LMFDB - Embedded newform 4034.2.a.b.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4034,2,Mod(1,4034)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4034, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4034 = 2 \cdot 2017 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4034.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:	$32.2116521754$
Analytic rank:	$1$
Dimension:	$35$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Character	$\chi$	$=$	4034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +0.00791248 q^{3} +1.00000 q^{4} -2.05271 q^{5} -0.00791248 q^{6} -2.16347 q^{7} -1.00000 q^{8} -2.99994 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +0.00791248 q^{3} +1.00000 q^{4} -2.05271 q^{5} -0.00791248 q^{6} -2.16347 q^{7} -1.00000 q^{8} -2.99994 q^{9} +2.05271 q^{10} +3.51446 q^{11} +0.00791248 q^{12} +0.954466 q^{13} +2.16347 q^{14} -0.0162420 q^{15} +1.00000 q^{16} +1.50277 q^{17} +2.99994 q^{18} +5.51294 q^{19} -2.05271 q^{20} -0.0171184 q^{21} -3.51446 q^{22} +2.04363 q^{23} -0.00791248 q^{24} -0.786397 q^{25} -0.954466 q^{26} -0.0474744 q^{27} -2.16347 q^{28} -8.64347 q^{29} +0.0162420 q^{30} -1.46030 q^{31} -1.00000 q^{32} +0.0278081 q^{33} -1.50277 q^{34} +4.44098 q^{35} -2.99994 q^{36} -11.7587 q^{37} -5.51294 q^{38} +0.00755219 q^{39} +2.05271 q^{40} +1.30333 q^{41} +0.0171184 q^{42} +9.55197 q^{43} +3.51446 q^{44} +6.15799 q^{45} -2.04363 q^{46} +8.01046 q^{47} +0.00791248 q^{48} -2.31938 q^{49} +0.786397 q^{50} +0.0118906 q^{51} +0.954466 q^{52} +2.71410 q^{53} +0.0474744 q^{54} -7.21415 q^{55} +2.16347 q^{56} +0.0436211 q^{57} +8.64347 q^{58} +10.0846 q^{59} -0.0162420 q^{60} +6.16426 q^{61} +1.46030 q^{62} +6.49029 q^{63} +1.00000 q^{64} -1.95924 q^{65} -0.0278081 q^{66} +6.69007 q^{67} +1.50277 q^{68} +0.0161701 q^{69} -4.44098 q^{70} +6.36626 q^{71} +2.99994 q^{72} +9.38700 q^{73} +11.7587 q^{74} -0.00622235 q^{75} +5.51294 q^{76} -7.60344 q^{77} -0.00755219 q^{78} -5.92668 q^{79} -2.05271 q^{80} +8.99944 q^{81} -1.30333 q^{82} -13.8283 q^{83} -0.0171184 q^{84} -3.08474 q^{85} -9.55197 q^{86} -0.0683913 q^{87} -3.51446 q^{88} -10.2331 q^{89} -6.15799 q^{90} -2.06496 q^{91} +2.04363 q^{92} -0.0115546 q^{93} -8.01046 q^{94} -11.3165 q^{95} -0.00791248 q^{96} -5.93870 q^{97} +2.31938 q^{98} -10.5432 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 35 q - 35 q^{2} - 6 q^{3} + 35 q^{4} + 6 q^{5} + 6 q^{6} - 14 q^{7} - 35 q^{8} + 23 q^{9}+O(q^{10}) $ 35 * q - 35 * q^2 - 6 * q^3 + 35 * q^4 + 6 * q^5 + 6 * q^6 - 14 * q^7 - 35 * q^8 + 23 * q^9	\( 35 q - 35 q^{2} - 6 q^{3} + 35 q^{4} + 6 q^{5} + 6 q^{6} - 14 q^{7} - 35 q^{8} + 23 q^{9} - 6 q^{10} - 9 q^{11} - 6 q^{12} - 7 q^{13} + 14 q^{14} - 19 q^{15} + 35 q^{16} + 17 q^{17} - 23 q^{18} - 25 q^{19} + 6 q^{20} - 15 q^{21} + 9 q^{22} - 12 q^{23} + 6 q^{24} + 7 q^{25} + 7 q^{26} - 27 q^{27} - 14 q^{28} - 13 q^{29} + 19 q^{30} - 69 q^{31} - 35 q^{32} + q^{33} - 17 q^{34} - 4 q^{35} + 23 q^{36} - 22 q^{37} + 25 q^{38} - 38 q^{39} - 6 q^{40} + 15 q^{42} - 32 q^{43} - 9 q^{44} + 9 q^{45} + 12 q^{46} - 18 q^{47} - 6 q^{48} - 19 q^{49} - 7 q^{50} - 21 q^{51} - 7 q^{52} + 20 q^{53} + 27 q^{54} - 54 q^{55} + 14 q^{56} + 28 q^{57} + 13 q^{58} - 21 q^{59} - 19 q^{60} - 67 q^{61} + 69 q^{62} - 28 q^{63} + 35 q^{64} + 22 q^{65} - q^{66} - 18 q^{67} + 17 q^{68} - 42 q^{69} + 4 q^{70} - 36 q^{71} - 23 q^{72} - 18 q^{73} + 22 q^{74} - 49 q^{75} - 25 q^{76} + 20 q^{77} + 38 q^{78} - 92 q^{79} + 6 q^{80} - 25 q^{81} + 42 q^{83} - 15 q^{84} - 29 q^{85} + 32 q^{86} - 40 q^{87} + 9 q^{88} - 8 q^{89} - 9 q^{90} - 89 q^{91} - 12 q^{92} - q^{93} + 18 q^{94} - 62 q^{95} + 6 q^{96} - 40 q^{97} + 19 q^{98} - 64 q^{99}+O(q^{100}) \) 35 * q - 35 * q^2 - 6 * q^3 + 35 * q^4 + 6 * q^5 + 6 * q^6 - 14 * q^7 - 35 * q^8 + 23 * q^9 - 6 * q^10 - 9 * q^11 - 6 * q^12 - 7 * q^13 + 14 * q^14 - 19 * q^15 + 35 * q^16 + 17 * q^17 - 23 * q^18 - 25 * q^19 + 6 * q^20 - 15 * q^21 + 9 * q^22 - 12 * q^23 + 6 * q^24 + 7 * q^25 + 7 * q^26 - 27 * q^27 - 14 * q^28 - 13 * q^29 + 19 * q^30 - 69 * q^31 - 35 * q^32 + q^33 - 17 * q^34 - 4 * q^35 + 23 * q^36 - 22 * q^37 + 25 * q^38 - 38 * q^39 - 6 * q^40 + 15 * q^42 - 32 * q^43 - 9 * q^44 + 9 * q^45 + 12 * q^46 - 18 * q^47 - 6 * q^48 - 19 * q^49 - 7 * q^50 - 21 * q^51 - 7 * q^52 + 20 * q^53 + 27 * q^54 - 54 * q^55 + 14 * q^56 + 28 * q^57 + 13 * q^58 - 21 * q^59 - 19 * q^60 - 67 * q^61 + 69 * q^62 - 28 * q^63 + 35 * q^64 + 22 * q^65 - q^66 - 18 * q^67 + 17 * q^68 - 42 * q^69 + 4 * q^70 - 36 * q^71 - 23 * q^72 - 18 * q^73 + 22 * q^74 - 49 * q^75 - 25 * q^76 + 20 * q^77 + 38 * q^78 - 92 * q^79 + 6 * q^80 - 25 * q^81 + 42 * q^83 - 15 * q^84 - 29 * q^85 + 32 * q^86 - 40 * q^87 + 9 * q^88 - 8 * q^89 - 9 * q^90 - 89 * q^91 - 12 * q^92 - q^93 + 18 * q^94 - 62 * q^95 + 6 * q^96 - 40 * q^97 + 19 * q^98 - 64 * 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
$3$	0.00791248	0.00456827	0.00228414	−	0.999997i	$-0.499273\pi$
$3$	0.00791248	0.00456827	0.00228414	+	0.999997i	$0.499273\pi$
$4$	1.00000	0.500000
$5$	−2.05271	−0.917998	−0.458999	−	0.888437i	$-0.651792\pi$
$5$	−2.05271	−0.917998	−0.458999	+	0.888437i	$0.651792\pi$
$6$	−0.00791248	−0.00323026
$7$	−2.16347	−0.817716	−0.408858	−	0.912598i	$-0.634073\pi$
$7$	−2.16347	−0.817716	−0.408858	+	0.912598i	$0.634073\pi$
$8$	−1.00000	−0.353553
$9$	−2.99994	−0.999979
$10$	2.05271	0.649123
$11$	3.51446	1.05965	0.529825	−	0.848107i	$-0.322258\pi$
$11$	3.51446	1.05965	0.529825	+	0.848107i	$0.322258\pi$
$12$	0.00791248	0.00228414
$13$	0.954466	0.264721	0.132361	−	0.991202i	$-0.457744\pi$
$13$	0.954466	0.264721	0.132361	+	0.991202i	$0.457744\pi$
$14$	2.16347	0.578213
$15$	−0.0162420	−0.00419367
$16$	1.00000	0.250000
$17$	1.50277	0.364475	0.182238	−	0.983255i	$-0.441666\pi$
$17$	1.50277	0.364475	0.182238	+	0.983255i	$0.441666\pi$
$18$	2.99994	0.707092
$19$	5.51294	1.26476	0.632378	−	0.774660i	$-0.282079\pi$
$19$	5.51294	1.26476	0.632378	+	0.774660i	$0.282079\pi$
$20$	−2.05271	−0.458999
$21$	−0.0171184	−0.00373555
$22$	−3.51446	−0.749285
$23$	2.04363	0.426125	0.213063	−	0.977039i	$-0.431656\pi$
$23$	2.04363	0.426125	0.213063	+	0.977039i	$0.431656\pi$
$24$	−0.00791248	−0.00161513
$25$	−0.786397	−0.157279
$26$	−0.954466	−0.187186
$27$	−0.0474744	−0.00913645
$28$	−2.16347	−0.408858
$29$	−8.64347	−1.60505	−0.802526	−	0.596617i	$-0.796511\pi$
$29$	−8.64347	−1.60505	−0.802526	+	0.596617i	$0.796511\pi$
$30$	0.0162420	0.00296537
$31$	−1.46030	−0.262277	−0.131139	−	0.991364i	$-0.541863\pi$
$31$	−1.46030	−0.262277	−0.131139	+	0.991364i	$0.541863\pi$
$32$	−1.00000	−0.176777
$33$	0.0278081	0.00484077
$34$	−1.50277	−0.257723
$35$	4.44098	0.750662
$36$	−2.99994	−0.499990
$37$	−11.7587	−1.93312	−0.966559	−	0.256446i	$-0.917448\pi$
$37$	−11.7587	−1.93312	−0.966559	+	0.256446i	$0.917448\pi$
$38$	−5.51294	−0.894318
$39$	0.00755219	0.00120932
$40$	2.05271	0.324561
$41$	1.30333	0.203546	0.101773	−	0.994808i	$-0.467549\pi$
$41$	1.30333	0.203546	0.101773	+	0.994808i	$0.467549\pi$
$42$	0.0171184	0.00264143
$43$	9.55197	1.45666	0.728331	−	0.685226i	$-0.240297\pi$
$43$	9.55197	1.45666	0.728331	+	0.685226i	$0.240297\pi$
$44$	3.51446	0.529825
$45$	6.15799	0.917979
$46$	−2.04363	−0.301316
$47$	8.01046	1.16845	0.584223	−	0.811593i	$-0.301399\pi$
$47$	8.01046	1.16845	0.584223	+	0.811593i	$0.301399\pi$
$48$	0.00791248	0.00114207
$49$	−2.31938	−0.331340
$50$	0.786397	0.111213
$51$	0.0118906	0.00166502
$52$	0.954466	0.132361
$53$	2.71410	0.372810	0.186405	−	0.982473i	$-0.440316\pi$
$53$	2.71410	0.372810	0.186405	+	0.982473i	$0.440316\pi$
$54$	0.0474744	0.00646044
$55$	−7.21415	−0.972756
$56$	2.16347	0.289106
$57$	0.0436211	0.00577775
$58$	8.64347	1.13494
$59$	10.0846	1.31290	0.656452	−	0.754367i	$-0.272056\pi$
$59$	10.0846	1.31290	0.656452	+	0.754367i	$0.272056\pi$
$60$	−0.0162420	−0.00209683
$61$	6.16426	0.789252	0.394626	−	0.918842i	$-0.370874\pi$
$61$	6.16426	0.789252	0.394626	+	0.918842i	$0.370874\pi$
$62$	1.46030	0.185458
$63$	6.49029	0.817699
$64$	1.00000	0.125000
$65$	−1.95924	−0.243014
$66$	−0.0278081	−0.00342294
$67$	6.69007	0.817323	0.408661	−	0.912686i	$-0.365996\pi$
$67$	6.69007	0.817323	0.408661	+	0.912686i	$0.365996\pi$
$68$	1.50277	0.182238
$69$	0.0161701	0.00194666
$70$	−4.44098	−0.530798
$71$	6.36626	0.755536	0.377768	−	0.925900i	$-0.376692\pi$
$71$	6.36626	0.755536	0.377768	+	0.925900i	$0.376692\pi$
$72$	2.99994	0.353546
$73$	9.38700	1.09867	0.549333	−	0.835604i	$-0.314882\pi$
$73$	9.38700	1.09867	0.549333	+	0.835604i	$0.314882\pi$
$74$	11.7587	1.36692
$75$	−0.00622235	−0.000718495 0
$76$	5.51294	0.632378
$77$	−7.60344	−0.866492
$78$	−0.00755219	−0.000855117 0
$79$	−5.92668	−0.666804	−0.333402	−	0.942785i	$-0.608197\pi$
$79$	−5.92668	−0.666804	−0.333402	+	0.942785i	$0.608197\pi$
$80$	−2.05271	−0.229500
$81$	8.99944	0.999937
$82$	−1.30333	−0.143928
$83$	−13.8283	−1.51785	−0.758925	−	0.651178i	$-0.774275\pi$
$83$	−13.8283	−1.51785	−0.758925	+	0.651178i	$0.774275\pi$
$84$	−0.0171184	−0.00186778
$85$	−3.08474	−0.334588
$86$	−9.55197	−1.03001
$87$	−0.0683913	−0.00733232
$88$	−3.51446	−0.374643
$89$	−10.2331	−1.08470	−0.542351	−	0.840152i	$-0.682466\pi$
$89$	−10.2331	−1.08470	−0.542351	+	0.840152i	$0.682466\pi$
$90$	−6.15799	−0.649109
$91$	−2.06496	−0.216467
$92$	2.04363	0.213063
$93$	−0.0115546	−0.00119815
$94$	−8.01046	−0.826216
$95$	−11.3165	−1.16104
$96$	−0.00791248	−0.000807564 0
$97$	−5.93870	−0.602983	−0.301492	−	0.953469i	$-0.597485\pi$
$97$	−5.93870	−0.602983	−0.301492	+	0.953469i	$0.597485\pi$
$98$	2.31938	0.234293
$99$	−10.5432	−1.05963
$100$	−0.786397	−0.0786397
$101$	0.631951	0.0628815	0.0314407	−	0.999506i	$-0.489990\pi$
$101$	0.631951	0.0628815	0.0314407	+	0.999506i	$0.489990\pi$
$102$	−0.0118906	−0.00117735
$103$	13.1398	1.29470	0.647352	−	0.762191i	$-0.275876\pi$
$103$	13.1398	1.29470	0.647352	+	0.762191i	$0.275876\pi$
$104$	−0.954466	−0.0935931
$105$	0.0351391	0.00342923
$106$	−2.71410	−0.263617
$107$	−2.85138	−0.275653	−0.137826	−	0.990456i	$-0.544012\pi$
$107$	−2.85138	−0.275653	−0.137826	+	0.990456i	$0.544012\pi$
$108$	−0.0474744	−0.00456822
$109$	−15.9944	−1.53198	−0.765991	−	0.642852i	$-0.777751\pi$
$109$	−15.9944	−1.53198	−0.765991	+	0.642852i	$0.777751\pi$
$110$	7.21415	0.687842
$111$	−0.0930404	−0.00883100
$112$	−2.16347	−0.204429
$113$	−15.5522	−1.46303	−0.731513	−	0.681828i	$-0.761185\pi$
$113$	−15.5522	−1.46303	−0.731513	+	0.681828i	$0.761185\pi$
$114$	−0.0436211	−0.00408549
$115$	−4.19496	−0.391182
$116$	−8.64347	−0.802526
$117$	−2.86334	−0.264716
$118$	−10.0846	−0.928364
$119$	−3.25120	−0.298037
$120$	0.0162420	0.00148268
$121$	1.35142	0.122856
$122$	−6.16426	−0.558086
$123$	0.0103126	0.000929852 0
$124$	−1.46030	−0.131139
$125$	11.8778	1.06238
$126$	−6.49029	−0.578201
$127$	−4.97035	−0.441047	−0.220524	−	0.975382i	$-0.570777\pi$
$127$	−4.97035	−0.441047	−0.220524	+	0.975382i	$0.570777\pi$
$128$	−1.00000	−0.0883883
$129$	0.0755797	0.00665442
$130$	1.95924	0.171837
$131$	19.1198	1.67050	0.835251	−	0.549868i	$-0.185322\pi$
$131$	19.1198	1.67050	0.835251	+	0.549868i	$0.185322\pi$
$132$	0.0278081	0.00242038
$133$	−11.9271	−1.03421
$134$	−6.69007	−0.577934
$135$	0.0974510	0.00838724
$136$	−1.50277	−0.128861
$137$	11.0041	0.940148	0.470074	−	0.882627i	$-0.344227\pi$
$137$	11.0041	0.940148	0.470074	+	0.882627i	$0.344227\pi$
$138$	−0.0161701	−0.00137649
$139$	−3.01281	−0.255543	−0.127771	−	0.991804i	$-0.540782\pi$
$139$	−3.01281	−0.255543	−0.127771	+	0.991804i	$0.540782\pi$
$140$	4.44098	0.375331
$141$	0.0633826	0.00533778
$142$	−6.36626	−0.534244
$143$	3.35443	0.280512
$144$	−2.99994	−0.249995
$145$	17.7425	1.47344
$146$	−9.38700	−0.776874
$147$	−0.0183521	−0.00151365
$148$	−11.7587	−0.966559
$149$	−21.3046	−1.74534	−0.872670	−	0.488311i	$-0.837613\pi$
$149$	−21.3046	−1.74534	−0.872670	+	0.488311i	$0.837613\pi$
$150$	0.00622235	0.000508053 0
$151$	−21.3100	−1.73418	−0.867092	−	0.498149i	$-0.834013\pi$
$151$	−21.3100	−1.73418	−0.867092	+	0.498149i	$0.834013\pi$
$152$	−5.51294	−0.447159
$153$	−4.50821	−0.364468
$154$	7.60344	0.612703
$155$	2.99756	0.240770
$156$	0.00755219	0.000604659 0
$157$	−9.61299	−0.767200	−0.383600	−	0.923499i	$-0.625316\pi$
$157$	−9.61299	−0.767200	−0.383600	+	0.923499i	$0.625316\pi$
$158$	5.92668	0.471502
$159$	0.0214753	0.00170310
$160$	2.05271	0.162281
$161$	−4.42133	−0.348450
$162$	−8.99944	−0.707063
$163$	−12.0713	−0.945500	−0.472750	−	0.881197i	$-0.656739\pi$
$163$	−12.0713	−0.945500	−0.472750	+	0.881197i	$0.656739\pi$
$164$	1.30333	0.101773
$165$	−0.0570818	−0.00444381
$166$	13.8283	1.07328
$167$	−9.63848	−0.745848	−0.372924	−	0.927862i	$-0.621645\pi$
$167$	−9.63848	−0.745848	−0.372924	+	0.927862i	$0.621645\pi$
$168$	0.0171184	0.00132072
$169$	−12.0890	−0.929923
$170$	3.08474	0.236589
$171$	−16.5385	−1.26473
$172$	9.55197	0.728331
$173$	15.0750	1.14613	0.573064	−	0.819511i	$-0.305755\pi$
$173$	15.0750	1.14613	0.573064	+	0.819511i	$0.305755\pi$
$174$	0.0683913	0.00518473
$175$	1.70135	0.128610
$176$	3.51446	0.264912
$177$	0.0797943	0.00599771
$178$	10.2331	0.767000
$179$	−21.0872	−1.57613	−0.788067	−	0.615590i	$-0.788918\pi$
$179$	−21.0872	−1.57613	−0.788067	+	0.615590i	$0.788918\pi$
$180$	6.15799	0.458989
$181$	−17.6060	−1.30864	−0.654321	−	0.756217i	$-0.727046\pi$
$181$	−17.6060	−1.30864	−0.654321	+	0.756217i	$0.727046\pi$
$182$	2.06496	0.153065
$183$	0.0487746	0.00360552
$184$	−2.04363	−0.150658
$185$	24.1371	1.77460
$186$	0.0115546	0.000847223 0
$187$	5.28142	0.386216
$188$	8.01046	0.584223
$189$	0.102710	0.00747102
$190$	11.3165	0.820982
$191$	−0.0895558	−0.00648003	−0.00324001	−	0.999995i	$-0.501031\pi$
$191$	−0.0895558	−0.00648003	−0.00324001	+	0.999995i	$0.501031\pi$
$192$	0.00791248	0.000571034 0
$193$	−23.8473	−1.71657	−0.858285	−	0.513174i	$-0.828469\pi$
$193$	−23.8473	−1.71657	−0.858285	+	0.513174i	$0.828469\pi$
$194$	5.93870	0.426374
$195$	−0.0155024	−0.00111015
$196$	−2.31938	−0.165670
$197$	2.83030	0.201650	0.100825	−	0.994904i	$-0.467852\pi$
$197$	2.83030	0.201650	0.100825	+	0.994904i	$0.467852\pi$
$198$	10.5432	0.749269
$199$	4.83453	0.342711	0.171355	−	0.985209i	$-0.445185\pi$
$199$	4.83453	0.342711	0.171355	+	0.985209i	$0.445185\pi$
$200$	0.786397	0.0556067
$201$	0.0529351	0.00373375
$202$	−0.631951	−0.0444639
$203$	18.6999	1.31248
$204$	0.0118906	0.000832511 0
$205$	−2.67535	−0.186854
$206$	−13.1398	−0.915494
$207$	−6.13075	−0.426116
$208$	0.954466	0.0661803
$209$	19.3750	1.34020
$210$	−0.0351391	−0.00242483
$211$	−4.16218	−0.286537	−0.143268	−	0.989684i	$-0.545761\pi$
$211$	−4.16218	−0.286537	−0.143268	+	0.989684i	$0.545761\pi$
$212$	2.71410	0.186405
$213$	0.0503729	0.00345149
$214$	2.85138	0.194916
$215$	−19.6074	−1.33721
$216$	0.0474744	0.00323022
$217$	3.15932	0.214468
$218$	15.9944	1.08327
$219$	0.0742745	0.00501900
$220$	−7.21415	−0.486378
$221$	1.43434	0.0964843
$222$	0.0930404	0.00624446
$223$	−9.26530	−0.620450	−0.310225	−	0.950663i	$-0.600404\pi$
$223$	−9.26530	−0.620450	−0.310225	+	0.950663i	$0.600404\pi$
$224$	2.16347	0.144553
$225$	2.35914	0.157276
$226$	15.5522	1.03452
$227$	−2.17585	−0.144417	−0.0722083	−	0.997390i	$-0.523005\pi$
$227$	−2.17585	−0.144417	−0.0722083	+	0.997390i	$0.523005\pi$
$228$	0.0436211	0.00288888
$229$	−23.2673	−1.53754	−0.768772	−	0.639523i	$-0.779132\pi$
$229$	−23.2673	−1.53754	−0.768772	+	0.639523i	$0.779132\pi$
$230$	4.19496	0.276608
$231$	−0.0601621	−0.00395837
$232$	8.64347	0.567472
$233$	22.0290	1.44317	0.721584	−	0.692327i	$-0.243414\pi$
$233$	22.0290	1.44317	0.721584	+	0.692327i	$0.243414\pi$
$234$	2.86334	0.187182
$235$	−16.4431	−1.07263
$236$	10.0846	0.656452
$237$	−0.0468948	−0.00304614
$238$	3.25120	0.210744
$239$	−9.58138	−0.619768	−0.309884	−	0.950774i	$-0.600290\pi$
$239$	−9.58138	−0.619768	−0.309884	+	0.950774i	$0.600290\pi$
$240$	−0.0162420	−0.00104842
$241$	3.18232	0.204991	0.102496	−	0.994733i	$-0.467317\pi$
$241$	3.18232	0.204991	0.102496	+	0.994733i	$0.467317\pi$
$242$	−1.35142	−0.0868725
$243$	0.213631	0.0137044
$244$	6.16426	0.394626
$245$	4.76101	0.304170
$246$	−0.0103126	−0.000657504 0
$247$	5.26192	0.334808
$248$	1.46030	0.0927291
$249$	−0.109416	−0.00693395
$250$	−11.8778	−0.751216
$251$	−18.6446	−1.17684	−0.588418	−	0.808557i	$-0.700249\pi$
$251$	−18.6446	−1.17684	−0.588418	+	0.808557i	$0.700249\pi$
$252$	6.49029	0.408850
$253$	7.18224	0.451543
$254$	4.97035	0.311867
$255$	−0.0244080	−0.00152849
$256$	1.00000	0.0625000
$257$	−2.10623	−0.131383	−0.0656914	−	0.997840i	$-0.520925\pi$
$257$	−2.10623	−0.131383	−0.0656914	+	0.997840i	$0.520925\pi$
$258$	−0.0755797	−0.00470539
$259$	25.4396	1.58074
$260$	−1.95924	−0.121507
$261$	25.9299	1.60502
$262$	−19.1198	−1.18122
$263$	−21.9082	−1.35092	−0.675458	−	0.737399i	$-0.736054\pi$
$263$	−21.9082	−1.35092	−0.675458	+	0.737399i	$0.736054\pi$
$264$	−0.0278081	−0.00171147
$265$	−5.57125	−0.342239
$266$	11.9271	0.731298
$267$	−0.0809689	−0.00495521
$268$	6.69007	0.408661
$269$	−26.0898	−1.59072	−0.795362	−	0.606135i	$-0.792719\pi$
$269$	−26.0898	−1.59072	−0.795362	+	0.606135i	$0.792719\pi$
$270$	−0.0974510	−0.00593068
$271$	9.63585	0.585336	0.292668	−	0.956214i	$-0.405457\pi$
$271$	9.63585	0.585336	0.292668	+	0.956214i	$0.405457\pi$
$272$	1.50277	0.0911188
$273$	−0.0163390	−0.000988879 0
$274$	−11.0041	−0.664785
$275$	−2.76376	−0.166661
$276$	0.0161701	0.000973328 0
$277$	−10.3646	−0.622750	−0.311375	−	0.950287i	$-0.600790\pi$
$277$	−10.3646	−0.622750	−0.311375	+	0.950287i	$0.600790\pi$
$278$	3.01281	0.180696
$279$	4.38080	0.262272
$280$	−4.44098	−0.265399
$281$	28.9878	1.72927	0.864634	−	0.502402i	$-0.167550\pi$
$281$	28.9878	1.72927	0.864634	+	0.502402i	$0.167550\pi$
$282$	−0.0633826	−0.00377438
$283$	−28.9915	−1.72336	−0.861682	−	0.507448i	$-0.830589\pi$
$283$	−28.9915	−1.72336	−0.861682	+	0.507448i	$0.830589\pi$
$284$	6.36626	0.377768
$285$	−0.0895412	−0.00530396
$286$	−3.35443	−0.198352
$287$	−2.81972	−0.166443
$288$	2.99994	0.176773
$289$	−14.7417	−0.867158
$290$	−17.7425	−1.04188
$291$	−0.0469898	−0.00275459
$292$	9.38700	0.549333
$293$	−28.1735	−1.64592	−0.822958	−	0.568102i	$-0.807678\pi$
$293$	−28.1735	−1.64592	−0.822958	+	0.568102i	$0.807678\pi$
$294$	0.0183521	0.00107031
$295$	−20.7008	−1.20524
$296$	11.7587	0.683460
$297$	−0.166847	−0.00968143
$298$	21.3046	1.23414
$299$	1.95057	0.112804
$300$	−0.00622235	−0.000359248 0
$301$	−20.6654	−1.19114
$302$	21.3100	1.22625
$303$	0.00500030	0.000287260 0
$304$	5.51294	0.316189
$305$	−12.6534	−0.724532
$306$	4.50821	0.257717
$307$	13.5638	0.774127	0.387063	−	0.922053i	$-0.373489\pi$
$307$	13.5638	0.774127	0.387063	+	0.922053i	$0.373489\pi$
$308$	−7.60344	−0.433246
$309$	0.103969	0.00591456
$310$	−2.99756	−0.170250
$311$	9.24744	0.524374	0.262187	−	0.965017i	$-0.415556\pi$
$311$	9.24744	0.524374	0.262187	+	0.965017i	$0.415556\pi$
$312$	−0.00755219	−0.000427559 0
$313$	−14.7084	−0.831368	−0.415684	−	0.909509i	$-0.636458\pi$
$313$	−14.7084	−0.831368	−0.415684	+	0.909509i	$0.636458\pi$
$314$	9.61299	0.542492
$315$	−13.3227	−0.750646
$316$	−5.92668	−0.333402
$317$	−2.80759	−0.157690	−0.0788451	−	0.996887i	$-0.525123\pi$
$317$	−2.80759	−0.157690	−0.0788451	+	0.996887i	$0.525123\pi$
$318$	−0.0214753	−0.00120427
$319$	−30.3771	−1.70079
$320$	−2.05271	−0.114750
$321$	−0.0225615	−0.00125926
$322$	4.42133	0.246391
$323$	8.28469	0.460972
$324$	8.99944	0.499969
$325$	−0.750589	−0.0416352
$326$	12.0713	0.668569
$327$	−0.126555	−0.00699851
$328$	−1.30333	−0.0719642
$329$	−17.3304	−0.955458
$330$	0.0570818	0.00314225
$331$	20.2301	1.11194	0.555972	−	0.831201i	$-0.312346\pi$
$331$	20.2301	1.11194	0.555972	+	0.831201i	$0.312346\pi$
$332$	−13.8283	−0.758925
$333$	35.2753	1.93308
$334$	9.63848	0.527394
$335$	−13.7328	−0.750301
$336$	−0.0171184	−0.000933888 0
$337$	11.4622	0.624387	0.312193	−	0.950019i	$-0.398936\pi$
$337$	11.4622	0.624387	0.312193	+	0.950019i	$0.398936\pi$
$338$	12.0890	0.657555
$339$	−0.123056	−0.00668350
$340$	−3.08474	−0.167294
$341$	−5.13216	−0.277922
$342$	16.5385	0.894299
$343$	20.1622	1.08866
$344$	−9.55197	−0.515007
$345$	−0.0331926	−0.00178703
$346$	−15.0750	−0.810434
$347$	28.0605	1.50637	0.753184	−	0.657810i	$-0.228517\pi$
$347$	28.0605	1.50637	0.753184	+	0.657810i	$0.228517\pi$
$348$	−0.0683913	−0.00366616
$349$	3.24741	0.173830	0.0869149	−	0.996216i	$-0.472299\pi$
$349$	3.24741	0.173830	0.0869149	+	0.996216i	$0.472299\pi$
$350$	−1.70135	−0.0909410
$351$	−0.0453127	−0.00241861
$352$	−3.51446	−0.187321
$353$	27.4709	1.46213	0.731065	−	0.682308i	$-0.239024\pi$
$353$	27.4709	1.46213	0.731065	+	0.682308i	$0.239024\pi$
$354$	−0.0797943	−0.00424102
$355$	−13.0681	−0.693580
$356$	−10.2331	−0.542351
$357$	−0.0257251	−0.00136152
$358$	21.0872	1.11449
$359$	15.3559	0.810455	0.405227	−	0.914216i	$-0.367192\pi$
$359$	15.3559	0.810455	0.405227	+	0.914216i	$0.367192\pi$
$360$	−6.15799	−0.324555
$361$	11.3926	0.599608
$362$	17.6060	0.925350
$363$	0.0106931	0.000561241 0
$364$	−2.06496	−0.108233
$365$	−19.2688	−1.00857
$366$	−0.0487746	−0.00254949
$367$	26.2089	1.36809	0.684046	−	0.729439i	$-0.260219\pi$
$367$	26.2089	1.36809	0.684046	+	0.729439i	$0.260219\pi$
$368$	2.04363	0.106531
$369$	−3.90990	−0.203541
$370$	−24.1371	−1.25483
$371$	−5.87188	−0.304853
$372$	−0.0115546	−0.000599077 0
$373$	−3.25830	−0.168709	−0.0843543	−	0.996436i	$-0.526883\pi$
$373$	−3.25830	−0.168709	−0.0843543	+	0.996436i	$0.526883\pi$
$374$	−5.28142	−0.273096
$375$	0.0939826	0.00485324
$376$	−8.01046	−0.413108
$377$	−8.24990	−0.424891
$378$	−0.102710	−0.00528281
$379$	13.5494	0.695987	0.347994	−	0.937497i	$-0.386863\pi$
$379$	13.5494	0.695987	0.347994	+	0.937497i	$0.386863\pi$
$380$	−11.3165	−0.580522
$381$	−0.0393278	−0.00201482
$382$	0.0895558	0.00458207
$383$	−5.87559	−0.300229	−0.150114	−	0.988669i	$-0.547964\pi$
$383$	−5.87559	−0.300229	−0.150114	+	0.988669i	$0.547964\pi$
$384$	−0.00791248	−0.000403782 0
$385$	15.6076	0.795438
$386$	23.8473	1.21380
$387$	−28.6553	−1.45663
$388$	−5.93870	−0.301492
$389$	26.7611	1.35684	0.678421	−	0.734674i	$-0.262665\pi$
$389$	26.7611	1.35684	0.678421	+	0.734674i	$0.262665\pi$
$390$	0.0155024	0.000784996 0
$391$	3.07110	0.155312
$392$	2.31938	0.117146
$393$	0.151285	0.00763131
$394$	−2.83030	−0.142588
$395$	12.1657	0.612125
$396$	−10.5432	−0.529813
$397$	−11.4504	−0.574682	−0.287341	−	0.957828i	$-0.592771\pi$
$397$	−11.4504	−0.574682	−0.287341	+	0.957828i	$0.592771\pi$
$398$	−4.83453	−0.242333
$399$	−0.0943730	−0.00472456
$400$	−0.786397	−0.0393199
$401$	−15.3106	−0.764574	−0.382287	−	0.924044i	$-0.624864\pi$
$401$	−15.3106	−0.764574	−0.382287	+	0.924044i	$0.624864\pi$
$402$	−0.0529351	−0.00264016
$403$	−1.39381	−0.0694304
$404$	0.631951	0.0314407
$405$	−18.4732	−0.917941
$406$	−18.6999	−0.928062
$407$	−41.3254	−2.04843
$408$	−0.0118906	−0.000588674 0
$409$	15.9969	0.790993	0.395497	−	0.918467i	$-0.370572\pi$
$409$	15.9969	0.790993	0.395497	+	0.918467i	$0.370572\pi$
$410$	2.67535	0.132126
$411$	0.0870701	0.00429485
$412$	13.1398	0.647352
$413$	−21.8178	−1.07358
$414$	6.13075	0.301310
$415$	28.3854	1.39338
$416$	−0.954466	−0.0467965
$417$	−0.0238388	−0.00116739
$418$	−19.3750	−0.947663
$419$	−15.4439	−0.754485	−0.377243	−	0.926114i	$-0.623128\pi$
$419$	−15.4439	−0.754485	−0.377243	+	0.926114i	$0.623128\pi$
$420$	0.0351391	0.00171461
$421$	−22.8408	−1.11319	−0.556596	−	0.830783i	$-0.687893\pi$
$421$	−22.8408	−1.11319	−0.556596	+	0.830783i	$0.687893\pi$
$422$	4.16218	0.202612
$423$	−24.0309	−1.16842
$424$	−2.71410	−0.131808
$425$	−1.18177	−0.0573245
$426$	−0.0503729	−0.00244057
$427$	−13.3362	−0.645385
$428$	−2.85138	−0.137826
$429$	0.0265419	0.00128145
$430$	19.6074	0.945552
$431$	−38.7999	−1.86893	−0.934464	−	0.356058i	$-0.884120\pi$
$431$	−38.7999	−1.86893	−0.934464	+	0.356058i	$0.884120\pi$
$432$	−0.0474744	−0.00228411
$433$	5.31619	0.255480	0.127740	−	0.991808i	$-0.459228\pi$
$433$	5.31619	0.255480	0.127740	+	0.991808i	$0.459228\pi$
$434$	−3.15932	−0.151652
$435$	0.140387	0.00673105
$436$	−15.9944	−0.765991
$437$	11.2664	0.538945
$438$	−0.0742745	−0.00354897
$439$	−15.9586	−0.761662	−0.380831	−	0.924645i	$-0.624362\pi$
$439$	−15.9586	−0.761662	−0.380831	+	0.924645i	$0.624362\pi$
$440$	7.21415	0.343921
$441$	6.95800	0.331333
$442$	−1.43434	−0.0682247
$443$	34.4260	1.63563	0.817814	−	0.575482i	$-0.195186\pi$
$443$	34.4260	1.63563	0.817814	+	0.575482i	$0.195186\pi$
$444$	−0.0930404	−0.00441550
$445$	21.0055	0.995754
$446$	9.26530	0.438724
$447$	−0.168572	−0.00797319
$448$	−2.16347	−0.102215
$449$	−15.7358	−0.742617	−0.371308	−	0.928510i	$-0.621091\pi$
$449$	−15.7358	−0.742617	−0.371308	+	0.928510i	$0.621091\pi$
$450$	−2.35914	−0.111211
$451$	4.58049	0.215687
$452$	−15.5522	−0.731513
$453$	−0.168615	−0.00792222
$454$	2.17585	0.102118
$455$	4.23876	0.198716
$456$	−0.0436211	−0.00204274
$457$	−30.0062	−1.40363	−0.701816	−	0.712358i	$-0.747627\pi$
$457$	−30.0062	−1.40363	−0.701816	+	0.712358i	$0.747627\pi$
$458$	23.2673	1.08721
$459$	−0.0713431	−0.00333001
$460$	−4.19496	−0.195591
$461$	−9.25095	−0.430860	−0.215430	−	0.976519i	$-0.569115\pi$
$461$	−9.25095	−0.430860	−0.215430	+	0.976519i	$0.569115\pi$
$462$	0.0601621	0.00279899
$463$	6.06645	0.281932	0.140966	−	0.990014i	$-0.454979\pi$
$463$	6.06645	0.281932	0.140966	+	0.990014i	$0.454979\pi$
$464$	−8.64347	−0.401263
$465$	0.0237182	0.00109990
$466$	−22.0290	−1.02047
$467$	0.750961	0.0347503	0.0173752	−	0.999849i	$-0.494469\pi$
$467$	0.750961	0.0347503	0.0173752	+	0.999849i	$0.494469\pi$
$468$	−2.86334	−0.132358
$469$	−14.4738	−0.668338
$470$	16.4431	0.758465
$471$	−0.0760626	−0.00350478
$472$	−10.0846	−0.464182
$473$	33.5700	1.54355
$474$	0.0468948	0.00215395
$475$	−4.33536	−0.198920
$476$	−3.25120	−0.149019
$477$	−8.14213	−0.372802
$478$	9.58138	0.438242
$479$	27.1845	1.24209	0.621047	−	0.783774i	$-0.286708\pi$
$479$	27.1845	1.24209	0.621047	+	0.783774i	$0.286708\pi$
$480$	0.0162420	0.000741342 0
$481$	−11.2233	−0.511737
$482$	−3.18232	−0.144951
$483$	−0.0349837	−0.00159181
$484$	1.35142	0.0614281
$485$	12.1904	0.553537
$486$	−0.213631	−0.00969050
$487$	−0.526772	−0.0238703	−0.0119352	−	0.999929i	$-0.503799\pi$
$487$	−0.526772	−0.0238703	−0.0119352	+	0.999929i	$0.503799\pi$
$488$	−6.16426	−0.279043
$489$	−0.0955142	−0.00431930
$490$	−4.76101	−0.215080
$491$	17.2936	0.780450	0.390225	−	0.920719i	$-0.372397\pi$
$491$	17.2936	0.780450	0.390225	+	0.920719i	$0.372397\pi$
$492$	0.0103126	0.000464926 0
$493$	−12.9891	−0.585002
$494$	−5.26192	−0.236745
$495$	21.6420	0.972736
$496$	−1.46030	−0.0655693
$497$	−13.7732	−0.617814
$498$	0.109416	0.00490304
$499$	10.7319	0.480427	0.240213	−	0.970720i	$-0.422783\pi$
$499$	10.7319	0.480427	0.240213	+	0.970720i	$0.422783\pi$
$500$	11.8778	0.531190
$501$	−0.0762642	−0.00340724
$502$	18.6446	0.832149
$503$	23.8730	1.06445	0.532223	−	0.846604i	$-0.321357\pi$
$503$	23.8730	1.06445	0.532223	+	0.846604i	$0.321357\pi$
$504$	−6.49029	−0.289100
$505$	−1.29721	−0.0577251
$506$	−7.18224	−0.319289
$507$	−0.0956539	−0.00424814
$508$	−4.97035	−0.220524
$509$	13.0185	0.577034	0.288517	−	0.957475i	$-0.406838\pi$
$509$	13.0185	0.577034	0.288517	+	0.957475i	$0.406838\pi$
$510$	0.0244080	0.00108080
$511$	−20.3085	−0.898397
$512$	−1.00000	−0.0441942
$513$	−0.261724	−0.0115554
$514$	2.10623	0.0929016
$515$	−26.9722	−1.18854
$516$	0.0755797	0.00332721
$517$	28.1524	1.23814
$518$	−25.4396	−1.11775
$519$	0.119280	0.00523582
$520$	1.95924	0.0859183
$521$	−12.5763	−0.550977	−0.275488	−	0.961304i	$-0.588840\pi$
$521$	−12.5763	−0.550977	−0.275488	+	0.961304i	$0.588840\pi$
$522$	−25.9299	−1.13492
$523$	−13.1452	−0.574801	−0.287401	−	0.957810i	$-0.592791\pi$
$523$	−13.1452	−0.574801	−0.287401	+	0.957810i	$0.592791\pi$
$524$	19.1198	0.835251
$525$	0.0134619	0.000587525 0
$526$	21.9082	0.955241
$527$	−2.19449	−0.0955936
$528$	0.0278081	0.00121019
$529$	−18.8236	−0.818417
$530$	5.57125	0.242000
$531$	−30.2532	−1.31288
$532$	−11.9271	−0.517106
$533$	1.24398	0.0538828
$534$	0.0809689	0.00350387
$535$	5.85304	0.253049
$536$	−6.69007	−0.288967
$537$	−0.166852	−0.00720021
$538$	26.0898	1.12481
$539$	−8.15137	−0.351104
$540$	0.0974510	0.00419362
$541$	−40.6361	−1.74708	−0.873540	−	0.486752i	$-0.838182\pi$
$541$	−40.6361	−1.74708	−0.873540	+	0.486752i	$0.838182\pi$
$542$	−9.63585	−0.413895
$543$	−0.139307	−0.00597823
$544$	−1.50277	−0.0644307
$545$	32.8317	1.40636
$546$	0.0163390	0.000699243 0
$547$	26.2707	1.12326	0.561628	−	0.827390i	$-0.310175\pi$
$547$	26.2707	1.12326	0.561628	+	0.827390i	$0.310175\pi$
$548$	11.0041	0.470074
$549$	−18.4924	−0.789236
$550$	2.76376	0.117847
$551$	−47.6510	−2.03000
$552$	−0.0161701	−0.000688247 0
$553$	12.8222	0.545256
$554$	10.3646	0.440351
$555$	0.190985	0.00810685
$556$	−3.01281	−0.127771
$557$	−6.39720	−0.271058	−0.135529	−	0.990773i	$-0.543273\pi$
$557$	−6.39720	−0.271058	−0.135529	+	0.990773i	$0.543273\pi$
$558$	−4.38080	−0.185454
$559$	9.11703	0.385609
$560$	4.44098	0.187666
$561$	0.0417891	0.00176434
$562$	−28.9878	−1.22278
$563$	−15.8572	−0.668303	−0.334151	−	0.942519i	$-0.608450\pi$
$563$	−15.8572	−0.668303	−0.334151	+	0.942519i	$0.608450\pi$
$564$	0.0633826	0.00266889
$565$	31.9241	1.34305
$566$	28.9915	1.21860
$567$	−19.4700	−0.817665
$568$	−6.36626	−0.267122
$569$	−29.4337	−1.23392	−0.616961	−	0.786993i	$-0.711637\pi$
$569$	−29.4337	−1.23392	−0.616961	+	0.786993i	$0.711637\pi$
$570$	0.0895412	0.00375047
$571$	−25.0635	−1.04888	−0.524438	−	0.851449i	$-0.675724\pi$
$571$	−25.0635	−1.04888	−0.524438	+	0.851449i	$0.675724\pi$
$572$	3.35443	0.140256
$573$	−0.000708608 0	−2.96025e−5 0
$574$	2.81972	0.117693
$575$	−1.60710	−0.0670208
$576$	−2.99994	−0.124997
$577$	13.5581	0.564432	0.282216	−	0.959351i	$-0.408931\pi$
$577$	13.5581	0.564432	0.282216	+	0.959351i	$0.408931\pi$
$578$	14.7417	0.613173
$579$	−0.188692	−0.00784175
$580$	17.7425	0.736718
$581$	29.9171	1.24117
$582$	0.0469898	0.00194779
$583$	9.53859	0.395048
$584$	−9.38700	−0.388437
$585$	5.87759	0.243008
$586$	28.1735	1.16384
$587$	10.7242	0.442633	0.221317	−	0.975202i	$-0.428965\pi$
$587$	10.7242	0.442633	0.221317	+	0.975202i	$0.428965\pi$
$588$	−0.0183521	−0.000756826 0
$589$	−8.05055	−0.331717
$590$	20.7008	0.852236
$591$	0.0223947	0.000921194 0
$592$	−11.7587	−0.483279
$593$	47.6262	1.95578	0.977888	−	0.209131i	$-0.0670636\pi$
$593$	47.6262	1.95578	0.977888	+	0.209131i	$0.0670636\pi$
$594$	0.166847	0.00684580
$595$	6.67376	0.273598
$596$	−21.3046	−0.872670
$597$	0.0382531	0.00156559
$598$	−1.95057	−0.0797648
$599$	−10.7706	−0.440074	−0.220037	−	0.975492i	$-0.570618\pi$
$599$	−10.7706	−0.440074	−0.220037	+	0.975492i	$0.570618\pi$
$600$	0.00622235	0.000254026 0
$601$	−26.7770	−1.09226	−0.546129	−	0.837701i	$-0.683899\pi$
$601$	−26.7770	−1.09226	−0.546129	+	0.837701i	$0.683899\pi$
$602$	20.6654	0.842260
$603$	−20.0698	−0.817305
$604$	−21.3100	−0.867092
$605$	−2.77406	−0.112782
$606$	−0.00500030	−0.000203123 0
$607$	−26.8906	−1.09145	−0.545727	−	0.837963i	$-0.683747\pi$
$607$	−26.8906	−1.09145	−0.545727	+	0.837963i	$0.683747\pi$
$608$	−5.51294	−0.223579
$609$	0.147963	0.00599576
$610$	12.6534	0.512322
$611$	7.64572	0.309313
$612$	−4.50821	−0.182234
$613$	2.22491	0.0898634	0.0449317	−	0.998990i	$-0.485693\pi$
$613$	2.22491	0.0898634	0.0449317	+	0.998990i	$0.485693\pi$
$614$	−13.5638	−0.547390
$615$	−0.0211686	−0.000853602 0
$616$	7.60344	0.306351
$617$	29.8195	1.20049	0.600244	−	0.799817i	$-0.295070\pi$
$617$	29.8195	1.20049	0.600244	+	0.799817i	$0.295070\pi$
$618$	−0.103969	−0.00418223
$619$	1.95243	0.0784749	0.0392374	−	0.999230i	$-0.487507\pi$
$619$	1.95243	0.0784749	0.0392374	+	0.999230i	$0.487507\pi$
$620$	2.99756	0.120385
$621$	−0.0970199	−0.00389327
$622$	−9.24744	−0.370788
$623$	22.1390	0.886979
$624$	0.00755219	0.000302330 0
$625$	−20.4496	−0.817984
$626$	14.7084	0.587866
$627$	0.153304	0.00612239
$628$	−9.61299	−0.383600
$629$	−17.6706	−0.704573
$630$	13.3227	0.530787
$631$	−12.4835	−0.496962	−0.248481	−	0.968637i	$-0.579931\pi$
$631$	−12.4835	−0.496962	−0.248481	+	0.968637i	$0.579931\pi$
$632$	5.92668	0.235751
$633$	−0.0329332	−0.00130898
$634$	2.80759	0.111504
$635$	10.2027	0.404880
$636$	0.0214753	0.000851549 0
$637$	−2.21377	−0.0877127
$638$	30.3771	1.20264
$639$	−19.0984	−0.755520
$640$	2.05271	0.0811403
$641$	20.2019	0.797926	0.398963	−	0.916967i	$-0.369370\pi$
$641$	20.2019	0.797926	0.398963	+	0.916967i	$0.369370\pi$
$642$	0.0225615	0.000890430 0
$643$	3.08728	0.121751	0.0608753	−	0.998145i	$-0.480611\pi$
$643$	3.08728	0.121751	0.0608753	+	0.998145i	$0.480611\pi$
$644$	−4.42133	−0.174225
$645$	−0.155143	−0.00610875
$646$	−8.28469	−0.325957
$647$	43.2135	1.69890	0.849450	−	0.527670i	$-0.176934\pi$
$647$	43.2135	1.69890	0.849450	+	0.527670i	$0.176934\pi$
$648$	−8.99944	−0.353531
$649$	35.4420	1.39122
$650$	0.750589	0.0294405
$651$	0.0249980	0.000979750 0
$652$	−12.0713	−0.472750
$653$	22.0752	0.863869	0.431935	−	0.901905i	$-0.357831\pi$
$653$	22.0752	0.863869	0.431935	+	0.901905i	$0.357831\pi$
$654$	0.126555	0.00494869
$655$	−39.2473	−1.53352
$656$	1.30333	0.0508864
$657$	−28.1604	−1.09864
$658$	17.3304	0.675611
$659$	−28.9574	−1.12802	−0.564011	−	0.825767i	$-0.690742\pi$
$659$	−28.9574	−1.12802	−0.564011	+	0.825767i	$0.690742\pi$
$660$	−0.0570818	−0.00222191
$661$	5.39662	0.209904	0.104952	−	0.994477i	$-0.466531\pi$
$661$	5.39662	0.209904	0.104952	+	0.994477i	$0.466531\pi$
$662$	−20.2301	−0.786264
$663$	0.0113492	0.000440767 0
$664$	13.8283	0.536641
$665$	24.4829	0.949404
$666$	−35.2753	−1.36689
$667$	−17.6640	−0.683954
$668$	−9.63848	−0.372924
$669$	−0.0733115	−0.00283439
$670$	13.7328	0.530543
$671$	21.6640	0.836331
$672$	0.0171184	0.000660358 0
$673$	−25.2498	−0.973310	−0.486655	−	0.873594i	$-0.661783\pi$
$673$	−25.2498	−0.973310	−0.486655	+	0.873594i	$0.661783\pi$
$674$	−11.4622	−0.441508
$675$	0.0373337	0.00143698
$676$	−12.0890	−0.464961
$677$	−17.8787	−0.687136	−0.343568	−	0.939128i	$-0.611636\pi$
$677$	−17.8787	−0.687136	−0.343568	+	0.939128i	$0.611636\pi$
$678$	0.123056	0.00472595
$679$	12.8482	0.493069
$680$	3.08474	0.118295
$681$	−0.0172164	−0.000659734 0
$682$	5.13216	0.196521
$683$	9.79701	0.374872	0.187436	−	0.982277i	$-0.439982\pi$
$683$	9.79701	0.374872	0.187436	+	0.982277i	$0.439982\pi$
$684$	−16.5385	−0.632365
$685$	−22.5883	−0.863054
$686$	−20.1622	−0.769798
$687$	−0.184102	−0.00702392
$688$	9.55197	0.364165
$689$	2.59052	0.0986908
$690$	0.0331926	0.00126362
$691$	−16.7243	−0.636221	−0.318111	−	0.948054i	$-0.603048\pi$
$691$	−16.7243	−0.636221	−0.318111	+	0.948054i	$0.603048\pi$
$692$	15.0750	0.573064
$693$	22.8098	0.866474
$694$	−28.0605	−1.06516
$695$	6.18441	0.234588
$696$	0.0683913	0.00259237
$697$	1.95860	0.0741873
$698$	−3.24741	−0.122916
$699$	0.174304	0.00659279
$700$	1.70135	0.0643050
$701$	33.9617	1.28272	0.641358	−	0.767242i	$-0.278371\pi$
$701$	33.9617	1.28272	0.641358	+	0.767242i	$0.278371\pi$
$702$	0.0453127	0.00171022
$703$	−64.8250	−2.44492
$704$	3.51446	0.132456
$705$	−0.130106	−0.00490007
$706$	−27.4709	−1.03388
$707$	−1.36721	−0.0514192
$708$	0.0797943	0.00299885
$709$	49.8391	1.87175	0.935873	−	0.352338i	$-0.114613\pi$
$709$	49.8391	1.87175	0.935873	+	0.352338i	$0.114613\pi$
$710$	13.0681	0.490435
$711$	17.7797	0.666790
$712$	10.2331	0.383500
$713$	−2.98430	−0.111763
$714$	0.0257251	0.000962737 0
$715$	−6.88566	−0.257509
$716$	−21.0872	−0.788067
$717$	−0.0758125	−0.00283127
$718$	−15.3559	−0.573078
$719$	41.9472	1.56437	0.782183	−	0.623048i	$-0.214106\pi$
$719$	41.9472	1.56437	0.782183	+	0.623048i	$0.214106\pi$
$720$	6.15799	0.229495
$721$	−28.4276	−1.05870
$722$	−11.3926	−0.423987
$723$	0.0251800	0.000936456 0
$724$	−17.6060	−0.654321
$725$	6.79720	0.252442
$726$	−0.0106931	−0.000396857 0
$727$	−1.49161	−0.0553208	−0.0276604	−	0.999617i	$-0.508806\pi$
$727$	−1.49161	−0.0553208	−0.0276604	+	0.999617i	$0.508806\pi$
$728$	2.06496	0.0765326
$729$	−26.9966	−0.999875
$730$	19.2688	0.713169
$731$	14.3544	0.530917
$732$	0.0487746	0.00180276
$733$	14.3682	0.530701	0.265350	−	0.964152i	$-0.414512\pi$
$733$	14.3682	0.530701	0.265350	+	0.964152i	$0.414512\pi$
$734$	−26.2089	−0.967388
$735$	0.0376714	0.00138953
$736$	−2.04363	−0.0753290
$737$	23.5120	0.866075
$738$	3.90990	0.143925
$739$	−19.9642	−0.734395	−0.367198	−	0.930143i	$-0.619683\pi$
$739$	−19.9642	−0.734395	−0.367198	+	0.930143i	$0.619683\pi$
$740$	24.1371	0.887299
$741$	0.0416348	0.00152949
$742$	5.87188	0.215564
$743$	2.43540	0.0893462	0.0446731	−	0.999002i	$-0.485775\pi$
$743$	2.43540	0.0893462	0.0446731	+	0.999002i	$0.485775\pi$
$744$	0.0115546	0.000423612 0
$745$	43.7321	1.60222
$746$	3.25830	0.119295
$747$	41.4840	1.51782
$748$	5.28142	0.193108
$749$	6.16888	0.225406
$750$	−0.0939826	−0.00343176
$751$	12.4353	0.453771	0.226885	−	0.973921i	$-0.427146\pi$
$751$	12.4353	0.453771	0.226885	+	0.973921i	$0.427146\pi$
$752$	8.01046	0.292112
$753$	−0.147525	−0.00537611
$754$	8.24990	0.300444
$755$	43.7432	1.59198
$756$	0.102710	0.00373551
$757$	25.0773	0.911449	0.455724	−	0.890121i	$-0.349380\pi$
$757$	25.0773	0.911449	0.455724	+	0.890121i	$0.349380\pi$
$758$	−13.5494	−0.492137
$759$	0.0568293	0.00206277
$760$	11.3165	0.410491
$761$	41.6756	1.51074	0.755370	−	0.655298i	$-0.227457\pi$
$761$	41.6756	1.51074	0.755370	+	0.655298i	$0.227457\pi$
$762$	0.0393278	0.00142470
$763$	34.6034	1.25273
$764$	−0.0895558	−0.00324001
$765$	9.25404	0.334581
$766$	5.87559	0.212294
$767$	9.62542	0.347554
$768$	0.00791248	0.000285517 0
$769$	−45.0099	−1.62310	−0.811549	−	0.584284i	$-0.801375\pi$
$769$	−45.0099	−1.62310	−0.811549	+	0.584284i	$0.801375\pi$
$770$	−15.6076	−0.562460
$771$	−0.0166655	−0.000600192 0
$772$	−23.8473	−0.858285
$773$	−32.1169	−1.15516	−0.577582	−	0.816333i	$-0.696004\pi$
$773$	−32.1169	−1.15516	−0.577582	+	0.816333i	$0.696004\pi$
$774$	28.6553	1.02999
$775$	1.14837	0.0412508
$776$	5.93870	0.213187
$777$	0.201290	0.00722126
$778$	−26.7611	−0.959432
$779$	7.18517	0.257436
$780$	−0.0155024	−0.000555076 0
$781$	22.3739	0.800603
$782$	−3.07110	−0.109822
$783$	0.410344	0.0146645
$784$	−2.31938	−0.0828350
$785$	19.7326	0.704288
$786$	−0.151285	−0.00539615
$787$	−14.4690	−0.515765	−0.257883	−	0.966176i	$-0.583025\pi$
$787$	−14.4690	−0.515765	−0.257883	+	0.966176i	$0.583025\pi$
$788$	2.83030	0.100825
$789$	−0.173348	−0.00617135
$790$	−12.1657	−0.432838
$791$	33.6467	1.19634
$792$	10.5432	0.374635
$793$	5.88357	0.208932
$794$	11.4504	0.406361
$795$	−0.0440824	−0.00156344
$796$	4.83453	0.171355
$797$	−21.6420	−0.766598	−0.383299	−	0.923624i	$-0.625212\pi$
$797$	−21.6420	−0.766598	−0.383299	+	0.923624i	$0.625212\pi$
$798$	0.0943730	0.00334077
$799$	12.0379	0.425870
$800$	0.786397	0.0278033
$801$	30.6985	1.08468
$802$	15.3106	0.540636
$803$	32.9902	1.16420
$804$	0.0529351	0.00186688
$805$	9.07569	0.319876
$806$	1.39381	0.0490947
$807$	−0.206435	−0.00726686
$808$	−0.631951	−0.0222320
$809$	−46.0508	−1.61906	−0.809530	−	0.587078i	$-0.800278\pi$
$809$	−46.0508	−1.61906	−0.809530	+	0.587078i	$0.800278\pi$
$810$	18.4732	0.649082
$811$	−24.3274	−0.854252	−0.427126	−	0.904192i	$-0.640474\pi$
$811$	−24.3274	−0.854252	−0.427126	+	0.904192i	$0.640474\pi$
$812$	18.6999	0.656239
$813$	0.0762434	0.00267397
$814$	41.3254	1.44846
$815$	24.7789	0.867967
$816$	0.0118906	0.000416255 0
$817$	52.6595	1.84232
$818$	−15.9969	−0.559317
$819$	6.19476	0.216462
$820$	−2.67535	−0.0934272
$821$	45.2783	1.58023	0.790113	−	0.612962i	$-0.210022\pi$
$821$	45.2783	1.58023	0.790113	+	0.612962i	$0.210022\pi$
$822$	−0.0870701	−0.00303692
$823$	−5.98289	−0.208550	−0.104275	−	0.994548i	$-0.533252\pi$
$823$	−5.98289	−0.208550	−0.104275	+	0.994548i	$0.533252\pi$
$824$	−13.1398	−0.457747
$825$	−0.0218682	−0.000761353 0
$826$	21.8178	0.759138
$827$	−34.8423	−1.21159	−0.605793	−	0.795622i	$-0.707144\pi$
$827$	−34.8423	−1.21159	−0.605793	+	0.795622i	$0.707144\pi$
$828$	−6.13075	−0.213058
$829$	36.5489	1.26939	0.634697	−	0.772761i	$-0.281125\pi$
$829$	36.5489	1.26939	0.634697	+	0.772761i	$0.281125\pi$
$830$	−28.3854	−0.985271
$831$	−0.0820099	−0.00284489
$832$	0.954466	0.0330902
$833$	−3.48549	−0.120765
$834$	0.0238388	0.000825469 0
$835$	19.7850	0.684687
$836$	19.3750	0.670099
$837$	0.0693268	0.00239628
$838$	15.4439	0.533502
$839$	−15.5166	−0.535692	−0.267846	−	0.963462i	$-0.586312\pi$
$839$	−15.5166	−0.535692	−0.267846	+	0.963462i	$0.586312\pi$
$840$	−0.0351391	−0.00121242
$841$	45.7096	1.57619
$842$	22.8408	0.787146
$843$	0.229366	0.00789977
$844$	−4.16218	−0.143268
$845$	24.8152	0.853667
$846$	24.0309	0.826199
$847$	−2.92376	−0.100462
$848$	2.71410	0.0932026
$849$	−0.229394	−0.00787280
$850$	1.18177	0.0405345
$851$	−24.0304	−0.823750
$852$	0.0503729	0.00172575
$853$	−4.98034	−0.170524	−0.0852619	−	0.996359i	$-0.527173\pi$
$853$	−4.98034	−0.170524	−0.0852619	+	0.996359i	$0.527173\pi$
$854$	13.3362	0.456356
$855$	33.9487	1.16102
$856$	2.85138	0.0974580
$857$	17.1263	0.585024	0.292512	−	0.956262i	$-0.405509\pi$
$857$	17.1263	0.585024	0.292512	+	0.956262i	$0.405509\pi$
$858$	−0.0265419	−0.000906124 0
$859$	−42.4388	−1.44799	−0.723996	−	0.689804i	$-0.757697\pi$
$859$	−42.4388	−1.44799	−0.723996	+	0.689804i	$0.757697\pi$
$860$	−19.6074	−0.668606
$861$	−0.0223109	−0.000760355 0
$862$	38.7999	1.32153
$863$	−2.06570	−0.0703174	−0.0351587	−	0.999382i	$-0.511194\pi$
$863$	−2.06570	−0.0703174	−0.0351587	+	0.999382i	$0.511194\pi$
$864$	0.0474744	0.00161511
$865$	−30.9444	−1.05214
$866$	−5.31619	−0.180651
$867$	−0.116643	−0.00396141
$868$	3.15932	0.107234
$869$	−20.8291	−0.706578
$870$	−0.140387	−0.00475957
$871$	6.38545	0.216363
$872$	15.9944	0.541637
$873$	17.8157	0.602971
$874$	−11.2664	−0.381091
$875$	−25.6973	−0.868726
$876$	0.0742745	0.00250950
$877$	−55.6239	−1.87828	−0.939142	−	0.343529i	$-0.888378\pi$
$877$	−55.6239	−1.87828	−0.939142	+	0.343529i	$0.888378\pi$
$878$	15.9586	0.538576
$879$	−0.222923	−0.00751899
$880$	−7.21415	−0.243189
$881$	−1.18516	−0.0399291	−0.0199645	−	0.999801i	$-0.506355\pi$
$881$	−1.18516	−0.0399291	−0.0199645	+	0.999801i	$0.506355\pi$
$882$	−6.95800	−0.234288
$883$	25.0978	0.844608	0.422304	−	0.906454i	$-0.361221\pi$
$883$	25.0978	0.844608	0.422304	+	0.906454i	$0.361221\pi$
$884$	1.43434	0.0482422
$885$	−0.163794	−0.00550588
$886$	−34.4260	−1.15656
$887$	−34.5437	−1.15986	−0.579932	−	0.814665i	$-0.696921\pi$
$887$	−34.5437	−1.15986	−0.579932	+	0.814665i	$0.696921\pi$
$888$	0.0930404	0.00312223
$889$	10.7532	0.360651
$890$	−21.0055	−0.704105
$891$	31.6281	1.05958
$892$	−9.26530	−0.310225
$893$	44.1613	1.47780
$894$	0.168572	0.00563789
$895$	43.2859	1.44689
$896$	2.16347	0.0722766
$897$	0.0154339	0.000515321 0
$898$	15.7358	0.525109
$899$	12.6221	0.420969
$900$	2.35914	0.0786381
$901$	4.07867	0.135880
$902$	−4.58049	−0.152514
$903$	−0.163515	−0.00544143
$904$	15.5522	0.517258
$905$	36.1399	1.20133
$906$	0.168615	0.00560186
$907$	2.57989	0.0856639	0.0428319	−	0.999082i	$-0.486362\pi$
$907$	2.57989	0.0856639	0.0428319	+	0.999082i	$0.486362\pi$
$908$	−2.17585	−0.0722083
$909$	−1.89581	−0.0628802
$910$	−4.23876	−0.140514
$911$	−4.86955	−0.161335	−0.0806677	−	0.996741i	$-0.525705\pi$
$911$	−4.86955	−0.161335	−0.0806677	+	0.996741i	$0.525705\pi$
$912$	0.0436211	0.00144444
$913$	−48.5989	−1.60839
$914$	30.0062	0.992517
$915$	−0.100120	−0.00330986
$916$	−23.2673	−0.768772
$917$	−41.3651	−1.36600
$918$	0.0713431	0.00235467
$919$	19.9790	0.659048	0.329524	−	0.944147i	$-0.393112\pi$
$919$	19.9790	0.659048	0.329524	+	0.944147i	$0.393112\pi$
$920$	4.19496	0.138304
$921$	0.107323	0.00353642
$922$	9.25095	0.304664
$923$	6.07638	0.200006
$924$	−0.0601621	−0.00197919
$925$	9.24700	0.304040
$926$	−6.06645	−0.199356
$927$	−39.4186	−1.29468
$928$	8.64347	0.283736
$929$	23.0619	0.756638	0.378319	−	0.925675i	$-0.376502\pi$
$929$	23.0619	0.756638	0.378319	+	0.925675i	$0.376502\pi$
$930$	−0.0237182	−0.000777749 0
$931$	−12.7866	−0.419064
$932$	22.0290	0.721584
$933$	0.0731702	0.00239548
$934$	−0.750961	−0.0245722
$935$	−10.8412	−0.354545
$936$	2.86334	0.0935911
$937$	−19.8441	−0.648277	−0.324139	−	0.946010i	$-0.605074\pi$
$937$	−19.8441	−0.648277	−0.324139	+	0.946010i	$0.605074\pi$
$938$	14.4738	0.472586
$939$	−0.116380	−0.00379791
$940$	−16.4431	−0.536316
$941$	−57.3716	−1.87026	−0.935131	−	0.354302i	$-0.884718\pi$
$941$	−57.3716	−1.87026	−0.935131	+	0.354302i	$0.884718\pi$
$942$	0.0760626	0.00247825
$943$	2.66351	0.0867359
$944$	10.0846	0.328226
$945$	−0.210833	−0.00685838
$946$	−33.5700	−1.09145
$947$	−33.6348	−1.09298	−0.546492	−	0.837464i	$-0.684037\pi$
$947$	−33.6348	−1.09298	−0.546492	+	0.837464i	$0.684037\pi$
$948$	−0.0468948	−0.00152307
$949$	8.95957	0.290840
$950$	4.33536	0.140658
$951$	−0.0222150	−0.000720371 0
$952$	3.25120	0.105372
$953$	22.2753	0.721568	0.360784	−	0.932649i	$-0.382509\pi$
$953$	22.2753	0.721568	0.360784	+	0.932649i	$0.382509\pi$
$954$	8.14213	0.263611
$955$	0.183832	0.00594865
$956$	−9.58138	−0.309884
$957$	−0.240358	−0.00776968
$958$	−27.1845	−0.878293
$959$	−23.8072	−0.768774
$960$	−0.0162420	−0.000524208 0
$961$	−28.8675	−0.931211
$962$	11.2233	0.361853
$963$	8.55395	0.275647
$964$	3.18232	0.102496
$965$	48.9516	1.57581
$966$	0.0349837	0.00112558
$967$	43.1127	1.38641	0.693205	−	0.720741i	$-0.256198\pi$
$967$	43.1127	1.38641	0.693205	+	0.720741i	$0.256198\pi$
$968$	−1.35142	−0.0434362
$969$	0.0655524	0.00210585
$970$	−12.1904	−0.391410
$971$	33.2052	1.06560	0.532802	−	0.846240i	$-0.321139\pi$
$971$	33.2052	1.06560	0.532802	+	0.846240i	$0.321139\pi$
$972$	0.213631	0.00685222
$973$	6.51813	0.208962
$974$	0.526772	0.0168789
$975$	−0.00593902	−0.000190201 0
$976$	6.16426	0.197313
$977$	2.70459	0.0865275	0.0432638	−	0.999064i	$-0.486224\pi$
$977$	2.70459	0.0865275	0.0432638	+	0.999064i	$0.486224\pi$
$978$	0.0955142	0.00305421
$979$	−35.9637	−1.14940
$980$	4.76101	0.152085
$981$	47.9821	1.53195
$982$	−17.2936	−0.551862
$983$	−3.73141	−0.119013	−0.0595067	−	0.998228i	$-0.518953\pi$
$983$	−3.73141	−0.119013	−0.0595067	+	0.998228i	$0.518953\pi$
$984$	−0.0103126	−0.000328752 0
$985$	−5.80977	−0.185115
$986$	12.9891	0.413659
$987$	−0.137127	−0.00436479
$988$	5.26192	0.167404
$989$	19.5206	0.620720
$990$	−21.6420	−0.687828
$991$	−60.3487	−1.91704	−0.958520	−	0.285025i	$-0.907998\pi$
$991$	−60.3487	−1.91704	−0.958520	+	0.285025i	$0.907998\pi$
$992$	1.46030	0.0463645
$993$	0.160070	0.00507967
$994$	13.7732	0.436860
$995$	−9.92386	−0.314608
$996$	−0.109416	−0.00346698
$997$	50.2852	1.59255	0.796274	−	0.604936i	$-0.206801\pi$
$997$	50.2852	1.59255	0.796274	+	0.604936i	$0.206801\pi$
$998$	−10.7319	−0.339713
$999$	0.558237	0.0176618

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4034.2.a.b.1.18	✓	35

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4034.2.a.b.1.18	✓	35	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:	\( N \)	\(=\)	\( 4034 = 2 \cdot 2017 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4034.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +0.00791248 q^{3} +1.00000 q^{4} -2.05271 q^{5} -0.00791248 q^{6} -2.16347 q^{7} -1.00000 q^{8} -2.99994 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +0.00791248 q^{3} +1.00000 q^{4} -2.05271 q^{5} -0.00791248 q^{6} -2.16347 q^{7} -1.00000 q^{8} -2.99994 q^{9} +2.05271 q^{10} +3.51446 q^{11} +0.00791248 q^{12} +0.954466 q^{13} +2.16347 q^{14} -0.0162420 q^{15} +1.00000 q^{16} +1.50277 q^{17} +2.99994 q^{18} +5.51294 q^{19} -2.05271 q^{20} -0.0171184 q^{21} -3.51446 q^{22} +2.04363 q^{23} -0.00791248 q^{24} -0.786397 q^{25} -0.954466 q^{26} -0.0474744 q^{27} -2.16347 q^{28} -8.64347 q^{29} +0.0162420 q^{30} -1.46030 q^{31} -1.00000 q^{32} +0.0278081 q^{33} -1.50277 q^{34} +4.44098 q^{35} -2.99994 q^{36} -11.7587 q^{37} -5.51294 q^{38} +0.00755219 q^{39} +2.05271 q^{40} +1.30333 q^{41} +0.0171184 q^{42} +9.55197 q^{43} +3.51446 q^{44} +6.15799 q^{45} -2.04363 q^{46} +8.01046 q^{47} +0.00791248 q^{48} -2.31938 q^{49} +0.786397 q^{50} +0.0118906 q^{51} +0.954466 q^{52} +2.71410 q^{53} +0.0474744 q^{54} -7.21415 q^{55} +2.16347 q^{56} +0.0436211 q^{57} +8.64347 q^{58} +10.0846 q^{59} -0.0162420 q^{60} +6.16426 q^{61} +1.46030 q^{62} +6.49029 q^{63} +1.00000 q^{64} -1.95924 q^{65} -0.0278081 q^{66} +6.69007 q^{67} +1.50277 q^{68} +0.0161701 q^{69} -4.44098 q^{70} +6.36626 q^{71} +2.99994 q^{72} +9.38700 q^{73} +11.7587 q^{74} -0.00622235 q^{75} +5.51294 q^{76} -7.60344 q^{77} -0.00755219 q^{78} -5.92668 q^{79} -2.05271 q^{80} +8.99944 q^{81} -1.30333 q^{82} -13.8283 q^{83} -0.0171184 q^{84} -3.08474 q^{85} -9.55197 q^{86} -0.0683913 q^{87} -3.51446 q^{88} -10.2331 q^{89} -6.15799 q^{90} -2.06496 q^{91} +2.04363 q^{92} -0.0115546 q^{93} -8.01046 q^{94} -11.3165 q^{95} -0.00791248 q^{96} -5.93870 q^{97} +2.31938 q^{98} -10.5432 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 35 q - 35 q^{2} - 6 q^{3} + 35 q^{4} + 6 q^{5} + 6 q^{6} - 14 q^{7} - 35 q^{8} + 23 q^{9}+O(q^{10}) \) 35 * q - 35 * q^2 - 6 * q^3 + 35 * q^4 + 6 * q^5 + 6 * q^6 - 14 * q^7 - 35 * q^8 + 23 * q^9	\( 35 q - 35 q^{2} - 6 q^{3} + 35 q^{4} + 6 q^{5} + 6 q^{6} - 14 q^{7} - 35 q^{8} + 23 q^{9} - 6 q^{10} - 9 q^{11} - 6 q^{12} - 7 q^{13} + 14 q^{14} - 19 q^{15} + 35 q^{16} + 17 q^{17} - 23 q^{18} - 25 q^{19} + 6 q^{20} - 15 q^{21} + 9 q^{22} - 12 q^{23} + 6 q^{24} + 7 q^{25} + 7 q^{26} - 27 q^{27} - 14 q^{28} - 13 q^{29} + 19 q^{30} - 69 q^{31} - 35 q^{32} + q^{33} - 17 q^{34} - 4 q^{35} + 23 q^{36} - 22 q^{37} + 25 q^{38} - 38 q^{39} - 6 q^{40} + 15 q^{42} - 32 q^{43} - 9 q^{44} + 9 q^{45} + 12 q^{46} - 18 q^{47} - 6 q^{48} - 19 q^{49} - 7 q^{50} - 21 q^{51} - 7 q^{52} + 20 q^{53} + 27 q^{54} - 54 q^{55} + 14 q^{56} + 28 q^{57} + 13 q^{58} - 21 q^{59} - 19 q^{60} - 67 q^{61} + 69 q^{62} - 28 q^{63} + 35 q^{64} + 22 q^{65} - q^{66} - 18 q^{67} + 17 q^{68} - 42 q^{69} + 4 q^{70} - 36 q^{71} - 23 q^{72} - 18 q^{73} + 22 q^{74} - 49 q^{75} - 25 q^{76} + 20 q^{77} + 38 q^{78} - 92 q^{79} + 6 q^{80} - 25 q^{81} + 42 q^{83} - 15 q^{84} - 29 q^{85} + 32 q^{86} - 40 q^{87} + 9 q^{88} - 8 q^{89} - 9 q^{90} - 89 q^{91} - 12 q^{92} - q^{93} + 18 q^{94} - 62 q^{95} + 6 q^{96} - 40 q^{97} + 19 q^{98} - 64 q^{99}+O(q^{100}) \) 35 * q - 35 * q^2 - 6 * q^3 + 35 * q^4 + 6 * q^5 + 6 * q^6 - 14 * q^7 - 35 * q^8 + 23 * q^9 - 6 * q^10 - 9 * q^11 - 6 * q^12 - 7 * q^13 + 14 * q^14 - 19 * q^15 + 35 * q^16 + 17 * q^17 - 23 * q^18 - 25 * q^19 + 6 * q^20 - 15 * q^21 + 9 * q^22 - 12 * q^23 + 6 * q^24 + 7 * q^25 + 7 * q^26 - 27 * q^27 - 14 * q^28 - 13 * q^29 + 19 * q^30 - 69 * q^31 - 35 * q^32 + q^33 - 17 * q^34 - 4 * q^35 + 23 * q^36 - 22 * q^37 + 25 * q^38 - 38 * q^39 - 6 * q^40 + 15 * q^42 - 32 * q^43 - 9 * q^44 + 9 * q^45 + 12 * q^46 - 18 * q^47 - 6 * q^48 - 19 * q^49 - 7 * q^50 - 21 * q^51 - 7 * q^52 + 20 * q^53 + 27 * q^54 - 54 * q^55 + 14 * q^56 + 28 * q^57 + 13 * q^58 - 21 * q^59 - 19 * q^60 - 67 * q^61 + 69 * q^62 - 28 * q^63 + 35 * q^64 + 22 * q^65 - q^66 - 18 * q^67 + 17 * q^68 - 42 * q^69 + 4 * q^70 - 36 * q^71 - 23 * q^72 - 18 * q^73 + 22 * q^74 - 49 * q^75 - 25 * q^76 + 20 * q^77 + 38 * q^78 - 92 * q^79 + 6 * q^80 - 25 * q^81 + 42 * q^83 - 15 * q^84 - 29 * q^85 + 32 * q^86 - 40 * q^87 + 9 * q^88 - 8 * q^89 - 9 * q^90 - 89 * q^91 - 12 * q^92 - q^93 + 18 * q^94 - 62 * q^95 + 6 * q^96 - 40 * q^97 + 19 * q^98 - 64 * q^99

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