} + 14 q^{25} - 3 q^{26} - 12 q^{27} - 19 q^{28} - 12 q^{29} - 11 q^{30} + 16 q^{31} - 21 q^{32} - 19 q^{33} - 7 q^{34} - 11 q^{35} - 13 q^{36} - q^{37} - 24 q^{38} + 6 q^{39} + 30 q^{40} + 3 q^{41} + 22 q^{42} - 23 q^{43} + 23 q^{44} - 22 q^{45} + 3 q^{46} - 35 q^{47} - 21 q^{48} + 3 q^{49} - 2 q^{50} - 34 q^{51} - 45 q^{53} + 55 q^{54} + 17 q^{55} - 17 q^{56} - 34 q^{57} + 3 q^{58} - 11 q^{59} + 93 q^{60} + 4 q^{61} - 7 q^{62} + q^{63} + 15 q^{64} + 5 q^{65} - 35 q^{66} - 19 q^{67} + q^{68} + 3 q^{69} + 14 q^{70} + 19 q^{71} + 4 q^{72} + 10 q^{73} - 15 q^{74} - 3 q^{75} - 4 q^{76} - 39 q^{77} + 16 q^{78} + 17 q^{79} - 90 q^{80} + 4 q^{81} - 3 q^{82} - 12 q^{83} + 42 q^{84} + 14 q^{85} + 17 q^{86} + 3 q^{87} - 2 q^{88} - 20 q^{89} + 65 q^{90} + 11 q^{91} - 11 q^{92} - 2 q^{93} + 13 q^{94} + 12 q^{95} + 14 q^{96} - 12 q^{97} + 75 q^{98} - 4 q^{99}+O(q^{100}) \) 12 * q - 3 * q^2 - 3 * q^3 + 11 * q^4 - 16 * q^5 - 2 * q^6 - 7 * q^7 - 9 * q^8 + 3 * q^9 - 6 * q^11 - 21 * q^12 - 15 * q^13 - 8 * q^14 + 6 * q^15 + 17 * q^16 - 18 * q^17 - 12 * q^18 - 6 * q^19 - 39 * q^20 - q^21 - 5 * q^22 - 12 * q^23 + 4 * q^24 + 14 * q^25 - 3 * q^26 - 12 * q^27 - 19 * q^28 - 12 * q^29 - 11 * q^30 + 16 * q^31 - 21 * q^32 - 19 * q^33 - 7 * q^34 - 11 * q^35 - 13 * q^36 - q^37 - 24 * q^38 + 6 * q^39 + 30 * q^40 + 3 * q^41 + 22 * q^42 - 23 * q^43 + 23 * q^44 - 22 * q^45 + 3 * q^46 - 35 * q^47 - 21 * q^48 + 3 * q^49 - 2 * q^50 - 34 * q^51 - 45 * q^53 + 55 * q^54 + 17 * q^55 - 17 * q^56 - 34 * q^57 + 3 * q^58 - 11 * q^59 + 93 * q^60 + 4 * q^61 - 7 * q^62 + q^63 + 15 * q^64 + 5 * q^65 - 35 * q^66 - 19 * q^67 + q^68 + 3 * q^69 + 14 * q^70 + 19 * q^71 + 4 * q^72 + 10 * q^73 - 15 * q^74 - 3 * q^75 - 4 * q^76 - 39 * q^77 + 16 * q^78 + 17 * q^79 - 90 * q^80 + 4 * q^81 - 3 * q^82 - 12 * q^83 + 42 * q^84 + 14 * q^85 + 17 * q^86 + 3 * q^87 - 2 * q^88 - 20 * q^89 + 65 * q^90 + 11 * q^91 - 11 * q^92 - 2 * q^93 + 13 * q^94 + 12 * q^95 + 14 * q^96 - 12 * q^97 + 75 * q^98 - 4 * q^99

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