LMFDB - Embedded newform 855.2.da.b.199.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [855,2,Mod(199,855)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(855, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 9, 8]))

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

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

chi := DirichletCharacter("855.199");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 855 = 3^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	855.da (of order $18$, degree $6$, 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:	$6.82720937282$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$8$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 95)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			199.7
Character	$\chi$	$=$	855.199
Dual form			855.2.da.b.739.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.45670 - 0.256855i) q^{2} +(0.176607 - 0.0642796i) q^{4} +(0.869056 - 2.06028i) q^{5} +(-2.81448 - 1.62494i) q^{7} +(-2.32124 + 1.34017i) q^{8} +O(q^{10})$	\(q+(1.45670 - 0.256855i) q^{2} +(0.176607 - 0.0642796i) q^{4} +(0.869056 - 2.06028i) q^{5} +(-2.81448 - 1.62494i) q^{7} +(-2.32124 + 1.34017i) q^{8} +(0.736759 - 3.22442i) q^{10} +(-2.09200 - 3.62344i) q^{11} +(-1.14682 + 1.36673i) q^{13} +(-4.51721 - 1.64413i) q^{14} +(-3.32506 + 2.79006i) q^{16} +(-6.23606 + 1.09959i) q^{17} +(4.09399 - 1.49640i) q^{19} +(0.0210474 - 0.419722i) q^{20} +(-3.97810 - 4.74092i) q^{22} +(0.490346 + 1.34721i) q^{23} +(-3.48948 - 3.58099i) q^{25} +(-1.31952 + 2.28547i) q^{26} +(-0.601506 - 0.106062i) q^{28} +(-0.0589345 + 0.334234i) q^{29} +(1.38932 - 2.40638i) q^{31} +(-0.681187 + 0.811808i) q^{32} +(-8.80161 + 3.20352i) q^{34} +(-5.79376 + 4.38644i) q^{35} +2.70482i q^{37} +(5.57935 - 3.23137i) q^{38} +(0.743832 + 5.94709i) q^{40} +(5.46819 - 4.58835i) q^{41} +(3.38403 - 9.29755i) q^{43} +(-0.602374 - 0.505452i) q^{44} +(1.06032 + 1.83654i) q^{46} +(-0.438674 - 0.0773501i) q^{47} +(1.78085 + 3.08452i) q^{49} +(-6.00292 - 4.32013i) q^{50} +(-0.114683 + 0.315090i) q^{52} +(-2.47532 - 6.80087i) q^{53} +(-9.28335 + 1.16111i) q^{55} +8.71078 q^{56} +0.502015i q^{58} +(0.545712 + 3.09489i) q^{59} +(2.88074 - 1.04850i) q^{61} +(1.40573 - 3.86222i) q^{62} +(3.55679 - 6.16055i) q^{64} +(1.81918 + 3.55053i) q^{65} +(-8.42261 - 1.48513i) q^{67} +(-1.03065 + 0.595046i) q^{68} +(-7.31307 + 7.87786i) q^{70} +(12.1153 + 4.40959i) q^{71} +(-1.17133 - 1.39594i) q^{73} +(0.694747 + 3.94011i) q^{74} +(0.626839 - 0.527435i) q^{76} +13.5974i q^{77} +(-0.535235 + 0.449116i) q^{79} +(2.85863 + 9.27527i) q^{80} +(6.78695 - 8.08837i) q^{82} +(-0.478899 - 0.276493i) q^{83} +(-3.15403 + 13.8036i) q^{85} +(2.54139 - 14.4129i) q^{86} +(9.71206 + 5.60726i) q^{88} +(5.23109 + 4.38940i) q^{89} +(5.44854 - 1.98311i) q^{91} +(0.173197 + 0.206408i) q^{92} -0.658883 q^{94} +(0.474906 - 9.73522i) q^{95} +(-13.0001 + 2.29226i) q^{97} +(3.38643 + 4.03579i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 18 q^{4} + 6 q^{5}+O(q^{10}) $ 48 * q - 18 * q^4 + 6 * q^5	$ 48 q - 18 q^{4} + 6 q^{5} - 15 q^{10} + 12 q^{11} - 6 q^{14} - 42 q^{16} + 12 q^{19} - 42 q^{20} + 12 q^{25} - 12 q^{26} - 42 q^{31} - 36 q^{34} - 6 q^{35} + 66 q^{40} - 6 q^{41} + 6 q^{44} - 6 q^{46} + 12 q^{49} + 18 q^{50} - 36 q^{56} + 36 q^{59} + 48 q^{61} + 18 q^{65} - 123 q^{70} + 24 q^{71} - 84 q^{74} + 66 q^{76} + 48 q^{79} + 39 q^{80} - 84 q^{85} + 42 q^{86} + 12 q^{89} - 30 q^{91} - 72 q^{94} + 63 q^{95}+O(q^{100}) $ 48 * q - 18 * q^4 + 6 * q^5 - 15 * q^10 + 12 * q^11 - 6 * q^14 - 42 * q^16 + 12 * q^19 - 42 * q^20 + 12 * q^25 - 12 * q^26 - 42 * q^31 - 36 * q^34 - 6 * q^35 + 66 * q^40 - 6 * q^41 + 6 * q^44 - 6 * q^46 + 12 * q^49 + 18 * q^50 - 36 * q^56 + 36 * q^59 + 48 * q^61 + 18 * q^65 - 123 * q^70 + 24 * q^71 - 84 * q^74 + 66 * q^76 + 48 * q^79 + 39 * q^80 - 84 * q^85 + 42 * q^86 + 12 * q^89 - 30 * q^91 - 72 * q^94 + 63 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/855\mathbb{Z}\right)^\times$.

$n$	$172$	$191$	$496$
$\chi(n)$	$-1$	$1$	$e\left(\frac{4}{9}\right)$

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 $

$2$	1.45670	−	0.256855i	1.03004	−	0.181624i	0.367010	−	0.930217i	$-0.380381\pi$
$2$	1.45670	−	0.256855i	1.03004	−	0.181624i	0.663030	+	0.748593i	$0.269270\pi$
$3$		0			0
$3$		0			0
$4$	0.176607	−	0.0642796i	0.0883034	−	0.0321398i
$5$	0.869056	−	2.06028i	0.388654	−	0.921384i
$5$	0.869056	−	2.06028i	0.388654	−	0.921384i
$6$		0			0
$7$	−2.81448	−	1.62494i	−1.06377	−	0.614169i	−0.137298	−	0.990530i	$-0.543842\pi$
$7$	−2.81448	−	1.62494i	−1.06377	−	0.614169i	−0.926473	+	0.376361i	$0.877175\pi$
$8$	−2.32124	+	1.34017i	−0.820684	+	0.473822i
$9$		0			0
$10$	0.736759	−	3.22442i	0.232984	−	1.01965i
$11$	−2.09200	−	3.62344i	−0.630760	−	1.09251i	−0.987397	−	0.158265i	$-0.949410\pi$
$11$	−2.09200	−	3.62344i	−0.630760	−	1.09251i	0.356636	−	0.934243i	$-0.383924\pi$
$12$		0			0
$13$	−1.14682	+	1.36673i	−0.318070	+	0.379062i	−0.901263	−	0.433272i	$-0.857359\pi$
$13$	−1.14682	+	1.36673i	−0.318070	+	0.379062i	0.583193	+	0.812334i	$0.301803\pi$
$14$	−4.51721	−	1.64413i	−1.20728	−	0.439412i
$15$		0			0
$16$	−3.32506	+	2.79006i	−0.831266	+	0.697515i
$17$	−6.23606	+	1.09959i	−1.51247	+	0.266689i	−0.867467	−	0.497495i	$-0.834253\pi$
$17$	−6.23606	+	1.09959i	−1.51247	+	0.266689i	−0.644999	+	0.764183i	$0.723142\pi$
$18$		0			0
$19$	4.09399	−	1.49640i	0.939226	−	0.343298i
$19$	4.09399	−	1.49640i	0.939226	−	0.343298i
$20$	0.0210474	−	0.419722i	0.00470635	−	0.0938526i
$21$		0			0
$22$	−3.97810	−	4.74092i	−0.848134	−	1.01077i
$23$	0.490346	+	1.34721i	0.102244	+	0.280914i	0.980258	−	0.197721i	$-0.0633540\pi$
$23$	0.490346	+	1.34721i	0.102244	+	0.280914i	−0.878014	+	0.478635i	$0.841132\pi$
$24$		0			0
$25$	−3.48948	−	3.58099i	−0.697897	−	0.716199i
$26$	−1.31952	+	2.28547i	−0.258779	+	0.448218i
$27$		0			0
$28$	−0.601506	−	0.106062i	−0.113674	−	0.0200438i
$29$	−0.0589345	+	0.334234i	−0.0109439	+	0.0620657i	−0.989791	−	0.142529i	$-0.954477\pi$
$29$	−0.0589345	+	0.334234i	−0.0109439	+	0.0620657i	0.978847	+	0.204595i	$0.0655877\pi$
$30$		0			0
$31$	1.38932	−	2.40638i	0.249530	−	0.432199i	−0.713866	−	0.700283i	$-0.753057\pi$
$31$	1.38932	−	2.40638i	0.249530	−	0.432199i	0.963395	+	0.268084i	$0.0863906\pi$
$32$	−0.681187	+	0.811808i	−0.120418	+	0.143509i
$33$		0			0
$34$	−8.80161	+	3.20352i	−1.50946	+	0.549400i
$35$	−5.79376	+	4.38644i	−0.979324	+	0.741443i
$36$		0			0
$37$			2.70482i			0.444670i	0.974970	+	0.222335i	$0.0713679\pi$
$37$			2.70482i			0.444670i	−0.974970	+	0.222335i	$0.928632\pi$
$38$	5.57935	−	3.23137i	0.905090	−	0.524197i
$39$		0			0
$40$	0.743832	+	5.94709i	0.117610	+	0.940317i
$41$	5.46819	−	4.58835i	0.853987	−	0.716581i	−0.106677	−	0.994294i	$-0.534021\pi$
$41$	5.46819	−	4.58835i	0.853987	−	0.716581i	0.960664	+	0.277713i	$0.0895765\pi$
$42$		0			0
$43$	3.38403	−	9.29755i	0.516060	−	1.41786i	−0.358767	−	0.933427i	$-0.616803\pi$
$43$	3.38403	−	9.29755i	0.516060	−	1.41786i	0.874827	−	0.484436i	$-0.160975\pi$
$44$	−0.602374	−	0.505452i	−0.0908113	−	0.0761997i
$45$		0			0
$46$	1.06032	+	1.83654i	0.156336	+	0.270782i
$47$	−0.438674	−	0.0773501i	−0.0639872	−	0.0112827i	0.141563	−	0.989929i	$-0.454787\pi$
$47$	−0.438674	−	0.0773501i	−0.0639872	−	0.0112827i	−0.205550	+	0.978647i	$0.565898\pi$
$48$		0			0
$49$	1.78085	+	3.08452i	0.254407	+	0.440645i
$50$	−6.00292	−	4.32013i	−0.848940	−	0.610959i
$51$		0			0
$52$	−0.114683	+	0.315090i	−0.0159037	+	0.0436952i
$53$	−2.47532	−	6.80087i	−0.340011	−	0.934172i	−0.985391	−	0.170310i	$-0.945523\pi$
$53$	−2.47532	−	6.80087i	−0.340011	−	0.934172i	0.645380	−	0.763862i	$-0.276699\pi$
$54$		0			0
$55$	−9.28335	+	1.16111i	−1.25177	+	0.156565i
$56$	8.71078			1.16403
$57$		0			0
$58$			0.502015i			0.0659178i
$59$	0.545712	+	3.09489i	0.0710457	+	0.402920i	0.999504	+	0.0314842i	$0.0100234\pi$
$59$	0.545712	+	3.09489i	0.0710457	+	0.402920i	−0.928459	+	0.371436i	$0.878866\pi$
$60$		0			0
$61$	2.88074	−	1.04850i	0.368841	−	0.134247i	−0.150948	−	0.988542i	$-0.548233\pi$
$61$	2.88074	−	1.04850i	0.368841	−	0.134247i	0.519789	+	0.854295i	$0.326010\pi$
$62$	1.40573	−	3.86222i	0.178528	−	0.490503i
$63$		0			0
$64$	3.55679	−	6.16055i	0.444599	−	0.770068i
$65$	1.81918	+	3.55053i	0.225642	+	0.440389i
$66$		0			0
$67$	−8.42261	−	1.48513i	−1.02899	−	0.181438i	−0.366426	−	0.930447i	$-0.619419\pi$
$67$	−8.42261	−	1.48513i	−1.02899	−	0.181438i	−0.662559	+	0.749009i	$0.730530\pi$
$68$	−1.03065	+	0.595046i	−0.124985	+	0.0721599i
$69$		0			0
$70$	−7.31307	+	7.87786i	−0.874080	+	0.941585i
$71$	12.1153	+	4.40959i	1.43782	+	0.523322i	0.939161	−	0.343478i	$-0.111605\pi$
$71$	12.1153	+	4.40959i	1.43782	+	0.523322i	0.498656	+	0.866800i	$0.333827\pi$
$72$		0			0
$73$	−1.17133	−	1.39594i	−0.137094	−	0.163382i	0.693129	−	0.720813i	$-0.256232\pi$
$73$	−1.17133	−	1.39594i	−0.137094	−	0.163382i	−0.830223	+	0.557431i	$0.811787\pi$
$74$	0.694747	+	3.94011i	0.0807627	+	0.458028i
$75$		0			0
$76$	0.626839	−	0.527435i	0.0719034	−	0.0605010i
$77$			13.5974i			1.54957i
$78$		0			0
$79$	−0.535235	+	0.449116i	−0.0602187	+	0.0505295i	−0.672400	−	0.740188i	$-0.734737\pi$
$79$	−0.535235	+	0.449116i	−0.0602187	+	0.0505295i	0.612182	+	0.790717i	$0.290292\pi$
$80$	2.85863	+	9.27527i	0.319604	+	1.03701i
$81$		0			0
$82$	6.78695	−	8.08837i	0.749493	−	0.893211i
$83$	−0.478899	−	0.276493i	−0.0525660	−	0.0303490i	0.473487	−	0.880801i	$-0.342995\pi$
$83$	−0.478899	−	0.276493i	−0.0525660	−	0.0303490i	−0.526053	+	0.850452i	$0.676329\pi$
$84$		0			0
$85$	−3.15403	+	13.8036i	−0.342103	+	1.49721i
$86$	2.54139	−	14.4129i	0.274045	−	1.55419i
$87$		0			0
$88$	9.71206	+	5.60726i	1.03531	+	0.597736i
$89$	5.23109	+	4.38940i	0.554494	+	0.465276i	0.876459	−	0.481476i	$-0.159899\pi$
$89$	5.23109	+	4.38940i	0.554494	+	0.465276i	−0.321965	+	0.946751i	$0.604343\pi$
$90$		0			0
$91$	5.44854	−	1.98311i	0.571162	−	0.207886i
$92$	0.173197	+	0.206408i	0.0180570	+	0.0215195i
$93$		0			0
$94$	−0.658883			−0.0679586
$95$	0.474906	−	9.73522i	0.0487244	−	0.998812i
$96$		0			0
$97$	−13.0001	+	2.29226i	−1.31996	+	0.232744i	−0.788863	−	0.614569i	$-0.789330\pi$
$97$	−13.0001	+	2.29226i	−1.31996	+	0.232744i	−0.531094	+	0.847313i	$0.678219\pi$
$98$	3.38643	+	4.03579i	0.342081	+	0.407676i
$99$		0			0
$100$	−0.846451	−	0.408125i	−0.0846451	−	0.0408125i
$101$	−13.2339	−	11.1046i	−1.31683	−	1.10495i	−0.986968	−	0.160916i	$-0.948555\pi$
$101$	−13.2339	−	11.1046i	−1.31683	−	1.10495i	−0.329857	−	0.944031i	$-0.607001\pi$
$102$		0			0
$103$	11.9759	−	6.91430i	1.18002	−	0.681286i	0.224003	−	0.974589i	$-0.428088\pi$
$103$	11.9759	−	6.91430i	1.18002	−	0.681286i	0.956020	+	0.293302i	$0.0947542\pi$
$104$	0.830401	−	4.70944i	0.0814275	−	0.461798i
$105$		0			0
$106$	−5.35262	−	9.27101i	−0.519893	−	0.900481i
$107$	2.82722	+	1.63230i	0.273318	+	0.157800i	0.630394	−	0.776275i	$-0.282893\pi$
$107$	2.82722	+	1.63230i	0.273318	+	0.157800i	−0.357077	+	0.934075i	$0.616226\pi$
$108$		0			0
$109$	−3.02669	−	1.10163i	−0.289905	−	0.105517i	0.192974	−	0.981204i	$-0.438187\pi$
$109$	−3.02669	−	1.10163i	−0.289905	−	0.105517i	−0.482879	+	0.875687i	$0.660409\pi$
$110$	−13.2248	+	4.07587i	−1.26094	+	0.388619i
$111$		0			0
$112$	13.8920	−	2.44953i	1.31267	−	0.231459i
$113$		−	4.71007i		−	0.443086i	−0.975151	−	0.221543i	$-0.928891\pi$
$113$		−	4.71007i		−	0.443086i	0.975151	−	0.221543i	$-0.0711093\pi$
$114$		0			0
$115$	3.20177	+	0.160557i	0.298567	+	0.0149720i
$116$	0.0110762	+	0.0628163i	0.00102840	+	0.00583234i
$117$		0			0
$118$	1.58988	+	4.36815i	0.146360	+	0.402121i
$119$	19.3380	+	7.03845i	1.77271	+	0.645214i
$120$		0			0
$121$	−3.25289	+	5.63416i	−0.295717	+	0.512197i
$122$	3.92705	−	2.26729i	0.355539	−	0.205270i
$123$		0			0
$124$	0.0906829	−	0.514288i	0.00814356	−	0.0461844i
$125$	−10.4104	+	4.07722i	−0.931134	+	0.364677i
$126$		0			0
$127$	0.380538	−	0.453507i	0.0337673	−	0.0402423i	−0.748897	−	0.662687i	$-0.769416\pi$
$127$	0.380538	−	0.453507i	0.0337673	−	0.0402423i	0.782664	+	0.622445i	$0.213860\pi$
$128$	4.32371	−	11.8793i	0.382165	−	1.04999i
$129$		0			0
$130$	3.56197	+	4.70478i	0.312406	+	0.412636i
$131$	3.56830	+	20.2369i	0.311764	+	1.76810i	0.589817	+	0.807537i	$0.299200\pi$
$131$	3.56830	+	20.2369i	0.311764	+	1.76810i	−0.278053	+	0.960566i	$0.589689\pi$
$132$		0			0
$133$	−13.9540	−	2.44090i	−1.20997	−	0.211653i
$134$	−12.6507			−1.09285
$135$		0			0
$136$	13.0018	−	10.9098i	1.11489	−	0.935506i
$137$	−2.99407	−	8.22613i	−0.255800	−	0.702806i	−0.999415	−	0.0341973i	$-0.989113\pi$
$137$	−2.99407	−	8.22613i	−0.255800	−	0.702806i	0.743615	−	0.668608i	$-0.233110\pi$
$138$		0			0
$139$	−5.89041	−	4.94264i	−0.499618	−	0.419229i	0.357840	−	0.933783i	$-0.383513\pi$
$139$	−5.89041	−	4.94264i	−0.499618	−	0.419229i	−0.857458	+	0.514553i	$0.827958\pi$
$140$	−0.741259	+	1.14710i	−0.0626478	+	0.0969472i
$141$		0			0
$142$	18.7809	+	3.31158i	1.57606	+	0.277901i
$143$	7.35139	+	1.29625i	0.614754	+	0.108398i
$144$		0			0
$145$	0.637397	+	0.411889i	0.0529329	+	0.0342055i
$146$	−2.06483	−	1.73260i	−0.170887	−	0.143391i
$147$		0			0
$148$	0.173865	+	0.477690i	0.0142916	+	0.0392659i
$149$	−11.4457	+	9.60412i	−0.937672	+	0.786800i	−0.977179	−	0.212419i	$-0.931866\pi$
$149$	−11.4457	+	9.60412i	−0.937672	+	0.786800i	0.0395067	+	0.999219i	$0.487421\pi$
$150$		0			0
$151$	13.1424			1.06951			0.534757	−	0.845006i	$-0.320403\pi$
$151$	13.1424			1.06951			0.534757	+	0.845006i	$0.320403\pi$
$152$	−7.49772	+	8.96017i	−0.608145	+	0.726765i
$153$		0			0
$154$	3.49257	+	19.8074i	0.281440	+	1.59612i
$155$	−3.75041	−	4.95367i	−0.301240	−	0.397888i
$156$		0			0
$157$	−3.70654	+	10.1836i	−0.295814	+	0.812742i	0.699374	+	0.714756i	$0.253462\pi$
$157$	−3.70654	+	10.1836i	−0.295814	+	0.812742i	−0.995188	+	0.0979861i	$0.968760\pi$
$158$	−0.664318	+	0.791704i	−0.0528503	+	0.0629846i
$159$		0			0
$160$	1.08056	+	2.10894i	0.0854256	+	0.166726i
$161$	0.809073	−	4.58848i	0.0637639	−	0.361623i
$162$		0			0
$163$	7.31405	−	4.22277i	0.572881	−	0.330753i	−0.185418	−	0.982660i	$-0.559364\pi$
$163$	7.31405	−	4.22277i	0.572881	−	0.330753i	0.758299	+	0.651907i	$0.226031\pi$
$164$	0.670782	−	1.16183i	0.0523792	−	0.0907235i
$165$		0			0
$166$	−0.768630	−	0.279758i	−0.0596573	−	0.0217135i
$167$	6.80663	+	18.7011i	0.526713	+	1.44713i	0.862919	+	0.505343i	$0.168634\pi$
$167$	6.80663	+	18.7011i	0.526713	+	1.44713i	−0.336206	+	0.941788i	$0.609144\pi$
$168$		0			0
$169$	1.70468	+	9.66772i	0.131129	+	0.743671i
$170$	−1.04895	+	20.9178i	−0.0804506	+	1.60432i
$171$		0			0
$172$		−	1.85954i		−	0.141788i
$173$	11.5430	−	2.03534i	0.877597	−	0.154744i	0.283340	−	0.959019i	$-0.408557\pi$
$173$	11.5430	−	2.03534i	0.877597	−	0.154744i	0.594257	+	0.804275i	$0.297446\pi$
$174$		0			0
$175$	4.00217	+	15.7488i	0.302536	+	1.19050i
$176$	17.0656	+	6.21138i	1.28637	+	0.468200i
$177$		0			0
$178$	8.74755	+	5.05040i	0.655657	+	0.378544i
$179$	−3.54189	−	6.13473i	−0.264733	−	0.458532i	0.702760	−	0.711427i	$-0.251951\pi$
$179$	−3.54189	−	6.13473i	−0.264733	−	0.458532i	−0.967494	+	0.252895i	$0.918617\pi$
$180$		0			0
$181$	1.61176	−	9.14076i	0.119801	−	0.679427i	−0.864459	−	0.502703i	$-0.832339\pi$
$181$	1.61176	−	9.14076i	0.119801	−	0.679427i	0.984260	−	0.176724i	$-0.0565500\pi$
$182$	7.42750	−	4.28827i	0.550563	−	0.317868i
$183$		0			0
$184$	−2.94371	−	2.47007i	−0.217013	−	0.182096i
$185$	5.57268	+	2.35064i	0.409712	+	0.172823i
$186$		0			0
$187$	17.0301	+	20.2957i	1.24536	+	1.48417i
$188$	−0.0824448	+	0.0145373i	−0.00601291	+	0.00106024i
$189$		0			0
$190$	−1.80874	−	14.3032i	−0.131220	−	1.03767i
$191$	−8.12426			−0.587850			−0.293925	−	0.955828i	$-0.594962\pi$
$191$	−8.12426			−0.587850			−0.293925	+	0.955828i	$0.594962\pi$
$192$		0			0
$193$	4.96452	+	5.91649i	0.357354	+	0.425878i	0.914531	−	0.404516i	$-0.132560\pi$
$193$	4.96452	+	5.91649i	0.357354	+	0.425878i	−0.557177	+	0.830394i	$0.688115\pi$
$194$	−18.3484	+	6.67827i	−1.31734	+	0.479472i
$195$		0			0
$196$	0.512781	+	0.430275i	0.0366272	+	0.0307339i
$197$	−3.08965	−	1.78381i	−0.220129	−	0.127091i	0.385881	−	0.922548i	$-0.373897\pi$
$197$	−3.08965	−	1.78381i	−0.220129	−	0.127091i	−0.606010	+	0.795457i	$0.707231\pi$
$198$		0			0
$199$	1.52279	−	8.63615i	0.107947	−	0.612201i	−0.882055	−	0.471147i	$-0.843840\pi$
$199$	1.52279	−	8.63615i	0.107947	−	0.612201i	0.990002	−	0.141053i	$-0.0450489\pi$
$200$	12.8991	+	3.63586i	0.912103	+	0.257094i
$201$		0			0
$202$	−22.1301	−	12.7768i	−1.55707	−	0.898974i
$203$	0.708979	−	0.844928i	0.0497606	−	0.0593023i
$204$		0			0
$205$	−4.70112	−	15.2535i	−0.328340	−	1.06535i
$206$	15.6693	−	13.1481i	1.09173	−	0.916073i
$207$		0			0
$208$		−	7.74414i		−	0.536960i
$209$	−13.9867	−	11.7039i	−0.967483	−	0.809574i
$210$		0			0
$211$	2.05203	+	11.6376i	0.141267	+	0.801167i	0.970289	+	0.241950i	$0.0777870\pi$
$211$	2.05203	+	11.6376i	0.141267	+	0.801167i	−0.829021	+	0.559217i	$0.811102\pi$
$212$	−0.874315	−	1.04197i	−0.0600482	−	0.0715627i
$213$		0			0
$214$	4.53767	+	1.65158i	0.310189	+	0.112899i
$215$	−16.2146	−	15.0521i	−1.10583	−	1.02655i
$216$		0			0
$217$	−7.82043	+	4.51513i	−0.530886	+	0.306507i
$218$	−4.69193	−	0.827314i	−0.317778	−	0.0560328i
$219$		0			0
$220$	−1.56487	+	0.801791i	−0.105503	+	0.0540568i
$221$	5.64880	−	9.78401i	0.379979	−	0.658144i
$222$		0			0
$223$	3.04316	−	8.36101i	0.203785	−	0.559895i	−0.795131	−	0.606437i	$-0.792598\pi$
$223$	3.04316	−	8.36101i	0.203785	−	0.559895i	0.998916	+	0.0465426i	$0.0148203\pi$
$224$	3.23632	−	1.17792i	0.216236	−	0.0787034i
$225$		0			0
$226$	−1.20980	−	6.86114i	−0.0804750	−	0.456396i
$227$		−	26.4080i		−	1.75276i	−0.481620	−	0.876380i	$-0.659951\pi$
$227$		−	26.4080i		−	1.75276i	0.481620	−	0.876380i	$-0.340049\pi$
$228$		0			0
$229$	−21.7852			−1.43961			−0.719804	−	0.694177i	$-0.755768\pi$
$229$	−21.7852			−1.43961			−0.719804	+	0.694177i	$0.755768\pi$
$230$	4.70525	−	0.588509i	0.310255	−	0.0388051i
$231$		0			0
$232$	−0.311129	−	0.854821i	−0.0204266	−	0.0561217i
$233$	−3.42052	+	9.39780i	−0.224086	+	0.615670i	−0.999883	−	0.0153122i	$-0.995126\pi$
$233$	−3.42052	+	9.39780i	−0.224086	+	0.615670i	0.775797	+	0.630982i	$0.217348\pi$
$234$		0			0
$235$	−0.540595	+	0.836568i	−0.0352645	+	0.0545717i
$236$	0.295315	+	0.511500i	0.0192234	+	0.0332958i
$237$		0			0
$238$	29.9774	+	5.28583i	1.94315	+	0.342630i
$239$	−8.91823	−	15.4468i	−0.576872	−	0.999172i	−0.995835	−	0.0911689i	$-0.970940\pi$
$239$	−8.91823	−	15.4468i	−0.576872	−	0.999172i	0.418963	−	0.908003i	$-0.362394\pi$
$240$		0			0
$241$	−13.1332	−	11.0201i	−0.845984	−	0.709864i	0.112918	−	0.993604i	$-0.463980\pi$
$241$	−13.1332	−	11.0201i	−0.845984	−	0.709864i	−0.958901	+	0.283740i	$0.908425\pi$
$242$	−3.29131	+	9.04279i	−0.211573	+	0.581293i
$243$		0			0
$244$	0.441361	−	0.370346i	0.0282552	−	0.0237090i
$245$	7.90262	−	0.988419i	0.504880	−	0.0631478i
$246$		0			0
$247$	−2.64990	+	7.31147i	−0.168609	+	0.465218i
$248$			7.44772i			0.472931i
$249$		0			0
$250$	−14.1175	+	8.61323i	−0.892872	+	0.544749i
$251$	9.11112	−	3.31618i	0.575089	−	0.209315i	−0.0380697	−	0.999275i	$-0.512121\pi$
$251$	9.11112	−	3.31618i	0.575089	−	0.209315i	0.613159	+	0.789960i	$0.289899\pi$
$252$		0			0
$253$	3.85575	−	4.59511i	0.242409	−	0.288892i
$254$	0.437843	−	0.758366i	0.0274727	−	0.0475841i
$255$		0			0
$256$	0.776555	−	4.40406i	0.0485347	−	0.275254i
$257$	−9.89795	−	1.74528i	−0.617417	−	0.108867i	−0.143813	−	0.989605i	$-0.545936\pi$
$257$	−9.89795	−	1.74528i	−0.617417	−	0.108867i	−0.473605	+	0.880738i	$0.657047\pi$
$258$		0			0
$259$	4.39517	−	7.61265i	0.273102	−	0.473027i
$260$	0.549507	+	0.510111i	0.0340790	+	0.0316357i
$261$		0			0
$262$	10.3959	+	28.5624i	0.642259	+	1.76459i
$263$	14.0324	+	16.7232i	0.865276	+	1.03120i	0.999192	+	0.0402026i	$0.0128003\pi$
$263$	14.0324	+	16.7232i	0.865276	+	1.03120i	−0.133916	+	0.990993i	$0.542755\pi$
$264$		0			0
$265$	−16.1629	−	0.810506i	−0.992877	−	0.0497890i
$266$	−20.9537	+	0.0285081i	−1.28475	+	0.00174794i
$267$		0			0
$268$	−1.58295	+	0.279117i	−0.0966943	+	0.0170498i
$269$	11.8393	−	9.93433i	0.721853	−	0.605707i	−0.206044	−	0.978543i	$-0.566059\pi$
$269$	11.8393	−	9.93433i	0.721853	−	0.605707i	0.927897	+	0.372836i	$0.121615\pi$
$270$		0			0
$271$	−4.85182	−	1.76592i	−0.294727	−	0.107272i	0.190425	−	0.981702i	$-0.439013\pi$
$271$	−4.85182	−	1.76592i	−0.294727	−	0.107272i	−0.485152	+	0.874430i	$0.661236\pi$
$272$	17.6674	−	21.0552i	1.07124	−	1.27666i
$273$		0			0
$274$	−6.47437	−	11.2139i	−0.391131	−	0.677459i
$275$	−5.67554	+	20.1354i	−0.342248	+	1.21421i
$276$		0			0
$277$	4.82402	−	2.78515i	0.289847	−	0.167343i	−0.348026	−	0.937485i	$-0.613148\pi$
$277$	4.82402	−	2.78515i	0.289847	−	0.167343i	0.637873	+	0.770142i	$0.279814\pi$
$278$	−9.85009	−	5.68695i	−0.590769	−	0.341081i
$279$		0			0
$280$	7.57016	−	17.9466i	0.452403	−	1.07252i
$281$	25.6282	−	9.32789i	1.52885	−	0.556455i	0.565509	−	0.824742i	$-0.308680\pi$
$281$	25.6282	−	9.32789i	1.52885	−	0.556455i	0.963339	+	0.268287i	$0.0864576\pi$
$282$		0			0
$283$	−14.8172	+	2.61267i	−0.880792	+	0.155307i	−0.595714	−	0.803197i	$-0.703131\pi$
$283$	−14.8172	+	2.61267i	−0.880792	+	0.155307i	−0.285078	+	0.958504i	$0.592020\pi$
$284$	2.42308			0.143784
$285$		0			0
$286$	11.0417			0.652910
$287$	−22.8459	+	4.02834i	−1.34855	+	0.237786i
$288$		0			0
$289$	21.7045	−	7.89981i	1.27674	−	0.464694i
$290$	1.03429	+	0.436279i	0.0607356	+	0.0256192i
$291$		0			0
$292$	−0.296596	−	0.171240i	−0.0173570	−	0.0100210i
$293$	−6.77995	+	3.91441i	−0.396089	+	0.228682i	−0.684795	−	0.728736i	$-0.740108\pi$
$293$	−6.77995	+	3.91441i	−0.396089	+	0.228682i	0.288706	+	0.957418i	$0.406775\pi$
$294$		0			0
$295$	6.85058	+	1.56531i	0.398856	+	0.0911361i
$296$	−3.62492	−	6.27855i	−0.210694	−	0.364933i
$297$		0			0
$298$	−14.2061	+	16.9302i	−0.822938	+	0.980740i
$299$	−2.40361	−	0.874843i	−0.139004	−	0.0505935i
$300$		0			0
$301$	−24.6322	+	20.6689i	−1.41978	+	1.19133i
$302$	19.1445	−	3.37569i	1.10164	−	0.194249i
$303$		0			0
$304$	−9.43773	+	16.3981i	−0.541291	+	0.940496i
$305$	0.343317	−	6.84633i	0.0196583	−	0.392020i
$306$		0			0
$307$	−10.1011	−	12.0381i	−0.576503	−	0.687049i	0.396449	−	0.918057i	$-0.370242\pi$
$307$	−10.1011	−	12.0381i	−0.576503	−	0.687049i	−0.972952	+	0.231008i	$0.925798\pi$
$308$	0.874039	+	2.40140i	0.0498030	+	0.136833i
$309$		0			0
$310$	−6.73558	−	6.25269i	−0.382555	−	0.355129i
$311$	8.99061	−	15.5722i	0.509810	−	0.883018i	−0.490125	−	0.871652i	$-0.663049\pi$
$311$	8.99061	−	15.5722i	0.509810	−	0.883018i	0.999935	−	0.0113654i	$-0.00361781\pi$
$312$		0			0
$313$	−20.8784	−	3.68143i	−1.18012	−	0.208087i	−0.451031	−	0.892508i	$-0.648944\pi$
$313$	−20.8784	−	3.68143i	−1.18012	−	0.208087i	−0.729087	+	0.684422i	$0.760055\pi$
$314$	−2.78359	+	15.7865i	−0.157087	+	0.890884i
$315$		0			0
$316$	−0.0656572	+	0.113722i	−0.00369351	+	0.00639734i
$317$	1.96977	−	2.34748i	0.110633	−	0.131848i	−0.707886	−	0.706327i	$-0.750351\pi$
$317$	1.96977	−	2.34748i	0.110633	−	0.131848i	0.818519	+	0.574479i	$0.194795\pi$
$318$		0			0
$319$	1.33437	−	0.485670i	0.0747102	−	0.0271923i
$320$	−9.60138	−	12.6818i	−0.536733	−	0.708936i
$321$		0			0
$322$		−	6.89184i		−	0.384067i
$323$	−23.8850	+	13.8333i	−1.32899	+	0.769708i
$324$		0			0
$325$	8.89604	−	0.662415i	0.493464	−	0.0367442i
$326$	9.56972	−	8.02995i	0.530018	−	0.444738i
$327$		0			0
$328$	−6.54382	+	17.9790i	−0.361322	+	0.992724i
$329$	1.10895	+	0.930518i	0.0611383	+	0.0513011i
$330$		0			0
$331$	12.9754	+	22.4741i	0.713195	+	1.23529i	0.963652	+	0.267162i	$0.0860858\pi$
$331$	12.9754	+	22.4741i	0.713195	+	1.23529i	−0.250457	+	0.968128i	$0.580581\pi$
$332$	−0.102350	−	0.0180470i	−0.00561717	−	0.000990459i
$333$		0			0
$334$	14.7187	+	25.4935i	0.805369	+	1.39494i
$335$	−10.3795	+	16.0622i	−0.567093	+	0.877574i
$336$		0			0
$337$	3.43986	−	9.45093i	0.187381	−	0.514825i	−0.810058	−	0.586350i	$-0.800564\pi$
$337$	3.43986	−	9.45093i	0.187381	−	0.514825i	0.997439	+	0.0715252i	$0.0227866\pi$
$338$	4.96641	+	13.6451i	0.270137	+	0.742195i
$339$		0			0
$340$	0.330267	+	2.64055i	0.0179112	+	0.143204i
$341$	−11.6258			−0.629574
$342$		0			0
$343$			11.1741i			0.603343i
$344$	4.60514	+	26.1171i	0.248293	+	1.40814i
$345$		0			0
$346$	16.2918	−	5.92975i	0.875855	−	0.318785i
$347$	−2.33190	+	6.40683i	−0.125183	+	0.343937i	−0.986414	−	0.164276i	$-0.947471\pi$
$347$	−2.33190	+	6.40683i	−0.125183	+	0.343937i	0.861232	+	0.508213i	$0.169694\pi$
$348$		0			0
$349$	15.7983	−	27.3634i	0.845663	−	1.46473i	−0.0393817	−	0.999224i	$-0.512539\pi$
$349$	15.7983	−	27.3634i	0.845663	−	1.46473i	0.885044	−	0.465507i	$-0.154128\pi$
$350$	9.87511	+	21.9133i	0.527847	+	1.17131i
$351$		0			0
$352$	4.36658	+	0.769945i	0.232739	+	0.0410382i
$353$	−5.46165	+	3.15328i	−0.290694	+	0.167832i	−0.638255	−	0.769825i	$-0.720343\pi$
$353$	−5.46165	+	3.15328i	−0.290694	+	0.167832i	0.347561	+	0.937658i	$0.387010\pi$
$354$		0			0
$355$	19.6138	−	21.1286i	1.04099	−	1.12139i
$356$	1.20600	+	0.438946i	0.0639176	+	0.0232641i
$357$		0			0
$358$	−6.73520	−	8.02670i	−0.355966	−	0.424224i
$359$	0.725269	+	4.11321i	0.0382782	+	0.217087i	0.997947	−	0.0640469i	$-0.0204007\pi$
$359$	0.725269	+	4.11321i	0.0382782	+	0.217087i	−0.959669	+	0.281134i	$0.909290\pi$
$360$		0			0
$361$	14.5216	−	12.2525i	0.764293	−	0.644870i
$362$		−	13.7293i		−	0.721596i
$363$		0			0
$364$	0.834776	−	0.700460i	0.0437542	−	0.0367141i
$365$	−3.89398	+	1.20012i	−0.203820	+	0.0628171i
$366$		0			0
$367$	10.6516	−	12.6941i	0.556010	−	0.662627i	−0.412687	−	0.910873i	$-0.635410\pi$
$367$	10.6516	−	12.6941i	0.556010	−	0.662627i	0.968697	+	0.248246i	$0.0798541\pi$
$368$	−5.38924	−	3.11148i	−0.280933	−	0.162197i
$369$		0			0
$370$	8.72148	+	1.99280i	0.453408	+	0.103601i
$371$	−4.08428	+	23.1631i	−0.212045	+	1.20257i
$372$		0			0
$373$	−32.0433	−	18.5002i	−1.65914	−	0.957905i	−0.973113	−	0.230330i	$-0.926020\pi$
$373$	−32.0433	−	18.5002i	−1.65914	−	0.957905i	−0.686028	−	0.727576i	$-0.740647\pi$
$374$	30.0207	+	25.1904i	1.55233	+	1.30256i
$375$		0			0
$376$	1.12193	−	0.408350i	0.0578592	−	0.0210590i
$377$	−0.389219	−	0.463853i	−0.0200458	−	0.0238897i
$378$		0			0
$379$	−31.5147			−1.61880			−0.809400	−	0.587257i	$-0.800208\pi$
$379$	−31.5147			−1.61880			−0.809400	+	0.587257i	$0.800208\pi$
$380$	−0.541904	−	1.74983i	−0.0277991	−	0.0897645i
$381$		0			0
$382$	−11.8346	+	2.08676i	−0.605510	+	0.106768i
$383$	−1.99144	−	2.37331i	−0.101758	−	0.121270i	0.712762	−	0.701406i	$-0.247444\pi$
$383$	−1.99144	−	2.37331i	−0.101758	−	0.121270i	−0.814520	+	0.580136i	$0.803000\pi$
$384$		0			0
$385$	28.0145	+	11.8169i	1.42775	+	0.602247i
$386$	8.75148	+	7.34337i	0.445439	+	0.373768i
$387$		0			0
$388$	−2.14856	+	1.24047i	−0.109076	+	0.0629753i
$389$	4.52037	−	25.6363i	0.229192	−	1.29981i	−0.625316	−	0.780372i	$-0.715030\pi$
$389$	4.52037	−	25.6363i	0.229192	−	1.29981i	0.854507	−	0.519439i	$-0.173859\pi$
$390$		0			0
$391$	−4.53920	−	7.86213i	−0.229557	−	0.397605i
$392$	−8.26756	−	4.77328i	−0.417575	−	0.241087i
$393$		0			0
$394$	−4.95887	−	1.80488i	−0.249824	−	0.0909285i
$395$	0.460153	+	1.49304i	0.0231528	+	0.0751230i
$396$		0			0
$397$	−12.4684	+	2.19851i	−0.625770	+	0.110340i	−0.477536	−	0.878612i	$-0.658470\pi$
$397$	−12.4684	+	2.19851i	−0.625770	+	0.110340i	−0.148234	+	0.988952i	$0.547359\pi$
$398$		−	12.9714i		−	0.650197i
$399$		0			0
$400$	21.5939	+	2.17116i	1.07970	+	0.108558i
$401$	1.60135	+	9.08170i	0.0799675	+	0.453518i	0.998330	+	0.0577770i	$0.0184012\pi$
$401$	1.60135	+	9.08170i	0.0799675	+	0.453518i	−0.918362	+	0.395741i	$0.870488\pi$
$402$		0			0
$403$	1.69556	+	4.65851i	0.0844618	+	0.232057i
$404$	−3.05100	−	1.11047i	−0.151793	−	0.0552481i
$405$		0			0
$406$	0.815744	−	1.41291i	0.0404847	−	0.0701215i
$407$	9.80076	−	5.65847i	0.485806	−	0.280480i
$408$		0			0
$409$	−5.98343	+	33.9337i	−0.295861	+	1.67791i	0.367819	+	0.929897i	$0.380105\pi$
$409$	−5.98343	+	33.9337i	−0.295861	+	1.67791i	−0.663680	+	0.748016i	$0.731007\pi$
$410$	−10.7660	−	21.0123i	−0.531697	−	1.03772i
$411$		0			0
$412$	1.67058	−	1.99092i	0.0823036	−	0.0980856i
$413$	3.49311	−	9.59724i	0.171885	−	0.472249i
$414$		0			0
$415$	−0.985842	+	0.746378i	−0.0483931	+	0.0366382i
$416$	−0.328320	−	1.86199i	−0.0160972	−	0.0912917i
$417$		0			0
$418$	−23.3806	−	13.4564i	−1.14358	−	0.658176i
$419$	−7.86047			−0.384009			−0.192005	−	0.981394i	$-0.561499\pi$
$419$	−7.86047			−0.384009			−0.192005	+	0.981394i	$0.561499\pi$
$420$		0			0
$421$	8.03752	−	6.74428i	0.391725	−	0.328696i	−0.425560	−	0.904930i	$-0.639923\pi$
$421$	8.03752	−	6.74428i	0.391725	−	0.328696i	0.817285	+	0.576234i	$0.195478\pi$
$422$	5.97836	+	16.4254i	0.291022	+	0.799577i
$423$		0			0
$424$	14.8601	+	12.4691i	0.721672	+	0.605555i
$425$	25.6982	+	18.4943i	1.24655	+	0.897105i
$426$		0			0
$427$	−9.81153	−	1.73004i	−0.474813	−	0.0837223i
$428$	0.604230	+	0.106542i	0.0292066	+	0.00514991i
$429$		0			0
$430$	−27.4860	−	17.7616i	−1.32549	−	0.856540i
$431$	−22.8988	−	19.2144i	−1.10300	−	0.925525i	−0.105375	−	0.994433i	$-0.533604\pi$
$431$	−22.8988	−	19.2144i	−1.10300	−	0.925525i	−0.997623	+	0.0689073i	$0.978049\pi$
$432$		0			0
$433$	2.32566	+	6.38969i	0.111764	+	0.307069i	0.982947	−	0.183890i	$-0.0588689\pi$
$433$	2.32566	+	6.38969i	0.111764	+	0.307069i	−0.871183	+	0.490959i	$0.836647\pi$
$434$	−10.2323	+	8.58589i	−0.491165	+	0.412136i
$435$		0			0
$436$	−0.605347			−0.0289908
$437$	4.02345	+	4.78173i	0.192468	+	0.228741i
$438$		0			0
$439$	−1.38329	−	7.84504i	−0.0660209	−	0.374423i	−0.999860	−	0.0167300i	$-0.994674\pi$
$439$	−1.38329	−	7.84504i	−0.0660209	−	0.374423i	0.933839	−	0.357693i	$-0.116437\pi$
$440$	19.9928	−	15.1365i	0.953121	−	0.721605i
$441$		0			0
$442$	5.71552	−	15.7033i	0.271859	−	0.746928i
$443$	14.0059	−	16.6916i	0.665440	−	0.793041i	−0.322715	−	0.946496i	$-0.604596\pi$
$443$	14.0059	−	16.6916i	0.665440	−	0.793041i	0.988156	+	0.153455i	$0.0490401\pi$
$444$		0			0
$445$	13.5895	−	6.96285i	0.644204	−	0.330071i
$446$	2.28539	−	12.9611i	0.108217	−	0.613726i
$447$		0			0
$448$	−20.0210	+	11.5591i	−0.945904	+	0.546118i
$449$	−9.39185	+	16.2672i	−0.443229	+	0.767695i	−0.997927	−	0.0643569i	$-0.979500\pi$
$449$	−9.39185	+	16.2672i	−0.443229	+	0.767695i	0.554698	+	0.832052i	$0.312834\pi$
$450$		0			0
$451$	−28.0651	−	10.2148i	−1.32153	−	0.480998i
$452$	−0.302761	−	0.831830i	−0.0142407	−	0.0391260i
$453$		0			0
$454$	−6.78303	−	38.4685i	−0.318343	−	1.80541i
$455$	0.649339	−	12.9489i	0.0304415	−	0.607055i
$456$		0			0
$457$			28.2368i			1.32086i	0.750887	+	0.660431i	$0.229627\pi$
$457$			28.2368i			1.32086i	−0.750887	+	0.660431i	$0.770373\pi$
$458$	−31.7345	+	5.59564i	−1.48285	+	0.261467i
$459$		0			0
$460$	0.575775	−	0.177453i	0.0268457	−	0.00827381i
$461$	−0.184187	−	0.0670386i	−0.00857845	−	0.00312230i	0.337727	−	0.941244i	$-0.390342\pi$
$461$	−0.184187	−	0.0670386i	−0.00857845	−	0.00312230i	−0.346306	+	0.938122i	$0.612564\pi$
$462$		0			0
$463$	12.0933	+	6.98206i	0.562022	+	0.324484i	0.753957	−	0.656924i	$-0.228143\pi$
$463$	12.0933	+	6.98206i	0.562022	+	0.324484i	−0.191935	+	0.981408i	$0.561476\pi$
$464$	−0.736571	−	1.27578i	−0.0341945	−	0.0592266i
$465$		0			0
$466$	−2.56879	+	14.5683i	−0.118997	+	0.674865i
$467$	27.8016	−	16.0512i	1.28650	−	0.742763i	0.308474	−	0.951233i	$-0.400182\pi$
$467$	27.8016	−	16.0512i	1.28650	−	0.742763i	0.978029	+	0.208470i	$0.0668483\pi$
$468$		0			0
$469$	21.2920	+	17.8661i	0.983172	+	0.824979i
$470$	−0.572606	+	1.35748i	−0.0264124	+	0.0626159i
$471$		0			0
$472$	−5.41441	−	6.45264i	−0.249218	−	0.297007i
$473$	−40.7685	+	7.18859i	−1.87454	+	0.330532i
$474$		0			0
$475$	−19.6445	−	9.43889i	−0.901353	−	0.433086i
$476$	3.86765			0.177273
$477$		0			0
$478$	−16.9588	−	20.2107i	−0.775675	−	0.924414i
$479$	1.86271	−	0.677972i	0.0851095	−	0.0309773i	−0.299114	−	0.954217i	$-0.596691\pi$
$479$	1.86271	−	0.677972i	0.0851095	−	0.0309773i	0.384224	+	0.923240i	$0.374469\pi$
$480$		0			0
$481$	−3.69675	−	3.10194i	−0.168557	−	0.141436i
$482$	−21.9616	−	12.6796i	−1.00033	−	0.577538i
$483$		0			0
$484$	−0.212320	+	1.20413i	−0.00965091	+	0.0547330i
$485$	−6.57509	+	28.7758i	−0.298560	+	1.30664i
$486$		0			0
$487$	−7.43843	−	4.29458i	−0.337068	−	0.194606i	0.321907	−	0.946771i	$-0.395676\pi$
$487$	−7.43843	−	4.29458i	−0.337068	−	0.194606i	−0.658975	+	0.752165i	$0.729010\pi$
$488$	−5.28173	+	6.29452i	−0.239093	+	0.284939i
$489$		0			0
$490$	11.2578	−	3.46965i	0.508577	−	0.156743i
$491$	−19.8407	+	16.6483i	−0.895398	+	0.751328i	−0.969285	−	0.245938i	$-0.920904\pi$
$491$	−19.8407	+	16.6483i	−0.895398	+	0.751328i	0.0738874	+	0.997267i	$0.476459\pi$
$492$		0			0
$493$		−	2.14910i		−	0.0967908i
$494$	−1.98211	+	11.3312i	−0.0891794	+	0.509817i
$495$		0			0
$496$	2.09435	+	11.8777i	0.0940391	+	0.533322i
$497$	−26.9328	−	32.0972i	−1.20810	−	1.43976i
$498$		0			0
$499$	−19.9251	−	7.25214i	−0.891970	−	0.324650i	−0.144939	−	0.989441i	$-0.546299\pi$
$499$	−19.9251	−	7.25214i	−0.891970	−	0.324650i	−0.747030	+	0.664790i	$0.768521\pi$
$500$	−1.57646	+	1.38924i	−0.0705016	+	0.0621287i
$501$		0			0
$502$	12.4204	−	7.17090i	0.554348	−	0.320053i
$503$	25.1285	+	4.43084i	1.12043	+	0.197561i	0.703028	−	0.711162i	$-0.251831\pi$
$503$	25.1285	+	4.43084i	1.12043	+	0.197561i	0.417398	+	0.908724i	$0.362942\pi$
$504$		0			0
$505$	−34.3795	+	17.6150i	−1.52987	+	0.783859i
$506$	4.43639	−	7.68405i	0.197221	−	0.341597i
$507$		0			0
$508$	0.0380543	−	0.104553i	0.00168839	−	0.00463880i
$509$	16.0130	−	5.82825i	0.709763	−	0.258333i	0.0381894	−	0.999271i	$-0.487841\pi$
$509$	16.0130	−	5.82825i	0.709763	−	0.258333i	0.671574	+	0.740938i	$0.265619\pi$
$510$		0			0
$511$	1.02837	+	5.83218i	0.0454924	+	0.258000i
$512$			18.6685i			0.825039i
$513$		0			0
$514$	−14.8666			−0.655738
$515$	−3.83763	−	30.6826i	−0.169106	−	1.35204i
$516$		0			0
$517$	0.637430	+	1.75133i	0.0280342	+	0.0770232i
$518$	4.44708	−	12.2183i	0.195393	−	0.536839i
$519$		0			0
$520$	−8.98108	−	5.80362i	−0.393847	−	0.254506i
$521$	10.8909	+	18.8635i	0.477137	+	0.826426i	0.999657	−	0.0262016i	$-0.00834118\pi$
$521$	10.8909	+	18.8635i	0.477137	+	0.826426i	−0.522520	+	0.852627i	$0.675008\pi$
$522$		0			0
$523$	17.2199	+	3.03633i	0.752973	+	0.132769i	0.536944	−	0.843618i	$-0.319578\pi$
$523$	17.2199	+	3.03633i	0.752973	+	0.132769i	0.216028	+	0.976387i	$0.430690\pi$
$524$	1.93100	+	3.34460i	0.0843563	+	0.146109i
$525$		0			0
$526$	24.7364	+	20.7563i	1.07856	+	0.905018i
$527$	−6.01788	+	16.5340i	−0.262143	+	0.720232i
$528$		0			0
$529$	16.0445	−	13.4629i	0.697586	−	0.585344i
$530$	−23.7526	+	2.97085i	−1.03175	+	0.129046i
$531$		0			0
$532$	−2.62127	+	0.465879i	−0.113647	+	0.0201984i
$533$			12.7355i			0.551637i
$534$		0			0
$535$	5.82000	−	4.40630i	0.251621	−	0.190501i
$536$	21.5413	−	7.84038i	0.930441	−	0.338653i
$537$		0			0
$538$	14.6945	−	17.5123i	0.633527	−	0.755008i
$539$	7.45104	−	12.9056i	0.320939	−	0.555883i
$540$		0			0
$541$	2.57157	−	14.5841i	0.110560	−	0.627018i	−0.878293	−	0.478123i	$-0.841317\pi$
$541$	2.57157	−	14.5841i	0.110560	−	0.627018i	0.988853	−	0.148895i	$-0.0475717\pi$
$542$	−7.52121	−	1.32619i	−0.323064	−	0.0569648i
$543$		0			0
$544$	3.35527	−	5.81150i	0.143856	−	0.249166i
$545$	−4.90002	+	5.27845i	−0.209894	+	0.226104i
$546$		0			0
$547$	9.08867	+	24.9709i	0.388603	+	1.06768i	0.967631	+	0.252371i	$0.0812103\pi$
$547$	9.08867	+	24.9709i	0.388603	+	1.06768i	−0.579027	+	0.815308i	$0.696567\pi$
$548$	−1.05754	−	1.26033i	−0.0451761	−	0.0538388i
$549$		0			0
$550$	−3.09568	+	30.7889i	−0.132000	+	1.31284i
$551$	0.258871	+	1.45654i	0.0110283	+	0.0620507i
$552$		0			0
$553$	2.23619	−	0.394301i	0.0950926	−	0.0167674i
$554$	6.31176	−	5.29619i	0.268161	−	0.225014i
$555$		0			0
$556$	−1.35800	−	0.494271i	−0.0575919	−	0.0209618i
$557$	−10.3330	+	12.3143i	−0.437821	+	0.521775i	−0.939162	−	0.343475i	$-0.888396\pi$
$557$	−10.3330	+	12.3143i	−0.437821	+	0.521775i	0.501340	+	0.865250i	$0.332840\pi$
$558$		0			0
$559$	8.82633	+	15.2877i	0.373314	+	0.646599i
$560$	7.02620	−	30.7501i	0.296911	−	1.29943i
$561$		0			0
$562$	34.9365	−	20.1706i	1.47371	−	0.850847i
$563$	1.75929	+	1.01573i	0.0741452	+	0.0428078i	0.536614	−	0.843828i	$-0.319703\pi$
$563$	1.75929	+	1.01573i	0.0741452	+	0.0428078i	−0.462469	+	0.886635i	$0.653036\pi$
$564$		0			0
$565$	−9.70404	−	4.09331i	−0.408252	−	0.172207i
$566$	−20.9131	+	7.61175i	−0.879044	+	0.319946i
$567$		0			0
$568$	−34.0321	+	6.00077i	−1.42795	+	0.251787i
$569$	−12.8224			−0.537543			−0.268772	−	0.963204i	$-0.586618\pi$
$569$	−12.8224			−0.537543			−0.268772	+	0.963204i	$0.586618\pi$
$570$		0			0
$571$	12.9168			0.540551			0.270276	−	0.962783i	$-0.412885\pi$
$571$	12.9168			0.540551			0.270276	+	0.962783i	$0.412885\pi$
$572$	1.38163	−	0.243618i	0.0577688	−	0.0101862i
$573$		0			0
$574$	−32.2448	+	11.7362i	−1.34587	+	0.489858i
$575$	3.11331	−	6.45701i	0.129834	−	0.269276i
$576$		0			0
$577$	7.02658	+	4.05680i	0.292520	+	0.168887i	0.639078	−	0.769142i	$-0.279316\pi$
$577$	7.02658	+	4.05680i	0.292520	+	0.168887i	−0.346558	+	0.938029i	$0.612649\pi$
$578$	29.5878	−	17.0825i	1.23069	−	0.710540i
$579$		0			0
$580$	0.139045	+	0.0317708i	0.00577352	+	0.00131921i
$581$	0.898567	+	1.55636i	0.0372788	+	0.0645689i
$582$		0			0
$583$	−19.4642	+	23.1966i	−0.806126	+	0.960703i
$584$	4.58975	+	1.67053i	0.189925	+	0.0691271i
$585$		0			0
$586$	−8.87090	+	7.44357i	−0.366454	+	0.307491i
$587$	32.0670	−	5.65427i	1.32355	−	0.233377i	0.533174	−	0.846005i	$-0.320999\pi$
$587$	32.0670	−	5.65427i	1.32355	−	0.233377i	0.790371	+	0.612629i	$0.209888\pi$
$588$		0			0
$589$	2.08697	−	11.9307i	0.0859921	−	0.491595i
$590$	10.3813	+	0.520581i	0.427391	+	0.0214320i
$591$		0			0
$592$	−7.54661	−	8.99370i	−0.310164	−	0.369639i
$593$	−3.92476	−	10.7832i	−0.161171	−	0.442812i	0.832652	−	0.553797i	$-0.186822\pi$
$593$	−3.92476	−	10.7832i	−0.161171	−	0.442812i	−0.993822	+	0.110985i	$0.964599\pi$
$594$		0			0
$595$	31.3070	−	33.7248i	1.28346	−	1.38258i
$596$	−1.40405	+	2.43188i	−0.0575120	+	0.0996138i
$597$		0			0
$598$	−3.72604	−	0.657002i	−0.152369	−	0.0268668i
$599$	5.76684	−	32.7054i	0.235627	−	1.33631i	−0.605663	−	0.795721i	$-0.707092\pi$
$599$	5.76684	−	32.7054i	0.235627	−	1.33631i	0.841290	−	0.540584i	$-0.181797\pi$
$600$		0			0
$601$	−13.6590	+	23.6581i	−0.557163	+	0.965034i	0.440569	+	0.897719i	$0.354777\pi$
$601$	−13.6590	+	23.6581i	−0.557163	+	0.965034i	−0.997732	+	0.0673154i	$0.978557\pi$
$602$	−30.5728	+	36.4352i	−1.24605	+	1.48499i
$603$		0			0
$604$	2.32104	−	0.844789i	0.0944417	−	0.0343740i
$605$	8.78100	+	11.5983i	0.356998	+	0.471536i
$606$		0			0
$607$		−	25.7405i		−	1.04478i	−0.852708	−	0.522388i	$-0.825041\pi$
$607$		−	25.7405i		−	1.04478i	0.852708	−	0.522388i	$-0.174959\pi$
$608$	−1.57399	+	4.34286i	−0.0638335	+	0.176126i
$609$		0			0
$610$	−1.25841	−	10.0612i	−0.0509513	−	0.407367i
$611$	0.608796	−	0.510841i	0.0246293	−	0.0206664i
$612$		0			0
$613$	13.8873	−	38.1551i	0.560904	−	1.54107i	−0.257411	−	0.966302i	$-0.582869\pi$
$613$	13.8873	−	38.1551i	0.560904	−	1.54107i	0.818315	−	0.574770i	$-0.194908\pi$
$614$	−17.8063	−	14.9413i	−0.718606	−	0.602982i
$615$		0			0
$616$	−18.2229	−	31.5630i	−0.734222	−	1.27171i
$617$	13.9954	+	2.46776i	0.563433	+	0.0993485i	0.448108	−	0.893979i	$-0.352098\pi$
$617$	13.9954	+	2.46776i	0.563433	+	0.0993485i	0.115325	+	0.993328i	$0.463209\pi$
$618$		0			0
$619$	−14.7818	−	25.6028i	−0.594129	−	1.02906i	−0.993669	−	0.112346i	$-0.964164\pi$
$619$	−14.7818	−	25.6028i	−0.594129	−	1.02906i	0.399540	−	0.916716i	$-0.369170\pi$
$620$	−0.980768	−	0.633777i	−0.0393886	−	0.0254531i
$621$		0			0
$622$	9.09680	−	24.9932i	0.364748	−	1.00214i
$623$	−7.59026	−	20.8541i	−0.304097	−	0.835500i
$624$		0			0
$625$	−0.647023	+	24.9916i	−0.0258809	+	0.999665i
$626$	−31.3591			−1.25336
$627$		0			0
$628$			2.03675i			0.0812753i
$629$	−2.97418	−	16.8674i	−0.118588	−	0.672548i
$630$		0			0
$631$	1.60465	−	0.584045i	0.0638801	−	0.0232505i	−0.309882	−	0.950775i	$-0.600290\pi$
$631$	1.60465	−	0.584045i	0.0638801	−	0.0232505i	0.373763	+	0.927524i	$0.378067\pi$
$632$	0.640520	−	1.75981i	0.0254785	−	0.0700017i
$633$		0			0
$634$	2.26640	−	3.92552i	0.0900102	−	0.155902i
$635$	−0.603642	−	1.17814i	−0.0239548	−	0.0467529i
$636$		0			0
$637$	−6.25800	−	1.10345i	−0.247951	−	0.0437204i
$638$	1.81902	−	1.05021i	0.0720158	−	0.0415783i
$639$		0			0
$640$	−20.7171	−	19.2318i	−0.818915	−	0.760204i
$641$	2.59543	+	0.944659i	0.102513	+	0.0373118i	0.392768	−	0.919638i	$-0.371518\pi$
$641$	2.59543	+	0.944659i	0.102513	+	0.0373118i	−0.290254	+	0.956950i	$0.593740\pi$
$642$		0			0
$643$	13.9466	+	16.6209i	0.550000	+	0.655465i	0.967398	−	0.253259i	$-0.0815025\pi$
$643$	13.9466	+	16.6209i	0.550000	+	0.655465i	−0.417398	+	0.908724i	$0.637058\pi$
$644$	−0.152058	−	0.862364i	−0.00599193	−	0.0339819i
$645$		0			0
$646$	−31.2400	+	26.2860i	−1.22912	+	1.03421i
$647$		−	28.0268i		−	1.10185i	−0.834556	−	0.550923i	$-0.814276\pi$
$647$		−	28.0268i		−	1.10185i	0.834556	−	0.550923i	$-0.185724\pi$
$648$		0			0
$649$	10.0725	−	8.45185i	0.395381	−	0.331764i
$650$	12.7887	−	3.24993i	0.501614	−	0.127473i
$651$		0			0
$652$	1.02027	−	1.21591i	0.0399570	−	0.0476189i
$653$	6.57580	+	3.79654i	0.257331	+	0.148570i	0.623116	−	0.782129i	$-0.285866\pi$
$653$	6.57580	+	3.79654i	0.257331	+	0.148570i	−0.365785	+	0.930699i	$0.619200\pi$
$654$		0			0
$655$	44.7946	+	10.2353i	1.75027	+	0.399925i
$656$	−5.38029	+	30.5131i	−0.210065	+	1.19134i
$657$		0			0
$658$	1.85441	+	1.07064i	0.0722924	+	0.0417380i
$659$	5.50322	+	4.61775i	0.214375	+	0.179882i	0.743652	−	0.668567i	$-0.233092\pi$
$659$	5.50322	+	4.61775i	0.214375	+	0.179882i	−0.529277	+	0.848449i	$0.677537\pi$
$660$		0			0
$661$	27.1268	−	9.87335i	1.05511	−	0.384029i	0.244521	−	0.969644i	$-0.421369\pi$
$661$	27.1268	−	9.87335i	1.05511	−	0.384029i	0.810589	+	0.585615i	$0.199147\pi$
$662$	24.6739	+	29.4052i	0.958978	+	1.14287i
$663$		0			0
$664$	1.48219			0.0575201
$665$	−17.1557	+	26.6278i	−0.665271	+	1.03258i
$666$		0			0
$667$	−0.479183	+	0.0844929i	−0.0185540	+	0.00327158i
$668$	2.40419	+	2.86521i	0.0930210	+	0.110858i
$669$		0			0
$670$	−10.9941	+	26.0638i	−0.424740	+	1.00693i
$671$	−9.82569	−	8.24473i	−0.379316	−	0.318284i
$672$		0			0
$673$	−20.1949	+	11.6595i	−0.778457	+	0.449442i	−0.835883	−	0.548907i	$-0.815044\pi$
$673$	−20.1949	+	11.6595i	−0.778457	+	0.449442i	0.0574263	+	0.998350i	$0.481711\pi$
$674$	2.58331	−	14.6507i	0.0995054	−	0.564323i
$675$		0			0
$676$	0.922496	+	1.59781i	0.0354806	+	0.0614542i
$677$	−15.1640	−	8.75493i	−0.582799	−	0.336479i	0.179446	−	0.983768i	$-0.442570\pi$
$677$	−15.1640	−	8.75493i	−0.582799	−	0.336479i	−0.762245	+	0.647289i	$0.775903\pi$
$678$		0			0
$679$	40.3132	+	14.6728i	1.54708	+	0.563090i
$680$	−11.1779	−	36.2685i	−0.428653	−	1.39083i
$681$		0			0
$682$	−16.9353	+	2.98615i	−0.648487	+	0.114346i
$683$			22.0114i			0.842243i	0.907004	+	0.421122i	$0.138363\pi$
$683$			22.0114i			0.842243i	−0.907004	+	0.421122i	$0.861637\pi$
$684$		0			0
$685$	−19.5501	−	0.980363i	−0.746971	−	0.0374577i
$686$	2.87012	+	16.2772i	0.109582	+	0.621468i
$687$		0			0
$688$	14.6886	+	40.3566i	0.559997	+	1.53858i
$689$	12.1337	+	4.41629i	0.462256	+	0.168247i
$690$		0			0
$691$	1.32811	−	2.30036i	0.0505238	−	0.0875098i	−0.839657	−	0.543116i	$-0.817244\pi$
$691$	1.32811	−	2.30036i	0.0505238	−	0.0875098i	0.890181	+	0.455607i	$0.150578\pi$
$692$	1.90774	−	1.10143i	0.0725214	−	0.0418702i
$693$		0			0
$694$	−1.75124	+	9.93178i	−0.0664762	+	0.377005i
$695$	−15.3023	+	7.84045i	−0.580450	+	0.297405i
$696$		0			0
$697$	−29.0546	+	34.6260i	−1.10052	+	1.31155i
$698$	15.9849	−	43.9181i	0.605037	−	1.66232i
$699$		0			0
$700$	1.71914	+	2.52409i	0.0649773	+	0.0954016i
$701$	1.27931	+	7.25535i	0.0483190	+	0.274031i	0.999389	−	0.0349439i	$-0.0111253\pi$
$701$	1.27931	+	7.25535i	0.0483190	+	0.274031i	−0.951070	+	0.308975i	$0.900014\pi$
$702$		0			0
$703$	4.04750	+	11.0735i	0.152654	+	0.417646i
$704$	−29.7632			−1.12174
$705$		0			0
$706$	−7.14603	+	5.99623i	−0.268944	+	0.225671i
$707$	19.2023	+	52.7579i	0.722177	+	1.98416i
$708$		0			0
$709$	4.58997	+	3.85144i	0.172380	+	0.144644i	0.724896	−	0.688858i	$-0.241888\pi$
$709$	4.58997	+	3.85144i	0.172380	+	0.144644i	−0.552516	+	0.833502i	$0.686332\pi$
$710$	23.1444	−	35.8159i	0.868594	−	1.34415i
$711$		0			0
$712$	−18.0252	−	3.17833i	−0.675522	−	0.119113i
$713$	3.92316	+	0.691759i	0.146923	+	0.0259066i
$714$		0			0
$715$	9.05941	−	14.0194i	0.338803	−	0.524296i
$716$	−1.01986	−	0.855765i	−0.0381140	−	0.0319814i
$717$		0			0
$718$	2.11300	+	5.80541i	0.0788563	+	0.216656i
$719$	10.4040	−	8.73002i	0.388005	−	0.325575i	−0.427831	−	0.903859i	$-0.640722\pi$
$719$	10.4040	−	8.73002i	0.388005	−	0.325575i	0.815835	+	0.578284i	$0.196278\pi$
$720$		0			0
$721$	−44.9412			−1.67370
$722$	18.0064	−	21.5782i	0.670128	−	0.803056i
$723$		0			0
$724$	−0.302916	−	1.71792i	−0.0112578	−	0.0638461i
$725$	1.40254	−	0.955259i	0.0520890	−	0.0354774i
$726$		0			0
$727$	14.1065	−	38.7574i	0.523183	−	1.43743i	−0.343776	−	0.939052i	$-0.611706\pi$
$727$	14.1065	−	38.7574i	0.523183	−	1.43743i	0.866958	−	0.498381i	$-0.166072\pi$
$728$	−9.98969	+	11.9052i	−0.370242	+	0.441238i
$729$		0			0
$730$	−5.36409	+	2.74840i	−0.198534	+	0.101723i
$731$	−10.8796	+	61.7011i	−0.402395	+	2.28210i
$732$		0			0
$733$	−0.107256	+	0.0619240i	−0.00396158	+	0.00228722i	−0.501979	−	0.864880i	$-0.667395\pi$
$733$	−0.107256	+	0.0619240i	−0.00396158	+	0.00228722i	0.498018	+	0.867167i	$0.334061\pi$
$734$	12.2556	−	21.2274i	0.452364	−	0.783517i
$735$		0			0
$736$	−1.42770	−	0.519639i	−0.0526256	−	0.0191541i
$737$	12.2388	+	33.6257i	0.450821	+	1.23862i
$738$		0			0
$739$	6.34049	+	35.9587i	0.233239	+	1.32276i	0.846291	+	0.532720i	$0.178830\pi$
$739$	6.34049	+	35.9587i	0.233239	+	1.32276i	−0.613053	+	0.790042i	$0.710059\pi$
$740$	1.13527	+	0.0569295i	0.0417334	+	0.00209277i
$741$		0			0
$742$			34.7907i			1.27721i
$743$	8.92430	−	1.57359i	0.327401	−	0.0577296i	−0.00753195	−	0.999972i	$-0.502398\pi$
$743$	8.92430	−	1.57359i	0.327401	−	0.0577296i	0.334933	+	0.942242i	$0.391286\pi$
$744$		0			0
$745$	9.84015	+	31.9279i	0.360515	+	1.16975i
$746$	−51.4293	−	18.7187i	−1.88296	−	0.685341i
$747$		0			0
$748$	4.31223	+	2.48967i	0.157671	+	0.0910312i
$749$	−5.30476	−	9.18812i	−0.193832	−	0.335727i
$750$		0			0
$751$	−0.709544	+	4.02402i	−0.0258916	+	0.146839i	−0.995013	−	0.0997456i	$-0.968197\pi$
$751$	−0.709544	+	4.02402i	−0.0258916	+	0.146839i	0.969121	+	0.246584i	$0.0793082\pi$
$752$	1.67443	−	0.966732i	0.0610602	−	0.0352531i
$753$		0			0
$754$	−0.686117	−	0.575721i	−0.0249869	−	0.0209665i
$755$	11.4215	−	27.0770i	0.415670	−	0.985432i
$756$		0			0
$757$	22.1503	+	26.3977i	0.805066	+	0.959441i	0.999771	−	0.0214214i	$-0.00681915\pi$
$757$	22.1503	+	26.3977i	0.805066	+	0.959441i	−0.194704	+	0.980862i	$0.562375\pi$
$758$	−45.9073	+	8.09470i	−1.66743	+	0.294013i
$759$		0			0
$760$	11.9445	+	23.2343i	0.433272	+	0.842796i
$761$	−20.5813			−0.746072			−0.373036	−	0.927817i	$-0.621683\pi$
$761$	−20.5813			−0.746072			−0.373036	+	0.927817i	$0.621683\pi$
$762$		0			0
$763$	6.72848	+	8.01868i	0.243587	+	0.290296i
$764$	−1.43480	+	0.522224i	−0.0519092	+	0.0188934i
$765$		0			0
$766$	−3.51052	−	2.94568i	−0.126840	−	0.106432i
$767$	−4.85570	−	2.80344i	−0.175329	−	0.101226i
$768$		0			0
$769$	5.27109	−	29.8939i	0.190081	−	1.07800i	−0.729172	−	0.684331i	$-0.760094\pi$
$769$	5.27109	−	29.8939i	0.190081	−	1.07800i	0.919252	−	0.393669i	$-0.128794\pi$
$770$	43.8439	+	10.0180i	1.58002	+	0.361025i
$771$		0			0
$772$	1.25708	+	0.725774i	0.0452432	+	0.0261212i
$773$	12.5488	−	14.9551i	0.451350	−	0.537898i	−0.491605	−	0.870818i	$-0.663590\pi$
$773$	12.5488	−	14.9551i	0.451350	−	0.537898i	0.942955	+	0.332921i	$0.108034\pi$
$774$		0			0
$775$	−13.4652	+	3.42186i	−0.483686	+	0.122917i
$776$	27.1043	−	22.7432i	0.972988	−	0.816434i
$777$		0			0
$778$		−	38.5054i		−	1.38048i
$779$	15.5207	−	26.9673i	0.556087	−	0.966204i
$780$		0			0
$781$	−9.36716	−	53.1238i	−0.335183	−	1.90092i
$782$	−8.63167	−	10.2868i	−0.308668	−	0.367856i
$783$		0			0
$784$	−14.5274	−	5.28754i	−0.518836	−	0.188841i
$785$	17.7599	+	16.4866i	0.633878	+	0.588433i
$786$		0			0
$787$	30.5046	−	17.6118i	1.08737	−	0.627793i	0.154495	−	0.987994i	$-0.450625\pi$
$787$	30.5046	−	17.6118i	1.08737	−	0.627793i	0.932875	+	0.360200i	$0.117292\pi$
$788$	−0.660316	−	0.116432i	−0.0235228	−	0.00414770i
$789$		0			0
$790$	1.05380	+	2.05671i	0.0374925	+	0.0731746i
$791$	−7.65357	+	13.2564i	−0.272129	+	0.471342i
$792$		0			0
$793$	−1.87067	+	5.13963i	−0.0664295	+	0.182514i
$794$	−17.5979	+	6.40513i	−0.624528	+	0.227309i
$795$		0			0
$796$	−0.286194	−	1.62309i	−0.0101439	−	0.0575288i
$797$			28.7940i			1.01994i	0.860193	+	0.509969i	$0.170343\pi$
$797$			28.7940i			1.01994i	−0.860193	+	0.509969i	$0.829657\pi$
$798$		0			0
$799$	2.82065			0.0997874
$800$	5.28407	−	0.393461i	0.186820	−	0.0139109i
$801$		0			0
$802$	4.66536	+	12.8180i	0.164740	+	0.452618i
$803$	−2.60768	+	7.16455i	−0.0920232	+	0.252832i
$804$		0			0
$805$	−8.75041	−	5.65456i	−0.308412	−	0.199297i
$806$	3.66648	+	6.35052i	0.129146	+	0.223688i
$807$		0			0
$808$	45.6012	+	8.04072i	1.60425	+	0.282872i
$809$	24.0034	+	41.5751i	0.843915	+	1.46170i	0.886560	+	0.462613i	$0.153088\pi$
$809$	24.0034	+	41.5751i	0.843915	+	1.46170i	−0.0426458	+	0.999090i	$0.513579\pi$
$810$		0			0
$811$	−7.37613	−	6.18931i	−0.259011	−	0.217336i	0.504030	−	0.863686i	$-0.331850\pi$
$811$	−7.37613	−	6.18931i	−0.259011	−	0.217336i	−0.763041	+	0.646350i	$0.776295\pi$
$812$	0.0708988	−	0.194793i	0.00248806	−	0.00683589i
$813$		0			0
$814$	12.8233	−	10.7601i	0.449458	−	0.377140i
$815$	−2.34375	−	18.7388i	−0.0820981	−	0.656391i
$816$		0			0
$817$	−0.0586768	−	43.1280i	−0.00205284	−	1.50886i
$818$			50.9680i			1.78205i
$819$		0			0
$820$	−1.81074	−	2.39169i	−0.0632338	−	0.0835214i
$821$	−24.1743	+	8.79872i	−0.843688	+	0.307077i	−0.727464	−	0.686146i	$-0.759301\pi$
$821$	−24.1743	+	8.79872i	−0.843688	+	0.307077i	−0.116224	+	0.993223i	$0.537079\pi$
$822$		0			0
$823$	8.65091	−	10.3098i	0.301552	−	0.359376i	−0.593896	−	0.804542i	$-0.702411\pi$
$823$	8.65091	−	10.3098i	0.301552	−	0.359376i	0.895448	+	0.445166i	$0.146855\pi$
$824$	−18.5327	+	32.0996i	−0.645617	+	1.11824i
$825$		0			0
$826$	2.62330	−	14.8775i	0.0912764	−	0.517654i
$827$	0.169788	+	0.0299383i	0.00590412	+	0.00104106i	0.176599	−	0.984283i	$-0.443490\pi$
$827$	0.169788	+	0.0299383i	0.00590412	+	0.00104106i	−0.170695	+	0.985324i	$0.554601\pi$
$828$		0			0
$829$	−21.1895	+	36.7014i	−0.735943	+	1.27469i	0.218365	+	0.975867i	$0.429928\pi$
$829$	−21.1895	+	36.7014i	−0.735943	+	1.27469i	−0.954308	+	0.298824i	$0.903406\pi$
$830$	−1.24436	+	1.34046i	−0.0431925	+	0.0465282i
$831$		0			0
$832$	4.34078	+	11.9262i	0.150490	+	0.413467i
$833$	−14.4971	−	17.2770i	−0.502296	−	0.598614i
$834$		0			0
$835$	44.4447	+	2.22873i	1.53807	+	0.0771284i
$836$	−3.22247	−	1.16792i	−0.111452	−	0.0403934i
$837$		0			0
$838$	−11.4503	+	2.01900i	−0.395545	+	0.0697452i
$839$	34.5791	−	29.0153i	1.19380	−	1.00172i	0.194019	−	0.980998i	$-0.437848\pi$
$839$	34.5791	−	29.0153i	1.19380	−	1.00172i	0.999785	−	0.0207231i	$-0.00659684\pi$
$840$		0			0
$841$	27.1428	+	9.87919i	0.935960	+	0.340662i
$842$	9.97593	−	11.8888i	0.343793	−	0.409717i
$843$		0			0
$844$	1.11046	+	1.92338i	0.0382237	+	0.0662055i
$845$	21.3997	+	4.88968i	0.736170	+	0.168210i
$846$		0			0
$847$	18.3103	−	10.5715i	0.629151	−	0.363240i
$848$	27.2054	+	15.7070i	0.934238	+	0.539382i
$849$		0			0
$850$	42.1849	+	20.3399i	1.44693	+	0.697652i
$851$	−3.64397	+	1.32630i	−0.124914	+	0.0454649i
$852$		0			0
$853$	45.6364	−	8.04694i	1.56256	−	0.275522i	0.675566	−	0.737299i	$-0.263899\pi$
$853$	45.6364	−	8.04694i	1.56256	−	0.275522i	0.886996	+	0.461778i	$0.152788\pi$
$854$	−14.7368			−0.504283
$855$		0			0
$856$	−8.75023			−0.299077
$857$	−21.5607	+	3.80174i	−0.736501	+	0.129865i	−0.529302	−	0.848434i	$-0.677546\pi$
$857$	−21.5607	+	3.80174i	−0.736501	+	0.129865i	−0.207199	+	0.978299i	$0.566435\pi$
$858$		0			0
$859$	31.3876	−	11.4242i	1.07093	−	0.389787i	0.254406	−	0.967097i	$-0.418120\pi$
$859$	31.3876	−	11.4242i	1.07093	−	0.389787i	0.816525	+	0.577310i	$0.195898\pi$
$860$	−3.83116	−	1.61604i	−0.130641	−	0.0551065i
$861$		0			0
$862$	−38.2920	−	22.1079i	−1.30423	−	0.752998i
$863$	23.4913	−	13.5627i	0.799653	−	0.461680i	−0.0436971	−	0.999045i	$-0.513914\pi$
$863$	23.4913	−	13.5627i	0.799653	−	0.461680i	0.843350	+	0.537365i	$0.180580\pi$
$864$		0			0
$865$	5.83814	−	25.5506i	0.198503	−	0.868745i
$866$	5.02900	+	8.71049i	0.170892	+	0.295994i
$867$		0			0
$868$	−1.09091	+	1.30010i	−0.0370279	+	0.0441282i
$869$	2.74705	+	0.999846i	0.0931875	+	0.0339175i
$870$		0			0
$871$	11.6890	−	9.80822i	0.396066	−	0.332339i
$872$	8.50206	−	1.49914i	0.287916	−	0.0507674i
$873$		0			0
$874$	7.08916	+	5.93209i	0.239794	+	0.200656i
$875$	35.9250	+	5.44102i	1.21449	+	0.183940i
$876$		0			0
$877$	31.5495	+	37.5992i	1.06535	+	1.26963i	0.961430	+	0.275049i	$0.0886941\pi$
$877$	31.5495	+	37.5992i	1.06535	+	1.26963i	0.103920	+	0.994586i	$0.466861\pi$
$878$	−4.03008	−	11.0725i	−0.136008	−	0.373680i
$879$		0			0
$880$	27.6282	−	29.7619i	0.931345	−	1.00327i
$881$	18.9889	−	32.8898i	0.639753	−	1.10808i	−0.345734	−	0.938332i	$-0.612370\pi$
$881$	18.9889	−	32.8898i	0.639753	−	1.10808i	0.985487	−	0.169751i	$-0.0542965\pi$
$882$		0			0
$883$	32.7055	+	5.76686i	1.10063	+	0.194070i	0.694320	−	0.719666i	$-0.255705\pi$
$883$	32.7055	+	5.76686i	1.10063	+	0.194070i	0.406307	+	0.913737i	$0.366816\pi$
$884$	0.368704	−	2.09103i	0.0124009	−	0.0703288i
$885$		0			0
$886$	16.1150	−	27.9121i	0.541395	−	0.937724i
$887$	−16.8748	+	20.1106i	−0.566601	+	0.675248i	−0.970930	−	0.239365i	$-0.923061\pi$
$887$	−16.8748	+	20.1106i	−0.566601	+	0.675248i	0.404329	+	0.914614i	$0.367505\pi$
$888$		0			0
$889$	−1.80794	+	0.658035i	−0.0606362	+	0.0220698i
$890$	18.0073	−	13.6333i	0.603607	−	0.456989i
$891$		0			0
$892$		−	1.67222i		−	0.0559902i
$893$	−1.91167	+	0.339762i	−0.0639718	+	0.0113697i
$894$		0			0
$895$	−15.7174	+	1.96585i	−0.525373	+	0.0657110i
$896$	−31.4721	+	26.4082i	−1.05141	+	0.882236i
$897$		0			0
$898$	−9.50278	+	26.1087i	−0.317112	+	0.871258i
$899$	0.722415	+	0.606178i	0.0240939	+	0.0202172i
$900$		0			0
$901$	22.9143	+	39.6888i	0.763387	+	1.32223i
$902$	−43.5060	−	7.67129i	−1.44859	−	0.255426i
$903$		0			0
$904$	6.31229	+	10.9332i	0.209944	+	0.363633i
$905$	−17.4318	−	11.2645i	−0.579452	−	0.374445i
$906$		0			0
$907$	−2.71140	+	7.44950i	−0.0900305	+	0.247357i	−0.976533	−	0.215366i	$-0.930905\pi$
$907$	−2.71140	+	7.44950i	−0.0900305	+	0.247357i	0.886503	+	0.462723i	$0.153128\pi$
$908$	−1.69750	−	4.66383i	−0.0563334	−	0.154775i
$909$		0			0
$910$	−2.38011	−	19.0295i	−0.0788998	−	0.630820i
$911$	0.619746			0.0205331			0.0102665	−	0.999947i	$-0.496732\pi$
$911$	0.619746			0.0205331			0.0102665	+	0.999947i	$0.496732\pi$
$912$		0			0
$913$			2.31369i			0.0765718i
$914$	7.25277	+	41.1325i	0.239900	+	1.36054i
$915$		0			0
$916$	−3.84742	+	1.40035i	−0.127122	+	0.0462687i
$917$	22.8407	−	62.7544i	0.754268	−	2.07233i
$918$		0			0
$919$	−17.5287	+	30.3606i	−0.578219	+	1.00150i	0.417465	+	0.908693i	$0.362919\pi$
$919$	−17.5287	+	30.3606i	−0.578219	+	1.00150i	−0.995684	+	0.0928113i	$0.970415\pi$
$920$	−7.64727	+	3.91823i	−0.252123	+	0.129180i
$921$		0			0
$922$	−0.285524	−	0.0503456i	−0.00940324	−	0.00165804i
$923$	−19.9207	+	11.5012i	−0.655699	+	0.378568i
$924$		0			0
$925$	9.68595	−	9.43843i	0.318472	−	0.310334i
$926$	19.4096	+	7.06452i	0.637840	+	0.232155i
$927$		0			0
$928$	−0.231188	−	0.275519i	−0.00758912	−	0.00904437i
$929$	2.09132	+	11.8605i	0.0686140	+	0.389129i	0.999704	+	0.0243392i	$0.00774816\pi$
$929$	2.09132	+	11.8605i	0.0686140	+	0.389129i	−0.931090	+	0.364790i	$0.881141\pi$
$930$		0			0
$931$	11.9065	+	9.96313i	0.390218	+	0.326528i
$932$			1.87959i			0.0615679i
$933$		0			0
$934$	36.3756	−	30.5228i	1.19025	−	0.998735i
$935$	56.6148	−	17.4486i	1.85150	−	0.570631i
$936$		0			0
$937$	9.59711	−	11.4374i	0.313524	−	0.373643i	−0.586152	−	0.810201i	$-0.699358\pi$
$937$	9.59711	−	11.4374i	0.313524	−	0.373643i	0.899676	+	0.436558i	$0.143802\pi$
$938$	35.6049	+	20.5565i	1.16254	+	0.671194i
$939$		0			0
$940$	−0.0416984	+	0.182493i	−0.00136005	+	0.00595226i
$941$	−3.37221	+	19.1248i	−0.109931	+	0.623450i	0.879205	+	0.476444i	$0.158075\pi$
$941$	−3.37221	+	19.1248i	−0.109931	+	0.623450i	−0.989136	+	0.147006i	$0.953036\pi$
$942$		0			0
$943$	8.86280	+	5.11694i	0.288612	+	0.166630i
$944$	−10.4494	−	8.76813i	−0.340101	−	0.285378i
$945$		0			0
$946$	−57.5409	+	20.9432i	−1.87082	+	0.680922i
$947$	10.7583	+	12.8212i	0.349598	+	0.416634i	0.911975	−	0.410247i	$-0.134557\pi$
$947$	10.7583	+	12.8212i	0.349598	+	0.416634i	−0.562377	+	0.826881i	$0.690113\pi$
$948$		0			0
$949$	3.25117			0.105538
$950$	−31.0405	−	8.70381i	−1.00709	−	0.282389i
$951$		0			0
$952$	−54.3209	+	9.57824i	−1.76055	+	0.310433i
$953$	34.1817	+	40.7361i	1.10725	+	1.31957i	0.942864	+	0.333177i	$0.108121\pi$
$953$	34.1817	+	40.7361i	1.10725	+	1.31957i	0.164389	+	0.986396i	$0.447435\pi$
$954$		0			0
$955$	−7.06043	+	16.7382i	−0.228470	+	0.541636i
$956$	−2.56794	−	2.15475i	−0.0830530	−	0.0696897i
$957$		0			0
$958$	2.53927	−	1.46605i	0.0820400	−	0.0473658i
$959$	−4.94022	+	28.0174i	−0.159528	+	0.904729i
$960$		0			0
$961$	11.6396	+	20.1603i	0.375470	+	0.650332i
$962$	−6.18179	−	3.56906i	−0.199309	−	0.115071i
$963$		0			0
$964$	−3.02778	−	1.10202i	−0.0975181	−	0.0354937i
$965$	16.5040	−	5.08653i	0.531284	−	0.163741i
$966$		0			0
$967$	29.5719	−	5.21432i	0.950967	−	0.167681i	0.323416	−	0.946257i	$-0.395169\pi$
$967$	29.5719	−	5.21432i	0.950967	−	0.167681i	0.627551	+	0.778576i	$0.284057\pi$
$968$		−	17.4377i		−	0.560469i
$969$		0			0
$970$	−2.18670	+	43.6065i	−0.0702107	+	1.40012i
$971$	−4.19210	−	23.7746i	−0.134531	−	0.762962i	−0.975185	−	0.221390i	$-0.928940\pi$
$971$	−4.19210	−	23.7746i	−0.134531	−	0.762962i	0.840654	−	0.541572i	$-0.182171\pi$
$972$		0			0
$973$	8.54693	+	23.4825i	0.274002	+	0.752814i
$974$	−11.9386	−	4.34531i	−0.382538	−	0.139233i
$975$		0			0
$976$	−6.65325	+	11.5238i	−0.212965	+	0.368867i
$977$	−8.29375	+	4.78840i	−0.265341	+	0.153195i	−0.626768	−	0.779206i	$-0.715623\pi$
$977$	−8.29375	+	4.78840i	−0.265341	+	0.153195i	0.361428	+	0.932400i	$0.382289\pi$
$978$		0			0
$979$	4.96134	−	28.1372i	0.158565	−	0.899267i
$980$	1.33212	−	0.682539i	0.0425530	−	0.0218029i
$981$		0			0
$982$	−24.6257	+	29.3477i	−0.785837	+	0.936524i
$983$	−10.6613	+	29.2916i	−0.340042	+	0.934257i	0.645340	+	0.763896i	$0.276716\pi$
$983$	−10.6613	+	29.2916i	−0.340042	+	0.934257i	−0.985382	+	0.170362i	$0.945506\pi$
$984$		0			0
$985$	−6.36023	+	4.81531i	−0.202654	+	0.153428i
$986$	−0.552008	−	3.13060i	−0.0175795	−	0.0996985i
$987$		0			0
$988$	0.00198853	+	1.46159i	6.32636e−5	+	0.0464994i
$989$	14.1851			0.451061
$990$		0			0
$991$	−37.2791	+	31.2808i	−1.18421	+	0.993669i	−0.184266	+	0.982876i	$0.558991\pi$
$991$	−37.2791	+	31.2808i	−1.18421	+	0.993669i	−0.999942	+	0.0107922i	$0.996565\pi$
$992$	1.00713	+	2.76706i	0.0319763	+	0.0878542i
$993$		0			0
$994$	−47.4772	−	39.8381i	−1.50589	−	1.26359i
$995$	−16.4695	−	10.6427i	−0.522118	−	0.337395i
$996$		0			0
$997$	−31.4108	−	5.53857i	−0.994790	−	0.175408i	−0.347523	−	0.937672i	$-0.612977\pi$
$997$	−31.4108	−	5.53857i	−0.994790	−	0.175408i	−0.647267	+	0.762263i	$0.724088\pi$
$998$	−30.8876	−	5.44631i	−0.977729	−	0.172400i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	855.2.da.b.199.7		48
3.2	odd	2		95.2.p.a.9.2	✓	48
5.4	even	2	inner	855.2.da.b.199.2		48
15.2	even	4		475.2.l.f.351.2		48
15.8	even	4		475.2.l.f.351.7		48
15.14	odd	2		95.2.p.a.9.7	yes	48
19.17	even	9	inner	855.2.da.b.739.2		48
57.17	odd	18		95.2.p.a.74.7	yes	48
57.32	even	18		1805.2.b.l.1084.7		24
57.44	odd	18		1805.2.b.k.1084.18		24
95.74	even	18	inner	855.2.da.b.739.7		48
285.17	even	36		475.2.l.f.226.2		48
285.32	odd	36		9025.2.a.ct.1.18		24
285.44	odd	18		1805.2.b.k.1084.7		24
285.74	odd	18		95.2.p.a.74.2	yes	48
285.89	even	18		1805.2.b.l.1084.18		24
285.158	even	36		9025.2.a.cu.1.18		24
285.188	even	36		475.2.l.f.226.7		48
285.203	odd	36		9025.2.a.ct.1.7		24
285.272	even	36		9025.2.a.cu.1.7		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.p.a.9.2	✓	48	3.2	odd	2
95.2.p.a.9.7	yes	48	15.14	odd	2
95.2.p.a.74.2	yes	48	285.74	odd	18
95.2.p.a.74.7	yes	48	57.17	odd	18
475.2.l.f.226.2		48	285.17	even	36
475.2.l.f.226.7		48	285.188	even	36
475.2.l.f.351.2		48	15.2	even	4
475.2.l.f.351.7		48	15.8	even	4
855.2.da.b.199.2		48	5.4	even	2	inner
855.2.da.b.199.7		48	1.1	even	1	trivial
855.2.da.b.739.2		48	19.17	even	9	inner
855.2.da.b.739.7		48	95.74	even	18	inner
1805.2.b.k.1084.7		24	285.44	odd	18
1805.2.b.k.1084.18		24	57.44	odd	18
1805.2.b.l.1084.7		24	57.32	even	18
1805.2.b.l.1084.18		24	285.89	even	18
9025.2.a.ct.1.7		24	285.203	odd	36
9025.2.a.ct.1.18		24	285.32	odd	36
9025.2.a.cu.1.7		24	285.272	even	36
9025.2.a.cu.1.18		24	285.158	even	36

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:	\( N \)	\(=\)	\( 855 = 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	855.da (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.45670 - 0.256855i) q^{2} +(0.176607 - 0.0642796i) q^{4} +(0.869056 - 2.06028i) q^{5} +(-2.81448 - 1.62494i) q^{7} +(-2.32124 + 1.34017i) q^{8} +O(q^{10})\)	\(q+(1.45670 - 0.256855i) q^{2} +(0.176607 - 0.0642796i) q^{4} +(0.869056 - 2.06028i) q^{5} +(-2.81448 - 1.62494i) q^{7} +(-2.32124 + 1.34017i) q^{8} +(0.736759 - 3.22442i) q^{10} +(-2.09200 - 3.62344i) q^{11} +(-1.14682 + 1.36673i) q^{13} +(-4.51721 - 1.64413i) q^{14} +(-3.32506 + 2.79006i) q^{16} +(-6.23606 + 1.09959i) q^{17} +(4.09399 - 1.49640i) q^{19} +(0.0210474 - 0.419722i) q^{20} +(-3.97810 - 4.74092i) q^{22} +(0.490346 + 1.34721i) q^{23} +(-3.48948 - 3.58099i) q^{25} +(-1.31952 + 2.28547i) q^{26} +(-0.601506 - 0.106062i) q^{28} +(-0.0589345 + 0.334234i) q^{29} +(1.38932 - 2.40638i) q^{31} +(-0.681187 + 0.811808i) q^{32} +(-8.80161 + 3.20352i) q^{34} +(-5.79376 + 4.38644i) q^{35} +2.70482i q^{37} +(5.57935 - 3.23137i) q^{38} +(0.743832 + 5.94709i) q^{40} +(5.46819 - 4.58835i) q^{41} +(3.38403 - 9.29755i) q^{43} +(-0.602374 - 0.505452i) q^{44} +(1.06032 + 1.83654i) q^{46} +(-0.438674 - 0.0773501i) q^{47} +(1.78085 + 3.08452i) q^{49} +(-6.00292 - 4.32013i) q^{50} +(-0.114683 + 0.315090i) q^{52} +(-2.47532 - 6.80087i) q^{53} +(-9.28335 + 1.16111i) q^{55} +8.71078 q^{56} +0.502015i q^{58} +(0.545712 + 3.09489i) q^{59} +(2.88074 - 1.04850i) q^{61} +(1.40573 - 3.86222i) q^{62} +(3.55679 - 6.16055i) q^{64} +(1.81918 + 3.55053i) q^{65} +(-8.42261 - 1.48513i) q^{67} +(-1.03065 + 0.595046i) q^{68} +(-7.31307 + 7.87786i) q^{70} +(12.1153 + 4.40959i) q^{71} +(-1.17133 - 1.39594i) q^{73} +(0.694747 + 3.94011i) q^{74} +(0.626839 - 0.527435i) q^{76} +13.5974i q^{77} +(-0.535235 + 0.449116i) q^{79} +(2.85863 + 9.27527i) q^{80} +(6.78695 - 8.08837i) q^{82} +(-0.478899 - 0.276493i) q^{83} +(-3.15403 + 13.8036i) q^{85} +(2.54139 - 14.4129i) q^{86} +(9.71206 + 5.60726i) q^{88} +(5.23109 + 4.38940i) q^{89} +(5.44854 - 1.98311i) q^{91} +(0.173197 + 0.206408i) q^{92} -0.658883 q^{94} +(0.474906 - 9.73522i) q^{95} +(-13.0001 + 2.29226i) q^{97} +(3.38643 + 4.03579i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 18 q^{4} + 6 q^{5}+O(q^{10}) \) 48 * q - 18 * q^4 + 6 * q^5	\( 48 q - 18 q^{4} + 6 q^{5} - 15 q^{10} + 12 q^{11} - 6 q^{14} - 42 q^{16} + 12 q^{19} - 42 q^{20} + 12 q^{25} - 12 q^{26} - 42 q^{31} - 36 q^{34} - 6 q^{35} + 66 q^{40} - 6 q^{41} + 6 q^{44} - 6 q^{46} + 12 q^{49} + 18 q^{50} - 36 q^{56} + 36 q^{59} + 48 q^{61} + 18 q^{65} - 123 q^{70} + 24 q^{71} - 84 q^{74} + 66 q^{76} + 48 q^{79} + 39 q^{80} - 84 q^{85} + 42 q^{86} + 12 q^{89} - 30 q^{91} - 72 q^{94} + 63 q^{95}+O(q^{100}) \) 48 * q - 18 * q^4 + 6 * q^5 - 15 * q^10 + 12 * q^11 - 6 * q^14 - 42 * q^16 + 12 * q^19 - 42 * q^20 + 12 * q^25 - 12 * q^26 - 42 * q^31 - 36 * q^34 - 6 * q^35 + 66 * q^40 - 6 * q^41 + 6 * q^44 - 6 * q^46 + 12 * q^49 + 18 * q^50 - 36 * q^56 + 36 * q^59 + 48 * q^61 + 18 * q^65 - 123 * q^70 + 24 * q^71 - 84 * q^74 + 66 * q^76 + 48 * q^79 + 39 * q^80 - 84 * q^85 + 42 * q^86 + 12 * q^89 - 30 * q^91 - 72 * q^94 + 63 * q^95

Introduction

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