LMFDB - Embedded newform 4010.2.a.o.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4010,2,Mod(1,4010)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4010, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4010.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4010 = 2 \cdot 5 \cdot 401 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4010.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:	$32.0200112105$
Analytic rank:	$0$
Dimension:	$22$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Character	$\chi$	$=$	4010.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.85051 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.85051 q^{6} -3.61831 q^{7} +1.00000 q^{8} +0.424381 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.85051 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.85051 q^{6} -3.61831 q^{7} +1.00000 q^{8} +0.424381 q^{9} -1.00000 q^{10} -4.59294 q^{11} -1.85051 q^{12} -5.49546 q^{13} -3.61831 q^{14} +1.85051 q^{15} +1.00000 q^{16} -7.18108 q^{17} +0.424381 q^{18} -8.33365 q^{19} -1.00000 q^{20} +6.69571 q^{21} -4.59294 q^{22} +2.32286 q^{23} -1.85051 q^{24} +1.00000 q^{25} -5.49546 q^{26} +4.76620 q^{27} -3.61831 q^{28} -0.581970 q^{29} +1.85051 q^{30} +2.15710 q^{31} +1.00000 q^{32} +8.49927 q^{33} -7.18108 q^{34} +3.61831 q^{35} +0.424381 q^{36} +0.265192 q^{37} -8.33365 q^{38} +10.1694 q^{39} -1.00000 q^{40} -1.58892 q^{41} +6.69571 q^{42} +9.22858 q^{43} -4.59294 q^{44} -0.424381 q^{45} +2.32286 q^{46} +6.13655 q^{47} -1.85051 q^{48} +6.09217 q^{49} +1.00000 q^{50} +13.2886 q^{51} -5.49546 q^{52} +8.25346 q^{53} +4.76620 q^{54} +4.59294 q^{55} -3.61831 q^{56} +15.4215 q^{57} -0.581970 q^{58} -0.454039 q^{59} +1.85051 q^{60} +1.76150 q^{61} +2.15710 q^{62} -1.53554 q^{63} +1.00000 q^{64} +5.49546 q^{65} +8.49927 q^{66} -5.09275 q^{67} -7.18108 q^{68} -4.29847 q^{69} +3.61831 q^{70} -12.0315 q^{71} +0.424381 q^{72} -6.51022 q^{73} +0.265192 q^{74} -1.85051 q^{75} -8.33365 q^{76} +16.6187 q^{77} +10.1694 q^{78} -15.9616 q^{79} -1.00000 q^{80} -10.0930 q^{81} -1.58892 q^{82} -0.411030 q^{83} +6.69571 q^{84} +7.18108 q^{85} +9.22858 q^{86} +1.07694 q^{87} -4.59294 q^{88} -3.77783 q^{89} -0.424381 q^{90} +19.8843 q^{91} +2.32286 q^{92} -3.99173 q^{93} +6.13655 q^{94} +8.33365 q^{95} -1.85051 q^{96} +11.9192 q^{97} +6.09217 q^{98} -1.94916 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 22 q^{2} + 2 q^{3} + 22 q^{4} - 22 q^{5} + 2 q^{6} + 13 q^{7} + 22 q^{8} + 32 q^{9}+O(q^{10}) $ 22 * q + 22 * q^2 + 2 * q^3 + 22 * q^4 - 22 * q^5 + 2 * q^6 + 13 * q^7 + 22 * q^8 + 32 * q^9	\( 22 q + 22 q^{2} + 2 q^{3} + 22 q^{4} - 22 q^{5} + 2 q^{6} + 13 q^{7} + 22 q^{8} + 32 q^{9} - 22 q^{10} - 3 q^{11} + 2 q^{12} + 6 q^{13} + 13 q^{14} - 2 q^{15} + 22 q^{16} + 17 q^{17} + 32 q^{18} + 13 q^{19} - 22 q^{20} + 16 q^{21} - 3 q^{22} + 19 q^{23} + 2 q^{24} + 22 q^{25} + 6 q^{26} + 14 q^{27} + 13 q^{28} + 14 q^{29} - 2 q^{30} + 13 q^{31} + 22 q^{32} + 12 q^{33} + 17 q^{34} - 13 q^{35} + 32 q^{36} + 35 q^{37} + 13 q^{38} + 30 q^{39} - 22 q^{40} - 5 q^{41} + 16 q^{42} + 19 q^{43} - 3 q^{44} - 32 q^{45} + 19 q^{46} + 29 q^{47} + 2 q^{48} + 61 q^{49} + 22 q^{50} + q^{51} + 6 q^{52} + 29 q^{53} + 14 q^{54} + 3 q^{55} + 13 q^{56} + 33 q^{57} + 14 q^{58} - 4 q^{59} - 2 q^{60} + 20 q^{61} + 13 q^{62} + 50 q^{63} + 22 q^{64} - 6 q^{65} + 12 q^{66} + 48 q^{67} + 17 q^{68} + 19 q^{69} - 13 q^{70} + 2 q^{71} + 32 q^{72} + 16 q^{73} + 35 q^{74} + 2 q^{75} + 13 q^{76} + 53 q^{77} + 30 q^{78} + 29 q^{79} - 22 q^{80} + 54 q^{81} - 5 q^{82} + 13 q^{83} + 16 q^{84} - 17 q^{85} + 19 q^{86} + 56 q^{87} - 3 q^{88} + 20 q^{89} - 32 q^{90} + 42 q^{91} + 19 q^{92} + 50 q^{93} + 29 q^{94} - 13 q^{95} + 2 q^{96} + 36 q^{97} + 61 q^{98} - q^{99}+O(q^{100}) \) 22 * q + 22 * q^2 + 2 * q^3 + 22 * q^4 - 22 * q^5 + 2 * q^6 + 13 * q^7 + 22 * q^8 + 32 * q^9 - 22 * q^10 - 3 * q^11 + 2 * q^12 + 6 * q^13 + 13 * q^14 - 2 * q^15 + 22 * q^16 + 17 * q^17 + 32 * q^18 + 13 * q^19 - 22 * q^20 + 16 * q^21 - 3 * q^22 + 19 * q^23 + 2 * q^24 + 22 * q^25 + 6 * q^26 + 14 * q^27 + 13 * q^28 + 14 * q^29 - 2 * q^30 + 13 * q^31 + 22 * q^32 + 12 * q^33 + 17 * q^34 - 13 * q^35 + 32 * q^36 + 35 * q^37 + 13 * q^38 + 30 * q^39 - 22 * q^40 - 5 * q^41 + 16 * q^42 + 19 * q^43 - 3 * q^44 - 32 * q^45 + 19 * q^46 + 29 * q^47 + 2 * q^48 + 61 * q^49 + 22 * q^50 + q^51 + 6 * q^52 + 29 * q^53 + 14 * q^54 + 3 * q^55 + 13 * q^56 + 33 * q^57 + 14 * q^58 - 4 * q^59 - 2 * q^60 + 20 * q^61 + 13 * q^62 + 50 * q^63 + 22 * q^64 - 6 * q^65 + 12 * q^66 + 48 * q^67 + 17 * q^68 + 19 * q^69 - 13 * q^70 + 2 * q^71 + 32 * q^72 + 16 * q^73 + 35 * q^74 + 2 * q^75 + 13 * q^76 + 53 * q^77 + 30 * q^78 + 29 * q^79 - 22 * q^80 + 54 * q^81 - 5 * q^82 + 13 * q^83 + 16 * q^84 - 17 * q^85 + 19 * q^86 + 56 * q^87 - 3 * q^88 + 20 * q^89 - 32 * q^90 + 42 * q^91 + 19 * q^92 + 50 * q^93 + 29 * q^94 - 13 * q^95 + 2 * q^96 + 36 * q^97 + 61 * q^98 - 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
$3$	−1.85051	−1.06839	−0.534196	−	0.845361i	$-0.679385\pi$
$3$	−1.85051	−1.06839	−0.534196	+	0.845361i	$0.679385\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−1.85051	−0.755467
$7$	−3.61831	−1.36759	−0.683797	−	0.729673i	$-0.739672\pi$
$7$	−3.61831	−1.36759	−0.683797	+	0.729673i	$0.739672\pi$
$8$	1.00000	0.353553
$9$	0.424381	0.141460
$10$	−1.00000	−0.316228
$11$	−4.59294	−1.38482	−0.692412	−	0.721503i	$-0.743452\pi$
$11$	−4.59294	−1.38482	−0.692412	+	0.721503i	$0.743452\pi$
$12$	−1.85051	−0.534196
$13$	−5.49546	−1.52417	−0.762083	−	0.647479i	$-0.775823\pi$
$13$	−5.49546	−1.52417	−0.762083	+	0.647479i	$0.775823\pi$
$14$	−3.61831	−0.967034
$15$	1.85051	0.477799
$16$	1.00000	0.250000
$17$	−7.18108	−1.74167	−0.870833	−	0.491578i	$-0.836420\pi$
$17$	−7.18108	−1.74167	−0.870833	+	0.491578i	$0.836420\pi$
$18$	0.424381	0.100028
$19$	−8.33365	−1.91187	−0.955935	−	0.293577i	$-0.905154\pi$
$19$	−8.33365	−1.91187	−0.955935	+	0.293577i	$0.905154\pi$
$20$	−1.00000	−0.223607
$21$	6.69571	1.46112
$22$	−4.59294	−0.979218
$23$	2.32286	0.484349	0.242175	−	0.970233i	$-0.422139\pi$
$23$	2.32286	0.484349	0.242175	+	0.970233i	$0.422139\pi$
$24$	−1.85051	−0.377733
$25$	1.00000	0.200000
$26$	−5.49546	−1.07775
$27$	4.76620	0.917256
$28$	−3.61831	−0.683797
$29$	−0.581970	−0.108069	−0.0540346	−	0.998539i	$-0.517208\pi$
$29$	−0.581970	−0.108069	−0.0540346	+	0.998539i	$0.517208\pi$
$30$	1.85051	0.337855
$31$	2.15710	0.387426	0.193713	−	0.981058i	$-0.437947\pi$
$31$	2.15710	0.387426	0.193713	+	0.981058i	$0.437947\pi$
$32$	1.00000	0.176777
$33$	8.49927	1.47953
$34$	−7.18108	−1.23154
$35$	3.61831	0.611606
$36$	0.424381	0.0707302
$37$	0.265192	0.0435974	0.0217987	−	0.999762i	$-0.493061\pi$
$37$	0.265192	0.0435974	0.0217987	+	0.999762i	$0.493061\pi$
$38$	−8.33365	−1.35190
$39$	10.1694	1.62841
$40$	−1.00000	−0.158114
$41$	−1.58892	−0.248147	−0.124074	−	0.992273i	$-0.539596\pi$
$41$	−1.58892	−0.248147	−0.124074	+	0.992273i	$0.539596\pi$
$42$	6.69571	1.03317
$43$	9.22858	1.40735	0.703673	−	0.710524i	$-0.251542\pi$
$43$	9.22858	1.40735	0.703673	+	0.710524i	$0.251542\pi$
$44$	−4.59294	−0.692412
$45$	−0.424381	−0.0632631
$46$	2.32286	0.342487
$47$	6.13655	0.895108	0.447554	−	0.894257i	$-0.352295\pi$
$47$	6.13655	0.895108	0.447554	+	0.894257i	$0.352295\pi$
$48$	−1.85051	−0.267098
$49$	6.09217	0.870311
$50$	1.00000	0.141421
$51$	13.2886	1.86078
$52$	−5.49546	−0.762083
$53$	8.25346	1.13370	0.566850	−	0.823821i	$-0.308162\pi$
$53$	8.25346	1.13370	0.566850	+	0.823821i	$0.308162\pi$
$54$	4.76620	0.648598
$55$	4.59294	0.619312
$56$	−3.61831	−0.483517
$57$	15.4215	2.04263
$58$	−0.581970	−0.0764164
$59$	−0.454039	−0.0591108	−0.0295554	−	0.999563i	$-0.509409\pi$
$59$	−0.454039	−0.0591108	−0.0295554	+	0.999563i	$0.509409\pi$
$60$	1.85051	0.238900
$61$	1.76150	0.225536	0.112768	−	0.993621i	$-0.464028\pi$
$61$	1.76150	0.225536	0.112768	+	0.993621i	$0.464028\pi$
$62$	2.15710	0.273952
$63$	−1.53554	−0.193460
$64$	1.00000	0.125000
$65$	5.49546	0.681628
$66$	8.49927	1.04619
$67$	−5.09275	−0.622179	−0.311089	−	0.950381i	$-0.600694\pi$
$67$	−5.09275	−0.622179	−0.311089	+	0.950381i	$0.600694\pi$
$68$	−7.18108	−0.870833
$69$	−4.29847	−0.517475
$70$	3.61831	0.432471
$71$	−12.0315	−1.42788	−0.713940	−	0.700207i	$-0.753091\pi$
$71$	−12.0315	−1.42788	−0.713940	+	0.700207i	$0.753091\pi$
$72$	0.424381	0.0500138
$73$	−6.51022	−0.761963	−0.380982	−	0.924583i	$-0.624414\pi$
$73$	−6.51022	−0.761963	−0.380982	+	0.924583i	$0.624414\pi$
$74$	0.265192	0.0308280
$75$	−1.85051	−0.213678
$76$	−8.33365	−0.955935
$77$	16.6187	1.89387
$78$	10.1694	1.15146
$79$	−15.9616	−1.79582	−0.897909	−	0.440182i	$-0.854914\pi$
$79$	−15.9616	−1.79582	−0.897909	+	0.440182i	$0.854914\pi$
$80$	−1.00000	−0.111803
$81$	−10.0930	−1.12145
$82$	−1.58892	−0.175466
$83$	−0.411030	−0.0451164	−0.0225582	−	0.999746i	$-0.507181\pi$
$83$	−0.411030	−0.0451164	−0.0225582	+	0.999746i	$0.507181\pi$
$84$	6.69571	0.730562
$85$	7.18108	0.778897
$86$	9.22858	0.995143
$87$	1.07694	0.115460
$88$	−4.59294	−0.489609
$89$	−3.77783	−0.400449	−0.200225	−	0.979750i	$-0.564167\pi$
$89$	−3.77783	−0.400449	−0.200225	+	0.979750i	$0.564167\pi$
$90$	−0.424381	−0.0447337
$91$	19.8843	2.08444
$92$	2.32286	0.242175
$93$	−3.99173	−0.413923
$94$	6.13655	0.632937
$95$	8.33365	0.855015
$96$	−1.85051	−0.188867
$97$	11.9192	1.21021	0.605106	−	0.796145i	$-0.293131\pi$
$97$	11.9192	1.21021	0.605106	+	0.796145i	$0.293131\pi$
$98$	6.09217	0.615403
$99$	−1.94916	−0.195898
$100$	1.00000	0.100000
$101$	−17.4273	−1.73408	−0.867039	−	0.498240i	$-0.833980\pi$
$101$	−17.4273	−1.73408	−0.867039	+	0.498240i	$0.833980\pi$
$102$	13.2886	1.31577
$103$	−9.39587	−0.925802	−0.462901	−	0.886410i	$-0.653192\pi$
$103$	−9.39587	−0.925802	−0.462901	+	0.886410i	$0.653192\pi$
$104$	−5.49546	−0.538874
$105$	−6.69571	−0.653435
$106$	8.25346	0.801647
$107$	−14.7124	−1.42230	−0.711150	−	0.703040i	$-0.751826\pi$
$107$	−14.7124	−1.42230	−0.711150	+	0.703040i	$0.751826\pi$
$108$	4.76620	0.458628
$109$	−1.86134	−0.178284	−0.0891420	−	0.996019i	$-0.528412\pi$
$109$	−1.86134	−0.178284	−0.0891420	+	0.996019i	$0.528412\pi$
$110$	4.59294	0.437920
$111$	−0.490741	−0.0465791
$112$	−3.61831	−0.341898
$113$	11.8353	1.11337	0.556684	−	0.830724i	$-0.312073\pi$
$113$	11.8353	1.11337	0.556684	+	0.830724i	$0.312073\pi$
$114$	15.4215	1.44435
$115$	−2.32286	−0.216608
$116$	−0.581970	−0.0540346
$117$	−2.33217	−0.215609
$118$	−0.454039	−0.0417977
$119$	25.9834	2.38189
$120$	1.85051	0.168928
$121$	10.0951	0.917735
$122$	1.76150	0.159478
$123$	2.94030	0.265118
$124$	2.15710	0.193713
$125$	−1.00000	−0.0894427
$126$	−1.53554	−0.136797
$127$	−11.0622	−0.981608	−0.490804	−	0.871270i	$-0.663297\pi$
$127$	−11.0622	−0.981608	−0.490804	+	0.871270i	$0.663297\pi$
$128$	1.00000	0.0883883
$129$	−17.0776	−1.50360
$130$	5.49546	0.481984
$131$	−19.7802	−1.72821	−0.864103	−	0.503315i	$-0.832114\pi$
$131$	−19.7802	−1.72821	−0.864103	+	0.503315i	$0.832114\pi$
$132$	8.49927	0.739767
$133$	30.1537	2.61466
$134$	−5.09275	−0.439947
$135$	−4.76620	−0.410210
$136$	−7.18108	−0.615772
$137$	20.9998	1.79414	0.897069	−	0.441890i	$-0.145692\pi$
$137$	20.9998	1.79414	0.897069	+	0.441890i	$0.145692\pi$
$138$	−4.29847	−0.365910
$139$	−3.49684	−0.296598	−0.148299	−	0.988943i	$-0.547380\pi$
$139$	−3.49684	−0.296598	−0.148299	+	0.988943i	$0.547380\pi$
$140$	3.61831	0.305803
$141$	−11.3557	−0.956325
$142$	−12.0315	−1.00966
$143$	25.2403	2.11070
$144$	0.424381	0.0353651
$145$	0.581970	0.0483300
$146$	−6.51022	−0.538789
$147$	−11.2736	−0.929833
$148$	0.265192	0.0217987
$149$	12.3597	1.01254	0.506272	−	0.862374i	$-0.331023\pi$
$149$	12.3597	1.01254	0.506272	+	0.862374i	$0.331023\pi$
$150$	−1.85051	−0.151093
$151$	13.7002	1.11491	0.557455	−	0.830207i	$-0.311778\pi$
$151$	13.7002	1.11491	0.557455	+	0.830207i	$0.311778\pi$
$152$	−8.33365	−0.675948
$153$	−3.04752	−0.246377
$154$	16.6187	1.33917
$155$	−2.15710	−0.173262
$156$	10.1694	0.814203
$157$	−11.7760	−0.939825	−0.469912	−	0.882713i	$-0.655714\pi$
$157$	−11.7760	−0.939825	−0.469912	+	0.882713i	$0.655714\pi$
$158$	−15.9616	−1.26983
$159$	−15.2731	−1.21124
$160$	−1.00000	−0.0790569
$161$	−8.40482	−0.662393
$162$	−10.0930	−0.792984
$163$	−8.87568	−0.695197	−0.347598	−	0.937644i	$-0.613003\pi$
$163$	−8.87568	−0.695197	−0.347598	+	0.937644i	$0.613003\pi$
$164$	−1.58892	−0.124074
$165$	−8.49927	−0.661667
$166$	−0.411030	−0.0319021
$167$	−2.66584	−0.206289	−0.103144	−	0.994666i	$-0.532890\pi$
$167$	−2.66584	−0.206289	−0.103144	+	0.994666i	$0.532890\pi$
$168$	6.69571	0.516586
$169$	17.2001	1.32308
$170$	7.18108	0.550763
$171$	−3.53665	−0.270454
$172$	9.22858	0.703673
$173$	0.476012	0.0361905	0.0180953	−	0.999836i	$-0.494240\pi$
$173$	0.476012	0.0361905	0.0180953	+	0.999836i	$0.494240\pi$
$174$	1.07694	0.0816426
$175$	−3.61831	−0.273519
$176$	−4.59294	−0.346206
$177$	0.840203	0.0631535
$178$	−3.77783	−0.283160
$179$	4.22392	0.315711	0.157855	−	0.987462i	$-0.449542\pi$
$179$	4.22392	0.315711	0.157855	+	0.987462i	$0.449542\pi$
$180$	−0.424381	−0.0316315
$181$	−10.2891	−0.764783	−0.382391	−	0.924000i	$-0.624899\pi$
$181$	−10.2891	−0.764783	−0.382391	+	0.924000i	$0.624899\pi$
$182$	19.8843	1.47392
$183$	−3.25966	−0.240961
$184$	2.32286	0.171243
$185$	−0.265192	−0.0194973
$186$	−3.99173	−0.292688
$187$	32.9822	2.41190
$188$	6.13655	0.447554
$189$	−17.2456	−1.25443
$190$	8.33365	0.604587
$191$	−17.0343	−1.23256	−0.616281	−	0.787526i	$-0.711361\pi$
$191$	−17.0343	−1.23256	−0.616281	+	0.787526i	$0.711361\pi$
$192$	−1.85051	−0.133549
$193$	−0.333107	−0.0239775	−0.0119888	−	0.999928i	$-0.503816\pi$
$193$	−0.333107	−0.0239775	−0.0119888	+	0.999928i	$0.503816\pi$
$194$	11.9192	0.855749
$195$	−10.1694	−0.728245
$196$	6.09217	0.435155
$197$	5.20471	0.370820	0.185410	−	0.982661i	$-0.440639\pi$
$197$	5.20471	0.370820	0.185410	+	0.982661i	$0.440639\pi$
$198$	−1.94916	−0.138521
$199$	−8.62992	−0.611759	−0.305879	−	0.952070i	$-0.598950\pi$
$199$	−8.62992	−0.611759	−0.305879	+	0.952070i	$0.598950\pi$
$200$	1.00000	0.0707107
$201$	9.42418	0.664731
$202$	−17.4273	−1.22618
$203$	2.10575	0.147795
$204$	13.2886	0.930391
$205$	1.58892	0.110975
$206$	−9.39587	−0.654641
$207$	0.985778	0.0685163
$208$	−5.49546	−0.381042
$209$	38.2759	2.64760
$210$	−6.69571	−0.462048
$211$	−15.1603	−1.04368	−0.521838	−	0.853045i	$-0.674753\pi$
$211$	−15.1603	−1.04368	−0.521838	+	0.853045i	$0.674753\pi$
$212$	8.25346	0.566850
$213$	22.2644	1.52553
$214$	−14.7124	−1.00572
$215$	−9.22858	−0.629384
$216$	4.76620	0.324299
$217$	−7.80506	−0.529842
$218$	−1.86134	−0.126066
$219$	12.0472	0.814075
$220$	4.59294	0.309656
$221$	39.4633	2.65459
$222$	−0.490741	−0.0329364
$223$	12.6131	0.844635	0.422317	−	0.906448i	$-0.361217\pi$
$223$	12.6131	0.844635	0.422317	+	0.906448i	$0.361217\pi$
$224$	−3.61831	−0.241759
$225$	0.424381	0.0282921
$226$	11.8353	0.787271
$227$	−8.09619	−0.537363	−0.268681	−	0.963229i	$-0.586588\pi$
$227$	−8.09619	−0.537363	−0.268681	+	0.963229i	$0.586588\pi$
$228$	15.4215	1.02131
$229$	9.61111	0.635120	0.317560	−	0.948238i	$-0.397136\pi$
$229$	9.61111	0.635120	0.317560	+	0.948238i	$0.397136\pi$
$230$	−2.32286	−0.153165
$231$	−30.7530	−2.02340
$232$	−0.581970	−0.0382082
$233$	17.2382	1.12932	0.564658	−	0.825325i	$-0.309008\pi$
$233$	17.2382	1.12932	0.564658	+	0.825325i	$0.309008\pi$
$234$	−2.33217	−0.152459
$235$	−6.13655	−0.400304
$236$	−0.454039	−0.0295554
$237$	29.5370	1.91864
$238$	25.9834	1.68425
$239$	−17.2681	−1.11698	−0.558490	−	0.829511i	$-0.688619\pi$
$239$	−17.2681	−1.11698	−0.558490	+	0.829511i	$0.688619\pi$
$240$	1.85051	0.119450
$241$	0.820430	0.0528485	0.0264243	−	0.999651i	$-0.491588\pi$
$241$	0.820430	0.0528485	0.0264243	+	0.999651i	$0.491588\pi$
$242$	10.0951	0.648937
$243$	4.37865	0.280891
$244$	1.76150	0.112768
$245$	−6.09217	−0.389215
$246$	2.94030	0.187467
$247$	45.7972	2.91401
$248$	2.15710	0.136976
$249$	0.760615	0.0482020
$250$	−1.00000	−0.0632456
$251$	−20.9512	−1.32243	−0.661213	−	0.750199i	$-0.729958\pi$
$251$	−20.9512	−1.32243	−0.661213	+	0.750199i	$0.729958\pi$
$252$	−1.53554	−0.0967302
$253$	−10.6687	−0.670738
$254$	−11.0622	−0.694102
$255$	−13.2886	−0.832167
$256$	1.00000	0.0625000
$257$	−16.1061	−1.00467	−0.502336	−	0.864673i	$-0.667526\pi$
$257$	−16.1061	−1.00467	−0.502336	+	0.864673i	$0.667526\pi$
$258$	−17.0776	−1.06320
$259$	−0.959549	−0.0596235
$260$	5.49546	0.340814
$261$	−0.246977	−0.0152875
$262$	−19.7802	−1.22203
$263$	−13.8883	−0.856387	−0.428194	−	0.903687i	$-0.640850\pi$
$263$	−13.8883	−0.856387	−0.428194	+	0.903687i	$0.640850\pi$
$264$	8.49927	0.523094
$265$	−8.25346	−0.507006
$266$	30.1537	1.84884
$267$	6.99091	0.427837
$268$	−5.09275	−0.311089
$269$	32.6056	1.98800	0.993998	−	0.109400i	$-0.0348928\pi$
$269$	32.6056	1.98800	0.993998	+	0.109400i	$0.0348928\pi$
$270$	−4.76620	−0.290062
$271$	−18.4311	−1.11961	−0.559806	−	0.828624i	$-0.689124\pi$
$271$	−18.4311	−1.11961	−0.559806	+	0.828624i	$0.689124\pi$
$272$	−7.18108	−0.435417
$273$	−36.7960	−2.22700
$274$	20.9998	1.26865
$275$	−4.59294	−0.276965
$276$	−4.29847	−0.258737
$277$	−18.7363	−1.12576	−0.562879	−	0.826540i	$-0.690306\pi$
$277$	−18.7363	−1.12576	−0.562879	+	0.826540i	$0.690306\pi$
$278$	−3.49684	−0.209727
$279$	0.915433	0.0548055
$280$	3.61831	0.216235
$281$	16.8001	1.00221	0.501104	−	0.865387i	$-0.332927\pi$
$281$	16.8001	1.00221	0.501104	+	0.865387i	$0.332927\pi$
$282$	−11.3557	−0.676224
$283$	−3.09470	−0.183961	−0.0919805	−	0.995761i	$-0.529320\pi$
$283$	−3.09470	−0.183961	−0.0919805	+	0.995761i	$0.529320\pi$
$284$	−12.0315	−0.713940
$285$	−15.4215	−0.913490
$286$	25.2403	1.49249
$287$	5.74919	0.339364
$288$	0.424381	0.0250069
$289$	34.5678	2.03340
$290$	0.581970	0.0341745
$291$	−22.0566	−1.29298
$292$	−6.51022	−0.380982
$293$	5.26165	0.307389	0.153694	−	0.988118i	$-0.450883\pi$
$293$	5.26165	0.307389	0.153694	+	0.988118i	$0.450883\pi$
$294$	−11.2736	−0.657491
$295$	0.454039	0.0264352
$296$	0.265192	0.0154140
$297$	−21.8909	−1.27024
$298$	12.3597	0.715977
$299$	−12.7652	−0.738229
$300$	−1.85051	−0.106839
$301$	−33.3919	−1.92468
$302$	13.7002	0.788360
$303$	32.2493	1.85267
$304$	−8.33365	−0.477968
$305$	−1.76150	−0.100863
$306$	−3.04752	−0.174215
$307$	1.49559	0.0853581	0.0426790	−	0.999089i	$-0.486411\pi$
$307$	1.49559	0.0853581	0.0426790	+	0.999089i	$0.486411\pi$
$308$	16.6187	0.946937
$309$	17.3871	0.989119
$310$	−2.15710	−0.122515
$311$	14.2765	0.809546	0.404773	−	0.914417i	$-0.367351\pi$
$311$	14.2765	0.809546	0.404773	+	0.914417i	$0.367351\pi$
$312$	10.1694	0.575728
$313$	16.9199	0.956371	0.478185	−	0.878259i	$-0.341295\pi$
$313$	16.9199	0.956371	0.478185	+	0.878259i	$0.341295\pi$
$314$	−11.7760	−0.664556
$315$	1.53554	0.0865181
$316$	−15.9616	−0.897909
$317$	−26.5629	−1.49192	−0.745959	−	0.665991i	$-0.768009\pi$
$317$	−26.5629	−1.49192	−0.745959	+	0.665991i	$0.768009\pi$
$318$	−15.2731	−0.856473
$319$	2.67295	0.149657
$320$	−1.00000	−0.0559017
$321$	27.2254	1.51957
$322$	−8.40482	−0.468383
$323$	59.8446	3.32984
$324$	−10.0930	−0.560725
$325$	−5.49546	−0.304833
$326$	−8.87568	−0.491578
$327$	3.44442	0.190477
$328$	−1.58892	−0.0877332
$329$	−22.2039	−1.22414
$330$	−8.49927	−0.467870
$331$	15.2308	0.837160	0.418580	−	0.908180i	$-0.362528\pi$
$331$	15.2308	0.837160	0.418580	+	0.908180i	$0.362528\pi$
$332$	−0.411030	−0.0225582
$333$	0.112543	0.00616730
$334$	−2.66584	−0.145868
$335$	5.09275	0.278247
$336$	6.69571	0.365281
$337$	21.1597	1.15264	0.576321	−	0.817224i	$-0.304488\pi$
$337$	21.1597	1.15264	0.576321	+	0.817224i	$0.304488\pi$
$338$	17.2001	0.935560
$339$	−21.9013	−1.18951
$340$	7.18108	0.389448
$341$	−9.90743	−0.536517
$342$	−3.53665	−0.191240
$343$	3.28480	0.177362
$344$	9.22858	0.497572
$345$	4.29847	0.231422
$346$	0.476012	0.0255906
$347$	0.108780	0.00583962	0.00291981	−	0.999996i	$-0.499071\pi$
$347$	0.108780	0.00583962	0.00291981	+	0.999996i	$0.499071\pi$
$348$	1.07694	0.0577301
$349$	−5.65639	−0.302780	−0.151390	−	0.988474i	$-0.548375\pi$
$349$	−5.65639	−0.302780	−0.151390	+	0.988474i	$0.548375\pi$
$350$	−3.61831	−0.193407
$351$	−26.1925	−1.39805
$352$	−4.59294	−0.244804
$353$	5.91432	0.314788	0.157394	−	0.987536i	$-0.449691\pi$
$353$	5.91432	0.314788	0.157394	+	0.987536i	$0.449691\pi$
$354$	0.840203	0.0446563
$355$	12.0315	0.638567
$356$	−3.77783	−0.200225
$357$	−48.0824	−2.54479
$358$	4.22392	0.223241
$359$	−5.07563	−0.267882	−0.133941	−	0.990989i	$-0.542763\pi$
$359$	−5.07563	−0.267882	−0.133941	+	0.990989i	$0.542763\pi$
$360$	−0.424381	−0.0223669
$361$	50.4497	2.65525
$362$	−10.2891	−0.540783
$363$	−18.6810	−0.980501
$364$	19.8843	1.04222
$365$	6.51022	0.340760
$366$	−3.25966	−0.170385
$367$	8.08860	0.422221	0.211111	−	0.977462i	$-0.432292\pi$
$367$	8.08860	0.422221	0.211111	+	0.977462i	$0.432292\pi$
$368$	2.32286	0.121087
$369$	−0.674307	−0.0351030
$370$	−0.265192	−0.0137867
$371$	−29.8636	−1.55044
$372$	−3.99173	−0.206962
$373$	−5.23464	−0.271039	−0.135520	−	0.990775i	$-0.543270\pi$
$373$	−5.23464	−0.271039	−0.135520	+	0.990775i	$0.543270\pi$
$374$	32.9822	1.70547
$375$	1.85051	0.0955598
$376$	6.13655	0.316468
$377$	3.19819	0.164715
$378$	−17.2456	−0.887018
$379$	22.5118	1.15635	0.578176	−	0.815912i	$-0.303765\pi$
$379$	22.5118	1.15635	0.578176	+	0.815912i	$0.303765\pi$
$380$	8.33365	0.427507
$381$	20.4706	1.04874
$382$	−17.0343	−0.871553
$383$	−30.6721	−1.56727	−0.783634	−	0.621222i	$-0.786636\pi$
$383$	−30.6721	−1.56727	−0.783634	+	0.621222i	$0.786636\pi$
$384$	−1.85051	−0.0944334
$385$	−16.6187	−0.846966
$386$	−0.333107	−0.0169547
$387$	3.91644	0.199084
$388$	11.9192	0.605106
$389$	21.4678	1.08846	0.544230	−	0.838936i	$-0.316822\pi$
$389$	21.4678	1.08846	0.544230	+	0.838936i	$0.316822\pi$
$390$	−10.1694	−0.514947
$391$	−16.6806	−0.843575
$392$	6.09217	0.307701
$393$	36.6035	1.84640
$394$	5.20471	0.262209
$395$	15.9616	0.803114
$396$	−1.94916	−0.0979489
$397$	−37.4285	−1.87848	−0.939241	−	0.343258i	$-0.888470\pi$
$397$	−37.4285	−1.87848	−0.939241	+	0.343258i	$0.888470\pi$
$398$	−8.62992	−0.432579
$399$	−55.7997	−2.79348
$400$	1.00000	0.0500000
$401$	−1.00000	−0.0499376
$401$	−1.00000	−0.0499376
$402$	9.42418	0.470036
$403$	−11.8543	−0.590502
$404$	−17.4273	−0.867039
$405$	10.0930	0.501527
$406$	2.10575	0.104507
$407$	−1.21801	−0.0603746
$408$	13.2886	0.657886
$409$	−27.4902	−1.35930	−0.679652	−	0.733534i	$-0.737869\pi$
$409$	−27.4902	−1.35930	−0.679652	+	0.733534i	$0.737869\pi$
$410$	1.58892	0.0784710
$411$	−38.8604	−1.91684
$412$	−9.39587	−0.462901
$413$	1.64285	0.0808396
$414$	0.985778	0.0484483
$415$	0.411030	0.0201767
$416$	−5.49546	−0.269437
$417$	6.47093	0.316883
$418$	38.2759	1.87214
$419$	−8.46902	−0.413739	−0.206869	−	0.978369i	$-0.566327\pi$
$419$	−8.46902	−0.413739	−0.206869	+	0.978369i	$0.566327\pi$
$420$	−6.69571	−0.326717
$421$	4.47613	0.218153	0.109077	−	0.994033i	$-0.465211\pi$
$421$	4.47613	0.218153	0.109077	+	0.994033i	$0.465211\pi$
$422$	−15.1603	−0.737990
$423$	2.60424	0.126622
$424$	8.25346	0.400823
$425$	−7.18108	−0.348333
$426$	22.2644	1.07872
$427$	−6.37364	−0.308442
$428$	−14.7124	−0.711150
$429$	−46.7074	−2.25505
$430$	−9.22858	−0.445042
$431$	25.8562	1.24545	0.622726	−	0.782440i	$-0.286025\pi$
$431$	25.8562	1.24545	0.622726	+	0.782440i	$0.286025\pi$
$432$	4.76620	0.229314
$433$	18.2486	0.876969	0.438485	−	0.898739i	$-0.355515\pi$
$433$	18.2486	0.876969	0.438485	+	0.898739i	$0.355515\pi$
$434$	−7.80506	−0.374655
$435$	−1.07694	−0.0516353
$436$	−1.86134	−0.0891420
$437$	−19.3579	−0.926013
$438$	12.0472	0.575638
$439$	1.03546	0.0494198	0.0247099	−	0.999695i	$-0.492134\pi$
$439$	1.03546	0.0494198	0.0247099	+	0.999695i	$0.492134\pi$
$440$	4.59294	0.218960
$441$	2.58541	0.123115
$442$	39.4633	1.87708
$443$	−31.7109	−1.50663	−0.753314	−	0.657661i	$-0.771546\pi$
$443$	−31.7109	−1.50663	−0.753314	+	0.657661i	$0.771546\pi$
$444$	−0.490741	−0.0232895
$445$	3.77783	0.179086
$446$	12.6131	0.597247
$447$	−22.8717	−1.08179
$448$	−3.61831	−0.170949
$449$	−27.8156	−1.31270	−0.656350	−	0.754457i	$-0.727900\pi$
$449$	−27.8156	−1.31270	−0.656350	+	0.754457i	$0.727900\pi$
$450$	0.424381	0.0200055
$451$	7.29780	0.343640
$452$	11.8353	0.556684
$453$	−25.3524	−1.19116
$454$	−8.09619	−0.379973
$455$	−19.8843	−0.932189
$456$	15.4215	0.722177
$457$	−18.1136	−0.847321	−0.423660	−	0.905821i	$-0.639255\pi$
$457$	−18.1136	−0.847321	−0.423660	+	0.905821i	$0.639255\pi$
$458$	9.61111	0.449098
$459$	−34.2265	−1.59755
$460$	−2.32286	−0.108304
$461$	1.87167	0.0871723	0.0435861	−	0.999050i	$-0.486122\pi$
$461$	1.87167	0.0871723	0.0435861	+	0.999050i	$0.486122\pi$
$462$	−30.7530	−1.43076
$463$	16.3893	0.761676	0.380838	−	0.924642i	$-0.375635\pi$
$463$	16.3893	0.761676	0.380838	+	0.924642i	$0.375635\pi$
$464$	−0.581970	−0.0270173
$465$	3.99173	0.185112
$466$	17.2382	0.798546
$467$	29.6244	1.37086	0.685428	−	0.728141i	$-0.259615\pi$
$467$	29.6244	1.37086	0.685428	+	0.728141i	$0.259615\pi$
$468$	−2.33217	−0.107805
$469$	18.4272	0.850887
$470$	−6.13655	−0.283058
$471$	21.7915	1.00410
$472$	−0.454039	−0.0208988
$473$	−42.3863	−1.94892
$474$	29.5370	1.35668
$475$	−8.33365	−0.382374
$476$	25.9834	1.19095
$477$	3.50262	0.160374
$478$	−17.2681	−0.789825
$479$	22.5334	1.02958	0.514788	−	0.857318i	$-0.327871\pi$
$479$	22.5334	1.02958	0.514788	+	0.857318i	$0.327871\pi$
$480$	1.85051	0.0844638
$481$	−1.45735	−0.0664496
$482$	0.820430	0.0373696
$483$	15.5532	0.707695
$484$	10.0951	0.458868
$485$	−11.9192	−0.541223
$486$	4.37865	0.198620
$487$	11.4035	0.516742	0.258371	−	0.966046i	$-0.416814\pi$
$487$	11.4035	0.516742	0.258371	+	0.966046i	$0.416814\pi$
$488$	1.76150	0.0797391
$489$	16.4245	0.742742
$490$	−6.09217	−0.275216
$491$	−1.30359	−0.0588300	−0.0294150	−	0.999567i	$-0.509364\pi$
$491$	−1.30359	−0.0588300	−0.0294150	+	0.999567i	$0.509364\pi$
$492$	2.94030	0.132559
$493$	4.17917	0.188220
$494$	45.7972	2.06051
$495$	1.94916	0.0876081
$496$	2.15710	0.0968566
$497$	43.5338	1.95276
$498$	0.760615	0.0340840
$499$	−43.0384	−1.92666	−0.963332	−	0.268313i	$-0.913534\pi$
$499$	−43.0384	−1.92666	−0.963332	+	0.268313i	$0.913534\pi$
$500$	−1.00000	−0.0447214
$501$	4.93315	0.220397
$502$	−20.9512	−0.935096
$503$	9.99761	0.445771	0.222886	−	0.974845i	$-0.428452\pi$
$503$	9.99761	0.445771	0.222886	+	0.974845i	$0.428452\pi$
$504$	−1.53554	−0.0683986
$505$	17.4273	0.775503
$506$	−10.6687	−0.474284
$507$	−31.8289	−1.41357
$508$	−11.0622	−0.490804
$509$	−42.7266	−1.89382	−0.946911	−	0.321496i	$-0.895814\pi$
$509$	−42.7266	−1.89382	−0.946911	+	0.321496i	$0.895814\pi$
$510$	−13.2886	−0.588431
$511$	23.5560	1.04206
$512$	1.00000	0.0441942
$513$	−39.7199	−1.75368
$514$	−16.1061	−0.710410
$515$	9.39587	0.414031
$516$	−17.0776	−0.751798
$517$	−28.1848	−1.23957
$518$	−0.959549	−0.0421601
$519$	−0.880864	−0.0386656
$520$	5.49546	0.240992
$521$	−20.0388	−0.877917	−0.438959	−	0.898507i	$-0.644653\pi$
$521$	−20.0388	−0.877917	−0.438959	+	0.898507i	$0.644653\pi$
$522$	−0.246977	−0.0108099
$523$	35.8781	1.56884	0.784421	−	0.620229i	$-0.212960\pi$
$523$	35.8781	1.56884	0.784421	+	0.620229i	$0.212960\pi$
$524$	−19.7802	−0.864103
$525$	6.69571	0.292225
$526$	−13.8883	−0.605557
$527$	−15.4903	−0.674768
$528$	8.49927	0.369883
$529$	−17.6043	−0.765406
$530$	−8.25346	−0.358507
$531$	−0.192686	−0.00836185
$532$	30.1537	1.30733
$533$	8.73182	0.378217
$534$	6.99091	0.302526
$535$	14.7124	0.636072
$536$	−5.09275	−0.219973
$537$	−7.81641	−0.337303
$538$	32.6056	1.40573
$539$	−27.9810	−1.20523
$540$	−4.76620	−0.205105
$541$	−19.3879	−0.833552	−0.416776	−	0.909009i	$-0.636840\pi$
$541$	−19.3879	−0.833552	−0.416776	+	0.909009i	$0.636840\pi$
$542$	−18.4311	−0.791685
$543$	19.0401	0.817087
$544$	−7.18108	−0.307886
$545$	1.86134	0.0797310
$546$	−36.7960	−1.57472
$547$	−7.90177	−0.337855	−0.168928	−	0.985628i	$-0.554030\pi$
$547$	−7.90177	−0.337855	−0.168928	+	0.985628i	$0.554030\pi$
$548$	20.9998	0.897069
$549$	0.747546	0.0319045
$550$	−4.59294	−0.195844
$551$	4.84994	0.206614
$552$	−4.29847	−0.182955
$553$	57.7539	2.45595
$554$	−18.7363	−0.796031
$555$	0.490741	0.0208308
$556$	−3.49684	−0.148299
$557$	−31.8483	−1.34946	−0.674729	−	0.738066i	$-0.735739\pi$
$557$	−31.8483	−1.34946	−0.674729	+	0.738066i	$0.735739\pi$
$558$	0.915433	0.0387534
$559$	−50.7153	−2.14503
$560$	3.61831	0.152902
$561$	−61.0339	−2.57685
$562$	16.8001	0.708668
$563$	36.3909	1.53369	0.766847	−	0.641830i	$-0.221825\pi$
$563$	36.3909	1.53369	0.766847	+	0.641830i	$0.221825\pi$
$564$	−11.3557	−0.478163
$565$	−11.8353	−0.497914
$566$	−3.09470	−0.130080
$567$	36.5198	1.53369
$568$	−12.0315	−0.504832
$569$	30.2491	1.26811	0.634055	−	0.773288i	$-0.281389\pi$
$569$	30.2491	1.26811	0.634055	+	0.773288i	$0.281389\pi$
$570$	−15.4215	−0.645935
$571$	−4.43415	−0.185563	−0.0927817	−	0.995686i	$-0.529576\pi$
$571$	−4.43415	−0.185563	−0.0927817	+	0.995686i	$0.529576\pi$
$572$	25.2403	1.05535
$573$	31.5222	1.31686
$574$	5.74919	0.239967
$575$	2.32286	0.0968699
$576$	0.424381	0.0176826
$577$	5.75491	0.239580	0.119790	−	0.992799i	$-0.461778\pi$
$577$	5.75491	0.239580	0.119790	+	0.992799i	$0.461778\pi$
$578$	34.5678	1.43783
$579$	0.616417	0.0256174
$580$	0.581970	0.0241650
$581$	1.48724	0.0617009
$582$	−22.0566	−0.914275
$583$	−37.9076	−1.56997
$584$	−6.51022	−0.269395
$585$	2.33217	0.0964234
$586$	5.26165	0.217357
$587$	5.88281	0.242810	0.121405	−	0.992603i	$-0.461260\pi$
$587$	5.88281	0.242810	0.121405	+	0.992603i	$0.461260\pi$
$588$	−11.2736	−0.464916
$589$	−17.9765	−0.740709
$590$	0.454039	0.0186925
$591$	−9.63135	−0.396181
$592$	0.265192	0.0108993
$593$	41.2608	1.69438	0.847190	−	0.531290i	$-0.178293\pi$
$593$	41.2608	1.69438	0.847190	+	0.531290i	$0.178293\pi$
$594$	−21.8909	−0.898194
$595$	−25.9834	−1.06521
$596$	12.3597	0.506272
$597$	15.9697	0.653598
$598$	−12.7652	−0.522007
$599$	−10.7374	−0.438720	−0.219360	−	0.975644i	$-0.570397\pi$
$599$	−10.7374	−0.438720	−0.219360	+	0.975644i	$0.570397\pi$
$600$	−1.85051	−0.0755467
$601$	37.4381	1.52713	0.763565	−	0.645731i	$-0.223447\pi$
$601$	37.4381	1.52713	0.763565	+	0.645731i	$0.223447\pi$
$602$	−33.3919	−1.36095
$603$	−2.16127	−0.0880137
$604$	13.7002	0.557455
$605$	−10.0951	−0.410424
$606$	32.2493	1.31004
$607$	12.3673	0.501975	0.250987	−	0.967990i	$-0.419245\pi$
$607$	12.3673	0.501975	0.250987	+	0.967990i	$0.419245\pi$
$608$	−8.33365	−0.337974
$609$	−3.89671	−0.157902
$610$	−1.76150	−0.0713209
$611$	−33.7232	−1.36429
$612$	−3.04752	−0.123188
$613$	33.6124	1.35759	0.678797	−	0.734326i	$-0.262502\pi$
$613$	33.6124	1.35759	0.678797	+	0.734326i	$0.262502\pi$
$614$	1.49559	0.0603573
$615$	−2.94030	−0.118564
$616$	16.6187	0.669586
$617$	28.8368	1.16093	0.580464	−	0.814286i	$-0.302871\pi$
$617$	28.8368	1.16093	0.580464	+	0.814286i	$0.302871\pi$
$618$	17.3871	0.699413
$619$	29.1708	1.17247	0.586236	−	0.810140i	$-0.300609\pi$
$619$	29.1708	1.17247	0.586236	+	0.810140i	$0.300609\pi$
$620$	−2.15710	−0.0866312
$621$	11.0712	0.444273
$622$	14.2765	0.572435
$623$	13.6694	0.547652
$624$	10.1694	0.407102
$625$	1.00000	0.0400000
$626$	16.9199	0.676256
$627$	−70.8300	−2.82868
$628$	−11.7760	−0.469912
$629$	−1.90437	−0.0759321
$630$	1.53554	0.0611775
$631$	24.8722	0.990146	0.495073	−	0.868851i	$-0.335141\pi$
$631$	24.8722	0.990146	0.495073	+	0.868851i	$0.335141\pi$
$632$	−15.9616	−0.634917
$633$	28.0542	1.11505
$634$	−26.5629	−1.05495
$635$	11.0622	0.438989
$636$	−15.2731	−0.605618
$637$	−33.4793	−1.32650
$638$	2.67295	0.105823
$639$	−5.10596	−0.201989
$640$	−1.00000	−0.0395285
$641$	26.1033	1.03102	0.515509	−	0.856884i	$-0.327603\pi$
$641$	26.1033	1.03102	0.515509	+	0.856884i	$0.327603\pi$
$642$	27.2254	1.07450
$643$	12.4557	0.491206	0.245603	−	0.969370i	$-0.421014\pi$
$643$	12.4557	0.491206	0.245603	+	0.969370i	$0.421014\pi$
$644$	−8.40482	−0.331196
$645$	17.0776	0.672428
$646$	59.8446	2.35455
$647$	−22.8730	−0.899232	−0.449616	−	0.893222i	$-0.648439\pi$
$647$	−22.8730	−0.899232	−0.449616	+	0.893222i	$0.648439\pi$
$648$	−10.0930	−0.396492
$649$	2.08537	0.0818580
$650$	−5.49546	−0.215550
$651$	14.4433	0.566078
$652$	−8.87568	−0.347598
$653$	23.0198	0.900834	0.450417	−	0.892818i	$-0.351275\pi$
$653$	23.0198	0.900834	0.450417	+	0.892818i	$0.351275\pi$
$654$	3.44442	0.134688
$655$	19.7802	0.772877
$656$	−1.58892	−0.0620368
$657$	−2.76281	−0.107788
$658$	−22.2039	−0.865600
$659$	−30.9672	−1.20631	−0.603156	−	0.797623i	$-0.706090\pi$
$659$	−30.9672	−1.20631	−0.603156	+	0.797623i	$0.706090\pi$
$660$	−8.49927	−0.330834
$661$	9.54274	0.371170	0.185585	−	0.982628i	$-0.440582\pi$
$661$	9.54274	0.371170	0.185585	+	0.982628i	$0.440582\pi$
$662$	15.2308	0.591961
$663$	−73.0272	−2.83614
$664$	−0.411030	−0.0159511
$665$	−30.1537	−1.16931
$666$	0.112543	0.00436094
$667$	−1.35183	−0.0523432
$668$	−2.66584	−0.103144
$669$	−23.3406	−0.902401
$670$	5.09275	0.196750
$671$	−8.09044	−0.312328
$672$	6.69571	0.258293
$673$	−14.5059	−0.559160	−0.279580	−	0.960122i	$-0.590195\pi$
$673$	−14.5059	−0.559160	−0.279580	+	0.960122i	$0.590195\pi$
$674$	21.1597	0.815040
$675$	4.76620	0.183451
$676$	17.2001	0.661541
$677$	−17.2703	−0.663751	−0.331875	−	0.943323i	$-0.607681\pi$
$677$	−17.2703	−0.663751	−0.331875	+	0.943323i	$0.607681\pi$
$678$	−21.9013	−0.841113
$679$	−43.1274	−1.65508
$680$	7.18108	0.275382
$681$	14.9821	0.574114
$682$	−9.90743	−0.379375
$683$	−38.2419	−1.46329	−0.731643	−	0.681688i	$-0.761246\pi$
$683$	−38.2419	−1.46329	−0.731643	+	0.681688i	$0.761246\pi$
$684$	−3.53665	−0.135227
$685$	−20.9998	−0.802363
$686$	3.28480	0.125414
$687$	−17.7854	−0.678557
$688$	9.22858	0.351836
$689$	−45.3565	−1.72795
$690$	4.29847	0.163640
$691$	−10.8346	−0.412169	−0.206085	−	0.978534i	$-0.566072\pi$
$691$	−10.8346	−0.412169	−0.206085	+	0.978534i	$0.566072\pi$
$692$	0.476012	0.0180953
$693$	7.05266	0.267908
$694$	0.108780	0.00412923
$695$	3.49684	0.132643
$696$	1.07694	0.0408213
$697$	11.4101	0.432189
$698$	−5.65639	−0.214097
$699$	−31.8995	−1.20655
$700$	−3.61831	−0.136759
$701$	22.7838	0.860532	0.430266	−	0.902702i	$-0.358420\pi$
$701$	22.7838	0.860532	0.430266	+	0.902702i	$0.358420\pi$
$702$	−26.1925	−0.988571
$703$	−2.21002	−0.0833525
$704$	−4.59294	−0.173103
$705$	11.3557	0.427682
$706$	5.91432	0.222588
$707$	63.0573	2.37151
$708$	0.840203	0.0315768
$709$	36.4029	1.36714	0.683571	−	0.729884i	$-0.260426\pi$
$709$	36.4029	1.36714	0.683571	+	0.729884i	$0.260426\pi$
$710$	12.0315	0.451535
$711$	−6.77380	−0.254037
$712$	−3.77783	−0.141580
$713$	5.01064	0.187650
$714$	−48.0824	−1.79944
$715$	−25.2403	−0.943934
$716$	4.22392	0.157855
$717$	31.9548	1.19337
$718$	−5.07563	−0.189421
$719$	44.5952	1.66312	0.831561	−	0.555434i	$-0.187448\pi$
$719$	44.5952	1.66312	0.831561	+	0.555434i	$0.187448\pi$
$720$	−0.424381	−0.0158158
$721$	33.9972	1.26612
$722$	50.4497	1.87754
$723$	−1.51821	−0.0564629
$724$	−10.2891	−0.382391
$725$	−0.581970	−0.0216138
$726$	−18.6810	−0.693319
$727$	−47.2366	−1.75191	−0.875954	−	0.482395i	$-0.839767\pi$
$727$	−47.2366	−1.75191	−0.875954	+	0.482395i	$0.839767\pi$
$728$	19.8843	0.736960
$729$	22.1764	0.821348
$730$	6.51022	0.240954
$731$	−66.2711	−2.45113
$732$	−3.25966	−0.120481
$733$	17.8127	0.657927	0.328964	−	0.944343i	$-0.393301\pi$
$733$	17.8127	0.657927	0.328964	+	0.944343i	$0.393301\pi$
$734$	8.08860	0.298556
$735$	11.2736	0.415834
$736$	2.32286	0.0856217
$737$	23.3907	0.861608
$738$	−0.674307	−0.0248216
$739$	8.86112	0.325961	0.162981	−	0.986629i	$-0.447889\pi$
$739$	8.86112	0.325961	0.162981	+	0.986629i	$0.447889\pi$
$740$	−0.265192	−0.00974867
$741$	−84.7482	−3.11330
$742$	−29.8636	−1.09633
$743$	−15.6835	−0.575372	−0.287686	−	0.957725i	$-0.592886\pi$
$743$	−15.6835	−0.575372	−0.287686	+	0.957725i	$0.592886\pi$
$744$	−3.99173	−0.146344
$745$	−12.3597	−0.452823
$746$	−5.23464	−0.191654
$747$	−0.174434	−0.00638219
$748$	32.9822	1.20595
$749$	53.2340	1.94513
$750$	1.85051	0.0675710
$751$	−18.0340	−0.658070	−0.329035	−	0.944318i	$-0.606723\pi$
$751$	−18.0340	−0.658070	−0.329035	+	0.944318i	$0.606723\pi$
$752$	6.13655	0.223777
$753$	38.7703	1.41287
$754$	3.19819	0.116471
$755$	−13.7002	−0.498603
$756$	−17.2456	−0.627217
$757$	−37.0335	−1.34600	−0.673002	−	0.739640i	$-0.734996\pi$
$757$	−37.0335	−1.34600	−0.673002	+	0.739640i	$0.734996\pi$
$758$	22.5118	0.817664
$759$	19.7426	0.716611
$760$	8.33365	0.302293
$761$	−51.3144	−1.86015	−0.930073	−	0.367376i	$-0.880256\pi$
$761$	−51.3144	−1.86015	−0.930073	+	0.367376i	$0.880256\pi$
$762$	20.4706	0.741573
$763$	6.73491	0.243820
$764$	−17.0343	−0.616281
$765$	3.04752	0.110183
$766$	−30.6721	−1.10823
$767$	2.49515	0.0900947
$768$	−1.85051	−0.0667745
$769$	47.3171	1.70630	0.853150	−	0.521666i	$-0.174689\pi$
$769$	47.3171	1.70630	0.853150	+	0.521666i	$0.174689\pi$
$770$	−16.6187	−0.598896
$771$	29.8045	1.07338
$772$	−0.333107	−0.0119888
$773$	23.1573	0.832910	0.416455	−	0.909156i	$-0.363272\pi$
$773$	23.1573	0.832910	0.416455	+	0.909156i	$0.363272\pi$
$774$	3.91644	0.140773
$775$	2.15710	0.0774853
$776$	11.9192	0.427874
$777$	1.77565	0.0637012
$778$	21.4678	0.769657
$779$	13.2415	0.474425
$780$	−10.1694	−0.364123
$781$	55.2601	1.97736
$782$	−16.6806	−0.596498
$783$	−2.77379	−0.0991271
$784$	6.09217	0.217578
$785$	11.7760	0.420302
$786$	36.6035	1.30560
$787$	−11.1905	−0.398899	−0.199450	−	0.979908i	$-0.563915\pi$
$787$	−11.1905	−0.398899	−0.199450	+	0.979908i	$0.563915\pi$
$788$	5.20471	0.185410
$789$	25.7004	0.914957
$790$	15.9616	0.567887
$791$	−42.8237	−1.52264
$792$	−1.94916	−0.0692603
$793$	−9.68022	−0.343755
$794$	−37.4285	−1.32829
$795$	15.2731	0.541681
$796$	−8.62992	−0.305879
$797$	−18.9772	−0.672207	−0.336103	−	0.941825i	$-0.609109\pi$
$797$	−18.9772	−0.672207	−0.336103	+	0.941825i	$0.609109\pi$
$798$	−55.7997	−1.97529
$799$	−44.0670	−1.55898
$800$	1.00000	0.0353553
$801$	−1.60324	−0.0566478
$802$	−1.00000	−0.0353112
$803$	29.9010	1.05518
$804$	9.42418	0.332365
$805$	8.40482	0.296231
$806$	−11.8543	−0.417548
$807$	−60.3369	−2.12396
$808$	−17.4273	−0.613089
$809$	−45.7945	−1.61005	−0.805024	−	0.593242i	$-0.797848\pi$
$809$	−45.7945	−1.61005	−0.805024	+	0.593242i	$0.797848\pi$
$810$	10.0930	0.354633
$811$	13.5084	0.474344	0.237172	−	0.971468i	$-0.423779\pi$
$811$	13.5084	0.474344	0.237172	+	0.971468i	$0.423779\pi$
$812$	2.10575	0.0738973
$813$	34.1070	1.19618
$814$	−1.21801	−0.0426913
$815$	8.87568	0.310901
$816$	13.2886	0.465195
$817$	−76.9078	−2.69066
$818$	−27.4902	−0.961174
$819$	8.43852	0.294866
$820$	1.58892	0.0554874
$821$	12.4024	0.432845	0.216423	−	0.976300i	$-0.430561\pi$
$821$	12.4024	0.432845	0.216423	+	0.976300i	$0.430561\pi$
$822$	−38.8604	−1.35541
$823$	16.2181	0.565326	0.282663	−	0.959219i	$-0.408782\pi$
$823$	16.2181	0.565326	0.282663	+	0.959219i	$0.408782\pi$
$824$	−9.39587	−0.327321
$825$	8.49927	0.295907
$826$	1.64285	0.0571622
$827$	14.0459	0.488423	0.244211	−	0.969722i	$-0.421471\pi$
$827$	14.0459	0.488423	0.244211	+	0.969722i	$0.421471\pi$
$828$	0.985778	0.0342582
$829$	−2.45144	−0.0851419	−0.0425709	−	0.999093i	$-0.513555\pi$
$829$	−2.45144	−0.0851419	−0.0425709	+	0.999093i	$0.513555\pi$
$830$	0.411030	0.0142671
$831$	34.6717	1.20275
$832$	−5.49546	−0.190521
$833$	−43.7484	−1.51579
$834$	6.47093	0.224070
$835$	2.66584	0.0922551
$836$	38.2759	1.32380
$837$	10.2812	0.355369
$838$	−8.46902	−0.292557
$839$	−22.9632	−0.792778	−0.396389	−	0.918083i	$-0.629737\pi$
$839$	−22.9632	−0.792778	−0.396389	+	0.918083i	$0.629737\pi$
$840$	−6.69571	−0.231024
$841$	−28.6613	−0.988321
$842$	4.47613	0.154258
$843$	−31.0887	−1.07075
$844$	−15.1603	−0.521838
$845$	−17.2001	−0.591700
$846$	2.60424	0.0895355
$847$	−36.5272	−1.25509
$848$	8.25346	0.283425
$849$	5.72678	0.196542
$850$	−7.18108	−0.246309
$851$	0.616004	0.0211164
$852$	22.2644	0.762767
$853$	−38.5749	−1.32078	−0.660389	−	0.750923i	$-0.729609\pi$
$853$	−38.5749	−1.32078	−0.660389	+	0.750923i	$0.729609\pi$
$854$	−6.37364	−0.218101
$855$	3.53665	0.120951
$856$	−14.7124	−0.502859
$857$	30.2155	1.03214	0.516070	−	0.856546i	$-0.327394\pi$
$857$	30.2155	1.03214	0.516070	+	0.856546i	$0.327394\pi$
$858$	−46.7074	−1.59456
$859$	38.0808	1.29930	0.649650	−	0.760233i	$-0.274915\pi$
$859$	38.0808	1.29930	0.649650	+	0.760233i	$0.274915\pi$
$860$	−9.22858	−0.314692
$861$	−10.6389	−0.362574
$862$	25.8562	0.880667
$863$	13.0702	0.444916	0.222458	−	0.974942i	$-0.428592\pi$
$863$	13.0702	0.444916	0.222458	+	0.974942i	$0.428592\pi$
$864$	4.76620	0.162150
$865$	−0.476012	−0.0161849
$866$	18.2486	0.620111
$867$	−63.9681	−2.17247
$868$	−7.80506	−0.264921
$869$	73.3105	2.48689
$870$	−1.07694	−0.0365117
$871$	27.9870	0.948304
$872$	−1.86134	−0.0630329
$873$	5.05829	0.171197
$874$	−19.3579	−0.654790
$875$	3.61831	0.122321
$876$	12.0472	0.407037
$877$	−27.5112	−0.928986	−0.464493	−	0.885577i	$-0.653763\pi$
$877$	−27.5112	−0.928986	−0.464493	+	0.885577i	$0.653763\pi$
$878$	1.03546	0.0349451
$879$	−9.73673	−0.328412
$880$	4.59294	0.154828
$881$	−46.0146	−1.55027	−0.775136	−	0.631794i	$-0.782319\pi$
$881$	−46.0146	−1.55027	−0.775136	+	0.631794i	$0.782319\pi$
$882$	2.58541	0.0870551
$883$	28.6610	0.964519	0.482260	−	0.876028i	$-0.339816\pi$
$883$	28.6610	0.964519	0.482260	+	0.876028i	$0.339816\pi$
$884$	39.4633	1.32729
$885$	−0.840203	−0.0282431
$886$	−31.7109	−1.06535
$887$	−8.76011	−0.294136	−0.147068	−	0.989126i	$-0.546984\pi$
$887$	−8.76011	−0.294136	−0.147068	+	0.989126i	$0.546984\pi$
$888$	−0.490741	−0.0164682
$889$	40.0263	1.34244
$890$	3.77783	0.126633
$891$	46.3567	1.55301
$892$	12.6131	0.422317
$893$	−51.1399	−1.71133
$894$	−22.8717	−0.764943
$895$	−4.22392	−0.141190
$896$	−3.61831	−0.120879
$897$	23.6221	0.788718
$898$	−27.8156	−0.928219
$899$	−1.25537	−0.0418688
$900$	0.424381	0.0141460
$901$	−59.2687	−1.97453
$902$	7.29780	0.242990
$903$	61.7919	2.05631
$904$	11.8353	0.393635
$905$	10.2891	0.342021
$906$	−25.3524	−0.842278
$907$	−23.2468	−0.771898	−0.385949	−	0.922520i	$-0.626126\pi$
$907$	−23.2468	−0.771898	−0.385949	+	0.922520i	$0.626126\pi$
$908$	−8.09619	−0.268681
$909$	−7.39581	−0.245304
$910$	−19.8843	−0.659157
$911$	−7.91575	−0.262261	−0.131130	−	0.991365i	$-0.541861\pi$
$911$	−7.91575	−0.262261	−0.131130	+	0.991365i	$0.541861\pi$
$912$	15.4215	0.510657
$913$	1.88784	0.0624783
$914$	−18.1136	−0.599146
$915$	3.25966	0.107761
$916$	9.61111	0.317560
$917$	71.5710	2.36348
$918$	−34.2265	−1.12964
$919$	10.8959	0.359423	0.179711	−	0.983719i	$-0.442484\pi$
$919$	10.8959	0.359423	0.179711	+	0.983719i	$0.442484\pi$
$920$	−2.32286	−0.0765824
$921$	−2.76761	−0.0911959
$922$	1.87167	0.0616401
$923$	66.1188	2.17633
$924$	−30.7530	−1.01170
$925$	0.265192	0.00871947
$926$	16.3893	0.538587
$927$	−3.98743	−0.130964
$928$	−0.581970	−0.0191041
$929$	−39.4849	−1.29546	−0.647730	−	0.761870i	$-0.724281\pi$
$929$	−39.4849	−1.29546	−0.647730	+	0.761870i	$0.724281\pi$
$930$	3.99173	0.130894
$931$	−50.7701	−1.66392
$932$	17.2382	0.564658
$933$	−26.4188	−0.864912
$934$	29.6244	0.969341
$935$	−32.9822	−1.07863
$936$	−2.33217	−0.0762294
$937$	−33.3711	−1.09019	−0.545094	−	0.838375i	$-0.683506\pi$
$937$	−33.3711	−1.09019	−0.545094	+	0.838375i	$0.683506\pi$
$938$	18.4272	0.601668
$939$	−31.3105	−1.02178
$940$	−6.13655	−0.200152
$941$	39.0022	1.27144	0.635718	−	0.771921i	$-0.280704\pi$
$941$	39.0022	1.27144	0.635718	+	0.771921i	$0.280704\pi$
$942$	21.7915	0.710006
$943$	−3.69083	−0.120190
$944$	−0.454039	−0.0147777
$945$	17.2456	0.561000
$946$	−42.3863	−1.37810
$947$	−36.4771	−1.18535	−0.592673	−	0.805443i	$-0.701927\pi$
$947$	−36.4771	−1.18535	−0.592673	+	0.805443i	$0.701927\pi$
$948$	29.5370	0.959318
$949$	35.7766	1.16136
$950$	−8.33365	−0.270379
$951$	49.1548	1.59395
$952$	25.9834	0.842126
$953$	3.23106	0.104664	0.0523321	−	0.998630i	$-0.483335\pi$
$953$	3.23106	0.104664	0.0523321	+	0.998630i	$0.483335\pi$
$954$	3.50262	0.113401
$955$	17.0343	0.551219
$956$	−17.2681	−0.558490
$957$	−4.94632	−0.159892
$958$	22.5334	0.728020
$959$	−75.9840	−2.45365
$960$	1.85051	0.0597249
$961$	−26.3469	−0.849901
$962$	−1.45735	−0.0469870
$963$	−6.24367	−0.201199
$964$	0.820430	0.0264243
$965$	0.333107	0.0107231
$966$	15.5532	0.500416
$967$	48.7029	1.56618	0.783090	−	0.621908i	$-0.213642\pi$
$967$	48.7029	1.56618	0.783090	+	0.621908i	$0.213642\pi$
$968$	10.0951	0.324468
$969$	−110.743	−3.55757
$970$	−11.9192	−0.382703
$971$	−46.9889	−1.50795	−0.753974	−	0.656905i	$-0.771865\pi$
$971$	−46.9889	−1.50795	−0.753974	+	0.656905i	$0.771865\pi$
$972$	4.37865	0.140445
$973$	12.6527	0.405626
$974$	11.4035	0.365391
$975$	10.1694	0.325681
$976$	1.76150	0.0563841
$977$	−1.04819	−0.0335344	−0.0167672	−	0.999859i	$-0.505337\pi$
$977$	−1.04819	−0.0335344	−0.0167672	+	0.999859i	$0.505337\pi$
$978$	16.4245	0.525198
$979$	17.3514	0.554552
$980$	−6.09217	−0.194607
$981$	−0.789918	−0.0252201
$982$	−1.30359	−0.0415991
$983$	35.7503	1.14026	0.570129	−	0.821555i	$-0.306893\pi$
$983$	35.7503	1.14026	0.570129	+	0.821555i	$0.306893\pi$
$984$	2.94030	0.0937334
$985$	−5.20471	−0.165836
$986$	4.17917	0.133092
$987$	41.0886	1.30786
$988$	45.7972	1.45700
$989$	21.4367	0.681647
$990$	1.94916	0.0619483
$991$	18.0421	0.573127	0.286564	−	0.958061i	$-0.407487\pi$
$991$	18.0421	0.573127	0.286564	+	0.958061i	$0.407487\pi$
$992$	2.15710	0.0684880
$993$	−28.1847	−0.894414
$994$	43.5338	1.38081
$995$	8.62992	0.273587
$996$	0.760615	0.0241010
$997$	−17.4120	−0.551443	−0.275721	−	0.961238i	$-0.588917\pi$
$997$	−17.4120	−0.551443	−0.275721	+	0.961238i	$0.588917\pi$
$998$	−43.0384	−1.36236
$999$	1.26396	0.0399900

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4010.2.a.o.1.5	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4010.2.a.o.1.5	✓	22	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:	\( N \)	\(=\)	\( 4010 = 2 \cdot 5 \cdot 401 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4010.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.85051 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.85051 q^{6} -3.61831 q^{7} +1.00000 q^{8} +0.424381 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.85051 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.85051 q^{6} -3.61831 q^{7} +1.00000 q^{8} +0.424381 q^{9} -1.00000 q^{10} -4.59294 q^{11} -1.85051 q^{12} -5.49546 q^{13} -3.61831 q^{14} +1.85051 q^{15} +1.00000 q^{16} -7.18108 q^{17} +0.424381 q^{18} -8.33365 q^{19} -1.00000 q^{20} +6.69571 q^{21} -4.59294 q^{22} +2.32286 q^{23} -1.85051 q^{24} +1.00000 q^{25} -5.49546 q^{26} +4.76620 q^{27} -3.61831 q^{28} -0.581970 q^{29} +1.85051 q^{30} +2.15710 q^{31} +1.00000 q^{32} +8.49927 q^{33} -7.18108 q^{34} +3.61831 q^{35} +0.424381 q^{36} +0.265192 q^{37} -8.33365 q^{38} +10.1694 q^{39} -1.00000 q^{40} -1.58892 q^{41} +6.69571 q^{42} +9.22858 q^{43} -4.59294 q^{44} -0.424381 q^{45} +2.32286 q^{46} +6.13655 q^{47} -1.85051 q^{48} +6.09217 q^{49} +1.00000 q^{50} +13.2886 q^{51} -5.49546 q^{52} +8.25346 q^{53} +4.76620 q^{54} +4.59294 q^{55} -3.61831 q^{56} +15.4215 q^{57} -0.581970 q^{58} -0.454039 q^{59} +1.85051 q^{60} +1.76150 q^{61} +2.15710 q^{62} -1.53554 q^{63} +1.00000 q^{64} +5.49546 q^{65} +8.49927 q^{66} -5.09275 q^{67} -7.18108 q^{68} -4.29847 q^{69} +3.61831 q^{70} -12.0315 q^{71} +0.424381 q^{72} -6.51022 q^{73} +0.265192 q^{74} -1.85051 q^{75} -8.33365 q^{76} +16.6187 q^{77} +10.1694 q^{78} -15.9616 q^{79} -1.00000 q^{80} -10.0930 q^{81} -1.58892 q^{82} -0.411030 q^{83} +6.69571 q^{84} +7.18108 q^{85} +9.22858 q^{86} +1.07694 q^{87} -4.59294 q^{88} -3.77783 q^{89} -0.424381 q^{90} +19.8843 q^{91} +2.32286 q^{92} -3.99173 q^{93} +6.13655 q^{94} +8.33365 q^{95} -1.85051 q^{96} +11.9192 q^{97} +6.09217 q^{98} -1.94916 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 22 q^{2} + 2 q^{3} + 22 q^{4} - 22 q^{5} + 2 q^{6} + 13 q^{7} + 22 q^{8} + 32 q^{9}+O(q^{10}) \) 22 * q + 22 * q^2 + 2 * q^3 + 22 * q^4 - 22 * q^5 + 2 * q^6 + 13 * q^7 + 22 * q^8 + 32 * q^9	\( 22 q + 22 q^{2} + 2 q^{3} + 22 q^{4} - 22 q^{5} + 2 q^{6} + 13 q^{7} + 22 q^{8} + 32 q^{9} - 22 q^{10} - 3 q^{11} + 2 q^{12} + 6 q^{13} + 13 q^{14} - 2 q^{15} + 22 q^{16} + 17 q^{17} + 32 q^{18} + 13 q^{19} - 22 q^{20} + 16 q^{21} - 3 q^{22} + 19 q^{23} + 2 q^{24} + 22 q^{25} + 6 q^{26} + 14 q^{27} + 13 q^{28} + 14 q^{29} - 2 q^{30} + 13 q^{31} + 22 q^{32} + 12 q^{33} + 17 q^{34} - 13 q^{35} + 32 q^{36} + 35 q^{37} + 13 q^{38} + 30 q^{39} - 22 q^{40} - 5 q^{41} + 16 q^{42} + 19 q^{43} - 3 q^{44} - 32 q^{45} + 19 q^{46} + 29 q^{47} + 2 q^{48} + 61 q^{49} + 22 q^{50} + q^{51} + 6 q^{52} + 29 q^{53} + 14 q^{54} + 3 q^{55} + 13 q^{56} + 33 q^{57} + 14 q^{58} - 4 q^{59} - 2 q^{60} + 20 q^{61} + 13 q^{62} + 50 q^{63} + 22 q^{64} - 6 q^{65} + 12 q^{66} + 48 q^{67} + 17 q^{68} + 19 q^{69} - 13 q^{70} + 2 q^{71} + 32 q^{72} + 16 q^{73} + 35 q^{74} + 2 q^{75} + 13 q^{76} + 53 q^{77} + 30 q^{78} + 29 q^{79} - 22 q^{80} + 54 q^{81} - 5 q^{82} + 13 q^{83} + 16 q^{84} - 17 q^{85} + 19 q^{86} + 56 q^{87} - 3 q^{88} + 20 q^{89} - 32 q^{90} + 42 q^{91} + 19 q^{92} + 50 q^{93} + 29 q^{94} - 13 q^{95} + 2 q^{96} + 36 q^{97} + 61 q^{98} - q^{99}+O(q^{100}) \) 22 * q + 22 * q^2 + 2 * q^3 + 22 * q^4 - 22 * q^5 + 2 * q^6 + 13 * q^7 + 22 * q^8 + 32 * q^9 - 22 * q^10 - 3 * q^11 + 2 * q^12 + 6 * q^13 + 13 * q^14 - 2 * q^15 + 22 * q^16 + 17 * q^17 + 32 * q^18 + 13 * q^19 - 22 * q^20 + 16 * q^21 - 3 * q^22 + 19 * q^23 + 2 * q^24 + 22 * q^25 + 6 * q^26 + 14 * q^27 + 13 * q^28 + 14 * q^29 - 2 * q^30 + 13 * q^31 + 22 * q^32 + 12 * q^33 + 17 * q^34 - 13 * q^35 + 32 * q^36 + 35 * q^37 + 13 * q^38 + 30 * q^39 - 22 * q^40 - 5 * q^41 + 16 * q^42 + 19 * q^43 - 3 * q^44 - 32 * q^45 + 19 * q^46 + 29 * q^47 + 2 * q^48 + 61 * q^49 + 22 * q^50 + q^51 + 6 * q^52 + 29 * q^53 + 14 * q^54 + 3 * q^55 + 13 * q^56 + 33 * q^57 + 14 * q^58 - 4 * q^59 - 2 * q^60 + 20 * q^61 + 13 * q^62 + 50 * q^63 + 22 * q^64 - 6 * q^65 + 12 * q^66 + 48 * q^67 + 17 * q^68 + 19 * q^69 - 13 * q^70 + 2 * q^71 + 32 * q^72 + 16 * q^73 + 35 * q^74 + 2 * q^75 + 13 * q^76 + 53 * q^77 + 30 * q^78 + 29 * q^79 - 22 * q^80 + 54 * q^81 - 5 * q^82 + 13 * q^83 + 16 * q^84 - 17 * q^85 + 19 * q^86 + 56 * q^87 - 3 * q^88 + 20 * q^89 - 32 * q^90 + 42 * q^91 + 19 * q^92 + 50 * q^93 + 29 * q^94 - 13 * q^95 + 2 * q^96 + 36 * q^97 + 61 * q^98 - q^99

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