LMFDB - Embedded newform 4029.2.a.f.1.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4029,2,Mod(1,4029)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4029, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("4029.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4029 = 3 \cdot 17 \cdot 79 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4029.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$32.1717269744$
Analytic rank:	$1$
Dimension:	$22$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
Character	$\chi$	$=$	4029.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.12169 q^{2} -1.00000 q^{3} +2.50157 q^{4} +3.09428 q^{5} -2.12169 q^{6} -1.64576 q^{7} +1.06418 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.12169 q^{2} -1.00000 q^{3} +2.50157 q^{4} +3.09428 q^{5} -2.12169 q^{6} -1.64576 q^{7} +1.06418 q^{8} +1.00000 q^{9} +6.56509 q^{10} -5.87310 q^{11} -2.50157 q^{12} -3.07987 q^{13} -3.49179 q^{14} -3.09428 q^{15} -2.74528 q^{16} +1.00000 q^{17} +2.12169 q^{18} +1.33625 q^{19} +7.74055 q^{20} +1.64576 q^{21} -12.4609 q^{22} -2.78466 q^{23} -1.06418 q^{24} +4.57454 q^{25} -6.53454 q^{26} -1.00000 q^{27} -4.11698 q^{28} -3.85741 q^{29} -6.56509 q^{30} +2.87372 q^{31} -7.95300 q^{32} +5.87310 q^{33} +2.12169 q^{34} -5.09243 q^{35} +2.50157 q^{36} -4.78383 q^{37} +2.83511 q^{38} +3.07987 q^{39} +3.29286 q^{40} -2.97818 q^{41} +3.49179 q^{42} -7.66890 q^{43} -14.6920 q^{44} +3.09428 q^{45} -5.90819 q^{46} +8.11431 q^{47} +2.74528 q^{48} -4.29148 q^{49} +9.70576 q^{50} -1.00000 q^{51} -7.70452 q^{52} +8.21045 q^{53} -2.12169 q^{54} -18.1730 q^{55} -1.75138 q^{56} -1.33625 q^{57} -8.18423 q^{58} -10.4426 q^{59} -7.74055 q^{60} +5.25363 q^{61} +6.09714 q^{62} -1.64576 q^{63} -11.3832 q^{64} -9.52997 q^{65} +12.4609 q^{66} -9.59740 q^{67} +2.50157 q^{68} +2.78466 q^{69} -10.8046 q^{70} -14.4554 q^{71} +1.06418 q^{72} +3.61069 q^{73} -10.1498 q^{74} -4.57454 q^{75} +3.34273 q^{76} +9.66571 q^{77} +6.53454 q^{78} +1.00000 q^{79} -8.49467 q^{80} +1.00000 q^{81} -6.31878 q^{82} +4.50715 q^{83} +4.11698 q^{84} +3.09428 q^{85} -16.2710 q^{86} +3.85741 q^{87} -6.25002 q^{88} +16.1062 q^{89} +6.56509 q^{90} +5.06873 q^{91} -6.96602 q^{92} -2.87372 q^{93} +17.2161 q^{94} +4.13473 q^{95} +7.95300 q^{96} -1.41509 q^{97} -9.10519 q^{98} -5.87310 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + q^{2} - 22 q^{3} + 19 q^{4} + q^{5} - q^{6} - 15 q^{7} + 15 q^{8} + 22 q^{9}+O(q^{10}) $ 22 * q + q^2 - 22 * q^3 + 19 * q^4 + q^5 - q^6 - 15 * q^7 + 15 * q^8 + 22 * q^9	\( 22 q + q^{2} - 22 q^{3} + 19 q^{4} + q^{5} - q^{6} - 15 q^{7} + 15 q^{8} + 22 q^{9} - 13 q^{10} - 23 q^{11} - 19 q^{12} - 18 q^{13} - 9 q^{14} - q^{15} + 21 q^{16} + 22 q^{17} + q^{18} - 30 q^{19} - 7 q^{20} + 15 q^{21} + 4 q^{22} - 3 q^{23} - 15 q^{24} + 19 q^{25} - 7 q^{26} - 22 q^{27} - 25 q^{28} - 7 q^{29} + 13 q^{30} - 10 q^{31} + 31 q^{32} + 23 q^{33} + q^{34} - 11 q^{35} + 19 q^{36} - q^{37} - 29 q^{38} + 18 q^{39} - 59 q^{40} + 9 q^{42} - 43 q^{43} - 80 q^{44} + q^{45} - 43 q^{46} + 2 q^{47} - 21 q^{48} + 43 q^{49} + 25 q^{50} - 22 q^{51} - 5 q^{52} - q^{53} - q^{54} - 19 q^{55} - 8 q^{56} + 30 q^{57} - 43 q^{58} - 28 q^{59} + 7 q^{60} - 29 q^{61} - 3 q^{62} - 15 q^{63} + 23 q^{64} + 19 q^{65} - 4 q^{66} - 16 q^{67} + 19 q^{68} + 3 q^{69} - 5 q^{70} - q^{71} + 15 q^{72} - 19 q^{73} - 24 q^{74} - 19 q^{75} - 72 q^{76} + 24 q^{77} + 7 q^{78} + 22 q^{79} - 82 q^{80} + 22 q^{81} - 81 q^{82} - 29 q^{83} + 25 q^{84} + q^{85} - 42 q^{86} + 7 q^{87} - 43 q^{88} - 28 q^{89} - 13 q^{90} - 96 q^{91} - 11 q^{92} + 10 q^{93} - 63 q^{94} - 23 q^{95} - 31 q^{96} - 51 q^{97} + 12 q^{98} - 23 q^{99}+O(q^{100}) \) 22 * q + q^2 - 22 * q^3 + 19 * q^4 + q^5 - q^6 - 15 * q^7 + 15 * q^8 + 22 * q^9 - 13 * q^10 - 23 * q^11 - 19 * q^12 - 18 * q^13 - 9 * q^14 - q^15 + 21 * q^16 + 22 * q^17 + q^18 - 30 * q^19 - 7 * q^20 + 15 * q^21 + 4 * q^22 - 3 * q^23 - 15 * q^24 + 19 * q^25 - 7 * q^26 - 22 * q^27 - 25 * q^28 - 7 * q^29 + 13 * q^30 - 10 * q^31 + 31 * q^32 + 23 * q^33 + q^34 - 11 * q^35 + 19 * q^36 - q^37 - 29 * q^38 + 18 * q^39 - 59 * q^40 + 9 * q^42 - 43 * q^43 - 80 * q^44 + q^45 - 43 * q^46 + 2 * q^47 - 21 * q^48 + 43 * q^49 + 25 * q^50 - 22 * q^51 - 5 * q^52 - q^53 - q^54 - 19 * q^55 - 8 * q^56 + 30 * q^57 - 43 * q^58 - 28 * q^59 + 7 * q^60 - 29 * q^61 - 3 * q^62 - 15 * q^63 + 23 * q^64 + 19 * q^65 - 4 * q^66 - 16 * q^67 + 19 * q^68 + 3 * q^69 - 5 * q^70 - q^71 + 15 * q^72 - 19 * q^73 - 24 * q^74 - 19 * q^75 - 72 * q^76 + 24 * q^77 + 7 * q^78 + 22 * q^79 - 82 * q^80 + 22 * q^81 - 81 * q^82 - 29 * q^83 + 25 * q^84 + q^85 - 42 * q^86 + 7 * q^87 - 43 * q^88 - 28 * q^89 - 13 * q^90 - 96 * q^91 - 11 * q^92 + 10 * q^93 - 63 * q^94 - 23 * q^95 - 31 * q^96 - 51 * q^97 + 12 * q^98 - 23 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	2.12169	1.50026	0.750131	−	0.661289i	$-0.229990\pi$
$2$	2.12169	1.50026	0.750131	+	0.661289i	$0.229990\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	2.50157	1.25079
$5$	3.09428	1.38380	0.691901	−	0.721992i	$-0.256773\pi$
$5$	3.09428	1.38380	0.691901	+	0.721992i	$0.256773\pi$
$6$	−2.12169	−0.866177
$7$	−1.64576	−0.622038	−0.311019	−	0.950404i	$-0.600670\pi$
$7$	−1.64576	−0.622038	−0.311019	+	0.950404i	$0.600670\pi$
$8$	1.06418	0.376244
$9$	1.00000	0.333333
$10$	6.56509	2.07607
$11$	−5.87310	−1.77081	−0.885403	−	0.464824i	$-0.846118\pi$
$11$	−5.87310	−1.77081	−0.885403	+	0.464824i	$0.846118\pi$
$12$	−2.50157	−0.722141
$13$	−3.07987	−0.854203	−0.427101	−	0.904204i	$-0.640465\pi$
$13$	−3.07987	−0.854203	−0.427101	+	0.904204i	$0.640465\pi$
$14$	−3.49179	−0.933220
$15$	−3.09428	−0.798938
$16$	−2.74528	−0.686321
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	2.12169	0.500087
$19$	1.33625	0.306557	0.153278	−	0.988183i	$-0.451017\pi$
$19$	1.33625	0.306557	0.153278	+	0.988183i	$0.451017\pi$
$20$	7.74055	1.73084
$21$	1.64576	0.359134
$22$	−12.4609	−2.65667
$23$	−2.78466	−0.580642	−0.290321	−	0.956929i	$-0.593762\pi$
$23$	−2.78466	−0.580642	−0.290321	+	0.956929i	$0.593762\pi$
$24$	−1.06418	−0.217224
$25$	4.57454	0.914908
$26$	−6.53454	−1.28153
$27$	−1.00000	−0.192450
$28$	−4.11698	−0.778037
$29$	−3.85741	−0.716303	−0.358152	−	0.933663i	$-0.616593\pi$
$29$	−3.85741	−0.716303	−0.358152	+	0.933663i	$0.616593\pi$
$30$	−6.56509	−1.19862
$31$	2.87372	0.516135	0.258068	−	0.966127i	$-0.416914\pi$
$31$	2.87372	0.516135	0.258068	+	0.966127i	$0.416914\pi$
$32$	−7.95300	−1.40591
$33$	5.87310	1.02238
$34$	2.12169	0.363867
$35$	−5.09243	−0.860778
$36$	2.50157	0.416928
$37$	−4.78383	−0.786457	−0.393228	−	0.919441i	$-0.628642\pi$
$37$	−4.78383	−0.786457	−0.393228	+	0.919441i	$0.628642\pi$
$38$	2.83511	0.459916
$39$	3.07987	0.493174
$40$	3.29286	0.520647
$41$	−2.97818	−0.465114	−0.232557	−	0.972583i	$-0.574709\pi$
$41$	−2.97818	−0.465114	−0.232557	+	0.972583i	$0.574709\pi$
$42$	3.49179	0.538795
$43$	−7.66890	−1.16950	−0.584748	−	0.811215i	$-0.698807\pi$
$43$	−7.66890	−1.16950	−0.584748	+	0.811215i	$0.698807\pi$
$44$	−14.6920	−2.21490
$45$	3.09428	0.461267
$46$	−5.90819	−0.871114
$47$	8.11431	1.18359	0.591797	−	0.806087i	$-0.298419\pi$
$47$	8.11431	1.18359	0.591797	+	0.806087i	$0.298419\pi$
$48$	2.74528	0.396248
$49$	−4.29148	−0.613068
$50$	9.70576	1.37260
$51$	−1.00000	−0.140028
$52$	−7.70452	−1.06842
$53$	8.21045	1.12779	0.563896	−	0.825846i	$-0.309302\pi$
$53$	8.21045	1.12779	0.563896	+	0.825846i	$0.309302\pi$
$54$	−2.12169	−0.288726
$55$	−18.1730	−2.45044
$56$	−1.75138	−0.234038
$57$	−1.33625	−0.176991
$58$	−8.18423	−1.07464
$59$	−10.4426	−1.35952	−0.679758	−	0.733436i	$-0.737915\pi$
$59$	−10.4426	−1.35952	−0.679758	+	0.733436i	$0.737915\pi$
$60$	−7.74055	−0.999301
$61$	5.25363	0.672659	0.336329	−	0.941744i	$-0.390814\pi$
$61$	5.25363	0.672659	0.336329	+	0.941744i	$0.390814\pi$
$62$	6.09714	0.774338
$63$	−1.64576	−0.207346
$64$	−11.3832	−1.42290
$65$	−9.52997	−1.18205
$66$	12.4609	1.53383
$67$	−9.59740	−1.17251	−0.586255	−	0.810127i	$-0.699398\pi$
$67$	−9.59740	−1.17251	−0.586255	+	0.810127i	$0.699398\pi$
$68$	2.50157	0.303360
$69$	2.78466	0.335234
$70$	−10.8046	−1.29139
$71$	−14.4554	−1.71553	−0.857767	−	0.514038i	$-0.828149\pi$
$71$	−14.4554	−1.71553	−0.857767	+	0.514038i	$0.828149\pi$
$72$	1.06418	0.125415
$73$	3.61069	0.422599	0.211300	−	0.977421i	$-0.432230\pi$
$73$	3.61069	0.422599	0.211300	+	0.977421i	$0.432230\pi$
$74$	−10.1498	−1.17989
$75$	−4.57454	−0.528222
$76$	3.34273	0.383437
$77$	9.66571	1.10151
$78$	6.53454	0.739891
$79$	1.00000	0.112509
$79$	1.00000	0.112509
$80$	−8.49467	−0.949733
$81$	1.00000	0.111111
$82$	−6.31878	−0.697793
$83$	4.50715	0.494724	0.247362	−	0.968923i	$-0.420436\pi$
$83$	4.50715	0.494724	0.247362	+	0.968923i	$0.420436\pi$
$84$	4.11698	0.449200
$85$	3.09428	0.335621
$86$	−16.2710	−1.75455
$87$	3.85741	0.413558
$88$	−6.25002	−0.666255
$89$	16.1062	1.70725	0.853625	−	0.520888i	$-0.174399\pi$
$89$	16.1062	1.70725	0.853625	+	0.520888i	$0.174399\pi$
$90$	6.56509	0.692022
$91$	5.06873	0.531347
$92$	−6.96602	−0.726258
$93$	−2.87372	−0.297991
$94$	17.2161	1.77570
$95$	4.13473	0.424214
$96$	7.95300	0.811700
$97$	−1.41509	−0.143680	−0.0718401	−	0.997416i	$-0.522887\pi$
$97$	−1.41509	−0.143680	−0.0718401	+	0.997416i	$0.522887\pi$
$98$	−9.10519	−0.919763
$99$	−5.87310	−0.590269
$100$	11.4435	1.14435
$101$	−1.75984	−0.175111	−0.0875553	−	0.996160i	$-0.527905\pi$
$101$	−1.75984	−0.175111	−0.0875553	+	0.996160i	$0.527905\pi$
$102$	−2.12169	−0.210079
$103$	4.11686	0.405646	0.202823	−	0.979215i	$-0.434988\pi$
$103$	4.11686	0.405646	0.202823	+	0.979215i	$0.434988\pi$
$104$	−3.27753	−0.321389
$105$	5.09243	0.496970
$106$	17.4200	1.69198
$107$	−1.93346	−0.186915	−0.0934573	−	0.995623i	$-0.529792\pi$
$107$	−1.93346	−0.186915	−0.0934573	+	0.995623i	$0.529792\pi$
$108$	−2.50157	−0.240714
$109$	−4.72261	−0.452344	−0.226172	−	0.974087i	$-0.572621\pi$
$109$	−4.72261	−0.452344	−0.226172	+	0.974087i	$0.572621\pi$
$110$	−38.5575	−3.67631
$111$	4.78383	0.454061
$112$	4.51808	0.426918
$113$	−2.20973	−0.207874	−0.103937	−	0.994584i	$-0.533144\pi$
$113$	−2.20973	−0.207874	−0.103937	+	0.994584i	$0.533144\pi$
$114$	−2.83511	−0.265532
$115$	−8.61650	−0.803493
$116$	−9.64959	−0.895942
$117$	−3.07987	−0.284734
$118$	−22.1561	−2.03963
$119$	−1.64576	−0.150866
$120$	−3.29286	−0.300596
$121$	23.4933	2.13575
$122$	11.1466	1.00916
$123$	2.97818	0.268534
$124$	7.18881	0.645574
$125$	−1.31649	−0.117751
$126$	−3.49179	−0.311073
$127$	−8.49752	−0.754033	−0.377017	−	0.926206i	$-0.623050\pi$
$127$	−8.49752	−0.754033	−0.377017	+	0.926206i	$0.623050\pi$
$128$	−8.24571	−0.728824
$129$	7.66890	0.675209
$130$	−20.2197	−1.77338
$131$	6.63412	0.579626	0.289813	−	0.957083i	$-0.406407\pi$
$131$	6.63412	0.579626	0.289813	+	0.957083i	$0.406407\pi$
$132$	14.6920	1.27877
$133$	−2.19915	−0.190690
$134$	−20.3627	−1.75907
$135$	−3.09428	−0.266313
$136$	1.06418	0.0912525
$137$	8.27453	0.706941	0.353470	−	0.935446i	$-0.385002\pi$
$137$	8.27453	0.706941	0.353470	+	0.935446i	$0.385002\pi$
$138$	5.90819	0.502938
$139$	10.2754	0.871550	0.435775	−	0.900056i	$-0.356474\pi$
$139$	10.2754	0.871550	0.435775	+	0.900056i	$0.356474\pi$
$140$	−12.7391	−1.07665
$141$	−8.11431	−0.683349
$142$	−30.6698	−2.57375
$143$	18.0884	1.51263
$144$	−2.74528	−0.228774
$145$	−11.9359	−0.991222
$146$	7.66077	0.634010
$147$	4.29148	0.353955
$148$	−11.9671	−0.983689
$149$	−7.82915	−0.641389	−0.320694	−	0.947183i	$-0.603916\pi$
$149$	−7.82915	−0.641389	−0.320694	+	0.947183i	$0.603916\pi$
$150$	−9.70576	−0.792472
$151$	2.89107	0.235272	0.117636	−	0.993057i	$-0.462468\pi$
$151$	2.89107	0.235272	0.117636	+	0.993057i	$0.462468\pi$
$152$	1.42201	0.115340
$153$	1.00000	0.0808452
$154$	20.5076	1.65255
$155$	8.89208	0.714229
$156$	7.70452	0.616855
$157$	23.4457	1.87117	0.935584	−	0.353103i	$-0.114873\pi$
$157$	23.4457	1.87117	0.935584	+	0.353103i	$0.114873\pi$
$158$	2.12169	0.168793
$159$	−8.21045	−0.651131
$160$	−24.6088	−1.94549
$161$	4.58288	0.361181
$162$	2.12169	0.166696
$163$	−3.35593	−0.262857	−0.131428	−	0.991326i	$-0.541956\pi$
$163$	−3.35593	−0.262857	−0.131428	+	0.991326i	$0.541956\pi$
$164$	−7.45014	−0.581758
$165$	18.1730	1.41477
$166$	9.56277	0.742215
$167$	−19.0238	−1.47211	−0.736054	−	0.676923i	$-0.763313\pi$
$167$	−19.0238	−1.47211	−0.736054	+	0.676923i	$0.763313\pi$
$168$	1.75138	0.135122
$169$	−3.51438	−0.270337
$170$	6.56509	0.503520
$171$	1.33625	0.102186
$172$	−19.1843	−1.46279
$173$	−4.70361	−0.357609	−0.178804	−	0.983885i	$-0.557223\pi$
$173$	−4.70361	−0.357609	−0.178804	+	0.983885i	$0.557223\pi$
$174$	8.18423	0.620445
$175$	−7.52859	−0.569108
$176$	16.1233	1.21534
$177$	10.4426	0.784917
$178$	34.1723	2.56132
$179$	−12.7953	−0.956369	−0.478185	−	0.878259i	$-0.658705\pi$
$179$	−12.7953	−0.956369	−0.478185	+	0.878259i	$0.658705\pi$
$180$	7.74055	0.576946
$181$	−6.11511	−0.454533	−0.227266	−	0.973833i	$-0.572979\pi$
$181$	−6.11511	−0.454533	−0.227266	+	0.973833i	$0.572979\pi$
$182$	10.7543	0.797160
$183$	−5.25363	−0.388360
$184$	−2.96337	−0.218463
$185$	−14.8025	−1.08830
$186$	−6.09714	−0.447064
$187$	−5.87310	−0.429484
$188$	20.2985	1.48042
$189$	1.64576	0.119711
$190$	8.77261	0.636432
$191$	26.5971	1.92450	0.962249	−	0.272171i	$-0.0877416\pi$
$191$	26.5971	1.92450	0.962249	+	0.272171i	$0.0877416\pi$
$192$	11.3832	0.821514
$193$	−18.1099	−1.30358	−0.651790	−	0.758400i	$-0.725981\pi$
$193$	−18.1099	−1.30358	−0.651790	+	0.758400i	$0.725981\pi$
$194$	−3.00237	−0.215558
$195$	9.52997	0.682456
$196$	−10.7354	−0.766817
$197$	8.81518	0.628056	0.314028	−	0.949414i	$-0.398321\pi$
$197$	8.81518	0.628056	0.314028	+	0.949414i	$0.398321\pi$
$198$	−12.4609	−0.885558
$199$	23.7431	1.68310	0.841550	−	0.540179i	$-0.181643\pi$
$199$	23.7431	1.68310	0.841550	+	0.540179i	$0.181643\pi$
$200$	4.86812	0.344228
$201$	9.59740	0.676949
$202$	−3.73384	−0.262712
$203$	6.34837	0.445568
$204$	−2.50157	−0.175145
$205$	−9.21532	−0.643626
$206$	8.73470	0.608575
$207$	−2.78466	−0.193547
$208$	8.45513	0.586258
$209$	−7.84793	−0.542853
$210$	10.8046	0.745586
$211$	−4.04315	−0.278342	−0.139171	−	0.990268i	$-0.544444\pi$
$211$	−4.04315	−0.278342	−0.139171	+	0.990268i	$0.544444\pi$
$212$	20.5390	1.41063
$213$	14.4554	0.990464
$214$	−4.10220	−0.280421
$215$	−23.7297	−1.61835
$216$	−1.06418	−0.0724082
$217$	−4.72945	−0.321056
$218$	−10.0199	−0.678634
$219$	−3.61069	−0.243988
$220$	−45.4610	−3.06498
$221$	−3.07987	−0.207175
$222$	10.1498	0.681211
$223$	−12.4658	−0.834770	−0.417385	−	0.908730i	$-0.637053\pi$
$223$	−12.4658	−0.834770	−0.417385	+	0.908730i	$0.637053\pi$
$224$	13.0887	0.874527
$225$	4.57454	0.304969
$226$	−4.68837	−0.311866
$227$	−3.99417	−0.265102	−0.132551	−	0.991176i	$-0.542317\pi$
$227$	−3.99417	−0.265102	−0.132551	+	0.991176i	$0.542317\pi$
$228$	−3.34273	−0.221377
$229$	−4.52903	−0.299287	−0.149643	−	0.988740i	$-0.547813\pi$
$229$	−4.52903	−0.299287	−0.149643	+	0.988740i	$0.547813\pi$
$230$	−18.2816	−1.20545
$231$	−9.66571	−0.635957
$232$	−4.10497	−0.269505
$233$	−3.45970	−0.226652	−0.113326	−	0.993558i	$-0.536151\pi$
$233$	−3.45970	−0.226652	−0.113326	+	0.993558i	$0.536151\pi$
$234$	−6.53454	−0.427176
$235$	25.1079	1.63786
$236$	−26.1230	−1.70046
$237$	−1.00000	−0.0649570
$238$	−3.49179	−0.226339
$239$	−12.3470	−0.798659	−0.399329	−	0.916808i	$-0.630757\pi$
$239$	−12.3470	−0.798659	−0.399329	+	0.916808i	$0.630757\pi$
$240$	8.49467	0.548328
$241$	16.9096	1.08924	0.544621	−	0.838682i	$-0.316674\pi$
$241$	16.9096	1.08924	0.544621	+	0.838682i	$0.316674\pi$
$242$	49.8455	3.20419
$243$	−1.00000	−0.0641500
$244$	13.1423	0.841352
$245$	−13.2790	−0.848365
$246$	6.31878	0.402871
$247$	−4.11548	−0.261862
$248$	3.05815	0.194193
$249$	−4.50715	−0.285629
$250$	−2.79319	−0.176657
$251$	19.6350	1.23935	0.619676	−	0.784858i	$-0.287264\pi$
$251$	19.6350	1.23935	0.619676	+	0.784858i	$0.287264\pi$
$252$	−4.11698	−0.259346
$253$	16.3546	1.02820
$254$	−18.0291	−1.13125
$255$	−3.09428	−0.193771
$256$	5.27164	0.329477
$257$	21.8923	1.36560	0.682802	−	0.730603i	$-0.260761\pi$
$257$	21.8923	1.36560	0.682802	+	0.730603i	$0.260761\pi$
$258$	16.2710	1.01299
$259$	7.87303	0.489206
$260$	−23.8399	−1.47849
$261$	−3.85741	−0.238768
$262$	14.0755	0.869590
$263$	−26.3879	−1.62715	−0.813573	−	0.581463i	$-0.802481\pi$
$263$	−26.3879	−1.62715	−0.813573	+	0.581463i	$0.802481\pi$
$264$	6.25002	0.384662
$265$	25.4054	1.56064
$266$	−4.66591	−0.286085
$267$	−16.1062	−0.985681
$268$	−24.0086	−1.46656
$269$	−10.3089	−0.628542	−0.314271	−	0.949333i	$-0.601760\pi$
$269$	−10.3089	−0.628542	−0.314271	+	0.949333i	$0.601760\pi$
$270$	−6.56509	−0.399539
$271$	4.78409	0.290613	0.145306	−	0.989387i	$-0.453583\pi$
$271$	4.78409	0.290613	0.145306	+	0.989387i	$0.453583\pi$
$272$	−2.74528	−0.166457
$273$	−5.06873	−0.306773
$274$	17.5560	1.06060
$275$	−26.8667	−1.62012
$276$	6.96602	0.419305
$277$	−11.6449	−0.699676	−0.349838	−	0.936810i	$-0.613763\pi$
$277$	−11.6449	−0.699676	−0.349838	+	0.936810i	$0.613763\pi$
$278$	21.8013	1.30755
$279$	2.87372	0.172045
$280$	−5.41925	−0.323862
$281$	−18.4640	−1.10147	−0.550736	−	0.834680i	$-0.685653\pi$
$281$	−18.4640	−1.10147	−0.550736	+	0.834680i	$0.685653\pi$
$282$	−17.2161	−1.02520
$283$	4.39374	0.261181	0.130590	−	0.991436i	$-0.458313\pi$
$283$	4.39374	0.261181	0.130590	+	0.991436i	$0.458313\pi$
$284$	−36.1611	−2.14577
$285$	−4.13473	−0.244920
$286$	38.3780	2.26934
$287$	4.90137	0.289319
$288$	−7.95300	−0.468635
$289$	1.00000	0.0588235
$290$	−25.3243	−1.48709
$291$	1.41509	0.0829538
$292$	9.03240	0.528581
$293$	−27.1944	−1.58871	−0.794357	−	0.607451i	$-0.792192\pi$
$293$	−27.1944	−1.58871	−0.794357	+	0.607451i	$0.792192\pi$
$294$	9.10519	0.531025
$295$	−32.3124	−1.88130
$296$	−5.09085	−0.295900
$297$	5.87310	0.340792
$298$	−16.6110	−0.962251
$299$	8.57640	0.495986
$300$	−11.4435	−0.660693
$301$	12.6212	0.727471
$302$	6.13396	0.352970
$303$	1.75984	0.101100
$304$	−3.66839	−0.210397
$305$	16.2562	0.930826
$306$	2.12169	0.121289
$307$	−29.2253	−1.66798	−0.833989	−	0.551781i	$-0.813948\pi$
$307$	−29.2253	−1.66798	−0.833989	+	0.551781i	$0.813948\pi$
$308$	24.1794	1.37775
$309$	−4.11686	−0.234200
$310$	18.8662	1.07153
$311$	−18.2738	−1.03621	−0.518107	−	0.855316i	$-0.673363\pi$
$311$	−18.2738	−1.03621	−0.518107	+	0.855316i	$0.673363\pi$
$312$	3.27753	0.185554
$313$	11.7589	0.664652	0.332326	−	0.943165i	$-0.392167\pi$
$313$	11.7589	0.664652	0.332326	+	0.943165i	$0.392167\pi$
$314$	49.7445	2.80724
$315$	−5.09243	−0.286926
$316$	2.50157	0.140724
$317$	−21.2457	−1.19328	−0.596638	−	0.802511i	$-0.703497\pi$
$317$	−21.2457	−1.19328	−0.596638	+	0.802511i	$0.703497\pi$
$318$	−17.4200	−0.976867
$319$	22.6550	1.26843
$320$	−35.2229	−1.96902
$321$	1.93346	0.107915
$322$	9.72345	0.541867
$323$	1.33625	0.0743510
$324$	2.50157	0.138976
$325$	−14.0890	−0.781517
$326$	−7.12025	−0.394354
$327$	4.72261	0.261161
$328$	−3.16932	−0.174996
$329$	−13.3542	−0.736241
$330$	38.5575	2.12252
$331$	8.97080	0.493080	0.246540	−	0.969133i	$-0.420706\pi$
$331$	8.97080	0.493080	0.246540	+	0.969133i	$0.420706\pi$
$332$	11.2750	0.618793
$333$	−4.78383	−0.262152
$334$	−40.3627	−2.20855
$335$	−29.6970	−1.62252
$336$	−4.51808	−0.246481
$337$	9.31094	0.507199	0.253600	−	0.967309i	$-0.418385\pi$
$337$	9.31094	0.507199	0.253600	+	0.967309i	$0.418385\pi$
$338$	−7.45644	−0.405577
$339$	2.20973	0.120016
$340$	7.74055	0.419790
$341$	−16.8776	−0.913975
$342$	2.83511	0.153305
$343$	18.5831	1.00339
$344$	−8.16107	−0.440016
$345$	8.61650	0.463897
$346$	−9.97960	−0.536506
$347$	−23.2082	−1.24588	−0.622941	−	0.782269i	$-0.714062\pi$
$347$	−23.2082	−1.24588	−0.622941	+	0.782269i	$0.714062\pi$
$348$	9.64959	0.517272
$349$	−32.3325	−1.73072	−0.865360	−	0.501151i	$-0.832910\pi$
$349$	−32.3325	−1.73072	−0.865360	+	0.501151i	$0.832910\pi$
$350$	−15.9733	−0.853811
$351$	3.07987	0.164391
$352$	46.7088	2.48959
$353$	33.3229	1.77360	0.886800	−	0.462154i	$-0.152923\pi$
$353$	33.3229	1.77360	0.886800	+	0.462154i	$0.152923\pi$
$354$	22.1561	1.17758
$355$	−44.7288	−2.37396
$356$	40.2907	2.13540
$357$	1.64576	0.0871028
$358$	−27.1478	−1.43480
$359$	20.8358	1.09967	0.549835	−	0.835273i	$-0.314691\pi$
$359$	20.8358	1.09967	0.549835	+	0.835273i	$0.314691\pi$
$360$	3.29286	0.173549
$361$	−17.2144	−0.906023
$362$	−12.9744	−0.681918
$363$	−23.4933	−1.23308
$364$	12.6798	0.664601
$365$	11.1725	0.584794
$366$	−11.1466	−0.582641
$367$	17.9492	0.936941	0.468470	−	0.883479i	$-0.344805\pi$
$367$	17.9492	0.936941	0.468470	+	0.883479i	$0.344805\pi$
$368$	7.64468	0.398507
$369$	−2.97818	−0.155038
$370$	−31.4063	−1.63274
$371$	−13.5124	−0.701530
$372$	−7.18881	−0.372722
$373$	33.1264	1.71522	0.857611	−	0.514299i	$-0.171948\pi$
$373$	33.1264	1.71522	0.857611	+	0.514299i	$0.171948\pi$
$374$	−12.4609	−0.644338
$375$	1.31649	0.0679834
$376$	8.63508	0.445320
$377$	11.8803	0.611868
$378$	3.49179	0.179598
$379$	−29.3175	−1.50594	−0.752969	−	0.658056i	$-0.771379\pi$
$379$	−29.3175	−1.50594	−0.752969	+	0.658056i	$0.771379\pi$
$380$	10.3433	0.530601
$381$	8.49752	0.435341
$382$	56.4308	2.88725
$383$	9.72406	0.496876	0.248438	−	0.968648i	$-0.420083\pi$
$383$	9.72406	0.496876	0.248438	+	0.968648i	$0.420083\pi$
$384$	8.24571	0.420787
$385$	29.9084	1.52427
$386$	−38.4236	−1.95571
$387$	−7.66890	−0.389832
$388$	−3.53994	−0.179713
$389$	−29.1273	−1.47681	−0.738406	−	0.674357i	$-0.764421\pi$
$389$	−29.1273	−1.47681	−0.738406	+	0.674357i	$0.764421\pi$
$390$	20.2197	1.02386
$391$	−2.78466	−0.140826
$392$	−4.56690	−0.230663
$393$	−6.63412	−0.334647
$394$	18.7031	0.942248
$395$	3.09428	0.155690
$396$	−14.6920	−0.738299
$397$	31.3565	1.57374	0.786868	−	0.617121i	$-0.211701\pi$
$397$	31.3565	1.57374	0.786868	+	0.617121i	$0.211701\pi$
$398$	50.3754	2.52509
$399$	2.19915	0.110095
$400$	−12.5584	−0.627921
$401$	11.4748	0.573026	0.286513	−	0.958076i	$-0.407504\pi$
$401$	11.4748	0.573026	0.286513	+	0.958076i	$0.407504\pi$
$402$	20.3627	1.01560
$403$	−8.85069	−0.440884
$404$	−4.40236	−0.219026
$405$	3.09428	0.153756
$406$	13.4693	0.668469
$407$	28.0959	1.39266
$408$	−1.06418	−0.0526847
$409$	21.5753	1.06683	0.533414	−	0.845854i	$-0.320909\pi$
$409$	21.5753	1.06683	0.533414	+	0.845854i	$0.320909\pi$
$410$	−19.5521	−0.965607
$411$	−8.27453	−0.408152
$412$	10.2986	0.507376
$413$	17.1861	0.845671
$414$	−5.90819	−0.290371
$415$	13.9464	0.684600
$416$	24.4942	1.20093
$417$	−10.2754	−0.503190
$418$	−16.6509	−0.814422
$419$	−2.06124	−0.100698	−0.0503491	−	0.998732i	$-0.516033\pi$
$419$	−2.06124	−0.100698	−0.0503491	+	0.998732i	$0.516033\pi$
$420$	12.7391	0.621603
$421$	23.8976	1.16470	0.582349	−	0.812939i	$-0.302134\pi$
$421$	23.8976	1.16470	0.582349	+	0.812939i	$0.302134\pi$
$422$	−8.57831	−0.417585
$423$	8.11431	0.394531
$424$	8.73738	0.424325
$425$	4.57454	0.221898
$426$	30.6698	1.48596
$427$	−8.64621	−0.418420
$428$	−4.83668	−0.233790
$429$	−18.0884	−0.873316
$430$	−50.3470	−2.42795
$431$	2.20896	0.106402	0.0532010	−	0.998584i	$-0.483058\pi$
$431$	2.20896	0.106402	0.0532010	+	0.998584i	$0.483058\pi$
$432$	2.74528	0.132083
$433$	−6.01766	−0.289190	−0.144595	−	0.989491i	$-0.546188\pi$
$433$	−6.01766	−0.289190	−0.144595	+	0.989491i	$0.546188\pi$
$434$	−10.0344	−0.481668
$435$	11.9359	0.572282
$436$	−11.8139	−0.565785
$437$	−3.72100	−0.178000
$438$	−7.66077	−0.366046
$439$	−41.2658	−1.96951	−0.984755	−	0.173945i	$-0.944349\pi$
$439$	−41.2658	−1.96951	−0.984755	+	0.173945i	$0.944349\pi$
$440$	−19.3393	−0.921965
$441$	−4.29148	−0.204356
$442$	−6.53454	−0.310816
$443$	2.26797	0.107755	0.0538773	−	0.998548i	$-0.482842\pi$
$443$	2.26797	0.107755	0.0538773	+	0.998548i	$0.482842\pi$
$444$	11.9671	0.567933
$445$	49.8369	2.36250
$446$	−26.4485	−1.25237
$447$	7.82915	0.370306
$448$	18.7341	0.885101
$449$	9.79315	0.462168	0.231084	−	0.972934i	$-0.425773\pi$
$449$	9.79315	0.462168	0.231084	+	0.972934i	$0.425773\pi$
$450$	9.70576	0.457534
$451$	17.4912	0.823627
$452$	−5.52781	−0.260006
$453$	−2.89107	−0.135834
$454$	−8.47439	−0.397723
$455$	15.6840	0.735279
$456$	−1.42201	−0.0665917
$457$	4.47379	0.209275	0.104638	−	0.994510i	$-0.466632\pi$
$457$	4.47379	0.209275	0.104638	+	0.994510i	$0.466632\pi$
$458$	−9.60921	−0.449009
$459$	−1.00000	−0.0466760
$460$	−21.5548	−1.00500
$461$	38.0543	1.77237	0.886183	−	0.463336i	$-0.153348\pi$
$461$	38.0543	1.77237	0.886183	+	0.463336i	$0.153348\pi$
$462$	−20.5076	−0.954102
$463$	−27.5924	−1.28233	−0.641163	−	0.767405i	$-0.721548\pi$
$463$	−27.5924	−1.28233	−0.641163	+	0.767405i	$0.721548\pi$
$464$	10.5897	0.491614
$465$	−8.89208	−0.412360
$466$	−7.34041	−0.340038
$467$	26.5652	1.22929	0.614646	−	0.788803i	$-0.289299\pi$
$467$	26.5652	1.22929	0.614646	+	0.788803i	$0.289299\pi$
$468$	−7.70452	−0.356142
$469$	15.7950	0.729346
$470$	53.2712	2.45722
$471$	−23.4457	−1.08032
$472$	−11.1128	−0.511510
$473$	45.0402	2.07095
$474$	−2.12169	−0.0974525
$475$	6.11273	0.280471
$476$	−4.11698	−0.188702
$477$	8.21045	0.375931
$478$	−26.1964	−1.19820
$479$	18.4710	0.843963	0.421981	−	0.906604i	$-0.361335\pi$
$479$	18.4710	0.843963	0.421981	+	0.906604i	$0.361335\pi$
$480$	24.6088	1.12323
$481$	14.7336	0.671794
$482$	35.8769	1.63415
$483$	−4.58288	−0.208528
$484$	58.7701	2.67137
$485$	−4.37866	−0.198825
$486$	−2.12169	−0.0962418
$487$	27.0392	1.22526	0.612631	−	0.790369i	$-0.290111\pi$
$487$	27.0392	1.22526	0.612631	+	0.790369i	$0.290111\pi$
$488$	5.59080	0.253084
$489$	3.35593	0.151760
$490$	−28.1740	−1.27277
$491$	16.3313	0.737019	0.368510	−	0.929624i	$-0.379868\pi$
$491$	16.3313	0.737019	0.368510	+	0.929624i	$0.379868\pi$
$492$	7.45014	0.335878
$493$	−3.85741	−0.173729
$494$	−8.73178	−0.392861
$495$	−18.1730	−0.816815
$496$	−7.88918	−0.354234
$497$	23.7900	1.06713
$498$	−9.56277	−0.428518
$499$	−33.0730	−1.48055	−0.740275	−	0.672304i	$-0.765305\pi$
$499$	−33.0730	−1.48055	−0.740275	+	0.672304i	$0.765305\pi$
$500$	−3.29330	−0.147281
$501$	19.0238	0.849922
$502$	41.6594	1.85935
$503$	−44.2101	−1.97123	−0.985616	−	0.168998i	$-0.945947\pi$
$503$	−44.2101	−1.97123	−0.985616	+	0.168998i	$0.945947\pi$
$504$	−1.75138	−0.0780127
$505$	−5.44543	−0.242318
$506$	34.6994	1.54257
$507$	3.51438	0.156079
$508$	−21.2572	−0.943134
$509$	−16.0099	−0.709627	−0.354814	−	0.934937i	$-0.615456\pi$
$509$	−16.0099	−0.709627	−0.354814	+	0.934937i	$0.615456\pi$
$510$	−6.56509	−0.290707
$511$	−5.94233	−0.262873
$512$	27.6762	1.22313
$513$	−1.33625	−0.0589969
$514$	46.4487	2.04876
$515$	12.7387	0.561334
$516$	19.1843	0.844541
$517$	−47.6562	−2.09592
$518$	16.7041	0.733938
$519$	4.70361	0.206465
$520$	−10.1416	−0.444738
$521$	10.5827	0.463636	0.231818	−	0.972759i	$-0.425533\pi$
$521$	10.5827	0.463636	0.231818	+	0.972759i	$0.425533\pi$
$522$	−8.18423	−0.358214
$523$	7.45832	0.326130	0.163065	−	0.986615i	$-0.447862\pi$
$523$	7.45832	0.326130	0.163065	+	0.986615i	$0.447862\pi$
$524$	16.5957	0.724987
$525$	7.52859	0.328575
$526$	−55.9869	−2.44115
$527$	2.87372	0.125181
$528$	−16.1233	−0.701678
$529$	−15.2457	−0.662855
$530$	53.9024	2.34137
$531$	−10.4426	−0.453172
$532$	−5.50132	−0.238513
$533$	9.17242	0.397302
$534$	−34.1723	−1.47878
$535$	−5.98265	−0.258653
$536$	−10.2133	−0.441149
$537$	12.7953	0.552160
$538$	−21.8722	−0.942978
$539$	25.2043	1.08562
$540$	−7.74055	−0.333100
$541$	−5.67087	−0.243810	−0.121905	−	0.992542i	$-0.538900\pi$
$541$	−5.67087	−0.243810	−0.121905	+	0.992542i	$0.538900\pi$
$542$	10.1504	0.435995
$543$	6.11511	0.262425
$544$	−7.95300	−0.340982
$545$	−14.6130	−0.625954
$546$	−10.7543	−0.460240
$547$	−33.4525	−1.43033	−0.715163	−	0.698957i	$-0.753648\pi$
$547$	−33.4525	−1.43033	−0.715163	+	0.698957i	$0.753648\pi$
$548$	20.6993	0.884231
$549$	5.25363	0.224220
$550$	−57.0029	−2.43061
$551$	−5.15447	−0.219588
$552$	2.96337	0.126130
$553$	−1.64576	−0.0699848
$554$	−24.7069	−1.04970
$555$	14.8025	0.628331
$556$	25.7047	1.09012
$557$	28.6569	1.21423	0.607117	−	0.794613i	$-0.292326\pi$
$557$	28.6569	1.21423	0.607117	+	0.794613i	$0.292326\pi$
$558$	6.09714	0.258113
$559$	23.6192	0.998987
$560$	13.9802	0.590770
$561$	5.87310	0.247962
$562$	−39.1749	−1.65250
$563$	−16.8611	−0.710612	−0.355306	−	0.934750i	$-0.615623\pi$
$563$	−16.8611	−0.710612	−0.355306	+	0.934750i	$0.615623\pi$
$564$	−20.2985	−0.854722
$565$	−6.83752	−0.287657
$566$	9.32216	0.391840
$567$	−1.64576	−0.0691154
$568$	−15.3831	−0.645459
$569$	−13.6026	−0.570252	−0.285126	−	0.958490i	$-0.592035\pi$
$569$	−13.6026	−0.570252	−0.285126	+	0.958490i	$0.592035\pi$
$570$	−8.77261	−0.367444
$571$	−33.1247	−1.38622	−0.693112	−	0.720830i	$-0.743761\pi$
$571$	−33.1247	−1.38622	−0.693112	+	0.720830i	$0.743761\pi$
$572$	45.2494	1.89197
$573$	−26.5971	−1.11111
$574$	10.3992	0.434054
$575$	−12.7385	−0.531234
$576$	−11.3832	−0.474302
$577$	27.3140	1.13710	0.568549	−	0.822650i	$-0.307505\pi$
$577$	27.3140	1.13710	0.568549	+	0.822650i	$0.307505\pi$
$578$	2.12169	0.0882507
$579$	18.1099	0.752622
$580$	−29.8585	−1.23981
$581$	−7.41768	−0.307737
$582$	3.00237	0.124452
$583$	−48.2208	−1.99710
$584$	3.84242	0.159000
$585$	−9.52997	−0.394016
$586$	−57.6981	−2.38349
$587$	6.23443	0.257323	0.128661	−	0.991689i	$-0.458932\pi$
$587$	6.23443	0.257323	0.128661	+	0.991689i	$0.458932\pi$
$588$	10.7354	0.442722
$589$	3.84001	0.158225
$590$	−68.5569	−2.82244
$591$	−8.81518	−0.362608
$592$	13.1330	0.539762
$593$	−28.5617	−1.17289	−0.586443	−	0.809990i	$-0.699472\pi$
$593$	−28.5617	−1.17289	−0.586443	+	0.809990i	$0.699472\pi$
$594$	12.4609	0.511277
$595$	−5.09243	−0.208769
$596$	−19.5852	−0.802240
$597$	−23.7431	−0.971739
$598$	18.1965	0.744109
$599$	8.61978	0.352195	0.176097	−	0.984373i	$-0.443653\pi$
$599$	8.61978	0.352195	0.176097	+	0.984373i	$0.443653\pi$
$600$	−4.86812	−0.198740
$601$	−10.8192	−0.441324	−0.220662	−	0.975350i	$-0.570822\pi$
$601$	−10.8192	−0.441324	−0.220662	+	0.975350i	$0.570822\pi$
$602$	26.7782	1.09140
$603$	−9.59740	−0.390836
$604$	7.23222	0.294275
$605$	72.6947	2.95546
$606$	3.73384	0.151677
$607$	15.7012	0.637293	0.318647	−	0.947874i	$-0.396772\pi$
$607$	15.7012	0.637293	0.318647	+	0.947874i	$0.396772\pi$
$608$	−10.6272	−0.430990
$609$	−6.34837	−0.257249
$610$	34.4906	1.39648
$611$	−24.9911	−1.01103
$612$	2.50157	0.101120
$613$	34.9648	1.41221	0.706107	−	0.708105i	$-0.250450\pi$
$613$	34.9648	1.41221	0.706107	+	0.708105i	$0.250450\pi$
$614$	−62.0071	−2.50240
$615$	9.21532	0.371597
$616$	10.2860	0.414436
$617$	13.0584	0.525711	0.262855	−	0.964835i	$-0.415336\pi$
$617$	13.0584	0.525711	0.262855	+	0.964835i	$0.415336\pi$
$618$	−8.73470	−0.351361
$619$	−37.2500	−1.49721	−0.748603	−	0.663019i	$-0.769275\pi$
$619$	−37.2500	−1.49721	−0.748603	+	0.663019i	$0.769275\pi$
$620$	22.2442	0.893347
$621$	2.78466	0.111745
$622$	−38.7714	−1.55459
$623$	−26.5069	−1.06198
$624$	−8.45513	−0.338476
$625$	−26.9463	−1.07785
$626$	24.9487	0.997152
$627$	7.84793	0.313416
$628$	58.6510	2.34043
$629$	−4.78383	−0.190744
$630$	−10.8046	−0.430464
$631$	−2.73082	−0.108712	−0.0543562	−	0.998522i	$-0.517311\pi$
$631$	−2.73082	−0.108712	−0.0543562	+	0.998522i	$0.517311\pi$
$632$	1.06418	0.0423307
$633$	4.04315	0.160701
$634$	−45.0767	−1.79023
$635$	−26.2937	−1.04343
$636$	−20.5390	−0.814425
$637$	13.2172	0.523685
$638$	48.0668	1.90298
$639$	−14.4554	−0.571845
$640$	−25.5145	−1.00855
$641$	−33.1051	−1.30757	−0.653787	−	0.756678i	$-0.726821\pi$
$641$	−33.1051	−1.30757	−0.653787	+	0.756678i	$0.726821\pi$
$642$	4.10220	0.161901
$643$	−3.14341	−0.123964	−0.0619820	−	0.998077i	$-0.519742\pi$
$643$	−3.14341	−0.123964	−0.0619820	+	0.998077i	$0.519742\pi$
$644$	11.4644	0.451760
$645$	23.7297	0.934355
$646$	2.83511	0.111546
$647$	27.6396	1.08663	0.543313	−	0.839530i	$-0.317170\pi$
$647$	27.6396	1.08663	0.543313	+	0.839530i	$0.317170\pi$
$648$	1.06418	0.0418049
$649$	61.3307	2.40744
$650$	−29.8925	−1.17248
$651$	4.72945	0.185362
$652$	−8.39510	−0.328777
$653$	−12.1705	−0.476270	−0.238135	−	0.971232i	$-0.576536\pi$
$653$	−12.1705	−0.476270	−0.238135	+	0.971232i	$0.576536\pi$
$654$	10.0199	0.391810
$655$	20.5278	0.802087
$656$	8.17596	0.319218
$657$	3.61069	0.140866
$658$	−28.3335	−1.10455
$659$	34.7996	1.35560	0.677800	−	0.735247i	$-0.262934\pi$
$659$	34.7996	1.35560	0.677800	+	0.735247i	$0.262934\pi$
$660$	45.4610	1.76957
$661$	−23.3744	−0.909158	−0.454579	−	0.890706i	$-0.650210\pi$
$661$	−23.3744	−0.909158	−0.454579	+	0.890706i	$0.650210\pi$
$662$	19.0333	0.739749
$663$	3.07987	0.119612
$664$	4.79641	0.186137
$665$	−6.80477	−0.263877
$666$	−10.1498	−0.393297
$667$	10.7416	0.415915
$668$	−47.5895	−1.84129
$669$	12.4658	0.481955
$670$	−63.0079	−2.43421
$671$	−30.8551	−1.19115
$672$	−13.0887	−0.504908
$673$	−13.9199	−0.536574	−0.268287	−	0.963339i	$-0.586458\pi$
$673$	−13.9199	−0.536574	−0.268287	+	0.963339i	$0.586458\pi$
$674$	19.7549	0.760932
$675$	−4.57454	−0.176074
$676$	−8.79148	−0.338134
$677$	−5.15341	−0.198062	−0.0990308	−	0.995084i	$-0.531574\pi$
$677$	−5.15341	−0.198062	−0.0990308	+	0.995084i	$0.531574\pi$
$678$	4.68837	0.180056
$679$	2.32889	0.0893746
$680$	3.29286	0.126275
$681$	3.99417	0.153057
$682$	−35.8091	−1.37120
$683$	28.1295	1.07635	0.538173	−	0.842834i	$-0.319115\pi$
$683$	28.1295	1.07635	0.538173	+	0.842834i	$0.319115\pi$
$684$	3.34273	0.127812
$685$	25.6037	0.978266
$686$	39.4275	1.50535
$687$	4.52903	0.172793
$688$	21.0533	0.802650
$689$	−25.2871	−0.963363
$690$	18.2816	0.695967
$691$	28.9552	1.10151	0.550753	−	0.834668i	$-0.314341\pi$
$691$	28.9552	1.10151	0.550753	+	0.834668i	$0.314341\pi$
$692$	−11.7664	−0.447292
$693$	9.66571	0.367170
$694$	−49.2406	−1.86915
$695$	31.7950	1.20605
$696$	4.10497	0.155599
$697$	−2.97818	−0.112807
$698$	−68.5996	−2.59653
$699$	3.45970	0.130858
$700$	−18.8333	−0.711832
$701$	25.3644	0.958002	0.479001	−	0.877814i	$-0.340999\pi$
$701$	25.3644	0.958002	0.479001	+	0.877814i	$0.340999\pi$
$702$	6.53454	0.246630
$703$	−6.39240	−0.241094
$704$	66.8549	2.51969
$705$	−25.1079	−0.945619
$706$	70.7009	2.66086
$707$	2.89627	0.108926
$708$	26.1230	0.981763
$709$	41.1161	1.54415	0.772075	−	0.635532i	$-0.219219\pi$
$709$	41.1161	1.54415	0.772075	+	0.635532i	$0.219219\pi$
$710$	−94.9007	−3.56156
$711$	1.00000	0.0375029
$712$	17.1398	0.642342
$713$	−8.00233	−0.299690
$714$	3.49179	0.130677
$715$	55.9705	2.09318
$716$	−32.0085	−1.19621
$717$	12.3470	0.461106
$718$	44.2071	1.64979
$719$	−28.9444	−1.07944	−0.539721	−	0.841844i	$-0.681470\pi$
$719$	−28.9444	−1.07944	−0.539721	+	0.841844i	$0.681470\pi$
$720$	−8.49467	−0.316578
$721$	−6.77535	−0.252327
$722$	−36.5237	−1.35927
$723$	−16.9096	−0.628874
$724$	−15.2974	−0.568523
$725$	−17.6459	−0.655351
$726$	−49.8455	−1.84994
$727$	−7.21004	−0.267406	−0.133703	−	0.991021i	$-0.542687\pi$
$727$	−7.21004	−0.267406	−0.133703	+	0.991021i	$0.542687\pi$
$728$	5.39403	0.199916
$729$	1.00000	0.0370370
$730$	23.7045	0.877344
$731$	−7.66890	−0.283644
$732$	−13.1423	−0.485755
$733$	30.8841	1.14073	0.570366	−	0.821391i	$-0.306801\pi$
$733$	30.8841	1.14073	0.570366	+	0.821391i	$0.306801\pi$
$734$	38.0826	1.40566
$735$	13.2790	0.489804
$736$	22.1464	0.816327
$737$	56.3665	2.07629
$738$	−6.31878	−0.232598
$739$	11.3417	0.417211	0.208605	−	0.978000i	$-0.433108\pi$
$739$	11.3417	0.417211	0.208605	+	0.978000i	$0.433108\pi$
$740$	−37.0295	−1.36123
$741$	4.11548	0.151186
$742$	−28.6692	−1.05248
$743$	3.46121	0.126980	0.0634898	−	0.997982i	$-0.479777\pi$
$743$	3.46121	0.126980	0.0634898	+	0.997982i	$0.479777\pi$
$744$	−3.05815	−0.112117
$745$	−24.2255	−0.887555
$746$	70.2841	2.57328
$747$	4.50715	0.164908
$748$	−14.6920	−0.537192
$749$	3.18201	0.116268
$750$	2.79319	0.101993
$751$	−7.61928	−0.278031	−0.139016	−	0.990290i	$-0.544394\pi$
$751$	−7.61928	−0.278031	−0.139016	+	0.990290i	$0.544394\pi$
$752$	−22.2761	−0.812326
$753$	−19.6350	−0.715540
$754$	25.2064	0.917963
$755$	8.94577	0.325570
$756$	4.11698	0.149733
$757$	−33.5165	−1.21818	−0.609089	−	0.793102i	$-0.708465\pi$
$757$	−33.5165	−1.21818	−0.609089	+	0.793102i	$0.708465\pi$
$758$	−62.2026	−2.25930
$759$	−16.3546	−0.593634
$760$	4.40009	0.159608
$761$	28.7904	1.04365	0.521825	−	0.853052i	$-0.325251\pi$
$761$	28.7904	1.04365	0.521825	+	0.853052i	$0.325251\pi$
$762$	18.0291	0.653126
$763$	7.77227	0.281375
$764$	66.5345	2.40713
$765$	3.09428	0.111874
$766$	20.6315	0.745445
$767$	32.1620	1.16130
$768$	−5.27164	−0.190224
$769$	6.52353	0.235244	0.117622	−	0.993058i	$-0.462473\pi$
$769$	6.52353	0.235244	0.117622	+	0.993058i	$0.462473\pi$
$770$	63.4563	2.28681
$771$	−21.8923	−0.788432
$772$	−45.3032	−1.63050
$773$	−16.2293	−0.583729	−0.291864	−	0.956460i	$-0.594276\pi$
$773$	−16.2293	−0.583729	−0.291864	+	0.956460i	$0.594276\pi$
$774$	−16.2710	−0.584850
$775$	13.1459	0.472216
$776$	−1.50590	−0.0540588
$777$	−7.87303	−0.282443
$778$	−61.7991	−2.21560
$779$	−3.97960	−0.142584
$780$	23.8399	0.853606
$781$	84.8977	3.03788
$782$	−5.90819	−0.211276
$783$	3.85741	0.137853
$784$	11.7813	0.420762
$785$	72.5474	2.58933
$786$	−14.0755	−0.502058
$787$	−29.1903	−1.04052	−0.520262	−	0.854007i	$-0.674166\pi$
$787$	−29.1903	−1.04052	−0.520262	+	0.854007i	$0.674166\pi$
$788$	22.0518	0.785563
$789$	26.3879	0.939433
$790$	6.56509	0.233576
$791$	3.63669	0.129306
$792$	−6.25002	−0.222085
$793$	−16.1805	−0.574587
$794$	66.5287	2.36102
$795$	−25.4054	−0.901036
$796$	59.3949	2.10520
$797$	−44.6631	−1.58205	−0.791024	−	0.611785i	$-0.790452\pi$
$797$	−44.6631	−1.58205	−0.791024	+	0.611785i	$0.790452\pi$
$798$	4.66591	0.165171
$799$	8.11431	0.287064
$800$	−36.3813	−1.28627
$801$	16.1062	0.569083
$802$	24.3461	0.859689
$803$	−21.2059	−0.748342
$804$	24.0086	0.846717
$805$	14.1807	0.499804
$806$	−18.7784	−0.661442
$807$	10.3089	0.362889
$808$	−1.87278	−0.0658843
$809$	11.2171	0.394373	0.197186	−	0.980366i	$-0.436820\pi$
$809$	11.2171	0.394373	0.197186	+	0.980366i	$0.436820\pi$
$810$	6.56509	0.230674
$811$	29.2939	1.02865	0.514324	−	0.857596i	$-0.328043\pi$
$811$	29.2939	1.02865	0.514324	+	0.857596i	$0.328043\pi$
$812$	15.8809	0.557310
$813$	−4.78409	−0.167785
$814$	59.6108	2.08936
$815$	−10.3842	−0.363742
$816$	2.74528	0.0961042
$817$	−10.2476	−0.358517
$818$	45.7760	1.60052
$819$	5.06873	0.177116
$820$	−23.0528	−0.805038
$821$	−41.4284	−1.44586	−0.722931	−	0.690921i	$-0.757205\pi$
$821$	−41.4284	−1.44586	−0.722931	+	0.690921i	$0.757205\pi$
$822$	−17.5560	−0.612336
$823$	39.7684	1.38624	0.693119	−	0.720823i	$-0.256236\pi$
$823$	39.7684	1.38624	0.693119	+	0.720823i	$0.256236\pi$
$824$	4.38107	0.152622
$825$	26.8667	0.935379
$826$	36.4635	1.26873
$827$	9.08559	0.315937	0.157969	−	0.987444i	$-0.449506\pi$
$827$	9.08559	0.315937	0.157969	+	0.987444i	$0.449506\pi$
$828$	−6.96602	−0.242086
$829$	−40.5296	−1.40765	−0.703826	−	0.710373i	$-0.748526\pi$
$829$	−40.5296	−1.40765	−0.703826	+	0.710373i	$0.748526\pi$
$830$	29.5899	1.02708
$831$	11.6449	0.403958
$832$	35.0589	1.21545
$833$	−4.29148	−0.148691
$834$	−21.8013	−0.754916
$835$	−58.8650	−2.03711
$836$	−19.6322	−0.678993
$837$	−2.87372	−0.0993303
$838$	−4.37332	−0.151074
$839$	−0.986086	−0.0340435	−0.0170217	−	0.999855i	$-0.505418\pi$
$839$	−0.986086	−0.0340435	−0.0170217	+	0.999855i	$0.505418\pi$
$840$	5.41925	0.186982
$841$	−14.1204	−0.486910
$842$	50.7033	1.74735
$843$	18.4640	0.635935
$844$	−10.1142	−0.348146
$845$	−10.8745	−0.374093
$846$	17.2161	0.591901
$847$	−38.6643	−1.32852
$848$	−22.5400	−0.774027
$849$	−4.39374	−0.150793
$850$	9.70576	0.332905
$851$	13.3213	0.456650
$852$	36.1611	1.23886
$853$	32.8566	1.12499	0.562494	−	0.826802i	$-0.309842\pi$
$853$	32.8566	1.12499	0.562494	+	0.826802i	$0.309842\pi$
$854$	−18.3446	−0.627739
$855$	4.13473	0.141405
$856$	−2.05754	−0.0703254
$857$	18.3194	0.625778	0.312889	−	0.949790i	$-0.398703\pi$
$857$	18.3194	0.625778	0.312889	+	0.949790i	$0.398703\pi$
$858$	−38.3780	−1.31020
$859$	−13.2189	−0.451022	−0.225511	−	0.974241i	$-0.572405\pi$
$859$	−13.2189	−0.451022	−0.225511	+	0.974241i	$0.572405\pi$
$860$	−59.3615	−2.02421
$861$	−4.90137	−0.167038
$862$	4.68674	0.159631
$863$	17.5888	0.598730	0.299365	−	0.954139i	$-0.403225\pi$
$863$	17.5888	0.598730	0.299365	+	0.954139i	$0.403225\pi$
$864$	7.95300	0.270567
$865$	−14.5543	−0.494859
$866$	−12.7676	−0.433861
$867$	−1.00000	−0.0339618
$868$	−11.8311	−0.401572
$869$	−5.87310	−0.199231
$870$	25.3243	0.858573
$871$	29.5588	1.00156
$872$	−5.02570	−0.170192
$873$	−1.41509	−0.0478934
$874$	−7.89482	−0.267046
$875$	2.16663	0.0732455
$876$	−9.03240	−0.305177
$877$	−21.1920	−0.715605	−0.357802	−	0.933797i	$-0.616474\pi$
$877$	−21.1920	−0.715605	−0.357802	+	0.933797i	$0.616474\pi$
$878$	−87.5533	−2.95478
$879$	27.1944	0.917244
$880$	49.8900	1.68179
$881$	−23.4469	−0.789946	−0.394973	−	0.918693i	$-0.629246\pi$
$881$	−23.4469	−0.789946	−0.394973	+	0.918693i	$0.629246\pi$
$882$	−9.10519	−0.306588
$883$	27.7760	0.934738	0.467369	−	0.884062i	$-0.345202\pi$
$883$	27.7760	0.934738	0.467369	+	0.884062i	$0.345202\pi$
$884$	−7.70452	−0.259131
$885$	32.3124	1.08617
$886$	4.81194	0.161660
$887$	8.01047	0.268965	0.134483	−	0.990916i	$-0.457063\pi$
$887$	8.01047	0.268965	0.134483	+	0.990916i	$0.457063\pi$
$888$	5.09085	0.170838
$889$	13.9849	0.469038
$890$	105.738	3.54436
$891$	−5.87310	−0.196756
$892$	−31.1840	−1.04412
$893$	10.8428	0.362839
$894$	16.6110	0.555556
$895$	−39.5923	−1.32343
$896$	13.5704	0.453357
$897$	−8.57640	−0.286358
$898$	20.7780	0.693372
$899$	−11.0851	−0.369709
$900$	11.4435	0.381451
$901$	8.21045	0.273530
$902$	37.1108	1.23566
$903$	−12.6212	−0.420006
$904$	−2.35155	−0.0782114
$905$	−18.9218	−0.628983
$906$	−6.13396	−0.203787
$907$	−2.82883	−0.0939298	−0.0469649	−	0.998897i	$-0.514955\pi$
$907$	−2.82883	−0.0939298	−0.0469649	+	0.998897i	$0.514955\pi$
$908$	−9.99169	−0.331586
$909$	−1.75984	−0.0583702
$910$	33.2767	1.10311
$911$	38.0241	1.25980	0.629898	−	0.776678i	$-0.283097\pi$
$911$	38.0241	1.25980	0.629898	+	0.776678i	$0.283097\pi$
$912$	3.66839	0.121473
$913$	−26.4709	−0.876060
$914$	9.49200	0.313968
$915$	−16.2562	−0.537413
$916$	−11.3297	−0.374344
$917$	−10.9182	−0.360549
$918$	−2.12169	−0.0700262
$919$	13.2328	0.436511	0.218256	−	0.975892i	$-0.429963\pi$
$919$	13.2328	0.436511	0.218256	+	0.975892i	$0.429963\pi$
$920$	−9.16949	−0.302309
$921$	29.2253	0.963007
$922$	80.7395	2.65901
$923$	44.5206	1.46541
$924$	−24.1794	−0.795445
$925$	−21.8838	−0.719536
$926$	−58.5425	−1.92382
$927$	4.11686	0.135215
$928$	30.6780	1.00705
$929$	22.2807	0.731008	0.365504	−	0.930810i	$-0.380897\pi$
$929$	22.2807	0.731008	0.365504	+	0.930810i	$0.380897\pi$
$930$	−18.8662	−0.618648
$931$	−5.73449	−0.187940
$932$	−8.65468	−0.283494
$933$	18.2738	0.598258
$934$	56.3632	1.84426
$935$	−18.1730	−0.594320
$936$	−3.27753	−0.107130
$937$	−6.25175	−0.204236	−0.102118	−	0.994772i	$-0.532562\pi$
$937$	−6.25175	−0.204236	−0.102118	+	0.994772i	$0.532562\pi$
$938$	33.5121	1.09421
$939$	−11.7589	−0.383737
$940$	62.8092	2.04861
$941$	−7.77168	−0.253350	−0.126675	−	0.991944i	$-0.540430\pi$
$941$	−7.77168	−0.253350	−0.126675	+	0.991944i	$0.540430\pi$
$942$	−49.7445	−1.62076
$943$	8.29322	0.270065
$944$	28.6680	0.933065
$945$	5.09243	0.165657
$946$	95.5614	3.10697
$947$	8.37337	0.272098	0.136049	−	0.990702i	$-0.456560\pi$
$947$	8.37337	0.272098	0.136049	+	0.990702i	$0.456560\pi$
$948$	−2.50157	−0.0812472
$949$	−11.1205	−0.360986
$950$	12.9693	0.420780
$951$	21.2457	0.688938
$952$	−1.75138	−0.0567626
$953$	13.8177	0.447598	0.223799	−	0.974635i	$-0.428154\pi$
$953$	13.8177	0.447598	0.223799	+	0.974635i	$0.428154\pi$
$954$	17.4200	0.563994
$955$	82.2987	2.66312
$956$	−30.8868	−0.998951
$957$	−22.6550	−0.732331
$958$	39.1898	1.26617
$959$	−13.6179	−0.439744
$960$	35.2229	1.13681
$961$	−22.7417	−0.733605
$962$	31.2601	1.00787
$963$	−1.93346	−0.0623048
$964$	42.3005	1.36241
$965$	−56.0370	−1.80390
$966$	−9.72345	−0.312847
$967$	−46.4038	−1.49224	−0.746122	−	0.665809i	$-0.768087\pi$
$967$	−46.4038	−1.49224	−0.746122	+	0.665809i	$0.768087\pi$
$968$	25.0011	0.803564
$969$	−1.33625	−0.0429266
$970$	−9.29017	−0.298289
$971$	−12.7845	−0.410273	−0.205137	−	0.978733i	$-0.565764\pi$
$971$	−12.7845	−0.410273	−0.205137	+	0.978733i	$0.565764\pi$
$972$	−2.50157	−0.0802379
$973$	−16.9109	−0.542137
$974$	57.3687	1.83821
$975$	14.0890	0.451209
$976$	−14.4227	−0.461660
$977$	9.13947	0.292398	0.146199	−	0.989255i	$-0.453296\pi$
$977$	9.13947	0.292398	0.146199	+	0.989255i	$0.453296\pi$
$978$	7.12025	0.227680
$979$	−94.5931	−3.02321
$980$	−33.2184	−1.06112
$981$	−4.72261	−0.150781
$982$	34.6499	1.10572
$983$	37.5313	1.19706	0.598531	−	0.801100i	$-0.295751\pi$
$983$	37.5313	1.19706	0.598531	+	0.801100i	$0.295751\pi$
$984$	3.16932	0.101034
$985$	27.2766	0.869104
$986$	−8.18423	−0.260639
$987$	13.3542	0.425069
$988$	−10.2952	−0.327533
$989$	21.3553	0.679058
$990$	−38.5575	−1.22544
$991$	−6.28062	−0.199511	−0.0997553	−	0.995012i	$-0.531806\pi$
$991$	−6.28062	−0.199511	−0.0997553	+	0.995012i	$0.531806\pi$
$992$	−22.8547	−0.725637
$993$	−8.97080	−0.284680
$994$	50.4751	1.60097
$995$	73.4676	2.32908
$996$	−11.2750	−0.357260
$997$	−48.8513	−1.54714	−0.773568	−	0.633713i	$-0.781530\pi$
$997$	−48.8513	−1.54714	−0.773568	+	0.633713i	$0.781530\pi$
$998$	−70.1706	−2.22121
$999$	4.78383	0.151354

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4029.2.a.f.1.19	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4029.2.a.f.1.19	✓	22	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 4029 = 3 \cdot 17 \cdot 79 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4029.a (trivial)

\(f(q)\)	\(=\)	\(q+2.12169 q^{2} -1.00000 q^{3} +2.50157 q^{4} +3.09428 q^{5} -2.12169 q^{6} -1.64576 q^{7} +1.06418 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.12169 q^{2} -1.00000 q^{3} +2.50157 q^{4} +3.09428 q^{5} -2.12169 q^{6} -1.64576 q^{7} +1.06418 q^{8} +1.00000 q^{9} +6.56509 q^{10} -5.87310 q^{11} -2.50157 q^{12} -3.07987 q^{13} -3.49179 q^{14} -3.09428 q^{15} -2.74528 q^{16} +1.00000 q^{17} +2.12169 q^{18} +1.33625 q^{19} +7.74055 q^{20} +1.64576 q^{21} -12.4609 q^{22} -2.78466 q^{23} -1.06418 q^{24} +4.57454 q^{25} -6.53454 q^{26} -1.00000 q^{27} -4.11698 q^{28} -3.85741 q^{29} -6.56509 q^{30} +2.87372 q^{31} -7.95300 q^{32} +5.87310 q^{33} +2.12169 q^{34} -5.09243 q^{35} +2.50157 q^{36} -4.78383 q^{37} +2.83511 q^{38} +3.07987 q^{39} +3.29286 q^{40} -2.97818 q^{41} +3.49179 q^{42} -7.66890 q^{43} -14.6920 q^{44} +3.09428 q^{45} -5.90819 q^{46} +8.11431 q^{47} +2.74528 q^{48} -4.29148 q^{49} +9.70576 q^{50} -1.00000 q^{51} -7.70452 q^{52} +8.21045 q^{53} -2.12169 q^{54} -18.1730 q^{55} -1.75138 q^{56} -1.33625 q^{57} -8.18423 q^{58} -10.4426 q^{59} -7.74055 q^{60} +5.25363 q^{61} +6.09714 q^{62} -1.64576 q^{63} -11.3832 q^{64} -9.52997 q^{65} +12.4609 q^{66} -9.59740 q^{67} +2.50157 q^{68} +2.78466 q^{69} -10.8046 q^{70} -14.4554 q^{71} +1.06418 q^{72} +3.61069 q^{73} -10.1498 q^{74} -4.57454 q^{75} +3.34273 q^{76} +9.66571 q^{77} +6.53454 q^{78} +1.00000 q^{79} -8.49467 q^{80} +1.00000 q^{81} -6.31878 q^{82} +4.50715 q^{83} +4.11698 q^{84} +3.09428 q^{85} -16.2710 q^{86} +3.85741 q^{87} -6.25002 q^{88} +16.1062 q^{89} +6.56509 q^{90} +5.06873 q^{91} -6.96602 q^{92} -2.87372 q^{93} +17.2161 q^{94} +4.13473 q^{95} +7.95300 q^{96} -1.41509 q^{97} -9.10519 q^{98} -5.87310 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + q^{2} - 22 q^{3} + 19 q^{4} + q^{5} - q^{6} - 15 q^{7} + 15 q^{8} + 22 q^{9}+O(q^{10}) \) 22 * q + q^2 - 22 * q^3 + 19 * q^4 + q^5 - q^6 - 15 * q^7 + 15 * q^8 + 22 * q^9	\( 22 q + q^{2} - 22 q^{3} + 19 q^{4} + q^{5} - q^{6} - 15 q^{7} + 15 q^{8} + 22 q^{9} - 13 q^{10} - 23 q^{11} - 19 q^{12} - 18 q^{13} - 9 q^{14} - q^{15} + 21 q^{16} + 22 q^{17} + q^{18} - 30 q^{19} - 7 q^{20} + 15 q^{21} + 4 q^{22} - 3 q^{23} - 15 q^{24} + 19 q^{25} - 7 q^{26} - 22 q^{27} - 25 q^{28} - 7 q^{29} + 13 q^{30} - 10 q^{31} + 31 q^{32} + 23 q^{33} + q^{34} - 11 q^{35} + 19 q^{36} - q^{37} - 29 q^{38} + 18 q^{39} - 59 q^{40} + 9 q^{42} - 43 q^{43} - 80 q^{44} + q^{45} - 43 q^{46} + 2 q^{47} - 21 q^{48} + 43 q^{49} + 25 q^{50} - 22 q^{51} - 5 q^{52} - q^{53} - q^{54} - 19 q^{55} - 8 q^{56} + 30 q^{57} - 43 q^{58} - 28 q^{59} + 7 q^{60} - 29 q^{61} - 3 q^{62} - 15 q^{63} + 23 q^{64} + 19 q^{65} - 4 q^{66} - 16 q^{67} + 19 q^{68} + 3 q^{69} - 5 q^{70} - q^{71} + 15 q^{72} - 19 q^{73} - 24 q^{74} - 19 q^{75} - 72 q^{76} + 24 q^{77} + 7 q^{78} + 22 q^{79} - 82 q^{80} + 22 q^{81} - 81 q^{82} - 29 q^{83} + 25 q^{84} + q^{85} - 42 q^{86} + 7 q^{87} - 43 q^{88} - 28 q^{89} - 13 q^{90} - 96 q^{91} - 11 q^{92} + 10 q^{93} - 63 q^{94} - 23 q^{95} - 31 q^{96} - 51 q^{97} + 12 q^{98} - 23 q^{99}+O(q^{100}) \) 22 * q + q^2 - 22 * q^3 + 19 * q^4 + q^5 - q^6 - 15 * q^7 + 15 * q^8 + 22 * q^9 - 13 * q^10 - 23 * q^11 - 19 * q^12 - 18 * q^13 - 9 * q^14 - q^15 + 21 * q^16 + 22 * q^17 + q^18 - 30 * q^19 - 7 * q^20 + 15 * q^21 + 4 * q^22 - 3 * q^23 - 15 * q^24 + 19 * q^25 - 7 * q^26 - 22 * q^27 - 25 * q^28 - 7 * q^29 + 13 * q^30 - 10 * q^31 + 31 * q^32 + 23 * q^33 + q^34 - 11 * q^35 + 19 * q^36 - q^37 - 29 * q^38 + 18 * q^39 - 59 * q^40 + 9 * q^42 - 43 * q^43 - 80 * q^44 + q^45 - 43 * q^46 + 2 * q^47 - 21 * q^48 + 43 * q^49 + 25 * q^50 - 22 * q^51 - 5 * q^52 - q^53 - q^54 - 19 * q^55 - 8 * q^56 + 30 * q^57 - 43 * q^58 - 28 * q^59 + 7 * q^60 - 29 * q^61 - 3 * q^62 - 15 * q^63 + 23 * q^64 + 19 * q^65 - 4 * q^66 - 16 * q^67 + 19 * q^68 + 3 * q^69 - 5 * q^70 - q^71 + 15 * q^72 - 19 * q^73 - 24 * q^74 - 19 * q^75 - 72 * q^76 + 24 * q^77 + 7 * q^78 + 22 * q^79 - 82 * q^80 + 22 * q^81 - 81 * q^82 - 29 * q^83 + 25 * q^84 + q^85 - 42 * q^86 + 7 * q^87 - 43 * q^88 - 28 * q^89 - 13 * q^90 - 96 * q^91 - 11 * q^92 + 10 * q^93 - 63 * q^94 - 23 * q^95 - 31 * q^96 - 51 * q^97 + 12 * q^98 - 23 * q^99

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