LMFDB - Embedded newform 4022.2.a.e.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4022,2,Mod(1,4022)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4022, 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("4022.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4022 = 2 \cdot 2011 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4022.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:	$32.1158316930$
Analytic rank:	$0$
Dimension:	$46$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Character	$\chi$	$=$	4022.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.56761 q^{3} +1.00000 q^{4} +4.10115 q^{5} +2.56761 q^{6} -1.16645 q^{7} -1.00000 q^{8} +3.59263 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.56761 q^{3} +1.00000 q^{4} +4.10115 q^{5} +2.56761 q^{6} -1.16645 q^{7} -1.00000 q^{8} +3.59263 q^{9} -4.10115 q^{10} +5.35832 q^{11} -2.56761 q^{12} +1.37161 q^{13} +1.16645 q^{14} -10.5302 q^{15} +1.00000 q^{16} +3.45448 q^{17} -3.59263 q^{18} -1.92408 q^{19} +4.10115 q^{20} +2.99499 q^{21} -5.35832 q^{22} +5.84516 q^{23} +2.56761 q^{24} +11.8195 q^{25} -1.37161 q^{26} -1.52163 q^{27} -1.16645 q^{28} -5.05552 q^{29} +10.5302 q^{30} -2.27739 q^{31} -1.00000 q^{32} -13.7581 q^{33} -3.45448 q^{34} -4.78379 q^{35} +3.59263 q^{36} +5.95064 q^{37} +1.92408 q^{38} -3.52176 q^{39} -4.10115 q^{40} +7.36033 q^{41} -2.99499 q^{42} +4.21771 q^{43} +5.35832 q^{44} +14.7339 q^{45} -5.84516 q^{46} +1.52516 q^{47} -2.56761 q^{48} -5.63939 q^{49} -11.8195 q^{50} -8.86977 q^{51} +1.37161 q^{52} +12.4831 q^{53} +1.52163 q^{54} +21.9753 q^{55} +1.16645 q^{56} +4.94030 q^{57} +5.05552 q^{58} -0.747945 q^{59} -10.5302 q^{60} +2.08364 q^{61} +2.27739 q^{62} -4.19062 q^{63} +1.00000 q^{64} +5.62518 q^{65} +13.7581 q^{66} -10.7495 q^{67} +3.45448 q^{68} -15.0081 q^{69} +4.78379 q^{70} -0.416439 q^{71} -3.59263 q^{72} -3.92946 q^{73} -5.95064 q^{74} -30.3478 q^{75} -1.92408 q^{76} -6.25022 q^{77} +3.52176 q^{78} -3.27640 q^{79} +4.10115 q^{80} -6.87091 q^{81} -7.36033 q^{82} +10.1637 q^{83} +2.99499 q^{84} +14.1674 q^{85} -4.21771 q^{86} +12.9806 q^{87} -5.35832 q^{88} +9.96062 q^{89} -14.7339 q^{90} -1.59991 q^{91} +5.84516 q^{92} +5.84745 q^{93} -1.52516 q^{94} -7.89096 q^{95} +2.56761 q^{96} +5.35401 q^{97} +5.63939 q^{98} +19.2505 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 46 q - 46 q^{2} + 8 q^{3} + 46 q^{4} + 14 q^{5} - 8 q^{6} + 28 q^{7} - 46 q^{8} + 58 q^{9}+O(q^{10}) $ 46 * q - 46 * q^2 + 8 * q^3 + 46 * q^4 + 14 * q^5 - 8 * q^6 + 28 * q^7 - 46 * q^8 + 58 * q^9	\( 46 q - 46 q^{2} + 8 q^{3} + 46 q^{4} + 14 q^{5} - 8 q^{6} + 28 q^{7} - 46 q^{8} + 58 q^{9} - 14 q^{10} - 6 q^{11} + 8 q^{12} + 37 q^{13} - 28 q^{14} + 9 q^{15} + 46 q^{16} + 6 q^{17} - 58 q^{18} + 18 q^{19} + 14 q^{20} + 19 q^{21} + 6 q^{22} - 4 q^{23} - 8 q^{24} + 86 q^{25} - 37 q^{26} + 32 q^{27} + 28 q^{28} + 15 q^{29} - 9 q^{30} + 18 q^{31} - 46 q^{32} + 37 q^{33} - 6 q^{34} - 2 q^{35} + 58 q^{36} + 74 q^{37} - 18 q^{38} - 3 q^{39} - 14 q^{40} - 18 q^{41} - 19 q^{42} + 25 q^{43} - 6 q^{44} + 94 q^{45} + 4 q^{46} + 18 q^{47} + 8 q^{48} + 92 q^{49} - 86 q^{50} - 10 q^{51} + 37 q^{52} + 17 q^{53} - 32 q^{54} + 37 q^{55} - 28 q^{56} + 43 q^{57} - 15 q^{58} - 24 q^{59} + 9 q^{60} + 46 q^{61} - 18 q^{62} + 80 q^{63} + 46 q^{64} + 24 q^{65} - 37 q^{66} + 61 q^{67} + 6 q^{68} + 59 q^{69} + 2 q^{70} - 8 q^{71} - 58 q^{72} + 101 q^{73} - 74 q^{74} + 34 q^{75} + 18 q^{76} + 40 q^{77} + 3 q^{78} + 9 q^{79} + 14 q^{80} + 58 q^{81} + 18 q^{82} + 18 q^{83} + 19 q^{84} + 60 q^{85} - 25 q^{86} + 20 q^{87} + 6 q^{88} - 25 q^{89} - 94 q^{90} + 51 q^{91} - 4 q^{92} + 63 q^{93} - 18 q^{94} - 31 q^{95} - 8 q^{96} + 76 q^{97} - 92 q^{98} + 21 q^{99}+O(q^{100}) \) 46 * q - 46 * q^2 + 8 * q^3 + 46 * q^4 + 14 * q^5 - 8 * q^6 + 28 * q^7 - 46 * q^8 + 58 * q^9 - 14 * q^10 - 6 * q^11 + 8 * q^12 + 37 * q^13 - 28 * q^14 + 9 * q^15 + 46 * q^16 + 6 * q^17 - 58 * q^18 + 18 * q^19 + 14 * q^20 + 19 * q^21 + 6 * q^22 - 4 * q^23 - 8 * q^24 + 86 * q^25 - 37 * q^26 + 32 * q^27 + 28 * q^28 + 15 * q^29 - 9 * q^30 + 18 * q^31 - 46 * q^32 + 37 * q^33 - 6 * q^34 - 2 * q^35 + 58 * q^36 + 74 * q^37 - 18 * q^38 - 3 * q^39 - 14 * q^40 - 18 * q^41 - 19 * q^42 + 25 * q^43 - 6 * q^44 + 94 * q^45 + 4 * q^46 + 18 * q^47 + 8 * q^48 + 92 * q^49 - 86 * q^50 - 10 * q^51 + 37 * q^52 + 17 * q^53 - 32 * q^54 + 37 * q^55 - 28 * q^56 + 43 * q^57 - 15 * q^58 - 24 * q^59 + 9 * q^60 + 46 * q^61 - 18 * q^62 + 80 * q^63 + 46 * q^64 + 24 * q^65 - 37 * q^66 + 61 * q^67 + 6 * q^68 + 59 * q^69 + 2 * q^70 - 8 * q^71 - 58 * q^72 + 101 * q^73 - 74 * q^74 + 34 * q^75 + 18 * q^76 + 40 * q^77 + 3 * q^78 + 9 * q^79 + 14 * q^80 + 58 * q^81 + 18 * q^82 + 18 * q^83 + 19 * q^84 + 60 * q^85 - 25 * q^86 + 20 * q^87 + 6 * q^88 - 25 * q^89 - 94 * q^90 + 51 * q^91 - 4 * q^92 + 63 * q^93 - 18 * q^94 - 31 * q^95 - 8 * q^96 + 76 * q^97 - 92 * q^98 + 21 * 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
$3$	−2.56761	−1.48241	−0.741205	−	0.671278i	$-0.765746\pi$
$3$	−2.56761	−1.48241	−0.741205	+	0.671278i	$0.765746\pi$
$4$	1.00000	0.500000
$5$	4.10115	1.83409	0.917046	−	0.398782i	$-0.130567\pi$
$5$	4.10115	1.83409	0.917046	+	0.398782i	$0.130567\pi$
$6$	2.56761	1.04822
$7$	−1.16645	−0.440877	−0.220438	−	0.975401i	$-0.570749\pi$
$7$	−1.16645	−0.440877	−0.220438	+	0.975401i	$0.570749\pi$
$8$	−1.00000	−0.353553
$9$	3.59263	1.19754
$10$	−4.10115	−1.29690
$11$	5.35832	1.61560	0.807798	−	0.589460i	$-0.200659\pi$
$11$	5.35832	1.61560	0.807798	+	0.589460i	$0.200659\pi$
$12$	−2.56761	−0.741205
$13$	1.37161	0.380416	0.190208	−	0.981744i	$-0.439084\pi$
$13$	1.37161	0.380416	0.190208	+	0.981744i	$0.439084\pi$
$14$	1.16645	0.311747
$15$	−10.5302	−2.71888
$16$	1.00000	0.250000
$17$	3.45448	0.837835	0.418917	−	0.908024i	$-0.362410\pi$
$17$	3.45448	0.837835	0.418917	+	0.908024i	$0.362410\pi$
$18$	−3.59263	−0.846790
$19$	−1.92408	−0.441415	−0.220708	−	0.975340i	$-0.570837\pi$
$19$	−1.92408	−0.441415	−0.220708	+	0.975340i	$0.570837\pi$
$20$	4.10115	0.917046
$21$	2.99499	0.653561
$22$	−5.35832	−1.14240
$23$	5.84516	1.21880	0.609400	−	0.792863i	$-0.291410\pi$
$23$	5.84516	1.21880	0.609400	+	0.792863i	$0.291410\pi$
$24$	2.56761	0.524111
$25$	11.8195	2.36389
$26$	−1.37161	−0.268995
$27$	−1.52163	−0.292839
$28$	−1.16645	−0.220438
$29$	−5.05552	−0.938786	−0.469393	−	0.882989i	$-0.655527\pi$
$29$	−5.05552	−0.938786	−0.469393	+	0.882989i	$0.655527\pi$
$30$	10.5302	1.92254
$31$	−2.27739	−0.409031	−0.204516	−	0.978863i	$-0.565562\pi$
$31$	−2.27739	−0.409031	−0.204516	+	0.978863i	$0.565562\pi$
$32$	−1.00000	−0.176777
$33$	−13.7581	−2.39498
$34$	−3.45448	−0.592439
$35$	−4.78379	−0.808609
$36$	3.59263	0.598771
$37$	5.95064	0.978278	0.489139	−	0.872206i	$-0.337311\pi$
$37$	5.95064	0.978278	0.489139	+	0.872206i	$0.337311\pi$
$38$	1.92408	0.312128
$39$	−3.52176	−0.563933
$40$	−4.10115	−0.648449
$41$	7.36033	1.14949	0.574746	−	0.818332i	$-0.305101\pi$
$41$	7.36033	1.14949	0.574746	+	0.818332i	$0.305101\pi$
$42$	−2.99499	−0.462137
$43$	4.21771	0.643195	0.321597	−	0.946877i	$-0.395780\pi$
$43$	4.21771	0.643195	0.321597	+	0.946877i	$0.395780\pi$
$44$	5.35832	0.807798
$45$	14.7339	2.19640
$46$	−5.84516	−0.861822
$47$	1.52516	0.222468	0.111234	−	0.993794i	$-0.464520\pi$
$47$	1.52516	0.222468	0.111234	+	0.993794i	$0.464520\pi$
$48$	−2.56761	−0.370603
$49$	−5.63939	−0.805628
$50$	−11.8195	−1.67152
$51$	−8.86977	−1.24202
$52$	1.37161	0.190208
$53$	12.4831	1.71469	0.857346	−	0.514740i	$-0.172112\pi$
$53$	12.4831	1.71469	0.857346	+	0.514740i	$0.172112\pi$
$54$	1.52163	0.207068
$55$	21.9753	2.96315
$56$	1.16645	0.155874
$57$	4.94030	0.654358
$58$	5.05552	0.663822
$59$	−0.747945	−0.0973742	−0.0486871	−	0.998814i	$-0.515504\pi$
$59$	−0.747945	−0.0973742	−0.0486871	+	0.998814i	$0.515504\pi$
$60$	−10.5302	−1.35944
$61$	2.08364	0.266783	0.133392	−	0.991063i	$-0.457413\pi$
$61$	2.08364	0.266783	0.133392	+	0.991063i	$0.457413\pi$
$62$	2.27739	0.289229
$63$	−4.19062	−0.527969
$64$	1.00000	0.125000
$65$	5.62518	0.697718
$66$	13.7581	1.69350
$67$	−10.7495	−1.31327	−0.656633	−	0.754210i	$-0.728020\pi$
$67$	−10.7495	−1.31327	−0.656633	+	0.754210i	$0.728020\pi$
$68$	3.45448	0.418917
$69$	−15.0081	−1.80676
$70$	4.78379	0.571773
$71$	−0.416439	−0.0494222	−0.0247111	−	0.999695i	$-0.507867\pi$
$71$	−0.416439	−0.0494222	−0.0247111	+	0.999695i	$0.507867\pi$
$72$	−3.59263	−0.423395
$73$	−3.92946	−0.459909	−0.229954	−	0.973201i	$-0.573858\pi$
$73$	−3.92946	−0.459909	−0.229954	+	0.973201i	$0.573858\pi$
$74$	−5.95064	−0.691747
$75$	−30.3478	−3.50426
$76$	−1.92408	−0.220708
$77$	−6.25022	−0.712279
$78$	3.52176	0.398761
$79$	−3.27640	−0.368624	−0.184312	−	0.982868i	$-0.559006\pi$
$79$	−3.27640	−0.368624	−0.184312	+	0.982868i	$0.559006\pi$
$80$	4.10115	0.458523
$81$	−6.87091	−0.763435
$82$	−7.36033	−0.812813
$83$	10.1637	1.11562	0.557808	−	0.829970i	$-0.311643\pi$
$83$	10.1637	1.11562	0.557808	+	0.829970i	$0.311643\pi$
$84$	2.99499	0.326780
$85$	14.1674	1.53667
$86$	−4.21771	−0.454807
$87$	12.9806	1.39167
$88$	−5.35832	−0.571199
$89$	9.96062	1.05582	0.527912	−	0.849299i	$-0.322975\pi$
$89$	9.96062	1.05582	0.527912	+	0.849299i	$0.322975\pi$
$90$	−14.7339	−1.55309
$91$	−1.59991	−0.167717
$92$	5.84516	0.609400
$93$	5.84745	0.606353
$94$	−1.52516	−0.157309
$95$	−7.89096	−0.809596
$96$	2.56761	0.262056
$97$	5.35401	0.543617	0.271809	−	0.962351i	$-0.412378\pi$
$97$	5.35401	0.543617	0.271809	+	0.962351i	$0.412378\pi$
$98$	5.63939	0.569665
$99$	19.2505	1.93474
$100$	11.8195	1.18195
$101$	−2.48909	−0.247673	−0.123837	−	0.992303i	$-0.539520\pi$
$101$	−2.48909	−0.247673	−0.123837	+	0.992303i	$0.539520\pi$
$102$	8.86977	0.878238
$103$	−19.7312	−1.94417	−0.972086	−	0.234625i	$-0.924614\pi$
$103$	−19.7312	−1.94417	−0.972086	+	0.234625i	$0.924614\pi$
$104$	−1.37161	−0.134497
$105$	12.2829	1.19869
$106$	−12.4831	−1.21247
$107$	9.20697	0.890072	0.445036	−	0.895513i	$-0.353191\pi$
$107$	9.20697	0.890072	0.445036	+	0.895513i	$0.353191\pi$
$108$	−1.52163	−0.146419
$109$	−16.8268	−1.61172	−0.805858	−	0.592109i	$-0.798296\pi$
$109$	−16.8268	−1.61172	−0.805858	+	0.592109i	$0.798296\pi$
$110$	−21.9753	−2.09526
$111$	−15.2789	−1.45021
$112$	−1.16645	−0.110219
$113$	9.83229	0.924944	0.462472	−	0.886634i	$-0.346963\pi$
$113$	9.83229	0.924944	0.462472	+	0.886634i	$0.346963\pi$
$114$	−4.94030	−0.462701
$115$	23.9719	2.23539
$116$	−5.05552	−0.469393
$117$	4.92768	0.455564
$118$	0.747945	0.0688540
$119$	−4.02948	−0.369382
$120$	10.5302	0.961269
$121$	17.7116	1.61015
$122$	−2.08364	−0.188644
$123$	−18.8985	−1.70402
$124$	−2.27739	−0.204516
$125$	27.9677	2.50151
$126$	4.19062	0.373330
$127$	−20.2539	−1.79725	−0.898624	−	0.438720i	$-0.855432\pi$
$127$	−20.2539	−1.79725	−0.898624	+	0.438720i	$0.855432\pi$
$128$	−1.00000	−0.0883883
$129$	−10.8294	−0.953479
$130$	−5.62518	−0.493361
$131$	−6.29020	−0.549577	−0.274788	−	0.961505i	$-0.588608\pi$
$131$	−6.29020	−0.549577	−0.274788	+	0.961505i	$0.588608\pi$
$132$	−13.7581	−1.19749
$133$	2.24435	0.194610
$134$	10.7495	0.928620
$135$	−6.24046	−0.537093
$136$	−3.45448	−0.296219
$137$	2.53916	0.216935	0.108467	−	0.994100i	$-0.465406\pi$
$137$	2.53916	0.216935	0.108467	+	0.994100i	$0.465406\pi$
$138$	15.0081	1.27757
$139$	−21.7219	−1.84243	−0.921216	−	0.389052i	$-0.872803\pi$
$139$	−21.7219	−1.84243	−0.921216	+	0.389052i	$0.872803\pi$
$140$	−4.78379	−0.404304
$141$	−3.91603	−0.329789
$142$	0.416439	0.0349468
$143$	7.34953	0.614598
$144$	3.59263	0.299386
$145$	−20.7335	−1.72182
$146$	3.92946	0.325205
$147$	14.4798	1.19427
$148$	5.95064	0.489139
$149$	2.28014	0.186796	0.0933982	−	0.995629i	$-0.470227\pi$
$149$	2.28014	0.186796	0.0933982	+	0.995629i	$0.470227\pi$
$150$	30.3478	2.47789
$151$	−15.3774	−1.25139	−0.625697	−	0.780066i	$-0.715185\pi$
$151$	−15.3774	−1.25139	−0.625697	+	0.780066i	$0.715185\pi$
$152$	1.92408	0.156064
$153$	12.4107	1.00334
$154$	6.25022	0.503657
$155$	−9.33993	−0.750201
$156$	−3.52176	−0.281966
$157$	−12.3874	−0.988626	−0.494313	−	0.869284i	$-0.664580\pi$
$157$	−12.3874	−0.988626	−0.494313	+	0.869284i	$0.664580\pi$
$158$	3.27640	0.260657
$159$	−32.0519	−2.54188
$160$	−4.10115	−0.324225
$161$	−6.81809	−0.537341
$162$	6.87091	0.539830
$163$	−8.48455	−0.664561	−0.332280	−	0.943181i	$-0.607818\pi$
$163$	−8.48455	−0.664561	−0.332280	+	0.943181i	$0.607818\pi$
$164$	7.36033	0.574746
$165$	−56.4240	−4.39261
$166$	−10.1637	−0.788859
$167$	−15.6574	−1.21161	−0.605805	−	0.795614i	$-0.707149\pi$
$167$	−15.6574	−1.21161	−0.605805	+	0.795614i	$0.707149\pi$
$168$	−2.99499	−0.231069
$169$	−11.1187	−0.855284
$170$	−14.1674	−1.08659
$171$	−6.91251	−0.528613
$172$	4.21771	0.321597
$173$	10.6678	0.811060	0.405530	−	0.914082i	$-0.367087\pi$
$173$	10.6678	0.811060	0.405530	+	0.914082i	$0.367087\pi$
$174$	−12.9806	−0.984057
$175$	−13.7868	−1.04219
$176$	5.35832	0.403899
$177$	1.92043	0.144349
$178$	−9.96062	−0.746580
$179$	−2.37806	−0.177745	−0.0888723	−	0.996043i	$-0.528326\pi$
$179$	−2.37806	−0.177745	−0.0888723	+	0.996043i	$0.528326\pi$
$180$	14.7339	1.09820
$181$	8.88171	0.660173	0.330086	−	0.943951i	$-0.392922\pi$
$181$	8.88171	0.660173	0.330086	+	0.943951i	$0.392922\pi$
$182$	1.59991	0.118594
$183$	−5.34999	−0.395482
$184$	−5.84516	−0.430911
$185$	24.4045	1.79425
$186$	−5.84745	−0.428756
$187$	18.5102	1.35360
$188$	1.52516	0.111234
$189$	1.77491	0.129106
$190$	7.89096	0.572471
$191$	5.53783	0.400704	0.200352	−	0.979724i	$-0.435791\pi$
$191$	5.53783	0.400704	0.200352	+	0.979724i	$0.435791\pi$
$192$	−2.56761	−0.185301
$193$	−1.47356	−0.106069	−0.0530347	−	0.998593i	$-0.516889\pi$
$193$	−1.47356	−0.106069	−0.0530347	+	0.998593i	$0.516889\pi$
$194$	−5.35401	−0.384396
$195$	−14.4433	−1.03430
$196$	−5.63939	−0.402814
$197$	2.79678	0.199262	0.0996312	−	0.995024i	$-0.468234\pi$
$197$	2.79678	0.199262	0.0996312	+	0.995024i	$0.468234\pi$
$198$	−19.2505	−1.36807
$199$	22.9527	1.62707	0.813537	−	0.581513i	$-0.197539\pi$
$199$	22.9527	1.62707	0.813537	+	0.581513i	$0.197539\pi$
$200$	−11.8195	−0.835762
$201$	27.6007	1.94680
$202$	2.48909	0.175132
$203$	5.89701	0.413889
$204$	−8.86977	−0.621008
$205$	30.1859	2.10827
$206$	19.7312	1.37474
$207$	20.9995	1.45956
$208$	1.37161	0.0951040
$209$	−10.3099	−0.713148
$210$	−12.2829	−0.847602
$211$	2.73130	0.188030	0.0940151	−	0.995571i	$-0.470030\pi$
$211$	2.73130	0.188030	0.0940151	+	0.995571i	$0.470030\pi$
$212$	12.4831	0.857346
$213$	1.06925	0.0732641
$214$	−9.20697	−0.629376
$215$	17.2975	1.17968
$216$	1.52163	0.103534
$217$	2.65646	0.180333
$218$	16.8268	1.13966
$219$	10.0893	0.681774
$220$	21.9753	1.48158
$221$	4.73820	0.318726
$222$	15.2789	1.02545
$223$	21.2213	1.42109	0.710543	−	0.703654i	$-0.248449\pi$
$223$	21.2213	1.42109	0.710543	+	0.703654i	$0.248449\pi$
$224$	1.16645	0.0779368
$225$	42.4629	2.83086
$226$	−9.83229	−0.654034
$227$	−25.1937	−1.67216	−0.836082	−	0.548605i	$-0.815159\pi$
$227$	−25.1937	−1.67216	−0.836082	+	0.548605i	$0.815159\pi$
$228$	4.94030	0.327179
$229$	−8.06393	−0.532879	−0.266440	−	0.963852i	$-0.585847\pi$
$229$	−8.06393	−0.532879	−0.266440	+	0.963852i	$0.585847\pi$
$230$	−23.9719	−1.58066
$231$	16.0481	1.05589
$232$	5.05552	0.331911
$233$	6.81229	0.446288	0.223144	−	0.974786i	$-0.428368\pi$
$233$	6.81229	0.446288	0.223144	+	0.974786i	$0.428368\pi$
$234$	−4.92768	−0.322133
$235$	6.25493	0.408027
$236$	−0.747945	−0.0486871
$237$	8.41253	0.546453
$238$	4.02948	0.261193
$239$	−18.8312	−1.21809	−0.609044	−	0.793136i	$-0.708447\pi$
$239$	−18.8312	−1.21809	−0.609044	+	0.793136i	$0.708447\pi$
$240$	−10.5302	−0.679719
$241$	−7.75562	−0.499584	−0.249792	−	0.968300i	$-0.580362\pi$
$241$	−7.75562	−0.499584	−0.249792	+	0.968300i	$0.580362\pi$
$242$	−17.7116	−1.13855
$243$	22.2067	1.42456
$244$	2.08364	0.133392
$245$	−23.1280	−1.47759
$246$	18.8985	1.20492
$247$	−2.63909	−0.167921
$248$	2.27739	0.144614
$249$	−26.0965	−1.65380
$250$	−27.9677	−1.76883
$251$	1.25838	0.0794284	0.0397142	−	0.999211i	$-0.487355\pi$
$251$	1.25838	0.0794284	0.0397142	+	0.999211i	$0.487355\pi$
$252$	−4.19062	−0.263984
$253$	31.3203	1.96909
$254$	20.2539	1.27085
$255$	−36.3763	−2.27797
$256$	1.00000	0.0625000
$257$	17.0569	1.06398	0.531991	−	0.846750i	$-0.321444\pi$
$257$	17.0569	1.06398	0.531991	+	0.846750i	$0.321444\pi$
$258$	10.8294	0.674211
$259$	−6.94112	−0.431300
$260$	5.62518	0.348859
$261$	−18.1626	−1.12424
$262$	6.29020	0.388610
$263$	10.9277	0.673830	0.336915	−	0.941535i	$-0.390616\pi$
$263$	10.9277	0.673830	0.336915	+	0.941535i	$0.390616\pi$
$264$	13.7581	0.846752
$265$	51.1953	3.14490
$266$	−2.24435	−0.137610
$267$	−25.5750	−1.56516
$268$	−10.7495	−0.656633
$269$	4.50599	0.274735	0.137367	−	0.990520i	$-0.456136\pi$
$269$	4.50599	0.274735	0.137367	+	0.990520i	$0.456136\pi$
$270$	6.24046	0.379782
$271$	26.7449	1.62464	0.812319	−	0.583214i	$-0.198205\pi$
$271$	26.7449	1.62464	0.812319	+	0.583214i	$0.198205\pi$
$272$	3.45448	0.209459
$273$	4.10796	0.248625
$274$	−2.53916	−0.153396
$275$	63.3325	3.81909
$276$	−15.0081	−0.903381
$277$	32.1621	1.93243	0.966215	−	0.257736i	$-0.0829765\pi$
$277$	32.1621	1.93243	0.966215	+	0.257736i	$0.0829765\pi$
$278$	21.7219	1.30280
$279$	−8.18181	−0.489832
$280$	4.78379	0.285886
$281$	−11.8516	−0.707008	−0.353504	−	0.935433i	$-0.615010\pi$
$281$	−11.8516	−0.707008	−0.353504	+	0.935433i	$0.615010\pi$
$282$	3.91603	0.233196
$283$	−19.5991	−1.16504	−0.582522	−	0.812815i	$-0.697934\pi$
$283$	−19.5991	−1.16504	−0.582522	+	0.812815i	$0.697934\pi$
$284$	−0.416439	−0.0247111
$285$	20.2609	1.20015
$286$	−7.34953	−0.434587
$287$	−8.58547	−0.506784
$288$	−3.59263	−0.211698
$289$	−5.06655	−0.298033
$290$	20.7335	1.21751
$291$	−13.7470	−0.805865
$292$	−3.92946	−0.229954
$293$	−17.7471	−1.03680	−0.518400	−	0.855139i	$-0.673472\pi$
$293$	−17.7471	−1.03680	−0.518400	+	0.855139i	$0.673472\pi$
$294$	−14.4798	−0.844477
$295$	−3.06744	−0.178593
$296$	−5.95064	−0.345874
$297$	−8.15341	−0.473109
$298$	−2.28014	−0.132085
$299$	8.01728	0.463651
$300$	−30.3478	−1.75213
$301$	−4.91975	−0.283570
$302$	15.3774	0.884869
$303$	6.39101	0.367154
$304$	−1.92408	−0.110354
$305$	8.54535	0.489305
$306$	−12.4107	−0.709470
$307$	19.8580	1.13336	0.566678	−	0.823939i	$-0.308228\pi$
$307$	19.8580	1.13336	0.566678	+	0.823939i	$0.308228\pi$
$308$	−6.25022	−0.356139
$309$	50.6620	2.88206
$310$	9.33993	0.530472
$311$	30.0347	1.70311	0.851557	−	0.524262i	$-0.175659\pi$
$311$	30.0347	1.70311	0.851557	+	0.524262i	$0.175659\pi$
$312$	3.52176	0.199380
$313$	15.5642	0.879743	0.439872	−	0.898061i	$-0.355024\pi$
$313$	15.5642	0.879743	0.439872	+	0.898061i	$0.355024\pi$
$314$	12.3874	0.699064
$315$	−17.1864	−0.968343
$316$	−3.27640	−0.184312
$317$	−20.9669	−1.17762	−0.588810	−	0.808271i	$-0.700404\pi$
$317$	−20.9669	−1.17762	−0.588810	+	0.808271i	$0.700404\pi$
$318$	32.0519	1.79738
$319$	−27.0891	−1.51670
$320$	4.10115	0.229261
$321$	−23.6399	−1.31945
$322$	6.81809	0.379957
$323$	−6.64671	−0.369833
$324$	−6.87091	−0.381717
$325$	16.2117	0.899263
$326$	8.48455	0.469916
$327$	43.2047	2.38923
$328$	−7.36033	−0.406406
$329$	−1.77903	−0.0980810
$330$	56.4240	3.10604
$331$	13.1657	0.723654	0.361827	−	0.932245i	$-0.382153\pi$
$331$	13.1657	0.723654	0.361827	+	0.932245i	$0.382153\pi$
$332$	10.1637	0.557808
$333$	21.3784	1.17153
$334$	15.6574	0.856737
$335$	−44.0856	−2.40865
$336$	2.99499	0.163390
$337$	−8.29108	−0.451644	−0.225822	−	0.974169i	$-0.572507\pi$
$337$	−8.29108	−0.451644	−0.225822	+	0.974169i	$0.572507\pi$
$338$	11.1187	0.604777
$339$	−25.2455	−1.37115
$340$	14.1674	0.768333
$341$	−12.2030	−0.660829
$342$	6.91251	0.373786
$343$	14.7432	0.796060
$344$	−4.21771	−0.227404
$345$	−61.5505	−3.31377
$346$	−10.6678	−0.573506
$347$	6.36995	0.341957	0.170978	−	0.985275i	$-0.445307\pi$
$347$	6.36995	0.341957	0.170978	+	0.985275i	$0.445307\pi$
$348$	12.9806	0.695833
$349$	10.0906	0.540136	0.270068	−	0.962841i	$-0.412954\pi$
$349$	10.0906	0.540136	0.270068	+	0.962841i	$0.412954\pi$
$350$	13.7868	0.736937
$351$	−2.08709	−0.111400
$352$	−5.35832	−0.285600
$353$	30.0583	1.59984	0.799922	−	0.600105i	$-0.204874\pi$
$353$	30.0583	1.59984	0.799922	+	0.600105i	$0.204874\pi$
$354$	−1.92043	−0.102070
$355$	−1.70788	−0.0906449
$356$	9.96062	0.527912
$357$	10.3461	0.547576
$358$	2.37806	0.125684
$359$	2.11507	0.111629	0.0558146	−	0.998441i	$-0.482224\pi$
$359$	2.11507	0.111629	0.0558146	+	0.998441i	$0.482224\pi$
$360$	−14.7339	−0.776545
$361$	−15.2979	−0.805153
$362$	−8.88171	−0.466813
$363$	−45.4766	−2.38690
$364$	−1.59991	−0.0838583
$365$	−16.1153	−0.843515
$366$	5.34999	0.279648
$367$	19.4501	1.01529	0.507644	−	0.861567i	$-0.330516\pi$
$367$	19.4501	1.01529	0.507644	+	0.861567i	$0.330516\pi$
$368$	5.84516	0.304700
$369$	26.4429	1.37656
$370$	−24.4045	−1.26873
$371$	−14.5610	−0.755968
$372$	5.84745	0.303176
$373$	29.3917	1.52185	0.760923	−	0.648842i	$-0.224746\pi$
$373$	29.3917	1.52185	0.760923	+	0.648842i	$0.224746\pi$
$374$	−18.5102	−0.957141
$375$	−71.8101	−3.70826
$376$	−1.52516	−0.0786543
$377$	−6.93419	−0.357129
$378$	−1.77491	−0.0912916
$379$	−30.2258	−1.55259	−0.776297	−	0.630368i	$-0.782904\pi$
$379$	−30.2258	−1.55259	−0.776297	+	0.630368i	$0.782904\pi$
$380$	−7.89096	−0.404798
$381$	52.0043	2.66426
$382$	−5.53783	−0.283340
$383$	13.2128	0.675141	0.337570	−	0.941300i	$-0.390395\pi$
$383$	13.2128	0.675141	0.337570	+	0.941300i	$0.390395\pi$
$384$	2.56761	0.131028
$385$	−25.6331	−1.30638
$386$	1.47356	0.0750025
$387$	15.1527	0.770253
$388$	5.35401	0.271809
$389$	15.9504	0.808718	0.404359	−	0.914600i	$-0.367495\pi$
$389$	15.9504	0.808718	0.404359	+	0.914600i	$0.367495\pi$
$390$	14.4433	0.731364
$391$	20.1920	1.02115
$392$	5.63939	0.284832
$393$	16.1508	0.814699
$394$	−2.79678	−0.140900
$395$	−13.4370	−0.676091
$396$	19.2505	0.967372
$397$	−19.6598	−0.986697	−0.493348	−	0.869832i	$-0.664227\pi$
$397$	−19.6598	−0.986697	−0.493348	+	0.869832i	$0.664227\pi$
$398$	−22.9527	−1.15052
$399$	−5.76261	−0.288492
$400$	11.8195	0.590973
$401$	−4.02940	−0.201219	−0.100609	−	0.994926i	$-0.532079\pi$
$401$	−4.02940	−0.201219	−0.100609	+	0.994926i	$0.532079\pi$
$402$	−27.6007	−1.37660
$403$	−3.12369	−0.155602
$404$	−2.48909	−0.123837
$405$	−28.1787	−1.40021
$406$	−5.89701	−0.292664
$407$	31.8854	1.58050
$408$	8.86977	0.439119
$409$	32.1461	1.58952	0.794760	−	0.606924i	$-0.207597\pi$
$409$	32.1461	1.58952	0.794760	+	0.606924i	$0.207597\pi$
$410$	−30.1859	−1.49077
$411$	−6.51957	−0.321587
$412$	−19.7312	−0.972086
$413$	0.872442	0.0429300
$414$	−20.9995	−1.03207
$415$	41.6831	2.04614
$416$	−1.37161	−0.0672487
$417$	55.7735	2.73124
$418$	10.3099	0.504272
$419$	−21.7677	−1.06342	−0.531712	−	0.846925i	$-0.678451\pi$
$419$	−21.7677	−1.06342	−0.531712	+	0.846925i	$0.678451\pi$
$420$	12.2829	0.599345
$421$	−39.9504	−1.94706	−0.973531	−	0.228555i	$-0.926600\pi$
$421$	−39.9504	−1.94706	−0.973531	+	0.228555i	$0.926600\pi$
$422$	−2.73130	−0.132957
$423$	5.47934	0.266415
$424$	−12.4831	−0.606235
$425$	40.8301	1.98055
$426$	−1.06925	−0.0518055
$427$	−2.43047	−0.117619
$428$	9.20697	0.445036
$429$	−18.8707	−0.911087
$430$	−17.2975	−0.834158
$431$	−10.9470	−0.527298	−0.263649	−	0.964619i	$-0.584926\pi$
$431$	−10.9470	−0.527298	−0.263649	+	0.964619i	$0.584926\pi$
$432$	−1.52163	−0.0732096
$433$	−33.7324	−1.62108	−0.810538	−	0.585686i	$-0.800825\pi$
$433$	−33.7324	−1.62108	−0.810538	+	0.585686i	$0.800825\pi$
$434$	−2.65646	−0.127514
$435$	53.2354	2.55244
$436$	−16.8268	−0.805858
$437$	−11.2466	−0.537997
$438$	−10.0893	−0.482087
$439$	18.0866	0.863227	0.431614	−	0.902059i	$-0.357944\pi$
$439$	18.0866	0.863227	0.431614	+	0.902059i	$0.357944\pi$
$440$	−21.9753	−1.04763
$441$	−20.2602	−0.964773
$442$	−4.73820	−0.225373
$443$	−18.1565	−0.862644	−0.431322	−	0.902198i	$-0.641953\pi$
$443$	−18.1565	−0.862644	−0.431322	+	0.902198i	$0.641953\pi$
$444$	−15.2789	−0.725105
$445$	40.8500	1.93648
$446$	−21.2213	−1.00486
$447$	−5.85451	−0.276909
$448$	−1.16645	−0.0551096
$449$	16.1679	0.763010	0.381505	−	0.924367i	$-0.375406\pi$
$449$	16.1679	0.763010	0.381505	+	0.924367i	$0.375406\pi$
$450$	−42.4629	−2.00172
$451$	39.4390	1.85711
$452$	9.83229	0.462472
$453$	39.4831	1.85508
$454$	25.1937	1.18240
$455$	−6.56150	−0.307608
$456$	−4.94030	−0.231351
$457$	5.71213	0.267202	0.133601	−	0.991035i	$-0.457346\pi$
$457$	5.71213	0.267202	0.133601	+	0.991035i	$0.457346\pi$
$458$	8.06393	0.376802
$459$	−5.25646	−0.245350
$460$	23.9719	1.11770
$461$	20.1981	0.940721	0.470360	−	0.882474i	$-0.344124\pi$
$461$	20.1981	0.940721	0.470360	+	0.882474i	$0.344124\pi$
$462$	−16.0481	−0.746627
$463$	28.6624	1.33205	0.666026	−	0.745928i	$-0.267994\pi$
$463$	28.6624	1.33205	0.666026	+	0.745928i	$0.267994\pi$
$464$	−5.05552	−0.234696
$465$	23.9813	1.11211
$466$	−6.81229	−0.315573
$467$	10.8578	0.502440	0.251220	−	0.967930i	$-0.419168\pi$
$467$	10.8578	0.502440	0.251220	+	0.967930i	$0.419168\pi$
$468$	4.92768	0.227782
$469$	12.5388	0.578989
$470$	−6.25493	−0.288518
$471$	31.8061	1.46555
$472$	0.747945	0.0344270
$473$	22.5998	1.03914
$474$	−8.41253	−0.386400
$475$	−22.7416	−1.04346
$476$	−4.02948	−0.184691
$477$	44.8473	2.05342
$478$	18.8312	0.861318
$479$	32.9143	1.50389	0.751947	−	0.659224i	$-0.229115\pi$
$479$	32.9143	1.50389	0.751947	+	0.659224i	$0.229115\pi$
$480$	10.5302	0.480634
$481$	8.16195	0.372153
$482$	7.75562	0.353259
$483$	17.5062	0.796560
$484$	17.7116	0.805074
$485$	21.9576	0.997044
$486$	−22.2067	−1.00732
$487$	28.9242	1.31068	0.655340	−	0.755334i	$-0.272526\pi$
$487$	28.9242	1.31068	0.655340	+	0.755334i	$0.272526\pi$
$488$	−2.08364	−0.0943221
$489$	21.7850	0.985152
$490$	23.1280	1.04482
$491$	−11.7035	−0.528170	−0.264085	−	0.964499i	$-0.585070\pi$
$491$	−11.7035	−0.528170	−0.264085	+	0.964499i	$0.585070\pi$
$492$	−18.8985	−0.852009
$493$	−17.4642	−0.786548
$494$	2.63909	0.118738
$495$	78.9491	3.54850
$496$	−2.27739	−0.102258
$497$	0.485756	0.0217891
$498$	26.0965	1.16941
$499$	21.3828	0.957226	0.478613	−	0.878026i	$-0.341140\pi$
$499$	21.3828	0.957226	0.478613	+	0.878026i	$0.341140\pi$
$500$	27.9677	1.25075
$501$	40.2022	1.79610
$502$	−1.25838	−0.0561644
$503$	−30.9696	−1.38087	−0.690434	−	0.723395i	$-0.742580\pi$
$503$	−30.9696	−1.38087	−0.690434	+	0.723395i	$0.742580\pi$
$504$	4.19062	0.186665
$505$	−10.2081	−0.454256
$506$	−31.3203	−1.39236
$507$	28.5485	1.26788
$508$	−20.2539	−0.898624
$509$	−21.0799	−0.934352	−0.467176	−	0.884164i	$-0.654729\pi$
$509$	−21.0799	−0.934352	−0.467176	+	0.884164i	$0.654729\pi$
$510$	36.3763	1.61077
$511$	4.58352	0.202763
$512$	−1.00000	−0.0441942
$513$	2.92775	0.129263
$514$	−17.0569	−0.752349
$515$	−80.9206	−3.56579
$516$	−10.8294	−0.476739
$517$	8.17232	0.359418
$518$	6.94112	0.304975
$519$	−27.3908	−1.20232
$520$	−5.62518	−0.246681
$521$	−25.4303	−1.11412	−0.557061	−	0.830472i	$-0.688071\pi$
$521$	−25.4303	−1.11412	−0.557061	+	0.830472i	$0.688071\pi$
$522$	18.1626	0.794955
$523$	14.6493	0.640567	0.320284	−	0.947322i	$-0.396222\pi$
$523$	14.6493	0.640567	0.320284	+	0.947322i	$0.396222\pi$
$524$	−6.29020	−0.274788
$525$	35.3992	1.54495
$526$	−10.9277	−0.476470
$527$	−7.86721	−0.342701
$528$	−13.7581	−0.598744
$529$	11.1659	0.485473
$530$	−51.1953	−2.22378
$531$	−2.68709	−0.116610
$532$	2.24435	0.0973049
$533$	10.0955	0.437285
$534$	25.5750	1.10674
$535$	37.7592	1.63247
$536$	10.7495	0.464310
$537$	6.10593	0.263490
$538$	−4.50599	−0.194267
$539$	−30.2177	−1.30157
$540$	−6.24046	−0.268546
$541$	−32.4447	−1.39490	−0.697452	−	0.716631i	$-0.745683\pi$
$541$	−32.4447	−1.39490	−0.697452	+	0.716631i	$0.745683\pi$
$542$	−26.7449	−1.14879
$543$	−22.8048	−0.978647
$544$	−3.45448	−0.148110
$545$	−69.0093	−2.95604
$546$	−4.10796	−0.175804
$547$	34.4635	1.47355	0.736777	−	0.676136i	$-0.236347\pi$
$547$	34.4635	1.47355	0.736777	+	0.676136i	$0.236347\pi$
$548$	2.53916	0.108467
$549$	7.48575	0.319484
$550$	−63.3325	−2.70051
$551$	9.72724	0.414394
$552$	15.0081	0.638787
$553$	3.82176	0.162518
$554$	−32.1621	−1.36643
$555$	−62.6612	−2.65982
$556$	−21.7219	−0.921216
$557$	−7.77793	−0.329562	−0.164781	−	0.986330i	$-0.552692\pi$
$557$	−7.77793	−0.329562	−0.164781	+	0.986330i	$0.552692\pi$
$558$	8.18181	0.346364
$559$	5.78505	0.244681
$560$	−4.78379	−0.202152
$561$	−47.5271	−2.00659
$562$	11.8516	0.499930
$563$	−16.2161	−0.683427	−0.341713	−	0.939804i	$-0.611007\pi$
$563$	−16.2161	−0.683427	−0.341713	+	0.939804i	$0.611007\pi$
$564$	−3.91603	−0.164894
$565$	40.3237	1.69643
$566$	19.5991	0.823810
$567$	8.01458	0.336581
$568$	0.416439	0.0174734
$569$	−14.0238	−0.587910	−0.293955	−	0.955819i	$-0.594972\pi$
$569$	−14.0238	−0.587910	−0.293955	+	0.955819i	$0.594972\pi$
$570$	−20.2609	−0.848637
$571$	−8.65971	−0.362398	−0.181199	−	0.983446i	$-0.557998\pi$
$571$	−8.65971	−0.362398	−0.181199	+	0.983446i	$0.557998\pi$
$572$	7.34953	0.307299
$573$	−14.2190	−0.594007
$574$	8.58547	0.358350
$575$	69.0867	2.88111
$576$	3.59263	0.149693
$577$	−13.8017	−0.574573	−0.287286	−	0.957845i	$-0.592753\pi$
$577$	−13.8017	−0.574573	−0.287286	+	0.957845i	$0.592753\pi$
$578$	5.06655	0.210741
$579$	3.78354	0.157239
$580$	−20.7335	−0.860910
$581$	−11.8555	−0.491849
$582$	13.7470	0.569832
$583$	66.8887	2.77025
$584$	3.92946	0.162602
$585$	20.2092	0.835547
$586$	17.7471	0.733128
$587$	6.79188	0.280331	0.140165	−	0.990128i	$-0.455237\pi$
$587$	6.79188	0.280331	0.140165	+	0.990128i	$0.455237\pi$
$588$	14.4798	0.597136
$589$	4.38189	0.180553
$590$	3.06744	0.126284
$591$	−7.18104	−0.295389
$592$	5.95064	0.244570
$593$	15.6819	0.643979	0.321990	−	0.946743i	$-0.395648\pi$
$593$	15.6819	0.643979	0.321990	+	0.946743i	$0.395648\pi$
$594$	8.15341	0.334538
$595$	−16.5255	−0.677481
$596$	2.28014	0.0933982
$597$	−58.9336	−2.41199
$598$	−8.01728	−0.327851
$599$	17.4694	0.713779	0.356890	−	0.934147i	$-0.383837\pi$
$599$	17.4694	0.713779	0.356890	+	0.934147i	$0.383837\pi$
$600$	30.3478	1.23894
$601$	−23.8275	−0.971945	−0.485973	−	0.873974i	$-0.661535\pi$
$601$	−23.8275	−0.971945	−0.485973	+	0.873974i	$0.661535\pi$
$602$	4.91975	0.200514
$603$	−38.6191	−1.57269
$604$	−15.3774	−0.625697
$605$	72.6381	2.95316
$606$	−6.39101	−0.259617
$607$	−14.7225	−0.597568	−0.298784	−	0.954321i	$-0.596581\pi$
$607$	−14.7225	−0.597568	−0.298784	+	0.954321i	$0.596581\pi$
$608$	1.92408	0.0780319
$609$	−15.1412	−0.613554
$610$	−8.54535	−0.345991
$611$	2.09193	0.0846304
$612$	12.4107	0.501671
$613$	−28.0863	−1.13439	−0.567197	−	0.823582i	$-0.691972\pi$
$613$	−28.0863	−1.13439	−0.567197	+	0.823582i	$0.691972\pi$
$614$	−19.8580	−0.801404
$615$	−77.5056	−3.12533
$616$	6.25022	0.251829
$617$	−6.22081	−0.250440	−0.125220	−	0.992129i	$-0.539964\pi$
$617$	−6.22081	−0.250440	−0.125220	+	0.992129i	$0.539964\pi$
$618$	−50.6620	−2.03793
$619$	−31.5722	−1.26899	−0.634497	−	0.772926i	$-0.718793\pi$
$619$	−31.5722	−1.26899	−0.634497	+	0.772926i	$0.718793\pi$
$620$	−9.33993	−0.375101
$621$	−8.89419	−0.356912
$622$	−30.0347	−1.20428
$623$	−11.6186	−0.465488
$624$	−3.52176	−0.140983
$625$	55.6025	2.22410
$626$	−15.5642	−0.622072
$627$	26.4717	1.05718
$628$	−12.3874	−0.494313
$629$	20.5564	0.819636
$630$	17.1864	0.684722
$631$	22.4727	0.894624	0.447312	−	0.894378i	$-0.352381\pi$
$631$	22.4727	0.894624	0.447312	+	0.894378i	$0.352381\pi$
$632$	3.27640	0.130328
$633$	−7.01291	−0.278738
$634$	20.9669	0.832704
$635$	−83.0646	−3.29632
$636$	−32.0519	−1.27094
$637$	−7.73504	−0.306474
$638$	27.0891	1.07247
$639$	−1.49611	−0.0591852
$640$	−4.10115	−0.162112
$641$	0.408453	0.0161329	0.00806645	−	0.999967i	$-0.497432\pi$
$641$	0.408453	0.0161329	0.00806645	+	0.999967i	$0.497432\pi$
$642$	23.6399	0.932994
$643$	12.5532	0.495048	0.247524	−	0.968882i	$-0.420383\pi$
$643$	12.5532	0.495048	0.247524	+	0.968882i	$0.420383\pi$
$644$	−6.81809	−0.268670
$645$	−44.4132	−1.74877
$646$	6.64671	0.261511
$647$	−23.0960	−0.907996	−0.453998	−	0.891003i	$-0.650003\pi$
$647$	−23.0960	−0.907996	−0.453998	+	0.891003i	$0.650003\pi$
$648$	6.87091	0.269915
$649$	−4.00773	−0.157317
$650$	−16.2117	−0.635875
$651$	−6.82077	−0.267327
$652$	−8.48455	−0.332280
$653$	35.3111	1.38183	0.690914	−	0.722937i	$-0.257208\pi$
$653$	35.3111	1.38183	0.690914	+	0.722937i	$0.257208\pi$
$654$	−43.2047	−1.68944
$655$	−25.7971	−1.00797
$656$	7.36033	0.287373
$657$	−14.1171	−0.550760
$658$	1.77903	0.0693537
$659$	−4.42396	−0.172333	−0.0861664	−	0.996281i	$-0.527462\pi$
$659$	−4.42396	−0.172333	−0.0861664	+	0.996281i	$0.527462\pi$
$660$	−56.4240	−2.19630
$661$	−24.1250	−0.938354	−0.469177	−	0.883104i	$-0.655449\pi$
$661$	−24.1250	−0.938354	−0.469177	+	0.883104i	$0.655449\pi$
$662$	−13.1657	−0.511701
$663$	−12.1659	−0.472483
$664$	−10.1637	−0.394430
$665$	9.20442	0.356932
$666$	−21.3784	−0.828397
$667$	−29.5503	−1.14419
$668$	−15.6574	−0.605805
$669$	−54.4882	−2.10663
$670$	44.0856	1.70317
$671$	11.1648	0.431014
$672$	−2.99499	−0.115534
$673$	−7.40802	−0.285558	−0.142779	−	0.989755i	$-0.545604\pi$
$673$	−7.40802	−0.285558	−0.142779	+	0.989755i	$0.545604\pi$
$674$	8.29108	0.319360
$675$	−17.9849	−0.692239
$676$	−11.1187	−0.427642
$677$	−46.7061	−1.79506	−0.897532	−	0.440950i	$-0.854642\pi$
$677$	−46.7061	−1.79506	−0.897532	+	0.440950i	$0.854642\pi$
$678$	25.2455	0.969548
$679$	−6.24519	−0.239668
$680$	−14.1674	−0.543294
$681$	64.6876	2.47883
$682$	12.2030	0.467277
$683$	20.2374	0.774361	0.387181	−	0.922004i	$-0.373449\pi$
$683$	20.2374	0.774361	0.387181	+	0.922004i	$0.373449\pi$
$684$	−6.91251	−0.264307
$685$	10.4135	0.397878
$686$	−14.7432	−0.562899
$687$	20.7050	0.789946
$688$	4.21771	0.160799
$689$	17.1220	0.652296
$690$	61.5505	2.34319
$691$	−5.78746	−0.220165	−0.110083	−	0.993922i	$-0.535112\pi$
$691$	−5.78746	−0.220165	−0.110083	+	0.993922i	$0.535112\pi$
$692$	10.6678	0.405530
$693$	−22.4547	−0.852984
$694$	−6.36995	−0.241800
$695$	−89.0851	−3.37919
$696$	−12.9806	−0.492028
$697$	25.4261	0.963084
$698$	−10.0906	−0.381934
$699$	−17.4913	−0.661582
$700$	−13.7868	−0.521093
$701$	9.96132	0.376234	0.188117	−	0.982147i	$-0.439762\pi$
$701$	9.96132	0.376234	0.188117	+	0.982147i	$0.439762\pi$
$702$	2.08709	0.0787720
$703$	−11.4495	−0.431827
$704$	5.35832	0.201949
$705$	−16.0602	−0.604863
$706$	−30.0583	−1.13126
$707$	2.90340	0.109193
$708$	1.92043	0.0721743
$709$	−22.2219	−0.834562	−0.417281	−	0.908778i	$-0.637017\pi$
$709$	−22.2219	−0.834562	−0.417281	+	0.908778i	$0.637017\pi$
$710$	1.70788	0.0640957
$711$	−11.7709	−0.441443
$712$	−9.96062	−0.373290
$713$	−13.3117	−0.498528
$714$	−10.3461	−0.387195
$715$	30.1415	1.12723
$716$	−2.37806	−0.0888723
$717$	48.3512	1.80571
$718$	−2.11507	−0.0789338
$719$	4.04248	0.150759	0.0753796	−	0.997155i	$-0.475983\pi$
$719$	4.04248	0.150759	0.0753796	+	0.997155i	$0.475983\pi$
$720$	14.7339	0.549101
$721$	23.0155	0.857141
$722$	15.2979	0.569329
$723$	19.9134	0.740588
$724$	8.88171	0.330086
$725$	−59.7535	−2.21919
$726$	45.4766	1.68779
$727$	2.47732	0.0918786	0.0459393	−	0.998944i	$-0.485372\pi$
$727$	2.47732	0.0918786	0.0459393	+	0.998944i	$0.485372\pi$
$728$	1.59991	0.0592968
$729$	−36.4055	−1.34835
$730$	16.1153	0.596455
$731$	14.5700	0.538891
$732$	−5.34999	−0.197741
$733$	45.8979	1.69528	0.847639	−	0.530573i	$-0.178023\pi$
$733$	45.8979	1.69528	0.847639	+	0.530573i	$0.178023\pi$
$734$	−19.4501	−0.717918
$735$	59.3838	2.19040
$736$	−5.84516	−0.215455
$737$	−57.5996	−2.12171
$738$	−26.4429	−0.973378
$739$	−24.5969	−0.904812	−0.452406	−	0.891812i	$-0.649434\pi$
$739$	−24.5969	−0.904812	−0.452406	+	0.891812i	$0.649434\pi$
$740$	24.4045	0.897126
$741$	6.77616	0.248928
$742$	14.5610	0.534550
$743$	−0.261380	−0.00958911	−0.00479456	−	0.999989i	$-0.501526\pi$
$743$	−0.261380	−0.00958911	−0.00479456	+	0.999989i	$0.501526\pi$
$744$	−5.84745	−0.214378
$745$	9.35121	0.342602
$746$	−29.3917	−1.07611
$747$	36.5145	1.33600
$748$	18.5102	0.676801
$749$	−10.7395	−0.392412
$750$	71.8101	2.62214
$751$	1.74594	0.0637103	0.0318551	−	0.999492i	$-0.489858\pi$
$751$	1.74594	0.0637103	0.0318551	+	0.999492i	$0.489858\pi$
$752$	1.52516	0.0556170
$753$	−3.23104	−0.117746
$754$	6.93419	0.252528
$755$	−63.0650	−2.29517
$756$	1.77491	0.0645529
$757$	−47.4391	−1.72420	−0.862102	−	0.506734i	$-0.830853\pi$
$757$	−47.4391	−1.72420	−0.862102	+	0.506734i	$0.830853\pi$
$758$	30.2258	1.09785
$759$	−80.4182	−2.91900
$760$	7.89096	0.286235
$761$	−25.5600	−0.926551	−0.463275	−	0.886214i	$-0.653326\pi$
$761$	−25.5600	−0.926551	−0.463275	+	0.886214i	$0.653326\pi$
$762$	−52.0043	−1.88392
$763$	19.6276	0.710568
$764$	5.53783	0.200352
$765$	50.8980	1.84022
$766$	−13.2128	−0.477397
$767$	−1.02589	−0.0370427
$768$	−2.56761	−0.0926507
$769$	−6.95306	−0.250734	−0.125367	−	0.992110i	$-0.540011\pi$
$769$	−6.95306	−0.250734	−0.125367	+	0.992110i	$0.540011\pi$
$770$	25.6331	0.923753
$771$	−43.7956	−1.57726
$772$	−1.47356	−0.0530347
$773$	23.2365	0.835759	0.417879	−	0.908503i	$-0.362773\pi$
$773$	23.2365	0.835759	0.417879	+	0.908503i	$0.362773\pi$
$774$	−15.1527	−0.544651
$775$	−26.9175	−0.966907
$776$	−5.35401	−0.192198
$777$	17.8221	0.639364
$778$	−15.9504	−0.571850
$779$	−14.1619	−0.507403
$780$	−14.4433	−0.517152
$781$	−2.23142	−0.0798463
$782$	−20.1920	−0.722064
$783$	7.69265	0.274913
$784$	−5.63939	−0.201407
$785$	−50.8028	−1.81323
$786$	−16.1508	−0.576079
$787$	40.2452	1.43459	0.717293	−	0.696772i	$-0.245381\pi$
$787$	40.2452	1.43459	0.717293	+	0.696772i	$0.245381\pi$
$788$	2.79678	0.0996312
$789$	−28.0581	−0.998893
$790$	13.4370	0.478069
$791$	−11.4689	−0.407787
$792$	−19.2505	−0.684035
$793$	2.85795	0.101489
$794$	19.6598	0.697700
$795$	−131.450	−4.66204
$796$	22.9527	0.813537
$797$	46.8988	1.66124	0.830620	−	0.556840i	$-0.187986\pi$
$797$	46.8988	1.66124	0.830620	+	0.556840i	$0.187986\pi$
$798$	5.76261	0.203994
$799$	5.26865	0.186391
$800$	−11.8195	−0.417881
$801$	35.7848	1.26439
$802$	4.02940	0.142283
$803$	−21.0553	−0.743026
$804$	27.6007	0.973400
$805$	−27.9620	−0.985532
$806$	3.12369	0.110027
$807$	−11.5696	−0.407270
$808$	2.48909	0.0875658
$809$	−25.1413	−0.883922	−0.441961	−	0.897034i	$-0.645717\pi$
$809$	−25.1413	−0.883922	−0.441961	+	0.897034i	$0.645717\pi$
$810$	28.1787	0.990098
$811$	37.9832	1.33377	0.666885	−	0.745161i	$-0.267627\pi$
$811$	37.9832	1.33377	0.666885	+	0.745161i	$0.267627\pi$
$812$	5.89701	0.206945
$813$	−68.6705	−2.40838
$814$	−31.8854	−1.11758
$815$	−34.7964	−1.21887
$816$	−8.86977	−0.310504
$817$	−8.11522	−0.283916
$818$	−32.1461	−1.12396
$819$	−5.74790	−0.200848
$820$	30.1859	1.05414
$821$	45.2063	1.57771	0.788856	−	0.614578i	$-0.210674\pi$
$821$	45.2063	1.57771	0.788856	+	0.614578i	$0.210674\pi$
$822$	6.51957	0.227396
$823$	−41.5323	−1.44773	−0.723863	−	0.689944i	$-0.757635\pi$
$823$	−41.5323	−1.44773	−0.723863	+	0.689944i	$0.757635\pi$
$824$	19.7312	0.687369
$825$	−162.613	−5.66147
$826$	−0.872442	−0.0303561
$827$	22.2401	0.773365	0.386683	−	0.922213i	$-0.373621\pi$
$827$	22.2401	0.773365	0.386683	+	0.922213i	$0.373621\pi$
$828$	20.9995	0.729782
$829$	−16.2307	−0.563716	−0.281858	−	0.959456i	$-0.590951\pi$
$829$	−16.2307	−0.563716	−0.281858	+	0.959456i	$0.590951\pi$
$830$	−41.6831	−1.44684
$831$	−82.5797	−2.86466
$832$	1.37161	0.0475520
$833$	−19.4812	−0.674983
$834$	−55.7735	−1.93128
$835$	−64.2136	−2.22220
$836$	−10.3099	−0.356574
$837$	3.46536	0.119780
$838$	21.7677	0.751954
$839$	53.4480	1.84523	0.922615	−	0.385722i	$-0.126048\pi$
$839$	53.4480	1.84523	0.922615	+	0.385722i	$0.126048\pi$
$840$	−12.2829	−0.423801
$841$	−3.44175	−0.118681
$842$	39.9504	1.37678
$843$	30.4303	1.04808
$844$	2.73130	0.0940151
$845$	−45.5995	−1.56867
$846$	−5.47934	−0.188384
$847$	−20.6597	−0.709877
$848$	12.4831	0.428673
$849$	50.3228	1.72707
$850$	−40.8301	−1.40046
$851$	34.7824	1.19233
$852$	1.06925	0.0366320
$853$	24.3991	0.835409	0.417704	−	0.908583i	$-0.362835\pi$
$853$	24.3991	0.835409	0.417704	+	0.908583i	$0.362835\pi$
$854$	2.43047	0.0831689
$855$	−28.3493	−0.969525
$856$	−9.20697	−0.314688
$857$	−13.2759	−0.453497	−0.226748	−	0.973953i	$-0.572809\pi$
$857$	−13.2759	−0.453497	−0.226748	+	0.973953i	$0.572809\pi$
$858$	18.8707	0.644236
$859$	6.04232	0.206161	0.103081	−	0.994673i	$-0.467130\pi$
$859$	6.04232	0.206161	0.103081	+	0.994673i	$0.467130\pi$
$860$	17.2975	0.589839
$861$	22.0441	0.751262
$862$	10.9470	0.372856
$863$	−22.4278	−0.763451	−0.381726	−	0.924276i	$-0.624670\pi$
$863$	−22.4278	−0.763451	−0.381726	+	0.924276i	$0.624670\pi$
$864$	1.52163	0.0517670
$865$	43.7504	1.48756
$866$	33.7324	1.14627
$867$	13.0089	0.441807
$868$	2.65646	0.0901663
$869$	−17.5560	−0.595548
$870$	−53.2354	−1.80485
$871$	−14.7442	−0.499588
$872$	16.8268	0.569828
$873$	19.2350	0.651005
$874$	11.2466	0.380421
$875$	−32.6229	−1.10286
$876$	10.0893	0.340887
$877$	41.6550	1.40659	0.703295	−	0.710898i	$-0.251711\pi$
$877$	41.6550	1.40659	0.703295	+	0.710898i	$0.251711\pi$
$878$	−18.0866	−0.610394
$879$	45.5678	1.53696
$880$	21.9753	0.740788
$881$	−28.2007	−0.950104	−0.475052	−	0.879958i	$-0.657571\pi$
$881$	−28.2007	−0.950104	−0.475052	+	0.879958i	$0.657571\pi$
$882$	20.2602	0.682197
$883$	26.2471	0.883287	0.441643	−	0.897191i	$-0.354396\pi$
$883$	26.2471	0.883287	0.441643	+	0.897191i	$0.354396\pi$
$884$	4.73820	0.159363
$885$	7.87599	0.264749
$886$	18.1565	0.609981
$887$	−57.9214	−1.94481	−0.972406	−	0.233297i	$-0.925049\pi$
$887$	−57.9214	−1.94481	−0.972406	+	0.233297i	$0.925049\pi$
$888$	15.2789	0.512727
$889$	23.6252	0.792365
$890$	−40.8500	−1.36930
$891$	−36.8166	−1.23340
$892$	21.2213	0.710543
$893$	−2.93454	−0.0982007
$894$	5.85451	0.195804
$895$	−9.75279	−0.326000
$896$	1.16645	0.0389684
$897$	−20.5852	−0.687321
$898$	−16.1679	−0.539530
$899$	11.5134	0.383993
$900$	42.4629	1.41543
$901$	43.1228	1.43663
$902$	−39.4390	−1.31318
$903$	12.6320	0.420367
$904$	−9.83229	−0.327017
$905$	36.4253	1.21082
$906$	−39.4831	−1.31174
$907$	−25.6981	−0.853291	−0.426645	−	0.904419i	$-0.640305\pi$
$907$	−25.6981	−0.853291	−0.426645	+	0.904419i	$0.640305\pi$
$908$	−25.1937	−0.836082
$909$	−8.94236	−0.296599
$910$	6.56150	0.217512
$911$	−39.8075	−1.31888	−0.659440	−	0.751757i	$-0.729207\pi$
$911$	−39.8075	−1.31888	−0.659440	+	0.751757i	$0.729207\pi$
$912$	4.94030	0.163590
$913$	54.4606	1.80238
$914$	−5.71213	−0.188941
$915$	−21.9411	−0.725351
$916$	−8.06393	−0.266440
$917$	7.33720	0.242296
$918$	5.25646	0.173489
$919$	−34.6989	−1.14461	−0.572305	−	0.820041i	$-0.693951\pi$
$919$	−34.6989	−1.14461	−0.572305	+	0.820041i	$0.693951\pi$
$920$	−23.9719	−0.790330
$921$	−50.9877	−1.68010
$922$	−20.1981	−0.665190
$923$	−0.571192	−0.0188010
$924$	16.0481	0.527945
$925$	70.3333	2.31255
$926$	−28.6624	−0.941904
$927$	−70.8868	−2.32823
$928$	5.05552	0.165955
$929$	1.69260	0.0555323	0.0277661	−	0.999614i	$-0.491161\pi$
$929$	1.69260	0.0555323	0.0277661	+	0.999614i	$0.491161\pi$
$930$	−23.9813	−0.786378
$931$	10.8507	0.355616
$932$	6.81229	0.223144
$933$	−77.1175	−2.52471
$934$	−10.8578	−0.355279
$935$	75.9133	2.48263
$936$	−4.92768	−0.161066
$937$	−11.6411	−0.380299	−0.190150	−	0.981755i	$-0.560897\pi$
$937$	−11.6411	−0.380299	−0.190150	+	0.981755i	$0.560897\pi$
$938$	−12.5388	−0.409407
$939$	−39.9629	−1.30414
$940$	6.25493	0.204013
$941$	43.5174	1.41863	0.709314	−	0.704893i	$-0.249005\pi$
$941$	43.5174	1.41863	0.709314	+	0.704893i	$0.249005\pi$
$942$	−31.8061	−1.03630
$943$	43.0223	1.40100
$944$	−0.747945	−0.0243436
$945$	7.27918	0.236792
$946$	−22.5998	−0.734784
$947$	−24.6521	−0.801086	−0.400543	−	0.916278i	$-0.631178\pi$
$947$	−24.6521	−0.801086	−0.400543	+	0.916278i	$0.631178\pi$
$948$	8.41253	0.273226
$949$	−5.38969	−0.174957
$950$	22.7416	0.737836
$951$	53.8349	1.74572
$952$	4.02948	0.130596
$953$	40.0782	1.29826	0.649130	−	0.760677i	$-0.275133\pi$
$953$	40.0782	1.29826	0.649130	+	0.760677i	$0.275133\pi$
$954$	−44.8473	−1.45198
$955$	22.7115	0.734927
$956$	−18.8312	−0.609044
$957$	69.5542	2.24837
$958$	−32.9143	−1.06341
$959$	−2.96180	−0.0956416
$960$	−10.5302	−0.339860
$961$	−25.8135	−0.832693
$962$	−8.16195	−0.263152
$963$	33.0772	1.06590
$964$	−7.75562	−0.249792
$965$	−6.04332	−0.194541
$966$	−17.5062	−0.563253
$967$	12.5131	0.402394	0.201197	−	0.979551i	$-0.435517\pi$
$967$	12.5131	0.402394	0.201197	+	0.979551i	$0.435517\pi$
$968$	−17.7116	−0.569273
$969$	17.0662	0.548244
$970$	−21.9576	−0.705017
$971$	46.5064	1.49246	0.746230	−	0.665688i	$-0.231862\pi$
$971$	46.5064	1.49246	0.746230	+	0.665688i	$0.231862\pi$
$972$	22.2067	0.712281
$973$	25.3376	0.812286
$974$	−28.9242	−0.926790
$975$	−41.6253	−1.33308
$976$	2.08364	0.0666958
$977$	−1.94368	−0.0621839	−0.0310920	−	0.999517i	$-0.509898\pi$
$977$	−1.94368	−0.0621839	−0.0310920	+	0.999517i	$0.509898\pi$
$978$	−21.7850	−0.696608
$979$	53.3722	1.70578
$980$	−23.1280	−0.738797
$981$	−60.4524	−1.93010
$982$	11.7035	0.373473
$983$	−13.9534	−0.445044	−0.222522	−	0.974928i	$-0.571429\pi$
$983$	−13.9534	−0.445044	−0.222522	+	0.974928i	$0.571429\pi$
$984$	18.8985	0.602461
$985$	11.4700	0.365466
$986$	17.4642	0.556173
$987$	4.56785	0.145396
$988$	−2.63909	−0.0839607
$989$	24.6532	0.783925
$990$	−78.9491	−2.50917
$991$	−7.85326	−0.249467	−0.124733	−	0.992190i	$-0.539808\pi$
$991$	−7.85326	−0.249467	−0.124733	+	0.992190i	$0.539808\pi$
$992$	2.27739	0.0723072
$993$	−33.8045	−1.07275
$994$	−0.485756	−0.0154072
$995$	94.1326	2.98420
$996$	−26.0965	−0.826900
$997$	−45.7457	−1.44878	−0.724391	−	0.689389i	$-0.757879\pi$
$997$	−45.7457	−1.44878	−0.724391	+	0.689389i	$0.757879\pi$
$998$	−21.3828	−0.676861
$999$	−9.05469	−0.286478

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4022.2.a.e.1.6	✓	46

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4022.2.a.e.1.6	✓	46	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:	\( N \)	\(=\)	\( 4022 = 2 \cdot 2011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4022.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.56761 q^{3} +1.00000 q^{4} +4.10115 q^{5} +2.56761 q^{6} -1.16645 q^{7} -1.00000 q^{8} +3.59263 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.56761 q^{3} +1.00000 q^{4} +4.10115 q^{5} +2.56761 q^{6} -1.16645 q^{7} -1.00000 q^{8} +3.59263 q^{9} -4.10115 q^{10} +5.35832 q^{11} -2.56761 q^{12} +1.37161 q^{13} +1.16645 q^{14} -10.5302 q^{15} +1.00000 q^{16} +3.45448 q^{17} -3.59263 q^{18} -1.92408 q^{19} +4.10115 q^{20} +2.99499 q^{21} -5.35832 q^{22} +5.84516 q^{23} +2.56761 q^{24} +11.8195 q^{25} -1.37161 q^{26} -1.52163 q^{27} -1.16645 q^{28} -5.05552 q^{29} +10.5302 q^{30} -2.27739 q^{31} -1.00000 q^{32} -13.7581 q^{33} -3.45448 q^{34} -4.78379 q^{35} +3.59263 q^{36} +5.95064 q^{37} +1.92408 q^{38} -3.52176 q^{39} -4.10115 q^{40} +7.36033 q^{41} -2.99499 q^{42} +4.21771 q^{43} +5.35832 q^{44} +14.7339 q^{45} -5.84516 q^{46} +1.52516 q^{47} -2.56761 q^{48} -5.63939 q^{49} -11.8195 q^{50} -8.86977 q^{51} +1.37161 q^{52} +12.4831 q^{53} +1.52163 q^{54} +21.9753 q^{55} +1.16645 q^{56} +4.94030 q^{57} +5.05552 q^{58} -0.747945 q^{59} -10.5302 q^{60} +2.08364 q^{61} +2.27739 q^{62} -4.19062 q^{63} +1.00000 q^{64} +5.62518 q^{65} +13.7581 q^{66} -10.7495 q^{67} +3.45448 q^{68} -15.0081 q^{69} +4.78379 q^{70} -0.416439 q^{71} -3.59263 q^{72} -3.92946 q^{73} -5.95064 q^{74} -30.3478 q^{75} -1.92408 q^{76} -6.25022 q^{77} +3.52176 q^{78} -3.27640 q^{79} +4.10115 q^{80} -6.87091 q^{81} -7.36033 q^{82} +10.1637 q^{83} +2.99499 q^{84} +14.1674 q^{85} -4.21771 q^{86} +12.9806 q^{87} -5.35832 q^{88} +9.96062 q^{89} -14.7339 q^{90} -1.59991 q^{91} +5.84516 q^{92} +5.84745 q^{93} -1.52516 q^{94} -7.89096 q^{95} +2.56761 q^{96} +5.35401 q^{97} +5.63939 q^{98} +19.2505 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 46 q - 46 q^{2} + 8 q^{3} + 46 q^{4} + 14 q^{5} - 8 q^{6} + 28 q^{7} - 46 q^{8} + 58 q^{9}+O(q^{10}) \) 46 * q - 46 * q^2 + 8 * q^3 + 46 * q^4 + 14 * q^5 - 8 * q^6 + 28 * q^7 - 46 * q^8 + 58 * q^9	\( 46 q - 46 q^{2} + 8 q^{3} + 46 q^{4} + 14 q^{5} - 8 q^{6} + 28 q^{7} - 46 q^{8} + 58 q^{9} - 14 q^{10} - 6 q^{11} + 8 q^{12} + 37 q^{13} - 28 q^{14} + 9 q^{15} + 46 q^{16} + 6 q^{17} - 58 q^{18} + 18 q^{19} + 14 q^{20} + 19 q^{21} + 6 q^{22} - 4 q^{23} - 8 q^{24} + 86 q^{25} - 37 q^{26} + 32 q^{27} + 28 q^{28} + 15 q^{29} - 9 q^{30} + 18 q^{31} - 46 q^{32} + 37 q^{33} - 6 q^{34} - 2 q^{35} + 58 q^{36} + 74 q^{37} - 18 q^{38} - 3 q^{39} - 14 q^{40} - 18 q^{41} - 19 q^{42} + 25 q^{43} - 6 q^{44} + 94 q^{45} + 4 q^{46} + 18 q^{47} + 8 q^{48} + 92 q^{49} - 86 q^{50} - 10 q^{51} + 37 q^{52} + 17 q^{53} - 32 q^{54} + 37 q^{55} - 28 q^{56} + 43 q^{57} - 15 q^{58} - 24 q^{59} + 9 q^{60} + 46 q^{61} - 18 q^{62} + 80 q^{63} + 46 q^{64} + 24 q^{65} - 37 q^{66} + 61 q^{67} + 6 q^{68} + 59 q^{69} + 2 q^{70} - 8 q^{71} - 58 q^{72} + 101 q^{73} - 74 q^{74} + 34 q^{75} + 18 q^{76} + 40 q^{77} + 3 q^{78} + 9 q^{79} + 14 q^{80} + 58 q^{81} + 18 q^{82} + 18 q^{83} + 19 q^{84} + 60 q^{85} - 25 q^{86} + 20 q^{87} + 6 q^{88} - 25 q^{89} - 94 q^{90} + 51 q^{91} - 4 q^{92} + 63 q^{93} - 18 q^{94} - 31 q^{95} - 8 q^{96} + 76 q^{97} - 92 q^{98} + 21 q^{99}+O(q^{100}) \) 46 * q - 46 * q^2 + 8 * q^3 + 46 * q^4 + 14 * q^5 - 8 * q^6 + 28 * q^7 - 46 * q^8 + 58 * q^9 - 14 * q^10 - 6 * q^11 + 8 * q^12 + 37 * q^13 - 28 * q^14 + 9 * q^15 + 46 * q^16 + 6 * q^17 - 58 * q^18 + 18 * q^19 + 14 * q^20 + 19 * q^21 + 6 * q^22 - 4 * q^23 - 8 * q^24 + 86 * q^25 - 37 * q^26 + 32 * q^27 + 28 * q^28 + 15 * q^29 - 9 * q^30 + 18 * q^31 - 46 * q^32 + 37 * q^33 - 6 * q^34 - 2 * q^35 + 58 * q^36 + 74 * q^37 - 18 * q^38 - 3 * q^39 - 14 * q^40 - 18 * q^41 - 19 * q^42 + 25 * q^43 - 6 * q^44 + 94 * q^45 + 4 * q^46 + 18 * q^47 + 8 * q^48 + 92 * q^49 - 86 * q^50 - 10 * q^51 + 37 * q^52 + 17 * q^53 - 32 * q^54 + 37 * q^55 - 28 * q^56 + 43 * q^57 - 15 * q^58 - 24 * q^59 + 9 * q^60 + 46 * q^61 - 18 * q^62 + 80 * q^63 + 46 * q^64 + 24 * q^65 - 37 * q^66 + 61 * q^67 + 6 * q^68 + 59 * q^69 + 2 * q^70 - 8 * q^71 - 58 * q^72 + 101 * q^73 - 74 * q^74 + 34 * q^75 + 18 * q^76 + 40 * q^77 + 3 * q^78 + 9 * q^79 + 14 * q^80 + 58 * q^81 + 18 * q^82 + 18 * q^83 + 19 * q^84 + 60 * q^85 - 25 * q^86 + 20 * q^87 + 6 * q^88 - 25 * q^89 - 94 * q^90 + 51 * q^91 - 4 * q^92 + 63 * q^93 - 18 * q^94 - 31 * q^95 - 8 * q^96 + 76 * q^97 - 92 * q^98 + 21 * q^99

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