LMFDB - Embedded newform 855.2.da.b.199.1

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			199.1
Character	$\chi$	$=$	855.199
Dual form			855.2.da.b.739.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.93197 + 0.340658i) q^{2} +(1.73706 - 0.632239i) q^{4} +(2.15043 - 0.612911i) q^{5} +(0.586358 + 0.338534i) q^{7} +(0.257316 - 0.148561i) q^{8} +O(q^{10})$	\(q+(-1.93197 + 0.340658i) q^{2} +(1.73706 - 0.632239i) q^{4} +(2.15043 - 0.612911i) q^{5} +(0.586358 + 0.338534i) q^{7} +(0.257316 - 0.148561i) q^{8} +(-3.94576 + 1.91668i) q^{10} +(1.42035 + 2.46011i) q^{11} +(-3.06393 + 3.65145i) q^{13} +(-1.24815 - 0.454289i) q^{14} +(-3.27865 + 2.75111i) q^{16} +(-5.10518 + 0.900181i) q^{17} +(3.00824 + 3.15444i) q^{19} +(3.34792 - 2.42425i) q^{20} +(-3.58212 - 4.26900i) q^{22} +(0.359434 + 0.987537i) q^{23} +(4.24868 - 2.63604i) q^{25} +(4.67552 - 8.09823i) q^{26} +(1.23257 + 0.217336i) q^{28} +(-0.247630 + 1.40438i) q^{29} +(-0.135532 + 0.234748i) q^{31} +(5.01508 - 5.97674i) q^{32} +(9.55639 - 3.47824i) q^{34} +(1.46841 + 0.368607i) q^{35} -0.603754i q^{37} +(-6.88641 - 5.06949i) q^{38} +(0.462285 - 0.477182i) q^{40} +(-5.15980 + 4.32958i) q^{41} +(-1.92538 + 5.28994i) q^{43} +(4.02261 + 3.37537i) q^{44} +(-1.03083 - 1.78544i) q^{46} +(7.77543 + 1.37102i) q^{47} +(-3.27079 - 5.66517i) q^{49} +(-7.31032 + 6.54009i) q^{50} +(-3.01365 + 8.27993i) q^{52} +(2.35594 + 6.47288i) q^{53} +(4.56218 + 4.41974i) q^{55} +0.201172 q^{56} -2.79757i q^{58} +(-1.75779 - 9.96889i) q^{59} +(7.02134 - 2.55556i) q^{61} +(0.181874 - 0.499695i) q^{62} +(-3.37297 + 5.84216i) q^{64} +(-4.35075 + 9.73010i) q^{65} +(-4.05478 - 0.714967i) q^{67} +(-8.29889 + 4.79137i) q^{68} +(-2.96249 - 0.211912i) q^{70} +(-7.14680 - 2.60122i) q^{71} +(10.3665 + 12.3543i) q^{73} +(0.205674 + 1.16643i) q^{74} +(7.21986 + 3.57753i) q^{76} +1.92334i q^{77} +(-11.3733 + 9.54332i) q^{79} +(-5.36431 + 7.92559i) q^{80} +(8.49365 - 10.1223i) q^{82} +(12.2815 + 7.09076i) q^{83} +(-10.4266 + 5.06480i) q^{85} +(1.91771 - 10.8759i) q^{86} +(0.730955 + 0.422017i) q^{88} +(6.31059 + 5.29521i) q^{89} +(-3.03270 + 1.10381i) q^{91} +(1.24872 + 1.48817i) q^{92} -15.4889 q^{94} +(8.40240 + 4.93961i) q^{95} +(-5.64144 + 0.994738i) q^{97} +(8.24894 + 9.83071i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.93197	+	0.340658i	−1.36611	+	0.240881i	−0.808144	−	0.588985i	$-0.799528\pi$
$2$	−1.93197	+	0.340658i	−1.36611	+	0.240881i	−0.557963	+	0.829866i	$0.688417\pi$
$3$		0			0
$3$		0			0
$4$	1.73706	−	0.632239i	0.868531	−	0.316120i
$5$	2.15043	−	0.612911i	0.961701	−	0.274102i
$5$	2.15043	−	0.612911i	0.961701	−	0.274102i
$6$		0			0
$7$	0.586358	+	0.338534i	0.221622	+	0.127954i	0.606701	−	0.794930i	$-0.292492\pi$
$7$	0.586358	+	0.338534i	0.221622	+	0.127954i	−0.385079	+	0.922884i	$0.625826\pi$
$8$	0.257316	−	0.148561i	0.0909749	−	0.0525244i
$9$		0			0
$10$	−3.94576	+	1.91668i	−1.24776	+	0.606109i
$11$	1.42035	+	2.46011i	0.428250	+	0.741751i	0.996718	−	0.0809546i	$-0.0257969\pi$
$11$	1.42035	+	2.46011i	0.428250	+	0.741751i	−0.568468	+	0.822706i	$0.692464\pi$
$12$		0			0
$13$	−3.06393	+	3.65145i	−0.849781	+	1.01273i	0.149930	+	0.988697i	$0.452095\pi$
$13$	−3.06393	+	3.65145i	−0.849781	+	1.01273i	−0.999711	+	0.0240334i	$0.992349\pi$
$14$	−1.24815	−	0.454289i	−0.333581	−	0.121414i
$15$		0			0
$16$	−3.27865	+	2.75111i	−0.819663	+	0.687779i
$17$	−5.10518	+	0.900181i	−1.23819	+	0.218326i	−0.754139	−	0.656715i	$-0.771946\pi$
$17$	−5.10518	+	0.900181i	−1.23819	+	0.218326i	−0.484049	+	0.875041i	$0.660834\pi$
$18$		0			0
$19$	3.00824	+	3.15444i	0.690138	+	0.723678i
$19$	3.00824	+	3.15444i	0.690138	+	0.723678i
$20$	3.34792	−	2.42425i	0.748618	−	0.542079i
$21$		0			0
$22$	−3.58212	−	4.26900i	−0.763710	−	0.910154i
$23$	0.359434	+	0.987537i	0.0749472	+	0.205916i	0.971509	−	0.237003i	$-0.0761652\pi$
$23$	0.359434	+	0.987537i	0.0749472	+	0.205916i	−0.896562	+	0.442919i	$0.853943\pi$
$24$		0			0
$25$	4.24868	−	2.63604i	0.849736	−	0.527208i
$26$	4.67552	−	8.09823i	0.916944	−	1.58819i
$27$		0			0
$28$	1.23257	+	0.217336i	0.232935	+	0.0410727i
$29$	−0.247630	+	1.40438i	−0.0459838	+	0.260787i	−0.999129	−	0.0417259i	$-0.986714\pi$
$29$	−0.247630	+	1.40438i	−0.0459838	+	0.260787i	0.953145	+	0.302513i	$0.0978255\pi$
$30$		0			0
$31$	−0.135532	+	0.234748i	−0.0243422	+	0.0421620i	−0.877940	−	0.478771i	$-0.841082\pi$
$31$	−0.135532	+	0.234748i	−0.0243422	+	0.0421620i	0.853598	+	0.520933i	$0.174416\pi$
$32$	5.01508	−	5.97674i	0.886549	−	1.05655i
$33$		0			0
$34$	9.55639	−	3.47824i	1.63891	−	0.596513i
$35$	1.46841	+	0.368607i	0.248207	+	0.0623060i
$36$		0			0
$37$		−	0.603754i		−	0.0992566i	−0.998768	−	0.0496283i	$-0.984196\pi$
$37$		−	0.603754i		−	0.0992566i	0.998768	−	0.0496283i	$-0.0158037\pi$
$38$	−6.88641	−	5.06949i	−1.11712	−	0.822380i
$39$		0			0
$40$	0.462285	−	0.477182i	0.0730936	−	0.0754492i
$41$	−5.15980	+	4.32958i	−0.805825	+	0.676167i	−0.949607	−	0.313442i	$-0.898518\pi$
$41$	−5.15980	+	4.32958i	−0.805825	+	0.676167i	0.143783	+	0.989609i	$0.454073\pi$
$42$		0			0
$43$	−1.92538	+	5.28994i	−0.293618	+	0.806709i	0.701912	+	0.712264i	$0.252330\pi$
$43$	−1.92538	+	5.28994i	−0.293618	+	0.806709i	−0.995530	+	0.0944453i	$0.969892\pi$
$44$	4.02261	+	3.37537i	0.606431	+	0.508856i
$45$		0			0
$46$	−1.03083	−	1.78544i	−0.151987	−	0.263249i
$47$	7.77543	+	1.37102i	1.13416	+	0.199983i	0.709051	−	0.705157i	$-0.249124\pi$
$47$	7.77543	+	1.37102i	1.13416	+	0.199983i	0.425112	+	0.905141i	$0.360235\pi$
$48$		0			0
$49$	−3.27079	−	5.66517i	−0.467256	−	0.809311i
$50$	−7.31032	+	6.54009i	−1.03384	+	0.924908i
$51$		0			0
$52$	−3.01365	+	8.27993i	−0.417918	+	1.14822i
$53$	2.35594	+	6.47288i	0.323613	+	0.889118i	0.989689	+	0.143235i	$0.0457503\pi$
$53$	2.35594	+	6.47288i	0.323613	+	0.889118i	−0.666076	+	0.745884i	$0.732027\pi$
$54$		0			0
$55$	4.56218	+	4.41974i	0.615164	+	0.595958i
$56$	0.201172			0.0268828
$57$		0			0
$58$		−	2.79757i		−	0.367339i
$59$	−1.75779	−	9.96889i	−0.228844	−	1.29784i	−0.855198	−	0.518301i	$-0.826565\pi$
$59$	−1.75779	−	9.96889i	−0.228844	−	1.29784i	0.626354	−	0.779539i	$-0.284546\pi$
$60$		0			0
$61$	7.02134	−	2.55556i	0.898990	−	0.327206i	0.149142	−	0.988816i	$-0.452349\pi$
$61$	7.02134	−	2.55556i	0.898990	−	0.327206i	0.749848	+	0.661610i	$0.230127\pi$
$62$	0.181874	−	0.499695i	0.0230980	−	0.0634614i
$63$		0			0
$64$	−3.37297	+	5.84216i	−0.421622	+	0.730270i
$65$	−4.35075	+	9.73010i	−0.539644	+	1.20687i
$66$		0			0
$67$	−4.05478	−	0.714967i	−0.495370	−	0.0873472i	−0.0796188	−	0.996825i	$-0.525370\pi$
$67$	−4.05478	−	0.714967i	−0.495370	−	0.0873472i	−0.415752	+	0.909478i	$0.636481\pi$
$68$	−8.29889	+	4.79137i	−1.00639	+	0.581039i
$69$		0			0
$70$	−2.96249	−	0.211912i	−0.354085	−	0.0253283i
$71$	−7.14680	−	2.60122i	−0.848169	−	0.308708i	−0.118875	−	0.992909i	$-0.537929\pi$
$71$	−7.14680	−	2.60122i	−0.848169	−	0.308708i	−0.729294	+	0.684201i	$0.760151\pi$
$72$		0			0
$73$	10.3665	+	12.3543i	1.21330	+	1.44596i	0.859879	+	0.510497i	$0.170539\pi$
$73$	10.3665	+	12.3543i	1.21330	+	1.44596i	0.353425	+	0.935463i	$0.385017\pi$
$74$	0.205674	+	1.16643i	0.0239091	+	0.135595i
$75$		0			0
$76$	7.21986	+	3.57753i	0.828175	+	0.410371i
$77$			1.92334i			0.219185i
$78$		0			0
$79$	−11.3733	+	9.54332i	−1.27959	+	1.07371i	−0.286294	+	0.958142i	$0.592423\pi$
$79$	−11.3733	+	9.54332i	−1.27959	+	1.07371i	−0.993300	+	0.115565i	$0.963132\pi$
$80$	−5.36431	+	7.92559i	−0.599748	+	0.886108i
$81$		0			0
$82$	8.49365	−	10.1223i	0.937966	−	1.11782i
$83$	12.2815	+	7.09076i	1.34808	+	0.778312i	0.987977	−	0.154603i	$-0.0494098\pi$
$83$	12.2815	+	7.09076i	1.34808	+	0.778312i	0.360098	+	0.932914i	$0.382743\pi$
$84$		0			0
$85$	−10.4266	+	5.06480i	−1.13092	+	0.549354i
$86$	1.91771	−	10.8759i	0.206792	−	1.17278i
$87$		0			0
$88$	0.730955	+	0.422017i	0.0779201	+	0.0449872i
$89$	6.31059	+	5.29521i	0.668921	+	0.561291i	0.912746	−	0.408528i	$-0.133958\pi$
$89$	6.31059	+	5.29521i	0.668921	+	0.561291i	−0.243825	+	0.969819i	$0.578402\pi$
$90$		0			0
$91$	−3.03270	+	1.10381i	−0.317913	+	0.115711i
$92$	1.24872	+	1.48817i	0.130188	+	0.155152i
$93$		0			0
$94$	−15.4889			−1.59756
$95$	8.40240	+	4.93961i	0.862068	+	0.506793i
$96$		0			0
$97$	−5.64144	+	0.994738i	−0.572801	+	0.101000i	−0.452543	−	0.891742i	$-0.649483\pi$
$97$	−5.64144	+	0.994738i	−0.572801	+	0.101000i	−0.120258	+	0.992743i	$0.538372\pi$
$98$	8.24894	+	9.83071i	0.833269	+	0.993051i
$99$		0			0
$100$	5.71362	−	7.26515i	0.571362	−	0.726515i
$101$	1.54918	+	1.29992i	0.154149	+	0.129347i	0.716601	−	0.697484i	$-0.245697\pi$
$101$	1.54918	+	1.29992i	0.154149	+	0.129347i	−0.562451	+	0.826831i	$0.690142\pi$
$102$		0			0
$103$	−15.7927	+	9.11792i	−1.55610	+	0.898415i	−0.558477	+	0.829520i	$0.688614\pi$
$103$	−15.7927	+	9.11792i	−1.55610	+	0.898415i	−0.997624	+	0.0688957i	$0.978052\pi$
$104$	−0.245934	+	1.39476i	−0.0241158	+	0.136767i
$105$		0			0
$106$	−6.75663	−	11.7028i	−0.656262	−	1.13668i
$107$	−5.38097	−	3.10671i	−0.520198	−	0.300337i	0.216817	−	0.976212i	$-0.430432\pi$
$107$	−5.38097	−	3.10671i	−0.520198	−	0.300337i	−0.737016	+	0.675876i	$0.763766\pi$
$108$		0			0
$109$	15.0243	+	5.46840i	1.43907	+	0.523777i	0.939515	−	0.342507i	$-0.111276\pi$
$109$	15.0243	+	5.46840i	1.43907	+	0.523777i	0.499551	+	0.866284i	$0.333498\pi$
$110$	−10.3196	−	6.98466i	−0.983935	−	0.665961i
$111$		0			0
$112$	−2.85381	+	0.503203i	−0.269659	+	0.0475482i
$113$			7.88392i			0.741657i	0.928701	+	0.370828i	$0.120926\pi$
$113$			7.88392i			0.741657i	−0.928701	+	0.370828i	$0.879074\pi$
$114$		0			0
$115$	1.37821	+	1.90333i	0.128519	+	0.177486i
$116$	0.457755	+	2.59606i	0.0425015	+	0.241038i
$117$		0			0
$118$	6.79196	+	18.6608i	0.625251	+	1.71786i
$119$	−3.29820	−	1.20045i	−0.302346	−	0.110045i
$120$		0			0
$121$	1.46524	−	2.53787i	0.133204	−	0.230715i
$122$	−12.6944	+	7.32913i	−1.14930	+	0.663548i
$123$		0			0
$124$	−0.0870104	+	0.493461i	−0.00781376	+	0.0443141i
$125$	7.52082	−	8.27268i	0.672683	−	0.739931i
$126$		0			0
$127$	10.1395	−	12.0838i	0.899736	−	1.07226i	−0.0972942	−	0.995256i	$-0.531019\pi$
$127$	10.1395	−	12.0838i	0.899736	−	1.07226i	0.997030	−	0.0770082i	$-0.0245368\pi$
$128$	−0.810645	+	2.22723i	−0.0716516	+	0.196861i
$129$		0			0
$130$	5.09087	−	20.2803i	0.446499	−	1.77870i
$131$	0.706095	+	4.00446i	0.0616918	+	0.349872i	0.999992	+	0.00404921i	$0.00128891\pi$
$131$	0.706095	+	4.00446i	0.0616918	+	0.349872i	−0.938300	+	0.345822i	$0.887600\pi$
$132$		0			0
$133$	0.696022	+	2.86802i	0.0603527	+	0.248689i
$134$	8.07726			0.697769
$135$		0			0
$136$	−1.17991	+	0.990064i	−0.101177	+	0.0848973i
$137$	0.893360	+	2.45449i	0.0763249	+	0.209701i	0.971987	−	0.235034i	$-0.0755201\pi$
$137$	0.893360	+	2.45449i	0.0763249	+	0.209701i	−0.895662	+	0.444735i	$0.853298\pi$
$138$		0			0
$139$	−6.87238	−	5.76661i	−0.582908	−	0.489118i	0.302993	−	0.952993i	$-0.402014\pi$
$139$	−6.87238	−	5.76661i	−0.582908	−	0.489118i	−0.885901	+	0.463875i	$0.846459\pi$
$140$	2.78377	−	0.288092i	0.235271	−	0.0243483i
$141$		0			0
$142$	14.6935	+	2.59086i	1.23305	+	0.217420i
$143$	−13.3348	−	2.35129i	−1.11511	−	0.196624i
$144$		0			0
$145$	0.328249	+	3.17179i	0.0272596	+	0.263403i
$146$	−24.2363	−	20.3367i	−2.00581	−	1.68307i
$147$		0			0
$148$	−0.381717	−	1.04876i	−0.0313770	−	0.0862075i
$149$	−1.32378	+	1.11078i	−0.108448	+	0.0909989i	−0.695399	−	0.718623i	$-0.744773\pi$
$149$	−1.32378	+	1.11078i	−0.108448	+	0.0909989i	0.586951	+	0.809622i	$0.300328\pi$
$150$		0			0
$151$	11.0738			0.901177			0.450589	−	0.892732i	$-0.351214\pi$
$151$	11.0738			0.901177			0.450589	+	0.892732i	$0.351214\pi$
$152$	1.24270	+	0.364779i	0.100796	+	0.0295875i
$153$		0			0
$154$	−0.655201	−	3.71583i	−0.0527976	−	0.299430i
$155$	−0.147572	+	0.587878i	−0.0118533	+	0.0472195i
$156$		0			0
$157$	0.671940	−	1.84614i	0.0536267	−	0.147338i	−0.909987	−	0.414637i	$-0.863909\pi$
$157$	0.671940	−	1.84614i	0.0536267	−	0.147338i	0.963614	+	0.267298i	$0.0861310\pi$
$158$	18.7218	−	22.3118i	1.48943	−	1.77503i
$159$		0			0
$160$	7.12136	−	15.9263i	0.562993	−	1.25909i
$161$	−0.123558	+	0.700730i	−0.00973771	+	0.0552253i
$162$		0			0
$163$	17.4341	−	10.0656i	1.36554	−	0.788395i	0.375186	−	0.926950i	$-0.377579\pi$
$163$	17.4341	−	10.0656i	1.36554	−	0.788395i	0.990355	+	0.138555i	$0.0442457\pi$
$164$	−6.22556	+	10.7830i	−0.486134	+	0.842009i
$165$		0			0
$166$	−26.1431	−	9.51530i	−2.02910	−	0.738530i
$167$	−6.10733	−	16.7798i	−0.472600	−	1.29846i	−0.915656	−	0.401963i	$-0.868328\pi$
$167$	−6.10733	−	16.7798i	−0.472600	−	1.29846i	0.443056	−	0.896494i	$-0.353894\pi$
$168$		0			0
$169$	−1.68799	−	9.57308i	−0.129846	−	0.736391i
$170$	18.4185	−	13.3369i	1.41263	−	1.02289i
$171$		0			0
$172$			10.4063i			0.793470i
$173$	−2.68082	+	0.472701i	−0.203819	+	0.0359388i	−0.274625	−	0.961551i	$-0.588554\pi$
$173$	−2.68082	+	0.472701i	−0.203819	+	0.0359388i	0.0708064	+	0.997490i	$0.477443\pi$
$174$		0			0
$175$	3.38364	−	0.107341i	0.255779	−	0.00811421i
$176$	−11.4249	−	4.15831i	−0.861181	−	0.313444i
$177$		0			0
$178$	−13.9957	−	8.08042i	−1.04902	−	0.605653i
$179$	−3.85817	−	6.68254i	−0.288373	−	0.499477i	0.685049	−	0.728497i	$-0.259781\pi$
$179$	−3.85817	−	6.68254i	−0.288373	−	0.499477i	−0.973422	+	0.229021i	$0.926448\pi$
$180$		0			0
$181$	−0.185874	+	1.05414i	−0.0138159	+	0.0783537i	−0.990936	−	0.134334i	$-0.957111\pi$
$181$	−0.185874	+	1.05414i	−0.0138159	+	0.0783537i	0.977120	+	0.212688i	$0.0682217\pi$
$182$	5.48305	−	3.16564i	0.406431	−	0.234653i
$183$		0			0
$184$	0.239198	+	0.200711i	0.0176339	+	0.0147966i
$185$	−0.370048	−	1.29833i	−0.0272064	−	0.0954551i
$186$		0			0
$187$	−9.46566	−	11.2807i	−0.692198	−	0.824929i
$188$	14.3732	−	2.53439i	1.04827	−	0.184839i
$189$		0			0
$190$	−17.9159	−	6.68082i	−1.29975	−	0.484677i
$191$	−5.38296			−0.389497			−0.194749	−	0.980853i	$-0.562389\pi$
$191$	−5.38296			−0.389497			−0.194749	+	0.980853i	$0.562389\pi$
$192$		0			0
$193$	9.94387	+	11.8506i	0.715775	+	0.853028i	0.994213	−	0.107426i	$-0.0342610\pi$
$193$	9.94387	+	11.8506i	0.715775	+	0.853028i	−0.278438	+	0.960454i	$0.589817\pi$
$194$	10.5602	−	3.84360i	0.758179	−	0.275954i
$195$		0			0
$196$	−9.26331	−	7.77284i	−0.661665	−	0.555203i
$197$	18.3882	+	10.6164i	1.31010	+	0.756388i	0.982113	−	0.188294i	$-0.0602958\pi$
$197$	18.3882	+	10.6164i	1.31010	+	0.756388i	0.327989	+	0.944682i	$0.393629\pi$
$198$		0			0
$199$	−1.31646	+	7.46602i	−0.0933214	+	0.529252i	0.901927	+	0.431888i	$0.142152\pi$
$199$	−1.31646	+	7.46602i	−0.0933214	+	0.529252i	−0.995249	+	0.0973643i	$0.968959\pi$
$200$	0.701639	−	1.30949i	0.0496134	−	0.0925946i
$201$		0			0
$202$	−3.43580	−	1.98366i	−0.241742	−	0.139570i
$203$	−0.620630	+	0.739638i	−0.0435597	+	0.0519124i
$204$		0			0
$205$	−8.44212	+	12.4729i	−0.589623	+	0.871149i
$206$	27.4049	−	22.9954i	1.90939	−	1.60217i
$207$		0			0
$208$		−	20.4011i		−	1.41456i
$209$	−3.48752	+	11.8810i	−0.241237	+	0.821826i
$210$		0			0
$211$	−2.30936	−	13.0971i	−0.158983	−	0.901639i	−0.955053	−	0.296434i	$-0.904202\pi$
$211$	−2.30936	−	13.0971i	−0.158983	−	0.901639i	0.796070	−	0.605204i	$-0.206909\pi$
$212$	8.18481	+	9.75428i	0.562135	+	0.669927i
$213$		0			0
$214$	11.4542	+	4.16898i	0.782992	+	0.284986i
$215$	−0.898132	+	12.5557i	−0.0612521	+	0.856294i
$216$		0			0
$217$	−0.158940	+	0.0917642i	−0.0107896	+	0.00622936i
$218$	−30.8893	−	5.44661i	−2.09209	−	0.368891i
$219$		0			0
$220$	10.7191	+	4.79299i	0.722683	+	0.323143i
$221$	12.3550	−	21.3994i	0.831084	−	1.43948i
$222$		0			0
$223$	6.79915	−	18.6805i	0.455304	−	1.25094i	−0.473640	−	0.880719i	$-0.657060\pi$
$223$	6.79915	−	18.6805i	0.455304	−	1.25094i	0.928944	−	0.370220i	$-0.120718\pi$
$224$	4.96396	−	1.80673i	0.331668	−	0.120717i
$225$		0			0
$226$	−2.68572	−	15.2315i	−0.178651	−	1.01318i
$227$		−	27.3022i		−	1.81211i	−0.423163	−	0.906054i	$-0.639080\pi$
$227$		−	27.3022i		−	1.81211i	0.423163	−	0.906054i	$-0.360920\pi$
$228$		0			0
$229$	14.6429			0.967633			0.483816	−	0.875170i	$-0.339250\pi$
$229$	14.6429			0.967633			0.483816	+	0.875170i	$0.339250\pi$
$230$	−3.31104	−	3.20766i	−0.218323	−	0.211507i
$231$		0			0
$232$	0.144918	+	0.398158i	0.00951431	+	0.0261403i
$233$	−2.26737	+	6.22953i	−0.148540	+	0.408110i	−0.991540	−	0.129804i	$-0.958565\pi$
$233$	−2.26737	+	6.22953i	−0.148540	+	0.408110i	0.843000	+	0.537914i	$0.180788\pi$
$234$		0			0
$235$	17.5608	−	1.81737i	1.14554	−	0.118552i
$236$	−9.35611	−	16.2053i	−0.609031	−	1.05487i
$237$		0			0
$238$	6.78096	+	1.19567i	0.439544	+	0.0775036i
$239$	6.33959	+	10.9805i	0.410074	+	0.710269i	0.994897	−	0.100892i	$-0.0321695\pi$
$239$	6.33959	+	10.9805i	0.410074	+	0.710269i	−0.584823	+	0.811161i	$0.698836\pi$
$240$		0			0
$241$	10.8118	+	9.07218i	0.696450	+	0.584391i	0.920761	−	0.390127i	$-0.127569\pi$
$241$	10.8118	+	9.07218i	0.696450	+	0.584391i	−0.224311	+	0.974518i	$0.572013\pi$
$242$	−1.96625	+	5.40222i	−0.126395	+	0.347268i
$243$		0			0
$244$	10.5808	−	8.87833i	0.677365	−	0.568377i
$245$	−10.5058	−	10.1778i	−0.671194	−	0.650239i
$246$		0			0
$247$	−20.7353	+	1.31946i	−1.31936	+	0.0839555i
$248$			0.0805392i			0.00511425i
$249$		0			0
$250$	−11.7118	+	18.5446i	−0.740721	+	1.17286i
$251$	6.55337	−	2.38523i	0.413645	−	0.150554i	−0.126811	−	0.991927i	$-0.540474\pi$
$251$	6.55337	−	2.38523i	0.413645	−	0.150554i	0.540456	+	0.841372i	$0.318252\pi$
$252$		0			0
$253$	−1.91893	+	2.28689i	−0.120642	+	0.143776i
$254$	−15.4728	+	26.7996i	−0.970847	+	1.68156i
$255$		0			0
$256$	3.15026	−	17.8660i	0.196891	−	1.11663i
$257$	−15.5410	−	2.74031i	−0.969424	−	0.170936i	−0.333553	−	0.942731i	$-0.608248\pi$
$257$	−15.5410	−	2.74031i	−0.969424	−	0.170936i	−0.635871	+	0.771796i	$0.719359\pi$
$258$		0			0
$259$	0.204391	−	0.354016i	0.0127003	−	0.0219975i
$260$	−1.40578	+	19.6525i	−0.0871825	+	1.21880i
$261$		0			0
$262$	−2.72830	−	7.49595i	−0.168555	−	0.463102i
$263$	−12.7872	−	15.2391i	−0.788490	−	0.939686i	0.210794	−	0.977531i	$-0.432395\pi$
$263$	−12.7872	−	15.2391i	−0.788490	−	0.939686i	−0.999284	+	0.0378448i	$0.987951\pi$
$264$		0			0
$265$	9.03357	+	12.4755i	0.554928	+	0.766363i
$266$	−2.32170	−	5.30381i	−0.142353	−	0.325198i
$267$		0			0
$268$	−7.49544	+	1.32165i	−0.457857	+	0.0807325i
$269$	−8.70147	+	7.30140i	−0.530538	+	0.445174i	−0.868287	−	0.496062i	$-0.834779\pi$
$269$	−8.70147	+	7.30140i	−0.530538	+	0.445174i	0.337749	+	0.941236i	$0.390334\pi$
$270$		0			0
$271$	−22.4471	−	8.17007i	−1.36356	−	0.496296i	−0.446409	−	0.894829i	$-0.647297\pi$
$271$	−22.4471	−	8.17007i	−1.36356	−	0.496296i	−0.917154	+	0.398533i	$0.869519\pi$
$272$	14.2616	−	16.9963i	0.864737	−	1.03055i
$273$		0			0
$274$	−2.56208	−	4.43766i	−0.154781	−	0.268089i
$275$	12.5195	+	6.70813i	0.754957	+	0.404516i
$276$		0			0
$277$	−4.06428	+	2.34652i	−0.244199	+	0.140988i	−0.617105	−	0.786881i	$-0.711695\pi$
$277$	−4.06428	+	2.34652i	−0.244199	+	0.140988i	0.372906	+	0.927869i	$0.378361\pi$
$278$	15.2417	+	8.79978i	0.914134	+	0.527776i
$279$		0			0
$280$	0.432606	−	0.123301i	0.0258532	−	0.00736862i
$281$	21.1014	−	7.68028i	1.25880	−	0.458167i	0.375436	−	0.926848i	$-0.377493\pi$
$281$	21.1014	−	7.68028i	1.25880	−	0.458167i	0.883367	+	0.468681i	$0.155271\pi$
$282$		0			0
$283$	−10.7176	+	1.88981i	−0.637097	+	0.112337i	−0.482862	−	0.875697i	$-0.660403\pi$
$283$	−10.7176	+	1.88981i	−0.637097	+	0.112337i	−0.154236	+	0.988034i	$0.549291\pi$
$284$	−14.0590			−0.834250
$285$		0			0
$286$	26.5634			1.57073
$287$	−4.49119	+	0.791919i	−0.265107	+	0.0467455i
$288$		0			0
$289$	9.27778	−	3.37683i	0.545752	−	0.198637i
$290$	−1.71466	−	6.01598i	−0.100688	−	0.353271i
$291$		0			0
$292$	25.8181	+	14.9061i	1.51089	+	0.872312i
$293$	10.8004	−	6.23561i	0.630965	−	0.364288i	−0.150161	−	0.988662i	$-0.547979\pi$
$293$	10.8004	−	6.23561i	0.630965	−	0.364288i	0.781126	+	0.624374i	$0.214646\pi$
$294$		0			0
$295$	−9.89003	−	20.3600i	−0.575820	−	1.18541i
$296$	−0.0896946	−	0.155356i	−0.00521339	−	0.00902986i
$297$		0			0
$298$	2.17910	−	2.59695i	0.126232	−	0.150437i
$299$	−4.70722	−	1.71329i	−0.272226	−	0.0990821i
$300$		0			0
$301$	−2.91979	+	2.44999i	−0.168294	+	0.141215i
$302$	−21.3943	+	3.77239i	−1.23110	+	0.217077i
$303$		0			0
$304$	−18.5412	−	2.06628i	−1.06341	−	0.118510i
$305$	13.5326	−	9.79900i	0.774872	−	0.561089i
$306$		0			0
$307$	2.68594	+	3.20098i	0.153295	+	0.182689i	0.837226	−	0.546857i	$-0.184176\pi$
$307$	2.68594	+	3.20098i	0.153295	+	0.182689i	−0.683932	+	0.729546i	$0.739731\pi$
$308$	1.21601	+	3.34096i	0.0692886	+	0.190369i
$309$		0			0
$310$	0.0848388	−	1.18603i	0.00481852	−	0.0673621i
$311$	−6.04544	+	10.4710i	−0.342806	+	0.593757i	−0.984953	−	0.172825i	$-0.944711\pi$
$311$	−6.04544	+	10.4710i	−0.342806	+	0.593757i	0.642147	+	0.766582i	$0.278044\pi$
$312$		0			0
$313$	−9.43307	−	1.66330i	−0.533188	−	0.0940155i	−0.0994297	−	0.995045i	$-0.531702\pi$
$313$	−9.43307	−	1.66330i	−0.533188	−	0.0940155i	−0.433759	+	0.901029i	$0.642813\pi$
$314$	−0.669264	+	3.79558i	−0.0377688	+	0.214197i
$315$		0			0
$316$	−13.7224	+	23.7680i	−0.771948	+	1.33705i
$317$	−7.17941	+	8.55609i	−0.403236	+	0.480558i	−0.929004	−	0.370070i	$-0.879334\pi$
$317$	−7.17941	+	8.55609i	−0.403236	+	0.480558i	0.525768	+	0.850628i	$0.323778\pi$
$318$		0			0
$319$	−3.80665	+	1.38551i	−0.213132	+	0.0775735i
$320$	−3.67261	+	14.6305i	−0.205305	+	0.817868i
$321$		0			0
$322$		−	1.39588i		−	0.0777893i
$323$	−18.1972	−	13.3960i	−1.01252	−	0.745374i
$324$		0			0
$325$	−3.39229	+	23.5905i	−0.188170	+	1.30857i
$326$	−30.2531	+	25.3854i	−1.67556	+	1.40597i
$327$		0			0
$328$	−0.684489	+	1.88062i	−0.0377946	+	0.103840i
$329$	4.09505	+	3.43615i	0.225767	+	0.189441i
$330$		0			0
$331$	10.8439	+	18.7822i	0.596034	+	1.03236i	0.993400	+	0.114701i	$0.0365911\pi$
$331$	10.8439	+	18.7822i	0.596034	+	1.03236i	−0.397366	+	0.917660i	$0.630076\pi$
$332$	25.8169	+	4.55221i	1.41688	+	0.249835i
$333$		0			0
$334$	17.5153	+	30.3374i	0.958396	+	1.65999i
$335$	−9.15773	+	0.947733i	−0.500340	+	0.0517802i
$336$		0			0
$337$	0.0180757	−	0.0496626i	0.000984647	−	0.00270530i	−0.939199	−	0.343372i	$-0.888431\pi$
$337$	0.0180757	−	0.0496626i	0.000984647	−	0.00270530i	0.940184	+	0.340667i	$0.110653\pi$
$338$	6.52229	+	17.9198i	0.354766	+	0.974711i
$339$		0			0
$340$	−14.9095	+	15.3900i	−0.808580	+	0.834638i
$341$	−0.770008			−0.0416983
$342$		0			0
$343$		−	9.16856i		−	0.495056i
$344$	0.290450	+	1.64722i	0.0156600	+	0.0888124i
$345$		0			0
$346$	5.01823	−	1.82649i	0.269782	−	0.0981925i
$347$	−8.68262	+	23.8553i	−0.466107	+	1.28062i	0.454715	+	0.890637i	$0.349741\pi$
$347$	−8.68262	+	23.8553i	−0.466107	+	1.28062i	−0.920822	+	0.389982i	$0.872481\pi$
$348$		0			0
$349$	−7.80995	+	13.5272i	−0.418057	+	0.724096i	−0.995744	−	0.0921622i	$-0.970622\pi$
$349$	−7.80995	+	13.5272i	−0.418057	+	0.724096i	0.577687	+	0.816259i	$0.303956\pi$
$350$	−6.50050	+	1.36004i	−0.347467	+	0.0726973i
$351$		0			0
$352$	21.8266	+	3.84862i	1.16336	+	0.205132i
$353$	10.8004	−	6.23564i	0.574850	−	0.331890i	−0.184234	−	0.982882i	$-0.558981\pi$
$353$	10.8004	−	6.23564i	0.574850	−	0.331890i	0.759084	+	0.650993i	$0.225647\pi$
$354$		0			0
$355$	−16.9630	−	1.21339i	−0.900302	−	0.0644001i
$356$	14.3097	+	5.20831i	0.758414	+	0.276040i
$357$		0			0
$358$	9.73031	+	11.5961i	0.514263	+	0.612875i
$359$	−5.84204	−	33.1318i	−0.308331	−	1.74863i	−0.607396	−	0.794399i	$-0.707786\pi$
$359$	−5.84204	−	33.1318i	−0.308331	−	1.74863i	0.299065	−	0.954233i	$-0.403325\pi$
$360$		0			0
$361$	−0.900964	+	18.9786i	−0.0474191	+	0.998875i
$362$		−	2.09989i		−	0.110368i
$363$		0			0
$364$	−4.57011	+	3.83478i	−0.239539	+	0.200997i
$365$	29.8644	+	20.2133i	1.56318	+	1.05801i
$366$		0			0
$367$	16.4618	−	19.6184i	0.859299	−	1.02407i	−0.140125	−	0.990134i	$-0.544750\pi$
$367$	16.4618	−	19.6184i	0.859299	−	1.02407i	0.999424	−	0.0339392i	$-0.0108053\pi$
$368$	−3.89529	−	2.24894i	−0.203056	−	0.117234i
$369$		0			0
$370$	1.15721	+	2.38227i	0.0601603	+	0.123848i
$371$	−0.809867	+	4.59299i	−0.0420462	+	0.238456i
$372$		0			0
$373$	−18.8456	−	10.8805i	−0.975788	−	0.563372i	−0.0747923	−	0.997199i	$-0.523829\pi$
$373$	−18.8456	−	10.8805i	−0.975788	−	0.563372i	−0.900996	+	0.433828i	$0.857163\pi$
$374$	22.1302	+	18.5695i	1.14433	+	0.960204i
$375$		0			0
$376$	2.20442	−	0.802344i	0.113684	−	0.0413777i
$377$	−4.36930	−	5.20713i	−0.225031	−	0.268181i
$378$		0			0
$379$	6.63029			0.340575			0.170288	−	0.985394i	$-0.445530\pi$
$379$	6.63029			0.340575			0.170288	+	0.985394i	$0.445530\pi$
$380$	17.7185	+	3.26809i	0.908940	+	0.167649i
$381$		0			0
$382$	10.3997	−	1.83375i	0.532095	−	0.0938226i
$383$	17.3693	+	20.7000i	0.887532	+	1.05772i	0.997960	+	0.0638349i	$0.0203331\pi$
$383$	17.3693	+	20.7000i	0.887532	+	1.05772i	−0.110429	+	0.993884i	$0.535222\pi$
$384$		0			0
$385$	1.17884	+	4.13600i	0.0600790	+	0.210790i
$386$	−23.2482	−	19.5076i	−1.18330	−	0.992910i
$387$		0			0
$388$	−9.17062	+	5.29466i	−0.465568	+	0.268796i
$389$	4.51305	−	25.5948i	0.228821	−	1.29771i	−0.626424	−	0.779483i	$-0.715482\pi$
$389$	4.51305	−	25.5948i	0.228821	−	1.29771i	0.855245	−	0.518224i	$-0.173407\pi$
$390$		0			0
$391$	−2.72394	−	4.71800i	−0.137755	−	0.238599i
$392$	−1.68325	−	0.971827i	−0.0850171	−	0.0490847i
$393$		0			0
$394$	−39.1419	−	14.2465i	−1.97194	−	0.717727i
$395$	−18.6082	+	27.4930i	−0.936281	+	1.38332i
$396$		0			0
$397$	−21.0231	+	3.70695i	−1.05512	+	0.186046i	−0.674191	−	0.738557i	$-0.735507\pi$
$397$	−21.0231	+	3.70695i	−1.05512	+	0.186046i	−0.380930	+	0.924604i	$0.624396\pi$
$398$		−	14.8726i		−	0.745494i
$399$		0			0
$400$	−6.67789	+	20.3313i	−0.333894	+	1.01656i
$401$	−4.52547	−	25.6652i	−0.225991	−	1.28166i	−0.860781	−	0.508975i	$-0.830025\pi$
$401$	−4.52547	−	25.6652i	−0.225991	−	1.28166i	0.634790	−	0.772685i	$-0.281087\pi$
$402$		0			0
$403$	−0.441911	−	1.21414i	−0.0220131	−	0.0604806i
$404$	3.51289	+	1.27859i	0.174773	+	0.0636120i
$405$		0			0
$406$	0.947073	−	1.64038i	0.0470024	−	0.0814106i
$407$	1.48530	−	0.857540i	0.0736237	−	0.0425067i
$408$		0			0
$409$	4.05420	−	22.9925i	0.200467	−	1.13691i	−0.703948	−	0.710252i	$-0.748581\pi$
$409$	4.05420	−	22.9925i	0.200467	−	1.13691i	0.904415	−	0.426654i	$-0.140308\pi$
$410$	12.0609	−	26.9732i	0.595645	−	1.33211i
$411$		0			0
$412$	−21.6682	+	25.8232i	−1.06752	+	1.27222i
$413$	2.34412	−	6.44041i	0.115346	−	0.316912i
$414$		0			0
$415$	30.7566	+	7.72067i	1.50978	+	0.378993i
$416$	6.45791	+	36.6246i	0.316625	+	1.79567i
$417$		0			0
$418$	2.69043	−	24.1417i	0.131593	−	1.18081i
$419$	21.9951			1.07453			0.537265	−	0.843413i	$-0.319457\pi$
$419$	21.9951			1.07453			0.537265	+	0.843413i	$0.319457\pi$
$420$		0			0
$421$	2.85822	−	2.39833i	0.139301	−	0.116888i	−0.570475	−	0.821315i	$-0.693241\pi$
$421$	2.85822	−	2.39833i	0.139301	−	0.116888i	0.709776	+	0.704428i	$0.248796\pi$
$422$	8.92323	+	24.5164i	0.434376	+	1.19344i
$423$		0			0
$424$	1.56784	+	1.31557i	0.0761410	+	0.0638899i
$425$	−19.3174	+	17.2820i	−0.937030	+	0.838303i
$426$		0			0
$427$	4.98216	+	0.878489i	0.241104	+	0.0425131i
$428$	−11.3113	−	1.99448i	−0.546751	−	0.0964069i
$429$		0			0
$430$	−2.54205	−	24.5632i	−0.122588	−	1.18454i
$431$	19.0853	+	16.0145i	0.919307	+	0.771390i	0.973867	−	0.227120i	$-0.0729310\pi$
$431$	19.0853	+	16.0145i	0.919307	+	0.771390i	−0.0545594	+	0.998511i	$0.517375\pi$
$432$		0			0
$433$	−3.75273	−	10.3105i	−0.180345	−	0.495492i	0.816274	−	0.577666i	$-0.196036\pi$
$433$	−3.75273	−	10.3105i	−0.180345	−	0.495492i	−0.996618	+	0.0821730i	$0.973814\pi$
$434$	0.275807	−	0.231430i	0.0132392	−	0.0111090i
$435$		0			0
$436$	29.5555			1.41545
$437$	−2.03386	+	4.10456i	−0.0972927	+	0.196348i
$438$		0			0
$439$	1.47943	+	8.39029i	0.0706096	+	0.400447i	0.999544	+	0.0302020i	$0.00961507\pi$
$439$	1.47943	+	8.39029i	0.0706096	+	0.400447i	−0.928934	+	0.370245i	$0.879274\pi$
$440$	1.83052	+	0.459507i	0.0872668	+	0.0219061i
$441$		0			0
$442$	−16.5795	+	45.5518i	−0.788606	+	2.16668i
$443$	6.05322	−	7.21394i	0.287597	−	0.342745i	−0.602831	−	0.797869i	$-0.705961\pi$
$443$	6.05322	−	7.21394i	0.287597	−	0.342745i	0.890428	+	0.455124i	$0.150405\pi$
$444$		0			0
$445$	16.8160	+	7.51914i	0.797153	+	0.356441i
$446$	−6.77206	+	38.4063i	−0.320667	+	1.81859i
$447$		0			0
$448$	−3.95554	+	2.28373i	−0.186881	+	0.107896i
$449$	−4.86372	+	8.42421i	−0.229533	+	0.397563i	−0.957670	−	0.287869i	$-0.907053\pi$
$449$	−4.86372	+	8.42421i	−0.229533	+	0.397563i	0.728137	+	0.685432i	$0.240387\pi$
$450$		0			0
$451$	−17.9799	−	6.54416i	−0.846642	−	0.308153i
$452$	4.98452	+	13.6949i	0.234452	+	0.644152i
$453$		0			0
$454$	9.30069	+	52.7468i	0.436503	+	2.47553i
$455$	−5.84506	+	4.23244i	−0.274021	+	0.198420i
$456$		0			0
$457$		−	10.4686i		−	0.489700i	−0.969561	−	0.244850i	$-0.921261\pi$
$457$		−	10.4686i		−	0.489700i	0.969561	−	0.244850i	$-0.0787387\pi$
$458$	−28.2897	+	4.98823i	−1.32189	+	0.233085i
$459$		0			0
$460$	3.59739	+	2.43484i	0.167729	+	0.113525i
$461$	−21.3065	−	7.75492i	−0.992342	−	0.361183i	−0.205715	−	0.978612i	$-0.565952\pi$
$461$	−21.3065	−	7.75492i	−0.992342	−	0.361183i	−0.786626	+	0.617429i	$0.788174\pi$
$462$		0			0
$463$	30.8631	+	17.8188i	1.43433	+	0.828110i	0.997447	−	0.0714094i	$-0.0227497\pi$
$463$	30.8631	+	17.8188i	1.43433	+	0.828110i	0.436881	+	0.899519i	$0.356083\pi$
$464$	−3.05172	−	5.28573i	−0.141672	−	0.245384i
$465$		0			0
$466$	2.25833	−	12.8076i	0.104615	−	0.593303i
$467$	2.51286	−	1.45080i	0.116281	−	0.0671350i	−0.440731	−	0.897639i	$-0.645281\pi$
$467$	2.51286	−	1.45080i	0.116281	−	0.0671350i	0.557013	+	0.830504i	$0.311948\pi$
$468$		0			0
$469$	−2.13551	−	1.79191i	−0.0986088	−	0.0827426i
$470$	−33.3078	+	9.49332i	−1.53637	+	0.437894i
$471$		0			0
$472$	−1.93330	−	2.30402i	−0.0889873	−	0.106051i
$473$	−15.7486	+	2.77689i	−0.724119	+	0.127682i
$474$		0			0
$475$	21.0963	+	5.47235i	0.967964	+	0.251089i
$476$	−6.48816			−0.297384
$477$		0			0
$478$	−15.9885	−	19.0543i	−0.731296	−	0.871524i
$479$	−27.5809	+	10.0386i	−1.26020	+	0.458676i	−0.883837	−	0.467795i	$-0.845048\pi$
$479$	−27.5809	+	10.0386i	−1.26020	+	0.458676i	−0.376365	+	0.926471i	$0.622826\pi$
$480$		0			0
$481$	2.20458	+	1.84986i	0.100520	+	0.0843464i
$482$	−23.9786	−	13.8440i	−1.09219	−	0.630578i
$483$		0			0
$484$	0.940673	−	5.33482i	0.0427578	−	0.242492i
$485$	−11.5218	+	5.59681i	−0.523179	+	0.254138i
$486$		0			0
$487$	−2.95906	−	1.70841i	−0.134088	−	0.0774157i	0.431456	−	0.902134i	$-0.358000\pi$
$487$	−2.95906	−	1.70841i	−0.134088	−	0.0774157i	−0.565543	+	0.824719i	$0.691334\pi$
$488$	1.42705	−	1.70069i	0.0645993	−	0.0769865i
$489$		0			0
$490$	23.7641	+	16.0844i	1.07355	+	0.726617i
$491$	19.2938	−	16.1894i	0.870717	−	0.730618i	−0.0935323	−	0.995616i	$-0.529816\pi$
$491$	19.2938	−	16.1894i	0.870717	−	0.730618i	0.964249	+	0.264998i	$0.0853714\pi$
$492$		0			0
$493$		−	7.39253i		−	0.332943i
$494$	39.6105	−	9.61281i	1.78216	−	0.432501i
$495$		0			0
$496$	−0.201457	−	1.14252i	−0.00904569	−	0.0513007i
$497$	−3.30998	−	3.94468i	−0.148473	−	0.176943i
$498$		0			0
$499$	−32.6388	−	11.8795i	−1.46111	−	0.531801i	−0.515441	−	0.856925i	$-0.672372\pi$
$499$	−32.6388	−	11.8795i	−1.46111	−	0.531801i	−0.945671	+	0.325124i	$0.894594\pi$
$500$	7.83383	−	19.1251i	0.350340	−	0.855301i
$501$		0			0
$502$	−11.8483	+	6.84064i	−0.528817	+	0.305313i
$503$	22.1171	+	3.89983i	0.986151	+	0.173885i	0.643391	−	0.765538i	$-0.277527\pi$
$503$	22.1171	+	3.89983i	0.986151	+	0.173885i	0.342760	+	0.939423i	$0.388638\pi$
$504$		0			0
$505$	4.12814	+	1.84587i	0.183700	+	0.0821402i
$506$	2.92826	−	5.07189i	0.130177	−	0.225473i
$507$		0			0
$508$	9.97312	−	27.4009i	0.442486	−	1.21572i
$509$	−2.20641	+	0.803067i	−0.0977974	+	0.0355953i	−0.390455	−	0.920622i	$-0.627682\pi$
$509$	−2.20641	+	0.803067i	−0.0977974	+	0.0355953i	0.292658	+	0.956217i	$0.405460\pi$
$510$		0			0
$511$	1.89612	+	10.7534i	0.0838794	+	0.475704i
$512$			30.8493i			1.36336i
$513$		0			0
$514$	30.9583			1.36551
$515$	−28.3726	+	29.2869i	−1.25025	+	1.29054i
$516$		0			0
$517$	7.67094	+	21.0757i	0.337367	+	0.926909i
$518$	−0.274279	+	0.753575i	−0.0120511	+	0.0331102i
$519$		0			0
$520$	0.326000	+	3.15006i	0.0142961	+	0.138139i
$521$	0.761964	+	1.31976i	0.0333822	+	0.0578197i	0.882234	−	0.470811i	$-0.156039\pi$
$521$	0.761964	+	1.31976i	0.0333822	+	0.0578197i	−0.848852	+	0.528631i	$0.822705\pi$
$522$		0			0
$523$	−13.2229	−	2.33156i	−0.578198	−	0.101952i	−0.123101	−	0.992394i	$-0.539284\pi$
$523$	−13.2229	−	2.33156i	−0.578198	−	0.101952i	−0.455096	+	0.890442i	$0.650395\pi$
$524$	3.75831	+	6.50958i	0.164183	+	0.284372i
$525$		0			0
$526$	29.8957	+	25.0855i	1.30351	+	1.09378i
$527$	0.480599	−	1.32043i	0.0209352	−	0.0575190i
$528$		0			0
$529$	16.7730	−	14.0742i	0.729260	−	0.611922i
$530$	−21.7024	−	21.0249i	−0.942693	−	0.913262i
$531$		0			0
$532$	3.02231	+	4.54188i	0.131034	+	0.196915i
$533$		−	32.1063i		−	1.39068i
$534$		0			0
$535$	−13.4755	−	3.38269i	−0.582598	−	0.146247i
$536$	−1.14958	+	0.418412i	−0.0496541	+	0.0180726i
$537$		0			0
$538$	14.3237	−	17.0703i	0.617537	−	0.735952i
$539$	9.29130	−	16.0930i	0.400205	−	0.693175i
$540$		0			0
$541$	2.81801	−	15.9817i	0.121156	−	0.687109i	−0.862361	−	0.506294i	$-0.831015\pi$
$541$	2.81801	−	15.9817i	0.121156	−	0.687109i	0.983517	−	0.180815i	$-0.0578737\pi$
$542$	46.1502	+	8.13752i	1.98232	+	0.349537i
$543$		0			0
$544$	−20.2227	+	35.0268i	−0.867043	+	1.50176i
$545$	35.6603	+	2.55084i	1.52752	+	0.109266i
$546$		0			0
$547$	−3.39107	−	9.31688i	−0.144992	−	0.398361i	0.845845	−	0.533429i	$-0.179097\pi$
$547$	−3.39107	−	9.31688i	−0.144992	−	0.398361i	−0.990836	+	0.135068i	$0.956875\pi$
$548$	3.10364	+	3.69878i	0.132581	+	0.158004i
$549$		0			0
$550$	−26.4725	−	8.69501i	−1.12879	−	0.370757i
$551$	−5.17496	+	3.44358i	−0.220461	+	0.146702i
$552$		0			0
$553$	−9.89954	+	1.74556i	−0.420971	+	0.0742286i
$554$	7.05270	−	5.91792i	0.299641	−	0.251428i
$555$		0			0
$556$	−15.5836	−	5.67198i	−0.660894	−	0.240546i
$557$	14.7090	−	17.5295i	0.623240	−	0.742748i	−0.358384	−	0.933574i	$-0.616672\pi$
$557$	14.7090	−	17.5295i	0.623240	−	0.742748i	0.981624	+	0.190826i	$0.0611166\pi$
$558$		0			0
$559$	−13.4167	−	23.2385i	−0.567467	−	0.982882i
$560$	−5.82849	+	2.83123i	−0.246299	+	0.119641i
$561$		0			0
$562$	−38.1508	+	22.0264i	−1.60930	+	0.929128i
$563$	−10.8081	−	6.24004i	−0.455505	−	0.262986i	0.254647	−	0.967034i	$-0.418041\pi$
$563$	−10.8081	−	6.24004i	−0.455505	−	0.262986i	−0.710153	+	0.704048i	$0.751374\pi$
$564$		0			0
$565$	4.83214	+	16.9538i	0.203290	+	0.713252i
$566$	20.0623	−	7.30209i	0.843283	−	0.306930i
$567$		0			0
$568$	−2.22543	+	0.392403i	−0.0933768	+	0.0164649i
$569$	1.90233			0.0797500			0.0398750	−	0.999205i	$-0.487304\pi$
$569$	1.90233			0.0797500			0.0398750	+	0.999205i	$0.487304\pi$
$570$		0			0
$571$	−12.2153			−0.511193			−0.255596	−	0.966784i	$-0.582272\pi$
$571$	−12.2153			−0.511193			−0.255596	+	0.966784i	$0.582272\pi$
$572$	−24.6500	+	4.34646i	−1.03067	+	0.181734i
$573$		0			0
$574$	8.40707	−	3.05992i	0.350904	−	0.127719i
$575$	4.13031	+	3.24825i	0.172246	+	0.135461i
$576$		0			0
$577$	−21.9021	−	12.6452i	−0.911796	−	0.526425i	−0.0307872	−	0.999526i	$-0.509801\pi$
$577$	−21.9021	−	12.6452i	−0.911796	−	0.526425i	−0.881008	+	0.473100i	$0.843135\pi$
$578$	−16.7740	+	9.68448i	−0.697707	+	0.402821i
$579$		0			0
$580$	2.57552	+	5.30207i	0.106943	+	0.220157i
$581$	4.80092	+	8.31544i	0.199176	+	0.344982i
$582$		0			0
$583$	−12.5778	+	14.9896i	−0.520917	+	0.620805i
$584$	4.50283	+	1.63890i	0.186328	+	0.0678180i
$585$		0			0
$586$	−18.7418	+	15.7262i	−0.774216	+	0.649644i
$587$	6.22574	−	1.09777i	0.256964	−	0.0453097i	−0.0436821	−	0.999045i	$-0.513909\pi$
$587$	6.22574	−	1.09777i	0.256964	−	0.0453097i	0.300646	+	0.953736i	$0.402798\pi$
$588$		0			0
$589$	−1.14821	+	0.278652i	−0.0473112	+	0.0114817i
$590$	26.0430	+	35.9658i	1.07217	+	1.48069i
$591$		0			0
$592$	1.66100	+	1.97950i	0.0682666	+	0.0813569i
$593$	0.199642	+	0.548512i	0.00819832	+	0.0225247i	0.943724	−	0.330733i	$-0.107296\pi$
$593$	0.199642	+	0.548512i	0.00819832	+	0.0225247i	−0.935526	+	0.353258i	$0.885074\pi$
$594$		0			0
$595$	−7.82832	−	0.559972i	−0.320930	−	0.0229566i
$596$	−1.59721	+	2.76645i	−0.0654242	+	0.113318i
$597$		0			0
$598$	9.67784	+	1.70646i	0.395756	+	0.0697825i
$599$	7.38388	−	41.8761i	0.301697	−	1.71101i	−0.336961	−	0.941519i	$-0.609399\pi$
$599$	7.38388	−	41.8761i	0.301697	−	1.71101i	0.638658	−	0.769491i	$-0.279490\pi$
$600$		0			0
$601$	−8.13809	+	14.0956i	−0.331960	+	0.574971i	−0.982896	−	0.184161i	$-0.941043\pi$
$601$	−8.13809	+	14.0956i	−0.331960	+	0.574971i	0.650936	+	0.759132i	$0.274377\pi$
$602$	4.80632	−	5.72795i	0.195891	−	0.233454i
$603$		0			0
$604$	19.2360	−	7.00132i	0.782701	−	0.284880i
$605$	1.59540	−	6.35557i	0.0648624	−	0.258391i
$606$		0			0
$607$			6.86749i			0.278743i	0.990240	+	0.139371i	$0.0445082\pi$
$607$			6.86749i			0.278743i	−0.990240	+	0.139371i	$0.955492\pi$
$608$	33.9398	−	2.15972i	1.37644	−	0.0875881i
$609$		0			0
$610$	−22.8063	+	23.5413i	−0.923402	+	0.953160i
$611$	−28.8296	+	24.1909i	−1.16632	+	0.978658i
$612$		0			0
$613$	1.99841	−	5.49059i	0.0807150	−	0.221763i	−0.892770	−	0.450512i	$-0.851241\pi$
$613$	1.99841	−	5.49059i	0.0807150	−	0.221763i	0.973485	+	0.228749i	$0.0734636\pi$
$614$	−6.27958	−	5.26920i	−0.253423	−	0.212647i
$615$		0			0
$616$	0.285734	+	0.494906i	0.0115126	+	0.0199403i
$617$	−37.9767	−	6.69631i	−1.52888	−	0.269583i	−0.654966	−	0.755658i	$-0.727317\pi$
$617$	−37.9767	−	6.69631i	−1.52888	−	0.269583i	−0.873917	+	0.486075i	$0.838428\pi$
$618$		0			0
$619$	5.46007	+	9.45712i	0.219459	+	0.380114i	0.954643	−	0.297754i	$-0.0962375\pi$
$619$	5.46007	+	9.45712i	0.219459	+	0.380114i	−0.735184	+	0.677868i	$0.762904\pi$
$620$	0.115338	+	1.11448i	0.00463207	+	0.0447586i
$621$		0			0
$622$	8.11256	−	22.2891i	0.325284	−	0.893711i
$623$	1.90765	+	5.24123i	0.0764285	+	0.209986i
$624$		0			0
$625$	11.1026	−	22.3994i	0.444103	−	0.895976i
$626$	18.7910			0.751039
$627$		0			0
$628$		−	3.63169i		−	0.144920i
$629$	0.543488	+	3.08228i	0.0216703	+	0.122898i
$630$		0			0
$631$	−7.62467	+	2.77515i	−0.303533	+	0.110477i	−0.489297	−	0.872117i	$-0.662746\pi$
$631$	−7.62467	+	2.77515i	−0.303533	+	0.110477i	0.185763	+	0.982595i	$0.440524\pi$
$632$	−1.50876	+	4.14528i	−0.0600152	+	0.164890i
$633$		0			0
$634$	10.9557	−	18.9758i	0.435106	−	0.753626i
$635$	14.3980	−	32.2000i	0.571367	−	1.27782i
$636$		0			0
$637$	30.7076	+	5.41457i	1.21668	+	0.214533i
$638$	6.88234	−	3.97352i	0.272474	−	0.157313i
$639$		0			0
$640$	−0.378141	+	5.28635i	−0.0149473	+	0.208961i
$641$	13.0690	+	4.75673i	0.516195	+	0.187880i	0.586964	−	0.809613i	$-0.300323\pi$
$641$	13.0690	+	4.75673i	0.516195	+	0.187880i	−0.0707688	+	0.997493i	$0.522545\pi$
$642$		0			0
$643$	−24.4957	−	29.1929i	−0.966017	−	1.15125i	−0.988456	−	0.151506i	$-0.951588\pi$
$643$	−24.4957	−	29.1929i	−0.966017	−	1.15125i	0.0224393	−	0.999748i	$-0.492857\pi$
$644$	0.228402	+	1.29533i	0.00900029	+	0.0510432i
$645$		0			0
$646$	39.7198	+	19.6816i	1.56276	+	0.774364i
$647$		−	28.6072i		−	1.12466i	−0.826912	−	0.562332i	$-0.809904\pi$
$647$		−	28.6072i		−	1.12466i	0.826912	−	0.562332i	$-0.190096\pi$
$648$		0			0
$649$	22.0279	−	18.4836i	0.864671	−	0.725545i
$650$	−1.48249	−	46.7317i	−0.0581482	−	1.83297i
$651$		0			0
$652$	23.9202	−	28.5070i	0.936787	−	1.11642i
$653$	−10.2937	−	5.94304i	−0.402822	−	0.232569i	0.284879	−	0.958563i	$-0.408047\pi$
$653$	−10.2937	−	5.94304i	−0.402822	−	0.232569i	−0.687701	+	0.725994i	$0.741380\pi$
$654$		0			0
$655$	3.97278	+	8.17854i	0.155230	+	0.319562i
$656$	5.00599	−	28.3904i	0.195451	−	1.10846i
$657$		0			0
$658$	−9.08204	−	5.24352i	−0.354055	−	0.204414i
$659$	−28.2769	−	23.7271i	−1.10151	−	0.924278i	−0.103986	−	0.994579i	$-0.533160\pi$
$659$	−28.2769	−	23.7271i	−1.10151	−	0.924278i	−0.997526	+	0.0703009i	$0.977604\pi$
$660$		0			0
$661$	8.49572	−	3.09219i	0.330445	−	0.120272i	−0.171469	−	0.985189i	$-0.554851\pi$
$661$	8.49572	−	3.09219i	0.330445	−	0.120272i	0.501914	+	0.864917i	$0.332629\pi$
$662$	−27.3483	−	32.5925i	−1.06292	−	1.26674i
$663$		0			0
$664$	4.21365			0.163521
$665$	3.25458	+	5.74087i	0.126207	+	0.222621i
$666$		0			0
$667$	−1.47588	+	0.260238i	−0.0571465	+	0.0100765i
$668$	−21.2176	−	25.2862i	−0.820935	−	0.978353i
$669$		0			0
$670$	17.3696	−	4.95064i	0.671045	−	0.191260i
$671$	16.2597	+	13.6435i	0.627698	+	0.526701i
$672$		0			0
$673$	34.4994	−	19.9182i	1.32985	−	0.767791i	0.344577	−	0.938758i	$-0.388022\pi$
$673$	34.4994	−	19.9182i	1.32985	−	0.767791i	0.985277	+	0.170967i	$0.0546891\pi$
$674$	−0.0180037	+	0.102104i	−0.000693478	+	0.00393291i
$675$		0			0
$676$	−8.98462	−	15.5618i	−0.345562	−	0.598532i
$677$	15.6221	+	9.01941i	0.600405	+	0.346644i	0.769201	−	0.639007i	$-0.220655\pi$
$677$	15.6221	+	9.01941i	0.600405	+	0.346644i	−0.168796	+	0.985651i	$0.553988\pi$
$678$		0			0
$679$	−3.64465	−	1.32655i	−0.139869	−	0.0509081i
$680$	−1.93050	+	2.85224i	−0.0740311	+	0.109379i
$681$		0			0
$682$	1.48763	−	0.262309i	0.0569643	−	0.0100443i
$683$		−	15.4271i		−	0.590301i	−0.955451	−	0.295151i	$-0.904630\pi$
$683$		−	15.4271i		−	0.590301i	0.955451	−	0.295151i	$-0.0953698\pi$
$684$		0			0
$685$	3.42549	+	4.73065i	0.130881	+	0.180749i
$686$	3.12334	+	17.7134i	0.119250	+	0.676299i
$687$		0			0
$688$	−8.24059	−	22.6408i	−0.314169	−	0.863173i
$689$	−30.8538	−	11.2299i	−1.17544	−	0.427824i
$690$		0			0
$691$	−1.51912	+	2.63119i	−0.0577901	+	0.100095i	−0.893473	−	0.449117i	$-0.851739\pi$
$691$	−1.51912	+	2.63119i	−0.0577901	+	0.100095i	0.835683	+	0.549212i	$0.185072\pi$
$692$	−4.35789	+	2.51603i	−0.165662	+	0.0956452i
$693$		0			0
$694$	8.64803	−	49.0454i	0.328275	−	1.86174i
$695$	−18.3130	−	8.18853i	−0.694651	−	0.310609i
$696$		0			0
$697$	22.4443	−	26.7481i	0.850138	−	1.01315i
$698$	10.4804	−	28.7947i	0.396689	−	1.08990i
$699$		0			0
$700$	5.80972	−	2.32572i	0.219587	−	0.0879041i
$701$	7.95179	+	45.0968i	0.300335	+	1.70328i	0.644690	+	0.764444i	$0.276987\pi$
$701$	7.95179	+	45.0968i	0.300335	+	1.70328i	−0.344355	+	0.938840i	$0.611902\pi$
$702$		0			0
$703$	1.90451	−	1.81624i	0.0718298	−	0.0685008i
$704$	−19.1631			−0.722238
$705$		0			0
$706$	−18.7419	+	15.7263i	−0.705360	+	0.591867i
$707$	0.468309	+	1.28667i	0.0176126	+	0.0483901i
$708$		0			0
$709$	−16.8950	−	14.1766i	−0.634506	−	0.532414i	0.267819	−	0.963469i	$-0.413697\pi$
$709$	−16.8950	−	14.1766i	−0.634506	−	0.532414i	−0.902326	+	0.431055i	$0.858141\pi$
$710$	33.1853	−	3.43435i	1.24542	−	0.128889i
$711$		0			0
$712$	2.41048	+	0.425032i	0.0903365	+	0.0159288i
$713$	−0.280537	−	0.0494663i	−0.0105062	−	0.00185253i
$714$		0			0
$715$	−30.1167	+	3.11678i	−1.12630	+	0.116561i
$716$	−10.9268	−	9.16871i	−0.408355	−	0.342651i
$717$		0			0
$718$	22.5732	+	62.0195i	0.842426	+	2.31455i
$719$	−5.43476	+	4.56031i	−0.202682	+	0.170071i	−0.738479	−	0.674276i	$-0.764456\pi$
$719$	−5.43476	+	4.56031i	−0.202682	+	0.170071i	0.535797	+	0.844347i	$0.320011\pi$
$720$		0			0
$721$	−12.3469			−0.459822
$722$	−4.72459	−	36.9730i	−0.175831	−	1.37599i
$723$		0			0
$724$	0.343596	+	1.94863i	0.0127696	+	0.0724202i
$725$	2.64990	+	6.61953i	0.0984149	+	0.245843i
$726$		0			0
$727$	9.64932	−	26.5113i	0.357873	−	0.983249i	−0.621893	−	0.783103i	$-0.713636\pi$
$727$	9.64932	−	26.5113i	0.357873	−	0.983249i	0.979766	−	0.200147i	$-0.0641418\pi$
$728$	−0.616378	+	0.734570i	−0.0228445	+	0.0272250i
$729$		0			0
$730$	−64.5829	−	28.8778i	−2.39032	−	1.06882i
$731$	5.06752	−	28.7393i	0.187429	−	1.06296i
$732$		0			0
$733$	−0.897082	+	0.517931i	−0.0331345	+	0.0191302i	−0.516476	−	0.856302i	$-0.672756\pi$
$733$	−0.897082	+	0.517931i	−0.0331345	+	0.0191302i	0.483341	+	0.875432i	$0.339423\pi$
$734$	−25.1205	+	43.5100i	−0.927214	+	1.60598i
$735$		0			0
$736$	7.70484	+	2.80433i	0.284004	+	0.103369i
$737$	−4.00029	−	10.9907i	−0.147353	−	0.404848i
$738$		0			0
$739$	−3.37137	−	19.1200i	−0.124018	−	0.703340i	−0.981886	−	0.189471i	$-0.939323\pi$
$739$	−3.37137	−	19.1200i	−0.124018	−	0.703340i	0.857868	−	0.513869i	$-0.171788\pi$
$740$	−1.46365	−	2.02132i	−0.0538049	−	0.0743053i
$741$		0			0
$742$		−	9.14938i		−	0.335884i
$743$	12.5098	−	2.20582i	0.458941	−	0.0809237i	0.0606022	−	0.998162i	$-0.480698\pi$
$743$	12.5098	−	2.20582i	0.458941	−	0.0809237i	0.398339	+	0.917238i	$0.369587\pi$
$744$		0			0
$745$	−2.16588	+	3.20002i	−0.0793518	+	0.117240i
$746$	40.1156	+	14.6009i	1.46874	+	0.534576i
$747$		0			0
$748$	−23.5746	−	13.6108i	−0.861972	−	0.497660i
$749$	−2.10345	−	3.64328i	−0.0768584	−	0.133123i
$750$		0			0
$751$	−0.801897	+	4.54778i	−0.0292616	+	0.165951i	−0.995937	−	0.0900552i	$-0.971296\pi$
$751$	−0.801897	+	4.54778i	−0.0292616	+	0.165951i	0.966675	+	0.256006i	$0.0824068\pi$
$752$	−29.2647	+	16.8960i	−1.06717	+	0.616134i
$753$		0			0
$754$	10.2152	+	8.57157i	0.372016	+	0.312158i
$755$	23.8135	−	6.78728i	0.866663	−	0.247014i
$756$		0			0
$757$	−4.37741	−	5.21680i	−0.159100	−	0.189608i	0.680606	−	0.732650i	$-0.261717\pi$
$757$	−4.37741	−	5.21680i	−0.159100	−	0.189608i	−0.839705	+	0.543042i	$0.817272\pi$
$758$	−12.8095	+	2.25866i	−0.465262	+	0.0820382i
$759$		0			0
$760$	2.89591	+	0.0227681i	0.105046	+	0.000825885i
$761$	−24.4864			−0.887632			−0.443816	−	0.896118i	$-0.646376\pi$
$761$	−24.4864			−0.887632			−0.443816	+	0.896118i	$0.646376\pi$
$762$		0			0
$763$	6.95837	+	8.29266i	0.251910	+	0.300215i
$764$	−9.35053	+	3.40332i	−0.338290	+	0.123128i
$765$		0			0
$766$	−40.6086	−	34.0746i	−1.46725	−	1.23117i
$767$	41.7867	+	24.1255i	1.50883	+	0.871123i
$768$		0			0
$769$	−0.519478	+	2.94611i	−0.0187329	+	0.106239i	−0.992741	−	0.120276i	$-0.961622\pi$
$769$	−0.519478	+	2.94611i	−0.0187329	+	0.106239i	0.974008	+	0.226515i	$0.0727333\pi$
$770$	−3.68643	−	7.58904i	−0.132850	−	0.273490i
$771$		0			0
$772$	24.7656	+	14.2984i	0.891332	+	0.514611i
$773$	−12.7042	+	15.1403i	−0.456938	+	0.544557i	−0.944491	−	0.328536i	$-0.893445\pi$
$773$	−12.7042	+	15.1403i	−0.456938	+	0.544557i	0.487554	+	0.873093i	$0.337889\pi$
$774$		0			0
$775$	0.0429739	+	1.35464i	0.00154367	+	0.0486600i
$776$	−1.30385	+	1.09406i	−0.0468056	+	0.0392745i
$777$		0			0
$778$			50.9857i			1.82792i
$779$	−29.1793	−	3.25183i	−1.04546	−	0.116509i
$780$		0			0
$781$	−3.75163	−	21.2765i	−0.134244	−	0.761335i
$782$	6.86978	+	8.18709i	0.245663	+	0.292770i
$783$		0			0
$784$	26.3093	+	9.57581i	0.939618	+	0.341993i
$785$	0.313440	−	4.38183i	0.0111871	−	0.156394i
$786$		0			0
$787$	20.3920	−	11.7733i	0.726895	−	0.419673i	−0.0903901	−	0.995906i	$-0.528811\pi$
$787$	20.3920	−	11.7733i	0.726895	−	0.419673i	0.817285	+	0.576233i	$0.195478\pi$
$788$	38.6535	+	6.81565i	1.37697	+	0.242798i
$789$		0			0
$790$	26.5847	−	59.4546i	0.945843	−	2.11530i
$791$	−2.66897	+	4.62280i	−0.0948977	+	0.164368i
$792$		0			0
$793$	−12.1814	+	33.4681i	−0.432574	+	1.18849i
$794$	39.3532	−	14.3234i	1.39659	−	0.508318i
$795$		0			0
$796$	2.43353	+	13.8013i	0.0862543	+	0.489173i
$797$		−	5.96976i		−	0.211460i	−0.994395	−	0.105730i	$-0.966282\pi$
$797$		−	5.96976i		−	0.211460i	0.994395	−	0.105730i	$-0.0337179\pi$
$798$		0			0
$799$	−40.9291			−1.44797
$800$	5.55254	−	38.6132i	0.196312	−	1.36518i
$801$		0			0
$802$	17.4861	+	48.0427i	0.617456	+	1.69645i
$803$	−15.6689	+	43.0500i	−0.552945	+	1.51920i
$804$		0			0
$805$	0.163783	+	1.58260i	0.00577260	+	0.0557793i
$806$	1.26736	+	2.19514i	0.0446409	+	0.0773204i
$807$		0			0
$808$	0.591747	+	0.104341i	0.0208176	+	0.00367070i
$809$	12.9533	+	22.4358i	0.455414	+	0.788801i	0.998712	−	0.0507393i	$-0.0161577\pi$
$809$	12.9533	+	22.4358i	0.455414	+	0.788801i	−0.543297	+	0.839540i	$0.682824\pi$
$810$		0			0
$811$	21.1791	+	17.7713i	0.743698	+	0.624036i	0.933828	−	0.357723i	$-0.116447\pi$
$811$	21.1791	+	17.7713i	0.743698	+	0.624036i	−0.190130	+	0.981759i	$0.560891\pi$
$812$	−0.610445	+	1.67718i	−0.0214224	+	0.0588576i
$813$		0			0
$814$	−2.57743	+	2.16272i	−0.0903388	+	0.0758032i
$815$	31.3214	−	32.3308i	1.09714	−	1.13250i
$816$		0			0
$817$	−22.4788	+	9.83993i	−0.786434	+	0.344256i
$818$			45.8018i			1.60142i
$819$		0			0
$820$	−6.77861	+	27.0037i	−0.236719	+	0.943011i
$821$	−9.72970	+	3.54132i	−0.339569	+	0.123593i	−0.506175	−	0.862431i	$-0.668941\pi$
$821$	−9.72970	+	3.54132i	−0.339569	+	0.123593i	0.166607	+	0.986023i	$0.446719\pi$
$822$		0			0
$823$	27.2218	−	32.4417i	0.948893	−	1.13085i	−0.0423901	−	0.999101i	$-0.513497\pi$
$823$	27.2218	−	32.4417i	0.948893	−	1.13085i	0.991284	−	0.131746i	$-0.0420583\pi$
$824$	−2.70914	+	4.69237i	−0.0943775	+	0.163467i
$825$		0			0
$826$	−2.33478	+	13.2412i	−0.0812374	+	0.460720i
$827$	22.2391	+	3.92136i	0.773330	+	0.136359i	0.546369	−	0.837545i	$-0.316010\pi$
$827$	22.2391	+	3.92136i	0.773330	+	0.136359i	0.226962	+	0.973904i	$0.427121\pi$
$828$		0			0
$829$	−6.32446	+	10.9543i	−0.219657	+	0.380458i	−0.954703	−	0.297560i	$-0.903827\pi$
$829$	−6.32446	+	10.9543i	−0.219657	+	0.380458i	0.735046	+	0.678017i	$0.237161\pi$
$830$	−62.0508	−	4.43860i	−2.15381	−	0.154066i
$831$		0			0
$832$	−10.9978	−	30.2162i	−0.381280	−	1.04756i
$833$	21.7977	+	25.9774i	0.755244	+	0.900065i
$834$		0			0
$835$	−23.4179	−	32.3404i	−0.810409	−	1.11919i
$836$	1.45358	+	22.8430i	0.0502732	+	0.790041i
$837$		0			0
$838$	−42.4938	+	7.49280i	−1.46792	+	0.258834i
$839$	35.3478	−	29.6603i	1.22034	−	1.02399i	0.221535	−	0.975152i	$-0.428893\pi$
$839$	35.3478	−	29.6603i	1.22034	−	1.02399i	0.998807	−	0.0488360i	$-0.0155512\pi$
$840$		0			0
$841$	25.3401	+	9.22305i	0.873797	+	0.318036i
$842$	−4.70498	+	5.60717i	−0.162144	+	0.193236i
$843$		0			0
$844$	−12.2920	−	21.2903i	−0.423108	−	0.732844i
$845$	−9.49735	−	19.5516i	−0.326719	−	0.672596i
$846$		0			0
$847$	1.71831	−	0.992066i	0.0590418	−	0.0340878i
$848$	−25.5319	−	14.7409i	−0.876770	−	0.506203i
$849$		0			0
$850$	31.4333	−	39.9690i	1.07815	−	1.37092i
$851$	0.596230	−	0.217010i	0.0204385	−	0.00743900i
$852$		0			0
$853$	36.8941	−	6.50543i	1.26323	−	0.222742i	0.498386	−	0.866955i	$-0.333926\pi$
$853$	36.8941	−	6.50543i	1.26323	−	0.222742i	0.764846	+	0.644214i	$0.222815\pi$
$854$	−9.92463			−0.339614
$855$		0			0
$856$	−1.84615			−0.0631000
$857$	33.3201	−	5.87524i	1.13819	−	0.200694i	0.427379	−	0.904073i	$-0.359437\pi$
$857$	33.3201	−	5.87524i	1.13819	−	0.200694i	0.710816	+	0.703378i	$0.248326\pi$
$858$		0			0
$859$	−19.9349	+	7.25572i	−0.680171	+	0.247562i	−0.658921	−	0.752212i	$-0.728987\pi$
$859$	−19.9349	+	7.25572i	−0.680171	+	0.247562i	−0.0212498	+	0.999774i	$0.506765\pi$
$860$	6.37811	+	22.3779i	0.217492	+	0.763081i
$861$		0			0
$862$	−42.3277	−	24.4379i	−1.44169	−	0.832358i
$863$	−25.2353	+	14.5696i	−0.859019	+	0.495955i	−0.863684	−	0.504034i	$-0.831848\pi$
$863$	−25.2353	+	14.5696i	−0.859019	+	0.495955i	0.00466481	+	0.999989i	$0.498515\pi$
$864$		0			0
$865$	−5.47519	+	2.65961i	−0.186162	+	0.0904296i
$866$	10.7625	+	18.6412i	0.365725	+	0.633454i
$867$		0			0
$868$	−0.218072	+	0.259888i	−0.00740185	+	0.00882119i
$869$	−39.6316	−	14.4247i	−1.34441	−	0.489325i
$870$		0			0
$871$	15.0342	−	12.6152i	0.509416	−	0.427450i
$872$	4.67838	−	0.824925i	0.158430	−	0.0279355i
$873$		0			0
$874$	2.53110	−	8.62273i	0.0856157	−	0.291668i
$875$	7.21047	−	2.30470i	0.243758	−	0.0779129i
$876$		0			0
$877$	4.13842	+	4.93198i	0.139745	+	0.166541i	0.831377	−	0.555708i	$-0.187553\pi$
$877$	4.13842	+	4.93198i	0.139745	+	0.166541i	−0.691633	+	0.722249i	$0.743108\pi$
$878$	−5.71644	−	15.7058i	−0.192920	−	0.530045i
$879$		0			0
$880$	−27.1170	−	1.93972i	−0.914114	−	0.0653881i
$881$	7.19996	−	12.4707i	0.242573	−	0.420148i	−0.718874	−	0.695141i	$-0.755342\pi$
$881$	7.19996	−	12.4707i	0.242573	−	0.420148i	0.961446	+	0.274993i	$0.0886754\pi$
$882$		0			0
$883$	25.4096	+	4.48039i	0.855100	+	0.150777i	0.583980	−	0.811768i	$-0.301495\pi$
$883$	25.4096	+	4.48039i	0.855100	+	0.150777i	0.271121	+	0.962545i	$0.412606\pi$
$884$	7.93179	−	44.9834i	0.266775	−	1.51296i
$885$		0			0
$886$	−9.23713	+	15.9992i	−0.310327	+	0.537503i
$887$	−16.6762	+	19.8739i	−0.559931	+	0.667300i	−0.969532	−	0.244965i	$-0.921224\pi$
$887$	−16.6762	+	19.8739i	−0.559931	+	0.667300i	0.409601	+	0.912265i	$0.365668\pi$
$888$		0			0
$889$	10.0362	−	3.65286i	0.336602	−	0.122513i
$890$	−35.0493	−	8.79825i	−1.17486	−	0.294918i
$891$		0			0
$892$		−	36.7479i		−	1.23041i
$893$	19.0656	+	28.6515i	0.638005	+	0.958785i
$894$		0			0
$895$	−12.3925	−	12.0056i	−0.414236	−	0.401303i
$896$	−1.22932	+	1.03152i	−0.0410687	+	0.0344607i
$897$		0			0
$898$	6.52677	−	17.9321i	0.217801	−	0.598404i
$899$	−0.296114	−	0.248469i	−0.00987595	−	0.00828690i
$900$		0			0
$901$	−17.8542	−	30.9245i	−0.594811	−	1.03024i
$902$	36.9660	+	6.51810i	1.23083	+	0.217029i
$903$		0			0
$904$	1.17125	+	2.02866i	0.0389551	+	0.0674722i
$905$	0.246387	+	2.38078i	0.00819018	+	0.0791398i
$906$		0			0
$907$	−10.2352	+	28.1209i	−0.339853	+	0.933740i	0.645582	+	0.763691i	$0.276615\pi$
$907$	−10.2352	+	28.1209i	−0.339853	+	0.933740i	−0.985436	+	0.170049i	$0.945607\pi$
$908$	−17.2615	−	47.4255i	−0.572843	−	1.57387i
$909$		0			0
$910$	9.85065	−	10.1681i	0.326546	−	0.337069i
$911$	−3.36120			−0.111362			−0.0556808	−	0.998449i	$-0.517733\pi$
$911$	−3.36120			−0.111362			−0.0556808	+	0.998449i	$0.517733\pi$
$912$		0			0
$913$			40.2853i			1.33325i
$914$	3.56621	+	20.2250i	0.117960	+	0.668982i
$915$		0			0
$916$	25.4357	−	9.25784i	0.840419	−	0.305888i
$917$	−0.941622	+	2.58708i	−0.0310951	+	0.0854330i
$918$		0			0
$919$	3.46233	−	5.99694i	0.114212	−	0.197821i	−0.803253	−	0.595639i	$-0.796899\pi$
$919$	3.46233	−	5.99694i	0.114212	−	0.197821i	0.917464	+	0.397818i	$0.130232\pi$
$920$	0.637396	+	0.285007i	0.0210143	+	0.00939642i
$921$		0			0
$922$	43.8052	+	7.72404i	1.44265	+	0.254378i
$923$	31.3955	−	18.1262i	1.03340	−	0.596632i
$924$		0			0
$925$	−1.59152	−	2.56516i	−0.0523289	−	0.0843419i
$926$	−65.6965	−	23.9116i	−2.15892	−	0.785783i
$927$		0			0
$928$	7.15173	+	8.52310i	0.234767	+	0.279785i
$929$	4.74769	+	26.9255i	0.155767	+	0.883396i	0.958082	+	0.286495i	$0.0924903\pi$
$929$	4.74769	+	26.9255i	0.155767	+	0.883396i	−0.802315	+	0.596901i	$0.796399\pi$
$930$		0			0
$931$	8.03112	−	27.3597i	0.263209	−	0.896679i
$932$			12.2546i			0.401413i
$933$		0			0
$934$	−4.36053	+	3.65892i	−0.142681	+	0.119724i
$935$	−27.2693	−	18.4568i	−0.891802	−	0.603602i
$936$		0			0
$937$	−23.8716	+	28.4491i	−0.779851	+	0.929390i	−0.998927	−	0.0463175i	$-0.985251\pi$
$937$	−23.8716	+	28.4491i	−0.779851	+	0.929390i	0.219076	+	0.975708i	$0.429696\pi$
$938$	4.73616	+	2.73443i	0.154641	+	0.0892822i
$939$		0			0
$940$	29.3552	−	14.2595i	0.957461	−	0.465094i
$941$	−8.80177	+	49.9173i	−0.286929	+	1.62726i	0.411382	+	0.911463i	$0.365046\pi$
$941$	−8.80177	+	49.9173i	−0.286929	+	1.62726i	−0.698311	+	0.715794i	$0.746065\pi$
$942$		0			0
$943$	−6.13023	−	3.53929i	−0.199628	−	0.115255i
$944$	33.1887	+	27.8487i	1.08020	+	0.906396i
$945$		0			0
$946$	29.4797	−	10.7297i	0.958468	−	0.348854i
$947$	2.61402	+	3.11527i	0.0849442	+	0.101233i	0.806842	−	0.590767i	$-0.201175\pi$
$947$	2.61402	+	3.11527i	0.0849442	+	0.101233i	−0.721898	+	0.691999i	$0.756730\pi$
$948$		0			0
$949$	−76.8732			−2.49541
$950$	−42.6215	−	3.38579i	−1.38282	−	0.109849i
$951$		0			0
$952$	−1.02702	+	0.181091i	−0.0332859	+	0.00586921i
$953$	9.53460	+	11.3629i	0.308856	+	0.368080i	0.898036	−	0.439921i	$-0.144994\pi$
$953$	9.53460	+	11.3629i	0.308856	+	0.368080i	−0.589180	+	0.808002i	$0.700549\pi$
$954$		0			0
$955$	−11.5757	+	3.29927i	−0.374580	+	0.106762i
$956$	17.9546	+	15.0657i	0.580692	+	0.487258i
$957$		0			0
$958$	49.8656	−	28.7899i	1.61108	−	0.930160i
$959$	−0.307098	+	1.74164i	−0.00991671	+	0.0562405i
$960$		0			0
$961$	15.4633	+	26.7832i	0.498815	+	0.863973i
$962$	−4.88934	−	2.82286i	−0.157639	−	0.0910128i
$963$		0			0
$964$	24.5166	+	8.92330i	0.789626	+	0.287400i
$965$	28.6470	+	19.3893i	0.922178	+	0.624162i
$966$		0			0
$967$	−55.8584	+	9.84935i	−1.79629	+	0.316734i	−0.969372	−	0.245595i	$-0.921017\pi$
$967$	−55.8584	+	9.84935i	−1.79629	+	0.316734i	−0.826914	+	0.562329i	$0.809905\pi$
$968$		−	0.870712i		−	0.0279858i
$969$		0			0
$970$	20.3532	−	14.7379i	0.653501	−	0.473204i
$971$	2.18689	+	12.4025i	0.0701805	+	0.398014i	0.999581	+	0.0289410i	$0.00921350\pi$
$971$	2.18689	+	12.4025i	0.0701805	+	0.398014i	−0.929401	+	0.369073i	$0.879675\pi$
$972$		0			0
$973$	−2.07748	−	5.70783i	−0.0666010	−	0.182985i
$974$	6.29879	+	2.29257i	0.201826	+	0.0734588i
$975$		0			0
$976$	−15.9899	+	27.6953i	−0.511824	+	0.886505i
$977$	31.9540	−	18.4486i	1.02230	−	0.590224i	0.107529	−	0.994202i	$-0.465706\pi$
$977$	31.9540	−	18.4486i	1.02230	−	0.590224i	0.914769	+	0.403978i	$0.132373\pi$
$978$		0			0
$979$	−4.06359	+	23.0458i	−0.129873	+	0.736546i
$980$	−24.6841	−	11.0374i	−0.788506	−	0.352575i
$981$		0			0
$982$	−31.7599	+	37.8500i	−1.01350	+	1.20784i
$983$	3.26993	−	8.98405i	0.104295	−	0.286547i	−0.876559	−	0.481295i	$-0.840167\pi$
$983$	3.26993	−	8.98405i	0.104295	−	0.286547i	0.980853	+	0.194748i	$0.0623889\pi$
$984$		0			0
$985$	46.0493	+	11.5595i	1.46725	+	0.368317i
$986$	2.51832	+	14.2821i	0.0801997	+	0.454835i
$987$		0			0
$988$	−35.1843	+	15.4017i	−1.11936	+	0.489992i
$989$	−5.91606			−0.188120
$990$		0			0
$991$	−12.4584	+	10.4538i	−0.395755	+	0.332077i	−0.818850	−	0.574008i	$-0.805388\pi$
$991$	−12.4584	+	10.4538i	−0.395755	+	0.332077i	0.423095	+	0.906085i	$0.360944\pi$
$992$	0.723325	+	1.98732i	0.0229656	+	0.0630974i
$993$		0			0
$994$	7.73855	+	6.49342i	0.245452	+	0.205959i
$995$	1.74505	+	16.8620i	0.0553218	+	0.534561i
$996$		0			0
$997$	36.0838	+	6.36254i	1.14278	+	0.201504i	0.712823	−	0.701344i	$-0.247416\pi$
$997$	36.0838	+	6.36254i	1.14278	+	0.201504i	0.429961	+	0.902848i	$0.358527\pi$
$998$	67.1039	+	11.8322i	2.12414	+	0.374543i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	855.2.da.b.199.1		48
3.2	odd	2		95.2.p.a.9.8	yes	48
5.4	even	2	inner	855.2.da.b.199.8		48
15.2	even	4		475.2.l.f.351.8		48
15.8	even	4		475.2.l.f.351.1		48
15.14	odd	2		95.2.p.a.9.1	✓	48
19.17	even	9	inner	855.2.da.b.739.8		48
57.17	odd	18		95.2.p.a.74.1	yes	48
57.32	even	18		1805.2.b.l.1084.21		24
57.44	odd	18		1805.2.b.k.1084.4		24
95.74	even	18	inner	855.2.da.b.739.1		48
285.17	even	36		475.2.l.f.226.8		48
285.32	odd	36		9025.2.a.ct.1.4		24
285.44	odd	18		1805.2.b.k.1084.21		24
285.74	odd	18		95.2.p.a.74.8	yes	48
285.89	even	18		1805.2.b.l.1084.4		24
285.158	even	36		9025.2.a.cu.1.4		24
285.188	even	36		475.2.l.f.226.1		48
285.203	odd	36		9025.2.a.ct.1.21		24
285.272	even	36		9025.2.a.cu.1.21		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.p.a.9.1	✓	48	15.14	odd	2
95.2.p.a.9.8	yes	48	3.2	odd	2
95.2.p.a.74.1	yes	48	57.17	odd	18
95.2.p.a.74.8	yes	48	285.74	odd	18
475.2.l.f.226.1		48	285.188	even	36
475.2.l.f.226.8		48	285.17	even	36
475.2.l.f.351.1		48	15.8	even	4
475.2.l.f.351.8		48	15.2	even	4
855.2.da.b.199.1		48	1.1	even	1	trivial
855.2.da.b.199.8		48	5.4	even	2	inner
855.2.da.b.739.1		48	95.74	even	18	inner
855.2.da.b.739.8		48	19.17	even	9	inner
1805.2.b.k.1084.4		24	57.44	odd	18
1805.2.b.k.1084.21		24	285.44	odd	18
1805.2.b.l.1084.4		24	285.89	even	18
1805.2.b.l.1084.21		24	57.32	even	18
9025.2.a.ct.1.4		24	285.32	odd	36
9025.2.a.ct.1.21		24	285.203	odd	36
9025.2.a.cu.1.4		24	285.158	even	36
9025.2.a.cu.1.21		24	285.272	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)

\(f(q)\)	\(=\)	\(q+(-1.93197 + 0.340658i) q^{2} +(1.73706 - 0.632239i) q^{4} +(2.15043 - 0.612911i) q^{5} +(0.586358 + 0.338534i) q^{7} +(0.257316 - 0.148561i) q^{8} +O(q^{10})\)	\(q+(-1.93197 + 0.340658i) q^{2} +(1.73706 - 0.632239i) q^{4} +(2.15043 - 0.612911i) q^{5} +(0.586358 + 0.338534i) q^{7} +(0.257316 - 0.148561i) q^{8} +(-3.94576 + 1.91668i) q^{10} +(1.42035 + 2.46011i) q^{11} +(-3.06393 + 3.65145i) q^{13} +(-1.24815 - 0.454289i) q^{14} +(-3.27865 + 2.75111i) q^{16} +(-5.10518 + 0.900181i) q^{17} +(3.00824 + 3.15444i) q^{19} +(3.34792 - 2.42425i) q^{20} +(-3.58212 - 4.26900i) q^{22} +(0.359434 + 0.987537i) q^{23} +(4.24868 - 2.63604i) q^{25} +(4.67552 - 8.09823i) q^{26} +(1.23257 + 0.217336i) q^{28} +(-0.247630 + 1.40438i) q^{29} +(-0.135532 + 0.234748i) q^{31} +(5.01508 - 5.97674i) q^{32} +(9.55639 - 3.47824i) q^{34} +(1.46841 + 0.368607i) q^{35} -0.603754i q^{37} +(-6.88641 - 5.06949i) q^{38} +(0.462285 - 0.477182i) q^{40} +(-5.15980 + 4.32958i) q^{41} +(-1.92538 + 5.28994i) q^{43} +(4.02261 + 3.37537i) q^{44} +(-1.03083 - 1.78544i) q^{46} +(7.77543 + 1.37102i) q^{47} +(-3.27079 - 5.66517i) q^{49} +(-7.31032 + 6.54009i) q^{50} +(-3.01365 + 8.27993i) q^{52} +(2.35594 + 6.47288i) q^{53} +(4.56218 + 4.41974i) q^{55} +0.201172 q^{56} -2.79757i q^{58} +(-1.75779 - 9.96889i) q^{59} +(7.02134 - 2.55556i) q^{61} +(0.181874 - 0.499695i) q^{62} +(-3.37297 + 5.84216i) q^{64} +(-4.35075 + 9.73010i) q^{65} +(-4.05478 - 0.714967i) q^{67} +(-8.29889 + 4.79137i) q^{68} +(-2.96249 - 0.211912i) q^{70} +(-7.14680 - 2.60122i) q^{71} +(10.3665 + 12.3543i) q^{73} +(0.205674 + 1.16643i) q^{74} +(7.21986 + 3.57753i) q^{76} +1.92334i q^{77} +(-11.3733 + 9.54332i) q^{79} +(-5.36431 + 7.92559i) q^{80} +(8.49365 - 10.1223i) q^{82} +(12.2815 + 7.09076i) q^{83} +(-10.4266 + 5.06480i) q^{85} +(1.91771 - 10.8759i) q^{86} +(0.730955 + 0.422017i) q^{88} +(6.31059 + 5.29521i) q^{89} +(-3.03270 + 1.10381i) q^{91} +(1.24872 + 1.48817i) q^{92} -15.4889 q^{94} +(8.40240 + 4.93961i) q^{95} +(-5.64144 + 0.994738i) q^{97} +(8.24894 + 9.83071i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 18 q^{4} + 6 q^{5}+O(q^{10}) \) 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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