LMFDB - Embedded newform 6015.2.a.i.1.5

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:	$0$
Dimension:	$43$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
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)

$f(q)$	$=$	$q-2.53356 q^{2} +1.00000 q^{3} +4.41894 q^{4} +1.00000 q^{5} -2.53356 q^{6} +1.97049 q^{7} -6.12853 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.53356 q^{2} +1.00000 q^{3} +4.41894 q^{4} +1.00000 q^{5} -2.53356 q^{6} +1.97049 q^{7} -6.12853 q^{8} +1.00000 q^{9} -2.53356 q^{10} -0.158135 q^{11} +4.41894 q^{12} +2.27749 q^{13} -4.99236 q^{14} +1.00000 q^{15} +6.68913 q^{16} -6.99684 q^{17} -2.53356 q^{18} +8.08598 q^{19} +4.41894 q^{20} +1.97049 q^{21} +0.400645 q^{22} +4.62259 q^{23} -6.12853 q^{24} +1.00000 q^{25} -5.77015 q^{26} +1.00000 q^{27} +8.70748 q^{28} +8.37663 q^{29} -2.53356 q^{30} +6.03721 q^{31} -4.69027 q^{32} -0.158135 q^{33} +17.7269 q^{34} +1.97049 q^{35} +4.41894 q^{36} -1.90302 q^{37} -20.4863 q^{38} +2.27749 q^{39} -6.12853 q^{40} +1.34588 q^{41} -4.99236 q^{42} +5.41037 q^{43} -0.698789 q^{44} +1.00000 q^{45} -11.7116 q^{46} -7.64565 q^{47} +6.68913 q^{48} -3.11716 q^{49} -2.53356 q^{50} -6.99684 q^{51} +10.0641 q^{52} -5.03921 q^{53} -2.53356 q^{54} -0.158135 q^{55} -12.0762 q^{56} +8.08598 q^{57} -21.2227 q^{58} +1.77026 q^{59} +4.41894 q^{60} -11.0651 q^{61} -15.2957 q^{62} +1.97049 q^{63} -1.49517 q^{64} +2.27749 q^{65} +0.400645 q^{66} +11.0357 q^{67} -30.9186 q^{68} +4.62259 q^{69} -4.99236 q^{70} +10.3764 q^{71} -6.12853 q^{72} +9.55858 q^{73} +4.82141 q^{74} +1.00000 q^{75} +35.7315 q^{76} -0.311604 q^{77} -5.77015 q^{78} -8.60680 q^{79} +6.68913 q^{80} +1.00000 q^{81} -3.40987 q^{82} +7.62285 q^{83} +8.70748 q^{84} -6.99684 q^{85} -13.7075 q^{86} +8.37663 q^{87} +0.969135 q^{88} +2.00964 q^{89} -2.53356 q^{90} +4.48777 q^{91} +20.4269 q^{92} +6.03721 q^{93} +19.3707 q^{94} +8.08598 q^{95} -4.69027 q^{96} -7.58545 q^{97} +7.89752 q^{98} -0.158135 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 43 q + 3 q^{2} + 43 q^{3} + 61 q^{4} + 43 q^{5} + 3 q^{6} + 14 q^{7} + 18 q^{8} + 43 q^{9}+O(q^{10}) $ 43 * q + 3 * q^2 + 43 * q^3 + 61 * q^4 + 43 * q^5 + 3 * q^6 + 14 * q^7 + 18 * q^8 + 43 * q^9	\( 43 q + 3 q^{2} + 43 q^{3} + 61 q^{4} + 43 q^{5} + 3 q^{6} + 14 q^{7} + 18 q^{8} + 43 q^{9} + 3 q^{10} + 19 q^{11} + 61 q^{12} + 8 q^{13} + 6 q^{14} + 43 q^{15} + 85 q^{16} + 40 q^{17} + 3 q^{18} + 43 q^{19} + 61 q^{20} + 14 q^{21} + 19 q^{22} + 12 q^{23} + 18 q^{24} + 43 q^{25} + 43 q^{27} + 36 q^{28} + 41 q^{29} + 3 q^{30} + 33 q^{31} + 4 q^{32} + 19 q^{33} + 20 q^{34} + 14 q^{35} + 61 q^{36} + 12 q^{37} + 10 q^{38} + 8 q^{39} + 18 q^{40} + 47 q^{41} + 6 q^{42} + 73 q^{43} + 5 q^{44} + 43 q^{45} + 21 q^{46} + 32 q^{47} + 85 q^{48} + 87 q^{49} + 3 q^{50} + 40 q^{51} + 18 q^{52} + 17 q^{53} + 3 q^{54} + 19 q^{55} + 15 q^{56} + 43 q^{57} - 16 q^{58} + 21 q^{59} + 61 q^{60} + 77 q^{61} + 15 q^{62} + 14 q^{63} + 112 q^{64} + 8 q^{65} + 19 q^{66} + 26 q^{67} + 50 q^{68} + 12 q^{69} + 6 q^{70} + 2 q^{71} + 18 q^{72} + 49 q^{73} - 34 q^{74} + 43 q^{75} + 50 q^{76} - 2 q^{77} + 59 q^{79} + 85 q^{80} + 43 q^{81} - 45 q^{82} - 3 q^{83} + 36 q^{84} + 40 q^{85} - 35 q^{86} + 41 q^{87} - 13 q^{88} + 57 q^{89} + 3 q^{90} + 11 q^{91} - 9 q^{92} + 33 q^{93} + 52 q^{94} + 43 q^{95} + 4 q^{96} + 7 q^{97} - 32 q^{98} + 19 q^{99}+O(q^{100}) \) 43 * q + 3 * q^2 + 43 * q^3 + 61 * q^4 + 43 * q^5 + 3 * q^6 + 14 * q^7 + 18 * q^8 + 43 * q^9 + 3 * q^10 + 19 * q^11 + 61 * q^12 + 8 * q^13 + 6 * q^14 + 43 * q^15 + 85 * q^16 + 40 * q^17 + 3 * q^18 + 43 * q^19 + 61 * q^20 + 14 * q^21 + 19 * q^22 + 12 * q^23 + 18 * q^24 + 43 * q^25 + 43 * q^27 + 36 * q^28 + 41 * q^29 + 3 * q^30 + 33 * q^31 + 4 * q^32 + 19 * q^33 + 20 * q^34 + 14 * q^35 + 61 * q^36 + 12 * q^37 + 10 * q^38 + 8 * q^39 + 18 * q^40 + 47 * q^41 + 6 * q^42 + 73 * q^43 + 5 * q^44 + 43 * q^45 + 21 * q^46 + 32 * q^47 + 85 * q^48 + 87 * q^49 + 3 * q^50 + 40 * q^51 + 18 * q^52 + 17 * q^53 + 3 * q^54 + 19 * q^55 + 15 * q^56 + 43 * q^57 - 16 * q^58 + 21 * q^59 + 61 * q^60 + 77 * q^61 + 15 * q^62 + 14 * q^63 + 112 * q^64 + 8 * q^65 + 19 * q^66 + 26 * q^67 + 50 * q^68 + 12 * q^69 + 6 * q^70 + 2 * q^71 + 18 * q^72 + 49 * q^73 - 34 * q^74 + 43 * q^75 + 50 * q^76 - 2 * q^77 + 59 * q^79 + 85 * q^80 + 43 * q^81 - 45 * q^82 - 3 * q^83 + 36 * q^84 + 40 * q^85 - 35 * q^86 + 41 * q^87 - 13 * q^88 + 57 * q^89 + 3 * q^90 + 11 * q^91 - 9 * q^92 + 33 * q^93 + 52 * q^94 + 43 * q^95 + 4 * q^96 + 7 * q^97 - 32 * q^98 + 19 * 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 $

$2$	−2.53356	−1.79150	−0.895749	−	0.444559i	$-0.853360\pi$
$2$	−2.53356	−1.79150	−0.895749	+	0.444559i	$0.853360\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	4.41894	2.20947
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−2.53356	−1.03432
$7$	1.97049	0.744776	0.372388	−	0.928077i	$-0.378539\pi$
$7$	1.97049	0.744776	0.372388	+	0.928077i	$0.378539\pi$
$8$	−6.12853	−2.16676
$9$	1.00000	0.333333
$10$	−2.53356	−0.801183
$11$	−0.158135	−0.0476795	−0.0238398	−	0.999716i	$-0.507589\pi$
$11$	−0.158135	−0.0476795	−0.0238398	+	0.999716i	$0.507589\pi$
$12$	4.41894	1.27564
$13$	2.27749	0.631661	0.315830	−	0.948816i	$-0.397717\pi$
$13$	2.27749	0.631661	0.315830	+	0.948816i	$0.397717\pi$
$14$	−4.99236	−1.33427
$15$	1.00000	0.258199
$16$	6.68913	1.67228
$17$	−6.99684	−1.69698	−0.848492	−	0.529209i	$-0.822489\pi$
$17$	−6.99684	−1.69698	−0.848492	+	0.529209i	$0.822489\pi$
$18$	−2.53356	−0.597166
$19$	8.08598	1.85505	0.927526	−	0.373759i	$-0.121931\pi$
$19$	8.08598	1.85505	0.927526	+	0.373759i	$0.121931\pi$
$20$	4.41894	0.988104
$21$	1.97049	0.429997
$22$	0.400645	0.0854178
$23$	4.62259	0.963876	0.481938	−	0.876205i	$-0.339933\pi$
$23$	4.62259	0.963876	0.481938	+	0.876205i	$0.339933\pi$
$24$	−6.12853	−1.25098
$25$	1.00000	0.200000
$26$	−5.77015	−1.13162
$27$	1.00000	0.192450
$28$	8.70748	1.64556
$29$	8.37663	1.55550	0.777751	−	0.628573i	$-0.216361\pi$
$29$	8.37663	1.55550	0.777751	+	0.628573i	$0.216361\pi$
$30$	−2.53356	−0.462563
$31$	6.03721	1.08432	0.542158	−	0.840277i	$-0.317607\pi$
$31$	6.03721	1.08432	0.542158	+	0.840277i	$0.317607\pi$
$32$	−4.69027	−0.829130
$33$	−0.158135	−0.0275278
$34$	17.7269	3.04014
$35$	1.97049	0.333074
$36$	4.41894	0.736489
$37$	−1.90302	−0.312854	−0.156427	−	0.987690i	$-0.549998\pi$
$37$	−1.90302	−0.312854	−0.156427	+	0.987690i	$0.549998\pi$
$38$	−20.4863	−3.32332
$39$	2.27749	0.364689
$40$	−6.12853	−0.969005
$41$	1.34588	0.210191	0.105096	−	0.994462i	$-0.466485\pi$
$41$	1.34588	0.210191	0.105096	+	0.994462i	$0.466485\pi$
$42$	−4.99236	−0.770339
$43$	5.41037	0.825073	0.412537	−	0.910941i	$-0.364643\pi$
$43$	5.41037	0.825073	0.412537	+	0.910941i	$0.364643\pi$
$44$	−0.698789	−0.105346
$45$	1.00000	0.149071
$46$	−11.7116	−1.72678
$47$	−7.64565	−1.11523	−0.557616	−	0.830099i	$-0.688284\pi$
$47$	−7.64565	−1.11523	−0.557616	+	0.830099i	$0.688284\pi$
$48$	6.68913	0.965492
$49$	−3.11716	−0.445309
$50$	−2.53356	−0.358300
$51$	−6.99684	−0.979754
$52$	10.0641	1.39563
$53$	−5.03921	−0.692189	−0.346095	−	0.938200i	$-0.612492\pi$
$53$	−5.03921	−0.692189	−0.346095	+	0.938200i	$0.612492\pi$
$54$	−2.53356	−0.344774
$55$	−0.158135	−0.0213229
$56$	−12.0762	−1.61375
$57$	8.08598	1.07101
$58$	−21.2227	−2.78668
$59$	1.77026	0.230469	0.115234	−	0.993338i	$-0.463238\pi$
$59$	1.77026	0.230469	0.115234	+	0.993338i	$0.463238\pi$
$60$	4.41894	0.570482
$61$	−11.0651	−1.41674	−0.708370	−	0.705841i	$-0.750569\pi$
$61$	−11.0651	−1.41674	−0.708370	+	0.705841i	$0.750569\pi$
$62$	−15.2957	−1.94255
$63$	1.97049	0.248259
$64$	−1.49517	−0.186896
$65$	2.27749	0.282487
$66$	0.400645	0.0493160
$67$	11.0357	1.34823	0.674113	−	0.738628i	$-0.264526\pi$
$67$	11.0357	1.34823	0.674113	+	0.738628i	$0.264526\pi$
$68$	−30.9186	−3.74943
$69$	4.62259	0.556494
$70$	−4.99236	−0.596702
$71$	10.3764	1.23145	0.615724	−	0.787962i	$-0.288864\pi$
$71$	10.3764	1.23145	0.615724	+	0.787962i	$0.288864\pi$
$72$	−6.12853	−0.722254
$73$	9.55858	1.11875	0.559374	−	0.828916i	$-0.311042\pi$
$73$	9.55858	1.11875	0.559374	+	0.828916i	$0.311042\pi$
$74$	4.82141	0.560477
$75$	1.00000	0.115470
$76$	35.7315	4.09868
$77$	−0.311604	−0.0355106
$78$	−5.77015	−0.653341
$79$	−8.60680	−0.968341	−0.484171	−	0.874974i	$-0.660879\pi$
$79$	−8.60680	−0.968341	−0.484171	+	0.874974i	$0.660879\pi$
$80$	6.68913	0.747867
$81$	1.00000	0.111111
$82$	−3.40987	−0.376557
$83$	7.62285	0.836717	0.418358	−	0.908282i	$-0.362606\pi$
$83$	7.62285	0.836717	0.418358	+	0.908282i	$0.362606\pi$
$84$	8.70748	0.950064
$85$	−6.99684	−0.758914
$86$	−13.7075	−1.47812
$87$	8.37663	0.898069
$88$	0.969135	0.103310
$89$	2.00964	0.213022	0.106511	−	0.994312i	$-0.466032\pi$
$89$	2.00964	0.213022	0.106511	+	0.994312i	$0.466032\pi$
$90$	−2.53356	−0.267061
$91$	4.48777	0.470446
$92$	20.4269	2.12965
$93$	6.03721	0.626030
$94$	19.3707	1.99794
$95$	8.08598	0.829605
$96$	−4.69027	−0.478698
$97$	−7.58545	−0.770186	−0.385093	−	0.922878i	$-0.625831\pi$
$97$	−7.58545	−0.770186	−0.385093	+	0.922878i	$0.625831\pi$
$98$	7.89752	0.797770
$99$	−0.158135	−0.0158932
$100$	4.41894	0.441894
$101$	−12.8000	−1.27364	−0.636822	−	0.771011i	$-0.719751\pi$
$101$	−12.8000	−1.27364	−0.636822	+	0.771011i	$0.719751\pi$
$102$	17.7269	1.75523
$103$	9.28910	0.915283	0.457641	−	0.889137i	$-0.348694\pi$
$103$	9.28910	0.915283	0.457641	+	0.889137i	$0.348694\pi$
$104$	−13.9576	−1.36866
$105$	1.97049	0.192300
$106$	12.7672	1.24006
$107$	−17.9855	−1.73872	−0.869360	−	0.494180i	$-0.835468\pi$
$107$	−17.9855	−1.73872	−0.869360	+	0.494180i	$0.835468\pi$
$108$	4.41894	0.425212
$109$	−0.980898	−0.0939530	−0.0469765	−	0.998896i	$-0.514959\pi$
$109$	−0.980898	−0.0939530	−0.0469765	+	0.998896i	$0.514959\pi$
$110$	0.400645	0.0382000
$111$	−1.90302	−0.180626
$112$	13.1809	1.24548
$113$	−9.61883	−0.904863	−0.452432	−	0.891799i	$-0.649443\pi$
$113$	−9.61883	−0.904863	−0.452432	+	0.891799i	$0.649443\pi$
$114$	−20.4863	−1.91872
$115$	4.62259	0.431059
$116$	37.0158	3.43683
$117$	2.27749	0.210554
$118$	−4.48507	−0.412884
$119$	−13.7872	−1.26387
$120$	−6.12853	−0.559455
$121$	−10.9750	−0.997727
$122$	28.0341	2.53809
$123$	1.34588	0.121354
$124$	26.6781	2.39576
$125$	1.00000	0.0894427
$126$	−4.99236	−0.444755
$127$	−13.9335	−1.23640	−0.618200	−	0.786021i	$-0.712138\pi$
$127$	−13.9335	−1.23640	−0.618200	+	0.786021i	$0.712138\pi$
$128$	13.1686	1.16395
$129$	5.41037	0.476356
$130$	−5.77015	−0.506076
$131$	18.2315	1.59289	0.796447	−	0.604709i	$-0.206710\pi$
$131$	18.2315	1.59289	0.796447	+	0.604709i	$0.206710\pi$
$132$	−0.698789	−0.0608217
$133$	15.9334	1.38160
$134$	−27.9596	−2.41534
$135$	1.00000	0.0860663
$136$	42.8803	3.67696
$137$	−7.12050	−0.608345	−0.304172	−	0.952617i	$-0.598380\pi$
$137$	−7.12050	−0.608345	−0.304172	+	0.952617i	$0.598380\pi$
$138$	−11.7116	−0.996959
$139$	18.3963	1.56035	0.780175	−	0.625561i	$-0.215130\pi$
$139$	18.3963	1.56035	0.780175	+	0.625561i	$0.215130\pi$
$140$	8.70748	0.735916
$141$	−7.64565	−0.643880
$142$	−26.2892	−2.20614
$143$	−0.360150	−0.0301173
$144$	6.68913	0.557427
$145$	8.37663	0.695641
$146$	−24.2173	−2.00423
$147$	−3.11716	−0.257099
$148$	−8.40931	−0.691241
$149$	17.3618	1.42233	0.711167	−	0.703023i	$-0.248167\pi$
$149$	17.3618	1.42233	0.711167	+	0.703023i	$0.248167\pi$
$150$	−2.53356	−0.206864
$151$	−16.7680	−1.36456	−0.682279	−	0.731092i	$-0.739011\pi$
$151$	−16.7680	−1.36456	−0.682279	+	0.731092i	$0.739011\pi$
$152$	−49.5552	−4.01945
$153$	−6.99684	−0.565661
$154$	0.789468	0.0636171
$155$	6.03721	0.484921
$156$	10.0641	0.805770
$157$	18.2345	1.45527	0.727634	−	0.685965i	$-0.240620\pi$
$157$	18.2345	1.45527	0.727634	+	0.685965i	$0.240620\pi$
$158$	21.8059	1.73478
$159$	−5.03921	−0.399636
$160$	−4.69027	−0.370798
$161$	9.10877	0.717872
$162$	−2.53356	−0.199055
$163$	7.93870	0.621807	0.310904	−	0.950441i	$-0.399368\pi$
$163$	7.93870	0.621807	0.310904	+	0.950441i	$0.399368\pi$
$164$	5.94736	0.464411
$165$	−0.158135	−0.0123108
$166$	−19.3130	−1.49898
$167$	−6.30284	−0.487728	−0.243864	−	0.969809i	$-0.578415\pi$
$167$	−6.30284	−0.487728	−0.243864	+	0.969809i	$0.578415\pi$
$168$	−12.0762	−0.931700
$169$	−7.81306	−0.601005
$170$	17.7269	1.35959
$171$	8.08598	0.618351
$172$	23.9081	1.82297
$173$	−14.4731	−1.10037	−0.550186	−	0.835042i	$-0.685443\pi$
$173$	−14.4731	−1.10037	−0.550186	+	0.835042i	$0.685443\pi$
$174$	−21.2227	−1.60889
$175$	1.97049	0.148955
$176$	−1.05779	−0.0797336
$177$	1.77026	0.133061
$178$	−5.09155	−0.381628
$179$	19.1815	1.43369	0.716847	−	0.697230i	$-0.245584\pi$
$179$	19.1815	1.43369	0.716847	+	0.697230i	$0.245584\pi$
$180$	4.41894	0.329368
$181$	−10.6959	−0.795021	−0.397511	−	0.917598i	$-0.630126\pi$
$181$	−10.6959	−0.795021	−0.397511	+	0.917598i	$0.630126\pi$
$182$	−11.3700	−0.842803
$183$	−11.0651	−0.817956
$184$	−28.3297	−2.08849
$185$	−1.90302	−0.139912
$186$	−15.2957	−1.12153
$187$	1.10645	0.0809113
$188$	−33.7857	−2.46407
$189$	1.97049	0.143332
$190$	−20.4863	−1.48624
$191$	7.81154	0.565223	0.282611	−	0.959234i	$-0.408799\pi$
$191$	7.81154	0.565223	0.282611	+	0.959234i	$0.408799\pi$
$192$	−1.49517	−0.107905
$193$	23.7699	1.71100	0.855498	−	0.517806i	$-0.173251\pi$
$193$	23.7699	1.71100	0.855498	+	0.517806i	$0.173251\pi$
$194$	19.2182	1.37979
$195$	2.27749	0.163094
$196$	−13.7745	−0.983895
$197$	14.0060	0.997887	0.498943	−	0.866635i	$-0.333722\pi$
$197$	14.0060	0.997887	0.498943	+	0.866635i	$0.333722\pi$
$198$	0.400645	0.0284726
$199$	11.0362	0.782339	0.391169	−	0.920319i	$-0.372071\pi$
$199$	11.0362	0.782339	0.391169	+	0.920319i	$0.372071\pi$
$200$	−6.12853	−0.433352
$201$	11.0357	0.778398
$202$	32.4295	2.28173
$203$	16.5061	1.15850
$204$	−30.9186	−2.16474
$205$	1.34588	0.0940003
$206$	−23.5345	−1.63973
$207$	4.62259	0.321292
$208$	15.2344	1.05631
$209$	−1.27868	−0.0884480
$210$	−4.99236	−0.344506
$211$	10.9238	0.752025	0.376013	−	0.926615i	$-0.377295\pi$
$211$	10.9238	0.752025	0.376013	+	0.926615i	$0.377295\pi$
$212$	−22.2680	−1.52937
$213$	10.3764	0.710977
$214$	45.5673	3.11491
$215$	5.41037	0.368984
$216$	−6.12853	−0.416993
$217$	11.8963	0.807572
$218$	2.48516	0.168317
$219$	9.55858	0.645909
$220$	−0.698789	−0.0471123
$221$	−15.9352	−1.07192
$222$	4.82141	0.323592
$223$	−12.7616	−0.854582	−0.427291	−	0.904114i	$-0.640532\pi$
$223$	−12.7616	−0.854582	−0.427291	+	0.904114i	$0.640532\pi$
$224$	−9.24214	−0.617516
$225$	1.00000	0.0666667
$226$	24.3699	1.62106
$227$	−7.23907	−0.480474	−0.240237	−	0.970714i	$-0.577225\pi$
$227$	−7.23907	−0.480474	−0.240237	+	0.970714i	$0.577225\pi$
$228$	35.7315	2.36637
$229$	12.3926	0.818928	0.409464	−	0.912326i	$-0.365716\pi$
$229$	12.3926	0.818928	0.409464	+	0.912326i	$0.365716\pi$
$230$	−11.7116	−0.772241
$231$	−0.311604	−0.0205020
$232$	−51.3364	−3.37040
$233$	−9.74378	−0.638336	−0.319168	−	0.947698i	$-0.603403\pi$
$233$	−9.74378	−0.638336	−0.319168	+	0.947698i	$0.603403\pi$
$234$	−5.77015	−0.377207
$235$	−7.64565	−0.498747
$236$	7.82268	0.509213
$237$	−8.60680	−0.559072
$238$	34.9308	2.26423
$239$	7.56242	0.489172	0.244586	−	0.969628i	$-0.421348\pi$
$239$	7.56242	0.489172	0.244586	+	0.969628i	$0.421348\pi$
$240$	6.68913	0.431781
$241$	−0.738193	−0.0475512	−0.0237756	−	0.999717i	$-0.507569\pi$
$241$	−0.738193	−0.0475512	−0.0237756	+	0.999717i	$0.507569\pi$
$242$	27.8058	1.78743
$243$	1.00000	0.0641500
$244$	−48.8960	−3.13024
$245$	−3.11716	−0.199148
$246$	−3.40987	−0.217405
$247$	18.4157	1.17176
$248$	−36.9992	−2.34945
$249$	7.62285	0.483079
$250$	−2.53356	−0.160237
$251$	11.9734	0.755757	0.377879	−	0.925855i	$-0.376654\pi$
$251$	11.9734	0.755757	0.377879	+	0.925855i	$0.376654\pi$
$252$	8.70748	0.548520
$253$	−0.730993	−0.0459571
$254$	35.3014	2.21501
$255$	−6.99684	−0.438159
$256$	−30.3732	−1.89833
$257$	−29.6338	−1.84851	−0.924253	−	0.381780i	$-0.875311\pi$
$257$	−29.6338	−1.84851	−0.924253	+	0.381780i	$0.875311\pi$
$258$	−13.7075	−0.853392
$259$	−3.74988	−0.233006
$260$	10.0641	0.624147
$261$	8.37663	0.518500
$262$	−46.1906	−2.85367
$263$	28.1396	1.73516	0.867580	−	0.497298i	$-0.165674\pi$
$263$	28.1396	1.73516	0.867580	+	0.497298i	$0.165674\pi$
$264$	0.969135	0.0596461
$265$	−5.03921	−0.309556
$266$	−40.3682	−2.47513
$267$	2.00964	0.122988
$268$	48.7661	2.97886
$269$	−3.81053	−0.232332	−0.116166	−	0.993230i	$-0.537060\pi$
$269$	−3.81053	−0.232332	−0.116166	+	0.993230i	$0.537060\pi$
$270$	−2.53356	−0.154188
$271$	5.69943	0.346216	0.173108	−	0.984903i	$-0.444619\pi$
$271$	5.69943	0.346216	0.173108	+	0.984903i	$0.444619\pi$
$272$	−46.8028	−2.83783
$273$	4.48777	0.271612
$274$	18.0402	1.08985
$275$	−0.158135	−0.00953590
$276$	20.4269	1.22956
$277$	−27.0050	−1.62258	−0.811288	−	0.584647i	$-0.801233\pi$
$277$	−27.0050	−1.62258	−0.811288	+	0.584647i	$0.801233\pi$
$278$	−46.6081	−2.79537
$279$	6.03721	0.361439
$280$	−12.0762	−0.721692
$281$	−17.1116	−1.02079	−0.510397	−	0.859939i	$-0.670502\pi$
$281$	−17.1116	−1.02079	−0.510397	+	0.859939i	$0.670502\pi$
$282$	19.3707	1.15351
$283$	−17.5695	−1.04440	−0.522200	−	0.852823i	$-0.674889\pi$
$283$	−17.5695	−1.04440	−0.522200	+	0.852823i	$0.674889\pi$
$284$	45.8525	2.72084
$285$	8.08598	0.478972
$286$	0.912463	0.0539551
$287$	2.65205	0.156545
$288$	−4.69027	−0.276377
$289$	31.9558	1.87975
$290$	−21.2227	−1.24624
$291$	−7.58545	−0.444667
$292$	42.2388	2.47184
$293$	−17.6934	−1.03366	−0.516829	−	0.856088i	$-0.672888\pi$
$293$	−17.6934	−1.03366	−0.516829	+	0.856088i	$0.672888\pi$
$294$	7.89752	0.460593
$295$	1.77026	0.103069
$296$	11.6627	0.677880
$297$	−0.158135	−0.00917593
$298$	−43.9872	−2.54811
$299$	10.5279	0.608843
$300$	4.41894	0.255127
$301$	10.6611	0.614495
$302$	42.4827	2.44460
$303$	−12.8000	−0.735338
$304$	54.0882	3.10217
$305$	−11.0651	−0.633586
$306$	17.7269	1.01338
$307$	7.97925	0.455400	0.227700	−	0.973731i	$-0.426879\pi$
$307$	7.97925	0.455400	0.227700	+	0.973731i	$0.426879\pi$
$308$	−1.37696	−0.0784594
$309$	9.28910	0.528439
$310$	−15.2957	−0.868735
$311$	−8.17612	−0.463626	−0.231813	−	0.972760i	$-0.574466\pi$
$311$	−8.17612	−0.463626	−0.231813	+	0.972760i	$0.574466\pi$
$312$	−13.9576	−0.790195
$313$	−3.86533	−0.218481	−0.109241	−	0.994015i	$-0.534842\pi$
$313$	−3.86533	−0.218481	−0.109241	+	0.994015i	$0.534842\pi$
$314$	−46.1981	−2.60711
$315$	1.97049	0.111025
$316$	−38.0329	−2.13952
$317$	−5.78149	−0.324721	−0.162360	−	0.986732i	$-0.551911\pi$
$317$	−5.78149	−0.324721	−0.162360	+	0.986732i	$0.551911\pi$
$318$	12.7672	0.715947
$319$	−1.32464	−0.0741655
$320$	−1.49517	−0.0835826
$321$	−17.9855	−1.00385
$322$	−23.0776	−1.28607
$323$	−56.5764	−3.14799
$324$	4.41894	0.245496
$325$	2.27749	0.126332
$326$	−20.1132	−1.11397
$327$	−0.980898	−0.0542438
$328$	−8.24826	−0.455434
$329$	−15.0657	−0.830599
$330$	0.400645	0.0220548
$331$	−8.42544	−0.463104	−0.231552	−	0.972823i	$-0.574380\pi$
$331$	−8.42544	−0.463104	−0.231552	+	0.972823i	$0.574380\pi$
$332$	33.6849	1.84870
$333$	−1.90302	−0.104285
$334$	15.9686	0.873764
$335$	11.0357	0.602945
$336$	13.1809	0.719076
$337$	−13.3758	−0.728628	−0.364314	−	0.931276i	$-0.618697\pi$
$337$	−13.3758	−0.728628	−0.364314	+	0.931276i	$0.618697\pi$
$338$	19.7949	1.07670
$339$	−9.61883	−0.522423
$340$	−30.9186	−1.67680
$341$	−0.954695	−0.0516996
$342$	−20.4863	−1.10777
$343$	−19.9358	−1.07643
$344$	−33.1576	−1.78774
$345$	4.62259	0.248872
$346$	36.6686	1.97132
$347$	15.4165	0.827599	0.413800	−	0.910368i	$-0.364201\pi$
$347$	15.4165	0.827599	0.413800	+	0.910368i	$0.364201\pi$
$348$	37.0158	1.98426
$349$	14.8281	0.793728	0.396864	−	0.917878i	$-0.370099\pi$
$349$	14.8281	0.793728	0.396864	+	0.917878i	$0.370099\pi$
$350$	−4.99236	−0.266853
$351$	2.27749	0.121563
$352$	0.741696	0.0395325
$353$	−20.3738	−1.08439	−0.542194	−	0.840253i	$-0.682406\pi$
$353$	−20.3738	−1.08439	−0.542194	+	0.840253i	$0.682406\pi$
$354$	−4.48507	−0.238379
$355$	10.3764	0.550720
$356$	8.88048	0.470664
$357$	−13.7872	−0.729697
$358$	−48.5976	−2.56846
$359$	−5.16739	−0.272724	−0.136362	−	0.990659i	$-0.543541\pi$
$359$	−5.16739	−0.272724	−0.136362	+	0.990659i	$0.543541\pi$
$360$	−6.12853	−0.323002
$361$	46.3831	2.44122
$362$	27.0988	1.42428
$363$	−10.9750	−0.576038
$364$	19.8312	1.03944
$365$	9.55858	0.500319
$366$	28.0341	1.46537
$367$	−13.8201	−0.721404	−0.360702	−	0.932681i	$-0.617463\pi$
$367$	−13.8201	−0.721404	−0.360702	+	0.932681i	$0.617463\pi$
$368$	30.9211	1.61187
$369$	1.34588	0.0700637
$370$	4.82141	0.250653
$371$	−9.92973	−0.515526
$372$	26.6781	1.38319
$373$	5.33973	0.276481	0.138240	−	0.990399i	$-0.455855\pi$
$373$	5.33973	0.276481	0.138240	+	0.990399i	$0.455855\pi$
$374$	−2.80325	−0.144953
$375$	1.00000	0.0516398
$376$	46.8566	2.41644
$377$	19.0777	0.982549
$378$	−4.99236	−0.256780
$379$	−1.23206	−0.0632866	−0.0316433	−	0.999499i	$-0.510074\pi$
$379$	−1.23206	−0.0632866	−0.0316433	+	0.999499i	$0.510074\pi$
$380$	35.7315	1.83298
$381$	−13.9335	−0.713835
$382$	−19.7910	−1.01260
$383$	−23.9784	−1.22524	−0.612619	−	0.790378i	$-0.709884\pi$
$383$	−23.9784	−1.22524	−0.612619	+	0.790378i	$0.709884\pi$
$384$	13.1686	0.672010
$385$	−0.311604	−0.0158808
$386$	−60.2226	−3.06525
$387$	5.41037	0.275024
$388$	−33.5196	−1.70170
$389$	13.8416	0.701798	0.350899	−	0.936413i	$-0.385876\pi$
$389$	13.8416	0.701798	0.350899	+	0.936413i	$0.385876\pi$
$390$	−5.77015	−0.292183
$391$	−32.3435	−1.63568
$392$	19.1036	0.964877
$393$	18.2315	0.919657
$394$	−35.4851	−1.78771
$395$	−8.60680	−0.433055
$396$	−0.698789	−0.0351155
$397$	−13.6426	−0.684703	−0.342352	−	0.939572i	$-0.611223\pi$
$397$	−13.6426	−0.684703	−0.342352	+	0.939572i	$0.611223\pi$
$398$	−27.9610	−1.40156
$399$	15.9334	0.797666
$400$	6.68913	0.334456
$401$	1.00000	0.0499376
$401$	1.00000	0.0499376
$402$	−27.9596	−1.39450
$403$	13.7497	0.684920
$404$	−56.5622	−2.81407
$405$	1.00000	0.0496904
$406$	−41.8192	−2.07545
$407$	0.300933	0.0149167
$408$	42.8803	2.12289
$409$	1.16973	0.0578396	0.0289198	−	0.999582i	$-0.490793\pi$
$409$	1.16973	0.0578396	0.0289198	+	0.999582i	$0.490793\pi$
$410$	−3.40987	−0.168401
$411$	−7.12050	−0.351228
$412$	41.0480	2.02229
$413$	3.48829	0.171648
$414$	−11.7116	−0.575594
$415$	7.62285	0.374191
$416$	−10.6820	−0.523729
$417$	18.3963	0.900869
$418$	3.23961	0.158454
$419$	−34.4624	−1.68360	−0.841800	−	0.539789i	$-0.818504\pi$
$419$	−34.4624	−1.68360	−0.841800	+	0.539789i	$0.818504\pi$
$420$	8.70748	0.424882
$421$	20.2664	0.987726	0.493863	−	0.869540i	$-0.335585\pi$
$421$	20.2664	0.987726	0.493863	+	0.869540i	$0.335585\pi$
$422$	−27.6761	−1.34725
$423$	−7.64565	−0.371744
$424$	30.8829	1.49981
$425$	−6.99684	−0.339397
$426$	−26.2892	−1.27371
$427$	−21.8037	−1.05515
$428$	−79.4766	−3.84165
$429$	−0.360150	−0.0173882
$430$	−13.7075	−0.661034
$431$	33.3866	1.60818	0.804088	−	0.594510i	$-0.202654\pi$
$431$	33.3866	1.60818	0.804088	+	0.594510i	$0.202654\pi$
$432$	6.68913	0.321831
$433$	−2.68684	−0.129121	−0.0645605	−	0.997914i	$-0.520565\pi$
$433$	−2.68684	−0.129121	−0.0645605	+	0.997914i	$0.520565\pi$
$434$	−30.1400	−1.44677
$435$	8.37663	0.401629
$436$	−4.33452	−0.207586
$437$	37.3782	1.78804
$438$	−24.2173	−1.15715
$439$	30.7101	1.46571	0.732856	−	0.680384i	$-0.238187\pi$
$439$	30.7101	1.46571	0.732856	+	0.680384i	$0.238187\pi$
$440$	0.969135	0.0462017
$441$	−3.11716	−0.148436
$442$	40.3728	1.92034
$443$	−4.31524	−0.205023	−0.102512	−	0.994732i	$-0.532688\pi$
$443$	−4.31524	−0.205023	−0.102512	+	0.994732i	$0.532688\pi$
$444$	−8.40931	−0.399088
$445$	2.00964	0.0952662
$446$	32.3324	1.53098
$447$	17.3618	0.821185
$448$	−2.94622	−0.139196
$449$	−16.3222	−0.770291	−0.385145	−	0.922856i	$-0.625849\pi$
$449$	−16.3222	−0.770291	−0.385145	+	0.922856i	$0.625849\pi$
$450$	−2.53356	−0.119433
$451$	−0.212831	−0.0100218
$452$	−42.5050	−1.99927
$453$	−16.7680	−0.787828
$454$	18.3406	0.860768
$455$	4.48777	0.210390
$456$	−49.5552	−2.32063
$457$	−34.5484	−1.61610	−0.808052	−	0.589111i	$-0.799478\pi$
$457$	−34.5484	−1.61610	−0.808052	+	0.589111i	$0.799478\pi$
$458$	−31.3975	−1.46711
$459$	−6.99684	−0.326585
$460$	20.4269	0.952410
$461$	17.4683	0.813579	0.406789	−	0.913522i	$-0.366648\pi$
$461$	17.4683	0.813579	0.406789	+	0.913522i	$0.366648\pi$
$462$	0.789468	0.0367294
$463$	29.1091	1.35281	0.676407	−	0.736528i	$-0.263536\pi$
$463$	29.1091	1.35281	0.676407	+	0.736528i	$0.263536\pi$
$464$	56.0324	2.60124
$465$	6.03721	0.279969
$466$	24.6865	1.14358
$467$	9.85725	0.456139	0.228070	−	0.973645i	$-0.426759\pi$
$467$	9.85725	0.456139	0.228070	+	0.973645i	$0.426759\pi$
$468$	10.0641	0.465211
$469$	21.7458	1.00413
$470$	19.3707	0.893505
$471$	18.2345	0.840199
$472$	−10.8491	−0.499370
$473$	−0.855569	−0.0393391
$474$	21.8059	1.00158
$475$	8.08598	0.371010
$476$	−60.9249	−2.79249
$477$	−5.03921	−0.230730
$478$	−19.1599	−0.876352
$479$	5.12854	0.234329	0.117165	−	0.993113i	$-0.462620\pi$
$479$	5.12854	0.234329	0.117165	+	0.993113i	$0.462620\pi$
$480$	−4.69027	−0.214080
$481$	−4.33409	−0.197617
$482$	1.87026	0.0851879
$483$	9.10877	0.414464
$484$	−48.4978	−2.20445
$485$	−7.58545	−0.344438
$486$	−2.53356	−0.114925
$487$	2.82110	0.127836	0.0639180	−	0.997955i	$-0.479640\pi$
$487$	2.82110	0.127836	0.0639180	+	0.997955i	$0.479640\pi$
$488$	67.8127	3.06974
$489$	7.93870	0.359001
$490$	7.89752	0.356774
$491$	19.5534	0.882432	0.441216	−	0.897401i	$-0.354547\pi$
$491$	19.5534	0.882432	0.441216	+	0.897401i	$0.354547\pi$
$492$	5.94736	0.268128
$493$	−58.6100	−2.63966
$494$	−46.6573	−2.09921
$495$	−0.158135	−0.00710764
$496$	40.3837	1.81328
$497$	20.4465	0.917153
$498$	−19.3130	−0.865435
$499$	−17.5681	−0.786454	−0.393227	−	0.919441i	$-0.628641\pi$
$499$	−17.5681	−0.786454	−0.393227	+	0.919441i	$0.628641\pi$
$500$	4.41894	0.197621
$501$	−6.30284	−0.281590
$502$	−30.3355	−1.35394
$503$	33.8950	1.51130	0.755652	−	0.654973i	$-0.227320\pi$
$503$	33.8950	1.51130	0.755652	+	0.654973i	$0.227320\pi$
$504$	−12.0762	−0.537917
$505$	−12.8000	−0.569591
$506$	1.85202	0.0823322
$507$	−7.81306	−0.346990
$508$	−61.5713	−2.73178
$509$	31.7876	1.40896	0.704481	−	0.709723i	$-0.251180\pi$
$509$	31.7876	1.40896	0.704481	+	0.709723i	$0.251180\pi$
$510$	17.7269	0.784962
$511$	18.8351	0.833216
$512$	50.6152	2.23690
$513$	8.08598	0.357005
$514$	75.0791	3.31160
$515$	9.28910	0.409327
$516$	23.9081	1.05249
$517$	1.20905	0.0531738
$518$	9.50055	0.417430
$519$	−14.4731	−0.635300
$520$	−13.9576	−0.612082
$521$	3.31702	0.145321	0.0726607	−	0.997357i	$-0.476851\pi$
$521$	3.31702	0.145321	0.0726607	+	0.997357i	$0.476851\pi$
$522$	−21.2227	−0.928893
$523$	17.7122	0.774499	0.387250	−	0.921975i	$-0.373425\pi$
$523$	17.7122	0.774499	0.387250	+	0.921975i	$0.373425\pi$
$524$	80.5638	3.51945
$525$	1.97049	0.0859993
$526$	−71.2933	−3.10854
$527$	−42.2414	−1.84007
$528$	−1.05779	−0.0460342
$529$	−1.63168	−0.0709425
$530$	12.7672	0.554570
$531$	1.77026	0.0768229
$532$	70.4086	3.05260
$533$	3.06522	0.132769
$534$	−5.09155	−0.220333
$535$	−17.9855	−0.777579
$536$	−67.6326	−2.92128
$537$	19.1815	0.827744
$538$	9.65422	0.416223
$539$	0.492932	0.0212321
$540$	4.41894	0.190161
$541$	23.5337	1.01179	0.505897	−	0.862594i	$-0.331162\pi$
$541$	23.5337	1.01179	0.505897	+	0.862594i	$0.331162\pi$
$542$	−14.4399	−0.620245
$543$	−10.6959	−0.459006
$544$	32.8171	1.40702
$545$	−0.980898	−0.0420170
$546$	−11.3700	−0.486593
$547$	34.4038	1.47100	0.735500	−	0.677525i	$-0.236947\pi$
$547$	34.4038	1.47100	0.735500	+	0.677525i	$0.236947\pi$
$548$	−31.4650	−1.34412
$549$	−11.0651	−0.472247
$550$	0.400645	0.0170836
$551$	67.7333	2.88554
$552$	−28.3297	−1.20579
$553$	−16.9596	−0.721197
$554$	68.4189	2.90684
$555$	−1.90302	−0.0807785
$556$	81.2919	3.44754
$557$	−18.3966	−0.779490	−0.389745	−	0.920923i	$-0.627437\pi$
$557$	−18.3966	−0.779490	−0.389745	+	0.920923i	$0.627437\pi$
$558$	−15.2957	−0.647517
$559$	12.3220	0.521166
$560$	13.1809	0.556994
$561$	1.10645	0.0467142
$562$	43.3534	1.82875
$563$	14.1516	0.596421	0.298210	−	0.954500i	$-0.403610\pi$
$563$	14.1516	0.596421	0.298210	+	0.954500i	$0.403610\pi$
$564$	−33.7857	−1.42263
$565$	−9.61883	−0.404667
$566$	44.5135	1.87104
$567$	1.97049	0.0827529
$568$	−63.5918	−2.66825
$569$	−20.0450	−0.840330	−0.420165	−	0.907448i	$-0.638028\pi$
$569$	−20.0450	−0.840330	−0.420165	+	0.907448i	$0.638028\pi$
$570$	−20.4863	−0.858079
$571$	−5.26503	−0.220335	−0.110167	−	0.993913i	$-0.535139\pi$
$571$	−5.26503	−0.220335	−0.110167	+	0.993913i	$0.535139\pi$
$572$	−1.59148	−0.0665432
$573$	7.81154	0.326332
$574$	−6.71912	−0.280451
$575$	4.62259	0.192775
$576$	−1.49517	−0.0622988
$577$	−4.07425	−0.169613	−0.0848065	−	0.996397i	$-0.527027\pi$
$577$	−4.07425	−0.169613	−0.0848065	+	0.996397i	$0.527027\pi$
$578$	−80.9620	−3.36758
$579$	23.7699	0.987844
$580$	37.0158	1.53700
$581$	15.0208	0.623167
$582$	19.2182	0.796621
$583$	0.796876	0.0330032
$584$	−58.5800	−2.42406
$585$	2.27749	0.0941624
$586$	44.8273	1.85180
$587$	46.8724	1.93463	0.967316	−	0.253573i	$-0.0816058\pi$
$587$	46.8724	1.93463	0.967316	+	0.253573i	$0.0816058\pi$
$588$	−13.7745	−0.568052
$589$	48.8168	2.01146
$590$	−4.48507	−0.184647
$591$	14.0060	0.576130
$592$	−12.7295	−0.523180
$593$	−37.0130	−1.51994	−0.759971	−	0.649956i	$-0.774787\pi$
$593$	−37.0130	−1.51994	−0.759971	+	0.649956i	$0.774787\pi$
$594$	0.400645	0.0164387
$595$	−13.7872	−0.565221
$596$	76.7207	3.14260
$597$	11.0362	0.451683
$598$	−26.6730	−1.09074
$599$	18.6150	0.760587	0.380294	−	0.924866i	$-0.375823\pi$
$599$	18.6150	0.760587	0.380294	+	0.924866i	$0.375823\pi$
$600$	−6.12853	−0.250196
$601$	17.3673	0.708426	0.354213	−	0.935165i	$-0.384749\pi$
$601$	17.3673	0.708426	0.354213	+	0.935165i	$0.384749\pi$
$602$	−27.0105	−1.10087
$603$	11.0357	0.449409
$604$	−74.0966	−3.01495
$605$	−10.9750	−0.446197
$606$	32.4295	1.31736
$607$	37.5400	1.52370	0.761851	−	0.647753i	$-0.224291\pi$
$607$	37.5400	1.52370	0.761851	+	0.647753i	$0.224291\pi$
$608$	−37.9254	−1.53808
$609$	16.5061	0.668860
$610$	28.0341	1.13507
$611$	−17.4129	−0.704449
$612$	−30.9186	−1.24981
$613$	−8.96887	−0.362249	−0.181125	−	0.983460i	$-0.557974\pi$
$613$	−8.96887	−0.362249	−0.181125	+	0.983460i	$0.557974\pi$
$614$	−20.2159	−0.815848
$615$	1.34588	0.0542711
$616$	1.90967	0.0769429
$617$	−5.99680	−0.241422	−0.120711	−	0.992688i	$-0.538517\pi$
$617$	−5.99680	−0.241422	−0.120711	+	0.992688i	$0.538517\pi$
$618$	−23.5345	−0.946697
$619$	−18.2735	−0.734476	−0.367238	−	0.930127i	$-0.619697\pi$
$619$	−18.2735	−0.734476	−0.367238	+	0.930127i	$0.619697\pi$
$620$	26.6781	1.07142
$621$	4.62259	0.185498
$622$	20.7147	0.830585
$623$	3.95998	0.158653
$624$	15.2344	0.609864
$625$	1.00000	0.0400000
$626$	9.79305	0.391409
$627$	−1.27868	−0.0510655
$628$	80.5769	3.21537
$629$	13.3151	0.530908
$630$	−4.99236	−0.198901
$631$	12.5044	0.497792	0.248896	−	0.968530i	$-0.419932\pi$
$631$	12.5044	0.497792	0.248896	+	0.968530i	$0.419932\pi$
$632$	52.7470	2.09816
$633$	10.9238	0.434182
$634$	14.6478	0.581737
$635$	−13.9335	−0.552935
$636$	−22.2680	−0.882982
$637$	−7.09929	−0.281284
$638$	3.35605	0.132867
$639$	10.3764	0.410482
$640$	13.1686	0.520536
$641$	32.2586	1.27414	0.637069	−	0.770807i	$-0.280147\pi$
$641$	32.2586	1.27414	0.637069	+	0.770807i	$0.280147\pi$
$642$	45.5673	1.79840
$643$	9.90049	0.390437	0.195219	−	0.980760i	$-0.437458\pi$
$643$	9.90049	0.390437	0.195219	+	0.980760i	$0.437458\pi$
$644$	40.2511	1.58612
$645$	5.41037	0.213033
$646$	143.340	5.63963
$647$	−42.1385	−1.65664	−0.828318	−	0.560258i	$-0.810702\pi$
$647$	−42.1385	−1.65664	−0.828318	+	0.560258i	$0.810702\pi$
$648$	−6.12853	−0.240751
$649$	−0.279941	−0.0109886
$650$	−5.77015	−0.226324
$651$	11.8963	0.466252
$652$	35.0806	1.37386
$653$	−24.6257	−0.963679	−0.481839	−	0.876260i	$-0.660031\pi$
$653$	−24.6257	−0.963679	−0.481839	+	0.876260i	$0.660031\pi$
$654$	2.48516	0.0971776
$655$	18.2315	0.712364
$656$	9.00276	0.351499
$657$	9.55858	0.372916
$658$	38.1699	1.48802
$659$	−33.5682	−1.30763	−0.653816	−	0.756653i	$-0.726833\pi$
$659$	−33.5682	−1.30763	−0.653816	+	0.756653i	$0.726833\pi$
$660$	−0.698789	−0.0272003
$661$	7.95823	0.309539	0.154770	−	0.987951i	$-0.450536\pi$
$661$	7.95823	0.309539	0.154770	+	0.987951i	$0.450536\pi$
$662$	21.3464	0.829650
$663$	−15.9352	−0.618872
$664$	−46.7169	−1.81297
$665$	15.9334	0.617870
$666$	4.82141	0.186826
$667$	38.7217	1.49931
$668$	−27.8518	−1.07762
$669$	−12.7616	−0.493393
$670$	−27.9596	−1.08018
$671$	1.74978	0.0675495
$672$	−9.24214	−0.356523
$673$	−39.3036	−1.51504	−0.757521	−	0.652810i	$-0.773590\pi$
$673$	−39.3036	−1.51504	−0.757521	+	0.652810i	$0.773590\pi$
$674$	33.8885	1.30534
$675$	1.00000	0.0384900
$676$	−34.5254	−1.32790
$677$	39.4000	1.51427	0.757133	−	0.653261i	$-0.226599\pi$
$677$	39.4000	1.51427	0.757133	+	0.653261i	$0.226599\pi$
$678$	24.3699	0.935920
$679$	−14.9471	−0.573616
$680$	42.8803	1.64439
$681$	−7.23907	−0.277402
$682$	2.41878	0.0926198
$683$	−4.60584	−0.176237	−0.0881187	−	0.996110i	$-0.528085\pi$
$683$	−4.60584	−0.176237	−0.0881187	+	0.996110i	$0.528085\pi$
$684$	35.7315	1.36623
$685$	−7.12050	−0.272060
$686$	50.5086	1.92843
$687$	12.3926	0.472808
$688$	36.1906	1.37976
$689$	−11.4767	−0.437229
$690$	−11.7116	−0.445854
$691$	−44.7663	−1.70299	−0.851495	−	0.524363i	$-0.824304\pi$
$691$	−44.7663	−1.70299	−0.851495	+	0.524363i	$0.824304\pi$
$692$	−63.9559	−2.43124
$693$	−0.311604	−0.0118369
$694$	−39.0586	−1.48264
$695$	18.3963	0.697810
$696$	−51.3364	−1.94590
$697$	−9.41691	−0.356691
$698$	−37.5678	−1.42196
$699$	−9.74378	−0.368543
$700$	8.70748	0.329112
$701$	−17.0872	−0.645376	−0.322688	−	0.946505i	$-0.604586\pi$
$701$	−17.0872	−0.645376	−0.322688	+	0.946505i	$0.604586\pi$
$702$	−5.77015	−0.217780
$703$	−15.3878	−0.580360
$704$	0.236439	0.00891113
$705$	−7.64565	−0.287952
$706$	51.6183	1.94268
$707$	−25.2222	−0.948579
$708$	7.82268	0.293994
$709$	7.48333	0.281042	0.140521	−	0.990078i	$-0.455122\pi$
$709$	7.48333	0.281042	0.140521	+	0.990078i	$0.455122\pi$
$710$	−26.2892	−0.986614
$711$	−8.60680	−0.322780
$712$	−12.3161	−0.461567
$713$	27.9076	1.04515
$714$	34.9308	1.30725
$715$	−0.360150	−0.0134689
$716$	84.7620	3.16770
$717$	7.56242	0.282424
$718$	13.0919	0.488585
$719$	−35.2839	−1.31587	−0.657935	−	0.753075i	$-0.728570\pi$
$719$	−35.2839	−1.31587	−0.657935	+	0.753075i	$0.728570\pi$
$720$	6.68913	0.249289
$721$	18.3041	0.681681
$722$	−117.515	−4.37344
$723$	−0.738193	−0.0274537
$724$	−47.2646	−1.75657
$725$	8.37663	0.311100
$726$	27.8058	1.03197
$727$	−10.9530	−0.406226	−0.203113	−	0.979155i	$-0.565106\pi$
$727$	−10.9530	−0.406226	−0.203113	+	0.979155i	$0.565106\pi$
$728$	−27.5034	−1.01934
$729$	1.00000	0.0370370
$730$	−24.2173	−0.896321
$731$	−37.8555	−1.40014
$732$	−48.8960	−1.80725
$733$	28.3261	1.04625	0.523125	−	0.852256i	$-0.324766\pi$
$733$	28.3261	1.04625	0.523125	+	0.852256i	$0.324766\pi$
$734$	35.0141	1.29239
$735$	−3.11716	−0.114978
$736$	−21.6812	−0.799179
$737$	−1.74513	−0.0642827
$738$	−3.40987	−0.125519
$739$	27.6533	1.01724	0.508622	−	0.860990i	$-0.330155\pi$
$739$	27.6533	1.01724	0.508622	+	0.860990i	$0.330155\pi$
$740$	−8.40931	−0.309132
$741$	18.4157	0.676518
$742$	25.1576	0.923564
$743$	8.52719	0.312832	0.156416	−	0.987691i	$-0.450006\pi$
$743$	8.52719	0.312832	0.156416	+	0.987691i	$0.450006\pi$
$744$	−36.9992	−1.35646
$745$	17.3618	0.636087
$746$	−13.5285	−0.495315
$747$	7.62285	0.278906
$748$	4.88931	0.178771
$749$	−35.4402	−1.29496
$750$	−2.53356	−0.0925126
$751$	−28.2063	−1.02926	−0.514632	−	0.857411i	$-0.672071\pi$
$751$	−28.2063	−1.02926	−0.514632	+	0.857411i	$0.672071\pi$
$752$	−51.1427	−1.86498
$753$	11.9734	0.436337
$754$	−48.3344	−1.76024
$755$	−16.7680	−0.610249
$756$	8.70748	0.316688
$757$	−34.9985	−1.27204	−0.636020	−	0.771672i	$-0.719421\pi$
$757$	−34.9985	−1.27204	−0.636020	+	0.771672i	$0.719421\pi$
$758$	3.12150	0.113378
$759$	−0.730993	−0.0265334
$760$	−49.5552	−1.79755
$761$	−7.19585	−0.260849	−0.130425	−	0.991458i	$-0.541634\pi$
$761$	−7.19585	−0.260849	−0.130425	+	0.991458i	$0.541634\pi$
$762$	35.3014	1.27884
$763$	−1.93285	−0.0699739
$764$	34.5187	1.24884
$765$	−6.99684	−0.252971
$766$	60.7507	2.19501
$767$	4.03175	0.145578
$768$	−30.3732	−1.09600
$769$	−3.00949	−0.108525	−0.0542625	−	0.998527i	$-0.517281\pi$
$769$	−3.00949	−0.108525	−0.0542625	+	0.998527i	$0.517281\pi$
$770$	0.789468	0.0284504
$771$	−29.6338	−1.06724
$772$	105.038	3.78039
$773$	52.4861	1.88779	0.943897	−	0.330240i	$-0.107130\pi$
$773$	52.4861	1.88779	0.943897	+	0.330240i	$0.107130\pi$
$774$	−13.7075	−0.492706
$775$	6.03721	0.216863
$776$	46.4877	1.66881
$777$	−3.74988	−0.134526
$778$	−35.0686	−1.25727
$779$	10.8828	0.389915
$780$	10.0641	0.360351
$781$	−1.64087	−0.0587148
$782$	81.9443	2.93032
$783$	8.37663	0.299356
$784$	−20.8511	−0.744681
$785$	18.2345	0.650816
$786$	−46.1906	−1.64757
$787$	−4.65725	−0.166013	−0.0830065	−	0.996549i	$-0.526452\pi$
$787$	−4.65725	−0.166013	−0.0830065	+	0.996549i	$0.526452\pi$
$788$	61.8916	2.20480
$789$	28.1396	1.00180
$790$	21.8059	0.775818
$791$	−18.9538	−0.673921
$792$	0.969135	0.0344367
$793$	−25.2006	−0.894899
$794$	34.5644	1.22665
$795$	−5.03921	−0.178722
$796$	48.7685	1.72855
$797$	20.0022	0.708514	0.354257	−	0.935148i	$-0.384734\pi$
$797$	20.0022	0.708514	0.354257	+	0.935148i	$0.384734\pi$
$798$	−40.3682	−1.42902
$799$	53.4954	1.89253
$800$	−4.69027	−0.165826
$801$	2.00964	0.0710072
$802$	−2.53356	−0.0894632
$803$	−1.51155	−0.0533413
$804$	48.7661	1.71985
$805$	9.10877	0.321042
$806$	−34.8356	−1.22703
$807$	−3.81053	−0.134137
$808$	78.4449	2.75968
$809$	−22.8308	−0.802690	−0.401345	−	0.915927i	$-0.631457\pi$
$809$	−22.8308	−0.802690	−0.401345	+	0.915927i	$0.631457\pi$
$810$	−2.53356	−0.0890203
$811$	−50.1389	−1.76061	−0.880307	−	0.474404i	$-0.842663\pi$
$811$	−50.1389	−1.76061	−0.880307	+	0.474404i	$0.842663\pi$
$812$	72.9394	2.55967
$813$	5.69943	0.199888
$814$	−0.762434	−0.0267233
$815$	7.93870	0.278081
$816$	−46.8028	−1.63842
$817$	43.7481	1.53055
$818$	−2.96359	−0.103620
$819$	4.48777	0.156815
$820$	5.94736	0.207691
$821$	18.5280	0.646631	0.323316	−	0.946291i	$-0.395202\pi$
$821$	18.5280	0.646631	0.323316	+	0.946291i	$0.395202\pi$
$822$	18.0402	0.629225
$823$	33.9547	1.18359	0.591793	−	0.806090i	$-0.298420\pi$
$823$	33.9547	1.18359	0.591793	+	0.806090i	$0.298420\pi$
$824$	−56.9285	−1.98320
$825$	−0.158135	−0.00550556
$826$	−8.83780	−0.307506
$827$	49.5879	1.72434	0.862170	−	0.506619i	$-0.169105\pi$
$827$	49.5879	1.72434	0.862170	+	0.506619i	$0.169105\pi$
$828$	20.4269	0.709885
$829$	−55.0364	−1.91149	−0.955747	−	0.294190i	$-0.904950\pi$
$829$	−55.0364	−1.91149	−0.955747	+	0.294190i	$0.904950\pi$
$830$	−19.3130	−0.670363
$831$	−27.0050	−0.936794
$832$	−3.40523	−0.118055
$833$	21.8103	0.755681
$834$	−46.6081	−1.61391
$835$	−6.30284	−0.218119
$836$	−5.65039	−0.195423
$837$	6.03721	0.208677
$838$	87.3127	3.01617
$839$	6.55209	0.226203	0.113102	−	0.993583i	$-0.463921\pi$
$839$	6.55209	0.226203	0.113102	+	0.993583i	$0.463921\pi$
$840$	−12.0762	−0.416669
$841$	41.1680	1.41958
$842$	−51.3463	−1.76951
$843$	−17.1116	−0.589356
$844$	48.2716	1.66158
$845$	−7.81306	−0.268777
$846$	19.3707	0.665980
$847$	−21.6261	−0.743083
$848$	−33.7079	−1.15754
$849$	−17.5695	−0.602985
$850$	17.7269	0.608029
$851$	−8.79686	−0.301552
$852$	45.8525	1.57088
$853$	48.6287	1.66501	0.832507	−	0.554014i	$-0.186905\pi$
$853$	48.6287	1.66501	0.832507	+	0.554014i	$0.186905\pi$
$854$	55.2410	1.89031
$855$	8.08598	0.276535
$856$	110.224	3.76739
$857$	36.4417	1.24483	0.622413	−	0.782689i	$-0.286152\pi$
$857$	36.4417	1.24483	0.622413	+	0.782689i	$0.286152\pi$
$858$	0.912463	0.0311510
$859$	−4.10026	−0.139899	−0.0699496	−	0.997551i	$-0.522284\pi$
$859$	−4.10026	−0.139899	−0.0699496	+	0.997551i	$0.522284\pi$
$860$	23.9081	0.815258
$861$	2.65205	0.0903815
$862$	−84.5870	−2.88105
$863$	1.75895	0.0598755	0.0299377	−	0.999552i	$-0.490469\pi$
$863$	1.75895	0.0598755	0.0299377	+	0.999552i	$0.490469\pi$
$864$	−4.69027	−0.159566
$865$	−14.4731	−0.492101
$866$	6.80726	0.231320
$867$	31.9558	1.08528
$868$	52.5689	1.78431
$869$	1.36104	0.0461700
$870$	−21.2227	−0.719517
$871$	25.1336	0.851621
$872$	6.01146	0.203574
$873$	−7.58545	−0.256729
$874$	−94.6999	−3.20327
$875$	1.97049	0.0666148
$876$	42.2388	1.42712
$877$	48.1536	1.62603	0.813015	−	0.582243i	$-0.197825\pi$
$877$	48.1536	1.62603	0.813015	+	0.582243i	$0.197825\pi$
$878$	−77.8058	−2.62582
$879$	−17.6934	−0.596783
$880$	−1.05779	−0.0356579
$881$	42.9221	1.44608	0.723041	−	0.690805i	$-0.242744\pi$
$881$	42.9221	1.44608	0.723041	+	0.690805i	$0.242744\pi$
$882$	7.89752	0.265923
$883$	−1.26017	−0.0424083	−0.0212041	−	0.999775i	$-0.506750\pi$
$883$	−1.26017	−0.0424083	−0.0212041	+	0.999775i	$0.506750\pi$
$884$	−70.4167	−2.36837
$885$	1.77026	0.0595067
$886$	10.9329	0.367299
$887$	33.3916	1.12118	0.560590	−	0.828093i	$-0.310574\pi$
$887$	33.3916	1.12118	0.560590	+	0.828093i	$0.310574\pi$
$888$	11.6627	0.391374
$889$	−27.4559	−0.920841
$890$	−5.09155	−0.170669
$891$	−0.158135	−0.00529772
$892$	−56.3929	−1.88817
$893$	−61.8226	−2.06882
$894$	−43.9872	−1.47115
$895$	19.1815	0.641168
$896$	25.9487	0.866886
$897$	10.5279	0.351516
$898$	41.3532	1.37998
$899$	50.5715	1.68665
$900$	4.41894	0.147298
$901$	35.2586	1.17463
$902$	0.539220	0.0179541
$903$	10.6611	0.354779
$904$	58.9492	1.96062
$905$	−10.6959	−0.355544
$906$	42.4827	1.41139
$907$	26.4730	0.879022	0.439511	−	0.898237i	$-0.355152\pi$
$907$	26.4730	0.879022	0.439511	+	0.898237i	$0.355152\pi$
$908$	−31.9890	−1.06159
$909$	−12.8000	−0.424548
$910$	−11.3700	−0.376913
$911$	−4.23219	−0.140219	−0.0701094	−	0.997539i	$-0.522335\pi$
$911$	−4.23219	−0.140219	−0.0701094	+	0.997539i	$0.522335\pi$
$912$	54.0882	1.79104
$913$	−1.20544	−0.0398943
$914$	87.5304	2.89525
$915$	−11.0651	−0.365801
$916$	54.7623	1.80940
$917$	35.9250	1.18635
$918$	17.7269	0.585076
$919$	−28.8289	−0.950978	−0.475489	−	0.879722i	$-0.657729\pi$
$919$	−28.8289	−0.950978	−0.475489	+	0.879722i	$0.657729\pi$
$920$	−28.3297	−0.934001
$921$	7.97925	0.262925
$922$	−44.2570	−1.45753
$923$	23.6320	0.777857
$924$	−1.37696	−0.0452986
$925$	−1.90302	−0.0625708
$926$	−73.7496	−2.42356
$927$	9.28910	0.305094
$928$	−39.2886	−1.28971
$929$	−49.6970	−1.63051	−0.815254	−	0.579104i	$-0.803402\pi$
$929$	−49.6970	−1.63051	−0.815254	+	0.579104i	$0.803402\pi$
$930$	−15.2957	−0.501564
$931$	−25.2053	−0.826071
$932$	−43.0571	−1.41038
$933$	−8.17612	−0.267674
$934$	−24.9740	−0.817173
$935$	1.10645	0.0361847
$936$	−13.9576	−0.456219
$937$	45.4098	1.48347	0.741736	−	0.670692i	$-0.234003\pi$
$937$	45.4098	1.48347	0.741736	+	0.670692i	$0.234003\pi$
$938$	−55.0943	−1.79889
$939$	−3.86533	−0.126140
$940$	−33.7857	−1.10197
$941$	43.3625	1.41358	0.706789	−	0.707424i	$-0.250143\pi$
$941$	43.3625	1.41358	0.706789	+	0.707424i	$0.250143\pi$
$942$	−46.1981	−1.50522
$943$	6.22145	0.202598
$944$	11.8415	0.385409
$945$	1.97049	0.0641001
$946$	2.16764	0.0704759
$947$	8.60285	0.279555	0.139778	−	0.990183i	$-0.455361\pi$
$947$	8.60285	0.279555	0.139778	+	0.990183i	$0.455361\pi$
$948$	−38.0329	−1.23525
$949$	21.7695	0.706669
$950$	−20.4863	−0.664665
$951$	−5.78149	−0.187478
$952$	84.4954	2.73851
$953$	−6.50664	−0.210771	−0.105385	−	0.994431i	$-0.533608\pi$
$953$	−6.50664	−0.210771	−0.105385	+	0.994431i	$0.533608\pi$
$954$	12.7672	0.413352
$955$	7.81154	0.252775
$956$	33.4179	1.08081
$957$	−1.32464	−0.0428195
$958$	−12.9935	−0.419800
$959$	−14.0309	−0.453081
$960$	−1.49517	−0.0482564
$961$	5.44795	0.175740
$962$	10.9807	0.354032
$963$	−17.9855	−0.579573
$964$	−3.26203	−0.105063
$965$	23.7699	0.765181
$966$	−23.0776	−0.742511
$967$	5.15068	0.165635	0.0828173	−	0.996565i	$-0.473608\pi$
$967$	5.15068	0.165635	0.0828173	+	0.996565i	$0.473608\pi$
$968$	67.2605	2.16184
$969$	−56.5764	−1.81749
$970$	19.2182	0.617060
$971$	13.8023	0.442936	0.221468	−	0.975168i	$-0.428915\pi$
$971$	13.8023	0.442936	0.221468	+	0.975168i	$0.428915\pi$
$972$	4.41894	0.141737
$973$	36.2497	1.16211
$974$	−7.14742	−0.229018
$975$	2.27749	0.0729379
$976$	−74.0158	−2.36919
$977$	50.9753	1.63084	0.815422	−	0.578867i	$-0.196505\pi$
$977$	50.9753	1.63084	0.815422	+	0.578867i	$0.196505\pi$
$978$	−20.1132	−0.643149
$979$	−0.317795	−0.0101568
$980$	−13.7745	−0.440011
$981$	−0.980898	−0.0313177
$982$	−49.5397	−1.58088
$983$	−37.1280	−1.18420	−0.592100	−	0.805864i	$-0.701701\pi$
$983$	−37.1280	−1.18420	−0.592100	+	0.805864i	$0.701701\pi$
$984$	−8.24826	−0.262945
$985$	14.0060	0.446268
$986$	148.492	4.72895
$987$	−15.0657	−0.479546
$988$	81.3779	2.58897
$989$	25.0099	0.795269
$990$	0.400645	0.0127333
$991$	−61.6336	−1.95786	−0.978928	−	0.204207i	$-0.934538\pi$
$991$	−61.6336	−1.95786	−0.978928	+	0.204207i	$0.934538\pi$
$992$	−28.3162	−0.899039
$993$	−8.42544	−0.267373
$994$	−51.8026	−1.64308
$995$	11.0362	0.349872
$996$	33.6849	1.06735
$997$	10.8579	0.343873	0.171937	−	0.985108i	$-0.444998\pi$
$997$	10.8579	0.343873	0.171937	+	0.985108i	$0.444998\pi$
$998$	44.5098	1.40893
$999$	−1.90302	−0.0602088

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6015.2.a.i.1.5	✓	43

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6015.2.a.i.1.5	✓	43	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)

\(f(q)\)	\(=\)	\(q-2.53356 q^{2} +1.00000 q^{3} +4.41894 q^{4} +1.00000 q^{5} -2.53356 q^{6} +1.97049 q^{7} -6.12853 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.53356 q^{2} +1.00000 q^{3} +4.41894 q^{4} +1.00000 q^{5} -2.53356 q^{6} +1.97049 q^{7} -6.12853 q^{8} +1.00000 q^{9} -2.53356 q^{10} -0.158135 q^{11} +4.41894 q^{12} +2.27749 q^{13} -4.99236 q^{14} +1.00000 q^{15} +6.68913 q^{16} -6.99684 q^{17} -2.53356 q^{18} +8.08598 q^{19} +4.41894 q^{20} +1.97049 q^{21} +0.400645 q^{22} +4.62259 q^{23} -6.12853 q^{24} +1.00000 q^{25} -5.77015 q^{26} +1.00000 q^{27} +8.70748 q^{28} +8.37663 q^{29} -2.53356 q^{30} +6.03721 q^{31} -4.69027 q^{32} -0.158135 q^{33} +17.7269 q^{34} +1.97049 q^{35} +4.41894 q^{36} -1.90302 q^{37} -20.4863 q^{38} +2.27749 q^{39} -6.12853 q^{40} +1.34588 q^{41} -4.99236 q^{42} +5.41037 q^{43} -0.698789 q^{44} +1.00000 q^{45} -11.7116 q^{46} -7.64565 q^{47} +6.68913 q^{48} -3.11716 q^{49} -2.53356 q^{50} -6.99684 q^{51} +10.0641 q^{52} -5.03921 q^{53} -2.53356 q^{54} -0.158135 q^{55} -12.0762 q^{56} +8.08598 q^{57} -21.2227 q^{58} +1.77026 q^{59} +4.41894 q^{60} -11.0651 q^{61} -15.2957 q^{62} +1.97049 q^{63} -1.49517 q^{64} +2.27749 q^{65} +0.400645 q^{66} +11.0357 q^{67} -30.9186 q^{68} +4.62259 q^{69} -4.99236 q^{70} +10.3764 q^{71} -6.12853 q^{72} +9.55858 q^{73} +4.82141 q^{74} +1.00000 q^{75} +35.7315 q^{76} -0.311604 q^{77} -5.77015 q^{78} -8.60680 q^{79} +6.68913 q^{80} +1.00000 q^{81} -3.40987 q^{82} +7.62285 q^{83} +8.70748 q^{84} -6.99684 q^{85} -13.7075 q^{86} +8.37663 q^{87} +0.969135 q^{88} +2.00964 q^{89} -2.53356 q^{90} +4.48777 q^{91} +20.4269 q^{92} +6.03721 q^{93} +19.3707 q^{94} +8.08598 q^{95} -4.69027 q^{96} -7.58545 q^{97} +7.89752 q^{98} -0.158135 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 43 q + 3 q^{2} + 43 q^{3} + 61 q^{4} + 43 q^{5} + 3 q^{6} + 14 q^{7} + 18 q^{8} + 43 q^{9}+O(q^{10}) \) 43 * q + 3 * q^2 + 43 * q^3 + 61 * q^4 + 43 * q^5 + 3 * q^6 + 14 * q^7 + 18 * q^8 + 43 * q^9	\( 43 q + 3 q^{2} + 43 q^{3} + 61 q^{4} + 43 q^{5} + 3 q^{6} + 14 q^{7} + 18 q^{8} + 43 q^{9} + 3 q^{10} + 19 q^{11} + 61 q^{12} + 8 q^{13} + 6 q^{14} + 43 q^{15} + 85 q^{16} + 40 q^{17} + 3 q^{18} + 43 q^{19} + 61 q^{20} + 14 q^{21} + 19 q^{22} + 12 q^{23} + 18 q^{24} + 43 q^{25} + 43 q^{27} + 36 q^{28} + 41 q^{29} + 3 q^{30} + 33 q^{31} + 4 q^{32} + 19 q^{33} + 20 q^{34} + 14 q^{35} + 61 q^{36} + 12 q^{37} + 10 q^{38} + 8 q^{39} + 18 q^{40} + 47 q^{41} + 6 q^{42} + 73 q^{43} + 5 q^{44} + 43 q^{45} + 21 q^{46} + 32 q^{47} + 85 q^{48} + 87 q^{49} + 3 q^{50} + 40 q^{51} + 18 q^{52} + 17 q^{53} + 3 q^{54} + 19 q^{55} + 15 q^{56} + 43 q^{57} - 16 q^{58} + 21 q^{59} + 61 q^{60} + 77 q^{61} + 15 q^{62} + 14 q^{63} + 112 q^{64} + 8 q^{65} + 19 q^{66} + 26 q^{67} + 50 q^{68} + 12 q^{69} + 6 q^{70} + 2 q^{71} + 18 q^{72} + 49 q^{73} - 34 q^{74} + 43 q^{75} + 50 q^{76} - 2 q^{77} + 59 q^{79} + 85 q^{80} + 43 q^{81} - 45 q^{82} - 3 q^{83} + 36 q^{84} + 40 q^{85} - 35 q^{86} + 41 q^{87} - 13 q^{88} + 57 q^{89} + 3 q^{90} + 11 q^{91} - 9 q^{92} + 33 q^{93} + 52 q^{94} + 43 q^{95} + 4 q^{96} + 7 q^{97} - 32 q^{98} + 19 q^{99}+O(q^{100}) \) 43 * q + 3 * q^2 + 43 * q^3 + 61 * q^4 + 43 * q^5 + 3 * q^6 + 14 * q^7 + 18 * q^8 + 43 * q^9 + 3 * q^10 + 19 * q^11 + 61 * q^12 + 8 * q^13 + 6 * q^14 + 43 * q^15 + 85 * q^16 + 40 * q^17 + 3 * q^18 + 43 * q^19 + 61 * q^20 + 14 * q^21 + 19 * q^22 + 12 * q^23 + 18 * q^24 + 43 * q^25 + 43 * q^27 + 36 * q^28 + 41 * q^29 + 3 * q^30 + 33 * q^31 + 4 * q^32 + 19 * q^33 + 20 * q^34 + 14 * q^35 + 61 * q^36 + 12 * q^37 + 10 * q^38 + 8 * q^39 + 18 * q^40 + 47 * q^41 + 6 * q^42 + 73 * q^43 + 5 * q^44 + 43 * q^45 + 21 * q^46 + 32 * q^47 + 85 * q^48 + 87 * q^49 + 3 * q^50 + 40 * q^51 + 18 * q^52 + 17 * q^53 + 3 * q^54 + 19 * q^55 + 15 * q^56 + 43 * q^57 - 16 * q^58 + 21 * q^59 + 61 * q^60 + 77 * q^61 + 15 * q^62 + 14 * q^63 + 112 * q^64 + 8 * q^65 + 19 * q^66 + 26 * q^67 + 50 * q^68 + 12 * q^69 + 6 * q^70 + 2 * q^71 + 18 * q^72 + 49 * q^73 - 34 * q^74 + 43 * q^75 + 50 * q^76 - 2 * q^77 + 59 * q^79 + 85 * q^80 + 43 * q^81 - 45 * q^82 - 3 * q^83 + 36 * q^84 + 40 * q^85 - 35 * q^86 + 41 * q^87 - 13 * q^88 + 57 * q^89 + 3 * q^90 + 11 * q^91 - 9 * q^92 + 33 * q^93 + 52 * q^94 + 43 * q^95 + 4 * q^96 + 7 * q^97 - 32 * q^98 + 19 * q^99

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