LMFDB - Embedded newform 4034.2.a.a.1.7

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:	$1$
Dimension:	$33$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
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)

$f(q)$	$=$	$q+1.00000 q^{2} -2.63161 q^{3} +1.00000 q^{4} +1.62454 q^{5} -2.63161 q^{6} +2.40683 q^{7} +1.00000 q^{8} +3.92538 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.63161 q^{3} +1.00000 q^{4} +1.62454 q^{5} -2.63161 q^{6} +2.40683 q^{7} +1.00000 q^{8} +3.92538 q^{9} +1.62454 q^{10} -3.88889 q^{11} -2.63161 q^{12} -0.435673 q^{13} +2.40683 q^{14} -4.27516 q^{15} +1.00000 q^{16} -1.47261 q^{17} +3.92538 q^{18} -4.69089 q^{19} +1.62454 q^{20} -6.33385 q^{21} -3.88889 q^{22} +6.93055 q^{23} -2.63161 q^{24} -2.36087 q^{25} -0.435673 q^{26} -2.43524 q^{27} +2.40683 q^{28} -0.515056 q^{29} -4.27516 q^{30} -0.199735 q^{31} +1.00000 q^{32} +10.2340 q^{33} -1.47261 q^{34} +3.91000 q^{35} +3.92538 q^{36} -11.2575 q^{37} -4.69089 q^{38} +1.14652 q^{39} +1.62454 q^{40} -11.0337 q^{41} -6.33385 q^{42} -7.50752 q^{43} -3.88889 q^{44} +6.37694 q^{45} +6.93055 q^{46} -7.60261 q^{47} -2.63161 q^{48} -1.20715 q^{49} -2.36087 q^{50} +3.87533 q^{51} -0.435673 q^{52} -3.42960 q^{53} -2.43524 q^{54} -6.31766 q^{55} +2.40683 q^{56} +12.3446 q^{57} -0.515056 q^{58} +7.97306 q^{59} -4.27516 q^{60} +10.4511 q^{61} -0.199735 q^{62} +9.44774 q^{63} +1.00000 q^{64} -0.707768 q^{65} +10.2340 q^{66} +1.39854 q^{67} -1.47261 q^{68} -18.2385 q^{69} +3.91000 q^{70} +9.93637 q^{71} +3.92538 q^{72} -0.642060 q^{73} -11.2575 q^{74} +6.21289 q^{75} -4.69089 q^{76} -9.35991 q^{77} +1.14652 q^{78} +14.4809 q^{79} +1.62454 q^{80} -5.36754 q^{81} -11.0337 q^{82} +5.55412 q^{83} -6.33385 q^{84} -2.39231 q^{85} -7.50752 q^{86} +1.35543 q^{87} -3.88889 q^{88} -14.8885 q^{89} +6.37694 q^{90} -1.04859 q^{91} +6.93055 q^{92} +0.525625 q^{93} -7.60261 q^{94} -7.62054 q^{95} -2.63161 q^{96} +7.29323 q^{97} -1.20715 q^{98} -15.2654 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 33 q + 33 q^{2} - 14 q^{3} + 33 q^{4} - 22 q^{5} - 14 q^{6} - 12 q^{7} + 33 q^{8} + 17 q^{9}+O(q^{10}) $ 33 * q + 33 * q^2 - 14 * q^3 + 33 * q^4 - 22 * q^5 - 14 * q^6 - 12 * q^7 + 33 * q^8 + 17 * q^9	\( 33 q + 33 q^{2} - 14 q^{3} + 33 q^{4} - 22 q^{5} - 14 q^{6} - 12 q^{7} + 33 q^{8} + 17 q^{9} - 22 q^{10} - 19 q^{11} - 14 q^{12} - 29 q^{13} - 12 q^{14} - 5 q^{15} + 33 q^{16} - 47 q^{17} + 17 q^{18} - 35 q^{19} - 22 q^{20} - 31 q^{21} - 19 q^{22} - 2 q^{23} - 14 q^{24} + 13 q^{25} - 29 q^{26} - 47 q^{27} - 12 q^{28} - 29 q^{29} - 5 q^{30} - 53 q^{31} + 33 q^{32} - 23 q^{33} - 47 q^{34} - 14 q^{35} + 17 q^{36} - 42 q^{37} - 35 q^{38} - 22 q^{40} - 42 q^{41} - 31 q^{42} - 26 q^{43} - 19 q^{44} - 55 q^{45} - 2 q^{46} - 14 q^{48} - 21 q^{49} + 13 q^{50} - 13 q^{51} - 29 q^{52} - 40 q^{53} - 47 q^{54} - 34 q^{55} - 12 q^{56} - 30 q^{57} - 29 q^{58} - 45 q^{59} - 5 q^{60} - 93 q^{61} - 53 q^{62} + 4 q^{63} + 33 q^{64} - 26 q^{65} - 23 q^{66} - 28 q^{67} - 47 q^{68} - 60 q^{69} - 14 q^{70} + 4 q^{71} + 17 q^{72} - 52 q^{73} - 42 q^{74} - 41 q^{75} - 35 q^{76} - 38 q^{77} - 38 q^{79} - 22 q^{80} + 25 q^{81} - 42 q^{82} - 42 q^{83} - 31 q^{84} - 21 q^{85} - 26 q^{86} + 12 q^{87} - 19 q^{88} - 58 q^{89} - 55 q^{90} - 79 q^{91} - 2 q^{92} + 25 q^{93} + 16 q^{95} - 14 q^{96} - 64 q^{97} - 21 q^{98} - 38 q^{99}+O(q^{100}) \) 33 * q + 33 * q^2 - 14 * q^3 + 33 * q^4 - 22 * q^5 - 14 * q^6 - 12 * q^7 + 33 * q^8 + 17 * q^9 - 22 * q^10 - 19 * q^11 - 14 * q^12 - 29 * q^13 - 12 * q^14 - 5 * q^15 + 33 * q^16 - 47 * q^17 + 17 * q^18 - 35 * q^19 - 22 * q^20 - 31 * q^21 - 19 * q^22 - 2 * q^23 - 14 * q^24 + 13 * q^25 - 29 * q^26 - 47 * q^27 - 12 * q^28 - 29 * q^29 - 5 * q^30 - 53 * q^31 + 33 * q^32 - 23 * q^33 - 47 * q^34 - 14 * q^35 + 17 * q^36 - 42 * q^37 - 35 * q^38 - 22 * q^40 - 42 * q^41 - 31 * q^42 - 26 * q^43 - 19 * q^44 - 55 * q^45 - 2 * q^46 - 14 * q^48 - 21 * q^49 + 13 * q^50 - 13 * q^51 - 29 * q^52 - 40 * q^53 - 47 * q^54 - 34 * q^55 - 12 * q^56 - 30 * q^57 - 29 * q^58 - 45 * q^59 - 5 * q^60 - 93 * q^61 - 53 * q^62 + 4 * q^63 + 33 * q^64 - 26 * q^65 - 23 * q^66 - 28 * q^67 - 47 * q^68 - 60 * q^69 - 14 * q^70 + 4 * q^71 + 17 * q^72 - 52 * q^73 - 42 * q^74 - 41 * q^75 - 35 * q^76 - 38 * q^77 - 38 * q^79 - 22 * q^80 + 25 * q^81 - 42 * q^82 - 42 * q^83 - 31 * q^84 - 21 * q^85 - 26 * q^86 + 12 * q^87 - 19 * q^88 - 58 * q^89 - 55 * q^90 - 79 * q^91 - 2 * q^92 + 25 * q^93 + 16 * q^95 - 14 * q^96 - 64 * q^97 - 21 * q^98 - 38 * 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
$3$	−2.63161	−1.51936	−0.759681	−	0.650296i	$-0.774645\pi$
$3$	−2.63161	−1.51936	−0.759681	+	0.650296i	$0.774645\pi$
$4$	1.00000	0.500000
$5$	1.62454	0.726517	0.363258	−	0.931688i	$-0.381664\pi$
$5$	1.62454	0.726517	0.363258	+	0.931688i	$0.381664\pi$
$6$	−2.63161	−1.07435
$7$	2.40683	0.909698	0.454849	−	0.890569i	$-0.349693\pi$
$7$	2.40683	0.909698	0.454849	+	0.890569i	$0.349693\pi$
$8$	1.00000	0.353553
$9$	3.92538	1.30846
$10$	1.62454	0.513725
$11$	−3.88889	−1.17254	−0.586272	−	0.810114i	$-0.699405\pi$
$11$	−3.88889	−1.17254	−0.586272	+	0.810114i	$0.699405\pi$
$12$	−2.63161	−0.759681
$13$	−0.435673	−0.120834	−0.0604169	−	0.998173i	$-0.519243\pi$
$13$	−0.435673	−0.120834	−0.0604169	+	0.998173i	$0.519243\pi$
$14$	2.40683	0.643254
$15$	−4.27516	−1.10384
$16$	1.00000	0.250000
$17$	−1.47261	−0.357160	−0.178580	−	0.983925i	$-0.557150\pi$
$17$	−1.47261	−0.357160	−0.178580	+	0.983925i	$0.557150\pi$
$18$	3.92538	0.925220
$19$	−4.69089	−1.07616	−0.538082	−	0.842893i	$-0.680851\pi$
$19$	−4.69089	−1.07616	−0.538082	+	0.842893i	$0.680851\pi$
$20$	1.62454	0.363258
$21$	−6.33385	−1.38216
$22$	−3.88889	−0.829114
$23$	6.93055	1.44512	0.722560	−	0.691309i	$-0.242965\pi$
$23$	6.93055	1.44512	0.722560	+	0.691309i	$0.242965\pi$
$24$	−2.63161	−0.537175
$25$	−2.36087	−0.472174
$26$	−0.435673	−0.0854424
$27$	−2.43524	−0.468661
$28$	2.40683	0.454849
$29$	−0.515056	−0.0956435	−0.0478218	−	0.998856i	$-0.515228\pi$
$29$	−0.515056	−0.0956435	−0.0478218	+	0.998856i	$0.515228\pi$
$30$	−4.27516	−0.780534
$31$	−0.199735	−0.0358735	−0.0179367	−	0.999839i	$-0.505710\pi$
$31$	−0.199735	−0.0358735	−0.0179367	+	0.999839i	$0.505710\pi$
$32$	1.00000	0.176777
$33$	10.2340	1.78152
$34$	−1.47261	−0.252550
$35$	3.91000	0.660911
$36$	3.92538	0.654230
$37$	−11.2575	−1.85071	−0.925357	−	0.379097i	$-0.876235\pi$
$37$	−11.2575	−1.85071	−0.925357	+	0.379097i	$0.876235\pi$
$38$	−4.69089	−0.760962
$39$	1.14652	0.183590
$40$	1.62454	0.256862
$41$	−11.0337	−1.72318	−0.861590	−	0.507605i	$-0.830531\pi$
$41$	−11.0337	−1.72318	−0.861590	+	0.507605i	$0.830531\pi$
$42$	−6.33385	−0.977335
$43$	−7.50752	−1.14489	−0.572443	−	0.819944i	$-0.694004\pi$
$43$	−7.50752	−1.14489	−0.572443	+	0.819944i	$0.694004\pi$
$44$	−3.88889	−0.586272
$45$	6.37694	0.950617
$46$	6.93055	1.02185
$47$	−7.60261	−1.10895	−0.554477	−	0.832199i	$-0.687082\pi$
$47$	−7.60261	−1.10895	−0.554477	+	0.832199i	$0.687082\pi$
$48$	−2.63161	−0.379840
$49$	−1.20715	−0.172450
$50$	−2.36087	−0.333877
$51$	3.87533	0.542655
$52$	−0.435673	−0.0604169
$53$	−3.42960	−0.471091	−0.235546	−	0.971863i	$-0.575688\pi$
$53$	−3.42960	−0.471091	−0.235546	+	0.971863i	$0.575688\pi$
$54$	−2.43524	−0.331394
$55$	−6.31766	−0.851873
$56$	2.40683	0.321627
$57$	12.3446	1.63508
$58$	−0.515056	−0.0676302
$59$	7.97306	1.03800	0.519002	−	0.854773i	$-0.326304\pi$
$59$	7.97306	1.03800	0.519002	+	0.854773i	$0.326304\pi$
$60$	−4.27516	−0.551921
$61$	10.4511	1.33813	0.669065	−	0.743204i	$-0.266695\pi$
$61$	10.4511	1.33813	0.669065	+	0.743204i	$0.266695\pi$
$62$	−0.199735	−0.0253664
$63$	9.44774	1.19030
$64$	1.00000	0.125000
$65$	−0.707768	−0.0877878
$66$	10.2340	1.25972
$67$	1.39854	0.170859	0.0854296	−	0.996344i	$-0.472774\pi$
$67$	1.39854	0.170859	0.0854296	+	0.996344i	$0.472774\pi$
$68$	−1.47261	−0.178580
$69$	−18.2385	−2.19566
$70$	3.91000	0.467334
$71$	9.93637	1.17923	0.589615	−	0.807685i	$-0.299280\pi$
$71$	9.93637	1.17923	0.589615	+	0.807685i	$0.299280\pi$
$72$	3.92538	0.462610
$73$	−0.642060	−0.0751475	−0.0375737	−	0.999294i	$-0.511963\pi$
$73$	−0.642060	−0.0751475	−0.0375737	+	0.999294i	$0.511963\pi$
$74$	−11.2575	−1.30865
$75$	6.21289	0.717402
$76$	−4.69089	−0.538082
$77$	−9.35991	−1.06666
$78$	1.14652	0.129818
$79$	14.4809	1.62923	0.814614	−	0.580003i	$-0.196949\pi$
$79$	14.4809	1.62923	0.814614	+	0.580003i	$0.196949\pi$
$80$	1.62454	0.181629
$81$	−5.36754	−0.596394
$82$	−11.0337	−1.21847
$83$	5.55412	0.609644	0.304822	−	0.952409i	$-0.401403\pi$
$83$	5.55412	0.609644	0.304822	+	0.952409i	$0.401403\pi$
$84$	−6.33385	−0.691080
$85$	−2.39231	−0.259482
$86$	−7.50752	−0.809557
$87$	1.35543	0.145317
$88$	−3.88889	−0.414557
$89$	−14.8885	−1.57817	−0.789086	−	0.614282i	$-0.789446\pi$
$89$	−14.8885	−1.57817	−0.789086	+	0.614282i	$0.789446\pi$
$90$	6.37694	0.672188
$91$	−1.04859	−0.109922
$92$	6.93055	0.722560
$93$	0.525625	0.0545048
$94$	−7.60261	−0.784149
$95$	−7.62054	−0.781850
$96$	−2.63161	−0.268588
$97$	7.29323	0.740516	0.370258	−	0.928929i	$-0.379269\pi$
$97$	7.29323	0.740516	0.370258	+	0.928929i	$0.379269\pi$
$98$	−1.20715	−0.121940
$99$	−15.2654	−1.53423
$100$	−2.36087	−0.236087
$101$	−14.4304	−1.43588	−0.717941	−	0.696104i	$-0.754915\pi$
$101$	−14.4304	−1.43588	−0.717941	+	0.696104i	$0.754915\pi$
$102$	3.87533	0.383715
$103$	11.1566	1.09930	0.549648	−	0.835397i	$-0.314762\pi$
$103$	11.1566	1.09930	0.549648	+	0.835397i	$0.314762\pi$
$104$	−0.435673	−0.0427212
$105$	−10.2896	−1.00416
$106$	−3.42960	−0.333112
$107$	−8.13602	−0.786539	−0.393269	−	0.919423i	$-0.628656\pi$
$107$	−8.13602	−0.786539	−0.393269	+	0.919423i	$0.628656\pi$
$108$	−2.43524	−0.234331
$109$	7.14934	0.684783	0.342391	−	0.939557i	$-0.388763\pi$
$109$	7.14934	0.684783	0.342391	+	0.939557i	$0.388763\pi$
$110$	−6.31766	−0.602365
$111$	29.6252	2.81190
$112$	2.40683	0.227424
$113$	−11.4205	−1.07435	−0.537174	−	0.843471i	$-0.680508\pi$
$113$	−11.4205	−1.07435	−0.537174	+	0.843471i	$0.680508\pi$
$114$	12.3446	1.15618
$115$	11.2590	1.04990
$116$	−0.515056	−0.0478218
$117$	−1.71018	−0.158106
$118$	7.97306	0.733980
$119$	−3.54432	−0.324907
$120$	−4.27516	−0.390267
$121$	4.12346	0.374860
$122$	10.4511	0.946201
$123$	29.0365	2.61813
$124$	−0.199735	−0.0179367
$125$	−11.9580	−1.06956
$126$	9.44774	0.841671
$127$	−12.2949	−1.09100	−0.545499	−	0.838112i	$-0.683660\pi$
$127$	−12.2949	−1.09100	−0.545499	+	0.838112i	$0.683660\pi$
$128$	1.00000	0.0883883
$129$	19.7569	1.73950
$130$	−0.707768	−0.0620753
$131$	7.48838	0.654263	0.327132	−	0.944979i	$-0.393918\pi$
$131$	7.48838	0.654263	0.327132	+	0.944979i	$0.393918\pi$
$132$	10.2340	0.890759
$133$	−11.2902	−0.978983
$134$	1.39854	0.120816
$135$	−3.95614	−0.340490
$136$	−1.47261	−0.126275
$137$	−6.72146	−0.574253	−0.287126	−	0.957893i	$-0.592700\pi$
$137$	−6.72146	−0.574253	−0.287126	+	0.957893i	$0.592700\pi$
$138$	−18.2385	−1.55257
$139$	−14.9701	−1.26975	−0.634875	−	0.772615i	$-0.718948\pi$
$139$	−14.9701	−1.26975	−0.634875	+	0.772615i	$0.718948\pi$
$140$	3.91000	0.330455
$141$	20.0071	1.68490
$142$	9.93637	0.833841
$143$	1.69428	0.141683
$144$	3.92538	0.327115
$145$	−0.836730	−0.0694866
$146$	−0.642060	−0.0531373
$147$	3.17674	0.262013
$148$	−11.2575	−0.925357
$149$	20.7917	1.70332	0.851660	−	0.524094i	$-0.175596\pi$
$149$	20.7917	1.70332	0.851660	+	0.524094i	$0.175596\pi$
$150$	6.21289	0.507280
$151$	−7.73591	−0.629540	−0.314770	−	0.949168i	$-0.601927\pi$
$151$	−7.73591	−0.629540	−0.314770	+	0.949168i	$0.601927\pi$
$152$	−4.69089	−0.380481
$153$	−5.78054	−0.467329
$154$	−9.35991	−0.754243
$155$	−0.324478	−0.0260627
$156$	1.14652	0.0917951
$157$	−12.9993	−1.03745	−0.518727	−	0.854940i	$-0.673594\pi$
$157$	−12.9993	−1.03745	−0.518727	+	0.854940i	$0.673594\pi$
$158$	14.4809	1.15204
$159$	9.02536	0.715758
$160$	1.62454	0.128431
$161$	16.6807	1.31462
$162$	−5.36754	−0.421714
$163$	−2.01069	−0.157490	−0.0787448	−	0.996895i	$-0.525091\pi$
$163$	−2.01069	−0.157490	−0.0787448	+	0.996895i	$0.525091\pi$
$164$	−11.0337	−0.861590
$165$	16.6256	1.29430
$166$	5.55412	0.431084
$167$	2.55685	0.197855	0.0989274	−	0.995095i	$-0.468459\pi$
$167$	2.55685	0.197855	0.0989274	+	0.995095i	$0.468459\pi$
$168$	−6.33385	−0.488667
$169$	−12.8102	−0.985399
$170$	−2.39231	−0.183482
$171$	−18.4135	−1.40812
$172$	−7.50752	−0.572443
$173$	−20.3577	−1.54777	−0.773883	−	0.633328i	$-0.781688\pi$
$173$	−20.3577	−1.54777	−0.773883	+	0.633328i	$0.781688\pi$
$174$	1.35543	0.102755
$175$	−5.68222	−0.429535
$176$	−3.88889	−0.293136
$177$	−20.9820	−1.57710
$178$	−14.8885	−1.11594
$179$	−9.96328	−0.744691	−0.372345	−	0.928094i	$-0.621446\pi$
$179$	−9.96328	−0.744691	−0.372345	+	0.928094i	$0.621446\pi$
$180$	6.37694	0.475309
$181$	13.7393	1.02124	0.510618	−	0.859808i	$-0.329417\pi$
$181$	13.7393	1.02124	0.510618	+	0.859808i	$0.329417\pi$
$182$	−1.04859	−0.0777268
$183$	−27.5033	−2.03310
$184$	6.93055	0.510927
$185$	−18.2882	−1.34457
$186$	0.525625	0.0385407
$187$	5.72681	0.418785
$188$	−7.60261	−0.554477
$189$	−5.86121	−0.426340
$190$	−7.62054	−0.552852
$191$	19.1234	1.38372	0.691862	−	0.722030i	$-0.256791\pi$
$191$	19.1234	1.38372	0.691862	+	0.722030i	$0.256791\pi$
$192$	−2.63161	−0.189920
$193$	9.35669	0.673509	0.336755	−	0.941592i	$-0.390671\pi$
$193$	9.35669	0.673509	0.336755	+	0.941592i	$0.390671\pi$
$194$	7.29323	0.523624
$195$	1.86257	0.133381
$196$	−1.20715	−0.0862248
$197$	−1.91194	−0.136220	−0.0681100	−	0.997678i	$-0.521697\pi$
$197$	−1.91194	−0.136220	−0.0681100	+	0.997678i	$0.521697\pi$
$198$	−15.2654	−1.08486
$199$	−4.08285	−0.289425	−0.144713	−	0.989474i	$-0.546226\pi$
$199$	−4.08285	−0.289425	−0.144713	+	0.989474i	$0.546226\pi$
$200$	−2.36087	−0.166939
$201$	−3.68042	−0.259597
$202$	−14.4304	−1.01532
$203$	−1.23966	−0.0870067
$204$	3.87533	0.271327
$205$	−17.9247	−1.25192
$206$	11.1566	0.777319
$207$	27.2050	1.89088
$208$	−0.435673	−0.0302085
$209$	18.2423	1.26185
$210$	−10.2896	−0.710050
$211$	−17.3412	−1.19382	−0.596910	−	0.802308i	$-0.703605\pi$
$211$	−17.3412	−1.19382	−0.596910	+	0.802308i	$0.703605\pi$
$212$	−3.42960	−0.235546
$213$	−26.1487	−1.79168
$214$	−8.13602	−0.556167
$215$	−12.1963	−0.831779
$216$	−2.43524	−0.165697
$217$	−0.480729	−0.0326340
$218$	7.14934	0.484214
$219$	1.68965	0.114176
$220$	−6.31766	−0.425936
$221$	0.641574	0.0431570
$222$	29.6252	1.98832
$223$	0.403446	0.0270167	0.0135084	−	0.999909i	$-0.495700\pi$
$223$	0.403446	0.0270167	0.0135084	+	0.999909i	$0.495700\pi$
$224$	2.40683	0.160813
$225$	−9.26730	−0.617820
$226$	−11.4205	−0.759679
$227$	−24.9262	−1.65441	−0.827205	−	0.561901i	$-0.810070\pi$
$227$	−24.9262	−1.65441	−0.827205	+	0.561901i	$0.810070\pi$
$228$	12.3446	0.817540
$229$	−16.9217	−1.11822	−0.559110	−	0.829093i	$-0.688857\pi$
$229$	−16.9217	−1.11822	−0.559110	+	0.829093i	$0.688857\pi$
$230$	11.2590	0.742394
$231$	24.6317	1.62064
$232$	−0.515056	−0.0338151
$233$	7.94745	0.520655	0.260327	−	0.965520i	$-0.416169\pi$
$233$	7.94745	0.520655	0.260327	+	0.965520i	$0.416169\pi$
$234$	−1.71018	−0.111798
$235$	−12.3507	−0.805674
$236$	7.97306	0.519002
$237$	−38.1081	−2.47539
$238$	−3.54432	−0.229744
$239$	−10.3402	−0.668853	−0.334427	−	0.942422i	$-0.608543\pi$
$239$	−10.3402	−0.668853	−0.334427	+	0.942422i	$0.608543\pi$
$240$	−4.27516	−0.275960
$241$	14.0421	0.904530	0.452265	−	0.891884i	$-0.350616\pi$
$241$	14.0421	0.904530	0.452265	+	0.891884i	$0.350616\pi$
$242$	4.12346	0.265066
$243$	21.4310	1.37480
$244$	10.4511	0.669065
$245$	−1.96106	−0.125288
$246$	29.0365	1.85130
$247$	2.04369	0.130037
$248$	−0.199735	−0.0126832
$249$	−14.6163	−0.926270
$250$	−11.9580	−0.756292
$251$	−26.3034	−1.66026	−0.830128	−	0.557573i	$-0.811733\pi$
$251$	−26.3034	−1.66026	−0.830128	+	0.557573i	$0.811733\pi$
$252$	9.44774	0.595151
$253$	−26.9521	−1.69447
$254$	−12.2949	−0.771452
$255$	6.29563	0.394248
$256$	1.00000	0.0625000
$257$	25.4771	1.58922	0.794610	−	0.607120i	$-0.207675\pi$
$257$	25.4771	1.58922	0.794610	+	0.607120i	$0.207675\pi$
$258$	19.7569	1.23001
$259$	−27.0948	−1.68359
$260$	−0.707768	−0.0438939
$261$	−2.02179	−0.125146
$262$	7.48838	0.462634
$263$	23.1755	1.42906	0.714532	−	0.699603i	$-0.246640\pi$
$263$	23.1755	1.42906	0.714532	+	0.699603i	$0.246640\pi$
$264$	10.2340	0.629862
$265$	−5.57152	−0.342256
$266$	−11.2902	−0.692246
$267$	39.1806	2.39781
$268$	1.39854	0.0854296
$269$	−31.2481	−1.90523	−0.952615	−	0.304178i	$-0.901618\pi$
$269$	−31.2481	−1.90523	−0.952615	+	0.304178i	$0.901618\pi$
$270$	−3.95614	−0.240763
$271$	−20.1390	−1.22336	−0.611678	−	0.791107i	$-0.709505\pi$
$271$	−20.1390	−1.22336	−0.611678	+	0.791107i	$0.709505\pi$
$272$	−1.47261	−0.0892899
$273$	2.75949	0.167012
$274$	−6.72146	−0.406058
$275$	9.18115	0.553644
$276$	−18.2385	−1.09783
$277$	13.3105	0.799748	0.399874	−	0.916570i	$-0.369054\pi$
$277$	13.3105	0.799748	0.399874	+	0.916570i	$0.369054\pi$
$278$	−14.9701	−0.897849
$279$	−0.784036	−0.0469390
$280$	3.91000	0.233667
$281$	−1.58836	−0.0947538	−0.0473769	−	0.998877i	$-0.515086\pi$
$281$	−1.58836	−0.0947538	−0.0473769	+	0.998877i	$0.515086\pi$
$282$	20.0071	1.19141
$283$	−22.5496	−1.34044	−0.670218	−	0.742164i	$-0.733799\pi$
$283$	−22.5496	−1.34044	−0.670218	+	0.742164i	$0.733799\pi$
$284$	9.93637	0.589615
$285$	20.0543	1.18791
$286$	1.69428	0.100185
$287$	−26.5564	−1.56757
$288$	3.92538	0.231305
$289$	−14.8314	−0.872437
$290$	−0.836730	−0.0491345
$291$	−19.1930	−1.12511
$292$	−0.642060	−0.0375737
$293$	−30.7268	−1.79508	−0.897540	−	0.440934i	$-0.854647\pi$
$293$	−30.7268	−1.79508	−0.897540	+	0.440934i	$0.854647\pi$
$294$	3.17674	0.185271
$295$	12.9526	0.754128
$296$	−11.2575	−0.654326
$297$	9.47036	0.549526
$298$	20.7917	1.20443
$299$	−3.01945	−0.174619
$300$	6.21289	0.358701
$301$	−18.0694	−1.04150
$302$	−7.73591	−0.445152
$303$	37.9753	2.18162
$304$	−4.69089	−0.269041
$305$	16.9783	0.972174
$306$	−5.78054	−0.330451
$307$	21.9144	1.25072	0.625361	−	0.780335i	$-0.284952\pi$
$307$	21.9144	1.25072	0.625361	+	0.780335i	$0.284952\pi$
$308$	−9.35991	−0.533331
$309$	−29.3599	−1.67023
$310$	−0.324478	−0.0184291
$311$	23.7656	1.34763	0.673813	−	0.738902i	$-0.264655\pi$
$311$	23.7656	1.34763	0.673813	+	0.738902i	$0.264655\pi$
$312$	1.14652	0.0649090
$313$	−6.65967	−0.376427	−0.188213	−	0.982128i	$-0.560270\pi$
$313$	−6.65967	−0.376427	−0.188213	+	0.982128i	$0.560270\pi$
$314$	−12.9993	−0.733591
$315$	15.3482	0.864775
$316$	14.4809	0.814614
$317$	6.98642	0.392397	0.196198	−	0.980564i	$-0.437140\pi$
$317$	6.98642	0.392397	0.196198	+	0.980564i	$0.437140\pi$
$318$	9.02536	0.506117
$319$	2.00300	0.112146
$320$	1.62454	0.0908146
$321$	21.4108	1.19504
$322$	16.6807	0.929578
$323$	6.90783	0.384362
$324$	−5.36754	−0.298197
$325$	1.02857	0.0570545
$326$	−2.01069	−0.111362
$327$	−18.8143	−1.04043
$328$	−11.0337	−0.609236
$329$	−18.2982	−1.00881
$330$	16.6256	0.915210
$331$	−27.0434	−1.48644	−0.743221	−	0.669046i	$-0.766703\pi$
$331$	−27.0434	−1.48644	−0.743221	+	0.669046i	$0.766703\pi$
$332$	5.55412	0.304822
$333$	−44.1898	−2.42158
$334$	2.55685	0.139905
$335$	2.27199	0.124132
$336$	−6.33385	−0.345540
$337$	−18.7181	−1.01964	−0.509821	−	0.860281i	$-0.670288\pi$
$337$	−18.7181	−1.01964	−0.509821	+	0.860281i	$0.670288\pi$
$338$	−12.8102	−0.696782
$339$	30.0542	1.63232
$340$	−2.39231	−0.129741
$341$	0.776748	0.0420632
$342$	−18.4135	−0.995688
$343$	−19.7532	−1.06658
$344$	−7.50752	−0.404779
$345$	−29.6292	−1.59518
$346$	−20.3577	−1.09444
$347$	23.1668	1.24366	0.621830	−	0.783152i	$-0.286390\pi$
$347$	23.1668	1.24366	0.621830	+	0.783152i	$0.286390\pi$
$348$	1.35543	0.0726586
$349$	12.7816	0.684183	0.342091	−	0.939667i	$-0.388865\pi$
$349$	12.7816	0.684183	0.342091	+	0.939667i	$0.388865\pi$
$350$	−5.68222	−0.303727
$351$	1.06097	0.0566301
$352$	−3.88889	−0.207279
$353$	−33.5835	−1.78747	−0.893735	−	0.448596i	$-0.851924\pi$
$353$	−33.5835	−1.78747	−0.893735	+	0.448596i	$0.851924\pi$
$354$	−20.9820	−1.11518
$355$	16.1420	0.856730
$356$	−14.8885	−0.789086
$357$	9.32727	0.493652
$358$	−9.96328	−0.526576
$359$	31.6318	1.66946	0.834730	−	0.550659i	$-0.185624\pi$
$359$	31.6318	1.66946	0.834730	+	0.550659i	$0.185624\pi$
$360$	6.37694	0.336094
$361$	3.00442	0.158127
$362$	13.7393	0.722123
$363$	−10.8514	−0.569548
$364$	−1.04859	−0.0549611
$365$	−1.04305	−0.0545959
$366$	−27.5033	−1.43762
$367$	8.62772	0.450364	0.225182	−	0.974317i	$-0.427702\pi$
$367$	8.62772	0.450364	0.225182	+	0.974317i	$0.427702\pi$
$368$	6.93055	0.361280
$369$	−43.3116	−2.25471
$370$	−18.2882	−0.950758
$371$	−8.25447	−0.428551
$372$	0.525625	0.0272524
$373$	5.25163	0.271919	0.135959	−	0.990714i	$-0.456588\pi$
$373$	5.25163	0.271919	0.135959	+	0.990714i	$0.456588\pi$
$374$	5.72681	0.296126
$375$	31.4689	1.62505
$376$	−7.60261	−0.392074
$377$	0.224396	0.0115570
$378$	−5.86121	−0.301468
$379$	−13.6498	−0.701144	−0.350572	−	0.936536i	$-0.614013\pi$
$379$	−13.6498	−0.701144	−0.350572	+	0.936536i	$0.614013\pi$
$380$	−7.62054	−0.390925
$381$	32.3555	1.65762
$382$	19.1234	0.978440
$383$	10.6673	0.545073	0.272536	−	0.962145i	$-0.412137\pi$
$383$	10.6673	0.545073	0.272536	+	0.962145i	$0.412137\pi$
$384$	−2.63161	−0.134294
$385$	−15.2056	−0.774947
$386$	9.35669	0.476243
$387$	−29.4699	−1.49804
$388$	7.29323	0.370258
$389$	26.1453	1.32562	0.662810	−	0.748788i	$-0.269364\pi$
$389$	26.1453	1.32562	0.662810	+	0.748788i	$0.269364\pi$
$390$	1.86257	0.0943149
$391$	−10.2060	−0.516138
$392$	−1.20715	−0.0609702
$393$	−19.7065	−0.994062
$394$	−1.91194	−0.0963220
$395$	23.5248	1.18366
$396$	−15.2654	−0.767113
$397$	−11.0050	−0.552325	−0.276163	−	0.961111i	$-0.589063\pi$
$397$	−11.0050	−0.552325	−0.276163	+	0.961111i	$0.589063\pi$
$398$	−4.08285	−0.204655
$399$	29.7114	1.48743
$400$	−2.36087	−0.118043
$401$	38.9649	1.94582	0.972908	−	0.231192i	$-0.0742626\pi$
$401$	38.9649	1.94582	0.972908	+	0.231192i	$0.0742626\pi$
$402$	−3.68042	−0.183563
$403$	0.0870191	0.00433473
$404$	−14.4304	−0.717941
$405$	−8.71979	−0.433290
$406$	−1.23966	−0.0615230
$407$	43.7790	2.17004
$408$	3.87533	0.191857
$409$	5.54873	0.274367	0.137184	−	0.990546i	$-0.456195\pi$
$409$	5.54873	0.274367	0.137184	+	0.990546i	$0.456195\pi$
$410$	−17.9247	−0.885240
$411$	17.6883	0.872497
$412$	11.1566	0.549648
$413$	19.1898	0.944271
$414$	27.2050	1.33705
$415$	9.02290	0.442917
$416$	−0.435673	−0.0213606
$417$	39.3956	1.92921
$418$	18.2423	0.892262
$419$	−1.42707	−0.0697168	−0.0348584	−	0.999392i	$-0.511098\pi$
$419$	−1.42707	−0.0697168	−0.0348584	+	0.999392i	$0.511098\pi$
$420$	−10.2896	−0.502081
$421$	30.5365	1.48826	0.744129	−	0.668036i	$-0.232865\pi$
$421$	30.5365	1.48826	0.744129	+	0.668036i	$0.232865\pi$
$422$	−17.3412	−0.844158
$423$	−29.8431	−1.45102
$424$	−3.42960	−0.166556
$425$	3.47663	0.168641
$426$	−26.1487	−1.26691
$427$	25.1541	1.21729
$428$	−8.13602	−0.393269
$429$	−4.45869	−0.215268
$430$	−12.1963	−0.588157
$431$	4.89885	0.235969	0.117985	−	0.993015i	$-0.462357\pi$
$431$	4.89885	0.235969	0.117985	+	0.993015i	$0.462357\pi$
$432$	−2.43524	−0.117165
$433$	40.9064	1.96584	0.982919	−	0.184041i	$-0.0589179\pi$
$433$	40.9064	1.96584	0.982919	+	0.184041i	$0.0589179\pi$
$434$	−0.480729	−0.0230757
$435$	2.20195	0.105575
$436$	7.14934	0.342391
$437$	−32.5104	−1.55518
$438$	1.68965	0.0807347
$439$	−13.9887	−0.667645	−0.333822	−	0.942636i	$-0.608339\pi$
$439$	−13.9887	−0.667645	−0.333822	+	0.942636i	$0.608339\pi$
$440$	−6.31766	−0.301183
$441$	−4.73851	−0.225643
$442$	0.641574	0.0305166
$443$	−0.229220	−0.0108906	−0.00544529	−	0.999985i	$-0.501733\pi$
$443$	−0.229220	−0.0108906	−0.00544529	+	0.999985i	$0.501733\pi$
$444$	29.6252	1.40595
$445$	−24.1869	−1.14657
$446$	0.403446	0.0191037
$447$	−54.7156	−2.58796
$448$	2.40683	0.113712
$449$	35.5225	1.67641	0.838204	−	0.545357i	$-0.183606\pi$
$449$	35.5225	1.67641	0.838204	+	0.545357i	$0.183606\pi$
$450$	−9.26730	−0.436865
$451$	42.9090	2.02050
$452$	−11.4205	−0.537174
$453$	20.3579	0.956499
$454$	−24.9262	−1.16984
$455$	−1.70348	−0.0798604
$456$	12.3446	0.578088
$457$	20.1742	0.943708	0.471854	−	0.881677i	$-0.343585\pi$
$457$	20.1742	0.943708	0.471854	+	0.881677i	$0.343585\pi$
$458$	−16.9217	−0.790701
$459$	3.58614	0.167387
$460$	11.2590	0.524952
$461$	−19.2420	−0.896189	−0.448095	−	0.893986i	$-0.647897\pi$
$461$	−19.2420	−0.896189	−0.448095	+	0.893986i	$0.647897\pi$
$462$	24.6317	1.14597
$463$	−31.8819	−1.48168	−0.740839	−	0.671683i	$-0.765572\pi$
$463$	−31.8819	−1.48168	−0.740839	+	0.671683i	$0.765572\pi$
$464$	−0.515056	−0.0239109
$465$	0.853899	0.0395986
$466$	7.94745	0.368159
$467$	32.0908	1.48498	0.742492	−	0.669855i	$-0.233644\pi$
$467$	32.0908	1.48498	0.742492	+	0.669855i	$0.233644\pi$
$468$	−1.71018	−0.0790531
$469$	3.36606	0.155430
$470$	−12.3507	−0.569697
$471$	34.2090	1.57627
$472$	7.97306	0.366990
$473$	29.1959	1.34243
$474$	−38.1081	−1.75036
$475$	11.0746	0.508136
$476$	−3.54432	−0.162454
$477$	−13.4625	−0.616404
$478$	−10.3402	−0.472951
$479$	33.2746	1.52035	0.760177	−	0.649716i	$-0.225112\pi$
$479$	33.2746	1.52035	0.760177	+	0.649716i	$0.225112\pi$
$480$	−4.27516	−0.195133
$481$	4.90456	0.223629
$482$	14.0421	0.639599
$483$	−43.8971	−1.99739
$484$	4.12346	0.187430
$485$	11.8482	0.537997
$486$	21.4310	0.972129
$487$	2.01597	0.0913522	0.0456761	−	0.998956i	$-0.485456\pi$
$487$	2.01597	0.0913522	0.0456761	+	0.998956i	$0.485456\pi$
$488$	10.4511	0.473100
$489$	5.29136	0.239284
$490$	−1.96106	−0.0885917
$491$	20.7960	0.938509	0.469255	−	0.883063i	$-0.344523\pi$
$491$	20.7960	0.938509	0.469255	+	0.883063i	$0.344523\pi$
$492$	29.0365	1.30907
$493$	0.758475	0.0341600
$494$	2.04369	0.0919500
$495$	−24.7992	−1.11464
$496$	−0.199735	−0.00896837
$497$	23.9152	1.07274
$498$	−14.6163	−0.654972
$499$	−28.3471	−1.26899	−0.634496	−	0.772926i	$-0.718792\pi$
$499$	−28.3471	−1.26899	−0.634496	+	0.772926i	$0.718792\pi$
$500$	−11.9580	−0.534779
$501$	−6.72863	−0.300613
$502$	−26.3034	−1.17398
$503$	−4.78924	−0.213542	−0.106771	−	0.994284i	$-0.534051\pi$
$503$	−4.78924	−0.213542	−0.106771	+	0.994284i	$0.534051\pi$
$504$	9.44774	0.420836
$505$	−23.4428	−1.04319
$506$	−26.9521	−1.19817
$507$	33.7114	1.49718
$508$	−12.2949	−0.545499
$509$	−5.68118	−0.251814	−0.125907	−	0.992042i	$-0.540184\pi$
$509$	−5.68118	−0.251814	−0.125907	+	0.992042i	$0.540184\pi$
$510$	6.29563	0.278775
$511$	−1.54533	−0.0683615
$512$	1.00000	0.0441942
$513$	11.4234	0.504356
$514$	25.4771	1.12375
$515$	18.1244	0.798656
$516$	19.7569	0.869748
$517$	29.5657	1.30030
$518$	−27.0948	−1.19048
$519$	53.5735	2.35162
$520$	−0.707768	−0.0310377
$521$	9.89674	0.433584	0.216792	−	0.976218i	$-0.430441\pi$
$521$	9.89674	0.433584	0.216792	+	0.976218i	$0.430441\pi$
$522$	−2.02179	−0.0884914
$523$	−18.4680	−0.807547	−0.403774	−	0.914859i	$-0.632302\pi$
$523$	−18.4680	−0.807547	−0.403774	+	0.914859i	$0.632302\pi$
$524$	7.48838	0.327132
$525$	14.9534	0.652619
$526$	23.1755	1.01050
$527$	0.294131	0.0128126
$528$	10.2340	0.445380
$529$	25.0325	1.08837
$530$	−5.57152	−0.242011
$531$	31.2973	1.35819
$532$	−11.2902	−0.489492
$533$	4.80709	0.208218
$534$	39.1806	1.69551
$535$	−13.2173	−0.571433
$536$	1.39854	0.0604078
$537$	26.2195	1.13145
$538$	−31.2481	−1.34720
$539$	4.69446	0.202205
$540$	−3.95614	−0.170245
$541$	−24.3961	−1.04887	−0.524436	−	0.851450i	$-0.675724\pi$
$541$	−24.3961	−1.04887	−0.524436	+	0.851450i	$0.675724\pi$
$542$	−20.1390	−0.865043
$543$	−36.1566	−1.55163
$544$	−1.47261	−0.0631375
$545$	11.6144	0.497506
$546$	2.75949	0.118095
$547$	15.4187	0.659255	0.329627	−	0.944111i	$-0.393077\pi$
$547$	15.4187	0.659255	0.329627	+	0.944111i	$0.393077\pi$
$548$	−6.72146	−0.287126
$549$	41.0246	1.75089
$550$	9.18115	0.391486
$551$	2.41607	0.102928
$552$	−18.2385	−0.776283
$553$	34.8531	1.48211
$554$	13.3105	0.565507
$555$	48.1274	2.04290
$556$	−14.9701	−0.634875
$557$	−1.73587	−0.0735513	−0.0367756	−	0.999324i	$-0.511709\pi$
$557$	−1.73587	−0.0735513	−0.0367756	+	0.999324i	$0.511709\pi$
$558$	−0.784036	−0.0331909
$559$	3.27082	0.138341
$560$	3.91000	0.165228
$561$	−15.0707	−0.636287
$562$	−1.58836	−0.0670011
$563$	8.20158	0.345656	0.172828	−	0.984952i	$-0.444710\pi$
$563$	8.20158	0.345656	0.172828	+	0.984952i	$0.444710\pi$
$564$	20.0071	0.842451
$565$	−18.5530	−0.780532
$566$	−22.5496	−0.947832
$567$	−12.9188	−0.542538
$568$	9.93637	0.416921
$569$	−17.0790	−0.715989	−0.357994	−	0.933724i	$-0.616539\pi$
$569$	−17.0790	−0.715989	−0.357994	+	0.933724i	$0.616539\pi$
$570$	20.0543	0.839982
$571$	30.8691	1.29183	0.645916	−	0.763408i	$-0.276476\pi$
$571$	30.8691	1.29183	0.645916	+	0.763408i	$0.276476\pi$
$572$	1.69428	0.0708415
$573$	−50.3255	−2.10238
$574$	−26.5564	−1.10844
$575$	−16.3621	−0.682347
$576$	3.92538	0.163557
$577$	−14.4092	−0.599864	−0.299932	−	0.953961i	$-0.596964\pi$
$577$	−14.4092	−0.599864	−0.299932	+	0.953961i	$0.596964\pi$
$578$	−14.8314	−0.616906
$579$	−24.6232	−1.02330
$580$	−0.836730	−0.0347433
$581$	13.3679	0.554592
$582$	−19.1930	−0.795574
$583$	13.3373	0.552375
$584$	−0.642060	−0.0265686
$585$	−2.77826	−0.114867
$586$	−30.7268	−1.26931
$587$	−28.1979	−1.16385	−0.581926	−	0.813241i	$-0.697701\pi$
$587$	−28.1979	−1.16385	−0.581926	+	0.813241i	$0.697701\pi$
$588$	3.17674	0.131007
$589$	0.936935	0.0386057
$590$	12.9526	0.533249
$591$	5.03148	0.206967
$592$	−11.2575	−0.462679
$593$	27.2438	1.11877	0.559384	−	0.828909i	$-0.311038\pi$
$593$	27.2438	1.11877	0.559384	+	0.828909i	$0.311038\pi$
$594$	9.47036	0.388574
$595$	−5.75789	−0.236051
$596$	20.7917	0.851660
$597$	10.7445	0.439742
$598$	−3.01945	−0.123475
$599$	−7.91876	−0.323552	−0.161776	−	0.986828i	$-0.551722\pi$
$599$	−7.91876	−0.323552	−0.161776	+	0.986828i	$0.551722\pi$
$600$	6.21289	0.253640
$601$	−48.2467	−1.96802	−0.984011	−	0.178107i	$-0.943003\pi$
$601$	−48.2467	−1.96802	−0.984011	+	0.178107i	$0.943003\pi$
$602$	−18.0694	−0.736452
$603$	5.48981	0.223562
$604$	−7.73591	−0.314770
$605$	6.69873	0.272342
$606$	37.9753	1.54264
$607$	8.96820	0.364008	0.182004	−	0.983298i	$-0.441742\pi$
$607$	8.96820	0.364008	0.182004	+	0.983298i	$0.441742\pi$
$608$	−4.69089	−0.190241
$609$	3.26229	0.132195
$610$	16.9783	0.687431
$611$	3.31225	0.133999
$612$	−5.78054	−0.233664
$613$	−9.55351	−0.385863	−0.192931	−	0.981212i	$-0.561799\pi$
$613$	−9.55351	−0.385863	−0.192931	+	0.981212i	$0.561799\pi$
$614$	21.9144	0.884395
$615$	47.1710	1.90212
$616$	−9.35991	−0.377122
$617$	20.0536	0.807329	0.403664	−	0.914907i	$-0.367736\pi$
$617$	20.0536	0.807329	0.403664	+	0.914907i	$0.367736\pi$
$618$	−29.3599	−1.18103
$619$	45.1892	1.81631	0.908153	−	0.418639i	$-0.137493\pi$
$619$	45.1892	1.81631	0.908153	+	0.418639i	$0.137493\pi$
$620$	−0.324478	−0.0130313
$621$	−16.8775	−0.677271
$622$	23.7656	0.952916
$623$	−35.8340	−1.43566
$624$	1.14652	0.0458976
$625$	−7.62196	−0.304879
$626$	−6.65967	−0.266174
$627$	−48.0067	−1.91720
$628$	−12.9993	−0.518727
$629$	16.5778	0.661000
$630$	15.3482	0.611488
$631$	−43.1897	−1.71936	−0.859678	−	0.510837i	$-0.829336\pi$
$631$	−43.1897	−1.71936	−0.859678	+	0.510837i	$0.829336\pi$
$632$	14.4809	0.576019
$633$	45.6354	1.81384
$634$	6.98642	0.277466
$635$	−19.9736	−0.792628
$636$	9.02536	0.357879
$637$	0.525921	0.0208378
$638$	2.00300	0.0792994
$639$	39.0040	1.54297
$640$	1.62454	0.0642156
$641$	−6.78287	−0.267907	−0.133954	−	0.990988i	$-0.542767\pi$
$641$	−6.78287	−0.267907	−0.133954	+	0.990988i	$0.542767\pi$
$642$	21.4108	0.845018
$643$	29.4134	1.15995	0.579975	−	0.814634i	$-0.303062\pi$
$643$	29.4134	1.15995	0.579975	+	0.814634i	$0.303062\pi$
$644$	16.6807	0.657311
$645$	32.0959	1.26377
$646$	6.90783	0.271785
$647$	−7.66965	−0.301525	−0.150763	−	0.988570i	$-0.548173\pi$
$647$	−7.66965	−0.301525	−0.150763	+	0.988570i	$0.548173\pi$
$648$	−5.36754	−0.210857
$649$	−31.0064	−1.21711
$650$	1.02857	0.0403437
$651$	1.26509	0.0495829
$652$	−2.01069	−0.0787448
$653$	−0.896945	−0.0351002	−0.0175501	−	0.999846i	$-0.505587\pi$
$653$	−0.896945	−0.0351002	−0.0175501	+	0.999846i	$0.505587\pi$
$654$	−18.8143	−0.735697
$655$	12.1652	0.475333
$656$	−11.0337	−0.430795
$657$	−2.52033	−0.0983274
$658$	−18.2982	−0.713339
$659$	−19.3774	−0.754836	−0.377418	−	0.926043i	$-0.623188\pi$
$659$	−19.3774	−0.754836	−0.377418	+	0.926043i	$0.623188\pi$
$660$	16.6256	0.647152
$661$	−40.7353	−1.58442	−0.792210	−	0.610248i	$-0.791070\pi$
$661$	−40.7353	−1.58442	−0.792210	+	0.610248i	$0.791070\pi$
$662$	−27.0434	−1.05107
$663$	−1.68837	−0.0655710
$664$	5.55412	0.215542
$665$	−18.3414	−0.711248
$666$	−44.1898	−1.71232
$667$	−3.56962	−0.138216
$668$	2.55685	0.0989274
$669$	−1.06171	−0.0410482
$670$	2.27199	0.0877746
$671$	−40.6433	−1.56902
$672$	−6.33385	−0.244334
$673$	5.43445	0.209483	0.104741	−	0.994499i	$-0.466599\pi$
$673$	5.43445	0.209483	0.104741	+	0.994499i	$0.466599\pi$
$674$	−18.7181	−0.720995
$675$	5.74927	0.221289
$676$	−12.8102	−0.492700
$677$	12.4547	0.478673	0.239336	−	0.970937i	$-0.423070\pi$
$677$	12.4547	0.478673	0.239336	+	0.970937i	$0.423070\pi$
$678$	30.0542	1.15423
$679$	17.5536	0.673646
$680$	−2.39231	−0.0917409
$681$	65.5960	2.51365
$682$	0.776748	0.0297432
$683$	1.34841	0.0515956	0.0257978	−	0.999667i	$-0.491787\pi$
$683$	1.34841	0.0515956	0.0257978	+	0.999667i	$0.491787\pi$
$684$	−18.4135	−0.704058
$685$	−10.9193	−0.417204
$686$	−19.7532	−0.754182
$687$	44.5315	1.69898
$688$	−7.50752	−0.286222
$689$	1.49418	0.0569237
$690$	−29.6292	−1.12796
$691$	9.91303	0.377109	0.188555	−	0.982063i	$-0.439620\pi$
$691$	9.91303	0.377109	0.188555	+	0.982063i	$0.439620\pi$
$692$	−20.3577	−0.773883
$693$	−36.7412	−1.39568
$694$	23.1668	0.879400
$695$	−24.3196	−0.922495
$696$	1.35543	0.0513774
$697$	16.2483	0.615450
$698$	12.7816	0.483790
$699$	−20.9146	−0.791063
$700$	−5.68222	−0.214768
$701$	40.7476	1.53902	0.769508	−	0.638637i	$-0.220502\pi$
$701$	40.7476	1.53902	0.769508	+	0.638637i	$0.220502\pi$
$702$	1.06097	0.0400436
$703$	52.8074	1.99167
$704$	−3.88889	−0.146568
$705$	32.5024	1.22411
$706$	−33.5835	−1.26393
$707$	−34.7316	−1.30622
$708$	−20.9820	−0.788552
$709$	47.9857	1.80214	0.901071	−	0.433672i	$-0.142782\pi$
$709$	47.9857	1.80214	0.901071	+	0.433672i	$0.142782\pi$
$710$	16.1420	0.605800
$711$	56.8430	2.13178
$712$	−14.8885	−0.557968
$713$	−1.38427	−0.0518415
$714$	9.32727	0.349064
$715$	2.75243	0.102935
$716$	−9.96328	−0.372345
$717$	27.2114	1.01623
$718$	31.6318	1.18049
$719$	−33.6453	−1.25476	−0.627378	−	0.778715i	$-0.715872\pi$
$719$	−33.6453	−1.25476	−0.627378	+	0.778715i	$0.715872\pi$
$720$	6.37694	0.237654
$721$	26.8522	1.00003
$722$	3.00442	0.111813
$723$	−36.9533	−1.37431
$724$	13.7393	0.510618
$725$	1.21598	0.0451603
$726$	−10.8514	−0.402731
$727$	41.0275	1.52163	0.760813	−	0.648971i	$-0.224800\pi$
$727$	41.0275	1.52163	0.760813	+	0.648971i	$0.224800\pi$
$728$	−1.04859	−0.0388634
$729$	−40.2954	−1.49242
$730$	−1.04305	−0.0386051
$731$	11.0556	0.408907
$732$	−27.5033	−1.01655
$733$	−7.86587	−0.290532	−0.145266	−	0.989393i	$-0.546404\pi$
$733$	−7.86587	−0.290532	−0.145266	+	0.989393i	$0.546404\pi$
$734$	8.62772	0.318455
$735$	5.16075	0.190357
$736$	6.93055	0.255463
$737$	−5.43878	−0.200340
$738$	−43.3116	−1.59432
$739$	−16.2185	−0.596606	−0.298303	−	0.954471i	$-0.596421\pi$
$739$	−16.2185	−0.596606	−0.298303	+	0.954471i	$0.596421\pi$
$740$	−18.2882	−0.672287
$741$	−5.37820	−0.197573
$742$	−8.25447	−0.303031
$743$	−34.0315	−1.24849	−0.624247	−	0.781227i	$-0.714594\pi$
$743$	−34.0315	−1.24849	−0.624247	+	0.781227i	$0.714594\pi$
$744$	0.525625	0.0192704
$745$	33.7769	1.23749
$746$	5.25163	0.192276
$747$	21.8020	0.797695
$748$	5.72681	0.209393
$749$	−19.5820	−0.715512
$750$	31.4689	1.14908
$751$	18.9617	0.691921	0.345960	−	0.938249i	$-0.387553\pi$
$751$	18.9617	0.691921	0.345960	+	0.938249i	$0.387553\pi$
$752$	−7.60261	−0.277239
$753$	69.2203	2.52253
$754$	0.224396	0.00817202
$755$	−12.5673	−0.457371
$756$	−5.86121	−0.213170
$757$	33.9233	1.23296	0.616482	−	0.787369i	$-0.288557\pi$
$757$	33.9233	1.23296	0.616482	+	0.787369i	$0.288557\pi$
$758$	−13.6498	−0.495783
$759$	70.9276	2.57451
$760$	−7.62054	−0.276426
$761$	−10.2553	−0.371755	−0.185878	−	0.982573i	$-0.559513\pi$
$761$	−10.2553	−0.371755	−0.185878	+	0.982573i	$0.559513\pi$
$762$	32.3555	1.17211
$763$	17.2073	0.622945
$764$	19.1234	0.691862
$765$	−9.39072	−0.339522
$766$	10.6673	0.385425
$767$	−3.47365	−0.125426
$768$	−2.63161	−0.0949601
$769$	2.56815	0.0926098	0.0463049	−	0.998927i	$-0.485255\pi$
$769$	2.56815	0.0926098	0.0463049	+	0.998927i	$0.485255\pi$
$770$	−15.2056	−0.547970
$771$	−67.0459	−2.41460
$772$	9.35669	0.336755
$773$	−3.62780	−0.130483	−0.0652415	−	0.997870i	$-0.520782\pi$
$773$	−3.62780	−0.130483	−0.0652415	+	0.997870i	$0.520782\pi$
$774$	−29.4699	−1.05927
$775$	0.471548	0.0169385
$776$	7.29323	0.261812
$777$	71.3031	2.55798
$778$	26.1453	0.937354
$779$	51.7580	1.85442
$780$	1.86257	0.0666907
$781$	−38.6414	−1.38270
$782$	−10.2060	−0.364965
$783$	1.25428	0.0448244
$784$	−1.20715	−0.0431124
$785$	−21.1178	−0.753728
$786$	−19.7065	−0.702908
$787$	5.28716	0.188467	0.0942334	−	0.995550i	$-0.469960\pi$
$787$	5.28716	0.188467	0.0942334	+	0.995550i	$0.469960\pi$
$788$	−1.91194	−0.0681100
$789$	−60.9889	−2.17126
$790$	23.5248	0.836975
$791$	−27.4872	−0.977332
$792$	−15.2654	−0.542431
$793$	−4.55327	−0.161691
$794$	−11.0050	−0.390553
$795$	14.6621	0.520010
$796$	−4.08285	−0.144713
$797$	−36.5030	−1.29300	−0.646501	−	0.762913i	$-0.723768\pi$
$797$	−36.5030	−1.29300	−0.646501	+	0.762913i	$0.723768\pi$
$798$	29.7114	1.05177
$799$	11.1956	0.396074
$800$	−2.36087	−0.0834693
$801$	−58.4428	−2.06497
$802$	38.9649	1.37590
$803$	2.49690	0.0881137
$804$	−3.68042	−0.129798
$805$	27.0985	0.955095
$806$	0.0870191	0.00306512
$807$	82.2329	2.89473
$808$	−14.4304	−0.507661
$809$	8.55440	0.300757	0.150378	−	0.988629i	$-0.451951\pi$
$809$	8.55440	0.300757	0.150378	+	0.988629i	$0.451951\pi$
$810$	−8.71979	−0.306382
$811$	−27.3412	−0.960078	−0.480039	−	0.877247i	$-0.659377\pi$
$811$	−27.3412	−0.960078	−0.480039	+	0.877247i	$0.659377\pi$
$812$	−1.23966	−0.0435034
$813$	52.9980	1.85872
$814$	43.7790	1.53445
$815$	−3.26645	−0.114419
$816$	3.87533	0.135664
$817$	35.2169	1.23208
$818$	5.54873	0.194007
$819$	−4.11612	−0.143829
$820$	−17.9247	−0.625959
$821$	−46.6196	−1.62703	−0.813517	−	0.581541i	$-0.802450\pi$
$821$	−46.6196	−1.62703	−0.813517	+	0.581541i	$0.802450\pi$
$822$	17.6883	0.616949
$823$	−44.5835	−1.55408	−0.777041	−	0.629450i	$-0.783280\pi$
$823$	−44.5835	−1.55408	−0.777041	+	0.629450i	$0.783280\pi$
$824$	11.1566	0.388660
$825$	−24.1612	−0.841186
$826$	19.1898	0.667700
$827$	−17.5379	−0.609852	−0.304926	−	0.952376i	$-0.598632\pi$
$827$	−17.5379	−0.609852	−0.304926	+	0.952376i	$0.598632\pi$
$828$	27.2050	0.945440
$829$	−17.3862	−0.603847	−0.301924	−	0.953332i	$-0.597629\pi$
$829$	−17.3862	−0.603847	−0.301924	+	0.953332i	$0.597629\pi$
$830$	9.02290	0.313189
$831$	−35.0279	−1.21511
$832$	−0.435673	−0.0151042
$833$	1.77765	0.0615920
$834$	39.3956	1.36416
$835$	4.15370	0.143745
$836$	18.2423	0.630925
$837$	0.486402	0.0168125
$838$	−1.42707	−0.0492972
$839$	41.5687	1.43511	0.717556	−	0.696501i	$-0.245261\pi$
$839$	41.5687	1.43511	0.717556	+	0.696501i	$0.245261\pi$
$840$	−10.2896	−0.355025
$841$	−28.7347	−0.990852
$842$	30.5365	1.05236
$843$	4.17996	0.143965
$844$	−17.3412	−0.596910
$845$	−20.8107	−0.715909
$846$	−29.8431	−1.02603
$847$	9.92449	0.341010
$848$	−3.42960	−0.117773
$849$	59.3419	2.03661
$850$	3.47663	0.119247
$851$	−78.0203	−2.67450
$852$	−26.1487	−0.895838
$853$	1.63153	0.0558625	0.0279312	−	0.999610i	$-0.491108\pi$
$853$	1.63153	0.0558625	0.0279312	+	0.999610i	$0.491108\pi$
$854$	25.1541	0.860757
$855$	−29.9135	−1.02302
$856$	−8.13602	−0.278083
$857$	−15.5894	−0.532524	−0.266262	−	0.963901i	$-0.585789\pi$
$857$	−15.5894	−0.532524	−0.266262	+	0.963901i	$0.585789\pi$
$858$	−4.45869	−0.152217
$859$	15.0600	0.513840	0.256920	−	0.966433i	$-0.417292\pi$
$859$	15.0600	0.513840	0.256920	+	0.966433i	$0.417292\pi$
$860$	−12.1963	−0.415890
$861$	69.8860	2.38171
$862$	4.89885	0.166856
$863$	33.8583	1.15255	0.576275	−	0.817256i	$-0.304506\pi$
$863$	33.8583	1.15255	0.576275	+	0.817256i	$0.304506\pi$
$864$	−2.43524	−0.0828484
$865$	−33.0719	−1.12448
$866$	40.9064	1.39006
$867$	39.0306	1.32555
$868$	−0.480729	−0.0163170
$869$	−56.3146	−1.91034
$870$	2.20195	0.0746530
$871$	−0.609307	−0.0206456
$872$	7.14934	0.242107
$873$	28.6287	0.968935
$874$	−32.5104	−1.09968
$875$	−28.7810	−0.972975
$876$	1.68965	0.0570881
$877$	−30.9548	−1.04527	−0.522634	−	0.852557i	$-0.675051\pi$
$877$	−30.9548	−1.04527	−0.522634	+	0.852557i	$0.675051\pi$
$878$	−13.9887	−0.472096
$879$	80.8610	2.72737
$880$	−6.31766	−0.212968
$881$	12.1845	0.410506	0.205253	−	0.978709i	$-0.434198\pi$
$881$	12.1845	0.410506	0.205253	+	0.978709i	$0.434198\pi$
$882$	−4.73851	−0.159554
$883$	3.21656	0.108246	0.0541230	−	0.998534i	$-0.482764\pi$
$883$	3.21656	0.108246	0.0541230	+	0.998534i	$0.482764\pi$
$884$	0.641574	0.0215785
$885$	−34.0861	−1.14579
$886$	−0.229220	−0.00770080
$887$	22.7194	0.762841	0.381421	−	0.924402i	$-0.375435\pi$
$887$	22.7194	0.762841	0.381421	+	0.924402i	$0.375435\pi$
$888$	29.6252	0.994158
$889$	−29.5918	−0.992479
$890$	−24.1869	−0.810747
$891$	20.8738	0.699298
$892$	0.403446	0.0135084
$893$	35.6630	1.19342
$894$	−54.7156	−1.82996
$895$	−16.1858	−0.541030
$896$	2.40683	0.0804067
$897$	7.94602	0.265310
$898$	35.5225	1.18540
$899$	0.102875	0.00343107
$900$	−9.26730	−0.308910
$901$	5.05044	0.168255
$902$	42.9090	1.42871
$903$	47.5515	1.58242
$904$	−11.4205	−0.379839
$905$	22.3201	0.741945
$906$	20.3579	0.676347
$907$	−0.459264	−0.0152496	−0.00762480	−	0.999971i	$-0.502427\pi$
$907$	−0.459264	−0.0152496	−0.00762480	+	0.999971i	$0.502427\pi$
$908$	−24.9262	−0.827205
$909$	−56.6449	−1.87879
$910$	−1.70348	−0.0564698
$911$	0.633327	0.0209831	0.0104915	−	0.999945i	$-0.496660\pi$
$911$	0.633327	0.0209831	0.0104915	+	0.999945i	$0.496660\pi$
$912$	12.3446	0.408770
$913$	−21.5994	−0.714835
$914$	20.1742	0.667302
$915$	−44.6802	−1.47708
$916$	−16.9217	−0.559110
$917$	18.0233	0.595182
$918$	3.58614	0.118360
$919$	−51.7778	−1.70799	−0.853996	−	0.520280i	$-0.825828\pi$
$919$	−51.7778	−1.70799	−0.853996	+	0.520280i	$0.825828\pi$
$920$	11.2590	0.371197
$921$	−57.6703	−1.90030
$922$	−19.2420	−0.633701
$923$	−4.32900	−0.142491
$924$	24.6317	0.810322
$925$	26.5774	0.873858
$926$	−31.8819	−1.04770
$927$	43.7940	1.43838
$928$	−0.515056	−0.0169075
$929$	31.9194	1.04724	0.523621	−	0.851951i	$-0.324581\pi$
$929$	31.9194	1.04724	0.523621	+	0.851951i	$0.324581\pi$
$930$	0.853899	0.0280005
$931$	5.66259	0.185584
$932$	7.94745	0.260327
$933$	−62.5420	−2.04753
$934$	32.0908	1.05004
$935$	9.30343	0.304255
$936$	−1.71018	−0.0558990
$937$	41.7633	1.36435	0.682174	−	0.731190i	$-0.261035\pi$
$937$	41.7633	1.36435	0.682174	+	0.731190i	$0.261035\pi$
$938$	3.36606	0.109906
$939$	17.5257	0.571928
$940$	−12.3507	−0.402837
$941$	−14.2881	−0.465778	−0.232889	−	0.972503i	$-0.574818\pi$
$941$	−14.2881	−0.465778	−0.232889	+	0.972503i	$0.574818\pi$
$942$	34.2090	1.11459
$943$	−76.4698	−2.49020
$944$	7.97306	0.259501
$945$	−9.52177	−0.309743
$946$	29.1959	0.949241
$947$	56.4876	1.83560	0.917801	−	0.397041i	$-0.129963\pi$
$947$	56.4876	1.83560	0.917801	+	0.397041i	$0.129963\pi$
$948$	−38.1081	−1.23769
$949$	0.279728	0.00908036
$950$	11.0746	0.359306
$951$	−18.3856	−0.596192
$952$	−3.54432	−0.114872
$953$	−0.542101	−0.0175604	−0.00878018	−	0.999961i	$-0.502795\pi$
$953$	−0.542101	−0.0175604	−0.00878018	+	0.999961i	$0.502795\pi$
$954$	−13.4625	−0.435863
$955$	31.0668	1.00530
$956$	−10.3402	−0.334427
$957$	−5.27111	−0.170391
$958$	33.2746	1.07505
$959$	−16.1774	−0.522397
$960$	−4.27516	−0.137980
$961$	−30.9601	−0.998713
$962$	4.90456	0.158130
$963$	−31.9369	−1.02915
$964$	14.0421	0.452265
$965$	15.2003	0.489316
$966$	−43.8971	−1.41237
$967$	26.9720	0.867360	0.433680	−	0.901067i	$-0.357215\pi$
$967$	26.9720	0.867360	0.433680	+	0.901067i	$0.357215\pi$
$968$	4.12346	0.132533
$969$	−18.1787	−0.583985
$970$	11.8482	0.380421
$971$	−29.5039	−0.946824	−0.473412	−	0.880841i	$-0.656978\pi$
$971$	−29.5039	−0.946824	−0.473412	+	0.880841i	$0.656978\pi$
$972$	21.4310	0.687399
$973$	−36.0306	−1.15509
$974$	2.01597	0.0645957
$975$	−2.70678	−0.0866865
$976$	10.4511	0.334532
$977$	41.5171	1.32825	0.664125	−	0.747622i	$-0.268804\pi$
$977$	41.5171	1.32825	0.664125	+	0.747622i	$0.268804\pi$
$978$	5.29136	0.169199
$979$	57.8995	1.85048
$980$	−1.96106	−0.0626438
$981$	28.0639	0.896010
$982$	20.7960	0.663626
$983$	34.5612	1.10233	0.551165	−	0.834396i	$-0.314183\pi$
$983$	34.5612	1.10233	0.551165	+	0.834396i	$0.314183\pi$
$984$	29.0365	0.925650
$985$	−3.10602	−0.0989661
$986$	0.758475	0.0241548
$987$	48.1538	1.53275
$988$	2.04369	0.0650185
$989$	−52.0313	−1.65450
$990$	−24.7992	−0.788170
$991$	−43.1040	−1.36924	−0.684621	−	0.728899i	$-0.740032\pi$
$991$	−43.1040	−1.36924	−0.684621	+	0.728899i	$0.740032\pi$
$992$	−0.199735	−0.00634159
$993$	71.1678	2.25844
$994$	23.9152	0.758544
$995$	−6.63275	−0.210272
$996$	−14.6163	−0.463135
$997$	23.4843	0.743754	0.371877	−	0.928282i	$-0.378714\pi$
$997$	23.4843	0.743754	0.371877	+	0.928282i	$0.378714\pi$
$998$	−28.3471	−0.897313
$999$	27.4146	0.867358

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4034.2.a.a.1.7	✓	33

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4034.2.a.a.1.7	✓	33	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.63161 q^{3} +1.00000 q^{4} +1.62454 q^{5} -2.63161 q^{6} +2.40683 q^{7} +1.00000 q^{8} +3.92538 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.63161 q^{3} +1.00000 q^{4} +1.62454 q^{5} -2.63161 q^{6} +2.40683 q^{7} +1.00000 q^{8} +3.92538 q^{9} +1.62454 q^{10} -3.88889 q^{11} -2.63161 q^{12} -0.435673 q^{13} +2.40683 q^{14} -4.27516 q^{15} +1.00000 q^{16} -1.47261 q^{17} +3.92538 q^{18} -4.69089 q^{19} +1.62454 q^{20} -6.33385 q^{21} -3.88889 q^{22} +6.93055 q^{23} -2.63161 q^{24} -2.36087 q^{25} -0.435673 q^{26} -2.43524 q^{27} +2.40683 q^{28} -0.515056 q^{29} -4.27516 q^{30} -0.199735 q^{31} +1.00000 q^{32} +10.2340 q^{33} -1.47261 q^{34} +3.91000 q^{35} +3.92538 q^{36} -11.2575 q^{37} -4.69089 q^{38} +1.14652 q^{39} +1.62454 q^{40} -11.0337 q^{41} -6.33385 q^{42} -7.50752 q^{43} -3.88889 q^{44} +6.37694 q^{45} +6.93055 q^{46} -7.60261 q^{47} -2.63161 q^{48} -1.20715 q^{49} -2.36087 q^{50} +3.87533 q^{51} -0.435673 q^{52} -3.42960 q^{53} -2.43524 q^{54} -6.31766 q^{55} +2.40683 q^{56} +12.3446 q^{57} -0.515056 q^{58} +7.97306 q^{59} -4.27516 q^{60} +10.4511 q^{61} -0.199735 q^{62} +9.44774 q^{63} +1.00000 q^{64} -0.707768 q^{65} +10.2340 q^{66} +1.39854 q^{67} -1.47261 q^{68} -18.2385 q^{69} +3.91000 q^{70} +9.93637 q^{71} +3.92538 q^{72} -0.642060 q^{73} -11.2575 q^{74} +6.21289 q^{75} -4.69089 q^{76} -9.35991 q^{77} +1.14652 q^{78} +14.4809 q^{79} +1.62454 q^{80} -5.36754 q^{81} -11.0337 q^{82} +5.55412 q^{83} -6.33385 q^{84} -2.39231 q^{85} -7.50752 q^{86} +1.35543 q^{87} -3.88889 q^{88} -14.8885 q^{89} +6.37694 q^{90} -1.04859 q^{91} +6.93055 q^{92} +0.525625 q^{93} -7.60261 q^{94} -7.62054 q^{95} -2.63161 q^{96} +7.29323 q^{97} -1.20715 q^{98} -15.2654 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 33 q + 33 q^{2} - 14 q^{3} + 33 q^{4} - 22 q^{5} - 14 q^{6} - 12 q^{7} + 33 q^{8} + 17 q^{9}+O(q^{10}) \) 33 * q + 33 * q^2 - 14 * q^3 + 33 * q^4 - 22 * q^5 - 14 * q^6 - 12 * q^7 + 33 * q^8 + 17 * q^9	\( 33 q + 33 q^{2} - 14 q^{3} + 33 q^{4} - 22 q^{5} - 14 q^{6} - 12 q^{7} + 33 q^{8} + 17 q^{9} - 22 q^{10} - 19 q^{11} - 14 q^{12} - 29 q^{13} - 12 q^{14} - 5 q^{15} + 33 q^{16} - 47 q^{17} + 17 q^{18} - 35 q^{19} - 22 q^{20} - 31 q^{21} - 19 q^{22} - 2 q^{23} - 14 q^{24} + 13 q^{25} - 29 q^{26} - 47 q^{27} - 12 q^{28} - 29 q^{29} - 5 q^{30} - 53 q^{31} + 33 q^{32} - 23 q^{33} - 47 q^{34} - 14 q^{35} + 17 q^{36} - 42 q^{37} - 35 q^{38} - 22 q^{40} - 42 q^{41} - 31 q^{42} - 26 q^{43} - 19 q^{44} - 55 q^{45} - 2 q^{46} - 14 q^{48} - 21 q^{49} + 13 q^{50} - 13 q^{51} - 29 q^{52} - 40 q^{53} - 47 q^{54} - 34 q^{55} - 12 q^{56} - 30 q^{57} - 29 q^{58} - 45 q^{59} - 5 q^{60} - 93 q^{61} - 53 q^{62} + 4 q^{63} + 33 q^{64} - 26 q^{65} - 23 q^{66} - 28 q^{67} - 47 q^{68} - 60 q^{69} - 14 q^{70} + 4 q^{71} + 17 q^{72} - 52 q^{73} - 42 q^{74} - 41 q^{75} - 35 q^{76} - 38 q^{77} - 38 q^{79} - 22 q^{80} + 25 q^{81} - 42 q^{82} - 42 q^{83} - 31 q^{84} - 21 q^{85} - 26 q^{86} + 12 q^{87} - 19 q^{88} - 58 q^{89} - 55 q^{90} - 79 q^{91} - 2 q^{92} + 25 q^{93} + 16 q^{95} - 14 q^{96} - 64 q^{97} - 21 q^{98} - 38 q^{99}+O(q^{100}) \) 33 * q + 33 * q^2 - 14 * q^3 + 33 * q^4 - 22 * q^5 - 14 * q^6 - 12 * q^7 + 33 * q^8 + 17 * q^9 - 22 * q^10 - 19 * q^11 - 14 * q^12 - 29 * q^13 - 12 * q^14 - 5 * q^15 + 33 * q^16 - 47 * q^17 + 17 * q^18 - 35 * q^19 - 22 * q^20 - 31 * q^21 - 19 * q^22 - 2 * q^23 - 14 * q^24 + 13 * q^25 - 29 * q^26 - 47 * q^27 - 12 * q^28 - 29 * q^29 - 5 * q^30 - 53 * q^31 + 33 * q^32 - 23 * q^33 - 47 * q^34 - 14 * q^35 + 17 * q^36 - 42 * q^37 - 35 * q^38 - 22 * q^40 - 42 * q^41 - 31 * q^42 - 26 * q^43 - 19 * q^44 - 55 * q^45 - 2 * q^46 - 14 * q^48 - 21 * q^49 + 13 * q^50 - 13 * q^51 - 29 * q^52 - 40 * q^53 - 47 * q^54 - 34 * q^55 - 12 * q^56 - 30 * q^57 - 29 * q^58 - 45 * q^59 - 5 * q^60 - 93 * q^61 - 53 * q^62 + 4 * q^63 + 33 * q^64 - 26 * q^65 - 23 * q^66 - 28 * q^67 - 47 * q^68 - 60 * q^69 - 14 * q^70 + 4 * q^71 + 17 * q^72 - 52 * q^73 - 42 * q^74 - 41 * q^75 - 35 * q^76 - 38 * q^77 - 38 * q^79 - 22 * q^80 + 25 * q^81 - 42 * q^82 - 42 * q^83 - 31 * q^84 - 21 * q^85 - 26 * q^86 + 12 * q^87 - 19 * q^88 - 58 * q^89 - 55 * q^90 - 79 * q^91 - 2 * q^92 + 25 * q^93 + 16 * q^95 - 14 * q^96 - 64 * q^97 - 21 * q^98 - 38 * q^99

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