LMFDB - Embedded newform 8015.2.a.j.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8015,2,Mod(1,8015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8015, 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("8015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8015 = 5 \cdot 7 \cdot 229 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8015.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:	$64.0000972201$
Analytic rank:	$1$
Dimension:	$45$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	8015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.24619 q^{2} -2.43741 q^{3} +3.04539 q^{4} -1.00000 q^{5} +5.47490 q^{6} +1.00000 q^{7} -2.34814 q^{8} +2.94098 q^{9} +O(q^{10})$	\(q-2.24619 q^{2} -2.43741 q^{3} +3.04539 q^{4} -1.00000 q^{5} +5.47490 q^{6} +1.00000 q^{7} -2.34814 q^{8} +2.94098 q^{9} +2.24619 q^{10} +1.14908 q^{11} -7.42286 q^{12} +4.80403 q^{13} -2.24619 q^{14} +2.43741 q^{15} -0.816398 q^{16} -3.50679 q^{17} -6.60600 q^{18} +0.197880 q^{19} -3.04539 q^{20} -2.43741 q^{21} -2.58105 q^{22} -0.962736 q^{23} +5.72338 q^{24} +1.00000 q^{25} -10.7908 q^{26} +0.143863 q^{27} +3.04539 q^{28} +8.64229 q^{29} -5.47490 q^{30} -1.42016 q^{31} +6.53006 q^{32} -2.80078 q^{33} +7.87694 q^{34} -1.00000 q^{35} +8.95641 q^{36} -7.38160 q^{37} -0.444477 q^{38} -11.7094 q^{39} +2.34814 q^{40} +9.00264 q^{41} +5.47490 q^{42} +3.53476 q^{43} +3.49938 q^{44} -2.94098 q^{45} +2.16249 q^{46} +3.51739 q^{47} +1.98990 q^{48} +1.00000 q^{49} -2.24619 q^{50} +8.54750 q^{51} +14.6301 q^{52} -12.7340 q^{53} -0.323144 q^{54} -1.14908 q^{55} -2.34814 q^{56} -0.482316 q^{57} -19.4123 q^{58} +9.36095 q^{59} +7.42286 q^{60} -10.2127 q^{61} +3.18995 q^{62} +2.94098 q^{63} -13.0350 q^{64} -4.80403 q^{65} +6.29108 q^{66} -13.0584 q^{67} -10.6795 q^{68} +2.34658 q^{69} +2.24619 q^{70} +2.95253 q^{71} -6.90582 q^{72} +0.0874720 q^{73} +16.5805 q^{74} -2.43741 q^{75} +0.602622 q^{76} +1.14908 q^{77} +26.3016 q^{78} -9.09873 q^{79} +0.816398 q^{80} -9.17358 q^{81} -20.2217 q^{82} -11.0703 q^{83} -7.42286 q^{84} +3.50679 q^{85} -7.93975 q^{86} -21.0648 q^{87} -2.69819 q^{88} +9.84309 q^{89} +6.60600 q^{90} +4.80403 q^{91} -2.93190 q^{92} +3.46151 q^{93} -7.90074 q^{94} -0.197880 q^{95} -15.9165 q^{96} -7.29301 q^{97} -2.24619 q^{98} +3.37941 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 45 q - 6 q^{2} + 34 q^{4} - 45 q^{5} + q^{6} + 45 q^{7} - 15 q^{8} + 29 q^{9}+O(q^{10}) $ 45 * q - 6 * q^2 + 34 * q^4 - 45 * q^5 + q^6 + 45 * q^7 - 15 * q^8 + 29 * q^9	\( 45 q - 6 q^{2} + 34 q^{4} - 45 q^{5} + q^{6} + 45 q^{7} - 15 q^{8} + 29 q^{9} + 6 q^{10} - q^{11} - 3 q^{12} - 21 q^{13} - 6 q^{14} + 8 q^{16} - 7 q^{17} - 36 q^{18} - 20 q^{19} - 34 q^{20} - 34 q^{22} - 22 q^{23} - 11 q^{24} + 45 q^{25} - q^{26} + 12 q^{27} + 34 q^{28} + 10 q^{29} - q^{30} - 27 q^{31} - 26 q^{32} - 39 q^{33} - 13 q^{34} - 45 q^{35} - 3 q^{36} - 72 q^{37} + 2 q^{38} - 37 q^{39} + 15 q^{40} - 4 q^{41} + q^{42} - 49 q^{43} + 5 q^{44} - 29 q^{45} - 67 q^{46} + 2 q^{47} + 8 q^{48} + 45 q^{49} - 6 q^{50} - 49 q^{51} - 47 q^{52} - 35 q^{53} - 12 q^{54} + q^{55} - 15 q^{56} - 77 q^{57} - 50 q^{58} + 4 q^{59} + 3 q^{60} - 36 q^{61} + 17 q^{62} + 29 q^{63} + 5 q^{64} + 21 q^{65} - 8 q^{66} - 80 q^{67} + 27 q^{68} + 9 q^{69} + 6 q^{70} - 12 q^{71} - 97 q^{72} - 55 q^{73} + 32 q^{74} - 37 q^{76} - q^{77} + 20 q^{78} - 94 q^{79} - 8 q^{80} - 19 q^{81} - 36 q^{82} + 24 q^{83} - 3 q^{84} + 7 q^{85} - 3 q^{86} - 4 q^{87} - 95 q^{88} + q^{89} + 36 q^{90} - 21 q^{91} - 65 q^{92} - 71 q^{93} - 53 q^{94} + 20 q^{95} - 13 q^{96} - 110 q^{97} - 6 q^{98} - 27 q^{99}+O(q^{100}) \) 45 * q - 6 * q^2 + 34 * q^4 - 45 * q^5 + q^6 + 45 * q^7 - 15 * q^8 + 29 * q^9 + 6 * q^10 - q^11 - 3 * q^12 - 21 * q^13 - 6 * q^14 + 8 * q^16 - 7 * q^17 - 36 * q^18 - 20 * q^19 - 34 * q^20 - 34 * q^22 - 22 * q^23 - 11 * q^24 + 45 * q^25 - q^26 + 12 * q^27 + 34 * q^28 + 10 * q^29 - q^30 - 27 * q^31 - 26 * q^32 - 39 * q^33 - 13 * q^34 - 45 * q^35 - 3 * q^36 - 72 * q^37 + 2 * q^38 - 37 * q^39 + 15 * q^40 - 4 * q^41 + q^42 - 49 * q^43 + 5 * q^44 - 29 * q^45 - 67 * q^46 + 2 * q^47 + 8 * q^48 + 45 * q^49 - 6 * q^50 - 49 * q^51 - 47 * q^52 - 35 * q^53 - 12 * q^54 + q^55 - 15 * q^56 - 77 * q^57 - 50 * q^58 + 4 * q^59 + 3 * q^60 - 36 * q^61 + 17 * q^62 + 29 * q^63 + 5 * q^64 + 21 * q^65 - 8 * q^66 - 80 * q^67 + 27 * q^68 + 9 * q^69 + 6 * q^70 - 12 * q^71 - 97 * q^72 - 55 * q^73 + 32 * q^74 - 37 * q^76 - q^77 + 20 * q^78 - 94 * q^79 - 8 * q^80 - 19 * q^81 - 36 * q^82 + 24 * q^83 - 3 * q^84 + 7 * q^85 - 3 * q^86 - 4 * q^87 - 95 * q^88 + q^89 + 36 * q^90 - 21 * q^91 - 65 * q^92 - 71 * q^93 - 53 * q^94 + 20 * q^95 - 13 * q^96 - 110 * q^97 - 6 * q^98 - 27 * 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 $

$2$	−2.24619	−1.58830	−0.794149	−	0.607723i	$-0.792083\pi$
$2$	−2.24619	−1.58830	−0.794149	+	0.607723i	$0.792083\pi$
$3$	−2.43741	−1.40724	−0.703620	−	0.710576i	$-0.748434\pi$
$3$	−2.43741	−1.40724	−0.703620	+	0.710576i	$0.748434\pi$
$4$	3.04539	1.52269
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	5.47490	2.23512
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−2.34814	−0.830192
$9$	2.94098	0.980326
$10$	2.24619	0.710309
$11$	1.14908	0.346460	0.173230	−	0.984881i	$-0.444580\pi$
$11$	1.14908	0.346460	0.173230	+	0.984881i	$0.444580\pi$
$12$	−7.42286	−2.14279
$13$	4.80403	1.33240	0.666199	−	0.745774i	$-0.267920\pi$
$13$	4.80403	1.33240	0.666199	+	0.745774i	$0.267920\pi$
$14$	−2.24619	−0.600320
$15$	2.43741	0.629337
$16$	−0.816398	−0.204099
$17$	−3.50679	−0.850522	−0.425261	−	0.905071i	$-0.639818\pi$
$17$	−3.50679	−0.850522	−0.425261	+	0.905071i	$0.639818\pi$
$18$	−6.60600	−1.55705
$19$	0.197880	0.0453968	0.0226984	−	0.999742i	$-0.492774\pi$
$19$	0.197880	0.0453968	0.0226984	+	0.999742i	$0.492774\pi$
$20$	−3.04539	−0.680969
$21$	−2.43741	−0.531887
$22$	−2.58105	−0.550282
$23$	−0.962736	−0.200744	−0.100372	−	0.994950i	$-0.532003\pi$
$23$	−0.962736	−0.200744	−0.100372	+	0.994950i	$0.532003\pi$
$24$	5.72338	1.16828
$25$	1.00000	0.200000
$26$	−10.7908	−2.11625
$27$	0.143863	0.0276864
$28$	3.04539	0.575524
$29$	8.64229	1.60483	0.802417	−	0.596764i	$-0.203547\pi$
$29$	8.64229	1.60483	0.802417	+	0.596764i	$0.203547\pi$
$30$	−5.47490	−0.999575
$31$	−1.42016	−0.255068	−0.127534	−	0.991834i	$-0.540706\pi$
$31$	−1.42016	−0.255068	−0.127534	+	0.991834i	$0.540706\pi$
$32$	6.53006	1.15436
$33$	−2.80078	−0.487553
$34$	7.87694	1.35088
$35$	−1.00000	−0.169031
$36$	8.95641	1.49273
$37$	−7.38160	−1.21353	−0.606764	−	0.794882i	$-0.707533\pi$
$37$	−7.38160	−1.21353	−0.606764	+	0.794882i	$0.707533\pi$
$38$	−0.444477	−0.0721038
$39$	−11.7094	−1.87500
$40$	2.34814	0.371273
$41$	9.00264	1.40598	0.702988	−	0.711202i	$-0.251849\pi$
$41$	9.00264	1.40598	0.702988	+	0.711202i	$0.251849\pi$
$42$	5.47490	0.844795
$43$	3.53476	0.539046	0.269523	−	0.962994i	$-0.413134\pi$
$43$	3.53476	0.539046	0.269523	+	0.962994i	$0.413134\pi$
$44$	3.49938	0.527552
$45$	−2.94098	−0.438415
$46$	2.16249	0.318842
$47$	3.51739	0.513064	0.256532	−	0.966536i	$-0.417420\pi$
$47$	3.51739	0.513064	0.256532	+	0.966536i	$0.417420\pi$
$48$	1.98990	0.287217
$49$	1.00000	0.142857
$50$	−2.24619	−0.317660
$51$	8.54750	1.19689
$52$	14.6301	2.02883
$53$	−12.7340	−1.74915	−0.874576	−	0.484888i	$-0.838860\pi$
$53$	−12.7340	−1.74915	−0.874576	+	0.484888i	$0.838860\pi$
$54$	−0.323144	−0.0439743
$55$	−1.14908	−0.154942
$56$	−2.34814	−0.313783
$57$	−0.482316	−0.0638843
$58$	−19.4123	−2.54895
$59$	9.36095	1.21869	0.609346	−	0.792904i	$-0.291432\pi$
$59$	9.36095	1.21869	0.609346	+	0.792904i	$0.291432\pi$
$60$	7.42286	0.958287
$61$	−10.2127	−1.30760	−0.653798	−	0.756669i	$-0.726826\pi$
$61$	−10.2127	−1.30760	−0.653798	+	0.756669i	$0.726826\pi$
$62$	3.18995	0.405123
$63$	2.94098	0.370528
$64$	−13.0350	−1.62937
$65$	−4.80403	−0.595866
$66$	6.29108	0.774379
$67$	−13.0584	−1.59534	−0.797672	−	0.603092i	$-0.793935\pi$
$67$	−13.0584	−1.59534	−0.797672	+	0.603092i	$0.793935\pi$
$68$	−10.6795	−1.29508
$69$	2.34658	0.282495
$70$	2.24619	0.268471
$71$	2.95253	0.350400	0.175200	−	0.984533i	$-0.443943\pi$
$71$	2.95253	0.350400	0.175200	+	0.984533i	$0.443943\pi$
$72$	−6.90582	−0.813859
$73$	0.0874720	0.0102378	0.00511891	−	0.999987i	$-0.498371\pi$
$73$	0.0874720	0.0102378	0.00511891	+	0.999987i	$0.498371\pi$
$74$	16.5805	1.92745
$75$	−2.43741	−0.281448
$76$	0.602622	0.0691254
$77$	1.14908	0.130950
$78$	26.3016	2.97807
$79$	−9.09873	−1.02369	−0.511844	−	0.859079i	$-0.671037\pi$
$79$	−9.09873	−1.02369	−0.511844	+	0.859079i	$0.671037\pi$
$80$	0.816398	0.0912761
$81$	−9.17358	−1.01929
$82$	−20.2217	−2.23311
$83$	−11.0703	−1.21512	−0.607561	−	0.794273i	$-0.707852\pi$
$83$	−11.0703	−1.21512	−0.607561	+	0.794273i	$0.707852\pi$
$84$	−7.42286	−0.809900
$85$	3.50679	0.380365
$86$	−7.93975	−0.856165
$87$	−21.0648	−2.25839
$88$	−2.69819	−0.287628
$89$	9.84309	1.04337	0.521683	−	0.853140i	$-0.325305\pi$
$89$	9.84309	1.04337	0.521683	+	0.853140i	$0.325305\pi$
$90$	6.60600	0.696334
$91$	4.80403	0.503599
$92$	−2.93190	−0.305672
$93$	3.46151	0.358941
$94$	−7.90074	−0.814900
$95$	−0.197880	−0.0203021
$96$	−15.9165	−1.62447
$97$	−7.29301	−0.740493	−0.370246	−	0.928934i	$-0.620727\pi$
$97$	−7.29301	−0.740493	−0.370246	+	0.928934i	$0.620727\pi$
$98$	−2.24619	−0.226900
$99$	3.37941	0.339644
$100$	3.04539	0.304539
$101$	−9.01500	−0.897026	−0.448513	−	0.893776i	$-0.648046\pi$
$101$	−9.01500	−0.897026	−0.448513	+	0.893776i	$0.648046\pi$
$102$	−19.1993	−1.90102
$103$	−14.5041	−1.42913	−0.714565	−	0.699569i	$-0.753375\pi$
$103$	−14.5041	−1.42913	−0.714565	+	0.699569i	$0.753375\pi$
$104$	−11.2805	−1.10615
$105$	2.43741	0.237867
$106$	28.6031	2.77818
$107$	14.8791	1.43842	0.719211	−	0.694792i	$-0.244504\pi$
$107$	14.8791	1.43842	0.719211	+	0.694792i	$0.244504\pi$
$108$	0.438118	0.0421579
$109$	5.38812	0.516089	0.258044	−	0.966133i	$-0.416922\pi$
$109$	5.38812	0.516089	0.258044	+	0.966133i	$0.416922\pi$
$110$	2.58105	0.246094
$111$	17.9920	1.70773
$112$	−0.816398	−0.0771424
$113$	−14.2534	−1.34084	−0.670422	−	0.741980i	$-0.733887\pi$
$113$	−14.2534	−1.34084	−0.670422	+	0.741980i	$0.733887\pi$
$114$	1.08337	0.101467
$115$	0.962736	0.0897756
$116$	26.3191	2.44367
$117$	14.1285	1.30618
$118$	−21.0265	−1.93565
$119$	−3.50679	−0.321467
$120$	−5.72338	−0.522471
$121$	−9.67962	−0.879965
$122$	22.9396	2.07685
$123$	−21.9431	−1.97855
$124$	−4.32492	−0.388389
$125$	−1.00000	−0.0894427
$126$	−6.60600	−0.588510
$127$	3.05354	0.270958	0.135479	−	0.990780i	$-0.456743\pi$
$127$	3.05354	0.270958	0.135479	+	0.990780i	$0.456743\pi$
$128$	16.2190	1.43357
$129$	−8.61566	−0.758567
$130$	10.7908	0.946414
$131$	−11.1368	−0.973026	−0.486513	−	0.873673i	$-0.661731\pi$
$131$	−11.1368	−0.973026	−0.486513	+	0.873673i	$0.661731\pi$
$132$	−8.52944	−0.742393
$133$	0.197880	0.0171584
$134$	29.3318	2.53388
$135$	−0.143863	−0.0123817
$136$	8.23444	0.706097
$137$	10.3569	0.884849	0.442424	−	0.896806i	$-0.354119\pi$
$137$	10.3569	0.884849	0.442424	+	0.896806i	$0.354119\pi$
$138$	−5.27088	−0.448687
$139$	−18.3333	−1.55501	−0.777505	−	0.628876i	$-0.783515\pi$
$139$	−18.3333	−1.55501	−0.777505	+	0.628876i	$0.783515\pi$
$140$	−3.04539	−0.257382
$141$	−8.57333	−0.722005
$142$	−6.63194	−0.556540
$143$	5.52020	0.461623
$144$	−2.40101	−0.200084
$145$	−8.64229	−0.717703
$146$	−0.196479	−0.0162607
$147$	−2.43741	−0.201034
$148$	−22.4798	−1.84783
$149$	21.4086	1.75386	0.876930	−	0.480618i	$-0.159588\pi$
$149$	21.4086	1.75386	0.876930	+	0.480618i	$0.159588\pi$
$150$	5.47490	0.447024
$151$	7.33163	0.596639	0.298320	−	0.954466i	$-0.403574\pi$
$151$	7.33163	0.596639	0.298320	+	0.954466i	$0.403574\pi$
$152$	−0.464650	−0.0376881
$153$	−10.3134	−0.833789
$154$	−2.58105	−0.207987
$155$	1.42016	0.114070
$156$	−35.6596	−2.85506
$157$	−0.750297	−0.0598802	−0.0299401	−	0.999552i	$-0.509532\pi$
$157$	−0.750297	−0.0598802	−0.0299401	+	0.999552i	$0.509532\pi$
$158$	20.4375	1.62592
$159$	31.0381	2.46148
$160$	−6.53006	−0.516247
$161$	−0.962736	−0.0758742
$162$	20.6056	1.61893
$163$	16.2939	1.27624	0.638120	−	0.769937i	$-0.279712\pi$
$163$	16.2939	1.27624	0.638120	+	0.769937i	$0.279712\pi$
$164$	27.4165	2.14087
$165$	2.80078	0.218040
$166$	24.8660	1.92998
$167$	2.36931	0.183342	0.0916712	−	0.995789i	$-0.470779\pi$
$167$	2.36931	0.183342	0.0916712	+	0.995789i	$0.470779\pi$
$168$	5.72338	0.441568
$169$	10.0787	0.775284
$170$	−7.87694	−0.604133
$171$	0.581961	0.0445037
$172$	10.7647	0.820801
$173$	−0.308936	−0.0234880	−0.0117440	−	0.999931i	$-0.503738\pi$
$173$	−0.308936	−0.0234880	−0.0117440	+	0.999931i	$0.503738\pi$
$174$	47.3157	3.58699
$175$	1.00000	0.0755929
$176$	−0.938105	−0.0707123
$177$	−22.8165	−1.71499
$178$	−22.1095	−1.65718
$179$	−12.6970	−0.949022	−0.474511	−	0.880250i	$-0.657375\pi$
$179$	−12.6970	−0.949022	−0.474511	+	0.880250i	$0.657375\pi$
$180$	−8.95641	−0.667571
$181$	4.98051	0.370198	0.185099	−	0.982720i	$-0.440739\pi$
$181$	4.98051	0.370198	0.185099	+	0.982720i	$0.440739\pi$
$182$	−10.7908	−0.799866
$183$	24.8925	1.84010
$184$	2.26064	0.166656
$185$	7.38160	0.542706
$186$	−7.77521	−0.570106
$187$	−4.02958	−0.294672
$188$	10.7118	0.781239
$189$	0.143863	0.0104645
$190$	0.444477	0.0322458
$191$	19.5718	1.41617	0.708084	−	0.706129i	$-0.249560\pi$
$191$	19.5718	1.41617	0.708084	+	0.706129i	$0.249560\pi$
$192$	31.7716	2.29292
$193$	−12.6950	−0.913804	−0.456902	−	0.889517i	$-0.651041\pi$
$193$	−12.6950	−0.913804	−0.456902	+	0.889517i	$0.651041\pi$
$194$	16.3815	1.17612
$195$	11.7094	0.838527
$196$	3.04539	0.217528
$197$	−6.94554	−0.494849	−0.247425	−	0.968907i	$-0.579584\pi$
$197$	−6.94554	−0.494849	−0.247425	+	0.968907i	$0.579584\pi$
$198$	−7.59081	−0.539456
$199$	−27.5085	−1.95003	−0.975013	−	0.222147i	$-0.928693\pi$
$199$	−27.5085	−1.95003	−0.975013	+	0.222147i	$0.928693\pi$
$200$	−2.34814	−0.166038
$201$	31.8288	2.24503
$202$	20.2494	1.42475
$203$	8.64229	0.606570
$204$	26.0304	1.82249
$205$	−9.00264	−0.628771
$206$	32.5790	2.26989
$207$	−2.83138	−0.196795
$208$	−3.92200	−0.271942
$209$	0.227380	0.0157282
$210$	−5.47490	−0.377804
$211$	16.3344	1.12450	0.562252	−	0.826966i	$-0.309935\pi$
$211$	16.3344	1.12450	0.562252	+	0.826966i	$0.309935\pi$
$212$	−38.7800	−2.66342
$213$	−7.19652	−0.493097
$214$	−33.4214	−2.28464
$215$	−3.53476	−0.241068
$216$	−0.337810	−0.0229850
$217$	−1.42016	−0.0964065
$218$	−12.1028	−0.819703
$219$	−0.213205	−0.0144071
$220$	−3.49938	−0.235928
$221$	−16.8467	−1.13323
$222$	−40.4135	−2.71238
$223$	−9.71968	−0.650878	−0.325439	−	0.945563i	$-0.605512\pi$
$223$	−9.71968	−0.650878	−0.325439	+	0.945563i	$0.605512\pi$
$224$	6.53006	0.436308
$225$	2.94098	0.196065
$226$	32.0158	2.12966
$227$	27.1783	1.80388	0.901942	−	0.431857i	$-0.142142\pi$
$227$	27.1783	1.80388	0.901942	+	0.431857i	$0.142142\pi$
$228$	−1.46884	−0.0972761
$229$	1.00000	0.0660819
$229$	1.00000	0.0660819
$230$	−2.16249	−0.142590
$231$	−2.80078	−0.184278
$232$	−20.2933	−1.33232
$233$	−12.6602	−0.829398	−0.414699	−	0.909959i	$-0.636113\pi$
$233$	−12.6602	−0.829398	−0.414699	+	0.909959i	$0.636113\pi$
$234$	−31.7354	−2.07461
$235$	−3.51739	−0.229449
$236$	28.5077	1.85569
$237$	22.1774	1.44057
$238$	7.87694	0.510586
$239$	2.63120	0.170198	0.0850991	−	0.996372i	$-0.472879\pi$
$239$	2.63120	0.170198	0.0850991	+	0.996372i	$0.472879\pi$
$240$	−1.98990	−0.128447
$241$	27.2344	1.75432	0.877160	−	0.480198i	$-0.159435\pi$
$241$	27.2344	1.75432	0.877160	+	0.480198i	$0.159435\pi$
$242$	21.7423	1.39765
$243$	21.9282	1.40670
$244$	−31.1015	−1.99107
$245$	−1.00000	−0.0638877
$246$	49.2885	3.14252
$247$	0.950623	0.0604867
$248$	3.33472	0.211755
$249$	26.9828	1.70997
$250$	2.24619	0.142062
$251$	−4.50244	−0.284191	−0.142096	−	0.989853i	$-0.545384\pi$
$251$	−4.50244	−0.284191	−0.142096	+	0.989853i	$0.545384\pi$
$252$	8.95641	0.564201
$253$	−1.10626	−0.0695499
$254$	−6.85884	−0.430362
$255$	−8.54750	−0.535265
$256$	−10.3610	−0.647563
$257$	−7.29431	−0.455006	−0.227503	−	0.973777i	$-0.573056\pi$
$257$	−7.29431	−0.455006	−0.227503	+	0.973777i	$0.573056\pi$
$258$	19.3524	1.20483
$259$	−7.38160	−0.458670
$260$	−14.6301	−0.907322
$261$	25.4168	1.57326
$262$	25.0154	1.54546
$263$	−11.8686	−0.731850	−0.365925	−	0.930644i	$-0.619247\pi$
$263$	−11.8686	−0.731850	−0.365925	+	0.930644i	$0.619247\pi$
$264$	6.57661	0.404762
$265$	12.7340	0.782245
$266$	−0.444477	−0.0272527
$267$	−23.9917	−1.46827
$268$	−39.7680	−2.42922
$269$	14.1066	0.860093	0.430047	−	0.902807i	$-0.358497\pi$
$269$	14.1066	0.860093	0.430047	+	0.902807i	$0.358497\pi$
$270$	0.323144	0.0196659
$271$	20.9294	1.27137	0.635685	−	0.771948i	$-0.280718\pi$
$271$	20.9294	1.27137	0.635685	+	0.771948i	$0.280718\pi$
$272$	2.86294	0.173591
$273$	−11.7094	−0.708685
$274$	−23.2636	−1.40540
$275$	1.14908	0.0692920
$276$	7.14625	0.430154
$277$	−24.7812	−1.48896	−0.744480	−	0.667645i	$-0.767302\pi$
$277$	−24.7812	−1.48896	−0.744480	+	0.667645i	$0.767302\pi$
$278$	41.1801	2.46982
$279$	−4.17665	−0.250049
$280$	2.34814	0.140328
$281$	9.64040	0.575098	0.287549	−	0.957766i	$-0.407160\pi$
$281$	9.64040	0.575098	0.287549	+	0.957766i	$0.407160\pi$
$282$	19.2574	1.14676
$283$	4.53000	0.269280	0.134640	−	0.990895i	$-0.457012\pi$
$283$	4.53000	0.269280	0.134640	+	0.990895i	$0.457012\pi$
$284$	8.99158	0.533552
$285$	0.482316	0.0285699
$286$	−12.3994	−0.733195
$287$	9.00264	0.531409
$288$	19.2048	1.13165
$289$	−4.70240	−0.276612
$290$	19.4123	1.13993
$291$	17.7761	1.04205
$292$	0.266386	0.0155891
$293$	−14.7618	−0.862392	−0.431196	−	0.902258i	$-0.641908\pi$
$293$	−14.7618	−0.862392	−0.431196	+	0.902258i	$0.641908\pi$
$294$	5.47490	0.319303
$295$	−9.36095	−0.545016
$296$	17.3330	1.00746
$297$	0.165310	0.00959224
$298$	−48.0878	−2.78565
$299$	−4.62501	−0.267471
$300$	−7.42286	−0.428559
$301$	3.53476	0.203740
$302$	−16.4683	−0.947642
$303$	21.9733	1.26233
$304$	−0.161549	−0.00926547
$305$	10.2127	0.584775
$306$	23.1659	1.32431
$307$	−20.8977	−1.19270	−0.596348	−	0.802726i	$-0.703382\pi$
$307$	−20.8977	−1.19270	−0.596348	+	0.802726i	$0.703382\pi$
$308$	3.49938	0.199396
$309$	35.3524	2.01113
$310$	−3.18995	−0.181177
$311$	23.6937	1.34354	0.671772	−	0.740758i	$-0.265533\pi$
$311$	23.6937	1.34354	0.671772	+	0.740758i	$0.265533\pi$
$312$	27.4953	1.55661
$313$	25.7338	1.45456	0.727280	−	0.686341i	$-0.240784\pi$
$313$	25.7338	1.45456	0.727280	+	0.686341i	$0.240784\pi$
$314$	1.68531	0.0951077
$315$	−2.94098	−0.165705
$316$	−27.7092	−1.55876
$317$	−23.9873	−1.34726	−0.673629	−	0.739069i	$-0.735266\pi$
$317$	−23.9873	−1.34726	−0.673629	+	0.739069i	$0.735266\pi$
$318$	−69.7175	−3.90956
$319$	9.93067	0.556011
$320$	13.0350	0.728678
$321$	−36.2666	−2.02420
$322$	2.16249	0.120511
$323$	−0.693925	−0.0386110
$324$	−27.9371	−1.55206
$325$	4.80403	0.266480
$326$	−36.5993	−2.02705
$327$	−13.1331	−0.726261
$328$	−21.1394	−1.16723
$329$	3.51739	0.193920
$330$	−6.29108	−0.346313
$331$	4.68214	0.257354	0.128677	−	0.991687i	$-0.458927\pi$
$331$	4.68214	0.257354	0.128677	+	0.991687i	$0.458927\pi$
$332$	−33.7133	−1.85026
$333$	−21.7091	−1.18965
$334$	−5.32192	−0.291203
$335$	13.0584	0.713459
$336$	1.98990	0.108558
$337$	−17.1413	−0.933744	−0.466872	−	0.884325i	$-0.654619\pi$
$337$	−17.1413	−0.933744	−0.466872	+	0.884325i	$0.654619\pi$
$338$	−22.6387	−1.23138
$339$	34.7413	1.88689
$340$	10.6795	0.579179
$341$	−1.63187	−0.0883707
$342$	−1.30720	−0.0706852
$343$	1.00000	0.0539949
$344$	−8.30010	−0.447511
$345$	−2.34658	−0.126336
$346$	0.693931	0.0373060
$347$	−16.9608	−0.910502	−0.455251	−	0.890363i	$-0.650450\pi$
$347$	−16.9608	−0.910502	−0.455251	+	0.890363i	$0.650450\pi$
$348$	−64.1505	−3.43883
$349$	15.9903	0.855942	0.427971	−	0.903793i	$-0.359229\pi$
$349$	15.9903	0.855942	0.427971	+	0.903793i	$0.359229\pi$
$350$	−2.24619	−0.120064
$351$	0.691121	0.0368893
$352$	7.50355	0.399941
$353$	22.6606	1.20610	0.603050	−	0.797704i	$-0.293952\pi$
$353$	22.6606	1.20610	0.603050	+	0.797704i	$0.293952\pi$
$354$	51.2503	2.72392
$355$	−2.95253	−0.156704
$356$	29.9760	1.58872
$357$	8.54750	0.452382
$358$	28.5200	1.50733
$359$	−12.4673	−0.657999	−0.328999	−	0.944330i	$-0.606711\pi$
$359$	−12.4673	−0.657999	−0.328999	+	0.944330i	$0.606711\pi$
$360$	6.90582	0.363969
$361$	−18.9608	−0.997939
$362$	−11.1872	−0.587986
$363$	23.5932	1.23832
$364$	14.6301	0.766827
$365$	−0.0874720	−0.00457850
$366$	−55.9133	−2.92263
$367$	14.4137	0.752387	0.376194	−	0.926541i	$-0.377233\pi$
$367$	14.4137	0.752387	0.376194	+	0.926541i	$0.377233\pi$
$368$	0.785975	0.0409718
$369$	26.4765	1.37831
$370$	−16.5805	−0.861980
$371$	−12.7340	−0.661118
$372$	10.5416	0.546557
$373$	1.16134	0.0601318	0.0300659	−	0.999548i	$-0.490428\pi$
$373$	1.16134	0.0601318	0.0300659	+	0.999548i	$0.490428\pi$
$374$	9.05121	0.468027
$375$	2.43741	0.125867
$376$	−8.25932	−0.425942
$377$	41.5178	2.13828
$378$	−0.323144	−0.0166207
$379$	29.4459	1.51253	0.756266	−	0.654264i	$-0.227021\pi$
$379$	29.4459	1.51253	0.756266	+	0.654264i	$0.227021\pi$
$380$	−0.602622	−0.0309138
$381$	−7.44273	−0.381303
$382$	−43.9621	−2.24930
$383$	−0.470007	−0.0240162	−0.0120081	−	0.999928i	$-0.503822\pi$
$383$	−0.470007	−0.0240162	−0.0120081	+	0.999928i	$0.503822\pi$
$384$	−39.5324	−2.01738
$385$	−1.14908	−0.0585624
$386$	28.5154	1.45139
$387$	10.3956	0.528440
$388$	−22.2100	−1.12754
$389$	−22.4224	−1.13686	−0.568429	−	0.822732i	$-0.692449\pi$
$389$	−22.4224	−1.13686	−0.568429	+	0.822732i	$0.692449\pi$
$390$	−26.3016	−1.33183
$391$	3.37612	0.170737
$392$	−2.34814	−0.118599
$393$	27.1449	1.36928
$394$	15.6010	0.785968
$395$	9.09873	0.457807
$396$	10.2916	0.517173
$397$	−12.0366	−0.604098	−0.302049	−	0.953292i	$-0.597671\pi$
$397$	−12.0366	−0.604098	−0.302049	+	0.953292i	$0.597671\pi$
$398$	61.7894	3.09722
$399$	−0.482316	−0.0241460
$400$	−0.816398	−0.0408199
$401$	−5.09455	−0.254410	−0.127205	−	0.991876i	$-0.540601\pi$
$401$	−5.09455	−0.254410	−0.127205	+	0.991876i	$0.540601\pi$
$402$	−71.4937	−3.56578
$403$	−6.82247	−0.339851
$404$	−27.4542	−1.36590
$405$	9.17358	0.455839
$406$	−19.4123	−0.963414
$407$	−8.48204	−0.420439
$408$	−20.0707	−0.993648
$409$	−13.6106	−0.673001	−0.336501	−	0.941683i	$-0.609243\pi$
$409$	−13.6106	−0.673001	−0.336501	+	0.941683i	$0.609243\pi$
$410$	20.2217	0.998677
$411$	−25.2440	−1.24519
$412$	−44.1705	−2.17613
$413$	9.36095	0.460622
$414$	6.35984	0.312569
$415$	11.0703	0.543419
$416$	31.3706	1.53807
$417$	44.6858	2.18827
$418$	−0.510739	−0.0249811
$419$	−30.6919	−1.49940	−0.749699	−	0.661779i	$-0.769802\pi$
$419$	−30.6919	−1.49940	−0.749699	+	0.661779i	$0.769802\pi$
$420$	7.42286	0.362198
$421$	−12.8081	−0.624228	−0.312114	−	0.950045i	$-0.601037\pi$
$421$	−12.8081	−0.624228	−0.312114	+	0.950045i	$0.601037\pi$
$422$	−36.6901	−1.78605
$423$	10.3446	0.502970
$424$	29.9012	1.45213
$425$	−3.50679	−0.170104
$426$	16.1648	0.783186
$427$	−10.2127	−0.494225
$428$	45.3127	2.19027
$429$	−13.4550	−0.649614
$430$	7.93975	0.382889
$431$	14.1874	0.683385	0.341693	−	0.939812i	$-0.389000\pi$
$431$	14.1874	0.683385	0.341693	+	0.939812i	$0.389000\pi$
$432$	−0.117449	−0.00565078
$433$	7.35827	0.353616	0.176808	−	0.984245i	$-0.443423\pi$
$433$	7.35827	0.353616	0.176808	+	0.984245i	$0.443423\pi$
$434$	3.18995	0.153122
$435$	21.0648	1.00998
$436$	16.4089	0.785844
$437$	−0.190506	−0.00911316
$438$	0.478901	0.0228828
$439$	27.0279	1.28997	0.644985	−	0.764195i	$-0.276864\pi$
$439$	27.0279	1.28997	0.644985	+	0.764195i	$0.276864\pi$
$440$	2.69819	0.128631
$441$	2.94098	0.140047
$442$	37.8410	1.79991
$443$	−28.5907	−1.35838	−0.679192	−	0.733960i	$-0.737670\pi$
$443$	−28.5907	−1.35838	−0.679192	+	0.733960i	$0.737670\pi$
$444$	54.7926	2.60034
$445$	−9.84309	−0.466607
$446$	21.8323	1.03379
$447$	−52.1816	−2.46810
$448$	−13.0350	−0.615846
$449$	24.1139	1.13801	0.569003	−	0.822336i	$-0.307329\pi$
$449$	24.1139	1.13801	0.569003	+	0.822336i	$0.307329\pi$
$450$	−6.60600	−0.311410
$451$	10.3447	0.487114
$452$	−43.4070	−2.04169
$453$	−17.8702	−0.839615
$454$	−61.0476	−2.86511
$455$	−4.80403	−0.225216
$456$	1.13254	0.0530362
$457$	−20.8262	−0.974210	−0.487105	−	0.873343i	$-0.661947\pi$
$457$	−20.8262	−0.974210	−0.487105	+	0.873343i	$0.661947\pi$
$458$	−2.24619	−0.104958
$459$	−0.504497	−0.0235479
$460$	2.93190	0.136701
$461$	34.0741	1.58699	0.793495	−	0.608577i	$-0.208259\pi$
$461$	34.0741	1.58699	0.793495	+	0.608577i	$0.208259\pi$
$462$	6.29108	0.292688
$463$	28.1816	1.30971	0.654855	−	0.755754i	$-0.272729\pi$
$463$	28.1816	1.30971	0.654855	+	0.755754i	$0.272729\pi$
$464$	−7.05555	−0.327546
$465$	−3.46151	−0.160523
$466$	28.4373	1.31733
$467$	26.6044	1.23110	0.615552	−	0.788096i	$-0.288933\pi$
$467$	26.6044	1.23110	0.615552	+	0.788096i	$0.288933\pi$
$468$	43.0269	1.98892
$469$	−13.0584	−0.602983
$470$	7.90074	0.364434
$471$	1.82878	0.0842659
$472$	−21.9808	−1.01175
$473$	4.06171	0.186758
$474$	−49.8147	−2.28806
$475$	0.197880	0.00907937
$476$	−10.6795	−0.489496
$477$	−37.4505	−1.71474
$478$	−5.91019	−0.270326
$479$	−32.6312	−1.49096	−0.745478	−	0.666530i	$-0.767779\pi$
$479$	−32.6312	−1.49096	−0.745478	+	0.666530i	$0.767779\pi$
$480$	15.9165	0.726484
$481$	−35.4614	−1.61690
$482$	−61.1737	−2.78638
$483$	2.34658	0.106773
$484$	−29.4782	−1.33992
$485$	7.29301	0.331158
$486$	−49.2550	−2.23425
$487$	9.58712	0.434434	0.217217	−	0.976123i	$-0.430302\pi$
$487$	9.58712	0.434434	0.217217	+	0.976123i	$0.430302\pi$
$488$	23.9807	1.08556
$489$	−39.7150	−1.79598
$490$	2.24619	0.101473
$491$	−10.3458	−0.466898	−0.233449	−	0.972369i	$-0.575001\pi$
$491$	−10.3458	−0.466898	−0.233449	+	0.972369i	$0.575001\pi$
$492$	−66.8253	−3.01272
$493$	−30.3067	−1.36495
$494$	−2.13528	−0.0960709
$495$	−3.37941	−0.151893
$496$	1.15941	0.0520592
$497$	2.95253	0.132439
$498$	−60.6087	−2.71594
$499$	21.9642	0.983254	0.491627	−	0.870806i	$-0.336402\pi$
$499$	21.9642	0.983254	0.491627	+	0.870806i	$0.336402\pi$
$500$	−3.04539	−0.136194
$501$	−5.77498	−0.258007
$502$	10.1133	0.451381
$503$	15.3925	0.686316	0.343158	−	0.939278i	$-0.388503\pi$
$503$	15.3925	0.686316	0.343158	+	0.939278i	$0.388503\pi$
$504$	−6.90582	−0.307610
$505$	9.01500	0.401162
$506$	2.48487	0.110466
$507$	−24.5659	−1.09101
$508$	9.29920	0.412585
$509$	−0.972481	−0.0431045	−0.0215522	−	0.999768i	$-0.506861\pi$
$509$	−0.972481	−0.0431045	−0.0215522	+	0.999768i	$0.506861\pi$
$510$	19.1993	0.850161
$511$	0.0874720	0.00386954
$512$	−9.16516	−0.405047
$513$	0.0284676	0.00125688
$514$	16.3844	0.722686
$515$	14.5041	0.639126
$516$	−26.2380	−1.15506
$517$	4.04176	0.177756
$518$	16.5805	0.728506
$519$	0.753005	0.0330533
$520$	11.2805	0.494684
$521$	31.8244	1.39425	0.697126	−	0.716949i	$-0.254462\pi$
$521$	31.8244	1.39425	0.697126	+	0.716949i	$0.254462\pi$
$522$	−57.0910	−2.49881
$523$	0.694270	0.0303583	0.0151791	−	0.999885i	$-0.495168\pi$
$523$	0.694270	0.0303583	0.0151791	+	0.999885i	$0.495168\pi$
$524$	−33.9158	−1.48162
$525$	−2.43741	−0.106377
$526$	26.6592	1.16240
$527$	4.98019	0.216941
$528$	2.28655	0.0995092
$529$	−22.0731	−0.959702
$530$	−28.6031	−1.24244
$531$	27.5304	1.19472
$532$	0.602622	0.0261270
$533$	43.2489	1.87332
$534$	53.8899	2.33204
$535$	−14.8791	−0.643282
$536$	30.6630	1.32444
$537$	30.9479	1.33550
$538$	−31.6861	−1.36608
$539$	1.14908	0.0494943
$540$	−0.438118	−0.0188536
$541$	−21.1545	−0.909505	−0.454752	−	0.890618i	$-0.650272\pi$
$541$	−21.1545	−0.909505	−0.454752	+	0.890618i	$0.650272\pi$
$542$	−47.0115	−2.01932
$543$	−12.1396	−0.520958
$544$	−22.8996	−0.981812
$545$	−5.38812	−0.230802
$546$	26.3016	1.12560
$547$	−5.67267	−0.242546	−0.121273	−	0.992619i	$-0.538698\pi$
$547$	−5.67267	−0.242546	−0.121273	+	0.992619i	$0.538698\pi$
$548$	31.5407	1.34735
$549$	−30.0352	−1.28187
$550$	−2.58105	−0.110056
$551$	1.71014	0.0728544
$552$	−5.51010	−0.234526
$553$	−9.09873	−0.386918
$554$	55.6634	2.36491
$555$	−17.9920	−0.763718
$556$	−55.8320	−2.36780
$557$	26.7402	1.13302	0.566510	−	0.824055i	$-0.308293\pi$
$557$	26.7402	1.13302	0.566510	+	0.824055i	$0.308293\pi$
$558$	9.38156	0.397153
$559$	16.9811	0.718223
$560$	0.816398	0.0344991
$561$	9.82174	0.414674
$562$	−21.6542	−0.913428
$563$	29.5136	1.24385	0.621925	−	0.783077i	$-0.286351\pi$
$563$	29.5136	1.24385	0.621925	+	0.783077i	$0.286351\pi$
$564$	−26.1091	−1.09939
$565$	14.2534	0.599644
$566$	−10.1753	−0.427698
$567$	−9.17358	−0.385254
$568$	−6.93294	−0.290900
$569$	−22.4097	−0.939464	−0.469732	−	0.882809i	$-0.655649\pi$
$569$	−22.4097	−0.939464	−0.469732	+	0.882809i	$0.655649\pi$
$570$	−1.08337	−0.0453776
$571$	−8.50487	−0.355918	−0.177959	−	0.984038i	$-0.556949\pi$
$571$	−8.50487	−0.355918	−0.177959	+	0.984038i	$0.556949\pi$
$572$	16.8111	0.702909
$573$	−47.7046	−1.99289
$574$	−20.2217	−0.844036
$575$	−0.962736	−0.0401489
$576$	−38.3356	−1.59732
$577$	−27.9151	−1.16212	−0.581061	−	0.813860i	$-0.697362\pi$
$577$	−27.9151	−1.16212	−0.581061	+	0.813860i	$0.697362\pi$
$578$	10.5625	0.439342
$579$	30.9429	1.28594
$580$	−26.3191	−1.09284
$581$	−11.0703	−0.459273
$582$	−39.9285	−1.65509
$583$	−14.6324	−0.606011
$584$	−0.205396	−0.00849937
$585$	−14.1285	−0.584143
$586$	33.1578	1.36974
$587$	−14.5436	−0.600277	−0.300139	−	0.953896i	$-0.597033\pi$
$587$	−14.5436	−0.600277	−0.300139	+	0.953896i	$0.597033\pi$
$588$	−7.42286	−0.306114
$589$	−0.281021	−0.0115793
$590$	21.0265	0.865648
$591$	16.9291	0.696372
$592$	6.02633	0.247680
$593$	−21.9238	−0.900303	−0.450151	−	0.892952i	$-0.648630\pi$
$593$	−21.9238	−0.900303	−0.450151	+	0.892952i	$0.648630\pi$
$594$	−0.371317	−0.0152353
$595$	3.50679	0.143765
$596$	65.1974	2.67059
$597$	67.0496	2.74416
$598$	10.3887	0.424824
$599$	−45.8142	−1.87192	−0.935959	−	0.352109i	$-0.885465\pi$
$599$	−45.8142	−1.87192	−0.935959	+	0.352109i	$0.885465\pi$
$600$	5.72338	0.233656
$601$	14.9981	0.611785	0.305893	−	0.952066i	$-0.401045\pi$
$601$	14.9981	0.611785	0.305893	+	0.952066i	$0.401045\pi$
$602$	−7.93975	−0.323600
$603$	−38.4046	−1.56396
$604$	22.3276	0.908498
$605$	9.67962	0.393533
$606$	−49.3562	−2.00496
$607$	17.1568	0.696372	0.348186	−	0.937425i	$-0.386798\pi$
$607$	17.1568	0.696372	0.348186	+	0.937425i	$0.386798\pi$
$608$	1.29217	0.0524044
$609$	−21.0648	−0.853590
$610$	−22.9396	−0.928797
$611$	16.8977	0.683606
$612$	−31.4083	−1.26960
$613$	16.4363	0.663854	0.331927	−	0.943305i	$-0.392301\pi$
$613$	16.4363	0.663854	0.331927	+	0.943305i	$0.392301\pi$
$614$	46.9403	1.89436
$615$	21.9431	0.884832
$616$	−2.69819	−0.108713
$617$	−40.5367	−1.63194	−0.815972	−	0.578091i	$-0.803798\pi$
$617$	−40.5367	−1.63194	−0.815972	+	0.578091i	$0.803798\pi$
$618$	−79.4084	−3.19427
$619$	−10.3747	−0.416994	−0.208497	−	0.978023i	$-0.566857\pi$
$619$	−10.3747	−0.416994	−0.208497	+	0.978023i	$0.566857\pi$
$620$	4.32492	0.173693
$621$	−0.138502	−0.00555789
$622$	−53.2205	−2.13395
$623$	9.84309	0.394355
$624$	9.55953	0.382687
$625$	1.00000	0.0400000
$626$	−57.8031	−2.31028
$627$	−0.554218	−0.0221333
$628$	−2.28494	−0.0911792
$629$	25.8858	1.03213
$630$	6.60600	0.263190
$631$	23.3842	0.930910	0.465455	−	0.885072i	$-0.345891\pi$
$631$	23.3842	0.930910	0.465455	+	0.885072i	$0.345891\pi$
$632$	21.3651	0.849858
$633$	−39.8136	−1.58245
$634$	53.8800	2.13985
$635$	−3.05354	−0.121176
$636$	94.5229	3.74808
$637$	4.80403	0.190343
$638$	−22.3062	−0.883111
$639$	8.68331	0.343506
$640$	−16.2190	−0.641112
$641$	−23.1244	−0.913357	−0.456679	−	0.889632i	$-0.650961\pi$
$641$	−23.1244	−0.913357	−0.456679	+	0.889632i	$0.650961\pi$
$642$	81.4618	3.21504
$643$	9.10711	0.359149	0.179575	−	0.983744i	$-0.442528\pi$
$643$	9.10711	0.359149	0.179575	+	0.983744i	$0.442528\pi$
$644$	−2.93190	−0.115533
$645$	8.61566	0.339241
$646$	1.55869	0.0613259
$647$	31.1237	1.22360	0.611800	−	0.791012i	$-0.290446\pi$
$647$	31.1237	1.22360	0.611800	+	0.791012i	$0.290446\pi$
$648$	21.5408	0.846204
$649$	10.7565	0.422228
$650$	−10.7908	−0.423249
$651$	3.46151	0.135667
$652$	49.6213	1.94332
$653$	15.6211	0.611303	0.305651	−	0.952144i	$-0.401126\pi$
$653$	15.6211	0.611303	0.305651	+	0.952144i	$0.401126\pi$
$654$	29.4994	1.15352
$655$	11.1368	0.435150
$656$	−7.34973	−0.286959
$657$	0.257253	0.0100364
$658$	−7.90074	−0.308003
$659$	−42.3029	−1.64789	−0.823943	−	0.566673i	$-0.808230\pi$
$659$	−42.3029	−1.64789	−0.823943	+	0.566673i	$0.808230\pi$
$660$	8.52944	0.332008
$661$	46.9846	1.82749	0.913745	−	0.406289i	$-0.133177\pi$
$661$	46.9846	1.82749	0.913745	+	0.406289i	$0.133177\pi$
$662$	−10.5170	−0.408755
$663$	41.0624	1.59473
$664$	25.9946	1.00878
$665$	−0.197880	−0.00767347
$666$	48.7629	1.88952
$667$	−8.32024	−0.322161
$668$	7.21545	0.279174
$669$	23.6909	0.915941
$670$	−29.3318	−1.13319
$671$	−11.7351	−0.453030
$672$	−15.9165	−0.613991
$673$	−48.6740	−1.87624	−0.938122	−	0.346306i	$-0.887436\pi$
$673$	−48.6740	−1.87624	−0.938122	+	0.346306i	$0.887436\pi$
$674$	38.5026	1.48306
$675$	0.143863	0.00553728
$676$	30.6935	1.18052
$677$	17.7977	0.684022	0.342011	−	0.939696i	$-0.388892\pi$
$677$	17.7977	0.684022	0.342011	+	0.939696i	$0.388892\pi$
$678$	−78.0357	−2.99694
$679$	−7.29301	−0.279880
$680$	−8.23444	−0.315776
$681$	−66.2446	−2.53850
$682$	3.66550	0.140359
$683$	−4.16968	−0.159548	−0.0797742	−	0.996813i	$-0.525420\pi$
$683$	−4.16968	−0.159548	−0.0797742	+	0.996813i	$0.525420\pi$
$684$	1.77230	0.0677655
$685$	−10.3569	−0.395716
$686$	−2.24619	−0.0857601
$687$	−2.43741	−0.0929931
$688$	−2.88577	−0.110019
$689$	−61.1746	−2.33057
$690$	5.27088	0.200659
$691$	−23.0386	−0.876430	−0.438215	−	0.898870i	$-0.644389\pi$
$691$	−23.0386	−0.876430	−0.438215	+	0.898870i	$0.644389\pi$
$692$	−0.940831	−0.0357650
$693$	3.37941	0.128373
$694$	38.0972	1.44615
$695$	18.3333	0.695422
$696$	49.4631	1.87490
$697$	−31.5704	−1.19581
$698$	−35.9173	−1.35949
$699$	30.8582	1.16716
$700$	3.04539	0.115105
$701$	−35.9894	−1.35930	−0.679651	−	0.733536i	$-0.737869\pi$
$701$	−35.9894	−1.35930	−0.679651	+	0.733536i	$0.737869\pi$
$702$	−1.55239	−0.0585913
$703$	−1.46067	−0.0550903
$704$	−14.9782	−0.564513
$705$	8.57333	0.322890
$706$	−50.9000	−1.91565
$707$	−9.01500	−0.339044
$708$	−69.4851	−2.61141
$709$	−24.5948	−0.923678	−0.461839	−	0.886964i	$-0.652810\pi$
$709$	−24.5948	−0.923678	−0.461839	+	0.886964i	$0.652810\pi$
$710$	6.63194	0.248892
$711$	−26.7592	−1.00355
$712$	−23.1129	−0.866194
$713$	1.36723	0.0512033
$714$	−19.1993	−0.718517
$715$	−5.52020	−0.206444
$716$	−38.6674	−1.44507
$717$	−6.41332	−0.239510
$718$	28.0040	1.04510
$719$	−2.87651	−0.107276	−0.0536378	−	0.998560i	$-0.517082\pi$
$719$	−2.87651	−0.107276	−0.0536378	+	0.998560i	$0.517082\pi$
$720$	2.40101	0.0894803
$721$	−14.5041	−0.540160
$722$	42.5897	1.58503
$723$	−66.3814	−2.46875
$724$	15.1676	0.563698
$725$	8.64229	0.320967
$726$	−52.9949	−1.96683
$727$	47.2634	1.75290	0.876452	−	0.481490i	$-0.159904\pi$
$727$	47.2634	1.75290	0.876452	+	0.481490i	$0.159904\pi$
$728$	−11.2805	−0.418084
$729$	−25.9273	−0.960272
$730$	0.196479	0.00727202
$731$	−12.3957	−0.458470
$732$	75.8071	2.80191
$733$	−11.8058	−0.436057	−0.218029	−	0.975942i	$-0.569963\pi$
$733$	−11.8058	−0.436057	−0.218029	+	0.975942i	$0.569963\pi$
$734$	−32.3759	−1.19502
$735$	2.43741	0.0899053
$736$	−6.28673	−0.231732
$737$	−15.0052	−0.552723
$738$	−59.4714	−2.18917
$739$	−16.4976	−0.606874	−0.303437	−	0.952852i	$-0.598134\pi$
$739$	−16.4976	−0.606874	−0.303437	+	0.952852i	$0.598134\pi$
$740$	22.4798	0.826375
$741$	−2.31706	−0.0851193
$742$	28.6031	1.05005
$743$	−22.3174	−0.818747	−0.409374	−	0.912367i	$-0.634253\pi$
$743$	−22.3174	−0.818747	−0.409374	+	0.912367i	$0.634253\pi$
$744$	−8.12809	−0.297990
$745$	−21.4086	−0.784350
$746$	−2.60859	−0.0955073
$747$	−32.5574	−1.19121
$748$	−12.2716	−0.448695
$749$	14.8791	0.543672
$750$	−5.47490	−0.199915
$751$	21.5474	0.786275	0.393137	−	0.919480i	$-0.371390\pi$
$751$	21.5474	0.786275	0.393137	+	0.919480i	$0.371390\pi$
$752$	−2.87159	−0.104716
$753$	10.9743	0.399925
$754$	−93.2571	−3.39622
$755$	−7.33163	−0.266825
$756$	0.438118	0.0159342
$757$	−18.0255	−0.655147	−0.327574	−	0.944826i	$-0.606231\pi$
$757$	−18.0255	−0.655147	−0.327574	+	0.944826i	$0.606231\pi$
$758$	−66.1411	−2.40235
$759$	2.69641	0.0978734
$760$	0.464650	0.0168546
$761$	−31.1528	−1.12929	−0.564644	−	0.825335i	$-0.690986\pi$
$761$	−31.1528	−1.12929	−0.564644	+	0.825335i	$0.690986\pi$
$762$	16.7178	0.605622
$763$	5.38812	0.195063
$764$	59.6037	2.15639
$765$	10.3134	0.372882
$766$	1.05573	0.0381449
$767$	44.9703	1.62378
$768$	25.2540	0.911276
$769$	5.44134	0.196220	0.0981099	−	0.995176i	$-0.468720\pi$
$769$	5.44134	0.196220	0.0981099	+	0.995176i	$0.468720\pi$
$770$	2.58105	0.0930146
$771$	17.7792	0.640303
$772$	−38.6611	−1.39144
$773$	18.2172	0.655228	0.327614	−	0.944812i	$-0.393755\pi$
$773$	18.2172	0.655228	0.327614	+	0.944812i	$0.393755\pi$
$774$	−23.3506	−0.839321
$775$	−1.42016	−0.0510135
$776$	17.1250	0.614751
$777$	17.9920	0.645460
$778$	50.3650	1.80567
$779$	1.78144	0.0638269
$780$	35.6596	1.27682
$781$	3.39268	0.121400
$782$	−7.58341	−0.271182
$783$	1.24330	0.0444321
$784$	−0.816398	−0.0291571
$785$	0.750297	0.0267793
$786$	−60.9728	−2.17483
$787$	52.1010	1.85720	0.928601	−	0.371081i	$-0.121013\pi$
$787$	52.1010	1.85720	0.928601	+	0.371081i	$0.121013\pi$
$788$	−21.1518	−0.753503
$789$	28.9287	1.02989
$790$	−20.4375	−0.727134
$791$	−14.2534	−0.506791
$792$	−7.93533	−0.281970
$793$	−49.0619	−1.74224
$794$	27.0365	0.959488
$795$	−31.0381	−1.10081
$796$	−83.7740	−2.96929
$797$	13.2548	0.469510	0.234755	−	0.972055i	$-0.424571\pi$
$797$	13.2548	0.469510	0.234755	+	0.972055i	$0.424571\pi$
$798$	1.08337	0.0383510
$799$	−12.3348	−0.436373
$800$	6.53006	0.230873
$801$	28.9483	1.02284
$802$	11.4433	0.404079
$803$	0.100512	0.00354700
$804$	96.9310	3.41849
$805$	0.962736	0.0339320
$806$	15.3246	0.539786
$807$	−34.3835	−1.21036
$808$	21.1685	0.744704
$809$	−38.8517	−1.36595	−0.682976	−	0.730441i	$-0.739315\pi$
$809$	−38.8517	−1.36595	−0.682976	+	0.730441i	$0.739315\pi$
$810$	−20.6056	−0.724009
$811$	−27.3431	−0.960147	−0.480073	−	0.877228i	$-0.659390\pi$
$811$	−27.3431	−0.960147	−0.480073	+	0.877228i	$0.659390\pi$
$812$	26.3191	0.923620
$813$	−51.0136	−1.78912
$814$	19.0523	0.667783
$815$	−16.2939	−0.570752
$816$	−6.97816	−0.244285
$817$	0.699459	0.0244710
$818$	30.5721	1.06893
$819$	14.1285	0.493691
$820$	−27.4165	−0.957426
$821$	−53.5502	−1.86891	−0.934457	−	0.356075i	$-0.884115\pi$
$821$	−53.5502	−1.86891	−0.934457	+	0.356075i	$0.884115\pi$
$822$	56.7029	1.97774
$823$	−36.8245	−1.28362	−0.641810	−	0.766864i	$-0.721816\pi$
$823$	−36.8245	−1.28362	−0.641810	+	0.766864i	$0.721816\pi$
$824$	34.0576	1.18645
$825$	−2.80078	−0.0975105
$826$	−21.0265	−0.731606
$827$	20.5425	0.714331	0.357166	−	0.934041i	$-0.383743\pi$
$827$	20.5425	0.714331	0.357166	+	0.934041i	$0.383743\pi$
$828$	−8.62265	−0.299658
$829$	−16.8078	−0.583759	−0.291879	−	0.956455i	$-0.594281\pi$
$829$	−16.8078	−0.583759	−0.291879	+	0.956455i	$0.594281\pi$
$830$	−24.8660	−0.863111
$831$	60.4021	2.09532
$832$	−62.6205	−2.17097
$833$	−3.50679	−0.121503
$834$	−100.373	−3.47563
$835$	−2.36931	−0.0819932
$836$	0.692459	0.0239492
$837$	−0.204308	−0.00706191
$838$	68.9399	2.38149
$839$	16.5309	0.570711	0.285355	−	0.958422i	$-0.407888\pi$
$839$	16.5309	0.570711	0.285355	+	0.958422i	$0.407888\pi$
$840$	−5.72338	−0.197475
$841$	45.6892	1.57549
$842$	28.7694	0.991460
$843$	−23.4976	−0.809301
$844$	49.7444	1.71227
$845$	−10.0787	−0.346718
$846$	−23.2359	−0.798867
$847$	−9.67962	−0.332596
$848$	10.3960	0.357001
$849$	−11.0415	−0.378942
$850$	7.87694	0.270177
$851$	7.10653	0.243609
$852$	−21.9162	−0.750836
$853$	−25.7491	−0.881633	−0.440816	−	0.897597i	$-0.645311\pi$
$853$	−25.7491	−0.881633	−0.440816	+	0.897597i	$0.645311\pi$
$854$	22.9396	0.784977
$855$	−0.581961	−0.0199027
$856$	−34.9383	−1.19417
$857$	−44.7649	−1.52914	−0.764569	−	0.644541i	$-0.777048\pi$
$857$	−44.7649	−1.52914	−0.764569	+	0.644541i	$0.777048\pi$
$858$	30.2226	1.03178
$859$	−34.2370	−1.16815	−0.584076	−	0.811699i	$-0.698543\pi$
$859$	−34.2370	−1.16815	−0.584076	+	0.811699i	$0.698543\pi$
$860$	−10.7647	−0.367073
$861$	−21.9431	−0.747820
$862$	−31.8678	−1.08542
$863$	−12.7772	−0.434940	−0.217470	−	0.976067i	$-0.569780\pi$
$863$	−12.7772	−0.434940	−0.217470	+	0.976067i	$0.569780\pi$
$864$	0.939434	0.0319602
$865$	0.308936	0.0105042
$866$	−16.5281	−0.561648
$867$	11.4617	0.389259
$868$	−4.32492	−0.146797
$869$	−10.4552	−0.354667
$870$	−47.3157	−1.60415
$871$	−62.7332	−2.12563
$872$	−12.6521	−0.428453
$873$	−21.4486	−0.725924
$874$	0.427914	0.0144744
$875$	−1.00000	−0.0338062
$876$	−0.649293	−0.0219376
$877$	29.0730	0.981724	0.490862	−	0.871237i	$-0.336682\pi$
$877$	29.0730	0.981724	0.490862	+	0.871237i	$0.336682\pi$
$878$	−60.7098	−2.04886
$879$	35.9805	1.21359
$880$	0.938105	0.0316235
$881$	−48.3263	−1.62815	−0.814077	−	0.580757i	$-0.802757\pi$
$881$	−48.3263	−1.62815	−0.814077	+	0.580757i	$0.802757\pi$
$882$	−6.60600	−0.222436
$883$	−7.38644	−0.248573	−0.124287	−	0.992246i	$-0.539664\pi$
$883$	−7.38644	−0.248573	−0.124287	+	0.992246i	$0.539664\pi$
$884$	−51.3048	−1.72557
$885$	22.8165	0.766968
$886$	64.2202	2.15752
$887$	−43.4485	−1.45886	−0.729429	−	0.684056i	$-0.760214\pi$
$887$	−43.4485	−1.45886	−0.729429	+	0.684056i	$0.760214\pi$
$888$	−42.2477	−1.41774
$889$	3.05354	0.102412
$890$	22.1095	0.741111
$891$	−10.5412	−0.353142
$892$	−29.6002	−0.991087
$893$	0.696023	0.0232915
$894$	117.210	3.92009
$895$	12.6970	0.424415
$896$	16.2190	0.541838
$897$	11.2731	0.376396
$898$	−54.1645	−1.80749
$899$	−12.2734	−0.409341
$900$	8.95641	0.298547
$901$	44.6556	1.48769
$902$	−23.2363	−0.773683
$903$	−8.61566	−0.286711
$904$	33.4689	1.11316
$905$	−4.98051	−0.165558
$906$	40.1399	1.33356
$907$	9.59538	0.318609	0.159305	−	0.987229i	$-0.449075\pi$
$907$	9.59538	0.318609	0.159305	+	0.987229i	$0.449075\pi$
$908$	82.7683	2.74676
$909$	−26.5129	−0.879378
$910$	10.7908	0.357711
$911$	−8.87647	−0.294091	−0.147045	−	0.989130i	$-0.546976\pi$
$911$	−8.87647	−0.294091	−0.147045	+	0.989130i	$0.546976\pi$
$912$	0.393762	0.0130387
$913$	−12.7206	−0.420991
$914$	46.7797	1.54734
$915$	−24.8925	−0.822919
$916$	3.04539	0.100622
$917$	−11.1368	−0.367769
$918$	1.13320	0.0374011
$919$	−31.3928	−1.03555	−0.517777	−	0.855516i	$-0.673240\pi$
$919$	−31.3928	−1.03555	−0.517777	+	0.855516i	$0.673240\pi$
$920$	−2.26064	−0.0745310
$921$	50.9364	1.67841
$922$	−76.5370	−2.52061
$923$	14.1840	0.466873
$924$	−8.52944	−0.280598
$925$	−7.38160	−0.242706
$926$	−63.3014	−2.08021
$927$	−42.6562	−1.40101
$928$	56.4347	1.85256
$929$	−24.4725	−0.802918	−0.401459	−	0.915877i	$-0.631497\pi$
$929$	−24.4725	−0.802918	−0.401459	+	0.915877i	$0.631497\pi$
$930$	7.77521	0.254959
$931$	0.197880	0.00648526
$932$	−38.5552	−1.26292
$933$	−57.7512	−1.89069
$934$	−59.7586	−1.95536
$935$	4.02958	0.131781
$936$	−33.1758	−1.08438
$937$	11.1959	0.365755	0.182877	−	0.983136i	$-0.441459\pi$
$937$	11.1959	0.365755	0.182877	+	0.983136i	$0.441459\pi$
$938$	29.3318	0.957717
$939$	−62.7239	−2.04692
$940$	−10.7118	−0.349381
$941$	−12.7067	−0.414225	−0.207113	−	0.978317i	$-0.566407\pi$
$941$	−12.7067	−0.414225	−0.207113	+	0.978317i	$0.566407\pi$
$942$	−4.10780	−0.133839
$943$	−8.66716	−0.282242
$944$	−7.64226	−0.248735
$945$	−0.143863	−0.00467986
$946$	−9.12339	−0.296627
$947$	−16.0225	−0.520661	−0.260331	−	0.965520i	$-0.583832\pi$
$947$	−16.0225	−0.520661	−0.260331	+	0.965520i	$0.583832\pi$
$948$	67.5386	2.19355
$949$	0.420218	0.0136409
$950$	−0.444477	−0.0144208
$951$	58.4668	1.89592
$952$	8.23444	0.266880
$953$	46.8613	1.51799	0.758994	−	0.651098i	$-0.225691\pi$
$953$	46.8613	1.51799	0.758994	+	0.651098i	$0.225691\pi$
$954$	84.1210	2.72352
$955$	−19.5718	−0.633329
$956$	8.01302	0.259160
$957$	−24.2051	−0.782441
$958$	73.2959	2.36808
$959$	10.3569	0.334441
$960$	−31.7716	−1.02543
$961$	−28.9832	−0.934941
$962$	79.6532	2.56812
$963$	43.7592	1.41012
$964$	82.9392	2.67129
$965$	12.6950	0.408665
$966$	−5.27088	−0.169588
$967$	8.48322	0.272802	0.136401	−	0.990654i	$-0.456446\pi$
$967$	8.48322	0.272802	0.136401	+	0.990654i	$0.456446\pi$
$968$	22.7291	0.730541
$969$	1.69138	0.0543350
$970$	−16.3815	−0.525979
$971$	25.7840	0.827447	0.413723	−	0.910403i	$-0.364228\pi$
$971$	25.7840	0.827447	0.413723	+	0.910403i	$0.364228\pi$
$972$	66.7799	2.14197
$973$	−18.3333	−0.587739
$974$	−21.5345	−0.690011
$975$	−11.7094	−0.375001
$976$	8.33759	0.266880
$977$	27.9068	0.892818	0.446409	−	0.894829i	$-0.352703\pi$
$977$	27.9068	0.892818	0.446409	+	0.894829i	$0.352703\pi$
$978$	89.2077	2.85255
$979$	11.3105	0.361484
$980$	−3.04539	−0.0972813
$981$	15.8463	0.505935
$982$	23.2386	0.741574
$983$	−38.8536	−1.23924	−0.619619	−	0.784903i	$-0.712713\pi$
$983$	−38.8536	−1.23924	−0.619619	+	0.784903i	$0.712713\pi$
$984$	51.5255	1.64257
$985$	6.94554	0.221303
$986$	68.0748	2.16794
$987$	−8.57333	−0.272892
$988$	2.89501	0.0921026
$989$	−3.40304	−0.108210
$990$	7.59081	0.241252
$991$	−16.4467	−0.522447	−0.261223	−	0.965278i	$-0.584126\pi$
$991$	−16.4467	−0.522447	−0.261223	+	0.965278i	$0.584126\pi$
$992$	−9.27371	−0.294441
$993$	−11.4123	−0.362159
$994$	−6.63194	−0.210352
$995$	27.5085	0.872078
$996$	82.1731	2.60376
$997$	−42.3335	−1.34071	−0.670357	−	0.742039i	$-0.733859\pi$
$997$	−42.3335	−1.34071	−0.670357	+	0.742039i	$0.733859\pi$
$998$	−49.3359	−1.56170
$999$	−1.06194	−0.0335982

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8015.2.a.j.1.7	✓	45

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8015.2.a.j.1.7	✓	45	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:	\( N \)	\(=\)	\( 8015 = 5 \cdot 7 \cdot 229 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8015.a (trivial)

\(f(q)\)	\(=\)	\(q-2.24619 q^{2} -2.43741 q^{3} +3.04539 q^{4} -1.00000 q^{5} +5.47490 q^{6} +1.00000 q^{7} -2.34814 q^{8} +2.94098 q^{9} +O(q^{10})\)	\(q-2.24619 q^{2} -2.43741 q^{3} +3.04539 q^{4} -1.00000 q^{5} +5.47490 q^{6} +1.00000 q^{7} -2.34814 q^{8} +2.94098 q^{9} +2.24619 q^{10} +1.14908 q^{11} -7.42286 q^{12} +4.80403 q^{13} -2.24619 q^{14} +2.43741 q^{15} -0.816398 q^{16} -3.50679 q^{17} -6.60600 q^{18} +0.197880 q^{19} -3.04539 q^{20} -2.43741 q^{21} -2.58105 q^{22} -0.962736 q^{23} +5.72338 q^{24} +1.00000 q^{25} -10.7908 q^{26} +0.143863 q^{27} +3.04539 q^{28} +8.64229 q^{29} -5.47490 q^{30} -1.42016 q^{31} +6.53006 q^{32} -2.80078 q^{33} +7.87694 q^{34} -1.00000 q^{35} +8.95641 q^{36} -7.38160 q^{37} -0.444477 q^{38} -11.7094 q^{39} +2.34814 q^{40} +9.00264 q^{41} +5.47490 q^{42} +3.53476 q^{43} +3.49938 q^{44} -2.94098 q^{45} +2.16249 q^{46} +3.51739 q^{47} +1.98990 q^{48} +1.00000 q^{49} -2.24619 q^{50} +8.54750 q^{51} +14.6301 q^{52} -12.7340 q^{53} -0.323144 q^{54} -1.14908 q^{55} -2.34814 q^{56} -0.482316 q^{57} -19.4123 q^{58} +9.36095 q^{59} +7.42286 q^{60} -10.2127 q^{61} +3.18995 q^{62} +2.94098 q^{63} -13.0350 q^{64} -4.80403 q^{65} +6.29108 q^{66} -13.0584 q^{67} -10.6795 q^{68} +2.34658 q^{69} +2.24619 q^{70} +2.95253 q^{71} -6.90582 q^{72} +0.0874720 q^{73} +16.5805 q^{74} -2.43741 q^{75} +0.602622 q^{76} +1.14908 q^{77} +26.3016 q^{78} -9.09873 q^{79} +0.816398 q^{80} -9.17358 q^{81} -20.2217 q^{82} -11.0703 q^{83} -7.42286 q^{84} +3.50679 q^{85} -7.93975 q^{86} -21.0648 q^{87} -2.69819 q^{88} +9.84309 q^{89} +6.60600 q^{90} +4.80403 q^{91} -2.93190 q^{92} +3.46151 q^{93} -7.90074 q^{94} -0.197880 q^{95} -15.9165 q^{96} -7.29301 q^{97} -2.24619 q^{98} +3.37941 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 45 q - 6 q^{2} + 34 q^{4} - 45 q^{5} + q^{6} + 45 q^{7} - 15 q^{8} + 29 q^{9}+O(q^{10}) \) 45 * q - 6 * q^2 + 34 * q^4 - 45 * q^5 + q^6 + 45 * q^7 - 15 * q^8 + 29 * q^9	\( 45 q - 6 q^{2} + 34 q^{4} - 45 q^{5} + q^{6} + 45 q^{7} - 15 q^{8} + 29 q^{9} + 6 q^{10} - q^{11} - 3 q^{12} - 21 q^{13} - 6 q^{14} + 8 q^{16} - 7 q^{17} - 36 q^{18} - 20 q^{19} - 34 q^{20} - 34 q^{22} - 22 q^{23} - 11 q^{24} + 45 q^{25} - q^{26} + 12 q^{27} + 34 q^{28} + 10 q^{29} - q^{30} - 27 q^{31} - 26 q^{32} - 39 q^{33} - 13 q^{34} - 45 q^{35} - 3 q^{36} - 72 q^{37} + 2 q^{38} - 37 q^{39} + 15 q^{40} - 4 q^{41} + q^{42} - 49 q^{43} + 5 q^{44} - 29 q^{45} - 67 q^{46} + 2 q^{47} + 8 q^{48} + 45 q^{49} - 6 q^{50} - 49 q^{51} - 47 q^{52} - 35 q^{53} - 12 q^{54} + q^{55} - 15 q^{56} - 77 q^{57} - 50 q^{58} + 4 q^{59} + 3 q^{60} - 36 q^{61} + 17 q^{62} + 29 q^{63} + 5 q^{64} + 21 q^{65} - 8 q^{66} - 80 q^{67} + 27 q^{68} + 9 q^{69} + 6 q^{70} - 12 q^{71} - 97 q^{72} - 55 q^{73} + 32 q^{74} - 37 q^{76} - q^{77} + 20 q^{78} - 94 q^{79} - 8 q^{80} - 19 q^{81} - 36 q^{82} + 24 q^{83} - 3 q^{84} + 7 q^{85} - 3 q^{86} - 4 q^{87} - 95 q^{88} + q^{89} + 36 q^{90} - 21 q^{91} - 65 q^{92} - 71 q^{93} - 53 q^{94} + 20 q^{95} - 13 q^{96} - 110 q^{97} - 6 q^{98} - 27 q^{99}+O(q^{100}) \) 45 * q - 6 * q^2 + 34 * q^4 - 45 * q^5 + q^6 + 45 * q^7 - 15 * q^8 + 29 * q^9 + 6 * q^10 - q^11 - 3 * q^12 - 21 * q^13 - 6 * q^14 + 8 * q^16 - 7 * q^17 - 36 * q^18 - 20 * q^19 - 34 * q^20 - 34 * q^22 - 22 * q^23 - 11 * q^24 + 45 * q^25 - q^26 + 12 * q^27 + 34 * q^28 + 10 * q^29 - q^30 - 27 * q^31 - 26 * q^32 - 39 * q^33 - 13 * q^34 - 45 * q^35 - 3 * q^36 - 72 * q^37 + 2 * q^38 - 37 * q^39 + 15 * q^40 - 4 * q^41 + q^42 - 49 * q^43 + 5 * q^44 - 29 * q^45 - 67 * q^46 + 2 * q^47 + 8 * q^48 + 45 * q^49 - 6 * q^50 - 49 * q^51 - 47 * q^52 - 35 * q^53 - 12 * q^54 + q^55 - 15 * q^56 - 77 * q^57 - 50 * q^58 + 4 * q^59 + 3 * q^60 - 36 * q^61 + 17 * q^62 + 29 * q^63 + 5 * q^64 + 21 * q^65 - 8 * q^66 - 80 * q^67 + 27 * q^68 + 9 * q^69 + 6 * q^70 - 12 * q^71 - 97 * q^72 - 55 * q^73 + 32 * q^74 - 37 * q^76 - q^77 + 20 * q^78 - 94 * q^79 - 8 * q^80 - 19 * q^81 - 36 * q^82 + 24 * q^83 - 3 * q^84 + 7 * q^85 - 3 * q^86 - 4 * q^87 - 95 * q^88 + q^89 + 36 * q^90 - 21 * q^91 - 65 * q^92 - 71 * q^93 - 53 * q^94 + 20 * q^95 - 13 * q^96 - 110 * q^97 - 6 * q^98 - 27 * q^99

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