LMFDB - Embedded newform 2415.2.a.w.1.4

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			1.4
Root			$-0.910389$ 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)

$f(q)$	$=$	$q-0.910389 q^{2} +1.00000 q^{3} -1.17119 q^{4} +1.00000 q^{5} -0.910389 q^{6} +1.00000 q^{7} +2.88702 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.910389 q^{2} +1.00000 q^{3} -1.17119 q^{4} +1.00000 q^{5} -0.910389 q^{6} +1.00000 q^{7} +2.88702 q^{8} +1.00000 q^{9} -0.910389 q^{10} +6.14865 q^{11} -1.17119 q^{12} -0.958000 q^{13} -0.910389 q^{14} +1.00000 q^{15} -0.285922 q^{16} +7.38130 q^{17} -0.910389 q^{18} +7.20837 q^{19} -1.17119 q^{20} +1.00000 q^{21} -5.59766 q^{22} -1.00000 q^{23} +2.88702 q^{24} +1.00000 q^{25} +0.872152 q^{26} +1.00000 q^{27} -1.17119 q^{28} -5.63401 q^{29} -0.910389 q^{30} -3.58105 q^{31} -5.51373 q^{32} +6.14865 q^{33} -6.71985 q^{34} +1.00000 q^{35} -1.17119 q^{36} -10.3012 q^{37} -6.56242 q^{38} -0.958000 q^{39} +2.88702 q^{40} +2.09597 q^{41} -0.910389 q^{42} -10.0640 q^{43} -7.20125 q^{44} +1.00000 q^{45} +0.910389 q^{46} +12.5398 q^{47} -0.285922 q^{48} +1.00000 q^{49} -0.910389 q^{50} +7.38130 q^{51} +1.12200 q^{52} -0.521736 q^{53} -0.910389 q^{54} +6.14865 q^{55} +2.88702 q^{56} +7.20837 q^{57} +5.12913 q^{58} -6.80974 q^{59} -1.17119 q^{60} +7.27476 q^{61} +3.26014 q^{62} +1.00000 q^{63} +5.59149 q^{64} -0.958000 q^{65} -5.59766 q^{66} -1.03891 q^{67} -8.64492 q^{68} -1.00000 q^{69} -0.910389 q^{70} -2.96196 q^{71} +2.88702 q^{72} -5.64068 q^{73} +9.37814 q^{74} +1.00000 q^{75} -8.44239 q^{76} +6.14865 q^{77} +0.872152 q^{78} +15.4517 q^{79} -0.285922 q^{80} +1.00000 q^{81} -1.90815 q^{82} +9.16624 q^{83} -1.17119 q^{84} +7.38130 q^{85} +9.16213 q^{86} -5.63401 q^{87} +17.7513 q^{88} -11.9206 q^{89} -0.910389 q^{90} -0.958000 q^{91} +1.17119 q^{92} -3.58105 q^{93} -11.4161 q^{94} +7.20837 q^{95} -5.51373 q^{96} +11.7617 q^{97} -0.910389 q^{98} +6.14865 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.910389	−0.643742	−0.321871	−	0.946784i	$-0.604312\pi$
$2$	−0.910389	−0.643742	−0.321871	+	0.946784i	$0.604312\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.17119	−0.585596
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−0.910389	−0.371665
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	2.88702	1.02071
$9$	1.00000	0.333333
$10$	−0.910389	−0.287890
$11$	6.14865	1.85389	0.926943	−	0.375201i	$-0.122426\pi$
$11$	6.14865	1.85389	0.926943	+	0.375201i	$0.122426\pi$
$12$	−1.17119	−0.338094
$13$	−0.958000	−0.265701	−0.132851	−	0.991136i	$-0.542413\pi$
$13$	−0.958000	−0.265701	−0.132851	+	0.991136i	$0.542413\pi$
$14$	−0.910389	−0.243312
$15$	1.00000	0.258199
$16$	−0.285922	−0.0714806
$17$	7.38130	1.79023	0.895114	−	0.445838i	$-0.147094\pi$
$17$	7.38130	1.79023	0.895114	+	0.445838i	$0.147094\pi$
$18$	−0.910389	−0.214581
$19$	7.20837	1.65371	0.826857	−	0.562413i	$-0.190127\pi$
$19$	7.20837	1.65371	0.826857	+	0.562413i	$0.190127\pi$
$20$	−1.17119	−0.261887
$21$	1.00000	0.218218
$22$	−5.59766	−1.19342
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	2.88702	0.589310
$25$	1.00000	0.200000
$26$	0.872152	0.171043
$27$	1.00000	0.192450
$28$	−1.17119	−0.221335
$29$	−5.63401	−1.04621	−0.523104	−	0.852269i	$-0.675226\pi$
$29$	−5.63401	−1.04621	−0.523104	+	0.852269i	$0.675226\pi$
$30$	−0.910389	−0.166213
$31$	−3.58105	−0.643175	−0.321587	−	0.946880i	$-0.604216\pi$
$31$	−3.58105	−0.643175	−0.321587	+	0.946880i	$0.604216\pi$
$32$	−5.51373	−0.974700
$33$	6.14865	1.07034
$34$	−6.71985	−1.15244
$35$	1.00000	0.169031
$36$	−1.17119	−0.195199
$37$	−10.3012	−1.69352	−0.846758	−	0.531979i	$-0.821449\pi$
$37$	−10.3012	−1.69352	−0.846758	+	0.531979i	$0.821449\pi$
$38$	−6.56242	−1.06456
$39$	−0.958000	−0.153403
$40$	2.88702	0.456478
$41$	2.09597	0.327336	0.163668	−	0.986515i	$-0.447667\pi$
$41$	2.09597	0.327336	0.163668	+	0.986515i	$0.447667\pi$
$42$	−0.910389	−0.140476
$43$	−10.0640	−1.53474	−0.767371	−	0.641204i	$-0.778435\pi$
$43$	−10.0640	−1.53474	−0.767371	+	0.641204i	$0.778435\pi$
$44$	−7.20125	−1.08563
$45$	1.00000	0.149071
$46$	0.910389	0.134229
$47$	12.5398	1.82912	0.914562	−	0.404445i	$-0.132535\pi$
$47$	12.5398	1.82912	0.914562	+	0.404445i	$0.132535\pi$
$48$	−0.285922	−0.0412693
$49$	1.00000	0.142857
$50$	−0.910389	−0.128748
$51$	7.38130	1.03359
$52$	1.12200	0.155594
$53$	−0.521736	−0.0716660	−0.0358330	−	0.999358i	$-0.511408\pi$
$53$	−0.521736	−0.0716660	−0.0358330	+	0.999358i	$0.511408\pi$
$54$	−0.910389	−0.123888
$55$	6.14865	0.829083
$56$	2.88702	0.385794
$57$	7.20837	0.954772
$58$	5.12913	0.673488
$59$	−6.80974	−0.886553	−0.443276	−	0.896385i	$-0.646184\pi$
$59$	−6.80974	−0.886553	−0.443276	+	0.896385i	$0.646184\pi$
$60$	−1.17119	−0.151200
$61$	7.27476	0.931437	0.465719	−	0.884933i	$-0.345796\pi$
$61$	7.27476	0.931437	0.465719	+	0.884933i	$0.345796\pi$
$62$	3.26014	0.414039
$63$	1.00000	0.125988
$64$	5.59149	0.698936
$65$	−0.958000	−0.118825
$66$	−5.59766	−0.689024
$67$	−1.03891	−0.126923	−0.0634617	−	0.997984i	$-0.520214\pi$
$67$	−1.03891	−0.126923	−0.0634617	+	0.997984i	$0.520214\pi$
$68$	−8.64492	−1.04835
$69$	−1.00000	−0.120386
$70$	−0.910389	−0.108812
$71$	−2.96196	−0.351520	−0.175760	−	0.984433i	$-0.556238\pi$
$71$	−2.96196	−0.351520	−0.175760	+	0.984433i	$0.556238\pi$
$72$	2.88702	0.340238
$73$	−5.64068	−0.660191	−0.330096	−	0.943948i	$-0.607081\pi$
$73$	−5.64068	−0.660191	−0.330096	+	0.943948i	$0.607081\pi$
$74$	9.37814	1.09019
$75$	1.00000	0.115470
$76$	−8.44239	−0.968408
$77$	6.14865	0.700703
$78$	0.872152	0.0987518
$79$	15.4517	1.73845	0.869226	−	0.494415i	$-0.164618\pi$
$79$	15.4517	1.73845	0.869226	+	0.494415i	$0.164618\pi$
$80$	−0.285922	−0.0319671
$81$	1.00000	0.111111
$82$	−1.90815	−0.210720
$83$	9.16624	1.00613	0.503063	−	0.864250i	$-0.332207\pi$
$83$	9.16624	1.00613	0.503063	+	0.864250i	$0.332207\pi$
$84$	−1.17119	−0.127788
$85$	7.38130	0.800614
$86$	9.16213	0.987978
$87$	−5.63401	−0.604029
$88$	17.7513	1.89229
$89$	−11.9206	−1.26358	−0.631792	−	0.775138i	$-0.717680\pi$
$89$	−11.9206	−1.26358	−0.631792	+	0.775138i	$0.717680\pi$
$90$	−0.910389	−0.0959634
$91$	−0.958000	−0.100426
$92$	1.17119	0.122105
$93$	−3.58105	−0.371337
$94$	−11.4161	−1.17748
$95$	7.20837	0.739563
$96$	−5.51373	−0.562743
$97$	11.7617	1.19422	0.597111	−	0.802158i	$-0.296315\pi$
$97$	11.7617	1.19422	0.597111	+	0.802158i	$0.296315\pi$
$98$	−0.910389	−0.0919631
$99$	6.14865	0.617962
$100$	−1.17119	−0.117119
$101$	−7.46288	−0.742585	−0.371292	−	0.928516i	$-0.621085\pi$
$101$	−7.46288	−0.742585	−0.371292	+	0.928516i	$0.621085\pi$
$102$	−6.71985	−0.665364
$103$	−5.33569	−0.525741	−0.262871	−	0.964831i	$-0.584669\pi$
$103$	−5.33569	−0.525741	−0.262871	+	0.964831i	$0.584669\pi$
$104$	−2.76576	−0.271205
$105$	1.00000	0.0975900
$106$	0.474983	0.0461344
$107$	−14.4972	−1.40149	−0.700747	−	0.713410i	$-0.747150\pi$
$107$	−14.4972	−1.40149	−0.700747	+	0.713410i	$0.747150\pi$
$108$	−1.17119	−0.112698
$109$	−18.5715	−1.77883	−0.889415	−	0.457101i	$-0.848888\pi$
$109$	−18.5715	−1.77883	−0.889415	+	0.457101i	$0.848888\pi$
$110$	−5.59766	−0.533716
$111$	−10.3012	−0.977751
$112$	−0.285922	−0.0270171
$113$	3.23566	0.304385	0.152193	−	0.988351i	$-0.451367\pi$
$113$	3.23566	0.304385	0.152193	+	0.988351i	$0.451367\pi$
$114$	−6.56242	−0.614627
$115$	−1.00000	−0.0932505
$116$	6.59851	0.612656
$117$	−0.958000	−0.0885671
$118$	6.19951	0.570711
$119$	7.38130	0.676642
$120$	2.88702	0.263547
$121$	26.8059	2.43690
$122$	−6.62286	−0.599605
$123$	2.09597	0.188987
$124$	4.19410	0.376641
$125$	1.00000	0.0894427
$126$	−0.910389	−0.0811039
$127$	11.4681	1.01763	0.508816	−	0.860875i	$-0.330083\pi$
$127$	11.4681	1.01763	0.508816	+	0.860875i	$0.330083\pi$
$128$	5.93704	0.524766
$129$	−10.0640	−0.886084
$130$	0.872152	0.0764928
$131$	3.04286	0.265856	0.132928	−	0.991126i	$-0.457562\pi$
$131$	3.04286	0.265856	0.132928	+	0.991126i	$0.457562\pi$
$132$	−7.20125	−0.626788
$133$	7.20837	0.625045
$134$	0.945814	0.0817059
$135$	1.00000	0.0860663
$136$	21.3099	1.82731
$137$	8.99771	0.768726	0.384363	−	0.923182i	$-0.374421\pi$
$137$	8.99771	0.768726	0.384363	+	0.923182i	$0.374421\pi$
$138$	0.910389	0.0774974
$139$	13.8537	1.17505	0.587526	−	0.809205i	$-0.300102\pi$
$139$	13.8537	1.17505	0.587526	+	0.809205i	$0.300102\pi$
$140$	−1.17119	−0.0989838
$141$	12.5398	1.05605
$142$	2.69653	0.226288
$143$	−5.89040	−0.492580
$144$	−0.285922	−0.0238269
$145$	−5.63401	−0.467879
$146$	5.13521	0.424993
$147$	1.00000	0.0824786
$148$	12.0647	0.991716
$149$	−10.0164	−0.820579	−0.410289	−	0.911955i	$-0.634572\pi$
$149$	−10.0164	−0.820579	−0.410289	+	0.911955i	$0.634572\pi$
$150$	−0.910389	−0.0743329
$151$	16.1836	1.31700	0.658502	−	0.752579i	$-0.271191\pi$
$151$	16.1836	1.31700	0.658502	+	0.752579i	$0.271191\pi$
$152$	20.8107	1.68797
$153$	7.38130	0.596743
$154$	−5.59766	−0.451072
$155$	−3.58105	−0.287637
$156$	1.12200	0.0898321
$157$	−6.23720	−0.497783	−0.248891	−	0.968531i	$-0.580066\pi$
$157$	−6.23720	−0.497783	−0.248891	+	0.968531i	$0.580066\pi$
$158$	−14.0670	−1.11911
$159$	−0.521736	−0.0413764
$160$	−5.51373	−0.435899
$161$	−1.00000	−0.0788110
$162$	−0.910389	−0.0715269
$163$	−14.6035	−1.14384	−0.571918	−	0.820311i	$-0.693800\pi$
$163$	−14.6035	−1.14384	−0.571918	+	0.820311i	$0.693800\pi$
$164$	−2.45479	−0.191687
$165$	6.14865	0.478671
$166$	−8.34484	−0.647685
$167$	−2.46123	−0.190456	−0.0952278	−	0.995456i	$-0.530358\pi$
$167$	−2.46123	−0.190456	−0.0952278	+	0.995456i	$0.530358\pi$
$168$	2.88702	0.222738
$169$	−12.0822	−0.929403
$170$	−6.71985	−0.515389
$171$	7.20837	0.551238
$172$	11.7869	0.898739
$173$	−14.0651	−1.06935	−0.534675	−	0.845058i	$-0.679566\pi$
$173$	−14.0651	−1.06935	−0.534675	+	0.845058i	$0.679566\pi$
$174$	5.12913	0.388839
$175$	1.00000	0.0755929
$176$	−1.75804	−0.132517
$177$	−6.80974	−0.511851
$178$	10.8524	0.813422
$179$	−12.0068	−0.897432	−0.448716	−	0.893674i	$-0.648119\pi$
$179$	−12.0068	−0.897432	−0.448716	+	0.893674i	$0.648119\pi$
$180$	−1.17119	−0.0872955
$181$	11.7464	0.873100	0.436550	−	0.899680i	$-0.356200\pi$
$181$	11.7464	0.873100	0.436550	+	0.899680i	$0.356200\pi$
$182$	0.872152	0.0646482
$183$	7.27476	0.537766
$184$	−2.88702	−0.212834
$185$	−10.3012	−0.757363
$186$	3.26014	0.239045
$187$	45.3850	3.31888
$188$	−14.6866	−1.07113
$189$	1.00000	0.0727393
$190$	−6.56242	−0.476088
$191$	−20.5702	−1.48841	−0.744205	−	0.667951i	$-0.767172\pi$
$191$	−20.5702	−1.48841	−0.744205	+	0.667951i	$0.767172\pi$
$192$	5.59149	0.403531
$193$	20.1396	1.44968	0.724841	−	0.688916i	$-0.241913\pi$
$193$	20.1396	1.44968	0.724841	+	0.688916i	$0.241913\pi$
$194$	−10.7077	−0.768771
$195$	−0.958000	−0.0686038
$196$	−1.17119	−0.0836566
$197$	−1.85832	−0.132400	−0.0661999	−	0.997806i	$-0.521088\pi$
$197$	−1.85832	−0.132400	−0.0661999	+	0.997806i	$0.521088\pi$
$198$	−5.59766	−0.397808
$199$	−4.56622	−0.323691	−0.161845	−	0.986816i	$-0.551745\pi$
$199$	−4.56622	−0.323691	−0.161845	+	0.986816i	$0.551745\pi$
$200$	2.88702	0.204143
$201$	−1.03891	−0.0732792
$202$	6.79412	0.478033
$203$	−5.63401	−0.395430
$204$	−8.64492	−0.605266
$205$	2.09597	0.146389
$206$	4.85755	0.338442
$207$	−1.00000	−0.0695048
$208$	0.273914	0.0189925
$209$	44.3217	3.06580
$210$	−0.910389	−0.0628228
$211$	15.3033	1.05352	0.526762	−	0.850013i	$-0.323406\pi$
$211$	15.3033	1.05352	0.526762	+	0.850013i	$0.323406\pi$
$212$	0.611054	0.0419674
$213$	−2.96196	−0.202950
$214$	13.1981	0.902201
$215$	−10.0640	−0.686357
$216$	2.88702	0.196437
$217$	−3.58105	−0.243097
$218$	16.9073	1.14511
$219$	−5.64068	−0.381162
$220$	−7.20125	−0.485508
$221$	−7.07128	−0.475666
$222$	9.37814	0.629420
$223$	−15.6303	−1.04668	−0.523341	−	0.852123i	$-0.675315\pi$
$223$	−15.6303	−1.04668	−0.523341	+	0.852123i	$0.675315\pi$
$224$	−5.51373	−0.368402
$225$	1.00000	0.0666667
$226$	−2.94571	−0.195946
$227$	15.0505	0.998934	0.499467	−	0.866333i	$-0.333529\pi$
$227$	15.0505	0.998934	0.499467	+	0.866333i	$0.333529\pi$
$228$	−8.44239	−0.559111
$229$	−11.1333	−0.735709	−0.367854	−	0.929883i	$-0.619907\pi$
$229$	−11.1333	−0.735709	−0.367854	+	0.929883i	$0.619907\pi$
$230$	0.910389	0.0600292
$231$	6.14865	0.404551
$232$	−16.2655	−1.06788
$233$	−12.1308	−0.794714	−0.397357	−	0.917664i	$-0.630072\pi$
$233$	−12.1308	−0.794714	−0.397357	+	0.917664i	$0.630072\pi$
$234$	0.872152	0.0570144
$235$	12.5398	0.818009
$236$	7.97552	0.519162
$237$	15.4517	1.00370
$238$	−6.71985	−0.435583
$239$	30.1372	1.94941	0.974706	−	0.223492i	$-0.0717457\pi$
$239$	30.1372	1.94941	0.974706	+	0.223492i	$0.0717457\pi$
$240$	−0.285922	−0.0184562
$241$	0.328171	0.0211394	0.0105697	−	0.999944i	$-0.496636\pi$
$241$	0.328171	0.0211394	0.0105697	+	0.999944i	$0.496636\pi$
$242$	−24.4037	−1.56873
$243$	1.00000	0.0641500
$244$	−8.52014	−0.545446
$245$	1.00000	0.0638877
$246$	−1.90815	−0.121659
$247$	−6.90562	−0.439394
$248$	−10.3385	−0.656498
$249$	9.16624	0.580887
$250$	−0.910389	−0.0575780
$251$	1.24387	0.0785124	0.0392562	−	0.999229i	$-0.487501\pi$
$251$	1.24387	0.0785124	0.0392562	+	0.999229i	$0.487501\pi$
$252$	−1.17119	−0.0737782
$253$	−6.14865	−0.386562
$254$	−10.4405	−0.655093
$255$	7.38130	0.462235
$256$	−16.5880	−1.03675
$257$	−3.02678	−0.188805	−0.0944025	−	0.995534i	$-0.530094\pi$
$257$	−3.02678	−0.188805	−0.0944025	+	0.995534i	$0.530094\pi$
$258$	9.16213	0.570409
$259$	−10.3012	−0.640089
$260$	1.12200	0.0695836
$261$	−5.63401	−0.348736
$262$	−2.77019	−0.171143
$263$	−18.5208	−1.14204	−0.571022	−	0.820935i	$-0.693453\pi$
$263$	−18.5208	−1.14204	−0.571022	+	0.820935i	$0.693453\pi$
$264$	17.7513	1.09251
$265$	−0.521736	−0.0320500
$266$	−6.56242	−0.402368
$267$	−11.9206	−0.729531
$268$	1.21677	0.0743259
$269$	−14.7422	−0.898847	−0.449423	−	0.893319i	$-0.648371\pi$
$269$	−14.7422	−0.898847	−0.449423	+	0.893319i	$0.648371\pi$
$270$	−0.910389	−0.0554045
$271$	21.3012	1.29396	0.646978	−	0.762508i	$-0.276032\pi$
$271$	21.3012	1.29396	0.646978	+	0.762508i	$0.276032\pi$
$272$	−2.11048	−0.127967
$273$	−0.958000	−0.0579808
$274$	−8.19141	−0.494861
$275$	6.14865	0.370777
$276$	1.17119	0.0704975
$277$	3.36847	0.202392	0.101196	−	0.994867i	$-0.467733\pi$
$277$	3.36847	0.202392	0.101196	+	0.994867i	$0.467733\pi$
$278$	−12.6122	−0.756431
$279$	−3.58105	−0.214392
$280$	2.88702	0.172532
$281$	0.595566	0.0355285	0.0177642	−	0.999842i	$-0.494345\pi$
$281$	0.595566	0.0355285	0.0177642	+	0.999842i	$0.494345\pi$
$282$	−11.4161	−0.679821
$283$	−18.5187	−1.10082	−0.550411	−	0.834894i	$-0.685529\pi$
$283$	−18.5187	−1.10082	−0.550411	+	0.834894i	$0.685529\pi$
$284$	3.46902	0.205849
$285$	7.20837	0.426987
$286$	5.36255	0.317095
$287$	2.09597	0.123721
$288$	−5.51373	−0.324900
$289$	37.4836	2.20492
$290$	5.12913	0.301193
$291$	11.7617	0.689485
$292$	6.60632	0.386606
$293$	−3.63324	−0.212256	−0.106128	−	0.994352i	$-0.533845\pi$
$293$	−3.63324	−0.212256	−0.106128	+	0.994352i	$0.533845\pi$
$294$	−0.910389	−0.0530949
$295$	−6.80974	−0.396478
$296$	−29.7399	−1.72860
$297$	6.14865	0.356781
$298$	9.11885	0.528241
$299$	0.958000	0.0554026
$300$	−1.17119	−0.0676188
$301$	−10.0640	−0.580078
$302$	−14.7334	−0.847810
$303$	−7.46288	−0.428731
$304$	−2.06103	−0.118208
$305$	7.27476	0.416551
$306$	−6.71985	−0.384148
$307$	−9.24435	−0.527603	−0.263801	−	0.964577i	$-0.584976\pi$
$307$	−9.24435	−0.527603	−0.263801	+	0.964577i	$0.584976\pi$
$308$	−7.20125	−0.410329
$309$	−5.33569	−0.303537
$310$	3.26014	0.185164
$311$	25.9986	1.47425	0.737123	−	0.675758i	$-0.236184\pi$
$311$	25.9986	1.47425	0.737123	+	0.675758i	$0.236184\pi$
$312$	−2.76576	−0.156580
$313$	5.81865	0.328889	0.164445	−	0.986386i	$-0.447417\pi$
$313$	5.81865	0.328889	0.164445	+	0.986386i	$0.447417\pi$
$314$	5.67827	0.320444
$315$	1.00000	0.0563436
$316$	−18.0969	−1.01803
$317$	−6.23771	−0.350345	−0.175172	−	0.984538i	$-0.556048\pi$
$317$	−6.23771	−0.350345	−0.175172	+	0.984538i	$0.556048\pi$
$318$	0.474983	0.0266357
$319$	−34.6415	−1.93955
$320$	5.59149	0.312574
$321$	−14.4972	−0.809153
$322$	0.910389	0.0507340
$323$	53.2071	2.96052
$324$	−1.17119	−0.0650663
$325$	−0.958000	−0.0531403
$326$	13.2949	0.736335
$327$	−18.5715	−1.02701
$328$	6.05111	0.334117
$329$	12.5398	0.691344
$330$	−5.59766	−0.308141
$331$	10.9065	0.599474	0.299737	−	0.954022i	$-0.403101\pi$
$331$	10.9065	0.599474	0.299737	+	0.954022i	$0.403101\pi$
$332$	−10.7354	−0.589183
$333$	−10.3012	−0.564505
$334$	2.24067	0.122604
$335$	−1.03891	−0.0567619
$336$	−0.285922	−0.0155983
$337$	7.17672	0.390941	0.195470	−	0.980710i	$-0.437377\pi$
$337$	7.17672	0.390941	0.195470	+	0.980710i	$0.437377\pi$
$338$	10.9995	0.598296
$339$	3.23566	0.175737
$340$	−8.64492	−0.468837
$341$	−22.0186	−1.19237
$342$	−6.56242	−0.354855
$343$	1.00000	0.0539949
$344$	−29.0549	−1.56653
$345$	−1.00000	−0.0538382
$346$	12.8047	0.688386
$347$	−6.77054	−0.363461	−0.181731	−	0.983348i	$-0.558170\pi$
$347$	−6.77054	−0.363461	−0.181731	+	0.983348i	$0.558170\pi$
$348$	6.59851	0.353717
$349$	18.5747	0.994280	0.497140	−	0.867670i	$-0.334383\pi$
$349$	18.5747	0.994280	0.497140	+	0.867670i	$0.334383\pi$
$350$	−0.910389	−0.0486623
$351$	−0.958000	−0.0511342
$352$	−33.9020	−1.80698
$353$	−17.0879	−0.909498	−0.454749	−	0.890620i	$-0.650271\pi$
$353$	−17.0879	−0.909498	−0.454749	+	0.890620i	$0.650271\pi$
$354$	6.19951	0.329500
$355$	−2.96196	−0.157204
$356$	13.9614	0.739950
$357$	7.38130	0.390660
$358$	10.9309	0.577715
$359$	28.5200	1.50523	0.752613	−	0.658463i	$-0.228793\pi$
$359$	28.5200	1.50523	0.752613	+	0.658463i	$0.228793\pi$
$360$	2.88702	0.152159
$361$	32.9606	1.73477
$362$	−10.6937	−0.562051
$363$	26.8059	1.40694
$364$	1.12200	0.0588089
$365$	−5.64068	−0.295246
$366$	−6.62286	−0.346182
$367$	−6.25157	−0.326329	−0.163165	−	0.986599i	$-0.552170\pi$
$367$	−6.25157	−0.326329	−0.163165	+	0.986599i	$0.552170\pi$
$368$	0.285922	0.0149047
$369$	2.09597	0.109112
$370$	9.37814	0.487546
$371$	−0.521736	−0.0270872
$372$	4.19410	0.217454
$373$	−11.6683	−0.604163	−0.302082	−	0.953282i	$-0.597681\pi$
$373$	−11.6683	−0.604163	−0.302082	+	0.953282i	$0.597681\pi$
$374$	−41.3180	−2.13650
$375$	1.00000	0.0516398
$376$	36.2028	1.86701
$377$	5.39738	0.277979
$378$	−0.910389	−0.0468253
$379$	−1.68449	−0.0865262	−0.0432631	−	0.999064i	$-0.513775\pi$
$379$	−1.68449	−0.0865262	−0.0432631	+	0.999064i	$0.513775\pi$
$380$	−8.44239	−0.433085
$381$	11.4681	0.587530
$382$	18.7269	0.958152
$383$	−18.2471	−0.932382	−0.466191	−	0.884684i	$-0.654374\pi$
$383$	−18.2471	−0.932382	−0.466191	+	0.884684i	$0.654374\pi$
$384$	5.93704	0.302974
$385$	6.14865	0.313364
$386$	−18.3349	−0.933221
$387$	−10.0640	−0.511581
$388$	−13.7753	−0.699333
$389$	11.6770	0.592047	0.296023	−	0.955181i	$-0.404339\pi$
$389$	11.6770	0.592047	0.296023	+	0.955181i	$0.404339\pi$
$390$	0.872152	0.0441631
$391$	−7.38130	−0.373288
$392$	2.88702	0.145816
$393$	3.04286	0.153492
$394$	1.69179	0.0852313
$395$	15.4517	0.777459
$396$	−7.20125	−0.361876
$397$	4.89817	0.245832	0.122916	−	0.992417i	$-0.460775\pi$
$397$	4.89817	0.245832	0.122916	+	0.992417i	$0.460775\pi$
$398$	4.15703	0.208373
$399$	7.20837	0.360870
$400$	−0.285922	−0.0142961
$401$	6.13735	0.306485	0.153242	−	0.988189i	$-0.451028\pi$
$401$	6.13735	0.306485	0.153242	+	0.988189i	$0.451028\pi$
$402$	0.945814	0.0471729
$403$	3.43064	0.170892
$404$	8.74047	0.434855
$405$	1.00000	0.0496904
$406$	5.12913	0.254555
$407$	−63.3387	−3.13959
$408$	21.3099	1.05500
$409$	−18.8608	−0.932607	−0.466303	−	0.884625i	$-0.654414\pi$
$409$	−18.8608	−0.932607	−0.466303	+	0.884625i	$0.654414\pi$
$410$	−1.90815	−0.0942368
$411$	8.99771	0.443824
$412$	6.24912	0.307872
$413$	−6.80974	−0.335085
$414$	0.910389	0.0447432
$415$	9.16624	0.449953
$416$	5.28216	0.258979
$417$	13.8537	0.678417
$418$	−40.3500	−1.97358
$419$	−1.73803	−0.0849082	−0.0424541	−	0.999098i	$-0.513518\pi$
$419$	−1.73803	−0.0849082	−0.0424541	+	0.999098i	$0.513518\pi$
$420$	−1.17119	−0.0571484
$421$	−9.07184	−0.442134	−0.221067	−	0.975259i	$-0.570954\pi$
$421$	−9.07184	−0.442134	−0.221067	+	0.975259i	$0.570954\pi$
$422$	−13.9320	−0.678197
$423$	12.5398	0.609708
$424$	−1.50626	−0.0731506
$425$	7.38130	0.358046
$426$	2.69653	0.130647
$427$	7.27476	0.352050
$428$	16.9790	0.820710
$429$	−5.89040	−0.284391
$430$	9.16213	0.441837
$431$	−14.9149	−0.718428	−0.359214	−	0.933255i	$-0.616955\pi$
$431$	−14.9149	−0.718428	−0.359214	+	0.933255i	$0.616955\pi$
$432$	−0.285922	−0.0137564
$433$	24.5663	1.18058	0.590290	−	0.807191i	$-0.299013\pi$
$433$	24.5663	1.18058	0.590290	+	0.807191i	$0.299013\pi$
$434$	3.26014	0.156492
$435$	−5.63401	−0.270130
$436$	21.7508	1.04168
$437$	−7.20837	−0.344823
$438$	5.13521	0.245370
$439$	7.94249	0.379074	0.189537	−	0.981874i	$-0.439301\pi$
$439$	7.94249	0.379074	0.189537	+	0.981874i	$0.439301\pi$
$440$	17.7513	0.846258
$441$	1.00000	0.0476190
$442$	6.43761	0.306206
$443$	−6.10397	−0.290009	−0.145004	−	0.989431i	$-0.546320\pi$
$443$	−6.10397	−0.290009	−0.145004	+	0.989431i	$0.546320\pi$
$444$	12.0647	0.572568
$445$	−11.9206	−0.565092
$446$	14.2296	0.673793
$447$	−10.0164	−0.473761
$448$	5.59149	0.264173
$449$	37.2102	1.75606	0.878029	−	0.478608i	$-0.158858\pi$
$449$	37.2102	1.75606	0.878029	+	0.478608i	$0.158858\pi$
$450$	−0.910389	−0.0429161
$451$	12.8874	0.606844
$452$	−3.78958	−0.178247
$453$	16.1836	0.760372
$454$	−13.7018	−0.643056
$455$	−0.958000	−0.0449117
$456$	20.8107	0.974550
$457$	−37.8112	−1.76874	−0.884368	−	0.466791i	$-0.845410\pi$
$457$	−37.8112	−1.76874	−0.884368	+	0.466791i	$0.845410\pi$
$458$	10.1356	0.473606
$459$	7.38130	0.344529
$460$	1.17119	0.0546071
$461$	−1.80500	−0.0840671	−0.0420336	−	0.999116i	$-0.513384\pi$
$461$	−1.80500	−0.0840671	−0.0420336	+	0.999116i	$0.513384\pi$
$462$	−5.59766	−0.260427
$463$	−33.1126	−1.53887	−0.769436	−	0.638724i	$-0.779463\pi$
$463$	−33.1126	−1.53887	−0.769436	+	0.638724i	$0.779463\pi$
$464$	1.61089	0.0747836
$465$	−3.58105	−0.166067
$466$	11.0437	0.511591
$467$	−0.938332	−0.0434208	−0.0217104	−	0.999764i	$-0.506911\pi$
$467$	−0.938332	−0.0434208	−0.0217104	+	0.999764i	$0.506911\pi$
$468$	1.12200	0.0518646
$469$	−1.03891	−0.0479725
$470$	−11.4161	−0.526587
$471$	−6.23720	−0.287395
$472$	−19.6598	−0.904918
$473$	−61.8798	−2.84524
$474$	−14.0670	−0.646121
$475$	7.20837	0.330743
$476$	−8.64492	−0.396239
$477$	−0.521736	−0.0238887
$478$	−27.4365	−1.25492
$479$	9.53793	0.435799	0.217900	−	0.975971i	$-0.430079\pi$
$479$	9.53793	0.435799	0.217900	+	0.975971i	$0.430079\pi$
$480$	−5.51373	−0.251666
$481$	9.86860	0.449969
$482$	−0.298764	−0.0136083
$483$	−1.00000	−0.0455016
$484$	−31.3948	−1.42704
$485$	11.7617	0.534073
$486$	−0.910389	−0.0412961
$487$	3.82667	0.173403	0.0867014	−	0.996234i	$-0.472367\pi$
$487$	3.82667	0.173403	0.0867014	+	0.996234i	$0.472367\pi$
$488$	21.0024	0.950732
$489$	−14.6035	−0.660394
$490$	−0.910389	−0.0411272
$491$	3.29041	0.148494	0.0742470	−	0.997240i	$-0.476345\pi$
$491$	3.29041	0.148494	0.0742470	+	0.997240i	$0.476345\pi$
$492$	−2.45479	−0.110670
$493$	−41.5863	−1.87295
$494$	6.28679	0.282856
$495$	6.14865	0.276361
$496$	1.02390	0.0459745
$497$	−2.96196	−0.132862
$498$	−8.34484	−0.373941
$499$	−42.6166	−1.90778	−0.953891	−	0.300153i	$-0.902962\pi$
$499$	−42.6166	−1.90778	−0.953891	+	0.300153i	$0.902962\pi$
$500$	−1.17119	−0.0523773
$501$	−2.46123	−0.109960
$502$	−1.13241	−0.0505417
$503$	−11.7199	−0.522564	−0.261282	−	0.965263i	$-0.584145\pi$
$503$	−11.7199	−0.522564	−0.261282	+	0.965263i	$0.584145\pi$
$504$	2.88702	0.128598
$505$	−7.46288	−0.332094
$506$	5.59766	0.248846
$507$	−12.0822	−0.536591
$508$	−13.4314	−0.595922
$509$	9.36211	0.414968	0.207484	−	0.978238i	$-0.433472\pi$
$509$	9.36211	0.414968	0.207484	+	0.978238i	$0.433472\pi$
$510$	−6.71985	−0.297560
$511$	−5.64068	−0.249529
$512$	3.22743	0.142633
$513$	7.20837	0.318257
$514$	2.75554	0.121542
$515$	−5.33569	−0.235119
$516$	11.7869	0.518887
$517$	77.1031	3.39099
$518$	9.37814	0.412052
$519$	−14.0651	−0.617390
$520$	−2.76576	−0.121287
$521$	−15.9483	−0.698706	−0.349353	−	0.936991i	$-0.613599\pi$
$521$	−15.9483	−0.698706	−0.349353	+	0.936991i	$0.613599\pi$
$522$	5.12913	0.224496
$523$	16.8091	0.735013	0.367506	−	0.930021i	$-0.380212\pi$
$523$	16.8091	0.735013	0.367506	+	0.930021i	$0.380212\pi$
$524$	−3.56378	−0.155684
$525$	1.00000	0.0436436
$526$	16.8612	0.735181
$527$	−26.4328	−1.15143
$528$	−1.75804	−0.0765087
$529$	1.00000	0.0434783
$530$	0.474983	0.0206319
$531$	−6.80974	−0.295518
$532$	−8.44239	−0.366024
$533$	−2.00794	−0.0869736
$534$	10.8524	0.469629
$535$	−14.4972	−0.626767
$536$	−2.99936	−0.129553
$537$	−12.0068	−0.518133
$538$	13.4211	0.578625
$539$	6.14865	0.264841
$540$	−1.17119	−0.0504001
$541$	30.1884	1.29790	0.648950	−	0.760831i	$-0.275208\pi$
$541$	30.1884	1.29790	0.648950	+	0.760831i	$0.275208\pi$
$542$	−19.3924	−0.832974
$543$	11.7464	0.504084
$544$	−40.6985	−1.74493
$545$	−18.5715	−0.795517
$546$	0.872152	0.0373247
$547$	15.0942	0.645380	0.322690	−	0.946505i	$-0.395413\pi$
$547$	15.0942	0.645380	0.322690	+	0.946505i	$0.395413\pi$
$548$	−10.5381	−0.450163
$549$	7.27476	0.310479
$550$	−5.59766	−0.238685
$551$	−40.6120	−1.73013
$552$	−2.88702	−0.122880
$553$	15.4517	0.657073
$554$	−3.06662	−0.130288
$555$	−10.3012	−0.437264
$556$	−16.2253	−0.688107
$557$	−40.7052	−1.72474	−0.862368	−	0.506282i	$-0.831019\pi$
$557$	−40.7052	−1.72474	−0.862368	+	0.506282i	$0.831019\pi$
$558$	3.26014	0.138013
$559$	9.64128	0.407783
$560$	−0.285922	−0.0120824
$561$	45.3850	1.91616
$562$	−0.542196	−0.0228712
$563$	−10.5653	−0.445275	−0.222638	−	0.974901i	$-0.571467\pi$
$563$	−10.5653	−0.445275	−0.222638	+	0.974901i	$0.571467\pi$
$564$	−14.6866	−0.618416
$565$	3.23566	0.136125
$566$	16.8592	0.708646
$567$	1.00000	0.0419961
$568$	−8.55122	−0.358801
$569$	35.9696	1.50792	0.753962	−	0.656918i	$-0.228140\pi$
$569$	35.9696	1.50792	0.753962	+	0.656918i	$0.228140\pi$
$570$	−6.56242	−0.274869
$571$	16.2421	0.679711	0.339856	−	0.940478i	$-0.389622\pi$
$571$	16.2421	0.679711	0.339856	+	0.940478i	$0.389622\pi$
$572$	6.89880	0.288453
$573$	−20.5702	−0.859334
$574$	−1.90815	−0.0796446
$575$	−1.00000	−0.0417029
$576$	5.59149	0.232979
$577$	−30.2443	−1.25909	−0.629543	−	0.776966i	$-0.716758\pi$
$577$	−30.2443	−1.25909	−0.629543	+	0.776966i	$0.716758\pi$
$578$	−34.1246	−1.41940
$579$	20.1396	0.836974
$580$	6.59851	0.273988
$581$	9.16624	0.380280
$582$	−10.7077	−0.443850
$583$	−3.20797	−0.132861
$584$	−16.2847	−0.673867
$585$	−0.958000	−0.0396084
$586$	3.30766	0.136638
$587$	−37.8910	−1.56393	−0.781965	−	0.623322i	$-0.785783\pi$
$587$	−37.8910	−1.56393	−0.781965	+	0.623322i	$0.785783\pi$
$588$	−1.17119	−0.0482992
$589$	−25.8135	−1.06363
$590$	6.19951	0.255230
$591$	−1.85832	−0.0764411
$592$	2.94536	0.121053
$593$	2.83382	0.116371	0.0581855	−	0.998306i	$-0.481469\pi$
$593$	2.83382	0.116371	0.0581855	+	0.998306i	$0.481469\pi$
$594$	−5.59766	−0.229675
$595$	7.38130	0.302604
$596$	11.7312	0.480528
$597$	−4.56622	−0.186883
$598$	−0.872152	−0.0356649
$599$	−48.1172	−1.96602	−0.983008	−	0.183563i	$-0.941237\pi$
$599$	−48.1172	−1.96602	−0.983008	+	0.183563i	$0.941237\pi$
$600$	2.88702	0.117862
$601$	−26.4575	−1.07922	−0.539611	−	0.841914i	$-0.681429\pi$
$601$	−26.4575	−1.07922	−0.539611	+	0.841914i	$0.681429\pi$
$602$	9.16213	0.373420
$603$	−1.03891	−0.0423078
$604$	−18.9541	−0.771232
$605$	26.8059	1.08981
$606$	6.79412	0.275992
$607$	1.71924	0.0697819	0.0348909	−	0.999391i	$-0.488892\pi$
$607$	1.71924	0.0697819	0.0348909	+	0.999391i	$0.488892\pi$
$608$	−39.7450	−1.61187
$609$	−5.63401	−0.228301
$610$	−6.62286	−0.268152
$611$	−12.0132	−0.486001
$612$	−8.64492	−0.349450
$613$	−22.9353	−0.926348	−0.463174	−	0.886267i	$-0.653289\pi$
$613$	−22.9353	−0.926348	−0.463174	+	0.886267i	$0.653289\pi$
$614$	8.41595	0.339640
$615$	2.09597	0.0845178
$616$	17.7513	0.715218
$617$	11.4180	0.459670	0.229835	−	0.973230i	$-0.426181\pi$
$617$	11.4180	0.459670	0.229835	+	0.973230i	$0.426181\pi$
$618$	4.85755	0.195399
$619$	−4.65260	−0.187004	−0.0935019	−	0.995619i	$-0.529806\pi$
$619$	−4.65260	−0.187004	−0.0935019	+	0.995619i	$0.529806\pi$
$620$	4.19410	0.168439
$621$	−1.00000	−0.0401286
$622$	−23.6688	−0.949034
$623$	−11.9206	−0.477590
$624$	0.273914	0.0109653
$625$	1.00000	0.0400000
$626$	−5.29723	−0.211720
$627$	44.3217	1.77004
$628$	7.30496	0.291500
$629$	−76.0366	−3.03178
$630$	−0.910389	−0.0362707
$631$	13.5452	0.539224	0.269612	−	0.962969i	$-0.413105\pi$
$631$	13.5452	0.539224	0.269612	+	0.962969i	$0.413105\pi$
$632$	44.6093	1.77446
$633$	15.3033	0.608252
$634$	5.67874	0.225532
$635$	11.4681	0.455099
$636$	0.611054	0.0242299
$637$	−0.958000	−0.0379573
$638$	31.5372	1.24857
$639$	−2.96196	−0.117173
$640$	5.93704	0.234682
$641$	26.2470	1.03669	0.518347	−	0.855170i	$-0.326548\pi$
$641$	26.2470	1.03669	0.518347	+	0.855170i	$0.326548\pi$
$642$	13.1981	0.520886
$643$	16.1617	0.637354	0.318677	−	0.947863i	$-0.396761\pi$
$643$	16.1617	0.637354	0.318677	+	0.947863i	$0.396761\pi$
$644$	1.17119	0.0461515
$645$	−10.0640	−0.396269
$646$	−48.4392	−1.90581
$647$	−32.4457	−1.27557	−0.637785	−	0.770214i	$-0.720149\pi$
$647$	−32.4457	−1.27557	−0.637785	+	0.770214i	$0.720149\pi$
$648$	2.88702	0.113413
$649$	−41.8707	−1.64357
$650$	0.872152	0.0342086
$651$	−3.58105	−0.140352
$652$	17.1035	0.669826
$653$	8.73339	0.341764	0.170882	−	0.985292i	$-0.445338\pi$
$653$	8.73339	0.341764	0.170882	+	0.985292i	$0.445338\pi$
$654$	16.9073	0.661128
$655$	3.04286	0.118894
$656$	−0.599285	−0.0233982
$657$	−5.64068	−0.220064
$658$	−11.4161	−0.445047
$659$	−16.3484	−0.636845	−0.318423	−	0.947949i	$-0.603153\pi$
$659$	−16.3484	−0.636845	−0.318423	+	0.947949i	$0.603153\pi$
$660$	−7.20125	−0.280308
$661$	−7.27031	−0.282782	−0.141391	−	0.989954i	$-0.545157\pi$
$661$	−7.27031	−0.282782	−0.141391	+	0.989954i	$0.545157\pi$
$662$	−9.92912	−0.385906
$663$	−7.07128	−0.274626
$664$	26.4631	1.02697
$665$	7.20837	0.279529
$666$	9.37814	0.363396
$667$	5.63401	0.218150
$668$	2.88257	0.111530
$669$	−15.6303	−0.604302
$670$	0.945814	0.0365400
$671$	44.7299	1.72678
$672$	−5.51373	−0.212697
$673$	49.6493	1.91384	0.956919	−	0.290355i	$-0.0937734\pi$
$673$	49.6493	1.91384	0.956919	+	0.290355i	$0.0937734\pi$
$674$	−6.53360	−0.251665
$675$	1.00000	0.0384900
$676$	14.1506	0.544255
$677$	−17.1308	−0.658389	−0.329195	−	0.944262i	$-0.606777\pi$
$677$	−17.1308	−0.658389	−0.329195	+	0.944262i	$0.606777\pi$
$678$	−2.94571	−0.113129
$679$	11.7617	0.451374
$680$	21.3099	0.817199
$681$	15.0505	0.576735
$682$	20.0455	0.767581
$683$	10.7480	0.411259	0.205629	−	0.978630i	$-0.434076\pi$
$683$	10.7480	0.411259	0.205629	+	0.978630i	$0.434076\pi$
$684$	−8.44239	−0.322803
$685$	8.99771	0.343785
$686$	−0.910389	−0.0347588
$687$	−11.1333	−0.424762
$688$	2.87752	0.109704
$689$	0.499823	0.0190418
$690$	0.910389	0.0346579
$691$	49.6272	1.88791	0.943953	−	0.330079i	$-0.107075\pi$
$691$	49.6272	1.88791	0.943953	+	0.330079i	$0.107075\pi$
$692$	16.4730	0.626208
$693$	6.14865	0.233568
$694$	6.16382	0.233975
$695$	13.8537	0.525500
$696$	−16.2655	−0.616541
$697$	15.4710	0.586006
$698$	−16.9102	−0.640060
$699$	−12.1308	−0.458828
$700$	−1.17119	−0.0442669
$701$	0.0532155	0.00200992	0.00100496	−	0.999999i	$-0.499680\pi$
$701$	0.0532155	0.00200992	0.00100496	+	0.999999i	$0.499680\pi$
$702$	0.872152	0.0329173
$703$	−74.2552	−2.80059
$704$	34.3801	1.29575
$705$	12.5398	0.472278
$706$	15.5566	0.585482
$707$	−7.46288	−0.280671
$708$	7.97552	0.299738
$709$	22.6909	0.852176	0.426088	−	0.904682i	$-0.359891\pi$
$709$	22.6909	0.852176	0.426088	+	0.904682i	$0.359891\pi$
$710$	2.69653	0.101199
$711$	15.4517	0.579484
$712$	−34.4151	−1.28976
$713$	3.58105	0.134111
$714$	−6.71985	−0.251484
$715$	−5.89040	−0.220289
$716$	14.0623	0.525533
$717$	30.1372	1.12549
$718$	−25.9643	−0.968978
$719$	0.709639	0.0264651	0.0132325	−	0.999912i	$-0.495788\pi$
$719$	0.709639	0.0264651	0.0132325	+	0.999912i	$0.495788\pi$
$720$	−0.285922	−0.0106557
$721$	−5.33569	−0.198711
$722$	−30.0069	−1.11674
$723$	0.328171	0.0122048
$724$	−13.7572	−0.511284
$725$	−5.63401	−0.209242
$726$	−24.4037	−0.905708
$727$	−33.9906	−1.26064	−0.630322	−	0.776334i	$-0.717077\pi$
$727$	−33.9906	−1.26064	−0.630322	+	0.776334i	$0.717077\pi$
$728$	−2.76576	−0.102506
$729$	1.00000	0.0370370
$730$	5.13521	0.190063
$731$	−74.2852	−2.74754
$732$	−8.52014	−0.314914
$733$	25.9303	0.957756	0.478878	−	0.877881i	$-0.341044\pi$
$733$	25.9303	0.957756	0.478878	+	0.877881i	$0.341044\pi$
$734$	5.69136	0.210072
$735$	1.00000	0.0368856
$736$	5.51373	0.203239
$737$	−6.38791	−0.235302
$738$	−1.90815	−0.0702399
$739$	1.80823	0.0665167	0.0332584	−	0.999447i	$-0.489412\pi$
$739$	1.80823	0.0665167	0.0332584	+	0.999447i	$0.489412\pi$
$740$	12.0647	0.443509
$741$	−6.90562	−0.253684
$742$	0.474983	0.0174372
$743$	37.1166	1.36167	0.680837	−	0.732435i	$-0.261616\pi$
$743$	37.1166	1.36167	0.680837	+	0.732435i	$0.261616\pi$
$744$	−10.3385	−0.379029
$745$	−10.0164	−0.366974
$746$	10.6227	0.388925
$747$	9.16624	0.335375
$748$	−53.1546	−1.94352
$749$	−14.4972	−0.529715
$750$	−0.910389	−0.0332427
$751$	−43.6106	−1.59137	−0.795686	−	0.605709i	$-0.792890\pi$
$751$	−43.6106	−1.59137	−0.795686	+	0.605709i	$0.792890\pi$
$752$	−3.58542	−0.130747
$753$	1.24387	0.0453292
$754$	−4.91371	−0.178947
$755$	16.1836	0.588982
$756$	−1.17119	−0.0425959
$757$	−3.82259	−0.138934	−0.0694672	−	0.997584i	$-0.522130\pi$
$757$	−3.82259	−0.138934	−0.0694672	+	0.997584i	$0.522130\pi$
$758$	1.53354	0.0557006
$759$	−6.14865	−0.223182
$760$	20.8107	0.754883
$761$	26.8627	0.973773	0.486887	−	0.873465i	$-0.338132\pi$
$761$	26.8627	0.973773	0.486887	+	0.873465i	$0.338132\pi$
$762$	−10.4405	−0.378218
$763$	−18.5715	−0.672334
$764$	24.0917	0.871608
$765$	7.38130	0.266871
$766$	16.6119	0.600213
$767$	6.52373	0.235558
$768$	−16.5880	−0.598567
$769$	43.1627	1.55649	0.778243	−	0.627963i	$-0.216111\pi$
$769$	43.1627	1.55649	0.778243	+	0.627963i	$0.216111\pi$
$770$	−5.59766	−0.201726
$771$	−3.02678	−0.109007
$772$	−23.5874	−0.848928
$773$	25.3328	0.911156	0.455578	−	0.890196i	$-0.349433\pi$
$773$	25.3328	0.911156	0.455578	+	0.890196i	$0.349433\pi$
$774$	9.16213	0.329326
$775$	−3.58105	−0.128635
$776$	33.9563	1.21896
$777$	−10.3012	−0.369555
$778$	−10.6306	−0.381125
$779$	15.1085	0.541320
$780$	1.12200	0.0401741
$781$	−18.2120	−0.651677
$782$	6.71985	0.240301
$783$	−5.63401	−0.201343
$784$	−0.285922	−0.0102115
$785$	−6.23720	−0.222615
$786$	−2.77019	−0.0988093
$787$	−8.14551	−0.290356	−0.145178	−	0.989406i	$-0.546376\pi$
$787$	−8.14551	−0.290356	−0.145178	+	0.989406i	$0.546376\pi$
$788$	2.17645	0.0775329
$789$	−18.5208	−0.659359
$790$	−14.0670	−0.500483
$791$	3.23566	0.115047
$792$	17.7513	0.630763
$793$	−6.96922	−0.247484
$794$	−4.45923	−0.158252
$795$	−0.521736	−0.0185041
$796$	5.34792	0.189552
$797$	−43.1333	−1.52786	−0.763930	−	0.645299i	$-0.776733\pi$
$797$	−43.1333	−1.52786	−0.763930	+	0.645299i	$0.776733\pi$
$798$	−6.56242	−0.232307
$799$	92.5603	3.27455
$800$	−5.51373	−0.194940
$801$	−11.9206	−0.421195
$802$	−5.58738	−0.197297
$803$	−34.6825	−1.22392
$804$	1.21677	0.0429121
$805$	−1.00000	−0.0352454
$806$	−3.12322	−0.110011
$807$	−14.7422	−0.518949
$808$	−21.5455	−0.757967
$809$	−6.75939	−0.237647	−0.118824	−	0.992915i	$-0.537912\pi$
$809$	−6.75939	−0.237647	−0.118824	+	0.992915i	$0.537912\pi$
$810$	−0.910389	−0.0319878
$811$	−17.8672	−0.627401	−0.313701	−	0.949522i	$-0.601569\pi$
$811$	−17.8672	−0.627401	−0.313701	+	0.949522i	$0.601569\pi$
$812$	6.59851	0.231562
$813$	21.3012	0.747066
$814$	57.6629	2.02108
$815$	−14.6035	−0.511539
$816$	−2.11048	−0.0738815
$817$	−72.5448	−2.53802
$818$	17.1707	0.600358
$819$	−0.958000	−0.0334752
$820$	−2.45479	−0.0857249
$821$	−33.3593	−1.16425	−0.582124	−	0.813100i	$-0.697778\pi$
$821$	−33.3593	−1.16425	−0.582124	+	0.813100i	$0.697778\pi$
$822$	−8.19141	−0.285708
$823$	−46.8917	−1.63454	−0.817271	−	0.576253i	$-0.804514\pi$
$823$	−46.8917	−1.63454	−0.817271	+	0.576253i	$0.804514\pi$
$824$	−15.4042	−0.536632
$825$	6.14865	0.214068
$826$	6.19951	0.215709
$827$	37.9953	1.32123	0.660614	−	0.750726i	$-0.270296\pi$
$827$	37.9953	1.32123	0.660614	+	0.750726i	$0.270296\pi$
$828$	1.17119	0.0407018
$829$	−5.47089	−0.190012	−0.0950059	−	0.995477i	$-0.530287\pi$
$829$	−5.47089	−0.190012	−0.0950059	+	0.995477i	$0.530287\pi$
$830$	−8.34484	−0.289654
$831$	3.36847	0.116851
$832$	−5.35664	−0.185708
$833$	7.38130	0.255747
$834$	−12.6122	−0.436726
$835$	−2.46123	−0.0851743
$836$	−51.9093	−1.79532
$837$	−3.58105	−0.123779
$838$	1.58228	0.0546589
$839$	−3.31418	−0.114418	−0.0572092	−	0.998362i	$-0.518220\pi$
$839$	−3.31418	−0.114418	−0.0572092	+	0.998362i	$0.518220\pi$
$840$	2.88702	0.0996116
$841$	2.74202	0.0945523
$842$	8.25890	0.284620
$843$	0.595566	0.0205124
$844$	−17.9231	−0.616939
$845$	−12.0822	−0.415642
$846$	−11.4161	−0.392495
$847$	26.8059	0.921060
$848$	0.149176	0.00512273
$849$	−18.5187	−0.635560
$850$	−6.71985	−0.230489
$851$	10.3012	0.353122
$852$	3.46902	0.118847
$853$	12.0402	0.412247	0.206124	−	0.978526i	$-0.433915\pi$
$853$	12.0402	0.412247	0.206124	+	0.978526i	$0.433915\pi$
$854$	−6.62286	−0.226630
$855$	7.20837	0.246521
$856$	−41.8536	−1.43053
$857$	−21.5328	−0.735545	−0.367773	−	0.929916i	$-0.619880\pi$
$857$	−21.5328	−0.735545	−0.367773	+	0.929916i	$0.619880\pi$
$858$	5.36255	0.183075
$859$	−24.1410	−0.823681	−0.411840	−	0.911256i	$-0.635114\pi$
$859$	−24.1410	−0.823681	−0.411840	+	0.911256i	$0.635114\pi$
$860$	11.7869	0.401928
$861$	2.09597	0.0714305
$862$	13.5784	0.462482
$863$	2.19350	0.0746677	0.0373339	−	0.999303i	$-0.488114\pi$
$863$	2.19350	0.0746677	0.0373339	+	0.999303i	$0.488114\pi$
$864$	−5.51373	−0.187581
$865$	−14.0651	−0.478228
$866$	−22.3649	−0.759989
$867$	37.4836	1.27301
$868$	4.19410	0.142357
$869$	95.0070	3.22289
$870$	5.12913	0.173894
$871$	0.995278	0.0337237
$872$	−53.6163	−1.81568
$873$	11.7617	0.398074
$874$	6.56242	0.221977
$875$	1.00000	0.0338062
$876$	6.60632	0.223207
$877$	29.8461	1.00783	0.503916	−	0.863753i	$-0.331892\pi$
$877$	29.8461	1.00783	0.503916	+	0.863753i	$0.331892\pi$
$878$	−7.23075	−0.244026
$879$	−3.63324	−0.122546
$880$	−1.75804	−0.0592634
$881$	−43.7768	−1.47488	−0.737438	−	0.675415i	$-0.763965\pi$
$881$	−43.7768	−1.47488	−0.737438	+	0.675415i	$0.763965\pi$
$882$	−0.910389	−0.0306544
$883$	−17.3470	−0.583774	−0.291887	−	0.956453i	$-0.594283\pi$
$883$	−17.3470	−0.583774	−0.291887	+	0.956453i	$0.594283\pi$
$884$	8.28183	0.278548
$885$	−6.80974	−0.228907
$886$	5.55699	0.186691
$887$	−42.9094	−1.44076	−0.720378	−	0.693582i	$-0.756032\pi$
$887$	−42.9094	−1.44076	−0.720378	+	0.693582i	$0.756032\pi$
$888$	−29.7399	−0.998005
$889$	11.4681	0.384629
$890$	10.8524	0.363773
$891$	6.14865	0.205987
$892$	18.3061	0.612933
$893$	90.3918	3.02485
$894$	9.11885	0.304980
$895$	−12.0068	−0.401344
$896$	5.93704	0.198343
$897$	0.958000	0.0319867
$898$	−33.8757	−1.13045
$899$	20.1756	0.672895
$900$	−1.17119	−0.0390398
$901$	−3.85109	−0.128298
$902$	−11.7325	−0.390651
$903$	−10.0640	−0.334908
$904$	9.34141	0.310691
$905$	11.7464	0.390462
$906$	−14.7334	−0.489484
$907$	−41.2635	−1.37013	−0.685066	−	0.728481i	$-0.740226\pi$
$907$	−41.2635	−1.37013	−0.685066	+	0.728481i	$0.740226\pi$
$908$	−17.6270	−0.584972
$909$	−7.46288	−0.247528
$910$	0.872152	0.0289116
$911$	−24.5707	−0.814064	−0.407032	−	0.913414i	$-0.633436\pi$
$911$	−24.5707	−0.814064	−0.407032	+	0.913414i	$0.633436\pi$
$912$	−2.06103	−0.0682477
$913$	56.3600	1.86524
$914$	34.4229	1.13861
$915$	7.27476	0.240496
$916$	13.0392	0.430828
$917$	3.04286	0.100484
$918$	−6.71985	−0.221788
$919$	−7.58773	−0.250296	−0.125148	−	0.992138i	$-0.539941\pi$
$919$	−7.58773	−0.250296	−0.125148	+	0.992138i	$0.539941\pi$
$920$	−2.88702	−0.0951821
$921$	−9.24435	−0.304612
$922$	1.64325	0.0541175
$923$	2.83755	0.0933992
$924$	−7.20125	−0.236904
$925$	−10.3012	−0.338703
$926$	30.1453	0.990636
$927$	−5.33569	−0.175247
$928$	31.0644	1.01974
$929$	−4.18988	−0.137466	−0.0687328	−	0.997635i	$-0.521896\pi$
$929$	−4.18988	−0.137466	−0.0687328	+	0.997635i	$0.521896\pi$
$930$	3.26014	0.106904
$931$	7.20837	0.236245
$932$	14.2075	0.465381
$933$	25.9986	0.851157
$934$	0.854247	0.0279518
$935$	45.3850	1.48425
$936$	−2.76576	−0.0904018
$937$	11.6174	0.379523	0.189761	−	0.981830i	$-0.439229\pi$
$937$	11.6174	0.379523	0.189761	+	0.981830i	$0.439229\pi$
$938$	0.945814	0.0308819
$939$	5.81865	0.189884
$940$	−14.6866	−0.479023
$941$	24.1854	0.788422	0.394211	−	0.919020i	$-0.371018\pi$
$941$	24.1854	0.788422	0.394211	+	0.919020i	$0.371018\pi$
$942$	5.67827	0.185008
$943$	−2.09597	−0.0682542
$944$	1.94706	0.0633713
$945$	1.00000	0.0325300
$946$	56.3347	1.83160
$947$	55.0793	1.78984	0.894918	−	0.446231i	$-0.147234\pi$
$947$	55.0793	1.78984	0.894918	+	0.446231i	$0.147234\pi$
$948$	−18.0969	−0.587760
$949$	5.40377	0.175414
$950$	−6.56242	−0.212913
$951$	−6.23771	−0.202272
$952$	21.3099	0.690659
$953$	−16.1621	−0.523542	−0.261771	−	0.965130i	$-0.584306\pi$
$953$	−16.1621	−0.523542	−0.261771	+	0.965130i	$0.584306\pi$
$954$	0.474983	0.0153781
$955$	−20.5702	−0.665637
$956$	−35.2964	−1.14157
$957$	−34.6415	−1.11980
$958$	−8.68322	−0.280542
$959$	8.99771	0.290551
$960$	5.59149	0.180464
$961$	−18.1761	−0.586326
$962$	−8.98426	−0.289664
$963$	−14.4972	−0.467165
$964$	−0.384352	−0.0123791
$965$	20.1396	0.648317
$966$	0.910389	0.0292913
$967$	−13.7709	−0.442844	−0.221422	−	0.975178i	$-0.571070\pi$
$967$	−13.7709	−0.442844	−0.221422	+	0.975178i	$0.571070\pi$
$968$	77.3890	2.48738
$969$	53.2071	1.70926
$970$	−10.7077	−0.343805
$971$	7.95625	0.255328	0.127664	−	0.991817i	$-0.459252\pi$
$971$	7.95625	0.255328	0.127664	+	0.991817i	$0.459252\pi$
$972$	−1.17119	−0.0375660
$973$	13.8537	0.444128
$974$	−3.48375	−0.111627
$975$	−0.958000	−0.0306805
$976$	−2.08002	−0.0665797
$977$	36.5559	1.16953	0.584763	−	0.811204i	$-0.301187\pi$
$977$	36.5559	1.16953	0.584763	+	0.811204i	$0.301187\pi$
$978$	13.2949	0.425123
$979$	−73.2957	−2.34254
$980$	−1.17119	−0.0374124
$981$	−18.5715	−0.592943
$982$	−2.99555	−0.0955918
$983$	−53.5523	−1.70805	−0.854026	−	0.520230i	$-0.825846\pi$
$983$	−53.5523	−1.70805	−0.854026	+	0.520230i	$0.825846\pi$
$984$	6.05111	0.192902
$985$	−1.85832	−0.0592110
$986$	37.8597	1.20570
$987$	12.5398	0.399148
$988$	8.08781	0.257307
$989$	10.0640	0.320016
$990$	−5.59766	−0.177905
$991$	10.4036	0.330482	0.165241	−	0.986253i	$-0.447160\pi$
$991$	10.4036	0.330482	0.165241	+	0.986253i	$0.447160\pi$
$992$	19.7449	0.626902
$993$	10.9065	0.346106
$994$	2.69653	0.0855288
$995$	−4.56622	−0.144759
$996$	−10.7354	−0.340165
$997$	32.3481	1.02448	0.512238	−	0.858844i	$-0.328817\pi$
$997$	32.3481	1.02448	0.512238	+	0.858844i	$0.328817\pi$
$998$	38.7977	1.22812
$999$	−10.3012	−0.325917

Twists

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

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

\(f(q)\)	\(=\)	\(q-0.910389 q^{2} +1.00000 q^{3} -1.17119 q^{4} +1.00000 q^{5} -0.910389 q^{6} +1.00000 q^{7} +2.88702 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.910389 q^{2} +1.00000 q^{3} -1.17119 q^{4} +1.00000 q^{5} -0.910389 q^{6} +1.00000 q^{7} +2.88702 q^{8} +1.00000 q^{9} -0.910389 q^{10} +6.14865 q^{11} -1.17119 q^{12} -0.958000 q^{13} -0.910389 q^{14} +1.00000 q^{15} -0.285922 q^{16} +7.38130 q^{17} -0.910389 q^{18} +7.20837 q^{19} -1.17119 q^{20} +1.00000 q^{21} -5.59766 q^{22} -1.00000 q^{23} +2.88702 q^{24} +1.00000 q^{25} +0.872152 q^{26} +1.00000 q^{27} -1.17119 q^{28} -5.63401 q^{29} -0.910389 q^{30} -3.58105 q^{31} -5.51373 q^{32} +6.14865 q^{33} -6.71985 q^{34} +1.00000 q^{35} -1.17119 q^{36} -10.3012 q^{37} -6.56242 q^{38} -0.958000 q^{39} +2.88702 q^{40} +2.09597 q^{41} -0.910389 q^{42} -10.0640 q^{43} -7.20125 q^{44} +1.00000 q^{45} +0.910389 q^{46} +12.5398 q^{47} -0.285922 q^{48} +1.00000 q^{49} -0.910389 q^{50} +7.38130 q^{51} +1.12200 q^{52} -0.521736 q^{53} -0.910389 q^{54} +6.14865 q^{55} +2.88702 q^{56} +7.20837 q^{57} +5.12913 q^{58} -6.80974 q^{59} -1.17119 q^{60} +7.27476 q^{61} +3.26014 q^{62} +1.00000 q^{63} +5.59149 q^{64} -0.958000 q^{65} -5.59766 q^{66} -1.03891 q^{67} -8.64492 q^{68} -1.00000 q^{69} -0.910389 q^{70} -2.96196 q^{71} +2.88702 q^{72} -5.64068 q^{73} +9.37814 q^{74} +1.00000 q^{75} -8.44239 q^{76} +6.14865 q^{77} +0.872152 q^{78} +15.4517 q^{79} -0.285922 q^{80} +1.00000 q^{81} -1.90815 q^{82} +9.16624 q^{83} -1.17119 q^{84} +7.38130 q^{85} +9.16213 q^{86} -5.63401 q^{87} +17.7513 q^{88} -11.9206 q^{89} -0.910389 q^{90} -0.958000 q^{91} +1.17119 q^{92} -3.58105 q^{93} -11.4161 q^{94} +7.20837 q^{95} -5.51373 q^{96} +11.7617 q^{97} -0.910389 q^{98} +6.14865 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 2 q^{2} + 10 q^{3} + 16 q^{4} + 10 q^{5} + 2 q^{6} + 10 q^{7} + 6 q^{8} + 10 q^{9}+O(q^{10}) \) 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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