LMFDB - Embedded newform 2415.2.a.w.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2415,2,Mod(1,2415)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2415, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("2415.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2415 = 3 \cdot 5 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2415.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:	$19.2838720881$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} - 16x^{8} + 30x^{7} + 87x^{6} - 143x^{5} - 196x^{4} + 244x^{3} + 160x^{2} - 89x - 12 $ x^10 - 2x^9 - 16x^8 + 30x^7 + 87x^6 - 143x^5 - 196x^4 + 244x^3 + 160x^2 - 89*x - 12
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$1.88703$ of defining polynomial
Character	$\chi$	$=$	2415.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.88703 q^{2} +1.00000 q^{3} +1.56089 q^{4} +1.00000 q^{5} +1.88703 q^{6} +1.00000 q^{7} -0.828610 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.88703 q^{2} +1.00000 q^{3} +1.56089 q^{4} +1.00000 q^{5} +1.88703 q^{6} +1.00000 q^{7} -0.828610 q^{8} +1.00000 q^{9} +1.88703 q^{10} -2.76344 q^{11} +1.56089 q^{12} +5.73169 q^{13} +1.88703 q^{14} +1.00000 q^{15} -4.68540 q^{16} +4.82653 q^{17} +1.88703 q^{18} +4.18325 q^{19} +1.56089 q^{20} +1.00000 q^{21} -5.21470 q^{22} -1.00000 q^{23} -0.828610 q^{24} +1.00000 q^{25} +10.8159 q^{26} +1.00000 q^{27} +1.56089 q^{28} -8.32979 q^{29} +1.88703 q^{30} +5.10382 q^{31} -7.18428 q^{32} -2.76344 q^{33} +9.10782 q^{34} +1.00000 q^{35} +1.56089 q^{36} +3.98441 q^{37} +7.89393 q^{38} +5.73169 q^{39} -0.828610 q^{40} -3.49426 q^{41} +1.88703 q^{42} +6.13541 q^{43} -4.31343 q^{44} +1.00000 q^{45} -1.88703 q^{46} +10.7297 q^{47} -4.68540 q^{48} +1.00000 q^{49} +1.88703 q^{50} +4.82653 q^{51} +8.94656 q^{52} -7.60272 q^{53} +1.88703 q^{54} -2.76344 q^{55} -0.828610 q^{56} +4.18325 q^{57} -15.7186 q^{58} -0.943685 q^{59} +1.56089 q^{60} -14.7835 q^{61} +9.63107 q^{62} +1.00000 q^{63} -4.18618 q^{64} +5.73169 q^{65} -5.21470 q^{66} -3.94831 q^{67} +7.53369 q^{68} -1.00000 q^{69} +1.88703 q^{70} +0.189223 q^{71} -0.828610 q^{72} +14.6936 q^{73} +7.51872 q^{74} +1.00000 q^{75} +6.52961 q^{76} -2.76344 q^{77} +10.8159 q^{78} +8.77235 q^{79} -4.68540 q^{80} +1.00000 q^{81} -6.59378 q^{82} -9.38891 q^{83} +1.56089 q^{84} +4.82653 q^{85} +11.5777 q^{86} -8.32979 q^{87} +2.28981 q^{88} -8.69381 q^{89} +1.88703 q^{90} +5.73169 q^{91} -1.56089 q^{92} +5.10382 q^{93} +20.2472 q^{94} +4.18325 q^{95} -7.18428 q^{96} +8.78399 q^{97} +1.88703 q^{98} -2.76344 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 2 q^{2} + 10 q^{3} + 16 q^{4} + 10 q^{5} + 2 q^{6} + 10 q^{7} + 6 q^{8} + 10 q^{9}+O(q^{10}) $ 10 * q + 2 * q^2 + 10 * q^3 + 16 * q^4 + 10 * q^5 + 2 * q^6 + 10 * q^7 + 6 * q^8 + 10 * q^9	\( 10 q + 2 q^{2} + 10 q^{3} + 16 q^{4} + 10 q^{5} + 2 q^{6} + 10 q^{7} + 6 q^{8} + 10 q^{9} + 2 q^{10} + 9 q^{11} + 16 q^{12} + 14 q^{13} + 2 q^{14} + 10 q^{15} + 20 q^{16} + 8 q^{17} + 2 q^{18} + 13 q^{19} + 16 q^{20} + 10 q^{21} - 10 q^{23} + 6 q^{24} + 10 q^{25} - 11 q^{26} + 10 q^{27} + 16 q^{28} + 10 q^{29} + 2 q^{30} + 8 q^{31} - 11 q^{32} + 9 q^{33} - 5 q^{34} + 10 q^{35} + 16 q^{36} + 8 q^{37} - 10 q^{38} + 14 q^{39} + 6 q^{40} - 5 q^{41} + 2 q^{42} + 4 q^{43} + 3 q^{44} + 10 q^{45} - 2 q^{46} + q^{47} + 20 q^{48} + 10 q^{49} + 2 q^{50} + 8 q^{51} + 14 q^{52} + 9 q^{53} + 2 q^{54} + 9 q^{55} + 6 q^{56} + 13 q^{57} - 28 q^{58} - 17 q^{59} + 16 q^{60} + 19 q^{61} - 28 q^{62} + 10 q^{63} + 24 q^{64} + 14 q^{65} + 8 q^{68} - 10 q^{69} + 2 q^{70} + 6 q^{72} + 6 q^{73} + 3 q^{74} + 10 q^{75} + 15 q^{76} + 9 q^{77} - 11 q^{78} + 32 q^{79} + 20 q^{80} + 10 q^{81} + 14 q^{82} - 2 q^{83} + 16 q^{84} + 8 q^{85} + 2 q^{86} + 10 q^{87} - 3 q^{88} + 10 q^{89} + 2 q^{90} + 14 q^{91} - 16 q^{92} + 8 q^{93} - 10 q^{94} + 13 q^{95} - 11 q^{96} + 18 q^{97} + 2 q^{98} + 9 q^{99}+O(q^{100}) \) 10 * q + 2 * q^2 + 10 * q^3 + 16 * q^4 + 10 * q^5 + 2 * q^6 + 10 * q^7 + 6 * q^8 + 10 * q^9 + 2 * q^10 + 9 * q^11 + 16 * q^12 + 14 * q^13 + 2 * q^14 + 10 * q^15 + 20 * q^16 + 8 * q^17 + 2 * q^18 + 13 * q^19 + 16 * q^20 + 10 * q^21 - 10 * q^23 + 6 * q^24 + 10 * q^25 - 11 * q^26 + 10 * q^27 + 16 * q^28 + 10 * q^29 + 2 * q^30 + 8 * q^31 - 11 * q^32 + 9 * q^33 - 5 * q^34 + 10 * q^35 + 16 * q^36 + 8 * q^37 - 10 * q^38 + 14 * q^39 + 6 * q^40 - 5 * q^41 + 2 * q^42 + 4 * q^43 + 3 * q^44 + 10 * q^45 - 2 * q^46 + q^47 + 20 * q^48 + 10 * q^49 + 2 * q^50 + 8 * q^51 + 14 * q^52 + 9 * q^53 + 2 * q^54 + 9 * q^55 + 6 * q^56 + 13 * q^57 - 28 * q^58 - 17 * q^59 + 16 * q^60 + 19 * q^61 - 28 * q^62 + 10 * q^63 + 24 * q^64 + 14 * q^65 + 8 * q^68 - 10 * q^69 + 2 * q^70 + 6 * q^72 + 6 * q^73 + 3 * q^74 + 10 * q^75 + 15 * q^76 + 9 * q^77 - 11 * q^78 + 32 * q^79 + 20 * q^80 + 10 * q^81 + 14 * q^82 - 2 * q^83 + 16 * q^84 + 8 * q^85 + 2 * q^86 + 10 * q^87 - 3 * q^88 + 10 * q^89 + 2 * q^90 + 14 * q^91 - 16 * q^92 + 8 * q^93 - 10 * q^94 + 13 * q^95 - 11 * q^96 + 18 * q^97 + 2 * q^98 + 9 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.88703	1.33433	0.667167	−	0.744908i	$-0.267507\pi$
$2$	1.88703	1.33433	0.667167	+	0.744908i	$0.267507\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.56089	0.780446
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	1.88703	0.770378
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−0.828610	−0.292958
$9$	1.00000	0.333333
$10$	1.88703	0.596732
$11$	−2.76344	−0.833209	−0.416604	−	0.909088i	$-0.636780\pi$
$11$	−2.76344	−0.833209	−0.416604	+	0.909088i	$0.636780\pi$
$12$	1.56089	0.450591
$13$	5.73169	1.58969	0.794843	−	0.606816i	$-0.207553\pi$
$13$	5.73169	1.58969	0.794843	+	0.606816i	$0.207553\pi$
$14$	1.88703	0.504331
$15$	1.00000	0.258199
$16$	−4.68540	−1.17135
$17$	4.82653	1.17061	0.585303	−	0.810815i	$-0.300976\pi$
$17$	4.82653	1.17061	0.585303	+	0.810815i	$0.300976\pi$
$18$	1.88703	0.444778
$19$	4.18325	0.959704	0.479852	−	0.877350i	$-0.340690\pi$
$19$	4.18325	0.959704	0.479852	+	0.877350i	$0.340690\pi$
$20$	1.56089	0.349026
$21$	1.00000	0.218218
$22$	−5.21470	−1.11178
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−0.828610	−0.169139
$25$	1.00000	0.200000
$26$	10.8159	2.12117
$27$	1.00000	0.192450
$28$	1.56089	0.294981
$29$	−8.32979	−1.54680	−0.773402	−	0.633916i	$-0.781446\pi$
$29$	−8.32979	−1.54680	−0.773402	+	0.633916i	$0.781446\pi$
$30$	1.88703	0.344523
$31$	5.10382	0.916673	0.458336	−	0.888779i	$-0.348446\pi$
$31$	5.10382	0.916673	0.458336	+	0.888779i	$0.348446\pi$
$32$	−7.18428	−1.27001
$33$	−2.76344	−0.481053
$34$	9.10782	1.56198
$35$	1.00000	0.169031
$36$	1.56089	0.260149
$37$	3.98441	0.655033	0.327517	−	0.944845i	$-0.393788\pi$
$37$	3.98441	0.655033	0.327517	+	0.944845i	$0.393788\pi$
$38$	7.89393	1.28056
$39$	5.73169	0.917805
$40$	−0.828610	−0.131015
$41$	−3.49426	−0.545712	−0.272856	−	0.962055i	$-0.587968\pi$
$41$	−3.49426	−0.545712	−0.272856	+	0.962055i	$0.587968\pi$
$42$	1.88703	0.291175
$43$	6.13541	0.935641	0.467820	−	0.883824i	$-0.345039\pi$
$43$	6.13541	0.935641	0.467820	+	0.883824i	$0.345039\pi$
$44$	−4.31343	−0.650275
$45$	1.00000	0.149071
$46$	−1.88703	−0.278228
$47$	10.7297	1.56508	0.782540	−	0.622600i	$-0.213924\pi$
$47$	10.7297	1.56508	0.782540	+	0.622600i	$0.213924\pi$
$48$	−4.68540	−0.676279
$49$	1.00000	0.142857
$50$	1.88703	0.266867
$51$	4.82653	0.675849
$52$	8.94656	1.24066
$53$	−7.60272	−1.04431	−0.522157	−	0.852850i	$-0.674872\pi$
$53$	−7.60272	−1.04431	−0.522157	+	0.852850i	$0.674872\pi$
$54$	1.88703	0.256793
$55$	−2.76344	−0.372622
$56$	−0.828610	−0.110728
$57$	4.18325	0.554085
$58$	−15.7186	−2.06395
$59$	−0.943685	−0.122857	−0.0614286	−	0.998111i	$-0.519566\pi$
$59$	−0.943685	−0.122857	−0.0614286	+	0.998111i	$0.519566\pi$
$60$	1.56089	0.201510
$61$	−14.7835	−1.89283	−0.946417	−	0.322948i	$-0.895326\pi$
$61$	−14.7835	−1.89283	−0.946417	+	0.322948i	$0.895326\pi$
$62$	9.63107	1.22315
$63$	1.00000	0.125988
$64$	−4.18618	−0.523272
$65$	5.73169	0.710929
$66$	−5.21470	−0.641886
$67$	−3.94831	−0.482363	−0.241182	−	0.970480i	$-0.577535\pi$
$67$	−3.94831	−0.482363	−0.241182	+	0.970480i	$0.577535\pi$
$68$	7.53369	0.913595
$69$	−1.00000	−0.120386
$70$	1.88703	0.225544
$71$	0.189223	0.0224567	0.0112283	−	0.999937i	$-0.496426\pi$
$71$	0.189223	0.0224567	0.0112283	+	0.999937i	$0.496426\pi$
$72$	−0.828610	−0.0976526
$73$	14.6936	1.71976	0.859879	−	0.510497i	$-0.170539\pi$
$73$	14.6936	1.71976	0.859879	+	0.510497i	$0.170539\pi$
$74$	7.51872	0.874033
$75$	1.00000	0.115470
$76$	6.52961	0.748997
$77$	−2.76344	−0.314923
$78$	10.8159	1.22466
$79$	8.77235	0.986966	0.493483	−	0.869755i	$-0.335723\pi$
$79$	8.77235	0.986966	0.493483	+	0.869755i	$0.335723\pi$
$80$	−4.68540	−0.523844
$81$	1.00000	0.111111
$82$	−6.59378	−0.728161
$83$	−9.38891	−1.03057	−0.515283	−	0.857020i	$-0.672313\pi$
$83$	−9.38891	−1.03057	−0.515283	+	0.857020i	$0.672313\pi$
$84$	1.56089	0.170307
$85$	4.82653	0.523511
$86$	11.5777	1.24846
$87$	−8.32979	−0.893047
$88$	2.28981	0.244095
$89$	−8.69381	−0.921542	−0.460771	−	0.887519i	$-0.652427\pi$
$89$	−8.69381	−0.921542	−0.460771	+	0.887519i	$0.652427\pi$
$90$	1.88703	0.198911
$91$	5.73169	0.600845
$92$	−1.56089	−0.162734
$93$	5.10382	0.529241
$94$	20.2472	2.08834
$95$	4.18325	0.429192
$96$	−7.18428	−0.733243
$97$	8.78399	0.891880	0.445940	−	0.895063i	$-0.352870\pi$
$97$	8.78399	0.891880	0.445940	+	0.895063i	$0.352870\pi$
$98$	1.88703	0.190619
$99$	−2.76344	−0.277736
$100$	1.56089	0.156089
$101$	−8.41512	−0.837335	−0.418668	−	0.908139i	$-0.637503\pi$
$101$	−8.41512	−0.837335	−0.418668	+	0.908139i	$0.637503\pi$
$102$	9.10782	0.901808
$103$	8.44094	0.831710	0.415855	−	0.909431i	$-0.363482\pi$
$103$	8.44094	0.831710	0.415855	+	0.909431i	$0.363482\pi$
$104$	−4.74934	−0.465711
$105$	1.00000	0.0975900
$106$	−14.3466	−1.39346
$107$	−10.1994	−0.986009	−0.493004	−	0.870027i	$-0.664101\pi$
$107$	−10.1994	−0.986009	−0.493004	+	0.870027i	$0.664101\pi$
$108$	1.56089	0.150197
$109$	−13.6876	−1.31104	−0.655519	−	0.755179i	$-0.727550\pi$
$109$	−13.6876	−1.31104	−0.655519	+	0.755179i	$0.727550\pi$
$110$	−5.21470	−0.497202
$111$	3.98441	0.378184
$112$	−4.68540	−0.442729
$113$	17.7930	1.67383	0.836913	−	0.547336i	$-0.184358\pi$
$113$	17.7930	1.67383	0.836913	+	0.547336i	$0.184358\pi$
$114$	7.89393	0.739334
$115$	−1.00000	−0.0932505
$116$	−13.0019	−1.20720
$117$	5.73169	0.529895
$118$	−1.78076	−0.163933
$119$	4.82653	0.442447
$120$	−0.828610	−0.0756414
$121$	−3.36340	−0.305763
$122$	−27.8970	−2.52567
$123$	−3.49426	−0.315067
$124$	7.96651	0.715414
$125$	1.00000	0.0894427
$126$	1.88703	0.168110
$127$	−17.4250	−1.54622	−0.773108	−	0.634274i	$-0.781299\pi$
$127$	−17.4250	−1.54622	−0.773108	+	0.634274i	$0.781299\pi$
$128$	6.46911	0.571794
$129$	6.13541	0.540192
$130$	10.8159	0.948616
$131$	−21.2884	−1.85997	−0.929987	−	0.367591i	$-0.880183\pi$
$131$	−21.2884	−1.85997	−0.929987	+	0.367591i	$0.880183\pi$
$132$	−4.31343	−0.375436
$133$	4.18325	0.362734
$134$	−7.45060	−0.643634
$135$	1.00000	0.0860663
$136$	−3.99931	−0.342938
$137$	16.8918	1.44316	0.721580	−	0.692331i	$-0.243416\pi$
$137$	16.8918	1.44316	0.721580	+	0.692331i	$0.243416\pi$
$138$	−1.88703	−0.160635
$139$	−13.9494	−1.18317	−0.591584	−	0.806243i	$-0.701497\pi$
$139$	−13.9494	−1.18317	−0.591584	+	0.806243i	$0.701497\pi$
$140$	1.56089	0.131920
$141$	10.7297	0.903600
$142$	0.357070	0.0299647
$143$	−15.8392	−1.32454
$144$	−4.68540	−0.390450
$145$	−8.32979	−0.691751
$146$	27.7274	2.29473
$147$	1.00000	0.0824786
$148$	6.21924	0.511218
$149$	−2.66203	−0.218082	−0.109041	−	0.994037i	$-0.534778\pi$
$149$	−2.66203	−0.218082	−0.109041	+	0.994037i	$0.534778\pi$
$150$	1.88703	0.154076
$151$	−2.18060	−0.177454	−0.0887272	−	0.996056i	$-0.528280\pi$
$151$	−2.18060	−0.177454	−0.0887272	+	0.996056i	$0.528280\pi$
$152$	−3.46628	−0.281153
$153$	4.82653	0.390202
$154$	−5.21470	−0.420213
$155$	5.10382	0.409948
$156$	8.94656	0.716298
$157$	−12.5707	−1.00325	−0.501624	−	0.865086i	$-0.667264\pi$
$157$	−12.5707	−1.00325	−0.501624	+	0.865086i	$0.667264\pi$
$158$	16.5537	1.31694
$159$	−7.60272	−0.602935
$160$	−7.18428	−0.567967
$161$	−1.00000	−0.0788110
$162$	1.88703	0.148259
$163$	−20.3288	−1.59227	−0.796137	−	0.605117i	$-0.793126\pi$
$163$	−20.3288	−1.59227	−0.796137	+	0.605117i	$0.793126\pi$
$164$	−5.45416	−0.425899
$165$	−2.76344	−0.215134
$166$	−17.7172	−1.37512
$167$	−12.0470	−0.932227	−0.466114	−	0.884725i	$-0.654346\pi$
$167$	−12.0470	−0.932227	−0.466114	+	0.884725i	$0.654346\pi$
$168$	−0.828610	−0.0639286
$169$	19.8523	1.52710
$170$	9.10782	0.698538
$171$	4.18325	0.319901
$172$	9.57671	0.730217
$173$	20.7346	1.57642	0.788209	−	0.615407i	$-0.211008\pi$
$173$	20.7346	1.57642	0.788209	+	0.615407i	$0.211008\pi$
$174$	−15.7186	−1.19162
$175$	1.00000	0.0755929
$176$	12.9478	0.975979
$177$	−0.943685	−0.0709317
$178$	−16.4055	−1.22964
$179$	1.40660	0.105135	0.0525673	−	0.998617i	$-0.483260\pi$
$179$	1.40660	0.105135	0.0525673	+	0.998617i	$0.483260\pi$
$180$	1.56089	0.116342
$181$	7.52723	0.559494	0.279747	−	0.960074i	$-0.409749\pi$
$181$	7.52723	0.559494	0.279747	+	0.960074i	$0.409749\pi$
$182$	10.8159	0.801727
$183$	−14.7835	−1.09283
$184$	0.828610	0.0610859
$185$	3.98441	0.292940
$186$	9.63107	0.706184
$187$	−13.3378	−0.975359
$188$	16.7478	1.22146
$189$	1.00000	0.0727393
$190$	7.89393	0.572686
$191$	5.72468	0.414223	0.207112	−	0.978317i	$-0.433594\pi$
$191$	5.72468	0.414223	0.207112	+	0.978317i	$0.433594\pi$
$192$	−4.18618	−0.302111
$193$	−7.49392	−0.539424	−0.269712	−	0.962941i	$-0.586928\pi$
$193$	−7.49392	−0.539424	−0.269712	+	0.962941i	$0.586928\pi$
$194$	16.5757	1.19006
$195$	5.73169	0.410455
$196$	1.56089	0.111492
$197$	−22.5090	−1.60370	−0.801848	−	0.597528i	$-0.796150\pi$
$197$	−22.5090	−1.60370	−0.801848	+	0.597528i	$0.796150\pi$
$198$	−5.21470	−0.370593
$199$	−11.3634	−0.805532	−0.402766	−	0.915303i	$-0.631951\pi$
$199$	−11.3634	−0.805532	−0.402766	+	0.915303i	$0.631951\pi$
$200$	−0.828610	−0.0585916
$201$	−3.94831	−0.278493
$202$	−15.8796	−1.11728
$203$	−8.32979	−0.584637
$204$	7.53369	0.527464
$205$	−3.49426	−0.244050
$206$	15.9283	1.10978
$207$	−1.00000	−0.0695048
$208$	−26.8553	−1.86208
$209$	−11.5602	−0.799633
$210$	1.88703	0.130218
$211$	−10.2089	−0.702807	−0.351403	−	0.936224i	$-0.614295\pi$
$211$	−10.2089	−0.702807	−0.351403	+	0.936224i	$0.614295\pi$
$212$	−11.8670	−0.815031
$213$	0.189223	0.0129654
$214$	−19.2465	−1.31566
$215$	6.13541	0.418431
$216$	−0.828610	−0.0563798
$217$	5.10382	0.346470
$218$	−25.8290	−1.74936
$219$	14.6936	0.992903
$220$	−4.31343	−0.290812
$221$	27.6642	1.86089
$222$	7.51872	0.504623
$223$	4.68318	0.313609	0.156805	−	0.987630i	$-0.449881\pi$
$223$	4.68318	0.313609	0.156805	+	0.987630i	$0.449881\pi$
$224$	−7.18428	−0.480020
$225$	1.00000	0.0666667
$226$	33.5760	2.23344
$227$	−1.11647	−0.0741027	−0.0370513	−	0.999313i	$-0.511797\pi$
$227$	−1.11647	−0.0741027	−0.0370513	+	0.999313i	$0.511797\pi$
$228$	6.52961	0.432434
$229$	−9.16628	−0.605725	−0.302862	−	0.953034i	$-0.597942\pi$
$229$	−9.16628	−0.605725	−0.302862	+	0.953034i	$0.597942\pi$
$230$	−1.88703	−0.124427
$231$	−2.76344	−0.181821
$232$	6.90215	0.453148
$233$	10.6638	0.698607	0.349303	−	0.937010i	$-0.386418\pi$
$233$	10.6638	0.698607	0.349303	+	0.937010i	$0.386418\pi$
$234$	10.8159	0.707057
$235$	10.7297	0.699925
$236$	−1.47299	−0.0958835
$237$	8.77235	0.569825
$238$	9.10782	0.590372
$239$	−26.2437	−1.69756	−0.848780	−	0.528746i	$-0.822663\pi$
$239$	−26.2437	−1.69756	−0.848780	+	0.528746i	$0.822663\pi$
$240$	−4.68540	−0.302441
$241$	24.8799	1.60265	0.801327	−	0.598227i	$-0.204128\pi$
$241$	24.8799	1.60265	0.801327	+	0.598227i	$0.204128\pi$
$242$	−6.34684	−0.407990
$243$	1.00000	0.0641500
$244$	−23.0755	−1.47725
$245$	1.00000	0.0638877
$246$	−6.59378	−0.420404
$247$	23.9771	1.52563
$248$	−4.22907	−0.268546
$249$	−9.38891	−0.594998
$250$	1.88703	0.119346
$251$	15.4628	0.976003	0.488001	−	0.872843i	$-0.337726\pi$
$251$	15.4628	0.976003	0.488001	+	0.872843i	$0.337726\pi$
$252$	1.56089	0.0983270
$253$	2.76344	0.173736
$254$	−32.8815	−2.06317
$255$	4.82653	0.302249
$256$	20.5798	1.28624
$257$	−25.5019	−1.59076	−0.795382	−	0.606109i	$-0.792730\pi$
$257$	−25.5019	−1.59076	−0.795382	+	0.606109i	$0.792730\pi$
$258$	11.5777	0.720797
$259$	3.98441	0.247579
$260$	8.94656	0.554842
$261$	−8.32979	−0.515601
$262$	−40.1719	−2.48183
$263$	19.8175	1.22200	0.610999	−	0.791631i	$-0.290768\pi$
$263$	19.8175	1.22200	0.610999	+	0.791631i	$0.290768\pi$
$264$	2.28981	0.140928
$265$	−7.60272	−0.467031
$266$	7.89393	0.484008
$267$	−8.69381	−0.532052
$268$	−6.16290	−0.376459
$269$	26.7170	1.62897	0.814483	−	0.580188i	$-0.197021\pi$
$269$	26.7170	1.62897	0.814483	+	0.580188i	$0.197021\pi$
$270$	1.88703	0.114841
$271$	−9.96933	−0.605593	−0.302797	−	0.953055i	$-0.597920\pi$
$271$	−9.96933	−0.605593	−0.302797	+	0.953055i	$0.597920\pi$
$272$	−22.6142	−1.37119
$273$	5.73169	0.346898
$274$	31.8753	1.92566
$275$	−2.76344	−0.166642
$276$	−1.56089	−0.0939547
$277$	2.62532	0.157740	0.0788700	−	0.996885i	$-0.474869\pi$
$277$	2.62532	0.157740	0.0788700	+	0.996885i	$0.474869\pi$
$278$	−26.3229	−1.57874
$279$	5.10382	0.305558
$280$	−0.828610	−0.0495189
$281$	−21.0523	−1.25588	−0.627939	−	0.778263i	$-0.716101\pi$
$281$	−21.0523	−1.25588	−0.627939	+	0.778263i	$0.716101\pi$
$282$	20.2472	1.20570
$283$	14.9895	0.891033	0.445516	−	0.895274i	$-0.353020\pi$
$283$	14.9895	0.891033	0.445516	+	0.895274i	$0.353020\pi$
$284$	0.295357	0.0175262
$285$	4.18325	0.247794
$286$	−29.8891	−1.76738
$287$	−3.49426	−0.206260
$288$	−7.18428	−0.423338
$289$	6.29538	0.370317
$290$	−15.7186	−0.923027
$291$	8.78399	0.514927
$292$	22.9352	1.34218
$293$	15.9314	0.930723	0.465361	−	0.885121i	$-0.345924\pi$
$293$	15.9314	0.930723	0.465361	+	0.885121i	$0.345924\pi$
$294$	1.88703	0.110054
$295$	−0.943685	−0.0549434
$296$	−3.30152	−0.191897
$297$	−2.76344	−0.160351
$298$	−5.02334	−0.290994
$299$	−5.73169	−0.331472
$300$	1.56089	0.0901182
$301$	6.13541	0.353639
$302$	−4.11486	−0.236783
$303$	−8.41512	−0.483436
$304$	−19.6002	−1.12415
$305$	−14.7835	−0.846501
$306$	9.10782	0.520659
$307$	−11.2105	−0.639818	−0.319909	−	0.947448i	$-0.603652\pi$
$307$	−11.2105	−0.639818	−0.319909	+	0.947448i	$0.603652\pi$
$308$	−4.31343	−0.245781
$309$	8.44094	0.480188
$310$	9.63107	0.547008
$311$	−23.6492	−1.34103	−0.670513	−	0.741898i	$-0.733926\pi$
$311$	−23.6492	−1.34103	−0.670513	+	0.741898i	$0.733926\pi$
$312$	−4.74934	−0.268878
$313$	5.05393	0.285665	0.142832	−	0.989747i	$-0.454379\pi$
$313$	5.05393	0.285665	0.142832	+	0.989747i	$0.454379\pi$
$314$	−23.7212	−1.33867
$315$	1.00000	0.0563436
$316$	13.6927	0.770274
$317$	31.6774	1.77918	0.889590	−	0.456761i	$-0.150990\pi$
$317$	31.6774	1.77918	0.889590	+	0.456761i	$0.150990\pi$
$318$	−14.3466	−0.804516
$319$	23.0189	1.28881
$320$	−4.18618	−0.234014
$321$	−10.1994	−0.569272
$322$	−1.88703	−0.105160
$323$	20.1906	1.12343
$324$	1.56089	0.0867163
$325$	5.73169	0.317937
$326$	−38.3611	−2.12462
$327$	−13.6876	−0.756928
$328$	2.89538	0.159870
$329$	10.7297	0.591545
$330$	−5.21470	−0.287060
$331$	−33.5974	−1.84668	−0.923341	−	0.383982i	$-0.874552\pi$
$331$	−33.5974	−1.84668	−0.923341	+	0.383982i	$0.874552\pi$
$332$	−14.6551	−0.804302
$333$	3.98441	0.218344
$334$	−22.7331	−1.24390
$335$	−3.94831	−0.215719
$336$	−4.68540	−0.255609
$337$	−18.5561	−1.01081	−0.505407	−	0.862881i	$-0.668658\pi$
$337$	−18.5561	−1.01081	−0.505407	+	0.862881i	$0.668658\pi$
$338$	37.4619	2.03766
$339$	17.7930	0.966384
$340$	7.53369	0.408572
$341$	−14.1041	−0.763780
$342$	7.89393	0.426855
$343$	1.00000	0.0539949
$344$	−5.08386	−0.274103
$345$	−1.00000	−0.0538382
$346$	39.1268	2.10347
$347$	9.38261	0.503685	0.251842	−	0.967768i	$-0.418964\pi$
$347$	9.38261	0.503685	0.251842	+	0.967768i	$0.418964\pi$
$348$	−13.0019	−0.696975
$349$	18.4351	0.986808	0.493404	−	0.869800i	$-0.335753\pi$
$349$	18.4351	0.986808	0.493404	+	0.869800i	$0.335753\pi$
$350$	1.88703	0.100866
$351$	5.73169	0.305935
$352$	19.8533	1.05819
$353$	29.5543	1.57302	0.786509	−	0.617579i	$-0.211886\pi$
$353$	29.5543	1.57302	0.786509	+	0.617579i	$0.211886\pi$
$354$	−1.78076	−0.0946465
$355$	0.189223	0.0100429
$356$	−13.5701	−0.719214
$357$	4.82653	0.255447
$358$	2.65431	0.140285
$359$	−1.02873	−0.0542944	−0.0271472	−	0.999631i	$-0.508642\pi$
$359$	−1.02873	−0.0542944	−0.0271472	+	0.999631i	$0.508642\pi$
$360$	−0.828610	−0.0436716
$361$	−1.50041	−0.0789691
$362$	14.2041	0.746552
$363$	−3.36340	−0.176532
$364$	8.94656	0.468927
$365$	14.6936	0.769100
$366$	−27.8970	−1.45820
$367$	−20.8876	−1.09032	−0.545161	−	0.838331i	$-0.683532\pi$
$367$	−20.8876	−1.09032	−0.545161	+	0.838331i	$0.683532\pi$
$368$	4.68540	0.244243
$369$	−3.49426	−0.181904
$370$	7.51872	0.390880
$371$	−7.60272	−0.394713
$372$	7.96651	0.413044
$373$	5.93540	0.307323	0.153662	−	0.988124i	$-0.450893\pi$
$373$	5.93540	0.307323	0.153662	+	0.988124i	$0.450893\pi$
$374$	−25.1689	−1.30145
$375$	1.00000	0.0516398
$376$	−8.89070	−0.458503
$377$	−47.7438	−2.45893
$378$	1.88703	0.0970585
$379$	−24.6244	−1.26487	−0.632435	−	0.774613i	$-0.717945\pi$
$379$	−24.6244	−1.26487	−0.632435	+	0.774613i	$0.717945\pi$
$380$	6.52961	0.334962
$381$	−17.4250	−0.892708
$382$	10.8027	0.552712
$383$	15.1784	0.775579	0.387789	−	0.921748i	$-0.373239\pi$
$383$	15.1784	0.775579	0.387789	+	0.921748i	$0.373239\pi$
$384$	6.46911	0.330125
$385$	−2.76344	−0.140838
$386$	−14.1413	−0.719771
$387$	6.13541	0.311880
$388$	13.7109	0.696064
$389$	−35.8307	−1.81669	−0.908344	−	0.418225i	$-0.862653\pi$
$389$	−35.8307	−1.81669	−0.908344	+	0.418225i	$0.862653\pi$
$390$	10.8159	0.547684
$391$	−4.82653	−0.244088
$392$	−0.828610	−0.0418511
$393$	−21.2884	−1.07386
$394$	−42.4751	−2.13987
$395$	8.77235	0.441385
$396$	−4.31343	−0.216758
$397$	−11.9122	−0.597857	−0.298928	−	0.954276i	$-0.596629\pi$
$397$	−11.9122	−0.597857	−0.298928	+	0.954276i	$0.596629\pi$
$398$	−21.4432	−1.07485
$399$	4.18325	0.209424
$400$	−4.68540	−0.234270
$401$	13.8828	0.693276	0.346638	−	0.937999i	$-0.387323\pi$
$401$	13.8828	0.693276	0.346638	+	0.937999i	$0.387323\pi$
$402$	−7.45060	−0.371602
$403$	29.2535	1.45722
$404$	−13.1351	−0.653495
$405$	1.00000	0.0496904
$406$	−15.7186	−0.780100
$407$	−11.0107	−0.545780
$408$	−3.99931	−0.197995
$409$	33.6644	1.66460	0.832298	−	0.554328i	$-0.187025\pi$
$409$	33.6644	1.66460	0.832298	+	0.554328i	$0.187025\pi$
$410$	−6.59378	−0.325644
$411$	16.8918	0.833209
$412$	13.1754	0.649105
$413$	−0.943685	−0.0464357
$414$	−1.88703	−0.0927426
$415$	−9.38891	−0.460883
$416$	−41.1781	−2.01892
$417$	−13.9494	−0.683103
$418$	−21.8144	−1.06698
$419$	8.67518	0.423810	0.211905	−	0.977290i	$-0.432033\pi$
$419$	8.67518	0.423810	0.211905	+	0.977290i	$0.432033\pi$
$420$	1.56089	0.0761638
$421$	35.4978	1.73006	0.865029	−	0.501721i	$-0.167300\pi$
$421$	35.4978	1.73006	0.865029	+	0.501721i	$0.167300\pi$
$422$	−19.2644	−0.937778
$423$	10.7297	0.521694
$424$	6.29969	0.305940
$425$	4.82653	0.234121
$426$	0.357070	0.0173001
$427$	−14.7835	−0.715424
$428$	−15.9201	−0.769527
$429$	−15.8392	−0.764723
$430$	11.5777	0.558327
$431$	−10.2558	−0.494002	−0.247001	−	0.969015i	$-0.579445\pi$
$431$	−10.2558	−0.494002	−0.247001	+	0.969015i	$0.579445\pi$
$432$	−4.68540	−0.225426
$433$	−1.48709	−0.0714650	−0.0357325	−	0.999361i	$-0.511376\pi$
$433$	−1.48709	−0.0714650	−0.0357325	+	0.999361i	$0.511376\pi$
$434$	9.63107	0.462306
$435$	−8.32979	−0.399383
$436$	−21.3649	−1.02319
$437$	−4.18325	−0.200112
$438$	27.7274	1.32486
$439$	13.1518	0.627702	0.313851	−	0.949472i	$-0.398381\pi$
$439$	13.1518	0.627702	0.313851	+	0.949472i	$0.398381\pi$
$440$	2.28981	0.109163
$441$	1.00000	0.0476190
$442$	52.2032	2.48305
$443$	−30.6473	−1.45610	−0.728048	−	0.685526i	$-0.759572\pi$
$443$	−30.6473	−1.45610	−0.728048	+	0.685526i	$0.759572\pi$
$444$	6.21924	0.295152
$445$	−8.69381	−0.412126
$446$	8.83732	0.418459
$447$	−2.66203	−0.125910
$448$	−4.18618	−0.197778
$449$	−2.87735	−0.135790	−0.0678952	−	0.997692i	$-0.521628\pi$
$449$	−2.87735	−0.135790	−0.0678952	+	0.997692i	$0.521628\pi$
$450$	1.88703	0.0889556
$451$	9.65618	0.454692
$452$	27.7730	1.30633
$453$	−2.18060	−0.102453
$454$	−2.10681	−0.0988777
$455$	5.73169	0.268706
$456$	−3.46628	−0.162324
$457$	11.4730	0.536684	0.268342	−	0.963324i	$-0.413524\pi$
$457$	11.4730	0.536684	0.268342	+	0.963324i	$0.413524\pi$
$458$	−17.2971	−0.808239
$459$	4.82653	0.225283
$460$	−1.56089	−0.0727770
$461$	−4.97184	−0.231561	−0.115781	−	0.993275i	$-0.536937\pi$
$461$	−4.97184	−0.231561	−0.115781	+	0.993275i	$0.536937\pi$
$462$	−5.21470	−0.242610
$463$	7.48612	0.347910	0.173955	−	0.984754i	$-0.444345\pi$
$463$	7.48612	0.347910	0.173955	+	0.984754i	$0.444345\pi$
$464$	39.0284	1.81185
$465$	5.10382	0.236684
$466$	20.1229	0.932174
$467$	30.6919	1.42025	0.710125	−	0.704075i	$-0.248638\pi$
$467$	30.6919	1.42025	0.710125	+	0.704075i	$0.248638\pi$
$468$	8.94656	0.413555
$469$	−3.94831	−0.182316
$470$	20.2472	0.933934
$471$	−12.5707	−0.579225
$472$	0.781946	0.0359920
$473$	−16.9548	−0.779584
$474$	16.5537	0.760337
$475$	4.18325	0.191941
$476$	7.53369	0.345306
$477$	−7.60272	−0.348105
$478$	−49.5226	−2.26511
$479$	−38.3822	−1.75373	−0.876864	−	0.480738i	$-0.840369\pi$
$479$	−38.3822	−1.75373	−0.876864	+	0.480738i	$0.840369\pi$
$480$	−7.18428	−0.327916
$481$	22.8374	1.04130
$482$	46.9491	2.13847
$483$	−1.00000	−0.0455016
$484$	−5.24990	−0.238632
$485$	8.78399	0.398861
$486$	1.88703	0.0855975
$487$	10.9845	0.497754	0.248877	−	0.968535i	$-0.419939\pi$
$487$	10.9845	0.497754	0.248877	+	0.968535i	$0.419939\pi$
$488$	12.2498	0.554520
$489$	−20.3288	−0.919299
$490$	1.88703	0.0852475
$491$	−28.8020	−1.29982	−0.649909	−	0.760012i	$-0.725193\pi$
$491$	−28.8020	−1.29982	−0.649909	+	0.760012i	$0.725193\pi$
$492$	−5.45416	−0.245893
$493$	−40.2040	−1.81070
$494$	45.2456	2.03569
$495$	−2.76344	−0.124207
$496$	−23.9134	−1.07374
$497$	0.189223	0.00848782
$498$	−17.7172	−0.793925
$499$	13.4792	0.603414	0.301707	−	0.953401i	$-0.402444\pi$
$499$	13.4792	0.603414	0.301707	+	0.953401i	$0.402444\pi$
$500$	1.56089	0.0698052
$501$	−12.0470	−0.538222
$502$	29.1788	1.30231
$503$	25.5683	1.14003	0.570017	−	0.821633i	$-0.306937\pi$
$503$	25.5683	1.14003	0.570017	+	0.821633i	$0.306937\pi$
$504$	−0.828610	−0.0369092
$505$	−8.41512	−0.374468
$506$	5.21470	0.231822
$507$	19.8523	0.881671
$508$	−27.1985	−1.20674
$509$	−40.1726	−1.78062	−0.890310	−	0.455355i	$-0.849513\pi$
$509$	−40.1726	−1.78062	−0.890310	+	0.455355i	$0.849513\pi$
$510$	9.10782	0.403301
$511$	14.6936	0.650008
$512$	25.8965	1.14447
$513$	4.18325	0.184695
$514$	−48.1229	−2.12261
$515$	8.44094	0.371952
$516$	9.57671	0.421591
$517$	−29.6508	−1.30404
$518$	7.51872	0.330354
$519$	20.7346	0.910146
$520$	−4.74934	−0.208272
$521$	−32.8518	−1.43926	−0.719632	−	0.694356i	$-0.755689\pi$
$521$	−32.8518	−1.43926	−0.719632	+	0.694356i	$0.755689\pi$
$522$	−15.7186	−0.687984
$523$	−14.5456	−0.636036	−0.318018	−	0.948085i	$-0.603017\pi$
$523$	−14.5456	−0.636036	−0.318018	+	0.948085i	$0.603017\pi$
$524$	−33.2289	−1.45161
$525$	1.00000	0.0436436
$526$	37.3962	1.63055
$527$	24.6337	1.07306
$528$	12.9478	0.563482
$529$	1.00000	0.0434783
$530$	−14.3466	−0.623175
$531$	−0.943685	−0.0409524
$532$	6.52961	0.283094
$533$	−20.0280	−0.867510
$534$	−16.4055	−0.709936
$535$	−10.1994	−0.440956
$536$	3.27161	0.141312
$537$	1.40660	0.0606995
$538$	50.4159	2.17358
$539$	−2.76344	−0.119030
$540$	1.56089	0.0671701
$541$	7.06454	0.303728	0.151864	−	0.988401i	$-0.451472\pi$
$541$	7.06454	0.303728	0.151864	+	0.988401i	$0.451472\pi$
$542$	−18.8124	−0.808064
$543$	7.52723	0.323024
$544$	−34.6751	−1.48668
$545$	−13.6876	−0.586314
$546$	10.8159	0.462877
$547$	−13.1927	−0.564078	−0.282039	−	0.959403i	$-0.591011\pi$
$547$	−13.1927	−0.564078	−0.282039	+	0.959403i	$0.591011\pi$
$548$	26.3662	1.12631
$549$	−14.7835	−0.630944
$550$	−5.21470	−0.222356
$551$	−34.8456	−1.48447
$552$	0.828610	0.0352680
$553$	8.77235	0.373038
$554$	4.95406	0.210478
$555$	3.98441	0.169129
$556$	−21.7734	−0.923400
$557$	35.6655	1.51120	0.755598	−	0.655035i	$-0.227346\pi$
$557$	35.6655	1.51120	0.755598	+	0.655035i	$0.227346\pi$
$558$	9.63107	0.407716
$559$	35.1663	1.48737
$560$	−4.68540	−0.197994
$561$	−13.3378	−0.563124
$562$	−39.7265	−1.67576
$563$	12.1370	0.511512	0.255756	−	0.966741i	$-0.417676\pi$
$563$	12.1370	0.511512	0.255756	+	0.966741i	$0.417676\pi$
$564$	16.7478	0.705211
$565$	17.7930	0.748558
$566$	28.2857	1.18893
$567$	1.00000	0.0419961
$568$	−0.156792	−0.00657885
$569$	−6.55611	−0.274846	−0.137423	−	0.990512i	$-0.543882\pi$
$569$	−6.55611	−0.274846	−0.137423	+	0.990512i	$0.543882\pi$
$570$	7.89393	0.330640
$571$	−11.9562	−0.500353	−0.250177	−	0.968200i	$-0.580489\pi$
$571$	−11.9562	−0.500353	−0.250177	+	0.968200i	$0.580489\pi$
$572$	−24.7233	−1.03373
$573$	5.72468	0.239152
$574$	−6.59378	−0.275219
$575$	−1.00000	−0.0417029
$576$	−4.18618	−0.174424
$577$	−20.8650	−0.868621	−0.434310	−	0.900763i	$-0.643008\pi$
$577$	−20.8650	−0.868621	−0.434310	+	0.900763i	$0.643008\pi$
$578$	11.8796	0.494126
$579$	−7.49392	−0.311437
$580$	−13.0019	−0.539875
$581$	−9.38891	−0.389517
$582$	16.5757	0.687084
$583$	21.0097	0.870131
$584$	−12.1753	−0.503817
$585$	5.73169	0.236976
$586$	30.0631	1.24189
$587$	−10.3965	−0.429109	−0.214554	−	0.976712i	$-0.568830\pi$
$587$	−10.3965	−0.429109	−0.214554	+	0.976712i	$0.568830\pi$
$588$	1.56089	0.0643701
$589$	21.3505	0.879734
$590$	−1.78076	−0.0733129
$591$	−22.5090	−0.925895
$592$	−18.6686	−0.767273
$593$	5.97284	0.245275	0.122638	−	0.992452i	$-0.460865\pi$
$593$	5.97284	0.245275	0.122638	+	0.992452i	$0.460865\pi$
$594$	−5.21470	−0.213962
$595$	4.82653	0.197868
$596$	−4.15515	−0.170201
$597$	−11.3634	−0.465074
$598$	−10.8159	−0.442295
$599$	18.7374	0.765591	0.382796	−	0.923833i	$-0.374961\pi$
$599$	18.7374	0.765591	0.382796	+	0.923833i	$0.374961\pi$
$600$	−0.828610	−0.0338279
$601$	16.7255	0.682247	0.341123	−	0.940019i	$-0.389193\pi$
$601$	16.7255	0.682247	0.341123	+	0.940019i	$0.389193\pi$
$602$	11.5777	0.471872
$603$	−3.94831	−0.160788
$604$	−3.40368	−0.138494
$605$	−3.36340	−0.136741
$606$	−15.8796	−0.645065
$607$	−6.97185	−0.282979	−0.141489	−	0.989940i	$-0.545189\pi$
$607$	−6.97185	−0.282979	−0.141489	+	0.989940i	$0.545189\pi$
$608$	−30.0537	−1.21884
$609$	−8.32979	−0.337540
$610$	−27.8970	−1.12951
$611$	61.4991	2.48799
$612$	7.53369	0.304532
$613$	25.0901	1.01338	0.506690	−	0.862128i	$-0.330869\pi$
$613$	25.0901	1.01338	0.506690	+	0.862128i	$0.330869\pi$
$614$	−21.1546	−0.853730
$615$	−3.49426	−0.140902
$616$	2.28981	0.0922592
$617$	−14.0523	−0.565724	−0.282862	−	0.959161i	$-0.591284\pi$
$617$	−14.0523	−0.565724	−0.282862	+	0.959161i	$0.591284\pi$
$618$	15.9283	0.640731
$619$	11.7007	0.470289	0.235145	−	0.971960i	$-0.424444\pi$
$619$	11.7007	0.470289	0.235145	+	0.971960i	$0.424444\pi$
$620$	7.96651	0.319943
$621$	−1.00000	−0.0401286
$622$	−44.6269	−1.78938
$623$	−8.69381	−0.348310
$624$	−26.8553	−1.07507
$625$	1.00000	0.0400000
$626$	9.53693	0.381172
$627$	−11.5602	−0.461669
$628$	−19.6214	−0.782981
$629$	19.2309	0.766786
$630$	1.88703	0.0751812
$631$	21.6403	0.861486	0.430743	−	0.902475i	$-0.358251\pi$
$631$	21.6403	0.861486	0.430743	+	0.902475i	$0.358251\pi$
$632$	−7.26885	−0.289139
$633$	−10.2089	−0.405766
$634$	59.7763	2.37402
$635$	−17.4250	−0.691489
$636$	−11.8670	−0.470558
$637$	5.73169	0.227098
$638$	43.4374	1.71970
$639$	0.189223	0.00748555
$640$	6.46911	0.255714
$641$	25.7386	1.01661	0.508307	−	0.861176i	$-0.330272\pi$
$641$	25.7386	1.01661	0.508307	+	0.861176i	$0.330272\pi$
$642$	−19.2465	−0.759599
$643$	20.7802	0.819490	0.409745	−	0.912200i	$-0.365618\pi$
$643$	20.7802	0.819490	0.409745	+	0.912200i	$0.365618\pi$
$644$	−1.56089	−0.0615078
$645$	6.13541	0.241581
$646$	38.1003	1.49904
$647$	10.4913	0.412456	0.206228	−	0.978504i	$-0.433881\pi$
$647$	10.4913	0.412456	0.206228	+	0.978504i	$0.433881\pi$
$648$	−0.828610	−0.0325509
$649$	2.60782	0.102366
$650$	10.8159	0.424234
$651$	5.10382	0.200034
$652$	−31.7311	−1.24268
$653$	−32.9451	−1.28924	−0.644621	−	0.764502i	$-0.722985\pi$
$653$	−32.9451	−1.28924	−0.644621	+	0.764502i	$0.722985\pi$
$654$	−25.8290	−1.00999
$655$	−21.2884	−0.831806
$656$	16.3720	0.639219
$657$	14.6936	0.573253
$658$	20.2472	0.789318
$659$	26.8160	1.04460	0.522301	−	0.852761i	$-0.325074\pi$
$659$	26.8160	1.04460	0.522301	+	0.852761i	$0.325074\pi$
$660$	−4.31343	−0.167900
$661$	33.9080	1.31887	0.659434	−	0.751762i	$-0.270796\pi$
$661$	33.9080	1.31887	0.659434	+	0.751762i	$0.270796\pi$
$662$	−63.3994	−2.46409
$663$	27.6642	1.07439
$664$	7.77974	0.301912
$665$	4.18325	0.162220
$666$	7.51872	0.291344
$667$	8.32979	0.322531
$668$	−18.8041	−0.727553
$669$	4.68318	0.181062
$670$	−7.45060	−0.287842
$671$	40.8533	1.57713
$672$	−7.18428	−0.277140
$673$	38.9754	1.50239	0.751196	−	0.660080i	$-0.229477\pi$
$673$	38.9754	1.50239	0.751196	+	0.660080i	$0.229477\pi$
$674$	−35.0159	−1.34876
$675$	1.00000	0.0384900
$676$	30.9873	1.19182
$677$	−13.6260	−0.523691	−0.261845	−	0.965110i	$-0.584331\pi$
$677$	−13.6260	−0.523691	−0.261845	+	0.965110i	$0.584331\pi$
$678$	33.5760	1.28948
$679$	8.78399	0.337099
$680$	−3.99931	−0.153367
$681$	−1.11647	−0.0427832
$682$	−26.6149	−1.01914
$683$	0.835032	0.0319516	0.0159758	−	0.999872i	$-0.494915\pi$
$683$	0.835032	0.0319516	0.0159758	+	0.999872i	$0.494915\pi$
$684$	6.52961	0.249666
$685$	16.8918	0.645401
$686$	1.88703	0.0720472
$687$	−9.16628	−0.349715
$688$	−28.7468	−1.09596
$689$	−43.5764	−1.66013
$690$	−1.88703	−0.0718381
$691$	−46.4748	−1.76799	−0.883993	−	0.467500i	$-0.845155\pi$
$691$	−46.4748	−1.76799	−0.883993	+	0.467500i	$0.845155\pi$
$692$	32.3644	1.23031
$693$	−2.76344	−0.104974
$694$	17.7053	0.672084
$695$	−13.9494	−0.529129
$696$	6.90215	0.261625
$697$	−16.8651	−0.638813
$698$	34.7876	1.31673
$699$	10.6638	0.403341
$700$	1.56089	0.0589962
$701$	23.1813	0.875545	0.437772	−	0.899086i	$-0.355768\pi$
$701$	23.1813	0.875545	0.437772	+	0.899086i	$0.355768\pi$
$702$	10.8159	0.408219
$703$	16.6678	0.628638
$704$	11.5683	0.435995
$705$	10.7297	0.404102
$706$	55.7700	2.09893
$707$	−8.41512	−0.316483
$708$	−1.47299	−0.0553584
$709$	19.2114	0.721499	0.360749	−	0.932663i	$-0.382521\pi$
$709$	19.2114	0.721499	0.360749	+	0.932663i	$0.382521\pi$
$710$	0.357070	0.0134006
$711$	8.77235	0.328989
$712$	7.20378	0.269973
$713$	−5.10382	−0.191139
$714$	9.10782	0.340852
$715$	−15.8392	−0.592352
$716$	2.19556	0.0820519
$717$	−26.2437	−0.980087
$718$	−1.94125	−0.0724469
$719$	−36.1631	−1.34866	−0.674328	−	0.738432i	$-0.735567\pi$
$719$	−36.1631	−1.34866	−0.674328	+	0.738432i	$0.735567\pi$
$720$	−4.68540	−0.174615
$721$	8.44094	0.314357
$722$	−2.83133	−0.105371
$723$	24.8799	0.925292
$724$	11.7492	0.436655
$725$	−8.32979	−0.309361
$726$	−6.34684	−0.235553
$727$	5.62523	0.208628	0.104314	−	0.994544i	$-0.466735\pi$
$727$	5.62523	0.208628	0.104314	+	0.994544i	$0.466735\pi$
$728$	−4.74934	−0.176022
$729$	1.00000	0.0370370
$730$	27.7274	1.02624
$731$	29.6127	1.09527
$732$	−23.0755	−0.852894
$733$	−4.23048	−0.156256	−0.0781281	−	0.996943i	$-0.524894\pi$
$733$	−4.23048	−0.156256	−0.0781281	+	0.996943i	$0.524894\pi$
$734$	−39.4155	−1.45485
$735$	1.00000	0.0368856
$736$	7.18428	0.264816
$737$	10.9109	0.401909
$738$	−6.59378	−0.242720
$739$	41.0958	1.51173	0.755866	−	0.654726i	$-0.227216\pi$
$739$	41.0958	1.51173	0.755866	+	0.654726i	$0.227216\pi$
$740$	6.21924	0.228624
$741$	23.9771	0.880821
$742$	−14.3466	−0.526679
$743$	−37.6532	−1.38136	−0.690682	−	0.723159i	$-0.742689\pi$
$743$	−37.6532	−1.38136	−0.690682	+	0.723159i	$0.742689\pi$
$744$	−4.22907	−0.155045
$745$	−2.66203	−0.0975293
$746$	11.2003	0.410072
$747$	−9.38891	−0.343522
$748$	−20.8189	−0.761215
$749$	−10.1994	−0.372676
$750$	1.88703	0.0689047
$751$	−18.4973	−0.674977	−0.337489	−	0.941330i	$-0.609577\pi$
$751$	−18.4973	−0.674977	−0.337489	+	0.941330i	$0.609577\pi$
$752$	−50.2727	−1.83326
$753$	15.4628	0.563495
$754$	−90.0941	−3.28103
$755$	−2.18060	−0.0793600
$756$	1.56089	0.0567691
$757$	−16.8077	−0.610887	−0.305444	−	0.952210i	$-0.598805\pi$
$757$	−16.8077	−0.610887	−0.305444	+	0.952210i	$0.598805\pi$
$758$	−46.4671	−1.68776
$759$	2.76344	0.100307
$760$	−3.46628	−0.125735
$761$	−41.2345	−1.49475	−0.747374	−	0.664404i	$-0.768686\pi$
$761$	−41.2345	−1.49475	−0.747374	+	0.664404i	$0.768686\pi$
$762$	−32.8815	−1.19117
$763$	−13.6876	−0.495526
$764$	8.93561	0.323279
$765$	4.82653	0.174504
$766$	28.6421	1.03488
$767$	−5.40891	−0.195304
$768$	20.5798	0.742609
$769$	25.8135	0.930859	0.465429	−	0.885085i	$-0.345900\pi$
$769$	25.8135	0.930859	0.465429	+	0.885085i	$0.345900\pi$
$770$	−5.21470	−0.187925
$771$	−25.5019	−0.918428
$772$	−11.6972	−0.420991
$773$	47.9254	1.72376	0.861879	−	0.507114i	$-0.169288\pi$
$773$	47.9254	1.72376	0.861879	+	0.507114i	$0.169288\pi$
$774$	11.5777	0.416152
$775$	5.10382	0.183335
$776$	−7.27850	−0.261283
$777$	3.98441	0.142940
$778$	−67.6137	−2.42407
$779$	−14.6174	−0.523721
$780$	8.94656	0.320338
$781$	−0.522907	−0.0187111
$782$	−9.10782	−0.325695
$783$	−8.32979	−0.297682
$784$	−4.68540	−0.167336
$785$	−12.5707	−0.448666
$786$	−40.1719	−1.43288
$787$	26.6300	0.949255	0.474628	−	0.880187i	$-0.342583\pi$
$787$	26.6300	0.949255	0.474628	+	0.880187i	$0.342583\pi$
$788$	−35.1341	−1.25160
$789$	19.8175	0.705521
$790$	16.5537	0.588954
$791$	17.7930	0.632647
$792$	2.28981	0.0813650
$793$	−84.7345	−3.00901
$794$	−22.4787	−0.797740
$795$	−7.60272	−0.269641
$796$	−17.7371	−0.628675
$797$	−5.39533	−0.191112	−0.0955562	−	0.995424i	$-0.530463\pi$
$797$	−5.39533	−0.191112	−0.0955562	+	0.995424i	$0.530463\pi$
$798$	7.89393	0.279442
$799$	51.7870	1.83209
$800$	−7.18428	−0.254003
$801$	−8.69381	−0.307181
$802$	26.1974	0.925061
$803$	−40.6050	−1.43292
$804$	−6.16290	−0.217349
$805$	−1.00000	−0.0352454
$806$	55.2023	1.94442
$807$	26.7170	0.940483
$808$	6.97285	0.245304
$809$	−12.9256	−0.454441	−0.227221	−	0.973843i	$-0.572964\pi$
$809$	−12.9256	−0.454441	−0.227221	+	0.973843i	$0.572964\pi$
$810$	1.88703	0.0663036
$811$	40.5729	1.42471	0.712354	−	0.701821i	$-0.247629\pi$
$811$	40.5729	1.42471	0.712354	+	0.701821i	$0.247629\pi$
$812$	−13.0019	−0.456278
$813$	−9.96933	−0.349640
$814$	−20.7775	−0.728252
$815$	−20.3288	−0.712086
$816$	−22.6142	−0.791656
$817$	25.6659	0.897938
$818$	63.5258	2.22113
$819$	5.73169	0.200282
$820$	−5.45416	−0.190468
$821$	28.0878	0.980270	0.490135	−	0.871647i	$-0.336948\pi$
$821$	28.0878	0.980270	0.490135	+	0.871647i	$0.336948\pi$
$822$	31.8753	1.11178
$823$	−26.8209	−0.934916	−0.467458	−	0.884015i	$-0.654830\pi$
$823$	−26.8209	−0.934916	−0.467458	+	0.884015i	$0.654830\pi$
$824$	−6.99425	−0.243656
$825$	−2.76344	−0.0962107
$826$	−1.78076	−0.0619607
$827$	−42.9862	−1.49478	−0.747389	−	0.664386i	$-0.768693\pi$
$827$	−42.9862	−1.49478	−0.747389	+	0.664386i	$0.768693\pi$
$828$	−1.56089	−0.0542448
$829$	−5.46109	−0.189672	−0.0948358	−	0.995493i	$-0.530233\pi$
$829$	−5.46109	−0.189672	−0.0948358	+	0.995493i	$0.530233\pi$
$830$	−17.7172	−0.614972
$831$	2.62532	0.0910712
$832$	−23.9939	−0.831838
$833$	4.82653	0.167229
$834$	−26.3229	−0.911487
$835$	−12.0470	−0.416905
$836$	−18.0442	−0.624071
$837$	5.10382	0.176414
$838$	16.3703	0.565504
$839$	18.8628	0.651218	0.325609	−	0.945505i	$-0.394431\pi$
$839$	18.8628	0.651218	0.325609	+	0.945505i	$0.394431\pi$
$840$	−0.828610	−0.0285898
$841$	40.3854	1.39260
$842$	66.9856	2.30848
$843$	−21.0523	−0.725081
$844$	−15.9349	−0.548503
$845$	19.8523	0.682939
$846$	20.2472	0.696113
$847$	−3.36340	−0.115568
$848$	35.6218	1.22326
$849$	14.9895	0.514438
$850$	9.10782	0.312396
$851$	−3.98441	−0.136584
$852$	0.295357	0.0101188
$853$	0.949259	0.0325020	0.0162510	−	0.999868i	$-0.494827\pi$
$853$	0.949259	0.0325020	0.0162510	+	0.999868i	$0.494827\pi$
$854$	−27.8970	−0.954614
$855$	4.18325	0.143064
$856$	8.45128	0.288859
$857$	9.44081	0.322492	0.161246	−	0.986914i	$-0.448449\pi$
$857$	9.44081	0.322492	0.161246	+	0.986914i	$0.448449\pi$
$858$	−29.8891	−1.02040
$859$	−24.7189	−0.843397	−0.421698	−	0.906736i	$-0.638566\pi$
$859$	−24.7189	−0.843397	−0.421698	+	0.906736i	$0.638566\pi$
$860$	9.57671	0.326563
$861$	−3.49426	−0.119084
$862$	−19.3529	−0.659164
$863$	21.1933	0.721429	0.360715	−	0.932676i	$-0.382533\pi$
$863$	21.1933	0.721429	0.360715	+	0.932676i	$0.382533\pi$
$864$	−7.18428	−0.244414
$865$	20.7346	0.704996
$866$	−2.80619	−0.0953582
$867$	6.29538	0.213802
$868$	7.96651	0.270401
$869$	−24.2419	−0.822349
$870$	−15.7186	−0.532910
$871$	−22.6305	−0.766806
$872$	11.3417	0.384079
$873$	8.78399	0.297293
$874$	−7.89393	−0.267016
$875$	1.00000	0.0338062
$876$	22.9352	0.774908
$877$	25.0644	0.846364	0.423182	−	0.906045i	$-0.360913\pi$
$877$	25.0644	0.846364	0.423182	+	0.906045i	$0.360913\pi$
$878$	24.8179	0.837564
$879$	15.9314	0.537353
$880$	12.9478	0.436471
$881$	49.9375	1.68244	0.841219	−	0.540695i	$-0.181839\pi$
$881$	49.9375	1.68244	0.841219	+	0.540695i	$0.181839\pi$
$882$	1.88703	0.0635397
$883$	5.34720	0.179948	0.0899739	−	0.995944i	$-0.471322\pi$
$883$	5.34720	0.179948	0.0899739	+	0.995944i	$0.471322\pi$
$884$	43.1808	1.45233
$885$	−0.943685	−0.0317216
$886$	−57.8324	−1.94292
$887$	−30.5018	−1.02415	−0.512076	−	0.858940i	$-0.671123\pi$
$887$	−30.5018	−1.02415	−0.512076	+	0.858940i	$0.671123\pi$
$888$	−3.30152	−0.110792
$889$	−17.4250	−0.584415
$890$	−16.4055	−0.549914
$891$	−2.76344	−0.0925787
$892$	7.30994	0.244755
$893$	44.8848	1.50201
$894$	−5.02334	−0.168006
$895$	1.40660	0.0470176
$896$	6.46911	0.216118
$897$	−5.73169	−0.191376
$898$	−5.42965	−0.181190
$899$	−42.5137	−1.41791
$900$	1.56089	0.0520298
$901$	−36.6947	−1.22248
$902$	18.2215	0.606710
$903$	6.13541	0.204174
$904$	−14.7435	−0.490360
$905$	7.52723	0.250213
$906$	−4.11486	−0.136707
$907$	3.92377	0.130287	0.0651433	−	0.997876i	$-0.479250\pi$
$907$	3.92377	0.130287	0.0651433	+	0.997876i	$0.479250\pi$
$908$	−1.74269	−0.0578332
$909$	−8.41512	−0.279112
$910$	10.8159	0.358543
$911$	8.44911	0.279932	0.139966	−	0.990156i	$-0.455301\pi$
$911$	8.44911	0.279932	0.139966	+	0.990156i	$0.455301\pi$
$912$	−19.6002	−0.649027
$913$	25.9457	0.858677
$914$	21.6499	0.716115
$915$	−14.7835	−0.488727
$916$	−14.3076	−0.472736
$917$	−21.2884	−0.703004
$918$	9.10782	0.300603
$919$	5.55929	0.183384	0.0916920	−	0.995787i	$-0.470772\pi$
$919$	5.55929	0.183384	0.0916920	+	0.995787i	$0.470772\pi$
$920$	0.828610	0.0273185
$921$	−11.2105	−0.369399
$922$	−9.38202	−0.308980
$923$	1.08457	0.0356990
$924$	−4.31343	−0.141902
$925$	3.98441	0.131007
$926$	14.1266	0.464228
$927$	8.44094	0.277237
$928$	59.8436	1.96446
$929$	51.1223	1.67727	0.838635	−	0.544694i	$-0.183354\pi$
$929$	51.1223	1.67727	0.838635	+	0.544694i	$0.183354\pi$
$930$	9.63107	0.315815
$931$	4.18325	0.137101
$932$	16.6450	0.545225
$933$	−23.6492	−0.774242
$934$	57.9166	1.89509
$935$	−13.3378	−0.436194
$936$	−4.74934	−0.155237
$937$	22.7884	0.744464	0.372232	−	0.928140i	$-0.378593\pi$
$937$	22.7884	0.744464	0.372232	+	0.928140i	$0.378593\pi$
$938$	−7.45060	−0.243271
$939$	5.05393	0.164929
$940$	16.7478	0.546254
$941$	1.02341	0.0333621	0.0166810	−	0.999861i	$-0.494690\pi$
$941$	1.02341	0.0333621	0.0166810	+	0.999861i	$0.494690\pi$
$942$	−23.7212	−0.772880
$943$	3.49426	0.113789
$944$	4.42154	0.143909
$945$	1.00000	0.0325300
$946$	−31.9943	−1.04023
$947$	−28.3311	−0.920638	−0.460319	−	0.887754i	$-0.652265\pi$
$947$	−28.3311	−0.920638	−0.460319	+	0.887754i	$0.652265\pi$
$948$	13.6927	0.444718
$949$	84.2193	2.73388
$950$	7.89393	0.256113
$951$	31.6774	1.02721
$952$	−3.99931	−0.129618
$953$	28.9150	0.936648	0.468324	−	0.883557i	$-0.344858\pi$
$953$	28.9150	0.936648	0.468324	+	0.883557i	$0.344858\pi$
$954$	−14.3466	−0.464488
$955$	5.72468	0.185246
$956$	−40.9635	−1.32486
$957$	23.0189	0.744095
$958$	−72.4285	−2.34006
$959$	16.8918	0.545463
$960$	−4.18618	−0.135108
$961$	−4.95105	−0.159711
$962$	43.0950	1.38944
$963$	−10.1994	−0.328670
$964$	38.8348	1.25079
$965$	−7.49392	−0.241238
$966$	−1.88703	−0.0607143
$967$	35.6299	1.14578	0.572890	−	0.819632i	$-0.305822\pi$
$967$	35.6299	1.14578	0.572890	+	0.819632i	$0.305822\pi$
$968$	2.78694	0.0895757
$969$	20.1906	0.648615
$970$	16.5757	0.532213
$971$	8.82435	0.283187	0.141593	−	0.989925i	$-0.454777\pi$
$971$	8.82435	0.283187	0.141593	+	0.989925i	$0.454777\pi$
$972$	1.56089	0.0500657
$973$	−13.9494	−0.447196
$974$	20.7281	0.664170
$975$	5.73169	0.183561
$976$	69.2666	2.21717
$977$	32.1161	1.02749	0.513743	−	0.857944i	$-0.328259\pi$
$977$	32.1161	1.02749	0.513743	+	0.857944i	$0.328259\pi$
$978$	−38.3611	−1.22665
$979$	24.0248	0.767837
$980$	1.56089	0.0498609
$981$	−13.6876	−0.437013
$982$	−54.3504	−1.73439
$983$	−37.5582	−1.19792	−0.598960	−	0.800779i	$-0.704419\pi$
$983$	−37.5582	−1.19792	−0.598960	+	0.800779i	$0.704419\pi$
$984$	2.89538	0.0923013
$985$	−22.5090	−0.717195
$986$	−75.8662	−2.41607
$987$	10.7297	0.341529
$988$	37.4257	1.19067
$989$	−6.13541	−0.195095
$990$	−5.21470	−0.165734
$991$	38.3530	1.21832	0.609161	−	0.793046i	$-0.291506\pi$
$991$	38.3530	1.21832	0.609161	+	0.793046i	$0.291506\pi$
$992$	−36.6673	−1.16419
$993$	−33.5974	−1.06618
$994$	0.357070	0.0113256
$995$	−11.3634	−0.360245
$996$	−14.6551	−0.464364
$997$	−4.68847	−0.148485	−0.0742426	−	0.997240i	$-0.523654\pi$
$997$	−4.68847	−0.148485	−0.0742426	+	0.997240i	$0.523654\pi$
$998$	25.4358	0.805155
$999$	3.98441	0.126061

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2415.2.a.w.1.7	✓	10
3.2	odd	2		7245.2.a.bv.1.4		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2415.2.a.w.1.7	✓	10	1.1	even	1	trivial
7245.2.a.bv.1.4		10	3.2	odd	2

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:	\( N \)	\(=\)	\( 2415 = 3 \cdot 5 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2415.a (trivial)

\(f(q)\)	\(=\)	\(q+1.88703 q^{2} +1.00000 q^{3} +1.56089 q^{4} +1.00000 q^{5} +1.88703 q^{6} +1.00000 q^{7} -0.828610 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.88703 q^{2} +1.00000 q^{3} +1.56089 q^{4} +1.00000 q^{5} +1.88703 q^{6} +1.00000 q^{7} -0.828610 q^{8} +1.00000 q^{9} +1.88703 q^{10} -2.76344 q^{11} +1.56089 q^{12} +5.73169 q^{13} +1.88703 q^{14} +1.00000 q^{15} -4.68540 q^{16} +4.82653 q^{17} +1.88703 q^{18} +4.18325 q^{19} +1.56089 q^{20} +1.00000 q^{21} -5.21470 q^{22} -1.00000 q^{23} -0.828610 q^{24} +1.00000 q^{25} +10.8159 q^{26} +1.00000 q^{27} +1.56089 q^{28} -8.32979 q^{29} +1.88703 q^{30} +5.10382 q^{31} -7.18428 q^{32} -2.76344 q^{33} +9.10782 q^{34} +1.00000 q^{35} +1.56089 q^{36} +3.98441 q^{37} +7.89393 q^{38} +5.73169 q^{39} -0.828610 q^{40} -3.49426 q^{41} +1.88703 q^{42} +6.13541 q^{43} -4.31343 q^{44} +1.00000 q^{45} -1.88703 q^{46} +10.7297 q^{47} -4.68540 q^{48} +1.00000 q^{49} +1.88703 q^{50} +4.82653 q^{51} +8.94656 q^{52} -7.60272 q^{53} +1.88703 q^{54} -2.76344 q^{55} -0.828610 q^{56} +4.18325 q^{57} -15.7186 q^{58} -0.943685 q^{59} +1.56089 q^{60} -14.7835 q^{61} +9.63107 q^{62} +1.00000 q^{63} -4.18618 q^{64} +5.73169 q^{65} -5.21470 q^{66} -3.94831 q^{67} +7.53369 q^{68} -1.00000 q^{69} +1.88703 q^{70} +0.189223 q^{71} -0.828610 q^{72} +14.6936 q^{73} +7.51872 q^{74} +1.00000 q^{75} +6.52961 q^{76} -2.76344 q^{77} +10.8159 q^{78} +8.77235 q^{79} -4.68540 q^{80} +1.00000 q^{81} -6.59378 q^{82} -9.38891 q^{83} +1.56089 q^{84} +4.82653 q^{85} +11.5777 q^{86} -8.32979 q^{87} +2.28981 q^{88} -8.69381 q^{89} +1.88703 q^{90} +5.73169 q^{91} -1.56089 q^{92} +5.10382 q^{93} +20.2472 q^{94} +4.18325 q^{95} -7.18428 q^{96} +8.78399 q^{97} +1.88703 q^{98} -2.76344 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 2 q^{2} + 10 q^{3} + 16 q^{4} + 10 q^{5} + 2 q^{6} + 10 q^{7} + 6 q^{8} + 10 q^{9}+O(q^{10}) \) 10 * q + 2 * q^2 + 10 * q^3 + 16 * q^4 + 10 * q^5 + 2 * q^6 + 10 * q^7 + 6 * q^8 + 10 * q^9	\( 10 q + 2 q^{2} + 10 q^{3} + 16 q^{4} + 10 q^{5} + 2 q^{6} + 10 q^{7} + 6 q^{8} + 10 q^{9} + 2 q^{10} + 9 q^{11} + 16 q^{12} + 14 q^{13} + 2 q^{14} + 10 q^{15} + 20 q^{16} + 8 q^{17} + 2 q^{18} + 13 q^{19} + 16 q^{20} + 10 q^{21} - 10 q^{23} + 6 q^{24} + 10 q^{25} - 11 q^{26} + 10 q^{27} + 16 q^{28} + 10 q^{29} + 2 q^{30} + 8 q^{31} - 11 q^{32} + 9 q^{33} - 5 q^{34} + 10 q^{35} + 16 q^{36} + 8 q^{37} - 10 q^{38} + 14 q^{39} + 6 q^{40} - 5 q^{41} + 2 q^{42} + 4 q^{43} + 3 q^{44} + 10 q^{45} - 2 q^{46} + q^{47} + 20 q^{48} + 10 q^{49} + 2 q^{50} + 8 q^{51} + 14 q^{52} + 9 q^{53} + 2 q^{54} + 9 q^{55} + 6 q^{56} + 13 q^{57} - 28 q^{58} - 17 q^{59} + 16 q^{60} + 19 q^{61} - 28 q^{62} + 10 q^{63} + 24 q^{64} + 14 q^{65} + 8 q^{68} - 10 q^{69} + 2 q^{70} + 6 q^{72} + 6 q^{73} + 3 q^{74} + 10 q^{75} + 15 q^{76} + 9 q^{77} - 11 q^{78} + 32 q^{79} + 20 q^{80} + 10 q^{81} + 14 q^{82} - 2 q^{83} + 16 q^{84} + 8 q^{85} + 2 q^{86} + 10 q^{87} - 3 q^{88} + 10 q^{89} + 2 q^{90} + 14 q^{91} - 16 q^{92} + 8 q^{93} - 10 q^{94} + 13 q^{95} - 11 q^{96} + 18 q^{97} + 2 q^{98} + 9 q^{99}+O(q^{100}) \) 10 * q + 2 * q^2 + 10 * q^3 + 16 * q^4 + 10 * q^5 + 2 * q^6 + 10 * q^7 + 6 * q^8 + 10 * q^9 + 2 * q^10 + 9 * q^11 + 16 * q^12 + 14 * q^13 + 2 * q^14 + 10 * q^15 + 20 * q^16 + 8 * q^17 + 2 * q^18 + 13 * q^19 + 16 * q^20 + 10 * q^21 - 10 * q^23 + 6 * q^24 + 10 * q^25 - 11 * q^26 + 10 * q^27 + 16 * q^28 + 10 * q^29 + 2 * q^30 + 8 * q^31 - 11 * q^32 + 9 * q^33 - 5 * q^34 + 10 * q^35 + 16 * q^36 + 8 * q^37 - 10 * q^38 + 14 * q^39 + 6 * q^40 - 5 * q^41 + 2 * q^42 + 4 * q^43 + 3 * q^44 + 10 * q^45 - 2 * q^46 + q^47 + 20 * q^48 + 10 * q^49 + 2 * q^50 + 8 * q^51 + 14 * q^52 + 9 * q^53 + 2 * q^54 + 9 * q^55 + 6 * q^56 + 13 * q^57 - 28 * q^58 - 17 * q^59 + 16 * q^60 + 19 * q^61 - 28 * q^62 + 10 * q^63 + 24 * q^64 + 14 * q^65 + 8 * q^68 - 10 * q^69 + 2 * q^70 + 6 * q^72 + 6 * q^73 + 3 * q^74 + 10 * q^75 + 15 * q^76 + 9 * q^77 - 11 * q^78 + 32 * q^79 + 20 * q^80 + 10 * q^81 + 14 * q^82 - 2 * q^83 + 16 * q^84 + 8 * q^85 + 2 * q^86 + 10 * q^87 - 3 * q^88 + 10 * q^89 + 2 * q^90 + 14 * q^91 - 16 * q^92 + 8 * q^93 - 10 * q^94 + 13 * q^95 - 11 * q^96 + 18 * q^97 + 2 * q^98 + 9 * q^99

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