LMFDB - Embedded newform 2415.2.a.w.1.6

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			1.6
Root			$0.509075$ 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)

$f(q)$	$=$	$q+0.509075 q^{2} +1.00000 q^{3} -1.74084 q^{4} +1.00000 q^{5} +0.509075 q^{6} +1.00000 q^{7} -1.90437 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.509075 q^{2} +1.00000 q^{3} -1.74084 q^{4} +1.00000 q^{5} +0.509075 q^{6} +1.00000 q^{7} -1.90437 q^{8} +1.00000 q^{9} +0.509075 q^{10} -0.761333 q^{11} -1.74084 q^{12} +0.924242 q^{13} +0.509075 q^{14} +1.00000 q^{15} +2.51222 q^{16} -2.41409 q^{17} +0.509075 q^{18} +5.39028 q^{19} -1.74084 q^{20} +1.00000 q^{21} -0.387576 q^{22} -1.00000 q^{23} -1.90437 q^{24} +1.00000 q^{25} +0.470509 q^{26} +1.00000 q^{27} -1.74084 q^{28} -1.88380 q^{29} +0.509075 q^{30} +7.21511 q^{31} +5.08765 q^{32} -0.761333 q^{33} -1.22895 q^{34} +1.00000 q^{35} -1.74084 q^{36} -1.31648 q^{37} +2.74406 q^{38} +0.924242 q^{39} -1.90437 q^{40} +8.00631 q^{41} +0.509075 q^{42} +2.57448 q^{43} +1.32536 q^{44} +1.00000 q^{45} -0.509075 q^{46} -11.6052 q^{47} +2.51222 q^{48} +1.00000 q^{49} +0.509075 q^{50} -2.41409 q^{51} -1.60896 q^{52} +3.28848 q^{53} +0.509075 q^{54} -0.761333 q^{55} -1.90437 q^{56} +5.39028 q^{57} -0.958995 q^{58} +11.7070 q^{59} -1.74084 q^{60} +9.31336 q^{61} +3.67304 q^{62} +1.00000 q^{63} -2.43443 q^{64} +0.924242 q^{65} -0.387576 q^{66} +9.89577 q^{67} +4.20255 q^{68} -1.00000 q^{69} +0.509075 q^{70} -5.91491 q^{71} -1.90437 q^{72} -0.915369 q^{73} -0.670190 q^{74} +1.00000 q^{75} -9.38362 q^{76} -0.761333 q^{77} +0.470509 q^{78} -3.95437 q^{79} +2.51222 q^{80} +1.00000 q^{81} +4.07582 q^{82} +12.9943 q^{83} -1.74084 q^{84} -2.41409 q^{85} +1.31060 q^{86} -1.88380 q^{87} +1.44986 q^{88} -9.31311 q^{89} +0.509075 q^{90} +0.924242 q^{91} +1.74084 q^{92} +7.21511 q^{93} -5.90793 q^{94} +5.39028 q^{95} +5.08765 q^{96} +0.412782 q^{97} +0.509075 q^{98} -0.761333 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.509075	0.359971	0.179985	−	0.983669i	$-0.442395\pi$
$2$	0.509075	0.359971	0.179985	+	0.983669i	$0.442395\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.74084	−0.870421
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	0.509075	0.207829
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−1.90437	−0.673297
$9$	1.00000	0.333333
$10$	0.509075	0.160984
$11$	−0.761333	−0.229550	−0.114775	−	0.993391i	$-0.536615\pi$
$11$	−0.761333	−0.229550	−0.114775	+	0.993391i	$0.536615\pi$
$12$	−1.74084	−0.502538
$13$	0.924242	0.256339	0.128169	−	0.991752i	$-0.459090\pi$
$13$	0.924242	0.256339	0.128169	+	0.991752i	$0.459090\pi$
$14$	0.509075	0.136056
$15$	1.00000	0.258199
$16$	2.51222	0.628054
$17$	−2.41409	−0.585502	−0.292751	−	0.956189i	$-0.594571\pi$
$17$	−2.41409	−0.585502	−0.292751	+	0.956189i	$0.594571\pi$
$18$	0.509075	0.119990
$19$	5.39028	1.23661	0.618307	−	0.785937i	$-0.287819\pi$
$19$	5.39028	1.23661	0.618307	+	0.785937i	$0.287819\pi$
$20$	−1.74084	−0.389264
$21$	1.00000	0.218218
$22$	−0.387576	−0.0826314
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−1.90437	−0.388728
$25$	1.00000	0.200000
$26$	0.470509	0.0922744
$27$	1.00000	0.192450
$28$	−1.74084	−0.328988
$29$	−1.88380	−0.349812	−0.174906	−	0.984585i	$-0.555962\pi$
$29$	−1.88380	−0.349812	−0.174906	+	0.984585i	$0.555962\pi$
$30$	0.509075	0.0929440
$31$	7.21511	1.29587	0.647936	−	0.761695i	$-0.275632\pi$
$31$	7.21511	1.29587	0.647936	+	0.761695i	$0.275632\pi$
$32$	5.08765	0.899378
$33$	−0.761333	−0.132531
$34$	−1.22895	−0.210764
$35$	1.00000	0.169031
$36$	−1.74084	−0.290140
$37$	−1.31648	−0.216429	−0.108214	−	0.994128i	$-0.534513\pi$
$37$	−1.31648	−0.216429	−0.108214	+	0.994128i	$0.534513\pi$
$38$	2.74406	0.445145
$39$	0.924242	0.147997
$40$	−1.90437	−0.301108
$41$	8.00631	1.25038	0.625188	−	0.780474i	$-0.285022\pi$
$41$	8.00631	1.25038	0.625188	+	0.780474i	$0.285022\pi$
$42$	0.509075	0.0785521
$43$	2.57448	0.392604	0.196302	−	0.980543i	$-0.437107\pi$
$43$	2.57448	0.392604	0.196302	+	0.980543i	$0.437107\pi$
$44$	1.32536	0.199806
$45$	1.00000	0.149071
$46$	−0.509075	−0.0750591
$47$	−11.6052	−1.69280	−0.846398	−	0.532551i	$-0.821233\pi$
$47$	−11.6052	−1.69280	−0.846398	+	0.532551i	$0.821233\pi$
$48$	2.51222	0.362607
$49$	1.00000	0.142857
$50$	0.509075	0.0719941
$51$	−2.41409	−0.338040
$52$	−1.60896	−0.223123
$53$	3.28848	0.451708	0.225854	−	0.974161i	$-0.427483\pi$
$53$	3.28848	0.451708	0.225854	+	0.974161i	$0.427483\pi$
$54$	0.509075	0.0692764
$55$	−0.761333	−0.102658
$56$	−1.90437	−0.254482
$57$	5.39028	0.713960
$58$	−0.958995	−0.125922
$59$	11.7070	1.52412	0.762062	−	0.647504i	$-0.224187\pi$
$59$	11.7070	1.52412	0.762062	+	0.647504i	$0.224187\pi$
$60$	−1.74084	−0.224742
$61$	9.31336	1.19245	0.596227	−	0.802816i	$-0.296666\pi$
$61$	9.31336	1.19245	0.596227	+	0.802816i	$0.296666\pi$
$62$	3.67304	0.466476
$63$	1.00000	0.125988
$64$	−2.43443	−0.304304
$65$	0.924242	0.114638
$66$	−0.387576	−0.0477073
$67$	9.89577	1.20896	0.604481	−	0.796620i	$-0.293381\pi$
$67$	9.89577	1.20896	0.604481	+	0.796620i	$0.293381\pi$
$68$	4.20255	0.509634
$69$	−1.00000	−0.120386
$70$	0.509075	0.0608462
$71$	−5.91491	−0.701970	−0.350985	−	0.936381i	$-0.614153\pi$
$71$	−5.91491	−0.701970	−0.350985	+	0.936381i	$0.614153\pi$
$72$	−1.90437	−0.224432
$73$	−0.915369	−0.107136	−0.0535679	−	0.998564i	$-0.517059\pi$
$73$	−0.915369	−0.107136	−0.0535679	+	0.998564i	$0.517059\pi$
$74$	−0.670190	−0.0779079
$75$	1.00000	0.115470
$76$	−9.38362	−1.07638
$77$	−0.761333	−0.0867619
$78$	0.470509	0.0532747
$79$	−3.95437	−0.444901	−0.222451	−	0.974944i	$-0.571406\pi$
$79$	−3.95437	−0.444901	−0.222451	+	0.974944i	$0.571406\pi$
$80$	2.51222	0.280874
$81$	1.00000	0.111111
$82$	4.07582	0.450099
$83$	12.9943	1.42631	0.713153	−	0.701009i	$-0.247267\pi$
$83$	12.9943	1.42631	0.713153	+	0.701009i	$0.247267\pi$
$84$	−1.74084	−0.189941
$85$	−2.41409	−0.261845
$86$	1.31060	0.141326
$87$	−1.88380	−0.201964
$88$	1.44986	0.154556
$89$	−9.31311	−0.987188	−0.493594	−	0.869692i	$-0.664317\pi$
$89$	−9.31311	−0.987188	−0.493594	+	0.869692i	$0.664317\pi$
$90$	0.509075	0.0536613
$91$	0.924242	0.0968869
$92$	1.74084	0.181495
$93$	7.21511	0.748172
$94$	−5.90793	−0.609357
$95$	5.39028	0.553031
$96$	5.08765	0.519256
$97$	0.412782	0.0419116	0.0209558	−	0.999780i	$-0.493329\pi$
$97$	0.412782	0.0419116	0.0209558	+	0.999780i	$0.493329\pi$
$98$	0.509075	0.0514244
$99$	−0.761333	−0.0765168
$100$	−1.74084	−0.174084
$101$	9.42096	0.937420	0.468710	−	0.883352i	$-0.344719\pi$
$101$	9.42096	0.937420	0.468710	+	0.883352i	$0.344719\pi$
$102$	−1.22895	−0.121684
$103$	−11.9140	−1.17392	−0.586960	−	0.809616i	$-0.699675\pi$
$103$	−11.9140	−1.17392	−0.586960	+	0.809616i	$0.699675\pi$
$104$	−1.76010	−0.172592
$105$	1.00000	0.0975900
$106$	1.67409	0.162602
$107$	13.7542	1.32967	0.664835	−	0.746990i	$-0.268502\pi$
$107$	13.7542	1.32967	0.664835	+	0.746990i	$0.268502\pi$
$108$	−1.74084	−0.167513
$109$	14.4553	1.38457	0.692286	−	0.721624i	$-0.256604\pi$
$109$	14.4553	1.38457	0.692286	+	0.721624i	$0.256604\pi$
$110$	−0.387576	−0.0369539
$111$	−1.31648	−0.124955
$112$	2.51222	0.237382
$113$	2.65306	0.249579	0.124789	−	0.992183i	$-0.460174\pi$
$113$	2.65306	0.249579	0.124789	+	0.992183i	$0.460174\pi$
$114$	2.74406	0.257005
$115$	−1.00000	−0.0932505
$116$	3.27939	0.304484
$117$	0.924242	0.0854462
$118$	5.95975	0.548640
$119$	−2.41409	−0.221299
$120$	−1.90437	−0.173844
$121$	−10.4204	−0.947307
$122$	4.74121	0.429249
$123$	8.00631	0.721905
$124$	−12.5604	−1.12795
$125$	1.00000	0.0894427
$126$	0.509075	0.0453520
$127$	−8.82437	−0.783036	−0.391518	−	0.920170i	$-0.628050\pi$
$127$	−8.82437	−0.783036	−0.391518	+	0.920170i	$0.628050\pi$
$128$	−11.4146	−1.00892
$129$	2.57448	0.226670
$130$	0.470509	0.0412664
$131$	15.0629	1.31605	0.658024	−	0.752997i	$-0.271392\pi$
$131$	15.0629	1.31605	0.658024	+	0.752997i	$0.271392\pi$
$132$	1.32536	0.115358
$133$	5.39028	0.467396
$134$	5.03770	0.435191
$135$	1.00000	0.0860663
$136$	4.59732	0.394217
$137$	−15.5460	−1.32818	−0.664091	−	0.747652i	$-0.731181\pi$
$137$	−15.5460	−1.32818	−0.664091	+	0.747652i	$0.731181\pi$
$138$	−0.509075	−0.0433354
$139$	13.8494	1.17469	0.587344	−	0.809338i	$-0.300174\pi$
$139$	13.8494	1.17469	0.587344	+	0.809338i	$0.300174\pi$
$140$	−1.74084	−0.147128
$141$	−11.6052	−0.977336
$142$	−3.01113	−0.252689
$143$	−0.703656	−0.0588427
$144$	2.51222	0.209351
$145$	−1.88380	−0.156441
$146$	−0.465992	−0.0385658
$147$	1.00000	0.0824786
$148$	2.29179	0.188384
$149$	−19.8485	−1.62605	−0.813025	−	0.582229i	$-0.802181\pi$
$149$	−19.8485	−1.62605	−0.813025	+	0.582229i	$0.802181\pi$
$150$	0.509075	0.0415658
$151$	0.130161	0.0105923	0.00529617	−	0.999986i	$-0.498314\pi$
$151$	0.130161	0.0105923	0.00529617	+	0.999986i	$0.498314\pi$
$152$	−10.2651	−0.832608
$153$	−2.41409	−0.195167
$154$	−0.387576	−0.0312317
$155$	7.21511	0.579532
$156$	−1.60896	−0.128820
$157$	0.623238	0.0497398	0.0248699	−	0.999691i	$-0.492083\pi$
$157$	0.623238	0.0497398	0.0248699	+	0.999691i	$0.492083\pi$
$158$	−2.01307	−0.160151
$159$	3.28848	0.260794
$160$	5.08765	0.402214
$161$	−1.00000	−0.0788110
$162$	0.509075	0.0399967
$163$	−0.125443	−0.00982544	−0.00491272	−	0.999988i	$-0.501564\pi$
$163$	−0.125443	−0.00982544	−0.00491272	+	0.999988i	$0.501564\pi$
$164$	−13.9377	−1.08835
$165$	−0.761333	−0.0592697
$166$	6.61506	0.513428
$167$	6.46729	0.500454	0.250227	−	0.968187i	$-0.419495\pi$
$167$	6.46729	0.500454	0.250227	+	0.968187i	$0.419495\pi$
$168$	−1.90437	−0.146925
$169$	−12.1458	−0.934290
$170$	−1.22895	−0.0942564
$171$	5.39028	0.412205
$172$	−4.48176	−0.341731
$173$	9.63972	0.732895	0.366447	−	0.930439i	$-0.380574\pi$
$173$	9.63972	0.732895	0.366447	+	0.930439i	$0.380574\pi$
$174$	−0.958995	−0.0727012
$175$	1.00000	0.0755929
$176$	−1.91263	−0.144170
$177$	11.7070	0.879953
$178$	−4.74108	−0.355359
$179$	−14.7008	−1.09879	−0.549395	−	0.835563i	$-0.685142\pi$
$179$	−14.7008	−1.09879	−0.549395	+	0.835563i	$0.685142\pi$
$180$	−1.74084	−0.129755
$181$	18.8304	1.39965	0.699825	−	0.714314i	$-0.253261\pi$
$181$	18.8304	1.39965	0.699825	+	0.714314i	$0.253261\pi$
$182$	0.470509	0.0348765
$183$	9.31336	0.688464
$184$	1.90437	0.140392
$185$	−1.31648	−0.0967898
$186$	3.67304	0.269320
$187$	1.83792	0.134402
$188$	20.2029	1.47345
$189$	1.00000	0.0727393
$190$	2.74406	0.199075
$191$	16.5527	1.19771	0.598856	−	0.800856i	$-0.295622\pi$
$191$	16.5527	1.19771	0.598856	+	0.800856i	$0.295622\pi$
$192$	−2.43443	−0.175690
$193$	19.3140	1.39025	0.695127	−	0.718887i	$-0.255348\pi$
$193$	19.3140	1.39025	0.695127	+	0.718887i	$0.255348\pi$
$194$	0.210137	0.0150870
$195$	0.924242	0.0661864
$196$	−1.74084	−0.124346
$197$	−15.9063	−1.13328	−0.566638	−	0.823967i	$-0.691756\pi$
$197$	−15.9063	−1.13328	−0.566638	+	0.823967i	$0.691756\pi$
$198$	−0.387576	−0.0275438
$199$	−24.3016	−1.72270	−0.861348	−	0.508015i	$-0.830379\pi$
$199$	−24.3016	−1.72270	−0.861348	+	0.508015i	$0.830379\pi$
$200$	−1.90437	−0.134659
$201$	9.89577	0.697994
$202$	4.79598	0.337444
$203$	−1.88380	−0.132217
$204$	4.20255	0.294237
$205$	8.00631	0.559185
$206$	−6.06512	−0.422577
$207$	−1.00000	−0.0695048
$208$	2.32190	0.160995
$209$	−4.10379	−0.283865
$210$	0.509075	0.0351295
$211$	−7.30661	−0.503008	−0.251504	−	0.967856i	$-0.580925\pi$
$211$	−7.30661	−0.503008	−0.251504	+	0.967856i	$0.580925\pi$
$212$	−5.72473	−0.393176
$213$	−5.91491	−0.405283
$214$	7.00193	0.478642
$215$	2.57448	0.175578
$216$	−1.90437	−0.129576
$217$	7.21511	0.489794
$218$	7.35886	0.498405
$219$	−0.915369	−0.0618549
$220$	1.32536	0.0893558
$221$	−2.23120	−0.150087
$222$	−0.670190	−0.0449802
$223$	28.4927	1.90802	0.954008	−	0.299782i	$-0.0969140\pi$
$223$	28.4927	1.90802	0.954008	+	0.299782i	$0.0969140\pi$
$224$	5.08765	0.339933
$225$	1.00000	0.0666667
$226$	1.35061	0.0898411
$227$	−11.9421	−0.792626	−0.396313	−	0.918115i	$-0.629710\pi$
$227$	−11.9421	−0.792626	−0.396313	+	0.918115i	$0.629710\pi$
$228$	−9.38362	−0.621445
$229$	−18.7123	−1.23655	−0.618273	−	0.785964i	$-0.712167\pi$
$229$	−18.7123	−1.23655	−0.618273	+	0.785964i	$0.712167\pi$
$230$	−0.509075	−0.0335674
$231$	−0.761333	−0.0500920
$232$	3.58745	0.235528
$233$	18.7571	1.22882	0.614408	−	0.788988i	$-0.289395\pi$
$233$	18.7571	1.22882	0.614408	+	0.788988i	$0.289395\pi$
$234$	0.470509	0.0307581
$235$	−11.6052	−0.757041
$236$	−20.3801	−1.32663
$237$	−3.95437	−0.256864
$238$	−1.22895	−0.0796612
$239$	−4.50726	−0.291550	−0.145775	−	0.989318i	$-0.546568\pi$
$239$	−4.50726	−0.291550	−0.145775	+	0.989318i	$0.546568\pi$
$240$	2.51222	0.162163
$241$	23.6728	1.52490	0.762448	−	0.647049i	$-0.223997\pi$
$241$	23.6728	1.52490	0.762448	+	0.647049i	$0.223997\pi$
$242$	−5.30476	−0.341003
$243$	1.00000	0.0641500
$244$	−16.2131	−1.03794
$245$	1.00000	0.0638877
$246$	4.07582	0.259865
$247$	4.98192	0.316992
$248$	−13.7402	−0.872507
$249$	12.9943	0.823478
$250$	0.509075	0.0321968
$251$	−11.8311	−0.746772	−0.373386	−	0.927676i	$-0.621803\pi$
$251$	−11.8311	−0.746772	−0.373386	+	0.927676i	$0.621803\pi$
$252$	−1.74084	−0.109663
$253$	0.761333	0.0478646
$254$	−4.49227	−0.281870
$255$	−2.41409	−0.151176
$256$	−0.942031	−0.0588769
$257$	−11.8697	−0.740410	−0.370205	−	0.928950i	$-0.620713\pi$
$257$	−11.8697	−0.740410	−0.370205	+	0.928950i	$0.620713\pi$
$258$	1.31060	0.0815946
$259$	−1.31648	−0.0818023
$260$	−1.60896	−0.0997835
$261$	−1.88380	−0.116604
$262$	7.66813	0.473739
$263$	−15.9080	−0.980929	−0.490465	−	0.871461i	$-0.663173\pi$
$263$	−15.9080	−0.980929	−0.490465	+	0.871461i	$0.663173\pi$
$264$	1.44986	0.0892327
$265$	3.28848	0.202010
$266$	2.74406	0.168249
$267$	−9.31311	−0.569953
$268$	−17.2270	−1.05231
$269$	8.42550	0.513712	0.256856	−	0.966450i	$-0.417313\pi$
$269$	8.42550	0.513712	0.256856	+	0.966450i	$0.417313\pi$
$270$	0.509075	0.0309813
$271$	−10.3893	−0.631108	−0.315554	−	0.948908i	$-0.602190\pi$
$271$	−10.3893	−0.631108	−0.315554	+	0.948908i	$0.602190\pi$
$272$	−6.06471	−0.367727
$273$	0.924242	0.0559377
$274$	−7.91408	−0.478107
$275$	−0.761333	−0.0459101
$276$	1.74084	0.104786
$277$	22.6197	1.35908	0.679542	−	0.733636i	$-0.262178\pi$
$277$	22.6197	1.35908	0.679542	+	0.733636i	$0.262178\pi$
$278$	7.05037	0.422853
$279$	7.21511	0.431957
$280$	−1.90437	−0.113808
$281$	0.912057	0.0544088	0.0272044	−	0.999630i	$-0.491340\pi$
$281$	0.912057	0.0544088	0.0272044	+	0.999630i	$0.491340\pi$
$282$	−5.90793	−0.351812
$283$	−24.9192	−1.48129	−0.740646	−	0.671895i	$-0.765481\pi$
$283$	−24.9192	−1.48129	−0.740646	+	0.671895i	$0.765481\pi$
$284$	10.2969	0.611010
$285$	5.39028	0.319292
$286$	−0.358214	−0.0211816
$287$	8.00631	0.472598
$288$	5.08765	0.299793
$289$	−11.1722	−0.657187
$290$	−0.958995	−0.0563141
$291$	0.412782	0.0241977
$292$	1.59351	0.0932533
$293$	−4.80031	−0.280437	−0.140219	−	0.990121i	$-0.544781\pi$
$293$	−4.80031	−0.280437	−0.140219	+	0.990121i	$0.544781\pi$
$294$	0.509075	0.0296899
$295$	11.7070	0.681609
$296$	2.50707	0.145721
$297$	−0.761333	−0.0441770
$298$	−10.1044	−0.585330
$299$	−0.924242	−0.0534503
$300$	−1.74084	−0.100508
$301$	2.57448	0.148390
$302$	0.0662618	0.00381294
$303$	9.42096	0.541220
$304$	13.5415	0.776660
$305$	9.31336	0.533282
$306$	−1.22895	−0.0702546
$307$	−11.0693	−0.631757	−0.315878	−	0.948800i	$-0.602299\pi$
$307$	−11.0693	−0.631757	−0.315878	+	0.948800i	$0.602299\pi$
$308$	1.32536	0.0755194
$309$	−11.9140	−0.677763
$310$	3.67304	0.208614
$311$	−24.9723	−1.41605	−0.708026	−	0.706186i	$-0.750414\pi$
$311$	−24.9723	−1.41605	−0.708026	+	0.706186i	$0.750414\pi$
$312$	−1.76010	−0.0996461
$313$	11.9930	0.677887	0.338944	−	0.940807i	$-0.389930\pi$
$313$	11.9930	0.677887	0.338944	+	0.940807i	$0.389930\pi$
$314$	0.317275	0.0179049
$315$	1.00000	0.0563436
$316$	6.88393	0.387251
$317$	−26.4737	−1.48691	−0.743455	−	0.668786i	$-0.766814\pi$
$317$	−26.4737	−1.48691	−0.743455	+	0.668786i	$0.766814\pi$
$318$	1.67409	0.0938781
$319$	1.43420	0.0802996
$320$	−2.43443	−0.136089
$321$	13.7542	0.767686
$322$	−0.509075	−0.0283697
$323$	−13.0126	−0.724041
$324$	−1.74084	−0.0967135
$325$	0.924242	0.0512677
$326$	−0.0638599	−0.00353687
$327$	14.4553	0.799383
$328$	−15.2470	−0.841874
$329$	−11.6052	−0.639817
$330$	−0.387576	−0.0213353
$331$	−14.0540	−0.772479	−0.386240	−	0.922398i	$-0.626226\pi$
$331$	−14.0540	−0.772479	−0.386240	+	0.922398i	$0.626226\pi$
$332$	−22.6210	−1.24149
$333$	−1.31648	−0.0721429
$334$	3.29234	0.180149
$335$	9.89577	0.540664
$336$	2.51222	0.137053
$337$	−24.5431	−1.33695	−0.668473	−	0.743737i	$-0.733052\pi$
$337$	−24.5431	−1.33695	−0.668473	+	0.743737i	$0.733052\pi$
$338$	−6.18312	−0.336317
$339$	2.65306	0.144094
$340$	4.20255	0.227915
$341$	−5.49310	−0.297468
$342$	2.74406	0.148382
$343$	1.00000	0.0539949
$344$	−4.90276	−0.264339
$345$	−1.00000	−0.0538382
$346$	4.90735	0.263821
$347$	−13.2460	−0.711084	−0.355542	−	0.934660i	$-0.615704\pi$
$347$	−13.2460	−0.711084	−0.355542	+	0.934660i	$0.615704\pi$
$348$	3.27939	0.175794
$349$	−19.4027	−1.03860	−0.519301	−	0.854591i	$-0.673808\pi$
$349$	−19.4027	−1.03860	−0.519301	+	0.854591i	$0.673808\pi$
$350$	0.509075	0.0272112
$351$	0.924242	0.0493324
$352$	−3.87339	−0.206453
$353$	−15.5103	−0.825529	−0.412765	−	0.910838i	$-0.635437\pi$
$353$	−15.5103	−0.825529	−0.412765	+	0.910838i	$0.635437\pi$
$354$	5.95975	0.316757
$355$	−5.91491	−0.313931
$356$	16.2127	0.859269
$357$	−2.41409	−0.127767
$358$	−7.48383	−0.395533
$359$	−9.78214	−0.516282	−0.258141	−	0.966107i	$-0.583110\pi$
$359$	−9.78214	−0.516282	−0.258141	+	0.966107i	$0.583110\pi$
$360$	−1.90437	−0.100369
$361$	10.0551	0.529215
$362$	9.58608	0.503833
$363$	−10.4204	−0.546928
$364$	−1.60896	−0.0843324
$365$	−0.915369	−0.0479126
$366$	4.74121	0.247827
$367$	10.8208	0.564840	0.282420	−	0.959291i	$-0.408863\pi$
$367$	10.8208	0.564840	0.282420	+	0.959291i	$0.408863\pi$
$368$	−2.51222	−0.130958
$369$	8.00631	0.416792
$370$	−0.670190	−0.0348415
$371$	3.28848	0.170730
$372$	−12.5604	−0.651225
$373$	−33.2129	−1.71970	−0.859851	−	0.510546i	$-0.829443\pi$
$373$	−33.2129	−1.71970	−0.859851	+	0.510546i	$0.829443\pi$
$374$	0.935642	0.0483809
$375$	1.00000	0.0516398
$376$	22.1007	1.13975
$377$	−1.74109	−0.0896704
$378$	0.509075	0.0261840
$379$	16.4231	0.843596	0.421798	−	0.906690i	$-0.361399\pi$
$379$	16.4231	0.843596	0.421798	+	0.906690i	$0.361399\pi$
$380$	−9.38362	−0.481370
$381$	−8.82437	−0.452086
$382$	8.42658	0.431141
$383$	−20.8881	−1.06733	−0.533666	−	0.845695i	$-0.679186\pi$
$383$	−20.8881	−1.06733	−0.533666	+	0.845695i	$0.679186\pi$
$384$	−11.4146	−0.582499
$385$	−0.761333	−0.0388011
$386$	9.83229	0.500451
$387$	2.57448	0.130868
$388$	−0.718588	−0.0364808
$389$	10.9950	0.557468	0.278734	−	0.960368i	$-0.410085\pi$
$389$	10.9950	0.557468	0.278734	+	0.960368i	$0.410085\pi$
$390$	0.470509	0.0238252
$391$	2.41409	0.122086
$392$	−1.90437	−0.0961853
$393$	15.0629	0.759821
$394$	−8.09751	−0.407946
$395$	−3.95437	−0.198966
$396$	1.32536	0.0666018
$397$	35.7288	1.79317	0.896587	−	0.442867i	$-0.146038\pi$
$397$	35.7288	1.79317	0.896587	+	0.442867i	$0.146038\pi$
$398$	−12.3714	−0.620120
$399$	5.39028	0.269851
$400$	2.51222	0.125611
$401$	−0.434319	−0.0216888	−0.0108444	−	0.999941i	$-0.503452\pi$
$401$	−0.434319	−0.0216888	−0.0108444	+	0.999941i	$0.503452\pi$
$402$	5.03770	0.251257
$403$	6.66851	0.332182
$404$	−16.4004	−0.815951
$405$	1.00000	0.0496904
$406$	−0.958995	−0.0475941
$407$	1.00228	0.0496813
$408$	4.59732	0.227601
$409$	1.05128	0.0519822	0.0259911	−	0.999662i	$-0.491726\pi$
$409$	1.05128	0.0519822	0.0259911	+	0.999662i	$0.491726\pi$
$410$	4.07582	0.201290
$411$	−15.5460	−0.766826
$412$	20.7404	1.02180
$413$	11.7070	0.576065
$414$	−0.509075	−0.0250197
$415$	12.9943	0.637863
$416$	4.70222	0.230545
$417$	13.8494	0.678206
$418$	−2.08914	−0.102183
$419$	−11.9060	−0.581647	−0.290824	−	0.956777i	$-0.593929\pi$
$419$	−11.9060	−0.581647	−0.290824	+	0.956777i	$0.593929\pi$
$420$	−1.74084	−0.0849444
$421$	33.6506	1.64003	0.820014	−	0.572343i	$-0.193965\pi$
$421$	33.6506	1.64003	0.820014	+	0.572343i	$0.193965\pi$
$422$	−3.71962	−0.181068
$423$	−11.6052	−0.564265
$424$	−6.26249	−0.304134
$425$	−2.41409	−0.117100
$426$	−3.01113	−0.145890
$427$	9.31336	0.450705
$428$	−23.9439	−1.15737
$429$	−0.703656	−0.0339728
$430$	1.31060	0.0632029
$431$	25.1785	1.21281	0.606403	−	0.795158i	$-0.292612\pi$
$431$	25.1785	1.21281	0.606403	+	0.795158i	$0.292612\pi$
$432$	2.51222	0.120869
$433$	−16.8717	−0.810801	−0.405401	−	0.914139i	$-0.632868\pi$
$433$	−16.8717	−0.810801	−0.405401	+	0.914139i	$0.632868\pi$
$434$	3.67304	0.176311
$435$	−1.88380	−0.0903212
$436$	−25.1645	−1.20516
$437$	−5.39028	−0.257852
$438$	−0.465992	−0.0222659
$439$	−12.7477	−0.608413	−0.304207	−	0.952606i	$-0.598391\pi$
$439$	−12.7477	−0.608413	−0.304207	+	0.952606i	$0.598391\pi$
$440$	1.44986	0.0691194
$441$	1.00000	0.0476190
$442$	−1.13585	−0.0540269
$443$	−5.30425	−0.252012	−0.126006	−	0.992029i	$-0.540216\pi$
$443$	−5.30425	−0.252012	−0.126006	+	0.992029i	$0.540216\pi$
$444$	2.29179	0.108764
$445$	−9.31311	−0.441484
$446$	14.5050	0.686830
$447$	−19.8485	−0.938800
$448$	−2.43443	−0.115016
$449$	29.7445	1.40373	0.701865	−	0.712310i	$-0.252351\pi$
$449$	29.7445	1.40373	0.701865	+	0.712310i	$0.252351\pi$
$450$	0.509075	0.0239980
$451$	−6.09547	−0.287024
$452$	−4.61856	−0.217239
$453$	0.130161	0.00611550
$454$	−6.07944	−0.285322
$455$	0.924242	0.0433292
$456$	−10.2651	−0.480707
$457$	10.0919	0.472080	0.236040	−	0.971743i	$-0.424150\pi$
$457$	10.0919	0.472080	0.236040	+	0.971743i	$0.424150\pi$
$458$	−9.52599	−0.445120
$459$	−2.41409	−0.112680
$460$	1.74084	0.0811672
$461$	−7.92746	−0.369219	−0.184609	−	0.982812i	$-0.559102\pi$
$461$	−7.92746	−0.369219	−0.184609	+	0.982812i	$0.559102\pi$
$462$	−0.387576	−0.0180317
$463$	−8.90942	−0.414056	−0.207028	−	0.978335i	$-0.566379\pi$
$463$	−8.90942	−0.414056	−0.207028	+	0.978335i	$0.566379\pi$
$464$	−4.73250	−0.219701
$465$	7.21511	0.334593
$466$	9.54876	0.442338
$467$	−36.4990	−1.68897	−0.844486	−	0.535578i	$-0.820094\pi$
$467$	−36.4990	−1.68897	−0.844486	+	0.535578i	$0.820094\pi$
$468$	−1.60896	−0.0743742
$469$	9.89577	0.456944
$470$	−5.90793	−0.272513
$471$	0.623238	0.0287173
$472$	−22.2945	−1.02619
$473$	−1.96003	−0.0901224
$474$	−2.01307	−0.0924635
$475$	5.39028	0.247323
$476$	4.20255	0.192623
$477$	3.28848	0.150569
$478$	−2.29453	−0.104950
$479$	−39.8881	−1.82253	−0.911266	−	0.411818i	$-0.864894\pi$
$479$	−39.8881	−1.82253	−0.911266	+	0.411818i	$0.864894\pi$
$480$	5.08765	0.232218
$481$	−1.21675	−0.0554790
$482$	12.0512	0.548918
$483$	−1.00000	−0.0455016
$484$	18.1402	0.824556
$485$	0.412782	0.0187435
$486$	0.509075	0.0230921
$487$	22.1569	1.00402	0.502012	−	0.864861i	$-0.332593\pi$
$487$	22.1569	1.00402	0.502012	+	0.864861i	$0.332593\pi$
$488$	−17.7361	−0.802876
$489$	−0.125443	−0.00567272
$490$	0.509075	0.0229977
$491$	−6.89334	−0.311092	−0.155546	−	0.987829i	$-0.549714\pi$
$491$	−6.89334	−0.311092	−0.155546	+	0.987829i	$0.549714\pi$
$492$	−13.9377	−0.628361
$493$	4.54765	0.204816
$494$	2.53617	0.114108
$495$	−0.761333	−0.0342194
$496$	18.1259	0.813878
$497$	−5.91491	−0.265320
$498$	6.61506	0.296428
$499$	22.9687	1.02822	0.514109	−	0.857725i	$-0.328123\pi$
$499$	22.9687	1.02822	0.514109	+	0.857725i	$0.328123\pi$
$500$	−1.74084	−0.0778528
$501$	6.46729	0.288937
$502$	−6.02292	−0.268816
$503$	29.0408	1.29486	0.647432	−	0.762123i	$-0.275843\pi$
$503$	29.0408	1.29486	0.647432	+	0.762123i	$0.275843\pi$
$504$	−1.90437	−0.0848274
$505$	9.42096	0.419227
$506$	0.387576	0.0172298
$507$	−12.1458	−0.539413
$508$	15.3618	0.681571
$509$	−30.4293	−1.34876	−0.674378	−	0.738386i	$-0.735588\pi$
$509$	−30.4293	−1.34876	−0.674378	+	0.738386i	$0.735588\pi$
$510$	−1.22895	−0.0544190
$511$	−0.915369	−0.0404935
$512$	22.3497	0.987725
$513$	5.39028	0.237987
$514$	−6.04256	−0.266526
$515$	−11.9140	−0.524993
$516$	−4.48176	−0.197298
$517$	8.83544	0.388582
$518$	−0.670190	−0.0294464
$519$	9.63972	0.423137
$520$	−1.76010	−0.0771855
$521$	−16.4000	−0.718496	−0.359248	−	0.933242i	$-0.616967\pi$
$521$	−16.4000	−0.718496	−0.359248	+	0.933242i	$0.616967\pi$
$522$	−0.958995	−0.0419741
$523$	−11.6436	−0.509138	−0.254569	−	0.967055i	$-0.581934\pi$
$523$	−11.6436	−0.509138	−0.254569	+	0.967055i	$0.581934\pi$
$524$	−26.2221	−1.14552
$525$	1.00000	0.0436436
$526$	−8.09837	−0.353106
$527$	−17.4179	−0.758736
$528$	−1.91263	−0.0832366
$529$	1.00000	0.0434783
$530$	1.67409	0.0727177
$531$	11.7070	0.508041
$532$	−9.38362	−0.406832
$533$	7.39978	0.320520
$534$	−4.74108	−0.205167
$535$	13.7542	0.594647
$536$	−18.8452	−0.813990
$537$	−14.7008	−0.634387
$538$	4.28922	0.184921
$539$	−0.761333	−0.0327929
$540$	−1.74084	−0.0749139
$541$	−6.59530	−0.283554	−0.141777	−	0.989899i	$-0.545282\pi$
$541$	−6.59530	−0.283554	−0.141777	+	0.989899i	$0.545282\pi$
$542$	−5.28896	−0.227180
$543$	18.8304	0.808088
$544$	−12.2820	−0.526588
$545$	14.4553	0.619199
$546$	0.470509	0.0201359
$547$	−30.1481	−1.28904	−0.644520	−	0.764587i	$-0.722943\pi$
$547$	−30.1481	−1.28904	−0.644520	+	0.764587i	$0.722943\pi$
$548$	27.0631	1.15608
$549$	9.31336	0.397485
$550$	−0.387576	−0.0165263
$551$	−10.1542	−0.432583
$552$	1.90437	0.0810554
$553$	−3.95437	−0.168157
$554$	11.5151	0.489231
$555$	−1.31648	−0.0558816
$556$	−24.1096	−1.02247
$557$	−14.7761	−0.626082	−0.313041	−	0.949740i	$-0.601348\pi$
$557$	−14.7761	−0.626082	−0.313041	+	0.949740i	$0.601348\pi$
$558$	3.67304	0.155492
$559$	2.37944	0.100640
$560$	2.51222	0.106160
$561$	1.83792	0.0775972
$562$	0.464306	0.0195856
$563$	−2.66015	−0.112112	−0.0560560	−	0.998428i	$-0.517853\pi$
$563$	−2.66015	−0.112112	−0.0560560	+	0.998428i	$0.517853\pi$
$564$	20.2029	0.850694
$565$	2.65306	0.111615
$566$	−12.6858	−0.533222
$567$	1.00000	0.0419961
$568$	11.2642	0.472634
$569$	23.1613	0.970970	0.485485	−	0.874245i	$-0.338643\pi$
$569$	23.1613	0.970970	0.485485	+	0.874245i	$0.338643\pi$
$570$	2.74406	0.114936
$571$	36.8271	1.54117	0.770583	−	0.637340i	$-0.219965\pi$
$571$	36.8271	1.54117	0.770583	+	0.637340i	$0.219965\pi$
$572$	1.22495	0.0512179
$573$	16.5527	0.691500
$574$	4.07582	0.170121
$575$	−1.00000	−0.0417029
$576$	−2.43443	−0.101435
$577$	−17.0956	−0.711700	−0.355850	−	0.934543i	$-0.615809\pi$
$577$	−17.0956	−0.711700	−0.355850	+	0.934543i	$0.615809\pi$
$578$	−5.68748	−0.236568
$579$	19.3140	0.802663
$580$	3.27939	0.136169
$581$	12.9943	0.539093
$582$	0.210137	0.00871046
$583$	−2.50363	−0.103690
$584$	1.74320	0.0721342
$585$	0.924242	0.0382127
$586$	−2.44372	−0.100949
$587$	6.56002	0.270761	0.135380	−	0.990794i	$-0.456774\pi$
$587$	6.56002	0.270761	0.135380	+	0.990794i	$0.456774\pi$
$588$	−1.74084	−0.0717911
$589$	38.8914	1.60249
$590$	5.95975	0.245359
$591$	−15.9063	−0.654298
$592$	−3.30729	−0.135929
$593$	−3.11525	−0.127928	−0.0639639	−	0.997952i	$-0.520374\pi$
$593$	−3.11525	−0.127928	−0.0639639	+	0.997952i	$0.520374\pi$
$594$	−0.387576	−0.0159024
$595$	−2.41409	−0.0989680
$596$	34.5530	1.41535
$597$	−24.3016	−0.994599
$598$	−0.470509	−0.0192406
$599$	−7.32395	−0.299248	−0.149624	−	0.988743i	$-0.547806\pi$
$599$	−7.32395	−0.299248	−0.149624	+	0.988743i	$0.547806\pi$
$600$	−1.90437	−0.0777456
$601$	12.2887	0.501267	0.250634	−	0.968082i	$-0.419361\pi$
$601$	12.2887	0.501267	0.250634	+	0.968082i	$0.419361\pi$
$602$	1.31060	0.0534162
$603$	9.89577	0.402987
$604$	−0.226590	−0.00921980
$605$	−10.4204	−0.423648
$606$	4.79598	0.194823
$607$	−33.7011	−1.36789	−0.683943	−	0.729535i	$-0.739736\pi$
$607$	−33.7011	−1.36789	−0.683943	+	0.729535i	$0.739736\pi$
$608$	27.4238	1.11218
$609$	−1.88380	−0.0763353
$610$	4.74121	0.191966
$611$	−10.7260	−0.433929
$612$	4.20255	0.169878
$613$	−14.4449	−0.583424	−0.291712	−	0.956506i	$-0.594225\pi$
$613$	−14.4449	−0.583424	−0.291712	+	0.956506i	$0.594225\pi$
$614$	−5.63509	−0.227414
$615$	8.00631	0.322846
$616$	1.44986	0.0584165
$617$	0.405073	0.0163076	0.00815381	−	0.999967i	$-0.497405\pi$
$617$	0.405073	0.0163076	0.00815381	+	0.999967i	$0.497405\pi$
$618$	−6.06512	−0.243975
$619$	19.0112	0.764123	0.382062	−	0.924137i	$-0.375214\pi$
$619$	19.0112	0.764123	0.382062	+	0.924137i	$0.375214\pi$
$620$	−12.5604	−0.504437
$621$	−1.00000	−0.0401286
$622$	−12.7128	−0.509737
$623$	−9.31311	−0.373122
$624$	2.32190	0.0929502
$625$	1.00000	0.0400000
$626$	6.10537	0.244020
$627$	−4.10379	−0.163890
$628$	−1.08496	−0.0432946
$629$	3.17811	0.126719
$630$	0.509075	0.0202821
$631$	20.8176	0.828737	0.414368	−	0.910109i	$-0.364003\pi$
$631$	20.8176	0.828737	0.414368	+	0.910109i	$0.364003\pi$
$632$	7.53059	0.299551
$633$	−7.30661	−0.290412
$634$	−13.4771	−0.535244
$635$	−8.82437	−0.350185
$636$	−5.72473	−0.227000
$637$	0.924242	0.0366198
$638$	0.730114	0.0289055
$639$	−5.91491	−0.233990
$640$	−11.4146	−0.451202
$641$	−40.8160	−1.61213	−0.806067	−	0.591824i	$-0.798408\pi$
$641$	−40.8160	−1.61213	−0.806067	+	0.591824i	$0.798408\pi$
$642$	7.00193	0.276344
$643$	−10.9629	−0.432336	−0.216168	−	0.976356i	$-0.569356\pi$
$643$	−10.9629	−0.432336	−0.216168	+	0.976356i	$0.569356\pi$
$644$	1.74084	0.0685988
$645$	2.57448	0.101370
$646$	−6.62440	−0.260633
$647$	−32.3997	−1.27376	−0.636881	−	0.770962i	$-0.719776\pi$
$647$	−32.3997	−1.27376	−0.636881	+	0.770962i	$0.719776\pi$
$648$	−1.90437	−0.0748108
$649$	−8.91293	−0.349863
$650$	0.470509	0.0184549
$651$	7.21511	0.282782
$652$	0.218376	0.00855227
$653$	37.5472	1.46934	0.734668	−	0.678427i	$-0.237338\pi$
$653$	37.5472	1.46934	0.734668	+	0.678427i	$0.237338\pi$
$654$	7.35886	0.287754
$655$	15.0629	0.588555
$656$	20.1136	0.785304
$657$	−0.915369	−0.0357119
$658$	−5.90793	−0.230315
$659$	−11.9589	−0.465851	−0.232926	−	0.972495i	$-0.574830\pi$
$659$	−11.9589	−0.465851	−0.232926	+	0.972495i	$0.574830\pi$
$660$	1.32536	0.0515896
$661$	39.6457	1.54204	0.771020	−	0.636811i	$-0.219747\pi$
$661$	39.6457	1.54204	0.771020	+	0.636811i	$0.219747\pi$
$662$	−7.15456	−0.278070
$663$	−2.23120	−0.0866527
$664$	−24.7459	−0.960327
$665$	5.39028	0.209026
$666$	−0.670190	−0.0259693
$667$	1.88380	0.0729409
$668$	−11.2585	−0.435606
$669$	28.4927	1.10159
$670$	5.03770	0.194623
$671$	−7.09057	−0.273728
$672$	5.08765	0.196260
$673$	−19.9248	−0.768046	−0.384023	−	0.923324i	$-0.625462\pi$
$673$	−19.9248	−0.768046	−0.384023	+	0.923324i	$0.625462\pi$
$674$	−12.4943	−0.481261
$675$	1.00000	0.0384900
$676$	21.1439	0.813226
$677$	36.7077	1.41079	0.705396	−	0.708814i	$-0.250769\pi$
$677$	36.7077	1.41079	0.705396	+	0.708814i	$0.250769\pi$
$678$	1.35061	0.0518698
$679$	0.412782	0.0158411
$680$	4.59732	0.176299
$681$	−11.9421	−0.457623
$682$	−2.79640	−0.107080
$683$	−6.26472	−0.239713	−0.119856	−	0.992791i	$-0.538243\pi$
$683$	−6.26472	−0.239713	−0.119856	+	0.992791i	$0.538243\pi$
$684$	−9.38362	−0.358792
$685$	−15.5460	−0.593981
$686$	0.509075	0.0194366
$687$	−18.7123	−0.713920
$688$	6.46764	0.246577
$689$	3.03936	0.115790
$690$	−0.509075	−0.0193802
$691$	23.8039	0.905545	0.452772	−	0.891626i	$-0.350435\pi$
$691$	23.8039	0.905545	0.452772	+	0.891626i	$0.350435\pi$
$692$	−16.7812	−0.637927
$693$	−0.761333	−0.0289206
$694$	−6.74323	−0.255969
$695$	13.8494	0.525336
$696$	3.58745	0.135982
$697$	−19.3279	−0.732098
$698$	−9.87743	−0.373866
$699$	18.7571	0.709457
$700$	−1.74084	−0.0657976
$701$	−24.8384	−0.938134	−0.469067	−	0.883163i	$-0.655410\pi$
$701$	−24.8384	−0.938134	−0.469067	+	0.883163i	$0.655410\pi$
$702$	0.470509	0.0177582
$703$	−7.09621	−0.267639
$704$	1.85341	0.0698532
$705$	−11.6052	−0.437078
$706$	−7.89591	−0.297166
$707$	9.42096	0.354312
$708$	−20.3801	−0.765930
$709$	4.44717	0.167017	0.0835085	−	0.996507i	$-0.473387\pi$
$709$	4.44717	0.167017	0.0835085	+	0.996507i	$0.473387\pi$
$710$	−3.01113	−0.113006
$711$	−3.95437	−0.148300
$712$	17.7356	0.664671
$713$	−7.21511	−0.270208
$714$	−1.22895	−0.0459924
$715$	−0.703656	−0.0263152
$716$	25.5918	0.956411
$717$	−4.50726	−0.168327
$718$	−4.97985	−0.185846
$719$	−34.3986	−1.28285	−0.641426	−	0.767185i	$-0.721657\pi$
$719$	−34.3986	−1.28285	−0.641426	+	0.767185i	$0.721657\pi$
$720$	2.51222	0.0936247
$721$	−11.9140	−0.443700
$722$	5.11879	0.190502
$723$	23.6728	0.880399
$724$	−32.7807	−1.21829
$725$	−1.88380	−0.0699625
$726$	−5.30476	−0.196878
$727$	21.3606	0.792220	0.396110	−	0.918203i	$-0.370360\pi$
$727$	21.3606	0.792220	0.396110	+	0.918203i	$0.370360\pi$
$728$	−1.76010	−0.0652337
$729$	1.00000	0.0370370
$730$	−0.465992	−0.0172471
$731$	−6.21501	−0.229871
$732$	−16.2131	−0.599253
$733$	−42.3277	−1.56341	−0.781705	−	0.623649i	$-0.785650\pi$
$733$	−42.3277	−1.56341	−0.781705	+	0.623649i	$0.785650\pi$
$734$	5.50859	0.203326
$735$	1.00000	0.0368856
$736$	−5.08765	−0.187533
$737$	−7.53397	−0.277518
$738$	4.07582	0.150033
$739$	46.2354	1.70080	0.850398	−	0.526140i	$-0.176361\pi$
$739$	46.2354	1.70080	0.850398	+	0.526140i	$0.176361\pi$
$740$	2.29179	0.0842479
$741$	4.98192	0.183015
$742$	1.67409	0.0614577
$743$	37.6427	1.38098	0.690489	−	0.723343i	$-0.257395\pi$
$743$	37.6427	1.38098	0.690489	+	0.723343i	$0.257395\pi$
$744$	−13.7402	−0.503742
$745$	−19.8485	−0.727192
$746$	−16.9079	−0.619042
$747$	12.9943	0.475435
$748$	−3.19954	−0.116987
$749$	13.7542	0.502568
$750$	0.509075	0.0185888
$751$	0.732988	0.0267471	0.0133736	−	0.999911i	$-0.495743\pi$
$751$	0.732988	0.0267471	0.0133736	+	0.999911i	$0.495743\pi$
$752$	−29.1548	−1.06317
$753$	−11.8311	−0.431149
$754$	−0.886344	−0.0322787
$755$	0.130161	0.00473704
$756$	−1.74084	−0.0633138
$757$	29.4223	1.06937	0.534686	−	0.845051i	$-0.320430\pi$
$757$	29.4223	1.06937	0.534686	+	0.845051i	$0.320430\pi$
$758$	8.36058	0.303670
$759$	0.761333	0.0276346
$760$	−10.2651	−0.372354
$761$	−15.0260	−0.544692	−0.272346	−	0.962199i	$-0.587799\pi$
$761$	−15.0260	−0.544692	−0.272346	+	0.962199i	$0.587799\pi$
$762$	−4.49227	−0.162738
$763$	14.4553	0.523319
$764$	−28.8157	−1.04251
$765$	−2.41409	−0.0872815
$766$	−10.6336	−0.384208
$767$	10.8201	0.390692
$768$	−0.942031	−0.0339926
$769$	16.1893	0.583802	0.291901	−	0.956449i	$-0.405712\pi$
$769$	16.1893	0.583802	0.291901	+	0.956449i	$0.405712\pi$
$770$	−0.387576	−0.0139673
$771$	−11.8697	−0.427476
$772$	−33.6227	−1.21011
$773$	−5.31416	−0.191137	−0.0955686	−	0.995423i	$-0.530467\pi$
$773$	−5.31416	−0.191137	−0.0955686	+	0.995423i	$0.530467\pi$
$774$	1.31060	0.0471087
$775$	7.21511	0.259174
$776$	−0.786090	−0.0282190
$777$	−1.31648	−0.0472286
$778$	5.59728	0.200672
$779$	43.1562	1.54623
$780$	−1.60896	−0.0576100
$781$	4.50321	0.161138
$782$	1.22895	0.0439473
$783$	−1.88380	−0.0673214
$784$	2.51222	0.0897220
$785$	0.623238	0.0222443
$786$	7.66813	0.273513
$787$	−13.0875	−0.466519	−0.233259	−	0.972415i	$-0.574939\pi$
$787$	−13.0875	−0.466519	−0.233259	+	0.972415i	$0.574939\pi$
$788$	27.6904	0.986428
$789$	−15.9080	−0.566340
$790$	−2.01307	−0.0716219
$791$	2.65306	0.0943320
$792$	1.44986	0.0515185
$793$	8.60781	0.305672
$794$	18.1886	0.645491
$795$	3.28848	0.116631
$796$	42.3053	1.49947
$797$	−19.9982	−0.708372	−0.354186	−	0.935175i	$-0.615242\pi$
$797$	−19.9982	−0.708372	−0.354186	+	0.935175i	$0.615242\pi$
$798$	2.74406	0.0971386
$799$	28.0160	0.991136
$800$	5.08765	0.179876
$801$	−9.31311	−0.329063
$802$	−0.221101	−0.00780735
$803$	0.696900	0.0245931
$804$	−17.2270	−0.607549
$805$	−1.00000	−0.0352454
$806$	3.39478	0.119576
$807$	8.42550	0.296592
$808$	−17.9410	−0.631162
$809$	10.7942	0.379504	0.189752	−	0.981832i	$-0.439232\pi$
$809$	10.7942	0.379504	0.189752	+	0.981832i	$0.439232\pi$
$810$	0.509075	0.0178871
$811$	−33.2421	−1.16729	−0.583644	−	0.812010i	$-0.698374\pi$
$811$	−33.2421	−1.16729	−0.583644	+	0.812010i	$0.698374\pi$
$812$	3.27939	0.115084
$813$	−10.3893	−0.364370
$814$	0.510237	0.0178838
$815$	−0.125443	−0.00439407
$816$	−6.06471	−0.212307
$817$	13.8771	0.485500
$818$	0.535179	0.0187121
$819$	0.924242	0.0322956
$820$	−13.9377	−0.486727
$821$	9.83580	0.343272	0.171636	−	0.985160i	$-0.445095\pi$
$821$	9.83580	0.343272	0.171636	+	0.985160i	$0.445095\pi$
$822$	−7.91408	−0.276035
$823$	−22.3759	−0.779976	−0.389988	−	0.920820i	$-0.627521\pi$
$823$	−22.3759	−0.779976	−0.389988	+	0.920820i	$0.627521\pi$
$824$	22.6887	0.790397
$825$	−0.761333	−0.0265062
$826$	5.95975	0.207366
$827$	12.2920	0.427436	0.213718	−	0.976895i	$-0.431443\pi$
$827$	12.2920	0.427436	0.213718	+	0.976895i	$0.431443\pi$
$828$	1.74084	0.0604984
$829$	20.2282	0.702555	0.351277	−	0.936271i	$-0.385747\pi$
$829$	20.2282	0.702555	0.351277	+	0.936271i	$0.385747\pi$
$830$	6.61506	0.229612
$831$	22.6197	0.784668
$832$	−2.25001	−0.0780050
$833$	−2.41409	−0.0836432
$834$	7.05037	0.244134
$835$	6.46729	0.223810
$836$	7.14406	0.247082
$837$	7.21511	0.249391
$838$	−6.06107	−0.209376
$839$	37.1749	1.28342	0.641710	−	0.766947i	$-0.278225\pi$
$839$	37.1749	1.28342	0.641710	+	0.766947i	$0.278225\pi$
$840$	−1.90437	−0.0657070
$841$	−25.4513	−0.877631
$842$	17.1307	0.590362
$843$	0.912057	0.0314129
$844$	12.7197	0.437829
$845$	−12.1458	−0.417827
$846$	−5.90793	−0.203119
$847$	−10.4204	−0.358048
$848$	8.26138	0.283697
$849$	−24.9192	−0.855225
$850$	−1.22895	−0.0421527
$851$	1.31648	0.0451285
$852$	10.2969	0.352767
$853$	−31.2010	−1.06830	−0.534151	−	0.845389i	$-0.679369\pi$
$853$	−31.2010	−1.06830	−0.534151	+	0.845389i	$0.679369\pi$
$854$	4.74121	0.162241
$855$	5.39028	0.184344
$856$	−26.1931	−0.895263
$857$	−26.1920	−0.894703	−0.447351	−	0.894358i	$-0.647633\pi$
$857$	−26.1920	−0.894703	−0.447351	+	0.894358i	$0.647633\pi$
$858$	−0.358214	−0.0122292
$859$	−3.44130	−0.117416	−0.0587078	−	0.998275i	$-0.518698\pi$
$859$	−3.44130	−0.117416	−0.0587078	+	0.998275i	$0.518698\pi$
$860$	−4.48176	−0.152827
$861$	8.00631	0.272854
$862$	12.8178	0.436574
$863$	21.0957	0.718106	0.359053	−	0.933317i	$-0.383100\pi$
$863$	21.0957	0.718106	0.359053	+	0.933317i	$0.383100\pi$
$864$	5.08765	0.173085
$865$	9.63972	0.327760
$866$	−8.58896	−0.291865
$867$	−11.1722	−0.379427
$868$	−12.5604	−0.426327
$869$	3.01059	0.102127
$870$	−0.958995	−0.0325130
$871$	9.14609	0.309904
$872$	−27.5283	−0.932227
$873$	0.412782	0.0139705
$874$	−2.74406	−0.0928191
$875$	1.00000	0.0338062
$876$	1.59351	0.0538398
$877$	−31.5221	−1.06443	−0.532213	−	0.846611i	$-0.678639\pi$
$877$	−31.5221	−1.06443	−0.532213	+	0.846611i	$0.678639\pi$
$878$	−6.48953	−0.219011
$879$	−4.80031	−0.161910
$880$	−1.91263	−0.0644748
$881$	42.3955	1.42834	0.714170	−	0.699972i	$-0.246804\pi$
$881$	42.3955	1.42834	0.714170	+	0.699972i	$0.246804\pi$
$882$	0.509075	0.0171415
$883$	−20.9460	−0.704890	−0.352445	−	0.935832i	$-0.614650\pi$
$883$	−20.9460	−0.704890	−0.352445	+	0.935832i	$0.614650\pi$
$884$	3.88417	0.130639
$885$	11.7070	0.393527
$886$	−2.70026	−0.0907171
$887$	−40.8644	−1.37209	−0.686046	−	0.727558i	$-0.740655\pi$
$887$	−40.8644	−1.37209	−0.686046	+	0.727558i	$0.740655\pi$
$888$	2.50707	0.0841319
$889$	−8.82437	−0.295960
$890$	−4.74108	−0.158921
$891$	−0.761333	−0.0255056
$892$	−49.6014	−1.66078
$893$	−62.5554	−2.09334
$894$	−10.1044	−0.337941
$895$	−14.7008	−0.491394
$896$	−11.4146	−0.381335
$897$	−0.924242	−0.0308596
$898$	15.1422	0.505301
$899$	−13.5918	−0.453312
$900$	−1.74084	−0.0580281
$901$	−7.93869	−0.264476
$902$	−3.10305	−0.103320
$903$	2.57448	0.0856732
$904$	−5.05241	−0.168041
$905$	18.8304	0.625943
$906$	0.0662618	0.00220140
$907$	−0.678799	−0.0225391	−0.0112696	−	0.999936i	$-0.503587\pi$
$907$	−0.678799	−0.0225391	−0.0112696	+	0.999936i	$0.503587\pi$
$908$	20.7893	0.689918
$909$	9.42096	0.312473
$910$	0.470509	0.0155972
$911$	24.8835	0.824428	0.412214	−	0.911087i	$-0.364756\pi$
$911$	24.8835	0.824428	0.412214	+	0.911087i	$0.364756\pi$
$912$	13.5415	0.448405
$913$	−9.89296	−0.327409
$914$	5.13755	0.169935
$915$	9.31336	0.307890
$916$	32.5752	1.07632
$917$	15.0629	0.497419
$918$	−1.22895	−0.0405615
$919$	−24.6135	−0.811926	−0.405963	−	0.913890i	$-0.633064\pi$
$919$	−24.6135	−0.811926	−0.405963	+	0.913890i	$0.633064\pi$
$920$	1.90437	0.0627853
$921$	−11.0693	−0.364745
$922$	−4.03568	−0.132908
$923$	−5.46681	−0.179942
$924$	1.32536	0.0436011
$925$	−1.31648	−0.0432857
$926$	−4.53557	−0.149048
$927$	−11.9140	−0.391307
$928$	−9.58410	−0.314613
$929$	−3.64018	−0.119431	−0.0597153	−	0.998215i	$-0.519019\pi$
$929$	−3.64018	−0.119431	−0.0597153	+	0.998215i	$0.519019\pi$
$930$	3.67304	0.120444
$931$	5.39028	0.176659
$932$	−32.6531	−1.06959
$933$	−24.9723	−0.817558
$934$	−18.5807	−0.607980
$935$	1.83792	0.0601066
$936$	−1.76010	−0.0575307
$937$	−28.8801	−0.943472	−0.471736	−	0.881740i	$-0.656372\pi$
$937$	−28.8801	−0.943472	−0.471736	+	0.881740i	$0.656372\pi$
$938$	5.03770	0.164487
$939$	11.9930	0.391378
$940$	20.2029	0.658945
$941$	14.4311	0.470441	0.235221	−	0.971942i	$-0.424419\pi$
$941$	14.4311	0.470441	0.235221	+	0.971942i	$0.424419\pi$
$942$	0.317275	0.0103374
$943$	−8.00631	−0.260721
$944$	29.4105	0.957232
$945$	1.00000	0.0325300
$946$	−0.997805	−0.0324414
$947$	−19.1426	−0.622051	−0.311026	−	0.950402i	$-0.600672\pi$
$947$	−19.1426	−0.622051	−0.311026	+	0.950402i	$0.600672\pi$
$948$	6.88393	0.223580
$949$	−0.846023	−0.0274631
$950$	2.74406	0.0890290
$951$	−26.4737	−0.858468
$952$	4.59732	0.149000
$953$	47.8256	1.54922	0.774611	−	0.632438i	$-0.217946\pi$
$953$	47.8256	1.54922	0.774611	+	0.632438i	$0.217946\pi$
$954$	1.67409	0.0542006
$955$	16.5527	0.535633
$956$	7.84642	0.253771
$957$	1.43420	0.0463610
$958$	−20.3060	−0.656058
$959$	−15.5460	−0.502006
$960$	−2.43443	−0.0785710
$961$	21.0578	0.679285
$962$	−0.619418	−0.0199708
$963$	13.7542	0.443223
$964$	−41.2105	−1.32730
$965$	19.3140	0.621740
$966$	−0.509075	−0.0163792
$967$	−24.6321	−0.792116	−0.396058	−	0.918226i	$-0.629622\pi$
$967$	−24.6321	−0.792116	−0.396058	+	0.918226i	$0.629622\pi$
$968$	19.8443	0.637819
$969$	−13.0126	−0.418025
$970$	0.210137	0.00674709
$971$	−14.3595	−0.460817	−0.230408	−	0.973094i	$-0.574006\pi$
$971$	−14.3595	−0.460817	−0.230408	+	0.973094i	$0.574006\pi$
$972$	−1.74084	−0.0558375
$973$	13.8494	0.443990
$974$	11.2795	0.361419
$975$	0.924242	0.0295994
$976$	23.3972	0.748926
$977$	52.8013	1.68926	0.844632	−	0.535347i	$-0.179819\pi$
$977$	52.8013	1.68926	0.844632	+	0.535347i	$0.179819\pi$
$978$	−0.0638599	−0.00204201
$979$	7.09038	0.226609
$980$	−1.74084	−0.0556092
$981$	14.4553	0.461524
$982$	−3.50923	−0.111984
$983$	38.6553	1.23291	0.616457	−	0.787389i	$-0.288568\pi$
$983$	38.6553	1.23291	0.616457	+	0.787389i	$0.288568\pi$
$984$	−15.2470	−0.486056
$985$	−15.9063	−0.506817
$986$	2.31510	0.0737277
$987$	−11.6052	−0.369398
$988$	−8.67274	−0.275917
$989$	−2.57448	−0.0818636
$990$	−0.387576	−0.0123180
$991$	−41.9614	−1.33295	−0.666474	−	0.745529i	$-0.732197\pi$
$991$	−41.9614	−1.33295	−0.666474	+	0.745529i	$0.732197\pi$
$992$	36.7080	1.16548
$993$	−14.0540	−0.445991
$994$	−3.01113	−0.0955074
$995$	−24.3016	−0.770413
$996$	−22.6210	−0.716772
$997$	−39.1555	−1.24007	−0.620033	−	0.784575i	$-0.712881\pi$
$997$	−39.1555	−1.24007	−0.620033	+	0.784575i	$0.712881\pi$
$998$	11.6928	0.370128
$999$	−1.31648	−0.0416517

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2415.2.a.w.1.6	✓	10
3.2	odd	2		7245.2.a.bv.1.5		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2415.2.a.w.1.6	✓	10	1.1	even	1	trivial
7245.2.a.bv.1.5		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)

\(f(q)\)	\(=\)	\(q+0.509075 q^{2} +1.00000 q^{3} -1.74084 q^{4} +1.00000 q^{5} +0.509075 q^{6} +1.00000 q^{7} -1.90437 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.509075 q^{2} +1.00000 q^{3} -1.74084 q^{4} +1.00000 q^{5} +0.509075 q^{6} +1.00000 q^{7} -1.90437 q^{8} +1.00000 q^{9} +0.509075 q^{10} -0.761333 q^{11} -1.74084 q^{12} +0.924242 q^{13} +0.509075 q^{14} +1.00000 q^{15} +2.51222 q^{16} -2.41409 q^{17} +0.509075 q^{18} +5.39028 q^{19} -1.74084 q^{20} +1.00000 q^{21} -0.387576 q^{22} -1.00000 q^{23} -1.90437 q^{24} +1.00000 q^{25} +0.470509 q^{26} +1.00000 q^{27} -1.74084 q^{28} -1.88380 q^{29} +0.509075 q^{30} +7.21511 q^{31} +5.08765 q^{32} -0.761333 q^{33} -1.22895 q^{34} +1.00000 q^{35} -1.74084 q^{36} -1.31648 q^{37} +2.74406 q^{38} +0.924242 q^{39} -1.90437 q^{40} +8.00631 q^{41} +0.509075 q^{42} +2.57448 q^{43} +1.32536 q^{44} +1.00000 q^{45} -0.509075 q^{46} -11.6052 q^{47} +2.51222 q^{48} +1.00000 q^{49} +0.509075 q^{50} -2.41409 q^{51} -1.60896 q^{52} +3.28848 q^{53} +0.509075 q^{54} -0.761333 q^{55} -1.90437 q^{56} +5.39028 q^{57} -0.958995 q^{58} +11.7070 q^{59} -1.74084 q^{60} +9.31336 q^{61} +3.67304 q^{62} +1.00000 q^{63} -2.43443 q^{64} +0.924242 q^{65} -0.387576 q^{66} +9.89577 q^{67} +4.20255 q^{68} -1.00000 q^{69} +0.509075 q^{70} -5.91491 q^{71} -1.90437 q^{72} -0.915369 q^{73} -0.670190 q^{74} +1.00000 q^{75} -9.38362 q^{76} -0.761333 q^{77} +0.470509 q^{78} -3.95437 q^{79} +2.51222 q^{80} +1.00000 q^{81} +4.07582 q^{82} +12.9943 q^{83} -1.74084 q^{84} -2.41409 q^{85} +1.31060 q^{86} -1.88380 q^{87} +1.44986 q^{88} -9.31311 q^{89} +0.509075 q^{90} +0.924242 q^{91} +1.74084 q^{92} +7.21511 q^{93} -5.90793 q^{94} +5.39028 q^{95} +5.08765 q^{96} +0.412782 q^{97} +0.509075 q^{98} -0.761333 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 2 q^{2} + 10 q^{3} + 16 q^{4} + 10 q^{5} + 2 q^{6} + 10 q^{7} + 6 q^{8} + 10 q^{9}+O(q^{10}) \) 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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