LMFDB - Embedded newform 6015.2.a.f.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6015,2,Mod(1,6015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6015, 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("6015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6015 = 3 \cdot 5 \cdot 401 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6015.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$48.0300168158$
Analytic rank:	$1$
Dimension:	$36$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	6015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.15201 q^{2} -1.00000 q^{3} +2.63116 q^{4} -1.00000 q^{5} +2.15201 q^{6} -1.35819 q^{7} -1.35826 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.15201 q^{2} -1.00000 q^{3} +2.63116 q^{4} -1.00000 q^{5} +2.15201 q^{6} -1.35819 q^{7} -1.35826 q^{8} +1.00000 q^{9} +2.15201 q^{10} +4.78172 q^{11} -2.63116 q^{12} -0.182116 q^{13} +2.92283 q^{14} +1.00000 q^{15} -2.33933 q^{16} -6.29594 q^{17} -2.15201 q^{18} +1.86484 q^{19} -2.63116 q^{20} +1.35819 q^{21} -10.2903 q^{22} -0.622104 q^{23} +1.35826 q^{24} +1.00000 q^{25} +0.391916 q^{26} -1.00000 q^{27} -3.57360 q^{28} +1.22405 q^{29} -2.15201 q^{30} +2.29507 q^{31} +7.75077 q^{32} -4.78172 q^{33} +13.5489 q^{34} +1.35819 q^{35} +2.63116 q^{36} +7.08834 q^{37} -4.01315 q^{38} +0.182116 q^{39} +1.35826 q^{40} +4.92662 q^{41} -2.92283 q^{42} -4.83286 q^{43} +12.5814 q^{44} -1.00000 q^{45} +1.33878 q^{46} -6.82178 q^{47} +2.33933 q^{48} -5.15533 q^{49} -2.15201 q^{50} +6.29594 q^{51} -0.479176 q^{52} -3.38125 q^{53} +2.15201 q^{54} -4.78172 q^{55} +1.84477 q^{56} -1.86484 q^{57} -2.63417 q^{58} +0.207201 q^{59} +2.63116 q^{60} +3.57051 q^{61} -4.93902 q^{62} -1.35819 q^{63} -12.0011 q^{64} +0.182116 q^{65} +10.2903 q^{66} +7.23627 q^{67} -16.5656 q^{68} +0.622104 q^{69} -2.92283 q^{70} -13.2701 q^{71} -1.35826 q^{72} -11.3122 q^{73} -15.2542 q^{74} -1.00000 q^{75} +4.90668 q^{76} -6.49446 q^{77} -0.391916 q^{78} +9.03049 q^{79} +2.33933 q^{80} +1.00000 q^{81} -10.6022 q^{82} -15.5209 q^{83} +3.57360 q^{84} +6.29594 q^{85} +10.4004 q^{86} -1.22405 q^{87} -6.49481 q^{88} +0.441236 q^{89} +2.15201 q^{90} +0.247347 q^{91} -1.63685 q^{92} -2.29507 q^{93} +14.6806 q^{94} -1.86484 q^{95} -7.75077 q^{96} +12.3300 q^{97} +11.0943 q^{98} +4.78172 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 7 q^{2} - 36 q^{3} + 45 q^{4} - 36 q^{5} + 7 q^{6} + 2 q^{7} - 24 q^{8} + 36 q^{9}+O(q^{10}) $ 36 * q - 7 * q^2 - 36 * q^3 + 45 * q^4 - 36 * q^5 + 7 * q^6 + 2 * q^7 - 24 * q^8 + 36 * q^9	\( 36 q - 7 q^{2} - 36 q^{3} + 45 q^{4} - 36 q^{5} + 7 q^{6} + 2 q^{7} - 24 q^{8} + 36 q^{9} + 7 q^{10} - q^{11} - 45 q^{12} - 8 q^{13} - 4 q^{14} + 36 q^{15} + 63 q^{16} - 50 q^{17} - 7 q^{18} + 15 q^{19} - 45 q^{20} - 2 q^{21} + 7 q^{22} - 32 q^{23} + 24 q^{24} + 36 q^{25} - 12 q^{26} - 36 q^{27} - 10 q^{28} + 7 q^{29} - 7 q^{30} + 7 q^{31} - 50 q^{32} + q^{33} + 8 q^{34} - 2 q^{35} + 45 q^{36} - 10 q^{37} - 48 q^{38} + 8 q^{39} + 24 q^{40} - 31 q^{41} + 4 q^{42} + 27 q^{43} - 9 q^{44} - 36 q^{45} + 23 q^{46} - 46 q^{47} - 63 q^{48} + 48 q^{49} - 7 q^{50} + 50 q^{51} - 14 q^{52} - 39 q^{53} + 7 q^{54} + q^{55} - 29 q^{56} - 15 q^{57} - 26 q^{58} - 9 q^{59} + 45 q^{60} + 5 q^{61} - 65 q^{62} + 2 q^{63} + 90 q^{64} + 8 q^{65} - 7 q^{66} + 18 q^{67} - 128 q^{68} + 32 q^{69} + 4 q^{70} + 4 q^{71} - 24 q^{72} - 45 q^{73} - 22 q^{74} - 36 q^{75} + 26 q^{76} - 38 q^{77} + 12 q^{78} + 25 q^{79} - 63 q^{80} + 36 q^{81} - 5 q^{82} - 71 q^{83} + 10 q^{84} + 50 q^{85} + 3 q^{86} - 7 q^{87} - 9 q^{88} - 39 q^{89} + 7 q^{90} + 19 q^{91} - 95 q^{92} - 7 q^{93} + 16 q^{94} - 15 q^{95} + 50 q^{96} - 61 q^{97} - 76 q^{98} - q^{99}+O(q^{100}) \) 36 * q - 7 * q^2 - 36 * q^3 + 45 * q^4 - 36 * q^5 + 7 * q^6 + 2 * q^7 - 24 * q^8 + 36 * q^9 + 7 * q^10 - q^11 - 45 * q^12 - 8 * q^13 - 4 * q^14 + 36 * q^15 + 63 * q^16 - 50 * q^17 - 7 * q^18 + 15 * q^19 - 45 * q^20 - 2 * q^21 + 7 * q^22 - 32 * q^23 + 24 * q^24 + 36 * q^25 - 12 * q^26 - 36 * q^27 - 10 * q^28 + 7 * q^29 - 7 * q^30 + 7 * q^31 - 50 * q^32 + q^33 + 8 * q^34 - 2 * q^35 + 45 * q^36 - 10 * q^37 - 48 * q^38 + 8 * q^39 + 24 * q^40 - 31 * q^41 + 4 * q^42 + 27 * q^43 - 9 * q^44 - 36 * q^45 + 23 * q^46 - 46 * q^47 - 63 * q^48 + 48 * q^49 - 7 * q^50 + 50 * q^51 - 14 * q^52 - 39 * q^53 + 7 * q^54 + q^55 - 29 * q^56 - 15 * q^57 - 26 * q^58 - 9 * q^59 + 45 * q^60 + 5 * q^61 - 65 * q^62 + 2 * q^63 + 90 * q^64 + 8 * q^65 - 7 * q^66 + 18 * q^67 - 128 * q^68 + 32 * q^69 + 4 * q^70 + 4 * q^71 - 24 * q^72 - 45 * q^73 - 22 * q^74 - 36 * q^75 + 26 * q^76 - 38 * q^77 + 12 * q^78 + 25 * q^79 - 63 * q^80 + 36 * q^81 - 5 * q^82 - 71 * q^83 + 10 * q^84 + 50 * q^85 + 3 * q^86 - 7 * q^87 - 9 * q^88 - 39 * q^89 + 7 * q^90 + 19 * q^91 - 95 * q^92 - 7 * q^93 + 16 * q^94 - 15 * q^95 + 50 * q^96 - 61 * q^97 - 76 * q^98 - q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.15201	−1.52170	−0.760851	−	0.648926i	$-0.775218\pi$
$2$	−2.15201	−1.52170	−0.760851	+	0.648926i	$0.775218\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	2.63116	1.31558
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	2.15201	0.878555
$7$	−1.35819	−0.513346	−0.256673	−	0.966498i	$-0.582626\pi$
$7$	−1.35819	−0.513346	−0.256673	+	0.966498i	$0.582626\pi$
$8$	−1.35826	−0.480217
$9$	1.00000	0.333333
$10$	2.15201	0.680526
$11$	4.78172	1.44174	0.720871	−	0.693069i	$-0.243742\pi$
$11$	4.78172	1.44174	0.720871	+	0.693069i	$0.243742\pi$
$12$	−2.63116	−0.759550
$13$	−0.182116	−0.0505099	−0.0252549	−	0.999681i	$-0.508040\pi$
$13$	−0.182116	−0.0505099	−0.0252549	+	0.999681i	$0.508040\pi$
$14$	2.92283	0.781160
$15$	1.00000	0.258199
$16$	−2.33933	−0.584831
$17$	−6.29594	−1.52699	−0.763494	−	0.645814i	$-0.776518\pi$
$17$	−6.29594	−1.52699	−0.763494	+	0.645814i	$0.776518\pi$
$18$	−2.15201	−0.507234
$19$	1.86484	0.427823	0.213911	−	0.976853i	$-0.431380\pi$
$19$	1.86484	0.427823	0.213911	+	0.976853i	$0.431380\pi$
$20$	−2.63116	−0.588345
$21$	1.35819	0.296380
$22$	−10.2903	−2.19390
$23$	−0.622104	−0.129718	−0.0648588	−	0.997894i	$-0.520660\pi$
$23$	−0.622104	−0.129718	−0.0648588	+	0.997894i	$0.520660\pi$
$24$	1.35826	0.277253
$25$	1.00000	0.200000
$26$	0.391916	0.0768610
$27$	−1.00000	−0.192450
$28$	−3.57360	−0.675347
$29$	1.22405	0.227300	0.113650	−	0.993521i	$-0.463746\pi$
$29$	1.22405	0.227300	0.113650	+	0.993521i	$0.463746\pi$
$30$	−2.15201	−0.392902
$31$	2.29507	0.412207	0.206103	−	0.978530i	$-0.433922\pi$
$31$	2.29507	0.412207	0.206103	+	0.978530i	$0.433922\pi$
$32$	7.75077	1.37016
$33$	−4.78172	−0.832390
$34$	13.5489	2.32362
$35$	1.35819	0.229575
$36$	2.63116	0.438526
$37$	7.08834	1.16532	0.582658	−	0.812718i	$-0.302013\pi$
$37$	7.08834	1.16532	0.582658	+	0.812718i	$0.302013\pi$
$38$	−4.01315	−0.651019
$39$	0.182116	0.0291619
$40$	1.35826	0.214760
$41$	4.92662	0.769409	0.384705	−	0.923040i	$-0.374303\pi$
$41$	4.92662	0.769409	0.384705	+	0.923040i	$0.374303\pi$
$42$	−2.92283	−0.451003
$43$	−4.83286	−0.737004	−0.368502	−	0.929627i	$-0.620129\pi$
$43$	−4.83286	−0.737004	−0.368502	+	0.929627i	$0.620129\pi$
$44$	12.5814	1.89672
$45$	−1.00000	−0.149071
$46$	1.33878	0.197392
$47$	−6.82178	−0.995059	−0.497529	−	0.867447i	$-0.665759\pi$
$47$	−6.82178	−0.995059	−0.497529	+	0.867447i	$0.665759\pi$
$48$	2.33933	0.337653
$49$	−5.15533	−0.736476
$50$	−2.15201	−0.304341
$51$	6.29594	0.881607
$52$	−0.479176	−0.0664497
$53$	−3.38125	−0.464451	−0.232226	−	0.972662i	$-0.574601\pi$
$53$	−3.38125	−0.464451	−0.232226	+	0.972662i	$0.574601\pi$
$54$	2.15201	0.292852
$55$	−4.78172	−0.644767
$56$	1.84477	0.246517
$57$	−1.86484	−0.247004
$58$	−2.63417	−0.345883
$59$	0.207201	0.0269752	0.0134876	−	0.999909i	$-0.495707\pi$
$59$	0.207201	0.0269752	0.0134876	+	0.999909i	$0.495707\pi$
$60$	2.63116	0.339681
$61$	3.57051	0.457157	0.228579	−	0.973525i	$-0.426592\pi$
$61$	3.57051	0.457157	0.228579	+	0.973525i	$0.426592\pi$
$62$	−4.93902	−0.627256
$63$	−1.35819	−0.171115
$64$	−12.0011	−1.50014
$65$	0.182116	0.0225887
$66$	10.2903	1.26665
$67$	7.23627	0.884051	0.442026	−	0.897002i	$-0.354260\pi$
$67$	7.23627	0.884051	0.442026	+	0.897002i	$0.354260\pi$
$68$	−16.5656	−2.00887
$69$	0.622104	0.0748925
$70$	−2.92283	−0.349345
$71$	−13.2701	−1.57487	−0.787434	−	0.616399i	$-0.788591\pi$
$71$	−13.2701	−1.57487	−0.787434	+	0.616399i	$0.788591\pi$
$72$	−1.35826	−0.160072
$73$	−11.3122	−1.32399	−0.661994	−	0.749509i	$-0.730289\pi$
$73$	−11.3122	−1.32399	−0.661994	+	0.749509i	$0.730289\pi$
$74$	−15.2542	−1.77326
$75$	−1.00000	−0.115470
$76$	4.90668	0.562835
$77$	−6.49446	−0.740112
$78$	−0.391916	−0.0443757
$79$	9.03049	1.01601	0.508005	−	0.861354i	$-0.330383\pi$
$79$	9.03049	1.01601	0.508005	+	0.861354i	$0.330383\pi$
$80$	2.33933	0.261545
$81$	1.00000	0.111111
$82$	−10.6022	−1.17081
$83$	−15.5209	−1.70364	−0.851819	−	0.523836i	$-0.824500\pi$
$83$	−15.5209	−1.70364	−0.851819	+	0.523836i	$0.824500\pi$
$84$	3.57360	0.389912
$85$	6.29594	0.682890
$86$	10.4004	1.12150
$87$	−1.22405	−0.131232
$88$	−6.49481	−0.692349
$89$	0.441236	0.0467709	0.0233854	−	0.999727i	$-0.492556\pi$
$89$	0.441236	0.0467709	0.0233854	+	0.999727i	$0.492556\pi$
$90$	2.15201	0.226842
$91$	0.247347	0.0259290
$92$	−1.63685	−0.170654
$93$	−2.29507	−0.237988
$94$	14.6806	1.51418
$95$	−1.86484	−0.191328
$96$	−7.75077	−0.791060
$97$	12.3300	1.25192	0.625962	−	0.779854i	$-0.284707\pi$
$97$	12.3300	1.25192	0.625962	+	0.779854i	$0.284707\pi$
$98$	11.0943	1.12070
$99$	4.78172	0.480581
$100$	2.63116	0.263116
$101$	−4.92703	−0.490257	−0.245129	−	0.969491i	$-0.578830\pi$
$101$	−4.92703	−0.490257	−0.245129	+	0.969491i	$0.578830\pi$
$102$	−13.5489	−1.34154
$103$	−6.06511	−0.597613	−0.298806	−	0.954314i	$-0.596588\pi$
$103$	−6.06511	−0.597613	−0.298806	+	0.954314i	$0.596588\pi$
$104$	0.247361	0.0242557
$105$	−1.35819	−0.132545
$106$	7.27650	0.706756
$107$	11.4131	1.10335	0.551673	−	0.834061i	$-0.313990\pi$
$107$	11.4131	1.10335	0.551673	+	0.834061i	$0.313990\pi$
$108$	−2.63116	−0.253183
$109$	−8.70886	−0.834158	−0.417079	−	0.908870i	$-0.636946\pi$
$109$	−8.70886	−0.834158	−0.417079	+	0.908870i	$0.636946\pi$
$110$	10.2903	0.981143
$111$	−7.08834	−0.672795
$112$	3.17724	0.300221
$113$	4.72358	0.444357	0.222179	−	0.975006i	$-0.428683\pi$
$113$	4.72358	0.444357	0.222179	+	0.975006i	$0.428683\pi$
$114$	4.01315	0.375866
$115$	0.622104	0.0580115
$116$	3.22066	0.299031
$117$	−0.182116	−0.0168366
$118$	−0.445899	−0.0410483
$119$	8.55105	0.783874
$120$	−1.35826	−0.123991
$121$	11.8648	1.07862
$122$	−7.68379	−0.695657
$123$	−4.92662	−0.444219
$124$	6.03869	0.542290
$125$	−1.00000	−0.0894427
$126$	2.92283	0.260387
$127$	8.09240	0.718085	0.359042	−	0.933321i	$-0.383103\pi$
$127$	8.09240	0.718085	0.359042	+	0.933321i	$0.383103\pi$
$128$	10.3250	0.912609
$129$	4.83286	0.425509
$130$	−0.391916	−0.0343733
$131$	−17.7466	−1.55053	−0.775263	−	0.631639i	$-0.782383\pi$
$131$	−17.7466	−1.55053	−0.775263	+	0.631639i	$0.782383\pi$
$132$	−12.5814	−1.09507
$133$	−2.53279	−0.219621
$134$	−15.5725	−1.34526
$135$	1.00000	0.0860663
$136$	8.55151	0.733286
$137$	16.6059	1.41874	0.709368	−	0.704838i	$-0.248980\pi$
$137$	16.6059	1.41874	0.709368	+	0.704838i	$0.248980\pi$
$138$	−1.33878	−0.113964
$139$	11.5551	0.980091	0.490045	−	0.871697i	$-0.336980\pi$
$139$	11.5551	0.980091	0.490045	+	0.871697i	$0.336980\pi$
$140$	3.57360	0.302024
$141$	6.82178	0.574498
$142$	28.5573	2.39648
$143$	−0.870827	−0.0728222
$144$	−2.33933	−0.194944
$145$	−1.22405	−0.101652
$146$	24.3439	2.01472
$147$	5.15533	0.425205
$148$	18.6505	1.53306
$149$	−2.77352	−0.227215	−0.113608	−	0.993526i	$-0.536241\pi$
$149$	−2.77352	−0.227215	−0.113608	+	0.993526i	$0.536241\pi$
$150$	2.15201	0.175711
$151$	9.62960	0.783646	0.391823	−	0.920041i	$-0.371845\pi$
$151$	9.62960	0.783646	0.391823	+	0.920041i	$0.371845\pi$
$152$	−2.53293	−0.205448
$153$	−6.29594	−0.508996
$154$	13.9762	1.12623
$155$	−2.29507	−0.184344
$156$	0.479176	0.0383648
$157$	15.6910	1.25228	0.626141	−	0.779710i	$-0.284634\pi$
$157$	15.6910	1.25228	0.626141	+	0.779710i	$0.284634\pi$
$158$	−19.4337	−1.54606
$159$	3.38125	0.268151
$160$	−7.75077	−0.612753
$161$	0.844932	0.0665900
$162$	−2.15201	−0.169078
$163$	3.38664	0.265262	0.132631	−	0.991165i	$-0.457657\pi$
$163$	3.38664	0.265262	0.132631	+	0.991165i	$0.457657\pi$
$164$	12.9627	1.01222
$165$	4.78172	0.372256
$166$	33.4011	2.59243
$167$	10.7650	0.833018	0.416509	−	0.909132i	$-0.363253\pi$
$167$	10.7650	0.833018	0.416509	+	0.909132i	$0.363253\pi$
$168$	−1.84477	−0.142327
$169$	−12.9668	−0.997449
$170$	−13.5489	−1.03916
$171$	1.86484	0.142608
$172$	−12.7160	−0.969587
$173$	−3.84918	−0.292648	−0.146324	−	0.989237i	$-0.546744\pi$
$173$	−3.84918	−0.292648	−0.146324	+	0.989237i	$0.546744\pi$
$174$	2.63417	0.199696
$175$	−1.35819	−0.102669
$176$	−11.1860	−0.843176
$177$	−0.207201	−0.0155742
$178$	−0.949545	−0.0711714
$179$	−1.49704	−0.111894	−0.0559471	−	0.998434i	$-0.517818\pi$
$179$	−1.49704	−0.111894	−0.0559471	+	0.998434i	$0.517818\pi$
$180$	−2.63116	−0.196115
$181$	17.8528	1.32699	0.663496	−	0.748180i	$-0.269072\pi$
$181$	17.8528	1.32699	0.663496	+	0.748180i	$0.269072\pi$
$182$	−0.532294	−0.0394563
$183$	−3.57051	−0.263940
$184$	0.844978	0.0622926
$185$	−7.08834	−0.521145
$186$	4.93902	0.362146
$187$	−30.1054	−2.20152
$188$	−17.9492	−1.30908
$189$	1.35819	0.0987935
$190$	4.01315	0.291145
$191$	−2.67836	−0.193799	−0.0968997	−	0.995294i	$-0.530893\pi$
$191$	−2.67836	−0.193799	−0.0968997	+	0.995294i	$0.530893\pi$
$192$	12.0011	0.866106
$193$	13.2967	0.957120	0.478560	−	0.878055i	$-0.341159\pi$
$193$	13.2967	0.957120	0.478560	+	0.878055i	$0.341159\pi$
$194$	−26.5343	−1.90505
$195$	−0.182116	−0.0130416
$196$	−13.5645	−0.968892
$197$	−15.9697	−1.13779	−0.568895	−	0.822410i	$-0.692629\pi$
$197$	−15.9697	−1.13779	−0.568895	+	0.822410i	$0.692629\pi$
$198$	−10.2903	−0.731301
$199$	25.1961	1.78610	0.893052	−	0.449954i	$-0.148559\pi$
$199$	25.1961	1.78610	0.893052	+	0.449954i	$0.148559\pi$
$200$	−1.35826	−0.0960434
$201$	−7.23627	−0.510407
$202$	10.6030	0.746026
$203$	−1.66249	−0.116684
$204$	16.5656	1.15982
$205$	−4.92662	−0.344090
$206$	13.0522	0.909389
$207$	−0.622104	−0.0432392
$208$	0.426028	0.0295398
$209$	8.91712	0.616810
$210$	2.92283	0.201695
$211$	3.90494	0.268827	0.134414	−	0.990925i	$-0.457085\pi$
$211$	3.90494	0.268827	0.134414	+	0.990925i	$0.457085\pi$
$212$	−8.89661	−0.611022
$213$	13.2701	0.909250
$214$	−24.5611	−1.67896
$215$	4.83286	0.329598
$216$	1.35826	0.0924178
$217$	−3.11713	−0.211605
$218$	18.7416	1.26934
$219$	11.3122	0.764404
$220$	−12.5814	−0.848241
$221$	1.14659	0.0771280
$222$	15.2542	1.02379
$223$	−27.0114	−1.80882	−0.904408	−	0.426669i	$-0.859687\pi$
$223$	−27.0114	−1.80882	−0.904408	+	0.426669i	$0.859687\pi$
$224$	−10.5270	−0.703364
$225$	1.00000	0.0666667
$226$	−10.1652	−0.676180
$227$	−20.7965	−1.38031	−0.690155	−	0.723662i	$-0.742458\pi$
$227$	−20.7965	−1.38031	−0.690155	+	0.723662i	$0.742458\pi$
$228$	−4.90668	−0.324953
$229$	−17.4126	−1.15065	−0.575327	−	0.817923i	$-0.695125\pi$
$229$	−17.4126	−1.15065	−0.575327	+	0.817923i	$0.695125\pi$
$230$	−1.33878	−0.0882762
$231$	6.49446	0.427304
$232$	−1.66257	−0.109153
$233$	6.20679	0.406621	0.203310	−	0.979114i	$-0.434830\pi$
$233$	6.20679	0.406621	0.203310	+	0.979114i	$0.434830\pi$
$234$	0.391916	0.0256203
$235$	6.82178	0.445004
$236$	0.545178	0.0354880
$237$	−9.03049	−0.586593
$238$	−18.4020	−1.19282
$239$	10.3811	0.671501	0.335750	−	0.941951i	$-0.391010\pi$
$239$	10.3811	0.671501	0.335750	+	0.941951i	$0.391010\pi$
$240$	−2.33933	−0.151003
$241$	16.3054	1.05032	0.525161	−	0.851003i	$-0.324005\pi$
$241$	16.3054	1.05032	0.525161	+	0.851003i	$0.324005\pi$
$242$	−25.5332	−1.64134
$243$	−1.00000	−0.0641500
$244$	9.39458	0.601426
$245$	5.15533	0.329362
$246$	10.6022	0.675969
$247$	−0.339617	−0.0216093
$248$	−3.11730	−0.197949
$249$	15.5209	0.983596
$250$	2.15201	0.136105
$251$	0.855112	0.0539742	0.0269871	−	0.999636i	$-0.491409\pi$
$251$	0.855112	0.0539742	0.0269871	+	0.999636i	$0.491409\pi$
$252$	−3.57360	−0.225116
$253$	−2.97472	−0.187019
$254$	−17.4150	−1.09271
$255$	−6.29594	−0.394267
$256$	1.78271	0.111419
$257$	−21.1972	−1.32224	−0.661122	−	0.750278i	$-0.729920\pi$
$257$	−21.1972	−1.32224	−0.661122	+	0.750278i	$0.729920\pi$
$258$	−10.4004	−0.647499
$259$	−9.62727	−0.598210
$260$	0.479176	0.0297172
$261$	1.22405	0.0757667
$262$	38.1909	2.35944
$263$	13.4377	0.828606	0.414303	−	0.910139i	$-0.364025\pi$
$263$	13.4377	0.828606	0.414303	+	0.910139i	$0.364025\pi$
$264$	6.49481	0.399728
$265$	3.38125	0.207709
$266$	5.45061	0.334198
$267$	−0.441236	−0.0270032
$268$	19.0398	1.16304
$269$	5.00124	0.304931	0.152466	−	0.988309i	$-0.451279\pi$
$269$	5.00124	0.304931	0.152466	+	0.988309i	$0.451279\pi$
$270$	−2.15201	−0.130967
$271$	17.7040	1.07544	0.537720	−	0.843124i	$-0.319286\pi$
$271$	17.7040	1.07544	0.537720	+	0.843124i	$0.319286\pi$
$272$	14.7282	0.893031
$273$	−0.247347	−0.0149701
$274$	−35.7361	−2.15890
$275$	4.78172	0.288348
$276$	1.63685	0.0985270
$277$	−19.8138	−1.19050	−0.595248	−	0.803542i	$-0.702946\pi$
$277$	−19.8138	−1.19050	−0.595248	+	0.803542i	$0.702946\pi$
$278$	−24.8667	−1.49141
$279$	2.29507	0.137402
$280$	−1.84477	−0.110246
$281$	−15.0863	−0.899974	−0.449987	−	0.893035i	$-0.648571\pi$
$281$	−15.0863	−0.899974	−0.449987	+	0.893035i	$0.648571\pi$
$282$	−14.6806	−0.874214
$283$	−22.1562	−1.31705	−0.658525	−	0.752559i	$-0.728819\pi$
$283$	−22.1562	−1.31705	−0.658525	+	0.752559i	$0.728819\pi$
$284$	−34.9156	−2.07186
$285$	1.86484	0.110463
$286$	1.87403	0.110814
$287$	−6.69127	−0.394973
$288$	7.75077	0.456719
$289$	22.6388	1.33170
$290$	2.63417	0.154684
$291$	−12.3300	−0.722798
$292$	−29.7641	−1.74181
$293$	−7.65251	−0.447065	−0.223532	−	0.974697i	$-0.571759\pi$
$293$	−7.65251	−0.447065	−0.223532	+	0.974697i	$0.571759\pi$
$294$	−11.0943	−0.647035
$295$	−0.207201	−0.0120637
$296$	−9.62779	−0.559604
$297$	−4.78172	−0.277463
$298$	5.96864	0.345754
$299$	0.113295	0.00655202
$300$	−2.63116	−0.151910
$301$	6.56392	0.378338
$302$	−20.7230	−1.19248
$303$	4.92703	0.283050
$304$	−4.36246	−0.250204
$305$	−3.57051	−0.204447
$306$	13.5489	0.774541
$307$	−11.4225	−0.651919	−0.325959	−	0.945384i	$-0.605687\pi$
$307$	−11.4225	−0.651919	−0.325959	+	0.945384i	$0.605687\pi$
$308$	−17.0879	−0.973676
$309$	6.06511	0.345032
$310$	4.93902	0.280517
$311$	−29.6287	−1.68009	−0.840045	−	0.542517i	$-0.817471\pi$
$311$	−29.6287	−1.68009	−0.840045	+	0.542517i	$0.817471\pi$
$312$	−0.247361	−0.0140040
$313$	25.4722	1.43977	0.719887	−	0.694091i	$-0.244194\pi$
$313$	25.4722	1.43977	0.719887	+	0.694091i	$0.244194\pi$
$314$	−33.7673	−1.90560
$315$	1.35819	0.0765251
$316$	23.7606	1.33664
$317$	9.41161	0.528609	0.264304	−	0.964439i	$-0.414858\pi$
$317$	9.41161	0.528609	0.264304	+	0.964439i	$0.414858\pi$
$318$	−7.27650	−0.408046
$319$	5.85305	0.327708
$320$	12.0011	0.670883
$321$	−11.4131	−0.637017
$322$	−1.81831	−0.101330
$323$	−11.7409	−0.653281
$324$	2.63116	0.146175
$325$	−0.182116	−0.0101020
$326$	−7.28810	−0.403650
$327$	8.70886	0.481601
$328$	−6.69163	−0.369483
$329$	9.26524	0.510809
$330$	−10.2903	−0.566463
$331$	−5.65320	−0.310728	−0.155364	−	0.987857i	$-0.549655\pi$
$331$	−5.65320	−0.310728	−0.155364	+	0.987857i	$0.549655\pi$
$332$	−40.8379	−2.24127
$333$	7.08834	0.388438
$334$	−23.1663	−1.26761
$335$	−7.23627	−0.395360
$336$	−3.17724	−0.173333
$337$	17.1185	0.932502	0.466251	−	0.884652i	$-0.345604\pi$
$337$	17.1185	0.932502	0.466251	+	0.884652i	$0.345604\pi$
$338$	27.9048	1.51782
$339$	−4.72358	−0.256550
$340$	16.5656	0.898396
$341$	10.9744	0.594296
$342$	−4.01315	−0.217006
$343$	16.5092	0.891413
$344$	6.56427	0.353922
$345$	−0.622104	−0.0334929
$346$	8.28349	0.445323
$347$	2.41113	0.129436	0.0647181	−	0.997904i	$-0.479385\pi$
$347$	2.41113	0.129436	0.0647181	+	0.997904i	$0.479385\pi$
$348$	−3.22066	−0.172646
$349$	6.67367	0.357233	0.178617	−	0.983919i	$-0.442838\pi$
$349$	6.67367	0.357233	0.178617	+	0.983919i	$0.442838\pi$
$350$	2.92283	0.156232
$351$	0.182116	0.00972063
$352$	37.0620	1.97541
$353$	−13.0085	−0.692372	−0.346186	−	0.938166i	$-0.612523\pi$
$353$	−13.0085	−0.692372	−0.346186	+	0.938166i	$0.612523\pi$
$354$	0.445899	0.0236992
$355$	13.2701	0.704302
$356$	1.16096	0.0615308
$357$	−8.55105	−0.452570
$358$	3.22165	0.170270
$359$	−1.17365	−0.0619426	−0.0309713	−	0.999520i	$-0.509860\pi$
$359$	−1.17365	−0.0619426	−0.0309713	+	0.999520i	$0.509860\pi$
$360$	1.35826	0.0715865
$361$	−15.5224	−0.816968
$362$	−38.4195	−2.01929
$363$	−11.8648	−0.622741
$364$	0.650810	0.0341117
$365$	11.3122	0.592105
$366$	7.68379	0.401638
$367$	−4.38481	−0.228885	−0.114443	−	0.993430i	$-0.536508\pi$
$367$	−4.38481	−0.228885	−0.114443	+	0.993430i	$0.536508\pi$
$368$	1.45530	0.0758629
$369$	4.92662	0.256470
$370$	15.2542	0.793027
$371$	4.59237	0.238424
$372$	−6.03869	−0.313092
$373$	−13.2746	−0.687335	−0.343667	−	0.939091i	$-0.611669\pi$
$373$	−13.2746	−0.687335	−0.343667	+	0.939091i	$0.611669\pi$
$374$	64.7872	3.35006
$375$	1.00000	0.0516398
$376$	9.26574	0.477844
$377$	−0.222919	−0.0114809
$378$	−2.92283	−0.150334
$379$	10.1819	0.523010	0.261505	−	0.965202i	$-0.415781\pi$
$379$	10.1819	0.523010	0.261505	+	0.965202i	$0.415781\pi$
$380$	−4.90668	−0.251707
$381$	−8.09240	−0.414586
$382$	5.76387	0.294905
$383$	−6.65712	−0.340163	−0.170081	−	0.985430i	$-0.554403\pi$
$383$	−6.65712	−0.340163	−0.170081	+	0.985430i	$0.554403\pi$
$384$	−10.3250	−0.526895
$385$	6.49446	0.330988
$386$	−28.6148	−1.45645
$387$	−4.83286	−0.245668
$388$	32.4422	1.64700
$389$	2.12808	0.107898	0.0539489	−	0.998544i	$-0.482819\pi$
$389$	2.12808	0.107898	0.0539489	+	0.998544i	$0.482819\pi$
$390$	0.391916	0.0198454
$391$	3.91673	0.198077
$392$	7.00227	0.353668
$393$	17.7466	0.895197
$394$	34.3669	1.73138
$395$	−9.03049	−0.454373
$396$	12.5814	0.632242
$397$	23.7869	1.19383	0.596915	−	0.802304i	$-0.296393\pi$
$397$	23.7869	1.19383	0.596915	+	0.802304i	$0.296393\pi$
$398$	−54.2223	−2.71792
$399$	2.53279	0.126798
$400$	−2.33933	−0.116966
$401$	−1.00000	−0.0499376
$401$	−1.00000	−0.0499376
$402$	15.5725	0.776688
$403$	−0.417969	−0.0208205
$404$	−12.9638	−0.644972
$405$	−1.00000	−0.0496904
$406$	3.57769	0.177558
$407$	33.8944	1.68008
$408$	−8.55151	−0.423363
$409$	−31.2166	−1.54356	−0.771781	−	0.635889i	$-0.780634\pi$
$409$	−31.2166	−1.54356	−0.771781	+	0.635889i	$0.780634\pi$
$410$	10.6022	0.523603
$411$	−16.6059	−0.819108
$412$	−15.9583	−0.786207
$413$	−0.281417	−0.0138476
$414$	1.33878	0.0657972
$415$	15.5209	0.761890
$416$	−1.41154	−0.0692064
$417$	−11.5551	−0.565856
$418$	−19.1898	−0.938602
$419$	−32.2997	−1.57794	−0.788971	−	0.614430i	$-0.789386\pi$
$419$	−32.2997	−1.57794	−0.788971	+	0.614430i	$0.789386\pi$
$420$	−3.57360	−0.174374
$421$	1.12145	0.0546560	0.0273280	−	0.999627i	$-0.491300\pi$
$421$	1.12145	0.0546560	0.0273280	+	0.999627i	$0.491300\pi$
$422$	−8.40348	−0.409075
$423$	−6.82178	−0.331686
$424$	4.59262	0.223037
$425$	−6.29594	−0.305398
$426$	−28.5573	−1.38361
$427$	−4.84942	−0.234680
$428$	30.0297	1.45154
$429$	0.870827	0.0420439
$430$	−10.4004	−0.501550
$431$	−2.85650	−0.137593	−0.0687964	−	0.997631i	$-0.521916\pi$
$431$	−2.85650	−0.137593	−0.0687964	+	0.997631i	$0.521916\pi$
$432$	2.33933	0.112551
$433$	−25.2692	−1.21436	−0.607180	−	0.794564i	$-0.707699\pi$
$433$	−25.2692	−1.21436	−0.607180	+	0.794564i	$0.707699\pi$
$434$	6.70811	0.321999
$435$	1.22405	0.0586886
$436$	−22.9144	−1.09740
$437$	−1.16012	−0.0554962
$438$	−24.3439	−1.16320
$439$	28.5758	1.36385	0.681924	−	0.731423i	$-0.261144\pi$
$439$	28.5758	1.36385	0.681924	+	0.731423i	$0.261144\pi$
$440$	6.49481	0.309628
$441$	−5.15533	−0.245492
$442$	−2.46748	−0.117366
$443$	5.82925	0.276956	0.138478	−	0.990366i	$-0.455779\pi$
$443$	5.82925	0.276956	0.138478	+	0.990366i	$0.455779\pi$
$444$	−18.6505	−0.885115
$445$	−0.441236	−0.0209166
$446$	58.1288	2.75248
$447$	2.77352	0.131183
$448$	16.2997	0.770090
$449$	32.1469	1.51711	0.758553	−	0.651612i	$-0.225907\pi$
$449$	32.1469	1.51711	0.758553	+	0.651612i	$0.225907\pi$
$450$	−2.15201	−0.101447
$451$	23.5577	1.10929
$452$	12.4285	0.584587
$453$	−9.62960	−0.452438
$454$	44.7543	2.10042
$455$	−0.247347	−0.0115958
$456$	2.53293	0.118615
$457$	3.72064	0.174044	0.0870221	−	0.996206i	$-0.472265\pi$
$457$	3.72064	0.174044	0.0870221	+	0.996206i	$0.472265\pi$
$458$	37.4721	1.75095
$459$	6.29594	0.293869
$460$	1.63685	0.0763187
$461$	−16.2087	−0.754916	−0.377458	−	0.926027i	$-0.623202\pi$
$461$	−16.2087	−0.754916	−0.377458	+	0.926027i	$0.623202\pi$
$462$	−13.9762	−0.650230
$463$	−10.8010	−0.501965	−0.250982	−	0.967992i	$-0.580754\pi$
$463$	−10.8010	−0.501965	−0.250982	+	0.967992i	$0.580754\pi$
$464$	−2.86345	−0.132932
$465$	2.29507	0.106431
$466$	−13.3571	−0.618756
$467$	9.48349	0.438843	0.219422	−	0.975630i	$-0.429583\pi$
$467$	9.48349	0.438843	0.219422	+	0.975630i	$0.429583\pi$
$468$	−0.479176	−0.0221499
$469$	−9.82820	−0.453824
$470$	−14.6806	−0.677164
$471$	−15.6910	−0.723005
$472$	−0.281432	−0.0129540
$473$	−23.1094	−1.06257
$474$	19.4337	0.892621
$475$	1.86484	0.0855646
$476$	22.4992	1.03125
$477$	−3.38125	−0.154817
$478$	−22.3404	−1.02182
$479$	−10.5960	−0.484144	−0.242072	−	0.970258i	$-0.577827\pi$
$479$	−10.5960	−0.484144	−0.242072	+	0.970258i	$0.577827\pi$
$480$	7.75077	0.353773
$481$	−1.29090	−0.0588599
$482$	−35.0894	−1.59828
$483$	−0.844932	−0.0384458
$484$	31.2182	1.41901
$485$	−12.3300	−0.559877
$486$	2.15201	0.0976173
$487$	16.5531	0.750091	0.375045	−	0.927006i	$-0.377627\pi$
$487$	16.5531	0.750091	0.375045	+	0.927006i	$0.377627\pi$
$488$	−4.84968	−0.219535
$489$	−3.38664	−0.153149
$490$	−11.0943	−0.501191
$491$	−24.0305	−1.08448	−0.542240	−	0.840224i	$-0.682424\pi$
$491$	−24.0305	−1.08448	−0.542240	+	0.840224i	$0.682424\pi$
$492$	−12.9627	−0.584405
$493$	−7.70653	−0.347085
$494$	0.730859	0.0328829
$495$	−4.78172	−0.214922
$496$	−5.36892	−0.241071
$497$	18.0232	0.808452
$498$	−33.4011	−1.49674
$499$	−28.6211	−1.28126	−0.640628	−	0.767852i	$-0.721326\pi$
$499$	−28.6211	−1.28126	−0.640628	+	0.767852i	$0.721326\pi$
$500$	−2.63116	−0.117669
$501$	−10.7650	−0.480943
$502$	−1.84021	−0.0821327
$503$	−20.3997	−0.909579	−0.454789	−	0.890599i	$-0.650285\pi$
$503$	−20.3997	−0.909579	−0.454789	+	0.890599i	$0.650285\pi$
$504$	1.84477	0.0821725
$505$	4.92703	0.219250
$506$	6.40164	0.284588
$507$	12.9668	0.575877
$508$	21.2924	0.944697
$509$	−8.18651	−0.362861	−0.181430	−	0.983404i	$-0.558073\pi$
$509$	−8.18651	−0.362861	−0.181430	+	0.983404i	$0.558073\pi$
$510$	13.5489	0.599957
$511$	15.3640	0.679663
$512$	−24.4864	−1.08216
$513$	−1.86484	−0.0823346
$514$	45.6166	2.01206
$515$	6.06511	0.267261
$516$	12.7160	0.559791
$517$	−32.6198	−1.43462
$518$	20.7180	0.910297
$519$	3.84918	0.168960
$520$	−0.247361	−0.0108475
$521$	−15.2566	−0.668402	−0.334201	−	0.942502i	$-0.608466\pi$
$521$	−15.2566	−0.668402	−0.334201	+	0.942502i	$0.608466\pi$
$522$	−2.63417	−0.115294
$523$	−15.8477	−0.692972	−0.346486	−	0.938055i	$-0.612625\pi$
$523$	−15.8477	−0.692972	−0.346486	+	0.938055i	$0.612625\pi$
$524$	−46.6940	−2.03984
$525$	1.35819	0.0592761
$526$	−28.9182	−1.26089
$527$	−14.4496	−0.629435
$528$	11.1860	0.486808
$529$	−22.6130	−0.983173
$530$	−7.27650	−0.316071
$531$	0.207201	0.00899175
$532$	−6.66418	−0.288929
$533$	−0.897217	−0.0388628
$534$	0.949545	0.0410908
$535$	−11.4131	−0.493431
$536$	−9.82873	−0.424536
$537$	1.49704	0.0646021
$538$	−10.7627	−0.464015
$539$	−24.6513	−1.06181
$540$	2.63116	0.113227
$541$	−31.2215	−1.34232	−0.671159	−	0.741313i	$-0.734203\pi$
$541$	−31.2215	−1.34232	−0.671159	+	0.741313i	$0.734203\pi$
$542$	−38.0992	−1.63650
$543$	−17.8528	−0.766139
$544$	−48.7984	−2.09221
$545$	8.70886	0.373047
$546$	0.532294	0.0227801
$547$	−5.57411	−0.238332	−0.119166	−	0.992874i	$-0.538022\pi$
$547$	−5.57411	−0.238332	−0.119166	+	0.992874i	$0.538022\pi$
$548$	43.6927	1.86646
$549$	3.57051	0.152386
$550$	−10.2903	−0.438780
$551$	2.28265	0.0972442
$552$	−0.844978	−0.0359646
$553$	−12.2651	−0.521564
$554$	42.6395	1.81158
$555$	7.08834	0.300883
$556$	30.4033	1.28939
$557$	−28.6727	−1.21490	−0.607451	−	0.794357i	$-0.707808\pi$
$557$	−28.6727	−1.21490	−0.607451	+	0.794357i	$0.707808\pi$
$558$	−4.93902	−0.209085
$559$	0.880140	0.0372260
$560$	−3.17724	−0.134263
$561$	30.1054	1.27105
$562$	32.4659	1.36949
$563$	39.2143	1.65269	0.826343	−	0.563168i	$-0.190417\pi$
$563$	39.2143	1.65269	0.826343	+	0.563168i	$0.190417\pi$
$564$	17.9492	0.755797
$565$	−4.72358	−0.198723
$566$	47.6804	2.00416
$567$	−1.35819	−0.0570384
$568$	18.0242	0.756278
$569$	43.5515	1.82577	0.912886	−	0.408214i	$-0.133848\pi$
$569$	43.5515	1.82577	0.912886	+	0.408214i	$0.133848\pi$
$570$	−4.01315	−0.168092
$571$	−25.9465	−1.08583	−0.542914	−	0.839789i	$-0.682679\pi$
$571$	−25.9465	−1.08583	−0.542914	+	0.839789i	$0.682679\pi$
$572$	−2.29128	−0.0958033
$573$	2.67836	0.111890
$574$	14.3997	0.601032
$575$	−0.622104	−0.0259435
$576$	−12.0011	−0.500046
$577$	−34.0838	−1.41893	−0.709464	−	0.704742i	$-0.751063\pi$
$577$	−34.0838	−1.41893	−0.709464	+	0.704742i	$0.751063\pi$
$578$	−48.7190	−2.02644
$579$	−13.2967	−0.552594
$580$	−3.22066	−0.133731
$581$	21.0802	0.874555
$582$	26.5343	1.09988
$583$	−16.1682	−0.669619
$584$	15.3648	0.635801
$585$	0.182116	0.00752957
$586$	16.4683	0.680299
$587$	−26.1441	−1.07908	−0.539541	−	0.841960i	$-0.681402\pi$
$587$	−26.1441	−1.07908	−0.539541	+	0.841960i	$0.681402\pi$
$588$	13.5645	0.559390
$589$	4.27993	0.176352
$590$	0.445899	0.0183574
$591$	15.9697	0.656904
$592$	−16.5819	−0.681513
$593$	−21.1152	−0.867098	−0.433549	−	0.901130i	$-0.642739\pi$
$593$	−21.1152	−0.867098	−0.433549	+	0.901130i	$0.642739\pi$
$594$	10.2903	0.422217
$595$	−8.55105	−0.350559
$596$	−7.29756	−0.298920
$597$	−25.1961	−1.03121
$598$	−0.243812	−0.00997023
$599$	−40.5059	−1.65503	−0.827513	−	0.561447i	$-0.810245\pi$
$599$	−40.5059	−1.65503	−0.827513	+	0.561447i	$0.810245\pi$
$600$	1.35826	0.0554507
$601$	10.9157	0.445261	0.222630	−	0.974903i	$-0.428536\pi$
$601$	10.9157	0.445261	0.222630	+	0.974903i	$0.428536\pi$
$602$	−14.1256	−0.575718
$603$	7.23627	0.294684
$604$	25.3370	1.03095
$605$	−11.8648	−0.482373
$606$	−10.6030	−0.430718
$607$	1.71356	0.0695513	0.0347756	−	0.999395i	$-0.488928\pi$
$607$	1.71356	0.0695513	0.0347756	+	0.999395i	$0.488928\pi$
$608$	14.4539	0.586184
$609$	1.66249	0.0673673
$610$	7.68379	0.311107
$611$	1.24235	0.0502603
$612$	−16.5656	−0.669625
$613$	−29.6529	−1.19767	−0.598834	−	0.800873i	$-0.704369\pi$
$613$	−29.6529	−1.19767	−0.598834	+	0.800873i	$0.704369\pi$
$614$	24.5814	0.992026
$615$	4.92662	0.198661
$616$	8.82115	0.355414
$617$	34.7995	1.40097	0.700487	−	0.713665i	$-0.252966\pi$
$617$	34.7995	1.40097	0.700487	+	0.713665i	$0.252966\pi$
$618$	−13.0522	−0.525036
$619$	−23.8960	−0.960460	−0.480230	−	0.877143i	$-0.659447\pi$
$619$	−23.8960	−0.960460	−0.480230	+	0.877143i	$0.659447\pi$
$620$	−6.03869	−0.242520
$621$	0.622104	0.0249642
$622$	63.7613	2.55660
$623$	−0.599280	−0.0240096
$624$	−0.426028	−0.0170548
$625$	1.00000	0.0400000
$626$	−54.8165	−2.19091
$627$	−8.91712	−0.356116
$628$	41.2856	1.64747
$629$	−44.6277	−1.77942
$630$	−2.92283	−0.116448
$631$	−21.9460	−0.873656	−0.436828	−	0.899545i	$-0.643898\pi$
$631$	−21.9460	−0.873656	−0.436828	+	0.899545i	$0.643898\pi$
$632$	−12.2657	−0.487905
$633$	−3.90494	−0.155208
$634$	−20.2539	−0.804385
$635$	−8.09240	−0.321137
$636$	8.89661	0.352774
$637$	0.938868	0.0371993
$638$	−12.5958	−0.498674
$639$	−13.2701	−0.524956
$640$	−10.3250	−0.408131
$641$	36.8198	1.45430	0.727148	−	0.686481i	$-0.240846\pi$
$641$	36.8198	1.45430	0.727148	+	0.686481i	$0.240846\pi$
$642$	24.5611	0.969350
$643$	11.8691	0.468072	0.234036	−	0.972228i	$-0.424807\pi$
$643$	11.8691	0.468072	0.234036	+	0.972228i	$0.424807\pi$
$644$	2.22315	0.0876044
$645$	−4.83286	−0.190294
$646$	25.2666	0.994099
$647$	−37.1891	−1.46205	−0.731027	−	0.682349i	$-0.760959\pi$
$647$	−37.1891	−1.46205	−0.731027	+	0.682349i	$0.760959\pi$
$648$	−1.35826	−0.0533574
$649$	0.990775	0.0388913
$650$	0.391916	0.0153722
$651$	3.11713	0.122170
$652$	8.91079	0.348974
$653$	−20.5555	−0.804400	−0.402200	−	0.915552i	$-0.631754\pi$
$653$	−20.5555	−0.804400	−0.402200	+	0.915552i	$0.631754\pi$
$654$	−18.7416	−0.732854
$655$	17.7466	0.693416
$656$	−11.5250	−0.449975
$657$	−11.3122	−0.441329
$658$	−19.9389	−0.777300
$659$	−4.07278	−0.158653	−0.0793264	−	0.996849i	$-0.525277\pi$
$659$	−4.07278	−0.158653	−0.0793264	+	0.996849i	$0.525277\pi$
$660$	12.5814	0.489732
$661$	31.6343	1.23043	0.615216	−	0.788359i	$-0.289069\pi$
$661$	31.6343	1.23043	0.615216	+	0.788359i	$0.289069\pi$
$662$	12.1657	0.472835
$663$	−1.14659	−0.0445299
$664$	21.0814	0.818116
$665$	2.53279	0.0982176
$666$	−15.2542	−0.591088
$667$	−0.761485	−0.0294848
$668$	28.3243	1.09590
$669$	27.0114	1.04432
$670$	15.5725	0.601620
$671$	17.0732	0.659103
$672$	10.5270	0.406087
$673$	−13.1639	−0.507433	−0.253716	−	0.967279i	$-0.581653\pi$
$673$	−13.1639	−0.507433	−0.253716	+	0.967279i	$0.581653\pi$
$674$	−36.8392	−1.41899
$675$	−1.00000	−0.0384900
$676$	−34.1178	−1.31222
$677$	41.3760	1.59021	0.795104	−	0.606473i	$-0.207416\pi$
$677$	41.3760	1.59021	0.795104	+	0.606473i	$0.207416\pi$
$678$	10.1652	0.390393
$679$	−16.7464	−0.642670
$680$	−8.55151	−0.327935
$681$	20.7965	0.796922
$682$	−23.6170	−0.904341
$683$	−19.5392	−0.747645	−0.373823	−	0.927500i	$-0.621953\pi$
$683$	−19.5392	−0.747645	−0.373823	+	0.927500i	$0.621953\pi$
$684$	4.90668	0.187612
$685$	−16.6059	−0.634478
$686$	−35.5280	−1.35647
$687$	17.4126	0.664331
$688$	11.3056	0.431023
$689$	0.615780	0.0234594
$690$	1.33878	0.0509663
$691$	−5.39099	−0.205083	−0.102541	−	0.994729i	$-0.532697\pi$
$691$	−5.39099	−0.205083	−0.102541	+	0.994729i	$0.532697\pi$
$692$	−10.1278	−0.385001
$693$	−6.49446	−0.246704
$694$	−5.18878	−0.196963
$695$	−11.5551	−0.438310
$696$	1.66257	0.0630197
$697$	−31.0177	−1.17488
$698$	−14.3618	−0.543603
$699$	−6.20679	−0.234763
$700$	−3.57360	−0.135069
$701$	−42.3836	−1.60080	−0.800402	−	0.599463i	$-0.795381\pi$
$701$	−42.3836	−1.60080	−0.800402	+	0.599463i	$0.795381\pi$
$702$	−0.391916	−0.0147919
$703$	13.2186	0.498549
$704$	−57.3859	−2.16281
$705$	−6.82178	−0.256923
$706$	27.9944	1.05358
$707$	6.69182	0.251672
$708$	−0.545178	−0.0204890
$709$	−17.1615	−0.644513	−0.322257	−	0.946652i	$-0.604441\pi$
$709$	−17.1615	−0.644513	−0.322257	+	0.946652i	$0.604441\pi$
$710$	−28.5573	−1.07174
$711$	9.03049	0.338670
$712$	−0.599312	−0.0224602
$713$	−1.42777	−0.0534705
$714$	18.4020	0.688676
$715$	0.870827	0.0325671
$716$	−3.93895	−0.147206
$717$	−10.3811	−0.387691
$718$	2.52570	0.0942583
$719$	−36.4377	−1.35890	−0.679448	−	0.733724i	$-0.737781\pi$
$719$	−36.4377	−1.35890	−0.679448	+	0.733724i	$0.737781\pi$
$720$	2.33933	0.0871815
$721$	8.23754	0.306782
$722$	33.4044	1.24318
$723$	−16.3054	−0.606404
$724$	46.9736	1.74576
$725$	1.22405	0.0454600
$726$	25.5332	0.947627
$727$	−23.5560	−0.873644	−0.436822	−	0.899548i	$-0.643896\pi$
$727$	−23.5560	−0.873644	−0.436822	+	0.899548i	$0.643896\pi$
$728$	−0.335962	−0.0124516
$729$	1.00000	0.0370370
$730$	−24.3439	−0.901008
$731$	30.4274	1.12540
$732$	−9.39458	−0.347234
$733$	−35.4904	−1.31087	−0.655435	−	0.755252i	$-0.727515\pi$
$733$	−35.4904	−1.31087	−0.655435	+	0.755252i	$0.727515\pi$
$734$	9.43616	0.348295
$735$	−5.15533	−0.190157
$736$	−4.82179	−0.177733
$737$	34.6018	1.27457
$738$	−10.6022	−0.390271
$739$	−17.0068	−0.625605	−0.312803	−	0.949818i	$-0.601268\pi$
$739$	−17.0068	−0.625605	−0.312803	+	0.949818i	$0.601268\pi$
$740$	−18.6505	−0.685607
$741$	0.339617	0.0124761
$742$	−9.88284	−0.362811
$743$	14.4014	0.528337	0.264169	−	0.964476i	$-0.414902\pi$
$743$	14.4014	0.528337	0.264169	+	0.964476i	$0.414902\pi$
$744$	3.11730	0.114286
$745$	2.77352	0.101614
$746$	28.5672	1.04592
$747$	−15.5209	−0.567879
$748$	−79.2120	−2.89628
$749$	−15.5011	−0.566398
$750$	−2.15201	−0.0785804
$751$	38.2439	1.39554	0.697771	−	0.716321i	$-0.254176\pi$
$751$	38.2439	1.39554	0.697771	+	0.716321i	$0.254176\pi$
$752$	15.9584	0.581942
$753$	−0.855112	−0.0311620
$754$	0.479724	0.0174705
$755$	−9.62960	−0.350457
$756$	3.57360	0.129971
$757$	0.142902	0.00519385	0.00259692	−	0.999997i	$-0.499173\pi$
$757$	0.142902	0.00519385	0.00259692	+	0.999997i	$0.499173\pi$
$758$	−21.9116	−0.795865
$759$	2.97472	0.107976
$760$	2.53293	0.0918791
$761$	−51.1338	−1.85360	−0.926799	−	0.375558i	$-0.877451\pi$
$761$	−51.1338	−1.85360	−0.926799	+	0.375558i	$0.877451\pi$
$762$	17.4150	0.630877
$763$	11.8283	0.428212
$764$	−7.04719	−0.254958
$765$	6.29594	0.227630
$766$	14.3262	0.517627
$767$	−0.0377346	−0.00136252
$768$	−1.78271	−0.0643280
$769$	−41.7480	−1.50547	−0.752735	−	0.658324i	$-0.771266\pi$
$769$	−41.7480	−1.50547	−0.752735	+	0.658324i	$0.771266\pi$
$770$	−13.9762	−0.503666
$771$	21.1972	0.763398
$772$	34.9858	1.25917
$773$	−5.65654	−0.203452	−0.101726	−	0.994812i	$-0.532436\pi$
$773$	−5.65654	−0.203452	−0.101726	+	0.994812i	$0.532436\pi$
$774$	10.4004	0.373834
$775$	2.29507	0.0824414
$776$	−16.7473	−0.601195
$777$	9.62727	0.345377
$778$	−4.57965	−0.164188
$779$	9.18735	0.329171
$780$	−0.479176	−0.0171572
$781$	−63.4537	−2.27055
$782$	−8.42884	−0.301415
$783$	−1.22405	−0.0437439
$784$	12.0600	0.430714
$785$	−15.6910	−0.560037
$786$	−38.1909	−1.36222
$787$	2.14069	0.0763072	0.0381536	−	0.999272i	$-0.487852\pi$
$787$	2.14069	0.0763072	0.0381536	+	0.999272i	$0.487852\pi$
$788$	−42.0187	−1.49685
$789$	−13.4377	−0.478396
$790$	19.4337	0.691421
$791$	−6.41550	−0.228109
$792$	−6.49481	−0.230783
$793$	−0.650247	−0.0230910
$794$	−51.1897	−1.81666
$795$	−3.38125	−0.119921
$796$	66.2949	2.34976
$797$	54.5685	1.93292	0.966458	−	0.256825i	$-0.0826764\pi$
$797$	54.5685	1.93292	0.966458	+	0.256825i	$0.0826764\pi$
$798$	−5.45061	−0.192949
$799$	42.9495	1.51944
$800$	7.75077	0.274031
$801$	0.441236	0.0155903
$802$	2.15201	0.0759902
$803$	−54.0915	−1.90885
$804$	−19.0398	−0.671481
$805$	−0.844932	−0.0297800
$806$	0.899474	0.0316826
$807$	−5.00124	−0.176052
$808$	6.69218	0.235430
$809$	−41.8203	−1.47032	−0.735161	−	0.677892i	$-0.762893\pi$
$809$	−41.8203	−1.47032	−0.735161	+	0.677892i	$0.762893\pi$
$810$	2.15201	0.0756140
$811$	21.9134	0.769483	0.384741	−	0.923024i	$-0.374291\pi$
$811$	21.9134	0.769483	0.384741	+	0.923024i	$0.374291\pi$
$812$	−4.37426	−0.153506
$813$	−17.7040	−0.620905
$814$	−72.9412	−2.55659
$815$	−3.38664	−0.118629
$816$	−14.7282	−0.515592
$817$	−9.01249	−0.315307
$818$	67.1785	2.34884
$819$	0.247347	0.00864301
$820$	−12.9627	−0.452678
$821$	28.8630	1.00732	0.503662	−	0.863901i	$-0.331986\pi$
$821$	28.8630	1.00732	0.503662	+	0.863901i	$0.331986\pi$
$822$	35.7361	1.24644
$823$	−40.9699	−1.42812	−0.714060	−	0.700084i	$-0.753146\pi$
$823$	−40.9699	−1.42812	−0.714060	+	0.700084i	$0.753146\pi$
$824$	8.23798	0.286984
$825$	−4.78172	−0.166478
$826$	0.605613	0.0210720
$827$	26.2522	0.912880	0.456440	−	0.889754i	$-0.349124\pi$
$827$	26.2522	0.912880	0.456440	+	0.889754i	$0.349124\pi$
$828$	−1.63685	−0.0568846
$829$	−31.5940	−1.09731	−0.548653	−	0.836050i	$-0.684859\pi$
$829$	−31.5940	−1.09731	−0.548653	+	0.836050i	$0.684859\pi$
$830$	−33.4011	−1.15937
$831$	19.8138	0.687333
$832$	2.18559	0.0757718
$833$	32.4576	1.12459
$834$	24.8667	0.861064
$835$	−10.7650	−0.372537
$836$	23.4624	0.811462
$837$	−2.29507	−0.0793292
$838$	69.5093	2.40116
$839$	20.9587	0.723574	0.361787	−	0.932261i	$-0.382167\pi$
$839$	20.9587	0.723574	0.361787	+	0.932261i	$0.382167\pi$
$840$	1.84477	0.0636505
$841$	−27.5017	−0.948335
$842$	−2.41337	−0.0831702
$843$	15.0863	0.519600
$844$	10.2745	0.353664
$845$	12.9668	0.446073
$846$	14.6806	0.504728
$847$	−16.1146	−0.553705
$848$	7.90986	0.271626
$849$	22.1562	0.760399
$850$	13.5489	0.464725
$851$	−4.40968	−0.151162
$852$	34.9156	1.19619
$853$	−13.5785	−0.464920	−0.232460	−	0.972606i	$-0.574678\pi$
$853$	−13.5785	−0.464920	−0.232460	+	0.972606i	$0.574678\pi$
$854$	10.4360	0.357113
$855$	−1.86484	−0.0637761
$856$	−15.5019	−0.529845
$857$	−2.43319	−0.0831161	−0.0415581	−	0.999136i	$-0.513232\pi$
$857$	−2.43319	−0.0831161	−0.0415581	+	0.999136i	$0.513232\pi$
$858$	−1.87403	−0.0639783
$859$	37.5213	1.28021	0.640104	−	0.768288i	$-0.278891\pi$
$859$	37.5213	1.28021	0.640104	+	0.768288i	$0.278891\pi$
$860$	12.7160	0.433612
$861$	6.69127	0.228038
$862$	6.14723	0.209375
$863$	−28.0203	−0.953824	−0.476912	−	0.878951i	$-0.658244\pi$
$863$	−28.0203	−0.953824	−0.476912	+	0.878951i	$0.658244\pi$
$864$	−7.75077	−0.263687
$865$	3.84918	0.130876
$866$	54.3796	1.84790
$867$	−22.6388	−0.768855
$868$	−8.20166	−0.278383
$869$	43.1813	1.46482
$870$	−2.63417	−0.0893067
$871$	−1.31784	−0.0446533
$872$	11.8289	0.400577
$873$	12.3300	0.417308
$874$	2.49660	0.0844487
$875$	1.35819	0.0459151
$876$	29.7641	1.00563
$877$	−21.7447	−0.734267	−0.367133	−	0.930168i	$-0.619661\pi$
$877$	−21.7447	−0.734267	−0.367133	+	0.930168i	$0.619661\pi$
$878$	−61.4954	−2.07537
$879$	7.65251	0.258113
$880$	11.1860	0.377080
$881$	−20.7562	−0.699295	−0.349647	−	0.936881i	$-0.613699\pi$
$881$	−20.7562	−0.699295	−0.349647	+	0.936881i	$0.613699\pi$
$882$	11.0943	0.373566
$883$	5.52328	0.185873	0.0929367	−	0.995672i	$-0.470375\pi$
$883$	5.52328	0.185873	0.0929367	+	0.995672i	$0.470375\pi$
$884$	3.01686	0.101468
$885$	0.207201	0.00696498
$886$	−12.5446	−0.421445
$887$	−12.5116	−0.420097	−0.210049	−	0.977691i	$-0.567362\pi$
$887$	−12.5116	−0.420097	−0.210049	+	0.977691i	$0.567362\pi$
$888$	9.62779	0.323088
$889$	−10.9910	−0.368626
$890$	0.949545	0.0318288
$891$	4.78172	0.160194
$892$	−71.0712	−2.37964
$893$	−12.7215	−0.425709
$894$	−5.96864	−0.199621
$895$	1.49704	0.0500406
$896$	−14.0233	−0.468484
$897$	−0.113295	−0.00378281
$898$	−69.1805	−2.30858
$899$	2.80928	0.0936947
$900$	2.63116	0.0877052
$901$	21.2882	0.709212
$902$	−50.6965	−1.68801
$903$	−6.56392	−0.218434
$904$	−6.41585	−0.213388
$905$	−17.8528	−0.593449
$906$	20.7230	0.688476
$907$	−34.9398	−1.16016	−0.580079	−	0.814560i	$-0.696978\pi$
$907$	−34.9398	−1.16016	−0.580079	+	0.814560i	$0.696978\pi$
$908$	−54.7188	−1.81591
$909$	−4.92703	−0.163419
$910$	0.532294	0.0176454
$911$	51.2163	1.69687	0.848436	−	0.529298i	$-0.177545\pi$
$911$	51.2163	1.69687	0.848436	+	0.529298i	$0.177545\pi$
$912$	4.36246	0.144456
$913$	−74.2164	−2.45621
$914$	−8.00686	−0.264844
$915$	3.57051	0.118037
$916$	−45.8152	−1.51378
$917$	24.1031	0.795956
$918$	−13.5489	−0.447181
$919$	−12.7503	−0.420595	−0.210297	−	0.977637i	$-0.567443\pi$
$919$	−12.7503	−0.420595	−0.210297	+	0.977637i	$0.567443\pi$
$920$	−0.844978	−0.0278581
$921$	11.4225	0.376385
$922$	34.8814	1.14876
$923$	2.41669	0.0795463
$924$	17.0879	0.562152
$925$	7.08834	0.233063
$926$	23.2439	0.763841
$927$	−6.06511	−0.199204
$928$	9.48733	0.311437
$929$	33.6878	1.10526	0.552631	−	0.833426i	$-0.313624\pi$
$929$	33.6878	1.10526	0.552631	+	0.833426i	$0.313624\pi$
$930$	−4.93902	−0.161957
$931$	−9.61385	−0.315081
$932$	16.3311	0.534941
$933$	29.6287	0.970000
$934$	−20.4086	−0.667789
$935$	30.1054	0.984551
$936$	0.247361	0.00808523
$937$	13.4324	0.438818	0.219409	−	0.975633i	$-0.429587\pi$
$937$	13.4324	0.438818	0.219409	+	0.975633i	$0.429587\pi$
$938$	21.1504	0.690585
$939$	−25.4722	−0.831254
$940$	17.9492	0.585438
$941$	−33.0222	−1.07649	−0.538247	−	0.842787i	$-0.680913\pi$
$941$	−33.0222	−1.07649	−0.538247	+	0.842787i	$0.680913\pi$
$942$	33.7673	1.10020
$943$	−3.06487	−0.0998060
$944$	−0.484710	−0.0157760
$945$	−1.35819	−0.0441818
$946$	49.7316	1.61691
$947$	23.5418	0.765007	0.382504	−	0.923954i	$-0.375062\pi$
$947$	23.5418	0.765007	0.382504	+	0.923954i	$0.375062\pi$
$948$	−23.7606	−0.771710
$949$	2.06012	0.0668744
$950$	−4.01315	−0.130204
$951$	−9.41161	−0.305192
$952$	−11.6145	−0.376429
$953$	−32.7941	−1.06230	−0.531152	−	0.847276i	$-0.678241\pi$
$953$	−32.7941	−1.06230	−0.531152	+	0.847276i	$0.678241\pi$
$954$	7.27650	0.235585
$955$	2.67836	0.0866697
$956$	27.3144	0.883412
$957$	−5.85305	−0.189202
$958$	22.8027	0.736723
$959$	−22.5539	−0.728303
$960$	−12.0011	−0.387334
$961$	−25.7327	−0.830086
$962$	2.77803	0.0895673
$963$	11.4131	0.367782
$964$	42.9021	1.38178
$965$	−13.2967	−0.428037
$966$	1.81831	0.0585030
$967$	28.1946	0.906677	0.453339	−	0.891338i	$-0.350233\pi$
$967$	28.1946	0.906677	0.453339	+	0.891338i	$0.350233\pi$
$968$	−16.1155	−0.517971
$969$	11.7409	0.377172
$970$	26.5343	0.851966
$971$	29.7681	0.955303	0.477651	−	0.878549i	$-0.341488\pi$
$971$	29.7681	0.955303	0.477651	+	0.878549i	$0.341488\pi$
$972$	−2.63116	−0.0843944
$973$	−15.6940	−0.503126
$974$	−35.6224	−1.14141
$975$	0.182116	0.00583238
$976$	−8.35259	−0.267360
$977$	−34.7139	−1.11059	−0.555297	−	0.831652i	$-0.687396\pi$
$977$	−34.7139	−1.11059	−0.555297	+	0.831652i	$0.687396\pi$
$978$	7.28810	0.233048
$979$	2.10986	0.0674315
$980$	13.5645	0.433302
$981$	−8.70886	−0.278053
$982$	51.7139	1.65026
$983$	−13.9346	−0.444446	−0.222223	−	0.974996i	$-0.571331\pi$
$983$	−13.9346	−0.444446	−0.222223	+	0.974996i	$0.571331\pi$
$984$	6.69163	0.213321
$985$	15.9697	0.508836
$986$	16.5846	0.528160
$987$	−9.26524	−0.294916
$988$	−0.893585	−0.0284287
$989$	3.00654	0.0956024
$990$	10.2903	0.327048
$991$	6.71006	0.213152	0.106576	−	0.994305i	$-0.466011\pi$
$991$	6.71006	0.213152	0.106576	+	0.994305i	$0.466011\pi$
$992$	17.7886	0.564788
$993$	5.65320	0.179399
$994$	−38.7862	−1.23022
$995$	−25.1961	−0.798770
$996$	40.8379	1.29400
$997$	16.3338	0.517296	0.258648	−	0.965972i	$-0.416723\pi$
$997$	16.3338	0.517296	0.258648	+	0.965972i	$0.416723\pi$
$998$	61.5929	1.94969
$999$	−7.08834	−0.224265

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6015.2.a.f.1.7	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6015.2.a.f.1.7	✓	36	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:	\( N \)	\(=\)	\( 6015 = 3 \cdot 5 \cdot 401 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6015.a (trivial)

\(f(q)\)	\(=\)	\(q-2.15201 q^{2} -1.00000 q^{3} +2.63116 q^{4} -1.00000 q^{5} +2.15201 q^{6} -1.35819 q^{7} -1.35826 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.15201 q^{2} -1.00000 q^{3} +2.63116 q^{4} -1.00000 q^{5} +2.15201 q^{6} -1.35819 q^{7} -1.35826 q^{8} +1.00000 q^{9} +2.15201 q^{10} +4.78172 q^{11} -2.63116 q^{12} -0.182116 q^{13} +2.92283 q^{14} +1.00000 q^{15} -2.33933 q^{16} -6.29594 q^{17} -2.15201 q^{18} +1.86484 q^{19} -2.63116 q^{20} +1.35819 q^{21} -10.2903 q^{22} -0.622104 q^{23} +1.35826 q^{24} +1.00000 q^{25} +0.391916 q^{26} -1.00000 q^{27} -3.57360 q^{28} +1.22405 q^{29} -2.15201 q^{30} +2.29507 q^{31} +7.75077 q^{32} -4.78172 q^{33} +13.5489 q^{34} +1.35819 q^{35} +2.63116 q^{36} +7.08834 q^{37} -4.01315 q^{38} +0.182116 q^{39} +1.35826 q^{40} +4.92662 q^{41} -2.92283 q^{42} -4.83286 q^{43} +12.5814 q^{44} -1.00000 q^{45} +1.33878 q^{46} -6.82178 q^{47} +2.33933 q^{48} -5.15533 q^{49} -2.15201 q^{50} +6.29594 q^{51} -0.479176 q^{52} -3.38125 q^{53} +2.15201 q^{54} -4.78172 q^{55} +1.84477 q^{56} -1.86484 q^{57} -2.63417 q^{58} +0.207201 q^{59} +2.63116 q^{60} +3.57051 q^{61} -4.93902 q^{62} -1.35819 q^{63} -12.0011 q^{64} +0.182116 q^{65} +10.2903 q^{66} +7.23627 q^{67} -16.5656 q^{68} +0.622104 q^{69} -2.92283 q^{70} -13.2701 q^{71} -1.35826 q^{72} -11.3122 q^{73} -15.2542 q^{74} -1.00000 q^{75} +4.90668 q^{76} -6.49446 q^{77} -0.391916 q^{78} +9.03049 q^{79} +2.33933 q^{80} +1.00000 q^{81} -10.6022 q^{82} -15.5209 q^{83} +3.57360 q^{84} +6.29594 q^{85} +10.4004 q^{86} -1.22405 q^{87} -6.49481 q^{88} +0.441236 q^{89} +2.15201 q^{90} +0.247347 q^{91} -1.63685 q^{92} -2.29507 q^{93} +14.6806 q^{94} -1.86484 q^{95} -7.75077 q^{96} +12.3300 q^{97} +11.0943 q^{98} +4.78172 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 7 q^{2} - 36 q^{3} + 45 q^{4} - 36 q^{5} + 7 q^{6} + 2 q^{7} - 24 q^{8} + 36 q^{9}+O(q^{10}) \) 36 * q - 7 * q^2 - 36 * q^3 + 45 * q^4 - 36 * q^5 + 7 * q^6 + 2 * q^7 - 24 * q^8 + 36 * q^9	\( 36 q - 7 q^{2} - 36 q^{3} + 45 q^{4} - 36 q^{5} + 7 q^{6} + 2 q^{7} - 24 q^{8} + 36 q^{9} + 7 q^{10} - q^{11} - 45 q^{12} - 8 q^{13} - 4 q^{14} + 36 q^{15} + 63 q^{16} - 50 q^{17} - 7 q^{18} + 15 q^{19} - 45 q^{20} - 2 q^{21} + 7 q^{22} - 32 q^{23} + 24 q^{24} + 36 q^{25} - 12 q^{26} - 36 q^{27} - 10 q^{28} + 7 q^{29} - 7 q^{30} + 7 q^{31} - 50 q^{32} + q^{33} + 8 q^{34} - 2 q^{35} + 45 q^{36} - 10 q^{37} - 48 q^{38} + 8 q^{39} + 24 q^{40} - 31 q^{41} + 4 q^{42} + 27 q^{43} - 9 q^{44} - 36 q^{45} + 23 q^{46} - 46 q^{47} - 63 q^{48} + 48 q^{49} - 7 q^{50} + 50 q^{51} - 14 q^{52} - 39 q^{53} + 7 q^{54} + q^{55} - 29 q^{56} - 15 q^{57} - 26 q^{58} - 9 q^{59} + 45 q^{60} + 5 q^{61} - 65 q^{62} + 2 q^{63} + 90 q^{64} + 8 q^{65} - 7 q^{66} + 18 q^{67} - 128 q^{68} + 32 q^{69} + 4 q^{70} + 4 q^{71} - 24 q^{72} - 45 q^{73} - 22 q^{74} - 36 q^{75} + 26 q^{76} - 38 q^{77} + 12 q^{78} + 25 q^{79} - 63 q^{80} + 36 q^{81} - 5 q^{82} - 71 q^{83} + 10 q^{84} + 50 q^{85} + 3 q^{86} - 7 q^{87} - 9 q^{88} - 39 q^{89} + 7 q^{90} + 19 q^{91} - 95 q^{92} - 7 q^{93} + 16 q^{94} - 15 q^{95} + 50 q^{96} - 61 q^{97} - 76 q^{98} - q^{99}+O(q^{100}) \) 36 * q - 7 * q^2 - 36 * q^3 + 45 * q^4 - 36 * q^5 + 7 * q^6 + 2 * q^7 - 24 * q^8 + 36 * q^9 + 7 * q^10 - q^11 - 45 * q^12 - 8 * q^13 - 4 * q^14 + 36 * q^15 + 63 * q^16 - 50 * q^17 - 7 * q^18 + 15 * q^19 - 45 * q^20 - 2 * q^21 + 7 * q^22 - 32 * q^23 + 24 * q^24 + 36 * q^25 - 12 * q^26 - 36 * q^27 - 10 * q^28 + 7 * q^29 - 7 * q^30 + 7 * q^31 - 50 * q^32 + q^33 + 8 * q^34 - 2 * q^35 + 45 * q^36 - 10 * q^37 - 48 * q^38 + 8 * q^39 + 24 * q^40 - 31 * q^41 + 4 * q^42 + 27 * q^43 - 9 * q^44 - 36 * q^45 + 23 * q^46 - 46 * q^47 - 63 * q^48 + 48 * q^49 - 7 * q^50 + 50 * q^51 - 14 * q^52 - 39 * q^53 + 7 * q^54 + q^55 - 29 * q^56 - 15 * q^57 - 26 * q^58 - 9 * q^59 + 45 * q^60 + 5 * q^61 - 65 * q^62 + 2 * q^63 + 90 * q^64 + 8 * q^65 - 7 * q^66 + 18 * q^67 - 128 * q^68 + 32 * q^69 + 4 * q^70 + 4 * q^71 - 24 * q^72 - 45 * q^73 - 22 * q^74 - 36 * q^75 + 26 * q^76 - 38 * q^77 + 12 * q^78 + 25 * q^79 - 63 * q^80 + 36 * q^81 - 5 * q^82 - 71 * q^83 + 10 * q^84 + 50 * q^85 + 3 * q^86 - 7 * q^87 - 9 * q^88 - 39 * q^89 + 7 * q^90 + 19 * q^91 - 95 * q^92 - 7 * q^93 + 16 * q^94 - 15 * q^95 + 50 * q^96 - 61 * q^97 - 76 * q^98 - q^99

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