LMFDB - Embedded newform 540.2.y.a.127.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [540,2,Mod(127,540)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(540, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 8, 3]))

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

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

chi := DirichletCharacter("540.127");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 540 = 2^{2} \cdot 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	540.y (of order $12$, degree $4$, not 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:	$4.31192170915$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$32$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 180)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			127.10
Character	$\chi$	$=$	540.127
Dual form			540.2.y.a.523.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.755096 + 1.19576i) q^{2} +(-0.859661 - 1.80582i) q^{4} +(-1.61454 + 1.54701i) q^{5} +(0.797301 + 2.97557i) q^{7} +(2.80844 + 0.335623i) q^{8} +O(q^{10})$	\(q+(-0.755096 + 1.19576i) q^{2} +(-0.859661 - 1.80582i) q^{4} +(-1.61454 + 1.54701i) q^{5} +(0.797301 + 2.97557i) q^{7} +(2.80844 + 0.335623i) q^{8} +(-0.630711 - 3.09874i) q^{10} +(-2.54830 - 1.47126i) q^{11} +(-2.11632 - 0.567067i) q^{13} +(-4.16009 - 1.29346i) q^{14} +(-2.52197 + 3.10478i) q^{16} +(0.109902 + 0.109902i) q^{17} +2.50211 q^{19} +(4.18158 + 1.58567i) q^{20} +(3.68348 - 1.93620i) q^{22} +(-1.26276 + 4.71270i) q^{23} +(0.213509 - 4.99544i) q^{25} +(2.27610 - 2.10242i) q^{26} +(4.68793 - 3.99776i) q^{28} +(-9.13227 - 5.27252i) q^{29} +(-8.05006 + 4.64770i) q^{31} +(-1.80823 - 5.36006i) q^{32} +(-0.214403 + 0.0484295i) q^{34} +(-5.89052 - 3.57075i) q^{35} +(-5.45569 - 5.45569i) q^{37} +(-1.88933 + 2.99191i) q^{38} +(-5.05357 + 3.80282i) q^{40} +(-2.78349 - 4.82114i) q^{41} +(1.54239 - 0.413282i) q^{43} +(-0.466160 + 5.86656i) q^{44} +(-4.68173 - 5.06850i) q^{46} +(0.721510 + 2.69271i) q^{47} +(-2.15614 + 1.24485i) q^{49} +(5.81210 + 4.02734i) q^{50} +(0.795299 + 4.30918i) q^{52} +(3.28818 - 3.28818i) q^{53} +(6.39041 - 1.56683i) q^{55} +(1.24051 + 8.62431i) q^{56} +(13.2004 - 6.93870i) q^{58} +(2.97451 + 5.15200i) q^{59} +(-2.48830 + 4.30987i) q^{61} +(0.521051 - 13.1354i) q^{62} +(7.77471 + 1.88516i) q^{64} +(4.29416 - 2.35842i) q^{65} +(0.726612 + 0.194695i) q^{67} +(0.103985 - 0.292942i) q^{68} +(8.71765 - 4.34736i) q^{70} -1.38203i q^{71} +(-6.06724 + 6.06724i) q^{73} +(10.6432 - 2.40410i) q^{74} +(-2.15096 - 4.51835i) q^{76} +(2.34608 - 8.75569i) q^{77} +(-5.25956 + 9.10982i) q^{79} +(-0.731307 - 8.91432i) q^{80} +(7.86671 + 0.312055i) q^{82} +(4.30492 - 1.15350i) q^{83} +(-0.347462 - 0.00742201i) q^{85} +(-0.670467 + 2.15639i) q^{86} +(-6.66297 - 4.98723i) q^{88} +13.8844i q^{89} -6.74939i q^{91} +(9.59583 - 1.77100i) q^{92} +(-3.76463 - 1.17051i) q^{94} +(-4.03976 + 3.87079i) q^{95} +(3.85933 - 1.03410i) q^{97} +(0.139559 - 3.51820i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q + 2 q^{2} + 4 q^{5} + 8 q^{8}+O(q^{10}) $ 128 * q + 2 * q^2 + 4 * q^5 + 8 * q^8	$ 128 q + 2 q^{2} + 4 q^{5} + 8 q^{8} - 8 q^{10} - 4 q^{13} - 4 q^{16} + 16 q^{17} + 18 q^{20} - 10 q^{22} - 4 q^{25} + 48 q^{26} + 8 q^{28} - 18 q^{32} - 16 q^{37} + 34 q^{38} - 2 q^{40} + 8 q^{41} - 40 q^{46} - 38 q^{50} - 18 q^{52} + 64 q^{53} + 32 q^{56} - 10 q^{58} - 8 q^{61} - 44 q^{62} - 12 q^{65} - 58 q^{68} - 22 q^{70} - 16 q^{73} - 32 q^{76} + 60 q^{77} - 132 q^{80} - 4 q^{85} - 32 q^{86} - 10 q^{88} - 52 q^{92} - 4 q^{97} - 164 q^{98}+O(q^{100}) $ 128 * q + 2 * q^2 + 4 * q^5 + 8 * q^8 - 8 * q^10 - 4 * q^13 - 4 * q^16 + 16 * q^17 + 18 * q^20 - 10 * q^22 - 4 * q^25 + 48 * q^26 + 8 * q^28 - 18 * q^32 - 16 * q^37 + 34 * q^38 - 2 * q^40 + 8 * q^41 - 40 * q^46 - 38 * q^50 - 18 * q^52 + 64 * q^53 + 32 * q^56 - 10 * q^58 - 8 * q^61 - 44 * q^62 - 12 * q^65 - 58 * q^68 - 22 * q^70 - 16 * q^73 - 32 * q^76 + 60 * q^77 - 132 * q^80 - 4 * q^85 - 32 * q^86 - 10 * q^88 - 52 * q^92 - 4 * q^97 - 164 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/540\mathbb{Z}\right)^\times$.

$n$	$217$	$271$	$461$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.755096	+	1.19576i	−0.533933	+	0.845527i
$2$	−0.755096	+	1.19576i	−0.533933	+	0.845527i
$3$		0			0
$3$		0			0
$4$	−0.859661	−	1.80582i	−0.429830	−	0.902910i
$5$	−1.61454	+	1.54701i	−0.722046	+	0.691845i
$5$	−1.61454	+	1.54701i	−0.722046	+	0.691845i
$6$		0			0
$7$	0.797301	+	2.97557i	0.301352	+	1.12466i	0.936041	+	0.351892i	$0.114461\pi$
$7$	0.797301	+	2.97557i	0.301352	+	1.12466i	−0.634689	+	0.772767i	$0.718872\pi$
$8$	2.80844	+	0.335623i	0.992935	+	0.118661i
$9$		0			0
$10$	−0.630711	−	3.09874i	−0.199448	−	0.979908i
$11$	−2.54830	−	1.47126i	−0.768342	−	0.443602i	0.0639409	−	0.997954i	$-0.479633\pi$
$11$	−2.54830	−	1.47126i	−0.768342	−	0.443602i	−0.832283	+	0.554351i	$0.812966\pi$
$12$		0			0
$13$	−2.11632	−	0.567067i	−0.586963	−	0.157276i	−0.0468980	−	0.998900i	$-0.514934\pi$
$13$	−2.11632	−	0.567067i	−0.586963	−	0.157276i	−0.540065	+	0.841623i	$0.681600\pi$
$14$	−4.16009	−	1.29346i	−1.11183	−	0.345692i
$15$		0			0
$16$	−2.52197	+	3.10478i	−0.630492	+	0.776196i
$17$	0.109902	+	0.109902i	0.0266552	+	0.0266552i	0.720309	−	0.693654i	$-0.244000\pi$
$17$	0.109902	+	0.109902i	0.0266552	+	0.0266552i	−0.693654	+	0.720309i	$0.744000\pi$
$18$		0			0
$19$	2.50211			0.574023			0.287011	−	0.957927i	$-0.407338\pi$
$19$	2.50211			0.574023			0.287011	+	0.957927i	$0.407338\pi$
$20$	4.18158	+	1.58567i	0.935031	+	0.354567i
$21$		0			0
$22$	3.68348	−	1.93620i	0.785321	−	0.412799i
$23$	−1.26276	+	4.71270i	−0.263305	+	0.982666i	0.699975	+	0.714167i	$0.253194\pi$
$23$	−1.26276	+	4.71270i	−0.263305	+	0.982666i	−0.963280	+	0.268499i	$0.913472\pi$
$24$		0			0
$25$	0.213509	−	4.99544i	0.0427018	−	0.999088i
$26$	2.27610	−	2.10242i	0.446380	−	0.412318i
$27$		0			0
$28$	4.68793	−	3.99776i	0.885936	−	0.755506i
$29$	−9.13227	−	5.27252i	−1.69582	−	0.979082i	−0.949643	−	0.313335i	$-0.898554\pi$
$29$	−9.13227	−	5.27252i	−1.69582	−	0.979082i	−0.746178	−	0.665747i	$-0.768113\pi$
$30$		0			0
$31$	−8.05006	+	4.64770i	−1.44583	+	0.834752i	−0.998229	−	0.0594800i	$-0.981056\pi$
$31$	−8.05006	+	4.64770i	−1.44583	+	0.834752i	−0.447604	+	0.894232i	$0.647722\pi$
$32$	−1.80823	−	5.36006i	−0.319653	−	0.947535i
$33$		0			0
$34$	−0.214403	+	0.0484295i	−0.0367698	+	0.00830559i
$35$	−5.89052	−	3.57075i	−0.995679	−	0.603568i
$36$		0			0
$37$	−5.45569	−	5.45569i	−0.896910	−	0.896910i	0.0982513	−	0.995162i	$-0.468675\pi$
$37$	−5.45569	−	5.45569i	−0.896910	−	0.896910i	−0.995162	+	0.0982513i	$0.968675\pi$
$38$	−1.88933	+	2.99191i	−0.306490	+	0.485351i
$39$		0			0
$40$	−5.05357	+	3.80282i	−0.799040	+	0.601278i
$41$	−2.78349	−	4.82114i	−0.434708	−	0.752936i	0.562564	−	0.826754i	$-0.309815\pi$
$41$	−2.78349	−	4.82114i	−0.434708	−	0.752936i	−0.997272	+	0.0738176i	$0.976482\pi$
$42$		0			0
$43$	1.54239	−	0.413282i	0.235212	−	0.0630249i	−0.139288	−	0.990252i	$-0.544481\pi$
$43$	1.54239	−	0.413282i	0.235212	−	0.0630249i	0.374499	+	0.927227i	$0.377815\pi$
$44$	−0.466160	+	5.86656i	−0.0702763	+	0.884417i
$45$		0			0
$46$	−4.68173	−	5.06850i	−0.690283	−	0.747309i
$47$	0.721510	+	2.69271i	0.105243	+	0.392772i	0.998373	−	0.0570272i	$-0.0181622\pi$
$47$	0.721510	+	2.69271i	0.105243	+	0.392772i	−0.893130	+	0.449799i	$0.851496\pi$
$48$		0			0
$49$	−2.15614	+	1.24485i	−0.308020	+	0.177835i
$50$	5.81210	+	4.02734i	0.821955	+	0.569552i
$51$		0			0
$52$	0.795299	+	4.30918i	0.110288	+	0.597576i
$53$	3.28818	−	3.28818i	0.451666	−	0.451666i	−0.444241	−	0.895907i	$-0.646527\pi$
$53$	3.28818	−	3.28818i	0.451666	−	0.451666i	0.895907	+	0.444241i	$0.146527\pi$
$54$		0			0
$55$	6.39041	−	1.56683i	0.861682	−	0.211272i
$56$	1.24051	+	8.62431i	0.165770	+	1.15247i
$57$		0			0
$58$	13.2004	−	6.93870i	1.73329	−	0.911096i
$59$	2.97451	+	5.15200i	0.387248	+	0.670734i	0.992078	−	0.125621i	$-0.0400923\pi$
$59$	2.97451	+	5.15200i	0.387248	+	0.670734i	−0.604830	+	0.796355i	$0.706759\pi$
$60$		0			0
$61$	−2.48830	+	4.30987i	−0.318595	+	0.551822i	−0.980195	−	0.198034i	$-0.936544\pi$
$61$	−2.48830	+	4.30987i	−0.318595	+	0.551822i	0.661600	+	0.749857i	$0.269878\pi$
$62$	0.521051	−	13.1354i	0.0661735	−	1.66819i
$63$		0			0
$64$	7.77471	+	1.88516i	0.971839	+	0.235645i
$65$	4.29416	−	2.35842i	0.532625	−	0.292526i
$66$		0			0
$67$	0.726612	+	0.194695i	0.0887698	+	0.0237858i	0.302931	−	0.953013i	$-0.402035\pi$
$67$	0.726612	+	0.194695i	0.0887698	+	0.0237858i	−0.214161	+	0.976798i	$0.568702\pi$
$68$	0.103985	−	0.292942i	0.0126100	−	0.0355245i
$69$		0			0
$70$	8.71765	−	4.34736i	1.04196	−	0.519608i
$71$		−	1.38203i		−	0.164016i	−0.996632	−	0.0820081i	$-0.973867\pi$
$71$		−	1.38203i		−	0.164016i	0.996632	−	0.0820081i	$-0.0261334\pi$
$72$		0			0
$73$	−6.06724	+	6.06724i	−0.710117	+	0.710117i	−0.966560	−	0.256442i	$-0.917450\pi$
$73$	−6.06724	+	6.06724i	−0.710117	+	0.710117i	0.256442	+	0.966560i	$0.417450\pi$
$74$	10.6432	−	2.40410i	1.23725	−	0.279471i
$75$		0			0
$76$	−2.15096	−	4.51835i	−0.246732	−	0.518291i
$77$	2.34608	−	8.75569i	0.267360	−	0.997803i
$78$		0			0
$79$	−5.25956	+	9.10982i	−0.591747	+	1.02494i	0.402250	+	0.915530i	$0.368228\pi$
$79$	−5.25956	+	9.10982i	−0.591747	+	1.02494i	−0.993997	+	0.109406i	$0.965105\pi$
$80$	−0.731307	−	8.91432i	−0.0817626	−	0.996652i
$81$		0			0
$82$	7.86671	+	0.312055i	0.868733	+	0.0344607i
$83$	4.30492	−	1.15350i	0.472526	−	0.126613i	−0.0146943	−	0.999892i	$-0.504678\pi$
$83$	4.30492	−	1.15350i	0.472526	−	0.126613i	0.487220	+	0.873279i	$0.338011\pi$
$84$		0			0
$85$	−0.347462	−	0.00742201i	−0.0376876	−	0.000805030i
$86$	−0.670467	+	2.15639i	−0.0722983	+	0.232529i
$87$		0			0
$88$	−6.66297	−	4.98723i	−0.710275	−	0.531640i
$89$			13.8844i			1.47174i	0.677122	+	0.735871i	$0.263227\pi$
$89$			13.8844i			1.47174i	−0.677122	+	0.735871i	$0.736773\pi$
$90$		0			0
$91$		−	6.74939i		−	0.707528i
$92$	9.59583	−	1.77100i	1.00043	−	0.184639i
$93$		0			0
$94$	−3.76463	−	1.17051i	−0.388292	−	0.120728i
$95$	−4.03976	+	3.87079i	−0.414471	+	0.397135i
$96$		0			0
$97$	3.85933	−	1.03410i	0.391855	−	0.104997i	−0.0575111	−	0.998345i	$-0.518316\pi$
$97$	3.85933	−	1.03410i	0.391855	−	0.104997i	0.449366	+	0.893348i	$0.351650\pi$
$98$	0.139559	−	3.51820i	0.0140976	−	0.355391i
$99$		0			0
$100$	−9.20441	+	3.90882i	−0.920441	+	0.390882i
$101$	2.84896	−	4.93454i	0.283482	−	0.491005i	−0.688758	−	0.724991i	$-0.741844\pi$
$101$	2.84896	−	4.93454i	0.283482	−	0.491005i	0.972240	+	0.233986i	$0.0751770\pi$
$102$		0			0
$103$	−0.854408	+	3.18870i	−0.0841874	+	0.314192i	−0.995159	−	0.0982773i	$-0.968667\pi$
$103$	−0.854408	+	3.18870i	−0.0841874	+	0.314192i	0.910972	+	0.412469i	$0.135333\pi$
$104$	−5.75326	−	2.30286i	−0.564153	−	0.225814i
$105$		0			0
$106$	1.44897	+	6.41475i	0.140736	+	0.623056i
$107$	−2.25402	+	2.25402i	−0.217904	+	0.217904i	−0.807615	−	0.589711i	$-0.799242\pi$
$107$	−2.25402	+	2.25402i	−0.217904	+	0.217904i	0.589711	+	0.807615i	$0.299242\pi$
$108$		0			0
$109$			16.8675i			1.61562i	0.589445	+	0.807809i	$0.299347\pi$
$109$			16.8675i			1.61562i	−0.589445	+	0.807809i	$0.700653\pi$
$110$	−2.95182	+	8.82447i	−0.281445	+	0.841380i
$111$		0			0
$112$	−11.2493	−	5.02884i	−1.06296	−	0.475181i
$113$	15.9361	+	4.27006i	1.49914	+	0.401694i	0.912812	−	0.408379i	$-0.133906\pi$
$113$	15.9361	+	4.27006i	1.49914	+	0.401694i	0.586329	+	0.810073i	$0.300573\pi$
$114$		0			0
$115$	−5.25181	−	9.56238i	−0.489734	−	0.891696i
$116$	−1.67056	+	21.0238i	−0.155108	+	1.95201i
$117$		0			0
$118$	−8.40658	−	0.333470i	−0.773888	−	0.0306984i
$119$	−0.239397	+	0.414647i	−0.0219455	+	0.0380106i
$120$		0			0
$121$	−1.17077	−	2.02784i	−0.106434	−	0.184349i
$122$	−3.27464	−	6.22977i	−0.296472	−	0.564017i
$123$		0			0
$124$	15.3132	+	10.5415i	1.37517	+	0.946655i
$125$	7.38328	+	8.39566i	0.660381	+	0.750931i
$126$		0			0
$127$	−2.50315	+	2.50315i	−0.222119	+	0.222119i	−0.809390	−	0.587271i	$-0.800202\pi$
$127$	−2.50315	+	2.50315i	−0.222119	+	0.222119i	0.587271	+	0.809390i	$0.300202\pi$
$128$	−8.12484	+	7.87318i	−0.718141	+	0.695897i
$129$		0			0
$130$	−0.422406	+	6.91560i	−0.0370475	+	0.606538i
$131$	1.89068	−	1.09158i	0.165189	−	0.0953722i	−0.415126	−	0.909764i	$-0.636263\pi$
$131$	1.89068	−	1.09158i	0.165189	−	0.0953722i	0.580316	+	0.814392i	$0.302929\pi$
$132$		0			0
$133$	1.99493	+	7.44519i	0.172983	+	0.645580i
$134$	−0.781470	+	0.721837i	−0.0675087	+	0.0623572i
$135$		0			0
$136$	0.271769	+	0.345540i	0.0233040	+	0.0296298i
$137$	−9.49360	+	2.54380i	−0.811093	+	0.217332i	−0.640449	−	0.768001i	$-0.721252\pi$
$137$	−9.49360	+	2.54380i	−0.811093	+	0.217332i	−0.170644	+	0.985333i	$0.554585\pi$
$138$		0			0
$139$	−6.69866	−	11.6024i	−0.568173	−	0.984104i	−0.996747	−	0.0805971i	$-0.974317\pi$
$139$	−6.69866	−	11.6024i	−0.568173	−	0.984104i	0.428574	−	0.903507i	$-0.359016\pi$
$140$	−1.38429	+	13.7068i	−0.116994	+	1.15844i
$141$		0			0
$142$	1.65256	+	1.04356i	0.138680	+	0.0875738i
$143$	4.55873	+	4.55873i	0.381220	+	0.381220i
$144$		0			0
$145$	22.9011	−	5.61501i	1.90183	−	0.466302i
$146$	−2.67359	−	11.8363i	−0.221268	−	0.979578i
$147$		0			0
$148$	−5.16195	+	14.5420i	−0.424310	+	1.19535i
$149$	−2.71903	+	1.56984i	−0.222752	+	0.128606i	−0.607224	−	0.794531i	$-0.707717\pi$
$149$	−2.71903	+	1.56984i	−0.222752	+	0.128606i	0.384472	+	0.923137i	$0.374384\pi$
$150$		0			0
$151$	14.0987	+	8.13990i	1.14734	+	0.662416i	0.948237	−	0.317563i	$-0.102864\pi$
$151$	14.0987	+	8.13990i	1.14734	+	0.662416i	0.199101	+	0.979979i	$0.436198\pi$
$152$	7.02703	+	0.839765i	0.569967	+	0.0681140i
$153$		0			0
$154$	8.69814	+	9.41672i	0.700916	+	0.758821i
$155$	5.80713	−	19.9575i	0.466440	−	1.60302i
$156$		0			0
$157$	−0.337873	+	1.26096i	−0.0269652	+	0.100635i	−0.978097	−	0.208150i	$-0.933256\pi$
$157$	−0.337873	+	1.26096i	−0.0269652	+	0.100635i	0.951132	+	0.308785i	$0.0999225\pi$
$158$	−6.92165	−	13.1679i	−0.550657	−	1.04758i
$159$		0			0
$160$	11.2116	+	5.85671i	0.886351	+	0.463013i
$161$	−15.0298			−1.18451
$162$		0			0
$163$	11.7230	+	11.7230i	0.918216	+	0.918216i	0.996900	−	0.0786833i	$-0.0250716\pi$
$163$	11.7230	+	11.7230i	0.918216	+	0.918216i	−0.0786833	+	0.996900i	$0.525072\pi$
$164$	−6.31326	+	9.17103i	−0.492983	+	0.716137i
$165$		0			0
$166$	−1.87132	+	6.01863i	−0.145243	+	0.467136i
$167$	7.18609	+	1.92551i	0.556076	+	0.149000i	0.525903	−	0.850545i	$-0.323727\pi$
$167$	7.18609	+	1.92551i	0.556076	+	0.149000i	0.0301731	+	0.999545i	$0.490394\pi$
$168$		0			0
$169$	−7.10107	−	4.09980i	−0.546236	−	0.315369i
$170$	0.271242	−	0.409876i	0.0208033	−	0.0314360i
$171$		0			0
$172$	−2.07224	−	2.42999i	−0.158007	−	0.185285i
$173$	3.87498	+	14.4616i	0.294609	+	1.09950i	0.941527	+	0.336937i	$0.109391\pi$
$173$	3.87498	+	14.4616i	0.294609	+	1.09950i	−0.646918	+	0.762559i	$0.723942\pi$
$174$		0			0
$175$	15.0345	−	3.34756i	1.13650	−	0.253052i
$176$	10.9947	−	4.20145i	0.828756	−	0.316696i
$177$		0			0
$178$	−16.6023	−	10.4840i	−1.24440	−	0.785812i
$179$	−17.1196			−1.27958			−0.639788	−	0.768551i	$-0.720978\pi$
$179$	−17.1196			−1.27958			−0.639788	+	0.768551i	$0.720978\pi$
$180$		0			0
$181$	6.55984			0.487589			0.243794	−	0.969827i	$-0.421608\pi$
$181$	6.55984			0.487589			0.243794	+	0.969827i	$0.421608\pi$
$182$	8.07062	+	5.09644i	0.598234	+	0.377773i
$183$		0			0
$184$	−5.12809	+	12.8115i	−0.378048	+	0.944479i
$185$	17.2485	+	0.368438i	1.26813	+	0.0270881i
$186$		0			0
$187$	−0.118369	−	0.441759i	−0.00865600	−	0.0323046i
$188$	4.24230	−	3.61773i	0.309401	−	0.263850i
$189$		0			0
$190$	−1.57811	−	7.75338i	−0.114488	−	0.562490i
$191$	−13.7567	−	7.94243i	−0.995399	−	0.574694i	−0.0885153	−	0.996075i	$-0.528212\pi$
$191$	−13.7567	−	7.94243i	−0.995399	−	0.574694i	−0.906884	+	0.421381i	$0.861546\pi$
$192$		0			0
$193$	0.708340	+	0.189799i	0.0509874	+	0.0136620i	0.284223	−	0.958758i	$-0.408265\pi$
$193$	0.708340	+	0.189799i	0.0509874	+	0.0136620i	−0.233235	+	0.972420i	$0.574931\pi$
$194$	−1.67763	+	5.39566i	−0.120447	+	0.387386i
$195$		0			0
$196$	4.10152	+	2.82345i	0.292966	+	0.201675i
$197$	−3.91134	−	3.91134i	−0.278671	−	0.278671i	0.553907	−	0.832578i	$-0.313136\pi$
$197$	−3.91134	−	3.91134i	−0.278671	−	0.278671i	−0.832578	+	0.553907i	$0.813136\pi$
$198$		0			0
$199$	−23.0871			−1.63660			−0.818299	−	0.574792i	$-0.805083\pi$
$199$	−23.0871			−1.63660			−0.818299	+	0.574792i	$0.805083\pi$
$200$	2.27621	−	13.9578i	0.160953	−	0.986962i
$201$		0			0
$202$	3.74927	+	7.13271i	0.263797	+	0.501856i
$203$	8.40757	−	31.3775i	0.590096	−	2.20227i
$204$		0			0
$205$	11.9524	+	3.47786i	0.834794	+	0.242904i
$206$	−3.16774	−	3.42943i	−0.220707	−	0.238940i
$207$		0			0
$208$	7.09792	−	5.14060i	0.492152	−	0.356437i
$209$	−6.37612	−	3.68126i	−0.441046	−	0.254638i
$210$		0			0
$211$	4.08882	−	2.36068i	0.281486	−	0.162516i	−0.352610	−	0.935770i	$-0.614706\pi$
$211$	4.08882	−	2.36068i	0.281486	−	0.162516i	0.634096	+	0.773254i	$0.281372\pi$
$212$	−8.76458	−	3.11114i	−0.601954	−	0.213674i
$213$		0			0
$214$	−0.993253	−	4.39725i	−0.0678974	−	0.300590i
$215$	−1.85090	+	3.05335i	−0.126231	+	0.208237i
$216$		0			0
$217$	−20.2479	−	20.2479i	−1.37452	−	1.37452i
$218$	−20.1694	−	12.7366i	−1.36605	−	0.862632i
$219$		0			0
$220$	−8.32300	−	10.1930i	−0.561137	−	0.687210i
$221$	−0.170267	−	0.294911i	−0.0114534	−	0.0198379i
$222$		0			0
$223$	−3.75372	+	1.00581i	−0.251368	+	0.0673538i	−0.382303	−	0.924037i	$-0.624869\pi$
$223$	−3.75372	+	1.00581i	−0.251368	+	0.0673538i	0.130935	+	0.991391i	$0.458202\pi$
$224$	14.5075	−	9.65411i	0.969325	−	0.645042i
$225$		0			0
$226$	−17.1392	+	15.8314i	−1.14008	+	1.05309i
$227$	3.39226	+	12.6601i	0.225152	+	0.840280i	0.982343	+	0.187087i	$0.0599045\pi$
$227$	3.39226	+	12.6601i	0.225152	+	0.840280i	−0.757191	+	0.653194i	$0.773429\pi$
$228$		0			0
$229$	21.5102	−	12.4189i	1.42143	−	0.820664i	0.425010	−	0.905189i	$-0.360271\pi$
$229$	21.5102	−	12.4189i	1.42143	−	0.820664i	0.996421	+	0.0845251i	$0.0269373\pi$
$230$	15.3999	+	0.940627i	1.01544	+	0.0620231i
$231$		0			0
$232$	−23.8779	−	17.8726i	−1.56766	−	1.17339i
$233$	−9.75670	+	9.75670i	−0.639183	+	0.639183i	−0.950354	−	0.311171i	$-0.899279\pi$
$233$	−9.75670	+	9.75670i	−0.639183	+	0.639183i	0.311171	+	0.950354i	$0.399279\pi$
$234$		0			0
$235$	−5.33056	−	3.23132i	−0.347728	−	0.210788i
$236$	6.74652	−	9.80040i	0.439161	−	0.637952i
$237$		0			0
$238$	−0.315049	−	0.599358i	−0.0204216	−	0.0388506i
$239$	13.6160	+	23.5836i	0.880746	+	1.52550i	0.850513	+	0.525954i	$0.176292\pi$
$239$	13.6160	+	23.5836i	0.880746	+	1.52550i	0.0302330	+	0.999543i	$0.490375\pi$
$240$		0			0
$241$	3.38831	−	5.86872i	0.218260	−	0.378037i	−0.736016	−	0.676964i	$-0.763295\pi$
$241$	3.38831	−	5.86872i	0.218260	−	0.378037i	0.954276	+	0.298927i	$0.0966286\pi$
$242$	3.30884	+	0.131254i	0.212700	+	0.00843735i
$243$		0			0
$244$	9.92195	+	0.788404i	0.635187	+	0.0504724i
$245$	1.55539	−	5.34544i	0.0993702	−	0.341507i
$246$		0			0
$247$	−5.29527	−	1.41886i	−0.336930	−	0.0902801i
$248$	−24.1680	+	10.3510i	−1.53467	+	0.657291i
$249$		0			0
$250$	−15.6142	+	2.48907i	−0.987531	+	0.157423i
$251$			15.8630i			1.00127i	0.865660	+	0.500633i	$0.166899\pi$
$251$			15.8630i			1.00127i	−0.865660	+	0.500633i	$0.833101\pi$
$252$		0			0
$253$	10.1515	−	10.1515i	0.638221	−	0.638221i
$254$	−1.10304	−	4.88328i	−0.0692107	−	0.306404i
$255$		0			0
$256$	−3.27936	−	15.6603i	−0.204960	−	0.978770i
$257$	−2.81588	+	10.5090i	−0.175650	+	0.655534i	0.820790	+	0.571230i	$0.193533\pi$
$257$	−2.81588	+	10.5090i	−0.175650	+	0.655534i	−0.996440	+	0.0843041i	$0.973133\pi$
$258$		0			0
$259$	11.8840	−	20.5836i	0.738433	−	1.27900i
$260$	−7.95041	−	5.72703i	−0.493063	−	0.355176i
$261$		0			0
$262$	−0.122377	+	3.08504i	−0.00756046	+	0.190595i
$263$	26.9654	−	7.22535i	1.66276	−	0.445534i	0.699613	−	0.714522i	$-0.253356\pi$
$263$	26.9654	−	7.22535i	1.66276	−	0.445534i	0.963144	+	0.268988i	$0.0866892\pi$
$264$		0			0
$265$	−0.222060	+	10.3958i	−0.0136410	+	0.638607i
$266$	−10.4090	−	3.23638i	−0.638216	−	0.198435i
$267$		0			0
$268$	−0.273056	−	1.47950i	−0.0166795	−	0.0903750i
$269$		−	7.41454i		−	0.452073i	−0.974119	−	0.226036i	$-0.927423\pi$
$269$		−	7.41454i		−	0.452073i	0.974119	−	0.226036i	$-0.0725768\pi$
$270$		0			0
$271$		−	27.8976i		−	1.69466i	−0.531068	−	0.847329i	$-0.678209\pi$
$271$		−	27.8976i		−	1.69466i	0.531068	−	0.847329i	$-0.321791\pi$
$272$	−0.618393	+	0.0640528i	−0.0374956	+	0.00388377i
$273$		0			0
$274$	4.12681	−	13.2728i	0.249310	−	0.801841i
$275$	−7.89369	+	12.4158i	−0.476007	+	0.748698i
$276$		0			0
$277$	−18.5281	+	4.96460i	−1.11325	+	0.298294i	−0.768148	−	0.640272i	$-0.778822\pi$
$277$	−18.5281	+	4.96460i	−1.11325	+	0.298294i	−0.345100	+	0.938566i	$0.612155\pi$
$278$	18.9318	+	0.750981i	1.13545	+	0.0450409i
$279$		0			0
$280$	−15.3448	−	12.0053i	−0.917025	−	0.717451i
$281$	0.979069	−	1.69580i	0.0584064	−	0.101163i	−0.835344	−	0.549728i	$-0.814731\pi$
$281$	0.979069	−	1.69580i	0.0584064	−	0.101163i	0.893750	+	0.448565i	$0.148065\pi$
$282$		0			0
$283$	5.67568	−	21.1819i	0.337384	−	1.25913i	−0.563877	−	0.825859i	$-0.690691\pi$
$283$	5.67568	−	21.1819i	0.337384	−	1.25913i	0.901261	−	0.433276i	$-0.142643\pi$
$284$	−2.49569	+	1.18807i	−0.148092	+	0.0704992i
$285$		0			0
$286$	−8.89340	+	2.00885i	−0.525878	+	0.118786i
$287$	12.1264	−	12.1264i	0.715797	−	0.715797i
$288$		0			0
$289$		−	16.9758i		−	0.998579i
$290$	−10.5784	+	31.6240i	−0.621182	+	1.85702i
$291$		0			0
$292$	16.1721	+	5.74058i	0.946402	+	0.335942i
$293$	−2.50910	−	0.672311i	−0.146583	−	0.0392768i	0.184781	−	0.982780i	$-0.440842\pi$
$293$	−2.50910	−	0.672311i	−0.146583	−	0.0392768i	−0.331364	+	0.943503i	$0.607509\pi$
$294$		0			0
$295$	−12.7727	−	3.71654i	−0.743655	−	0.216385i
$296$	−13.4909	−	17.1531i	−0.784145	−	0.997002i
$297$		0			0
$298$	0.175993	−	4.43668i	0.0101950	−	0.257010i
$299$	5.34484	−	9.25753i	0.309100	−	0.535377i
$300$		0			0
$301$	2.45950	+	4.25997i	0.141763	+	0.245541i
$302$	−20.3792	+	10.7122i	−1.17269	+	0.616419i
$303$		0			0
$304$	−6.31023	+	7.76850i	−0.361917	+	0.445554i
$305$	−2.64994	−	10.8079i	−0.151735	−	0.618859i
$306$		0			0
$307$	−10.2092	+	10.2092i	−0.582668	+	0.582668i	−0.935636	−	0.352968i	$-0.885173\pi$
$307$	−10.2092	+	10.2092i	−0.582668	+	0.582668i	0.352968	+	0.935636i	$0.385173\pi$
$308$	−17.8280	+	3.29032i	−1.01585	+	0.187484i
$309$		0			0
$310$	19.4793	+	22.0137i	1.10635	+	1.25029i
$311$	12.5706	−	7.25766i	0.712815	−	0.411544i	−0.0992874	−	0.995059i	$-0.531656\pi$
$311$	12.5706	−	7.25766i	0.712815	−	0.411544i	0.812102	+	0.583515i	$0.198323\pi$
$312$		0			0
$313$	0.695535	+	2.59577i	0.0393139	+	0.146722i	0.982793	−	0.184711i	$-0.0591348\pi$
$313$	0.695535	+	2.59577i	0.0393139	+	0.146722i	−0.943479	+	0.331432i	$0.892468\pi$
$314$	−1.25267	−	1.35616i	−0.0706924	−	0.0765324i
$315$		0			0
$316$	20.9721	+	1.66646i	1.17977	+	0.0937456i
$317$	−7.86762	+	2.10812i	−0.441890	+	0.118404i	−0.472902	−	0.881115i	$-0.656794\pi$
$317$	−7.86762	+	2.10812i	−0.441890	+	0.118404i	0.0310123	+	0.999519i	$0.490127\pi$
$318$		0			0
$319$	15.5145	+	26.8719i	0.868646	+	1.50454i
$320$	−15.4690	+	8.98390i	−0.864743	+	0.502215i
$321$		0			0
$322$	11.3489	−	17.9719i	0.632450	−	1.00154i
$323$	0.274987	+	0.274987i	0.0153007	+	0.0153007i
$324$		0			0
$325$	−3.28460	+	10.4509i	−0.182197	+	0.579711i
$326$	−22.8698	+	5.16585i	−1.26664	+	0.286110i
$327$		0			0
$328$	−6.19918	−	14.4741i	−0.342293	−	0.799199i
$329$	−7.43708	+	4.29380i	−0.410020	+	0.236725i
$330$		0			0
$331$	−9.07230	−	5.23789i	−0.498659	−	0.287901i	0.229501	−	0.973308i	$-0.426291\pi$
$331$	−9.07230	−	5.23789i	−0.498659	−	0.287901i	−0.728159	+	0.685408i	$0.759624\pi$
$332$	−5.78378	−	6.78229i	−0.317426	−	0.372226i
$333$		0			0
$334$	−7.72862	+	7.13886i	−0.422891	+	0.390621i
$335$	−1.47434	+	0.809734i	−0.0805520	+	0.0442405i
$336$		0			0
$337$	−4.91055	+	18.3264i	−0.267495	+	0.998303i	0.693211	+	0.720735i	$0.256195\pi$
$337$	−4.91055	+	18.3264i	−0.267495	+	0.998303i	−0.960706	+	0.277569i	$0.910471\pi$
$338$	10.2643	−	5.39539i	0.558307	−	0.293471i
$339$		0			0
$340$	0.285297	+	0.633835i	0.0154724	+	0.0343745i
$341$	27.3520			1.48119
$342$		0			0
$343$	9.82465	+	9.82465i	0.530481	+	0.530481i
$344$	4.47042	−	0.643017i	0.241029	−	0.0346691i
$345$		0			0
$346$	−20.2185	−	6.28638i	−1.08696	−	0.337958i
$347$	−28.0317	−	7.51108i	−1.50482	−	0.403216i	−0.590110	−	0.807323i	$-0.700916\pi$
$347$	−28.0317	−	7.51108i	−1.50482	−	0.403216i	−0.914712	+	0.404107i	$0.867582\pi$
$348$		0			0
$349$	−20.2315	−	11.6807i	−1.08297	−	0.625252i	−0.151273	−	0.988492i	$-0.548337\pi$
$349$	−20.2315	−	11.6807i	−1.08297	−	0.625252i	−0.931696	+	0.363240i	$0.881671\pi$
$350$	−7.34963	+	20.5053i	−0.392854	+	1.09605i
$351$		0			0
$352$	−3.27814	+	16.3194i	−0.174725	+	0.869829i
$353$	−0.686242	−	2.56109i	−0.0365250	−	0.136313i	0.945256	−	0.326330i	$-0.105812\pi$
$353$	−0.686242	−	2.56109i	−0.0365250	−	0.136313i	−0.981781	+	0.190017i	$0.939146\pi$
$354$		0			0
$355$	2.13801	+	2.23134i	0.113474	+	0.118427i
$356$	25.0727	−	11.9359i	1.32885	−	0.632599i
$357$		0			0
$358$	12.9269	−	20.4708i	0.683209	−	1.08192i
$359$	0.819643			0.0432591			0.0216296	−	0.999766i	$-0.493115\pi$
$359$	0.819643			0.0432591			0.0216296	+	0.999766i	$0.493115\pi$
$360$		0			0
$361$	−12.7395			−0.670498
$362$	−4.95330	+	7.84396i	−0.260340	+	0.412269i
$363$		0			0
$364$	−12.1882	+	5.80218i	−0.638834	+	0.304117i
$365$	0.409738	−	19.1819i	0.0214467	−	1.00403i
$366$		0			0
$367$	1.14470	+	4.27209i	0.0597529	+	0.223001i	0.989345	−	0.145588i	$-0.0465075\pi$
$367$	1.14470	+	4.27209i	0.0597529	+	0.223001i	−0.929592	+	0.368589i	$0.879841\pi$
$368$	−11.4473	−	15.8059i	−0.596730	−	0.823939i
$369$		0			0
$370$	−13.4648	+	20.3468i	−0.700003	+	1.05778i
$371$	12.4059	+	7.16254i	0.644081	+	0.371860i
$372$		0			0
$373$	−0.122931	−	0.0329392i	−0.00636511	−	0.00170553i	0.255635	−	0.966773i	$-0.417715\pi$
$373$	−0.122931	−	0.0329392i	−0.00636511	−	0.00170553i	−0.262000	+	0.965068i	$0.584382\pi$
$374$	0.617616	+	0.192030i	0.0319362	+	0.00992965i
$375$		0			0
$376$	1.12258	+	7.80448i	0.0578928	+	0.402485i
$377$	16.3370	+	16.3370i	0.841397	+	0.841397i
$378$		0			0
$379$	−6.17768			−0.317326			−0.158663	−	0.987333i	$-0.550718\pi$
$379$	−6.17768			−0.317326			−0.158663	+	0.987333i	$0.550718\pi$
$380$	10.4628	+	3.96752i	0.536729	+	0.203529i
$381$		0			0
$382$	19.8848	−	10.4523i	1.01740	−	0.534788i
$383$	−1.84190	+	6.87408i	−0.0941169	+	0.351249i	−0.996884	−	0.0788806i	$-0.974865\pi$
$383$	−1.84190	+	6.87408i	−0.0941169	+	0.351249i	0.902767	+	0.430129i	$0.141532\pi$
$384$		0			0
$385$	9.75730	+	17.7659i	0.497278	+	0.905432i
$386$	−0.761817	+	0.703684i	−0.0387755	+	0.0358166i
$387$		0			0
$388$	−5.18511	−	6.08027i	−0.263234	−	0.308679i
$389$	4.40423	+	2.54279i	0.223304	+	0.128924i	0.607479	−	0.794336i	$-0.292181\pi$
$389$	4.40423	+	2.54279i	0.223304	+	0.128924i	−0.384175	+	0.923260i	$0.625514\pi$
$390$		0			0
$391$	−0.656717	+	0.379156i	−0.0332116	+	0.0191747i
$392$	−6.47320	+	2.77244i	−0.326946	+	0.140029i
$393$		0			0
$394$	7.63044	−	1.72357i	0.384416	−	0.0868321i
$395$	−5.60121	−	22.8448i	−0.281828	−	1.14945i
$396$		0			0
$397$	16.5129	+	16.5129i	0.828760	+	0.828760i	0.987345	−	0.158586i	$-0.0506934\pi$
$397$	16.5129	+	16.5129i	0.828760	+	0.828760i	−0.158586	+	0.987345i	$0.550693\pi$
$398$	17.4329	−	27.6065i	0.873835	−	1.38379i
$399$		0			0
$400$	14.9713	+	13.2612i	0.748565	+	0.663062i
$401$	−2.77254	−	4.80218i	−0.138454	−	0.239809i	0.788458	−	0.615089i	$-0.210880\pi$
$401$	−2.77254	−	4.80218i	−0.138454	−	0.239809i	−0.926912	+	0.375280i	$0.877547\pi$
$402$		0			0
$403$	19.6721	−	5.27112i	0.979937	−	0.262573i
$404$	−11.3600	−	0.902675i	−0.565183	−	0.0449098i
$405$		0			0
$406$	31.1713	+	33.7464i	1.54700	+	1.67481i
$407$	5.87599	+	21.9295i	0.291262	+	1.08701i
$408$		0			0
$409$	14.6386	−	8.45162i	0.723834	−	0.417906i	−0.0923283	−	0.995729i	$-0.529431\pi$
$409$	14.6386	−	8.45162i	0.723834	−	0.417906i	0.816162	+	0.577823i	$0.196098\pi$
$410$	−13.1839	+	11.6661i	−0.651107	+	0.576146i
$411$		0			0
$412$	6.49271	−	1.19829i	0.319873	−	0.0590354i
$413$	−12.9586	+	12.9586i	−0.637649	+	0.637649i
$414$		0			0
$415$	−5.16600	+	8.52213i	−0.253589	+	0.418335i
$416$	0.787290	+	12.3690i	0.0386001	+	0.606441i
$417$		0			0
$418$	9.21646	−	4.84458i	0.450792	−	0.236956i
$419$	−12.4670	−	21.5935i	−0.609053	−	1.05491i	−0.991397	−	0.130891i	$-0.958216\pi$
$419$	−12.4670	−	21.5935i	−0.609053	−	1.05491i	0.382343	−	0.924020i	$-0.375117\pi$
$420$		0			0
$421$	10.4510	−	18.1017i	0.509353	−	0.882225i	−0.490589	−	0.871391i	$-0.663218\pi$
$421$	10.4510	−	18.1017i	0.509353	−	0.882225i	0.999941	−	0.0108333i	$-0.00344842\pi$
$422$	−0.264654	+	6.67177i	−0.0128832	+	0.324777i
$423$		0			0
$424$	10.3383	−	8.13108i	0.502070	−	0.394880i
$425$	0.572475	−	0.525545i	0.0277691	−	0.0254927i
$426$		0			0
$427$	−14.8082	−	3.96786i	−0.716621	−	0.192018i
$428$	6.00804	+	2.13266i	0.290409	+	0.103086i
$429$		0			0
$430$	−2.25345	−	4.51880i	−0.108671	−	0.217916i
$431$		−	3.32701i		−	0.160257i	−0.996785	−	0.0801283i	$-0.974467\pi$
$431$		−	3.32701i		−	0.160257i	0.996785	−	0.0801283i	$-0.0255330\pi$
$432$		0			0
$433$	−20.7044	+	20.7044i	−0.994989	+	0.994989i	−0.999988	−	0.00499808i	$-0.998409\pi$
$433$	−20.7044	+	20.7044i	−0.994989	+	0.994989i	0.00499808	+	0.999988i	$0.498409\pi$
$434$	39.5006	−	8.92241i	1.89609	−	0.428290i
$435$		0			0
$436$	30.4597	−	14.5004i	1.45876	−	0.694441i
$437$	−3.15957	+	11.7917i	−0.151143	+	0.564072i
$438$		0			0
$439$	−10.1704	+	17.6157i	−0.485409	+	0.840753i	−0.999859	−	0.0167673i	$-0.994663\pi$
$439$	−10.1704	+	17.6157i	−0.485409	+	0.840753i	0.514451	+	0.857520i	$0.327996\pi$
$440$	18.4730	−	2.25559i	0.880664	−	0.107531i
$441$		0			0
$442$	0.481209	+	0.0190885i	0.0228888	+	0.000907947i
$443$	−34.3766	+	9.21119i	−1.63328	+	0.437637i	−0.954865	−	0.297040i	$-0.904001\pi$
$443$	−34.3766	+	9.21119i	−1.63328	+	0.437637i	−0.678417	+	0.734677i	$0.737334\pi$
$444$		0			0
$445$	−21.4793	−	22.4169i	−1.01822	−	1.06267i
$446$	1.63172	−	5.24801i	0.0772642	−	0.248501i
$447$		0			0
$448$	0.589370	+	24.6372i	0.0278451	+	1.16400i
$449$		−	23.6611i		−	1.11664i	−0.829627	−	0.558318i	$-0.811447\pi$
$449$		−	23.6611i		−	1.11664i	0.829627	−	0.558318i	$-0.188553\pi$
$450$		0			0
$451$			16.3810i			0.771350i
$452$	−5.98866	−	32.4485i	−0.281683	−	1.52625i
$453$		0			0
$454$	−17.6999	−	5.50327i	−0.830696	−	0.258281i
$455$	10.4414	+	10.8972i	0.489500	+	0.510868i
$456$		0			0
$457$	31.3670	−	8.40476i	1.46729	−	0.393158i	0.565286	−	0.824895i	$-0.308766\pi$
$457$	31.3670	−	8.40476i	1.46729	−	0.393158i	0.901999	+	0.431737i	$0.142099\pi$
$458$	−1.39227	+	35.0983i	−0.0650567	+	1.64004i
$459$		0			0
$460$	−12.7531	+	17.7042i	−0.594619	+	0.825464i
$461$	−4.00376	+	6.93472i	−0.186474	+	0.322982i	−0.944072	−	0.329739i	$-0.893039\pi$
$461$	−4.00376	+	6.93472i	−0.186474	+	0.322982i	0.757598	+	0.652721i	$0.226373\pi$
$462$		0			0
$463$	−3.28645	+	12.2652i	−0.152734	+	0.570013i	0.846554	+	0.532302i	$0.178673\pi$
$463$	−3.28645	+	12.2652i	−0.152734	+	0.570013i	−0.999289	+	0.0377103i	$0.987994\pi$
$464$	39.4013	−	15.0566i	1.82916	−	0.698985i
$465$		0			0
$466$	−4.29938	−	19.0339i	−0.199165	−	0.881727i
$467$	−3.31787	+	3.31787i	−0.153533	+	0.153533i	−0.779694	−	0.626161i	$-0.784625\pi$
$467$	−3.31787	+	3.31787i	−0.153533	+	0.153533i	0.626161	+	0.779694i	$0.284625\pi$
$468$		0			0
$469$			2.31732i			0.107004i
$470$	7.88895	−	3.93409i	0.363890	−	0.181466i
$471$		0			0
$472$	6.62461	+	15.4674i	0.304923	+	0.711946i
$473$	−4.53852	−	1.21609i	−0.208681	−	0.0559160i
$474$		0			0
$475$	0.534222	−	12.4991i	0.0245118	−	0.573499i
$476$	0.954578	+	0.0758513i	0.0437530	+	0.00347664i
$477$		0			0
$478$	−38.4816	−	1.52648i	−1.76011	−	0.0698196i
$479$	−9.05300	+	15.6803i	−0.413642	+	0.716449i	−0.995285	−	0.0969950i	$-0.969077\pi$
$479$	−9.05300	+	15.6803i	−0.413642	+	0.716449i	0.581643	+	0.813444i	$0.302410\pi$
$480$		0			0
$481$	8.45227	+	14.6398i	0.385390	+	0.667516i
$482$	4.45905	+	8.48303i	0.203104	+	0.386391i
$483$		0			0
$484$	−2.65544	+	3.85745i	−0.120702	+	0.175339i
$485$	−4.63128	+	7.64003i	−0.210296	+	0.346916i
$486$		0			0
$487$	5.02861	−	5.02861i	0.227868	−	0.227868i	−0.583933	−	0.811802i	$-0.698487\pi$
$487$	5.02861	−	5.02861i	0.227868	−	0.227868i	0.811802	+	0.583933i	$0.198487\pi$
$488$	−8.43476	+	11.2689i	−0.381824	+	0.510119i
$489$		0			0
$490$	5.21737	+	5.89618i	0.235697	+	0.266362i
$491$	−25.2747	+	14.5924i	−1.14063	+	0.658545i	−0.946587	−	0.322448i	$-0.895494\pi$
$491$	−25.2747	+	14.5924i	−1.14063	+	0.658545i	−0.194046	+	0.980992i	$0.562161\pi$
$492$		0			0
$493$	−0.424196	−	1.58312i	−0.0191048	−	0.0713001i
$494$	5.69505	−	5.26047i	0.256232	−	0.236680i
$495$		0			0
$496$	5.87187	−	36.7150i	0.263655	−	1.64855i
$497$	4.11231	−	1.10189i	0.184462	−	0.0494266i
$498$		0			0
$499$	7.76008	+	13.4409i	0.347389	+	0.601695i	0.985785	−	0.168013i	$-0.0537350\pi$
$499$	7.76008	+	13.4409i	0.347389	+	0.601695i	−0.638396	+	0.769708i	$0.720402\pi$
$500$	8.81393	−	20.5503i	0.394171	−	0.919037i
$501$		0			0
$502$	−18.9683	−	11.9781i	−0.846596	−	0.534609i
$503$	8.16997	+	8.16997i	0.364281	+	0.364281i	0.865386	−	0.501105i	$-0.167073\pi$
$503$	8.16997	+	8.16997i	0.364281	+	0.364281i	−0.501105	+	0.865386i	$0.667073\pi$
$504$		0			0
$505$	3.03402	+	12.3744i	0.135012	+	0.550654i
$506$	4.47336	+	19.8041i	0.198865	+	0.880400i
$507$		0			0
$508$	6.67210	+	2.36838i	0.296027	+	0.105080i
$509$	7.00348	−	4.04346i	0.310424	−	0.179223i	−0.336692	−	0.941615i	$-0.609308\pi$
$509$	7.00348	−	4.04346i	0.310424	−	0.179223i	0.647116	+	0.762392i	$0.275975\pi$
$510$		0			0
$511$	−22.8909	−	13.2161i	−1.01263	−	0.584645i
$512$	21.2021	+	7.90374i	0.937011	+	0.349299i
$513$		0			0
$514$	−10.4399	−	11.3024i	−0.460486	−	0.498528i
$515$	−3.55347	−	6.47007i	−0.156585	−	0.285105i
$516$		0			0
$517$	2.12306	−	7.92337i	0.0933721	−	0.348469i
$518$	15.6394	+	29.7529i	0.687157	+	1.30727i
$519$		0			0
$520$	12.8514	−	5.18228i	0.563573	−	0.227258i
$521$	17.0484			0.746904			0.373452	−	0.927649i	$-0.378174\pi$
$521$	17.0484			0.746904			0.373452	+	0.927649i	$0.378174\pi$
$522$		0			0
$523$	15.5907	+	15.5907i	0.681732	+	0.681732i	0.960390	−	0.278658i	$-0.0898897\pi$
$523$	15.5907	+	15.5907i	0.681732	+	0.681732i	−0.278658	+	0.960390i	$0.589890\pi$
$524$	−3.59655	−	2.47583i	−0.157116	−	0.108157i
$525$		0			0
$526$	−11.7217	+	37.6998i	−0.511090	+	1.64379i
$527$	−1.39551	−	0.373927i	−0.0607895	−	0.0162885i
$528$		0			0
$529$	−0.696383	−	0.402057i	−0.0302775	−	0.0174807i
$530$	−12.2631	−	8.11533i	−0.532676	−	0.352507i
$531$		0			0
$532$	11.7297	−	10.0028i	0.508547	−	0.433677i
$533$	3.15685	+	11.7815i	0.136738	+	0.510315i
$534$		0			0
$535$	0.152220	−	7.12620i	0.00658105	−	0.308092i
$536$	1.97531	+	0.790658i	0.0853202	+	0.0341512i
$537$		0			0
$538$	8.86598	+	5.59869i	0.382240	+	0.241377i
$539$	7.32599			0.315553
$540$		0			0
$541$	−5.34524			−0.229810			−0.114905	−	0.993376i	$-0.536656\pi$
$541$	−5.34524			−0.229810			−0.114905	+	0.993376i	$0.536656\pi$
$542$	33.3587	+	21.0654i	1.43288	+	0.904835i
$543$		0			0
$544$	0.390355	−	0.787813i	0.0167363	−	0.0337772i
$545$	−26.0943	−	27.2334i	−1.11776	−	1.16655i
$546$		0			0
$547$	5.20421	+	19.4224i	0.222516	+	0.830441i	0.983385	+	0.181535i	$0.0581065\pi$
$547$	5.20421	+	19.4224i	0.222516	+	0.830441i	−0.760869	+	0.648906i	$0.775227\pi$
$548$	12.7549	+	14.9569i	0.544863	+	0.638928i
$549$		0			0
$550$	−8.88572	−	18.8140i	−0.378888	−	0.802232i
$551$	−22.8499	−	13.1924i	−0.973439	−	0.562015i
$552$		0			0
$553$	−31.3004	−	8.38691i	−1.33103	−	0.356648i
$554$	8.05407	−	25.9039i	0.342185	−	1.10055i
$555$		0			0
$556$	−15.1933	+	22.0707i	−0.644339	+	0.936006i
$557$	−29.0569	−	29.0569i	−1.23118	−	1.23118i	−0.963512	−	0.267667i	$-0.913747\pi$
$557$	−29.0569	−	29.0569i	−1.23118	−	1.23118i	−0.267667	−	0.963512i	$-0.586253\pi$
$558$		0			0
$559$	−3.49855			−0.147973
$560$	25.9421	−	9.28346i	1.09625	−	0.392298i
$561$		0			0
$562$	1.28847	+	2.45122i	0.0543507	+	0.103398i
$563$	1.68072	−	6.27254i	0.0708340	−	0.264356i	−0.921422	−	0.388562i	$-0.872972\pi$
$563$	1.68072	−	6.27254i	0.0708340	−	0.264356i	0.992256	+	0.124206i	$0.0396385\pi$
$564$		0			0
$565$	−32.3354	+	17.7591i	−1.36036	+	0.747131i
$566$	21.0427	+	22.7811i	0.884491	+	0.957561i
$567$		0			0
$568$	0.463840	−	3.88134i	0.0194623	−	0.162857i
$569$	20.9363	+	12.0876i	0.877694	+	0.506737i	0.869897	−	0.493233i	$-0.164185\pi$
$569$	20.9363	+	12.0876i	0.877694	+	0.506737i	0.00779641	+	0.999970i	$0.497518\pi$
$570$		0			0
$571$	6.45998	−	3.72967i	0.270342	−	0.156082i	−0.358701	−	0.933452i	$-0.616780\pi$
$571$	6.45998	−	3.72967i	0.270342	−	0.156082i	0.629043	+	0.777371i	$0.283447\pi$
$572$	4.31328	−	12.1512i	0.180347	−	0.508067i
$573$		0			0
$574$	5.34360	+	23.6567i	0.223037	+	0.987413i
$575$	23.2724	+	7.31426i	0.970526	+	0.305026i
$576$		0			0
$577$	12.6994	+	12.6994i	0.528685	+	0.528685i	0.920180	−	0.391495i	$-0.128042\pi$
$577$	12.6994	+	12.6994i	0.528685	+	0.528685i	−0.391495	+	0.920180i	$0.628042\pi$
$578$	20.2990	+	12.8184i	0.844325	+	0.533175i
$579$		0			0
$580$	−29.8269	−	36.5283i	−1.23849	−	1.51675i
$581$	6.86463	+	11.8899i	0.284793	+	0.493276i
$582$		0			0
$583$	−13.2171	+	3.54150i	−0.547394	+	0.146674i
$584$	−19.0758	+	15.0032i	−0.789363	+	0.620837i
$585$		0			0
$586$	2.69853	−	2.49261i	0.111475	−	0.102969i
$587$	0.439709	+	1.64102i	0.0181487	+	0.0677320i	0.974406	−	0.224794i	$-0.0721709\pi$
$587$	0.439709	+	1.64102i	0.0181487	+	0.0677320i	−0.956258	+	0.292526i	$0.905504\pi$
$588$		0			0
$589$	−20.1421	+	11.6290i	−0.829941	+	0.479167i
$590$	14.0887	−	12.4667i	0.580022	−	0.513245i
$591$		0			0
$592$	30.6978	−	3.17966i	1.26167	−	0.130683i
$593$	18.2428	−	18.2428i	0.749143	−	0.749143i	−0.225176	−	0.974318i	$-0.572296\pi$
$593$	18.2428	−	18.2428i	0.749143	−	0.749143i	0.974318	+	0.225176i	$0.0722956\pi$
$594$		0			0
$595$	−0.254947	−	1.03982i	−0.0104518	−	0.0426283i
$596$	5.17229	+	3.56056i	0.211865	+	0.145846i
$597$		0			0
$598$	7.03387	+	13.3814i	0.287636	+	0.547208i
$599$	3.28022	+	5.68150i	0.134026	+	0.232140i	0.925225	−	0.379419i	$-0.123876\pi$
$599$	3.28022	+	5.68150i	0.134026	+	0.232140i	−0.791199	+	0.611559i	$0.790543\pi$
$600$		0			0
$601$	3.09788	−	5.36568i	0.126365	−	0.218871i	−0.795901	−	0.605427i	$-0.793002\pi$
$601$	3.09788	−	5.36568i	0.126365	−	0.218871i	0.922266	+	0.386557i	$0.126336\pi$
$602$	−6.95104	−	0.275732i	−0.283303	−	0.0112380i
$603$		0			0
$604$	2.57908	−	32.4573i	0.104941	−	1.32067i
$605$	5.02735	+	1.46283i	0.204391	+	0.0594727i
$606$		0			0
$607$	13.3799	+	3.58513i	0.543072	+	0.145516i	0.519918	−	0.854216i	$-0.325962\pi$
$607$	13.3799	+	3.58513i	0.543072	+	0.145516i	0.0231542	+	0.999732i	$0.492629\pi$
$608$	−4.52439	−	13.4115i	−0.183488	−	0.543906i
$609$		0			0
$610$	14.9246	+	4.99233i	0.604279	+	0.202134i
$611$		−	6.10779i		−	0.247095i
$612$		0			0
$613$	3.19784	−	3.19784i	0.129160	−	0.129160i	−0.639572	−	0.768731i	$-0.720888\pi$
$613$	3.19784	−	3.19784i	0.129160	−	0.129160i	0.768731	+	0.639572i	$0.220888\pi$
$614$	−4.49876	−	19.9166i	−0.181555	−	0.803767i
$615$		0			0
$616$	9.52744	−	23.8025i	0.383872	−	0.959028i
$617$	−3.12380	+	11.6582i	−0.125759	+	0.469340i	−0.999866	−	0.0163946i	$-0.994781\pi$
$617$	−3.12380	+	11.6582i	−0.125759	+	0.469340i	0.874106	+	0.485735i	$0.161448\pi$
$618$		0			0
$619$	19.7044	−	34.1290i	0.791986	−	1.37176i	−0.132749	−	0.991150i	$-0.542380\pi$
$619$	19.7044	−	34.1290i	0.791986	−	1.37176i	0.924735	−	0.380611i	$-0.124286\pi$
$620$	−41.0317	+	6.67002i	−1.64787	+	0.267874i
$621$		0			0
$622$	−0.813651	+	20.5116i	−0.0326244	+	0.822441i
$623$	−41.3139	+	11.0700i	−1.65521	+	0.443511i
$624$		0			0
$625$	−24.9088	−	2.13314i	−0.996353	−	0.0853256i
$626$	−3.62910	−	1.12837i	−0.145048	−	0.0450986i
$627$		0			0
$628$	2.56752	−	0.473859i	0.102455	−	0.0189090i
$629$		−	1.19919i		−	0.0478147i
$630$		0			0
$631$			25.3333i			1.00850i	0.863557	+	0.504251i	$0.168232\pi$
$631$			25.3333i			1.00850i	−0.863557	+	0.504251i	$0.831768\pi$
$632$	−17.8286	+	23.8192i	−0.709186	+	0.947477i
$633$		0			0
$634$	3.42001	−	10.9996i	0.135826	−	0.436849i
$635$	0.169045	−	7.91386i	0.00670835	−	0.314052i
$636$		0			0
$637$	5.26900	−	1.41183i	0.208766	−	0.0559386i
$638$	−43.8472	−	1.73932i	−1.73593	−	0.0688604i
$639$		0			0
$640$	0.938020	−	25.2808i	0.0370785	−	0.999312i
$641$	8.65919	−	14.9981i	0.342017	−	0.592391i	−0.642790	−	0.766042i	$-0.722223\pi$
$641$	8.65919	−	14.9981i	0.342017	−	0.592391i	0.984807	+	0.173651i	$0.0555565\pi$
$642$		0			0
$643$	−6.76281	+	25.2391i	−0.266699	+	0.995335i	0.694503	+	0.719490i	$0.255624\pi$
$643$	−6.76281	+	25.2391i	−0.266699	+	0.995335i	−0.961202	+	0.275845i	$0.911042\pi$
$644$	12.9205	+	27.1410i	0.509139	+	1.06951i
$645$		0			0
$646$	−0.536459	+	0.121176i	−0.0211067	+	0.00476759i
$647$	31.0498	−	31.0498i	1.22069	−	1.22069i	0.253307	−	0.967386i	$-0.418482\pi$
$647$	31.0498	−	31.0498i	1.22069	−	1.22069i	0.967386	−	0.253307i	$-0.0815183\pi$
$648$		0			0
$649$		−	17.5051i		−	0.687137i
$650$	−10.0165	−	11.8190i	−0.392880	−	0.463580i
$651$		0			0
$652$	11.0918	−	31.2474i	0.434389	−	1.22374i
$653$	−18.2190	−	4.88176i	−0.712963	−	0.191038i	−0.115934	−	0.993257i	$-0.536986\pi$
$653$	−18.2190	−	4.88176i	−0.712963	−	0.191038i	−0.597030	+	0.802219i	$0.703653\pi$
$654$		0			0
$655$	−1.36389	+	4.68732i	−0.0532917	+	0.183149i
$656$	21.9885	+	3.51664i	0.858506	+	0.137302i
$657$		0			0
$658$	0.481375	−	12.1352i	0.0187660	−	0.473078i
$659$	−2.45423	+	4.25085i	−0.0956033	+	0.165590i	−0.909860	−	0.414915i	$-0.863811\pi$
$659$	−2.45423	+	4.25085i	−0.0956033	+	0.165590i	0.814257	+	0.580505i	$0.197145\pi$
$660$		0			0
$661$	−14.5092	−	25.1307i	−0.564343	−	0.977471i	−0.997110	−	0.0759653i	$-0.975796\pi$
$661$	−14.5092	−	25.1307i	−0.564343	−	0.977471i	0.432767	−	0.901506i	$-0.357537\pi$
$662$	13.1137	−	6.89314i	0.509678	−	0.267909i
$663$		0			0
$664$	12.4773	−	1.79471i	0.484212	−	0.0696481i
$665$	−14.7387	−	8.93441i	−0.571542	−	0.346461i
$666$		0			0
$667$	36.3797	−	36.3797i	1.40863	−	1.40863i
$668$	−2.70048	−	14.6321i	−0.104485	−	0.566131i
$669$		0			0
$670$	0.145028	−	2.37438i	0.00560290	−	0.0917303i
$671$	12.6819	−	7.32190i	0.489579	−	0.282659i
$672$		0			0
$673$	9.79936	+	36.5717i	0.377738	+	1.40974i	0.849303	+	0.527905i	$0.177022\pi$
$673$	9.79936	+	36.5717i	0.377738	+	1.40974i	−0.471565	+	0.881831i	$0.656311\pi$
$674$	−18.2060	−	19.7100i	−0.701268	−	0.759201i
$675$		0			0
$676$	−1.29900	+	16.3477i	−0.0499614	+	0.628757i
$677$	33.1042	−	8.87024i	1.27230	−	0.340911i	0.441387	−	0.897317i	$-0.354487\pi$
$677$	33.1042	−	8.87024i	1.27230	−	0.340911i	0.830911	+	0.556406i	$0.187820\pi$
$678$		0			0
$679$	6.15409	+	10.6592i	0.236172	+	0.409063i
$680$	−0.973338	−	0.137461i	−0.0373258	−	0.00527138i
$681$		0			0
$682$	−20.6534	+	32.7063i	−0.790858	+	1.25239i
$683$	3.26162	+	3.26162i	0.124802	+	0.124802i	0.766749	−	0.641947i	$-0.221873\pi$
$683$	3.26162	+	3.26162i	0.124802	+	0.124802i	−0.641947	+	0.766749i	$0.721873\pi$
$684$		0			0
$685$	11.3926	−	18.7938i	0.435287	−	0.718074i
$686$	−19.1664	+	4.32932i	−0.731777	+	0.165294i
$687$		0			0
$688$	−2.60670	+	5.83106i	−0.0993796	+	0.222307i
$689$	−8.82347	+	5.09424i	−0.336148	+	0.194075i
$690$		0			0
$691$	31.7466	+	18.3289i	1.20770	+	0.697265i	0.962256	−	0.272146i	$-0.0877334\pi$
$691$	31.7466	+	18.3289i	1.20770	+	0.697265i	0.245443	+	0.969411i	$0.421067\pi$
$692$	22.7839	−	19.4296i	0.866114	−	0.738602i
$693$		0			0
$694$	30.1480	−	27.8475i	1.14440	−	1.05708i
$695$	28.7643	+	8.36971i	1.09109	+	0.317481i
$696$		0			0
$697$	0.223943	−	0.835767i	0.00848245	−	0.0316569i
$698$	29.2440	−	15.3719i	1.10690	−	0.581836i
$699$		0			0
$700$	−18.9697	−	24.2718i	−0.716986	−	0.917389i
$701$	−1.37716			−0.0520147			−0.0260074	−	0.999662i	$-0.508279\pi$
$701$	−1.37716			−0.0520147			−0.0260074	+	0.999662i	$0.508279\pi$
$702$		0			0
$703$	−13.6507	−	13.6507i	−0.514847	−	0.514847i
$704$	−17.0388	−	16.2426i	−0.642172	−	0.612166i
$705$		0			0
$706$	3.58062	+	1.11329i	0.134758	+	0.0418993i
$707$	16.9545	+	4.54296i	0.637641	+	0.170855i
$708$		0			0
$709$	−19.7595	−	11.4081i	−0.742082	−	0.428441i	0.0807437	−	0.996735i	$-0.474270\pi$
$709$	−19.7595	−	11.4081i	−0.742082	−	0.428441i	−0.822826	+	0.568294i	$0.807604\pi$
$710$	−4.28254	+	0.871659i	−0.160721	+	0.0327128i
$711$		0			0
$712$	−4.65992	+	38.9935i	−0.174638	+	1.46134i
$713$	−11.7379	−	43.8065i	−0.439588	−	1.64056i
$714$		0			0
$715$	−14.4127	−	0.307864i	−0.539003	−	0.0115135i
$716$	14.7170	+	30.9148i	0.550001	+	1.15534i
$717$		0			0
$718$	−0.618909	+	0.980092i	−0.0230975	+	0.0365767i
$719$	−37.1216			−1.38440			−0.692201	−	0.721705i	$-0.743359\pi$
$719$	−37.1216			−1.38440			−0.692201	+	0.721705i	$0.743359\pi$
$720$		0			0
$721$	−10.1694			−0.378728
$722$	9.61952	−	15.2333i	0.358001	−	0.566924i
$723$		0			0
$724$	−5.63923	−	11.8459i	−0.209580	−	0.440249i
$725$	−28.2884	+	44.4940i	−1.05060	+	1.65246i
$726$		0			0
$727$	4.49460	+	16.7741i	0.166695	+	0.622116i	0.997818	+	0.0660262i	$0.0210321\pi$
$727$	4.49460	+	16.7741i	0.166695	+	0.622116i	−0.831123	+	0.556089i	$0.812301\pi$
$728$	2.26525	−	18.9553i	0.0839559	−	0.702530i
$729$		0			0
$730$	22.6275	+	14.9741i	0.837482	+	0.554218i
$731$	0.214933	+	0.124091i	0.00794957	+	0.00458969i
$732$		0			0
$733$	32.4504	+	8.69507i	1.19858	+	0.321160i	0.802273	−	0.596957i	$-0.203624\pi$
$733$	32.4504	+	8.69507i	1.19858	+	0.321160i	0.396311	+	0.918117i	$0.370290\pi$
$734$	−5.97273	−	1.85705i	−0.220457	−	0.0685450i
$735$		0			0
$736$	27.5437	−	1.75316i	1.01528	−	0.0646224i
$737$	−1.56518	−	1.56518i	−0.0576541	−	0.0576541i
$738$		0			0
$739$	−11.2724			−0.414663			−0.207331	−	0.978271i	$-0.566478\pi$
$739$	−11.2724			−0.414663			−0.207331	+	0.978271i	$0.566478\pi$
$740$	−14.1625	−	31.4644i	−0.520624	−	1.15665i
$741$		0			0
$742$	−17.9323	+	9.42599i	−0.658314	+	0.346039i
$743$	0.797903	−	2.97781i	0.0292722	−	0.109245i	−0.949744	−	0.313028i	$-0.898657\pi$
$743$	0.797903	−	2.97781i	0.0292722	−	0.109245i	0.979016	+	0.203782i	$0.0653234\pi$
$744$		0			0
$745$	1.96145	−	6.74095i	0.0718619	−	0.246969i
$746$	0.132212	−	0.122123i	0.00484061	−	0.00447123i
$747$		0			0
$748$	−0.695981	+	0.593516i	−0.0254476	+	0.0217011i
$749$	−8.50411	−	4.90985i	−0.310733	−	0.179402i
$750$		0			0
$751$	−19.7254	+	11.3884i	−0.719789	+	0.415570i	−0.814675	−	0.579918i	$-0.803085\pi$
$751$	−19.7254	+	11.3884i	−0.719789	+	0.415570i	0.0948862	+	0.995488i	$0.469751\pi$
$752$	−10.1799	−	4.55080i	−0.371223	−	0.165950i
$753$		0			0
$754$	−31.8710	+	7.19904i	−1.16067	+	0.262173i
$755$	−35.3556	+	8.66866i	−1.28672	+	0.315485i
$756$		0			0
$757$	−2.14675	−	2.14675i	−0.0780251	−	0.0780251i	0.667017	−	0.745042i	$-0.267571\pi$
$757$	−2.14675	−	2.14675i	−0.0780251	−	0.0780251i	−0.745042	+	0.667017i	$0.767571\pi$
$758$	4.66474	−	7.38699i	0.169431	−	0.268308i
$759$		0			0
$760$	−12.6446	+	9.51505i	−0.458667	+	0.345147i
$761$	7.84977	+	13.5962i	0.284554	+	0.492862i	0.972501	−	0.232899i	$-0.0748212\pi$
$761$	7.84977	+	13.5962i	0.284554	+	0.492862i	−0.687947	+	0.725761i	$0.741488\pi$
$762$		0			0
$763$	−50.1905	+	13.4485i	−1.81702	+	0.486869i
$764$	−2.51651	+	31.6699i	−0.0910441	+	1.14578i
$765$		0			0
$766$	−6.82890	−	7.39305i	−0.246738	−	0.267122i
$767$	−3.37350	−	12.5901i	−0.121810	−	0.454601i
$768$		0			0
$769$	4.81835	−	2.78187i	0.173754	−	0.100317i	−0.410601	−	0.911815i	$-0.634681\pi$
$769$	4.81835	−	2.78187i	0.173754	−	0.100317i	0.584355	+	0.811498i	$0.301348\pi$
$770$	−28.6113	−	1.74758i	−1.03108	−	0.0629785i
$771$		0			0
$772$	−0.266189	−	1.44230i	−0.00958034	−	0.0519094i
$773$	−5.06450	+	5.06450i	−0.182157	+	0.182157i	−0.792295	−	0.610138i	$-0.791114\pi$
$773$	−5.06450	+	5.06450i	−0.182157	+	0.182157i	0.610138	+	0.792295i	$0.291114\pi$
$774$		0			0
$775$	21.4986	+	41.2059i	0.772251	+	1.48016i
$776$	11.1858	−	1.60894i	0.401546	−	0.0577576i
$777$		0			0
$778$	−6.36617	+	3.34634i	−0.228238	+	0.119972i
$779$	−6.96459	−	12.0630i	−0.249532	−	0.432202i
$780$		0			0
$781$	−2.03332	+	3.52182i	−0.0727580	+	0.126021i
$782$	0.0425069	−	1.07157i	0.00152004	−	0.0383193i
$783$		0			0
$784$	1.57273	−	9.83382i	0.0561690	−	0.351208i
$785$	−1.40521	−	2.55857i	−0.0501540	−	0.0913192i
$786$		0			0
$787$	−42.9849	−	11.5178i	−1.53225	−	0.410564i	−0.608496	−	0.793557i	$-0.708227\pi$
$787$	−42.9849	−	11.5178i	−1.53225	−	0.410564i	−0.923751	+	0.382993i	$0.874893\pi$
$788$	−3.70075	+	10.4256i	−0.131834	+	0.371396i
$789$		0			0
$790$	31.5463	+	10.5524i	1.12237	+	0.375436i
$791$			50.8234i			1.80707i
$792$		0			0
$793$	7.71005	−	7.71005i	0.273792	−	0.273792i
$794$	−32.2142	+	7.27657i	−1.14324	+	0.258236i
$795$		0			0
$796$	19.8470	+	41.6911i	0.703460	+	1.47770i
$797$	−5.05676	+	18.8721i	−0.179120	+	0.668484i	0.816693	+	0.577072i	$0.195805\pi$
$797$	−5.05676	+	18.8721i	−0.179120	+	0.668484i	−0.995813	+	0.0914122i	$0.970862\pi$
$798$		0			0
$799$	−0.216640	+	0.375231i	−0.00766416	+	0.0132747i
$800$	−27.1620	+	7.88850i	−0.960320	+	0.278901i
$801$		0			0
$802$	7.83576	+	0.310827i	0.276690	+	0.0109757i
$803$	24.3877	−	6.53466i	0.860623	−	0.230603i
$804$		0			0
$805$	24.2662	−	23.2512i	0.855272	−	0.819498i
$806$	−8.55134	+	27.5032i	−0.301208	+	0.968759i
$807$		0			0
$808$	9.65729	−	12.9022i	0.339742	−	0.453898i
$809$		−	13.0099i		−	0.457403i	−0.973497	−	0.228701i	$-0.926552\pi$
$809$		−	13.0099i		−	0.457403i	0.973497	−	0.228701i	$-0.0734479\pi$
$810$		0			0
$811$		−	37.7797i		−	1.32662i	−0.748343	−	0.663312i	$-0.769150\pi$
$811$		−	37.7797i		−	1.32662i	0.748343	−	0.663312i	$-0.230850\pi$
$812$	−63.8897	+	11.7914i	−2.24209	+	0.413798i
$813$		0			0
$814$	−30.6593	−	9.53263i	−1.07461	−	0.334119i
$815$	−37.0629	−	0.791687i	−1.29826	−	0.0277316i
$816$		0			0
$817$	3.85922	−	1.03407i	0.135017	−	0.0361777i
$818$	−0.947505	+	23.8860i	−0.0331287	+	0.835154i
$819$		0			0
$820$	−3.99464	−	24.5737i	−0.139499	−	0.858151i
$821$	−17.8689	+	30.9499i	−0.623629	+	1.08016i	0.365175	+	0.930939i	$0.381009\pi$
$821$	−17.8689	+	30.9499i	−0.623629	+	1.08016i	−0.988804	+	0.149219i	$0.952324\pi$
$822$		0			0
$823$	9.77082	−	36.4652i	0.340589	−	1.27110i	−0.557092	−	0.830451i	$-0.688083\pi$
$823$	9.77082	−	36.4652i	0.340589	−	1.27110i	0.897681	−	0.440646i	$-0.145251\pi$
$824$	−3.46976	+	8.66851i	−0.120875	+	0.301982i
$825$		0			0
$826$	−5.71031	−	25.2802i	−0.198687	−	0.879611i
$827$	−15.8276	+	15.8276i	−0.550380	+	0.550380i	−0.926550	−	0.376171i	$-0.877241\pi$
$827$	−15.8276	+	15.8276i	−0.550380	+	0.550380i	0.376171	+	0.926550i	$0.377241\pi$
$828$		0			0
$829$			30.6554i			1.06471i	0.846522	+	0.532353i	$0.178692\pi$
$829$			30.6554i			1.06471i	−0.846522	+	0.532353i	$0.821308\pi$
$830$	−6.28956	−	12.6123i	−0.218314	−	0.437779i
$831$		0			0
$832$	−15.3848	−	8.39839i	−0.533372	−	0.291162i
$833$	−0.373777	−	0.100153i	−0.0129506	−	0.00347010i
$834$		0			0
$835$	−14.5810	+	8.00814i	−0.504598	+	0.277133i
$836$	−1.16638	+	14.6788i	−0.0403402	+	0.507675i
$837$		0			0
$838$	35.2343	+	1.39767i	1.21715	+	0.0482816i
$839$	−6.18963	+	10.7208i	−0.213690	+	0.370122i	−0.952866	−	0.303390i	$-0.901882\pi$
$839$	−6.18963	+	10.7208i	−0.213690	+	0.370122i	0.739177	+	0.673512i	$0.235215\pi$
$840$		0			0
$841$	41.0989	+	71.1854i	1.41720	+	2.45467i
$842$	13.7537	+	26.1654i	0.473984	+	0.901720i
$843$		0			0
$844$	−7.77796	−	5.35429i	−0.267729	−	0.184302i
$845$	17.8074	−	4.36612i	0.612594	−	0.150199i
$846$		0			0
$847$	5.10051	−	5.10051i	0.175256	−	0.175256i
$848$	1.91640	+	18.5018i	0.0658095	+	0.635353i
$849$		0			0
$850$	0.196150	+	1.08138i	0.00672787	+	0.0370909i
$851$	32.6003	−	18.8218i	1.11752	−	0.645203i
$852$		0			0
$853$	−9.66844	−	36.0831i	−0.331041	−	1.23546i	−0.908098	−	0.418758i	$-0.862465\pi$
$853$	−9.66844	−	36.0831i	−0.331041	−	1.23546i	0.577056	−	0.816704i	$-0.304201\pi$
$854$	15.9262	−	14.7109i	0.544984	−	0.503397i
$855$		0			0
$856$	−7.08678	+	5.57378i	−0.242221	+	0.190508i
$857$	0.390753	−	0.104702i	0.0133479	−	0.00357655i	−0.252139	−	0.967691i	$-0.581134\pi$
$857$	0.390753	−	0.104702i	0.0133479	−	0.00357655i	0.265487	+	0.964114i	$0.414467\pi$
$858$		0			0
$859$	−17.7770	−	30.7906i	−0.606543	−	1.05056i	−0.991806	−	0.127756i	$-0.959223\pi$
$859$	−17.7770	−	30.7906i	−0.606543	−	1.05056i	0.385263	−	0.922807i	$-0.374111\pi$
$860$	7.10495	+	0.717548i	0.242277	+	0.0244682i
$861$		0			0
$862$	3.97829	+	2.51221i	0.135501	+	0.0855664i
$863$	16.1777	+	16.1777i	0.550695	+	0.550695i	0.926641	−	0.375946i	$-0.122682\pi$
$863$	16.1777	+	16.1777i	0.550695	+	0.550695i	−0.375946	+	0.926641i	$0.622682\pi$
$864$		0			0
$865$	−28.6286	−	17.3543i	−0.973402	−	0.590063i
$866$	−9.12358	−	40.3912i	−0.310032	−	1.37255i
$867$		0			0
$868$	−19.1577	+	53.9703i	−0.650255	+	1.83187i
$869$	26.8059	−	15.4764i	0.909328	−	0.525001i
$870$		0			0
$871$	−1.42734	−	0.824076i	−0.0483636	−	0.0279228i
$872$	−5.66114	+	47.3715i	−0.191710	+	1.60420i
$873$		0			0
$874$	−11.7142	−	12.6819i	−0.396238	−	0.428972i
$875$	−19.0952	+	28.6633i	−0.645534	+	0.968998i
$876$		0			0
$877$	3.22095	−	12.0208i	0.108764	−	0.405912i	−0.889981	−	0.455997i	$-0.849283\pi$
$877$	3.22095	−	12.0208i	0.108764	−	0.405912i	0.998745	+	0.0500851i	$0.0159493\pi$
$878$	−13.3844	−	25.4629i	−0.451703	−	0.859332i
$879$		0			0
$880$	−11.2517	+	23.7923i	−0.379295	+	0.802039i
$881$	−25.7791			−0.868521			−0.434261	−	0.900787i	$-0.642990\pi$
$881$	−25.7791			−0.868521			−0.434261	+	0.900787i	$0.642990\pi$
$882$		0			0
$883$	−38.5747	−	38.5747i	−1.29814	−	1.29814i	−0.929618	−	0.368526i	$-0.879863\pi$
$883$	−38.5747	−	38.5747i	−1.29814	−	1.29814i	−0.368526	−	0.929618i	$-0.620137\pi$
$884$	−0.386184	+	0.560995i	−0.0129888	+	0.0188683i
$885$		0			0
$886$	14.9433	−	48.0613i	0.502031	−	1.61465i
$887$	−19.0351	−	5.10044i	−0.639136	−	0.171256i	−0.0753240	−	0.997159i	$-0.523999\pi$
$887$	−19.0351	−	5.10044i	−0.639136	−	0.171256i	−0.563812	+	0.825903i	$0.690666\pi$
$888$		0			0
$889$	−9.44407	−	5.45254i	−0.316744	−	0.182872i
$890$	43.0241	−	8.75703i	1.44217	−	0.293536i
$891$		0			0
$892$	5.04323	+	5.91389i	0.168860	+	0.198012i
$893$	1.80529	+	6.73745i	0.0604119	+	0.225460i
$894$		0			0
$895$	27.6403	−	26.4842i	0.923913	−	0.885268i
$896$	−29.9051	−	17.8987i	−0.999060	−	0.597955i
$897$		0			0
$898$	28.2929	+	17.8664i	0.944145	+	0.596209i
$899$	98.0204			3.26916
$900$		0			0
$901$	0.722757			0.0240785
$902$	−19.5876	−	12.3692i	−0.652197	−	0.411849i
$903$		0			0
$904$	43.3225	+	17.3408i	1.44088	+	0.576745i
$905$	−10.5911	+	10.1481i	−0.352062	+	0.337336i
$906$		0			0
$907$	8.36622	+	31.2232i	0.277796	+	1.03675i	0.953945	+	0.299983i	$0.0969810\pi$
$907$	8.36622	+	31.2232i	0.277796	+	1.03675i	−0.676149	+	0.736765i	$0.736352\pi$
$908$	19.9457	−	17.0092i	0.661920	−	0.564470i
$909$		0			0
$910$	−20.9146	+	4.25692i	−0.693313	+	0.141115i
$911$	−8.49642	−	4.90541i	−0.281499	−	0.162523i	0.352603	−	0.935773i	$-0.385297\pi$
$911$	−8.49642	−	4.90541i	−0.281499	−	0.162523i	−0.634102	+	0.773250i	$0.718630\pi$
$912$		0			0
$913$	−12.6673	−	3.39420i	−0.419227	−	0.112332i
$914$	−13.6350	+	43.8536i	−0.451007	+	1.45055i
$915$		0			0
$916$	−40.9177	−	28.1674i	−1.35196	−	0.930678i
$917$	4.75553	+	4.75553i	0.157041	+	0.157041i
$918$		0			0
$919$	−8.58129			−0.283071			−0.141535	−	0.989933i	$-0.545204\pi$
$919$	−8.58129			−0.283071			−0.141535	+	0.989933i	$0.545204\pi$
$920$	−11.5401	−	28.6180i	−0.380465	−	0.943508i
$921$		0			0
$922$	−5.26901	−	10.0239i	−0.173525	−	0.330120i
$923$	−0.783702	+	2.92481i	−0.0257959	+	0.0962714i
$924$		0			0
$925$	−28.4184	+	26.0887i	−0.934392	+	0.857793i
$926$	−12.1846	−	13.1912i	−0.400411	−	0.433490i
$927$		0			0
$928$	−11.7478	+	58.4835i	−0.385639	+	1.91982i
$929$	12.5313	+	7.23495i	0.411138	+	0.237371i	0.691279	−	0.722588i	$-0.257048\pi$
$929$	12.5313	+	7.23495i	0.411138	+	0.237371i	−0.280140	+	0.959959i	$0.590381\pi$
$930$		0			0
$931$	−5.39489	+	3.11474i	−0.176810	+	0.102082i
$932$	26.0063	+	9.23139i	0.851865	+	0.302384i
$933$		0			0
$934$	−1.46205	−	6.47268i	−0.0478398	−	0.211792i
$935$	0.874519	+	0.530122i	0.0285998	+	0.0173368i
$936$		0			0
$937$	−36.3423	−	36.3423i	−1.18725	−	1.18725i	−0.977825	−	0.209425i	$-0.932841\pi$
$937$	−36.3423	−	36.3423i	−1.18725	−	1.18725i	−0.209425	−	0.977825i	$-0.567159\pi$
$938$	−2.77094	−	1.74980i	−0.0904744	−	0.0571328i
$939$		0			0
$940$	−1.25270	+	12.4039i	−0.0408586	+	0.404570i
$941$	−4.83638	−	8.37686i	−0.157662	−	0.273078i	0.776363	−	0.630286i	$-0.217062\pi$
$941$	−4.83638	−	8.37686i	−0.157662	−	0.273078i	−0.934025	+	0.357208i	$0.883729\pi$
$942$		0			0
$943$	26.2355	−	7.02978i	0.854345	−	0.228921i
$944$	−23.4975	−	3.75798i	−0.764778	−	0.122312i
$945$		0			0
$946$	4.88116	−	4.50869i	0.158700	−	0.146590i
$947$	0.883755	+	3.29822i	0.0287182	+	0.107178i	0.978797	−	0.204832i	$-0.0656647\pi$
$947$	0.883755	+	3.29822i	0.0287182	+	0.107178i	−0.950079	+	0.312009i	$0.898998\pi$
$948$		0			0
$949$	16.2808	−	9.39972i	0.528497	−	0.305128i
$950$	14.5425	+	10.0768i	0.471821	+	0.326936i
$951$		0			0
$952$	−0.811497	+	1.08417i	−0.0263008	+	0.0351380i
$953$	35.7615	−	35.7615i	1.15843	−	1.15843i	0.173614	−	0.984814i	$-0.444456\pi$
$953$	35.7615	−	35.7615i	1.15843	−	1.15843i	0.984814	−	0.173614i	$-0.0555445\pi$
$954$		0			0
$955$	34.4978	−	8.45836i	1.11632	−	0.273706i
$956$	30.8826	−	44.8619i	0.998815	−	1.45094i
$957$		0			0
$958$	−11.9139	−	22.6653i	−0.384920	−	0.732282i
$959$	−15.1385	−	26.2207i	−0.488848	−	0.846710i
$960$		0			0
$961$	27.7023	−	47.9818i	0.893622	−	1.54780i
$962$	−23.8878	−	0.947578i	−0.770175	−	0.0305511i
$963$		0			0
$964$	−13.5106	−	1.07356i	−0.435148	−	0.0345772i
$965$	−1.43727	+	0.789371i	−0.0462673	+	0.0254107i
$966$		0			0
$967$	−23.2284	−	6.22403i	−0.746975	−	0.200151i	−0.134799	−	0.990873i	$-0.543039\pi$
$967$	−23.2284	−	6.22403i	−0.746975	−	0.200151i	−0.612176	+	0.790722i	$0.709706\pi$
$968$	−2.60746	−	6.08800i	−0.0838069	−	0.195676i
$969$		0			0
$970$	−5.63854	−	11.3068i	−0.181043	−	0.363041i
$971$		−	42.1591i		−	1.35295i	−0.736466	−	0.676475i	$-0.763507\pi$
$971$		−	42.1591i		−	1.35295i	0.736466	−	0.676475i	$-0.236493\pi$
$972$		0			0
$973$	29.1829	−	29.1829i	0.935562	−	0.935562i
$974$	2.21591	+	9.81008i	0.0710022	+	0.314335i
$975$		0			0
$976$	−7.10579	−	18.5950i	−0.227451	−	0.595211i
$977$	7.46641	−	27.8650i	0.238872	−	0.891481i	−0.737494	−	0.675354i	$-0.763991\pi$
$977$	7.46641	−	27.8650i	0.238872	−	0.891481i	0.976365	−	0.216127i	$-0.0693424\pi$
$978$		0			0
$979$	20.4276	−	35.3816i	0.652868	−	1.13080i
$980$	−10.9900	+	1.78651i	−0.351063	+	0.0570679i
$981$		0			0
$982$	1.63594	−	41.2410i	0.0522050	−	1.31605i
$983$	26.7632	−	7.17118i	0.853613	−	0.228725i	0.194625	−	0.980878i	$-0.437651\pi$
$983$	26.7632	−	7.17118i	0.853613	−	0.228725i	0.658989	+	0.752153i	$0.270984\pi$
$984$		0			0
$985$	12.3659	+	0.264144i	0.394011	+	0.00841632i
$986$	2.21333	+	0.688173i	0.0704868	+	0.0219159i
$987$		0			0
$988$	1.98992	+	10.7820i	0.0633079	+	0.343022i
$989$			7.79069i			0.247730i
$990$		0			0
$991$		−	10.8415i		−	0.344392i	−0.985063	−	0.172196i	$-0.944914\pi$
$991$		−	10.8415i		−	0.344392i	0.985063	−	0.172196i	$-0.0550862\pi$
$992$	39.4684	+	34.7447i	1.25312	+	1.10315i
$993$		0			0
$994$	−1.78760	+	5.74935i	−0.0566992	+	0.182358i
$995$	37.2751	−	35.7160i	1.18170	−	1.13227i
$996$		0			0
$997$	32.8355	−	8.79826i	1.03991	−	0.278644i	0.301835	−	0.953360i	$-0.402401\pi$
$997$	32.8355	−	8.79826i	1.03991	−	0.278644i	0.738077	+	0.674717i	$0.235734\pi$
$998$	−21.9316	−	0.869977i	−0.694232	−	0.0275386i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	540.2.y.a.127.10		128
3.2	odd	2		180.2.x.a.7.23	✓	128
4.3	odd	2	inner	540.2.y.a.127.6		128
5.3	odd	4	inner	540.2.y.a.343.27		128
9.4	even	3	inner	540.2.y.a.307.12		128
9.5	odd	6		180.2.x.a.67.21	yes	128
12.11	even	2		180.2.x.a.7.27	yes	128
15.2	even	4		900.2.bf.e.43.27		128
15.8	even	4		180.2.x.a.43.6	yes	128
15.14	odd	2		900.2.bf.e.7.10		128
20.3	even	4	inner	540.2.y.a.343.12		128
36.23	even	6		180.2.x.a.67.6	yes	128
36.31	odd	6	inner	540.2.y.a.307.27		128
45.13	odd	12	inner	540.2.y.a.523.6		128
45.14	odd	6		900.2.bf.e.607.12		128
45.23	even	12		180.2.x.a.103.27	yes	128
45.32	even	12		900.2.bf.e.643.6		128
60.23	odd	4		180.2.x.a.43.21	yes	128
60.47	odd	4		900.2.bf.e.43.12		128
60.59	even	2		900.2.bf.e.7.6		128
180.23	odd	12		180.2.x.a.103.23	yes	128
180.59	even	6		900.2.bf.e.607.27		128
180.103	even	12	inner	540.2.y.a.523.10		128
180.167	odd	12		900.2.bf.e.643.10		128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
180.2.x.a.7.23	✓	128	3.2	odd	2
180.2.x.a.7.27	yes	128	12.11	even	2
180.2.x.a.43.6	yes	128	15.8	even	4
180.2.x.a.43.21	yes	128	60.23	odd	4
180.2.x.a.67.6	yes	128	36.23	even	6
180.2.x.a.67.21	yes	128	9.5	odd	6
180.2.x.a.103.23	yes	128	180.23	odd	12
180.2.x.a.103.27	yes	128	45.23	even	12
540.2.y.a.127.6		128	4.3	odd	2	inner
540.2.y.a.127.10		128	1.1	even	1	trivial
540.2.y.a.307.12		128	9.4	even	3	inner
540.2.y.a.307.27		128	36.31	odd	6	inner
540.2.y.a.343.12		128	20.3	even	4	inner
540.2.y.a.343.27		128	5.3	odd	4	inner
540.2.y.a.523.6		128	45.13	odd	12	inner
540.2.y.a.523.10		128	180.103	even	12	inner
900.2.bf.e.7.6		128	60.59	even	2
900.2.bf.e.7.10		128	15.14	odd	2
900.2.bf.e.43.12		128	60.47	odd	4
900.2.bf.e.43.27		128	15.2	even	4
900.2.bf.e.607.12		128	45.14	odd	6
900.2.bf.e.607.27		128	180.59	even	6
900.2.bf.e.643.6		128	45.32	even	12
900.2.bf.e.643.10		128	180.167	odd	12

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:	\( N \)	\(=\)	\( 540 = 2^{2} \cdot 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	540.y (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.755096 + 1.19576i) q^{2} +(-0.859661 - 1.80582i) q^{4} +(-1.61454 + 1.54701i) q^{5} +(0.797301 + 2.97557i) q^{7} +(2.80844 + 0.335623i) q^{8} +O(q^{10})\)	\(q+(-0.755096 + 1.19576i) q^{2} +(-0.859661 - 1.80582i) q^{4} +(-1.61454 + 1.54701i) q^{5} +(0.797301 + 2.97557i) q^{7} +(2.80844 + 0.335623i) q^{8} +(-0.630711 - 3.09874i) q^{10} +(-2.54830 - 1.47126i) q^{11} +(-2.11632 - 0.567067i) q^{13} +(-4.16009 - 1.29346i) q^{14} +(-2.52197 + 3.10478i) q^{16} +(0.109902 + 0.109902i) q^{17} +2.50211 q^{19} +(4.18158 + 1.58567i) q^{20} +(3.68348 - 1.93620i) q^{22} +(-1.26276 + 4.71270i) q^{23} +(0.213509 - 4.99544i) q^{25} +(2.27610 - 2.10242i) q^{26} +(4.68793 - 3.99776i) q^{28} +(-9.13227 - 5.27252i) q^{29} +(-8.05006 + 4.64770i) q^{31} +(-1.80823 - 5.36006i) q^{32} +(-0.214403 + 0.0484295i) q^{34} +(-5.89052 - 3.57075i) q^{35} +(-5.45569 - 5.45569i) q^{37} +(-1.88933 + 2.99191i) q^{38} +(-5.05357 + 3.80282i) q^{40} +(-2.78349 - 4.82114i) q^{41} +(1.54239 - 0.413282i) q^{43} +(-0.466160 + 5.86656i) q^{44} +(-4.68173 - 5.06850i) q^{46} +(0.721510 + 2.69271i) q^{47} +(-2.15614 + 1.24485i) q^{49} +(5.81210 + 4.02734i) q^{50} +(0.795299 + 4.30918i) q^{52} +(3.28818 - 3.28818i) q^{53} +(6.39041 - 1.56683i) q^{55} +(1.24051 + 8.62431i) q^{56} +(13.2004 - 6.93870i) q^{58} +(2.97451 + 5.15200i) q^{59} +(-2.48830 + 4.30987i) q^{61} +(0.521051 - 13.1354i) q^{62} +(7.77471 + 1.88516i) q^{64} +(4.29416 - 2.35842i) q^{65} +(0.726612 + 0.194695i) q^{67} +(0.103985 - 0.292942i) q^{68} +(8.71765 - 4.34736i) q^{70} -1.38203i q^{71} +(-6.06724 + 6.06724i) q^{73} +(10.6432 - 2.40410i) q^{74} +(-2.15096 - 4.51835i) q^{76} +(2.34608 - 8.75569i) q^{77} +(-5.25956 + 9.10982i) q^{79} +(-0.731307 - 8.91432i) q^{80} +(7.86671 + 0.312055i) q^{82} +(4.30492 - 1.15350i) q^{83} +(-0.347462 - 0.00742201i) q^{85} +(-0.670467 + 2.15639i) q^{86} +(-6.66297 - 4.98723i) q^{88} +13.8844i q^{89} -6.74939i q^{91} +(9.59583 - 1.77100i) q^{92} +(-3.76463 - 1.17051i) q^{94} +(-4.03976 + 3.87079i) q^{95} +(3.85933 - 1.03410i) q^{97} +(0.139559 - 3.51820i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q + 2 q^{2} + 4 q^{5} + 8 q^{8}+O(q^{10}) \) 128 * q + 2 * q^2 + 4 * q^5 + 8 * q^8	\( 128 q + 2 q^{2} + 4 q^{5} + 8 q^{8} - 8 q^{10} - 4 q^{13} - 4 q^{16} + 16 q^{17} + 18 q^{20} - 10 q^{22} - 4 q^{25} + 48 q^{26} + 8 q^{28} - 18 q^{32} - 16 q^{37} + 34 q^{38} - 2 q^{40} + 8 q^{41} - 40 q^{46} - 38 q^{50} - 18 q^{52} + 64 q^{53} + 32 q^{56} - 10 q^{58} - 8 q^{61} - 44 q^{62} - 12 q^{65} - 58 q^{68} - 22 q^{70} - 16 q^{73} - 32 q^{76} + 60 q^{77} - 132 q^{80} - 4 q^{85} - 32 q^{86} - 10 q^{88} - 52 q^{92} - 4 q^{97} - 164 q^{98}+O(q^{100}) \) 128 * q + 2 * q^2 + 4 * q^5 + 8 * q^8 - 8 * q^10 - 4 * q^13 - 4 * q^16 + 16 * q^17 + 18 * q^20 - 10 * q^22 - 4 * q^25 + 48 * q^26 + 8 * q^28 - 18 * q^32 - 16 * q^37 + 34 * q^38 - 2 * q^40 + 8 * q^41 - 40 * q^46 - 38 * q^50 - 18 * q^52 + 64 * q^53 + 32 * q^56 - 10 * q^58 - 8 * q^61 - 44 * q^62 - 12 * q^65 - 58 * q^68 - 22 * q^70 - 16 * q^73 - 32 * q^76 + 60 * q^77 - 132 * q^80 - 4 * q^85 - 32 * q^86 - 10 * q^88 - 52 * q^92 - 4 * q^97 - 164 * q^98

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