LMFDB - Embedded newform 2415.2.a.v.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("2415.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$19.2838720881$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} - 16x^{8} + 30x^{7} + 83x^{6} - 137x^{5} - 164x^{4} + 208x^{3} + 108x^{2} - 83x - 12 $ x^10 - 2x^9 - 16x^8 + 30x^7 + 83x^6 - 137x^5 - 164x^4 + 208x^3 + 108x^2 - 83*x - 12
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$1.24544$ of defining polynomial
Character	$\chi$	$=$	2415.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.24544 q^{2} +1.00000 q^{3} -0.448869 q^{4} +1.00000 q^{5} +1.24544 q^{6} -1.00000 q^{7} -3.04993 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.24544 q^{2} +1.00000 q^{3} -0.448869 q^{4} +1.00000 q^{5} +1.24544 q^{6} -1.00000 q^{7} -3.04993 q^{8} +1.00000 q^{9} +1.24544 q^{10} -0.513578 q^{11} -0.448869 q^{12} +2.59846 q^{13} -1.24544 q^{14} +1.00000 q^{15} -2.90078 q^{16} +6.83646 q^{17} +1.24544 q^{18} +3.28337 q^{19} -0.448869 q^{20} -1.00000 q^{21} -0.639633 q^{22} +1.00000 q^{23} -3.04993 q^{24} +1.00000 q^{25} +3.23623 q^{26} +1.00000 q^{27} +0.448869 q^{28} +3.52655 q^{29} +1.24544 q^{30} -9.77146 q^{31} +2.48710 q^{32} -0.513578 q^{33} +8.51442 q^{34} -1.00000 q^{35} -0.448869 q^{36} +3.63412 q^{37} +4.08925 q^{38} +2.59846 q^{39} -3.04993 q^{40} -4.10804 q^{41} -1.24544 q^{42} +6.67992 q^{43} +0.230530 q^{44} +1.00000 q^{45} +1.24544 q^{46} -2.57796 q^{47} -2.90078 q^{48} +1.00000 q^{49} +1.24544 q^{50} +6.83646 q^{51} -1.16637 q^{52} +13.4477 q^{53} +1.24544 q^{54} -0.513578 q^{55} +3.04993 q^{56} +3.28337 q^{57} +4.39212 q^{58} -12.0645 q^{59} -0.448869 q^{60} +15.3185 q^{61} -12.1698 q^{62} -1.00000 q^{63} +8.89910 q^{64} +2.59846 q^{65} -0.639633 q^{66} +0.956941 q^{67} -3.06868 q^{68} +1.00000 q^{69} -1.24544 q^{70} +11.3266 q^{71} -3.04993 q^{72} +9.42809 q^{73} +4.52609 q^{74} +1.00000 q^{75} -1.47380 q^{76} +0.513578 q^{77} +3.23623 q^{78} -3.35770 q^{79} -2.90078 q^{80} +1.00000 q^{81} -5.11633 q^{82} +5.30873 q^{83} +0.448869 q^{84} +6.83646 q^{85} +8.31947 q^{86} +3.52655 q^{87} +1.56638 q^{88} -5.91016 q^{89} +1.24544 q^{90} -2.59846 q^{91} -0.448869 q^{92} -9.77146 q^{93} -3.21071 q^{94} +3.28337 q^{95} +2.48710 q^{96} -1.11970 q^{97} +1.24544 q^{98} -0.513578 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	\( 10 q + 2 q^{2} + 10 q^{3} + 16 q^{4} + 10 q^{5} + 2 q^{6} - 10 q^{7} + 6 q^{8} + 10 q^{9} + 2 q^{10} - q^{11} + 16 q^{12} - 2 q^{13} - 2 q^{14} + 10 q^{15} + 36 q^{16} + 8 q^{17} + 2 q^{18} + 11 q^{19} + 16 q^{20} - 10 q^{21} + 10 q^{23} + 6 q^{24} + 10 q^{25} + 15 q^{26} + 10 q^{27} - 16 q^{28} + 6 q^{29} + 2 q^{30} + 16 q^{31} - q^{32} - q^{33} + 21 q^{34} - 10 q^{35} + 16 q^{36} - 6 q^{38} - 2 q^{39} + 6 q^{40} + 23 q^{41} - 2 q^{42} + 4 q^{43} - q^{44} + 10 q^{45} + 2 q^{46} + 21 q^{47} + 36 q^{48} + 10 q^{49} + 2 q^{50} + 8 q^{51} + 10 q^{52} - q^{53} + 2 q^{54} - q^{55} - 6 q^{56} + 11 q^{57} + 8 q^{58} + 15 q^{59} + 16 q^{60} + 29 q^{61} + 12 q^{62} - 10 q^{63} + 80 q^{64} - 2 q^{65} + 32 q^{67} - 28 q^{68} + 10 q^{69} - 2 q^{70} - 4 q^{71} + 6 q^{72} + 18 q^{73} - 49 q^{74} + 10 q^{75} + 49 q^{76} + q^{77} + 15 q^{78} + 8 q^{79} + 36 q^{80} + 10 q^{81} + 6 q^{82} + 2 q^{83} - 16 q^{84} + 8 q^{85} - 14 q^{86} + 6 q^{87} - 69 q^{88} + 6 q^{89} + 2 q^{90} + 2 q^{91} + 16 q^{92} + 16 q^{93} - 2 q^{94} + 11 q^{95} - q^{96} - 2 q^{97} + 2 q^{98} - q^{99}+O(q^{100}) \) 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 - q^11 + 16 * q^12 - 2 * q^13 - 2 * q^14 + 10 * q^15 + 36 * q^16 + 8 * q^17 + 2 * q^18 + 11 * q^19 + 16 * q^20 - 10 * q^21 + 10 * q^23 + 6 * q^24 + 10 * q^25 + 15 * q^26 + 10 * q^27 - 16 * q^28 + 6 * q^29 + 2 * q^30 + 16 * q^31 - q^32 - q^33 + 21 * q^34 - 10 * q^35 + 16 * q^36 - 6 * q^38 - 2 * q^39 + 6 * q^40 + 23 * q^41 - 2 * q^42 + 4 * q^43 - q^44 + 10 * q^45 + 2 * q^46 + 21 * q^47 + 36 * q^48 + 10 * q^49 + 2 * q^50 + 8 * q^51 + 10 * q^52 - q^53 + 2 * q^54 - q^55 - 6 * q^56 + 11 * q^57 + 8 * q^58 + 15 * q^59 + 16 * q^60 + 29 * q^61 + 12 * q^62 - 10 * q^63 + 80 * q^64 - 2 * q^65 + 32 * q^67 - 28 * q^68 + 10 * q^69 - 2 * q^70 - 4 * q^71 + 6 * q^72 + 18 * q^73 - 49 * q^74 + 10 * q^75 + 49 * q^76 + q^77 + 15 * q^78 + 8 * q^79 + 36 * q^80 + 10 * q^81 + 6 * q^82 + 2 * q^83 - 16 * q^84 + 8 * q^85 - 14 * q^86 + 6 * q^87 - 69 * q^88 + 6 * q^89 + 2 * q^90 + 2 * q^91 + 16 * q^92 + 16 * q^93 - 2 * q^94 + 11 * q^95 - q^96 - 2 * q^97 + 2 * q^98 - q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.24544	0.880662	0.440331	−	0.897836i	$-0.354861\pi$
$2$	1.24544	0.880662	0.440331	+	0.897836i	$0.354861\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−0.448869	−0.224435
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	1.24544	0.508450
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−3.04993	−1.07831
$9$	1.00000	0.333333
$10$	1.24544	0.393844
$11$	−0.513578	−0.154850	−0.0774249	−	0.996998i	$-0.524670\pi$
$11$	−0.513578	−0.154850	−0.0774249	+	0.996998i	$0.524670\pi$
$12$	−0.448869	−0.129577
$13$	2.59846	0.720682	0.360341	−	0.932821i	$-0.382660\pi$
$13$	2.59846	0.720682	0.360341	+	0.932821i	$0.382660\pi$
$14$	−1.24544	−0.332859
$15$	1.00000	0.258199
$16$	−2.90078	−0.725194
$17$	6.83646	1.65808	0.829042	−	0.559186i	$-0.188886\pi$
$17$	6.83646	1.65808	0.829042	+	0.559186i	$0.188886\pi$
$18$	1.24544	0.293554
$19$	3.28337	0.753257	0.376628	−	0.926364i	$-0.377083\pi$
$19$	3.28337	0.753257	0.376628	+	0.926364i	$0.377083\pi$
$20$	−0.448869	−0.100370
$21$	−1.00000	−0.218218
$22$	−0.639633	−0.136370
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	−3.04993	−0.622564
$25$	1.00000	0.200000
$26$	3.23623	0.634677
$27$	1.00000	0.192450
$28$	0.448869	0.0848283
$29$	3.52655	0.654864	0.327432	−	0.944875i	$-0.393817\pi$
$29$	3.52655	0.654864	0.327432	+	0.944875i	$0.393817\pi$
$30$	1.24544	0.227386
$31$	−9.77146	−1.75501	−0.877503	−	0.479571i	$-0.840792\pi$
$31$	−9.77146	−1.75501	−0.877503	+	0.479571i	$0.840792\pi$
$32$	2.48710	0.439662
$33$	−0.513578	−0.0894025
$34$	8.51442	1.46021
$35$	−1.00000	−0.169031
$36$	−0.448869	−0.0748116
$37$	3.63412	0.597445	0.298723	−	0.954340i	$-0.403439\pi$
$37$	3.63412	0.597445	0.298723	+	0.954340i	$0.403439\pi$
$38$	4.08925	0.663365
$39$	2.59846	0.416086
$40$	−3.04993	−0.482236
$41$	−4.10804	−0.641567	−0.320784	−	0.947152i	$-0.603946\pi$
$41$	−4.10804	−0.641567	−0.320784	+	0.947152i	$0.603946\pi$
$42$	−1.24544	−0.192176
$43$	6.67992	1.01868	0.509339	−	0.860566i	$-0.329890\pi$
$43$	6.67992	1.01868	0.509339	+	0.860566i	$0.329890\pi$
$44$	0.230530	0.0347537
$45$	1.00000	0.149071
$46$	1.24544	0.183631
$47$	−2.57796	−0.376035	−0.188017	−	0.982166i	$-0.560206\pi$
$47$	−2.57796	−0.376035	−0.188017	+	0.982166i	$0.560206\pi$
$48$	−2.90078	−0.418691
$49$	1.00000	0.142857
$50$	1.24544	0.176132
$51$	6.83646	0.957295
$52$	−1.16637	−0.161746
$53$	13.4477	1.84718	0.923592	−	0.383378i	$-0.125239\pi$
$53$	13.4477	1.84718	0.923592	+	0.383378i	$0.125239\pi$
$54$	1.24544	0.169483
$55$	−0.513578	−0.0692509
$56$	3.04993	0.407564
$57$	3.28337	0.434893
$58$	4.39212	0.576714
$59$	−12.0645	−1.57066	−0.785331	−	0.619076i	$-0.787507\pi$
$59$	−12.0645	−1.57066	−0.785331	+	0.619076i	$0.787507\pi$
$60$	−0.448869	−0.0579488
$61$	15.3185	1.96133	0.980667	−	0.195685i	$-0.0626929\pi$
$61$	15.3185	1.96133	0.980667	+	0.195685i	$0.0626929\pi$
$62$	−12.1698	−1.54557
$63$	−1.00000	−0.125988
$64$	8.89910	1.11239
$65$	2.59846	0.322299
$66$	−0.639633	−0.0787334
$67$	0.956941	0.116909	0.0584545	−	0.998290i	$-0.481383\pi$
$67$	0.956941	0.116909	0.0584545	+	0.998290i	$0.481383\pi$
$68$	−3.06868	−0.372132
$69$	1.00000	0.120386
$70$	−1.24544	−0.148859
$71$	11.3266	1.34421	0.672107	−	0.740454i	$-0.265389\pi$
$71$	11.3266	1.34421	0.672107	+	0.740454i	$0.265389\pi$
$72$	−3.04993	−0.359438
$73$	9.42809	1.10347	0.551737	−	0.834018i	$-0.313965\pi$
$73$	9.42809	1.10347	0.551737	+	0.834018i	$0.313965\pi$
$74$	4.52609	0.526147
$75$	1.00000	0.115470
$76$	−1.47380	−0.169057
$77$	0.513578	0.0585277
$78$	3.23623	0.366431
$79$	−3.35770	−0.377771	−0.188885	−	0.981999i	$-0.560487\pi$
$79$	−3.35770	−0.377771	−0.188885	+	0.981999i	$0.560487\pi$
$80$	−2.90078	−0.324317
$81$	1.00000	0.111111
$82$	−5.11633	−0.565004
$83$	5.30873	0.582709	0.291355	−	0.956615i	$-0.405894\pi$
$83$	5.30873	0.582709	0.291355	+	0.956615i	$0.405894\pi$
$84$	0.448869	0.0489757
$85$	6.83646	0.741518
$86$	8.31947	0.897111
$87$	3.52655	0.378086
$88$	1.56638	0.166976
$89$	−5.91016	−0.626476	−0.313238	−	0.949675i	$-0.601414\pi$
$89$	−5.91016	−0.626476	−0.313238	+	0.949675i	$0.601414\pi$
$90$	1.24544	0.131281
$91$	−2.59846	−0.272392
$92$	−0.448869	−0.0467979
$93$	−9.77146	−1.01325
$94$	−3.21071	−0.331159
$95$	3.28337	0.336867
$96$	2.48710	0.253839
$97$	−1.11970	−0.113688	−0.0568441	−	0.998383i	$-0.518104\pi$
$97$	−1.11970	−0.113688	−0.0568441	+	0.998383i	$0.518104\pi$
$98$	1.24544	0.125809
$99$	−0.513578	−0.0516166
$100$	−0.448869	−0.0448869
$101$	16.6251	1.65426	0.827131	−	0.562009i	$-0.189971\pi$
$101$	16.6251	1.65426	0.827131	+	0.562009i	$0.189971\pi$
$102$	8.51442	0.843053
$103$	−10.1220	−0.997353	−0.498676	−	0.866788i	$-0.666180\pi$
$103$	−10.1220	−0.997353	−0.498676	+	0.866788i	$0.666180\pi$
$104$	−7.92511	−0.777121
$105$	−1.00000	−0.0975900
$106$	16.7484	1.62674
$107$	−2.23019	−0.215601	−0.107800	−	0.994173i	$-0.534381\pi$
$107$	−2.23019	−0.215601	−0.107800	+	0.994173i	$0.534381\pi$
$108$	−0.448869	−0.0431925
$109$	−10.2161	−0.978522	−0.489261	−	0.872138i	$-0.662733\pi$
$109$	−10.2161	−0.978522	−0.489261	+	0.872138i	$0.662733\pi$
$110$	−0.639633	−0.0609866
$111$	3.63412	0.344935
$112$	2.90078	0.274098
$113$	0.659740	0.0620631	0.0310316	−	0.999518i	$-0.490121\pi$
$113$	0.659740	0.0620631	0.0310316	+	0.999518i	$0.490121\pi$
$114$	4.08925	0.382994
$115$	1.00000	0.0932505
$116$	−1.58296	−0.146974
$117$	2.59846	0.240227
$118$	−15.0256	−1.38322
$119$	−6.83646	−0.626697
$120$	−3.04993	−0.278419
$121$	−10.7362	−0.976022
$122$	19.0783	1.72727
$123$	−4.10804	−0.370409
$124$	4.38611	0.393884
$125$	1.00000	0.0894427
$126$	−1.24544	−0.110953
$127$	−11.5796	−1.02752	−0.513762	−	0.857933i	$-0.671749\pi$
$127$	−11.5796	−1.02752	−0.513762	+	0.857933i	$0.671749\pi$
$128$	6.10913	0.539976
$129$	6.67992	0.588134
$130$	3.23623	0.283836
$131$	7.12321	0.622358	0.311179	−	0.950351i	$-0.399276\pi$
$131$	7.12321	0.622358	0.311179	+	0.950351i	$0.399276\pi$
$132$	0.230530	0.0200650
$133$	−3.28337	−0.284704
$134$	1.19182	0.102957
$135$	1.00000	0.0860663
$136$	−20.8507	−1.78793
$137$	−19.8549	−1.69632	−0.848159	−	0.529742i	$-0.822289\pi$
$137$	−19.8549	−1.69632	−0.848159	+	0.529742i	$0.822289\pi$
$138$	1.24544	0.106019
$139$	9.96496	0.845216	0.422608	−	0.906312i	$-0.361115\pi$
$139$	9.96496	0.845216	0.422608	+	0.906312i	$0.361115\pi$
$140$	0.448869	0.0379364
$141$	−2.57796	−0.217104
$142$	14.1066	1.18380
$143$	−1.33451	−0.111597
$144$	−2.90078	−0.241731
$145$	3.52655	0.292864
$146$	11.7422	0.971788
$147$	1.00000	0.0824786
$148$	−1.63124	−0.134087
$149$	−12.7648	−1.04573	−0.522867	−	0.852415i	$-0.675137\pi$
$149$	−12.7648	−1.04573	−0.522867	+	0.852415i	$0.675137\pi$
$150$	1.24544	0.101690
$151$	−1.37398	−0.111813	−0.0559063	−	0.998436i	$-0.517805\pi$
$151$	−1.37398	−0.111813	−0.0559063	+	0.998436i	$0.517805\pi$
$152$	−10.0140	−0.812247
$153$	6.83646	0.552695
$154$	0.639633	0.0515431
$155$	−9.77146	−0.784863
$156$	−1.16637	−0.0933842
$157$	−23.7228	−1.89328	−0.946641	−	0.322289i	$-0.895548\pi$
$157$	−23.7228	−1.89328	−0.946641	+	0.322289i	$0.895548\pi$
$158$	−4.18182	−0.332688
$159$	13.4477	1.06647
$160$	2.48710	0.196623
$161$	−1.00000	−0.0788110
$162$	1.24544	0.0978513
$163$	6.66240	0.521840	0.260920	−	0.965360i	$-0.415974\pi$
$163$	6.66240	0.521840	0.260920	+	0.965360i	$0.415974\pi$
$164$	1.84397	0.143990
$165$	−0.513578	−0.0399820
$166$	6.61173	0.513170
$167$	−10.8967	−0.843214	−0.421607	−	0.906779i	$-0.638534\pi$
$167$	−10.8967	−0.843214	−0.421607	+	0.906779i	$0.638534\pi$
$168$	3.04993	0.235307
$169$	−6.24802	−0.480617
$170$	8.51442	0.653026
$171$	3.28337	0.251086
$172$	−2.99841	−0.228627
$173$	18.8161	1.43056	0.715279	−	0.698839i	$-0.246300\pi$
$173$	18.8161	1.43056	0.715279	+	0.698839i	$0.246300\pi$
$174$	4.39212	0.332966
$175$	−1.00000	−0.0755929
$176$	1.48978	0.112296
$177$	−12.0645	−0.906822
$178$	−7.36078	−0.551714
$179$	−10.1709	−0.760206	−0.380103	−	0.924944i	$-0.624111\pi$
$179$	−10.1709	−0.760206	−0.380103	+	0.924944i	$0.624111\pi$
$180$	−0.448869	−0.0334568
$181$	−13.9159	−1.03436	−0.517180	−	0.855877i	$-0.673018\pi$
$181$	−13.9159	−1.03436	−0.517180	+	0.855877i	$0.673018\pi$
$182$	−3.23623	−0.239885
$183$	15.3185	1.13238
$184$	−3.04993	−0.224844
$185$	3.63412	0.267186
$186$	−12.1698	−0.892334
$187$	−3.51106	−0.256754
$188$	1.15717	0.0843952
$189$	−1.00000	−0.0727393
$190$	4.08925	0.296666
$191$	−11.5540	−0.836015	−0.418007	−	0.908444i	$-0.637271\pi$
$191$	−11.5540	−0.836015	−0.418007	+	0.908444i	$0.637271\pi$
$192$	8.89910	0.642237
$193$	8.49197	0.611265	0.305633	−	0.952150i	$-0.401132\pi$
$193$	8.49197	0.611265	0.305633	+	0.952150i	$0.401132\pi$
$194$	−1.39452	−0.100121
$195$	2.59846	0.186079
$196$	−0.448869	−0.0320621
$197$	17.5745	1.25213	0.626065	−	0.779771i	$-0.284664\pi$
$197$	17.5745	1.25213	0.626065	+	0.779771i	$0.284664\pi$
$198$	−0.639633	−0.0454567
$199$	−11.5756	−0.820576	−0.410288	−	0.911956i	$-0.634572\pi$
$199$	−11.5756	−0.820576	−0.410288	+	0.911956i	$0.634572\pi$
$200$	−3.04993	−0.215663
$201$	0.956941	0.0674974
$202$	20.7057	1.45685
$203$	−3.52655	−0.247515
$204$	−3.06868	−0.214850
$205$	−4.10804	−0.286918
$206$	−12.6064	−0.878330
$207$	1.00000	0.0695048
$208$	−7.53754	−0.522635
$209$	−1.68627	−0.116642
$210$	−1.24544	−0.0859438
$211$	11.2148	0.772061	0.386031	−	0.922486i	$-0.373846\pi$
$211$	11.2148	0.772061	0.386031	+	0.922486i	$0.373846\pi$
$212$	−6.03626	−0.414572
$213$	11.3266	0.776083
$214$	−2.77758	−0.189871
$215$	6.67992	0.455567
$216$	−3.04993	−0.207521
$217$	9.77146	0.663330
$218$	−12.7235	−0.861747
$219$	9.42809	0.637091
$220$	0.230530	0.0155423
$221$	17.7642	1.19495
$222$	4.52609	0.303771
$223$	−20.6615	−1.38360	−0.691798	−	0.722091i	$-0.743181\pi$
$223$	−20.6615	−1.38360	−0.691798	+	0.722091i	$0.743181\pi$
$224$	−2.48710	−0.166177
$225$	1.00000	0.0666667
$226$	0.821669	0.0546566
$227$	−3.27159	−0.217143	−0.108571	−	0.994089i	$-0.534628\pi$
$227$	−3.27159	−0.217143	−0.108571	+	0.994089i	$0.534628\pi$
$228$	−1.47380	−0.0976051
$229$	21.8072	1.44106	0.720530	−	0.693424i	$-0.243899\pi$
$229$	21.8072	1.44106	0.720530	+	0.693424i	$0.243899\pi$
$230$	1.24544	0.0821221
$231$	0.513578	0.0337910
$232$	−10.7557	−0.706148
$233$	−12.2781	−0.804368	−0.402184	−	0.915559i	$-0.631749\pi$
$233$	−12.2781	−0.804368	−0.402184	+	0.915559i	$0.631749\pi$
$234$	3.23623	0.211559
$235$	−2.57796	−0.168168
$236$	5.41538	0.352511
$237$	−3.35770	−0.218106
$238$	−8.51442	−0.551908
$239$	−0.726877	−0.0470178	−0.0235089	−	0.999724i	$-0.507484\pi$
$239$	−0.726877	−0.0470178	−0.0235089	+	0.999724i	$0.507484\pi$
$240$	−2.90078	−0.187244
$241$	16.7541	1.07923	0.539614	−	0.841913i	$-0.318570\pi$
$241$	16.7541	1.07923	0.539614	+	0.841913i	$0.318570\pi$
$242$	−13.3714	−0.859545
$243$	1.00000	0.0641500
$244$	−6.87601	−0.440191
$245$	1.00000	0.0638877
$246$	−5.11633	−0.326205
$247$	8.53170	0.542859
$248$	29.8023	1.89245
$249$	5.30873	0.336427
$250$	1.24544	0.0787688
$251$	3.89139	0.245622	0.122811	−	0.992430i	$-0.460809\pi$
$251$	3.89139	0.245622	0.122811	+	0.992430i	$0.460809\pi$
$252$	0.448869	0.0282761
$253$	−0.513578	−0.0322884
$254$	−14.4218	−0.904901
$255$	6.83646	0.428115
$256$	−10.1896	−0.636852
$257$	−15.6797	−0.978072	−0.489036	−	0.872264i	$-0.662651\pi$
$257$	−15.6797	−0.978072	−0.489036	+	0.872264i	$0.662651\pi$
$258$	8.31947	0.517947
$259$	−3.63412	−0.225813
$260$	−1.16637	−0.0723351
$261$	3.52655	0.218288
$262$	8.87156	0.548087
$263$	−6.12841	−0.377894	−0.188947	−	0.981987i	$-0.560507\pi$
$263$	−6.12841	−0.377894	−0.188947	+	0.981987i	$0.560507\pi$
$264$	1.56638	0.0964039
$265$	13.4477	0.826085
$266$	−4.08925	−0.250728
$267$	−5.91016	−0.361696
$268$	−0.429542	−0.0262384
$269$	−9.15405	−0.558132	−0.279066	−	0.960272i	$-0.590025\pi$
$269$	−9.15405	−0.558132	−0.279066	+	0.960272i	$0.590025\pi$
$270$	1.24544	0.0757953
$271$	−0.635165	−0.0385835	−0.0192918	−	0.999814i	$-0.506141\pi$
$271$	−0.635165	−0.0385835	−0.0192918	+	0.999814i	$0.506141\pi$
$272$	−19.8310	−1.20243
$273$	−2.59846	−0.157266
$274$	−24.7282	−1.49388
$275$	−0.513578	−0.0309699
$276$	−0.448869	−0.0270188
$277$	−0.334446	−0.0200949	−0.0100475	−	0.999950i	$-0.503198\pi$
$277$	−0.334446	−0.0200949	−0.0100475	+	0.999950i	$0.503198\pi$
$278$	12.4108	0.744350
$279$	−9.77146	−0.585002
$280$	3.04993	0.182268
$281$	−9.92415	−0.592025	−0.296013	−	0.955184i	$-0.595657\pi$
$281$	−9.92415	−0.592025	−0.296013	+	0.955184i	$0.595657\pi$
$282$	−3.21071	−0.191195
$283$	−15.7403	−0.935661	−0.467831	−	0.883818i	$-0.654964\pi$
$283$	−15.7403	−0.935661	−0.467831	+	0.883818i	$0.654964\pi$
$284$	−5.08415	−0.301689
$285$	3.28337	0.194490
$286$	−1.66206	−0.0982796
$287$	4.10804	0.242490
$288$	2.48710	0.146554
$289$	29.7371	1.74924
$290$	4.39212	0.257914
$291$	−1.11970	−0.0656379
$292$	−4.23198	−0.247658
$293$	−5.76835	−0.336991	−0.168495	−	0.985702i	$-0.553891\pi$
$293$	−5.76835	−0.336991	−0.168495	+	0.985702i	$0.553891\pi$
$294$	1.24544	0.0726358
$295$	−12.0645	−0.702421
$296$	−11.0838	−0.644233
$297$	−0.513578	−0.0298008
$298$	−15.8978	−0.920937
$299$	2.59846	0.150273
$300$	−0.448869	−0.0259155
$301$	−6.67992	−0.385024
$302$	−1.71121	−0.0984691
$303$	16.6251	0.955089
$304$	−9.52433	−0.546258
$305$	15.3185	0.877135
$306$	8.51442	0.486737
$307$	18.5242	1.05723	0.528615	−	0.848862i	$-0.322712\pi$
$307$	18.5242	1.05723	0.528615	+	0.848862i	$0.322712\pi$
$308$	−0.230530	−0.0131356
$309$	−10.1220	−0.575822
$310$	−12.1698	−0.691199
$311$	−27.4938	−1.55903	−0.779515	−	0.626384i	$-0.784534\pi$
$311$	−27.4938	−1.55903	−0.779515	+	0.626384i	$0.784534\pi$
$312$	−7.92511	−0.448671
$313$	31.4783	1.77926	0.889631	−	0.456681i	$-0.150962\pi$
$313$	31.4783	1.77926	0.889631	+	0.456681i	$0.150962\pi$
$314$	−29.5454	−1.66734
$315$	−1.00000	−0.0563436
$316$	1.50717	0.0847848
$317$	−11.5990	−0.651464	−0.325732	−	0.945462i	$-0.605611\pi$
$317$	−11.5990	−0.651464	−0.325732	+	0.945462i	$0.605611\pi$
$318$	16.7484	0.939201
$319$	−1.81116	−0.101405
$320$	8.89910	0.497475
$321$	−2.23019	−0.124477
$322$	−1.24544	−0.0694059
$323$	22.4466	1.24896
$324$	−0.448869	−0.0249372
$325$	2.59846	0.144136
$326$	8.29765	0.459564
$327$	−10.2161	−0.564950
$328$	12.5292	0.691810
$329$	2.57796	0.142128
$330$	−0.639633	−0.0352106
$331$	32.0508	1.76167	0.880836	−	0.473422i	$-0.156982\pi$
$331$	32.0508	1.76167	0.880836	+	0.473422i	$0.156982\pi$
$332$	−2.38293	−0.130780
$333$	3.63412	0.199148
$334$	−13.5713	−0.742587
$335$	0.956941	0.0522833
$336$	2.90078	0.158250
$337$	10.9882	0.598566	0.299283	−	0.954164i	$-0.403253\pi$
$337$	10.9882	0.598566	0.299283	+	0.954164i	$0.403253\pi$
$338$	−7.78156	−0.423261
$339$	0.659740	0.0358321
$340$	−3.06868	−0.166422
$341$	5.01841	0.271762
$342$	4.08925	0.221122
$343$	−1.00000	−0.0539949
$344$	−20.3733	−1.09845
$345$	1.00000	0.0538382
$346$	23.4343	1.25984
$347$	−10.8796	−0.584050	−0.292025	−	0.956411i	$-0.594329\pi$
$347$	−10.8796	−0.584050	−0.292025	+	0.956411i	$0.594329\pi$
$348$	−1.58296	−0.0848556
$349$	−6.79268	−0.363604	−0.181802	−	0.983335i	$-0.558193\pi$
$349$	−6.79268	−0.363604	−0.181802	+	0.983335i	$0.558193\pi$
$350$	−1.24544	−0.0665718
$351$	2.59846	0.138695
$352$	−1.27732	−0.0680815
$353$	−30.6513	−1.63140	−0.815702	−	0.578472i	$-0.803649\pi$
$353$	−30.6513	−1.63140	−0.815702	+	0.578472i	$0.803649\pi$
$354$	−15.0256	−0.798603
$355$	11.3266	0.601151
$356$	2.65289	0.140603
$357$	−6.83646	−0.361824
$358$	−12.6672	−0.669484
$359$	−15.1730	−0.800802	−0.400401	−	0.916340i	$-0.631129\pi$
$359$	−15.1730	−0.800802	−0.400401	+	0.916340i	$0.631129\pi$
$360$	−3.04993	−0.160745
$361$	−8.21948	−0.432604
$362$	−17.3315	−0.910922
$363$	−10.7362	−0.563506
$364$	1.16637	0.0611343
$365$	9.42809	0.493489
$366$	19.0783	0.997241
$367$	25.0010	1.30504	0.652521	−	0.757771i	$-0.273712\pi$
$367$	25.0010	1.30504	0.652521	+	0.757771i	$0.273712\pi$
$368$	−2.90078	−0.151213
$369$	−4.10804	−0.213856
$370$	4.52609	0.235300
$371$	−13.4477	−0.698170
$372$	4.38611	0.227409
$373$	36.1580	1.87219	0.936094	−	0.351749i	$-0.114413\pi$
$373$	36.1580	1.87219	0.936094	+	0.351749i	$0.114413\pi$
$374$	−4.37282	−0.226113
$375$	1.00000	0.0516398
$376$	7.86260	0.405483
$377$	9.16359	0.471949
$378$	−1.24544	−0.0640587
$379$	−36.2815	−1.86365	−0.931827	−	0.362902i	$-0.881786\pi$
$379$	−36.2815	−1.86365	−0.931827	+	0.362902i	$0.881786\pi$
$380$	−1.47380	−0.0756046
$381$	−11.5796	−0.593241
$382$	−14.3898	−0.736247
$383$	15.8895	0.811917	0.405959	−	0.913891i	$-0.366938\pi$
$383$	15.8895	0.811917	0.405959	+	0.913891i	$0.366938\pi$
$384$	6.10913	0.311755
$385$	0.513578	0.0261744
$386$	10.5763	0.538318
$387$	6.67992	0.339559
$388$	0.502599	0.0255156
$389$	−10.1435	−0.514298	−0.257149	−	0.966372i	$-0.582783\pi$
$389$	−10.1435	−0.514298	−0.257149	+	0.966372i	$0.582783\pi$
$390$	3.23623	0.163873
$391$	6.83646	0.345734
$392$	−3.04993	−0.154045
$393$	7.12321	0.359318
$394$	21.8880	1.10270
$395$	−3.35770	−0.168944
$396$	0.230530	0.0115846
$397$	−27.3807	−1.37420	−0.687099	−	0.726564i	$-0.741116\pi$
$397$	−27.3807	−1.37420	−0.687099	+	0.726564i	$0.741116\pi$
$398$	−14.4168	−0.722650
$399$	−3.28337	−0.164374
$400$	−2.90078	−0.145039
$401$	−32.4155	−1.61875	−0.809376	−	0.587291i	$-0.800195\pi$
$401$	−32.4155	−1.61875	−0.809376	+	0.587291i	$0.800195\pi$
$402$	1.19182	0.0594424
$403$	−25.3907	−1.26480
$404$	−7.46251	−0.371274
$405$	1.00000	0.0496904
$406$	−4.39212	−0.217977
$407$	−1.86640	−0.0925143
$408$	−20.8507	−1.03226
$409$	35.2650	1.74374	0.871872	−	0.489734i	$-0.162906\pi$
$409$	35.2650	1.74374	0.871872	+	0.489734i	$0.162906\pi$
$410$	−5.11633	−0.252677
$411$	−19.8549	−0.979370
$412$	4.54347	0.223841
$413$	12.0645	0.593654
$414$	1.24544	0.0612102
$415$	5.30873	0.260595
$416$	6.46263	0.316857
$417$	9.96496	0.487986
$418$	−2.10015	−0.102722
$419$	32.2756	1.57677	0.788384	−	0.615183i	$-0.210918\pi$
$419$	32.2756	1.57677	0.788384	+	0.615183i	$0.210918\pi$
$420$	0.448869	0.0219026
$421$	−15.1190	−0.736853	−0.368426	−	0.929657i	$-0.620103\pi$
$421$	−15.1190	−0.736853	−0.368426	+	0.929657i	$0.620103\pi$
$422$	13.9674	0.679925
$423$	−2.57796	−0.125345
$424$	−41.0145	−1.99184
$425$	6.83646	0.331617
$426$	14.1066	0.683467
$427$	−15.3185	−0.741314
$428$	1.00106	0.0483883
$429$	−1.33451	−0.0644308
$430$	8.31947	0.401200
$431$	−32.7669	−1.57832	−0.789162	−	0.614185i	$-0.789485\pi$
$431$	−32.7669	−1.57832	−0.789162	+	0.614185i	$0.789485\pi$
$432$	−2.90078	−0.139564
$433$	−22.5352	−1.08297	−0.541487	−	0.840709i	$-0.682138\pi$
$433$	−22.5352	−1.08297	−0.541487	+	0.840709i	$0.682138\pi$
$434$	12.1698	0.584169
$435$	3.52655	0.169085
$436$	4.58568	0.219614
$437$	3.28337	0.157065
$438$	11.7422	0.561062
$439$	15.9307	0.760333	0.380167	−	0.924918i	$-0.375867\pi$
$439$	15.9307	0.760333	0.380167	+	0.924918i	$0.375867\pi$
$440$	1.56638	0.0746741
$441$	1.00000	0.0476190
$442$	22.1244	1.05235
$443$	39.3837	1.87117	0.935587	−	0.353096i	$-0.114871\pi$
$443$	39.3837	1.87117	0.935587	+	0.353096i	$0.114871\pi$
$444$	−1.63124	−0.0774154
$445$	−5.91016	−0.280169
$446$	−25.7327	−1.21848
$447$	−12.7648	−0.603754
$448$	−8.89910	−0.420443
$449$	−13.2470	−0.625165	−0.312582	−	0.949891i	$-0.601194\pi$
$449$	−13.2470	−0.625165	−0.312582	+	0.949891i	$0.601194\pi$
$450$	1.24544	0.0587108
$451$	2.10980	0.0993465
$452$	−0.296137	−0.0139291
$453$	−1.37398	−0.0645550
$454$	−4.07458	−0.191229
$455$	−2.59846	−0.121818
$456$	−10.0140	−0.468951
$457$	−25.3844	−1.18743	−0.593715	−	0.804675i	$-0.702339\pi$
$457$	−25.3844	−1.18743	−0.593715	+	0.804675i	$0.702339\pi$
$458$	27.1596	1.26909
$459$	6.83646	0.319098
$460$	−0.448869	−0.0209286
$461$	−36.5927	−1.70429	−0.852146	−	0.523304i	$-0.824699\pi$
$461$	−36.5927	−1.70429	−0.852146	+	0.523304i	$0.824699\pi$
$462$	0.639633	0.0297584
$463$	16.2626	0.755786	0.377893	−	0.925849i	$-0.376649\pi$
$463$	16.2626	0.755786	0.377893	+	0.925849i	$0.376649\pi$
$464$	−10.2297	−0.474904
$465$	−9.77146	−0.453141
$466$	−15.2917	−0.708376
$467$	22.5008	1.04121	0.520606	−	0.853797i	$-0.325706\pi$
$467$	22.5008	1.04121	0.520606	+	0.853797i	$0.325706\pi$
$468$	−1.16637	−0.0539154
$469$	−0.956941	−0.0441874
$470$	−3.21071	−0.148099
$471$	−23.7228	−1.09309
$472$	36.7958	1.69366
$473$	−3.43066	−0.157742
$474$	−4.18182	−0.192078
$475$	3.28337	0.150651
$476$	3.06868	0.140653
$477$	13.4477	0.615728
$478$	−0.905285	−0.0414068
$479$	4.20541	0.192150	0.0960749	−	0.995374i	$-0.469371\pi$
$479$	4.20541	0.192150	0.0960749	+	0.995374i	$0.469371\pi$
$480$	2.48710	0.113520
$481$	9.44310	0.430568
$482$	20.8663	0.950435
$483$	−1.00000	−0.0455016
$484$	4.81917	0.219053
$485$	−1.11970	−0.0508429
$486$	1.24544	0.0564945
$487$	−7.61192	−0.344929	−0.172464	−	0.985016i	$-0.555173\pi$
$487$	−7.61192	−0.344929	−0.172464	+	0.985016i	$0.555173\pi$
$488$	−46.7204	−2.11493
$489$	6.66240	0.301284
$490$	1.24544	0.0562634
$491$	−4.34856	−0.196248	−0.0981239	−	0.995174i	$-0.531284\pi$
$491$	−4.34856	−0.196248	−0.0981239	+	0.995174i	$0.531284\pi$
$492$	1.84397	0.0831327
$493$	24.1091	1.08582
$494$	10.6257	0.478075
$495$	−0.513578	−0.0230836
$496$	28.3448	1.27272
$497$	−11.3266	−0.508066
$498$	6.61173	0.296279
$499$	8.83646	0.395574	0.197787	−	0.980245i	$-0.436625\pi$
$499$	8.83646	0.395574	0.197787	+	0.980245i	$0.436625\pi$
$500$	−0.448869	−0.0200741
$501$	−10.8967	−0.486830
$502$	4.84651	0.216310
$503$	−38.8186	−1.73084	−0.865419	−	0.501049i	$-0.832948\pi$
$503$	−38.8186	−1.73084	−0.865419	+	0.501049i	$0.832948\pi$
$504$	3.04993	0.135855
$505$	16.6251	0.739808
$506$	−0.639633	−0.0284352
$507$	−6.24802	−0.277484
$508$	5.19773	0.230612
$509$	−15.9459	−0.706789	−0.353395	−	0.935474i	$-0.614973\pi$
$509$	−15.9459	−0.706789	−0.353395	+	0.935474i	$0.614973\pi$
$510$	8.51442	0.377025
$511$	−9.42809	−0.417074
$512$	−24.9089	−1.10083
$513$	3.28337	0.144964
$514$	−19.5282	−0.861351
$515$	−10.1220	−0.446030
$516$	−2.99841	−0.131998
$517$	1.32399	0.0582288
$518$	−4.52609	−0.198865
$519$	18.8161	0.825933
$520$	−7.92511	−0.347539
$521$	44.9257	1.96823	0.984116	−	0.177527i	$-0.0568097\pi$
$521$	44.9257	1.96823	0.984116	+	0.177527i	$0.0568097\pi$
$522$	4.39212	0.192238
$523$	−27.2355	−1.19093	−0.595463	−	0.803383i	$-0.703031\pi$
$523$	−27.2355	−1.19093	−0.595463	+	0.803383i	$0.703031\pi$
$524$	−3.19739	−0.139679
$525$	−1.00000	−0.0436436
$526$	−7.63259	−0.332797
$527$	−66.8022	−2.90995
$528$	1.48978	0.0648342
$529$	1.00000	0.0434783
$530$	16.7484	0.727502
$531$	−12.0645	−0.523554
$532$	1.47380	0.0638975
$533$	−10.6746	−0.462366
$534$	−7.36078	−0.318532
$535$	−2.23019	−0.0964196
$536$	−2.91860	−0.126064
$537$	−10.1709	−0.438905
$538$	−11.4009	−0.491526
$539$	−0.513578	−0.0221214
$540$	−0.448869	−0.0193163
$541$	23.7081	1.01929	0.509645	−	0.860385i	$-0.329777\pi$
$541$	23.7081	1.01929	0.509645	+	0.860385i	$0.329777\pi$
$542$	−0.791062	−0.0339790
$543$	−13.9159	−0.597188
$544$	17.0030	0.728996
$545$	−10.2161	−0.437608
$546$	−3.23623	−0.138498
$547$	18.4904	0.790594	0.395297	−	0.918553i	$-0.370642\pi$
$547$	18.4904	0.790594	0.395297	+	0.918553i	$0.370642\pi$
$548$	8.91225	0.380713
$549$	15.3185	0.653778
$550$	−0.639633	−0.0272740
$551$	11.5790	0.493281
$552$	−3.04993	−0.129814
$553$	3.35770	0.142784
$554$	−0.416534	−0.0176968
$555$	3.63412	0.154260
$556$	−4.47296	−0.189696
$557$	−26.8202	−1.13641	−0.568203	−	0.822888i	$-0.692361\pi$
$557$	−26.8202	−1.13641	−0.568203	+	0.822888i	$0.692361\pi$
$558$	−12.1698	−0.515189
$559$	17.3575	0.734143
$560$	2.90078	0.122580
$561$	−3.51106	−0.148237
$562$	−12.3600	−0.521374
$563$	6.56937	0.276866	0.138433	−	0.990372i	$-0.455793\pi$
$563$	6.56937	0.276866	0.138433	+	0.990372i	$0.455793\pi$
$564$	1.15717	0.0487256
$565$	0.659740	0.0277555
$566$	−19.6036	−0.824001
$567$	−1.00000	−0.0419961
$568$	−34.5452	−1.44948
$569$	−2.92728	−0.122718	−0.0613590	−	0.998116i	$-0.519543\pi$
$569$	−2.92728	−0.122718	−0.0613590	+	0.998116i	$0.519543\pi$
$570$	4.08925	0.171280
$571$	34.2338	1.43264	0.716321	−	0.697771i	$-0.245825\pi$
$571$	34.2338	1.43264	0.716321	+	0.697771i	$0.245825\pi$
$572$	0.599021	0.0250463
$573$	−11.5540	−0.482673
$574$	5.11633	0.213551
$575$	1.00000	0.0417029
$576$	8.89910	0.370796
$577$	−13.3635	−0.556331	−0.278165	−	0.960533i	$-0.589726\pi$
$577$	−13.3635	−0.556331	−0.278165	+	0.960533i	$0.589726\pi$
$578$	37.0359	1.54049
$579$	8.49197	0.352914
$580$	−1.58296	−0.0657289
$581$	−5.30873	−0.220243
$582$	−1.39452	−0.0578048
$583$	−6.90645	−0.286036
$584$	−28.7550	−1.18989
$585$	2.59846	0.107433
$586$	−7.18416	−0.296775
$587$	−27.4290	−1.13212	−0.566058	−	0.824365i	$-0.691532\pi$
$587$	−27.4290	−1.13212	−0.566058	+	0.824365i	$0.691532\pi$
$588$	−0.448869	−0.0185111
$589$	−32.0833	−1.32197
$590$	−15.0256	−0.618595
$591$	17.5745	0.722918
$592$	−10.5418	−0.433264
$593$	42.8174	1.75830	0.879150	−	0.476546i	$-0.158111\pi$
$593$	42.8174	1.75830	0.879150	+	0.476546i	$0.158111\pi$
$594$	−0.639633	−0.0262445
$595$	−6.83646	−0.280267
$596$	5.72973	0.234699
$597$	−11.5756	−0.473760
$598$	3.23623	0.132339
$599$	−5.18595	−0.211892	−0.105946	−	0.994372i	$-0.533787\pi$
$599$	−5.18595	−0.211892	−0.105946	+	0.994372i	$0.533787\pi$
$600$	−3.04993	−0.124513
$601$	4.87661	0.198921	0.0994605	−	0.995042i	$-0.468288\pi$
$601$	4.87661	0.198921	0.0994605	+	0.995042i	$0.468288\pi$
$602$	−8.31947	−0.339076
$603$	0.956941	0.0389697
$604$	0.616736	0.0250946
$605$	−10.7362	−0.436490
$606$	20.7057	0.841110
$607$	2.38934	0.0969804	0.0484902	−	0.998824i	$-0.484559\pi$
$607$	2.38934	0.0969804	0.0484902	+	0.998824i	$0.484559\pi$
$608$	8.16608	0.331178
$609$	−3.52655	−0.142903
$610$	19.0783	0.772459
$611$	−6.69872	−0.271001
$612$	−3.06868	−0.124044
$613$	21.5734	0.871341	0.435671	−	0.900106i	$-0.356511\pi$
$613$	21.5734	0.871341	0.435671	+	0.900106i	$0.356511\pi$
$614$	23.0708	0.931061
$615$	−4.10804	−0.165652
$616$	−1.56638	−0.0631112
$617$	−10.8894	−0.438391	−0.219195	−	0.975681i	$-0.570343\pi$
$617$	−10.8894	−0.438391	−0.219195	+	0.975681i	$0.570343\pi$
$618$	−12.6064	−0.507104
$619$	48.4354	1.94678	0.973391	−	0.229152i	$-0.0735954\pi$
$619$	48.4354	1.94678	0.973391	+	0.229152i	$0.0735954\pi$
$620$	4.38611	0.176150
$621$	1.00000	0.0401286
$622$	−34.2420	−1.37298
$623$	5.91016	0.236786
$624$	−7.53754	−0.301743
$625$	1.00000	0.0400000
$626$	39.2045	1.56693
$627$	−1.68627	−0.0673431
$628$	10.6484	0.424918
$629$	24.8445	0.990615
$630$	−1.24544	−0.0496197
$631$	42.5661	1.69453	0.847265	−	0.531170i	$-0.178247\pi$
$631$	42.5661	1.69453	0.847265	+	0.531170i	$0.178247\pi$
$632$	10.2407	0.407355
$633$	11.2148	0.445750
$634$	−14.4459	−0.573719
$635$	−11.5796	−0.459523
$636$	−6.03626	−0.239353
$637$	2.59846	0.102955
$638$	−2.25570	−0.0893039
$639$	11.3266	0.448072
$640$	6.10913	0.241484
$641$	26.6125	1.05113	0.525565	−	0.850753i	$-0.323854\pi$
$641$	26.6125	1.05113	0.525565	+	0.850753i	$0.323854\pi$
$642$	−2.77758	−0.109622
$643$	−12.8631	−0.507273	−0.253636	−	0.967300i	$-0.581627\pi$
$643$	−12.8631	−0.507273	−0.253636	+	0.967300i	$0.581627\pi$
$644$	0.448869	0.0176879
$645$	6.67992	0.263022
$646$	27.9560	1.09991
$647$	44.0219	1.73068	0.865340	−	0.501185i	$-0.167102\pi$
$647$	44.0219	1.73068	0.865340	+	0.501185i	$0.167102\pi$
$648$	−3.04993	−0.119813
$649$	6.19606	0.243216
$650$	3.23623	0.126935
$651$	9.77146	0.382974
$652$	−2.99055	−0.117119
$653$	−14.0315	−0.549096	−0.274548	−	0.961573i	$-0.588528\pi$
$653$	−14.0315	−0.549096	−0.274548	+	0.961573i	$0.588528\pi$
$654$	−12.7235	−0.497530
$655$	7.12321	0.278327
$656$	11.9165	0.465261
$657$	9.42809	0.367825
$658$	3.21071	0.125166
$659$	−3.12638	−0.121786	−0.0608932	−	0.998144i	$-0.519395\pi$
$659$	−3.12638	−0.121786	−0.0608932	+	0.998144i	$0.519395\pi$
$660$	0.230530	0.00897335
$661$	−16.6293	−0.646804	−0.323402	−	0.946262i	$-0.604827\pi$
$661$	−16.6293	−0.646804	−0.323402	+	0.946262i	$0.604827\pi$
$662$	39.9175	1.55144
$663$	17.7642	0.689906
$664$	−16.1913	−0.628343
$665$	−3.28337	−0.127324
$666$	4.52609	0.175382
$667$	3.52655	0.136549
$668$	4.89121	0.189247
$669$	−20.6615	−0.798819
$670$	1.19182	0.0460439
$671$	−7.86725	−0.303712
$672$	−2.48710	−0.0959421
$673$	17.8900	0.689607	0.344804	−	0.938675i	$-0.387946\pi$
$673$	17.8900	0.689607	0.344804	+	0.938675i	$0.387946\pi$
$674$	13.6852	0.527134
$675$	1.00000	0.0384900
$676$	2.80455	0.107867
$677$	9.64059	0.370518	0.185259	−	0.982690i	$-0.440688\pi$
$677$	9.64059	0.370518	0.185259	+	0.982690i	$0.440688\pi$
$678$	0.821669	0.0315560
$679$	1.11970	0.0429701
$680$	−20.8507	−0.799588
$681$	−3.27159	−0.125368
$682$	6.25015	0.239331
$683$	−20.6009	−0.788272	−0.394136	−	0.919052i	$-0.628956\pi$
$683$	−20.6009	−0.788272	−0.394136	+	0.919052i	$0.628956\pi$
$684$	−1.47380	−0.0563523
$685$	−19.8549	−0.758616
$686$	−1.24544	−0.0475513
$687$	21.8072	0.831996
$688$	−19.3770	−0.738740
$689$	34.9433	1.33123
$690$	1.24544	0.0474132
$691$	−4.99909	−0.190174	−0.0950871	−	0.995469i	$-0.530313\pi$
$691$	−4.99909	−0.190174	−0.0950871	+	0.995469i	$0.530313\pi$
$692$	−8.44595	−0.321067
$693$	0.513578	0.0195092
$694$	−13.5500	−0.514351
$695$	9.96496	0.377992
$696$	−10.7557	−0.407695
$697$	−28.0844	−1.06377
$698$	−8.45991	−0.320212
$699$	−12.2781	−0.464402
$700$	0.448869	0.0169657
$701$	27.0169	1.02042	0.510208	−	0.860051i	$-0.329568\pi$
$701$	27.0169	1.02042	0.510208	+	0.860051i	$0.329568\pi$
$702$	3.23623	0.122144
$703$	11.9322	0.450030
$704$	−4.57039	−0.172253
$705$	−2.57796	−0.0970917
$706$	−38.1745	−1.43672
$707$	−16.6251	−0.625252
$708$	5.41538	0.203522
$709$	0.460881	0.0173087	0.00865437	−	0.999963i	$-0.497245\pi$
$709$	0.460881	0.0173087	0.00865437	+	0.999963i	$0.497245\pi$
$710$	14.1066	0.529411
$711$	−3.35770	−0.125924
$712$	18.0256	0.675537
$713$	−9.77146	−0.365944
$714$	−8.51442	−0.318644
$715$	−1.33451	−0.0499079
$716$	4.56539	0.170617
$717$	−0.726877	−0.0271457
$718$	−18.8972	−0.705236
$719$	−1.93809	−0.0722786	−0.0361393	−	0.999347i	$-0.511506\pi$
$719$	−1.93809	−0.0722786	−0.0361393	+	0.999347i	$0.511506\pi$
$720$	−2.90078	−0.108106
$721$	10.1220	0.376964
$722$	−10.2369	−0.380978
$723$	16.7541	0.623092
$724$	6.24642	0.232146
$725$	3.52655	0.130973
$726$	−13.3714	−0.496259
$727$	8.09802	0.300339	0.150169	−	0.988660i	$-0.452018\pi$
$727$	8.09802	0.300339	0.150169	+	0.988660i	$0.452018\pi$
$728$	7.92511	0.293724
$729$	1.00000	0.0370370
$730$	11.7422	0.434597
$731$	45.6670	1.68905
$732$	−6.87601	−0.254145
$733$	−38.4857	−1.42150	−0.710751	−	0.703444i	$-0.751645\pi$
$733$	−38.4857	−1.42150	−0.710751	+	0.703444i	$0.751645\pi$
$734$	31.1373	1.14930
$735$	1.00000	0.0368856
$736$	2.48710	0.0916759
$737$	−0.491464	−0.0181033
$738$	−5.11633	−0.188335
$739$	2.18045	0.0802090	0.0401045	−	0.999195i	$-0.487231\pi$
$739$	2.18045	0.0802090	0.0401045	+	0.999195i	$0.487231\pi$
$740$	−1.63124	−0.0599657
$741$	8.53170	0.313420
$742$	−16.7484	−0.614851
$743$	5.67180	0.208078	0.104039	−	0.994573i	$-0.466823\pi$
$743$	5.67180	0.208078	0.104039	+	0.994573i	$0.466823\pi$
$744$	29.8023	1.09260
$745$	−12.7648	−0.467666
$746$	45.0327	1.64877
$747$	5.30873	0.194236
$748$	1.57601	0.0576245
$749$	2.23019	0.0814894
$750$	1.24544	0.0454772
$751$	6.94365	0.253377	0.126689	−	0.991943i	$-0.459565\pi$
$751$	6.94365	0.253377	0.126689	+	0.991943i	$0.459565\pi$
$752$	7.47810	0.272698
$753$	3.89139	0.141810
$754$	11.4127	0.415627
$755$	−1.37398	−0.0500041
$756$	0.448869	0.0163252
$757$	−28.4727	−1.03486	−0.517429	−	0.855726i	$-0.673111\pi$
$757$	−28.4727	−1.03486	−0.517429	+	0.855726i	$0.673111\pi$
$758$	−45.1866	−1.64125
$759$	−0.513578	−0.0186417
$760$	−10.0140	−0.363248
$761$	38.3730	1.39102	0.695511	−	0.718516i	$-0.255178\pi$
$761$	38.3730	1.39102	0.695511	+	0.718516i	$0.255178\pi$
$762$	−14.4218	−0.522445
$763$	10.2161	0.369846
$764$	5.18622	0.187631
$765$	6.83646	0.247173
$766$	19.7895	0.715024
$767$	−31.3490	−1.13195
$768$	−10.1896	−0.367687
$769$	32.3392	1.16618	0.583090	−	0.812407i	$-0.301843\pi$
$769$	32.3392	1.16618	0.583090	+	0.812407i	$0.301843\pi$
$770$	0.639633	0.0230508
$771$	−15.6797	−0.564690
$772$	−3.81179	−0.137189
$773$	7.60831	0.273652	0.136826	−	0.990595i	$-0.456310\pi$
$773$	7.60831	0.273652	0.136826	+	0.990595i	$0.456310\pi$
$774$	8.31947	0.299037
$775$	−9.77146	−0.351001
$776$	3.41500	0.122591
$777$	−3.63412	−0.130373
$778$	−12.6332	−0.452923
$779$	−13.4882	−0.483265
$780$	−1.16637	−0.0417627
$781$	−5.81708	−0.208151
$782$	8.51442	0.304475
$783$	3.52655	0.126029
$784$	−2.90078	−0.103599
$785$	−23.7228	−0.846702
$786$	8.87156	0.316438
$787$	−44.2852	−1.57860	−0.789299	−	0.614010i	$-0.789556\pi$
$787$	−44.2852	−1.57860	−0.789299	+	0.614010i	$0.789556\pi$
$788$	−7.88865	−0.281022
$789$	−6.12841	−0.218177
$790$	−4.18182	−0.148783
$791$	−0.659740	−0.0234576
$792$	1.56638	0.0556588
$793$	39.8045	1.41350
$794$	−34.1011	−1.21020
$795$	13.4477	0.476941
$796$	5.19595	0.184166
$797$	−8.88275	−0.314643	−0.157322	−	0.987547i	$-0.550286\pi$
$797$	−8.88275	−0.314643	−0.157322	+	0.987547i	$0.550286\pi$
$798$	−4.08925	−0.144758
$799$	−17.6241	−0.623497
$800$	2.48710	0.0879324
$801$	−5.91016	−0.208825
$802$	−40.3717	−1.42557
$803$	−4.84206	−0.170873
$804$	−0.429542	−0.0151488
$805$	−1.00000	−0.0352454
$806$	−31.6227	−1.11386
$807$	−9.15405	−0.322238
$808$	−50.7055	−1.78381
$809$	−29.9867	−1.05428	−0.527139	−	0.849779i	$-0.676735\pi$
$809$	−29.9867	−1.05428	−0.527139	+	0.849779i	$0.676735\pi$
$810$	1.24544	0.0437604
$811$	46.8307	1.64445	0.822225	−	0.569163i	$-0.192733\pi$
$811$	46.8307	1.64445	0.822225	+	0.569163i	$0.192733\pi$
$812$	1.58296	0.0555510
$813$	−0.635165	−0.0222762
$814$	−2.32450	−0.0814738
$815$	6.66240	0.233374
$816$	−19.8310	−0.694225
$817$	21.9327	0.767326
$818$	43.9206	1.53565
$819$	−2.59846	−0.0907974
$820$	1.84397	0.0643943
$821$	6.58921	0.229965	0.114982	−	0.993368i	$-0.463319\pi$
$821$	6.58921	0.229965	0.114982	+	0.993368i	$0.463319\pi$
$822$	−24.7282	−0.862493
$823$	−32.2561	−1.12438	−0.562189	−	0.827009i	$-0.690041\pi$
$823$	−32.2561	−1.12438	−0.562189	+	0.827009i	$0.690041\pi$
$824$	30.8715	1.07546
$825$	−0.513578	−0.0178805
$826$	15.0256	0.522809
$827$	−42.8135	−1.48877	−0.744386	−	0.667749i	$-0.767258\pi$
$827$	−42.8135	−1.48877	−0.744386	+	0.667749i	$0.767258\pi$
$828$	−0.448869	−0.0155993
$829$	−23.7559	−0.825075	−0.412537	−	0.910941i	$-0.635357\pi$
$829$	−23.7559	−0.825075	−0.412537	+	0.910941i	$0.635357\pi$
$830$	6.61173	0.229496
$831$	−0.334446	−0.0116018
$832$	23.1239	0.801678
$833$	6.83646	0.236869
$834$	12.4108	0.429751
$835$	−10.8967	−0.377097
$836$	0.756914	0.0261784
$837$	−9.77146	−0.337751
$838$	40.1975	1.38860
$839$	−34.8611	−1.20354	−0.601770	−	0.798669i	$-0.705538\pi$
$839$	−34.8611	−1.20354	−0.601770	+	0.798669i	$0.705538\pi$
$840$	3.04993	0.105233
$841$	−16.5634	−0.571153
$842$	−18.8298	−0.648918
$843$	−9.92415	−0.341806
$844$	−5.03400	−0.173277
$845$	−6.24802	−0.214939
$846$	−3.21071	−0.110386
$847$	10.7362	0.368901
$848$	−39.0088	−1.33957
$849$	−15.7403	−0.540204
$850$	8.51442	0.292042
$851$	3.63412	0.124576
$852$	−5.08415	−0.174180
$853$	−9.00983	−0.308491	−0.154245	−	0.988033i	$-0.549295\pi$
$853$	−9.00983	−0.308491	−0.154245	+	0.988033i	$0.549295\pi$
$854$	−19.0783	−0.652847
$855$	3.28337	0.112289
$856$	6.80192	0.232485
$857$	4.87327	0.166468	0.0832338	−	0.996530i	$-0.473475\pi$
$857$	4.87327	0.166468	0.0832338	+	0.996530i	$0.473475\pi$
$858$	−1.66206	−0.0567418
$859$	56.3790	1.92363	0.961814	−	0.273706i	$-0.0882494\pi$
$859$	56.3790	1.92363	0.961814	+	0.273706i	$0.0882494\pi$
$860$	−2.99841	−0.102245
$861$	4.10804	0.140001
$862$	−40.8093	−1.38997
$863$	8.51273	0.289777	0.144888	−	0.989448i	$-0.453718\pi$
$863$	8.51273	0.289777	0.144888	+	0.989448i	$0.453718\pi$
$864$	2.48710	0.0846130
$865$	18.8161	0.639765
$866$	−28.0664	−0.953734
$867$	29.7371	1.00993
$868$	−4.38611	−0.148874
$869$	1.72444	0.0584977
$870$	4.39212	0.148907
$871$	2.48657	0.0842542
$872$	31.1583	1.05515
$873$	−1.11970	−0.0378961
$874$	4.08925	0.138321
$875$	−1.00000	−0.0338062
$876$	−4.23198	−0.142985
$877$	0.689117	0.0232698	0.0116349	−	0.999932i	$-0.496296\pi$
$877$	0.689117	0.0232698	0.0116349	+	0.999932i	$0.496296\pi$
$878$	19.8409	0.669596
$879$	−5.76835	−0.194562
$880$	1.48978	0.0502204
$881$	−52.4384	−1.76669	−0.883347	−	0.468719i	$-0.844716\pi$
$881$	−52.4384	−1.76669	−0.883347	+	0.468719i	$0.844716\pi$
$882$	1.24544	0.0419363
$883$	−30.6601	−1.03179	−0.515897	−	0.856651i	$-0.672541\pi$
$883$	−30.6601	−1.03179	−0.515897	+	0.856651i	$0.672541\pi$
$884$	−7.97382	−0.268189
$885$	−12.0645	−0.405543
$886$	49.0501	1.64787
$887$	−17.4761	−0.586790	−0.293395	−	0.955991i	$-0.594785\pi$
$887$	−17.4761	−0.586790	−0.293395	+	0.955991i	$0.594785\pi$
$888$	−11.0838	−0.371948
$889$	11.5796	0.388368
$890$	−7.36078	−0.246734
$891$	−0.513578	−0.0172055
$892$	9.27431	0.310527
$893$	−8.46441	−0.283251
$894$	−15.8978	−0.531703
$895$	−10.1709	−0.339974
$896$	−6.10913	−0.204092
$897$	2.59846	0.0867599
$898$	−16.4984	−0.550559
$899$	−34.4595	−1.14929
$900$	−0.448869	−0.0149623
$901$	91.9346	3.06278
$902$	2.62764	0.0874907
$903$	−6.67992	−0.222294
$904$	−2.01216	−0.0669234
$905$	−13.9159	−0.462580
$906$	−1.71121	−0.0568511
$907$	7.11311	0.236187	0.118093	−	0.993002i	$-0.462322\pi$
$907$	7.11311	0.236187	0.118093	+	0.993002i	$0.462322\pi$
$908$	1.46852	0.0487344
$909$	16.6251	0.551421
$910$	−3.23623	−0.107280
$911$	−44.2763	−1.46694	−0.733469	−	0.679723i	$-0.762100\pi$
$911$	−44.2763	−1.46694	−0.733469	+	0.679723i	$0.762100\pi$
$912$	−9.52433	−0.315382
$913$	−2.72645	−0.0902323
$914$	−31.6148	−1.04572
$915$	15.3185	0.506414
$916$	−9.78858	−0.323424
$917$	−7.12321	−0.235229
$918$	8.51442	0.281018
$919$	24.1328	0.796067	0.398033	−	0.917371i	$-0.369693\pi$
$919$	24.1328	0.796067	0.398033	+	0.917371i	$0.369693\pi$
$920$	−3.04993	−0.100553
$921$	18.5242	0.610392
$922$	−45.5741	−1.50090
$923$	29.4316	0.968752
$924$	−0.230530	−0.00758387
$925$	3.63412	0.119489
$926$	20.2541	0.665592
$927$	−10.1220	−0.332451
$928$	8.77089	0.287919
$929$	47.9060	1.57174	0.785872	−	0.618389i	$-0.212214\pi$
$929$	47.9060	1.57174	0.785872	+	0.618389i	$0.212214\pi$
$930$	−12.1698	−0.399064
$931$	3.28337	0.107608
$932$	5.51128	0.180528
$933$	−27.4938	−0.900106
$934$	28.0235	0.916956
$935$	−3.51106	−0.114824
$936$	−7.92511	−0.259040
$937$	−29.6109	−0.967347	−0.483674	−	0.875248i	$-0.660698\pi$
$937$	−29.6109	−0.967347	−0.483674	+	0.875248i	$0.660698\pi$
$938$	−1.19182	−0.0389142
$939$	31.4783	1.02726
$940$	1.15717	0.0377427
$941$	−17.4819	−0.569893	−0.284946	−	0.958543i	$-0.591976\pi$
$941$	−17.4819	−0.569893	−0.284946	+	0.958543i	$0.591976\pi$
$942$	−29.5454	−0.962640
$943$	−4.10804	−0.133776
$944$	34.9964	1.13903
$945$	−1.00000	−0.0325300
$946$	−4.27270	−0.138917
$947$	−17.3544	−0.563942	−0.281971	−	0.959423i	$-0.590988\pi$
$947$	−17.3544	−0.563942	−0.281971	+	0.959423i	$0.590988\pi$
$948$	1.50717	0.0489505
$949$	24.4985	0.795254
$950$	4.08925	0.132673
$951$	−11.5990	−0.376123
$952$	20.8507	0.675775
$953$	−19.0365	−0.616652	−0.308326	−	0.951281i	$-0.599769\pi$
$953$	−19.0365	−0.616652	−0.308326	+	0.951281i	$0.599769\pi$
$954$	16.7484	0.542248
$955$	−11.5540	−0.373877
$956$	0.326273	0.0105524
$957$	−1.81116	−0.0585465
$958$	5.23760	0.169219
$959$	19.8549	0.641148
$960$	8.89910	0.287217
$961$	64.4815	2.08005
$962$	11.7609	0.379185
$963$	−2.23019	−0.0718669
$964$	−7.52041	−0.242216
$965$	8.49197	0.273366
$966$	−1.24544	−0.0400715
$967$	−0.435745	−0.0140126	−0.00700630	−	0.999975i	$-0.502230\pi$
$967$	−0.435745	−0.0140126	−0.00700630	+	0.999975i	$0.502230\pi$
$968$	32.7448	1.05246
$969$	22.4466	0.721089
$970$	−1.39452	−0.0447754
$971$	4.94414	0.158665	0.0793325	−	0.996848i	$-0.474721\pi$
$971$	4.94414	0.158665	0.0793325	+	0.996848i	$0.474721\pi$
$972$	−0.448869	−0.0143975
$973$	−9.96496	−0.319462
$974$	−9.48021	−0.303766
$975$	2.59846	0.0832172
$976$	−44.4356	−1.42235
$977$	−41.4751	−1.32690	−0.663452	−	0.748218i	$-0.730910\pi$
$977$	−41.4751	−1.32690	−0.663452	+	0.748218i	$0.730910\pi$
$978$	8.29765	0.265330
$979$	3.03533	0.0970097
$980$	−0.448869	−0.0143386
$981$	−10.2161	−0.326174
$982$	−5.41589	−0.172828
$983$	−13.0214	−0.415317	−0.207658	−	0.978201i	$-0.566584\pi$
$983$	−13.0214	−0.415317	−0.207658	+	0.978201i	$0.566584\pi$
$984$	12.5292	0.399417
$985$	17.5745	0.559970
$986$	30.0265	0.956240
$987$	2.57796	0.0820575
$988$	−3.82962	−0.121836
$989$	6.67992	0.212409
$990$	−0.639633	−0.0203289
$991$	3.97487	0.126266	0.0631330	−	0.998005i	$-0.479891\pi$
$991$	3.97487	0.126266	0.0631330	+	0.998005i	$0.479891\pi$
$992$	−24.3026	−0.771610
$993$	32.0508	1.01710
$994$	−14.1066	−0.447434
$995$	−11.5756	−0.366973
$996$	−2.38293	−0.0755059
$997$	33.8775	1.07291	0.536456	−	0.843928i	$-0.319763\pi$
$997$	33.8775	1.07291	0.536456	+	0.843928i	$0.319763\pi$
$998$	11.0053	0.348367
$999$	3.63412	0.114978

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+1.24544 q^{2} +1.00000 q^{3} -0.448869 q^{4} +1.00000 q^{5} +1.24544 q^{6} -1.00000 q^{7} -3.04993 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.24544 q^{2} +1.00000 q^{3} -0.448869 q^{4} +1.00000 q^{5} +1.24544 q^{6} -1.00000 q^{7} -3.04993 q^{8} +1.00000 q^{9} +1.24544 q^{10} -0.513578 q^{11} -0.448869 q^{12} +2.59846 q^{13} -1.24544 q^{14} +1.00000 q^{15} -2.90078 q^{16} +6.83646 q^{17} +1.24544 q^{18} +3.28337 q^{19} -0.448869 q^{20} -1.00000 q^{21} -0.639633 q^{22} +1.00000 q^{23} -3.04993 q^{24} +1.00000 q^{25} +3.23623 q^{26} +1.00000 q^{27} +0.448869 q^{28} +3.52655 q^{29} +1.24544 q^{30} -9.77146 q^{31} +2.48710 q^{32} -0.513578 q^{33} +8.51442 q^{34} -1.00000 q^{35} -0.448869 q^{36} +3.63412 q^{37} +4.08925 q^{38} +2.59846 q^{39} -3.04993 q^{40} -4.10804 q^{41} -1.24544 q^{42} +6.67992 q^{43} +0.230530 q^{44} +1.00000 q^{45} +1.24544 q^{46} -2.57796 q^{47} -2.90078 q^{48} +1.00000 q^{49} +1.24544 q^{50} +6.83646 q^{51} -1.16637 q^{52} +13.4477 q^{53} +1.24544 q^{54} -0.513578 q^{55} +3.04993 q^{56} +3.28337 q^{57} +4.39212 q^{58} -12.0645 q^{59} -0.448869 q^{60} +15.3185 q^{61} -12.1698 q^{62} -1.00000 q^{63} +8.89910 q^{64} +2.59846 q^{65} -0.639633 q^{66} +0.956941 q^{67} -3.06868 q^{68} +1.00000 q^{69} -1.24544 q^{70} +11.3266 q^{71} -3.04993 q^{72} +9.42809 q^{73} +4.52609 q^{74} +1.00000 q^{75} -1.47380 q^{76} +0.513578 q^{77} +3.23623 q^{78} -3.35770 q^{79} -2.90078 q^{80} +1.00000 q^{81} -5.11633 q^{82} +5.30873 q^{83} +0.448869 q^{84} +6.83646 q^{85} +8.31947 q^{86} +3.52655 q^{87} +1.56638 q^{88} -5.91016 q^{89} +1.24544 q^{90} -2.59846 q^{91} -0.448869 q^{92} -9.77146 q^{93} -3.21071 q^{94} +3.28337 q^{95} +2.48710 q^{96} -1.11970 q^{97} +1.24544 q^{98} -0.513578 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 2 q^{2} + 10 q^{3} + 16 q^{4} + 10 q^{5} + 2 q^{6} - 10 q^{7} + 6 q^{8} + 10 q^{9}+O(q^{10}) \) 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	\( 10 q + 2 q^{2} + 10 q^{3} + 16 q^{4} + 10 q^{5} + 2 q^{6} - 10 q^{7} + 6 q^{8} + 10 q^{9} + 2 q^{10} - q^{11} + 16 q^{12} - 2 q^{13} - 2 q^{14} + 10 q^{15} + 36 q^{16} + 8 q^{17} + 2 q^{18} + 11 q^{19} + 16 q^{20} - 10 q^{21} + 10 q^{23} + 6 q^{24} + 10 q^{25} + 15 q^{26} + 10 q^{27} - 16 q^{28} + 6 q^{29} + 2 q^{30} + 16 q^{31} - q^{32} - q^{33} + 21 q^{34} - 10 q^{35} + 16 q^{36} - 6 q^{38} - 2 q^{39} + 6 q^{40} + 23 q^{41} - 2 q^{42} + 4 q^{43} - q^{44} + 10 q^{45} + 2 q^{46} + 21 q^{47} + 36 q^{48} + 10 q^{49} + 2 q^{50} + 8 q^{51} + 10 q^{52} - q^{53} + 2 q^{54} - q^{55} - 6 q^{56} + 11 q^{57} + 8 q^{58} + 15 q^{59} + 16 q^{60} + 29 q^{61} + 12 q^{62} - 10 q^{63} + 80 q^{64} - 2 q^{65} + 32 q^{67} - 28 q^{68} + 10 q^{69} - 2 q^{70} - 4 q^{71} + 6 q^{72} + 18 q^{73} - 49 q^{74} + 10 q^{75} + 49 q^{76} + q^{77} + 15 q^{78} + 8 q^{79} + 36 q^{80} + 10 q^{81} + 6 q^{82} + 2 q^{83} - 16 q^{84} + 8 q^{85} - 14 q^{86} + 6 q^{87} - 69 q^{88} + 6 q^{89} + 2 q^{90} + 2 q^{91} + 16 q^{92} + 16 q^{93} - 2 q^{94} + 11 q^{95} - q^{96} - 2 q^{97} + 2 q^{98} - q^{99}+O(q^{100}) \) 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 - q^11 + 16 * q^12 - 2 * q^13 - 2 * q^14 + 10 * q^15 + 36 * q^16 + 8 * q^17 + 2 * q^18 + 11 * q^19 + 16 * q^20 - 10 * q^21 + 10 * q^23 + 6 * q^24 + 10 * q^25 + 15 * q^26 + 10 * q^27 - 16 * q^28 + 6 * q^29 + 2 * q^30 + 16 * q^31 - q^32 - q^33 + 21 * q^34 - 10 * q^35 + 16 * q^36 - 6 * q^38 - 2 * q^39 + 6 * q^40 + 23 * q^41 - 2 * q^42 + 4 * q^43 - q^44 + 10 * q^45 + 2 * q^46 + 21 * q^47 + 36 * q^48 + 10 * q^49 + 2 * q^50 + 8 * q^51 + 10 * q^52 - q^53 + 2 * q^54 - q^55 - 6 * q^56 + 11 * q^57 + 8 * q^58 + 15 * q^59 + 16 * q^60 + 29 * q^61 + 12 * q^62 - 10 * q^63 + 80 * q^64 - 2 * q^65 + 32 * q^67 - 28 * q^68 + 10 * q^69 - 2 * q^70 - 4 * q^71 + 6 * q^72 + 18 * q^73 - 49 * q^74 + 10 * q^75 + 49 * q^76 + q^77 + 15 * q^78 + 8 * q^79 + 36 * q^80 + 10 * q^81 + 6 * q^82 + 2 * q^83 - 16 * q^84 + 8 * q^85 - 14 * q^86 + 6 * q^87 - 69 * q^88 + 6 * q^89 + 2 * q^90 + 2 * q^91 + 16 * q^92 + 16 * q^93 - 2 * q^94 + 11 * q^95 - q^96 - 2 * q^97 + 2 * q^98 - q^99

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