LMFDB - Embedded newform 6015.2.a.h.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6015,2,Mod(1,6015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6015, 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("6015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6015 = 3 \cdot 5 \cdot 401 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6015.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:	$48.0300168158$
Analytic rank:	$0$
Dimension:	$39$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	6015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.73278 q^{2} +1.00000 q^{3} +5.46807 q^{4} -1.00000 q^{5} -2.73278 q^{6} -1.71200 q^{7} -9.47746 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.73278 q^{2} +1.00000 q^{3} +5.46807 q^{4} -1.00000 q^{5} -2.73278 q^{6} -1.71200 q^{7} -9.47746 q^{8} +1.00000 q^{9} +2.73278 q^{10} -4.31366 q^{11} +5.46807 q^{12} +6.69453 q^{13} +4.67852 q^{14} -1.00000 q^{15} +14.9636 q^{16} +2.29187 q^{17} -2.73278 q^{18} +2.15108 q^{19} -5.46807 q^{20} -1.71200 q^{21} +11.7883 q^{22} -1.55568 q^{23} -9.47746 q^{24} +1.00000 q^{25} -18.2946 q^{26} +1.00000 q^{27} -9.36135 q^{28} +4.71374 q^{29} +2.73278 q^{30} +2.30777 q^{31} -21.9374 q^{32} -4.31366 q^{33} -6.26316 q^{34} +1.71200 q^{35} +5.46807 q^{36} +10.2899 q^{37} -5.87843 q^{38} +6.69453 q^{39} +9.47746 q^{40} +2.57185 q^{41} +4.67852 q^{42} +2.31757 q^{43} -23.5874 q^{44} -1.00000 q^{45} +4.25132 q^{46} -0.498820 q^{47} +14.9636 q^{48} -4.06905 q^{49} -2.73278 q^{50} +2.29187 q^{51} +36.6061 q^{52} +8.10086 q^{53} -2.73278 q^{54} +4.31366 q^{55} +16.2254 q^{56} +2.15108 q^{57} -12.8816 q^{58} +0.0343004 q^{59} -5.46807 q^{60} -10.4745 q^{61} -6.30663 q^{62} -1.71200 q^{63} +30.0227 q^{64} -6.69453 q^{65} +11.7883 q^{66} -1.88257 q^{67} +12.5321 q^{68} -1.55568 q^{69} -4.67852 q^{70} -0.812646 q^{71} -9.47746 q^{72} -10.2482 q^{73} -28.1200 q^{74} +1.00000 q^{75} +11.7623 q^{76} +7.38500 q^{77} -18.2946 q^{78} -10.6392 q^{79} -14.9636 q^{80} +1.00000 q^{81} -7.02828 q^{82} +4.04540 q^{83} -9.36135 q^{84} -2.29187 q^{85} -6.33339 q^{86} +4.71374 q^{87} +40.8826 q^{88} -10.1106 q^{89} +2.73278 q^{90} -11.4610 q^{91} -8.50656 q^{92} +2.30777 q^{93} +1.36316 q^{94} -2.15108 q^{95} -21.9374 q^{96} -10.3510 q^{97} +11.1198 q^{98} -4.31366 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 39 q + 39 q^{3} + 48 q^{4} - 39 q^{5} + 22 q^{7} + 3 q^{8} + 39 q^{9}+O(q^{10}) $ 39 * q + 39 * q^3 + 48 * q^4 - 39 * q^5 + 22 * q^7 + 3 * q^8 + 39 * q^9	\( 39 q + 39 q^{3} + 48 q^{4} - 39 q^{5} + 22 q^{7} + 3 q^{8} + 39 q^{9} - q^{11} + 48 q^{12} + 30 q^{13} + 8 q^{14} - 39 q^{15} + 58 q^{16} + 32 q^{17} + 27 q^{19} - 48 q^{20} + 22 q^{21} + 23 q^{22} - 8 q^{23} + 3 q^{24} + 39 q^{25} - 4 q^{26} + 39 q^{27} + 60 q^{28} - 9 q^{29} + 19 q^{31} + q^{32} - q^{33} + 26 q^{34} - 22 q^{35} + 48 q^{36} + 44 q^{37} + 14 q^{38} + 30 q^{39} - 3 q^{40} + 31 q^{41} + 8 q^{42} + 75 q^{43} + q^{44} - 39 q^{45} + 19 q^{46} - 16 q^{47} + 58 q^{48} + 91 q^{49} + 32 q^{51} + 94 q^{52} + 17 q^{53} + q^{55} + 27 q^{56} + 27 q^{57} + 26 q^{58} - q^{59} - 48 q^{60} + 55 q^{61} + 11 q^{62} + 22 q^{63} + 77 q^{64} - 30 q^{65} + 23 q^{66} + 84 q^{67} + 36 q^{68} - 8 q^{69} - 8 q^{70} - 2 q^{71} + 3 q^{72} + 79 q^{73} + 20 q^{74} + 39 q^{75} + 58 q^{76} + 32 q^{77} - 4 q^{78} + 29 q^{79} - 58 q^{80} + 39 q^{81} + 53 q^{82} + 9 q^{83} + 60 q^{84} - 32 q^{85} - 17 q^{86} - 9 q^{87} + 57 q^{88} + 37 q^{89} + 71 q^{91} + 7 q^{92} + 19 q^{93} + 32 q^{94} - 27 q^{95} + q^{96} + 91 q^{97} - 9 q^{98} - q^{99}+O(q^{100}) \) 39 * q + 39 * q^3 + 48 * q^4 - 39 * q^5 + 22 * q^7 + 3 * q^8 + 39 * q^9 - q^11 + 48 * q^12 + 30 * q^13 + 8 * q^14 - 39 * q^15 + 58 * q^16 + 32 * q^17 + 27 * q^19 - 48 * q^20 + 22 * q^21 + 23 * q^22 - 8 * q^23 + 3 * q^24 + 39 * q^25 - 4 * q^26 + 39 * q^27 + 60 * q^28 - 9 * q^29 + 19 * q^31 + q^32 - q^33 + 26 * q^34 - 22 * q^35 + 48 * q^36 + 44 * q^37 + 14 * q^38 + 30 * q^39 - 3 * q^40 + 31 * q^41 + 8 * q^42 + 75 * q^43 + q^44 - 39 * q^45 + 19 * q^46 - 16 * q^47 + 58 * q^48 + 91 * q^49 + 32 * q^51 + 94 * q^52 + 17 * q^53 + q^55 + 27 * q^56 + 27 * q^57 + 26 * q^58 - q^59 - 48 * q^60 + 55 * q^61 + 11 * q^62 + 22 * q^63 + 77 * q^64 - 30 * q^65 + 23 * q^66 + 84 * q^67 + 36 * q^68 - 8 * q^69 - 8 * q^70 - 2 * q^71 + 3 * q^72 + 79 * q^73 + 20 * q^74 + 39 * q^75 + 58 * q^76 + 32 * q^77 - 4 * q^78 + 29 * q^79 - 58 * q^80 + 39 * q^81 + 53 * q^82 + 9 * q^83 + 60 * q^84 - 32 * q^85 - 17 * q^86 - 9 * q^87 + 57 * q^88 + 37 * q^89 + 71 * q^91 + 7 * q^92 + 19 * q^93 + 32 * q^94 - 27 * q^95 + q^96 + 91 * q^97 - 9 * q^98 - 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 $

$2$	−2.73278	−1.93237	−0.966183	−	0.257859i	$-0.916983\pi$
$2$	−2.73278	−1.93237	−0.966183	+	0.257859i	$0.916983\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	5.46807	2.73403
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−2.73278	−1.11565
$7$	−1.71200	−0.647076	−0.323538	−	0.946215i	$-0.604872\pi$
$7$	−1.71200	−0.647076	−0.323538	+	0.946215i	$0.604872\pi$
$8$	−9.47746	−3.35079
$9$	1.00000	0.333333
$10$	2.73278	0.864180
$11$	−4.31366	−1.30062	−0.650309	−	0.759670i	$-0.725361\pi$
$11$	−4.31366	−1.30062	−0.650309	+	0.759670i	$0.725361\pi$
$12$	5.46807	1.57850
$13$	6.69453	1.85673	0.928364	−	0.371673i	$-0.121216\pi$
$13$	6.69453	1.85673	0.928364	+	0.371673i	$0.121216\pi$
$14$	4.67852	1.25039
$15$	−1.00000	−0.258199
$16$	14.9636	3.74091
$17$	2.29187	0.555859	0.277930	−	0.960601i	$-0.410352\pi$
$17$	2.29187	0.555859	0.277930	+	0.960601i	$0.410352\pi$
$18$	−2.73278	−0.644122
$19$	2.15108	0.493492	0.246746	−	0.969080i	$-0.420639\pi$
$19$	2.15108	0.493492	0.246746	+	0.969080i	$0.420639\pi$
$20$	−5.46807	−1.22270
$21$	−1.71200	−0.373590
$22$	11.7883	2.51327
$23$	−1.55568	−0.324381	−0.162191	−	0.986759i	$-0.551856\pi$
$23$	−1.55568	−0.324381	−0.162191	+	0.986759i	$0.551856\pi$
$24$	−9.47746	−1.93458
$25$	1.00000	0.200000
$26$	−18.2946	−3.58787
$27$	1.00000	0.192450
$28$	−9.36135	−1.76913
$29$	4.71374	0.875319	0.437659	−	0.899141i	$-0.355808\pi$
$29$	4.71374	0.875319	0.437659	+	0.899141i	$0.355808\pi$
$30$	2.73278	0.498935
$31$	2.30777	0.414488	0.207244	−	0.978289i	$-0.433551\pi$
$31$	2.30777	0.414488	0.207244	+	0.978289i	$0.433551\pi$
$32$	−21.9374	−3.87802
$33$	−4.31366	−0.750912
$34$	−6.26316	−1.07412
$35$	1.71200	0.289381
$36$	5.46807	0.911345
$37$	10.2899	1.69165	0.845825	−	0.533461i	$-0.179109\pi$
$37$	10.2899	1.69165	0.845825	+	0.533461i	$0.179109\pi$
$38$	−5.87843	−0.953607
$39$	6.69453	1.07198
$40$	9.47746	1.49852
$41$	2.57185	0.401655	0.200828	−	0.979627i	$-0.435637\pi$
$41$	2.57185	0.401655	0.200828	+	0.979627i	$0.435637\pi$
$42$	4.67852	0.721912
$43$	2.31757	0.353426	0.176713	−	0.984262i	$-0.443454\pi$
$43$	2.31757	0.353426	0.176713	+	0.984262i	$0.443454\pi$
$44$	−23.5874	−3.55594
$45$	−1.00000	−0.149071
$46$	4.25132	0.626823
$47$	−0.498820	−0.0727603	−0.0363802	−	0.999338i	$-0.511583\pi$
$47$	−0.498820	−0.0727603	−0.0363802	+	0.999338i	$0.511583\pi$
$48$	14.9636	2.15982
$49$	−4.06905	−0.581292
$50$	−2.73278	−0.386473
$51$	2.29187	0.320925
$52$	36.6061	5.07636
$53$	8.10086	1.11274	0.556369	−	0.830935i	$-0.312194\pi$
$53$	8.10086	1.11274	0.556369	+	0.830935i	$0.312194\pi$
$54$	−2.73278	−0.371884
$55$	4.31366	0.581654
$56$	16.2254	2.16822
$57$	2.15108	0.284918
$58$	−12.8816	−1.69144
$59$	0.0343004	0.00446554	0.00223277	−	0.999998i	$-0.499289\pi$
$59$	0.0343004	0.00446554	0.00223277	+	0.999998i	$0.499289\pi$
$60$	−5.46807	−0.705925
$61$	−10.4745	−1.34113	−0.670564	−	0.741852i	$-0.733948\pi$
$61$	−10.4745	−1.34113	−0.670564	+	0.741852i	$0.733948\pi$
$62$	−6.30663	−0.800942
$63$	−1.71200	−0.215692
$64$	30.0227	3.75283
$65$	−6.69453	−0.830354
$66$	11.7883	1.45104
$67$	−1.88257	−0.229992	−0.114996	−	0.993366i	$-0.536686\pi$
$67$	−1.88257	−0.229992	−0.114996	+	0.993366i	$0.536686\pi$
$68$	12.5321	1.51974
$69$	−1.55568	−0.187282
$70$	−4.67852	−0.559190
$71$	−0.812646	−0.0964433	−0.0482217	−	0.998837i	$-0.515355\pi$
$71$	−0.812646	−0.0964433	−0.0482217	+	0.998837i	$0.515355\pi$
$72$	−9.47746	−1.11693
$73$	−10.2482	−1.19946	−0.599731	−	0.800202i	$-0.704726\pi$
$73$	−10.2482	−1.19946	−0.599731	+	0.800202i	$0.704726\pi$
$74$	−28.1200	−3.26888
$75$	1.00000	0.115470
$76$	11.7623	1.34922
$77$	7.38500	0.841599
$78$	−18.2946	−2.07146
$79$	−10.6392	−1.19700	−0.598501	−	0.801122i	$-0.704237\pi$
$79$	−10.6392	−1.19700	−0.598501	+	0.801122i	$0.704237\pi$
$80$	−14.9636	−1.67299
$81$	1.00000	0.111111
$82$	−7.02828	−0.776144
$83$	4.04540	0.444040	0.222020	−	0.975042i	$-0.428735\pi$
$83$	4.04540	0.444040	0.222020	+	0.975042i	$0.428735\pi$
$84$	−9.36135	−1.02141
$85$	−2.29187	−0.248588
$86$	−6.33339	−0.682947
$87$	4.71374	0.505366
$88$	40.8826	4.35810
$89$	−10.1106	−1.07172	−0.535860	−	0.844307i	$-0.680013\pi$
$89$	−10.1106	−1.07172	−0.535860	+	0.844307i	$0.680013\pi$
$90$	2.73278	0.288060
$91$	−11.4610	−1.20144
$92$	−8.50656	−0.886870
$93$	2.30777	0.239305
$94$	1.36316	0.140599
$95$	−2.15108	−0.220696
$96$	−21.9374	−2.23897
$97$	−10.3510	−1.05098	−0.525492	−	0.850799i	$-0.676119\pi$
$97$	−10.3510	−1.05098	−0.525492	+	0.850799i	$0.676119\pi$
$98$	11.1198	1.12327
$99$	−4.31366	−0.433539
$100$	5.46807	0.546807
$101$	4.10770	0.408731	0.204366	−	0.978895i	$-0.434487\pi$
$101$	4.10770	0.408731	0.204366	+	0.978895i	$0.434487\pi$
$102$	−6.26316	−0.620145
$103$	−11.4912	−1.13226	−0.566130	−	0.824316i	$-0.691560\pi$
$103$	−11.4912	−1.13226	−0.566130	+	0.824316i	$0.691560\pi$
$104$	−63.4471	−6.22150
$105$	1.71200	0.167074
$106$	−22.1378	−2.15022
$107$	3.74907	0.362436	0.181218	−	0.983443i	$-0.441996\pi$
$107$	3.74907	0.362436	0.181218	+	0.983443i	$0.441996\pi$
$108$	5.46807	0.526165
$109$	−9.47092	−0.907150	−0.453575	−	0.891218i	$-0.649852\pi$
$109$	−9.47092	−0.907150	−0.453575	+	0.891218i	$0.649852\pi$
$110$	−11.7883	−1.12397
$111$	10.2899	0.976674
$112$	−25.6178	−2.42065
$113$	−2.41569	−0.227249	−0.113625	−	0.993524i	$-0.536246\pi$
$113$	−2.41569	−0.227249	−0.113625	+	0.993524i	$0.536246\pi$
$114$	−5.87843	−0.550565
$115$	1.55568	0.145068
$116$	25.7750	2.39315
$117$	6.69453	0.618909
$118$	−0.0937354	−0.00862905
$119$	−3.92368	−0.359683
$120$	9.47746	0.865170
$121$	7.60769	0.691608
$122$	28.6246	2.59155
$123$	2.57185	0.231896
$124$	12.6191	1.13322
$125$	−1.00000	−0.0894427
$126$	4.67852	0.416796
$127$	19.0279	1.68845	0.844224	−	0.535990i	$-0.180062\pi$
$127$	19.0279	1.68845	0.844224	+	0.535990i	$0.180062\pi$
$128$	−38.1705	−3.37383
$129$	2.31757	0.204050
$130$	18.2946	1.60455
$131$	5.48769	0.479462	0.239731	−	0.970839i	$-0.422941\pi$
$131$	5.48769	0.479462	0.239731	+	0.970839i	$0.422941\pi$
$132$	−23.5874	−2.05302
$133$	−3.68266	−0.319327
$134$	5.14463	0.444428
$135$	−1.00000	−0.0860663
$136$	−21.7211	−1.86257
$137$	−4.11472	−0.351544	−0.175772	−	0.984431i	$-0.556242\pi$
$137$	−4.11472	−0.351544	−0.175772	+	0.984431i	$0.556242\pi$
$138$	4.25132	0.361897
$139$	−2.63013	−0.223085	−0.111542	−	0.993760i	$-0.535579\pi$
$139$	−2.63013	−0.223085	−0.111542	+	0.993760i	$0.535579\pi$
$140$	9.36135	0.791179
$141$	−0.498820	−0.0420082
$142$	2.22078	0.186364
$143$	−28.8779	−2.41489
$144$	14.9636	1.24697
$145$	−4.71374	−0.391455
$146$	28.0061	2.31780
$147$	−4.06905	−0.335609
$148$	56.2659	4.62503
$149$	−0.250366	−0.0205108	−0.0102554	−	0.999947i	$-0.503264\pi$
$149$	−0.250366	−0.0205108	−0.0102554	+	0.999947i	$0.503264\pi$
$150$	−2.73278	−0.223130
$151$	−16.7372	−1.36205	−0.681027	−	0.732258i	$-0.738467\pi$
$151$	−16.7372	−1.36205	−0.681027	+	0.732258i	$0.738467\pi$
$152$	−20.3868	−1.65359
$153$	2.29187	0.185286
$154$	−20.1816	−1.62628
$155$	−2.30777	−0.185365
$156$	36.6061	2.93084
$157$	17.9633	1.43363	0.716815	−	0.697264i	$-0.245599\pi$
$157$	17.9633	1.43363	0.716815	+	0.697264i	$0.245599\pi$
$158$	29.0745	2.31305
$159$	8.10086	0.642440
$160$	21.9374	1.73430
$161$	2.66333	0.209900
$162$	−2.73278	−0.214707
$163$	10.0195	0.784788	0.392394	−	0.919797i	$-0.371647\pi$
$163$	10.0195	0.784788	0.392394	+	0.919797i	$0.371647\pi$
$164$	14.0630	1.09814
$165$	4.31366	0.335818
$166$	−11.0552	−0.858047
$167$	19.7478	1.52813	0.764064	−	0.645141i	$-0.223201\pi$
$167$	19.7478	1.52813	0.764064	+	0.645141i	$0.223201\pi$
$168$	16.2254	1.25182
$169$	31.8167	2.44744
$170$	6.26316	0.480362
$171$	2.15108	0.164497
$172$	12.6726	0.966278
$173$	16.2195	1.23314	0.616572	−	0.787298i	$-0.288521\pi$
$173$	16.2195	1.23314	0.616572	+	0.787298i	$0.288521\pi$
$174$	−12.8816	−0.976551
$175$	−1.71200	−0.129415
$176$	−64.5481	−4.86550
$177$	0.0343004	0.00257818
$178$	27.6300	2.07096
$179$	−18.6263	−1.39219	−0.696097	−	0.717947i	$-0.745082\pi$
$179$	−18.6263	−1.39219	−0.696097	+	0.717947i	$0.745082\pi$
$180$	−5.46807	−0.407566
$181$	19.3451	1.43791	0.718956	−	0.695055i	$-0.244620\pi$
$181$	19.3451	1.43791	0.718956	+	0.695055i	$0.244620\pi$
$182$	31.3205	2.32163
$183$	−10.4745	−0.774301
$184$	14.7439	1.08693
$185$	−10.2899	−0.756529
$186$	−6.30663	−0.462424
$187$	−9.88634	−0.722960
$188$	−2.72758	−0.198929
$189$	−1.71200	−0.124530
$190$	5.87843	0.426466
$191$	15.4616	1.11876	0.559381	−	0.828910i	$-0.311039\pi$
$191$	15.4616	1.11876	0.559381	+	0.828910i	$0.311039\pi$
$192$	30.0227	2.16670
$193$	−3.46771	−0.249611	−0.124806	−	0.992181i	$-0.539831\pi$
$193$	−3.46771	−0.249611	−0.124806	+	0.992181i	$0.539831\pi$
$194$	28.2869	2.03088
$195$	−6.69453	−0.479405
$196$	−22.2498	−1.58927
$197$	−8.46550	−0.603142	−0.301571	−	0.953444i	$-0.597511\pi$
$197$	−8.46550	−0.603142	−0.301571	+	0.953444i	$0.597511\pi$
$198$	11.7883	0.837756
$199$	10.4342	0.739661	0.369830	−	0.929099i	$-0.379416\pi$
$199$	10.4342	0.739661	0.369830	+	0.929099i	$0.379416\pi$
$200$	−9.47746	−0.670158
$201$	−1.88257	−0.132786
$202$	−11.2254	−0.789818
$203$	−8.06993	−0.566398
$204$	12.5321	0.877421
$205$	−2.57185	−0.179626
$206$	31.4029	2.18794
$207$	−1.55568	−0.108127
$208$	100.174	6.94585
$209$	−9.27904	−0.641845
$210$	−4.67852	−0.322849
$211$	16.0086	1.10208	0.551038	−	0.834480i	$-0.314232\pi$
$211$	16.0086	1.10208	0.551038	+	0.834480i	$0.314232\pi$
$212$	44.2961	3.04227
$213$	−0.812646	−0.0556816
$214$	−10.2454	−0.700358
$215$	−2.31757	−0.158057
$216$	−9.47746	−0.644859
$217$	−3.95091	−0.268205
$218$	25.8819	1.75294
$219$	−10.2482	−0.692510
$220$	23.5874	1.59026
$221$	15.3430	1.03208
$222$	−28.1200	−1.88729
$223$	−18.7932	−1.25848	−0.629242	−	0.777210i	$-0.716634\pi$
$223$	−18.7932	−1.25848	−0.629242	+	0.777210i	$0.716634\pi$
$224$	37.5569	2.50937
$225$	1.00000	0.0666667
$226$	6.60154	0.439128
$227$	25.1202	1.66728	0.833642	−	0.552305i	$-0.186252\pi$
$227$	25.1202	1.66728	0.833642	+	0.552305i	$0.186252\pi$
$228$	11.7623	0.778975
$229$	28.1760	1.86192	0.930961	−	0.365119i	$-0.118972\pi$
$229$	28.1760	1.86192	0.930961	+	0.365119i	$0.118972\pi$
$230$	−4.25132	−0.280324
$231$	7.38500	0.485898
$232$	−44.6742	−2.93301
$233$	−2.71865	−0.178105	−0.0890524	−	0.996027i	$-0.528384\pi$
$233$	−2.71865	−0.178105	−0.0890524	+	0.996027i	$0.528384\pi$
$234$	−18.2946	−1.19596
$235$	0.498820	0.0325394
$236$	0.187557	0.0122089
$237$	−10.6392	−0.691090
$238$	10.7225	0.695039
$239$	−22.1956	−1.43571	−0.717855	−	0.696192i	$-0.754876\pi$
$239$	−22.1956	−1.43571	−0.717855	+	0.696192i	$0.754876\pi$
$240$	−14.9636	−0.965899
$241$	28.4003	1.82942	0.914712	−	0.404106i	$-0.132417\pi$
$241$	28.4003	1.82942	0.914712	+	0.404106i	$0.132417\pi$
$242$	−20.7901	−1.33644
$243$	1.00000	0.0641500
$244$	−57.2755	−3.66669
$245$	4.06905	0.259962
$246$	−7.02828	−0.448107
$247$	14.4005	0.916280
$248$	−21.8718	−1.38886
$249$	4.04540	0.256367
$250$	2.73278	0.172836
$251$	−8.17384	−0.515928	−0.257964	−	0.966154i	$-0.583052\pi$
$251$	−8.17384	−0.515928	−0.257964	+	0.966154i	$0.583052\pi$
$252$	−9.36135	−0.589710
$253$	6.71067	0.421896
$254$	−51.9989	−3.26270
$255$	−2.29187	−0.143522
$256$	44.2661	2.76663
$257$	16.9883	1.05970	0.529851	−	0.848091i	$-0.322248\pi$
$257$	16.9883	1.05970	0.529851	+	0.848091i	$0.322248\pi$
$258$	−6.33339	−0.394300
$259$	−17.6163	−1.09463
$260$	−36.6061	−2.27022
$261$	4.71374	0.291773
$262$	−14.9966	−0.926495
$263$	5.01956	0.309520	0.154760	−	0.987952i	$-0.450540\pi$
$263$	5.01956	0.309520	0.154760	+	0.987952i	$0.450540\pi$
$264$	40.8826	2.51615
$265$	−8.10086	−0.497632
$266$	10.0639	0.617057
$267$	−10.1106	−0.618758
$268$	−10.2940	−0.628806
$269$	−24.4564	−1.49113	−0.745566	−	0.666432i	$-0.767821\pi$
$269$	−24.4564	−1.49113	−0.745566	+	0.666432i	$0.767821\pi$
$270$	2.73278	0.166312
$271$	−22.0105	−1.33705	−0.668523	−	0.743692i	$-0.733073\pi$
$271$	−22.0105	−1.33705	−0.668523	+	0.743692i	$0.733073\pi$
$272$	34.2947	2.07942
$273$	−11.4610	−0.693654
$274$	11.2446	0.679312
$275$	−4.31366	−0.260124
$276$	−8.50656	−0.512035
$277$	23.7348	1.42609	0.713043	−	0.701120i	$-0.247316\pi$
$277$	23.7348	1.42609	0.713043	+	0.701120i	$0.247316\pi$
$278$	7.18757	0.431082
$279$	2.30777	0.138163
$280$	−16.2254	−0.969656
$281$	−14.7352	−0.879029	−0.439514	−	0.898236i	$-0.644849\pi$
$281$	−14.7352	−0.879029	−0.439514	+	0.898236i	$0.644849\pi$
$282$	1.36316	0.0811751
$283$	24.9343	1.48219	0.741097	−	0.671398i	$-0.234306\pi$
$283$	24.9343	1.48219	0.741097	+	0.671398i	$0.234306\pi$
$284$	−4.44360	−0.263679
$285$	−2.15108	−0.127419
$286$	78.9169	4.66646
$287$	−4.40301	−0.259901
$288$	−21.9374	−1.29267
$289$	−11.7474	−0.691021
$290$	12.8816	0.756433
$291$	−10.3510	−0.606785
$292$	−56.0379	−3.27937
$293$	20.9390	1.22327	0.611636	−	0.791139i	$-0.290512\pi$
$293$	20.9390	1.22327	0.611636	+	0.791139i	$0.290512\pi$
$294$	11.1198	0.648519
$295$	−0.0343004	−0.00199705
$296$	−97.5221	−5.66836
$297$	−4.31366	−0.250304
$298$	0.684194	0.0396343
$299$	−10.4145	−0.602288
$300$	5.46807	0.315699
$301$	−3.96768	−0.228693
$302$	45.7391	2.63199
$303$	4.10770	0.235981
$304$	32.1880	1.84611
$305$	10.4745	0.599771
$306$	−6.26316	−0.358041
$307$	−6.51501	−0.371832	−0.185916	−	0.982566i	$-0.559525\pi$
$307$	−6.51501	−0.371832	−0.185916	+	0.982566i	$0.559525\pi$
$308$	40.3817	2.30096
$309$	−11.4912	−0.653711
$310$	6.30663	0.358192
$311$	24.0358	1.36294	0.681472	−	0.731844i	$-0.261340\pi$
$311$	24.0358	1.36294	0.681472	+	0.731844i	$0.261340\pi$
$312$	−63.4471	−3.59198
$313$	27.5340	1.55632	0.778158	−	0.628069i	$-0.216154\pi$
$313$	27.5340	1.55632	0.778158	+	0.628069i	$0.216154\pi$
$314$	−49.0898	−2.77030
$315$	1.71200	0.0964605
$316$	−58.1759	−3.27265
$317$	14.7656	0.829320	0.414660	−	0.909976i	$-0.363901\pi$
$317$	14.7656	0.829320	0.414660	+	0.909976i	$0.363901\pi$
$318$	−22.1378	−1.24143
$319$	−20.3335	−1.13846
$320$	−30.0227	−1.67832
$321$	3.74907	0.209252
$322$	−7.27828	−0.405603
$323$	4.92999	0.274312
$324$	5.46807	0.303782
$325$	6.69453	0.371345
$326$	−27.3811	−1.51650
$327$	−9.47092	−0.523743
$328$	−24.3746	−1.34586
$329$	0.853981	0.0470815
$330$	−11.7883	−0.648923
$331$	1.79871	0.0988658	0.0494329	−	0.998777i	$-0.484259\pi$
$331$	1.79871	0.0988658	0.0494329	+	0.998777i	$0.484259\pi$
$332$	22.1205	1.21402
$333$	10.2899	0.563883
$334$	−53.9662	−2.95290
$335$	1.88257	0.102856
$336$	−25.6178	−1.39757
$337$	17.4718	0.951752	0.475876	−	0.879512i	$-0.342131\pi$
$337$	17.4718	0.951752	0.475876	+	0.879512i	$0.342131\pi$
$338$	−86.9479	−4.72934
$339$	−2.41569	−0.131202
$340$	−12.5321	−0.679647
$341$	−9.95495	−0.539091
$342$	−5.87843	−0.317869
$343$	18.9502	1.02322
$344$	−21.9646	−1.18425
$345$	1.55568	0.0837549
$346$	−44.3242	−2.38288
$347$	−2.62074	−0.140689	−0.0703443	−	0.997523i	$-0.522410\pi$
$347$	−2.62074	−0.140689	−0.0703443	+	0.997523i	$0.522410\pi$
$348$	25.7750	1.38169
$349$	27.4084	1.46714	0.733568	−	0.679616i	$-0.237854\pi$
$349$	27.4084	1.46714	0.733568	+	0.679616i	$0.237854\pi$
$350$	4.67852	0.250078
$351$	6.69453	0.357327
$352$	94.6304	5.04382
$353$	−6.70016	−0.356614	−0.178307	−	0.983975i	$-0.557062\pi$
$353$	−6.70016	−0.356614	−0.178307	+	0.983975i	$0.557062\pi$
$354$	−0.0937354	−0.00498198
$355$	0.812646	0.0431308
$356$	−55.2854	−2.93012
$357$	−3.92368	−0.207663
$358$	50.9015	2.69023
$359$	7.30638	0.385616	0.192808	−	0.981236i	$-0.438241\pi$
$359$	7.30638	0.385616	0.192808	+	0.981236i	$0.438241\pi$
$360$	9.47746	0.499506
$361$	−14.3728	−0.756466
$362$	−52.8659	−2.77857
$363$	7.60769	0.399300
$364$	−62.6698	−3.28479
$365$	10.2482	0.536416
$366$	28.6246	1.49623
$367$	−18.4042	−0.960694	−0.480347	−	0.877079i	$-0.659489\pi$
$367$	−18.4042	−0.960694	−0.480347	+	0.877079i	$0.659489\pi$
$368$	−23.2786	−1.21348
$369$	2.57185	0.133885
$370$	28.1200	1.46189
$371$	−13.8687	−0.720027
$372$	12.6191	0.654268
$373$	−5.69127	−0.294683	−0.147341	−	0.989086i	$-0.547072\pi$
$373$	−5.69127	−0.294683	−0.147341	+	0.989086i	$0.547072\pi$
$374$	27.0171	1.39702
$375$	−1.00000	−0.0516398
$376$	4.72754	0.243804
$377$	31.5562	1.62523
$378$	4.67852	0.240637
$379$	−15.4931	−0.795829	−0.397915	−	0.917422i	$-0.630266\pi$
$379$	−15.4931	−0.795829	−0.397915	+	0.917422i	$0.630266\pi$
$380$	−11.7623	−0.603392
$381$	19.0279	0.974826
$382$	−42.2531	−2.16186
$383$	14.6540	0.748784	0.374392	−	0.927270i	$-0.377851\pi$
$383$	14.6540	0.748784	0.374392	+	0.927270i	$0.377851\pi$
$384$	−38.1705	−1.94788
$385$	−7.38500	−0.376375
$386$	9.47648	0.482340
$387$	2.31757	0.117809
$388$	−56.5999	−2.87342
$389$	35.9615	1.82332	0.911660	−	0.410944i	$-0.134801\pi$
$389$	35.9615	1.82332	0.911660	+	0.410944i	$0.134801\pi$
$390$	18.2946	0.926385
$391$	−3.56541	−0.180310
$392$	38.5642	1.94779
$393$	5.48769	0.276817
$394$	23.1343	1.16549
$395$	10.6392	0.535316
$396$	−23.5874	−1.18531
$397$	−21.1553	−1.06175	−0.530877	−	0.847449i	$-0.678137\pi$
$397$	−21.1553	−1.06175	−0.530877	+	0.847449i	$0.678137\pi$
$398$	−28.5143	−1.42929
$399$	−3.68266	−0.184364
$400$	14.9636	0.748182
$401$	−1.00000	−0.0499376
$401$	−1.00000	−0.0499376
$402$	5.14463	0.256591
$403$	15.4494	0.769591
$404$	22.4612	1.11749
$405$	−1.00000	−0.0496904
$406$	22.0533	1.09449
$407$	−44.3872	−2.20019
$408$	−21.7211	−1.07535
$409$	−4.88321	−0.241459	−0.120730	−	0.992685i	$-0.538523\pi$
$409$	−4.88321	−0.241459	−0.120730	+	0.992685i	$0.538523\pi$
$410$	7.02828	0.347102
$411$	−4.11472	−0.202964
$412$	−62.8346	−3.09564
$413$	−0.0587225	−0.00288954
$414$	4.25132	0.208941
$415$	−4.04540	−0.198581
$416$	−146.860	−7.20042
$417$	−2.63013	−0.128798
$418$	25.3576	1.24028
$419$	−0.698245	−0.0341115	−0.0170557	−	0.999855i	$-0.505429\pi$
$419$	−0.698245	−0.0341115	−0.0170557	+	0.999855i	$0.505429\pi$
$420$	9.36135	0.456787
$421$	16.5350	0.805867	0.402933	−	0.915229i	$-0.367991\pi$
$421$	16.5350	0.805867	0.402933	+	0.915229i	$0.367991\pi$
$422$	−43.7479	−2.12961
$423$	−0.498820	−0.0242534
$424$	−76.7756	−3.72855
$425$	2.29187	0.111172
$426$	2.22078	0.107597
$427$	17.9325	0.867813
$428$	20.5001	0.990912
$429$	−28.8779	−1.39424
$430$	6.33339	0.305423
$431$	8.22154	0.396018	0.198009	−	0.980200i	$-0.436553\pi$
$431$	8.22154	0.396018	0.198009	+	0.980200i	$0.436553\pi$
$432$	14.9636	0.719939
$433$	−14.3270	−0.688511	−0.344256	−	0.938876i	$-0.611869\pi$
$433$	−14.3270	−0.688511	−0.344256	+	0.938876i	$0.611869\pi$
$434$	10.7970	0.518271
$435$	−4.71374	−0.226006
$436$	−51.7877	−2.48018
$437$	−3.34639	−0.160080
$438$	28.0061	1.33818
$439$	−13.2935	−0.634464	−0.317232	−	0.948348i	$-0.602753\pi$
$439$	−13.2935	−0.634464	−0.317232	+	0.948348i	$0.602753\pi$
$440$	−40.8826	−1.94900
$441$	−4.06905	−0.193764
$442$	−41.9289	−1.99435
$443$	36.6470	1.74115	0.870575	−	0.492036i	$-0.163747\pi$
$443$	36.6470	1.74115	0.870575	+	0.492036i	$0.163747\pi$
$444$	56.2659	2.67026
$445$	10.1106	0.479288
$446$	51.3575	2.43185
$447$	−0.250366	−0.0118419
$448$	−51.3989	−2.42837
$449$	31.7359	1.49771	0.748856	−	0.662733i	$-0.230604\pi$
$449$	31.7359	1.49771	0.748856	+	0.662733i	$0.230604\pi$
$450$	−2.73278	−0.128824
$451$	−11.0941	−0.522400
$452$	−13.2092	−0.621307
$453$	−16.7372	−0.786383
$454$	−68.6478	−3.22180
$455$	11.4610	0.537302
$456$	−20.3868	−0.954699
$457$	−10.5119	−0.491728	−0.245864	−	0.969304i	$-0.579072\pi$
$457$	−10.5119	−0.491728	−0.245864	+	0.969304i	$0.579072\pi$
$458$	−76.9987	−3.59791
$459$	2.29187	0.106975
$460$	8.50656	0.396620
$461$	4.19605	0.195430	0.0977148	−	0.995214i	$-0.468847\pi$
$461$	4.19605	0.195430	0.0977148	+	0.995214i	$0.468847\pi$
$462$	−20.1816	−0.938932
$463$	−17.7989	−0.827183	−0.413592	−	0.910462i	$-0.635726\pi$
$463$	−17.7989	−0.827183	−0.413592	+	0.910462i	$0.635726\pi$
$464$	70.5347	3.27449
$465$	−2.30777	−0.107020
$466$	7.42947	0.344163
$467$	−27.9987	−1.29562	−0.647812	−	0.761800i	$-0.724316\pi$
$467$	−27.9987	−1.29562	−0.647812	+	0.761800i	$0.724316\pi$
$468$	36.6061	1.69212
$469$	3.22296	0.148822
$470$	−1.36316	−0.0628780
$471$	17.9633	0.827706
$472$	−0.325081	−0.0149631
$473$	−9.99720	−0.459672
$474$	29.0745	1.33544
$475$	2.15108	0.0986984
$476$	−21.4550	−0.983386
$477$	8.10086	0.370913
$478$	60.6555	2.77432
$479$	−14.4726	−0.661269	−0.330635	−	0.943759i	$-0.607263\pi$
$479$	−14.4726	−0.661269	−0.330635	+	0.943759i	$0.607263\pi$
$480$	21.9374	1.00130
$481$	68.8860	3.14093
$482$	−77.6117	−3.53512
$483$	2.66333	0.121186
$484$	41.5994	1.89088
$485$	10.3510	0.470014
$486$	−2.73278	−0.123961
$487$	−10.5645	−0.478723	−0.239362	−	0.970931i	$-0.576938\pi$
$487$	−10.5645	−0.478723	−0.239362	+	0.970931i	$0.576938\pi$
$488$	99.2721	4.49384
$489$	10.0195	0.453098
$490$	−11.1198	−0.502341
$491$	13.5372	0.610926	0.305463	−	0.952204i	$-0.401189\pi$
$491$	13.5372	0.610926	0.305463	+	0.952204i	$0.401189\pi$
$492$	14.0630	0.634011
$493$	10.8032	0.486554
$494$	−39.3533	−1.77059
$495$	4.31366	0.193885
$496$	34.5327	1.55056
$497$	1.39125	0.0624062
$498$	−11.0552	−0.495394
$499$	12.1099	0.542113	0.271057	−	0.962563i	$-0.412627\pi$
$499$	12.1099	0.542113	0.271057	+	0.962563i	$0.412627\pi$
$500$	−5.46807	−0.244539
$501$	19.7478	0.882265
$502$	22.3373	0.996962
$503$	1.34609	0.0600191	0.0300095	−	0.999550i	$-0.490446\pi$
$503$	1.34609	0.0600191	0.0300095	+	0.999550i	$0.490446\pi$
$504$	16.2254	0.722739
$505$	−4.10770	−0.182790
$506$	−18.3388	−0.815258
$507$	31.8167	1.41303
$508$	104.046	4.61628
$509$	−0.270181	−0.0119755	−0.00598777	−	0.999982i	$-0.501906\pi$
$509$	−0.270181	−0.0119755	−0.00598777	+	0.999982i	$0.501906\pi$
$510$	6.26316	0.277337
$511$	17.5450	0.776143
$512$	−44.6284	−1.97232
$513$	2.15108	0.0949726
$514$	−46.4252	−2.04773
$515$	11.4912	0.506362
$516$	12.6726	0.557881
$517$	2.15174	0.0946334
$518$	48.1415	2.11522
$519$	16.2195	0.711956
$520$	63.4471	2.78234
$521$	26.6154	1.16604	0.583020	−	0.812458i	$-0.301871\pi$
$521$	26.6154	1.16604	0.583020	+	0.812458i	$0.301871\pi$
$522$	−12.8816	−0.563812
$523$	6.26098	0.273773	0.136887	−	0.990587i	$-0.456290\pi$
$523$	6.26098	0.273773	0.136887	+	0.990587i	$0.456290\pi$
$524$	30.0071	1.31087
$525$	−1.71200	−0.0747179
$526$	−13.7173	−0.598105
$527$	5.28910	0.230397
$528$	−64.5481	−2.80910
$529$	−20.5799	−0.894777
$530$	22.1378	0.961607
$531$	0.0343004	0.00148851
$532$	−20.1370	−0.873051
$533$	17.2173	0.745764
$534$	27.6300	1.19567
$535$	−3.74907	−0.162086
$536$	17.8419	0.770654
$537$	−18.6263	−0.803784
$538$	66.8338	2.88141
$539$	17.5525	0.756039
$540$	−5.46807	−0.235308
$541$	2.72176	0.117018	0.0585088	−	0.998287i	$-0.481365\pi$
$541$	2.72176	0.117018	0.0585088	+	0.998287i	$0.481365\pi$
$542$	60.1499	2.58366
$543$	19.3451	0.830179
$544$	−50.2775	−2.15563
$545$	9.47092	0.405690
$546$	31.3205	1.34039
$547$	21.9169	0.937100	0.468550	−	0.883437i	$-0.344777\pi$
$547$	21.9169	0.937100	0.468550	+	0.883437i	$0.344777\pi$
$548$	−22.4996	−0.961134
$549$	−10.4745	−0.447043
$550$	11.7883	0.502654
$551$	10.1396	0.431963
$552$	14.7439	0.627541
$553$	18.2143	0.774552
$554$	−64.8619	−2.75572
$555$	−10.2899	−0.436782
$556$	−14.3817	−0.609922
$557$	−7.05282	−0.298838	−0.149419	−	0.988774i	$-0.547740\pi$
$557$	−7.05282	−0.298838	−0.149419	+	0.988774i	$0.547740\pi$
$558$	−6.30663	−0.266981
$559$	15.5150	0.656215
$560$	25.6178	1.08255
$561$	−9.88634	−0.417401
$562$	40.2680	1.69860
$563$	1.92206	0.0810052	0.0405026	−	0.999179i	$-0.487104\pi$
$563$	1.92206	0.0810052	0.0405026	+	0.999179i	$0.487104\pi$
$564$	−2.72758	−0.114852
$565$	2.41569	0.101629
$566$	−68.1400	−2.86414
$567$	−1.71200	−0.0718974
$568$	7.70182	0.323161
$569$	−6.94111	−0.290987	−0.145493	−	0.989359i	$-0.546477\pi$
$569$	−6.94111	−0.290987	−0.145493	+	0.989359i	$0.546477\pi$
$570$	5.87843	0.246220
$571$	−39.3491	−1.64671	−0.823355	−	0.567527i	$-0.807900\pi$
$571$	−39.3491	−1.64671	−0.823355	+	0.567527i	$0.807900\pi$
$572$	−157.906	−6.60240
$573$	15.4616	0.645918
$574$	12.0324	0.502225
$575$	−1.55568	−0.0648763
$576$	30.0227	1.25094
$577$	−33.5351	−1.39609	−0.698043	−	0.716056i	$-0.745946\pi$
$577$	−33.5351	−1.39609	−0.698043	+	0.716056i	$0.745946\pi$
$578$	32.1029	1.33530
$579$	−3.46771	−0.144113
$580$	−25.7750	−1.07025
$581$	−6.92573	−0.287328
$582$	28.2869	1.17253
$583$	−34.9444	−1.44725
$584$	97.1270	4.01914
$585$	−6.69453	−0.276785
$586$	−57.2217	−2.36381
$587$	−18.1586	−0.749486	−0.374743	−	0.927129i	$-0.622269\pi$
$587$	−18.1586	−0.749486	−0.374743	+	0.927129i	$0.622269\pi$
$588$	−22.2498	−0.917567
$589$	4.96421	0.204547
$590$	0.0937354	0.00385903
$591$	−8.46550	−0.348224
$592$	153.974	6.32831
$593$	−39.2981	−1.61378	−0.806890	−	0.590702i	$-0.798851\pi$
$593$	−39.2981	−1.61378	−0.806890	+	0.590702i	$0.798851\pi$
$594$	11.7883	0.483679
$595$	3.92368	0.160855
$596$	−1.36902	−0.0560771
$597$	10.4342	0.427043
$598$	28.4606	1.16384
$599$	−23.8735	−0.975445	−0.487723	−	0.872999i	$-0.662172\pi$
$599$	−23.8735	−0.975445	−0.487723	+	0.872999i	$0.662172\pi$
$600$	−9.47746	−0.386916
$601$	−0.504084	−0.0205620	−0.0102810	−	0.999947i	$-0.503273\pi$
$601$	−0.504084	−0.0205620	−0.0102810	+	0.999947i	$0.503273\pi$
$602$	10.8428	0.441919
$603$	−1.88257	−0.0766640
$604$	−91.5202	−3.72390
$605$	−7.60769	−0.309296
$606$	−11.2254	−0.456002
$607$	25.8767	1.05030	0.525151	−	0.851009i	$-0.324009\pi$
$607$	25.8767	1.05030	0.525151	+	0.851009i	$0.324009\pi$
$608$	−47.1891	−1.91377
$609$	−8.06993	−0.327010
$610$	−28.6246	−1.15898
$611$	−3.33936	−0.135096
$612$	12.5321	0.506579
$613$	16.6449	0.672283	0.336142	−	0.941811i	$-0.390878\pi$
$613$	16.6449	0.672283	0.336142	+	0.941811i	$0.390878\pi$
$614$	17.8041	0.718514
$615$	−2.57185	−0.103707
$616$	−69.9911	−2.82002
$617$	31.3414	1.26176	0.630879	−	0.775881i	$-0.282694\pi$
$617$	31.3414	1.26176	0.630879	+	0.775881i	$0.282694\pi$
$618$	31.4029	1.26321
$619$	19.9957	0.803696	0.401848	−	0.915706i	$-0.368368\pi$
$619$	19.9957	0.803696	0.401848	+	0.915706i	$0.368368\pi$
$620$	−12.6191	−0.506793
$621$	−1.55568	−0.0624272
$622$	−65.6844	−2.63370
$623$	17.3094	0.693485
$624$	100.174	4.01019
$625$	1.00000	0.0400000
$626$	−75.2443	−3.00737
$627$	−9.27904	−0.370569
$628$	98.2247	3.91959
$629$	23.5831	0.940319
$630$	−4.67852	−0.186397
$631$	35.0721	1.39620	0.698100	−	0.716001i	$-0.254029\pi$
$631$	35.0721	1.39620	0.698100	+	0.716001i	$0.254029\pi$
$632$	100.833	4.01090
$633$	16.0086	0.636284
$634$	−40.3511	−1.60255
$635$	−19.0279	−0.755097
$636$	44.2961	1.75645
$637$	−27.2403	−1.07930
$638$	55.5668	2.19991
$639$	−0.812646	−0.0321478
$640$	38.1705	1.50882
$641$	−18.7291	−0.739755	−0.369877	−	0.929081i	$-0.620600\pi$
$641$	−18.7291	−0.739755	−0.369877	+	0.929081i	$0.620600\pi$
$642$	−10.2454	−0.404352
$643$	−11.5939	−0.457219	−0.228610	−	0.973518i	$-0.573418\pi$
$643$	−11.5939	−0.457219	−0.228610	+	0.973518i	$0.573418\pi$
$644$	14.5633	0.573873
$645$	−2.31757	−0.0912541
$646$	−13.4726	−0.530071
$647$	−47.9021	−1.88323	−0.941613	−	0.336696i	$-0.890691\pi$
$647$	−47.9021	−1.88323	−0.941613	+	0.336696i	$0.890691\pi$
$648$	−9.47746	−0.372310
$649$	−0.147961	−0.00580796
$650$	−18.2946	−0.717575
$651$	−3.95091	−0.154848
$652$	54.7874	2.14564
$653$	−17.7246	−0.693615	−0.346808	−	0.937936i	$-0.612734\pi$
$653$	−17.7246	−0.693615	−0.346808	+	0.937936i	$0.612734\pi$
$654$	25.8819	1.01206
$655$	−5.48769	−0.214422
$656$	38.4842	1.50256
$657$	−10.2482	−0.399821
$658$	−2.33374	−0.0909786
$659$	−12.8909	−0.502157	−0.251078	−	0.967967i	$-0.580785\pi$
$659$	−12.8909	−0.502157	−0.251078	+	0.967967i	$0.580785\pi$
$660$	23.5874	0.918139
$661$	−16.6864	−0.649027	−0.324514	−	0.945881i	$-0.605201\pi$
$661$	−16.6864	−0.649027	−0.324514	+	0.945881i	$0.605201\pi$
$662$	−4.91546	−0.191045
$663$	15.3430	0.595871
$664$	−38.3401	−1.48788
$665$	3.68266	0.142807
$666$	−28.1200	−1.08963
$667$	−7.33306	−0.283937
$668$	107.982	4.17795
$669$	−18.7932	−0.726586
$670$	−5.14463	−0.198754
$671$	45.1837	1.74430
$672$	37.5569	1.44879
$673$	11.7915	0.454528	0.227264	−	0.973833i	$-0.427022\pi$
$673$	11.7915	0.454528	0.227264	+	0.973833i	$0.427022\pi$
$674$	−47.7466	−1.83913
$675$	1.00000	0.0384900
$676$	173.976	6.69137
$677$	35.9867	1.38308	0.691541	−	0.722337i	$-0.256932\pi$
$677$	35.9867	1.38308	0.691541	+	0.722337i	$0.256932\pi$
$678$	6.60154	0.253531
$679$	17.7209	0.680066
$680$	21.7211	0.832965
$681$	25.1202	0.962607
$682$	27.2047	1.04172
$683$	7.39613	0.283005	0.141503	−	0.989938i	$-0.454807\pi$
$683$	7.39613	0.283005	0.141503	+	0.989938i	$0.454807\pi$
$684$	11.7623	0.449742
$685$	4.11472	0.157215
$686$	−51.7868	−1.97723
$687$	28.1760	1.07498
$688$	34.6792	1.32213
$689$	54.2314	2.06605
$690$	−4.25132	−0.161845
$691$	0.0700223	0.00266377	0.00133189	−	0.999999i	$-0.499576\pi$
$691$	0.0700223	0.00266377	0.00133189	+	0.999999i	$0.499576\pi$
$692$	88.6892	3.37146
$693$	7.38500	0.280533
$694$	7.16189	0.271862
$695$	2.63013	0.0997666
$696$	−44.6742	−1.69337
$697$	5.89433	0.223264
$698$	−74.9009	−2.83504
$699$	−2.71865	−0.102829
$700$	−9.36135	−0.353826
$701$	42.7979	1.61645	0.808227	−	0.588871i	$-0.200427\pi$
$701$	42.7979	1.61645	0.808227	+	0.588871i	$0.200427\pi$
$702$	−18.2946	−0.690487
$703$	22.1344	0.834816
$704$	−129.508	−4.88100
$705$	0.498820	0.0187866
$706$	18.3101	0.689108
$707$	−7.03239	−0.264480
$708$	0.187557	0.00704883
$709$	11.0492	0.414960	0.207480	−	0.978239i	$-0.433474\pi$
$709$	11.0492	0.414960	0.207480	+	0.978239i	$0.433474\pi$
$710$	−2.22078	−0.0833444
$711$	−10.6392	−0.399001
$712$	95.8227	3.59111
$713$	−3.59015	−0.134452
$714$	10.7225	0.401281
$715$	28.8779	1.07997
$716$	−101.850	−3.80631
$717$	−22.1956	−0.828908
$718$	−19.9667	−0.745151
$719$	−40.3122	−1.50339	−0.751696	−	0.659509i	$-0.770764\pi$
$719$	−40.3122	−1.50339	−0.751696	+	0.659509i	$0.770764\pi$
$720$	−14.9636	−0.557662
$721$	19.6730	0.732659
$722$	39.2778	1.46177
$723$	28.4003	1.05622
$724$	105.781	3.93130
$725$	4.71374	0.175064
$726$	−20.7901	−0.771593
$727$	7.48031	0.277430	0.138715	−	0.990332i	$-0.455703\pi$
$727$	7.48031	0.277430	0.138715	+	0.990332i	$0.455703\pi$
$728$	108.622	4.02578
$729$	1.00000	0.0370370
$730$	−28.0061	−1.03655
$731$	5.31155	0.196455
$732$	−57.2755	−2.11697
$733$	9.68626	0.357770	0.178885	−	0.983870i	$-0.442751\pi$
$733$	9.68626	0.357770	0.178885	+	0.983870i	$0.442751\pi$
$734$	50.2947	1.85641
$735$	4.06905	0.150089
$736$	34.1275	1.25796
$737$	8.12075	0.299132
$738$	−7.02828	−0.258715
$739$	24.1467	0.888251	0.444126	−	0.895964i	$-0.353514\pi$
$739$	24.1467	0.888251	0.444126	+	0.895964i	$0.353514\pi$
$740$	−56.2659	−2.06838
$741$	14.4005	0.529015
$742$	37.9001	1.39136
$743$	38.7390	1.42120	0.710598	−	0.703598i	$-0.248425\pi$
$743$	38.7390	1.42120	0.710598	+	0.703598i	$0.248425\pi$
$744$	−21.8718	−0.801860
$745$	0.250366	0.00917269
$746$	15.5530	0.569435
$747$	4.04540	0.148013
$748$	−54.0592	−1.97660
$749$	−6.41841	−0.234524
$750$	2.73278	0.0997869
$751$	−23.4468	−0.855586	−0.427793	−	0.903877i	$-0.640709\pi$
$751$	−23.4468	−0.855586	−0.427793	+	0.903877i	$0.640709\pi$
$752$	−7.46416	−0.272190
$753$	−8.17384	−0.297871
$754$	−86.2361	−3.14053
$755$	16.7372	0.609129
$756$	−9.36135	−0.340469
$757$	34.9630	1.27075	0.635375	−	0.772203i	$-0.280845\pi$
$757$	34.9630	1.27075	0.635375	+	0.772203i	$0.280845\pi$
$758$	42.3393	1.53783
$759$	6.71067	0.243582
$760$	20.3868	0.739507
$761$	48.4869	1.75765	0.878825	−	0.477145i	$-0.158328\pi$
$761$	48.4869	1.75765	0.878825	+	0.477145i	$0.158328\pi$
$762$	−51.9989	−1.88372
$763$	16.2143	0.586995
$764$	84.5452	3.05874
$765$	−2.29187	−0.0828626
$766$	−40.0461	−1.44692
$767$	0.229625	0.00829128
$768$	44.2661	1.59732
$769$	45.2021	1.63003	0.815016	−	0.579439i	$-0.196728\pi$
$769$	45.2021	1.63003	0.815016	+	0.579439i	$0.196728\pi$
$770$	20.1816	0.727293
$771$	16.9883	0.611819
$772$	−18.9617	−0.682446
$773$	−27.2533	−0.980234	−0.490117	−	0.871657i	$-0.663046\pi$
$773$	−27.2533	−0.980234	−0.490117	+	0.871657i	$0.663046\pi$
$774$	−6.33339	−0.227649
$775$	2.30777	0.0828976
$776$	98.1010	3.52162
$777$	−17.6163	−0.631983
$778$	−98.2748	−3.52332
$779$	5.53225	0.198214
$780$	−36.6061	−1.31071
$781$	3.50548	0.125436
$782$	9.74346	0.348425
$783$	4.71374	0.168455
$784$	−60.8877	−2.17456
$785$	−17.9633	−0.641138
$786$	−14.9966	−0.534912
$787$	−47.2046	−1.68266	−0.841331	−	0.540521i	$-0.818227\pi$
$787$	−47.2046	−1.68266	−0.841331	+	0.540521i	$0.818227\pi$
$788$	−46.2900	−1.64901
$789$	5.01956	0.178701
$790$	−29.0745	−1.03443
$791$	4.13567	0.147048
$792$	40.8826	1.45270
$793$	−70.1221	−2.49011
$794$	57.8127	2.05170
$795$	−8.10086	−0.287308
$796$	57.0549	2.02226
$797$	26.3485	0.933312	0.466656	−	0.884439i	$-0.345459\pi$
$797$	26.3485	0.933312	0.466656	+	0.884439i	$0.345459\pi$
$798$	10.0639	0.356258
$799$	−1.14323	−0.0404445
$800$	−21.9374	−0.775603
$801$	−10.1106	−0.357240
$802$	2.73278	0.0964977
$803$	44.2073	1.56004
$804$	−10.2940	−0.363041
$805$	−2.66333	−0.0938699
$806$	−42.2199	−1.48713
$807$	−24.4564	−0.860905
$808$	−38.9305	−1.36957
$809$	−15.3032	−0.538032	−0.269016	−	0.963136i	$-0.586698\pi$
$809$	−15.3032	−0.538032	−0.269016	+	0.963136i	$0.586698\pi$
$810$	2.73278	0.0960200
$811$	−10.6266	−0.373150	−0.186575	−	0.982441i	$-0.559739\pi$
$811$	−10.6266	−0.373150	−0.186575	+	0.982441i	$0.559739\pi$
$812$	−44.1269	−1.54855
$813$	−22.0105	−0.771943
$814$	121.300	4.25157
$815$	−10.0195	−0.350968
$816$	34.2947	1.20055
$817$	4.98528	0.174413
$818$	13.3447	0.466587
$819$	−11.4610	−0.400481
$820$	−14.0630	−0.491103
$821$	−20.1510	−0.703274	−0.351637	−	0.936136i	$-0.614375\pi$
$821$	−20.1510	−0.703274	−0.351637	+	0.936136i	$0.614375\pi$
$822$	11.2446	0.392201
$823$	−47.2101	−1.64564	−0.822820	−	0.568301i	$-0.807601\pi$
$823$	−47.2101	−1.64564	−0.822820	+	0.568301i	$0.807601\pi$
$824$	108.907	3.79396
$825$	−4.31366	−0.150182
$826$	0.160475	0.00558365
$827$	−26.9499	−0.937141	−0.468571	−	0.883426i	$-0.655231\pi$
$827$	−26.9499	−0.937141	−0.468571	+	0.883426i	$0.655231\pi$
$828$	−8.50656	−0.295623
$829$	−8.01121	−0.278241	−0.139120	−	0.990275i	$-0.544428\pi$
$829$	−8.01121	−0.278241	−0.139120	+	0.990275i	$0.544428\pi$
$830$	11.0552	0.383730
$831$	23.7348	0.823352
$832$	200.988	6.96799
$833$	−9.32570	−0.323116
$834$	7.18757	0.248885
$835$	−19.7478	−0.683399
$836$	−50.7385	−1.75483
$837$	2.30777	0.0797683
$838$	1.90815	0.0659159
$839$	−22.5149	−0.777302	−0.388651	−	0.921385i	$-0.627059\pi$
$839$	−22.5149	−0.777302	−0.388651	+	0.921385i	$0.627059\pi$
$840$	−16.2254	−0.559831
$841$	−6.78069	−0.233817
$842$	−45.1865	−1.55723
$843$	−14.7352	−0.507508
$844$	87.5360	3.01311
$845$	−31.8167	−1.09453
$846$	1.36316	0.0468665
$847$	−13.0244	−0.447523
$848$	121.218	4.16266
$849$	24.9343	0.855745
$850$	−6.26316	−0.214825
$851$	−16.0078	−0.548740
$852$	−4.44360	−0.152235
$853$	4.33838	0.148543	0.0742716	−	0.997238i	$-0.476337\pi$
$853$	4.33838	0.148543	0.0742716	+	0.997238i	$0.476337\pi$
$854$	−49.0054	−1.67693
$855$	−2.15108	−0.0735655
$856$	−35.5316	−1.21445
$857$	−11.9414	−0.407912	−0.203956	−	0.978980i	$-0.565380\pi$
$857$	−11.9414	−0.407912	−0.203956	+	0.978980i	$0.565380\pi$
$858$	78.9169	2.69418
$859$	43.0816	1.46992	0.734962	−	0.678108i	$-0.237200\pi$
$859$	43.0816	1.46992	0.734962	+	0.678108i	$0.237200\pi$
$860$	−12.6726	−0.432133
$861$	−4.40301	−0.150054
$862$	−22.4676	−0.765250
$863$	−19.1077	−0.650433	−0.325216	−	0.945640i	$-0.605437\pi$
$863$	−19.1077	−0.650433	−0.325216	+	0.945640i	$0.605437\pi$
$864$	−21.9374	−0.746325
$865$	−16.2195	−0.551479
$866$	39.1525	1.33045
$867$	−11.7474	−0.398961
$868$	−21.6039	−0.733283
$869$	45.8939	1.55684
$870$	12.8816	0.436727
$871$	−12.6029	−0.427032
$872$	89.7603	3.03967
$873$	−10.3510	−0.350328
$874$	9.14495	0.309332
$875$	1.71200	0.0578763
$876$	−56.0379	−1.89335
$877$	25.0398	0.845534	0.422767	−	0.906238i	$-0.361059\pi$
$877$	25.0398	0.845534	0.422767	+	0.906238i	$0.361059\pi$
$878$	36.3282	1.22602
$879$	20.9390	0.706256
$880$	64.5481	2.17592
$881$	56.4289	1.90114	0.950569	−	0.310514i	$-0.100501\pi$
$881$	56.4289	1.90114	0.950569	+	0.310514i	$0.100501\pi$
$882$	11.1198	0.374423
$883$	41.5066	1.39681	0.698405	−	0.715703i	$-0.253893\pi$
$883$	41.5066	1.39681	0.698405	+	0.715703i	$0.253893\pi$
$884$	83.8963	2.82174
$885$	−0.0343004	−0.00115300
$886$	−100.148	−3.36454
$887$	35.0626	1.17729	0.588643	−	0.808393i	$-0.299662\pi$
$887$	35.0626	1.17729	0.588643	+	0.808393i	$0.299662\pi$
$888$	−97.5221	−3.27263
$889$	−32.5757	−1.09256
$890$	−27.6300	−0.926159
$891$	−4.31366	−0.144513
$892$	−102.762	−3.44074
$893$	−1.07300	−0.0359066
$894$	0.684194	0.0228829
$895$	18.6263	0.622608
$896$	65.3480	2.18312
$897$	−10.4145	−0.347731
$898$	−86.7272	−2.89413
$899$	10.8782	0.362809
$900$	5.46807	0.182269
$901$	18.5661	0.618526
$902$	30.3176	1.00947
$903$	−3.96768	−0.132036
$904$	22.8946	0.761463
$905$	−19.3451	−0.643054
$906$	45.7391	1.51958
$907$	−38.9027	−1.29174	−0.645872	−	0.763446i	$-0.723506\pi$
$907$	−38.9027	−1.29174	−0.645872	+	0.763446i	$0.723506\pi$
$908$	137.359	4.55841
$909$	4.10770	0.136244
$910$	−31.3205	−1.03826
$911$	−30.4511	−1.00889	−0.504445	−	0.863444i	$-0.668303\pi$
$911$	−30.4511	−1.00889	−0.504445	+	0.863444i	$0.668303\pi$
$912$	32.1880	1.06585
$913$	−17.4505	−0.577526
$914$	28.7268	0.950197
$915$	10.4745	0.346278
$916$	154.068	5.09056
$917$	−9.39495	−0.310248
$918$	−6.26316	−0.206715
$919$	50.9883	1.68195	0.840974	−	0.541076i	$-0.181983\pi$
$919$	50.9883	1.68195	0.840974	+	0.541076i	$0.181983\pi$
$920$	−14.7439	−0.486091
$921$	−6.51501	−0.214677
$922$	−11.4669	−0.377641
$923$	−5.44028	−0.179069
$924$	40.3817	1.32846
$925$	10.2899	0.338330
$926$	48.6403	1.59842
$927$	−11.4912	−0.377420
$928$	−103.407	−3.39450
$929$	39.3116	1.28977	0.644886	−	0.764279i	$-0.276905\pi$
$929$	39.3116	1.28977	0.644886	+	0.764279i	$0.276905\pi$
$930$	6.30663	0.206802
$931$	−8.75285	−0.286863
$932$	−14.8658	−0.486945
$933$	24.0358	0.786896
$934$	76.5141	2.50362
$935$	9.88634	0.323318
$936$	−63.4471	−2.07383
$937$	−5.96271	−0.194793	−0.0973967	−	0.995246i	$-0.531052\pi$
$937$	−5.96271	−0.194793	−0.0973967	+	0.995246i	$0.531052\pi$
$938$	−8.80763	−0.287579
$939$	27.5340	0.898539
$940$	2.72758	0.0889638
$941$	29.9851	0.977487	0.488743	−	0.872428i	$-0.337455\pi$
$941$	29.9851	0.977487	0.488743	+	0.872428i	$0.337455\pi$
$942$	−49.0898	−1.59943
$943$	−4.00097	−0.130289
$944$	0.513259	0.0167052
$945$	1.71200	0.0556915
$946$	27.3201	0.888254
$947$	−28.4459	−0.924367	−0.462183	−	0.886784i	$-0.652934\pi$
$947$	−28.4459	−0.924367	−0.462183	+	0.886784i	$0.652934\pi$
$948$	−58.1759	−1.88946
$949$	−68.6069	−2.22707
$950$	−5.87843	−0.190721
$951$	14.7656	0.478808
$952$	37.1865	1.20522
$953$	−27.9235	−0.904531	−0.452265	−	0.891883i	$-0.649384\pi$
$953$	−27.9235	−0.904531	−0.452265	+	0.891883i	$0.649384\pi$
$954$	−22.1378	−0.716739
$955$	−15.4616	−0.500326
$956$	−121.367	−3.92528
$957$	−20.3335	−0.657288
$958$	39.5503	1.27781
$959$	7.04442	0.227476
$960$	−30.0227	−0.968977
$961$	−25.6742	−0.828200
$962$	−188.250	−6.06943
$963$	3.74907	0.120812
$964$	155.295	5.00171
$965$	3.46771	0.111630
$966$	−7.27828	−0.234175
$967$	49.9783	1.60719	0.803597	−	0.595174i	$-0.202917\pi$
$967$	49.9783	1.60719	0.803597	+	0.595174i	$0.202917\pi$
$968$	−72.1015	−2.31743
$969$	4.92999	0.158374
$970$	−28.2869	−0.908239
$971$	−35.1858	−1.12917	−0.564583	−	0.825376i	$-0.690963\pi$
$971$	−35.1858	−1.12917	−0.564583	+	0.825376i	$0.690963\pi$
$972$	5.46807	0.175388
$973$	4.50280	0.144353
$974$	28.8704	0.925068
$975$	6.69453	0.214396
$976$	−156.737	−5.01704
$977$	−9.06963	−0.290163	−0.145082	−	0.989420i	$-0.546344\pi$
$977$	−9.06963	−0.290163	−0.145082	+	0.989420i	$0.546344\pi$
$978$	−27.3811	−0.875550
$979$	43.6137	1.39390
$980$	22.2498	0.710744
$981$	−9.47092	−0.302383
$982$	−36.9942	−1.18053
$983$	0.742484	0.0236816	0.0118408	−	0.999930i	$-0.496231\pi$
$983$	0.742484	0.0236816	0.0118408	+	0.999930i	$0.496231\pi$
$984$	−24.3746	−0.777033
$985$	8.46550	0.269733
$986$	−29.5229	−0.940200
$987$	0.853981	0.0271825
$988$	78.7428	2.50514
$989$	−3.60539	−0.114645
$990$	−11.7883	−0.374656
$991$	−25.8344	−0.820657	−0.410328	−	0.911938i	$-0.634586\pi$
$991$	−25.8344	−0.820657	−0.410328	+	0.911938i	$0.634586\pi$
$992$	−50.6265	−1.60739
$993$	1.79871	0.0570802
$994$	−3.80198	−0.120592
$995$	−10.4342	−0.330786
$996$	22.1205	0.700915
$997$	54.3632	1.72170	0.860850	−	0.508860i	$-0.169933\pi$
$997$	54.3632	1.72170	0.860850	+	0.508860i	$0.169933\pi$
$998$	−33.0936	−1.04756
$999$	10.2899	0.325558

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6015.2.a.h.1.1	✓	39

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6015.2.a.h.1.1	✓	39	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:	\( N \)	\(=\)	\( 6015 = 3 \cdot 5 \cdot 401 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6015.a (trivial)

\(f(q)\)	\(=\)	\(q-2.73278 q^{2} +1.00000 q^{3} +5.46807 q^{4} -1.00000 q^{5} -2.73278 q^{6} -1.71200 q^{7} -9.47746 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.73278 q^{2} +1.00000 q^{3} +5.46807 q^{4} -1.00000 q^{5} -2.73278 q^{6} -1.71200 q^{7} -9.47746 q^{8} +1.00000 q^{9} +2.73278 q^{10} -4.31366 q^{11} +5.46807 q^{12} +6.69453 q^{13} +4.67852 q^{14} -1.00000 q^{15} +14.9636 q^{16} +2.29187 q^{17} -2.73278 q^{18} +2.15108 q^{19} -5.46807 q^{20} -1.71200 q^{21} +11.7883 q^{22} -1.55568 q^{23} -9.47746 q^{24} +1.00000 q^{25} -18.2946 q^{26} +1.00000 q^{27} -9.36135 q^{28} +4.71374 q^{29} +2.73278 q^{30} +2.30777 q^{31} -21.9374 q^{32} -4.31366 q^{33} -6.26316 q^{34} +1.71200 q^{35} +5.46807 q^{36} +10.2899 q^{37} -5.87843 q^{38} +6.69453 q^{39} +9.47746 q^{40} +2.57185 q^{41} +4.67852 q^{42} +2.31757 q^{43} -23.5874 q^{44} -1.00000 q^{45} +4.25132 q^{46} -0.498820 q^{47} +14.9636 q^{48} -4.06905 q^{49} -2.73278 q^{50} +2.29187 q^{51} +36.6061 q^{52} +8.10086 q^{53} -2.73278 q^{54} +4.31366 q^{55} +16.2254 q^{56} +2.15108 q^{57} -12.8816 q^{58} +0.0343004 q^{59} -5.46807 q^{60} -10.4745 q^{61} -6.30663 q^{62} -1.71200 q^{63} +30.0227 q^{64} -6.69453 q^{65} +11.7883 q^{66} -1.88257 q^{67} +12.5321 q^{68} -1.55568 q^{69} -4.67852 q^{70} -0.812646 q^{71} -9.47746 q^{72} -10.2482 q^{73} -28.1200 q^{74} +1.00000 q^{75} +11.7623 q^{76} +7.38500 q^{77} -18.2946 q^{78} -10.6392 q^{79} -14.9636 q^{80} +1.00000 q^{81} -7.02828 q^{82} +4.04540 q^{83} -9.36135 q^{84} -2.29187 q^{85} -6.33339 q^{86} +4.71374 q^{87} +40.8826 q^{88} -10.1106 q^{89} +2.73278 q^{90} -11.4610 q^{91} -8.50656 q^{92} +2.30777 q^{93} +1.36316 q^{94} -2.15108 q^{95} -21.9374 q^{96} -10.3510 q^{97} +11.1198 q^{98} -4.31366 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 39 q + 39 q^{3} + 48 q^{4} - 39 q^{5} + 22 q^{7} + 3 q^{8} + 39 q^{9}+O(q^{10}) \) 39 * q + 39 * q^3 + 48 * q^4 - 39 * q^5 + 22 * q^7 + 3 * q^8 + 39 * q^9	\( 39 q + 39 q^{3} + 48 q^{4} - 39 q^{5} + 22 q^{7} + 3 q^{8} + 39 q^{9} - q^{11} + 48 q^{12} + 30 q^{13} + 8 q^{14} - 39 q^{15} + 58 q^{16} + 32 q^{17} + 27 q^{19} - 48 q^{20} + 22 q^{21} + 23 q^{22} - 8 q^{23} + 3 q^{24} + 39 q^{25} - 4 q^{26} + 39 q^{27} + 60 q^{28} - 9 q^{29} + 19 q^{31} + q^{32} - q^{33} + 26 q^{34} - 22 q^{35} + 48 q^{36} + 44 q^{37} + 14 q^{38} + 30 q^{39} - 3 q^{40} + 31 q^{41} + 8 q^{42} + 75 q^{43} + q^{44} - 39 q^{45} + 19 q^{46} - 16 q^{47} + 58 q^{48} + 91 q^{49} + 32 q^{51} + 94 q^{52} + 17 q^{53} + q^{55} + 27 q^{56} + 27 q^{57} + 26 q^{58} - q^{59} - 48 q^{60} + 55 q^{61} + 11 q^{62} + 22 q^{63} + 77 q^{64} - 30 q^{65} + 23 q^{66} + 84 q^{67} + 36 q^{68} - 8 q^{69} - 8 q^{70} - 2 q^{71} + 3 q^{72} + 79 q^{73} + 20 q^{74} + 39 q^{75} + 58 q^{76} + 32 q^{77} - 4 q^{78} + 29 q^{79} - 58 q^{80} + 39 q^{81} + 53 q^{82} + 9 q^{83} + 60 q^{84} - 32 q^{85} - 17 q^{86} - 9 q^{87} + 57 q^{88} + 37 q^{89} + 71 q^{91} + 7 q^{92} + 19 q^{93} + 32 q^{94} - 27 q^{95} + q^{96} + 91 q^{97} - 9 q^{98} - q^{99}+O(q^{100}) \) 39 * q + 39 * q^3 + 48 * q^4 - 39 * q^5 + 22 * q^7 + 3 * q^8 + 39 * q^9 - q^11 + 48 * q^12 + 30 * q^13 + 8 * q^14 - 39 * q^15 + 58 * q^16 + 32 * q^17 + 27 * q^19 - 48 * q^20 + 22 * q^21 + 23 * q^22 - 8 * q^23 + 3 * q^24 + 39 * q^25 - 4 * q^26 + 39 * q^27 + 60 * q^28 - 9 * q^29 + 19 * q^31 + q^32 - q^33 + 26 * q^34 - 22 * q^35 + 48 * q^36 + 44 * q^37 + 14 * q^38 + 30 * q^39 - 3 * q^40 + 31 * q^41 + 8 * q^42 + 75 * q^43 + q^44 - 39 * q^45 + 19 * q^46 - 16 * q^47 + 58 * q^48 + 91 * q^49 + 32 * q^51 + 94 * q^52 + 17 * q^53 + q^55 + 27 * q^56 + 27 * q^57 + 26 * q^58 - q^59 - 48 * q^60 + 55 * q^61 + 11 * q^62 + 22 * q^63 + 77 * q^64 - 30 * q^65 + 23 * q^66 + 84 * q^67 + 36 * q^68 - 8 * q^69 - 8 * q^70 - 2 * q^71 + 3 * q^72 + 79 * q^73 + 20 * q^74 + 39 * q^75 + 58 * q^76 + 32 * q^77 - 4 * q^78 + 29 * q^79 - 58 * q^80 + 39 * q^81 + 53 * q^82 + 9 * q^83 + 60 * q^84 - 32 * q^85 - 17 * q^86 - 9 * q^87 + 57 * q^88 + 37 * q^89 + 71 * q^91 + 7 * q^92 + 19 * q^93 + 32 * q^94 - 27 * q^95 + q^96 + 91 * q^97 - 9 * q^98 - q^99

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