LMFDB - Embedded newform 8043.2.a.o.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8043,2,Mod(1,8043)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8043, 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("8043.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8043 = 3 \cdot 7 \cdot 383 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8043.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$64.2236783457$
Analytic rank:	$1$
Dimension:	$41$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Character	$\chi$	$=$	8043.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.81957 q^{2} -1.00000 q^{3} +1.31084 q^{4} +0.0545380 q^{5} +1.81957 q^{6} +1.00000 q^{7} +1.25397 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.81957 q^{2} -1.00000 q^{3} +1.31084 q^{4} +0.0545380 q^{5} +1.81957 q^{6} +1.00000 q^{7} +1.25397 q^{8} +1.00000 q^{9} -0.0992358 q^{10} -4.37533 q^{11} -1.31084 q^{12} -4.14228 q^{13} -1.81957 q^{14} -0.0545380 q^{15} -4.90338 q^{16} -0.737867 q^{17} -1.81957 q^{18} -2.61449 q^{19} +0.0714907 q^{20} -1.00000 q^{21} +7.96124 q^{22} -3.28992 q^{23} -1.25397 q^{24} -4.99703 q^{25} +7.53718 q^{26} -1.00000 q^{27} +1.31084 q^{28} -1.83606 q^{29} +0.0992358 q^{30} +4.69240 q^{31} +6.41411 q^{32} +4.37533 q^{33} +1.34260 q^{34} +0.0545380 q^{35} +1.31084 q^{36} +10.8584 q^{37} +4.75725 q^{38} +4.14228 q^{39} +0.0683891 q^{40} +11.3665 q^{41} +1.81957 q^{42} +3.22453 q^{43} -5.73538 q^{44} +0.0545380 q^{45} +5.98625 q^{46} +12.8747 q^{47} +4.90338 q^{48} +1.00000 q^{49} +9.09245 q^{50} +0.737867 q^{51} -5.42988 q^{52} -0.678812 q^{53} +1.81957 q^{54} -0.238622 q^{55} +1.25397 q^{56} +2.61449 q^{57} +3.34085 q^{58} +2.96920 q^{59} -0.0714907 q^{60} +3.60089 q^{61} -8.53816 q^{62} +1.00000 q^{63} -1.86417 q^{64} -0.225912 q^{65} -7.96124 q^{66} -6.62048 q^{67} -0.967228 q^{68} +3.28992 q^{69} -0.0992358 q^{70} +4.46606 q^{71} +1.25397 q^{72} -3.31321 q^{73} -19.7576 q^{74} +4.99703 q^{75} -3.42719 q^{76} -4.37533 q^{77} -7.53718 q^{78} -7.81112 q^{79} -0.267420 q^{80} +1.00000 q^{81} -20.6821 q^{82} -1.78859 q^{83} -1.31084 q^{84} -0.0402418 q^{85} -5.86726 q^{86} +1.83606 q^{87} -5.48654 q^{88} -12.9560 q^{89} -0.0992358 q^{90} -4.14228 q^{91} -4.31257 q^{92} -4.69240 q^{93} -23.4264 q^{94} -0.142589 q^{95} -6.41411 q^{96} -12.4769 q^{97} -1.81957 q^{98} -4.37533 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 41 q - 4 q^{2} - 41 q^{3} + 34 q^{4} + 5 q^{5} + 4 q^{6} + 41 q^{7} - 15 q^{8} + 41 q^{9}+O(q^{10}) $ 41 * q - 4 * q^2 - 41 * q^3 + 34 * q^4 + 5 * q^5 + 4 * q^6 + 41 * q^7 - 15 * q^8 + 41 * q^9	\( 41 q - 4 q^{2} - 41 q^{3} + 34 q^{4} + 5 q^{5} + 4 q^{6} + 41 q^{7} - 15 q^{8} + 41 q^{9} - 18 q^{10} - 17 q^{11} - 34 q^{12} - 38 q^{13} - 4 q^{14} - 5 q^{15} + 16 q^{16} + 4 q^{17} - 4 q^{18} - 15 q^{19} + 23 q^{20} - 41 q^{21} - 31 q^{22} - 8 q^{23} + 15 q^{24} + 16 q^{25} + 15 q^{26} - 41 q^{27} + 34 q^{28} - 27 q^{29} + 18 q^{30} - 23 q^{31} - 24 q^{32} + 17 q^{33} - 9 q^{34} + 5 q^{35} + 34 q^{36} - 81 q^{37} + 38 q^{39} - 52 q^{40} + 29 q^{41} + 4 q^{42} - 47 q^{43} - 20 q^{44} + 5 q^{45} - 40 q^{46} + 26 q^{47} - 16 q^{48} + 41 q^{49} - 23 q^{50} - 4 q^{51} - 64 q^{52} - 66 q^{53} + 4 q^{54} - 14 q^{55} - 15 q^{56} + 15 q^{57} - 50 q^{58} + 41 q^{59} - 23 q^{60} - 47 q^{61} + 5 q^{62} + 41 q^{63} - 37 q^{64} - 24 q^{65} + 31 q^{66} - 73 q^{67} + 10 q^{68} + 8 q^{69} - 18 q^{70} + q^{71} - 15 q^{72} - 14 q^{73} + 18 q^{74} - 16 q^{75} - 37 q^{76} - 17 q^{77} - 15 q^{78} - 80 q^{79} + 63 q^{80} + 41 q^{81} - 31 q^{82} + 20 q^{83} - 34 q^{84} - 82 q^{85} - 39 q^{86} + 27 q^{87} - 132 q^{88} + 17 q^{89} - 18 q^{90} - 38 q^{91} - 26 q^{92} + 23 q^{93} - 9 q^{94} - q^{95} + 24 q^{96} - 73 q^{97} - 4 q^{98} - 17 q^{99}+O(q^{100}) \) 41 * q - 4 * q^2 - 41 * q^3 + 34 * q^4 + 5 * q^5 + 4 * q^6 + 41 * q^7 - 15 * q^8 + 41 * q^9 - 18 * q^10 - 17 * q^11 - 34 * q^12 - 38 * q^13 - 4 * q^14 - 5 * q^15 + 16 * q^16 + 4 * q^17 - 4 * q^18 - 15 * q^19 + 23 * q^20 - 41 * q^21 - 31 * q^22 - 8 * q^23 + 15 * q^24 + 16 * q^25 + 15 * q^26 - 41 * q^27 + 34 * q^28 - 27 * q^29 + 18 * q^30 - 23 * q^31 - 24 * q^32 + 17 * q^33 - 9 * q^34 + 5 * q^35 + 34 * q^36 - 81 * q^37 + 38 * q^39 - 52 * q^40 + 29 * q^41 + 4 * q^42 - 47 * q^43 - 20 * q^44 + 5 * q^45 - 40 * q^46 + 26 * q^47 - 16 * q^48 + 41 * q^49 - 23 * q^50 - 4 * q^51 - 64 * q^52 - 66 * q^53 + 4 * q^54 - 14 * q^55 - 15 * q^56 + 15 * q^57 - 50 * q^58 + 41 * q^59 - 23 * q^60 - 47 * q^61 + 5 * q^62 + 41 * q^63 - 37 * q^64 - 24 * q^65 + 31 * q^66 - 73 * q^67 + 10 * q^68 + 8 * q^69 - 18 * q^70 + q^71 - 15 * q^72 - 14 * q^73 + 18 * q^74 - 16 * q^75 - 37 * q^76 - 17 * q^77 - 15 * q^78 - 80 * q^79 + 63 * q^80 + 41 * q^81 - 31 * q^82 + 20 * q^83 - 34 * q^84 - 82 * q^85 - 39 * q^86 + 27 * q^87 - 132 * q^88 + 17 * q^89 - 18 * q^90 - 38 * q^91 - 26 * q^92 + 23 * q^93 - 9 * q^94 - q^95 + 24 * q^96 - 73 * q^97 - 4 * q^98 - 17 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.81957	−1.28663	−0.643316	−	0.765601i	$-0.722442\pi$
$2$	−1.81957	−1.28663	−0.643316	+	0.765601i	$0.722442\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.31084	0.655421
$5$	0.0545380	0.0243901	0.0121951	−	0.999926i	$-0.496118\pi$
$5$	0.0545380	0.0243901	0.0121951	+	0.999926i	$0.496118\pi$
$6$	1.81957	0.742837
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.25397	0.443346
$9$	1.00000	0.333333
$10$	−0.0992358	−0.0313811
$11$	−4.37533	−1.31921	−0.659606	−	0.751611i	$-0.729277\pi$
$11$	−4.37533	−1.31921	−0.659606	+	0.751611i	$0.729277\pi$
$12$	−1.31084	−0.378408
$13$	−4.14228	−1.14886	−0.574431	−	0.818553i	$-0.694777\pi$
$13$	−4.14228	−1.14886	−0.574431	+	0.818553i	$0.694777\pi$
$14$	−1.81957	−0.486301
$15$	−0.0545380	−0.0140817
$16$	−4.90338	−1.22584
$17$	−0.737867	−0.178959	−0.0894795	−	0.995989i	$-0.528520\pi$
$17$	−0.737867	−0.178959	−0.0894795	+	0.995989i	$0.528520\pi$
$18$	−1.81957	−0.428877
$19$	−2.61449	−0.599805	−0.299903	−	0.953970i	$-0.596954\pi$
$19$	−2.61449	−0.599805	−0.299903	+	0.953970i	$0.596954\pi$
$20$	0.0714907	0.0159858
$21$	−1.00000	−0.218218
$22$	7.96124	1.69734
$23$	−3.28992	−0.685996	−0.342998	−	0.939336i	$-0.611442\pi$
$23$	−3.28992	−0.685996	−0.342998	+	0.939336i	$0.611442\pi$
$24$	−1.25397	−0.255966
$25$	−4.99703	−0.999405
$26$	7.53718	1.47816
$27$	−1.00000	−0.192450
$28$	1.31084	0.247726
$29$	−1.83606	−0.340948	−0.170474	−	0.985362i	$-0.554530\pi$
$29$	−1.83606	−0.340948	−0.170474	+	0.985362i	$0.554530\pi$
$30$	0.0992358	0.0181179
$31$	4.69240	0.842780	0.421390	−	0.906879i	$-0.361542\pi$
$31$	4.69240	0.842780	0.421390	+	0.906879i	$0.361542\pi$
$32$	6.41411	1.13386
$33$	4.37533	0.761648
$34$	1.34260	0.230254
$35$	0.0545380	0.00921860
$36$	1.31084	0.218474
$37$	10.8584	1.78511	0.892555	−	0.450939i	$-0.148911\pi$
$37$	10.8584	1.78511	0.892555	+	0.450939i	$0.148911\pi$
$38$	4.75725	0.771729
$39$	4.14228	0.663296
$40$	0.0683891	0.0108133
$41$	11.3665	1.77515	0.887573	−	0.460668i	$-0.152390\pi$
$41$	11.3665	1.77515	0.887573	+	0.460668i	$0.152390\pi$
$42$	1.81957	0.280766
$43$	3.22453	0.491736	0.245868	−	0.969303i	$-0.420927\pi$
$43$	3.22453	0.491736	0.245868	+	0.969303i	$0.420927\pi$
$44$	−5.73538	−0.864640
$45$	0.0545380	0.00813004
$46$	5.98625	0.882625
$47$	12.8747	1.87797	0.938983	−	0.343964i	$-0.111770\pi$
$47$	12.8747	1.87797	0.938983	+	0.343964i	$0.111770\pi$
$48$	4.90338	0.707741
$49$	1.00000	0.142857
$50$	9.09245	1.28587
$51$	0.737867	0.103322
$52$	−5.42988	−0.752989
$53$	−0.678812	−0.0932421	−0.0466210	−	0.998913i	$-0.514845\pi$
$53$	−0.678812	−0.0932421	−0.0466210	+	0.998913i	$0.514845\pi$
$54$	1.81957	0.247612
$55$	−0.238622	−0.0321758
$56$	1.25397	0.167569
$57$	2.61449	0.346298
$58$	3.34085	0.438675
$59$	2.96920	0.386557	0.193279	−	0.981144i	$-0.438088\pi$
$59$	2.96920	0.386557	0.193279	+	0.981144i	$0.438088\pi$
$60$	−0.0714907	−0.00922942
$61$	3.60089	0.461046	0.230523	−	0.973067i	$-0.425956\pi$
$61$	3.60089	0.461046	0.230523	+	0.973067i	$0.425956\pi$
$62$	−8.53816	−1.08435
$63$	1.00000	0.125988
$64$	−1.86417	−0.233022
$65$	−0.225912	−0.0280209
$66$	−7.96124	−0.979961
$67$	−6.62048	−0.808820	−0.404410	−	0.914578i	$-0.632523\pi$
$67$	−6.62048	−0.808820	−0.404410	+	0.914578i	$0.632523\pi$
$68$	−0.967228	−0.117294
$69$	3.28992	0.396060
$70$	−0.0992358	−0.0118609
$71$	4.46606	0.530024	0.265012	−	0.964245i	$-0.414624\pi$
$71$	4.46606	0.530024	0.265012	+	0.964245i	$0.414624\pi$
$72$	1.25397	0.147782
$73$	−3.31321	−0.387782	−0.193891	−	0.981023i	$-0.562111\pi$
$73$	−3.31321	−0.387782	−0.193891	+	0.981023i	$0.562111\pi$
$74$	−19.7576	−2.29678
$75$	4.99703	0.577007
$76$	−3.42719	−0.393125
$77$	−4.37533	−0.498616
$78$	−7.53718	−0.853417
$79$	−7.81112	−0.878820	−0.439410	−	0.898287i	$-0.644812\pi$
$79$	−7.81112	−0.878820	−0.439410	+	0.898287i	$0.644812\pi$
$80$	−0.267420	−0.0298985
$81$	1.00000	0.111111
$82$	−20.6821	−2.28396
$83$	−1.78859	−0.196323	−0.0981614	−	0.995171i	$-0.531296\pi$
$83$	−1.78859	−0.196323	−0.0981614	+	0.995171i	$0.531296\pi$
$84$	−1.31084	−0.143025
$85$	−0.0402418	−0.00436484
$86$	−5.86726	−0.632683
$87$	1.83606	0.196846
$88$	−5.48654	−0.584867
$89$	−12.9560	−1.37334	−0.686668	−	0.726971i	$-0.740927\pi$
$89$	−12.9560	−1.37334	−0.686668	+	0.726971i	$0.740927\pi$
$90$	−0.0992358	−0.0104604
$91$	−4.14228	−0.434229
$92$	−4.31257	−0.449617
$93$	−4.69240	−0.486579
$94$	−23.4264	−2.41625
$95$	−0.142589	−0.0146293
$96$	−6.41411	−0.654637
$97$	−12.4769	−1.26684	−0.633419	−	0.773809i	$-0.718349\pi$
$97$	−12.4769	−1.26684	−0.633419	+	0.773809i	$0.718349\pi$
$98$	−1.81957	−0.183805
$99$	−4.37533	−0.439738
$100$	−6.55032	−0.655032
$101$	3.81344	0.379451	0.189726	−	0.981837i	$-0.439240\pi$
$101$	3.81344	0.379451	0.189726	+	0.981837i	$0.439240\pi$
$102$	−1.34260	−0.132937
$103$	2.14592	0.211444	0.105722	−	0.994396i	$-0.466285\pi$
$103$	2.14592	0.211444	0.105722	+	0.994396i	$0.466285\pi$
$104$	−5.19430	−0.509343
$105$	−0.0545380	−0.00532236
$106$	1.23515	0.119968
$107$	16.9935	1.64282	0.821410	−	0.570338i	$-0.193188\pi$
$107$	16.9935	1.64282	0.821410	+	0.570338i	$0.193188\pi$
$108$	−1.31084	−0.126136
$109$	13.8355	1.32521	0.662603	−	0.748971i	$-0.269452\pi$
$109$	13.8355	1.32521	0.662603	+	0.748971i	$0.269452\pi$
$110$	0.434190	0.0413984
$111$	−10.8584	−1.03063
$112$	−4.90338	−0.463326
$113$	16.4259	1.54522	0.772609	−	0.634882i	$-0.218951\pi$
$113$	16.4259	1.54522	0.772609	+	0.634882i	$0.218951\pi$
$114$	−4.75725	−0.445558
$115$	−0.179426	−0.0167315
$116$	−2.40679	−0.223465
$117$	−4.14228	−0.382954
$118$	−5.40268	−0.497357
$119$	−0.737867	−0.0676402
$120$	−0.0683891	−0.00624304
$121$	8.14355	0.740323
$122$	−6.55207	−0.593197
$123$	−11.3665	−1.02488
$124$	6.15100	0.552376
$125$	−0.545218	−0.0487658
$126$	−1.81957	−0.162100
$127$	10.1715	0.902575	0.451287	−	0.892379i	$-0.350965\pi$
$127$	10.1715	0.902575	0.451287	+	0.892379i	$0.350965\pi$
$128$	−9.43621	−0.834051
$129$	−3.22453	−0.283904
$130$	0.411063	0.0360526
$131$	−2.24899	−0.196495	−0.0982475	−	0.995162i	$-0.531324\pi$
$131$	−2.24899	−0.196495	−0.0982475	+	0.995162i	$0.531324\pi$
$132$	5.73538	0.499200
$133$	−2.61449	−0.226705
$134$	12.0464	1.04065
$135$	−0.0545380	−0.00469388
$136$	−0.925264	−0.0793407
$137$	−11.1976	−0.956675	−0.478337	−	0.878176i	$-0.658760\pi$
$137$	−11.1976	−0.956675	−0.478337	+	0.878176i	$0.658760\pi$
$138$	−5.98625	−0.509584
$139$	−19.5406	−1.65741	−0.828706	−	0.559684i	$-0.810923\pi$
$139$	−19.5406	−1.65741	−0.828706	+	0.559684i	$0.810923\pi$
$140$	0.0714907	0.00604207
$141$	−12.8747	−1.08424
$142$	−8.12632	−0.681945
$143$	18.1239	1.51559
$144$	−4.90338	−0.408615
$145$	−0.100135	−0.00831577
$146$	6.02863	0.498933
$147$	−1.00000	−0.0824786
$148$	14.2337	1.17000
$149$	−0.742136	−0.0607981	−0.0303991	−	0.999538i	$-0.509678\pi$
$149$	−0.742136	−0.0607981	−0.0303991	+	0.999538i	$0.509678\pi$
$150$	−9.09245	−0.742395
$151$	18.5392	1.50870	0.754349	−	0.656473i	$-0.227952\pi$
$151$	18.5392	1.50870	0.754349	+	0.656473i	$0.227952\pi$
$152$	−3.27850	−0.265921
$153$	−0.737867	−0.0596530
$154$	7.96124	0.641535
$155$	0.255914	0.0205555
$156$	5.42988	0.434738
$157$	−15.8976	−1.26877	−0.634384	−	0.773018i	$-0.718746\pi$
$157$	−15.8976	−1.26877	−0.634384	+	0.773018i	$0.718746\pi$
$158$	14.2129	1.13072
$159$	0.678812	0.0538333
$160$	0.349812	0.0276551
$161$	−3.28992	−0.259282
$162$	−1.81957	−0.142959
$163$	19.7909	1.55015	0.775073	−	0.631871i	$-0.217713\pi$
$163$	19.7909	1.55015	0.775073	+	0.631871i	$0.217713\pi$
$164$	14.8997	1.16347
$165$	0.238622	0.0185767
$166$	3.25446	0.252595
$167$	−11.6029	−0.897861	−0.448931	−	0.893567i	$-0.648195\pi$
$167$	−11.6029	−0.897861	−0.448931	+	0.893567i	$0.648195\pi$
$168$	−1.25397	−0.0967460
$169$	4.15848	0.319883
$170$	0.0732229	0.00561594
$171$	−2.61449	−0.199935
$172$	4.22685	0.322294
$173$	13.8802	1.05529	0.527644	−	0.849465i	$-0.323075\pi$
$173$	13.8802	1.05529	0.527644	+	0.849465i	$0.323075\pi$
$174$	−3.34085	−0.253269
$175$	−4.99703	−0.377740
$176$	21.4539	1.61715
$177$	−2.96920	−0.223179
$178$	23.5744	1.76698
$179$	7.36976	0.550842	0.275421	−	0.961324i	$-0.411183\pi$
$179$	7.36976	0.550842	0.275421	+	0.961324i	$0.411183\pi$
$180$	0.0714907	0.00532861
$181$	15.9406	1.18486	0.592429	−	0.805622i	$-0.298169\pi$
$181$	15.9406	1.18486	0.592429	+	0.805622i	$0.298169\pi$
$182$	7.53718	0.558693
$183$	−3.60089	−0.266185
$184$	−4.12547	−0.304134
$185$	0.592195	0.0435391
$186$	8.53816	0.626049
$187$	3.22842	0.236085
$188$	16.8767	1.23086
$189$	−1.00000	−0.0727393
$190$	0.259451	0.0188226
$191$	0.973904	0.0704692	0.0352346	−	0.999379i	$-0.488782\pi$
$191$	0.973904	0.0704692	0.0352346	+	0.999379i	$0.488782\pi$
$192$	1.86417	0.134535
$193$	−20.9720	−1.50960	−0.754799	−	0.655956i	$-0.772266\pi$
$193$	−20.9720	−1.50960	−0.754799	+	0.655956i	$0.772266\pi$
$194$	22.7026	1.62995
$195$	0.225912	0.0161779
$196$	1.31084	0.0936316
$197$	−8.06480	−0.574593	−0.287297	−	0.957842i	$-0.592757\pi$
$197$	−8.06480	−0.574593	−0.287297	+	0.957842i	$0.592757\pi$
$198$	7.96124	0.565780
$199$	−22.5607	−1.59929	−0.799644	−	0.600474i	$-0.794978\pi$
$199$	−22.5607	−1.59929	−0.799644	+	0.600474i	$0.794978\pi$
$200$	−6.26613	−0.443082
$201$	6.62048	0.466973
$202$	−6.93883	−0.488214
$203$	−1.83606	−0.128866
$204$	0.967228	0.0677195
$205$	0.619905	0.0432960
$206$	−3.90466	−0.272051
$207$	−3.28992	−0.228665
$208$	20.3112	1.40833
$209$	11.4393	0.791271
$210$	0.0992358	0.00684792
$211$	−14.9658	−1.03029	−0.515143	−	0.857104i	$-0.672261\pi$
$211$	−14.9658	−1.03029	−0.515143	+	0.857104i	$0.672261\pi$
$212$	−0.889816	−0.0611128
$213$	−4.46606	−0.306009
$214$	−30.9208	−2.11370
$215$	0.175859	0.0119935
$216$	−1.25397	−0.0853219
$217$	4.69240	0.318541
$218$	−25.1748	−1.70505
$219$	3.31321	0.223886
$220$	−0.312796	−0.0210887
$221$	3.05645	0.205599
$222$	19.7576	1.32605
$223$	7.13703	0.477931	0.238965	−	0.971028i	$-0.423192\pi$
$223$	7.13703	0.477931	0.238965	+	0.971028i	$0.423192\pi$
$224$	6.41411	0.428560
$225$	−4.99703	−0.333135
$226$	−29.8881	−1.98813
$227$	14.3461	0.952187	0.476093	−	0.879395i	$-0.342052\pi$
$227$	14.3461	0.952187	0.476093	+	0.879395i	$0.342052\pi$
$228$	3.42719	0.226971
$229$	−1.93514	−0.127878	−0.0639388	−	0.997954i	$-0.520366\pi$
$229$	−1.93514	−0.127878	−0.0639388	+	0.997954i	$0.520366\pi$
$230$	0.326478	0.0215273
$231$	4.37533	0.287876
$232$	−2.30237	−0.151158
$233$	0.949228	0.0621860	0.0310930	−	0.999516i	$-0.490101\pi$
$233$	0.949228	0.0621860	0.0310930	+	0.999516i	$0.490101\pi$
$234$	7.53718	0.492721
$235$	0.702160	0.0458038
$236$	3.89216	0.253358
$237$	7.81112	0.507387
$238$	1.34260	0.0870280
$239$	−24.4283	−1.58014	−0.790069	−	0.613018i	$-0.789955\pi$
$239$	−24.4283	−1.58014	−0.790069	+	0.613018i	$0.789955\pi$
$240$	0.267420	0.0172619
$241$	−22.7683	−1.46664	−0.733318	−	0.679886i	$-0.762029\pi$
$241$	−22.7683	−1.46664	−0.733318	+	0.679886i	$0.762029\pi$
$242$	−14.8178	−0.952523
$243$	−1.00000	−0.0641500
$244$	4.72020	0.302180
$245$	0.0545380	0.00348430
$246$	20.6821	1.31864
$247$	10.8300	0.689093
$248$	5.88414	0.373643
$249$	1.78859	0.113347
$250$	0.992063	0.0627436
$251$	7.60068	0.479751	0.239875	−	0.970804i	$-0.422893\pi$
$251$	7.60068	0.479751	0.239875	+	0.970804i	$0.422893\pi$
$252$	1.31084	0.0825753
$253$	14.3945	0.904975
$254$	−18.5078	−1.16128
$255$	0.0402418	0.00252004
$256$	20.8982	1.30614
$257$	1.66669	0.103965	0.0519825	−	0.998648i	$-0.483446\pi$
$257$	1.66669	0.103965	0.0519825	+	0.998648i	$0.483446\pi$
$258$	5.86726	0.365280
$259$	10.8584	0.674708
$260$	−0.296135	−0.0183655
$261$	−1.83606	−0.113649
$262$	4.09219	0.252817
$263$	15.0060	0.925308	0.462654	−	0.886539i	$-0.346897\pi$
$263$	15.0060	0.925308	0.462654	+	0.886539i	$0.346897\pi$
$264$	5.48654	0.337673
$265$	−0.0370211	−0.00227419
$266$	4.75725	0.291686
$267$	12.9560	0.792896
$268$	−8.67841	−0.530118
$269$	9.41081	0.573787	0.286893	−	0.957962i	$-0.407377\pi$
$269$	9.41081	0.573787	0.286893	+	0.957962i	$0.407377\pi$
$270$	0.0992358	0.00603930
$271$	13.3441	0.810599	0.405300	−	0.914184i	$-0.367167\pi$
$271$	13.3441	0.810599	0.405300	+	0.914184i	$0.367167\pi$
$272$	3.61804	0.219376
$273$	4.14228	0.250702
$274$	20.3748	1.23089
$275$	21.8637	1.31843
$276$	4.31257	0.259586
$277$	−29.8415	−1.79300	−0.896500	−	0.443043i	$-0.853899\pi$
$277$	−29.8415	−1.79300	−0.896500	+	0.443043i	$0.853899\pi$
$278$	35.5555	2.13248
$279$	4.69240	0.280927
$280$	0.0683891	0.00408703
$281$	12.2405	0.730208	0.365104	−	0.930967i	$-0.381033\pi$
$281$	12.2405	0.730208	0.365104	+	0.930967i	$0.381033\pi$
$282$	23.4264	1.39502
$283$	−24.4356	−1.45255	−0.726273	−	0.687406i	$-0.758749\pi$
$283$	−24.4356	−1.45255	−0.726273	+	0.687406i	$0.758749\pi$
$284$	5.85430	0.347389
$285$	0.142589	0.00844625
$286$	−32.9777	−1.95001
$287$	11.3665	0.670942
$288$	6.41411	0.377955
$289$	−16.4556	−0.967974
$290$	0.182203	0.0106993
$291$	12.4769	0.731409
$292$	−4.34310	−0.254161
$293$	−13.8860	−0.811229	−0.405615	−	0.914044i	$-0.632942\pi$
$293$	−13.8860	−0.811229	−0.405615	+	0.914044i	$0.632942\pi$
$294$	1.81957	0.106120
$295$	0.161934	0.00942818
$296$	13.6161	0.791421
$297$	4.37533	0.253883
$298$	1.35037	0.0782248
$299$	13.6278	0.788115
$300$	6.55032	0.378183
$301$	3.22453	0.185859
$302$	−33.7334	−1.94114
$303$	−3.81344	−0.219076
$304$	12.8198	0.735268
$305$	0.196385	0.0112450
$306$	1.34260	0.0767515
$307$	−8.13024	−0.464017	−0.232009	−	0.972714i	$-0.574530\pi$
$307$	−8.13024	−0.464017	−0.232009	+	0.972714i	$0.574530\pi$
$308$	−5.73538	−0.326803
$309$	−2.14592	−0.122077
$310$	−0.465654	−0.0264474
$311$	−8.03940	−0.455873	−0.227936	−	0.973676i	$-0.573198\pi$
$311$	−8.03940	−0.455873	−0.227936	+	0.973676i	$0.573198\pi$
$312$	5.19430	0.294069
$313$	−20.8034	−1.17588	−0.587938	−	0.808906i	$-0.700060\pi$
$313$	−20.8034	−1.17588	−0.587938	+	0.808906i	$0.700060\pi$
$314$	28.9268	1.63244
$315$	0.0545380	0.00307287
$316$	−10.2392	−0.575997
$317$	14.4430	0.811198	0.405599	−	0.914051i	$-0.367063\pi$
$317$	14.4430	0.811198	0.405599	+	0.914051i	$0.367063\pi$
$318$	−1.23515	−0.0692637
$319$	8.03338	0.449783
$320$	−0.101668	−0.00568343
$321$	−16.9935	−0.948483
$322$	5.98625	0.333601
$323$	1.92915	0.107341
$324$	1.31084	0.0728246
$325$	20.6991	1.14818
$326$	−36.0111	−1.99447
$327$	−13.8355	−0.765108
$328$	14.2532	0.787003
$329$	12.8747	0.709804
$330$	−0.434190	−0.0239014
$331$	−27.5060	−1.51187	−0.755933	−	0.654648i	$-0.772817\pi$
$331$	−27.5060	−1.51187	−0.755933	+	0.654648i	$0.772817\pi$
$332$	−2.34455	−0.128674
$333$	10.8584	0.595036
$334$	21.1124	1.15522
$335$	−0.361068	−0.0197272
$336$	4.90338	0.267501
$337$	17.9946	0.980226	0.490113	−	0.871659i	$-0.336955\pi$
$337$	17.9946	0.980226	0.490113	+	0.871659i	$0.336955\pi$
$338$	−7.56665	−0.411572
$339$	−16.4259	−0.892132
$340$	−0.0527507	−0.00286081
$341$	−20.5308	−1.11181
$342$	4.75725	0.257243
$343$	1.00000	0.0539949
$344$	4.04346	0.218009
$345$	0.179426	0.00965996
$346$	−25.2559	−1.35777
$347$	−27.5277	−1.47777	−0.738883	−	0.673834i	$-0.764646\pi$
$347$	−27.5277	−1.47777	−0.738883	+	0.673834i	$0.764646\pi$
$348$	2.40679	0.129017
$349$	1.93035	0.103329	0.0516646	−	0.998664i	$-0.483547\pi$
$349$	1.93035	0.103329	0.0516646	+	0.998664i	$0.483547\pi$
$350$	9.09245	0.486012
$351$	4.14228	0.221099
$352$	−28.0639	−1.49581
$353$	4.85614	0.258466	0.129233	−	0.991614i	$-0.458748\pi$
$353$	4.85614	0.258466	0.129233	+	0.991614i	$0.458748\pi$
$354$	5.40268	0.287149
$355$	0.243570	0.0129273
$356$	−16.9833	−0.900114
$357$	0.737867	0.0390521
$358$	−13.4098	−0.708731
$359$	20.8631	1.10111	0.550555	−	0.834799i	$-0.314416\pi$
$359$	20.8631	1.10111	0.550555	+	0.834799i	$0.314416\pi$
$360$	0.0683891	0.00360442
$361$	−12.1644	−0.640234
$362$	−29.0052	−1.52448
$363$	−8.14355	−0.427426
$364$	−5.42988	−0.284603
$365$	−0.180696	−0.00945806
$366$	6.55207	0.342482
$367$	19.2173	1.00313	0.501567	−	0.865119i	$-0.332757\pi$
$367$	19.2173	1.00313	0.501567	+	0.865119i	$0.332757\pi$
$368$	16.1317	0.840925
$369$	11.3665	0.591715
$370$	−1.07754	−0.0560187
$371$	−0.678812	−0.0352422
$372$	−6.15100	−0.318915
$373$	3.56401	0.184538	0.0922688	−	0.995734i	$-0.470588\pi$
$373$	3.56401	0.184538	0.0922688	+	0.995734i	$0.470588\pi$
$374$	−5.87434	−0.303755
$375$	0.545218	0.0281549
$376$	16.1445	0.832588
$377$	7.60548	0.391702
$378$	1.81957	0.0935887
$379$	−33.7905	−1.73570	−0.867852	−	0.496824i	$-0.834500\pi$
$379$	−33.7905	−1.73570	−0.867852	+	0.496824i	$0.834500\pi$
$380$	−0.186912	−0.00958838
$381$	−10.1715	−0.521102
$382$	−1.77209	−0.0906680
$383$	1.00000	0.0510976
$383$	1.00000	0.0510976
$384$	9.43621	0.481540
$385$	−0.238622	−0.0121613
$386$	38.1601	1.94230
$387$	3.22453	0.163912
$388$	−16.3553	−0.830313
$389$	−22.9512	−1.16367	−0.581836	−	0.813306i	$-0.697665\pi$
$389$	−22.9512	−1.16367	−0.581836	+	0.813306i	$0.697665\pi$
$390$	−0.411063	−0.0208150
$391$	2.42753	0.122765
$392$	1.25397	0.0633351
$393$	2.24899	0.113446
$394$	14.6745	0.739290
$395$	−0.426003	−0.0214345
$396$	−5.73538	−0.288213
$397$	−19.9859	−1.00306	−0.501532	−	0.865139i	$-0.667230\pi$
$397$	−19.9859	−1.00306	−0.501532	+	0.865139i	$0.667230\pi$
$398$	41.0509	2.05769
$399$	2.61449	0.130888
$400$	24.5023	1.22511
$401$	−1.89771	−0.0947673	−0.0473836	−	0.998877i	$-0.515088\pi$
$401$	−1.89771	−0.0947673	−0.0473836	+	0.998877i	$0.515088\pi$
$402$	−12.0464	−0.600822
$403$	−19.4372	−0.968238
$404$	4.99882	0.248701
$405$	0.0545380	0.00271001
$406$	3.34085	0.165803
$407$	−47.5091	−2.35494
$408$	0.925264	0.0458074
$409$	16.0114	0.791715	0.395858	−	0.918312i	$-0.370447\pi$
$409$	16.0114	0.791715	0.395858	+	0.918312i	$0.370447\pi$
$410$	−1.12796	−0.0557060
$411$	11.1976	0.552336
$412$	2.81297	0.138585
$413$	2.96920	0.146105
$414$	5.98625	0.294208
$415$	−0.0975459	−0.00478834
$416$	−26.5690	−1.30265
$417$	19.5406	0.956908
$418$	−20.8146	−1.01807
$419$	−0.755385	−0.0369030	−0.0184515	−	0.999830i	$-0.505874\pi$
$419$	−0.755385	−0.0369030	−0.0184515	+	0.999830i	$0.505874\pi$
$420$	−0.0714907	−0.00348839
$421$	23.0388	1.12284	0.561422	−	0.827529i	$-0.310254\pi$
$421$	23.0388	1.12284	0.561422	+	0.827529i	$0.310254\pi$
$422$	27.2313	1.32560
$423$	12.8747	0.625989
$424$	−0.851211	−0.0413385
$425$	3.68714	0.178853
$426$	8.12632	0.393721
$427$	3.60089	0.174259
$428$	22.2758	1.07674
$429$	−18.1239	−0.875028
$430$	−0.319989	−0.0154312
$431$	−12.8743	−0.620131	−0.310065	−	0.950715i	$-0.600351\pi$
$431$	−12.8743	−0.620131	−0.310065	+	0.950715i	$0.600351\pi$
$432$	4.90338	0.235914
$433$	−8.52437	−0.409655	−0.204828	−	0.978798i	$-0.565663\pi$
$433$	−8.52437	−0.409655	−0.204828	+	0.978798i	$0.565663\pi$
$434$	−8.53816	−0.409845
$435$	0.100135	0.00480111
$436$	18.1362	0.868568
$437$	8.60147	0.411464
$438$	−6.02863	−0.288059
$439$	−7.28234	−0.347567	−0.173784	−	0.984784i	$-0.555599\pi$
$439$	−7.28234	−0.347567	−0.173784	+	0.984784i	$0.555599\pi$
$440$	−0.299225	−0.0142650
$441$	1.00000	0.0476190
$442$	−5.56144	−0.264530
$443$	10.5467	0.501089	0.250544	−	0.968105i	$-0.419390\pi$
$443$	10.5467	0.501089	0.250544	+	0.968105i	$0.419390\pi$
$444$	−14.2337	−0.675499
$445$	−0.706596	−0.0334958
$446$	−12.9863	−0.614921
$447$	0.742136	0.0351018
$448$	−1.86417	−0.0880740
$449$	−7.24726	−0.342019	−0.171010	−	0.985269i	$-0.554703\pi$
$449$	−7.24726	−0.342019	−0.171010	+	0.985269i	$0.554703\pi$
$450$	9.09245	0.428622
$451$	−49.7321	−2.34179
$452$	21.5318	1.01277
$453$	−18.5392	−0.871048
$454$	−26.1038	−1.22511
$455$	−0.225912	−0.0105909
$456$	3.27850	0.153530
$457$	−33.7167	−1.57720	−0.788600	−	0.614907i	$-0.789194\pi$
$457$	−33.7167	−1.57720	−0.788600	+	0.614907i	$0.789194\pi$
$458$	3.52113	0.164531
$459$	0.737867	0.0344407
$460$	−0.235199	−0.0109662
$461$	−32.5551	−1.51624	−0.758121	−	0.652114i	$-0.773882\pi$
$461$	−32.5551	−1.51624	−0.758121	+	0.652114i	$0.773882\pi$
$462$	−7.96124	−0.370390
$463$	21.1876	0.984670	0.492335	−	0.870406i	$-0.336143\pi$
$463$	21.1876	0.984670	0.492335	+	0.870406i	$0.336143\pi$
$464$	9.00290	0.417949
$465$	−0.255914	−0.0118677
$466$	−1.72719	−0.0800104
$467$	−11.5230	−0.533221	−0.266610	−	0.963804i	$-0.585904\pi$
$467$	−11.5230	−0.533221	−0.266610	+	0.963804i	$0.585904\pi$
$468$	−5.42988	−0.250996
$469$	−6.62048	−0.305705
$470$	−1.27763	−0.0589327
$471$	15.8976	0.732523
$472$	3.72329	0.171379
$473$	−14.1084	−0.648704
$474$	−14.2129	−0.652820
$475$	13.0647	0.599448
$476$	−0.967228	−0.0443328
$477$	−0.678812	−0.0310807
$478$	44.4491	2.03306
$479$	42.3677	1.93583	0.967915	−	0.251279i	$-0.0808510\pi$
$479$	42.3677	1.93583	0.967915	+	0.251279i	$0.0808510\pi$
$480$	−0.349812	−0.0159667
$481$	−44.9785	−2.05084
$482$	41.4286	1.88702
$483$	3.28992	0.149697
$484$	10.6749	0.485223
$485$	−0.680466	−0.0308984
$486$	1.81957	0.0825375
$487$	−10.2405	−0.464040	−0.232020	−	0.972711i	$-0.574533\pi$
$487$	−10.2405	−0.464040	−0.232020	+	0.972711i	$0.574533\pi$
$488$	4.51541	0.204403
$489$	−19.7909	−0.894977
$490$	−0.0992358	−0.00448302
$491$	27.8957	1.25892	0.629458	−	0.777035i	$-0.283277\pi$
$491$	27.8957	1.25892	0.629458	+	0.777035i	$0.283277\pi$
$492$	−14.8997	−0.671729
$493$	1.35477	0.0610157
$494$	−19.7059	−0.886609
$495$	−0.238622	−0.0107253
$496$	−23.0086	−1.03312
$497$	4.46606	0.200330
$498$	−3.25446	−0.145836
$499$	−37.8413	−1.69401	−0.847005	−	0.531585i	$-0.821596\pi$
$499$	−37.8413	−1.69401	−0.847005	+	0.531585i	$0.821596\pi$
$500$	−0.714695	−0.0319621
$501$	11.6029	0.518381
$502$	−13.8300	−0.617262
$503$	22.1116	0.985909	0.492955	−	0.870055i	$-0.335917\pi$
$503$	22.1116	0.985909	0.492955	+	0.870055i	$0.335917\pi$
$504$	1.25397	0.0558563
$505$	0.207977	0.00925487
$506$	−26.1919	−1.16437
$507$	−4.15848	−0.184685
$508$	13.3332	0.591567
$509$	20.0767	0.889886	0.444943	−	0.895559i	$-0.353224\pi$
$509$	20.0767	0.889886	0.444943	+	0.895559i	$0.353224\pi$
$510$	−0.0732229	−0.00324236
$511$	−3.31321	−0.146568
$512$	−19.1534	−0.846468
$513$	2.61449	0.115433
$514$	−3.03265	−0.133765
$515$	0.117034	0.00515715
$516$	−4.22685	−0.186077
$517$	−56.3311	−2.47744
$518$	−19.7576	−0.868101
$519$	−13.8802	−0.609271
$520$	−0.283287	−0.0124229
$521$	43.3042	1.89719	0.948595	−	0.316492i	$-0.102505\pi$
$521$	43.3042	1.89719	0.948595	+	0.316492i	$0.102505\pi$
$522$	3.34085	0.146225
$523$	26.7892	1.17141	0.585705	−	0.810524i	$-0.300818\pi$
$523$	26.7892	1.17141	0.585705	+	0.810524i	$0.300818\pi$
$524$	−2.94807	−0.128787
$525$	4.99703	0.218088
$526$	−27.3045	−1.19053
$527$	−3.46237	−0.150823
$528$	−21.4539	−0.933662
$529$	−12.1764	−0.529409
$530$	0.0673625	0.00292604
$531$	2.96920	0.128852
$532$	−3.42719	−0.148587
$533$	−47.0831	−2.03940
$534$	−23.5744	−1.02017
$535$	0.926789	0.0400686
$536$	−8.30189	−0.358587
$537$	−7.36976	−0.318029
$538$	−17.1236	−0.738253
$539$	−4.37533	−0.188459
$540$	−0.0714907	−0.00307647
$541$	18.7795	0.807394	0.403697	−	0.914893i	$-0.367725\pi$
$541$	18.7795	0.807394	0.403697	+	0.914893i	$0.367725\pi$
$542$	−24.2806	−1.04294
$543$	−15.9406	−0.684079
$544$	−4.73276	−0.202915
$545$	0.754563	0.0323219
$546$	−7.53718	−0.322561
$547$	−26.6260	−1.13845	−0.569224	−	0.822183i	$-0.692756\pi$
$547$	−26.6260	−1.13845	−0.569224	+	0.822183i	$0.692756\pi$
$548$	−14.6783	−0.627025
$549$	3.60089	0.153682
$550$	−39.7825	−1.69633
$551$	4.80036	0.204502
$552$	4.12547	0.175592
$553$	−7.81112	−0.332163
$554$	54.2987	2.30693
$555$	−0.592195	−0.0251373
$556$	−25.6147	−1.08630
$557$	−42.3741	−1.79545	−0.897724	−	0.440557i	$-0.854781\pi$
$557$	−42.3741	−1.79545	−0.897724	+	0.440557i	$0.854781\pi$
$558$	−8.53816	−0.361449
$559$	−13.3569	−0.564936
$560$	−0.267420	−0.0113006
$561$	−3.22842	−0.136304
$562$	−22.2725	−0.939509
$563$	−18.5333	−0.781085	−0.390543	−	0.920585i	$-0.627713\pi$
$563$	−18.5333	−0.781085	−0.390543	+	0.920585i	$0.627713\pi$
$564$	−16.8767	−0.710637
$565$	0.895836	0.0376881
$566$	44.4623	1.86889
$567$	1.00000	0.0419961
$568$	5.60031	0.234984
$569$	9.57726	0.401499	0.200750	−	0.979643i	$-0.435662\pi$
$569$	9.57726	0.401499	0.200750	+	0.979643i	$0.435662\pi$
$570$	−0.259451	−0.0108672
$571$	22.2580	0.931468	0.465734	−	0.884925i	$-0.345790\pi$
$571$	22.2580	0.931468	0.465734	+	0.884925i	$0.345790\pi$
$572$	23.7575	0.993352
$573$	−0.973904	−0.0406854
$574$	−20.6821	−0.863255
$575$	16.4398	0.685588
$576$	−1.86417	−0.0776739
$577$	38.1173	1.58684	0.793422	−	0.608672i	$-0.208298\pi$
$577$	38.1173	1.58684	0.793422	+	0.608672i	$0.208298\pi$
$578$	29.9421	1.24543
$579$	20.9720	0.871567
$580$	−0.131261	−0.00545033
$581$	−1.78859	−0.0742030
$582$	−22.7026	−0.941055
$583$	2.97003	0.123006
$584$	−4.15467	−0.171922
$585$	−0.225912	−0.00934030
$586$	25.2666	1.04375
$587$	−38.2929	−1.58052	−0.790259	−	0.612773i	$-0.790054\pi$
$587$	−38.2929	−1.58052	−0.790259	+	0.612773i	$0.790054\pi$
$588$	−1.31084	−0.0540583
$589$	−12.2682	−0.505504
$590$	−0.294651	−0.0121306
$591$	8.06480	0.331742
$592$	−53.2428	−2.18827
$593$	−31.7130	−1.30230	−0.651149	−	0.758950i	$-0.725713\pi$
$593$	−31.7130	−1.30230	−0.651149	+	0.758950i	$0.725713\pi$
$594$	−7.96124	−0.326654
$595$	−0.0402418	−0.00164975
$596$	−0.972823	−0.0398484
$597$	22.5607	0.923349
$598$	−24.7967	−1.01401
$599$	−9.05610	−0.370022	−0.185011	−	0.982736i	$-0.559232\pi$
$599$	−9.05610	−0.370022	−0.185011	+	0.982736i	$0.559232\pi$
$600$	6.26613	0.255814
$601$	19.3613	0.789764	0.394882	−	0.918732i	$-0.370785\pi$
$601$	19.3613	0.789764	0.394882	+	0.918732i	$0.370785\pi$
$602$	−5.86726	−0.239132
$603$	−6.62048	−0.269607
$604$	24.3020	0.988834
$605$	0.444133	0.0180566
$606$	6.93883	0.281871
$607$	37.4186	1.51877	0.759387	−	0.650639i	$-0.225499\pi$
$607$	37.4186	1.51877	0.759387	+	0.650639i	$0.225499\pi$
$608$	−16.7696	−0.680098
$609$	1.83606	0.0744010
$610$	−0.357337	−0.0144682
$611$	−53.3305	−2.15752
$612$	−0.967228	−0.0390979
$613$	−41.1615	−1.66250	−0.831249	−	0.555900i	$-0.812374\pi$
$613$	−41.1615	−1.66250	−0.831249	+	0.555900i	$0.812374\pi$
$614$	14.7936	0.597019
$615$	−0.619905	−0.0249970
$616$	−5.48654	−0.221059
$617$	−23.8478	−0.960075	−0.480037	−	0.877248i	$-0.659377\pi$
$617$	−23.8478	−0.960075	−0.480037	+	0.877248i	$0.659377\pi$
$618$	3.90466	0.157068
$619$	−0.508420	−0.0204351	−0.0102176	−	0.999948i	$-0.503252\pi$
$619$	−0.508420	−0.0204351	−0.0102176	+	0.999948i	$0.503252\pi$
$620$	0.335463	0.0134725
$621$	3.28992	0.132020
$622$	14.6283	0.586540
$623$	−12.9560	−0.519072
$624$	−20.3112	−0.813097
$625$	24.9554	0.998216
$626$	37.8533	1.51292
$627$	−11.4393	−0.456840
$628$	−20.8393	−0.831577
$629$	−8.01205	−0.319462
$630$	−0.0992358	−0.00395365
$631$	13.7149	0.545981	0.272991	−	0.962017i	$-0.411987\pi$
$631$	13.7149	0.545981	0.272991	+	0.962017i	$0.411987\pi$
$632$	−9.79492	−0.389621
$633$	14.9658	0.594836
$634$	−26.2800	−1.04371
$635$	0.554733	0.0220139
$636$	0.889816	0.0352835
$637$	−4.14228	−0.164123
$638$	−14.6173	−0.578705
$639$	4.46606	0.176675
$640$	−0.514632	−0.0203426
$641$	−19.7775	−0.781163	−0.390582	−	0.920568i	$-0.627726\pi$
$641$	−19.7775	−0.781163	−0.390582	+	0.920568i	$0.627726\pi$
$642$	30.9208	1.22035
$643$	−7.65166	−0.301752	−0.150876	−	0.988553i	$-0.548209\pi$
$643$	−7.65166	−0.301752	−0.150876	+	0.988553i	$0.548209\pi$
$644$	−4.31257	−0.169939
$645$	−0.175859	−0.00692445
$646$	−3.51022	−0.138108
$647$	−0.122957	−0.00483392	−0.00241696	−	0.999997i	$-0.500769\pi$
$647$	−0.122957	−0.00483392	−0.00241696	+	0.999997i	$0.500769\pi$
$648$	1.25397	0.0492606
$649$	−12.9913	−0.509951
$650$	−37.6635	−1.47728
$651$	−4.69240	−0.183910
$652$	25.9428	1.01600
$653$	27.5485	1.07806	0.539028	−	0.842288i	$-0.318792\pi$
$653$	27.5485	1.07806	0.539028	+	0.842288i	$0.318792\pi$
$654$	25.1748	0.984412
$655$	−0.122655	−0.00479254
$656$	−55.7341	−2.17605
$657$	−3.31321	−0.129261
$658$	−23.4264	−0.913257
$659$	15.1469	0.590038	0.295019	−	0.955491i	$-0.404674\pi$
$659$	15.1469	0.590038	0.295019	+	0.955491i	$0.404674\pi$
$660$	0.312796	0.0121756
$661$	−26.3415	−1.02456	−0.512282	−	0.858817i	$-0.671200\pi$
$661$	−26.3415	−1.02456	−0.512282	+	0.858817i	$0.671200\pi$
$662$	50.0492	1.94522
$663$	−3.05645	−0.118703
$664$	−2.24283	−0.0870389
$665$	−0.142589	−0.00552937
$666$	−19.7576	−0.765593
$667$	6.04050	0.233889
$668$	−15.2096	−0.588478
$669$	−7.13703	−0.275933
$670$	0.656989	0.0253817
$671$	−15.7551	−0.608218
$672$	−6.41411	−0.247429
$673$	−0.892392	−0.0343992	−0.0171996	−	0.999852i	$-0.505475\pi$
$673$	−0.892392	−0.0343992	−0.0171996	+	0.999852i	$0.505475\pi$
$674$	−32.7424	−1.26119
$675$	4.99703	0.192336
$676$	5.45111	0.209658
$677$	28.2598	1.08611	0.543056	−	0.839697i	$-0.317267\pi$
$677$	28.2598	1.08611	0.543056	+	0.839697i	$0.317267\pi$
$678$	29.8881	1.14785
$679$	−12.4769	−0.478820
$680$	−0.0504621	−0.00193513
$681$	−14.3461	−0.549745
$682$	37.3573	1.43049
$683$	−1.84970	−0.0707767	−0.0353883	−	0.999374i	$-0.511267\pi$
$683$	−1.84970	−0.0707767	−0.0353883	+	0.999374i	$0.511267\pi$
$684$	−3.42719	−0.131042
$685$	−0.610694	−0.0233334
$686$	−1.81957	−0.0694716
$687$	1.93514	0.0738302
$688$	−15.8111	−0.602792
$689$	2.81183	0.107122
$690$	−0.326478	−0.0124288
$691$	−28.7961	−1.09546	−0.547729	−	0.836656i	$-0.684507\pi$
$691$	−28.7961	−1.09546	−0.547729	+	0.836656i	$0.684507\pi$
$692$	18.1947	0.691659
$693$	−4.37533	−0.166205
$694$	50.0887	1.90134
$695$	−1.06571	−0.0404245
$696$	2.30237	0.0872710
$697$	−8.38695	−0.317678
$698$	−3.51241	−0.132947
$699$	−0.949228	−0.0359031
$700$	−6.55032	−0.247579
$701$	7.98243	0.301492	0.150746	−	0.988573i	$-0.451832\pi$
$701$	7.98243	0.301492	0.150746	+	0.988573i	$0.451832\pi$
$702$	−7.53718	−0.284472
$703$	−28.3892	−1.07072
$704$	8.15639	0.307405
$705$	−0.702160	−0.0264449
$706$	−8.83609	−0.332551
$707$	3.81344	0.143419
$708$	−3.89216	−0.146276
$709$	−13.7362	−0.515875	−0.257937	−	0.966162i	$-0.583043\pi$
$709$	−13.7362	−0.515875	−0.257937	+	0.966162i	$0.583043\pi$
$710$	−0.443193	−0.0166327
$711$	−7.81112	−0.292940
$712$	−16.2465	−0.608863
$713$	−15.4376	−0.578144
$714$	−1.34260	−0.0502456
$715$	0.988439	0.0369655
$716$	9.66060	0.361034
$717$	24.4283	0.912293
$718$	−37.9618	−1.41672
$719$	−25.9494	−0.967748	−0.483874	−	0.875138i	$-0.660771\pi$
$719$	−25.9494	−0.967748	−0.483874	+	0.875138i	$0.660771\pi$
$720$	−0.267420	−0.00996617
$721$	2.14592	0.0799183
$722$	22.1341	0.823745
$723$	22.7683	0.846763
$724$	20.8957	0.776582
$725$	9.17484	0.340745
$726$	14.8178	0.549939
$727$	22.1155	0.820220	0.410110	−	0.912036i	$-0.365490\pi$
$727$	22.1155	0.820220	0.410110	+	0.912036i	$0.365490\pi$
$728$	−5.19430	−0.192514
$729$	1.00000	0.0370370
$730$	0.328789	0.0121690
$731$	−2.37927	−0.0880006
$732$	−4.72020	−0.174464
$733$	−26.8789	−0.992794	−0.496397	−	0.868096i	$-0.665344\pi$
$733$	−26.8789	−0.992794	−0.496397	+	0.868096i	$0.665344\pi$
$734$	−34.9672	−1.29066
$735$	−0.0545380	−0.00201166
$736$	−21.1019	−0.777827
$737$	28.9668	1.06701
$738$	−20.6821	−0.761319
$739$	−45.5422	−1.67530	−0.837648	−	0.546210i	$-0.816070\pi$
$739$	−45.5422	−1.67530	−0.837648	+	0.546210i	$0.816070\pi$
$740$	0.776275	0.0285364
$741$	−10.8300	−0.397848
$742$	1.23515	0.0453437
$743$	−15.5173	−0.569273	−0.284637	−	0.958636i	$-0.591873\pi$
$743$	−15.5173	−0.569273	−0.284637	+	0.958636i	$0.591873\pi$
$744$	−5.88414	−0.215723
$745$	−0.0404746	−0.00148287
$746$	−6.48498	−0.237432
$747$	−1.78859	−0.0654409
$748$	4.23195	0.154735
$749$	16.9935	0.620928
$750$	−0.992063	−0.0362250
$751$	39.6374	1.44639	0.723195	−	0.690644i	$-0.242673\pi$
$751$	39.6374	1.44639	0.723195	+	0.690644i	$0.242673\pi$
$752$	−63.1294	−2.30209
$753$	−7.60068	−0.276984
$754$	−13.8387	−0.503976
$755$	1.01109	0.0367974
$756$	−1.31084	−0.0476749
$757$	−6.94788	−0.252525	−0.126263	−	0.991997i	$-0.540298\pi$
$757$	−6.94788	−0.252525	−0.126263	+	0.991997i	$0.540298\pi$
$758$	61.4843	2.23321
$759$	−14.3945	−0.522488
$760$	−0.178803	−0.00648585
$761$	17.5742	0.637065	0.318533	−	0.947912i	$-0.396810\pi$
$761$	17.5742	0.637065	0.318533	+	0.947912i	$0.396810\pi$
$762$	18.5078	0.670466
$763$	13.8355	0.500881
$764$	1.27664	0.0461870
$765$	−0.0402418	−0.00145495
$766$	−1.81957	−0.0657438
$767$	−12.2993	−0.444101
$768$	−20.8982	−0.754099
$769$	26.6804	0.962121	0.481060	−	0.876687i	$-0.340252\pi$
$769$	26.6804	0.962121	0.481060	+	0.876687i	$0.340252\pi$
$770$	0.434190	0.0156471
$771$	−1.66669	−0.0600242
$772$	−27.4910	−0.989423
$773$	34.3374	1.23503	0.617516	−	0.786558i	$-0.288139\pi$
$773$	34.3374	1.23503	0.617516	+	0.786558i	$0.288139\pi$
$774$	−5.86726	−0.210894
$775$	−23.4481	−0.842279
$776$	−15.6457	−0.561647
$777$	−10.8584	−0.389543
$778$	41.7614	1.49722
$779$	−29.7175	−1.06474
$780$	0.296135	0.0106033
$781$	−19.5405	−0.699214
$782$	−4.41706	−0.157954
$783$	1.83606	0.0656155
$784$	−4.90338	−0.175121
$785$	−0.867024	−0.0309454
$786$	−4.09219	−0.145964
$787$	33.2657	1.18579	0.592896	−	0.805279i	$-0.297984\pi$
$787$	33.2657	1.18579	0.592896	+	0.805279i	$0.297984\pi$
$788$	−10.5717	−0.376601
$789$	−15.0060	−0.534227
$790$	0.775143	0.0275784
$791$	16.4259	0.584038
$792$	−5.48654	−0.194956
$793$	−14.9159	−0.529678
$794$	36.3658	1.29057
$795$	0.0370211	0.00131300
$796$	−29.5736	−1.04821
$797$	−45.8535	−1.62421	−0.812107	−	0.583508i	$-0.801680\pi$
$797$	−45.8535	−1.62421	−0.812107	+	0.583508i	$0.801680\pi$
$798$	−4.75725	−0.168405
$799$	−9.49981	−0.336079
$800$	−32.0515	−1.13319
$801$	−12.9560	−0.457779
$802$	3.45303	0.121931
$803$	14.4964	0.511567
$804$	8.67841	0.306064
$805$	−0.179426	−0.00632393
$806$	35.3675	1.24577
$807$	−9.41081	−0.331276
$808$	4.78194	0.168228
$809$	44.9258	1.57951	0.789754	−	0.613424i	$-0.210208\pi$
$809$	44.9258	1.57951	0.789754	+	0.613424i	$0.210208\pi$
$810$	−0.0992358	−0.00348679
$811$	−21.5122	−0.755394	−0.377697	−	0.925929i	$-0.623284\pi$
$811$	−21.5122	−0.755394	−0.377697	+	0.925929i	$0.623284\pi$
$812$	−2.40679	−0.0844617
$813$	−13.3441	−0.468000
$814$	86.4463	3.02994
$815$	1.07936	0.0378083
$816$	−3.61804	−0.126657
$817$	−8.43050	−0.294946
$818$	−29.1340	−1.01865
$819$	−4.14228	−0.144743
$820$	0.812598	0.0283771
$821$	50.9133	1.77689	0.888444	−	0.458986i	$-0.151787\pi$
$821$	50.9133	1.77689	0.888444	+	0.458986i	$0.151787\pi$
$822$	−20.3748	−0.710654
$823$	37.4112	1.30407	0.652036	−	0.758188i	$-0.273915\pi$
$823$	37.4112	1.30407	0.652036	+	0.758188i	$0.273915\pi$
$824$	2.69092	0.0937428
$825$	−21.8637	−0.761195
$826$	−5.40268	−0.187983
$827$	−29.2200	−1.01608	−0.508039	−	0.861334i	$-0.669629\pi$
$827$	−29.2200	−1.01608	−0.508039	+	0.861334i	$0.669629\pi$
$828$	−4.31257	−0.149872
$829$	8.12688	0.282258	0.141129	−	0.989991i	$-0.454927\pi$
$829$	8.12688	0.282258	0.141129	+	0.989991i	$0.454927\pi$
$830$	0.177492	0.00616083
$831$	29.8415	1.03519
$832$	7.72193	0.267710
$833$	−0.737867	−0.0255656
$834$	−35.5555	−1.23119
$835$	−0.632800	−0.0218990
$836$	14.9951	0.518616
$837$	−4.69240	−0.162193
$838$	1.37448	0.0474805
$839$	9.33818	0.322390	0.161195	−	0.986923i	$-0.448465\pi$
$839$	9.33818	0.322390	0.161195	+	0.986923i	$0.448465\pi$
$840$	−0.0683891	−0.00235965
$841$	−25.6289	−0.883754
$842$	−41.9208	−1.44469
$843$	−12.2405	−0.421586
$844$	−19.6178	−0.675272
$845$	0.226795	0.00780199
$846$	−23.4264	−0.805417
$847$	8.14355	0.279816
$848$	3.32847	0.114300
$849$	24.4356	0.838628
$850$	−6.70902	−0.230117
$851$	−35.7233	−1.22458
$852$	−5.85430	−0.200565
$853$	−47.7267	−1.63413	−0.817065	−	0.576545i	$-0.804401\pi$
$853$	−47.7267	−1.63413	−0.817065	+	0.576545i	$0.804401\pi$
$854$	−6.55207	−0.224207
$855$	−0.142589	−0.00487644
$856$	21.3093	0.728337
$857$	−53.5456	−1.82908	−0.914542	−	0.404492i	$-0.867448\pi$
$857$	−53.5456	−1.82908	−0.914542	+	0.404492i	$0.867448\pi$
$858$	32.9777	1.12584
$859$	55.3464	1.88840	0.944198	−	0.329379i	$-0.106840\pi$
$859$	55.3464	1.88840	0.944198	+	0.329379i	$0.106840\pi$
$860$	0.230524	0.00786080
$861$	−11.3665	−0.387368
$862$	23.4256	0.797880
$863$	11.6333	0.396001	0.198000	−	0.980202i	$-0.436555\pi$
$863$	11.6333	0.396001	0.198000	+	0.980202i	$0.436555\pi$
$864$	−6.41411	−0.218212
$865$	0.756996	0.0257386
$866$	15.5107	0.527075
$867$	16.4556	0.558860
$868$	6.15100	0.208779
$869$	34.1763	1.15935
$870$	−0.182203	−0.00617726
$871$	27.4239	0.929223
$872$	17.3494	0.587524
$873$	−12.4769	−0.422279
$874$	−15.6510	−0.529403
$875$	−0.545218	−0.0184317
$876$	4.34310	0.146740
$877$	55.9494	1.88928	0.944638	−	0.328114i	$-0.106413\pi$
$877$	55.9494	1.88928	0.944638	+	0.328114i	$0.106413\pi$
$878$	13.2508	0.447191
$879$	13.8860	0.468363
$880$	1.17005	0.0394425
$881$	41.1229	1.38547	0.692733	−	0.721194i	$-0.256406\pi$
$881$	41.1229	1.38547	0.692733	+	0.721194i	$0.256406\pi$
$882$	−1.81957	−0.0612682
$883$	−3.73676	−0.125752	−0.0628761	−	0.998021i	$-0.520027\pi$
$883$	−3.73676	−0.125752	−0.0628761	+	0.998021i	$0.520027\pi$
$884$	4.00653	0.134754
$885$	−0.161934	−0.00544336
$886$	−19.1905	−0.644717
$887$	11.4159	0.383308	0.191654	−	0.981463i	$-0.438615\pi$
$887$	11.4159	0.383308	0.191654	+	0.981463i	$0.438615\pi$
$888$	−13.6161	−0.456927
$889$	10.1715	0.341141
$890$	1.28570	0.0430968
$891$	−4.37533	−0.146579
$892$	9.35552	0.313246
$893$	−33.6607	−1.12641
$894$	−1.35037	−0.0451631
$895$	0.401932	0.0134351
$896$	−9.43621	−0.315242
$897$	−13.6278	−0.455018
$898$	13.1869	0.440053
$899$	−8.61554	−0.287344
$900$	−6.55032	−0.218344
$901$	0.500873	0.0166865
$902$	90.4912	3.01303
$903$	−3.22453	−0.107306
$904$	20.5976	0.685066
$905$	0.869371	0.0288989
$906$	33.7334	1.12072
$907$	−34.8777	−1.15809	−0.579047	−	0.815294i	$-0.696575\pi$
$907$	−34.8777	−1.15809	−0.579047	+	0.815294i	$0.696575\pi$
$908$	18.8055	0.624084
$909$	3.81344	0.126484
$910$	0.411063	0.0136266
$911$	−18.7994	−0.622852	−0.311426	−	0.950270i	$-0.600807\pi$
$911$	−18.7994	−0.622852	−0.311426	+	0.950270i	$0.600807\pi$
$912$	−12.8198	−0.424507
$913$	7.82566	0.258992
$914$	61.3499	2.02928
$915$	−0.196385	−0.00649229
$916$	−2.53666	−0.0838138
$917$	−2.24899	−0.0742681
$918$	−1.34260	−0.0443125
$919$	43.5808	1.43760	0.718800	−	0.695217i	$-0.244692\pi$
$919$	43.5808	1.43760	0.718800	+	0.695217i	$0.244692\pi$
$920$	−0.224995	−0.00741786
$921$	8.13024	0.267900
$922$	59.2363	1.95084
$923$	−18.4997	−0.608924
$924$	5.73538	0.188680
$925$	−54.2597	−1.78405
$926$	−38.5523	−1.26691
$927$	2.14592	0.0704813
$928$	−11.7767	−0.386589
$929$	4.41382	0.144813	0.0724064	−	0.997375i	$-0.476932\pi$
$929$	4.41382	0.144813	0.0724064	+	0.997375i	$0.476932\pi$
$930$	0.465654	0.0152694
$931$	−2.61449	−0.0856865
$932$	1.24429	0.0407580
$933$	8.03940	0.263198
$934$	20.9669	0.686059
$935$	0.176071	0.00575815
$936$	−5.19430	−0.169781
$937$	41.9961	1.37195	0.685977	−	0.727623i	$-0.259375\pi$
$937$	41.9961	1.37195	0.685977	+	0.727623i	$0.259375\pi$
$938$	12.0464	0.393330
$939$	20.8034	0.678893
$940$	0.920421	0.0300208
$941$	22.9649	0.748634	0.374317	−	0.927301i	$-0.377877\pi$
$941$	22.9649	0.748634	0.374317	+	0.927301i	$0.377877\pi$
$942$	−28.9268	−0.942488
$943$	−37.3948	−1.21774
$944$	−14.5591	−0.473859
$945$	−0.0545380	−0.00177412
$946$	25.6712	0.834644
$947$	−50.7159	−1.64804	−0.824022	−	0.566557i	$-0.808275\pi$
$947$	−50.7159	−1.64804	−0.824022	+	0.566557i	$0.808275\pi$
$948$	10.2392	0.332552
$949$	13.7243	0.445508
$950$	−23.7721	−0.771269
$951$	−14.4430	−0.468345
$952$	−0.925264	−0.0299880
$953$	−55.9545	−1.81254	−0.906272	−	0.422695i	$-0.861084\pi$
$953$	−55.9545	−1.81254	−0.906272	+	0.422695i	$0.861084\pi$
$954$	1.23515	0.0399894
$955$	0.0531148	0.00171875
$956$	−32.0217	−1.03566
$957$	−8.03338	−0.259682
$958$	−77.0911	−2.49070
$959$	−11.1976	−0.361589
$960$	0.101668	0.00328133
$961$	−8.98136	−0.289721
$962$	81.8417	2.63868
$963$	16.9935	0.547607
$964$	−29.8457	−0.961265
$965$	−1.14377	−0.0368193
$966$	−5.98625	−0.192605
$967$	−14.9570	−0.480984	−0.240492	−	0.970651i	$-0.577309\pi$
$967$	−14.9570	−0.480984	−0.240492	+	0.970651i	$0.577309\pi$
$968$	10.2118	0.328219
$969$	−1.92915	−0.0619731
$970$	1.23816	0.0397548
$971$	3.99471	0.128196	0.0640982	−	0.997944i	$-0.479583\pi$
$971$	3.99471	0.128196	0.0640982	+	0.997944i	$0.479583\pi$
$972$	−1.31084	−0.0420453
$973$	−19.5406	−0.626443
$974$	18.6333	0.597048
$975$	−20.6991	−0.662901
$976$	−17.6565	−0.565171
$977$	−26.8621	−0.859394	−0.429697	−	0.902973i	$-0.641380\pi$
$977$	−26.8621	−0.859394	−0.429697	+	0.902973i	$0.641380\pi$
$978$	36.0111	1.15151
$979$	56.6869	1.81172
$980$	0.0714907	0.00228369
$981$	13.8355	0.441735
$982$	−50.7583	−1.61976
$983$	44.9356	1.43322	0.716612	−	0.697472i	$-0.245692\pi$
$983$	44.9356	1.43322	0.716612	+	0.697472i	$0.245692\pi$
$984$	−14.2532	−0.454376
$985$	−0.439838	−0.0140144
$986$	−2.46510	−0.0785048
$987$	−12.8747	−0.409806
$988$	14.1964	0.451646
$989$	−10.6084	−0.337329
$990$	0.434190	0.0137995
$991$	−51.5100	−1.63627	−0.818135	−	0.575026i	$-0.804992\pi$
$991$	−51.5100	−1.63627	−0.818135	+	0.575026i	$0.804992\pi$
$992$	30.0976	0.955599
$993$	27.5060	0.872877
$994$	−8.12632	−0.257751
$995$	−1.23042	−0.0390068
$996$	2.34455	0.0742901
$997$	−39.4069	−1.24803	−0.624015	−	0.781413i	$-0.714499\pi$
$997$	−39.4069	−1.24803	−0.624015	+	0.781413i	$0.714499\pi$
$998$	68.8550	2.17957
$999$	−10.8584	−0.343544

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8043.2.a.o.1.10	✓	41

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8043.2.a.o.1.10	✓	41	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:	\( N \)	\(=\)	\( 8043 = 3 \cdot 7 \cdot 383 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8043.a (trivial)

\(f(q)\)	\(=\)	\(q-1.81957 q^{2} -1.00000 q^{3} +1.31084 q^{4} +0.0545380 q^{5} +1.81957 q^{6} +1.00000 q^{7} +1.25397 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.81957 q^{2} -1.00000 q^{3} +1.31084 q^{4} +0.0545380 q^{5} +1.81957 q^{6} +1.00000 q^{7} +1.25397 q^{8} +1.00000 q^{9} -0.0992358 q^{10} -4.37533 q^{11} -1.31084 q^{12} -4.14228 q^{13} -1.81957 q^{14} -0.0545380 q^{15} -4.90338 q^{16} -0.737867 q^{17} -1.81957 q^{18} -2.61449 q^{19} +0.0714907 q^{20} -1.00000 q^{21} +7.96124 q^{22} -3.28992 q^{23} -1.25397 q^{24} -4.99703 q^{25} +7.53718 q^{26} -1.00000 q^{27} +1.31084 q^{28} -1.83606 q^{29} +0.0992358 q^{30} +4.69240 q^{31} +6.41411 q^{32} +4.37533 q^{33} +1.34260 q^{34} +0.0545380 q^{35} +1.31084 q^{36} +10.8584 q^{37} +4.75725 q^{38} +4.14228 q^{39} +0.0683891 q^{40} +11.3665 q^{41} +1.81957 q^{42} +3.22453 q^{43} -5.73538 q^{44} +0.0545380 q^{45} +5.98625 q^{46} +12.8747 q^{47} +4.90338 q^{48} +1.00000 q^{49} +9.09245 q^{50} +0.737867 q^{51} -5.42988 q^{52} -0.678812 q^{53} +1.81957 q^{54} -0.238622 q^{55} +1.25397 q^{56} +2.61449 q^{57} +3.34085 q^{58} +2.96920 q^{59} -0.0714907 q^{60} +3.60089 q^{61} -8.53816 q^{62} +1.00000 q^{63} -1.86417 q^{64} -0.225912 q^{65} -7.96124 q^{66} -6.62048 q^{67} -0.967228 q^{68} +3.28992 q^{69} -0.0992358 q^{70} +4.46606 q^{71} +1.25397 q^{72} -3.31321 q^{73} -19.7576 q^{74} +4.99703 q^{75} -3.42719 q^{76} -4.37533 q^{77} -7.53718 q^{78} -7.81112 q^{79} -0.267420 q^{80} +1.00000 q^{81} -20.6821 q^{82} -1.78859 q^{83} -1.31084 q^{84} -0.0402418 q^{85} -5.86726 q^{86} +1.83606 q^{87} -5.48654 q^{88} -12.9560 q^{89} -0.0992358 q^{90} -4.14228 q^{91} -4.31257 q^{92} -4.69240 q^{93} -23.4264 q^{94} -0.142589 q^{95} -6.41411 q^{96} -12.4769 q^{97} -1.81957 q^{98} -4.37533 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 41 q - 4 q^{2} - 41 q^{3} + 34 q^{4} + 5 q^{5} + 4 q^{6} + 41 q^{7} - 15 q^{8} + 41 q^{9}+O(q^{10}) \) 41 * q - 4 * q^2 - 41 * q^3 + 34 * q^4 + 5 * q^5 + 4 * q^6 + 41 * q^7 - 15 * q^8 + 41 * q^9	\( 41 q - 4 q^{2} - 41 q^{3} + 34 q^{4} + 5 q^{5} + 4 q^{6} + 41 q^{7} - 15 q^{8} + 41 q^{9} - 18 q^{10} - 17 q^{11} - 34 q^{12} - 38 q^{13} - 4 q^{14} - 5 q^{15} + 16 q^{16} + 4 q^{17} - 4 q^{18} - 15 q^{19} + 23 q^{20} - 41 q^{21} - 31 q^{22} - 8 q^{23} + 15 q^{24} + 16 q^{25} + 15 q^{26} - 41 q^{27} + 34 q^{28} - 27 q^{29} + 18 q^{30} - 23 q^{31} - 24 q^{32} + 17 q^{33} - 9 q^{34} + 5 q^{35} + 34 q^{36} - 81 q^{37} + 38 q^{39} - 52 q^{40} + 29 q^{41} + 4 q^{42} - 47 q^{43} - 20 q^{44} + 5 q^{45} - 40 q^{46} + 26 q^{47} - 16 q^{48} + 41 q^{49} - 23 q^{50} - 4 q^{51} - 64 q^{52} - 66 q^{53} + 4 q^{54} - 14 q^{55} - 15 q^{56} + 15 q^{57} - 50 q^{58} + 41 q^{59} - 23 q^{60} - 47 q^{61} + 5 q^{62} + 41 q^{63} - 37 q^{64} - 24 q^{65} + 31 q^{66} - 73 q^{67} + 10 q^{68} + 8 q^{69} - 18 q^{70} + q^{71} - 15 q^{72} - 14 q^{73} + 18 q^{74} - 16 q^{75} - 37 q^{76} - 17 q^{77} - 15 q^{78} - 80 q^{79} + 63 q^{80} + 41 q^{81} - 31 q^{82} + 20 q^{83} - 34 q^{84} - 82 q^{85} - 39 q^{86} + 27 q^{87} - 132 q^{88} + 17 q^{89} - 18 q^{90} - 38 q^{91} - 26 q^{92} + 23 q^{93} - 9 q^{94} - q^{95} + 24 q^{96} - 73 q^{97} - 4 q^{98} - 17 q^{99}+O(q^{100}) \) 41 * q - 4 * q^2 - 41 * q^3 + 34 * q^4 + 5 * q^5 + 4 * q^6 + 41 * q^7 - 15 * q^8 + 41 * q^9 - 18 * q^10 - 17 * q^11 - 34 * q^12 - 38 * q^13 - 4 * q^14 - 5 * q^15 + 16 * q^16 + 4 * q^17 - 4 * q^18 - 15 * q^19 + 23 * q^20 - 41 * q^21 - 31 * q^22 - 8 * q^23 + 15 * q^24 + 16 * q^25 + 15 * q^26 - 41 * q^27 + 34 * q^28 - 27 * q^29 + 18 * q^30 - 23 * q^31 - 24 * q^32 + 17 * q^33 - 9 * q^34 + 5 * q^35 + 34 * q^36 - 81 * q^37 + 38 * q^39 - 52 * q^40 + 29 * q^41 + 4 * q^42 - 47 * q^43 - 20 * q^44 + 5 * q^45 - 40 * q^46 + 26 * q^47 - 16 * q^48 + 41 * q^49 - 23 * q^50 - 4 * q^51 - 64 * q^52 - 66 * q^53 + 4 * q^54 - 14 * q^55 - 15 * q^56 + 15 * q^57 - 50 * q^58 + 41 * q^59 - 23 * q^60 - 47 * q^61 + 5 * q^62 + 41 * q^63 - 37 * q^64 - 24 * q^65 + 31 * q^66 - 73 * q^67 + 10 * q^68 + 8 * q^69 - 18 * q^70 + q^71 - 15 * q^72 - 14 * q^73 + 18 * q^74 - 16 * q^75 - 37 * q^76 - 17 * q^77 - 15 * q^78 - 80 * q^79 + 63 * q^80 + 41 * q^81 - 31 * q^82 + 20 * q^83 - 34 * q^84 - 82 * q^85 - 39 * q^86 + 27 * q^87 - 132 * q^88 + 17 * q^89 - 18 * q^90 - 38 * q^91 - 26 * q^92 + 23 * q^93 - 9 * q^94 - q^95 + 24 * q^96 - 73 * q^97 - 4 * q^98 - 17 * q^99

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