LMFDB - Embedded newform 8021.2.a.a.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8021,2,Mod(1,8021)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8021, 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("8021.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8021 = 13 \cdot 617 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8021.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$64.0480074613$
Analytic rank:	$1$
Dimension:	$134$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Character	$\chi$	$=$	8021.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.38388 q^{2} +0.0725376 q^{3} +3.68286 q^{4} -3.05924 q^{5} -0.172921 q^{6} -4.27004 q^{7} -4.01173 q^{8} -2.99474 q^{9} +O(q^{10})$	\(q-2.38388 q^{2} +0.0725376 q^{3} +3.68286 q^{4} -3.05924 q^{5} -0.172921 q^{6} -4.27004 q^{7} -4.01173 q^{8} -2.99474 q^{9} +7.29285 q^{10} +2.46731 q^{11} +0.267146 q^{12} +1.00000 q^{13} +10.1792 q^{14} -0.221910 q^{15} +2.19774 q^{16} -1.27222 q^{17} +7.13908 q^{18} +0.997990 q^{19} -11.2668 q^{20} -0.309739 q^{21} -5.88175 q^{22} -0.383553 q^{23} -0.291001 q^{24} +4.35895 q^{25} -2.38388 q^{26} -0.434844 q^{27} -15.7260 q^{28} -4.72422 q^{29} +0.529005 q^{30} -3.53003 q^{31} +2.78431 q^{32} +0.178972 q^{33} +3.03282 q^{34} +13.0631 q^{35} -11.0292 q^{36} +6.07208 q^{37} -2.37908 q^{38} +0.0725376 q^{39} +12.2728 q^{40} -1.30094 q^{41} +0.738378 q^{42} -9.71207 q^{43} +9.08674 q^{44} +9.16162 q^{45} +0.914343 q^{46} +9.52442 q^{47} +0.159419 q^{48} +11.2333 q^{49} -10.3912 q^{50} -0.0922840 q^{51} +3.68286 q^{52} -11.0135 q^{53} +1.03661 q^{54} -7.54808 q^{55} +17.1303 q^{56} +0.0723917 q^{57} +11.2619 q^{58} -1.91373 q^{59} -0.817263 q^{60} -6.27105 q^{61} +8.41516 q^{62} +12.7877 q^{63} -11.0329 q^{64} -3.05924 q^{65} -0.426648 q^{66} -1.81943 q^{67} -4.68542 q^{68} -0.0278220 q^{69} -31.1408 q^{70} -0.711972 q^{71} +12.0141 q^{72} +0.825468 q^{73} -14.4751 q^{74} +0.316188 q^{75} +3.67546 q^{76} -10.5355 q^{77} -0.172921 q^{78} +4.55458 q^{79} -6.72343 q^{80} +8.95267 q^{81} +3.10129 q^{82} +10.8981 q^{83} -1.14072 q^{84} +3.89204 q^{85} +23.1524 q^{86} -0.342683 q^{87} -9.89817 q^{88} +0.955601 q^{89} -21.8402 q^{90} -4.27004 q^{91} -1.41257 q^{92} -0.256060 q^{93} -22.7050 q^{94} -3.05309 q^{95} +0.201967 q^{96} -1.49314 q^{97} -26.7787 q^{98} -7.38893 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 134 q - 6 q^{2} - 33 q^{3} + 98 q^{4} - 8 q^{5} - 16 q^{6} - 32 q^{7} - 15 q^{8} + 101 q^{9}+O(q^{10}) $ 134 * q - 6 * q^2 - 33 * q^3 + 98 * q^4 - 8 * q^5 - 16 * q^6 - 32 * q^7 - 15 * q^8 + 101 * q^9	\( 134 q - 6 q^{2} - 33 q^{3} + 98 q^{4} - 8 q^{5} - 16 q^{6} - 32 q^{7} - 15 q^{8} + 101 q^{9} - 33 q^{10} - 47 q^{11} - 53 q^{12} + 134 q^{13} - 28 q^{14} - 30 q^{15} + 30 q^{16} - 17 q^{17} - 14 q^{18} - 87 q^{19} - 12 q^{20} - 24 q^{21} - 52 q^{22} - 44 q^{23} - 36 q^{24} + 58 q^{25} - 6 q^{26} - 117 q^{27} - 71 q^{28} - 42 q^{29} - 21 q^{30} - 82 q^{31} - 31 q^{32} + 12 q^{33} - 30 q^{34} - 54 q^{35} + 32 q^{36} - 55 q^{37} - 12 q^{38} - 33 q^{39} - 86 q^{40} - 16 q^{41} + 6 q^{42} - 148 q^{43} - 54 q^{44} - 24 q^{45} - 57 q^{46} - 21 q^{47} - 82 q^{48} + 12 q^{49} - 17 q^{50} - 123 q^{51} + 98 q^{52} - 17 q^{53} - 10 q^{54} - 148 q^{55} - 47 q^{56} - q^{57} - 58 q^{58} - 64 q^{59} - 16 q^{60} - 112 q^{61} - 15 q^{62} - 58 q^{63} - 65 q^{64} - 8 q^{65} - 20 q^{66} - 110 q^{67} - 8 q^{68} - 57 q^{69} - 40 q^{70} - 78 q^{71} - 28 q^{72} - 43 q^{73} - 52 q^{74} - 150 q^{75} - 96 q^{76} - 24 q^{77} - 16 q^{78} - 228 q^{79} + 20 q^{80} + 54 q^{81} - 89 q^{82} - 12 q^{83} + 6 q^{84} - 77 q^{85} + 29 q^{86} - 77 q^{87} - 95 q^{88} - 32 q^{89} - 46 q^{90} - 32 q^{91} - 62 q^{92} - 9 q^{93} - 87 q^{94} - 61 q^{95} - 54 q^{96} - 38 q^{97} + 6 q^{98} - 193 q^{99}+O(q^{100}) \) 134 * q - 6 * q^2 - 33 * q^3 + 98 * q^4 - 8 * q^5 - 16 * q^6 - 32 * q^7 - 15 * q^8 + 101 * q^9 - 33 * q^10 - 47 * q^11 - 53 * q^12 + 134 * q^13 - 28 * q^14 - 30 * q^15 + 30 * q^16 - 17 * q^17 - 14 * q^18 - 87 * q^19 - 12 * q^20 - 24 * q^21 - 52 * q^22 - 44 * q^23 - 36 * q^24 + 58 * q^25 - 6 * q^26 - 117 * q^27 - 71 * q^28 - 42 * q^29 - 21 * q^30 - 82 * q^31 - 31 * q^32 + 12 * q^33 - 30 * q^34 - 54 * q^35 + 32 * q^36 - 55 * q^37 - 12 * q^38 - 33 * q^39 - 86 * q^40 - 16 * q^41 + 6 * q^42 - 148 * q^43 - 54 * q^44 - 24 * q^45 - 57 * q^46 - 21 * q^47 - 82 * q^48 + 12 * q^49 - 17 * q^50 - 123 * q^51 + 98 * q^52 - 17 * q^53 - 10 * q^54 - 148 * q^55 - 47 * q^56 - q^57 - 58 * q^58 - 64 * q^59 - 16 * q^60 - 112 * q^61 - 15 * q^62 - 58 * q^63 - 65 * q^64 - 8 * q^65 - 20 * q^66 - 110 * q^67 - 8 * q^68 - 57 * q^69 - 40 * q^70 - 78 * q^71 - 28 * q^72 - 43 * q^73 - 52 * q^74 - 150 * q^75 - 96 * q^76 - 24 * q^77 - 16 * q^78 - 228 * q^79 + 20 * q^80 + 54 * q^81 - 89 * q^82 - 12 * q^83 + 6 * q^84 - 77 * q^85 + 29 * q^86 - 77 * q^87 - 95 * q^88 - 32 * q^89 - 46 * q^90 - 32 * q^91 - 62 * q^92 - 9 * q^93 - 87 * q^94 - 61 * q^95 - 54 * q^96 - 38 * q^97 + 6 * q^98 - 193 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−2.38388	−1.68565	−0.842827	−	0.538184i	$-0.819110\pi$
$2$	−2.38388	−1.68565	−0.842827	+	0.538184i	$0.819110\pi$
$3$	0.0725376	0.0418796	0.0209398	−	0.999781i	$-0.493334\pi$
$3$	0.0725376	0.0418796	0.0209398	+	0.999781i	$0.493334\pi$
$4$	3.68286	1.84143
$5$	−3.05924	−1.36813	−0.684067	−	0.729419i	$-0.739790\pi$
$5$	−3.05924	−1.36813	−0.684067	+	0.729419i	$0.739790\pi$
$6$	−0.172921	−0.0705945
$7$	−4.27004	−1.61392	−0.806962	−	0.590603i	$-0.798890\pi$
$7$	−4.27004	−1.61392	−0.806962	+	0.590603i	$0.798890\pi$
$8$	−4.01173	−1.41836
$9$	−2.99474	−0.998246
$10$	7.29285	2.30620
$11$	2.46731	0.743921	0.371960	−	0.928249i	$-0.378686\pi$
$11$	2.46731	0.743921	0.371960	+	0.928249i	$0.378686\pi$
$12$	0.267146	0.0771183
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	10.1792	2.72052
$15$	−0.221910	−0.0572969
$16$	2.19774	0.549436
$17$	−1.27222	−0.308560	−0.154280	−	0.988027i	$-0.549306\pi$
$17$	−1.27222	−0.308560	−0.154280	+	0.988027i	$0.549306\pi$
$18$	7.13908	1.68270
$19$	0.997990	0.228954	0.114477	−	0.993426i	$-0.463481\pi$
$19$	0.997990	0.228954	0.114477	+	0.993426i	$0.463481\pi$
$20$	−11.2668	−2.51932
$21$	−0.309739	−0.0675905
$22$	−5.88175	−1.25399
$23$	−0.383553	−0.0799764	−0.0399882	−	0.999200i	$-0.512732\pi$
$23$	−0.383553	−0.0799764	−0.0399882	+	0.999200i	$0.512732\pi$
$24$	−0.291001	−0.0594004
$25$	4.35895	0.871790
$26$	−2.38388	−0.467516
$27$	−0.434844	−0.0836857
$28$	−15.7260	−2.97193
$29$	−4.72422	−0.877265	−0.438633	−	0.898666i	$-0.644537\pi$
$29$	−4.72422	−0.877265	−0.438633	+	0.898666i	$0.644537\pi$
$30$	0.529005	0.0965827
$31$	−3.53003	−0.634013	−0.317006	−	0.948423i	$-0.602678\pi$
$31$	−3.53003	−0.634013	−0.317006	+	0.948423i	$0.602678\pi$
$32$	2.78431	0.492202
$33$	0.178972	0.0311551
$34$	3.03282	0.520125
$35$	13.0631	2.20806
$36$	−11.0292	−1.83820
$37$	6.07208	0.998244	0.499122	−	0.866532i	$-0.333656\pi$
$37$	6.07208	0.998244	0.499122	+	0.866532i	$0.333656\pi$
$38$	−2.37908	−0.385938
$39$	0.0725376	0.0116153
$40$	12.2728	1.94051
$41$	−1.30094	−0.203173	−0.101587	−	0.994827i	$-0.532392\pi$
$41$	−1.30094	−0.203173	−0.101587	+	0.994827i	$0.532392\pi$
$42$	0.738378	0.113934
$43$	−9.71207	−1.48108	−0.740538	−	0.672014i	$-0.765429\pi$
$43$	−9.71207	−1.48108	−0.740538	+	0.672014i	$0.765429\pi$
$44$	9.08674	1.36988
$45$	9.16162	1.36573
$46$	0.914343	0.134813
$47$	9.52442	1.38928	0.694640	−	0.719357i	$-0.255564\pi$
$47$	9.52442	1.38928	0.694640	+	0.719357i	$0.255564\pi$
$48$	0.159419	0.0230102
$49$	11.2333	1.60475
$50$	−10.3912	−1.46954
$51$	−0.0922840	−0.0129223
$52$	3.68286	0.510721
$53$	−11.0135	−1.51283	−0.756413	−	0.654095i	$-0.773050\pi$
$53$	−11.0135	−1.51283	−0.756413	+	0.654095i	$0.773050\pi$
$54$	1.03661	0.141065
$55$	−7.54808	−1.01778
$56$	17.1303	2.28913
$57$	0.0723917	0.00958852
$58$	11.2619	1.47877
$59$	−1.91373	−0.249147	−0.124574	−	0.992210i	$-0.539756\pi$
$59$	−1.91373	−0.249147	−0.124574	+	0.992210i	$0.539756\pi$
$60$	−0.817263	−0.105508
$61$	−6.27105	−0.802925	−0.401463	−	0.915875i	$-0.631498\pi$
$61$	−6.27105	−0.802925	−0.401463	+	0.915875i	$0.631498\pi$
$62$	8.41516	1.06873
$63$	12.7877	1.61109
$64$	−11.0329	−1.37912
$65$	−3.05924	−0.379452
$66$	−0.426648	−0.0525167
$67$	−1.81943	−0.222279	−0.111139	−	0.993805i	$-0.535450\pi$
$67$	−1.81943	−0.222279	−0.111139	+	0.993805i	$0.535450\pi$
$68$	−4.68542	−0.568191
$69$	−0.0278220	−0.00334938
$70$	−31.1408	−3.72203
$71$	−0.711972	−0.0844955	−0.0422478	−	0.999107i	$-0.513452\pi$
$71$	−0.711972	−0.0844955	−0.0422478	+	0.999107i	$0.513452\pi$
$72$	12.0141	1.41587
$73$	0.825468	0.0966137	0.0483069	−	0.998833i	$-0.484617\pi$
$73$	0.825468	0.0966137	0.0483069	+	0.998833i	$0.484617\pi$
$74$	−14.4751	−1.68269
$75$	0.316188	0.0365102
$76$	3.67546	0.421604
$77$	−10.5355	−1.20063
$78$	−0.172921	−0.0195794
$79$	4.55458	0.512430	0.256215	−	0.966620i	$-0.417524\pi$
$79$	4.55458	0.512430	0.256215	+	0.966620i	$0.417524\pi$
$80$	−6.72343	−0.751702
$81$	8.95267	0.994741
$82$	3.10129	0.342480
$83$	10.8981	1.19622	0.598112	−	0.801413i	$-0.295918\pi$
$83$	10.8981	1.19622	0.598112	+	0.801413i	$0.295918\pi$
$84$	−1.14072	−0.124463
$85$	3.89204	0.422151
$86$	23.1524	2.49658
$87$	−0.342683	−0.0367395
$88$	−9.89817	−1.05515
$89$	0.955601	0.101294	0.0506468	−	0.998717i	$-0.483872\pi$
$89$	0.955601	0.101294	0.0506468	+	0.998717i	$0.483872\pi$
$90$	−21.8402	−2.30216
$91$	−4.27004	−0.447622
$92$	−1.41257	−0.147271
$93$	−0.256060	−0.0265522
$94$	−22.7050	−2.34185
$95$	−3.05309	−0.313240
$96$	0.201967	0.0206132
$97$	−1.49314	−0.151605	−0.0758025	−	0.997123i	$-0.524152\pi$
$97$	−1.49314	−0.151605	−0.0758025	+	0.997123i	$0.524152\pi$
$98$	−26.7787	−2.70506
$99$	−7.38893	−0.742616
$100$	16.0534	1.60534
$101$	6.85917	0.682513	0.341256	−	0.939970i	$-0.389148\pi$
$101$	6.85917	0.682513	0.341256	+	0.939970i	$0.389148\pi$
$102$	0.219994	0.0217826
$103$	12.3642	1.21828	0.609138	−	0.793064i	$-0.291515\pi$
$103$	12.3642	1.21828	0.609138	+	0.793064i	$0.291515\pi$
$104$	−4.01173	−0.393383
$105$	0.947564	0.0924728
$106$	26.2549	2.55010
$107$	3.30425	0.319434	0.159717	−	0.987163i	$-0.448942\pi$
$107$	3.30425	0.319434	0.159717	+	0.987163i	$0.448942\pi$
$108$	−1.60147	−0.154101
$109$	1.91827	0.183737	0.0918684	−	0.995771i	$-0.470716\pi$
$109$	1.91827	0.183737	0.0918684	+	0.995771i	$0.470716\pi$
$110$	17.9937	1.71563
$111$	0.440454	0.0418060
$112$	−9.38446	−0.886748
$113$	12.0944	1.13775	0.568875	−	0.822424i	$-0.307379\pi$
$113$	12.0944	1.13775	0.568875	+	0.822424i	$0.307379\pi$
$114$	−0.172573	−0.0161629
$115$	1.17338	0.109418
$116$	−17.3986	−1.61542
$117$	−2.99474	−0.276864
$118$	4.56210	0.419976
$119$	5.43245	0.497992
$120$	0.890243	0.0812677
$121$	−4.91240	−0.446582
$122$	14.9494	1.35345
$123$	−0.0943672	−0.00850880
$124$	−13.0006	−1.16749
$125$	1.96113	0.175409
$126$	−30.4842	−2.71575
$127$	10.6555	0.945526	0.472763	−	0.881190i	$-0.343257\pi$
$127$	10.6555	0.945526	0.472763	+	0.881190i	$0.343257\pi$
$128$	20.7325	1.83251
$129$	−0.704490	−0.0620269
$130$	7.29285	0.639625
$131$	12.3178	1.07621	0.538107	−	0.842877i	$-0.319140\pi$
$131$	12.3178	1.07621	0.538107	+	0.842877i	$0.319140\pi$
$132$	0.659130	0.0573699
$133$	−4.26146	−0.369515
$134$	4.33729	0.374685
$135$	1.33029	0.114493
$136$	5.10382	0.437649
$137$	15.6891	1.34041	0.670204	−	0.742177i	$-0.266206\pi$
$137$	15.6891	1.34041	0.670204	+	0.742177i	$0.266206\pi$
$138$	0.0663242	0.00564589
$139$	7.26944	0.616586	0.308293	−	0.951291i	$-0.400242\pi$
$139$	7.26944	0.616586	0.308293	+	0.951291i	$0.400242\pi$
$140$	48.1095	4.06600
$141$	0.690879	0.0581825
$142$	1.69725	0.142430
$143$	2.46731	0.206326
$144$	−6.58167	−0.548472
$145$	14.4525	1.20022
$146$	−1.96781	−0.162857
$147$	0.814834	0.0672064
$148$	22.3626	1.83820
$149$	−8.85272	−0.725243	−0.362621	−	0.931937i	$-0.618118\pi$
$149$	−8.85272	−0.725243	−0.362621	+	0.931937i	$0.618118\pi$
$150$	−0.753752	−0.0615436
$151$	17.7747	1.44648	0.723242	−	0.690595i	$-0.242651\pi$
$151$	17.7747	1.44648	0.723242	+	0.690595i	$0.242651\pi$
$152$	−4.00367	−0.324740
$153$	3.80998	0.308018
$154$	25.1153	2.02385
$155$	10.7992	0.867414
$156$	0.267146	0.0213888
$157$	18.0511	1.44063	0.720316	−	0.693646i	$-0.243997\pi$
$157$	18.0511	1.44063	0.720316	+	0.693646i	$0.243997\pi$
$158$	−10.8575	−0.863780
$159$	−0.798895	−0.0633565
$160$	−8.51789	−0.673398
$161$	1.63779	0.129076
$162$	−21.3421	−1.67679
$163$	−8.17059	−0.639970	−0.319985	−	0.947423i	$-0.603678\pi$
$163$	−8.17059	−0.639970	−0.319985	+	0.947423i	$0.603678\pi$
$164$	−4.79119	−0.374129
$165$	−0.547519	−0.0426243
$166$	−25.9798	−2.01642
$167$	12.8700	0.995908	0.497954	−	0.867203i	$-0.334085\pi$
$167$	12.8700	0.995908	0.497954	+	0.867203i	$0.334085\pi$
$168$	1.24259	0.0958677
$169$	1.00000	0.0769231
$170$	−9.27813	−0.711600
$171$	−2.98872	−0.228553
$172$	−35.7682	−2.72730
$173$	6.51353	0.495214	0.247607	−	0.968861i	$-0.420356\pi$
$173$	6.51353	0.495214	0.247607	+	0.968861i	$0.420356\pi$
$174$	0.816914	0.0619301
$175$	−18.6129	−1.40700
$176$	5.42251	0.408737
$177$	−0.138818	−0.0104342
$178$	−2.27803	−0.170746
$179$	−2.87992	−0.215255	−0.107628	−	0.994191i	$-0.534325\pi$
$179$	−2.87992	−0.215255	−0.107628	+	0.994191i	$0.534325\pi$
$180$	33.7410	2.51490
$181$	−8.19581	−0.609190	−0.304595	−	0.952482i	$-0.598521\pi$
$181$	−8.19581	−0.609190	−0.304595	+	0.952482i	$0.598521\pi$
$182$	10.1792	0.754536
$183$	−0.454886	−0.0336262
$184$	1.53871	0.113435
$185$	−18.5760	−1.36573
$186$	0.610415	0.0447578
$187$	−3.13896	−0.229544
$188$	35.0771	2.55826
$189$	1.85680	0.135062
$190$	7.27818	0.528015
$191$	8.70060	0.629554	0.314777	−	0.949166i	$-0.398070\pi$
$191$	8.70060	0.629554	0.314777	+	0.949166i	$0.398070\pi$
$192$	−0.800303	−0.0577569
$193$	5.83949	0.420336	0.210168	−	0.977665i	$-0.432599\pi$
$193$	5.83949	0.420336	0.210168	+	0.977665i	$0.432599\pi$
$194$	3.55945	0.255554
$195$	−0.221910	−0.0158913
$196$	41.3706	2.95504
$197$	−3.31836	−0.236423	−0.118212	−	0.992988i	$-0.537716\pi$
$197$	−3.31836	−0.236423	−0.118212	+	0.992988i	$0.537716\pi$
$198$	17.6143	1.25179
$199$	−27.2437	−1.93125	−0.965627	−	0.259931i	$-0.916300\pi$
$199$	−27.2437	−1.93125	−0.965627	+	0.259931i	$0.916300\pi$
$200$	−17.4869	−1.23651
$201$	−0.131977	−0.00930894
$202$	−16.3514	−1.15048
$203$	20.1726	1.41584
$204$	−0.339869	−0.0237956
$205$	3.97990	0.277968
$206$	−29.4746	−2.05359
$207$	1.14864	0.0798361
$208$	2.19774	0.152386
$209$	2.46234	0.170324
$210$	−2.25888	−0.155877
$211$	−11.8659	−0.816884	−0.408442	−	0.912784i	$-0.633928\pi$
$211$	−11.8659	−0.816884	−0.408442	+	0.912784i	$0.633928\pi$
$212$	−40.5613	−2.78576
$213$	−0.0516447	−0.00353864
$214$	−7.87692	−0.538455
$215$	29.7116	2.02631
$216$	1.74448	0.118697
$217$	15.0734	1.02325
$218$	−4.57291	−0.309717
$219$	0.0598774	0.00404614
$220$	−27.7985	−1.87418
$221$	−1.27222	−0.0855790
$222$	−1.04999	−0.0704705
$223$	15.5717	1.04276	0.521378	−	0.853326i	$-0.325418\pi$
$223$	15.5717	1.04276	0.521378	+	0.853326i	$0.325418\pi$
$224$	−11.8891	−0.794377
$225$	−13.0539	−0.870261
$226$	−28.8317	−1.91785
$227$	−17.2347	−1.14391	−0.571954	−	0.820286i	$-0.693814\pi$
$227$	−17.2347	−1.14391	−0.571954	+	0.820286i	$0.693814\pi$
$228$	0.266609	0.0176566
$229$	3.08595	0.203925	0.101963	−	0.994788i	$-0.467488\pi$
$229$	3.08595	0.203925	0.101963	+	0.994788i	$0.467488\pi$
$230$	−2.79719	−0.184442
$231$	−0.764219	−0.0502819
$232$	18.9523	1.24428
$233$	29.0422	1.90261	0.951307	−	0.308244i	$-0.0997412\pi$
$233$	29.0422	1.90261	0.951307	+	0.308244i	$0.0997412\pi$
$234$	7.13908	0.466696
$235$	−29.1375	−1.90072
$236$	−7.04802	−0.458787
$237$	0.330378	0.0214604
$238$	−12.9503	−0.839442
$239$	6.12984	0.396507	0.198253	−	0.980151i	$-0.436473\pi$
$239$	6.12984	0.396507	0.198253	+	0.980151i	$0.436473\pi$
$240$	−0.487701	−0.0314810
$241$	−12.0507	−0.776253	−0.388126	−	0.921606i	$-0.626878\pi$
$241$	−12.0507	−0.776253	−0.388126	+	0.921606i	$0.626878\pi$
$242$	11.7106	0.752783
$243$	1.95394	0.125345
$244$	−23.0954	−1.47853
$245$	−34.3653	−2.19552
$246$	0.224960	0.0143429
$247$	0.997990	0.0635006
$248$	14.1615	0.899259
$249$	0.790523	0.0500974
$250$	−4.67508	−0.295678
$251$	−10.2379	−0.646211	−0.323105	−	0.946363i	$-0.604727\pi$
$251$	−10.2379	−0.646211	−0.323105	+	0.946363i	$0.604727\pi$
$252$	47.0952	2.96672
$253$	−0.946343	−0.0594961
$254$	−25.4015	−1.59383
$255$	0.282319	0.0176795
$256$	−27.3579	−1.70987
$257$	−31.7414	−1.97997	−0.989986	−	0.141167i	$-0.954915\pi$
$257$	−31.7414	−1.97997	−0.989986	+	0.141167i	$0.954915\pi$
$258$	1.67942	0.104556
$259$	−25.9280	−1.61109
$260$	−11.2668	−0.698735
$261$	14.1478	0.875727
$262$	−29.3642	−1.81412
$263$	15.7889	0.973584	0.486792	−	0.873518i	$-0.338167\pi$
$263$	15.7889	0.973584	0.486792	+	0.873518i	$0.338167\pi$
$264$	−0.717989	−0.0441892
$265$	33.6930	2.06975
$266$	10.1588	0.622875
$267$	0.0693170	0.00424213
$268$	−6.70071	−0.409311
$269$	8.45013	0.515213	0.257607	−	0.966250i	$-0.417066\pi$
$269$	8.45013	0.515213	0.257607	+	0.966250i	$0.417066\pi$
$270$	−3.17125	−0.192996
$271$	−5.72517	−0.347779	−0.173890	−	0.984765i	$-0.555634\pi$
$271$	−5.72517	−0.347779	−0.173890	+	0.984765i	$0.555634\pi$
$272$	−2.79602	−0.169534
$273$	−0.309739	−0.0187462
$274$	−37.4008	−2.25947
$275$	10.7549	0.648542
$276$	−0.102465	−0.00616765
$277$	−22.3451	−1.34259	−0.671293	−	0.741192i	$-0.734261\pi$
$277$	−22.3451	−1.34259	−0.671293	+	0.741192i	$0.734261\pi$
$278$	−17.3294	−1.03935
$279$	10.5715	0.632901
$280$	−52.4056	−3.13183
$281$	6.08074	0.362747	0.181373	−	0.983414i	$-0.441946\pi$
$281$	6.08074	0.362747	0.181373	+	0.983414i	$0.441946\pi$
$282$	−1.64697	−0.0980755
$283$	−11.4280	−0.679327	−0.339663	−	0.940547i	$-0.610313\pi$
$283$	−11.4280	−0.679327	−0.339663	+	0.940547i	$0.610313\pi$
$284$	−2.62209	−0.155593
$285$	−0.221464	−0.0131184
$286$	−5.88175	−0.347795
$287$	5.55508	0.327906
$288$	−8.33829	−0.491339
$289$	−15.3814	−0.904791
$290$	−34.4530	−2.02315
$291$	−0.108308	−0.00634915
$292$	3.04008	0.177907
$293$	10.6980	0.624983	0.312491	−	0.949921i	$-0.398836\pi$
$293$	10.6980	0.624983	0.312491	+	0.949921i	$0.398836\pi$
$294$	−1.94246	−0.113287
$295$	5.85457	0.340866
$296$	−24.3596	−1.41587
$297$	−1.07289	−0.0622555
$298$	21.1038	1.22251
$299$	−0.383553	−0.0221815
$300$	1.16448	0.0672310
$301$	41.4710	2.39035
$302$	−42.3726	−2.43827
$303$	0.497547	0.0285834
$304$	2.19333	0.125796
$305$	19.1846	1.09851
$306$	−9.08251	−0.519213
$307$	−28.0803	−1.60263	−0.801314	−	0.598243i	$-0.795866\pi$
$307$	−28.0803	−1.60263	−0.801314	+	0.598243i	$0.795866\pi$
$308$	−38.8008	−2.21088
$309$	0.896866	0.0510209
$310$	−25.7440	−1.46216
$311$	−16.3006	−0.924325	−0.462162	−	0.886795i	$-0.652926\pi$
$311$	−16.3006	−0.924325	−0.462162	+	0.886795i	$0.652926\pi$
$312$	−0.291001	−0.0164747
$313$	−24.1431	−1.36465	−0.682326	−	0.731048i	$-0.739031\pi$
$313$	−24.1431	−1.36465	−0.682326	+	0.731048i	$0.739031\pi$
$314$	−43.0315	−2.42841
$315$	−39.1205	−2.20419
$316$	16.7739	0.943605
$317$	9.14823	0.513816	0.256908	−	0.966436i	$-0.417296\pi$
$317$	9.14823	0.513816	0.256908	+	0.966436i	$0.417296\pi$
$318$	1.90447	0.106797
$319$	−11.6561	−0.652616
$320$	33.7524	1.88682
$321$	0.239682	0.0133778
$322$	−3.90428	−0.217577
$323$	−1.26967	−0.0706461
$324$	32.9715	1.83175
$325$	4.35895	0.241791
$326$	19.4777	1.07877
$327$	0.139147	0.00769482
$328$	5.21903	0.288173
$329$	−40.6697	−2.24219
$330$	1.30522	0.0718499
$331$	11.9367	0.656102	0.328051	−	0.944660i	$-0.393608\pi$
$331$	11.9367	0.656102	0.328051	+	0.944660i	$0.393608\pi$
$332$	40.1363	2.20276
$333$	−18.1843	−0.996493
$334$	−30.6804	−1.67876
$335$	5.56607	0.304107
$336$	−0.680726	−0.0371367
$337$	−18.4406	−1.00453	−0.502263	−	0.864715i	$-0.667499\pi$
$337$	−18.4406	−1.00453	−0.502263	+	0.864715i	$0.667499\pi$
$338$	−2.38388	−0.129666
$339$	0.877302	0.0476485
$340$	14.3338	0.777361
$341$	−8.70967	−0.471655
$342$	7.12473	0.385261
$343$	−18.0762	−0.976025
$344$	38.9622	2.10070
$345$	0.0851142	0.00458240
$346$	−15.5274	−0.834760
$347$	−17.0338	−0.914425	−0.457212	−	0.889358i	$-0.651152\pi$
$347$	−17.0338	−0.914425	−0.457212	+	0.889358i	$0.651152\pi$
$348$	−1.26206	−0.0676533
$349$	34.5070	1.84712	0.923559	−	0.383456i	$-0.125266\pi$
$349$	34.5070	1.84712	0.923559	+	0.383456i	$0.125266\pi$
$350$	44.3708	2.37172
$351$	−0.434844	−0.0232102
$352$	6.86975	0.366159
$353$	−11.9159	−0.634218	−0.317109	−	0.948389i	$-0.602712\pi$
$353$	−11.9159	−0.634218	−0.317109	+	0.948389i	$0.602712\pi$
$354$	0.330924	0.0175884
$355$	2.17809	0.115601
$356$	3.51935	0.186525
$357$	0.394057	0.0208557
$358$	6.86537	0.362846
$359$	26.4579	1.39640	0.698198	−	0.715905i	$-0.253985\pi$
$359$	26.4579	1.39640	0.698198	+	0.715905i	$0.253985\pi$
$360$	−36.7540	−1.93710
$361$	−18.0040	−0.947580
$362$	19.5378	1.02688
$363$	−0.356334	−0.0187027
$364$	−15.7260	−0.824265
$365$	−2.52531	−0.132181
$366$	1.08439	0.0566821
$367$	−12.1968	−0.636668	−0.318334	−	0.947979i	$-0.603123\pi$
$367$	−12.1968	−0.636668	−0.318334	+	0.947979i	$0.603123\pi$
$368$	−0.842952	−0.0439419
$369$	3.89598	0.202817
$370$	44.2828	2.30215
$371$	47.0283	2.44159
$372$	−0.943034	−0.0488940
$373$	13.3334	0.690379	0.345190	−	0.938533i	$-0.387815\pi$
$373$	13.3334	0.690379	0.345190	+	0.938533i	$0.387815\pi$
$374$	7.48290	0.386932
$375$	0.142255	0.00734603
$376$	−38.2094	−1.97050
$377$	−4.72422	−0.243310
$378$	−4.42638	−0.227669
$379$	−12.2663	−0.630079	−0.315040	−	0.949079i	$-0.602018\pi$
$379$	−12.2663	−0.630079	−0.315040	+	0.949079i	$0.602018\pi$
$380$	−11.2441	−0.576810
$381$	0.772927	0.0395982
$382$	−20.7412	−1.06121
$383$	38.0672	1.94514	0.972571	−	0.232605i	$-0.0747250\pi$
$383$	38.0672	1.94514	0.972571	+	0.232605i	$0.0747250\pi$
$384$	1.50389	0.0767450
$385$	32.2306	1.64262
$386$	−13.9206	−0.708540
$387$	29.0851	1.47848
$388$	−5.49901	−0.279170
$389$	−16.7141	−0.847439	−0.423719	−	0.905794i	$-0.639276\pi$
$389$	−16.7141	−0.847439	−0.423719	+	0.905794i	$0.639276\pi$
$390$	0.529005	0.0267872
$391$	0.487966	0.0246775
$392$	−45.0648	−2.27612
$393$	0.893505	0.0450714
$394$	7.91055	0.398528
$395$	−13.9335	−0.701073
$396$	−27.2124	−1.36748
$397$	−15.3935	−0.772579	−0.386290	−	0.922378i	$-0.626243\pi$
$397$	−15.3935	−0.772579	−0.386290	+	0.922378i	$0.626243\pi$
$398$	64.9456	3.25543
$399$	−0.309116	−0.0154751
$400$	9.57986	0.478993
$401$	21.8936	1.09332	0.546658	−	0.837356i	$-0.315900\pi$
$401$	21.8936	1.09332	0.546658	+	0.837356i	$0.315900\pi$
$402$	0.314617	0.0156917
$403$	−3.53003	−0.175843
$404$	25.2614	1.25680
$405$	−27.3884	−1.36094
$406$	−48.0890	−2.38662
$407$	14.9817	0.742614
$408$	0.370219	0.0183286
$409$	−25.2287	−1.24748	−0.623739	−	0.781633i	$-0.714387\pi$
$409$	−25.2287	−1.24748	−0.623739	+	0.781633i	$0.714387\pi$
$410$	−9.48758	−0.468558
$411$	1.13805	0.0561358
$412$	45.5355	2.24337
$413$	8.17173	0.402104
$414$	−2.73822	−0.134576
$415$	−33.3400	−1.63659
$416$	2.78431	0.136512
$417$	0.527307	0.0258224
$418$	−5.86992	−0.287107
$419$	−18.4756	−0.902594	−0.451297	−	0.892374i	$-0.649039\pi$
$419$	−18.4756	−0.902594	−0.451297	+	0.892374i	$0.649039\pi$
$420$	3.48975	0.170282
$421$	−2.85206	−0.139001	−0.0695004	−	0.997582i	$-0.522141\pi$
$421$	−2.85206	−0.139001	−0.0695004	+	0.997582i	$0.522141\pi$
$422$	28.2869	1.37698
$423$	−28.5232	−1.38684
$424$	44.1833	2.14573
$425$	−5.54556	−0.268999
$426$	0.123115	0.00596492
$427$	26.7776	1.29586
$428$	12.1691	0.588215
$429$	0.178972	0.00864086
$430$	−70.8286	−3.41566
$431$	−33.4160	−1.60959	−0.804795	−	0.593552i	$-0.797725\pi$
$431$	−33.4160	−1.60959	−0.804795	+	0.593552i	$0.797725\pi$
$432$	−0.955675	−0.0459799
$433$	28.3945	1.36455	0.682276	−	0.731095i	$-0.260990\pi$
$433$	28.3945	1.36455	0.682276	+	0.731095i	$0.260990\pi$
$434$	−35.9331	−1.72484
$435$	1.04835	0.0502646
$436$	7.06472	0.338339
$437$	−0.382782	−0.0183110
$438$	−0.142740	−0.00682040
$439$	−8.88657	−0.424133	−0.212066	−	0.977255i	$-0.568019\pi$
$439$	−8.88657	−0.424133	−0.212066	+	0.977255i	$0.568019\pi$
$440$	30.2809	1.44358
$441$	−33.6407	−1.60194
$442$	3.03282	0.144257
$443$	34.8510	1.65582	0.827911	−	0.560859i	$-0.189529\pi$
$443$	34.8510	1.65582	0.827911	+	0.560859i	$0.189529\pi$
$444$	1.62213	0.0769829
$445$	−2.92341	−0.138583
$446$	−37.1209	−1.75773
$447$	−0.642154	−0.0303729
$448$	47.1112	2.22579
$449$	6.71237	0.316776	0.158388	−	0.987377i	$-0.449370\pi$
$449$	6.71237	0.316776	0.158388	+	0.987377i	$0.449370\pi$
$450$	31.1189	1.46696
$451$	−3.20982	−0.151145
$452$	44.5422	2.09509
$453$	1.28933	0.0605781
$454$	41.0854	1.92823
$455$	13.0631	0.612407
$456$	−0.290416	−0.0136000
$457$	−12.9944	−0.607853	−0.303926	−	0.952696i	$-0.598298\pi$
$457$	−12.9944	−0.607853	−0.303926	+	0.952696i	$0.598298\pi$
$458$	−7.35653	−0.343748
$459$	0.553219	0.0258220
$460$	4.32140	0.201486
$461$	−28.0745	−1.30756	−0.653779	−	0.756686i	$-0.726817\pi$
$461$	−28.0745	−1.30756	−0.653779	+	0.756686i	$0.726817\pi$
$462$	1.82180	0.0847580
$463$	16.3439	0.759566	0.379783	−	0.925076i	$-0.375999\pi$
$463$	16.3439	0.759566	0.379783	+	0.925076i	$0.375999\pi$
$464$	−10.3826	−0.482001
$465$	0.783349	0.0363269
$466$	−69.2329	−3.20715
$467$	7.07365	0.327330	0.163665	−	0.986516i	$-0.447668\pi$
$467$	7.07365	0.327330	0.163665	+	0.986516i	$0.447668\pi$
$468$	−11.0292	−0.509825
$469$	7.76904	0.358741
$470$	69.4602	3.20396
$471$	1.30938	0.0603330
$472$	7.67739	0.353380
$473$	−23.9626	−1.10180
$474$	−0.787580	−0.0361747
$475$	4.35019	0.199600
$476$	20.0070	0.917018
$477$	32.9826	1.51017
$478$	−14.6128	−0.668373
$479$	30.3242	1.38555	0.692774	−	0.721154i	$-0.256388\pi$
$479$	30.3242	1.38555	0.692774	+	0.721154i	$0.256388\pi$
$480$	−0.617867	−0.0282016
$481$	6.07208	0.276863
$482$	28.7273	1.30849
$483$	0.118801	0.00540564
$484$	−18.0917	−0.822350
$485$	4.56786	0.207416
$486$	−4.65794	−0.211288
$487$	−9.57286	−0.433788	−0.216894	−	0.976195i	$-0.569593\pi$
$487$	−9.57286	−0.433788	−0.216894	+	0.976195i	$0.569593\pi$
$488$	25.1578	1.13884
$489$	−0.592675	−0.0268017
$490$	81.9225	3.70088
$491$	−21.2584	−0.959378	−0.479689	−	0.877439i	$-0.659250\pi$
$491$	−21.2584	−0.959378	−0.479689	+	0.877439i	$0.659250\pi$
$492$	−0.347541	−0.0156684
$493$	6.01026	0.270689
$494$	−2.37908	−0.107040
$495$	22.6045	1.01600
$496$	−7.75811	−0.348349
$497$	3.04015	0.136369
$498$	−1.88451	−0.0844468
$499$	−0.956576	−0.0428222	−0.0214111	−	0.999771i	$-0.506816\pi$
$499$	−0.956576	−0.0428222	−0.0214111	+	0.999771i	$0.506816\pi$
$500$	7.22256	0.323003
$501$	0.933556	0.0417082
$502$	24.4059	1.08929
$503$	8.33514	0.371645	0.185823	−	0.982583i	$-0.440505\pi$
$503$	8.33514	0.371645	0.185823	+	0.982583i	$0.440505\pi$
$504$	−51.3007	−2.28511
$505$	−20.9838	−0.933769
$506$	2.25596	0.100290
$507$	0.0725376	0.00322151
$508$	39.2429	1.74112
$509$	28.7913	1.27615	0.638075	−	0.769974i	$-0.279731\pi$
$509$	28.7913	1.27615	0.638075	+	0.769974i	$0.279731\pi$
$510$	−0.673013	−0.0298015
$511$	−3.52478	−0.155927
$512$	23.7527	1.04973
$513$	−0.433969	−0.0191602
$514$	75.6674	3.33755
$515$	−37.8249	−1.66677
$516$	−2.59454	−0.114218
$517$	23.4997	1.03351
$518$	61.8092	2.71574
$519$	0.472475	0.0207394
$520$	12.2728	0.538200
$521$	−20.7726	−0.910066	−0.455033	−	0.890475i	$-0.650373\pi$
$521$	−20.7726	−0.910066	−0.455033	+	0.890475i	$0.650373\pi$
$522$	−33.7266	−1.47617
$523$	2.94231	0.128658	0.0643292	−	0.997929i	$-0.479509\pi$
$523$	2.94231	0.128658	0.0643292	+	0.997929i	$0.479509\pi$
$524$	45.3649	1.98177
$525$	−1.35013	−0.0589247
$526$	−37.6387	−1.64113
$527$	4.49099	0.195631
$528$	0.393335	0.0171177
$529$	−22.8529	−0.993604
$530$	−80.3200	−3.48888
$531$	5.73113	0.248710
$532$	−15.6944	−0.680437
$533$	−1.30094	−0.0563501
$534$	−0.165243	−0.00715077
$535$	−10.1085	−0.437028
$536$	7.29906	0.315272
$537$	−0.208902	−0.00901480
$538$	−20.1440	−0.868472
$539$	27.7159	1.19381
$540$	4.89928	0.210831
$541$	2.54836	0.109562	0.0547812	−	0.998498i	$-0.482554\pi$
$541$	2.54836	0.109562	0.0547812	+	0.998498i	$0.482554\pi$
$542$	13.6481	0.586236
$543$	−0.594504	−0.0255126
$544$	−3.54227	−0.151874
$545$	−5.86845	−0.251377
$546$	0.738378	0.0315997
$547$	29.7942	1.27391	0.636954	−	0.770902i	$-0.280194\pi$
$547$	29.7942	1.27391	0.636954	+	0.770902i	$0.280194\pi$
$548$	57.7807	2.46827
$549$	18.7801	0.801517
$550$	−25.6382	−1.09322
$551$	−4.71472	−0.200854
$552$	0.111614	0.00475063
$553$	−19.4482	−0.827024
$554$	53.2679	2.26314
$555$	−1.34745	−0.0571962
$556$	26.7723	1.13540
$557$	6.02751	0.255394	0.127697	−	0.991813i	$-0.459242\pi$
$557$	6.02751	0.255394	0.127697	+	0.991813i	$0.459242\pi$
$558$	−25.2012	−1.06685
$559$	−9.71207	−0.410777
$560$	28.7093	1.21319
$561$	−0.227693	−0.00961320
$562$	−14.4957	−0.611466
$563$	−35.0784	−1.47838	−0.739188	−	0.673499i	$-0.764791\pi$
$563$	−35.0784	−1.47838	−0.739188	+	0.673499i	$0.764791\pi$
$564$	2.54441	0.107139
$565$	−36.9998	−1.55659
$566$	27.2430	1.14511
$567$	−38.2283	−1.60544
$568$	2.85624	0.119845
$569$	2.47185	0.103625	0.0518127	−	0.998657i	$-0.483500\pi$
$569$	2.47185	0.103625	0.0518127	+	0.998657i	$0.483500\pi$
$570$	0.527942	0.0221130
$571$	−6.18518	−0.258842	−0.129421	−	0.991590i	$-0.541312\pi$
$571$	−6.18518	−0.258842	−0.129421	+	0.991590i	$0.541312\pi$
$572$	9.08674	0.379936
$573$	0.631121	0.0263654
$574$	−13.2426	−0.552736
$575$	−1.67189	−0.0697226
$576$	33.0408	1.37670
$577$	−22.5398	−0.938345	−0.469173	−	0.883106i	$-0.655448\pi$
$577$	−22.5398	−0.938345	−0.469173	+	0.883106i	$0.655448\pi$
$578$	36.6674	1.52516
$579$	0.423582	0.0176035
$580$	53.2266	2.21012
$581$	−46.5354	−1.93061
$582$	0.258194	0.0107025
$583$	−27.1737	−1.12542
$584$	−3.31156	−0.137033
$585$	9.16162	0.378787
$586$	−25.5027	−1.05350
$587$	−12.5970	−0.519935	−0.259968	−	0.965617i	$-0.583712\pi$
$587$	−12.5970	−0.519935	−0.259968	+	0.965617i	$0.583712\pi$
$588$	3.00092	0.123756
$589$	−3.52294	−0.145160
$590$	−13.9566	−0.574583
$591$	−0.240706	−0.00990130
$592$	13.3449	0.548471
$593$	−37.3313	−1.53301	−0.766507	−	0.642236i	$-0.778007\pi$
$593$	−37.3313	−1.53301	−0.766507	+	0.642236i	$0.778007\pi$
$594$	2.55764	0.104941
$595$	−16.6192	−0.681320
$596$	−32.6033	−1.33548
$597$	−1.97619	−0.0808801
$598$	0.914343	0.0373903
$599$	9.83716	0.401935	0.200968	−	0.979598i	$-0.435591\pi$
$599$	9.83716	0.401935	0.200968	+	0.979598i	$0.435591\pi$
$600$	−1.26846	−0.0517846
$601$	−20.3438	−0.829842	−0.414921	−	0.909857i	$-0.636191\pi$
$601$	−20.3438	−0.829842	−0.414921	+	0.909857i	$0.636191\pi$
$602$	−98.8616	−4.02930
$603$	5.44872	0.221889
$604$	65.4617	2.66360
$605$	15.0282	0.610984
$606$	−1.18609	−0.0481817
$607$	−12.8597	−0.521960	−0.260980	−	0.965344i	$-0.584046\pi$
$607$	−12.8597	−0.521960	−0.260980	+	0.965344i	$0.584046\pi$
$608$	2.77872	0.112692
$609$	1.46327	0.0592948
$610$	−45.7338	−1.85171
$611$	9.52442	0.385317
$612$	14.0316	0.567195
$613$	31.9646	1.29104	0.645518	−	0.763745i	$-0.276641\pi$
$613$	31.9646	1.29104	0.645518	+	0.763745i	$0.276641\pi$
$614$	66.9400	2.70148
$615$	0.288692	0.0116412
$616$	42.2656	1.70293
$617$	1.00000	0.0402585
$617$	1.00000	0.0402585
$618$	−2.13802	−0.0860036
$619$	−13.9613	−0.561153	−0.280576	−	0.959832i	$-0.590526\pi$
$619$	−13.9613	−0.561153	−0.280576	+	0.959832i	$0.590526\pi$
$620$	39.7720	1.59728
$621$	0.166786	0.00669288
$622$	38.8587	1.55809
$623$	−4.08046	−0.163480
$624$	0.159419	0.00638187
$625$	−27.7943	−1.11177
$626$	57.5542	2.30033
$627$	0.178612	0.00713310
$628$	66.4795	2.65282
$629$	−7.72505	−0.308018
$630$	93.2585	3.71551
$631$	−6.64143	−0.264391	−0.132196	−	0.991224i	$-0.542203\pi$
$631$	−6.64143	−0.264391	−0.132196	+	0.991224i	$0.542203\pi$
$632$	−18.2717	−0.726811
$633$	−0.860725	−0.0342107
$634$	−21.8082	−0.866116
$635$	−32.5979	−1.29361
$636$	−2.94222	−0.116667
$637$	11.2333	0.445078
$638$	27.7867	1.10008
$639$	2.13217	0.0843473
$640$	−63.4258	−2.50713
$641$	10.9178	0.431228	0.215614	−	0.976479i	$-0.430825\pi$
$641$	10.9178	0.431228	0.215614	+	0.976479i	$0.430825\pi$
$642$	−0.571372	−0.0225503
$643$	−18.3957	−0.725454	−0.362727	−	0.931895i	$-0.618154\pi$
$643$	−18.3957	−0.725454	−0.362727	+	0.931895i	$0.618154\pi$
$644$	6.03175	0.237684
$645$	2.15520	0.0848611
$646$	3.02673	0.119085
$647$	9.93421	0.390554	0.195277	−	0.980748i	$-0.437439\pi$
$647$	9.93421	0.390554	0.195277	+	0.980748i	$0.437439\pi$
$648$	−35.9157	−1.41090
$649$	−4.72177	−0.185346
$650$	−10.3912	−0.407576
$651$	1.09339	0.0428532
$652$	−30.0912	−1.17846
$653$	−19.6078	−0.767312	−0.383656	−	0.923476i	$-0.625335\pi$
$653$	−19.6078	−0.767312	−0.383656	+	0.923476i	$0.625335\pi$
$654$	−0.331708	−0.0129708
$655$	−37.6832	−1.47240
$656$	−2.85914	−0.111631
$657$	−2.47206	−0.0964443
$658$	96.9515	3.77956
$659$	20.1274	0.784052	0.392026	−	0.919954i	$-0.371774\pi$
$659$	20.1274	0.784052	0.392026	+	0.919954i	$0.371774\pi$
$660$	−2.01644	−0.0784897
$661$	−4.93888	−0.192100	−0.0960502	−	0.995376i	$-0.530621\pi$
$661$	−4.93888	−0.192100	−0.0960502	+	0.995376i	$0.530621\pi$
$662$	−28.4557	−1.10596
$663$	−0.0922840	−0.00358401
$664$	−43.7203	−1.69668
$665$	13.0368	0.505546
$666$	43.3491	1.67974
$667$	1.81199	0.0701605
$668$	47.3983	1.83390
$669$	1.12953	0.0436702
$670$	−13.2688	−0.512619
$671$	−15.4726	−0.597313
$672$	−0.862409	−0.0332682
$673$	45.9981	1.77310	0.886548	−	0.462636i	$-0.153096\pi$
$673$	45.9981	1.77310	0.886548	+	0.462636i	$0.153096\pi$
$674$	43.9602	1.69328
$675$	−1.89546	−0.0729564
$676$	3.68286	0.141649
$677$	19.3094	0.742119	0.371060	−	0.928609i	$-0.378995\pi$
$677$	19.3094	0.742119	0.371060	+	0.928609i	$0.378995\pi$
$678$	−2.09138	−0.0803189
$679$	6.37575	0.244679
$680$	−15.6138	−0.598762
$681$	−1.25016	−0.0479064
$682$	20.7628	0.795047
$683$	37.1164	1.42022	0.710110	−	0.704091i	$-0.248645\pi$
$683$	37.1164	1.42022	0.710110	+	0.704091i	$0.248645\pi$
$684$	−11.0070	−0.420864
$685$	−47.9967	−1.83386
$686$	43.0915	1.64524
$687$	0.223847	0.00854031
$688$	−21.3446	−0.813757
$689$	−11.0135	−0.419582
$690$	−0.202902	−0.00772434
$691$	2.20217	0.0837745	0.0418872	−	0.999122i	$-0.486663\pi$
$691$	2.20217	0.0837745	0.0418872	+	0.999122i	$0.486663\pi$
$692$	23.9884	0.911903
$693$	31.5511	1.19853
$694$	40.6066	1.54140
$695$	−22.2390	−0.843572
$696$	1.37475	0.0521099
$697$	1.65509	0.0626910
$698$	−82.2604	−3.11360
$699$	2.10665	0.0796807
$700$	−68.5487	−2.59090
$701$	3.88779	0.146840	0.0734199	−	0.997301i	$-0.476609\pi$
$701$	3.88779	0.146840	0.0734199	+	0.997301i	$0.476609\pi$
$702$	1.03661	0.0391244
$703$	6.05987	0.228552
$704$	−27.2216	−1.02595
$705$	−2.11356	−0.0796014
$706$	28.4060	1.06907
$707$	−29.2889	−1.10152
$708$	−0.511246	−0.0192138
$709$	13.5534	0.509009	0.254504	−	0.967072i	$-0.418088\pi$
$709$	13.5534	0.509009	0.254504	+	0.967072i	$0.418088\pi$
$710$	−5.19230	−0.194864
$711$	−13.6398	−0.511531
$712$	−3.83362	−0.143671
$713$	1.35396	0.0507060
$714$	−0.939382	−0.0351555
$715$	−7.54808	−0.282282
$716$	−10.6063	−0.396378
$717$	0.444644	0.0166055
$718$	−63.0724	−2.35384
$719$	48.4984	1.80869	0.904343	−	0.426807i	$-0.140362\pi$
$719$	48.4984	1.80869	0.904343	+	0.426807i	$0.140362\pi$
$720$	20.1349	0.750384
$721$	−52.7955	−1.96621
$722$	42.9193	1.59729
$723$	−0.874127	−0.0325091
$724$	−30.1840	−1.12178
$725$	−20.5926	−0.764791
$726$	0.849455	0.0315262
$727$	38.6817	1.43462	0.717312	−	0.696752i	$-0.245372\pi$
$727$	38.6817	1.43462	0.717312	+	0.696752i	$0.245372\pi$
$728$	17.1303	0.634890
$729$	−26.7163	−0.989492
$730$	6.02001	0.222811
$731$	12.3559	0.457000
$732$	−1.67528	−0.0619203
$733$	−32.9949	−1.21869	−0.609347	−	0.792904i	$-0.708568\pi$
$733$	−32.9949	−1.21869	−0.609347	+	0.792904i	$0.708568\pi$
$734$	29.0757	1.07320
$735$	−2.49277	−0.0919473
$736$	−1.06793	−0.0393645
$737$	−4.48909	−0.165358
$738$	−9.28754	−0.341879
$739$	19.5545	0.719322	0.359661	−	0.933083i	$-0.382892\pi$
$739$	19.5545	0.719322	0.359661	+	0.933083i	$0.382892\pi$
$740$	−68.4126	−2.51490
$741$	0.0723917	0.00265938
$742$	−112.110	−4.11567
$743$	−26.5914	−0.975542	−0.487771	−	0.872972i	$-0.662190\pi$
$743$	−26.5914	−0.975542	−0.487771	+	0.872972i	$0.662190\pi$
$744$	1.02724	0.0376606
$745$	27.0826	0.992229
$746$	−31.7853	−1.16374
$747$	−32.6370	−1.19413
$748$	−11.5604	−0.422689
$749$	−14.1093	−0.515542
$750$	−0.339119	−0.0123829
$751$	−14.7040	−0.536556	−0.268278	−	0.963342i	$-0.586455\pi$
$751$	−14.7040	−0.536556	−0.268278	+	0.963342i	$0.586455\pi$
$752$	20.9323	0.763321
$753$	−0.742632	−0.0270630
$754$	11.2619	0.410136
$755$	−54.3770	−1.97898
$756$	6.83834	0.248708
$757$	−12.1814	−0.442740	−0.221370	−	0.975190i	$-0.571053\pi$
$757$	−12.1814	−0.442740	−0.221370	+	0.975190i	$0.571053\pi$
$758$	29.2414	1.06210
$759$	−0.0686454	−0.00249167
$760$	12.2482	0.444288
$761$	−19.8061	−0.717970	−0.358985	−	0.933343i	$-0.616877\pi$
$761$	−19.8061	−0.717970	−0.358985	+	0.933343i	$0.616877\pi$
$762$	−1.84256	−0.0667489
$763$	−8.19109	−0.296537
$764$	32.0431	1.15928
$765$	−11.6556	−0.421410
$766$	−90.7474	−3.27884
$767$	−1.91373	−0.0691009
$768$	−1.98447	−0.0716086
$769$	46.1661	1.66479	0.832397	−	0.554181i	$-0.186968\pi$
$769$	46.1661	1.66479	0.832397	+	0.554181i	$0.186968\pi$
$770$	−76.8338	−2.76890
$771$	−2.30244	−0.0829204
$772$	21.5060	0.774019
$773$	−29.4075	−1.05771	−0.528857	−	0.848711i	$-0.677379\pi$
$773$	−29.4075	−1.05771	−0.528857	+	0.848711i	$0.677379\pi$
$774$	−69.3353	−2.49220
$775$	−15.3872	−0.552726
$776$	5.99006	0.215031
$777$	−1.88076	−0.0674718
$778$	39.8443	1.42849
$779$	−1.29833	−0.0465174
$780$	−0.817263	−0.0292627
$781$	−1.75665	−0.0628580
$782$	−1.16325	−0.0415977
$783$	2.05430	0.0734146
$784$	24.6878	0.881709
$785$	−55.2225	−1.97098
$786$	−2.13001	−0.0759748
$787$	−15.1455	−0.539880	−0.269940	−	0.962877i	$-0.587004\pi$
$787$	−15.1455	−0.539880	−0.269940	+	0.962877i	$0.587004\pi$
$788$	−12.2210	−0.435357
$789$	1.14529	0.0407733
$790$	33.2158	1.18177
$791$	−51.6438	−1.83624
$792$	29.6424	1.05330
$793$	−6.27105	−0.222691
$794$	36.6963	1.30230
$795$	2.44401	0.0866801
$796$	−100.335	−3.55627
$797$	11.5353	0.408601	0.204301	−	0.978908i	$-0.434508\pi$
$797$	11.5353	0.408601	0.204301	+	0.978908i	$0.434508\pi$
$798$	0.736893	0.0260857
$799$	−12.1172	−0.428676
$800$	12.1367	0.429097
$801$	−2.86178	−0.101116
$802$	−52.1917	−1.84295
$803$	2.03668	0.0718729
$804$	−0.486053	−0.0171418
$805$	−5.01039	−0.176593
$806$	8.41516	0.296411
$807$	0.612952	0.0215769
$808$	−27.5171	−0.968050
$809$	13.6513	0.479954	0.239977	−	0.970779i	$-0.422860\pi$
$809$	13.6513	0.479954	0.239977	+	0.970779i	$0.422860\pi$
$810$	65.2905	2.29407
$811$	11.8884	0.417459	0.208730	−	0.977973i	$-0.433067\pi$
$811$	11.8884	0.417459	0.208730	+	0.977973i	$0.433067\pi$
$812$	74.2929	2.60717
$813$	−0.415290	−0.0145649
$814$	−35.7144	−1.25179
$815$	24.9958	0.875565
$816$	−0.202817	−0.00710000
$817$	−9.69254	−0.339099
$818$	60.1420	2.10282
$819$	12.7877	0.446837
$820$	14.6574	0.511859
$821$	47.8997	1.67171	0.835855	−	0.548950i	$-0.184972\pi$
$821$	47.8997	1.67171	0.835855	+	0.548950i	$0.184972\pi$
$822$	−2.71296	−0.0946255
$823$	3.92822	0.136929	0.0684646	−	0.997654i	$-0.478190\pi$
$823$	3.92822	0.136929	0.0684646	+	0.997654i	$0.478190\pi$
$824$	−49.6017	−1.72796
$825$	0.780131	0.0271607
$826$	−19.4804	−0.677809
$827$	−7.76641	−0.270065	−0.135032	−	0.990841i	$-0.543114\pi$
$827$	−7.76641	−0.270065	−0.135032	+	0.990841i	$0.543114\pi$
$828$	4.23029	0.147013
$829$	−9.22162	−0.320280	−0.160140	−	0.987094i	$-0.551195\pi$
$829$	−9.22162	−0.320280	−0.160140	+	0.987094i	$0.551195\pi$
$830$	79.4783	2.75873
$831$	−1.62086	−0.0562269
$832$	−11.0329	−0.382499
$833$	−14.2912	−0.495162
$834$	−1.25703	−0.0435276
$835$	−39.3723	−1.36254
$836$	9.06847	0.313640
$837$	1.53501	0.0530578
$838$	44.0436	1.52146
$839$	19.2824	0.665704	0.332852	−	0.942979i	$-0.391989\pi$
$839$	19.2824	0.665704	0.332852	+	0.942979i	$0.391989\pi$
$840$	−3.80137	−0.131160
$841$	−6.68176	−0.230405
$842$	6.79895	0.234307
$843$	0.441082	0.0151917
$844$	−43.7005	−1.50423
$845$	−3.05924	−0.105241
$846$	67.9957	2.33774
$847$	20.9762	0.720750
$848$	−24.2049	−0.831201
$849$	−0.828963	−0.0284499
$850$	13.2199	0.453440
$851$	−2.32897	−0.0798359
$852$	−0.190200	−0.00651616
$853$	−36.6757	−1.25575	−0.627877	−	0.778313i	$-0.716076\pi$
$853$	−36.6757	−1.25575	−0.627877	+	0.778313i	$0.716076\pi$
$854$	−63.8346	−2.18437
$855$	9.14320	0.312691
$856$	−13.2558	−0.453072
$857$	−9.77484	−0.333902	−0.166951	−	0.985965i	$-0.553392\pi$
$857$	−9.77484	−0.333902	−0.166951	+	0.985965i	$0.553392\pi$
$858$	−0.426648	−0.0145655
$859$	−27.9366	−0.953183	−0.476592	−	0.879125i	$-0.658128\pi$
$859$	−27.9366	−0.953183	−0.476592	+	0.879125i	$0.658128\pi$
$860$	109.424	3.73131
$861$	0.402952	0.0137326
$862$	79.6595	2.71321
$863$	−16.3864	−0.557801	−0.278900	−	0.960320i	$-0.589970\pi$
$863$	−16.3864	−0.557801	−0.278900	+	0.960320i	$0.589970\pi$
$864$	−1.21074	−0.0411903
$865$	−19.9264	−0.677519
$866$	−67.6889	−2.30016
$867$	−1.11573	−0.0378923
$868$	55.5132	1.88424
$869$	11.2375	0.381207
$870$	−2.49914	−0.0847287
$871$	−1.81943	−0.0616490
$872$	−7.69558	−0.260605
$873$	4.47155	0.151339
$874$	0.912505	0.0308659
$875$	−8.37410	−0.283096
$876$	0.220520	0.00745069
$877$	47.1694	1.59280	0.796399	−	0.604772i	$-0.206736\pi$
$877$	47.1694	1.59280	0.796399	+	0.604772i	$0.206736\pi$
$878$	21.1845	0.714941
$879$	0.776006	0.0261740
$880$	−16.5887	−0.559207
$881$	−36.2487	−1.22125	−0.610625	−	0.791920i	$-0.709082\pi$
$881$	−36.2487	−1.22125	−0.610625	+	0.791920i	$0.709082\pi$
$882$	80.1952	2.70031
$883$	57.9434	1.94995	0.974975	−	0.222315i	$-0.0713612\pi$
$883$	57.9434	1.94995	0.974975	+	0.222315i	$0.0713612\pi$
$884$	−4.68542	−0.157588
$885$	0.424676	0.0142753
$886$	−83.0805	−2.79114
$887$	53.9569	1.81170	0.905848	−	0.423603i	$-0.139235\pi$
$887$	53.9569	1.81170	0.905848	+	0.423603i	$0.139235\pi$
$888$	−1.76698	−0.0592961
$889$	−45.4996	−1.52601
$890$	6.96905	0.233603
$891$	22.0890	0.740009
$892$	57.3483	1.92016
$893$	9.50528	0.318082
$894$	1.53082	0.0511981
$895$	8.81037	0.294498
$896$	−88.5288	−2.95754
$897$	−0.0278220	−0.000928950 0
$898$	−16.0015	−0.533976
$899$	16.6767	0.556197
$900$	−48.0758	−1.60253
$901$	14.0117	0.466797
$902$	7.65182	0.254778
$903$	3.00820	0.100107
$904$	−48.5197	−1.61374
$905$	25.0730	0.833453
$906$	−3.07361	−0.102114
$907$	7.32727	0.243298	0.121649	−	0.992573i	$-0.461182\pi$
$907$	7.32727	0.243298	0.121649	+	0.992573i	$0.461182\pi$
$908$	−63.4730	−2.10643
$909$	−20.5414	−0.681316
$910$	−31.1408	−1.03231
$911$	5.48479	0.181719	0.0908596	−	0.995864i	$-0.471039\pi$
$911$	5.48479	0.181719	0.0908596	+	0.995864i	$0.471039\pi$
$912$	0.159099	0.00526828
$913$	26.8890	0.889895
$914$	30.9770	1.02463
$915$	1.39161	0.0460051
$916$	11.3651	0.375515
$917$	−52.5977	−1.73693
$918$	−1.31880	−0.0435270
$919$	−42.3124	−1.39576	−0.697879	−	0.716215i	$-0.745873\pi$
$919$	−42.3124	−1.39576	−0.697879	+	0.716215i	$0.745873\pi$
$920$	−4.70729	−0.155195
$921$	−2.03688	−0.0671174
$922$	66.9260	2.20409
$923$	−0.711972	−0.0234348
$924$	−2.81451	−0.0925907
$925$	26.4679	0.870259
$926$	−38.9618	−1.28037
$927$	−37.0274	−1.21614
$928$	−13.1537	−0.431792
$929$	−36.9977	−1.21386	−0.606928	−	0.794757i	$-0.707598\pi$
$929$	−36.9977	−1.21386	−0.606928	+	0.794757i	$0.707598\pi$
$930$	−1.86741	−0.0612347
$931$	11.2107	0.367415
$932$	106.958	3.50353
$933$	−1.18241	−0.0387103
$934$	−16.8627	−0.551765
$935$	9.60285	0.314047
$936$	12.0141	0.392693
$937$	8.92499	0.291567	0.145783	−	0.989317i	$-0.453430\pi$
$937$	8.92499	0.291567	0.145783	+	0.989317i	$0.453430\pi$
$938$	−18.5204	−0.604714
$939$	−1.75128	−0.0571510
$940$	−107.309	−3.50005
$941$	−17.2917	−0.563693	−0.281846	−	0.959460i	$-0.590947\pi$
$941$	−17.2917	−0.563693	−0.281846	+	0.959460i	$0.590947\pi$
$942$	−3.12140	−0.101701
$943$	0.498981	0.0162490
$944$	−4.20590	−0.136890
$945$	−5.68040	−0.184783
$946$	57.1239	1.85726
$947$	13.5805	0.441308	0.220654	−	0.975352i	$-0.429181\pi$
$947$	13.5805	0.441308	0.220654	+	0.975352i	$0.429181\pi$
$948$	1.21674	0.0395178
$949$	0.825468	0.0267958
$950$	−10.3703	−0.336457
$951$	0.663591	0.0215184
$952$	−21.7935	−0.706332
$953$	3.84702	0.124617	0.0623086	−	0.998057i	$-0.480154\pi$
$953$	3.84702	0.124617	0.0623086	+	0.998057i	$0.480154\pi$
$954$	−78.6265	−2.54563
$955$	−26.6172	−0.861314
$956$	22.5754	0.730139
$957$	−0.845504	−0.0273313
$958$	−72.2891	−2.33556
$959$	−66.9931	−2.16332
$960$	2.44832	0.0790192
$961$	−18.5389	−0.598028
$962$	−14.4751	−0.466695
$963$	−9.89536	−0.318874
$964$	−44.3810	−1.42942
$965$	−17.8644	−0.575075
$966$	−0.283207	−0.00911204
$967$	−37.8233	−1.21632	−0.608158	−	0.793816i	$-0.708091\pi$
$967$	−37.8233	−1.21632	−0.608158	+	0.793816i	$0.708091\pi$
$968$	19.7072	0.633415
$969$	−0.0920985	−0.00295863
$970$	−10.8892	−0.349632
$971$	−59.3493	−1.90461	−0.952305	−	0.305148i	$-0.901294\pi$
$971$	−59.3493	−1.90461	−0.952305	+	0.305148i	$0.901294\pi$
$972$	7.19608	0.230814
$973$	−31.0408	−0.995123
$974$	22.8205	0.731216
$975$	0.316188	0.0101261
$976$	−13.7822	−0.441156
$977$	7.75157	0.247995	0.123997	−	0.992283i	$-0.460429\pi$
$977$	7.75157	0.247995	0.123997	+	0.992283i	$0.460429\pi$
$978$	1.41286	0.0451784
$979$	2.35776	0.0753544
$980$	−126.562	−4.04289
$981$	−5.74471	−0.183415
$982$	50.6774	1.61718
$983$	2.70192	0.0861779	0.0430889	−	0.999071i	$-0.486280\pi$
$983$	2.70192	0.0861779	0.0430889	+	0.999071i	$0.486280\pi$
$984$	0.378576	0.0120686
$985$	10.1516	0.323458
$986$	−14.3277	−0.456288
$987$	−2.95008	−0.0939021
$988$	3.67546	0.116932
$989$	3.72510	0.118451
$990$	−53.8864	−1.71262
$991$	−45.6185	−1.44912	−0.724560	−	0.689212i	$-0.757957\pi$
$991$	−45.6185	−1.44912	−0.724560	+	0.689212i	$0.757957\pi$
$992$	−9.82872	−0.312062
$993$	0.865862	0.0274773
$994$	−7.24734	−0.229872
$995$	83.3450	2.64221
$996$	2.91139	0.0922508
$997$	12.9654	0.410619	0.205310	−	0.978697i	$-0.434180\pi$
$997$	12.9654	0.410619	0.205310	+	0.978697i	$0.434180\pi$
$998$	2.28036	0.0721835
$999$	−2.64041	−0.0835387

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8021.2.a.a.1.11	✓	134

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8021.2.a.a.1.11	✓	134	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:	\( N \)	\(=\)	\( 8021 = 13 \cdot 617 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8021.a (trivial)

\(f(q)\)	\(=\)	\(q-2.38388 q^{2} +0.0725376 q^{3} +3.68286 q^{4} -3.05924 q^{5} -0.172921 q^{6} -4.27004 q^{7} -4.01173 q^{8} -2.99474 q^{9} +O(q^{10})\)	\(q-2.38388 q^{2} +0.0725376 q^{3} +3.68286 q^{4} -3.05924 q^{5} -0.172921 q^{6} -4.27004 q^{7} -4.01173 q^{8} -2.99474 q^{9} +7.29285 q^{10} +2.46731 q^{11} +0.267146 q^{12} +1.00000 q^{13} +10.1792 q^{14} -0.221910 q^{15} +2.19774 q^{16} -1.27222 q^{17} +7.13908 q^{18} +0.997990 q^{19} -11.2668 q^{20} -0.309739 q^{21} -5.88175 q^{22} -0.383553 q^{23} -0.291001 q^{24} +4.35895 q^{25} -2.38388 q^{26} -0.434844 q^{27} -15.7260 q^{28} -4.72422 q^{29} +0.529005 q^{30} -3.53003 q^{31} +2.78431 q^{32} +0.178972 q^{33} +3.03282 q^{34} +13.0631 q^{35} -11.0292 q^{36} +6.07208 q^{37} -2.37908 q^{38} +0.0725376 q^{39} +12.2728 q^{40} -1.30094 q^{41} +0.738378 q^{42} -9.71207 q^{43} +9.08674 q^{44} +9.16162 q^{45} +0.914343 q^{46} +9.52442 q^{47} +0.159419 q^{48} +11.2333 q^{49} -10.3912 q^{50} -0.0922840 q^{51} +3.68286 q^{52} -11.0135 q^{53} +1.03661 q^{54} -7.54808 q^{55} +17.1303 q^{56} +0.0723917 q^{57} +11.2619 q^{58} -1.91373 q^{59} -0.817263 q^{60} -6.27105 q^{61} +8.41516 q^{62} +12.7877 q^{63} -11.0329 q^{64} -3.05924 q^{65} -0.426648 q^{66} -1.81943 q^{67} -4.68542 q^{68} -0.0278220 q^{69} -31.1408 q^{70} -0.711972 q^{71} +12.0141 q^{72} +0.825468 q^{73} -14.4751 q^{74} +0.316188 q^{75} +3.67546 q^{76} -10.5355 q^{77} -0.172921 q^{78} +4.55458 q^{79} -6.72343 q^{80} +8.95267 q^{81} +3.10129 q^{82} +10.8981 q^{83} -1.14072 q^{84} +3.89204 q^{85} +23.1524 q^{86} -0.342683 q^{87} -9.89817 q^{88} +0.955601 q^{89} -21.8402 q^{90} -4.27004 q^{91} -1.41257 q^{92} -0.256060 q^{93} -22.7050 q^{94} -3.05309 q^{95} +0.201967 q^{96} -1.49314 q^{97} -26.7787 q^{98} -7.38893 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 134 q - 6 q^{2} - 33 q^{3} + 98 q^{4} - 8 q^{5} - 16 q^{6} - 32 q^{7} - 15 q^{8} + 101 q^{9}+O(q^{10}) \) 134 * q - 6 * q^2 - 33 * q^3 + 98 * q^4 - 8 * q^5 - 16 * q^6 - 32 * q^7 - 15 * q^8 + 101 * q^9	\( 134 q - 6 q^{2} - 33 q^{3} + 98 q^{4} - 8 q^{5} - 16 q^{6} - 32 q^{7} - 15 q^{8} + 101 q^{9} - 33 q^{10} - 47 q^{11} - 53 q^{12} + 134 q^{13} - 28 q^{14} - 30 q^{15} + 30 q^{16} - 17 q^{17} - 14 q^{18} - 87 q^{19} - 12 q^{20} - 24 q^{21} - 52 q^{22} - 44 q^{23} - 36 q^{24} + 58 q^{25} - 6 q^{26} - 117 q^{27} - 71 q^{28} - 42 q^{29} - 21 q^{30} - 82 q^{31} - 31 q^{32} + 12 q^{33} - 30 q^{34} - 54 q^{35} + 32 q^{36} - 55 q^{37} - 12 q^{38} - 33 q^{39} - 86 q^{40} - 16 q^{41} + 6 q^{42} - 148 q^{43} - 54 q^{44} - 24 q^{45} - 57 q^{46} - 21 q^{47} - 82 q^{48} + 12 q^{49} - 17 q^{50} - 123 q^{51} + 98 q^{52} - 17 q^{53} - 10 q^{54} - 148 q^{55} - 47 q^{56} - q^{57} - 58 q^{58} - 64 q^{59} - 16 q^{60} - 112 q^{61} - 15 q^{62} - 58 q^{63} - 65 q^{64} - 8 q^{65} - 20 q^{66} - 110 q^{67} - 8 q^{68} - 57 q^{69} - 40 q^{70} - 78 q^{71} - 28 q^{72} - 43 q^{73} - 52 q^{74} - 150 q^{75} - 96 q^{76} - 24 q^{77} - 16 q^{78} - 228 q^{79} + 20 q^{80} + 54 q^{81} - 89 q^{82} - 12 q^{83} + 6 q^{84} - 77 q^{85} + 29 q^{86} - 77 q^{87} - 95 q^{88} - 32 q^{89} - 46 q^{90} - 32 q^{91} - 62 q^{92} - 9 q^{93} - 87 q^{94} - 61 q^{95} - 54 q^{96} - 38 q^{97} + 6 q^{98} - 193 q^{99}+O(q^{100}) \) 134 * q - 6 * q^2 - 33 * q^3 + 98 * q^4 - 8 * q^5 - 16 * q^6 - 32 * q^7 - 15 * q^8 + 101 * q^9 - 33 * q^10 - 47 * q^11 - 53 * q^12 + 134 * q^13 - 28 * q^14 - 30 * q^15 + 30 * q^16 - 17 * q^17 - 14 * q^18 - 87 * q^19 - 12 * q^20 - 24 * q^21 - 52 * q^22 - 44 * q^23 - 36 * q^24 + 58 * q^25 - 6 * q^26 - 117 * q^27 - 71 * q^28 - 42 * q^29 - 21 * q^30 - 82 * q^31 - 31 * q^32 + 12 * q^33 - 30 * q^34 - 54 * q^35 + 32 * q^36 - 55 * q^37 - 12 * q^38 - 33 * q^39 - 86 * q^40 - 16 * q^41 + 6 * q^42 - 148 * q^43 - 54 * q^44 - 24 * q^45 - 57 * q^46 - 21 * q^47 - 82 * q^48 + 12 * q^49 - 17 * q^50 - 123 * q^51 + 98 * q^52 - 17 * q^53 - 10 * q^54 - 148 * q^55 - 47 * q^56 - q^57 - 58 * q^58 - 64 * q^59 - 16 * q^60 - 112 * q^61 - 15 * q^62 - 58 * q^63 - 65 * q^64 - 8 * q^65 - 20 * q^66 - 110 * q^67 - 8 * q^68 - 57 * q^69 - 40 * q^70 - 78 * q^71 - 28 * q^72 - 43 * q^73 - 52 * q^74 - 150 * q^75 - 96 * q^76 - 24 * q^77 - 16 * q^78 - 228 * q^79 + 20 * q^80 + 54 * q^81 - 89 * q^82 - 12 * q^83 + 6 * q^84 - 77 * q^85 + 29 * q^86 - 77 * q^87 - 95 * q^88 - 32 * q^89 - 46 * q^90 - 32 * q^91 - 62 * q^92 - 9 * q^93 - 87 * q^94 - 61 * q^95 - 54 * q^96 - 38 * q^97 + 6 * q^98 - 193 * q^99

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