LMFDB - Embedded newform 8034.2.a.o.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8034,2,Mod(1,8034)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8034, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8034 = 2 \cdot 3 \cdot 13 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8034.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:	$64.1518129839$
Analytic rank:	$1$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 3x^{6} - 4x^{5} + 14x^{4} + 3x^{3} - 12x^{2} - 3x + 1 $ x^7 - 3x^6 - 4x^5 + 14x^4 + 3x^3 - 12x^2 - 3x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-0.519850$ of defining polynomial
Character	$\chi$	$=$	8034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.94146 q^{5} +1.00000 q^{6} -3.14882 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.94146 q^{5} +1.00000 q^{6} -3.14882 q^{7} -1.00000 q^{8} +1.00000 q^{9} +2.94146 q^{10} +0.137087 q^{11} -1.00000 q^{12} +1.00000 q^{13} +3.14882 q^{14} +2.94146 q^{15} +1.00000 q^{16} -2.74850 q^{17} -1.00000 q^{18} -4.14882 q^{19} -2.94146 q^{20} +3.14882 q^{21} -0.137087 q^{22} +7.19107 q^{23} +1.00000 q^{24} +3.65220 q^{25} -1.00000 q^{26} -1.00000 q^{27} -3.14882 q^{28} -10.1077 q^{29} -2.94146 q^{30} +4.60157 q^{31} -1.00000 q^{32} -0.137087 q^{33} +2.74850 q^{34} +9.26214 q^{35} +1.00000 q^{36} -0.829880 q^{37} +4.14882 q^{38} -1.00000 q^{39} +2.94146 q^{40} +4.33657 q^{41} -3.14882 q^{42} -9.96834 q^{43} +0.137087 q^{44} -2.94146 q^{45} -7.19107 q^{46} +6.77316 q^{47} -1.00000 q^{48} +2.91507 q^{49} -3.65220 q^{50} +2.74850 q^{51} +1.00000 q^{52} +5.15156 q^{53} +1.00000 q^{54} -0.403237 q^{55} +3.14882 q^{56} +4.14882 q^{57} +10.1077 q^{58} +10.3965 q^{59} +2.94146 q^{60} -8.47985 q^{61} -4.60157 q^{62} -3.14882 q^{63} +1.00000 q^{64} -2.94146 q^{65} +0.137087 q^{66} +12.7124 q^{67} -2.74850 q^{68} -7.19107 q^{69} -9.26214 q^{70} -4.30422 q^{71} -1.00000 q^{72} +1.09602 q^{73} +0.829880 q^{74} -3.65220 q^{75} -4.14882 q^{76} -0.431663 q^{77} +1.00000 q^{78} -2.76399 q^{79} -2.94146 q^{80} +1.00000 q^{81} -4.33657 q^{82} +8.49113 q^{83} +3.14882 q^{84} +8.08460 q^{85} +9.96834 q^{86} +10.1077 q^{87} -0.137087 q^{88} +3.36617 q^{89} +2.94146 q^{90} -3.14882 q^{91} +7.19107 q^{92} -4.60157 q^{93} -6.77316 q^{94} +12.2036 q^{95} +1.00000 q^{96} -10.0536 q^{97} -2.91507 q^{98} +0.137087 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - 7 q^{2} - 7 q^{3} + 7 q^{4} + 2 q^{5} + 7 q^{6} - 9 q^{7} - 7 q^{8} + 7 q^{9}+O(q^{10}) $ 7 * q - 7 * q^2 - 7 * q^3 + 7 * q^4 + 2 * q^5 + 7 * q^6 - 9 * q^7 - 7 * q^8 + 7 * q^9	$ 7 q - 7 q^{2} - 7 q^{3} + 7 q^{4} + 2 q^{5} + 7 q^{6} - 9 q^{7} - 7 q^{8} + 7 q^{9} - 2 q^{10} - 7 q^{12} + 7 q^{13} + 9 q^{14} - 2 q^{15} + 7 q^{16} + 3 q^{17} - 7 q^{18} - 16 q^{19} + 2 q^{20} + 9 q^{21} + 6 q^{23} + 7 q^{24} + 15 q^{25} - 7 q^{26} - 7 q^{27} - 9 q^{28} - 5 q^{29} + 2 q^{30} - 16 q^{31} - 7 q^{32} - 3 q^{34} - 10 q^{35} + 7 q^{36} + 17 q^{37} + 16 q^{38} - 7 q^{39} - 2 q^{40} + 12 q^{41} - 9 q^{42} - 22 q^{43} + 2 q^{45} - 6 q^{46} - 7 q^{48} - 2 q^{49} - 15 q^{50} - 3 q^{51} + 7 q^{52} + 2 q^{53} + 7 q^{54} - 16 q^{55} + 9 q^{56} + 16 q^{57} + 5 q^{58} - 3 q^{59} - 2 q^{60} - 6 q^{61} + 16 q^{62} - 9 q^{63} + 7 q^{64} + 2 q^{65} + q^{67} + 3 q^{68} - 6 q^{69} + 10 q^{70} + 15 q^{71} - 7 q^{72} + 17 q^{73} - 17 q^{74} - 15 q^{75} - 16 q^{76} - 10 q^{77} + 7 q^{78} - 27 q^{79} + 2 q^{80} + 7 q^{81} - 12 q^{82} + 12 q^{83} + 9 q^{84} + 15 q^{85} + 22 q^{86} + 5 q^{87} - 9 q^{89} - 2 q^{90} - 9 q^{91} + 6 q^{92} + 16 q^{93} - 12 q^{95} + 7 q^{96} - 3 q^{97} + 2 q^{98}+O(q^{100}) $ 7 * q - 7 * q^2 - 7 * q^3 + 7 * q^4 + 2 * q^5 + 7 * q^6 - 9 * q^7 - 7 * q^8 + 7 * q^9 - 2 * q^10 - 7 * q^12 + 7 * q^13 + 9 * q^14 - 2 * q^15 + 7 * q^16 + 3 * q^17 - 7 * q^18 - 16 * q^19 + 2 * q^20 + 9 * q^21 + 6 * q^23 + 7 * q^24 + 15 * q^25 - 7 * q^26 - 7 * q^27 - 9 * q^28 - 5 * q^29 + 2 * q^30 - 16 * q^31 - 7 * q^32 - 3 * q^34 - 10 * q^35 + 7 * q^36 + 17 * q^37 + 16 * q^38 - 7 * q^39 - 2 * q^40 + 12 * q^41 - 9 * q^42 - 22 * q^43 + 2 * q^45 - 6 * q^46 - 7 * q^48 - 2 * q^49 - 15 * q^50 - 3 * q^51 + 7 * q^52 + 2 * q^53 + 7 * q^54 - 16 * q^55 + 9 * q^56 + 16 * q^57 + 5 * q^58 - 3 * q^59 - 2 * q^60 - 6 * q^61 + 16 * q^62 - 9 * q^63 + 7 * q^64 + 2 * q^65 + q^67 + 3 * q^68 - 6 * q^69 + 10 * q^70 + 15 * q^71 - 7 * q^72 + 17 * q^73 - 17 * q^74 - 15 * q^75 - 16 * q^76 - 10 * q^77 + 7 * q^78 - 27 * q^79 + 2 * q^80 + 7 * q^81 - 12 * q^82 + 12 * q^83 + 9 * q^84 + 15 * q^85 + 22 * q^86 + 5 * q^87 - 9 * q^89 - 2 * q^90 - 9 * q^91 + 6 * q^92 + 16 * q^93 - 12 * q^95 + 7 * q^96 - 3 * q^97 + 2 * q^98

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
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	−2.94146	−1.31546	−0.657731	−	0.753253i	$-0.728484\pi$
$5$	−2.94146	−1.31546	−0.657731	+	0.753253i	$0.728484\pi$
$6$	1.00000	0.408248
$7$	−3.14882	−1.19014	−0.595071	−	0.803673i	$-0.702876\pi$
$7$	−3.14882	−1.19014	−0.595071	+	0.803673i	$0.702876\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	2.94146	0.930172
$11$	0.137087	0.0413334	0.0206667	−	0.999786i	$-0.493421\pi$
$11$	0.137087	0.0413334	0.0206667	+	0.999786i	$0.493421\pi$
$12$	−1.00000	−0.288675
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	3.14882	0.841558
$15$	2.94146	0.759482
$16$	1.00000	0.250000
$17$	−2.74850	−0.666609	−0.333304	−	0.942819i	$-0.608164\pi$
$17$	−2.74850	−0.666609	−0.333304	+	0.942819i	$0.608164\pi$
$18$	−1.00000	−0.235702
$19$	−4.14882	−0.951805	−0.475902	−	0.879498i	$-0.657878\pi$
$19$	−4.14882	−0.951805	−0.475902	+	0.879498i	$0.657878\pi$
$20$	−2.94146	−0.657731
$21$	3.14882	0.687129
$22$	−0.137087	−0.0292271
$23$	7.19107	1.49944	0.749721	−	0.661754i	$-0.230188\pi$
$23$	7.19107	1.49944	0.749721	+	0.661754i	$0.230188\pi$
$24$	1.00000	0.204124
$25$	3.65220	0.730440
$26$	−1.00000	−0.196116
$27$	−1.00000	−0.192450
$28$	−3.14882	−0.595071
$29$	−10.1077	−1.87695	−0.938475	−	0.345346i	$-0.887762\pi$
$29$	−10.1077	−1.87695	−0.938475	+	0.345346i	$0.887762\pi$
$30$	−2.94146	−0.537035
$31$	4.60157	0.826467	0.413233	−	0.910625i	$-0.364399\pi$
$31$	4.60157	0.826467	0.413233	+	0.910625i	$0.364399\pi$
$32$	−1.00000	−0.176777
$33$	−0.137087	−0.0238638
$34$	2.74850	0.471363
$35$	9.26214	1.56559
$36$	1.00000	0.166667
$37$	−0.829880	−0.136431	−0.0682157	−	0.997671i	$-0.521731\pi$
$37$	−0.829880	−0.136431	−0.0682157	+	0.997671i	$0.521731\pi$
$38$	4.14882	0.673027
$39$	−1.00000	−0.160128
$40$	2.94146	0.465086
$41$	4.33657	0.677259	0.338630	−	0.940920i	$-0.390037\pi$
$41$	4.33657	0.677259	0.338630	+	0.940920i	$0.390037\pi$
$42$	−3.14882	−0.485873
$43$	−9.96834	−1.52016	−0.760079	−	0.649831i	$-0.774840\pi$
$43$	−9.96834	−1.52016	−0.760079	+	0.649831i	$0.774840\pi$
$44$	0.137087	0.0206667
$45$	−2.94146	−0.438487
$46$	−7.19107	−1.06027
$47$	6.77316	0.987967	0.493984	−	0.869471i	$-0.335540\pi$
$47$	6.77316	0.987967	0.493984	+	0.869471i	$0.335540\pi$
$48$	−1.00000	−0.144338
$49$	2.91507	0.416438
$50$	−3.65220	−0.516499
$51$	2.74850	0.384867
$52$	1.00000	0.138675
$53$	5.15156	0.707621	0.353810	−	0.935317i	$-0.384886\pi$
$53$	5.15156	0.707621	0.353810	+	0.935317i	$0.384886\pi$
$54$	1.00000	0.136083
$55$	−0.403237	−0.0543725
$56$	3.14882	0.420779
$57$	4.14882	0.549525
$58$	10.1077	1.32720
$59$	10.3965	1.35351	0.676755	−	0.736208i	$-0.263386\pi$
$59$	10.3965	1.35351	0.676755	+	0.736208i	$0.263386\pi$
$60$	2.94146	0.379741
$61$	−8.47985	−1.08573	−0.542867	−	0.839819i	$-0.682661\pi$
$61$	−8.47985	−1.08573	−0.542867	+	0.839819i	$0.682661\pi$
$62$	−4.60157	−0.584400
$63$	−3.14882	−0.396714
$64$	1.00000	0.125000
$65$	−2.94146	−0.364843
$66$	0.137087	0.0168743
$67$	12.7124	1.55306	0.776532	−	0.630078i	$-0.216977\pi$
$67$	12.7124	1.55306	0.776532	+	0.630078i	$0.216977\pi$
$68$	−2.74850	−0.333304
$69$	−7.19107	−0.865703
$70$	−9.26214	−1.10704
$71$	−4.30422	−0.510817	−0.255409	−	0.966833i	$-0.582210\pi$
$71$	−4.30422	−0.510817	−0.255409	+	0.966833i	$0.582210\pi$
$72$	−1.00000	−0.117851
$73$	1.09602	0.128280	0.0641400	−	0.997941i	$-0.479570\pi$
$73$	1.09602	0.128280	0.0641400	+	0.997941i	$0.479570\pi$
$74$	0.829880	0.0964716
$75$	−3.65220	−0.421720
$76$	−4.14882	−0.475902
$77$	−0.431663	−0.0491926
$78$	1.00000	0.113228
$79$	−2.76399	−0.310973	−0.155486	−	0.987838i	$-0.549694\pi$
$79$	−2.76399	−0.310973	−0.155486	+	0.987838i	$0.549694\pi$
$80$	−2.94146	−0.328865
$81$	1.00000	0.111111
$82$	−4.33657	−0.478895
$83$	8.49113	0.932022	0.466011	−	0.884779i	$-0.345691\pi$
$83$	8.49113	0.932022	0.466011	+	0.884779i	$0.345691\pi$
$84$	3.14882	0.343564
$85$	8.08460	0.876898
$86$	9.96834	1.07491
$87$	10.1077	1.08366
$88$	−0.137087	−0.0146136
$89$	3.36617	0.356814	0.178407	−	0.983957i	$-0.442906\pi$
$89$	3.36617	0.356814	0.178407	+	0.983957i	$0.442906\pi$
$90$	2.94146	0.310057
$91$	−3.14882	−0.330086
$92$	7.19107	0.749721
$93$	−4.60157	−0.477161
$94$	−6.77316	−0.698598
$95$	12.2036	1.25206
$96$	1.00000	0.102062
$97$	−10.0536	−1.02078	−0.510392	−	0.859942i	$-0.670500\pi$
$97$	−10.0536	−1.02078	−0.510392	+	0.859942i	$0.670500\pi$
$98$	−2.91507	−0.294466
$99$	0.137087	0.0137778
$100$	3.65220	0.365220
$101$	15.0153	1.49408	0.747038	−	0.664781i	$-0.231475\pi$
$101$	15.0153	1.49408	0.747038	+	0.664781i	$0.231475\pi$
$102$	−2.74850	−0.272142
$103$	1.00000	0.0985329
$103$	1.00000	0.0985329
$104$	−1.00000	−0.0980581
$105$	−9.26214	−0.903892
$106$	−5.15156	−0.500363
$107$	3.93656	0.380561	0.190281	−	0.981730i	$-0.439060\pi$
$107$	3.93656	0.380561	0.190281	+	0.981730i	$0.439060\pi$
$108$	−1.00000	−0.0962250
$109$	12.7707	1.22322	0.611608	−	0.791161i	$-0.290523\pi$
$109$	12.7707	1.22322	0.611608	+	0.791161i	$0.290523\pi$
$110$	0.403237	0.0384472
$111$	0.829880	0.0787687
$112$	−3.14882	−0.297536
$113$	−5.01087	−0.471383	−0.235691	−	0.971828i	$-0.575735\pi$
$113$	−5.01087	−0.471383	−0.235691	+	0.971828i	$0.575735\pi$
$114$	−4.14882	−0.388573
$115$	−21.1523	−1.97246
$116$	−10.1077	−0.938475
$117$	1.00000	0.0924500
$118$	−10.3965	−0.957076
$119$	8.65452	0.793359
$120$	−2.94146	−0.268518
$121$	−10.9812	−0.998292
$122$	8.47985	0.767730
$123$	−4.33657	−0.391016
$124$	4.60157	0.413233
$125$	3.96450	0.354596
$126$	3.14882	0.280519
$127$	8.01336	0.711071	0.355536	−	0.934663i	$-0.384299\pi$
$127$	8.01336	0.711071	0.355536	+	0.934663i	$0.384299\pi$
$128$	−1.00000	−0.0883883
$129$	9.96834	0.877663
$130$	2.94146	0.257983
$131$	16.7419	1.46274	0.731372	−	0.681979i	$-0.238880\pi$
$131$	16.7419	1.46274	0.731372	+	0.681979i	$0.238880\pi$
$132$	−0.137087	−0.0119319
$133$	13.0639	1.13278
$134$	−12.7124	−1.09818
$135$	2.94146	0.253161
$136$	2.74850	0.235682
$137$	−6.21021	−0.530574	−0.265287	−	0.964169i	$-0.585467\pi$
$137$	−6.21021	−0.530574	−0.265287	+	0.964169i	$0.585467\pi$
$138$	7.19107	0.612144
$139$	−4.22377	−0.358255	−0.179128	−	0.983826i	$-0.557328\pi$
$139$	−4.22377	−0.358255	−0.179128	+	0.983826i	$0.557328\pi$
$140$	9.26214	0.782793
$141$	−6.77316	−0.570403
$142$	4.30422	0.361202
$143$	0.137087	0.0114638
$144$	1.00000	0.0833333
$145$	29.7314	2.46906
$146$	−1.09602	−0.0907076
$147$	−2.91507	−0.240431
$148$	−0.829880	−0.0682157
$149$	12.6682	1.03782	0.518909	−	0.854830i	$-0.326338\pi$
$149$	12.6682	1.03782	0.518909	+	0.854830i	$0.326338\pi$
$150$	3.65220	0.298201
$151$	−0.585495	−0.0476469	−0.0238235	−	0.999716i	$-0.507584\pi$
$151$	−0.585495	−0.0476469	−0.0238235	+	0.999716i	$0.507584\pi$
$152$	4.14882	0.336514
$153$	−2.74850	−0.222203
$154$	0.431663	0.0347844
$155$	−13.5353	−1.08719
$156$	−1.00000	−0.0800641
$157$	6.17311	0.492668	0.246334	−	0.969185i	$-0.420774\pi$
$157$	6.17311	0.492668	0.246334	+	0.969185i	$0.420774\pi$
$158$	2.76399	0.219891
$159$	−5.15156	−0.408545
$160$	2.94146	0.232543
$161$	−22.6434	−1.78455
$162$	−1.00000	−0.0785674
$163$	19.0187	1.48966	0.744829	−	0.667255i	$-0.232531\pi$
$163$	19.0187	1.48966	0.744829	+	0.667255i	$0.232531\pi$
$164$	4.33657	0.338630
$165$	0.403237	0.0313920
$166$	−8.49113	−0.659039
$167$	−14.1560	−1.09543	−0.547713	−	0.836666i	$-0.684502\pi$
$167$	−14.1560	−1.09543	−0.547713	+	0.836666i	$0.684502\pi$
$168$	−3.14882	−0.242937
$169$	1.00000	0.0769231
$170$	−8.08460	−0.620061
$171$	−4.14882	−0.317268
$172$	−9.96834	−0.760079
$173$	−1.79096	−0.136164	−0.0680821	−	0.997680i	$-0.521688\pi$
$173$	−1.79096	−0.136164	−0.0680821	+	0.997680i	$0.521688\pi$
$174$	−10.1077	−0.766262
$175$	−11.5001	−0.869327
$176$	0.137087	0.0103333
$177$	−10.3965	−0.781450
$178$	−3.36617	−0.252305
$179$	−16.8883	−1.26229	−0.631144	−	0.775666i	$-0.717414\pi$
$179$	−16.8883	−1.26229	−0.631144	+	0.775666i	$0.717414\pi$
$180$	−2.94146	−0.219244
$181$	22.9822	1.70826	0.854129	−	0.520062i	$-0.174091\pi$
$181$	22.9822	1.70826	0.854129	+	0.520062i	$0.174091\pi$
$182$	3.14882	0.233406
$183$	8.47985	0.626849
$184$	−7.19107	−0.530133
$185$	2.44106	0.179470
$186$	4.60157	0.337404
$187$	−0.376784	−0.0275532
$188$	6.77316	0.493984
$189$	3.14882	0.229043
$190$	−12.2036	−0.885342
$191$	−1.01677	−0.0735712	−0.0367856	−	0.999323i	$-0.511712\pi$
$191$	−1.01677	−0.0735712	−0.0367856	+	0.999323i	$0.511712\pi$
$192$	−1.00000	−0.0721688
$193$	4.27406	0.307653	0.153827	−	0.988098i	$-0.450840\pi$
$193$	4.27406	0.307653	0.153827	+	0.988098i	$0.450840\pi$
$194$	10.0536	0.721803
$195$	2.94146	0.210642
$196$	2.91507	0.208219
$197$	22.0133	1.56838	0.784190	−	0.620521i	$-0.213079\pi$
$197$	22.0133	1.56838	0.784190	+	0.620521i	$0.213079\pi$
$198$	−0.137087	−0.00974237
$199$	−24.9686	−1.76997	−0.884987	−	0.465615i	$-0.845833\pi$
$199$	−24.9686	−1.76997	−0.884987	+	0.465615i	$0.845833\pi$
$200$	−3.65220	−0.258250
$201$	−12.7124	−0.896662
$202$	−15.0153	−1.05647
$203$	31.8273	2.23384
$204$	2.74850	0.192433
$205$	−12.7559	−0.890909
$206$	−1.00000	−0.0696733
$207$	7.19107	0.499814
$208$	1.00000	0.0693375
$209$	−0.568751	−0.0393413
$210$	9.26214	0.639148
$211$	4.72118	0.325020	0.162510	−	0.986707i	$-0.448041\pi$
$211$	4.72118	0.325020	0.162510	+	0.986707i	$0.448041\pi$
$212$	5.15156	0.353810
$213$	4.30422	0.294921
$214$	−3.93656	−0.269098
$215$	29.3215	1.99971
$216$	1.00000	0.0680414
$217$	−14.4895	−0.983613
$218$	−12.7707	−0.864944
$219$	−1.09602	−0.0740625
$220$	−0.403237	−0.0271863
$221$	−2.74850	−0.184884
$222$	−0.829880	−0.0556979
$223$	−26.6098	−1.78193	−0.890963	−	0.454076i	$-0.849970\pi$
$223$	−26.6098	−1.78193	−0.890963	+	0.454076i	$0.849970\pi$
$224$	3.14882	0.210389
$225$	3.65220	0.243480
$226$	5.01087	0.333318
$227$	0.507530	0.0336860	0.0168430	−	0.999858i	$-0.494638\pi$
$227$	0.507530	0.0336860	0.0168430	+	0.999858i	$0.494638\pi$
$228$	4.14882	0.274762
$229$	−1.12067	−0.0740556	−0.0370278	−	0.999314i	$-0.511789\pi$
$229$	−1.12067	−0.0740556	−0.0370278	+	0.999314i	$0.511789\pi$
$230$	21.1523	1.39474
$231$	0.431663	0.0284014
$232$	10.1077	0.663602
$233$	−3.05262	−0.199984	−0.0999920	−	0.994988i	$-0.531882\pi$
$233$	−3.05262	−0.199984	−0.0999920	+	0.994988i	$0.531882\pi$
$234$	−1.00000	−0.0653720
$235$	−19.9230	−1.29963
$236$	10.3965	0.676755
$237$	2.76399	0.179540
$238$	−8.65452	−0.560989
$239$	1.15111	0.0744589	0.0372294	−	0.999307i	$-0.488147\pi$
$239$	1.15111	0.0744589	0.0372294	+	0.999307i	$0.488147\pi$
$240$	2.94146	0.189871
$241$	1.40880	0.0907489	0.0453745	−	0.998970i	$-0.485552\pi$
$241$	1.40880	0.0907489	0.0453745	+	0.998970i	$0.485552\pi$
$242$	10.9812	0.705899
$243$	−1.00000	−0.0641500
$244$	−8.47985	−0.542867
$245$	−8.57456	−0.547809
$246$	4.33657	0.276490
$247$	−4.14882	−0.263983
$248$	−4.60157	−0.292200
$249$	−8.49113	−0.538103
$250$	−3.96450	−0.250737
$251$	−3.13575	−0.197927	−0.0989634	−	0.995091i	$-0.531553\pi$
$251$	−3.13575	−0.197927	−0.0989634	+	0.995091i	$0.531553\pi$
$252$	−3.14882	−0.198357
$253$	0.985804	0.0619770
$254$	−8.01336	−0.502803
$255$	−8.08460	−0.506277
$256$	1.00000	0.0625000
$257$	6.85244	0.427443	0.213722	−	0.976895i	$-0.431441\pi$
$257$	6.85244	0.427443	0.213722	+	0.976895i	$0.431441\pi$
$258$	−9.96834	−0.620602
$259$	2.61314	0.162373
$260$	−2.94146	−0.182422
$261$	−10.1077	−0.625650
$262$	−16.7419	−1.03432
$263$	−18.0045	−1.11020	−0.555102	−	0.831782i	$-0.687321\pi$
$263$	−18.0045	−1.11020	−0.555102	+	0.831782i	$0.687321\pi$
$264$	0.137087	0.00843714
$265$	−15.1531	−0.930848
$266$	−13.0639	−0.800998
$267$	−3.36617	−0.206006
$268$	12.7124	0.776532
$269$	−13.9664	−0.851548	−0.425774	−	0.904829i	$-0.639998\pi$
$269$	−13.9664	−0.851548	−0.425774	+	0.904829i	$0.639998\pi$
$270$	−2.94146	−0.179012
$271$	−17.6408	−1.07160	−0.535801	−	0.844345i	$-0.679990\pi$
$271$	−17.6408	−1.07160	−0.535801	+	0.844345i	$0.679990\pi$
$272$	−2.74850	−0.166652
$273$	3.14882	0.190575
$274$	6.21021	0.375173
$275$	0.500670	0.0301916
$276$	−7.19107	−0.432851
$277$	2.39614	0.143970	0.0719849	−	0.997406i	$-0.477067\pi$
$277$	2.39614	0.143970	0.0719849	+	0.997406i	$0.477067\pi$
$278$	4.22377	0.253325
$279$	4.60157	0.275489
$280$	−9.26214	−0.553518
$281$	−2.16737	−0.129294	−0.0646472	−	0.997908i	$-0.520592\pi$
$281$	−2.16737	−0.129294	−0.0646472	+	0.997908i	$0.520592\pi$
$282$	6.77316	0.403336
$283$	−6.62007	−0.393522	−0.196761	−	0.980451i	$-0.563042\pi$
$283$	−6.62007	−0.393522	−0.196761	+	0.980451i	$0.563042\pi$
$284$	−4.30422	−0.255409
$285$	−12.2036	−0.722879
$286$	−0.137087	−0.00810614
$287$	−13.6551	−0.806035
$288$	−1.00000	−0.0589256
$289$	−9.44576	−0.555633
$290$	−29.7314	−1.74589
$291$	10.0536	0.589350
$292$	1.09602	0.0641400
$293$	17.4690	1.02055	0.510275	−	0.860011i	$-0.329543\pi$
$293$	17.4690	1.02055	0.510275	+	0.860011i	$0.329543\pi$
$294$	2.91507	0.170010
$295$	−30.5809	−1.78049
$296$	0.829880	0.0482358
$297$	−0.137087	−0.00795461
$298$	−12.6682	−0.733848
$299$	7.19107	0.415870
$300$	−3.65220	−0.210860
$301$	31.3885	1.80920
$302$	0.585495	0.0336915
$303$	−15.0153	−0.862605
$304$	−4.14882	−0.237951
$305$	24.9432	1.42824
$306$	2.74850	0.157121
$307$	−21.1127	−1.20496	−0.602482	−	0.798132i	$-0.705822\pi$
$307$	−21.1127	−1.20496	−0.602482	+	0.798132i	$0.705822\pi$
$308$	−0.431663	−0.0245963
$309$	−1.00000	−0.0568880
$310$	13.5353	0.768756
$311$	−15.4624	−0.876793	−0.438397	−	0.898782i	$-0.644453\pi$
$311$	−15.4624	−0.876793	−0.438397	+	0.898782i	$0.644453\pi$
$312$	1.00000	0.0566139
$313$	26.0600	1.47300	0.736499	−	0.676438i	$-0.236477\pi$
$313$	26.0600	1.47300	0.736499	+	0.676438i	$0.236477\pi$
$314$	−6.17311	−0.348369
$315$	9.26214	0.521862
$316$	−2.76399	−0.155486
$317$	−14.1968	−0.797373	−0.398687	−	0.917087i	$-0.630534\pi$
$317$	−14.1968	−0.797373	−0.398687	+	0.917087i	$0.630534\pi$
$318$	5.15156	0.288885
$319$	−1.38564	−0.0775807
$320$	−2.94146	−0.164433
$321$	−3.93656	−0.219717
$322$	22.6434	1.26187
$323$	11.4030	0.634481
$324$	1.00000	0.0555556
$325$	3.65220	0.202588
$326$	−19.0187	−1.05335
$327$	−12.7707	−0.706224
$328$	−4.33657	−0.239447
$329$	−21.3275	−1.17582
$330$	−0.403237	−0.0221975
$331$	20.5911	1.13179	0.565896	−	0.824477i	$-0.308530\pi$
$331$	20.5911	1.13179	0.565896	+	0.824477i	$0.308530\pi$
$332$	8.49113	0.466011
$333$	−0.829880	−0.0454772
$334$	14.1560	0.774583
$335$	−37.3930	−2.04300
$336$	3.14882	0.171782
$337$	−5.93953	−0.323547	−0.161773	−	0.986828i	$-0.551721\pi$
$337$	−5.93953	−0.323547	−0.161773	+	0.986828i	$0.551721\pi$
$338$	−1.00000	−0.0543928
$339$	5.01087	0.272153
$340$	8.08460	0.438449
$341$	0.630817	0.0341607
$342$	4.14882	0.224342
$343$	12.8627	0.694521
$344$	9.96834	0.537457
$345$	21.1523	1.13880
$346$	1.79096	0.0962827
$347$	8.09109	0.434353	0.217176	−	0.976132i	$-0.430315\pi$
$347$	8.09109	0.434353	0.217176	+	0.976132i	$0.430315\pi$
$348$	10.1077	0.541829
$349$	−14.5290	−0.777719	−0.388859	−	0.921297i	$-0.627131\pi$
$349$	−14.5290	−0.777719	−0.388859	+	0.921297i	$0.627131\pi$
$350$	11.5001	0.614707
$351$	−1.00000	−0.0533761
$352$	−0.137087	−0.00730678
$353$	8.63553	0.459623	0.229811	−	0.973235i	$-0.426189\pi$
$353$	8.63553	0.459623	0.229811	+	0.973235i	$0.426189\pi$
$354$	10.3965	0.552568
$355$	12.6607	0.671961
$356$	3.36617	0.178407
$357$	−8.65452	−0.458046
$358$	16.8883	0.892572
$359$	−6.80238	−0.359016	−0.179508	−	0.983757i	$-0.557451\pi$
$359$	−6.80238	−0.359016	−0.179508	+	0.983757i	$0.557451\pi$
$360$	2.94146	0.155029
$361$	−1.78729	−0.0940680
$362$	−22.9822	−1.20792
$363$	10.9812	0.576364
$364$	−3.14882	−0.165043
$365$	−3.22392	−0.168747
$366$	−8.47985	−0.443249
$367$	−28.3418	−1.47943	−0.739714	−	0.672921i	$-0.765039\pi$
$367$	−28.3418	−1.47943	−0.739714	+	0.672921i	$0.765039\pi$
$368$	7.19107	0.374860
$369$	4.33657	0.225753
$370$	−2.44106	−0.126905
$371$	−16.2213	−0.842169
$372$	−4.60157	−0.238580
$373$	0.827118	0.0428265	0.0214133	−	0.999771i	$-0.493183\pi$
$373$	0.827118	0.0428265	0.0214133	+	0.999771i	$0.493183\pi$
$374$	0.376784	0.0194830
$375$	−3.96450	−0.204726
$376$	−6.77316	−0.349299
$377$	−10.1077	−0.520572
$378$	−3.14882	−0.161958
$379$	−4.67824	−0.240305	−0.120153	−	0.992755i	$-0.538338\pi$
$379$	−4.67824	−0.240305	−0.120153	+	0.992755i	$0.538338\pi$
$380$	12.2036	0.626031
$381$	−8.01336	−0.410537
$382$	1.01677	0.0520227
$383$	34.0161	1.73814	0.869070	−	0.494688i	$-0.164718\pi$
$383$	34.0161	1.73814	0.869070	+	0.494688i	$0.164718\pi$
$384$	1.00000	0.0510310
$385$	1.26972	0.0647110
$386$	−4.27406	−0.217544
$387$	−9.96834	−0.506719
$388$	−10.0536	−0.510392
$389$	−17.2938	−0.876828	−0.438414	−	0.898773i	$-0.644460\pi$
$389$	−17.2938	−0.876828	−0.438414	+	0.898773i	$0.644460\pi$
$390$	−2.94146	−0.148947
$391$	−19.7646	−0.999540
$392$	−2.91507	−0.147233
$393$	−16.7419	−0.844516
$394$	−22.0133	−1.10901
$395$	8.13016	0.409073
$396$	0.137087	0.00688890
$397$	−11.9604	−0.600276	−0.300138	−	0.953896i	$-0.597033\pi$
$397$	−11.9604	−0.600276	−0.300138	+	0.953896i	$0.597033\pi$
$398$	24.9686	1.25156
$399$	−13.0639	−0.654012
$400$	3.65220	0.182610
$401$	−3.41345	−0.170460	−0.0852298	−	0.996361i	$-0.527162\pi$
$401$	−3.41345	−0.170460	−0.0852298	+	0.996361i	$0.527162\pi$
$402$	12.7124	0.634035
$403$	4.60157	0.229221
$404$	15.0153	0.747038
$405$	−2.94146	−0.146162
$406$	−31.8273	−1.57956
$407$	−0.113766	−0.00563918
$408$	−2.74850	−0.136071
$409$	−24.8064	−1.22660	−0.613298	−	0.789852i	$-0.710158\pi$
$409$	−24.8064	−1.22660	−0.613298	+	0.789852i	$0.710158\pi$
$410$	12.7559	0.629968
$411$	6.21021	0.306327
$412$	1.00000	0.0492665
$413$	−32.7367	−1.61087
$414$	−7.19107	−0.353422
$415$	−24.9763	−1.22604
$416$	−1.00000	−0.0490290
$417$	4.22377	0.206839
$418$	0.568751	0.0278185
$419$	6.00013	0.293125	0.146563	−	0.989201i	$-0.453179\pi$
$419$	6.00013	0.293125	0.146563	+	0.989201i	$0.453179\pi$
$420$	−9.26214	−0.451946
$421$	−1.38513	−0.0675070	−0.0337535	−	0.999430i	$-0.510746\pi$
$421$	−1.38513	−0.0675070	−0.0337535	+	0.999430i	$0.510746\pi$
$422$	−4.72118	−0.229824
$423$	6.77316	0.329322
$424$	−5.15156	−0.250182
$425$	−10.0381	−0.486918
$426$	−4.30422	−0.208540
$427$	26.7015	1.29218
$428$	3.93656	0.190281
$429$	−0.137087	−0.00661864
$430$	−29.3215	−1.41401
$431$	−23.5209	−1.13296	−0.566481	−	0.824075i	$-0.691696\pi$
$431$	−23.5209	−1.13296	−0.566481	+	0.824075i	$0.691696\pi$
$432$	−1.00000	−0.0481125
$433$	−13.5308	−0.650249	−0.325125	−	0.945671i	$-0.605406\pi$
$433$	−13.5308	−0.650249	−0.325125	+	0.945671i	$0.605406\pi$
$434$	14.4895	0.695519
$435$	−29.7314	−1.42551
$436$	12.7707	0.611608
$437$	−29.8344	−1.42718
$438$	1.09602	0.0523701
$439$	−29.4705	−1.40655	−0.703275	−	0.710918i	$-0.748280\pi$
$439$	−29.4705	−1.40655	−0.703275	+	0.710918i	$0.748280\pi$
$440$	0.403237	0.0192236
$441$	2.91507	0.138813
$442$	2.74850	0.130733
$443$	−38.0382	−1.80725	−0.903625	−	0.428324i	$-0.859104\pi$
$443$	−38.0382	−1.80725	−0.903625	+	0.428324i	$0.859104\pi$
$444$	0.829880	0.0393844
$445$	−9.90147	−0.469375
$446$	26.6098	1.26001
$447$	−12.6682	−0.599184
$448$	−3.14882	−0.148768
$449$	21.2124	1.00108	0.500538	−	0.865715i	$-0.333136\pi$
$449$	21.2124	1.00108	0.500538	+	0.865715i	$0.333136\pi$
$450$	−3.65220	−0.172166
$451$	0.594489	0.0279934
$452$	−5.01087	−0.235691
$453$	0.585495	0.0275090
$454$	−0.507530	−0.0238196
$455$	9.26214	0.434216
$456$	−4.14882	−0.194286
$457$	28.9591	1.35465	0.677324	−	0.735684i	$-0.263139\pi$
$457$	28.9591	1.35465	0.677324	+	0.735684i	$0.263139\pi$
$458$	1.12067	0.0523652
$459$	2.74850	0.128289
$460$	−21.1523	−0.986229
$461$	−15.5870	−0.725960	−0.362980	−	0.931797i	$-0.618241\pi$
$461$	−15.5870	−0.725960	−0.362980	+	0.931797i	$0.618241\pi$
$462$	−0.431663	−0.0200828
$463$	−15.6494	−0.727290	−0.363645	−	0.931538i	$-0.618468\pi$
$463$	−15.6494	−0.727290	−0.363645	+	0.931538i	$0.618468\pi$
$464$	−10.1077	−0.469238
$465$	13.5353	0.627687
$466$	3.05262	0.141410
$467$	28.3998	1.31419	0.657093	−	0.753809i	$-0.271786\pi$
$467$	28.3998	1.31419	0.657093	+	0.753809i	$0.271786\pi$
$468$	1.00000	0.0462250
$469$	−40.0290	−1.84837
$470$	19.9230	0.918980
$471$	−6.17311	−0.284442
$472$	−10.3965	−0.478538
$473$	−1.36653	−0.0628333
$474$	−2.76399	−0.126954
$475$	−15.1523	−0.695236
$476$	8.65452	0.396679
$477$	5.15156	0.235874
$478$	−1.15111	−0.0526504
$479$	33.2339	1.51850	0.759249	−	0.650801i	$-0.225567\pi$
$479$	33.2339	1.51850	0.759249	+	0.650801i	$0.225567\pi$
$480$	−2.94146	−0.134259
$481$	−0.829880	−0.0378393
$482$	−1.40880	−0.0641692
$483$	22.6434	1.03031
$484$	−10.9812	−0.499146
$485$	29.5722	1.34280
$486$	1.00000	0.0453609
$487$	−34.4329	−1.56031	−0.780153	−	0.625589i	$-0.784859\pi$
$487$	−34.4329	−1.56031	−0.780153	+	0.625589i	$0.784859\pi$
$488$	8.47985	0.383865
$489$	−19.0187	−0.860055
$490$	8.57456	0.387359
$491$	27.1694	1.22614	0.613070	−	0.790029i	$-0.289934\pi$
$491$	27.1694	1.22614	0.613070	+	0.790029i	$0.289934\pi$
$492$	−4.33657	−0.195508
$493$	27.7810	1.25119
$494$	4.14882	0.186664
$495$	−0.403237	−0.0181242
$496$	4.60157	0.206617
$497$	13.5532	0.607945
$498$	8.49113	0.380496
$499$	−18.9505	−0.848343	−0.424171	−	0.905582i	$-0.639435\pi$
$499$	−18.9505	−0.848343	−0.424171	+	0.905582i	$0.639435\pi$
$500$	3.96450	0.177298
$501$	14.1560	0.632445
$502$	3.13575	0.139955
$503$	28.6947	1.27943	0.639717	−	0.768610i	$-0.279052\pi$
$503$	28.6947	1.27943	0.639717	+	0.768610i	$0.279052\pi$
$504$	3.14882	0.140260
$505$	−44.1669	−1.96540
$506$	−0.985804	−0.0438244
$507$	−1.00000	−0.0444116
$508$	8.01336	0.355536
$509$	12.8280	0.568590	0.284295	−	0.958737i	$-0.408240\pi$
$509$	12.8280	0.568590	0.284295	+	0.958737i	$0.408240\pi$
$510$	8.08460	0.357992
$511$	−3.45118	−0.152671
$512$	−1.00000	−0.0441942
$513$	4.14882	0.183175
$514$	−6.85244	−0.302248
$515$	−2.94146	−0.129616
$516$	9.96834	0.438832
$517$	0.928515	0.0408360
$518$	−2.61314	−0.114815
$519$	1.79096	0.0786145
$520$	2.94146	0.128992
$521$	−15.9227	−0.697587	−0.348793	−	0.937200i	$-0.613408\pi$
$521$	−15.9227	−0.697587	−0.348793	+	0.937200i	$0.613408\pi$
$522$	10.1077	0.442402
$523$	14.6818	0.641989	0.320995	−	0.947081i	$-0.395983\pi$
$523$	14.6818	0.641989	0.320995	+	0.947081i	$0.395983\pi$
$524$	16.7419	0.731372
$525$	11.5001	0.501906
$526$	18.0045	0.785032
$527$	−12.6474	−0.550930
$528$	−0.137087	−0.00596596
$529$	28.7115	1.24832
$530$	15.1531	0.658209
$531$	10.3965	0.451170
$532$	13.0639	0.566391
$533$	4.33657	0.187838
$534$	3.36617	0.145669
$535$	−11.5792	−0.500614
$536$	−12.7124	−0.549091
$537$	16.8883	0.728782
$538$	13.9664	0.602136
$539$	0.399619	0.0172128
$540$	2.94146	0.126580
$541$	15.0939	0.648936	0.324468	−	0.945897i	$-0.394815\pi$
$541$	15.0939	0.648936	0.324468	+	0.945897i	$0.394815\pi$
$542$	17.6408	0.757736
$543$	−22.9822	−0.986263
$544$	2.74850	0.117841
$545$	−37.5647	−1.60909
$546$	−3.14882	−0.134757
$547$	−17.7084	−0.757157	−0.378579	−	0.925569i	$-0.623587\pi$
$547$	−17.7084	−0.757157	−0.378579	+	0.925569i	$0.623587\pi$
$548$	−6.21021	−0.265287
$549$	−8.47985	−0.361911
$550$	−0.500670	−0.0213487
$551$	41.9350	1.78649
$552$	7.19107	0.306072
$553$	8.70330	0.370102
$554$	−2.39614	−0.101802
$555$	−2.44106	−0.103617
$556$	−4.22377	−0.179128
$557$	−11.4351	−0.484521	−0.242260	−	0.970211i	$-0.577889\pi$
$557$	−11.4351	−0.484521	−0.242260	+	0.970211i	$0.577889\pi$
$558$	−4.60157	−0.194800
$559$	−9.96834	−0.421616
$560$	9.26214	0.391397
$561$	0.376784	0.0159078
$562$	2.16737	0.0914249
$563$	16.6028	0.699726	0.349863	−	0.936801i	$-0.386228\pi$
$563$	16.6028	0.699726	0.349863	+	0.936801i	$0.386228\pi$
$564$	−6.77316	−0.285202
$565$	14.7393	0.620086
$566$	6.62007	0.278262
$567$	−3.14882	−0.132238
$568$	4.30422	0.180601
$569$	−13.7295	−0.575571	−0.287785	−	0.957695i	$-0.592919\pi$
$569$	−13.7295	−0.575571	−0.287785	+	0.957695i	$0.592919\pi$
$570$	12.2036	0.511152
$571$	−30.7554	−1.28707	−0.643536	−	0.765416i	$-0.722533\pi$
$571$	−30.7554	−1.28707	−0.643536	+	0.765416i	$0.722533\pi$
$572$	0.137087	0.00573191
$573$	1.01677	0.0424764
$574$	13.6551	0.569953
$575$	26.2632	1.09525
$576$	1.00000	0.0416667
$577$	39.7020	1.65282	0.826408	−	0.563072i	$-0.190380\pi$
$577$	39.7020	1.65282	0.826408	+	0.563072i	$0.190380\pi$
$578$	9.44576	0.392892
$579$	−4.27406	−0.177624
$580$	29.7314	1.23453
$581$	−26.7370	−1.10924
$582$	−10.0536	−0.416733
$583$	0.706213	0.0292484
$584$	−1.09602	−0.0453538
$585$	−2.94146	−0.121614
$586$	−17.4690	−0.721638
$587$	−41.6041	−1.71718	−0.858592	−	0.512659i	$-0.828661\pi$
$587$	−41.6041	−1.71718	−0.858592	+	0.512659i	$0.828661\pi$
$588$	−2.91507	−0.120215
$589$	−19.0911	−0.786635
$590$	30.5809	1.25900
$591$	−22.0133	−0.905505
$592$	−0.829880	−0.0341079
$593$	−2.62330	−0.107726	−0.0538630	−	0.998548i	$-0.517153\pi$
$593$	−2.62330	−0.107726	−0.0538630	+	0.998548i	$0.517153\pi$
$594$	0.137087	0.00562476
$595$	−25.4570	−1.04363
$596$	12.6682	0.518909
$597$	24.9686	1.02190
$598$	−7.19107	−0.294065
$599$	−10.0121	−0.409084	−0.204542	−	0.978858i	$-0.565570\pi$
$599$	−10.0121	−0.409084	−0.204542	+	0.978858i	$0.565570\pi$
$600$	3.65220	0.149100
$601$	−7.82992	−0.319389	−0.159694	−	0.987166i	$-0.551051\pi$
$601$	−7.82992	−0.319389	−0.159694	+	0.987166i	$0.551051\pi$
$602$	−31.3885	−1.27930
$603$	12.7124	0.517688
$604$	−0.585495	−0.0238235
$605$	32.3008	1.31321
$606$	15.0153	0.609954
$607$	−32.5823	−1.32248	−0.661238	−	0.750176i	$-0.729969\pi$
$607$	−32.5823	−1.32248	−0.661238	+	0.750176i	$0.729969\pi$
$608$	4.14882	0.168257
$609$	−31.8273	−1.28971
$610$	−24.9432	−1.00992
$611$	6.77316	0.274013
$612$	−2.74850	−0.111101
$613$	36.6489	1.48023	0.740117	−	0.672479i	$-0.234770\pi$
$613$	36.6489	1.48023	0.740117	+	0.672479i	$0.234770\pi$
$614$	21.1127	0.852039
$615$	12.7559	0.514366
$616$	0.431663	0.0173922
$617$	11.2017	0.450962	0.225481	−	0.974248i	$-0.427605\pi$
$617$	11.2017	0.450962	0.225481	+	0.974248i	$0.427605\pi$
$618$	1.00000	0.0402259
$619$	−32.1143	−1.29078	−0.645390	−	0.763853i	$-0.723305\pi$
$619$	−32.1143	−1.29078	−0.645390	+	0.763853i	$0.723305\pi$
$620$	−13.5353	−0.543593
$621$	−7.19107	−0.288568
$622$	15.4624	0.619986
$623$	−10.5995	−0.424659
$624$	−1.00000	−0.0400320
$625$	−29.9224	−1.19690
$626$	−26.0600	−1.04157
$627$	0.568751	0.0227137
$628$	6.17311	0.246334
$629$	2.28092	0.0909464
$630$	−9.26214	−0.369012
$631$	−0.248116	−0.00987734	−0.00493867	−	0.999988i	$-0.501572\pi$
$631$	−0.248116	−0.00987734	−0.00493867	+	0.999988i	$0.501572\pi$
$632$	2.76399	0.109946
$633$	−4.72118	−0.187650
$634$	14.1968	0.563828
$635$	−23.5710	−0.935387
$636$	−5.15156	−0.204272
$637$	2.91507	0.115499
$638$	1.38564	0.0548579
$639$	−4.30422	−0.170272
$640$	2.94146	0.116272
$641$	9.62837	0.380298	0.190149	−	0.981755i	$-0.439103\pi$
$641$	9.62837	0.380298	0.190149	+	0.981755i	$0.439103\pi$
$642$	3.93656	0.155364
$643$	19.8045	0.781014	0.390507	−	0.920600i	$-0.372300\pi$
$643$	19.8045	0.781014	0.390507	+	0.920600i	$0.372300\pi$
$644$	−22.6434	−0.892274
$645$	−29.3215	−1.15453
$646$	−11.4030	−0.448646
$647$	−7.50452	−0.295033	−0.147517	−	0.989060i	$-0.547128\pi$
$647$	−7.50452	−0.295033	−0.147517	+	0.989060i	$0.547128\pi$
$648$	−1.00000	−0.0392837
$649$	1.42523	0.0559452
$650$	−3.65220	−0.143251
$651$	14.4895	0.567889
$652$	19.0187	0.744829
$653$	6.80345	0.266239	0.133120	−	0.991100i	$-0.457501\pi$
$653$	6.80345	0.266239	0.133120	+	0.991100i	$0.457501\pi$
$654$	12.7707	0.499376
$655$	−49.2456	−1.92418
$656$	4.33657	0.169315
$657$	1.09602	0.0427600
$658$	21.3275	0.831431
$659$	−17.2877	−0.673433	−0.336717	−	0.941606i	$-0.609316\pi$
$659$	−17.2877	−0.673433	−0.336717	+	0.941606i	$0.609316\pi$
$660$	0.403237	0.0156960
$661$	46.3068	1.80112	0.900562	−	0.434727i	$-0.143155\pi$
$661$	46.3068	1.80112	0.900562	+	0.434727i	$0.143155\pi$
$662$	−20.5911	−0.800298
$663$	2.74850	0.106743
$664$	−8.49113	−0.329520
$665$	−38.4269	−1.49013
$666$	0.829880	0.0321572
$667$	−72.6851	−2.81438
$668$	−14.1560	−0.547713
$669$	26.6098	1.02880
$670$	37.3930	1.44462
$671$	−1.16248	−0.0448771
$672$	−3.14882	−0.121468
$673$	17.3880	0.670257	0.335129	−	0.942172i	$-0.391220\pi$
$673$	17.3880	0.670257	0.335129	+	0.942172i	$0.391220\pi$
$674$	5.93953	0.228782
$675$	−3.65220	−0.140573
$676$	1.00000	0.0384615
$677$	32.6958	1.25660	0.628300	−	0.777971i	$-0.283751\pi$
$677$	32.6958	1.25660	0.628300	+	0.777971i	$0.283751\pi$
$678$	−5.01087	−0.192441
$679$	31.6568	1.21488
$680$	−8.08460	−0.310030
$681$	−0.507530	−0.0194486
$682$	−0.630817	−0.0241552
$683$	30.8958	1.18219	0.591097	−	0.806601i	$-0.298695\pi$
$683$	30.8958	1.18219	0.591097	+	0.806601i	$0.298695\pi$
$684$	−4.14882	−0.158634
$685$	18.2671	0.697950
$686$	−12.8627	−0.491101
$687$	1.12067	0.0427560
$688$	−9.96834	−0.380039
$689$	5.15156	0.196259
$690$	−21.1523	−0.805253
$691$	4.36777	0.166158	0.0830789	−	0.996543i	$-0.473525\pi$
$691$	4.36777	0.166158	0.0830789	+	0.996543i	$0.473525\pi$
$692$	−1.79096	−0.0680821
$693$	−0.431663	−0.0163975
$694$	−8.09109	−0.307134
$695$	12.4241	0.471271
$696$	−10.1077	−0.383131
$697$	−11.9191	−0.451467
$698$	14.5290	0.549930
$699$	3.05262	0.115461
$700$	−11.5001	−0.434664
$701$	17.1484	0.647684	0.323842	−	0.946111i	$-0.395025\pi$
$701$	17.1484	0.647684	0.323842	+	0.946111i	$0.395025\pi$
$702$	1.00000	0.0377426
$703$	3.44302	0.129856
$704$	0.137087	0.00516667
$705$	19.9230	0.750344
$706$	−8.63553	−0.325002
$707$	−47.2804	−1.77816
$708$	−10.3965	−0.390725
$709$	−41.8599	−1.57208	−0.786040	−	0.618175i	$-0.787872\pi$
$709$	−41.8599	−1.57208	−0.786040	+	0.618175i	$0.787872\pi$
$710$	−12.6607	−0.475148
$711$	−2.76399	−0.103658
$712$	−3.36617	−0.126153
$713$	33.0902	1.23924
$714$	8.65452	0.323887
$715$	−0.403237	−0.0150802
$716$	−16.8883	−0.631144
$717$	−1.15111	−0.0429889
$718$	6.80238	0.253863
$719$	−35.0705	−1.30791	−0.653955	−	0.756533i	$-0.726892\pi$
$719$	−35.0705	−1.30791	−0.653955	+	0.756533i	$0.726892\pi$
$720$	−2.94146	−0.109622
$721$	−3.14882	−0.117268
$722$	1.78729	0.0665161
$723$	−1.40880	−0.0523939
$724$	22.9822	0.854129
$725$	−36.9153	−1.37100
$726$	−10.9812	−0.407551
$727$	38.5964	1.43146	0.715732	−	0.698376i	$-0.246093\pi$
$727$	38.5964	1.43146	0.715732	+	0.698376i	$0.246093\pi$
$728$	3.14882	0.116703
$729$	1.00000	0.0370370
$730$	3.22392	0.119322
$731$	27.3980	1.01335
$732$	8.47985	0.313424
$733$	−44.4750	−1.64272	−0.821361	−	0.570409i	$-0.806785\pi$
$733$	−44.4750	−1.64272	−0.821361	+	0.570409i	$0.806785\pi$
$734$	28.3418	1.04611
$735$	8.57456	0.316278
$736$	−7.19107	−0.265066
$737$	1.74271	0.0641934
$738$	−4.33657	−0.159632
$739$	31.4615	1.15733	0.578664	−	0.815566i	$-0.303574\pi$
$739$	31.4615	1.15733	0.578664	+	0.815566i	$0.303574\pi$
$740$	2.44106	0.0897352
$741$	4.14882	0.152411
$742$	16.2213	0.595503
$743$	2.00052	0.0733919	0.0366959	−	0.999326i	$-0.488317\pi$
$743$	2.00052	0.0733919	0.0366959	+	0.999326i	$0.488317\pi$
$744$	4.60157	0.168702
$745$	−37.2630	−1.36521
$746$	−0.827118	−0.0302829
$747$	8.49113	0.310674
$748$	−0.376784	−0.0137766
$749$	−12.3955	−0.452922
$750$	3.96450	0.144763
$751$	−21.1577	−0.772055	−0.386027	−	0.922487i	$-0.626153\pi$
$751$	−21.1577	−0.772055	−0.386027	+	0.922487i	$0.626153\pi$
$752$	6.77316	0.246992
$753$	3.13575	0.114273
$754$	10.1077	0.368100
$755$	1.72221	0.0626777
$756$	3.14882	0.114521
$757$	1.41669	0.0514906	0.0257453	−	0.999669i	$-0.491804\pi$
$757$	1.41669	0.0514906	0.0257453	+	0.999669i	$0.491804\pi$
$758$	4.67824	0.169921
$759$	−0.985804	−0.0357824
$760$	−12.2036	−0.442671
$761$	−12.0808	−0.437929	−0.218964	−	0.975733i	$-0.570268\pi$
$761$	−12.0808	−0.437929	−0.218964	+	0.975733i	$0.570268\pi$
$762$	8.01336	0.290294
$763$	−40.2128	−1.45580
$764$	−1.01677	−0.0367856
$765$	8.08460	0.292299
$766$	−34.0161	−1.22905
$767$	10.3965	0.375396
$768$	−1.00000	−0.0360844
$769$	−22.6133	−0.815458	−0.407729	−	0.913103i	$-0.633679\pi$
$769$	−22.6133	−0.815458	−0.407729	+	0.913103i	$0.633679\pi$
$770$	−1.26972	−0.0457576
$771$	−6.85244	−0.246784
$772$	4.27406	0.153827
$773$	−17.5110	−0.629828	−0.314914	−	0.949120i	$-0.601976\pi$
$773$	−17.5110	−0.629828	−0.314914	+	0.949120i	$0.601976\pi$
$774$	9.96834	0.358305
$775$	16.8059	0.603684
$776$	10.0536	0.360902
$777$	−2.61314	−0.0937460
$778$	17.2938	0.620011
$779$	−17.9917	−0.644618
$780$	2.94146	0.105321
$781$	−0.590055	−0.0211138
$782$	19.7646	0.706782
$783$	10.1077	0.361219
$784$	2.91507	0.104110
$785$	−18.1580	−0.648086
$786$	16.7419	0.597163
$787$	−5.13840	−0.183164	−0.0915821	−	0.995798i	$-0.529192\pi$
$787$	−5.13840	−0.183164	−0.0915821	+	0.995798i	$0.529192\pi$
$788$	22.0133	0.784190
$789$	18.0045	0.640976
$790$	−8.13016	−0.289258
$791$	15.7783	0.561013
$792$	−0.137087	−0.00487119
$793$	−8.47985	−0.301128
$794$	11.9604	0.424459
$795$	15.1531	0.537425
$796$	−24.9686	−0.884987
$797$	49.0785	1.73845	0.869225	−	0.494417i	$-0.164618\pi$
$797$	49.0785	1.73845	0.869225	+	0.494417i	$0.164618\pi$
$798$	13.0639	0.462457
$799$	−18.6160	−0.658587
$800$	−3.65220	−0.129125
$801$	3.36617	0.118938
$802$	3.41345	0.120533
$803$	0.150251	0.00530225
$804$	−12.7124	−0.448331
$805$	66.6046	2.34751
$806$	−4.60157	−0.162083
$807$	13.9664	0.491642
$808$	−15.0153	−0.528236
$809$	−25.8699	−0.909537	−0.454769	−	0.890610i	$-0.650278\pi$
$809$	−25.8699	−0.909537	−0.454769	+	0.890610i	$0.650278\pi$
$810$	2.94146	0.103352
$811$	24.3422	0.854771	0.427385	−	0.904070i	$-0.359435\pi$
$811$	24.3422	0.854771	0.427385	+	0.904070i	$0.359435\pi$
$812$	31.8273	1.11692
$813$	17.6408	0.618689
$814$	0.113766	0.00398750
$815$	−55.9428	−1.95959
$816$	2.74850	0.0962167
$817$	41.3569	1.44689
$818$	24.8064	0.867334
$819$	−3.14882	−0.110029
$820$	−12.7559	−0.445454
$821$	−35.0414	−1.22295	−0.611477	−	0.791262i	$-0.709424\pi$
$821$	−35.0414	−1.22295	−0.611477	+	0.791262i	$0.709424\pi$
$822$	−6.21021	−0.216606
$823$	7.32602	0.255369	0.127685	−	0.991815i	$-0.459245\pi$
$823$	7.32602	0.255369	0.127685	+	0.991815i	$0.459245\pi$
$824$	−1.00000	−0.0348367
$825$	−0.500670	−0.0174311
$826$	32.7367	1.13906
$827$	−13.6740	−0.475493	−0.237746	−	0.971327i	$-0.576409\pi$
$827$	−13.6740	−0.475493	−0.237746	+	0.971327i	$0.576409\pi$
$828$	7.19107	0.249907
$829$	0.164027	0.00569690	0.00284845	−	0.999996i	$-0.499093\pi$
$829$	0.164027	0.00569690	0.00284845	+	0.999996i	$0.499093\pi$
$830$	24.9763	0.866941
$831$	−2.39614	−0.0831210
$832$	1.00000	0.0346688
$833$	−8.01206	−0.277601
$834$	−4.22377	−0.146257
$835$	41.6394	1.44099
$836$	−0.568751	−0.0196707
$837$	−4.60157	−0.159054
$838$	−6.00013	−0.207271
$839$	−38.6390	−1.33397	−0.666983	−	0.745073i	$-0.732415\pi$
$839$	−38.6390	−1.33397	−0.666983	+	0.745073i	$0.732415\pi$
$840$	9.26214	0.319574
$841$	73.1654	2.52294
$842$	1.38513	0.0477346
$843$	2.16737	0.0746481
$844$	4.72118	0.162510
$845$	−2.94146	−0.101189
$846$	−6.77316	−0.232866
$847$	34.5778	1.18811
$848$	5.15156	0.176905
$849$	6.62007	0.227200
$850$	10.0381	0.344303
$851$	−5.96773	−0.204571
$852$	4.30422	0.147460
$853$	−45.2760	−1.55022	−0.775110	−	0.631827i	$-0.782305\pi$
$853$	−45.2760	−1.55022	−0.775110	+	0.631827i	$0.782305\pi$
$854$	−26.7015	−0.913708
$855$	12.2036	0.417354
$856$	−3.93656	−0.134549
$857$	8.54449	0.291874	0.145937	−	0.989294i	$-0.453380\pi$
$857$	8.54449	0.291874	0.145937	+	0.989294i	$0.453380\pi$
$858$	0.137087	0.00468008
$859$	−51.2047	−1.74708	−0.873540	−	0.486752i	$-0.838182\pi$
$859$	−51.2047	−1.74708	−0.873540	+	0.486752i	$0.838182\pi$
$860$	29.3215	0.999855
$861$	13.6551	0.465364
$862$	23.5209	0.801126
$863$	11.8317	0.402755	0.201378	−	0.979514i	$-0.435458\pi$
$863$	11.8317	0.402755	0.201378	+	0.979514i	$0.435458\pi$
$864$	1.00000	0.0340207
$865$	5.26804	0.179119
$866$	13.5308	0.459796
$867$	9.44576	0.320795
$868$	−14.4895	−0.491806
$869$	−0.378908	−0.0128536
$870$	29.7314	1.00799
$871$	12.7124	0.430742
$872$	−12.7707	−0.432472
$873$	−10.0536	−0.340261
$874$	29.8344	1.00917
$875$	−12.4835	−0.422019
$876$	−1.09602	−0.0370312
$877$	−9.41928	−0.318067	−0.159033	−	0.987273i	$-0.550838\pi$
$877$	−9.41928	−0.318067	−0.159033	+	0.987273i	$0.550838\pi$
$878$	29.4705	0.994582
$879$	−17.4690	−0.589215
$880$	−0.403237	−0.0135931
$881$	−44.7004	−1.50600	−0.752998	−	0.658023i	$-0.771393\pi$
$881$	−44.7004	−1.50600	−0.752998	+	0.658023i	$0.771393\pi$
$882$	−2.91507	−0.0981555
$883$	38.4515	1.29400	0.646998	−	0.762492i	$-0.276024\pi$
$883$	38.4515	1.29400	0.646998	+	0.762492i	$0.276024\pi$
$884$	−2.74850	−0.0924420
$885$	30.5809	1.02797
$886$	38.0382	1.27792
$887$	−18.0261	−0.605259	−0.302629	−	0.953108i	$-0.597864\pi$
$887$	−18.0261	−0.605259	−0.302629	+	0.953108i	$0.597864\pi$
$888$	−0.829880	−0.0278490
$889$	−25.2326	−0.846276
$890$	9.90147	0.331898
$891$	0.137087	0.00459260
$892$	−26.6098	−0.890963
$893$	−28.1006	−0.940352
$894$	12.6682	0.423687
$895$	49.6762	1.66049
$896$	3.14882	0.105195
$897$	−7.19107	−0.240103
$898$	−21.2124	−0.707867
$899$	−46.5112	−1.55124
$900$	3.65220	0.121740
$901$	−14.1590	−0.471706
$902$	−0.594489	−0.0197943
$903$	−31.3885	−1.04454
$904$	5.01087	0.166659
$905$	−67.6014	−2.24715
$906$	−0.585495	−0.0194518
$907$	23.7118	0.787338	0.393669	−	0.919252i	$-0.371206\pi$
$907$	23.7118	0.787338	0.393669	+	0.919252i	$0.371206\pi$
$908$	0.507530	0.0168430
$909$	15.0153	0.498025
$910$	−9.26214	−0.307037
$911$	45.2061	1.49774	0.748872	−	0.662714i	$-0.230596\pi$
$911$	45.2061	1.49774	0.748872	+	0.662714i	$0.230596\pi$
$912$	4.14882	0.137381
$913$	1.16403	0.0385236
$914$	−28.9591	−0.957881
$915$	−24.9432	−0.824596
$916$	−1.12067	−0.0370278
$917$	−52.7171	−1.74087
$918$	−2.74850	−0.0907139
$919$	−30.0324	−0.990677	−0.495339	−	0.868700i	$-0.664956\pi$
$919$	−30.0324	−0.990677	−0.495339	+	0.868700i	$0.664956\pi$
$920$	21.1523	0.697369
$921$	21.1127	0.695687
$922$	15.5870	0.513331
$923$	−4.30422	−0.141675
$924$	0.431663	0.0142007
$925$	−3.03089	−0.0996550
$926$	15.6494	0.514272
$927$	1.00000	0.0328443
$928$	10.1077	0.331801
$929$	3.27154	0.107336	0.0536678	−	0.998559i	$-0.482909\pi$
$929$	3.27154	0.107336	0.0536678	+	0.998559i	$0.482909\pi$
$930$	−13.5353	−0.443842
$931$	−12.0941	−0.396368
$932$	−3.05262	−0.0999920
$933$	15.4624	0.506217
$934$	−28.3998	−0.929270
$935$	1.10830	0.0362452
$936$	−1.00000	−0.0326860
$937$	−13.6534	−0.446036	−0.223018	−	0.974814i	$-0.571591\pi$
$937$	−13.6534	−0.446036	−0.223018	+	0.974814i	$0.571591\pi$
$938$	40.0290	1.30699
$939$	−26.0600	−0.850436
$940$	−19.9230	−0.649817
$941$	−7.40560	−0.241416	−0.120708	−	0.992688i	$-0.538516\pi$
$941$	−7.40560	−0.241416	−0.120708	+	0.992688i	$0.538516\pi$
$942$	6.17311	0.201131
$943$	31.1846	1.01551
$944$	10.3965	0.338378
$945$	−9.26214	−0.301297
$946$	1.36653	0.0444298
$947$	29.3314	0.953143	0.476572	−	0.879136i	$-0.341879\pi$
$947$	29.3314	0.953143	0.476572	+	0.879136i	$0.341879\pi$
$948$	2.76399	0.0897701
$949$	1.09602	0.0355785
$950$	15.1523	0.491606
$951$	14.1968	0.460364
$952$	−8.65452	−0.280495
$953$	−24.9809	−0.809209	−0.404605	−	0.914492i	$-0.632591\pi$
$953$	−24.9809	−0.809209	−0.404605	+	0.914492i	$0.632591\pi$
$954$	−5.15156	−0.166788
$955$	2.99080	0.0967801
$956$	1.15111	0.0372294
$957$	1.38564	0.0447913
$958$	−33.2339	−1.07374
$959$	19.5548	0.631459
$960$	2.94146	0.0949353
$961$	−9.82555	−0.316953
$962$	0.829880	0.0267564
$963$	3.93656	0.126854
$964$	1.40880	0.0453745
$965$	−12.5720	−0.404706
$966$	−22.6434	−0.728539
$967$	−21.5596	−0.693308	−0.346654	−	0.937993i	$-0.612682\pi$
$967$	−21.5596	−0.693308	−0.346654	+	0.937993i	$0.612682\pi$
$968$	10.9812	0.352949
$969$	−11.4030	−0.366318
$970$	−29.5722	−0.949505
$971$	−5.37257	−0.172414	−0.0862070	−	0.996277i	$-0.527475\pi$
$971$	−5.37257	−0.172414	−0.0862070	+	0.996277i	$0.527475\pi$
$972$	−1.00000	−0.0320750
$973$	13.2999	0.426375
$974$	34.4329	1.10330
$975$	−3.65220	−0.116964
$976$	−8.47985	−0.271433
$977$	−10.9763	−0.351162	−0.175581	−	0.984465i	$-0.556180\pi$
$977$	−10.9763	−0.351162	−0.175581	+	0.984465i	$0.556180\pi$
$978$	19.0187	0.608151
$979$	0.461460	0.0147483
$980$	−8.57456	−0.273904
$981$	12.7707	0.407739
$982$	−27.1694	−0.867012
$983$	32.6451	1.04122	0.520609	−	0.853795i	$-0.325705\pi$
$983$	32.6451	1.04122	0.520609	+	0.853795i	$0.325705\pi$
$984$	4.33657	0.138245
$985$	−64.7512	−2.06314
$986$	−27.7810	−0.884726
$987$	21.3275	0.678861
$988$	−4.14882	−0.131992
$989$	−71.6830	−2.27939
$990$	0.403237	0.0128157
$991$	−47.8870	−1.52118	−0.760590	−	0.649233i	$-0.775090\pi$
$991$	−47.8870	−1.52118	−0.760590	+	0.649233i	$0.775090\pi$
$992$	−4.60157	−0.146100
$993$	−20.5911	−0.653440
$994$	−13.5532	−0.429882
$995$	73.4441	2.32833
$996$	−8.49113	−0.269052
$997$	23.8769	0.756190	0.378095	−	0.925767i	$-0.376579\pi$
$997$	23.8769	0.756190	0.378095	+	0.925767i	$0.376579\pi$
$998$	18.9505	0.599869
$999$	0.829880	0.0262562

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8034.2.a.o.1.1	✓	7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8034.2.a.o.1.1	✓	7	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:	\( N \)	\(=\)	\( 8034 = 2 \cdot 3 \cdot 13 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8034.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.94146 q^{5} +1.00000 q^{6} -3.14882 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.94146 q^{5} +1.00000 q^{6} -3.14882 q^{7} -1.00000 q^{8} +1.00000 q^{9} +2.94146 q^{10} +0.137087 q^{11} -1.00000 q^{12} +1.00000 q^{13} +3.14882 q^{14} +2.94146 q^{15} +1.00000 q^{16} -2.74850 q^{17} -1.00000 q^{18} -4.14882 q^{19} -2.94146 q^{20} +3.14882 q^{21} -0.137087 q^{22} +7.19107 q^{23} +1.00000 q^{24} +3.65220 q^{25} -1.00000 q^{26} -1.00000 q^{27} -3.14882 q^{28} -10.1077 q^{29} -2.94146 q^{30} +4.60157 q^{31} -1.00000 q^{32} -0.137087 q^{33} +2.74850 q^{34} +9.26214 q^{35} +1.00000 q^{36} -0.829880 q^{37} +4.14882 q^{38} -1.00000 q^{39} +2.94146 q^{40} +4.33657 q^{41} -3.14882 q^{42} -9.96834 q^{43} +0.137087 q^{44} -2.94146 q^{45} -7.19107 q^{46} +6.77316 q^{47} -1.00000 q^{48} +2.91507 q^{49} -3.65220 q^{50} +2.74850 q^{51} +1.00000 q^{52} +5.15156 q^{53} +1.00000 q^{54} -0.403237 q^{55} +3.14882 q^{56} +4.14882 q^{57} +10.1077 q^{58} +10.3965 q^{59} +2.94146 q^{60} -8.47985 q^{61} -4.60157 q^{62} -3.14882 q^{63} +1.00000 q^{64} -2.94146 q^{65} +0.137087 q^{66} +12.7124 q^{67} -2.74850 q^{68} -7.19107 q^{69} -9.26214 q^{70} -4.30422 q^{71} -1.00000 q^{72} +1.09602 q^{73} +0.829880 q^{74} -3.65220 q^{75} -4.14882 q^{76} -0.431663 q^{77} +1.00000 q^{78} -2.76399 q^{79} -2.94146 q^{80} +1.00000 q^{81} -4.33657 q^{82} +8.49113 q^{83} +3.14882 q^{84} +8.08460 q^{85} +9.96834 q^{86} +10.1077 q^{87} -0.137087 q^{88} +3.36617 q^{89} +2.94146 q^{90} -3.14882 q^{91} +7.19107 q^{92} -4.60157 q^{93} -6.77316 q^{94} +12.2036 q^{95} +1.00000 q^{96} -10.0536 q^{97} -2.91507 q^{98} +0.137087 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - 7 q^{2} - 7 q^{3} + 7 q^{4} + 2 q^{5} + 7 q^{6} - 9 q^{7} - 7 q^{8} + 7 q^{9}+O(q^{10}) \) 7 * q - 7 * q^2 - 7 * q^3 + 7 * q^4 + 2 * q^5 + 7 * q^6 - 9 * q^7 - 7 * q^8 + 7 * q^9	\( 7 q - 7 q^{2} - 7 q^{3} + 7 q^{4} + 2 q^{5} + 7 q^{6} - 9 q^{7} - 7 q^{8} + 7 q^{9} - 2 q^{10} - 7 q^{12} + 7 q^{13} + 9 q^{14} - 2 q^{15} + 7 q^{16} + 3 q^{17} - 7 q^{18} - 16 q^{19} + 2 q^{20} + 9 q^{21} + 6 q^{23} + 7 q^{24} + 15 q^{25} - 7 q^{26} - 7 q^{27} - 9 q^{28} - 5 q^{29} + 2 q^{30} - 16 q^{31} - 7 q^{32} - 3 q^{34} - 10 q^{35} + 7 q^{36} + 17 q^{37} + 16 q^{38} - 7 q^{39} - 2 q^{40} + 12 q^{41} - 9 q^{42} - 22 q^{43} + 2 q^{45} - 6 q^{46} - 7 q^{48} - 2 q^{49} - 15 q^{50} - 3 q^{51} + 7 q^{52} + 2 q^{53} + 7 q^{54} - 16 q^{55} + 9 q^{56} + 16 q^{57} + 5 q^{58} - 3 q^{59} - 2 q^{60} - 6 q^{61} + 16 q^{62} - 9 q^{63} + 7 q^{64} + 2 q^{65} + q^{67} + 3 q^{68} - 6 q^{69} + 10 q^{70} + 15 q^{71} - 7 q^{72} + 17 q^{73} - 17 q^{74} - 15 q^{75} - 16 q^{76} - 10 q^{77} + 7 q^{78} - 27 q^{79} + 2 q^{80} + 7 q^{81} - 12 q^{82} + 12 q^{83} + 9 q^{84} + 15 q^{85} + 22 q^{86} + 5 q^{87} - 9 q^{89} - 2 q^{90} - 9 q^{91} + 6 q^{92} + 16 q^{93} - 12 q^{95} + 7 q^{96} - 3 q^{97} + 2 q^{98}+O(q^{100}) \) 7 * q - 7 * q^2 - 7 * q^3 + 7 * q^4 + 2 * q^5 + 7 * q^6 - 9 * q^7 - 7 * q^8 + 7 * q^9 - 2 * q^10 - 7 * q^12 + 7 * q^13 + 9 * q^14 - 2 * q^15 + 7 * q^16 + 3 * q^17 - 7 * q^18 - 16 * q^19 + 2 * q^20 + 9 * q^21 + 6 * q^23 + 7 * q^24 + 15 * q^25 - 7 * q^26 - 7 * q^27 - 9 * q^28 - 5 * q^29 + 2 * q^30 - 16 * q^31 - 7 * q^32 - 3 * q^34 - 10 * q^35 + 7 * q^36 + 17 * q^37 + 16 * q^38 - 7 * q^39 - 2 * q^40 + 12 * q^41 - 9 * q^42 - 22 * q^43 + 2 * q^45 - 6 * q^46 - 7 * q^48 - 2 * q^49 - 15 * q^50 - 3 * q^51 + 7 * q^52 + 2 * q^53 + 7 * q^54 - 16 * q^55 + 9 * q^56 + 16 * q^57 + 5 * q^58 - 3 * q^59 - 2 * q^60 - 6 * q^61 + 16 * q^62 - 9 * q^63 + 7 * q^64 + 2 * q^65 + q^67 + 3 * q^68 - 6 * q^69 + 10 * q^70 + 15 * q^71 - 7 * q^72 + 17 * q^73 - 17 * q^74 - 15 * q^75 - 16 * q^76 - 10 * q^77 + 7 * q^78 - 27 * q^79 + 2 * q^80 + 7 * q^81 - 12 * q^82 + 12 * q^83 + 9 * q^84 + 15 * q^85 + 22 * q^86 + 5 * q^87 - 9 * q^89 - 2 * q^90 - 9 * q^91 + 6 * q^92 + 16 * q^93 - 12 * q^95 + 7 * q^96 - 3 * q^97 + 2 * q^98

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