LMFDB - Embedded newform 7942.2.a.cc.1.3

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:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 6 x^{15} - 14 x^{14} + 128 x^{13} + 39 x^{12} - 1110 x^{11} + 348 x^{10} + 4996 x^{9} + \cdots - 359 $ x^16 - 6x^15 - 14x^14 + 128x^13 + 39x^12 - 1110x^11 + 348x^10 + 4996x^9 - 2932x^8 - 12256x^7 + 8993x^6 + 15430x^5 - 12896x^4 - 7688x^3 + 7371x^2 - 64*x - 359
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-1.89187$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} -2.89187 q^{3} +1.00000 q^{4} +2.32159 q^{5} +2.89187 q^{6} +0.619749 q^{7} -1.00000 q^{8} +5.36293 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.89187 q^{3} +1.00000 q^{4} +2.32159 q^{5} +2.89187 q^{6} +0.619749 q^{7} -1.00000 q^{8} +5.36293 q^{9} -2.32159 q^{10} -1.00000 q^{11} -2.89187 q^{12} -5.40808 q^{13} -0.619749 q^{14} -6.71375 q^{15} +1.00000 q^{16} -2.11092 q^{17} -5.36293 q^{18} +2.32159 q^{20} -1.79224 q^{21} +1.00000 q^{22} +1.91700 q^{23} +2.89187 q^{24} +0.389790 q^{25} +5.40808 q^{26} -6.83331 q^{27} +0.619749 q^{28} +8.17634 q^{29} +6.71375 q^{30} -2.15765 q^{31} -1.00000 q^{32} +2.89187 q^{33} +2.11092 q^{34} +1.43880 q^{35} +5.36293 q^{36} -8.95912 q^{37} +15.6395 q^{39} -2.32159 q^{40} +3.78171 q^{41} +1.79224 q^{42} +4.48084 q^{43} -1.00000 q^{44} +12.4505 q^{45} -1.91700 q^{46} +6.91886 q^{47} -2.89187 q^{48} -6.61591 q^{49} -0.389790 q^{50} +6.10453 q^{51} -5.40808 q^{52} +13.0641 q^{53} +6.83331 q^{54} -2.32159 q^{55} -0.619749 q^{56} -8.17634 q^{58} -0.481748 q^{59} -6.71375 q^{60} -10.4685 q^{61} +2.15765 q^{62} +3.32367 q^{63} +1.00000 q^{64} -12.5554 q^{65} -2.89187 q^{66} +12.9284 q^{67} -2.11092 q^{68} -5.54373 q^{69} -1.43880 q^{70} +0.861495 q^{71} -5.36293 q^{72} +0.742559 q^{73} +8.95912 q^{74} -1.12722 q^{75} -0.619749 q^{77} -15.6395 q^{78} +13.7382 q^{79} +2.32159 q^{80} +3.67226 q^{81} -3.78171 q^{82} -9.63754 q^{83} -1.79224 q^{84} -4.90070 q^{85} -4.48084 q^{86} -23.6449 q^{87} +1.00000 q^{88} -12.1655 q^{89} -12.4505 q^{90} -3.35165 q^{91} +1.91700 q^{92} +6.23965 q^{93} -6.91886 q^{94} +2.89187 q^{96} -8.77484 q^{97} +6.61591 q^{98} -5.36293 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16 q^{2} - 10 q^{3} + 16 q^{4} + 10 q^{6} + 6 q^{7} - 16 q^{8} + 20 q^{9}+O(q^{10}) $ 16 * q - 16 * q^2 - 10 * q^3 + 16 * q^4 + 10 * q^6 + 6 * q^7 - 16 * q^8 + 20 * q^9	$ 16 q - 16 q^{2} - 10 q^{3} + 16 q^{4} + 10 q^{6} + 6 q^{7} - 16 q^{8} + 20 q^{9} - 16 q^{11} - 10 q^{12} + 2 q^{13} - 6 q^{14} + 8 q^{15} + 16 q^{16} - 20 q^{18} - 6 q^{21} + 16 q^{22} - 6 q^{23} + 10 q^{24} + 18 q^{25} - 2 q^{26} - 46 q^{27} + 6 q^{28} - 28 q^{29} - 8 q^{30} - 8 q^{31} - 16 q^{32} + 10 q^{33} + 14 q^{35} + 20 q^{36} - 32 q^{37} + 24 q^{39} - 24 q^{41} + 6 q^{42} + 28 q^{43} - 16 q^{44} - 16 q^{45} + 6 q^{46} + 32 q^{47} - 10 q^{48} + 16 q^{49} - 18 q^{50} - 14 q^{51} + 2 q^{52} - 16 q^{53} + 46 q^{54} - 6 q^{56} + 28 q^{58} - 30 q^{59} + 8 q^{60} - 8 q^{61} + 8 q^{62} - 8 q^{63} + 16 q^{64} - 26 q^{65} - 10 q^{66} - 44 q^{67} - 16 q^{69} - 14 q^{70} - 36 q^{71} - 20 q^{72} + 10 q^{73} + 32 q^{74} - 76 q^{75} - 6 q^{77} - 24 q^{78} + 16 q^{79} + 48 q^{81} + 24 q^{82} + 12 q^{83} - 6 q^{84} - 4 q^{85} - 28 q^{86} + 24 q^{87} + 16 q^{88} - 32 q^{89} + 16 q^{90} + 24 q^{91} - 6 q^{92} - 14 q^{93} - 32 q^{94} + 10 q^{96} - 52 q^{97} - 16 q^{98} - 20 q^{99}+O(q^{100}) $ 16 * q - 16 * q^2 - 10 * q^3 + 16 * q^4 + 10 * q^6 + 6 * q^7 - 16 * q^8 + 20 * q^9 - 16 * q^11 - 10 * q^12 + 2 * q^13 - 6 * q^14 + 8 * q^15 + 16 * q^16 - 20 * q^18 - 6 * q^21 + 16 * q^22 - 6 * q^23 + 10 * q^24 + 18 * q^25 - 2 * q^26 - 46 * q^27 + 6 * q^28 - 28 * q^29 - 8 * q^30 - 8 * q^31 - 16 * q^32 + 10 * q^33 + 14 * q^35 + 20 * q^36 - 32 * q^37 + 24 * q^39 - 24 * q^41 + 6 * q^42 + 28 * q^43 - 16 * q^44 - 16 * q^45 + 6 * q^46 + 32 * q^47 - 10 * q^48 + 16 * q^49 - 18 * q^50 - 14 * q^51 + 2 * q^52 - 16 * q^53 + 46 * q^54 - 6 * q^56 + 28 * q^58 - 30 * q^59 + 8 * q^60 - 8 * q^61 + 8 * q^62 - 8 * q^63 + 16 * q^64 - 26 * q^65 - 10 * q^66 - 44 * q^67 - 16 * q^69 - 14 * q^70 - 36 * q^71 - 20 * q^72 + 10 * q^73 + 32 * q^74 - 76 * q^75 - 6 * q^77 - 24 * q^78 + 16 * q^79 + 48 * q^81 + 24 * q^82 + 12 * q^83 - 6 * q^84 - 4 * q^85 - 28 * q^86 + 24 * q^87 + 16 * q^88 - 32 * q^89 + 16 * q^90 + 24 * q^91 - 6 * q^92 - 14 * q^93 - 32 * q^94 + 10 * q^96 - 52 * q^97 - 16 * q^98 - 20 * 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
$3$	−2.89187	−1.66962	−0.834812	−	0.550535i	$-0.814424\pi$
$3$	−2.89187	−1.66962	−0.834812	+	0.550535i	$0.814424\pi$
$4$	1.00000	0.500000
$5$	2.32159	1.03825	0.519124	−	0.854699i	$-0.326258\pi$
$5$	2.32159	1.03825	0.519124	+	0.854699i	$0.326258\pi$
$6$	2.89187	1.18060
$7$	0.619749	0.234243	0.117122	−	0.993118i	$-0.462633\pi$
$7$	0.619749	0.234243	0.117122	+	0.993118i	$0.462633\pi$
$8$	−1.00000	−0.353553
$9$	5.36293	1.78764
$10$	−2.32159	−0.734152
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−2.89187	−0.834812
$13$	−5.40808	−1.49993	−0.749966	−	0.661476i	$-0.769930\pi$
$13$	−5.40808	−1.49993	−0.749966	+	0.661476i	$0.769930\pi$
$14$	−0.619749	−0.165635
$15$	−6.71375	−1.73348
$16$	1.00000	0.250000
$17$	−2.11092	−0.511974	−0.255987	−	0.966680i	$-0.582400\pi$
$17$	−2.11092	−0.511974	−0.255987	+	0.966680i	$0.582400\pi$
$18$	−5.36293	−1.26406
$19$	0	0
$19$	0	0
$20$	2.32159	0.519124
$21$	−1.79224	−0.391098
$22$	1.00000	0.213201
$23$	1.91700	0.399723	0.199861	−	0.979824i	$-0.435951\pi$
$23$	1.91700	0.399723	0.199861	+	0.979824i	$0.435951\pi$
$24$	2.89187	0.590301
$25$	0.389790	0.0779581
$26$	5.40808	1.06061
$27$	−6.83331	−1.31507
$28$	0.619749	0.117122
$29$	8.17634	1.51831	0.759154	−	0.650911i	$-0.225613\pi$
$29$	8.17634	1.51831	0.759154	+	0.650911i	$0.225613\pi$
$30$	6.71375	1.22576
$31$	−2.15765	−0.387525	−0.193763	−	0.981048i	$-0.562069\pi$
$31$	−2.15765	−0.387525	−0.193763	+	0.981048i	$0.562069\pi$
$32$	−1.00000	−0.176777
$33$	2.89187	0.503411
$34$	2.11092	0.362020
$35$	1.43880	0.243202
$36$	5.36293	0.893822
$37$	−8.95912	−1.47287	−0.736435	−	0.676508i	$-0.763493\pi$
$37$	−8.95912	−1.47287	−0.736435	+	0.676508i	$0.763493\pi$
$38$	0	0
$39$	15.6395	2.50432
$40$	−2.32159	−0.367076
$41$	3.78171	0.590604	0.295302	−	0.955404i	$-0.404580\pi$
$41$	3.78171	0.590604	0.295302	+	0.955404i	$0.404580\pi$
$42$	1.79224	0.276548
$43$	4.48084	0.683322	0.341661	−	0.939823i	$-0.389011\pi$
$43$	4.48084	0.683322	0.341661	+	0.939823i	$0.389011\pi$
$44$	−1.00000	−0.150756
$45$	12.4505	1.85602
$46$	−1.91700	−0.282647
$47$	6.91886	1.00922	0.504610	−	0.863347i	$-0.331636\pi$
$47$	6.91886	1.00922	0.504610	+	0.863347i	$0.331636\pi$
$48$	−2.89187	−0.417406
$49$	−6.61591	−0.945130
$50$	−0.389790	−0.0551247
$51$	6.10453	0.854805
$52$	−5.40808	−0.749966
$53$	13.0641	1.79449	0.897246	−	0.441531i	$-0.145565\pi$
$53$	13.0641	1.79449	0.897246	+	0.441531i	$0.145565\pi$
$54$	6.83331	0.929895
$55$	−2.32159	−0.313043
$56$	−0.619749	−0.0828174
$57$	0	0
$58$	−8.17634	−1.07361
$59$	−0.481748	−0.0627183	−0.0313591	−	0.999508i	$-0.509984\pi$
$59$	−0.481748	−0.0627183	−0.0313591	+	0.999508i	$0.509984\pi$
$60$	−6.71375	−0.866742
$61$	−10.4685	−1.34036	−0.670178	−	0.742200i	$-0.733782\pi$
$61$	−10.4685	−1.34036	−0.670178	+	0.742200i	$0.733782\pi$
$62$	2.15765	0.274022
$63$	3.32367	0.418743
$64$	1.00000	0.125000
$65$	−12.5554	−1.55730
$66$	−2.89187	−0.355965
$67$	12.9284	1.57945	0.789727	−	0.613459i	$-0.210222\pi$
$67$	12.9284	1.57945	0.789727	+	0.613459i	$0.210222\pi$
$68$	−2.11092	−0.255987
$69$	−5.54373	−0.667387
$70$	−1.43880	−0.171970
$71$	0.861495	0.102241	0.0511203	−	0.998693i	$-0.483721\pi$
$71$	0.861495	0.102241	0.0511203	+	0.998693i	$0.483721\pi$
$72$	−5.36293	−0.632028
$73$	0.742559	0.0869099	0.0434550	−	0.999055i	$-0.486163\pi$
$73$	0.742559	0.0869099	0.0434550	+	0.999055i	$0.486163\pi$
$74$	8.95912	1.04148
$75$	−1.12722	−0.130161
$76$	0	0
$77$	−0.619749	−0.0706270
$78$	−15.6395	−1.77082
$79$	13.7382	1.54566	0.772832	−	0.634611i	$-0.218840\pi$
$79$	13.7382	1.54566	0.772832	+	0.634611i	$0.218840\pi$
$80$	2.32159	0.259562
$81$	3.67226	0.408029
$82$	−3.78171	−0.417620
$83$	−9.63754	−1.05786	−0.528929	−	0.848666i	$-0.677406\pi$
$83$	−9.63754	−1.05786	−0.528929	+	0.848666i	$0.677406\pi$
$84$	−1.79224	−0.195549
$85$	−4.90070	−0.531556
$86$	−4.48084	−0.483182
$87$	−23.6449	−2.53500
$88$	1.00000	0.106600
$89$	−12.1655	−1.28954	−0.644771	−	0.764376i	$-0.723047\pi$
$89$	−12.1655	−1.28954	−0.644771	+	0.764376i	$0.723047\pi$
$90$	−12.4505	−1.31240
$91$	−3.35165	−0.351349
$92$	1.91700	0.199861
$93$	6.23965	0.647021
$94$	−6.91886	−0.713626
$95$	0	0
$96$	2.89187	0.295151
$97$	−8.77484	−0.890950	−0.445475	−	0.895294i	$-0.646965\pi$
$97$	−8.77484	−0.890950	−0.445475	+	0.895294i	$0.646965\pi$
$98$	6.61591	0.668308
$99$	−5.36293	−0.538995
$100$	0.389790	0.0389790
$101$	14.3939	1.43224	0.716121	−	0.697976i	$-0.245916\pi$
$101$	14.3939	1.43224	0.716121	+	0.697976i	$0.245916\pi$
$102$	−6.10453	−0.604438
$103$	−16.6584	−1.64140	−0.820699	−	0.571360i	$-0.806416\pi$
$103$	−16.6584	−1.64140	−0.820699	+	0.571360i	$0.806416\pi$
$104$	5.40808	0.530306
$105$	−4.16084	−0.406056
$106$	−13.0641	−1.26890
$107$	0.00662935	0.000640884 0	0.000320442	−	1.00000i	$-0.499898\pi$
$107$	0.00662935	0.000640884 0	0.000320442		1.00000i	$0.499898\pi$
$108$	−6.83331	−0.657535
$109$	−0.514933	−0.0493216	−0.0246608	−	0.999696i	$-0.507851\pi$
$109$	−0.514933	−0.0493216	−0.0246608	+	0.999696i	$0.507851\pi$
$110$	2.32159	0.221355
$111$	25.9087	2.45914
$112$	0.619749	0.0585608
$113$	−5.66743	−0.533147	−0.266574	−	0.963815i	$-0.585892\pi$
$113$	−5.66743	−0.533147	−0.266574	+	0.963815i	$0.585892\pi$
$114$	0	0
$115$	4.45050	0.415011
$116$	8.17634	0.759154
$117$	−29.0032	−2.68135
$118$	0.481748	0.0443485
$119$	−1.30824	−0.119926
$120$	6.71375	0.612879
$121$	1.00000	0.0909091
$122$	10.4685	0.947775
$123$	−10.9362	−0.986086
$124$	−2.15765	−0.193763
$125$	−10.7030	−0.957308
$126$	−3.32367	−0.296096
$127$	2.31759	0.205653	0.102826	−	0.994699i	$-0.467211\pi$
$127$	2.31759	0.205653	0.102826	+	0.994699i	$0.467211\pi$
$128$	−1.00000	−0.0883883
$129$	−12.9580	−1.14089
$130$	12.5554	1.10118
$131$	−12.7061	−1.11014	−0.555071	−	0.831803i	$-0.687309\pi$
$131$	−12.7061	−1.11014	−0.555071	+	0.831803i	$0.687309\pi$
$132$	2.89187	0.251705
$133$	0	0
$134$	−12.9284	−1.11684
$135$	−15.8642	−1.36537
$136$	2.11092	0.181010
$137$	6.24091	0.533197	0.266598	−	0.963808i	$-0.414100\pi$
$137$	6.24091	0.533197	0.266598	+	0.963808i	$0.414100\pi$
$138$	5.54373	0.471914
$139$	−13.2842	−1.12675	−0.563374	−	0.826202i	$-0.690497\pi$
$139$	−13.2842	−1.12675	−0.563374	+	0.826202i	$0.690497\pi$
$140$	1.43880	0.121601
$141$	−20.0085	−1.68502
$142$	−0.861495	−0.0722951
$143$	5.40808	0.452247
$144$	5.36293	0.446911
$145$	18.9821	1.57638
$146$	−0.742559	−0.0614546
$147$	19.1324	1.57801
$148$	−8.95912	−0.736435
$149$	18.9794	1.55485	0.777427	−	0.628973i	$-0.216524\pi$
$149$	18.9794	1.55485	0.777427	+	0.628973i	$0.216524\pi$
$150$	1.12722	0.0920375
$151$	9.04462	0.736040	0.368020	−	0.929818i	$-0.380036\pi$
$151$	9.04462	0.736040	0.368020	+	0.929818i	$0.380036\pi$
$152$	0	0
$153$	−11.3207	−0.915228
$154$	0.619749	0.0499408
$155$	−5.00918	−0.402347
$156$	15.6395	1.25216
$157$	−9.51959	−0.759746	−0.379873	−	0.925039i	$-0.624032\pi$
$157$	−9.51959	−0.759746	−0.379873	+	0.925039i	$0.624032\pi$
$158$	−13.7382	−1.09295
$159$	−37.7797	−2.99613
$160$	−2.32159	−0.183538
$161$	1.18806	0.0936323
$162$	−3.67226	−0.288520
$163$	−2.53944	−0.198904	−0.0994520	−	0.995042i	$-0.531709\pi$
$163$	−2.53944	−0.198904	−0.0994520	+	0.995042i	$0.531709\pi$
$164$	3.78171	0.295302
$165$	6.71375	0.522665
$166$	9.63754	0.748018
$167$	−4.96767	−0.384410	−0.192205	−	0.981355i	$-0.561564\pi$
$167$	−4.96767	−0.384410	−0.192205	+	0.981355i	$0.561564\pi$
$168$	1.79224	0.138274
$169$	16.2474	1.24980
$170$	4.90070	0.375867
$171$	0	0
$172$	4.48084	0.341661
$173$	−1.31861	−0.100252	−0.0501261	−	0.998743i	$-0.515962\pi$
$173$	−1.31861	−0.100252	−0.0501261	+	0.998743i	$0.515962\pi$
$174$	23.6449	1.79252
$175$	0.241572	0.0182611
$176$	−1.00000	−0.0753778
$177$	1.39316	0.104716
$178$	12.1655	0.911844
$179$	11.7844	0.880806	0.440403	−	0.897800i	$-0.354835\pi$
$179$	11.7844	0.880806	0.440403	+	0.897800i	$0.354835\pi$
$180$	12.4505	0.928009
$181$	21.4956	1.59775	0.798877	−	0.601495i	$-0.205428\pi$
$181$	21.4956	1.59775	0.798877	+	0.601495i	$0.205428\pi$
$182$	3.35165	0.248441
$183$	30.2736	2.23789
$184$	−1.91700	−0.141323
$185$	−20.7994	−1.52920
$186$	−6.23965	−0.457513
$187$	2.11092	0.154366
$188$	6.91886	0.504610
$189$	−4.23494	−0.308046
$190$	0	0
$191$	19.9002	1.43993	0.719966	−	0.694010i	$-0.244157\pi$
$191$	19.9002	1.43993	0.719966	+	0.694010i	$0.244157\pi$
$192$	−2.89187	−0.208703
$193$	−18.6371	−1.34153	−0.670763	−	0.741672i	$-0.734033\pi$
$193$	−18.6371	−1.34153	−0.670763	+	0.741672i	$0.734033\pi$
$194$	8.77484	0.629997
$195$	36.3085	2.60011
$196$	−6.61591	−0.472565
$197$	−23.9710	−1.70786	−0.853931	−	0.520386i	$-0.825788\pi$
$197$	−23.9710	−1.70786	−0.853931	+	0.520386i	$0.825788\pi$
$198$	5.36293	0.381127
$199$	−13.1332	−0.930990	−0.465495	−	0.885050i	$-0.654124\pi$
$199$	−13.1332	−0.930990	−0.465495	+	0.885050i	$0.654124\pi$
$200$	−0.389790	−0.0275623
$201$	−37.3872	−2.63709
$202$	−14.3939	−1.01275
$203$	5.06728	0.355653
$204$	6.10453	0.427402
$205$	8.77959	0.613193
$206$	16.6584	1.16064
$207$	10.2808	0.714563
$208$	−5.40808	−0.374983
$209$	0	0
$210$	4.16084	0.287125
$211$	10.6845	0.735550	0.367775	−	0.929915i	$-0.380120\pi$
$211$	10.6845	0.735550	0.367775	+	0.929915i	$0.380120\pi$
$212$	13.0641	0.897246
$213$	−2.49134	−0.170704
$214$	−0.00662935	−0.000453173 0
$215$	10.4027	0.709457
$216$	6.83331	0.464948
$217$	−1.33720	−0.0907751
$218$	0.514933	0.0348757
$219$	−2.14739	−0.145107
$220$	−2.32159	−0.156522
$221$	11.4160	0.767927
$222$	−25.9087	−1.73888
$223$	5.53560	0.370691	0.185346	−	0.982673i	$-0.440660\pi$
$223$	5.53560	0.370691	0.185346	+	0.982673i	$0.440660\pi$
$224$	−0.619749	−0.0414087
$225$	2.09042	0.139361
$226$	5.66743	0.376992
$227$	−19.4971	−1.29407	−0.647033	−	0.762462i	$-0.723990\pi$
$227$	−19.4971	−1.29407	−0.647033	+	0.762462i	$0.723990\pi$
$228$	0	0
$229$	−11.7003	−0.773176	−0.386588	−	0.922253i	$-0.626346\pi$
$229$	−11.7003	−0.773176	−0.386588	+	0.922253i	$0.626346\pi$
$230$	−4.45050	−0.293457
$231$	1.79224	0.117920
$232$	−8.17634	−0.536803
$233$	−4.24414	−0.278043	−0.139021	−	0.990289i	$-0.544396\pi$
$233$	−4.24414	−0.278043	−0.139021	+	0.990289i	$0.544396\pi$
$234$	29.0032	1.89600
$235$	16.0628	1.04782
$236$	−0.481748	−0.0313591
$237$	−39.7290	−2.58068
$238$	1.30824	0.0848008
$239$	21.6536	1.40065	0.700327	−	0.713822i	$-0.253037\pi$
$239$	21.6536	1.40065	0.700327	+	0.713822i	$0.253037\pi$
$240$	−6.71375	−0.433371
$241$	3.32772	0.214358	0.107179	−	0.994240i	$-0.465818\pi$
$241$	3.32772	0.214358	0.107179	+	0.994240i	$0.465818\pi$
$242$	−1.00000	−0.0642824
$243$	9.88021	0.633816
$244$	−10.4685	−0.670178
$245$	−15.3594	−0.981279
$246$	10.9362	0.697268
$247$	0	0
$248$	2.15765	0.137011
$249$	27.8705	1.76622
$250$	10.7030	0.676919
$251$	2.71655	0.171467	0.0857335	−	0.996318i	$-0.472677\pi$
$251$	2.71655	0.171467	0.0857335	+	0.996318i	$0.472677\pi$
$252$	3.32367	0.209372
$253$	−1.91700	−0.120521
$254$	−2.31759	−0.145418
$255$	14.1722	0.887499
$256$	1.00000	0.0625000
$257$	−12.2152	−0.761965	−0.380983	−	0.924582i	$-0.624414\pi$
$257$	−12.2152	−0.761965	−0.380983	+	0.924582i	$0.624414\pi$
$258$	12.9580	0.806732
$259$	−5.55241	−0.345010
$260$	−12.5554	−0.778650
$261$	43.8492	2.71420
$262$	12.7061	0.784989
$263$	30.2313	1.86414	0.932072	−	0.362273i	$-0.117999\pi$
$263$	30.2313	1.86414	0.932072	+	0.362273i	$0.117999\pi$
$264$	−2.89187	−0.177983
$265$	30.3295	1.86313
$266$	0	0
$267$	35.1811	2.15305
$268$	12.9284	0.789727
$269$	−31.0692	−1.89432	−0.947161	−	0.320759i	$-0.896062\pi$
$269$	−31.0692	−1.89432	−0.947161	+	0.320759i	$0.896062\pi$
$270$	15.8642	0.965462
$271$	29.0175	1.76269	0.881344	−	0.472475i	$-0.156639\pi$
$271$	29.0175	1.76269	0.881344	+	0.472475i	$0.156639\pi$
$272$	−2.11092	−0.127994
$273$	9.69256	0.586620
$274$	−6.24091	−0.377027
$275$	−0.389790	−0.0235052
$276$	−5.54373	−0.333694
$277$	18.5680	1.11564	0.557822	−	0.829960i	$-0.311637\pi$
$277$	18.5680	1.11564	0.557822	+	0.829960i	$0.311637\pi$
$278$	13.2842	0.796731
$279$	−11.5713	−0.692757
$280$	−1.43880	−0.0859850
$281$	−5.54419	−0.330739	−0.165369	−	0.986232i	$-0.552882\pi$
$281$	−5.54419	−0.330739	−0.165369	+	0.986232i	$0.552882\pi$
$282$	20.0085	1.19149
$283$	−30.4821	−1.81197	−0.905986	−	0.423307i	$-0.860869\pi$
$283$	−30.4821	−1.81197	−0.905986	+	0.423307i	$0.860869\pi$
$284$	0.861495	0.0511203
$285$	0	0
$286$	−5.40808	−0.319787
$287$	2.34371	0.138345
$288$	−5.36293	−0.316014
$289$	−12.5440	−0.737882
$290$	−18.9821	−1.11467
$291$	25.3757	1.48755
$292$	0.742559	0.0434550
$293$	7.21344	0.421414	0.210707	−	0.977549i	$-0.432423\pi$
$293$	7.21344	0.421414	0.210707	+	0.977549i	$0.432423\pi$
$294$	−19.1324	−1.11582
$295$	−1.11842	−0.0651171
$296$	8.95912	0.520739
$297$	6.83331	0.396509
$298$	−18.9794	−1.09945
$299$	−10.3673	−0.599557
$300$	−1.12722	−0.0650803
$301$	2.77700	0.160063
$302$	−9.04462	−0.520459
$303$	−41.6252	−2.39131
$304$	0	0
$305$	−24.3036	−1.39162
$306$	11.3207	0.647164
$307$	7.84149	0.447538	0.223769	−	0.974642i	$-0.428164\pi$
$307$	7.84149	0.447538	0.223769	+	0.974642i	$0.428164\pi$
$308$	−0.619749	−0.0353135
$309$	48.1739	2.74052
$310$	5.00918	0.284502
$311$	17.4791	0.991149	0.495574	−	0.868565i	$-0.334958\pi$
$311$	17.4791	0.991149	0.495574	+	0.868565i	$0.334958\pi$
$312$	−15.6395	−0.885412
$313$	−13.4316	−0.759198	−0.379599	−	0.925151i	$-0.623938\pi$
$313$	−13.4316	−0.759198	−0.379599	+	0.925151i	$0.623938\pi$
$314$	9.51959	0.537221
$315$	7.71621	0.434759
$316$	13.7382	0.772832
$317$	−28.7600	−1.61532	−0.807661	−	0.589648i	$-0.799267\pi$
$317$	−28.7600	−1.61532	−0.807661	+	0.589648i	$0.799267\pi$
$318$	37.7797	2.11858
$319$	−8.17634	−0.457787
$320$	2.32159	0.129781
$321$	−0.0191713	−0.00107004
$322$	−1.18806	−0.0662081
$323$	0	0
$324$	3.67226	0.204015
$325$	−2.10802	−0.116932
$326$	2.53944	0.140646
$327$	1.48912	0.0823486
$328$	−3.78171	−0.208810
$329$	4.28796	0.236403
$330$	−6.71375	−0.369580
$331$	24.4732	1.34517	0.672584	−	0.740021i	$-0.265184\pi$
$331$	24.4732	1.34517	0.672584	+	0.740021i	$0.265184\pi$
$332$	−9.63754	−0.528929
$333$	−48.0472	−2.63297
$334$	4.96767	0.271819
$335$	30.0144	1.63986
$336$	−1.79224	−0.0977745
$337$	17.0286	0.927608	0.463804	−	0.885938i	$-0.346484\pi$
$337$	17.0286	0.927608	0.463804	+	0.885938i	$0.346484\pi$
$338$	−16.2474	−0.883740
$339$	16.3895	0.890155
$340$	−4.90070	−0.265778
$341$	2.15765	0.116843
$342$	0	0
$343$	−8.43845	−0.455633
$344$	−4.48084	−0.241591
$345$	−12.8703	−0.692913
$346$	1.31861	0.0708890
$347$	−34.4158	−1.84754	−0.923768	−	0.382952i	$-0.874907\pi$
$347$	−34.4158	−1.84754	−0.923768	+	0.382952i	$0.874907\pi$
$348$	−23.6449	−1.26750
$349$	6.30432	0.337462	0.168731	−	0.985662i	$-0.446033\pi$
$349$	6.30432	0.337462	0.168731	+	0.985662i	$0.446033\pi$
$350$	−0.241572	−0.0129126
$351$	36.9551	1.97252
$352$	1.00000	0.0533002
$353$	−0.0980516	−0.00521876	−0.00260938	−	0.999997i	$-0.500831\pi$
$353$	−0.0980516	−0.00521876	−0.00260938	+	0.999997i	$0.500831\pi$
$354$	−1.39316	−0.0740454
$355$	2.00004	0.106151
$356$	−12.1655	−0.644771
$357$	3.78327	0.200232
$358$	−11.7844	−0.622824
$359$	16.0003	0.844462	0.422231	−	0.906488i	$-0.361247\pi$
$359$	16.0003	0.844462	0.422231	+	0.906488i	$0.361247\pi$
$360$	−12.4505	−0.656201
$361$	0	0
$362$	−21.4956	−1.12978
$363$	−2.89187	−0.151784
$364$	−3.35165	−0.175674
$365$	1.72392	0.0902340
$366$	−30.2736	−1.58243
$367$	27.5175	1.43640	0.718201	−	0.695836i	$-0.244966\pi$
$367$	27.5175	1.43640	0.718201	+	0.695836i	$0.244966\pi$
$368$	1.91700	0.0999307
$369$	20.2811	1.05579
$370$	20.7994	1.08131
$371$	8.09646	0.420347
$372$	6.23965	0.323511
$373$	0.106435	0.00551101	0.00275550	−	0.999996i	$-0.499123\pi$
$373$	0.106435	0.00551101	0.00275550	+	0.999996i	$0.499123\pi$
$374$	−2.11092	−0.109153
$375$	30.9518	1.59834
$376$	−6.91886	−0.356813
$377$	−44.2183	−2.27736
$378$	4.23494	0.217822
$379$	−24.2776	−1.24705	−0.623527	−	0.781802i	$-0.714301\pi$
$379$	−24.2776	−1.24705	−0.623527	+	0.781802i	$0.714301\pi$
$380$	0	0
$381$	−6.70217	−0.343363
$382$	−19.9002	−1.01819
$383$	−9.18773	−0.469471	−0.234736	−	0.972059i	$-0.575422\pi$
$383$	−9.18773	−0.469471	−0.234736	+	0.972059i	$0.575422\pi$
$384$	2.89187	0.147575
$385$	−1.43880	−0.0733283
$386$	18.6371	0.948602
$387$	24.0305	1.22154
$388$	−8.77484	−0.445475
$389$	−16.1614	−0.819414	−0.409707	−	0.912217i	$-0.634369\pi$
$389$	−16.1614	−0.819414	−0.409707	+	0.912217i	$0.634369\pi$
$390$	−36.3085	−1.83855
$391$	−4.04665	−0.204648
$392$	6.61591	0.334154
$393$	36.7446	1.85352
$394$	23.9710	1.20764
$395$	31.8944	1.60478
$396$	−5.36293	−0.269498
$397$	15.0342	0.754547	0.377274	−	0.926102i	$-0.376862\pi$
$397$	15.0342	0.754547	0.377274	+	0.926102i	$0.376862\pi$
$398$	13.1332	0.658309
$399$	0	0
$400$	0.389790	0.0194895
$401$	−33.5824	−1.67702	−0.838512	−	0.544883i	$-0.816574\pi$
$401$	−33.5824	−1.67702	−0.838512	+	0.544883i	$0.816574\pi$
$402$	37.3872	1.86471
$403$	11.6687	0.581261
$404$	14.3939	0.716121
$405$	8.52549	0.423635
$406$	−5.06728	−0.251485
$407$	8.95912	0.444087
$408$	−6.10453	−0.302219
$409$	21.8421	1.08002	0.540012	−	0.841657i	$-0.318420\pi$
$409$	21.8421	1.08002	0.540012	+	0.841657i	$0.318420\pi$
$410$	−8.77959	−0.433593
$411$	−18.0479	−0.890239
$412$	−16.6584	−0.820699
$413$	−0.298563	−0.0146913
$414$	−10.2808	−0.505272
$415$	−22.3744	−1.09832
$416$	5.40808	0.265153
$417$	38.4161	1.88125
$418$	0	0
$419$	−23.3426	−1.14036	−0.570180	−	0.821520i	$-0.693126\pi$
$419$	−23.3426	−1.14036	−0.570180	+	0.821520i	$0.693126\pi$
$420$	−4.16084	−0.203028
$421$	−23.2798	−1.13459	−0.567294	−	0.823515i	$-0.692010\pi$
$421$	−23.2798	−1.13459	−0.567294	+	0.823515i	$0.692010\pi$
$422$	−10.6845	−0.520112
$423$	37.1054	1.80413
$424$	−13.0641	−0.634449
$425$	−0.822818	−0.0399125
$426$	2.49134	0.120706
$427$	−6.48785	−0.313969
$428$	0.00662935	0.000320442 0
$429$	−15.6395	−0.755082
$430$	−10.4027	−0.501662
$431$	6.03661	0.290774	0.145387	−	0.989375i	$-0.453557\pi$
$431$	6.03661	0.290774	0.145387	+	0.989375i	$0.453557\pi$
$432$	−6.83331	−0.328768
$433$	16.8667	0.810563	0.405281	−	0.914192i	$-0.367174\pi$
$433$	16.8667	0.810563	0.405281	+	0.914192i	$0.367174\pi$
$434$	1.33720	0.0641877
$435$	−54.8939	−2.63196
$436$	−0.514933	−0.0246608
$437$	0	0
$438$	2.14739	0.102606
$439$	3.95501	0.188762	0.0943811	−	0.995536i	$-0.469913\pi$
$439$	3.95501	0.188762	0.0943811	+	0.995536i	$0.469913\pi$
$440$	2.32159	0.110678
$441$	−35.4807	−1.68956
$442$	−11.4160	−0.543006
$443$	−19.0506	−0.905123	−0.452561	−	0.891733i	$-0.649490\pi$
$443$	−19.0506	−0.905123	−0.452561	+	0.891733i	$0.649490\pi$
$444$	25.9087	1.22957
$445$	−28.2434	−1.33886
$446$	−5.53560	−0.262118
$447$	−54.8861	−2.59602
$448$	0.619749	0.0292804
$449$	−29.3987	−1.38741	−0.693705	−	0.720259i	$-0.744023\pi$
$449$	−29.3987	−1.38741	−0.693705	+	0.720259i	$0.744023\pi$
$450$	−2.09042	−0.0985434
$451$	−3.78171	−0.178074
$452$	−5.66743	−0.266574
$453$	−26.1559	−1.22891
$454$	19.4971	0.915042
$455$	−7.78117	−0.364787
$456$	0	0
$457$	−36.6925	−1.71640	−0.858200	−	0.513315i	$-0.828417\pi$
$457$	−36.6925	−1.71640	−0.858200	+	0.513315i	$0.828417\pi$
$458$	11.7003	0.546718
$459$	14.4246	0.673282
$460$	4.45050	0.207506
$461$	−11.3329	−0.527824	−0.263912	−	0.964547i	$-0.585013\pi$
$461$	−11.3329	−0.527824	−0.263912	+	0.964547i	$0.585013\pi$
$462$	−1.79224	−0.0833824
$463$	−36.9188	−1.71576	−0.857880	−	0.513850i	$-0.828219\pi$
$463$	−36.9188	−1.71576	−0.857880	+	0.513850i	$0.828219\pi$
$464$	8.17634	0.379577
$465$	14.4859	0.671768
$466$	4.24414	0.196606
$467$	−16.4547	−0.761434	−0.380717	−	0.924692i	$-0.624323\pi$
$467$	−16.4547	−0.761434	−0.380717	+	0.924692i	$0.624323\pi$
$468$	−29.0032	−1.34067
$469$	8.01235	0.369976
$470$	−16.0628	−0.740921
$471$	27.5294	1.26849
$472$	0.481748	0.0221743
$473$	−4.48084	−0.206029
$474$	39.7290	1.82481
$475$	0	0
$476$	−1.30824	−0.0599632
$477$	70.0619	3.20791
$478$	−21.6536	−0.990413
$479$	24.0495	1.09885	0.549424	−	0.835544i	$-0.314847\pi$
$479$	24.0495	1.09885	0.549424	+	0.835544i	$0.314847\pi$
$480$	6.71375	0.306439
$481$	48.4517	2.20921
$482$	−3.32772	−0.151574
$483$	−3.43572	−0.156331
$484$	1.00000	0.0454545
$485$	−20.3716	−0.925027
$486$	−9.88021	−0.448175
$487$	−21.1149	−0.956806	−0.478403	−	0.878140i	$-0.658784\pi$
$487$	−21.1149	−0.956806	−0.478403	+	0.878140i	$0.658784\pi$
$488$	10.4685	0.473888
$489$	7.34373	0.332095
$490$	15.3594	0.693869
$491$	−13.4381	−0.606451	−0.303225	−	0.952919i	$-0.598063\pi$
$491$	−13.4381	−0.606451	−0.303225	+	0.952919i	$0.598063\pi$
$492$	−10.9362	−0.493043
$493$	−17.2596	−0.777335
$494$	0	0
$495$	−12.4505	−0.559610
$496$	−2.15765	−0.0968813
$497$	0.533911	0.0239492
$498$	−27.8705	−1.24891
$499$	4.37364	0.195791	0.0978955	−	0.995197i	$-0.468789\pi$
$499$	4.37364	0.195791	0.0978955	+	0.995197i	$0.468789\pi$
$500$	−10.7030	−0.478654
$501$	14.3659	0.641821
$502$	−2.71655	−0.121245
$503$	−14.6289	−0.652270	−0.326135	−	0.945323i	$-0.605746\pi$
$503$	−14.6289	−0.652270	−0.326135	+	0.945323i	$0.605746\pi$
$504$	−3.32367	−0.148048
$505$	33.4167	1.48702
$506$	1.91700	0.0852212
$507$	−46.9853	−2.08669
$508$	2.31759	0.102826
$509$	−1.11532	−0.0494356	−0.0247178	−	0.999694i	$-0.507869\pi$
$509$	−1.11532	−0.0494356	−0.0247178	+	0.999694i	$0.507869\pi$
$510$	−14.1722	−0.627556
$511$	0.460200	0.0203581
$512$	−1.00000	−0.0441942
$513$	0	0
$514$	12.2152	0.538791
$515$	−38.6740	−1.70418
$516$	−12.9580	−0.570445
$517$	−6.91886	−0.304291
$518$	5.55241	0.243959
$519$	3.81326	0.167383
$520$	12.5554	0.550589
$521$	−32.9296	−1.44267	−0.721337	−	0.692584i	$-0.756472\pi$
$521$	−32.9296	−1.44267	−0.721337	+	0.692584i	$0.756472\pi$
$522$	−43.8492	−1.91923
$523$	−1.24956	−0.0546393	−0.0273196	−	0.999627i	$-0.508697\pi$
$523$	−1.24956	−0.0546393	−0.0273196	+	0.999627i	$0.508697\pi$
$524$	−12.7061	−0.555071
$525$	−0.698596	−0.0304892
$526$	−30.2313	−1.31815
$527$	4.55463	0.198403
$528$	2.89187	0.125853
$529$	−19.3251	−0.840222
$530$	−30.3295	−1.31743
$531$	−2.58359	−0.112118
$532$	0	0
$533$	−20.4518	−0.885865
$534$	−35.1811	−1.52244
$535$	0.0153907	0.000665396 0
$536$	−12.9284	−0.558421
$537$	−34.0790	−1.47062
$538$	31.0692	1.33949
$539$	6.61591	0.284967
$540$	−15.8642	−0.682685
$541$	−27.6391	−1.18830	−0.594150	−	0.804355i	$-0.702511\pi$
$541$	−27.6391	−1.18830	−0.594150	+	0.804355i	$0.702511\pi$
$542$	−29.0175	−1.24641
$543$	−62.1625	−2.66765
$544$	2.11092	0.0905051
$545$	−1.19546	−0.0512081
$546$	−9.69256	−0.414803
$547$	−33.5431	−1.43420	−0.717100	−	0.696970i	$-0.754531\pi$
$547$	−33.5431	−1.43420	−0.717100	+	0.696970i	$0.754531\pi$
$548$	6.24091	0.266598
$549$	−56.1420	−2.39608
$550$	0.389790	0.0166207
$551$	0	0
$552$	5.54373	0.235957
$553$	8.51421	0.362061
$554$	−18.5680	−0.788880
$555$	60.1493	2.55320
$556$	−13.2842	−0.563374
$557$	−25.5181	−1.08124	−0.540618	−	0.841269i	$-0.681809\pi$
$557$	−25.5181	−1.08124	−0.540618	+	0.841269i	$0.681809\pi$
$558$	11.5713	0.489853
$559$	−24.2328	−1.02494
$560$	1.43880	0.0608006
$561$	−6.10453	−0.257733
$562$	5.54419	0.233868
$563$	−4.25894	−0.179493	−0.0897464	−	0.995965i	$-0.528606\pi$
$563$	−4.25894	−0.179493	−0.0897464	+	0.995965i	$0.528606\pi$
$564$	−20.0085	−0.842509
$565$	−13.1575	−0.553539
$566$	30.4821	1.28126
$567$	2.27588	0.0955780
$568$	−0.861495	−0.0361475
$569$	42.9292	1.79968	0.899842	−	0.436215i	$-0.143681\pi$
$569$	42.9292	1.79968	0.899842	+	0.436215i	$0.143681\pi$
$570$	0	0
$571$	5.03496	0.210707	0.105353	−	0.994435i	$-0.466403\pi$
$571$	5.03496	0.210707	0.105353	+	0.994435i	$0.466403\pi$
$572$	5.40808	0.226123
$573$	−57.5490	−2.40414
$574$	−2.34371	−0.0978246
$575$	0.747230	0.0311616
$576$	5.36293	0.223456
$577$	−6.40331	−0.266573	−0.133287	−	0.991078i	$-0.542553\pi$
$577$	−6.40331	−0.266573	−0.133287	+	0.991078i	$0.542553\pi$
$578$	12.5440	0.521762
$579$	53.8961	2.23985
$580$	18.9821	0.788190
$581$	−5.97286	−0.247796
$582$	−25.3757	−1.05186
$583$	−13.0641	−0.541060
$584$	−0.742559	−0.0307273
$585$	−67.3336	−2.78390
$586$	−7.21344	−0.297984
$587$	5.17993	0.213799	0.106899	−	0.994270i	$-0.465908\pi$
$587$	5.17993	0.213799	0.106899	+	0.994270i	$0.465908\pi$
$588$	19.1324	0.789006
$589$	0	0
$590$	1.11842	0.0460448
$591$	69.3211	2.85149
$592$	−8.95912	−0.368218
$593$	8.73765	0.358812	0.179406	−	0.983775i	$-0.442582\pi$
$593$	8.73765	0.358812	0.179406	+	0.983775i	$0.442582\pi$
$594$	−6.83331	−0.280374
$595$	−3.03721	−0.124513
$596$	18.9794	0.777427
$597$	37.9797	1.55440
$598$	10.3673	0.423951
$599$	−17.6096	−0.719509	−0.359755	−	0.933047i	$-0.617140\pi$
$599$	−17.6096	−0.719509	−0.359755	+	0.933047i	$0.617140\pi$
$600$	1.12722	0.0460188
$601$	−5.24893	−0.214108	−0.107054	−	0.994253i	$-0.534142\pi$
$601$	−5.24893	−0.214108	−0.107054	+	0.994253i	$0.534142\pi$
$602$	−2.77700	−0.113182
$603$	69.3341	2.82350
$604$	9.04462	0.368020
$605$	2.32159	0.0943861
$606$	41.6252	1.69091
$607$	−46.2940	−1.87901	−0.939507	−	0.342529i	$-0.888716\pi$
$607$	−46.2940	−1.87901	−0.939507	+	0.342529i	$0.888716\pi$
$608$	0	0
$609$	−14.6539	−0.593807
$610$	24.3036	0.984025
$611$	−37.4178	−1.51376
$612$	−11.3207	−0.457614
$613$	−8.68969	−0.350973	−0.175487	−	0.984482i	$-0.556150\pi$
$613$	−8.68969	−0.350973	−0.175487	+	0.984482i	$0.556150\pi$
$614$	−7.84149	−0.316457
$615$	−25.3895	−1.02380
$616$	0.619749	0.0249704
$617$	22.3672	0.900470	0.450235	−	0.892910i	$-0.351340\pi$
$617$	22.3672	0.900470	0.450235	+	0.892910i	$0.351340\pi$
$618$	−48.1739	−1.93784
$619$	−41.5812	−1.67129	−0.835644	−	0.549272i	$-0.814905\pi$
$619$	−41.5812	−1.67129	−0.835644	+	0.549272i	$0.814905\pi$
$620$	−5.00918	−0.201173
$621$	−13.0995	−0.525664
$622$	−17.4791	−0.700848
$623$	−7.53957	−0.302066
$624$	15.6395	0.626081
$625$	−26.7970	−1.07188
$626$	13.4316	0.536834
$627$	0	0
$628$	−9.51959	−0.379873
$629$	18.9120	0.754072
$630$	−7.71621	−0.307421
$631$	32.5792	1.29696	0.648479	−	0.761232i	$-0.275405\pi$
$631$	32.5792	1.29696	0.648479	+	0.761232i	$0.275405\pi$
$632$	−13.7382	−0.546475
$633$	−30.8982	−1.22809
$634$	28.7600	1.14220
$635$	5.38050	0.213518
$636$	−37.7797	−1.49806
$637$	35.7794	1.41763
$638$	8.17634	0.323704
$639$	4.62014	0.182770
$640$	−2.32159	−0.0917690
$641$	−38.7763	−1.53157	−0.765786	−	0.643096i	$-0.777650\pi$
$641$	−38.7763	−1.53157	−0.765786	+	0.643096i	$0.777650\pi$
$642$	0.0191713	0.000756629 0
$643$	5.13255	0.202408	0.101204	−	0.994866i	$-0.467731\pi$
$643$	5.13255	0.202408	0.101204	+	0.994866i	$0.467731\pi$
$644$	1.18806	0.0468162
$645$	−30.0833	−1.18453
$646$	0	0
$647$	3.97575	0.156303	0.0781514	−	0.996942i	$-0.475098\pi$
$647$	3.97575	0.156303	0.0781514	+	0.996942i	$0.475098\pi$
$648$	−3.67226	−0.144260
$649$	0.481748	0.0189103
$650$	2.10802	0.0826833
$651$	3.86701	0.151560
$652$	−2.53944	−0.0994520
$653$	−4.02352	−0.157452	−0.0787262	−	0.996896i	$-0.525085\pi$
$653$	−4.02352	−0.157452	−0.0787262	+	0.996896i	$0.525085\pi$
$654$	−1.48912	−0.0582292
$655$	−29.4985	−1.15260
$656$	3.78171	0.147651
$657$	3.98229	0.155364
$658$	−4.28796	−0.167162
$659$	−1.46203	−0.0569526	−0.0284763	−	0.999594i	$-0.509066\pi$
$659$	−1.46203	−0.0569526	−0.0284763	+	0.999594i	$0.509066\pi$
$660$	6.71375	0.261332
$661$	39.8928	1.55165	0.775825	−	0.630948i	$-0.217334\pi$
$661$	39.8928	1.55165	0.775825	+	0.630948i	$0.217334\pi$
$662$	−24.4732	−0.951177
$663$	−33.0138	−1.28215
$664$	9.63754	0.374009
$665$	0	0
$666$	48.0472	1.86179
$667$	15.6741	0.606903
$668$	−4.96767	−0.192205
$669$	−16.0082	−0.618915
$670$	−30.0144	−1.15956
$671$	10.4685	0.404133
$672$	1.79224	0.0691370
$673$	35.6620	1.37467	0.687334	−	0.726342i	$-0.258781\pi$
$673$	35.6620	1.37467	0.687334	+	0.726342i	$0.258781\pi$
$674$	−17.0286	−0.655918
$675$	−2.66356	−0.102520
$676$	16.2474	0.624898
$677$	37.6649	1.44758	0.723790	−	0.690020i	$-0.242398\pi$
$677$	37.6649	1.44758	0.723790	+	0.690020i	$0.242398\pi$
$678$	−16.3895	−0.629435
$679$	−5.43820	−0.208699
$680$	4.90070	0.187933
$681$	56.3830	2.16060
$682$	−2.15765	−0.0826206
$683$	18.0520	0.690739	0.345369	−	0.938467i	$-0.387754\pi$
$683$	18.0520	0.690739	0.345369	+	0.938467i	$0.387754\pi$
$684$	0	0
$685$	14.4888	0.553590
$686$	8.43845	0.322181
$687$	33.8357	1.29091
$688$	4.48084	0.170830
$689$	−70.6517	−2.69162
$690$	12.8703	0.489964
$691$	26.0974	0.992793	0.496396	−	0.868096i	$-0.334656\pi$
$691$	26.0974	0.992793	0.496396	+	0.868096i	$0.334656\pi$
$692$	−1.31861	−0.0501261
$693$	−3.32367	−0.126256
$694$	34.4158	1.30641
$695$	−30.8404	−1.16984
$696$	23.6449	0.896259
$697$	−7.98290	−0.302374
$698$	−6.30432	−0.238622
$699$	12.2735	0.464227
$700$	0.241572	0.00913057
$701$	−24.9874	−0.943762	−0.471881	−	0.881662i	$-0.656425\pi$
$701$	−24.9874	−0.943762	−0.471881	+	0.881662i	$0.656425\pi$
$702$	−36.9551	−1.39478
$703$	0	0
$704$	−1.00000	−0.0376889
$705$	−46.4515	−1.74947
$706$	0.0980516	0.00369022
$707$	8.92058	0.335493
$708$	1.39316	0.0523580
$709$	−48.3712	−1.81662	−0.908310	−	0.418299i	$-0.862627\pi$
$709$	−48.3712	−1.81662	−0.908310	+	0.418299i	$0.862627\pi$
$710$	−2.00004	−0.0750602
$711$	73.6768	2.76310
$712$	12.1655	0.455922
$713$	−4.13622	−0.154903
$714$	−3.78327	−0.141585
$715$	12.5554	0.469544
$716$	11.7844	0.440403
$717$	−62.6195	−2.33857
$718$	−16.0003	−0.597125
$719$	−10.2500	−0.382262	−0.191131	−	0.981565i	$-0.561216\pi$
$719$	−10.2500	−0.382262	−0.191131	+	0.981565i	$0.561216\pi$
$720$	12.4505	0.464004
$721$	−10.3240	−0.384486
$722$	0	0
$723$	−9.62336	−0.357897
$724$	21.4956	0.798877
$725$	3.18706	0.118364
$726$	2.89187	0.107328
$727$	36.9962	1.37211	0.686057	−	0.727548i	$-0.259340\pi$
$727$	36.9962	1.37211	0.686057	+	0.727548i	$0.259340\pi$
$728$	3.35165	0.124221
$729$	−39.5891	−1.46626
$730$	−1.72392	−0.0638051
$731$	−9.45871	−0.349843
$732$	30.2736	1.11895
$733$	1.52188	0.0562121	0.0281060	−	0.999605i	$-0.491052\pi$
$733$	1.52188	0.0562121	0.0281060	+	0.999605i	$0.491052\pi$
$734$	−27.5175	−1.01569
$735$	44.4176	1.63837
$736$	−1.91700	−0.0706617
$737$	−12.9284	−0.476223
$738$	−20.2811	−0.746556
$739$	0.458020	0.0168485	0.00842427	−	0.999965i	$-0.497318\pi$
$739$	0.458020	0.0168485	0.00842427	+	0.999965i	$0.497318\pi$
$740$	−20.7994	−0.764602
$741$	0	0
$742$	−8.09646	−0.297230
$743$	−2.67829	−0.0982569	−0.0491284	−	0.998792i	$-0.515644\pi$
$743$	−2.67829	−0.0982569	−0.0491284	+	0.998792i	$0.515644\pi$
$744$	−6.23965	−0.228757
$745$	44.0625	1.61432
$746$	−0.106435	−0.00389687
$747$	−51.6855	−1.89107
$748$	2.11092	0.0771830
$749$	0.00410854	0.000150123 0
$750$	−30.9518	−1.13020
$751$	−0.642767	−0.0234549	−0.0117274	−	0.999931i	$-0.503733\pi$
$751$	−0.642767	−0.0234549	−0.0117274	+	0.999931i	$0.503733\pi$
$752$	6.91886	0.252305
$753$	−7.85591	−0.286285
$754$	44.2183	1.61034
$755$	20.9979	0.764192
$756$	−4.23494	−0.154023
$757$	6.09908	0.221675	0.110837	−	0.993839i	$-0.464647\pi$
$757$	6.09908	0.221675	0.110837	+	0.993839i	$0.464647\pi$
$758$	24.2776	0.881800
$759$	5.54373	0.201225
$760$	0	0
$761$	3.82471	0.138646	0.0693229	−	0.997594i	$-0.477916\pi$
$761$	3.82471	0.138646	0.0693229	+	0.997594i	$0.477916\pi$
$762$	6.70217	0.242794
$763$	−0.319129	−0.0115533
$764$	19.9002	0.719966
$765$	−26.2822	−0.950233
$766$	9.18773	0.331966
$767$	2.60533	0.0940732
$768$	−2.89187	−0.104352
$769$	29.0596	1.04791	0.523957	−	0.851745i	$-0.324455\pi$
$769$	29.0596	1.04791	0.523957	+	0.851745i	$0.324455\pi$
$770$	1.43880	0.0518509
$771$	35.3249	1.27220
$772$	−18.6371	−0.670763
$773$	−30.7089	−1.10452	−0.552261	−	0.833671i	$-0.686235\pi$
$773$	−30.7089	−1.10452	−0.552261	+	0.833671i	$0.686235\pi$
$774$	−24.0305	−0.863757
$775$	−0.841030	−0.0302107
$776$	8.77484	0.314998
$777$	16.0569	0.576037
$778$	16.1614	0.579413
$779$	0	0
$780$	36.3085	1.30005
$781$	−0.861495	−0.0308267
$782$	4.04665	0.144708
$783$	−55.8715	−1.99668
$784$	−6.61591	−0.236283
$785$	−22.1006	−0.788804
$786$	−36.7446	−1.31064
$787$	−36.8187	−1.31245	−0.656223	−	0.754567i	$-0.727847\pi$
$787$	−36.8187	−1.31245	−0.656223	+	0.754567i	$0.727847\pi$
$788$	−23.9710	−0.853931
$789$	−87.4252	−3.11242
$790$	−31.8944	−1.13475
$791$	−3.51239	−0.124886
$792$	5.36293	0.190564
$793$	56.6146	2.01044
$794$	−15.0342	−0.533545
$795$	−87.7091	−3.11072
$796$	−13.1332	−0.465495
$797$	22.9649	0.813458	0.406729	−	0.913549i	$-0.366669\pi$
$797$	22.9649	0.813458	0.406729	+	0.913549i	$0.366669\pi$
$798$	0	0
$799$	−14.6052	−0.516695
$800$	−0.389790	−0.0137812
$801$	−65.2429	−2.30524
$802$	33.5824	1.18584
$803$	−0.742559	−0.0262043
$804$	−37.3872	−1.31855
$805$	2.75819	0.0972136
$806$	−11.6687	−0.411014
$807$	89.8482	3.16281
$808$	−14.3939	−0.506374
$809$	41.7631	1.46831	0.734157	−	0.678980i	$-0.237578\pi$
$809$	41.7631	1.46831	0.734157	+	0.678980i	$0.237578\pi$
$810$	−8.52549	−0.299555
$811$	−42.0544	−1.47673	−0.738365	−	0.674401i	$-0.764402\pi$
$811$	−42.0544	−1.47673	−0.738365	+	0.674401i	$0.764402\pi$
$812$	5.06728	0.177827
$813$	−83.9150	−2.94303
$814$	−8.95912	−0.314017
$815$	−5.89553	−0.206512
$816$	6.10453	0.213701
$817$	0	0
$818$	−21.8421	−0.763692
$819$	−17.9747	−0.628087
$820$	8.77959	0.306596
$821$	−5.15499	−0.179910	−0.0899552	−	0.995946i	$-0.528672\pi$
$821$	−5.15499	−0.179910	−0.0899552	+	0.995946i	$0.528672\pi$
$822$	18.0479	0.629494
$823$	−43.7778	−1.52600	−0.763000	−	0.646399i	$-0.776274\pi$
$823$	−43.7778	−1.52600	−0.763000	+	0.646399i	$0.776274\pi$
$824$	16.6584	0.580322
$825$	1.12722	0.0392449
$826$	0.298563	0.0103883
$827$	24.6212	0.856161	0.428081	−	0.903741i	$-0.359190\pi$
$827$	24.6212	0.856161	0.428081	+	0.903741i	$0.359190\pi$
$828$	10.2808	0.357281
$829$	22.3734	0.777062	0.388531	−	0.921436i	$-0.372983\pi$
$829$	22.3734	0.777062	0.388531	+	0.921436i	$0.372983\pi$
$830$	22.3744	0.776628
$831$	−53.6964	−1.86271
$832$	−5.40808	−0.187492
$833$	13.9657	0.483882
$834$	−38.4161	−1.33024
$835$	−11.5329	−0.399113
$836$	0	0
$837$	14.7439	0.509623
$838$	23.3426	0.806356
$839$	37.3558	1.28967	0.644833	−	0.764323i	$-0.276927\pi$
$839$	37.3558	1.28967	0.644833	+	0.764323i	$0.276927\pi$
$840$	4.16084	0.143563
$841$	37.8525	1.30526
$842$	23.2798	0.802275
$843$	16.0331	0.552209
$844$	10.6845	0.367775
$845$	37.7197	1.29760
$846$	−37.1054	−1.27571
$847$	0.619749	0.0212948
$848$	13.0641	0.448623
$849$	88.1504	3.02531
$850$	0.822818	0.0282224
$851$	−17.1747	−0.588740
$852$	−2.49134	−0.0853518
$853$	−39.2497	−1.34388	−0.671942	−	0.740604i	$-0.734539\pi$
$853$	−39.2497	−1.34388	−0.671942	+	0.740604i	$0.734539\pi$
$854$	6.48785	0.222010
$855$	0	0
$856$	−0.00662935	−0.000226587 0
$857$	11.8591	0.405098	0.202549	−	0.979272i	$-0.435077\pi$
$857$	11.8591	0.405098	0.202549	+	0.979272i	$0.435077\pi$
$858$	15.6395	0.533923
$859$	4.76206	0.162479	0.0812396	−	0.996695i	$-0.474112\pi$
$859$	4.76206	0.162479	0.0812396	+	0.996695i	$0.474112\pi$
$860$	10.4027	0.354729
$861$	−6.77771	−0.230984
$862$	−6.03661	−0.205608
$863$	−34.6110	−1.17817	−0.589086	−	0.808070i	$-0.700512\pi$
$863$	−34.6110	−1.17817	−0.589086	+	0.808070i	$0.700512\pi$
$864$	6.83331	0.232474
$865$	−3.06128	−0.104087
$866$	−16.8667	−0.573154
$867$	36.2757	1.23199
$868$	−1.33720	−0.0453875
$869$	−13.7382	−0.466035
$870$	54.8939	1.86108
$871$	−69.9178	−2.36907
$872$	0.514933	0.0174378
$873$	−47.0589	−1.59270
$874$	0	0
$875$	−6.63319	−0.224243
$876$	−2.14739	−0.0725535
$877$	−9.62162	−0.324899	−0.162449	−	0.986717i	$-0.551939\pi$
$877$	−9.62162	−0.324899	−0.162449	+	0.986717i	$0.551939\pi$
$878$	−3.95501	−0.133475
$879$	−20.8604	−0.703603
$880$	−2.32159	−0.0782609
$881$	28.6583	0.965523	0.482762	−	0.875752i	$-0.339634\pi$
$881$	28.6583	0.965523	0.482762	+	0.875752i	$0.339634\pi$
$882$	35.4807	1.19470
$883$	−20.9891	−0.706340	−0.353170	−	0.935559i	$-0.614896\pi$
$883$	−20.9891	−0.706340	−0.353170	+	0.935559i	$0.614896\pi$
$884$	11.4160	0.383963
$885$	3.23434	0.108721
$886$	19.0506	0.640019
$887$	21.4493	0.720196	0.360098	−	0.932914i	$-0.382743\pi$
$887$	21.4493	0.720196	0.360098	+	0.932914i	$0.382743\pi$
$888$	−25.9087	−0.869438
$889$	1.43632	0.0481727
$890$	28.2434	0.946720
$891$	−3.67226	−0.123025
$892$	5.53560	0.185346
$893$	0	0
$894$	54.8861	1.83566
$895$	27.3585	0.914495
$896$	−0.619749	−0.0207044
$897$	29.9810	1.00104
$898$	29.3987	0.981047
$899$	−17.6417	−0.588382
$900$	2.09042	0.0696807
$901$	−27.5773	−0.918734
$902$	3.78171	0.125917
$903$	−8.03072	−0.267246
$904$	5.66743	0.188496
$905$	49.9039	1.65886
$906$	26.1559	0.868971
$907$	−45.0480	−1.49579	−0.747897	−	0.663815i	$-0.768936\pi$
$907$	−45.0480	−1.49579	−0.747897	+	0.663815i	$0.768936\pi$
$908$	−19.4971	−0.647033
$909$	77.1933	2.56034
$910$	7.78117	0.257943
$911$	8.62181	0.285653	0.142827	−	0.989748i	$-0.454381\pi$
$911$	8.62181	0.285653	0.142827	+	0.989748i	$0.454381\pi$
$912$	0	0
$913$	9.63754	0.318956
$914$	36.6925	1.21368
$915$	70.2830	2.32349
$916$	−11.7003	−0.386588
$917$	−7.87462	−0.260043
$918$	−14.4246	−0.476083
$919$	17.2872	0.570252	0.285126	−	0.958490i	$-0.407965\pi$
$919$	17.2872	0.570252	0.285126	+	0.958490i	$0.407965\pi$
$920$	−4.45050	−0.146729
$921$	−22.6766	−0.747220
$922$	11.3329	0.373228
$923$	−4.65904	−0.153354
$924$	1.79224	0.0589602
$925$	−3.49218	−0.114822
$926$	36.9188	1.21323
$927$	−89.3378	−2.93424
$928$	−8.17634	−0.268402
$929$	56.2674	1.84608	0.923038	−	0.384710i	$-0.125699\pi$
$929$	56.2674	1.84608	0.923038	+	0.384710i	$0.125699\pi$
$930$	−14.4859	−0.475012
$931$	0	0
$932$	−4.24414	−0.139021
$933$	−50.5474	−1.65485
$934$	16.4547	0.538415
$935$	4.90070	0.160270
$936$	29.0032	0.947999
$937$	−1.44602	−0.0472395	−0.0236197	−	0.999721i	$-0.507519\pi$
$937$	−1.44602	−0.0472395	−0.0236197	+	0.999721i	$0.507519\pi$
$938$	−8.01235	−0.261613
$939$	38.8425	1.26758
$940$	16.0628	0.523910
$941$	−1.49320	−0.0486769	−0.0243385	−	0.999704i	$-0.507748\pi$
$941$	−1.49320	−0.0486769	−0.0243385	+	0.999704i	$0.507748\pi$
$942$	−27.5294	−0.896958
$943$	7.24955	0.236078
$944$	−0.481748	−0.0156796
$945$	−9.83179	−0.319828
$946$	4.48084	0.145685
$947$	52.0491	1.69137	0.845684	−	0.533684i	$-0.179193\pi$
$947$	52.0491	1.69137	0.845684	+	0.533684i	$0.179193\pi$
$948$	−39.7290	−1.29034
$949$	−4.01582	−0.130359
$950$	0	0
$951$	83.1702	2.69698
$952$	1.30824	0.0424004
$953$	−25.1001	−0.813073	−0.406537	−	0.913634i	$-0.633264\pi$
$953$	−25.1001	−0.813073	−0.406537	+	0.913634i	$0.633264\pi$
$954$	−70.0619	−2.26834
$955$	46.2003	1.49501
$956$	21.6536	0.700327
$957$	23.6449	0.764333
$958$	−24.0495	−0.777003
$959$	3.86780	0.124898
$960$	−6.71375	−0.216685
$961$	−26.3446	−0.849824
$962$	−48.4517	−1.56214
$963$	0.0355528	0.00114567
$964$	3.32772	0.107179
$965$	−43.2677	−1.39284
$966$	3.43572	0.110543
$967$	12.8951	0.414678	0.207339	−	0.978269i	$-0.433520\pi$
$967$	12.8951	0.414678	0.207339	+	0.978269i	$0.433520\pi$
$968$	−1.00000	−0.0321412
$969$	0	0
$970$	20.3716	0.654093
$971$	−51.6032	−1.65602	−0.828012	−	0.560710i	$-0.810528\pi$
$971$	−51.6032	−1.65602	−0.828012	+	0.560710i	$0.810528\pi$
$972$	9.88021	0.316908
$973$	−8.23285	−0.263933
$974$	21.1149	0.676564
$975$	6.09612	0.195232
$976$	−10.4685	−0.335089
$977$	−7.48552	−0.239483	−0.119742	−	0.992805i	$-0.538207\pi$
$977$	−7.48552	−0.239483	−0.119742	+	0.992805i	$0.538207\pi$
$978$	−7.34373	−0.234826
$979$	12.1655	0.388812
$980$	−15.3594	−0.490640
$981$	−2.76155	−0.0881696
$982$	13.4381	0.428825
$983$	−3.85099	−0.122828	−0.0614138	−	0.998112i	$-0.519561\pi$
$983$	−3.85099	−0.122828	−0.0614138	+	0.998112i	$0.519561\pi$
$984$	10.9362	0.348634
$985$	−55.6509	−1.77318
$986$	17.2596	0.549659
$987$	−12.4002	−0.394704
$988$	0	0
$989$	8.58979	0.273139
$990$	12.4505	0.395704
$991$	3.30740	0.105063	0.0525316	−	0.998619i	$-0.483271\pi$
$991$	3.30740	0.105063	0.0525316	+	0.998619i	$0.483271\pi$
$992$	2.15765	0.0685054
$993$	−70.7734	−2.24592
$994$	−0.533911	−0.0169346
$995$	−30.4900	−0.966598
$996$	27.8705	0.883112
$997$	−44.8228	−1.41955	−0.709776	−	0.704427i	$-0.751204\pi$
$997$	−44.8228	−1.41955	−0.709776	+	0.704427i	$0.751204\pi$
$998$	−4.37364	−0.138445
$999$	61.2205	1.93693

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7942.2.a.cc.1.3	✓	16
19.18	odd	2		7942.2.a.cd.1.14	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7942.2.a.cc.1.3	✓	16	1.1	even	1	trivial
7942.2.a.cd.1.14	yes	16	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.89187 q^{3} +1.00000 q^{4} +2.32159 q^{5} +2.89187 q^{6} +0.619749 q^{7} -1.00000 q^{8} +5.36293 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.89187 q^{3} +1.00000 q^{4} +2.32159 q^{5} +2.89187 q^{6} +0.619749 q^{7} -1.00000 q^{8} +5.36293 q^{9} -2.32159 q^{10} -1.00000 q^{11} -2.89187 q^{12} -5.40808 q^{13} -0.619749 q^{14} -6.71375 q^{15} +1.00000 q^{16} -2.11092 q^{17} -5.36293 q^{18} +2.32159 q^{20} -1.79224 q^{21} +1.00000 q^{22} +1.91700 q^{23} +2.89187 q^{24} +0.389790 q^{25} +5.40808 q^{26} -6.83331 q^{27} +0.619749 q^{28} +8.17634 q^{29} +6.71375 q^{30} -2.15765 q^{31} -1.00000 q^{32} +2.89187 q^{33} +2.11092 q^{34} +1.43880 q^{35} +5.36293 q^{36} -8.95912 q^{37} +15.6395 q^{39} -2.32159 q^{40} +3.78171 q^{41} +1.79224 q^{42} +4.48084 q^{43} -1.00000 q^{44} +12.4505 q^{45} -1.91700 q^{46} +6.91886 q^{47} -2.89187 q^{48} -6.61591 q^{49} -0.389790 q^{50} +6.10453 q^{51} -5.40808 q^{52} +13.0641 q^{53} +6.83331 q^{54} -2.32159 q^{55} -0.619749 q^{56} -8.17634 q^{58} -0.481748 q^{59} -6.71375 q^{60} -10.4685 q^{61} +2.15765 q^{62} +3.32367 q^{63} +1.00000 q^{64} -12.5554 q^{65} -2.89187 q^{66} +12.9284 q^{67} -2.11092 q^{68} -5.54373 q^{69} -1.43880 q^{70} +0.861495 q^{71} -5.36293 q^{72} +0.742559 q^{73} +8.95912 q^{74} -1.12722 q^{75} -0.619749 q^{77} -15.6395 q^{78} +13.7382 q^{79} +2.32159 q^{80} +3.67226 q^{81} -3.78171 q^{82} -9.63754 q^{83} -1.79224 q^{84} -4.90070 q^{85} -4.48084 q^{86} -23.6449 q^{87} +1.00000 q^{88} -12.1655 q^{89} -12.4505 q^{90} -3.35165 q^{91} +1.91700 q^{92} +6.23965 q^{93} -6.91886 q^{94} +2.89187 q^{96} -8.77484 q^{97} +6.61591 q^{98} -5.36293 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{2} - 10 q^{3} + 16 q^{4} + 10 q^{6} + 6 q^{7} - 16 q^{8} + 20 q^{9}+O(q^{10}) \) 16 * q - 16 * q^2 - 10 * q^3 + 16 * q^4 + 10 * q^6 + 6 * q^7 - 16 * q^8 + 20 * q^9	\( 16 q - 16 q^{2} - 10 q^{3} + 16 q^{4} + 10 q^{6} + 6 q^{7} - 16 q^{8} + 20 q^{9} - 16 q^{11} - 10 q^{12} + 2 q^{13} - 6 q^{14} + 8 q^{15} + 16 q^{16} - 20 q^{18} - 6 q^{21} + 16 q^{22} - 6 q^{23} + 10 q^{24} + 18 q^{25} - 2 q^{26} - 46 q^{27} + 6 q^{28} - 28 q^{29} - 8 q^{30} - 8 q^{31} - 16 q^{32} + 10 q^{33} + 14 q^{35} + 20 q^{36} - 32 q^{37} + 24 q^{39} - 24 q^{41} + 6 q^{42} + 28 q^{43} - 16 q^{44} - 16 q^{45} + 6 q^{46} + 32 q^{47} - 10 q^{48} + 16 q^{49} - 18 q^{50} - 14 q^{51} + 2 q^{52} - 16 q^{53} + 46 q^{54} - 6 q^{56} + 28 q^{58} - 30 q^{59} + 8 q^{60} - 8 q^{61} + 8 q^{62} - 8 q^{63} + 16 q^{64} - 26 q^{65} - 10 q^{66} - 44 q^{67} - 16 q^{69} - 14 q^{70} - 36 q^{71} - 20 q^{72} + 10 q^{73} + 32 q^{74} - 76 q^{75} - 6 q^{77} - 24 q^{78} + 16 q^{79} + 48 q^{81} + 24 q^{82} + 12 q^{83} - 6 q^{84} - 4 q^{85} - 28 q^{86} + 24 q^{87} + 16 q^{88} - 32 q^{89} + 16 q^{90} + 24 q^{91} - 6 q^{92} - 14 q^{93} - 32 q^{94} + 10 q^{96} - 52 q^{97} - 16 q^{98} - 20 q^{99}+O(q^{100}) \) 16 * q - 16 * q^2 - 10 * q^3 + 16 * q^4 + 10 * q^6 + 6 * q^7 - 16 * q^8 + 20 * q^9 - 16 * q^11 - 10 * q^12 + 2 * q^13 - 6 * q^14 + 8 * q^15 + 16 * q^16 - 20 * q^18 - 6 * q^21 + 16 * q^22 - 6 * q^23 + 10 * q^24 + 18 * q^25 - 2 * q^26 - 46 * q^27 + 6 * q^28 - 28 * q^29 - 8 * q^30 - 8 * q^31 - 16 * q^32 + 10 * q^33 + 14 * q^35 + 20 * q^36 - 32 * q^37 + 24 * q^39 - 24 * q^41 + 6 * q^42 + 28 * q^43 - 16 * q^44 - 16 * q^45 + 6 * q^46 + 32 * q^47 - 10 * q^48 + 16 * q^49 - 18 * q^50 - 14 * q^51 + 2 * q^52 - 16 * q^53 + 46 * q^54 - 6 * q^56 + 28 * q^58 - 30 * q^59 + 8 * q^60 - 8 * q^61 + 8 * q^62 - 8 * q^63 + 16 * q^64 - 26 * q^65 - 10 * q^66 - 44 * q^67 - 16 * q^69 - 14 * q^70 - 36 * q^71 - 20 * q^72 + 10 * q^73 + 32 * q^74 - 76 * q^75 - 6 * q^77 - 24 * q^78 + 16 * q^79 + 48 * q^81 + 24 * q^82 + 12 * q^83 - 6 * q^84 - 4 * q^85 - 28 * q^86 + 24 * q^87 + 16 * q^88 - 32 * q^89 + 16 * q^90 + 24 * q^91 - 6 * q^92 - 14 * q^93 - 32 * q^94 + 10 * q^96 - 52 * q^97 - 16 * q^98 - 20 * q^99

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