LMFDB - Embedded newform 864.2.bn.a.35.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [864,2,Mod(35,864)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(864, base_ring=CyclotomicField(24))

chi = DirichletCharacter(H, H._module([12, 9, 4]))

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

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

chi := DirichletCharacter("864.35");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 864 = 2^{5} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	864.bn (of order $24$, degree $8$, 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:	$6.89907473464$
Analytic rank:	$0$
Dimension:	$368$
Relative dimension:	$46$ over $\Q(\zeta_{24})$
Twist minimal:	no (minimal twist has level 288)
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			35.17
Character	$\chi$	$=$	864.35
Dual form			864.2.bn.a.395.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.488984 - 1.32699i) q^{2} +(-1.52179 + 1.29775i) q^{4} +(1.11620 + 0.856491i) q^{5} +(-1.82515 + 0.489046i) q^{7} +(2.46623 + 1.38481i) q^{8} +O(q^{10})$	\(q+(-0.488984 - 1.32699i) q^{2} +(-1.52179 + 1.29775i) q^{4} +(1.11620 + 0.856491i) q^{5} +(-1.82515 + 0.489046i) q^{7} +(2.46623 + 1.38481i) q^{8} +(0.590748 - 1.90000i) q^{10} +(-0.267076 + 2.02865i) q^{11} +(-2.31610 + 0.304921i) q^{13} +(1.54143 + 2.18281i) q^{14} +(0.631682 - 3.94981i) q^{16} -2.43543 q^{17} +(-7.41946 - 3.07324i) q^{19} +(-2.81014 + 0.145153i) q^{20} +(2.82258 - 0.637569i) q^{22} +(1.78352 - 6.65621i) q^{23} +(-0.781767 - 2.91760i) q^{25} +(1.53716 + 2.92434i) q^{26} +(2.14282 - 3.11281i) q^{28} +(-1.15634 - 1.50698i) q^{29} +(-5.12880 + 2.96111i) q^{31} +(-5.55023 + 1.09316i) q^{32} +(1.19089 + 3.23178i) q^{34} +(-2.45609 - 1.01735i) q^{35} +(-0.701864 - 1.69445i) q^{37} +(-0.450151 + 11.3483i) q^{38} +(1.56673 + 3.65804i) q^{40} +(8.50981 + 2.28020i) q^{41} +(-2.85610 - 0.376012i) q^{43} +(-2.22624 - 3.43377i) q^{44} +(-9.70481 + 0.888066i) q^{46} +(-8.82446 - 5.09480i) q^{47} +(-2.97019 + 1.71484i) q^{49} +(-3.48934 + 2.46405i) q^{50} +(3.12891 - 3.46975i) q^{52} +(-0.0950263 - 0.229414i) q^{53} +(-2.03563 + 2.03563i) q^{55} +(-5.17847 - 1.32139i) q^{56} +(-1.43431 + 2.27134i) q^{58} +(3.55726 - 4.63591i) q^{59} +(-2.88644 + 2.21485i) q^{61} +(6.43726 + 5.35791i) q^{62} +(4.16458 + 6.83054i) q^{64} +(-2.84640 - 1.64337i) q^{65} +(-6.10177 + 0.803313i) q^{67} +(3.70621 - 3.16058i) q^{68} +(-0.149015 + 3.75667i) q^{70} +(-8.45963 + 8.45963i) q^{71} +(7.58174 + 7.58174i) q^{73} +(-1.90531 + 1.75992i) q^{74} +(15.2792 - 4.95180i) q^{76} +(-0.504648 - 3.83319i) q^{77} +(0.353898 - 0.612970i) q^{79} +(4.08806 - 3.86775i) q^{80} +(-1.13537 - 12.4074i) q^{82} +(7.19271 + 9.37372i) q^{83} +(-2.71843 - 2.08592i) q^{85} +(0.897624 + 3.97387i) q^{86} +(-3.46797 + 4.63326i) q^{88} +(0.251664 + 0.251664i) q^{89} +(4.07810 - 1.68920i) q^{91} +(5.92395 + 12.4439i) q^{92} +(-2.44572 + 14.2012i) q^{94} +(-5.64941 - 9.78506i) q^{95} +(6.37184 - 11.0363i) q^{97} +(3.72795 + 3.10287i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 368 q + 12 q^{2} - 4 q^{4} + 12 q^{5} - 4 q^{7}+O(q^{10}) $ 368 * q + 12 * q^2 - 4 * q^4 + 12 * q^5 - 4 * q^7	$ 368 q + 12 q^{2} - 4 q^{4} + 12 q^{5} - 4 q^{7} - 16 q^{10} + 12 q^{11} - 4 q^{13} + 12 q^{14} - 4 q^{16} - 16 q^{19} + 12 q^{20} - 4 q^{22} + 12 q^{23} - 4 q^{25} - 16 q^{28} + 12 q^{29} + 12 q^{32} - 12 q^{34} - 16 q^{37} + 12 q^{38} - 4 q^{40} + 12 q^{41} - 4 q^{43} - 16 q^{46} + 24 q^{47} + 168 q^{50} - 4 q^{52} - 16 q^{55} + 12 q^{56} + 32 q^{58} + 12 q^{59} - 4 q^{61} - 16 q^{64} + 24 q^{65} - 4 q^{67} + 60 q^{68} - 4 q^{70} - 16 q^{73} + 12 q^{74} - 28 q^{76} + 12 q^{77} - 8 q^{79} - 16 q^{82} + 132 q^{83} - 24 q^{85} + 12 q^{86} - 4 q^{88} - 16 q^{91} - 216 q^{92} - 20 q^{94} - 8 q^{97}+O(q^{100}) $ 368 * q + 12 * q^2 - 4 * q^4 + 12 * q^5 - 4 * q^7 - 16 * q^10 + 12 * q^11 - 4 * q^13 + 12 * q^14 - 4 * q^16 - 16 * q^19 + 12 * q^20 - 4 * q^22 + 12 * q^23 - 4 * q^25 - 16 * q^28 + 12 * q^29 + 12 * q^32 - 12 * q^34 - 16 * q^37 + 12 * q^38 - 4 * q^40 + 12 * q^41 - 4 * q^43 - 16 * q^46 + 24 * q^47 + 168 * q^50 - 4 * q^52 - 16 * q^55 + 12 * q^56 + 32 * q^58 + 12 * q^59 - 4 * q^61 - 16 * q^64 + 24 * q^65 - 4 * q^67 + 60 * q^68 - 4 * q^70 - 16 * q^73 + 12 * q^74 - 28 * q^76 + 12 * q^77 - 8 * q^79 - 16 * q^82 + 132 * q^83 - 24 * q^85 + 12 * q^86 - 4 * q^88 - 16 * q^91 - 216 * q^92 - 20 * q^94 - 8 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/864\mathbb{Z}\right)^\times$.

$n$	$325$	$353$	$703$
$\chi(n)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.488984	−	1.32699i	−0.345764	−	0.938321i
$2$	−0.488984	−	1.32699i	−0.345764	−	0.938321i
$3$		0			0
$3$		0			0
$4$	−1.52179	+	1.29775i	−0.760894	+	0.648876i
$5$	1.11620	+	0.856491i	0.499180	+	0.383035i	0.827441	−	0.561553i	$-0.189796\pi$
$5$	1.11620	+	0.856491i	0.499180	+	0.383035i	−0.328261	+	0.944587i	$0.606462\pi$
$6$		0			0
$7$	−1.82515	+	0.489046i	−0.689840	+	0.184842i	−0.586675	−	0.809822i	$-0.699564\pi$
$7$	−1.82515	+	0.489046i	−0.689840	+	0.184842i	−0.103165	+	0.994664i	$0.532897\pi$
$8$	2.46623	+	1.38481i	0.871944	+	0.489606i
$9$		0			0
$10$	0.590748	−	1.90000i	0.186811	−	0.600831i
$11$	−0.267076	+	2.02865i	−0.0805265	+	0.611660i	0.902833	+	0.429991i	$0.141483\pi$
$11$	−0.267076	+	2.02865i	−0.0805265	+	0.611660i	−0.983360	+	0.181669i	$0.941850\pi$
$12$		0			0
$13$	−2.31610	+	0.304921i	−0.642371	+	0.0845698i	−0.444673	−	0.895693i	$-0.646680\pi$
$13$	−2.31610	+	0.304921i	−0.642371	+	0.0845698i	−0.197698	+	0.980263i	$0.563347\pi$
$14$	1.54143	+	2.18281i	0.411963	+	0.583380i
$15$		0			0
$16$	0.631682	−	3.94981i	0.157920	−	0.987452i
$17$	−2.43543			−0.590678			−0.295339	−	0.955393i	$-0.595433\pi$
$17$	−2.43543			−0.590678			−0.295339	+	0.955393i	$0.595433\pi$
$18$		0			0
$19$	−7.41946	−	3.07324i	−1.70214	−	0.705050i	−0.702166	−	0.712013i	$-0.747784\pi$
$19$	−7.41946	−	3.07324i	−1.70214	−	0.705050i	−0.999976	+	0.00696315i	$0.997784\pi$
$20$	−2.81014	+	0.145153i	−0.628365	+	0.0324572i
$21$		0			0
$22$	2.82258	−	0.637569i	0.601777	−	0.135930i
$23$	1.78352	−	6.65621i	0.371891	−	1.38791i	−0.485944	−	0.873990i	$-0.661524\pi$
$23$	1.78352	−	6.65621i	0.371891	−	1.38791i	0.857835	−	0.513925i	$-0.171809\pi$
$24$		0			0
$25$	−0.781767	−	2.91760i	−0.156353	−	0.583519i
$26$	1.53716	+	2.92434i	0.301462	+	0.573509i
$27$		0			0
$28$	2.14282	−	3.11281i	0.404956	−	0.588266i
$29$	−1.15634	−	1.50698i	−0.214728	−	0.279839i	0.673554	−	0.739138i	$-0.264767\pi$
$29$	−1.15634	−	1.50698i	−0.214728	−	0.279839i	−0.888281	+	0.459300i	$0.848100\pi$
$30$		0			0
$31$	−5.12880	+	2.96111i	−0.921159	+	0.531831i	−0.884005	−	0.467478i	$-0.845163\pi$
$31$	−5.12880	+	2.96111i	−0.921159	+	0.531831i	−0.0371544	+	0.999310i	$0.511829\pi$
$32$	−5.55023	+	1.09316i	−0.981150	+	0.193245i
$33$		0			0
$34$	1.19089	+	3.23178i	0.204235	+	0.554246i
$35$	−2.45609	−	1.01735i	−0.415156	−	0.171963i
$36$		0			0
$37$	−0.701864	−	1.69445i	−0.115386	−	0.278566i	0.855627	−	0.517592i	$-0.173172\pi$
$37$	−0.701864	−	1.69445i	−0.115386	−	0.278566i	−0.971013	+	0.239027i	$0.923172\pi$
$38$	−0.450151	+	11.3483i	−0.0730242	+	1.84094i
$39$		0			0
$40$	1.56673	+	3.65804i	0.247722	+	0.578386i
$41$	8.50981	+	2.28020i	1.32901	+	0.356107i	0.852345	−	0.522979i	$-0.175180\pi$
$41$	8.50981	+	2.28020i	1.32901	+	0.356107i	0.476663	+	0.879086i	$0.341846\pi$
$42$		0			0
$43$	−2.85610	−	0.376012i	−0.435551	−	0.0573414i	−0.0904370	−	0.995902i	$-0.528826\pi$
$43$	−2.85610	−	0.376012i	−0.435551	−	0.0573414i	−0.345114	+	0.938561i	$0.612160\pi$
$44$	−2.22624	−	3.43377i	−0.335619	−	0.517660i
$45$		0			0
$46$	−9.70481	+	0.888066i	−1.43090	+	0.130938i
$47$	−8.82446	−	5.09480i	−1.28718	−	0.743153i	−0.309029	−	0.951053i	$-0.600004\pi$
$47$	−8.82446	−	5.09480i	−1.28718	−	0.743153i	−0.978150	+	0.207899i	$0.933337\pi$
$48$		0			0
$49$	−2.97019	+	1.71484i	−0.424313	+	0.244977i
$50$	−3.48934	+	2.46405i	−0.493467	+	0.348470i
$51$		0			0
$52$	3.12891	−	3.46975i	0.433901	−	0.481168i
$53$	−0.0950263	−	0.229414i	−0.0130529	−	0.0315124i	0.917219	−	0.398384i	$-0.130429\pi$
$53$	−0.0950263	−	0.229414i	−0.0130529	−	0.0315124i	−0.930272	+	0.366872i	$0.880429\pi$
$54$		0			0
$55$	−2.03563	+	2.03563i	−0.274484	+	0.274484i
$56$	−5.17847	−	1.32139i	−0.692002	−	0.176578i
$57$		0			0
$58$	−1.43431	+	2.27134i	−0.188334	+	0.298242i
$59$	3.55726	−	4.63591i	0.463116	−	0.603544i	−0.502161	−	0.864774i	$-0.667461\pi$
$59$	3.55726	−	4.63591i	0.463116	−	0.603544i	0.965277	+	0.261230i	$0.0841281\pi$
$60$		0			0
$61$	−2.88644	+	2.21485i	−0.369571	+	0.283582i	−0.776804	−	0.629743i	$-0.783160\pi$
$61$	−2.88644	+	2.21485i	−0.369571	+	0.283582i	0.407233	+	0.913324i	$0.366494\pi$
$62$	6.43726	+	5.35791i	0.817533	+	0.680455i
$63$		0			0
$64$	4.16458	+	6.83054i	0.520573	+	0.853817i
$65$	−2.84640	−	1.64337i	−0.353052	−	0.203835i
$66$		0			0
$67$	−6.10177	+	0.803313i	−0.745450	+	0.0981403i	−0.493676	−	0.869646i	$-0.664347\pi$
$67$	−6.10177	+	0.803313i	−0.745450	+	0.0981403i	−0.251774	+	0.967786i	$0.581014\pi$
$68$	3.70621	−	3.16058i	0.449443	−	0.383277i
$69$		0			0
$70$	−0.149015	+	3.75667i	−0.0178107	+	0.449008i
$71$	−8.45963	+	8.45963i	−1.00397	+	1.00397i	−0.00398084	+	0.999992i	$0.501267\pi$
$71$	−8.45963	+	8.45963i	−1.00397	+	1.00397i	−0.999992	+	0.00398084i	$0.998733\pi$
$72$		0			0
$73$	7.58174	+	7.58174i	0.887376	+	0.887376i	0.994270	−	0.106894i	$-0.0340907\pi$
$73$	7.58174	+	7.58174i	0.887376	+	0.887376i	−0.106894	+	0.994270i	$0.534091\pi$
$74$	−1.90531	+	1.75992i	−0.221488	+	0.204587i
$75$		0			0
$76$	15.2792	−	4.95180i	1.75264	−	0.568010i
$77$	−0.504648	−	3.83319i	−0.0575100	−	0.436832i
$78$		0			0
$79$	0.353898	−	0.612970i	0.0398167	−	0.0689645i	−0.845430	−	0.534086i	$-0.820656\pi$
$79$	0.353898	−	0.612970i	0.0398167	−	0.0689645i	0.885247	+	0.465121i	$0.153989\pi$
$80$	4.08806	−	3.86775i	0.457059	−	0.432428i
$81$		0			0
$82$	−1.13537	−	12.4074i	−0.125381	−	1.37017i
$83$	7.19271	+	9.37372i	0.789503	+	1.02890i	0.998697	+	0.0510258i	$0.0162491\pi$
$83$	7.19271	+	9.37372i	0.789503	+	1.02890i	−0.209195	+	0.977874i	$0.567084\pi$
$84$		0			0
$85$	−2.71843	−	2.08592i	−0.294855	−	0.226250i
$86$	0.897624	+	3.97387i	0.0967932	+	0.428513i
$87$		0			0
$88$	−3.46797	+	4.63326i	−0.369687	+	0.493907i
$89$	0.251664	+	0.251664i	0.0266763	+	0.0266763i	0.720319	−	0.693643i	$-0.243995\pi$
$89$	0.251664	+	0.251664i	0.0266763	+	0.0266763i	−0.693643	+	0.720319i	$0.743995\pi$
$90$		0			0
$91$	4.07810	−	1.68920i	0.427501	−	0.177077i
$92$	5.92395	+	12.4439i	0.617615	+	1.29737i
$93$		0			0
$94$	−2.44572	+	14.2012i	−0.252256	+	1.46474i
$95$	−5.64941	−	9.78506i	−0.579617	−	1.00393i
$96$		0			0
$97$	6.37184	−	11.0363i	0.646962	−	1.12057i	−0.336882	−	0.941547i	$-0.609372\pi$
$97$	6.37184	−	11.0363i	0.646962	−	1.12057i	0.983845	−	0.179025i	$-0.0572942\pi$
$98$	3.72795	+	3.10287i	0.376579	+	0.313437i
$99$		0			0
$100$	4.97600	+	3.42542i	0.497600	+	0.342542i
$101$	0.342223	−	2.59944i	0.0340525	−	0.258654i	−0.965948	−	0.258738i	$-0.916693\pi$
$101$	0.342223	−	2.59944i	0.0340525	−	0.258654i	1.00000		8.39140e-5i	$2.67107e-5\pi$
$102$		0			0
$103$	−3.07865	+	11.4897i	−0.303348	+	1.13211i	0.631010	+	0.775775i	$0.282641\pi$
$103$	−3.07865	+	11.4897i	−0.303348	+	1.13211i	−0.934358	+	0.356336i	$0.884026\pi$
$104$	−6.13430	−	2.45536i	−0.601517	−	0.240768i
$105$		0			0
$106$	−0.257963	+	0.238278i	−0.0250556	+	0.0231437i
$107$	−12.8146	+	5.30797i	−1.23883	+	0.513141i	−0.903349	−	0.428906i	$-0.858899\pi$
$107$	−12.8146	+	5.30797i	−1.23883	+	0.513141i	−0.335482	+	0.942047i	$0.608899\pi$
$108$		0			0
$109$	−5.41896	+	13.0825i	−0.519043	+	1.25308i	0.419449	+	0.907779i	$0.362223\pi$
$109$	−5.41896	+	13.0825i	−0.519043	+	1.25308i	−0.938492	+	0.345301i	$0.887777\pi$
$110$	3.69664	+	1.70586i	0.352461	+	0.162648i
$111$		0			0
$112$	0.778728	+	7.51789i	0.0735828	+	0.710374i
$113$	0.766183	+	1.32707i	0.0720764	+	0.124840i	0.899811	−	0.436280i	$-0.143704\pi$
$113$	0.766183	+	1.32707i	0.0720764	+	0.124840i	−0.827735	+	0.561120i	$0.810371\pi$
$114$		0			0
$115$	7.69176	−	5.90209i	0.717260	−	0.550373i
$116$	3.71539	+	0.792653i	0.344966	+	0.0735960i
$117$		0			0
$118$	−7.89124	−	2.45355i	−0.726447	−	0.225867i
$119$	4.44501	−	1.19104i	0.407473	−	0.109182i
$120$		0			0
$121$	6.58111	+	1.76340i	0.598283	+	0.160309i
$122$	4.35050	+	2.74725i	0.393875	+	0.248724i
$123$		0			0
$124$	3.96216	−	11.1621i	0.355812	−	1.00239i
$125$	4.31835	−	10.4254i	0.386245	−	0.932478i
$126$		0			0
$127$		−	12.6029i		−	1.11833i	−0.829057	−	0.559164i	$-0.811122\pi$
$127$		−	12.6029i		−	1.11833i	0.829057	−	0.559164i	$-0.188878\pi$
$128$	7.02762	−	8.86637i	0.621160	−	0.783684i
$129$		0			0
$130$	−0.788885	+	4.58071i	−0.0691898	+	0.401755i
$131$	0.970201	+	7.36941i	0.0847668	+	0.643868i	0.980105	+	0.198481i	$0.0636007\pi$
$131$	0.970201	+	7.36941i	0.0847668	+	0.643868i	−0.895338	+	0.445387i	$0.853066\pi$
$132$		0			0
$133$	15.0446	+	1.98065i	1.30453	+	0.171744i
$134$	4.04966	+	7.70416i	0.349837	+	0.665538i
$135$		0			0
$136$	−6.00632	−	3.37261i	−0.515038	−	0.289199i
$137$	−1.84464	−	6.88430i	−0.157598	−	0.588165i	−0.998869	−	0.0475507i	$-0.984858\pi$
$137$	−1.84464	−	6.88430i	−0.157598	−	0.588165i	0.841270	−	0.540615i	$-0.181808\pi$
$138$		0			0
$139$	11.7231	−	15.2778i	0.994340	−	1.29585i	0.0393458	−	0.999226i	$-0.487473\pi$
$139$	11.7231	−	15.2778i	0.994340	−	1.29585i	0.954994	−	0.296624i	$-0.0958607\pi$
$140$	5.05792	−	1.63921i	0.427472	−	0.138539i
$141$		0			0
$142$	15.3624	+	7.08919i	1.28919	+	0.594912i
$143$		−	4.77999i		−	0.399723i
$144$		0			0
$145$		−	2.67249i		−	0.221938i
$146$	6.35352	−	13.7682i	0.525821	−	1.13947i
$147$		0			0
$148$	3.26706	+	1.66775i	0.268551	+	0.137088i
$149$	−10.9615	+	14.2853i	−0.898002	+	1.17030i	0.0867315	+	0.996232i	$0.472358\pi$
$149$	−10.9615	+	14.2853i	−0.898002	+	1.17030i	−0.984734	+	0.174068i	$0.944309\pi$
$150$		0			0
$151$	−3.66761	−	13.6877i	−0.298465	−	1.11389i	−0.938426	−	0.345481i	$-0.887716\pi$
$151$	−3.66761	−	13.6877i	−0.298465	−	1.11389i	0.639960	−	0.768408i	$-0.278951\pi$
$152$	−14.0422	−	17.8539i	−1.13898	−	1.44814i
$153$		0			0
$154$	−4.83982	+	2.54403i	−0.390004	+	0.205004i
$155$	−8.26094	−	1.08757i	−0.663534	−	0.0873560i
$156$		0			0
$157$	0.985606	+	7.48642i	0.0786599	+	0.597481i	0.984696	+	0.174281i	$0.0557601\pi$
$157$	0.985606	+	7.48642i	0.0786599	+	0.597481i	−0.906036	+	0.423200i	$0.860907\pi$
$158$	−0.986454	−	0.169886i	−0.0784781	−	0.0135154i
$159$		0			0
$160$	−7.13145	−	3.53353i	−0.563791	−	0.279350i
$161$			13.0208i			1.02618i
$162$		0			0
$163$	−5.33350	+	12.8762i	−0.417752	+	1.00854i	0.565246	+	0.824923i	$0.308781\pi$
$163$	−5.33350	+	12.8762i	−0.417752	+	1.00854i	−0.982997	+	0.183619i	$0.941219\pi$
$164$	−15.9093	+	7.57364i	−1.24230	+	0.591402i
$165$		0			0
$166$	8.92169	−	14.1282i	0.692457	−	1.09656i
$167$	7.48145	+	2.00465i	0.578932	+	0.155124i	0.536390	−	0.843970i	$-0.319788\pi$
$167$	7.48145	+	2.00465i	0.578932	+	0.155124i	0.0425421	+	0.999095i	$0.486454\pi$
$168$		0			0
$169$	−7.28569	+	1.95219i	−0.560437	+	0.150169i
$170$	−1.43872	+	4.62730i	−0.110345	+	0.354898i
$171$		0			0
$172$	4.83435	−	3.13429i	0.368616	−	0.238988i
$173$	10.9308	−	8.38746i	0.831050	−	0.637687i	−0.103059	−	0.994675i	$-0.532863\pi$
$173$	10.9308	−	8.38746i	0.831050	−	0.637687i	0.934109	+	0.356988i	$0.116196\pi$
$174$		0			0
$175$	2.85368	+	4.94272i	0.215718	+	0.373634i
$176$	7.84405	+	2.33636i	0.591268	+	0.176110i
$177$		0			0
$178$	0.210895	−	0.457014i	0.0158072	−	0.0342546i
$179$	−0.702535	+	1.69607i	−0.0525099	+	0.126770i	−0.947958	−	0.318397i	$-0.896856\pi$
$179$	−0.702535	+	1.69607i	−0.0525099	+	0.126770i	0.895448	+	0.445167i	$0.146856\pi$
$180$		0			0
$181$	−9.16779	+	3.79742i	−0.681437	+	0.282260i	−0.696427	−	0.717627i	$-0.745228\pi$
$181$	−9.16779	+	3.79742i	−0.681437	+	0.282260i	0.0149906	+	0.999888i	$0.495228\pi$
$182$	−4.23568	−	4.58559i	−0.313970	−	0.339907i
$183$		0			0
$184$	13.6162	−	13.9459i	1.00380	−	1.02810i
$185$	0.667860	−	2.49249i	0.0491020	−	0.183251i
$186$		0			0
$187$	0.650445	−	4.94062i	0.0475652	−	0.361294i
$188$	20.0407	−	3.69874i	1.46162	−	0.269758i
$189$		0			0
$190$	−10.2222	+	12.2814i	−0.741595	+	0.890989i
$191$	13.1754	−	22.8204i	0.953338	−	1.65123i	0.215211	−	0.976567i	$-0.430956\pi$
$191$	13.1754	−	22.8204i	0.953338	−	1.65123i	0.738127	−	0.674662i	$-0.235711\pi$
$192$		0			0
$193$	−8.88327	−	15.3863i	−0.639432	−	1.10753i	−0.985558	−	0.169340i	$-0.945836\pi$
$193$	−8.88327	−	15.3863i	−0.639432	−	1.10753i	0.346126	−	0.938188i	$-0.387497\pi$
$194$	−17.7608	−	3.05875i	−1.27515	−	0.219605i
$195$		0			0
$196$	2.29456	−	6.46419i	0.163897	−	0.461728i
$197$	−4.46253	+	1.84844i	−0.317942	+	0.131696i	−0.535947	−	0.844252i	$-0.680045\pi$
$197$	−4.46253	+	1.84844i	−0.317942	+	0.131696i	0.218005	+	0.975948i	$0.430045\pi$
$198$		0			0
$199$	−11.7416	−	11.7416i	−0.832339	−	0.832339i	0.155497	−	0.987836i	$-0.450302\pi$
$199$	−11.7416	−	11.7416i	−0.832339	−	0.832339i	−0.987836	+	0.155497i	$0.950302\pi$
$200$	2.11231	−	8.27806i	0.149363	−	0.585348i
$201$		0			0
$202$	−3.61677	+	0.816961i	−0.254475	+	0.0574812i
$203$	2.84748	+	2.18495i	0.199854	+	0.153353i
$204$		0			0
$205$	7.54569	+	9.83373i	0.527014	+	0.686818i
$206$	16.7521	−	1.53294i	1.16717	−	0.106805i
$207$		0			0
$208$	−0.258661	+	9.34077i	−0.0179349	+	0.647666i
$209$	8.21608	−	14.2307i	0.568318	−	0.984356i
$210$		0			0
$211$	0.359364	+	2.72964i	0.0247397	+	0.187916i	0.999352	−	0.0359805i	$-0.0114554\pi$
$211$	0.359364	+	2.72964i	0.0247397	+	0.187916i	−0.974613	+	0.223897i	$0.928122\pi$
$212$	0.442332	+	0.225799i	0.0303795	+	0.0155079i
$213$		0			0
$214$	13.3097	+	14.4093i	0.909834	+	0.984996i
$215$	−2.86593	−	2.86593i	−0.195455	−	0.195455i
$216$		0			0
$217$	7.91268	−	7.91268i	0.537148	−	0.537148i
$218$	20.0101	+	0.793739i	1.35526	+	0.0537588i
$219$		0			0
$220$	0.456056	−	5.73954i	0.0307473	−	0.386959i
$221$	5.64070	−	0.742612i	0.379434	−	0.0499535i
$222$		0			0
$223$	−16.4398	−	9.49150i	−1.10089	−	0.635598i	−0.164433	−	0.986388i	$-0.552580\pi$
$223$	−16.4398	−	9.49150i	−1.10089	−	0.635598i	−0.936454	+	0.350791i	$0.885913\pi$
$224$	9.59536	−	4.70949i	0.641117	−	0.314666i
$225$		0			0
$226$	1.38635	−	1.66563i	0.0922187	−	0.110796i
$227$	−9.35398	+	7.17756i	−0.620845	+	0.476391i	−0.870649	−	0.491905i	$-0.836301\pi$
$227$	−9.35398	+	7.17756i	−0.620845	+	0.476391i	0.249804	+	0.968297i	$0.419634\pi$
$228$		0			0
$229$	−0.0323442	+	0.0421518i	−0.00213736	+	0.00278547i	−0.794421	−	0.607368i	$-0.792225\pi$
$229$	−0.0323442	+	0.0421518i	−0.00213736	+	0.00278547i	0.792283	+	0.610153i	$0.208892\pi$
$230$	−11.5931	−	7.32083i	−0.764429	−	0.482721i
$231$		0			0
$232$	−0.764929	−	5.31788i	−0.0502201	−	0.349136i
$233$	11.6368	−	11.6368i	0.762353	−	0.762353i	−0.214394	−	0.976747i	$-0.568778\pi$
$233$	11.6368	−	11.6368i	0.762353	−	0.762353i	0.976747	+	0.214394i	$0.0687776\pi$
$234$		0			0
$235$	−5.48622	−	13.2449i	−0.357881	−	0.864002i
$236$	0.602863	+	11.6713i	0.0392431	+	0.759738i
$237$		0			0
$238$	−3.75403	−	5.31607i	−0.243338	−	0.344590i
$239$	−25.0656	+	14.4717i	−1.62136	+	0.936094i	−0.634806	+	0.772672i	$0.718920\pi$
$239$	−25.0656	+	14.4717i	−1.62136	+	0.936094i	−0.986556	+	0.163422i	$0.947747\pi$
$240$		0			0
$241$	10.0975	+	5.82980i	0.650438	+	0.375531i	0.788624	−	0.614876i	$-0.210794\pi$
$241$	10.0975	+	5.82980i	0.650438	+	0.375531i	−0.138186	+	0.990406i	$0.544127\pi$
$242$	−0.878047	−	9.59532i	−0.0564430	−	0.616811i
$243$		0			0
$244$	1.51824	−	7.11641i	0.0971951	−	0.455582i
$245$	−4.78407	−	0.629835i	−0.305643	−	0.0402387i
$246$		0			0
$247$	18.1213	+	4.85559i	1.15303	+	0.308954i
$248$	−16.7494	+	0.200357i	−1.06359	+	0.0127227i
$249$		0			0
$250$	−15.9460	−	0.632528i	−1.00851	−	0.0400046i
$251$	−0.0941454	−	0.227287i	−0.00594241	−	0.0143462i	0.920880	−	0.389845i	$-0.127471\pi$
$251$	−0.0941454	−	0.227287i	−0.00594241	−	0.0143462i	−0.926823	+	0.375499i	$0.877471\pi$
$252$		0			0
$253$	13.0267	+	5.39586i	0.818985	+	0.339235i
$254$	−16.7239	+	6.16263i	−1.04935	+	0.386678i
$255$		0			0
$256$	−15.2020	−	4.99004i	−0.950122	−	0.311878i
$257$	25.5643	−	14.7596i	1.59466	−	0.920676i	0.602165	−	0.798372i	$-0.294305\pi$
$257$	25.5643	−	14.7596i	1.59466	−	0.920676i	0.992493	−	0.122304i	$-0.0390283\pi$
$258$		0			0
$259$	2.10967	+	2.74937i	0.131088	+	0.170838i
$260$	6.46430	−	1.19306i	0.400899	−	0.0739903i
$261$		0			0
$262$	9.30469	−	4.89097i	0.574846	−	0.302165i
$263$	−1.50892	−	5.63138i	−0.0930443	−	0.347246i	0.903671	−	0.428227i	$-0.140861\pi$
$263$	−1.50892	−	5.63138i	−0.0930443	−	0.347246i	−0.996716	+	0.0809806i	$0.974195\pi$
$264$		0			0
$265$	0.0904225	−	0.337461i	0.00555461	−	0.0207301i
$266$	−4.72825	−	20.9324i	−0.289908	−	1.28345i
$267$		0			0
$268$	8.24310	−	9.14106i	0.503528	−	0.558379i
$269$	9.53560	+	3.94978i	0.581396	+	0.240822i	0.653944	−	0.756543i	$-0.273113\pi$
$269$	9.53560	+	3.94978i	0.581396	+	0.240822i	−0.0725482	+	0.997365i	$0.523113\pi$
$270$		0			0
$271$	−29.3045			−1.78012			−0.890060	−	0.455843i	$-0.849338\pi$
$271$	−29.3045			−1.78012			−0.890060	+	0.455843i	$0.849338\pi$
$272$	−1.53841	+	9.61947i	−0.0932801	+	0.583266i
$273$		0			0
$274$	−8.23337	+	5.81413i	−0.497396	+	0.351244i
$275$	6.12756	−	0.806709i	0.369506	−	0.0486464i
$276$		0			0
$277$	−4.29079	+	32.5918i	−0.257809	+	1.95825i	0.0269033	+	0.999638i	$0.491435\pi$
$277$	−4.29079	+	32.5918i	−0.257809	+	1.95825i	−0.284712	+	0.958613i	$0.591898\pi$
$278$	−26.0059	−	8.08577i	−1.55973	−	0.484953i
$279$		0			0
$280$	−4.64846	−	5.91024i	−0.277798	−	0.353205i
$281$	3.50616	−	0.939472i	0.209160	−	0.0560442i	−0.152718	−	0.988270i	$-0.548803\pi$
$281$	3.50616	−	0.939472i	0.209160	−	0.0560442i	0.361878	+	0.932226i	$0.382136\pi$
$282$		0			0
$283$	26.0124	+	19.9600i	1.54628	+	1.18650i	0.909684	+	0.415301i	$0.136324\pi$
$283$	26.0124	+	19.9600i	1.54628	+	1.18650i	0.636593	+	0.771200i	$0.280343\pi$
$284$	1.89527	−	23.8523i	0.112464	−	1.41537i
$285$		0			0
$286$	−6.34298	+	2.33734i	−0.375068	+	0.138210i
$287$	−16.6468			−0.982627
$288$		0			0
$289$	−11.0687			−0.651100
$290$	−3.54636	+	1.30681i	−0.208249	+	0.0767383i
$291$		0			0
$292$	−21.3770	−	1.69859i	−1.25100	−	0.0994026i
$293$	8.71623	+	6.68820i	0.509208	+	0.390729i	0.831165	−	0.556025i	$-0.187674\pi$
$293$	8.71623	+	6.68820i	0.509208	+	0.390729i	−0.321958	+	0.946754i	$0.604341\pi$
$294$		0			0
$295$	7.94123	−	2.12785i	0.462357	−	0.123888i
$296$	0.615538	−	5.15085i	0.0357774	−	0.299387i
$297$		0			0
$298$	24.3164	+	7.56049i	1.40861	+	0.437967i
$299$	−2.10121	+	15.9603i	−0.121516	+	0.923007i
$300$		0			0
$301$	5.39668	−	0.710486i	0.311059	−	0.0409518i
$302$	−16.3700	+	11.5599i	−0.941987	+	0.665199i
$303$		0			0
$304$	−16.8255	+	27.3641i	−0.965006	+	1.56944i
$305$	−5.11885			−0.293104
$306$		0			0
$307$	4.11369	+	1.70395i	0.234781	+	0.0972494i	0.496972	−	0.867767i	$-0.334445\pi$
$307$	4.11369	+	1.70395i	0.234781	+	0.0972494i	−0.262191	+	0.965016i	$0.584445\pi$
$308$	5.74249	+	5.17839i	0.327209	+	0.295066i
$309$		0			0
$310$	2.59627	+	11.4940i	0.147458	+	0.652813i
$311$	−1.65374	+	6.17183i	−0.0937747	+	0.349972i	−0.996831	−	0.0795505i	$-0.974651\pi$
$311$	−1.65374	+	6.17183i	−0.0937747	+	0.349972i	0.903056	+	0.429523i	$0.141318\pi$
$312$		0			0
$313$	0.183093	+	0.683314i	0.0103490	+	0.0386232i	0.970907	−	0.239456i	$-0.0769690\pi$
$313$	0.183093	+	0.683314i	0.0103490	+	0.0386232i	−0.960558	+	0.278079i	$0.910302\pi$
$314$	9.45243	−	4.96863i	0.533432	−	0.280396i
$315$		0			0
$316$	0.256924	+	1.39208i	0.0144531	+	0.0783108i
$317$	−7.91717	−	10.3179i	−0.444673	−	0.579509i	0.516211	−	0.856462i	$-0.327342\pi$
$317$	−7.91717	−	10.3179i	−0.444673	−	0.579509i	−0.960884	+	0.276953i	$0.910675\pi$
$318$		0			0
$319$	3.36596	−	1.94334i	0.188457	−	0.108806i
$320$	−1.20178	+	11.1912i	−0.0671818	+	0.625606i
$321$		0			0
$322$	17.2784	−	6.36695i	0.962887	−	0.354816i
$323$	18.0696	+	7.48466i	1.00542	+	0.416457i
$324$		0			0
$325$	2.70029	+	6.51907i	0.149785	+	0.361613i
$326$	19.6945	+	0.781221i	1.09078	+	0.0432678i
$327$		0			0
$328$	17.8295	+	17.4080i	0.984469	+	0.961195i
$329$	18.5975	+	4.98319i	1.02531	+	0.274732i
$330$		0			0
$331$	15.2702	+	2.01036i	0.839324	+	0.110499i	0.537919	−	0.842997i	$-0.319211\pi$
$331$	15.2702	+	2.01036i	0.839324	+	0.110499i	0.301406	+	0.953496i	$0.402544\pi$
$332$	−23.1105	−	4.93047i	−1.26836	−	0.270595i
$333$		0			0
$334$	−0.998169	−	10.9080i	−0.0546174	−	0.596861i
$335$	−7.49883	−	4.32945i	−0.409705	−	0.236543i
$336$		0			0
$337$	16.8932	−	9.75332i	0.920234	−	0.531297i	0.0365240	−	0.999333i	$-0.488371\pi$
$337$	16.8932	−	9.75332i	0.920234	−	0.531297i	0.883710	+	0.468036i	$0.155038\pi$
$338$	6.15312	+	8.71342i	0.334686	+	0.473947i
$339$		0			0
$340$	6.84388	−	0.353510i	0.371162	−	0.0191718i
$341$	−4.63727	−	11.1954i	−0.251122	−	0.606262i
$342$		0			0
$343$	13.9351	−	13.9351i	0.752424	−	0.752424i
$344$	−6.52309	−	4.88250i	−0.351701	−	0.263247i
$345$		0			0
$346$	−16.4750	−	10.4036i	−0.885703	−	0.559303i
$347$	6.52389	−	8.50210i	0.350221	−	0.456417i	−0.584712	−	0.811241i	$-0.698793\pi$
$347$	6.52389	−	8.50210i	0.350221	−	0.456417i	0.934933	+	0.354824i	$0.115459\pi$
$348$		0			0
$349$	−16.6173	+	12.7509i	−0.889502	+	0.682539i	−0.948860	−	0.315698i	$-0.897761\pi$
$349$	−16.6173	+	12.7509i	−0.889502	+	0.682539i	0.0593575	+	0.998237i	$0.481095\pi$
$350$	5.16351	−	6.20370i	0.276001	−	0.331602i
$351$		0			0
$352$	−0.735302	−	11.5514i	−0.0391917	−	0.615692i
$353$	14.7391	+	8.50962i	0.784483	+	0.452922i	0.838017	−	0.545645i	$-0.183715\pi$
$353$	14.7391	+	8.50962i	0.784483	+	0.452922i	−0.0535337	+	0.998566i	$0.517048\pi$
$354$		0			0
$355$	−16.6882	+	2.19705i	−0.885720	+	0.116607i
$356$	−0.709576	−	0.0563820i	−0.0376074	−	0.00298824i
$357$		0			0
$358$	2.59419	+	0.102903i	0.137107	+	0.00543861i
$359$	−0.817007	+	0.817007i	−0.0431200	+	0.0431200i	−0.728338	−	0.685218i	$-0.759707\pi$
$359$	−0.817007	+	0.817007i	−0.0431200	+	0.0431200i	0.685218	+	0.728338i	$0.259707\pi$
$360$		0			0
$361$	32.1686	+	32.1686i	1.69308	+	1.69308i
$362$	9.52204	+	10.3087i	0.500467	+	0.541811i
$363$		0			0
$364$	−4.01384	+	7.86298i	−0.210382	+	0.412132i
$365$	1.96905	+	14.9564i	0.103065	+	0.782856i
$366$		0			0
$367$	−1.94461	+	3.36816i	−0.101508	+	0.175816i	−0.912306	−	0.409509i	$-0.865700\pi$
$367$	−1.94461	+	3.36816i	−0.101508	+	0.175816i	0.810798	+	0.585326i	$0.199033\pi$
$368$	−25.1641	−	11.2492i	−1.31177	−	0.586404i
$369$		0			0
$370$	−3.63407	+	0.332546i	−0.188926	+	0.0172882i
$371$	0.285631	+	0.372241i	0.0148292	+	0.0193258i
$372$		0			0
$373$	−15.7325	−	12.0720i	−0.814600	−	0.625065i	0.115112	−	0.993353i	$-0.463277\pi$
$373$	−15.7325	−	12.0720i	−0.814600	−	0.625065i	−0.929712	+	0.368288i	$0.879944\pi$
$374$	−6.87419	+	1.55275i	−0.355456	+	0.0802910i
$375$		0			0
$376$	−14.7078	−	24.7852i	−0.758496	−	1.27820i
$377$	3.13772	+	3.13772i	0.161601	+	0.161601i
$378$		0			0
$379$	15.9789	−	6.61869i	0.820783	−	0.339979i	0.0675356	−	0.997717i	$-0.478486\pi$
$379$	15.9789	−	6.61869i	0.820783	−	0.339979i	0.753247	+	0.657737i	$0.228486\pi$
$380$	21.2958	+	7.55927i	1.09245	+	0.387782i
$381$		0			0
$382$	−36.7250	−	6.32473i	−1.87901	−	0.323601i
$383$	14.1781	+	24.5572i	0.724468	+	1.25482i	0.959193	+	0.282753i	$0.0912478\pi$
$383$	14.1781	+	24.5572i	0.724468	+	1.25482i	−0.234725	+	0.972062i	$0.575419\pi$
$384$		0			0
$385$	2.71980	−	4.71083i	0.138614	−	0.240086i
$386$	−16.0736	+	19.3116i	−0.818125	+	0.982936i
$387$		0			0
$388$	4.62585	+	25.0641i	0.234842	+	1.27243i
$389$	−3.41327	+	25.9264i	−0.173060	+	1.31452i	0.655745	+	0.754982i	$0.272355\pi$
$389$	−3.41327	+	25.9264i	−0.173060	+	1.31452i	−0.828805	+	0.559538i	$0.810979\pi$
$390$		0			0
$391$	−4.34364	+	16.2107i	−0.219668	+	0.819810i
$392$	−9.69990	+	0.116031i	−0.489919	+	0.00586044i
$393$		0			0
$394$	4.63496	+	5.01786i	0.233506	+	0.252796i
$395$	0.920026	−	0.381087i	0.0462915	−	0.0191746i
$396$		0			0
$397$	13.7375	−	33.1654i	0.689468	−	1.66452i	−0.0563826	−	0.998409i	$-0.517957\pi$
$397$	13.7375	−	33.1654i	0.689468	−	1.66452i	0.745850	−	0.666113i	$-0.232043\pi$
$398$	−9.83948	+	21.3224i	−0.493209	+	1.06879i
$399$		0			0
$400$	−12.0178	+	1.24484i	−0.600888	+	0.0622420i
$401$	−13.1884	−	22.8429i	−0.658595	−	1.14072i	−0.980980	−	0.194111i	$-0.937818\pi$
$401$	−13.1884	−	22.8429i	−0.658595	−	1.14072i	0.322385	−	0.946609i	$-0.395516\pi$
$402$		0			0
$403$	10.9759	−	8.42211i	0.546749	−	0.419535i
$404$	2.85264	+	4.39992i	0.141924	+	0.218904i
$405$		0			0
$406$	1.50702	−	4.84697i	0.0747923	−	0.240551i
$407$	3.62489	−	0.971286i	0.179679	−	0.0481448i
$408$		0			0
$409$	−30.7010	−	8.22630i	−1.51807	−	0.406764i	−0.598961	−	0.800778i	$-0.704419\pi$
$409$	−30.7010	−	8.22630i	−1.51807	−	0.406764i	−0.919104	+	0.394014i	$0.871086\pi$
$410$	9.35951	−	14.8216i	0.462233	−	0.731985i
$411$		0			0
$412$	−10.2257	−	21.4802i	−0.503783	−	1.05825i
$413$	−4.22534	+	10.2009i	−0.207915	+	0.501952i
$414$		0			0
$415$			16.6235i			0.816013i
$416$	12.5216	−	4.22425i	0.613920	−	0.207111i
$417$		0			0
$418$	−22.9015	−	3.94406i	−1.12015	−	0.192910i
$419$	2.89873	+	22.0180i	0.141612	+	1.07565i	0.903697	+	0.428173i	$0.140843\pi$
$419$	2.89873	+	22.0180i	0.141612	+	1.07565i	−0.762084	+	0.647478i	$0.775824\pi$
$420$		0			0
$421$	−20.7380	−	2.73021i	−1.01071	−	0.133062i	−0.393056	−	0.919515i	$-0.628582\pi$
$421$	−20.7380	−	2.73021i	−1.01071	−	0.133062i	−0.617651	+	0.786452i	$0.711915\pi$
$422$	3.44648	−	1.81162i	0.167772	−	0.0881885i
$423$		0			0
$424$	0.0833386	−	0.697381i	0.00404728	−	0.0338678i
$425$	1.90394	+	7.10559i	0.0923545	+	0.344672i
$426$		0			0
$427$	4.18501	−	5.45402i	0.202527	−	0.263938i
$428$	12.6126	−	24.7077i	0.609655	−	1.19429i
$429$		0			0
$430$	−2.40166	+	5.20444i	−0.115818	+	0.250981i
$431$			25.8563i			1.24545i	0.782439	+	0.622727i	$0.213975\pi$
$431$			25.8563i			1.24545i	−0.782439	+	0.622727i	$0.786025\pi$
$432$		0			0
$433$		−	27.0878i		−	1.30176i	−0.759181	−	0.650879i	$-0.774400\pi$
$433$		−	27.0878i		−	1.30176i	0.759181	−	0.650879i	$-0.225600\pi$
$434$	−14.3692	−	6.63084i	−0.689743	−	0.318291i
$435$		0			0
$436$	−8.73137	−	26.9413i	−0.418157	−	1.29026i
$437$	−33.6889	+	43.9043i	−1.61156	+	2.10023i
$438$		0			0
$439$	1.62046	+	6.04765i	0.0773405	+	0.288639i	0.993754	−	0.111595i	$-0.0355958\pi$
$439$	1.62046	+	6.04765i	0.0773405	+	0.288639i	−0.916413	+	0.400233i	$0.868929\pi$
$440$	−7.83929	+	2.20136i	−0.373724	+	0.104946i
$441$		0			0
$442$	−3.74365	−	7.12201i	−0.178067	−	0.338759i
$443$	2.78748	+	0.366978i	0.132437	+	0.0174357i	0.196453	−	0.980513i	$-0.437058\pi$
$443$	2.78748	+	0.366978i	0.132437	+	0.0174357i	−0.0640162	+	0.997949i	$0.520391\pi$
$444$		0			0
$445$	0.0653595	+	0.496455i	0.00309834	+	0.0235342i
$446$	−4.55631	+	26.4565i	−0.215748	+	1.25275i
$447$		0			0
$448$	−10.9414	−	10.4300i	−0.516933	−	0.492774i
$449$			31.2741i			1.47592i	0.674846	+	0.737959i	$0.264210\pi$
$449$			31.2741i			1.47592i	−0.674846	+	0.737959i	$0.735790\pi$
$450$		0			0
$451$	−6.89848	+	16.6544i	−0.324837	+	0.784225i
$452$	−2.88817	−	1.02520i	−0.135848	−	0.0482214i
$453$		0			0
$454$	14.0985	+	8.90289i	0.661674	+	0.417833i
$455$	5.99877	+	1.60737i	0.281227	+	0.0753545i
$456$		0			0
$457$	−9.71728	+	2.60374i	−0.454555	+	0.121798i	−0.478830	−	0.877908i	$-0.658939\pi$
$457$	−9.71728	+	2.60374i	−0.454555	+	0.121798i	0.0242748	+	0.999705i	$0.492272\pi$
$458$	0.0717506	+	0.0223088i	0.00335269	+	0.00104242i
$459$		0			0
$460$	−4.04578	+	18.9637i	−0.188635	+	0.884188i
$461$	−18.6488	+	14.3097i	−0.868559	+	0.666469i	−0.943735	−	0.330701i	$-0.892715\pi$
$461$	−18.6488	+	14.3097i	−0.868559	+	0.666469i	0.0751762	+	0.997170i	$0.476048\pi$
$462$		0			0
$463$	−5.92320	−	10.2593i	−0.275274	−	0.476789i	0.694930	−	0.719077i	$-0.255435\pi$
$463$	−5.92320	−	10.2593i	−0.275274	−	0.476789i	−0.970204	+	0.242288i	$0.922102\pi$
$464$	−6.68271	+	3.61541i	−0.310237	+	0.167841i
$465$		0			0
$466$	−21.1321	−	9.75168i	−0.978927	−	0.451738i
$467$	1.37856	−	3.32815i	0.0637923	−	0.154008i	−0.888769	−	0.458356i	$-0.848438\pi$
$467$	1.37856	−	3.32815i	0.0637923	−	0.154008i	0.952561	+	0.304348i	$0.0984385\pi$
$468$		0			0
$469$	10.7438	−	4.45021i	0.496101	−	0.205492i
$470$	−14.8931	+	13.7567i	−0.686969	+	0.634548i
$471$		0			0
$472$	15.1929	−	6.50708i	0.699309	−	0.299513i
$473$	1.52559	−	5.69359i	0.0701468	−	0.261791i
$474$		0			0
$475$	−3.16618	+	24.0496i	−0.145274	+	1.10347i
$476$	−5.21869	+	7.58102i	−0.239198	+	0.347476i
$477$		0			0
$478$	31.4604	+	26.1854i	1.43897	+	1.19769i
$479$	12.0894	−	20.9395i	0.552381	−	0.956752i	−0.445721	−	0.895172i	$-0.647053\pi$
$479$	12.0894	−	20.9395i	0.552381	−	0.956752i	0.998102	−	0.0615801i	$-0.0196140\pi$
$480$		0			0
$481$	2.14226	+	3.71050i	0.0976786	+	0.169184i
$482$	2.79855	−	16.2500i	0.127470	−	0.740165i
$483$		0			0
$484$	−12.3035	+	5.85712i	−0.559251	+	0.266233i
$485$	16.5648	−	6.86136i	0.752168	−	0.311558i
$486$		0			0
$487$	−5.63800	−	5.63800i	−0.255482	−	0.255482i	0.567732	−	0.823214i	$-0.307821\pi$
$487$	−5.63800	−	5.63800i	−0.255482	−	0.255482i	−0.823214	+	0.567732i	$0.807821\pi$
$488$	−10.1858	+	1.46513i	−0.461089	+	0.0663235i
$489$		0			0
$490$	1.50355	+	6.65638i	0.0679236	+	0.300705i
$491$	−7.11189	−	5.45714i	−0.320955	−	0.246277i	0.435700	−	0.900092i	$-0.356501\pi$
$491$	−7.11189	−	5.45714i	−0.320955	−	0.246277i	−0.756655	+	0.653815i	$0.773168\pi$
$492$		0			0
$493$	2.81619	+	3.67013i	0.126835	+	0.165295i
$494$	−2.41773	−	26.4211i	−0.108779	−	1.18874i
$495$		0			0
$496$	8.45606	+	22.1282i	0.379688	+	0.993587i
$497$	11.3029	−	19.5772i	0.507004	−	0.878157i
$498$		0			0
$499$	2.11489	+	16.0642i	0.0946756	+	0.719132i	0.971283	+	0.237926i	$0.0764677\pi$
$499$	2.11489	+	16.0642i	0.0946756	+	0.719132i	−0.876608	+	0.481206i	$0.840199\pi$
$500$	6.95799	+	21.4694i	0.311171	+	0.960142i
$501$		0			0
$502$	−0.255571	+	0.236070i	−0.0114067	+	0.0105363i
$503$	−5.54544	−	5.54544i	−0.247259	−	0.247259i	0.572586	−	0.819845i	$-0.305940\pi$
$503$	−5.54544	−	5.54544i	−0.247259	−	0.247259i	−0.819845	+	0.572586i	$0.805940\pi$
$504$		0			0
$505$	2.60839	−	2.60839i	0.116072	−	0.116072i
$506$	0.790355	−	19.9248i	0.0351355	−	0.885766i
$507$		0			0
$508$	16.3555	+	19.1790i	0.725656	+	0.850930i
$509$	1.19804	−	0.157724i	0.0531020	−	0.00699101i	−0.103928	−	0.994585i	$-0.533141\pi$
$509$	1.19804	−	0.157724i	0.0531020	−	0.00699101i	0.157030	+	0.987594i	$0.449808\pi$
$510$		0			0
$511$	−17.5456	−	10.1300i	−0.776172	−	0.448123i
$512$	0.811799	+	22.6128i	0.0358768	+	0.999356i
$513$		0			0
$514$	−32.0863	−	26.7063i	−1.41527	−	1.17796i
$515$	−13.2772	+	10.1880i	−0.585063	+	0.448935i
$516$		0			0
$517$	12.6924	−	16.5410i	0.558209	−	0.727472i
$518$	2.61679	−	4.14390i	0.114975	−	0.182072i
$519$		0			0
$520$	−4.74411	−	7.99465i	−0.208043	−	0.350589i
$521$	−23.8022	+	23.8022i	−1.04279	+	1.04279i	−0.0437498	+	0.999043i	$0.513930\pi$
$521$	−23.8022	+	23.8022i	−1.04279	+	1.04279i	−0.999043	+	0.0437498i	$0.986070\pi$
$522$		0			0
$523$	5.58541	+	13.4844i	0.244233	+	0.589630i	0.997695	−	0.0678614i	$-0.0216176\pi$
$523$	5.58541	+	13.4844i	0.244233	+	0.589630i	−0.753462	+	0.657491i	$0.771618\pi$
$524$	−11.0401	−	9.95560i	−0.482289	−	0.434912i
$525$		0			0
$526$	−6.73493	+	4.75598i	−0.293657	+	0.207371i
$527$	12.4908	−	7.21157i	0.544108	−	0.314141i
$528$		0			0
$529$	−21.2055	−	12.2430i	−0.921979	−	0.532305i
$530$	−0.492022	+	0.0450238i	−0.0213721	+	0.00195571i
$531$		0			0
$532$	−25.4650	+	16.5100i	−1.10405	+	0.715798i
$533$	−20.4049	−	2.68635i	−0.883832	−	0.116359i
$534$		0			0
$535$	−18.8499	−	5.05081i	−0.814951	−	0.218365i
$536$	−16.1608	−	6.46866i	−0.698041	−	0.279403i
$537$		0			0
$538$	0.578541	−	14.5850i	0.0249427	−	0.628804i
$539$	−2.68554	−	6.48346i	−0.115674	−	0.279262i
$540$		0			0
$541$	13.6258	+	5.64398i	0.585818	+	0.242654i	0.655850	−	0.754891i	$-0.272310\pi$
$541$	13.6258	+	5.64398i	0.585818	+	0.242654i	−0.0700324	+	0.997545i	$0.522310\pi$
$542$	14.3294	+	38.8867i	0.615502	+	1.67033i
$543$		0			0
$544$	13.5172	−	2.66231i	0.579544	−	0.114146i
$545$	−17.2537	+	9.96145i	−0.739069	+	0.426702i
$546$		0			0
$547$	−4.60452	−	6.00073i	−0.196875	−	0.256573i	0.684475	−	0.729036i	$-0.260031\pi$
$547$	−4.60452	−	6.00073i	−0.196875	−	0.256573i	−0.881350	+	0.472464i	$0.843365\pi$
$548$	11.7413	+	8.08256i	0.501562	+	0.345270i
$549$		0			0
$550$	−4.06677	−	7.73672i	−0.173408	−	0.329895i
$551$	3.94815	+	14.7347i	0.168197	+	0.627719i
$552$		0			0
$553$	−0.346145	+	1.29183i	−0.0147196	+	0.0549343i
$554$	45.3470	−	10.2431i	1.92661	−	0.435186i
$555$		0			0
$556$	1.98676	+	38.4633i	0.0842575	+	1.63121i
$557$	−30.8241	−	12.7678i	−1.30606	−	0.540988i	−0.382328	−	0.924027i	$-0.624878\pi$
$557$	−30.8241	−	12.7678i	−1.30606	−	0.540988i	−0.923732	+	0.383038i	$0.874878\pi$
$558$		0			0
$559$	6.72967			0.284635
$560$	−5.56979	+	9.05846i	−0.235367	+	0.382790i
$561$		0			0
$562$	−2.96112	−	4.19324i	−0.124907	−	0.176881i
$563$	−3.34318	+	0.440137i	−0.140898	+	0.0185496i	−0.200645	−	0.979664i	$-0.564304\pi$
$563$	−3.34318	+	0.440137i	−0.140898	+	0.0185496i	0.0597472	+	0.998214i	$0.480971\pi$
$564$		0			0
$565$	−0.281408	+	2.13750i	−0.0118389	+	0.0899255i
$566$	13.7670	−	44.2783i	0.578672	−	1.86115i
$567$		0			0
$568$	−32.5784	+	9.14838i	−1.36696	+	0.383858i
$569$	−19.0496	+	5.10434i	−0.798602	+	0.213985i	−0.634970	−	0.772537i	$-0.718988\pi$
$569$	−19.0496	+	5.10434i	−0.798602	+	0.213985i	−0.163632	+	0.986521i	$0.552321\pi$
$570$		0			0
$571$	−10.3555	−	7.94609i	−0.433366	−	0.332533i	0.368933	−	0.929456i	$-0.379723\pi$
$571$	−10.3555	−	7.94609i	−0.433366	−	0.332533i	−0.802299	+	0.596923i	$0.796390\pi$
$572$	6.20324	+	7.27413i	0.259370	+	0.304147i
$573$		0			0
$574$	8.14000	+	22.0900i	0.339757	+	0.922020i
$575$	−20.8144			−0.868021
$576$		0			0
$577$	−7.81056			−0.325158			−0.162579	−	0.986696i	$-0.551981\pi$
$577$	−7.81056			−0.325158			−0.162579	+	0.986696i	$0.551981\pi$
$578$	5.41242	+	14.6880i	0.225127	+	0.610941i
$579$		0			0
$580$	3.46823	+	4.06696i	0.144010	+	0.168872i
$581$	−17.7119	−	13.5908i	−0.734814	−	0.563843i
$582$		0			0
$583$	0.490779	−	0.131504i	0.0203260	−	0.00544633i
$584$	8.19902	+	29.1976i	0.339278	+	1.20821i
$585$		0			0
$586$	4.61305	−	14.8367i	0.190563	−	0.612900i
$587$	3.76407	−	28.5910i	0.155360	−	1.18007i	−0.719075	−	0.694932i	$-0.755434\pi$
$587$	3.76407	−	28.5910i	0.155360	−	1.18007i	0.874435	−	0.485143i	$-0.161232\pi$
$588$		0			0
$589$	47.1531	−	6.20783i	1.94291	−	0.255789i
$590$	−6.70676	−	9.49743i	−0.276113	−	0.391003i
$591$		0			0
$592$	−7.13610	+	1.70187i	−0.293292	+	0.0699466i
$593$	−3.63338			−0.149205			−0.0746025	−	0.997213i	$-0.523769\pi$
$593$	−3.63338			−0.149205			−0.0746025	+	0.997213i	$0.523769\pi$
$594$		0			0
$595$	5.98164	+	2.47767i	0.245223	+	0.101575i
$596$	−1.85769	−	35.9646i	−0.0760941	−	1.47317i
$597$		0			0
$598$	22.2065	−	5.01605i	0.908093	−	0.205121i
$599$	3.81505	−	14.2380i	0.155879	−	0.581748i	−0.843150	−	0.537679i	$-0.819301\pi$
$599$	3.81505	−	14.2380i	0.155879	−	0.581748i	0.999028	−	0.0440689i	$-0.0140321\pi$
$600$		0			0
$601$	−0.791171	−	2.95269i	−0.0322726	−	0.120443i	0.947910	−	0.318537i	$-0.103191\pi$
$601$	−0.791171	−	2.95269i	−0.0322726	−	0.120443i	−0.980183	+	0.198094i	$0.936525\pi$
$602$	−3.58170	−	6.81391i	−0.145979	−	0.277714i
$603$		0			0
$604$	23.3445	+	16.0701i	0.949876	+	0.653884i
$605$	5.83550	+	7.60498i	0.237247	+	0.309186i
$606$		0			0
$607$	36.1165	−	20.8519i	1.46592	−	0.846351i	0.466648	−	0.884443i	$-0.345461\pi$
$607$	36.1165	−	20.8519i	1.46592	−	0.846351i	0.999274	+	0.0380925i	$0.0121282\pi$
$608$	44.5392	+	8.94652i	1.80630	+	0.362829i
$609$		0			0
$610$	2.50304	+	6.79264i	0.101345	+	0.275026i
$611$	21.9918	+	9.10932i	0.889695	+	0.368524i
$612$		0			0
$613$	−2.40339	−	5.80229i	−0.0970720	−	0.234352i	0.867883	−	0.496769i	$-0.165480\pi$
$613$	−2.40339	−	5.80229i	−0.0970720	−	0.234352i	−0.964955	+	0.262417i	$0.915480\pi$
$614$	0.249585	−	6.29202i	0.0100724	−	0.253925i
$615$		0			0
$616$	4.06367	−	10.1524i	0.163730	−	0.409050i
$617$	23.9110	+	6.40693i	0.962620	+	0.257933i	0.705709	−	0.708502i	$-0.250629\pi$
$617$	23.9110	+	6.40693i	0.962620	+	0.257933i	0.256911	+	0.966435i	$0.417295\pi$
$618$		0			0
$619$	29.2836	+	3.85526i	1.17701	+	0.154956i	0.693548	−	0.720411i	$-0.256047\pi$
$619$	29.2836	+	3.85526i	1.17701	+	0.154956i	0.483460	+	0.875367i	$0.339380\pi$
$620$	13.9828	−	9.06559i	0.561563	−	0.364083i
$621$		0			0
$622$	8.99858	−	0.823440i	0.360810	−	0.0330169i
$623$	−0.582398	−	0.336248i	−0.0233333	−	0.0134715i
$624$		0			0
$625$	0.670208	−	0.386945i	0.0268083	−	0.0154778i
$626$	0.817219	−	0.577092i	0.0326626	−	0.0230652i
$627$		0			0
$628$	−11.2154	−	10.1137i	−0.447543	−	0.403580i
$629$	1.70934	+	4.12671i	0.0681557	+	0.164543i
$630$		0			0
$631$	−7.09696	+	7.09696i	−0.282526	+	0.282526i	−0.834115	−	0.551590i	$-0.814021\pi$
$631$	−7.09696	+	7.09696i	−0.282526	+	0.282526i	0.551590	+	0.834115i	$0.314021\pi$
$632$	1.72164	−	1.02164i	0.0684833	−	0.0406387i
$633$		0			0
$634$	−9.82029	+	15.5513i	−0.390014	+	0.617619i
$635$	10.7943	−	14.0674i	0.428358	−	0.558248i
$636$		0			0
$637$	6.35637	−	4.87741i	0.251849	−	0.193250i
$638$	−4.22468	−	3.51632i	−0.167257	−	0.139212i
$639$		0			0
$640$	15.4382	−	3.87756i	0.610249	−	0.153274i
$641$	−31.5504	−	18.2156i	−1.24616	−	0.719473i	−0.275822	−	0.961209i	$-0.588950\pi$
$641$	−31.5504	−	18.2156i	−1.24616	−	0.719473i	−0.970342	+	0.241735i	$0.922283\pi$
$642$		0			0
$643$	2.35622	−	0.310202i	0.0929203	−	0.0122332i	−0.0839227	−	0.996472i	$-0.526745\pi$
$643$	2.35622	−	0.310202i	0.0929203	−	0.0122332i	0.176843	+	0.984239i	$0.443412\pi$
$644$	−16.8977	−	19.8149i	−0.665864	−	0.780815i
$645$		0			0
$646$	1.09631	−	27.6380i	0.0431338	−	1.08740i
$647$	26.9732	−	26.9732i	1.06043	−	1.06043i	0.0623730	−	0.998053i	$-0.480133\pi$
$647$	26.9732	−	26.9732i	1.06043	−	1.06043i	0.998053	−	0.0623730i	$-0.0198668\pi$
$648$		0			0
$649$	8.45456	+	8.45456i	0.331871	+	0.331871i
$650$	7.33032	−	6.77097i	0.287519	−	0.265579i
$651$		0			0
$652$	−8.59365	−	26.5164i	−0.336553	−	1.03846i
$653$	−4.78292	−	36.3299i	−0.187170	−	1.42170i	−0.784711	−	0.619861i	$-0.787189\pi$
$653$	−4.78292	−	36.3299i	−0.187170	−	1.42170i	0.597541	−	0.801838i	$-0.296144\pi$
$654$		0			0
$655$	−5.22889	+	9.05671i	−0.204310	+	0.353875i
$656$	14.3818	−	32.1717i	0.561516	−	1.25610i
$657$		0			0
$658$	−2.48127	−	27.1153i	−0.0967298	−	1.05707i
$659$	5.77717	+	7.52896i	0.225047	+	0.293287i	0.892206	−	0.451628i	$-0.149157\pi$
$659$	5.77717	+	7.52896i	0.225047	+	0.293287i	−0.667159	+	0.744915i	$0.732490\pi$
$660$		0			0
$661$	−25.1285	−	19.2818i	−0.977387	−	0.749975i	−0.00913641	−	0.999958i	$-0.502908\pi$
$661$	−25.1285	−	19.2818i	−0.977387	−	0.749975i	−0.968250	+	0.249983i	$0.919575\pi$
$662$	−4.79916	−	21.2463i	−0.186525	−	0.825763i
$663$		0			0
$664$	4.75802	+	33.0783i	0.184647	+	1.28369i
$665$	15.0963	+	15.0963i	0.585411	+	0.585411i
$666$		0			0
$667$	−12.0931	+	5.00914i	−0.468248	+	0.193955i
$668$	−13.9867	+	6.65841i	−0.541163	+	0.257622i
$669$		0			0
$670$	−2.07832	+	12.0679i	−0.0802924	+	0.466223i
$671$	−3.72224	−	6.44710i	−0.143695	−	0.248888i
$672$		0			0
$673$	−5.21641	+	9.03509i	−0.201078	+	0.348277i	−0.948876	−	0.315649i	$-0.897778\pi$
$673$	−5.21641	+	9.03509i	−0.201078	+	0.348277i	0.747798	+	0.663926i	$0.231111\pi$
$674$	−21.2031	−	17.6479i	−0.816711	−	0.679771i
$675$		0			0
$676$	8.55381	−	12.4258i	0.328993	−	0.477917i
$677$	1.66924	−	12.6791i	0.0641541	−	0.487299i	−0.928963	−	0.370173i	$-0.879299\pi$
$677$	1.66924	−	12.6791i	0.0641541	−	0.487299i	0.993117	−	0.117126i	$-0.0373681\pi$
$678$		0			0
$679$	−6.23225	+	23.2591i	−0.239172	+	0.892601i
$680$	−3.81565	−	8.90888i	−0.146324	−	0.341640i
$681$		0			0
$682$	−12.5885	+	11.6279i	−0.482040	+	0.445257i
$683$	43.1914	−	17.8904i	1.65267	−	0.684559i	0.655189	−	0.755465i	$-0.272589\pi$
$683$	43.1914	−	17.8904i	1.65267	−	0.684559i	0.997483	+	0.0709064i	$0.0225892\pi$
$684$		0			0
$685$	3.83735	−	9.26418i	0.146618	−	0.353966i
$686$	−25.3057	−	11.6776i	−0.966177	−	0.445854i
$687$		0			0
$688$	−3.28932	+	11.0435i	−0.125404	+	0.421030i
$689$	0.290044	+	0.502370i	0.0110498	+	0.0191388i
$690$		0			0
$691$	23.2193	−	17.8168i	0.883305	−	0.677784i	−0.0640578	−	0.997946i	$-0.520404\pi$
$691$	23.2193	−	17.8168i	0.883305	−	0.677784i	0.947363	+	0.320163i	$0.103738\pi$
$692$	−5.74946	+	26.9494i	−0.218562	+	1.02446i
$693$		0			0
$694$	−14.4723	−	4.49972i	−0.549359	−	0.170807i
$695$	26.1707	−	7.01241i	0.992710	−	0.265996i
$696$		0			0
$697$	−20.7250	−	5.55325i	−0.785016	−	0.210344i
$698$	25.0458	+	15.8159i	0.947999	+	0.598642i
$699$		0			0
$700$	−10.7571	−	3.81840i	−0.406581	−	0.144322i
$701$	10.7323	−	25.9101i	0.405354	−	0.978611i	−0.580990	−	0.813911i	$-0.697334\pi$
$701$	10.7323	−	25.9101i	0.405354	−	0.978611i	0.986344	−	0.164700i	$-0.0526655\pi$
$702$		0			0
$703$			14.7289i			0.555511i
$704$	−14.9690	+	6.62419i	−0.564166	+	0.249659i
$705$		0			0
$706$	4.08497	−	23.7197i	0.153740	−	0.892701i
$707$	0.646640	+	4.91172i	0.0243194	+	0.184724i
$708$		0			0
$709$	−36.0201	−	4.74214i	−1.35276	−	0.178095i	−0.580948	−	0.813941i	$-0.697318\pi$
$709$	−36.0201	−	4.74214i	−1.35276	−	0.178095i	−0.771816	+	0.635846i	$0.780651\pi$
$710$	11.0757	+	21.0708i	0.415665	+	0.790771i
$711$		0			0
$712$	0.272153	+	0.969168i	0.0101994	+	0.0363211i
$713$	10.5624	+	39.4195i	0.395566	+	1.47627i
$714$		0			0
$715$	4.09402	−	5.33543i	0.153108	−	0.199534i
$716$	−1.13197	−	3.49277i	−0.0423036	−	0.130531i
$717$		0			0
$718$	1.48366	+	0.684654i	0.0553697	+	0.0255511i
$719$		−	7.09333i		−	0.264536i	−0.991214	−	0.132268i	$-0.957774\pi$
$719$		−	7.09333i		−	0.264536i	0.991214	−	0.132268i	$-0.0422260\pi$
$720$		0			0
$721$		−	22.4759i		−	0.837047i
$722$	26.9574	−	58.4172i	1.00325	−	2.17406i
$723$		0			0
$724$	9.02333	−	17.6764i	0.335349	−	0.656938i
$725$	−3.49276	+	4.55185i	−0.129718	+	0.169052i
$726$		0			0
$727$	6.69956	+	25.0031i	0.248473	+	0.927313i	0.971606	+	0.236605i	$0.0760346\pi$
$727$	6.69956	+	25.0031i	0.248473	+	0.927313i	−0.723133	+	0.690709i	$0.757299\pi$
$728$	12.3968	+	1.48144i	0.459455	+	0.0549059i
$729$		0			0
$730$	18.8842	−	9.92638i	0.698935	−	0.367392i
$731$	6.95582	+	0.915751i	0.257270	+	0.0338703i
$732$		0			0
$733$	3.03813	+	23.0769i	0.112216	+	0.852364i	0.951279	+	0.308330i	$0.0997702\pi$
$733$	3.03813	+	23.0769i	0.112216	+	0.852364i	−0.839064	+	0.544033i	$0.816896\pi$
$734$	5.42038	+	0.933491i	0.200070	+	0.0344558i
$735$		0			0
$736$	−2.62266	+	38.8931i	−0.0966726	+	1.43362i
$737$		−	12.5929i		−	0.463865i
$738$		0			0
$739$	−11.4867	+	27.7313i	−0.422544	+	1.02011i	0.559051	+	0.829133i	$0.311166\pi$
$739$	−11.4867	+	27.7313i	−0.422544	+	1.02011i	−0.981594	+	0.190977i	$0.938834\pi$
$740$	2.21829	+	4.65975i	0.0815458	+	0.171296i
$741$		0			0
$742$	0.354290	−	0.561049i	0.0130064	−	0.0205967i
$743$	42.1135	+	11.2843i	1.54500	+	0.413980i	0.927876	−	0.372889i	$-0.121633\pi$
$743$	42.1135	+	11.2843i	1.54500	+	0.413980i	0.617119	+	0.786870i	$0.288300\pi$
$744$		0			0
$745$	−24.4705	+	6.55685i	−0.896530	+	0.240225i
$746$	−8.32643	+	26.7799i	−0.304852	+	0.980482i
$747$		0			0
$748$	5.42186	+	8.36269i	0.198243	+	0.305770i
$749$	20.7926	−	15.9547i	0.759745	−	0.582973i
$750$		0			0
$751$	−17.2507	−	29.8791i	−0.629486	−	1.09030i	−0.987655	−	0.156645i	$-0.949932\pi$
$751$	−17.2507	−	29.8791i	−0.629486	−	1.09030i	0.358169	−	0.933657i	$-0.383401\pi$
$752$	−25.6977	+	31.6366i	−0.937100	+	1.15367i
$753$		0			0
$754$	2.62942	−	5.69801i	0.0957577	−	0.207509i
$755$	7.62960	−	18.4195i	0.277670	−	0.670354i
$756$		0			0
$757$	−22.0802	+	9.14594i	−0.802520	+	0.332415i	−0.745965	−	0.665985i	$-0.768012\pi$
$757$	−22.0802	+	9.14594i	−0.802520	+	0.332415i	−0.0565548	+	0.998399i	$0.518012\pi$
$758$	−16.5964	−	17.9674i	−0.602807	−	0.652605i
$759$		0			0
$760$	−0.382255	−	31.9556i	−0.0138658	−	1.15915i
$761$	8.69339	−	32.4442i	0.315135	−	1.17610i	−0.608728	−	0.793379i	$-0.708320\pi$
$761$	8.69339	−	32.4442i	0.315135	−	1.17610i	0.923864	−	0.382722i	$-0.125013\pi$
$762$		0			0
$763$	3.49243	−	26.5277i	0.126435	−	0.960366i
$764$	9.56511	+	51.8263i	0.346054	+	1.87501i
$765$		0			0
$766$	25.6542	−	30.8223i	0.926925	−	1.11365i
$767$	−6.82539	+	11.8219i	−0.246451	+	0.426865i
$768$		0			0
$769$	−7.39426	−	12.8072i	−0.266644	−	0.461841i	0.701349	−	0.712818i	$-0.252581\pi$
$769$	−7.39426	−	12.8072i	−0.266644	−	0.461841i	−0.967993	+	0.250977i	$0.919248\pi$
$770$	−7.58116	−	1.30562i	−0.273206	−	0.0470512i
$771$		0			0
$772$	33.4860	+	11.8864i	1.20519	+	0.427800i
$773$	−21.4021	+	8.86506i	−0.769781	+	0.318854i	−0.732784	−	0.680461i	$-0.761779\pi$
$773$	−21.4021	+	8.86506i	−0.769781	+	0.318854i	−0.0369976	+	0.999315i	$0.511779\pi$
$774$		0			0
$775$	12.6489	+	12.6489i	0.454360	+	0.454360i
$776$	30.9977	−	18.3944i	1.11275	−	0.660319i
$777$		0			0
$778$	36.0730	−	8.14823i	1.29328	−	0.292128i
$779$	−56.1306	−	43.0705i	−2.01109	−	1.54316i
$780$		0			0
$781$	−14.9022	−	19.4210i	−0.533243	−	0.694936i
$782$	23.6354	−	2.16282i	0.845199	−	0.0773423i
$783$		0			0
$784$	4.89707	+	12.8149i	0.174895	+	0.457675i
$785$	−5.31192	+	9.20051i	−0.189591	+	0.328380i
$786$		0			0
$787$	3.95176	+	30.0166i	0.140865	+	1.06998i	0.905149	+	0.425095i	$0.139759\pi$
$787$	3.95176	+	30.0166i	0.140865	+	1.06998i	−0.764284	+	0.644880i	$0.776907\pi$
$788$	4.39221	−	8.60419i	0.156466	−	0.306511i
$789$		0			0
$790$	−0.955576	−	1.03452i	−0.0339979	−	0.0368064i
$791$	−2.04739	−	2.04739i	−0.0727969	−	0.0727969i
$792$		0			0
$793$	6.00994	−	6.00994i	0.213419	−	0.213419i
$794$	−50.7275	−	2.01220i	−1.80025	−	0.0714103i
$795$		0			0
$796$	33.1059	+	2.63055i	1.17341	+	0.0932374i
$797$	−23.7635	+	3.12852i	−0.841745	+	0.110818i	−0.539054	−	0.842271i	$-0.681218\pi$
$797$	−23.7635	+	3.12852i	−0.841745	+	0.110818i	−0.302691	+	0.953089i	$0.597885\pi$
$798$		0			0
$799$	21.4913	+	12.4080i	0.760308	+	0.438964i
$800$	7.52839	+	15.3387i	0.266169	+	0.542305i
$801$		0			0
$802$	−23.8633	+	28.6706i	−0.842643	+	1.01239i
$803$	−17.4056	+	13.3558i	−0.614229	+	0.471315i
$804$		0			0
$805$	−11.1522	+	14.5338i	−0.393063	+	0.512249i
$806$	−16.5431	−	10.4466i	−0.582705	−	0.367966i
$807$		0			0
$808$	4.44374	−	5.93691i	0.156330	−	0.208860i
$809$	22.2499	−	22.2499i	0.782266	−	0.782266i	−0.197947	−	0.980213i	$-0.563427\pi$
$809$	22.2499	−	22.2499i	0.782266	−	0.782266i	0.980213	+	0.197947i	$0.0634273\pi$
$810$		0			0
$811$	4.32863	+	10.4502i	0.151999	+	0.366957i	0.981477	−	0.191582i	$-0.0613619\pi$
$811$	4.32863	+	10.4502i	0.151999	+	0.366957i	−0.829478	+	0.558540i	$0.811362\pi$
$812$	−7.16878	+	0.370292i	−0.251575	+	0.0129947i
$813$		0			0
$814$	−3.06140	−	4.33523i	−0.107302	−	0.151950i
$815$	−16.9816	+	9.80434i	−0.594840	+	0.343431i
$816$		0			0
$817$	20.0351	+	11.5673i	0.700941	+	0.404688i
$818$	4.09610	+	44.7623i	0.143217	+	1.56508i
$819$		0			0
$820$	−24.2447	−	5.17243i	−0.846661	−	0.180629i
$821$	−2.77656	−	0.365542i	−0.0969028	−	0.0127575i	0.0819188	−	0.996639i	$-0.473895\pi$
$821$	−2.77656	−	0.365542i	−0.0969028	−	0.0127575i	−0.178822	+	0.983882i	$0.557229\pi$
$822$		0			0
$823$	1.28354	+	0.343922i	0.0447412	+	0.0119884i	0.281120	−	0.959673i	$-0.409294\pi$
$823$	1.28354	+	0.343922i	0.0447412	+	0.0119884i	−0.236379	+	0.971661i	$0.575961\pi$
$824$	−23.5037	+	24.0728i	−0.818790	+	0.838616i
$825$		0			0
$826$	15.6025	+	0.618904i	0.542882	+	0.0215344i
$827$	10.4122	+	25.1373i	0.362068	+	0.874109i	0.994998	+	0.0998998i	$0.0318522\pi$
$827$	10.4122	+	25.1373i	0.362068	+	0.874109i	−0.632930	+	0.774209i	$0.718148\pi$
$828$		0			0
$829$	−4.97111	−	2.05910i	−0.172654	−	0.0715156i	0.294682	−	0.955595i	$-0.404786\pi$
$829$	−4.97111	−	2.05910i	−0.172654	−	0.0715156i	−0.467336	+	0.884080i	$0.654786\pi$
$830$	22.0591	−	8.12861i	0.765683	−	0.282148i
$831$		0			0
$832$	−11.7284	−	14.5504i	−0.406608	−	0.504443i
$833$	7.23368	−	4.17637i	0.250632	−	0.144703i
$834$		0			0
$835$	6.63384	+	8.64539i	0.229574	+	0.299186i
$836$	5.96474	+	32.3185i	0.206295	+	1.11776i
$837$		0			0
$838$	27.8002	−	14.6130i	0.960342	−	0.504799i
$839$	−11.8082	−	44.0688i	−0.407664	−	1.52142i	−0.799089	−	0.601213i	$-0.794684\pi$
$839$	−11.8082	−	44.0688i	−0.407664	−	1.52142i	0.391425	−	0.920210i	$-0.371982\pi$
$840$		0			0
$841$	6.57190	−	24.5267i	0.226617	−	0.845748i
$842$	6.51759	+	28.8540i	0.224611	+	0.994376i
$843$		0			0
$844$	−4.08928	−	3.68757i	−0.140759	−	0.126932i
$845$	−9.80433	−	4.06109i	−0.337279	−	0.139706i
$846$		0			0
$847$	−12.8739			−0.442351
$848$	−0.966167	+	0.230419i	−0.0331783	+	0.00791263i
$849$		0			0
$850$	8.49803	−	6.00102i	0.291480	−	0.205833i
$851$	−12.5304	+	1.64966i	−0.429536	+	0.0565495i
$852$		0			0
$853$	−0.849458	+	6.45227i	−0.0290849	+	0.220922i	−0.999815	−	0.0192528i	$-0.993871\pi$
$853$	−0.849458	+	6.45227i	−0.0290849	+	0.220922i	0.970730	+	0.240174i	$0.0772046\pi$
$854$	−9.28382	−	2.88653i	−0.317686	−	0.0987751i
$855$		0			0
$856$	−38.9542	−	4.65512i	−1.33143	−	0.159109i
$857$	−7.49146	+	2.00733i	−0.255903	+	0.0685691i	−0.384490	−	0.923129i	$-0.625623\pi$
$857$	−7.49146	+	2.00733i	−0.255903	+	0.0685691i	0.128586	+	0.991698i	$0.458956\pi$
$858$		0			0
$859$	−38.4937	−	29.5372i	−1.31339	−	1.00780i	−0.998273	−	0.0587440i	$-0.981290\pi$
$859$	−38.4937	−	29.5372i	−1.31339	−	1.00780i	−0.315114	−	0.949054i	$-0.602043\pi$
$860$	8.08060	+	0.642074i	0.275546	+	0.0218946i
$861$		0			0
$862$	34.3110	−	12.6433i	1.16864	−	0.430633i
$863$	1.63134			0.0555313			0.0277657	−	0.999614i	$-0.491161\pi$
$863$	1.63134			0.0555313			0.0277657	+	0.999614i	$0.491161\pi$
$864$		0			0
$865$	19.3847			0.659100
$866$	−35.9452	+	13.2455i	−1.22147	+	0.450101i
$867$		0			0
$868$	−1.77273	+	22.3101i	−0.0601705	+	0.757255i
$869$	1.14898	+	0.881645i	0.0389765	+	0.0299077i
$870$		0			0
$871$	13.8874	−	3.72111i	0.470556	−	0.126085i
$872$	−31.4813	+	24.7603i	−1.06609	+	0.838489i
$873$		0			0
$874$	74.7338	+	23.2363i	2.52791	+	0.785979i
$875$	−2.78310	+	21.1398i	−0.0940861	+	0.714655i
$876$		0			0
$877$	10.3125	−	1.35766i	0.348227	−	0.0458450i	0.0456159	−	0.998959i	$-0.485475\pi$
$877$	10.3125	−	1.35766i	0.348227	−	0.0458450i	0.302611	+	0.953114i	$0.402142\pi$
$878$	7.23277	−	5.10754i	0.244094	−	0.172371i
$879$		0			0
$880$	6.75447	+	9.32621i	0.227693	+	0.314386i
$881$	−27.9243			−0.940795			−0.470397	−	0.882455i	$-0.655889\pi$
$881$	−27.9243			−0.940795			−0.470397	+	0.882455i	$0.655889\pi$
$882$		0			0
$883$	−43.4627	−	18.0028i	−1.46264	−	0.605843i	−0.497469	−	0.867482i	$-0.665737\pi$
$883$	−43.4627	−	18.0028i	−1.46264	−	0.605843i	−0.965166	+	0.261638i	$0.915737\pi$
$884$	−7.62022	+	8.45032i	−0.256296	+	0.284215i
$885$		0			0
$886$	−0.876057	−	3.87839i	−0.0294317	−	0.130297i
$887$	1.55524	−	5.80423i	0.0522198	−	0.194887i	−0.934888	−	0.354942i	$-0.884501\pi$
$887$	1.55524	−	5.80423i	0.0522198	−	0.194887i	0.987108	+	0.160055i	$0.0511672\pi$
$888$		0			0
$889$	6.16341	+	23.0022i	0.206714	+	0.771468i
$890$	0.626829	−	0.329490i	0.0210114	−	0.0110445i
$891$		0			0
$892$	37.3354	−	6.89067i	1.25008	−	0.230717i
$893$	49.8152	+	64.9204i	1.66700	+	2.17248i
$894$		0			0
$895$	−2.23684	+	1.29144i	−0.0747693	+	0.0431681i
$896$	−8.49036	+	19.6192i	−0.283643	+	0.655433i
$897$		0			0
$898$	41.5004	−	15.2926i	1.38489	−	0.510319i
$899$	10.3930	+	4.30492i	0.346625	+	0.143577i
$900$		0			0
$901$	0.231430	+	0.558721i	0.00771004	+	0.0186137i
$902$	25.4734	+	1.01045i	0.848172	+	0.0336443i
$903$		0			0
$904$	0.0518421	+	4.33388i	0.00172424	+	0.144143i
$905$	−13.4856	−	3.61345i	−0.448275	−	0.120115i
$906$		0			0
$907$	−30.6906	−	4.04050i	−1.01907	−	0.134162i	−0.397563	−	0.917575i	$-0.630144\pi$
$907$	−30.6906	−	4.04050i	−1.01907	−	0.134162i	−0.621502	+	0.783412i	$0.713477\pi$
$908$	4.92009	−	23.0619i	0.163279	−	0.765335i
$909$		0			0
$910$	−0.800352	−	8.74627i	−0.0265314	−	0.289936i
$911$	11.0798	+	6.39693i	0.367090	+	0.211940i	0.672186	−	0.740382i	$-0.265355\pi$
$911$	11.0798	+	6.39693i	0.367090	+	0.211940i	−0.305096	+	0.952322i	$0.598689\pi$
$912$		0			0
$913$	−20.9370	+	12.0880i	−0.692912	+	0.400053i
$914$	8.20673	+	11.6215i	0.271454	+	0.384406i
$915$		0			0
$916$	−0.00548150	−	0.106121i	−0.000181114	−	0.00350633i
$917$	−5.37474	−	12.9758i	−0.177489	−	0.428497i
$918$		0			0
$919$	15.3396	−	15.3396i	0.506006	−	0.506006i	−0.407292	−	0.913298i	$-0.633527\pi$
$919$	15.3396	−	15.3396i	0.506006	−	0.506006i	0.913298	+	0.407292i	$0.133527\pi$
$920$	27.1429	−	3.90427i	0.894876	−	0.128720i
$921$		0			0
$922$	28.1077	+	17.7494i	0.925679	+	0.584547i
$923$	17.0138	−	22.1729i	0.560017	−	0.729829i
$924$		0			0
$925$	−4.39502	+	3.37242i	−0.144507	+	0.110884i
$926$	−10.7176	+	12.8766i	−0.352202	+	0.423152i
$927$		0			0
$928$	8.06534	+	7.10000i	0.264758	+	0.233069i
$929$	−25.1555	−	14.5235i	−0.825324	−	0.476501i	0.0269247	−	0.999637i	$-0.491429\pi$
$929$	−25.1555	−	14.5235i	−0.825324	−	0.476501i	−0.852249	+	0.523136i	$0.824762\pi$
$930$		0			0
$931$	27.3073	−	3.59508i	0.894962	−	0.117824i
$932$	−2.60708	+	32.8105i	−0.0853977	+	1.07474i
$933$		0			0
$934$	−5.09050	−	0.201924i	−0.166566	−	0.00660716i
$935$	4.95762	−	4.95762i	0.162132	−	0.162132i
$936$		0			0
$937$	−12.3300	−	12.3300i	−0.402803	−	0.402803i	0.476416	−	0.879220i	$-0.341936\pi$
$937$	−12.3300	−	12.3300i	−0.402803	−	0.402803i	−0.879220	+	0.476416i	$0.841936\pi$
$938$	−11.1589	−	12.0807i	−0.364351	−	0.394450i
$939$		0			0
$940$	25.5374	+	13.0362i	0.832940	+	0.425194i
$941$	−2.90717	−	22.0821i	−0.0947710	−	0.719857i	−0.971190	−	0.238307i	$-0.923407\pi$
$941$	−2.90717	−	22.0821i	−0.0947710	−	0.719857i	0.876419	−	0.481550i	$-0.159926\pi$
$942$		0			0
$943$	30.3549	−	52.5762i	0.988492	−	1.71212i
$944$	−16.0639	−	16.9789i	−0.522835	−	0.552616i
$945$		0			0
$946$	−8.30131	+	0.759634i	−0.269899	+	0.0246978i
$947$	−8.67334	−	11.3033i	−0.281846	−	0.367308i	0.630881	−	0.775880i	$-0.282694\pi$
$947$	−8.67334	−	11.3033i	−0.281846	−	0.367308i	−0.912726	+	0.408571i	$0.866027\pi$
$948$		0			0
$949$	−19.8719	−	15.2483i	−0.645070	−	0.494979i
$950$	33.4617	−	7.55837i	1.08564	−	0.245226i
$951$		0			0
$952$	12.6118	+	3.21814i	0.408750	+	0.104300i
$953$	14.1164	+	14.1164i	0.457276	+	0.457276i	0.897760	−	0.440484i	$-0.145193\pi$
$953$	14.1164	+	14.1164i	0.457276	+	0.457276i	−0.440484	+	0.897760i	$0.645193\pi$
$954$		0			0
$955$	34.2519	−	14.1876i	1.10837	−	0.459100i
$956$	19.3640	−	54.5518i	0.626277	−	1.76433i
$957$		0			0
$958$	−33.6980	−	5.80343i	−1.08873	−	0.187500i
$959$	6.73348	+	11.6627i	0.217435	+	0.376609i
$960$		0			0
$961$	2.03637	−	3.52709i	0.0656893	−	0.113777i
$962$	3.87626	−	4.65713i	0.124976	−	0.150152i
$963$		0			0
$964$	−22.9319	+	4.23234i	−0.738588	+	0.136314i
$965$	3.26269	−	24.7826i	0.105030	−	0.797781i
$966$		0			0
$967$	−14.5828	+	54.4238i	−0.468951	+	1.75015i	0.174494	+	0.984658i	$0.444171\pi$
$967$	−14.5828	+	54.4238i	−0.468951	+	1.75015i	−0.643445	+	0.765492i	$0.722496\pi$
$968$	13.7885	+	13.4626i	0.443181	+	0.432703i
$969$		0			0
$970$	−17.2049	−	18.6262i	−0.552415	−	0.598050i
$971$	−30.1234	+	12.4775i	−0.966706	+	0.400423i	−0.809485	−	0.587141i	$-0.800253\pi$
$971$	−30.1234	+	12.4775i	−0.966706	+	0.400423i	−0.157221	+	0.987563i	$0.550253\pi$
$972$		0			0
$973$	−13.9248	+	33.6174i	−0.446408	+	1.07772i
$974$	−4.72466	+	10.2384i	−0.151388	+	0.328061i
$975$		0			0
$976$	6.92490	+	12.8000i	0.221661	+	0.409717i
$977$	−22.7901	−	39.4736i	−0.729119	−	1.26287i	−0.957256	−	0.289242i	$-0.906597\pi$
$977$	−22.7901	−	39.4736i	−0.729119	−	1.26287i	0.228137	−	0.973629i	$-0.426737\pi$
$978$		0			0
$979$	−0.577750	+	0.443323i	−0.0184650	+	0.0141687i
$980$	8.09772	−	5.25006i	0.258672	−	0.167707i
$981$		0			0
$982$	−3.76396	+	12.1058i	−0.120113	+	0.386313i
$983$	26.5342	−	7.10983i	0.846311	−	0.226768i	0.190494	−	0.981688i	$-0.438991\pi$
$983$	26.5342	−	7.10983i	0.846311	−	0.226768i	0.655817	+	0.754920i	$0.272324\pi$
$984$		0			0
$985$	−6.56425	−	1.75889i	−0.209154	−	0.0560428i
$986$	3.49315	−	5.53169i	0.111244	−	0.176165i
$987$		0			0
$988$	−33.8782	+	16.1278i	−1.07781	+	0.513093i
$989$	−7.59674	+	18.3401i	−0.241562	+	0.583183i
$990$		0			0
$991$			13.4151i			0.426145i	0.977036	+	0.213073i	$0.0683471\pi$
$991$			13.4151i			0.426145i	−0.977036	+	0.213073i	$0.931653\pi$
$992$	25.2290	−	22.0414i	0.801022	−	0.699816i
$993$		0			0
$994$	−31.5056	−	5.42586i	−0.999298	−	0.172098i
$995$	−3.04941	−	23.1626i	−0.0966727	−	0.734302i
$996$		0			0
$997$	46.7347	+	6.15274i	1.48010	+	0.194859i	0.826911	−	0.562333i	$-0.190096\pi$
$997$	46.7347	+	6.15274i	1.48010	+	0.194859i	0.653192	+	0.757192i	$0.273429\pi$
$998$	20.2828	−	10.6616i	0.642042	−	0.337486i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.bn.a.35.17		368
3.2	odd	2		288.2.bf.a.227.30	yes	368
9.4	even	3		288.2.bf.a.131.44	yes	368
9.5	odd	6	inner	864.2.bn.a.611.3		368
32.11	odd	8	inner	864.2.bn.a.683.3		368
96.11	even	8		288.2.bf.a.11.44	✓	368
288.139	odd	24		288.2.bf.a.203.30	yes	368
288.203	even	24	inner	864.2.bn.a.395.17		368

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.bf.a.11.44	✓	368	96.11	even	8
288.2.bf.a.131.44	yes	368	9.4	even	3
288.2.bf.a.203.30	yes	368	288.139	odd	24
288.2.bf.a.227.30	yes	368	3.2	odd	2
864.2.bn.a.35.17		368	1.1	even	1	trivial
864.2.bn.a.395.17		368	288.203	even	24	inner
864.2.bn.a.611.3		368	9.5	odd	6	inner
864.2.bn.a.683.3		368	32.11	odd	8	inner

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:	\( N \)	\(=\)	\( 864 = 2^{5} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	864.bn (of order \(24\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.488984 - 1.32699i) q^{2} +(-1.52179 + 1.29775i) q^{4} +(1.11620 + 0.856491i) q^{5} +(-1.82515 + 0.489046i) q^{7} +(2.46623 + 1.38481i) q^{8} +O(q^{10})\)	\(q+(-0.488984 - 1.32699i) q^{2} +(-1.52179 + 1.29775i) q^{4} +(1.11620 + 0.856491i) q^{5} +(-1.82515 + 0.489046i) q^{7} +(2.46623 + 1.38481i) q^{8} +(0.590748 - 1.90000i) q^{10} +(-0.267076 + 2.02865i) q^{11} +(-2.31610 + 0.304921i) q^{13} +(1.54143 + 2.18281i) q^{14} +(0.631682 - 3.94981i) q^{16} -2.43543 q^{17} +(-7.41946 - 3.07324i) q^{19} +(-2.81014 + 0.145153i) q^{20} +(2.82258 - 0.637569i) q^{22} +(1.78352 - 6.65621i) q^{23} +(-0.781767 - 2.91760i) q^{25} +(1.53716 + 2.92434i) q^{26} +(2.14282 - 3.11281i) q^{28} +(-1.15634 - 1.50698i) q^{29} +(-5.12880 + 2.96111i) q^{31} +(-5.55023 + 1.09316i) q^{32} +(1.19089 + 3.23178i) q^{34} +(-2.45609 - 1.01735i) q^{35} +(-0.701864 - 1.69445i) q^{37} +(-0.450151 + 11.3483i) q^{38} +(1.56673 + 3.65804i) q^{40} +(8.50981 + 2.28020i) q^{41} +(-2.85610 - 0.376012i) q^{43} +(-2.22624 - 3.43377i) q^{44} +(-9.70481 + 0.888066i) q^{46} +(-8.82446 - 5.09480i) q^{47} +(-2.97019 + 1.71484i) q^{49} +(-3.48934 + 2.46405i) q^{50} +(3.12891 - 3.46975i) q^{52} +(-0.0950263 - 0.229414i) q^{53} +(-2.03563 + 2.03563i) q^{55} +(-5.17847 - 1.32139i) q^{56} +(-1.43431 + 2.27134i) q^{58} +(3.55726 - 4.63591i) q^{59} +(-2.88644 + 2.21485i) q^{61} +(6.43726 + 5.35791i) q^{62} +(4.16458 + 6.83054i) q^{64} +(-2.84640 - 1.64337i) q^{65} +(-6.10177 + 0.803313i) q^{67} +(3.70621 - 3.16058i) q^{68} +(-0.149015 + 3.75667i) q^{70} +(-8.45963 + 8.45963i) q^{71} +(7.58174 + 7.58174i) q^{73} +(-1.90531 + 1.75992i) q^{74} +(15.2792 - 4.95180i) q^{76} +(-0.504648 - 3.83319i) q^{77} +(0.353898 - 0.612970i) q^{79} +(4.08806 - 3.86775i) q^{80} +(-1.13537 - 12.4074i) q^{82} +(7.19271 + 9.37372i) q^{83} +(-2.71843 - 2.08592i) q^{85} +(0.897624 + 3.97387i) q^{86} +(-3.46797 + 4.63326i) q^{88} +(0.251664 + 0.251664i) q^{89} +(4.07810 - 1.68920i) q^{91} +(5.92395 + 12.4439i) q^{92} +(-2.44572 + 14.2012i) q^{94} +(-5.64941 - 9.78506i) q^{95} +(6.37184 - 11.0363i) q^{97} +(3.72795 + 3.10287i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 368 q + 12 q^{2} - 4 q^{4} + 12 q^{5} - 4 q^{7}+O(q^{10}) \) 368 * q + 12 * q^2 - 4 * q^4 + 12 * q^5 - 4 * q^7	\( 368 q + 12 q^{2} - 4 q^{4} + 12 q^{5} - 4 q^{7} - 16 q^{10} + 12 q^{11} - 4 q^{13} + 12 q^{14} - 4 q^{16} - 16 q^{19} + 12 q^{20} - 4 q^{22} + 12 q^{23} - 4 q^{25} - 16 q^{28} + 12 q^{29} + 12 q^{32} - 12 q^{34} - 16 q^{37} + 12 q^{38} - 4 q^{40} + 12 q^{41} - 4 q^{43} - 16 q^{46} + 24 q^{47} + 168 q^{50} - 4 q^{52} - 16 q^{55} + 12 q^{56} + 32 q^{58} + 12 q^{59} - 4 q^{61} - 16 q^{64} + 24 q^{65} - 4 q^{67} + 60 q^{68} - 4 q^{70} - 16 q^{73} + 12 q^{74} - 28 q^{76} + 12 q^{77} - 8 q^{79} - 16 q^{82} + 132 q^{83} - 24 q^{85} + 12 q^{86} - 4 q^{88} - 16 q^{91} - 216 q^{92} - 20 q^{94} - 8 q^{97}+O(q^{100}) \) 368 * q + 12 * q^2 - 4 * q^4 + 12 * q^5 - 4 * q^7 - 16 * q^10 + 12 * q^11 - 4 * q^13 + 12 * q^14 - 4 * q^16 - 16 * q^19 + 12 * q^20 - 4 * q^22 + 12 * q^23 - 4 * q^25 - 16 * q^28 + 12 * q^29 + 12 * q^32 - 12 * q^34 - 16 * q^37 + 12 * q^38 - 4 * q^40 + 12 * q^41 - 4 * q^43 - 16 * q^46 + 24 * q^47 + 168 * q^50 - 4 * q^52 - 16 * q^55 + 12 * q^56 + 32 * q^58 + 12 * q^59 - 4 * q^61 - 16 * q^64 + 24 * q^65 - 4 * q^67 + 60 * q^68 - 4 * q^70 - 16 * q^73 + 12 * q^74 - 28 * q^76 + 12 * q^77 - 8 * q^79 - 16 * q^82 + 132 * q^83 - 24 * q^85 + 12 * q^86 - 4 * q^88 - 16 * q^91 - 216 * q^92 - 20 * q^94 - 8 * q^97

Introduction

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