LMFDB - Embedded newform 7935.2.a.bq.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7935,2,Mod(1,7935)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7935, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("7935.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7935 = 3 \cdot 5 \cdot 23^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7935.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:	$63.3612940039$
Analytic rank:	$1$
Dimension:	$15$
Coefficient field:	$\mathbb{Q}[x]/(x^{15} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{15} - 21x^{13} + 172x^{11} - 696x^{9} + 1466x^{7} - 1583x^{5} + 803x^{3} - 11x^{2} - 143x + 11 $ x^15 - 21x^13 + 172x^11 - 696x^9 + 1466x^7 - 1583x^5 + 803x^3 - 11x^2 - 143x + 11
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 345)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$0.0791955$ of defining polynomial
Character	$\chi$	$=$	7935.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.0791955 q^{2} -1.00000 q^{3} -1.99373 q^{4} +1.00000 q^{5} -0.0791955 q^{6} -1.92769 q^{7} -0.316285 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.0791955 q^{2} -1.00000 q^{3} -1.99373 q^{4} +1.00000 q^{5} -0.0791955 q^{6} -1.92769 q^{7} -0.316285 q^{8} +1.00000 q^{9} +0.0791955 q^{10} +0.702190 q^{11} +1.99373 q^{12} +0.202244 q^{13} -0.152664 q^{14} -1.00000 q^{15} +3.96241 q^{16} -0.628976 q^{17} +0.0791955 q^{18} +2.05993 q^{19} -1.99373 q^{20} +1.92769 q^{21} +0.0556103 q^{22} +0.316285 q^{24} +1.00000 q^{25} +0.0160169 q^{26} -1.00000 q^{27} +3.84329 q^{28} -4.38757 q^{29} -0.0791955 q^{30} -5.60513 q^{31} +0.946376 q^{32} -0.702190 q^{33} -0.0498121 q^{34} -1.92769 q^{35} -1.99373 q^{36} -0.211397 q^{37} +0.163137 q^{38} -0.202244 q^{39} -0.316285 q^{40} +1.31783 q^{41} +0.152664 q^{42} -6.47631 q^{43} -1.39998 q^{44} +1.00000 q^{45} +4.52947 q^{47} -3.96241 q^{48} -3.28401 q^{49} +0.0791955 q^{50} +0.628976 q^{51} -0.403220 q^{52} -0.0863594 q^{53} -0.0791955 q^{54} +0.702190 q^{55} +0.609700 q^{56} -2.05993 q^{57} -0.347476 q^{58} +7.30129 q^{59} +1.99373 q^{60} +7.77288 q^{61} -0.443901 q^{62} -1.92769 q^{63} -7.84987 q^{64} +0.202244 q^{65} -0.0556103 q^{66} -4.96543 q^{67} +1.25401 q^{68} -0.152664 q^{70} -0.552143 q^{71} -0.316285 q^{72} +15.3268 q^{73} -0.0167417 q^{74} -1.00000 q^{75} -4.10693 q^{76} -1.35360 q^{77} -0.0160169 q^{78} +6.35949 q^{79} +3.96241 q^{80} +1.00000 q^{81} +0.104366 q^{82} +13.8516 q^{83} -3.84329 q^{84} -0.628976 q^{85} -0.512895 q^{86} +4.38757 q^{87} -0.222092 q^{88} -11.9104 q^{89} +0.0791955 q^{90} -0.389864 q^{91} +5.60513 q^{93} +0.358714 q^{94} +2.05993 q^{95} -0.946376 q^{96} +4.06742 q^{97} -0.260079 q^{98} +0.702190 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 15 q - 15 q^{3} + 12 q^{4} + 15 q^{5} + 5 q^{7} + 15 q^{9}+O(q^{10}) $ 15 * q - 15 * q^3 + 12 * q^4 + 15 * q^5 + 5 * q^7 + 15 * q^9	$ 15 q - 15 q^{3} + 12 q^{4} + 15 q^{5} + 5 q^{7} + 15 q^{9} - 13 q^{11} - 12 q^{12} - 24 q^{13} - 15 q^{14} - 15 q^{15} + 2 q^{16} - 2 q^{17} - 13 q^{19} + 12 q^{20} - 5 q^{21} + 9 q^{22} + 15 q^{25} - 9 q^{26} - 15 q^{27} - q^{28} - 3 q^{29} - 22 q^{31} + 13 q^{33} - q^{34} + 5 q^{35} + 12 q^{36} + 6 q^{37} + 17 q^{38} + 24 q^{39} - 20 q^{41} + 15 q^{42} + 4 q^{43} + 18 q^{44} + 15 q^{45} + 7 q^{47} - 2 q^{48} - 10 q^{49} + 2 q^{51} - 55 q^{52} - 4 q^{53} - 13 q^{55} - 25 q^{56} + 13 q^{57} + 2 q^{58} + 9 q^{59} - 12 q^{60} - 13 q^{61} - 7 q^{62} + 5 q^{63} - 26 q^{64} - 24 q^{65} - 9 q^{66} + 32 q^{67} - 27 q^{68} - 15 q^{70} + 14 q^{71} - 43 q^{73} + 11 q^{74} - 15 q^{75} - 88 q^{76} - 21 q^{77} + 9 q^{78} - 33 q^{79} + 2 q^{80} + 15 q^{81} - 35 q^{82} + 12 q^{83} + q^{84} - 2 q^{85} - 77 q^{86} + 3 q^{87} + 37 q^{88} - 29 q^{89} - 20 q^{91} + 22 q^{93} - 20 q^{94} - 13 q^{95} - 18 q^{97} - 19 q^{98} - 13 q^{99}+O(q^{100}) $ 15 * q - 15 * q^3 + 12 * q^4 + 15 * q^5 + 5 * q^7 + 15 * q^9 - 13 * q^11 - 12 * q^12 - 24 * q^13 - 15 * q^14 - 15 * q^15 + 2 * q^16 - 2 * q^17 - 13 * q^19 + 12 * q^20 - 5 * q^21 + 9 * q^22 + 15 * q^25 - 9 * q^26 - 15 * q^27 - q^28 - 3 * q^29 - 22 * q^31 + 13 * q^33 - q^34 + 5 * q^35 + 12 * q^36 + 6 * q^37 + 17 * q^38 + 24 * q^39 - 20 * q^41 + 15 * q^42 + 4 * q^43 + 18 * q^44 + 15 * q^45 + 7 * q^47 - 2 * q^48 - 10 * q^49 + 2 * q^51 - 55 * q^52 - 4 * q^53 - 13 * q^55 - 25 * q^56 + 13 * q^57 + 2 * q^58 + 9 * q^59 - 12 * q^60 - 13 * q^61 - 7 * q^62 + 5 * q^63 - 26 * q^64 - 24 * q^65 - 9 * q^66 + 32 * q^67 - 27 * q^68 - 15 * q^70 + 14 * q^71 - 43 * q^73 + 11 * q^74 - 15 * q^75 - 88 * q^76 - 21 * q^77 + 9 * q^78 - 33 * q^79 + 2 * q^80 + 15 * q^81 - 35 * q^82 + 12 * q^83 + q^84 - 2 * q^85 - 77 * q^86 + 3 * q^87 + 37 * q^88 - 29 * q^89 - 20 * q^91 + 22 * q^93 - 20 * q^94 - 13 * q^95 - 18 * q^97 - 19 * q^98 - 13 * 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 $

$2$	0.0791955	0.0559997	0.0279999	−	0.999608i	$-0.491086\pi$
$2$	0.0791955	0.0559997	0.0279999	+	0.999608i	$0.491086\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.99373	−0.996864
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−0.0791955	−0.0323314
$7$	−1.92769	−0.728598	−0.364299	−	0.931282i	$-0.618691\pi$
$7$	−1.92769	−0.728598	−0.364299	+	0.931282i	$0.618691\pi$
$8$	−0.316285	−0.111824
$9$	1.00000	0.333333
$10$	0.0791955	0.0250438
$11$	0.702190	0.211718	0.105859	−	0.994381i	$-0.466241\pi$
$11$	0.702190	0.211718	0.105859	+	0.994381i	$0.466241\pi$
$12$	1.99373	0.575540
$13$	0.202244	0.0560925	0.0280463	−	0.999607i	$-0.491071\pi$
$13$	0.202244	0.0560925	0.0280463	+	0.999607i	$0.491071\pi$
$14$	−0.152664	−0.0408013
$15$	−1.00000	−0.258199
$16$	3.96241	0.990602
$17$	−0.628976	−0.152549	−0.0762746	−	0.997087i	$-0.524303\pi$
$17$	−0.628976	−0.152549	−0.0762746	+	0.997087i	$0.524303\pi$
$18$	0.0791955	0.0186666
$19$	2.05993	0.472579	0.236290	−	0.971683i	$-0.424069\pi$
$19$	2.05993	0.472579	0.236290	+	0.971683i	$0.424069\pi$
$20$	−1.99373	−0.445811
$21$	1.92769	0.420656
$22$	0.0556103	0.0118562
$23$	0	0
$23$	0	0
$24$	0.316285	0.0645615
$25$	1.00000	0.200000
$26$	0.0160169	0.00314116
$27$	−1.00000	−0.192450
$28$	3.84329	0.726313
$29$	−4.38757	−0.814751	−0.407375	−	0.913261i	$-0.633556\pi$
$29$	−4.38757	−0.814751	−0.407375	+	0.913261i	$0.633556\pi$
$30$	−0.0791955	−0.0144591
$31$	−5.60513	−1.00671	−0.503356	−	0.864079i	$-0.667901\pi$
$31$	−5.60513	−1.00671	−0.503356	+	0.864079i	$0.667901\pi$
$32$	0.946376	0.167297
$33$	−0.702190	−0.122236
$34$	−0.0498121	−0.00854271
$35$	−1.92769	−0.325839
$36$	−1.99373	−0.332288
$37$	−0.211397	−0.0347535	−0.0173767	−	0.999849i	$-0.505531\pi$
$37$	−0.211397	−0.0347535	−0.0173767	+	0.999849i	$0.505531\pi$
$38$	0.163137	0.0264643
$39$	−0.202244	−0.0323850
$40$	−0.316285	−0.0500091
$41$	1.31783	0.205810	0.102905	−	0.994691i	$-0.467186\pi$
$41$	1.31783	0.205810	0.102905	+	0.994691i	$0.467186\pi$
$42$	0.152664	0.0235566
$43$	−6.47631	−0.987629	−0.493814	−	0.869567i	$-0.664398\pi$
$43$	−6.47631	−0.987629	−0.493814	+	0.869567i	$0.664398\pi$
$44$	−1.39998	−0.211054
$45$	1.00000	0.149071
$46$	0	0
$47$	4.52947	0.660691	0.330345	−	0.943860i	$-0.392835\pi$
$47$	4.52947	0.660691	0.330345	+	0.943860i	$0.392835\pi$
$48$	−3.96241	−0.571924
$49$	−3.28401	−0.469145
$50$	0.0791955	0.0111999
$51$	0.628976	0.0880743
$52$	−0.403220	−0.0559166
$53$	−0.0863594	−0.0118624	−0.00593119	−	0.999982i	$-0.501888\pi$
$53$	−0.0863594	−0.0118624	−0.00593119	+	0.999982i	$0.501888\pi$
$54$	−0.0791955	−0.0107771
$55$	0.702190	0.0946832
$56$	0.609700	0.0814746
$57$	−2.05993	−0.272844
$58$	−0.347476	−0.0456258
$59$	7.30129	0.950548	0.475274	−	0.879838i	$-0.342349\pi$
$59$	7.30129	0.950548	0.475274	+	0.879838i	$0.342349\pi$
$60$	1.99373	0.257389
$61$	7.77288	0.995215	0.497607	−	0.867402i	$-0.334212\pi$
$61$	7.77288	0.995215	0.497607	+	0.867402i	$0.334212\pi$
$62$	−0.443901	−0.0563755
$63$	−1.92769	−0.242866
$64$	−7.84987	−0.981233
$65$	0.202244	0.0250853
$66$	−0.0556103	−0.00684515
$67$	−4.96543	−0.606624	−0.303312	−	0.952891i	$-0.598092\pi$
$67$	−4.96543	−0.606624	−0.303312	+	0.952891i	$0.598092\pi$
$68$	1.25401	0.152071
$69$	0	0
$70$	−0.152664	−0.0182469
$71$	−0.552143	−0.0655273	−0.0327636	−	0.999463i	$-0.510431\pi$
$71$	−0.552143	−0.0655273	−0.0327636	+	0.999463i	$0.510431\pi$
$72$	−0.316285	−0.0372746
$73$	15.3268	1.79387	0.896934	−	0.442164i	$-0.145789\pi$
$73$	15.3268	1.79387	0.896934	+	0.442164i	$0.145789\pi$
$74$	−0.0167417	−0.00194619
$75$	−1.00000	−0.115470
$76$	−4.10693	−0.471097
$77$	−1.35360	−0.154257
$78$	−0.0160169	−0.00181355
$79$	6.35949	0.715499	0.357750	−	0.933818i	$-0.383544\pi$
$79$	6.35949	0.715499	0.357750	+	0.933818i	$0.383544\pi$
$80$	3.96241	0.443011
$81$	1.00000	0.111111
$82$	0.104366	0.0115253
$83$	13.8516	1.52041	0.760203	−	0.649686i	$-0.225099\pi$
$83$	13.8516	1.52041	0.760203	+	0.649686i	$0.225099\pi$
$84$	−3.84329	−0.419337
$85$	−0.628976	−0.0682221
$86$	−0.512895	−0.0553069
$87$	4.38757	0.470397
$88$	−0.222092	−0.0236751
$89$	−11.9104	−1.26250	−0.631252	−	0.775578i	$-0.717458\pi$
$89$	−11.9104	−1.26250	−0.631252	+	0.775578i	$0.717458\pi$
$90$	0.0791955	0.00834794
$91$	−0.389864	−0.0408689
$92$	0	0
$93$	5.60513	0.581225
$94$	0.358714	0.0369985
$95$	2.05993	0.211344
$96$	−0.946376	−0.0965891
$97$	4.06742	0.412984	0.206492	−	0.978448i	$-0.433795\pi$
$97$	4.06742	0.412984	0.206492	+	0.978448i	$0.433795\pi$
$98$	−0.260079	−0.0262720
$99$	0.702190	0.0705727
$100$	−1.99373	−0.199373
$101$	4.76216	0.473852	0.236926	−	0.971528i	$-0.423860\pi$
$101$	4.76216	0.473852	0.236926	+	0.971528i	$0.423860\pi$
$102$	0.0498121	0.00493214
$103$	13.7414	1.35398	0.676991	−	0.735991i	$-0.263284\pi$
$103$	13.7414	1.35398	0.676991	+	0.735991i	$0.263284\pi$
$104$	−0.0639670	−0.00627248
$105$	1.92769	0.188123
$106$	−0.00683928	−0.000664290 0
$107$	−6.72302	−0.649939	−0.324970	−	0.945724i	$-0.605354\pi$
$107$	−6.72302	−0.649939	−0.324970	+	0.945724i	$0.605354\pi$
$108$	1.99373	0.191847
$109$	−5.69952	−0.545915	−0.272957	−	0.962026i	$-0.588002\pi$
$109$	−5.69952	−0.545915	−0.272957	+	0.962026i	$0.588002\pi$
$110$	0.0556103	0.00530223
$111$	0.211397	0.0200649
$112$	−7.63829	−0.721751
$113$	3.24001	0.304795	0.152397	−	0.988319i	$-0.451301\pi$
$113$	3.24001	0.304795	0.152397	+	0.988319i	$0.451301\pi$
$114$	−0.163137	−0.0152792
$115$	0	0
$116$	8.74762	0.812196
$117$	0.202244	0.0186975
$118$	0.578230	0.0532304
$119$	1.21247	0.111147
$120$	0.316285	0.0288728
$121$	−10.5069	−0.955175
$122$	0.615577	0.0557317
$123$	−1.31783	−0.118825
$124$	11.1751	1.00355
$125$	1.00000	0.0894427
$126$	−0.152664	−0.0136004
$127$	12.7386	1.13037	0.565184	−	0.824965i	$-0.308805\pi$
$127$	12.7386	1.13037	0.565184	+	0.824965i	$0.308805\pi$
$128$	−2.51443	−0.222246
$129$	6.47631	0.570208
$130$	0.0160169	0.00140477
$131$	3.41280	0.298178	0.149089	−	0.988824i	$-0.452366\pi$
$131$	3.41280	0.298178	0.149089	+	0.988824i	$0.452366\pi$
$132$	1.39998	0.121852
$133$	−3.97090	−0.344320
$134$	−0.393240	−0.0339707
$135$	−1.00000	−0.0860663
$136$	0.198936	0.0170586
$137$	−13.9986	−1.19598	−0.597990	−	0.801503i	$-0.704034\pi$
$137$	−13.9986	−1.19598	−0.597990	+	0.801503i	$0.704034\pi$
$138$	0	0
$139$	8.43073	0.715086	0.357543	−	0.933897i	$-0.383615\pi$
$139$	8.43073	0.715086	0.357543	+	0.933897i	$0.383615\pi$
$140$	3.84329	0.324817
$141$	−4.52947	−0.381450
$142$	−0.0437273	−0.00366951
$143$	0.142014	0.0118758
$144$	3.96241	0.330201
$145$	−4.38757	−0.364368
$146$	1.21382	0.100456
$147$	3.28401	0.270861
$148$	0.421469	0.0346445
$149$	−9.92042	−0.812712	−0.406356	−	0.913715i	$-0.633201\pi$
$149$	−9.92042	−0.812712	−0.406356	+	0.913715i	$0.633201\pi$
$150$	−0.0791955	−0.00646629
$151$	−8.48032	−0.690119	−0.345059	−	0.938581i	$-0.612141\pi$
$151$	−8.48032	−0.690119	−0.345059	+	0.938581i	$0.612141\pi$
$152$	−0.651525	−0.0528456
$153$	−0.628976	−0.0508497
$154$	−0.107199	−0.00863837
$155$	−5.60513	−0.450215
$156$	0.403220	0.0322835
$157$	1.30294	0.103986	0.0519928	−	0.998647i	$-0.483443\pi$
$157$	1.30294	0.103986	0.0519928	+	0.998647i	$0.483443\pi$
$158$	0.503644	0.0400677
$159$	0.0863594	0.00684875
$160$	0.946376	0.0748176
$161$	0	0
$162$	0.0791955	0.00622219
$163$	−3.81931	−0.299152	−0.149576	−	0.988750i	$-0.547791\pi$
$163$	−3.81931	−0.299152	−0.149576	+	0.988750i	$0.547791\pi$
$164$	−2.62739	−0.205165
$165$	−0.702190	−0.0546654
$166$	1.09698	0.0851423
$167$	15.8295	1.22492	0.612462	−	0.790500i	$-0.290179\pi$
$167$	15.8295	1.22492	0.612462	+	0.790500i	$0.290179\pi$
$168$	−0.609700	−0.0470394
$169$	−12.9591	−0.996854
$170$	−0.0498121	−0.00382042
$171$	2.05993	0.157526
$172$	12.9120	0.984532
$173$	6.27485	0.477068	0.238534	−	0.971134i	$-0.423333\pi$
$173$	6.27485	0.477068	0.238534	+	0.971134i	$0.423333\pi$
$174$	0.347476	0.0263421
$175$	−1.92769	−0.145720
$176$	2.78236	0.209728
$177$	−7.30129	−0.548799
$178$	−0.943253	−0.0706998
$179$	−17.3147	−1.29416	−0.647079	−	0.762423i	$-0.724010\pi$
$179$	−17.3147	−1.29416	−0.647079	+	0.762423i	$0.724010\pi$
$180$	−1.99373	−0.148604
$181$	−4.93595	−0.366886	−0.183443	−	0.983030i	$-0.558724\pi$
$181$	−4.93595	−0.366886	−0.183443	+	0.983030i	$0.558724\pi$
$182$	−0.0308755	−0.00228865
$183$	−7.77288	−0.574588
$184$	0	0
$185$	−0.211397	−0.0155422
$186$	0.443901	0.0325484
$187$	−0.441661	−0.0322974
$188$	−9.03053	−0.658619
$189$	1.92769	0.140219
$190$	0.163137	0.0118352
$191$	−23.5194	−1.70181	−0.850904	−	0.525322i	$-0.823945\pi$
$191$	−23.5194	−1.70181	−0.850904	+	0.525322i	$0.823945\pi$
$192$	7.84987	0.566515
$193$	−8.55125	−0.615533	−0.307766	−	0.951462i	$-0.599582\pi$
$193$	−8.55125	−0.615533	−0.307766	+	0.951462i	$0.599582\pi$
$194$	0.322122	0.0231270
$195$	−0.202244	−0.0144830
$196$	6.54743	0.467673
$197$	−16.8793	−1.20260	−0.601299	−	0.799024i	$-0.705350\pi$
$197$	−16.8793	−1.20260	−0.601299	+	0.799024i	$0.705350\pi$
$198$	0.0556103	0.00395205
$199$	6.52006	0.462195	0.231097	−	0.972931i	$-0.425768\pi$
$199$	6.52006	0.462195	0.231097	+	0.972931i	$0.425768\pi$
$200$	−0.316285	−0.0223648
$201$	4.96543	0.350234
$202$	0.377141	0.0265356
$203$	8.45787	0.593626
$204$	−1.25401	−0.0877981
$205$	1.31783	0.0920412
$206$	1.08826	0.0758226
$207$	0	0
$208$	0.801375	0.0555653
$209$	1.44646	0.100054
$210$	0.152664	0.0105348
$211$	19.4339	1.33789	0.668944	−	0.743313i	$-0.266747\pi$
$211$	19.4339	1.33789	0.668944	+	0.743313i	$0.266747\pi$
$212$	0.172177	0.0118252
$213$	0.552143	0.0378322
$214$	−0.532434	−0.0363964
$215$	−6.47631	−0.441681
$216$	0.316285	0.0215205
$217$	10.8050	0.733488
$218$	−0.451376	−0.0305711
$219$	−15.3268	−1.03569
$220$	−1.39998	−0.0943863
$221$	−0.127207	−0.00855687
$222$	0.0167417	0.00112363
$223$	−17.2099	−1.15246	−0.576229	−	0.817288i	$-0.695476\pi$
$223$	−17.2099	−1.15246	−0.576229	+	0.817288i	$0.695476\pi$
$224$	−1.82432	−0.121892
$225$	1.00000	0.0666667
$226$	0.256595	0.0170684
$227$	−21.4471	−1.42349	−0.711746	−	0.702436i	$-0.752095\pi$
$227$	−21.4471	−1.42349	−0.711746	+	0.702436i	$0.752095\pi$
$228$	4.10693	0.271988
$229$	−16.9490	−1.12002	−0.560010	−	0.828486i	$-0.689203\pi$
$229$	−16.9490	−1.12002	−0.560010	+	0.828486i	$0.689203\pi$
$230$	0	0
$231$	1.35360	0.0890606
$232$	1.38772	0.0911085
$233$	−29.7925	−1.95177	−0.975886	−	0.218281i	$-0.929955\pi$
$233$	−29.7925	−1.95177	−0.975886	+	0.218281i	$0.929955\pi$
$234$	0.0160169	0.00104705
$235$	4.52947	0.295470
$236$	−14.5568	−0.947567
$237$	−6.35949	−0.413094
$238$	0.0960223	0.00622420
$239$	6.96610	0.450600	0.225300	−	0.974289i	$-0.427664\pi$
$239$	6.96610	0.450600	0.225300	+	0.974289i	$0.427664\pi$
$240$	−3.96241	−0.255772
$241$	28.7894	1.85449	0.927243	−	0.374461i	$-0.122172\pi$
$241$	28.7894	1.85449	0.927243	+	0.374461i	$0.122172\pi$
$242$	−0.832102	−0.0534895
$243$	−1.00000	−0.0641500
$244$	−15.4970	−0.992094
$245$	−3.28401	−0.209808
$246$	−0.104366	−0.00665415
$247$	0.416608	0.0265082
$248$	1.77282	0.112574
$249$	−13.8516	−0.877807
$250$	0.0791955	0.00500877
$251$	23.4134	1.47784	0.738919	−	0.673794i	$-0.235337\pi$
$251$	23.4134	1.47784	0.738919	+	0.673794i	$0.235337\pi$
$252$	3.84329	0.242104
$253$	0	0
$254$	1.00884	0.0633003
$255$	0.628976	0.0393880
$256$	15.5006	0.968788
$257$	−12.5063	−0.780118	−0.390059	−	0.920790i	$-0.627545\pi$
$257$	−12.5063	−0.780118	−0.390059	+	0.920790i	$0.627545\pi$
$258$	0.512895	0.0319315
$259$	0.407508	0.0253213
$260$	−0.403220	−0.0250067
$261$	−4.38757	−0.271584
$262$	0.270278	0.0166979
$263$	15.6431	0.964594	0.482297	−	0.876008i	$-0.339803\pi$
$263$	15.6431	0.964594	0.482297	+	0.876008i	$0.339803\pi$
$264$	0.222092	0.0136688
$265$	−0.0863594	−0.00530502
$266$	−0.314477	−0.0192818
$267$	11.9104	0.728907
$268$	9.89971	0.604721
$269$	−30.5760	−1.86425	−0.932127	−	0.362132i	$-0.882049\pi$
$269$	−30.5760	−1.86425	−0.932127	+	0.362132i	$0.882049\pi$
$270$	−0.0791955	−0.00481969
$271$	−30.8842	−1.87608	−0.938040	−	0.346527i	$-0.887361\pi$
$271$	−30.8842	−1.87608	−0.938040	+	0.346527i	$0.887361\pi$
$272$	−2.49226	−0.151116
$273$	0.389864	0.0235957
$274$	−1.10863	−0.0669746
$275$	0.702190	0.0423436
$276$	0	0
$277$	1.78368	0.107171	0.0535854	−	0.998563i	$-0.482935\pi$
$277$	1.78368	0.107171	0.0535854	+	0.998563i	$0.482935\pi$
$278$	0.667677	0.0400446
$279$	−5.60513	−0.335570
$280$	0.609700	0.0364366
$281$	−2.81479	−0.167916	−0.0839582	−	0.996469i	$-0.526756\pi$
$281$	−2.81479	−0.167916	−0.0839582	+	0.996469i	$0.526756\pi$
$282$	−0.358714	−0.0213611
$283$	16.1119	0.957754	0.478877	−	0.877882i	$-0.341044\pi$
$283$	16.1119	0.957754	0.478877	+	0.877882i	$0.341044\pi$
$284$	1.10082	0.0653218
$285$	−2.05993	−0.122019
$286$	0.0112469	0.000665041 0
$287$	−2.54037	−0.149953
$288$	0.946376	0.0557657
$289$	−16.6044	−0.976729
$290$	−0.347476	−0.0204045
$291$	−4.06742	−0.238437
$292$	−30.5575	−1.78824
$293$	−7.63275	−0.445910	−0.222955	−	0.974829i	$-0.571570\pi$
$293$	−7.63275	−0.445910	−0.222955	+	0.974829i	$0.571570\pi$
$294$	0.260079	0.0151681
$295$	7.30129	0.425098
$296$	0.0668619	0.00388627
$297$	−0.702190	−0.0407452
$298$	−0.785653	−0.0455117
$299$	0	0
$300$	1.99373	0.115108
$301$	12.4843	0.719585
$302$	−0.671604	−0.0386465
$303$	−4.76216	−0.273579
$304$	8.16227	0.468138
$305$	7.77288	0.445074
$306$	−0.0498121	−0.00284757
$307$	13.6608	0.779660	0.389830	−	0.920887i	$-0.372534\pi$
$307$	13.6608	0.779660	0.389830	+	0.920887i	$0.372534\pi$
$308$	2.69872	0.153774
$309$	−13.7414	−0.781722
$310$	−0.443901	−0.0252119
$311$	−26.5240	−1.50404	−0.752018	−	0.659143i	$-0.770919\pi$
$311$	−26.5240	−1.50404	−0.752018	+	0.659143i	$0.770919\pi$
$312$	0.0639670	0.00362142
$313$	−1.90802	−0.107848	−0.0539238	−	0.998545i	$-0.517173\pi$
$313$	−1.90802	−0.107848	−0.0539238	+	0.998545i	$0.517173\pi$
$314$	0.103187	0.00582316
$315$	−1.92769	−0.108613
$316$	−12.6791	−0.713255
$317$	−1.59205	−0.0894185	−0.0447092	−	0.999000i	$-0.514236\pi$
$317$	−1.59205	−0.0894185	−0.0447092	+	0.999000i	$0.514236\pi$
$318$	0.00683928	0.000383528 0
$319$	−3.08090	−0.172498
$320$	−7.84987	−0.438821
$321$	6.72302	0.375243
$322$	0	0
$323$	−1.29564	−0.0720916
$324$	−1.99373	−0.110763
$325$	0.202244	0.0112185
$326$	−0.302473	−0.0167524
$327$	5.69952	0.315184
$328$	−0.416810	−0.0230145
$329$	−8.73141	−0.481378
$330$	−0.0556103	−0.00306125
$331$	−29.1250	−1.60086	−0.800428	−	0.599429i	$-0.795394\pi$
$331$	−29.1250	−1.60086	−0.800428	+	0.599429i	$0.795394\pi$
$332$	−27.6162	−1.51564
$333$	−0.211397	−0.0115845
$334$	1.25363	0.0685954
$335$	−4.96543	−0.271290
$336$	7.63829	0.416703
$337$	17.8316	0.971350	0.485675	−	0.874139i	$-0.338574\pi$
$337$	17.8316	0.971350	0.485675	+	0.874139i	$0.338574\pi$
$338$	−1.02630	−0.0558235
$339$	−3.24001	−0.175973
$340$	1.25401	0.0680081
$341$	−3.93586	−0.213139
$342$	0.163137	0.00882144
$343$	19.8244	1.07042
$344$	2.04836	0.110440
$345$	0	0
$346$	0.496940	0.0267157
$347$	−7.94157	−0.426326	−0.213163	−	0.977017i	$-0.568377\pi$
$347$	−7.94157	−0.426326	−0.213163	+	0.977017i	$0.568377\pi$
$348$	−8.74762	−0.468921
$349$	12.7001	0.679822	0.339911	−	0.940458i	$-0.389603\pi$
$349$	12.7001	0.679822	0.339911	+	0.940458i	$0.389603\pi$
$350$	−0.152664	−0.00816026
$351$	−0.202244	−0.0107950
$352$	0.664535	0.0354199
$353$	9.32881	0.496522	0.248261	−	0.968693i	$-0.420141\pi$
$353$	9.32881	0.496522	0.248261	+	0.968693i	$0.420141\pi$
$354$	−0.578230	−0.0307326
$355$	−0.552143	−0.0293047
$356$	23.7462	1.25854
$357$	−1.21247	−0.0641708
$358$	−1.37124	−0.0724725
$359$	30.4273	1.60589	0.802944	−	0.596054i	$-0.203266\pi$
$359$	30.4273	1.60589	0.802944	+	0.596054i	$0.203266\pi$
$360$	−0.316285	−0.0166697
$361$	−14.7567	−0.776669
$362$	−0.390905	−0.0205455
$363$	10.5069	0.551471
$364$	0.777284	0.0407407
$365$	15.3268	0.802242
$366$	−0.615577	−0.0321767
$367$	−15.0369	−0.784922	−0.392461	−	0.919769i	$-0.628376\pi$
$367$	−15.0369	−0.784922	−0.392461	+	0.919769i	$0.628376\pi$
$368$	0	0
$369$	1.31783	0.0686035
$370$	−0.0167417	−0.000870361 0
$371$	0.166474	0.00864291
$372$	−11.1751	−0.579402
$373$	−17.5589	−0.909166	−0.454583	−	0.890704i	$-0.650212\pi$
$373$	−17.5589	−0.909166	−0.454583	+	0.890704i	$0.650212\pi$
$374$	−0.0349776	−0.00180865
$375$	−1.00000	−0.0516398
$376$	−1.43260	−0.0738810
$377$	−0.887361	−0.0457014
$378$	0.152664	0.00785221
$379$	−16.2697	−0.835719	−0.417859	−	0.908512i	$-0.637220\pi$
$379$	−16.2697	−0.835719	−0.417859	+	0.908512i	$0.637220\pi$
$380$	−4.10693	−0.210681
$381$	−12.7386	−0.652619
$382$	−1.86264	−0.0953007
$383$	2.60840	0.133283	0.0666414	−	0.997777i	$-0.478772\pi$
$383$	2.60840	0.133283	0.0666414	+	0.997777i	$0.478772\pi$
$384$	2.51443	0.128314
$385$	−1.35360	−0.0689860
$386$	−0.677221	−0.0344697
$387$	−6.47631	−0.329210
$388$	−8.10933	−0.411689
$389$	−4.89704	−0.248290	−0.124145	−	0.992264i	$-0.539619\pi$
$389$	−4.89704	−0.248290	−0.124145	+	0.992264i	$0.539619\pi$
$390$	−0.0160169	−0.000811045 0
$391$	0	0
$392$	1.03869	0.0524615
$393$	−3.41280	−0.172153
$394$	−1.33676	−0.0673452
$395$	6.35949	0.319981
$396$	−1.39998	−0.0703514
$397$	5.55080	0.278587	0.139293	−	0.990251i	$-0.455517\pi$
$397$	5.55080	0.278587	0.139293	+	0.990251i	$0.455517\pi$
$398$	0.516360	0.0258828
$399$	3.97090	0.198794
$400$	3.96241	0.198120
$401$	−13.3353	−0.665935	−0.332968	−	0.942938i	$-0.608050\pi$
$401$	−13.3353	−0.665935	−0.332968	+	0.942938i	$0.608050\pi$
$402$	0.393240	0.0196130
$403$	−1.13361	−0.0564689
$404$	−9.49444	−0.472366
$405$	1.00000	0.0496904
$406$	0.669826	0.0332429
$407$	−0.148441	−0.00735794
$408$	−0.198936	−0.00984880
$409$	−22.4344	−1.10931	−0.554655	−	0.832081i	$-0.687150\pi$
$409$	−22.4344	−1.10931	−0.554655	+	0.832081i	$0.687150\pi$
$410$	0.104366	0.00515428
$411$	13.9986	0.690500
$412$	−27.3966	−1.34974
$413$	−14.0746	−0.692567
$414$	0	0
$415$	13.8516	0.679946
$416$	0.191399	0.00938412
$417$	−8.43073	−0.412855
$418$	0.114553	0.00560297
$419$	15.9309	0.778274	0.389137	−	0.921180i	$-0.372773\pi$
$419$	15.9309	0.778274	0.389137	+	0.921180i	$0.372773\pi$
$420$	−3.84329	−0.187533
$421$	−12.8838	−0.627917	−0.313958	−	0.949437i	$-0.601655\pi$
$421$	−12.8838	−0.627917	−0.313958	+	0.949437i	$0.601655\pi$
$422$	1.53908	0.0749213
$423$	4.52947	0.220230
$424$	0.0273142	0.00132650
$425$	−0.628976	−0.0305098
$426$	0.0437273	0.00211859
$427$	−14.9837	−0.725112
$428$	13.4039	0.647901
$429$	−0.142014	−0.00685650
$430$	−0.512895	−0.0247340
$431$	−28.6683	−1.38091	−0.690453	−	0.723377i	$-0.742589\pi$
$431$	−28.6683	−1.38091	−0.690453	+	0.723377i	$0.742589\pi$
$432$	−3.96241	−0.190641
$433$	39.8345	1.91432	0.957162	−	0.289554i	$-0.0935069\pi$
$433$	39.8345	1.91432	0.957162	+	0.289554i	$0.0935069\pi$
$434$	0.855704	0.0410751
$435$	4.38757	0.210368
$436$	11.3633	0.544203
$437$	0	0
$438$	−1.21382	−0.0579984
$439$	−12.9227	−0.616765	−0.308382	−	0.951262i	$-0.599788\pi$
$439$	−12.9227	−0.616765	−0.308382	+	0.951262i	$0.599788\pi$
$440$	−0.222092	−0.0105878
$441$	−3.28401	−0.156382
$442$	−0.0100742	−0.000479182 0
$443$	0.634587	0.0301502	0.0150751	−	0.999886i	$-0.495201\pi$
$443$	0.634587	0.0301502	0.0150751	+	0.999886i	$0.495201\pi$
$444$	−0.421469	−0.0200020
$445$	−11.9104	−0.564609
$446$	−1.36294	−0.0645373
$447$	9.92042	0.469220
$448$	15.1321	0.714925
$449$	−18.0275	−0.850771	−0.425385	−	0.905012i	$-0.639861\pi$
$449$	−18.0275	−0.850771	−0.425385	+	0.905012i	$0.639861\pi$
$450$	0.0791955	0.00373331
$451$	0.925366	0.0435738
$452$	−6.45971	−0.303839
$453$	8.48032	0.398440
$454$	−1.69851	−0.0797152
$455$	−0.389864	−0.0182771
$456$	0.651525	0.0305104
$457$	−25.4244	−1.18930	−0.594651	−	0.803984i	$-0.702710\pi$
$457$	−25.4244	−1.18930	−0.594651	+	0.803984i	$0.702710\pi$
$458$	−1.34228	−0.0627208
$459$	0.628976	0.0293581
$460$	0	0
$461$	10.3079	0.480086	0.240043	−	0.970762i	$-0.422839\pi$
$461$	10.3079	0.480086	0.240043	+	0.970762i	$0.422839\pi$
$462$	0.107199	0.00498737
$463$	−9.22528	−0.428735	−0.214368	−	0.976753i	$-0.568769\pi$
$463$	−9.22528	−0.428735	−0.214368	+	0.976753i	$0.568769\pi$
$464$	−17.3853	−0.807094
$465$	5.60513	0.259932
$466$	−2.35943	−0.109299
$467$	16.4376	0.760642	0.380321	−	0.924854i	$-0.375813\pi$
$467$	16.4376	0.760642	0.380321	+	0.924854i	$0.375813\pi$
$468$	−0.403220	−0.0186389
$469$	9.57180	0.441985
$470$	0.358714	0.0165462
$471$	−1.30294	−0.0600361
$472$	−2.30929	−0.106294
$473$	−4.54760	−0.209099
$474$	−0.503644	−0.0231331
$475$	2.05993	0.0945159
$476$	−2.41734	−0.110799
$477$	−0.0863594	−0.00395412
$478$	0.551684	0.0252334
$479$	−29.2726	−1.33750	−0.668750	−	0.743488i	$-0.733170\pi$
$479$	−29.2726	−1.33750	−0.668750	+	0.743488i	$0.733170\pi$
$480$	−0.946376	−0.0431960
$481$	−0.0427539	−0.00194941
$482$	2.27999	0.103851
$483$	0	0
$484$	20.9480	0.952180
$485$	4.06742	0.184692
$486$	−0.0791955	−0.00359238
$487$	−16.5657	−0.750662	−0.375331	−	0.926891i	$-0.622471\pi$
$487$	−16.5657	−0.750662	−0.375331	+	0.926891i	$0.622471\pi$
$488$	−2.45845	−0.111289
$489$	3.81931	0.172715
$490$	−0.260079	−0.0117492
$491$	26.3462	1.18899	0.594495	−	0.804100i	$-0.297352\pi$
$491$	26.3462	1.18899	0.594495	+	0.804100i	$0.297352\pi$
$492$	2.62739	0.118452
$493$	2.75968	0.124290
$494$	0.0329935	0.00148445
$495$	0.702190	0.0315611
$496$	−22.2098	−0.997250
$497$	1.06436	0.0477431
$498$	−1.09698	−0.0491569
$499$	−36.7104	−1.64338	−0.821692	−	0.569932i	$-0.806969\pi$
$499$	−36.7104	−1.64338	−0.821692	+	0.569932i	$0.806969\pi$
$500$	−1.99373	−0.0891622
$501$	−15.8295	−0.707210
$502$	1.85423	0.0827585
$503$	18.4845	0.824183	0.412091	−	0.911142i	$-0.364798\pi$
$503$	18.4845	0.824183	0.412091	+	0.911142i	$0.364798\pi$
$504$	0.609700	0.0271582
$505$	4.76216	0.211913
$506$	0	0
$507$	12.9591	0.575534
$508$	−25.3973	−1.12682
$509$	−18.7784	−0.832338	−0.416169	−	0.909287i	$-0.636628\pi$
$509$	−18.7784	−0.832338	−0.416169	+	0.909287i	$0.636628\pi$
$510$	0.0498121	0.00220572
$511$	−29.5453	−1.30701
$512$	6.25643	0.276498
$513$	−2.05993	−0.0909479
$514$	−0.990439	−0.0436864
$515$	13.7414	0.605519
$516$	−12.9120	−0.568420
$517$	3.18055	0.139880
$518$	0.0322728	0.00141799
$519$	−6.27485	−0.275435
$520$	−0.0639670	−0.00280514
$521$	21.2172	0.929540	0.464770	−	0.885431i	$-0.346137\pi$
$521$	21.2172	0.929540	0.464770	+	0.885431i	$0.346137\pi$
$522$	−0.347476	−0.0152086
$523$	−21.6409	−0.946291	−0.473146	−	0.880984i	$-0.656882\pi$
$523$	−21.6409	−0.946291	−0.473146	+	0.880984i	$0.656882\pi$
$524$	−6.80419	−0.297243
$525$	1.92769	0.0841313
$526$	1.23886	0.0540170
$527$	3.52549	0.153573
$528$	−2.78236	−0.121087
$529$	0	0
$530$	−0.00683928	−0.000297079 0
$531$	7.30129	0.316849
$532$	7.91689	0.343241
$533$	0.266524	0.0115444
$534$	0.943253	0.0408186
$535$	−6.72302	−0.290662
$536$	1.57049	0.0678350
$537$	17.3147	0.747182
$538$	−2.42149	−0.104398
$539$	−2.30600	−0.0993264
$540$	1.99373	0.0857964
$541$	1.51455	0.0651155	0.0325577	−	0.999470i	$-0.489635\pi$
$541$	1.51455	0.0651155	0.0325577	+	0.999470i	$0.489635\pi$
$542$	−2.44589	−0.105060
$543$	4.93595	0.211822
$544$	−0.595248	−0.0255211
$545$	−5.69952	−0.244140
$546$	0.0308755	0.00132135
$547$	−29.3921	−1.25671	−0.628357	−	0.777925i	$-0.716272\pi$
$547$	−29.3921	−1.25671	−0.628357	+	0.777925i	$0.716272\pi$
$548$	27.9094	1.19223
$549$	7.77288	0.331738
$550$	0.0556103	0.00237123
$551$	−9.03806	−0.385034
$552$	0	0
$553$	−12.2591	−0.521311
$554$	0.141259	0.00600154
$555$	0.211397	0.00897331
$556$	−16.8086	−0.712843
$557$	−8.77669	−0.371880	−0.185940	−	0.982561i	$-0.559533\pi$
$557$	−8.77669	−0.371880	−0.185940	+	0.982561i	$0.559533\pi$
$558$	−0.443901	−0.0187918
$559$	−1.30980	−0.0553986
$560$	−7.63829	−0.322777
$561$	0.441661	0.0186469
$562$	−0.222919	−0.00940327
$563$	22.5912	0.952105	0.476053	−	0.879417i	$-0.342067\pi$
$563$	22.5912	0.952105	0.476053	+	0.879417i	$0.342067\pi$
$564$	9.03053	0.380254
$565$	3.24001	0.136308
$566$	1.27599	0.0536340
$567$	−1.92769	−0.0809554
$568$	0.174635	0.00732751
$569$	25.9142	1.08638	0.543190	−	0.839610i	$-0.317216\pi$
$569$	25.9142	1.08638	0.543190	+	0.839610i	$0.317216\pi$
$570$	−0.163137	−0.00683305
$571$	20.5927	0.861777	0.430888	−	0.902405i	$-0.358200\pi$
$571$	20.5927	0.861777	0.430888	+	0.902405i	$0.358200\pi$
$572$	−0.283137	−0.0118386
$573$	23.5194	0.982539
$574$	−0.201186	−0.00839733
$575$	0	0
$576$	−7.84987	−0.327078
$577$	−42.7382	−1.77921	−0.889607	−	0.456727i	$-0.849022\pi$
$577$	−42.7382	−1.77921	−0.889607	+	0.456727i	$0.849022\pi$
$578$	−1.31499	−0.0546965
$579$	8.55125	0.355378
$580$	8.74762	0.363225
$581$	−26.7015	−1.10777
$582$	−0.322122	−0.0133524
$583$	−0.0606407	−0.00251148
$584$	−4.84765	−0.200597
$585$	0.202244	0.00836178
$586$	−0.604480	−0.0249708
$587$	−9.10582	−0.375837	−0.187919	−	0.982185i	$-0.560174\pi$
$587$	−9.10582	−0.375837	−0.187919	+	0.982185i	$0.560174\pi$
$588$	−6.54743	−0.270011
$589$	−11.5462	−0.475751
$590$	0.578230	0.0238054
$591$	16.8793	0.694321
$592$	−0.837642	−0.0344269
$593$	−16.3034	−0.669502	−0.334751	−	0.942307i	$-0.608652\pi$
$593$	−16.3034	−0.669502	−0.334751	+	0.942307i	$0.608652\pi$
$594$	−0.0556103	−0.00228172
$595$	1.21247	0.0497065
$596$	19.7786	0.810164
$597$	−6.52006	−0.266848
$598$	0	0
$599$	41.8367	1.70940	0.854701	−	0.519121i	$-0.173740\pi$
$599$	41.8367	1.70940	0.854701	+	0.519121i	$0.173740\pi$
$600$	0.316285	0.0129123
$601$	7.20493	0.293895	0.146948	−	0.989144i	$-0.453055\pi$
$601$	7.20493	0.293895	0.146948	+	0.989144i	$0.453055\pi$
$602$	0.988703	0.0402965
$603$	−4.96543	−0.202208
$604$	16.9075	0.687955
$605$	−10.5069	−0.427167
$606$	−0.377141	−0.0153203
$607$	−4.94504	−0.200713	−0.100356	−	0.994952i	$-0.531998\pi$
$607$	−4.94504	−0.200713	−0.100356	+	0.994952i	$0.531998\pi$
$608$	1.94946	0.0790612
$609$	−8.45787	−0.342730
$610$	0.615577	0.0249240
$611$	0.916059	0.0370598
$612$	1.25401	0.0506903
$613$	10.3897	0.419635	0.209818	−	0.977741i	$-0.432713\pi$
$613$	10.3897	0.419635	0.209818	+	0.977741i	$0.432713\pi$
$614$	1.08187	0.0436608
$615$	−1.31783	−0.0531400
$616$	0.428125	0.0172497
$617$	0.636064	0.0256070	0.0128035	−	0.999918i	$-0.495924\pi$
$617$	0.636064	0.0256070	0.0128035	+	0.999918i	$0.495924\pi$
$618$	−1.08826	−0.0437762
$619$	−34.5730	−1.38961	−0.694803	−	0.719200i	$-0.744509\pi$
$619$	−34.5730	−1.38961	−0.694803	+	0.719200i	$0.744509\pi$
$620$	11.1751	0.448803
$621$	0	0
$622$	−2.10058	−0.0842256
$623$	22.9596	0.919858
$624$	−0.801375	−0.0320807
$625$	1.00000	0.0400000
$626$	−0.151106	−0.00603943
$627$	−1.44646	−0.0577660
$628$	−2.59770	−0.103659
$629$	0.132964	0.00530162
$630$	−0.152664	−0.00608230
$631$	15.4349	0.614454	0.307227	−	0.951636i	$-0.400599\pi$
$631$	15.4349	0.614454	0.307227	+	0.951636i	$0.400599\pi$
$632$	−2.01142	−0.0800098
$633$	−19.4339	−0.772430
$634$	−0.126083	−0.00500741
$635$	12.7386	0.505516
$636$	−0.172177	−0.00682727
$637$	−0.664173	−0.0263155
$638$	−0.243994	−0.00965981
$639$	−0.552143	−0.0218424
$640$	−2.51443	−0.0993914
$641$	13.8540	0.547198	0.273599	−	0.961844i	$-0.411786\pi$
$641$	13.8540	0.547198	0.273599	+	0.961844i	$0.411786\pi$
$642$	0.532434	0.0210135
$643$	−33.7556	−1.33119	−0.665596	−	0.746312i	$-0.731823\pi$
$643$	−33.7556	−1.33119	−0.665596	+	0.746312i	$0.731823\pi$
$644$	0	0
$645$	6.47631	0.255005
$646$	−0.102609	−0.00403711
$647$	−16.6712	−0.655413	−0.327706	−	0.944780i	$-0.606276\pi$
$647$	−16.6712	−0.655413	−0.327706	+	0.944780i	$0.606276\pi$
$648$	−0.316285	−0.0124249
$649$	5.12689	0.201248
$650$	0.0160169	0.000628233 0
$651$	−10.8050	−0.423479
$652$	7.61467	0.298214
$653$	−9.64726	−0.377526	−0.188763	−	0.982023i	$-0.560448\pi$
$653$	−9.64726	−0.377526	−0.188763	+	0.982023i	$0.560448\pi$
$654$	0.451376	0.0176502
$655$	3.41280	0.133349
$656$	5.22178	0.203876
$657$	15.3268	0.597956
$658$	−0.691489	−0.0269570
$659$	−31.1013	−1.21153	−0.605767	−	0.795642i	$-0.707134\pi$
$659$	−31.1013	−1.21153	−0.605767	+	0.795642i	$0.707134\pi$
$660$	1.39998	0.0544940
$661$	41.9241	1.63066	0.815329	−	0.578998i	$-0.196556\pi$
$661$	41.9241	1.63066	0.815329	+	0.578998i	$0.196556\pi$
$662$	−2.30657	−0.0896475
$663$	0.127207	0.00494031
$664$	−4.38105	−0.170018
$665$	−3.97090	−0.153985
$666$	−0.0167417	−0.000648728 0
$667$	0	0
$668$	−31.5597	−1.22108
$669$	17.2099	0.665372
$670$	−0.393240	−0.0151922
$671$	5.45803	0.210705
$672$	1.82432	0.0703746
$673$	−15.2915	−0.589443	−0.294721	−	0.955583i	$-0.595227\pi$
$673$	−15.2915	−0.589443	−0.294721	+	0.955583i	$0.595227\pi$
$674$	1.41219	0.0543953
$675$	−1.00000	−0.0384900
$676$	25.8369	0.993728
$677$	−42.8457	−1.64669	−0.823347	−	0.567539i	$-0.807896\pi$
$677$	−42.8457	−1.64669	−0.823347	+	0.567539i	$0.807896\pi$
$678$	−0.256595	−0.00985446
$679$	−7.84073	−0.300900
$680$	0.198936	0.00762885
$681$	21.4471	0.821854
$682$	−0.311703	−0.0119357
$683$	−18.3519	−0.702217	−0.351109	−	0.936335i	$-0.614195\pi$
$683$	−18.3519	−0.702217	−0.351109	+	0.936335i	$0.614195\pi$
$684$	−4.10693	−0.157032
$685$	−13.9986	−0.534859
$686$	1.57000	0.0599430
$687$	16.9490	0.646644
$688$	−25.6618	−0.978347
$689$	−0.0174657	−0.000665390 0
$690$	0	0
$691$	−18.4567	−0.702127	−0.351064	−	0.936352i	$-0.614180\pi$
$691$	−18.4567	−0.702127	−0.351064	+	0.936352i	$0.614180\pi$
$692$	−12.5103	−0.475572
$693$	−1.35360	−0.0514192
$694$	−0.628937	−0.0238741
$695$	8.43073	0.319796
$696$	−1.38772	−0.0526015
$697$	−0.828884	−0.0313962
$698$	1.00579	0.0380699
$699$	29.7925	1.12686
$700$	3.84329	0.145263
$701$	21.8534	0.825393	0.412697	−	0.910869i	$-0.364587\pi$
$701$	21.8534	0.825393	0.412697	+	0.910869i	$0.364587\pi$
$702$	−0.0160169	−0.000604517 0
$703$	−0.435463	−0.0164238
$704$	−5.51209	−0.207745
$705$	−4.52947	−0.170590
$706$	0.738800	0.0278051
$707$	−9.17996	−0.345248
$708$	14.5568	0.547078
$709$	−29.3336	−1.10165	−0.550823	−	0.834622i	$-0.685686\pi$
$709$	−29.3336	−1.10165	−0.550823	+	0.834622i	$0.685686\pi$
$710$	−0.0437273	−0.00164105
$711$	6.35949	0.238500
$712$	3.76710	0.141178
$713$	0	0
$714$	−0.0960223	−0.00359355
$715$	0.142014	0.00531102
$716$	34.5207	1.29010
$717$	−6.96610	−0.260154
$718$	2.40970	0.0899293
$719$	−7.87919	−0.293844	−0.146922	−	0.989148i	$-0.546937\pi$
$719$	−7.87919	−0.293844	−0.146922	+	0.989148i	$0.546937\pi$
$720$	3.96241	0.147670
$721$	−26.4892	−0.986509
$722$	−1.16867	−0.0434932
$723$	−28.7894	−1.07069
$724$	9.84094	0.365736
$725$	−4.38757	−0.162950
$726$	0.832102	0.0308822
$727$	−11.2690	−0.417944	−0.208972	−	0.977922i	$-0.567012\pi$
$727$	−11.2690	−0.417944	−0.208972	+	0.977922i	$0.567012\pi$
$728$	0.123308	0.00457012
$729$	1.00000	0.0370370
$730$	1.21382	0.0449253
$731$	4.07345	0.150662
$732$	15.4970	0.572786
$733$	−39.0478	−1.44226	−0.721132	−	0.692797i	$-0.756378\pi$
$733$	−39.0478	−1.44226	−0.721132	+	0.692797i	$0.756378\pi$
$734$	−1.19086	−0.0439554
$735$	3.28401	0.121133
$736$	0	0
$737$	−3.48667	−0.128433
$738$	0.104366	0.00384177
$739$	21.8913	0.805283	0.402642	−	0.915358i	$-0.368092\pi$
$739$	21.8913	0.805283	0.402642	+	0.915358i	$0.368092\pi$
$740$	0.421469	0.0154935
$741$	−0.416608	−0.0153045
$742$	0.0131840	0.000484000 0
$743$	29.4228	1.07942	0.539709	−	0.841852i	$-0.318534\pi$
$743$	29.4228	1.07942	0.539709	+	0.841852i	$0.318534\pi$
$744$	−1.77282	−0.0649948
$745$	−9.92042	−0.363456
$746$	−1.39059	−0.0509130
$747$	13.8516	0.506802
$748$	0.880551	0.0321961
$749$	12.9599	0.473545
$750$	−0.0791955	−0.00289181
$751$	12.0925	0.441261	0.220630	−	0.975357i	$-0.429189\pi$
$751$	12.0925	0.441261	0.220630	+	0.975357i	$0.429189\pi$
$752$	17.9476	0.654482
$753$	−23.4134	−0.853230
$754$	−0.0702750	−0.00255927
$755$	−8.48032	−0.308631
$756$	−3.84329	−0.139779
$757$	4.87804	0.177295	0.0886477	−	0.996063i	$-0.471745\pi$
$757$	4.87804	0.177295	0.0886477	+	0.996063i	$0.471745\pi$
$758$	−1.28849	−0.0468000
$759$	0	0
$760$	−0.651525	−0.0236333
$761$	13.8511	0.502101	0.251050	−	0.967974i	$-0.419224\pi$
$761$	13.8511	0.502101	0.251050	+	0.967974i	$0.419224\pi$
$762$	−1.00884	−0.0365464
$763$	10.9869	0.397752
$764$	46.8914	1.69647
$765$	−0.628976	−0.0227407
$766$	0.206573	0.00746380
$767$	1.47665	0.0533186
$768$	−15.5006	−0.559330
$769$	5.06641	0.182699	0.0913496	−	0.995819i	$-0.470882\pi$
$769$	5.06641	0.182699	0.0913496	+	0.995819i	$0.470882\pi$
$770$	−0.107199	−0.00386320
$771$	12.5063	0.450402
$772$	17.0489	0.613603
$773$	50.0060	1.79859	0.899295	−	0.437342i	$-0.144080\pi$
$773$	50.0060	1.79859	0.899295	+	0.437342i	$0.144080\pi$
$774$	−0.512895	−0.0184356
$775$	−5.60513	−0.201342
$776$	−1.28647	−0.0461815
$777$	−0.407508	−0.0146193
$778$	−0.387824	−0.0139042
$779$	2.71463	0.0972618
$780$	0.403220	0.0144376
$781$	−0.387709	−0.0138733
$782$	0	0
$783$	4.38757	0.156799
$784$	−13.0126	−0.464736
$785$	1.30294	0.0465038
$786$	−0.270278	−0.00964051
$787$	−7.35404	−0.262143	−0.131072	−	0.991373i	$-0.541842\pi$
$787$	−7.35404	−0.262143	−0.131072	+	0.991373i	$0.541842\pi$
$788$	33.6527	1.19883
$789$	−15.6431	−0.556909
$790$	0.503644	0.0179188
$791$	−6.24574	−0.222073
$792$	−0.222092	−0.00789171
$793$	1.57202	0.0558241
$794$	0.439599	0.0156008
$795$	0.0863594	0.00306285
$796$	−12.9992	−0.460745
$797$	18.0089	0.637910	0.318955	−	0.947770i	$-0.396668\pi$
$797$	18.0089	0.637910	0.318955	+	0.947770i	$0.396668\pi$
$798$	0.314477	0.0111324
$799$	−2.84893	−0.100788
$800$	0.946376	0.0334594
$801$	−11.9104	−0.420834
$802$	−1.05610	−0.0372922
$803$	10.7623	0.379794
$804$	−9.89971	−0.349136
$805$	0	0
$806$	−0.0897766	−0.00316224
$807$	30.5760	1.07633
$808$	−1.50620	−0.0529880
$809$	−13.6103	−0.478511	−0.239256	−	0.970957i	$-0.576903\pi$
$809$	−13.6103	−0.478511	−0.239256	+	0.970957i	$0.576903\pi$
$810$	0.0791955	0.00278265
$811$	−18.3829	−0.645510	−0.322755	−	0.946483i	$-0.604609\pi$
$811$	−18.3829	−0.645510	−0.322755	+	0.946483i	$0.604609\pi$
$812$	−16.8627	−0.591764
$813$	30.8842	1.08316
$814$	−0.0117559	−0.000412043 0
$815$	−3.81931	−0.133785
$816$	2.49226	0.0872466
$817$	−13.3407	−0.466733
$818$	−1.77670	−0.0621210
$819$	−0.389864	−0.0136230
$820$	−2.62739	−0.0917526
$821$	43.0981	1.50413	0.752067	−	0.659086i	$-0.229057\pi$
$821$	43.0981	1.50413	0.752067	+	0.659086i	$0.229057\pi$
$822$	1.10863	0.0386678
$823$	38.3845	1.33800	0.668999	−	0.743263i	$-0.266723\pi$
$823$	38.3845	1.33800	0.668999	+	0.743263i	$0.266723\pi$
$824$	−4.34621	−0.151407
$825$	−0.702190	−0.0244471
$826$	−1.11465	−0.0387836
$827$	−39.4343	−1.37127	−0.685633	−	0.727948i	$-0.740474\pi$
$827$	−39.4343	−1.37127	−0.685633	+	0.727948i	$0.740474\pi$
$828$	0	0
$829$	−14.3301	−0.497705	−0.248853	−	0.968541i	$-0.580053\pi$
$829$	−14.3301	−0.497705	−0.248853	+	0.968541i	$0.580053\pi$
$830$	1.09698	0.0380768
$831$	−1.78368	−0.0618751
$832$	−1.58759	−0.0550398
$833$	2.06557	0.0715676
$834$	−0.667677	−0.0231198
$835$	15.8295	0.547802
$836$	−2.88384	−0.0997399
$837$	5.60513	0.193742
$838$	1.26165	0.0435831
$839$	−35.3622	−1.22084	−0.610420	−	0.792078i	$-0.708999\pi$
$839$	−35.3622	−1.22084	−0.610420	+	0.792078i	$0.708999\pi$
$840$	−0.609700	−0.0210367
$841$	−9.74925	−0.336181
$842$	−1.02034	−0.0351632
$843$	2.81479	0.0969466
$844$	−38.7460	−1.33369
$845$	−12.9591	−0.445806
$846$	0.358714	0.0123328
$847$	20.2541	0.695939
$848$	−0.342191	−0.0117509
$849$	−16.1119	−0.552960
$850$	−0.0498121	−0.00170854
$851$	0	0
$852$	−1.10082	−0.0377136
$853$	−36.9288	−1.26442	−0.632208	−	0.774798i	$-0.717851\pi$
$853$	−36.9288	−1.26442	−0.632208	+	0.774798i	$0.717851\pi$
$854$	−1.18664	−0.0406060
$855$	2.05993	0.0704480
$856$	2.12639	0.0726787
$857$	−47.4356	−1.62037	−0.810185	−	0.586175i	$-0.800633\pi$
$857$	−47.4356	−1.62037	−0.810185	+	0.586175i	$0.800633\pi$
$858$	−0.0112469	−0.000383962 0
$859$	−33.0836	−1.12880	−0.564398	−	0.825502i	$-0.690892\pi$
$859$	−33.0836	−1.12880	−0.564398	+	0.825502i	$0.690892\pi$
$860$	12.9120	0.440296
$861$	2.54037	0.0865755
$862$	−2.27041	−0.0773303
$863$	33.1464	1.12832	0.564158	−	0.825667i	$-0.309201\pi$
$863$	33.1464	1.12832	0.564158	+	0.825667i	$0.309201\pi$
$864$	−0.946376	−0.0321964
$865$	6.27485	0.213351
$866$	3.15471	0.107202
$867$	16.6044	0.563915
$868$	−21.5421	−0.731188
$869$	4.46557	0.151484
$870$	0.347476	0.0117805
$871$	−1.00423	−0.0340270
$872$	1.80267	0.0610462
$873$	4.06742	0.137661
$874$	0	0
$875$	−1.92769	−0.0651678
$876$	30.5575	1.03244
$877$	−5.61438	−0.189584	−0.0947921	−	0.995497i	$-0.530219\pi$
$877$	−5.61438	−0.189584	−0.0947921	+	0.995497i	$0.530219\pi$
$878$	−1.02342	−0.0345386
$879$	7.63275	0.257446
$880$	2.78236	0.0937934
$881$	−38.6554	−1.30233	−0.651167	−	0.758935i	$-0.725720\pi$
$881$	−38.6554	−1.30233	−0.651167	+	0.758935i	$0.725720\pi$
$882$	−0.260079	−0.00875732
$883$	−45.7749	−1.54045	−0.770224	−	0.637773i	$-0.779856\pi$
$883$	−45.7749	−1.54045	−0.770224	+	0.637773i	$0.779856\pi$
$884$	0.253616	0.00853003
$885$	−7.30129	−0.245430
$886$	0.0502565	0.00168840
$887$	−5.97450	−0.200604	−0.100302	−	0.994957i	$-0.531981\pi$
$887$	−5.97450	−0.200604	−0.100302	+	0.994957i	$0.531981\pi$
$888$	−0.0668619	−0.00224374
$889$	−24.5561	−0.823584
$890$	−0.943253	−0.0316179
$891$	0.702190	0.0235242
$892$	34.3118	1.14884
$893$	9.33037	0.312229
$894$	0.785653	0.0262762
$895$	−17.3147	−0.578765
$896$	4.84703	0.161928
$897$	0	0
$898$	−1.42770	−0.0476429
$899$	24.5929	0.820219
$900$	−1.99373	−0.0664576
$901$	0.0543180	0.00180960
$902$	0.0732849	0.00244012
$903$	−12.4843	−0.415452
$904$	−1.02477	−0.0340833
$905$	−4.93595	−0.164076
$906$	0.671604	0.0223125
$907$	57.6657	1.91476	0.957379	−	0.288836i	$-0.0932682\pi$
$907$	57.6657	1.91476	0.957379	+	0.288836i	$0.0932682\pi$
$908$	42.7596	1.41903
$909$	4.76216	0.157951
$910$	−0.0308755	−0.00102351
$911$	−40.0359	−1.32645	−0.663224	−	0.748421i	$-0.730812\pi$
$911$	−40.0359	−1.32645	−0.663224	+	0.748421i	$0.730812\pi$
$912$	−8.16227	−0.270280
$913$	9.72642	0.321898
$914$	−2.01350	−0.0666005
$915$	−7.77288	−0.256963
$916$	33.7917	1.11651
$917$	−6.57882	−0.217252
$918$	0.0498121	0.00164405
$919$	23.4018	0.771956	0.385978	−	0.922508i	$-0.373864\pi$
$919$	23.4018	0.771956	0.385978	+	0.922508i	$0.373864\pi$
$920$	0	0
$921$	−13.6608	−0.450137
$922$	0.816338	0.0268847
$923$	−0.111668	−0.00367559
$924$	−2.69872	−0.0887813
$925$	−0.211397	−0.00695070
$926$	−0.730601	−0.0240090
$927$	13.7414	0.451327
$928$	−4.15229	−0.136306
$929$	42.9123	1.40791	0.703953	−	0.710247i	$-0.251417\pi$
$929$	42.9123	1.40791	0.703953	+	0.710247i	$0.251417\pi$
$930$	0.443901	0.0145561
$931$	−6.76482	−0.221708
$932$	59.3981	1.94565
$933$	26.5240	0.868356
$934$	1.30179	0.0425958
$935$	−0.441661	−0.0144438
$936$	−0.0639670	−0.00209083
$937$	40.8908	1.33585	0.667923	−	0.744230i	$-0.267184\pi$
$937$	40.8908	1.33585	0.667923	+	0.744230i	$0.267184\pi$
$938$	0.758044	0.0247510
$939$	1.90802	0.0622658
$940$	−9.03053	−0.294543
$941$	−4.97986	−0.162339	−0.0811695	−	0.996700i	$-0.525865\pi$
$941$	−4.97986	−0.162339	−0.0811695	+	0.996700i	$0.525865\pi$
$942$	−0.103187	−0.00336200
$943$	0	0
$944$	28.9307	0.941614
$945$	1.92769	0.0627077
$946$	−0.360150	−0.0117095
$947$	43.4234	1.41107	0.705535	−	0.708675i	$-0.250707\pi$
$947$	43.4234	1.41107	0.705535	+	0.708675i	$0.250707\pi$
$948$	12.6791	0.411798
$949$	3.09976	0.100623
$950$	0.163137	0.00529286
$951$	1.59205	0.0516258
$952$	−0.383487	−0.0124289
$953$	33.9521	1.09981	0.549907	−	0.835226i	$-0.314663\pi$
$953$	33.9521	1.09981	0.549907	+	0.835226i	$0.314663\pi$
$954$	−0.00683928	−0.000221430 0
$955$	−23.5194	−0.761071
$956$	−13.8885	−0.449186
$957$	3.08090	0.0995915
$958$	−2.31826	−0.0748996
$959$	26.9849	0.871389
$960$	7.84987	0.253353
$961$	0.417485	0.0134673
$962$	−0.00338592	−0.000109166 0
$963$	−6.72302	−0.216646
$964$	−57.3981	−1.84867
$965$	−8.55125	−0.275275
$966$	0	0
$967$	16.6593	0.535727	0.267863	−	0.963457i	$-0.413682\pi$
$967$	16.6593	0.535727	0.267863	+	0.963457i	$0.413682\pi$
$968$	3.32319	0.106811
$969$	1.29564	0.0416221
$970$	0.322122	0.0103427
$971$	5.24268	0.168246	0.0841228	−	0.996455i	$-0.473191\pi$
$971$	5.24268	0.168246	0.0841228	+	0.996455i	$0.473191\pi$
$972$	1.99373	0.0639489
$973$	−16.2518	−0.521010
$974$	−1.31193	−0.0420369
$975$	−0.202244	−0.00647700
$976$	30.7993	0.985862
$977$	−60.4240	−1.93313	−0.966567	−	0.256415i	$-0.917459\pi$
$977$	−60.4240	−1.93313	−0.966567	+	0.256415i	$0.917459\pi$
$978$	0.302473	0.00967201
$979$	−8.36338	−0.267295
$980$	6.54743	0.209150
$981$	−5.69952	−0.181972
$982$	2.08650	0.0665830
$983$	41.3752	1.31966	0.659831	−	0.751414i	$-0.270628\pi$
$983$	41.3752	1.31966	0.659831	+	0.751414i	$0.270628\pi$
$984$	0.416810	0.0132874
$985$	−16.8793	−0.537818
$986$	0.218554	0.00696018
$987$	8.73141	0.277924
$988$	−0.830604	−0.0264250
$989$	0	0
$990$	0.0556103	0.00176741
$991$	−36.7606	−1.16774	−0.583870	−	0.811847i	$-0.698462\pi$
$991$	−36.7606	−1.16774	−0.583870	+	0.811847i	$0.698462\pi$
$992$	−5.30456	−0.168420
$993$	29.1250	0.924255
$994$	0.0842926	0.00267360
$995$	6.52006	0.206700
$996$	27.6162	0.875054
$997$	−17.9932	−0.569851	−0.284925	−	0.958550i	$-0.591969\pi$
$997$	−17.9932	−0.569851	−0.284925	+	0.958550i	$0.591969\pi$
$998$	−2.90730	−0.0920290
$999$	0.211397	0.00668831

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7935.2.a.bq.1.8		15
23.11	odd	22		345.2.m.a.121.2	✓	30
23.21	odd	22		345.2.m.a.211.2	yes	30
23.22	odd	2		7935.2.a.bp.1.8		15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
345.2.m.a.121.2	✓	30	23.11	odd	22
345.2.m.a.211.2	yes	30	23.21	odd	22
7935.2.a.bp.1.8		15	23.22	odd	2
7935.2.a.bq.1.8		15	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 7935 = 3 \cdot 5 \cdot 23^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7935.a (trivial)

\(f(q)\)	\(=\)	\(q+0.0791955 q^{2} -1.00000 q^{3} -1.99373 q^{4} +1.00000 q^{5} -0.0791955 q^{6} -1.92769 q^{7} -0.316285 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.0791955 q^{2} -1.00000 q^{3} -1.99373 q^{4} +1.00000 q^{5} -0.0791955 q^{6} -1.92769 q^{7} -0.316285 q^{8} +1.00000 q^{9} +0.0791955 q^{10} +0.702190 q^{11} +1.99373 q^{12} +0.202244 q^{13} -0.152664 q^{14} -1.00000 q^{15} +3.96241 q^{16} -0.628976 q^{17} +0.0791955 q^{18} +2.05993 q^{19} -1.99373 q^{20} +1.92769 q^{21} +0.0556103 q^{22} +0.316285 q^{24} +1.00000 q^{25} +0.0160169 q^{26} -1.00000 q^{27} +3.84329 q^{28} -4.38757 q^{29} -0.0791955 q^{30} -5.60513 q^{31} +0.946376 q^{32} -0.702190 q^{33} -0.0498121 q^{34} -1.92769 q^{35} -1.99373 q^{36} -0.211397 q^{37} +0.163137 q^{38} -0.202244 q^{39} -0.316285 q^{40} +1.31783 q^{41} +0.152664 q^{42} -6.47631 q^{43} -1.39998 q^{44} +1.00000 q^{45} +4.52947 q^{47} -3.96241 q^{48} -3.28401 q^{49} +0.0791955 q^{50} +0.628976 q^{51} -0.403220 q^{52} -0.0863594 q^{53} -0.0791955 q^{54} +0.702190 q^{55} +0.609700 q^{56} -2.05993 q^{57} -0.347476 q^{58} +7.30129 q^{59} +1.99373 q^{60} +7.77288 q^{61} -0.443901 q^{62} -1.92769 q^{63} -7.84987 q^{64} +0.202244 q^{65} -0.0556103 q^{66} -4.96543 q^{67} +1.25401 q^{68} -0.152664 q^{70} -0.552143 q^{71} -0.316285 q^{72} +15.3268 q^{73} -0.0167417 q^{74} -1.00000 q^{75} -4.10693 q^{76} -1.35360 q^{77} -0.0160169 q^{78} +6.35949 q^{79} +3.96241 q^{80} +1.00000 q^{81} +0.104366 q^{82} +13.8516 q^{83} -3.84329 q^{84} -0.628976 q^{85} -0.512895 q^{86} +4.38757 q^{87} -0.222092 q^{88} -11.9104 q^{89} +0.0791955 q^{90} -0.389864 q^{91} +5.60513 q^{93} +0.358714 q^{94} +2.05993 q^{95} -0.946376 q^{96} +4.06742 q^{97} -0.260079 q^{98} +0.702190 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q - 15 q^{3} + 12 q^{4} + 15 q^{5} + 5 q^{7} + 15 q^{9}+O(q^{10}) \) 15 * q - 15 * q^3 + 12 * q^4 + 15 * q^5 + 5 * q^7 + 15 * q^9	\( 15 q - 15 q^{3} + 12 q^{4} + 15 q^{5} + 5 q^{7} + 15 q^{9} - 13 q^{11} - 12 q^{12} - 24 q^{13} - 15 q^{14} - 15 q^{15} + 2 q^{16} - 2 q^{17} - 13 q^{19} + 12 q^{20} - 5 q^{21} + 9 q^{22} + 15 q^{25} - 9 q^{26} - 15 q^{27} - q^{28} - 3 q^{29} - 22 q^{31} + 13 q^{33} - q^{34} + 5 q^{35} + 12 q^{36} + 6 q^{37} + 17 q^{38} + 24 q^{39} - 20 q^{41} + 15 q^{42} + 4 q^{43} + 18 q^{44} + 15 q^{45} + 7 q^{47} - 2 q^{48} - 10 q^{49} + 2 q^{51} - 55 q^{52} - 4 q^{53} - 13 q^{55} - 25 q^{56} + 13 q^{57} + 2 q^{58} + 9 q^{59} - 12 q^{60} - 13 q^{61} - 7 q^{62} + 5 q^{63} - 26 q^{64} - 24 q^{65} - 9 q^{66} + 32 q^{67} - 27 q^{68} - 15 q^{70} + 14 q^{71} - 43 q^{73} + 11 q^{74} - 15 q^{75} - 88 q^{76} - 21 q^{77} + 9 q^{78} - 33 q^{79} + 2 q^{80} + 15 q^{81} - 35 q^{82} + 12 q^{83} + q^{84} - 2 q^{85} - 77 q^{86} + 3 q^{87} + 37 q^{88} - 29 q^{89} - 20 q^{91} + 22 q^{93} - 20 q^{94} - 13 q^{95} - 18 q^{97} - 19 q^{98} - 13 q^{99}+O(q^{100}) \) 15 * q - 15 * q^3 + 12 * q^4 + 15 * q^5 + 5 * q^7 + 15 * q^9 - 13 * q^11 - 12 * q^12 - 24 * q^13 - 15 * q^14 - 15 * q^15 + 2 * q^16 - 2 * q^17 - 13 * q^19 + 12 * q^20 - 5 * q^21 + 9 * q^22 + 15 * q^25 - 9 * q^26 - 15 * q^27 - q^28 - 3 * q^29 - 22 * q^31 + 13 * q^33 - q^34 + 5 * q^35 + 12 * q^36 + 6 * q^37 + 17 * q^38 + 24 * q^39 - 20 * q^41 + 15 * q^42 + 4 * q^43 + 18 * q^44 + 15 * q^45 + 7 * q^47 - 2 * q^48 - 10 * q^49 + 2 * q^51 - 55 * q^52 - 4 * q^53 - 13 * q^55 - 25 * q^56 + 13 * q^57 + 2 * q^58 + 9 * q^59 - 12 * q^60 - 13 * q^61 - 7 * q^62 + 5 * q^63 - 26 * q^64 - 24 * q^65 - 9 * q^66 + 32 * q^67 - 27 * q^68 - 15 * q^70 + 14 * q^71 - 43 * q^73 + 11 * q^74 - 15 * q^75 - 88 * q^76 - 21 * q^77 + 9 * q^78 - 33 * q^79 + 2 * q^80 + 15 * q^81 - 35 * q^82 + 12 * q^83 + q^84 - 2 * q^85 - 77 * q^86 + 3 * q^87 + 37 * q^88 - 29 * q^89 - 20 * q^91 + 22 * q^93 - 20 * q^94 - 13 * q^95 - 18 * q^97 - 19 * q^98 - 13 * q^99

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