LMFDB - Embedded newform 4031.2.a.e.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4031,2,Mod(1,4031)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4031, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4031.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4031 = 29 \cdot 139 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4031.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:	$32.1876970548$
Analytic rank:	$0$
Dimension:	$103$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Character	$\chi$	$=$	4031.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.20982 q^{2} -3.43245 q^{3} +2.88331 q^{4} +3.18051 q^{5} +7.58510 q^{6} +4.63810 q^{7} -1.95196 q^{8} +8.78169 q^{9} +O(q^{10})$	\(q-2.20982 q^{2} -3.43245 q^{3} +2.88331 q^{4} +3.18051 q^{5} +7.58510 q^{6} +4.63810 q^{7} -1.95196 q^{8} +8.78169 q^{9} -7.02836 q^{10} +5.96685 q^{11} -9.89681 q^{12} -2.55639 q^{13} -10.2494 q^{14} -10.9169 q^{15} -1.45314 q^{16} +3.08767 q^{17} -19.4060 q^{18} -0.685938 q^{19} +9.17040 q^{20} -15.9200 q^{21} -13.1857 q^{22} +7.54619 q^{23} +6.70000 q^{24} +5.11564 q^{25} +5.64916 q^{26} -19.8454 q^{27} +13.3731 q^{28} -1.00000 q^{29} +24.1245 q^{30} +1.64314 q^{31} +7.11510 q^{32} -20.4809 q^{33} -6.82319 q^{34} +14.7515 q^{35} +25.3204 q^{36} +3.25824 q^{37} +1.51580 q^{38} +8.77467 q^{39} -6.20822 q^{40} +6.64257 q^{41} +35.1804 q^{42} -9.32244 q^{43} +17.2043 q^{44} +27.9303 q^{45} -16.6757 q^{46} -7.07988 q^{47} +4.98783 q^{48} +14.5119 q^{49} -11.3047 q^{50} -10.5983 q^{51} -7.37086 q^{52} +2.14930 q^{53} +43.8547 q^{54} +18.9776 q^{55} -9.05338 q^{56} +2.35444 q^{57} +2.20982 q^{58} +13.1088 q^{59} -31.4769 q^{60} -2.28175 q^{61} -3.63105 q^{62} +40.7303 q^{63} -12.8168 q^{64} -8.13062 q^{65} +45.2591 q^{66} +13.0569 q^{67} +8.90271 q^{68} -25.9019 q^{69} -32.5982 q^{70} -6.74370 q^{71} -17.1415 q^{72} +0.584169 q^{73} -7.20012 q^{74} -17.5592 q^{75} -1.97777 q^{76} +27.6748 q^{77} -19.3905 q^{78} +8.11201 q^{79} -4.62173 q^{80} +41.7731 q^{81} -14.6789 q^{82} -5.13561 q^{83} -45.9024 q^{84} +9.82036 q^{85} +20.6009 q^{86} +3.43245 q^{87} -11.6470 q^{88} -0.784141 q^{89} -61.7209 q^{90} -11.8568 q^{91} +21.7580 q^{92} -5.64000 q^{93} +15.6453 q^{94} -2.18163 q^{95} -24.4222 q^{96} -1.48449 q^{97} -32.0688 q^{98} +52.3990 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 103 q + q^{2} + 2 q^{3} + 127 q^{4} + 9 q^{5} + 19 q^{6} + 18 q^{7} + 149 q^{9}+O(q^{10}) $ 103 * q + q^2 + 2 * q^3 + 127 * q^4 + 9 * q^5 + 19 * q^6 + 18 * q^7 + 149 * q^9	\( 103 q + q^{2} + 2 q^{3} + 127 q^{4} + 9 q^{5} + 19 q^{6} + 18 q^{7} + 149 q^{9} + 20 q^{10} + 9 q^{11} + 36 q^{13} - 10 q^{14} + 16 q^{15} + 179 q^{16} + 21 q^{17} + 7 q^{18} + 42 q^{19} + 24 q^{20} + 28 q^{21} + 32 q^{22} + 25 q^{23} + 68 q^{24} + 194 q^{25} - 5 q^{26} + 14 q^{27} + 59 q^{28} - 103 q^{29} + 84 q^{30} + 34 q^{31} + 11 q^{32} + 42 q^{33} + 54 q^{34} + 35 q^{35} + 214 q^{36} + 34 q^{37} + 9 q^{38} + 23 q^{39} + 46 q^{40} + 16 q^{41} + 13 q^{42} + 68 q^{43} - 6 q^{44} + 25 q^{45} + 60 q^{46} + 6 q^{47} + 5 q^{48} + 257 q^{49} - 51 q^{50} + 68 q^{51} + 37 q^{52} + 35 q^{53} + 30 q^{54} + 66 q^{55} - 54 q^{56} + 78 q^{57} - q^{58} + 10 q^{59} - 24 q^{60} + 70 q^{61} + 29 q^{62} + 26 q^{63} + 276 q^{64} + 95 q^{65} + 77 q^{66} + 71 q^{67} - 21 q^{68} - 20 q^{69} + 48 q^{70} + 32 q^{71} + 32 q^{72} + 94 q^{73} + 35 q^{74} + 7 q^{75} + 134 q^{76} + 17 q^{77} + 58 q^{78} + 110 q^{79} + 78 q^{80} + 267 q^{81} - 71 q^{82} + 35 q^{83} + 96 q^{84} + 71 q^{85} + 33 q^{86} - 2 q^{87} + 100 q^{88} + 22 q^{89} - 134 q^{90} + 108 q^{91} - 11 q^{92} + 78 q^{93} + 90 q^{94} + 12 q^{95} + 177 q^{96} + 44 q^{97} - 18 q^{98} + 83 q^{99}+O(q^{100}) \) 103 * q + q^2 + 2 * q^3 + 127 * q^4 + 9 * q^5 + 19 * q^6 + 18 * q^7 + 149 * q^9 + 20 * q^10 + 9 * q^11 + 36 * q^13 - 10 * q^14 + 16 * q^15 + 179 * q^16 + 21 * q^17 + 7 * q^18 + 42 * q^19 + 24 * q^20 + 28 * q^21 + 32 * q^22 + 25 * q^23 + 68 * q^24 + 194 * q^25 - 5 * q^26 + 14 * q^27 + 59 * q^28 - 103 * q^29 + 84 * q^30 + 34 * q^31 + 11 * q^32 + 42 * q^33 + 54 * q^34 + 35 * q^35 + 214 * q^36 + 34 * q^37 + 9 * q^38 + 23 * q^39 + 46 * q^40 + 16 * q^41 + 13 * q^42 + 68 * q^43 - 6 * q^44 + 25 * q^45 + 60 * q^46 + 6 * q^47 + 5 * q^48 + 257 * q^49 - 51 * q^50 + 68 * q^51 + 37 * q^52 + 35 * q^53 + 30 * q^54 + 66 * q^55 - 54 * q^56 + 78 * q^57 - q^58 + 10 * q^59 - 24 * q^60 + 70 * q^61 + 29 * q^62 + 26 * q^63 + 276 * q^64 + 95 * q^65 + 77 * q^66 + 71 * q^67 - 21 * q^68 - 20 * q^69 + 48 * q^70 + 32 * q^71 + 32 * q^72 + 94 * q^73 + 35 * q^74 + 7 * q^75 + 134 * q^76 + 17 * q^77 + 58 * q^78 + 110 * q^79 + 78 * q^80 + 267 * q^81 - 71 * q^82 + 35 * q^83 + 96 * q^84 + 71 * q^85 + 33 * q^86 - 2 * q^87 + 100 * q^88 + 22 * q^89 - 134 * q^90 + 108 * q^91 - 11 * q^92 + 78 * q^93 + 90 * q^94 + 12 * q^95 + 177 * q^96 + 44 * q^97 - 18 * q^98 + 83 * 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 $

$2$	−2.20982	−1.56258	−0.781290	−	0.624168i	$-0.785438\pi$
$2$	−2.20982	−1.56258	−0.781290	+	0.624168i	$0.785438\pi$
$3$	−3.43245	−1.98172	−0.990862	−	0.134878i	$-0.956936\pi$
$3$	−3.43245	−1.98172	−0.990862	+	0.134878i	$0.956936\pi$
$4$	2.88331	1.44166
$5$	3.18051	1.42237	0.711184	−	0.703006i	$-0.248159\pi$
$5$	3.18051	1.42237	0.711184	+	0.703006i	$0.248159\pi$
$6$	7.58510	3.09660
$7$	4.63810	1.75304	0.876518	−	0.481369i	$-0.159860\pi$
$7$	4.63810	1.75304	0.876518	+	0.481369i	$0.159860\pi$
$8$	−1.95196	−0.690122
$9$	8.78169	2.92723
$10$	−7.02836	−2.22256
$11$	5.96685	1.79907	0.899536	−	0.436846i	$-0.143905\pi$
$11$	5.96685	1.79907	0.899536	+	0.436846i	$0.143905\pi$
$12$	−9.89681	−2.85696
$13$	−2.55639	−0.709015	−0.354507	−	0.935053i	$-0.615351\pi$
$13$	−2.55639	−0.709015	−0.354507	+	0.935053i	$0.615351\pi$
$14$	−10.2494	−2.73926
$15$	−10.9169	−2.81874
$16$	−1.45314	−0.363285
$17$	3.08767	0.748869	0.374435	−	0.927253i	$-0.377837\pi$
$17$	3.08767	0.748869	0.374435	+	0.927253i	$0.377837\pi$
$18$	−19.4060	−4.57403
$19$	−0.685938	−0.157365	−0.0786824	−	0.996900i	$-0.525071\pi$
$19$	−0.685938	−0.157365	−0.0786824	+	0.996900i	$0.525071\pi$
$20$	9.17040	2.05056
$21$	−15.9200	−3.47403
$22$	−13.1857	−2.81119
$23$	7.54619	1.57349	0.786745	−	0.617278i	$-0.211765\pi$
$23$	7.54619	1.57349	0.786745	+	0.617278i	$0.211765\pi$
$24$	6.70000	1.36763
$25$	5.11564	1.02313
$26$	5.64916	1.10789
$27$	−19.8454	−3.81924
$28$	13.3731	2.52727
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	24.1245	4.40451
$31$	1.64314	0.295117	0.147558	−	0.989053i	$-0.452859\pi$
$31$	1.64314	0.295117	0.147558	+	0.989053i	$0.452859\pi$
$32$	7.11510	1.25778
$33$	−20.4809	−3.56527
$34$	−6.82319	−1.17017
$35$	14.7515	2.49346
$36$	25.3204	4.22006
$37$	3.25824	0.535651	0.267826	−	0.963467i	$-0.413695\pi$
$37$	3.25824	0.535651	0.267826	+	0.963467i	$0.413695\pi$
$38$	1.51580	0.245895
$39$	8.77467	1.40507
$40$	−6.20822	−0.981607
$41$	6.64257	1.03740	0.518698	−	0.854958i	$-0.326417\pi$
$41$	6.64257	1.03740	0.518698	+	0.854958i	$0.326417\pi$
$42$	35.1804	5.42846
$43$	−9.32244	−1.42166	−0.710830	−	0.703364i	$-0.751680\pi$
$43$	−9.32244	−1.42166	−0.710830	+	0.703364i	$0.751680\pi$
$44$	17.2043	2.59364
$45$	27.9303	4.16360
$46$	−16.6757	−2.45870
$47$	−7.07988	−1.03271	−0.516353	−	0.856376i	$-0.672711\pi$
$47$	−7.07988	−1.03271	−0.516353	+	0.856376i	$0.672711\pi$
$48$	4.98783	0.719931
$49$	14.5119	2.07314
$50$	−11.3047	−1.59872
$51$	−10.5983	−1.48405
$52$	−7.37086	−1.02215
$53$	2.14930	0.295229	0.147614	−	0.989045i	$-0.452841\pi$
$53$	2.14930	0.295229	0.147614	+	0.989045i	$0.452841\pi$
$54$	43.8547	5.96787
$55$	18.9776	2.55894
$56$	−9.05338	−1.20981
$57$	2.35444	0.311854
$58$	2.20982	0.290164
$59$	13.1088	1.70662	0.853312	−	0.521400i	$-0.174590\pi$
$59$	13.1088	1.70662	0.853312	+	0.521400i	$0.174590\pi$
$60$	−31.4769	−4.06365
$61$	−2.28175	−0.292148	−0.146074	−	0.989274i	$-0.546664\pi$
$61$	−2.28175	−0.292148	−0.146074	+	0.989274i	$0.546664\pi$
$62$	−3.63105	−0.461144
$63$	40.7303	5.13154
$64$	−12.8168	−1.60210
$65$	−8.13062	−1.00848
$66$	45.2591	5.57101
$67$	13.0569	1.59516	0.797578	−	0.603216i	$-0.206114\pi$
$67$	13.0569	1.59516	0.797578	+	0.603216i	$0.206114\pi$
$68$	8.90271	1.07961
$69$	−25.9019	−3.11822
$70$	−32.5982	−3.89623
$71$	−6.74370	−0.800329	−0.400165	−	0.916443i	$-0.631047\pi$
$71$	−6.74370	−0.800329	−0.400165	+	0.916443i	$0.631047\pi$
$72$	−17.1415	−2.02015
$73$	0.584169	0.0683718	0.0341859	−	0.999415i	$-0.489116\pi$
$73$	0.584169	0.0683718	0.0341859	+	0.999415i	$0.489116\pi$
$74$	−7.20012	−0.836998
$75$	−17.5592	−2.02756
$76$	−1.97777	−0.226866
$77$	27.6748	3.15384
$78$	−19.3905	−2.19554
$79$	8.11201	0.912672	0.456336	−	0.889807i	$-0.349161\pi$
$79$	8.11201	0.912672	0.456336	+	0.889807i	$0.349161\pi$
$80$	−4.62173	−0.516725
$81$	41.7731	4.64145
$82$	−14.6789	−1.62101
$83$	−5.13561	−0.563706	−0.281853	−	0.959458i	$-0.590949\pi$
$83$	−5.13561	−0.563706	−0.281853	+	0.959458i	$0.590949\pi$
$84$	−45.9024	−5.00836
$85$	9.82036	1.06517
$86$	20.6009	2.22146
$87$	3.43245	0.367997
$88$	−11.6470	−1.24158
$89$	−0.784141	−0.0831188	−0.0415594	−	0.999136i	$-0.513233\pi$
$89$	−0.784141	−0.0831188	−0.0415594	+	0.999136i	$0.513233\pi$
$90$	−61.7209	−6.50595
$91$	−11.8568	−1.24293
$92$	21.7580	2.26843
$93$	−5.64000	−0.584840
$94$	15.6453	1.61369
$95$	−2.18163	−0.223831
$96$	−24.4222	−2.49258
$97$	−1.48449	−0.150727	−0.0753634	−	0.997156i	$-0.524012\pi$
$97$	−1.48449	−0.150727	−0.0753634	+	0.997156i	$0.524012\pi$
$98$	−32.0688	−3.23944
$99$	52.3990	5.26630
$100$	14.7500	1.47500
$101$	−7.74620	−0.770776	−0.385388	−	0.922755i	$-0.625932\pi$
$101$	−7.74620	−0.770776	−0.385388	+	0.922755i	$0.625932\pi$
$102$	23.4203	2.31895
$103$	−10.2244	−1.00744	−0.503720	−	0.863867i	$-0.668036\pi$
$103$	−10.2244	−1.00744	−0.503720	+	0.863867i	$0.668036\pi$
$104$	4.98997	0.489306
$105$	−50.6338	−4.94135
$106$	−4.74957	−0.461319
$107$	−15.5545	−1.50371	−0.751854	−	0.659329i	$-0.770840\pi$
$107$	−15.5545	−1.50371	−0.751854	+	0.659329i	$0.770840\pi$
$108$	−57.2203	−5.50603
$109$	8.22581	0.787890	0.393945	−	0.919134i	$-0.371110\pi$
$109$	8.22581	0.787890	0.393945	+	0.919134i	$0.371110\pi$
$110$	−41.9372	−3.99855
$111$	−11.1837	−1.06151
$112$	−6.73981	−0.636852
$113$	−4.25866	−0.400621	−0.200311	−	0.979732i	$-0.564195\pi$
$113$	−4.25866	−0.400621	−0.200311	+	0.979732i	$0.564195\pi$
$114$	−5.20290	−0.487296
$115$	24.0007	2.23808
$116$	−2.88331	−0.267709
$117$	−22.4494	−2.07545
$118$	−28.9682	−2.66674
$119$	14.3209	1.31280
$120$	21.3094	1.94527
$121$	24.6033	2.23666
$122$	5.04225	0.456504
$123$	−22.8003	−2.05583
$124$	4.73769	0.425457
$125$	0.367806	0.0328976
$126$	−90.0068	−8.01844
$127$	11.5015	1.02059	0.510296	−	0.859999i	$-0.329536\pi$
$127$	11.5015	1.02059	0.510296	+	0.859999i	$0.329536\pi$
$128$	14.0927	1.24563
$129$	31.9988	2.81734
$130$	17.9672	1.57583
$131$	−2.83492	−0.247688	−0.123844	−	0.992302i	$-0.539522\pi$
$131$	−2.83492	−0.247688	−0.123844	+	0.992302i	$0.539522\pi$
$132$	−59.0528	−5.13988
$133$	−3.18145	−0.275866
$134$	−28.8535	−2.49256
$135$	−63.1184	−5.43236
$136$	−6.02700	−0.516811
$137$	−14.7774	−1.26252	−0.631258	−	0.775573i	$-0.717461\pi$
$137$	−14.7774	−1.26252	−0.631258	+	0.775573i	$0.717461\pi$
$138$	57.2386	4.87247
$139$	1.00000	0.0848189
$139$	1.00000	0.0848189
$140$	42.5332	3.59471
$141$	24.3013	2.04654
$142$	14.9024	1.25058
$143$	−15.2536	−1.27557
$144$	−12.7610	−1.06342
$145$	−3.18051	−0.264127
$146$	−1.29091	−0.106836
$147$	−49.8115	−4.10838
$148$	9.39451	0.772224
$149$	14.0313	1.14949	0.574746	−	0.818332i	$-0.305101\pi$
$149$	14.0313	1.14949	0.574746	+	0.818332i	$0.305101\pi$
$150$	38.8026	3.16822
$151$	−6.65093	−0.541245	−0.270623	−	0.962686i	$-0.587230\pi$
$151$	−6.65093	−0.541245	−0.270623	+	0.962686i	$0.587230\pi$
$152$	1.33892	0.108601
$153$	27.1150	2.19211
$154$	−61.1564	−4.92812
$155$	5.22603	0.419765
$156$	25.3001	2.02563
$157$	0.154213	0.0123075	0.00615375	−	0.999981i	$-0.498041\pi$
$157$	0.154213	0.0123075	0.00615375	+	0.999981i	$0.498041\pi$
$158$	−17.9261	−1.42612
$159$	−7.37736	−0.585062
$160$	22.6296	1.78903
$161$	35.0000	2.75838
$162$	−92.3110	−7.25264
$163$	−8.60250	−0.673799	−0.336900	−	0.941541i	$-0.609378\pi$
$163$	−8.60250	−0.673799	−0.336900	+	0.941541i	$0.609378\pi$
$164$	19.1526	1.49557
$165$	−65.1397	−5.07112
$166$	11.3488	0.880836
$167$	−3.75245	−0.290373	−0.145186	−	0.989404i	$-0.546378\pi$
$167$	−3.75245	−0.290373	−0.145186	+	0.989404i	$0.546378\pi$
$168$	31.0752	2.39751
$169$	−6.46488	−0.497298
$170$	−21.7012	−1.66441
$171$	−6.02369	−0.460643
$172$	−26.8795	−2.04954
$173$	−2.07535	−0.157786	−0.0788930	−	0.996883i	$-0.525139\pi$
$173$	−2.07535	−0.157786	−0.0788930	+	0.996883i	$0.525139\pi$
$174$	−7.58510	−0.575025
$175$	23.7269	1.79358
$176$	−8.67067	−0.653576
$177$	−44.9954	−3.38206
$178$	1.73281	0.129880
$179$	−9.16202	−0.684801	−0.342401	−	0.939554i	$-0.611240\pi$
$179$	−9.16202	−0.684801	−0.342401	+	0.939554i	$0.611240\pi$
$180$	80.5316	6.00247
$181$	13.8145	1.02683	0.513413	−	0.858142i	$-0.328381\pi$
$181$	13.8145	1.02683	0.513413	+	0.858142i	$0.328381\pi$
$182$	26.2014	1.94217
$183$	7.83198	0.578956
$184$	−14.7299	−1.08590
$185$	10.3629	0.761893
$186$	12.4634	0.913860
$187$	18.4236	1.34727
$188$	−20.4135	−1.48881
$189$	−92.0447	−6.69527
$190$	4.82102	0.349753
$191$	14.9728	1.08339	0.541695	−	0.840575i	$-0.317783\pi$
$191$	14.9728	1.08339	0.541695	+	0.840575i	$0.317783\pi$
$192$	43.9930	3.17492
$193$	23.5397	1.69443	0.847213	−	0.531253i	$-0.178279\pi$
$193$	23.5397	1.69443	0.847213	+	0.531253i	$0.178279\pi$
$194$	3.28045	0.235523
$195$	27.9079	1.99853
$196$	41.8425	2.98875
$197$	7.97132	0.567933	0.283966	−	0.958834i	$-0.408350\pi$
$197$	7.97132	0.567933	0.283966	+	0.958834i	$0.408350\pi$
$198$	−115.792	−8.22901
$199$	1.42405	0.100948	0.0504739	−	0.998725i	$-0.483927\pi$
$199$	1.42405	0.100948	0.0504739	+	0.998725i	$0.483927\pi$
$200$	−9.98553	−0.706083
$201$	−44.8172	−3.16116
$202$	17.1177	1.20440
$203$	−4.63810	−0.325531
$204$	−30.5581	−2.13949
$205$	21.1268	1.47556
$206$	22.5941	1.57421
$207$	66.2683	4.60597
$208$	3.71479	0.257575
$209$	−4.09288	−0.283111
$210$	111.892	7.72126
$211$	−22.0627	−1.51886	−0.759430	−	0.650589i	$-0.774522\pi$
$211$	−22.0627	−1.51886	−0.759430	+	0.650589i	$0.774522\pi$
$212$	6.19710	0.425618
$213$	23.1474	1.58603
$214$	34.3726	2.34966
$215$	−29.6501	−2.02212
$216$	38.7373	2.63574
$217$	7.62105	0.517351
$218$	−18.1776	−1.23114
$219$	−2.00513	−0.135494
$220$	54.7184	3.68911
$221$	−7.89328	−0.530959
$222$	24.7140	1.65870
$223$	−10.2133	−0.683936	−0.341968	−	0.939712i	$-0.611093\pi$
$223$	−10.2133	−0.683936	−0.341968	+	0.939712i	$0.611093\pi$
$224$	33.0005	2.20494
$225$	44.9240	2.99493
$226$	9.41088	0.626003
$227$	−23.8241	−1.58126	−0.790629	−	0.612295i	$-0.790246\pi$
$227$	−23.8241	−1.58126	−0.790629	+	0.612295i	$0.790246\pi$
$228$	6.78859	0.449586
$229$	3.54433	0.234216	0.117108	−	0.993119i	$-0.462638\pi$
$229$	3.54433	0.234216	0.117108	+	0.993119i	$0.462638\pi$
$230$	−53.0373	−3.49718
$231$	−94.9924	−6.25004
$232$	1.95196	0.128152
$233$	14.0040	0.917435	0.458717	−	0.888582i	$-0.348309\pi$
$233$	14.0040	0.917435	0.458717	+	0.888582i	$0.348309\pi$
$234$	49.6092	3.24306
$235$	−22.5176	−1.46889
$236$	37.7968	2.46036
$237$	−27.8440	−1.80866
$238$	−31.6466	−2.05135
$239$	0.755896	0.0488949	0.0244474	−	0.999701i	$-0.492217\pi$
$239$	0.755896	0.0488949	0.0244474	+	0.999701i	$0.492217\pi$
$240$	15.8638	1.02401
$241$	16.5236	1.06438	0.532191	−	0.846625i	$-0.321369\pi$
$241$	16.5236	1.06438	0.532191	+	0.846625i	$0.321369\pi$
$242$	−54.3688	−3.49496
$243$	−83.8478	−5.37884
$244$	−6.57899	−0.421176
$245$	46.1554	2.94876
$246$	50.3845	3.21240
$247$	1.75352	0.111574
$248$	−3.20734	−0.203667
$249$	17.6277	1.11711
$250$	−0.812786	−0.0514051
$251$	−14.3208	−0.903923	−0.451962	−	0.892037i	$-0.649276\pi$
$251$	−14.3208	−0.903923	−0.451962	+	0.892037i	$0.649276\pi$
$252$	117.438	7.39791
$253$	45.0270	2.83082
$254$	−25.4162	−1.59476
$255$	−33.7079	−2.11087
$256$	−5.50867	−0.344292
$257$	−8.59151	−0.535924	−0.267962	−	0.963429i	$-0.586350\pi$
$257$	−8.59151	−0.535924	−0.267962	+	0.963429i	$0.586350\pi$
$258$	−70.7116	−4.40231
$259$	15.1120	0.939016
$260$	−23.4431	−1.45388
$261$	−8.78169	−0.543573
$262$	6.26466	0.387032
$263$	−4.39937	−0.271277	−0.135638	−	0.990758i	$-0.543309\pi$
$263$	−4.39937	−0.271277	−0.135638	+	0.990758i	$0.543309\pi$
$264$	39.9779	2.46047
$265$	6.83587	0.419924
$266$	7.03043	0.431063
$267$	2.69152	0.164719
$268$	37.6471	2.29967
$269$	24.7144	1.50687	0.753433	−	0.657525i	$-0.228397\pi$
$269$	24.7144	1.50687	0.753433	+	0.657525i	$0.228397\pi$
$270$	139.480	8.48850
$271$	22.0718	1.34077	0.670384	−	0.742014i	$-0.266129\pi$
$271$	22.0718	1.34077	0.670384	+	0.742014i	$0.266129\pi$
$272$	−4.48682	−0.272053
$273$	40.6978	2.46314
$274$	32.6554	1.97278
$275$	30.5243	1.84068
$276$	−74.6832	−4.49540
$277$	1.83140	0.110038	0.0550192	−	0.998485i	$-0.482478\pi$
$277$	1.83140	0.110038	0.0550192	+	0.998485i	$0.482478\pi$
$278$	−2.20982	−0.132536
$279$	14.4296	0.863875
$280$	−28.7944	−1.72079
$281$	−4.75990	−0.283952	−0.141976	−	0.989870i	$-0.545346\pi$
$281$	−4.75990	−0.283952	−0.141976	+	0.989870i	$0.545346\pi$
$282$	−53.7016	−3.19788
$283$	−25.4288	−1.51159	−0.755793	−	0.654811i	$-0.772748\pi$
$283$	−25.4288	−1.51159	−0.755793	+	0.654811i	$0.772748\pi$
$284$	−19.4442	−1.15380
$285$	7.48833	0.443571
$286$	33.7077	1.99318
$287$	30.8089	1.81859
$288$	62.4826	3.68182
$289$	−7.46631	−0.439195
$290$	7.02836	0.412719
$291$	5.09542	0.298699
$292$	1.68434	0.0985686
$293$	14.7586	0.862206	0.431103	−	0.902303i	$-0.358125\pi$
$293$	14.7586	0.862206	0.431103	+	0.902303i	$0.358125\pi$
$294$	110.075	6.41968
$295$	41.6928	2.42745
$296$	−6.35995	−0.369664
$297$	−118.414	−6.87109
$298$	−31.0068	−1.79617
$299$	−19.2910	−1.11563
$300$	−50.6286	−2.92304
$301$	−43.2384	−2.49222
$302$	14.6974	0.845739
$303$	26.5884	1.52747
$304$	0.996764	0.0571683
$305$	−7.25712	−0.415541
$306$	−59.9192	−3.42535
$307$	−11.3034	−0.645121	−0.322560	−	0.946549i	$-0.604544\pi$
$307$	−11.3034	−0.645121	−0.322560	+	0.946549i	$0.604544\pi$
$308$	79.7951	4.54675
$309$	35.0947	1.99647
$310$	−11.5486	−0.655916
$311$	−18.2778	−1.03644	−0.518220	−	0.855247i	$-0.673405\pi$
$311$	−18.2778	−1.03644	−0.518220	+	0.855247i	$0.673405\pi$
$312$	−17.1278	−0.969670
$313$	−7.02356	−0.396995	−0.198498	−	0.980101i	$-0.563606\pi$
$313$	−7.02356	−0.396995	−0.198498	+	0.980101i	$0.563606\pi$
$314$	−0.340782	−0.0192315
$315$	129.543	7.29894
$316$	23.3894	1.31576
$317$	−24.9945	−1.40383	−0.701914	−	0.712261i	$-0.747671\pi$
$317$	−24.9945	−1.40383	−0.701914	+	0.712261i	$0.747671\pi$
$318$	16.3026	0.914207
$319$	−5.96685	−0.334079
$320$	−40.7640	−2.27878
$321$	53.3899	2.97994
$322$	−77.3437	−4.31020
$323$	−2.11795	−0.117846
$324$	120.445	6.69137
$325$	−13.0776	−0.725413
$326$	19.0100	1.05287
$327$	−28.2347	−1.56138
$328$	−12.9660	−0.715929
$329$	−32.8372	−1.81037
$330$	143.947	7.92402
$331$	−18.4354	−1.01330	−0.506650	−	0.862152i	$-0.669117\pi$
$331$	−18.4354	−1.01330	−0.506650	+	0.862152i	$0.669117\pi$
$332$	−14.8076	−0.812670
$333$	28.6129	1.56797
$334$	8.29224	0.453731
$335$	41.5277	2.26890
$336$	23.1340	1.26207
$337$	20.4994	1.11668	0.558338	−	0.829614i	$-0.311439\pi$
$337$	20.4994	1.11668	0.558338	+	0.829614i	$0.311439\pi$
$338$	14.2862	0.777068
$339$	14.6176	0.793921
$340$	28.3151	1.53560
$341$	9.80437	0.530937
$342$	13.3113	0.719792
$343$	34.8411	1.88124
$344$	18.1970	0.981118
$345$	−82.3813	−4.43526
$346$	4.58615	0.246553
$347$	−9.78387	−0.525226	−0.262613	−	0.964901i	$-0.584584\pi$
$347$	−9.78387	−0.525226	−0.262613	+	0.964901i	$0.584584\pi$
$348$	9.89681	0.530525
$349$	−28.2003	−1.50953	−0.754764	−	0.655996i	$-0.772249\pi$
$349$	−28.2003	−1.50953	−0.754764	+	0.655996i	$0.772249\pi$
$350$	−52.4321	−2.80261
$351$	50.7325	2.70790
$352$	42.4547	2.26284
$353$	−29.3869	−1.56411	−0.782054	−	0.623211i	$-0.785828\pi$
$353$	−29.3869	−1.56411	−0.782054	+	0.623211i	$0.785828\pi$
$354$	99.4318	5.28474
$355$	−21.4484	−1.13836
$356$	−2.26092	−0.119829
$357$	−49.1557	−2.60160
$358$	20.2464	1.07006
$359$	−16.8296	−0.888233	−0.444117	−	0.895969i	$-0.646482\pi$
$359$	−16.8296	−0.888233	−0.444117	+	0.895969i	$0.646482\pi$
$360$	−54.5187	−2.87339
$361$	−18.5295	−0.975236
$362$	−30.5277	−1.60450
$363$	−84.4494	−4.43245
$364$	−34.1868	−1.79187
$365$	1.85796	0.0972499
$366$	−17.3073	−0.904665
$367$	−15.0965	−0.788032	−0.394016	−	0.919104i	$-0.628915\pi$
$367$	−15.0965	−0.788032	−0.394016	+	0.919104i	$0.628915\pi$
$368$	−10.9657	−0.571626
$369$	58.3330	3.03670
$370$	−22.9001	−1.19052
$371$	9.96866	0.517547
$372$	−16.2619	−0.843138
$373$	−31.3584	−1.62368	−0.811838	−	0.583882i	$-0.801533\pi$
$373$	−31.3584	−1.62368	−0.811838	+	0.583882i	$0.801533\pi$
$374$	−40.7130	−2.10522
$375$	−1.26248	−0.0651939
$376$	13.8196	0.712693
$377$	2.55639	0.131661
$378$	203.402	10.4619
$379$	−21.1971	−1.08882	−0.544411	−	0.838819i	$-0.683247\pi$
$379$	−21.1971	−1.08882	−0.544411	+	0.838819i	$0.683247\pi$
$380$	−6.29032	−0.322687
$381$	−39.4782	−2.02253
$382$	−33.0871	−1.69288
$383$	5.70238	0.291378	0.145689	−	0.989330i	$-0.453460\pi$
$383$	5.70238	0.291378	0.145689	+	0.989330i	$0.453460\pi$
$384$	−48.3724	−2.46849
$385$	88.0200	4.48592
$386$	−52.0186	−2.64768
$387$	−81.8668	−4.16153
$388$	−4.28024	−0.217296
$389$	10.5132	0.533041	0.266520	−	0.963829i	$-0.414126\pi$
$389$	10.5132	0.533041	0.266520	+	0.963829i	$0.414126\pi$
$390$	−61.6715	−3.12286
$391$	23.3001	1.17834
$392$	−28.3267	−1.43072
$393$	9.73071	0.490849
$394$	−17.6152	−0.887440
$395$	25.8003	1.29816
$396$	151.083	7.59219
$397$	23.6950	1.18922	0.594610	−	0.804014i	$-0.297306\pi$
$397$	23.6950	1.18922	0.594610	+	0.804014i	$0.297306\pi$
$398$	−3.14689	−0.157739
$399$	10.9201	0.546691
$400$	−7.43375	−0.371688
$401$	7.50109	0.374587	0.187293	−	0.982304i	$-0.440029\pi$
$401$	7.50109	0.374587	0.187293	+	0.982304i	$0.440029\pi$
$402$	99.0380	4.93956
$403$	−4.20051	−0.209242
$404$	−22.3347	−1.11119
$405$	132.860	6.60185
$406$	10.2494	0.508668
$407$	19.4414	0.963675
$408$	20.6874	1.02418
$409$	15.9197	0.787178	0.393589	−	0.919287i	$-0.371233\pi$
$409$	15.9197	0.787178	0.393589	+	0.919287i	$0.371233\pi$
$410$	−46.6864	−2.30568
$411$	50.7226	2.50196
$412$	−29.4801	−1.45238
$413$	60.8000	2.99177
$414$	−146.441	−7.19719
$415$	−16.3339	−0.801798
$416$	−18.1890	−0.891787
$417$	−3.43245	−0.168088
$418$	9.04454	0.442383
$419$	−21.3766	−1.04432	−0.522158	−	0.852849i	$-0.674873\pi$
$419$	−21.3766	−1.04432	−0.522158	+	0.852849i	$0.674873\pi$
$420$	−145.993	−7.12373
$421$	−25.6838	−1.25175	−0.625875	−	0.779923i	$-0.715258\pi$
$421$	−25.6838	−1.25175	−0.625875	+	0.779923i	$0.715258\pi$
$422$	48.7547	2.37334
$423$	−62.1733	−3.02297
$424$	−4.19534	−0.203744
$425$	15.7954	0.766190
$426$	−51.1516	−2.47830
$427$	−10.5830	−0.512146
$428$	−44.8484	−2.16783
$429$	52.3571	2.52783
$430$	65.5215	3.15973
$431$	−24.4779	−1.17906	−0.589530	−	0.807746i	$-0.700687\pi$
$431$	−24.4779	−1.17906	−0.589530	+	0.807746i	$0.700687\pi$
$432$	28.8381	1.38747
$433$	2.61167	0.125509	0.0627544	−	0.998029i	$-0.480012\pi$
$433$	2.61167	0.125509	0.0627544	+	0.998029i	$0.480012\pi$
$434$	−16.8412	−0.808401
$435$	10.9169	0.523427
$436$	23.7176	1.13587
$437$	−5.17622	−0.247612
$438$	4.43098	0.211720
$439$	−23.4901	−1.12112	−0.560560	−	0.828114i	$-0.689414\pi$
$439$	−23.4901	−1.12112	−0.560560	+	0.828114i	$0.689414\pi$
$440$	−37.0435	−1.76598
$441$	127.439	6.06855
$442$	17.4427	0.829666
$443$	3.16121	0.150193	0.0750967	−	0.997176i	$-0.476073\pi$
$443$	3.16121	0.150193	0.0750967	+	0.997176i	$0.476073\pi$
$444$	−32.2462	−1.53034
$445$	−2.49397	−0.118225
$446$	22.5696	1.06870
$447$	−48.1618	−2.27798
$448$	−59.4456	−2.80854
$449$	−25.1203	−1.18550	−0.592750	−	0.805386i	$-0.701958\pi$
$449$	−25.1203	−1.18550	−0.592750	+	0.805386i	$0.701958\pi$
$450$	−99.2741	−4.67982
$451$	39.6352	1.86635
$452$	−12.2790	−0.577558
$453$	22.8290	1.07260
$454$	52.6469	2.47084
$455$	−37.7106	−1.76790
$456$	−4.59578	−0.215217
$457$	4.59355	0.214877	0.107439	−	0.994212i	$-0.465735\pi$
$457$	4.59355	0.214877	0.107439	+	0.994212i	$0.465735\pi$
$458$	−7.83234	−0.365981
$459$	−61.2759	−2.86011
$460$	69.2016	3.22654
$461$	16.8307	0.783886	0.391943	−	0.919990i	$-0.371803\pi$
$461$	16.8307	0.783886	0.391943	+	0.919990i	$0.371803\pi$
$462$	209.916	9.76618
$463$	24.7171	1.14870	0.574350	−	0.818610i	$-0.305255\pi$
$463$	24.7171	1.14870	0.574350	+	0.818610i	$0.305255\pi$
$464$	1.45314	0.0674604
$465$	−17.9381	−0.831858
$466$	−30.9464	−1.43357
$467$	−12.3322	−0.570666	−0.285333	−	0.958428i	$-0.592104\pi$
$467$	−12.3322	−0.570666	−0.285333	+	0.958428i	$0.592104\pi$
$468$	−64.7287	−2.99208
$469$	60.5592	2.79637
$470$	49.7599	2.29525
$471$	−0.529327	−0.0243901
$472$	−25.5879	−1.17778
$473$	−55.6256	−2.55767
$474$	61.5304	2.82618
$475$	−3.50901	−0.161005
$476$	41.2916	1.89260
$477$	18.8745	0.864203
$478$	−1.67040	−0.0764021
$479$	26.7437	1.22195	0.610976	−	0.791649i	$-0.290777\pi$
$479$	26.7437	1.22195	0.610976	+	0.791649i	$0.290777\pi$
$480$	−77.6751	−3.54537
$481$	−8.32932	−0.379784
$482$	−36.5143	−1.66318
$483$	−120.136	−5.46636
$484$	70.9389	3.22449
$485$	−4.72143	−0.214389
$486$	185.289	8.40486
$487$	3.08308	0.139708	0.0698538	−	0.997557i	$-0.477747\pi$
$487$	3.08308	0.139708	0.0698538	+	0.997557i	$0.477747\pi$
$488$	4.45388	0.201618
$489$	29.5276	1.33528
$490$	−101.995	−4.60767
$491$	30.3636	1.37029	0.685144	−	0.728408i	$-0.259739\pi$
$491$	30.3636	1.37029	0.685144	+	0.728408i	$0.259739\pi$
$492$	−65.7403	−2.96380
$493$	−3.08767	−0.139062
$494$	−3.87497	−0.174343
$495$	166.656	7.49061
$496$	−2.38772	−0.107212
$497$	−31.2779	−1.40301
$498$	−38.9541	−1.74557
$499$	32.9849	1.47661	0.738304	−	0.674468i	$-0.235627\pi$
$499$	32.9849	1.47661	0.738304	+	0.674468i	$0.235627\pi$
$500$	1.06050	0.0474270
$501$	12.8801	0.575439
$502$	31.6465	1.41245
$503$	−32.1519	−1.43358	−0.716792	−	0.697287i	$-0.754390\pi$
$503$	−32.1519	−1.43358	−0.716792	+	0.697287i	$0.754390\pi$
$504$	−79.5040	−3.54139
$505$	−24.6369	−1.09633
$506$	−99.5016	−4.42338
$507$	22.1903	0.985508
$508$	33.1624	1.47134
$509$	1.95906	0.0868337	0.0434168	−	0.999057i	$-0.486176\pi$
$509$	1.95906	0.0868337	0.0434168	+	0.999057i	$0.486176\pi$
$510$	74.4884	3.29840
$511$	2.70943	0.119858
$512$	−16.0122	−0.707645
$513$	13.6127	0.601014
$514$	18.9857	0.837424
$515$	−32.5188	−1.43295
$516$	92.2625	4.06163
$517$	−42.2446	−1.85791
$518$	−33.3949	−1.46729
$519$	7.12353	0.312688
$520$	15.8706	0.695973
$521$	11.6802	0.511721	0.255860	−	0.966714i	$-0.417641\pi$
$521$	11.6802	0.511721	0.255860	+	0.966714i	$0.417641\pi$
$522$	19.4060	0.849376
$523$	33.7684	1.47659	0.738295	−	0.674478i	$-0.235631\pi$
$523$	33.7684	1.47659	0.738295	+	0.674478i	$0.235631\pi$
$524$	−8.17395	−0.357081
$525$	−81.4412	−3.55438
$526$	9.72182	0.423891
$527$	5.07347	0.221004
$528$	29.7616	1.29521
$529$	33.9450	1.47587
$530$	−15.1060	−0.656165
$531$	115.118	4.99569
$532$	−9.17309	−0.397704
$533$	−16.9810	−0.735529
$534$	−5.94779	−0.257386
$535$	−49.4712	−2.13883
$536$	−25.4866	−1.10085
$537$	31.4481	1.35709
$538$	−54.6145	−2.35460
$539$	86.5906	3.72972
$540$	−181.990	−7.83160
$541$	3.64938	0.156899	0.0784496	−	0.996918i	$-0.475003\pi$
$541$	3.64938	0.156899	0.0784496	+	0.996918i	$0.475003\pi$
$542$	−48.7748	−2.09506
$543$	−47.4177	−2.03489
$544$	21.9691	0.941916
$545$	26.1623	1.12067
$546$	−89.9348	−3.84885
$547$	10.1953	0.435921	0.217961	−	0.975958i	$-0.430060\pi$
$547$	10.1953	0.435921	0.217961	+	0.975958i	$0.430060\pi$
$548$	−42.6078	−1.82011
$549$	−20.0376	−0.855184
$550$	−67.4532	−2.87621
$551$	0.685938	0.0292219
$552$	50.5595	2.15195
$553$	37.6243	1.59995
$554$	−4.04708	−0.171944
$555$	−35.5700	−1.50986
$556$	2.88331	0.122280
$557$	−35.7380	−1.51427	−0.757133	−	0.653261i	$-0.773401\pi$
$557$	−35.7380	−1.51427	−0.757133	+	0.653261i	$0.773401\pi$
$558$	−31.8868	−1.34987
$559$	23.8318	1.00798
$560$	−21.4360	−0.905838
$561$	−63.2382	−2.66992
$562$	10.5185	0.443697
$563$	−8.53228	−0.359593	−0.179796	−	0.983704i	$-0.557544\pi$
$563$	−8.53228	−0.359593	−0.179796	+	0.983704i	$0.557544\pi$
$564$	70.0682	2.95040
$565$	−13.5447	−0.569831
$566$	56.1931	2.36197
$567$	193.748	8.13663
$568$	13.1634	0.552325
$569$	32.9874	1.38290	0.691452	−	0.722422i	$-0.256971\pi$
$569$	32.9874	1.38290	0.691452	+	0.722422i	$0.256971\pi$
$570$	−16.5479	−0.693114
$571$	−27.0200	−1.13075	−0.565376	−	0.824833i	$-0.691269\pi$
$571$	−27.0200	−1.13075	−0.565376	+	0.824833i	$0.691269\pi$
$572$	−43.9808	−1.83893
$573$	−51.3932	−2.14698
$574$	−68.0822	−2.84169
$575$	38.6036	1.60988
$576$	−112.553	−4.68972
$577$	−16.8300	−0.700644	−0.350322	−	0.936629i	$-0.613928\pi$
$577$	−16.8300	−0.700644	−0.350322	+	0.936629i	$0.613928\pi$
$578$	16.4992	0.686277
$579$	−80.7988	−3.35789
$580$	−9.17040	−0.380780
$581$	−23.8195	−0.988198
$582$	−11.2600	−0.466741
$583$	12.8245	0.531138
$584$	−1.14027	−0.0471849
$585$	−71.4006	−2.95205
$586$	−32.6139	−1.34727
$587$	−32.0500	−1.32285	−0.661423	−	0.750013i	$-0.730047\pi$
$587$	−32.0500	−1.32285	−0.661423	+	0.750013i	$0.730047\pi$
$588$	−143.622	−5.92287
$589$	−1.12709	−0.0464410
$590$	−92.1336	−3.79308
$591$	−27.3611	−1.12549
$592$	−4.73468	−0.194594
$593$	1.65260	0.0678643	0.0339322	−	0.999424i	$-0.489197\pi$
$593$	1.65260	0.0678643	0.0339322	+	0.999424i	$0.489197\pi$
$594$	261.674	10.7366
$595$	45.5478	1.86728
$596$	40.4567	1.65717
$597$	−4.88796	−0.200051
$598$	42.6297	1.74326
$599$	22.6178	0.924139	0.462069	−	0.886844i	$-0.347107\pi$
$599$	22.6178	0.924139	0.462069	+	0.886844i	$0.347107\pi$
$600$	34.2748	1.39926
$601$	17.2647	0.704242	0.352121	−	0.935955i	$-0.385461\pi$
$601$	17.2647	0.704242	0.352121	+	0.935955i	$0.385461\pi$
$602$	95.5491	3.89429
$603$	114.662	4.66939
$604$	−19.1767	−0.780289
$605$	78.2510	3.18135
$606$	−58.7557	−2.38679
$607$	−5.13190	−0.208297	−0.104149	−	0.994562i	$-0.533212\pi$
$607$	−5.13190	−0.208297	−0.104149	+	0.994562i	$0.533212\pi$
$608$	−4.88051	−0.197931
$609$	15.9200	0.645112
$610$	16.0369	0.649317
$611$	18.0989	0.732204
$612$	78.1808	3.16027
$613$	3.59021	0.145007	0.0725036	−	0.997368i	$-0.476901\pi$
$613$	3.59021	0.145007	0.0725036	+	0.997368i	$0.476901\pi$
$614$	24.9786	1.00805
$615$	−72.5165	−2.92415
$616$	−54.0201	−2.17653
$617$	6.33574	0.255067	0.127534	−	0.991834i	$-0.459294\pi$
$617$	6.33574	0.255067	0.127534	+	0.991834i	$0.459294\pi$
$618$	−77.5531	−3.11964
$619$	12.7828	0.513783	0.256892	−	0.966440i	$-0.417302\pi$
$619$	12.7828	0.513783	0.256892	+	0.966440i	$0.417302\pi$
$620$	15.0683	0.605156
$621$	−149.757	−6.00954
$622$	40.3907	1.61952
$623$	−3.63692	−0.145710
$624$	−12.7508	−0.510442
$625$	−24.4084	−0.976336
$626$	15.5208	0.620337
$627$	14.0486	0.561047
$628$	0.444643	0.0177432
$629$	10.0604	0.401133
$630$	−286.268	−11.4052
$631$	−26.7259	−1.06394	−0.531971	−	0.846762i	$-0.678549\pi$
$631$	−26.7259	−1.06394	−0.531971	+	0.846762i	$0.678549\pi$
$632$	−15.8343	−0.629855
$633$	75.7291	3.00996
$634$	55.2333	2.19359
$635$	36.5806	1.45166
$636$	−21.2712	−0.843458
$637$	−37.0982	−1.46988
$638$	13.1857	0.522026
$639$	−59.2211	−2.34275
$640$	44.8219	1.77174
$641$	−26.3137	−1.03933	−0.519664	−	0.854371i	$-0.673943\pi$
$641$	−26.3137	−1.03933	−0.519664	+	0.854371i	$0.673943\pi$
$642$	−117.982	−4.65639
$643$	−47.0487	−1.85542	−0.927710	−	0.373303i	$-0.878225\pi$
$643$	−47.0487	−1.85542	−0.927710	+	0.373303i	$0.878225\pi$
$644$	100.916	3.97664
$645$	101.772	4.00729
$646$	4.68028	0.184143
$647$	12.4424	0.489160	0.244580	−	0.969629i	$-0.421350\pi$
$647$	12.4424	0.489160	0.244580	+	0.969629i	$0.421350\pi$
$648$	−81.5393	−3.20317
$649$	78.2184	3.07034
$650$	28.8991	1.13352
$651$	−26.1588	−1.02525
$652$	−24.8037	−0.971387
$653$	−9.44189	−0.369490	−0.184745	−	0.982787i	$-0.559146\pi$
$653$	−9.44189	−0.369490	−0.184745	+	0.982787i	$0.559146\pi$
$654$	62.3935	2.43978
$655$	−9.01649	−0.352303
$656$	−9.65259	−0.376870
$657$	5.12999	0.200140
$658$	72.5643	2.82885
$659$	29.9022	1.16482	0.582412	−	0.812894i	$-0.302109\pi$
$659$	29.9022	1.16482	0.582412	+	0.812894i	$0.302109\pi$
$660$	−187.818	−7.31080
$661$	−27.5708	−1.07238	−0.536191	−	0.844097i	$-0.680137\pi$
$661$	−27.5708	−1.07238	−0.536191	+	0.844097i	$0.680137\pi$
$662$	40.7389	1.58336
$663$	27.0933	1.05222
$664$	10.0245	0.389026
$665$	−10.1186	−0.392383
$666$	−63.2293	−2.45009
$667$	−7.54619	−0.292190
$668$	−10.8195	−0.418618
$669$	35.0567	1.35537
$670$	−91.7687	−3.54533
$671$	−13.6148	−0.525595
$672$	−113.273	−4.36958
$673$	23.0221	0.887436	0.443718	−	0.896166i	$-0.353659\pi$
$673$	23.0221	0.887436	0.443718	+	0.896166i	$0.353659\pi$
$674$	−45.3001	−1.74489
$675$	−101.522	−3.90758
$676$	−18.6402	−0.716933
$677$	−29.7568	−1.14365	−0.571824	−	0.820376i	$-0.693764\pi$
$677$	−29.7568	−1.14365	−0.571824	+	0.820376i	$0.693764\pi$
$678$	−32.3024	−1.24056
$679$	−6.88520	−0.264230
$680$	−19.1689	−0.735095
$681$	81.7748	3.13362
$682$	−21.6659	−0.829631
$683$	23.6830	0.906207	0.453103	−	0.891458i	$-0.350317\pi$
$683$	23.6830	0.906207	0.453103	+	0.891458i	$0.350317\pi$
$684$	−17.3682	−0.664089
$685$	−46.9996	−1.79576
$686$	−76.9927	−2.93960
$687$	−12.1657	−0.464152
$688$	13.5468	0.516468
$689$	−5.49444	−0.209322
$690$	182.048	6.93044
$691$	−41.1247	−1.56446	−0.782229	−	0.622991i	$-0.785917\pi$
$691$	−41.1247	−1.56446	−0.782229	+	0.622991i	$0.785917\pi$
$692$	−5.98388	−0.227473
$693$	243.032	9.23201
$694$	21.6206	0.820707
$695$	3.18051	0.120644
$696$	−6.70000	−0.253963
$697$	20.5101	0.776874
$698$	62.3177	2.35876
$699$	−48.0681	−1.81810
$700$	68.4119	2.58573
$701$	1.50959	0.0570163	0.0285082	−	0.999594i	$-0.490924\pi$
$701$	1.50959	0.0570163	0.0285082	+	0.999594i	$0.490924\pi$
$702$	−112.110	−4.23131
$703$	−2.23495	−0.0842927
$704$	−76.4760	−2.88230
$705$	77.2906	2.91093
$706$	64.9398	2.44404
$707$	−35.9276	−1.35120
$708$	−129.736	−4.87576
$709$	−22.1543	−0.832023	−0.416012	−	0.909359i	$-0.636572\pi$
$709$	−22.1543	−0.832023	−0.416012	+	0.909359i	$0.636572\pi$
$710$	47.3971	1.77878
$711$	71.2372	2.67160
$712$	1.53061	0.0573621
$713$	12.3995	0.464363
$714$	108.625	4.06520
$715$	−48.5142	−1.81433
$716$	−26.4169	−0.987247
$717$	−2.59457	−0.0968961
$718$	37.1905	1.38794
$719$	42.4642	1.58365	0.791824	−	0.610749i	$-0.209132\pi$
$719$	42.4642	1.58365	0.791824	+	0.610749i	$0.209132\pi$
$720$	−40.5866	−1.51257
$721$	−47.4218	−1.76608
$722$	40.9469	1.52388
$723$	−56.7165	−2.10931
$724$	39.8316	1.48033
$725$	−5.11564	−0.189990
$726$	186.618	6.92605
$727$	−8.48538	−0.314705	−0.157353	−	0.987542i	$-0.550296\pi$
$727$	−8.48538	−0.314705	−0.157353	+	0.987542i	$0.550296\pi$
$728$	23.1439	0.857772
$729$	162.484	6.01792
$730$	−4.10575	−0.151961
$731$	−28.7846	−1.06464
$732$	22.5820	0.834656
$733$	−15.1957	−0.561264	−0.280632	−	0.959815i	$-0.590544\pi$
$733$	−15.1957	−0.561264	−0.280632	+	0.959815i	$0.590544\pi$
$734$	33.3606	1.23136
$735$	−158.426	−5.84363
$736$	53.6919	1.97911
$737$	77.9086	2.86980
$738$	−128.906	−4.74508
$739$	26.0977	0.960021	0.480011	−	0.877263i	$-0.340633\pi$
$739$	26.0977	0.960021	0.480011	+	0.877263i	$0.340633\pi$
$740$	29.8793	1.09839
$741$	−6.01888	−0.221109
$742$	−22.0290	−0.808708
$743$	19.9100	0.730426	0.365213	−	0.930924i	$-0.380996\pi$
$743$	19.9100	0.730426	0.365213	+	0.930924i	$0.380996\pi$
$744$	11.0090	0.403611
$745$	44.6268	1.63500
$746$	69.2965	2.53712
$747$	−45.0994	−1.65010
$748$	53.1211	1.94230
$749$	−72.1432	−2.63606
$750$	2.78985	0.101871
$751$	−39.5021	−1.44145	−0.720726	−	0.693220i	$-0.756192\pi$
$751$	−39.5021	−1.44145	−0.720726	+	0.693220i	$0.756192\pi$
$752$	10.2881	0.375167
$753$	49.1555	1.79133
$754$	−5.64916	−0.205730
$755$	−21.1534	−0.769850
$756$	−265.393	−9.65227
$757$	11.8395	0.430314	0.215157	−	0.976580i	$-0.430974\pi$
$757$	11.8395	0.430314	0.215157	+	0.976580i	$0.430974\pi$
$758$	46.8418	1.70137
$759$	−154.553	−5.60991
$760$	4.25845	0.154470
$761$	1.95134	0.0707359	0.0353680	−	0.999374i	$-0.488740\pi$
$761$	1.95134	0.0707359	0.0353680	+	0.999374i	$0.488740\pi$
$762$	87.2399	3.16037
$763$	38.1521	1.38120
$764$	43.1711	1.56188
$765$	86.2394	3.11799
$766$	−12.6013	−0.455302
$767$	−33.5113	−1.21002
$768$	18.9082	0.682291
$769$	−6.74699	−0.243303	−0.121651	−	0.992573i	$-0.538819\pi$
$769$	−6.74699	−0.243303	−0.121651	+	0.992573i	$0.538819\pi$
$770$	−194.509	−7.00960
$771$	29.4899	1.06205
$772$	67.8723	2.44278
$773$	−1.97553	−0.0710549	−0.0355274	−	0.999369i	$-0.511311\pi$
$773$	−1.97553	−0.0710549	−0.0355274	+	0.999369i	$0.511311\pi$
$774$	180.911	6.50272
$775$	8.40573	0.301943
$776$	2.89766	0.104020
$777$	−51.8712	−1.86087
$778$	−23.2323	−0.832919
$779$	−4.55639	−0.163250
$780$	80.4672	2.88119
$781$	−40.2386	−1.43985
$782$	−51.4891	−1.84125
$783$	19.8454	0.709215
$784$	−21.0879	−0.753139
$785$	0.490475	0.0175058
$786$	−21.5031	−0.766991
$787$	−25.6043	−0.912695	−0.456347	−	0.889802i	$-0.650843\pi$
$787$	−25.6043	−0.912695	−0.456347	+	0.889802i	$0.650843\pi$
$788$	22.9838	0.818763
$789$	15.1006	0.537595
$790$	−57.0141	−2.02847
$791$	−19.7521	−0.702304
$792$	−102.281	−3.63439
$793$	5.83303	0.207137
$794$	−52.3618	−1.85825
$795$	−23.4638	−0.832174
$796$	4.10596	0.145532
$797$	−2.57779	−0.0913099	−0.0456549	−	0.998957i	$-0.514537\pi$
$797$	−2.57779	−0.0913099	−0.0456549	+	0.998957i	$0.514537\pi$
$798$	−24.1316	−0.854248
$799$	−21.8603	−0.773362
$800$	36.3983	1.28687
$801$	−6.88609	−0.243308
$802$	−16.5761	−0.585321
$803$	3.48565	0.123006
$804$	−129.222	−4.55730
$805$	111.318	3.92344
$806$	9.28237	0.326958
$807$	−84.8310	−2.98619
$808$	15.1203	0.531929
$809$	−32.4352	−1.14036	−0.570180	−	0.821520i	$-0.693127\pi$
$809$	−32.4352	−1.14036	−0.570180	+	0.821520i	$0.693127\pi$
$810$	−293.596	−10.3159
$811$	−41.3450	−1.45182	−0.725909	−	0.687791i	$-0.758581\pi$
$811$	−41.3450	−1.45182	−0.725909	+	0.687791i	$0.758581\pi$
$812$	−13.3731	−0.469303
$813$	−75.7604	−2.65703
$814$	−42.9621	−1.50582
$815$	−27.3603	−0.958390
$816$	15.4008	0.539134
$817$	6.39461	0.223719
$818$	−35.1797	−1.23003
$819$	−104.123	−3.63834
$820$	60.9150	2.12725
$821$	−14.5416	−0.507506	−0.253753	−	0.967269i	$-0.581665\pi$
$821$	−14.5416	−0.507506	−0.253753	+	0.967269i	$0.581665\pi$
$822$	−112.088	−3.90951
$823$	16.9678	0.591462	0.295731	−	0.955271i	$-0.404437\pi$
$823$	16.9678	0.591462	0.295731	+	0.955271i	$0.404437\pi$
$824$	19.9576	0.695257
$825$	−104.773	−3.64773
$826$	−134.357	−4.67489
$827$	36.9842	1.28607	0.643033	−	0.765839i	$-0.277676\pi$
$827$	36.9842	1.28607	0.643033	+	0.765839i	$0.277676\pi$
$828$	191.072	6.64022
$829$	45.1488	1.56808	0.784041	−	0.620710i	$-0.213155\pi$
$829$	45.1488	1.56808	0.784041	+	0.620710i	$0.213155\pi$
$830$	36.0949	1.25287
$831$	−6.28620	−0.218066
$832$	32.7648	1.13591
$833$	44.8081	1.55251
$834$	7.58510	0.262650
$835$	−11.9347	−0.413017
$836$	−11.8011	−0.408148
$837$	−32.6087	−1.12712
$838$	47.2385	1.63183
$839$	−52.2683	−1.80450	−0.902251	−	0.431212i	$-0.858086\pi$
$839$	−52.2683	−1.80450	−0.902251	+	0.431212i	$0.858086\pi$
$840$	98.8351	3.41013
$841$	1.00000	0.0344828
$842$	56.7566	1.95596
$843$	16.3381	0.562714
$844$	−63.6137	−2.18967
$845$	−20.5616	−0.707341
$846$	137.392	4.72363
$847$	114.112	3.92095
$848$	−3.12323	−0.107252
$849$	87.2830	2.99555
$850$	−34.9050	−1.19723
$851$	24.5873	0.842841
$852$	66.7411	2.28651
$853$	42.0639	1.44024	0.720120	−	0.693849i	$-0.244087\pi$
$853$	42.0639	1.44024	0.720120	+	0.693849i	$0.244087\pi$
$854$	23.3865	0.800268
$855$	−19.1584	−0.655204
$856$	30.3617	1.03774
$857$	−9.03502	−0.308630	−0.154315	−	0.988022i	$-0.549317\pi$
$857$	−9.03502	−0.308630	−0.154315	+	0.988022i	$0.549317\pi$
$858$	−115.700	−3.94993
$859$	−11.6751	−0.398349	−0.199174	−	0.979964i	$-0.563826\pi$
$859$	−11.6751	−0.398349	−0.199174	+	0.979964i	$0.563826\pi$
$860$	−85.4905	−2.91520
$861$	−105.750	−3.60395
$862$	54.0919	1.84238
$863$	−35.8692	−1.22100	−0.610501	−	0.792016i	$-0.709032\pi$
$863$	−35.8692	−1.22100	−0.610501	+	0.792016i	$0.709032\pi$
$864$	−141.202	−4.80378
$865$	−6.60067	−0.224430
$866$	−5.77132	−0.196118
$867$	25.6277	0.870363
$868$	21.9739	0.745841
$869$	48.4031	1.64196
$870$	−24.1245	−0.817896
$871$	−33.3786	−1.13099
$872$	−16.0564	−0.543740
$873$	−13.0363	−0.441212
$874$	11.4385	0.386913
$875$	1.70592	0.0576707
$876$	−5.78141	−0.195336
$877$	21.4576	0.724570	0.362285	−	0.932067i	$-0.381997\pi$
$877$	21.4576	0.724570	0.362285	+	0.932067i	$0.381997\pi$
$878$	51.9088	1.75184
$879$	−50.6581	−1.70865
$880$	−27.5772	−0.929626
$881$	16.0281	0.540002	0.270001	−	0.962860i	$-0.412976\pi$
$881$	16.0281	0.540002	0.270001	+	0.962860i	$0.412976\pi$
$882$	−281.618	−9.48259
$883$	−19.2491	−0.647785	−0.323893	−	0.946094i	$-0.604992\pi$
$883$	−19.2491	−0.647785	−0.323893	+	0.946094i	$0.604992\pi$
$884$	−22.7588	−0.765460
$885$	−143.108	−4.81053
$886$	−6.98570	−0.234689
$887$	−10.2589	−0.344461	−0.172231	−	0.985057i	$-0.555097\pi$
$887$	−10.2589	−0.344461	−0.172231	+	0.985057i	$0.555097\pi$
$888$	21.8302	0.732573
$889$	53.3450	1.78913
$890$	5.51123	0.184737
$891$	249.254	8.35031
$892$	−29.4482	−0.985999
$893$	4.85635	0.162512
$894$	106.429	3.55952
$895$	−29.1399	−0.974039
$896$	65.3632	2.18363
$897$	66.2153	2.21087
$898$	55.5114	1.85244
$899$	−1.64314	−0.0548018
$900$	129.530	4.31766
$901$	6.63632	0.221088
$902$	−87.5867	−2.91632
$903$	148.414	4.93889
$904$	8.31273	0.276477
$905$	43.9373	1.46052
$906$	−50.4480	−1.67602
$907$	35.1978	1.16872	0.584362	−	0.811493i	$-0.301345\pi$
$907$	35.1978	1.16872	0.584362	+	0.811493i	$0.301345\pi$
$908$	−68.6922	−2.27963
$909$	−68.0248	−2.25624
$910$	83.3337	2.76249
$911$	−45.7595	−1.51608	−0.758039	−	0.652209i	$-0.773842\pi$
$911$	−45.7595	−1.51608	−0.758039	+	0.652209i	$0.773842\pi$
$912$	−3.42134	−0.113292
$913$	−30.6434	−1.01415
$914$	−10.1509	−0.335763
$915$	24.9097	0.823489
$916$	10.2194	0.337659
$917$	−13.1486	−0.434206
$918$	135.409	4.46915
$919$	−2.52235	−0.0832046	−0.0416023	−	0.999134i	$-0.513246\pi$
$919$	−2.52235	−0.0832046	−0.0416023	+	0.999134i	$0.513246\pi$
$920$	−46.8485	−1.54455
$921$	38.7984	1.27845
$922$	−37.1929	−1.22488
$923$	17.2395	0.567445
$924$	−273.893	−9.01040
$925$	16.6680	0.548040
$926$	−54.6203	−1.79493
$927$	−89.7876	−2.94901
$928$	−7.11510	−0.233565
$929$	15.5843	0.511303	0.255652	−	0.966769i	$-0.417710\pi$
$929$	15.5843	0.511303	0.255652	+	0.966769i	$0.417710\pi$
$930$	39.6399	1.29984
$931$	−9.95429	−0.326239
$932$	40.3780	1.32262
$933$	62.7376	2.05394
$934$	27.2519	0.891711
$935$	58.5966	1.91631
$936$	43.8204	1.43231
$937$	−14.4114	−0.470800	−0.235400	−	0.971899i	$-0.575640\pi$
$937$	−14.4114	−0.470800	−0.235400	+	0.971899i	$0.575640\pi$
$938$	−133.825	−4.36955
$939$	24.1080	0.786735
$940$	−64.9253	−2.11763
$941$	−30.5096	−0.994585	−0.497292	−	0.867583i	$-0.665672\pi$
$941$	−30.5096	−0.994585	−0.497292	+	0.867583i	$0.665672\pi$
$942$	1.16972	0.0381115
$943$	50.1261	1.63233
$944$	−19.0490	−0.619992
$945$	−292.749	−9.52313
$946$	122.923	3.99656
$947$	46.6458	1.51578	0.757892	−	0.652380i	$-0.226229\pi$
$947$	46.6458	1.51578	0.757892	+	0.652380i	$0.226229\pi$
$948$	−80.2830	−2.60747
$949$	−1.49336	−0.0484766
$950$	7.75429	0.251582
$951$	85.7922	2.78200
$952$	−27.9538	−0.905988
$953$	−30.2992	−0.981486	−0.490743	−	0.871304i	$-0.663275\pi$
$953$	−30.2992	−0.981486	−0.490743	+	0.871304i	$0.663275\pi$
$954$	−41.7092	−1.35039
$955$	47.6210	1.54098
$956$	2.17948	0.0704895
$957$	20.4809	0.662053
$958$	−59.0988	−1.90940
$959$	−68.5389	−2.21324
$960$	139.920	4.51591
$961$	−28.3001	−0.912906
$962$	18.4063	0.593444
$963$	−136.595	−4.40170
$964$	47.6428	1.53447
$965$	74.8683	2.41010
$966$	265.478	8.54162
$967$	13.1955	0.424339	0.212169	−	0.977233i	$-0.431947\pi$
$967$	13.1955	0.424339	0.212169	+	0.977233i	$0.431947\pi$
$968$	−48.0246	−1.54357
$969$	7.26974	0.233538
$970$	10.4335	0.335000
$971$	27.3306	0.877079	0.438540	−	0.898712i	$-0.355496\pi$
$971$	27.3306	0.877079	0.438540	+	0.898712i	$0.355496\pi$
$972$	−241.759	−7.75443
$973$	4.63810	0.148691
$974$	−6.81305	−0.218304
$975$	44.8881	1.43757
$976$	3.31570	0.106133
$977$	46.6600	1.49279	0.746393	−	0.665506i	$-0.231784\pi$
$977$	46.6600	1.49279	0.746393	+	0.665506i	$0.231784\pi$
$978$	−65.2507	−2.08649
$979$	−4.67885	−0.149537
$980$	133.080	4.25110
$981$	72.2365	2.30633
$982$	−67.0980	−2.14118
$983$	23.3498	0.744745	0.372372	−	0.928083i	$-0.378544\pi$
$983$	23.3498	0.744745	0.372372	+	0.928083i	$0.378544\pi$
$984$	44.5052	1.41877
$985$	25.3529	0.807809
$986$	6.82319	0.217295
$987$	112.712	3.58766
$988$	5.05595	0.160851
$989$	−70.3489	−2.23697
$990$	−368.279	−11.7047
$991$	48.5697	1.54287	0.771433	−	0.636310i	$-0.219540\pi$
$991$	48.5697	1.54287	0.771433	+	0.636310i	$0.219540\pi$
$992$	11.6911	0.371193
$993$	63.2785	2.00808
$994$	69.1186	2.19231
$995$	4.52919	0.143585
$996$	50.8262	1.61049
$997$	−11.7339	−0.371615	−0.185808	−	0.982586i	$-0.559490\pi$
$997$	−11.7339	−0.371615	−0.185808	+	0.982586i	$0.559490\pi$
$998$	−72.8908	−2.30732
$999$	−64.6609	−2.04578

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4031.2.a.e.1.16	✓	103

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4031.2.a.e.1.16	✓	103	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:	\( N \)	\(=\)	\( 4031 = 29 \cdot 139 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4031.a (trivial)

\(f(q)\)	\(=\)	\(q-2.20982 q^{2} -3.43245 q^{3} +2.88331 q^{4} +3.18051 q^{5} +7.58510 q^{6} +4.63810 q^{7} -1.95196 q^{8} +8.78169 q^{9} +O(q^{10})\)	\(q-2.20982 q^{2} -3.43245 q^{3} +2.88331 q^{4} +3.18051 q^{5} +7.58510 q^{6} +4.63810 q^{7} -1.95196 q^{8} +8.78169 q^{9} -7.02836 q^{10} +5.96685 q^{11} -9.89681 q^{12} -2.55639 q^{13} -10.2494 q^{14} -10.9169 q^{15} -1.45314 q^{16} +3.08767 q^{17} -19.4060 q^{18} -0.685938 q^{19} +9.17040 q^{20} -15.9200 q^{21} -13.1857 q^{22} +7.54619 q^{23} +6.70000 q^{24} +5.11564 q^{25} +5.64916 q^{26} -19.8454 q^{27} +13.3731 q^{28} -1.00000 q^{29} +24.1245 q^{30} +1.64314 q^{31} +7.11510 q^{32} -20.4809 q^{33} -6.82319 q^{34} +14.7515 q^{35} +25.3204 q^{36} +3.25824 q^{37} +1.51580 q^{38} +8.77467 q^{39} -6.20822 q^{40} +6.64257 q^{41} +35.1804 q^{42} -9.32244 q^{43} +17.2043 q^{44} +27.9303 q^{45} -16.6757 q^{46} -7.07988 q^{47} +4.98783 q^{48} +14.5119 q^{49} -11.3047 q^{50} -10.5983 q^{51} -7.37086 q^{52} +2.14930 q^{53} +43.8547 q^{54} +18.9776 q^{55} -9.05338 q^{56} +2.35444 q^{57} +2.20982 q^{58} +13.1088 q^{59} -31.4769 q^{60} -2.28175 q^{61} -3.63105 q^{62} +40.7303 q^{63} -12.8168 q^{64} -8.13062 q^{65} +45.2591 q^{66} +13.0569 q^{67} +8.90271 q^{68} -25.9019 q^{69} -32.5982 q^{70} -6.74370 q^{71} -17.1415 q^{72} +0.584169 q^{73} -7.20012 q^{74} -17.5592 q^{75} -1.97777 q^{76} +27.6748 q^{77} -19.3905 q^{78} +8.11201 q^{79} -4.62173 q^{80} +41.7731 q^{81} -14.6789 q^{82} -5.13561 q^{83} -45.9024 q^{84} +9.82036 q^{85} +20.6009 q^{86} +3.43245 q^{87} -11.6470 q^{88} -0.784141 q^{89} -61.7209 q^{90} -11.8568 q^{91} +21.7580 q^{92} -5.64000 q^{93} +15.6453 q^{94} -2.18163 q^{95} -24.4222 q^{96} -1.48449 q^{97} -32.0688 q^{98} +52.3990 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 103 q + q^{2} + 2 q^{3} + 127 q^{4} + 9 q^{5} + 19 q^{6} + 18 q^{7} + 149 q^{9}+O(q^{10}) \) 103 * q + q^2 + 2 * q^3 + 127 * q^4 + 9 * q^5 + 19 * q^6 + 18 * q^7 + 149 * q^9	\( 103 q + q^{2} + 2 q^{3} + 127 q^{4} + 9 q^{5} + 19 q^{6} + 18 q^{7} + 149 q^{9} + 20 q^{10} + 9 q^{11} + 36 q^{13} - 10 q^{14} + 16 q^{15} + 179 q^{16} + 21 q^{17} + 7 q^{18} + 42 q^{19} + 24 q^{20} + 28 q^{21} + 32 q^{22} + 25 q^{23} + 68 q^{24} + 194 q^{25} - 5 q^{26} + 14 q^{27} + 59 q^{28} - 103 q^{29} + 84 q^{30} + 34 q^{31} + 11 q^{32} + 42 q^{33} + 54 q^{34} + 35 q^{35} + 214 q^{36} + 34 q^{37} + 9 q^{38} + 23 q^{39} + 46 q^{40} + 16 q^{41} + 13 q^{42} + 68 q^{43} - 6 q^{44} + 25 q^{45} + 60 q^{46} + 6 q^{47} + 5 q^{48} + 257 q^{49} - 51 q^{50} + 68 q^{51} + 37 q^{52} + 35 q^{53} + 30 q^{54} + 66 q^{55} - 54 q^{56} + 78 q^{57} - q^{58} + 10 q^{59} - 24 q^{60} + 70 q^{61} + 29 q^{62} + 26 q^{63} + 276 q^{64} + 95 q^{65} + 77 q^{66} + 71 q^{67} - 21 q^{68} - 20 q^{69} + 48 q^{70} + 32 q^{71} + 32 q^{72} + 94 q^{73} + 35 q^{74} + 7 q^{75} + 134 q^{76} + 17 q^{77} + 58 q^{78} + 110 q^{79} + 78 q^{80} + 267 q^{81} - 71 q^{82} + 35 q^{83} + 96 q^{84} + 71 q^{85} + 33 q^{86} - 2 q^{87} + 100 q^{88} + 22 q^{89} - 134 q^{90} + 108 q^{91} - 11 q^{92} + 78 q^{93} + 90 q^{94} + 12 q^{95} + 177 q^{96} + 44 q^{97} - 18 q^{98} + 83 q^{99}+O(q^{100}) \) 103 * q + q^2 + 2 * q^3 + 127 * q^4 + 9 * q^5 + 19 * q^6 + 18 * q^7 + 149 * q^9 + 20 * q^10 + 9 * q^11 + 36 * q^13 - 10 * q^14 + 16 * q^15 + 179 * q^16 + 21 * q^17 + 7 * q^18 + 42 * q^19 + 24 * q^20 + 28 * q^21 + 32 * q^22 + 25 * q^23 + 68 * q^24 + 194 * q^25 - 5 * q^26 + 14 * q^27 + 59 * q^28 - 103 * q^29 + 84 * q^30 + 34 * q^31 + 11 * q^32 + 42 * q^33 + 54 * q^34 + 35 * q^35 + 214 * q^36 + 34 * q^37 + 9 * q^38 + 23 * q^39 + 46 * q^40 + 16 * q^41 + 13 * q^42 + 68 * q^43 - 6 * q^44 + 25 * q^45 + 60 * q^46 + 6 * q^47 + 5 * q^48 + 257 * q^49 - 51 * q^50 + 68 * q^51 + 37 * q^52 + 35 * q^53 + 30 * q^54 + 66 * q^55 - 54 * q^56 + 78 * q^57 - q^58 + 10 * q^59 - 24 * q^60 + 70 * q^61 + 29 * q^62 + 26 * q^63 + 276 * q^64 + 95 * q^65 + 77 * q^66 + 71 * q^67 - 21 * q^68 - 20 * q^69 + 48 * q^70 + 32 * q^71 + 32 * q^72 + 94 * q^73 + 35 * q^74 + 7 * q^75 + 134 * q^76 + 17 * q^77 + 58 * q^78 + 110 * q^79 + 78 * q^80 + 267 * q^81 - 71 * q^82 + 35 * q^83 + 96 * q^84 + 71 * q^85 + 33 * q^86 - 2 * q^87 + 100 * q^88 + 22 * q^89 - 134 * q^90 + 108 * q^91 - 11 * q^92 + 78 * q^93 + 90 * q^94 + 12 * q^95 + 177 * q^96 + 44 * q^97 - 18 * q^98 + 83 * q^99

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