LMFDB - Embedded newform 4034.2.a.d.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4034,2,Mod(1,4034)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4034, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4034 = 2 \cdot 2017 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4034.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:	$32.2116521754$
Analytic rank:	$0$
Dimension:	$52$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Character	$\chi$	$=$	4034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.49412 q^{3} +1.00000 q^{4} +2.01405 q^{5} -2.49412 q^{6} +2.26153 q^{7} +1.00000 q^{8} +3.22062 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.49412 q^{3} +1.00000 q^{4} +2.01405 q^{5} -2.49412 q^{6} +2.26153 q^{7} +1.00000 q^{8} +3.22062 q^{9} +2.01405 q^{10} -3.70387 q^{11} -2.49412 q^{12} -3.55865 q^{13} +2.26153 q^{14} -5.02328 q^{15} +1.00000 q^{16} +6.88697 q^{17} +3.22062 q^{18} +2.37414 q^{19} +2.01405 q^{20} -5.64052 q^{21} -3.70387 q^{22} -2.90483 q^{23} -2.49412 q^{24} -0.943592 q^{25} -3.55865 q^{26} -0.550262 q^{27} +2.26153 q^{28} +5.51423 q^{29} -5.02328 q^{30} -6.05211 q^{31} +1.00000 q^{32} +9.23790 q^{33} +6.88697 q^{34} +4.55484 q^{35} +3.22062 q^{36} +4.05981 q^{37} +2.37414 q^{38} +8.87569 q^{39} +2.01405 q^{40} +5.33998 q^{41} -5.64052 q^{42} -1.25313 q^{43} -3.70387 q^{44} +6.48651 q^{45} -2.90483 q^{46} +6.32993 q^{47} -2.49412 q^{48} -1.88548 q^{49} -0.943592 q^{50} -17.1769 q^{51} -3.55865 q^{52} +12.2322 q^{53} -0.550262 q^{54} -7.45980 q^{55} +2.26153 q^{56} -5.92139 q^{57} +5.51423 q^{58} -4.09159 q^{59} -5.02328 q^{60} +2.55932 q^{61} -6.05211 q^{62} +7.28354 q^{63} +1.00000 q^{64} -7.16730 q^{65} +9.23790 q^{66} +15.7411 q^{67} +6.88697 q^{68} +7.24498 q^{69} +4.55484 q^{70} +0.641025 q^{71} +3.22062 q^{72} -8.54143 q^{73} +4.05981 q^{74} +2.35343 q^{75} +2.37414 q^{76} -8.37642 q^{77} +8.87569 q^{78} +2.47415 q^{79} +2.01405 q^{80} -8.28945 q^{81} +5.33998 q^{82} +5.59401 q^{83} -5.64052 q^{84} +13.8707 q^{85} -1.25313 q^{86} -13.7531 q^{87} -3.70387 q^{88} +8.40142 q^{89} +6.48651 q^{90} -8.04799 q^{91} -2.90483 q^{92} +15.0947 q^{93} +6.32993 q^{94} +4.78164 q^{95} -2.49412 q^{96} -7.21256 q^{97} -1.88548 q^{98} -11.9288 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q + 52 q^{2} + 16 q^{3} + 52 q^{4} + 24 q^{5} + 16 q^{6} + 12 q^{7} + 52 q^{8} + 70 q^{9}+O(q^{10}) $ 52 * q + 52 * q^2 + 16 * q^3 + 52 * q^4 + 24 * q^5 + 16 * q^6 + 12 * q^7 + 52 * q^8 + 70 * q^9	\( 52 q + 52 q^{2} + 16 q^{3} + 52 q^{4} + 24 q^{5} + 16 q^{6} + 12 q^{7} + 52 q^{8} + 70 q^{9} + 24 q^{10} + 19 q^{11} + 16 q^{12} + 27 q^{13} + 12 q^{14} + 5 q^{15} + 52 q^{16} + 43 q^{17} + 70 q^{18} + 35 q^{19} + 24 q^{20} + 29 q^{21} + 19 q^{22} + 2 q^{23} + 16 q^{24} + 88 q^{25} + 27 q^{26} + 49 q^{27} + 12 q^{28} + 31 q^{29} + 5 q^{30} + 59 q^{31} + 52 q^{32} + 45 q^{33} + 43 q^{34} + 18 q^{35} + 70 q^{36} + 60 q^{37} + 35 q^{38} + 6 q^{39} + 24 q^{40} + 56 q^{41} + 29 q^{42} + 34 q^{43} + 19 q^{44} + 61 q^{45} + 2 q^{46} - 4 q^{47} + 16 q^{48} + 102 q^{49} + 88 q^{50} + 23 q^{51} + 27 q^{52} + 30 q^{53} + 49 q^{54} + 24 q^{55} + 12 q^{56} + 32 q^{57} + 31 q^{58} + 27 q^{59} + 5 q^{60} + 107 q^{61} + 59 q^{62} - 4 q^{63} + 52 q^{64} + 46 q^{65} + 45 q^{66} + 22 q^{67} + 43 q^{68} + 36 q^{69} + 18 q^{70} + 8 q^{71} + 70 q^{72} + 66 q^{73} + 60 q^{74} + 53 q^{75} + 35 q^{76} + 26 q^{77} + 6 q^{78} + 50 q^{79} + 24 q^{80} + 108 q^{81} + 56 q^{82} + 52 q^{83} + 29 q^{84} + 19 q^{85} + 34 q^{86} - 32 q^{87} + 19 q^{88} + 62 q^{89} + 61 q^{90} + 69 q^{91} + 2 q^{92} + 21 q^{93} - 4 q^{94} - 44 q^{95} + 16 q^{96} + 82 q^{97} + 102 q^{98} + 16 q^{99}+O(q^{100}) \) 52 * q + 52 * q^2 + 16 * q^3 + 52 * q^4 + 24 * q^5 + 16 * q^6 + 12 * q^7 + 52 * q^8 + 70 * q^9 + 24 * q^10 + 19 * q^11 + 16 * q^12 + 27 * q^13 + 12 * q^14 + 5 * q^15 + 52 * q^16 + 43 * q^17 + 70 * q^18 + 35 * q^19 + 24 * q^20 + 29 * q^21 + 19 * q^22 + 2 * q^23 + 16 * q^24 + 88 * q^25 + 27 * q^26 + 49 * q^27 + 12 * q^28 + 31 * q^29 + 5 * q^30 + 59 * q^31 + 52 * q^32 + 45 * q^33 + 43 * q^34 + 18 * q^35 + 70 * q^36 + 60 * q^37 + 35 * q^38 + 6 * q^39 + 24 * q^40 + 56 * q^41 + 29 * q^42 + 34 * q^43 + 19 * q^44 + 61 * q^45 + 2 * q^46 - 4 * q^47 + 16 * q^48 + 102 * q^49 + 88 * q^50 + 23 * q^51 + 27 * q^52 + 30 * q^53 + 49 * q^54 + 24 * q^55 + 12 * q^56 + 32 * q^57 + 31 * q^58 + 27 * q^59 + 5 * q^60 + 107 * q^61 + 59 * q^62 - 4 * q^63 + 52 * q^64 + 46 * q^65 + 45 * q^66 + 22 * q^67 + 43 * q^68 + 36 * q^69 + 18 * q^70 + 8 * q^71 + 70 * q^72 + 66 * q^73 + 60 * q^74 + 53 * q^75 + 35 * q^76 + 26 * q^77 + 6 * q^78 + 50 * q^79 + 24 * q^80 + 108 * q^81 + 56 * q^82 + 52 * q^83 + 29 * q^84 + 19 * q^85 + 34 * q^86 - 32 * q^87 + 19 * q^88 + 62 * q^89 + 61 * q^90 + 69 * q^91 + 2 * q^92 + 21 * q^93 - 4 * q^94 - 44 * q^95 + 16 * q^96 + 82 * q^97 + 102 * q^98 + 16 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−2.49412	−1.43998	−0.719990	−	0.693985i	$-0.755854\pi$
$3$	−2.49412	−1.43998	−0.719990	+	0.693985i	$0.755854\pi$
$4$	1.00000	0.500000
$5$	2.01405	0.900712	0.450356	−	0.892849i	$-0.351297\pi$
$5$	2.01405	0.900712	0.450356	+	0.892849i	$0.351297\pi$
$6$	−2.49412	−1.01822
$7$	2.26153	0.854778	0.427389	−	0.904068i	$-0.359433\pi$
$7$	2.26153	0.854778	0.427389	+	0.904068i	$0.359433\pi$
$8$	1.00000	0.353553
$9$	3.22062	1.07354
$10$	2.01405	0.636899
$11$	−3.70387	−1.11676	−0.558380	−	0.829585i	$-0.688577\pi$
$11$	−3.70387	−1.11676	−0.558380	+	0.829585i	$0.688577\pi$
$12$	−2.49412	−0.719990
$13$	−3.55865	−0.986991	−0.493496	−	0.869748i	$-0.664281\pi$
$13$	−3.55865	−0.986991	−0.493496	+	0.869748i	$0.664281\pi$
$14$	2.26153	0.604419
$15$	−5.02328	−1.29701
$16$	1.00000	0.250000
$17$	6.88697	1.67034	0.835168	−	0.549995i	$-0.185370\pi$
$17$	6.88697	1.67034	0.835168	+	0.549995i	$0.185370\pi$
$18$	3.22062	0.759108
$19$	2.37414	0.544665	0.272333	−	0.962203i	$-0.412205\pi$
$19$	2.37414	0.544665	0.272333	+	0.962203i	$0.412205\pi$
$20$	2.01405	0.450356
$21$	−5.64052	−1.23086
$22$	−3.70387	−0.789669
$23$	−2.90483	−0.605698	−0.302849	−	0.953038i	$-0.597938\pi$
$23$	−2.90483	−0.605698	−0.302849	+	0.953038i	$0.597938\pi$
$24$	−2.49412	−0.509110
$25$	−0.943592	−0.188718
$26$	−3.55865	−0.697908
$27$	−0.550262	−0.105898
$28$	2.26153	0.427389
$29$	5.51423	1.02397	0.511983	−	0.858995i	$-0.328911\pi$
$29$	5.51423	1.02397	0.511983	+	0.858995i	$0.328911\pi$
$30$	−5.02328	−0.917122
$31$	−6.05211	−1.08699	−0.543495	−	0.839412i	$-0.682899\pi$
$31$	−6.05211	−1.08699	−0.543495	+	0.839412i	$0.682899\pi$
$32$	1.00000	0.176777
$33$	9.23790	1.60811
$34$	6.88697	1.18111
$35$	4.55484	0.769909
$36$	3.22062	0.536771
$37$	4.05981	0.667428	0.333714	−	0.942674i	$-0.391698\pi$
$37$	4.05981	0.667428	0.333714	+	0.942674i	$0.391698\pi$
$38$	2.37414	0.385136
$39$	8.87569	1.42125
$40$	2.01405	0.318450
$41$	5.33998	0.833964	0.416982	−	0.908915i	$-0.363088\pi$
$41$	5.33998	0.833964	0.416982	+	0.908915i	$0.363088\pi$
$42$	−5.64052	−0.870351
$43$	−1.25313	−0.191101	−0.0955505	−	0.995425i	$-0.530461\pi$
$43$	−1.25313	−0.191101	−0.0955505	+	0.995425i	$0.530461\pi$
$44$	−3.70387	−0.558380
$45$	6.48651	0.966951
$46$	−2.90483	−0.428293
$47$	6.32993	0.923315	0.461658	−	0.887058i	$-0.347255\pi$
$47$	6.32993	0.923315	0.461658	+	0.887058i	$0.347255\pi$
$48$	−2.49412	−0.359995
$49$	−1.88548	−0.269355
$50$	−0.943592	−0.133444
$51$	−17.1769	−2.40525
$52$	−3.55865	−0.493496
$53$	12.2322	1.68023	0.840114	−	0.542410i	$-0.182488\pi$
$53$	12.2322	1.68023	0.840114	+	0.542410i	$0.182488\pi$
$54$	−0.550262	−0.0748811
$55$	−7.45980	−1.00588
$56$	2.26153	0.302210
$57$	−5.92139	−0.784307
$58$	5.51423	0.724054
$59$	−4.09159	−0.532679	−0.266340	−	0.963879i	$-0.585814\pi$
$59$	−4.09159	−0.532679	−0.266340	+	0.963879i	$0.585814\pi$
$60$	−5.02328	−0.648503
$61$	2.55932	0.327687	0.163843	−	0.986486i	$-0.447611\pi$
$61$	2.55932	0.327687	0.163843	+	0.986486i	$0.447611\pi$
$62$	−6.05211	−0.768618
$63$	7.28354	0.917639
$64$	1.00000	0.125000
$65$	−7.16730	−0.888994
$66$	9.23790	1.13711
$67$	15.7411	1.92308	0.961540	−	0.274665i	$-0.0885668\pi$
$67$	15.7411	1.92308	0.961540	+	0.274665i	$0.0885668\pi$
$68$	6.88697	0.835168
$69$	7.24498	0.872193
$70$	4.55484	0.544408
$71$	0.641025	0.0760757	0.0380379	−	0.999276i	$-0.487889\pi$
$71$	0.641025	0.0760757	0.0380379	+	0.999276i	$0.487889\pi$
$72$	3.22062	0.379554
$73$	−8.54143	−0.999699	−0.499849	−	0.866112i	$-0.666611\pi$
$73$	−8.54143	−0.999699	−0.499849	+	0.866112i	$0.666611\pi$
$74$	4.05981	0.471943
$75$	2.35343	0.271751
$76$	2.37414	0.272333
$77$	−8.37642	−0.954582
$78$	8.87569	1.00497
$79$	2.47415	0.278363	0.139182	−	0.990267i	$-0.455553\pi$
$79$	2.47415	0.278363	0.139182	+	0.990267i	$0.455553\pi$
$80$	2.01405	0.225178
$81$	−8.28945	−0.921050
$82$	5.33998	0.589702
$83$	5.59401	0.614022	0.307011	−	0.951706i	$-0.400671\pi$
$83$	5.59401	0.614022	0.307011	+	0.951706i	$0.400671\pi$
$84$	−5.64052	−0.615431
$85$	13.8707	1.50449
$86$	−1.25313	−0.135129
$87$	−13.7531	−1.47449
$88$	−3.70387	−0.394834
$89$	8.40142	0.890549	0.445275	−	0.895394i	$-0.353106\pi$
$89$	8.40142	0.890549	0.445275	+	0.895394i	$0.353106\pi$
$90$	6.48651	0.683738
$91$	−8.04799	−0.843658
$92$	−2.90483	−0.302849
$93$	15.0947	1.56524
$94$	6.32993	0.652882
$95$	4.78164	0.490586
$96$	−2.49412	−0.254555
$97$	−7.21256	−0.732324	−0.366162	−	0.930551i	$-0.619328\pi$
$97$	−7.21256	−0.732324	−0.366162	+	0.930551i	$0.619328\pi$
$98$	−1.88548	−0.190462
$99$	−11.9288	−1.19889
$100$	−0.943592	−0.0943592
$101$	−6.35568	−0.632414	−0.316207	−	0.948690i	$-0.602409\pi$
$101$	−6.35568	−0.632414	−0.316207	+	0.948690i	$0.602409\pi$
$102$	−17.1769	−1.70077
$103$	−11.2162	−1.10516	−0.552582	−	0.833459i	$-0.686357\pi$
$103$	−11.2162	−1.10516	−0.552582	+	0.833459i	$0.686357\pi$
$104$	−3.55865	−0.348954
$105$	−11.3603	−1.10865
$106$	12.2322	1.18810
$107$	−13.6183	−1.31653	−0.658267	−	0.752785i	$-0.728710\pi$
$107$	−13.6183	−1.31653	−0.658267	+	0.752785i	$0.728710\pi$
$108$	−0.550262	−0.0529490
$109$	0.0239725	0.00229615	0.00114807	−	0.999999i	$-0.499635\pi$
$109$	0.0239725	0.00229615	0.00114807	+	0.999999i	$0.499635\pi$
$110$	−7.45980	−0.711264
$111$	−10.1256	−0.961083
$112$	2.26153	0.213694
$113$	20.2362	1.90366	0.951831	−	0.306624i	$-0.0991994\pi$
$113$	20.2362	1.90366	0.951831	+	0.306624i	$0.0991994\pi$
$114$	−5.92139	−0.554589
$115$	−5.85048	−0.545560
$116$	5.51423	0.511983
$117$	−11.4611	−1.05958
$118$	−4.09159	−0.376661
$119$	15.5751	1.42777
$120$	−5.02328	−0.458561
$121$	2.71868	0.247153
$122$	2.55932	0.231710
$123$	−13.3185	−1.20089
$124$	−6.05211	−0.543495
$125$	−11.9707	−1.07069
$126$	7.28354	0.648869
$127$	−15.7777	−1.40004	−0.700022	−	0.714121i	$-0.746826\pi$
$127$	−15.7777	−1.40004	−0.700022	+	0.714121i	$0.746826\pi$
$128$	1.00000	0.0883883
$129$	3.12546	0.275182
$130$	−7.16730	−0.628614
$131$	−5.27108	−0.460536	−0.230268	−	0.973127i	$-0.573960\pi$
$131$	−5.27108	−0.460536	−0.230268	+	0.973127i	$0.573960\pi$
$132$	9.23790	0.804056
$133$	5.36919	0.465568
$134$	15.7411	1.35982
$135$	−1.10826	−0.0953835
$136$	6.88697	0.590553
$137$	14.6575	1.25228	0.626138	−	0.779712i	$-0.284635\pi$
$137$	14.6575	1.25228	0.626138	+	0.779712i	$0.284635\pi$
$138$	7.24498	0.616734
$139$	21.7180	1.84210	0.921048	−	0.389448i	$-0.127334\pi$
$139$	21.7180	1.84210	0.921048	+	0.389448i	$0.127334\pi$
$140$	4.55484	0.384954
$141$	−15.7876	−1.32956
$142$	0.641025	0.0537937
$143$	13.1808	1.10223
$144$	3.22062	0.268385
$145$	11.1059	0.922299
$146$	−8.54143	−0.706894
$147$	4.70261	0.387865
$148$	4.05981	0.333714
$149$	19.8344	1.62490	0.812449	−	0.583032i	$-0.198134\pi$
$149$	19.8344	1.62490	0.812449	+	0.583032i	$0.198134\pi$
$150$	2.35343	0.192157
$151$	−4.66734	−0.379823	−0.189911	−	0.981801i	$-0.560820\pi$
$151$	−4.66734	−0.379823	−0.189911	+	0.981801i	$0.560820\pi$
$152$	2.37414	0.192568
$153$	22.1803	1.79317
$154$	−8.37642	−0.674991
$155$	−12.1893	−0.979065
$156$	8.87569	0.710624
$157$	21.6430	1.72730	0.863652	−	0.504089i	$-0.168172\pi$
$157$	21.6430	1.72730	0.863652	+	0.504089i	$0.168172\pi$
$158$	2.47415	0.196833
$159$	−30.5087	−2.41949
$160$	2.01405	0.159225
$161$	−6.56935	−0.517738
$162$	−8.28945	−0.651281
$163$	10.8339	0.848576	0.424288	−	0.905527i	$-0.360524\pi$
$163$	10.8339	0.848576	0.424288	+	0.905527i	$0.360524\pi$
$164$	5.33998	0.416982
$165$	18.6056	1.44845
$166$	5.59401	0.434179
$167$	13.3377	1.03211	0.516053	−	0.856557i	$-0.327401\pi$
$167$	13.3377	1.03211	0.516053	+	0.856557i	$0.327401\pi$
$168$	−5.64052	−0.435176
$169$	−0.336031	−0.0258485
$170$	13.8707	1.06384
$171$	7.64621	0.584721
$172$	−1.25313	−0.0955505
$173$	−22.9937	−1.74818	−0.874088	−	0.485767i	$-0.838540\pi$
$173$	−22.9937	−1.74818	−0.874088	+	0.485767i	$0.838540\pi$
$174$	−13.7531	−1.04262
$175$	−2.13396	−0.161312
$176$	−3.70387	−0.279190
$177$	10.2049	0.767047
$178$	8.40142	0.629713
$179$	0.526188	0.0393292	0.0196646	−	0.999807i	$-0.493740\pi$
$179$	0.526188	0.0393292	0.0196646	+	0.999807i	$0.493740\pi$
$180$	6.48651	0.483476
$181$	22.4799	1.67092	0.835460	−	0.549551i	$-0.185201\pi$
$181$	22.4799	1.67092	0.835460	+	0.549551i	$0.185201\pi$
$182$	−8.04799	−0.596556
$183$	−6.38323	−0.471862
$184$	−2.90483	−0.214147
$185$	8.17666	0.601160
$186$	15.0947	1.10679
$187$	−25.5085	−1.86536
$188$	6.32993	0.461658
$189$	−1.24443	−0.0905192
$190$	4.78164	0.346897
$191$	11.3651	0.822349	0.411175	−	0.911557i	$-0.365119\pi$
$191$	11.3651	0.822349	0.411175	+	0.911557i	$0.365119\pi$
$192$	−2.49412	−0.179997
$193$	−6.87508	−0.494879	−0.247440	−	0.968903i	$-0.579589\pi$
$193$	−6.87508	−0.494879	−0.247440	+	0.968903i	$0.579589\pi$
$194$	−7.21256	−0.517832
$195$	17.8761	1.28013
$196$	−1.88548	−0.134677
$197$	19.5956	1.39613	0.698064	−	0.716035i	$-0.254045\pi$
$197$	19.5956	1.39613	0.698064	+	0.716035i	$0.254045\pi$
$198$	−11.9288	−0.847742
$199$	21.9514	1.55609	0.778045	−	0.628208i	$-0.216211\pi$
$199$	21.9514	1.55609	0.778045	+	0.628208i	$0.216211\pi$
$200$	−0.943592	−0.0667220
$201$	−39.2601	−2.76920
$202$	−6.35568	−0.447184
$203$	12.4706	0.875264
$204$	−17.1769	−1.20262
$205$	10.7550	0.751162
$206$	−11.2162	−0.781469
$207$	−9.35536	−0.650242
$208$	−3.55865	−0.246748
$209$	−8.79352	−0.608260
$210$	−11.3603	−0.783936
$211$	2.41930	0.166551	0.0832757	−	0.996527i	$-0.473462\pi$
$211$	2.41930	0.166551	0.0832757	+	0.996527i	$0.473462\pi$
$212$	12.2322	0.840114
$213$	−1.59879	−0.109547
$214$	−13.6183	−0.930930
$215$	−2.52388	−0.172127
$216$	−0.550262	−0.0374406
$217$	−13.6870	−0.929135
$218$	0.0239725	0.00162362
$219$	21.3033	1.43955
$220$	−7.45980	−0.502939
$221$	−24.5083	−1.64861
$222$	−10.1256	−0.679588
$223$	23.7336	1.58932	0.794660	−	0.607055i	$-0.207649\pi$
$223$	23.7336	1.58932	0.794660	+	0.607055i	$0.207649\pi$
$224$	2.26153	0.151105
$225$	−3.03895	−0.202597
$226$	20.2362	1.34609
$227$	3.74598	0.248629	0.124315	−	0.992243i	$-0.460327\pi$
$227$	3.74598	0.248629	0.124315	+	0.992243i	$0.460327\pi$
$228$	−5.92139	−0.392153
$229$	−6.05569	−0.400171	−0.200085	−	0.979778i	$-0.564122\pi$
$229$	−6.05569	−0.400171	−0.200085	+	0.979778i	$0.564122\pi$
$230$	−5.85048	−0.385769
$231$	20.8918	1.37458
$232$	5.51423	0.362027
$233$	−4.78829	−0.313691	−0.156846	−	0.987623i	$-0.550133\pi$
$233$	−4.78829	−0.313691	−0.156846	+	0.987623i	$0.550133\pi$
$234$	−11.4611	−0.749233
$235$	12.7488	0.831641
$236$	−4.09159	−0.266340
$237$	−6.17081	−0.400837
$238$	15.5751	1.00958
$239$	−23.7507	−1.53630	−0.768151	−	0.640268i	$-0.778823\pi$
$239$	−23.7507	−1.53630	−0.768151	+	0.640268i	$0.778823\pi$
$240$	−5.02328	−0.324252
$241$	14.2155	0.915700	0.457850	−	0.889029i	$-0.348620\pi$
$241$	14.2155	0.915700	0.457850	+	0.889029i	$0.348620\pi$
$242$	2.71868	0.174764
$243$	22.3257	1.43219
$244$	2.55932	0.163843
$245$	−3.79746	−0.242611
$246$	−13.3185	−0.849159
$247$	−8.44873	−0.537580
$248$	−6.05211	−0.384309
$249$	−13.9521	−0.884179
$250$	−11.9707	−0.757094
$251$	−0.0817027	−0.00515703	−0.00257852	−	0.999997i	$-0.500821\pi$
$251$	−0.0817027	−0.00515703	−0.00257852	+	0.999997i	$0.500821\pi$
$252$	7.28354	0.458820
$253$	10.7591	0.676420
$254$	−15.7777	−0.989980
$255$	−34.5952	−2.16644
$256$	1.00000	0.0625000
$257$	−8.34170	−0.520341	−0.260171	−	0.965563i	$-0.583779\pi$
$257$	−8.34170	−0.520341	−0.260171	+	0.965563i	$0.583779\pi$
$258$	3.12546	0.194583
$259$	9.18137	0.570503
$260$	−7.16730	−0.444497
$261$	17.7593	1.09927
$262$	−5.27108	−0.325648
$263$	−5.21436	−0.321531	−0.160766	−	0.986993i	$-0.551396\pi$
$263$	−5.21436	−0.321531	−0.160766	+	0.986993i	$0.551396\pi$
$264$	9.23790	0.568553
$265$	24.6364	1.51340
$266$	5.36919	0.329206
$267$	−20.9541	−1.28237
$268$	15.7411	0.961540
$269$	−8.22161	−0.501280	−0.250640	−	0.968080i	$-0.580641\pi$
$269$	−8.22161	−0.501280	−0.250640	+	0.968080i	$0.580641\pi$
$270$	−1.10826	−0.0674463
$271$	−15.5448	−0.944279	−0.472140	−	0.881524i	$-0.656518\pi$
$271$	−15.5448	−0.944279	−0.472140	+	0.881524i	$0.656518\pi$
$272$	6.88697	0.417584
$273$	20.0726	1.21485
$274$	14.6575	0.885493
$275$	3.49494	0.210753
$276$	7.24498	0.436097
$277$	−12.3455	−0.741768	−0.370884	−	0.928679i	$-0.620945\pi$
$277$	−12.3455	−0.741768	−0.370884	+	0.928679i	$0.620945\pi$
$278$	21.7180	1.30256
$279$	−19.4916	−1.16693
$280$	4.55484	0.272204
$281$	10.2175	0.609523	0.304761	−	0.952429i	$-0.401423\pi$
$281$	10.2175	0.609523	0.304761	+	0.952429i	$0.401423\pi$
$282$	−15.7876	−0.940137
$283$	17.1257	1.01802	0.509010	−	0.860761i	$-0.330012\pi$
$283$	17.1257	1.01802	0.509010	+	0.860761i	$0.330012\pi$
$284$	0.641025	0.0380379
$285$	−11.9260	−0.706434
$286$	13.1808	0.779396
$287$	12.0765	0.712854
$288$	3.22062	0.189777
$289$	30.4304	1.79002
$290$	11.1059	0.652164
$291$	17.9890	1.05453
$292$	−8.54143	−0.499849
$293$	−1.28713	−0.0751952	−0.0375976	−	0.999293i	$-0.511971\pi$
$293$	−1.28713	−0.0751952	−0.0375976	+	0.999293i	$0.511971\pi$
$294$	4.70261	0.274262
$295$	−8.24067	−0.479790
$296$	4.05981	0.235971
$297$	2.03810	0.118263
$298$	19.8344	1.14898
$299$	10.3373	0.597819
$300$	2.35343	0.135875
$301$	−2.83400	−0.163349
$302$	−4.66734	−0.268575
$303$	15.8518	0.910663
$304$	2.37414	0.136166
$305$	5.15460	0.295151
$306$	22.1803	1.26797
$307$	−2.79331	−0.159423	−0.0797113	−	0.996818i	$-0.525400\pi$
$307$	−2.79331	−0.159423	−0.0797113	+	0.996818i	$0.525400\pi$
$308$	−8.37642	−0.477291
$309$	27.9745	1.59141
$310$	−12.1893	−0.692304
$311$	−23.6621	−1.34175	−0.670877	−	0.741569i	$-0.734082\pi$
$311$	−23.6621	−1.34175	−0.670877	+	0.741569i	$0.734082\pi$
$312$	8.87569	0.502487
$313$	18.7782	1.06140	0.530702	−	0.847558i	$-0.321928\pi$
$313$	18.7782	1.06140	0.530702	+	0.847558i	$0.321928\pi$
$314$	21.6430	1.22139
$315$	14.6694	0.826529
$316$	2.47415	0.139182
$317$	22.9427	1.28859	0.644295	−	0.764777i	$-0.277151\pi$
$317$	22.9427	1.28859	0.644295	+	0.764777i	$0.277151\pi$
$318$	−30.5087	−1.71084
$319$	−20.4240	−1.14353
$320$	2.01405	0.112589
$321$	33.9657	1.89578
$322$	−6.56935	−0.366096
$323$	16.3506	0.909774
$324$	−8.28945	−0.460525
$325$	3.35791	0.186263
$326$	10.8339	0.600034
$327$	−0.0597902	−0.00330641
$328$	5.33998	0.294851
$329$	14.3153	0.789230
$330$	18.6056	1.02421
$331$	1.57418	0.0865249	0.0432625	−	0.999064i	$-0.486225\pi$
$331$	1.57418	0.0865249	0.0432625	+	0.999064i	$0.486225\pi$
$332$	5.59401	0.307011
$333$	13.0751	0.716511
$334$	13.3377	0.729809
$335$	31.7034	1.73214
$336$	−5.64052	−0.307716
$337$	−0.477872	−0.0260313	−0.0130157	−	0.999915i	$-0.504143\pi$
$337$	−0.477872	−0.0260313	−0.0130157	+	0.999915i	$0.504143\pi$
$338$	−0.336031	−0.0182777
$339$	−50.4715	−2.74123
$340$	13.8707	0.752246
$341$	22.4162	1.21391
$342$	7.64621	0.413460
$343$	−20.0948	−1.08502
$344$	−1.25313	−0.0675644
$345$	14.5918	0.785595
$346$	−22.9937	−1.23615
$347$	−20.1302	−1.08064	−0.540322	−	0.841458i	$-0.681698\pi$
$347$	−20.1302	−1.08064	−0.540322	+	0.841458i	$0.681698\pi$
$348$	−13.7531	−0.737246
$349$	15.7844	0.844920	0.422460	−	0.906382i	$-0.361167\pi$
$349$	15.7844	0.844920	0.422460	+	0.906382i	$0.361167\pi$
$350$	−2.13396	−0.114065
$351$	1.95819	0.104520
$352$	−3.70387	−0.197417
$353$	16.6971	0.888696	0.444348	−	0.895854i	$-0.353435\pi$
$353$	16.6971	0.888696	0.444348	+	0.895854i	$0.353435\pi$
$354$	10.2049	0.542384
$355$	1.29106	0.0685223
$356$	8.40142	0.445275
$357$	−38.8461	−2.05595
$358$	0.526188	0.0278099
$359$	−28.5977	−1.50933	−0.754663	−	0.656112i	$-0.772200\pi$
$359$	−28.5977	−1.50933	−0.754663	+	0.656112i	$0.772200\pi$
$360$	6.48651	0.341869
$361$	−13.3635	−0.703340
$362$	22.4799	1.18152
$363$	−6.78071	−0.355895
$364$	−8.04799	−0.421829
$365$	−17.2029	−0.900441
$366$	−6.38323	−0.333657
$367$	1.18623	0.0619208	0.0309604	−	0.999521i	$-0.490143\pi$
$367$	1.18623	0.0619208	0.0309604	+	0.999521i	$0.490143\pi$
$368$	−2.90483	−0.151425
$369$	17.1981	0.895295
$370$	8.17666	0.425084
$371$	27.6636	1.43622
$372$	15.0947	0.782622
$373$	−2.98533	−0.154574	−0.0772872	−	0.997009i	$-0.524626\pi$
$373$	−2.98533	−0.154574	−0.0772872	+	0.997009i	$0.524626\pi$
$374$	−25.5085	−1.31901
$375$	29.8564	1.54178
$376$	6.32993	0.326441
$377$	−19.6232	−1.01065
$378$	−1.24443	−0.0640067
$379$	3.12466	0.160503	0.0802516	−	0.996775i	$-0.474428\pi$
$379$	3.12466	0.160503	0.0802516	+	0.996775i	$0.474428\pi$
$380$	4.78164	0.245293
$381$	39.3514	2.01603
$382$	11.3651	0.581489
$383$	−9.08236	−0.464087	−0.232044	−	0.972705i	$-0.574541\pi$
$383$	−9.08236	−0.464087	−0.232044	+	0.972705i	$0.574541\pi$
$384$	−2.49412	−0.127277
$385$	−16.8706	−0.859803
$386$	−6.87508	−0.349932
$387$	−4.03587	−0.205155
$388$	−7.21256	−0.366162
$389$	−28.3345	−1.43661	−0.718307	−	0.695726i	$-0.755083\pi$
$389$	−28.3345	−1.43661	−0.718307	+	0.695726i	$0.755083\pi$
$390$	17.8761	0.905191
$391$	−20.0055	−1.01172
$392$	−1.88548	−0.0952312
$393$	13.1467	0.663163
$394$	19.5956	0.987212
$395$	4.98306	0.250725
$396$	−11.9288	−0.599444
$397$	18.5496	0.930976	0.465488	−	0.885054i	$-0.345879\pi$
$397$	18.5496	0.930976	0.465488	+	0.885054i	$0.345879\pi$
$398$	21.9514	1.10032
$399$	−13.3914	−0.670408
$400$	−0.943592	−0.0471796
$401$	−0.135001	−0.00674164	−0.00337082	−	0.999994i	$-0.501073\pi$
$401$	−0.135001	−0.00674164	−0.00337082	+	0.999994i	$0.501073\pi$
$402$	−39.2601	−1.95812
$403$	21.5373	1.07285
$404$	−6.35568	−0.316207
$405$	−16.6954	−0.829601
$406$	12.4706	0.618905
$407$	−15.0370	−0.745357
$408$	−17.1769	−0.850384
$409$	25.1046	1.24134	0.620672	−	0.784070i	$-0.286860\pi$
$409$	25.1046	1.24134	0.620672	+	0.784070i	$0.286860\pi$
$410$	10.7550	0.531151
$411$	−36.5576	−1.80325
$412$	−11.2162	−0.552582
$413$	−9.25325	−0.455322
$414$	−9.35536	−0.459791
$415$	11.2666	0.553057
$416$	−3.55865	−0.174477
$417$	−54.1672	−2.65258
$418$	−8.79352	−0.430105
$419$	27.8624	1.36117	0.680585	−	0.732669i	$-0.261726\pi$
$419$	27.8624	1.36117	0.680585	+	0.732669i	$0.261726\pi$
$420$	−11.3603	−0.554326
$421$	20.2765	0.988215	0.494107	−	0.869401i	$-0.335495\pi$
$421$	20.2765	0.988215	0.494107	+	0.869401i	$0.335495\pi$
$422$	2.41930	0.117770
$423$	20.3863	0.991217
$424$	12.2322	0.594050
$425$	−6.49849	−0.315223
$426$	−1.59879	−0.0774618
$427$	5.78797	0.280099
$428$	−13.6183	−0.658267
$429$	−32.8744	−1.58719
$430$	−2.52388	−0.121712
$431$	17.8164	0.858183	0.429092	−	0.903261i	$-0.358834\pi$
$431$	17.8164	0.858183	0.429092	+	0.903261i	$0.358834\pi$
$432$	−0.550262	−0.0264745
$433$	−36.7403	−1.76563	−0.882814	−	0.469722i	$-0.844354\pi$
$433$	−36.7403	−1.76563	−0.882814	+	0.469722i	$0.844354\pi$
$434$	−13.6870	−0.656998
$435$	−27.6995	−1.32809
$436$	0.0239725	0.00114807
$437$	−6.89647	−0.329903
$438$	21.3033	1.01791
$439$	−27.3337	−1.30456	−0.652282	−	0.757976i	$-0.726188\pi$
$439$	−27.3337	−1.30456	−0.652282	+	0.757976i	$0.726188\pi$
$440$	−7.45980	−0.355632
$441$	−6.07243	−0.289163
$442$	−24.5083	−1.16574
$443$	11.9975	0.570020	0.285010	−	0.958524i	$-0.408003\pi$
$443$	11.9975	0.570020	0.285010	+	0.958524i	$0.408003\pi$
$444$	−10.1256	−0.480541
$445$	16.9209	0.802128
$446$	23.7336	1.12382
$447$	−49.4694	−2.33982
$448$	2.26153	0.106847
$449$	−31.4885	−1.48603	−0.743017	−	0.669272i	$-0.766606\pi$
$449$	−31.4885	−1.48603	−0.743017	+	0.669272i	$0.766606\pi$
$450$	−3.03895	−0.143258
$451$	−19.7786	−0.931338
$452$	20.2362	0.951831
$453$	11.6409	0.546937
$454$	3.74598	0.175808
$455$	−16.2091	−0.759893
$456$	−5.92139	−0.277294
$457$	−5.43642	−0.254305	−0.127153	−	0.991883i	$-0.540584\pi$
$457$	−5.43642	−0.254305	−0.127153	+	0.991883i	$0.540584\pi$
$458$	−6.05569	−0.282964
$459$	−3.78964	−0.176885
$460$	−5.85048	−0.272780
$461$	−0.418075	−0.0194717	−0.00973585	−	0.999953i	$-0.503099\pi$
$461$	−0.418075	−0.0194717	−0.00973585	+	0.999953i	$0.503099\pi$
$462$	20.8918	0.971974
$463$	2.04479	0.0950296	0.0475148	−	0.998871i	$-0.484870\pi$
$463$	2.04479	0.0950296	0.0475148	+	0.998871i	$0.484870\pi$
$464$	5.51423	0.255992
$465$	30.4015	1.40983
$466$	−4.78829	−0.221813
$467$	−35.7920	−1.65626	−0.828129	−	0.560538i	$-0.810594\pi$
$467$	−35.7920	−1.65626	−0.828129	+	0.560538i	$0.810594\pi$
$468$	−11.4611	−0.529788
$469$	35.5989	1.64381
$470$	12.7488	0.588059
$471$	−53.9803	−2.48728
$472$	−4.09159	−0.188331
$473$	4.64145	0.213414
$474$	−6.17081	−0.283435
$475$	−2.24022	−0.102788
$476$	15.5751	0.713883
$477$	39.3955	1.80379
$478$	−23.7507	−1.08633
$479$	4.99316	0.228143	0.114072	−	0.993473i	$-0.463611\pi$
$479$	4.99316	0.228143	0.114072	+	0.993473i	$0.463611\pi$
$480$	−5.02328	−0.229281
$481$	−14.4474	−0.658745
$482$	14.2155	0.647498
$483$	16.3847	0.745532
$484$	2.71868	0.123576
$485$	−14.5265	−0.659613
$486$	22.3257	1.01271
$487$	−9.48550	−0.429829	−0.214915	−	0.976633i	$-0.568947\pi$
$487$	−9.48550	−0.429829	−0.214915	+	0.976633i	$0.568947\pi$
$488$	2.55932	0.115855
$489$	−27.0210	−1.22193
$490$	−3.79746	−0.171552
$491$	33.4510	1.50962	0.754811	−	0.655942i	$-0.227729\pi$
$491$	33.4510	1.50962	0.754811	+	0.655942i	$0.227729\pi$
$492$	−13.3185	−0.600446
$493$	37.9763	1.71037
$494$	−8.44873	−0.380126
$495$	−24.0252	−1.07985
$496$	−6.05211	−0.271748
$497$	1.44970	0.0650278
$498$	−13.9521	−0.625209
$499$	26.4188	1.18267	0.591334	−	0.806426i	$-0.298601\pi$
$499$	26.4188	1.18267	0.591334	+	0.806426i	$0.298601\pi$
$500$	−11.9707	−0.535346
$501$	−33.2659	−1.48621
$502$	−0.0817027	−0.00364657
$503$	−34.0270	−1.51719	−0.758594	−	0.651564i	$-0.774113\pi$
$503$	−34.0270	−1.51719	−0.758594	+	0.651564i	$0.774113\pi$
$504$	7.28354	0.324435
$505$	−12.8007	−0.569623
$506$	10.7591	0.478301
$507$	0.838101	0.0372214
$508$	−15.7777	−0.700022
$509$	26.3595	1.16836	0.584182	−	0.811623i	$-0.301415\pi$
$509$	26.3595	1.16836	0.584182	+	0.811623i	$0.301415\pi$
$510$	−34.5952	−1.53190
$511$	−19.3167	−0.854521
$512$	1.00000	0.0441942
$513$	−1.30640	−0.0576789
$514$	−8.34170	−0.367937
$515$	−22.5900	−0.995434
$516$	3.12546	0.137591
$517$	−23.4453	−1.03112
$518$	9.18137	0.403406
$519$	57.3489	2.51734
$520$	−7.16730	−0.314307
$521$	−43.5700	−1.90883	−0.954417	−	0.298476i	$-0.903522\pi$
$521$	−43.5700	−1.90883	−0.954417	+	0.298476i	$0.903522\pi$
$522$	17.7593	0.777302
$523$	−26.7780	−1.17092	−0.585461	−	0.810701i	$-0.699086\pi$
$523$	−26.7780	−1.17092	−0.585461	+	0.810701i	$0.699086\pi$
$524$	−5.27108	−0.230268
$525$	5.32235	0.232286
$526$	−5.21436	−0.227357
$527$	−41.6807	−1.81564
$528$	9.23790	0.402028
$529$	−14.5620	−0.633129
$530$	24.6364	1.07014
$531$	−13.1775	−0.571853
$532$	5.36919	0.232784
$533$	−19.0031	−0.823116
$534$	−20.9541	−0.906774
$535$	−27.4280	−1.18582
$536$	15.7411	0.679912
$537$	−1.31238	−0.0566332
$538$	−8.22161	−0.354459
$539$	6.98359	0.300804
$540$	−1.10826	−0.0476917
$541$	−27.6992	−1.19088	−0.595441	−	0.803399i	$-0.703023\pi$
$541$	−27.6992	−1.19088	−0.595441	+	0.803399i	$0.703023\pi$
$542$	−15.5448	−0.667706
$543$	−56.0676	−2.40609
$544$	6.88697	0.295276
$545$	0.0482819	0.00206817
$546$	20.0726	0.859029
$547$	−2.36790	−0.101244	−0.0506222	−	0.998718i	$-0.516120\pi$
$547$	−2.36790	−0.101244	−0.0506222	+	0.998718i	$0.516120\pi$
$548$	14.6575	0.626138
$549$	8.24259	0.351785
$550$	3.49494	0.149025
$551$	13.0916	0.557719
$552$	7.24498	0.308367
$553$	5.59536	0.237939
$554$	−12.3455	−0.524509
$555$	−20.3936	−0.865658
$556$	21.7180	0.921048
$557$	−23.7533	−1.00646	−0.503231	−	0.864152i	$-0.667855\pi$
$557$	−23.7533	−1.00646	−0.503231	+	0.864152i	$0.667855\pi$
$558$	−19.4916	−0.825143
$559$	4.45946	0.188615
$560$	4.55484	0.192477
$561$	63.6211	2.68609
$562$	10.2175	0.430998
$563$	−15.8021	−0.665980	−0.332990	−	0.942930i	$-0.608058\pi$
$563$	−15.8021	−0.665980	−0.332990	+	0.942930i	$0.608058\pi$
$564$	−15.7876	−0.664778
$565$	40.7568	1.71465
$566$	17.1257	0.719848
$567$	−18.7468	−0.787294
$568$	0.641025	0.0268968
$569$	−9.81604	−0.411510	−0.205755	−	0.978604i	$-0.565965\pi$
$569$	−9.81604	−0.411510	−0.205755	+	0.978604i	$0.565965\pi$
$570$	−11.9260	−0.499525
$571$	−23.6515	−0.989785	−0.494892	−	0.868954i	$-0.664792\pi$
$571$	−23.6515	−0.989785	−0.494892	+	0.868954i	$0.664792\pi$
$572$	13.1808	0.551116
$573$	−28.3459	−1.18417
$574$	12.0765	0.504064
$575$	2.74097	0.114306
$576$	3.22062	0.134193
$577$	−12.9868	−0.540646	−0.270323	−	0.962770i	$-0.587130\pi$
$577$	−12.9868	−0.540646	−0.270323	+	0.962770i	$0.587130\pi$
$578$	30.4304	1.26574
$579$	17.1473	0.712616
$580$	11.1059	0.461149
$581$	12.6510	0.524852
$582$	17.9890	0.745667
$583$	−45.3067	−1.87641
$584$	−8.54143	−0.353447
$585$	−23.0832	−0.954372
$586$	−1.28713	−0.0531710
$587$	35.9740	1.48480	0.742402	−	0.669955i	$-0.233686\pi$
$587$	35.9740	1.48480	0.742402	+	0.669955i	$0.233686\pi$
$588$	4.70261	0.193933
$589$	−14.3686	−0.592046
$590$	−8.24067	−0.339263
$591$	−48.8737	−2.01040
$592$	4.05981	0.166857
$593$	−6.08419	−0.249848	−0.124924	−	0.992166i	$-0.539869\pi$
$593$	−6.08419	−0.249848	−0.124924	+	0.992166i	$0.539869\pi$
$594$	2.03810	0.0836243
$595$	31.3691	1.28601
$596$	19.8344	0.812449
$597$	−54.7493	−2.24074
$598$	10.3373	0.422722
$599$	4.09711	0.167403	0.0837016	−	0.996491i	$-0.473326\pi$
$599$	4.09711	0.167403	0.0837016	+	0.996491i	$0.473326\pi$
$600$	2.35343	0.0960783
$601$	40.1134	1.63626	0.818130	−	0.575033i	$-0.195011\pi$
$601$	40.1134	1.63626	0.818130	+	0.575033i	$0.195011\pi$
$602$	−2.83400	−0.115505
$603$	50.6961	2.06451
$604$	−4.66734	−0.189911
$605$	5.47557	0.222614
$606$	15.8518	0.643936
$607$	−43.2460	−1.75530	−0.877652	−	0.479299i	$-0.840891\pi$
$607$	−43.2460	−1.75530	−0.877652	+	0.479299i	$0.840891\pi$
$608$	2.37414	0.0962841
$609$	−31.1031	−1.26036
$610$	5.15460	0.208704
$611$	−22.5260	−0.911304
$612$	22.1803	0.896587
$613$	20.9795	0.847356	0.423678	−	0.905813i	$-0.360739\pi$
$613$	20.9795	0.847356	0.423678	+	0.905813i	$0.360739\pi$
$614$	−2.79331	−0.112729
$615$	−26.8242	−1.08166
$616$	−8.37642	−0.337496
$617$	41.0688	1.65337	0.826684	−	0.562666i	$-0.190224\pi$
$617$	41.0688	1.65337	0.826684	+	0.562666i	$0.190224\pi$
$618$	27.9745	1.12530
$619$	35.2143	1.41538	0.707691	−	0.706522i	$-0.249737\pi$
$619$	35.2143	1.41538	0.707691	+	0.706522i	$0.249737\pi$
$620$	−12.1893	−0.489533
$621$	1.59842	0.0641422
$622$	−23.6621	−0.948763
$623$	19.0001	0.761222
$624$	8.87569	0.355312
$625$	−19.3917	−0.775667
$626$	18.7782	0.750526
$627$	21.9321	0.875882
$628$	21.6430	0.863652
$629$	27.9598	1.11483
$630$	14.6694	0.584444
$631$	−19.4169	−0.772975	−0.386488	−	0.922295i	$-0.626312\pi$
$631$	−19.4169	−0.772975	−0.386488	+	0.922295i	$0.626312\pi$
$632$	2.47415	0.0984163
$633$	−6.03401	−0.239830
$634$	22.9427	0.911171
$635$	−31.7771	−1.26104
$636$	−30.5087	−1.20975
$637$	6.70977	0.265851
$638$	−20.4240	−0.808594
$639$	2.06450	0.0816704
$640$	2.01405	0.0796124
$641$	2.74610	0.108464	0.0542322	−	0.998528i	$-0.482729\pi$
$641$	2.74610	0.108464	0.0542322	+	0.998528i	$0.482729\pi$
$642$	33.9657	1.34052
$643$	20.4085	0.804833	0.402417	−	0.915457i	$-0.368170\pi$
$643$	20.4085	0.804833	0.402417	+	0.915457i	$0.368170\pi$
$644$	−6.56935	−0.258869
$645$	6.29485	0.247859
$646$	16.3506	0.643307
$647$	−15.2695	−0.600305	−0.300152	−	0.953891i	$-0.597038\pi$
$647$	−15.2695	−0.600305	−0.300152	+	0.953891i	$0.597038\pi$
$648$	−8.28945	−0.325641
$649$	15.1547	0.594875
$650$	3.35791	0.131708
$651$	34.1370	1.33794
$652$	10.8339	0.424288
$653$	−45.6646	−1.78699	−0.893497	−	0.449070i	$-0.851755\pi$
$653$	−45.6646	−1.78699	−0.893497	+	0.449070i	$0.851755\pi$
$654$	−0.0597902	−0.00233798
$655$	−10.6162	−0.414810
$656$	5.33998	0.208491
$657$	−27.5087	−1.07322
$658$	14.3153	0.558070
$659$	13.9482	0.543344	0.271672	−	0.962390i	$-0.412423\pi$
$659$	13.9482	0.543344	0.271672	+	0.962390i	$0.412423\pi$
$660$	18.6056	0.724223
$661$	30.9262	1.20289	0.601445	−	0.798914i	$-0.294592\pi$
$661$	30.9262	1.20289	0.601445	+	0.798914i	$0.294592\pi$
$662$	1.57418	0.0611824
$663$	61.1266	2.37396
$664$	5.59401	0.217090
$665$	10.8138	0.419342
$666$	13.0751	0.506650
$667$	−16.0179	−0.620215
$668$	13.3377	0.516053
$669$	−59.1944	−2.28859
$670$	31.7034	1.22481
$671$	−9.47938	−0.365947
$672$	−5.64052	−0.217588
$673$	−9.57022	−0.368905	−0.184452	−	0.982841i	$-0.559051\pi$
$673$	−9.57022	−0.368905	−0.184452	+	0.982841i	$0.559051\pi$
$674$	−0.477872	−0.0184069
$675$	0.519222	0.0199849
$676$	−0.336031	−0.0129243
$677$	−25.9543	−0.997506	−0.498753	−	0.866744i	$-0.666209\pi$
$677$	−25.9543	−0.997506	−0.498753	+	0.866744i	$0.666209\pi$
$678$	−50.4715	−1.93834
$679$	−16.3114	−0.625975
$680$	13.8707	0.531918
$681$	−9.34291	−0.358021
$682$	22.4162	0.858362
$683$	−13.8477	−0.529869	−0.264935	−	0.964266i	$-0.585350\pi$
$683$	−13.8477	−0.529869	−0.264935	+	0.964266i	$0.585350\pi$
$684$	7.64621	0.292360
$685$	29.5210	1.12794
$686$	−20.0948	−0.767222
$687$	15.1036	0.576238
$688$	−1.25313	−0.0477753
$689$	−43.5302	−1.65837
$690$	14.5918	0.555499
$691$	−31.2996	−1.19069	−0.595347	−	0.803469i	$-0.702985\pi$
$691$	−31.2996	−1.19069	−0.595347	+	0.803469i	$0.702985\pi$
$692$	−22.9937	−0.874088
$693$	−26.9773	−1.02478
$694$	−20.1302	−0.764131
$695$	43.7412	1.65920
$696$	−13.7531	−0.521311
$697$	36.7763	1.39300
$698$	15.7844	0.597449
$699$	11.9426	0.451709
$700$	−2.13396	−0.0806561
$701$	−32.9107	−1.24302	−0.621510	−	0.783407i	$-0.713480\pi$
$701$	−32.9107	−1.24302	−0.621510	+	0.783407i	$0.713480\pi$
$702$	1.95819	0.0739070
$703$	9.63855	0.363525
$704$	−3.70387	−0.139595
$705$	−31.7970	−1.19755
$706$	16.6971	0.628403
$707$	−14.3736	−0.540574
$708$	10.2049	0.383524
$709$	−16.5984	−0.623366	−0.311683	−	0.950186i	$-0.600893\pi$
$709$	−16.5984	−0.623366	−0.311683	+	0.950186i	$0.600893\pi$
$710$	1.29106	0.0484526
$711$	7.96830	0.298834
$712$	8.40142	0.314857
$713$	17.5803	0.658388
$714$	−38.8461	−1.45378
$715$	26.5468	0.992794
$716$	0.526188	0.0196646
$717$	59.2369	2.21224
$718$	−28.5977	−1.06726
$719$	−46.7763	−1.74446	−0.872231	−	0.489094i	$-0.837328\pi$
$719$	−46.7763	−1.74446	−0.872231	+	0.489094i	$0.837328\pi$
$720$	6.48651	0.241738
$721$	−25.3657	−0.944669
$722$	−13.3635	−0.497336
$723$	−35.4551	−1.31859
$724$	22.4799	0.835460
$725$	−5.20318	−0.193241
$726$	−6.78071	−0.251656
$727$	9.39673	0.348505	0.174253	−	0.984701i	$-0.444249\pi$
$727$	9.39673	0.348505	0.174253	+	0.984701i	$0.444249\pi$
$728$	−8.04799	−0.298278
$729$	−30.8145	−1.14128
$730$	−17.2029	−0.636708
$731$	−8.63029	−0.319203
$732$	−6.38323	−0.235931
$733$	15.7585	0.582052	0.291026	−	0.956715i	$-0.406003\pi$
$733$	15.7585	0.582052	0.291026	+	0.956715i	$0.406003\pi$
$734$	1.18623	0.0437846
$735$	9.47131	0.349355
$736$	−2.90483	−0.107073
$737$	−58.3030	−2.14762
$738$	17.1981	0.633069
$739$	26.5556	0.976862	0.488431	−	0.872603i	$-0.337569\pi$
$739$	26.5556	0.976862	0.488431	+	0.872603i	$0.337569\pi$
$740$	8.17666	0.300580
$741$	21.0721	0.774104
$742$	27.6636	1.01556
$743$	−26.2022	−0.961267	−0.480633	−	0.876922i	$-0.659593\pi$
$743$	−26.2022	−0.961267	−0.480633	+	0.876922i	$0.659593\pi$
$744$	15.0947	0.553397
$745$	39.9476	1.46357
$746$	−2.98533	−0.109301
$747$	18.0162	0.659178
$748$	−25.5085	−0.932682
$749$	−30.7983	−1.12534
$750$	29.8564	1.09020
$751$	−28.1226	−1.02621	−0.513104	−	0.858326i	$-0.671505\pi$
$751$	−28.1226	−1.02621	−0.513104	+	0.858326i	$0.671505\pi$
$752$	6.32993	0.230829
$753$	0.203776	0.00742602
$754$	−19.6232	−0.714635
$755$	−9.40027	−0.342111
$756$	−1.24443	−0.0452596
$757$	−31.8928	−1.15916	−0.579582	−	0.814914i	$-0.696784\pi$
$757$	−31.8928	−1.15916	−0.579582	+	0.814914i	$0.696784\pi$
$758$	3.12466	0.113493
$759$	−26.8345	−0.974031
$760$	4.78164	0.173448
$761$	8.87040	0.321552	0.160776	−	0.986991i	$-0.448600\pi$
$761$	8.87040	0.321552	0.160776	+	0.986991i	$0.448600\pi$
$762$	39.3514	1.42555
$763$	0.0542145	0.00196270
$764$	11.3651	0.411175
$765$	44.6724	1.61513
$766$	−9.08236	−0.328159
$767$	14.5605	0.525750
$768$	−2.49412	−0.0899987
$769$	0.145034	0.00523005	0.00261503	−	0.999997i	$-0.499168\pi$
$769$	0.145034	0.00523005	0.00261503	+	0.999997i	$0.499168\pi$
$770$	−16.8706	−0.607973
$771$	20.8052	0.749280
$772$	−6.87508	−0.247440
$773$	−28.1788	−1.01352	−0.506761	−	0.862086i	$-0.669157\pi$
$773$	−28.1788	−1.01352	−0.506761	+	0.862086i	$0.669157\pi$
$774$	−4.03587	−0.145066
$775$	5.71072	0.205135
$776$	−7.21256	−0.258916
$777$	−22.8994	−0.821512
$778$	−28.3345	−1.01584
$779$	12.6779	0.454231
$780$	17.8761	0.640067
$781$	−2.37428	−0.0849583
$782$	−20.0055	−0.715394
$783$	−3.03427	−0.108436
$784$	−1.88548	−0.0673386
$785$	43.5902	1.55580
$786$	13.1467	0.468927
$787$	−4.62878	−0.164998	−0.0824990	−	0.996591i	$-0.526290\pi$
$787$	−4.62878	−0.164998	−0.0824990	+	0.996591i	$0.526290\pi$
$788$	19.5956	0.698064
$789$	13.0052	0.462998
$790$	4.98306	0.177289
$791$	45.7648	1.62721
$792$	−11.9288	−0.423871
$793$	−9.10770	−0.323424
$794$	18.5496	0.658299
$795$	−61.4460	−2.17927
$796$	21.9514	0.778045
$797$	23.3111	0.825721	0.412861	−	0.910794i	$-0.364530\pi$
$797$	23.3111	0.825721	0.412861	+	0.910794i	$0.364530\pi$
$798$	−13.3914	−0.474050
$799$	43.5941	1.54225
$800$	−0.943592	−0.0333610
$801$	27.0578	0.956041
$802$	−0.135001	−0.00476706
$803$	31.6364	1.11642
$804$	−39.2601	−1.38460
$805$	−13.2310	−0.466332
$806$	21.5373	0.758619
$807$	20.5057	0.721833
$808$	−6.35568	−0.223592
$809$	3.93721	0.138425	0.0692125	−	0.997602i	$-0.477951\pi$
$809$	3.93721	0.138425	0.0692125	+	0.997602i	$0.477951\pi$
$810$	−16.6954	−0.586616
$811$	−8.77345	−0.308077	−0.154039	−	0.988065i	$-0.549228\pi$
$811$	−8.77345	−0.308077	−0.154039	+	0.988065i	$0.549228\pi$
$812$	12.4706	0.437632
$813$	38.7706	1.35974
$814$	−15.0370	−0.527047
$815$	21.8200	0.764322
$816$	−17.1769	−0.601312
$817$	−2.97511	−0.104086
$818$	25.1046	0.877763
$819$	−25.9195	−0.905702
$820$	10.7550	0.375581
$821$	0.517055	0.0180453	0.00902267	−	0.999959i	$-0.497128\pi$
$821$	0.517055	0.0180453	0.00902267	+	0.999959i	$0.497128\pi$
$822$	−36.5576	−1.27509
$823$	16.0261	0.558636	0.279318	−	0.960199i	$-0.409892\pi$
$823$	16.0261	0.558636	0.279318	+	0.960199i	$0.409892\pi$
$824$	−11.2162	−0.390734
$825$	−8.71680	−0.303480
$826$	−9.25325	−0.321962
$827$	−49.1062	−1.70759	−0.853795	−	0.520609i	$-0.825705\pi$
$827$	−49.1062	−1.70759	−0.853795	+	0.520609i	$0.825705\pi$
$828$	−9.35536	−0.325121
$829$	−33.7931	−1.17368	−0.586841	−	0.809702i	$-0.699629\pi$
$829$	−33.7931	−1.17368	−0.586841	+	0.809702i	$0.699629\pi$
$830$	11.2666	0.391070
$831$	30.7911	1.06813
$832$	−3.55865	−0.123374
$833$	−12.9853	−0.449913
$834$	−54.1672	−1.87566
$835$	26.8629	0.929630
$836$	−8.79352	−0.304130
$837$	3.33024	0.115110
$838$	27.8624	0.962492
$839$	47.4779	1.63912	0.819559	−	0.572994i	$-0.194218\pi$
$839$	47.4779	1.63912	0.819559	+	0.572994i	$0.194218\pi$
$840$	−11.3603	−0.391968
$841$	1.40673	0.0485078
$842$	20.2765	0.698773
$843$	−25.4836	−0.877700
$844$	2.41930	0.0832757
$845$	−0.676784	−0.0232821
$846$	20.3863	0.700896
$847$	6.14838	0.211261
$848$	12.2322	0.420057
$849$	−42.7136	−1.46593
$850$	−6.49849	−0.222896
$851$	−11.7930	−0.404260
$852$	−1.59879	−0.0547737
$853$	−32.2823	−1.10533	−0.552663	−	0.833405i	$-0.686388\pi$
$853$	−32.2823	−1.10533	−0.552663	+	0.833405i	$0.686388\pi$
$854$	5.78797	0.198060
$855$	15.3999	0.526665
$856$	−13.6183	−0.465465
$857$	−8.60550	−0.293958	−0.146979	−	0.989140i	$-0.546955\pi$
$857$	−8.60550	−0.293958	−0.146979	+	0.989140i	$0.546955\pi$
$858$	−32.8744	−1.12231
$859$	−34.7924	−1.18710	−0.593551	−	0.804797i	$-0.702274\pi$
$859$	−34.7924	−1.18710	−0.593551	+	0.804797i	$0.702274\pi$
$860$	−2.52388	−0.0860635
$861$	−30.1203	−1.02650
$862$	17.8164	0.606827
$863$	1.13842	0.0387522	0.0193761	−	0.999812i	$-0.493832\pi$
$863$	1.13842	0.0387522	0.0193761	+	0.999812i	$0.493832\pi$
$864$	−0.550262	−0.0187203
$865$	−46.3105	−1.57460
$866$	−36.7403	−1.24849
$867$	−75.8970	−2.57760
$868$	−13.6870	−0.464568
$869$	−9.16393	−0.310865
$870$	−27.6995	−0.939103
$871$	−56.0170	−1.89806
$872$	0.0239725	0.000811811 0
$873$	−23.2289	−0.786180
$874$	−6.89647	−0.233277
$875$	−27.0721	−0.915204
$876$	21.3033	0.719773
$877$	31.2059	1.05375	0.526874	−	0.849943i	$-0.323364\pi$
$877$	31.2059	1.05375	0.526874	+	0.849943i	$0.323364\pi$
$878$	−27.3337	−0.922466
$879$	3.21026	0.108280
$880$	−7.45980	−0.251470
$881$	25.7583	0.867820	0.433910	−	0.900956i	$-0.357134\pi$
$881$	25.7583	0.867820	0.433910	+	0.900956i	$0.357134\pi$
$882$	−6.07243	−0.204469
$883$	−45.0254	−1.51523	−0.757613	−	0.652704i	$-0.773635\pi$
$883$	−45.0254	−1.51523	−0.757613	+	0.652704i	$0.773635\pi$
$884$	−24.5083	−0.824303
$885$	20.5532	0.690888
$886$	11.9975	0.403065
$887$	0.401785	0.0134906	0.00674530	−	0.999977i	$-0.497853\pi$
$887$	0.401785	0.0134906	0.00674530	+	0.999977i	$0.497853\pi$
$888$	−10.1256	−0.339794
$889$	−35.6817	−1.19673
$890$	16.9209	0.567190
$891$	30.7031	1.02859
$892$	23.7336	0.794660
$893$	15.0281	0.502898
$894$	−49.4694	−1.65450
$895$	1.05977	0.0354242
$896$	2.26153	0.0755524
$897$	−25.7823	−0.860847
$898$	−31.4885	−1.05079
$899$	−33.3727	−1.11304
$900$	−3.03895	−0.101298
$901$	84.2431	2.80655
$902$	−19.7786	−0.658556
$903$	7.06833	0.235219
$904$	20.2362	0.673046
$905$	45.2758	1.50502
$906$	11.6409	0.386743
$907$	−46.5912	−1.54704	−0.773518	−	0.633775i	$-0.781505\pi$
$907$	−46.5912	−1.54704	−0.773518	+	0.633775i	$0.781505\pi$
$908$	3.74598	0.124315
$909$	−20.4693	−0.678923
$910$	−16.2091	−0.537325
$911$	21.6758	0.718152	0.359076	−	0.933308i	$-0.383092\pi$
$911$	21.6758	0.718152	0.359076	+	0.933308i	$0.383092\pi$
$912$	−5.92139	−0.196077
$913$	−20.7195	−0.685715
$914$	−5.43642	−0.179821
$915$	−12.8562	−0.425012
$916$	−6.05569	−0.200085
$917$	−11.9207	−0.393656
$918$	−3.78964	−0.125077
$919$	−28.2429	−0.931646	−0.465823	−	0.884878i	$-0.654242\pi$
$919$	−28.2429	−0.931646	−0.465823	+	0.884878i	$0.654242\pi$
$920$	−5.85048	−0.192884
$921$	6.96684	0.229565
$922$	−0.418075	−0.0137686
$923$	−2.28118	−0.0750861
$924$	20.8918	0.687289
$925$	−3.83080	−0.125956
$926$	2.04479	0.0671960
$927$	−36.1231	−1.18644
$928$	5.51423	0.181013
$929$	42.2378	1.38578	0.692888	−	0.721045i	$-0.256338\pi$
$929$	42.2378	1.38578	0.692888	+	0.721045i	$0.256338\pi$
$930$	30.4015	0.996903
$931$	−4.47640	−0.146708
$932$	−4.78829	−0.156846
$933$	59.0160	1.93210
$934$	−35.7920	−1.17115
$935$	−51.3754	−1.68016
$936$	−11.4611	−0.374617
$937$	13.3743	0.436918	0.218459	−	0.975846i	$-0.429897\pi$
$937$	13.3743	0.436918	0.218459	+	0.975846i	$0.429897\pi$
$938$	35.5989	1.16235
$939$	−46.8349	−1.52840
$940$	12.7488	0.415820
$941$	−5.34684	−0.174302	−0.0871510	−	0.996195i	$-0.527776\pi$
$941$	−5.34684	−0.174302	−0.0871510	+	0.996195i	$0.527776\pi$
$942$	−53.9803	−1.75877
$943$	−15.5117	−0.505131
$944$	−4.09159	−0.133170
$945$	−2.50635	−0.0815317
$946$	4.64145	0.150906
$947$	−47.3436	−1.53846	−0.769231	−	0.638971i	$-0.779360\pi$
$947$	−47.3436	−1.53846	−0.769231	+	0.638971i	$0.779360\pi$
$948$	−6.17081	−0.200419
$949$	30.3959	0.986694
$950$	−2.24022	−0.0726823
$951$	−57.2218	−1.85554
$952$	15.5751	0.504792
$953$	−25.1830	−0.815757	−0.407879	−	0.913036i	$-0.633731\pi$
$953$	−25.1830	−0.815757	−0.407879	+	0.913036i	$0.633731\pi$
$954$	39.3955	1.27547
$955$	22.8899	0.740700
$956$	−23.7507	−0.768151
$957$	50.9399	1.64665
$958$	4.99316	0.161322
$959$	33.1484	1.07042
$960$	−5.02328	−0.162126
$961$	5.62799	0.181548
$962$	−14.4474	−0.465803
$963$	−43.8595	−1.41335
$964$	14.2155	0.457850
$965$	−13.8468	−0.445743
$966$	16.3847	0.527171
$967$	−18.1464	−0.583549	−0.291775	−	0.956487i	$-0.594246\pi$
$967$	−18.1464	−0.583549	−0.291775	+	0.956487i	$0.594246\pi$
$968$	2.71868	0.0873818
$969$	−40.7804	−1.31006
$970$	−14.5265	−0.466417
$971$	−21.7629	−0.698406	−0.349203	−	0.937047i	$-0.613548\pi$
$971$	−21.7629	−0.698406	−0.349203	+	0.937047i	$0.613548\pi$
$972$	22.3257	0.716096
$973$	49.1159	1.57458
$974$	−9.48550	−0.303935
$975$	−8.37502	−0.268215
$976$	2.55932	0.0819217
$977$	2.63198	0.0842045	0.0421023	−	0.999113i	$-0.486594\pi$
$977$	2.63198	0.0842045	0.0421023	+	0.999113i	$0.486594\pi$
$978$	−27.0210	−0.864036
$979$	−31.1178	−0.994530
$980$	−3.79746	−0.121305
$981$	0.0772064	0.00246501
$982$	33.4510	1.06746
$983$	48.1572	1.53598	0.767988	−	0.640464i	$-0.221258\pi$
$983$	48.1572	1.53598	0.767988	+	0.640464i	$0.221258\pi$
$984$	−13.3185	−0.424579
$985$	39.4666	1.25751
$986$	37.9763	1.20941
$987$	−35.7041	−1.13647
$988$	−8.44873	−0.268790
$989$	3.64014	0.115750
$990$	−24.0252	−0.763571
$991$	−0.147273	−0.00467829	−0.00233914	−	0.999997i	$-0.500745\pi$
$991$	−0.147273	−0.00467829	−0.00233914	+	0.999997i	$0.500745\pi$
$992$	−6.05211	−0.192155
$993$	−3.92620	−0.124594
$994$	1.44970	0.0459816
$995$	44.2112	1.40159
$996$	−13.9521	−0.442089
$997$	−26.1014	−0.826639	−0.413319	−	0.910586i	$-0.635631\pi$
$997$	−26.1014	−0.826639	−0.413319	+	0.910586i	$0.635631\pi$
$998$	26.4188	0.836273
$999$	−2.23396	−0.0706792

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4034.2.a.d.1.8	✓	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4034.2.a.d.1.8	✓	52	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:	\( N \)	\(=\)	\( 4034 = 2 \cdot 2017 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4034.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.49412 q^{3} +1.00000 q^{4} +2.01405 q^{5} -2.49412 q^{6} +2.26153 q^{7} +1.00000 q^{8} +3.22062 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.49412 q^{3} +1.00000 q^{4} +2.01405 q^{5} -2.49412 q^{6} +2.26153 q^{7} +1.00000 q^{8} +3.22062 q^{9} +2.01405 q^{10} -3.70387 q^{11} -2.49412 q^{12} -3.55865 q^{13} +2.26153 q^{14} -5.02328 q^{15} +1.00000 q^{16} +6.88697 q^{17} +3.22062 q^{18} +2.37414 q^{19} +2.01405 q^{20} -5.64052 q^{21} -3.70387 q^{22} -2.90483 q^{23} -2.49412 q^{24} -0.943592 q^{25} -3.55865 q^{26} -0.550262 q^{27} +2.26153 q^{28} +5.51423 q^{29} -5.02328 q^{30} -6.05211 q^{31} +1.00000 q^{32} +9.23790 q^{33} +6.88697 q^{34} +4.55484 q^{35} +3.22062 q^{36} +4.05981 q^{37} +2.37414 q^{38} +8.87569 q^{39} +2.01405 q^{40} +5.33998 q^{41} -5.64052 q^{42} -1.25313 q^{43} -3.70387 q^{44} +6.48651 q^{45} -2.90483 q^{46} +6.32993 q^{47} -2.49412 q^{48} -1.88548 q^{49} -0.943592 q^{50} -17.1769 q^{51} -3.55865 q^{52} +12.2322 q^{53} -0.550262 q^{54} -7.45980 q^{55} +2.26153 q^{56} -5.92139 q^{57} +5.51423 q^{58} -4.09159 q^{59} -5.02328 q^{60} +2.55932 q^{61} -6.05211 q^{62} +7.28354 q^{63} +1.00000 q^{64} -7.16730 q^{65} +9.23790 q^{66} +15.7411 q^{67} +6.88697 q^{68} +7.24498 q^{69} +4.55484 q^{70} +0.641025 q^{71} +3.22062 q^{72} -8.54143 q^{73} +4.05981 q^{74} +2.35343 q^{75} +2.37414 q^{76} -8.37642 q^{77} +8.87569 q^{78} +2.47415 q^{79} +2.01405 q^{80} -8.28945 q^{81} +5.33998 q^{82} +5.59401 q^{83} -5.64052 q^{84} +13.8707 q^{85} -1.25313 q^{86} -13.7531 q^{87} -3.70387 q^{88} +8.40142 q^{89} +6.48651 q^{90} -8.04799 q^{91} -2.90483 q^{92} +15.0947 q^{93} +6.32993 q^{94} +4.78164 q^{95} -2.49412 q^{96} -7.21256 q^{97} -1.88548 q^{98} -11.9288 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q + 52 q^{2} + 16 q^{3} + 52 q^{4} + 24 q^{5} + 16 q^{6} + 12 q^{7} + 52 q^{8} + 70 q^{9}+O(q^{10}) \) 52 * q + 52 * q^2 + 16 * q^3 + 52 * q^4 + 24 * q^5 + 16 * q^6 + 12 * q^7 + 52 * q^8 + 70 * q^9	\( 52 q + 52 q^{2} + 16 q^{3} + 52 q^{4} + 24 q^{5} + 16 q^{6} + 12 q^{7} + 52 q^{8} + 70 q^{9} + 24 q^{10} + 19 q^{11} + 16 q^{12} + 27 q^{13} + 12 q^{14} + 5 q^{15} + 52 q^{16} + 43 q^{17} + 70 q^{18} + 35 q^{19} + 24 q^{20} + 29 q^{21} + 19 q^{22} + 2 q^{23} + 16 q^{24} + 88 q^{25} + 27 q^{26} + 49 q^{27} + 12 q^{28} + 31 q^{29} + 5 q^{30} + 59 q^{31} + 52 q^{32} + 45 q^{33} + 43 q^{34} + 18 q^{35} + 70 q^{36} + 60 q^{37} + 35 q^{38} + 6 q^{39} + 24 q^{40} + 56 q^{41} + 29 q^{42} + 34 q^{43} + 19 q^{44} + 61 q^{45} + 2 q^{46} - 4 q^{47} + 16 q^{48} + 102 q^{49} + 88 q^{50} + 23 q^{51} + 27 q^{52} + 30 q^{53} + 49 q^{54} + 24 q^{55} + 12 q^{56} + 32 q^{57} + 31 q^{58} + 27 q^{59} + 5 q^{60} + 107 q^{61} + 59 q^{62} - 4 q^{63} + 52 q^{64} + 46 q^{65} + 45 q^{66} + 22 q^{67} + 43 q^{68} + 36 q^{69} + 18 q^{70} + 8 q^{71} + 70 q^{72} + 66 q^{73} + 60 q^{74} + 53 q^{75} + 35 q^{76} + 26 q^{77} + 6 q^{78} + 50 q^{79} + 24 q^{80} + 108 q^{81} + 56 q^{82} + 52 q^{83} + 29 q^{84} + 19 q^{85} + 34 q^{86} - 32 q^{87} + 19 q^{88} + 62 q^{89} + 61 q^{90} + 69 q^{91} + 2 q^{92} + 21 q^{93} - 4 q^{94} - 44 q^{95} + 16 q^{96} + 82 q^{97} + 102 q^{98} + 16 q^{99}+O(q^{100}) \) 52 * q + 52 * q^2 + 16 * q^3 + 52 * q^4 + 24 * q^5 + 16 * q^6 + 12 * q^7 + 52 * q^8 + 70 * q^9 + 24 * q^10 + 19 * q^11 + 16 * q^12 + 27 * q^13 + 12 * q^14 + 5 * q^15 + 52 * q^16 + 43 * q^17 + 70 * q^18 + 35 * q^19 + 24 * q^20 + 29 * q^21 + 19 * q^22 + 2 * q^23 + 16 * q^24 + 88 * q^25 + 27 * q^26 + 49 * q^27 + 12 * q^28 + 31 * q^29 + 5 * q^30 + 59 * q^31 + 52 * q^32 + 45 * q^33 + 43 * q^34 + 18 * q^35 + 70 * q^36 + 60 * q^37 + 35 * q^38 + 6 * q^39 + 24 * q^40 + 56 * q^41 + 29 * q^42 + 34 * q^43 + 19 * q^44 + 61 * q^45 + 2 * q^46 - 4 * q^47 + 16 * q^48 + 102 * q^49 + 88 * q^50 + 23 * q^51 + 27 * q^52 + 30 * q^53 + 49 * q^54 + 24 * q^55 + 12 * q^56 + 32 * q^57 + 31 * q^58 + 27 * q^59 + 5 * q^60 + 107 * q^61 + 59 * q^62 - 4 * q^63 + 52 * q^64 + 46 * q^65 + 45 * q^66 + 22 * q^67 + 43 * q^68 + 36 * q^69 + 18 * q^70 + 8 * q^71 + 70 * q^72 + 66 * q^73 + 60 * q^74 + 53 * q^75 + 35 * q^76 + 26 * q^77 + 6 * q^78 + 50 * q^79 + 24 * q^80 + 108 * q^81 + 56 * q^82 + 52 * q^83 + 29 * q^84 + 19 * q^85 + 34 * q^86 - 32 * q^87 + 19 * q^88 + 62 * q^89 + 61 * q^90 + 69 * q^91 + 2 * q^92 + 21 * q^93 - 4 * q^94 - 44 * q^95 + 16 * q^96 + 82 * q^97 + 102 * q^98 + 16 * q^99

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