LMFDB - Embedded newform 2415.2.a.w.1.9

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			1.9
Root			$2.51086$ 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)

$f(q)$	$=$	$q+2.51086 q^{2} +1.00000 q^{3} +4.30443 q^{4} +1.00000 q^{5} +2.51086 q^{6} +1.00000 q^{7} +5.78609 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.51086 q^{2} +1.00000 q^{3} +4.30443 q^{4} +1.00000 q^{5} +2.51086 q^{6} +1.00000 q^{7} +5.78609 q^{8} +1.00000 q^{9} +2.51086 q^{10} -2.18160 q^{11} +4.30443 q^{12} -3.86504 q^{13} +2.51086 q^{14} +1.00000 q^{15} +5.91923 q^{16} +7.23813 q^{17} +2.51086 q^{18} -1.03699 q^{19} +4.30443 q^{20} +1.00000 q^{21} -5.47769 q^{22} -1.00000 q^{23} +5.78609 q^{24} +1.00000 q^{25} -9.70458 q^{26} +1.00000 q^{27} +4.30443 q^{28} +10.4121 q^{29} +2.51086 q^{30} -3.03567 q^{31} +3.29018 q^{32} -2.18160 q^{33} +18.1739 q^{34} +1.00000 q^{35} +4.30443 q^{36} +2.86835 q^{37} -2.60375 q^{38} -3.86504 q^{39} +5.78609 q^{40} +5.78803 q^{41} +2.51086 q^{42} -10.1282 q^{43} -9.39053 q^{44} +1.00000 q^{45} -2.51086 q^{46} -3.49832 q^{47} +5.91923 q^{48} +1.00000 q^{49} +2.51086 q^{50} +7.23813 q^{51} -16.6368 q^{52} +11.4219 q^{53} +2.51086 q^{54} -2.18160 q^{55} +5.78609 q^{56} -1.03699 q^{57} +26.1435 q^{58} -10.9605 q^{59} +4.30443 q^{60} -4.05657 q^{61} -7.62214 q^{62} +1.00000 q^{63} -3.57727 q^{64} -3.86504 q^{65} -5.47769 q^{66} -11.8470 q^{67} +31.1560 q^{68} -1.00000 q^{69} +2.51086 q^{70} -9.35988 q^{71} +5.78609 q^{72} -8.75508 q^{73} +7.20204 q^{74} +1.00000 q^{75} -4.46367 q^{76} -2.18160 q^{77} -9.70458 q^{78} +6.27815 q^{79} +5.91923 q^{80} +1.00000 q^{81} +14.5329 q^{82} -10.6686 q^{83} +4.30443 q^{84} +7.23813 q^{85} -25.4304 q^{86} +10.4121 q^{87} -12.6229 q^{88} -10.6606 q^{89} +2.51086 q^{90} -3.86504 q^{91} -4.30443 q^{92} -3.03567 q^{93} -8.78381 q^{94} -1.03699 q^{95} +3.29018 q^{96} +16.6008 q^{97} +2.51086 q^{98} -2.18160 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	2.51086	1.77545	0.887724	−	0.460377i	$-0.152286\pi$
$2$	2.51086	1.77545	0.887724	+	0.460377i	$0.152286\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	4.30443	2.15221
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	2.51086	1.02505
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	5.78609	2.04569
$9$	1.00000	0.333333
$10$	2.51086	0.794004
$11$	−2.18160	−0.657777	−0.328889	−	0.944369i	$-0.606674\pi$
$11$	−2.18160	−0.657777	−0.328889	+	0.944369i	$0.606674\pi$
$12$	4.30443	1.24258
$13$	−3.86504	−1.07197	−0.535985	−	0.844228i	$-0.680059\pi$
$13$	−3.86504	−1.07197	−0.535985	+	0.844228i	$0.680059\pi$
$14$	2.51086	0.671056
$15$	1.00000	0.258199
$16$	5.91923	1.47981
$17$	7.23813	1.75550	0.877752	−	0.479116i	$-0.159043\pi$
$17$	7.23813	1.75550	0.877752	+	0.479116i	$0.159043\pi$
$18$	2.51086	0.591816
$19$	−1.03699	−0.237903	−0.118951	−	0.992900i	$-0.537953\pi$
$19$	−1.03699	−0.237903	−0.118951	+	0.992900i	$0.537953\pi$
$20$	4.30443	0.962499
$21$	1.00000	0.218218
$22$	−5.47769	−1.16785
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	5.78609	1.18108
$25$	1.00000	0.200000
$26$	−9.70458	−1.90322
$27$	1.00000	0.192450
$28$	4.30443	0.813460
$29$	10.4121	1.93349	0.966744	−	0.255747i	$-0.0823213\pi$
$29$	10.4121	1.93349	0.966744	+	0.255747i	$0.0823213\pi$
$30$	2.51086	0.458419
$31$	−3.03567	−0.545222	−0.272611	−	0.962124i	$-0.587887\pi$
$31$	−3.03567	−0.545222	−0.272611	+	0.962124i	$0.587887\pi$
$32$	3.29018	0.581627
$33$	−2.18160	−0.379768
$34$	18.1739	3.11680
$35$	1.00000	0.169031
$36$	4.30443	0.717404
$37$	2.86835	0.471555	0.235777	−	0.971807i	$-0.424236\pi$
$37$	2.86835	0.471555	0.235777	+	0.971807i	$0.424236\pi$
$38$	−2.60375	−0.422384
$39$	−3.86504	−0.618902
$40$	5.78609	0.914862
$41$	5.78803	0.903938	0.451969	−	0.892034i	$-0.350722\pi$
$41$	5.78803	0.903938	0.451969	+	0.892034i	$0.350722\pi$
$42$	2.51086	0.387434
$43$	−10.1282	−1.54453	−0.772265	−	0.635300i	$-0.780876\pi$
$43$	−10.1282	−1.54453	−0.772265	+	0.635300i	$0.780876\pi$
$44$	−9.39053	−1.41568
$45$	1.00000	0.149071
$46$	−2.51086	−0.370206
$47$	−3.49832	−0.510283	−0.255141	−	0.966904i	$-0.582122\pi$
$47$	−3.49832	−0.510283	−0.255141	+	0.966904i	$0.582122\pi$
$48$	5.91923	0.854367
$49$	1.00000	0.142857
$50$	2.51086	0.355089
$51$	7.23813	1.01354
$52$	−16.6368	−2.30711
$53$	11.4219	1.56892	0.784458	−	0.620182i	$-0.212941\pi$
$53$	11.4219	1.56892	0.784458	+	0.620182i	$0.212941\pi$
$54$	2.51086	0.341685
$55$	−2.18160	−0.294167
$56$	5.78609	0.773199
$57$	−1.03699	−0.137353
$58$	26.1435	3.43281
$59$	−10.9605	−1.42694	−0.713471	−	0.700685i	$-0.752878\pi$
$59$	−10.9605	−1.42694	−0.713471	+	0.700685i	$0.752878\pi$
$60$	4.30443	0.555699
$61$	−4.05657	−0.519390	−0.259695	−	0.965691i	$-0.583622\pi$
$61$	−4.05657	−0.519390	−0.259695	+	0.965691i	$0.583622\pi$
$62$	−7.62214	−0.968012
$63$	1.00000	0.125988
$64$	−3.57727	−0.447159
$65$	−3.86504	−0.479399
$66$	−5.47769	−0.674258
$67$	−11.8470	−1.44734	−0.723669	−	0.690147i	$-0.757546\pi$
$67$	−11.8470	−1.44734	−0.723669	+	0.690147i	$0.757546\pi$
$68$	31.1560	3.77822
$69$	−1.00000	−0.120386
$70$	2.51086	0.300105
$71$	−9.35988	−1.11081	−0.555407	−	0.831579i	$-0.687437\pi$
$71$	−9.35988	−1.11081	−0.555407	+	0.831579i	$0.687437\pi$
$72$	5.78609	0.681898
$73$	−8.75508	−1.02470	−0.512352	−	0.858775i	$-0.671226\pi$
$73$	−8.75508	−1.02470	−0.512352	+	0.858775i	$0.671226\pi$
$74$	7.20204	0.837220
$75$	1.00000	0.115470
$76$	−4.46367	−0.512017
$77$	−2.18160	−0.248616
$78$	−9.70458	−1.09883
$79$	6.27815	0.706347	0.353173	−	0.935558i	$-0.385103\pi$
$79$	6.27815	0.706347	0.353173	+	0.935558i	$0.385103\pi$
$80$	5.91923	0.661790
$81$	1.00000	0.111111
$82$	14.5329	1.60489
$83$	−10.6686	−1.17103	−0.585516	−	0.810661i	$-0.699108\pi$
$83$	−10.6686	−1.17103	−0.585516	+	0.810661i	$0.699108\pi$
$84$	4.30443	0.469651
$85$	7.23813	0.785085
$86$	−25.4304	−2.74223
$87$	10.4121	1.11630
$88$	−12.6229	−1.34561
$89$	−10.6606	−1.13003	−0.565013	−	0.825082i	$-0.691129\pi$
$89$	−10.6606	−1.13003	−0.565013	+	0.825082i	$0.691129\pi$
$90$	2.51086	0.264668
$91$	−3.86504	−0.405166
$92$	−4.30443	−0.448767
$93$	−3.03567	−0.314784
$94$	−8.78381	−0.905980
$95$	−1.03699	−0.106393
$96$	3.29018	0.335803
$97$	16.6008	1.68556	0.842778	−	0.538262i	$-0.180919\pi$
$97$	16.6008	1.68556	0.842778	+	0.538262i	$0.180919\pi$
$98$	2.51086	0.253635
$99$	−2.18160	−0.219259
$100$	4.30443	0.430443
$101$	−12.6404	−1.25776	−0.628882	−	0.777500i	$-0.716487\pi$
$101$	−12.6404	−1.25776	−0.628882	+	0.777500i	$0.716487\pi$
$102$	18.1739	1.79949
$103$	−14.4046	−1.41933	−0.709665	−	0.704540i	$-0.751154\pi$
$103$	−14.4046	−1.41933	−0.709665	+	0.704540i	$0.751154\pi$
$104$	−22.3635	−2.19292
$105$	1.00000	0.0975900
$106$	28.6788	2.78553
$107$	18.3850	1.77735	0.888673	−	0.458542i	$-0.151628\pi$
$107$	18.3850	1.77735	0.888673	+	0.458542i	$0.151628\pi$
$108$	4.30443	0.414194
$109$	19.8501	1.90130	0.950649	−	0.310267i	$-0.100419\pi$
$109$	19.8501	1.90130	0.950649	+	0.310267i	$0.100419\pi$
$110$	−5.47769	−0.522278
$111$	2.86835	0.272252
$112$	5.91923	0.559315
$113$	−3.89280	−0.366203	−0.183102	−	0.983094i	$-0.558614\pi$
$113$	−3.89280	−0.366203	−0.183102	+	0.983094i	$0.558614\pi$
$114$	−2.60375	−0.243863
$115$	−1.00000	−0.0932505
$116$	44.8183	4.16128
$117$	−3.86504	−0.357323
$118$	−27.5204	−2.53346
$119$	7.23813	0.663518
$120$	5.78609	0.528196
$121$	−6.24062	−0.567329
$122$	−10.1855	−0.922150
$123$	5.78803	0.521889
$124$	−13.0668	−1.17343
$125$	1.00000	0.0894427
$126$	2.51086	0.223685
$127$	−0.606134	−0.0537857	−0.0268929	−	0.999638i	$-0.508561\pi$
$127$	−0.606134	−0.0537857	−0.0268929	+	0.999638i	$0.508561\pi$
$128$	−15.5624	−1.37553
$129$	−10.1282	−0.891735
$130$	−9.70458	−0.851148
$131$	−3.10866	−0.271605	−0.135803	−	0.990736i	$-0.543361\pi$
$131$	−3.10866	−0.271605	−0.135803	+	0.990736i	$0.543361\pi$
$132$	−9.39053	−0.817341
$133$	−1.03699	−0.0899188
$134$	−29.7461	−2.56967
$135$	1.00000	0.0860663
$136$	41.8805	3.59122
$137$	−18.0184	−1.53942	−0.769709	−	0.638395i	$-0.779598\pi$
$137$	−18.0184	−1.53942	−0.769709	+	0.638395i	$0.779598\pi$
$138$	−2.51086	−0.213739
$139$	−12.6982	−1.07704	−0.538522	−	0.842611i	$-0.681017\pi$
$139$	−12.6982	−1.07704	−0.538522	+	0.842611i	$0.681017\pi$
$140$	4.30443	0.363790
$141$	−3.49832	−0.294612
$142$	−23.5014	−1.97219
$143$	8.43197	0.705117
$144$	5.91923	0.493269
$145$	10.4121	0.864682
$146$	−21.9828	−1.81931
$147$	1.00000	0.0824786
$148$	12.3466	1.01489
$149$	−12.7300	−1.04288	−0.521440	−	0.853288i	$-0.674605\pi$
$149$	−12.7300	−1.04288	−0.521440	+	0.853288i	$0.674605\pi$
$150$	2.51086	0.205011
$151$	−10.4553	−0.850837	−0.425419	−	0.904997i	$-0.639873\pi$
$151$	−10.4553	−0.850837	−0.425419	+	0.904997i	$0.639873\pi$
$152$	−6.00015	−0.486676
$153$	7.23813	0.585168
$154$	−5.47769	−0.441405
$155$	−3.03567	−0.243831
$156$	−16.6368	−1.33201
$157$	8.59702	0.686117	0.343059	−	0.939314i	$-0.388537\pi$
$157$	8.59702	0.686117	0.343059	+	0.939314i	$0.388537\pi$
$158$	15.7636	1.25408
$159$	11.4219	0.905814
$160$	3.29018	0.260112
$161$	−1.00000	−0.0788110
$162$	2.51086	0.197272
$163$	20.1903	1.58142	0.790712	−	0.612188i	$-0.209710\pi$
$163$	20.1903	1.58142	0.790712	+	0.612188i	$0.209710\pi$
$164$	24.9141	1.94547
$165$	−2.18160	−0.169837
$166$	−26.7874	−2.07911
$167$	−3.65724	−0.283005	−0.141503	−	0.989938i	$-0.545193\pi$
$167$	−3.65724	−0.283005	−0.141503	+	0.989938i	$0.545193\pi$
$168$	5.78609	0.446407
$169$	1.93853	0.149118
$170$	18.1739	1.39388
$171$	−1.03699	−0.0793009
$172$	−43.5959	−3.32416
$173$	−6.06289	−0.460953	−0.230477	−	0.973078i	$-0.574029\pi$
$173$	−6.06289	−0.460953	−0.230477	+	0.973078i	$0.574029\pi$
$174$	26.1435	1.98193
$175$	1.00000	0.0755929
$176$	−12.9134	−0.973384
$177$	−10.9605	−0.823845
$178$	−26.7674	−2.00630
$179$	8.16263	0.610104	0.305052	−	0.952336i	$-0.401326\pi$
$179$	8.16263	0.610104	0.305052	+	0.952336i	$0.401326\pi$
$180$	4.30443	0.320833
$181$	15.5295	1.15430	0.577149	−	0.816639i	$-0.304165\pi$
$181$	15.5295	1.15430	0.577149	+	0.816639i	$0.304165\pi$
$182$	−9.70458	−0.719351
$183$	−4.05657	−0.299870
$184$	−5.78609	−0.426557
$185$	2.86835	0.210886
$186$	−7.62214	−0.558882
$187$	−15.7907	−1.15473
$188$	−15.0583	−1.09824
$189$	1.00000	0.0727393
$190$	−2.60375	−0.188896
$191$	23.7441	1.71806	0.859030	−	0.511925i	$-0.171067\pi$
$191$	23.7441	1.71806	0.859030	+	0.511925i	$0.171067\pi$
$192$	−3.57727	−0.258167
$193$	10.9543	0.788509	0.394254	−	0.919001i	$-0.371003\pi$
$193$	10.9543	0.788509	0.394254	+	0.919001i	$0.371003\pi$
$194$	41.6823	2.99261
$195$	−3.86504	−0.276781
$196$	4.30443	0.307459
$197$	1.63608	0.116566	0.0582829	−	0.998300i	$-0.481437\pi$
$197$	1.63608	0.116566	0.0582829	+	0.998300i	$0.481437\pi$
$198$	−5.47769	−0.389283
$199$	4.52690	0.320903	0.160452	−	0.987044i	$-0.448705\pi$
$199$	4.52690	0.320903	0.160452	+	0.987044i	$0.448705\pi$
$200$	5.78609	0.409139
$201$	−11.8470	−0.835621
$202$	−31.7382	−2.23310
$203$	10.4121	0.730790
$204$	31.1560	2.18136
$205$	5.78803	0.404253
$206$	−36.1680	−2.51994
$207$	−1.00000	−0.0695048
$208$	−22.8781	−1.58631
$209$	2.26231	0.156487
$210$	2.51086	0.173266
$211$	23.1930	1.59667	0.798336	−	0.602212i	$-0.205714\pi$
$211$	23.1930	1.59667	0.798336	+	0.602212i	$0.205714\pi$
$212$	49.1646	3.37664
$213$	−9.35988	−0.641329
$214$	46.1622	3.15558
$215$	−10.1282	−0.690735
$216$	5.78609	0.393694
$217$	−3.03567	−0.206074
$218$	49.8410	3.37566
$219$	−8.75508	−0.591613
$220$	−9.39053	−0.633110
$221$	−27.9756	−1.88185
$222$	7.20204	0.483369
$223$	8.66306	0.580122	0.290061	−	0.957008i	$-0.406324\pi$
$223$	8.66306	0.580122	0.290061	+	0.957008i	$0.406324\pi$
$224$	3.29018	0.219834
$225$	1.00000	0.0666667
$226$	−9.77427	−0.650175
$227$	8.32346	0.552447	0.276224	−	0.961093i	$-0.410917\pi$
$227$	8.32346	0.552447	0.276224	+	0.961093i	$0.410917\pi$
$228$	−4.46367	−0.295613
$229$	14.1032	0.931965	0.465983	−	0.884794i	$-0.345701\pi$
$229$	14.1032	0.931965	0.465983	+	0.884794i	$0.345701\pi$
$230$	−2.51086	−0.165561
$231$	−2.18160	−0.143539
$232$	60.2457	3.95532
$233$	6.84220	0.448247	0.224124	−	0.974561i	$-0.428048\pi$
$233$	6.84220	0.448247	0.224124	+	0.974561i	$0.428048\pi$
$234$	−9.70458	−0.634408
$235$	−3.49832	−0.228205
$236$	−47.1789	−3.07108
$237$	6.27815	0.407809
$238$	18.1739	1.17804
$239$	−8.53974	−0.552390	−0.276195	−	0.961102i	$-0.589074\pi$
$239$	−8.53974	−0.552390	−0.276195	+	0.961102i	$0.589074\pi$
$240$	5.91923	0.382085
$241$	6.01936	0.387741	0.193870	−	0.981027i	$-0.437896\pi$
$241$	6.01936	0.387741	0.193870	+	0.981027i	$0.437896\pi$
$242$	−15.6693	−1.00726
$243$	1.00000	0.0641500
$244$	−17.4612	−1.11784
$245$	1.00000	0.0638877
$246$	14.5329	0.926586
$247$	4.00802	0.255024
$248$	−17.5646	−1.11536
$249$	−10.6686	−0.676096
$250$	2.51086	0.158801
$251$	−10.7940	−0.681310	−0.340655	−	0.940188i	$-0.610649\pi$
$251$	−10.7940	−0.681310	−0.340655	+	0.940188i	$0.610649\pi$
$252$	4.30443	0.271153
$253$	2.18160	0.137156
$254$	−1.52192	−0.0954937
$255$	7.23813	0.453269
$256$	−31.9205	−1.99503
$257$	2.28998	0.142845	0.0714224	−	0.997446i	$-0.477246\pi$
$257$	2.28998	0.142845	0.0714224	+	0.997446i	$0.477246\pi$
$258$	−25.4304	−1.58323
$259$	2.86835	0.178231
$260$	−16.6368	−1.03177
$261$	10.4121	0.644496
$262$	−7.80543	−0.482221
$263$	21.2381	1.30960	0.654800	−	0.755802i	$-0.272753\pi$
$263$	21.2381	1.30960	0.654800	+	0.755802i	$0.272753\pi$
$264$	−12.6229	−0.776888
$265$	11.4219	0.701640
$266$	−2.60375	−0.159646
$267$	−10.6606	−0.652421
$268$	−50.9944	−3.11498
$269$	−21.8063	−1.32956	−0.664778	−	0.747041i	$-0.731474\pi$
$269$	−21.8063	−1.32956	−0.664778	+	0.747041i	$0.731474\pi$
$270$	2.51086	0.152806
$271$	−10.1633	−0.617379	−0.308689	−	0.951163i	$-0.599890\pi$
$271$	−10.1633	−0.617379	−0.308689	+	0.951163i	$0.599890\pi$
$272$	42.8441	2.59781
$273$	−3.86504	−0.233923
$274$	−45.2417	−2.73315
$275$	−2.18160	−0.131555
$276$	−4.30443	−0.259096
$277$	−27.4752	−1.65083	−0.825414	−	0.564529i	$-0.809058\pi$
$277$	−27.4752	−1.65083	−0.825414	+	0.564529i	$0.809058\pi$
$278$	−31.8833	−1.91224
$279$	−3.03567	−0.181741
$280$	5.78609	0.345785
$281$	20.9027	1.24695	0.623475	−	0.781843i	$-0.285720\pi$
$281$	20.9027	1.24695	0.623475	+	0.781843i	$0.285720\pi$
$282$	−8.78381	−0.523068
$283$	13.5840	0.807485	0.403742	−	0.914873i	$-0.367709\pi$
$283$	13.5840	0.807485	0.403742	+	0.914873i	$0.367709\pi$
$284$	−40.2889	−2.39071
$285$	−1.03699	−0.0614262
$286$	21.1715	1.25190
$287$	5.78803	0.341656
$288$	3.29018	0.193876
$289$	35.3905	2.08179
$290$	26.1435	1.53520
$291$	16.6008	0.973156
$292$	−37.6856	−2.20538
$293$	−24.0583	−1.40550	−0.702752	−	0.711435i	$-0.748046\pi$
$293$	−24.0583	−1.40550	−0.702752	+	0.711435i	$0.748046\pi$
$294$	2.51086	0.146436
$295$	−10.9605	−0.638148
$296$	16.5966	0.964656
$297$	−2.18160	−0.126589
$298$	−31.9632	−1.85158
$299$	3.86504	0.223521
$300$	4.30443	0.248516
$301$	−10.1282	−0.583778
$302$	−26.2517	−1.51062
$303$	−12.6404	−0.726171
$304$	−6.13821	−0.352050
$305$	−4.05657	−0.232278
$306$	18.1739	1.03893
$307$	−7.54716	−0.430739	−0.215370	−	0.976533i	$-0.569096\pi$
$307$	−7.54716	−0.430739	−0.215370	+	0.976533i	$0.569096\pi$
$308$	−9.39053	−0.535075
$309$	−14.4046	−0.819450
$310$	−7.62214	−0.432908
$311$	−10.6496	−0.603881	−0.301941	−	0.953327i	$-0.597634\pi$
$311$	−10.6496	−0.603881	−0.301941	+	0.953327i	$0.597634\pi$
$312$	−22.3635	−1.26608
$313$	6.63242	0.374887	0.187443	−	0.982275i	$-0.439980\pi$
$313$	6.63242	0.374887	0.187443	+	0.982275i	$0.439980\pi$
$314$	21.5859	1.21816
$315$	1.00000	0.0563436
$316$	27.0238	1.52021
$317$	0.975934	0.0548139	0.0274070	−	0.999624i	$-0.491275\pi$
$317$	0.975934	0.0548139	0.0274070	+	0.999624i	$0.491275\pi$
$318$	28.6788	1.60822
$319$	−22.7151	−1.27180
$320$	−3.57727	−0.199976
$321$	18.3850	1.02615
$322$	−2.51086	−0.139925
$323$	−7.50590	−0.417639
$324$	4.30443	0.239135
$325$	−3.86504	−0.214394
$326$	50.6950	2.80774
$327$	19.8501	1.09772
$328$	33.4901	1.84918
$329$	−3.49832	−0.192869
$330$	−5.47769	−0.301537
$331$	0.736747	0.0404953	0.0202476	−	0.999795i	$-0.493555\pi$
$331$	0.736747	0.0404953	0.0202476	+	0.999795i	$0.493555\pi$
$332$	−45.9223	−2.52031
$333$	2.86835	0.157185
$334$	−9.18281	−0.502461
$335$	−11.8470	−0.647270
$336$	5.91923	0.322921
$337$	−21.8698	−1.19132	−0.595662	−	0.803235i	$-0.703110\pi$
$337$	−21.8698	−1.19132	−0.595662	+	0.803235i	$0.703110\pi$
$338$	4.86739	0.264751
$339$	−3.89280	−0.211428
$340$	31.1560	1.68967
$341$	6.62261	0.358634
$342$	−2.60375	−0.140795
$343$	1.00000	0.0539949
$344$	−58.6025	−3.15964
$345$	−1.00000	−0.0538382
$346$	−15.2231	−0.818398
$347$	14.1018	0.757024	0.378512	−	0.925596i	$-0.376436\pi$
$347$	14.1018	0.757024	0.378512	+	0.925596i	$0.376436\pi$
$348$	44.8183	2.40251
$349$	20.4978	1.09722	0.548612	−	0.836077i	$-0.315156\pi$
$349$	20.4978	1.09722	0.548612	+	0.836077i	$0.315156\pi$
$350$	2.51086	0.134211
$351$	−3.86504	−0.206301
$352$	−7.17786	−0.382581
$353$	20.1724	1.07367	0.536835	−	0.843687i	$-0.319620\pi$
$353$	20.1724	1.07367	0.536835	+	0.843687i	$0.319620\pi$
$354$	−27.5204	−1.46269
$355$	−9.35988	−0.496771
$356$	−45.8880	−2.43206
$357$	7.23813	0.383082
$358$	20.4952	1.08321
$359$	28.0596	1.48093	0.740465	−	0.672095i	$-0.234606\pi$
$359$	28.0596	1.48093	0.740465	+	0.672095i	$0.234606\pi$
$360$	5.78609	0.304954
$361$	−17.9246	−0.943402
$362$	38.9924	2.04939
$363$	−6.24062	−0.327548
$364$	−16.6368	−0.872004
$365$	−8.75508	−0.458262
$366$	−10.1855	−0.532403
$367$	6.22286	0.324830	0.162415	−	0.986723i	$-0.448072\pi$
$367$	6.22286	0.324830	0.162415	+	0.986723i	$0.448072\pi$
$368$	−5.91923	−0.308561
$369$	5.78803	0.301313
$370$	7.20204	0.374416
$371$	11.4219	0.592994
$372$	−13.0668	−0.677482
$373$	5.45251	0.282320	0.141160	−	0.989987i	$-0.454917\pi$
$373$	5.45251	0.282320	0.141160	+	0.989987i	$0.454917\pi$
$374$	−39.6482	−2.05016
$375$	1.00000	0.0516398
$376$	−20.2416	−1.04388
$377$	−40.2434	−2.07264
$378$	2.51086	0.129145
$379$	13.2886	0.682588	0.341294	−	0.939957i	$-0.389135\pi$
$379$	13.2886	0.682588	0.341294	+	0.939957i	$0.389135\pi$
$380$	−4.46367	−0.228981
$381$	−0.606134	−0.0310532
$382$	59.6181	3.05033
$383$	−6.59374	−0.336924	−0.168462	−	0.985708i	$-0.553880\pi$
$383$	−6.59374	−0.336924	−0.168462	+	0.985708i	$0.553880\pi$
$384$	−15.5624	−0.794165
$385$	−2.18160	−0.111185
$386$	27.5048	1.39996
$387$	−10.1282	−0.514844
$388$	71.4569	3.62767
$389$	31.6730	1.60588	0.802942	−	0.596057i	$-0.203267\pi$
$389$	31.6730	1.60588	0.802942	+	0.596057i	$0.203267\pi$
$390$	−9.70458	−0.491411
$391$	−7.23813	−0.366048
$392$	5.78609	0.292242
$393$	−3.10866	−0.156811
$394$	4.10797	0.206956
$395$	6.27815	0.315888
$396$	−9.39053	−0.471892
$397$	−30.4772	−1.52961	−0.764803	−	0.644265i	$-0.777163\pi$
$397$	−30.4772	−1.52961	−0.764803	+	0.644265i	$0.777163\pi$
$398$	11.3664	0.569747
$399$	−1.03699	−0.0519146
$400$	5.91923	0.295962
$401$	30.3834	1.51728	0.758638	−	0.651513i	$-0.225865\pi$
$401$	30.3834	1.51728	0.758638	+	0.651513i	$0.225865\pi$
$402$	−29.7461	−1.48360
$403$	11.7330	0.584461
$404$	−54.4096	−2.70698
$405$	1.00000	0.0496904
$406$	26.1435	1.29748
$407$	−6.25760	−0.310178
$408$	41.8805	2.07339
$409$	24.3325	1.20317	0.601583	−	0.798810i	$-0.294537\pi$
$409$	24.3325	1.20317	0.601583	+	0.798810i	$0.294537\pi$
$410$	14.5329	0.717730
$411$	−18.0184	−0.888783
$412$	−62.0036	−3.05470
$413$	−10.9605	−0.539333
$414$	−2.51086	−0.123402
$415$	−10.6686	−0.523702
$416$	−12.7167	−0.623487
$417$	−12.6982	−0.621832
$418$	5.68034	0.277834
$419$	−26.8854	−1.31344	−0.656718	−	0.754136i	$-0.728056\pi$
$419$	−26.8854	−1.31344	−0.656718	+	0.754136i	$0.728056\pi$
$420$	4.30443	0.210034
$421$	−33.1263	−1.61448	−0.807238	−	0.590226i	$-0.799039\pi$
$421$	−33.1263	−1.61448	−0.807238	+	0.590226i	$0.799039\pi$
$422$	58.2344	2.83481
$423$	−3.49832	−0.170094
$424$	66.0881	3.20952
$425$	7.23813	0.351101
$426$	−23.5014	−1.13865
$427$	−4.05657	−0.196311
$428$	79.1369	3.82523
$429$	8.43197	0.407099
$430$	−25.4304	−1.22636
$431$	−4.40299	−0.212085	−0.106042	−	0.994362i	$-0.533818\pi$
$431$	−4.40299	−0.212085	−0.106042	+	0.994362i	$0.533818\pi$
$432$	5.91923	0.284789
$433$	21.4239	1.02957	0.514783	−	0.857320i	$-0.327872\pi$
$433$	21.4239	1.02957	0.514783	+	0.857320i	$0.327872\pi$
$434$	−7.62214	−0.365874
$435$	10.4121	0.499224
$436$	85.4435	4.09200
$437$	1.03699	0.0496062
$438$	−21.9828	−1.05038
$439$	−18.3977	−0.878075	−0.439037	−	0.898469i	$-0.644680\pi$
$439$	−18.3977	−0.878075	−0.439037	+	0.898469i	$0.644680\pi$
$440$	−12.6229	−0.601775
$441$	1.00000	0.0476190
$442$	−70.2430	−3.34112
$443$	−28.8477	−1.37060	−0.685299	−	0.728262i	$-0.740328\pi$
$443$	−28.8477	−1.37060	−0.685299	+	0.728262i	$0.740328\pi$
$444$	12.3466	0.585945
$445$	−10.6606	−0.505363
$446$	21.7518	1.02998
$447$	−12.7300	−0.602107
$448$	−3.57727	−0.169010
$449$	−5.07335	−0.239426	−0.119713	−	0.992809i	$-0.538197\pi$
$449$	−5.07335	−0.239426	−0.119713	+	0.992809i	$0.538197\pi$
$450$	2.51086	0.118363
$451$	−12.6272	−0.594590
$452$	−16.7563	−0.788148
$453$	−10.4553	−0.491231
$454$	20.8990	0.980841
$455$	−3.86504	−0.181196
$456$	−6.00015	−0.280983
$457$	−24.3409	−1.13862	−0.569310	−	0.822123i	$-0.692790\pi$
$457$	−24.3409	−1.13862	−0.569310	+	0.822123i	$0.692790\pi$
$458$	35.4112	1.65466
$459$	7.23813	0.337847
$460$	−4.30443	−0.200695
$461$	−14.8050	−0.689537	−0.344769	−	0.938688i	$-0.612043\pi$
$461$	−14.8050	−0.689537	−0.344769	+	0.938688i	$0.612043\pi$
$462$	−5.47769	−0.254845
$463$	37.1272	1.72545	0.862724	−	0.505676i	$-0.168757\pi$
$463$	37.1272	1.72545	0.862724	+	0.505676i	$0.168757\pi$
$464$	61.6319	2.86119
$465$	−3.03567	−0.140776
$466$	17.1798	0.795839
$467$	−6.86921	−0.317869	−0.158935	−	0.987289i	$-0.550806\pi$
$467$	−6.86921	−0.317869	−0.158935	+	0.987289i	$0.550806\pi$
$468$	−16.6368	−0.769035
$469$	−11.8470	−0.547043
$470$	−8.78381	−0.405167
$471$	8.59702	0.396130
$472$	−63.4188	−2.91909
$473$	22.0956	1.01596
$474$	15.7636	0.724044
$475$	−1.03699	−0.0475806
$476$	31.1560	1.42803
$477$	11.4219	0.522972
$478$	−21.4421	−0.980739
$479$	7.49834	0.342608	0.171304	−	0.985218i	$-0.445202\pi$
$479$	7.49834	0.342608	0.171304	+	0.985218i	$0.445202\pi$
$480$	3.29018	0.150176
$481$	−11.0863	−0.505492
$482$	15.1138	0.688414
$483$	−1.00000	−0.0455016
$484$	−26.8623	−1.22101
$485$	16.6008	0.753803
$486$	2.51086	0.113895
$487$	−15.8310	−0.717373	−0.358687	−	0.933458i	$-0.616775\pi$
$487$	−15.8310	−0.717373	−0.358687	+	0.933458i	$0.616775\pi$
$488$	−23.4717	−1.06251
$489$	20.1903	0.913036
$490$	2.51086	0.113429
$491$	22.3864	1.01028	0.505142	−	0.863036i	$-0.331440\pi$
$491$	22.3864	1.01028	0.505142	+	0.863036i	$0.331440\pi$
$492$	24.9141	1.12322
$493$	75.3645	3.39424
$494$	10.0636	0.452782
$495$	−2.18160	−0.0980556
$496$	−17.9688	−0.806823
$497$	−9.35988	−0.419848
$498$	−26.7874	−1.20037
$499$	−12.7284	−0.569802	−0.284901	−	0.958557i	$-0.591961\pi$
$499$	−12.7284	−0.569802	−0.284901	+	0.958557i	$0.591961\pi$
$500$	4.30443	0.192500
$501$	−3.65724	−0.163393
$502$	−27.1022	−1.20963
$503$	15.7208	0.700957	0.350478	−	0.936571i	$-0.386019\pi$
$503$	15.7208	0.700957	0.350478	+	0.936571i	$0.386019\pi$
$504$	5.78609	0.257733
$505$	−12.6404	−0.562490
$506$	5.47769	0.243513
$507$	1.93853	0.0860932
$508$	−2.60906	−0.115758
$509$	−28.8217	−1.27750	−0.638749	−	0.769415i	$-0.720548\pi$
$509$	−28.8217	−1.27750	−0.638749	+	0.769415i	$0.720548\pi$
$510$	18.1739	0.804755
$511$	−8.75508	−0.387302
$512$	−49.0231	−2.16654
$513$	−1.03699	−0.0457844
$514$	5.74982	0.253613
$515$	−14.4046	−0.634743
$516$	−43.5959	−1.91920
$517$	7.63194	0.335652
$518$	7.20204	0.316440
$519$	−6.06289	−0.266131
$520$	−22.3635	−0.980704
$521$	1.55854	0.0682811	0.0341405	−	0.999417i	$-0.489131\pi$
$521$	1.55854	0.0682811	0.0341405	+	0.999417i	$0.489131\pi$
$522$	26.1435	1.14427
$523$	20.1499	0.881094	0.440547	−	0.897730i	$-0.354785\pi$
$523$	20.1499	0.881094	0.440547	+	0.897730i	$0.354785\pi$
$524$	−13.3810	−0.584552
$525$	1.00000	0.0436436
$526$	53.3260	2.32513
$527$	−21.9725	−0.957139
$528$	−12.9134	−0.561983
$529$	1.00000	0.0434783
$530$	28.6788	1.24573
$531$	−10.9605	−0.475647
$532$	−4.46367	−0.193524
$533$	−22.3710	−0.968993
$534$	−26.7674	−1.15834
$535$	18.3850	0.794853
$536$	−68.5477	−2.96081
$537$	8.16263	0.352244
$538$	−54.7527	−2.36056
$539$	−2.18160	−0.0939681
$540$	4.30443	0.185233
$541$	−3.94541	−0.169626	−0.0848132	−	0.996397i	$-0.527029\pi$
$541$	−3.94541	−0.169626	−0.0848132	+	0.996397i	$0.527029\pi$
$542$	−25.5187	−1.09612
$543$	15.5295	0.666434
$544$	23.8147	1.02105
$545$	19.8501	0.850287
$546$	−9.70458	−0.415318
$547$	38.3609	1.64019	0.820096	−	0.572226i	$-0.193920\pi$
$547$	38.3609	1.64019	0.820096	+	0.572226i	$0.193920\pi$
$548$	−77.5589	−3.31315
$549$	−4.05657	−0.173130
$550$	−5.47769	−0.233570
$551$	−10.7973	−0.459982
$552$	−5.78609	−0.246273
$553$	6.27815	0.266974
$554$	−68.9865	−2.93096
$555$	2.86835	0.121755
$556$	−54.6583	−2.31803
$557$	27.2431	1.15433	0.577164	−	0.816628i	$-0.304159\pi$
$557$	27.2431	1.15433	0.577164	+	0.816628i	$0.304159\pi$
$558$	−7.62214	−0.322671
$559$	39.1458	1.65569
$560$	5.91923	0.250133
$561$	−15.7907	−0.666684
$562$	52.4838	2.21389
$563$	11.5069	0.484959	0.242479	−	0.970157i	$-0.422039\pi$
$563$	11.5069	0.484959	0.242479	+	0.970157i	$0.422039\pi$
$564$	−15.0583	−0.634068
$565$	−3.89280	−0.163771
$566$	34.1075	1.43365
$567$	1.00000	0.0419961
$568$	−54.1572	−2.27238
$569$	15.9564	0.668929	0.334464	−	0.942408i	$-0.391445\pi$
$569$	15.9564	0.668929	0.334464	+	0.942408i	$0.391445\pi$
$570$	−2.60375	−0.109059
$571$	17.7204	0.741576	0.370788	−	0.928717i	$-0.379088\pi$
$571$	17.7204	0.741576	0.370788	+	0.928717i	$0.379088\pi$
$572$	36.2948	1.51756
$573$	23.7441	0.991923
$574$	14.5329	0.606593
$575$	−1.00000	−0.0417029
$576$	−3.57727	−0.149053
$577$	−29.4629	−1.22656	−0.613279	−	0.789866i	$-0.710150\pi$
$577$	−29.4629	−1.22656	−0.613279	+	0.789866i	$0.710150\pi$
$578$	88.8606	3.69611
$579$	10.9543	0.455246
$580$	44.8183	1.86098
$581$	−10.6686	−0.442609
$582$	41.6823	1.72779
$583$	−24.9180	−1.03200
$584$	−50.6577	−2.09623
$585$	−3.86504	−0.159800
$586$	−60.4072	−2.49540
$587$	−10.1910	−0.420629	−0.210315	−	0.977634i	$-0.567449\pi$
$587$	−10.1910	−0.420629	−0.210315	+	0.977634i	$0.567449\pi$
$588$	4.30443	0.177512
$589$	3.14797	0.129710
$590$	−27.5204	−1.13300
$591$	1.63608	0.0672993
$592$	16.9785	0.697810
$593$	43.2504	1.77608	0.888040	−	0.459767i	$-0.152067\pi$
$593$	43.2504	1.77608	0.888040	+	0.459767i	$0.152067\pi$
$594$	−5.47769	−0.224753
$595$	7.23813	0.296734
$596$	−54.7952	−2.24450
$597$	4.52690	0.185274
$598$	9.70458	0.396850
$599$	−21.3690	−0.873112	−0.436556	−	0.899677i	$-0.643802\pi$
$599$	−21.3690	−0.873112	−0.436556	+	0.899677i	$0.643802\pi$
$600$	5.78609	0.236216
$601$	30.5340	1.24551	0.622755	−	0.782417i	$-0.286013\pi$
$601$	30.5340	1.24551	0.622755	+	0.782417i	$0.286013\pi$
$602$	−25.4304	−1.03647
$603$	−11.8470	−0.482446
$604$	−45.0039	−1.83118
$605$	−6.24062	−0.253717
$606$	−31.7382	−1.28928
$607$	10.7987	0.438305	0.219152	−	0.975691i	$-0.429671\pi$
$607$	10.7987	0.438305	0.219152	+	0.975691i	$0.429671\pi$
$608$	−3.41190	−0.138371
$609$	10.4121	0.421922
$610$	−10.1855	−0.412398
$611$	13.5212	0.547008
$612$	31.1560	1.25941
$613$	−10.0540	−0.406078	−0.203039	−	0.979171i	$-0.565082\pi$
$613$	−10.0540	−0.406078	−0.203039	+	0.979171i	$0.565082\pi$
$614$	−18.9499	−0.764754
$615$	5.78803	0.233396
$616$	−12.6229	−0.508593
$617$	−34.6311	−1.39420	−0.697099	−	0.716975i	$-0.745526\pi$
$617$	−34.6311	−1.39420	−0.697099	+	0.716975i	$0.745526\pi$
$618$	−36.1680	−1.45489
$619$	−19.9992	−0.803837	−0.401919	−	0.915675i	$-0.631657\pi$
$619$	−19.9992	−0.803837	−0.401919	+	0.915675i	$0.631657\pi$
$620$	−13.0668	−0.524775
$621$	−1.00000	−0.0401286
$622$	−26.7396	−1.07216
$623$	−10.6606	−0.427110
$624$	−22.8781	−0.915856
$625$	1.00000	0.0400000
$626$	16.6531	0.665591
$627$	2.26231	0.0903478
$628$	37.0053	1.47667
$629$	20.7615	0.827816
$630$	2.51086	0.100035
$631$	−18.9931	−0.756105	−0.378053	−	0.925784i	$-0.623406\pi$
$631$	−18.9931	−0.756105	−0.378053	+	0.925784i	$0.623406\pi$
$632$	36.3259	1.44497
$633$	23.1930	0.921839
$634$	2.45043	0.0973192
$635$	−0.606134	−0.0240537
$636$	49.1646	1.94950
$637$	−3.86504	−0.153138
$638$	−57.0346	−2.25802
$639$	−9.35988	−0.370271
$640$	−15.5624	−0.615158
$641$	32.1003	1.26788	0.633942	−	0.773380i	$-0.281436\pi$
$641$	32.1003	1.26788	0.633942	+	0.773380i	$0.281436\pi$
$642$	46.1622	1.82188
$643$	−11.2097	−0.442069	−0.221034	−	0.975266i	$-0.570943\pi$
$643$	−11.2097	−0.442069	−0.221034	+	0.975266i	$0.570943\pi$
$644$	−4.30443	−0.169618
$645$	−10.1282	−0.398796
$646$	−18.8463	−0.741496
$647$	32.3860	1.27322	0.636612	−	0.771184i	$-0.280335\pi$
$647$	32.3860	1.27322	0.636612	+	0.771184i	$0.280335\pi$
$648$	5.78609	0.227299
$649$	23.9115	0.938610
$650$	−9.70458	−0.380645
$651$	−3.03567	−0.118977
$652$	86.9076	3.40356
$653$	−6.19380	−0.242382	−0.121191	−	0.992629i	$-0.538671\pi$
$653$	−6.19380	−0.242382	−0.121191	+	0.992629i	$0.538671\pi$
$654$	49.8410	1.94894
$655$	−3.10866	−0.121466
$656$	34.2607	1.33765
$657$	−8.75508	−0.341568
$658$	−8.78381	−0.342428
$659$	−36.1823	−1.40946	−0.704731	−	0.709475i	$-0.748932\pi$
$659$	−36.1823	−1.40946	−0.704731	+	0.709475i	$0.748932\pi$
$660$	−9.39053	−0.365526
$661$	47.3301	1.84093	0.920463	−	0.390829i	$-0.127812\pi$
$661$	47.3301	1.84093	0.920463	+	0.390829i	$0.127812\pi$
$662$	1.84987	0.0718972
$663$	−27.9756	−1.08648
$664$	−61.7296	−2.39557
$665$	−1.03699	−0.0402129
$666$	7.20204	0.279073
$667$	−10.4121	−0.403160
$668$	−15.7423	−0.609088
$669$	8.66306	0.334933
$670$	−29.7461	−1.14919
$671$	8.84980	0.341643
$672$	3.29018	0.126921
$673$	26.8770	1.03603	0.518016	−	0.855371i	$-0.326671\pi$
$673$	26.8770	1.03603	0.518016	+	0.855371i	$0.326671\pi$
$674$	−54.9121	−2.11513
$675$	1.00000	0.0384900
$676$	8.34427	0.320933
$677$	−24.4776	−0.940751	−0.470375	−	0.882466i	$-0.655881\pi$
$677$	−24.4776	−0.940751	−0.470375	+	0.882466i	$0.655881\pi$
$678$	−9.77427	−0.375379
$679$	16.6008	0.637080
$680$	41.8805	1.60604
$681$	8.32346	0.318956
$682$	16.6284	0.636736
$683$	27.7600	1.06221	0.531103	−	0.847307i	$-0.321778\pi$
$683$	27.7600	1.06221	0.531103	+	0.847307i	$0.321778\pi$
$684$	−4.46367	−0.170672
$685$	−18.0184	−0.688448
$686$	2.51086	0.0958651
$687$	14.1032	0.538070
$688$	−59.9510	−2.28561
$689$	−44.1460	−1.68183
$690$	−2.51086	−0.0955869
$691$	13.4938	0.513328	0.256664	−	0.966501i	$-0.417377\pi$
$691$	13.4938	0.513328	0.256664	+	0.966501i	$0.417377\pi$
$692$	−26.0973	−0.992069
$693$	−2.18160	−0.0828721
$694$	35.4077	1.34406
$695$	−12.6982	−0.481669
$696$	60.2457	2.28361
$697$	41.8945	1.58687
$698$	51.4672	1.94806
$699$	6.84220	0.258796
$700$	4.30443	0.162692
$701$	−44.7162	−1.68891	−0.844453	−	0.535630i	$-0.820074\pi$
$701$	−44.7162	−1.68891	−0.844453	+	0.535630i	$0.820074\pi$
$702$	−9.70458	−0.366276
$703$	−2.97447	−0.112184
$704$	7.80418	0.294131
$705$	−3.49832	−0.131754
$706$	50.6501	1.90624
$707$	−12.6404	−0.475390
$708$	−47.1789	−1.77309
$709$	1.65346	0.0620969	0.0310485	−	0.999518i	$-0.490115\pi$
$709$	1.65346	0.0620969	0.0310485	+	0.999518i	$0.490115\pi$
$710$	−23.5014	−0.881991
$711$	6.27815	0.235449
$712$	−61.6835	−2.31169
$713$	3.03567	0.113687
$714$	18.1739	0.680142
$715$	8.43197	0.315338
$716$	35.1355	1.31307
$717$	−8.53974	−0.318922
$718$	70.4538	2.62931
$719$	12.4903	0.465808	0.232904	−	0.972500i	$-0.425177\pi$
$719$	12.4903	0.465808	0.232904	+	0.972500i	$0.425177\pi$
$720$	5.91923	0.220597
$721$	−14.4046	−0.536456
$722$	−45.0063	−1.67496
$723$	6.01936	0.223862
$724$	66.8455	2.48429
$725$	10.4121	0.386698
$726$	−15.6693	−0.581544
$727$	35.2642	1.30788	0.653938	−	0.756548i	$-0.273116\pi$
$727$	35.2642	1.30788	0.653938	+	0.756548i	$0.273116\pi$
$728$	−22.3635	−0.828846
$729$	1.00000	0.0370370
$730$	−21.9828	−0.813620
$731$	−73.3089	−2.71143
$732$	−17.4612	−0.645384
$733$	−38.0198	−1.40429	−0.702147	−	0.712032i	$-0.747775\pi$
$733$	−38.0198	−1.40429	−0.702147	+	0.712032i	$0.747775\pi$
$734$	15.6247	0.576719
$735$	1.00000	0.0368856
$736$	−3.29018	−0.121278
$737$	25.8454	0.952026
$738$	14.5329	0.534965
$739$	28.5590	1.05056	0.525281	−	0.850929i	$-0.323960\pi$
$739$	28.5590	1.05056	0.525281	+	0.850929i	$0.323960\pi$
$740$	12.3466	0.453871
$741$	4.00802	0.147238
$742$	28.6788	1.05283
$743$	4.98847	0.183009	0.0915045	−	0.995805i	$-0.470832\pi$
$743$	4.98847	0.183009	0.0915045	+	0.995805i	$0.470832\pi$
$744$	−17.5646	−0.643951
$745$	−12.7300	−0.466390
$746$	13.6905	0.501244
$747$	−10.6686	−0.390344
$748$	−67.9699	−2.48522
$749$	18.3850	0.671773
$750$	2.51086	0.0916837
$751$	−28.1981	−1.02896	−0.514482	−	0.857501i	$-0.672016\pi$
$751$	−28.1981	−1.02896	−0.514482	+	0.857501i	$0.672016\pi$
$752$	−20.7074	−0.755121
$753$	−10.7940	−0.393355
$754$	−101.046	−3.67986
$755$	−10.4553	−0.380506
$756$	4.30443	0.156550
$757$	7.00546	0.254618	0.127309	−	0.991863i	$-0.459366\pi$
$757$	7.00546	0.254618	0.127309	+	0.991863i	$0.459366\pi$
$758$	33.3658	1.21190
$759$	2.18160	0.0791870
$760$	−6.00015	−0.217648
$761$	−5.17357	−0.187542	−0.0937709	−	0.995594i	$-0.529892\pi$
$761$	−5.17357	−0.187542	−0.0937709	+	0.995594i	$0.529892\pi$
$762$	−1.52192	−0.0551333
$763$	19.8501	0.718623
$764$	102.205	3.69763
$765$	7.23813	0.261695
$766$	−16.5560	−0.598192
$767$	42.3630	1.52964
$768$	−31.9205	−1.15183
$769$	32.8480	1.18453	0.592264	−	0.805744i	$-0.298234\pi$
$769$	32.8480	1.18453	0.592264	+	0.805744i	$0.298234\pi$
$770$	−5.47769	−0.197402
$771$	2.28998	0.0824715
$772$	47.1520	1.69704
$773$	−18.0259	−0.648348	−0.324174	−	0.945997i	$-0.605086\pi$
$773$	−18.0259	−0.648348	−0.324174	+	0.945997i	$0.605086\pi$
$774$	−25.4304	−0.914078
$775$	−3.03567	−0.109044
$776$	96.0538	3.44813
$777$	2.86835	0.102902
$778$	79.5265	2.85116
$779$	−6.00215	−0.215049
$780$	−16.6368	−0.595692
$781$	20.4195	0.730668
$782$	−18.1739	−0.649899
$783$	10.4121	0.372100
$784$	5.91923	0.211401
$785$	8.59702	0.306841
$786$	−7.80543	−0.278410
$787$	24.9915	0.890852	0.445426	−	0.895319i	$-0.353052\pi$
$787$	24.9915	0.890852	0.445426	+	0.895319i	$0.353052\pi$
$788$	7.04238	0.250874
$789$	21.2381	0.756098
$790$	15.7636	0.560842
$791$	−3.89280	−0.138412
$792$	−12.6229	−0.448537
$793$	15.6788	0.556770
$794$	−76.5239	−2.71573
$795$	11.4219	0.405092
$796$	19.4857	0.690652
$797$	−8.70000	−0.308170	−0.154085	−	0.988058i	$-0.549243\pi$
$797$	−8.70000	−0.308170	−0.154085	+	0.988058i	$0.549243\pi$
$798$	−2.60375	−0.0921717
$799$	−25.3213	−0.895804
$800$	3.29018	0.116325
$801$	−10.6606	−0.376675
$802$	76.2886	2.69384
$803$	19.1001	0.674027
$804$	−50.9944	−1.79844
$805$	−1.00000	−0.0352454
$806$	29.4599	1.03768
$807$	−21.8063	−0.767620
$808$	−73.1384	−2.57300
$809$	−8.31047	−0.292181	−0.146090	−	0.989271i	$-0.546669\pi$
$809$	−8.31047	−0.292181	−0.146090	+	0.989271i	$0.546669\pi$
$810$	2.51086	0.0882227
$811$	−20.4860	−0.719360	−0.359680	−	0.933076i	$-0.617114\pi$
$811$	−20.4860	−0.719360	−0.359680	+	0.933076i	$0.617114\pi$
$812$	44.8183	1.57281
$813$	−10.1633	−0.356444
$814$	−15.7120	−0.550704
$815$	20.1903	0.707235
$816$	42.8441	1.49985
$817$	10.5028	0.367448
$818$	61.0956	2.13616
$819$	−3.86504	−0.135055
$820$	24.9141	0.870039
$821$	−41.4487	−1.44657	−0.723285	−	0.690549i	$-0.757369\pi$
$821$	−41.4487	−1.44657	−0.723285	+	0.690549i	$0.757369\pi$
$822$	−45.2417	−1.57799
$823$	3.74123	0.130411	0.0652055	−	0.997872i	$-0.479230\pi$
$823$	3.74123	0.130411	0.0652055	+	0.997872i	$0.479230\pi$
$824$	−83.3465	−2.90351
$825$	−2.18160	−0.0759535
$826$	−27.5204	−0.957558
$827$	−26.4726	−0.920542	−0.460271	−	0.887778i	$-0.652248\pi$
$827$	−26.4726	−0.920542	−0.460271	+	0.887778i	$0.652248\pi$
$828$	−4.30443	−0.149589
$829$	21.6909	0.753357	0.376678	−	0.926344i	$-0.377066\pi$
$829$	21.6909	0.753357	0.376678	+	0.926344i	$0.377066\pi$
$830$	−26.7874	−0.929804
$831$	−27.4752	−0.953105
$832$	13.8263	0.479341
$833$	7.23813	0.250786
$834$	−31.8833	−1.10403
$835$	−3.65724	−0.126564
$836$	9.73793	0.336793
$837$	−3.03567	−0.104928
$838$	−67.5055	−2.33194
$839$	34.4618	1.18975	0.594877	−	0.803817i	$-0.297201\pi$
$839$	34.4618	1.18975	0.594877	+	0.803817i	$0.297201\pi$
$840$	5.78609	0.199639
$841$	79.4129	2.73837
$842$	−83.1755	−2.86642
$843$	20.9027	0.719927
$844$	99.8325	3.43638
$845$	1.93853	0.0666875
$846$	−8.78381	−0.301993
$847$	−6.24062	−0.214430
$848$	67.6087	2.32169
$849$	13.5840	0.466201
$850$	18.1739	0.623361
$851$	−2.86835	−0.0983259
$852$	−40.2889	−1.38028
$853$	−34.0265	−1.16504	−0.582522	−	0.812815i	$-0.697934\pi$
$853$	−34.0265	−1.16504	−0.582522	+	0.812815i	$0.697934\pi$
$854$	−10.1855	−0.348540
$855$	−1.03699	−0.0354645
$856$	106.377	3.63590
$857$	−49.0194	−1.67447	−0.837235	−	0.546843i	$-0.815830\pi$
$857$	−49.0194	−1.67447	−0.837235	+	0.546843i	$0.815830\pi$
$858$	21.1715	0.722783
$859$	38.3359	1.30800	0.654002	−	0.756493i	$-0.273089\pi$
$859$	38.3359	1.30800	0.654002	+	0.756493i	$0.273089\pi$
$860$	−43.5959	−1.48661
$861$	5.78803	0.197255
$862$	−11.0553	−0.376545
$863$	−46.2699	−1.57504	−0.787522	−	0.616286i	$-0.788636\pi$
$863$	−46.2699	−1.57504	−0.787522	+	0.616286i	$0.788636\pi$
$864$	3.29018	0.111934
$865$	−6.06289	−0.206145
$866$	53.7925	1.82794
$867$	35.3905	1.20192
$868$	−13.0668	−0.443516
$869$	−13.6964	−0.464619
$870$	26.1435	0.886347
$871$	45.7890	1.55150
$872$	114.855	3.88947
$873$	16.6008	0.561852
$874$	2.60375	0.0880731
$875$	1.00000	0.0338062
$876$	−37.6856	−1.27328
$877$	−10.7129	−0.361750	−0.180875	−	0.983506i	$-0.557893\pi$
$877$	−10.7129	−0.361750	−0.180875	+	0.983506i	$0.557893\pi$
$878$	−46.1941	−1.55898
$879$	−24.0583	−0.811468
$880$	−12.9134	−0.435310
$881$	31.5594	1.06326	0.531632	−	0.846975i	$-0.321579\pi$
$881$	31.5594	1.06326	0.531632	+	0.846975i	$0.321579\pi$
$882$	2.51086	0.0845451
$883$	8.90907	0.299814	0.149907	−	0.988700i	$-0.452103\pi$
$883$	8.90907	0.299814	0.149907	+	0.988700i	$0.452103\pi$
$884$	−120.419	−4.05013
$885$	−10.9605	−0.368435
$886$	−72.4327	−2.43342
$887$	−11.7729	−0.395295	−0.197648	−	0.980273i	$-0.563330\pi$
$887$	−11.7729	−0.395295	−0.197648	+	0.980273i	$0.563330\pi$
$888$	16.5966	0.556945
$889$	−0.606134	−0.0203291
$890$	−26.7674	−0.897245
$891$	−2.18160	−0.0730863
$892$	37.2895	1.24855
$893$	3.62774	0.121398
$894$	−31.9632	−1.06901
$895$	8.16263	0.272847
$896$	−15.5624	−0.519903
$897$	3.86504	0.129050
$898$	−12.7385	−0.425088
$899$	−31.6078	−1.05418
$900$	4.30443	0.143481
$901$	82.6730	2.75424
$902$	−31.7050	−1.05566
$903$	−10.1282	−0.337044
$904$	−22.5241	−0.749140
$905$	15.5295	0.516218
$906$	−26.2517	−0.872155
$907$	−18.2995	−0.607625	−0.303813	−	0.952732i	$-0.598260\pi$
$907$	−18.2995	−0.607625	−0.303813	+	0.952732i	$0.598260\pi$
$908$	35.8277	1.18898
$909$	−12.6404	−0.419255
$910$	−9.70458	−0.321704
$911$	18.3174	0.606882	0.303441	−	0.952850i	$-0.401864\pi$
$911$	18.3174	0.606882	0.303441	+	0.952850i	$0.401864\pi$
$912$	−6.13821	−0.203256
$913$	23.2746	0.770278
$914$	−61.1167	−2.02156
$915$	−4.05657	−0.134106
$916$	60.7062	2.00579
$917$	−3.10866	−0.102657
$918$	18.1739	0.599829
$919$	44.6232	1.47198	0.735991	−	0.676991i	$-0.236716\pi$
$919$	44.6232	1.47198	0.735991	+	0.676991i	$0.236716\pi$
$920$	−5.78609	−0.190762
$921$	−7.54716	−0.248687
$922$	−37.1733	−1.22424
$923$	36.1763	1.19076
$924$	−9.39053	−0.308926
$925$	2.86835	0.0943109
$926$	93.2213	3.06344
$927$	−14.4046	−0.473110
$928$	34.2579	1.12457
$929$	−23.5106	−0.771358	−0.385679	−	0.922633i	$-0.626033\pi$
$929$	−23.5106	−0.771358	−0.385679	+	0.922633i	$0.626033\pi$
$930$	−7.62214	−0.249940
$931$	−1.03699	−0.0339861
$932$	29.4517	0.964724
$933$	−10.6496	−0.348651
$934$	−17.2476	−0.564360
$935$	−15.7907	−0.516411
$936$	−22.3635	−0.730973
$937$	56.0103	1.82978	0.914889	−	0.403706i	$-0.132278\pi$
$937$	56.0103	1.82978	0.914889	+	0.403706i	$0.132278\pi$
$938$	−29.7461	−0.971245
$939$	6.63242	0.216441
$940$	−15.0583	−0.491147
$941$	−1.96370	−0.0640148	−0.0320074	−	0.999488i	$-0.510190\pi$
$941$	−1.96370	−0.0640148	−0.0320074	+	0.999488i	$0.510190\pi$
$942$	21.5859	0.703308
$943$	−5.78803	−0.188484
$944$	−64.8780	−2.11160
$945$	1.00000	0.0325300
$946$	55.4790	1.80378
$947$	−2.88445	−0.0937322	−0.0468661	−	0.998901i	$-0.514923\pi$
$947$	−2.88445	−0.0937322	−0.0468661	+	0.998901i	$0.514923\pi$
$948$	27.0238	0.877693
$949$	33.8387	1.09845
$950$	−2.60375	−0.0844768
$951$	0.975934	0.0316468
$952$	41.8805	1.35735
$953$	−29.3311	−0.950127	−0.475063	−	0.879952i	$-0.657575\pi$
$953$	−29.3311	−0.950127	−0.475063	+	0.879952i	$0.657575\pi$
$954$	28.6788	0.928509
$955$	23.7441	0.768340
$956$	−36.7587	−1.18886
$957$	−22.7151	−0.734276
$958$	18.8273	0.608283
$959$	−18.0184	−0.581845
$960$	−3.57727	−0.115456
$961$	−21.7847	−0.702733
$962$	−27.8362	−0.897474
$963$	18.3850	0.592448
$964$	25.9099	0.834501
$965$	10.9543	0.352632
$966$	−2.51086	−0.0807856
$967$	25.1425	0.808529	0.404264	−	0.914642i	$-0.367528\pi$
$967$	25.1425	0.808529	0.404264	+	0.914642i	$0.367528\pi$
$968$	−36.1088	−1.16058
$969$	−7.50590	−0.241124
$970$	41.6823	1.33834
$971$	−18.8829	−0.605981	−0.302991	−	0.952994i	$-0.597985\pi$
$971$	−18.8829	−0.605981	−0.302991	+	0.952994i	$0.597985\pi$
$972$	4.30443	0.138065
$973$	−12.6982	−0.407084
$974$	−39.7496	−1.27366
$975$	−3.86504	−0.123780
$976$	−24.0118	−0.768598
$977$	−43.8525	−1.40297	−0.701483	−	0.712686i	$-0.747478\pi$
$977$	−43.8525	−1.40297	−0.701483	+	0.712686i	$0.747478\pi$
$978$	50.6950	1.62105
$979$	23.2573	0.743305
$980$	4.30443	0.137500
$981$	19.8501	0.633766
$982$	56.2091	1.79371
$983$	22.3638	0.713295	0.356647	−	0.934239i	$-0.383920\pi$
$983$	22.3638	0.713295	0.356647	+	0.934239i	$0.383920\pi$
$984$	33.4901	1.06762
$985$	1.63608	0.0521298
$986$	189.230	6.02630
$987$	−3.49832	−0.111353
$988$	17.2522	0.548867
$989$	10.1282	0.322057
$990$	−5.47769	−0.174093
$991$	−11.1883	−0.355408	−0.177704	−	0.984084i	$-0.556867\pi$
$991$	−11.1883	−0.355408	−0.177704	+	0.984084i	$0.556867\pi$
$992$	−9.98789	−0.317116
$993$	0.736747	0.0233800
$994$	−23.5014	−0.745418
$995$	4.52690	0.143512
$996$	−45.9223	−1.45510
$997$	−17.1628	−0.543553	−0.271776	−	0.962360i	$-0.587611\pi$
$997$	−17.1628	−0.543553	−0.271776	+	0.962360i	$0.587611\pi$
$998$	−31.9593	−1.01165
$999$	2.86835	0.0907507

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2415.2.a.w.1.9	✓	10
3.2	odd	2		7245.2.a.bv.1.2		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2415.2.a.w.1.9	✓	10	1.1	even	1	trivial
7245.2.a.bv.1.2		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)

\(f(q)\)	\(=\)	\(q+2.51086 q^{2} +1.00000 q^{3} +4.30443 q^{4} +1.00000 q^{5} +2.51086 q^{6} +1.00000 q^{7} +5.78609 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.51086 q^{2} +1.00000 q^{3} +4.30443 q^{4} +1.00000 q^{5} +2.51086 q^{6} +1.00000 q^{7} +5.78609 q^{8} +1.00000 q^{9} +2.51086 q^{10} -2.18160 q^{11} +4.30443 q^{12} -3.86504 q^{13} +2.51086 q^{14} +1.00000 q^{15} +5.91923 q^{16} +7.23813 q^{17} +2.51086 q^{18} -1.03699 q^{19} +4.30443 q^{20} +1.00000 q^{21} -5.47769 q^{22} -1.00000 q^{23} +5.78609 q^{24} +1.00000 q^{25} -9.70458 q^{26} +1.00000 q^{27} +4.30443 q^{28} +10.4121 q^{29} +2.51086 q^{30} -3.03567 q^{31} +3.29018 q^{32} -2.18160 q^{33} +18.1739 q^{34} +1.00000 q^{35} +4.30443 q^{36} +2.86835 q^{37} -2.60375 q^{38} -3.86504 q^{39} +5.78609 q^{40} +5.78803 q^{41} +2.51086 q^{42} -10.1282 q^{43} -9.39053 q^{44} +1.00000 q^{45} -2.51086 q^{46} -3.49832 q^{47} +5.91923 q^{48} +1.00000 q^{49} +2.51086 q^{50} +7.23813 q^{51} -16.6368 q^{52} +11.4219 q^{53} +2.51086 q^{54} -2.18160 q^{55} +5.78609 q^{56} -1.03699 q^{57} +26.1435 q^{58} -10.9605 q^{59} +4.30443 q^{60} -4.05657 q^{61} -7.62214 q^{62} +1.00000 q^{63} -3.57727 q^{64} -3.86504 q^{65} -5.47769 q^{66} -11.8470 q^{67} +31.1560 q^{68} -1.00000 q^{69} +2.51086 q^{70} -9.35988 q^{71} +5.78609 q^{72} -8.75508 q^{73} +7.20204 q^{74} +1.00000 q^{75} -4.46367 q^{76} -2.18160 q^{77} -9.70458 q^{78} +6.27815 q^{79} +5.91923 q^{80} +1.00000 q^{81} +14.5329 q^{82} -10.6686 q^{83} +4.30443 q^{84} +7.23813 q^{85} -25.4304 q^{86} +10.4121 q^{87} -12.6229 q^{88} -10.6606 q^{89} +2.51086 q^{90} -3.86504 q^{91} -4.30443 q^{92} -3.03567 q^{93} -8.78381 q^{94} -1.03699 q^{95} +3.29018 q^{96} +16.6008 q^{97} +2.51086 q^{98} -2.18160 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 2 q^{2} + 10 q^{3} + 16 q^{4} + 10 q^{5} + 2 q^{6} + 10 q^{7} + 6 q^{8} + 10 q^{9}+O(q^{10}) \) 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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