LMFDB - Embedded newform 4010.2.a.n.1.19

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			1.19
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)

$f(q)$	$=$	$q+1.00000 q^{2} +2.70959 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.70959 q^{6} +0.508884 q^{7} +1.00000 q^{8} +4.34189 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +2.70959 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.70959 q^{6} +0.508884 q^{7} +1.00000 q^{8} +4.34189 q^{9} +1.00000 q^{10} -0.524738 q^{11} +2.70959 q^{12} +6.69930 q^{13} +0.508884 q^{14} +2.70959 q^{15} +1.00000 q^{16} -3.24778 q^{17} +4.34189 q^{18} +0.166143 q^{19} +1.00000 q^{20} +1.37887 q^{21} -0.524738 q^{22} +1.07275 q^{23} +2.70959 q^{24} +1.00000 q^{25} +6.69930 q^{26} +3.63599 q^{27} +0.508884 q^{28} +2.11316 q^{29} +2.70959 q^{30} -7.15091 q^{31} +1.00000 q^{32} -1.42183 q^{33} -3.24778 q^{34} +0.508884 q^{35} +4.34189 q^{36} -6.51587 q^{37} +0.166143 q^{38} +18.1524 q^{39} +1.00000 q^{40} +10.1111 q^{41} +1.37887 q^{42} -3.01682 q^{43} -0.524738 q^{44} +4.34189 q^{45} +1.07275 q^{46} -7.56055 q^{47} +2.70959 q^{48} -6.74104 q^{49} +1.00000 q^{50} -8.80017 q^{51} +6.69930 q^{52} +4.08848 q^{53} +3.63599 q^{54} -0.524738 q^{55} +0.508884 q^{56} +0.450180 q^{57} +2.11316 q^{58} -1.50718 q^{59} +2.70959 q^{60} +7.63061 q^{61} -7.15091 q^{62} +2.20952 q^{63} +1.00000 q^{64} +6.69930 q^{65} -1.42183 q^{66} -9.42485 q^{67} -3.24778 q^{68} +2.90670 q^{69} +0.508884 q^{70} -13.6484 q^{71} +4.34189 q^{72} +3.63586 q^{73} -6.51587 q^{74} +2.70959 q^{75} +0.166143 q^{76} -0.267031 q^{77} +18.1524 q^{78} +14.5900 q^{79} +1.00000 q^{80} -3.17363 q^{81} +10.1111 q^{82} +6.44014 q^{83} +1.37887 q^{84} -3.24778 q^{85} -3.01682 q^{86} +5.72581 q^{87} -0.524738 q^{88} -4.50501 q^{89} +4.34189 q^{90} +3.40917 q^{91} +1.07275 q^{92} -19.3761 q^{93} -7.56055 q^{94} +0.166143 q^{95} +2.70959 q^{96} +6.30646 q^{97} -6.74104 q^{98} -2.27836 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	2.70959	1.56438	0.782192	−	0.623037i	$-0.214102\pi$
$3$	2.70959	1.56438	0.782192	+	0.623037i	$0.214102\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	2.70959	1.10619
$7$	0.508884	0.192340	0.0961700	−	0.995365i	$-0.469341\pi$
$7$	0.508884	0.192340	0.0961700	+	0.995365i	$0.469341\pi$
$8$	1.00000	0.353553
$9$	4.34189	1.44730
$10$	1.00000	0.316228
$11$	−0.524738	−0.158214	−0.0791072	−	0.996866i	$-0.525207\pi$
$11$	−0.524738	−0.158214	−0.0791072	+	0.996866i	$0.525207\pi$
$12$	2.70959	0.782192
$13$	6.69930	1.85805	0.929026	−	0.370015i	$-0.120647\pi$
$13$	6.69930	1.85805	0.929026	+	0.370015i	$0.120647\pi$
$14$	0.508884	0.136005
$15$	2.70959	0.699614
$16$	1.00000	0.250000
$17$	−3.24778	−0.787703	−0.393851	−	0.919174i	$-0.628858\pi$
$17$	−3.24778	−0.787703	−0.393851	+	0.919174i	$0.628858\pi$
$18$	4.34189	1.02339
$19$	0.166143	0.0381158	0.0190579	−	0.999818i	$-0.493933\pi$
$19$	0.166143	0.0381158	0.0190579	+	0.999818i	$0.493933\pi$
$20$	1.00000	0.223607
$21$	1.37887	0.300894
$22$	−0.524738	−0.111874
$23$	1.07275	0.223683	0.111841	−	0.993726i	$-0.464325\pi$
$23$	1.07275	0.223683	0.111841	+	0.993726i	$0.464325\pi$
$24$	2.70959	0.553093
$25$	1.00000	0.200000
$26$	6.69930	1.31384
$27$	3.63599	0.699746
$28$	0.508884	0.0961700
$29$	2.11316	0.392404	0.196202	−	0.980563i	$-0.437139\pi$
$29$	2.11316	0.392404	0.196202	+	0.980563i	$0.437139\pi$
$30$	2.70959	0.494702
$31$	−7.15091	−1.28434	−0.642171	−	0.766561i	$-0.721966\pi$
$31$	−7.15091	−1.28434	−0.642171	+	0.766561i	$0.721966\pi$
$32$	1.00000	0.176777
$33$	−1.42183	−0.247508
$34$	−3.24778	−0.556990
$35$	0.508884	0.0860171
$36$	4.34189	0.723649
$37$	−6.51587	−1.07120	−0.535601	−	0.844471i	$-0.679915\pi$
$37$	−6.51587	−1.07120	−0.535601	+	0.844471i	$0.679915\pi$
$38$	0.166143	0.0269519
$39$	18.1524	2.90671
$40$	1.00000	0.158114
$41$	10.1111	1.57910	0.789548	−	0.613689i	$-0.210315\pi$
$41$	10.1111	1.57910	0.789548	+	0.613689i	$0.210315\pi$
$42$	1.37887	0.212764
$43$	−3.01682	−0.460061	−0.230031	−	0.973183i	$-0.573883\pi$
$43$	−3.01682	−0.460061	−0.230031	+	0.973183i	$0.573883\pi$
$44$	−0.524738	−0.0791072
$45$	4.34189	0.647251
$46$	1.07275	0.158168
$47$	−7.56055	−1.10282	−0.551410	−	0.834234i	$-0.685910\pi$
$47$	−7.56055	−1.10282	−0.551410	+	0.834234i	$0.685910\pi$
$48$	2.70959	0.391096
$49$	−6.74104	−0.963005
$50$	1.00000	0.141421
$51$	−8.80017	−1.23227
$52$	6.69930	0.929026
$53$	4.08848	0.561596	0.280798	−	0.959767i	$-0.409401\pi$
$53$	4.08848	0.561596	0.280798	+	0.959767i	$0.409401\pi$
$54$	3.63599	0.494795
$55$	−0.524738	−0.0707556
$56$	0.508884	0.0680025
$57$	0.450180	0.0596278
$58$	2.11316	0.277472
$59$	−1.50718	−0.196219	−0.0981093	−	0.995176i	$-0.531279\pi$
$59$	−1.50718	−0.196219	−0.0981093	+	0.995176i	$0.531279\pi$
$60$	2.70959	0.349807
$61$	7.63061	0.976999	0.488499	−	0.872564i	$-0.337544\pi$
$61$	7.63061	0.976999	0.488499	+	0.872564i	$0.337544\pi$
$62$	−7.15091	−0.908167
$63$	2.20952	0.278373
$64$	1.00000	0.125000
$65$	6.69930	0.830946
$66$	−1.42183	−0.175015
$67$	−9.42485	−1.15143	−0.575714	−	0.817651i	$-0.695276\pi$
$67$	−9.42485	−1.15143	−0.575714	+	0.817651i	$0.695276\pi$
$68$	−3.24778	−0.393851
$69$	2.90670	0.349926
$70$	0.508884	0.0608233
$71$	−13.6484	−1.61976	−0.809881	−	0.586594i	$-0.800469\pi$
$71$	−13.6484	−1.61976	−0.809881	+	0.586594i	$0.800469\pi$
$72$	4.34189	0.511697
$73$	3.63586	0.425545	0.212773	−	0.977102i	$-0.431751\pi$
$73$	3.63586	0.425545	0.212773	+	0.977102i	$0.431751\pi$
$74$	−6.51587	−0.757455
$75$	2.70959	0.312877
$76$	0.166143	0.0190579
$77$	−0.267031	−0.0304310
$78$	18.1524	2.05535
$79$	14.5900	1.64151	0.820754	−	0.571281i	$-0.193553\pi$
$79$	14.5900	1.64151	0.820754	+	0.571281i	$0.193553\pi$
$80$	1.00000	0.111803
$81$	−3.17363	−0.352626
$82$	10.1111	1.11659
$83$	6.44014	0.706897	0.353449	−	0.935454i	$-0.385009\pi$
$83$	6.44014	0.706897	0.353449	+	0.935454i	$0.385009\pi$
$84$	1.37887	0.150447
$85$	−3.24778	−0.352271
$86$	−3.01682	−0.325312
$87$	5.72581	0.613871
$88$	−0.524738	−0.0559372
$89$	−4.50501	−0.477530	−0.238765	−	0.971077i	$-0.576743\pi$
$89$	−4.50501	−0.477530	−0.238765	+	0.971077i	$0.576743\pi$
$90$	4.34189	0.457676
$91$	3.40917	0.357378
$92$	1.07275	0.111841
$93$	−19.3761	−2.00920
$94$	−7.56055	−0.779812
$95$	0.166143	0.0170459
$96$	2.70959	0.276547
$97$	6.30646	0.640324	0.320162	−	0.947363i	$-0.396263\pi$
$97$	6.30646	0.640324	0.320162	+	0.947363i	$0.396263\pi$
$98$	−6.74104	−0.680948
$99$	−2.27836	−0.228983
$100$	1.00000	0.100000
$101$	−9.00297	−0.895829	−0.447915	−	0.894076i	$-0.647833\pi$
$101$	−9.00297	−0.895829	−0.447915	+	0.894076i	$0.647833\pi$
$102$	−8.80017	−0.871346
$103$	−4.69017	−0.462136	−0.231068	−	0.972938i	$-0.574222\pi$
$103$	−4.69017	−0.462136	−0.231068	+	0.972938i	$0.574222\pi$
$104$	6.69930	0.656920
$105$	1.37887	0.134564
$106$	4.08848	0.397108
$107$	0.0168288	0.00162690	0.000813449	−	1.00000i	$-0.499741\pi$
$107$	0.0168288	0.00162690	0.000813449		1.00000i	$0.499741\pi$
$108$	3.63599	0.349873
$109$	−10.3599	−0.992294	−0.496147	−	0.868238i	$-0.665252\pi$
$109$	−10.3599	−0.992294	−0.496147	+	0.868238i	$0.665252\pi$
$110$	−0.524738	−0.0500318
$111$	−17.6554	−1.67577
$112$	0.508884	0.0480850
$113$	13.7131	1.29002	0.645008	−	0.764176i	$-0.276854\pi$
$113$	13.7131	1.29002	0.645008	+	0.764176i	$0.276854\pi$
$114$	0.450180	0.0421632
$115$	1.07275	0.100034
$116$	2.11316	0.196202
$117$	29.0877	2.68915
$118$	−1.50718	−0.138748
$119$	−1.65274	−0.151507
$120$	2.70959	0.247351
$121$	−10.7247	−0.974968
$122$	7.63061	0.690843
$123$	27.3971	2.47031
$124$	−7.15091	−0.642171
$125$	1.00000	0.0894427
$126$	2.20952	0.196840
$127$	−16.4826	−1.46260	−0.731299	−	0.682057i	$-0.761085\pi$
$127$	−16.4826	−1.46260	−0.731299	+	0.682057i	$0.761085\pi$
$128$	1.00000	0.0883883
$129$	−8.17436	−0.719712
$130$	6.69930	0.587567
$131$	15.5989	1.36288	0.681440	−	0.731874i	$-0.261354\pi$
$131$	15.5989	1.36288	0.681440	+	0.731874i	$0.261354\pi$
$132$	−1.42183	−0.123754
$133$	0.0845474	0.00733119
$134$	−9.42485	−0.814183
$135$	3.63599	0.312936
$136$	−3.24778	−0.278495
$137$	11.0287	0.942249	0.471125	−	0.882067i	$-0.343848\pi$
$137$	11.0287	0.942249	0.471125	+	0.882067i	$0.343848\pi$
$138$	2.90670	0.247435
$139$	−0.261140	−0.0221496	−0.0110748	−	0.999939i	$-0.503525\pi$
$139$	−0.261140	−0.0221496	−0.0110748	+	0.999939i	$0.503525\pi$
$140$	0.508884	0.0430085
$141$	−20.4860	−1.72523
$142$	−13.6484	−1.14535
$143$	−3.51538	−0.293971
$144$	4.34189	0.361825
$145$	2.11316	0.175488
$146$	3.63586	0.300906
$147$	−18.2655	−1.50651
$148$	−6.51587	−0.535601
$149$	−0.681585	−0.0558376	−0.0279188	−	0.999610i	$-0.508888\pi$
$149$	−0.681585	−0.0558376	−0.0279188	+	0.999610i	$0.508888\pi$
$150$	2.70959	0.221237
$151$	21.2590	1.73003	0.865015	−	0.501747i	$-0.167309\pi$
$151$	21.2590	1.73003	0.865015	+	0.501747i	$0.167309\pi$
$152$	0.166143	0.0134760
$153$	−14.1015	−1.14004
$154$	−0.267031	−0.0215179
$155$	−7.15091	−0.574375
$156$	18.1524	1.45335
$157$	11.7061	0.934245	0.467122	−	0.884193i	$-0.345291\pi$
$157$	11.7061	0.934245	0.467122	+	0.884193i	$0.345291\pi$
$158$	14.5900	1.16072
$159$	11.0781	0.878551
$160$	1.00000	0.0790569
$161$	0.545903	0.0430232
$162$	−3.17363	−0.249344
$163$	3.69501	0.289416	0.144708	−	0.989474i	$-0.453776\pi$
$163$	3.69501	0.289416	0.144708	+	0.989474i	$0.453776\pi$
$164$	10.1111	0.789548
$165$	−1.42183	−0.110689
$166$	6.44014	0.499852
$167$	−14.0535	−1.08749	−0.543747	−	0.839249i	$-0.682995\pi$
$167$	−14.0535	−1.08749	−0.543747	+	0.839249i	$0.682995\pi$
$168$	1.37887	0.106382
$169$	31.8806	2.45236
$170$	−3.24778	−0.249093
$171$	0.721375	0.0551649
$172$	−3.01682	−0.230031
$173$	−3.72711	−0.283367	−0.141683	−	0.989912i	$-0.545251\pi$
$173$	−3.72711	−0.283367	−0.141683	+	0.989912i	$0.545251\pi$
$174$	5.72581	0.434072
$175$	0.508884	0.0384680
$176$	−0.524738	−0.0395536
$177$	−4.08386	−0.306961
$178$	−4.50501	−0.337665
$179$	−18.9380	−1.41549	−0.707745	−	0.706468i	$-0.750287\pi$
$179$	−18.9380	−1.41549	−0.707745	+	0.706468i	$0.750287\pi$
$180$	4.34189	0.323626
$181$	17.7223	1.31728	0.658642	−	0.752456i	$-0.271131\pi$
$181$	17.7223	1.31728	0.658642	+	0.752456i	$0.271131\pi$
$182$	3.40917	0.252704
$183$	20.6758	1.52840
$184$	1.07275	0.0790839
$185$	−6.51587	−0.479056
$186$	−19.3761	−1.42072
$187$	1.70423	0.124626
$188$	−7.56055	−0.551410
$189$	1.85030	0.134589
$190$	0.166143	0.0120533
$191$	−12.0935	−0.875052	−0.437526	−	0.899206i	$-0.644145\pi$
$191$	−12.0935	−0.875052	−0.437526	+	0.899206i	$0.644145\pi$
$192$	2.70959	0.195548
$193$	2.16212	0.155633	0.0778165	−	0.996968i	$-0.475205\pi$
$193$	2.16212	0.155633	0.0778165	+	0.996968i	$0.475205\pi$
$194$	6.30646	0.452778
$195$	18.1524	1.29992
$196$	−6.74104	−0.481503
$197$	−6.57704	−0.468595	−0.234297	−	0.972165i	$-0.575279\pi$
$197$	−6.57704	−0.468595	−0.234297	+	0.972165i	$0.575279\pi$
$198$	−2.27836	−0.161916
$199$	−27.2755	−1.93351	−0.966753	−	0.255713i	$-0.917690\pi$
$199$	−27.2755	−1.93351	−0.966753	+	0.255713i	$0.917690\pi$
$200$	1.00000	0.0707107
$201$	−25.5375	−1.80128
$202$	−9.00297	−0.633447
$203$	1.07535	0.0754750
$204$	−8.80017	−0.616135
$205$	10.1111	0.706193
$206$	−4.69017	−0.326780
$207$	4.65775	0.323736
$208$	6.69930	0.464513
$209$	−0.0871815	−0.00603047
$210$	1.37887	0.0951509
$211$	−13.4299	−0.924554	−0.462277	−	0.886735i	$-0.652967\pi$
$211$	−13.4299	−0.924554	−0.462277	+	0.886735i	$0.652967\pi$
$212$	4.08848	0.280798
$213$	−36.9815	−2.53393
$214$	0.0168288	0.00115039
$215$	−3.01682	−0.205746
$216$	3.63599	0.247398
$217$	−3.63898	−0.247030
$218$	−10.3599	−0.701658
$219$	9.85170	0.665716
$220$	−0.524738	−0.0353778
$221$	−21.7579	−1.46359
$222$	−17.6554	−1.18495
$223$	16.6367	1.11407	0.557037	−	0.830487i	$-0.311938\pi$
$223$	16.6367	1.11407	0.557037	+	0.830487i	$0.311938\pi$
$224$	0.508884	0.0340012
$225$	4.34189	0.289460
$226$	13.7131	0.912179
$227$	1.15411	0.0766007	0.0383004	−	0.999266i	$-0.487806\pi$
$227$	1.15411	0.0766007	0.0383004	+	0.999266i	$0.487806\pi$
$228$	0.450180	0.0298139
$229$	22.7634	1.50425	0.752124	−	0.659021i	$-0.229029\pi$
$229$	22.7634	1.50425	0.752124	+	0.659021i	$0.229029\pi$
$230$	1.07275	0.0707348
$231$	−0.723544	−0.0476057
$232$	2.11316	0.138736
$233$	7.31865	0.479461	0.239730	−	0.970839i	$-0.422941\pi$
$233$	7.31865	0.479461	0.239730	+	0.970839i	$0.422941\pi$
$234$	29.0877	1.90152
$235$	−7.56055	−0.493196
$236$	−1.50718	−0.0981093
$237$	39.5331	2.56795
$238$	−1.65274	−0.107131
$239$	16.9160	1.09421	0.547104	−	0.837065i	$-0.315730\pi$
$239$	16.9160	1.09421	0.547104	+	0.837065i	$0.315730\pi$
$240$	2.70959	0.174903
$241$	21.7885	1.40352	0.701759	−	0.712414i	$-0.252398\pi$
$241$	21.7885	1.40352	0.701759	+	0.712414i	$0.252398\pi$
$242$	−10.7247	−0.689407
$243$	−19.5072	−1.25139
$244$	7.63061	0.488499
$245$	−6.74104	−0.430669
$246$	27.3971	1.74677
$247$	1.11304	0.0708211
$248$	−7.15091	−0.454083
$249$	17.4502	1.10586
$250$	1.00000	0.0632456
$251$	−3.28793	−0.207532	−0.103766	−	0.994602i	$-0.533089\pi$
$251$	−3.28793	−0.207532	−0.103766	+	0.994602i	$0.533089\pi$
$252$	2.20952	0.139187
$253$	−0.562910	−0.0353899
$254$	−16.4826	−1.03421
$255$	−8.80017	−0.551088
$256$	1.00000	0.0625000
$257$	−7.48856	−0.467124	−0.233562	−	0.972342i	$-0.575038\pi$
$257$	−7.48856	−0.467124	−0.233562	+	0.972342i	$0.575038\pi$
$258$	−8.17436	−0.508914
$259$	−3.31582	−0.206035
$260$	6.69930	0.415473
$261$	9.17512	0.567926
$262$	15.5989	0.963701
$263$	−13.6601	−0.842318	−0.421159	−	0.906987i	$-0.638377\pi$
$263$	−13.6601	−0.842318	−0.421159	+	0.906987i	$0.638377\pi$
$264$	−1.42183	−0.0875073
$265$	4.08848	0.251153
$266$	0.0845474	0.00518394
$267$	−12.2067	−0.747041
$268$	−9.42485	−0.575714
$269$	−29.8938	−1.82266	−0.911328	−	0.411680i	$-0.864942\pi$
$269$	−29.8938	−1.82266	−0.911328	+	0.411680i	$0.864942\pi$
$270$	3.63599	0.221279
$271$	6.79048	0.412492	0.206246	−	0.978500i	$-0.433875\pi$
$271$	6.79048	0.412492	0.206246	+	0.978500i	$0.433875\pi$
$272$	−3.24778	−0.196926
$273$	9.23745	0.559076
$274$	11.0287	0.666271
$275$	−0.524738	−0.0316429
$276$	2.90670	0.174963
$277$	21.9706	1.32008	0.660042	−	0.751229i	$-0.270539\pi$
$277$	21.9706	1.32008	0.660042	+	0.751229i	$0.270539\pi$
$278$	−0.261140	−0.0156621
$279$	−31.0485	−1.85883
$280$	0.508884	0.0304116
$281$	−23.9659	−1.42968	−0.714841	−	0.699287i	$-0.753501\pi$
$281$	−23.9659	−1.42968	−0.714841	+	0.699287i	$0.753501\pi$
$282$	−20.4860	−1.21993
$283$	15.1844	0.902619	0.451309	−	0.892367i	$-0.350957\pi$
$283$	15.1844	0.902619	0.451309	+	0.892367i	$0.350957\pi$
$284$	−13.6484	−0.809881
$285$	0.450180	0.0266663
$286$	−3.51538	−0.207869
$287$	5.14540	0.303723
$288$	4.34189	0.255849
$289$	−6.45192	−0.379524
$290$	2.11316	0.124089
$291$	17.0880	1.00171
$292$	3.63586	0.212773
$293$	−14.1153	−0.824624	−0.412312	−	0.911043i	$-0.635279\pi$
$293$	−14.1153	−0.824624	−0.412312	+	0.911043i	$0.635279\pi$
$294$	−18.2655	−1.06526
$295$	−1.50718	−0.0877517
$296$	−6.51587	−0.378727
$297$	−1.90794	−0.110710
$298$	−0.681585	−0.0394831
$299$	7.18664	0.415614
$300$	2.70959	0.156438
$301$	−1.53521	−0.0884882
$302$	21.2590	1.22332
$303$	−24.3944	−1.40142
$304$	0.166143	0.00952895
$305$	7.63061	0.436927
$306$	−14.1015	−0.806131
$307$	−18.5123	−1.05655	−0.528276	−	0.849073i	$-0.677161\pi$
$307$	−18.5123	−1.05655	−0.528276	+	0.849073i	$0.677161\pi$
$308$	−0.267031	−0.0152155
$309$	−12.7084	−0.722958
$310$	−7.15091	−0.406145
$311$	−30.4446	−1.72635	−0.863177	−	0.504902i	$-0.831529\pi$
$311$	−30.4446	−1.72635	−0.863177	+	0.504902i	$0.831529\pi$
$312$	18.1524	1.02768
$313$	−16.5007	−0.932677	−0.466338	−	0.884606i	$-0.654427\pi$
$313$	−16.5007	−0.932677	−0.466338	+	0.884606i	$0.654427\pi$
$314$	11.7061	0.660611
$315$	2.20952	0.124492
$316$	14.5900	0.820754
$317$	14.2115	0.798199	0.399100	−	0.916908i	$-0.369323\pi$
$317$	14.2115	0.798199	0.399100	+	0.916908i	$0.369323\pi$
$318$	11.0781	0.621230
$319$	−1.10886	−0.0620840
$320$	1.00000	0.0559017
$321$	0.0455991	0.00254509
$322$	0.545903	0.0304220
$323$	−0.539596	−0.0300239
$324$	−3.17363	−0.176313
$325$	6.69930	0.371610
$326$	3.69501	0.204648
$327$	−28.0710	−1.55233
$328$	10.1111	0.558294
$329$	−3.84744	−0.212116
$330$	−1.42183	−0.0782689
$331$	−5.18264	−0.284864	−0.142432	−	0.989805i	$-0.545492\pi$
$331$	−5.18264	−0.284864	−0.142432	+	0.989805i	$0.545492\pi$
$332$	6.44014	0.353449
$333$	−28.2912	−1.55035
$334$	−14.0535	−0.768974
$335$	−9.42485	−0.514934
$336$	1.37887	0.0752234
$337$	−4.05060	−0.220650	−0.110325	−	0.993896i	$-0.535189\pi$
$337$	−4.05060	−0.220650	−0.110325	+	0.993896i	$0.535189\pi$
$338$	31.8806	1.73408
$339$	37.1568	2.01808
$340$	−3.24778	−0.176136
$341$	3.75236	0.203201
$342$	0.721375	0.0390075
$343$	−6.99259	−0.377564
$344$	−3.01682	−0.162656
$345$	2.90670	0.156492
$346$	−3.72711	−0.200370
$347$	−4.06750	−0.218355	−0.109178	−	0.994022i	$-0.534822\pi$
$347$	−4.06750	−0.218355	−0.109178	+	0.994022i	$0.534822\pi$
$348$	5.72581	0.306935
$349$	10.7560	0.575758	0.287879	−	0.957667i	$-0.407050\pi$
$349$	10.7560	0.575758	0.287879	+	0.957667i	$0.407050\pi$
$350$	0.508884	0.0272010
$351$	24.3586	1.30016
$352$	−0.524738	−0.0279686
$353$	−15.8408	−0.843121	−0.421561	−	0.906800i	$-0.638518\pi$
$353$	−15.8408	−0.843121	−0.421561	+	0.906800i	$0.638518\pi$
$354$	−4.08386	−0.217055
$355$	−13.6484	−0.724380
$356$	−4.50501	−0.238765
$357$	−4.47826	−0.237015
$358$	−18.9380	−1.00090
$359$	6.41044	0.338330	0.169165	−	0.985588i	$-0.445893\pi$
$359$	6.41044	0.338330	0.169165	+	0.985588i	$0.445893\pi$
$360$	4.34189	0.228838
$361$	−18.9724	−0.998547
$362$	17.7223	0.931461
$363$	−29.0594	−1.52522
$364$	3.40917	0.178689
$365$	3.63586	0.190310
$366$	20.6758	1.08074
$367$	0.622097	0.0324732	0.0162366	−	0.999868i	$-0.494832\pi$
$367$	0.622097	0.0324732	0.0162366	+	0.999868i	$0.494832\pi$
$368$	1.07275	0.0559207
$369$	43.9015	2.28542
$370$	−6.51587	−0.338744
$371$	2.08056	0.108017
$372$	−19.3761	−1.00460
$373$	6.86343	0.355375	0.177688	−	0.984087i	$-0.443138\pi$
$373$	6.86343	0.355375	0.177688	+	0.984087i	$0.443138\pi$
$374$	1.70423	0.0881238
$375$	2.70959	0.139923
$376$	−7.56055	−0.389906
$377$	14.1567	0.729107
$378$	1.85030	0.0951690
$379$	21.2741	1.09278	0.546388	−	0.837532i	$-0.316002\pi$
$379$	21.2741	1.09278	0.546388	+	0.837532i	$0.316002\pi$
$380$	0.166143	0.00852295
$381$	−44.6612	−2.28806
$382$	−12.0935	−0.618755
$383$	−24.0014	−1.22641	−0.613207	−	0.789922i	$-0.710121\pi$
$383$	−24.0014	−1.22641	−0.613207	+	0.789922i	$0.710121\pi$
$384$	2.70959	0.138273
$385$	−0.267031	−0.0136091
$386$	2.16212	0.110049
$387$	−13.0987	−0.665846
$388$	6.30646	0.320162
$389$	−26.0471	−1.32064	−0.660321	−	0.750984i	$-0.729580\pi$
$389$	−26.0471	−1.32064	−0.660321	+	0.750984i	$0.729580\pi$
$390$	18.1524	0.919181
$391$	−3.48404	−0.176196
$392$	−6.74104	−0.340474
$393$	42.2666	2.13207
$394$	−6.57704	−0.331347
$395$	14.5900	0.734105
$396$	−2.27836	−0.114492
$397$	24.7247	1.24090	0.620448	−	0.784247i	$-0.286951\pi$
$397$	24.7247	1.24090	0.620448	+	0.784247i	$0.286951\pi$
$398$	−27.2755	−1.36719
$399$	0.229089	0.0114688
$400$	1.00000	0.0500000
$401$	1.00000	0.0499376
$401$	1.00000	0.0499376
$402$	−25.5375	−1.27369
$403$	−47.9061	−2.38637
$404$	−9.00297	−0.447915
$405$	−3.17363	−0.157699
$406$	1.07535	0.0533689
$407$	3.41912	0.169480
$408$	−8.80017	−0.435673
$409$	−37.1403	−1.83647	−0.918236	−	0.396034i	$-0.870386\pi$
$409$	−37.1403	−1.83647	−0.918236	+	0.396034i	$0.870386\pi$
$410$	10.1111	0.499354
$411$	29.8834	1.47404
$412$	−4.69017	−0.231068
$413$	−0.766982	−0.0377407
$414$	4.65775	0.228916
$415$	6.44014	0.316134
$416$	6.69930	0.328460
$417$	−0.707583	−0.0346505
$418$	−0.0871815	−0.00426418
$419$	−5.93748	−0.290065	−0.145032	−	0.989427i	$-0.546329\pi$
$419$	−5.93748	−0.290065	−0.145032	+	0.989427i	$0.546329\pi$
$420$	1.37887	0.0672819
$421$	−22.8842	−1.11531	−0.557654	−	0.830074i	$-0.688298\pi$
$421$	−22.8842	−1.11531	−0.557654	+	0.830074i	$0.688298\pi$
$422$	−13.4299	−0.653759
$423$	−32.8271	−1.59611
$424$	4.08848	0.198554
$425$	−3.24778	−0.157541
$426$	−36.9815	−1.79176
$427$	3.88309	0.187916
$428$	0.0168288	0.000813449 0
$429$	−9.52524	−0.459883
$430$	−3.01682	−0.145484
$431$	24.6927	1.18940	0.594702	−	0.803946i	$-0.297270\pi$
$431$	24.6927	1.18940	0.594702	+	0.803946i	$0.297270\pi$
$432$	3.63599	0.174937
$433$	6.93760	0.333400	0.166700	−	0.986008i	$-0.446689\pi$
$433$	6.93760	0.333400	0.166700	+	0.986008i	$0.446689\pi$
$434$	−3.63898	−0.174677
$435$	5.72581	0.274531
$436$	−10.3599	−0.496147
$437$	0.178229	0.00852585
$438$	9.85170	0.470732
$439$	28.6401	1.36692	0.683458	−	0.729990i	$-0.260475\pi$
$439$	28.6401	1.36692	0.683458	+	0.729990i	$0.260475\pi$
$440$	−0.524738	−0.0250159
$441$	−29.2689	−1.39376
$442$	−21.7579	−1.03492
$443$	27.5210	1.30756	0.653780	−	0.756684i	$-0.273182\pi$
$443$	27.5210	1.30756	0.653780	+	0.756684i	$0.273182\pi$
$444$	−17.6554	−0.837886
$445$	−4.50501	−0.213558
$446$	16.6367	0.787770
$447$	−1.84682	−0.0873515
$448$	0.508884	0.0240425
$449$	32.2677	1.52281	0.761404	−	0.648277i	$-0.224510\pi$
$449$	32.2677	1.52281	0.761404	+	0.648277i	$0.224510\pi$
$450$	4.34189	0.204679
$451$	−5.30570	−0.249836
$452$	13.7131	0.645008
$453$	57.6031	2.70643
$454$	1.15411	0.0541649
$455$	3.40917	0.159824
$456$	0.450180	0.0210816
$457$	−39.4463	−1.84522	−0.922611	−	0.385731i	$-0.873949\pi$
$457$	−39.4463	−1.84522	−0.922611	+	0.385731i	$0.873949\pi$
$458$	22.7634	1.06366
$459$	−11.8089	−0.551192
$460$	1.07275	0.0500170
$461$	10.5349	0.490661	0.245331	−	0.969440i	$-0.421104\pi$
$461$	10.5349	0.490661	0.245331	+	0.969440i	$0.421104\pi$
$462$	−0.723544	−0.0336623
$463$	15.9010	0.738984	0.369492	−	0.929234i	$-0.379532\pi$
$463$	15.9010	0.738984	0.369492	+	0.929234i	$0.379532\pi$
$464$	2.11316	0.0981011
$465$	−19.3761	−0.898544
$466$	7.31865	0.339030
$467$	22.1681	1.02582	0.512909	−	0.858443i	$-0.328568\pi$
$467$	22.1681	1.02582	0.512909	+	0.858443i	$0.328568\pi$
$468$	29.0877	1.34458
$469$	−4.79615	−0.221466
$470$	−7.56055	−0.348742
$471$	31.7186	1.46152
$472$	−1.50718	−0.0693738
$473$	1.58304	0.0727883
$474$	39.5331	1.81582
$475$	0.166143	0.00762316
$476$	−1.65274	−0.0757534
$477$	17.7517	0.812796
$478$	16.9160	0.773722
$479$	−3.54440	−0.161948	−0.0809739	−	0.996716i	$-0.525803\pi$
$479$	−3.54440	−0.161948	−0.0809739	+	0.996716i	$0.525803\pi$
$480$	2.70959	0.123675
$481$	−43.6518	−1.99035
$482$	21.7885	0.992437
$483$	1.47917	0.0673048
$484$	−10.7247	−0.487484
$485$	6.30646	0.286362
$486$	−19.5072	−0.884866
$487$	26.5658	1.20381	0.601907	−	0.798567i	$-0.294408\pi$
$487$	26.5658	1.20381	0.601907	+	0.798567i	$0.294408\pi$
$488$	7.63061	0.345421
$489$	10.0120	0.452757
$490$	−6.74104	−0.304529
$491$	−21.2415	−0.958615	−0.479308	−	0.877647i	$-0.659112\pi$
$491$	−21.2415	−0.958615	−0.479308	+	0.877647i	$0.659112\pi$
$492$	27.3971	1.23516
$493$	−6.86309	−0.309098
$494$	1.11304	0.0500781
$495$	−2.27836	−0.102405
$496$	−7.15091	−0.321086
$497$	−6.94543	−0.311545
$498$	17.4502	0.781960
$499$	6.76786	0.302971	0.151486	−	0.988459i	$-0.451594\pi$
$499$	6.76786	0.302971	0.151486	+	0.988459i	$0.451594\pi$
$500$	1.00000	0.0447214
$501$	−38.0793	−1.70126
$502$	−3.28793	−0.146747
$503$	−5.50315	−0.245373	−0.122687	−	0.992445i	$-0.539151\pi$
$503$	−5.50315	−0.245373	−0.122687	+	0.992445i	$0.539151\pi$
$504$	2.20952	0.0984198
$505$	−9.00297	−0.400627
$506$	−0.562910	−0.0250244
$507$	86.3835	3.83643
$508$	−16.4826	−0.731299
$509$	13.3529	0.591856	0.295928	−	0.955210i	$-0.404371\pi$
$509$	13.3529	0.591856	0.295928	+	0.955210i	$0.404371\pi$
$510$	−8.80017	−0.389678
$511$	1.85023	0.0818494
$512$	1.00000	0.0441942
$513$	0.604094	0.0266714
$514$	−7.48856	−0.330306
$515$	−4.69017	−0.206674
$516$	−8.17436	−0.359856
$517$	3.96731	0.174482
$518$	−3.31582	−0.145689
$519$	−10.0989	−0.443294
$520$	6.69930	0.293784
$521$	−13.9232	−0.609988	−0.304994	−	0.952354i	$-0.598655\pi$
$521$	−13.9232	−0.609988	−0.304994	+	0.952354i	$0.598655\pi$
$522$	9.17512	0.401584
$523$	16.1322	0.705410	0.352705	−	0.935735i	$-0.385262\pi$
$523$	16.1322	0.705410	0.352705	+	0.935735i	$0.385262\pi$
$524$	15.5989	0.681440
$525$	1.37887	0.0601787
$526$	−13.6601	−0.595609
$527$	23.2246	1.01168
$528$	−1.42183	−0.0618770
$529$	−21.8492	−0.949966
$530$	4.08848	0.177592
$531$	−6.54404	−0.283987
$532$	0.0845474	0.00366560
$533$	67.7376	2.93404
$534$	−12.2067	−0.528238
$535$	0.0168288	0.000727571 0
$536$	−9.42485	−0.407091
$537$	−51.3142	−2.21437
$538$	−29.8938	−1.28881
$539$	3.53728	0.152361
$540$	3.63599	0.156468
$541$	−8.26077	−0.355158	−0.177579	−	0.984107i	$-0.556827\pi$
$541$	−8.26077	−0.355158	−0.177579	+	0.984107i	$0.556827\pi$
$542$	6.79048	0.291676
$543$	48.0201	2.06074
$544$	−3.24778	−0.139247
$545$	−10.3599	−0.443767
$546$	9.23745	0.395326
$547$	−12.0205	−0.513960	−0.256980	−	0.966417i	$-0.582727\pi$
$547$	−12.0205	−0.513960	−0.256980	+	0.966417i	$0.582727\pi$
$548$	11.0287	0.471125
$549$	33.1313	1.41401
$550$	−0.524738	−0.0223749
$551$	0.351087	0.0149568
$552$	2.90670	0.123718
$553$	7.42464	0.315728
$554$	21.9706	0.933440
$555$	−17.6554	−0.749428
$556$	−0.261140	−0.0110748
$557$	28.4695	1.20629	0.603147	−	0.797630i	$-0.293913\pi$
$557$	28.4695	1.20629	0.603147	+	0.797630i	$0.293913\pi$
$558$	−31.0485	−1.31439
$559$	−20.2106	−0.854817
$560$	0.508884	0.0215043
$561$	4.61778	0.194963
$562$	−23.9659	−1.01094
$563$	−17.9916	−0.758253	−0.379127	−	0.925345i	$-0.623776\pi$
$563$	−17.9916	−0.758253	−0.379127	+	0.925345i	$0.623776\pi$
$564$	−20.4860	−0.862617
$565$	13.7131	0.576912
$566$	15.1844	0.638248
$567$	−1.61501	−0.0678241
$568$	−13.6484	−0.572673
$569$	−17.6739	−0.740930	−0.370465	−	0.928846i	$-0.620802\pi$
$569$	−17.6739	−0.740930	−0.370465	+	0.928846i	$0.620802\pi$
$570$	0.450180	0.0188560
$571$	10.3093	0.431430	0.215715	−	0.976456i	$-0.430792\pi$
$571$	10.3093	0.431430	0.215715	+	0.976456i	$0.430792\pi$
$572$	−3.51538	−0.146985
$573$	−32.7683	−1.36892
$574$	5.14540	0.214765
$575$	1.07275	0.0447366
$576$	4.34189	0.180912
$577$	−3.13686	−0.130589	−0.0652946	−	0.997866i	$-0.520799\pi$
$577$	−3.13686	−0.130589	−0.0652946	+	0.997866i	$0.520799\pi$
$578$	−6.45192	−0.268364
$579$	5.85847	0.243470
$580$	2.11316	0.0877442
$581$	3.27728	0.135965
$582$	17.0880	0.708318
$583$	−2.14538	−0.0888525
$584$	3.63586	0.150453
$585$	29.0877	1.20263
$586$	−14.1153	−0.583097
$587$	−11.1195	−0.458951	−0.229476	−	0.973314i	$-0.573701\pi$
$587$	−11.1195	−0.458951	−0.229476	+	0.973314i	$0.573701\pi$
$588$	−18.2655	−0.753255
$589$	−1.18807	−0.0489537
$590$	−1.50718	−0.0620498
$591$	−17.8211	−0.733062
$592$	−6.51587	−0.267801
$593$	−47.7905	−1.96252	−0.981260	−	0.192690i	$-0.938279\pi$
$593$	−47.7905	−1.96252	−0.981260	+	0.192690i	$0.938279\pi$
$594$	−1.90794	−0.0782838
$595$	−1.65274	−0.0677559
$596$	−0.681585	−0.0279188
$597$	−73.9054	−3.02475
$598$	7.18664	0.293884
$599$	4.88935	0.199773	0.0998867	−	0.994999i	$-0.468152\pi$
$599$	4.88935	0.199773	0.0998867	+	0.994999i	$0.468152\pi$
$600$	2.70959	0.110619
$601$	−1.79550	−0.0732401	−0.0366201	−	0.999329i	$-0.511659\pi$
$601$	−1.79550	−0.0732401	−0.0366201	+	0.999329i	$0.511659\pi$
$602$	−1.53521	−0.0625706
$603$	−40.9217	−1.66646
$604$	21.2590	0.865015
$605$	−10.7247	−0.436019
$606$	−24.3944	−0.990955
$607$	27.2537	1.10619	0.553097	−	0.833117i	$-0.313446\pi$
$607$	27.2537	1.10619	0.553097	+	0.833117i	$0.313446\pi$
$608$	0.166143	0.00673798
$609$	2.91377	0.118072
$610$	7.63061	0.308954
$611$	−50.6504	−2.04910
$612$	−14.1015	−0.570020
$613$	−26.9375	−1.08800	−0.543999	−	0.839086i	$-0.683090\pi$
$613$	−26.9375	−1.08800	−0.543999	+	0.839086i	$0.683090\pi$
$614$	−18.5123	−0.747095
$615$	27.3971	1.10476
$616$	−0.267031	−0.0107590
$617$	−46.9556	−1.89036	−0.945180	−	0.326549i	$-0.894114\pi$
$617$	−46.9556	−1.89036	−0.945180	+	0.326549i	$0.894114\pi$
$618$	−12.7084	−0.511209
$619$	5.08514	0.204389	0.102195	−	0.994764i	$-0.467414\pi$
$619$	5.08514	0.204389	0.102195	+	0.994764i	$0.467414\pi$
$620$	−7.15091	−0.287188
$621$	3.90049	0.156521
$622$	−30.4446	−1.22072
$623$	−2.29253	−0.0918482
$624$	18.1524	0.726677
$625$	1.00000	0.0400000
$626$	−16.5007	−0.659502
$627$	−0.236226	−0.00943397
$628$	11.7061	0.467122
$629$	21.1621	0.843789
$630$	2.20952	0.0880294
$631$	21.5933	0.859616	0.429808	−	0.902920i	$-0.358581\pi$
$631$	21.5933	0.859616	0.429808	+	0.902920i	$0.358581\pi$
$632$	14.5900	0.580361
$633$	−36.3896	−1.44636
$634$	14.2115	0.564412
$635$	−16.4826	−0.654093
$636$	11.0781	0.439276
$637$	−45.1602	−1.78931
$638$	−1.10886	−0.0439000
$639$	−59.2598	−2.34428
$640$	1.00000	0.0395285
$641$	27.8972	1.10187	0.550936	−	0.834547i	$-0.314271\pi$
$641$	27.8972	1.10187	0.550936	+	0.834547i	$0.314271\pi$
$642$	0.0455991	0.00179965
$643$	45.0320	1.77589	0.887945	−	0.459950i	$-0.152133\pi$
$643$	45.0320	1.77589	0.887945	+	0.459950i	$0.152133\pi$
$644$	0.545903	0.0215116
$645$	−8.17436	−0.321865
$646$	−0.539596	−0.0212301
$647$	−11.6824	−0.459284	−0.229642	−	0.973275i	$-0.573756\pi$
$647$	−11.6824	−0.459284	−0.229642	+	0.973275i	$0.573756\pi$
$648$	−3.17363	−0.124672
$649$	0.790877	0.0310446
$650$	6.69930	0.262768
$651$	−9.86017	−0.386450
$652$	3.69501	0.144708
$653$	−11.2683	−0.440963	−0.220481	−	0.975391i	$-0.570763\pi$
$653$	−11.2683	−0.440963	−0.220481	+	0.975391i	$0.570763\pi$
$654$	−28.0710	−1.09766
$655$	15.5989	0.609498
$656$	10.1111	0.394774
$657$	15.7865	0.615891
$658$	−3.84744	−0.149989
$659$	14.7900	0.576137	0.288069	−	0.957610i	$-0.406987\pi$
$659$	14.7900	0.576137	0.288069	+	0.957610i	$0.406987\pi$
$660$	−1.42183	−0.0553445
$661$	44.1284	1.71640	0.858198	−	0.513318i	$-0.171584\pi$
$661$	44.1284	1.71640	0.858198	+	0.513318i	$0.171584\pi$
$662$	−5.18264	−0.201429
$663$	−58.9550	−2.28962
$664$	6.44014	0.249926
$665$	0.0845474	0.00327861
$666$	−28.2912	−1.09626
$667$	2.26688	0.0877741
$668$	−14.0535	−0.543747
$669$	45.0786	1.74284
$670$	−9.42485	−0.364114
$671$	−4.00407	−0.154575
$672$	1.37887	0.0531910
$673$	39.8350	1.53553	0.767764	−	0.640733i	$-0.221369\pi$
$673$	39.8350	1.53553	0.767764	+	0.640733i	$0.221369\pi$
$674$	−4.05060	−0.156023
$675$	3.63599	0.139949
$676$	31.8806	1.22618
$677$	29.1904	1.12188	0.560938	−	0.827858i	$-0.310440\pi$
$677$	29.1904	1.12188	0.560938	+	0.827858i	$0.310440\pi$
$678$	37.1568	1.42700
$679$	3.20926	0.123160
$680$	−3.24778	−0.124547
$681$	3.12716	0.119833
$682$	3.75236	0.143685
$683$	−9.92190	−0.379651	−0.189826	−	0.981818i	$-0.560792\pi$
$683$	−9.92190	−0.379651	−0.189826	+	0.981818i	$0.560792\pi$
$684$	0.721375	0.0275825
$685$	11.0287	0.421387
$686$	−6.99259	−0.266978
$687$	61.6796	2.35322
$688$	−3.01682	−0.115015
$689$	27.3899	1.04347
$690$	2.90670	0.110656
$691$	−39.4119	−1.49930	−0.749650	−	0.661835i	$-0.769778\pi$
$691$	−39.4119	−1.49930	−0.749650	+	0.661835i	$0.769778\pi$
$692$	−3.72711	−0.141683
$693$	−1.15942	−0.0440427
$694$	−4.06750	−0.154400
$695$	−0.261140	−0.00990561
$696$	5.72581	0.217036
$697$	−32.8388	−1.24386
$698$	10.7560	0.407122
$699$	19.8306	0.750061
$700$	0.508884	0.0192340
$701$	1.37395	0.0518933	0.0259467	−	0.999663i	$-0.491740\pi$
$701$	1.37395	0.0518933	0.0259467	+	0.999663i	$0.491740\pi$
$702$	24.3586	0.919355
$703$	−1.08257	−0.0408297
$704$	−0.524738	−0.0197768
$705$	−20.4860	−0.771548
$706$	−15.8408	−0.596177
$707$	−4.58147	−0.172304
$708$	−4.08386	−0.153481
$709$	−37.9378	−1.42478	−0.712392	−	0.701782i	$-0.752388\pi$
$709$	−37.9378	−1.42478	−0.712392	+	0.701782i	$0.752388\pi$
$710$	−13.6484	−0.512214
$711$	63.3485	2.37575
$712$	−4.50501	−0.168832
$713$	−7.67111	−0.287285
$714$	−4.47826	−0.167595
$715$	−3.51538	−0.131468
$716$	−18.9380	−0.707745
$717$	45.8356	1.71176
$718$	6.41044	0.239235
$719$	5.37922	0.200611	0.100306	−	0.994957i	$-0.468018\pi$
$719$	5.37922	0.200611	0.100306	+	0.994957i	$0.468018\pi$
$720$	4.34189	0.161813
$721$	−2.38675	−0.0888873
$722$	−18.9724	−0.706079
$723$	59.0379	2.19564
$724$	17.7223	0.658642
$725$	2.11316	0.0784808
$726$	−29.0594	−1.07850
$727$	29.3086	1.08699	0.543497	−	0.839411i	$-0.317100\pi$
$727$	29.3086	1.08699	0.543497	+	0.839411i	$0.317100\pi$
$728$	3.40917	0.126352
$729$	−43.3357	−1.60503
$730$	3.63586	0.134569
$731$	9.79798	0.362391
$732$	20.6758	0.764201
$733$	25.9038	0.956780	0.478390	−	0.878147i	$-0.341221\pi$
$733$	25.9038	0.956780	0.478390	+	0.878147i	$0.341221\pi$
$734$	0.622097	0.0229620
$735$	−18.2655	−0.673732
$736$	1.07275	0.0395419
$737$	4.94557	0.182173
$738$	43.9015	1.61604
$739$	25.0755	0.922416	0.461208	−	0.887292i	$-0.347416\pi$
$739$	25.0755	0.922416	0.461208	+	0.887292i	$0.347416\pi$
$740$	−6.51587	−0.239528
$741$	3.01589	0.110791
$742$	2.08056	0.0763798
$743$	−15.2672	−0.560098	−0.280049	−	0.959986i	$-0.590351\pi$
$743$	−15.2672	−0.560098	−0.280049	+	0.959986i	$0.590351\pi$
$744$	−19.3761	−0.710361
$745$	−0.681585	−0.0249713
$746$	6.86343	0.251288
$747$	27.9624	1.02309
$748$	1.70423	0.0623130
$749$	0.00856388	0.000312917 0
$750$	2.70959	0.0989404
$751$	−29.2051	−1.06571	−0.532855	−	0.846207i	$-0.678881\pi$
$751$	−29.2051	−1.06571	−0.532855	+	0.846207i	$0.678881\pi$
$752$	−7.56055	−0.275705
$753$	−8.90894	−0.324660
$754$	14.1567	0.515557
$755$	21.2590	0.773693
$756$	1.85030	0.0672946
$757$	20.7484	0.754112	0.377056	−	0.926190i	$-0.376936\pi$
$757$	20.7484	0.754112	0.377056	+	0.926190i	$0.376936\pi$
$758$	21.2741	0.772710
$759$	−1.52526	−0.0553633
$760$	0.166143	0.00602664
$761$	5.10069	0.184900	0.0924500	−	0.995717i	$-0.470530\pi$
$761$	5.10069	0.184900	0.0924500	+	0.995717i	$0.470530\pi$
$762$	−44.6612	−1.61791
$763$	−5.27196	−0.190858
$764$	−12.0935	−0.437526
$765$	−14.1015	−0.509842
$766$	−24.0014	−0.867205
$767$	−10.0971	−0.364584
$768$	2.70959	0.0977740
$769$	22.1918	0.800255	0.400128	−	0.916459i	$-0.368966\pi$
$769$	22.1918	0.800255	0.400128	+	0.916459i	$0.368966\pi$
$770$	−0.267031	−0.00962312
$771$	−20.2910	−0.730761
$772$	2.16212	0.0778165
$773$	47.6997	1.71564	0.857820	−	0.513950i	$-0.171818\pi$
$773$	47.6997	1.71564	0.857820	+	0.513950i	$0.171818\pi$
$774$	−13.0987	−0.470824
$775$	−7.15091	−0.256868
$776$	6.30646	0.226389
$777$	−8.98453	−0.322318
$778$	−26.0471	−0.933834
$779$	1.67989	0.0601885
$780$	18.1524	0.649959
$781$	7.16181	0.256270
$782$	−3.48404	−0.124589
$783$	7.68343	0.274583
$784$	−6.74104	−0.240751
$785$	11.7061	0.417807
$786$	42.2666	1.50760
$787$	−12.0941	−0.431107	−0.215554	−	0.976492i	$-0.569156\pi$
$787$	−12.0941	−0.431107	−0.215554	+	0.976492i	$0.569156\pi$
$788$	−6.57704	−0.234297
$789$	−37.0133	−1.31771
$790$	14.5900	0.519091
$791$	6.97835	0.248122
$792$	−2.27836	−0.0809579
$793$	51.1197	1.81531
$794$	24.7247	0.877447
$795$	11.0781	0.392900
$796$	−27.2755	−0.966753
$797$	25.2863	0.895685	0.447842	−	0.894112i	$-0.352193\pi$
$797$	25.2863	0.895685	0.447842	+	0.894112i	$0.352193\pi$
$798$	0.229089	0.00810967
$799$	24.5550	0.868694
$800$	1.00000	0.0353553
$801$	−19.5603	−0.691129
$802$	1.00000	0.0353112
$803$	−1.90787	−0.0673274
$804$	−25.5375	−0.900638
$805$	0.545903	0.0192405
$806$	−47.9061	−1.68742
$807$	−81.0000	−2.85134
$808$	−9.00297	−0.316724
$809$	−7.80915	−0.274555	−0.137277	−	0.990533i	$-0.543835\pi$
$809$	−7.80915	−0.274555	−0.137277	+	0.990533i	$0.543835\pi$
$810$	−3.17363	−0.111510
$811$	1.79162	0.0629123	0.0314561	−	0.999505i	$-0.489986\pi$
$811$	1.79162	0.0629123	0.0314561	+	0.999505i	$0.489986\pi$
$812$	1.07535	0.0377375
$813$	18.3994	0.645297
$814$	3.41912	0.119840
$815$	3.69501	0.129431
$816$	−8.80017	−0.308067
$817$	−0.501224	−0.0175356
$818$	−37.1403	−1.29858
$819$	14.8022	0.517232
$820$	10.1111	0.353096
$821$	13.8418	0.483081	0.241540	−	0.970391i	$-0.422347\pi$
$821$	13.8418	0.483081	0.241540	+	0.970391i	$0.422347\pi$
$822$	29.8834	1.04230
$823$	−27.0549	−0.943075	−0.471537	−	0.881846i	$-0.656301\pi$
$823$	−27.0549	−0.943075	−0.471537	+	0.881846i	$0.656301\pi$
$824$	−4.69017	−0.163390
$825$	−1.42183	−0.0495016
$826$	−0.766982	−0.0266867
$827$	17.8559	0.620911	0.310456	−	0.950588i	$-0.399518\pi$
$827$	17.8559	0.620911	0.310456	+	0.950588i	$0.399518\pi$
$828$	4.65775	0.161868
$829$	−36.0591	−1.25239	−0.626193	−	0.779668i	$-0.715388\pi$
$829$	−36.0591	−1.25239	−0.626193	+	0.779668i	$0.715388\pi$
$830$	6.44014	0.223540
$831$	59.5313	2.06512
$832$	6.69930	0.232256
$833$	21.8934	0.758562
$834$	−0.707583	−0.0245016
$835$	−14.0535	−0.486342
$836$	−0.0871815	−0.00301523
$837$	−26.0006	−0.898714
$838$	−5.93748	−0.205107
$839$	42.0558	1.45193	0.725964	−	0.687733i	$-0.241394\pi$
$839$	42.0558	1.45193	0.725964	+	0.687733i	$0.241394\pi$
$840$	1.37887	0.0475755
$841$	−24.5345	−0.846019
$842$	−22.8842	−0.788642
$843$	−64.9377	−2.23657
$844$	−13.4299	−0.462277
$845$	31.8806	1.09673
$846$	−32.8271	−1.12862
$847$	−5.45760	−0.187525
$848$	4.08848	0.140399
$849$	41.1435	1.41204
$850$	−3.24778	−0.111398
$851$	−6.98987	−0.239610
$852$	−36.9815	−1.26697
$853$	3.02836	0.103689	0.0518445	−	0.998655i	$-0.483490\pi$
$853$	3.02836	0.103689	0.0518445	+	0.998655i	$0.483490\pi$
$854$	3.88309	0.132877
$855$	0.721375	0.0246705
$856$	0.0168288	0.000575195 0
$857$	7.74331	0.264506	0.132253	−	0.991216i	$-0.457779\pi$
$857$	7.74331	0.264506	0.132253	+	0.991216i	$0.457779\pi$
$858$	−9.52524	−0.325186
$859$	−3.49703	−0.119317	−0.0596585	−	0.998219i	$-0.519001\pi$
$859$	−3.49703	−0.119317	−0.0596585	+	0.998219i	$0.519001\pi$
$860$	−3.01682	−0.102873
$861$	13.9419	0.475140
$862$	24.6927	0.841036
$863$	−6.27209	−0.213505	−0.106752	−	0.994286i	$-0.534045\pi$
$863$	−6.27209	−0.213505	−0.106752	+	0.994286i	$0.534045\pi$
$864$	3.63599	0.123699
$865$	−3.72711	−0.126725
$866$	6.93760	0.235749
$867$	−17.4821	−0.593722
$868$	−3.63898	−0.123515
$869$	−7.65595	−0.259710
$870$	5.72581	0.194123
$871$	−63.1399	−2.13941
$872$	−10.3599	−0.350829
$873$	27.3820	0.926740
$874$	0.178229	0.00602869
$875$	0.508884	0.0172034
$876$	9.85170	0.332858
$877$	8.68715	0.293344	0.146672	−	0.989185i	$-0.453144\pi$
$877$	8.68715	0.293344	0.146672	+	0.989185i	$0.453144\pi$
$878$	28.6401	0.966556
$879$	−38.2467	−1.29003
$880$	−0.524738	−0.0176889
$881$	43.0913	1.45178	0.725892	−	0.687809i	$-0.241427\pi$
$881$	43.0913	1.45178	0.725892	+	0.687809i	$0.241427\pi$
$882$	−29.2689	−0.985534
$883$	−5.48644	−0.184633	−0.0923167	−	0.995730i	$-0.529427\pi$
$883$	−5.48644	−0.184633	−0.0923167	+	0.995730i	$0.529427\pi$
$884$	−21.7579	−0.731796
$885$	−4.08386	−0.137277
$886$	27.5210	0.924585
$887$	−10.0197	−0.336429	−0.168215	−	0.985750i	$-0.553800\pi$
$887$	−10.0197	−0.336429	−0.168215	+	0.985750i	$0.553800\pi$
$888$	−17.6554	−0.592475
$889$	−8.38775	−0.281316
$890$	−4.50501	−0.151008
$891$	1.66533	0.0557905
$892$	16.6367	0.557037
$893$	−1.25613	−0.0420349
$894$	−1.84682	−0.0617668
$895$	−18.9380	−0.633026
$896$	0.508884	0.0170006
$897$	19.4729	0.650181
$898$	32.2677	1.07679
$899$	−15.1110	−0.503981
$900$	4.34189	0.144730
$901$	−13.2785	−0.442370
$902$	−5.30570	−0.176660
$903$	−4.15980	−0.138429
$904$	13.7131	0.456089
$905$	17.7223	0.589108
$906$	57.6031	1.91374
$907$	21.1784	0.703219	0.351609	−	0.936147i	$-0.385635\pi$
$907$	21.1784	0.703219	0.351609	+	0.936147i	$0.385635\pi$
$908$	1.15411	0.0383004
$909$	−39.0900	−1.29653
$910$	3.40917	0.113013
$911$	37.2703	1.23482	0.617410	−	0.786641i	$-0.288182\pi$
$911$	37.2703	1.23482	0.617410	+	0.786641i	$0.288182\pi$
$912$	0.450180	0.0149069
$913$	−3.37938	−0.111841
$914$	−39.4463	−1.30477
$915$	20.6758	0.683522
$916$	22.7634	0.752124
$917$	7.93801	0.262136
$918$	−11.8089	−0.389752
$919$	−9.85101	−0.324955	−0.162477	−	0.986712i	$-0.551948\pi$
$919$	−9.85101	−0.324955	−0.162477	+	0.986712i	$0.551948\pi$
$920$	1.07275	0.0353674
$921$	−50.1608	−1.65285
$922$	10.5349	0.346950
$923$	−91.4345	−3.00960
$924$	−0.723544	−0.0238029
$925$	−6.51587	−0.214241
$926$	15.9010	0.522541
$927$	−20.3642	−0.668849
$928$	2.11316	0.0693679
$929$	4.31363	0.141526	0.0707628	−	0.997493i	$-0.477457\pi$
$929$	4.31363	0.141526	0.0707628	+	0.997493i	$0.477457\pi$
$930$	−19.3761	−0.635366
$931$	−1.11998	−0.0367057
$932$	7.31865	0.239730
$933$	−82.4924	−2.70068
$934$	22.1681	0.725362
$935$	1.70423	0.0557344
$936$	29.0877	0.950760
$937$	−37.4978	−1.22500	−0.612499	−	0.790471i	$-0.709836\pi$
$937$	−37.4978	−1.22500	−0.612499	+	0.790471i	$0.709836\pi$
$938$	−4.79615	−0.156600
$939$	−44.7103	−1.45906
$940$	−7.56055	−0.246598
$941$	25.4250	0.828831	0.414415	−	0.910088i	$-0.363986\pi$
$941$	25.4250	0.828831	0.414415	+	0.910088i	$0.363986\pi$
$942$	31.7186	1.03345
$943$	10.8467	0.353217
$944$	−1.50718	−0.0490547
$945$	1.85030	0.0601901
$946$	1.58304	0.0514691
$947$	2.83674	0.0921818	0.0460909	−	0.998937i	$-0.485324\pi$
$947$	2.83674	0.0921818	0.0460909	+	0.998937i	$0.485324\pi$
$948$	39.5331	1.28398
$949$	24.3577	0.790685
$950$	0.166143	0.00539039
$951$	38.5075	1.24869
$952$	−1.65274	−0.0535657
$953$	−34.3115	−1.11146	−0.555729	−	0.831363i	$-0.687561\pi$
$953$	−34.3115	−1.11146	−0.555729	+	0.831363i	$0.687561\pi$
$954$	17.7517	0.574734
$955$	−12.0935	−0.391335
$956$	16.9160	0.547104
$957$	−3.00455	−0.0971232
$958$	−3.54440	−0.114514
$959$	5.61235	0.181232
$960$	2.70959	0.0874517
$961$	20.1356	0.649535
$962$	−43.6518	−1.40739
$963$	0.0730687	0.00235461
$964$	21.7885	0.701759
$965$	2.16212	0.0696012
$966$	1.47917	0.0475917
$967$	20.8539	0.670615	0.335308	−	0.942109i	$-0.391160\pi$
$967$	20.8539	0.670615	0.335308	+	0.942109i	$0.391160\pi$
$968$	−10.7247	−0.344703
$969$	−1.46209	−0.0469689
$970$	6.30646	0.202488
$971$	−23.4479	−0.752479	−0.376240	−	0.926522i	$-0.622783\pi$
$971$	−23.4479	−0.752479	−0.376240	+	0.926522i	$0.622783\pi$
$972$	−19.5072	−0.625694
$973$	−0.132890	−0.00426026
$974$	26.5658	0.851224
$975$	18.1524	0.581341
$976$	7.63061	0.244250
$977$	31.4874	1.00737	0.503686	−	0.863887i	$-0.331977\pi$
$977$	31.4874	1.00737	0.503686	+	0.863887i	$0.331977\pi$
$978$	10.0120	0.320148
$979$	2.36395	0.0755522
$980$	−6.74104	−0.215335
$981$	−44.9814	−1.43615
$982$	−21.2415	−0.677843
$983$	12.1747	0.388313	0.194156	−	0.980971i	$-0.437803\pi$
$983$	12.1747	0.388313	0.194156	+	0.980971i	$0.437803\pi$
$984$	27.3971	0.873387
$985$	−6.57704	−0.209562
$986$	−6.86309	−0.218565
$987$	−10.4250	−0.331832
$988$	1.11304	0.0354106
$989$	−3.23628	−0.102908
$990$	−2.27836	−0.0724109
$991$	−56.2515	−1.78689	−0.893444	−	0.449175i	$-0.851718\pi$
$991$	−56.2515	−1.78689	−0.893444	+	0.449175i	$0.851718\pi$
$992$	−7.15091	−0.227042
$993$	−14.0429	−0.445636
$994$	−6.94543	−0.220296
$995$	−27.2755	−0.864690
$996$	17.4502	0.552929
$997$	38.9622	1.23395	0.616973	−	0.786984i	$-0.288359\pi$
$997$	38.9622	1.23395	0.616973	+	0.786984i	$0.288359\pi$
$998$	6.76786	0.214233
$999$	−23.6916	−0.749570

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4010.2.a.n.1.19	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4010.2.a.n.1.19	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +2.70959 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.70959 q^{6} +0.508884 q^{7} +1.00000 q^{8} +4.34189 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +2.70959 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.70959 q^{6} +0.508884 q^{7} +1.00000 q^{8} +4.34189 q^{9} +1.00000 q^{10} -0.524738 q^{11} +2.70959 q^{12} +6.69930 q^{13} +0.508884 q^{14} +2.70959 q^{15} +1.00000 q^{16} -3.24778 q^{17} +4.34189 q^{18} +0.166143 q^{19} +1.00000 q^{20} +1.37887 q^{21} -0.524738 q^{22} +1.07275 q^{23} +2.70959 q^{24} +1.00000 q^{25} +6.69930 q^{26} +3.63599 q^{27} +0.508884 q^{28} +2.11316 q^{29} +2.70959 q^{30} -7.15091 q^{31} +1.00000 q^{32} -1.42183 q^{33} -3.24778 q^{34} +0.508884 q^{35} +4.34189 q^{36} -6.51587 q^{37} +0.166143 q^{38} +18.1524 q^{39} +1.00000 q^{40} +10.1111 q^{41} +1.37887 q^{42} -3.01682 q^{43} -0.524738 q^{44} +4.34189 q^{45} +1.07275 q^{46} -7.56055 q^{47} +2.70959 q^{48} -6.74104 q^{49} +1.00000 q^{50} -8.80017 q^{51} +6.69930 q^{52} +4.08848 q^{53} +3.63599 q^{54} -0.524738 q^{55} +0.508884 q^{56} +0.450180 q^{57} +2.11316 q^{58} -1.50718 q^{59} +2.70959 q^{60} +7.63061 q^{61} -7.15091 q^{62} +2.20952 q^{63} +1.00000 q^{64} +6.69930 q^{65} -1.42183 q^{66} -9.42485 q^{67} -3.24778 q^{68} +2.90670 q^{69} +0.508884 q^{70} -13.6484 q^{71} +4.34189 q^{72} +3.63586 q^{73} -6.51587 q^{74} +2.70959 q^{75} +0.166143 q^{76} -0.267031 q^{77} +18.1524 q^{78} +14.5900 q^{79} +1.00000 q^{80} -3.17363 q^{81} +10.1111 q^{82} +6.44014 q^{83} +1.37887 q^{84} -3.24778 q^{85} -3.01682 q^{86} +5.72581 q^{87} -0.524738 q^{88} -4.50501 q^{89} +4.34189 q^{90} +3.40917 q^{91} +1.07275 q^{92} -19.3761 q^{93} -7.56055 q^{94} +0.166143 q^{95} +2.70959 q^{96} +6.30646 q^{97} -6.74104 q^{98} -2.27836 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 22 q^{2} + q^{3} + 22 q^{4} + 22 q^{5} + q^{6} + 22 q^{8} + 43 q^{9}+O(q^{10}) \) 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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