LMFDB - Embedded newform 6002.2.a.c.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6002,2,Mod(1,6002)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6002, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6002.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6002 = 2 \cdot 3001 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6002.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:	$47.9262112932$
Analytic rank:	$0$
Dimension:	$69$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Character	$\chi$	$=$	6002.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.90243 q^{3} +1.00000 q^{4} -0.692359 q^{5} +1.90243 q^{6} -4.50666 q^{7} -1.00000 q^{8} +0.619255 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.90243 q^{3} +1.00000 q^{4} -0.692359 q^{5} +1.90243 q^{6} -4.50666 q^{7} -1.00000 q^{8} +0.619255 q^{9} +0.692359 q^{10} +1.74701 q^{11} -1.90243 q^{12} +1.23547 q^{13} +4.50666 q^{14} +1.31717 q^{15} +1.00000 q^{16} +2.20000 q^{17} -0.619255 q^{18} -7.73195 q^{19} -0.692359 q^{20} +8.57362 q^{21} -1.74701 q^{22} +4.19141 q^{23} +1.90243 q^{24} -4.52064 q^{25} -1.23547 q^{26} +4.52921 q^{27} -4.50666 q^{28} -4.32577 q^{29} -1.31717 q^{30} +3.11219 q^{31} -1.00000 q^{32} -3.32357 q^{33} -2.20000 q^{34} +3.12023 q^{35} +0.619255 q^{36} +0.117969 q^{37} +7.73195 q^{38} -2.35040 q^{39} +0.692359 q^{40} -6.26276 q^{41} -8.57362 q^{42} -10.3379 q^{43} +1.74701 q^{44} -0.428747 q^{45} -4.19141 q^{46} +4.87073 q^{47} -1.90243 q^{48} +13.3100 q^{49} +4.52064 q^{50} -4.18536 q^{51} +1.23547 q^{52} -12.8758 q^{53} -4.52921 q^{54} -1.20956 q^{55} +4.50666 q^{56} +14.7095 q^{57} +4.32577 q^{58} +9.74483 q^{59} +1.31717 q^{60} -10.7532 q^{61} -3.11219 q^{62} -2.79077 q^{63} +1.00000 q^{64} -0.855391 q^{65} +3.32357 q^{66} -12.6840 q^{67} +2.20000 q^{68} -7.97389 q^{69} -3.12023 q^{70} +5.97188 q^{71} -0.619255 q^{72} +1.96041 q^{73} -0.117969 q^{74} +8.60022 q^{75} -7.73195 q^{76} -7.87317 q^{77} +2.35040 q^{78} -6.72381 q^{79} -0.692359 q^{80} -10.4743 q^{81} +6.26276 q^{82} -3.47077 q^{83} +8.57362 q^{84} -1.52319 q^{85} +10.3379 q^{86} +8.22949 q^{87} -1.74701 q^{88} -13.5881 q^{89} +0.428747 q^{90} -5.56785 q^{91} +4.19141 q^{92} -5.92074 q^{93} -4.87073 q^{94} +5.35329 q^{95} +1.90243 q^{96} -7.68573 q^{97} -13.3100 q^{98} +1.08184 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 69 q - 69 q^{2} + 11 q^{3} + 69 q^{4} - 2 q^{5} - 11 q^{6} + 23 q^{7} - 69 q^{8} + 72 q^{9}+O(q^{10}) $ 69 * q - 69 * q^2 + 11 * q^3 + 69 * q^4 - 2 * q^5 - 11 * q^6 + 23 * q^7 - 69 * q^8 + 72 * q^9	\( 69 q - 69 q^{2} + 11 q^{3} + 69 q^{4} - 2 q^{5} - 11 q^{6} + 23 q^{7} - 69 q^{8} + 72 q^{9} + 2 q^{10} - 14 q^{11} + 11 q^{12} + 31 q^{13} - 23 q^{14} + 34 q^{15} + 69 q^{16} - 4 q^{17} - 72 q^{18} + 17 q^{19} - 2 q^{20} - 11 q^{21} + 14 q^{22} + 33 q^{23} - 11 q^{24} + 119 q^{25} - 31 q^{26} + 44 q^{27} + 23 q^{28} - 25 q^{29} - 34 q^{30} + 49 q^{31} - 69 q^{32} + 10 q^{33} + 4 q^{34} - 11 q^{35} + 72 q^{36} + 73 q^{37} - 17 q^{38} + 31 q^{39} + 2 q^{40} - 46 q^{41} + 11 q^{42} + 76 q^{43} - 14 q^{44} + 9 q^{45} - 33 q^{46} + 23 q^{47} + 11 q^{48} + 100 q^{49} - 119 q^{50} + 25 q^{51} + 31 q^{52} + 30 q^{53} - 44 q^{54} + 81 q^{55} - 23 q^{56} + 12 q^{57} + 25 q^{58} - 3 q^{59} + 34 q^{60} + 13 q^{61} - 49 q^{62} + 65 q^{63} + 69 q^{64} - 27 q^{65} - 10 q^{66} + 105 q^{67} - 4 q^{68} + 19 q^{69} + 11 q^{70} + 51 q^{71} - 72 q^{72} + 43 q^{73} - 73 q^{74} + 77 q^{75} + 17 q^{76} - 19 q^{77} - 31 q^{78} + 89 q^{79} - 2 q^{80} + 73 q^{81} + 46 q^{82} - 10 q^{83} - 11 q^{84} + 44 q^{85} - 76 q^{86} + 57 q^{87} + 14 q^{88} - 28 q^{89} - 9 q^{90} + 76 q^{91} + 33 q^{92} + 59 q^{93} - 23 q^{94} + 72 q^{95} - 11 q^{96} + 89 q^{97} - 100 q^{98} - 17 q^{99}+O(q^{100}) \) 69 * q - 69 * q^2 + 11 * q^3 + 69 * q^4 - 2 * q^5 - 11 * q^6 + 23 * q^7 - 69 * q^8 + 72 * q^9 + 2 * q^10 - 14 * q^11 + 11 * q^12 + 31 * q^13 - 23 * q^14 + 34 * q^15 + 69 * q^16 - 4 * q^17 - 72 * q^18 + 17 * q^19 - 2 * q^20 - 11 * q^21 + 14 * q^22 + 33 * q^23 - 11 * q^24 + 119 * q^25 - 31 * q^26 + 44 * q^27 + 23 * q^28 - 25 * q^29 - 34 * q^30 + 49 * q^31 - 69 * q^32 + 10 * q^33 + 4 * q^34 - 11 * q^35 + 72 * q^36 + 73 * q^37 - 17 * q^38 + 31 * q^39 + 2 * q^40 - 46 * q^41 + 11 * q^42 + 76 * q^43 - 14 * q^44 + 9 * q^45 - 33 * q^46 + 23 * q^47 + 11 * q^48 + 100 * q^49 - 119 * q^50 + 25 * q^51 + 31 * q^52 + 30 * q^53 - 44 * q^54 + 81 * q^55 - 23 * q^56 + 12 * q^57 + 25 * q^58 - 3 * q^59 + 34 * q^60 + 13 * q^61 - 49 * q^62 + 65 * q^63 + 69 * q^64 - 27 * q^65 - 10 * q^66 + 105 * q^67 - 4 * q^68 + 19 * q^69 + 11 * q^70 + 51 * q^71 - 72 * q^72 + 43 * q^73 - 73 * q^74 + 77 * q^75 + 17 * q^76 - 19 * q^77 - 31 * q^78 + 89 * q^79 - 2 * q^80 + 73 * q^81 + 46 * q^82 - 10 * q^83 - 11 * q^84 + 44 * q^85 - 76 * q^86 + 57 * q^87 + 14 * q^88 - 28 * q^89 - 9 * q^90 + 76 * q^91 + 33 * q^92 + 59 * q^93 - 23 * q^94 + 72 * q^95 - 11 * q^96 + 89 * q^97 - 100 * q^98 - 17 * 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
$3$	−1.90243	−1.09837	−0.549185	−	0.835701i	$-0.685062\pi$
$3$	−1.90243	−1.09837	−0.549185	+	0.835701i	$0.685062\pi$
$4$	1.00000	0.500000
$5$	−0.692359	−0.309632	−0.154816	−	0.987943i	$-0.549479\pi$
$5$	−0.692359	−0.309632	−0.154816	+	0.987943i	$0.549479\pi$
$6$	1.90243	0.776665
$7$	−4.50666	−1.70336	−0.851678	−	0.524065i	$-0.824415\pi$
$7$	−4.50666	−1.70336	−0.851678	+	0.524065i	$0.824415\pi$
$8$	−1.00000	−0.353553
$9$	0.619255	0.206418
$10$	0.692359	0.218943
$11$	1.74701	0.526743	0.263371	−	0.964694i	$-0.415166\pi$
$11$	1.74701	0.526743	0.263371	+	0.964694i	$0.415166\pi$
$12$	−1.90243	−0.549185
$13$	1.23547	0.342658	0.171329	−	0.985214i	$-0.445194\pi$
$13$	1.23547	0.342658	0.171329	+	0.985214i	$0.445194\pi$
$14$	4.50666	1.20445
$15$	1.31717	0.340091
$16$	1.00000	0.250000
$17$	2.20000	0.533579	0.266790	−	0.963755i	$-0.414037\pi$
$17$	2.20000	0.533579	0.266790	+	0.963755i	$0.414037\pi$
$18$	−0.619255	−0.145960
$19$	−7.73195	−1.77383	−0.886916	−	0.461931i	$-0.847157\pi$
$19$	−7.73195	−1.77383	−0.886916	+	0.461931i	$0.847157\pi$
$20$	−0.692359	−0.154816
$21$	8.57362	1.87092
$22$	−1.74701	−0.372464
$23$	4.19141	0.873970	0.436985	−	0.899469i	$-0.356046\pi$
$23$	4.19141	0.873970	0.436985	+	0.899469i	$0.356046\pi$
$24$	1.90243	0.388333
$25$	−4.52064	−0.904128
$26$	−1.23547	−0.242296
$27$	4.52921	0.871647
$28$	−4.50666	−0.851678
$29$	−4.32577	−0.803276	−0.401638	−	0.915799i	$-0.631559\pi$
$29$	−4.32577	−0.803276	−0.401638	+	0.915799i	$0.631559\pi$
$30$	−1.31717	−0.240481
$31$	3.11219	0.558966	0.279483	−	0.960151i	$-0.409837\pi$
$31$	3.11219	0.558966	0.279483	+	0.960151i	$0.409837\pi$
$32$	−1.00000	−0.176777
$33$	−3.32357	−0.578559
$34$	−2.20000	−0.377297
$35$	3.12023	0.527414
$36$	0.619255	0.103209
$37$	0.117969	0.0193941	0.00969703	−	0.999953i	$-0.496913\pi$
$37$	0.117969	0.0193941	0.00969703	+	0.999953i	$0.496913\pi$
$38$	7.73195	1.25429
$39$	−2.35040	−0.376366
$40$	0.692359	0.109472
$41$	−6.26276	−0.978079	−0.489040	−	0.872262i	$-0.662653\pi$
$41$	−6.26276	−0.978079	−0.489040	+	0.872262i	$0.662653\pi$
$42$	−8.57362	−1.32294
$43$	−10.3379	−1.57651	−0.788257	−	0.615346i	$-0.789016\pi$
$43$	−10.3379	−1.57651	−0.788257	+	0.615346i	$0.789016\pi$
$44$	1.74701	0.263371
$45$	−0.428747	−0.0639138
$46$	−4.19141	−0.617990
$47$	4.87073	0.710469	0.355234	−	0.934777i	$-0.384401\pi$
$47$	4.87073	0.710469	0.355234	+	0.934777i	$0.384401\pi$
$48$	−1.90243	−0.274593
$49$	13.3100	1.90142
$50$	4.52064	0.639315
$51$	−4.18536	−0.586068
$52$	1.23547	0.171329
$53$	−12.8758	−1.76862	−0.884310	−	0.466900i	$-0.845371\pi$
$53$	−12.8758	−1.76862	−0.884310	+	0.466900i	$0.845371\pi$
$54$	−4.52921	−0.616347
$55$	−1.20956	−0.163097
$56$	4.50666	0.602227
$57$	14.7095	1.94832
$58$	4.32577	0.568002
$59$	9.74483	1.26867	0.634334	−	0.773059i	$-0.281274\pi$
$59$	9.74483	1.26867	0.634334	+	0.773059i	$0.281274\pi$
$60$	1.31717	0.170046
$61$	−10.7532	−1.37680	−0.688402	−	0.725330i	$-0.741687\pi$
$61$	−10.7532	−1.37680	−0.688402	+	0.725330i	$0.741687\pi$
$62$	−3.11219	−0.395249
$63$	−2.79077	−0.351604
$64$	1.00000	0.125000
$65$	−0.855391	−0.106098
$66$	3.32357	0.409103
$67$	−12.6840	−1.54960	−0.774800	−	0.632206i	$-0.782150\pi$
$67$	−12.6840	−1.54960	−0.774800	+	0.632206i	$0.782150\pi$
$68$	2.20000	0.266790
$69$	−7.97389	−0.959943
$70$	−3.12023	−0.372938
$71$	5.97188	0.708732	0.354366	−	0.935107i	$-0.384697\pi$
$71$	5.97188	0.708732	0.354366	+	0.935107i	$0.384697\pi$
$72$	−0.619255	−0.0729799
$73$	1.96041	0.229449	0.114724	−	0.993397i	$-0.463401\pi$
$73$	1.96041	0.229449	0.114724	+	0.993397i	$0.463401\pi$
$74$	−0.117969	−0.0137137
$75$	8.60022	0.993067
$76$	−7.73195	−0.886916
$77$	−7.87317	−0.897231
$78$	2.35040	0.266131
$79$	−6.72381	−0.756488	−0.378244	−	0.925706i	$-0.623472\pi$
$79$	−6.72381	−0.756488	−0.378244	+	0.925706i	$0.623472\pi$
$80$	−0.692359	−0.0774081
$81$	−10.4743	−1.16381
$82$	6.26276	0.691607
$83$	−3.47077	−0.380967	−0.190483	−	0.981690i	$-0.561006\pi$
$83$	−3.47077	−0.380967	−0.190483	+	0.981690i	$0.561006\pi$
$84$	8.57362	0.935458
$85$	−1.52319	−0.165213
$86$	10.3379	1.11476
$87$	8.22949	0.882294
$88$	−1.74701	−0.186232
$89$	−13.5881	−1.44033	−0.720167	−	0.693801i	$-0.755935\pi$
$89$	−13.5881	−1.44033	−0.720167	+	0.693801i	$0.755935\pi$
$90$	0.428747	0.0451939
$91$	−5.56785	−0.583669
$92$	4.19141	0.436985
$93$	−5.92074	−0.613952
$94$	−4.87073	−0.502377
$95$	5.35329	0.549236
$96$	1.90243	0.194166
$97$	−7.68573	−0.780367	−0.390184	−	0.920737i	$-0.627588\pi$
$97$	−7.68573	−0.780367	−0.390184	+	0.920737i	$0.627588\pi$
$98$	−13.3100	−1.34451
$99$	1.08184	0.108729
$100$	−4.52064	−0.452064
$101$	−16.6833	−1.66005	−0.830027	−	0.557724i	$-0.811675\pi$
$101$	−16.6833	−1.66005	−0.830027	+	0.557724i	$0.811675\pi$
$102$	4.18536	0.414412
$103$	−5.72510	−0.564111	−0.282056	−	0.959398i	$-0.591016\pi$
$103$	−5.72510	−0.564111	−0.282056	+	0.959398i	$0.591016\pi$
$104$	−1.23547	−0.121148
$105$	−5.93602	−0.579297
$106$	12.8758	1.25060
$107$	−5.08265	−0.491358	−0.245679	−	0.969351i	$-0.579011\pi$
$107$	−5.08265	−0.491358	−0.245679	+	0.969351i	$0.579011\pi$
$108$	4.52921	0.435823
$109$	−13.6294	−1.30546	−0.652731	−	0.757589i	$-0.726377\pi$
$109$	−13.6294	−1.30546	−0.652731	+	0.757589i	$0.726377\pi$
$110$	1.20956	0.115327
$111$	−0.224429	−0.0213019
$112$	−4.50666	−0.425839
$113$	18.9476	1.78244	0.891218	−	0.453575i	$-0.149852\pi$
$113$	18.9476	1.78244	0.891218	+	0.453575i	$0.149852\pi$
$114$	−14.7095	−1.37767
$115$	−2.90196	−0.270610
$116$	−4.32577	−0.401638
$117$	0.765072	0.0707310
$118$	−9.74483	−0.897084
$119$	−9.91466	−0.908875
$120$	−1.31717	−0.120240
$121$	−7.94796	−0.722542
$122$	10.7532	0.973547
$123$	11.9145	1.07429
$124$	3.11219	0.279483
$125$	6.59170	0.589580
$126$	2.79077	0.248621
$127$	10.9655	0.973035	0.486517	−	0.873671i	$-0.338267\pi$
$127$	10.9655	0.973035	0.486517	+	0.873671i	$0.338267\pi$
$128$	−1.00000	−0.0883883
$129$	19.6672	1.73160
$130$	0.855391	0.0750227
$131$	19.3690	1.69228	0.846141	−	0.532960i	$-0.178920\pi$
$131$	19.3690	1.69228	0.846141	+	0.532960i	$0.178920\pi$
$132$	−3.32357	−0.289280
$133$	34.8453	3.02147
$134$	12.6840	1.09573
$135$	−3.13584	−0.269890
$136$	−2.20000	−0.188649
$137$	0.0408129	0.00348688	0.00174344	−	0.999998i	$-0.499445\pi$
$137$	0.0408129	0.00348688	0.00174344	+	0.999998i	$0.499445\pi$
$138$	7.97389	0.678782
$139$	6.56547	0.556876	0.278438	−	0.960454i	$-0.410183\pi$
$139$	6.56547	0.556876	0.278438	+	0.960454i	$0.410183\pi$
$140$	3.12023	0.263707
$141$	−9.26624	−0.780358
$142$	−5.97188	−0.501149
$143$	2.15838	0.180493
$144$	0.619255	0.0516046
$145$	2.99499	0.248720
$146$	−1.96041	−0.162245
$147$	−25.3213	−2.08847
$148$	0.117969	0.00969703
$149$	−2.42416	−0.198595	−0.0992973	−	0.995058i	$-0.531659\pi$
$149$	−2.42416	−0.198595	−0.0992973	+	0.995058i	$0.531659\pi$
$150$	−8.60022	−0.702205
$151$	0.497924	0.0405205	0.0202602	−	0.999795i	$-0.493551\pi$
$151$	0.497924	0.0405205	0.0202602	+	0.999795i	$0.493551\pi$
$152$	7.73195	0.627144
$153$	1.36236	0.110140
$154$	7.87317	0.634438
$155$	−2.15475	−0.173074
$156$	−2.35040	−0.188183
$157$	5.45549	0.435395	0.217698	−	0.976016i	$-0.430145\pi$
$157$	5.45549	0.435395	0.217698	+	0.976016i	$0.430145\pi$
$158$	6.72381	0.534918
$159$	24.4953	1.94260
$160$	0.692359	0.0547358
$161$	−18.8893	−1.48868
$162$	10.4743	0.822938
$163$	0.974839	0.0763553	0.0381777	−	0.999271i	$-0.487845\pi$
$163$	0.974839	0.0763553	0.0381777	+	0.999271i	$0.487845\pi$
$164$	−6.26276	−0.489040
$165$	2.30110	0.179141
$166$	3.47077	0.269384
$167$	6.09401	0.471569	0.235784	−	0.971805i	$-0.424234\pi$
$167$	6.09401	0.471569	0.235784	+	0.971805i	$0.424234\pi$
$168$	−8.57362	−0.661469
$169$	−11.4736	−0.882585
$170$	1.52319	0.116824
$171$	−4.78805	−0.366151
$172$	−10.3379	−0.788257
$173$	−0.0648065	−0.00492714	−0.00246357	−	0.999997i	$-0.500784\pi$
$173$	−0.0648065	−0.00492714	−0.00246357	+	0.999997i	$0.500784\pi$
$174$	−8.22949	−0.623876
$175$	20.3730	1.54005
$176$	1.74701	0.131686
$177$	−18.5389	−1.39347
$178$	13.5881	1.01847
$179$	−19.6821	−1.47111	−0.735556	−	0.677464i	$-0.763079\pi$
$179$	−19.6821	−1.47111	−0.735556	+	0.677464i	$0.763079\pi$
$180$	−0.428747	−0.0319569
$181$	−14.0217	−1.04223	−0.521113	−	0.853488i	$-0.674483\pi$
$181$	−14.0217	−1.04223	−0.521113	+	0.853488i	$0.674483\pi$
$182$	5.56785	0.412716
$183$	20.4572	1.51224
$184$	−4.19141	−0.308995
$185$	−0.0816773	−0.00600503
$186$	5.92074	0.434129
$187$	3.84342	0.281059
$188$	4.87073	0.355234
$189$	−20.4116	−1.48473
$190$	−5.35329	−0.388368
$191$	−17.0067	−1.23056	−0.615280	−	0.788309i	$-0.710957\pi$
$191$	−17.0067	−1.23056	−0.615280	+	0.788309i	$0.710957\pi$
$192$	−1.90243	−0.137296
$193$	6.75865	0.486499	0.243249	−	0.969964i	$-0.421787\pi$
$193$	6.75865	0.486499	0.243249	+	0.969964i	$0.421787\pi$
$194$	7.68573	0.551803
$195$	1.62732	0.116535
$196$	13.3100	0.950711
$197$	−1.81768	−0.129504	−0.0647522	−	0.997901i	$-0.520626\pi$
$197$	−1.81768	−0.129504	−0.0647522	+	0.997901i	$0.520626\pi$
$198$	−1.08184	−0.0768833
$199$	−4.70299	−0.333386	−0.166693	−	0.986009i	$-0.553309\pi$
$199$	−4.70299	−0.333386	−0.166693	+	0.986009i	$0.553309\pi$
$200$	4.52064	0.319657
$201$	24.1305	1.70204
$202$	16.6833	1.17383
$203$	19.4948	1.36826
$204$	−4.18536	−0.293034
$205$	4.33608	0.302845
$206$	5.72510	0.398887
$207$	2.59555	0.180403
$208$	1.23547	0.0856646
$209$	−13.5078	−0.934353
$210$	5.93602	0.409624
$211$	16.4034	1.12926	0.564629	−	0.825345i	$-0.309019\pi$
$211$	16.4034	1.12926	0.564629	+	0.825345i	$0.309019\pi$
$212$	−12.8758	−0.884310
$213$	−11.3611	−0.778450
$214$	5.08265	0.347443
$215$	7.15754	0.488140
$216$	−4.52921	−0.308174
$217$	−14.0256	−0.952118
$218$	13.6294	0.923102
$219$	−3.72955	−0.252020
$220$	−1.20956	−0.0815484
$221$	2.71804	0.182835
$222$	0.224429	0.0150627
$223$	21.3659	1.43077	0.715383	−	0.698733i	$-0.246252\pi$
$223$	21.3659	1.43077	0.715383	+	0.698733i	$0.246252\pi$
$224$	4.50666	0.301114
$225$	−2.79943	−0.186629
$226$	−18.9476	−1.26037
$227$	25.7720	1.71054	0.855272	−	0.518179i	$-0.173390\pi$
$227$	25.7720	1.71054	0.855272	+	0.518179i	$0.173390\pi$
$228$	14.7095	0.974162
$229$	19.5360	1.29097	0.645487	−	0.763771i	$-0.276654\pi$
$229$	19.5360	1.29097	0.645487	+	0.763771i	$0.276654\pi$
$230$	2.90196	0.191350
$231$	14.9782	0.985492
$232$	4.32577	0.284001
$233$	5.78994	0.379312	0.189656	−	0.981851i	$-0.439263\pi$
$233$	5.78994	0.379312	0.189656	+	0.981851i	$0.439263\pi$
$234$	−0.765072	−0.0500143
$235$	−3.37230	−0.219984
$236$	9.74483	0.634334
$237$	12.7916	0.830904
$238$	9.91466	0.642672
$239$	−20.7606	−1.34289	−0.671445	−	0.741055i	$-0.734326\pi$
$239$	−20.7606	−1.34289	−0.671445	+	0.741055i	$0.734326\pi$
$240$	1.31717	0.0850228
$241$	−25.8445	−1.66479	−0.832396	−	0.554182i	$-0.813031\pi$
$241$	−25.8445	−1.66479	−0.832396	+	0.554182i	$0.813031\pi$
$242$	7.94796	0.510914
$243$	6.33901	0.406648
$244$	−10.7532	−0.688402
$245$	−9.21527	−0.588742
$246$	−11.9145	−0.759640
$247$	−9.55261	−0.607818
$248$	−3.11219	−0.197624
$249$	6.60292	0.418443
$250$	−6.59170	−0.416896
$251$	−11.3216	−0.714612	−0.357306	−	0.933987i	$-0.616305\pi$
$251$	−11.3216	−0.714612	−0.357306	+	0.933987i	$0.616305\pi$
$252$	−2.79077	−0.175802
$253$	7.32244	0.460358
$254$	−10.9655	−0.688040
$255$	2.89777	0.181466
$256$	1.00000	0.0625000
$257$	0.337216	0.0210350	0.0105175	−	0.999945i	$-0.496652\pi$
$257$	0.337216	0.0210350	0.0105175	+	0.999945i	$0.496652\pi$
$258$	−19.6672	−1.22442
$259$	−0.531648	−0.0330350
$260$	−0.855391	−0.0530491
$261$	−2.67876	−0.165811
$262$	−19.3690	−1.19662
$263$	13.2148	0.814857	0.407428	−	0.913237i	$-0.366426\pi$
$263$	13.2148	0.814857	0.407428	+	0.913237i	$0.366426\pi$
$264$	3.32357	0.204552
$265$	8.91465	0.547622
$266$	−34.8453	−2.13650
$267$	25.8504	1.58202
$268$	−12.6840	−0.774800
$269$	17.6742	1.07762	0.538809	−	0.842428i	$-0.318874\pi$
$269$	17.6742	1.07762	0.538809	+	0.842428i	$0.318874\pi$
$270$	3.13584	0.190841
$271$	7.04650	0.428044	0.214022	−	0.976829i	$-0.431344\pi$
$271$	7.04650	0.428044	0.214022	+	0.976829i	$0.431344\pi$
$272$	2.20000	0.133395
$273$	10.5925	0.641085
$274$	−0.0408129	−0.00246559
$275$	−7.89760	−0.476243
$276$	−7.97389	−0.479972
$277$	−7.74842	−0.465557	−0.232779	−	0.972530i	$-0.574782\pi$
$277$	−7.74842	−0.465557	−0.232779	+	0.972530i	$0.574782\pi$
$278$	−6.56547	−0.393771
$279$	1.92724	0.115381
$280$	−3.12023	−0.186469
$281$	2.88064	0.171845	0.0859224	−	0.996302i	$-0.472616\pi$
$281$	2.88064	0.171845	0.0859224	+	0.996302i	$0.472616\pi$
$282$	9.26624	0.551797
$283$	−17.6829	−1.05114	−0.525569	−	0.850751i	$-0.676147\pi$
$283$	−17.6829	−1.05114	−0.525569	+	0.850751i	$0.676147\pi$
$284$	5.97188	0.354366
$285$	−10.1843	−0.603265
$286$	−2.15838	−0.127628
$287$	28.2241	1.66602
$288$	−0.619255	−0.0364899
$289$	−12.1600	−0.715293
$290$	−2.99499	−0.175872
$291$	14.6216	0.857133
$292$	1.96041	0.114724
$293$	−13.3608	−0.780548	−0.390274	−	0.920699i	$-0.627620\pi$
$293$	−13.3608	−0.780548	−0.390274	+	0.920699i	$0.627620\pi$
$294$	25.3213	1.47677
$295$	−6.74692	−0.392821
$296$	−0.117969	−0.00685684
$297$	7.91257	0.459134
$298$	2.42416	0.140428
$299$	5.17837	0.299473
$300$	8.60022	0.496534
$301$	46.5893	2.68536
$302$	−0.497924	−0.0286523
$303$	31.7389	1.82335
$304$	−7.73195	−0.443458
$305$	7.44506	0.426303
$306$	−1.36236	−0.0778811
$307$	−20.9863	−1.19775	−0.598875	−	0.800842i	$-0.704386\pi$
$307$	−20.9863	−1.19775	−0.598875	+	0.800842i	$0.704386\pi$
$308$	−7.87317	−0.448615
$309$	10.8916	0.619603
$310$	2.15475	0.122382
$311$	7.59987	0.430949	0.215475	−	0.976509i	$-0.430870\pi$
$311$	7.59987	0.430949	0.215475	+	0.976509i	$0.430870\pi$
$312$	2.35040	0.133065
$313$	12.4177	0.701888	0.350944	−	0.936396i	$-0.385861\pi$
$313$	12.4177	0.701888	0.350944	+	0.936396i	$0.385861\pi$
$314$	−5.45549	−0.307871
$315$	1.93221	0.108868
$316$	−6.72381	−0.378244
$317$	−26.2743	−1.47571	−0.737857	−	0.674957i	$-0.764162\pi$
$317$	−26.2743	−1.47571	−0.737857	+	0.674957i	$0.764162\pi$
$318$	−24.4953	−1.37363
$319$	−7.55716	−0.423120
$320$	−0.692359	−0.0387041
$321$	9.66941	0.539694
$322$	18.8893	1.05266
$323$	−17.0103	−0.946479
$324$	−10.4743	−0.581905
$325$	−5.58512	−0.309807
$326$	−0.974839	−0.0539914
$327$	25.9291	1.43388
$328$	6.26276	0.345803
$329$	−21.9507	−1.21018
$330$	−2.30110	−0.126672
$331$	−0.813545	−0.0447165	−0.0223582	−	0.999750i	$-0.507117\pi$
$331$	−0.813545	−0.0447165	−0.0223582	+	0.999750i	$0.507117\pi$
$332$	−3.47077	−0.190483
$333$	0.0730532	0.00400329
$334$	−6.09401	−0.333450
$335$	8.78191	0.479807
$336$	8.57362	0.467729
$337$	14.2055	0.773824	0.386912	−	0.922117i	$-0.373542\pi$
$337$	14.2055	0.773824	0.386912	+	0.922117i	$0.373542\pi$
$338$	11.4736	0.624082
$339$	−36.0465	−1.95778
$340$	−1.52319	−0.0826067
$341$	5.43702	0.294431
$342$	4.78805	0.258908
$343$	−28.4368	−1.53544
$344$	10.3379	0.557382
$345$	5.52079	0.297230
$346$	0.0648065	0.00348402
$347$	29.3419	1.57515	0.787577	−	0.616216i	$-0.211335\pi$
$347$	29.3419	1.57515	0.787577	+	0.616216i	$0.211335\pi$
$348$	8.22949	0.441147
$349$	4.66114	0.249505	0.124752	−	0.992188i	$-0.460186\pi$
$349$	4.66114	0.249505	0.124752	+	0.992188i	$0.460186\pi$
$350$	−20.3730	−1.08898
$351$	5.59571	0.298677
$352$	−1.74701	−0.0931159
$353$	2.47569	0.131768	0.0658840	−	0.997827i	$-0.479013\pi$
$353$	2.47569	0.131768	0.0658840	+	0.997827i	$0.479013\pi$
$354$	18.5389	0.985331
$355$	−4.13469	−0.219446
$356$	−13.5881	−0.720167
$357$	18.8620	0.998282
$358$	19.6821	1.04023
$359$	8.34227	0.440288	0.220144	−	0.975467i	$-0.429347\pi$
$359$	8.34227	0.440288	0.220144	+	0.975467i	$0.429347\pi$
$360$	0.428747	0.0225969
$361$	40.7831	2.14648
$362$	14.0217	0.736965
$363$	15.1205	0.793619
$364$	−5.56785	−0.291835
$365$	−1.35731	−0.0710448
$366$	−20.4572	−1.06932
$367$	−11.0714	−0.577924	−0.288962	−	0.957340i	$-0.593310\pi$
$367$	−11.0714	−0.577924	−0.288962	+	0.957340i	$0.593310\pi$
$368$	4.19141	0.218493
$369$	−3.87825	−0.201893
$370$	0.0816773	0.00424620
$371$	58.0266	3.01259
$372$	−5.92074	−0.306976
$373$	22.7365	1.17725	0.588626	−	0.808406i	$-0.299669\pi$
$373$	22.7365	1.17725	0.588626	+	0.808406i	$0.299669\pi$
$374$	−3.84342	−0.198739
$375$	−12.5403	−0.647577
$376$	−4.87073	−0.251189
$377$	−5.34437	−0.275249
$378$	20.4116	1.04986
$379$	24.7598	1.27183	0.635913	−	0.771760i	$-0.280624\pi$
$379$	24.7598	1.27183	0.635913	+	0.771760i	$0.280624\pi$
$380$	5.35329	0.274618
$381$	−20.8612	−1.06875
$382$	17.0067	0.870138
$383$	−25.1188	−1.28351	−0.641755	−	0.766910i	$-0.721793\pi$
$383$	−25.1188	−1.28351	−0.641755	+	0.766910i	$0.721793\pi$
$384$	1.90243	0.0970832
$385$	5.45106	0.277812
$386$	−6.75865	−0.344006
$387$	−6.40179	−0.325421
$388$	−7.68573	−0.390184
$389$	−10.7146	−0.543253	−0.271627	−	0.962403i	$-0.587562\pi$
$389$	−10.7146	−0.543253	−0.271627	+	0.962403i	$0.587562\pi$
$390$	−1.62732	−0.0824028
$391$	9.22112	0.466332
$392$	−13.3100	−0.672254
$393$	−36.8483	−1.85875
$394$	1.81768	0.0915735
$395$	4.65529	0.234233
$396$	1.08184	0.0543647
$397$	−23.2910	−1.16894	−0.584470	−	0.811415i	$-0.698698\pi$
$397$	−23.2910	−1.16894	−0.584470	+	0.811415i	$0.698698\pi$
$398$	4.70299	0.235740
$399$	−66.2908	−3.31869
$400$	−4.52064	−0.226032
$401$	26.8546	1.34105	0.670527	−	0.741885i	$-0.266068\pi$
$401$	26.8546	1.34105	0.670527	+	0.741885i	$0.266068\pi$
$402$	−24.1305	−1.20352
$403$	3.84502	0.191534
$404$	−16.6833	−0.830027
$405$	7.25197	0.360353
$406$	−19.4948	−0.967509
$407$	0.206094	0.0102157
$408$	4.18536	0.207206
$409$	−21.7411	−1.07503	−0.537515	−	0.843254i	$-0.680637\pi$
$409$	−21.7411	−1.07503	−0.537515	+	0.843254i	$0.680637\pi$
$410$	−4.33608	−0.214144
$411$	−0.0776438	−0.00382988
$412$	−5.72510	−0.282056
$413$	−43.9166	−2.16099
$414$	−2.59555	−0.127564
$415$	2.40302	0.117960
$416$	−1.23547	−0.0605740
$417$	−12.4904	−0.611656
$418$	13.5078	0.660687
$419$	−4.24569	−0.207415	−0.103708	−	0.994608i	$-0.533071\pi$
$419$	−4.24569	−0.207415	−0.103708	+	0.994608i	$0.533071\pi$
$420$	−5.93602	−0.289648
$421$	−3.00716	−0.146560	−0.0732801	−	0.997311i	$-0.523347\pi$
$421$	−3.00716	−0.146560	−0.0732801	+	0.997311i	$0.523347\pi$
$422$	−16.4034	−0.798506
$423$	3.01622	0.146654
$424$	12.8758	0.625302
$425$	−9.94542	−0.482424
$426$	11.3611	0.550448
$427$	48.4609	2.34519
$428$	−5.08265	−0.245679
$429$	−4.10618	−0.198248
$430$	−7.15754	−0.345167
$431$	23.9960	1.15585	0.577923	−	0.816091i	$-0.303863\pi$
$431$	23.9960	1.15585	0.577923	+	0.816091i	$0.303863\pi$
$432$	4.52921	0.217912
$433$	38.1871	1.83515	0.917577	−	0.397558i	$-0.130142\pi$
$433$	38.1871	1.83515	0.917577	+	0.397558i	$0.130142\pi$
$434$	14.0256	0.673249
$435$	−5.69777	−0.273187
$436$	−13.6294	−0.652731
$437$	−32.4078	−1.55028
$438$	3.72955	0.178205
$439$	−17.1293	−0.817538	−0.408769	−	0.912638i	$-0.634042\pi$
$439$	−17.1293	−0.817538	−0.408769	+	0.912638i	$0.634042\pi$
$440$	1.20956	0.0576634
$441$	8.24225	0.392488
$442$	−2.71804	−0.129284
$443$	21.6098	1.02671	0.513357	−	0.858175i	$-0.328402\pi$
$443$	21.6098	1.02671	0.513357	+	0.858175i	$0.328402\pi$
$444$	−0.224429	−0.0106509
$445$	9.40783	0.445974
$446$	−21.3659	−1.01170
$447$	4.61180	0.218130
$448$	−4.50666	−0.212920
$449$	−2.31987	−0.109481	−0.0547407	−	0.998501i	$-0.517433\pi$
$449$	−2.31987	−0.109481	−0.0547407	+	0.998501i	$0.517433\pi$
$450$	2.79943	0.131966
$451$	−10.9411	−0.515196
$452$	18.9476	0.891218
$453$	−0.947267	−0.0445065
$454$	−25.7720	−1.20954
$455$	3.85495	0.180723
$456$	−14.7095	−0.688837
$457$	15.3374	0.717453	0.358727	−	0.933443i	$-0.383211\pi$
$457$	15.3374	0.717453	0.358727	+	0.933443i	$0.383211\pi$
$458$	−19.5360	−0.912857
$459$	9.96428	0.465093
$460$	−2.90196	−0.135305
$461$	−11.5780	−0.539242	−0.269621	−	0.962967i	$-0.586898\pi$
$461$	−11.5780	−0.539242	−0.269621	+	0.962967i	$0.586898\pi$
$462$	−14.9782	−0.696848
$463$	24.9996	1.16183	0.580916	−	0.813964i	$-0.302695\pi$
$463$	24.9996	1.16183	0.580916	+	0.813964i	$0.302695\pi$
$464$	−4.32577	−0.200819
$465$	4.09928	0.190099
$466$	−5.78994	−0.268214
$467$	32.0195	1.48168	0.740842	−	0.671679i	$-0.234427\pi$
$467$	32.0195	1.48168	0.740842	+	0.671679i	$0.234427\pi$
$468$	0.765072	0.0353655
$469$	57.1626	2.63952
$470$	3.37230	0.155552
$471$	−10.3787	−0.478226
$472$	−9.74483	−0.448542
$473$	−18.0604	−0.830418
$474$	−12.7916	−0.587538
$475$	34.9534	1.60377
$476$	−9.91466	−0.454438
$477$	−7.97337	−0.365076
$478$	20.7606	0.949566
$479$	−11.3944	−0.520624	−0.260312	−	0.965525i	$-0.583825\pi$
$479$	−11.3944	−0.520624	−0.260312	+	0.965525i	$0.583825\pi$
$480$	−1.31717	−0.0601202
$481$	0.145748	0.00664554
$482$	25.8445	1.17719
$483$	35.9356	1.63512
$484$	−7.94796	−0.361271
$485$	5.32128	0.241627
$486$	−6.33901	−0.287543
$487$	28.7353	1.30212	0.651060	−	0.759026i	$-0.274325\pi$
$487$	28.7353	1.30212	0.651060	+	0.759026i	$0.274325\pi$
$488$	10.7532	0.486773
$489$	−1.85457	−0.0838664
$490$	9.21527	0.416303
$491$	20.0082	0.902955	0.451478	−	0.892282i	$-0.350897\pi$
$491$	20.0082	0.902955	0.451478	+	0.892282i	$0.350897\pi$
$492$	11.9145	0.537147
$493$	−9.51671	−0.428611
$494$	9.55261	0.429792
$495$	−0.749025	−0.0336661
$496$	3.11219	0.139741
$497$	−26.9132	−1.20722
$498$	−6.60292	−0.295884
$499$	4.49152	0.201068	0.100534	−	0.994934i	$-0.467945\pi$
$499$	4.49152	0.201068	0.100534	+	0.994934i	$0.467945\pi$
$500$	6.59170	0.294790
$501$	−11.5935	−0.517958
$502$	11.3216	0.505307
$503$	−38.1998	−1.70324	−0.851622	−	0.524156i	$-0.824381\pi$
$503$	−38.1998	−1.70324	−0.851622	+	0.524156i	$0.824381\pi$
$504$	2.79077	0.124311
$505$	11.5509	0.514006
$506$	−7.32244	−0.325522
$507$	21.8278	0.969406
$508$	10.9655	0.486517
$509$	−5.57915	−0.247291	−0.123646	−	0.992326i	$-0.539459\pi$
$509$	−5.57915	−0.247291	−0.123646	+	0.992326i	$0.539459\pi$
$510$	−2.89777	−0.128316
$511$	−8.83490	−0.390833
$512$	−1.00000	−0.0441942
$513$	−35.0196	−1.54615
$514$	−0.337216	−0.0148740
$515$	3.96383	0.174667
$516$	19.6672	0.865798
$517$	8.50921	0.374235
$518$	0.531648	0.0233593
$519$	0.123290	0.00541183
$520$	0.855391	0.0375114
$521$	35.5305	1.55662	0.778311	−	0.627879i	$-0.216077\pi$
$521$	35.5305	1.55662	0.778311	+	0.627879i	$0.216077\pi$
$522$	2.67876	0.117246
$523$	−21.4134	−0.936343	−0.468172	−	0.883638i	$-0.655087\pi$
$523$	−21.4134	−0.936343	−0.468172	+	0.883638i	$0.655087\pi$
$524$	19.3690	0.846141
$525$	−38.7582	−1.69155
$526$	−13.2148	−0.576191
$527$	6.84683	0.298252
$528$	−3.32357	−0.144640
$529$	−5.43206	−0.236176
$530$	−8.91465	−0.387227
$531$	6.03453	0.261876
$532$	34.8453	1.51073
$533$	−7.73747	−0.335147
$534$	−25.8504	−1.11866
$535$	3.51902	0.152141
$536$	12.6840	0.547867
$537$	37.4440	1.61583
$538$	−17.6742	−0.761991
$539$	23.2526	1.00156
$540$	−3.13584	−0.134945
$541$	19.0748	0.820089	0.410045	−	0.912065i	$-0.365513\pi$
$541$	19.0748	0.820089	0.410045	+	0.912065i	$0.365513\pi$
$542$	−7.04650	−0.302673
$543$	26.6754	1.14475
$544$	−2.20000	−0.0943243
$545$	9.43646	0.404214
$546$	−10.5925	−0.453316
$547$	13.6153	0.582147	0.291073	−	0.956701i	$-0.405988\pi$
$547$	13.6153	0.582147	0.291073	+	0.956701i	$0.405988\pi$
$548$	0.0408129	0.00174344
$549$	−6.65896	−0.284197
$550$	7.89760	0.336755
$551$	33.4467	1.42488
$552$	7.97389	0.339391
$553$	30.3019	1.28857
$554$	7.74842	0.329199
$555$	0.155386	0.00659575
$556$	6.56547	0.278438
$557$	−34.1013	−1.44492	−0.722460	−	0.691413i	$-0.756989\pi$
$557$	−34.1013	−1.44492	−0.722460	+	0.691413i	$0.756989\pi$
$558$	−1.92724	−0.0815865
$559$	−12.7722	−0.540206
$560$	3.12023	0.131854
$561$	−7.31186	−0.308707
$562$	−2.88064	−0.121513
$563$	−23.7442	−1.00070	−0.500348	−	0.865824i	$-0.666795\pi$
$563$	−23.7442	−1.00070	−0.500348	+	0.865824i	$0.666795\pi$
$564$	−9.26624	−0.390179
$565$	−13.1185	−0.551900
$566$	17.6829	0.743266
$567$	47.2040	1.98238
$568$	−5.97188	−0.250575
$569$	3.10799	0.130294	0.0651469	−	0.997876i	$-0.479248\pi$
$569$	3.10799	0.130294	0.0651469	+	0.997876i	$0.479248\pi$
$570$	10.1843	0.426572
$571$	−12.7122	−0.531990	−0.265995	−	0.963974i	$-0.585701\pi$
$571$	−12.7122	−0.531990	−0.265995	+	0.963974i	$0.585701\pi$
$572$	2.15838	0.0902464
$573$	32.3541	1.35161
$574$	−28.2241	−1.17805
$575$	−18.9479	−0.790181
$576$	0.619255	0.0258023
$577$	36.7585	1.53028	0.765138	−	0.643866i	$-0.222671\pi$
$577$	36.7585	1.53028	0.765138	+	0.643866i	$0.222671\pi$
$578$	12.1600	0.505789
$579$	−12.8579	−0.534356
$580$	2.99499	0.124360
$581$	15.6416	0.648922
$582$	−14.6216	−0.606084
$583$	−22.4941	−0.931608
$584$	−1.96041	−0.0811224
$585$	−0.529705	−0.0219006
$586$	13.3608	0.551931
$587$	−7.56043	−0.312052	−0.156026	−	0.987753i	$-0.549868\pi$
$587$	−7.56043	−0.312052	−0.156026	+	0.987753i	$0.549868\pi$
$588$	−25.3213	−1.04423
$589$	−24.0633	−0.991511
$590$	6.74692	0.277766
$591$	3.45802	0.142244
$592$	0.117969	0.00484852
$593$	−48.2902	−1.98304	−0.991520	−	0.129957i	$-0.958516\pi$
$593$	−48.2902	−1.98304	−0.991520	+	0.129957i	$0.958516\pi$
$594$	−7.91257	−0.324657
$595$	6.86450	0.281417
$596$	−2.42416	−0.0992973
$597$	8.94713	0.366182
$598$	−5.17837	−0.211759
$599$	−25.2648	−1.03229	−0.516146	−	0.856501i	$-0.672634\pi$
$599$	−25.2648	−1.03229	−0.516146	+	0.856501i	$0.672634\pi$
$600$	−8.60022	−0.351102
$601$	16.3115	0.665362	0.332681	−	0.943039i	$-0.392047\pi$
$601$	16.3115	0.665362	0.332681	+	0.943039i	$0.392047\pi$
$602$	−46.5893	−1.89884
$603$	−7.85465	−0.319866
$604$	0.497924	0.0202602
$605$	5.50284	0.223722
$606$	−31.7389	−1.28931
$607$	43.8321	1.77909	0.889546	−	0.456846i	$-0.151021\pi$
$607$	43.8321	1.77909	0.889546	+	0.456846i	$0.151021\pi$
$608$	7.73195	0.313572
$609$	−37.0875	−1.50286
$610$	−7.44506	−0.301442
$611$	6.01765	0.243448
$612$	1.36236	0.0550702
$613$	9.23358	0.372941	0.186470	−	0.982461i	$-0.440295\pi$
$613$	9.23358	0.372941	0.186470	+	0.982461i	$0.440295\pi$
$614$	20.9863	0.846938
$615$	−8.24911	−0.332636
$616$	7.87317	0.317219
$617$	−10.9337	−0.440172	−0.220086	−	0.975480i	$-0.570634\pi$
$617$	−10.9337	−0.440172	−0.220086	+	0.975480i	$0.570634\pi$
$618$	−10.8916	−0.438126
$619$	−0.214494	−0.00862123	−0.00431061	−	0.999991i	$-0.501372\pi$
$619$	−0.214494	−0.00862123	−0.00431061	+	0.999991i	$0.501372\pi$
$620$	−2.15475	−0.0865370
$621$	18.9838	0.761793
$622$	−7.59987	−0.304727
$623$	61.2368	2.45340
$624$	−2.35040	−0.0940915
$625$	18.0394	0.721575
$626$	−12.4177	−0.496310
$627$	25.6977	1.02627
$628$	5.45549	0.217698
$629$	0.259533	0.0103483
$630$	−1.93221	−0.0769813
$631$	33.6031	1.33772	0.668859	−	0.743389i	$-0.266783\pi$
$631$	33.6031	1.33772	0.668859	+	0.743389i	$0.266783\pi$
$632$	6.72381	0.267459
$633$	−31.2064	−1.24034
$634$	26.2743	1.04349
$635$	−7.59210	−0.301283
$636$	24.4953	0.971301
$637$	16.4441	0.651538
$638$	7.55716	0.299191
$639$	3.69812	0.146295
$640$	0.692359	0.0273679
$641$	−4.55401	−0.179872	−0.0899362	−	0.995948i	$-0.528666\pi$
$641$	−4.55401	−0.179872	−0.0899362	+	0.995948i	$0.528666\pi$
$642$	−9.66941	−0.381621
$643$	3.63677	0.143420	0.0717100	−	0.997426i	$-0.477154\pi$
$643$	3.63677	0.143420	0.0717100	+	0.997426i	$0.477154\pi$
$644$	−18.8893	−0.744341
$645$	−13.6167	−0.536159
$646$	17.0103	0.669262
$647$	19.2704	0.757599	0.378799	−	0.925479i	$-0.376337\pi$
$647$	19.2704	0.757599	0.378799	+	0.925479i	$0.376337\pi$
$648$	10.4743	0.411469
$649$	17.0243	0.668262
$650$	5.58512	0.219067
$651$	26.6827	1.04578
$652$	0.974839	0.0381777
$653$	12.4616	0.487662	0.243831	−	0.969818i	$-0.421596\pi$
$653$	12.4616	0.487662	0.243831	+	0.969818i	$0.421596\pi$
$654$	−25.9291	−1.01391
$655$	−13.4103	−0.523985
$656$	−6.26276	−0.244520
$657$	1.21399	0.0473624
$658$	21.9507	0.855728
$659$	14.2923	0.556747	0.278374	−	0.960473i	$-0.410205\pi$
$659$	14.2923	0.556747	0.278374	+	0.960473i	$0.410205\pi$
$660$	2.30110	0.0895703
$661$	49.0192	1.90663	0.953313	−	0.301983i	$-0.0976485\pi$
$661$	49.0192	1.90663	0.953313	+	0.301983i	$0.0976485\pi$
$662$	0.813545	0.0316193
$663$	−5.17090	−0.200821
$664$	3.47077	0.134692
$665$	−24.1254	−0.935544
$666$	−0.0730532	−0.00283075
$667$	−18.1311	−0.702039
$668$	6.09401	0.235784
$669$	−40.6472	−1.57151
$670$	−8.78191	−0.339275
$671$	−18.7859	−0.725221
$672$	−8.57362	−0.330734
$673$	36.4892	1.40656	0.703278	−	0.710915i	$-0.251719\pi$
$673$	36.4892	1.40656	0.703278	+	0.710915i	$0.251719\pi$
$674$	−14.2055	−0.547176
$675$	−20.4749	−0.788080
$676$	−11.4736	−0.441293
$677$	17.5912	0.676085	0.338043	−	0.941131i	$-0.390235\pi$
$677$	17.5912	0.676085	0.338043	+	0.941131i	$0.390235\pi$
$678$	36.0465	1.38436
$679$	34.6369	1.32924
$680$	1.52319	0.0584118
$681$	−49.0294	−1.87881
$682$	−5.43702	−0.208194
$683$	7.06166	0.270207	0.135104	−	0.990831i	$-0.456863\pi$
$683$	7.06166	0.270207	0.135104	+	0.990831i	$0.456863\pi$
$684$	−4.78805	−0.183076
$685$	−0.0282572	−0.00107965
$686$	28.4368	1.08572
$687$	−37.1659	−1.41797
$688$	−10.3379	−0.394128
$689$	−15.9076	−0.606033
$690$	−5.52079	−0.210173
$691$	−33.0596	−1.25765	−0.628823	−	0.777548i	$-0.716463\pi$
$691$	−33.0596	−1.25765	−0.628823	+	0.777548i	$0.716463\pi$
$692$	−0.0648065	−0.00246357
$693$	−4.87550	−0.185205
$694$	−29.3419	−1.11380
$695$	−4.54567	−0.172427
$696$	−8.22949	−0.311938
$697$	−13.7781	−0.521883
$698$	−4.66114	−0.176427
$699$	−11.0150	−0.416625
$700$	20.3730	0.770026
$701$	21.6620	0.818163	0.409081	−	0.912498i	$-0.365849\pi$
$701$	21.6620	0.818163	0.409081	+	0.912498i	$0.365849\pi$
$702$	−5.59571	−0.211197
$703$	−0.912134	−0.0344018
$704$	1.74701	0.0658429
$705$	6.41557	0.241624
$706$	−2.47569	−0.0931740
$707$	75.1860	2.82766
$708$	−18.5389	−0.696734
$709$	24.9992	0.938864	0.469432	−	0.882969i	$-0.344459\pi$
$709$	24.9992	0.938864	0.469432	+	0.882969i	$0.344459\pi$
$710$	4.13469	0.155172
$711$	−4.16375	−0.156153
$712$	13.5881	0.509235
$713$	13.0445	0.488519
$714$	−18.8620	−0.705892
$715$	−1.49438	−0.0558865
$716$	−19.6821	−0.735556
$717$	39.4956	1.47499
$718$	−8.34227	−0.311331
$719$	−31.0767	−1.15897	−0.579483	−	0.814984i	$-0.696746\pi$
$719$	−31.0767	−1.15897	−0.579483	+	0.814984i	$0.696746\pi$
$720$	−0.428747	−0.0159785
$721$	25.8011	0.960882
$722$	−40.7831	−1.51779
$723$	49.1675	1.82856
$724$	−14.0217	−0.521113
$725$	19.5552	0.726264
$726$	−15.1205	−0.561173
$727$	−1.25553	−0.0465649	−0.0232824	−	0.999729i	$-0.507412\pi$
$727$	−1.25553	−0.0465649	−0.0232824	+	0.999729i	$0.507412\pi$
$728$	5.56785	0.206358
$729$	19.3633	0.717160
$730$	1.35731	0.0502363
$731$	−22.7434	−0.841195
$732$	20.4572	0.756120
$733$	39.8758	1.47285	0.736424	−	0.676521i	$-0.236513\pi$
$733$	39.8758	1.47285	0.736424	+	0.676521i	$0.236513\pi$
$734$	11.0714	0.408654
$735$	17.5314	0.646657
$736$	−4.19141	−0.154498
$737$	−22.1591	−0.816241
$738$	3.87825	0.142760
$739$	−45.0862	−1.65852	−0.829261	−	0.558861i	$-0.811238\pi$
$739$	−45.0862	−1.65852	−0.829261	+	0.558861i	$0.811238\pi$
$740$	−0.0816773	−0.00300252
$741$	18.1732	0.667610
$742$	−58.0266	−2.13022
$743$	22.9823	0.843140	0.421570	−	0.906796i	$-0.361479\pi$
$743$	22.9823	0.843140	0.421570	+	0.906796i	$0.361479\pi$
$744$	5.92074	0.217065
$745$	1.67839	0.0614913
$746$	−22.7365	−0.832443
$747$	−2.14929	−0.0786385
$748$	3.84342	0.140530
$749$	22.9058	0.836958
$750$	12.5403	0.457906
$751$	−46.3468	−1.69122	−0.845610	−	0.533802i	$-0.820763\pi$
$751$	−46.3468	−1.69122	−0.845610	+	0.533802i	$0.820763\pi$
$752$	4.87073	0.177617
$753$	21.5386	0.784909
$754$	5.34437	0.194631
$755$	−0.344742	−0.0125464
$756$	−20.4116	−0.742363
$757$	48.2136	1.75235	0.876177	−	0.481989i	$-0.160086\pi$
$757$	48.2136	1.75235	0.876177	+	0.481989i	$0.160086\pi$
$758$	−24.7598	−0.899317
$759$	−13.9304	−0.505643
$760$	−5.35329	−0.194184
$761$	−0.279773	−0.0101418	−0.00507088	−	0.999987i	$-0.501614\pi$
$761$	−0.279773	−0.0101418	−0.00507088	+	0.999987i	$0.501614\pi$
$762$	20.8612	0.755723
$763$	61.4232	2.22367
$764$	−17.0067	−0.615280
$765$	−0.943244	−0.0341031
$766$	25.1188	0.907579
$767$	12.0395	0.434720
$768$	−1.90243	−0.0686482
$769$	−51.6987	−1.86430	−0.932152	−	0.362066i	$-0.882071\pi$
$769$	−51.6987	−1.86430	−0.932152	+	0.362066i	$0.882071\pi$
$770$	−5.45106	−0.196443
$771$	−0.641532	−0.0231042
$772$	6.75865	0.243249
$773$	−4.16888	−0.149944	−0.0749721	−	0.997186i	$-0.523887\pi$
$773$	−4.16888	−0.149944	−0.0749721	+	0.997186i	$0.523887\pi$
$774$	6.40179	0.230108
$775$	−14.0691	−0.505376
$776$	7.68573	0.275902
$777$	1.01143	0.0362847
$778$	10.7146	0.384138
$779$	48.4234	1.73495
$780$	1.62732	0.0582676
$781$	10.4329	0.373320
$782$	−9.22112	−0.329747
$783$	−19.5923	−0.700173
$784$	13.3100	0.475355
$785$	−3.77716	−0.134813
$786$	36.8483	1.31434
$787$	−27.4709	−0.979233	−0.489616	−	0.871938i	$-0.662863\pi$
$787$	−27.4709	−0.979233	−0.489616	+	0.871938i	$0.662863\pi$
$788$	−1.81768	−0.0647522
$789$	−25.1402	−0.895015
$790$	−4.65529	−0.165628
$791$	−85.3901	−3.03612
$792$	−1.08184	−0.0384416
$793$	−13.2853	−0.471773
$794$	23.2910	0.826566
$795$	−16.9595	−0.601492
$796$	−4.70299	−0.166693
$797$	−15.3171	−0.542561	−0.271281	−	0.962500i	$-0.587447\pi$
$797$	−15.3171	−0.542561	−0.271281	+	0.962500i	$0.587447\pi$
$798$	66.2908	2.34667
$799$	10.7156	0.379091
$800$	4.52064	0.159829
$801$	−8.41448	−0.297311
$802$	−26.8546	−0.948268
$803$	3.42486	0.120861
$804$	24.1305	0.851018
$805$	13.0782	0.460944
$806$	−3.84502	−0.135435
$807$	−33.6241	−1.18362
$808$	16.6833	0.586917
$809$	9.03744	0.317739	0.158870	−	0.987300i	$-0.449215\pi$
$809$	9.03744	0.317739	0.158870	+	0.987300i	$0.449215\pi$
$810$	−7.25197	−0.254808
$811$	41.9339	1.47250	0.736249	−	0.676711i	$-0.236595\pi$
$811$	41.9339	1.47250	0.736249	+	0.676711i	$0.236595\pi$
$812$	19.4948	0.684132
$813$	−13.4055	−0.470151
$814$	−0.206094	−0.00722358
$815$	−0.674939	−0.0236421
$816$	−4.18536	−0.146517
$817$	79.9321	2.79647
$818$	21.7411	0.760161
$819$	−3.44792	−0.120480
$820$	4.33608	0.151423
$821$	45.3506	1.58275	0.791373	−	0.611334i	$-0.209367\pi$
$821$	45.3506	1.58275	0.791373	+	0.611334i	$0.209367\pi$
$822$	0.0776438	0.00270814
$823$	−23.4694	−0.818091	−0.409045	−	0.912514i	$-0.634138\pi$
$823$	−23.4694	−0.818091	−0.409045	+	0.912514i	$0.634138\pi$
$824$	5.72510	0.199443
$825$	15.0247	0.523091
$826$	43.9166	1.52805
$827$	−43.0104	−1.49562	−0.747808	−	0.663915i	$-0.768894\pi$
$827$	−43.0104	−1.49562	−0.747808	+	0.663915i	$0.768894\pi$
$828$	2.59555	0.0902017
$829$	17.1761	0.596549	0.298274	−	0.954480i	$-0.403589\pi$
$829$	17.1761	0.596549	0.298274	+	0.954480i	$0.403589\pi$
$830$	−2.40302	−0.0834101
$831$	14.7409	0.511355
$832$	1.23547	0.0428323
$833$	29.2819	1.01456
$834$	12.4904	0.432506
$835$	−4.21925	−0.146013
$836$	−13.5078	−0.467177
$837$	14.0958	0.487221
$838$	4.24569	0.146665
$839$	−13.3944	−0.462427	−0.231214	−	0.972903i	$-0.574270\pi$
$839$	−13.3944	−0.462427	−0.231214	+	0.972903i	$0.574270\pi$
$840$	5.93602	0.204812
$841$	−10.2877	−0.354748
$842$	3.00716	0.103634
$843$	−5.48023	−0.188749
$844$	16.4034	0.564629
$845$	7.94386	0.273277
$846$	−3.01622	−0.103700
$847$	35.8187	1.23075
$848$	−12.8758	−0.442155
$849$	33.6405	1.15454
$850$	9.94542	0.341125
$851$	0.494459	0.0169498
$852$	−11.3611	−0.389225
$853$	10.0221	0.343152	0.171576	−	0.985171i	$-0.445114\pi$
$853$	10.0221	0.343152	0.171576	+	0.985171i	$0.445114\pi$
$854$	−48.4609	−1.65830
$855$	3.31505	0.113372
$856$	5.08265	0.173721
$857$	−33.9153	−1.15852	−0.579262	−	0.815141i	$-0.696659\pi$
$857$	−33.9153	−1.15852	−0.579262	+	0.815141i	$0.696659\pi$
$858$	4.10618	0.140183
$859$	48.7250	1.66248	0.831238	−	0.555916i	$-0.187633\pi$
$859$	48.7250	1.66248	0.831238	+	0.555916i	$0.187633\pi$
$860$	7.15754	0.244070
$861$	−53.6945	−1.82990
$862$	−23.9960	−0.817307
$863$	21.3088	0.725360	0.362680	−	0.931914i	$-0.381862\pi$
$863$	21.3088	0.725360	0.362680	+	0.931914i	$0.381862\pi$
$864$	−4.52921	−0.154087
$865$	0.0448694	0.00152560
$866$	−38.1871	−1.29765
$867$	23.1336	0.785657
$868$	−14.0256	−0.476059
$869$	−11.7466	−0.398475
$870$	5.69777	0.193172
$871$	−15.6708	−0.530984
$872$	13.6294	0.461551
$873$	−4.75942	−0.161082
$874$	32.4078	1.09621
$875$	−29.7065	−1.00426
$876$	−3.72955	−0.126010
$877$	−8.10910	−0.273825	−0.136912	−	0.990583i	$-0.543718\pi$
$877$	−8.10910	−0.273825	−0.136912	+	0.990583i	$0.543718\pi$
$878$	17.1293	0.578087
$879$	25.4181	0.857331
$880$	−1.20956	−0.0407742
$881$	10.6187	0.357753	0.178877	−	0.983871i	$-0.442754\pi$
$881$	10.6187	0.357753	0.178877	+	0.983871i	$0.442754\pi$
$882$	−8.24225	−0.277531
$883$	23.0961	0.777246	0.388623	−	0.921397i	$-0.372951\pi$
$883$	23.0961	0.777246	0.388623	+	0.921397i	$0.372951\pi$
$884$	2.71804	0.0914177
$885$	12.8356	0.431463
$886$	−21.6098	−0.725997
$887$	−46.9010	−1.57478	−0.787391	−	0.616453i	$-0.788569\pi$
$887$	−46.9010	−1.57478	−0.787391	+	0.616453i	$0.788569\pi$
$888$	0.224429	0.00753135
$889$	−49.4179	−1.65742
$890$	−9.40783	−0.315351
$891$	−18.2987	−0.613029
$892$	21.3659	0.715383
$893$	−37.6602	−1.26025
$894$	−4.61180	−0.154242
$895$	13.6271	0.455504
$896$	4.50666	0.150557
$897$	−9.85152	−0.328933
$898$	2.31987	0.0774150
$899$	−13.4626	−0.449004
$900$	−2.79943	−0.0933143
$901$	−28.3267	−0.943699
$902$	10.9411	0.364299
$903$	−88.6331	−2.94953
$904$	−18.9476	−0.630186
$905$	9.70807	0.322707
$906$	0.947267	0.0314708
$907$	−6.42666	−0.213394	−0.106697	−	0.994292i	$-0.534027\pi$
$907$	−6.42666	−0.213394	−0.106697	+	0.994292i	$0.534027\pi$
$908$	25.7720	0.855272
$909$	−10.3312	−0.342665
$910$	−3.85495	−0.127790
$911$	3.06669	0.101604	0.0508020	−	0.998709i	$-0.483822\pi$
$911$	3.06669	0.101604	0.0508020	+	0.998709i	$0.483822\pi$
$912$	14.7095	0.487081
$913$	−6.06347	−0.200672
$914$	−15.3374	−0.507316
$915$	−14.1637	−0.468239
$916$	19.5360	0.645487
$917$	−87.2896	−2.88256
$918$	−9.96428	−0.328870
$919$	−3.38035	−0.111508	−0.0557538	−	0.998445i	$-0.517756\pi$
$919$	−3.38035	−0.111508	−0.0557538	+	0.998445i	$0.517756\pi$
$920$	2.90196	0.0956749
$921$	39.9250	1.31557
$922$	11.5780	0.381301
$923$	7.37809	0.242853
$924$	14.9782	0.492746
$925$	−0.533297	−0.0175347
$926$	−24.9996	−0.821539
$927$	−3.54530	−0.116443
$928$	4.32577	0.142000
$929$	−18.7569	−0.615394	−0.307697	−	0.951484i	$-0.599558\pi$
$929$	−18.7569	−0.615394	−0.307697	+	0.951484i	$0.599558\pi$
$930$	−4.09928	−0.134421
$931$	−102.912	−3.37280
$932$	5.78994	0.189656
$933$	−14.4583	−0.473342
$934$	−32.0195	−1.04771
$935$	−2.66103	−0.0870250
$936$	−0.765072	−0.0250072
$937$	27.8242	0.908978	0.454489	−	0.890752i	$-0.349822\pi$
$937$	27.8242	0.908978	0.454489	+	0.890752i	$0.349822\pi$
$938$	−57.1626	−1.86642
$939$	−23.6238	−0.770934
$940$	−3.37230	−0.109992
$941$	−1.46325	−0.0477006	−0.0238503	−	0.999716i	$-0.507593\pi$
$941$	−1.46325	−0.0477006	−0.0238503	+	0.999716i	$0.507593\pi$
$942$	10.3787	0.338157
$943$	−26.2498	−0.854812
$944$	9.74483	0.317167
$945$	14.1322	0.459719
$946$	18.0604	0.587194
$947$	−4.82345	−0.156741	−0.0783705	−	0.996924i	$-0.524972\pi$
$947$	−4.82345	−0.156741	−0.0783705	+	0.996924i	$0.524972\pi$
$948$	12.7916	0.415452
$949$	2.42203	0.0786226
$950$	−34.9534	−1.13404
$951$	49.9852	1.62088
$952$	9.91466	0.321336
$953$	−23.8493	−0.772554	−0.386277	−	0.922383i	$-0.626239\pi$
$953$	−23.8493	−0.772554	−0.386277	+	0.922383i	$0.626239\pi$
$954$	7.97337	0.258147
$955$	11.7747	0.381021
$956$	−20.7606	−0.671445
$957$	14.3770	0.464742
$958$	11.3944	0.368137
$959$	−0.183930	−0.00593939
$960$	1.31717	0.0425114
$961$	−21.3143	−0.687557
$962$	−0.145748	−0.00469911
$963$	−3.14746	−0.101425
$964$	−25.8445	−0.832396
$965$	−4.67942	−0.150636
$966$	−35.9356	−1.15621
$967$	35.6071	1.14505	0.572523	−	0.819888i	$-0.305965\pi$
$967$	35.6071	1.14505	0.572523	+	0.819888i	$0.305965\pi$
$968$	7.94796	0.255457
$969$	32.3610	1.03959
$970$	−5.32128	−0.170856
$971$	−12.2539	−0.393245	−0.196623	−	0.980479i	$-0.562997\pi$
$971$	−12.2539	−0.393245	−0.196623	+	0.980479i	$0.562997\pi$
$972$	6.33901	0.203324
$973$	−29.5883	−0.948558
$974$	−28.7353	−0.920738
$975$	10.6253	0.340283
$976$	−10.7532	−0.344201
$977$	34.8927	1.11632	0.558158	−	0.829735i	$-0.311508\pi$
$977$	34.8927	1.11632	0.558158	+	0.829735i	$0.311508\pi$
$978$	1.85457	0.0593025
$979$	−23.7385	−0.758685
$980$	−9.21527	−0.294371
$981$	−8.44009	−0.269471
$982$	−20.0082	−0.638486
$983$	−15.0825	−0.481058	−0.240529	−	0.970642i	$-0.577321\pi$
$983$	−15.0825	−0.481058	−0.240529	+	0.970642i	$0.577321\pi$
$984$	−11.9145	−0.379820
$985$	1.25849	0.0400988
$986$	9.51671	0.303074
$987$	41.7598	1.32923
$988$	−9.55261	−0.303909
$989$	−43.3304	−1.37783
$990$	0.749025	0.0238056
$991$	26.1589	0.830965	0.415482	−	0.909601i	$-0.363613\pi$
$991$	26.1589	0.830965	0.415482	+	0.909601i	$0.363613\pi$
$992$	−3.11219	−0.0988121
$993$	1.54772	0.0491153
$994$	26.9132	0.853636
$995$	3.25616	0.103227
$996$	6.60292	0.209221
$997$	−40.7854	−1.29169	−0.645843	−	0.763470i	$-0.723494\pi$
$997$	−40.7854	−1.29169	−0.645843	+	0.763470i	$0.723494\pi$
$998$	−4.49152	−0.142176
$999$	0.534309	0.0169048

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6002.2.a.c.1.16	✓	69

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6002.2.a.c.1.16	✓	69	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:	\( N \)	\(=\)	\( 6002 = 2 \cdot 3001 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6002.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.90243 q^{3} +1.00000 q^{4} -0.692359 q^{5} +1.90243 q^{6} -4.50666 q^{7} -1.00000 q^{8} +0.619255 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.90243 q^{3} +1.00000 q^{4} -0.692359 q^{5} +1.90243 q^{6} -4.50666 q^{7} -1.00000 q^{8} +0.619255 q^{9} +0.692359 q^{10} +1.74701 q^{11} -1.90243 q^{12} +1.23547 q^{13} +4.50666 q^{14} +1.31717 q^{15} +1.00000 q^{16} +2.20000 q^{17} -0.619255 q^{18} -7.73195 q^{19} -0.692359 q^{20} +8.57362 q^{21} -1.74701 q^{22} +4.19141 q^{23} +1.90243 q^{24} -4.52064 q^{25} -1.23547 q^{26} +4.52921 q^{27} -4.50666 q^{28} -4.32577 q^{29} -1.31717 q^{30} +3.11219 q^{31} -1.00000 q^{32} -3.32357 q^{33} -2.20000 q^{34} +3.12023 q^{35} +0.619255 q^{36} +0.117969 q^{37} +7.73195 q^{38} -2.35040 q^{39} +0.692359 q^{40} -6.26276 q^{41} -8.57362 q^{42} -10.3379 q^{43} +1.74701 q^{44} -0.428747 q^{45} -4.19141 q^{46} +4.87073 q^{47} -1.90243 q^{48} +13.3100 q^{49} +4.52064 q^{50} -4.18536 q^{51} +1.23547 q^{52} -12.8758 q^{53} -4.52921 q^{54} -1.20956 q^{55} +4.50666 q^{56} +14.7095 q^{57} +4.32577 q^{58} +9.74483 q^{59} +1.31717 q^{60} -10.7532 q^{61} -3.11219 q^{62} -2.79077 q^{63} +1.00000 q^{64} -0.855391 q^{65} +3.32357 q^{66} -12.6840 q^{67} +2.20000 q^{68} -7.97389 q^{69} -3.12023 q^{70} +5.97188 q^{71} -0.619255 q^{72} +1.96041 q^{73} -0.117969 q^{74} +8.60022 q^{75} -7.73195 q^{76} -7.87317 q^{77} +2.35040 q^{78} -6.72381 q^{79} -0.692359 q^{80} -10.4743 q^{81} +6.26276 q^{82} -3.47077 q^{83} +8.57362 q^{84} -1.52319 q^{85} +10.3379 q^{86} +8.22949 q^{87} -1.74701 q^{88} -13.5881 q^{89} +0.428747 q^{90} -5.56785 q^{91} +4.19141 q^{92} -5.92074 q^{93} -4.87073 q^{94} +5.35329 q^{95} +1.90243 q^{96} -7.68573 q^{97} -13.3100 q^{98} +1.08184 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 69 q - 69 q^{2} + 11 q^{3} + 69 q^{4} - 2 q^{5} - 11 q^{6} + 23 q^{7} - 69 q^{8} + 72 q^{9}+O(q^{10}) \) 69 * q - 69 * q^2 + 11 * q^3 + 69 * q^4 - 2 * q^5 - 11 * q^6 + 23 * q^7 - 69 * q^8 + 72 * q^9	\( 69 q - 69 q^{2} + 11 q^{3} + 69 q^{4} - 2 q^{5} - 11 q^{6} + 23 q^{7} - 69 q^{8} + 72 q^{9} + 2 q^{10} - 14 q^{11} + 11 q^{12} + 31 q^{13} - 23 q^{14} + 34 q^{15} + 69 q^{16} - 4 q^{17} - 72 q^{18} + 17 q^{19} - 2 q^{20} - 11 q^{21} + 14 q^{22} + 33 q^{23} - 11 q^{24} + 119 q^{25} - 31 q^{26} + 44 q^{27} + 23 q^{28} - 25 q^{29} - 34 q^{30} + 49 q^{31} - 69 q^{32} + 10 q^{33} + 4 q^{34} - 11 q^{35} + 72 q^{36} + 73 q^{37} - 17 q^{38} + 31 q^{39} + 2 q^{40} - 46 q^{41} + 11 q^{42} + 76 q^{43} - 14 q^{44} + 9 q^{45} - 33 q^{46} + 23 q^{47} + 11 q^{48} + 100 q^{49} - 119 q^{50} + 25 q^{51} + 31 q^{52} + 30 q^{53} - 44 q^{54} + 81 q^{55} - 23 q^{56} + 12 q^{57} + 25 q^{58} - 3 q^{59} + 34 q^{60} + 13 q^{61} - 49 q^{62} + 65 q^{63} + 69 q^{64} - 27 q^{65} - 10 q^{66} + 105 q^{67} - 4 q^{68} + 19 q^{69} + 11 q^{70} + 51 q^{71} - 72 q^{72} + 43 q^{73} - 73 q^{74} + 77 q^{75} + 17 q^{76} - 19 q^{77} - 31 q^{78} + 89 q^{79} - 2 q^{80} + 73 q^{81} + 46 q^{82} - 10 q^{83} - 11 q^{84} + 44 q^{85} - 76 q^{86} + 57 q^{87} + 14 q^{88} - 28 q^{89} - 9 q^{90} + 76 q^{91} + 33 q^{92} + 59 q^{93} - 23 q^{94} + 72 q^{95} - 11 q^{96} + 89 q^{97} - 100 q^{98} - 17 q^{99}+O(q^{100}) \) 69 * q - 69 * q^2 + 11 * q^3 + 69 * q^4 - 2 * q^5 - 11 * q^6 + 23 * q^7 - 69 * q^8 + 72 * q^9 + 2 * q^10 - 14 * q^11 + 11 * q^12 + 31 * q^13 - 23 * q^14 + 34 * q^15 + 69 * q^16 - 4 * q^17 - 72 * q^18 + 17 * q^19 - 2 * q^20 - 11 * q^21 + 14 * q^22 + 33 * q^23 - 11 * q^24 + 119 * q^25 - 31 * q^26 + 44 * q^27 + 23 * q^28 - 25 * q^29 - 34 * q^30 + 49 * q^31 - 69 * q^32 + 10 * q^33 + 4 * q^34 - 11 * q^35 + 72 * q^36 + 73 * q^37 - 17 * q^38 + 31 * q^39 + 2 * q^40 - 46 * q^41 + 11 * q^42 + 76 * q^43 - 14 * q^44 + 9 * q^45 - 33 * q^46 + 23 * q^47 + 11 * q^48 + 100 * q^49 - 119 * q^50 + 25 * q^51 + 31 * q^52 + 30 * q^53 - 44 * q^54 + 81 * q^55 - 23 * q^56 + 12 * q^57 + 25 * q^58 - 3 * q^59 + 34 * q^60 + 13 * q^61 - 49 * q^62 + 65 * q^63 + 69 * q^64 - 27 * q^65 - 10 * q^66 + 105 * q^67 - 4 * q^68 + 19 * q^69 + 11 * q^70 + 51 * q^71 - 72 * q^72 + 43 * q^73 - 73 * q^74 + 77 * q^75 + 17 * q^76 - 19 * q^77 - 31 * q^78 + 89 * q^79 - 2 * q^80 + 73 * q^81 + 46 * q^82 - 10 * q^83 - 11 * q^84 + 44 * q^85 - 76 * q^86 + 57 * q^87 + 14 * q^88 - 28 * q^89 - 9 * q^90 + 76 * q^91 + 33 * q^92 + 59 * q^93 - 23 * q^94 + 72 * q^95 - 11 * q^96 + 89 * q^97 - 100 * q^98 - 17 * q^99

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