LMFDB - Embedded newform 8007.2.a.i.1.18

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			1.18
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)

$f(q)$	$=$	$q-1.22360 q^{2} +1.00000 q^{3} -0.502806 q^{4} +1.43997 q^{5} -1.22360 q^{6} -1.77841 q^{7} +3.06243 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.22360 q^{2} +1.00000 q^{3} -0.502806 q^{4} +1.43997 q^{5} -1.22360 q^{6} -1.77841 q^{7} +3.06243 q^{8} +1.00000 q^{9} -1.76195 q^{10} -4.03409 q^{11} -0.502806 q^{12} +1.49492 q^{13} +2.17605 q^{14} +1.43997 q^{15} -2.74157 q^{16} +1.00000 q^{17} -1.22360 q^{18} +0.978337 q^{19} -0.724027 q^{20} -1.77841 q^{21} +4.93610 q^{22} +2.98194 q^{23} +3.06243 q^{24} -2.92648 q^{25} -1.82919 q^{26} +1.00000 q^{27} +0.894194 q^{28} +3.44515 q^{29} -1.76195 q^{30} +5.60765 q^{31} -2.77028 q^{32} -4.03409 q^{33} -1.22360 q^{34} -2.56085 q^{35} -0.502806 q^{36} +0.00295062 q^{37} -1.19709 q^{38} +1.49492 q^{39} +4.40981 q^{40} +8.32343 q^{41} +2.17605 q^{42} +2.89385 q^{43} +2.02836 q^{44} +1.43997 q^{45} -3.64870 q^{46} -6.47494 q^{47} -2.74157 q^{48} -3.83727 q^{49} +3.58084 q^{50} +1.00000 q^{51} -0.751657 q^{52} -3.00170 q^{53} -1.22360 q^{54} -5.80897 q^{55} -5.44624 q^{56} +0.978337 q^{57} -4.21548 q^{58} -4.07376 q^{59} -0.724027 q^{60} -3.04725 q^{61} -6.86151 q^{62} -1.77841 q^{63} +8.87285 q^{64} +2.15265 q^{65} +4.93610 q^{66} +10.5594 q^{67} -0.502806 q^{68} +2.98194 q^{69} +3.13346 q^{70} -12.5257 q^{71} +3.06243 q^{72} +4.54543 q^{73} -0.00361037 q^{74} -2.92648 q^{75} -0.491914 q^{76} +7.17424 q^{77} -1.82919 q^{78} -8.54162 q^{79} -3.94779 q^{80} +1.00000 q^{81} -10.1845 q^{82} +2.65805 q^{83} +0.894194 q^{84} +1.43997 q^{85} -3.54091 q^{86} +3.44515 q^{87} -12.3541 q^{88} -2.75226 q^{89} -1.76195 q^{90} -2.65858 q^{91} -1.49934 q^{92} +5.60765 q^{93} +7.92273 q^{94} +1.40878 q^{95} -2.77028 q^{96} +3.36257 q^{97} +4.69528 q^{98} -4.03409 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.22360	−0.865215	−0.432607	−	0.901582i	$-0.642406\pi$
$2$	−1.22360	−0.865215	−0.432607	+	0.901582i	$0.642406\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−0.502806	−0.251403
$5$	1.43997	0.643975	0.321987	−	0.946744i	$-0.395649\pi$
$5$	1.43997	0.643975	0.321987	+	0.946744i	$0.395649\pi$
$6$	−1.22360	−0.499532
$7$	−1.77841	−0.672174	−0.336087	−	0.941831i	$-0.609104\pi$
$7$	−1.77841	−0.672174	−0.336087	+	0.941831i	$0.609104\pi$
$8$	3.06243	1.08273
$9$	1.00000	0.333333
$10$	−1.76195	−0.557177
$11$	−4.03409	−1.21632	−0.608161	−	0.793814i	$-0.708093\pi$
$11$	−4.03409	−1.21632	−0.608161	+	0.793814i	$0.708093\pi$
$12$	−0.502806	−0.145148
$13$	1.49492	0.414617	0.207309	−	0.978276i	$-0.433530\pi$
$13$	1.49492	0.414617	0.207309	+	0.978276i	$0.433530\pi$
$14$	2.17605	0.581575
$15$	1.43997	0.371799
$16$	−2.74157	−0.685393
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−1.22360	−0.288405
$19$	0.978337	0.224446	0.112223	−	0.993683i	$-0.464203\pi$
$19$	0.978337	0.224446	0.112223	+	0.993683i	$0.464203\pi$
$20$	−0.724027	−0.161897
$21$	−1.77841	−0.388080
$22$	4.93610	1.05238
$23$	2.98194	0.621777	0.310889	−	0.950446i	$-0.399373\pi$
$23$	2.98194	0.621777	0.310889	+	0.950446i	$0.399373\pi$
$24$	3.06243	0.625116
$25$	−2.92648	−0.585296
$26$	−1.82919	−0.358733
$27$	1.00000	0.192450
$28$	0.894194	0.168987
$29$	3.44515	0.639748	0.319874	−	0.947460i	$-0.396359\pi$
$29$	3.44515	0.639748	0.319874	+	0.947460i	$0.396359\pi$
$30$	−1.76195	−0.321686
$31$	5.60765	1.00716	0.503582	−	0.863947i	$-0.332015\pi$
$31$	5.60765	1.00716	0.503582	+	0.863947i	$0.332015\pi$
$32$	−2.77028	−0.489720
$33$	−4.03409	−0.702244
$34$	−1.22360	−0.209845
$35$	−2.56085	−0.432863
$36$	−0.502806	−0.0838011
$37$	0.00295062	0.000485079 0	0.000242539	−	1.00000i	$-0.499923\pi$
$37$	0.00295062	0.000485079 0	0.000242539		1.00000i	$0.499923\pi$
$38$	−1.19709	−0.194194
$39$	1.49492	0.239379
$40$	4.40981	0.697253
$41$	8.32343	1.29990	0.649951	−	0.759976i	$-0.274789\pi$
$41$	8.32343	1.29990	0.649951	+	0.759976i	$0.274789\pi$
$42$	2.17605	0.335773
$43$	2.89385	0.441307	0.220654	−	0.975352i	$-0.429181\pi$
$43$	2.89385	0.441307	0.220654	+	0.975352i	$0.429181\pi$
$44$	2.02836	0.305787
$45$	1.43997	0.214658
$46$	−3.64870	−0.537971
$47$	−6.47494	−0.944467	−0.472234	−	0.881473i	$-0.656552\pi$
$47$	−6.47494	−0.944467	−0.472234	+	0.881473i	$0.656552\pi$
$48$	−2.74157	−0.395712
$49$	−3.83727	−0.548182
$50$	3.58084	0.506407
$51$	1.00000	0.140028
$52$	−0.751657	−0.104236
$53$	−3.00170	−0.412315	−0.206158	−	0.978519i	$-0.566096\pi$
$53$	−3.00170	−0.412315	−0.206158	+	0.978519i	$0.566096\pi$
$54$	−1.22360	−0.166511
$55$	−5.80897	−0.783281
$56$	−5.44624	−0.727785
$57$	0.978337	0.129584
$58$	−4.21548	−0.553519
$59$	−4.07376	−0.530359	−0.265179	−	0.964199i	$-0.585431\pi$
$59$	−4.07376	−0.530359	−0.265179	+	0.964199i	$0.585431\pi$
$60$	−0.724027	−0.0934715
$61$	−3.04725	−0.390160	−0.195080	−	0.980787i	$-0.562497\pi$
$61$	−3.04725	−0.390160	−0.195080	+	0.980787i	$0.562497\pi$
$62$	−6.86151	−0.871413
$63$	−1.77841	−0.224058
$64$	8.87285	1.10911
$65$	2.15265	0.267003
$66$	4.93610	0.607592
$67$	10.5594	1.29003	0.645016	−	0.764169i	$-0.276851\pi$
$67$	10.5594	1.29003	0.645016	+	0.764169i	$0.276851\pi$
$68$	−0.502806	−0.0609742
$69$	2.98194	0.358983
$70$	3.13346	0.374520
$71$	−12.5257	−1.48653	−0.743263	−	0.668999i	$-0.766723\pi$
$71$	−12.5257	−1.48653	−0.743263	+	0.668999i	$0.766723\pi$
$72$	3.06243	0.360911
$73$	4.54543	0.532002	0.266001	−	0.963973i	$-0.414298\pi$
$73$	4.54543	0.532002	0.266001	+	0.963973i	$0.414298\pi$
$74$	−0.00361037	−0.000419697 0
$75$	−2.92648	−0.337921
$76$	−0.491914	−0.0564264
$77$	7.17424	0.817581
$78$	−1.82919	−0.207115
$79$	−8.54162	−0.961007	−0.480504	−	0.876993i	$-0.659546\pi$
$79$	−8.54162	−0.961007	−0.480504	+	0.876993i	$0.659546\pi$
$80$	−3.94779	−0.441376
$81$	1.00000	0.111111
$82$	−10.1845	−1.12469
$83$	2.65805	0.291759	0.145879	−	0.989302i	$-0.453399\pi$
$83$	2.65805	0.291759	0.145879	+	0.989302i	$0.453399\pi$
$84$	0.894194	0.0975646
$85$	1.43997	0.156187
$86$	−3.54091	−0.381826
$87$	3.44515	0.369359
$88$	−12.3541	−1.31695
$89$	−2.75226	−0.291739	−0.145869	−	0.989304i	$-0.546598\pi$
$89$	−2.75226	−0.291739	−0.145869	+	0.989304i	$0.546598\pi$
$90$	−1.76195	−0.185726
$91$	−2.65858	−0.278695
$92$	−1.49934	−0.156317
$93$	5.60765	0.581486
$94$	7.92273	0.817167
$95$	1.40878	0.144538
$96$	−2.77028	−0.282740
$97$	3.36257	0.341418	0.170709	−	0.985322i	$-0.445394\pi$
$97$	3.36257	0.341418	0.170709	+	0.985322i	$0.445394\pi$
$98$	4.69528	0.474295
$99$	−4.03409	−0.405441
$100$	1.47145	0.147145
$101$	12.8388	1.27751	0.638753	−	0.769411i	$-0.279450\pi$
$101$	12.8388	1.27751	0.638753	+	0.769411i	$0.279450\pi$
$102$	−1.22360	−0.121154
$103$	−14.0201	−1.38144	−0.690718	−	0.723124i	$-0.742706\pi$
$103$	−14.0201	−1.38144	−0.690718	+	0.723124i	$0.742706\pi$
$104$	4.57810	0.448920
$105$	−2.56085	−0.249914
$106$	3.67287	0.356741
$107$	9.83296	0.950588	0.475294	−	0.879827i	$-0.342342\pi$
$107$	9.83296	0.950588	0.475294	+	0.879827i	$0.342342\pi$
$108$	−0.502806	−0.0483826
$109$	13.9552	1.33666	0.668331	−	0.743864i	$-0.267009\pi$
$109$	13.9552	1.33666	0.668331	+	0.743864i	$0.267009\pi$
$110$	7.10785	0.677706
$111$	0.00295062	0.000280060 0
$112$	4.87563	0.460704
$113$	4.18898	0.394066	0.197033	−	0.980397i	$-0.436869\pi$
$113$	4.18898	0.394066	0.197033	+	0.980397i	$0.436869\pi$
$114$	−1.19709	−0.112118
$115$	4.29391	0.400409
$116$	−1.73224	−0.160835
$117$	1.49492	0.138206
$118$	4.98465	0.458874
$119$	−1.77841	−0.163026
$120$	4.40981	0.402559
$121$	5.27384	0.479440
$122$	3.72861	0.337572
$123$	8.32343	0.750499
$124$	−2.81956	−0.253204
$125$	−11.4139	−1.02089
$126$	2.17605	0.193858
$127$	−4.75965	−0.422350	−0.211175	−	0.977448i	$-0.567729\pi$
$127$	−4.75965	−0.422350	−0.211175	+	0.977448i	$0.567729\pi$
$128$	−5.31626	−0.469895
$129$	2.89385	0.254789
$130$	−2.63398	−0.231015
$131$	−1.09758	−0.0958956	−0.0479478	−	0.998850i	$-0.515268\pi$
$131$	−1.09758	−0.0958956	−0.0479478	+	0.998850i	$0.515268\pi$
$132$	2.02836	0.176546
$133$	−1.73988	−0.150867
$134$	−12.9204	−1.11616
$135$	1.43997	0.123933
$136$	3.06243	0.262601
$137$	−11.5071	−0.983119	−0.491560	−	0.870844i	$-0.663573\pi$
$137$	−11.5071	−0.983119	−0.491560	+	0.870844i	$0.663573\pi$
$138$	−3.64870	−0.310598
$139$	18.1838	1.54233	0.771164	−	0.636637i	$-0.219675\pi$
$139$	18.1838	1.54233	0.771164	+	0.636637i	$0.219675\pi$
$140$	1.28761	0.108823
$141$	−6.47494	−0.545288
$142$	15.3264	1.28616
$143$	−6.03065	−0.504308
$144$	−2.74157	−0.228464
$145$	4.96091	0.411981
$146$	−5.56178	−0.460296
$147$	−3.83727	−0.316493
$148$	−0.00148359	−0.000121950 0
$149$	7.04423	0.577086	0.288543	−	0.957467i	$-0.406829\pi$
$149$	7.04423	0.577086	0.288543	+	0.957467i	$0.406829\pi$
$150$	3.58084	0.292374
$151$	6.11906	0.497962	0.248981	−	0.968508i	$-0.419904\pi$
$151$	6.11906	0.497962	0.248981	+	0.968508i	$0.419904\pi$
$152$	2.99609	0.243015
$153$	1.00000	0.0808452
$154$	−8.77839	−0.707383
$155$	8.07486	0.648588
$156$	−0.751657	−0.0601807
$157$	1.00000	0.0798087
$157$	1.00000	0.0798087
$158$	10.4515	0.831478
$159$	−3.00170	−0.238050
$160$	−3.98912	−0.315368
$161$	−5.30310	−0.417943
$162$	−1.22360	−0.0961350
$163$	19.5803	1.53365	0.766823	−	0.641859i	$-0.221837\pi$
$163$	19.5803	1.53365	0.766823	+	0.641859i	$0.221837\pi$
$164$	−4.18508	−0.326800
$165$	−5.80897	−0.452228
$166$	−3.25238	−0.252434
$167$	−21.2436	−1.64388	−0.821940	−	0.569574i	$-0.807108\pi$
$167$	−21.2436	−1.64388	−0.821940	+	0.569574i	$0.807108\pi$
$168$	−5.44624	−0.420187
$169$	−10.7652	−0.828093
$170$	−1.76195	−0.135135
$171$	0.978337	0.0748153
$172$	−1.45504	−0.110946
$173$	22.3508	1.69930	0.849650	−	0.527347i	$-0.176813\pi$
$173$	22.3508	1.69930	0.849650	+	0.527347i	$0.176813\pi$
$174$	−4.21548	−0.319574
$175$	5.20447	0.393421
$176$	11.0597	0.833659
$177$	−4.07376	−0.306203
$178$	3.36766	0.252417
$179$	6.82845	0.510383	0.255191	−	0.966891i	$-0.417862\pi$
$179$	6.82845	0.510383	0.255191	+	0.966891i	$0.417862\pi$
$180$	−0.724027	−0.0539658
$181$	0.0495339	0.00368183	0.00184091	−	0.999998i	$-0.499414\pi$
$181$	0.0495339	0.00368183	0.00184091	+	0.999998i	$0.499414\pi$
$182$	3.25304	0.241131
$183$	−3.04725	−0.225259
$184$	9.13198	0.673218
$185$	0.00424881	0.000312378 0
$186$	−6.86151	−0.503111
$187$	−4.03409	−0.295002
$188$	3.25564	0.237442
$189$	−1.77841	−0.129360
$190$	−1.72378	−0.125056
$191$	−13.2905	−0.961664	−0.480832	−	0.876813i	$-0.659665\pi$
$191$	−13.2905	−0.961664	−0.480832	+	0.876813i	$0.659665\pi$
$192$	8.87285	0.640343
$193$	10.7795	0.775928	0.387964	−	0.921675i	$-0.373179\pi$
$193$	10.7795	0.775928	0.387964	+	0.921675i	$0.373179\pi$
$194$	−4.11444	−0.295400
$195$	2.15265	0.154154
$196$	1.92941	0.137815
$197$	21.7139	1.54705	0.773525	−	0.633766i	$-0.218492\pi$
$197$	21.7139	1.54705	0.773525	+	0.633766i	$0.218492\pi$
$198$	4.93610	0.350793
$199$	4.44333	0.314979	0.157490	−	0.987521i	$-0.449660\pi$
$199$	4.44333	0.314979	0.157490	+	0.987521i	$0.449660\pi$
$200$	−8.96215	−0.633719
$201$	10.5594	0.744800
$202$	−15.7095	−1.10532
$203$	−6.12687	−0.430022
$204$	−0.502806	−0.0352035
$205$	11.9855	0.837104
$206$	17.1549	1.19524
$207$	2.98194	0.207259
$208$	−4.09844	−0.284176
$209$	−3.94670	−0.272999
$210$	3.13346	0.216229
$211$	−2.12234	−0.146108	−0.0730539	−	0.997328i	$-0.523275\pi$
$211$	−2.12234	−0.146108	−0.0730539	+	0.997328i	$0.523275\pi$
$212$	1.50927	0.103657
$213$	−12.5257	−0.858246
$214$	−12.0316	−0.822463
$215$	4.16705	0.284191
$216$	3.06243	0.208372
$217$	−9.97268	−0.676990
$218$	−17.0755	−1.15650
$219$	4.54543	0.307152
$220$	2.92079	0.196919
$221$	1.49492	0.100559
$222$	−0.00361037	−0.000242312 0
$223$	−19.9671	−1.33710	−0.668549	−	0.743668i	$-0.733084\pi$
$223$	−19.9671	−1.33710	−0.668549	+	0.743668i	$0.733084\pi$
$224$	4.92668	0.329177
$225$	−2.92648	−0.195099
$226$	−5.12563	−0.340952
$227$	25.6205	1.70049	0.850246	−	0.526386i	$-0.176453\pi$
$227$	25.6205	1.70049	0.850246	+	0.526386i	$0.176453\pi$
$228$	−0.491914	−0.0325778
$229$	28.3808	1.87545	0.937727	−	0.347372i	$-0.112926\pi$
$229$	28.3808	1.87545	0.937727	+	0.347372i	$0.112926\pi$
$230$	−5.25402	−0.346440
$231$	7.17424	0.472030
$232$	10.5505	0.692676
$233$	−3.26740	−0.214054	−0.107027	−	0.994256i	$-0.534133\pi$
$233$	−3.26740	−0.214054	−0.107027	+	0.994256i	$0.534133\pi$
$234$	−1.82919	−0.119578
$235$	−9.32373	−0.608213
$236$	2.04831	0.133334
$237$	−8.54162	−0.554838
$238$	2.17605	0.141053
$239$	22.1109	1.43024	0.715118	−	0.699003i	$-0.246373\pi$
$239$	22.1109	1.43024	0.715118	+	0.699003i	$0.246373\pi$
$240$	−3.94779	−0.254829
$241$	−23.4687	−1.51175	−0.755875	−	0.654716i	$-0.772788\pi$
$241$	−23.4687	−1.51175	−0.755875	+	0.654716i	$0.772788\pi$
$242$	−6.45307	−0.414819
$243$	1.00000	0.0641500
$244$	1.53217	0.0980875
$245$	−5.52556	−0.353015
$246$	−10.1845	−0.649343
$247$	1.46254	0.0930592
$248$	17.1730	1.09049
$249$	2.65805	0.168447
$250$	13.9660	0.883290
$251$	17.9834	1.13510	0.567551	−	0.823338i	$-0.307891\pi$
$251$	17.9834	1.13510	0.567551	+	0.823338i	$0.307891\pi$
$252$	0.894194	0.0563289
$253$	−12.0294	−0.756282
$254$	5.82390	0.365424
$255$	1.43997	0.0901745
$256$	−11.2407	−0.702546
$257$	26.0376	1.62418	0.812091	−	0.583530i	$-0.198329\pi$
$257$	26.0376	1.62418	0.812091	+	0.583530i	$0.198329\pi$
$258$	−3.54091	−0.220447
$259$	−0.00524740	−0.000326057 0
$260$	−1.08237	−0.0671254
$261$	3.44515	0.213249
$262$	1.34299	0.0829703
$263$	−28.6152	−1.76449	−0.882243	−	0.470794i	$-0.843968\pi$
$263$	−28.6152	−1.76449	−0.882243	+	0.470794i	$0.843968\pi$
$264$	−12.3541	−0.760343
$265$	−4.32236	−0.265521
$266$	2.12892	0.130532
$267$	−2.75226	−0.168435
$268$	−5.30932	−0.324318
$269$	4.81904	0.293822	0.146911	−	0.989150i	$-0.453067\pi$
$269$	4.81904	0.293822	0.146911	+	0.989150i	$0.453067\pi$
$270$	−1.76195	−0.107229
$271$	8.14633	0.494854	0.247427	−	0.968907i	$-0.420415\pi$
$271$	8.14633	0.494854	0.247427	+	0.968907i	$0.420415\pi$
$272$	−2.74157	−0.166232
$273$	−2.65858	−0.160905
$274$	14.0801	0.850610
$275$	11.8057	0.711909
$276$	−1.49934	−0.0902495
$277$	−27.2492	−1.63725	−0.818624	−	0.574330i	$-0.805263\pi$
$277$	−27.2492	−1.63725	−0.818624	+	0.574330i	$0.805263\pi$
$278$	−22.2496	−1.33444
$279$	5.60765	0.335721
$280$	−7.84244	−0.468675
$281$	−2.90218	−0.173130	−0.0865648	−	0.996246i	$-0.527589\pi$
$281$	−2.90218	−0.173130	−0.0865648	+	0.996246i	$0.527589\pi$
$282$	7.92273	0.471792
$283$	17.8270	1.05971	0.529854	−	0.848089i	$-0.322247\pi$
$283$	17.8270	1.05971	0.529854	+	0.848089i	$0.322247\pi$
$284$	6.29800	0.373717
$285$	1.40878	0.0834488
$286$	7.37909	0.436335
$287$	−14.8024	−0.873761
$288$	−2.77028	−0.163240
$289$	1.00000	0.0588235
$290$	−6.07017	−0.356452
$291$	3.36257	0.197118
$292$	−2.28547	−0.133747
$293$	−6.35919	−0.371508	−0.185754	−	0.982596i	$-0.559473\pi$
$293$	−6.35919	−0.371508	−0.185754	+	0.982596i	$0.559473\pi$
$294$	4.69528	0.273834
$295$	−5.86610	−0.341538
$296$	0.00903606	0.000525210 0
$297$	−4.03409	−0.234081
$298$	−8.61932	−0.499304
$299$	4.45777	0.257800
$300$	1.47145	0.0849544
$301$	−5.14643	−0.296635
$302$	−7.48727	−0.430844
$303$	12.8388	0.737569
$304$	−2.68218	−0.153834
$305$	−4.38795	−0.251253
$306$	−1.22360	−0.0699485
$307$	−6.77718	−0.386794	−0.193397	−	0.981121i	$-0.561951\pi$
$307$	−6.77718	−0.386794	−0.193397	+	0.981121i	$0.561951\pi$
$308$	−3.60725	−0.205542
$309$	−14.0201	−0.797573
$310$	−9.88039	−0.561168
$311$	−19.3852	−1.09923	−0.549617	−	0.835416i	$-0.685226\pi$
$311$	−19.3852	−1.09923	−0.549617	+	0.835416i	$0.685226\pi$
$312$	4.57810	0.259184
$313$	16.6914	0.943455	0.471727	−	0.881744i	$-0.343631\pi$
$313$	16.6914	0.943455	0.471727	+	0.881744i	$0.343631\pi$
$314$	−1.22360	−0.0690517
$315$	−2.56085	−0.144288
$316$	4.29478	0.241600
$317$	27.3880	1.53826	0.769131	−	0.639091i	$-0.220689\pi$
$317$	27.3880	1.53826	0.769131	+	0.639091i	$0.220689\pi$
$318$	3.67287	0.205965
$319$	−13.8980	−0.778140
$320$	12.7767	0.714237
$321$	9.83296	0.548822
$322$	6.48886	0.361610
$323$	0.978337	0.0544361
$324$	−0.502806	−0.0279337
$325$	−4.37487	−0.242674
$326$	−23.9584	−1.32693
$327$	13.9552	0.771722
$328$	25.4899	1.40745
$329$	11.5151	0.634847
$330$	7.10785	0.391274
$331$	23.1358	1.27166	0.635830	−	0.771829i	$-0.280658\pi$
$331$	23.1358	1.27166	0.635830	+	0.771829i	$0.280658\pi$
$332$	−1.33648	−0.0733490
$333$	0.00295062	0.000161693 0
$334$	25.9937	1.42231
$335$	15.2052	0.830748
$336$	4.87563	0.265987
$337$	10.7292	0.584459	0.292230	−	0.956348i	$-0.405603\pi$
$337$	10.7292	0.584459	0.292230	+	0.956348i	$0.405603\pi$
$338$	13.1723	0.716478
$339$	4.18898	0.227514
$340$	−0.724027	−0.0392659
$341$	−22.6217	−1.22504
$342$	−1.19709	−0.0647313
$343$	19.2731	1.04065
$344$	8.86220	0.477818
$345$	4.29391	0.231176
$346$	−27.3484	−1.47026
$347$	4.65783	0.250046	0.125023	−	0.992154i	$-0.460100\pi$
$347$	4.65783	0.250046	0.125023	+	0.992154i	$0.460100\pi$
$348$	−1.73224	−0.0928579
$349$	−24.5007	−1.31149	−0.655746	−	0.754982i	$-0.727646\pi$
$349$	−24.5007	−1.31149	−0.655746	+	0.754982i	$0.727646\pi$
$350$	−6.36819	−0.340394
$351$	1.49492	0.0797931
$352$	11.1755	0.595658
$353$	−18.7132	−0.996003	−0.498001	−	0.867176i	$-0.665933\pi$
$353$	−18.7132	−0.996003	−0.498001	+	0.867176i	$0.665933\pi$
$354$	4.98465	0.264931
$355$	−18.0366	−0.957285
$356$	1.38385	0.0733440
$357$	−1.77841	−0.0941232
$358$	−8.35529	−0.441591
$359$	29.6667	1.56575	0.782875	−	0.622180i	$-0.213753\pi$
$359$	29.6667	1.56575	0.782875	+	0.622180i	$0.213753\pi$
$360$	4.40981	0.232418
$361$	−18.0429	−0.949624
$362$	−0.0606096	−0.00318557
$363$	5.27384	0.276805
$364$	1.33675	0.0700648
$365$	6.54529	0.342596
$366$	3.72861	0.194897
$367$	22.8390	1.19219	0.596094	−	0.802915i	$-0.296719\pi$
$367$	22.8390	1.19219	0.596094	+	0.802915i	$0.296719\pi$
$368$	−8.17520	−0.426162
$369$	8.32343	0.433301
$370$	−0.00519883	−0.000270274 0
$371$	5.33824	0.277148
$372$	−2.81956	−0.146188
$373$	30.3342	1.57065	0.785324	−	0.619085i	$-0.212497\pi$
$373$	30.3342	1.57065	0.785324	+	0.619085i	$0.212497\pi$
$374$	4.93610	0.255240
$375$	−11.4139	−0.589412
$376$	−19.8291	−1.02261
$377$	5.15023	0.265250
$378$	2.17605	0.111924
$379$	−36.9670	−1.89887	−0.949434	−	0.313966i	$-0.898342\pi$
$379$	−36.9670	−1.89887	−0.949434	+	0.313966i	$0.898342\pi$
$380$	−0.708343	−0.0363372
$381$	−4.75965	−0.243844
$382$	16.2622	0.832046
$383$	−22.4314	−1.14619	−0.573096	−	0.819488i	$-0.694258\pi$
$383$	−22.4314	−1.14619	−0.573096	+	0.819488i	$0.694258\pi$
$384$	−5.31626	−0.271294
$385$	10.3307	0.526501
$386$	−13.1898	−0.671344
$387$	2.89385	0.147102
$388$	−1.69072	−0.0858335
$389$	27.9731	1.41829	0.709147	−	0.705061i	$-0.249080\pi$
$389$	27.9731	1.41829	0.709147	+	0.705061i	$0.249080\pi$
$390$	−2.63398	−0.133377
$391$	2.98194	0.150803
$392$	−11.7514	−0.593534
$393$	−1.09758	−0.0553653
$394$	−26.5691	−1.33853
$395$	−12.2997	−0.618865
$396$	2.02836	0.101929
$397$	−12.2729	−0.615957	−0.307978	−	0.951393i	$-0.599652\pi$
$397$	−12.2729	−0.615957	−0.307978	+	0.951393i	$0.599652\pi$
$398$	−5.43685	−0.272525
$399$	−1.73988	−0.0871030
$400$	8.02316	0.401158
$401$	1.26743	0.0632922	0.0316461	−	0.999499i	$-0.489925\pi$
$401$	1.26743	0.0632922	0.0316461	+	0.999499i	$0.489925\pi$
$402$	−12.9204	−0.644412
$403$	8.38301	0.417588
$404$	−6.45542	−0.321169
$405$	1.43997	0.0715528
$406$	7.49683	0.372061
$407$	−0.0119030	−0.000590012 0
$408$	3.06243	0.151613
$409$	−17.3814	−0.859455	−0.429727	−	0.902959i	$-0.641390\pi$
$409$	−17.3814	−0.859455	−0.429727	+	0.902959i	$0.641390\pi$
$410$	−14.6655	−0.724275
$411$	−11.5071	−0.567604
$412$	7.04937	0.347298
$413$	7.24480	0.356494
$414$	−3.64870	−0.179324
$415$	3.82751	0.187885
$416$	−4.14135	−0.203046
$417$	18.1838	0.890463
$418$	4.82917	0.236202
$419$	19.2565	0.940743	0.470372	−	0.882468i	$-0.344120\pi$
$419$	19.2565	0.940743	0.470372	+	0.882468i	$0.344120\pi$
$420$	1.28761	0.0628291
$421$	37.5063	1.82794	0.913972	−	0.405777i	$-0.132999\pi$
$421$	37.5063	1.82794	0.913972	+	0.405777i	$0.132999\pi$
$422$	2.59689	0.126415
$423$	−6.47494	−0.314822
$424$	−9.19249	−0.446427
$425$	−2.92648	−0.141955
$426$	15.3264	0.742567
$427$	5.41924	0.262255
$428$	−4.94407	−0.238981
$429$	−6.03065	−0.291163
$430$	−5.09880	−0.245886
$431$	9.74557	0.469428	0.234714	−	0.972065i	$-0.424585\pi$
$431$	9.74557	0.469428	0.234714	+	0.972065i	$0.424585\pi$
$432$	−2.74157	−0.131904
$433$	−34.3295	−1.64977	−0.824884	−	0.565302i	$-0.808760\pi$
$433$	−34.3295	−1.64977	−0.824884	+	0.565302i	$0.808760\pi$
$434$	12.2026	0.585741
$435$	4.96091	0.237858
$436$	−7.01674	−0.336041
$437$	2.91734	0.139555
$438$	−5.56178	−0.265752
$439$	6.96917	0.332621	0.166310	−	0.986073i	$-0.446815\pi$
$439$	6.96917	0.332621	0.166310	+	0.986073i	$0.446815\pi$
$440$	−17.7896	−0.848084
$441$	−3.83727	−0.182727
$442$	−1.82919	−0.0870055
$443$	−6.65599	−0.316235	−0.158118	−	0.987420i	$-0.550543\pi$
$443$	−6.65599	−0.316235	−0.158118	+	0.987420i	$0.550543\pi$
$444$	−0.00148359	−7.04080e−5 0
$445$	−3.96317	−0.187872
$446$	24.4318	1.15688
$447$	7.04423	0.333181
$448$	−15.7795	−0.745513
$449$	36.8460	1.73887	0.869435	−	0.494048i	$-0.164483\pi$
$449$	36.8460	1.73887	0.869435	+	0.494048i	$0.164483\pi$
$450$	3.58084	0.168802
$451$	−33.5774	−1.58110
$452$	−2.10625	−0.0990695
$453$	6.11906	0.287499
$454$	−31.3492	−1.47129
$455$	−3.82828	−0.179473
$456$	2.99609	0.140305
$457$	0.0138535	0.000648040 0	0.000324020	−	1.00000i	$-0.499897\pi$
$457$	0.0138535	0.000648040 0	0.000324020		1.00000i	$0.499897\pi$
$458$	−34.7267	−1.62267
$459$	1.00000	0.0466760
$460$	−2.15900	−0.100664
$461$	26.3681	1.22809	0.614043	−	0.789273i	$-0.289542\pi$
$461$	26.3681	1.22809	0.614043	+	0.789273i	$0.289542\pi$
$462$	−8.77839	−0.408408
$463$	−1.86513	−0.0866799	−0.0433399	−	0.999060i	$-0.513800\pi$
$463$	−1.86513	−0.0866799	−0.0433399	+	0.999060i	$0.513800\pi$
$464$	−9.44512	−0.438479
$465$	8.07486	0.374463
$466$	3.99798	0.185203
$467$	−30.2276	−1.39876	−0.699382	−	0.714748i	$-0.746541\pi$
$467$	−30.2276	−1.39876	−0.699382	+	0.714748i	$0.746541\pi$
$468$	−0.751657	−0.0347454
$469$	−18.7788	−0.867126
$470$	11.4085	0.526235
$471$	1.00000	0.0460776
$472$	−12.4756	−0.574237
$473$	−11.6740	−0.536772
$474$	10.4515	0.480054
$475$	−2.86309	−0.131367
$476$	0.894194	0.0409853
$477$	−3.00170	−0.137438
$478$	−27.0549	−1.23746
$479$	−21.5174	−0.983154	−0.491577	−	0.870834i	$-0.663579\pi$
$479$	−21.5174	−0.983154	−0.491577	+	0.870834i	$0.663579\pi$
$480$	−3.98912	−0.182078
$481$	0.00441095	0.000201122 0
$482$	28.7162	1.30799
$483$	−5.30310	−0.241299
$484$	−2.65172	−0.120533
$485$	4.84201	0.219864
$486$	−1.22360	−0.0555036
$487$	18.2971	0.829123	0.414561	−	0.910021i	$-0.363935\pi$
$487$	18.2971	0.829123	0.414561	+	0.910021i	$0.363935\pi$
$488$	−9.33198	−0.422439
$489$	19.5803	0.885451
$490$	6.76107	0.305434
$491$	−7.88733	−0.355950	−0.177975	−	0.984035i	$-0.556955\pi$
$491$	−7.88733	−0.355950	−0.177975	+	0.984035i	$0.556955\pi$
$492$	−4.18508	−0.188678
$493$	3.44515	0.155162
$494$	−1.78956	−0.0805162
$495$	−5.80897	−0.261094
$496$	−15.3738	−0.690303
$497$	22.2758	0.999204
$498$	−3.25238	−0.145743
$499$	−0.669836	−0.0299860	−0.0149930	−	0.999888i	$-0.504773\pi$
$499$	−0.669836	−0.0299860	−0.0149930	+	0.999888i	$0.504773\pi$
$500$	5.73899	0.256655
$501$	−21.2436	−0.949094
$502$	−22.0045	−0.982108
$503$	36.3297	1.61986	0.809931	−	0.586526i	$-0.199505\pi$
$503$	36.3297	1.61986	0.809931	+	0.586526i	$0.199505\pi$
$504$	−5.44624	−0.242595
$505$	18.4875	0.822682
$506$	14.7192	0.654346
$507$	−10.7652	−0.478099
$508$	2.39318	0.106180
$509$	27.2873	1.20949	0.604744	−	0.796420i	$-0.293276\pi$
$509$	27.2873	1.20949	0.604744	+	0.796420i	$0.293276\pi$
$510$	−1.76195	−0.0780203
$511$	−8.08362	−0.357598
$512$	24.3867	1.07775
$513$	0.978337	0.0431946
$514$	−31.8596	−1.40527
$515$	−20.1885	−0.889610
$516$	−1.45504	−0.0640547
$517$	26.1205	1.14878
$518$	0.00642071	0.000282110 0
$519$	22.3508	0.981091
$520$	6.59233	0.289093
$521$	8.24738	0.361324	0.180662	−	0.983545i	$-0.442176\pi$
$521$	8.24738	0.361324	0.180662	+	0.983545i	$0.442176\pi$
$522$	−4.21548	−0.184506
$523$	6.24833	0.273220	0.136610	−	0.990625i	$-0.456379\pi$
$523$	6.24833	0.273220	0.136610	+	0.990625i	$0.456379\pi$
$524$	0.551868	0.0241085
$525$	5.20447	0.227142
$526$	35.0135	1.52666
$527$	5.60765	0.244273
$528$	11.0597	0.481313
$529$	−14.1080	−0.613393
$530$	5.28883	0.229732
$531$	−4.07376	−0.176786
$532$	0.874823	0.0379284
$533$	12.4429	0.538962
$534$	3.36766	0.145733
$535$	14.1592	0.612155
$536$	32.3373	1.39676
$537$	6.82845	0.294670
$538$	−5.89657	−0.254219
$539$	15.4799	0.666766
$540$	−0.724027	−0.0311572
$541$	−9.55644	−0.410863	−0.205432	−	0.978671i	$-0.565860\pi$
$541$	−9.55644	−0.410863	−0.205432	+	0.978671i	$0.565860\pi$
$542$	−9.96784	−0.428155
$543$	0.0495339	0.00212570
$544$	−2.77028	−0.118775
$545$	20.0950	0.860777
$546$	3.25304	0.139217
$547$	13.6758	0.584736	0.292368	−	0.956306i	$-0.405557\pi$
$547$	13.6758	0.584736	0.292368	+	0.956306i	$0.405557\pi$
$548$	5.78585	0.247159
$549$	−3.04725	−0.130053
$550$	−14.4454	−0.615954
$551$	3.37052	0.143589
$552$	9.13198	0.388683
$553$	15.1905	0.645964
$554$	33.3421	1.41657
$555$	0.00424881	0.000180352 0
$556$	−9.14292	−0.387746
$557$	30.1391	1.27703	0.638517	−	0.769608i	$-0.279548\pi$
$557$	30.1391	1.27703	0.638517	+	0.769608i	$0.279548\pi$
$558$	−6.86151	−0.290471
$559$	4.32608	0.182974
$560$	7.02077	0.296682
$561$	−4.03409	−0.170319
$562$	3.55110	0.149794
$563$	17.6923	0.745643	0.372821	−	0.927903i	$-0.378390\pi$
$563$	17.6923	0.745643	0.372821	+	0.927903i	$0.378390\pi$
$564$	3.25564	0.137087
$565$	6.03201	0.253769
$566$	−21.8131	−0.916875
$567$	−1.77841	−0.0746860
$568$	−38.3591	−1.60951
$569$	−10.5912	−0.444008	−0.222004	−	0.975046i	$-0.571260\pi$
$569$	−10.5912	−0.444008	−0.222004	+	0.975046i	$0.571260\pi$
$570$	−1.72378	−0.0722011
$571$	35.4429	1.48324	0.741619	−	0.670821i	$-0.234058\pi$
$571$	35.4429	1.48324	0.741619	+	0.670821i	$0.234058\pi$
$572$	3.03225	0.126785
$573$	−13.2905	−0.555217
$574$	18.1122	0.755991
$575$	−8.72659	−0.363924
$576$	8.87285	0.369702
$577$	−45.9966	−1.91486	−0.957432	−	0.288658i	$-0.906791\pi$
$577$	−45.9966	−1.91486	−0.957432	+	0.288658i	$0.906791\pi$
$578$	−1.22360	−0.0508950
$579$	10.7795	0.447982
$580$	−2.49438	−0.103573
$581$	−4.72709	−0.196113
$582$	−4.11444	−0.170549
$583$	12.1091	0.501508
$584$	13.9201	0.576016
$585$	2.15265	0.0890010
$586$	7.78110	0.321434
$587$	39.0590	1.61214	0.806070	−	0.591821i	$-0.201591\pi$
$587$	39.0590	1.61214	0.806070	+	0.591821i	$0.201591\pi$
$588$	1.92941	0.0795673
$589$	5.48617	0.226054
$590$	7.17776	0.295504
$591$	21.7139	0.893190
$592$	−0.00808933	−0.000332470 0
$593$	24.6123	1.01071	0.505353	−	0.862913i	$-0.331362\pi$
$593$	24.6123	1.01071	0.505353	+	0.862913i	$0.331362\pi$
$594$	4.93610	0.202531
$595$	−2.56085	−0.104985
$596$	−3.54189	−0.145081
$597$	4.44333	0.181853
$598$	−5.45452	−0.223052
$599$	40.9930	1.67493	0.837465	−	0.546492i	$-0.184037\pi$
$599$	40.9930	1.67493	0.837465	+	0.546492i	$0.184037\pi$
$600$	−8.96215	−0.365878
$601$	18.9194	0.771739	0.385869	−	0.922553i	$-0.373902\pi$
$601$	18.9194	0.771739	0.385869	+	0.922553i	$0.373902\pi$
$602$	6.29717	0.256653
$603$	10.5594	0.430011
$604$	−3.07670	−0.125189
$605$	7.59419	0.308748
$606$	−15.7095	−0.638156
$607$	−14.0761	−0.571330	−0.285665	−	0.958330i	$-0.592214\pi$
$607$	−14.0761	−0.571330	−0.285665	+	0.958330i	$0.592214\pi$
$608$	−2.71026	−0.109916
$609$	−6.12687	−0.248273
$610$	5.36909	0.217388
$611$	−9.67954	−0.391592
$612$	−0.502806	−0.0203247
$613$	−41.7383	−1.68579	−0.842897	−	0.538074i	$-0.819152\pi$
$613$	−41.7383	−1.68579	−0.842897	+	0.538074i	$0.819152\pi$
$614$	8.29254	0.334660
$615$	11.9855	0.483302
$616$	21.9706	0.885221
$617$	42.2403	1.70053	0.850266	−	0.526354i	$-0.176441\pi$
$617$	42.2403	1.70053	0.850266	+	0.526354i	$0.176441\pi$
$618$	17.1549	0.690072
$619$	0.835762	0.0335921	0.0167960	−	0.999859i	$-0.494653\pi$
$619$	0.835762	0.0335921	0.0167960	+	0.999859i	$0.494653\pi$
$620$	−4.06009	−0.163057
$621$	2.98194	0.119661
$622$	23.7197	0.951074
$623$	4.89463	0.196099
$624$	−4.09844	−0.164069
$625$	−1.80330	−0.0721318
$626$	−20.4236	−0.816291
$627$	−3.94670	−0.157616
$628$	−0.502806	−0.0200642
$629$	0.00295062	0.000117649 0
$630$	3.13346	0.124840
$631$	−31.9472	−1.27180	−0.635898	−	0.771773i	$-0.719370\pi$
$631$	−31.9472	−1.27180	−0.635898	+	0.771773i	$0.719370\pi$
$632$	−26.1581	−1.04051
$633$	−2.12234	−0.0843553
$634$	−33.5119	−1.33093
$635$	−6.85376	−0.271983
$636$	1.50927	0.0598466
$637$	−5.73643	−0.227286
$638$	17.0056	0.673258
$639$	−12.5257	−0.495509
$640$	−7.65526	−0.302601
$641$	−14.6474	−0.578536	−0.289268	−	0.957248i	$-0.593412\pi$
$641$	−14.6474	−0.578536	−0.289268	+	0.957248i	$0.593412\pi$
$642$	−12.0316	−0.474849
$643$	−28.1866	−1.11157	−0.555786	−	0.831325i	$-0.687583\pi$
$643$	−28.1866	−1.11157	−0.555786	+	0.831325i	$0.687583\pi$
$644$	2.66643	0.105072
$645$	4.16705	0.164078
$646$	−1.19709	−0.0470990
$647$	33.0682	1.30005	0.650023	−	0.759915i	$-0.274759\pi$
$647$	33.0682	1.30005	0.650023	+	0.759915i	$0.274759\pi$
$648$	3.06243	0.120304
$649$	16.4339	0.645087
$650$	5.35308	0.209965
$651$	−9.97268	−0.390860
$652$	−9.84509	−0.385563
$653$	10.5888	0.414373	0.207187	−	0.978301i	$-0.433569\pi$
$653$	10.5888	0.414373	0.207187	+	0.978301i	$0.433569\pi$
$654$	−17.0755	−0.667705
$655$	−1.58048	−0.0617544
$656$	−22.8193	−0.890944
$657$	4.54543	0.177334
$658$	−14.0898	−0.549279
$659$	−35.0849	−1.36671	−0.683357	−	0.730085i	$-0.739481\pi$
$659$	−35.0849	−1.36671	−0.683357	+	0.730085i	$0.739481\pi$
$660$	2.92079	0.113691
$661$	39.3829	1.53182	0.765909	−	0.642949i	$-0.222289\pi$
$661$	39.3829	1.53182	0.765909	+	0.642949i	$0.222289\pi$
$662$	−28.3090	−1.10026
$663$	1.49492	0.0580580
$664$	8.14008	0.315896
$665$	−2.50538	−0.0971544
$666$	−0.00361037	−0.000139899 0
$667$	10.2732	0.397781
$668$	10.6814	0.413277
$669$	−19.9671	−0.771974
$670$	−18.6051	−0.718776
$671$	12.2929	0.474560
$672$	4.92668	0.190051
$673$	−31.4479	−1.21223	−0.606114	−	0.795378i	$-0.707273\pi$
$673$	−31.4479	−1.21223	−0.606114	+	0.795378i	$0.707273\pi$
$674$	−13.1283	−0.505683
$675$	−2.92648	−0.112640
$676$	5.41281	0.208185
$677$	−24.8759	−0.956059	−0.478030	−	0.878344i	$-0.658649\pi$
$677$	−24.8759	−0.956059	−0.478030	+	0.878344i	$0.658649\pi$
$678$	−5.12563	−0.196849
$679$	−5.98002	−0.229492
$680$	4.40981	0.169109
$681$	25.6205	0.981779
$682$	27.6799	1.05992
$683$	−43.0324	−1.64659	−0.823294	−	0.567616i	$-0.807866\pi$
$683$	−43.0324	−1.64659	−0.823294	+	0.567616i	$0.807866\pi$
$684$	−0.491914	−0.0188088
$685$	−16.5699	−0.633104
$686$	−23.5825	−0.900384
$687$	28.3808	1.08279
$688$	−7.93369	−0.302469
$689$	−4.48731	−0.170953
$690$	−5.25402	−0.200017
$691$	9.68382	0.368390	0.184195	−	0.982890i	$-0.441032\pi$
$691$	9.68382	0.368390	0.184195	+	0.982890i	$0.441032\pi$
$692$	−11.2381	−0.427209
$693$	7.17424	0.272527
$694$	−5.69932	−0.216343
$695$	26.1841	0.993220
$696$	10.5505	0.399917
$697$	8.32343	0.315273
$698$	29.9790	1.13472
$699$	−3.26740	−0.123584
$700$	−2.61684	−0.0989073
$701$	−5.20454	−0.196573	−0.0982864	−	0.995158i	$-0.531336\pi$
$701$	−5.20454	−0.196573	−0.0982864	+	0.995158i	$0.531336\pi$
$702$	−1.82919	−0.0690382
$703$	0.00288670	0.000108874 0
$704$	−35.7938	−1.34903
$705$	−9.32373	−0.351152
$706$	22.8974	0.861756
$707$	−22.8326	−0.858707
$708$	2.04831	0.0769804
$709$	50.1566	1.88367	0.941835	−	0.336076i	$-0.109100\pi$
$709$	50.1566	1.88367	0.941835	+	0.336076i	$0.109100\pi$
$710$	22.0696	0.828258
$711$	−8.54162	−0.320336
$712$	−8.42860	−0.315875
$713$	16.7217	0.626232
$714$	2.17605	0.0814368
$715$	−8.68396	−0.324762
$716$	−3.43339	−0.128312
$717$	22.1109	0.825747
$718$	−36.3001	−1.35471
$719$	−4.83288	−0.180236	−0.0901180	−	0.995931i	$-0.528724\pi$
$719$	−4.83288	−0.180236	−0.0901180	+	0.995931i	$0.528724\pi$
$720$	−3.94779	−0.147125
$721$	24.9333	0.928566
$722$	22.0772	0.821629
$723$	−23.4687	−0.872810
$724$	−0.0249060	−0.000925623 0
$725$	−10.0822	−0.374442
$726$	−6.45307	−0.239496
$727$	27.0232	1.00224	0.501118	−	0.865379i	$-0.332922\pi$
$727$	27.0232	1.00224	0.501118	+	0.865379i	$0.332922\pi$
$728$	−8.14172	−0.301752
$729$	1.00000	0.0370370
$730$	−8.00881	−0.296419
$731$	2.89385	0.107033
$732$	1.53217	0.0566308
$733$	−42.9678	−1.58705	−0.793526	−	0.608537i	$-0.791757\pi$
$733$	−42.9678	−1.58705	−0.793526	+	0.608537i	$0.791757\pi$
$734$	−27.9458	−1.03150
$735$	−5.52556	−0.203813
$736$	−8.26079	−0.304497
$737$	−42.5974	−1.56910
$738$	−10.1845	−0.374898
$739$	16.8426	0.619566	0.309783	−	0.950807i	$-0.399744\pi$
$739$	16.8426	0.619566	0.309783	+	0.950807i	$0.399744\pi$
$740$	−0.00213633	−7.85329e−5 0
$741$	1.46254	0.0537277
$742$	−6.53186	−0.239792
$743$	−26.9717	−0.989496	−0.494748	−	0.869037i	$-0.664740\pi$
$743$	−26.9717	−0.989496	−0.494748	+	0.869037i	$0.664740\pi$
$744$	17.1730	0.629594
$745$	10.1435	0.371629
$746$	−37.1169	−1.35895
$747$	2.65805	0.0972528
$748$	2.02836	0.0741643
$749$	−17.4870	−0.638961
$750$	13.9660	0.509968
$751$	−7.93966	−0.289722	−0.144861	−	0.989452i	$-0.546274\pi$
$751$	−7.93966	−0.289722	−0.144861	+	0.989452i	$0.546274\pi$
$752$	17.7515	0.647331
$753$	17.9834	0.655352
$754$	−6.30182	−0.229499
$755$	8.81127	0.320675
$756$	0.894194	0.0325215
$757$	−11.5997	−0.421600	−0.210800	−	0.977529i	$-0.567607\pi$
$757$	−11.5997	−0.421600	−0.210800	+	0.977529i	$0.567607\pi$
$758$	45.2328	1.64293
$759$	−12.0294	−0.436639
$760$	4.31428	0.156496
$761$	19.0430	0.690309	0.345154	−	0.938546i	$-0.387827\pi$
$761$	19.0430	0.690309	0.345154	+	0.938546i	$0.387827\pi$
$762$	5.82390	0.210978
$763$	−24.8179	−0.898470
$764$	6.68253	0.241765
$765$	1.43997	0.0520623
$766$	27.4471	0.991703
$767$	−6.08997	−0.219896
$768$	−11.2407	−0.405615
$769$	18.8111	0.678345	0.339173	−	0.940724i	$-0.389853\pi$
$769$	18.8111	0.678345	0.339173	+	0.940724i	$0.389853\pi$
$770$	−12.6406	−0.455537
$771$	26.0376	0.937722
$772$	−5.42002	−0.195071
$773$	43.1808	1.55310	0.776552	−	0.630053i	$-0.216967\pi$
$773$	43.1808	1.55310	0.776552	+	0.630053i	$0.216967\pi$
$774$	−3.54091	−0.127275
$775$	−16.4107	−0.589489
$776$	10.2976	0.369664
$777$	−0.00524740	−0.000188249 0
$778$	−34.2279	−1.22713
$779$	8.14312	0.291758
$780$	−1.08237	−0.0387549
$781$	50.5297	1.80810
$782$	−3.64870	−0.130477
$783$	3.44515	0.123120
$784$	10.5202	0.375720
$785$	1.43997	0.0513948
$786$	1.34299	0.0479029
$787$	−16.7278	−0.596282	−0.298141	−	0.954522i	$-0.596367\pi$
$787$	−16.7278	−0.596282	−0.298141	+	0.954522i	$0.596367\pi$
$788$	−10.9179	−0.388933
$789$	−28.6152	−1.01873
$790$	15.0499	0.535451
$791$	−7.44971	−0.264881
$792$	−12.3541	−0.438984
$793$	−4.55540	−0.161767
$794$	15.0170	0.532935
$795$	−4.32236	−0.153298
$796$	−2.23413	−0.0791868
$797$	40.8113	1.44561	0.722805	−	0.691052i	$-0.242853\pi$
$797$	40.8113	1.44561	0.722805	+	0.691052i	$0.242853\pi$
$798$	2.12892	0.0753628
$799$	−6.47494	−0.229067
$800$	8.10716	0.286632
$801$	−2.75226	−0.0972462
$802$	−1.55082	−0.0547614
$803$	−18.3366	−0.647086
$804$	−5.30932	−0.187245
$805$	−7.63631	−0.269145
$806$	−10.2574	−0.361303
$807$	4.81904	0.169638
$808$	39.3179	1.38320
$809$	41.2829	1.45143	0.725714	−	0.687996i	$-0.241509\pi$
$809$	41.2829	1.45143	0.725714	+	0.687996i	$0.241509\pi$
$810$	−1.76195	−0.0619085
$811$	−22.2285	−0.780548	−0.390274	−	0.920699i	$-0.627620\pi$
$811$	−22.2285	−0.780548	−0.390274	+	0.920699i	$0.627620\pi$
$812$	3.08063	0.108109
$813$	8.14633	0.285704
$814$	0.0145645	0.000510487 0
$815$	28.1950	0.987629
$816$	−2.74157	−0.0959742
$817$	2.83116	0.0990496
$818$	21.2679	0.743613
$819$	−2.65858	−0.0928983
$820$	−6.02639	−0.210451
$821$	53.4128	1.86412	0.932060	−	0.362303i	$-0.118009\pi$
$821$	53.4128	1.86412	0.932060	+	0.362303i	$0.118009\pi$
$822$	14.0801	0.491100
$823$	−46.8531	−1.63320	−0.816598	−	0.577206i	$-0.804143\pi$
$823$	−46.8531	−1.63320	−0.816598	+	0.577206i	$0.804143\pi$
$824$	−42.9354	−1.49573
$825$	11.8057	0.411021
$826$	−8.86473	−0.308444
$827$	−41.2175	−1.43327	−0.716637	−	0.697446i	$-0.754320\pi$
$827$	−41.2175	−1.43327	−0.716637	+	0.697446i	$0.754320\pi$
$828$	−1.49934	−0.0521056
$829$	43.5296	1.51185	0.755924	−	0.654660i	$-0.227188\pi$
$829$	43.5296	1.51185	0.755924	+	0.654660i	$0.227188\pi$
$830$	−4.68334	−0.162561
$831$	−27.2492	−0.945265
$832$	13.2642	0.459855
$833$	−3.83727	−0.132954
$834$	−22.2496	−0.770442
$835$	−30.5902	−1.05862
$836$	1.98442	0.0686327
$837$	5.60765	0.193829
$838$	−23.5623	−0.813945
$839$	−5.90659	−0.203918	−0.101959	−	0.994789i	$-0.532511\pi$
$839$	−5.90659	−0.203918	−0.101959	+	0.994789i	$0.532511\pi$
$840$	−7.84244	−0.270590
$841$	−17.1310	−0.590723
$842$	−45.8926	−1.58156
$843$	−2.90218	−0.0999564
$844$	1.06712	0.0367320
$845$	−15.5016	−0.533271
$846$	7.92273	0.272389
$847$	−9.37904	−0.322267
$848$	8.22937	0.282598
$849$	17.8270	0.611822
$850$	3.58084	0.122822
$851$	0.00879856	0.000301611 0
$852$	6.29800	0.215766
$853$	−33.8417	−1.15872	−0.579359	−	0.815073i	$-0.696697\pi$
$853$	−33.8417	−1.15872	−0.579359	+	0.815073i	$0.696697\pi$
$854$	−6.63097	−0.226907
$855$	1.40878	0.0481792
$856$	30.1127	1.02923
$857$	30.6365	1.04652	0.523261	−	0.852172i	$-0.324715\pi$
$857$	30.6365	1.04652	0.523261	+	0.852172i	$0.324715\pi$
$858$	7.37909	0.251918
$859$	20.2674	0.691514	0.345757	−	0.938324i	$-0.387622\pi$
$859$	20.2674	0.691514	0.345757	+	0.938324i	$0.387622\pi$
$860$	−2.09522	−0.0714465
$861$	−14.8024	−0.504466
$862$	−11.9247	−0.406156
$863$	2.70101	0.0919434	0.0459717	−	0.998943i	$-0.485362\pi$
$863$	2.70101	0.0919434	0.0459717	+	0.998943i	$0.485362\pi$
$864$	−2.77028	−0.0942467
$865$	32.1845	1.09431
$866$	42.0055	1.42740
$867$	1.00000	0.0339618
$868$	5.01433	0.170197
$869$	34.4576	1.16889
$870$	−6.07017	−0.205798
$871$	15.7855	0.534870
$872$	42.7367	1.44725
$873$	3.36257	0.113806
$874$	−3.56965	−0.120745
$875$	20.2986	0.686217
$876$	−2.28547	−0.0772189
$877$	6.05186	0.204357	0.102178	−	0.994766i	$-0.467419\pi$
$877$	6.05186	0.204357	0.102178	+	0.994766i	$0.467419\pi$
$878$	−8.52747	−0.287788
$879$	−6.35919	−0.214490
$880$	15.9257	0.536856
$881$	26.6644	0.898348	0.449174	−	0.893444i	$-0.351718\pi$
$881$	26.6644	0.898348	0.449174	+	0.893444i	$0.351718\pi$
$882$	4.69528	0.158098
$883$	−25.8013	−0.868283	−0.434142	−	0.900845i	$-0.642948\pi$
$883$	−25.8013	−0.868283	−0.434142	+	0.900845i	$0.642948\pi$
$884$	−0.751657	−0.0252810
$885$	−5.86610	−0.197187
$886$	8.14426	0.273612
$887$	−6.48143	−0.217625	−0.108813	−	0.994062i	$-0.534705\pi$
$887$	−6.48143	−0.217625	−0.108813	+	0.994062i	$0.534705\pi$
$888$	0.00903606	0.000303230 0
$889$	8.46459	0.283893
$890$	4.84933	0.162550
$891$	−4.03409	−0.135147
$892$	10.0396	0.336151
$893$	−6.33468	−0.211982
$894$	−8.61932	−0.288273
$895$	9.83278	0.328674
$896$	9.45446	0.315851
$897$	4.45777	0.148841
$898$	−45.0847	−1.50450
$899$	19.3192	0.644331
$900$	1.47145	0.0490485
$901$	−3.00170	−0.100001
$902$	41.0853	1.36799
$903$	−5.14643	−0.171263
$904$	12.8285	0.426668
$905$	0.0713274	0.00237100
$906$	−7.48727	−0.248748
$907$	−42.7587	−1.41978	−0.709890	−	0.704312i	$-0.751255\pi$
$907$	−42.7587	−1.41978	−0.709890	+	0.704312i	$0.751255\pi$
$908$	−12.8821	−0.427509
$909$	12.8388	0.425836
$910$	4.68428	0.155282
$911$	23.1259	0.766197	0.383098	−	0.923708i	$-0.374857\pi$
$911$	23.1259	0.766197	0.383098	+	0.923708i	$0.374857\pi$
$912$	−2.68218	−0.0888159
$913$	−10.7228	−0.354872
$914$	−0.0169511	−0.000560694 0
$915$	−4.38795	−0.145061
$916$	−14.2700	−0.471495
$917$	1.95193	0.0644585
$918$	−1.22360	−0.0403848
$919$	19.6361	0.647734	0.323867	−	0.946103i	$-0.395017\pi$
$919$	19.6361	0.647734	0.323867	+	0.946103i	$0.395017\pi$
$920$	13.1498	0.433536
$921$	−6.77718	−0.223316
$922$	−32.2640	−1.06256
$923$	−18.7250	−0.616339
$924$	−3.60725	−0.118670
$925$	−0.00863493	−0.000283915 0
$926$	2.28217	0.0749967
$927$	−14.0201	−0.460479
$928$	−9.54401	−0.313297
$929$	45.2482	1.48455	0.742273	−	0.670097i	$-0.233748\pi$
$929$	45.2482	1.48455	0.742273	+	0.670097i	$0.233748\pi$
$930$	−9.88039	−0.323991
$931$	−3.75415	−0.123037
$932$	1.64287	0.0538139
$933$	−19.3852	−0.634644
$934$	36.9864	1.21023
$935$	−5.80897	−0.189974
$936$	4.57810	0.149640
$937$	18.4117	0.601485	0.300743	−	0.953705i	$-0.402766\pi$
$937$	18.4117	0.601485	0.300743	+	0.953705i	$0.402766\pi$
$938$	22.9778	0.750251
$939$	16.6914	0.544704
$940$	4.68803	0.152907
$941$	−35.6431	−1.16193	−0.580966	−	0.813928i	$-0.697325\pi$
$941$	−35.6431	−1.16193	−0.580966	+	0.813928i	$0.697325\pi$
$942$	−1.22360	−0.0398670
$943$	24.8200	0.808249
$944$	11.1685	0.363504
$945$	−2.56085	−0.0833046
$946$	14.2843	0.464423
$947$	48.0440	1.56122	0.780611	−	0.625018i	$-0.214908\pi$
$947$	48.0440	1.56122	0.780611	+	0.625018i	$0.214908\pi$
$948$	4.29478	0.139488
$949$	6.79507	0.220577
$950$	3.50327	0.113661
$951$	27.3880	0.888116
$952$	−5.44624	−0.176514
$953$	35.2943	1.14329	0.571647	−	0.820500i	$-0.306305\pi$
$953$	35.2943	1.14329	0.571647	+	0.820500i	$0.306305\pi$
$954$	3.67287	0.118914
$955$	−19.1379	−0.619287
$956$	−11.1175	−0.359566
$957$	−13.8980	−0.449259
$958$	26.3286	0.850640
$959$	20.4643	0.660828
$960$	12.7767	0.412365
$961$	0.445750	0.0143790
$962$	−0.00539723	−0.000174014 0
$963$	9.83296	0.316863
$964$	11.8002	0.380059
$965$	15.5222	0.499678
$966$	6.48886	0.208776
$967$	20.8179	0.669459	0.334729	−	0.942314i	$-0.391355\pi$
$967$	20.8179	0.669459	0.334729	+	0.942314i	$0.391355\pi$
$968$	16.1508	0.519106
$969$	0.978337	0.0314287
$970$	−5.92468	−0.190230
$971$	0.0226047	0.000725421 0	0.000362710	−	1.00000i	$-0.499885\pi$
$971$	0.0226047	0.000725421 0	0.000362710		1.00000i	$0.499885\pi$
$972$	−0.502806	−0.0161275
$973$	−32.3381	−1.03671
$974$	−22.3884	−0.717370
$975$	−4.37487	−0.140108
$976$	8.35425	0.267413
$977$	11.1634	0.357148	0.178574	−	0.983926i	$-0.442852\pi$
$977$	11.1634	0.357148	0.178574	+	0.983926i	$0.442852\pi$
$978$	−23.9584	−0.766105
$979$	11.1028	0.354848
$980$	2.77829	0.0887492
$981$	13.9552	0.445554
$982$	9.65092	0.307973
$983$	−33.9837	−1.08391	−0.541956	−	0.840407i	$-0.682316\pi$
$983$	−33.9837	−1.08391	−0.541956	+	0.840407i	$0.682316\pi$
$984$	25.4899	0.812589
$985$	31.2674	0.996261
$986$	−4.21548	−0.134248
$987$	11.5151	0.366529
$988$	−0.735374	−0.0233954
$989$	8.62927	0.274395
$990$	7.10785	0.225902
$991$	−55.6265	−1.76703	−0.883517	−	0.468400i	$-0.844831\pi$
$991$	−55.6265	−1.76703	−0.883517	+	0.468400i	$0.844831\pi$
$992$	−15.5347	−0.493229
$993$	23.1358	0.734194
$994$	−27.2566	−0.864527
$995$	6.39826	0.202839
$996$	−1.33648	−0.0423481
$997$	−19.7876	−0.626680	−0.313340	−	0.949641i	$-0.601448\pi$
$997$	−19.7876	−0.626680	−0.313340	+	0.949641i	$0.601448\pi$
$998$	0.819610	0.0259443
$999$	0.00295062	9.33534e−5 0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.i.1.18	✓	63

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.i.1.18	✓	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)

\(f(q)\)	\(=\)	\(q-1.22360 q^{2} +1.00000 q^{3} -0.502806 q^{4} +1.43997 q^{5} -1.22360 q^{6} -1.77841 q^{7} +3.06243 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.22360 q^{2} +1.00000 q^{3} -0.502806 q^{4} +1.43997 q^{5} -1.22360 q^{6} -1.77841 q^{7} +3.06243 q^{8} +1.00000 q^{9} -1.76195 q^{10} -4.03409 q^{11} -0.502806 q^{12} +1.49492 q^{13} +2.17605 q^{14} +1.43997 q^{15} -2.74157 q^{16} +1.00000 q^{17} -1.22360 q^{18} +0.978337 q^{19} -0.724027 q^{20} -1.77841 q^{21} +4.93610 q^{22} +2.98194 q^{23} +3.06243 q^{24} -2.92648 q^{25} -1.82919 q^{26} +1.00000 q^{27} +0.894194 q^{28} +3.44515 q^{29} -1.76195 q^{30} +5.60765 q^{31} -2.77028 q^{32} -4.03409 q^{33} -1.22360 q^{34} -2.56085 q^{35} -0.502806 q^{36} +0.00295062 q^{37} -1.19709 q^{38} +1.49492 q^{39} +4.40981 q^{40} +8.32343 q^{41} +2.17605 q^{42} +2.89385 q^{43} +2.02836 q^{44} +1.43997 q^{45} -3.64870 q^{46} -6.47494 q^{47} -2.74157 q^{48} -3.83727 q^{49} +3.58084 q^{50} +1.00000 q^{51} -0.751657 q^{52} -3.00170 q^{53} -1.22360 q^{54} -5.80897 q^{55} -5.44624 q^{56} +0.978337 q^{57} -4.21548 q^{58} -4.07376 q^{59} -0.724027 q^{60} -3.04725 q^{61} -6.86151 q^{62} -1.77841 q^{63} +8.87285 q^{64} +2.15265 q^{65} +4.93610 q^{66} +10.5594 q^{67} -0.502806 q^{68} +2.98194 q^{69} +3.13346 q^{70} -12.5257 q^{71} +3.06243 q^{72} +4.54543 q^{73} -0.00361037 q^{74} -2.92648 q^{75} -0.491914 q^{76} +7.17424 q^{77} -1.82919 q^{78} -8.54162 q^{79} -3.94779 q^{80} +1.00000 q^{81} -10.1845 q^{82} +2.65805 q^{83} +0.894194 q^{84} +1.43997 q^{85} -3.54091 q^{86} +3.44515 q^{87} -12.3541 q^{88} -2.75226 q^{89} -1.76195 q^{90} -2.65858 q^{91} -1.49934 q^{92} +5.60765 q^{93} +7.92273 q^{94} +1.40878 q^{95} -2.77028 q^{96} +3.36257 q^{97} +4.69528 q^{98} -4.03409 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 63 q + 10 q^{2} + 63 q^{3} + 70 q^{4} + 19 q^{5} + 10 q^{6} + 11 q^{7} + 27 q^{8} + 63 q^{9}+O(q^{10}) \) 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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