LMFDB - Embedded newform 7942.2.a.bs.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7942,2,Mod(1,7942)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7942, 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("7942.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7942 = 2 \cdot 11 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7942.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:	$63.4171892853$
Analytic rank:	$1$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} - 21 x^{10} + 59 x^{9} + 162 x^{8} - 408 x^{7} - 581 x^{6} + 1236 x^{5} + 972 x^{4} + \cdots + 81 $ x^12 - 3x^11 - 21x^10 + 59x^9 + 162x^8 - 408x^7 - 581x^6 + 1236x^5 + 972x^4 - 1596x^3 - 621x^2 + 648*x + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 418)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Root			$1.87195$ of defining polynomial
Character	$\chi$	$=$	7942.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.87195 q^{3} +1.00000 q^{4} +3.81859 q^{5} -1.87195 q^{6} -2.96733 q^{7} -1.00000 q^{8} +0.504212 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.87195 q^{3} +1.00000 q^{4} +3.81859 q^{5} -1.87195 q^{6} -2.96733 q^{7} -1.00000 q^{8} +0.504212 q^{9} -3.81859 q^{10} +1.00000 q^{11} +1.87195 q^{12} -1.08537 q^{13} +2.96733 q^{14} +7.14822 q^{15} +1.00000 q^{16} -2.29885 q^{17} -0.504212 q^{18} +3.81859 q^{20} -5.55471 q^{21} -1.00000 q^{22} -7.37385 q^{23} -1.87195 q^{24} +9.58162 q^{25} +1.08537 q^{26} -4.67200 q^{27} -2.96733 q^{28} -7.32445 q^{29} -7.14822 q^{30} +8.37319 q^{31} -1.00000 q^{32} +1.87195 q^{33} +2.29885 q^{34} -11.3310 q^{35} +0.504212 q^{36} +9.10622 q^{37} -2.03176 q^{39} -3.81859 q^{40} -9.41379 q^{41} +5.55471 q^{42} -8.07120 q^{43} +1.00000 q^{44} +1.92538 q^{45} +7.37385 q^{46} -12.2614 q^{47} +1.87195 q^{48} +1.80506 q^{49} -9.58162 q^{50} -4.30334 q^{51} -1.08537 q^{52} -3.29423 q^{53} +4.67200 q^{54} +3.81859 q^{55} +2.96733 q^{56} +7.32445 q^{58} +0.00737709 q^{59} +7.14822 q^{60} +1.17369 q^{61} -8.37319 q^{62} -1.49616 q^{63} +1.00000 q^{64} -4.14457 q^{65} -1.87195 q^{66} -4.51665 q^{67} -2.29885 q^{68} -13.8035 q^{69} +11.3310 q^{70} -6.26636 q^{71} -0.504212 q^{72} -9.46560 q^{73} -9.10622 q^{74} +17.9363 q^{75} -2.96733 q^{77} +2.03176 q^{78} -0.124845 q^{79} +3.81859 q^{80} -10.2584 q^{81} +9.41379 q^{82} +10.9086 q^{83} -5.55471 q^{84} -8.77835 q^{85} +8.07120 q^{86} -13.7110 q^{87} -1.00000 q^{88} -4.14468 q^{89} -1.92538 q^{90} +3.22064 q^{91} -7.37385 q^{92} +15.6742 q^{93} +12.2614 q^{94} -1.87195 q^{96} +1.40370 q^{97} -1.80506 q^{98} +0.504212 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 12 q^{2} + 3 q^{3} + 12 q^{4} - 9 q^{5} - 3 q^{6} - 12 q^{7} - 12 q^{8} + 15 q^{9}+O(q^{10}) $ 12 * q - 12 * q^2 + 3 * q^3 + 12 * q^4 - 9 * q^5 - 3 * q^6 - 12 * q^7 - 12 * q^8 + 15 * q^9	\( 12 q - 12 q^{2} + 3 q^{3} + 12 q^{4} - 9 q^{5} - 3 q^{6} - 12 q^{7} - 12 q^{8} + 15 q^{9} + 9 q^{10} + 12 q^{11} + 3 q^{12} + 12 q^{14} + 21 q^{15} + 12 q^{16} - 33 q^{17} - 15 q^{18} - 9 q^{20} - 9 q^{21} - 12 q^{22} - 18 q^{23} - 3 q^{24} + 15 q^{25} + 21 q^{27} - 12 q^{28} - 15 q^{29} - 21 q^{30} + 9 q^{31} - 12 q^{32} + 3 q^{33} + 33 q^{34} - 30 q^{35} + 15 q^{36} + 9 q^{37} - 6 q^{39} + 9 q^{40} - 15 q^{41} + 9 q^{42} - 21 q^{43} + 12 q^{44} + 18 q^{46} - 27 q^{47} + 3 q^{48} + 18 q^{49} - 15 q^{50} - 6 q^{51} + 6 q^{53} - 21 q^{54} - 9 q^{55} + 12 q^{56} + 15 q^{58} + 48 q^{59} + 21 q^{60} + 12 q^{61} - 9 q^{62} - 66 q^{63} + 12 q^{64} - 36 q^{65} - 3 q^{66} - 3 q^{67} - 33 q^{68} - 24 q^{69} + 30 q^{70} - 3 q^{71} - 15 q^{72} - 30 q^{73} - 9 q^{74} + 21 q^{75} - 12 q^{77} + 6 q^{78} + 12 q^{79} - 9 q^{80} + 12 q^{81} + 15 q^{82} - 66 q^{83} - 9 q^{84} + 15 q^{85} + 21 q^{86} - 51 q^{87} - 12 q^{88} + 30 q^{89} + 54 q^{91} - 18 q^{92} - 66 q^{93} + 27 q^{94} - 3 q^{96} + 36 q^{97} - 18 q^{98} + 15 q^{99}+O(q^{100}) \) 12 * q - 12 * q^2 + 3 * q^3 + 12 * q^4 - 9 * q^5 - 3 * q^6 - 12 * q^7 - 12 * q^8 + 15 * q^9 + 9 * q^10 + 12 * q^11 + 3 * q^12 + 12 * q^14 + 21 * q^15 + 12 * q^16 - 33 * q^17 - 15 * q^18 - 9 * q^20 - 9 * q^21 - 12 * q^22 - 18 * q^23 - 3 * q^24 + 15 * q^25 + 21 * q^27 - 12 * q^28 - 15 * q^29 - 21 * q^30 + 9 * q^31 - 12 * q^32 + 3 * q^33 + 33 * q^34 - 30 * q^35 + 15 * q^36 + 9 * q^37 - 6 * q^39 + 9 * q^40 - 15 * q^41 + 9 * q^42 - 21 * q^43 + 12 * q^44 + 18 * q^46 - 27 * q^47 + 3 * q^48 + 18 * q^49 - 15 * q^50 - 6 * q^51 + 6 * q^53 - 21 * q^54 - 9 * q^55 + 12 * q^56 + 15 * q^58 + 48 * q^59 + 21 * q^60 + 12 * q^61 - 9 * q^62 - 66 * q^63 + 12 * q^64 - 36 * q^65 - 3 * q^66 - 3 * q^67 - 33 * q^68 - 24 * q^69 + 30 * q^70 - 3 * q^71 - 15 * q^72 - 30 * q^73 - 9 * q^74 + 21 * q^75 - 12 * q^77 + 6 * q^78 + 12 * q^79 - 9 * q^80 + 12 * q^81 + 15 * q^82 - 66 * q^83 - 9 * q^84 + 15 * q^85 + 21 * q^86 - 51 * q^87 - 12 * q^88 + 30 * q^89 + 54 * q^91 - 18 * q^92 - 66 * q^93 + 27 * q^94 - 3 * q^96 + 36 * q^97 - 18 * q^98 + 15 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	1.87195	1.08077	0.540387	−	0.841417i	$-0.318278\pi$
$3$	1.87195	1.08077	0.540387	+	0.841417i	$0.318278\pi$
$4$	1.00000	0.500000
$5$	3.81859	1.70772	0.853862	−	0.520499i	$-0.174254\pi$
$5$	3.81859	1.70772	0.853862	+	0.520499i	$0.174254\pi$
$6$	−1.87195	−0.764222
$7$	−2.96733	−1.12155	−0.560773	−	0.827970i	$-0.689496\pi$
$7$	−2.96733	−1.12155	−0.560773	+	0.827970i	$0.689496\pi$
$8$	−1.00000	−0.353553
$9$	0.504212	0.168071
$10$	−3.81859	−1.20754
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	1.87195	0.540387
$13$	−1.08537	−0.301026	−0.150513	−	0.988608i	$-0.548093\pi$
$13$	−1.08537	−0.301026	−0.150513	+	0.988608i	$0.548093\pi$
$14$	2.96733	0.793053
$15$	7.14822	1.84566
$16$	1.00000	0.250000
$17$	−2.29885	−0.557552	−0.278776	−	0.960356i	$-0.589929\pi$
$17$	−2.29885	−0.557552	−0.278776	+	0.960356i	$0.589929\pi$
$18$	−0.504212	−0.118844
$19$	0	0
$19$	0	0
$20$	3.81859	0.853862
$21$	−5.55471	−1.21214
$22$	−1.00000	−0.213201
$23$	−7.37385	−1.53755	−0.768777	−	0.639517i	$-0.779134\pi$
$23$	−7.37385	−1.53755	−0.768777	+	0.639517i	$0.779134\pi$
$24$	−1.87195	−0.382111
$25$	9.58162	1.91632
$26$	1.08537	0.212858
$27$	−4.67200	−0.899127
$28$	−2.96733	−0.560773
$29$	−7.32445	−1.36012	−0.680058	−	0.733158i	$-0.738045\pi$
$29$	−7.32445	−1.36012	−0.680058	+	0.733158i	$0.738045\pi$
$30$	−7.14822	−1.30508
$31$	8.37319	1.50387	0.751935	−	0.659238i	$-0.229121\pi$
$31$	8.37319	1.50387	0.751935	+	0.659238i	$0.229121\pi$
$32$	−1.00000	−0.176777
$33$	1.87195	0.325865
$34$	2.29885	0.394249
$35$	−11.3310	−1.91529
$36$	0.504212	0.0840353
$37$	9.10622	1.49705	0.748526	−	0.663105i	$-0.230762\pi$
$37$	9.10622	1.49705	0.748526	+	0.663105i	$0.230762\pi$
$38$	0	0
$39$	−2.03176	−0.325341
$40$	−3.81859	−0.603772
$41$	−9.41379	−1.47019	−0.735094	−	0.677966i	$-0.762862\pi$
$41$	−9.41379	−1.47019	−0.735094	+	0.677966i	$0.762862\pi$
$42$	5.55471	0.857110
$43$	−8.07120	−1.23085	−0.615423	−	0.788197i	$-0.711015\pi$
$43$	−8.07120	−1.23085	−0.615423	+	0.788197i	$0.711015\pi$
$44$	1.00000	0.150756
$45$	1.92538	0.287018
$46$	7.37385	1.08721
$47$	−12.2614	−1.78850	−0.894252	−	0.447564i	$-0.852292\pi$
$47$	−12.2614	−1.78850	−0.894252	+	0.447564i	$0.852292\pi$
$48$	1.87195	0.270193
$49$	1.80506	0.257866
$50$	−9.58162	−1.35505
$51$	−4.30334	−0.602588
$52$	−1.08537	−0.150513
$53$	−3.29423	−0.452498	−0.226249	−	0.974070i	$-0.572646\pi$
$53$	−3.29423	−0.452498	−0.226249	+	0.974070i	$0.572646\pi$
$54$	4.67200	0.635779
$55$	3.81859	0.514898
$56$	2.96733	0.396526
$57$	0	0
$58$	7.32445	0.961747
$59$	0.00737709	0.000960415 0	0.000480207	−	1.00000i	$-0.499847\pi$
$59$	0.00737709	0.000960415 0	0.000480207		1.00000i	$0.499847\pi$
$60$	7.14822	0.922831
$61$	1.17369	0.150276	0.0751378	−	0.997173i	$-0.476060\pi$
$61$	1.17369	0.150276	0.0751378	+	0.997173i	$0.476060\pi$
$62$	−8.37319	−1.06340
$63$	−1.49616	−0.188499
$64$	1.00000	0.125000
$65$	−4.14457	−0.514070
$66$	−1.87195	−0.230422
$67$	−4.51665	−0.551797	−0.275898	−	0.961187i	$-0.588975\pi$
$67$	−4.51665	−0.551797	−0.275898	+	0.961187i	$0.588975\pi$
$68$	−2.29885	−0.278776
$69$	−13.8035	−1.66175
$70$	11.3310	1.35432
$71$	−6.26636	−0.743680	−0.371840	−	0.928297i	$-0.621273\pi$
$71$	−6.26636	−0.743680	−0.371840	+	0.928297i	$0.621273\pi$
$72$	−0.504212	−0.0594219
$73$	−9.46560	−1.10787	−0.553933	−	0.832562i	$-0.686873\pi$
$73$	−9.46560	−1.10787	−0.553933	+	0.832562i	$0.686873\pi$
$74$	−9.10622	−1.05858
$75$	17.9363	2.07111
$76$	0	0
$77$	−2.96733	−0.338159
$78$	2.03176	0.230051
$79$	−0.124845	−0.0140461	−0.00702306	−	0.999975i	$-0.502236\pi$
$79$	−0.124845	−0.0140461	−0.00702306	+	0.999975i	$0.502236\pi$
$80$	3.81859	0.426931
$81$	−10.2584	−1.13982
$82$	9.41379	1.03958
$83$	10.9086	1.19738	0.598689	−	0.800982i	$-0.295689\pi$
$83$	10.9086	1.19738	0.598689	+	0.800982i	$0.295689\pi$
$84$	−5.55471	−0.606069
$85$	−8.77835	−0.952146
$86$	8.07120	0.870339
$87$	−13.7110	−1.46998
$88$	−1.00000	−0.106600
$89$	−4.14468	−0.439336	−0.219668	−	0.975575i	$-0.570497\pi$
$89$	−4.14468	−0.439336	−0.219668	+	0.975575i	$0.570497\pi$
$90$	−1.92538	−0.202953
$91$	3.22064	0.337615
$92$	−7.37385	−0.768777
$93$	15.6742	1.62534
$94$	12.2614	1.26466
$95$	0	0
$96$	−1.87195	−0.191056
$97$	1.40370	0.142524	0.0712620	−	0.997458i	$-0.477297\pi$
$97$	1.40370	0.142524	0.0712620	+	0.997458i	$0.477297\pi$
$98$	−1.80506	−0.182339
$99$	0.504212	0.0506752
$100$	9.58162	0.958162
$101$	−15.4837	−1.54069	−0.770343	−	0.637630i	$-0.779915\pi$
$101$	−15.4837	−1.54069	−0.770343	+	0.637630i	$0.779915\pi$
$102$	4.30334	0.426094
$103$	18.1886	1.79218	0.896089	−	0.443875i	$-0.146397\pi$
$103$	18.1886	1.79218	0.896089	+	0.443875i	$0.146397\pi$
$104$	1.08537	0.106429
$105$	−21.2111	−2.07000
$106$	3.29423	0.319964
$107$	11.2675	1.08927	0.544636	−	0.838672i	$-0.316668\pi$
$107$	11.2675	1.08927	0.544636	+	0.838672i	$0.316668\pi$
$108$	−4.67200	−0.449563
$109$	5.24997	0.502856	0.251428	−	0.967876i	$-0.419100\pi$
$109$	5.24997	0.502856	0.251428	+	0.967876i	$0.419100\pi$
$110$	−3.81859	−0.364088
$111$	17.0464	1.61797
$112$	−2.96733	−0.280387
$113$	0.0698227	0.00656837	0.00328418	−	0.999995i	$-0.498955\pi$
$113$	0.0698227	0.00656837	0.00328418	+	0.999995i	$0.498955\pi$
$114$	0	0
$115$	−28.1577	−2.62572
$116$	−7.32445	−0.680058
$117$	−0.547255	−0.0505937
$118$	−0.00737709	−0.000679116 0
$119$	6.82144	0.625321
$120$	−7.14822	−0.652540
$121$	1.00000	0.0909091
$122$	−1.17369	−0.106261
$123$	−17.6222	−1.58894
$124$	8.37319	0.751935
$125$	17.4953	1.56483
$126$	1.49616	0.133289
$127$	6.49536	0.576370	0.288185	−	0.957575i	$-0.406948\pi$
$127$	6.49536	0.576370	0.288185	+	0.957575i	$0.406948\pi$
$128$	−1.00000	−0.0883883
$129$	−15.1089	−1.33027
$130$	4.14457	0.363503
$131$	−6.56205	−0.573329	−0.286664	−	0.958031i	$-0.592546\pi$
$131$	−6.56205	−0.573329	−0.286664	+	0.958031i	$0.592546\pi$
$132$	1.87195	0.162933
$133$	0	0
$134$	4.51665	0.390179
$135$	−17.8404	−1.53546
$136$	2.29885	0.197124
$137$	−9.04069	−0.772398	−0.386199	−	0.922415i	$-0.626212\pi$
$137$	−9.04069	−0.772398	−0.386199	+	0.922415i	$0.626212\pi$
$138$	13.8035	1.17503
$139$	20.3343	1.72474	0.862368	−	0.506281i	$-0.168980\pi$
$139$	20.3343	1.72474	0.862368	+	0.506281i	$0.168980\pi$
$140$	−11.3310	−0.957646
$141$	−22.9527	−1.93297
$142$	6.26636	0.525861
$143$	−1.08537	−0.0907629
$144$	0.504212	0.0420177
$145$	−27.9691	−2.32270
$146$	9.46560	0.783379
$147$	3.37899	0.278695
$148$	9.10622	0.748526
$149$	−4.96885	−0.407064	−0.203532	−	0.979068i	$-0.565242\pi$
$149$	−4.96885	−0.407064	−0.203532	+	0.979068i	$0.565242\pi$
$150$	−17.9363	−1.46450
$151$	−3.08344	−0.250927	−0.125463	−	0.992098i	$-0.540042\pi$
$151$	−3.08344	−0.250927	−0.125463	+	0.992098i	$0.540042\pi$
$152$	0	0
$153$	−1.15911	−0.0937082
$154$	2.96733	0.239114
$155$	31.9738	2.56819
$156$	−2.03176	−0.162671
$157$	−7.91801	−0.631926	−0.315963	−	0.948771i	$-0.602328\pi$
$157$	−7.91801	−0.631926	−0.315963	+	0.948771i	$0.602328\pi$
$158$	0.124845	0.00993211
$159$	−6.16666	−0.489048
$160$	−3.81859	−0.301886
$161$	21.8807	1.72444
$162$	10.2584	0.805977
$163$	−2.60977	−0.204413	−0.102206	−	0.994763i	$-0.532590\pi$
$163$	−2.60977	−0.204413	−0.102206	+	0.994763i	$0.532590\pi$
$164$	−9.41379	−0.735094
$165$	7.14822	0.556488
$166$	−10.9086	−0.846674
$167$	11.1320	0.861419	0.430709	−	0.902491i	$-0.358263\pi$
$167$	11.1320	0.861419	0.430709	+	0.902491i	$0.358263\pi$
$168$	5.55471	0.428555
$169$	−11.8220	−0.909383
$170$	8.77835	0.673269
$171$	0	0
$172$	−8.07120	−0.615423
$173$	3.57818	0.272044	0.136022	−	0.990706i	$-0.456568\pi$
$173$	3.57818	0.272044	0.136022	+	0.990706i	$0.456568\pi$
$174$	13.7110	1.03943
$175$	−28.4318	−2.14924
$176$	1.00000	0.0753778
$177$	0.0138096	0.00103799
$178$	4.14468	0.310657
$179$	−8.94841	−0.668835	−0.334418	−	0.942425i	$-0.608540\pi$
$179$	−8.94841	−0.668835	−0.334418	+	0.942425i	$0.608540\pi$
$180$	1.92538	0.143509
$181$	−14.3106	−1.06370	−0.531849	−	0.846839i	$-0.678503\pi$
$181$	−14.3106	−1.06370	−0.531849	+	0.846839i	$0.678503\pi$
$182$	−3.22064	−0.238730
$183$	2.19709	0.162414
$184$	7.37385	0.543607
$185$	34.7729	2.55655
$186$	−15.6742	−1.14929
$187$	−2.29885	−0.168108
$188$	−12.2614	−0.894252
$189$	13.8634	1.00841
$190$	0	0
$191$	21.7899	1.57666	0.788330	−	0.615253i	$-0.210946\pi$
$191$	21.7899	1.57666	0.788330	+	0.615253i	$0.210946\pi$
$192$	1.87195	0.135097
$193$	0.295692	0.0212844	0.0106422	−	0.999943i	$-0.496612\pi$
$193$	0.295692	0.0212844	0.0106422	+	0.999943i	$0.496612\pi$
$194$	−1.40370	−0.100780
$195$	−7.75844	−0.555593
$196$	1.80506	0.128933
$197$	−12.7105	−0.905583	−0.452792	−	0.891616i	$-0.649572\pi$
$197$	−12.7105	−0.905583	−0.452792	+	0.891616i	$0.649572\pi$
$198$	−0.504212	−0.0358328
$199$	5.90529	0.418615	0.209307	−	0.977850i	$-0.432879\pi$
$199$	5.90529	0.418615	0.209307	+	0.977850i	$0.432879\pi$
$200$	−9.58162	−0.677523
$201$	−8.45496	−0.596367
$202$	15.4837	1.08943
$203$	21.7341	1.52543
$204$	−4.30334	−0.301294
$205$	−35.9474	−2.51067
$206$	−18.1886	−1.26726
$207$	−3.71798	−0.258418
$208$	−1.08537	−0.0752566
$209$	0	0
$210$	21.2111	1.46371
$211$	14.7186	1.01327	0.506636	−	0.862160i	$-0.330889\pi$
$211$	14.7186	1.01327	0.506636	+	0.862160i	$0.330889\pi$
$212$	−3.29423	−0.226249
$213$	−11.7303	−0.803749
$214$	−11.2675	−0.770232
$215$	−30.8206	−2.10195
$216$	4.67200	0.317889
$217$	−24.8460	−1.68666
$218$	−5.24997	−0.355573
$219$	−17.7192	−1.19735
$220$	3.81859	0.257449
$221$	2.49509	0.167838
$222$	−17.0464	−1.14408
$223$	−4.70824	−0.315287	−0.157643	−	0.987496i	$-0.550390\pi$
$223$	−4.70824	−0.315287	−0.157643	+	0.987496i	$0.550390\pi$
$224$	2.96733	0.198263
$225$	4.83116	0.322078
$226$	−0.0698227	−0.00464454
$227$	−18.3182	−1.21582	−0.607912	−	0.794005i	$-0.707993\pi$
$227$	−18.3182	−1.21582	−0.607912	+	0.794005i	$0.707993\pi$
$228$	0	0
$229$	0.455408	0.0300942	0.0150471	−	0.999887i	$-0.495210\pi$
$229$	0.455408	0.0300942	0.0150471	+	0.999887i	$0.495210\pi$
$230$	28.1577	1.85666
$231$	−5.55471	−0.365473
$232$	7.32445	0.480874
$233$	5.51851	0.361530	0.180765	−	0.983526i	$-0.442143\pi$
$233$	5.51851	0.361530	0.180765	+	0.983526i	$0.442143\pi$
$234$	0.547255	0.0357752
$235$	−46.8211	−3.05427
$236$	0.00737709	0.000480207 0
$237$	−0.233703	−0.0151807
$238$	−6.82144	−0.442168
$239$	−1.92490	−0.124512	−0.0622558	−	0.998060i	$-0.519829\pi$
$239$	−1.92490	−0.124512	−0.0622558	+	0.998060i	$0.519829\pi$
$240$	7.14822	0.461416
$241$	17.7954	1.14630	0.573151	−	0.819450i	$-0.305721\pi$
$241$	17.7954	1.14630	0.573151	+	0.819450i	$0.305721\pi$
$242$	−1.00000	−0.0642824
$243$	−5.18726	−0.332763
$244$	1.17369	0.0751378
$245$	6.89279	0.440364
$246$	17.6222	1.12355
$247$	0	0
$248$	−8.37319	−0.531698
$249$	20.4205	1.29409
$250$	−17.4953	−1.10650
$251$	5.57761	0.352055	0.176028	−	0.984385i	$-0.443675\pi$
$251$	5.57761	0.352055	0.176028	+	0.984385i	$0.443675\pi$
$252$	−1.49616	−0.0942495
$253$	−7.37385	−0.463590
$254$	−6.49536	−0.407555
$255$	−16.4327	−1.02905
$256$	1.00000	0.0625000
$257$	−12.9649	−0.808731	−0.404366	−	0.914597i	$-0.632508\pi$
$257$	−12.9649	−0.808731	−0.404366	+	0.914597i	$0.632508\pi$
$258$	15.1089	0.940640
$259$	−27.0212	−1.67901
$260$	−4.14457	−0.257035
$261$	−3.69307	−0.228596
$262$	6.56205	0.405405
$263$	−16.4999	−1.01743	−0.508713	−	0.860936i	$-0.669879\pi$
$263$	−16.4999	−1.01743	−0.508713	+	0.860936i	$0.669879\pi$
$264$	−1.87195	−0.115211
$265$	−12.5793	−0.772742
$266$	0	0
$267$	−7.75866	−0.474822
$268$	−4.51665	−0.275898
$269$	25.3288	1.54432	0.772162	−	0.635426i	$-0.219175\pi$
$269$	25.3288	1.54432	0.772162	+	0.635426i	$0.219175\pi$
$270$	17.8404	1.08573
$271$	−15.6943	−0.953359	−0.476680	−	0.879077i	$-0.658160\pi$
$271$	−15.6943	−0.953359	−0.476680	+	0.879077i	$0.658160\pi$
$272$	−2.29885	−0.139388
$273$	6.02890	0.364885
$274$	9.04069	0.546168
$275$	9.58162	0.577793
$276$	−13.8035	−0.830873
$277$	6.78919	0.407923	0.203961	−	0.978979i	$-0.434618\pi$
$277$	6.78919	0.407923	0.203961	+	0.978979i	$0.434618\pi$
$278$	−20.3343	−1.21957
$279$	4.22186	0.252756
$280$	11.3310	0.677158
$281$	2.32695	0.138814	0.0694071	−	0.997588i	$-0.477889\pi$
$281$	2.32695	0.138814	0.0694071	+	0.997588i	$0.477889\pi$
$282$	22.9527	1.36681
$283$	−27.9034	−1.65869	−0.829344	−	0.558739i	$-0.811285\pi$
$283$	−27.9034	−1.65869	−0.829344	+	0.558739i	$0.811285\pi$
$284$	−6.26636	−0.371840
$285$	0	0
$286$	1.08537	0.0641791
$287$	27.9338	1.64888
$288$	−0.504212	−0.0297110
$289$	−11.7153	−0.689135
$290$	27.9691	1.64240
$291$	2.62766	0.154036
$292$	−9.46560	−0.553933
$293$	−31.0448	−1.81366	−0.906829	−	0.421500i	$-0.861504\pi$
$293$	−31.0448	−1.81366	−0.906829	+	0.421500i	$0.861504\pi$
$294$	−3.37899	−0.197067
$295$	0.0281701	0.00164012
$296$	−9.10622	−0.529288
$297$	−4.67200	−0.271097
$298$	4.96885	0.287838
$299$	8.00333	0.462844
$300$	17.9363	1.03556
$301$	23.9499	1.38045
$302$	3.08344	0.177432
$303$	−28.9848	−1.66513
$304$	0	0
$305$	4.48184	0.256629
$306$	1.15911	0.0662617
$307$	26.6887	1.52321	0.761603	−	0.648044i	$-0.224413\pi$
$307$	26.6887	1.52321	0.761603	+	0.648044i	$0.224413\pi$
$308$	−2.96733	−0.169079
$309$	34.0482	1.93694
$310$	−31.9738	−1.81599
$311$	2.65525	0.150566	0.0752828	−	0.997162i	$-0.476014\pi$
$311$	2.65525	0.150566	0.0752828	+	0.997162i	$0.476014\pi$
$312$	2.03176	0.115026
$313$	−29.4836	−1.66651	−0.833257	−	0.552886i	$-0.813527\pi$
$313$	−29.4836	−1.66651	−0.833257	+	0.552886i	$0.813527\pi$
$314$	7.91801	0.446839
$315$	−5.71324	−0.321904
$316$	−0.124845	−0.00702306
$317$	−30.3931	−1.70705	−0.853523	−	0.521055i	$-0.825539\pi$
$317$	−30.3931	−1.70705	−0.853523	+	0.521055i	$0.825539\pi$
$318$	6.16666	0.345809
$319$	−7.32445	−0.410090
$320$	3.81859	0.213466
$321$	21.0923	1.17726
$322$	−21.8807	−1.21936
$323$	0	0
$324$	−10.2584	−0.569911
$325$	−10.3996	−0.576864
$326$	2.60977	0.144542
$327$	9.82770	0.543473
$328$	9.41379	0.519790
$329$	36.3835	2.00589
$330$	−7.14822	−0.393497
$331$	6.46346	0.355264	0.177632	−	0.984097i	$-0.443156\pi$
$331$	6.46346	0.355264	0.177632	+	0.984097i	$0.443156\pi$
$332$	10.9086	0.598689
$333$	4.59146	0.251611
$334$	−11.1320	−0.609115
$335$	−17.2472	−0.942317
$336$	−5.55471	−0.303034
$337$	−13.2628	−0.722469	−0.361234	−	0.932475i	$-0.617645\pi$
$337$	−13.2628	−0.722469	−0.361234	+	0.932475i	$0.617645\pi$
$338$	11.8220	0.643031
$339$	0.130705	0.00709892
$340$	−8.77835	−0.476073
$341$	8.37319	0.453434
$342$	0	0
$343$	15.4151	0.832338
$344$	8.07120	0.435170
$345$	−52.7099	−2.83781
$346$	−3.57818	−0.192364
$347$	2.70692	0.145315	0.0726576	−	0.997357i	$-0.476852\pi$
$347$	2.70692	0.145315	0.0726576	+	0.997357i	$0.476852\pi$
$348$	−13.7110	−0.734988
$349$	5.48025	0.293351	0.146676	−	0.989185i	$-0.453143\pi$
$349$	5.48025	0.293351	0.146676	+	0.989185i	$0.453143\pi$
$350$	28.4318	1.51975
$351$	5.07083	0.270661
$352$	−1.00000	−0.0533002
$353$	23.2866	1.23942	0.619711	−	0.784830i	$-0.287250\pi$
$353$	23.2866	1.23942	0.619711	+	0.784830i	$0.287250\pi$
$354$	−0.0138096	−0.000733970 0
$355$	−23.9286	−1.27000
$356$	−4.14468	−0.219668
$357$	12.7694	0.675830
$358$	8.94841	0.472938
$359$	12.4962	0.659523	0.329762	−	0.944064i	$-0.393032\pi$
$359$	12.4962	0.659523	0.329762	+	0.944064i	$0.393032\pi$
$360$	−1.92538	−0.101476
$361$	0	0
$362$	14.3106	0.752149
$363$	1.87195	0.0982521
$364$	3.22064	0.168808
$365$	−36.1452	−1.89193
$366$	−2.19709	−0.114844
$367$	17.7649	0.927319	0.463659	−	0.886014i	$-0.346536\pi$
$367$	17.7649	0.927319	0.463659	+	0.886014i	$0.346536\pi$
$368$	−7.37385	−0.384388
$369$	−4.74655	−0.247095
$370$	−34.7729	−1.80776
$371$	9.77509	0.507497
$372$	15.6742	0.812671
$373$	21.2672	1.10117	0.550587	−	0.834778i	$-0.314404\pi$
$373$	21.2672	1.10117	0.550587	+	0.834778i	$0.314404\pi$
$374$	2.29885	0.118871
$375$	32.7504	1.69122
$376$	12.2614	0.632331
$377$	7.94971	0.409431
$378$	−13.8634	−0.713055
$379$	−20.3995	−1.04785	−0.523926	−	0.851764i	$-0.675533\pi$
$379$	−20.3995	−1.04785	−0.523926	+	0.851764i	$0.675533\pi$
$380$	0	0
$381$	12.1590	0.622925
$382$	−21.7899	−1.11487
$383$	−17.1052	−0.874037	−0.437019	−	0.899452i	$-0.643966\pi$
$383$	−17.1052	−0.874037	−0.437019	+	0.899452i	$0.643966\pi$
$384$	−1.87195	−0.0955278
$385$	−11.3310	−0.577482
$386$	−0.295692	−0.0150503
$387$	−4.06959	−0.206869
$388$	1.40370	0.0712620
$389$	4.54851	0.230619	0.115309	−	0.993330i	$-0.463214\pi$
$389$	4.54851	0.230619	0.115309	+	0.993330i	$0.463214\pi$
$390$	7.75844	0.392864
$391$	16.9513	0.857267
$392$	−1.80506	−0.0911694
$393$	−12.2839	−0.619638
$394$	12.7105	0.640344
$395$	−0.476730	−0.0239869
$396$	0.504212	0.0253376
$397$	−12.8646	−0.645654	−0.322827	−	0.946458i	$-0.604633\pi$
$397$	−12.8646	−0.645654	−0.322827	+	0.946458i	$0.604633\pi$
$398$	−5.90529	−0.296005
$399$	0	0
$400$	9.58162	0.479081
$401$	23.0448	1.15080	0.575402	−	0.817871i	$-0.304845\pi$
$401$	23.0448	1.15080	0.575402	+	0.817871i	$0.304845\pi$
$402$	8.45496	0.421695
$403$	−9.08798	−0.452704
$404$	−15.4837	−0.770343
$405$	−39.1726	−1.94650
$406$	−21.7341	−1.07864
$407$	9.10622	0.451378
$408$	4.30334	0.213047
$409$	14.9884	0.741128	0.370564	−	0.928807i	$-0.379164\pi$
$409$	14.9884	0.741128	0.370564	+	0.928807i	$0.379164\pi$
$410$	35.9474	1.77532
$411$	−16.9238	−0.834788
$412$	18.1886	0.896089
$413$	−0.0218903	−0.00107715
$414$	3.71798	0.182729
$415$	41.6556	2.04479
$416$	1.08537	0.0532145
$417$	38.0650	1.86405
$418$	0	0
$419$	−30.8820	−1.50868	−0.754342	−	0.656482i	$-0.772044\pi$
$419$	−30.8820	−1.50868	−0.754342	+	0.656482i	$0.772044\pi$
$420$	−21.2111	−1.03500
$421$	38.1631	1.85996	0.929978	−	0.367614i	$-0.119825\pi$
$421$	38.1631	1.85996	0.929978	+	0.367614i	$0.119825\pi$
$422$	−14.7186	−0.716491
$423$	−6.18232	−0.300595
$424$	3.29423	0.159982
$425$	−22.0267	−1.06845
$426$	11.7303	0.568337
$427$	−3.48273	−0.168541
$428$	11.2675	0.544636
$429$	−2.03176	−0.0980941
$430$	30.8206	1.48630
$431$	−0.821524	−0.0395714	−0.0197857	−	0.999804i	$-0.506298\pi$
$431$	−0.821524	−0.0395714	−0.0197857	+	0.999804i	$0.506298\pi$
$432$	−4.67200	−0.224782
$433$	5.53382	0.265938	0.132969	−	0.991120i	$-0.457549\pi$
$433$	5.53382	0.265938	0.132969	+	0.991120i	$0.457549\pi$
$434$	24.8460	1.19265
$435$	−52.3568	−2.51032
$436$	5.24997	0.251428
$437$	0	0
$438$	17.7192	0.846655
$439$	−0.815891	−0.0389404	−0.0194702	−	0.999810i	$-0.506198\pi$
$439$	−0.815891	−0.0389404	−0.0194702	+	0.999810i	$0.506198\pi$
$440$	−3.81859	−0.182044
$441$	0.910134	0.0433397
$442$	−2.49509	−0.118679
$443$	−29.0886	−1.38204	−0.691022	−	0.722834i	$-0.742839\pi$
$443$	−29.0886	−1.38204	−0.691022	+	0.722834i	$0.742839\pi$
$444$	17.0464	0.808987
$445$	−15.8268	−0.750264
$446$	4.70824	0.222941
$447$	−9.30147	−0.439944
$448$	−2.96733	−0.140193
$449$	24.0614	1.13553	0.567764	−	0.823191i	$-0.307809\pi$
$449$	24.0614	1.13553	0.567764	+	0.823191i	$0.307809\pi$
$450$	−4.83116	−0.227743
$451$	−9.41379	−0.443278
$452$	0.0698227	0.00328418
$453$	−5.77206	−0.271195
$454$	18.3182	0.859717
$455$	12.2983	0.576554
$456$	0	0
$457$	−15.8385	−0.740896	−0.370448	−	0.928853i	$-0.620796\pi$
$457$	−15.8385	−0.740896	−0.370448	+	0.928853i	$0.620796\pi$
$458$	−0.455408	−0.0212798
$459$	10.7402	0.501310
$460$	−28.1577	−1.31286
$461$	−17.1067	−0.796737	−0.398368	−	0.917226i	$-0.630423\pi$
$461$	−17.1067	−0.796737	−0.398368	+	0.917226i	$0.630423\pi$
$462$	5.55471	0.258428
$463$	4.29074	0.199407	0.0997037	−	0.995017i	$-0.468211\pi$
$463$	4.29074	0.199407	0.0997037	+	0.995017i	$0.468211\pi$
$464$	−7.32445	−0.340029
$465$	59.8534	2.77564
$466$	−5.51851	−0.255640
$467$	31.5321	1.45913	0.729566	−	0.683910i	$-0.239722\pi$
$467$	31.5321	1.45913	0.729566	+	0.683910i	$0.239722\pi$
$468$	−0.547255	−0.0252969
$469$	13.4024	0.618866
$470$	46.8211	2.15970
$471$	−14.8222	−0.682969
$472$	−0.00737709	−0.000339558 0
$473$	−8.07120	−0.371114
$474$	0.233703	0.0107344
$475$	0	0
$476$	6.82144	0.312660
$477$	−1.66099	−0.0760516
$478$	1.92490	0.0880429
$479$	22.9595	1.04905	0.524524	−	0.851396i	$-0.324243\pi$
$479$	22.9595	1.04905	0.524524	+	0.851396i	$0.324243\pi$
$480$	−7.14822	−0.326270
$481$	−9.88358	−0.450653
$482$	−17.7954	−0.810558
$483$	40.9596	1.86373
$484$	1.00000	0.0454545
$485$	5.36015	0.243392
$486$	5.18726	0.235299
$487$	6.90006	0.312672	0.156336	−	0.987704i	$-0.450032\pi$
$487$	6.90006	0.312672	0.156336	+	0.987704i	$0.450032\pi$
$488$	−1.17369	−0.0531304
$489$	−4.88536	−0.220924
$490$	−6.89279	−0.311384
$491$	15.0255	0.678094	0.339047	−	0.940770i	$-0.389896\pi$
$491$	15.0255	0.678094	0.339047	+	0.940770i	$0.389896\pi$
$492$	−17.6222	−0.794469
$493$	16.8378	0.758336
$494$	0	0
$495$	1.92538	0.0865393
$496$	8.37319	0.375967
$497$	18.5944	0.834072
$498$	−20.4205	−0.915062
$499$	−21.6638	−0.969804	−0.484902	−	0.874569i	$-0.661145\pi$
$499$	−21.6638	−0.969804	−0.484902	+	0.874569i	$0.661145\pi$
$500$	17.4953	0.782414
$501$	20.8386	0.930998
$502$	−5.57761	−0.248941
$503$	19.9476	0.889417	0.444709	−	0.895675i	$-0.353307\pi$
$503$	19.9476	0.889417	0.444709	+	0.895675i	$0.353307\pi$
$504$	1.49616	0.0666445
$505$	−59.1259	−2.63107
$506$	7.37385	0.327808
$507$	−22.1302	−0.982837
$508$	6.49536	0.288185
$509$	3.02204	0.133950	0.0669748	−	0.997755i	$-0.478665\pi$
$509$	3.02204	0.133950	0.0669748	+	0.997755i	$0.478665\pi$
$510$	16.4327	0.727651
$511$	28.0876	1.24252
$512$	−1.00000	−0.0441942
$513$	0	0
$514$	12.9649	0.571859
$515$	69.4548	3.06055
$516$	−15.1089	−0.665133
$517$	−12.2614	−0.539254
$518$	27.0212	1.18724
$519$	6.69819	0.294018
$520$	4.14457	0.181751
$521$	13.2518	0.580571	0.290286	−	0.956940i	$-0.406250\pi$
$521$	13.2518	0.580571	0.290286	+	0.956940i	$0.406250\pi$
$522$	3.69307	0.161641
$523$	26.2954	1.14982	0.574909	−	0.818217i	$-0.305037\pi$
$523$	26.2954	1.14982	0.574909	+	0.818217i	$0.305037\pi$
$524$	−6.56205	−0.286664
$525$	−53.2231	−2.32285
$526$	16.4999	0.719429
$527$	−19.2487	−0.838486
$528$	1.87195	0.0814663
$529$	31.3736	1.36407
$530$	12.5793	0.546411
$531$	0.00371961	0.000161418 0
$532$	0	0
$533$	10.2174	0.442565
$534$	7.75866	0.335750
$535$	43.0260	1.86018
$536$	4.51665	0.195090
$537$	−16.7510	−0.722859
$538$	−25.3288	−1.09200
$539$	1.80506	0.0777495
$540$	−17.8404	−0.767731
$541$	−10.3901	−0.446707	−0.223353	−	0.974738i	$-0.571700\pi$
$541$	−10.3901	−0.446707	−0.223353	+	0.974738i	$0.571700\pi$
$542$	15.6943	0.674127
$543$	−26.7888	−1.14962
$544$	2.29885	0.0985622
$545$	20.0475	0.858739
$546$	−6.02890	−0.258013
$547$	6.15057	0.262979	0.131490	−	0.991318i	$-0.458024\pi$
$547$	6.15057	0.262979	0.131490	+	0.991318i	$0.458024\pi$
$548$	−9.04069	−0.386199
$549$	0.591789	0.0252569
$550$	−9.58162	−0.408561
$551$	0	0
$552$	13.8035	0.587516
$553$	0.370456	0.0157534
$554$	−6.78919	−0.288445
$555$	65.0933	2.76305
$556$	20.3343	0.862368
$557$	8.85759	0.375308	0.187654	−	0.982235i	$-0.439912\pi$
$557$	8.85759	0.375308	0.187654	+	0.982235i	$0.439912\pi$
$558$	−4.22186	−0.178726
$559$	8.76020	0.370517
$560$	−11.3310	−0.478823
$561$	−4.30334	−0.181687
$562$	−2.32695	−0.0981564
$563$	42.7035	1.79974	0.899870	−	0.436158i	$-0.143661\pi$
$563$	42.7035	1.79974	0.899870	+	0.436158i	$0.143661\pi$
$564$	−22.9527	−0.966483
$565$	0.266624	0.0112170
$566$	27.9034	1.17287
$567$	30.4401	1.27836
$568$	6.26636	0.262931
$569$	−3.77478	−0.158247	−0.0791235	−	0.996865i	$-0.525212\pi$
$569$	−3.77478	−0.158247	−0.0791235	+	0.996865i	$0.525212\pi$
$570$	0	0
$571$	−23.6048	−0.987831	−0.493915	−	0.869510i	$-0.664435\pi$
$571$	−23.6048	−0.987831	−0.493915	+	0.869510i	$0.664435\pi$
$572$	−1.08537	−0.0453814
$573$	40.7896	1.70401
$574$	−27.9338	−1.16594
$575$	−70.6534	−2.94645
$576$	0.504212	0.0210088
$577$	20.4844	0.852777	0.426388	−	0.904540i	$-0.359786\pi$
$577$	20.4844	0.852777	0.426388	+	0.904540i	$0.359786\pi$
$578$	11.7153	0.487292
$579$	0.553522	0.0230036
$580$	−27.9691	−1.16135
$581$	−32.3695	−1.34291
$582$	−2.62766	−0.108920
$583$	−3.29423	−0.136433
$584$	9.46560	0.391689
$585$	−2.08974	−0.0864001
$586$	31.0448	1.28245
$587$	−41.4799	−1.71206	−0.856030	−	0.516926i	$-0.827076\pi$
$587$	−41.4799	−1.71206	−0.856030	+	0.516926i	$0.827076\pi$
$588$	3.37899	0.139347
$589$	0	0
$590$	−0.0281701	−0.00115974
$591$	−23.7934	−0.978730
$592$	9.10622	0.374263
$593$	29.6247	1.21654	0.608270	−	0.793730i	$-0.291864\pi$
$593$	29.6247	1.21654	0.608270	+	0.793730i	$0.291864\pi$
$594$	4.67200	0.191695
$595$	26.0483	1.06788
$596$	−4.96885	−0.203532
$597$	11.0544	0.452428
$598$	−8.00333	−0.327280
$599$	−37.8359	−1.54593	−0.772966	−	0.634448i	$-0.781228\pi$
$599$	−37.8359	−1.54593	−0.772966	+	0.634448i	$0.781228\pi$
$600$	−17.9363	−0.732248
$601$	−8.20002	−0.334486	−0.167243	−	0.985916i	$-0.553486\pi$
$601$	−8.20002	−0.334486	−0.167243	+	0.985916i	$0.553486\pi$
$602$	−23.9499	−0.976126
$603$	−2.27735	−0.0927408
$604$	−3.08344	−0.125463
$605$	3.81859	0.155248
$606$	28.9848	1.17743
$607$	−26.2736	−1.06641	−0.533206	−	0.845986i	$-0.679013\pi$
$607$	−26.2736	−1.06641	−0.533206	+	0.845986i	$0.679013\pi$
$608$	0	0
$609$	40.6852	1.64865
$610$	−4.48184	−0.181464
$611$	13.3081	0.538387
$612$	−1.15911	−0.0468541
$613$	−35.6834	−1.44124	−0.720619	−	0.693331i	$-0.756142\pi$
$613$	−35.6834	−1.44124	−0.720619	+	0.693331i	$0.756142\pi$
$614$	−26.6887	−1.07707
$615$	−67.2919	−2.71347
$616$	2.96733	0.119557
$617$	8.95576	0.360545	0.180273	−	0.983617i	$-0.442302\pi$
$617$	8.95576	0.360545	0.180273	+	0.983617i	$0.442302\pi$
$618$	−34.0482	−1.36962
$619$	23.9758	0.963670	0.481835	−	0.876262i	$-0.339970\pi$
$619$	23.9758	0.963670	0.481835	+	0.876262i	$0.339970\pi$
$620$	31.9738	1.28410
$621$	34.4506	1.38246
$622$	−2.65525	−0.106466
$623$	12.2987	0.492735
$624$	−2.03176	−0.0813353
$625$	18.8993	0.755971
$626$	29.4836	1.17840
$627$	0	0
$628$	−7.91801	−0.315963
$629$	−20.9338	−0.834685
$630$	5.71324	0.227621
$631$	37.1038	1.47708	0.738540	−	0.674210i	$-0.235516\pi$
$631$	37.1038	1.47708	0.738540	+	0.674210i	$0.235516\pi$
$632$	0.124845	0.00496605
$633$	27.5526	1.09512
$634$	30.3931	1.20706
$635$	24.8031	0.984281
$636$	−6.16666	−0.244524
$637$	−1.95915	−0.0776245
$638$	7.32445	0.289978
$639$	−3.15957	−0.124991
$640$	−3.81859	−0.150943
$641$	−17.5501	−0.693188	−0.346594	−	0.938015i	$-0.612662\pi$
$641$	−17.5501	−0.693188	−0.346594	+	0.938015i	$0.612662\pi$
$642$	−21.0923	−0.832446
$643$	−16.0292	−0.632131	−0.316065	−	0.948737i	$-0.602362\pi$
$643$	−16.0292	−0.632131	−0.316065	+	0.948737i	$0.602362\pi$
$644$	21.8807	0.862219
$645$	−57.6947	−2.27173
$646$	0	0
$647$	−44.5692	−1.75220	−0.876099	−	0.482131i	$-0.839863\pi$
$647$	−44.5692	−1.75220	−0.876099	+	0.482131i	$0.839863\pi$
$648$	10.2584	0.402988
$649$	0.00737709	0.000289576 0
$650$	10.3996	0.407904
$651$	−46.5106	−1.82290
$652$	−2.60977	−0.102206
$653$	7.60550	0.297626	0.148813	−	0.988865i	$-0.452455\pi$
$653$	7.60550	0.297626	0.148813	+	0.988865i	$0.452455\pi$
$654$	−9.82770	−0.384294
$655$	−25.0578	−0.979088
$656$	−9.41379	−0.367547
$657$	−4.77267	−0.186200
$658$	−36.3835	−1.41838
$659$	6.85923	0.267198	0.133599	−	0.991036i	$-0.457347\pi$
$659$	6.85923	0.267198	0.133599	+	0.991036i	$0.457347\pi$
$660$	7.14822	0.278244
$661$	−1.36039	−0.0529129	−0.0264565	−	0.999650i	$-0.508422\pi$
$661$	−1.36039	−0.0529129	−0.0264565	+	0.999650i	$0.508422\pi$
$662$	−6.46346	−0.251209
$663$	4.67070	0.181395
$664$	−10.9086	−0.423337
$665$	0	0
$666$	−4.59146	−0.177916
$667$	54.0094	2.09125
$668$	11.1320	0.430709
$669$	−8.81360	−0.340754
$670$	17.2472	0.666319
$671$	1.17369	0.0453098
$672$	5.55471	0.214278
$673$	30.8455	1.18901	0.594504	−	0.804093i	$-0.297348\pi$
$673$	30.8455	1.18901	0.594504	+	0.804093i	$0.297348\pi$
$674$	13.2628	0.510863
$675$	−44.7653	−1.72302
$676$	−11.8220	−0.454692
$677$	−37.6823	−1.44825	−0.724125	−	0.689669i	$-0.757756\pi$
$677$	−37.6823	−1.44825	−0.724125	+	0.689669i	$0.757756\pi$
$678$	−0.130705	−0.00501969
$679$	−4.16524	−0.159847
$680$	8.77835	0.336634
$681$	−34.2909	−1.31403
$682$	−8.37319	−0.320626
$683$	33.0982	1.26647	0.633233	−	0.773961i	$-0.281727\pi$
$683$	33.0982	1.26647	0.633233	+	0.773961i	$0.281727\pi$
$684$	0	0
$685$	−34.5227	−1.31904
$686$	−15.4151	−0.588552
$687$	0.852503	0.0325250
$688$	−8.07120	−0.307711
$689$	3.57545	0.136214
$690$	52.7099	2.00663
$691$	−9.85841	−0.375032	−0.187516	−	0.982262i	$-0.560044\pi$
$691$	−9.85841	−0.375032	−0.187516	+	0.982262i	$0.560044\pi$
$692$	3.57818	0.136022
$693$	−1.49616	−0.0568346
$694$	−2.70692	−0.102753
$695$	77.6485	2.94538
$696$	13.7110	0.519715
$697$	21.6409	0.819706
$698$	−5.48025	−0.207431
$699$	10.3304	0.390732
$700$	−28.4318	−1.07462
$701$	17.1825	0.648974	0.324487	−	0.945890i	$-0.394808\pi$
$701$	17.1825	0.648974	0.324487	+	0.945890i	$0.394808\pi$
$702$	−5.07083	−0.191386
$703$	0	0
$704$	1.00000	0.0376889
$705$	−87.6469	−3.30097
$706$	−23.2866	−0.876404
$707$	45.9453	1.72795
$708$	0.0138096	0.000518995 0
$709$	−34.4823	−1.29501	−0.647505	−	0.762061i	$-0.724188\pi$
$709$	−34.4823	−1.29501	−0.647505	+	0.762061i	$0.724188\pi$
$710$	23.9286	0.898026
$711$	−0.0629482	−0.00236074
$712$	4.14468	0.155329
$713$	−61.7426	−2.31228
$714$	−12.7694	−0.477884
$715$	−4.14457	−0.154998
$716$	−8.94841	−0.334418
$717$	−3.60333	−0.134569
$718$	−12.4962	−0.466353
$719$	20.6583	0.770425	0.385213	−	0.922828i	$-0.374128\pi$
$719$	20.6583	0.770425	0.385213	+	0.922828i	$0.374128\pi$
$720$	1.92538	0.0717546
$721$	−53.9717	−2.01001
$722$	0	0
$723$	33.3122	1.23889
$724$	−14.3106	−0.531849
$725$	−70.1800	−2.60642
$726$	−1.87195	−0.0694747
$727$	−18.5327	−0.687341	−0.343671	−	0.939090i	$-0.611670\pi$
$727$	−18.5327	−0.687341	−0.343671	+	0.939090i	$0.611670\pi$
$728$	−3.22064	−0.119365
$729$	21.0649	0.780181
$730$	36.1452	1.33780
$731$	18.5544	0.686261
$732$	2.19709	0.0812069
$733$	−49.3980	−1.82456	−0.912278	−	0.409571i	$-0.865678\pi$
$733$	−49.3980	−1.82456	−0.912278	+	0.409571i	$0.865678\pi$
$734$	−17.7649	−0.655713
$735$	12.9030	0.475934
$736$	7.37385	0.271804
$737$	−4.51665	−0.166373
$738$	4.74655	0.174723
$739$	−10.9118	−0.401396	−0.200698	−	0.979653i	$-0.564321\pi$
$739$	−10.9118	−0.401396	−0.200698	+	0.979653i	$0.564321\pi$
$740$	34.7729	1.27828
$741$	0	0
$742$	−9.77509	−0.358855
$743$	−5.36485	−0.196817	−0.0984086	−	0.995146i	$-0.531375\pi$
$743$	−5.36485	−0.196817	−0.0984086	+	0.995146i	$0.531375\pi$
$744$	−15.6742	−0.574645
$745$	−18.9740	−0.695154
$746$	−21.2672	−0.778648
$747$	5.50026	0.201244
$748$	−2.29885	−0.0840542
$749$	−33.4345	−1.22167
$750$	−32.7504	−1.19588
$751$	−11.2786	−0.411562	−0.205781	−	0.978598i	$-0.565973\pi$
$751$	−11.2786	−0.411562	−0.205781	+	0.978598i	$0.565973\pi$
$752$	−12.2614	−0.447126
$753$	10.4410	0.380492
$754$	−7.94971	−0.289511
$755$	−11.7744	−0.428514
$756$	13.8634	0.504206
$757$	−1.61383	−0.0586558	−0.0293279	−	0.999570i	$-0.509337\pi$
$757$	−1.61383	−0.0586558	−0.0293279	+	0.999570i	$0.509337\pi$
$758$	20.3995	0.740944
$759$	−13.8035	−0.501035
$760$	0	0
$761$	8.37790	0.303699	0.151849	−	0.988404i	$-0.451477\pi$
$761$	8.37790	0.303699	0.151849	+	0.988404i	$0.451477\pi$
$762$	−12.1590	−0.440474
$763$	−15.5784	−0.563976
$764$	21.7899	0.788330
$765$	−4.42615	−0.160028
$766$	17.1052	0.618038
$767$	−0.00800684	−0.000289110 0
$768$	1.87195	0.0675483
$769$	−49.9882	−1.80262	−0.901310	−	0.433174i	$-0.857393\pi$
$769$	−49.9882	−1.80262	−0.901310	+	0.433174i	$0.857393\pi$
$770$	11.3310	0.408342
$771$	−24.2698	−0.874055
$772$	0.295692	0.0106422
$773$	−41.7519	−1.50171	−0.750855	−	0.660467i	$-0.770358\pi$
$773$	−41.7519	−1.50171	−0.750855	+	0.660467i	$0.770358\pi$
$774$	4.06959	0.146279
$775$	80.2287	2.88190
$776$	−1.40370	−0.0503898
$777$	−50.5824	−1.81463
$778$	−4.54851	−0.163072
$779$	0	0
$780$	−7.75844	−0.277797
$781$	−6.26636	−0.224228
$782$	−16.9513	−0.606179
$783$	34.2198	1.22292
$784$	1.80506	0.0644665
$785$	−30.2356	−1.07916
$786$	12.2839	0.438151
$787$	15.2904	0.545046	0.272523	−	0.962149i	$-0.412142\pi$
$787$	15.2904	0.545046	0.272523	+	0.962149i	$0.412142\pi$
$788$	−12.7105	−0.452792
$789$	−30.8870	−1.09961
$790$	0.476730	0.0169613
$791$	−0.207187	−0.00736673
$792$	−0.504212	−0.0179164
$793$	−1.27388	−0.0452369
$794$	12.8646	0.456546
$795$	−23.5479	−0.835159
$796$	5.90529	0.209307
$797$	17.9368	0.635352	0.317676	−	0.948199i	$-0.397098\pi$
$797$	17.9368	0.635352	0.317676	+	0.948199i	$0.397098\pi$
$798$	0	0
$799$	28.1870	0.997184
$800$	−9.58162	−0.338761
$801$	−2.08980	−0.0738394
$802$	−23.0448	−0.813742
$803$	−9.46560	−0.334034
$804$	−8.45496	−0.298184
$805$	83.5532	2.94486
$806$	9.08798	0.320110
$807$	47.4143	1.66906
$808$	15.4837	0.544715
$809$	32.1261	1.12950	0.564748	−	0.825264i	$-0.308974\pi$
$809$	32.1261	1.12950	0.564748	+	0.825264i	$0.308974\pi$
$810$	39.1726	1.37639
$811$	33.9239	1.19123	0.595615	−	0.803270i	$-0.296908\pi$
$811$	33.9239	1.19123	0.595615	+	0.803270i	$0.296908\pi$
$812$	21.7341	0.762716
$813$	−29.3790	−1.03036
$814$	−9.10622	−0.319173
$815$	−9.96562	−0.349081
$816$	−4.30334	−0.150647
$817$	0	0
$818$	−14.9884	−0.524057
$819$	1.62389	0.0567432
$820$	−35.9474	−1.25534
$821$	−21.1765	−0.739066	−0.369533	−	0.929218i	$-0.620482\pi$
$821$	−21.1765	−0.739066	−0.369533	+	0.929218i	$0.620482\pi$
$822$	16.9238	0.590284
$823$	14.8707	0.518359	0.259179	−	0.965829i	$-0.416548\pi$
$823$	14.8707	0.518359	0.259179	+	0.965829i	$0.416548\pi$
$824$	−18.1886	−0.633630
$825$	17.9363	0.624463
$826$	0.0218903	0.000761660 0
$827$	−18.7958	−0.653593	−0.326797	−	0.945095i	$-0.605969\pi$
$827$	−18.7958	−0.653593	−0.326797	+	0.945095i	$0.605969\pi$
$828$	−3.71798	−0.129209
$829$	−29.4697	−1.02352	−0.511762	−	0.859127i	$-0.671007\pi$
$829$	−29.4697	−1.02352	−0.511762	+	0.859127i	$0.671007\pi$
$830$	−41.6556	−1.44589
$831$	12.7090	0.440872
$832$	−1.08537	−0.0376283
$833$	−4.14956	−0.143774
$834$	−38.0650	−1.31808
$835$	42.5085	1.47107
$836$	0	0
$837$	−39.1195	−1.35217
$838$	30.8820	1.06680
$839$	10.9072	0.376558	0.188279	−	0.982116i	$-0.439709\pi$
$839$	10.9072	0.376558	0.188279	+	0.982116i	$0.439709\pi$
$840$	21.2111	0.731854
$841$	24.6475	0.849915
$842$	−38.1631	−1.31519
$843$	4.35594	0.150027
$844$	14.7186	0.506636
$845$	−45.1433	−1.55298
$846$	6.18232	0.212553
$847$	−2.96733	−0.101959
$848$	−3.29423	−0.113124
$849$	−52.2340	−1.79266
$850$	22.0267	0.755508
$851$	−67.1479	−2.30180
$852$	−11.7303	−0.401875
$853$	53.8255	1.84295	0.921474	−	0.388439i	$-0.126986\pi$
$853$	53.8255	1.84295	0.921474	+	0.388439i	$0.126986\pi$
$854$	3.48273	0.119177
$855$	0	0
$856$	−11.2675	−0.385116
$857$	−2.08805	−0.0713263	−0.0356632	−	0.999364i	$-0.511354\pi$
$857$	−2.08805	−0.0713263	−0.0356632	+	0.999364i	$0.511354\pi$
$858$	2.03176	0.0693630
$859$	52.6452	1.79623	0.898116	−	0.439758i	$-0.144936\pi$
$859$	52.6452	1.79623	0.898116	+	0.439758i	$0.144936\pi$
$860$	−30.8206	−1.05097
$861$	52.2909	1.78207
$862$	0.821524	0.0279812
$863$	−38.5995	−1.31394	−0.656972	−	0.753915i	$-0.728163\pi$
$863$	−38.5995	−1.31394	−0.656972	+	0.753915i	$0.728163\pi$
$864$	4.67200	0.158945
$865$	13.6636	0.464576
$866$	−5.53382	−0.188047
$867$	−21.9305	−0.744799
$868$	−24.8460	−0.843329
$869$	−0.124845	−0.00423506
$870$	52.3568	1.77506
$871$	4.90222	0.166105
$872$	−5.24997	−0.177786
$873$	0.707762	0.0239541
$874$	0	0
$875$	−51.9144	−1.75503
$876$	−17.7192	−0.598675
$877$	−46.2658	−1.56228	−0.781142	−	0.624353i	$-0.785363\pi$
$877$	−46.2658	−1.56228	−0.781142	+	0.624353i	$0.785363\pi$
$878$	0.815891	0.0275350
$879$	−58.1145	−1.96015
$880$	3.81859	0.128725
$881$	6.38988	0.215281	0.107640	−	0.994190i	$-0.465671\pi$
$881$	6.38988	0.215281	0.107640	+	0.994190i	$0.465671\pi$
$882$	−0.910134	−0.0306458
$883$	15.1988	0.511482	0.255741	−	0.966745i	$-0.417681\pi$
$883$	15.1988	0.511482	0.255741	+	0.966745i	$0.417681\pi$
$884$	2.49509	0.0839190
$885$	0.0527330	0.00177260
$886$	29.0886	0.977252
$887$	−18.7819	−0.630634	−0.315317	−	0.948986i	$-0.602111\pi$
$887$	−18.7819	−0.630634	−0.315317	+	0.948986i	$0.602111\pi$
$888$	−17.0464	−0.572040
$889$	−19.2739	−0.646425
$890$	15.8268	0.530517
$891$	−10.2584	−0.343670
$892$	−4.70824	−0.157643
$893$	0	0
$894$	9.30147	0.311088
$895$	−34.1703	−1.14219
$896$	2.96733	0.0991316
$897$	14.9819	0.500230
$898$	−24.0614	−0.802940
$899$	−61.3290	−2.04544
$900$	4.83116	0.161039
$901$	7.57294	0.252291
$902$	9.41379	0.313445
$903$	44.8332	1.49195
$904$	−0.0698227	−0.00232227
$905$	−54.6463	−1.81650
$906$	5.77206	0.191764
$907$	−29.7445	−0.987650	−0.493825	−	0.869561i	$-0.664402\pi$
$907$	−29.7445	−0.987650	−0.493825	+	0.869561i	$0.664402\pi$
$908$	−18.3182	−0.607912
$909$	−7.80707	−0.258944
$910$	−12.2983	−0.407685
$911$	−5.87840	−0.194760	−0.0973801	−	0.995247i	$-0.531046\pi$
$911$	−5.87840	−0.194760	−0.0973801	+	0.995247i	$0.531046\pi$
$912$	0	0
$913$	10.9086	0.361023
$914$	15.8385	0.523893
$915$	8.38980	0.277358
$916$	0.455408	0.0150471
$917$	19.4718	0.643015
$918$	−10.7402	−0.354480
$919$	−10.1909	−0.336166	−0.168083	−	0.985773i	$-0.553758\pi$
$919$	−10.1909	−0.336166	−0.168083	+	0.985773i	$0.553758\pi$
$920$	28.1577	0.928332
$921$	49.9601	1.64624
$922$	17.1067	0.563378
$923$	6.80130	0.223867
$924$	−5.55471	−0.182737
$925$	87.2523	2.86884
$926$	−4.29074	−0.141002
$927$	9.17092	0.301212
$928$	7.32445	0.240437
$929$	−33.4090	−1.09611	−0.548057	−	0.836441i	$-0.684632\pi$
$929$	−33.4090	−1.09611	−0.548057	+	0.836441i	$0.684632\pi$
$930$	−59.8534	−1.96267
$931$	0	0
$932$	5.51851	0.180765
$933$	4.97051	0.162727
$934$	−31.5321	−1.03176
$935$	−8.77835	−0.287083
$936$	0.547255	0.0178876
$937$	9.09093	0.296988	0.148494	−	0.988913i	$-0.452557\pi$
$937$	9.09093	0.296988	0.148494	+	0.988913i	$0.452557\pi$
$938$	−13.4024	−0.437604
$939$	−55.1920	−1.80112
$940$	−46.8211	−1.52714
$941$	−2.66159	−0.0867652	−0.0433826	−	0.999059i	$-0.513813\pi$
$941$	−2.66159	−0.0867652	−0.0433826	+	0.999059i	$0.513813\pi$
$942$	14.8222	0.482932
$943$	69.4159	2.26049
$944$	0.00737709	0.000240104 0
$945$	52.9385	1.72209
$946$	8.07120	0.262417
$947$	−39.7554	−1.29188	−0.645938	−	0.763390i	$-0.723534\pi$
$947$	−39.7554	−1.29188	−0.645938	+	0.763390i	$0.723534\pi$
$948$	−0.233703	−0.00759033
$949$	10.2736	0.333497
$950$	0	0
$951$	−56.8945	−1.84493
$952$	−6.82144	−0.221084
$953$	−49.1457	−1.59199	−0.795993	−	0.605306i	$-0.793051\pi$
$953$	−49.1457	−1.59199	−0.795993	+	0.605306i	$0.793051\pi$
$954$	1.66099	0.0537766
$955$	83.2065	2.69250
$956$	−1.92490	−0.0622558
$957$	−13.7110	−0.443215
$958$	−22.9595	−0.741789
$959$	26.8267	0.866281
$960$	7.14822	0.230708
$961$	39.1103	1.26162
$962$	9.88358	0.318659
$963$	5.68122	0.183075
$964$	17.7954	0.573151
$965$	1.12913	0.0363479
$966$	−40.9596	−1.31785
$967$	12.1854	0.391855	0.195928	−	0.980618i	$-0.437228\pi$
$967$	12.1854	0.391855	0.195928	+	0.980618i	$0.437228\pi$
$968$	−1.00000	−0.0321412
$969$	0	0
$970$	−5.36015	−0.172104
$971$	−25.4970	−0.818239	−0.409119	−	0.912481i	$-0.634164\pi$
$971$	−25.4970	−0.818239	−0.409119	+	0.912481i	$0.634164\pi$
$972$	−5.18726	−0.166382
$973$	−60.3388	−1.93437
$974$	−6.90006	−0.221092
$975$	−19.4675	−0.623459
$976$	1.17369	0.0375689
$977$	−46.3120	−1.48165	−0.740825	−	0.671698i	$-0.765565\pi$
$977$	−46.3120	−1.48165	−0.740825	+	0.671698i	$0.765565\pi$
$978$	4.88536	0.156217
$979$	−4.14468	−0.132465
$980$	6.89279	0.220182
$981$	2.64710	0.0845153
$982$	−15.0255	−0.479485
$983$	−40.2568	−1.28399	−0.641997	−	0.766707i	$-0.721894\pi$
$983$	−40.2568	−1.28399	−0.641997	+	0.766707i	$0.721894\pi$
$984$	17.6222	0.561775
$985$	−48.5360	−1.54649
$986$	−16.8378	−0.536224
$987$	68.1083	2.16791
$988$	0	0
$989$	59.5158	1.89249
$990$	−1.92538	−0.0611925
$991$	37.4591	1.18993	0.594964	−	0.803752i	$-0.297166\pi$
$991$	37.4591	1.18993	0.594964	+	0.803752i	$0.297166\pi$
$992$	−8.37319	−0.265849
$993$	12.0993	0.383959
$994$	−18.5944	−0.589778
$995$	22.5499	0.714879
$996$	20.4205	0.647047
$997$	−24.8793	−0.787936	−0.393968	−	0.919124i	$-0.628898\pi$
$997$	−24.8793	−0.787936	−0.393968	+	0.919124i	$0.628898\pi$
$998$	21.6638	0.685755
$999$	−42.5443	−1.34604

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7942.2.a.bs.1.9		12
19.14	odd	18		418.2.j.b.177.3	yes	24
19.15	odd	18		418.2.j.b.111.3	✓	24
19.18	odd	2		7942.2.a.bw.1.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.j.b.111.3	✓	24	19.15	odd	18
418.2.j.b.177.3	yes	24	19.14	odd	18
7942.2.a.bs.1.9		12	1.1	even	1	trivial
7942.2.a.bw.1.4		12	19.18	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 7942 = 2 \cdot 11 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7942.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.87195 q^{3} +1.00000 q^{4} +3.81859 q^{5} -1.87195 q^{6} -2.96733 q^{7} -1.00000 q^{8} +0.504212 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.87195 q^{3} +1.00000 q^{4} +3.81859 q^{5} -1.87195 q^{6} -2.96733 q^{7} -1.00000 q^{8} +0.504212 q^{9} -3.81859 q^{10} +1.00000 q^{11} +1.87195 q^{12} -1.08537 q^{13} +2.96733 q^{14} +7.14822 q^{15} +1.00000 q^{16} -2.29885 q^{17} -0.504212 q^{18} +3.81859 q^{20} -5.55471 q^{21} -1.00000 q^{22} -7.37385 q^{23} -1.87195 q^{24} +9.58162 q^{25} +1.08537 q^{26} -4.67200 q^{27} -2.96733 q^{28} -7.32445 q^{29} -7.14822 q^{30} +8.37319 q^{31} -1.00000 q^{32} +1.87195 q^{33} +2.29885 q^{34} -11.3310 q^{35} +0.504212 q^{36} +9.10622 q^{37} -2.03176 q^{39} -3.81859 q^{40} -9.41379 q^{41} +5.55471 q^{42} -8.07120 q^{43} +1.00000 q^{44} +1.92538 q^{45} +7.37385 q^{46} -12.2614 q^{47} +1.87195 q^{48} +1.80506 q^{49} -9.58162 q^{50} -4.30334 q^{51} -1.08537 q^{52} -3.29423 q^{53} +4.67200 q^{54} +3.81859 q^{55} +2.96733 q^{56} +7.32445 q^{58} +0.00737709 q^{59} +7.14822 q^{60} +1.17369 q^{61} -8.37319 q^{62} -1.49616 q^{63} +1.00000 q^{64} -4.14457 q^{65} -1.87195 q^{66} -4.51665 q^{67} -2.29885 q^{68} -13.8035 q^{69} +11.3310 q^{70} -6.26636 q^{71} -0.504212 q^{72} -9.46560 q^{73} -9.10622 q^{74} +17.9363 q^{75} -2.96733 q^{77} +2.03176 q^{78} -0.124845 q^{79} +3.81859 q^{80} -10.2584 q^{81} +9.41379 q^{82} +10.9086 q^{83} -5.55471 q^{84} -8.77835 q^{85} +8.07120 q^{86} -13.7110 q^{87} -1.00000 q^{88} -4.14468 q^{89} -1.92538 q^{90} +3.22064 q^{91} -7.37385 q^{92} +15.6742 q^{93} +12.2614 q^{94} -1.87195 q^{96} +1.40370 q^{97} -1.80506 q^{98} +0.504212 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{2} + 3 q^{3} + 12 q^{4} - 9 q^{5} - 3 q^{6} - 12 q^{7} - 12 q^{8} + 15 q^{9}+O(q^{10}) \) 12 * q - 12 * q^2 + 3 * q^3 + 12 * q^4 - 9 * q^5 - 3 * q^6 - 12 * q^7 - 12 * q^8 + 15 * q^9	\( 12 q - 12 q^{2} + 3 q^{3} + 12 q^{4} - 9 q^{5} - 3 q^{6} - 12 q^{7} - 12 q^{8} + 15 q^{9} + 9 q^{10} + 12 q^{11} + 3 q^{12} + 12 q^{14} + 21 q^{15} + 12 q^{16} - 33 q^{17} - 15 q^{18} - 9 q^{20} - 9 q^{21} - 12 q^{22} - 18 q^{23} - 3 q^{24} + 15 q^{25} + 21 q^{27} - 12 q^{28} - 15 q^{29} - 21 q^{30} + 9 q^{31} - 12 q^{32} + 3 q^{33} + 33 q^{34} - 30 q^{35} + 15 q^{36} + 9 q^{37} - 6 q^{39} + 9 q^{40} - 15 q^{41} + 9 q^{42} - 21 q^{43} + 12 q^{44} + 18 q^{46} - 27 q^{47} + 3 q^{48} + 18 q^{49} - 15 q^{50} - 6 q^{51} + 6 q^{53} - 21 q^{54} - 9 q^{55} + 12 q^{56} + 15 q^{58} + 48 q^{59} + 21 q^{60} + 12 q^{61} - 9 q^{62} - 66 q^{63} + 12 q^{64} - 36 q^{65} - 3 q^{66} - 3 q^{67} - 33 q^{68} - 24 q^{69} + 30 q^{70} - 3 q^{71} - 15 q^{72} - 30 q^{73} - 9 q^{74} + 21 q^{75} - 12 q^{77} + 6 q^{78} + 12 q^{79} - 9 q^{80} + 12 q^{81} + 15 q^{82} - 66 q^{83} - 9 q^{84} + 15 q^{85} + 21 q^{86} - 51 q^{87} - 12 q^{88} + 30 q^{89} + 54 q^{91} - 18 q^{92} - 66 q^{93} + 27 q^{94} - 3 q^{96} + 36 q^{97} - 18 q^{98} + 15 q^{99}+O(q^{100}) \) 12 * q - 12 * q^2 + 3 * q^3 + 12 * q^4 - 9 * q^5 - 3 * q^6 - 12 * q^7 - 12 * q^8 + 15 * q^9 + 9 * q^10 + 12 * q^11 + 3 * q^12 + 12 * q^14 + 21 * q^15 + 12 * q^16 - 33 * q^17 - 15 * q^18 - 9 * q^20 - 9 * q^21 - 12 * q^22 - 18 * q^23 - 3 * q^24 + 15 * q^25 + 21 * q^27 - 12 * q^28 - 15 * q^29 - 21 * q^30 + 9 * q^31 - 12 * q^32 + 3 * q^33 + 33 * q^34 - 30 * q^35 + 15 * q^36 + 9 * q^37 - 6 * q^39 + 9 * q^40 - 15 * q^41 + 9 * q^42 - 21 * q^43 + 12 * q^44 + 18 * q^46 - 27 * q^47 + 3 * q^48 + 18 * q^49 - 15 * q^50 - 6 * q^51 + 6 * q^53 - 21 * q^54 - 9 * q^55 + 12 * q^56 + 15 * q^58 + 48 * q^59 + 21 * q^60 + 12 * q^61 - 9 * q^62 - 66 * q^63 + 12 * q^64 - 36 * q^65 - 3 * q^66 - 3 * q^67 - 33 * q^68 - 24 * q^69 + 30 * q^70 - 3 * q^71 - 15 * q^72 - 30 * q^73 - 9 * q^74 + 21 * q^75 - 12 * q^77 + 6 * q^78 + 12 * q^79 - 9 * q^80 + 12 * q^81 + 15 * q^82 - 66 * q^83 - 9 * q^84 + 15 * q^85 + 21 * q^86 - 51 * q^87 - 12 * q^88 + 30 * q^89 + 54 * q^91 - 18 * q^92 - 66 * q^93 + 27 * q^94 - 3 * q^96 + 36 * q^97 - 18 * q^98 + 15 * q^99

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