LMFDB - Embedded newform 4033.2.a.d.1.72

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4033,2,Mod(1,4033)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4033, 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("4033.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4033 = 37 \cdot 109 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4033.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$32.2036671352$
Analytic rank:	$1$
Dimension:	$79$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.72
Character	$\chi$	$=$	4033.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.26042 q^{2} -0.287940 q^{3} +3.10951 q^{4} +3.74762 q^{5} -0.650866 q^{6} -2.77077 q^{7} +2.50796 q^{8} -2.91709 q^{9} +O(q^{10})$	\(q+2.26042 q^{2} -0.287940 q^{3} +3.10951 q^{4} +3.74762 q^{5} -0.650866 q^{6} -2.77077 q^{7} +2.50796 q^{8} -2.91709 q^{9} +8.47120 q^{10} -6.19834 q^{11} -0.895352 q^{12} -2.91323 q^{13} -6.26311 q^{14} -1.07909 q^{15} -0.549977 q^{16} -1.87707 q^{17} -6.59386 q^{18} -2.67486 q^{19} +11.6533 q^{20} +0.797816 q^{21} -14.0109 q^{22} -3.49676 q^{23} -0.722141 q^{24} +9.04466 q^{25} -6.58514 q^{26} +1.70377 q^{27} -8.61574 q^{28} +8.04895 q^{29} -2.43920 q^{30} +3.20477 q^{31} -6.25909 q^{32} +1.78475 q^{33} -4.24298 q^{34} -10.3838 q^{35} -9.07072 q^{36} -1.00000 q^{37} -6.04632 q^{38} +0.838836 q^{39} +9.39887 q^{40} +5.25605 q^{41} +1.80340 q^{42} -1.20841 q^{43} -19.2738 q^{44} -10.9321 q^{45} -7.90416 q^{46} -1.64892 q^{47} +0.158360 q^{48} +0.677178 q^{49} +20.4448 q^{50} +0.540485 q^{51} -9.05872 q^{52} -6.68007 q^{53} +3.85123 q^{54} -23.2290 q^{55} -6.94897 q^{56} +0.770200 q^{57} +18.1940 q^{58} -3.29977 q^{59} -3.35544 q^{60} +2.81439 q^{61} +7.24414 q^{62} +8.08259 q^{63} -13.0482 q^{64} -10.9177 q^{65} +4.03429 q^{66} -14.2813 q^{67} -5.83678 q^{68} +1.00686 q^{69} -23.4718 q^{70} -3.72787 q^{71} -7.31593 q^{72} -15.0229 q^{73} -2.26042 q^{74} -2.60432 q^{75} -8.31751 q^{76} +17.1742 q^{77} +1.89612 q^{78} +12.3047 q^{79} -2.06111 q^{80} +8.26069 q^{81} +11.8809 q^{82} +8.90084 q^{83} +2.48082 q^{84} -7.03456 q^{85} -2.73153 q^{86} -2.31762 q^{87} -15.5452 q^{88} +9.82309 q^{89} -24.7113 q^{90} +8.07190 q^{91} -10.8732 q^{92} -0.922782 q^{93} -3.72726 q^{94} -10.0244 q^{95} +1.80224 q^{96} +3.69047 q^{97} +1.53071 q^{98} +18.0811 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 79 q - 11 q^{2} - 11 q^{3} + 79 q^{4} - 16 q^{5} - 14 q^{6} - 15 q^{7} - 42 q^{8} + 76 q^{9}+O(q^{10}) $ 79 * q - 11 * q^2 - 11 * q^3 + 79 * q^4 - 16 * q^5 - 14 * q^6 - 15 * q^7 - 42 * q^8 + 76 * q^9	\( 79 q - 11 q^{2} - 11 q^{3} + 79 q^{4} - 16 q^{5} - 14 q^{6} - 15 q^{7} - 42 q^{8} + 76 q^{9} - 13 q^{10} - 5 q^{11} - 40 q^{12} - 18 q^{13} - 42 q^{14} - 49 q^{15} + 83 q^{16} - 62 q^{17} - 33 q^{18} - 25 q^{19} - 39 q^{20} - 15 q^{21} - 31 q^{22} - 94 q^{23} - 39 q^{24} + 71 q^{25} - 35 q^{26} - 47 q^{27} - 13 q^{28} - 17 q^{29} + 15 q^{30} - 37 q^{31} - 105 q^{32} - 60 q^{33} + 9 q^{34} - 60 q^{35} + 43 q^{36} - 79 q^{37} - 80 q^{38} - 41 q^{39} - 64 q^{40} - 37 q^{41} - 30 q^{42} - 20 q^{43} - 14 q^{44} - 8 q^{45} + 61 q^{46} - 148 q^{47} - 39 q^{48} + 82 q^{49} - 90 q^{50} - 45 q^{51} - 27 q^{52} - 70 q^{53} - 41 q^{54} - 105 q^{55} - 68 q^{56} - 31 q^{57} - 14 q^{58} - 96 q^{59} - 74 q^{60} - 21 q^{61} + 4 q^{62} - 60 q^{63} + 132 q^{64} - 15 q^{65} + 71 q^{66} - 44 q^{67} - 166 q^{68} - 72 q^{69} - 9 q^{70} - 55 q^{71} - 126 q^{72} - 27 q^{73} + 11 q^{74} - 39 q^{75} - 4 q^{76} - 104 q^{77} - 47 q^{78} - 49 q^{79} - 82 q^{80} + 55 q^{81} + 20 q^{82} - 52 q^{83} - 29 q^{84} + 3 q^{85} - 32 q^{86} - 113 q^{87} + 14 q^{88} - 68 q^{89} - 39 q^{90} - 30 q^{91} - 179 q^{92} - 53 q^{93} - 33 q^{94} - 86 q^{95} + 33 q^{96} - 57 q^{97} - 116 q^{98} + q^{99}+O(q^{100}) \) 79 * q - 11 * q^2 - 11 * q^3 + 79 * q^4 - 16 * q^5 - 14 * q^6 - 15 * q^7 - 42 * q^8 + 76 * q^9 - 13 * q^10 - 5 * q^11 - 40 * q^12 - 18 * q^13 - 42 * q^14 - 49 * q^15 + 83 * q^16 - 62 * q^17 - 33 * q^18 - 25 * q^19 - 39 * q^20 - 15 * q^21 - 31 * q^22 - 94 * q^23 - 39 * q^24 + 71 * q^25 - 35 * q^26 - 47 * q^27 - 13 * q^28 - 17 * q^29 + 15 * q^30 - 37 * q^31 - 105 * q^32 - 60 * q^33 + 9 * q^34 - 60 * q^35 + 43 * q^36 - 79 * q^37 - 80 * q^38 - 41 * q^39 - 64 * q^40 - 37 * q^41 - 30 * q^42 - 20 * q^43 - 14 * q^44 - 8 * q^45 + 61 * q^46 - 148 * q^47 - 39 * q^48 + 82 * q^49 - 90 * q^50 - 45 * q^51 - 27 * q^52 - 70 * q^53 - 41 * q^54 - 105 * q^55 - 68 * q^56 - 31 * q^57 - 14 * q^58 - 96 * q^59 - 74 * q^60 - 21 * q^61 + 4 * q^62 - 60 * q^63 + 132 * q^64 - 15 * q^65 + 71 * q^66 - 44 * q^67 - 166 * q^68 - 72 * q^69 - 9 * q^70 - 55 * q^71 - 126 * q^72 - 27 * q^73 + 11 * q^74 - 39 * q^75 - 4 * q^76 - 104 * q^77 - 47 * q^78 - 49 * q^79 - 82 * q^80 + 55 * q^81 + 20 * q^82 - 52 * q^83 - 29 * q^84 + 3 * q^85 - 32 * q^86 - 113 * q^87 + 14 * q^88 - 68 * q^89 - 39 * q^90 - 30 * q^91 - 179 * q^92 - 53 * q^93 - 33 * q^94 - 86 * q^95 + 33 * q^96 - 57 * q^97 - 116 * q^98 + 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 $

$2$	2.26042	1.59836	0.799180	−	0.601092i	$-0.205267\pi$
$2$	2.26042	1.59836	0.799180	+	0.601092i	$0.205267\pi$
$3$	−0.287940	−0.166242	−0.0831211	−	0.996539i	$-0.526489\pi$
$3$	−0.287940	−0.166242	−0.0831211	+	0.996539i	$0.526489\pi$
$4$	3.10951	1.55475
$5$	3.74762	1.67599	0.837993	−	0.545680i	$-0.183729\pi$
$5$	3.74762	1.67599	0.837993	+	0.545680i	$0.183729\pi$
$6$	−0.650866	−0.265715
$7$	−2.77077	−1.04725	−0.523627	−	0.851948i	$-0.675421\pi$
$7$	−2.77077	−1.04725	−0.523627	+	0.851948i	$0.675421\pi$
$8$	2.50796	0.886696
$9$	−2.91709	−0.972364
$10$	8.47120	2.67883
$11$	−6.19834	−1.86887	−0.934435	−	0.356134i	$-0.884095\pi$
$11$	−6.19834	−1.86887	−0.934435	+	0.356134i	$0.884095\pi$
$12$	−0.895352	−0.258466
$13$	−2.91323	−0.807985	−0.403993	−	0.914762i	$-0.632378\pi$
$13$	−2.91323	−0.807985	−0.403993	+	0.914762i	$0.632378\pi$
$14$	−6.26311	−1.67389
$15$	−1.07909	−0.278620
$16$	−0.549977	−0.137494
$17$	−1.87707	−0.455258	−0.227629	−	0.973748i	$-0.573097\pi$
$17$	−1.87707	−0.455258	−0.227629	+	0.973748i	$0.573097\pi$
$18$	−6.59386	−1.55419
$19$	−2.67486	−0.613656	−0.306828	−	0.951765i	$-0.599268\pi$
$19$	−2.67486	−0.613656	−0.306828	+	0.951765i	$0.599268\pi$
$20$	11.6533	2.60575
$21$	0.797816	0.174098
$22$	−14.0109	−2.98713
$23$	−3.49676	−0.729125	−0.364563	−	0.931179i	$-0.618781\pi$
$23$	−3.49676	−0.729125	−0.364563	+	0.931179i	$0.618781\pi$
$24$	−0.722141	−0.147406
$25$	9.04466	1.80893
$26$	−6.58514	−1.29145
$27$	1.70377	0.327890
$28$	−8.61574	−1.62822
$29$	8.04895	1.49465	0.747327	−	0.664457i	$-0.231337\pi$
$29$	8.04895	1.49465	0.747327	+	0.664457i	$0.231337\pi$
$30$	−2.43920	−0.445335
$31$	3.20477	0.575594	0.287797	−	0.957691i	$-0.407077\pi$
$31$	3.20477	0.575594	0.287797	+	0.957691i	$0.407077\pi$
$32$	−6.25909	−1.10646
$33$	1.78475	0.310685
$34$	−4.24298	−0.727665
$35$	−10.3838	−1.75518
$36$	−9.07072	−1.51179
$37$	−1.00000	−0.164399
$37$	−1.00000	−0.164399
$38$	−6.04632	−0.980843
$39$	0.838836	0.134321
$40$	9.39887	1.48609
$41$	5.25605	0.820858	0.410429	−	0.911893i	$-0.365379\pi$
$41$	5.25605	0.820858	0.410429	+	0.911893i	$0.365379\pi$
$42$	1.80340	0.278271
$43$	−1.20841	−0.184281	−0.0921407	−	0.995746i	$-0.529371\pi$
$43$	−1.20841	−0.184281	−0.0921407	+	0.995746i	$0.529371\pi$
$44$	−19.2738	−2.90563
$45$	−10.9321	−1.62967
$46$	−7.90416	−1.16540
$47$	−1.64892	−0.240520	−0.120260	−	0.992742i	$-0.538373\pi$
$47$	−1.64892	−0.240520	−0.120260	+	0.992742i	$0.538373\pi$
$48$	0.158360	0.0228574
$49$	0.677178	0.0967397
$50$	20.4448	2.89132
$51$	0.540485	0.0756830
$52$	−9.05872	−1.25622
$53$	−6.68007	−0.917578	−0.458789	−	0.888545i	$-0.651717\pi$
$53$	−6.68007	−0.917578	−0.458789	+	0.888545i	$0.651717\pi$
$54$	3.85123	0.524086
$55$	−23.2290	−3.13220
$56$	−6.94897	−0.928596
$57$	0.770200	0.102015
$58$	18.1940	2.38899
$59$	−3.29977	−0.429594	−0.214797	−	0.976659i	$-0.568909\pi$
$59$	−3.29977	−0.429594	−0.214797	+	0.976659i	$0.568909\pi$
$60$	−3.35544	−0.433185
$61$	2.81439	0.360345	0.180173	−	0.983635i	$-0.442334\pi$
$61$	2.81439	0.360345	0.180173	+	0.983635i	$0.442334\pi$
$62$	7.24414	0.920007
$63$	8.08259	1.01831
$64$	−13.0482	−1.63103
$65$	−10.9177	−1.35417
$66$	4.03429	0.496587
$67$	−14.2813	−1.74474	−0.872369	−	0.488847i	$-0.837418\pi$
$67$	−14.2813	−1.74474	−0.872369	+	0.488847i	$0.837418\pi$
$68$	−5.83678	−0.707813
$69$	1.00686	0.121211
$70$	−23.4718	−2.80541
$71$	−3.72787	−0.442416	−0.221208	−	0.975227i	$-0.571000\pi$
$71$	−3.72787	−0.442416	−0.221208	+	0.975227i	$0.571000\pi$
$72$	−7.31593	−0.862191
$73$	−15.0229	−1.75829	−0.879147	−	0.476550i	$-0.841887\pi$
$73$	−15.0229	−1.75829	−0.879147	+	0.476550i	$0.841887\pi$
$74$	−2.26042	−0.262769
$75$	−2.60432	−0.300721
$76$	−8.31751	−0.954084
$77$	17.1742	1.95718
$78$	1.89612	0.214694
$79$	12.3047	1.38439	0.692195	−	0.721711i	$-0.256644\pi$
$79$	12.3047	1.38439	0.692195	+	0.721711i	$0.256644\pi$
$80$	−2.06111	−0.230439
$81$	8.26069	0.917854
$82$	11.8809	1.31203
$83$	8.90084	0.976994	0.488497	−	0.872565i	$-0.337545\pi$
$83$	8.90084	0.976994	0.488497	+	0.872565i	$0.337545\pi$
$84$	2.48082	0.270679
$85$	−7.03456	−0.763006
$86$	−2.73153	−0.294548
$87$	−2.31762	−0.248475
$88$	−15.5452	−1.65712
$89$	9.82309	1.04125	0.520623	−	0.853787i	$-0.325700\pi$
$89$	9.82309	1.04125	0.520623	+	0.853787i	$0.325700\pi$
$90$	−24.7113	−2.60480
$91$	8.07190	0.846166
$92$	−10.8732	−1.13361
$93$	−0.922782	−0.0956881
$94$	−3.72726	−0.384438
$95$	−10.0244	−1.02848
$96$	1.80224	0.183941
$97$	3.69047	0.374711	0.187355	−	0.982292i	$-0.440008\pi$
$97$	3.69047	0.374711	0.187355	+	0.982292i	$0.440008\pi$
$98$	1.53071	0.154625
$99$	18.0811	1.81722
$100$	28.1244	2.81244
$101$	4.16888	0.414819	0.207409	−	0.978254i	$-0.433497\pi$
$101$	4.16888	0.414819	0.207409	+	0.978254i	$0.433497\pi$
$102$	1.22172	0.120969
$103$	8.06097	0.794271	0.397135	−	0.917760i	$-0.370004\pi$
$103$	8.06097	0.794271	0.397135	+	0.917760i	$0.370004\pi$
$104$	−7.30626	−0.716438
$105$	2.98991	0.291786
$106$	−15.0998	−1.46662
$107$	−6.91521	−0.668518	−0.334259	−	0.942481i	$-0.608486\pi$
$107$	−6.91521	−0.668518	−0.334259	+	0.942481i	$0.608486\pi$
$108$	5.29788	0.509788
$109$	−1.00000	−0.0957826
$109$	−1.00000	−0.0957826
$110$	−52.5074	−5.00638
$111$	0.287940	0.0273301
$112$	1.52386	0.143991
$113$	−15.6454	−1.47180	−0.735899	−	0.677091i	$-0.763240\pi$
$113$	−15.6454	−1.47180	−0.735899	+	0.677091i	$0.763240\pi$
$114$	1.74098	0.163057
$115$	−13.1045	−1.22200
$116$	25.0283	2.32382
$117$	8.49816	0.785656
$118$	−7.45888	−0.686646
$119$	5.20095	0.476770
$120$	−2.70631	−0.247051
$121$	27.4194	2.49267
$122$	6.36170	0.575961
$123$	−1.51343	−0.136461
$124$	9.96527	0.894907
$125$	15.1579	1.35576
$126$	18.2701	1.62763
$127$	−4.53560	−0.402470	−0.201235	−	0.979543i	$-0.564495\pi$
$127$	−4.53560	−0.402470	−0.201235	+	0.979543i	$0.564495\pi$
$128$	−16.9763	−1.50051
$129$	0.347951	0.0306354
$130$	−24.6786	−2.16446
$131$	−1.29025	−0.112730	−0.0563648	−	0.998410i	$-0.517951\pi$
$131$	−1.29025	−0.112730	−0.0563648	+	0.998410i	$0.517951\pi$
$132$	5.54969	0.483039
$133$	7.41144	0.642653
$134$	−32.2818	−2.78872
$135$	6.38507	0.549540
$136$	−4.70762	−0.403675
$137$	9.13910	0.780806	0.390403	−	0.920644i	$-0.372336\pi$
$137$	9.13910	0.780806	0.390403	+	0.920644i	$0.372336\pi$
$138$	2.27592	0.193739
$139$	15.6056	1.32365	0.661826	−	0.749658i	$-0.269782\pi$
$139$	15.6056	1.32365	0.661826	+	0.749658i	$0.269782\pi$
$140$	−32.2885	−2.72888
$141$	0.474791	0.0399846
$142$	−8.42655	−0.707140
$143$	18.0572	1.51002
$144$	1.60433	0.133694
$145$	30.1644	2.50502
$146$	−33.9580	−2.81039
$147$	−0.194987	−0.0160822
$148$	−3.10951	−0.255600
$149$	1.72639	0.141431	0.0707157	−	0.997497i	$-0.477472\pi$
$149$	1.72639	0.141431	0.0707157	+	0.997497i	$0.477472\pi$
$150$	−5.88686	−0.480660
$151$	−20.1295	−1.63811	−0.819056	−	0.573713i	$-0.805503\pi$
$151$	−20.1295	−1.63811	−0.819056	+	0.573713i	$0.805503\pi$
$152$	−6.70844	−0.544126
$153$	5.47560	0.442676
$154$	38.8209	3.12828
$155$	12.0103	0.964688
$156$	2.60837	0.208837
$157$	17.5579	1.40127	0.700635	−	0.713520i	$-0.252900\pi$
$157$	17.5579	1.40127	0.700635	+	0.713520i	$0.252900\pi$
$158$	27.8139	2.21275
$159$	1.92346	0.152540
$160$	−23.4567	−1.85442
$161$	9.68873	0.763579
$162$	18.6726	1.46706
$163$	6.72703	0.526901	0.263451	−	0.964673i	$-0.415139\pi$
$163$	6.72703	0.526901	0.263451	+	0.964673i	$0.415139\pi$
$164$	16.3437	1.27623
$165$	6.68857	0.520704
$166$	20.1197	1.56159
$167$	−6.68863	−0.517582	−0.258791	−	0.965933i	$-0.583324\pi$
$167$	−6.68863	−0.517582	−0.258791	+	0.965933i	$0.583324\pi$
$168$	2.00089	0.154372
$169$	−4.51307	−0.347160
$170$	−15.9011	−1.21956
$171$	7.80282	0.596696
$172$	−3.75757	−0.286512
$173$	−19.6335	−1.49270	−0.746352	−	0.665551i	$-0.768197\pi$
$173$	−19.6335	−1.49270	−0.746352	+	0.665551i	$0.768197\pi$
$174$	−5.23879	−0.397152
$175$	−25.0607	−1.89441
$176$	3.40894	0.256959
$177$	0.950137	0.0714167
$178$	22.2043	1.66428
$179$	−21.5886	−1.61361	−0.806803	−	0.590821i	$-0.798804\pi$
$179$	−21.5886	−1.61361	−0.806803	+	0.590821i	$0.798804\pi$
$180$	−33.9936	−2.53373
$181$	21.8170	1.62164	0.810822	−	0.585293i	$-0.199020\pi$
$181$	21.8170	1.62164	0.810822	+	0.585293i	$0.199020\pi$
$182$	18.2459	1.35248
$183$	−0.810375	−0.0599046
$184$	−8.76972	−0.646512
$185$	−3.74762	−0.275531
$186$	−2.08588	−0.152944
$187$	11.6347	0.850817
$188$	−5.12734	−0.373950
$189$	−4.72075	−0.343384
$190$	−22.6593	−1.64388
$191$	12.2973	0.889803	0.444901	−	0.895580i	$-0.353239\pi$
$191$	12.2973	0.889803	0.444901	+	0.895580i	$0.353239\pi$
$192$	3.75711	0.271146
$193$	−13.3847	−0.963451	−0.481725	−	0.876322i	$-0.659990\pi$
$193$	−13.3847	−0.963451	−0.481725	+	0.876322i	$0.659990\pi$
$194$	8.34202	0.598922
$195$	3.14364	0.225121
$196$	2.10569	0.150406
$197$	0.118401	0.00843572	0.00421786	−	0.999991i	$-0.498657\pi$
$197$	0.118401	0.00843572	0.00421786	+	0.999991i	$0.498657\pi$
$198$	40.8710	2.90457
$199$	−1.50753	−0.106866	−0.0534329	−	0.998571i	$-0.517016\pi$
$199$	−1.50753	−0.106866	−0.0534329	+	0.998571i	$0.517016\pi$
$200$	22.6836	1.60397
$201$	4.11216	0.290049
$202$	9.42342	0.663030
$203$	−22.3018	−1.56528
$204$	1.68064	0.117668
$205$	19.6977	1.37575
$206$	18.2212	1.26953
$207$	10.2004	0.708975
$208$	1.60221	0.111093
$209$	16.5797	1.14684
$210$	6.75846	0.466378
$211$	−28.0387	−1.93027	−0.965133	−	0.261762i	$-0.915697\pi$
$211$	−28.0387	−1.93027	−0.965133	+	0.261762i	$0.915697\pi$
$212$	−20.7717	−1.42661
$213$	1.07340	0.0735483
$214$	−15.6313	−1.06853
$215$	−4.52868	−0.308853
$216$	4.27297	0.290739
$217$	−8.87970	−0.602793
$218$	−2.26042	−0.153095
$219$	4.32569	0.292303
$220$	−72.2308	−4.86980
$221$	5.46836	0.367841
$222$	0.650866	0.0436833
$223$	−16.0010	−1.07151	−0.535755	−	0.844374i	$-0.679973\pi$
$223$	−16.0010	−1.07151	−0.535755	+	0.844374i	$0.679973\pi$
$224$	17.3425	1.15875
$225$	−26.3841	−1.75894
$226$	−35.3653	−2.35246
$227$	−16.7654	−1.11276	−0.556381	−	0.830927i	$-0.687810\pi$
$227$	−16.7654	−1.11276	−0.556381	+	0.830927i	$0.687810\pi$
$228$	2.39494	0.158609
$229$	−3.16426	−0.209100	−0.104550	−	0.994520i	$-0.533340\pi$
$229$	−3.16426	−0.209100	−0.104550	+	0.994520i	$0.533340\pi$
$230$	−29.6218	−1.95320
$231$	−4.94514	−0.325366
$232$	20.1864	1.32530
$233$	12.0970	0.792500	0.396250	−	0.918143i	$-0.370311\pi$
$233$	12.0970	0.792500	0.396250	+	0.918143i	$0.370311\pi$
$234$	19.2094	1.25576
$235$	−6.17954	−0.403109
$236$	−10.2607	−0.667913
$237$	−3.54302	−0.230144
$238$	11.7563	0.762050
$239$	−1.65173	−0.106841	−0.0534207	−	0.998572i	$-0.517012\pi$
$239$	−1.65173	−0.106841	−0.0534207	+	0.998572i	$0.517012\pi$
$240$	0.593475	0.0383086
$241$	−20.3495	−1.31083	−0.655414	−	0.755270i	$-0.727506\pi$
$241$	−20.3495	−1.31083	−0.655414	+	0.755270i	$0.727506\pi$
$242$	61.9795	3.98419
$243$	−7.48988	−0.480476
$244$	8.75136	0.560248
$245$	2.53781	0.162134
$246$	−3.42099	−0.218114
$247$	7.79250	0.495825
$248$	8.03743	0.510377
$249$	−2.56291	−0.162418
$250$	34.2632	2.16699
$251$	10.9059	0.688371	0.344186	−	0.938902i	$-0.388155\pi$
$251$	10.9059	0.688371	0.344186	+	0.938902i	$0.388155\pi$
$252$	25.1329	1.58322
$253$	21.6741	1.36264
$254$	−10.2524	−0.643291
$255$	2.02553	0.126844
$256$	−12.2772	−0.767326
$257$	−3.87567	−0.241757	−0.120879	−	0.992667i	$-0.538571\pi$
$257$	−3.87567	−0.241757	−0.120879	+	0.992667i	$0.538571\pi$
$258$	0.786516	0.0489663
$259$	2.77077	0.172167
$260$	−33.9486	−2.10541
$261$	−23.4795	−1.45335
$262$	−2.91651	−0.180183
$263$	−16.0538	−0.989920	−0.494960	−	0.868916i	$-0.664817\pi$
$263$	−16.0538	−0.989920	−0.494960	+	0.868916i	$0.664817\pi$
$264$	4.47607	0.275483
$265$	−25.0344	−1.53785
$266$	16.7530	1.02719
$267$	−2.82846	−0.173099
$268$	−44.4078	−2.71264
$269$	4.74910	0.289558	0.144779	−	0.989464i	$-0.453753\pi$
$269$	4.74910	0.289558	0.144779	+	0.989464i	$0.453753\pi$
$270$	14.4330	0.878362
$271$	7.00814	0.425714	0.212857	−	0.977083i	$-0.431723\pi$
$271$	7.00814	0.425714	0.212857	+	0.977083i	$0.431723\pi$
$272$	1.03235	0.0625953
$273$	−2.32422	−0.140668
$274$	20.6582	1.24801
$275$	−56.0619	−3.38066
$276$	3.13083	0.188454
$277$	8.88525	0.533863	0.266931	−	0.963716i	$-0.413990\pi$
$277$	8.88525	0.533863	0.266931	+	0.963716i	$0.413990\pi$
$278$	35.2753	2.11567
$279$	−9.34861	−0.559687
$280$	−26.0421	−1.55631
$281$	10.4145	0.621279	0.310640	−	0.950528i	$-0.399457\pi$
$281$	10.4145	0.621279	0.310640	+	0.950528i	$0.399457\pi$
$282$	1.07323	0.0639098
$283$	4.14695	0.246510	0.123255	−	0.992375i	$-0.460667\pi$
$283$	4.14695	0.246510	0.123255	+	0.992375i	$0.460667\pi$
$284$	−11.5918	−0.687848
$285$	2.88642	0.170977
$286$	40.8169	2.41355
$287$	−14.5633	−0.859646
$288$	18.2583	1.07588
$289$	−13.4766	−0.792741
$290$	68.1843	4.00392
$291$	−1.06263	−0.0622927
$292$	−46.7137	−2.73372
$293$	14.1178	0.824774	0.412387	−	0.911009i	$-0.364695\pi$
$293$	14.1178	0.824774	0.412387	+	0.911009i	$0.364695\pi$
$294$	−0.440752	−0.0257052
$295$	−12.3663	−0.719994
$296$	−2.50796	−0.145772
$297$	−10.5605	−0.612784
$298$	3.90237	0.226058
$299$	10.1869	0.589122
$300$	−8.09815	−0.467547
$301$	3.34824	0.192989
$302$	−45.5011	−2.61829
$303$	−1.20039	−0.0689604
$304$	1.47111	0.0843741
$305$	10.5473	0.603934
$306$	12.3772	0.707555
$307$	18.5974	1.06141	0.530704	−	0.847557i	$-0.321927\pi$
$307$	18.5974	1.06141	0.530704	+	0.847557i	$0.321927\pi$
$308$	53.4033	3.04293
$309$	−2.32107	−0.132041
$310$	27.1483	1.54192
$311$	16.5359	0.937664	0.468832	−	0.883287i	$-0.344675\pi$
$311$	16.5359	0.937664	0.468832	+	0.883287i	$0.344675\pi$
$312$	2.10376	0.119102
$313$	−22.2647	−1.25847	−0.629237	−	0.777214i	$-0.716632\pi$
$313$	−22.2647	−1.25847	−0.629237	+	0.777214i	$0.716632\pi$
$314$	39.6882	2.23973
$315$	30.2905	1.70668
$316$	38.2616	2.15239
$317$	−27.0925	−1.52166	−0.760832	−	0.648948i	$-0.775209\pi$
$317$	−27.0925	−1.52166	−0.760832	+	0.648948i	$0.775209\pi$
$318$	4.34783	0.243814
$319$	−49.8902	−2.79331
$320$	−48.8998	−2.73358
$321$	1.99116	0.111136
$322$	21.9006	1.22047
$323$	5.02092	0.279371
$324$	25.6867	1.42704
$325$	−26.3492	−1.46159
$326$	15.2059	0.842178
$327$	0.287940	0.0159231
$328$	13.1820	0.727852
$329$	4.56879	0.251886
$330$	15.1190	0.832273
$331$	17.3761	0.955075	0.477537	−	0.878611i	$-0.341530\pi$
$331$	17.3761	0.955075	0.477537	+	0.878611i	$0.341530\pi$
$332$	27.6772	1.51899
$333$	2.91709	0.159856
$334$	−15.1191	−0.827282
$335$	−53.5209	−2.92416
$336$	−0.438781	−0.0239374
$337$	10.5475	0.574559	0.287280	−	0.957847i	$-0.407249\pi$
$337$	10.5475	0.574559	0.287280	+	0.957847i	$0.407249\pi$
$338$	−10.2015	−0.554886
$339$	4.50495	0.244675
$340$	−21.8740	−1.18629
$341$	−19.8643	−1.07571
$342$	17.6377	0.953735
$343$	17.5191	0.945942
$344$	−3.03065	−0.163402
$345$	3.77332	0.203149
$346$	−44.3799	−2.38588
$347$	−29.0907	−1.56167	−0.780835	−	0.624737i	$-0.785206\pi$
$347$	−29.0907	−1.56167	−0.780835	+	0.624737i	$0.785206\pi$
$348$	−7.20665	−0.386317
$349$	−1.44108	−0.0771391	−0.0385696	−	0.999256i	$-0.512280\pi$
$349$	−1.44108	−0.0771391	−0.0385696	+	0.999256i	$0.512280\pi$
$350$	−56.6477	−3.02795
$351$	−4.96347	−0.264930
$352$	38.7960	2.06783
$353$	2.90600	0.154671	0.0773354	−	0.997005i	$-0.475359\pi$
$353$	2.90600	0.154671	0.0773354	+	0.997005i	$0.475359\pi$
$354$	2.14771	0.114150
$355$	−13.9706	−0.741484
$356$	30.5450	1.61888
$357$	−1.49756	−0.0792593
$358$	−48.7993	−2.57912
$359$	18.6829	0.986044	0.493022	−	0.870017i	$-0.335892\pi$
$359$	18.6829	0.986044	0.493022	+	0.870017i	$0.335892\pi$
$360$	−27.4173	−1.44502
$361$	−11.8451	−0.623427
$362$	49.3156	2.59197
$363$	−7.89515	−0.414388
$364$	25.0996	1.31558
$365$	−56.3000	−2.94688
$366$	−1.83179	−0.0957491
$367$	−4.56030	−0.238046	−0.119023	−	0.992892i	$-0.537976\pi$
$367$	−4.56030	−0.238046	−0.119023	+	0.992892i	$0.537976\pi$
$368$	1.92314	0.100251
$369$	−15.3324	−0.798172
$370$	−8.47120	−0.440397
$371$	18.5090	0.960937
$372$	−2.86940	−0.148771
$373$	−31.1436	−1.61255	−0.806276	−	0.591539i	$-0.798521\pi$
$373$	−31.1436	−1.61255	−0.806276	+	0.591539i	$0.798521\pi$
$374$	26.2994	1.35991
$375$	−4.36455	−0.225385
$376$	−4.13543	−0.213268
$377$	−23.4485	−1.20766
$378$	−10.6709	−0.548851
$379$	6.46391	0.332029	0.166014	−	0.986123i	$-0.446910\pi$
$379$	6.46391	0.332029	0.166014	+	0.986123i	$0.446910\pi$
$380$	−31.1709	−1.59903
$381$	1.30598	0.0669075
$382$	27.7971	1.42222
$383$	−25.7784	−1.31721	−0.658606	−	0.752488i	$-0.728854\pi$
$383$	−25.7784	−1.31721	−0.658606	+	0.752488i	$0.728854\pi$
$384$	4.88817	0.249448
$385$	64.3623	3.28021
$386$	−30.2550	−1.53994
$387$	3.52505	0.179189
$388$	11.4756	0.582583
$389$	29.4572	1.49354	0.746769	−	0.665084i	$-0.231604\pi$
$389$	29.4572	1.49354	0.746769	+	0.665084i	$0.231604\pi$
$390$	7.10595	0.359824
$391$	6.56368	0.331940
$392$	1.69833	0.0857787
$393$	0.371515	0.0187404
$394$	0.267636	0.0134833
$395$	46.1134	2.32022
$396$	56.2234	2.82533
$397$	33.4236	1.67748	0.838742	−	0.544528i	$-0.183291\pi$
$397$	33.4236	1.67748	0.838742	+	0.544528i	$0.183291\pi$
$398$	−3.40765	−0.170810
$399$	−2.13405	−0.106836
$400$	−4.97436	−0.248718
$401$	1.70947	0.0853668	0.0426834	−	0.999089i	$-0.486409\pi$
$401$	1.70947	0.0853668	0.0426834	+	0.999089i	$0.486409\pi$
$402$	9.29521	0.463603
$403$	−9.33625	−0.465072
$404$	12.9632	0.644941
$405$	30.9579	1.53831
$406$	−50.4115	−2.50188
$407$	6.19834	0.307240
$408$	1.35551	0.0671079
$409$	28.5467	1.41154	0.705772	−	0.708439i	$-0.250600\pi$
$409$	28.5467	1.41154	0.705772	+	0.708439i	$0.250600\pi$
$410$	44.5251	2.19894
$411$	−2.63151	−0.129803
$412$	25.0656	1.23490
$413$	9.14292	0.449894
$414$	23.0571	1.13320
$415$	33.3570	1.63743
$416$	18.2342	0.894005
$417$	−4.49348	−0.220047
$418$	37.4771	1.83307
$419$	1.65577	0.0808897	0.0404449	−	0.999182i	$-0.487122\pi$
$419$	1.65577	0.0808897	0.0404449	+	0.999182i	$0.487122\pi$
$420$	9.29716	0.453655
$421$	−36.0442	−1.75669	−0.878343	−	0.478031i	$-0.841351\pi$
$421$	−36.0442	−1.75669	−0.878343	+	0.478031i	$0.841351\pi$
$422$	−63.3793	−3.08526
$423$	4.81006	0.233873
$424$	−16.7533	−0.813613
$425$	−16.9775	−0.823530
$426$	2.42634	0.117557
$427$	−7.79802	−0.377373
$428$	−21.5029	−1.03938
$429$	−5.19939	−0.251029
$430$	−10.2367	−0.493659
$431$	21.8814	1.05399	0.526996	−	0.849868i	$-0.323318\pi$
$431$	21.8814	1.05399	0.526996	+	0.849868i	$0.323318\pi$
$432$	−0.937033	−0.0450830
$433$	26.5676	1.27676	0.638378	−	0.769723i	$-0.279606\pi$
$433$	26.5676	1.27676	0.638378	+	0.769723i	$0.279606\pi$
$434$	−20.0719	−0.963480
$435$	−8.68555	−0.416440
$436$	−3.10951	−0.148918
$437$	9.35336	0.447432
$438$	9.77788	0.467205
$439$	15.5829	0.743733	0.371866	−	0.928286i	$-0.378718\pi$
$439$	15.5829	0.743733	0.371866	+	0.928286i	$0.378718\pi$
$440$	−58.2574	−2.77731
$441$	−1.97539	−0.0940661
$442$	12.3608	0.587943
$443$	−4.22119	−0.200555	−0.100277	−	0.994960i	$-0.531973\pi$
$443$	−4.22119	−0.200555	−0.100277	+	0.994960i	$0.531973\pi$
$444$	0.895352	0.0424915
$445$	36.8132	1.74511
$446$	−36.1691	−1.71266
$447$	−0.497097	−0.0235119
$448$	36.1537	1.70810
$449$	−2.16780	−0.102305	−0.0511524	−	0.998691i	$-0.516289\pi$
$449$	−2.16780	−0.102305	−0.0511524	+	0.998691i	$0.516289\pi$
$450$	−59.6392	−2.81142
$451$	−32.5788	−1.53408
$452$	−48.6496	−2.28828
$453$	5.79608	0.272324
$454$	−37.8970	−1.77859
$455$	30.2504	1.41816
$456$	1.93163	0.0904568
$457$	−36.5229	−1.70847	−0.854235	−	0.519887i	$-0.825974\pi$
$457$	−36.5229	−1.70847	−0.854235	+	0.519887i	$0.825974\pi$
$458$	−7.15256	−0.334217
$459$	−3.19810	−0.149274
$460$	−40.7486	−1.89992
$461$	41.0182	1.91041	0.955203	−	0.295950i	$-0.0956363\pi$
$461$	41.0182	1.91041	0.955203	+	0.295950i	$0.0956363\pi$
$462$	−11.1781	−0.520052
$463$	10.3765	0.482238	0.241119	−	0.970496i	$-0.422486\pi$
$463$	10.3765	0.482238	0.241119	+	0.970496i	$0.422486\pi$
$464$	−4.42674	−0.205506
$465$	−3.45824	−0.160372
$466$	27.3443	1.26670
$467$	−12.0716	−0.558606	−0.279303	−	0.960203i	$-0.590103\pi$
$467$	−12.0716	−0.558606	−0.279303	+	0.960203i	$0.590103\pi$
$468$	26.4251	1.22150
$469$	39.5702	1.82718
$470$	−13.9684	−0.644313
$471$	−5.05561	−0.232950
$472$	−8.27569	−0.380919
$473$	7.49016	0.344398
$474$	−8.00873	−0.367853
$475$	−24.1932	−1.11006
$476$	16.1724	0.741260
$477$	19.4864	0.892220
$478$	−3.73360	−0.170771
$479$	−14.0928	−0.643917	−0.321959	−	0.946754i	$-0.604341\pi$
$479$	−14.0928	−0.643917	−0.321959	+	0.946754i	$0.604341\pi$
$480$	6.75412	0.308282
$481$	2.91323	0.132832
$482$	−45.9985	−2.09517
$483$	−2.78977	−0.126939
$484$	85.2609	3.87550
$485$	13.8305	0.628010
$486$	−16.9303	−0.767974
$487$	−39.1653	−1.77475	−0.887374	−	0.461050i	$-0.847473\pi$
$487$	−39.1653	−1.77475	−0.887374	+	0.461050i	$0.847473\pi$
$488$	7.05836	0.319517
$489$	−1.93698	−0.0875933
$490$	5.73651	0.259149
$491$	25.0350	1.12982	0.564908	−	0.825154i	$-0.308912\pi$
$491$	25.0350	1.12982	0.564908	+	0.825154i	$0.308912\pi$
$492$	−4.70602	−0.212164
$493$	−15.1085	−0.680452
$494$	17.6143	0.792506
$495$	67.7612	3.04564
$496$	−1.76255	−0.0791409
$497$	10.3291	0.463322
$498$	−5.79326	−0.259602
$499$	−28.7882	−1.28874	−0.644368	−	0.764716i	$-0.722879\pi$
$499$	−28.7882	−1.28874	−0.644368	+	0.764716i	$0.722879\pi$
$500$	47.1335	2.10787
$501$	1.92592	0.0860440
$502$	24.6518	1.10027
$503$	3.64064	0.162328	0.0811640	−	0.996701i	$-0.474136\pi$
$503$	3.64064	0.162328	0.0811640	+	0.996701i	$0.474136\pi$
$504$	20.2708	0.902933
$505$	15.6234	0.695231
$506$	48.9926	2.17799
$507$	1.29949	0.0577126
$508$	−14.1035	−0.625741
$509$	−34.6520	−1.53592	−0.767961	−	0.640496i	$-0.778729\pi$
$509$	−34.6520	−1.53592	−0.767961	+	0.640496i	$0.778729\pi$
$510$	4.57856	0.202742
$511$	41.6250	1.84138
$512$	6.20099	0.274048
$513$	−4.55734	−0.201212
$514$	−8.76064	−0.386415
$515$	30.2094	1.33119
$516$	1.08196	0.0476304
$517$	10.2206	0.449501
$518$	6.26311	0.275185
$519$	5.65326	0.248151
$520$	−27.3811	−1.20074
$521$	−33.8125	−1.48135	−0.740677	−	0.671862i	$-0.765495\pi$
$521$	−33.8125	−1.48135	−0.740677	+	0.671862i	$0.765495\pi$
$522$	−53.0736	−2.32297
$523$	−13.4398	−0.587682	−0.293841	−	0.955854i	$-0.594934\pi$
$523$	−13.4398	−0.587682	−0.293841	+	0.955854i	$0.594934\pi$
$524$	−4.01204	−0.175267
$525$	7.21598	0.314931
$526$	−36.2884	−1.58225
$527$	−6.01560	−0.262044
$528$	−0.981572	−0.0427174
$529$	−10.7727	−0.468377
$530$	−56.5882	−2.45804
$531$	9.62574	0.417722
$532$	23.0459	0.999167
$533$	−15.3121	−0.663241
$534$	−6.39351	−0.276674
$535$	−25.9156	−1.12043
$536$	−35.8169	−1.54705
$537$	6.21621	0.268249
$538$	10.7350	0.462817
$539$	−4.19738	−0.180794
$540$	19.8544	0.854399
$541$	3.91568	0.168348	0.0841741	−	0.996451i	$-0.473175\pi$
$541$	3.91568	0.168348	0.0841741	+	0.996451i	$0.473175\pi$
$542$	15.8414	0.680444
$543$	−6.28199	−0.269586
$544$	11.7488	0.503725
$545$	−3.74762	−0.160530
$546$	−5.25373	−0.224839
$547$	−17.6509	−0.754698	−0.377349	−	0.926071i	$-0.623164\pi$
$547$	−17.6509	−0.754698	−0.377349	+	0.926071i	$0.623164\pi$
$548$	28.4181	1.21396
$549$	−8.20982	−0.350387
$550$	−126.724	−5.40351
$551$	−21.5299	−0.917203
$552$	2.52515	0.107478
$553$	−34.0936	−1.44981
$554$	20.0844	0.853305
$555$	1.07909	0.0458048
$556$	48.5258	2.05795
$557$	−19.6703	−0.833458	−0.416729	−	0.909031i	$-0.636824\pi$
$557$	−19.6703	−0.833458	−0.416729	+	0.909031i	$0.636824\pi$
$558$	−21.1318	−0.894581
$559$	3.52039	0.148897
$560$	5.71085	0.241328
$561$	−3.35011	−0.141442
$562$	23.5413	0.993028
$563$	7.05355	0.297272	0.148636	−	0.988892i	$-0.452512\pi$
$563$	7.05355	0.297272	0.148636	+	0.988892i	$0.452512\pi$
$564$	1.47637	0.0621663
$565$	−58.6331	−2.46671
$566$	9.37385	0.394012
$567$	−22.8885	−0.961226
$568$	−9.34932	−0.392289
$569$	−9.69624	−0.406488	−0.203244	−	0.979128i	$-0.565148\pi$
$569$	−9.69624	−0.406488	−0.203244	+	0.979128i	$0.565148\pi$
$570$	6.52452	0.273282
$571$	−31.9842	−1.33850	−0.669249	−	0.743038i	$-0.733384\pi$
$571$	−31.9842	−1.33850	−0.669249	+	0.743038i	$0.733384\pi$
$572$	56.1490	2.34771
$573$	−3.54089	−0.147923
$574$	−32.9193	−1.37402
$575$	−31.6270	−1.31894
$576$	38.0629	1.58595
$577$	28.1398	1.17148	0.585738	−	0.810501i	$-0.300805\pi$
$577$	28.1398	1.17148	0.585738	+	0.810501i	$0.300805\pi$
$578$	−30.4628	−1.26708
$579$	3.85399	0.160166
$580$	93.7965	3.89469
$581$	−24.6622	−1.02316
$582$	−2.40200	−0.0995662
$583$	41.4053	1.71483
$584$	−37.6767	−1.55907
$585$	31.8479	1.31675
$586$	31.9123	1.31828
$587$	4.70689	0.194274	0.0971371	−	0.995271i	$-0.469031\pi$
$587$	4.70689	0.194274	0.0971371	+	0.995271i	$0.469031\pi$
$588$	−0.606312	−0.0250039
$589$	−8.57233	−0.353217
$590$	−27.9531	−1.15081
$591$	−0.0340924	−0.00140237
$592$	0.549977	0.0226039
$593$	12.3503	0.507166	0.253583	−	0.967314i	$-0.418391\pi$
$593$	12.3503	0.507166	0.253583	+	0.967314i	$0.418391\pi$
$594$	−23.8713	−0.979449
$595$	19.4912	0.799060
$596$	5.36822	0.219891
$597$	0.434078	0.0177656
$598$	23.0266	0.941630
$599$	2.42638	0.0991392	0.0495696	−	0.998771i	$-0.484215\pi$
$599$	2.42638	0.0991392	0.0495696	+	0.998771i	$0.484215\pi$
$600$	−6.53152	−0.266648
$601$	−35.5913	−1.45180	−0.725900	−	0.687800i	$-0.758577\pi$
$601$	−35.5913	−1.45180	−0.725900	+	0.687800i	$0.758577\pi$
$602$	7.56844	0.308466
$603$	41.6599	1.69652
$604$	−62.5927	−2.54686
$605$	102.758	4.17769
$606$	−2.71338	−0.110224
$607$	−6.90219	−0.280151	−0.140076	−	0.990141i	$-0.544735\pi$
$607$	−6.90219	−0.280151	−0.140076	+	0.990141i	$0.544735\pi$
$608$	16.7422	0.678986
$609$	6.42159	0.260216
$610$	23.8412	0.965304
$611$	4.80370	0.194337
$612$	17.0264	0.688252
$613$	−4.07913	−0.164755	−0.0823773	−	0.996601i	$-0.526251\pi$
$613$	−4.07913	−0.164755	−0.0823773	+	0.996601i	$0.526251\pi$
$614$	42.0379	1.69651
$615$	−5.67176	−0.228707
$616$	43.0721	1.73542
$617$	15.0006	0.603901	0.301950	−	0.953324i	$-0.402362\pi$
$617$	15.0006	0.603901	0.301950	+	0.953324i	$0.402362\pi$
$618$	−5.24661	−0.211050
$619$	−0.756491	−0.0304059	−0.0152030	−	0.999884i	$-0.504839\pi$
$619$	−0.756491	−0.0304059	−0.0152030	+	0.999884i	$0.504839\pi$
$620$	37.3460	1.49985
$621$	−5.95767	−0.239073
$622$	37.3781	1.49872
$623$	−27.2175	−1.09045
$624$	−0.461341	−0.0184684
$625$	11.5826	0.463304
$626$	−50.3275	−2.01149
$627$	−4.77396	−0.190654
$628$	54.5963	2.17863
$629$	1.87707	0.0748439
$630$	68.4693	2.72788
$631$	18.8224	0.749307	0.374654	−	0.927165i	$-0.377762\pi$
$631$	18.8224	0.749307	0.374654	+	0.927165i	$0.377762\pi$
$632$	30.8597	1.22753
$633$	8.07347	0.320892
$634$	−61.2404	−2.43217
$635$	−16.9977	−0.674534
$636$	5.98101	0.237163
$637$	−1.97278	−0.0781643
$638$	−112.773	−4.46472
$639$	10.8745	0.430189
$640$	−63.6209	−2.51484
$641$	−31.9589	−1.26230	−0.631150	−	0.775661i	$-0.717417\pi$
$641$	−31.9589	−1.26230	−0.631150	+	0.775661i	$0.717417\pi$
$642$	4.50087	0.177635
$643$	−35.1065	−1.38447	−0.692233	−	0.721674i	$-0.743373\pi$
$643$	−35.1065	−1.38447	−0.692233	+	0.721674i	$0.743373\pi$
$644$	30.1272	1.18718
$645$	1.30399	0.0513445
$646$	11.3494	0.446536
$647$	−37.3032	−1.46654	−0.733271	−	0.679937i	$-0.762007\pi$
$647$	−37.3032	−1.46654	−0.733271	+	0.679937i	$0.762007\pi$
$648$	20.7174	0.813858
$649$	20.4531	0.802855
$650$	−59.5603	−2.33615
$651$	2.55682	0.100210
$652$	20.9177	0.819202
$653$	−1.03669	−0.0405688	−0.0202844	−	0.999794i	$-0.506457\pi$
$653$	−1.03669	−0.0405688	−0.0202844	+	0.999794i	$0.506457\pi$
$654$	0.650866	0.0254509
$655$	−4.83537	−0.188933
$656$	−2.89071	−0.112863
$657$	43.8231	1.70970
$658$	10.3274	0.402604
$659$	46.5232	1.81229	0.906143	−	0.422972i	$-0.139013\pi$
$659$	46.5232	1.81229	0.906143	+	0.422972i	$0.139013\pi$
$660$	20.7982	0.809567
$661$	32.6899	1.27149	0.635744	−	0.771900i	$-0.280693\pi$
$661$	32.6899	1.27149	0.635744	+	0.771900i	$0.280693\pi$
$662$	39.2772	1.52655
$663$	−1.57456	−0.0611508
$664$	22.3229	0.866297
$665$	27.7753	1.07708
$666$	6.59386	0.255507
$667$	−28.1453	−1.08979
$668$	−20.7984	−0.804712
$669$	4.60734	0.178130
$670$	−120.980	−4.67386
$671$	−17.4445	−0.673439
$672$	−4.99360	−0.192632
$673$	−33.0430	−1.27371	−0.636857	−	0.770982i	$-0.719766\pi$
$673$	−33.0430	−1.27371	−0.636857	+	0.770982i	$0.719766\pi$
$674$	23.8418	0.918352
$675$	15.4100	0.593131
$676$	−14.0334	−0.539748
$677$	−28.4050	−1.09169	−0.545847	−	0.837885i	$-0.683792\pi$
$677$	−28.4050	−1.09169	−0.545847	+	0.837885i	$0.683792\pi$
$678$	10.1831	0.391079
$679$	−10.2255	−0.392417
$680$	−17.6424	−0.676554
$681$	4.82744	0.184988
$682$	−44.9016	−1.71937
$683$	−16.5963	−0.635038	−0.317519	−	0.948252i	$-0.602850\pi$
$683$	−16.5963	−0.635038	−0.317519	+	0.948252i	$0.602850\pi$
$684$	24.2629	0.927716
$685$	34.2499	1.30862
$686$	39.6006	1.51196
$687$	0.911117	0.0347613
$688$	0.664600	0.0253376
$689$	19.4606	0.741390
$690$	8.52929	0.324705
$691$	−44.9921	−1.71158	−0.855790	−	0.517323i	$-0.826929\pi$
$691$	−44.9921	−1.71158	−0.855790	+	0.517323i	$0.826929\pi$
$692$	−61.0504	−2.32079
$693$	−50.0987	−1.90309
$694$	−65.7573	−2.49611
$695$	58.4840	2.21842
$696$	−5.81248	−0.220321
$697$	−9.86601	−0.373702
$698$	−3.25744	−0.123296
$699$	−3.48321	−0.131747
$700$	−77.9264	−2.94534
$701$	−8.08732	−0.305454	−0.152727	−	0.988268i	$-0.548805\pi$
$701$	−8.08732	−0.305454	−0.152727	+	0.988268i	$0.548805\pi$
$702$	−11.2195	−0.423454
$703$	2.67486	0.100884
$704$	80.8774	3.04818
$705$	1.77934	0.0670137
$706$	6.56879	0.247220
$707$	−11.5510	−0.434421
$708$	2.95446	0.111035
$709$	−4.03142	−0.151403	−0.0757015	−	0.997131i	$-0.524120\pi$
$709$	−4.03142	−0.151403	−0.0757015	+	0.997131i	$0.524120\pi$
$710$	−31.5795	−1.18516
$711$	−35.8940	−1.34613
$712$	24.6359	0.923268
$713$	−11.2063	−0.419680
$714$	−3.38512	−0.126685
$715$	67.6716	2.53077
$716$	−67.1298	−2.50876
$717$	0.475598	0.0177615
$718$	42.2312	1.57605
$719$	−0.259088	−0.00966234	−0.00483117	−	0.999988i	$-0.501538\pi$
$719$	−0.259088	−0.00966234	−0.00483117	+	0.999988i	$0.501538\pi$
$720$	6.01243	0.224070
$721$	−22.3351	−0.831803
$722$	−26.7749	−0.996460
$723$	5.85944	0.217915
$724$	67.8401	2.52126
$725$	72.8001	2.70373
$726$	−17.8464	−0.662341
$727$	15.7917	0.585681	0.292841	−	0.956161i	$-0.405399\pi$
$727$	15.7917	0.585681	0.292841	+	0.956161i	$0.405399\pi$
$728$	20.2440	0.750292
$729$	−22.6254	−0.837979
$730$	−127.262	−4.71017
$731$	2.26828	0.0838955
$732$	−2.51987	−0.0931369
$733$	14.9685	0.552874	0.276437	−	0.961032i	$-0.410846\pi$
$733$	14.9685	0.552874	0.276437	+	0.961032i	$0.410846\pi$
$734$	−10.3082	−0.380482
$735$	−0.730736	−0.0269536
$736$	21.8865	0.806749
$737$	88.5204	3.26069
$738$	−34.6577	−1.27577
$739$	−52.2635	−1.92254	−0.961271	−	0.275603i	$-0.911122\pi$
$739$	−52.2635	−1.92254	−0.961271	+	0.275603i	$0.911122\pi$
$740$	−11.6533	−0.428382
$741$	−2.24377	−0.0824270
$742$	41.8380	1.53592
$743$	38.8641	1.42579	0.712893	−	0.701273i	$-0.247385\pi$
$743$	38.8641	1.42579	0.712893	+	0.701273i	$0.247385\pi$
$744$	−2.31430	−0.0848463
$745$	6.46985	0.237037
$746$	−70.3976	−2.57744
$747$	−25.9646	−0.949994
$748$	36.1783	1.32281
$749$	19.1605	0.700108
$750$	−9.86573	−0.360246
$751$	−53.2908	−1.94461	−0.972304	−	0.233719i	$-0.924910\pi$
$751$	−53.2908	−1.94461	−0.972304	+	0.233719i	$0.924910\pi$
$752$	0.906871	0.0330702
$753$	−3.14023	−0.114436
$754$	−53.0035	−1.93027
$755$	−75.4376	−2.74546
$756$	−14.6792	−0.533878
$757$	24.5049	0.890645	0.445323	−	0.895370i	$-0.353089\pi$
$757$	24.5049	0.890645	0.445323	+	0.895370i	$0.353089\pi$
$758$	14.6112	0.530702
$759$	−6.24084	−0.226528
$760$	−25.1407	−0.911948
$761$	−37.5435	−1.36095	−0.680476	−	0.732770i	$-0.738227\pi$
$761$	−37.5435	−1.36095	−0.680476	+	0.732770i	$0.738227\pi$
$762$	2.95207	0.106942
$763$	2.77077	0.100309
$764$	38.2386	1.38342
$765$	20.5205	0.741919
$766$	−58.2700	−2.10538
$767$	9.61301	0.347106
$768$	3.53510	0.127562
$769$	−51.2492	−1.84809	−0.924047	−	0.382280i	$-0.875139\pi$
$769$	−51.2492	−1.84809	−0.924047	+	0.382280i	$0.875139\pi$
$770$	145.486	5.24295
$771$	1.11596	0.0401903
$772$	−41.6198	−1.49793
$773$	13.2910	0.478044	0.239022	−	0.971014i	$-0.423173\pi$
$773$	13.2910	0.478044	0.239022	+	0.971014i	$0.423173\pi$
$774$	7.96811	0.286408
$775$	28.9861	1.04121
$776$	9.25554	0.332255
$777$	−0.797816	−0.0286215
$778$	66.5856	2.38721
$779$	−14.0592	−0.503724
$780$	9.77517	0.350007
$781$	23.1066	0.826818
$782$	14.8367	0.530559
$783$	13.7135	0.490082
$784$	−0.372432	−0.0133012
$785$	65.8002	2.34851
$786$	0.839780	0.0299540
$787$	32.8223	1.16999	0.584994	−	0.811038i	$-0.301097\pi$
$787$	32.8223	1.16999	0.584994	+	0.811038i	$0.301097\pi$
$788$	0.368169	0.0131155
$789$	4.62254	0.164567
$790$	104.236	3.70855
$791$	43.3499	1.54135
$792$	45.3466	1.61132
$793$	−8.19896	−0.291154
$794$	75.5515	2.68122
$795$	7.20840	0.255656
$796$	−4.68767	−0.166150
$797$	47.2321	1.67305	0.836524	−	0.547930i	$-0.184584\pi$
$797$	47.2321	1.67305	0.836524	+	0.547930i	$0.184584\pi$
$798$	−4.82385	−0.170762
$799$	3.09515	0.109499
$800$	−56.6114	−2.00151
$801$	−28.6548	−1.01247
$802$	3.86412	0.136447
$803$	93.1169	3.28602
$804$	12.7868	0.450955
$805$	36.3097	1.27975
$806$	−21.1039	−0.743352
$807$	−1.36746	−0.0481367
$808$	10.4554	0.367818
$809$	7.75533	0.272663	0.136331	−	0.990663i	$-0.456469\pi$
$809$	7.75533	0.272663	0.136331	+	0.990663i	$0.456469\pi$
$810$	69.9780	2.45878
$811$	28.3916	0.996962	0.498481	−	0.866900i	$-0.333891\pi$
$811$	28.3916	0.996962	0.498481	+	0.866900i	$0.333891\pi$
$812$	−69.3477	−2.43363
$813$	−2.01792	−0.0707717
$814$	14.0109	0.491081
$815$	25.2103	0.883080
$816$	−0.297254	−0.0104060
$817$	3.23234	0.113085
$818$	64.5276	2.25615
$819$	−23.5465	−0.822780
$820$	61.2501	2.13895
$821$	13.8510	0.483403	0.241701	−	0.970351i	$-0.422295\pi$
$821$	13.8510	0.483403	0.241701	+	0.970351i	$0.422295\pi$
$822$	−5.94833	−0.207472
$823$	−23.2902	−0.811844	−0.405922	−	0.913908i	$-0.633050\pi$
$823$	−23.2902	−0.811844	−0.405922	+	0.913908i	$0.633050\pi$
$824$	20.2165	0.704277
$825$	16.1425	0.562008
$826$	20.6669	0.719092
$827$	10.2746	0.357282	0.178641	−	0.983914i	$-0.442830\pi$
$827$	10.2746	0.357282	0.178641	+	0.983914i	$0.442830\pi$
$828$	31.7181	1.10228
$829$	−1.56760	−0.0544450	−0.0272225	−	0.999629i	$-0.508666\pi$
$829$	−1.56760	−0.0544450	−0.0272225	+	0.999629i	$0.508666\pi$
$830$	75.4009	2.61720
$831$	−2.55842	−0.0887506
$832$	38.0125	1.31785
$833$	−1.27111	−0.0440415
$834$	−10.1572	−0.351714
$835$	−25.0665	−0.867460
$836$	51.5547	1.78306
$837$	5.46019	0.188732
$838$	3.74274	0.129291
$839$	29.1483	1.00631	0.503156	−	0.864195i	$-0.332172\pi$
$839$	29.1483	1.00631	0.503156	+	0.864195i	$0.332172\pi$
$840$	7.49857	0.258725
$841$	35.7857	1.23399
$842$	−81.4751	−2.80782
$843$	−2.99876	−0.103283
$844$	−87.1866	−3.00109
$845$	−16.9133	−0.581835
$846$	10.8728	0.373813
$847$	−75.9730	−2.61046
$848$	3.67389	0.126162
$849$	−1.19407	−0.0409804
$850$	−38.3763	−1.31630
$851$	3.49676	0.119867
$852$	3.33775	0.114349
$853$	38.6563	1.32357	0.661783	−	0.749695i	$-0.269800\pi$
$853$	38.6563	1.32357	0.661783	+	0.749695i	$0.269800\pi$
$854$	−17.6268	−0.603178
$855$	29.2420	1.00006
$856$	−17.3430	−0.592773
$857$	14.6068	0.498960	0.249480	−	0.968380i	$-0.419740\pi$
$857$	14.6068	0.498960	0.249480	+	0.968380i	$0.419740\pi$
$858$	−11.7528	−0.401235
$859$	7.17921	0.244951	0.122476	−	0.992472i	$-0.460917\pi$
$859$	7.17921	0.244951	0.122476	+	0.992472i	$0.460917\pi$
$860$	−14.0820	−0.480191
$861$	4.19337	0.142909
$862$	49.4613	1.68466
$863$	2.51019	0.0854479	0.0427239	−	0.999087i	$-0.486396\pi$
$863$	2.51019	0.0854479	0.0427239	+	0.999087i	$0.486396\pi$
$864$	−10.6640	−0.362798
$865$	−73.5788	−2.50175
$866$	60.0539	2.04071
$867$	3.88045	0.131787
$868$	−27.6115	−0.937195
$869$	−76.2689	−2.58724
$870$	−19.6330	−0.665621
$871$	41.6048	1.40972
$872$	−2.50796	−0.0849301
$873$	−10.7654	−0.364355
$874$	21.1425	0.715157
$875$	−41.9990	−1.41982
$876$	13.4508	0.454459
$877$	32.5009	1.09748	0.548739	−	0.835994i	$-0.315108\pi$
$877$	32.5009	1.09748	0.548739	+	0.835994i	$0.315108\pi$
$878$	35.2240	1.18875
$879$	−4.06509	−0.137112
$880$	12.7754	0.430660
$881$	1.72391	0.0580801	0.0290400	−	0.999578i	$-0.490755\pi$
$881$	1.72391	0.0580801	0.0290400	+	0.999578i	$0.490755\pi$
$882$	−4.46521	−0.150352
$883$	−1.40012	−0.0471178	−0.0235589	−	0.999722i	$-0.507500\pi$
$883$	−1.40012	−0.0471178	−0.0235589	+	0.999722i	$0.507500\pi$
$884$	17.0039	0.571903
$885$	3.56075	0.119693
$886$	−9.54168	−0.320559
$887$	18.7078	0.628146	0.314073	−	0.949399i	$-0.398306\pi$
$887$	18.7078	0.628146	0.314073	+	0.949399i	$0.398306\pi$
$888$	0.722141	0.0242335
$889$	12.5671	0.421488
$890$	83.2134	2.78932
$891$	−51.2026	−1.71535
$892$	−49.7554	−1.66593
$893$	4.41065	0.147597
$894$	−1.12365	−0.0375804
$895$	−80.9058	−2.70438
$896$	47.0376	1.57141
$897$	−2.93321	−0.0979370
$898$	−4.90014	−0.163520
$899$	25.7951	0.860314
$900$	−82.0415	−2.73472
$901$	12.5390	0.417734
$902$	−73.6419	−2.45201
$903$	−0.964092	−0.0320830
$904$	−39.2380	−1.30504
$905$	81.7618	2.71785
$906$	13.1016	0.435271
$907$	−14.3928	−0.477905	−0.238952	−	0.971031i	$-0.576804\pi$
$907$	−14.3928	−0.477905	−0.238952	+	0.971031i	$0.576804\pi$
$908$	−52.1323	−1.73007
$909$	−12.1610	−0.403355
$910$	68.3788	2.26673
$911$	0.795451	0.0263545	0.0131772	−	0.999913i	$-0.495805\pi$
$911$	0.795451	0.0263545	0.0131772	+	0.999913i	$0.495805\pi$
$912$	−0.423592	−0.0140265
$913$	−55.1704	−1.82588
$914$	−82.5572	−2.73075
$915$	−3.03698	−0.100399
$916$	−9.83929	−0.325099
$917$	3.57499	0.118057
$918$	−7.22905	−0.238594
$919$	48.7226	1.60721	0.803605	−	0.595163i	$-0.202913\pi$
$919$	48.7226	1.60721	0.803605	+	0.595163i	$0.202913\pi$
$920$	−32.8656	−1.08355
$921$	−5.35493	−0.176451
$922$	92.7184	3.05352
$923$	10.8601	0.357466
$924$	−15.3769	−0.505864
$925$	−9.04466	−0.297387
$926$	23.4553	0.770790
$927$	−23.5146	−0.772320
$928$	−50.3791	−1.65378
$929$	21.9383	0.719773	0.359886	−	0.932996i	$-0.382815\pi$
$929$	21.9383	0.719773	0.359886	+	0.932996i	$0.382815\pi$
$930$	−7.81708	−0.256332
$931$	−1.81136	−0.0593649
$932$	37.6157	1.23214
$933$	−4.76134	−0.155879
$934$	−27.2868	−0.892853
$935$	43.6026	1.42596
$936$	21.3130	0.696638
$937$	8.30810	0.271414	0.135707	−	0.990749i	$-0.456669\pi$
$937$	8.30810	0.271414	0.135707	+	0.990749i	$0.456669\pi$
$938$	89.4454	2.92050
$939$	6.41089	0.209211
$940$	−19.2153	−0.626735
$941$	−8.22332	−0.268073	−0.134036	−	0.990976i	$-0.542794\pi$
$941$	−8.22332	−0.268073	−0.134036	+	0.990976i	$0.542794\pi$
$942$	−11.4278	−0.372338
$943$	−18.3792	−0.598508
$944$	1.81480	0.0590667
$945$	−17.6916	−0.575507
$946$	16.9309	0.550472
$947$	42.8014	1.39086	0.695429	−	0.718595i	$-0.255214\pi$
$947$	42.8014	1.39086	0.695429	+	0.718595i	$0.255214\pi$
$948$	−11.0171	−0.357817
$949$	43.7651	1.42068
$950$	−54.6869	−1.77428
$951$	7.80101	0.252965
$952$	13.0437	0.422750
$953$	22.3181	0.722954	0.361477	−	0.932381i	$-0.382273\pi$
$953$	22.3181	0.722954	0.361477	+	0.932381i	$0.382273\pi$
$954$	44.0474	1.42609
$955$	46.0857	1.49130
$956$	−5.13606	−0.166112
$957$	14.3654	0.464367
$958$	−31.8557	−1.02921
$959$	−25.3224	−0.817702
$960$	14.0802	0.454437
$961$	−20.7294	−0.668691
$962$	6.58514	0.212313
$963$	20.1723	0.650043
$964$	−63.2770	−2.03801
$965$	−50.1607	−1.61473
$966$	−6.30606	−0.202894
$967$	29.1000	0.935792	0.467896	−	0.883784i	$-0.345012\pi$
$967$	29.1000	0.935792	0.467896	+	0.883784i	$0.345012\pi$
$968$	68.7667	2.21025
$969$	−1.44572	−0.0464433
$970$	31.2627	1.00379
$971$	30.6692	0.984223	0.492112	−	0.870532i	$-0.336225\pi$
$971$	30.6692	0.984223	0.492112	+	0.870532i	$0.336225\pi$
$972$	−23.2899	−0.747022
$973$	−43.2396	−1.38620
$974$	−88.5300	−2.83669
$975$	7.58699	0.242978
$976$	−1.54785	−0.0495454
$977$	−15.5451	−0.497331	−0.248666	−	0.968589i	$-0.579992\pi$
$977$	−15.5451	−0.497331	−0.248666	+	0.968589i	$0.579992\pi$
$978$	−4.37839	−0.140006
$979$	−60.8868	−1.94595
$980$	7.89133	0.252079
$981$	2.91709	0.0931355
$982$	56.5898	1.80585
$983$	54.8056	1.74803	0.874014	−	0.485900i	$-0.161508\pi$
$983$	54.8056	1.74803	0.874014	+	0.485900i	$0.161508\pi$
$984$	−3.79561	−0.121000
$985$	0.443722	0.0141382
$986$	−34.1516	−1.08761
$987$	−1.31554	−0.0418741
$988$	24.2308	0.770886
$989$	4.22553	0.134364
$990$	153.169	4.86803
$991$	11.4857	0.364854	0.182427	−	0.983219i	$-0.441605\pi$
$991$	11.4857	0.364854	0.182427	+	0.983219i	$0.441605\pi$
$992$	−20.0590	−0.636873
$993$	−5.00326	−0.158774
$994$	23.3481	0.740555
$995$	−5.64964	−0.179106
$996$	−7.96938	−0.252520
$997$	17.5486	0.555768	0.277884	−	0.960615i	$-0.410367\pi$
$997$	17.5486	0.555768	0.277884	+	0.960615i	$0.410367\pi$
$998$	−65.0734	−2.05986
$999$	−1.70377	−0.0539048

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4033.2.a.d.1.72	✓	79

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4033.2.a.d.1.72	✓	79	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:	\( N \)	\(=\)	\( 4033 = 37 \cdot 109 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4033.a (trivial)

\(f(q)\)	\(=\)	\(q+2.26042 q^{2} -0.287940 q^{3} +3.10951 q^{4} +3.74762 q^{5} -0.650866 q^{6} -2.77077 q^{7} +2.50796 q^{8} -2.91709 q^{9} +O(q^{10})\)	\(q+2.26042 q^{2} -0.287940 q^{3} +3.10951 q^{4} +3.74762 q^{5} -0.650866 q^{6} -2.77077 q^{7} +2.50796 q^{8} -2.91709 q^{9} +8.47120 q^{10} -6.19834 q^{11} -0.895352 q^{12} -2.91323 q^{13} -6.26311 q^{14} -1.07909 q^{15} -0.549977 q^{16} -1.87707 q^{17} -6.59386 q^{18} -2.67486 q^{19} +11.6533 q^{20} +0.797816 q^{21} -14.0109 q^{22} -3.49676 q^{23} -0.722141 q^{24} +9.04466 q^{25} -6.58514 q^{26} +1.70377 q^{27} -8.61574 q^{28} +8.04895 q^{29} -2.43920 q^{30} +3.20477 q^{31} -6.25909 q^{32} +1.78475 q^{33} -4.24298 q^{34} -10.3838 q^{35} -9.07072 q^{36} -1.00000 q^{37} -6.04632 q^{38} +0.838836 q^{39} +9.39887 q^{40} +5.25605 q^{41} +1.80340 q^{42} -1.20841 q^{43} -19.2738 q^{44} -10.9321 q^{45} -7.90416 q^{46} -1.64892 q^{47} +0.158360 q^{48} +0.677178 q^{49} +20.4448 q^{50} +0.540485 q^{51} -9.05872 q^{52} -6.68007 q^{53} +3.85123 q^{54} -23.2290 q^{55} -6.94897 q^{56} +0.770200 q^{57} +18.1940 q^{58} -3.29977 q^{59} -3.35544 q^{60} +2.81439 q^{61} +7.24414 q^{62} +8.08259 q^{63} -13.0482 q^{64} -10.9177 q^{65} +4.03429 q^{66} -14.2813 q^{67} -5.83678 q^{68} +1.00686 q^{69} -23.4718 q^{70} -3.72787 q^{71} -7.31593 q^{72} -15.0229 q^{73} -2.26042 q^{74} -2.60432 q^{75} -8.31751 q^{76} +17.1742 q^{77} +1.89612 q^{78} +12.3047 q^{79} -2.06111 q^{80} +8.26069 q^{81} +11.8809 q^{82} +8.90084 q^{83} +2.48082 q^{84} -7.03456 q^{85} -2.73153 q^{86} -2.31762 q^{87} -15.5452 q^{88} +9.82309 q^{89} -24.7113 q^{90} +8.07190 q^{91} -10.8732 q^{92} -0.922782 q^{93} -3.72726 q^{94} -10.0244 q^{95} +1.80224 q^{96} +3.69047 q^{97} +1.53071 q^{98} +18.0811 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 79 q - 11 q^{2} - 11 q^{3} + 79 q^{4} - 16 q^{5} - 14 q^{6} - 15 q^{7} - 42 q^{8} + 76 q^{9}+O(q^{10}) \) 79 * q - 11 * q^2 - 11 * q^3 + 79 * q^4 - 16 * q^5 - 14 * q^6 - 15 * q^7 - 42 * q^8 + 76 * q^9	\( 79 q - 11 q^{2} - 11 q^{3} + 79 q^{4} - 16 q^{5} - 14 q^{6} - 15 q^{7} - 42 q^{8} + 76 q^{9} - 13 q^{10} - 5 q^{11} - 40 q^{12} - 18 q^{13} - 42 q^{14} - 49 q^{15} + 83 q^{16} - 62 q^{17} - 33 q^{18} - 25 q^{19} - 39 q^{20} - 15 q^{21} - 31 q^{22} - 94 q^{23} - 39 q^{24} + 71 q^{25} - 35 q^{26} - 47 q^{27} - 13 q^{28} - 17 q^{29} + 15 q^{30} - 37 q^{31} - 105 q^{32} - 60 q^{33} + 9 q^{34} - 60 q^{35} + 43 q^{36} - 79 q^{37} - 80 q^{38} - 41 q^{39} - 64 q^{40} - 37 q^{41} - 30 q^{42} - 20 q^{43} - 14 q^{44} - 8 q^{45} + 61 q^{46} - 148 q^{47} - 39 q^{48} + 82 q^{49} - 90 q^{50} - 45 q^{51} - 27 q^{52} - 70 q^{53} - 41 q^{54} - 105 q^{55} - 68 q^{56} - 31 q^{57} - 14 q^{58} - 96 q^{59} - 74 q^{60} - 21 q^{61} + 4 q^{62} - 60 q^{63} + 132 q^{64} - 15 q^{65} + 71 q^{66} - 44 q^{67} - 166 q^{68} - 72 q^{69} - 9 q^{70} - 55 q^{71} - 126 q^{72} - 27 q^{73} + 11 q^{74} - 39 q^{75} - 4 q^{76} - 104 q^{77} - 47 q^{78} - 49 q^{79} - 82 q^{80} + 55 q^{81} + 20 q^{82} - 52 q^{83} - 29 q^{84} + 3 q^{85} - 32 q^{86} - 113 q^{87} + 14 q^{88} - 68 q^{89} - 39 q^{90} - 30 q^{91} - 179 q^{92} - 53 q^{93} - 33 q^{94} - 86 q^{95} + 33 q^{96} - 57 q^{97} - 116 q^{98} + q^{99}+O(q^{100}) \) 79 * q - 11 * q^2 - 11 * q^3 + 79 * q^4 - 16 * q^5 - 14 * q^6 - 15 * q^7 - 42 * q^8 + 76 * q^9 - 13 * q^10 - 5 * q^11 - 40 * q^12 - 18 * q^13 - 42 * q^14 - 49 * q^15 + 83 * q^16 - 62 * q^17 - 33 * q^18 - 25 * q^19 - 39 * q^20 - 15 * q^21 - 31 * q^22 - 94 * q^23 - 39 * q^24 + 71 * q^25 - 35 * q^26 - 47 * q^27 - 13 * q^28 - 17 * q^29 + 15 * q^30 - 37 * q^31 - 105 * q^32 - 60 * q^33 + 9 * q^34 - 60 * q^35 + 43 * q^36 - 79 * q^37 - 80 * q^38 - 41 * q^39 - 64 * q^40 - 37 * q^41 - 30 * q^42 - 20 * q^43 - 14 * q^44 - 8 * q^45 + 61 * q^46 - 148 * q^47 - 39 * q^48 + 82 * q^49 - 90 * q^50 - 45 * q^51 - 27 * q^52 - 70 * q^53 - 41 * q^54 - 105 * q^55 - 68 * q^56 - 31 * q^57 - 14 * q^58 - 96 * q^59 - 74 * q^60 - 21 * q^61 + 4 * q^62 - 60 * q^63 + 132 * q^64 - 15 * q^65 + 71 * q^66 - 44 * q^67 - 166 * q^68 - 72 * q^69 - 9 * q^70 - 55 * q^71 - 126 * q^72 - 27 * q^73 + 11 * q^74 - 39 * q^75 - 4 * q^76 - 104 * q^77 - 47 * q^78 - 49 * q^79 - 82 * q^80 + 55 * q^81 + 20 * q^82 - 52 * q^83 - 29 * q^84 + 3 * q^85 - 32 * q^86 - 113 * q^87 + 14 * q^88 - 68 * q^89 - 39 * q^90 - 30 * q^91 - 179 * q^92 - 53 * q^93 - 33 * q^94 - 86 * q^95 + 33 * q^96 - 57 * q^97 - 116 * q^98 + q^99

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