LMFDB - Embedded newform 8029.2.a.d.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8029,2,Mod(1,8029)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8029, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("8029.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8029 = 7 \cdot 31 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8029.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:	$64.1118877829$
Analytic rank:	$1$
Dimension:	$66$
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Character	$\chi$	$=$	8029.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.49545 q^{2} -2.27678 q^{3} +4.22728 q^{4} -4.17212 q^{5} +5.68159 q^{6} +1.00000 q^{7} -5.55806 q^{8} +2.18372 q^{9} +O(q^{10})$	\(q-2.49545 q^{2} -2.27678 q^{3} +4.22728 q^{4} -4.17212 q^{5} +5.68159 q^{6} +1.00000 q^{7} -5.55806 q^{8} +2.18372 q^{9} +10.4113 q^{10} -4.41097 q^{11} -9.62457 q^{12} -3.12944 q^{13} -2.49545 q^{14} +9.49899 q^{15} +5.41532 q^{16} +0.137262 q^{17} -5.44937 q^{18} +1.70235 q^{19} -17.6367 q^{20} -2.27678 q^{21} +11.0074 q^{22} -4.43394 q^{23} +12.6545 q^{24} +12.4066 q^{25} +7.80937 q^{26} +1.85849 q^{27} +4.22728 q^{28} -9.68642 q^{29} -23.7043 q^{30} +1.00000 q^{31} -2.39754 q^{32} +10.0428 q^{33} -0.342531 q^{34} -4.17212 q^{35} +9.23119 q^{36} -1.00000 q^{37} -4.24812 q^{38} +7.12505 q^{39} +23.1889 q^{40} -11.0937 q^{41} +5.68159 q^{42} -10.5358 q^{43} -18.6464 q^{44} -9.11074 q^{45} +11.0647 q^{46} +7.71961 q^{47} -12.3295 q^{48} +1.00000 q^{49} -30.9600 q^{50} -0.312516 q^{51} -13.2290 q^{52} -6.29701 q^{53} -4.63777 q^{54} +18.4031 q^{55} -5.55806 q^{56} -3.87587 q^{57} +24.1720 q^{58} -1.32341 q^{59} +40.1549 q^{60} -2.44182 q^{61} -2.49545 q^{62} +2.18372 q^{63} -4.84770 q^{64} +13.0564 q^{65} -25.0613 q^{66} +8.55448 q^{67} +0.580246 q^{68} +10.0951 q^{69} +10.4113 q^{70} +14.3237 q^{71} -12.1372 q^{72} -0.114873 q^{73} +2.49545 q^{74} -28.2470 q^{75} +7.19629 q^{76} -4.41097 q^{77} -17.7802 q^{78} +7.44898 q^{79} -22.5934 q^{80} -10.7825 q^{81} +27.6839 q^{82} +2.70070 q^{83} -9.62457 q^{84} -0.572675 q^{85} +26.2915 q^{86} +22.0538 q^{87} +24.5165 q^{88} +0.294910 q^{89} +22.7354 q^{90} -3.12944 q^{91} -18.7435 q^{92} -2.27678 q^{93} -19.2639 q^{94} -7.10239 q^{95} +5.45866 q^{96} -15.8339 q^{97} -2.49545 q^{98} -9.63232 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 66 q - 5 q^{2} - 12 q^{3} + 63 q^{4} - 26 q^{5} - 19 q^{6} + 66 q^{7} - 15 q^{8} + 66 q^{9}+O(q^{10}) $ 66 * q - 5 * q^2 - 12 * q^3 + 63 * q^4 - 26 * q^5 - 19 * q^6 + 66 * q^7 - 15 * q^8 + 66 * q^9	\( 66 q - 5 q^{2} - 12 q^{3} + 63 q^{4} - 26 q^{5} - 19 q^{6} + 66 q^{7} - 15 q^{8} + 66 q^{9} - 6 q^{10} - 57 q^{11} - 29 q^{12} - 28 q^{13} - 5 q^{14} - 24 q^{15} + 69 q^{16} - 47 q^{17} + 8 q^{18} - 27 q^{19} - 77 q^{20} - 12 q^{21} - 12 q^{22} - 46 q^{23} - 57 q^{24} + 72 q^{25} - 21 q^{26} - 36 q^{27} + 63 q^{28} - 62 q^{29} + 2 q^{30} + 66 q^{31} - 40 q^{32} + 4 q^{33} - 46 q^{34} - 26 q^{35} + 62 q^{36} - 66 q^{37} - 31 q^{38} - 8 q^{39} - 37 q^{40} - 33 q^{41} - 19 q^{42} - 22 q^{43} - 84 q^{44} - 77 q^{45} - 14 q^{46} - 20 q^{47} - 43 q^{48} + 66 q^{49} - 10 q^{50} - 39 q^{51} - 41 q^{52} - 47 q^{53} - 65 q^{54} - 15 q^{55} - 15 q^{56} + 5 q^{57} + 24 q^{58} - 125 q^{59} - 77 q^{60} - 57 q^{61} - 5 q^{62} + 66 q^{63} + 81 q^{64} - 40 q^{65} + 33 q^{66} - 25 q^{67} - 107 q^{68} - 72 q^{69} - 6 q^{70} - 57 q^{71} + 38 q^{72} + 5 q^{73} + 5 q^{74} - 60 q^{75} - 33 q^{76} - 57 q^{77} - 19 q^{78} - 4 q^{79} - 132 q^{80} + 58 q^{81} + 8 q^{82} - 84 q^{83} - 29 q^{84} - 33 q^{85} - 60 q^{86} - 31 q^{87} + 21 q^{88} - 132 q^{89} - 61 q^{90} - 28 q^{91} - 100 q^{92} - 12 q^{93} - 35 q^{94} + 4 q^{95} - 198 q^{96} - 39 q^{97} - 5 q^{98} - 174 q^{99}+O(q^{100}) \) 66 * q - 5 * q^2 - 12 * q^3 + 63 * q^4 - 26 * q^5 - 19 * q^6 + 66 * q^7 - 15 * q^8 + 66 * q^9 - 6 * q^10 - 57 * q^11 - 29 * q^12 - 28 * q^13 - 5 * q^14 - 24 * q^15 + 69 * q^16 - 47 * q^17 + 8 * q^18 - 27 * q^19 - 77 * q^20 - 12 * q^21 - 12 * q^22 - 46 * q^23 - 57 * q^24 + 72 * q^25 - 21 * q^26 - 36 * q^27 + 63 * q^28 - 62 * q^29 + 2 * q^30 + 66 * q^31 - 40 * q^32 + 4 * q^33 - 46 * q^34 - 26 * q^35 + 62 * q^36 - 66 * q^37 - 31 * q^38 - 8 * q^39 - 37 * q^40 - 33 * q^41 - 19 * q^42 - 22 * q^43 - 84 * q^44 - 77 * q^45 - 14 * q^46 - 20 * q^47 - 43 * q^48 + 66 * q^49 - 10 * q^50 - 39 * q^51 - 41 * q^52 - 47 * q^53 - 65 * q^54 - 15 * q^55 - 15 * q^56 + 5 * q^57 + 24 * q^58 - 125 * q^59 - 77 * q^60 - 57 * q^61 - 5 * q^62 + 66 * q^63 + 81 * q^64 - 40 * q^65 + 33 * q^66 - 25 * q^67 - 107 * q^68 - 72 * q^69 - 6 * q^70 - 57 * q^71 + 38 * q^72 + 5 * q^73 + 5 * q^74 - 60 * q^75 - 33 * q^76 - 57 * q^77 - 19 * q^78 - 4 * q^79 - 132 * q^80 + 58 * q^81 + 8 * q^82 - 84 * q^83 - 29 * q^84 - 33 * q^85 - 60 * q^86 - 31 * q^87 + 21 * q^88 - 132 * q^89 - 61 * q^90 - 28 * q^91 - 100 * q^92 - 12 * q^93 - 35 * q^94 + 4 * q^95 - 198 * q^96 - 39 * q^97 - 5 * q^98 - 174 * 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 $

$2$	−2.49545	−1.76455	−0.882275	−	0.470734i	$-0.843989\pi$
$2$	−2.49545	−1.76455	−0.882275	+	0.470734i	$0.843989\pi$
$3$	−2.27678	−1.31450	−0.657249	−	0.753673i	$-0.728280\pi$
$3$	−2.27678	−1.31450	−0.657249	+	0.753673i	$0.728280\pi$
$4$	4.22728	2.11364
$5$	−4.17212	−1.86583	−0.932914	−	0.360098i	$-0.882743\pi$
$5$	−4.17212	−1.86583	−0.932914	+	0.360098i	$0.882743\pi$
$6$	5.68159	2.31950
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−5.55806	−1.96507
$9$	2.18372	0.727906
$10$	10.4113	3.29235
$11$	−4.41097	−1.32996	−0.664979	−	0.746862i	$-0.731560\pi$
$11$	−4.41097	−1.32996	−0.664979	+	0.746862i	$0.731560\pi$
$12$	−9.62457	−2.77837
$13$	−3.12944	−0.867951	−0.433976	−	0.900925i	$-0.642890\pi$
$13$	−3.12944	−0.867951	−0.433976	+	0.900925i	$0.642890\pi$
$14$	−2.49545	−0.666937
$15$	9.49899	2.45263
$16$	5.41532	1.35383
$17$	0.137262	0.0332910	0.0166455	−	0.999861i	$-0.494701\pi$
$17$	0.137262	0.0332910	0.0166455	+	0.999861i	$0.494701\pi$
$18$	−5.44937	−1.28443
$19$	1.70235	0.390545	0.195273	−	0.980749i	$-0.437441\pi$
$19$	1.70235	0.390545	0.195273	+	0.980749i	$0.437441\pi$
$20$	−17.6367	−3.94369
$21$	−2.27678	−0.496834
$22$	11.0074	2.34678
$23$	−4.43394	−0.924541	−0.462270	−	0.886739i	$-0.652965\pi$
$23$	−4.43394	−0.924541	−0.462270	+	0.886739i	$0.652965\pi$
$24$	12.6545	2.58308
$25$	12.4066	2.48132
$26$	7.80937	1.53154
$27$	1.85849	0.357667
$28$	4.22728	0.798880
$29$	−9.68642	−1.79872	−0.899362	−	0.437205i	$-0.855968\pi$
$29$	−9.68642	−1.79872	−0.899362	+	0.437205i	$0.855968\pi$
$30$	−23.7043	−4.32779
$31$	1.00000	0.179605
$31$	1.00000	0.179605
$32$	−2.39754	−0.423829
$33$	10.0428	1.74823
$34$	−0.342531	−0.0587437
$35$	−4.17212	−0.705217
$36$	9.23119	1.53853
$37$	−1.00000	−0.164399
$37$	−1.00000	−0.164399
$38$	−4.24812	−0.689137
$39$	7.12505	1.14092
$40$	23.1889	3.66649
$41$	−11.0937	−1.73255	−0.866275	−	0.499567i	$-0.833493\pi$
$41$	−11.0937	−1.73255	−0.866275	+	0.499567i	$0.833493\pi$
$42$	5.68159	0.876688
$43$	−10.5358	−1.60669	−0.803345	−	0.595514i	$-0.796948\pi$
$43$	−10.5358	−1.60669	−0.803345	+	0.595514i	$0.796948\pi$
$44$	−18.6464	−2.81105
$45$	−9.11074	−1.35815
$46$	11.0647	1.63140
$47$	7.71961	1.12602	0.563010	−	0.826450i	$-0.309643\pi$
$47$	7.71961	1.12602	0.563010	+	0.826450i	$0.309643\pi$
$48$	−12.3295	−1.77961
$49$	1.00000	0.142857
$50$	−30.9600	−4.37841
$51$	−0.312516	−0.0437610
$52$	−13.2290	−1.83454
$53$	−6.29701	−0.864961	−0.432481	−	0.901643i	$-0.642362\pi$
$53$	−6.29701	−0.864961	−0.432481	+	0.901643i	$0.642362\pi$
$54$	−4.63777	−0.631121
$55$	18.4031	2.48147
$56$	−5.55806	−0.742727
$57$	−3.87587	−0.513371
$58$	24.1720	3.17394
$59$	−1.32341	−0.172293	−0.0861463	−	0.996282i	$-0.527455\pi$
$59$	−1.32341	−0.172293	−0.0861463	+	0.996282i	$0.527455\pi$
$60$	40.1549	5.18397
$61$	−2.44182	−0.312644	−0.156322	−	0.987706i	$-0.549964\pi$
$61$	−2.44182	−0.312644	−0.156322	+	0.987706i	$0.549964\pi$
$62$	−2.49545	−0.316923
$63$	2.18372	0.275123
$64$	−4.84770	−0.605962
$65$	13.0564	1.61945
$66$	−25.0613	−3.08484
$67$	8.55448	1.04510	0.522548	−	0.852610i	$-0.324982\pi$
$67$	8.55448	1.04510	0.522548	+	0.852610i	$0.324982\pi$
$68$	0.580246	0.0703651
$69$	10.0951	1.21531
$70$	10.4113	1.24439
$71$	14.3237	1.69991	0.849955	−	0.526855i	$-0.176629\pi$
$71$	14.3237	1.69991	0.849955	+	0.526855i	$0.176629\pi$
$72$	−12.1372	−1.43039
$73$	−0.114873	−0.0134448	−0.00672241	−	0.999977i	$-0.502140\pi$
$73$	−0.114873	−0.0134448	−0.00672241	+	0.999977i	$0.502140\pi$
$74$	2.49545	0.290090
$75$	−28.2470	−3.26169
$76$	7.19629	0.825471
$77$	−4.41097	−0.502677
$78$	−17.7802	−2.01321
$79$	7.44898	0.838076	0.419038	−	0.907969i	$-0.362367\pi$
$79$	7.44898	0.838076	0.419038	+	0.907969i	$0.362367\pi$
$80$	−22.5934	−2.52601
$81$	−10.7825	−1.19806
$82$	27.6839	3.05717
$83$	2.70070	0.296440	0.148220	−	0.988954i	$-0.452646\pi$
$83$	2.70070	0.296440	0.148220	+	0.988954i	$0.452646\pi$
$84$	−9.62457	−1.05013
$85$	−0.572675	−0.0621153
$86$	26.2915	2.83509
$87$	22.0538	2.36442
$88$	24.5165	2.61346
$89$	0.294910	0.0312604	0.0156302	−	0.999878i	$-0.495025\pi$
$89$	0.294910	0.0312604	0.0156302	+	0.999878i	$0.495025\pi$
$90$	22.7354	2.39652
$91$	−3.12944	−0.328055
$92$	−18.7435	−1.95415
$93$	−2.27678	−0.236091
$94$	−19.2639	−1.98692
$95$	−7.10239	−0.728690
$96$	5.45866	0.557122
$97$	−15.8339	−1.60769	−0.803845	−	0.594839i	$-0.797216\pi$
$97$	−15.8339	−1.60769	−0.803845	+	0.594839i	$0.797216\pi$
$98$	−2.49545	−0.252079
$99$	−9.63232	−0.968085
$100$	52.4461	5.24461
$101$	−10.8645	−1.08106	−0.540528	−	0.841326i	$-0.681775\pi$
$101$	−10.8645	−1.08106	−0.540528	+	0.841326i	$0.681775\pi$
$102$	0.779868	0.0772184
$103$	−6.72576	−0.662709	−0.331355	−	0.943506i	$-0.607506\pi$
$103$	−6.72576	−0.662709	−0.331355	+	0.943506i	$0.607506\pi$
$104$	17.3936	1.70559
$105$	9.49899	0.927007
$106$	15.7139	1.52627
$107$	3.64014	0.351906	0.175953	−	0.984399i	$-0.443699\pi$
$107$	3.64014	0.351906	0.175953	+	0.984399i	$0.443699\pi$
$108$	7.85635	0.755978
$109$	2.78417	0.266675	0.133338	−	0.991071i	$-0.457431\pi$
$109$	2.78417	0.266675	0.133338	+	0.991071i	$0.457431\pi$
$110$	−45.9240	−4.37869
$111$	2.27678	0.216102
$112$	5.41532	0.511699
$113$	14.0563	1.32230	0.661150	−	0.750253i	$-0.270069\pi$
$113$	14.0563	1.32230	0.661150	+	0.750253i	$0.270069\pi$
$114$	9.67203	0.905869
$115$	18.4989	1.72503
$116$	−40.9472	−3.80185
$117$	−6.83383	−0.631787
$118$	3.30249	0.304019
$119$	0.137262	0.0125828
$120$	−52.7960	−4.81959
$121$	8.45667	0.768788
$122$	6.09345	0.551675
$123$	25.2580	2.27744
$124$	4.22728	0.379621
$125$	−30.9012	−2.76388
$126$	−5.44937	−0.485468
$127$	−6.15720	−0.546363	−0.273181	−	0.961963i	$-0.588076\pi$
$127$	−6.15720	−0.546363	−0.273181	+	0.961963i	$0.588076\pi$
$128$	16.8923	1.49308
$129$	23.9876	2.11199
$130$	−32.5816	−2.85760
$131$	−6.28986	−0.549548	−0.274774	−	0.961509i	$-0.588603\pi$
$131$	−6.28986	−0.549548	−0.274774	+	0.961509i	$0.588603\pi$
$132$	42.4537	3.69512
$133$	1.70235	0.147612
$134$	−21.3473	−1.84412
$135$	−7.75384	−0.667344
$136$	−0.762912	−0.0654192
$137$	8.03157	0.686183	0.343091	−	0.939302i	$-0.388526\pi$
$137$	8.03157	0.686183	0.343091	+	0.939302i	$0.388526\pi$
$138$	−25.1918	−2.14447
$139$	−5.60728	−0.475603	−0.237801	−	0.971314i	$-0.576427\pi$
$139$	−5.60728	−0.475603	−0.237801	+	0.971314i	$0.576427\pi$
$140$	−17.6367	−1.49057
$141$	−17.5758	−1.48015
$142$	−35.7441	−2.99958
$143$	13.8039	1.15434
$144$	11.8255	0.985461
$145$	40.4129	3.35611
$146$	0.286659	0.0237241
$147$	−2.27678	−0.187786
$148$	−4.22728	−0.347480
$149$	5.80206	0.475323	0.237662	−	0.971348i	$-0.423619\pi$
$149$	5.80206	0.475323	0.237662	+	0.971348i	$0.423619\pi$
$150$	70.4891	5.75541
$151$	−15.8639	−1.29098	−0.645492	−	0.763767i	$-0.723348\pi$
$151$	−15.8639	−1.29098	−0.645492	+	0.763767i	$0.723348\pi$
$152$	−9.46175	−0.767449
$153$	0.299742	0.0242327
$154$	11.0074	0.886999
$155$	−4.17212	−0.335113
$156$	30.1195	2.41149
$157$	−4.49290	−0.358572	−0.179286	−	0.983797i	$-0.557379\pi$
$157$	−4.49290	−0.358572	−0.179286	+	0.983797i	$0.557379\pi$
$158$	−18.5886	−1.47883
$159$	14.3369	1.13699
$160$	10.0028	0.790792
$161$	−4.43394	−0.349444
$162$	26.9073	2.11403
$163$	7.47443	0.585442	0.292721	−	0.956198i	$-0.405439\pi$
$163$	7.47443	0.585442	0.292721	+	0.956198i	$0.405439\pi$
$164$	−46.8963	−3.66199
$165$	−41.8998	−3.26189
$166$	−6.73946	−0.523084
$167$	−9.67189	−0.748433	−0.374217	−	0.927341i	$-0.622088\pi$
$167$	−9.67189	−0.748433	−0.374217	+	0.927341i	$0.622088\pi$
$168$	12.6545	0.976314
$169$	−3.20659	−0.246661
$170$	1.42908	0.109606
$171$	3.71745	0.284280
$172$	−44.5376	−3.39596
$173$	4.38303	0.333236	0.166618	−	0.986022i	$-0.446715\pi$
$173$	4.38303	0.333236	0.166618	+	0.986022i	$0.446715\pi$
$174$	−55.0343	−4.17214
$175$	12.4066	0.937850
$176$	−23.8868	−1.80054
$177$	3.01310	0.226478
$178$	−0.735935	−0.0551606
$179$	5.31586	0.397326	0.198663	−	0.980068i	$-0.436340\pi$
$179$	5.31586	0.397326	0.198663	+	0.980068i	$0.436340\pi$
$180$	−38.5136	−2.87064
$181$	7.66146	0.569472	0.284736	−	0.958606i	$-0.408094\pi$
$181$	7.66146	0.569472	0.284736	+	0.958606i	$0.408094\pi$
$182$	7.80937	0.578869
$183$	5.55949	0.410969
$184$	24.6441	1.81679
$185$	4.17212	0.306740
$186$	5.68159	0.416594
$187$	−0.605460	−0.0442756
$188$	32.6329	2.38000
$189$	1.85849	0.135185
$190$	17.7237	1.28581
$191$	−0.236244	−0.0170940	−0.00854700	−	0.999963i	$-0.502721\pi$
$191$	−0.236244	−0.0170940	−0.00854700	+	0.999963i	$0.502721\pi$
$192$	11.0371	0.796536
$193$	8.04006	0.578736	0.289368	−	0.957218i	$-0.406555\pi$
$193$	8.04006	0.578736	0.289368	+	0.957218i	$0.406555\pi$
$194$	39.5127	2.83685
$195$	−29.7266	−2.12876
$196$	4.22728	0.301948
$197$	9.37607	0.668017	0.334009	−	0.942570i	$-0.391599\pi$
$197$	9.37607	0.668017	0.334009	+	0.942570i	$0.391599\pi$
$198$	24.0370	1.70823
$199$	23.1033	1.63775	0.818876	−	0.573970i	$-0.194598\pi$
$199$	23.1033	1.63775	0.818876	+	0.573970i	$0.194598\pi$
$200$	−68.9566	−4.87597
$201$	−19.4766	−1.37378
$202$	27.1118	1.90758
$203$	−9.68642	−0.679854
$204$	−1.32109	−0.0924949
$205$	46.2844	3.23264
$206$	16.7838	1.16938
$207$	−9.68249	−0.672979
$208$	−16.9469	−1.17506
$209$	−7.50900	−0.519409
$210$	−23.7043	−1.63575
$211$	14.3111	0.985218	0.492609	−	0.870251i	$-0.336043\pi$
$211$	14.3111	0.985218	0.492609	+	0.870251i	$0.336043\pi$
$212$	−26.6192	−1.82822
$213$	−32.6119	−2.23453
$214$	−9.08379	−0.620955
$215$	43.9565	2.99781
$216$	−10.3296	−0.702840
$217$	1.00000	0.0678844
$218$	−6.94776	−0.470562
$219$	0.261539	0.0176732
$220$	77.7950	5.24494
$221$	−0.429555	−0.0288950
$222$	−5.68159	−0.381323
$223$	5.63928	0.377634	0.188817	−	0.982012i	$-0.439535\pi$
$223$	5.63928	0.377634	0.188817	+	0.982012i	$0.439535\pi$
$224$	−2.39754	−0.160192
$225$	27.0925	1.80617
$226$	−35.0767	−2.33327
$227$	−1.27294	−0.0844882	−0.0422441	−	0.999107i	$-0.513451\pi$
$227$	−1.27294	−0.0844882	−0.0422441	+	0.999107i	$0.513451\pi$
$228$	−16.3844	−1.08508
$229$	24.5142	1.61994	0.809972	−	0.586468i	$-0.199482\pi$
$229$	24.5142	1.61994	0.809972	+	0.586468i	$0.199482\pi$
$230$	−46.1632	−3.04391
$231$	10.0428	0.660768
$232$	53.8377	3.53462
$233$	25.7034	1.68388	0.841942	−	0.539568i	$-0.181412\pi$
$233$	25.7034	1.68388	0.841942	+	0.539568i	$0.181412\pi$
$234$	17.0535	1.11482
$235$	−32.2071	−2.10096
$236$	−5.59440	−0.364164
$237$	−16.9597	−1.10165
$238$	−0.342531	−0.0222030
$239$	5.87062	0.379739	0.189869	−	0.981809i	$-0.439194\pi$
$239$	5.87062	0.379739	0.189869	+	0.981809i	$0.439194\pi$
$240$	51.4401	3.32044
$241$	−26.0016	−1.67491	−0.837454	−	0.546508i	$-0.815957\pi$
$241$	−26.0016	−1.67491	−0.837454	+	0.546508i	$0.815957\pi$
$242$	−21.1032	−1.35657
$243$	18.9740	1.21718
$244$	−10.3223	−0.660815
$245$	−4.17212	−0.266547
$246$	−63.0301	−4.01865
$247$	−5.32740	−0.338974
$248$	−5.55806	−0.352937
$249$	−6.14889	−0.389670
$250$	77.1123	4.87701
$251$	1.91006	0.120562	0.0602811	−	0.998181i	$-0.480800\pi$
$251$	1.91006	0.120562	0.0602811	+	0.998181i	$0.480800\pi$
$252$	9.23119	0.581510
$253$	19.5580	1.22960
$254$	15.3650	0.964085
$255$	1.30385	0.0816505
$256$	−32.4584	−2.02865
$257$	16.3775	1.02160	0.510800	−	0.859700i	$-0.329349\pi$
$257$	16.3775	1.02160	0.510800	+	0.859700i	$0.329349\pi$
$258$	−59.8599	−3.72672
$259$	−1.00000	−0.0621370
$260$	55.1931	3.42293
$261$	−21.1524	−1.30930
$262$	15.6961	0.969705
$263$	20.9705	1.29310	0.646548	−	0.762874i	$-0.276212\pi$
$263$	20.9705	1.29310	0.646548	+	0.762874i	$0.276212\pi$
$264$	−55.8185	−3.43539
$265$	26.2719	1.61387
$266$	−4.24812	−0.260469
$267$	−0.671446	−0.0410918
$268$	36.1621	2.20895
$269$	−4.16993	−0.254245	−0.127123	−	0.991887i	$-0.540574\pi$
$269$	−4.16993	−0.254245	−0.127123	+	0.991887i	$0.540574\pi$
$270$	19.3493	1.17756
$271$	−3.82494	−0.232349	−0.116174	−	0.993229i	$-0.537063\pi$
$271$	−3.82494	−0.232349	−0.116174	+	0.993229i	$0.537063\pi$
$272$	0.743319	0.0450703
$273$	7.12505	0.431227
$274$	−20.0424	−1.21080
$275$	−54.7251	−3.30005
$276$	42.6748	2.56872
$277$	18.3828	1.10452	0.552258	−	0.833673i	$-0.313766\pi$
$277$	18.3828	1.10452	0.552258	+	0.833673i	$0.313766\pi$
$278$	13.9927	0.839225
$279$	2.18372	0.130736
$280$	23.1889	1.38580
$281$	30.0277	1.79130	0.895650	−	0.444759i	$-0.146711\pi$
$281$	30.0277	1.79130	0.895650	+	0.444759i	$0.146711\pi$
$282$	43.8596	2.61180
$283$	13.1803	0.783486	0.391743	−	0.920075i	$-0.371872\pi$
$283$	13.1803	0.783486	0.391743	+	0.920075i	$0.371872\pi$
$284$	60.5502	3.59300
$285$	16.1706	0.957862
$286$	−34.4469	−2.03689
$287$	−11.0937	−0.654843
$288$	−5.23555	−0.308508
$289$	−16.9812	−0.998892
$290$	−100.848	−5.92203
$291$	36.0503	2.11331
$292$	−0.485598	−0.0284175
$293$	4.55582	0.266154	0.133077	−	0.991106i	$-0.457514\pi$
$293$	4.55582	0.266154	0.133077	+	0.991106i	$0.457514\pi$
$294$	5.68159	0.331357
$295$	5.52140	0.321469
$296$	5.55806	0.323056
$297$	−8.19775	−0.475681
$298$	−14.4788	−0.838732
$299$	13.8758	0.802456
$300$	−119.408	−6.89403
$301$	−10.5358	−0.607272
$302$	39.5875	2.27801
$303$	24.7360	1.42105
$304$	9.21875	0.528731
$305$	10.1876	0.583339
$306$	−0.747993	−0.0427599
$307$	21.5873	1.23205	0.616027	−	0.787725i	$-0.288741\pi$
$307$	21.5873	1.23205	0.616027	+	0.787725i	$0.288741\pi$
$308$	−18.6464	−1.06248
$309$	15.3131	0.871130
$310$	10.4113	0.591323
$311$	6.91295	0.391997	0.195999	−	0.980604i	$-0.437205\pi$
$311$	6.91295	0.391997	0.195999	+	0.980604i	$0.437205\pi$
$312$	−39.6015	−2.24199
$313$	−13.3364	−0.753820	−0.376910	−	0.926250i	$-0.623013\pi$
$313$	−13.3364	−0.753820	−0.376910	+	0.926250i	$0.623013\pi$
$314$	11.2118	0.632719
$315$	−9.11074	−0.513332
$316$	31.4889	1.77139
$317$	21.1871	1.18999	0.594993	−	0.803731i	$-0.297155\pi$
$317$	21.1871	1.18999	0.594993	+	0.803731i	$0.297155\pi$
$318$	−35.7770	−2.00628
$319$	42.7265	2.39223
$320$	20.2252	1.13062
$321$	−8.28779	−0.462579
$322$	11.0647	0.616611
$323$	0.233668	0.0130016
$324$	−45.5807	−2.53226
$325$	−38.8257	−2.15366
$326$	−18.6521	−1.03304
$327$	−6.33894	−0.350544
$328$	61.6597	3.40459
$329$	7.71961	0.425596
$330$	104.559	5.75578
$331$	13.6397	0.749707	0.374854	−	0.927084i	$-0.377693\pi$
$331$	13.6397	0.749707	0.374854	+	0.927084i	$0.377693\pi$
$332$	11.4166	0.626568
$333$	−2.18372	−0.119667
$334$	24.1357	1.32065
$335$	−35.6903	−1.94997
$336$	−12.3295	−0.672628
$337$	7.24672	0.394754	0.197377	−	0.980328i	$-0.436758\pi$
$337$	7.24672	0.394754	0.197377	+	0.980328i	$0.436758\pi$
$338$	8.00188	0.435245
$339$	−32.0030	−1.73816
$340$	−2.42086	−0.131289
$341$	−4.41097	−0.238868
$342$	−9.27671	−0.501627
$343$	1.00000	0.0539949
$344$	58.5585	3.15726
$345$	−42.1180	−2.26756
$346$	−10.9376	−0.588011
$347$	−6.79166	−0.364595	−0.182298	−	0.983243i	$-0.558353\pi$
$347$	−6.79166	−0.364595	−0.182298	+	0.983243i	$0.558353\pi$
$348$	93.2277	4.99753
$349$	−13.5233	−0.723885	−0.361942	−	0.932200i	$-0.617886\pi$
$349$	−13.5233	−0.723885	−0.361942	+	0.932200i	$0.617886\pi$
$350$	−30.9600	−1.65488
$351$	−5.81604	−0.310437
$352$	10.5755	0.563675
$353$	14.3289	0.762650	0.381325	−	0.924441i	$-0.375468\pi$
$353$	14.3289	0.762650	0.381325	+	0.924441i	$0.375468\pi$
$354$	−7.51904	−0.399633
$355$	−59.7602	−3.17174
$356$	1.24667	0.0660733
$357$	−0.312516	−0.0165401
$358$	−13.2655	−0.701101
$359$	30.5463	1.61217	0.806085	−	0.591799i	$-0.201582\pi$
$359$	30.5463	1.61217	0.806085	+	0.591799i	$0.201582\pi$
$360$	50.6380	2.66886
$361$	−16.1020	−0.847475
$362$	−19.1188	−1.00486
$363$	−19.2540	−1.01057
$364$	−13.2290	−0.693389
$365$	0.479262	0.0250857
$366$	−13.8734	−0.725176
$367$	7.44651	0.388705	0.194352	−	0.980932i	$-0.437739\pi$
$367$	7.44651	0.388705	0.194352	+	0.980932i	$0.437739\pi$
$368$	−24.0112	−1.25167
$369$	−24.2256	−1.26114
$370$	−10.4113	−0.541259
$371$	−6.29701	−0.326925
$372$	−9.62457	−0.499011
$373$	27.5965	1.42889	0.714445	−	0.699691i	$-0.246679\pi$
$373$	27.5965	1.42889	0.714445	+	0.699691i	$0.246679\pi$
$374$	1.51090	0.0781266
$375$	70.3551	3.63312
$376$	−42.9060	−2.21271
$377$	30.3131	1.56120
$378$	−4.63777	−0.238541
$379$	−30.6453	−1.57414	−0.787070	−	0.616863i	$-0.788403\pi$
$379$	−30.6453	−1.57414	−0.787070	+	0.616863i	$0.788403\pi$
$380$	−30.0238	−1.54019
$381$	14.0186	0.718193
$382$	0.589535	0.0301632
$383$	−5.45400	−0.278686	−0.139343	−	0.990244i	$-0.544499\pi$
$383$	−5.45400	−0.278686	−0.139343	+	0.990244i	$0.544499\pi$
$384$	−38.4599	−1.96265
$385$	18.4031	0.937909
$386$	−20.0636	−1.02121
$387$	−23.0072	−1.16952
$388$	−66.9343	−3.39807
$389$	−7.40361	−0.375378	−0.187689	−	0.982228i	$-0.560100\pi$
$389$	−7.40361	−0.375378	−0.187689	+	0.982228i	$0.560100\pi$
$390$	74.1812	3.75631
$391$	−0.608613	−0.0307789
$392$	−5.55806	−0.280724
$393$	14.3206	0.722380
$394$	−23.3975	−1.17875
$395$	−31.0780	−1.56371
$396$	−40.7185	−2.04618
$397$	−4.78126	−0.239965	−0.119982	−	0.992776i	$-0.538284\pi$
$397$	−4.78126	−0.239965	−0.119982	+	0.992776i	$0.538284\pi$
$398$	−57.6532	−2.88990
$399$	−3.87587	−0.194036
$400$	67.1856	3.35928
$401$	−33.5970	−1.67775	−0.838877	−	0.544320i	$-0.816788\pi$
$401$	−33.5970	−1.67775	−0.838877	+	0.544320i	$0.816788\pi$
$402$	48.6030	2.42410
$403$	−3.12944	−0.155889
$404$	−45.9271	−2.28496
$405$	44.9860	2.23537
$406$	24.1720	1.19964
$407$	4.41097	0.218644
$408$	1.73698	0.0859934
$409$	−24.8875	−1.23061	−0.615303	−	0.788291i	$-0.710966\pi$
$409$	−24.8875	−1.23061	−0.615303	+	0.788291i	$0.710966\pi$
$410$	−115.500	−5.70416
$411$	−18.2861	−0.901987
$412$	−28.4317	−1.40073
$413$	−1.32341	−0.0651205
$414$	24.1622	1.18751
$415$	−11.2676	−0.553107
$416$	7.50296	0.367863
$417$	12.7665	0.625179
$418$	18.7383	0.916523
$419$	−10.4605	−0.511031	−0.255515	−	0.966805i	$-0.582245\pi$
$419$	−10.4605	−0.511031	−0.255515	+	0.966805i	$0.582245\pi$
$420$	40.1549	1.95936
$421$	−26.4178	−1.28753	−0.643763	−	0.765225i	$-0.722628\pi$
$421$	−26.4178	−1.28753	−0.643763	+	0.765225i	$0.722628\pi$
$422$	−35.7127	−1.73847
$423$	16.8575	0.819637
$424$	34.9992	1.69971
$425$	1.70296	0.0826055
$426$	81.3814	3.94294
$427$	−2.44182	−0.118168
$428$	15.3879	0.743801
$429$	−31.4284	−1.51738
$430$	−109.691	−5.28978
$431$	−11.3433	−0.546387	−0.273194	−	0.961959i	$-0.588080\pi$
$431$	−11.3433	−0.546387	−0.273194	+	0.961959i	$0.588080\pi$
$432$	10.0643	0.484219
$433$	27.7143	1.33186	0.665932	−	0.746013i	$-0.268034\pi$
$433$	27.7143	1.33186	0.665932	+	0.746013i	$0.268034\pi$
$434$	−2.49545	−0.119785
$435$	−92.0113	−4.41160
$436$	11.7695	0.563655
$437$	−7.54811	−0.361075
$438$	−0.652659	−0.0311852
$439$	35.5192	1.69524	0.847618	−	0.530606i	$-0.178036\pi$
$439$	35.5192	1.69524	0.847618	+	0.530606i	$0.178036\pi$
$440$	−102.286	−4.87627
$441$	2.18372	0.103987
$442$	1.07193	0.0509866
$443$	20.6845	0.982751	0.491375	−	0.870948i	$-0.336494\pi$
$443$	20.6845	0.982751	0.491375	+	0.870948i	$0.336494\pi$
$444$	9.62457	0.456762
$445$	−1.23040	−0.0583266
$446$	−14.0725	−0.666354
$447$	−13.2100	−0.624812
$448$	−4.84770	−0.229032
$449$	30.2653	1.42831	0.714154	−	0.699988i	$-0.246812\pi$
$449$	30.2653	1.42831	0.714154	+	0.699988i	$0.246812\pi$
$450$	−67.6080	−3.18707
$451$	48.9342	2.30422
$452$	59.4197	2.79487
$453$	36.1185	1.69700
$454$	3.17657	0.149084
$455$	13.0564	0.612094
$456$	21.5423	1.00881
$457$	5.62835	0.263283	0.131642	−	0.991297i	$-0.457975\pi$
$457$	5.62835	0.263283	0.131642	+	0.991297i	$0.457975\pi$
$458$	−61.1740	−2.85847
$459$	0.255101	0.0119071
$460$	78.2001	3.64610
$461$	−37.5254	−1.74773	−0.873866	−	0.486167i	$-0.838395\pi$
$461$	−37.5254	−1.74773	−0.873866	+	0.486167i	$0.838395\pi$
$462$	−25.0613	−1.16596
$463$	0.945476	0.0439400	0.0219700	−	0.999759i	$-0.493006\pi$
$463$	0.945476	0.0439400	0.0219700	+	0.999759i	$0.493006\pi$
$464$	−52.4551	−2.43517
$465$	9.49899	0.440505
$466$	−64.1415	−2.97130
$467$	12.1372	0.561641	0.280821	−	0.959760i	$-0.409393\pi$
$467$	12.1372	0.561641	0.280821	+	0.959760i	$0.409393\pi$
$468$	−28.8885	−1.33537
$469$	8.55448	0.395009
$470$	80.3713	3.70725
$471$	10.2293	0.471343
$472$	7.35557	0.338567
$473$	46.4730	2.13683
$474$	42.3220	1.94392
$475$	21.1203	0.969066
$476$	0.580246	0.0265955
$477$	−13.7509	−0.629611
$478$	−14.6498	−0.670068
$479$	−1.83806	−0.0839832	−0.0419916	−	0.999118i	$-0.513370\pi$
$479$	−1.83806	−0.0839832	−0.0419916	+	0.999118i	$0.513370\pi$
$480$	−22.7742	−1.03949
$481$	3.12944	0.142690
$482$	64.8856	2.95546
$483$	10.0951	0.459343
$484$	35.7487	1.62494
$485$	66.0610	2.99967
$486$	−47.3486	−2.14778
$487$	23.4454	1.06241	0.531207	−	0.847242i	$-0.321739\pi$
$487$	23.4454	1.06241	0.531207	+	0.847242i	$0.321739\pi$
$488$	13.5718	0.614367
$489$	−17.0176	−0.769563
$490$	10.4113	0.470336
$491$	2.81368	0.126980	0.0634898	−	0.997982i	$-0.479777\pi$
$491$	2.81368	0.126980	0.0634898	+	0.997982i	$0.479777\pi$
$492$	106.772	4.81368
$493$	−1.32958	−0.0598813
$494$	13.2943	0.598137
$495$	40.1872	1.80628
$496$	5.41532	0.243155
$497$	14.3237	0.642506
$498$	15.3443	0.687593
$499$	−6.57068	−0.294144	−0.147072	−	0.989126i	$-0.546985\pi$
$499$	−6.57068	−0.294144	−0.147072	+	0.989126i	$0.546985\pi$
$500$	−130.628	−5.84185
$501$	22.0207	0.983815
$502$	−4.76647	−0.212738
$503$	−18.9256	−0.843851	−0.421925	−	0.906631i	$-0.638646\pi$
$503$	−18.9256	−0.843851	−0.421925	+	0.906631i	$0.638646\pi$
$504$	−12.1372	−0.540636
$505$	45.3279	2.01706
$506$	−48.8060	−2.16969
$507$	7.30069	0.324235
$508$	−26.0282	−1.15481
$509$	−11.8876	−0.526908	−0.263454	−	0.964672i	$-0.584862\pi$
$509$	−11.8876	−0.526908	−0.263454	+	0.964672i	$0.584862\pi$
$510$	−3.25370	−0.144076
$511$	−0.114873	−0.00508166
$512$	47.2139	2.08658
$513$	3.16379	0.139685
$514$	−40.8692	−1.80266
$515$	28.0607	1.23650
$516$	101.402	4.46399
$517$	−34.0510	−1.49756
$518$	2.49545	0.109644
$519$	−9.97919	−0.438038
$520$	−72.5683	−3.18233
$521$	−21.7702	−0.953772	−0.476886	−	0.878965i	$-0.658234\pi$
$521$	−21.7702	−0.953772	−0.476886	+	0.878965i	$0.658234\pi$
$522$	52.7849	2.31033
$523$	−1.71331	−0.0749177	−0.0374588	−	0.999298i	$-0.511926\pi$
$523$	−1.71331	−0.0749177	−0.0374588	+	0.999298i	$0.511926\pi$
$524$	−26.5890	−1.16155
$525$	−28.2470	−1.23280
$526$	−52.3308	−2.28173
$527$	0.137262	0.00597924
$528$	54.3850	2.36680
$529$	−3.34016	−0.145224
$530$	−65.5602	−2.84776
$531$	−2.88995	−0.125413
$532$	7.19629	0.311999
$533$	34.7172	1.50377
$534$	1.67556	0.0725086
$535$	−15.1871	−0.656596
$536$	−47.5463	−2.05369
$537$	−12.1030	−0.522284
$538$	10.4059	0.448629
$539$	−4.41097	−0.189994
$540$	−32.7776	−1.41053
$541$	−15.2291	−0.654748	−0.327374	−	0.944895i	$-0.606164\pi$
$541$	−15.2291	−0.654748	−0.327374	+	0.944895i	$0.606164\pi$
$542$	9.54496	0.409991
$543$	−17.4435	−0.748570
$544$	−0.329092	−0.0141097
$545$	−11.6159	−0.497570
$546$	−17.7802	−0.760923
$547$	−10.1194	−0.432675	−0.216337	−	0.976319i	$-0.569411\pi$
$547$	−10.1194	−0.432675	−0.216337	+	0.976319i	$0.569411\pi$
$548$	33.9517	1.45034
$549$	−5.33226	−0.227575
$550$	136.564	5.82310
$551$	−16.4897	−0.702483
$552$	−56.1092	−2.38817
$553$	7.44898	0.316763
$554$	−45.8734	−1.94897
$555$	−9.49899	−0.403210
$556$	−23.7035	−1.00525
$557$	35.3475	1.49772	0.748861	−	0.662727i	$-0.230601\pi$
$557$	35.3475	1.49772	0.748861	+	0.662727i	$0.230601\pi$
$558$	−5.44937	−0.230690
$559$	32.9711	1.39453
$560$	−22.5934	−0.954743
$561$	1.37850	0.0582003
$562$	−74.9326	−3.16084
$563$	4.60288	0.193988	0.0969942	−	0.995285i	$-0.469077\pi$
$563$	4.60288	0.193988	0.0969942	+	0.995285i	$0.469077\pi$
$564$	−74.2979	−3.12851
$565$	−58.6444	−2.46719
$566$	−32.8907	−1.38250
$567$	−10.7825	−0.452824
$568$	−79.6120	−3.34044
$569$	7.53773	0.315998	0.157999	−	0.987439i	$-0.449496\pi$
$569$	7.53773	0.315998	0.157999	+	0.987439i	$0.449496\pi$
$570$	−40.3529	−1.69020
$571$	35.7834	1.49749	0.748745	−	0.662858i	$-0.230657\pi$
$571$	35.7834	1.49749	0.748745	+	0.662858i	$0.230657\pi$
$572$	58.3528	2.43985
$573$	0.537875	0.0224700
$574$	27.6839	1.15550
$575$	−55.0101	−2.29408
$576$	−10.5860	−0.441084
$577$	21.8924	0.911392	0.455696	−	0.890135i	$-0.349390\pi$
$577$	21.8924	0.911392	0.455696	+	0.890135i	$0.349390\pi$
$578$	42.3757	1.76259
$579$	−18.3054	−0.760748
$580$	170.837	7.09361
$581$	2.70070	0.112044
$582$	−89.9618	−3.72903
$583$	27.7760	1.15036
$584$	0.638469	0.0264200
$585$	28.5115	1.17881
$586$	−11.3688	−0.469642
$587$	−44.0039	−1.81624	−0.908118	−	0.418715i	$-0.862481\pi$
$587$	−44.0039	−1.81624	−0.908118	+	0.418715i	$0.862481\pi$
$588$	−9.62457	−0.396911
$589$	1.70235	0.0701440
$590$	−13.7784	−0.567248
$591$	−21.3472	−0.878108
$592$	−5.41532	−0.222568
$593$	−15.1912	−0.623829	−0.311914	−	0.950110i	$-0.600970\pi$
$593$	−15.1912	−0.623829	−0.311914	+	0.950110i	$0.600970\pi$
$594$	20.4571	0.839364
$595$	−0.572675	−0.0234774
$596$	24.5269	1.00466
$597$	−52.6012	−2.15282
$598$	−34.6263	−1.41597
$599$	−18.6617	−0.762494	−0.381247	−	0.924473i	$-0.624505\pi$
$599$	−18.6617	−0.762494	−0.381247	+	0.924473i	$0.624505\pi$
$600$	156.999	6.40945
$601$	−29.7294	−1.21269	−0.606345	−	0.795202i	$-0.707365\pi$
$601$	−29.7294	−1.21269	−0.606345	+	0.795202i	$0.707365\pi$
$602$	26.2915	1.07156
$603$	18.6806	0.760732
$604$	−67.0610	−2.72867
$605$	−35.2822	−1.43443
$606$	−61.7275	−2.50751
$607$	41.8315	1.69789	0.848944	−	0.528483i	$-0.177239\pi$
$607$	41.8315	1.69789	0.848944	+	0.528483i	$0.177239\pi$
$608$	−4.08144	−0.165524
$609$	22.0538	0.893667
$610$	−25.4226	−1.02933
$611$	−24.1581	−0.977331
$612$	1.26709	0.0512192
$613$	28.3600	1.14545	0.572725	−	0.819748i	$-0.305886\pi$
$613$	28.3600	1.14545	0.572725	+	0.819748i	$0.305886\pi$
$614$	−53.8702	−2.17402
$615$	−105.379	−4.24931
$616$	24.5165	0.987796
$617$	−38.2649	−1.54049	−0.770244	−	0.637750i	$-0.779865\pi$
$617$	−38.2649	−1.54049	−0.770244	+	0.637750i	$0.779865\pi$
$618$	−38.2130	−1.53715
$619$	−4.03092	−0.162016	−0.0810082	−	0.996713i	$-0.525814\pi$
$619$	−4.03092	−0.162016	−0.0810082	+	0.996713i	$0.525814\pi$
$620$	−17.6367	−0.708307
$621$	−8.24044	−0.330677
$622$	−17.2509	−0.691699
$623$	0.294910	0.0118153
$624$	38.5844	1.54461
$625$	66.8904	2.67562
$626$	33.2804	1.33015
$627$	17.0963	0.682762
$628$	−18.9927	−0.757892
$629$	−0.137262	−0.00547301
$630$	22.7354	0.905800
$631$	−0.792060	−0.0315314	−0.0157657	−	0.999876i	$-0.505019\pi$
$631$	−0.792060	−0.0315314	−0.0157657	+	0.999876i	$0.505019\pi$
$632$	−41.4019	−1.64688
$633$	−32.5832	−1.29507
$634$	−52.8714	−2.09979
$635$	25.6886	1.01942
$636$	60.6061	2.40319
$637$	−3.12944	−0.123993
$638$	−106.622	−4.22121
$639$	31.2789	1.23738
$640$	−70.4766	−2.78583
$641$	36.0422	1.42358	0.711790	−	0.702392i	$-0.247885\pi$
$641$	36.0422	1.42358	0.711790	+	0.702392i	$0.247885\pi$
$642$	20.6818	0.816245
$643$	−38.7588	−1.52850	−0.764250	−	0.644920i	$-0.776890\pi$
$643$	−38.7588	−1.52850	−0.764250	+	0.644920i	$0.776890\pi$
$644$	−18.7435	−0.738597
$645$	−100.079	−3.94061
$646$	−0.583107	−0.0229420
$647$	−1.82162	−0.0716151	−0.0358075	−	0.999359i	$-0.511400\pi$
$647$	−1.82162	−0.0716151	−0.0358075	+	0.999359i	$0.511400\pi$
$648$	59.9300	2.35427
$649$	5.83750	0.229142
$650$	96.8876	3.80025
$651$	−2.27678	−0.0892340
$652$	31.5965	1.23741
$653$	14.7936	0.578919	0.289460	−	0.957190i	$-0.406524\pi$
$653$	14.7936	0.578919	0.289460	+	0.957190i	$0.406524\pi$
$654$	15.8185	0.618553
$655$	26.2421	1.02536
$656$	−60.0761	−2.34558
$657$	−0.250849	−0.00978657
$658$	−19.2639	−0.750985
$659$	34.1642	1.33085	0.665425	−	0.746465i	$-0.268250\pi$
$659$	34.1642	1.33085	0.665425	+	0.746465i	$0.268250\pi$
$660$	−177.122	−6.89446
$661$	−10.0856	−0.392285	−0.196142	−	0.980575i	$-0.562841\pi$
$661$	−10.0856	−0.392285	−0.196142	+	0.980575i	$0.562841\pi$
$662$	−34.0373	−1.32290
$663$	0.978000	0.0379824
$664$	−15.0107	−0.582526
$665$	−7.10239	−0.275419
$666$	5.44937	0.211159
$667$	42.9490	1.66299
$668$	−40.8858	−1.58192
$669$	−12.8394	−0.496400
$670$	89.0634	3.44082
$671$	10.7708	0.415803
$672$	5.45866	0.210572
$673$	−29.3560	−1.13159	−0.565795	−	0.824546i	$-0.691431\pi$
$673$	−29.3560	−1.13159	−0.565795	+	0.824546i	$0.691431\pi$
$674$	−18.0838	−0.696563
$675$	23.0575	0.887484
$676$	−13.5551	−0.521351
$677$	12.1777	0.468027	0.234013	−	0.972233i	$-0.424814\pi$
$677$	12.1777	0.468027	0.234013	+	0.972233i	$0.424814\pi$
$678$	79.8618	3.06708
$679$	−15.8339	−0.607650
$680$	3.18296	0.122061
$681$	2.89821	0.111060
$682$	11.0074	0.421494
$683$	−33.3857	−1.27747	−0.638734	−	0.769428i	$-0.720541\pi$
$683$	−33.3857	−1.27747	−0.638734	+	0.769428i	$0.720541\pi$
$684$	15.7147	0.600866
$685$	−33.5087	−1.28030
$686$	−2.49545	−0.0952768
$687$	−55.8134	−2.12941
$688$	−57.0545	−2.17518
$689$	19.7061	0.750744
$690$	105.103	4.00122
$691$	−38.8474	−1.47782	−0.738912	−	0.673802i	$-0.764660\pi$
$691$	−38.8474	−1.47782	−0.738912	+	0.673802i	$0.764660\pi$
$692$	18.5283	0.704340
$693$	−9.63232	−0.365902
$694$	16.9483	0.643347
$695$	23.3942	0.887394
$696$	−122.577	−4.64625
$697$	−1.52275	−0.0576784
$698$	33.7467	1.27733
$699$	−58.5209	−2.21346
$700$	52.4461	1.98228
$701$	−39.3640	−1.48676	−0.743379	−	0.668870i	$-0.766778\pi$
$701$	−39.3640	−1.48676	−0.743379	+	0.668870i	$0.766778\pi$
$702$	14.5136	0.547782
$703$	−1.70235	−0.0642052
$704$	21.3830	0.805904
$705$	73.3285	2.76171
$706$	−35.7570	−1.34573
$707$	−10.8645	−0.408600
$708$	12.7372	0.478694
$709$	−27.8659	−1.04652	−0.523262	−	0.852172i	$-0.675285\pi$
$709$	−27.8659	−1.04652	−0.523262	+	0.852172i	$0.675285\pi$
$710$	149.129	5.59670
$711$	16.2665	0.610041
$712$	−1.63913	−0.0614290
$713$	−4.43394	−0.166052
$714$	0.779868	0.0291858
$715$	−57.5915	−2.15380
$716$	22.4716	0.839803
$717$	−13.3661	−0.499166
$718$	−76.2268	−2.84476
$719$	−2.30416	−0.0859305	−0.0429653	−	0.999077i	$-0.513680\pi$
$719$	−2.30416	−0.0859305	−0.0429653	+	0.999077i	$0.513680\pi$
$720$	−49.3375	−1.83870
$721$	−6.72576	−0.250480
$722$	40.1818	1.49541
$723$	59.1998	2.20166
$724$	32.3871	1.20366
$725$	−120.175	−4.46320
$726$	48.0473	1.78320
$727$	−14.6978	−0.545110	−0.272555	−	0.962140i	$-0.587869\pi$
$727$	−14.6978	−0.545110	−0.272555	+	0.962140i	$0.587869\pi$
$728$	17.3936	0.644651
$729$	−10.8519	−0.401923
$730$	−1.19598	−0.0442650
$731$	−1.44616	−0.0534883
$732$	23.5015	0.868641
$733$	18.7296	0.691792	0.345896	−	0.938273i	$-0.387575\pi$
$733$	18.7296	0.691792	0.345896	+	0.938273i	$0.387575\pi$
$734$	−18.5824	−0.685889
$735$	9.49899	0.350376
$736$	10.6305	0.391847
$737$	−37.7336	−1.38993
$738$	60.4538	2.22534
$739$	−5.05483	−0.185945	−0.0929725	−	0.995669i	$-0.529637\pi$
$739$	−5.05483	−0.185945	−0.0929725	+	0.995669i	$0.529637\pi$
$740$	17.6367	0.648338
$741$	12.1293	0.445581
$742$	15.7139	0.576875
$743$	−21.2333	−0.778973	−0.389487	−	0.921032i	$-0.627348\pi$
$743$	−21.2333	−0.778973	−0.389487	+	0.921032i	$0.627348\pi$
$744$	12.6545	0.463936
$745$	−24.2069	−0.886872
$746$	−68.8656	−2.52135
$747$	5.89757	0.215781
$748$	−2.55945	−0.0935827
$749$	3.64014	0.133008
$750$	−175.568	−6.41083
$751$	−25.7590	−0.939958	−0.469979	−	0.882678i	$-0.655739\pi$
$751$	−25.7590	−0.939958	−0.469979	+	0.882678i	$0.655739\pi$
$752$	41.8041	1.52444
$753$	−4.34879	−0.158479
$754$	−75.6449	−2.75482
$755$	66.1860	2.40876
$756$	7.85635	0.285733
$757$	−18.7968	−0.683181	−0.341590	−	0.939849i	$-0.610966\pi$
$757$	−18.7968	−0.683181	−0.341590	+	0.939849i	$0.610966\pi$
$758$	76.4737	2.77765
$759$	−44.5292	−1.61631
$760$	39.4755	1.43193
$761$	46.0031	1.66761	0.833805	−	0.552059i	$-0.186158\pi$
$761$	46.0031	1.66761	0.833805	+	0.552059i	$0.186158\pi$
$762$	−34.9827	−1.26729
$763$	2.78417	0.100794
$764$	−0.998668	−0.0361305
$765$	−1.25056	−0.0452141
$766$	13.6102	0.491756
$767$	4.14152	0.149542
$768$	73.9007	2.66666
$769$	20.7417	0.747965	0.373983	−	0.927436i	$-0.377992\pi$
$769$	20.7417	0.747965	0.373983	+	0.927436i	$0.377992\pi$
$770$	−45.9240	−1.65499
$771$	−37.2879	−1.34289
$772$	33.9876	1.22324
$773$	24.6179	0.885444	0.442722	−	0.896659i	$-0.354013\pi$
$773$	24.6179	0.885444	0.442722	+	0.896659i	$0.354013\pi$
$774$	57.4133	2.06368
$775$	12.4066	0.445658
$776$	88.0058	3.15922
$777$	2.27678	0.0816790
$778$	18.4754	0.662374
$779$	−18.8854	−0.676639
$780$	−125.662	−4.49943
$781$	−63.1814	−2.26081
$782$	1.51876	0.0543109
$783$	−18.0021	−0.643343
$784$	5.41532	0.193404
$785$	18.7449	0.669034
$786$	−35.7364	−1.27468
$787$	−15.9154	−0.567321	−0.283661	−	0.958925i	$-0.591549\pi$
$787$	−15.9154	−0.567321	−0.283661	+	0.958925i	$0.591549\pi$
$788$	39.6352	1.41195
$789$	−47.7451	−1.69977
$790$	77.5537	2.75924
$791$	14.0563	0.499783
$792$	53.5371	1.90236
$793$	7.64155	0.271359
$794$	11.9314	0.423430
$795$	−59.8153	−2.12143
$796$	97.6642	3.46162
$797$	−25.6508	−0.908599	−0.454299	−	0.890849i	$-0.650110\pi$
$797$	−25.6508	−0.908599	−0.454299	+	0.890849i	$0.650110\pi$
$798$	9.67203	0.342386
$799$	1.05961	0.0374863
$800$	−29.7453	−1.05165
$801$	0.644002	0.0227547
$802$	83.8397	2.96048
$803$	0.506700	0.0178810
$804$	−82.3332	−2.90367
$805$	18.4989	0.652002
$806$	7.80937	0.275073
$807$	9.49402	0.334205
$808$	60.3854	2.12435
$809$	0.00801039	0.000281630 0	0.000140815	−	1.00000i	$-0.499955\pi$
$809$	0.00801039	0.000281630 0	0.000140815		1.00000i	$0.499955\pi$
$810$	−112.260	−3.94443
$811$	49.1300	1.72519	0.862594	−	0.505896i	$-0.168838\pi$
$811$	49.1300	1.72519	0.862594	+	0.505896i	$0.168838\pi$
$812$	−40.9472	−1.43697
$813$	8.70855	0.305422
$814$	−11.0074	−0.385808
$815$	−31.1842	−1.09234
$816$	−1.69237	−0.0592449
$817$	−17.9355	−0.627485
$818$	62.1054	2.17147
$819$	−6.83383	−0.238793
$820$	195.657	6.83264
$821$	−13.9406	−0.486529	−0.243265	−	0.969960i	$-0.578218\pi$
$821$	−13.9406	−0.486529	−0.243265	+	0.969960i	$0.578218\pi$
$822$	45.6321	1.59160
$823$	30.8910	1.07679	0.538396	−	0.842692i	$-0.319031\pi$
$823$	30.8910	1.07679	0.538396	+	0.842692i	$0.319031\pi$
$824$	37.3822	1.30227
$825$	124.597	4.33791
$826$	3.30249	0.114908
$827$	−6.70491	−0.233152	−0.116576	−	0.993182i	$-0.537192\pi$
$827$	−6.70491	−0.233152	−0.116576	+	0.993182i	$0.537192\pi$
$828$	−40.9306	−1.42243
$829$	−34.5543	−1.20012	−0.600060	−	0.799955i	$-0.704857\pi$
$829$	−34.5543	−1.20012	−0.600060	+	0.799955i	$0.704857\pi$
$830$	28.1178	0.975985
$831$	−41.8536	−1.45188
$832$	15.1706	0.525945
$833$	0.137262	0.00475586
$834$	−31.8582	−1.10316
$835$	40.3523	1.39645
$836$	−31.7426	−1.09784
$837$	1.85849	0.0642388
$838$	26.1038	0.901739
$839$	−17.8552	−0.616428	−0.308214	−	0.951317i	$-0.599731\pi$
$839$	−17.8552	−0.616428	−0.308214	+	0.951317i	$0.599731\pi$
$840$	−52.7960	−1.82163
$841$	64.8268	2.23541
$842$	65.9244	2.27191
$843$	−68.3663	−2.35466
$844$	60.4970	2.08239
$845$	13.3783	0.460226
$846$	−42.0670	−1.44629
$847$	8.45667	0.290575
$848$	−34.1003	−1.17101
$849$	−30.0086	−1.02989
$850$	−4.24964	−0.145762
$851$	4.43394	0.151994
$852$	−137.859	−4.72299
$853$	57.0571	1.95360	0.976798	−	0.214161i	$-0.0687017\pi$
$853$	57.0571	1.95360	0.976798	+	0.214161i	$0.0687017\pi$
$854$	6.09345	0.208514
$855$	−15.5096	−0.530418
$856$	−20.2321	−0.691520
$857$	43.8891	1.49922	0.749612	−	0.661877i	$-0.230240\pi$
$857$	43.8891	1.49922	0.749612	+	0.661877i	$0.230240\pi$
$858$	78.4280	2.67749
$859$	1.62827	0.0555559	0.0277780	−	0.999614i	$-0.491157\pi$
$859$	1.62827	0.0555559	0.0277780	+	0.999614i	$0.491157\pi$
$860$	185.816	6.33628
$861$	25.2580	0.860790
$862$	28.3066	0.964128
$863$	−42.6396	−1.45147	−0.725734	−	0.687976i	$-0.758500\pi$
$863$	−42.6396	−1.45147	−0.725734	+	0.687976i	$0.758500\pi$
$864$	−4.45580	−0.151589
$865$	−18.2865	−0.621761
$866$	−69.1596	−2.35014
$867$	38.6623	1.31304
$868$	4.22728	0.143483
$869$	−32.8572	−1.11461
$870$	229.610	7.78450
$871$	−26.7707	−0.907092
$872$	−15.4746	−0.524036
$873$	−34.5768	−1.17025
$874$	18.8359	0.637135
$875$	−30.9012	−1.04465
$876$	1.10560	0.0373547
$877$	−3.04681	−0.102884	−0.0514418	−	0.998676i	$-0.516382\pi$
$877$	−3.04681	−0.102884	−0.0514418	+	0.998676i	$0.516382\pi$
$878$	−88.6363	−2.99133
$879$	−10.3726	−0.349859
$880$	99.6586	3.35949
$881$	−11.8347	−0.398720	−0.199360	−	0.979926i	$-0.563886\pi$
$881$	−11.8347	−0.398720	−0.199360	+	0.979926i	$0.563886\pi$
$882$	−5.44937	−0.183490
$883$	−39.7191	−1.33665	−0.668327	−	0.743868i	$-0.732989\pi$
$883$	−39.7191	−1.33665	−0.668327	+	0.743868i	$0.732989\pi$
$884$	−1.81585	−0.0610735
$885$	−12.5710	−0.422570
$886$	−51.6172	−1.73411
$887$	−22.8890	−0.768538	−0.384269	−	0.923221i	$-0.625547\pi$
$887$	−22.8890	−0.768538	−0.384269	+	0.923221i	$0.625547\pi$
$888$	−12.6545	−0.424656
$889$	−6.15720	−0.206506
$890$	3.07041	0.102920
$891$	47.5614	1.59337
$892$	23.8388	0.798182
$893$	13.1414	0.439762
$894$	32.9649	1.10251
$895$	−22.1784	−0.741342
$896$	16.8923	0.564331
$897$	−31.5920	−1.05483
$898$	−75.5256	−2.52032
$899$	−9.68642	−0.323060
$900$	114.528	3.81758
$901$	−0.864343	−0.0287954
$902$	−122.113	−4.06591
$903$	23.9876	0.798258
$904$	−78.1255	−2.59842
$905$	−31.9645	−1.06254
$906$	−90.1321	−2.99444
$907$	−36.4911	−1.21167	−0.605834	−	0.795591i	$-0.707160\pi$
$907$	−36.4911	−1.21167	−0.605834	+	0.795591i	$0.707160\pi$
$908$	−5.38109	−0.178578
$909$	−23.7250	−0.786907
$910$	−32.5816	−1.08007
$911$	−52.3926	−1.73585	−0.867923	−	0.496699i	$-0.834545\pi$
$911$	−52.3926	−1.73585	−0.867923	+	0.496699i	$0.834545\pi$
$912$	−20.9890	−0.695017
$913$	−11.9127	−0.394253
$914$	−14.0453	−0.464576
$915$	−23.1949	−0.766799
$916$	103.628	3.42398
$917$	−6.28986	−0.207710
$918$	−0.636591	−0.0210106
$919$	37.1988	1.22707	0.613537	−	0.789666i	$-0.289746\pi$
$919$	37.1988	1.22707	0.613537	+	0.789666i	$0.289746\pi$
$920$	−102.818	−3.38982
$921$	−49.1496	−1.61953
$922$	93.6428	3.08396
$923$	−44.8252	−1.47544
$924$	42.4537	1.39662
$925$	−12.4066	−0.407926
$926$	−2.35939	−0.0775343
$927$	−14.6872	−0.482390
$928$	23.2236	0.762351
$929$	−51.1906	−1.67951	−0.839755	−	0.542965i	$-0.817302\pi$
$929$	−51.1906	−1.67951	−0.839755	+	0.542965i	$0.817302\pi$
$930$	−23.7043	−0.777294
$931$	1.70235	0.0557922
$932$	108.655	3.55912
$933$	−15.7392	−0.515280
$934$	−30.2877	−0.991045
$935$	2.52605	0.0826107
$936$	37.9828	1.24151
$937$	21.5978	0.705569	0.352785	−	0.935705i	$-0.385235\pi$
$937$	21.5978	0.705569	0.352785	+	0.935705i	$0.385235\pi$
$938$	−21.3473	−0.697013
$939$	30.3641	0.990895
$940$	−136.148	−4.44067
$941$	−49.1646	−1.60272	−0.801361	−	0.598181i	$-0.795890\pi$
$941$	−49.1646	−1.60272	−0.801361	+	0.598181i	$0.795890\pi$
$942$	−25.5268	−0.831708
$943$	49.1890	1.60181
$944$	−7.16666	−0.233255
$945$	−7.75384	−0.252233
$946$	−115.971	−3.77054
$947$	−30.8042	−1.00100	−0.500502	−	0.865736i	$-0.666851\pi$
$947$	−30.8042	−1.00100	−0.500502	+	0.865736i	$0.666851\pi$
$948$	−71.6933	−2.32849
$949$	0.359487	0.0116694
$950$	−52.7047	−1.70997
$951$	−48.2383	−1.56424
$952$	−0.762912	−0.0247261
$953$	−52.7054	−1.70729	−0.853647	−	0.520852i	$-0.825614\pi$
$953$	−52.7054	−1.70729	−0.853647	+	0.520852i	$0.825614\pi$
$954$	34.3147	1.11098
$955$	0.985637	0.0318945
$956$	24.8167	0.802630
$957$	−97.2789	−3.14458
$958$	4.58680	0.148193
$959$	8.03157	0.259353
$960$	−46.0482	−1.48620
$961$	1.00000	0.0322581
$962$	−7.80937	−0.251784
$963$	7.94905	0.256154
$964$	−109.916	−3.54015
$965$	−33.5441	−1.07982
$966$	−25.1918	−0.810534
$967$	33.5840	1.07999	0.539994	−	0.841669i	$-0.318426\pi$
$967$	33.5840	1.07999	0.539994	+	0.841669i	$0.318426\pi$
$968$	−47.0027	−1.51072
$969$	−0.532010	−0.0170906
$970$	−164.852	−5.29308
$971$	52.0939	1.67177	0.835887	−	0.548902i	$-0.184954\pi$
$971$	52.0939	1.67177	0.835887	+	0.548902i	$0.184954\pi$
$972$	80.2082	2.57268
$973$	−5.60728	−0.179761
$974$	−58.5069	−1.87468
$975$	88.3975	2.83099
$976$	−13.2233	−0.423266
$977$	51.9144	1.66089	0.830444	−	0.557103i	$-0.188087\pi$
$977$	51.9144	1.66089	0.830444	+	0.557103i	$0.188087\pi$
$978$	42.4666	1.35793
$979$	−1.30084	−0.0415751
$980$	−17.6367	−0.563384
$981$	6.07985	0.194115
$982$	−7.02140	−0.224062
$983$	−34.3329	−1.09505	−0.547525	−	0.836789i	$-0.684430\pi$
$983$	−34.3329	−1.09505	−0.547525	+	0.836789i	$0.684430\pi$
$984$	−140.385	−4.47532
$985$	−39.1181	−1.24641
$986$	3.31790	0.105664
$987$	−17.5758	−0.559445
$988$	−22.5204	−0.716469
$989$	46.7150	1.48545
$990$	−100.285	−3.18727
$991$	51.0077	1.62031	0.810157	−	0.586213i	$-0.199382\pi$
$991$	51.0077	1.62031	0.810157	+	0.586213i	$0.199382\pi$
$992$	−2.39754	−0.0761219
$993$	−31.0546	−0.985489
$994$	−35.7441	−1.13373
$995$	−96.3899	−3.05576
$996$	−25.9931	−0.823622
$997$	−6.93913	−0.219764	−0.109882	−	0.993945i	$-0.535047\pi$
$997$	−6.93913	−0.219764	−0.109882	+	0.993945i	$0.535047\pi$
$998$	16.3968	0.519032
$999$	−1.85849	−0.0588000

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8029.2.a.d.1.6	✓	66

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8029.2.a.d.1.6	✓	66	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:	\( N \)	\(=\)	\( 8029 = 7 \cdot 31 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8029.a (trivial)

\(f(q)\)	\(=\)	\(q-2.49545 q^{2} -2.27678 q^{3} +4.22728 q^{4} -4.17212 q^{5} +5.68159 q^{6} +1.00000 q^{7} -5.55806 q^{8} +2.18372 q^{9} +O(q^{10})\)	\(q-2.49545 q^{2} -2.27678 q^{3} +4.22728 q^{4} -4.17212 q^{5} +5.68159 q^{6} +1.00000 q^{7} -5.55806 q^{8} +2.18372 q^{9} +10.4113 q^{10} -4.41097 q^{11} -9.62457 q^{12} -3.12944 q^{13} -2.49545 q^{14} +9.49899 q^{15} +5.41532 q^{16} +0.137262 q^{17} -5.44937 q^{18} +1.70235 q^{19} -17.6367 q^{20} -2.27678 q^{21} +11.0074 q^{22} -4.43394 q^{23} +12.6545 q^{24} +12.4066 q^{25} +7.80937 q^{26} +1.85849 q^{27} +4.22728 q^{28} -9.68642 q^{29} -23.7043 q^{30} +1.00000 q^{31} -2.39754 q^{32} +10.0428 q^{33} -0.342531 q^{34} -4.17212 q^{35} +9.23119 q^{36} -1.00000 q^{37} -4.24812 q^{38} +7.12505 q^{39} +23.1889 q^{40} -11.0937 q^{41} +5.68159 q^{42} -10.5358 q^{43} -18.6464 q^{44} -9.11074 q^{45} +11.0647 q^{46} +7.71961 q^{47} -12.3295 q^{48} +1.00000 q^{49} -30.9600 q^{50} -0.312516 q^{51} -13.2290 q^{52} -6.29701 q^{53} -4.63777 q^{54} +18.4031 q^{55} -5.55806 q^{56} -3.87587 q^{57} +24.1720 q^{58} -1.32341 q^{59} +40.1549 q^{60} -2.44182 q^{61} -2.49545 q^{62} +2.18372 q^{63} -4.84770 q^{64} +13.0564 q^{65} -25.0613 q^{66} +8.55448 q^{67} +0.580246 q^{68} +10.0951 q^{69} +10.4113 q^{70} +14.3237 q^{71} -12.1372 q^{72} -0.114873 q^{73} +2.49545 q^{74} -28.2470 q^{75} +7.19629 q^{76} -4.41097 q^{77} -17.7802 q^{78} +7.44898 q^{79} -22.5934 q^{80} -10.7825 q^{81} +27.6839 q^{82} +2.70070 q^{83} -9.62457 q^{84} -0.572675 q^{85} +26.2915 q^{86} +22.0538 q^{87} +24.5165 q^{88} +0.294910 q^{89} +22.7354 q^{90} -3.12944 q^{91} -18.7435 q^{92} -2.27678 q^{93} -19.2639 q^{94} -7.10239 q^{95} +5.45866 q^{96} -15.8339 q^{97} -2.49545 q^{98} -9.63232 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 66 q - 5 q^{2} - 12 q^{3} + 63 q^{4} - 26 q^{5} - 19 q^{6} + 66 q^{7} - 15 q^{8} + 66 q^{9}+O(q^{10}) \) 66 * q - 5 * q^2 - 12 * q^3 + 63 * q^4 - 26 * q^5 - 19 * q^6 + 66 * q^7 - 15 * q^8 + 66 * q^9	\( 66 q - 5 q^{2} - 12 q^{3} + 63 q^{4} - 26 q^{5} - 19 q^{6} + 66 q^{7} - 15 q^{8} + 66 q^{9} - 6 q^{10} - 57 q^{11} - 29 q^{12} - 28 q^{13} - 5 q^{14} - 24 q^{15} + 69 q^{16} - 47 q^{17} + 8 q^{18} - 27 q^{19} - 77 q^{20} - 12 q^{21} - 12 q^{22} - 46 q^{23} - 57 q^{24} + 72 q^{25} - 21 q^{26} - 36 q^{27} + 63 q^{28} - 62 q^{29} + 2 q^{30} + 66 q^{31} - 40 q^{32} + 4 q^{33} - 46 q^{34} - 26 q^{35} + 62 q^{36} - 66 q^{37} - 31 q^{38} - 8 q^{39} - 37 q^{40} - 33 q^{41} - 19 q^{42} - 22 q^{43} - 84 q^{44} - 77 q^{45} - 14 q^{46} - 20 q^{47} - 43 q^{48} + 66 q^{49} - 10 q^{50} - 39 q^{51} - 41 q^{52} - 47 q^{53} - 65 q^{54} - 15 q^{55} - 15 q^{56} + 5 q^{57} + 24 q^{58} - 125 q^{59} - 77 q^{60} - 57 q^{61} - 5 q^{62} + 66 q^{63} + 81 q^{64} - 40 q^{65} + 33 q^{66} - 25 q^{67} - 107 q^{68} - 72 q^{69} - 6 q^{70} - 57 q^{71} + 38 q^{72} + 5 q^{73} + 5 q^{74} - 60 q^{75} - 33 q^{76} - 57 q^{77} - 19 q^{78} - 4 q^{79} - 132 q^{80} + 58 q^{81} + 8 q^{82} - 84 q^{83} - 29 q^{84} - 33 q^{85} - 60 q^{86} - 31 q^{87} + 21 q^{88} - 132 q^{89} - 61 q^{90} - 28 q^{91} - 100 q^{92} - 12 q^{93} - 35 q^{94} + 4 q^{95} - 198 q^{96} - 39 q^{97} - 5 q^{98} - 174 q^{99}+O(q^{100}) \) 66 * q - 5 * q^2 - 12 * q^3 + 63 * q^4 - 26 * q^5 - 19 * q^6 + 66 * q^7 - 15 * q^8 + 66 * q^9 - 6 * q^10 - 57 * q^11 - 29 * q^12 - 28 * q^13 - 5 * q^14 - 24 * q^15 + 69 * q^16 - 47 * q^17 + 8 * q^18 - 27 * q^19 - 77 * q^20 - 12 * q^21 - 12 * q^22 - 46 * q^23 - 57 * q^24 + 72 * q^25 - 21 * q^26 - 36 * q^27 + 63 * q^28 - 62 * q^29 + 2 * q^30 + 66 * q^31 - 40 * q^32 + 4 * q^33 - 46 * q^34 - 26 * q^35 + 62 * q^36 - 66 * q^37 - 31 * q^38 - 8 * q^39 - 37 * q^40 - 33 * q^41 - 19 * q^42 - 22 * q^43 - 84 * q^44 - 77 * q^45 - 14 * q^46 - 20 * q^47 - 43 * q^48 + 66 * q^49 - 10 * q^50 - 39 * q^51 - 41 * q^52 - 47 * q^53 - 65 * q^54 - 15 * q^55 - 15 * q^56 + 5 * q^57 + 24 * q^58 - 125 * q^59 - 77 * q^60 - 57 * q^61 - 5 * q^62 + 66 * q^63 + 81 * q^64 - 40 * q^65 + 33 * q^66 - 25 * q^67 - 107 * q^68 - 72 * q^69 - 6 * q^70 - 57 * q^71 + 38 * q^72 + 5 * q^73 + 5 * q^74 - 60 * q^75 - 33 * q^76 - 57 * q^77 - 19 * q^78 - 4 * q^79 - 132 * q^80 + 58 * q^81 + 8 * q^82 - 84 * q^83 - 29 * q^84 - 33 * q^85 - 60 * q^86 - 31 * q^87 + 21 * q^88 - 132 * q^89 - 61 * q^90 - 28 * q^91 - 100 * q^92 - 12 * q^93 - 35 * q^94 + 4 * q^95 - 198 * q^96 - 39 * q^97 - 5 * q^98 - 174 * q^99

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