LMFDB - Embedded newform 90.2.l.b.47.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [90,2,Mod(23,90)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(90, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([10, 9]))

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

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

chi := DirichletCharacter("90.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 90 = 2 \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	90.l (of order $12$, degree $4$, 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:	$0.718653618192$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	16.0.9349208943630483456.9
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 48 x^{14} - 196 x^{13} + 642 x^{12} - 1668 x^{11} + 3580 x^{10} - 6328 x^{9} + \cdots + 25 $ x^16 - 8x^15 + 48x^14 - 196x^13 + 642x^12 - 1668x^11 + 3580x^10 - 6328x^9 + 9297x^8 - 11276x^7 + 11224x^6 - 9024x^5 + 5736x^4 - 2780x^3 + 972x^2 - 220*x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			47.3
Root			$0.500000 + 0.589118i$ of defining polynomial
Character	$\chi$	$=$	90.47
Dual form			90.2.l.b.23.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.258819 + 0.965926i) q^{2} +(-1.45865 + 0.933998i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(1.36868 + 1.76825i) q^{5} +(-1.27970 - 1.16721i) q^{6} +(-2.56188 + 0.686453i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(1.25529 - 2.72474i) q^{9} +O(q^{10})$	\(q+(0.258819 + 0.965926i) q^{2} +(-1.45865 + 0.933998i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(1.36868 + 1.76825i) q^{5} +(-1.27970 - 1.16721i) q^{6} +(-2.56188 + 0.686453i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(1.25529 - 2.72474i) q^{9} +(-1.35376 + 1.77970i) q^{10} +(4.15512 + 2.39896i) q^{11} +(0.796225 - 1.53819i) q^{12} +(0.581838 + 0.155903i) q^{13} +(-1.32613 - 2.29692i) q^{14} +(-3.64796 - 1.30092i) q^{15} +(0.500000 - 0.866025i) q^{16} +(4.40865 - 4.40865i) q^{17} +(2.95680 + 0.507306i) q^{18} -5.19145i q^{19} +(-2.06944 - 0.847015i) q^{20} +(3.09573 - 3.39408i) q^{21} +(-1.24179 + 4.63444i) q^{22} +(-0.681226 + 2.54237i) q^{23} +(1.69185 + 0.370982i) q^{24} +(-1.25345 + 4.84034i) q^{25} +0.602363i q^{26} +(0.713876 + 5.14688i) q^{27} +(1.87542 - 1.87542i) q^{28} +(-0.920201 + 1.59383i) q^{29} +(0.312426 - 3.86036i) q^{30} +(-2.03888 - 3.53145i) q^{31} +(0.965926 + 0.258819i) q^{32} +(-8.30148 + 0.381642i) q^{33} +(5.39948 + 3.11739i) q^{34} +(-4.72021 - 3.59052i) q^{35} +(0.275255 + 2.98735i) q^{36} +(0.632057 + 0.632057i) q^{37} +(5.01456 - 1.34365i) q^{38} +(-0.994309 + 0.316029i) q^{39} +(0.282544 - 2.21815i) q^{40} +(-5.58550 + 3.22479i) q^{41} +(4.07966 + 2.11179i) q^{42} +(-0.644420 - 2.40501i) q^{43} -4.79792 q^{44} +(6.53614 - 1.50961i) q^{45} -2.63206 q^{46} +(-1.02538 - 3.82678i) q^{47} +(0.0795432 + 1.73022i) q^{48} +(0.0298240 - 0.0172189i) q^{49} +(-4.99982 + 0.0420344i) q^{50} +(-2.31299 + 10.5483i) q^{51} +(-0.581838 + 0.155903i) q^{52} +(-1.31215 - 1.31215i) q^{53} +(-4.78674 + 2.02166i) q^{54} +(1.44505 + 10.6307i) q^{55} +(2.29692 + 1.32613i) q^{56} +(4.84881 + 7.57249i) q^{57} +(-1.77769 - 0.476331i) q^{58} +(-0.0645473 - 0.111799i) q^{59} +(3.80968 - 0.697355i) q^{60} +(6.27251 - 10.8643i) q^{61} +(2.88341 - 2.88341i) q^{62} +(-1.34550 + 7.84217i) q^{63} +1.00000i q^{64} +(0.520672 + 1.24222i) q^{65} +(-2.51722 - 7.91984i) q^{66} +(2.85782 - 10.6655i) q^{67} +(-1.61368 + 6.02233i) q^{68} +(-1.38090 - 4.34468i) q^{69} +(2.24650 - 5.48866i) q^{70} +10.4203i q^{71} +(-2.81431 + 1.03906i) q^{72} +(3.30021 - 3.30021i) q^{73} +(-0.446932 + 0.774109i) q^{74} +(-2.69253 - 8.23106i) q^{75} +(2.59573 + 4.49593i) q^{76} +(-12.2917 - 3.29355i) q^{77} +(-0.562606 - 0.878635i) q^{78} +(3.62792 + 2.09458i) q^{79} +(2.21569 - 0.301182i) q^{80} +(-5.84847 - 6.84072i) q^{81} +(-4.56054 - 4.56054i) q^{82} +(11.1098 - 2.97686i) q^{83} +(-0.983937 + 4.48722i) q^{84} +(13.8296 + 1.76160i) q^{85} +(2.15627 - 1.24492i) q^{86} +(-0.146391 - 3.18431i) q^{87} +(-1.24179 - 4.63444i) q^{88} +2.04989 q^{89} +(3.14985 + 5.92270i) q^{90} -1.59762 q^{91} +(-0.681226 - 2.54237i) q^{92} +(6.27237 + 3.24682i) q^{93} +(3.43100 - 1.98089i) q^{94} +(9.17981 - 7.10542i) q^{95} +(-1.65068 + 0.524648i) q^{96} +(-16.7115 + 4.47782i) q^{97} +(0.0243512 + 0.0243512i) q^{98} +(11.7525 - 8.31025i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 12 q^{5} + 8 q^{7}+O(q^{10}) $ 16 * q - 12 * q^5 + 8 * q^7	$ 16 q - 12 q^{5} + 8 q^{7} - 8 q^{10} - 24 q^{15} + 8 q^{16} - 12 q^{20} + 24 q^{21} + 8 q^{22} - 24 q^{23} - 16 q^{25} - 16 q^{28} - 12 q^{30} - 8 q^{31} + 24 q^{36} + 24 q^{38} - 4 q^{40} + 24 q^{41} + 24 q^{42} + 36 q^{45} - 32 q^{46} + 48 q^{47} + 24 q^{50} - 48 q^{51} + 24 q^{55} + 24 q^{56} + 24 q^{57} + 16 q^{58} + 12 q^{60} - 24 q^{61} - 48 q^{63} - 48 q^{66} - 16 q^{67} - 24 q^{68} + 16 q^{70} - 24 q^{72} + 16 q^{73} + 16 q^{76} - 72 q^{77} + 24 q^{81} - 16 q^{82} + 48 q^{83} - 4 q^{85} - 48 q^{86} - 48 q^{87} + 8 q^{88} + 12 q^{90} - 24 q^{92} + 72 q^{93} + 84 q^{95} - 48 q^{97}+O(q^{100}) $ 16 * q - 12 * q^5 + 8 * q^7 - 8 * q^10 - 24 * q^15 + 8 * q^16 - 12 * q^20 + 24 * q^21 + 8 * q^22 - 24 * q^23 - 16 * q^25 - 16 * q^28 - 12 * q^30 - 8 * q^31 + 24 * q^36 + 24 * q^38 - 4 * q^40 + 24 * q^41 + 24 * q^42 + 36 * q^45 - 32 * q^46 + 48 * q^47 + 24 * q^50 - 48 * q^51 + 24 * q^55 + 24 * q^56 + 24 * q^57 + 16 * q^58 + 12 * q^60 - 24 * q^61 - 48 * q^63 - 48 * q^66 - 16 * q^67 - 24 * q^68 + 16 * q^70 - 24 * q^72 + 16 * q^73 + 16 * q^76 - 72 * q^77 + 24 * q^81 - 16 * q^82 + 48 * q^83 - 4 * q^85 - 48 * q^86 - 48 * q^87 + 8 * q^88 + 12 * q^90 - 24 * q^92 + 72 * q^93 + 84 * q^95 - 48 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/90\mathbb{Z}\right)^\times$.

$n$	$11$	$37$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	0.258819	+	0.965926i	0.183013	+	0.683013i
$2$	0.258819	+	0.965926i	0.183013	+	0.683013i
$3$	−1.45865	+	0.933998i	−0.842150	+	0.539244i
$3$	−1.45865	+	0.933998i	−0.842150	+	0.539244i
$4$	−0.866025	+	0.500000i	−0.433013	+	0.250000i
$5$	1.36868	+	1.76825i	0.612091	+	0.790787i
$5$	1.36868	+	1.76825i	0.612091	+	0.790787i
$6$	−1.27970	−	1.16721i	−0.522435	−	0.476510i
$7$	−2.56188	+	0.686453i	−0.968299	+	0.259455i	−0.708109	−	0.706103i	$-0.750452\pi$
$7$	−2.56188	+	0.686453i	−0.968299	+	0.259455i	−0.260189	+	0.965558i	$0.583785\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	1.25529	−	2.72474i	0.418432	−	0.908248i
$10$	−1.35376	+	1.77970i	−0.428097	+	0.562790i
$11$	4.15512	+	2.39896i	1.25282	+	0.723314i	0.971668	−	0.236350i	$-0.0759512\pi$
$11$	4.15512	+	2.39896i	1.25282	+	0.723314i	0.281149	+	0.959664i	$0.409285\pi$
$12$	0.796225	−	1.53819i	0.229850	−	0.444037i
$13$	0.581838	+	0.155903i	0.161373	+	0.0432397i	0.338601	−	0.940930i	$-0.390046\pi$
$13$	0.581838	+	0.155903i	0.161373	+	0.0432397i	−0.177228	+	0.984170i	$0.556713\pi$
$14$	−1.32613	−	2.29692i	−0.354422	−	0.613877i
$15$	−3.64796	−	1.30092i	−0.941899	−	0.335895i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	4.40865	−	4.40865i	1.06926	−	1.06926i	0.0718393	−	0.997416i	$-0.477113\pi$
$17$	4.40865	−	4.40865i	1.06926	−	1.06926i	0.997416	−	0.0718393i	$-0.0228869\pi$
$18$	2.95680	+	0.507306i	0.696923	+	0.119573i
$19$		−	5.19145i		−	1.19100i	−0.803355	−	0.595501i	$-0.796954\pi$
$19$		−	5.19145i		−	1.19100i	0.803355	−	0.595501i	$-0.203046\pi$
$20$	−2.06944	−	0.847015i	−0.462740	−	0.189398i
$21$	3.09573	−	3.39408i	0.675543	−	0.740649i
$22$	−1.24179	+	4.63444i	−0.264751	+	0.988065i
$23$	−0.681226	+	2.54237i	−0.142046	+	0.530121i	0.857824	+	0.513944i	$0.171816\pi$
$23$	−0.681226	+	2.54237i	−0.142046	+	0.530121i	−0.999869	+	0.0161770i	$0.994850\pi$
$24$	1.69185	+	0.370982i	0.345348	+	0.0757264i
$25$	−1.25345	+	4.84034i	−0.250689	+	0.968068i
$26$			0.602363i			0.118133i
$27$	0.713876	+	5.14688i	0.137386	+	0.990518i
$28$	1.87542	−	1.87542i	0.354422	−	0.354422i
$29$	−0.920201	+	1.59383i	−0.170877	+	0.295968i	−0.938727	−	0.344662i	$-0.887993\pi$
$29$	−0.920201	+	1.59383i	−0.170877	+	0.295968i	0.767850	+	0.640630i	$0.221327\pi$
$30$	0.312426	−	3.86036i	0.0570409	−	0.704802i
$31$	−2.03888	−	3.53145i	−0.366194	−	0.634266i	0.622773	−	0.782402i	$-0.286006\pi$
$31$	−2.03888	−	3.53145i	−0.366194	−	0.634266i	−0.988967	+	0.148136i	$0.952673\pi$
$32$	0.965926	+	0.258819i	0.170753	+	0.0457532i
$33$	−8.30148	+	0.381642i	−1.44510	+	0.0664354i
$34$	5.39948	+	3.11739i	0.926002	+	0.534628i
$35$	−4.72021	−	3.59052i	−0.797861	−	0.606909i
$36$	0.275255	+	2.98735i	0.0458759	+	0.497891i
$37$	0.632057	+	0.632057i	0.103910	+	0.103910i	0.757150	−	0.653241i	$-0.226591\pi$
$37$	0.632057	+	0.632057i	0.103910	+	0.103910i	−0.653241	+	0.757150i	$0.726591\pi$
$38$	5.01456	−	1.34365i	0.813469	−	0.217968i
$39$	−0.994309	+	0.316029i	−0.159217	+	0.0506051i
$40$	0.282544	−	2.21815i	0.0446741	−	0.350720i
$41$	−5.58550	+	3.22479i	−0.872309	+	0.503628i	−0.868115	−	0.496363i	$-0.834668\pi$
$41$	−5.58550	+	3.22479i	−0.872309	+	0.503628i	−0.00419400	+	0.999991i	$0.501335\pi$
$42$	4.07966	+	2.11179i	0.629506	+	0.325856i
$43$	−0.644420	−	2.40501i	−0.0982731	−	0.366760i	0.899222	−	0.437492i	$-0.144133\pi$
$43$	−0.644420	−	2.40501i	−0.0982731	−	0.366760i	−0.997495	+	0.0707320i	$0.977466\pi$
$44$	−4.79792			−0.723314
$45$	6.53614	−	1.50961i	0.974350	−	0.225040i
$46$	−2.63206			−0.388076
$47$	−1.02538	−	3.82678i	−0.149568	−	0.558194i	−0.999509	−	0.0313173i	$-0.990030\pi$
$47$	−1.02538	−	3.82678i	−0.149568	−	0.558194i	0.849942	−	0.526876i	$-0.176637\pi$
$48$	0.0795432	+	1.73022i	0.0114811	+	0.249736i
$49$	0.0298240	−	0.0172189i	0.00426058	−	0.00245984i
$50$	−4.99982	+	0.0420344i	−0.707082	+	0.00594456i
$51$	−2.31299	+	10.5483i	−0.323883	+	1.47706i
$52$	−0.581838	+	0.155903i	−0.0806865	+	0.0216199i
$53$	−1.31215	−	1.31215i	−0.180237	−	0.180237i	0.611222	−	0.791459i	$-0.290678\pi$
$53$	−1.31215	−	1.31215i	−0.180237	−	0.180237i	−0.791459	+	0.611222i	$0.790678\pi$
$54$	−4.78674	+	2.02166i	−0.651393	+	0.275113i
$55$	1.44505	+	10.6307i	0.194850	+	1.43345i
$56$	2.29692	+	1.32613i	0.306938	+	0.177211i
$57$	4.84881	+	7.57249i	0.642240	+	1.00300i
$58$	−1.77769	−	0.476331i	−0.233422	−	0.0625453i
$59$	−0.0645473	−	0.111799i	−0.00840334	−	0.0145550i	0.861793	−	0.507260i	$-0.169342\pi$
$59$	−0.0645473	−	0.111799i	−0.00840334	−	0.0145550i	−0.870196	+	0.492705i	$0.836008\pi$
$60$	3.80968	−	0.697355i	0.491828	−	0.0900281i
$61$	6.27251	−	10.8643i	0.803113	−	1.39103i	−0.114445	−	0.993430i	$-0.536509\pi$
$61$	6.27251	−	10.8643i	0.803113	−	1.39103i	0.917558	−	0.397603i	$-0.130158\pi$
$62$	2.88341	−	2.88341i	0.366194	−	0.366194i
$63$	−1.34550	+	7.84217i	−0.169517	+	0.988020i
$64$			1.00000i			0.125000i
$65$	0.520672	+	1.24222i	0.0645815	+	0.154078i
$66$	−2.51722	−	7.91984i	−0.309848	−	0.974864i
$67$	2.85782	−	10.6655i	0.349138	−	1.30300i	−0.538566	−	0.842584i	$-0.681034\pi$
$67$	2.85782	−	10.6655i	0.349138	−	1.30300i	0.887703	−	0.460416i	$-0.152300\pi$
$68$	−1.61368	+	6.02233i	−0.195687	+	0.730315i
$69$	−1.38090	−	4.34468i	−0.166241	−	0.523039i
$70$	2.24650	−	5.48866i	0.268508	−	0.656021i
$71$			10.4203i			1.23666i	0.785919	+	0.618329i	$0.212190\pi$
$71$			10.4203i			1.23666i	−0.785919	+	0.618329i	$0.787810\pi$
$72$	−2.81431	+	1.03906i	−0.331670	+	0.122454i
$73$	3.30021	−	3.30021i	0.386261	−	0.386261i	−0.487091	−	0.873351i	$-0.661942\pi$
$73$	3.30021	−	3.30021i	0.386261	−	0.386261i	0.873351	+	0.487091i	$0.161942\pi$
$74$	−0.446932	+	0.774109i	−0.0519548	+	0.0899883i
$75$	−2.69253	−	8.23106i	−0.310907	−	0.950440i
$76$	2.59573	+	4.49593i	0.297750	+	0.515719i
$77$	−12.2917	−	3.29355i	−1.40077	−	0.375335i
$78$	−0.562606	−	0.878635i	−0.0637026	−	0.0994858i
$79$	3.62792	+	2.09458i	0.408173	+	0.235659i	0.690004	−	0.723805i	$-0.257609\pi$
$79$	3.62792	+	2.09458i	0.408173	+	0.235659i	−0.281832	+	0.959464i	$0.590942\pi$
$80$	2.21569	−	0.301182i	0.247722	−	0.0336731i
$81$	−5.84847	−	6.84072i	−0.649830	−	0.760080i
$82$	−4.56054	−	4.56054i	−0.503628	−	0.503628i
$83$	11.1098	−	2.97686i	1.21946	−	0.326753i	0.408992	−	0.912538i	$-0.365881\pi$
$83$	11.1098	−	2.97686i	1.21946	−	0.326753i	0.810466	+	0.585785i	$0.199214\pi$
$84$	−0.983937	+	4.48722i	−0.107356	+	0.489596i
$85$	13.8296	+	1.76160i	1.50004	+	0.191072i
$86$	2.15627	−	1.24492i	0.232517	−	0.134243i
$87$	−0.146391	−	3.18431i	−0.0156948	−	0.341393i
$88$	−1.24179	−	4.63444i	−0.132376	−	0.494033i
$89$	2.04989			0.217288			0.108644	−	0.994081i	$-0.465349\pi$
$89$	2.04989			0.217288			0.108644	+	0.994081i	$0.465349\pi$
$90$	3.14985	+	5.92270i	0.332024	+	0.624308i
$91$	−1.59762			−0.167476
$92$	−0.681226	−	2.54237i	−0.0710228	−	0.265061i
$93$	6.27237	+	3.24682i	0.650414	+	0.336679i
$94$	3.43100	−	1.98089i	0.353881	−	0.204313i
$95$	9.17981	−	7.10542i	0.941829	−	0.729001i
$96$	−1.65068	+	0.524648i	−0.168472	+	0.0535466i
$97$	−16.7115	+	4.47782i	−1.69679	+	0.454654i	−0.972128	−	0.234450i	$-0.924671\pi$
$97$	−16.7115	+	4.47782i	−1.69679	+	0.454654i	−0.724663	+	0.689104i	$0.758004\pi$
$98$	0.0243512	+	0.0243512i	0.00245984	+	0.00245984i
$99$	11.7525	−	8.31025i	1.18117	−	0.835211i
$100$	−1.33465	−	4.81858i	−0.133465	−	0.481858i
$101$	−10.3594	−	5.98097i	−1.03079	−	0.595129i	−0.113582	−	0.993529i	$-0.536232\pi$
$101$	−10.3594	−	5.98097i	−1.03079	−	0.595129i	−0.917212	+	0.398399i	$0.869566\pi$
$102$	−10.7876	+	0.495934i	−1.06813	+	0.0491048i
$103$	−10.4055	−	2.78816i	−1.02529	−	0.274725i	−0.293285	−	0.956025i	$-0.594748\pi$
$103$	−10.4055	−	2.78816i	−1.02529	−	0.274725i	−0.732004	+	0.681300i	$0.761415\pi$
$104$	−0.301182	−	0.521662i	−0.0295333	−	0.0511532i
$105$	10.2386	+	0.828632i	0.999190	+	0.0808662i
$106$	0.927828	−	1.60704i	0.0901186	−	0.156090i
$107$	4.35367	−	4.35367i	0.420885	−	0.420885i	−0.464623	−	0.885508i	$-0.653810\pi$
$107$	4.35367	−	4.35367i	0.420885	−	0.420885i	0.885508	+	0.464623i	$0.153810\pi$
$108$	−3.19168	−	4.10039i	−0.307119	−	0.394560i
$109$			15.4546i			1.48028i	0.672452	+	0.740141i	$0.265241\pi$
$109$			15.4546i			1.48028i	−0.672452	+	0.740141i	$0.734759\pi$
$110$	−9.89448	+	4.14724i	−0.943402	+	0.395424i
$111$	−1.51229	−	0.331607i	−0.143540	−	0.0314748i
$112$	−0.686453	+	2.56188i	−0.0648637	+	0.242075i
$113$	1.53568	−	5.73124i	0.144465	−	0.539150i	−0.855314	−	0.518110i	$-0.826636\pi$
$113$	1.53568	−	5.73124i	0.144465	−	0.539150i	0.999779	−	0.0210396i	$-0.00669762\pi$
$114$	−6.05950	+	6.64349i	−0.567524	+	0.622220i
$115$	−5.42794	+	2.27510i	−0.506158	+	0.212155i
$116$		−	1.84040i		−	0.170877i
$117$	1.15518	−	1.38966i	0.106796	−	0.128474i
$118$	0.0912837	−	0.0912837i	0.00840334	−	0.00840334i
$119$	−8.26810	+	14.3208i	−0.757935	+	1.31278i
$120$	1.65961	+	3.49938i	0.151501	+	0.319449i
$121$	6.01003	+	10.4097i	0.546367	+	0.946335i
$122$	12.1176	+	3.24689i	1.09707	+	0.293960i
$123$	5.13532	−	9.92068i	0.463036	−	0.894517i
$124$	3.53145	+	2.03888i	0.317133	+	0.183097i
$125$	−10.2745	+	4.40844i	−0.918980	+	0.394303i
$126$	−7.92319	+	0.730046i	−0.705854	+	0.0650377i
$127$	2.51837	+	2.51837i	0.223469	+	0.223469i	0.809957	−	0.586489i	$-0.199490\pi$
$127$	2.51837	+	2.51837i	0.223469	+	0.223469i	−0.586489	+	0.809957i	$0.699490\pi$
$128$	−0.965926	+	0.258819i	−0.0853766	+	0.0228766i
$129$	3.18625	+	2.90617i	0.280534	+	0.255874i
$130$	−1.06513	+	0.824441i	−0.0934182	+	0.0723082i
$131$	11.3102	−	6.52997i	0.988181	−	0.570526i	0.0834508	−	0.996512i	$-0.473406\pi$
$131$	11.3102	−	6.52997i	0.988181	−	0.570526i	0.904730	+	0.425985i	$0.140073\pi$
$132$	6.99847	−	4.48125i	0.609139	−	0.390043i
$133$	3.56369	+	13.2999i	0.309011	+	1.15325i
$134$	11.0417			0.953862
$135$	−8.12393	+	8.30673i	−0.699196	+	0.714930i
$136$	−6.23478			−0.534628
$137$	0.840942	+	3.13844i	0.0718465	+	0.268135i	0.992500	−	0.122246i	$-0.0390098\pi$
$137$	0.840942	+	3.13844i	0.0718465	+	0.268135i	−0.920653	+	0.390381i	$0.872343\pi$
$138$	3.83924	−	2.45834i	0.326818	−	0.209267i
$139$	−19.0478	+	10.9973i	−1.61561	+	0.932775i	−0.627578	+	0.778554i	$0.715953\pi$
$139$	−19.0478	+	10.9973i	−1.61561	+	0.932775i	−0.988036	+	0.154221i	$0.950713\pi$
$140$	5.88308	+	0.749378i	0.497211	+	0.0633340i
$141$	5.06988	+	4.62421i	0.426961	+	0.389429i
$142$	−10.0652	+	2.69696i	−0.844653	+	0.226324i
$143$	2.04360	+	2.04360i	0.170895	+	0.170895i
$144$	−1.73205	−	2.44949i	−0.144338	−	0.204124i
$145$	−4.07776	+	0.554295i	−0.338640	+	0.0460317i
$146$	4.04192	+	2.33360i	0.334512	+	0.193130i
$147$	−0.0274203	+	0.0529719i	−0.00226159	+	0.00436905i
$148$	−0.863406	−	0.231349i	−0.0709715	−	0.0190168i
$149$	6.56668	+	11.3738i	0.537964	+	0.931780i	0.999014	+	0.0444061i	$0.0141396\pi$
$149$	6.56668	+	11.3738i	0.537964	+	0.931780i	−0.461050	+	0.887374i	$0.652527\pi$
$150$	7.25371	−	4.73114i	0.592263	−	0.386296i
$151$	−0.167899	+	0.290810i	−0.0136634	+	0.0236658i	−0.872776	−	0.488120i	$-0.837683\pi$
$151$	−0.167899	+	0.290810i	−0.0136634	+	0.0236658i	0.859113	+	0.511786i	$0.171016\pi$
$152$	−3.67091	+	3.67091i	−0.297750	+	0.297750i
$153$	−6.47830	−	17.5466i	−0.523739	−	1.41856i
$154$		−	12.7253i		−	1.02543i
$155$	3.45392	−	8.43867i	0.277426	−	0.677810i
$156$	0.703083	−	0.770843i	0.0562917	−	0.0617169i
$157$	−1.17992	+	4.40352i	−0.0941678	+	0.351439i	−0.996892	−	0.0787808i	$-0.974897\pi$
$157$	−1.17992	+	4.40352i	−0.0941678	+	0.351439i	0.902724	+	0.430220i	$0.141564\pi$
$158$	−1.08423	+	4.04642i	−0.0862571	+	0.321916i
$159$	3.13950	+	0.688415i	0.248979	+	0.0545948i
$160$	0.864382	+	2.06224i	0.0683354	+	0.163035i
$161$		−	6.98088i		−	0.550170i
$162$	5.09393	−	7.41970i	0.400217	−	0.582946i
$163$	9.01496	−	9.01496i	0.706106	−	0.706106i	−0.259608	−	0.965714i	$-0.583593\pi$
$163$	9.01496	−	9.01496i	0.706106	−	0.706106i	0.965714	+	0.259608i	$0.0835932\pi$
$164$	3.22479	−	5.58550i	0.251814	−	0.436154i
$165$	−12.0369	−	14.1568i	−0.937070	−	1.10210i
$166$	5.75085	+	9.96076i	0.446353	+	0.773105i
$167$	−0.00858342	−	0.00229992i	−0.000664205	−	0.000177973i	0.258487	−	0.966015i	$-0.416776\pi$
$167$	−0.00858342	−	0.00229992i	−0.000664205	−	0.000177973i	−0.259151	+	0.965837i	$0.583443\pi$
$168$	−4.58899	+	0.210969i	−0.354048	+	0.0162766i
$169$	−10.9441	−	6.31858i	−0.841854	−	0.486045i
$170$	1.87780	+	13.8143i	0.144021	+	1.05951i
$171$	−14.1454	−	6.51681i	−1.08172	−	0.498353i
$172$	1.76059	+	1.76059i	0.134243	+	0.134243i
$173$	−10.0291	+	2.68729i	−0.762500	+	0.204311i	−0.619056	−	0.785347i	$-0.712484\pi$
$173$	−10.0291	+	2.68729i	−0.762500	+	0.204311i	−0.143444	+	0.989658i	$0.545818\pi$
$174$	3.03791	−	0.965562i	0.230304	−	0.0731991i
$175$	−0.111486	−	13.2608i	−0.00842753	−	1.00242i
$176$	4.15512	−	2.39896i	0.313204	−	0.180829i
$177$	0.198572	+	0.102788i	0.0149256	+	0.00772605i
$178$	0.530550	+	1.98004i	0.0397664	+	0.148410i
$179$	1.46292			0.109343			0.0546717	−	0.998504i	$-0.482589\pi$
$179$	1.46292			0.109343			0.0546717	+	0.998504i	$0.482589\pi$
$180$	−4.90565	+	4.57543i	−0.365646	+	0.341033i
$181$	−8.68576			−0.645607			−0.322804	−	0.946466i	$-0.604625\pi$
$181$	−8.68576			−0.645607			−0.322804	+	0.946466i	$0.604625\pi$
$182$	−0.413494	−	1.54318i	−0.0306502	−	0.114388i
$183$	0.997872	+	21.7057i	0.0737648	+	1.60453i
$184$	2.27943	−	1.31603i	0.168042	−	0.0970189i
$185$	−0.252556	+	1.98272i	−0.0185683	+	0.145772i
$186$	−1.51278	+	6.89898i	−0.110922	+	0.505858i
$187$	28.8947	−	7.74231i	2.11299	−	0.566174i
$188$	2.80140	+	2.80140i	0.204313	+	0.204313i
$189$	−5.36196	−	12.6956i	−0.390025	−	0.923472i
$190$	9.23922	+	7.02800i	0.670284	+	0.509865i
$191$	−4.33795	−	2.50452i	−0.313883	−	0.181220i	0.334780	−	0.942296i	$-0.391338\pi$
$191$	−4.33795	−	2.50452i	−0.313883	−	0.181220i	−0.648663	+	0.761076i	$0.724671\pi$
$192$	−0.933998	−	1.45865i	−0.0674055	−	0.105269i
$193$	−3.25355	−	0.871785i	−0.234195	−	0.0627524i	0.139812	−	0.990178i	$-0.455350\pi$
$193$	−3.25355	−	0.871785i	−0.234195	−	0.0627524i	−0.374008	+	0.927426i	$0.622017\pi$
$194$	−8.65048	−	14.9831i	−0.621069	−	1.07572i
$195$	−1.91971	−	1.32565i	−0.137473	−	0.0949318i
$196$	−0.0172189	+	0.0298240i	−0.00122992	+	0.00213029i
$197$	−15.5027	+	15.5027i	−1.10452	+	1.10452i	−0.110665	+	0.993858i	$0.535298\pi$
$197$	−15.5027	+	15.5027i	−1.10452	+	1.10452i	−0.993858	+	0.110665i	$0.964702\pi$
$198$	11.0688	+	9.20116i	0.786628	+	0.653898i
$199$		−	18.4607i		−	1.30864i	−0.756217	−	0.654321i	$-0.772955\pi$
$199$		−	18.4607i		−	1.30864i	0.756217	−	0.654321i	$-0.227045\pi$
$200$	4.30896	−	2.53631i	0.304689	−	0.179345i
$201$	5.79303	+	18.2264i	0.408609	+	1.28559i
$202$	3.09598	−	11.5544i	0.217832	−	0.812962i
$203$	1.26335	−	4.71488i	0.0886697	−	0.330920i
$204$	−3.27106	−	10.2916i	−0.229020	−	0.720558i
$205$	−13.3470	−	5.46289i	−0.932195	−	0.381545i
$206$		−	10.7726i		−	0.750564i
$207$	6.07217	+	5.04759i	0.422045	+	0.350832i
$208$	0.425935	−	0.425935i	0.0295333	−	0.0295333i
$209$	12.4541	−	21.5711i	0.861468	−	1.49211i
$210$	1.84956	+	10.1042i	0.127632	+	0.697259i
$211$	0.654465	+	1.13357i	0.0450552	+	0.0780380i	0.887674	−	0.460473i	$-0.152320\pi$
$211$	0.654465	+	1.13357i	0.0450552	+	0.0780380i	−0.842618	+	0.538511i	$0.818987\pi$
$212$	1.79243	+	0.480279i	0.123104	+	0.0329857i
$213$	−9.73251	−	15.1995i	−0.666860	−	1.04145i
$214$	5.33213	+	3.07851i	0.364497	+	0.210442i
$215$	3.37066	−	4.43117i	0.229877	−	0.302204i
$216$	3.13461	−	4.14418i	0.213283	−	0.281976i
$217$	7.64754	+	7.64754i	0.519149	+	0.519149i
$218$	−14.9280	+	3.99994i	−1.01105	+	0.270910i
$219$	−1.73145	+	7.89624i	−0.117001	+	0.533578i
$220$	−6.56681	−	8.48395i	−0.442734	−	0.571988i
$221$	3.25245	−	1.87780i	0.218783	−	0.126315i
$222$	−0.0711008	−	1.54658i	−0.00477197	−	0.103800i
$223$	5.42903	+	20.2614i	0.363555	+	1.35681i	0.869369	+	0.494163i	$0.164526\pi$
$223$	5.42903	+	20.2614i	0.363555	+	1.35681i	−0.505814	+	0.862643i	$0.668808\pi$
$224$	−2.65225			−0.177211
$225$	11.6152	+	9.49138i	0.774349	+	0.632758i
$226$	5.93342			0.394685
$227$	1.54126	+	5.75206i	0.102297	+	0.381778i	0.998025	−	0.0628257i	$-0.0200112\pi$
$227$	1.54126	+	5.75206i	0.102297	+	0.381778i	−0.895727	+	0.444604i	$0.853345\pi$
$228$	−7.98544	−	4.13357i	−0.528848	−	0.273752i
$229$	10.1822	−	5.87872i	0.672862	−	0.388477i	−0.124298	−	0.992245i	$-0.539668\pi$
$229$	10.1822	−	5.87872i	0.672862	−	0.388477i	0.797160	+	0.603768i	$0.206335\pi$
$230$	−3.60244	−	4.65415i	−0.237538	−	0.306885i
$231$	21.0054	−	6.67630i	1.38205	−	0.439268i
$232$	1.77769	−	0.476331i	0.116711	−	0.0312727i
$233$	13.4322	+	13.4322i	0.879973	+	0.879973i	0.993531	−	0.113558i	$-0.0362249\pi$
$233$	13.4322	+	13.4322i	0.879973	+	0.879973i	−0.113558	+	0.993531i	$0.536225\pi$
$234$	1.64129	+	0.756144i	0.107294	+	0.0494307i
$235$	5.36331	−	7.05077i	0.349864	−	0.459941i
$236$	0.111799	+	0.0645473i	0.00727751	+	0.00420167i
$237$	−7.24818	+	0.333219i	−0.470820	+	0.0216449i
$238$	−15.9727	−	4.27988i	−1.03536	−	0.277424i
$239$	−2.27943	−	3.94809i	−0.147444	−	0.255380i	0.782838	−	0.622225i	$-0.213771\pi$
$239$	−2.27943	−	3.94809i	−0.147444	−	0.255380i	−0.930282	+	0.366845i	$0.880438\pi$
$240$	−2.95061	+	2.50877i	−0.190461	+	0.161940i
$241$	8.03104	−	13.9102i	0.517325	−	0.896032i	−0.482473	−	0.875911i	$-0.660261\pi$
$241$	8.03104	−	13.9102i	0.517325	−	0.896032i	0.999798	−	0.0201215i	$-0.00640532\pi$
$242$	−8.49947	+	8.49947i	−0.546367	+	0.546367i
$243$	14.9201	+	4.51572i	0.957122	+	0.289684i
$244$			12.5450i			0.803113i
$245$	0.0712669	+	0.0291693i	0.00455307	+	0.00186356i
$246$	10.9118	+	2.39268i	0.695708	+	0.152552i
$247$	0.809364	−	3.02059i	0.0514986	−	0.192195i
$248$	−1.05540	+	3.93882i	−0.0670181	+	0.250115i
$249$	−13.4249	+	14.7187i	−0.850766	+	0.932760i
$250$	−6.91747	−	8.78343i	−0.437499	−	0.555513i
$251$			18.9981i			1.19915i	0.800319	+	0.599574i	$0.204663\pi$
$251$			18.9981i			1.19915i	−0.800319	+	0.599574i	$0.795337\pi$
$252$	−2.75584	−	7.46427i	−0.173602	−	0.470205i
$253$	−8.92963	+	8.92963i	−0.561401	+	0.561401i
$254$	−1.78075	+	3.08436i	−0.111734	+	0.193530i
$255$	−21.8179	+	10.3473i	−1.36629	+	0.647974i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	3.23709	+	0.867374i	0.201924	+	0.0541053i	0.358363	−	0.933582i	$-0.383335\pi$
$257$	3.23709	+	0.867374i	0.201924	+	0.0541053i	−0.156439	+	0.987688i	$0.550002\pi$
$258$	−1.98248	+	3.82985i	−0.123424	+	0.238436i
$259$	−2.05313	−	1.18538i	−0.127575	−	0.0736557i
$260$	−1.07203	−	0.815457i	−0.0664842	−	0.0505725i
$261$	3.18767	+	4.50804i	0.197312	+	0.279041i
$262$	9.23478	+	9.23478i	0.570526	+	0.570526i
$263$	−16.1748	+	4.33402i	−0.997380	+	0.267247i	−0.720347	−	0.693614i	$-0.756018\pi$
$263$	−16.1748	+	4.33402i	−0.997380	+	0.267247i	−0.277032	+	0.960861i	$0.589351\pi$
$264$	6.13989	+	5.60017i	0.377884	+	0.344667i
$265$	0.524304	−	4.11611i	0.0322078	−	0.252851i
$266$	−11.9243	+	6.88452i	−0.731128	+	0.422117i
$267$	−2.99006	+	1.91459i	−0.182989	+	0.117171i
$268$	2.85782	+	10.6655i	0.174569	+	0.651500i
$269$	0.535741			0.0326647			0.0163324	−	0.999867i	$-0.494801\pi$
$269$	0.535741			0.0326647			0.0163324	+	0.999867i	$0.494801\pi$
$270$	−10.1263	−	5.69717i	−0.616268	−	0.346719i
$271$	−15.5412			−0.944063			−0.472032	−	0.881582i	$-0.656479\pi$
$271$	−15.5412			−0.944063			−0.472032	+	0.881582i	$0.656479\pi$
$272$	−1.61368	−	6.02233i	−0.0978437	−	0.365158i
$273$	2.33036	−	1.49217i	0.141040	−	0.0903104i
$274$	−2.81385	+	1.62458i	−0.169991	+	0.0981442i
$275$	−16.8200	+	17.1052i	−1.01428	+	1.03148i
$276$	3.36824	+	3.07216i	0.202744	+	0.184922i
$277$	16.7200	−	4.48011i	1.00461	−	0.269184i	0.281232	−	0.959640i	$-0.409257\pi$
$277$	16.7200	−	4.48011i	1.00461	−	0.269184i	0.723374	+	0.690456i	$0.242590\pi$
$278$	−15.5525	−	15.5525i	−0.932775	−	0.932775i
$279$	−12.1817	+	1.12242i	−0.729298	+	0.0671978i
$280$	0.798810	+	5.87657i	0.0477380	+	0.351192i
$281$	−20.8909	−	12.0613i	−1.24624	−	0.719519i	−0.275886	−	0.961190i	$-0.588971\pi$
$281$	−20.8909	−	12.0613i	−1.24624	−	0.719519i	−0.970358	+	0.241671i	$0.922304\pi$
$282$	−3.15447	+	6.09396i	−0.187846	+	0.362890i
$283$	15.9876	+	4.28387i	0.950365	+	0.254649i	0.700517	−	0.713636i	$-0.252953\pi$
$283$	15.9876	+	4.28387i	0.950365	+	0.254649i	0.249848	+	0.968285i	$0.419619\pi$
$284$	−5.21013	−	9.02421i	−0.309164	−	0.535489i
$285$	−6.75364	+	18.9382i	−0.400051	+	1.12180i
$286$	−1.44505	+	2.50289i	−0.0854474	+	0.147999i
$287$	12.0957	−	12.0957i	0.713987	−	0.713987i
$288$	1.91774	−	2.30701i	0.113004	−	0.135942i
$289$		−	21.8725i		−	1.28661i
$290$	−1.59081	−	3.79535i	−0.0934156	−	0.222871i
$291$	20.1938	−	22.1400i	1.18378	−	1.29787i
$292$	−1.20796	+	4.50818i	−0.0706906	+	0.263821i
$293$	4.18032	−	15.6012i	0.244217	−	0.911431i	−0.729558	−	0.683919i	$-0.760274\pi$
$293$	4.18032	−	15.6012i	0.244217	−	0.911431i	0.973775	−	0.227512i	$-0.0730591\pi$
$294$	−0.0582638	−	0.0127758i	−0.00339801	−	0.000745100i
$295$	0.109345	−	0.267153i	0.00636631	−	0.0155542i
$296$		−	0.893864i		−	0.0519548i
$297$	−9.38093	+	23.0985i	−0.544337	+	1.34031i
$298$	−9.28669	+	9.28669i	−0.537964	+	0.537964i
$299$	−0.792727	+	1.37304i	−0.0458446	+	0.0794052i
$300$	6.44733	+	5.78204i	0.372237	+	0.333826i
$301$	3.30185	+	5.71897i	0.190315	+	0.329636i
$302$	−0.324356	−	0.0869109i	−0.0186646	−	0.00500116i
$303$	20.6968	−	0.951492i	1.18900	−	0.0546618i
$304$	−4.49593	−	2.59573i	−0.257859	−	0.148875i
$305$	27.7959	−	3.77833i	1.59159	−	0.216347i
$306$	15.2720	−	10.7990i	0.873043	−	0.617335i
$307$	−1.45642	−	1.45642i	−0.0831222	−	0.0831222i	0.664323	−	0.747445i	$-0.268720\pi$
$307$	−1.45642	−	1.45642i	−0.0831222	−	0.0831222i	−0.747445	+	0.664323i	$0.768720\pi$
$308$	12.2917	−	3.29355i	0.700384	−	0.187667i
$309$	17.7821	−	5.65183i	1.01159	−	0.321521i
$310$	9.04507	+	1.15215i	0.513725	+	0.0654376i
$311$	−1.81462	+	1.04767i	−0.102898	+	0.0594081i	−0.550566	−	0.834792i	$-0.685588\pi$
$311$	−1.81462	+	1.04767i	−0.102898	+	0.0594081i	0.447668	+	0.894200i	$0.352255\pi$
$312$	0.926549	+	0.479617i	0.0524555	+	0.0271530i
$313$	−5.11217	−	19.0789i	−0.288957	−	1.07840i	−0.945899	−	0.324461i	$-0.894817\pi$
$313$	−5.11217	−	19.0789i	−0.288957	−	1.07840i	0.656942	−	0.753941i	$-0.271850\pi$
$314$	−4.55886			−0.257271
$315$	−15.7085	+	8.35420i	−0.885074	+	0.470706i
$316$	−4.18916			−0.235659
$317$	8.82217	+	32.9248i	0.495503	+	1.84924i	0.527196	+	0.849743i	$0.323243\pi$
$317$	8.82217	+	32.9248i	0.495503	+	1.84924i	−0.0316937	+	0.999498i	$0.510090\pi$
$318$	0.147605	+	3.21070i	0.00827727	+	0.180047i
$319$	−7.64709	+	4.41505i	−0.428155	+	0.247195i
$320$	−1.76825	+	1.36868i	−0.0988484	+	0.0765114i
$321$	−2.28414	+	10.4168i	−0.127488	+	0.581408i
$322$	6.74301	−	1.80678i	0.375773	−	0.100688i
$323$	−22.8873	−	22.8873i	−1.27348	−	1.27348i
$324$	8.48528	+	3.00000i	0.471405	+	0.166667i
$325$	−1.48393	+	2.62088i	−0.0823135	+	0.145380i
$326$	11.0410	+	6.37454i	0.611506	+	0.353053i
$327$	−14.4346	−	22.5428i	−0.798233	−	1.24662i
$328$	6.22982	+	1.66927i	0.343984	+	0.0921703i
$329$	5.25381	+	9.09987i	0.289652	+	0.501692i
$330$	10.5590	−	15.2908i	0.581255	−	0.841730i
$331$	−12.0140	+	20.8088i	−0.660348	+	1.14376i	0.320176	+	0.947358i	$0.396258\pi$
$331$	−12.0140	+	20.8088i	−0.660348	+	1.14376i	−0.980524	+	0.196399i	$0.937075\pi$
$332$	−8.13293	+	8.13293i	−0.446353	+	0.446353i
$333$	2.51561	−	0.928776i	0.137855	−	0.0508966i
$334$		−	0.00888621i		−	0.000486232i
$335$	22.7708	−	9.54429i	1.24410	−	0.521460i
$336$	−1.39150	−	4.37802i	−0.0759124	−	0.238841i
$337$	3.17090	−	11.8340i	0.172730	−	0.644637i	−0.824197	−	0.566303i	$-0.808373\pi$
$337$	3.17090	−	11.8340i	0.172730	−	0.644637i	0.996927	−	0.0783338i	$-0.0249600\pi$
$338$	3.27074	−	12.2066i	0.177905	−	0.663949i
$339$	3.11295	+	9.79417i	0.169072	+	0.531947i
$340$	−12.8576	+	5.38923i	−0.697302	+	0.292272i
$341$		−	19.5648i		−	1.05949i
$342$	2.63366	−	15.3501i	0.142412	−	0.830037i
$343$	13.0634	−	13.0634i	0.705357	−	0.705357i
$344$	−1.24492	+	2.15627i	−0.0671217	+	0.116258i
$345$	5.79250	−	8.38826i	0.311858	−	0.451609i
$346$	−5.19145	−	8.99186i	−0.279094	−	0.483405i
$347$	−17.9559	−	4.81127i	−0.963924	−	0.258283i	−0.257663	−	0.966235i	$-0.582953\pi$
$347$	−17.9559	−	4.81127i	−0.963924	−	0.258283i	−0.706260	+	0.707952i	$0.749619\pi$
$348$	1.71893	+	2.68449i	0.0921444	+	0.143904i
$349$	27.2305	+	15.7215i	1.45761	+	0.841553i	0.998894	−	0.0470278i	$-0.0149749\pi$
$349$	27.2305	+	15.7215i	1.45761	+	0.841553i	0.458720	+	0.888581i	$0.348308\pi$
$350$	12.7801	−	3.53983i	0.683124	−	0.189212i
$351$	−0.387054	+	3.10595i	−0.0206594	+	0.165783i
$352$	3.39264	+	3.39264i	0.180829	+	0.180829i
$353$	11.7440	−	3.14681i	0.625073	−	0.167488i	0.0676398	−	0.997710i	$-0.478453\pi$
$353$	11.7440	−	3.14681i	0.625073	−	0.167488i	0.557433	+	0.830222i	$0.311786\pi$
$354$	−0.0478918	+	0.218409i	−0.00254542	+	0.0116083i
$355$	−18.4257	+	14.2620i	−0.977933	+	0.756947i
$356$	−1.77526	+	1.02494i	−0.0940883	+	0.0543219i
$357$	−1.31534	−	28.6113i	−0.0696153	−	1.51427i
$358$	0.378631	+	1.41307i	0.0200112	+	0.0746830i
$359$	−4.31606			−0.227793			−0.113896	−	0.993493i	$-0.536333\pi$
$359$	−4.31606			−0.227793			−0.113896	+	0.993493i	$0.536333\pi$
$360$	−5.68920	−	3.55429i	−0.299847	−	0.187327i
$361$	−7.95119			−0.418484
$362$	−2.24804	−	8.38980i	−0.118154	−	0.440958i
$363$	−18.4891	−	9.57068i	−0.970428	−	0.502330i
$364$	1.38358	−	0.798810i	0.0725192	−	0.0418690i
$365$	10.3525	+	1.31869i	0.541877	+	0.0690235i
$366$	−20.7078	+	6.58172i	−1.08242	+	0.344032i
$367$	−19.2008	+	5.14485i	−1.00228	+	0.268559i	−0.722399	−	0.691477i	$-0.756960\pi$
$367$	−19.2008	+	5.14485i	−1.00228	+	0.268559i	−0.279877	+	0.960036i	$0.590294\pi$
$368$	1.86115	+	1.86115i	0.0970189	+	0.0970189i
$369$	1.77528	+	19.2671i	0.0924174	+	1.00301i
$370$	−1.98053	+	0.269215i	−0.102963	+	0.0139958i
$371$	4.26229	+	2.46083i	0.221287	+	0.127760i
$372$	−7.05544	+	0.324358i	−0.365807	+	0.0168172i
$373$	2.53800	+	0.680056i	0.131413	+	0.0352120i	0.323926	−	0.946082i	$-0.394997\pi$
$373$	2.53800	+	0.680056i	0.131413	+	0.0352120i	−0.192513	+	0.981294i	$0.561664\pi$
$374$	14.9570	+	25.9063i	0.773408	+	1.33958i
$375$	10.8694	−	16.0267i	0.561293	−	0.827617i
$376$	−1.98089	+	3.43100i	−0.102157	+	0.176940i
$377$	−0.783892	+	0.783892i	−0.0403725	+	0.0403725i
$378$	10.8753	−	8.46512i	0.559363	−	0.435399i
$379$		−	3.03124i		−	0.155705i	−0.996965	−	0.0778523i	$-0.975194\pi$
$379$		−	3.03124i		−	0.155705i	0.996965	−	0.0778523i	$-0.0248063\pi$
$380$	−4.39724	+	10.7434i	−0.225574	+	0.551124i
$381$	−6.02555	−	1.32125i	−0.308698	−	0.0676899i
$382$	1.29643	−	4.83835i	0.0663313	−	0.247552i
$383$	−6.14717	+	22.9416i	−0.314106	+	1.17226i	0.610713	+	0.791852i	$0.290883\pi$
$383$	−6.14717	+	22.9416i	−0.314106	+	1.17226i	−0.924819	+	0.380407i	$0.875784\pi$
$384$	1.16721	−	1.27970i	0.0595638	−	0.0653043i
$385$	−10.9995	−	26.2426i	−0.560588	−	1.33745i
$386$		−	3.36832i		−	0.171443i
$387$	−7.36197	−	1.26311i	−0.374230	−	0.0642077i
$388$	12.2336	−	12.2336i	0.621069	−	0.621069i
$389$	3.33254	−	5.77213i	0.168966	−	0.292659i	−0.769090	−	0.639140i	$-0.779290\pi$
$389$	3.33254	−	5.77213i	0.168966	−	0.292659i	0.938057	+	0.346482i	$0.112624\pi$
$390$	0.783624	−	2.19740i	0.0396803	−	0.111270i
$391$	8.20515	+	14.2117i	0.414952	+	0.718718i
$392$	−0.0332644	−	0.00891317i	−0.00168011	−	0.000450183i
$393$	−10.3987	+	20.0887i	−0.524543	+	1.01334i
$394$	−18.9869	−	10.9621i	−0.956545	−	0.552261i
$395$	1.26170	+	9.28189i	0.0634829	+	0.467022i
$396$	−6.02281	+	13.0731i	−0.302658	+	0.656949i
$397$	−13.2242	−	13.2242i	−0.663703	−	0.663703i	0.292548	−	0.956251i	$-0.405497\pi$
$397$	−13.2242	−	13.2242i	−0.663703	−	0.663703i	−0.956251	+	0.292548i	$0.905497\pi$
$398$	17.8316	−	4.77797i	0.893819	−	0.239498i
$399$	−17.6202	−	16.0713i	−0.882114	−	0.804572i
$400$	3.56513	+	3.50569i	0.178257	+	0.175284i
$401$	4.66934	−	2.69585i	0.233176	−	0.134624i	−0.378860	−	0.925454i	$-0.623684\pi$
$401$	4.66934	−	2.69585i	0.233176	−	0.134624i	0.612036	+	0.790830i	$0.290351\pi$
$402$	−16.1060	+	10.3130i	−0.803294	+	0.514364i
$403$	−0.635736	−	2.37260i	−0.0316683	−	0.118188i
$404$	11.9619			0.595129
$405$	4.09146	−	19.7043i	0.203306	−	0.979115i
$406$	4.88121			0.242250
$407$	1.10999	+	4.14256i	0.0550204	+	0.205339i
$408$	9.09433	−	5.82327i	0.450237	−	0.288295i
$409$	−7.43574	+	4.29303i	−0.367674	+	0.212277i	−0.672442	−	0.740150i	$-0.734754\pi$
$409$	−7.43574	+	4.29303i	−0.367674	+	0.212277i	0.304768	+	0.952427i	$0.401421\pi$
$410$	1.82229	−	14.3061i	0.0899965	−	0.706528i
$411$	−4.15793	−	3.79243i	−0.205096	−	0.187067i
$412$	10.4055	−	2.78816i	0.512644	−	0.137363i
$413$	0.242107	+	0.242107i	0.0119133	+	0.0119133i
$414$	−3.30401	+	7.17168i	−0.162383	+	0.352469i
$415$	20.4696	+	15.5706i	1.00481	+	0.764329i
$416$	0.521662	+	0.301182i	0.0255766	+	0.0147666i
$417$	17.5126	−	33.8317i	0.857595	−	1.65675i
$418$	24.0595	+	6.44672i	1.17679	+	0.315319i
$419$	7.72749	+	13.3844i	0.377512	+	0.653871i	0.990700	−	0.136067i	$-0.0434462\pi$
$419$	7.72749	+	13.3844i	0.377512	+	0.653871i	−0.613187	+	0.789938i	$0.710113\pi$
$420$	−9.28125	+	4.40171i	−0.452878	+	0.214781i
$421$	9.45129	−	16.3701i	0.460628	−	0.797831i	−0.538364	−	0.842712i	$-0.680958\pi$
$421$	9.45129	−	16.3701i	0.460628	−	0.797831i	0.998992	+	0.0448812i	$0.0142909\pi$
$422$	−0.925553	+	0.925553i	−0.0450552	+	0.0450552i
$423$	−11.7142	−	2.00983i	−0.569562	−	0.0977214i
$424$			1.85566i			0.0901186i
$425$	15.8134	+	26.8654i	0.767060	+	1.30316i
$426$	12.1626	−	13.3348i	0.589280	−	0.646073i
$427$	−8.61157	+	32.1388i	−0.416743	+	1.55531i
$428$	−1.59355	+	5.94722i	−0.0770273	+	0.287470i
$429$	−4.88962	−	1.07217i	−0.236073	−	0.0517650i
$430$	5.15258	+	2.10894i	0.248479	+	0.101702i
$431$		−	3.91428i		−	0.188544i	−0.995546	−	0.0942720i	$-0.969948\pi$
$431$		−	3.91428i		−	0.188544i	0.995546	−	0.0942720i	$-0.0300523\pi$
$432$	4.81427	+	1.95521i	0.231627	+	0.0940699i
$433$	−27.2049	+	27.2049i	−1.30738	+	1.30738i	−0.384086	+	0.923297i	$0.625483\pi$
$433$	−27.2049	+	27.2049i	−1.30738	+	1.30738i	−0.923297	+	0.384086i	$0.874517\pi$
$434$	−5.40762	+	9.36628i	−0.259574	+	0.449596i
$435$	5.43030	−	4.61714i	0.260363	−	0.221375i
$436$	−7.72730	−	13.3841i	−0.370070	−	0.640981i
$437$	13.1986	+	3.53656i	0.631375	+	0.169176i
$438$	−8.07531	+	0.371245i	−0.385853	+	0.0177388i
$439$	−13.2725	−	7.66286i	−0.633460	−	0.365728i	0.148631	−	0.988893i	$-0.452513\pi$
$439$	−13.2725	−	7.66286i	−0.633460	−	0.365728i	−0.782091	+	0.623164i	$0.785847\pi$
$440$	6.49525	−	8.53886i	0.309649	−	0.407074i
$441$	−0.00947919	−	0.102878i	−0.000451390	−	0.00489894i
$442$	2.65561	+	2.65561i	0.126315	+	0.126315i
$443$	−26.8719	+	7.20031i	−1.27672	+	0.342097i	−0.832603	−	0.553870i	$-0.813150\pi$
$443$	−26.8719	+	7.20031i	−1.27672	+	0.342097i	−0.444120	+	0.895967i	$0.646484\pi$
$444$	1.47548	−	0.468963i	0.0700233	−	0.0222560i
$445$	2.80563	+	3.62472i	0.133000	+	0.171828i
$446$	−18.1659	+	10.4881i	−0.860180	+	0.496625i
$447$	−20.2016	−	10.4571i	−0.955503	−	0.494605i
$448$	−0.686453	−	2.56188i	−0.0324319	−	0.121037i
$449$	−24.3627			−1.14975			−0.574874	−	0.818242i	$-0.694949\pi$
$449$	−24.3627			−1.14975			−0.574874	+	0.818242i	$0.694949\pi$
$450$	−6.16172	+	13.6760i	−0.290466	+	0.644693i
$451$	−30.9446			−1.45712
$452$	1.53568	+	5.73124i	0.0722324	+	0.269575i
$453$	−0.0267105	−	0.581006i	−0.00125497	−	0.0272980i
$454$	−5.15716	+	2.97749i	−0.242037	+	0.139740i
$455$	−2.18662	−	2.82500i	−0.102511	−	0.132438i
$456$	1.92594	−	8.78319i	0.0901902	−	0.411310i
$457$	−12.6705	+	3.39506i	−0.592702	+	0.158814i	−0.542688	−	0.839935i	$-0.682593\pi$
$457$	−12.6705	+	3.39506i	−0.592702	+	0.158814i	−0.0500141	+	0.998749i	$0.515927\pi$
$458$	8.31377	+	8.31377i	0.388477	+	0.388477i
$459$	25.8380	+	19.5436i	1.20602	+	0.912216i
$460$	3.56318	−	4.68427i	0.166134	−	0.218405i
$461$	34.7684	+	20.0736i	1.61933	+	0.934919i	0.987094	+	0.160141i	$0.0511948\pi$
$461$	34.7684	+	20.0736i	1.61933	+	0.934919i	0.632233	+	0.774778i	$0.282139\pi$
$462$	11.8854	+	18.5617i	0.552959	+	0.863569i
$463$	−11.5688	−	3.09986i	−0.537649	−	0.144063i	−0.0202307	−	0.999795i	$-0.506440\pi$
$463$	−11.5688	−	3.09986i	−0.537649	−	0.144063i	−0.517418	+	0.855733i	$0.673107\pi$
$464$	0.920201	+	1.59383i	0.0427192	+	0.0739919i
$465$	2.84365	+	15.5350i	0.131871	+	0.720418i
$466$	−9.49800	+	16.4510i	−0.439986	+	0.762079i
$467$	8.63124	−	8.63124i	0.399406	−	0.399406i	−0.478617	−	0.878024i	$-0.658862\pi$
$467$	8.63124	−	8.63124i	0.399406	−	0.399406i	0.878024	+	0.478617i	$0.158862\pi$
$468$	−0.305583	+	1.78107i	−0.0141256	+	0.0823298i
$469$			29.2855i			1.35228i
$470$	8.19864	+	3.35568i	0.378175	+	0.154786i
$471$	−2.39179	−	7.52521i	−0.110208	−	0.346744i
$472$	−0.0334121	+	0.124696i	−0.00153792	+	0.00573959i
$473$	3.09188	−	11.5390i	0.142165	−	0.530565i
$474$	−2.19783	−	6.91496i	−0.100950	−	0.317615i
$475$	25.1284	+	6.50721i	1.15297	+	0.298571i
$476$		−	16.5362i		−	0.757935i
$477$	−5.22240	+	1.92813i	−0.239117	+	0.0882832i
$478$	3.22360	−	3.22360i	0.147444	−	0.147444i
$479$	5.13488	−	8.89388i	0.234619	−	0.406372i	−0.724543	−	0.689230i	$-0.757949\pi$
$479$	5.13488	−	8.89388i	0.234619	−	0.406372i	0.959162	+	0.282858i	$0.0912825\pi$
$480$	−3.18696	−	2.20075i	−0.145464	−	0.100450i
$481$	0.269215	+	0.466295i	0.0122752	+	0.0212612i
$482$	15.5148	+	4.15717i	0.706678	+	0.189354i
$483$	6.52013	+	10.1826i	0.296676	+	0.463326i
$484$	−10.4097	−	6.01003i	−0.473167	−	0.273183i
$485$	−30.7905	−	23.4214i	−1.39812	−	1.06351i
$486$	−0.500258	+	15.5804i	−0.0226921	+	0.706743i
$487$	17.5218	+	17.5218i	0.793987	+	0.793987i	0.982140	−	0.188153i	$-0.0602500\pi$
$487$	17.5218	+	17.5218i	0.793987	+	0.793987i	−0.188153	+	0.982140i	$0.560250\pi$
$488$	−12.1176	+	3.24689i	−0.548536	+	0.146980i
$489$	−4.72968	+	21.5696i	−0.213884	+	0.975411i
$490$	−0.00973020	+	0.0763881i	−0.000439566	+	0.00345086i
$491$	−7.70100	+	4.44617i	−0.347541	+	0.200653i	−0.663602	−	0.748086i	$-0.730973\pi$
$491$	−7.70100	+	4.44617i	−0.347541	+	0.200653i	0.316061	+	0.948739i	$0.397640\pi$
$492$	0.513021	+	11.1592i	0.0231288	+	0.503096i
$493$	2.96982	+	11.0835i	0.133754	+	0.499176i
$494$	3.12714			0.140697
$495$	30.7800	+	9.40730i	1.38346	+	0.422827i
$496$	−4.07776			−0.183097
$497$	−7.15302	−	26.6954i	−0.320857	−	1.19745i
$498$	−17.6918	−	9.15794i	−0.792788	−	0.410377i
$499$	25.4186	−	14.6754i	1.13789	−	0.656963i	0.191985	−	0.981398i	$-0.438507\pi$
$499$	25.4186	−	14.6754i	1.13789	−	0.656963i	0.945908	+	0.324435i	$0.105174\pi$
$500$	6.69377	−	8.95508i	0.299354	−	0.400483i
$501$	0.0146683	−	0.00466213i	0.000655331	−	0.000208288i
$502$	−18.3507	+	4.91707i	−0.819034	+	0.219459i
$503$	10.0766	+	10.0766i	0.449293	+	0.449293i	0.895120	−	0.445826i	$-0.147090\pi$
$503$	10.0766	+	10.0766i	0.449293	+	0.449293i	−0.445826	+	0.895120i	$0.647090\pi$
$504$	6.49666	−	4.59383i	0.289384	−	0.204626i
$505$	−3.60272	−	26.5040i	−0.160319	−	1.17941i
$506$	−10.9365	−	6.31420i	−0.486188	−	0.280701i
$507$	21.8651	−	1.00520i	0.971063	−	0.0446425i
$508$	−3.44015	−	0.921786i	−0.152632	−	0.0408976i
$509$	−15.0024	−	25.9849i	−0.664970	−	1.15176i	−0.979293	−	0.202446i	$-0.935111\pi$
$509$	−15.0024	−	25.9849i	−0.664970	−	1.15176i	0.314323	−	0.949316i	$-0.398223\pi$
$510$	−15.6416	−	18.3964i	−0.692623	−	0.814605i
$511$	−6.18930	+	10.7202i	−0.273799	+	0.474233i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	26.7198	−	3.70605i	1.17971	−	0.163626i
$514$			3.35128i			0.147819i
$515$	−9.31166	−	22.2157i	−0.410321	−	0.978943i
$516$	−4.21246	−	0.923688i	−0.185443	−	0.0406631i
$517$	4.91971	−	18.3606i	0.216369	−	0.807499i
$518$	0.613596	−	2.28997i	0.0269598	−	0.100615i
$519$	12.1190	−	13.2870i	0.531965	−	0.583234i
$520$	0.510211	−	1.24655i	0.0223742	−	0.0546649i
$521$		−	6.40485i		−	0.280602i	−0.990109	−	0.140301i	$-0.955193\pi$
$521$		−	6.40485i		−	0.280602i	0.990109	−	0.140301i	$-0.0448070\pi$
$522$	−3.52941	+	4.24582i	−0.154478	+	0.185834i
$523$	16.0596	−	16.0596i	0.702237	−	0.702237i	−0.262653	−	0.964890i	$-0.584597\pi$
$523$	16.0596	−	16.0596i	0.702237	−	0.702237i	0.964890	+	0.262653i	$0.0845974\pi$
$524$	−6.52997	+	11.3102i	−0.285263	+	0.494090i
$525$	12.5482	+	19.2387i	0.547647	+	0.839644i
$526$	−8.37268	−	14.5019i	−0.365066	−	0.632313i
$527$	−24.5576	−	6.58020i	−1.06975	−	0.286638i
$528$	−3.82023	+	7.38011i	−0.166254	+	0.321178i
$529$	13.9190	+	8.03614i	0.605174	+	0.349397i
$530$	4.11156	−	0.558889i	0.178595	−	0.0242766i
$531$	−0.385650	+	0.0355339i	−0.0167358	+	0.00154204i
$532$	−9.73618	−	9.73618i	−0.422117	−	0.422117i
$533$	−3.75261	+	1.00551i	−0.162544	+	0.0435535i
$534$	−2.62324	−	2.39264i	−0.113519	−	0.103540i
$535$	13.6572	+	1.73963i	0.590450	+	0.0752107i
$536$	−9.56244	+	5.52087i	−0.413034	+	0.238465i
$537$	−2.13388	+	1.36636i	−0.0920836	+	0.0589628i
$538$	0.138660	+	0.517486i	0.00597806	+	0.0223104i
$539$	0.165230			0.00711696
$540$	2.88216	−	11.2558i	0.124029	−	0.484373i
$541$	44.6389			1.91917			0.959587	−	0.281412i	$-0.0908026\pi$
$541$	44.6389			1.91917			0.959587	+	0.281412i	$0.0908026\pi$
$542$	−4.02237	−	15.0117i	−0.172776	−	0.644807i
$543$	12.6694	−	8.11248i	0.543698	−	0.348140i
$544$	5.39948	−	3.11739i	0.231501	−	0.133657i
$545$	−27.3276	+	21.1523i	−1.17059	+	0.906067i
$546$	2.04447	+	1.86475i	0.0874953	+	0.0798040i
$547$	5.15053	−	1.38008i	0.220221	−	0.0590080i	−0.147022	−	0.989133i	$-0.546969\pi$
$547$	5.15053	−	1.38008i	0.220221	−	0.0590080i	0.367242	+	0.930125i	$0.380302\pi$
$548$	−2.29750	−	2.29750i	−0.0981442	−	0.0981442i
$549$	−21.7286	−	30.7289i	−0.927355	−	1.31148i
$550$	−20.8757	−	11.8197i	−0.890144	−	0.503995i
$551$	8.27432	+	4.77718i	0.352498	+	0.203515i
$552$	−2.09571	+	4.04860i	−0.0891994	+	0.172320i
$553$	−10.7321	−	2.87566i	−0.456376	−	0.122286i
$554$	8.65490	+	14.9907i	0.367712	+	0.636895i
$555$	−1.48347	−	3.12797i	−0.0629697	−	0.132775i
$556$	10.9973	−	19.0478i	0.466388	−	0.807807i
$557$	4.10329	−	4.10329i	0.173862	−	0.173862i	−0.614812	−	0.788674i	$-0.710768\pi$
$557$	4.10329	−	4.10329i	0.173862	−	0.173862i	0.788674	+	0.614812i	$0.210768\pi$
$558$	−4.23703	−	11.4761i	−0.179368	−	0.485822i
$559$		−	1.49979i		−	0.0634344i
$560$	−5.46959	+	2.29256i	−0.231132	+	0.0968783i
$561$	−34.9158	+	38.2809i	−1.47415	+	1.61622i
$562$	6.24341	−	23.3007i	0.263362	−	0.982882i
$563$	1.53547	−	5.73047i	0.0647125	−	0.241510i	−0.925992	−	0.377544i	$-0.876769\pi$
$563$	1.53547	−	5.73047i	0.0647125	−	0.241510i	0.990704	+	0.136033i	$0.0434354\pi$
$564$	−6.70275	−	1.46975i	−0.282237	−	0.0618875i
$565$	12.2361	−	5.12874i	0.514778	−	0.215768i
$566$			16.5516i			0.695715i
$567$	19.6789	+	13.5104i	0.826436	+	0.567383i
$568$	7.36824	−	7.36824i	0.309164	−	0.309164i
$569$	17.6714	−	30.6077i	0.740822	−	1.28314i	−0.211300	−	0.977421i	$-0.567770\pi$
$569$	17.6714	−	30.6077i	0.740822	−	1.28314i	0.952122	−	0.305720i	$-0.0988971\pi$
$570$	−20.0409	−	1.62194i	−0.839420	−	0.0679358i
$571$	1.50529	+	2.60725i	0.0629946	+	0.109110i	0.895803	−	0.444452i	$-0.146602\pi$
$571$	1.50529	+	2.60725i	0.0629946	+	0.109110i	−0.832808	+	0.553562i	$0.813268\pi$
$572$	−2.79162	−	0.748011i	−0.116723	−	0.0312759i
$573$	8.66674	−	0.398435i	0.362058	−	0.0166448i
$574$	14.8142	+	8.55296i	0.618331	+	0.356993i
$575$	−11.4521	−	6.48410i	−0.477584	−	0.270405i
$576$	2.72474	+	1.25529i	0.113531	+	0.0523040i
$577$	−11.5350	−	11.5350i	−0.480208	−	0.480208i	0.424990	−	0.905198i	$-0.360278\pi$
$577$	−11.5350	−	11.5350i	−0.480208	−	0.480208i	−0.905198	+	0.424990i	$0.860278\pi$
$578$	21.1272	−	5.66101i	0.878774	−	0.235467i
$579$	5.56002	−	1.76718i	0.231066	−	0.0734415i
$580$	3.25430	−	2.51891i	0.135127	−	0.104592i
$581$	−26.4185	+	15.2527i	−1.09602	+	0.632789i
$582$	26.6122	+	13.7755i	1.10311	+	0.571011i
$583$	−2.30434	−	8.59992i	−0.0954361	−	0.356172i
$584$	−4.66721			−0.193130
$585$	4.03833	+	0.140652i	0.166964	+	0.00581526i
$586$	16.1515			0.667214
$587$	−2.95165	−	11.0157i	−0.121828	−	0.454666i	0.877879	−	0.478882i	$-0.158958\pi$
$587$	−2.95165	−	11.0157i	−0.121828	−	0.454666i	−0.999707	+	0.0242156i	$0.992291\pi$
$588$	−0.00273930	−	0.0595851i	−0.000112967	−	0.00245725i
$589$	−18.3333	+	10.5848i	−0.755412	+	0.436137i
$590$	0.286351	+	0.0364749i	0.0117889	+	0.00150165i
$591$	8.13346	−	37.0925i	0.334566	−	1.52578i
$592$	0.863406	−	0.231349i	0.0354858	−	0.00950838i
$593$	23.4664	+	23.4664i	0.963651	+	0.963651i	0.999362	−	0.0357109i	$-0.0113696\pi$
$593$	23.4664	+	23.4664i	0.963651	+	0.963651i	−0.0357109	+	0.999362i	$0.511370\pi$
$594$	−24.7394	−	3.08295i	−1.01507	−	0.126495i
$595$	−36.6391	+	4.98040i	−1.50206	+	0.204177i
$596$	−11.3738	−	6.56668i	−0.465890	−	0.268982i
$597$	17.2422	+	26.9276i	0.705678	+	1.10207i
$598$	−1.53143	−	0.410346i	−0.0626249	−	0.0167803i
$599$	−17.2683	−	29.9097i	−0.705566	−	1.22208i	−0.966487	−	0.256715i	$-0.917360\pi$
$599$	−17.2683	−	29.9097i	−0.705566	−	1.22208i	0.260922	−	0.965360i	$-0.415974\pi$
$600$	−3.91633	+	7.72414i	−0.159883	+	0.315337i
$601$	−1.57759	+	2.73247i	−0.0643513	+	0.111460i	−0.896406	−	0.443234i	$-0.853831\pi$
$601$	−1.57759	+	2.73247i	−0.0643513	+	0.111460i	0.832055	+	0.554694i	$0.187164\pi$
$602$	−4.66952	+	4.66952i	−0.190315	+	0.190315i
$603$	−25.4734	−	21.1752i	−1.03736	−	0.862320i
$604$		−	0.335798i		−	0.0136634i
$605$	−10.1812	+	24.8748i	−0.413924	+	1.01130i
$606$	6.27581	+	19.7454i	0.254937	+	0.802100i
$607$	1.32070	−	4.92890i	0.0536054	−	0.200058i	−0.933930	−	0.357456i	$-0.883644\pi$
$607$	1.32070	−	4.92890i	0.0536054	−	0.200058i	0.987535	+	0.157399i	$0.0503107\pi$
$608$	1.34365	−	5.01456i	0.0544921	−	0.203367i
$609$	2.56091	+	8.05731i	0.103773	+	0.326499i
$610$	10.8437	+	25.8709i	0.439048	+	1.04748i
$611$		−	2.38643i		−	0.0965446i
$612$	14.3837	+	11.9567i	0.581426	+	0.483320i
$613$	−9.09622	+	9.09622i	−0.367393	+	0.367393i	−0.866525	−	0.499133i	$-0.833652\pi$
$613$	−9.09622	+	9.09622i	−0.367393	+	0.367393i	0.499133	+	0.866525i	$0.333652\pi$
$614$	1.02984	−	1.78374i	0.0415611	−	0.0719859i
$615$	24.5709	−	4.49765i	0.990793	−	0.181363i
$616$	6.36265	+	11.0204i	0.256358	+	0.444026i
$617$	23.2998	+	6.24315i	0.938013	+	0.251340i	0.695268	−	0.718751i	$-0.255286\pi$
$617$	23.2998	+	6.24315i	0.938013	+	0.251340i	0.242745	+	0.970090i	$0.421952\pi$
$618$	10.0616	+	15.7134i	0.404737	+	0.632087i
$619$	26.9280	+	15.5469i	1.08233	+	0.624883i	0.931524	−	0.363680i	$-0.118480\pi$
$619$	26.9280	+	15.5469i	1.08233	+	0.624883i	0.150806	+	0.988563i	$0.451813\pi$
$620$	1.22815	+	9.03506i	0.0493236	+	0.362857i
$621$	−13.5716	−	1.69125i	−0.544609	−	0.0678677i
$622$	−1.48163	−	1.48163i	−0.0594081	−	0.0594081i
$623$	−5.25156	+	1.40715i	−0.210399	+	0.0563764i
$624$	−0.223466	+	1.01911i	−0.00894580	+	0.0407971i
$625$	−21.8577	−	12.1342i	−0.874310	−	0.485369i
$626$	17.1057	−	9.87595i	0.683679	−	0.394723i
$627$	1.98128	+	43.0967i	0.0791246	+	1.72112i
$628$	−1.17992	−	4.40352i	−0.0470839	−	0.175719i
$629$	5.57304			0.222212
$630$	−12.1352	−	13.0110i	−0.483478	−	0.518372i
$631$	46.1604			1.83762			0.918809	−	0.394703i	$-0.129153\pi$
$631$	46.1604			1.83762			0.918809	+	0.394703i	$0.129153\pi$
$632$	−1.08423	−	4.04642i	−0.0431285	−	0.160958i
$633$	−2.01338	−	1.04220i	−0.0800247	−	0.0414239i
$634$	−29.5196	+	17.0431i	−1.17237	+	0.676869i
$635$	−1.00628	+	7.89994i	−0.0399331	+	0.313500i
$636$	−3.06309	+	0.973565i	−0.121460	+	0.0386044i
$637$	0.0200372	−	0.00536896i	0.000793905	−	0.000212726i
$638$	−6.24383	−	6.24383i	−0.247195	−	0.247195i
$639$	28.3926	+	13.0805i	1.12319	+	0.517457i
$640$	−1.77970	−	1.35376i	−0.0703487	−	0.0535122i
$641$	−3.41084	−	1.96925i	−0.134720	−	0.0777808i	0.431125	−	0.902292i	$-0.358117\pi$
$641$	−3.41084	−	1.96925i	−0.134720	−	0.0777808i	−0.565845	+	0.824511i	$0.691450\pi$
$642$	−10.6530	+	0.489749i	−0.420441	+	0.0193288i
$643$	−29.9917	−	8.03625i	−1.18276	−	0.316919i	−0.386737	−	0.922190i	$-0.626398\pi$
$643$	−29.9917	−	8.03625i	−1.18276	−	0.316919i	−0.796019	+	0.605271i	$0.793065\pi$
$644$	3.49044	+	6.04562i	0.137543	+	0.238231i
$645$	−0.777892	+	9.61170i	−0.0306295	+	0.378460i
$646$	16.1838	−	28.0311i	0.636742	−	1.10287i
$647$	−18.0986	+	18.0986i	−0.711531	+	0.711531i	−0.966855	−	0.255325i	$-0.917818\pi$
$647$	−18.0986	+	18.0986i	−0.711531	+	0.711531i	0.255325	+	0.966855i	$0.417818\pi$
$648$	−0.701625	+	8.97261i	−0.0275624	+	0.352477i
$649$		−	0.619386i		−	0.0243130i
$650$	−2.91564	−	0.755031i	−0.114361	−	0.0296147i
$651$	−18.2978	−	4.01226i	−0.717149	−	0.157253i
$652$	−3.29971	+	12.3147i	−0.129226	+	0.482280i
$653$	3.63685	−	13.5729i	0.142321	−	0.531148i	−0.857539	−	0.514419i	$-0.828008\pi$
$653$	3.63685	−	13.5729i	0.142321	−	0.531148i	0.999860	−	0.0167299i	$-0.00532554\pi$
$654$	18.0387	−	19.7772i	0.705369	−	0.773350i
$655$	27.0267	+	11.0620i	1.05602	+	0.432227i
$656$			6.44958i			0.251814i
$657$	−4.84950	−	13.1350i	−0.189197	−	0.512444i
$658$	−7.43002	+	7.43002i	−0.289652	+	0.289652i
$659$	−18.2709	+	31.6462i	−0.711734	+	1.23276i	0.252471	+	0.967604i	$0.418757\pi$
$659$	−18.2709	+	31.6462i	−0.711734	+	1.23276i	−0.964206	+	0.265155i	$0.914577\pi$
$660$	17.5026	+	6.24169i	0.681289	+	0.242957i
$661$	−17.9365	−	31.0670i	−0.697650	−	1.20836i	−0.969279	−	0.245963i	$-0.920896\pi$
$661$	−17.9365	−	31.0670i	−0.697650	−	1.20836i	0.271629	−	0.962402i	$-0.412438\pi$
$662$	−23.2092	−	6.21890i	−0.902053	−	0.241704i
$663$	−2.99030	+	5.77683i	−0.116134	+	0.224353i
$664$	−9.96076	−	5.75085i	−0.386553	−	0.223176i
$665$	−18.6400	+	24.5047i	−0.722829	+	0.950253i
$666$	1.54822	+	2.18951i	0.0599922	+	0.0848418i
$667$	−3.42525	−	3.42525i	−0.132626	−	0.132626i
$668$	0.00858342	−	0.00229992i	0.000332102	−	8.89866e-5i
$669$	−26.8432	−	24.4835i	−1.03782	−	0.946588i
$670$	15.1126	+	19.5246i	0.583850	+	0.754302i
$671$	52.1261	−	30.0950i	2.01231	−	1.16181i
$672$	3.86870	−	2.47720i	0.149238	−	0.0955600i
$673$	−6.49200	−	24.2285i	−0.250248	−	0.933939i	−0.970673	−	0.240406i	$-0.922720\pi$
$673$	−6.49200	−	24.2285i	−0.250248	−	0.933939i	0.720424	−	0.693534i	$-0.243947\pi$
$674$	12.2514			0.471907
$675$	−25.8074	−	2.99594i	−0.993329	−	0.115314i
$676$	12.6372			0.486045
$677$	1.40152	+	5.23054i	0.0538647	+	0.201026i	0.987614	−	0.156901i	$-0.0501504\pi$
$677$	1.40152	+	5.23054i	0.0538647	+	0.201026i	−0.933750	+	0.357927i	$0.883484\pi$
$678$	−8.65475	+	5.54180i	−0.332384	+	0.212832i
$679$	39.7389	−	22.9433i	1.52504	−	0.880481i
$680$	−8.53340	−	11.0247i	−0.327241	−	0.422777i
$681$	−7.62057	−	6.95069i	−0.292021	−	0.266351i
$682$	18.8981	−	5.06374i	0.723647	−	0.193901i
$683$	14.3302	+	14.3302i	0.548331	+	0.548331i	0.925958	−	0.377627i	$-0.123260\pi$
$683$	14.3302	+	14.3302i	0.548331	+	0.548331i	−0.377627	+	0.925958i	$0.623260\pi$
$684$	15.5087	−	1.42897i	0.592989	−	0.0546382i
$685$	−4.39858	+	5.78251i	−0.168061	+	0.220938i
$686$	15.9993	+	9.23721i	0.610857	+	0.352678i
$687$	−9.36157	+	18.0852i	−0.357166	+	0.689992i
$688$	−2.40501	−	0.644420i	−0.0916900	−	0.0245683i
$689$	−0.558889	−	0.968025i	−0.0212920	−	0.0368788i
$690$	9.60164	+	3.42408i	0.365528	+	0.130353i
$691$	−5.85991	+	10.1497i	−0.222921	+	0.386111i	−0.955694	−	0.294363i	$-0.904893\pi$
$691$	−5.85991	+	10.1497i	−0.222921	+	0.386111i	0.732772	+	0.680474i	$0.238226\pi$
$692$	7.34182	−	7.34182i	0.279094	−	0.279094i
$693$	−24.4038	+	29.3574i	−0.927023	+	1.11519i
$694$		−	18.5893i		−	0.705641i
$695$	−45.5162	−	18.6297i	−1.72653	−	0.706664i
$696$	−2.14813	+	2.35516i	−0.0814246	+	0.0892720i
$697$	−10.4076	+	38.8415i	−0.394214	+	1.47123i
$698$	−8.13805	+	30.3716i	−0.308030	+	1.14958i
$699$	−32.1385	−	7.04717i	−1.21559	−	0.266549i
$700$	6.72694	+	11.4284i	0.254255	+	0.431954i
$701$			30.7235i			1.16041i	0.814471	+	0.580205i	$0.197028\pi$
$701$			30.7235i			1.16041i	−0.814471	+	0.580205i	$0.802972\pi$
$702$	−3.10029	+	0.430013i	−0.117013	+	0.0162298i
$703$	3.28129	−	3.28129i	0.123756	−	0.123756i
$704$	−2.39896	+	4.15512i	−0.0904143	+	0.156602i
$705$	−1.23776	+	15.2939i	−0.0466168	+	0.576001i
$706$	6.07917	+	10.5294i	0.228792	+	0.396280i
$707$	30.6451	+	8.21132i	1.15253	+	0.308818i
$708$	−0.223362	+	0.0102686i	−0.00839448	+	0.000385918i
$709$	−27.4879	−	15.8701i	−1.03233	−	0.596015i	−0.114678	−	0.993403i	$-0.536584\pi$
$709$	−27.4879	−	15.8701i	−1.03233	−	0.596015i	−0.917651	+	0.397387i	$0.869917\pi$
$710$	−18.5449	−	14.1066i	−0.695979	−	0.529410i
$711$	10.2613	−	7.25584i	0.384829	−	0.272115i
$712$	−1.44949	−	1.44949i	−0.0543219	−	0.0543219i
$713$	10.3672	−	2.77788i	0.388254	−	0.104032i
$714$	27.2960	−	8.67568i	1.02153	−	0.324679i
$715$	−0.816579	+	6.41065i	−0.0305383	+	0.239745i
$716$	−1.26692	+	0.731458i	−0.0473471	+	0.0273359i
$717$	7.01238	+	3.62988i	0.261882	+	0.135560i
$718$	−1.11708	−	4.16899i	−0.0416890	−	0.155585i
$719$	−7.79879			−0.290846			−0.145423	−	0.989370i	$-0.546454\pi$
$719$	−7.79879			−0.290846			−0.145423	+	0.989370i	$0.546454\pi$
$720$	1.96070	−	6.41527i	0.0730711	−	0.239083i
$721$	28.5717			1.06407
$722$	−2.05792	−	7.68026i	−0.0765878	−	0.285830i
$723$	1.27763	+	27.7910i	0.0475155	+	1.03356i
$724$	7.52209	−	4.34288i	0.279556	−	0.161402i
$725$	−6.56127	−	6.45187i	−0.243680	−	0.239616i
$726$	4.45923	−	20.3362i	0.165497	−	0.754747i
$727$	−42.7863	+	11.4645i	−1.58685	+	0.425196i	−0.941039	−	0.338297i	$-0.890149\pi$
$727$	−42.7863	+	11.4645i	−1.58685	+	0.425196i	−0.645815	+	0.763494i	$0.723482\pi$
$728$	1.12969	+	1.12969i	0.0418690	+	0.0418690i
$729$	−25.9808	+	7.34847i	−0.962250	+	0.272166i
$730$	1.40568	+	10.3411i	0.0520265	+	0.382741i
$731$	−13.4439	−	7.76182i	−0.497239	−	0.287081i
$732$	−11.7170	−	18.2987i	−0.433074	−	0.676341i
$733$	26.9304	+	7.21598i	0.994697	+	0.266528i	0.719222	−	0.694780i	$-0.244498\pi$
$733$	26.9304	+	7.21598i	0.994697	+	0.266528i	0.275475	+	0.961308i	$0.411165\pi$
$734$	−9.93909	−	17.2150i	−0.366858	−	0.635418i
$735$	−0.131197	+	0.0240154i	−0.00483928	+	0.000885821i
$736$	−1.31603	+	2.27943i	−0.0485095	+	0.0840208i
$737$	37.4607	−	37.4607i	1.37988	−	1.37988i
$738$	−18.1511	+	6.70149i	−0.668153	+	0.246685i
$739$			10.8068i			0.397536i	0.980047	+	0.198768i	$0.0636941\pi$
$739$			10.8068i			0.397536i	−0.980047	+	0.198768i	$0.936306\pi$
$740$	−0.772640	−	1.84336i	−0.0284028	−	0.0677634i
$741$	1.64065	+	5.16191i	0.0602707	+	0.189628i
$742$	−1.27382	+	4.75396i	−0.0467634	+	0.174523i
$743$	−5.75762	+	21.4877i	−0.211227	+	0.788309i	0.776234	+	0.630445i	$0.217127\pi$
$743$	−5.75762	+	21.4877i	−0.211227	+	0.788309i	−0.987461	+	0.157864i	$0.949539\pi$
$744$	−2.13939	−	6.73108i	−0.0784338	−	0.246773i
$745$	−11.1242	+	27.1787i	−0.407558	+	0.995749i
$746$			2.62754i			0.0962009i
$747$	5.83488	−	34.0082i	0.213487	−	1.24429i
$748$	−21.1524	+	21.1524i	−0.773408	+	0.773408i
$749$	−8.16498	+	14.1422i	−0.298342	+	0.516743i
$750$	18.2938	+	6.35101i	0.667997	+	0.231906i
$751$	−20.6235	−	35.7209i	−0.752561	−	1.30347i	−0.946578	−	0.322476i	$-0.895485\pi$
$751$	−20.6235	−	35.7209i	−0.752561	−	1.30347i	0.194017	−	0.980998i	$-0.437848\pi$
$752$	−3.82678	−	1.02538i	−0.139548	−	0.0373919i
$753$	−17.7442	−	27.7115i	−0.646634	−	1.00986i
$754$	−0.960067	−	0.554295i	−0.0349636	−	0.0201862i
$755$	−0.744025	+	0.101136i	−0.0270778	+	0.00368072i
$756$	10.9914	+	8.31377i	0.399754	+	0.302369i
$757$	−20.5246	−	20.5246i	−0.745978	−	0.745978i	0.227743	−	0.973721i	$-0.426865\pi$
$757$	−20.5246	−	20.5246i	−0.745978	−	0.745978i	−0.973721	+	0.227743i	$0.926865\pi$
$758$	2.92796	−	0.784544i	0.106348	−	0.0284959i
$759$	4.68491	−	21.3654i	0.170051	−	0.775516i
$760$	−11.5154	−	1.46681i	−0.417707	−	0.0532069i
$761$	39.8188	−	22.9894i	1.44343	−	0.833365i	0.445353	−	0.895355i	$-0.353078\pi$
$761$	39.8188	−	22.9894i	1.44343	−	0.833365i	0.998077	+	0.0619904i	$0.0197448\pi$
$762$	−0.283294	−	6.16220i	−0.0102626	−	0.223233i
$763$	−10.6089	−	39.5928i	−0.384066	−	1.43335i
$764$	5.00903			0.181220
$765$	22.1602	−	35.4709i	0.801203	−	1.28245i
$766$	−23.7508			−0.858153
$767$	−0.0201262	−	0.0751122i	−0.000726717	−	0.00271214i
$768$	1.53819	+	0.796225i	0.0555046	+	0.0287313i
$769$	26.6702	−	15.3980i	0.961752	−	0.555268i	0.0650399	−	0.997883i	$-0.479283\pi$
$769$	26.6702	−	15.3980i	0.961752	−	0.555268i	0.896712	+	0.442615i	$0.145949\pi$
$770$	22.5016	−	17.4168i	0.810900	−	0.627659i
$771$	−5.53189	+	1.75824i	−0.199226	+	0.0633215i
$772$	3.25355	−	0.871785i	0.117098	−	0.0313762i
$773$	29.6376	+	29.6376i	1.06599	+	1.06599i	0.997663	+	0.0683287i	$0.0217667\pi$
$773$	29.6376	+	29.6376i	1.06599	+	1.06599i	0.0683287	+	0.997663i	$0.478233\pi$
$774$	−0.685343	−	7.43803i	−0.0246341	−	0.267354i
$775$	19.6490	−	5.44239i	0.705814	−	0.195496i
$776$	14.9831	+	8.65048i	0.537861	+	0.310534i
$777$	4.10193	−	0.188577i	0.147156	−	0.00676517i
$778$	6.43797	+	1.72505i	0.230813	+	0.0618460i
$779$	16.7414	+	28.9969i	0.599821	+	1.03892i
$780$	2.32534	+	0.188194i	0.0832605	+	0.00673842i
$781$	−24.9978	+	43.2975i	−0.894492	+	1.54931i
$782$	−11.6038	+	11.6038i	−0.414952	+	0.414952i
$783$	−8.86018	−	3.59836i	−0.316637	−	0.128595i
$784$		−	0.0344378i		−	0.00122992i
$785$	−9.40147	+	3.94060i	−0.335553	+	0.140646i
$786$	−22.0955	−	4.84500i	−0.788122	−	0.172816i
$787$	−6.98316	+	26.0615i	−0.248923	+	0.928993i	0.722448	+	0.691425i	$0.243017\pi$
$787$	−6.98316	+	26.0615i	−0.248923	+	0.928993i	−0.971371	+	0.237568i	$0.923650\pi$
$788$	5.67439	−	21.1771i	0.202142	−	0.754403i
$789$	19.5453	−	21.4290i	0.695831	−	0.762893i
$790$	−8.63906	+	3.62104i	−0.307364	+	0.128831i
$791$			15.7369i			0.559540i
$792$	−14.1865	−	2.43401i	−0.504095	−	0.0864890i
$793$	5.34337	−	5.34337i	0.189749	−	0.189749i
$794$	9.35091	−	16.1963i	0.331852	−	0.574784i
$795$	3.07967	+	6.49365i	0.109225	+	0.230306i
$796$	9.23033	+	15.9874i	0.327161	+	0.566659i
$797$	6.28188	+	1.68322i	0.222515	+	0.0596228i	0.368354	−	0.929686i	$-0.379921\pi$
$797$	6.28188	+	1.68322i	0.222515	+	0.0596228i	−0.145839	+	0.989308i	$0.546588\pi$
$798$	10.9633	−	21.1794i	0.388095	−	0.749742i
$799$	−21.3915	−	12.3504i	−0.756778	−	0.436926i
$800$	−2.46351	+	4.35099i	−0.0870982	+	0.153831i
$801$	2.57321	−	5.58542i	0.0909200	−	0.197351i
$802$	3.81250	+	3.81250i	0.134624	+	0.134624i
$803$	21.6299	−	5.79571i	0.763302	−	0.204526i
$804$	−14.1301	−	12.8880i	−0.498330	−	0.454525i
$805$	12.3440	−	9.55456i	0.435068	−	0.336754i
$806$	2.12721	−	1.22815i	0.0749279	−	0.0432596i
$807$	−0.781457	+	0.500381i	−0.0275086	+	0.0176143i
$808$	3.09598	+	11.5544i	0.108916	+	0.406481i
$809$	−5.79431			−0.203717			−0.101859	−	0.994799i	$-0.532479\pi$
$809$	−5.79431			−0.203717			−0.101859	+	0.994799i	$0.532479\pi$
$810$	20.0919	−	1.14780i	0.705956	−	0.0403296i
$811$	1.90498			0.0668929			0.0334465	−	0.999441i	$-0.489352\pi$
$811$	1.90498			0.0668929			0.0334465	+	0.999441i	$0.489352\pi$
$812$	1.26335	+	4.71488i	0.0443349	+	0.165460i
$813$	22.6692	−	14.5155i	0.795042	−	0.509080i
$814$	−3.71411	+	2.14434i	−0.130180	+	0.0751592i
$815$	28.2793	+	3.60218i	0.990581	+	0.126179i
$816$	7.97863	+	7.27728i	0.279308	+	0.254756i
$817$	−12.4855	+	3.34547i	−0.436812	+	0.117043i
$818$	−6.07126	−	6.07126i	−0.212277	−	0.212277i
$819$	−2.00548	+	4.35310i	−0.0700773	+	0.152110i
$820$	14.2903	−	1.94250i	0.499038	−	0.0678349i
$821$	−33.4503	−	19.3125i	−1.16742	−	0.674012i	−0.214351	−	0.976757i	$-0.568764\pi$
$821$	−33.4503	−	19.3125i	−1.16742	−	0.674012i	−0.953072	+	0.302745i	$0.902097\pi$
$822$	2.58706	−	4.99781i	0.0902339	−	0.174319i
$823$	20.6711	+	5.53879i	0.720548	+	0.193070i	0.600416	−	0.799688i	$-0.295002\pi$
$823$	20.6711	+	5.53879i	0.720548	+	0.193070i	0.120132	+	0.992758i	$0.461668\pi$
$824$	5.38631	+	9.32936i	0.187641	+	0.325004i
$825$	8.55819	−	40.6603i	0.297958	−	1.41561i
$826$	−0.171196	+	0.296520i	−0.00595666	+	0.0103172i
$827$	23.1603	−	23.1603i	0.805364	−	0.805364i	−0.178564	−	0.983928i	$-0.557145\pi$
$827$	23.1603	−	23.1603i	0.805364	−	0.805364i	0.983928	+	0.178564i	$0.0571453\pi$
$828$	−7.78245	−	1.33526i	−0.270459	−	0.0464034i
$829$			34.1116i			1.18475i	0.805664	+	0.592373i	$0.201809\pi$
$829$			34.1116i			1.18475i	−0.805664	+	0.592373i	$0.798191\pi$
$830$	−9.74211	+	23.8020i	−0.338154	+	0.826181i
$831$	−20.2041	+	22.1513i	−0.700873	+	0.768421i
$832$	−0.155903	+	0.581838i	−0.00540497	+	0.0201716i
$833$	0.0555716	−	0.207396i	0.00192544	−	0.00718585i
$834$	37.2115	+	8.15957i	1.28853	+	0.282543i
$835$	−0.00768108	−	0.0183255i	−0.000265815	−	0.000634180i
$836$			24.9082i			0.861468i
$837$	16.7204	−	13.0149i	0.577942	−	0.449860i
$838$	−10.9283	+	10.9283i	−0.377512	+	0.377512i
$839$	18.8058	−	32.5726i	0.649249	−	1.12453i	−0.334054	−	0.942554i	$-0.608417\pi$
$839$	18.8058	−	32.5726i	0.649249	−	1.12453i	0.983303	−	0.181978i	$-0.0582500\pi$
$840$	−6.65389	−	7.82575i	−0.229581	−	0.270014i
$841$	12.8065	+	22.1814i	0.441602	+	0.764877i
$842$	18.2585	+	4.89235i	0.629229	+	0.168602i
$843$	41.7376	−	1.91880i	1.43752	−	0.0660868i
$844$	−1.13357	−	0.654465i	−0.0390190	−	0.0225276i
$845$	−3.80608	−	28.0000i	−0.130933	−	0.963231i
$846$	−1.09050	−	11.8352i	−0.0374921	−	0.406903i
$847$	−22.5427	−	22.5427i	−0.774577	−	0.774577i
$848$	−1.79243	+	0.480279i	−0.0615521	+	0.0164928i
$849$	−27.3214	+	8.68375i	−0.937667	+	0.298026i
$850$	−21.8572	+	22.2278i	−0.749695	+	0.762407i
$851$	−2.03750	+	1.17635i	−0.0698445	+	0.0403248i
$852$	16.0283	+	8.29688i	0.549122	+	0.284246i
$853$	−1.98742	−	7.41714i	−0.0680478	−	0.253958i	0.923519	−	0.383552i	$-0.125299\pi$
$853$	−1.98742	−	7.41714i	−0.0680478	−	0.253958i	−0.991567	+	0.129594i	$0.958633\pi$
$854$	−33.2726			−1.13856
$855$	−7.83709	−	33.9320i	−0.268023	−	1.16045i
$856$	−6.15702			−0.210442
$857$	1.87635	+	7.00264i	0.0640949	+	0.239206i	0.990540	−	0.137224i	$-0.0438182\pi$
$857$	1.87635	+	7.00264i	0.0640949	+	0.239206i	−0.926445	+	0.376430i	$0.877152\pi$
$858$	−0.229887	−	5.00051i	−0.00784823	−	0.170714i
$859$	−1.50446	+	0.868601i	−0.0513316	+	0.0296363i	−0.525446	−	0.850827i	$-0.676102\pi$
$859$	−1.50446	+	0.868601i	−0.0513316	+	0.0296363i	0.474115	+	0.880463i	$0.342768\pi$
$860$	−0.703491	+	5.52284i	−0.0239888	+	0.188327i
$861$	−6.34598	+	28.9407i	−0.216271	+	0.986297i
$862$	3.78090	−	1.01309i	0.128778	−	0.0345060i
$863$	−36.4612	−	36.4612i	−1.24115	−	1.24115i	−0.959523	−	0.281630i	$-0.909125\pi$
$863$	−36.4612	−	36.4612i	−1.24115	−	1.24115i	−0.281630	−	0.959523i	$-0.590875\pi$
$864$	−0.642559	+	5.15627i	−0.0218603	+	0.175420i
$865$	−18.4784	−	14.0560i	−0.628286	−	0.477918i
$866$	−33.3190	−	19.2368i	−1.13223	−	0.653692i
$867$	20.4288	+	31.9042i	0.693799	+	1.08352i
$868$	−10.4467	−	2.79919i	−0.354585	−	0.0950108i
$869$	10.0496	+	17.4065i	0.340911	+	0.590474i
$870$	5.86528	+	4.05026i	0.198852	+	0.137317i
$871$	3.32557	−	5.76006i	0.112683	−	0.195172i
$872$	10.9280	−	10.9280i	0.370070	−	0.370070i
$873$	−8.77688	+	51.1554i	−0.297052	+	1.73135i
$874$			13.6642i			0.462199i
$875$	23.2959	−	18.3469i	0.787544	−	0.620237i
$876$	−2.44864	−	7.70407i	−0.0827318	−	0.260296i
$877$	2.68194	−	10.0092i	0.0905628	−	0.337985i	−0.905747	−	0.423820i	$-0.860689\pi$
$877$	2.68194	−	10.0092i	0.0905628	−	0.337985i	0.996309	+	0.0858347i	$0.0273557\pi$
$878$	3.96659	−	14.8035i	0.133866	−	0.499594i
$879$	8.47386	+	26.6610i	0.285816	+	0.899254i
$880$	9.92900	+	4.06391i	0.334706	+	0.136994i
$881$		−	1.17719i		−	0.0396604i	−0.999803	−	0.0198302i	$-0.993687\pi$
$881$		−	1.17719i		−	0.0396604i	0.999803	−	0.0198302i	$-0.00631257\pi$
$882$	0.0969188	−	0.0357829i	0.00326343	−	0.00120487i
$883$	−22.1929	+	22.1929i	−0.746850	+	0.746850i	−0.973886	−	0.227036i	$-0.927097\pi$
$883$	−22.1929	+	22.1929i	−0.746850	+	0.746850i	0.227036	+	0.973886i	$0.427097\pi$
$884$	−1.87780	+	3.25245i	−0.0631573	+	0.109392i
$885$	0.0900247	+	0.491810i	0.00302615	+	0.0165320i
$886$	−13.9099	−	24.0927i	−0.467313	−	0.809410i
$887$	8.80492	+	2.35927i	0.295640	+	0.0792166i	0.403590	−	0.914940i	$-0.367762\pi$
$887$	8.80492	+	2.35927i	0.295640	+	0.0792166i	−0.107950	+	0.994156i	$0.534429\pi$
$888$	0.834867	+	1.30383i	0.0280163	+	0.0437537i
$889$	−8.18049	−	4.72301i	−0.274365	−	0.158405i
$890$	−2.77506	+	3.64818i	−0.0930203	+	0.122287i
$891$	−7.89049	−	42.4543i	−0.264341	−	1.42227i
$892$	−14.8324	−	14.8324i	−0.496625	−	0.496625i
$893$	−19.8666	+	5.32323i	−0.664809	+	0.178135i
$894$	4.87224	−	22.2197i	0.162952	−	0.743140i
$895$	2.00226	+	2.58681i	0.0669281	+	0.0864674i
$896$	2.29692	−	1.32613i	0.0767346	−	0.0443028i
$897$	−0.126112	−	2.74319i	−0.00421076	−	0.0915925i
$898$	−6.30553	−	23.5326i	−0.210418	−	0.785292i
$899$	7.50472			0.250296
$900$	−14.8048	−	2.41215i	−0.493493	−	0.0804051i
$901$	−11.5696			−0.385439
$902$	−8.00905	−	29.8902i	−0.266672	−	0.995234i
$903$	−10.1577	−	5.25803i	−0.338028	−	0.174976i
$904$	−5.13849	+	2.96671i	−0.170904	+	0.0986713i
$905$	−11.8880	−	15.3586i	−0.395170	−	0.510538i
$906$	0.554295	−	0.176176i	0.0184152	−	0.00585304i
$907$	7.35203	−	1.96997i	0.244120	−	0.0654118i	−0.134684	−	0.990889i	$-0.543002\pi$
$907$	7.35203	−	1.96997i	0.244120	−	0.0654118i	0.378804	+	0.925477i	$0.376335\pi$
$908$	−4.21080	−	4.21080i	−0.139740	−	0.139740i
$909$	−29.3007	+	20.7187i	−0.971842	+	0.687196i
$910$	2.16280	−	2.84328i	0.0716960	−	0.0942538i
$911$	39.2522	+	22.6623i	1.30048	+	0.750835i	0.980487	−	0.196583i	$-0.0629846\pi$
$911$	39.2522	+	22.6623i	1.30048	+	0.750835i	0.319997	+	0.947418i	$0.396318\pi$
$912$	8.98237	−	0.412945i	0.297436	−	0.0136740i
$913$	53.3039	+	14.2827i	1.76410	+	0.472690i
$914$	−6.55874	−	11.3601i	−0.216944	−	0.375758i
$915$	−37.0154	+	31.4726i	−1.22369	+	1.04045i
$916$	−5.87872	+	10.1822i	−0.194238	+	0.336431i
$917$	−24.4930	+	24.4930i	−0.808829	+	0.808829i
$918$	−12.1903	+	30.0159i	−0.402339	+	0.990672i
$919$			19.9726i			0.658836i	0.944184	+	0.329418i	$0.106852\pi$
$919$			19.9726i			0.658836i	−0.944184	+	0.329418i	$0.893148\pi$
$920$	5.44687	+	2.22939i	0.179578	+	0.0735009i
$921$	3.48469	+	0.764106i	0.114824	+	0.0251782i
$922$	−10.3908	+	38.7791i	−0.342204	+	1.27712i
$923$	−1.62455	+	6.06291i	−0.0534728	+	0.199563i
$924$	−14.8531	+	16.2845i	−0.488630	+	0.535722i
$925$	−3.85162	+	2.26712i	−0.126640	+	0.0745424i
$926$		−	11.9769i		−	0.393586i
$927$	−20.6590	+	24.8525i	−0.678532	+	0.816263i
$928$	−1.30136	+	1.30136i	−0.0427192	+	0.0427192i
$929$	−24.8920	+	43.1142i	−0.816681	+	1.41453i	0.0914341	+	0.995811i	$0.470855\pi$
$929$	−24.8920	+	43.1142i	−0.816681	+	1.41453i	−0.908115	+	0.418721i	$0.862478\pi$
$930$	−14.2697	+	6.76750i	−0.467920	+	0.221915i
$931$	−0.0893912	−	0.154830i	−0.00292968	−	0.00507435i
$932$	−18.3487	−	4.91653i	−0.601033	−	0.161046i
$933$	1.66837	−	3.22304i	0.0546199	−	0.105518i
$934$	10.5711	+	6.10321i	0.345896	+	0.199703i
$935$	53.2379	+	40.4964i	1.74106	+	1.32438i
$936$	−1.79947	+	0.165804i	−0.0588174	+	0.00541946i
$937$	28.6750	+	28.6750i	0.936771	+	0.936771i	0.998117	−	0.0613453i	$-0.0195391\pi$
$937$	28.6750	+	28.6750i	0.936771	+	0.936771i	−0.0613453	+	0.998117i	$0.519539\pi$
$938$	−28.2876	+	7.57964i	−0.923623	+	0.247484i
$939$	25.2765	+	23.0546i	0.824867	+	0.752357i
$940$	−1.11938	+	8.78780i	−0.0365100	+	0.286626i
$941$	−42.4585	+	24.5134i	−1.38411	+	0.799115i	−0.992643	−	0.121078i	$-0.961365\pi$
$941$	−42.4585	+	24.5134i	−1.38411	+	0.799115i	−0.391464	+	0.920193i	$0.628031\pi$
$942$	6.64976	−	4.25796i	0.216661	−	0.138732i
$943$	−4.39363	−	16.3972i	−0.143076	−	0.533967i
$944$	−0.129095			−0.00420167
$945$	15.1103	−	26.8575i	0.491539	−	0.873676i
$946$	11.9461			0.388401
$947$	11.6667	+	43.5407i	0.379117	+	1.41488i	0.847236	+	0.531217i	$0.178265\pi$
$947$	11.6667	+	43.5407i	0.379117	+	1.41488i	−0.468119	+	0.883665i	$0.655068\pi$
$948$	6.11050	−	3.91267i	0.198460	−	0.127078i
$949$	2.43470	−	1.40568i	0.0790339	−	0.0456302i
$950$	0.218220	+	25.9564i	0.00707998	+	0.842135i
$951$	−43.6201	−	39.7857i	−1.41448	−	1.29014i
$952$	15.9727	−	4.27988i	0.517679	−	0.138712i
$953$	−2.71971	−	2.71971i	−0.0881001	−	0.0881001i	0.661683	−	0.749783i	$-0.269842\pi$
$953$	−2.71971	−	2.71971i	−0.0881001	−	0.0881001i	−0.749783	+	0.661683i	$0.769842\pi$
$954$	−3.21409	−	4.54541i	−0.104060	−	0.147163i
$955$	−1.50863	−	11.0985i	−0.0488181	−	0.359138i
$956$	3.94809	+	2.27943i	0.127690	+	0.0737220i
$957$	7.03075	−	13.5824i	0.227272	−	0.439056i
$958$	9.91983	+	2.65801i	0.320495	+	0.0858764i
$959$	−4.30878	−	7.46303i	−0.139138	−	0.240994i
$960$	1.30092	−	3.64796i	0.0419869	−	0.117737i
$961$	7.18593	−	12.4464i	0.231804	−	0.401497i
$962$	−0.380728	+	0.380728i	−0.0122752	+	0.0122752i
$963$	−6.39750	−	17.3278i	−0.206156	−	0.558380i
$964$			16.0621i			0.517325i
$965$	−2.91151	−	6.94629i	−0.0937250	−	0.223609i
$966$	−8.14813	+	8.93342i	−0.262162	+	0.287428i
$967$	8.10886	−	30.2627i	0.260763	−	0.973182i	−0.704029	−	0.710171i	$-0.748618\pi$
$967$	8.10886	−	30.2627i	0.260763	−	0.973182i	0.964793	−	0.263011i	$-0.0847157\pi$
$968$	3.11102	−	11.6105i	0.0999920	−	0.373175i
$969$	54.7612	+	12.0078i	1.75918	+	0.385745i
$970$	14.6542	−	35.8032i	0.470517	−	1.14957i
$971$			31.9680i			1.02590i	0.858418	+	0.512951i	$0.171448\pi$
$971$			31.9680i			1.02590i	−0.858418	+	0.512951i	$0.828552\pi$
$972$	−15.1790	+	3.54930i	−0.486867	+	0.113844i
$973$	41.2491	−	41.2491i	1.32238	−	1.32238i
$974$	−12.3898	+	21.4597i	−0.396993	+	0.687613i
$975$	−0.283370	−	5.20892i	−0.00907512	−	0.166819i
$976$	−6.27251	−	10.8643i	−0.200778	−	0.347758i
$977$	−8.45932	−	2.26667i	−0.270638	−	0.0725171i	0.120948	−	0.992659i	$-0.461407\pi$
$977$	−8.45932	−	2.26667i	−0.270638	−	0.0725171i	−0.391585	+	0.920142i	$0.628073\pi$
$978$	−22.0588	+	1.01410i	−0.705361	+	0.0324275i
$979$	8.51754	+	4.91760i	0.272222	+	0.157167i
$980$	−0.0763036	+	0.0103720i	−0.00243743	+	0.000331323i
$981$	42.1098	+	19.4001i	1.34446	+	0.619397i
$982$	−6.28784	−	6.28784i	−0.200653	−	0.200653i
$983$	40.7397	−	10.9162i	1.29940	−	0.348172i	0.458174	−	0.888863i	$-0.348504\pi$
$983$	40.7397	−	10.9162i	1.29940	−	0.348172i	0.841222	+	0.540691i	$0.181837\pi$
$984$	−10.6462	+	3.38376i	−0.339388	+	0.107870i
$985$	−48.6309	−	6.19454i	−1.54951	−	0.197374i
$986$	−9.93720	+	5.73725i	−0.316465	+	0.182711i
$987$	−16.1627	−	8.36644i	−0.514465	−	0.266307i
$988$	0.809364	+	3.02059i	0.0257493	+	0.0960977i
$989$	6.55342			0.208387
$990$	−1.12032	+	32.1659i	−0.0356061	+	1.02230i
$991$	−13.9120			−0.441929			−0.220964	−	0.975282i	$-0.570920\pi$
$991$	−13.9120			−0.441929			−0.220964	+	0.975282i	$0.570920\pi$
$992$	−1.05540	−	3.93882i	−0.0335091	−	0.125058i
$993$	−1.91126	−	41.5738i	−0.0606521	−	1.31930i
$994$	23.9345	−	13.8186i	0.759156	−	0.438299i
$995$	32.6432	−	25.2667i	1.03486	−	0.801008i
$996$	4.26692	−	19.4592i	0.135203	−	0.616589i
$997$	29.2374	−	7.83414i	0.925958	−	0.248110i	0.235828	−	0.971795i	$-0.424220\pi$
$997$	29.2374	−	7.83414i	0.925958	−	0.248110i	0.690130	+	0.723685i	$0.257553\pi$
$998$	20.7542	+	20.7542i	0.656963	+	0.656963i
$999$	−2.80191	+	3.70433i	−0.0886486	+	0.117200i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	90.2.l.b.47.3	yes	16
3.2	odd	2		270.2.m.b.197.1		16
4.3	odd	2		720.2.cu.b.497.4		16
5.2	odd	4		450.2.p.h.443.2		16
5.3	odd	4	inner	90.2.l.b.83.3	yes	16
5.4	even	2		450.2.p.h.407.2		16
9.2	odd	6		810.2.f.c.647.4		16
9.4	even	3		270.2.m.b.17.1		16
9.5	odd	6	inner	90.2.l.b.77.3	yes	16
9.7	even	3		810.2.f.c.647.5		16
15.2	even	4		1350.2.q.h.143.3		16
15.8	even	4		270.2.m.b.143.1		16
15.14	odd	2		1350.2.q.h.1007.4		16
20.3	even	4		720.2.cu.b.353.3		16
36.23	even	6		720.2.cu.b.257.3		16
45.4	even	6		1350.2.q.h.557.3		16
45.13	odd	12		270.2.m.b.233.1		16
45.14	odd	6		450.2.p.h.257.2		16
45.22	odd	12		1350.2.q.h.1043.4		16
45.23	even	12	inner	90.2.l.b.23.3	✓	16
45.32	even	12		450.2.p.h.293.2		16
45.38	even	12		810.2.f.c.323.5		16
45.43	odd	12		810.2.f.c.323.4		16
180.23	odd	12		720.2.cu.b.113.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
90.2.l.b.23.3	✓	16	45.23	even	12	inner
90.2.l.b.47.3	yes	16	1.1	even	1	trivial
90.2.l.b.77.3	yes	16	9.5	odd	6	inner
90.2.l.b.83.3	yes	16	5.3	odd	4	inner
270.2.m.b.17.1		16	9.4	even	3
270.2.m.b.143.1		16	15.8	even	4
270.2.m.b.197.1		16	3.2	odd	2
270.2.m.b.233.1		16	45.13	odd	12
450.2.p.h.257.2		16	45.14	odd	6
450.2.p.h.293.2		16	45.32	even	12
450.2.p.h.407.2		16	5.4	even	2
450.2.p.h.443.2		16	5.2	odd	4
720.2.cu.b.113.4		16	180.23	odd	12
720.2.cu.b.257.3		16	36.23	even	6
720.2.cu.b.353.3		16	20.3	even	4
720.2.cu.b.497.4		16	4.3	odd	2
810.2.f.c.323.4		16	45.43	odd	12
810.2.f.c.323.5		16	45.38	even	12
810.2.f.c.647.4		16	9.2	odd	6
810.2.f.c.647.5		16	9.7	even	3
1350.2.q.h.143.3		16	15.2	even	4
1350.2.q.h.557.3		16	45.4	even	6
1350.2.q.h.1007.4		16	15.14	odd	2
1350.2.q.h.1043.4		16	45.22	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 90 = 2 \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	90.l (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.258819 + 0.965926i) q^{2} +(-1.45865 + 0.933998i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(1.36868 + 1.76825i) q^{5} +(-1.27970 - 1.16721i) q^{6} +(-2.56188 + 0.686453i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(1.25529 - 2.72474i) q^{9} +O(q^{10})\)	\(q+(0.258819 + 0.965926i) q^{2} +(-1.45865 + 0.933998i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(1.36868 + 1.76825i) q^{5} +(-1.27970 - 1.16721i) q^{6} +(-2.56188 + 0.686453i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(1.25529 - 2.72474i) q^{9} +(-1.35376 + 1.77970i) q^{10} +(4.15512 + 2.39896i) q^{11} +(0.796225 - 1.53819i) q^{12} +(0.581838 + 0.155903i) q^{13} +(-1.32613 - 2.29692i) q^{14} +(-3.64796 - 1.30092i) q^{15} +(0.500000 - 0.866025i) q^{16} +(4.40865 - 4.40865i) q^{17} +(2.95680 + 0.507306i) q^{18} -5.19145i q^{19} +(-2.06944 - 0.847015i) q^{20} +(3.09573 - 3.39408i) q^{21} +(-1.24179 + 4.63444i) q^{22} +(-0.681226 + 2.54237i) q^{23} +(1.69185 + 0.370982i) q^{24} +(-1.25345 + 4.84034i) q^{25} +0.602363i q^{26} +(0.713876 + 5.14688i) q^{27} +(1.87542 - 1.87542i) q^{28} +(-0.920201 + 1.59383i) q^{29} +(0.312426 - 3.86036i) q^{30} +(-2.03888 - 3.53145i) q^{31} +(0.965926 + 0.258819i) q^{32} +(-8.30148 + 0.381642i) q^{33} +(5.39948 + 3.11739i) q^{34} +(-4.72021 - 3.59052i) q^{35} +(0.275255 + 2.98735i) q^{36} +(0.632057 + 0.632057i) q^{37} +(5.01456 - 1.34365i) q^{38} +(-0.994309 + 0.316029i) q^{39} +(0.282544 - 2.21815i) q^{40} +(-5.58550 + 3.22479i) q^{41} +(4.07966 + 2.11179i) q^{42} +(-0.644420 - 2.40501i) q^{43} -4.79792 q^{44} +(6.53614 - 1.50961i) q^{45} -2.63206 q^{46} +(-1.02538 - 3.82678i) q^{47} +(0.0795432 + 1.73022i) q^{48} +(0.0298240 - 0.0172189i) q^{49} +(-4.99982 + 0.0420344i) q^{50} +(-2.31299 + 10.5483i) q^{51} +(-0.581838 + 0.155903i) q^{52} +(-1.31215 - 1.31215i) q^{53} +(-4.78674 + 2.02166i) q^{54} +(1.44505 + 10.6307i) q^{55} +(2.29692 + 1.32613i) q^{56} +(4.84881 + 7.57249i) q^{57} +(-1.77769 - 0.476331i) q^{58} +(-0.0645473 - 0.111799i) q^{59} +(3.80968 - 0.697355i) q^{60} +(6.27251 - 10.8643i) q^{61} +(2.88341 - 2.88341i) q^{62} +(-1.34550 + 7.84217i) q^{63} +1.00000i q^{64} +(0.520672 + 1.24222i) q^{65} +(-2.51722 - 7.91984i) q^{66} +(2.85782 - 10.6655i) q^{67} +(-1.61368 + 6.02233i) q^{68} +(-1.38090 - 4.34468i) q^{69} +(2.24650 - 5.48866i) q^{70} +10.4203i q^{71} +(-2.81431 + 1.03906i) q^{72} +(3.30021 - 3.30021i) q^{73} +(-0.446932 + 0.774109i) q^{74} +(-2.69253 - 8.23106i) q^{75} +(2.59573 + 4.49593i) q^{76} +(-12.2917 - 3.29355i) q^{77} +(-0.562606 - 0.878635i) q^{78} +(3.62792 + 2.09458i) q^{79} +(2.21569 - 0.301182i) q^{80} +(-5.84847 - 6.84072i) q^{81} +(-4.56054 - 4.56054i) q^{82} +(11.1098 - 2.97686i) q^{83} +(-0.983937 + 4.48722i) q^{84} +(13.8296 + 1.76160i) q^{85} +(2.15627 - 1.24492i) q^{86} +(-0.146391 - 3.18431i) q^{87} +(-1.24179 - 4.63444i) q^{88} +2.04989 q^{89} +(3.14985 + 5.92270i) q^{90} -1.59762 q^{91} +(-0.681226 - 2.54237i) q^{92} +(6.27237 + 3.24682i) q^{93} +(3.43100 - 1.98089i) q^{94} +(9.17981 - 7.10542i) q^{95} +(-1.65068 + 0.524648i) q^{96} +(-16.7115 + 4.47782i) q^{97} +(0.0243512 + 0.0243512i) q^{98} +(11.7525 - 8.31025i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 12 q^{5} + 8 q^{7}+O(q^{10}) \) 16 * q - 12 * q^5 + 8 * q^7	\( 16 q - 12 q^{5} + 8 q^{7} - 8 q^{10} - 24 q^{15} + 8 q^{16} - 12 q^{20} + 24 q^{21} + 8 q^{22} - 24 q^{23} - 16 q^{25} - 16 q^{28} - 12 q^{30} - 8 q^{31} + 24 q^{36} + 24 q^{38} - 4 q^{40} + 24 q^{41} + 24 q^{42} + 36 q^{45} - 32 q^{46} + 48 q^{47} + 24 q^{50} - 48 q^{51} + 24 q^{55} + 24 q^{56} + 24 q^{57} + 16 q^{58} + 12 q^{60} - 24 q^{61} - 48 q^{63} - 48 q^{66} - 16 q^{67} - 24 q^{68} + 16 q^{70} - 24 q^{72} + 16 q^{73} + 16 q^{76} - 72 q^{77} + 24 q^{81} - 16 q^{82} + 48 q^{83} - 4 q^{85} - 48 q^{86} - 48 q^{87} + 8 q^{88} + 12 q^{90} - 24 q^{92} + 72 q^{93} + 84 q^{95} - 48 q^{97}+O(q^{100}) \) 16 * q - 12 * q^5 + 8 * q^7 - 8 * q^10 - 24 * q^15 + 8 * q^16 - 12 * q^20 + 24 * q^21 + 8 * q^22 - 24 * q^23 - 16 * q^25 - 16 * q^28 - 12 * q^30 - 8 * q^31 + 24 * q^36 + 24 * q^38 - 4 * q^40 + 24 * q^41 + 24 * q^42 + 36 * q^45 - 32 * q^46 + 48 * q^47 + 24 * q^50 - 48 * q^51 + 24 * q^55 + 24 * q^56 + 24 * q^57 + 16 * q^58 + 12 * q^60 - 24 * q^61 - 48 * q^63 - 48 * q^66 - 16 * q^67 - 24 * q^68 + 16 * q^70 - 24 * q^72 + 16 * q^73 + 16 * q^76 - 72 * q^77 + 24 * q^81 - 16 * q^82 + 48 * q^83 - 4 * q^85 - 48 * q^86 - 48 * q^87 + 8 * q^88 + 12 * q^90 - 24 * q^92 + 72 * q^93 + 84 * q^95 - 48 * q^97

Introduction

L-functions

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