LMFDB - Embedded newform 4009.2.a.c.1.57

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4009,2,Mod(1,4009)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4009, 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("4009.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4009 = 19 \cdot 211 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4009.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:	$32.0120261703$
Analytic rank:	$1$
Dimension:	$71$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.57
Character	$\chi$	$=$	4009.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.47232 q^{2} +1.80615 q^{3} +0.167717 q^{4} -0.960908 q^{5} +2.65923 q^{6} -2.43987 q^{7} -2.69770 q^{8} +0.262192 q^{9} +O(q^{10})$	\(q+1.47232 q^{2} +1.80615 q^{3} +0.167717 q^{4} -0.960908 q^{5} +2.65923 q^{6} -2.43987 q^{7} -2.69770 q^{8} +0.262192 q^{9} -1.41476 q^{10} +5.44391 q^{11} +0.302923 q^{12} +2.57127 q^{13} -3.59226 q^{14} -1.73555 q^{15} -4.30731 q^{16} -6.76960 q^{17} +0.386029 q^{18} +1.00000 q^{19} -0.161161 q^{20} -4.40677 q^{21} +8.01516 q^{22} -0.962127 q^{23} -4.87246 q^{24} -4.07666 q^{25} +3.78573 q^{26} -4.94490 q^{27} -0.409207 q^{28} +2.70832 q^{29} -2.55528 q^{30} +1.24744 q^{31} -0.946316 q^{32} +9.83254 q^{33} -9.96700 q^{34} +2.34449 q^{35} +0.0439740 q^{36} -7.27123 q^{37} +1.47232 q^{38} +4.64411 q^{39} +2.59224 q^{40} -11.7087 q^{41} -6.48817 q^{42} +3.48905 q^{43} +0.913036 q^{44} -0.251942 q^{45} -1.41656 q^{46} -8.25004 q^{47} -7.77966 q^{48} -1.04706 q^{49} -6.00213 q^{50} -12.2269 q^{51} +0.431246 q^{52} +5.95700 q^{53} -7.28046 q^{54} -5.23110 q^{55} +6.58203 q^{56} +1.80615 q^{57} +3.98750 q^{58} -7.46552 q^{59} -0.291081 q^{60} +4.94471 q^{61} +1.83662 q^{62} -0.639713 q^{63} +7.22133 q^{64} -2.47076 q^{65} +14.4766 q^{66} -1.94823 q^{67} -1.13538 q^{68} -1.73775 q^{69} +3.45183 q^{70} -8.99743 q^{71} -0.707315 q^{72} -0.277878 q^{73} -10.7056 q^{74} -7.36307 q^{75} +0.167717 q^{76} -13.2824 q^{77} +6.83761 q^{78} -4.10087 q^{79} +4.13892 q^{80} -9.71783 q^{81} -17.2389 q^{82} +11.0621 q^{83} -0.739091 q^{84} +6.50497 q^{85} +5.13699 q^{86} +4.89164 q^{87} -14.6860 q^{88} -11.0863 q^{89} -0.370939 q^{90} -6.27356 q^{91} -0.161365 q^{92} +2.25306 q^{93} -12.1467 q^{94} -0.960908 q^{95} -1.70919 q^{96} -6.97622 q^{97} -1.54160 q^{98} +1.42735 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 71 q - 15 q^{2} - 8 q^{3} + 69 q^{4} - 18 q^{5} - 9 q^{6} - 19 q^{7} - 39 q^{8} + 63 q^{9}+O(q^{10}) $ 71 * q - 15 * q^2 - 8 * q^3 + 69 * q^4 - 18 * q^5 - 9 * q^6 - 19 * q^7 - 39 * q^8 + 63 * q^9	\( 71 q - 15 q^{2} - 8 q^{3} + 69 q^{4} - 18 q^{5} - 9 q^{6} - 19 q^{7} - 39 q^{8} + 63 q^{9} - 10 q^{10} - 52 q^{11} - 9 q^{12} - 15 q^{13} - 53 q^{14} - 33 q^{15} + 53 q^{16} - 10 q^{17} - 35 q^{18} + 71 q^{19} - 33 q^{20} - 38 q^{21} - 6 q^{22} - 65 q^{23} - 30 q^{24} + 51 q^{25} - 4 q^{26} - 23 q^{27} - 29 q^{28} - 97 q^{29} - 27 q^{30} - 53 q^{31} - 78 q^{32} - 17 q^{33} - 24 q^{34} - 38 q^{35} + 24 q^{36} - 33 q^{37} - 15 q^{38} - 86 q^{39} + 25 q^{40} - 69 q^{41} + 64 q^{42} - 10 q^{43} - 94 q^{44} - 34 q^{45} - 6 q^{46} - 37 q^{47} - q^{48} + 74 q^{49} - 41 q^{50} - 46 q^{51} - 30 q^{52} - 50 q^{53} - 17 q^{54} - 30 q^{55} - 116 q^{56} - 8 q^{57} + 11 q^{58} - 93 q^{59} - 56 q^{60} - 18 q^{61} - q^{62} - 84 q^{63} + 93 q^{64} - 78 q^{65} - 53 q^{66} - 5 q^{67} - 9 q^{68} - 69 q^{69} - 10 q^{70} - 221 q^{71} - 73 q^{72} - 34 q^{73} - 58 q^{74} - 70 q^{75} + 69 q^{76} - 2 q^{77} + 7 q^{78} - 68 q^{79} - 71 q^{80} + 39 q^{81} + 26 q^{82} - 45 q^{83} - 10 q^{84} - 44 q^{85} - 80 q^{86} - 7 q^{87} - 46 q^{88} - 143 q^{89} + 41 q^{90} - 30 q^{91} - 46 q^{92} + 32 q^{93} + 41 q^{94} - 18 q^{95} - 140 q^{96} - 18 q^{97} - 97 q^{98} - 142 q^{99}+O(q^{100}) \) 71 * q - 15 * q^2 - 8 * q^3 + 69 * q^4 - 18 * q^5 - 9 * q^6 - 19 * q^7 - 39 * q^8 + 63 * q^9 - 10 * q^10 - 52 * q^11 - 9 * q^12 - 15 * q^13 - 53 * q^14 - 33 * q^15 + 53 * q^16 - 10 * q^17 - 35 * q^18 + 71 * q^19 - 33 * q^20 - 38 * q^21 - 6 * q^22 - 65 * q^23 - 30 * q^24 + 51 * q^25 - 4 * q^26 - 23 * q^27 - 29 * q^28 - 97 * q^29 - 27 * q^30 - 53 * q^31 - 78 * q^32 - 17 * q^33 - 24 * q^34 - 38 * q^35 + 24 * q^36 - 33 * q^37 - 15 * q^38 - 86 * q^39 + 25 * q^40 - 69 * q^41 + 64 * q^42 - 10 * q^43 - 94 * q^44 - 34 * q^45 - 6 * q^46 - 37 * q^47 - q^48 + 74 * q^49 - 41 * q^50 - 46 * q^51 - 30 * q^52 - 50 * q^53 - 17 * q^54 - 30 * q^55 - 116 * q^56 - 8 * q^57 + 11 * q^58 - 93 * q^59 - 56 * q^60 - 18 * q^61 - q^62 - 84 * q^63 + 93 * q^64 - 78 * q^65 - 53 * q^66 - 5 * q^67 - 9 * q^68 - 69 * q^69 - 10 * q^70 - 221 * q^71 - 73 * q^72 - 34 * q^73 - 58 * q^74 - 70 * q^75 + 69 * q^76 - 2 * q^77 + 7 * q^78 - 68 * q^79 - 71 * q^80 + 39 * q^81 + 26 * q^82 - 45 * q^83 - 10 * q^84 - 44 * q^85 - 80 * q^86 - 7 * q^87 - 46 * q^88 - 143 * q^89 + 41 * q^90 - 30 * q^91 - 46 * q^92 + 32 * q^93 + 41 * q^94 - 18 * q^95 - 140 * q^96 - 18 * q^97 - 97 * q^98 - 142 * 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 $

$2$	1.47232	1.04109	0.520543	−	0.853836i	$-0.325730\pi$
$2$	1.47232	1.04109	0.520543	+	0.853836i	$0.325730\pi$
$3$	1.80615	1.04278	0.521392	−	0.853317i	$-0.325413\pi$
$3$	1.80615	1.04278	0.521392	+	0.853317i	$0.325413\pi$
$4$	0.167717	0.0838585
$5$	−0.960908	−0.429731	−0.214866	−	0.976644i	$-0.568931\pi$
$5$	−0.960908	−0.429731	−0.214866	+	0.976644i	$0.568931\pi$
$6$	2.65923	1.08563
$7$	−2.43987	−0.922183	−0.461091	−	0.887353i	$-0.652542\pi$
$7$	−2.43987	−0.922183	−0.461091	+	0.887353i	$0.652542\pi$
$8$	−2.69770	−0.953781
$9$	0.262192	0.0873973
$10$	−1.41476	−0.447387
$11$	5.44391	1.64140	0.820700	−	0.571359i	$-0.193584\pi$
$11$	5.44391	1.64140	0.820700	+	0.571359i	$0.193584\pi$
$12$	0.302923	0.0874463
$13$	2.57127	0.713142	0.356571	−	0.934268i	$-0.383946\pi$
$13$	2.57127	0.713142	0.356571	+	0.934268i	$0.383946\pi$
$14$	−3.59226	−0.960071
$15$	−1.73555	−0.448117
$16$	−4.30731	−1.07683
$17$	−6.76960	−1.64187	−0.820935	−	0.571021i	$-0.806547\pi$
$17$	−6.76960	−1.64187	−0.820935	+	0.571021i	$0.806547\pi$
$18$	0.386029	0.0909880
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	−0.161161	−0.0360366
$21$	−4.40677	−0.961637
$22$	8.01516	1.70884
$23$	−0.962127	−0.200617	−0.100309	−	0.994956i	$-0.531983\pi$
$23$	−0.962127	−0.200617	−0.100309	+	0.994956i	$0.531983\pi$
$24$	−4.87246	−0.994587
$25$	−4.07666	−0.815331
$26$	3.78573	0.742442
$27$	−4.94490	−0.951647
$28$	−0.409207	−0.0773329
$29$	2.70832	0.502922	0.251461	−	0.967867i	$-0.419089\pi$
$29$	2.70832	0.502922	0.251461	+	0.967867i	$0.419089\pi$
$30$	−2.55528	−0.466528
$31$	1.24744	0.224046	0.112023	−	0.993706i	$-0.464267\pi$
$31$	1.24744	0.224046	0.112023	+	0.993706i	$0.464267\pi$
$32$	−0.946316	−0.167287
$33$	9.83254	1.71162
$34$	−9.96700	−1.70933
$35$	2.34449	0.396291
$36$	0.0439740	0.00732901
$37$	−7.27123	−1.19538	−0.597691	−	0.801726i	$-0.703915\pi$
$37$	−7.27123	−1.19538	−0.597691	+	0.801726i	$0.703915\pi$
$38$	1.47232	0.238841
$39$	4.64411	0.743653
$40$	2.59224	0.409870
$41$	−11.7087	−1.82859	−0.914293	−	0.405053i	$-0.867253\pi$
$41$	−11.7087	−1.82859	−0.914293	+	0.405053i	$0.867253\pi$
$42$	−6.48817	−1.00115
$43$	3.48905	0.532076	0.266038	−	0.963963i	$-0.414285\pi$
$43$	3.48905	0.532076	0.266038	+	0.963963i	$0.414285\pi$
$44$	0.913036	0.137645
$45$	−0.251942	−0.0375573
$46$	−1.41656	−0.208860
$47$	−8.25004	−1.20339	−0.601696	−	0.798725i	$-0.705508\pi$
$47$	−8.25004	−1.20339	−0.601696	+	0.798725i	$0.705508\pi$
$48$	−7.77966	−1.12290
$49$	−1.04706	−0.149579
$50$	−6.00213	−0.848829
$51$	−12.2269	−1.71212
$52$	0.431246	0.0598031
$53$	5.95700	0.818256	0.409128	−	0.912477i	$-0.365833\pi$
$53$	5.95700	0.818256	0.409128	+	0.912477i	$0.365833\pi$
$54$	−7.28046	−0.990746
$55$	−5.23110	−0.705361
$56$	6.58203	0.879561
$57$	1.80615	0.239231
$58$	3.98750	0.523585
$59$	−7.46552	−0.971927	−0.485964	−	0.873979i	$-0.661531\pi$
$59$	−7.46552	−0.971927	−0.485964	+	0.873979i	$0.661531\pi$
$60$	−0.291081	−0.0375784
$61$	4.94471	0.633105	0.316553	−	0.948575i	$-0.397475\pi$
$61$	4.94471	0.633105	0.316553	+	0.948575i	$0.397475\pi$
$62$	1.83662	0.233251
$63$	−0.639713	−0.0805962
$64$	7.22133	0.902667
$65$	−2.47076	−0.306460
$66$	14.4766	1.78195
$67$	−1.94823	−0.238014	−0.119007	−	0.992893i	$-0.537971\pi$
$67$	−1.94823	−0.238014	−0.119007	+	0.992893i	$0.537971\pi$
$68$	−1.13538	−0.137685
$69$	−1.73775	−0.209200
$70$	3.45183	0.412572
$71$	−8.99743	−1.06780	−0.533899	−	0.845548i	$-0.679274\pi$
$71$	−8.99743	−1.06780	−0.533899	+	0.845548i	$0.679274\pi$
$72$	−0.707315	−0.0833579
$73$	−0.277878	−0.0325232	−0.0162616	−	0.999868i	$-0.505176\pi$
$73$	−0.277878	−0.0325232	−0.0162616	+	0.999868i	$0.505176\pi$
$74$	−10.7056	−1.24450
$75$	−7.36307	−0.850214
$76$	0.167717	0.0192385
$77$	−13.2824	−1.51367
$78$	6.83761	0.774206
$79$	−4.10087	−0.461384	−0.230692	−	0.973027i	$-0.574099\pi$
$79$	−4.10087	−0.461384	−0.230692	+	0.973027i	$0.574099\pi$
$80$	4.13892	0.462746
$81$	−9.71783	−1.07976
$82$	−17.2389	−1.90371
$83$	11.0621	1.21422	0.607111	−	0.794617i	$-0.292328\pi$
$83$	11.0621	1.21422	0.607111	+	0.794617i	$0.292328\pi$
$84$	−0.739091	−0.0806414
$85$	6.50497	0.705563
$86$	5.13699	0.553936
$87$	4.89164	0.524439
$88$	−14.6860	−1.56554
$89$	−11.0863	−1.17515	−0.587574	−	0.809170i	$-0.699917\pi$
$89$	−11.0863	−1.17515	−0.587574	+	0.809170i	$0.699917\pi$
$90$	−0.370939	−0.0391004
$91$	−6.27356	−0.657648
$92$	−0.161365	−0.0168235
$93$	2.25306	0.233632
$94$	−12.1467	−1.25283
$95$	−0.960908	−0.0985871
$96$	−1.70919	−0.174444
$97$	−6.97622	−0.708328	−0.354164	−	0.935183i	$-0.615234\pi$
$97$	−6.97622	−0.708328	−0.354164	+	0.935183i	$0.615234\pi$
$98$	−1.54160	−0.155725
$99$	1.42735	0.143454
$100$	−0.683725	−0.0683725
$101$	13.3422	1.32760	0.663798	−	0.747912i	$-0.268944\pi$
$101$	13.3422	1.32760	0.663798	+	0.747912i	$0.268944\pi$
$102$	−18.0019	−1.78246
$103$	1.97747	0.194846	0.0974229	−	0.995243i	$-0.468940\pi$
$103$	1.97747	0.194846	0.0974229	+	0.995243i	$0.468940\pi$
$104$	−6.93652	−0.680182
$105$	4.23450	0.413245
$106$	8.77059	0.851875
$107$	1.60897	0.155545	0.0777727	−	0.996971i	$-0.475219\pi$
$107$	1.60897	0.155545	0.0777727	+	0.996971i	$0.475219\pi$
$108$	−0.829344	−0.0798037
$109$	−5.95195	−0.570093	−0.285047	−	0.958514i	$-0.592009\pi$
$109$	−5.95195	−0.570093	−0.285047	+	0.958514i	$0.592009\pi$
$110$	−7.70183	−0.734341
$111$	−13.1330	−1.24653
$112$	10.5092	0.993030
$113$	−7.16937	−0.674438	−0.337219	−	0.941426i	$-0.609486\pi$
$113$	−7.16937	−0.674438	−0.337219	+	0.941426i	$0.609486\pi$
$114$	2.65923	0.249060
$115$	0.924516	0.0862115
$116$	0.454231	0.0421743
$117$	0.674166	0.0623267
$118$	−10.9916	−1.01186
$119$	16.5169	1.51410
$120$	4.68199	0.427405
$121$	18.6361	1.69419
$122$	7.28018	0.659117
$123$	−21.1477	−1.90682
$124$	0.209216	0.0187882
$125$	8.72183	0.780104
$126$	−0.941860	−0.0839076
$127$	12.0688	1.07093	0.535464	−	0.844558i	$-0.320137\pi$
$127$	12.0688	1.07093	0.535464	+	0.844558i	$0.320137\pi$
$128$	12.5247	1.10704
$129$	6.30177	0.554840
$130$	−3.63774	−0.319051
$131$	10.4096	0.909492	0.454746	−	0.890621i	$-0.349730\pi$
$131$	10.4096	0.909492	0.454746	+	0.890621i	$0.349730\pi$
$132$	1.64908	0.143534
$133$	−2.43987	−0.211563
$134$	−2.86841	−0.247793
$135$	4.75160	0.408952
$136$	18.2624	1.56599
$137$	−10.3487	−0.884151	−0.442075	−	0.896978i	$-0.645758\pi$
$137$	−10.3487	−0.884151	−0.442075	+	0.896978i	$0.645758\pi$
$138$	−2.55852	−0.217795
$139$	13.9590	1.18399	0.591996	−	0.805941i	$-0.298340\pi$
$139$	13.9590	1.18399	0.591996	+	0.805941i	$0.298340\pi$
$140$	0.393210	0.0332323
$141$	−14.9008	−1.25488
$142$	−13.2471	−1.11167
$143$	13.9978	1.17055
$144$	−1.12934	−0.0941117
$145$	−2.60244	−0.216121
$146$	−0.409125	−0.0338594
$147$	−1.89114	−0.155979
$148$	−1.21951	−0.100243
$149$	−13.6429	−1.11767	−0.558835	−	0.829279i	$-0.688752\pi$
$149$	−13.6429	−1.11767	−0.558835	+	0.829279i	$0.688752\pi$
$150$	−10.8408	−0.885145
$151$	−2.21276	−0.180072	−0.0900361	−	0.995939i	$-0.528698\pi$
$151$	−2.21276	−0.180072	−0.0900361	+	0.995939i	$0.528698\pi$
$152$	−2.69770	−0.218812
$153$	−1.77493	−0.143495
$154$	−19.5559	−1.57586
$155$	−1.19867	−0.0962797
$156$	0.778897	0.0623616
$157$	−12.8201	−1.02315	−0.511576	−	0.859238i	$-0.670938\pi$
$157$	−12.8201	−1.02315	−0.511576	+	0.859238i	$0.670938\pi$
$158$	−6.03778	−0.480340
$159$	10.7593	0.853264
$160$	0.909323	0.0718883
$161$	2.34746	0.185006
$162$	−14.3077	−1.12412
$163$	3.73814	0.292794	0.146397	−	0.989226i	$-0.453232\pi$
$163$	3.73814	0.292794	0.146397	+	0.989226i	$0.453232\pi$
$164$	−1.96374	−0.153343
$165$	−9.44817	−0.735539
$166$	16.2869	1.26411
$167$	−6.97277	−0.539569	−0.269784	−	0.962921i	$-0.586952\pi$
$167$	−6.97277	−0.539569	−0.269784	+	0.962921i	$0.586952\pi$
$168$	11.8882	0.917191
$169$	−6.38856	−0.491428
$170$	9.57738	0.734551
$171$	0.262192	0.0200503
$172$	0.585174	0.0446191
$173$	−0.664903	−0.0505517	−0.0252758	−	0.999681i	$-0.508046\pi$
$173$	−0.664903	−0.0505517	−0.0252758	+	0.999681i	$0.508046\pi$
$174$	7.20204	0.545985
$175$	9.94649	0.751884
$176$	−23.4486	−1.76750
$177$	−13.4839	−1.01351
$178$	−16.3226	−1.22343
$179$	−16.4707	−1.23108	−0.615538	−	0.788107i	$-0.711061\pi$
$179$	−16.4707	−1.23108	−0.615538	+	0.788107i	$0.711061\pi$
$180$	−0.0422550	−0.00314950
$181$	−5.49623	−0.408532	−0.204266	−	0.978915i	$-0.565481\pi$
$181$	−5.49623	−0.408532	−0.204266	+	0.978915i	$0.565481\pi$
$182$	−9.23666	−0.684667
$183$	8.93091	0.660192
$184$	2.59553	0.191345
$185$	6.98698	0.513693
$186$	3.31722	0.243231
$187$	−36.8531	−2.69497
$188$	−1.38367	−0.100915
$189$	12.0649	0.877592
$190$	−1.41476	−0.102638
$191$	−2.24925	−0.162750	−0.0813750	−	0.996684i	$-0.525931\pi$
$191$	−2.24925	−0.162750	−0.0813750	+	0.996684i	$0.525931\pi$
$192$	13.0428	0.941286
$193$	−13.8017	−0.993471	−0.496736	−	0.867902i	$-0.665468\pi$
$193$	−13.8017	−0.993471	−0.496736	+	0.867902i	$0.665468\pi$
$194$	−10.2712	−0.737429
$195$	−4.46257	−0.319571
$196$	−0.175609	−0.0125435
$197$	1.23946	0.0883079	0.0441540	−	0.999025i	$-0.485941\pi$
$197$	1.23946	0.0883079	0.0441540	+	0.999025i	$0.485941\pi$
$198$	2.10151	0.149348
$199$	7.35331	0.521262	0.260631	−	0.965438i	$-0.416069\pi$
$199$	7.35331	0.521262	0.260631	+	0.965438i	$0.416069\pi$
$200$	10.9976	0.777648
$201$	−3.51880	−0.248197
$202$	19.6439	1.38214
$203$	−6.60793	−0.463786
$204$	−2.05067	−0.143575
$205$	11.2510	0.785801
$206$	2.91146	0.202851
$207$	−0.252262	−0.0175334
$208$	−11.0753	−0.767931
$209$	5.44391	0.376563
$210$	6.23453	0.430224
$211$	1.00000	0.0688428
$211$	1.00000	0.0688428
$212$	0.999090	0.0686178
$213$	−16.2507	−1.11348
$214$	2.36892	0.161936
$215$	−3.35266	−0.228650
$216$	13.3399	0.907663
$217$	−3.04358	−0.206612
$218$	−8.76316	−0.593516
$219$	−0.501891	−0.0339146
$220$	−0.877344	−0.0591505
$221$	−17.4065	−1.17089
$222$	−19.3359	−1.29774
$223$	−1.07816	−0.0721988	−0.0360994	−	0.999348i	$-0.511493\pi$
$223$	−1.07816	−0.0721988	−0.0360994	+	0.999348i	$0.511493\pi$
$224$	2.30888	0.154269
$225$	−1.06887	−0.0712577
$226$	−10.5556	−0.702147
$227$	18.1778	1.20650	0.603250	−	0.797552i	$-0.293872\pi$
$227$	18.1778	1.20650	0.603250	+	0.797552i	$0.293872\pi$
$228$	0.302923	0.0200616
$229$	−19.9217	−1.31646	−0.658231	−	0.752816i	$-0.728695\pi$
$229$	−19.9217	−1.31646	−0.658231	+	0.752816i	$0.728695\pi$
$230$	1.36118	0.0897535
$231$	−23.9901	−1.57843
$232$	−7.30623	−0.479678
$233$	22.8234	1.49521	0.747607	−	0.664142i	$-0.231203\pi$
$233$	22.8234	1.49521	0.747607	+	0.664142i	$0.231203\pi$
$234$	0.992587	0.0648874
$235$	7.92753	0.517135
$236$	−1.25209	−0.0815044
$237$	−7.40681	−0.481124
$238$	24.3182	1.57631
$239$	5.72602	0.370385	0.185193	−	0.982702i	$-0.440709\pi$
$239$	5.72602	0.370385	0.185193	+	0.982702i	$0.440709\pi$
$240$	7.47554	0.482544
$241$	−0.109996	−0.00708544	−0.00354272	−	0.999994i	$-0.501128\pi$
$241$	−0.109996	−0.00708544	−0.00354272	+	0.999994i	$0.501128\pi$
$242$	27.4383	1.76380
$243$	−2.71719	−0.174308
$244$	0.829312	0.0530913
$245$	1.00612	0.0642789
$246$	−31.1360	−1.98516
$247$	2.57127	0.163606
$248$	−3.36521	−0.213691
$249$	19.9798	1.26617
$250$	12.8413	0.812155
$251$	18.6582	1.17770	0.588848	−	0.808244i	$-0.299582\pi$
$251$	18.6582	1.17770	0.588848	+	0.808244i	$0.299582\pi$
$252$	−0.107291	−0.00675868
$253$	−5.23773	−0.329293
$254$	17.7690	1.11493
$255$	11.7490	0.735749
$256$	3.99769	0.249856
$257$	27.3451	1.70574	0.852869	−	0.522124i	$-0.174860\pi$
$257$	27.3451	1.70574	0.852869	+	0.522124i	$0.174860\pi$
$258$	9.27820	0.577636
$259$	17.7408	1.10236
$260$	−0.414388	−0.0256992
$261$	0.710099	0.0439540
$262$	15.3262	0.946858
$263$	−21.6822	−1.33698	−0.668492	−	0.743719i	$-0.733060\pi$
$263$	−21.6822	−1.33698	−0.668492	+	0.743719i	$0.733060\pi$
$264$	−26.5252	−1.63252
$265$	−5.72413	−0.351630
$266$	−3.59226	−0.220255
$267$	−20.0236	−1.22543
$268$	−0.326751	−0.0199595
$269$	−21.9140	−1.33612	−0.668061	−	0.744107i	$-0.732875\pi$
$269$	−21.9140	−1.33612	−0.668061	+	0.744107i	$0.732875\pi$
$270$	6.99586	0.425754
$271$	20.3233	1.23455	0.617276	−	0.786747i	$-0.288236\pi$
$271$	20.3233	1.23455	0.617276	+	0.786747i	$0.288236\pi$
$272$	29.1588	1.76801
$273$	−11.3310	−0.685784
$274$	−15.2366	−0.920476
$275$	−22.1929	−1.33828
$276$	−0.291450	−0.0175432
$277$	23.6548	1.42128	0.710639	−	0.703557i	$-0.248406\pi$
$277$	23.6548	1.42128	0.710639	+	0.703557i	$0.248406\pi$
$278$	20.5521	1.23264
$279$	0.327068	0.0195810
$280$	−6.32473	−0.377975
$281$	−1.30154	−0.0776435	−0.0388218	−	0.999246i	$-0.512360\pi$
$281$	−1.30154	−0.0776435	−0.0388218	+	0.999246i	$0.512360\pi$
$282$	−21.9388	−1.30643
$283$	30.9446	1.83947	0.919733	−	0.392544i	$-0.128405\pi$
$283$	30.9446	1.83947	0.919733	+	0.392544i	$0.128405\pi$
$284$	−1.50902	−0.0895440
$285$	−1.73555	−0.102805
$286$	20.6092	1.21864
$287$	28.5676	1.68629
$288$	−0.248116	−0.0146204
$289$	28.8276	1.69574
$290$	−3.83162	−0.225001
$291$	−12.6001	−0.738632
$292$	−0.0466049	−0.00272734
$293$	−9.60430	−0.561089	−0.280545	−	0.959841i	$-0.590515\pi$
$293$	−9.60430	−0.561089	−0.280545	+	0.959841i	$0.590515\pi$
$294$	−2.78436	−0.162387
$295$	7.17368	0.417668
$296$	19.6156	1.14013
$297$	−26.9196	−1.56203
$298$	−20.0867	−1.16359
$299$	−2.47389	−0.143069
$300$	−1.23491	−0.0712977
$301$	−8.51282	−0.490671
$302$	−3.25789	−0.187470
$303$	24.0980	1.38439
$304$	−4.30731	−0.247041
$305$	−4.75141	−0.272065
$306$	−2.61327	−0.149391
$307$	32.5997	1.86056	0.930282	−	0.366845i	$-0.119562\pi$
$307$	32.5997	1.86056	0.930282	+	0.366845i	$0.119562\pi$
$308$	−2.22769	−0.126934
$309$	3.57161	0.203182
$310$	−1.76483	−0.100235
$311$	−0.580133	−0.0328963	−0.0164481	−	0.999865i	$-0.505236\pi$
$311$	−0.580133	−0.0328963	−0.0164481	+	0.999865i	$0.505236\pi$
$312$	−12.5284	−0.709283
$313$	−13.8370	−0.782115	−0.391058	−	0.920366i	$-0.627891\pi$
$313$	−13.8370	−0.782115	−0.391058	+	0.920366i	$0.627891\pi$
$314$	−18.8752	−1.06519
$315$	0.614705	0.0346347
$316$	−0.687786	−0.0386910
$317$	−12.7246	−0.714686	−0.357343	−	0.933973i	$-0.616317\pi$
$317$	−12.7246	−0.714686	−0.357343	+	0.933973i	$0.616317\pi$
$318$	15.8410	0.888321
$319$	14.7438	0.825496
$320$	−6.93904	−0.387904
$321$	2.90605	0.162200
$322$	3.45621	0.192607
$323$	−6.76960	−0.376671
$324$	−1.62985	−0.0905470
$325$	−10.4822	−0.581447
$326$	5.50372	0.304823
$327$	−10.7501	−0.594484
$328$	31.5865	1.74407
$329$	20.1290	1.10975
$330$	−13.9107	−0.765759
$331$	−18.5195	−1.01792	−0.508962	−	0.860789i	$-0.669971\pi$
$331$	−18.5195	−1.01792	−0.508962	+	0.860789i	$0.669971\pi$
$332$	1.85530	0.101823
$333$	−1.90646	−0.104473
$334$	−10.2661	−0.561737
$335$	1.87207	0.102282
$336$	18.9813	1.03552
$337$	1.33247	0.0725843	0.0362922	−	0.999341i	$-0.488445\pi$
$337$	1.33247	0.0725843	0.0362922	+	0.999341i	$0.488445\pi$
$338$	−9.40599	−0.511618
$339$	−12.9490	−0.703292
$340$	1.09099	0.0591675
$341$	6.79093	0.367750
$342$	0.386029	0.0208741
$343$	19.6337	1.06012
$344$	−9.41243	−0.507484
$345$	1.66982	0.0898999
$346$	−0.978948	−0.0526286
$347$	14.7242	0.790437	0.395218	−	0.918587i	$-0.370669\pi$
$347$	14.7242	0.790437	0.395218	+	0.918587i	$0.370669\pi$
$348$	0.820411	0.0439787
$349$	−11.7105	−0.626847	−0.313424	−	0.949613i	$-0.601476\pi$
$349$	−11.7105	−0.626847	−0.313424	+	0.949613i	$0.601476\pi$
$350$	14.6444	0.782775
$351$	−12.7147	−0.678660
$352$	−5.15166	−0.274584
$353$	−7.32901	−0.390084	−0.195042	−	0.980795i	$-0.562484\pi$
$353$	−7.32901	−0.390084	−0.195042	+	0.980795i	$0.562484\pi$
$354$	−19.8525	−1.05515
$355$	8.64571	0.458867
$356$	−1.85937	−0.0985462
$357$	29.8321	1.57888
$358$	−24.2501	−1.28166
$359$	27.0117	1.42562	0.712811	−	0.701356i	$-0.247422\pi$
$359$	27.0117	1.42562	0.712811	+	0.701356i	$0.247422\pi$
$360$	0.679665	0.0358215
$361$	1.00000	0.0526316
$362$	−8.09220	−0.425317
$363$	33.6597	1.76668
$364$	−1.05218	−0.0551493
$365$	0.267015	0.0139762
$366$	13.1491	0.687316
$367$	1.53187	0.0799627	0.0399814	−	0.999200i	$-0.487270\pi$
$367$	1.53187	0.0799627	0.0399814	+	0.999200i	$0.487270\pi$
$368$	4.14417	0.216030
$369$	−3.06992	−0.159813
$370$	10.2871	0.534799
$371$	−14.5343	−0.754582
$372$	0.377877	0.0195920
$373$	−8.55536	−0.442980	−0.221490	−	0.975163i	$-0.571092\pi$
$373$	−8.55536	−0.442980	−0.221490	+	0.975163i	$0.571092\pi$
$374$	−54.2595	−2.80569
$375$	15.7530	0.813480
$376$	22.2561	1.14777
$377$	6.96382	0.358655
$378$	17.7634	0.913648
$379$	36.0840	1.85351	0.926756	−	0.375663i	$-0.122585\pi$
$379$	36.0840	1.85351	0.926756	+	0.375663i	$0.122585\pi$
$380$	−0.161161	−0.00826737
$381$	21.7980	1.11675
$382$	−3.31161	−0.169437
$383$	35.3272	1.80514	0.902569	−	0.430546i	$-0.141679\pi$
$383$	35.3272	1.80514	0.902569	+	0.430546i	$0.141679\pi$
$384$	22.6216	1.15440
$385$	12.7632	0.650472
$386$	−20.3205	−1.03429
$387$	0.914801	0.0465020
$388$	−1.17003	−0.0593993
$389$	13.2520	0.671901	0.335951	−	0.941880i	$-0.390943\pi$
$389$	13.2520	0.671901	0.335951	+	0.941880i	$0.390943\pi$
$390$	−6.57031	−0.332701
$391$	6.51322	0.329388
$392$	2.82464	0.142666
$393$	18.8014	0.948403
$394$	1.82488	0.0919361
$395$	3.94056	0.198271
$396$	0.239391	0.0120298
$397$	−4.98691	−0.250286	−0.125143	−	0.992139i	$-0.539939\pi$
$397$	−4.98691	−0.250286	−0.125143	+	0.992139i	$0.539939\pi$
$398$	10.8264	0.542679
$399$	−4.40677	−0.220615
$400$	17.5594	0.877970
$401$	22.9580	1.14647	0.573233	−	0.819392i	$-0.305689\pi$
$401$	22.9580	1.14647	0.573233	+	0.819392i	$0.305689\pi$
$402$	−5.18078	−0.258394
$403$	3.20750	0.159777
$404$	2.23771	0.111330
$405$	9.33794	0.464006
$406$	−9.72897	−0.482841
$407$	−39.5839	−1.96210
$408$	32.9847	1.63298
$409$	20.0580	0.991806	0.495903	−	0.868378i	$-0.334837\pi$
$409$	20.0580	0.991806	0.495903	+	0.868378i	$0.334837\pi$
$410$	16.5650	0.818086
$411$	−18.6914	−0.921978
$412$	0.331655	0.0163395
$413$	18.2149	0.896295
$414$	−0.371409	−0.0182538
$415$	−10.6296	−0.521789
$416$	−2.43323	−0.119299
$417$	25.2122	1.23465
$418$	8.01516	0.392034
$419$	−19.4890	−0.952101	−0.476051	−	0.879418i	$-0.657932\pi$
$419$	−19.4890	−0.952101	−0.476051	+	0.879418i	$0.657932\pi$
$420$	0.710199	0.0346541
$421$	−37.8117	−1.84283	−0.921415	−	0.388581i	$-0.872965\pi$
$421$	−37.8117	−1.84283	−0.921415	+	0.388581i	$0.872965\pi$
$422$	1.47232	0.0716713
$423$	−2.16309	−0.105173
$424$	−16.0702	−0.780438
$425$	27.5973	1.33867
$426$	−23.9263	−1.15923
$427$	−12.0644	−0.583839
$428$	0.269852	0.0130438
$429$	25.2821	1.22063
$430$	−4.93618	−0.238044
$431$	−31.2194	−1.50379	−0.751894	−	0.659284i	$-0.770859\pi$
$431$	−31.2194	−1.50379	−0.751894	+	0.659284i	$0.770859\pi$
$432$	21.2992	1.02476
$433$	5.82043	0.279712	0.139856	−	0.990172i	$-0.455336\pi$
$433$	5.82043	0.279712	0.139856	+	0.990172i	$0.455336\pi$
$434$	−4.48111	−0.215100
$435$	−4.70042	−0.225368
$436$	−0.998243	−0.0478072
$437$	−0.962127	−0.0460248
$438$	−0.738942	−0.0353080
$439$	−27.5605	−1.31539	−0.657696	−	0.753283i	$-0.728469\pi$
$439$	−27.5605	−1.31539	−0.657696	+	0.753283i	$0.728469\pi$
$440$	14.1119	0.672760
$441$	−0.274529	−0.0130728
$442$	−25.6279	−1.21899
$443$	8.88533	0.422155	0.211077	−	0.977469i	$-0.432303\pi$
$443$	8.88533	0.422155	0.211077	+	0.977469i	$0.432303\pi$
$444$	−2.20262	−0.104532
$445$	10.6529	0.504998
$446$	−1.58739	−0.0751651
$447$	−24.6412	−1.16549
$448$	−17.6191	−0.832423
$449$	12.2982	0.580388	0.290194	−	0.956968i	$-0.406280\pi$
$449$	12.2982	0.580388	0.290194	+	0.956968i	$0.406280\pi$
$450$	−1.57371	−0.0741853
$451$	−63.7409	−3.00144
$452$	−1.20243	−0.0565573
$453$	−3.99659	−0.187776
$454$	26.7634	1.25607
$455$	6.02831	0.282612
$456$	−4.87246	−0.228174
$457$	−10.8681	−0.508389	−0.254194	−	0.967153i	$-0.581810\pi$
$457$	−10.8681	−0.508389	−0.254194	+	0.967153i	$0.581810\pi$
$458$	−29.3310	−1.37055
$459$	33.4750	1.56248
$460$	0.155057	0.00722957
$461$	6.02311	0.280524	0.140262	−	0.990114i	$-0.455205\pi$
$461$	6.02311	0.280524	0.140262	+	0.990114i	$0.455205\pi$
$462$	−35.3210	−1.64328
$463$	13.6464	0.634201	0.317101	−	0.948392i	$-0.397291\pi$
$463$	13.6464	0.634201	0.317101	+	0.948392i	$0.397291\pi$
$464$	−11.6656	−0.541560
$465$	−2.16499	−0.100399
$466$	33.6033	1.55664
$467$	−0.699809	−0.0323833	−0.0161917	−	0.999869i	$-0.505154\pi$
$467$	−0.699809	−0.0323833	−0.0161917	+	0.999869i	$0.505154\pi$
$468$	0.113069	0.00522662
$469$	4.75341	0.219492
$470$	11.6718	0.538382
$471$	−23.1550	−1.06693
$472$	20.1397	0.927006
$473$	18.9941	0.873349
$474$	−10.9052	−0.500891
$475$	−4.07666	−0.187050
$476$	2.77017	0.126971
$477$	1.56188	0.0715134
$478$	8.43051	0.385603
$479$	−11.3312	−0.517734	−0.258867	−	0.965913i	$-0.583349\pi$
$479$	−11.3312	−0.517734	−0.258867	+	0.965913i	$0.583349\pi$
$480$	1.64238	0.0749639
$481$	−18.6963	−0.852478
$482$	−0.161948	−0.00737655
$483$	4.23987	0.192921
$484$	3.12560	0.142073
$485$	6.70350	0.304390
$486$	−4.00056	−0.181469
$487$	−26.1728	−1.18600	−0.593002	−	0.805201i	$-0.702057\pi$
$487$	−26.1728	−1.18600	−0.593002	+	0.805201i	$0.702057\pi$
$488$	−13.3393	−0.603844
$489$	6.75165	0.305320
$490$	1.48133	0.0669198
$491$	20.0817	0.906276	0.453138	−	0.891440i	$-0.350305\pi$
$491$	20.0817	0.906276	0.453138	+	0.891440i	$0.350305\pi$
$492$	−3.54682	−0.159903
$493$	−18.3342	−0.825733
$494$	3.78573	0.170328
$495$	−1.37155	−0.0616466
$496$	−5.37309	−0.241259
$497$	21.9525	0.984706
$498$	29.4166	1.31819
$499$	−3.86476	−0.173010	−0.0865052	−	0.996251i	$-0.527570\pi$
$499$	−3.86476	−0.173010	−0.0865052	+	0.996251i	$0.527570\pi$
$500$	1.46280	0.0654184
$501$	−12.5939	−0.562654
$502$	27.4708	1.22608
$503$	−15.5551	−0.693569	−0.346784	−	0.937945i	$-0.612726\pi$
$503$	−15.5551	−0.693569	−0.346784	+	0.937945i	$0.612726\pi$
$504$	1.72575	0.0768712
$505$	−12.8206	−0.570509
$506$	−7.71160	−0.342822
$507$	−11.5387	−0.512453
$508$	2.02414	0.0898065
$509$	12.5569	0.556575	0.278287	−	0.960498i	$-0.410233\pi$
$509$	12.5569	0.556575	0.278287	+	0.960498i	$0.410233\pi$
$510$	17.2982	0.765978
$511$	0.677985	0.0299923
$512$	−19.1636	−0.846918
$513$	−4.94490	−0.218323
$514$	40.2606	1.77582
$515$	−1.90017	−0.0837314
$516$	1.05691	0.0465280
$517$	−44.9124	−1.97525
$518$	26.1201	1.14765
$519$	−1.20092	−0.0527144
$520$	6.66536	0.292295
$521$	2.59559	0.113715	0.0568574	−	0.998382i	$-0.481892\pi$
$521$	2.59559	0.113715	0.0568574	+	0.998382i	$0.481892\pi$
$522$	1.04549	0.0457599
$523$	−8.43959	−0.369038	−0.184519	−	0.982829i	$-0.559073\pi$
$523$	−8.43959	−0.369038	−0.184519	+	0.982829i	$0.559073\pi$
$524$	1.74587	0.0762686
$525$	17.9649	0.784052
$526$	−31.9231	−1.39191
$527$	−8.44465	−0.367855
$528$	−42.3517	−1.84312
$529$	−22.0743	−0.959753
$530$	−8.42773	−0.366077
$531$	−1.95740	−0.0849438
$532$	−0.409207	−0.0177414
$533$	−30.1062	−1.30404
$534$	−29.4811	−1.27577
$535$	−1.54608	−0.0668427
$536$	5.25573	0.227013
$537$	−29.7486	−1.28375
$538$	−32.2644	−1.39102
$539$	−5.70007	−0.245520
$540$	0.796924	0.0342941
$541$	−35.5524	−1.52852	−0.764258	−	0.644911i	$-0.776895\pi$
$541$	−35.5524	−1.52852	−0.764258	+	0.644911i	$0.776895\pi$
$542$	29.9223	1.28527
$543$	−9.92705	−0.426010
$544$	6.40618	0.274663
$545$	5.71928	0.244987
$546$	−16.6828	−0.713960
$547$	−2.52662	−0.108031	−0.0540153	−	0.998540i	$-0.517202\pi$
$547$	−2.52662	−0.108031	−0.0540153	+	0.998540i	$0.517202\pi$
$548$	−1.73566	−0.0741436
$549$	1.29646	0.0553317
$550$	−32.6750	−1.39327
$551$	2.70832	0.115378
$552$	4.68793	0.199531
$553$	10.0056	0.425480
$554$	34.8273	1.47967
$555$	12.6196	0.535671
$556$	2.34117	0.0992877
$557$	−15.4449	−0.654421	−0.327210	−	0.944952i	$-0.606109\pi$
$557$	−15.4449	−0.654421	−0.327210	+	0.944952i	$0.606109\pi$
$558$	0.481547	0.0203855
$559$	8.97131	0.379446
$560$	−10.0984	−0.426736
$561$	−66.5624	−2.81027
$562$	−1.91628	−0.0808335
$563$	−21.1070	−0.889553	−0.444776	−	0.895642i	$-0.646717\pi$
$563$	−21.1070	−0.889553	−0.444776	+	0.895642i	$0.646717\pi$
$564$	−2.49912	−0.105232
$565$	6.88911	0.289827
$566$	45.5603	1.91504
$567$	23.7102	0.995735
$568$	24.2724	1.01845
$569$	14.3221	0.600414	0.300207	−	0.953874i	$-0.402944\pi$
$569$	14.3221	0.600414	0.300207	+	0.953874i	$0.402944\pi$
$570$	−2.55528	−0.107029
$571$	35.2784	1.47635	0.738177	−	0.674607i	$-0.235687\pi$
$571$	35.2784	1.47635	0.738177	+	0.674607i	$0.235687\pi$
$572$	2.34766	0.0981608
$573$	−4.06249	−0.169713
$574$	42.0605	1.75557
$575$	3.92226	0.163570
$576$	1.89337	0.0788906
$577$	45.9769	1.91404	0.957021	−	0.290019i	$-0.0936616\pi$
$577$	45.9769	1.91404	0.957021	+	0.290019i	$0.0936616\pi$
$578$	42.4433	1.76541
$579$	−24.9281	−1.03598
$580$	−0.436474	−0.0181236
$581$	−26.9900	−1.11973
$582$	−18.5514	−0.768979
$583$	32.4293	1.34309
$584$	0.749632	0.0310200
$585$	−0.647812	−0.0267837
$586$	−14.1406	−0.584142
$587$	36.0661	1.48861	0.744304	−	0.667841i	$-0.232781\pi$
$587$	36.0661	1.48861	0.744304	+	0.667841i	$0.232781\pi$
$588$	−0.317177	−0.0130802
$589$	1.24744	0.0513997
$590$	10.5619	0.434828
$591$	2.23866	0.0920861
$592$	31.3194	1.28722
$593$	5.32695	0.218752	0.109376	−	0.994000i	$-0.465115\pi$
$593$	5.32695	0.218752	0.109376	+	0.994000i	$0.465115\pi$
$594$	−39.6342	−1.62621
$595$	−15.8713	−0.650658
$596$	−2.28815	−0.0937262
$597$	13.2812	0.543564
$598$	−3.64235	−0.148947
$599$	−28.7258	−1.17371	−0.586853	−	0.809694i	$-0.699633\pi$
$599$	−28.7258	−1.17371	−0.586853	+	0.809694i	$0.699633\pi$
$600$	19.8634	0.810918
$601$	−33.2840	−1.35768	−0.678842	−	0.734284i	$-0.737518\pi$
$601$	−33.2840	−1.35768	−0.678842	+	0.734284i	$0.737518\pi$
$602$	−12.5336	−0.510830
$603$	−0.510809	−0.0208017
$604$	−0.371118	−0.0151006
$605$	−17.9076	−0.728048
$606$	35.4799	1.44127
$607$	−37.9215	−1.53919	−0.769593	−	0.638535i	$-0.779541\pi$
$607$	−37.9215	−1.53919	−0.769593	+	0.638535i	$0.779541\pi$
$608$	−0.946316	−0.0383782
$609$	−11.9349	−0.483628
$610$	−6.99558	−0.283243
$611$	−21.2131	−0.858190
$612$	−0.297687	−0.0120333
$613$	1.28635	0.0519553	0.0259777	−	0.999663i	$-0.491730\pi$
$613$	1.28635	0.0519553	0.0259777	+	0.999663i	$0.491730\pi$
$614$	47.9971	1.93701
$615$	20.3210	0.819420
$616$	35.8320	1.44371
$617$	−27.5261	−1.10816	−0.554080	−	0.832463i	$-0.686930\pi$
$617$	−27.5261	−1.10816	−0.554080	+	0.832463i	$0.686930\pi$
$618$	5.25855	0.211530
$619$	14.2764	0.573817	0.286909	−	0.957958i	$-0.407372\pi$
$619$	14.2764	0.573817	0.286909	+	0.957958i	$0.407372\pi$
$620$	−0.201038	−0.00807387
$621$	4.75762	0.190917
$622$	−0.854139	−0.0342479
$623$	27.0492	1.08370
$624$	−20.0036	−0.800785
$625$	12.0024	0.480096
$626$	−20.3725	−0.814249
$627$	9.83254	0.392674
$628$	−2.15014	−0.0858000
$629$	49.2234	1.96266
$630$	0.905041	0.0360577
$631$	−34.6313	−1.37865	−0.689325	−	0.724452i	$-0.742093\pi$
$631$	−34.6313	−1.37865	−0.689325	+	0.724452i	$0.742093\pi$
$632$	11.0629	0.440060
$633$	1.80615	0.0717882
$634$	−18.7347	−0.744049
$635$	−11.5970	−0.460211
$636$	1.80451	0.0715535
$637$	−2.69226	−0.106671
$638$	21.7076	0.859412
$639$	−2.35905	−0.0933227
$640$	−12.0351	−0.475729
$641$	−37.6023	−1.48520	−0.742600	−	0.669735i	$-0.766408\pi$
$641$	−37.6023	−1.48520	−0.742600	+	0.669735i	$0.766408\pi$
$642$	4.27863	0.168864
$643$	−14.7808	−0.582899	−0.291449	−	0.956586i	$-0.594138\pi$
$643$	−14.7808	−0.582899	−0.291449	+	0.956586i	$0.594138\pi$
$644$	0.393709	0.0155143
$645$	−6.05542	−0.238432
$646$	−9.96700	−0.392147
$647$	−8.97140	−0.352702	−0.176351	−	0.984327i	$-0.556429\pi$
$647$	−8.97140	−0.352702	−0.176351	+	0.984327i	$0.556429\pi$
$648$	26.2158	1.02985
$649$	−40.6416	−1.59532
$650$	−15.4331	−0.605336
$651$	−5.49717	−0.215451
$652$	0.626950	0.0245532
$653$	−32.4600	−1.27026	−0.635129	−	0.772406i	$-0.719053\pi$
$653$	−32.4600	−1.27026	−0.635129	+	0.772406i	$0.719053\pi$
$654$	−15.8276	−0.618908
$655$	−10.0027	−0.390837
$656$	50.4328	1.96907
$657$	−0.0728574	−0.00284244
$658$	29.6362	1.15534
$659$	6.87033	0.267630	0.133815	−	0.991006i	$-0.457277\pi$
$659$	6.87033	0.267630	0.133815	+	0.991006i	$0.457277\pi$
$660$	−1.58462	−0.0616812
$661$	19.8527	0.772180	0.386090	−	0.922461i	$-0.373825\pi$
$661$	19.8527	0.772180	0.386090	+	0.922461i	$0.373825\pi$
$662$	−27.2666	−1.05975
$663$	−31.4388	−1.22098
$664$	−29.8422	−1.15810
$665$	2.34449	0.0909153
$666$	−2.80691	−0.108766
$667$	−2.60574	−0.100895
$668$	−1.16945	−0.0452475
$669$	−1.94732	−0.0752877
$670$	2.75628	0.106484
$671$	26.9185	1.03918
$672$	4.17020	0.160869
$673$	23.0100	0.886971	0.443485	−	0.896282i	$-0.353742\pi$
$673$	23.0100	0.886971	0.443485	+	0.896282i	$0.353742\pi$
$674$	1.96182	0.0755664
$675$	20.1587	0.775907
$676$	−1.07147	−0.0412104
$677$	−15.1748	−0.583216	−0.291608	−	0.956538i	$-0.594190\pi$
$677$	−15.1748	−0.583216	−0.291608	+	0.956538i	$0.594190\pi$
$678$	−19.0650	−0.732187
$679$	17.0210	0.653207
$680$	−17.5485	−0.672953
$681$	32.8318	1.25812
$682$	9.99840	0.382859
$683$	10.8415	0.414837	0.207418	−	0.978252i	$-0.433494\pi$
$683$	10.8415	0.414837	0.207418	+	0.978252i	$0.433494\pi$
$684$	0.0439740	0.00168139
$685$	9.94417	0.379947
$686$	28.9071	1.10368
$687$	−35.9816	−1.37278
$688$	−15.0284	−0.572953
$689$	15.3171	0.583533
$690$	2.45850	0.0935935
$691$	−0.502394	−0.0191120	−0.00955598	−	0.999954i	$-0.503042\pi$
$691$	−0.502394	−0.0191120	−0.00955598	+	0.999954i	$0.503042\pi$
$692$	−0.111516	−0.00423919
$693$	−3.48254	−0.132291
$694$	21.6787	0.822912
$695$	−13.4134	−0.508798
$696$	−13.1962	−0.500200
$697$	79.2630	3.00230
$698$	−17.2415	−0.652601
$699$	41.2227	1.55918
$700$	1.66820	0.0630519
$701$	27.6266	1.04344	0.521721	−	0.853116i	$-0.325290\pi$
$701$	27.6266	1.04344	0.521721	+	0.853116i	$0.325290\pi$
$702$	−18.7201	−0.706543
$703$	−7.27123	−0.274240
$704$	39.3123	1.48164
$705$	14.3183	0.539260
$706$	−10.7906	−0.406110
$707$	−32.5531	−1.22429
$708$	−2.26147	−0.0849914
$709$	−20.0730	−0.753857	−0.376928	−	0.926242i	$-0.623020\pi$
$709$	−20.0730	−0.753857	−0.376928	+	0.926242i	$0.623020\pi$
$710$	12.7292	0.477719
$711$	−1.07522	−0.0403237
$712$	29.9076	1.12083
$713$	−1.20019	−0.0449476
$714$	43.9223	1.64375
$715$	−13.4506	−0.503023
$716$	−2.76241	−0.103236
$717$	10.3421	0.386232
$718$	39.7698	1.48419
$719$	−33.7085	−1.25711	−0.628557	−	0.777763i	$-0.716354\pi$
$719$	−33.7085	−1.25711	−0.628557	+	0.777763i	$0.716354\pi$
$720$	1.08519	0.0404427
$721$	−4.82476	−0.179683
$722$	1.47232	0.0547940
$723$	−0.198669	−0.00738858
$724$	−0.921812	−0.0342589
$725$	−11.0409	−0.410048
$726$	49.5578	1.83926
$727$	28.2185	1.04657	0.523284	−	0.852158i	$-0.324707\pi$
$727$	28.2185	1.04657	0.523284	+	0.852158i	$0.324707\pi$
$728$	16.9242	0.627252
$729$	24.2458	0.897994
$730$	0.393131	0.0145504
$731$	−23.6195	−0.873599
$732$	1.49787	0.0553627
$733$	−31.6855	−1.17033	−0.585166	−	0.810914i	$-0.698971\pi$
$733$	−31.6855	−1.17033	−0.585166	+	0.810914i	$0.698971\pi$
$734$	2.25539	0.0832480
$735$	1.81721	0.0670290
$736$	0.910476	0.0335606
$737$	−10.6060	−0.390676
$738$	−4.51989	−0.166379
$739$	−35.9182	−1.32127	−0.660636	−	0.750706i	$-0.729713\pi$
$739$	−35.9182	−1.32127	−0.660636	+	0.750706i	$0.729713\pi$
$740$	1.17184	0.0430776
$741$	4.64411	0.170606
$742$	−21.3991	−0.785584
$743$	5.84754	0.214525	0.107263	−	0.994231i	$-0.465791\pi$
$743$	5.84754	0.214525	0.107263	+	0.994231i	$0.465791\pi$
$744$	−6.07809	−0.222834
$745$	13.1096	0.480298
$746$	−12.5962	−0.461180
$747$	2.90039	0.106120
$748$	−6.18089	−0.225996
$749$	−3.92568	−0.143441
$750$	23.1934	0.846902
$751$	−30.3583	−1.10779	−0.553895	−	0.832587i	$-0.686859\pi$
$751$	−30.3583	−1.10779	−0.553895	+	0.832587i	$0.686859\pi$
$752$	35.5354	1.29584
$753$	33.6996	1.22808
$754$	10.2530	0.373390
$755$	2.12626	0.0773826
$756$	2.02349	0.0735936
$757$	14.5564	0.529063	0.264531	−	0.964377i	$-0.414783\pi$
$757$	14.5564	0.529063	0.264531	+	0.964377i	$0.414783\pi$
$758$	53.1271	1.92966
$759$	−9.46015	−0.343382
$760$	2.59224	0.0940305
$761$	−49.4325	−1.79193	−0.895963	−	0.444129i	$-0.853513\pi$
$761$	−49.4325	−1.79193	−0.895963	+	0.444129i	$0.853513\pi$
$762$	32.0936	1.16263
$763$	14.5220	0.525730
$764$	−0.377238	−0.0136480
$765$	1.70555	0.0616643
$766$	52.0129	1.87930
$767$	−19.1959	−0.693123
$768$	7.22045	0.260546
$769$	35.9557	1.29660	0.648299	−	0.761386i	$-0.275481\pi$
$769$	35.9557	1.29660	0.648299	+	0.761386i	$0.275481\pi$
$770$	18.7914	0.677196
$771$	49.3894	1.77872
$772$	−2.31479	−0.0833110
$773$	9.76880	0.351359	0.175680	−	0.984447i	$-0.443788\pi$
$773$	9.76880	0.351359	0.175680	+	0.984447i	$0.443788\pi$
$774$	1.34688	0.0484125
$775$	−5.08537	−0.182672
$776$	18.8197	0.675590
$777$	32.0427	1.14952
$778$	19.5111	0.699506
$779$	−11.7087	−0.419506
$780$	−0.748448	−0.0267987
$781$	−48.9812	−1.75269
$782$	9.58952	0.342921
$783$	−13.3924	−0.478604
$784$	4.50999	0.161071
$785$	12.3189	0.439680
$786$	27.6816	0.987368
$787$	−14.7123	−0.524438	−0.262219	−	0.965008i	$-0.584454\pi$
$787$	−14.7123	−0.524438	−0.262219	+	0.965008i	$0.584454\pi$
$788$	0.207879	0.00740537
$789$	−39.1614	−1.39418
$790$	5.80176	0.206417
$791$	17.4923	0.621955
$792$	−3.85056	−0.136824
$793$	12.7142	0.451494
$794$	−7.34232	−0.260569
$795$	−10.3387	−0.366674
$796$	1.23328	0.0437123
$797$	−8.51544	−0.301632	−0.150816	−	0.988562i	$-0.548190\pi$
$797$	−8.51544	−0.301632	−0.150816	+	0.988562i	$0.548190\pi$
$798$	−6.48817	−0.229679
$799$	55.8495	1.97581
$800$	3.85780	0.136394
$801$	−2.90674	−0.102705
$802$	33.8014	1.19357
$803$	−1.51274	−0.0533835
$804$	−0.590162	−0.0208134
$805$	−2.25569	−0.0795028
$806$	4.72246	0.166341
$807$	−39.5801	−1.39329
$808$	−35.9932	−1.26624
$809$	−18.6064	−0.654165	−0.327083	−	0.944996i	$-0.606066\pi$
$809$	−18.6064	−0.654165	−0.327083	+	0.944996i	$0.606066\pi$
$810$	13.7484	0.483070
$811$	−46.9976	−1.65031	−0.825155	−	0.564907i	$-0.808912\pi$
$811$	−46.9976	−1.65031	−0.825155	+	0.564907i	$0.808912\pi$
$812$	−1.10826	−0.0388924
$813$	36.7070	1.28737
$814$	−58.2801	−2.04272
$815$	−3.59201	−0.125823
$816$	52.6652	1.84365
$817$	3.48905	0.122067
$818$	29.5318	1.03255
$819$	−1.64488	−0.0574766
$820$	1.88698	0.0658961
$821$	13.2110	0.461067	0.230533	−	0.973064i	$-0.425953\pi$
$821$	13.2110	0.461067	0.230533	+	0.973064i	$0.425953\pi$
$822$	−27.5196	−0.959857
$823$	48.4166	1.68770	0.843849	−	0.536581i	$-0.180285\pi$
$823$	48.4166	1.68770	0.843849	+	0.536581i	$0.180285\pi$
$824$	−5.33462	−0.185840
$825$	−40.0839	−1.39554
$826$	26.8180	0.933119
$827$	0.974032	0.0338704	0.0169352	−	0.999857i	$-0.494609\pi$
$827$	0.974032	0.0338704	0.0169352	+	0.999857i	$0.494609\pi$
$828$	−0.0423086	−0.00147033
$829$	−28.6206	−0.994036	−0.497018	−	0.867740i	$-0.665572\pi$
$829$	−28.6206	−0.994036	−0.497018	+	0.867740i	$0.665572\pi$
$830$	−15.6502	−0.543227
$831$	42.7242	1.48209
$832$	18.5680	0.643730
$833$	7.08815	0.245590
$834$	37.1203	1.28537
$835$	6.70019	0.231870
$836$	0.913036	0.0315780
$837$	−6.16845	−0.213213
$838$	−28.6940	−0.991218
$839$	−2.38517	−0.0823451	−0.0411725	−	0.999152i	$-0.513109\pi$
$839$	−2.38517	−0.0823451	−0.0411725	+	0.999152i	$0.513109\pi$
$840$	−11.4234	−0.394146
$841$	−21.6650	−0.747069
$842$	−55.6708	−1.91854
$843$	−2.35079	−0.0809654
$844$	0.167717	0.00577306
$845$	6.13882	0.211182
$846$	−3.18476	−0.109494
$847$	−45.4697	−1.56236
$848$	−25.6586	−0.881120
$849$	55.8907	1.91817
$850$	40.6320	1.39367
$851$	6.99585	0.239814
$852$	−2.72553	−0.0933750
$853$	1.93371	0.0662090	0.0331045	−	0.999452i	$-0.489461\pi$
$853$	1.93371	0.0662090	0.0331045	+	0.999452i	$0.489461\pi$
$854$	−17.7627	−0.607826
$855$	−0.251942	−0.00861624
$856$	−4.34053	−0.148356
$857$	−30.7649	−1.05091	−0.525455	−	0.850822i	$-0.676105\pi$
$857$	−30.7649	−1.05091	−0.525455	+	0.850822i	$0.676105\pi$
$858$	37.2233	1.27078
$859$	16.9374	0.577896	0.288948	−	0.957345i	$-0.406695\pi$
$859$	16.9374	0.577896	0.288948	+	0.957345i	$0.406695\pi$
$860$	−0.562298	−0.0191742
$861$	51.5974	1.75844
$862$	−45.9649	−1.56557
$863$	−33.4440	−1.13845	−0.569223	−	0.822183i	$-0.692756\pi$
$863$	−33.4440	−1.13845	−0.569223	+	0.822183i	$0.692756\pi$
$864$	4.67944	0.159198
$865$	0.638911	0.0217236
$866$	8.56951	0.291204
$867$	52.0670	1.76829
$868$	−0.510460	−0.0173261
$869$	−22.3248	−0.757316
$870$	−6.92050	−0.234627
$871$	−5.00942	−0.169738
$872$	16.0566	0.543744
$873$	−1.82911	−0.0619059
$874$	−1.41656	−0.0479157
$875$	−21.2801	−0.719399
$876$	−0.0841756	−0.00284403
$877$	−5.95151	−0.200968	−0.100484	−	0.994939i	$-0.532039\pi$
$877$	−5.95151	−0.200968	−0.100484	+	0.994939i	$0.532039\pi$
$878$	−40.5778	−1.36944
$879$	−17.3468	−0.585095
$880$	22.5319	0.759551
$881$	−54.4312	−1.83383	−0.916917	−	0.399077i	$-0.869331\pi$
$881$	−54.4312	−1.83383	−0.916917	+	0.399077i	$0.869331\pi$
$882$	−0.404194	−0.0136099
$883$	23.4270	0.788382	0.394191	−	0.919029i	$-0.371025\pi$
$883$	23.4270	0.788382	0.394191	+	0.919029i	$0.371025\pi$
$884$	−2.91937	−0.0981889
$885$	12.9568	0.435537
$886$	13.0820	0.439499
$887$	32.5791	1.09390	0.546950	−	0.837165i	$-0.315789\pi$
$887$	32.5791	1.09390	0.546950	+	0.837165i	$0.315789\pi$
$888$	35.4288	1.18891
$889$	−29.4461	−0.987592
$890$	15.6845	0.525746
$891$	−52.9030	−1.77232
$892$	−0.180825	−0.00605448
$893$	−8.25004	−0.276077
$894$	−36.2796	−1.21337
$895$	15.8268	0.529032
$896$	−30.5586	−1.02089
$897$	−4.46822	−0.149190
$898$	18.1068	0.604233
$899$	3.37846	0.112678
$900$	−0.179267	−0.00597557
$901$	−40.3265	−1.34347
$902$	−93.8468	−3.12476
$903$	−15.3755	−0.511664
$904$	19.3408	0.643266
$905$	5.28138	0.175559
$906$	−5.88425	−0.195491
$907$	7.46857	0.247990	0.123995	−	0.992283i	$-0.460429\pi$
$907$	7.46857	0.247990	0.123995	+	0.992283i	$0.460429\pi$
$908$	3.04872	0.101175
$909$	3.49821	0.116028
$910$	8.87559	0.294223
$911$	−43.9581	−1.45640	−0.728199	−	0.685366i	$-0.759642\pi$
$911$	−43.9581	−1.45640	−0.728199	+	0.685366i	$0.759642\pi$
$912$	−7.77966	−0.257610
$913$	60.2210	1.99302
$914$	−16.0013	−0.529276
$915$	−8.58178	−0.283705
$916$	−3.34121	−0.110397
$917$	−25.3980	−0.838717
$918$	49.2859	1.62668
$919$	−36.2610	−1.19614	−0.598070	−	0.801444i	$-0.704065\pi$
$919$	−36.2610	−1.19614	−0.598070	+	0.801444i	$0.704065\pi$
$920$	−2.49407	−0.0822269
$921$	58.8801	1.94017
$922$	8.86793	0.292050
$923$	−23.1348	−0.761493
$924$	−4.02354	−0.132365
$925$	29.6423	0.974633
$926$	20.0918	0.660258
$927$	0.518476	0.0170290
$928$	−2.56292	−0.0841321
$929$	−48.2703	−1.58370	−0.791848	−	0.610718i	$-0.790881\pi$
$929$	−48.2703	−1.58370	−0.791848	+	0.610718i	$0.790881\pi$
$930$	−3.18755	−0.104524
$931$	−1.04706	−0.0343159
$932$	3.82788	0.125386
$933$	−1.04781	−0.0343037
$934$	−1.03034	−0.0337138
$935$	35.4125	1.15811
$936$	−1.81870	−0.0594460
$937$	−11.5337	−0.376790	−0.188395	−	0.982093i	$-0.560328\pi$
$937$	−11.5337	−0.376790	−0.188395	+	0.982093i	$0.560328\pi$
$938$	6.99853	0.228510
$939$	−24.9918	−0.815577
$940$	1.32958	0.0433662
$941$	−53.2938	−1.73733	−0.868665	−	0.495401i	$-0.835021\pi$
$941$	−53.2938	−1.73733	−0.868665	+	0.495401i	$0.835021\pi$
$942$	−34.0915	−1.11076
$943$	11.2652	0.366846
$944$	32.1563	1.04660
$945$	−11.5933	−0.377129
$946$	27.9653	0.909231
$947$	−4.90289	−0.159323	−0.0796613	−	0.996822i	$-0.525384\pi$
$947$	−4.90289	−0.159323	−0.0796613	+	0.996822i	$0.525384\pi$
$948$	−1.24225	−0.0403463
$949$	−0.714500	−0.0231937
$950$	−6.00213	−0.194735
$951$	−22.9826	−0.745262
$952$	−44.5577	−1.44412
$953$	−12.9509	−0.419521	−0.209760	−	0.977753i	$-0.567268\pi$
$953$	−12.9509	−0.419521	−0.209760	+	0.977753i	$0.567268\pi$
$954$	2.29958	0.0744515
$955$	2.16132	0.0699388
$956$	0.960351	0.0310600
$957$	26.6296	0.860814
$958$	−16.6831	−0.539006
$959$	25.2495	0.815348
$960$	−12.5330	−0.404500
$961$	−29.4439	−0.949803
$962$	−27.5269	−0.887503
$963$	0.421860	0.0135942
$964$	−0.0184481	−0.000594175 0
$965$	13.2622	0.426926
$966$	6.24244	0.200847
$967$	47.6759	1.53315	0.766576	−	0.642153i	$-0.221959\pi$
$967$	47.6759	1.53315	0.766576	+	0.642153i	$0.221959\pi$
$968$	−50.2747	−1.61589
$969$	−12.2269	−0.392786
$970$	9.86968	0.316896
$971$	18.0216	0.578341	0.289170	−	0.957278i	$-0.406621\pi$
$971$	18.0216	0.578341	0.289170	+	0.957278i	$0.406621\pi$
$972$	−0.455719	−0.0146172
$973$	−34.0582	−1.09186
$974$	−38.5347	−1.23473
$975$	−18.9324	−0.606324
$976$	−21.2984	−0.681744
$977$	45.5980	1.45881	0.729405	−	0.684082i	$-0.239797\pi$
$977$	45.5980	1.45881	0.729405	+	0.684082i	$0.239797\pi$
$978$	9.94057	0.317865
$979$	−60.3530	−1.92889
$980$	0.168744	0.00539033
$981$	−1.56055	−0.0498246
$982$	29.5667	0.943510
$983$	−31.0122	−0.989136	−0.494568	−	0.869139i	$-0.664674\pi$
$983$	−31.0122	−0.989136	−0.494568	+	0.869139i	$0.664674\pi$
$984$	57.0500	1.81869
$985$	−1.19101	−0.0379487
$986$	−26.9938	−0.859658
$987$	36.3560	1.15723
$988$	0.431246	0.0137198
$989$	−3.35691	−0.106744
$990$	−2.01936	−0.0641794
$991$	−49.1434	−1.56109	−0.780545	−	0.625099i	$-0.785059\pi$
$991$	−49.1434	−1.56109	−0.780545	+	0.625099i	$0.785059\pi$
$992$	−1.18047	−0.0374799
$993$	−33.4491	−1.06147
$994$	32.3211	1.02516
$995$	−7.06586	−0.224003
$996$	3.35096	0.106179
$997$	40.8676	1.29429	0.647145	−	0.762367i	$-0.275963\pi$
$997$	40.8676	1.29429	0.647145	+	0.762367i	$0.275963\pi$
$998$	−5.69015	−0.180118
$999$	35.9555	1.13758

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4009.2.a.c.1.57	✓	71

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4009.2.a.c.1.57	✓	71	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 4009 = 19 \cdot 211 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4009.a (trivial)

\(f(q)\)	\(=\)	\(q+1.47232 q^{2} +1.80615 q^{3} +0.167717 q^{4} -0.960908 q^{5} +2.65923 q^{6} -2.43987 q^{7} -2.69770 q^{8} +0.262192 q^{9} +O(q^{10})\)	\(q+1.47232 q^{2} +1.80615 q^{3} +0.167717 q^{4} -0.960908 q^{5} +2.65923 q^{6} -2.43987 q^{7} -2.69770 q^{8} +0.262192 q^{9} -1.41476 q^{10} +5.44391 q^{11} +0.302923 q^{12} +2.57127 q^{13} -3.59226 q^{14} -1.73555 q^{15} -4.30731 q^{16} -6.76960 q^{17} +0.386029 q^{18} +1.00000 q^{19} -0.161161 q^{20} -4.40677 q^{21} +8.01516 q^{22} -0.962127 q^{23} -4.87246 q^{24} -4.07666 q^{25} +3.78573 q^{26} -4.94490 q^{27} -0.409207 q^{28} +2.70832 q^{29} -2.55528 q^{30} +1.24744 q^{31} -0.946316 q^{32} +9.83254 q^{33} -9.96700 q^{34} +2.34449 q^{35} +0.0439740 q^{36} -7.27123 q^{37} +1.47232 q^{38} +4.64411 q^{39} +2.59224 q^{40} -11.7087 q^{41} -6.48817 q^{42} +3.48905 q^{43} +0.913036 q^{44} -0.251942 q^{45} -1.41656 q^{46} -8.25004 q^{47} -7.77966 q^{48} -1.04706 q^{49} -6.00213 q^{50} -12.2269 q^{51} +0.431246 q^{52} +5.95700 q^{53} -7.28046 q^{54} -5.23110 q^{55} +6.58203 q^{56} +1.80615 q^{57} +3.98750 q^{58} -7.46552 q^{59} -0.291081 q^{60} +4.94471 q^{61} +1.83662 q^{62} -0.639713 q^{63} +7.22133 q^{64} -2.47076 q^{65} +14.4766 q^{66} -1.94823 q^{67} -1.13538 q^{68} -1.73775 q^{69} +3.45183 q^{70} -8.99743 q^{71} -0.707315 q^{72} -0.277878 q^{73} -10.7056 q^{74} -7.36307 q^{75} +0.167717 q^{76} -13.2824 q^{77} +6.83761 q^{78} -4.10087 q^{79} +4.13892 q^{80} -9.71783 q^{81} -17.2389 q^{82} +11.0621 q^{83} -0.739091 q^{84} +6.50497 q^{85} +5.13699 q^{86} +4.89164 q^{87} -14.6860 q^{88} -11.0863 q^{89} -0.370939 q^{90} -6.27356 q^{91} -0.161365 q^{92} +2.25306 q^{93} -12.1467 q^{94} -0.960908 q^{95} -1.70919 q^{96} -6.97622 q^{97} -1.54160 q^{98} +1.42735 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 71 q - 15 q^{2} - 8 q^{3} + 69 q^{4} - 18 q^{5} - 9 q^{6} - 19 q^{7} - 39 q^{8} + 63 q^{9}+O(q^{10}) \) 71 * q - 15 * q^2 - 8 * q^3 + 69 * q^4 - 18 * q^5 - 9 * q^6 - 19 * q^7 - 39 * q^8 + 63 * q^9	\( 71 q - 15 q^{2} - 8 q^{3} + 69 q^{4} - 18 q^{5} - 9 q^{6} - 19 q^{7} - 39 q^{8} + 63 q^{9} - 10 q^{10} - 52 q^{11} - 9 q^{12} - 15 q^{13} - 53 q^{14} - 33 q^{15} + 53 q^{16} - 10 q^{17} - 35 q^{18} + 71 q^{19} - 33 q^{20} - 38 q^{21} - 6 q^{22} - 65 q^{23} - 30 q^{24} + 51 q^{25} - 4 q^{26} - 23 q^{27} - 29 q^{28} - 97 q^{29} - 27 q^{30} - 53 q^{31} - 78 q^{32} - 17 q^{33} - 24 q^{34} - 38 q^{35} + 24 q^{36} - 33 q^{37} - 15 q^{38} - 86 q^{39} + 25 q^{40} - 69 q^{41} + 64 q^{42} - 10 q^{43} - 94 q^{44} - 34 q^{45} - 6 q^{46} - 37 q^{47} - q^{48} + 74 q^{49} - 41 q^{50} - 46 q^{51} - 30 q^{52} - 50 q^{53} - 17 q^{54} - 30 q^{55} - 116 q^{56} - 8 q^{57} + 11 q^{58} - 93 q^{59} - 56 q^{60} - 18 q^{61} - q^{62} - 84 q^{63} + 93 q^{64} - 78 q^{65} - 53 q^{66} - 5 q^{67} - 9 q^{68} - 69 q^{69} - 10 q^{70} - 221 q^{71} - 73 q^{72} - 34 q^{73} - 58 q^{74} - 70 q^{75} + 69 q^{76} - 2 q^{77} + 7 q^{78} - 68 q^{79} - 71 q^{80} + 39 q^{81} + 26 q^{82} - 45 q^{83} - 10 q^{84} - 44 q^{85} - 80 q^{86} - 7 q^{87} - 46 q^{88} - 143 q^{89} + 41 q^{90} - 30 q^{91} - 46 q^{92} + 32 q^{93} + 41 q^{94} - 18 q^{95} - 140 q^{96} - 18 q^{97} - 97 q^{98} - 142 q^{99}+O(q^{100}) \) 71 * q - 15 * q^2 - 8 * q^3 + 69 * q^4 - 18 * q^5 - 9 * q^6 - 19 * q^7 - 39 * q^8 + 63 * q^9 - 10 * q^10 - 52 * q^11 - 9 * q^12 - 15 * q^13 - 53 * q^14 - 33 * q^15 + 53 * q^16 - 10 * q^17 - 35 * q^18 + 71 * q^19 - 33 * q^20 - 38 * q^21 - 6 * q^22 - 65 * q^23 - 30 * q^24 + 51 * q^25 - 4 * q^26 - 23 * q^27 - 29 * q^28 - 97 * q^29 - 27 * q^30 - 53 * q^31 - 78 * q^32 - 17 * q^33 - 24 * q^34 - 38 * q^35 + 24 * q^36 - 33 * q^37 - 15 * q^38 - 86 * q^39 + 25 * q^40 - 69 * q^41 + 64 * q^42 - 10 * q^43 - 94 * q^44 - 34 * q^45 - 6 * q^46 - 37 * q^47 - q^48 + 74 * q^49 - 41 * q^50 - 46 * q^51 - 30 * q^52 - 50 * q^53 - 17 * q^54 - 30 * q^55 - 116 * q^56 - 8 * q^57 + 11 * q^58 - 93 * q^59 - 56 * q^60 - 18 * q^61 - q^62 - 84 * q^63 + 93 * q^64 - 78 * q^65 - 53 * q^66 - 5 * q^67 - 9 * q^68 - 69 * q^69 - 10 * q^70 - 221 * q^71 - 73 * q^72 - 34 * q^73 - 58 * q^74 - 70 * q^75 + 69 * q^76 - 2 * q^77 + 7 * q^78 - 68 * q^79 - 71 * q^80 + 39 * q^81 + 26 * q^82 - 45 * q^83 - 10 * q^84 - 44 * q^85 - 80 * q^86 - 7 * q^87 - 46 * q^88 - 143 * q^89 + 41 * q^90 - 30 * q^91 - 46 * q^92 + 32 * q^93 + 41 * q^94 - 18 * q^95 - 140 * q^96 - 18 * q^97 - 97 * q^98 - 142 * q^99

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