LMFDB - Embedded newform 600.2.d.g.349.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [600,2,Mod(349,600)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(600, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0, 1]))

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

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

chi := DirichletCharacter("600.349");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 600 = 2^{3} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	600.d (of order $2$, degree $1$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.79102412128$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.214798336.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} - 2x^{5} + 9x^{4} - 4x^{3} - 16x + 16 $ x^8 - 2x^7 - 2x^5 + 9x^4 - 4x^3 - 16*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			349.6
Root			$1.23291 + 0.692769i$ of defining polynomial
Character	$\chi$	$=$	600.349
Dual form			600.2.d.g.349.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.192769 + 1.40101i) q^{2} -1.00000 q^{3} +(-1.92568 + 0.540143i) q^{4} +(-0.192769 - 1.40101i) q^{6} -0.0802864i q^{7} +(-1.12796 - 2.59378i) q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(0.192769 + 1.40101i) q^{2} -1.00000 q^{3} +(-1.92568 + 0.540143i) q^{4} +(-0.192769 - 1.40101i) q^{6} -0.0802864i q^{7} +(-1.12796 - 2.59378i) q^{8} +1.00000 q^{9} -2.41649i q^{11} +(1.92568 - 0.540143i) q^{12} -5.26785 q^{13} +(0.112482 - 0.0154767i) q^{14} +(3.41649 - 2.08029i) q^{16} +0.255918i q^{17} +(0.192769 + 1.40101i) q^{18} -6.95864i q^{19} +0.0802864i q^{21} +(3.38554 - 0.465824i) q^{22} -1.64542i q^{23} +(1.12796 + 2.59378i) q^{24} +(-1.01548 - 7.38033i) q^{26} -1.00000 q^{27} +(0.0433661 + 0.154606i) q^{28} -4.51516i q^{29} +8.29484 q^{31} +(3.57310 + 4.38554i) q^{32} +2.41649i q^{33} +(-0.358545 + 0.0493330i) q^{34} +(-1.92568 + 0.540143i) q^{36} +2.67241 q^{37} +(9.74915 - 1.34141i) q^{38} +5.26785 q^{39} -8.11921 q^{41} +(-0.112482 + 0.0154767i) q^{42} +4.08890 q^{43} +(1.30525 + 4.65339i) q^{44} +(2.30525 - 0.317185i) q^{46} -5.70272i q^{47} +(-3.41649 + 2.08029i) q^{48} +6.99355 q^{49} -0.255918i q^{51} +(10.1442 - 2.84539i) q^{52} -11.5627 q^{53} +(-0.192769 - 1.40101i) q^{54} +(-0.208245 + 0.0905597i) q^{56} +6.95864i q^{57} +(6.32580 - 0.870381i) q^{58} -12.6963i q^{59} +11.9403i q^{61} +(1.59899 + 11.6212i) q^{62} -0.0802864i q^{63} +(-5.45542 + 5.85136i) q^{64} +(-3.38554 + 0.465824i) q^{66} -7.27979 q^{67} +(-0.138232 - 0.492816i) q^{68} +1.64542i q^{69} -11.3481 q^{71} +(-1.12796 - 2.59378i) q^{72} -12.0779i q^{73} +(0.515157 + 3.74408i) q^{74} +(3.75866 + 13.4001i) q^{76} -0.194011 q^{77} +(1.01548 + 7.38033i) q^{78} -5.50539 q^{79} +1.00000 q^{81} +(-1.56513 - 11.3751i) q^{82} +9.20811 q^{83} +(-0.0433661 - 0.154606i) q^{84} +(0.788212 + 5.72861i) q^{86} +4.51516i q^{87} +(-6.26785 + 2.72570i) q^{88} -11.9173 q^{89} +0.422937i q^{91} +(0.888760 + 3.16855i) q^{92} -8.29484 q^{93} +(7.98959 - 1.09931i) q^{94} +(-3.57310 - 4.38554i) q^{96} -8.50539i q^{97} +(1.34814 + 9.79807i) q^{98} -2.41649i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} - 8 q^{3} - 4 q^{4} + 2 q^{6} - 8 q^{8} + 8 q^{9}+O(q^{10}) $ 8 * q - 2 * q^2 - 8 * q^3 - 4 * q^4 + 2 * q^6 - 8 * q^8 + 8 * q^9	$ 8 q - 2 q^{2} - 8 q^{3} - 4 q^{4} + 2 q^{6} - 8 q^{8} + 8 q^{9} + 4 q^{12} + 6 q^{14} + 8 q^{16} - 2 q^{18} + 20 q^{22} + 8 q^{24} - 2 q^{26} - 8 q^{27} + 24 q^{28} + 8 q^{31} - 12 q^{32} - 12 q^{34} - 4 q^{36} + 14 q^{38} - 6 q^{42} - 8 q^{43} + 12 q^{44} + 20 q^{46} - 8 q^{48} + 24 q^{52} + 8 q^{53} + 2 q^{54} + 8 q^{56} - 20 q^{58} + 26 q^{62} + 32 q^{64} - 20 q^{66} + 24 q^{67} + 36 q^{68} - 40 q^{71} - 8 q^{72} - 8 q^{74} - 20 q^{76} - 24 q^{77} + 2 q^{78} + 16 q^{79} + 8 q^{81} - 16 q^{82} - 32 q^{83} - 24 q^{84} - 18 q^{86} - 8 q^{88} + 28 q^{92} - 8 q^{93} + 4 q^{94} + 12 q^{96} - 40 q^{98}+O(q^{100}) $ 8 * q - 2 * q^2 - 8 * q^3 - 4 * q^4 + 2 * q^6 - 8 * q^8 + 8 * q^9 + 4 * q^12 + 6 * q^14 + 8 * q^16 - 2 * q^18 + 20 * q^22 + 8 * q^24 - 2 * q^26 - 8 * q^27 + 24 * q^28 + 8 * q^31 - 12 * q^32 - 12 * q^34 - 4 * q^36 + 14 * q^38 - 6 * q^42 - 8 * q^43 + 12 * q^44 + 20 * q^46 - 8 * q^48 + 24 * q^52 + 8 * q^53 + 2 * q^54 + 8 * q^56 - 20 * q^58 + 26 * q^62 + 32 * q^64 - 20 * q^66 + 24 * q^67 + 36 * q^68 - 40 * q^71 - 8 * q^72 - 8 * q^74 - 20 * q^76 - 24 * q^77 + 2 * q^78 + 16 * q^79 + 8 * q^81 - 16 * q^82 - 32 * q^83 - 24 * q^84 - 18 * q^86 - 8 * q^88 + 28 * q^92 - 8 * q^93 + 4 * q^94 + 12 * q^96 - 40 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/600\mathbb{Z}\right)^\times$.

$n$	$151$	$301$	$401$	$577$
$\chi(n)$	$1$	$-1$	$1$	$-1$

Coefficient data

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

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

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

$2$	0.192769	+	1.40101i	0.136308	+	0.990667i
$2$	0.192769	+	1.40101i	0.136308	+	0.990667i
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$	−1.92568	+	0.540143i	−0.962840	+	0.270072i
$5$		0			0
$5$		0			0
$6$	−0.192769	−	1.40101i	−0.0786975	−	0.571962i
$7$		−	0.0802864i		−	0.0303454i	−0.999885	−	0.0151727i	$-0.995170\pi$
$7$		−	0.0802864i		−	0.0303454i	0.999885	−	0.0151727i	$-0.00482980\pi$
$8$	−1.12796	−	2.59378i	−0.398794	−	0.917041i
$9$	1.00000			0.333333
$10$		0			0
$11$		−	2.41649i		−	0.728599i	−0.931282	−	0.364300i	$-0.881308\pi$
$11$		−	2.41649i		−	0.728599i	0.931282	−	0.364300i	$-0.118692\pi$
$12$	1.92568	−	0.540143i	0.555896	−	0.155926i
$13$	−5.26785			−1.46104			−0.730520	−	0.682892i	$-0.760722\pi$
$13$	−5.26785			−1.46104			−0.730520	+	0.682892i	$0.760722\pi$
$14$	0.112482	−	0.0154767i	0.0300622	−	0.00413632i
$15$		0			0
$16$	3.41649	−	2.08029i	0.854123	−	0.520072i
$17$			0.255918i			0.0620692i	0.999518	+	0.0310346i	$0.00988021\pi$
$17$			0.255918i			0.0620692i	−0.999518	+	0.0310346i	$0.990120\pi$
$18$	0.192769	+	1.40101i	0.0454360	+	0.330222i
$19$		−	6.95864i		−	1.59642i	−0.602378	−	0.798211i	$-0.705780\pi$
$19$		−	6.95864i		−	1.59642i	0.602378	−	0.798211i	$-0.294220\pi$
$20$		0			0
$21$			0.0802864i			0.0175199i
$22$	3.38554	−	0.465824i	0.721799	−	0.0993139i
$23$		−	1.64542i		−	0.343093i	−0.985176	−	0.171546i	$-0.945124\pi$
$23$		−	1.64542i		−	0.343093i	0.985176	−	0.171546i	$-0.0548764\pi$
$24$	1.12796	+	2.59378i	0.230244	+	0.529454i
$25$		0			0
$26$	−1.01548	−	7.38033i	−0.199151	−	1.44740i
$27$	−1.00000			−0.192450
$28$	0.0433661	+	0.154606i	0.00819543	+	0.0292178i
$29$		−	4.51516i		−	0.838444i	−0.907884	−	0.419222i	$-0.862303\pi$
$29$		−	4.51516i		−	0.838444i	0.907884	−	0.419222i	$-0.137697\pi$
$30$		0			0
$31$	8.29484			1.48980			0.744899	−	0.667177i	$-0.232498\pi$
$31$	8.29484			1.48980			0.744899	+	0.667177i	$0.232498\pi$
$32$	3.57310	+	4.38554i	0.631641	+	0.775261i
$33$			2.41649i			0.420657i
$34$	−0.358545	+	0.0493330i	−0.0614899	+	0.00846053i
$35$		0			0
$36$	−1.92568	+	0.540143i	−0.320947	+	0.0900239i
$37$	2.67241			0.439341			0.219671	−	0.975574i	$-0.429502\pi$
$37$	2.67241			0.439341			0.219671	+	0.975574i	$0.429502\pi$
$38$	9.74915	−	1.34141i	1.58152	−	0.217605i
$39$	5.26785			0.843531
$40$		0			0
$41$	−8.11921			−1.26801			−0.634004	−	0.773330i	$-0.718590\pi$
$41$	−8.11921			−1.26801			−0.634004	+	0.773330i	$0.718590\pi$
$42$	−0.112482	+	0.0154767i	−0.0173564	+	0.00238811i
$43$	4.08890			0.623551			0.311776	−	0.950156i	$-0.399076\pi$
$43$	4.08890			0.623551			0.311776	+	0.950156i	$0.399076\pi$
$44$	1.30525	+	4.65339i	0.196774	+	0.701525i
$45$		0			0
$46$	2.30525	−	0.317185i	0.339891	−	0.0467663i
$47$		−	5.70272i		−	0.831827i	−0.909404	−	0.415914i	$-0.863462\pi$
$47$		−	5.70272i		−	0.831827i	0.909404	−	0.415914i	$-0.136538\pi$
$48$	−3.41649	+	2.08029i	−0.493128	+	0.300263i
$49$	6.99355			0.999079
$50$		0			0
$51$		−	0.255918i		−	0.0358357i
$52$	10.1442	−	2.84539i	1.40675	−	0.394585i
$53$	−11.5627			−1.58826			−0.794129	−	0.607749i	$-0.792073\pi$
$53$	−11.5627			−1.58826			−0.794129	+	0.607749i	$0.792073\pi$
$54$	−0.192769	−	1.40101i	−0.0262325	−	0.190654i
$55$		0			0
$56$	−0.208245	+	0.0905597i	−0.0278280	+	0.0121016i
$57$			6.95864i			0.921694i
$58$	6.32580	−	0.870381i	0.830618	−	0.114287i
$59$		−	12.6963i		−	1.65291i	−0.563000	−	0.826457i	$-0.690353\pi$
$59$		−	12.6963i		−	1.65291i	0.563000	−	0.826457i	$-0.309647\pi$
$60$		0			0
$61$			11.9403i			1.52879i	0.644746	+	0.764397i	$0.276963\pi$
$61$			11.9403i			1.52879i	−0.644746	+	0.764397i	$0.723037\pi$
$62$	1.59899	+	11.6212i	0.203071	+	1.47589i
$63$		−	0.0802864i		−	0.0101151i
$64$	−5.45542	+	5.85136i	−0.681927	+	0.731420i
$65$		0			0
$66$	−3.38554	+	0.465824i	−0.416731	+	0.0573389i
$67$	−7.27979			−0.889367			−0.444684	−	0.895688i	$-0.646684\pi$
$67$	−7.27979			−0.889367			−0.444684	+	0.895688i	$0.646684\pi$
$68$	−0.138232	−	0.492816i	−0.0167631	−	0.0597628i
$69$			1.64542i			0.198085i
$70$		0			0
$71$	−11.3481			−1.34678			−0.673388	−	0.739289i	$-0.735162\pi$
$71$	−11.3481			−1.34678			−0.673388	+	0.739289i	$0.735162\pi$
$72$	−1.12796	−	2.59378i	−0.132931	−	0.305680i
$73$		−	12.0779i		−	1.41361i	−0.707411	−	0.706803i	$-0.750137\pi$
$73$		−	12.0779i		−	1.41361i	0.707411	−	0.706803i	$-0.249863\pi$
$74$	0.515157	+	3.74408i	0.0598857	+	0.435241i
$75$		0			0
$76$	3.75866	+	13.4001i	0.431148	+	1.53710i
$77$	−0.194011			−0.0221096
$78$	1.01548	+	7.38033i	0.114980	+	0.835658i
$79$	−5.50539			−0.619405			−0.309702	−	0.950834i	$-0.600229\pi$
$79$	−5.50539			−0.619405			−0.309702	+	0.950834i	$0.600229\pi$
$80$		0			0
$81$	1.00000			0.111111
$82$	−1.56513	−	11.3751i	−0.172840	−	1.25617i
$83$	9.20811			1.01072			0.505361	−	0.862908i	$-0.331359\pi$
$83$	9.20811			1.01072			0.505361	+	0.862908i	$0.331359\pi$
$84$	−0.0433661	−	0.154606i	−0.00473163	−	0.0168689i
$85$		0			0
$86$	0.788212	+	5.72861i	0.0849950	+	0.617731i
$87$			4.51516i			0.484076i
$88$	−6.26785	+	2.72570i	−0.668155	+	0.290561i
$89$	−11.9173			−1.26323			−0.631615	−	0.775283i	$-0.717607\pi$
$89$	−11.9173			−1.26323			−0.631615	+	0.775283i	$0.717607\pi$
$90$		0			0
$91$			0.422937i			0.0443358i
$92$	0.888760	+	3.16855i	0.0926597	+	0.330344i
$93$	−8.29484			−0.860135
$94$	7.98959	−	1.09931i	0.824064	−	0.113385i
$95$		0			0
$96$	−3.57310	−	4.38554i	−0.364678	−	0.447597i
$97$		−	8.50539i		−	0.863592i	−0.901971	−	0.431796i	$-0.857880\pi$
$97$		−	8.50539i		−	0.863592i	0.901971	−	0.431796i	$-0.142120\pi$
$98$	1.34814	+	9.79807i	0.136183	+	0.989754i
$99$		−	2.41649i		−	0.242866i
$100$		0			0
$101$			7.56270i			0.752516i	0.926515	+	0.376258i	$0.122789\pi$
$101$			7.56270i			0.752516i	−0.926515	+	0.376258i	$0.877211\pi$
$102$	0.358545	−	0.0493330i	0.0355012	−	0.00488469i
$103$		−	1.78544i		−	0.175925i	−0.996124	−	0.0879624i	$-0.971964\pi$
$103$		−	1.78544i		−	0.175925i	0.996124	−	0.0879624i	$-0.0280355\pi$
$104$	5.94192	+	13.6637i	0.582653	+	1.33983i
$105$		0			0
$106$	−2.22893	−	16.1995i	−0.216492	−	1.57343i
$107$	−10.4705			−1.01222			−0.506110	−	0.862469i	$-0.668917\pi$
$107$	−10.4705			−1.01222			−0.506110	+	0.862469i	$0.668917\pi$
$108$	1.92568	−	0.540143i	0.185299	−	0.0519753i
$109$			3.64298i			0.348934i	0.984663	+	0.174467i	$0.0558203\pi$
$109$			3.64298i			0.348934i	−0.984663	+	0.174467i	$0.944180\pi$
$110$		0			0
$111$	−2.67241			−0.253654
$112$	−0.167019	−	0.274298i	−0.0157818	−	0.0259187i
$113$			8.83298i			0.830937i	0.909608	+	0.415468i	$0.136382\pi$
$113$			8.83298i			0.830937i	−0.909608	+	0.415468i	$0.863618\pi$
$114$	−9.74915	+	1.34141i	−0.913092	+	0.125634i
$115$		0			0
$116$	2.43883	+	8.69475i	0.226440	+	0.807287i
$117$	−5.26785			−0.487013
$118$	17.7877	−	2.44744i	1.63749	−	0.225305i
$119$	0.0205467			0.00188351
$120$		0			0
$121$	5.16057			0.469143
$122$	−16.7285	+	2.30171i	−1.51452	+	0.208387i
$123$	8.11921			0.732085
$124$	−15.9732	+	4.48040i	−1.43444	+	0.402352i
$125$		0			0
$126$	0.112482	−	0.0154767i	0.0100207	−	0.00137877i
$127$			8.69628i			0.771670i	0.922568	+	0.385835i	$0.126087\pi$
$127$			8.69628i			0.771670i	−0.922568	+	0.385835i	$0.873913\pi$
$128$	−9.24947	−	6.51516i	−0.817546	−	0.575864i
$129$	−4.08890			−0.360008
$130$		0			0
$131$		−	10.7916i		−	0.942868i	−0.881901	−	0.471434i	$-0.843736\pi$
$131$		−	10.7916i		−	0.942868i	0.881901	−	0.471434i	$-0.156264\pi$
$132$	−1.30525	−	4.65339i	−0.113608	−	0.405026i
$133$	−0.558684			−0.0484440
$134$	−1.40331	−	10.1991i	−0.121228	−	0.881066i
$135$		0			0
$136$	0.663796	−	0.288665i	0.0569200	−	0.0247528i
$137$		−	11.5421i		−	0.986112i	−0.869997	−	0.493056i	$-0.835880\pi$
$137$		−	11.5421i		−	0.986112i	0.869997	−	0.493056i	$-0.164120\pi$
$138$	−2.30525	+	0.317185i	−0.196236	+	0.0270006i
$139$		−	0.214558i		−	0.0181986i	−0.999959	−	0.00909928i	$-0.997104\pi$
$139$		−	0.214558i		−	0.0181986i	0.999959	−	0.00909928i	$-0.00289643\pi$
$140$		0			0
$141$			5.70272i			0.480256i
$142$	−2.18757	−	15.8989i	−0.183576	−	1.33421i
$143$			12.7297i			1.06451i
$144$	3.41649	−	2.08029i	0.284708	−	0.173357i
$145$		0			0
$146$	16.9212	−	2.32823i	1.40041	−	0.192686i
$147$	−6.99355			−0.576819
$148$	−5.14621	+	1.44348i	−0.423015	+	0.118654i
$149$			23.0475i			1.88813i	0.329762	+	0.944064i	$0.393031\pi$
$149$			23.0475i			1.88813i	−0.329762	+	0.944064i	$0.606969\pi$
$150$		0			0
$151$	9.48573			0.771938			0.385969	−	0.922512i	$-0.373867\pi$
$151$	9.48573			0.771938			0.385969	+	0.922512i	$0.373867\pi$
$152$	−18.0492	+	7.84906i	−1.46398	+	0.636643i
$153$			0.255918i			0.0206897i
$154$	−0.0373993	−	0.271812i	−0.00301372	−	0.0219033i
$155$		0			0
$156$	−10.1442	+	2.84539i	−0.812186	+	0.227814i
$157$	−6.34413			−0.506316			−0.253158	−	0.967425i	$-0.581469\pi$
$157$	−6.34413			−0.506316			−0.253158	+	0.967425i	$0.581469\pi$
$158$	−1.06127	−	7.71313i	−0.0844298	−	0.613624i
$159$	11.5627			0.916981
$160$		0			0
$161$	−0.132104			−0.0104113
$162$	0.192769	+	1.40101i	0.0151453	+	0.110074i
$163$	12.4100			0.972030			0.486015	−	0.873951i	$-0.338450\pi$
$163$	12.4100			0.972030			0.486015	+	0.873951i	$0.338450\pi$
$164$	15.6350	−	4.38554i	1.22089	−	0.342453i
$165$		0			0
$166$	1.77504	+	12.9007i	0.137769	+	1.00129i
$167$		−	23.2654i		−	1.80033i	−0.435547	−	0.900166i	$-0.643445\pi$
$167$		−	23.2654i		−	1.80033i	0.435547	−	0.900166i	$-0.356555\pi$
$168$	0.208245	−	0.0905597i	0.0160665	−	0.00698683i
$169$	14.7503			1.13464
$170$		0			0
$171$		−	6.95864i		−	0.532140i
$172$	−7.87391	+	2.20859i	−0.600380	+	0.168403i
$173$	−8.63897			−0.656809			−0.328404	−	0.944537i	$-0.606511\pi$
$173$	−8.63897			−0.656809			−0.328404	+	0.944537i	$0.606511\pi$
$174$	−6.32580	+	0.870381i	−0.479557	+	0.0659834i
$175$		0			0
$176$	−5.02699	−	8.25592i	−0.378924	−	0.622313i
$177$			12.6963i			0.954311i
$178$	−2.29728	−	16.6963i	−0.172188	−	1.25144i
$179$			9.40544i			0.702996i	0.936189	+	0.351498i	$0.114328\pi$
$179$			9.40544i			0.702996i	−0.936189	+	0.351498i	$0.885672\pi$
$180$		0			0
$181$		−	6.43487i		−	0.478300i	−0.970983	−	0.239150i	$-0.923131\pi$
$181$		−	6.43487i		−	0.478300i	0.970983	−	0.239150i	$-0.0768688\pi$
$182$	−0.592540	+	0.0815289i	−0.0439220	+	0.00604333i
$183$		−	11.9403i		−	0.882649i
$184$	−4.26785	+	1.85596i	−0.314630	+	0.136823i
$185$		0			0
$186$	−1.59899	−	11.6212i	−0.117243	−	0.852107i
$187$	0.618423			0.0452236
$188$	3.08029	+	10.9816i	0.224653	+	0.800917i
$189$			0.0802864i			0.00583997i
$190$		0			0
$191$	−5.56270			−0.402503			−0.201251	−	0.979540i	$-0.564501\pi$
$191$	−5.56270			−0.402503			−0.201251	+	0.979540i	$0.564501\pi$
$192$	5.45542	−	5.85136i	0.393711	−	0.422286i
$193$		−	18.4227i		−	1.32609i	−0.748578	−	0.663046i	$-0.769263\pi$
$193$		−	18.4227i		−	1.32609i	0.748578	−	0.663046i	$-0.230737\pi$
$194$	11.9162	−	1.63957i	0.855531	−	0.117714i
$195$		0			0
$196$	−13.4674	+	3.77752i	−0.961954	+	0.269823i
$197$	18.0239			1.28415			0.642074	−	0.766643i	$-0.278074\pi$
$197$	18.0239			1.28415			0.642074	+	0.766643i	$0.278074\pi$
$198$	3.38554	−	0.465824i	0.240600	−	0.0331046i
$199$	−20.1214			−1.42637			−0.713183	−	0.700977i	$-0.752747\pi$
$199$	−20.1214			−1.42637			−0.713183	+	0.700977i	$0.752747\pi$
$200$		0			0
$201$	7.27979			0.513476
$202$	−10.5954	+	1.45785i	−0.745493	+	0.102574i
$203$	−0.362505			−0.0254429
$204$	0.138232	+	0.492816i	0.00967820	+	0.0345040i
$205$		0			0
$206$	2.50143	−	0.344177i	0.174283	−	0.0239800i
$207$		−	1.64542i		−	0.114364i
$208$	−17.9976	+	10.9586i	−1.24791	+	0.759845i
$209$	−16.8155			−1.16315
$210$		0			0
$211$		−	3.25592i		−	0.224147i	−0.993700	−	0.112073i	$-0.964251\pi$
$211$		−	3.25592i		−	0.224147i	0.993700	−	0.112073i	$-0.0357492\pi$
$212$	22.2661	−	6.24551i	1.52924	−	0.428943i
$213$	11.3481			0.777562
$214$	−2.01838	−	14.6693i	−0.137974	−	1.00277i
$215$		0			0
$216$	1.12796	+	2.59378i	0.0767479	+	0.176485i
$217$		−	0.665963i		−	0.0452085i
$218$	−5.10387	+	0.702253i	−0.345678	+	0.0475626i
$219$			12.0779i			0.816146i
$220$		0			0
$221$		−	1.34814i		−	0.0906856i
$222$	−0.515157	−	3.74408i	−0.0345750	−	0.251286i
$223$			26.9911i			1.80746i	0.428104	+	0.903730i	$0.359182\pi$
$223$			26.9911i			1.80746i	−0.428104	+	0.903730i	$0.640818\pi$
$224$	0.352099	−	0.286871i	0.0235256	−	0.0191674i
$225$		0			0
$226$	−12.3751	+	1.70272i	−0.823181	+	0.113263i
$227$	19.8219			1.31563			0.657814	−	0.753180i	$-0.271481\pi$
$227$	19.8219			1.31563			0.657814	+	0.753180i	$0.271481\pi$
$228$	−3.75866	−	13.4001i	−0.248923	−	0.887444i
$229$			21.6797i			1.43264i	0.697773	+	0.716319i	$0.254174\pi$
$229$			21.6797i			1.43264i	−0.697773	+	0.716319i	$0.745826\pi$
$230$		0			0
$231$	0.194011			0.0127650
$232$	−11.7113	+	5.09291i	−0.768887	+	0.334366i
$233$			17.2733i			1.13161i	0.824538	+	0.565807i	$0.191435\pi$
$233$			17.2733i			1.13161i	−0.824538	+	0.565807i	$0.808565\pi$
$234$	−1.01548	−	7.38033i	−0.0663838	−	0.482468i
$235$		0			0
$236$	6.85781	+	24.4490i	0.446405	+	1.59149i
$237$	5.50539			0.357614
$238$	0.00396076	+	0.0287862i	0.000256738	+	0.00186594i
$239$	16.3718			1.05900			0.529502	−	0.848309i	$-0.322379\pi$
$239$	16.3718			1.05900			0.529502	+	0.848309i	$0.322379\pi$
$240$		0			0
$241$	−6.82654			−0.439736			−0.219868	−	0.975530i	$-0.570563\pi$
$241$	−6.82654			−0.439736			−0.219868	+	0.975530i	$0.570563\pi$
$242$	0.994797	+	7.23003i	0.0639480	+	0.464764i
$243$	−1.00000			−0.0641500
$244$	−6.44945	−	22.9931i	−0.412884	−	1.47198i
$245$		0			0
$246$	1.56513	+	11.3751i	0.0997890	+	0.725252i
$247$			36.6571i			2.33243i
$248$	−9.35624	−	21.5150i	−0.594122	−	1.36621i
$249$	−9.20811			−0.583540
$250$		0			0
$251$			2.96969i			0.187445i	0.995598	+	0.0937225i	$0.0298766\pi$
$251$			2.96969i			0.187445i	−0.995598	+	0.0937225i	$0.970123\pi$
$252$	0.0433661	+	0.154606i	0.00273181	+	0.00973925i
$253$	−3.97613			−0.249977
$254$	−12.1836	+	1.67637i	−0.764467	+	0.105185i
$255$		0			0
$256$	7.34482	−	14.2146i	0.459051	−	0.888410i
$257$		−	5.03031i		−	0.313782i	−0.987616	−	0.156891i	$-0.949853\pi$
$257$		−	5.03031i		−	0.313782i	0.987616	−	0.156891i	$-0.0501472\pi$
$258$	−0.788212	−	5.72861i	−0.0490719	−	0.356647i
$259$		−	0.214558i		−	0.0133320i
$260$		0			0
$261$		−	4.51516i		−	0.279481i
$262$	15.1192	−	2.08029i	0.934068	−	0.128521i
$263$		−	2.70585i		−	0.166850i	−0.996514	−	0.0834248i	$-0.973414\pi$
$263$		−	2.70585i		−	0.166850i	0.996514	−	0.0834248i	$-0.0265859\pi$
$264$	6.26785	−	2.72570i	0.385760	−	0.167755i
$265$		0			0
$266$	−0.107697	−	0.782724i	−0.00660331	−	0.0479919i
$267$	11.9173			0.729326
$268$	14.0185	−	3.93213i	0.856319	−	0.240193i
$269$		−	22.3718i		−	1.36403i	−0.731337	−	0.682017i	$-0.761103\pi$
$269$		−	22.3718i		−	1.36403i	0.731337	−	0.682017i	$-0.238897\pi$
$270$		0			0
$271$	−0.869741			−0.0528330			−0.0264165	−	0.999651i	$-0.508410\pi$
$271$	−0.869741			−0.0528330			−0.0264165	+	0.999651i	$0.508410\pi$
$272$	0.532383	+	0.874341i	0.0322804	+	0.0530147i
$273$		−	0.422937i		−	0.0255973i
$274$	16.1707	−	2.22496i	0.976908	−	0.134415i
$275$		0			0
$276$	−0.888760	−	3.16855i	−0.0534971	−	0.190724i
$277$	28.6733			1.72281			0.861406	−	0.507918i	$-0.169585\pi$
$277$	28.6733			1.72281			0.861406	+	0.507918i	$0.169585\pi$
$278$	0.300599	−	0.0413600i	0.0180287	−	0.00248061i
$279$	8.29484			0.496599
$280$		0			0
$281$	15.1429			0.903349			0.451674	−	0.892183i	$-0.350827\pi$
$281$	15.1429			0.903349			0.451674	+	0.892183i	$0.350827\pi$
$282$	−7.98959	+	1.09931i	−0.475773	+	0.0654627i
$283$	6.23225			0.370469			0.185234	−	0.982694i	$-0.440696\pi$
$283$	6.23225			0.370469			0.185234	+	0.982694i	$0.440696\pi$
$284$	21.8529	−	6.12962i	1.29673	−	0.363726i
$285$		0			0
$286$	−17.8345	+	2.45389i	−1.05458	+	0.145102i
$287$			0.651862i			0.0384782i
$288$	3.57310	+	4.38554i	0.210547	+	0.258420i
$289$	16.9345			0.996147
$290$		0			0
$291$			8.50539i			0.498595i
$292$	6.52377	+	23.2581i	0.381775	+	1.36108i
$293$	21.5054			1.25636			0.628179	−	0.778069i	$-0.283800\pi$
$293$	21.5054			1.25636			0.628179	+	0.778069i	$0.283800\pi$
$294$	−1.34814	−	9.79807i	−0.0786250	−	0.571435i
$295$		0			0
$296$	−3.01437	−	6.93165i	−0.175207	−	0.402894i
$297$			2.41649i			0.140219i
$298$	−32.2899	+	4.44284i	−1.87051	+	0.257367i
$299$			8.66781i			0.501272i
$300$		0			0
$301$		−	0.328283i		−	0.0189219i
$302$	1.82855	+	13.2896i	0.105221	+	0.764733i
$303$		−	7.56270i		−	0.434466i
$304$	−14.4760	−	23.7741i	−0.830253	−	1.36354i
$305$		0			0
$306$	−0.358545	+	0.0493330i	−0.0204966	+	0.00282018i
$307$	3.57706			0.204154			0.102077	−	0.994777i	$-0.467451\pi$
$307$	3.57706			0.204154			0.102077	+	0.994777i	$0.467451\pi$
$308$	0.373604	−	0.104794i	0.0212880	−	0.00597118i
$309$			1.78544i			0.101570i
$310$		0			0
$311$	−2.49461			−0.141456			−0.0707282	−	0.997496i	$-0.522532\pi$
$311$	−2.49461			−0.141456			−0.0707282	+	0.997496i	$0.522532\pi$
$312$	−5.94192	−	13.6637i	−0.336395	−	0.773553i
$313$			9.57246i			0.541068i	0.962710	+	0.270534i	$0.0872002\pi$
$313$			9.57246i			0.541068i	−0.962710	+	0.270534i	$0.912800\pi$
$314$	−1.22295	−	8.88821i	−0.0690150	−	0.501591i
$315$		0			0
$316$	10.6016	−	2.97370i	0.596388	−	0.167284i
$317$	−3.16702			−0.177877			−0.0889387	−	0.996037i	$-0.528348\pi$
$317$	−3.16702			−0.177877			−0.0889387	+	0.996037i	$0.528348\pi$
$318$	2.22893	+	16.1995i	0.124992	+	0.908423i
$319$	−10.9108			−0.610889
$320$		0			0
$321$	10.4705			0.584405
$322$	−0.0254656	−	0.185080i	−0.00141914	−	0.0103141i
$323$	1.78084			0.0990887
$324$	−1.92568	+	0.540143i	−0.106982	+	0.0300080i
$325$		0			0
$326$	2.39227	+	17.3866i	0.132495	+	0.962957i
$327$		−	3.64298i		−	0.201457i
$328$	9.15814	+	21.0595i	0.505674	+	1.16281i
$329$	−0.457851			−0.0252421
$330$		0			0
$331$		−	16.5118i		−	0.907573i	−0.891111	−	0.453786i	$-0.850073\pi$
$331$		−	16.5118i		−	0.907573i	0.891111	−	0.453786i	$-0.149927\pi$
$332$	−17.7319	+	4.97370i	−0.973163	+	0.272967i
$333$	2.67241			0.146447
$334$	32.5952	−	4.48484i	1.78353	−	0.245400i
$335$		0			0
$336$	0.167019	+	0.274298i	0.00911161	+	0.0149642i
$337$			11.8330i			0.644584i	0.946640	+	0.322292i	$0.104453\pi$
$337$			11.8330i			0.644584i	−0.946640	+	0.322292i	$0.895547\pi$
$338$	2.84339	+	20.6653i	0.154660	+	1.12405i
$339$		−	8.83298i		−	0.479742i
$340$		0			0
$341$		−	20.0444i		−	1.08547i
$342$	9.74915	−	1.34141i	0.527174	−	0.0725350i
$343$		−	1.12349i		−	0.0606628i
$344$	−4.61211	−	10.6057i	−0.248668	−	0.571822i
$345$		0			0
$346$	−1.66532	−	12.1033i	−0.0895283	−	0.650678i
$347$	23.9713			1.28684			0.643422	−	0.765511i	$-0.277514\pi$
$347$	23.9713			1.28684			0.643422	+	0.765511i	$0.277514\pi$
$348$	−2.43883	−	8.69475i	−0.130735	−	0.466087i
$349$		−	8.91570i		−	0.477247i	−0.971112	−	0.238623i	$-0.923304\pi$
$349$		−	8.91570i		−	0.477247i	0.971112	−	0.238623i	$-0.0766961\pi$
$350$		0			0
$351$	5.26785			0.281177
$352$	10.5976	−	8.63437i	0.564855	−	0.460213i
$353$		−	7.35606i		−	0.391524i	−0.980651	−	0.195762i	$-0.937282\pi$
$353$		−	7.35606i		−	0.391524i	0.980651	−	0.195762i	$-0.0627179\pi$
$354$	−17.7877	+	2.44744i	−0.945403	+	0.130080i
$355$		0			0
$356$	22.9489	−	6.43704i	1.21629	−	0.341162i
$357$	−0.0205467			−0.00108745
$358$	−13.1772	+	1.81307i	−0.696434	+	0.0958240i
$359$	−25.2114			−1.33061			−0.665304	−	0.746572i	$-0.731698\pi$
$359$	−25.2114			−1.33061			−0.665304	+	0.746572i	$0.731698\pi$
$360$		0			0
$361$	−29.4227			−1.54856
$362$	9.01534	−	1.24044i	0.473836	−	0.0651961i
$363$	−5.16057			−0.270860
$364$	−0.228446	−	0.814441i	−0.0119738	−	0.0426883i
$365$		0			0
$366$	16.7285	−	2.30171i	0.874411	−	0.120312i
$367$		−	5.86573i		−	0.306189i	−0.988212	−	0.153094i	$-0.951076\pi$
$367$		−	5.86573i		−	0.306189i	0.988212	−	0.153094i	$-0.0489238\pi$
$368$	−3.42294	−	5.62155i	−0.178433	−	0.293043i
$369$	−8.11921			−0.422669
$370$		0			0
$371$			0.928327i			0.0481963i
$372$	15.9732	−	4.48040i	0.828173	−	0.232298i
$373$	27.5063			1.42422			0.712111	−	0.702067i	$-0.247739\pi$
$373$	27.5063			1.42422			0.712111	+	0.702067i	$0.247739\pi$
$374$	0.119213	+	0.866420i	0.00616434	+	0.0448015i
$375$		0			0
$376$	−14.7916	+	6.43244i	−0.762820	+	0.331728i
$377$			23.7852i			1.22500i
$378$	−0.112482	+	0.0154767i	−0.00578547	+	0.000796035i
$379$			11.7549i			0.603807i	0.953339	+	0.301903i	$0.0976220\pi$
$379$			11.7549i			0.603807i	−0.953339	+	0.301903i	$0.902378\pi$
$380$		0			0
$381$		−	8.69628i		−	0.445524i
$382$	−1.07231	−	7.79341i	−0.0548643	−	0.398746i
$383$		−	34.3335i		−	1.75436i	−0.480162	−	0.877180i	$-0.659422\pi$
$383$		−	34.3335i		−	1.75436i	0.480162	−	0.877180i	$-0.340578\pi$
$384$	9.24947	+	6.51516i	0.472010	+	0.332475i
$385$		0			0
$386$	25.8104	−	3.55131i	1.31372	−	0.180757i
$387$	4.08890			0.207850
$388$	4.59413	+	16.3787i	0.233232	+	0.831501i
$389$			2.89515i			0.146790i	0.997303	+	0.0733951i	$0.0233834\pi$
$389$			2.89515i			0.146790i	−0.997303	+	0.0733951i	$0.976617\pi$
$390$		0			0
$391$	0.421092			0.0212955
$392$	−7.88844	−	18.1398i	−0.398427	−	0.916196i
$393$			10.7916i			0.544365i
$394$	3.47444	+	25.2517i	0.175040	+	1.27216i
$395$		0			0
$396$	1.30525	+	4.65339i	0.0655913	+	0.233842i
$397$	−22.9099			−1.14982			−0.574909	−	0.818218i	$-0.694962\pi$
$397$	−22.9099			−1.14982			−0.574909	+	0.818218i	$0.694962\pi$
$398$	−3.87877	−	28.1903i	−0.194425	−	1.41305i
$399$	0.558684			0.0279692
$400$		0			0
$401$	−12.4337			−0.620910			−0.310455	−	0.950588i	$-0.600481\pi$
$401$	−12.4337			−0.620910			−0.310455	+	0.950588i	$0.600481\pi$
$402$	1.40331	+	10.1991i	0.0699910	+	0.508684i
$403$	−43.6960			−2.17665
$404$	−4.08494	−	14.5633i	−0.203233	−	0.724553i
$405$		0			0
$406$	−0.0698797	−	0.507875i	−0.00346807	−	0.0252054i
$407$		−	6.45785i		−	0.320104i
$408$	−0.663796	+	0.288665i	−0.0328628	+	0.0142910i
$409$	32.0886			1.58668			0.793340	−	0.608778i	$-0.208340\pi$
$409$	32.0886			1.58668			0.793340	+	0.608778i	$0.208340\pi$
$410$		0			0
$411$			11.5421i			0.569332i
$412$	0.964394	+	3.43819i	0.0475123	+	0.169388i
$413$	−1.01934			−0.0501583
$414$	2.30525	−	0.317185i	0.113297	−	0.0155888i
$415$		0			0
$416$	−18.8226	−	23.1024i	−0.922853	−	1.13269i
$417$			0.214558i			0.0105069i
$418$	−3.24150	−	23.5587i	−0.158547	−	1.15230i
$419$			16.1364i			0.788317i	0.919043	+	0.394158i	$0.128964\pi$
$419$			16.1364i			0.788317i	−0.919043	+	0.394158i	$0.871036\pi$
$420$		0			0
$421$		−	28.7675i		−	1.40204i	−0.713141	−	0.701021i	$-0.752728\pi$
$421$		−	28.7675i		−	1.40204i	0.713141	−	0.701021i	$-0.247272\pi$
$422$	4.56159	−	0.627639i	0.222055	−	0.0305530i
$423$		−	5.70272i		−	0.277276i
$424$	13.0422	+	29.9911i	0.633388	+	1.45650i
$425$		0			0
$426$	2.18757	+	15.8989i	0.105988	+	0.770304i
$427$	0.958640			0.0463918
$428$	20.1628	−	5.65556i	0.974605	−	0.273372i
$429$		−	12.7297i		−	0.614596i
$430$		0			0
$431$	24.7297			1.19119			0.595594	−	0.803285i	$-0.296917\pi$
$431$	24.7297			1.19119			0.595594	+	0.803285i	$0.296917\pi$
$432$	−3.41649	+	2.08029i	−0.164376	+	0.100088i
$433$		−	4.48816i		−	0.215687i	−0.994168	−	0.107844i	$-0.965605\pi$
$433$		−	4.48816i		−	0.215687i	0.994168	−	0.107844i	$-0.0343946\pi$
$434$	0.933023	−	0.128377i	0.0447865	−	0.00616228i
$435$		0			0
$436$	−1.96773	−	7.01522i	−0.0942373	−	0.335968i
$437$	−11.4499			−0.547721
$438$	−16.9212	+	2.32823i	−0.808528	+	0.111247i
$439$	−5.96081			−0.284494			−0.142247	−	0.989831i	$-0.545433\pi$
$439$	−5.96081			−0.284494			−0.142247	+	0.989831i	$0.545433\pi$
$440$		0			0
$441$	6.99355			0.333026
$442$	1.88876	−	0.259879i	0.0898392	−	0.0123612i
$443$	−14.2924			−0.679053			−0.339526	−	0.940597i	$-0.610267\pi$
$443$	−14.2924			−0.679053			−0.339526	+	0.940597i	$0.610267\pi$
$444$	5.14621	−	1.44348i	0.244228	−	0.0685047i
$445$		0			0
$446$	−37.8149	+	5.20304i	−1.79059	+	0.246371i
$447$		−	23.0475i		−	1.09011i
$448$	0.469784	+	0.437996i	0.0221952	+	0.0206933i
$449$	−24.5529			−1.15872			−0.579362	−	0.815070i	$-0.696698\pi$
$449$	−24.5529			−1.15872			−0.579362	+	0.815070i	$0.696698\pi$
$450$		0			0
$451$			19.6200i			0.923870i
$452$	−4.77107	−	17.0095i	−0.224412	−	0.800060i
$453$	−9.48573			−0.445678
$454$	3.82105	+	27.7708i	0.179331	+	1.30335i
$455$		0			0
$456$	18.0492	−	7.84906i	0.845231	−	0.367566i
$457$		−	28.9108i		−	1.35239i	−0.736722	−	0.676196i	$-0.763627\pi$
$457$		−	28.9108i		−	1.35239i	0.736722	−	0.676196i	$-0.236373\pi$
$458$	−30.3736	+	4.17917i	−1.41927	+	0.195280i
$459$		−	0.255918i		−	0.0119452i
$460$		0			0
$461$			4.35458i			0.202813i	0.994845	+	0.101407i	$0.0323343\pi$
$461$			4.35458i			0.202813i	−0.994845	+	0.101407i	$0.967666\pi$
$462$	0.0373993	+	0.271812i	0.00173997	+	0.0126459i
$463$			11.1303i			0.517267i	0.965976	+	0.258634i	$0.0832722\pi$
$463$			11.1303i			0.517267i	−0.965976	+	0.258634i	$0.916728\pi$
$464$	−9.39282	−	15.4260i	−0.436051	−	0.716134i
$465$		0			0
$466$	−24.2002	+	3.32976i	−1.12105	+	0.154248i
$467$	−19.1257			−0.885030			−0.442515	−	0.896761i	$-0.645914\pi$
$467$	−19.1257			−0.885030			−0.442515	+	0.896761i	$0.645914\pi$
$468$	10.1442	−	2.84539i	0.468916	−	0.131528i
$469$			0.584467i			0.0269882i
$470$		0			0
$471$	6.34413			0.292322
$472$	−32.9314	+	14.3209i	−1.51579	+	0.659172i
$473$		−	9.88079i		−	0.454319i
$474$	1.06127	+	7.71313i	0.0487456	+	0.354276i
$475$		0			0
$476$	−0.0395664	+	0.0110982i	−0.00181352	+	0.000508684i
$477$	−11.5627			−0.529419
$478$	3.15597	+	22.9371i	0.144351	+	1.04912i
$479$	25.6358			1.17133			0.585666	−	0.810553i	$-0.300833\pi$
$479$	25.6358			1.17133			0.585666	+	0.810553i	$0.300833\pi$
$480$		0			0
$481$	−14.0779			−0.641895
$482$	−1.31594	−	9.56407i	−0.0599395	−	0.435632i
$483$	0.132104			0.00601096
$484$	−9.93761	+	2.78745i	−0.451710	+	0.126702i
$485$		0			0
$486$	−0.192769	−	1.40101i	−0.00874416	−	0.0635513i
$487$			12.8434i			0.581992i	0.956724	+	0.290996i	$0.0939866\pi$
$487$			12.8434i			0.581992i	−0.956724	+	0.290996i	$0.906013\pi$
$488$	30.9704	−	13.4681i	1.40197	−	0.609673i
$489$	−12.4100			−0.561202
$490$		0			0
$491$			16.9887i			0.766689i	0.923605	+	0.383344i	$0.125228\pi$
$491$			16.9887i			0.766689i	−0.923605	+	0.383344i	$0.874772\pi$
$492$	−15.6350	+	4.38554i	−0.704881	+	0.197715i
$493$	1.15551			0.0520415
$494$	−51.3571	+	7.06634i	−2.31066	+	0.317930i
$495$		0			0
$496$	28.3393	−	17.2557i	1.27247	−	0.774802i
$497$			0.911101i			0.0408684i
$498$	−1.77504	−	12.9007i	−0.0795412	−	0.578094i
$499$			14.0521i			0.629060i	0.949248	+	0.314530i	$0.101847\pi$
$499$			14.0521i			0.629060i	−0.949248	+	0.314530i	$0.898153\pi$
$500$		0			0
$501$			23.2654i			1.03942i
$502$	−4.16057	+	0.572463i	−0.185695	+	0.0255503i
$503$		−	9.53258i		−	0.425037i	−0.977157	−	0.212518i	$-0.931833\pi$
$503$		−	9.53258i		−	0.425037i	0.977157	−	0.212518i	$-0.0681665\pi$
$504$	−0.208245	+	0.0905597i	−0.00927599	+	0.00403385i
$505$		0			0
$506$	−0.766474	−	5.57062i	−0.0340739	−	0.247644i
$507$	−14.7503			−0.655082
$508$	−4.69723	−	16.7462i	−0.208406	−	0.742995i
$509$		−	30.3450i		−	1.34502i	−0.740088	−	0.672510i	$-0.765216\pi$
$509$		−	30.3450i		−	1.34502i	0.740088	−	0.672510i	$-0.234784\pi$
$510$		0			0
$511$	−0.969687			−0.0428964
$512$	21.3306	+	7.55007i	0.942690	+	0.333669i
$513$			6.95864i			0.307231i
$514$	7.04754	−	0.969687i	0.310854	−	0.0427710i
$515$		0			0
$516$	7.87391	−	2.20859i	0.346630	−	0.0972278i
$517$	−13.7806			−0.606069
$518$	0.300599	−	0.0413600i	0.0132075	−	0.00181726i
$519$	8.63897			0.379209
$520$		0			0
$521$	14.4245			0.631949			0.315975	−	0.948768i	$-0.397669\pi$
$521$	14.4245			0.631949			0.315975	+	0.948768i	$0.397669\pi$
$522$	6.32580	−	0.870381i	0.276873	−	0.0380955i
$523$	−28.2207			−1.23401			−0.617003	−	0.786961i	$-0.711654\pi$
$523$	−28.2207			−1.23401			−0.617003	+	0.786961i	$0.711654\pi$
$524$	5.82902	+	20.7812i	0.254642	+	0.907832i
$525$		0			0
$526$	3.79093	−	0.521603i	0.165292	−	0.0227430i
$527$			2.12280i			0.0924706i
$528$	5.02699	+	8.25592i	0.218772	+	0.359293i
$529$	20.2926			0.882287
$530$		0			0
$531$		−	12.6963i		−	0.550971i
$532$	1.07585	−	0.301769i	0.0466439	−	0.0130834i
$533$	42.7708			1.85261
$534$	2.29728	+	16.6963i	0.0994129	+	0.722519i
$535$		0			0
$536$	8.21130	+	18.8822i	0.354674	+	0.815586i
$537$		−	9.40544i		−	0.405875i
$538$	31.3432	−	4.31258i	1.35130	−	0.185929i
$539$		−	16.8999i		−	0.727928i
$540$		0			0
$541$		−	13.4695i		−	0.579100i	−0.957163	−	0.289550i	$-0.906494\pi$
$541$		−	13.4695i		−	0.579100i	0.957163	−	0.289550i	$-0.0935056\pi$
$542$	−0.167659	−	1.21852i	−0.00720156	−	0.0523399i
$543$			6.43487i			0.276147i
$544$	−1.12234	+	0.914421i	−0.0481198	+	0.0392055i
$545$		0			0
$546$	0.592540	−	0.0815289i	0.0253584	−	0.00348912i
$547$	4.42773			0.189316			0.0946581	−	0.995510i	$-0.469824\pi$
$547$	4.42773			0.189316			0.0946581	+	0.995510i	$0.469824\pi$
$548$	6.23441	+	22.2265i	0.266321	+	0.949469i
$549$			11.9403i			0.509598i
$550$		0			0
$551$	−31.4193			−1.33851
$552$	4.26785	−	1.85596i	0.181652	−	0.0789950i
$553$			0.442008i			0.0187961i
$554$	5.52731	+	40.1717i	0.234833	+	1.70673i
$555$		0			0
$556$	0.115892	+	0.413170i	0.00491492	+	0.0175223i
$557$	−40.2017			−1.70340			−0.851700	−	0.524030i	$-0.824428\pi$
$557$	−40.2017			−1.70340			−0.851700	+	0.524030i	$0.824428\pi$
$558$	1.59899	+	11.6212i	0.0676905	+	0.491964i
$559$	−21.5397			−0.911033
$560$		0			0
$561$	−0.618423			−0.0261099
$562$	2.91907	+	21.2154i	0.123134	+	0.894917i
$563$	−13.1128			−0.552637			−0.276319	−	0.961066i	$-0.589115\pi$
$563$	−13.1128			−0.552637			−0.276319	+	0.961066i	$0.589115\pi$
$564$	−3.08029	−	10.9816i	−0.129703	−	0.462410i
$565$		0			0
$566$	1.20138	+	8.73146i	0.0504978	+	0.367011i
$567$		−	0.0802864i		−	0.00337171i
$568$	12.8002	+	29.4346i	0.537086	+	1.23505i
$569$	11.0257			0.462222			0.231111	−	0.972927i	$-0.425764\pi$
$569$	11.0257			0.462222			0.231111	+	0.972927i	$0.425764\pi$
$570$		0			0
$571$			45.6960i			1.91232i	0.292847	+	0.956159i	$0.405397\pi$
$571$			45.6960i			1.91232i	−0.292847	+	0.956159i	$0.594603\pi$
$572$	−6.87587	−	24.5134i	−0.287495	−	1.02496i
$573$	5.56270			0.232385
$574$	−0.913268	+	0.125659i	−0.0381191	+	0.00524489i
$575$		0			0
$576$	−5.45542	+	5.85136i	−0.227309	+	0.243807i
$577$		−	17.2685i		−	0.718899i	−0.933165	−	0.359449i	$-0.882965\pi$
$577$		−	17.2685i		−	0.718899i	0.933165	−	0.359449i	$-0.117035\pi$
$578$	3.26444	+	23.7255i	0.135783	+	0.986850i
$579$			18.4227i			0.765620i
$580$		0			0
$581$		−	0.739286i		−	0.0306707i
$582$	−11.9162	+	1.63957i	−0.493941	+	0.0679625i
$583$			27.9411i			1.15720i
$584$	−31.3273	+	13.6233i	−1.29633	+	0.563737i
$585$		0			0
$586$	4.14557	+	30.1294i	0.171252	+	1.24463i
$587$	−34.7155			−1.43286			−0.716432	−	0.697657i	$-0.754226\pi$
$587$	−34.7155			−1.43286			−0.716432	+	0.697657i	$0.754226\pi$
$588$	13.4674	−	3.77752i	0.555384	−	0.155782i
$589$		−	57.7208i		−	2.37835i
$590$		0			0
$591$	−18.0239			−0.741403
$592$	9.13026	−	5.55938i	0.375251	−	0.228489i
$593$			9.34022i			0.383557i	0.981438	+	0.191778i	$0.0614255\pi$
$593$			9.34022i			0.383557i	−0.981438	+	0.191778i	$0.938575\pi$
$594$	−3.38554	+	0.465824i	−0.138910	+	0.0191130i
$595$		0			0
$596$	−12.4490	−	44.3822i	−0.509930	−	1.81797i
$597$	20.1214			0.823513
$598$	−12.1437	+	1.67088i	−0.496594	+	0.0683274i
$599$	13.9110			0.568389			0.284195	−	0.958767i	$-0.408274\pi$
$599$	13.9110			0.568389			0.284195	+	0.958767i	$0.408274\pi$
$600$		0			0
$601$	11.7330			0.478600			0.239300	−	0.970946i	$-0.423082\pi$
$601$	11.7330			0.478600			0.239300	+	0.970946i	$0.423082\pi$
$602$	0.459929	−	0.0632826i	0.0187453	−	0.00257921i
$603$	−7.27979			−0.296456
$604$	−18.2665	+	5.12365i	−0.743253	+	0.208478i
$605$		0			0
$606$	10.5954	−	1.45785i	0.430410	−	0.0592211i
$607$		−	10.8158i		−	0.438998i	−0.975613	−	0.219499i	$-0.929558\pi$
$607$		−	10.8158i		−	0.438998i	0.975613	−	0.219499i	$-0.0704423\pi$
$608$	30.5174	−	24.8639i	1.23764	−	1.00837i
$609$	0.362505			0.0146895
$610$		0			0
$611$			30.0411i			1.21533i
$612$	−0.138232	−	0.492816i	−0.00558771	−	0.0199209i
$613$	17.9632			0.725528			0.362764	−	0.931881i	$-0.381833\pi$
$613$	17.9632			0.725528			0.362764	+	0.931881i	$0.381833\pi$
$614$	0.689546	+	5.01152i	0.0278278	+	0.202248i
$615$		0			0
$616$	0.218837	+	0.503223i	0.00881718	+	0.0202754i
$617$			12.3576i			0.497500i	0.968568	+	0.248750i	$0.0800197\pi$
$617$			12.3576i			0.497500i	−0.968568	+	0.248750i	$0.919980\pi$
$618$	−2.50143	+	0.344177i	−0.100622	+	0.0138448i
$619$		−	4.99540i		−	0.200782i	−0.994948	−	0.100391i	$-0.967991\pi$
$619$		−	4.99540i		−	0.200782i	0.994948	−	0.100391i	$-0.0320094\pi$
$620$		0			0
$621$			1.64542i			0.0660283i
$622$	−0.480883	−	3.49498i	−0.0192816	−	0.140136i
$623$			0.956795i			0.0383332i
$624$	17.9976	−	10.9586i	0.720479	−	0.438697i
$625$		0			0
$626$	−13.4112	+	1.84527i	−0.536018	+	0.0737519i
$627$	16.8155			0.671546
$628$	12.2168	−	3.42674i	0.487502	−	0.136742i
$629$			0.683917i			0.0272696i
$630$		0			0
$631$	−17.9674			−0.715273			−0.357636	−	0.933861i	$-0.616417\pi$
$631$	−17.9674			−0.715273			−0.357636	+	0.933861i	$0.616417\pi$
$632$	6.20985	+	14.2798i	0.247015	+	0.568019i
$633$			3.25592i			0.129411i
$634$	−0.610502	−	4.43704i	−0.0242461	−	0.176217i
$635$		0			0
$636$	−22.2661	+	6.24551i	−0.882907	+	0.247651i
$637$	−36.8410			−1.45969
$638$	−2.10327	−	15.2862i	−0.0832691	−	0.605188i
$639$	−11.3481			−0.448925
$640$		0			0
$641$	27.3638			1.08081			0.540403	−	0.841406i	$-0.318272\pi$
$641$	27.3638			1.08081			0.540403	+	0.841406i	$0.318272\pi$
$642$	2.01838	+	14.6693i	0.0796591	+	0.578950i
$643$	−2.27518			−0.0897245			−0.0448623	−	0.998993i	$-0.514285\pi$
$643$	−2.27518			−0.0897245			−0.0448623	+	0.998993i	$0.514285\pi$
$644$	0.254391	−	0.0713553i	0.0100244	−	0.00281179i
$645$		0			0
$646$	0.343290	+	2.49498i	0.0135066	+	0.0981638i
$647$			12.4769i			0.490516i	0.969458	+	0.245258i	$0.0788726\pi$
$647$			12.4769i			0.490516i	−0.969458	+	0.245258i	$0.921127\pi$
$648$	−1.12796	−	2.59378i	−0.0443104	−	0.101893i
$649$	−30.6804			−1.20431
$650$		0			0
$651$			0.665963i			0.0261011i
$652$	−23.8978	+	6.70320i	−0.935909	+	0.262518i
$653$	−29.3055			−1.14681			−0.573406	−	0.819271i	$-0.694378\pi$
$653$	−29.3055			−1.14681			−0.573406	+	0.819271i	$0.694378\pi$
$654$	5.10387	−	0.702253i	0.199577	−	0.0274603i
$655$		0			0
$656$	−27.7392	+	16.8903i	−1.08303	+	0.659455i
$657$		−	12.0779i		−	0.471202i
$658$	−0.0882593	−	0.641455i	−0.00344070	−	0.0250065i
$659$		−	18.6009i		−	0.724589i	−0.932064	−	0.362295i	$-0.881993\pi$
$659$		−	18.6009i		−	0.724589i	0.932064	−	0.362295i	$-0.118007\pi$
$660$		0			0
$661$			16.1318i			0.627456i	0.949513	+	0.313728i	$0.101578\pi$
$661$			16.1318i			0.627456i	−0.949513	+	0.313728i	$0.898422\pi$
$662$	23.1333	−	3.18296i	0.899102	−	0.123709i
$663$			1.34814i			0.0523573i
$664$	−10.3864	−	23.8838i	−0.403069	−	0.926873i
$665$		0			0
$666$	0.515157	+	3.74408i	0.0199619	+	0.145080i
$667$	−7.42931			−0.287664
$668$	12.5667	+	44.8018i	0.486219	+	1.73343i
$669$		−	26.9911i		−	1.04354i
$670$		0			0
$671$	28.8535			1.11388
$672$	−0.352099	+	0.286871i	−0.0135825	+	0.0110663i
$673$			34.1385i			1.31594i	0.753043	+	0.657971i	$0.228585\pi$
$673$			34.1385i			1.31594i	−0.753043	+	0.657971i	$0.771415\pi$
$674$	−16.5782	+	2.28103i	−0.638567	+	0.0878619i
$675$		0			0
$676$	−28.4043	+	7.96725i	−1.09247	+	0.306433i
$677$	12.1940			0.468654			0.234327	−	0.972158i	$-0.424711\pi$
$677$	12.1940			0.468654			0.234327	+	0.972158i	$0.424711\pi$
$678$	12.3751	−	1.70272i	0.475264	−	0.0653926i
$679$	−0.682867			−0.0262060
$680$		0			0
$681$	−19.8219			−0.759578
$682$	28.0825	−	3.86393i	1.07533	−	0.147958i
$683$	−21.8567			−0.836322			−0.418161	−	0.908373i	$-0.637325\pi$
$683$	−21.8567			−0.836322			−0.418161	+	0.908373i	$0.637325\pi$
$684$	3.75866	+	13.4001i	0.143716	+	0.512366i
$685$		0			0
$686$	1.57403	−	0.216574i	0.0600966	−	0.00826883i
$687$		−	21.6797i		−	0.827134i
$688$	13.9697	−	8.50608i	0.532589	−	0.324291i
$689$	60.9106			2.32051
$690$		0			0
$691$			6.17780i			0.235015i	0.993072	+	0.117507i	$0.0374903\pi$
$691$			6.17780i			0.235015i	−0.993072	+	0.117507i	$0.962510\pi$
$692$	16.6359	−	4.66628i	0.632402	−	0.177385i
$693$	−0.194011			−0.00736988
$694$	4.62091	+	33.5841i	0.175407	+	1.27483i
$695$		0			0
$696$	11.7113	−	5.09291i	0.443917	−	0.193046i
$697$		−	2.07785i		−	0.0787043i
$698$	12.4910	−	1.71867i	0.472792	−	0.0650525i
$699$		−	17.2733i		−	0.653338i
$700$		0			0
$701$			33.9746i			1.28320i	0.767038	+	0.641601i	$0.221730\pi$
$701$			33.9746i			1.28320i	−0.767038	+	0.641601i	$0.778270\pi$
$702$	1.01548	+	7.38033i	0.0383267	+	0.278553i
$703$		−	18.5963i		−	0.701374i
$704$	14.1398	+	13.1830i	0.532912	+	0.496852i
$705$		0			0
$706$	10.3059	−	1.41802i	0.387869	−	0.0533678i
$707$	0.607181			0.0228354
$708$	−6.85781	−	24.4490i	−0.257732	−	0.918849i
$709$			22.3441i			0.839151i	0.907720	+	0.419576i	$0.137821\pi$
$709$			22.3441i			0.839151i	−0.907720	+	0.419576i	$0.862179\pi$
$710$		0			0
$711$	−5.50539			−0.206468
$712$	13.4422	+	30.9108i	0.503768	+	1.15843i
$713$		−	13.6485i		−	0.511139i
$714$	−0.00396076	−	0.0287862i	−0.000148228	−	0.00107730i
$715$		0			0
$716$	−5.08029	−	18.1119i	−0.189859	−	0.676873i
$717$	−16.3718			−0.611416
$718$	−4.85997	−	35.3216i	−0.181373	−	1.31819i
$719$	17.8427			0.665422			0.332711	−	0.943029i	$-0.392037\pi$
$719$	17.8427			0.665422			0.332711	+	0.943029i	$0.392037\pi$
$720$		0			0
$721$	−0.143347			−0.00533851
$722$	−5.67177	−	41.2216i	−0.211081	−	1.53411i
$723$	6.82654			0.253882
$724$	3.47575	+	12.3915i	0.129175	+	0.460527i
$725$		0			0
$726$	−0.994797	−	7.23003i	−0.0369204	−	0.268332i
$727$		−	23.9148i		−	0.886953i	−0.896286	−	0.443476i	$-0.853745\pi$
$727$		−	23.9148i		−	0.886953i	0.896286	−	0.443476i	$-0.146255\pi$
$728$	1.09701	−	0.477055i	0.0406577	−	0.0176808i
$729$	1.00000			0.0370370
$730$		0			0
$731$			1.04642i			0.0387034i
$732$	6.44945	+	22.9931i	0.238379	+	0.849850i
$733$	−15.6789			−0.579112			−0.289556	−	0.957161i	$-0.593508\pi$
$733$	−15.6789			−0.579112			−0.289556	+	0.957161i	$0.593508\pi$
$734$	8.21797	−	1.13073i	0.303331	−	0.0417360i
$735$		0			0
$736$	7.21603	−	5.87924i	0.265987	−	0.216712i
$737$			17.5915i			0.647992i
$738$	−1.56513	−	11.3751i	−0.0576132	−	0.418724i
$739$		−	22.3083i		−	0.820622i	−0.911946	−	0.410311i	$-0.865420\pi$
$739$		−	22.3083i		−	0.820622i	0.911946	−	0.410311i	$-0.134580\pi$
$740$		0			0
$741$		−	36.6571i		−	1.34663i
$742$	−1.30060	+	0.178952i	−0.0477465	+	0.00656955i
$743$		−	9.78057i		−	0.358814i	−0.983775	−	0.179407i	$-0.942582\pi$
$743$		−	9.78057i		−	0.358814i	0.983775	−	0.179407i	$-0.0574180\pi$
$744$	9.35624	+	21.5150i	0.343017	+	0.788779i
$745$		0			0
$746$	5.30235	+	38.5367i	0.194133	+	1.41093i
$747$	9.20811			0.336907
$748$	−1.19089	+	0.334037i	−0.0435431	+	0.0122136i
$749$			0.840636i			0.0307162i
$750$		0			0
$751$	−8.05399			−0.293894			−0.146947	−	0.989144i	$-0.546945\pi$
$751$	−8.05399			−0.293894			−0.146947	+	0.989144i	$0.546945\pi$
$752$	−11.8633	−	19.4833i	−0.432610	−	0.710483i
$753$		−	2.96969i		−	0.108221i
$754$	−33.3234	+	4.58504i	−1.21357	+	0.166977i
$755$		0			0
$756$	−0.0433661	−	0.154606i	−0.00157721	−	0.00562296i
$757$	28.4889			1.03545			0.517723	−	0.855549i	$-0.326780\pi$
$757$	28.4889			1.03545			0.517723	+	0.855549i	$0.326780\pi$
$758$	−16.4687	+	2.26597i	−0.598171	+	0.0823037i
$759$	3.97613			0.144324
$760$		0			0
$761$	−21.5005			−0.779393			−0.389697	−	0.920943i	$-0.627420\pi$
$761$	−21.5005			−0.779393			−0.389697	+	0.920943i	$0.627420\pi$
$762$	12.1836	−	1.67637i	0.441365	−	0.0607285i
$763$	0.292482			0.0105886
$764$	10.7120	−	3.00465i	0.387546	−	0.108705i
$765$		0			0
$766$	48.1017	−	6.61842i	1.73799	−	0.239133i
$767$			66.8821i			2.41497i
$768$	−7.34482	+	14.2146i	−0.265033	+	0.512924i
$769$	−23.5596			−0.849580			−0.424790	−	0.905292i	$-0.639652\pi$
$769$	−23.5596			−0.849580			−0.424790	+	0.905292i	$0.639652\pi$
$770$		0			0
$771$			5.03031i			0.181162i
$772$	9.95088	+	35.4762i	0.358140	+	1.27682i
$773$	31.1655			1.12094			0.560472	−	0.828173i	$-0.310620\pi$
$773$	31.1655			1.12094			0.560472	+	0.828173i	$0.310620\pi$
$774$	0.788212	+	5.72861i	0.0283317	+	0.205910i
$775$		0			0
$776$	−22.0611	+	9.59373i	−0.791949	+	0.344395i
$777$			0.214558i			0.00769722i
$778$	−4.05615	+	0.558095i	−0.145420	+	0.0200087i
$779$			56.4987i			2.02428i
$780$		0			0
$781$			27.4227i			0.981260i
$782$	0.0811733	+	0.589955i	0.00290275	+	0.0210968i
$783$			4.51516i			0.161359i
$784$	23.8934	−	14.5486i	0.853336	−	0.519593i
$785$		0			0
$786$	−15.1192	+	2.08029i	−0.539284	+	0.0742014i
$787$	−5.07812			−0.181015			−0.0905077	−	0.995896i	$-0.528849\pi$
$787$	−5.07812			−0.181015			−0.0905077	+	0.995896i	$0.528849\pi$
$788$	−34.7082	+	9.73547i	−1.23643	+	0.346812i
$789$			2.70585i			0.0963307i
$790$		0			0
$791$	0.709168			0.0252151
$792$	−6.26785	+	2.72570i	−0.222718	+	0.0968536i
$793$		−	62.8995i		−	2.23363i
$794$	−4.41632	−	32.0972i	−0.156729	−	1.13909i
$795$		0			0
$796$	38.7473	−	10.8684i	1.37336	−	0.385221i
$797$	−1.43418			−0.0508012			−0.0254006	−	0.999677i	$-0.508086\pi$
$797$	−1.43418			−0.0508012			−0.0254006	+	0.999677i	$0.508086\pi$
$798$	0.107697	+	0.782724i	0.00381242	+	0.0277081i
$799$	1.45943			0.0516309
$800$		0			0
$801$	−11.9173			−0.421076
$802$	−2.39683	−	17.4198i	−0.0846350	−	0.615115i
$803$	−29.1860			−1.02995
$804$	−14.0185	+	3.93213i	−0.494396	+	0.138675i
$805$		0			0
$806$	−8.42322	−	61.2187i	−0.296695	−	2.15634i
$807$			22.3718i			0.787525i
$808$	19.6160	−	8.53041i	0.690088	−	0.300099i
$809$	−23.7153			−0.833787			−0.416894	−	0.908955i	$-0.636881\pi$
$809$	−23.7153			−0.833787			−0.416894	+	0.908955i	$0.636881\pi$
$810$		0			0
$811$		−	47.8394i		−	1.67987i	−0.542689	−	0.839933i	$-0.682594\pi$
$811$		−	47.8394i		−	1.67987i	0.542689	−	0.839933i	$-0.317406\pi$
$812$	0.698070	−	0.195805i	0.0244974	−	0.00687140i
$813$	0.869741			0.0305031
$814$	9.04754	−	1.24487i	0.317116	−	0.0436327i
$815$		0			0
$816$	−0.532383	−	0.874341i	−0.0186371	−	0.0306081i
$817$		−	28.4532i		−	0.995451i
$818$	6.18568	+	44.9566i	0.216277	+	1.57187i
$819$			0.422937i			0.0147786i
$820$		0			0
$821$		−	51.9216i		−	1.81208i	−0.423195	−	0.906038i	$-0.639092\pi$
$821$		−	51.9216i		−	1.81208i	0.423195	−	0.906038i	$-0.360908\pi$
$822$	−16.1707	+	2.22496i	−0.564018	+	0.0776046i
$823$		−	27.8542i		−	0.970937i	−0.874254	−	0.485469i	$-0.838649\pi$
$823$		−	27.8542i		−	0.970937i	0.874254	−	0.485469i	$-0.161351\pi$
$824$	−4.63105	+	2.01391i	−0.161330	+	0.0701577i
$825$		0			0
$826$	−0.196496	−	1.42811i	−0.00683698	−	0.0496902i
$827$	43.9365			1.52782			0.763912	−	0.645321i	$-0.223276\pi$
$827$	43.9365			1.52782			0.763912	+	0.645321i	$0.223276\pi$
$828$	0.888760	+	3.16855i	0.0308866	+	0.110115i
$829$		−	41.6898i		−	1.44795i	−0.689827	−	0.723974i	$-0.742314\pi$
$829$		−	41.6898i		−	1.44795i	0.689827	−	0.723974i	$-0.257686\pi$
$830$		0			0
$831$	−28.6733			−0.994666
$832$	28.7383	−	30.8241i	0.996322	−	1.06863i
$833$			1.78978i			0.0620121i
$834$	−0.300599	+	0.0413600i	−0.0104089	+	0.00143218i
$835$		0			0
$836$	32.3813	−	9.08277i	1.11993	−	0.314134i
$837$	−8.29484			−0.286712
$838$	−22.6074	+	3.11060i	−0.780959	+	0.107454i
$839$	25.4733			0.879437			0.439719	−	0.898136i	$-0.355078\pi$
$839$	25.4733			0.879437			0.439719	+	0.898136i	$0.355078\pi$
$840$		0			0
$841$	8.61336			0.297012
$842$	40.3037	−	5.54547i	1.38896	−	0.191110i
$843$	−15.1429			−0.521549
$844$	1.75866	+	6.26986i	0.0605356	+	0.215817i
$845$		0			0
$846$	7.98959	−	1.09931i	0.274688	−	0.0377949i
$847$		−	0.414324i		−	0.0142363i
$848$	−39.5038	+	24.0537i	−1.35657	+	0.826008i
$849$	−6.23225			−0.213890
$850$		0			0
$851$		−	4.39722i		−	0.150735i
$852$	−21.8529	+	6.12962i	−0.748668	+	0.209997i
$853$	−12.5366			−0.429245			−0.214622	−	0.976697i	$-0.568852\pi$
$853$	−12.5366			−0.429245			−0.214622	+	0.976697i	$0.568852\pi$
$854$	0.184796	+	1.34307i	0.00632358	+	0.0459588i
$855$		0			0
$856$	11.8103	+	27.1581i	0.403667	+	0.928246i
$857$			2.61409i			0.0892956i	0.999003	+	0.0446478i	$0.0142166\pi$
$857$			2.61409i			0.0892956i	−0.999003	+	0.0446478i	$0.985783\pi$
$858$	17.8345	−	2.45389i	0.608860	−	0.0837744i
$859$		−	31.8438i		−	1.08650i	−0.839573	−	0.543248i	$-0.817195\pi$
$859$		−	31.8438i		−	1.08650i	0.839573	−	0.543248i	$-0.182805\pi$
$860$		0			0
$861$		−	0.651862i		−	0.0222154i
$862$	4.76711	+	34.6467i	0.162369	+	1.18007i
$863$			22.3335i			0.760241i	0.924937	+	0.380121i	$0.124118\pi$
$863$			22.3335i			0.760241i	−0.924937	+	0.380121i	$0.875882\pi$
$864$	−3.57310	−	4.38554i	−0.121559	−	0.149199i
$865$		0			0
$866$	6.28798	−	0.865177i	0.213674	−	0.0293999i
$867$	−16.9345			−0.575126
$868$	0.359715	+	1.28243i	0.0122095	+	0.0435286i
$869$			13.3037i			0.451298i
$870$		0			0
$871$	38.3488			1.29940
$872$	9.44910	−	4.10913i	0.319987	−	0.139153i
$873$		−	8.50539i		−	0.287864i
$874$	−2.20717	−	16.0414i	−0.0746588	−	0.542609i
$875$		0			0
$876$	−6.52377	−	23.2581i	−0.220418	−	0.785818i
$877$	37.4408			1.26429			0.632143	−	0.774852i	$-0.282176\pi$
$877$	37.4408			1.26429			0.632143	+	0.774852i	$0.282176\pi$
$878$	−1.14906	−	8.35117i	−0.0387788	−	0.281838i
$879$	−21.5054			−0.725359
$880$		0			0
$881$	53.1952			1.79219			0.896096	−	0.443860i	$-0.146391\pi$
$881$	53.1952			1.79219			0.896096	+	0.443860i	$0.146391\pi$
$882$	1.34814	+	9.79807i	0.0453942	+	0.329918i
$883$	36.0907			1.21455			0.607274	−	0.794493i	$-0.292263\pi$
$883$	36.0907			1.21455			0.607274	+	0.794493i	$0.292263\pi$
$884$	0.728188	+	2.59608i	0.0244916	+	0.0873157i
$885$		0			0
$886$	−2.75513	−	20.0239i	−0.0925604	−	0.672715i
$887$		−	43.3018i		−	1.45393i	−0.686673	−	0.726966i	$-0.740930\pi$
$887$		−	43.3018i		−	1.45393i	0.686673	−	0.726966i	$-0.259070\pi$
$888$	3.01437	+	6.93165i	0.101156	+	0.232611i
$889$	0.698192			0.0234166
$890$		0			0
$891$		−	2.41649i		−	0.0809555i
$892$	−14.5791	−	51.9763i	−0.488143	−	1.74029i
$893$	−39.6832			−1.32795
$894$	32.2899	−	4.44284i	1.07994	−	0.148591i
$895$		0			0
$896$	−0.523078	+	0.742606i	−0.0174748	+	0.0248087i
$897$		−	8.66781i		−	0.289410i
$898$	−4.73304	−	34.3990i	−0.157943	−	1.14791i
$899$		−	37.4525i		−	1.24911i
$900$		0			0
$901$		−	2.95910i		−	0.0985820i
$902$	−27.4879	+	3.78212i	−0.915247	+	0.125931i
$903$			0.328283i			0.0109246i
$904$	22.9108	−	9.96324i	0.762003	−	0.331372i
$905$		0			0
$906$	−1.82855	−	13.2896i	−0.0607496	−	0.441519i
$907$	8.75026			0.290548			0.145274	−	0.989391i	$-0.453594\pi$
$907$	8.75026			0.290548			0.145274	+	0.989391i	$0.453594\pi$
$908$	−38.1707	+	10.7067i	−1.26674	+	0.355314i
$909$			7.56270i			0.250839i
$910$		0			0
$911$	−13.7438			−0.455353			−0.227676	−	0.973737i	$-0.573113\pi$
$911$	−13.7438			−0.455353			−0.227676	+	0.973737i	$0.573113\pi$
$912$	14.4760	+	23.7741i	0.479347	+	0.787240i
$913$		−	22.2513i		−	0.736411i
$914$	40.5045	−	5.57310i	1.33977	−	0.184342i
$915$		0			0
$916$	−11.7102	−	41.7483i	−0.386915	−	1.37940i
$917$	−0.866420			−0.0286117
$918$	0.358545	−	0.0493330i	0.0118337	−	0.00162823i
$919$	0.989347			0.0326355			0.0163178	−	0.999867i	$-0.494806\pi$
$919$	0.989347			0.0326355			0.0163178	+	0.999867i	$0.494806\pi$
$920$		0			0
$921$	−3.57706			−0.117868
$922$	−6.10083	+	0.839427i	−0.200920	+	0.0276451i
$923$	59.7803			1.96769
$924$	−0.373604	+	0.104794i	−0.0122907	+	0.00344746i
$925$		0			0
$926$	−15.5936	+	2.14557i	−0.512439	+	0.0705076i
$927$		−	1.78544i		−	0.0586416i
$928$	19.8014	−	16.1331i	0.650012	−	0.529596i
$929$	8.49434			0.278690			0.139345	−	0.990244i	$-0.455500\pi$
$929$	8.49434			0.278690			0.139345	+	0.990244i	$0.455500\pi$
$930$		0			0
$931$		−	48.6656i		−	1.59495i
$932$	−9.33008	−	33.2629i	−0.305617	−	1.08956i
$933$	2.49461			0.0816699
$934$	−3.68683	−	26.7953i	−0.120637	−	0.876770i
$935$		0			0
$936$	5.94192	+	13.6637i	0.194218	+	0.446611i
$937$			18.6912i			0.610615i	0.952254	+	0.305308i	$0.0987593\pi$
$937$			18.6912i			0.610615i	−0.952254	+	0.305308i	$0.901241\pi$
$938$	−0.818847	+	0.112667i	−0.0267363	+	0.00367871i
$939$		−	9.57246i		−	0.312386i
$940$		0			0
$941$		−	3.03170i		−	0.0988305i	−0.998778	−	0.0494152i	$-0.984264\pi$
$941$		−	3.03170i		−	0.0988305i	0.998778	−	0.0494152i	$-0.0157358\pi$
$942$	1.22295	+	8.88821i	0.0398458	+	0.289594i
$943$			13.3595i			0.435045i
$944$	−26.4119	−	43.3767i	−0.859634	−	1.41179i
$945$		0			0
$946$	13.8431	−	1.90471i	0.450079	−	0.0619273i
$947$	−16.8327			−0.546990			−0.273495	−	0.961873i	$-0.588180\pi$
$947$	−16.8327			−0.546990			−0.273495	+	0.961873i	$0.588180\pi$
$948$	−10.6016	+	2.97370i	−0.344325	+	0.0965812i
$949$			63.6243i			2.06533i
$950$		0			0
$951$	3.16702			0.102698
$952$	−0.0231759	−	0.0532937i	−0.000751134	−	0.00172726i
$953$		−	1.73948i		−	0.0563473i	−0.999603	−	0.0281737i	$-0.991031\pi$
$953$		−	1.73948i		−	0.0563473i	0.999603	−	0.0281737i	$-0.00896914\pi$
$954$	−2.22893	−	16.1995i	−0.0721641	−	0.524478i
$955$		0			0
$956$	−31.5269	+	8.84312i	−1.01965	+	0.286007i
$957$	10.9108			0.352697
$958$	4.94179	+	35.9162i	0.159662	+	1.16040i
$959$	−0.926677			−0.0299240
$960$		0			0
$961$	37.8044			1.21950
$962$	−2.71377	−	19.7233i	−0.0874954	−	0.635904i
$963$	−10.4705			−0.337406
$964$	13.1457	−	3.68731i	0.423395	−	0.118760i
$965$		0			0
$966$	0.0254656	+	0.185080i	0.000819342	+	0.00595486i
$967$		−	17.3399i		−	0.557615i	−0.960347	−	0.278808i	$-0.910061\pi$
$967$		−	17.3399i		−	0.557615i	0.960347	−	0.278808i	$-0.0899392\pi$
$968$	−5.82091	−	13.3854i	−0.187091	−	0.430223i
$969$	−1.78084			−0.0572089
$970$		0			0
$971$		−	45.4054i		−	1.45713i	−0.684977	−	0.728565i	$-0.740188\pi$
$971$		−	45.4054i		−	1.45713i	0.684977	−	0.728565i	$-0.259812\pi$
$972$	1.92568	−	0.540143i	0.0617662	−	0.0173251i
$973$	−0.0172261			−0.000552243
$974$	−17.9938	+	2.47581i	−0.576560	+	0.0793302i
$975$		0			0
$976$	24.8392	+	40.7938i	0.795082	+	1.30578i
$977$			43.4336i			1.38957i	0.719220	+	0.694783i	$0.244499\pi$
$977$			43.4336i			1.38957i	−0.719220	+	0.694783i	$0.755501\pi$
$978$	−2.39227	−	17.3866i	−0.0764963	−	0.555964i
$979$			28.7980i			0.920388i
$980$		0			0
$981$			3.64298i			0.116311i
$982$	−23.8014	+	3.27489i	−0.759533	+	0.104506i
$983$			47.4465i			1.51331i	0.653815	+	0.756655i	$0.273168\pi$
$983$			47.4465i			1.51331i	−0.653815	+	0.756655i	$0.726832\pi$
$984$	−9.15814	−	21.0595i	−0.291951	−	0.671351i
$985$		0			0
$986$	0.222746	+	1.61889i	0.00709368	+	0.0515558i
$987$	0.457851			0.0145735
$988$	−19.8001	−	70.5898i	−0.629924	−	2.24576i
$989$		−	6.72794i		−	0.213936i
$990$		0			0
$991$	−28.8434			−0.916242			−0.458121	−	0.888890i	$-0.651477\pi$
$991$	−28.8434			−0.916242			−0.458121	+	0.888890i	$0.651477\pi$
$992$	29.6383	+	36.3773i	0.941018	+	1.15498i
$993$			16.5118i			0.523987i
$994$	−1.27646	+	0.175632i	−0.0404870	+	0.00557070i
$995$		0			0
$996$	17.7319	−	4.97370i	0.561856	−	0.157598i
$997$	33.1449			1.04971			0.524855	−	0.851192i	$-0.324119\pi$
$997$	33.1449			1.04971			0.524855	+	0.851192i	$0.324119\pi$
$998$	−19.6872	+	2.70881i	−0.623189	+	0.0857460i
$999$	−2.67241			−0.0845513

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	600.2.d.g.349.6		8
3.2	odd	2		1800.2.d.t.1549.3		8
4.3	odd	2		2400.2.d.h.49.5		8
5.2	odd	4		600.2.k.e.301.2	yes	8
5.3	odd	4		600.2.k.d.301.7	✓	8
5.4	even	2		600.2.d.h.349.3		8
8.3	odd	2		2400.2.d.g.49.5		8
8.5	even	2		600.2.d.h.349.4		8
12.11	even	2		7200.2.d.t.2449.5		8
15.2	even	4		1800.2.k.q.901.7		8
15.8	even	4		1800.2.k.t.901.2		8
15.14	odd	2		1800.2.d.s.1549.6		8
20.3	even	4		2400.2.k.d.1201.7		8
20.7	even	4		2400.2.k.e.1201.2		8
20.19	odd	2		2400.2.d.g.49.4		8
24.5	odd	2		1800.2.d.s.1549.5		8
24.11	even	2		7200.2.d.s.2449.5		8
40.3	even	4		2400.2.k.d.1201.3		8
40.13	odd	4		600.2.k.d.301.8	yes	8
40.19	odd	2		2400.2.d.h.49.4		8
40.27	even	4		2400.2.k.e.1201.6		8
40.29	even	2	inner	600.2.d.g.349.5		8
40.37	odd	4		600.2.k.e.301.1	yes	8
60.23	odd	4		7200.2.k.r.3601.5		8
60.47	odd	4		7200.2.k.s.3601.3		8
60.59	even	2		7200.2.d.s.2449.4		8
120.29	odd	2		1800.2.d.t.1549.4		8
120.53	even	4		1800.2.k.t.901.1		8
120.59	even	2		7200.2.d.t.2449.4		8
120.77	even	4		1800.2.k.q.901.8		8
120.83	odd	4		7200.2.k.r.3601.6		8
120.107	odd	4		7200.2.k.s.3601.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
600.2.d.g.349.5		8	40.29	even	2	inner
600.2.d.g.349.6		8	1.1	even	1	trivial
600.2.d.h.349.3		8	5.4	even	2
600.2.d.h.349.4		8	8.5	even	2
600.2.k.d.301.7	✓	8	5.3	odd	4
600.2.k.d.301.8	yes	8	40.13	odd	4
600.2.k.e.301.1	yes	8	40.37	odd	4
600.2.k.e.301.2	yes	8	5.2	odd	4
1800.2.d.s.1549.5		8	24.5	odd	2
1800.2.d.s.1549.6		8	15.14	odd	2
1800.2.d.t.1549.3		8	3.2	odd	2
1800.2.d.t.1549.4		8	120.29	odd	2
1800.2.k.q.901.7		8	15.2	even	4
1800.2.k.q.901.8		8	120.77	even	4
1800.2.k.t.901.1		8	120.53	even	4
1800.2.k.t.901.2		8	15.8	even	4
2400.2.d.g.49.4		8	20.19	odd	2
2400.2.d.g.49.5		8	8.3	odd	2
2400.2.d.h.49.4		8	40.19	odd	2
2400.2.d.h.49.5		8	4.3	odd	2
2400.2.k.d.1201.3		8	40.3	even	4
2400.2.k.d.1201.7		8	20.3	even	4
2400.2.k.e.1201.2		8	20.7	even	4
2400.2.k.e.1201.6		8	40.27	even	4
7200.2.d.s.2449.4		8	60.59	even	2
7200.2.d.s.2449.5		8	24.11	even	2
7200.2.d.t.2449.4		8	120.59	even	2
7200.2.d.t.2449.5		8	12.11	even	2
7200.2.k.r.3601.5		8	60.23	odd	4
7200.2.k.r.3601.6		8	120.83	odd	4
7200.2.k.s.3601.3		8	60.47	odd	4
7200.2.k.s.3601.4		8	120.107	odd	4

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:	\( N \)	\(=\)	\( 600 = 2^{3} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	600.d (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.192769 + 1.40101i) q^{2} -1.00000 q^{3} +(-1.92568 + 0.540143i) q^{4} +(-0.192769 - 1.40101i) q^{6} -0.0802864i q^{7} +(-1.12796 - 2.59378i) q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(0.192769 + 1.40101i) q^{2} -1.00000 q^{3} +(-1.92568 + 0.540143i) q^{4} +(-0.192769 - 1.40101i) q^{6} -0.0802864i q^{7} +(-1.12796 - 2.59378i) q^{8} +1.00000 q^{9} -2.41649i q^{11} +(1.92568 - 0.540143i) q^{12} -5.26785 q^{13} +(0.112482 - 0.0154767i) q^{14} +(3.41649 - 2.08029i) q^{16} +0.255918i q^{17} +(0.192769 + 1.40101i) q^{18} -6.95864i q^{19} +0.0802864i q^{21} +(3.38554 - 0.465824i) q^{22} -1.64542i q^{23} +(1.12796 + 2.59378i) q^{24} +(-1.01548 - 7.38033i) q^{26} -1.00000 q^{27} +(0.0433661 + 0.154606i) q^{28} -4.51516i q^{29} +8.29484 q^{31} +(3.57310 + 4.38554i) q^{32} +2.41649i q^{33} +(-0.358545 + 0.0493330i) q^{34} +(-1.92568 + 0.540143i) q^{36} +2.67241 q^{37} +(9.74915 - 1.34141i) q^{38} +5.26785 q^{39} -8.11921 q^{41} +(-0.112482 + 0.0154767i) q^{42} +4.08890 q^{43} +(1.30525 + 4.65339i) q^{44} +(2.30525 - 0.317185i) q^{46} -5.70272i q^{47} +(-3.41649 + 2.08029i) q^{48} +6.99355 q^{49} -0.255918i q^{51} +(10.1442 - 2.84539i) q^{52} -11.5627 q^{53} +(-0.192769 - 1.40101i) q^{54} +(-0.208245 + 0.0905597i) q^{56} +6.95864i q^{57} +(6.32580 - 0.870381i) q^{58} -12.6963i q^{59} +11.9403i q^{61} +(1.59899 + 11.6212i) q^{62} -0.0802864i q^{63} +(-5.45542 + 5.85136i) q^{64} +(-3.38554 + 0.465824i) q^{66} -7.27979 q^{67} +(-0.138232 - 0.492816i) q^{68} +1.64542i q^{69} -11.3481 q^{71} +(-1.12796 - 2.59378i) q^{72} -12.0779i q^{73} +(0.515157 + 3.74408i) q^{74} +(3.75866 + 13.4001i) q^{76} -0.194011 q^{77} +(1.01548 + 7.38033i) q^{78} -5.50539 q^{79} +1.00000 q^{81} +(-1.56513 - 11.3751i) q^{82} +9.20811 q^{83} +(-0.0433661 - 0.154606i) q^{84} +(0.788212 + 5.72861i) q^{86} +4.51516i q^{87} +(-6.26785 + 2.72570i) q^{88} -11.9173 q^{89} +0.422937i q^{91} +(0.888760 + 3.16855i) q^{92} -8.29484 q^{93} +(7.98959 - 1.09931i) q^{94} +(-3.57310 - 4.38554i) q^{96} -8.50539i q^{97} +(1.34814 + 9.79807i) q^{98} -2.41649i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} - 8 q^{3} - 4 q^{4} + 2 q^{6} - 8 q^{8} + 8 q^{9}+O(q^{10}) \) 8 * q - 2 * q^2 - 8 * q^3 - 4 * q^4 + 2 * q^6 - 8 * q^8 + 8 * q^9	\( 8 q - 2 q^{2} - 8 q^{3} - 4 q^{4} + 2 q^{6} - 8 q^{8} + 8 q^{9} + 4 q^{12} + 6 q^{14} + 8 q^{16} - 2 q^{18} + 20 q^{22} + 8 q^{24} - 2 q^{26} - 8 q^{27} + 24 q^{28} + 8 q^{31} - 12 q^{32} - 12 q^{34} - 4 q^{36} + 14 q^{38} - 6 q^{42} - 8 q^{43} + 12 q^{44} + 20 q^{46} - 8 q^{48} + 24 q^{52} + 8 q^{53} + 2 q^{54} + 8 q^{56} - 20 q^{58} + 26 q^{62} + 32 q^{64} - 20 q^{66} + 24 q^{67} + 36 q^{68} - 40 q^{71} - 8 q^{72} - 8 q^{74} - 20 q^{76} - 24 q^{77} + 2 q^{78} + 16 q^{79} + 8 q^{81} - 16 q^{82} - 32 q^{83} - 24 q^{84} - 18 q^{86} - 8 q^{88} + 28 q^{92} - 8 q^{93} + 4 q^{94} + 12 q^{96} - 40 q^{98}+O(q^{100}) \) 8 * q - 2 * q^2 - 8 * q^3 - 4 * q^4 + 2 * q^6 - 8 * q^8 + 8 * q^9 + 4 * q^12 + 6 * q^14 + 8 * q^16 - 2 * q^18 + 20 * q^22 + 8 * q^24 - 2 * q^26 - 8 * q^27 + 24 * q^28 + 8 * q^31 - 12 * q^32 - 12 * q^34 - 4 * q^36 + 14 * q^38 - 6 * q^42 - 8 * q^43 + 12 * q^44 + 20 * q^46 - 8 * q^48 + 24 * q^52 + 8 * q^53 + 2 * q^54 + 8 * q^56 - 20 * q^58 + 26 * q^62 + 32 * q^64 - 20 * q^66 + 24 * q^67 + 36 * q^68 - 40 * q^71 - 8 * q^72 - 8 * q^74 - 20 * q^76 - 24 * q^77 + 2 * q^78 + 16 * q^79 + 8 * q^81 - 16 * q^82 - 32 * q^83 - 24 * q^84 - 18 * q^86 - 8 * q^88 + 28 * q^92 - 8 * q^93 + 4 * q^94 + 12 * q^96 - 40 * q^98

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