LMFDB - Embedded newform 6034.2.a.m.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6034,2,Mod(1,6034)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6034, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6034 = 2 \cdot 7 \cdot 431 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6034.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:	$48.1817325796$
Analytic rank:	$1$
Dimension:	$21$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Character	$\chi$	$=$	6034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.87377 q^{3} +1.00000 q^{4} -1.03478 q^{5} +1.87377 q^{6} +1.00000 q^{7} +1.00000 q^{8} +0.510997 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.87377 q^{3} +1.00000 q^{4} -1.03478 q^{5} +1.87377 q^{6} +1.00000 q^{7} +1.00000 q^{8} +0.510997 q^{9} -1.03478 q^{10} -1.53135 q^{11} +1.87377 q^{12} -3.90213 q^{13} +1.00000 q^{14} -1.93894 q^{15} +1.00000 q^{16} +6.17967 q^{17} +0.510997 q^{18} -7.84007 q^{19} -1.03478 q^{20} +1.87377 q^{21} -1.53135 q^{22} -3.25866 q^{23} +1.87377 q^{24} -3.92923 q^{25} -3.90213 q^{26} -4.66381 q^{27} +1.00000 q^{28} -5.17036 q^{29} -1.93894 q^{30} -6.47426 q^{31} +1.00000 q^{32} -2.86939 q^{33} +6.17967 q^{34} -1.03478 q^{35} +0.510997 q^{36} -5.37684 q^{37} -7.84007 q^{38} -7.31167 q^{39} -1.03478 q^{40} +8.96633 q^{41} +1.87377 q^{42} -8.31944 q^{43} -1.53135 q^{44} -0.528770 q^{45} -3.25866 q^{46} -5.21669 q^{47} +1.87377 q^{48} +1.00000 q^{49} -3.92923 q^{50} +11.5793 q^{51} -3.90213 q^{52} +0.218836 q^{53} -4.66381 q^{54} +1.58461 q^{55} +1.00000 q^{56} -14.6904 q^{57} -5.17036 q^{58} -4.84226 q^{59} -1.93894 q^{60} -0.717905 q^{61} -6.47426 q^{62} +0.510997 q^{63} +1.00000 q^{64} +4.03785 q^{65} -2.86939 q^{66} +8.68318 q^{67} +6.17967 q^{68} -6.10597 q^{69} -1.03478 q^{70} +10.1587 q^{71} +0.510997 q^{72} -10.7760 q^{73} -5.37684 q^{74} -7.36245 q^{75} -7.84007 q^{76} -1.53135 q^{77} -7.31167 q^{78} +17.3211 q^{79} -1.03478 q^{80} -10.2719 q^{81} +8.96633 q^{82} +14.6313 q^{83} +1.87377 q^{84} -6.39461 q^{85} -8.31944 q^{86} -9.68803 q^{87} -1.53135 q^{88} -1.14751 q^{89} -0.528770 q^{90} -3.90213 q^{91} -3.25866 q^{92} -12.1312 q^{93} -5.21669 q^{94} +8.11275 q^{95} +1.87377 q^{96} +2.36608 q^{97} +1.00000 q^{98} -0.782516 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 21 q + 21 q^{2} - 6 q^{3} + 21 q^{4} - 11 q^{5} - 6 q^{6} + 21 q^{7} + 21 q^{8} + 5 q^{9}+O(q^{10}) $ 21 * q + 21 * q^2 - 6 * q^3 + 21 * q^4 - 11 * q^5 - 6 * q^6 + 21 * q^7 + 21 * q^8 + 5 * q^9	\( 21 q + 21 q^{2} - 6 q^{3} + 21 q^{4} - 11 q^{5} - 6 q^{6} + 21 q^{7} + 21 q^{8} + 5 q^{9} - 11 q^{10} - 34 q^{11} - 6 q^{12} - 19 q^{13} + 21 q^{14} - 24 q^{15} + 21 q^{16} - 17 q^{17} + 5 q^{18} - 15 q^{19} - 11 q^{20} - 6 q^{21} - 34 q^{22} - 32 q^{23} - 6 q^{24} + 6 q^{25} - 19 q^{26} - 3 q^{27} + 21 q^{28} - 46 q^{29} - 24 q^{30} + 7 q^{31} + 21 q^{32} - 13 q^{33} - 17 q^{34} - 11 q^{35} + 5 q^{36} - 34 q^{37} - 15 q^{38} - 25 q^{39} - 11 q^{40} - 27 q^{41} - 6 q^{42} - 47 q^{43} - 34 q^{44} - 13 q^{45} - 32 q^{46} - 7 q^{47} - 6 q^{48} + 21 q^{49} + 6 q^{50} - 29 q^{51} - 19 q^{52} - 57 q^{53} - 3 q^{54} + 17 q^{55} + 21 q^{56} - 28 q^{57} - 46 q^{58} - 30 q^{59} - 24 q^{60} - 17 q^{61} + 7 q^{62} + 5 q^{63} + 21 q^{64} - 40 q^{65} - 13 q^{66} - 38 q^{67} - 17 q^{68} - 13 q^{69} - 11 q^{70} - 66 q^{71} + 5 q^{72} - 15 q^{73} - 34 q^{74} + 15 q^{75} - 15 q^{76} - 34 q^{77} - 25 q^{78} - 17 q^{79} - 11 q^{80} - 11 q^{81} - 27 q^{82} - 19 q^{83} - 6 q^{84} - 28 q^{85} - 47 q^{86} + 45 q^{87} - 34 q^{88} - 39 q^{89} - 13 q^{90} - 19 q^{91} - 32 q^{92} - 25 q^{93} - 7 q^{94} - 35 q^{95} - 6 q^{96} + 21 q^{98} - 52 q^{99}+O(q^{100}) \) 21 * q + 21 * q^2 - 6 * q^3 + 21 * q^4 - 11 * q^5 - 6 * q^6 + 21 * q^7 + 21 * q^8 + 5 * q^9 - 11 * q^10 - 34 * q^11 - 6 * q^12 - 19 * q^13 + 21 * q^14 - 24 * q^15 + 21 * q^16 - 17 * q^17 + 5 * q^18 - 15 * q^19 - 11 * q^20 - 6 * q^21 - 34 * q^22 - 32 * q^23 - 6 * q^24 + 6 * q^25 - 19 * q^26 - 3 * q^27 + 21 * q^28 - 46 * q^29 - 24 * q^30 + 7 * q^31 + 21 * q^32 - 13 * q^33 - 17 * q^34 - 11 * q^35 + 5 * q^36 - 34 * q^37 - 15 * q^38 - 25 * q^39 - 11 * q^40 - 27 * q^41 - 6 * q^42 - 47 * q^43 - 34 * q^44 - 13 * q^45 - 32 * q^46 - 7 * q^47 - 6 * q^48 + 21 * q^49 + 6 * q^50 - 29 * q^51 - 19 * q^52 - 57 * q^53 - 3 * q^54 + 17 * q^55 + 21 * q^56 - 28 * q^57 - 46 * q^58 - 30 * q^59 - 24 * q^60 - 17 * q^61 + 7 * q^62 + 5 * q^63 + 21 * q^64 - 40 * q^65 - 13 * q^66 - 38 * q^67 - 17 * q^68 - 13 * q^69 - 11 * q^70 - 66 * q^71 + 5 * q^72 - 15 * q^73 - 34 * q^74 + 15 * q^75 - 15 * q^76 - 34 * q^77 - 25 * q^78 - 17 * q^79 - 11 * q^80 - 11 * q^81 - 27 * q^82 - 19 * q^83 - 6 * q^84 - 28 * q^85 - 47 * q^86 + 45 * q^87 - 34 * q^88 - 39 * q^89 - 13 * q^90 - 19 * q^91 - 32 * q^92 - 25 * q^93 - 7 * q^94 - 35 * q^95 - 6 * q^96 + 21 * q^98 - 52 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	1.87377	1.08182	0.540909	−	0.841081i	$-0.318080\pi$
$3$	1.87377	1.08182	0.540909	+	0.841081i	$0.318080\pi$
$4$	1.00000	0.500000
$5$	−1.03478	−0.462768	−0.231384	−	0.972863i	$-0.574325\pi$
$5$	−1.03478	−0.462768	−0.231384	+	0.972863i	$0.574325\pi$
$6$	1.87377	0.764962
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.00000	0.353553
$9$	0.510997	0.170332
$10$	−1.03478	−0.327226
$11$	−1.53135	−0.461720	−0.230860	−	0.972987i	$-0.574154\pi$
$11$	−1.53135	−0.461720	−0.230860	+	0.972987i	$0.574154\pi$
$12$	1.87377	0.540909
$13$	−3.90213	−1.08226	−0.541128	−	0.840940i	$-0.682003\pi$
$13$	−3.90213	−1.08226	−0.541128	+	0.840940i	$0.682003\pi$
$14$	1.00000	0.267261
$15$	−1.93894	−0.500631
$16$	1.00000	0.250000
$17$	6.17967	1.49879	0.749395	−	0.662123i	$-0.230344\pi$
$17$	6.17967	1.49879	0.749395	+	0.662123i	$0.230344\pi$
$18$	0.510997	0.120443
$19$	−7.84007	−1.79863	−0.899317	−	0.437296i	$-0.855936\pi$
$19$	−7.84007	−1.79863	−0.899317	+	0.437296i	$0.855936\pi$
$20$	−1.03478	−0.231384
$21$	1.87377	0.408889
$22$	−1.53135	−0.326485
$23$	−3.25866	−0.679478	−0.339739	−	0.940520i	$-0.610339\pi$
$23$	−3.25866	−0.679478	−0.339739	+	0.940520i	$0.610339\pi$
$24$	1.87377	0.382481
$25$	−3.92923	−0.785846
$26$	−3.90213	−0.765270
$27$	−4.66381	−0.897550
$28$	1.00000	0.188982
$29$	−5.17036	−0.960111	−0.480056	−	0.877238i	$-0.659383\pi$
$29$	−5.17036	−0.960111	−0.480056	+	0.877238i	$0.659383\pi$
$30$	−1.93894	−0.354000
$31$	−6.47426	−1.16281	−0.581406	−	0.813614i	$-0.697497\pi$
$31$	−6.47426	−1.16281	−0.581406	+	0.813614i	$0.697497\pi$
$32$	1.00000	0.176777
$33$	−2.86939	−0.499497
$34$	6.17967	1.05981
$35$	−1.03478	−0.174910
$36$	0.510997	0.0851662
$37$	−5.37684	−0.883947	−0.441973	−	0.897028i	$-0.645721\pi$
$37$	−5.37684	−0.883947	−0.441973	+	0.897028i	$0.645721\pi$
$38$	−7.84007	−1.27183
$39$	−7.31167	−1.17080
$40$	−1.03478	−0.163613
$41$	8.96633	1.40031	0.700153	−	0.713993i	$-0.253115\pi$
$41$	8.96633	1.40031	0.700153	+	0.713993i	$0.253115\pi$
$42$	1.87377	0.289128
$43$	−8.31944	−1.26870	−0.634351	−	0.773045i	$-0.718733\pi$
$43$	−8.31944	−1.26870	−0.634351	+	0.773045i	$0.718733\pi$
$44$	−1.53135	−0.230860
$45$	−0.528770	−0.0788243
$46$	−3.25866	−0.480464
$47$	−5.21669	−0.760932	−0.380466	−	0.924795i	$-0.624236\pi$
$47$	−5.21669	−0.760932	−0.380466	+	0.924795i	$0.624236\pi$
$48$	1.87377	0.270455
$49$	1.00000	0.142857
$50$	−3.92923	−0.555677
$51$	11.5793	1.62142
$52$	−3.90213	−0.541128
$53$	0.218836	0.0300594	0.0150297	−	0.999887i	$-0.495216\pi$
$53$	0.218836	0.0300594	0.0150297	+	0.999887i	$0.495216\pi$
$54$	−4.66381	−0.634664
$55$	1.58461	0.213669
$56$	1.00000	0.133631
$57$	−14.6904	−1.94580
$58$	−5.17036	−0.678901
$59$	−4.84226	−0.630408	−0.315204	−	0.949024i	$-0.602073\pi$
$59$	−4.84226	−0.630408	−0.315204	+	0.949024i	$0.602073\pi$
$60$	−1.93894	−0.250316
$61$	−0.717905	−0.0919183	−0.0459591	−	0.998943i	$-0.514634\pi$
$61$	−0.717905	−0.0919183	−0.0459591	+	0.998943i	$0.514634\pi$
$62$	−6.47426	−0.822232
$63$	0.510997	0.0643796
$64$	1.00000	0.125000
$65$	4.03785	0.500833
$66$	−2.86939	−0.353198
$67$	8.68318	1.06082	0.530410	−	0.847741i	$-0.322038\pi$
$67$	8.68318	1.06082	0.530410	+	0.847741i	$0.322038\pi$
$68$	6.17967	0.749395
$69$	−6.10597	−0.735073
$70$	−1.03478	−0.123680
$71$	10.1587	1.20562	0.602809	−	0.797886i	$-0.294048\pi$
$71$	10.1587	1.20562	0.602809	+	0.797886i	$0.294048\pi$
$72$	0.510997	0.0602216
$73$	−10.7760	−1.26123	−0.630616	−	0.776095i	$-0.717197\pi$
$73$	−10.7760	−1.26123	−0.630616	+	0.776095i	$0.717197\pi$
$74$	−5.37684	−0.625045
$75$	−7.36245	−0.850143
$76$	−7.84007	−0.899317
$77$	−1.53135	−0.174514
$78$	−7.31167	−0.827884
$79$	17.3211	1.94877	0.974385	−	0.224885i	$-0.0722005\pi$
$79$	17.3211	1.94877	0.974385	+	0.224885i	$0.0722005\pi$
$80$	−1.03478	−0.115692
$81$	−10.2719	−1.14132
$82$	8.96633	0.990166
$83$	14.6313	1.60600	0.802999	−	0.595980i	$-0.203236\pi$
$83$	14.6313	1.60600	0.802999	+	0.595980i	$0.203236\pi$
$84$	1.87377	0.204445
$85$	−6.39461	−0.693592
$86$	−8.31944	−0.897108
$87$	−9.68803	−1.03867
$88$	−1.53135	−0.163243
$89$	−1.14751	−0.121636	−0.0608178	−	0.998149i	$-0.519371\pi$
$89$	−1.14751	−0.121636	−0.0608178	+	0.998149i	$0.519371\pi$
$90$	−0.528770	−0.0557372
$91$	−3.90213	−0.409054
$92$	−3.25866	−0.339739
$93$	−12.1312	−1.25795
$94$	−5.21669	−0.538060
$95$	8.11275	0.832351
$96$	1.87377	0.191240
$97$	2.36608	0.240239	0.120120	−	0.992759i	$-0.461672\pi$
$97$	2.36608	0.240239	0.120120	+	0.992759i	$0.461672\pi$
$98$	1.00000	0.101015
$99$	−0.782516	−0.0786458
$100$	−3.92923	−0.392923
$101$	−11.1134	−1.10582	−0.552912	−	0.833240i	$-0.686483\pi$
$101$	−11.1134	−1.10582	−0.552912	+	0.833240i	$0.686483\pi$
$102$	11.5793	1.14652
$103$	19.9431	1.96505	0.982525	−	0.186129i	$-0.0595944\pi$
$103$	19.9431	1.96505	0.982525	+	0.186129i	$0.0595944\pi$
$104$	−3.90213	−0.382635
$105$	−1.93894	−0.189221
$106$	0.218836	0.0212552
$107$	5.25937	0.508443	0.254221	−	0.967146i	$-0.418181\pi$
$107$	5.25937	0.508443	0.254221	+	0.967146i	$0.418181\pi$
$108$	−4.66381	−0.448775
$109$	19.9697	1.91275	0.956373	−	0.292147i	$-0.0943698\pi$
$109$	19.9697	1.91275	0.956373	+	0.292147i	$0.0943698\pi$
$110$	1.58461	0.151087
$111$	−10.0749	−0.956270
$112$	1.00000	0.0944911
$113$	−9.69424	−0.911957	−0.455978	−	0.889991i	$-0.650711\pi$
$113$	−9.69424	−0.911957	−0.455978	+	0.889991i	$0.650711\pi$
$114$	−14.6904	−1.37589
$115$	3.37200	0.314441
$116$	−5.17036	−0.480056
$117$	−1.99398	−0.184343
$118$	−4.84226	−0.445766
$119$	6.17967	0.566490
$120$	−1.93894	−0.177000
$121$	−8.65496	−0.786815
$122$	−0.717905	−0.0649961
$123$	16.8008	1.51488
$124$	−6.47426	−0.581406
$125$	9.23979	0.826432
$126$	0.510997	0.0455232
$127$	1.70316	0.151131	0.0755656	−	0.997141i	$-0.475924\pi$
$127$	1.70316	0.151131	0.0755656	+	0.997141i	$0.475924\pi$
$128$	1.00000	0.0883883
$129$	−15.5887	−1.37251
$130$	4.03785	0.354143
$131$	10.6552	0.930953	0.465477	−	0.885060i	$-0.345883\pi$
$131$	10.6552	0.930953	0.465477	+	0.885060i	$0.345883\pi$
$132$	−2.86939	−0.249749
$133$	−7.84007	−0.679820
$134$	8.68318	0.750113
$135$	4.82602	0.415358
$136$	6.17967	0.529903
$137$	−8.13906	−0.695367	−0.347684	−	0.937612i	$-0.613032\pi$
$137$	−8.13906	−0.695367	−0.347684	+	0.937612i	$0.613032\pi$
$138$	−6.10597	−0.519775
$139$	−21.7449	−1.84438	−0.922189	−	0.386739i	$-0.873602\pi$
$139$	−21.7449	−1.84438	−0.922189	+	0.386739i	$0.873602\pi$
$140$	−1.03478	−0.0874549
$141$	−9.77485	−0.823191
$142$	10.1587	0.852501
$143$	5.97553	0.499699
$144$	0.510997	0.0425831
$145$	5.35018	0.444309
$146$	−10.7760	−0.891825
$147$	1.87377	0.154546
$148$	−5.37684	−0.441973
$149$	14.2511	1.16750	0.583748	−	0.811935i	$-0.301586\pi$
$149$	14.2511	1.16750	0.583748	+	0.811935i	$0.301586\pi$
$150$	−7.36245	−0.601142
$151$	−23.8297	−1.93923	−0.969615	−	0.244634i	$-0.921332\pi$
$151$	−23.8297	−1.93923	−0.969615	+	0.244634i	$0.921332\pi$
$152$	−7.84007	−0.635913
$153$	3.15779	0.255292
$154$	−1.53135	−0.123400
$155$	6.69944	0.538112
$156$	−7.31167	−0.585402
$157$	−0.198198	−0.0158179	−0.00790897	−	0.999969i	$-0.502518\pi$
$157$	−0.198198	−0.0158179	−0.00790897	+	0.999969i	$0.502518\pi$
$158$	17.3211	1.37799
$159$	0.410046	0.0325188
$160$	−1.03478	−0.0818066
$161$	−3.25866	−0.256819
$162$	−10.2719	−0.807035
$163$	−7.42722	−0.581745	−0.290872	−	0.956762i	$-0.593946\pi$
$163$	−7.42722	−0.581745	−0.290872	+	0.956762i	$0.593946\pi$
$164$	8.96633	0.700153
$165$	2.96919	0.231151
$166$	14.6313	1.13561
$167$	−4.10783	−0.317874	−0.158937	−	0.987289i	$-0.550807\pi$
$167$	−4.10783	−0.317874	−0.158937	+	0.987289i	$0.550807\pi$
$168$	1.87377	0.144564
$169$	2.22661	0.171278
$170$	−6.39461	−0.490444
$171$	−4.00625	−0.306366
$172$	−8.31944	−0.634351
$173$	23.7230	1.80363	0.901814	−	0.432125i	$-0.142236\pi$
$173$	23.7230	1.80363	0.901814	+	0.432125i	$0.142236\pi$
$174$	−9.68803	−0.734448
$175$	−3.92923	−0.297022
$176$	−1.53135	−0.115430
$177$	−9.07325	−0.681987
$178$	−1.14751	−0.0860094
$179$	9.25943	0.692082	0.346041	−	0.938219i	$-0.387526\pi$
$179$	9.25943	0.692082	0.346041	+	0.938219i	$0.387526\pi$
$180$	−0.528770	−0.0394122
$181$	−15.6697	−1.16472	−0.582358	−	0.812932i	$-0.697870\pi$
$181$	−15.6697	−1.16472	−0.582358	+	0.812932i	$0.697870\pi$
$182$	−3.90213	−0.289245
$183$	−1.34519	−0.0994390
$184$	−3.25866	−0.240232
$185$	5.56385	0.409062
$186$	−12.1312	−0.889506
$187$	−9.46325	−0.692021
$188$	−5.21669	−0.380466
$189$	−4.66381	−0.339242
$190$	8.11275	0.588561
$191$	−2.02195	−0.146303	−0.0731516	−	0.997321i	$-0.523306\pi$
$191$	−2.02195	−0.146303	−0.0731516	+	0.997321i	$0.523306\pi$
$192$	1.87377	0.135227
$193$	−1.77261	−0.127595	−0.0637977	−	0.997963i	$-0.520321\pi$
$193$	−1.77261	−0.127595	−0.0637977	+	0.997963i	$0.520321\pi$
$194$	2.36608	0.169875
$195$	7.56598	0.541811
$196$	1.00000	0.0714286
$197$	−26.7239	−1.90400	−0.952000	−	0.306099i	$-0.900976\pi$
$197$	−26.7239	−1.90400	−0.952000	+	0.306099i	$0.900976\pi$
$198$	−0.782516	−0.0556110
$199$	16.4847	1.16857	0.584284	−	0.811549i	$-0.301375\pi$
$199$	16.4847	1.16857	0.584284	+	0.811549i	$0.301375\pi$
$200$	−3.92923	−0.277838
$201$	16.2702	1.14761
$202$	−11.1134	−0.781936
$203$	−5.17036	−0.362888
$204$	11.5793	0.810710
$205$	−9.27819	−0.648017
$206$	19.9431	1.38950
$207$	−1.66517	−0.115737
$208$	−3.90213	−0.270564
$209$	12.0059	0.830466
$210$	−1.93894	−0.133799
$211$	−26.3090	−1.81119	−0.905595	−	0.424144i	$-0.860575\pi$
$211$	−26.3090	−1.81119	−0.905595	+	0.424144i	$0.860575\pi$
$212$	0.218836	0.0150297
$213$	19.0351	1.30426
$214$	5.25937	0.359523
$215$	8.60880	0.587115
$216$	−4.66381	−0.317332
$217$	−6.47426	−0.439501
$218$	19.9697	1.35252
$219$	−20.1916	−1.36442
$220$	1.58461	0.106835
$221$	−24.1139	−1.62207
$222$	−10.0749	−0.676185
$223$	18.4763	1.23727	0.618634	−	0.785679i	$-0.287686\pi$
$223$	18.4763	1.23727	0.618634	+	0.785679i	$0.287686\pi$
$224$	1.00000	0.0668153
$225$	−2.00782	−0.133855
$226$	−9.69424	−0.644851
$227$	−12.3181	−0.817583	−0.408792	−	0.912628i	$-0.634050\pi$
$227$	−12.3181	−0.817583	−0.408792	+	0.912628i	$0.634050\pi$
$228$	−14.6904	−0.972899
$229$	7.76057	0.512833	0.256416	−	0.966566i	$-0.417458\pi$
$229$	7.76057	0.512833	0.256416	+	0.966566i	$0.417458\pi$
$230$	3.37200	0.222343
$231$	−2.86939	−0.188792
$232$	−5.17036	−0.339451
$233$	−13.3591	−0.875181	−0.437590	−	0.899174i	$-0.644168\pi$
$233$	−13.3591	−0.875181	−0.437590	+	0.899174i	$0.644168\pi$
$234$	−1.99398	−0.130350
$235$	5.39813	0.352135
$236$	−4.84226	−0.315204
$237$	32.4556	2.10822
$238$	6.17967	0.400569
$239$	−0.728139	−0.0470994	−0.0235497	−	0.999723i	$-0.507497\pi$
$239$	−0.728139	−0.0470994	−0.0235497	+	0.999723i	$0.507497\pi$
$240$	−1.93894	−0.125158
$241$	−8.41243	−0.541892	−0.270946	−	0.962595i	$-0.587337\pi$
$241$	−8.41243	−0.541892	−0.270946	+	0.962595i	$0.587337\pi$
$242$	−8.65496	−0.556362
$243$	−5.25566	−0.337151
$244$	−0.717905	−0.0459591
$245$	−1.03478	−0.0661097
$246$	16.8008	1.07118
$247$	30.5930	1.94658
$248$	−6.47426	−0.411116
$249$	27.4157	1.73740
$250$	9.23979	0.584376
$251$	−18.9854	−1.19835	−0.599175	−	0.800618i	$-0.704505\pi$
$251$	−18.9854	−1.19835	−0.599175	+	0.800618i	$0.704505\pi$
$252$	0.510997	0.0321898
$253$	4.99016	0.313729
$254$	1.70316	0.106866
$255$	−11.9820	−0.750341
$256$	1.00000	0.0625000
$257$	1.45993	0.0910679	0.0455340	−	0.998963i	$-0.485501\pi$
$257$	1.45993	0.0910679	0.0455340	+	0.998963i	$0.485501\pi$
$258$	−15.5887	−0.970509
$259$	−5.37684	−0.334101
$260$	4.03785	0.250417
$261$	−2.64204	−0.163538
$262$	10.6552	0.658283
$263$	−7.36690	−0.454263	−0.227131	−	0.973864i	$-0.572935\pi$
$263$	−7.36690	−0.454263	−0.227131	+	0.973864i	$0.572935\pi$
$264$	−2.86939	−0.176599
$265$	−0.226447	−0.0139105
$266$	−7.84007	−0.480705
$267$	−2.15016	−0.131588
$268$	8.68318	0.530410
$269$	−14.2497	−0.868819	−0.434409	−	0.900716i	$-0.643043\pi$
$269$	−14.2497	−0.868819	−0.434409	+	0.900716i	$0.643043\pi$
$270$	4.82602	0.293702
$271$	−28.9629	−1.75937	−0.879686	−	0.475556i	$-0.842247\pi$
$271$	−28.9629	−1.75937	−0.879686	+	0.475556i	$0.842247\pi$
$272$	6.17967	0.374698
$273$	−7.31167	−0.442523
$274$	−8.13906	−0.491699
$275$	6.01703	0.362841
$276$	−6.10597	−0.367536
$277$	−7.43709	−0.446851	−0.223426	−	0.974721i	$-0.571724\pi$
$277$	−7.43709	−0.446851	−0.223426	+	0.974721i	$0.571724\pi$
$278$	−21.7449	−1.30417
$279$	−3.30833	−0.198064
$280$	−1.03478	−0.0618400
$281$	5.97650	0.356528	0.178264	−	0.983983i	$-0.442952\pi$
$281$	5.97650	0.356528	0.178264	+	0.983983i	$0.442952\pi$
$282$	−9.77485	−0.582084
$283$	2.60026	0.154569	0.0772847	−	0.997009i	$-0.475375\pi$
$283$	2.60026	0.154569	0.0772847	+	0.997009i	$0.475375\pi$
$284$	10.1587	0.602809
$285$	15.2014	0.900453
$286$	5.97553	0.353341
$287$	8.96633	0.529266
$288$	0.510997	0.0301108
$289$	21.1883	1.24637
$290$	5.35018	0.314174
$291$	4.43348	0.259895
$292$	−10.7760	−0.630616
$293$	25.2527	1.47528	0.737639	−	0.675195i	$-0.235941\pi$
$293$	25.2527	1.47528	0.737639	+	0.675195i	$0.235941\pi$
$294$	1.87377	0.109280
$295$	5.01067	0.291733
$296$	−5.37684	−0.312522
$297$	7.14193	0.414417
$298$	14.2511	0.825544
$299$	12.7157	0.735369
$300$	−7.36245	−0.425071
$301$	−8.31944	−0.479525
$302$	−23.8297	−1.37124
$303$	−20.8239	−1.19630
$304$	−7.84007	−0.449659
$305$	0.742874	0.0425368
$306$	3.15779	0.180519
$307$	7.22841	0.412547	0.206274	−	0.978494i	$-0.433866\pi$
$307$	7.22841	0.412547	0.206274	+	0.978494i	$0.433866\pi$
$308$	−1.53135	−0.0872569
$309$	37.3687	2.12583
$310$	6.69944	0.380503
$311$	−21.3815	−1.21243	−0.606216	−	0.795300i	$-0.707313\pi$
$311$	−21.3815	−1.21243	−0.606216	+	0.795300i	$0.707313\pi$
$312$	−7.31167	−0.413942
$313$	26.7729	1.51330	0.756648	−	0.653823i	$-0.226836\pi$
$313$	26.7729	1.51330	0.756648	+	0.653823i	$0.226836\pi$
$314$	−0.198198	−0.0111850
$315$	−0.528770	−0.0297928
$316$	17.3211	0.974385
$317$	16.3290	0.917128	0.458564	−	0.888661i	$-0.348364\pi$
$317$	16.3290	0.917128	0.458564	+	0.888661i	$0.348364\pi$
$318$	0.410046	0.0229943
$319$	7.91763	0.443302
$320$	−1.03478	−0.0578460
$321$	9.85483	0.550043
$322$	−3.25866	−0.181598
$323$	−48.4490	−2.69578
$324$	−10.2719	−0.570660
$325$	15.3324	0.850486
$326$	−7.42722	−0.411356
$327$	37.4185	2.06925
$328$	8.96633	0.495083
$329$	−5.21669	−0.287605
$330$	2.96919	0.163449
$331$	−18.7873	−1.03264	−0.516322	−	0.856394i	$-0.672699\pi$
$331$	−18.7873	−1.03264	−0.516322	+	0.856394i	$0.672699\pi$
$332$	14.6313	0.802999
$333$	−2.74755	−0.150565
$334$	−4.10783	−0.224771
$335$	−8.98519	−0.490913
$336$	1.87377	0.102222
$337$	9.78975	0.533282	0.266641	−	0.963796i	$-0.414086\pi$
$337$	9.78975	0.533282	0.266641	+	0.963796i	$0.414086\pi$
$338$	2.22661	0.121112
$339$	−18.1647	−0.986572
$340$	−6.39461	−0.346796
$341$	9.91437	0.536893
$342$	−4.00625	−0.216633
$343$	1.00000	0.0539949
$344$	−8.31944	−0.448554
$345$	6.31834	0.340168
$346$	23.7230	1.27536
$347$	13.4271	0.720803	0.360402	−	0.932797i	$-0.382640\pi$
$347$	13.4271	0.720803	0.360402	+	0.932797i	$0.382640\pi$
$348$	−9.68803	−0.519333
$349$	−15.0560	−0.805932	−0.402966	−	0.915215i	$-0.632021\pi$
$349$	−15.0560	−0.805932	−0.402966	+	0.915215i	$0.632021\pi$
$350$	−3.92923	−0.210026
$351$	18.1988	0.971379
$352$	−1.53135	−0.0816213
$353$	−12.3768	−0.658749	−0.329375	−	0.944199i	$-0.606838\pi$
$353$	−12.3768	−0.658749	−0.329375	+	0.944199i	$0.606838\pi$
$354$	−9.07325	−0.482238
$355$	−10.5120	−0.557921
$356$	−1.14751	−0.0608178
$357$	11.5793	0.612839
$358$	9.25943	0.489376
$359$	7.47502	0.394517	0.197258	−	0.980352i	$-0.436796\pi$
$359$	7.47502	0.394517	0.197258	+	0.980352i	$0.436796\pi$
$360$	−0.528770	−0.0278686
$361$	42.4667	2.23509
$362$	−15.6697	−0.823579
$363$	−16.2174	−0.851191
$364$	−3.90213	−0.204527
$365$	11.1508	0.583657
$366$	−1.34519	−0.0703140
$367$	12.5289	0.654004	0.327002	−	0.945024i	$-0.393962\pi$
$367$	12.5289	0.654004	0.327002	+	0.945024i	$0.393962\pi$
$368$	−3.25866	−0.169870
$369$	4.58177	0.238517
$370$	5.56385	0.289251
$371$	0.218836	0.0113614
$372$	−12.1312	−0.628976
$373$	−37.6943	−1.95174	−0.975868	−	0.218363i	$-0.929928\pi$
$373$	−37.6943	−1.95174	−0.975868	+	0.218363i	$0.929928\pi$
$374$	−9.46325	−0.489333
$375$	17.3132	0.894050
$376$	−5.21669	−0.269030
$377$	20.1754	1.03909
$378$	−4.66381	−0.239880
$379$	−14.1439	−0.726525	−0.363263	−	0.931687i	$-0.618337\pi$
$379$	−14.1439	−0.726525	−0.363263	+	0.931687i	$0.618337\pi$
$380$	8.11275	0.416175
$381$	3.19133	0.163497
$382$	−2.02195	−0.103452
$383$	17.4302	0.890643	0.445321	−	0.895371i	$-0.353089\pi$
$383$	17.4302	0.890643	0.445321	+	0.895371i	$0.353089\pi$
$384$	1.87377	0.0956202
$385$	1.58461	0.0807594
$386$	−1.77261	−0.0902235
$387$	−4.25121	−0.216101
$388$	2.36608	0.120120
$389$	20.3563	1.03211	0.516054	−	0.856556i	$-0.327400\pi$
$389$	20.3563	1.03211	0.516054	+	0.856556i	$0.327400\pi$
$390$	7.56598	0.383118
$391$	−20.1375	−1.01840
$392$	1.00000	0.0505076
$393$	19.9654	1.00712
$394$	−26.7239	−1.34633
$395$	−17.9235	−0.901829
$396$	−0.782516	−0.0393229
$397$	−31.8380	−1.59791	−0.798953	−	0.601394i	$-0.794612\pi$
$397$	−31.8380	−1.59791	−0.798953	+	0.601394i	$0.794612\pi$
$398$	16.4847	0.826302
$399$	−14.6904	−0.735442
$400$	−3.92923	−0.196461
$401$	4.64724	0.232072	0.116036	−	0.993245i	$-0.462981\pi$
$401$	4.64724	0.232072	0.116036	+	0.993245i	$0.462981\pi$
$402$	16.2702	0.811486
$403$	25.2634	1.25846
$404$	−11.1134	−0.552912
$405$	10.6291	0.528166
$406$	−5.17036	−0.256600
$407$	8.23383	0.408136
$408$	11.5793	0.573259
$409$	−19.1420	−0.946510	−0.473255	−	0.880925i	$-0.656921\pi$
$409$	−19.1420	−0.946510	−0.473255	+	0.880925i	$0.656921\pi$
$410$	−9.27819	−0.458217
$411$	−15.2507	−0.752261
$412$	19.9431	0.982525
$413$	−4.84226	−0.238272
$414$	−1.66517	−0.0818385
$415$	−15.1402	−0.743205
$416$	−3.90213	−0.191318
$417$	−40.7448	−1.99528
$418$	12.0059	0.587228
$419$	−0.149339	−0.00729566	−0.00364783	−	0.999993i	$-0.501161\pi$
$419$	−0.149339	−0.00729566	−0.00364783	+	0.999993i	$0.501161\pi$
$420$	−1.93894	−0.0946104
$421$	2.58441	0.125957	0.0629783	−	0.998015i	$-0.479940\pi$
$421$	2.58441	0.125957	0.0629783	+	0.998015i	$0.479940\pi$
$422$	−26.3090	−1.28070
$423$	−2.66571	−0.129611
$424$	0.218836	0.0106276
$425$	−24.2813	−1.17782
$426$	19.0351	0.922251
$427$	−0.717905	−0.0347419
$428$	5.25937	0.254221
$429$	11.1967	0.540584
$430$	8.60880	0.415153
$431$	−1.00000	−0.0481683
$431$	−1.00000	−0.0481683
$432$	−4.66381	−0.224388
$433$	20.2714	0.974181	0.487090	−	0.873352i	$-0.338058\pi$
$433$	20.2714	0.974181	0.487090	+	0.873352i	$0.338058\pi$
$434$	−6.47426	−0.310774
$435$	10.0250	0.480662
$436$	19.9697	0.956373
$437$	25.5481	1.22213
$438$	−20.1916	−0.964793
$439$	35.0205	1.67144	0.835718	−	0.549158i	$-0.185052\pi$
$439$	35.0205	1.67144	0.835718	+	0.549158i	$0.185052\pi$
$440$	1.58461	0.0755435
$441$	0.510997	0.0243332
$442$	−24.1139	−1.14698
$443$	14.5875	0.693073	0.346537	−	0.938036i	$-0.387358\pi$
$443$	14.5875	0.693073	0.346537	+	0.938036i	$0.387358\pi$
$444$	−10.0749	−0.478135
$445$	1.18742	0.0562891
$446$	18.4763	0.874880
$447$	26.7032	1.26302
$448$	1.00000	0.0472456
$449$	−41.6861	−1.96729	−0.983644	−	0.180122i	$-0.942351\pi$
$449$	−41.6861	−1.96729	−0.983644	+	0.180122i	$0.942351\pi$
$450$	−2.00782	−0.0946497
$451$	−13.7306	−0.646549
$452$	−9.69424	−0.455978
$453$	−44.6512	−2.09790
$454$	−12.3181	−0.578119
$455$	4.03785	0.189297
$456$	−14.6904	−0.687943
$457$	−7.67178	−0.358871	−0.179435	−	0.983770i	$-0.557427\pi$
$457$	−7.67178	−0.358871	−0.179435	+	0.983770i	$0.557427\pi$
$458$	7.76057	0.362628
$459$	−28.8208	−1.34524
$460$	3.37200	0.157220
$461$	20.3822	0.949295	0.474647	−	0.880176i	$-0.342576\pi$
$461$	20.3822	0.949295	0.474647	+	0.880176i	$0.342576\pi$
$462$	−2.86939	−0.133496
$463$	−29.2383	−1.35882	−0.679409	−	0.733760i	$-0.737764\pi$
$463$	−29.2383	−1.35882	−0.679409	+	0.733760i	$0.737764\pi$
$464$	−5.17036	−0.240028
$465$	12.5532	0.582140
$466$	−13.3591	−0.618846
$467$	−9.48920	−0.439108	−0.219554	−	0.975600i	$-0.570460\pi$
$467$	−9.48920	−0.439108	−0.219554	+	0.975600i	$0.570460\pi$
$468$	−1.99398	−0.0921716
$469$	8.68318	0.400952
$470$	5.39813	0.248997
$471$	−0.371377	−0.0171121
$472$	−4.84226	−0.222883
$473$	12.7400	0.585785
$474$	32.4556	1.49073
$475$	30.8054	1.41345
$476$	6.17967	0.283245
$477$	0.111824	0.00512008
$478$	−0.728139	−0.0333043
$479$	−5.45903	−0.249429	−0.124715	−	0.992193i	$-0.539802\pi$
$479$	−5.45903	−0.249429	−0.124715	+	0.992193i	$0.539802\pi$
$480$	−1.93894	−0.0884999
$481$	20.9811	0.956657
$482$	−8.41243	−0.383176
$483$	−6.10597	−0.277831
$484$	−8.65496	−0.393407
$485$	−2.44838	−0.111175
$486$	−5.25566	−0.238401
$487$	−2.15693	−0.0977396	−0.0488698	−	0.998805i	$-0.515562\pi$
$487$	−2.15693	−0.0977396	−0.0488698	+	0.998805i	$0.515562\pi$
$488$	−0.717905	−0.0324980
$489$	−13.9169	−0.629343
$490$	−1.03478	−0.0467466
$491$	3.49842	0.157881	0.0789407	−	0.996879i	$-0.474846\pi$
$491$	3.49842	0.157881	0.0789407	+	0.996879i	$0.474846\pi$
$492$	16.8008	0.757439
$493$	−31.9511	−1.43901
$494$	30.5930	1.37644
$495$	0.809732	0.0363948
$496$	−6.47426	−0.290703
$497$	10.1587	0.455681
$498$	27.4157	1.22853
$499$	36.7928	1.64707	0.823537	−	0.567263i	$-0.191998\pi$
$499$	36.7928	1.64707	0.823537	+	0.567263i	$0.191998\pi$
$500$	9.23979	0.413216
$501$	−7.69711	−0.343882
$502$	−18.9854	−0.847361
$503$	20.7073	0.923292	0.461646	−	0.887064i	$-0.347259\pi$
$503$	20.7073	0.923292	0.461646	+	0.887064i	$0.347259\pi$
$504$	0.510997	0.0227616
$505$	11.4999	0.511740
$506$	4.99016	0.221840
$507$	4.17214	0.185291
$508$	1.70316	0.0755656
$509$	−9.01048	−0.399383	−0.199691	−	0.979859i	$-0.563994\pi$
$509$	−9.01048	−0.399383	−0.199691	+	0.979859i	$0.563994\pi$
$510$	−11.9820	−0.530571
$511$	−10.7760	−0.476701
$512$	1.00000	0.0441942
$513$	36.5646	1.61437
$514$	1.45993	0.0643948
$515$	−20.6367	−0.909362
$516$	−15.5887	−0.686253
$517$	7.98859	0.351338
$518$	−5.37684	−0.236245
$519$	44.4514	1.95120
$520$	4.03785	0.177071
$521$	7.03599	0.308252	0.154126	−	0.988051i	$-0.450744\pi$
$521$	7.03599	0.308252	0.154126	+	0.988051i	$0.450744\pi$
$522$	−2.64204	−0.115639
$523$	−24.6139	−1.07629	−0.538145	−	0.842852i	$-0.680875\pi$
$523$	−24.6139	−1.07629	−0.538145	+	0.842852i	$0.680875\pi$
$524$	10.6552	0.465477
$525$	−7.36245	−0.321324
$526$	−7.36690	−0.321212
$527$	−40.0088	−1.74281
$528$	−2.86939	−0.124874
$529$	−12.3811	−0.538309
$530$	−0.226447	−0.00983622
$531$	−2.47438	−0.107379
$532$	−7.84007	−0.339910
$533$	−34.9878	−1.51549
$534$	−2.15016	−0.0930466
$535$	−5.44229	−0.235291
$536$	8.68318	0.375056
$537$	17.3500	0.748708
$538$	−14.2497	−0.614348
$539$	−1.53135	−0.0659600
$540$	4.82602	0.207679
$541$	45.5270	1.95736	0.978680	−	0.205390i	$-0.0658462\pi$
$541$	45.5270	1.95736	0.978680	+	0.205390i	$0.0658462\pi$
$542$	−28.9629	−1.24406
$543$	−29.3613	−1.26001
$544$	6.17967	0.264951
$545$	−20.6642	−0.885158
$546$	−7.31167	−0.312911
$547$	−8.46400	−0.361895	−0.180947	−	0.983493i	$-0.557916\pi$
$547$	−8.46400	−0.361895	−0.180947	+	0.983493i	$0.557916\pi$
$548$	−8.13906	−0.347684
$549$	−0.366847	−0.0156567
$550$	6.01703	0.256567
$551$	40.5359	1.72689
$552$	−6.10597	−0.259887
$553$	17.3211	0.736566
$554$	−7.43709	−0.315972
$555$	10.4253	0.442531
$556$	−21.7449	−0.922189
$557$	−27.9602	−1.18471	−0.592355	−	0.805677i	$-0.701802\pi$
$557$	−27.9602	−1.18471	−0.592355	+	0.805677i	$0.701802\pi$
$558$	−3.30833	−0.140053
$559$	32.4635	1.37306
$560$	−1.03478	−0.0437275
$561$	−17.7319	−0.748642
$562$	5.97650	0.252103
$563$	28.2756	1.19167	0.595836	−	0.803106i	$-0.296821\pi$
$563$	28.2756	1.19167	0.595836	+	0.803106i	$0.296821\pi$
$564$	−9.77485	−0.411596
$565$	10.0314	0.422024
$566$	2.60026	0.109297
$567$	−10.2719	−0.431378
$568$	10.1587	0.426250
$569$	2.18742	0.0917016	0.0458508	−	0.998948i	$-0.485400\pi$
$569$	2.18742	0.0917016	0.0458508	+	0.998948i	$0.485400\pi$
$570$	15.2014	0.636716
$571$	−39.0519	−1.63427	−0.817135	−	0.576446i	$-0.804439\pi$
$571$	−39.0519	−1.63427	−0.817135	+	0.576446i	$0.804439\pi$
$572$	5.97553	0.249850
$573$	−3.78866	−0.158274
$574$	8.96633	0.374248
$575$	12.8040	0.533965
$576$	0.510997	0.0212915
$577$	17.3073	0.720513	0.360257	−	0.932853i	$-0.382689\pi$
$577$	17.3073	0.720513	0.360257	+	0.932853i	$0.382689\pi$
$578$	21.1883	0.881319
$579$	−3.32146	−0.138035
$580$	5.35018	0.222154
$581$	14.6313	0.607010
$582$	4.43348	0.183774
$583$	−0.335114	−0.0138790
$584$	−10.7760	−0.445913
$585$	2.06333	0.0853081
$586$	25.2527	1.04318
$587$	−34.1661	−1.41019	−0.705093	−	0.709115i	$-0.749095\pi$
$587$	−34.1661	−1.41019	−0.705093	+	0.709115i	$0.749095\pi$
$588$	1.87377	0.0772728
$589$	50.7586	2.09147
$590$	5.01067	0.206286
$591$	−50.0743	−2.05978
$592$	−5.37684	−0.220987
$593$	−34.9695	−1.43602	−0.718012	−	0.696031i	$-0.754948\pi$
$593$	−34.9695	−1.43602	−0.718012	+	0.696031i	$0.754948\pi$
$594$	7.14193	0.293037
$595$	−6.39461	−0.262153
$596$	14.2511	0.583748
$597$	30.8884	1.26418
$598$	12.7157	0.519985
$599$	39.1226	1.59850	0.799252	−	0.600996i	$-0.205229\pi$
$599$	39.1226	1.59850	0.799252	+	0.600996i	$0.205229\pi$
$600$	−7.36245	−0.300571
$601$	28.9069	1.17914	0.589568	−	0.807718i	$-0.299298\pi$
$601$	28.9069	1.17914	0.589568	+	0.807718i	$0.299298\pi$
$602$	−8.31944	−0.339075
$603$	4.43708	0.180692
$604$	−23.8297	−0.969615
$605$	8.95599	0.364113
$606$	−20.8239	−0.845913
$607$	−20.1789	−0.819035	−0.409518	−	0.912302i	$-0.634303\pi$
$607$	−20.1789	−0.819035	−0.409518	+	0.912302i	$0.634303\pi$
$608$	−7.84007	−0.317957
$609$	−9.68803	−0.392579
$610$	0.742874	0.0300781
$611$	20.3562	0.823524
$612$	3.15779	0.127646
$613$	−24.4418	−0.987196	−0.493598	−	0.869690i	$-0.664319\pi$
$613$	−24.4418	−0.987196	−0.493598	+	0.869690i	$0.664319\pi$
$614$	7.22841	0.291715
$615$	−17.3852	−0.701037
$616$	−1.53135	−0.0616999
$617$	−32.5600	−1.31082	−0.655408	−	0.755275i	$-0.727504\pi$
$617$	−32.5600	−1.31082	−0.655408	+	0.755275i	$0.727504\pi$
$618$	37.3687	1.50319
$619$	3.93775	0.158271	0.0791357	−	0.996864i	$-0.474784\pi$
$619$	3.93775	0.158271	0.0791357	+	0.996864i	$0.474784\pi$
$620$	6.69944	0.269056
$621$	15.1978	0.609866
$622$	−21.3815	−0.857319
$623$	−1.14751	−0.0459739
$624$	−7.31167	−0.292701
$625$	10.0850	0.403399
$626$	26.7729	1.07006
$627$	22.4962	0.898413
$628$	−0.198198	−0.00790897
$629$	−33.2271	−1.32485
$630$	−0.528770	−0.0210667
$631$	42.2330	1.68127	0.840634	−	0.541604i	$-0.182183\pi$
$631$	42.2330	1.68127	0.840634	+	0.541604i	$0.182183\pi$
$632$	17.3211	0.688995
$633$	−49.2970	−1.95938
$634$	16.3290	0.648508
$635$	−1.76240	−0.0699387
$636$	0.410046	0.0162594
$637$	−3.90213	−0.154608
$638$	7.91763	0.313462
$639$	5.19107	0.205356
$640$	−1.03478	−0.0409033
$641$	−50.4987	−1.99458	−0.997289	−	0.0735892i	$-0.976555\pi$
$641$	−50.4987	−1.99458	−0.997289	+	0.0735892i	$0.976555\pi$
$642$	9.85483	0.388939
$643$	−30.2512	−1.19299	−0.596495	−	0.802617i	$-0.703440\pi$
$643$	−30.2512	−1.19299	−0.596495	+	0.802617i	$0.703440\pi$
$644$	−3.25866	−0.128409
$645$	16.1309	0.635152
$646$	−48.4490	−1.90620
$647$	−31.3945	−1.23425	−0.617123	−	0.786866i	$-0.711702\pi$
$647$	−31.3945	−1.23425	−0.617123	+	0.786866i	$0.711702\pi$
$648$	−10.2719	−0.403517
$649$	7.41520	0.291072
$650$	15.3324	0.601385
$651$	−12.1312	−0.475461
$652$	−7.42722	−0.290872
$653$	−3.00925	−0.117761	−0.0588805	−	0.998265i	$-0.518753\pi$
$653$	−3.00925	−0.117761	−0.0588805	+	0.998265i	$0.518753\pi$
$654$	37.4185	1.46318
$655$	−11.0258	−0.430815
$656$	8.96633	0.350077
$657$	−5.50648	−0.214828
$658$	−5.21669	−0.203368
$659$	−11.2106	−0.436704	−0.218352	−	0.975870i	$-0.570068\pi$
$659$	−11.2106	−0.436704	−0.218352	+	0.975870i	$0.570068\pi$
$660$	2.96919	0.115576
$661$	1.43340	0.0557527	0.0278763	−	0.999611i	$-0.491126\pi$
$661$	1.43340	0.0557527	0.0278763	+	0.999611i	$0.491126\pi$
$662$	−18.7873	−0.730190
$663$	−45.1837	−1.75479
$664$	14.6313	0.567806
$665$	8.11275	0.314599
$666$	−2.74755	−0.106465
$667$	16.8485	0.652375
$668$	−4.10783	−0.158937
$669$	34.6203	1.33850
$670$	−8.98519	−0.347128
$671$	1.09936	0.0424405
$672$	1.87377	0.0722821
$673$	23.9446	0.922998	0.461499	−	0.887141i	$-0.347312\pi$
$673$	23.9446	0.922998	0.461499	+	0.887141i	$0.347312\pi$
$674$	9.78975	0.377087
$675$	18.3252	0.705336
$676$	2.22661	0.0856388
$677$	−1.94721	−0.0748373	−0.0374187	−	0.999300i	$-0.511914\pi$
$677$	−1.94721	−0.0748373	−0.0374187	+	0.999300i	$0.511914\pi$
$678$	−18.1647	−0.697612
$679$	2.36608	0.0908019
$680$	−6.39461	−0.245222
$681$	−23.0813	−0.884477
$682$	9.91437	0.379641
$683$	−3.53111	−0.135114	−0.0675571	−	0.997715i	$-0.521520\pi$
$683$	−3.53111	−0.135114	−0.0675571	+	0.997715i	$0.521520\pi$
$684$	−4.00625	−0.153183
$685$	8.42214	0.321794
$686$	1.00000	0.0381802
$687$	14.5415	0.554792
$688$	−8.31944	−0.317176
$689$	−0.853924	−0.0325319
$690$	6.31834	0.240535
$691$	36.9712	1.40645	0.703225	−	0.710967i	$-0.251743\pi$
$691$	36.9712	1.40645	0.703225	+	0.710967i	$0.251743\pi$
$692$	23.7230	0.901814
$693$	−0.782516	−0.0297253
$694$	13.4271	0.509685
$695$	22.5012	0.853519
$696$	−9.68803	−0.367224
$697$	55.4090	2.09877
$698$	−15.0560	−0.569880
$699$	−25.0317	−0.946787
$700$	−3.92923	−0.148511
$701$	−39.2488	−1.48241	−0.741203	−	0.671281i	$-0.765744\pi$
$701$	−39.2488	−1.48241	−0.741203	+	0.671281i	$0.765744\pi$
$702$	18.1988	0.686869
$703$	42.1548	1.58990
$704$	−1.53135	−0.0577150
$705$	10.1148	0.380947
$706$	−12.3768	−0.465806
$707$	−11.1134	−0.417962
$708$	−9.07325	−0.340994
$709$	46.4330	1.74383	0.871913	−	0.489661i	$-0.162879\pi$
$709$	46.4330	1.74383	0.871913	+	0.489661i	$0.162879\pi$
$710$	−10.5120	−0.394510
$711$	8.85101	0.331939
$712$	−1.14751	−0.0430047
$713$	21.0974	0.790105
$714$	11.5793	0.433343
$715$	−6.18336	−0.231245
$716$	9.25943	0.346041
$717$	−1.36436	−0.0509530
$718$	7.47502	0.278965
$719$	47.0274	1.75383	0.876913	−	0.480649i	$-0.159599\pi$
$719$	47.0274	1.75383	0.876913	+	0.480649i	$0.159599\pi$
$720$	−0.528770	−0.0197061
$721$	19.9431	0.742719
$722$	42.4667	1.58045
$723$	−15.7629	−0.586229
$724$	−15.6697	−0.582358
$725$	20.3155	0.754499
$726$	−16.2174	−0.601883
$727$	11.2393	0.416841	0.208421	−	0.978039i	$-0.433168\pi$
$727$	11.2393	0.416841	0.208421	+	0.978039i	$0.433168\pi$
$728$	−3.90213	−0.144623
$729$	20.9678	0.776583
$730$	11.1508	0.412708
$731$	−51.4114	−1.90152
$732$	−1.34519	−0.0497195
$733$	−50.1259	−1.85144	−0.925722	−	0.378204i	$-0.876542\pi$
$733$	−50.1259	−1.85144	−0.925722	+	0.378204i	$0.876542\pi$
$734$	12.5289	0.462451
$735$	−1.93894	−0.0715187
$736$	−3.25866	−0.120116
$737$	−13.2970	−0.489801
$738$	4.58177	0.168657
$739$	49.2976	1.81344	0.906722	−	0.421730i	$-0.138577\pi$
$739$	49.2976	1.81344	0.906722	+	0.421730i	$0.138577\pi$
$740$	5.56385	0.204531
$741$	57.3240	2.10585
$742$	0.218836	0.00803371
$743$	29.3668	1.07736	0.538682	−	0.842509i	$-0.318922\pi$
$743$	29.3668	1.07736	0.538682	+	0.842509i	$0.318922\pi$
$744$	−12.1312	−0.444753
$745$	−14.7468	−0.540280
$746$	−37.6943	−1.38009
$747$	7.47657	0.273553
$748$	−9.46325	−0.346011
$749$	5.25937	0.192173
$750$	17.3132	0.632189
$751$	16.1753	0.590247	0.295123	−	0.955459i	$-0.404639\pi$
$751$	16.1753	0.590247	0.295123	+	0.955459i	$0.404639\pi$
$752$	−5.21669	−0.190233
$753$	−35.5742	−1.29640
$754$	20.1754	0.734745
$755$	24.6585	0.897414
$756$	−4.66381	−0.169621
$757$	4.92890	0.179144	0.0895720	−	0.995980i	$-0.471450\pi$
$757$	4.92890	0.179144	0.0895720	+	0.995980i	$0.471450\pi$
$758$	−14.1439	−0.513731
$759$	9.35039	0.339398
$760$	8.11275	0.294280
$761$	50.1125	1.81658	0.908289	−	0.418344i	$-0.137389\pi$
$761$	50.1125	1.81658	0.908289	+	0.418344i	$0.137389\pi$
$762$	3.19133	0.115610
$763$	19.9697	0.722950
$764$	−2.02195	−0.0731516
$765$	−3.26762	−0.118141
$766$	17.4302	0.629780
$767$	18.8951	0.682263
$768$	1.87377	0.0676137
$769$	38.4149	1.38528	0.692639	−	0.721285i	$-0.256448\pi$
$769$	38.4149	1.38528	0.692639	+	0.721285i	$0.256448\pi$
$770$	1.58461	0.0571055
$771$	2.73557	0.0985190
$772$	−1.77261	−0.0637977
$773$	28.9276	1.04045	0.520227	−	0.854028i	$-0.325847\pi$
$773$	28.9276	1.04045	0.520227	+	0.854028i	$0.325847\pi$
$774$	−4.25121	−0.152807
$775$	25.4388	0.913790
$776$	2.36608	0.0849374
$777$	−10.0749	−0.361436
$778$	20.3563	0.729810
$779$	−70.2967	−2.51864
$780$	7.56598	0.270906
$781$	−15.5566	−0.556658
$782$	−20.1375	−0.720115
$783$	24.1135	0.861748
$784$	1.00000	0.0357143
$785$	0.205092	0.00732004
$786$	19.9654	0.712144
$787$	−0.524550	−0.0186982	−0.00934910	−	0.999956i	$-0.502976\pi$
$787$	−0.524550	−0.0186982	−0.00934910	+	0.999956i	$0.502976\pi$
$788$	−26.7239	−0.952000
$789$	−13.8038	−0.491430
$790$	−17.9235	−0.637689
$791$	−9.69424	−0.344687
$792$	−0.782516	−0.0278055
$793$	2.80136	0.0994791
$794$	−31.8380	−1.12989
$795$	−0.424308	−0.0150487
$796$	16.4847	0.584284
$797$	−37.9437	−1.34404	−0.672018	−	0.740535i	$-0.734572\pi$
$797$	−37.9437	−1.34404	−0.672018	+	0.740535i	$0.734572\pi$
$798$	−14.6904	−0.520036
$799$	−32.2374	−1.14048
$800$	−3.92923	−0.138919
$801$	−0.586373	−0.0207185
$802$	4.64724	0.164100
$803$	16.5018	0.582335
$804$	16.2702	0.573807
$805$	3.37200	0.118847
$806$	25.2634	0.889865
$807$	−26.7006	−0.939905
$808$	−11.1134	−0.390968
$809$	−48.5107	−1.70555	−0.852773	−	0.522282i	$-0.825081\pi$
$809$	−48.5107	−1.70555	−0.852773	+	0.522282i	$0.825081\pi$
$810$	10.6291	0.373470
$811$	27.5821	0.968537	0.484269	−	0.874919i	$-0.339086\pi$
$811$	27.5821	0.968537	0.484269	+	0.874919i	$0.339086\pi$
$812$	−5.17036	−0.181444
$813$	−54.2697	−1.90332
$814$	8.23383	0.288596
$815$	7.68555	0.269213
$816$	11.5793	0.405355
$817$	65.2250	2.28193
$818$	−19.1420	−0.669284
$819$	−1.99398	−0.0696752
$820$	−9.27819	−0.324008
$821$	−38.4367	−1.34145	−0.670726	−	0.741705i	$-0.734017\pi$
$821$	−38.4367	−1.34145	−0.670726	+	0.741705i	$0.734017\pi$
$822$	−15.2507	−0.531929
$823$	−35.6103	−1.24130	−0.620649	−	0.784089i	$-0.713131\pi$
$823$	−35.6103	−1.24130	−0.620649	+	0.784089i	$0.713131\pi$
$824$	19.9431	0.694750
$825$	11.2745	0.392528
$826$	−4.84226	−0.168484
$827$	−27.7480	−0.964893	−0.482446	−	0.875926i	$-0.660252\pi$
$827$	−27.7480	−0.964893	−0.482446	+	0.875926i	$0.660252\pi$
$828$	−1.66517	−0.0578686
$829$	25.6964	0.892472	0.446236	−	0.894915i	$-0.352764\pi$
$829$	25.6964	0.892472	0.446236	+	0.894915i	$0.352764\pi$
$830$	−15.1402	−0.525525
$831$	−13.9354	−0.483412
$832$	−3.90213	−0.135282
$833$	6.17967	0.214113
$834$	−40.7448	−1.41088
$835$	4.25071	0.147102
$836$	12.0059	0.415233
$837$	30.1947	1.04368
$838$	−0.149339	−0.00515881
$839$	6.52203	0.225166	0.112583	−	0.993642i	$-0.464088\pi$
$839$	6.52203	0.225166	0.112583	+	0.993642i	$0.464088\pi$
$840$	−1.93894	−0.0668997
$841$	−2.26742	−0.0781868
$842$	2.58441	0.0890647
$843$	11.1986	0.385699
$844$	−26.3090	−0.905595
$845$	−2.30405	−0.0792618
$846$	−2.66571	−0.0916491
$847$	−8.65496	−0.297388
$848$	0.218836	0.00751484
$849$	4.87228	0.167216
$850$	−24.2813	−0.832843
$851$	17.5213	0.600623
$852$	19.0351	0.652130
$853$	−5.70019	−0.195171	−0.0975854	−	0.995227i	$-0.531112\pi$
$853$	−5.70019	−0.195171	−0.0975854	+	0.995227i	$0.531112\pi$
$854$	−0.717905	−0.0245662
$855$	4.14559	0.141776
$856$	5.25937	0.179762
$857$	15.2428	0.520684	0.260342	−	0.965516i	$-0.416165\pi$
$857$	15.2428	0.520684	0.260342	+	0.965516i	$0.416165\pi$
$858$	11.1967	0.382251
$859$	20.8271	0.710613	0.355307	−	0.934750i	$-0.384376\pi$
$859$	20.8271	0.710613	0.355307	+	0.934750i	$0.384376\pi$
$860$	8.60880	0.293558
$861$	16.8008	0.572570
$862$	−1.00000	−0.0340601
$863$	−0.909073	−0.0309452	−0.0154726	−	0.999880i	$-0.504925\pi$
$863$	−0.909073	−0.0309452	−0.0154726	+	0.999880i	$0.504925\pi$
$864$	−4.66381	−0.158666
$865$	−24.5481	−0.834661
$866$	20.2714	0.688850
$867$	39.7020	1.34835
$868$	−6.47426	−0.219751
$869$	−26.5246	−0.899786
$870$	10.0250	0.339879
$871$	−33.8829	−1.14808
$872$	19.9697	0.676258
$873$	1.20906	0.0409205
$874$	25.5481	0.864179
$875$	9.23979	0.312362
$876$	−20.1916	−0.682212
$877$	0.916470	0.0309470	0.0154735	−	0.999880i	$-0.495074\pi$
$877$	0.916470	0.0309470	0.0154735	+	0.999880i	$0.495074\pi$
$878$	35.0205	1.18188
$879$	47.3176	1.59598
$880$	1.58461	0.0534173
$881$	12.6324	0.425595	0.212797	−	0.977096i	$-0.431743\pi$
$881$	12.6324	0.425595	0.212797	+	0.977096i	$0.431743\pi$
$882$	0.510997	0.0172062
$883$	6.37879	0.214664	0.107332	−	0.994223i	$-0.465769\pi$
$883$	6.37879	0.214664	0.107332	+	0.994223i	$0.465769\pi$
$884$	−24.1139	−0.811037
$885$	9.38883	0.315602
$886$	14.5875	0.490077
$887$	−15.2730	−0.512817	−0.256408	−	0.966569i	$-0.582539\pi$
$887$	−15.2730	−0.512817	−0.256408	+	0.966569i	$0.582539\pi$
$888$	−10.0749	−0.338093
$889$	1.70316	0.0571222
$890$	1.18742	0.0398024
$891$	15.7298	0.526970
$892$	18.4763	0.618634
$893$	40.8992	1.36864
$894$	26.7032	0.893089
$895$	−9.58148	−0.320274
$896$	1.00000	0.0334077
$897$	23.8263	0.795537
$898$	−41.6861	−1.39108
$899$	33.4742	1.11643
$900$	−2.00782	−0.0669275
$901$	1.35233	0.0450527
$902$	−13.7306	−0.457179
$903$	−15.5887	−0.518759
$904$	−9.69424	−0.322425
$905$	16.2147	0.538994
$906$	−44.6512	−1.48344
$907$	32.6370	1.08369	0.541847	−	0.840477i	$-0.317725\pi$
$907$	32.6370	1.08369	0.541847	+	0.840477i	$0.317725\pi$
$908$	−12.3181	−0.408792
$909$	−5.67891	−0.188358
$910$	4.03785	0.133853
$911$	−36.0496	−1.19438	−0.597188	−	0.802101i	$-0.703715\pi$
$911$	−36.0496	−1.19438	−0.597188	+	0.802101i	$0.703715\pi$
$912$	−14.6904	−0.486449
$913$	−22.4057	−0.741521
$914$	−7.67178	−0.253760
$915$	1.39197	0.0460172
$916$	7.76057	0.256416
$917$	10.6552	0.351867
$918$	−28.8208	−0.951228
$919$	−24.2381	−0.799540	−0.399770	−	0.916616i	$-0.630910\pi$
$919$	−24.2381	−0.799540	−0.399770	+	0.916616i	$0.630910\pi$
$920$	3.37200	0.111172
$921$	13.5443	0.446301
$922$	20.3822	0.671253
$923$	−39.6406	−1.30479
$924$	−2.86939	−0.0943961
$925$	21.1268	0.694646
$926$	−29.2383	−0.960829
$927$	10.1909	0.334712
$928$	−5.17036	−0.169725
$929$	7.12909	0.233898	0.116949	−	0.993138i	$-0.462689\pi$
$929$	7.12909	0.233898	0.116949	+	0.993138i	$0.462689\pi$
$930$	12.5532	0.411635
$931$	−7.84007	−0.256948
$932$	−13.3591	−0.437590
$933$	−40.0639	−1.31163
$934$	−9.48920	−0.310496
$935$	9.79239	0.320245
$936$	−1.99398	−0.0651751
$937$	−14.5641	−0.475790	−0.237895	−	0.971291i	$-0.576457\pi$
$937$	−14.5641	−0.475790	−0.237895	+	0.971291i	$0.576457\pi$
$938$	8.68318	0.283516
$939$	50.1662	1.63711
$940$	5.39813	0.176068
$941$	−57.6067	−1.87793	−0.938963	−	0.344019i	$-0.888211\pi$
$941$	−57.6067	−1.87793	−0.938963	+	0.344019i	$0.888211\pi$
$942$	−0.371377	−0.0121001
$943$	−29.2183	−0.951478
$944$	−4.84226	−0.157602
$945$	4.82602	0.156990
$946$	12.7400	0.414213
$947$	−58.2225	−1.89198	−0.945989	−	0.324199i	$-0.894905\pi$
$947$	−58.2225	−1.89198	−0.945989	+	0.324199i	$0.894905\pi$
$948$	32.4556	1.05411
$949$	42.0492	1.36497
$950$	30.8054	0.999460
$951$	30.5967	0.992167
$952$	6.17967	0.200284
$953$	−28.9412	−0.937497	−0.468749	−	0.883332i	$-0.655295\pi$
$953$	−28.9412	−0.937497	−0.468749	+	0.883332i	$0.655295\pi$
$954$	0.111824	0.00362045
$955$	2.09227	0.0677044
$956$	−0.728139	−0.0235497
$957$	14.8358	0.479573
$958$	−5.45903	−0.176373
$959$	−8.13906	−0.262824
$960$	−1.93894	−0.0625789
$961$	10.9160	0.352130
$962$	20.9811	0.676458
$963$	2.68752	0.0866042
$964$	−8.41243	−0.270946
$965$	1.83426	0.0590470
$966$	−6.10597	−0.196456
$967$	−28.5526	−0.918189	−0.459094	−	0.888388i	$-0.651826\pi$
$967$	−28.5526	−0.918189	−0.459094	+	0.888388i	$0.651826\pi$
$968$	−8.65496	−0.278181
$969$	−90.7822	−2.91634
$970$	−2.44838	−0.0786126
$971$	3.16395	0.101536	0.0507680	−	0.998710i	$-0.483833\pi$
$971$	3.16395	0.101536	0.0507680	+	0.998710i	$0.483833\pi$
$972$	−5.25566	−0.168575
$973$	−21.7449	−0.697110
$974$	−2.15693	−0.0691123
$975$	28.7292	0.920072
$976$	−0.717905	−0.0229796
$977$	−21.6856	−0.693785	−0.346892	−	0.937905i	$-0.612763\pi$
$977$	−21.6856	−0.693785	−0.346892	+	0.937905i	$0.612763\pi$
$978$	−13.9169	−0.445012
$979$	1.75724	0.0561616
$980$	−1.03478	−0.0330549
$981$	10.2044	0.325803
$982$	3.49842	0.111639
$983$	10.7821	0.343895	0.171947	−	0.985106i	$-0.444994\pi$
$983$	10.7821	0.343895	0.171947	+	0.985106i	$0.444994\pi$
$984$	16.8008	0.535590
$985$	27.6534	0.881110
$986$	−31.9511	−1.01753
$987$	−9.77485	−0.311137
$988$	30.5930	0.973292
$989$	27.1103	0.862056
$990$	0.809732	0.0257350
$991$	−33.9689	−1.07906	−0.539529	−	0.841967i	$-0.681398\pi$
$991$	−33.9689	−1.07906	−0.539529	+	0.841967i	$0.681398\pi$
$992$	−6.47426	−0.205558
$993$	−35.2030	−1.11713
$994$	10.1587	0.322215
$995$	−17.0580	−0.540776
$996$	27.4157	0.868700
$997$	−11.0447	−0.349789	−0.174895	−	0.984587i	$-0.555958\pi$
$997$	−11.0447	−0.349789	−0.174895	+	0.984587i	$0.555958\pi$
$998$	36.7928	1.16466
$999$	25.0765	0.793387

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6034.2.a.m.1.18	✓	21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6034.2.a.m.1.18	✓	21	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:	\( N \)	\(=\)	\( 6034 = 2 \cdot 7 \cdot 431 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6034.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.87377 q^{3} +1.00000 q^{4} -1.03478 q^{5} +1.87377 q^{6} +1.00000 q^{7} +1.00000 q^{8} +0.510997 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.87377 q^{3} +1.00000 q^{4} -1.03478 q^{5} +1.87377 q^{6} +1.00000 q^{7} +1.00000 q^{8} +0.510997 q^{9} -1.03478 q^{10} -1.53135 q^{11} +1.87377 q^{12} -3.90213 q^{13} +1.00000 q^{14} -1.93894 q^{15} +1.00000 q^{16} +6.17967 q^{17} +0.510997 q^{18} -7.84007 q^{19} -1.03478 q^{20} +1.87377 q^{21} -1.53135 q^{22} -3.25866 q^{23} +1.87377 q^{24} -3.92923 q^{25} -3.90213 q^{26} -4.66381 q^{27} +1.00000 q^{28} -5.17036 q^{29} -1.93894 q^{30} -6.47426 q^{31} +1.00000 q^{32} -2.86939 q^{33} +6.17967 q^{34} -1.03478 q^{35} +0.510997 q^{36} -5.37684 q^{37} -7.84007 q^{38} -7.31167 q^{39} -1.03478 q^{40} +8.96633 q^{41} +1.87377 q^{42} -8.31944 q^{43} -1.53135 q^{44} -0.528770 q^{45} -3.25866 q^{46} -5.21669 q^{47} +1.87377 q^{48} +1.00000 q^{49} -3.92923 q^{50} +11.5793 q^{51} -3.90213 q^{52} +0.218836 q^{53} -4.66381 q^{54} +1.58461 q^{55} +1.00000 q^{56} -14.6904 q^{57} -5.17036 q^{58} -4.84226 q^{59} -1.93894 q^{60} -0.717905 q^{61} -6.47426 q^{62} +0.510997 q^{63} +1.00000 q^{64} +4.03785 q^{65} -2.86939 q^{66} +8.68318 q^{67} +6.17967 q^{68} -6.10597 q^{69} -1.03478 q^{70} +10.1587 q^{71} +0.510997 q^{72} -10.7760 q^{73} -5.37684 q^{74} -7.36245 q^{75} -7.84007 q^{76} -1.53135 q^{77} -7.31167 q^{78} +17.3211 q^{79} -1.03478 q^{80} -10.2719 q^{81} +8.96633 q^{82} +14.6313 q^{83} +1.87377 q^{84} -6.39461 q^{85} -8.31944 q^{86} -9.68803 q^{87} -1.53135 q^{88} -1.14751 q^{89} -0.528770 q^{90} -3.90213 q^{91} -3.25866 q^{92} -12.1312 q^{93} -5.21669 q^{94} +8.11275 q^{95} +1.87377 q^{96} +2.36608 q^{97} +1.00000 q^{98} -0.782516 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q + 21 q^{2} - 6 q^{3} + 21 q^{4} - 11 q^{5} - 6 q^{6} + 21 q^{7} + 21 q^{8} + 5 q^{9}+O(q^{10}) \) 21 * q + 21 * q^2 - 6 * q^3 + 21 * q^4 - 11 * q^5 - 6 * q^6 + 21 * q^7 + 21 * q^8 + 5 * q^9	\( 21 q + 21 q^{2} - 6 q^{3} + 21 q^{4} - 11 q^{5} - 6 q^{6} + 21 q^{7} + 21 q^{8} + 5 q^{9} - 11 q^{10} - 34 q^{11} - 6 q^{12} - 19 q^{13} + 21 q^{14} - 24 q^{15} + 21 q^{16} - 17 q^{17} + 5 q^{18} - 15 q^{19} - 11 q^{20} - 6 q^{21} - 34 q^{22} - 32 q^{23} - 6 q^{24} + 6 q^{25} - 19 q^{26} - 3 q^{27} + 21 q^{28} - 46 q^{29} - 24 q^{30} + 7 q^{31} + 21 q^{32} - 13 q^{33} - 17 q^{34} - 11 q^{35} + 5 q^{36} - 34 q^{37} - 15 q^{38} - 25 q^{39} - 11 q^{40} - 27 q^{41} - 6 q^{42} - 47 q^{43} - 34 q^{44} - 13 q^{45} - 32 q^{46} - 7 q^{47} - 6 q^{48} + 21 q^{49} + 6 q^{50} - 29 q^{51} - 19 q^{52} - 57 q^{53} - 3 q^{54} + 17 q^{55} + 21 q^{56} - 28 q^{57} - 46 q^{58} - 30 q^{59} - 24 q^{60} - 17 q^{61} + 7 q^{62} + 5 q^{63} + 21 q^{64} - 40 q^{65} - 13 q^{66} - 38 q^{67} - 17 q^{68} - 13 q^{69} - 11 q^{70} - 66 q^{71} + 5 q^{72} - 15 q^{73} - 34 q^{74} + 15 q^{75} - 15 q^{76} - 34 q^{77} - 25 q^{78} - 17 q^{79} - 11 q^{80} - 11 q^{81} - 27 q^{82} - 19 q^{83} - 6 q^{84} - 28 q^{85} - 47 q^{86} + 45 q^{87} - 34 q^{88} - 39 q^{89} - 13 q^{90} - 19 q^{91} - 32 q^{92} - 25 q^{93} - 7 q^{94} - 35 q^{95} - 6 q^{96} + 21 q^{98} - 52 q^{99}+O(q^{100}) \) 21 * q + 21 * q^2 - 6 * q^3 + 21 * q^4 - 11 * q^5 - 6 * q^6 + 21 * q^7 + 21 * q^8 + 5 * q^9 - 11 * q^10 - 34 * q^11 - 6 * q^12 - 19 * q^13 + 21 * q^14 - 24 * q^15 + 21 * q^16 - 17 * q^17 + 5 * q^18 - 15 * q^19 - 11 * q^20 - 6 * q^21 - 34 * q^22 - 32 * q^23 - 6 * q^24 + 6 * q^25 - 19 * q^26 - 3 * q^27 + 21 * q^28 - 46 * q^29 - 24 * q^30 + 7 * q^31 + 21 * q^32 - 13 * q^33 - 17 * q^34 - 11 * q^35 + 5 * q^36 - 34 * q^37 - 15 * q^38 - 25 * q^39 - 11 * q^40 - 27 * q^41 - 6 * q^42 - 47 * q^43 - 34 * q^44 - 13 * q^45 - 32 * q^46 - 7 * q^47 - 6 * q^48 + 21 * q^49 + 6 * q^50 - 29 * q^51 - 19 * q^52 - 57 * q^53 - 3 * q^54 + 17 * q^55 + 21 * q^56 - 28 * q^57 - 46 * q^58 - 30 * q^59 - 24 * q^60 - 17 * q^61 + 7 * q^62 + 5 * q^63 + 21 * q^64 - 40 * q^65 - 13 * q^66 - 38 * q^67 - 17 * q^68 - 13 * q^69 - 11 * q^70 - 66 * q^71 + 5 * q^72 - 15 * q^73 - 34 * q^74 + 15 * q^75 - 15 * q^76 - 34 * q^77 - 25 * q^78 - 17 * q^79 - 11 * q^80 - 11 * q^81 - 27 * q^82 - 19 * q^83 - 6 * q^84 - 28 * q^85 - 47 * q^86 + 45 * q^87 - 34 * q^88 - 39 * q^89 - 13 * q^90 - 19 * q^91 - 32 * q^92 - 25 * q^93 - 7 * q^94 - 35 * q^95 - 6 * q^96 + 21 * q^98 - 52 * q^99

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