LMFDB - Embedded newform 1305.2.c.j.784.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1305,2,Mod(784,1305)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1305, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

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

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

chi := DirichletCharacter("1305.784");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1305 = 3^{2} \cdot 5 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1305.c (of order $2$, degree $1$, minimal)

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:	no
Analytic conductor:	$10.4204774638$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	10.0.3899266318336.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} + 2x^{8} + 6x^{7} + 19x^{6} - 12x^{5} + 4x^{4} + 2x^{3} + 9x^{2} - 6x + 2 $ x^10 - 2x^9 + 2x^8 + 6x^7 + 19x^6 - 12x^5 + 4x^4 + 2x^3 + 9x^2 - 6*x + 2
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 435)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			784.10
Root			$-1.20964 - 1.20964i$ of defining polynomial
Character	$\chi$	$=$	1305.784
Dual form			1305.2.c.j.784.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.51908i q^{2} -4.34577 q^{4} +(1.27413 - 1.83755i) q^{5} -0.173311i q^{7} -5.90919i q^{8} +(4.62893 + 3.20964i) q^{10} -5.08250 q^{11} +1.82669i q^{13} +0.436584 q^{14} +6.19418 q^{16} -4.24598i q^{17} +8.62093 q^{19} +(-5.53709 + 7.98556i) q^{20} -12.8032i q^{22} -3.16348i q^{23} +(-1.75317 - 4.68256i) q^{25} -4.60158 q^{26} +0.753170i q^{28} +1.00000 q^{29} +3.22185 q^{31} +3.78527i q^{32} +10.6960 q^{34} +(-0.318467 - 0.220821i) q^{35} -1.97828i q^{37} +21.7168i q^{38} +(-10.8584 - 7.52909i) q^{40} +9.96541 q^{41} +7.91070i q^{43} +22.0874 q^{44} +7.96907 q^{46} -8.66893i q^{47} +6.96996 q^{49} +(11.7958 - 4.41638i) q^{50} -7.93837i q^{52} -5.40285i q^{53} +(-6.47578 + 9.33933i) q^{55} -1.02413 q^{56} +2.51908i q^{58} +7.66286 q^{59} +2.76215 q^{61} +8.11611i q^{62} +2.85296 q^{64} +(3.35663 + 2.32744i) q^{65} -8.13872i q^{67} +18.4520i q^{68} +(0.556267 - 0.802245i) q^{70} +6.25938 q^{71} -6.74356i q^{73} +4.98345 q^{74} -37.4646 q^{76} +0.880853i q^{77} -4.54763 q^{79} +(7.89221 - 11.3821i) q^{80} +25.1037i q^{82} +11.6224i q^{83} +(-7.80219 - 5.40994i) q^{85} -19.9277 q^{86} +30.0334i q^{88} -16.4911 q^{89} +0.316585 q^{91} +13.7478i q^{92} +21.8377 q^{94} +(10.9842 - 15.8414i) q^{95} -2.74419i q^{97} +17.5579i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 10 q^{4} + 4 q^{10} - 24 q^{11} + 12 q^{14} + 2 q^{16} + 4 q^{19} - 8 q^{20} + 2 q^{25} + 10 q^{29} + 4 q^{31} - 8 q^{34} - 2 q^{35} - 14 q^{40} + 28 q^{41} + 40 q^{44} - 12 q^{46} + 14 q^{49} + 12 q^{50}+ \cdots + 36 q^{95}+O(q^{100}) $ 10 * q - 10 * q^4 + 4 * q^10 - 24 * q^11 + 12 * q^14 + 2 * q^16 + 4 * q^19 - 8 * q^20 + 2 * q^25 + 10 * q^29 + 4 * q^31 - 8 * q^34 - 2 * q^35 - 14 * q^40 + 28 * q^41 + 40 * q^44 - 12 * q^46 + 14 * q^49 + 12 * q^50 + 2 * q^55 + 4 * q^56 + 8 * q^59 - 24 * q^61 + 18 * q^64 - 6 * q^65 + 20 * q^70 - 60 * q^71 + 4 * q^74 - 88 * q^76 + 36 * q^79 + 30 * q^80 - 14 * q^85 - 60 * q^86 - 44 * q^89 - 24 * q^91 + 100 * q^94 + 36 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1305\mathbb{Z}\right)^\times$.

$n$	$146$	$262$	$901$
$\chi(n)$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$			2.51908i			1.78126i	0.454729	+	0.890630i	$0.349736\pi$
$2$			2.51908i			1.78126i	−0.454729	+	0.890630i	$0.650264\pi$
$3$		0			0
$3$		0			0
$4$	−4.34577			−2.17289
$5$	1.27413	−	1.83755i	0.569810	−	0.821777i
$5$	1.27413	−	1.83755i	0.569810	−	0.821777i
$6$		0			0
$7$		−	0.173311i		−	0.0655054i	−0.999463	−	0.0327527i	$-0.989573\pi$
$7$		−	0.173311i		−	0.0655054i	0.999463	−	0.0327527i	$-0.0104274\pi$
$8$		−	5.90919i		−	2.08921i
$9$		0			0
$10$	4.62893	+	3.20964i	1.46380	+	1.01498i
$11$	−5.08250			−1.53243			−0.766215	−	0.642584i	$-0.777862\pi$
$11$	−5.08250			−1.53243			−0.766215	+	0.642584i	$0.777862\pi$
$12$		0			0
$13$			1.82669i			0.506632i	0.967384	+	0.253316i	$0.0815213\pi$
$13$			1.82669i			0.506632i	−0.967384	+	0.253316i	$0.918479\pi$
$14$	0.436584			0.116682
$15$		0			0
$16$	6.19418			1.54854
$17$		−	4.24598i		−	1.02980i	−0.857250	−	0.514901i	$-0.827829\pi$
$17$		−	4.24598i		−	1.02980i	0.857250	−	0.514901i	$-0.172171\pi$
$18$		0			0
$19$	8.62093			1.97778			0.988889	−	0.148656i	$-0.0474948\pi$
$19$	8.62093			1.97778			0.988889	+	0.148656i	$0.0474948\pi$
$20$	−5.53709	+	7.98556i	−1.23813	+	1.78563i
$21$		0			0
$22$		−	12.8032i		−	2.72966i
$23$		−	3.16348i		−	0.659632i	−0.944045	−	0.329816i	$-0.893013\pi$
$23$		−	3.16348i		−	0.659632i	0.944045	−	0.329816i	$-0.106987\pi$
$24$		0			0
$25$	−1.75317	−	4.68256i	−0.350634	−	0.936513i
$26$	−4.60158			−0.902444
$27$		0			0
$28$			0.753170i			0.142336i
$29$	1.00000			0.185695
$29$	1.00000			0.185695
$30$		0			0
$31$	3.22185			0.578662			0.289331	−	0.957229i	$-0.406567\pi$
$31$	3.22185			0.578662			0.289331	+	0.957229i	$0.406567\pi$
$32$			3.78527i			0.669147i
$33$		0			0
$34$	10.6960			1.83434
$35$	−0.318467	−	0.220821i	−0.0538308	−	0.0373256i
$36$		0			0
$37$		−	1.97828i		−	0.325227i	−0.986690	−	0.162614i	$-0.948008\pi$
$37$		−	1.97828i		−	0.325227i	0.986690	−	0.162614i	$-0.0519924\pi$
$38$			21.7168i			3.52294i
$39$		0			0
$40$	−10.8584	−	7.52909i	−1.71687	−	1.19045i
$41$	9.96541			1.55634			0.778168	−	0.628056i	$-0.216149\pi$
$41$	9.96541			1.55634			0.778168	+	0.628056i	$0.216149\pi$
$42$		0			0
$43$			7.91070i			1.20637i	0.797601	+	0.603185i	$0.206102\pi$
$43$			7.91070i			1.20637i	−0.797601	+	0.603185i	$0.793898\pi$
$44$	22.0874			3.32980
$45$		0			0
$46$	7.96907			1.17497
$47$		−	8.66893i		−	1.26449i	−0.774767	−	0.632246i	$-0.782133\pi$
$47$		−	8.66893i		−	1.26449i	0.774767	−	0.632246i	$-0.217867\pi$
$48$		0			0
$49$	6.96996			0.995709
$50$	11.7958	−	4.41638i	1.66817	−	0.624570i
$51$		0			0
$52$		−	7.93837i		−	1.10085i
$53$		−	5.40285i		−	0.742138i	−0.928605	−	0.371069i	$-0.878991\pi$
$53$		−	5.40285i		−	0.742138i	0.928605	−	0.371069i	$-0.121009\pi$
$54$		0			0
$55$	−6.47578	+	9.33933i	−0.873194	+	1.25932i
$56$	−1.02413			−0.136855
$57$		0			0
$58$			2.51908i			0.330772i
$59$	7.66286			0.997619			0.498810	−	0.866712i	$-0.333771\pi$
$59$	7.66286			0.997619			0.498810	+	0.866712i	$0.333771\pi$
$60$		0			0
$61$	2.76215			0.353657			0.176828	−	0.984242i	$-0.443416\pi$
$61$	2.76215			0.353657			0.176828	+	0.984242i	$0.443416\pi$
$62$			8.11611i			1.03075i
$63$		0			0
$64$	2.85296			0.356620
$65$	3.35663	+	2.32744i	0.416339	+	0.288684i
$66$		0			0
$67$		−	8.13872i		−	0.994303i	−0.867664	−	0.497152i	$-0.834379\pi$
$67$		−	8.13872i		−	0.994303i	0.867664	−	0.497152i	$-0.165621\pi$
$68$			18.4520i			2.23764i
$69$		0			0
$70$	0.556267	−	0.802245i	0.0664866	−	0.0958866i
$71$	6.25938			0.742852			0.371426	−	0.928463i	$-0.378869\pi$
$71$	6.25938			0.742852			0.371426	+	0.928463i	$0.378869\pi$
$72$		0			0
$73$		−	6.74356i		−	0.789274i	−0.918837	−	0.394637i	$-0.870870\pi$
$73$		−	6.74356i		−	0.789274i	0.918837	−	0.394637i	$-0.129130\pi$
$74$	4.98345			0.579314
$75$		0			0
$76$	−37.4646			−4.29748
$77$			0.880853i			0.100382i
$78$		0			0
$79$	−4.54763			−0.511649			−0.255824	−	0.966723i	$-0.582347\pi$
$79$	−4.54763			−0.511649			−0.255824	+	0.966723i	$0.582347\pi$
$80$	7.89221	−	11.3821i	0.882376	−	1.27256i
$81$		0			0
$82$			25.1037i			2.77224i
$83$			11.6224i			1.27573i	0.770149	+	0.637865i	$0.220182\pi$
$83$			11.6224i			1.27573i	−0.770149	+	0.637865i	$0.779818\pi$
$84$		0			0
$85$	−7.80219	−	5.40994i	−0.846267	−	0.586791i
$86$	−19.9277			−2.14886
$87$		0			0
$88$			30.0334i			3.20157i
$89$	−16.4911			−1.74805			−0.874024	−	0.485882i	$-0.838499\pi$
$89$	−16.4911			−1.74805			−0.874024	+	0.485882i	$0.838499\pi$
$90$		0			0
$91$	0.316585			0.0331872
$92$			13.7478i			1.43330i
$93$		0			0
$94$	21.8377			2.25239
$95$	10.9842	−	15.8414i	1.12696	−	1.62529i
$96$		0			0
$97$		−	2.74419i		−	0.278631i	−0.990248	−	0.139315i	$-0.955510\pi$
$97$		−	2.74419i		−	0.278631i	0.990248	−	0.139315i	$-0.0444901\pi$
$98$			17.5579i			1.77362i
$99$		0			0
$100$	7.61887	+	20.3493i	0.761887	+	2.03493i
$101$	−6.41474			−0.638290			−0.319145	−	0.947706i	$-0.603396\pi$
$101$	−6.41474			−0.638290			−0.319145	+	0.947706i	$0.603396\pi$
$102$		0			0
$103$		−	7.08642i		−	0.698245i	−0.937077	−	0.349123i	$-0.886480\pi$
$103$		−	7.08642i		−	0.698245i	0.937077	−	0.349123i	$-0.113520\pi$
$104$	10.7942			1.05846
$105$		0			0
$106$	13.6102			1.32194
$107$			0.925187i			0.0894412i	0.999000	+	0.0447206i	$0.0142398\pi$
$107$			0.925187i			0.0894412i	−0.999000	+	0.0447206i	$0.985760\pi$
$108$		0			0
$109$	−4.11700			−0.394337			−0.197169	−	0.980370i	$-0.563175\pi$
$109$	−4.11700			−0.394337			−0.197169	+	0.980370i	$0.563175\pi$
$110$	−23.5265	−	16.3130i	−2.24317	−	1.55538i
$111$		0			0
$112$		−	1.07352i		−	0.101438i
$113$		−	6.84626i		−	0.644042i	−0.946732	−	0.322021i	$-0.895638\pi$
$113$		−	6.84626i		−	0.644042i	0.946732	−	0.322021i	$-0.104362\pi$
$114$		0			0
$115$	−5.81305	−	4.03070i	−0.542070	−	0.375864i
$116$	−4.34577			−0.403495
$117$		0			0
$118$			19.3034i			1.77702i
$119$	−0.735875			−0.0674575
$120$		0			0
$121$	14.8318			1.34834
$122$			6.95807i			0.629954i
$123$		0			0
$124$	−14.0014			−1.25737
$125$	−10.8382	−	2.74467i	−0.969399	−	0.245491i
$126$		0			0
$127$			5.25850i			0.466617i	0.972403	+	0.233308i	$0.0749551\pi$
$127$			5.25850i			0.466617i	−0.972403	+	0.233308i	$0.925045\pi$
$128$			14.7574i			1.30438i
$129$		0			0
$130$	−5.86302	+	8.45562i	−0.514221	+	0.741607i
$131$	−17.7157			−1.54783			−0.773913	−	0.633293i	$-0.781703\pi$
$131$	−17.7157			−1.54783			−0.773913	+	0.633293i	$0.781703\pi$
$132$		0			0
$133$		−	1.49410i		−	0.129555i
$134$	20.5021			1.77111
$135$		0			0
$136$	−25.0903			−2.15147
$137$		−	1.14479i		−	0.0978057i	−0.998804	−	0.0489028i	$-0.984428\pi$
$137$		−	1.14479i		−	0.0978057i	0.998804	−	0.0489028i	$-0.0155725\pi$
$138$		0			0
$139$	−4.08670			−0.346630			−0.173315	−	0.984866i	$-0.555448\pi$
$139$	−4.08670			−0.346630			−0.173315	+	0.984866i	$0.555448\pi$
$140$	1.38399	+	0.959639i	0.116968	+	0.0811043i
$141$		0			0
$142$			15.7679i			1.32321i
$143$		−	9.28414i		−	0.776379i
$144$		0			0
$145$	1.27413	−	1.83755i	0.105811	−	0.152600i
$146$	16.9876			1.40590
$147$		0			0
$148$			8.59715i			0.706682i
$149$	1.50268			0.123105			0.0615523	−	0.998104i	$-0.480395\pi$
$149$	1.50268			0.123105			0.0615523	+	0.998104i	$0.480395\pi$
$150$		0			0
$151$	−21.4897			−1.74881			−0.874404	−	0.485199i	$-0.838747\pi$
$151$	−21.4897			−1.74881			−0.874404	+	0.485199i	$0.838747\pi$
$152$		−	50.9427i		−	4.13200i
$153$		0			0
$154$	−2.21894			−0.178807
$155$	4.10507	−	5.92031i	0.329727	−	0.475531i
$156$		0			0
$157$		−	11.1167i		−	0.887206i	−0.896223	−	0.443603i	$-0.853700\pi$
$157$		−	11.1167i		−	0.887206i	0.896223	−	0.443603i	$-0.146300\pi$
$158$		−	11.4559i		−	0.911379i
$159$		0			0
$160$	6.95561	+	4.82293i	0.549889	+	0.381286i
$161$	−0.548266			−0.0432094
$162$		0			0
$163$		−	12.2180i		−	0.956988i	−0.878091	−	0.478494i	$-0.841183\pi$
$163$		−	12.2180i		−	0.956988i	0.878091	−	0.478494i	$-0.158817\pi$
$164$	−43.3074			−3.38174
$165$		0			0
$166$	−29.2779			−2.27240
$167$			21.3634i			1.65315i	0.562826	+	0.826576i	$0.309714\pi$
$167$			21.3634i			1.65315i	−0.562826	+	0.826576i	$0.690286\pi$
$168$		0			0
$169$	9.66321			0.743324
$170$	13.6281	−	19.6544i	1.04523	−	1.50742i
$171$		0			0
$172$		−	34.3781i		−	2.62130i
$173$		−	13.1686i		−	1.00119i	−0.865682	−	0.500594i	$-0.833115\pi$
$173$		−	13.1686i		−	1.00119i	0.865682	−	0.500594i	$-0.166885\pi$
$174$		0			0
$175$	−0.811540	+	0.303844i	−0.0613466	+	0.0229684i
$176$	−31.4819			−2.37304
$177$		0			0
$178$		−	41.5423i		−	3.11373i
$179$	10.6947			0.799357			0.399679	−	0.916655i	$-0.369122\pi$
$179$	10.6947			0.799357			0.399679	+	0.916655i	$0.369122\pi$
$180$		0			0
$181$	−15.2511			−1.13361			−0.566804	−	0.823852i	$-0.691820\pi$
$181$	−15.2511			−1.13361			−0.566804	+	0.823852i	$0.691820\pi$
$182$			0.797504i			0.0591149i
$183$		0			0
$184$	−18.6936			−1.37811
$185$	−3.63519	−	2.52059i	−0.267264	−	0.185318i
$186$		0			0
$187$			21.5802i			1.57810i
$188$			37.6732i			2.74760i
$189$		0			0
$190$	39.9057	+	27.6701i	2.89507	+	2.00740i
$191$	25.7131			1.86053			0.930266	−	0.366885i	$-0.119576\pi$
$191$	25.7131			1.86053			0.930266	+	0.366885i	$0.119576\pi$
$192$		0			0
$193$		−	22.8935i		−	1.64791i	−0.566658	−	0.823953i	$-0.691764\pi$
$193$		−	22.8935i		−	1.64791i	0.566658	−	0.823953i	$-0.308236\pi$
$194$	6.91284			0.496313
$195$		0			0
$196$	−30.2899			−2.16356
$197$			0.840810i			0.0599052i	0.999551	+	0.0299526i	$0.00953564\pi$
$197$			0.840810i			0.0599052i	−0.999551	+	0.0299526i	$0.990464\pi$
$198$		0			0
$199$	26.5996			1.88560			0.942799	−	0.333361i	$-0.108183\pi$
$199$	26.5996			1.88560			0.942799	+	0.333361i	$0.108183\pi$
$200$	−27.6701	+	10.3598i	−1.95657	+	0.732549i
$201$		0			0
$202$		−	16.1592i		−	1.13696i
$203$		−	0.173311i		−	0.0121640i
$204$		0			0
$205$	12.6973	−	18.3119i	0.886815	−	1.27896i
$206$	17.8513			1.24376
$207$		0			0
$208$			11.3148i			0.784543i
$209$	−43.8159			−3.03081
$210$		0			0
$211$	1.86360			0.128296			0.0641478	−	0.997940i	$-0.479567\pi$
$211$	1.86360			0.128296			0.0641478	+	0.997940i	$0.479567\pi$
$212$			23.4795i			1.61258i
$213$		0			0
$214$	−2.33062			−0.159318
$215$	14.5363	+	10.0793i	0.991367	+	0.687401i
$216$		0			0
$217$		−	0.558382i		−	0.0379055i
$218$		−	10.3711i		−	0.702417i
$219$		0			0
$220$	28.1422	−	40.5866i	1.89735	−	2.73635i
$221$	7.75608			0.521731
$222$		0			0
$223$			25.0759i			1.67920i	0.543202	+	0.839602i	$0.317212\pi$
$223$			25.0759i			1.67920i	−0.543202	+	0.839602i	$0.682788\pi$
$224$	0.656028			0.0438327
$225$		0			0
$226$	17.2463			1.14721
$227$			20.3877i			1.35318i	0.736360	+	0.676590i	$0.236543\pi$
$227$			20.3877i			1.35318i	−0.736360	+	0.676590i	$0.763457\pi$
$228$		0			0
$229$	5.84179			0.386037			0.193018	−	0.981195i	$-0.438172\pi$
$229$	5.84179			0.386037			0.193018	+	0.981195i	$0.438172\pi$
$230$	10.1537	−	14.6435i	0.669512	−	0.965567i
$231$		0			0
$232$		−	5.90919i		−	0.387957i
$233$		−	14.1216i		−	0.925134i	−0.886584	−	0.462567i	$-0.846928\pi$
$233$		−	14.1216i		−	0.925134i	0.886584	−	0.462567i	$-0.153072\pi$
$234$		0			0
$235$	−15.9296	−	11.0454i	−1.03913	−	0.720520i
$236$	−33.3010			−2.16771
$237$		0			0
$238$		−	1.85373i		−	0.120159i
$239$	−6.39059			−0.413373			−0.206686	−	0.978407i	$-0.566268\pi$
$239$	−6.39059			−0.413373			−0.206686	+	0.978407i	$0.566268\pi$
$240$		0			0
$241$	−10.1713			−0.655188			−0.327594	−	0.944819i	$-0.606238\pi$
$241$	−10.1713			−0.655188			−0.327594	+	0.944819i	$0.606238\pi$
$242$			37.3624i			2.40175i
$243$		0			0
$244$	−12.0037			−0.768455
$245$	8.88066	−	12.8076i	0.567365	−	0.818251i
$246$		0			0
$247$			15.7478i			1.00201i
$248$		−	19.0385i		−	1.20895i
$249$		0			0
$250$	6.91406	−	27.3023i	0.437283	−	1.72675i
$251$	15.7587			0.994678			0.497339	−	0.867556i	$-0.334310\pi$
$251$	15.7587			0.994678			0.497339	+	0.867556i	$0.334310\pi$
$252$		0			0
$253$			16.0784i			1.01084i
$254$	−13.2466			−0.831165
$255$		0			0
$256$	−31.4691			−1.96682
$257$			12.3486i			0.770283i	0.922858	+	0.385142i	$0.125847\pi$
$257$			12.3486i			0.770283i	−0.922858	+	0.385142i	$0.874153\pi$
$258$		0			0
$259$	−0.342858			−0.0213041
$260$	−14.5871	−	10.1145i	−0.904656	−	0.627277i
$261$		0			0
$262$		−	44.6272i		−	2.75708i
$263$			4.16928i			0.257089i	0.991704	+	0.128545i	$0.0410305\pi$
$263$			4.16928i			0.257089i	−0.991704	+	0.128545i	$0.958969\pi$
$264$		0			0
$265$	−9.92799	−	6.88395i	−0.609872	−	0.422877i
$266$	3.76377			0.230771
$267$		0			0
$268$			35.3690i			2.16051i
$269$	−1.36011			−0.0829273			−0.0414636	−	0.999140i	$-0.513202\pi$
$269$	−1.36011			−0.0829273			−0.0414636	+	0.999140i	$0.513202\pi$
$270$		0			0
$271$	11.1448			0.676998			0.338499	−	0.940967i	$-0.390081\pi$
$271$	11.1448			0.676998			0.338499	+	0.940967i	$0.390081\pi$
$272$		−	26.3003i		−	1.59469i
$273$		0			0
$274$	2.88381			0.174217
$275$	8.91048	+	23.7991i	0.537322	+	1.43514i
$276$		0			0
$277$		−	0.704673i		−	0.0423397i	−0.999776	−	0.0211699i	$-0.993261\pi$
$277$		−	0.704673i		−	0.0423397i	0.999776	−	0.0211699i	$-0.00673908\pi$
$278$		−	10.2947i		−	0.617437i
$279$		0			0
$280$	−1.30487	+	1.88188i	−0.0779811	+	0.112464i
$281$	13.8119			0.823950			0.411975	−	0.911195i	$-0.364839\pi$
$281$	13.8119			0.823950			0.411975	+	0.911195i	$0.364839\pi$
$282$		0			0
$283$			8.92142i			0.530324i	0.964204	+	0.265162i	$0.0854254\pi$
$283$			8.92142i			0.530324i	−0.964204	+	0.265162i	$0.914575\pi$
$284$	−27.2018			−1.61413
$285$		0			0
$286$	23.3875			1.38293
$287$		−	1.72712i		−	0.101948i
$288$		0			0
$289$	−1.02833			−0.0604902
$290$	4.62893	+	3.20964i	0.271820	+	0.188477i
$291$		0			0
$292$			29.3060i			1.71500i
$293$			31.2817i			1.82750i	0.406278	+	0.913749i	$0.366826\pi$
$293$			31.2817i			1.82750i	−0.406278	+	0.913749i	$0.633174\pi$
$294$		0			0
$295$	9.76350	−	14.0809i	0.568453	−	0.819820i
$296$	−11.6900			−0.679469
$297$		0			0
$298$			3.78538i			0.219281i
$299$	5.77870			0.334191
$300$		0			0
$301$	1.37101			0.0790238
$302$		−	54.1343i		−	3.11508i
$303$		0			0
$304$	53.3996			3.06268
$305$	3.51934	−	5.07558i	0.201517	−	0.290627i
$306$		0			0
$307$			21.8533i			1.24723i	0.781730	+	0.623617i	$0.214338\pi$
$307$			21.8533i			1.24723i	−0.781730	+	0.623617i	$0.785662\pi$
$308$		−	3.82798i		−	0.218120i
$309$		0			0
$310$	14.9137	+	10.3410i	0.847043	+	0.587329i
$311$	−28.8838			−1.63785			−0.818925	−	0.573901i	$-0.805430\pi$
$311$	−28.8838			−1.63785			−0.818925	+	0.573901i	$0.805430\pi$
$312$		0			0
$313$			8.24232i			0.465884i	0.972491	+	0.232942i	$0.0748352\pi$
$313$			8.24232i			0.465884i	−0.972491	+	0.232942i	$0.925165\pi$
$314$	28.0038			1.58034
$315$		0			0
$316$	19.7630			1.11175
$317$		−	7.15829i		−	0.402050i	−0.979586	−	0.201025i	$-0.935573\pi$
$317$		−	7.15829i		−	0.402050i	0.979586	−	0.201025i	$-0.0644272\pi$
$318$		0			0
$319$	−5.08250			−0.284565
$320$	3.63505	−	5.24246i	0.203206	−	0.293062i
$321$		0			0
$322$		−	1.38113i		−	0.0769672i
$323$		−	36.6043i		−	2.03672i
$324$		0			0
$325$	8.55359	−	3.20250i	0.474468	−	0.177643i
$326$	30.7781			1.70464
$327$		0			0
$328$		−	58.8875i		−	3.25152i
$329$	−1.50242			−0.0828311
$330$		0			0
$331$	−24.6936			−1.35728			−0.678642	−	0.734470i	$-0.737431\pi$
$331$	−24.6936			−1.35728			−0.678642	+	0.734470i	$0.737431\pi$
$332$		−	50.5085i		−	2.77201i
$333$		0			0
$334$	−53.8162			−2.94469
$335$	−14.9553	−	10.3698i	−0.817095	−	0.566563i
$336$		0			0
$337$		−	11.7142i		−	0.638116i	−0.947735	−	0.319058i	$-0.896634\pi$
$337$		−	11.7142i		−	0.638116i	0.947735	−	0.319058i	$-0.103366\pi$
$338$			24.3424i			1.32405i
$339$		0			0
$340$	33.9065	+	23.5104i	1.83884	+	1.27503i
$341$	−16.3751			−0.886759
$342$		0			0
$343$		−	2.42115i		−	0.130730i
$344$	46.7458			2.52036
$345$		0			0
$346$	33.1727			1.78337
$347$			0.828990i			0.0445025i	0.999752	+	0.0222513i	$0.00708338\pi$
$347$			0.828990i			0.0445025i	−0.999752	+	0.0222513i	$0.992917\pi$
$348$		0			0
$349$	8.44370			0.451981			0.225991	−	0.974129i	$-0.427438\pi$
$349$	8.44370			0.451981			0.225991	+	0.974129i	$0.427438\pi$
$350$	−0.765407	−	2.04433i	−0.0409127	−	0.109274i
$351$		0			0
$352$		−	19.2386i		−	1.02542i
$353$			4.90553i			0.261095i	0.991442	+	0.130547i	$0.0416735\pi$
$353$			4.90553i			0.261095i	−0.991442	+	0.130547i	$0.958327\pi$
$354$		0			0
$355$	7.97528	−	11.5019i	0.423284	−	0.610458i
$356$	71.6664			3.79831
$357$		0			0
$358$			26.9407i			1.42386i
$359$	4.69044			0.247552			0.123776	−	0.992310i	$-0.460500\pi$
$359$	4.69044			0.247552			0.123776	+	0.992310i	$0.460500\pi$
$360$		0			0
$361$	55.3205			2.91161
$362$		−	38.4189i		−	2.01925i
$363$		0			0
$364$	−1.37581			−0.0721119
$365$	−12.3916	−	8.59219i	−0.648607	−	0.449736i
$366$		0			0
$367$		−	29.2460i		−	1.52663i	−0.646028	−	0.763314i	$-0.723571\pi$
$367$		−	29.2460i		−	1.52663i	0.646028	−	0.763314i	$-0.276429\pi$
$368$		−	19.5952i		−	1.02147i
$369$		0			0
$370$	6.34958	−	9.15733i	0.330099	−	0.476067i
$371$	−0.936373			−0.0486140
$372$		0			0
$373$			34.5171i			1.78723i	0.448839	+	0.893613i	$0.351838\pi$
$373$			34.5171i			1.78723i	−0.448839	+	0.893613i	$0.648162\pi$
$374$	−54.3622			−2.81100
$375$		0			0
$376$	−51.2263			−2.64179
$377$			1.82669i			0.0940793i
$378$		0			0
$379$	3.20131			0.164440			0.0822201	−	0.996614i	$-0.473799\pi$
$379$	3.20131			0.164440			0.0822201	+	0.996614i	$0.473799\pi$
$380$	−47.7349	+	68.8430i	−2.44875	+	3.53157i
$381$		0			0
$382$			64.7733i			3.31409i
$383$		−	19.4424i		−	0.993458i	−0.867906	−	0.496729i	$-0.834534\pi$
$383$		−	19.4424i		−	0.993458i	0.867906	−	0.496729i	$-0.165466\pi$
$384$		0			0
$385$	1.61861	+	1.12232i	0.0824920	+	0.0571989i
$386$	57.6705			2.93535
$387$		0			0
$388$			11.9256i			0.605432i
$389$	2.55875			0.129734			0.0648669	−	0.997894i	$-0.479338\pi$
$389$	2.55875			0.129734			0.0648669	+	0.997894i	$0.479338\pi$
$390$		0			0
$391$	−13.4321			−0.679289
$392$		−	41.1868i		−	2.08025i
$393$		0			0
$394$	−2.11807			−0.106707
$395$	−5.79429	+	8.35650i	−0.291542	+	0.420461i
$396$		0			0
$397$		−	30.6583i		−	1.53869i	−0.638831	−	0.769347i	$-0.720582\pi$
$397$		−	30.6583i		−	1.53869i	0.638831	−	0.769347i	$-0.279418\pi$
$398$			67.0067i			3.35874i
$399$		0			0
$400$	−10.8594	−	29.0046i	−0.542972	−	1.45023i
$401$	−11.1628			−0.557446			−0.278723	−	0.960372i	$-0.589911\pi$
$401$	−11.1628			−0.557446			−0.278723	+	0.960372i	$0.589911\pi$
$402$		0			0
$403$			5.88532i			0.293169i
$404$	27.8770			1.38693
$405$		0			0
$406$	0.436584			0.0216673
$407$			10.0546i			0.498388i
$408$		0			0
$409$	−13.3880			−0.661994			−0.330997	−	0.943632i	$-0.607385\pi$
$409$	−13.3880			−0.661994			−0.330997	+	0.943632i	$0.607385\pi$
$410$	46.1292	+	31.9854i	2.27816	+	1.57965i
$411$		0			0
$412$			30.7959i			1.51721i
$413$		−	1.32806i		−	0.0653495i
$414$		0			0
$415$	21.3568	+	14.8085i	1.04836	+	0.726923i
$416$	−6.91451			−0.339012
$417$		0			0
$418$		−	110.376i		−	5.39865i
$419$	29.2982			1.43131			0.715655	−	0.698454i	$-0.246128\pi$
$419$	29.2982			1.43131			0.715655	+	0.698454i	$0.246128\pi$
$420$		0			0
$421$	10.1098			0.492724			0.246362	−	0.969178i	$-0.420765\pi$
$421$	10.1098			0.492724			0.246362	+	0.969178i	$0.420765\pi$
$422$			4.69456i			0.228528i
$423$		0			0
$424$	−31.9264			−1.55048
$425$	−19.8821	+	7.44392i	−0.964422	+	0.361083i
$426$		0			0
$427$		−	0.478710i		−	0.0231664i
$428$		−	4.02065i		−	0.194345i
$429$		0			0
$430$	−25.3905	+	36.6181i	−1.22444	+	1.76588i
$431$	−30.3330			−1.46109			−0.730545	−	0.682865i	$-0.760734\pi$
$431$	−30.3330			−1.46109			−0.730545	+	0.682865i	$0.760734\pi$
$432$		0			0
$433$		−	6.50520i		−	0.312620i	−0.987708	−	0.156310i	$-0.950040\pi$
$433$		−	6.50520i		−	0.312620i	0.987708	−	0.156310i	$-0.0499599\pi$
$434$	1.40661			0.0675195
$435$		0			0
$436$	17.8915			0.856850
$437$		−	27.2722i		−	1.30460i
$438$		0			0
$439$	9.40248			0.448756			0.224378	−	0.974502i	$-0.427965\pi$
$439$	9.40248			0.448756			0.224378	+	0.974502i	$0.427965\pi$
$440$	55.1879	+	38.2666i	2.63098	+	1.82429i
$441$		0			0
$442$			19.5382i			0.929337i
$443$		−	28.1657i		−	1.33819i	−0.743175	−	0.669097i	$-0.766681\pi$
$443$		−	28.1657i		−	1.33819i	0.743175	−	0.669097i	$-0.233319\pi$
$444$		0			0
$445$	−21.0118	+	30.3031i	−0.996055	+	1.43651i
$446$	−63.1682			−2.99110
$447$		0			0
$448$		−	0.494450i		−	0.0233605i
$449$	−32.2625			−1.52256			−0.761281	−	0.648422i	$-0.775429\pi$
$449$	−32.2625			−1.52256			−0.761281	+	0.648422i	$0.775429\pi$
$450$		0			0
$451$	−50.6492			−2.38498
$452$			29.7523i			1.39943i
$453$		0			0
$454$	−51.3583			−2.41037
$455$	0.403372	−	0.581741i	0.0189104	−	0.0272724i
$456$		0			0
$457$		−	27.1466i		−	1.26986i	−0.772568	−	0.634932i	$-0.781028\pi$
$457$		−	27.1466i		−	1.26986i	0.772568	−	0.634932i	$-0.218972\pi$
$458$			14.7160i			0.687631i
$459$		0			0
$460$	25.2622	+	17.5165i	1.17786	+	0.816710i
$461$	−7.00940			−0.326460			−0.163230	−	0.986588i	$-0.552191\pi$
$461$	−7.00940			−0.326460			−0.163230	+	0.986588i	$0.552191\pi$
$462$		0			0
$463$		−	21.7590i		−	1.01123i	−0.862760	−	0.505613i	$-0.831266\pi$
$463$		−	21.7590i		−	1.01123i	0.862760	−	0.505613i	$-0.168734\pi$
$464$	6.19418			0.287558
$465$		0			0
$466$	35.5733			1.64790
$467$			30.7825i			1.42445i	0.701953	+	0.712223i	$0.252312\pi$
$467$			30.7825i			1.42445i	−0.701953	+	0.712223i	$0.747688\pi$
$468$		0			0
$469$	−1.41053			−0.0651322
$470$	27.8242	−	40.1279i	1.28343	−	1.85096i
$471$		0			0
$472$		−	45.2813i		−	2.08424i
$473$		−	40.2061i		−	1.84868i
$474$		0			0
$475$	−15.1140	−	40.3681i	−0.693476	−	1.85221i
$476$	3.19794			0.146577
$477$		0			0
$478$		−	16.0984i		−	0.736324i
$479$	−6.29237			−0.287506			−0.143753	−	0.989614i	$-0.545917\pi$
$479$	−6.29237			−0.287506			−0.143753	+	0.989614i	$0.545917\pi$
$480$		0			0
$481$	3.61370			0.164771
$482$		−	25.6222i		−	1.16706i
$483$		0			0
$484$	−64.4555			−2.92979
$485$	−5.04259	−	3.49647i	−0.228972	−	0.158766i
$486$		0			0
$487$			30.3406i			1.37487i	0.726248	+	0.687433i	$0.241262\pi$
$487$			30.3406i			1.37487i	−0.726248	+	0.687433i	$0.758738\pi$
$488$		−	16.3220i		−	0.738864i
$489$		0			0
$490$	32.2635	+	22.3711i	1.45752	+	1.01062i
$491$	−17.7822			−0.802502			−0.401251	−	0.915968i	$-0.631424\pi$
$491$	−17.7822			−0.802502			−0.401251	+	0.915968i	$0.631424\pi$
$492$		0			0
$493$		−	4.24598i		−	0.191229i
$494$	−39.6699			−1.78483
$495$		0			0
$496$	19.9567			0.896083
$497$		−	1.08482i		−	0.0486608i
$498$		0			0
$499$	−0.262248			−0.0117399			−0.00586993	−	0.999983i	$-0.501868\pi$
$499$	−0.262248			−0.0117399			−0.00586993	+	0.999983i	$0.501868\pi$
$500$	47.1004	+	11.9277i	2.10639	+	0.533424i
$501$		0			0
$502$			39.6974i			1.77178i
$503$			15.0486i			0.670986i	0.942043	+	0.335493i	$0.108903\pi$
$503$			15.0486i			0.670986i	−0.942043	+	0.335493i	$0.891097\pi$
$504$		0			0
$505$	−8.17323	+	11.7874i	−0.363704	+	0.524532i
$506$	−40.5028			−1.80057
$507$		0			0
$508$		−	22.8522i		−	1.01390i
$509$	39.8752			1.76744			0.883719	−	0.468019i	$-0.155032\pi$
$509$	39.8752			1.76744			0.883719	+	0.468019i	$0.155032\pi$
$510$		0			0
$511$	−1.16873			−0.0517017
$512$		−	49.7585i		−	2.19904i
$513$		0			0
$514$	−31.1071			−1.37207
$515$	−13.0216	−	9.02904i	−0.573802	−	0.397867i
$516$		0			0
$517$			44.0598i			1.93775i
$518$		−	0.863687i		−	0.0379482i
$519$		0			0
$520$	13.7533	−	19.8349i	0.603122	−	0.869820i
$521$	−18.3187			−0.802557			−0.401279	−	0.915956i	$-0.631434\pi$
$521$	−18.3187			−0.802557			−0.401279	+	0.915956i	$0.631434\pi$
$522$		0			0
$523$		−	6.04576i		−	0.264363i	−0.991226	−	0.132181i	$-0.957802\pi$
$523$		−	6.04576i		−	0.264363i	0.991226	−	0.132181i	$-0.0421981\pi$
$524$	76.9882			3.36325
$525$		0			0
$526$	−10.5028			−0.457942
$527$		−	13.6799i		−	0.595906i
$528$		0			0
$529$	12.9924			0.564886
$530$	17.3412	−	25.0094i	0.753254	−	1.08634i
$531$		0			0
$532$			6.49303i			0.281508i
$533$			18.2037i			0.788490i
$534$		0			0
$535$	1.70008	+	1.17881i	0.0735007	+	0.0509645i
$536$	−48.0932			−2.07731
$537$		0			0
$538$		−	3.42622i		−	0.147715i
$539$	−35.4248			−1.52585
$540$		0			0
$541$	−35.6643			−1.53333			−0.766664	−	0.642049i	$-0.778085\pi$
$541$	−35.6643			−1.53333			−0.766664	+	0.642049i	$0.778085\pi$
$542$			28.0746i			1.20591i
$543$		0			0
$544$	16.0722			0.689088
$545$	−5.24561	+	7.56519i	−0.224697	+	0.324057i
$546$		0			0
$547$			5.23087i			0.223656i	0.993728	+	0.111828i	$0.0356706\pi$
$547$			5.23087i			0.223656i	−0.993728	+	0.111828i	$0.964329\pi$
$548$			4.97498i			0.212520i
$549$		0			0
$550$	−59.9519	+	22.4462i	−2.55636	+	0.957110i
$551$	8.62093			0.367264
$552$		0			0
$553$			0.788155i			0.0335157i
$554$	1.77513			0.0754180
$555$		0			0
$556$	17.7599			0.753186
$557$			32.9893i			1.39780i	0.715219	+	0.698900i	$0.246327\pi$
$557$			32.9893i			1.39780i	−0.715219	+	0.698900i	$0.753673\pi$
$558$		0			0
$559$	−14.4504			−0.611186
$560$	−1.97264	−	1.36781i	−0.0833594	−	0.0578004i
$561$		0			0
$562$			34.7933i			1.46767i
$563$		−	5.94931i		−	0.250734i	−0.992110	−	0.125367i	$-0.959989\pi$
$563$		−	5.94931i		−	0.250734i	0.992110	−	0.125367i	$-0.0400108\pi$
$564$		0			0
$565$	−12.5803	−	8.72305i	−0.529259	−	0.366981i
$566$	−22.4738			−0.944644
$567$		0			0
$568$		−	36.9878i		−	1.55198i
$569$	−14.6940			−0.616003			−0.308002	−	0.951386i	$-0.599660\pi$
$569$	−14.6940			−0.616003			−0.308002	+	0.951386i	$0.599660\pi$
$570$		0			0
$571$	7.86509			0.329144			0.164572	−	0.986365i	$-0.447376\pi$
$571$	7.86509			0.329144			0.164572	+	0.986365i	$0.447376\pi$
$572$			40.3467i			1.68698i
$573$		0			0
$574$	4.35074			0.181597
$575$	−14.8132	+	5.54612i	−0.617753	+	0.231289i
$576$		0			0
$577$		−	29.7454i		−	1.23832i	−0.785265	−	0.619159i	$-0.787474\pi$
$577$		−	29.7454i		−	1.23832i	0.785265	−	0.619159i	$-0.212526\pi$
$578$		−	2.59045i		−	0.107749i
$579$		0			0
$580$	−5.53709	+	7.98556i	−0.229915	+	0.331582i
$581$	2.01430			0.0835671
$582$		0			0
$583$			27.4599i			1.13727i
$584$	−39.8489			−1.64896
$585$		0			0
$586$	−78.8013			−3.25525
$587$		−	46.1639i		−	1.90539i	−0.303929	−	0.952695i	$-0.598299\pi$
$587$		−	46.1639i		−	1.90539i	0.303929	−	0.952695i	$-0.401701\pi$
$588$		0			0
$589$	27.7754			1.14446
$590$	35.4709	+	24.5951i	1.46031	+	1.01256i
$591$		0			0
$592$		−	12.2538i		−	0.503629i
$593$			22.6806i			0.931382i	0.884948	+	0.465691i	$0.154194\pi$
$593$			22.6806i			0.931382i	−0.884948	+	0.465691i	$0.845806\pi$
$594$		0			0
$595$	−0.937602	+	1.35221i	−0.0384379	+	0.0554350i
$596$	−6.53031			−0.267492
$597$		0			0
$598$			14.5570i			0.595280i
$599$	22.8764			0.934704			0.467352	−	0.884071i	$-0.345208\pi$
$599$	22.8764			0.934704			0.467352	+	0.884071i	$0.345208\pi$
$600$		0			0
$601$	14.6918			0.599291			0.299646	−	0.954051i	$-0.403132\pi$
$601$	14.6918			0.599291			0.299646	+	0.954051i	$0.403132\pi$
$602$			3.45369i			0.140762i
$603$		0			0
$604$	93.3893			3.79996
$605$	18.8977	−	27.2541i	0.768299	−	1.10804i
$606$		0			0
$607$			20.9484i			0.850270i	0.905130	+	0.425135i	$0.139773\pi$
$607$			20.9484i			0.850270i	−0.905130	+	0.425135i	$0.860227\pi$
$608$			32.6325i			1.32342i
$609$		0			0
$610$	12.7858	+	8.86551i	0.517682	+	0.358954i
$611$	15.8354			0.640633
$612$		0			0
$613$		−	42.0373i		−	1.69787i	−0.528496	−	0.848936i	$-0.677244\pi$
$613$		−	42.0373i		−	1.69787i	0.528496	−	0.848936i	$-0.322756\pi$
$614$	−55.0503			−2.22165
$615$		0			0
$616$	5.20512			0.209720
$617$			44.6853i			1.79896i	0.436958	+	0.899482i	$0.356056\pi$
$617$			44.6853i			1.79896i	−0.436958	+	0.899482i	$0.643944\pi$
$618$		0			0
$619$	22.1966			0.892157			0.446079	−	0.894994i	$-0.352820\pi$
$619$	22.1966			0.892157			0.446079	+	0.894994i	$0.352820\pi$
$620$	−17.8397	+	25.7283i	−0.716459	+	1.03327i
$621$		0			0
$622$		−	72.7606i		−	2.91744i
$623$			2.85808i			0.114507i
$624$		0			0
$625$	−18.8528	+	16.4187i	−0.754112	+	0.656746i
$626$	−20.7631			−0.829859
$627$		0			0
$628$			48.3104i			1.92780i
$629$	−8.39974			−0.334919
$630$		0			0
$631$	−5.29765			−0.210896			−0.105448	−	0.994425i	$-0.533628\pi$
$631$	−5.29765			−0.210896			−0.105448	+	0.994425i	$0.533628\pi$
$632$			26.8728i			1.06894i
$633$		0			0
$634$	18.0323			0.716155
$635$	9.66275	+	6.70003i	0.383455	+	0.265883i
$636$		0			0
$637$			12.7320i			0.504458i
$638$		−	12.8032i		−	0.506884i
$639$		0			0
$640$	27.1174	+	18.8029i	1.07191	+	0.743248i
$641$	−3.21592			−0.127021			−0.0635107	−	0.997981i	$-0.520230\pi$
$641$	−3.21592			−0.127021			−0.0635107	+	0.997981i	$0.520230\pi$
$642$		0			0
$643$			32.0630i			1.26444i	0.774788	+	0.632221i	$0.217857\pi$
$643$			32.0630i			1.26444i	−0.774788	+	0.632221i	$0.782143\pi$
$644$	2.38264			0.0938891
$645$		0			0
$646$	92.2092			3.62792
$647$			9.26571i			0.364273i	0.983273	+	0.182136i	$0.0583012\pi$
$647$			9.26571i			0.364273i	−0.983273	+	0.182136i	$0.941699\pi$
$648$		0			0
$649$	−38.9465			−1.52878
$650$	8.06735	+	21.5472i	0.316427	+	0.845150i
$651$		0			0
$652$			53.0966i			2.07942i
$653$		−	22.2362i		−	0.870171i	−0.900389	−	0.435085i	$-0.856718\pi$
$653$		−	22.2362i		−	0.870171i	0.900389	−	0.435085i	$-0.143282\pi$
$654$		0			0
$655$	−22.5721	+	32.5534i	−0.881966	+	1.27197i
$656$	61.7275			2.41006
$657$		0			0
$658$		−	3.78472i		−	0.147544i
$659$	34.6708			1.35058			0.675291	−	0.737552i	$-0.264018\pi$
$659$	34.6708			1.35058			0.675291	+	0.737552i	$0.264018\pi$
$660$		0			0
$661$	−9.67217			−0.376204			−0.188102	−	0.982150i	$-0.560234\pi$
$661$	−9.67217			−0.376204			−0.188102	+	0.982150i	$0.560234\pi$
$662$		−	62.2052i		−	2.41767i
$663$		0			0
$664$	68.6792			2.66527
$665$	−2.74549	−	1.90369i	−0.106465	−	0.0738218i
$666$		0			0
$667$		−	3.16348i		−	0.122491i
$668$		−	92.8405i		−	3.59211i
$669$		0			0
$670$	26.1224	−	37.6736i	1.00920	−	1.45546i
$671$	−14.0386			−0.541954
$672$		0			0
$673$			24.7689i			0.954770i	0.878694	+	0.477385i	$0.158415\pi$
$673$			24.7689i			0.954770i	−0.878694	+	0.477385i	$0.841585\pi$
$674$	29.5091			1.13665
$675$		0			0
$676$	−41.9941			−1.61516
$677$			33.3636i			1.28227i	0.767430	+	0.641133i	$0.221535\pi$
$677$			33.3636i			1.28227i	−0.767430	+	0.641133i	$0.778465\pi$
$678$		0			0
$679$	−0.475599			−0.0182518
$680$	−31.9684	+	46.1046i	−1.22593	+	1.76803i
$681$		0			0
$682$		−	41.2501i		−	1.57955i
$683$			13.9516i			0.533842i	0.963718	+	0.266921i	$0.0860063\pi$
$683$			13.9516i			0.533842i	−0.963718	+	0.266921i	$0.913994\pi$
$684$		0			0
$685$	−2.10360	−	1.45861i	−0.0803744	−	0.0557306i
$686$	6.09907			0.232864
$687$		0			0
$688$			49.0003i			1.86812i
$689$	9.86932			0.375991
$690$		0			0
$691$	50.5611			1.92344			0.961718	−	0.274042i	$-0.0883607\pi$
$691$	50.5611			1.92344			0.961718	+	0.274042i	$0.0883607\pi$
$692$			57.2276i			2.17547i
$693$		0			0
$694$	−2.08829			−0.0792705
$695$	−5.20700	+	7.50952i	−0.197513	+	0.284852i
$696$		0			0
$697$		−	42.3129i		−	1.60272i
$698$			21.2704i			0.805096i
$699$		0			0
$700$	3.52676	−	1.32043i	0.133299	−	0.0499077i
$701$	24.0803			0.909499			0.454749	−	0.890620i	$-0.349729\pi$
$701$	24.0803			0.909499			0.454749	+	0.890620i	$0.349729\pi$
$702$		0			0
$703$		−	17.0546i		−	0.643227i
$704$	−14.5002			−0.546496
$705$		0			0
$706$	−12.3574			−0.465078
$707$			1.11174i			0.0418114i
$708$		0			0
$709$	−0.769569			−0.0289018			−0.0144509	−	0.999896i	$-0.504600\pi$
$709$	−0.769569			−0.0289018			−0.0144509	+	0.999896i	$0.504600\pi$
$710$	28.9743	+	20.0904i	1.08738	+	0.753979i
$711$		0			0
$712$			97.4487i			3.65205i
$713$		−	10.1923i		−	0.381703i
$714$		0			0
$715$	−17.0601	−	11.8292i	−0.638010	−	0.442388i
$716$	−46.4766			−1.73691
$717$		0			0
$718$			11.8156i			0.440955i
$719$	4.92456			0.183655			0.0918275	−	0.995775i	$-0.470729\pi$
$719$	4.92456			0.183655			0.0918275	+	0.995775i	$0.470729\pi$
$720$		0			0
$721$	−1.22815			−0.0457388
$722$			139.357i			5.18632i
$723$		0			0
$724$	66.2780			2.46320
$725$	−1.75317	−	4.68256i	−0.0651111	−	0.173906i
$726$		0			0
$727$			41.8838i			1.55339i	0.629880	+	0.776693i	$0.283104\pi$
$727$			41.8838i			1.55339i	−0.629880	+	0.776693i	$0.716896\pi$
$728$		−	1.87076i		−	0.0693350i
$729$		0			0
$730$	21.6444	−	31.2155i	0.801096	−	1.15534i
$731$	33.5887			1.24232
$732$		0			0
$733$			27.1372i			1.00234i	0.865350	+	0.501168i	$0.167096\pi$
$733$			27.1372i			1.00234i	−0.865350	+	0.501168i	$0.832904\pi$
$734$	73.6730			2.71932
$735$		0			0
$736$	11.9746			0.441390
$737$			41.3650i			1.52370i
$738$		0			0
$739$	3.41445			0.125603			0.0628013	−	0.998026i	$-0.479997\pi$
$739$	3.41445			0.125603			0.0628013	+	0.998026i	$0.479997\pi$
$740$	15.7977	+	10.9539i	0.580735	+	0.402674i
$741$		0			0
$742$		−	2.35880i		−	0.0865942i
$743$			3.73961i			0.137193i	0.997644	+	0.0685966i	$0.0218521\pi$
$743$			3.73961i			0.137193i	−0.997644	+	0.0685966i	$0.978148\pi$
$744$		0			0
$745$	1.91462	−	2.76125i	0.0701461	−	0.101164i
$746$	−86.9513			−3.18351
$747$		0			0
$748$		−	93.7825i		−	3.42903i
$749$	0.160345			0.00585888
$750$		0			0
$751$	−24.1900			−0.882707			−0.441354	−	0.897333i	$-0.645502\pi$
$751$	−24.1900			−0.882707			−0.441354	+	0.897333i	$0.645502\pi$
$752$		−	53.6969i		−	1.95812i
$753$		0			0
$754$	−4.60158			−0.167580
$755$	−27.3807	+	39.4884i	−0.996487	+	1.43713i
$756$		0			0
$757$		−	3.55451i		−	0.129191i	−0.997912	−	0.0645953i	$-0.979424\pi$
$757$		−	3.55451i		−	0.129191i	0.997912	−	0.0645953i	$-0.0205757\pi$
$758$			8.06436i			0.292911i
$759$		0			0
$760$	−93.6097	−	64.9078i	−3.39558	−	2.35445i
$761$	44.2390			1.60366			0.801832	−	0.597550i	$-0.203859\pi$
$761$	44.2390			1.60366			0.801832	+	0.597550i	$0.203859\pi$
$762$		0			0
$763$			0.713522i			0.0258312i
$764$	−111.743			−4.04272
$765$		0			0
$766$	48.9769			1.76961
$767$			13.9977i			0.505426i
$768$		0			0
$769$	−6.30558			−0.227385			−0.113692	−	0.993516i	$-0.536268\pi$
$769$	−6.30558			−0.227385			−0.113692	+	0.993516i	$0.536268\pi$
$770$	−2.82722	+	4.07741i	−0.101886	+	0.146940i
$771$		0			0
$772$			99.4897i			3.58071i
$773$		−	24.2649i		−	0.872747i	−0.899766	−	0.436374i	$-0.856263\pi$
$773$		−	24.2649i		−	0.872747i	0.899766	−	0.436374i	$-0.143737\pi$
$774$		0			0
$775$	−5.64845	−	15.0865i	−0.202898	−	0.541924i
$776$	−16.2159			−0.582118
$777$		0			0
$778$			6.44570i			0.231090i
$779$	85.9111			3.07809
$780$		0			0
$781$	−31.8133			−1.13837
$782$		−	33.8365i		−	1.20999i
$783$		0			0
$784$	43.1732			1.54190
$785$	−20.4274	−	14.1641i	−0.729085	−	0.505538i
$786$		0			0
$787$			39.1338i			1.39497i	0.716600	+	0.697484i	$0.245697\pi$
$787$			39.1338i			1.39497i	−0.716600	+	0.697484i	$0.754303\pi$
$788$		−	3.65397i		−	0.130167i
$789$		0			0
$790$	−21.0507	−	14.5963i	−0.748950	−	0.519312i
$791$	−1.18653			−0.0421882
$792$		0			0
$793$			5.04558i			0.179174i
$794$	77.2307			2.74081
$795$		0			0
$796$	−115.596			−4.09719
$797$			29.3166i			1.03845i	0.854638	+	0.519224i	$0.173779\pi$
$797$			29.3166i			1.03845i	−0.854638	+	0.519224i	$0.826221\pi$
$798$		0			0
$799$	−36.8081			−1.30218
$800$	17.7248	−	6.63622i	0.626665	−	0.234626i
$801$		0			0
$802$		−	28.1201i		−	0.992956i
$803$			34.2741i			1.20951i
$804$		0			0
$805$	−0.698564	+	1.00747i	−0.0246211	+	0.0355085i
$806$	−14.8256			−0.522210
$807$		0			0
$808$			37.9059i			1.33352i
$809$	−28.7412			−1.01049			−0.505244	−	0.862977i	$-0.668597\pi$
$809$	−28.7412			−1.01049			−0.505244	+	0.862977i	$0.668597\pi$
$810$		0			0
$811$	4.04326			0.141978			0.0709891	−	0.997477i	$-0.477384\pi$
$811$	4.04326			0.141978			0.0709891	+	0.997477i	$0.477384\pi$
$812$			0.753170i			0.0264311i
$813$		0			0
$814$	−25.3284			−0.887759
$815$	−22.4512	−	15.5674i	−0.786430	−	0.545301i
$816$		0			0
$817$			68.1976i			2.38593i
$818$		−	33.7255i		−	1.17918i
$819$		0			0
$820$	−55.1794	+	79.5794i	−1.92695	+	2.77903i
$821$	−1.38325			−0.0482758			−0.0241379	−	0.999709i	$-0.507684\pi$
$821$	−1.38325			−0.0482758			−0.0241379	+	0.999709i	$0.507684\pi$
$822$		0			0
$823$		−	11.7734i		−	0.410395i	−0.978721	−	0.205197i	$-0.934216\pi$
$823$		−	11.7734i		−	0.410395i	0.978721	−	0.205197i	$-0.0657836\pi$
$824$	−41.8749			−1.45878
$825$		0			0
$826$	3.34549			0.116404
$827$			19.4700i			0.677040i	0.940959	+	0.338520i	$0.109926\pi$
$827$			19.4700i			0.677040i	−0.940959	+	0.338520i	$0.890074\pi$
$828$		0			0
$829$	−16.9194			−0.587634			−0.293817	−	0.955862i	$-0.594926\pi$
$829$	−16.9194			−0.587634			−0.293817	+	0.955862i	$0.594926\pi$
$830$	−37.3039	+	53.7995i	−1.29484	+	1.86741i
$831$		0			0
$832$			5.21147i			0.180675i
$833$		−	29.5943i		−	1.02538i
$834$		0			0
$835$	39.2563	+	27.2198i	1.35852	+	0.941982i
$836$	190.414			6.58560
$837$		0			0
$838$			73.8045i			2.54953i
$839$	17.9764			0.620615			0.310308	−	0.950636i	$-0.399568\pi$
$839$	17.9764			0.620615			0.310308	+	0.950636i	$0.399568\pi$
$840$		0			0
$841$	1.00000			0.0344828
$842$			25.4675i			0.877669i
$843$		0			0
$844$	−8.09878			−0.278772
$845$	12.3122	−	17.7566i	0.423553	−	0.610846i
$846$		0			0
$847$		−	2.57051i		−	0.0883237i
$848$		−	33.4662i		−	1.14923i
$849$		0			0
$850$	−18.7518	−	50.0845i	−0.643183	−	1.71789i
$851$	−6.25826			−0.214530
$852$		0			0
$853$		−	25.1608i		−	0.861489i	−0.902474	−	0.430744i	$-0.858251\pi$
$853$		−	25.1608i		−	0.861489i	0.902474	−	0.430744i	$-0.141749\pi$
$854$	1.20591			0.0412654
$855$		0			0
$856$	5.46710			0.186862
$857$			27.8748i			0.952184i	0.879395	+	0.476092i	$0.157947\pi$
$857$			27.8748i			0.952184i	−0.879395	+	0.476092i	$0.842053\pi$
$858$		0			0
$859$	−21.0421			−0.717947			−0.358973	−	0.933348i	$-0.616873\pi$
$859$	−21.0421			−0.717947			−0.358973	+	0.933348i	$0.616873\pi$
$860$	−63.1714	−	43.8022i	−2.15413	−	1.49364i
$861$		0			0
$862$		−	76.4113i		−	2.60258i
$863$			29.1647i			0.992779i	0.868100	+	0.496390i	$0.165341\pi$
$863$			29.1647i			0.992779i	−0.868100	+	0.496390i	$0.834659\pi$
$864$		0			0
$865$	−24.1979	−	16.7785i	−0.822753	−	0.570486i
$866$	16.3871			0.556858
$867$		0			0
$868$			2.42660i			0.0823642i
$869$	23.1133			0.784066
$870$		0			0
$871$	14.8669			0.503746
$872$			24.3281i			0.823854i
$873$		0			0
$874$	68.7008			2.32384
$875$	−0.475682	+	1.87838i	−0.0160810	+	0.0635009i
$876$		0			0
$877$		−	11.5743i		−	0.390836i	−0.980720	−	0.195418i	$-0.937394\pi$
$877$		−	11.5743i		−	0.390836i	0.980720	−	0.195418i	$-0.0626064\pi$
$878$			23.6856i			0.799350i
$879$		0			0
$880$	−40.1121	+	57.8495i	−1.35218	+	1.95011i
$881$	−21.8843			−0.737299			−0.368650	−	0.929568i	$-0.620180\pi$
$881$	−21.8843			−0.737299			−0.368650	+	0.929568i	$0.620180\pi$
$882$		0			0
$883$		−	20.2591i		−	0.681773i	−0.940104	−	0.340887i	$-0.889273\pi$
$883$		−	20.2591i		−	0.681773i	0.940104	−	0.340887i	$-0.110727\pi$
$884$	−33.7062			−1.13366
$885$		0			0
$886$	70.9517			2.38367
$887$		−	37.5330i		−	1.26023i	−0.776500	−	0.630117i	$-0.783007\pi$
$887$		−	37.5330i		−	1.26023i	0.776500	−	0.630117i	$-0.216993\pi$
$888$		0			0
$889$	0.911356			0.0305659
$890$	−76.3360	−	52.9304i	−2.55879	−	1.77423i
$891$		0			0
$892$		−	108.974i		−	3.64872i
$893$		−	74.7342i		−	2.50089i
$894$		0			0
$895$	13.6264	−	19.6520i	0.455481	−	0.656893i
$896$	2.55762			0.0854439
$897$		0			0
$898$		−	81.2719i		−	2.71208i
$899$	3.22185			0.107455
$900$		0			0
$901$	−22.9404			−0.764254
$902$		−	127.589i		−	4.24826i
$903$		0			0
$904$	−40.4558			−1.34554
$905$	−19.4320	+	28.0247i	−0.645941	+	0.931573i
$906$		0			0
$907$		−	17.7096i		−	0.588037i	−0.955800	−	0.294018i	$-0.905007\pi$
$907$		−	17.7096i		−	0.588037i	0.955800	−	0.294018i	$-0.0949927\pi$
$908$		−	88.6004i		−	2.94031i
$909$		0			0
$910$	1.46545	+	1.01613i	0.0485793	+	0.0336843i
$911$	6.63407			0.219796			0.109898	−	0.993943i	$-0.464948\pi$
$911$	6.63407			0.219796			0.109898	+	0.993943i	$0.464948\pi$
$912$		0			0
$913$		−	59.0710i		−	1.95497i
$914$	68.3845			2.26196
$915$		0			0
$916$	−25.3871			−0.838813
$917$			3.07032i			0.101391i
$918$		0			0
$919$	−4.71782			−0.155626			−0.0778132	−	0.996968i	$-0.524794\pi$
$919$	−4.71782			−0.155626			−0.0778132	+	0.996968i	$0.524794\pi$
$920$	−23.8181	+	34.3504i	−0.785261	+	1.13250i
$921$		0			0
$922$		−	17.6572i		−	0.581510i
$923$			11.4339i			0.376353i
$924$		0			0
$925$	−9.26342	+	3.46826i	−0.304580	+	0.114036i
$926$	54.8127			1.80126
$927$		0			0
$928$			3.78527i			0.124257i
$929$	43.4668			1.42610			0.713049	−	0.701114i	$-0.247314\pi$
$929$	43.4668			1.42610			0.713049	+	0.701114i	$0.247314\pi$
$930$		0			0
$931$	60.0876			1.96929
$932$			61.3690i			2.01021i
$933$		0			0
$934$	−77.5437			−2.53731
$935$	39.6546	+	27.4960i	1.29684	+	0.899216i
$936$		0			0
$937$		−	50.9680i		−	1.66505i	−0.553986	−	0.832526i	$-0.686894\pi$
$937$		−	50.9680i		−	1.66505i	0.553986	−	0.832526i	$-0.313106\pi$
$938$		−	3.55324i		−	0.116017i
$939$		0			0
$940$	69.2263	+	48.0006i	2.25791	+	1.56561i
$941$	−11.0790			−0.361165			−0.180583	−	0.983560i	$-0.557798\pi$
$941$	−11.0790			−0.361165			−0.180583	+	0.983560i	$0.557798\pi$
$942$		0			0
$943$		−	31.5254i		−	1.02661i
$944$	47.4651			1.54486
$945$		0			0
$946$	101.282			3.29298
$947$			58.5923i			1.90399i	0.306107	+	0.951997i	$0.400974\pi$
$947$			58.5923i			1.90399i	−0.306107	+	0.951997i	$0.599026\pi$
$948$		0			0
$949$	12.3184			0.399872
$950$	101.690	−	38.0733i	3.29927	−	1.23526i
$951$		0			0
$952$			4.34842i			0.140933i
$953$		−	22.9017i		−	0.741859i	−0.928661	−	0.370929i	$-0.879039\pi$
$953$		−	22.9017i		−	0.741859i	0.928661	−	0.370929i	$-0.120961\pi$
$954$		0			0
$955$	32.7619	−	47.2490i	1.06015	−	1.52894i
$956$	27.7720			0.898211
$957$		0			0
$958$		−	15.8510i		−	0.512123i
$959$	−0.198404			−0.00640680
$960$		0			0
$961$	−20.6197			−0.665151
$962$			9.10321i			0.293499i
$963$		0			0
$964$	44.2019			1.42365
$965$	−42.0678	−	29.1693i	−1.35421	−	0.938993i
$966$		0			0
$967$			49.6623i			1.59703i	0.601973	+	0.798516i	$0.294381\pi$
$967$			49.6623i			1.59703i	−0.601973	+	0.798516i	$0.705619\pi$
$968$		−	87.6437i		−	2.81698i
$969$		0			0
$970$	8.80788	−	12.7027i	0.282804	−	0.407859i
$971$	6.90899			0.221720			0.110860	−	0.993836i	$-0.464639\pi$
$971$	6.90899			0.221720			0.110860	+	0.993836i	$0.464639\pi$
$972$		0			0
$973$			0.708271i			0.0227061i
$974$	−76.4305			−2.44899
$975$		0			0
$976$	17.1092			0.547653
$977$		−	8.17310i		−	0.261481i	−0.991417	−	0.130740i	$-0.958265\pi$
$977$		−	8.17310i		−	0.261481i	0.991417	−	0.130740i	$-0.0417354\pi$
$978$		0			0
$979$	83.8158			2.67876
$980$	−38.5933	+	55.6591i	−1.23282	+	1.77796i
$981$		0			0
$982$		−	44.7949i		−	1.42946i
$983$			24.1451i			0.770108i	0.922894	+	0.385054i	$0.125817\pi$
$983$			24.1451i			0.770108i	−0.922894	+	0.385054i	$0.874183\pi$
$984$		0			0
$985$	1.54503	+	1.07130i	0.0492287	+	0.0341346i
$986$	10.6960			0.340629
$987$		0			0
$988$		−	68.4362i		−	2.17724i
$989$	25.0253			0.795760
$990$		0			0
$991$	−51.7396			−1.64356			−0.821781	−	0.569803i	$-0.807020\pi$
$991$	−51.7396			−1.64356			−0.821781	+	0.569803i	$0.807020\pi$
$992$			12.1956i			0.387210i
$993$		0			0
$994$	2.73275			0.0866775
$995$	33.8915	−	48.8781i	1.07443	−	1.54954i
$996$		0			0
$997$			9.07880i			0.287528i	0.989612	+	0.143764i	$0.0459207\pi$
$997$			9.07880i			0.287528i	−0.989612	+	0.143764i	$0.954079\pi$
$998$		−	0.660625i		−	0.0209117i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1305.2.c.j.784.10		10
3.2	odd	2		435.2.c.e.349.1	✓	10
5.2	odd	4		6525.2.a.bl.1.1		5
5.3	odd	4		6525.2.a.bs.1.5		5
5.4	even	2	inner	1305.2.c.j.784.1		10
15.2	even	4		2175.2.a.z.1.5		5
15.8	even	4		2175.2.a.w.1.1		5
15.14	odd	2		435.2.c.e.349.10	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
435.2.c.e.349.1	✓	10	3.2	odd	2
435.2.c.e.349.10	yes	10	15.14	odd	2
1305.2.c.j.784.1		10	5.4	even	2	inner
1305.2.c.j.784.10		10	1.1	even	1	trivial
2175.2.a.w.1.1		5	15.8	even	4
2175.2.a.z.1.5		5	15.2	even	4
6525.2.a.bl.1.1		5	5.2	odd	4
6525.2.a.bs.1.5		5	5.3	odd	4

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:	\( N \)	\(=\)	\( 1305 = 3^{2} \cdot 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1305.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+2.51908i q^{2} -4.34577 q^{4} +(1.27413 - 1.83755i) q^{5} -0.173311i q^{7} -5.90919i q^{8} +(4.62893 + 3.20964i) q^{10} -5.08250 q^{11} +1.82669i q^{13} +0.436584 q^{14} +6.19418 q^{16} -4.24598i q^{17} +8.62093 q^{19} +(-5.53709 + 7.98556i) q^{20} -12.8032i q^{22} -3.16348i q^{23} +(-1.75317 - 4.68256i) q^{25} -4.60158 q^{26} +0.753170i q^{28} +1.00000 q^{29} +3.22185 q^{31} +3.78527i q^{32} +10.6960 q^{34} +(-0.318467 - 0.220821i) q^{35} -1.97828i q^{37} +21.7168i q^{38} +(-10.8584 - 7.52909i) q^{40} +9.96541 q^{41} +7.91070i q^{43} +22.0874 q^{44} +7.96907 q^{46} -8.66893i q^{47} +6.96996 q^{49} +(11.7958 - 4.41638i) q^{50} -7.93837i q^{52} -5.40285i q^{53} +(-6.47578 + 9.33933i) q^{55} -1.02413 q^{56} +2.51908i q^{58} +7.66286 q^{59} +2.76215 q^{61} +8.11611i q^{62} +2.85296 q^{64} +(3.35663 + 2.32744i) q^{65} -8.13872i q^{67} +18.4520i q^{68} +(0.556267 - 0.802245i) q^{70} +6.25938 q^{71} -6.74356i q^{73} +4.98345 q^{74} -37.4646 q^{76} +0.880853i q^{77} -4.54763 q^{79} +(7.89221 - 11.3821i) q^{80} +25.1037i q^{82} +11.6224i q^{83} +(-7.80219 - 5.40994i) q^{85} -19.9277 q^{86} +30.0334i q^{88} -16.4911 q^{89} +0.316585 q^{91} +13.7478i q^{92} +21.8377 q^{94} +(10.9842 - 15.8414i) q^{95} -2.74419i q^{97} +17.5579i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 10 q^{4} + 4 q^{10} - 24 q^{11} + 12 q^{14} + 2 q^{16} + 4 q^{19} - 8 q^{20} + 2 q^{25} + 10 q^{29} + 4 q^{31} - 8 q^{34} - 2 q^{35} - 14 q^{40} + 28 q^{41} + 40 q^{44} - 12 q^{46} + 14 q^{49} + 12 q^{50}+ \cdots + 36 q^{95}+O(q^{100}) \) 10 * q - 10 * q^4 + 4 * q^10 - 24 * q^11 + 12 * q^14 + 2 * q^16 + 4 * q^19 - 8 * q^20 + 2 * q^25 + 10 * q^29 + 4 * q^31 - 8 * q^34 - 2 * q^35 - 14 * q^40 + 28 * q^41 + 40 * q^44 - 12 * q^46 + 14 * q^49 + 12 * q^50 + 2 * q^55 + 4 * q^56 + 8 * q^59 - 24 * q^61 + 18 * q^64 - 6 * q^65 + 20 * q^70 - 60 * q^71 + 4 * q^74 - 88 * q^76 + 36 * q^79 + 30 * q^80 - 14 * q^85 - 60 * q^86 - 44 * q^89 - 24 * q^91 + 100 * q^94 + 36 * q^95

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