LMFDB - Embedded newform 8007.2.a.i.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8007,2,Mod(1,8007)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8007, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("8007.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8007 = 3 \cdot 17 \cdot 157 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8007.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:	$63.9362168984$
Analytic rank:	$0$
Dimension:	$63$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Character	$\chi$	$=$	8007.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.70479 q^{2} +1.00000 q^{3} +5.31589 q^{4} +4.10743 q^{5} -2.70479 q^{6} +3.26601 q^{7} -8.96878 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.70479 q^{2} +1.00000 q^{3} +5.31589 q^{4} +4.10743 q^{5} -2.70479 q^{6} +3.26601 q^{7} -8.96878 q^{8} +1.00000 q^{9} -11.1097 q^{10} +2.39019 q^{11} +5.31589 q^{12} -0.0451518 q^{13} -8.83386 q^{14} +4.10743 q^{15} +13.6269 q^{16} +1.00000 q^{17} -2.70479 q^{18} -7.19687 q^{19} +21.8346 q^{20} +3.26601 q^{21} -6.46495 q^{22} +5.99393 q^{23} -8.96878 q^{24} +11.8710 q^{25} +0.122126 q^{26} +1.00000 q^{27} +17.3617 q^{28} -5.23193 q^{29} -11.1097 q^{30} +8.94867 q^{31} -18.9203 q^{32} +2.39019 q^{33} -2.70479 q^{34} +13.4149 q^{35} +5.31589 q^{36} +2.60436 q^{37} +19.4660 q^{38} -0.0451518 q^{39} -36.8386 q^{40} +9.65073 q^{41} -8.83386 q^{42} -2.56103 q^{43} +12.7060 q^{44} +4.10743 q^{45} -16.2123 q^{46} +11.1792 q^{47} +13.6269 q^{48} +3.66680 q^{49} -32.1084 q^{50} +1.00000 q^{51} -0.240022 q^{52} -10.2143 q^{53} -2.70479 q^{54} +9.81751 q^{55} -29.2921 q^{56} -7.19687 q^{57} +14.1513 q^{58} +12.9398 q^{59} +21.8346 q^{60} -10.0547 q^{61} -24.2043 q^{62} +3.26601 q^{63} +23.9217 q^{64} -0.185458 q^{65} -6.46495 q^{66} -2.70112 q^{67} +5.31589 q^{68} +5.99393 q^{69} -36.2844 q^{70} -4.65122 q^{71} -8.96878 q^{72} -4.08599 q^{73} -7.04424 q^{74} +11.8710 q^{75} -38.2578 q^{76} +7.80636 q^{77} +0.122126 q^{78} +6.40550 q^{79} +55.9714 q^{80} +1.00000 q^{81} -26.1032 q^{82} +2.34525 q^{83} +17.3617 q^{84} +4.10743 q^{85} +6.92706 q^{86} -5.23193 q^{87} -21.4370 q^{88} +0.914319 q^{89} -11.1097 q^{90} -0.147466 q^{91} +31.8630 q^{92} +8.94867 q^{93} -30.2375 q^{94} -29.5606 q^{95} -18.9203 q^{96} +3.43487 q^{97} -9.91791 q^{98} +2.39019 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 63 q + 10 q^{2} + 63 q^{3} + 70 q^{4} + 19 q^{5} + 10 q^{6} + 11 q^{7} + 27 q^{8} + 63 q^{9}+O(q^{10}) $ 63 * q + 10 * q^2 + 63 * q^3 + 70 * q^4 + 19 * q^5 + 10 * q^6 + 11 * q^7 + 27 * q^8 + 63 * q^9	\( 63 q + 10 q^{2} + 63 q^{3} + 70 q^{4} + 19 q^{5} + 10 q^{6} + 11 q^{7} + 27 q^{8} + 63 q^{9} + 4 q^{10} + 23 q^{11} + 70 q^{12} + 10 q^{13} + 18 q^{14} + 19 q^{15} + 72 q^{16} + 63 q^{17} + 10 q^{18} + 6 q^{19} + 48 q^{20} + 11 q^{21} + 21 q^{22} + 44 q^{23} + 27 q^{24} + 110 q^{25} + 41 q^{26} + 63 q^{27} + 26 q^{28} + 35 q^{29} + 4 q^{30} + q^{31} + 54 q^{32} + 23 q^{33} + 10 q^{34} + 47 q^{35} + 70 q^{36} + 40 q^{37} + 38 q^{38} + 10 q^{39} - 10 q^{40} + 35 q^{41} + 18 q^{42} + 27 q^{43} + 46 q^{44} + 19 q^{45} + 8 q^{46} + 29 q^{47} + 72 q^{48} + 114 q^{49} + 27 q^{50} + 63 q^{51} - q^{52} + 75 q^{53} + 10 q^{54} + 5 q^{55} + 24 q^{56} + 6 q^{57} + 41 q^{58} + 105 q^{59} + 48 q^{60} + 5 q^{61} + 22 q^{62} + 11 q^{63} + 61 q^{64} + 49 q^{65} + 21 q^{66} + 4 q^{67} + 70 q^{68} + 44 q^{69} - 16 q^{70} + 16 q^{71} + 27 q^{72} + 39 q^{73} + 54 q^{74} + 110 q^{75} + 6 q^{76} + 88 q^{77} + 41 q^{78} + 16 q^{79} + 102 q^{80} + 63 q^{81} - 29 q^{82} + 73 q^{83} + 26 q^{84} + 19 q^{85} + 46 q^{86} + 35 q^{87} + 18 q^{88} + 88 q^{89} + 4 q^{90} - 15 q^{91} + 110 q^{92} + q^{93} - 8 q^{94} + 28 q^{95} + 54 q^{96} + 70 q^{97} + 33 q^{98} + 23 q^{99}+O(q^{100}) \) 63 * q + 10 * q^2 + 63 * q^3 + 70 * q^4 + 19 * q^5 + 10 * q^6 + 11 * q^7 + 27 * q^8 + 63 * q^9 + 4 * q^10 + 23 * q^11 + 70 * q^12 + 10 * q^13 + 18 * q^14 + 19 * q^15 + 72 * q^16 + 63 * q^17 + 10 * q^18 + 6 * q^19 + 48 * q^20 + 11 * q^21 + 21 * q^22 + 44 * q^23 + 27 * q^24 + 110 * q^25 + 41 * q^26 + 63 * q^27 + 26 * q^28 + 35 * q^29 + 4 * q^30 + q^31 + 54 * q^32 + 23 * q^33 + 10 * q^34 + 47 * q^35 + 70 * q^36 + 40 * q^37 + 38 * q^38 + 10 * q^39 - 10 * q^40 + 35 * q^41 + 18 * q^42 + 27 * q^43 + 46 * q^44 + 19 * q^45 + 8 * q^46 + 29 * q^47 + 72 * q^48 + 114 * q^49 + 27 * q^50 + 63 * q^51 - q^52 + 75 * q^53 + 10 * q^54 + 5 * q^55 + 24 * q^56 + 6 * q^57 + 41 * q^58 + 105 * q^59 + 48 * q^60 + 5 * q^61 + 22 * q^62 + 11 * q^63 + 61 * q^64 + 49 * q^65 + 21 * q^66 + 4 * q^67 + 70 * q^68 + 44 * q^69 - 16 * q^70 + 16 * q^71 + 27 * q^72 + 39 * q^73 + 54 * q^74 + 110 * q^75 + 6 * q^76 + 88 * q^77 + 41 * q^78 + 16 * q^79 + 102 * q^80 + 63 * q^81 - 29 * q^82 + 73 * q^83 + 26 * q^84 + 19 * q^85 + 46 * q^86 + 35 * q^87 + 18 * q^88 + 88 * q^89 + 4 * q^90 - 15 * q^91 + 110 * q^92 + q^93 - 8 * q^94 + 28 * q^95 + 54 * q^96 + 70 * q^97 + 33 * q^98 + 23 * 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 $

$2$	−2.70479	−1.91258	−0.956288	−	0.292428i	$-0.905537\pi$
$2$	−2.70479	−1.91258	−0.956288	+	0.292428i	$0.905537\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	5.31589	2.65794
$5$	4.10743	1.83690	0.918449	−	0.395540i	$-0.129443\pi$
$5$	4.10743	1.83690	0.918449	+	0.395540i	$0.129443\pi$
$6$	−2.70479	−1.10423
$7$	3.26601	1.23443	0.617217	−	0.786793i	$-0.288260\pi$
$7$	3.26601	1.23443	0.617217	+	0.786793i	$0.288260\pi$
$8$	−8.96878	−3.17094
$9$	1.00000	0.333333
$10$	−11.1097	−3.51320
$11$	2.39019	0.720668	0.360334	−	0.932823i	$-0.382663\pi$
$11$	2.39019	0.720668	0.360334	+	0.932823i	$0.382663\pi$
$12$	5.31589	1.53456
$13$	−0.0451518	−0.0125228	−0.00626142	−	0.999980i	$-0.501993\pi$
$13$	−0.0451518	−0.0125228	−0.00626142	+	0.999980i	$0.501993\pi$
$14$	−8.83386	−2.36095
$15$	4.10743	1.06053
$16$	13.6269	3.40672
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−2.70479	−0.637525
$19$	−7.19687	−1.65108	−0.825538	−	0.564347i	$-0.809128\pi$
$19$	−7.19687	−1.65108	−0.825538	+	0.564347i	$0.809128\pi$
$20$	21.8346	4.88237
$21$	3.26601	0.712701
$22$	−6.46495	−1.37833
$23$	5.99393	1.24982	0.624910	−	0.780697i	$-0.285136\pi$
$23$	5.99393	1.24982	0.624910	+	0.780697i	$0.285136\pi$
$24$	−8.96878	−1.83074
$25$	11.8710	2.37419
$26$	0.122126	0.0239509
$27$	1.00000	0.192450
$28$	17.3617	3.28106
$29$	−5.23193	−0.971545	−0.485772	−	0.874085i	$-0.661462\pi$
$29$	−5.23193	−0.971545	−0.485772	+	0.874085i	$0.661462\pi$
$30$	−11.1097	−2.02835
$31$	8.94867	1.60723	0.803614	−	0.595151i	$-0.202908\pi$
$31$	8.94867	1.60723	0.803614	+	0.595151i	$0.202908\pi$
$32$	−18.9203	−3.34467
$33$	2.39019	0.416078
$34$	−2.70479	−0.463868
$35$	13.4149	2.26753
$36$	5.31589	0.885981
$37$	2.60436	0.428154	0.214077	−	0.976817i	$-0.431326\pi$
$37$	2.60436	0.428154	0.214077	+	0.976817i	$0.431326\pi$
$38$	19.4660	3.15781
$39$	−0.0451518	−0.00723007
$40$	−36.8386	−5.82470
$41$	9.65073	1.50719	0.753595	−	0.657339i	$-0.228318\pi$
$41$	9.65073	1.50719	0.753595	+	0.657339i	$0.228318\pi$
$42$	−8.83386	−1.36309
$43$	−2.56103	−0.390554	−0.195277	−	0.980748i	$-0.562561\pi$
$43$	−2.56103	−0.390554	−0.195277	+	0.980748i	$0.562561\pi$
$44$	12.7060	1.91550
$45$	4.10743	0.612299
$46$	−16.2123	−2.39037
$47$	11.1792	1.63066	0.815329	−	0.578998i	$-0.196556\pi$
$47$	11.1792	1.63066	0.815329	+	0.578998i	$0.196556\pi$
$48$	13.6269	1.96687
$49$	3.66680	0.523828
$50$	−32.1084	−4.54082
$51$	1.00000	0.140028
$52$	−0.240022	−0.0332850
$53$	−10.2143	−1.40304	−0.701520	−	0.712650i	$-0.747495\pi$
$53$	−10.2143	−1.40304	−0.701520	+	0.712650i	$0.747495\pi$
$54$	−2.70479	−0.368075
$55$	9.81751	1.32379
$56$	−29.2921	−3.91432
$57$	−7.19687	−0.953249
$58$	14.1513	1.85815
$59$	12.9398	1.68462	0.842311	−	0.538991i	$-0.181195\pi$
$59$	12.9398	1.68462	0.842311	+	0.538991i	$0.181195\pi$
$60$	21.8346	2.81884
$61$	−10.0547	−1.28737	−0.643686	−	0.765289i	$-0.722596\pi$
$61$	−10.0547	−1.28737	−0.643686	+	0.765289i	$0.722596\pi$
$62$	−24.2043	−3.07394
$63$	3.26601	0.411478
$64$	23.9217	2.99021
$65$	−0.185458	−0.0230032
$66$	−6.46495	−0.795780
$67$	−2.70112	−0.329994	−0.164997	−	0.986294i	$-0.552761\pi$
$67$	−2.70112	−0.329994	−0.164997	+	0.986294i	$0.552761\pi$
$68$	5.31589	0.644646
$69$	5.99393	0.721584
$70$	−36.2844	−4.33682
$71$	−4.65122	−0.551998	−0.275999	−	0.961158i	$-0.589009\pi$
$71$	−4.65122	−0.551998	−0.275999	+	0.961158i	$0.589009\pi$
$72$	−8.96878	−1.05698
$73$	−4.08599	−0.478230	−0.239115	−	0.970991i	$-0.576857\pi$
$73$	−4.08599	−0.478230	−0.239115	+	0.970991i	$0.576857\pi$
$74$	−7.04424	−0.818877
$75$	11.8710	1.37074
$76$	−38.2578	−4.38847
$77$	7.80636	0.889617
$78$	0.122126	0.0138280
$79$	6.40550	0.720675	0.360338	−	0.932822i	$-0.382661\pi$
$79$	6.40550	0.720675	0.360338	+	0.932822i	$0.382661\pi$
$80$	55.9714	6.25780
$81$	1.00000	0.111111
$82$	−26.1032	−2.88262
$83$	2.34525	0.257424	0.128712	−	0.991682i	$-0.458916\pi$
$83$	2.34525	0.257424	0.128712	+	0.991682i	$0.458916\pi$
$84$	17.3617	1.89432
$85$	4.10743	0.445513
$86$	6.92706	0.746964
$87$	−5.23193	−0.560922
$88$	−21.4370	−2.28520
$89$	0.914319	0.0969176	0.0484588	−	0.998825i	$-0.484569\pi$
$89$	0.914319	0.0969176	0.0484588	+	0.998825i	$0.484569\pi$
$90$	−11.1097	−1.17107
$91$	−0.147466	−0.0154586
$92$	31.8630	3.32195
$93$	8.94867	0.927933
$94$	−30.2375	−3.11876
$95$	−29.5606	−3.03286
$96$	−18.9203	−1.93105
$97$	3.43487	0.348759	0.174379	−	0.984679i	$-0.444208\pi$
$97$	3.43487	0.348759	0.174379	+	0.984679i	$0.444208\pi$
$98$	−9.91791	−1.00186
$99$	2.39019	0.240223
$100$	63.1047	6.31047
$101$	−1.94178	−0.193215	−0.0966073	−	0.995323i	$-0.530799\pi$
$101$	−1.94178	−0.193215	−0.0966073	+	0.995323i	$0.530799\pi$
$102$	−2.70479	−0.267814
$103$	−16.5103	−1.62681	−0.813403	−	0.581700i	$-0.802388\pi$
$103$	−16.5103	−1.62681	−0.813403	+	0.581700i	$0.802388\pi$
$104$	0.404956	0.0397092
$105$	13.4149	1.30916
$106$	27.6275	2.68342
$107$	−16.6960	−1.61406	−0.807032	−	0.590508i	$-0.798927\pi$
$107$	−16.6960	−1.61406	−0.807032	+	0.590508i	$0.798927\pi$
$108$	5.31589	0.511522
$109$	−6.18540	−0.592454	−0.296227	−	0.955118i	$-0.595729\pi$
$109$	−6.18540	−0.592454	−0.296227	+	0.955118i	$0.595729\pi$
$110$	−26.5543	−2.53185
$111$	2.60436	0.247195
$112$	44.5055	4.20537
$113$	−5.14626	−0.484120	−0.242060	−	0.970261i	$-0.577823\pi$
$113$	−5.14626	−0.484120	−0.242060	+	0.970261i	$0.577823\pi$
$114$	19.4660	1.82316
$115$	24.6196	2.29579
$116$	−27.8123	−2.58231
$117$	−0.0451518	−0.00417428
$118$	−34.9995	−3.22197
$119$	3.26601	0.299394
$120$	−36.8386	−3.36289
$121$	−5.28701	−0.480637
$122$	27.1959	2.46220
$123$	9.65073	0.870177
$124$	47.5701	4.27192
$125$	28.2220	2.52425
$126$	−8.83386	−0.786983
$127$	−7.53189	−0.668347	−0.334174	−	0.942512i	$-0.608457\pi$
$127$	−7.53189	−0.668347	−0.334174	+	0.942512i	$0.608457\pi$
$128$	−26.8625	−2.37433
$129$	−2.56103	−0.225487
$130$	0.501624	0.0439953
$131$	−4.69947	−0.410594	−0.205297	−	0.978700i	$-0.565816\pi$
$131$	−4.69947	−0.410594	−0.205297	+	0.978700i	$0.565816\pi$
$132$	12.7060	1.10591
$133$	−23.5050	−2.03814
$134$	7.30596	0.631139
$135$	4.10743	0.353511
$136$	−8.96878	−0.769066
$137$	7.00580	0.598546	0.299273	−	0.954168i	$-0.403256\pi$
$137$	7.00580	0.598546	0.299273	+	0.954168i	$0.403256\pi$
$138$	−16.2123	−1.38008
$139$	−6.11216	−0.518427	−0.259213	−	0.965820i	$-0.583463\pi$
$139$	−6.11216	−0.518427	−0.259213	+	0.965820i	$0.583463\pi$
$140$	71.3120	6.02696
$141$	11.1792	0.941461
$142$	12.5806	1.05574
$143$	−0.107921	−0.00902482
$144$	13.6269	1.13557
$145$	−21.4898	−1.78463
$146$	11.0518	0.914650
$147$	3.66680	0.302432
$148$	13.8445	1.13801
$149$	−1.06095	−0.0869160	−0.0434580	−	0.999055i	$-0.513837\pi$
$149$	−1.06095	−0.0869160	−0.0434580	+	0.999055i	$0.513837\pi$
$150$	−32.1084	−2.62164
$151$	−5.86705	−0.477453	−0.238727	−	0.971087i	$-0.576730\pi$
$151$	−5.86705	−0.477453	−0.238727	+	0.971087i	$0.576730\pi$
$152$	64.5471	5.23546
$153$	1.00000	0.0808452
$154$	−21.1146	−1.70146
$155$	36.7560	2.95231
$156$	−0.240022	−0.0192171
$157$	1.00000	0.0798087
$157$	1.00000	0.0798087
$158$	−17.3255	−1.37835
$159$	−10.2143	−0.810046
$160$	−77.7138	−6.14381
$161$	19.5762	1.54282
$162$	−2.70479	−0.212508
$163$	10.0030	0.783492	0.391746	−	0.920073i	$-0.371871\pi$
$163$	10.0030	0.783492	0.391746	+	0.920073i	$0.371871\pi$
$164$	51.3022	4.00603
$165$	9.81751	0.764292
$166$	−6.34340	−0.492343
$167$	−6.77415	−0.524199	−0.262100	−	0.965041i	$-0.584415\pi$
$167$	−6.77415	−0.524199	−0.262100	+	0.965041i	$0.584415\pi$
$168$	−29.2921	−2.25993
$169$	−12.9980	−0.999843
$170$	−11.1097	−0.852077
$171$	−7.19687	−0.550358
$172$	−13.6142	−1.03807
$173$	−11.5732	−0.879893	−0.439947	−	0.898024i	$-0.645003\pi$
$173$	−11.5732	−0.879893	−0.439947	+	0.898024i	$0.645003\pi$
$174$	14.1513	1.07280
$175$	38.7706	2.93078
$176$	32.5708	2.45512
$177$	12.9398	0.972617
$178$	−2.47304	−0.185362
$179$	18.8021	1.40534	0.702669	−	0.711517i	$-0.251992\pi$
$179$	18.8021	1.40534	0.702669	+	0.711517i	$0.251992\pi$
$180$	21.8346	1.62746
$181$	−16.9748	−1.26172	−0.630862	−	0.775895i	$-0.717299\pi$
$181$	−16.9748	−1.26172	−0.630862	+	0.775895i	$0.717299\pi$
$182$	0.398864	0.0295658
$183$	−10.0547	−0.743265
$184$	−53.7582	−3.96311
$185$	10.6972	0.786475
$186$	−24.2043	−1.77474
$187$	2.39019	0.174788
$188$	59.4275	4.33420
$189$	3.26601	0.237567
$190$	79.9553	5.80056
$191$	19.0454	1.37808	0.689040	−	0.724723i	$-0.258032\pi$
$191$	19.0454	1.37808	0.689040	+	0.724723i	$0.258032\pi$
$192$	23.9217	1.72640
$193$	1.17280	0.0844197	0.0422099	−	0.999109i	$-0.486560\pi$
$193$	1.17280	0.0844197	0.0422099	+	0.999109i	$0.486560\pi$
$194$	−9.29061	−0.667027
$195$	−0.185458	−0.0132809
$196$	19.4923	1.39231
$197$	24.1467	1.72038	0.860189	−	0.509975i	$-0.170345\pi$
$197$	24.1467	1.72038	0.860189	+	0.509975i	$0.170345\pi$
$198$	−6.46495	−0.459444
$199$	−6.69545	−0.474628	−0.237314	−	0.971433i	$-0.576267\pi$
$199$	−6.69545	−0.474628	−0.237314	+	0.971433i	$0.576267\pi$
$200$	−106.468	−7.52842
$201$	−2.70112	−0.190522
$202$	5.25211	0.369537
$203$	−17.0875	−1.19931
$204$	5.31589	0.372187
$205$	39.6397	2.76855
$206$	44.6568	3.11139
$207$	5.99393	0.416607
$208$	−0.615278	−0.0426618
$209$	−17.2019	−1.18988
$210$	−36.2844	−2.50386
$211$	−11.8357	−0.814800	−0.407400	−	0.913250i	$-0.633565\pi$
$211$	−11.8357	−0.814800	−0.407400	+	0.913250i	$0.633565\pi$
$212$	−54.2980	−3.72920
$213$	−4.65122	−0.318696
$214$	45.1592	3.08702
$215$	−10.5193	−0.717408
$216$	−8.96878	−0.610248
$217$	29.2264	1.98402
$218$	16.7302	1.13311
$219$	−4.08599	−0.276106
$220$	52.1888	3.51857
$221$	−0.0451518	−0.00303724
$222$	−7.04424	−0.472779
$223$	−16.8323	−1.12718	−0.563588	−	0.826056i	$-0.690579\pi$
$223$	−16.8323	−1.12718	−0.563588	+	0.826056i	$0.690579\pi$
$224$	−61.7938	−4.12877
$225$	11.8710	0.791397
$226$	13.9196	0.925916
$227$	26.5338	1.76111	0.880554	−	0.473946i	$-0.157171\pi$
$227$	26.5338	1.76111	0.880554	+	0.473946i	$0.157171\pi$
$228$	−38.2578	−2.53368
$229$	−6.29588	−0.416043	−0.208022	−	0.978124i	$-0.566702\pi$
$229$	−6.29588	−0.416043	−0.208022	+	0.978124i	$0.566702\pi$
$230$	−66.5909	−4.39087
$231$	7.80636	0.513621
$232$	46.9240	3.08071
$233$	−27.2945	−1.78812	−0.894060	−	0.447947i	$-0.852155\pi$
$233$	−27.2945	−1.78812	−0.894060	+	0.447947i	$0.852155\pi$
$234$	0.122126	0.00798363
$235$	45.9179	2.99535
$236$	68.7867	4.47763
$237$	6.40550	0.416082
$238$	−8.83386	−0.572614
$239$	−8.50267	−0.549992	−0.274996	−	0.961445i	$-0.588677\pi$
$239$	−8.50267	−0.549992	−0.274996	+	0.961445i	$0.588677\pi$
$240$	55.9714	3.61294
$241$	29.9801	1.93119	0.965593	−	0.260059i	$-0.0837421\pi$
$241$	29.9801	1.93119	0.965593	+	0.260059i	$0.0837421\pi$
$242$	14.3003	0.919255
$243$	1.00000	0.0641500
$244$	−53.4497	−3.42176
$245$	15.0611	0.962218
$246$	−26.1032	−1.66428
$247$	0.324951	0.0206762
$248$	−80.2586	−5.09643
$249$	2.34525	0.148624
$250$	−76.3344	−4.82781
$251$	2.40989	0.152111	0.0760555	−	0.997104i	$-0.475767\pi$
$251$	2.40989	0.152111	0.0760555	+	0.997104i	$0.475767\pi$
$252$	17.3617	1.09369
$253$	14.3266	0.900706
$254$	20.3722	1.27826
$255$	4.10743	0.257217
$256$	24.8141	1.55088
$257$	5.25168	0.327591	0.163795	−	0.986494i	$-0.447626\pi$
$257$	5.25168	0.327591	0.163795	+	0.986494i	$0.447626\pi$
$258$	6.92706	0.431260
$259$	8.50585	0.528528
$260$	−0.985872	−0.0611412
$261$	−5.23193	−0.323848
$262$	12.7111	0.785293
$263$	25.0049	1.54187	0.770933	−	0.636917i	$-0.219790\pi$
$263$	25.0049	1.54187	0.770933	+	0.636917i	$0.219790\pi$
$264$	−21.4370	−1.31936
$265$	−41.9544	−2.57724
$266$	63.5761	3.89810
$267$	0.914319	0.0559554
$268$	−14.3588	−0.877106
$269$	−20.9028	−1.27446	−0.637232	−	0.770672i	$-0.719921\pi$
$269$	−20.9028	−1.27446	−0.637232	+	0.770672i	$0.719921\pi$
$270$	−11.1097	−0.676116
$271$	24.8412	1.50900	0.754499	−	0.656301i	$-0.227880\pi$
$271$	24.8412	1.50900	0.754499	+	0.656301i	$0.227880\pi$
$272$	13.6269	0.826251
$273$	−0.147466	−0.00892504
$274$	−18.9492	−1.14476
$275$	28.3738	1.71100
$276$	31.8630	1.91793
$277$	−8.51555	−0.511650	−0.255825	−	0.966723i	$-0.582347\pi$
$277$	−8.51555	−0.511650	−0.255825	+	0.966723i	$0.582347\pi$
$278$	16.5321	0.991530
$279$	8.94867	0.535743
$280$	−120.315	−7.19020
$281$	2.57756	0.153765	0.0768823	−	0.997040i	$-0.475503\pi$
$281$	2.57756	0.153765	0.0768823	+	0.997040i	$0.475503\pi$
$282$	−30.2375	−1.80061
$283$	−26.4449	−1.57199	−0.785993	−	0.618236i	$-0.787848\pi$
$283$	−26.4449	−1.57199	−0.785993	+	0.618236i	$0.787848\pi$
$284$	−24.7253	−1.46718
$285$	−29.5606	−1.75102
$286$	0.291904	0.0172606
$287$	31.5193	1.86053
$288$	−18.9203	−1.11489
$289$	1.00000	0.0588235
$290$	58.1253	3.41324
$291$	3.43487	0.201356
$292$	−21.7207	−1.27111
$293$	27.8140	1.62491	0.812456	−	0.583022i	$-0.198130\pi$
$293$	27.8140	1.62491	0.812456	+	0.583022i	$0.198130\pi$
$294$	−9.91791	−0.578425
$295$	53.1494	3.09448
$296$	−23.3579	−1.35765
$297$	2.39019	0.138693
$298$	2.86963	0.166233
$299$	−0.270636	−0.0156513
$300$	63.1047	3.64335
$301$	−8.36436	−0.482113
$302$	15.8691	0.913165
$303$	−1.94178	−0.111553
$304$	−98.0709	−5.62475
$305$	−41.2990	−2.36477
$306$	−2.70479	−0.154623
$307$	23.9519	1.36701	0.683504	−	0.729947i	$-0.260455\pi$
$307$	23.9519	1.36701	0.683504	+	0.729947i	$0.260455\pi$
$308$	41.4977	2.36455
$309$	−16.5103	−0.939237
$310$	−99.4172	−5.64652
$311$	−13.7463	−0.779479	−0.389739	−	0.920925i	$-0.627435\pi$
$311$	−13.7463	−0.779479	−0.389739	+	0.920925i	$0.627435\pi$
$312$	0.404956	0.0229261
$313$	12.4962	0.706329	0.353164	−	0.935561i	$-0.385106\pi$
$313$	12.4962	0.706329	0.353164	+	0.935561i	$0.385106\pi$
$314$	−2.70479	−0.152640
$315$	13.4149	0.755843
$316$	34.0509	1.91551
$317$	−19.9918	−1.12285	−0.561427	−	0.827527i	$-0.689747\pi$
$317$	−19.9918	−1.12285	−0.561427	+	0.827527i	$0.689747\pi$
$318$	27.6275	1.54927
$319$	−12.5053	−0.700161
$320$	98.2565	5.49271
$321$	−16.6960	−0.931880
$322$	−52.9495	−2.95076
$323$	−7.19687	−0.400445
$324$	5.31589	0.295327
$325$	−0.535995	−0.0297316
$326$	−27.0559	−1.49849
$327$	−6.18540	−0.342054
$328$	−86.5553	−4.77921
$329$	36.5114	2.01294
$330$	−26.5543	−1.46177
$331$	−27.9219	−1.53473	−0.767363	−	0.641213i	$-0.778432\pi$
$331$	−27.9219	−1.53473	−0.767363	+	0.641213i	$0.778432\pi$
$332$	12.4671	0.684219
$333$	2.60436	0.142718
$334$	18.3226	1.00257
$335$	−11.0947	−0.606165
$336$	44.5055	2.42797
$337$	10.5092	0.572472	0.286236	−	0.958159i	$-0.407596\pi$
$337$	10.5092	0.572472	0.286236	+	0.958159i	$0.407596\pi$
$338$	35.1568	1.91228
$339$	−5.14626	−0.279507
$340$	21.8346	1.18415
$341$	21.3890	1.15828
$342$	19.4660	1.05260
$343$	−10.8863	−0.587803
$344$	22.9694	1.23842
$345$	24.6196	1.32548
$346$	31.3030	1.68286
$347$	17.1823	0.922393	0.461197	−	0.887298i	$-0.347420\pi$
$347$	17.1823	0.922393	0.461197	+	0.887298i	$0.347420\pi$
$348$	−27.8123	−1.49090
$349$	27.7430	1.48505	0.742525	−	0.669818i	$-0.233628\pi$
$349$	27.7430	1.48505	0.742525	+	0.669818i	$0.233628\pi$
$350$	−104.866	−5.60534
$351$	−0.0451518	−0.00241002
$352$	−45.2230	−2.41040
$353$	−21.8607	−1.16353	−0.581763	−	0.813358i	$-0.697637\pi$
$353$	−21.8607	−1.16353	−0.581763	+	0.813358i	$0.697637\pi$
$354$	−34.9995	−1.86020
$355$	−19.1045	−1.01396
$356$	4.86042	0.257602
$357$	3.26601	0.172855
$358$	−50.8558	−2.68781
$359$	−17.7184	−0.935142	−0.467571	−	0.883956i	$-0.654871\pi$
$359$	−17.7184	−0.935142	−0.467571	+	0.883956i	$0.654871\pi$
$360$	−36.8386	−1.94157
$361$	32.7949	1.72605
$362$	45.9131	2.41314
$363$	−5.28701	−0.277496
$364$	−0.783912	−0.0410882
$365$	−16.7829	−0.878458
$366$	27.1959	1.42155
$367$	−17.1086	−0.893060	−0.446530	−	0.894769i	$-0.647340\pi$
$367$	−17.1086	−0.893060	−0.446530	+	0.894769i	$0.647340\pi$
$368$	81.6786	4.25779
$369$	9.65073	0.502397
$370$	−28.9337	−1.50419
$371$	−33.3599	−1.73196
$372$	47.5701	2.46640
$373$	7.74630	0.401088	0.200544	−	0.979685i	$-0.435729\pi$
$373$	7.74630	0.401088	0.200544	+	0.979685i	$0.435729\pi$
$374$	−6.46495	−0.334295
$375$	28.2220	1.45738
$376$	−100.264	−5.17072
$377$	0.236231	0.0121665
$378$	−8.83386	−0.454365
$379$	−28.5453	−1.46627	−0.733137	−	0.680081i	$-0.761944\pi$
$379$	−28.5453	−1.46627	−0.733137	+	0.680081i	$0.761944\pi$
$380$	−157.141	−8.06116
$381$	−7.53189	−0.385870
$382$	−51.5139	−2.63568
$383$	−24.7203	−1.26315	−0.631575	−	0.775315i	$-0.717591\pi$
$383$	−24.7203	−1.26315	−0.631575	+	0.775315i	$0.717591\pi$
$384$	−26.8625	−1.37082
$385$	32.0641	1.63414
$386$	−3.17217	−0.161459
$387$	−2.56103	−0.130185
$388$	18.2594	0.926981
$389$	−8.27196	−0.419405	−0.209703	−	0.977765i	$-0.567250\pi$
$389$	−8.27196	−0.419405	−0.209703	+	0.977765i	$0.567250\pi$
$390$	0.501624	0.0254007
$391$	5.99393	0.303126
$392$	−32.8867	−1.66103
$393$	−4.69947	−0.237057
$394$	−65.3116	−3.29035
$395$	26.3101	1.32381
$396$	12.7060	0.638498
$397$	−19.4806	−0.977703	−0.488851	−	0.872367i	$-0.662584\pi$
$397$	−19.4806	−0.977703	−0.488851	+	0.872367i	$0.662584\pi$
$398$	18.1098	0.907761
$399$	−23.5050	−1.17672
$400$	161.764	8.08821
$401$	−26.4504	−1.32087	−0.660434	−	0.750884i	$-0.729628\pi$
$401$	−26.4504	−1.32087	−0.660434	+	0.750884i	$0.729628\pi$
$402$	7.30596	0.364388
$403$	−0.404048	−0.0201271
$404$	−10.3223	−0.513554
$405$	4.10743	0.204100
$406$	46.2181	2.29377
$407$	6.22490	0.308557
$408$	−8.96878	−0.444021
$409$	21.0630	1.04150	0.520749	−	0.853710i	$-0.325653\pi$
$409$	21.0630	1.04150	0.520749	+	0.853710i	$0.325653\pi$
$410$	−107.217	−5.29507
$411$	7.00580	0.345571
$412$	−87.7668	−4.32396
$413$	42.2616	2.07956
$414$	−16.2123	−0.796792
$415$	9.63293	0.472862
$416$	0.854285	0.0418848
$417$	−6.11216	−0.299314
$418$	46.5274	2.27573
$419$	3.06846	0.149904	0.0749520	−	0.997187i	$-0.476120\pi$
$419$	3.06846	0.149904	0.0749520	+	0.997187i	$0.476120\pi$
$420$	71.3120	3.47967
$421$	−14.4700	−0.705225	−0.352612	−	0.935770i	$-0.614707\pi$
$421$	−14.4700	−0.705225	−0.352612	+	0.935770i	$0.614707\pi$
$422$	32.0130	1.55837
$423$	11.1792	0.543553
$424$	91.6097	4.44896
$425$	11.8710	0.575826
$426$	12.5806	0.609530
$427$	−32.8387	−1.58918
$428$	−88.7541	−4.29009
$429$	−0.107921	−0.00521048
$430$	28.4524	1.37210
$431$	−3.82214	−0.184106	−0.0920529	−	0.995754i	$-0.529343\pi$
$431$	−3.82214	−0.184106	−0.0920529	+	0.995754i	$0.529343\pi$
$432$	13.6269	0.655624
$433$	5.35097	0.257151	0.128576	−	0.991700i	$-0.458960\pi$
$433$	5.35097	0.257151	0.128576	+	0.991700i	$0.458960\pi$
$434$	−79.0513	−3.79458
$435$	−21.4898	−1.03036
$436$	−32.8809	−1.57471
$437$	−43.1375	−2.06355
$438$	11.0518	0.528073
$439$	−1.59733	−0.0762366	−0.0381183	−	0.999273i	$-0.512136\pi$
$439$	−1.59733	−0.0762366	−0.0381183	+	0.999273i	$0.512136\pi$
$440$	−88.0511	−4.19767
$441$	3.66680	0.174609
$442$	0.122126	0.00580894
$443$	−1.92161	−0.0912985	−0.0456492	−	0.998958i	$-0.514536\pi$
$443$	−1.92161	−0.0912985	−0.0456492	+	0.998958i	$0.514536\pi$
$444$	13.8445	0.657030
$445$	3.75550	0.178028
$446$	45.5279	2.15581
$447$	−1.06095	−0.0501810
$448$	78.1284	3.69122
$449$	16.2491	0.766843	0.383421	−	0.923574i	$-0.374746\pi$
$449$	16.2491	0.766843	0.383421	+	0.923574i	$0.374746\pi$
$450$	−32.1084	−1.51361
$451$	23.0670	1.08618
$452$	−27.3570	−1.28676
$453$	−5.86705	−0.275658
$454$	−71.7682	−3.36825
$455$	−0.605706	−0.0283959
$456$	64.5471	3.02270
$457$	5.95528	0.278576	0.139288	−	0.990252i	$-0.455519\pi$
$457$	5.95528	0.278576	0.139288	+	0.990252i	$0.455519\pi$
$458$	17.0290	0.795714
$459$	1.00000	0.0466760
$460$	130.875	6.10208
$461$	5.60306	0.260960	0.130480	−	0.991451i	$-0.458348\pi$
$461$	5.60306	0.260960	0.130480	+	0.991451i	$0.458348\pi$
$462$	−21.1146	−0.982339
$463$	−20.0805	−0.933219	−0.466610	−	0.884463i	$-0.654525\pi$
$463$	−20.0805	−0.933219	−0.466610	+	0.884463i	$0.654525\pi$
$464$	−71.2949	−3.30978
$465$	36.7560	1.70452
$466$	73.8258	3.41992
$467$	−8.87296	−0.410591	−0.205296	−	0.978700i	$-0.565816\pi$
$467$	−8.87296	−0.410591	−0.205296	+	0.978700i	$0.565816\pi$
$468$	−0.240022	−0.0110950
$469$	−8.82187	−0.407356
$470$	−124.198	−5.72883
$471$	1.00000	0.0460776
$472$	−116.054	−5.34184
$473$	−6.12135	−0.281460
$474$	−17.3255	−0.795788
$475$	−85.4337	−3.91997
$476$	17.3617	0.795773
$477$	−10.2143	−0.467680
$478$	22.9979	1.05190
$479$	−38.7268	−1.76947	−0.884735	−	0.466094i	$-0.845661\pi$
$479$	−38.7268	−1.76947	−0.884735	+	0.466094i	$0.845661\pi$
$480$	−77.7138	−3.54713
$481$	−0.117591	−0.00536171
$482$	−81.0898	−3.69354
$483$	19.5762	0.890748
$484$	−28.1052	−1.27751
$485$	14.1085	0.640634
$486$	−2.70479	−0.122692
$487$	−3.43610	−0.155705	−0.0778524	−	0.996965i	$-0.524806\pi$
$487$	−3.43610	−0.155705	−0.0778524	+	0.996965i	$0.524806\pi$
$488$	90.1784	4.08218
$489$	10.0030	0.452349
$490$	−40.7371	−1.84032
$491$	−6.85807	−0.309501	−0.154750	−	0.987954i	$-0.549457\pi$
$491$	−6.85807	−0.309501	−0.154750	+	0.987954i	$0.549457\pi$
$492$	51.3022	2.31288
$493$	−5.23193	−0.235634
$494$	−0.878925	−0.0395447
$495$	9.81751	0.441264
$496$	121.942	5.47538
$497$	−15.1909	−0.681405
$498$	−6.34340	−0.284254
$499$	−11.5293	−0.516122	−0.258061	−	0.966129i	$-0.583084\pi$
$499$	−11.5293	−0.516122	−0.258061	+	0.966129i	$0.583084\pi$
$500$	150.025	6.70931
$501$	−6.77415	−0.302647
$502$	−6.51825	−0.290924
$503$	34.6633	1.54556	0.772779	−	0.634675i	$-0.218866\pi$
$503$	34.6633	1.54556	0.772779	+	0.634675i	$0.218866\pi$
$504$	−29.2921	−1.30477
$505$	−7.97573	−0.354915
$506$	−38.7504	−1.72267
$507$	−12.9980	−0.577260
$508$	−40.0387	−1.77643
$509$	29.5396	1.30932	0.654659	−	0.755924i	$-0.272812\pi$
$509$	29.5396	1.30932	0.654659	+	0.755924i	$0.272812\pi$
$510$	−11.1097	−0.491947
$511$	−13.3449	−0.590343
$512$	−13.3918	−0.591839
$513$	−7.19687	−0.317750
$514$	−14.2047	−0.626542
$515$	−67.8148	−2.98828
$516$	−13.6142	−0.599331
$517$	26.7204	1.17516
$518$	−23.0065	−1.01085
$519$	−11.5732	−0.508007
$520$	1.66333	0.0729418
$521$	−28.2716	−1.23860	−0.619301	−	0.785153i	$-0.712584\pi$
$521$	−28.2716	−1.23860	−0.619301	+	0.785153i	$0.712584\pi$
$522$	14.1513	0.619384
$523$	−19.1246	−0.836260	−0.418130	−	0.908387i	$-0.637314\pi$
$523$	−19.1246	−0.836260	−0.418130	+	0.908387i	$0.637314\pi$
$524$	−24.9818	−1.09134
$525$	38.7706	1.69209
$526$	−67.6329	−2.94893
$527$	8.94867	0.389810
$528$	32.5708	1.41746
$529$	12.9272	0.562050
$530$	113.478	4.92917
$531$	12.9398	0.561541
$532$	−124.950	−5.41727
$533$	−0.435747	−0.0188743
$534$	−2.47304	−0.107019
$535$	−68.5776	−2.96487
$536$	24.2257	1.04639
$537$	18.8021	0.811372
$538$	56.5376	2.43751
$539$	8.76433	0.377506
$540$	21.8346	0.939612
$541$	−11.7347	−0.504516	−0.252258	−	0.967660i	$-0.581173\pi$
$541$	−11.7347	−0.504516	−0.252258	+	0.967660i	$0.581173\pi$
$542$	−67.1903	−2.88607
$543$	−16.9748	−0.728457
$544$	−18.9203	−0.811201
$545$	−25.4061	−1.08828
$546$	0.398864	0.0170698
$547$	21.0039	0.898063	0.449032	−	0.893516i	$-0.351769\pi$
$547$	21.0039	0.898063	0.449032	+	0.893516i	$0.351769\pi$
$548$	37.2420	1.59090
$549$	−10.0547	−0.429124
$550$	−76.7451	−3.27242
$551$	37.6535	1.60409
$552$	−53.7582	−2.28810
$553$	20.9204	0.889626
$554$	23.0328	0.978569
$555$	10.6972	0.454071
$556$	−32.4916	−1.37795
$557$	21.8774	0.926976	0.463488	−	0.886103i	$-0.346598\pi$
$557$	21.8774	0.926976	0.463488	+	0.886103i	$0.346598\pi$
$558$	−24.2043	−1.02465
$559$	0.115635	0.00489085
$560$	182.803	7.72484
$561$	2.39019	0.100914
$562$	−6.97177	−0.294086
$563$	−7.72854	−0.325719	−0.162860	−	0.986649i	$-0.552072\pi$
$563$	−7.72854	−0.325719	−0.162860	+	0.986649i	$0.552072\pi$
$564$	59.4275	2.50235
$565$	−21.1379	−0.889278
$566$	71.5279	3.00654
$567$	3.26601	0.137159
$568$	41.7157	1.75035
$569$	12.0772	0.506304	0.253152	−	0.967427i	$-0.418533\pi$
$569$	12.0772	0.506304	0.253152	+	0.967427i	$0.418533\pi$
$570$	79.9553	3.34896
$571$	−22.0839	−0.924183	−0.462092	−	0.886832i	$-0.652901\pi$
$571$	−22.0839	−0.924183	−0.462092	+	0.886832i	$0.652901\pi$
$572$	−0.573696	−0.0239875
$573$	19.0454	0.795635
$574$	−85.2532	−3.55840
$575$	71.1536	2.96731
$576$	23.9217	0.996737
$577$	27.9197	1.16231	0.581157	−	0.813791i	$-0.302600\pi$
$577$	27.9197	1.16231	0.581157	+	0.813791i	$0.302600\pi$
$578$	−2.70479	−0.112504
$579$	1.17280	0.0487397
$580$	−114.237	−4.74344
$581$	7.65959	0.317773
$582$	−9.29061	−0.385108
$583$	−24.4140	−1.01113
$584$	36.6464	1.51644
$585$	−0.185458	−0.00766773
$586$	−75.2311	−3.10777
$587$	33.9439	1.40101	0.700507	−	0.713645i	$-0.252957\pi$
$587$	33.9439	1.40101	0.700507	+	0.713645i	$0.252957\pi$
$588$	19.4923	0.803848
$589$	−64.4024	−2.65365
$590$	−143.758	−5.91842
$591$	24.1467	0.993261
$592$	35.4893	1.45860
$593$	−9.64117	−0.395915	−0.197958	−	0.980211i	$-0.563431\pi$
$593$	−9.64117	−0.395915	−0.197958	+	0.980211i	$0.563431\pi$
$594$	−6.46495	−0.265260
$595$	13.4149	0.549957
$596$	−5.63987	−0.231018
$597$	−6.69545	−0.274026
$598$	0.732014	0.0299343
$599$	32.0357	1.30894	0.654472	−	0.756086i	$-0.272891\pi$
$599$	32.0357	1.30894	0.654472	+	0.756086i	$0.272891\pi$
$600$	−106.468	−4.34654
$601$	22.7983	0.929963	0.464981	−	0.885320i	$-0.346061\pi$
$601$	22.7983	0.929963	0.464981	+	0.885320i	$0.346061\pi$
$602$	22.6238	0.922078
$603$	−2.70112	−0.109998
$604$	−31.1886	−1.26904
$605$	−21.7160	−0.882882
$606$	5.25211	0.213353
$607$	27.6170	1.12094	0.560470	−	0.828175i	$-0.310621\pi$
$607$	27.6170	1.12094	0.560470	+	0.828175i	$0.310621\pi$
$608$	136.167	5.52230
$609$	−17.0875	−0.692421
$610$	111.705	4.52280
$611$	−0.504762	−0.0204205
$612$	5.31589	0.214882
$613$	−31.0444	−1.25387	−0.626935	−	0.779071i	$-0.715691\pi$
$613$	−31.0444	−1.25387	−0.626935	+	0.779071i	$0.715691\pi$
$614$	−64.7849	−2.61450
$615$	39.6397	1.59843
$616$	−70.0135	−2.82093
$617$	39.1252	1.57512	0.787560	−	0.616238i	$-0.211344\pi$
$617$	39.1252	1.57512	0.787560	+	0.616238i	$0.211344\pi$
$618$	44.6568	1.79636
$619$	−3.27025	−0.131442	−0.0657211	−	0.997838i	$-0.520935\pi$
$619$	−3.27025	−0.131442	−0.0657211	+	0.997838i	$0.520935\pi$
$620$	195.391	7.84708
$621$	5.99393	0.240528
$622$	37.1807	1.49081
$623$	2.98617	0.119638
$624$	−0.615278	−0.0246308
$625$	56.5648	2.26259
$626$	−33.7997	−1.35091
$627$	−17.2019	−0.686976
$628$	5.31589	0.212127
$629$	2.60436	0.103843
$630$	−36.2844	−1.44561
$631$	−25.4032	−1.01129	−0.505643	−	0.862743i	$-0.668745\pi$
$631$	−25.4032	−1.01129	−0.505643	+	0.862743i	$0.668745\pi$
$632$	−57.4495	−2.28522
$633$	−11.8357	−0.470425
$634$	54.0737	2.14754
$635$	−30.9367	−1.22769
$636$	−54.2980	−2.15306
$637$	−0.165562	−0.00655982
$638$	33.8242	1.33911
$639$	−4.65122	−0.183999
$640$	−110.336	−4.36140
$641$	15.4227	0.609161	0.304581	−	0.952487i	$-0.401484\pi$
$641$	15.4227	0.609161	0.304581	+	0.952487i	$0.401484\pi$
$642$	45.1592	1.78229
$643$	35.5453	1.40177	0.700885	−	0.713274i	$-0.252789\pi$
$643$	35.5453	1.40177	0.700885	+	0.713274i	$0.252789\pi$
$644$	104.065	4.10073
$645$	−10.5193	−0.414196
$646$	19.4660	0.765880
$647$	38.4687	1.51236	0.756181	−	0.654363i	$-0.227063\pi$
$647$	38.4687	1.51236	0.756181	+	0.654363i	$0.227063\pi$
$648$	−8.96878	−0.352327
$649$	30.9286	1.21405
$650$	1.44975	0.0568640
$651$	29.2264	1.14547
$652$	53.1746	2.08248
$653$	−19.9590	−0.781057	−0.390529	−	0.920591i	$-0.627708\pi$
$653$	−19.9590	−0.781057	−0.390529	+	0.920591i	$0.627708\pi$
$654$	16.7302	0.654203
$655$	−19.3027	−0.754220
$656$	131.509	5.13458
$657$	−4.08599	−0.159410
$658$	−98.7557	−3.84990
$659$	−17.1028	−0.666232	−0.333116	−	0.942886i	$-0.608100\pi$
$659$	−17.1028	−0.666232	−0.333116	+	0.942886i	$0.608100\pi$
$660$	52.1888	2.03145
$661$	−30.5703	−1.18905	−0.594524	−	0.804078i	$-0.702659\pi$
$661$	−30.5703	−1.18905	−0.594524	+	0.804078i	$0.702659\pi$
$662$	75.5229	2.93528
$663$	−0.0451518	−0.00175355
$664$	−21.0340	−0.816277
$665$	−96.5452	−3.74386
$666$	−7.04424	−0.272959
$667$	−31.3598	−1.21426
$668$	−36.0106	−1.39329
$669$	−16.8323	−0.650775
$670$	30.0087	1.15934
$671$	−24.0326	−0.927768
$672$	−61.7938	−2.38375
$673$	39.8486	1.53605	0.768026	−	0.640419i	$-0.221239\pi$
$673$	39.8486	1.53605	0.768026	+	0.640419i	$0.221239\pi$
$674$	−28.4252	−1.09490
$675$	11.8710	0.456913
$676$	−69.0957	−2.65753
$677$	28.4235	1.09241	0.546203	−	0.837653i	$-0.316073\pi$
$677$	28.4235	1.09241	0.546203	+	0.837653i	$0.316073\pi$
$678$	13.9196	0.534578
$679$	11.2183	0.430520
$680$	−36.8386	−1.41270
$681$	26.5338	1.01678
$682$	−57.8527	−2.21529
$683$	−13.4436	−0.514405	−0.257202	−	0.966358i	$-0.582801\pi$
$683$	−13.4436	−0.514405	−0.257202	+	0.966358i	$0.582801\pi$
$684$	−38.2578	−1.46282
$685$	28.7758	1.09947
$686$	29.4451	1.12422
$687$	−6.29588	−0.240203
$688$	−34.8989	−1.33051
$689$	0.461193	0.0175701
$690$	−66.5909	−2.53507
$691$	1.98155	0.0753816	0.0376908	−	0.999289i	$-0.488000\pi$
$691$	1.98155	0.0753816	0.0376908	+	0.999289i	$0.488000\pi$
$692$	−61.5218	−2.33871
$693$	7.80636	0.296539
$694$	−46.4745	−1.76415
$695$	−25.1053	−0.952297
$696$	46.9240	1.77865
$697$	9.65073	0.365547
$698$	−75.0391	−2.84027
$699$	−27.2945	−1.03237
$700$	206.100	7.78986
$701$	2.94724	0.111316	0.0556578	−	0.998450i	$-0.482274\pi$
$701$	2.94724	0.111316	0.0556578	+	0.998450i	$0.482274\pi$
$702$	0.122126	0.00460935
$703$	−18.7432	−0.706914
$704$	57.1773	2.15495
$705$	45.9179	1.72937
$706$	59.1285	2.22533
$707$	−6.34187	−0.238511
$708$	68.7867	2.58516
$709$	33.7349	1.26694	0.633470	−	0.773767i	$-0.281630\pi$
$709$	33.7349	1.26694	0.633470	+	0.773767i	$0.281630\pi$
$710$	51.6737	1.93928
$711$	6.40550	0.240225
$712$	−8.20032	−0.307320
$713$	53.6376	2.00875
$714$	−8.83386	−0.330599
$715$	−0.443278	−0.0165777
$716$	99.9500	3.73531
$717$	−8.50267	−0.317538
$718$	47.9246	1.78853
$719$	10.9339	0.407764	0.203882	−	0.978995i	$-0.434644\pi$
$719$	10.9339	0.407764	0.203882	+	0.978995i	$0.434644\pi$
$720$	55.9714	2.08593
$721$	−53.9227	−2.00819
$722$	−88.7034	−3.30120
$723$	29.9801	1.11497
$724$	−90.2359	−3.35359
$725$	−62.1080	−2.30663
$726$	14.3003	0.530732
$727$	14.7686	0.547737	0.273869	−	0.961767i	$-0.411697\pi$
$727$	14.7686	0.547737	0.273869	+	0.961767i	$0.411697\pi$
$728$	1.32259	0.0490184
$729$	1.00000	0.0370370
$730$	45.3943	1.68012
$731$	−2.56103	−0.0947233
$732$	−53.4497	−1.97556
$733$	35.4884	1.31079	0.655397	−	0.755284i	$-0.272501\pi$
$733$	35.4884	1.31079	0.655397	+	0.755284i	$0.272501\pi$
$734$	46.2751	1.70804
$735$	15.0611	0.555537
$736$	−113.407	−4.18024
$737$	−6.45618	−0.237816
$738$	−26.1032	−0.960872
$739$	26.8090	0.986186	0.493093	−	0.869977i	$-0.335866\pi$
$739$	26.8090	0.986186	0.493093	+	0.869977i	$0.335866\pi$
$740$	56.8652	2.09041
$741$	0.324951	0.0119374
$742$	90.2316	3.31251
$743$	35.1118	1.28813	0.644063	−	0.764973i	$-0.277248\pi$
$743$	35.1118	1.28813	0.644063	+	0.764973i	$0.277248\pi$
$744$	−80.2586	−2.94242
$745$	−4.35775	−0.159656
$746$	−20.9521	−0.767111
$747$	2.34525	0.0858081
$748$	12.7060	0.464576
$749$	−54.5293	−1.99246
$750$	−76.3344	−2.78734
$751$	−8.56723	−0.312623	−0.156311	−	0.987708i	$-0.549960\pi$
$751$	−8.56723	−0.312623	−0.156311	+	0.987708i	$0.549960\pi$
$752$	152.338	5.55520
$753$	2.40989	0.0878213
$754$	−0.638955	−0.0232694
$755$	−24.0985	−0.877033
$756$	17.3617	0.631440
$757$	14.8205	0.538660	0.269330	−	0.963048i	$-0.413198\pi$
$757$	14.8205	0.538660	0.269330	+	0.963048i	$0.413198\pi$
$758$	77.2090	2.80436
$759$	14.3266	0.520023
$760$	265.123	9.61701
$761$	−48.5603	−1.76031	−0.880154	−	0.474688i	$-0.842561\pi$
$761$	−48.5603	−1.76031	−0.880154	+	0.474688i	$0.842561\pi$
$762$	20.3722	0.738006
$763$	−20.2016	−0.731346
$764$	101.243	3.66286
$765$	4.10743	0.148504
$766$	66.8633	2.41587
$767$	−0.584256	−0.0210963
$768$	24.8141	0.895400
$769$	9.76416	0.352105	0.176052	−	0.984381i	$-0.443667\pi$
$769$	9.76416	0.352105	0.176052	+	0.984381i	$0.443667\pi$
$770$	−86.7265	−3.12541
$771$	5.25168	0.189135
$772$	6.23445	0.224383
$773$	19.5940	0.704746	0.352373	−	0.935860i	$-0.385375\pi$
$773$	19.5940	0.704746	0.352373	+	0.935860i	$0.385375\pi$
$774$	6.92706	0.248988
$775$	106.229	3.81587
$776$	−30.8066	−1.10589
$777$	8.50585	0.305146
$778$	22.3739	0.802144
$779$	−69.4550	−2.48849
$780$	−0.985872	−0.0352999
$781$	−11.1173	−0.397807
$782$	−16.2123	−0.579751
$783$	−5.23193	−0.186974
$784$	49.9670	1.78454
$785$	4.10743	0.146600
$786$	12.7111	0.453389
$787$	−39.7808	−1.41803	−0.709016	−	0.705193i	$-0.750861\pi$
$787$	−39.7808	−1.41803	−0.709016	+	0.705193i	$0.750861\pi$
$788$	128.361	4.57267
$789$	25.0049	0.890196
$790$	−71.1634	−2.53188
$791$	−16.8077	−0.597614
$792$	−21.4370	−0.761732
$793$	0.453987	0.0161216
$794$	52.6909	1.86993
$795$	−41.9544	−1.48797
$796$	−35.5923	−1.26153
$797$	−54.6933	−1.93734	−0.968668	−	0.248359i	$-0.920109\pi$
$797$	−54.6933	−1.93734	−0.968668	+	0.248359i	$0.920109\pi$
$798$	63.5761	2.25057
$799$	11.1792	0.395493
$800$	−224.602	−7.94088
$801$	0.914319	0.0323059
$802$	71.5427	2.52626
$803$	−9.76629	−0.344645
$804$	−14.3588	−0.506397
$805$	80.4078	2.83400
$806$	1.09286	0.0384945
$807$	−20.9028	−0.735813
$808$	17.4154	0.612672
$809$	4.50986	0.158558	0.0792791	−	0.996852i	$-0.474738\pi$
$809$	4.50986	0.158558	0.0792791	+	0.996852i	$0.474738\pi$
$810$	−11.1097	−0.390356
$811$	−40.1171	−1.40870	−0.704351	−	0.709852i	$-0.748762\pi$
$811$	−40.1171	−1.40870	−0.704351	+	0.709852i	$0.748762\pi$
$812$	−90.8353	−3.18769
$813$	24.8412	0.871220
$814$	−16.8371	−0.590138
$815$	41.0864	1.43919
$816$	13.6269	0.477036
$817$	18.4314	0.644834
$818$	−56.9710	−1.99194
$819$	−0.147466	−0.00515288
$820$	210.720	7.35866
$821$	−4.27573	−0.149224	−0.0746120	−	0.997213i	$-0.523772\pi$
$821$	−4.27573	−0.149224	−0.0746120	+	0.997213i	$0.523772\pi$
$822$	−18.9492	−0.660930
$823$	−15.4427	−0.538298	−0.269149	−	0.963098i	$-0.586742\pi$
$823$	−15.4427	−0.538298	−0.269149	+	0.963098i	$0.586742\pi$
$824$	148.077	5.15851
$825$	28.3738	0.987849
$826$	−114.309	−3.97731
$827$	−17.4456	−0.606642	−0.303321	−	0.952888i	$-0.598096\pi$
$827$	−17.4456	−0.606642	−0.303321	+	0.952888i	$0.598096\pi$
$828$	31.8630	1.10732
$829$	16.7459	0.581608	0.290804	−	0.956783i	$-0.406077\pi$
$829$	16.7459	0.581608	0.290804	+	0.956783i	$0.406077\pi$
$830$	−26.0550	−0.904384
$831$	−8.51555	−0.295401
$832$	−1.08011	−0.0374459
$833$	3.66680	0.127047
$834$	16.5321	0.572460
$835$	−27.8243	−0.962900
$836$	−91.4431	−3.16263
$837$	8.94867	0.309311
$838$	−8.29954	−0.286703
$839$	−44.9423	−1.55158	−0.775790	−	0.630991i	$-0.782649\pi$
$839$	−44.9423	−1.55158	−0.775790	+	0.630991i	$0.782649\pi$
$840$	−120.315	−4.15127
$841$	−1.62692	−0.0561007
$842$	39.1383	1.34879
$843$	2.57756	0.0887760
$844$	−62.9170	−2.16569
$845$	−53.3882	−1.83661
$846$	−30.2375	−1.03959
$847$	−17.2674	−0.593315
$848$	−139.189	−4.77977
$849$	−26.4449	−0.907586
$850$	−32.1084	−1.10131
$851$	15.6103	0.535115
$852$	−24.7253	−0.847076
$853$	43.6052	1.49301	0.746507	−	0.665377i	$-0.231729\pi$
$853$	43.6052	1.49301	0.746507	+	0.665377i	$0.231729\pi$
$854$	88.8218	3.03942
$855$	−29.5606	−1.01095
$856$	149.743	5.11810
$857$	12.7052	0.434002	0.217001	−	0.976171i	$-0.430373\pi$
$857$	12.7052	0.434002	0.217001	+	0.976171i	$0.430373\pi$
$858$	0.291904	0.00996543
$859$	−11.0653	−0.377544	−0.188772	−	0.982021i	$-0.560451\pi$
$859$	−11.0653	−0.377544	−0.188772	+	0.982021i	$0.560451\pi$
$860$	−55.9192	−1.90683
$861$	31.5193	1.07418
$862$	10.3381	0.352116
$863$	−6.74699	−0.229670	−0.114835	−	0.993385i	$-0.536634\pi$
$863$	−6.74699	−0.229670	−0.114835	+	0.993385i	$0.536634\pi$
$864$	−18.9203	−0.643682
$865$	−47.5360	−1.61627
$866$	−14.4732	−0.491821
$867$	1.00000	0.0339618
$868$	155.364	5.27341
$869$	15.3103	0.519368
$870$	58.1253	1.97063
$871$	0.121960	0.00413247
$872$	55.4755	1.87864
$873$	3.43487	0.116253
$874$	116.678	3.94669
$875$	92.1731	3.11602
$876$	−21.7207	−0.733874
$877$	−25.2555	−0.852818	−0.426409	−	0.904530i	$-0.640222\pi$
$877$	−25.2555	−0.852818	−0.426409	+	0.904530i	$0.640222\pi$
$878$	4.32045	0.145808
$879$	27.8140	0.938144
$880$	133.782	4.50980
$881$	2.21253	0.0745420	0.0372710	−	0.999305i	$-0.488134\pi$
$881$	2.21253	0.0745420	0.0372710	+	0.999305i	$0.488134\pi$
$882$	−9.91791	−0.333954
$883$	38.8450	1.30724	0.653620	−	0.756823i	$-0.273249\pi$
$883$	38.8450	1.30724	0.653620	+	0.756823i	$0.273249\pi$
$884$	−0.240022	−0.00807280
$885$	53.1494	1.78660
$886$	5.19755	0.174615
$887$	2.02195	0.0678903	0.0339452	−	0.999424i	$-0.489193\pi$
$887$	2.02195	0.0678903	0.0339452	+	0.999424i	$0.489193\pi$
$888$	−23.3579	−0.783840
$889$	−24.5992	−0.825031
$890$	−10.1578	−0.340491
$891$	2.39019	0.0800742
$892$	−89.4787	−2.99597
$893$	−80.4554	−2.69234
$894$	2.86963	0.0959749
$895$	77.2284	2.58146
$896$	−87.7331	−2.93096
$897$	−0.270636	−0.00903628
$898$	−43.9504	−1.46664
$899$	−46.8188	−1.56149
$900$	63.1047	2.10349
$901$	−10.2143	−0.340287
$902$	−62.3915	−2.07741
$903$	−8.36436	−0.278348
$904$	46.1557	1.53512
$905$	−69.7226	−2.31766
$906$	15.8691	0.527216
$907$	−53.3461	−1.77133	−0.885664	−	0.464327i	$-0.846296\pi$
$907$	−53.3461	−1.77133	−0.885664	+	0.464327i	$0.846296\pi$
$908$	141.050	4.68092
$909$	−1.94178	−0.0644049
$910$	1.63831	0.0543093
$911$	−12.7830	−0.423519	−0.211759	−	0.977322i	$-0.567919\pi$
$911$	−12.7830	−0.423519	−0.211759	+	0.977322i	$0.567919\pi$
$912$	−98.0709	−3.24745
$913$	5.60557	0.185517
$914$	−16.1078	−0.532798
$915$	−41.2990	−1.36530
$916$	−33.4682	−1.10582
$917$	−15.3485	−0.506852
$918$	−2.70479	−0.0892714
$919$	−41.8260	−1.37971	−0.689856	−	0.723947i	$-0.742326\pi$
$919$	−41.8260	−1.37971	−0.689856	+	0.723947i	$0.742326\pi$
$920$	−220.808	−7.27982
$921$	23.9519	0.789242
$922$	−15.1551	−0.499106
$923$	0.210011	0.00691258
$924$	41.4977	1.36518
$925$	30.9162	1.01652
$926$	54.3135	1.78485
$927$	−16.5103	−0.542269
$928$	98.9897	3.24950
$929$	−6.07357	−0.199267	−0.0996336	−	0.995024i	$-0.531767\pi$
$929$	−6.07357	−0.199267	−0.0996336	+	0.995024i	$0.531767\pi$
$930$	−99.4172	−3.26002
$931$	−26.3895	−0.864880
$932$	−145.094	−4.75272
$933$	−13.7463	−0.450032
$934$	23.9995	0.785287
$935$	9.81751	0.321067
$936$	0.404956	0.0132364
$937$	36.8311	1.20322	0.601610	−	0.798790i	$-0.294526\pi$
$937$	36.8311	1.20322	0.601610	+	0.798790i	$0.294526\pi$
$938$	23.8613	0.779099
$939$	12.4962	0.407799
$940$	244.094	7.96147
$941$	45.0715	1.46929	0.734645	−	0.678452i	$-0.237349\pi$
$941$	45.0715	1.46929	0.734645	+	0.678452i	$0.237349\pi$
$942$	−2.70479	−0.0881268
$943$	57.8458	1.88372
$944$	176.330	5.73904
$945$	13.4149	0.436386
$946$	16.5570	0.538313
$947$	−39.9350	−1.29771	−0.648856	−	0.760911i	$-0.724752\pi$
$947$	−39.9350	−1.29771	−0.648856	+	0.760911i	$0.724752\pi$
$948$	34.0509	1.10592
$949$	0.184490	0.00598879
$950$	231.080	7.49723
$951$	−19.9918	−0.648280
$952$	−29.2921	−0.949362
$953$	29.2735	0.948262	0.474131	−	0.880454i	$-0.342762\pi$
$953$	29.2735	0.948262	0.474131	+	0.880454i	$0.342762\pi$
$954$	27.6275	0.894473
$955$	78.2278	2.53139
$956$	−45.1992	−1.46185
$957$	−12.5053	−0.404238
$958$	104.748	3.38425
$959$	22.8810	0.738865
$960$	98.2565	3.17122
$961$	49.0786	1.58318
$962$	0.318060	0.0102547
$963$	−16.6960	−0.538021
$964$	159.371	5.13298
$965$	4.81717	0.155070
$966$	−52.9495	−1.70362
$967$	58.9191	1.89471	0.947356	−	0.320182i	$-0.103744\pi$
$967$	58.9191	1.89471	0.947356	+	0.320182i	$0.103744\pi$
$968$	47.4180	1.52407
$969$	−7.19687	−0.231197
$970$	−38.1605	−1.22526
$971$	29.0228	0.931387	0.465693	−	0.884946i	$-0.345805\pi$
$971$	29.0228	0.931387	0.465693	+	0.884946i	$0.345805\pi$
$972$	5.31589	0.170507
$973$	−19.9624	−0.639964
$974$	9.29394	0.297797
$975$	−0.535995	−0.0171656
$976$	−137.014	−4.38572
$977$	6.31830	0.202140	0.101070	−	0.994879i	$-0.467773\pi$
$977$	6.31830	0.202140	0.101070	+	0.994879i	$0.467773\pi$
$978$	−27.0559	−0.865152
$979$	2.18539	0.0698454
$980$	80.0631	2.55752
$981$	−6.18540	−0.197485
$982$	18.5496	0.591943
$983$	41.4778	1.32293	0.661467	−	0.749974i	$-0.269934\pi$
$983$	41.4778	1.32293	0.661467	+	0.749974i	$0.269934\pi$
$984$	−86.5553	−2.75928
$985$	99.1807	3.16016
$986$	14.1513	0.450668
$987$	36.5114	1.16217
$988$	1.72740	0.0549561
$989$	−15.3507	−0.488122
$990$	−26.5543	−0.843951
$991$	−24.6527	−0.783118	−0.391559	−	0.920153i	$-0.628064\pi$
$991$	−24.6527	−0.783118	−0.391559	+	0.920153i	$0.628064\pi$
$992$	−169.312	−5.37565
$993$	−27.9219	−0.886075
$994$	41.0882	1.30324
$995$	−27.5011	−0.871842
$996$	12.4671	0.395034
$997$	60.3762	1.91213	0.956066	−	0.293150i	$-0.0947036\pi$
$997$	60.3762	1.91213	0.956066	+	0.293150i	$0.0947036\pi$
$998$	31.1843	0.987122
$999$	2.60436	0.0823983

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.i.1.2	✓	63

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.i.1.2	✓	63	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:	\( N \)	\(=\)	\( 8007 = 3 \cdot 17 \cdot 157 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8007.a (trivial)

\(f(q)\)	\(=\)	\(q-2.70479 q^{2} +1.00000 q^{3} +5.31589 q^{4} +4.10743 q^{5} -2.70479 q^{6} +3.26601 q^{7} -8.96878 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.70479 q^{2} +1.00000 q^{3} +5.31589 q^{4} +4.10743 q^{5} -2.70479 q^{6} +3.26601 q^{7} -8.96878 q^{8} +1.00000 q^{9} -11.1097 q^{10} +2.39019 q^{11} +5.31589 q^{12} -0.0451518 q^{13} -8.83386 q^{14} +4.10743 q^{15} +13.6269 q^{16} +1.00000 q^{17} -2.70479 q^{18} -7.19687 q^{19} +21.8346 q^{20} +3.26601 q^{21} -6.46495 q^{22} +5.99393 q^{23} -8.96878 q^{24} +11.8710 q^{25} +0.122126 q^{26} +1.00000 q^{27} +17.3617 q^{28} -5.23193 q^{29} -11.1097 q^{30} +8.94867 q^{31} -18.9203 q^{32} +2.39019 q^{33} -2.70479 q^{34} +13.4149 q^{35} +5.31589 q^{36} +2.60436 q^{37} +19.4660 q^{38} -0.0451518 q^{39} -36.8386 q^{40} +9.65073 q^{41} -8.83386 q^{42} -2.56103 q^{43} +12.7060 q^{44} +4.10743 q^{45} -16.2123 q^{46} +11.1792 q^{47} +13.6269 q^{48} +3.66680 q^{49} -32.1084 q^{50} +1.00000 q^{51} -0.240022 q^{52} -10.2143 q^{53} -2.70479 q^{54} +9.81751 q^{55} -29.2921 q^{56} -7.19687 q^{57} +14.1513 q^{58} +12.9398 q^{59} +21.8346 q^{60} -10.0547 q^{61} -24.2043 q^{62} +3.26601 q^{63} +23.9217 q^{64} -0.185458 q^{65} -6.46495 q^{66} -2.70112 q^{67} +5.31589 q^{68} +5.99393 q^{69} -36.2844 q^{70} -4.65122 q^{71} -8.96878 q^{72} -4.08599 q^{73} -7.04424 q^{74} +11.8710 q^{75} -38.2578 q^{76} +7.80636 q^{77} +0.122126 q^{78} +6.40550 q^{79} +55.9714 q^{80} +1.00000 q^{81} -26.1032 q^{82} +2.34525 q^{83} +17.3617 q^{84} +4.10743 q^{85} +6.92706 q^{86} -5.23193 q^{87} -21.4370 q^{88} +0.914319 q^{89} -11.1097 q^{90} -0.147466 q^{91} +31.8630 q^{92} +8.94867 q^{93} -30.2375 q^{94} -29.5606 q^{95} -18.9203 q^{96} +3.43487 q^{97} -9.91791 q^{98} +2.39019 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 63 q + 10 q^{2} + 63 q^{3} + 70 q^{4} + 19 q^{5} + 10 q^{6} + 11 q^{7} + 27 q^{8} + 63 q^{9}+O(q^{10}) \) 63 * q + 10 * q^2 + 63 * q^3 + 70 * q^4 + 19 * q^5 + 10 * q^6 + 11 * q^7 + 27 * q^8 + 63 * q^9	\( 63 q + 10 q^{2} + 63 q^{3} + 70 q^{4} + 19 q^{5} + 10 q^{6} + 11 q^{7} + 27 q^{8} + 63 q^{9} + 4 q^{10} + 23 q^{11} + 70 q^{12} + 10 q^{13} + 18 q^{14} + 19 q^{15} + 72 q^{16} + 63 q^{17} + 10 q^{18} + 6 q^{19} + 48 q^{20} + 11 q^{21} + 21 q^{22} + 44 q^{23} + 27 q^{24} + 110 q^{25} + 41 q^{26} + 63 q^{27} + 26 q^{28} + 35 q^{29} + 4 q^{30} + q^{31} + 54 q^{32} + 23 q^{33} + 10 q^{34} + 47 q^{35} + 70 q^{36} + 40 q^{37} + 38 q^{38} + 10 q^{39} - 10 q^{40} + 35 q^{41} + 18 q^{42} + 27 q^{43} + 46 q^{44} + 19 q^{45} + 8 q^{46} + 29 q^{47} + 72 q^{48} + 114 q^{49} + 27 q^{50} + 63 q^{51} - q^{52} + 75 q^{53} + 10 q^{54} + 5 q^{55} + 24 q^{56} + 6 q^{57} + 41 q^{58} + 105 q^{59} + 48 q^{60} + 5 q^{61} + 22 q^{62} + 11 q^{63} + 61 q^{64} + 49 q^{65} + 21 q^{66} + 4 q^{67} + 70 q^{68} + 44 q^{69} - 16 q^{70} + 16 q^{71} + 27 q^{72} + 39 q^{73} + 54 q^{74} + 110 q^{75} + 6 q^{76} + 88 q^{77} + 41 q^{78} + 16 q^{79} + 102 q^{80} + 63 q^{81} - 29 q^{82} + 73 q^{83} + 26 q^{84} + 19 q^{85} + 46 q^{86} + 35 q^{87} + 18 q^{88} + 88 q^{89} + 4 q^{90} - 15 q^{91} + 110 q^{92} + q^{93} - 8 q^{94} + 28 q^{95} + 54 q^{96} + 70 q^{97} + 33 q^{98} + 23 q^{99}+O(q^{100}) \) 63 * q + 10 * q^2 + 63 * q^3 + 70 * q^4 + 19 * q^5 + 10 * q^6 + 11 * q^7 + 27 * q^8 + 63 * q^9 + 4 * q^10 + 23 * q^11 + 70 * q^12 + 10 * q^13 + 18 * q^14 + 19 * q^15 + 72 * q^16 + 63 * q^17 + 10 * q^18 + 6 * q^19 + 48 * q^20 + 11 * q^21 + 21 * q^22 + 44 * q^23 + 27 * q^24 + 110 * q^25 + 41 * q^26 + 63 * q^27 + 26 * q^28 + 35 * q^29 + 4 * q^30 + q^31 + 54 * q^32 + 23 * q^33 + 10 * q^34 + 47 * q^35 + 70 * q^36 + 40 * q^37 + 38 * q^38 + 10 * q^39 - 10 * q^40 + 35 * q^41 + 18 * q^42 + 27 * q^43 + 46 * q^44 + 19 * q^45 + 8 * q^46 + 29 * q^47 + 72 * q^48 + 114 * q^49 + 27 * q^50 + 63 * q^51 - q^52 + 75 * q^53 + 10 * q^54 + 5 * q^55 + 24 * q^56 + 6 * q^57 + 41 * q^58 + 105 * q^59 + 48 * q^60 + 5 * q^61 + 22 * q^62 + 11 * q^63 + 61 * q^64 + 49 * q^65 + 21 * q^66 + 4 * q^67 + 70 * q^68 + 44 * q^69 - 16 * q^70 + 16 * q^71 + 27 * q^72 + 39 * q^73 + 54 * q^74 + 110 * q^75 + 6 * q^76 + 88 * q^77 + 41 * q^78 + 16 * q^79 + 102 * q^80 + 63 * q^81 - 29 * q^82 + 73 * q^83 + 26 * q^84 + 19 * q^85 + 46 * q^86 + 35 * q^87 + 18 * q^88 + 88 * q^89 + 4 * q^90 - 15 * q^91 + 110 * q^92 + q^93 - 8 * q^94 + 28 * q^95 + 54 * q^96 + 70 * q^97 + 33 * q^98 + 23 * q^99

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