LMFDB - Embedded newform 4010.2.a.n.1.20

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			1.20
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)

$f(q)$	$=$	$q+1.00000 q^{2} +2.88697 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.88697 q^{6} -3.00491 q^{7} +1.00000 q^{8} +5.33461 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +2.88697 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.88697 q^{6} -3.00491 q^{7} +1.00000 q^{8} +5.33461 q^{9} +1.00000 q^{10} -0.352693 q^{11} +2.88697 q^{12} +5.21119 q^{13} -3.00491 q^{14} +2.88697 q^{15} +1.00000 q^{16} +4.16107 q^{17} +5.33461 q^{18} -6.47701 q^{19} +1.00000 q^{20} -8.67510 q^{21} -0.352693 q^{22} -0.961461 q^{23} +2.88697 q^{24} +1.00000 q^{25} +5.21119 q^{26} +6.73995 q^{27} -3.00491 q^{28} -2.72879 q^{29} +2.88697 q^{30} +6.42537 q^{31} +1.00000 q^{32} -1.01821 q^{33} +4.16107 q^{34} -3.00491 q^{35} +5.33461 q^{36} +4.88720 q^{37} -6.47701 q^{38} +15.0446 q^{39} +1.00000 q^{40} -5.34619 q^{41} -8.67510 q^{42} +12.7527 q^{43} -0.352693 q^{44} +5.33461 q^{45} -0.961461 q^{46} +5.29179 q^{47} +2.88697 q^{48} +2.02950 q^{49} +1.00000 q^{50} +12.0129 q^{51} +5.21119 q^{52} +6.33046 q^{53} +6.73995 q^{54} -0.352693 q^{55} -3.00491 q^{56} -18.6989 q^{57} -2.72879 q^{58} +1.94152 q^{59} +2.88697 q^{60} -2.76793 q^{61} +6.42537 q^{62} -16.0300 q^{63} +1.00000 q^{64} +5.21119 q^{65} -1.01821 q^{66} +14.5511 q^{67} +4.16107 q^{68} -2.77571 q^{69} -3.00491 q^{70} -12.4237 q^{71} +5.33461 q^{72} +0.815631 q^{73} +4.88720 q^{74} +2.88697 q^{75} -6.47701 q^{76} +1.05981 q^{77} +15.0446 q^{78} -15.8948 q^{79} +1.00000 q^{80} +3.45423 q^{81} -5.34619 q^{82} +9.30950 q^{83} -8.67510 q^{84} +4.16107 q^{85} +12.7527 q^{86} -7.87795 q^{87} -0.352693 q^{88} -4.43001 q^{89} +5.33461 q^{90} -15.6592 q^{91} -0.961461 q^{92} +18.5499 q^{93} +5.29179 q^{94} -6.47701 q^{95} +2.88697 q^{96} -18.8373 q^{97} +2.02950 q^{98} -1.88148 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 22 q^{2} + q^{3} + 22 q^{4} + 22 q^{5} + q^{6} + 22 q^{8} + 43 q^{9}+O(q^{10}) $ 22 * q + 22 * q^2 + q^3 + 22 * q^4 + 22 * q^5 + q^6 + 22 * q^8 + 43 * q^9	\( 22 q + 22 q^{2} + q^{3} + 22 q^{4} + 22 q^{5} + q^{6} + 22 q^{8} + 43 q^{9} + 22 q^{10} + 12 q^{11} + q^{12} + 10 q^{13} + q^{15} + 22 q^{16} + 24 q^{17} + 43 q^{18} + 13 q^{19} + 22 q^{20} + 13 q^{21} + 12 q^{22} + 7 q^{23} + q^{24} + 22 q^{25} + 10 q^{26} - 5 q^{27} + 22 q^{29} + q^{30} + 14 q^{31} + 22 q^{32} + 31 q^{33} + 24 q^{34} + 43 q^{36} + 35 q^{37} + 13 q^{38} + 4 q^{39} + 22 q^{40} + 29 q^{41} + 13 q^{42} + 7 q^{43} + 12 q^{44} + 43 q^{45} + 7 q^{46} - 21 q^{47} + q^{48} + 32 q^{49} + 22 q^{50} - 6 q^{51} + 10 q^{52} + 29 q^{53} - 5 q^{54} + 12 q^{55} - 13 q^{57} + 22 q^{58} + 12 q^{59} + q^{60} + 24 q^{61} + 14 q^{62} - 8 q^{63} + 22 q^{64} + 10 q^{65} + 31 q^{66} + 25 q^{67} + 24 q^{68} + 3 q^{69} + 31 q^{71} + 43 q^{72} + 30 q^{73} + 35 q^{74} + q^{75} + 13 q^{76} + 10 q^{77} + 4 q^{78} + 35 q^{79} + 22 q^{80} + 74 q^{81} + 29 q^{82} - 33 q^{83} + 13 q^{84} + 24 q^{85} + 7 q^{86} - 24 q^{87} + 12 q^{88} + 38 q^{89} + 43 q^{90} - 32 q^{91} + 7 q^{92} + 3 q^{93} - 21 q^{94} + 13 q^{95} + q^{96} + 11 q^{97} + 32 q^{98} - 41 q^{99}+O(q^{100}) \) 22 * q + 22 * q^2 + q^3 + 22 * q^4 + 22 * q^5 + q^6 + 22 * q^8 + 43 * q^9 + 22 * q^10 + 12 * q^11 + q^12 + 10 * q^13 + q^15 + 22 * q^16 + 24 * q^17 + 43 * q^18 + 13 * q^19 + 22 * q^20 + 13 * q^21 + 12 * q^22 + 7 * q^23 + q^24 + 22 * q^25 + 10 * q^26 - 5 * q^27 + 22 * q^29 + q^30 + 14 * q^31 + 22 * q^32 + 31 * q^33 + 24 * q^34 + 43 * q^36 + 35 * q^37 + 13 * q^38 + 4 * q^39 + 22 * q^40 + 29 * q^41 + 13 * q^42 + 7 * q^43 + 12 * q^44 + 43 * q^45 + 7 * q^46 - 21 * q^47 + q^48 + 32 * q^49 + 22 * q^50 - 6 * q^51 + 10 * q^52 + 29 * q^53 - 5 * q^54 + 12 * q^55 - 13 * q^57 + 22 * q^58 + 12 * q^59 + q^60 + 24 * q^61 + 14 * q^62 - 8 * q^63 + 22 * q^64 + 10 * q^65 + 31 * q^66 + 25 * q^67 + 24 * q^68 + 3 * q^69 + 31 * q^71 + 43 * q^72 + 30 * q^73 + 35 * q^74 + q^75 + 13 * q^76 + 10 * q^77 + 4 * q^78 + 35 * q^79 + 22 * q^80 + 74 * q^81 + 29 * q^82 - 33 * q^83 + 13 * q^84 + 24 * q^85 + 7 * q^86 - 24 * q^87 + 12 * q^88 + 38 * q^89 + 43 * q^90 - 32 * q^91 + 7 * q^92 + 3 * q^93 - 21 * q^94 + 13 * q^95 + q^96 + 11 * q^97 + 32 * q^98 - 41 * 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
$3$	2.88697	1.66679	0.833397	−	0.552675i	$-0.186393\pi$
$3$	2.88697	1.66679	0.833397	+	0.552675i	$0.186393\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	2.88697	1.17860
$7$	−3.00491	−1.13575	−0.567875	−	0.823115i	$-0.692234\pi$
$7$	−3.00491	−1.13575	−0.567875	+	0.823115i	$0.692234\pi$
$8$	1.00000	0.353553
$9$	5.33461	1.77820
$10$	1.00000	0.316228
$11$	−0.352693	−0.106341	−0.0531704	−	0.998585i	$-0.516933\pi$
$11$	−0.352693	−0.106341	−0.0531704	+	0.998585i	$0.516933\pi$
$12$	2.88697	0.833397
$13$	5.21119	1.44532	0.722662	−	0.691201i	$-0.242918\pi$
$13$	5.21119	1.44532	0.722662	+	0.691201i	$0.242918\pi$
$14$	−3.00491	−0.803097
$15$	2.88697	0.745413
$16$	1.00000	0.250000
$17$	4.16107	1.00921	0.504603	−	0.863351i	$-0.331639\pi$
$17$	4.16107	1.00921	0.504603	+	0.863351i	$0.331639\pi$
$18$	5.33461	1.25738
$19$	−6.47701	−1.48593	−0.742964	−	0.669332i	$-0.766581\pi$
$19$	−6.47701	−1.48593	−0.742964	+	0.669332i	$0.766581\pi$
$20$	1.00000	0.223607
$21$	−8.67510	−1.89306
$22$	−0.352693	−0.0751944
$23$	−0.961461	−0.200478	−0.100239	−	0.994963i	$-0.531961\pi$
$23$	−0.961461	−0.200478	−0.100239	+	0.994963i	$0.531961\pi$
$24$	2.88697	0.589301
$25$	1.00000	0.200000
$26$	5.21119	1.02200
$27$	6.73995	1.29710
$28$	−3.00491	−0.567875
$29$	−2.72879	−0.506724	−0.253362	−	0.967372i	$-0.581536\pi$
$29$	−2.72879	−0.506724	−0.253362	+	0.967372i	$0.581536\pi$
$30$	2.88697	0.527087
$31$	6.42537	1.15403	0.577015	−	0.816734i	$-0.304217\pi$
$31$	6.42537	1.15403	0.577015	+	0.816734i	$0.304217\pi$
$32$	1.00000	0.176777
$33$	−1.01821	−0.177248
$34$	4.16107	0.713617
$35$	−3.00491	−0.507923
$36$	5.33461	0.889102
$37$	4.88720	0.803451	0.401726	−	0.915760i	$-0.368411\pi$
$37$	4.88720	0.803451	0.401726	+	0.915760i	$0.368411\pi$
$38$	−6.47701	−1.05071
$39$	15.0446	2.40906
$40$	1.00000	0.158114
$41$	−5.34619	−0.834935	−0.417467	−	0.908692i	$-0.637082\pi$
$41$	−5.34619	−0.834935	−0.417467	+	0.908692i	$0.637082\pi$
$42$	−8.67510	−1.33860
$43$	12.7527	1.94476	0.972382	−	0.233394i	$-0.0749830\pi$
$43$	12.7527	1.94476	0.972382	+	0.233394i	$0.0749830\pi$
$44$	−0.352693	−0.0531704
$45$	5.33461	0.795237
$46$	−0.961461	−0.141760
$47$	5.29179	0.771886	0.385943	−	0.922523i	$-0.373876\pi$
$47$	5.29179	0.771886	0.385943	+	0.922523i	$0.373876\pi$
$48$	2.88697	0.416699
$49$	2.02950	0.289928
$50$	1.00000	0.141421
$51$	12.0129	1.68214
$52$	5.21119	0.722662
$53$	6.33046	0.869556	0.434778	−	0.900538i	$-0.356827\pi$
$53$	6.33046	0.869556	0.434778	+	0.900538i	$0.356827\pi$
$54$	6.73995	0.917192
$55$	−0.352693	−0.0475571
$56$	−3.00491	−0.401548
$57$	−18.6989	−2.47674
$58$	−2.72879	−0.358308
$59$	1.94152	0.252764	0.126382	−	0.991982i	$-0.459664\pi$
$59$	1.94152	0.252764	0.126382	+	0.991982i	$0.459664\pi$
$60$	2.88697	0.372707
$61$	−2.76793	−0.354397	−0.177199	−	0.984175i	$-0.556704\pi$
$61$	−2.76793	−0.354397	−0.177199	+	0.984175i	$0.556704\pi$
$62$	6.42537	0.816022
$63$	−16.0300	−2.01959
$64$	1.00000	0.125000
$65$	5.21119	0.646369
$66$	−1.01821	−0.125334
$67$	14.5511	1.77770	0.888848	−	0.458203i	$-0.151507\pi$
$67$	14.5511	1.77770	0.888848	+	0.458203i	$0.151507\pi$
$68$	4.16107	0.504603
$69$	−2.77571	−0.334156
$70$	−3.00491	−0.359156
$71$	−12.4237	−1.47442	−0.737212	−	0.675662i	$-0.763858\pi$
$71$	−12.4237	−1.47442	−0.737212	+	0.675662i	$0.763858\pi$
$72$	5.33461	0.628690
$73$	0.815631	0.0954623	0.0477312	−	0.998860i	$-0.484801\pi$
$73$	0.815631	0.0954623	0.0477312	+	0.998860i	$0.484801\pi$
$74$	4.88720	0.568126
$75$	2.88697	0.333359
$76$	−6.47701	−0.742964
$77$	1.05981	0.120777
$78$	15.0446	1.70346
$79$	−15.8948	−1.78830	−0.894152	−	0.447764i	$-0.852220\pi$
$79$	−15.8948	−1.78830	−0.894152	+	0.447764i	$0.852220\pi$
$80$	1.00000	0.111803
$81$	3.45423	0.383804
$82$	−5.34619	−0.590388
$83$	9.30950	1.02185	0.510925	−	0.859625i	$-0.329303\pi$
$83$	9.30950	1.02185	0.510925	+	0.859625i	$0.329303\pi$
$84$	−8.67510	−0.946531
$85$	4.16107	0.451331
$86$	12.7527	1.37516
$87$	−7.87795	−0.844605
$88$	−0.352693	−0.0375972
$89$	−4.43001	−0.469580	−0.234790	−	0.972046i	$-0.575440\pi$
$89$	−4.43001	−0.469580	−0.234790	+	0.972046i	$0.575440\pi$
$90$	5.33461	0.562317
$91$	−15.6592	−1.64153
$92$	−0.961461	−0.100239
$93$	18.5499	1.92353
$94$	5.29179	0.545806
$95$	−6.47701	−0.664527
$96$	2.88697	0.294650
$97$	−18.8373	−1.91264	−0.956318	−	0.292330i	$-0.905570\pi$
$97$	−18.8373	−1.91264	−0.956318	+	0.292330i	$0.905570\pi$
$98$	2.02950	0.205010
$99$	−1.88148	−0.189096
$100$	1.00000	0.100000
$101$	−14.6388	−1.45661	−0.728306	−	0.685252i	$-0.759692\pi$
$101$	−14.6388	−1.45661	−0.728306	+	0.685252i	$0.759692\pi$
$102$	12.0129	1.18945
$103$	0.403241	0.0397325	0.0198663	−	0.999803i	$-0.493676\pi$
$103$	0.403241	0.0397325	0.0198663	+	0.999803i	$0.493676\pi$
$104$	5.21119	0.511000
$105$	−8.67510	−0.846603
$106$	6.33046	0.614869
$107$	−18.6153	−1.79961	−0.899803	−	0.436297i	$-0.856290\pi$
$107$	−18.6153	−1.79961	−0.899803	+	0.436297i	$0.856290\pi$
$108$	6.73995	0.648552
$109$	19.6377	1.88095	0.940475	−	0.339862i	$-0.110380\pi$
$109$	19.6377	1.88095	0.940475	+	0.339862i	$0.110380\pi$
$110$	−0.352693	−0.0336279
$111$	14.1092	1.33919
$112$	−3.00491	−0.283937
$113$	−5.90817	−0.555794	−0.277897	−	0.960611i	$-0.589637\pi$
$113$	−5.90817	−0.555794	−0.277897	+	0.960611i	$0.589637\pi$
$114$	−18.6989	−1.75132
$115$	−0.961461	−0.0896567
$116$	−2.72879	−0.253362
$117$	27.7997	2.57008
$118$	1.94152	0.178731
$119$	−12.5036	−1.14621
$120$	2.88697	0.263543
$121$	−10.8756	−0.988692
$122$	−2.76793	−0.250597
$123$	−15.4343	−1.39166
$124$	6.42537	0.577015
$125$	1.00000	0.0894427
$126$	−16.0300	−1.42807
$127$	−1.80126	−0.159836	−0.0799182	−	0.996801i	$-0.525466\pi$
$127$	−1.80126	−0.159836	−0.0799182	+	0.996801i	$0.525466\pi$
$128$	1.00000	0.0883883
$129$	36.8166	3.24152
$130$	5.21119	0.457052
$131$	−6.64364	−0.580458	−0.290229	−	0.956957i	$-0.593731\pi$
$131$	−6.64364	−0.580458	−0.290229	+	0.956957i	$0.593731\pi$
$132$	−1.01821	−0.0886242
$133$	19.4628	1.68764
$134$	14.5511	1.25702
$135$	6.73995	0.580083
$136$	4.16107	0.356809
$137$	7.33813	0.626939	0.313470	−	0.949598i	$-0.398509\pi$
$137$	7.33813	0.626939	0.313470	+	0.949598i	$0.398509\pi$
$138$	−2.77571	−0.236284
$139$	−16.9588	−1.43842	−0.719212	−	0.694791i	$-0.755497\pi$
$139$	−16.9588	−1.43842	−0.719212	+	0.694791i	$0.755497\pi$
$140$	−3.00491	−0.253961
$141$	15.2772	1.28658
$142$	−12.4237	−1.04258
$143$	−1.83795	−0.153697
$144$	5.33461	0.444551
$145$	−2.72879	−0.226614
$146$	0.815631	0.0675021
$147$	5.85910	0.483250
$148$	4.88720	0.401726
$149$	15.4659	1.26702	0.633508	−	0.773736i	$-0.281614\pi$
$149$	15.4659	1.26702	0.633508	+	0.773736i	$0.281614\pi$
$150$	2.88697	0.235720
$151$	−22.6342	−1.84194	−0.920972	−	0.389628i	$-0.872604\pi$
$151$	−22.6342	−1.84194	−0.920972	+	0.389628i	$0.872604\pi$
$152$	−6.47701	−0.525355
$153$	22.1977	1.79458
$154$	1.05981	0.0854020
$155$	6.42537	0.516098
$156$	15.0446	1.20453
$157$	−7.26165	−0.579543	−0.289771	−	0.957096i	$-0.593579\pi$
$157$	−7.26165	−0.579543	−0.289771	+	0.957096i	$0.593579\pi$
$158$	−15.8948	−1.26452
$159$	18.2759	1.44937
$160$	1.00000	0.0790569
$161$	2.88911	0.227693
$162$	3.45423	0.271390
$163$	11.1134	0.870468	0.435234	−	0.900317i	$-0.356666\pi$
$163$	11.1134	0.870468	0.435234	+	0.900317i	$0.356666\pi$
$164$	−5.34619	−0.417467
$165$	−1.01821	−0.0792679
$166$	9.30950	0.722557
$167$	−16.7808	−1.29854	−0.649268	−	0.760560i	$-0.724925\pi$
$167$	−16.7808	−1.29854	−0.649268	+	0.760560i	$0.724925\pi$
$168$	−8.67510	−0.669298
$169$	14.1565	1.08896
$170$	4.16107	0.319139
$171$	−34.5523	−2.64228
$172$	12.7527	0.972382
$173$	20.4096	1.55171	0.775856	−	0.630910i	$-0.217318\pi$
$173$	20.4096	1.55171	0.775856	+	0.630910i	$0.217318\pi$
$174$	−7.87795	−0.597226
$175$	−3.00491	−0.227150
$176$	−0.352693	−0.0265852
$177$	5.60510	0.421305
$178$	−4.43001	−0.332043
$179$	−7.84475	−0.586344	−0.293172	−	0.956060i	$-0.594711\pi$
$179$	−7.84475	−0.586344	−0.293172	+	0.956060i	$0.594711\pi$
$180$	5.33461	0.397618
$181$	−21.5993	−1.60547	−0.802733	−	0.596338i	$-0.796622\pi$
$181$	−21.5993	−1.60547	−0.802733	+	0.596338i	$0.796622\pi$
$182$	−15.6592	−1.16074
$183$	−7.99094	−0.590707
$184$	−0.961461	−0.0708798
$185$	4.88720	0.359314
$186$	18.5499	1.36014
$187$	−1.46758	−0.107320
$188$	5.29179	0.385943
$189$	−20.2530	−1.47319
$190$	−6.47701	−0.469892
$191$	19.6697	1.42325	0.711623	−	0.702562i	$-0.247960\pi$
$191$	19.6697	1.42325	0.711623	+	0.702562i	$0.247960\pi$
$192$	2.88697	0.208349
$193$	−4.02360	−0.289625	−0.144813	−	0.989459i	$-0.546258\pi$
$193$	−4.02360	−0.289625	−0.144813	+	0.989459i	$0.546258\pi$
$194$	−18.8373	−1.35244
$195$	15.0446	1.07736
$196$	2.02950	0.144964
$197$	3.59063	0.255822	0.127911	−	0.991786i	$-0.459173\pi$
$197$	3.59063	0.255822	0.127911	+	0.991786i	$0.459173\pi$
$198$	−1.88148	−0.133711
$199$	9.12209	0.646648	0.323324	−	0.946288i	$-0.395200\pi$
$199$	9.12209	0.646648	0.323324	+	0.946288i	$0.395200\pi$
$200$	1.00000	0.0707107
$201$	42.0085	2.96305
$202$	−14.6388	−1.02998
$203$	8.19978	0.575512
$204$	12.0129	0.841070
$205$	−5.34619	−0.373394
$206$	0.403241	0.0280951
$207$	−5.12902	−0.356491
$208$	5.21119	0.361331
$209$	2.28439	0.158015
$210$	−8.67510	−0.598639
$211$	4.24631	0.292328	0.146164	−	0.989260i	$-0.453307\pi$
$211$	4.24631	0.292328	0.146164	+	0.989260i	$0.453307\pi$
$212$	6.33046	0.434778
$213$	−35.8669	−2.45756
$214$	−18.6153	−1.27251
$215$	12.7527	0.869725
$216$	6.73995	0.458596
$217$	−19.3077	−1.31069
$218$	19.6377	1.33003
$219$	2.35470	0.159116
$220$	−0.352693	−0.0237785
$221$	21.6841	1.45863
$222$	14.1092	0.946949
$223$	−9.67104	−0.647621	−0.323810	−	0.946122i	$-0.604964\pi$
$223$	−9.67104	−0.647621	−0.323810	+	0.946122i	$0.604964\pi$
$224$	−3.00491	−0.200774
$225$	5.33461	0.355641
$226$	−5.90817	−0.393006
$227$	10.7364	0.712602	0.356301	−	0.934371i	$-0.384038\pi$
$227$	10.7364	0.712602	0.356301	+	0.934371i	$0.384038\pi$
$228$	−18.6989	−1.23837
$229$	7.66550	0.506550	0.253275	−	0.967394i	$-0.418492\pi$
$229$	7.66550	0.506550	0.253275	+	0.967394i	$0.418492\pi$
$230$	−0.961461	−0.0633969
$231$	3.05965	0.201310
$232$	−2.72879	−0.179154
$233$	−14.4301	−0.945346	−0.472673	−	0.881238i	$-0.656711\pi$
$233$	−14.4301	−0.945346	−0.472673	+	0.881238i	$0.656711\pi$
$234$	27.7997	1.81732
$235$	5.29179	0.345198
$236$	1.94152	0.126382
$237$	−45.8878	−2.98073
$238$	−12.5036	−0.810491
$239$	−15.1537	−0.980208	−0.490104	−	0.871664i	$-0.663041\pi$
$239$	−15.1537	−0.980208	−0.490104	+	0.871664i	$0.663041\pi$
$240$	2.88697	0.186353
$241$	14.8455	0.956284	0.478142	−	0.878283i	$-0.341310\pi$
$241$	14.8455	0.956284	0.478142	+	0.878283i	$0.341310\pi$
$242$	−10.8756	−0.699111
$243$	−10.2476	−0.657383
$244$	−2.76793	−0.177199
$245$	2.02950	0.129660
$246$	−15.4343	−0.984055
$247$	−33.7529	−2.14765
$248$	6.42537	0.408011
$249$	26.8763	1.70321
$250$	1.00000	0.0632456
$251$	2.34934	0.148289	0.0741445	−	0.997248i	$-0.476377\pi$
$251$	2.34934	0.148289	0.0741445	+	0.997248i	$0.476377\pi$
$252$	−16.0300	−1.00980
$253$	0.339100	0.0213191
$254$	−1.80126	−0.113021
$255$	12.0129	0.752276
$256$	1.00000	0.0625000
$257$	−15.1618	−0.945768	−0.472884	−	0.881125i	$-0.656787\pi$
$257$	−15.1618	−0.945768	−0.472884	+	0.881125i	$0.656787\pi$
$258$	36.8166	2.29210
$259$	−14.6856	−0.912520
$260$	5.21119	0.323184
$261$	−14.5570	−0.901058
$262$	−6.64364	−0.410446
$263$	−0.0193164	−0.00119110	−0.000595550	−	1.00000i	$-0.500190\pi$
$263$	−0.0193164	−0.00119110	−0.000595550		1.00000i	$0.500190\pi$
$264$	−1.01821	−0.0626668
$265$	6.33046	0.388877
$266$	19.4628	1.19334
$267$	−12.7893	−0.782693
$268$	14.5511	0.888848
$269$	29.7435	1.81350	0.906748	−	0.421674i	$-0.138557\pi$
$269$	29.7435	1.81350	0.906748	+	0.421674i	$0.138557\pi$
$270$	6.73995	0.410181
$271$	14.6993	0.892916	0.446458	−	0.894805i	$-0.352685\pi$
$271$	14.6993	0.892916	0.446458	+	0.894805i	$0.352685\pi$
$272$	4.16107	0.252302
$273$	−45.2076	−2.73609
$274$	7.33813	0.443313
$275$	−0.352693	−0.0212682
$276$	−2.77571	−0.167078
$277$	16.3679	0.983454	0.491727	−	0.870749i	$-0.336366\pi$
$277$	16.3679	0.983454	0.491727	+	0.870749i	$0.336366\pi$
$278$	−16.9588	−1.01712
$279$	34.2768	2.05210
$280$	−3.00491	−0.179578
$281$	−7.15437	−0.426794	−0.213397	−	0.976966i	$-0.568453\pi$
$281$	−7.15437	−0.426794	−0.213397	+	0.976966i	$0.568453\pi$
$282$	15.2772	0.909746
$283$	−26.2064	−1.55781	−0.778903	−	0.627144i	$-0.784224\pi$
$283$	−26.2064	−1.55781	−0.778903	+	0.627144i	$0.784224\pi$
$284$	−12.4237	−0.737212
$285$	−18.6989	−1.10763
$286$	−1.83795	−0.108680
$287$	16.0648	0.948277
$288$	5.33461	0.314345
$289$	0.314478	0.0184987
$290$	−2.72879	−0.160240
$291$	−54.3827	−3.18797
$292$	0.815631	0.0477312
$293$	−31.5675	−1.84419	−0.922096	−	0.386960i	$-0.873525\pi$
$293$	−31.5675	−1.84419	−0.922096	+	0.386960i	$0.873525\pi$
$294$	5.85910	0.341710
$295$	1.94152	0.113039
$296$	4.88720	0.284063
$297$	−2.37713	−0.137935
$298$	15.4659	0.895916
$299$	−5.01036	−0.289757
$300$	2.88697	0.166679
$301$	−38.3207	−2.20877
$302$	−22.6342	−1.30245
$303$	−42.2617	−2.42787
$304$	−6.47701	−0.371482
$305$	−2.76793	−0.158491
$306$	22.1977	1.26896
$307$	−27.1426	−1.54911	−0.774555	−	0.632507i	$-0.782026\pi$
$307$	−27.1426	−1.54911	−0.774555	+	0.632507i	$0.782026\pi$
$308$	1.05981	0.0603883
$309$	1.16415	0.0662259
$310$	6.42537	0.364936
$311$	−1.43517	−0.0813810	−0.0406905	−	0.999172i	$-0.512956\pi$
$311$	−1.43517	−0.0813810	−0.0406905	+	0.999172i	$0.512956\pi$
$312$	15.0446	0.851731
$313$	5.93627	0.335538	0.167769	−	0.985826i	$-0.446344\pi$
$313$	5.93627	0.335538	0.167769	+	0.985826i	$0.446344\pi$
$314$	−7.26165	−0.409799
$315$	−16.0300	−0.903190
$316$	−15.8948	−0.894152
$317$	16.3797	0.919978	0.459989	−	0.887925i	$-0.347853\pi$
$317$	16.3797	0.919978	0.459989	+	0.887925i	$0.347853\pi$
$318$	18.2759	1.02486
$319$	0.962426	0.0538855
$320$	1.00000	0.0559017
$321$	−53.7418	−2.99957
$322$	2.88911	0.161004
$323$	−26.9513	−1.49961
$324$	3.45423	0.191902
$325$	5.21119	0.289065
$326$	11.1134	0.615514
$327$	56.6935	3.13516
$328$	−5.34619	−0.295194
$329$	−15.9013	−0.876670
$330$	−1.01821	−0.0560509
$331$	−28.3742	−1.55959	−0.779794	−	0.626036i	$-0.784676\pi$
$331$	−28.3742	−1.55959	−0.779794	+	0.626036i	$0.784676\pi$
$332$	9.30950	0.510925
$333$	26.0713	1.42870
$334$	−16.7808	−0.918203
$335$	14.5511	0.795009
$336$	−8.67510	−0.473265
$337$	18.0605	0.983820	0.491910	−	0.870646i	$-0.336299\pi$
$337$	18.0605	0.983820	0.491910	+	0.870646i	$0.336299\pi$
$338$	14.1565	0.770014
$339$	−17.0567	−0.926394
$340$	4.16107	0.225666
$341$	−2.26618	−0.122721
$342$	−34.5523	−1.86837
$343$	14.9359	0.806464
$344$	12.7527	0.687578
$345$	−2.77571	−0.149439
$346$	20.4096	1.09723
$347$	−15.0623	−0.808584	−0.404292	−	0.914630i	$-0.632482\pi$
$347$	−15.0623	−0.808584	−0.404292	+	0.914630i	$0.632482\pi$
$348$	−7.87795	−0.422302
$349$	−12.8012	−0.685230	−0.342615	−	0.939476i	$-0.611313\pi$
$349$	−12.8012	−0.685230	−0.342615	+	0.939476i	$0.611313\pi$
$350$	−3.00491	−0.160619
$351$	35.1232	1.87474
$352$	−0.352693	−0.0187986
$353$	34.5622	1.83956	0.919779	−	0.392436i	$-0.128368\pi$
$353$	34.5622	1.83956	0.919779	+	0.392436i	$0.128368\pi$
$354$	5.60510	0.297908
$355$	−12.4237	−0.659382
$356$	−4.43001	−0.234790
$357$	−36.0977	−1.91049
$358$	−7.84475	−0.414608
$359$	12.3118	0.649790	0.324895	−	0.945750i	$-0.394671\pi$
$359$	12.3118	0.649790	0.324895	+	0.945750i	$0.394671\pi$
$360$	5.33461	0.281159
$361$	22.9516	1.20798
$362$	−21.5993	−1.13524
$363$	−31.3976	−1.64795
$364$	−15.6592	−0.820764
$365$	0.815631	0.0426921
$366$	−7.99094	−0.417693
$367$	−28.0300	−1.46316	−0.731578	−	0.681758i	$-0.761216\pi$
$367$	−28.0300	−1.46316	−0.731578	+	0.681758i	$0.761216\pi$
$368$	−0.961461	−0.0501196
$369$	−28.5198	−1.48468
$370$	4.88720	0.254074
$371$	−19.0225	−0.987598
$372$	18.5499	0.961765
$373$	31.0946	1.61002	0.805010	−	0.593262i	$-0.202160\pi$
$373$	31.0946	1.61002	0.805010	+	0.593262i	$0.202160\pi$
$374$	−1.46758	−0.0758867
$375$	2.88697	0.149083
$376$	5.29179	0.272903
$377$	−14.2203	−0.732381
$378$	−20.2530	−1.04170
$379$	32.3312	1.66074	0.830371	−	0.557211i	$-0.188128\pi$
$379$	32.3312	1.66074	0.830371	+	0.557211i	$0.188128\pi$
$380$	−6.47701	−0.332264
$381$	−5.20020	−0.266414
$382$	19.6697	1.00639
$383$	−9.07708	−0.463817	−0.231908	−	0.972738i	$-0.574497\pi$
$383$	−9.07708	−0.463817	−0.231908	+	0.972738i	$0.574497\pi$
$384$	2.88697	0.147325
$385$	1.05981	0.0540130
$386$	−4.02360	−0.204796
$387$	68.0305	3.45819
$388$	−18.8373	−0.956318
$389$	2.98986	0.151592	0.0757959	−	0.997123i	$-0.475850\pi$
$389$	2.98986	0.151592	0.0757959	+	0.997123i	$0.475850\pi$
$390$	15.0446	0.761811
$391$	−4.00070	−0.202324
$392$	2.02950	0.102505
$393$	−19.1800	−0.967504
$394$	3.59063	0.180893
$395$	−15.8948	−0.799754
$396$	−1.88148	−0.0945479
$397$	23.9459	1.20181	0.600906	−	0.799320i	$-0.294807\pi$
$397$	23.9459	1.20181	0.600906	+	0.799320i	$0.294807\pi$
$398$	9.12209	0.457249
$399$	56.1887	2.81295
$400$	1.00000	0.0500000
$401$	1.00000	0.0499376
$401$	1.00000	0.0499376
$402$	42.0085	2.09519
$403$	33.4838	1.66795
$404$	−14.6388	−0.728306
$405$	3.45423	0.171642
$406$	8.19978	0.406948
$407$	−1.72368	−0.0854397
$408$	12.0129	0.594726
$409$	−12.3505	−0.610692	−0.305346	−	0.952241i	$-0.598772\pi$
$409$	−12.3505	−0.610692	−0.305346	+	0.952241i	$0.598772\pi$
$410$	−5.34619	−0.264030
$411$	21.1850	1.04498
$412$	0.403241	0.0198663
$413$	−5.83408	−0.287077
$414$	−5.12902	−0.252078
$415$	9.30950	0.456985
$416$	5.21119	0.255500
$417$	−48.9595	−2.39756
$418$	2.28439	0.111733
$419$	−8.78143	−0.429001	−0.214500	−	0.976724i	$-0.568812\pi$
$419$	−8.78143	−0.429001	−0.214500	+	0.976724i	$0.568812\pi$
$420$	−8.67510	−0.423301
$421$	−15.3913	−0.750126	−0.375063	−	0.926999i	$-0.622379\pi$
$421$	−15.3913	−0.750126	−0.375063	+	0.926999i	$0.622379\pi$
$422$	4.24631	0.206707
$423$	28.2296	1.37257
$424$	6.33046	0.307435
$425$	4.16107	0.201841
$426$	−35.8669	−1.73776
$427$	8.31739	0.402507
$428$	−18.6153	−0.899803
$429$	−5.30611	−0.256182
$430$	12.7527	0.614989
$431$	−31.0498	−1.49562	−0.747808	−	0.663915i	$-0.768894\pi$
$431$	−31.0498	−1.49562	−0.747808	+	0.663915i	$0.768894\pi$
$432$	6.73995	0.324276
$433$	9.03970	0.434420	0.217210	−	0.976125i	$-0.430304\pi$
$433$	9.03970	0.434420	0.217210	+	0.976125i	$0.430304\pi$
$434$	−19.3077	−0.926797
$435$	−7.87795	−0.377719
$436$	19.6377	0.940475
$437$	6.22739	0.297896
$438$	2.35470	0.112512
$439$	25.5201	1.21801	0.609004	−	0.793167i	$-0.291569\pi$
$439$	25.5201	1.21801	0.609004	+	0.793167i	$0.291569\pi$
$440$	−0.352693	−0.0168140
$441$	10.8266	0.515551
$442$	21.6841	1.03141
$443$	−24.6233	−1.16989	−0.584944	−	0.811073i	$-0.698884\pi$
$443$	−24.6233	−1.16989	−0.584944	+	0.811073i	$0.698884\pi$
$444$	14.1092	0.669594
$445$	−4.43001	−0.210002
$446$	−9.67104	−0.457937
$447$	44.6496	2.11186
$448$	−3.00491	−0.141969
$449$	6.91809	0.326485	0.163242	−	0.986586i	$-0.447805\pi$
$449$	6.91809	0.326485	0.163242	+	0.986586i	$0.447805\pi$
$450$	5.33461	0.251476
$451$	1.88556	0.0887877
$452$	−5.90817	−0.277897
$453$	−65.3443	−3.07014
$454$	10.7364	0.503886
$455$	−15.6592	−0.734114
$456$	−18.6989	−0.875658
$457$	−5.81648	−0.272084	−0.136042	−	0.990703i	$-0.543438\pi$
$457$	−5.81648	−0.272084	−0.136042	+	0.990703i	$0.543438\pi$
$458$	7.66550	0.358185
$459$	28.0454	1.30905
$460$	−0.961461	−0.0448283
$461$	34.6966	1.61598	0.807991	−	0.589194i	$-0.200555\pi$
$461$	34.6966	1.61598	0.807991	+	0.589194i	$0.200555\pi$
$462$	3.05965	0.142348
$463$	20.2015	0.938844	0.469422	−	0.882974i	$-0.344462\pi$
$463$	20.2015	0.938844	0.469422	+	0.882974i	$0.344462\pi$
$464$	−2.72879	−0.126681
$465$	18.5499	0.860229
$466$	−14.4301	−0.668461
$467$	32.6777	1.51214	0.756072	−	0.654488i	$-0.227116\pi$
$467$	32.6777	1.51214	0.756072	+	0.654488i	$0.227116\pi$
$468$	27.7997	1.28504
$469$	−43.7247	−2.01902
$470$	5.29179	0.244092
$471$	−20.9642	−0.965979
$472$	1.94152	0.0893655
$473$	−4.49778	−0.206808
$474$	−45.8878	−2.10770
$475$	−6.47701	−0.297186
$476$	−12.5036	−0.573103
$477$	33.7706	1.54625
$478$	−15.1537	−0.693112
$479$	−39.1837	−1.79035	−0.895175	−	0.445715i	$-0.852950\pi$
$479$	−39.1837	−1.79035	−0.895175	+	0.445715i	$0.852950\pi$
$480$	2.88697	0.131772
$481$	25.4682	1.16125
$482$	14.8455	0.676195
$483$	8.34077	0.379518
$484$	−10.8756	−0.494346
$485$	−18.8373	−0.855356
$486$	−10.2476	−0.464840
$487$	−7.84738	−0.355599	−0.177799	−	0.984067i	$-0.556898\pi$
$487$	−7.84738	−0.355599	−0.177799	+	0.984067i	$0.556898\pi$
$488$	−2.76793	−0.125298
$489$	32.0840	1.45089
$490$	2.02950	0.0916833
$491$	3.56851	0.161045	0.0805223	−	0.996753i	$-0.474341\pi$
$491$	3.56851	0.161045	0.0805223	+	0.996753i	$0.474341\pi$
$492$	−15.4343	−0.695832
$493$	−11.3547	−0.511389
$494$	−33.7529	−1.51862
$495$	−1.88148	−0.0845662
$496$	6.42537	0.288507
$497$	37.3322	1.67458
$498$	26.8763	1.20435
$499$	−34.6315	−1.55032	−0.775160	−	0.631765i	$-0.782331\pi$
$499$	−34.6315	−1.55032	−0.775160	+	0.631765i	$0.782331\pi$
$500$	1.00000	0.0447214
$501$	−48.4457	−2.16439
$502$	2.34934	0.104856
$503$	−31.6666	−1.41194	−0.705972	−	0.708240i	$-0.749490\pi$
$503$	−31.6666	−1.41194	−0.705972	+	0.708240i	$0.749490\pi$
$504$	−16.0300	−0.714034
$505$	−14.6388	−0.651417
$506$	0.339100	0.0150749
$507$	40.8695	1.81508
$508$	−1.80126	−0.0799182
$509$	4.06497	0.180177	0.0900884	−	0.995934i	$-0.471285\pi$
$509$	4.06497	0.180177	0.0900884	+	0.995934i	$0.471285\pi$
$510$	12.0129	0.531940
$511$	−2.45090	−0.108421
$512$	1.00000	0.0441942
$513$	−43.6547	−1.92740
$514$	−15.1618	−0.668759
$515$	0.403241	0.0177689
$516$	36.8166	1.62076
$517$	−1.86637	−0.0820831
$518$	−14.6856	−0.645249
$519$	58.9219	2.58639
$520$	5.21119	0.228526
$521$	−15.4701	−0.677758	−0.338879	−	0.940830i	$-0.610048\pi$
$521$	−15.4701	−0.677758	−0.338879	+	0.940830i	$0.610048\pi$
$522$	−14.5570	−0.637144
$523$	26.1289	1.14254	0.571269	−	0.820763i	$-0.306451\pi$
$523$	26.1289	1.14254	0.571269	+	0.820763i	$0.306451\pi$
$524$	−6.64364	−0.290229
$525$	−8.67510	−0.378612
$526$	−0.0193164	−0.000842235 0
$527$	26.7364	1.16465
$528$	−1.01821	−0.0443121
$529$	−22.0756	−0.959808
$530$	6.33046	0.274978
$531$	10.3572	0.449465
$532$	19.4628	0.843821
$533$	−27.8600	−1.20675
$534$	−12.7893	−0.553447
$535$	−18.6153	−0.804808
$536$	14.5511	0.628510
$537$	−22.6476	−0.977315
$538$	29.7435	1.28233
$539$	−0.715789	−0.0308312
$540$	6.73995	0.290041
$541$	−2.11443	−0.0909065	−0.0454532	−	0.998966i	$-0.514473\pi$
$541$	−2.11443	−0.0909065	−0.0454532	+	0.998966i	$0.514473\pi$
$542$	14.6993	0.631387
$543$	−62.3567	−2.67598
$544$	4.16107	0.178404
$545$	19.6377	0.841187
$546$	−45.2076	−1.93471
$547$	−13.0000	−0.555838	−0.277919	−	0.960604i	$-0.589645\pi$
$547$	−13.0000	−0.555838	−0.277919	+	0.960604i	$0.589645\pi$
$548$	7.33813	0.313470
$549$	−14.7658	−0.630190
$550$	−0.352693	−0.0150389
$551$	17.6744	0.752955
$552$	−2.77571	−0.118142
$553$	47.7624	2.03107
$554$	16.3679	0.695407
$555$	14.1092	0.598903
$556$	−16.9588	−0.719212
$557$	−11.0659	−0.468878	−0.234439	−	0.972131i	$-0.575325\pi$
$557$	−11.0659	−0.468878	−0.234439	+	0.972131i	$0.575325\pi$
$558$	34.2768	1.45105
$559$	66.4567	2.81082
$560$	−3.00491	−0.126981
$561$	−4.23686	−0.178880
$562$	−7.15437	−0.301789
$563$	−33.9085	−1.42907	−0.714537	−	0.699598i	$-0.753362\pi$
$563$	−33.9085	−1.42907	−0.714537	+	0.699598i	$0.753362\pi$
$564$	15.2772	0.643288
$565$	−5.90817	−0.248559
$566$	−26.2064	−1.10154
$567$	−10.3797	−0.435905
$568$	−12.4237	−0.521288
$569$	8.62359	0.361520	0.180760	−	0.983527i	$-0.442144\pi$
$569$	8.62359	0.361520	0.180760	+	0.983527i	$0.442144\pi$
$570$	−18.6989	−0.783213
$571$	−4.58073	−0.191697	−0.0958487	−	0.995396i	$-0.530557\pi$
$571$	−4.58073	−0.191697	−0.0958487	+	0.995396i	$0.530557\pi$
$572$	−1.83795	−0.0768486
$573$	56.7857	2.37226
$574$	16.0648	0.670533
$575$	−0.961461	−0.0400957
$576$	5.33461	0.222275
$577$	6.49955	0.270580	0.135290	−	0.990806i	$-0.456803\pi$
$577$	6.49955	0.270580	0.135290	+	0.990806i	$0.456803\pi$
$578$	0.314478	0.0130805
$579$	−11.6160	−0.482746
$580$	−2.72879	−0.113307
$581$	−27.9742	−1.16057
$582$	−54.3827	−2.25423
$583$	−2.23271	−0.0924694
$584$	0.815631	0.0337510
$585$	27.7997	1.14938
$586$	−31.5675	−1.30404
$587$	30.5997	1.26298	0.631492	−	0.775383i	$-0.282443\pi$
$587$	30.5997	1.26298	0.631492	+	0.775383i	$0.282443\pi$
$588$	5.85910	0.241625
$589$	−41.6171	−1.71480
$590$	1.94152	0.0799309
$591$	10.3661	0.426403
$592$	4.88720	0.200863
$593$	43.8214	1.79953	0.899765	−	0.436376i	$-0.143738\pi$
$593$	43.8214	1.79953	0.899765	+	0.436376i	$0.143738\pi$
$594$	−2.37713	−0.0975350
$595$	−12.5036	−0.512599
$596$	15.4659	0.633508
$597$	26.3352	1.07783
$598$	−5.01036	−0.204889
$599$	−4.26116	−0.174106	−0.0870531	−	0.996204i	$-0.527745\pi$
$599$	−4.26116	−0.174106	−0.0870531	+	0.996204i	$0.527745\pi$
$600$	2.88697	0.117860
$601$	−32.8134	−1.33849	−0.669244	−	0.743043i	$-0.733382\pi$
$601$	−32.8134	−1.33849	−0.669244	+	0.743043i	$0.733382\pi$
$602$	−38.3207	−1.56183
$603$	77.6242	3.16110
$604$	−22.6342	−0.920972
$605$	−10.8756	−0.442156
$606$	−42.2617	−1.71677
$607$	−1.94263	−0.0788491	−0.0394245	−	0.999223i	$-0.512552\pi$
$607$	−1.94263	−0.0788491	−0.0394245	+	0.999223i	$0.512552\pi$
$608$	−6.47701	−0.262677
$609$	23.6725	0.959260
$610$	−2.76793	−0.112070
$611$	27.5765	1.11563
$612$	22.1977	0.897288
$613$	24.8459	1.00352	0.501759	−	0.865007i	$-0.332686\pi$
$613$	24.8459	1.00352	0.501759	+	0.865007i	$0.332686\pi$
$614$	−27.1426	−1.09539
$615$	−15.4343	−0.622371
$616$	1.05981	0.0427010
$617$	−30.2735	−1.21876	−0.609382	−	0.792877i	$-0.708582\pi$
$617$	−30.2735	−1.21876	−0.609382	+	0.792877i	$0.708582\pi$
$618$	1.16415	0.0468288
$619$	21.5728	0.867085	0.433543	−	0.901133i	$-0.357263\pi$
$619$	21.5728	0.867085	0.433543	+	0.901133i	$0.357263\pi$
$620$	6.42537	0.258049
$621$	−6.48020	−0.260042
$622$	−1.43517	−0.0575451
$623$	13.3118	0.533325
$624$	15.0446	0.602265
$625$	1.00000	0.0400000
$626$	5.93627	0.237261
$627$	6.59498	0.263378
$628$	−7.26165	−0.289771
$629$	20.3360	0.810849
$630$	−16.0300	−0.638652
$631$	6.00569	0.239083	0.119541	−	0.992829i	$-0.461858\pi$
$631$	6.00569	0.239083	0.119541	+	0.992829i	$0.461858\pi$
$632$	−15.8948	−0.632261
$633$	12.2590	0.487251
$634$	16.3797	0.650523
$635$	−1.80126	−0.0714810
$636$	18.2759	0.724686
$637$	10.5761	0.419040
$638$	0.962426	0.0381028
$639$	−66.2757	−2.62183
$640$	1.00000	0.0395285
$641$	−50.3961	−1.99053	−0.995264	−	0.0972137i	$-0.969007\pi$
$641$	−50.3961	−1.99053	−0.995264	+	0.0972137i	$0.969007\pi$
$642$	−53.7418	−2.12102
$643$	−0.192012	−0.00757220	−0.00378610	−	0.999993i	$-0.501205\pi$
$643$	−0.192012	−0.00757220	−0.00378610	+	0.999993i	$0.501205\pi$
$644$	2.88911	0.113847
$645$	36.8166	1.44965
$646$	−26.9513	−1.06038
$647$	−0.370379	−0.0145611	−0.00728054	−	0.999973i	$-0.502317\pi$
$647$	−0.370379	−0.0145611	−0.00728054	+	0.999973i	$0.502317\pi$
$648$	3.45423	0.135695
$649$	−0.684759	−0.0268791
$650$	5.21119	0.204400
$651$	−55.7407	−2.18465
$652$	11.1134	0.435234
$653$	13.0031	0.508851	0.254426	−	0.967092i	$-0.418114\pi$
$653$	13.0031	0.508851	0.254426	+	0.967092i	$0.418114\pi$
$654$	56.6935	2.21689
$655$	−6.64364	−0.259589
$656$	−5.34619	−0.208734
$657$	4.35107	0.169751
$658$	−15.9013	−0.619899
$659$	11.7857	0.459104	0.229552	−	0.973296i	$-0.426274\pi$
$659$	11.7857	0.459104	0.229552	+	0.973296i	$0.426274\pi$
$660$	−1.01821	−0.0396339
$661$	33.3806	1.29835	0.649177	−	0.760637i	$-0.275113\pi$
$661$	33.3806	1.29835	0.649177	+	0.760637i	$0.275113\pi$
$662$	−28.3742	−1.10280
$663$	62.6015	2.43124
$664$	9.30950	0.361279
$665$	19.4628	0.754737
$666$	26.0713	1.01024
$667$	2.62363	0.101587
$668$	−16.7808	−0.649268
$669$	−27.9200	−1.07945
$670$	14.5511	0.562157
$671$	0.976230	0.0376869
$672$	−8.67510	−0.334649
$673$	−3.96535	−0.152853	−0.0764265	−	0.997075i	$-0.524351\pi$
$673$	−3.96535	−0.152853	−0.0764265	+	0.997075i	$0.524351\pi$
$674$	18.0605	0.695666
$675$	6.73995	0.259421
$676$	14.1565	0.544482
$677$	37.9898	1.46007	0.730033	−	0.683412i	$-0.239505\pi$
$677$	37.9898	1.46007	0.730033	+	0.683412i	$0.239505\pi$
$678$	−17.0567	−0.655059
$679$	56.6043	2.17228
$680$	4.16107	0.159570
$681$	30.9958	1.18776
$682$	−2.26618	−0.0867765
$683$	−0.559071	−0.0213923	−0.0106961	−	0.999943i	$-0.503405\pi$
$683$	−0.559071	−0.0213923	−0.0106961	+	0.999943i	$0.503405\pi$
$684$	−34.5523	−1.32114
$685$	7.33813	0.280376
$686$	14.9359	0.570256
$687$	22.1301	0.844315
$688$	12.7527	0.486191
$689$	32.9893	1.25679
$690$	−2.77571	−0.105670
$691$	−51.4835	−1.95852	−0.979262	−	0.202599i	$-0.935061\pi$
$691$	−51.4835	−1.95852	−0.979262	+	0.202599i	$0.935061\pi$
$692$	20.4096	0.775856
$693$	5.65368	0.214765
$694$	−15.0623	−0.571755
$695$	−16.9588	−0.643282
$696$	−7.87795	−0.298613
$697$	−22.2459	−0.842622
$698$	−12.8012	−0.484531
$699$	−41.6592	−1.57570
$700$	−3.00491	−0.113575
$701$	33.3342	1.25901	0.629507	−	0.776995i	$-0.283257\pi$
$701$	33.3342	1.25901	0.629507	+	0.776995i	$0.283257\pi$
$702$	35.1232	1.32564
$703$	−31.6545	−1.19387
$704$	−0.352693	−0.0132926
$705$	15.2772	0.575374
$706$	34.5622	1.30076
$707$	43.9882	1.65435
$708$	5.60510	0.210653
$709$	−7.60498	−0.285611	−0.142806	−	0.989751i	$-0.545612\pi$
$709$	−7.60498	−0.285611	−0.142806	+	0.989751i	$0.545612\pi$
$710$	−12.4237	−0.466254
$711$	−84.7925	−3.17997
$712$	−4.43001	−0.166021
$713$	−6.17774	−0.231358
$714$	−36.0977	−1.35092
$715$	−1.83795	−0.0687355
$716$	−7.84475	−0.293172
$717$	−43.7482	−1.63381
$718$	12.3118	0.459471
$719$	−49.3059	−1.83880	−0.919399	−	0.393325i	$-0.871325\pi$
$719$	−49.3059	−1.83880	−0.919399	+	0.393325i	$0.871325\pi$
$720$	5.33461	0.198809
$721$	−1.21170	−0.0451262
$722$	22.9516	0.854171
$723$	42.8586	1.59393
$724$	−21.5993	−0.802733
$725$	−2.72879	−0.101345
$726$	−31.3976	−1.16527
$727$	−11.2405	−0.416886	−0.208443	−	0.978035i	$-0.566840\pi$
$727$	−11.2405	−0.416886	−0.208443	+	0.978035i	$0.566840\pi$
$728$	−15.6592	−0.580368
$729$	−39.9472	−1.47953
$730$	0.815631	0.0301878
$731$	53.0647	1.96267
$732$	−7.99094	−0.295354
$733$	−21.3435	−0.788341	−0.394171	−	0.919037i	$-0.628968\pi$
$733$	−21.3435	−0.788341	−0.394171	+	0.919037i	$0.628968\pi$
$734$	−28.0300	−1.03461
$735$	5.85910	0.216116
$736$	−0.961461	−0.0354399
$737$	−5.13206	−0.189042
$738$	−28.5198	−1.04983
$739$	24.6330	0.906141	0.453070	−	0.891475i	$-0.350329\pi$
$739$	24.6330	0.906141	0.453070	+	0.891475i	$0.350329\pi$
$740$	4.88720	0.179657
$741$	−97.4438	−3.57969
$742$	−19.0225	−0.698338
$743$	−4.96765	−0.182245	−0.0911227	−	0.995840i	$-0.529046\pi$
$743$	−4.96765	−0.182245	−0.0911227	+	0.995840i	$0.529046\pi$
$744$	18.5499	0.680071
$745$	15.4659	0.566627
$746$	31.0946	1.13846
$747$	49.6625	1.81706
$748$	−1.46758	−0.0536600
$749$	55.9372	2.04390
$750$	2.88697	0.105417
$751$	19.9985	0.729757	0.364879	−	0.931055i	$-0.381110\pi$
$751$	19.9985	0.729757	0.364879	+	0.931055i	$0.381110\pi$
$752$	5.29179	0.192972
$753$	6.78248	0.247167
$754$	−14.2203	−0.517871
$755$	−22.6342	−0.823743
$756$	−20.2530	−0.736593
$757$	38.9336	1.41507	0.707533	−	0.706680i	$-0.249808\pi$
$757$	38.9336	1.41507	0.707533	+	0.706680i	$0.249808\pi$
$758$	32.3312	1.17432
$759$	0.978974	0.0355345
$760$	−6.47701	−0.234946
$761$	23.5934	0.855262	0.427631	−	0.903953i	$-0.359348\pi$
$761$	23.5934	0.855262	0.427631	+	0.903953i	$0.359348\pi$
$762$	−5.20020	−0.188383
$763$	−59.0096	−2.13629
$764$	19.6697	0.711623
$765$	22.1977	0.802558
$766$	−9.07708	−0.327968
$767$	10.1176	0.365326
$768$	2.88697	0.104175
$769$	−32.5356	−1.17327	−0.586633	−	0.809853i	$-0.699547\pi$
$769$	−32.5356	−1.17327	−0.586633	+	0.809853i	$0.699547\pi$
$770$	1.05981	0.0381929
$771$	−43.7718	−1.57640
$772$	−4.02360	−0.144813
$773$	−9.89787	−0.356002	−0.178001	−	0.984030i	$-0.556963\pi$
$773$	−9.89787	−0.356002	−0.178001	+	0.984030i	$0.556963\pi$
$774$	68.0305	2.44531
$775$	6.42537	0.230806
$776$	−18.8373	−0.676219
$777$	−42.3970	−1.52098
$778$	2.98986	0.107192
$779$	34.6273	1.24065
$780$	15.0446	0.538682
$781$	4.38176	0.156792
$782$	−4.00070	−0.143065
$783$	−18.3919	−0.657274
$784$	2.02950	0.0724820
$785$	−7.26165	−0.259179
$786$	−19.1800	−0.684128
$787$	17.3495	0.618442	0.309221	−	0.950990i	$-0.399932\pi$
$787$	17.3495	0.618442	0.309221	+	0.950990i	$0.399932\pi$
$788$	3.59063	0.127911
$789$	−0.0557659	−0.00198532
$790$	−15.8948	−0.565511
$791$	17.7535	0.631243
$792$	−1.88148	−0.0668554
$793$	−14.4242	−0.512219
$794$	23.9459	0.849809
$795$	18.2759	0.648179
$796$	9.12209	0.323324
$797$	35.2007	1.24687	0.623437	−	0.781873i	$-0.285736\pi$
$797$	35.2007	1.24687	0.623437	+	0.781873i	$0.285736\pi$
$798$	56.1887	1.98906
$799$	22.0195	0.778993
$800$	1.00000	0.0353553
$801$	−23.6324	−0.835008
$802$	1.00000	0.0353112
$803$	−0.287667	−0.0101516
$804$	42.0085	1.48153
$805$	2.88911	0.101828
$806$	33.4838	1.17942
$807$	85.8688	3.02272
$808$	−14.6388	−0.514990
$809$	−27.2405	−0.957726	−0.478863	−	0.877890i	$-0.658951\pi$
$809$	−27.2405	−0.957726	−0.478863	+	0.877890i	$0.658951\pi$
$810$	3.45423	0.121369
$811$	12.8028	0.449566	0.224783	−	0.974409i	$-0.427833\pi$
$811$	12.8028	0.449566	0.224783	+	0.974409i	$0.427833\pi$
$812$	8.19978	0.287756
$813$	42.4363	1.48831
$814$	−1.72368	−0.0604150
$815$	11.1134	0.389285
$816$	12.0129	0.420535
$817$	−82.5992	−2.88978
$818$	−12.3505	−0.431825
$819$	−83.5356	−2.91897
$820$	−5.34619	−0.186697
$821$	7.55619	0.263713	0.131856	−	0.991269i	$-0.457906\pi$
$821$	7.55619	0.263713	0.131856	+	0.991269i	$0.457906\pi$
$822$	21.1850	0.738911
$823$	30.2519	1.05451	0.527257	−	0.849706i	$-0.323220\pi$
$823$	30.2519	1.05451	0.527257	+	0.849706i	$0.323220\pi$
$824$	0.403241	0.0140476
$825$	−1.01821	−0.0354497
$826$	−5.83408	−0.202994
$827$	−4.92810	−0.171367	−0.0856833	−	0.996322i	$-0.527307\pi$
$827$	−4.92810	−0.171367	−0.0856833	+	0.996322i	$0.527307\pi$
$828$	−5.12902	−0.178246
$829$	1.99520	0.0692962	0.0346481	−	0.999400i	$-0.488969\pi$
$829$	1.99520	0.0692962	0.0346481	+	0.999400i	$0.488969\pi$
$830$	9.30950	0.323137
$831$	47.2538	1.63922
$832$	5.21119	0.180666
$833$	8.44487	0.292597
$834$	−48.9595	−1.69533
$835$	−16.7808	−0.580723
$836$	2.28439	0.0790074
$837$	43.3067	1.49690
$838$	−8.78143	−0.303349
$839$	25.3194	0.874123	0.437061	−	0.899432i	$-0.356019\pi$
$839$	25.3194	0.874123	0.437061	+	0.899432i	$0.356019\pi$
$840$	−8.67510	−0.299319
$841$	−21.5537	−0.743231
$842$	−15.3913	−0.530419
$843$	−20.6545	−0.711378
$844$	4.24631	0.146164
$845$	14.1565	0.487000
$846$	28.2296	0.970554
$847$	32.6802	1.12291
$848$	6.33046	0.217389
$849$	−75.6570	−2.59654
$850$	4.16107	0.142723
$851$	−4.69885	−0.161075
$852$	−35.8669	−1.22878
$853$	30.2487	1.03570	0.517848	−	0.855473i	$-0.326733\pi$
$853$	30.2487	1.03570	0.517848	+	0.855473i	$0.326733\pi$
$854$	8.31739	0.284615
$855$	−34.5523	−1.18166
$856$	−18.6153	−0.636257
$857$	−32.5698	−1.11256	−0.556282	−	0.830993i	$-0.687773\pi$
$857$	−32.5698	−1.11256	−0.556282	+	0.830993i	$0.687773\pi$
$858$	−5.30611	−0.181148
$859$	0.962287	0.0328328	0.0164164	−	0.999865i	$-0.494774\pi$
$859$	0.962287	0.0328328	0.0164164	+	0.999865i	$0.494774\pi$
$860$	12.7527	0.434863
$861$	46.3787	1.58058
$862$	−31.0498	−1.05756
$863$	−25.4056	−0.864816	−0.432408	−	0.901678i	$-0.642336\pi$
$863$	−25.4056	−0.864816	−0.432408	+	0.901678i	$0.642336\pi$
$864$	6.73995	0.229298
$865$	20.4096	0.693947
$866$	9.03970	0.307181
$867$	0.907888	0.0308335
$868$	−19.3077	−0.655345
$869$	5.60598	0.190170
$870$	−7.87795	−0.267087
$871$	75.8284	2.56935
$872$	19.6377	0.665016
$873$	−100.489	−3.40105
$874$	6.22739	0.210645
$875$	−3.00491	−0.101585
$876$	2.35470	0.0795580
$877$	29.9193	1.01030	0.505152	−	0.863031i	$-0.331437\pi$
$877$	29.9193	1.01030	0.505152	+	0.863031i	$0.331437\pi$
$878$	25.5201	0.861261
$879$	−91.1345	−3.07389
$880$	−0.352693	−0.0118893
$881$	−3.74904	−0.126308	−0.0631542	−	0.998004i	$-0.520116\pi$
$881$	−3.74904	−0.126308	−0.0631542	+	0.998004i	$0.520116\pi$
$882$	10.8266	0.364550
$883$	−28.9136	−0.973020	−0.486510	−	0.873675i	$-0.661730\pi$
$883$	−28.9136	−0.973020	−0.486510	+	0.873675i	$0.661730\pi$
$884$	21.6841	0.729316
$885$	5.60510	0.188413
$886$	−24.6233	−0.827236
$887$	21.4540	0.720356	0.360178	−	0.932884i	$-0.382716\pi$
$887$	21.4540	0.720356	0.360178	+	0.932884i	$0.382716\pi$
$888$	14.1092	0.473474
$889$	5.41264	0.181534
$890$	−4.43001	−0.148494
$891$	−1.21828	−0.0408140
$892$	−9.67104	−0.323810
$893$	−34.2749	−1.14697
$894$	44.6496	1.49331
$895$	−7.84475	−0.262221
$896$	−3.00491	−0.100387
$897$	−14.4648	−0.482965
$898$	6.91809	0.230860
$899$	−17.5335	−0.584775
$900$	5.33461	0.177820
$901$	26.3415	0.877562
$902$	1.88556	0.0627824
$903$	−110.631	−3.68156
$904$	−5.90817	−0.196503
$905$	−21.5993	−0.717986
$906$	−65.3443	−2.17092
$907$	25.3205	0.840753	0.420377	−	0.907350i	$-0.361898\pi$
$907$	25.3205	0.840753	0.420377	+	0.907350i	$0.361898\pi$
$908$	10.7364	0.356301
$909$	−78.0922	−2.59015
$910$	−15.6592	−0.519097
$911$	−11.0469	−0.366001	−0.183001	−	0.983113i	$-0.558581\pi$
$911$	−11.0469	−0.366001	−0.183001	+	0.983113i	$0.558581\pi$
$912$	−18.6989	−0.619184
$913$	−3.28339	−0.108664
$914$	−5.81648	−0.192392
$915$	−7.99094	−0.264172
$916$	7.66550	0.253275
$917$	19.9636	0.659255
$918$	28.0454	0.925636
$919$	6.33984	0.209132	0.104566	−	0.994518i	$-0.466655\pi$
$919$	6.33984	0.209132	0.104566	+	0.994518i	$0.466655\pi$
$920$	−0.961461	−0.0316984
$921$	−78.3599	−2.58205
$922$	34.6966	1.14267
$923$	−64.7424	−2.13102
$924$	3.05965	0.100655
$925$	4.88720	0.160690
$926$	20.2015	0.663863
$927$	2.15113	0.0706525
$928$	−2.72879	−0.0895770
$929$	−23.6478	−0.775859	−0.387929	−	0.921689i	$-0.626810\pi$
$929$	−23.6478	−0.775859	−0.387929	+	0.921689i	$0.626810\pi$
$930$	18.5499	0.608274
$931$	−13.1451	−0.430812
$932$	−14.4301	−0.472673
$933$	−4.14330	−0.135645
$934$	32.6777	1.06925
$935$	−1.46758	−0.0479950
$936$	27.7997	0.908661
$937$	−9.20610	−0.300750	−0.150375	−	0.988629i	$-0.548048\pi$
$937$	−9.20610	−0.300750	−0.150375	+	0.988629i	$0.548048\pi$
$938$	−43.7247	−1.42766
$939$	17.1379	0.559273
$940$	5.29179	0.172599
$941$	−13.6278	−0.444253	−0.222127	−	0.975018i	$-0.571300\pi$
$941$	−13.6278	−0.444253	−0.222127	+	0.975018i	$0.571300\pi$
$942$	−20.9642	−0.683050
$943$	5.14015	0.167386
$944$	1.94152	0.0631910
$945$	−20.2530	−0.658829
$946$	−4.49778	−0.146235
$947$	−16.6379	−0.540659	−0.270329	−	0.962768i	$-0.587133\pi$
$947$	−16.6379	−0.540659	−0.270329	+	0.962768i	$0.587133\pi$
$948$	−45.8878	−1.49037
$949$	4.25041	0.137974
$950$	−6.47701	−0.210142
$951$	47.2879	1.53341
$952$	−12.5036	−0.405245
$953$	2.48046	0.0803499	0.0401750	−	0.999193i	$-0.487208\pi$
$953$	2.48046	0.0803499	0.0401750	+	0.999193i	$0.487208\pi$
$954$	33.7706	1.09336
$955$	19.6697	0.636495
$956$	−15.1537	−0.490104
$957$	2.77850	0.0898160
$958$	−39.1837	−1.26597
$959$	−22.0504	−0.712046
$960$	2.88697	0.0931766
$961$	10.2853	0.331785
$962$	25.4682	0.821126
$963$	−99.3052	−3.20006
$964$	14.8455	0.478142
$965$	−4.02360	−0.129524
$966$	8.34077	0.268360
$967$	−41.6153	−1.33826	−0.669129	−	0.743147i	$-0.733332\pi$
$967$	−41.6153	−1.33826	−0.669129	+	0.743147i	$0.733332\pi$
$968$	−10.8756	−0.349555
$969$	−77.8076	−2.49954
$970$	−18.8373	−0.604828
$971$	41.8002	1.34143	0.670715	−	0.741715i	$-0.265987\pi$
$971$	41.8002	1.34143	0.670715	+	0.741715i	$0.265987\pi$
$972$	−10.2476	−0.328692
$973$	50.9596	1.63369
$974$	−7.84738	−0.251446
$975$	15.0446	0.481812
$976$	−2.76793	−0.0885993
$977$	−16.6292	−0.532014	−0.266007	−	0.963971i	$-0.585704\pi$
$977$	−16.6292	−0.532014	−0.266007	+	0.963971i	$0.585704\pi$
$978$	32.0840	1.02593
$979$	1.56243	0.0499355
$980$	2.02950	0.0648299
$981$	104.759	3.34471
$982$	3.56851	0.113876
$983$	−8.82919	−0.281607	−0.140804	−	0.990038i	$-0.544969\pi$
$983$	−8.82919	−0.281607	−0.140804	+	0.990038i	$0.544969\pi$
$984$	−15.4343	−0.492028
$985$	3.59063	0.114407
$986$	−11.3547	−0.361607
$987$	−45.9068	−1.46123
$988$	−33.7529	−1.07382
$989$	−12.2612	−0.389883
$990$	−1.88148	−0.0597973
$991$	16.9783	0.539333	0.269666	−	0.962954i	$-0.413087\pi$
$991$	16.9783	0.539333	0.269666	+	0.962954i	$0.413087\pi$
$992$	6.42537	0.204006
$993$	−81.9156	−2.59951
$994$	37.3322	1.18410
$995$	9.12209	0.289190
$996$	26.8763	0.851607
$997$	7.62169	0.241381	0.120691	−	0.992690i	$-0.461489\pi$
$997$	7.62169	0.241381	0.120691	+	0.992690i	$0.461489\pi$
$998$	−34.6315	−1.09624
$999$	32.9395	1.04216

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4010.2.a.n.1.20	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4010.2.a.n.1.20	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +2.88697 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.88697 q^{6} -3.00491 q^{7} +1.00000 q^{8} +5.33461 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +2.88697 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.88697 q^{6} -3.00491 q^{7} +1.00000 q^{8} +5.33461 q^{9} +1.00000 q^{10} -0.352693 q^{11} +2.88697 q^{12} +5.21119 q^{13} -3.00491 q^{14} +2.88697 q^{15} +1.00000 q^{16} +4.16107 q^{17} +5.33461 q^{18} -6.47701 q^{19} +1.00000 q^{20} -8.67510 q^{21} -0.352693 q^{22} -0.961461 q^{23} +2.88697 q^{24} +1.00000 q^{25} +5.21119 q^{26} +6.73995 q^{27} -3.00491 q^{28} -2.72879 q^{29} +2.88697 q^{30} +6.42537 q^{31} +1.00000 q^{32} -1.01821 q^{33} +4.16107 q^{34} -3.00491 q^{35} +5.33461 q^{36} +4.88720 q^{37} -6.47701 q^{38} +15.0446 q^{39} +1.00000 q^{40} -5.34619 q^{41} -8.67510 q^{42} +12.7527 q^{43} -0.352693 q^{44} +5.33461 q^{45} -0.961461 q^{46} +5.29179 q^{47} +2.88697 q^{48} +2.02950 q^{49} +1.00000 q^{50} +12.0129 q^{51} +5.21119 q^{52} +6.33046 q^{53} +6.73995 q^{54} -0.352693 q^{55} -3.00491 q^{56} -18.6989 q^{57} -2.72879 q^{58} +1.94152 q^{59} +2.88697 q^{60} -2.76793 q^{61} +6.42537 q^{62} -16.0300 q^{63} +1.00000 q^{64} +5.21119 q^{65} -1.01821 q^{66} +14.5511 q^{67} +4.16107 q^{68} -2.77571 q^{69} -3.00491 q^{70} -12.4237 q^{71} +5.33461 q^{72} +0.815631 q^{73} +4.88720 q^{74} +2.88697 q^{75} -6.47701 q^{76} +1.05981 q^{77} +15.0446 q^{78} -15.8948 q^{79} +1.00000 q^{80} +3.45423 q^{81} -5.34619 q^{82} +9.30950 q^{83} -8.67510 q^{84} +4.16107 q^{85} +12.7527 q^{86} -7.87795 q^{87} -0.352693 q^{88} -4.43001 q^{89} +5.33461 q^{90} -15.6592 q^{91} -0.961461 q^{92} +18.5499 q^{93} +5.29179 q^{94} -6.47701 q^{95} +2.88697 q^{96} -18.8373 q^{97} +2.02950 q^{98} -1.88148 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 22 q^{2} + q^{3} + 22 q^{4} + 22 q^{5} + q^{6} + 22 q^{8} + 43 q^{9}+O(q^{10}) \) 22 * q + 22 * q^2 + q^3 + 22 * q^4 + 22 * q^5 + q^6 + 22 * q^8 + 43 * q^9	\( 22 q + 22 q^{2} + q^{3} + 22 q^{4} + 22 q^{5} + q^{6} + 22 q^{8} + 43 q^{9} + 22 q^{10} + 12 q^{11} + q^{12} + 10 q^{13} + q^{15} + 22 q^{16} + 24 q^{17} + 43 q^{18} + 13 q^{19} + 22 q^{20} + 13 q^{21} + 12 q^{22} + 7 q^{23} + q^{24} + 22 q^{25} + 10 q^{26} - 5 q^{27} + 22 q^{29} + q^{30} + 14 q^{31} + 22 q^{32} + 31 q^{33} + 24 q^{34} + 43 q^{36} + 35 q^{37} + 13 q^{38} + 4 q^{39} + 22 q^{40} + 29 q^{41} + 13 q^{42} + 7 q^{43} + 12 q^{44} + 43 q^{45} + 7 q^{46} - 21 q^{47} + q^{48} + 32 q^{49} + 22 q^{50} - 6 q^{51} + 10 q^{52} + 29 q^{53} - 5 q^{54} + 12 q^{55} - 13 q^{57} + 22 q^{58} + 12 q^{59} + q^{60} + 24 q^{61} + 14 q^{62} - 8 q^{63} + 22 q^{64} + 10 q^{65} + 31 q^{66} + 25 q^{67} + 24 q^{68} + 3 q^{69} + 31 q^{71} + 43 q^{72} + 30 q^{73} + 35 q^{74} + q^{75} + 13 q^{76} + 10 q^{77} + 4 q^{78} + 35 q^{79} + 22 q^{80} + 74 q^{81} + 29 q^{82} - 33 q^{83} + 13 q^{84} + 24 q^{85} + 7 q^{86} - 24 q^{87} + 12 q^{88} + 38 q^{89} + 43 q^{90} - 32 q^{91} + 7 q^{92} + 3 q^{93} - 21 q^{94} + 13 q^{95} + q^{96} + 11 q^{97} + 32 q^{98} - 41 q^{99}+O(q^{100}) \) 22 * q + 22 * q^2 + q^3 + 22 * q^4 + 22 * q^5 + q^6 + 22 * q^8 + 43 * q^9 + 22 * q^10 + 12 * q^11 + q^12 + 10 * q^13 + q^15 + 22 * q^16 + 24 * q^17 + 43 * q^18 + 13 * q^19 + 22 * q^20 + 13 * q^21 + 12 * q^22 + 7 * q^23 + q^24 + 22 * q^25 + 10 * q^26 - 5 * q^27 + 22 * q^29 + q^30 + 14 * q^31 + 22 * q^32 + 31 * q^33 + 24 * q^34 + 43 * q^36 + 35 * q^37 + 13 * q^38 + 4 * q^39 + 22 * q^40 + 29 * q^41 + 13 * q^42 + 7 * q^43 + 12 * q^44 + 43 * q^45 + 7 * q^46 - 21 * q^47 + q^48 + 32 * q^49 + 22 * q^50 - 6 * q^51 + 10 * q^52 + 29 * q^53 - 5 * q^54 + 12 * q^55 - 13 * q^57 + 22 * q^58 + 12 * q^59 + q^60 + 24 * q^61 + 14 * q^62 - 8 * q^63 + 22 * q^64 + 10 * q^65 + 31 * q^66 + 25 * q^67 + 24 * q^68 + 3 * q^69 + 31 * q^71 + 43 * q^72 + 30 * q^73 + 35 * q^74 + q^75 + 13 * q^76 + 10 * q^77 + 4 * q^78 + 35 * q^79 + 22 * q^80 + 74 * q^81 + 29 * q^82 - 33 * q^83 + 13 * q^84 + 24 * q^85 + 7 * q^86 - 24 * q^87 + 12 * q^88 + 38 * q^89 + 43 * q^90 - 32 * q^91 + 7 * q^92 + 3 * q^93 - 21 * q^94 + 13 * q^95 + q^96 + 11 * q^97 + 32 * q^98 - 41 * q^99

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