LMFDB - Embedded newform 600.2.k.e.301.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [600,2,Mod(301,600)]

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, 0]))

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

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

chi := DirichletCharacter("600.301");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 600 = 2^{3} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	600.k (of order $2$, degree $1$, 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:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			301.1
Root			$1.23291 + 0.692769i$ of defining polynomial
Character	$\chi$	$=$	600.301
Dual form			600.2.k.e.301.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.40101 - 0.192769i) q^{2} -1.00000i q^{3} +(1.92568 + 0.540143i) q^{4} +(-0.192769 + 1.40101i) q^{6} +0.0802864 q^{7} +(-2.59378 - 1.12796i) q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+(-1.40101 - 0.192769i) q^{2} -1.00000i q^{3} +(1.92568 + 0.540143i) q^{4} +(-0.192769 + 1.40101i) q^{6} +0.0802864 q^{7} +(-2.59378 - 1.12796i) q^{8} -1.00000 q^{9} +2.41649i q^{11} +(0.540143 - 1.92568i) q^{12} -5.26785i q^{13} +(-0.112482 - 0.0154767i) q^{14} +(3.41649 + 2.08029i) q^{16} -0.255918 q^{17} +(1.40101 + 0.192769i) q^{18} -6.95864i q^{19} -0.0802864i q^{21} +(0.465824 - 3.38554i) q^{22} -1.64542 q^{23} +(-1.12796 + 2.59378i) q^{24} +(-1.01548 + 7.38033i) q^{26} +1.00000i q^{27} +(0.154606 + 0.0433661i) q^{28} -4.51516i q^{29} +8.29484 q^{31} +(-4.38554 - 3.57310i) q^{32} +2.41649 q^{33} +(0.358545 + 0.0493330i) q^{34} +(-1.92568 - 0.540143i) q^{36} -2.67241i q^{37} +(-1.34141 + 9.74915i) q^{38} -5.26785 q^{39} -8.11921 q^{41} +(-0.0154767 + 0.112482i) q^{42} +4.08890i q^{43} +(-1.30525 + 4.65339i) q^{44} +(2.30525 + 0.317185i) q^{46} +5.70272 q^{47} +(2.08029 - 3.41649i) q^{48} -6.99355 q^{49} +0.255918i q^{51} +(2.84539 - 10.1442i) q^{52} -11.5627i q^{53} +(0.192769 - 1.40101i) q^{54} +(-0.208245 - 0.0905597i) q^{56} -6.95864 q^{57} +(-0.870381 + 6.32580i) q^{58} -12.6963i q^{59} -11.9403i q^{61} +(-11.6212 - 1.59899i) q^{62} -0.0802864 q^{63} +(5.45542 + 5.85136i) q^{64} +(-3.38554 - 0.465824i) q^{66} +7.27979i q^{67} +(-0.492816 - 0.138232i) q^{68} +1.64542i q^{69} -11.3481 q^{71} +(2.59378 + 1.12796i) q^{72} -12.0779 q^{73} +(-0.515157 + 3.74408i) q^{74} +(3.75866 - 13.4001i) q^{76} +0.194011i q^{77} +(7.38033 + 1.01548i) q^{78} +5.50539 q^{79} +1.00000 q^{81} +(11.3751 + 1.56513i) q^{82} +9.20811i q^{83} +(0.0433661 - 0.154606i) q^{84} +(0.788212 - 5.72861i) q^{86} -4.51516 q^{87} +(2.72570 - 6.26785i) q^{88} +11.9173 q^{89} -0.422937i q^{91} +(-3.16855 - 0.888760i) q^{92} -8.29484i q^{93} +(-7.98959 - 1.09931i) q^{94} +(-3.57310 + 4.38554i) q^{96} +8.50539 q^{97} +(9.79807 + 1.34814i) q^{98} -2.41649i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{2} + 4 q^{4} + 2 q^{6} - 8 q^{7} - 4 q^{8} - 8 q^{9}+O(q^{10}) $ 8 * q + 2 * q^2 + 4 * q^4 + 2 * q^6 - 8 * q^7 - 4 * q^8 - 8 * q^9	$ 8 q + 2 q^{2} + 4 q^{4} + 2 q^{6} - 8 q^{7} - 4 q^{8} - 8 q^{9} - 6 q^{14} + 8 q^{16} - 2 q^{18} - 12 q^{22} - 8 q^{23} - 8 q^{24} - 2 q^{26} + 4 q^{28} + 8 q^{31} - 28 q^{32} + 12 q^{34} - 4 q^{36} - 30 q^{38} + 6 q^{42} - 12 q^{44} + 20 q^{46} + 8 q^{48} + 20 q^{52} - 2 q^{54} + 8 q^{56} - 8 q^{57} - 12 q^{58} - 30 q^{62} + 8 q^{63} - 32 q^{64} - 20 q^{66} + 28 q^{68} - 40 q^{71} + 4 q^{72} + 16 q^{73} + 8 q^{74} - 20 q^{76} + 22 q^{78} - 16 q^{79} + 8 q^{81} + 24 q^{82} + 24 q^{84} - 18 q^{86} - 24 q^{87} + 8 q^{88} + 36 q^{92} - 4 q^{94} + 12 q^{96} + 8 q^{97} + 48 q^{98}+O(q^{100}) $ 8 * q + 2 * q^2 + 4 * q^4 + 2 * q^6 - 8 * q^7 - 4 * q^8 - 8 * q^9 - 6 * q^14 + 8 * q^16 - 2 * q^18 - 12 * q^22 - 8 * q^23 - 8 * q^24 - 2 * q^26 + 4 * q^28 + 8 * q^31 - 28 * q^32 + 12 * q^34 - 4 * q^36 - 30 * q^38 + 6 * q^42 - 12 * q^44 + 20 * q^46 + 8 * q^48 + 20 * q^52 - 2 * q^54 + 8 * q^56 - 8 * q^57 - 12 * q^58 - 30 * q^62 + 8 * q^63 - 32 * q^64 - 20 * q^66 + 28 * q^68 - 40 * q^71 + 4 * q^72 + 16 * q^73 + 8 * q^74 - 20 * q^76 + 22 * q^78 - 16 * q^79 + 8 * q^81 + 24 * q^82 + 24 * q^84 - 18 * q^86 - 24 * q^87 + 8 * q^88 + 36 * q^92 - 4 * q^94 + 12 * q^96 + 8 * q^97 + 48 * 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 $

$2$	−1.40101	−	0.192769i	−0.990667	−	0.136308i
$2$	−1.40101	−	0.192769i	−0.990667	−	0.136308i
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	1.92568	+	0.540143i	0.962840	+	0.270072i
$5$		0			0
$5$		0			0
$6$	−0.192769	+	1.40101i	−0.0786975	+	0.571962i
$7$	0.0802864			0.0303454			0.0151727	−	0.999885i	$-0.495170\pi$
$7$	0.0802864			0.0303454			0.0151727	+	0.999885i	$0.495170\pi$
$8$	−2.59378	−	1.12796i	−0.917041	−	0.398794i
$9$	−1.00000			−0.333333
$10$		0			0
$11$			2.41649i			0.728599i	0.931282	+	0.364300i	$0.118692\pi$
$11$			2.41649i			0.728599i	−0.931282	+	0.364300i	$0.881308\pi$
$12$	0.540143	−	1.92568i	0.155926	−	0.555896i
$13$		−	5.26785i		−	1.46104i	−0.682892	−	0.730520i	$-0.739278\pi$
$13$		−	5.26785i		−	1.46104i	0.682892	−	0.730520i	$-0.260722\pi$
$14$	−0.112482	−	0.0154767i	−0.0300622	−	0.00413632i
$15$		0			0
$16$	3.41649	+	2.08029i	0.854123	+	0.520072i
$17$	−0.255918			−0.0620692			−0.0310346	−	0.999518i	$-0.509880\pi$
$17$	−0.255918			−0.0620692			−0.0310346	+	0.999518i	$0.509880\pi$
$18$	1.40101	+	0.192769i	0.330222	+	0.0454360i
$19$		−	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
$22$	0.465824	−	3.38554i	0.0993139	−	0.721799i
$23$	−1.64542			−0.343093			−0.171546	−	0.985176i	$-0.554876\pi$
$23$	−1.64542			−0.343093			−0.171546	+	0.985176i	$0.554876\pi$
$24$	−1.12796	+	2.59378i	−0.230244	+	0.529454i
$25$		0			0
$26$	−1.01548	+	7.38033i	−0.199151	+	1.44740i
$27$			1.00000i			0.192450i
$28$	0.154606	+	0.0433661i	0.0292178	+	0.00819543i
$29$		−	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	$0.232498\pi$
$32$	−4.38554	−	3.57310i	−0.775261	−	0.631641i
$33$	2.41649			0.420657
$34$	0.358545	+	0.0493330i	0.0614899	+	0.00846053i
$35$		0			0
$36$	−1.92568	−	0.540143i	−0.320947	−	0.0900239i
$37$		−	2.67241i		−	0.439341i	−0.975574	−	0.219671i	$-0.929502\pi$
$37$		−	2.67241i		−	0.439341i	0.975574	−	0.219671i	$-0.0704983\pi$
$38$	−1.34141	+	9.74915i	−0.217605	+	1.58152i
$39$	−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	$0.718590\pi$
$42$	−0.0154767	+	0.112482i	−0.00238811	+	0.0173564i
$43$			4.08890i			0.623551i	0.950156	+	0.311776i	$0.100924\pi$
$43$			4.08890i			0.623551i	−0.950156	+	0.311776i	$0.899076\pi$
$44$	−1.30525	+	4.65339i	−0.196774	+	0.701525i
$45$		0			0
$46$	2.30525	+	0.317185i	0.339891	+	0.0467663i
$47$	5.70272			0.831827			0.415914	−	0.909404i	$-0.363462\pi$
$47$	5.70272			0.831827			0.415914	+	0.909404i	$0.363462\pi$
$48$	2.08029	−	3.41649i	0.300263	−	0.493128i
$49$	−6.99355			−0.999079
$50$		0			0
$51$			0.255918i			0.0358357i
$52$	2.84539	−	10.1442i	0.394585	−	1.40675i
$53$		−	11.5627i		−	1.58826i	−0.607749	−	0.794129i	$-0.707927\pi$
$53$		−	11.5627i		−	1.58826i	0.607749	−	0.794129i	$-0.292073\pi$
$54$	0.192769	−	1.40101i	0.0262325	−	0.190654i
$55$		0			0
$56$	−0.208245	−	0.0905597i	−0.0278280	−	0.0121016i
$57$	−6.95864			−0.921694
$58$	−0.870381	+	6.32580i	−0.114287	+	0.830618i
$59$		−	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	$-0.723037\pi$
$61$		−	11.9403i		−	1.52879i	0.644746	−	0.764397i	$-0.276963\pi$
$62$	−11.6212	−	1.59899i	−1.47589	−	0.203071i
$63$	−0.0802864			−0.0101151
$64$	5.45542	+	5.85136i	0.681927	+	0.731420i
$65$		0			0
$66$	−3.38554	−	0.465824i	−0.416731	−	0.0573389i
$67$			7.27979i			0.889367i	0.895688	+	0.444684i	$0.146684\pi$
$67$			7.27979i			0.889367i	−0.895688	+	0.444684i	$0.853316\pi$
$68$	−0.492816	−	0.138232i	−0.0597628	−	0.0167631i
$69$			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	$0.735162\pi$
$72$	2.59378	+	1.12796i	0.305680	+	0.132931i
$73$	−12.0779			−1.41361			−0.706803	−	0.707411i	$-0.749863\pi$
$73$	−12.0779			−1.41361			−0.706803	+	0.707411i	$0.749863\pi$
$74$	−0.515157	+	3.74408i	−0.0598857	+	0.435241i
$75$		0			0
$76$	3.75866	−	13.4001i	0.431148	−	1.53710i
$77$			0.194011i			0.0221096i
$78$	7.38033	+	1.01548i	0.835658	+	0.114980i
$79$	5.50539			0.619405			0.309702	−	0.950834i	$-0.399771\pi$
$79$	5.50539			0.619405			0.309702	+	0.950834i	$0.399771\pi$
$80$		0			0
$81$	1.00000			0.111111
$82$	11.3751	+	1.56513i	1.25617	+	0.172840i
$83$			9.20811i			1.01072i	0.862908	+	0.505361i	$0.168641\pi$
$83$			9.20811i			1.01072i	−0.862908	+	0.505361i	$0.831359\pi$
$84$	0.0433661	−	0.154606i	0.00473163	−	0.0168689i
$85$		0			0
$86$	0.788212	−	5.72861i	0.0849950	−	0.617731i
$87$	−4.51516			−0.484076
$88$	2.72570	−	6.26785i	0.290561	−	0.668155i
$89$	11.9173			1.26323			0.631615	−	0.775283i	$-0.282393\pi$
$89$	11.9173			1.26323			0.631615	+	0.775283i	$0.282393\pi$
$90$		0			0
$91$		−	0.422937i		−	0.0443358i
$92$	−3.16855	−	0.888760i	−0.330344	−	0.0926597i
$93$		−	8.29484i		−	0.860135i
$94$	−7.98959	−	1.09931i	−0.824064	−	0.113385i
$95$		0			0
$96$	−3.57310	+	4.38554i	−0.364678	+	0.447597i
$97$	8.50539			0.863592			0.431796	−	0.901971i	$-0.357880\pi$
$97$	8.50539			0.863592			0.431796	+	0.901971i	$0.357880\pi$
$98$	9.79807	+	1.34814i	0.989754	+	0.136183i
$99$		−	2.41649i		−	0.242866i
$100$		0			0
$101$		−	7.56270i		−	0.752516i	−0.926515	−	0.376258i	$-0.877211\pi$
$101$		−	7.56270i		−	0.752516i	0.926515	−	0.376258i	$-0.122789\pi$
$102$	0.0493330	−	0.358545i	0.00488469	−	0.0355012i
$103$	−1.78544			−0.175925			−0.0879624	−	0.996124i	$-0.528036\pi$
$103$	−1.78544			−0.175925			−0.0879624	+	0.996124i	$0.528036\pi$
$104$	−5.94192	+	13.6637i	−0.582653	+	1.33983i
$105$		0			0
$106$	−2.22893	+	16.1995i	−0.216492	+	1.57343i
$107$			10.4705i			1.01222i	0.862469	+	0.506110i	$0.168917\pi$
$107$			10.4705i			1.01222i	−0.862469	+	0.506110i	$0.831083\pi$
$108$	−0.540143	+	1.92568i	−0.0519753	+	0.185299i
$109$			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
$112$	0.274298	+	0.167019i	0.0259187	+	0.0157818i
$113$	8.83298			0.830937			0.415468	−	0.909608i	$-0.363618\pi$
$113$	8.83298			0.830937			0.415468	+	0.909608i	$0.363618\pi$
$114$	9.74915	+	1.34141i	0.913092	+	0.125634i
$115$		0			0
$116$	2.43883	−	8.69475i	0.226440	−	0.807287i
$117$			5.26785i			0.487013i
$118$	−2.44744	+	17.7877i	−0.225305	+	1.63749i
$119$	−0.0205467			−0.00188351
$120$		0			0
$121$	5.16057			0.469143
$122$	−2.30171	+	16.7285i	−0.208387	+	1.51452i
$123$			8.11921i			0.732085i
$124$	15.9732	+	4.48040i	1.43444	+	0.402352i
$125$		0			0
$126$	0.112482	+	0.0154767i	0.0100207	+	0.00137877i
$127$	−8.69628			−0.771670			−0.385835	−	0.922568i	$-0.626087\pi$
$127$	−8.69628			−0.771670			−0.385835	+	0.922568i	$0.626087\pi$
$128$	−6.51516	−	9.24947i	−0.575864	−	0.817546i
$129$	4.08890			0.360008
$130$		0			0
$131$			10.7916i			0.942868i	0.881901	+	0.471434i	$0.156264\pi$
$131$			10.7916i			0.942868i	−0.881901	+	0.471434i	$0.843736\pi$
$132$	4.65339	+	1.30525i	0.405026	+	0.113608i
$133$		−	0.558684i		−	0.0484440i
$134$	1.40331	−	10.1991i	0.121228	−	0.881066i
$135$		0			0
$136$	0.663796	+	0.288665i	0.0569200	+	0.0247528i
$137$	11.5421			0.986112			0.493056	−	0.869997i	$-0.335880\pi$
$137$	11.5421			0.986112			0.493056	+	0.869997i	$0.335880\pi$
$138$	0.317185	−	2.30525i	0.0270006	−	0.196236i
$139$		−	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
$142$	15.8989	+	2.18757i	1.33421	+	0.183576i
$143$	12.7297			1.06451
$144$	−3.41649	−	2.08029i	−0.284708	−	0.173357i
$145$		0			0
$146$	16.9212	+	2.32823i	1.40041	+	0.192686i
$147$			6.99355i			0.576819i
$148$	1.44348	−	5.14621i	0.118654	−	0.423015i
$149$			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	$0.373867\pi$
$152$	−7.84906	+	18.0492i	−0.636643	+	1.46398i
$153$	0.255918			0.0206897
$154$	0.0373993	−	0.271812i	0.00301372	−	0.0219033i
$155$		0			0
$156$	−10.1442	−	2.84539i	−0.812186	−	0.227814i
$157$			6.34413i			0.506316i	0.967425	+	0.253158i	$0.0814693\pi$
$157$			6.34413i			0.506316i	−0.967425	+	0.253158i	$0.918531\pi$
$158$	−7.71313	−	1.06127i	−0.613624	−	0.0844298i
$159$	−11.5627			−0.916981
$160$		0			0
$161$	−0.132104			−0.0104113
$162$	−1.40101	−	0.192769i	−0.110074	−	0.0151453i
$163$			12.4100i			0.972030i	0.873951	+	0.486015i	$0.161550\pi$
$163$			12.4100i			0.972030i	−0.873951	+	0.486015i	$0.838450\pi$
$164$	−15.6350	−	4.38554i	−1.22089	−	0.342453i
$165$		0			0
$166$	1.77504	−	12.9007i	0.137769	−	1.00129i
$167$	23.2654			1.80033			0.900166	−	0.435547i	$-0.143445\pi$
$167$	23.2654			1.80033			0.900166	+	0.435547i	$0.143445\pi$
$168$	−0.0905597	+	0.208245i	−0.00698683	+	0.0160665i
$169$	−14.7503			−1.13464
$170$		0			0
$171$			6.95864i			0.532140i
$172$	−2.20859	+	7.87391i	−0.168403	+	0.600380i
$173$		−	8.63897i		−	0.656809i	−0.944537	−	0.328404i	$-0.893489\pi$
$173$		−	8.63897i		−	0.656809i	0.944537	−	0.328404i	$-0.106511\pi$
$174$	6.32580	+	0.870381i	0.479557	+	0.0659834i
$175$		0			0
$176$	−5.02699	+	8.25592i	−0.378924	+	0.622313i
$177$	−12.6963			−0.954311
$178$	−16.6963	−	2.29728i	−1.25144	−	0.172188i
$179$			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	$0.0768688\pi$
$181$			6.43487i			0.478300i	−0.970983	+	0.239150i	$0.923131\pi$
$182$	−0.0815289	+	0.592540i	−0.00604333	+	0.0439220i
$183$	−11.9403			−0.882649
$184$	4.26785	+	1.85596i	0.314630	+	0.136823i
$185$		0			0
$186$	−1.59899	+	11.6212i	−0.117243	+	0.852107i
$187$		−	0.618423i		−	0.0452236i
$188$	10.9816	+	3.08029i	0.800917	+	0.224653i
$189$			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	$0.564501\pi$
$192$	5.85136	−	5.45542i	0.422286	−	0.393711i
$193$	−18.4227			−1.32609			−0.663046	−	0.748578i	$-0.730737\pi$
$193$	−18.4227			−1.32609			−0.663046	+	0.748578i	$0.730737\pi$
$194$	−11.9162	−	1.63957i	−0.855531	−	0.117714i
$195$		0			0
$196$	−13.4674	−	3.77752i	−0.961954	−	0.269823i
$197$		−	18.0239i		−	1.28415i	−0.766643	−	0.642074i	$-0.778074\pi$
$197$		−	18.0239i		−	1.28415i	0.766643	−	0.642074i	$-0.221926\pi$
$198$	−0.465824	+	3.38554i	−0.0331046	+	0.240600i
$199$	20.1214			1.42637			0.713183	−	0.700977i	$-0.247253\pi$
$199$	20.1214			1.42637			0.713183	+	0.700977i	$0.247253\pi$
$200$		0			0
$201$	7.27979			0.513476
$202$	−1.45785	+	10.5954i	−0.102574	+	0.745493i
$203$		−	0.362505i		−	0.0254429i
$204$	−0.138232	+	0.492816i	−0.00967820	+	0.0345040i
$205$		0			0
$206$	2.50143	+	0.344177i	0.174283	+	0.0239800i
$207$	1.64542			0.114364
$208$	10.9586	−	17.9976i	0.759845	−	1.24791i
$209$	16.8155			1.16315
$210$		0			0
$211$			3.25592i			0.224147i	0.993700	+	0.112073i	$0.0357492\pi$
$211$			3.25592i			0.224147i	−0.993700	+	0.112073i	$0.964251\pi$
$212$	6.24551	−	22.2661i	0.428943	−	1.52924i
$213$			11.3481i			0.777562i
$214$	2.01838	−	14.6693i	0.137974	−	1.00277i
$215$		0			0
$216$	1.12796	−	2.59378i	0.0767479	−	0.176485i
$217$	0.665963			0.0452085
$218$	0.702253	−	5.10387i	0.0475626	−	0.345678i
$219$			12.0779i			0.816146i
$220$		0			0
$221$			1.34814i			0.0906856i
$222$	3.74408	+	0.515157i	0.251286	+	0.0345750i
$223$	26.9911			1.80746			0.903730	−	0.428104i	$-0.140818\pi$
$223$	26.9911			1.80746			0.903730	+	0.428104i	$0.140818\pi$
$224$	−0.352099	−	0.286871i	−0.0235256	−	0.0191674i
$225$		0			0
$226$	−12.3751	−	1.70272i	−0.823181	−	0.113263i
$227$		−	19.8219i		−	1.31563i	−0.753180	−	0.657814i	$-0.771481\pi$
$227$		−	19.8219i		−	1.31563i	0.753180	−	0.657814i	$-0.228519\pi$
$228$	−13.4001	−	3.75866i	−0.887444	−	0.248923i
$229$			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
$232$	−5.09291	+	11.7113i	−0.334366	+	0.768887i
$233$	17.2733			1.13161			0.565807	−	0.824538i	$-0.308565\pi$
$233$	17.2733			1.13161			0.565807	+	0.824538i	$0.308565\pi$
$234$	1.01548	−	7.38033i	0.0663838	−	0.482468i
$235$		0			0
$236$	6.85781	−	24.4490i	0.446405	−	1.59149i
$237$		−	5.50539i		−	0.357614i
$238$	0.0287862	+	0.00396076i	0.00186594	+	0.000256738i
$239$	−16.3718			−1.05900			−0.529502	−	0.848309i	$-0.677621\pi$
$239$	−16.3718			−1.05900			−0.529502	+	0.848309i	$0.677621\pi$
$240$		0			0
$241$	−6.82654			−0.439736			−0.219868	−	0.975530i	$-0.570563\pi$
$241$	−6.82654			−0.439736			−0.219868	+	0.975530i	$0.570563\pi$
$242$	−7.23003	−	0.994797i	−0.464764	−	0.0639480i
$243$		−	1.00000i		−	0.0641500i
$244$	6.44945	−	22.9931i	0.412884	−	1.47198i
$245$		0			0
$246$	1.56513	−	11.3751i	0.0997890	−	0.725252i
$247$	−36.6571			−2.33243
$248$	−21.5150	−	9.35624i	−1.36621	−	0.594122i
$249$	9.20811			0.583540
$250$		0			0
$251$		−	2.96969i		−	0.187445i	−0.995598	−	0.0937225i	$-0.970123\pi$
$251$		−	2.96969i		−	0.187445i	0.995598	−	0.0937225i	$-0.0298766\pi$
$252$	−0.154606	−	0.0433661i	−0.00973925	−	0.00273181i
$253$		−	3.97613i		−	0.249977i
$254$	12.1836	+	1.67637i	0.764467	+	0.105185i
$255$		0			0
$256$	7.34482	+	14.2146i	0.459051	+	0.888410i
$257$	5.03031			0.313782			0.156891	−	0.987616i	$-0.449853\pi$
$257$	5.03031			0.313782			0.156891	+	0.987616i	$0.449853\pi$
$258$	−5.72861	−	0.788212i	−0.356647	−	0.0490719i
$259$		−	0.214558i		−	0.0133320i
$260$		0			0
$261$			4.51516i			0.279481i
$262$	2.08029	−	15.1192i	0.128521	−	0.934068i
$263$	−2.70585			−0.166850			−0.0834248	−	0.996514i	$-0.526586\pi$
$263$	−2.70585			−0.166850			−0.0834248	+	0.996514i	$0.526586\pi$
$264$	−6.26785	−	2.72570i	−0.385760	−	0.167755i
$265$		0			0
$266$	−0.107697	+	0.782724i	−0.00660331	+	0.0479919i
$267$		−	11.9173i		−	0.729326i
$268$	−3.93213	+	14.0185i	−0.240193	+	0.856319i
$269$		−	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	$0.508410\pi$
$272$	−0.874341	−	0.532383i	−0.0530147	−	0.0322804i
$273$	−0.422937			−0.0255973
$274$	−16.1707	−	2.22496i	−0.976908	−	0.134415i
$275$		0			0
$276$	−0.888760	+	3.16855i	−0.0534971	+	0.190724i
$277$		−	28.6733i		−	1.72281i	−0.507918	−	0.861406i	$-0.669585\pi$
$277$		−	28.6733i		−	1.72281i	0.507918	−	0.861406i	$-0.330415\pi$
$278$	−0.0413600	+	0.300599i	−0.00248061	+	0.0180287i
$279$	−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	$0.350827\pi$
$282$	−1.09931	+	7.98959i	−0.0654627	+	0.475773i
$283$			6.23225i			0.370469i	0.982694	+	0.185234i	$0.0593044\pi$
$283$			6.23225i			0.370469i	−0.982694	+	0.185234i	$0.940696\pi$
$284$	−21.8529	−	6.12962i	−1.29673	−	0.363726i
$285$		0			0
$286$	−17.8345	−	2.45389i	−1.05458	−	0.145102i
$287$	−0.651862			−0.0384782
$288$	4.38554	+	3.57310i	0.258420	+	0.210547i
$289$	−16.9345			−0.996147
$290$		0			0
$291$		−	8.50539i		−	0.498595i
$292$	−23.2581	−	6.52377i	−1.36108	−	0.381775i
$293$			21.5054i			1.25636i	0.778069	+	0.628179i	$0.216200\pi$
$293$			21.5054i			1.25636i	−0.778069	+	0.628179i	$0.783800\pi$
$294$	1.34814	−	9.79807i	0.0786250	−	0.571435i
$295$		0			0
$296$	−3.01437	+	6.93165i	−0.175207	+	0.402894i
$297$	−2.41649			−0.140219
$298$	4.44284	−	32.2899i	0.257367	−	1.87051i
$299$			8.66781i			0.501272i
$300$		0			0
$301$			0.328283i			0.0189219i
$302$	−13.2896	−	1.82855i	−0.764733	−	0.105221i
$303$	−7.56270			−0.434466
$304$	14.4760	−	23.7741i	0.830253	−	1.36354i
$305$		0			0
$306$	−0.358545	−	0.0493330i	−0.0204966	−	0.00282018i
$307$		−	3.57706i		−	0.204154i	−0.994777	−	0.102077i	$-0.967451\pi$
$307$		−	3.57706i		−	0.204154i	0.994777	−	0.102077i	$-0.0325488\pi$
$308$	−0.104794	+	0.373604i	−0.00597118	+	0.0212880i
$309$			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	$0.522532\pi$
$312$	13.6637	+	5.94192i	0.773553	+	0.336395i
$313$	9.57246			0.541068			0.270534	−	0.962710i	$-0.412800\pi$
$313$	9.57246			0.541068			0.270534	+	0.962710i	$0.412800\pi$
$314$	1.22295	−	8.88821i	0.0690150	−	0.501591i
$315$		0			0
$316$	10.6016	+	2.97370i	0.596388	+	0.167284i
$317$			3.16702i			0.177877i	0.996037	+	0.0889387i	$0.0283475\pi$
$317$			3.16702i			0.177877i	−0.996037	+	0.0889387i	$0.971652\pi$
$318$	16.1995	+	2.22893i	0.908423	+	0.124992i
$319$	10.9108			0.610889
$320$		0			0
$321$	10.4705			0.584405
$322$	0.185080	+	0.0254656i	0.0103141	+	0.00141914i
$323$			1.78084i			0.0990887i
$324$	1.92568	+	0.540143i	0.106982	+	0.0300080i
$325$		0			0
$326$	2.39227	−	17.3866i	0.132495	−	0.962957i
$327$	3.64298			0.201457
$328$	21.0595	+	9.15814i	1.16281	+	0.505674i
$329$	0.457851			0.0252421
$330$		0			0
$331$			16.5118i			0.907573i	0.891111	+	0.453786i	$0.149927\pi$
$331$			16.5118i			0.907573i	−0.891111	+	0.453786i	$0.850073\pi$
$332$	−4.97370	+	17.7319i	−0.272967	+	0.973163i
$333$			2.67241i			0.146447i
$334$	−32.5952	−	4.48484i	−1.78353	−	0.245400i
$335$		0			0
$336$	0.167019	−	0.274298i	0.00911161	−	0.0149642i
$337$	−11.8330			−0.644584			−0.322292	−	0.946640i	$-0.604453\pi$
$337$	−11.8330			−0.644584			−0.322292	+	0.946640i	$0.604453\pi$
$338$	20.6653	+	2.84339i	1.12405	+	0.154660i
$339$		−	8.83298i		−	0.479742i
$340$		0			0
$341$			20.0444i			1.08547i
$342$	1.34141	−	9.74915i	0.0725350	−	0.527174i
$343$	−1.12349			−0.0606628
$344$	4.61211	−	10.6057i	0.248668	−	0.571822i
$345$		0			0
$346$	−1.66532	+	12.1033i	−0.0895283	+	0.650678i
$347$		−	23.9713i		−	1.28684i	−0.765511	−	0.643422i	$-0.777514\pi$
$347$		−	23.9713i		−	1.28684i	0.765511	−	0.643422i	$-0.222486\pi$
$348$	−8.69475	−	2.43883i	−0.466087	−	0.130735i
$349$		−	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
$352$	8.63437	−	10.5976i	0.460213	−	0.564855i
$353$	−7.35606			−0.391524			−0.195762	−	0.980651i	$-0.562718\pi$
$353$	−7.35606			−0.391524			−0.195762	+	0.980651i	$0.562718\pi$
$354$	17.7877	+	2.44744i	0.945403	+	0.130080i
$355$		0			0
$356$	22.9489	+	6.43704i	1.21629	+	0.341162i
$357$			0.0205467i			0.00108745i
$358$	1.81307	−	13.1772i	0.0958240	−	0.696434i
$359$	25.2114			1.33061			0.665304	−	0.746572i	$-0.268302\pi$
$359$	25.2114			1.33061			0.665304	+	0.746572i	$0.268302\pi$
$360$		0			0
$361$	−29.4227			−1.54856
$362$	1.24044	−	9.01534i	0.0651961	−	0.473836i
$363$		−	5.16057i		−	0.270860i
$364$	0.228446	−	0.814441i	0.0119738	−	0.0426883i
$365$		0			0
$366$	16.7285	+	2.30171i	0.874411	+	0.120312i
$367$	5.86573			0.306189			0.153094	−	0.988212i	$-0.451076\pi$
$367$	5.86573			0.306189			0.153094	+	0.988212i	$0.451076\pi$
$368$	−5.62155	−	3.42294i	−0.293043	−	0.178433i
$369$	8.11921			0.422669
$370$		0			0
$371$		−	0.928327i		−	0.0481963i
$372$	4.48040	−	15.9732i	0.232298	−	0.828173i
$373$			27.5063i			1.42422i	0.702067	+	0.712111i	$0.252261\pi$
$373$			27.5063i			1.42422i	−0.702067	+	0.712111i	$0.747739\pi$
$374$	−0.119213	+	0.866420i	−0.00616434	+	0.0448015i
$375$		0			0
$376$	−14.7916	−	6.43244i	−0.762820	−	0.331728i
$377$	−23.7852			−1.22500
$378$	0.0154767	−	0.112482i	0.000796035	−	0.00578547i
$379$			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
$382$	7.79341	+	1.07231i	0.398746	+	0.0548643i
$383$	−34.3335			−1.75436			−0.877180	−	0.480162i	$-0.840578\pi$
$383$	−34.3335			−1.75436			−0.877180	+	0.480162i	$0.840578\pi$
$384$	−9.24947	+	6.51516i	−0.472010	+	0.332475i
$385$		0			0
$386$	25.8104	+	3.55131i	1.31372	+	0.180757i
$387$		−	4.08890i		−	0.207850i
$388$	16.3787	+	4.59413i	0.831501	+	0.233232i
$389$			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
$392$	18.1398	+	7.88844i	0.916196	+	0.398427i
$393$	10.7916			0.544365
$394$	−3.47444	+	25.2517i	−0.175040	+	1.27216i
$395$		0			0
$396$	1.30525	−	4.65339i	0.0655913	−	0.233842i
$397$			22.9099i			1.14982i	0.818218	+	0.574909i	$0.194962\pi$
$397$			22.9099i			1.14982i	−0.818218	+	0.574909i	$0.805038\pi$
$398$	−28.1903	−	3.87877i	−1.41305	−	0.194425i
$399$	−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	$0.600481\pi$
$402$	−10.1991	−	1.40331i	−0.508684	−	0.0699910i
$403$		−	43.6960i		−	2.17665i
$404$	4.08494	−	14.5633i	0.203233	−	0.724553i
$405$		0			0
$406$	−0.0698797	+	0.507875i	−0.00346807	+	0.0252054i
$407$	6.45785			0.320104
$408$	0.288665	−	0.663796i	0.0142910	−	0.0328628i
$409$	−32.0886			−1.58668			−0.793340	−	0.608778i	$-0.791660\pi$
$409$	−32.0886			−1.58668			−0.793340	+	0.608778i	$0.791660\pi$
$410$		0			0
$411$		−	11.5421i		−	0.569332i
$412$	−3.43819	−	0.964394i	−0.169388	−	0.0475123i
$413$		−	1.01934i		−	0.0501583i
$414$	−2.30525	−	0.317185i	−0.113297	−	0.0155888i
$415$		0			0
$416$	−18.8226	+	23.1024i	−0.922853	+	1.13269i
$417$	−0.214558			−0.0105069
$418$	−23.5587	−	3.24150i	−1.15230	−	0.158547i
$419$			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	$0.247272\pi$
$421$			28.7675i			1.40204i	−0.713141	+	0.701021i	$0.752728\pi$
$422$	0.627639	−	4.56159i	0.0305530	−	0.222055i
$423$	−5.70272			−0.277276
$424$	−13.0422	+	29.9911i	−0.633388	+	1.45650i
$425$		0			0
$426$	2.18757	−	15.8989i	0.105988	−	0.770304i
$427$		−	0.958640i		−	0.0463918i
$428$	−5.65556	+	20.1628i	−0.273372	+	0.974605i
$429$		−	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	$0.296917\pi$
$432$	−2.08029	+	3.41649i	−0.100088	+	0.164376i
$433$	−4.48816			−0.215687			−0.107844	−	0.994168i	$-0.534395\pi$
$433$	−4.48816			−0.215687			−0.107844	+	0.994168i	$0.534395\pi$
$434$	−0.933023	−	0.128377i	−0.0447865	−	0.00616228i
$435$		0			0
$436$	−1.96773	+	7.01522i	−0.0942373	+	0.335968i
$437$			11.4499i			0.547721i
$438$	2.32823	−	16.9212i	0.111247	−	0.808528i
$439$	5.96081			0.284494			0.142247	−	0.989831i	$-0.454567\pi$
$439$	5.96081			0.284494			0.142247	+	0.989831i	$0.454567\pi$
$440$		0			0
$441$	6.99355			0.333026
$442$	0.259879	−	1.88876i	0.0123612	−	0.0898392i
$443$		−	14.2924i		−	0.679053i	−0.940597	−	0.339526i	$-0.889733\pi$
$443$		−	14.2924i		−	0.679053i	0.940597	−	0.339526i	$-0.110267\pi$
$444$	−5.14621	−	1.44348i	−0.244228	−	0.0685047i
$445$		0			0
$446$	−37.8149	−	5.20304i	−1.79059	−	0.246371i
$447$	23.0475			1.09011
$448$	0.437996	+	0.469784i	0.0206933	+	0.0221952i
$449$	24.5529			1.15872			0.579362	−	0.815070i	$-0.303302\pi$
$449$	24.5529			1.15872			0.579362	+	0.815070i	$0.303302\pi$
$450$		0			0
$451$		−	19.6200i		−	0.923870i
$452$	17.0095	+	4.77107i	0.800060	+	0.224412i
$453$		−	9.48573i		−	0.445678i
$454$	−3.82105	+	27.7708i	−0.179331	+	1.30335i
$455$		0			0
$456$	18.0492	+	7.84906i	0.845231	+	0.367566i
$457$	28.9108			1.35239			0.676196	−	0.736722i	$-0.263627\pi$
$457$	28.9108			1.35239			0.676196	+	0.736722i	$0.263627\pi$
$458$	4.17917	−	30.3736i	0.195280	−	1.41927i
$459$		−	0.255918i		−	0.0119452i
$460$		0			0
$461$		−	4.35458i		−	0.202813i	−0.994845	−	0.101407i	$-0.967666\pi$
$461$		−	4.35458i		−	0.202813i	0.994845	−	0.101407i	$-0.0323343\pi$
$462$	−0.271812	−	0.0373993i	−0.0126459	−	0.00173997i
$463$	11.1303			0.517267			0.258634	−	0.965976i	$-0.416728\pi$
$463$	11.1303			0.517267			0.258634	+	0.965976i	$0.416728\pi$
$464$	9.39282	−	15.4260i	0.436051	−	0.716134i
$465$		0			0
$466$	−24.2002	−	3.32976i	−1.12105	−	0.154248i
$467$			19.1257i			0.885030i	0.896761	+	0.442515i	$0.145914\pi$
$467$			19.1257i			0.885030i	−0.896761	+	0.442515i	$0.854086\pi$
$468$	−2.84539	+	10.1442i	−0.131528	+	0.468916i
$469$			0.584467i			0.0269882i
$470$		0			0
$471$	6.34413			0.292322
$472$	−14.3209	+	32.9314i	−0.659172	+	1.51579i
$473$	−9.88079			−0.454319
$474$	−1.06127	+	7.71313i	−0.0487456	+	0.354276i
$475$		0			0
$476$	−0.0395664	−	0.0110982i	−0.00181352	−	0.000508684i
$477$			11.5627i			0.529419i
$478$	22.9371	+	3.15597i	1.04912	+	0.144351i
$479$	−25.6358			−1.17133			−0.585666	−	0.810553i	$-0.699167\pi$
$479$	−25.6358			−1.17133			−0.585666	+	0.810553i	$0.699167\pi$
$480$		0			0
$481$	−14.0779			−0.641895
$482$	9.56407	+	1.31594i	0.435632	+	0.0599395i
$483$			0.132104i			0.00601096i
$484$	9.93761	+	2.78745i	0.451710	+	0.126702i
$485$		0			0
$486$	−0.192769	+	1.40101i	−0.00874416	+	0.0635513i
$487$	−12.8434			−0.581992			−0.290996	−	0.956724i	$-0.593987\pi$
$487$	−12.8434			−0.581992			−0.290996	+	0.956724i	$0.593987\pi$
$488$	−13.4681	+	30.9704i	−0.609673	+	1.40197i
$489$	12.4100			0.561202
$490$		0			0
$491$		−	16.9887i		−	0.766689i	−0.923605	−	0.383344i	$-0.874772\pi$
$491$		−	16.9887i		−	0.766689i	0.923605	−	0.383344i	$-0.125228\pi$
$492$	−4.38554	+	15.6350i	−0.197715	+	0.704881i
$493$			1.15551i			0.0520415i
$494$	51.3571	+	7.06634i	2.31066	+	0.317930i
$495$		0			0
$496$	28.3393	+	17.2557i	1.27247	+	0.774802i
$497$	−0.911101			−0.0408684
$498$	−12.9007	−	1.77504i	−0.578094	−	0.0795412i
$499$			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
$502$	−0.572463	+	4.16057i	−0.0255503	+	0.185695i
$503$	−9.53258			−0.425037			−0.212518	−	0.977157i	$-0.568167\pi$
$503$	−9.53258			−0.425037			−0.212518	+	0.977157i	$0.568167\pi$
$504$	0.208245	+	0.0905597i	0.00927599	+	0.00403385i
$505$		0			0
$506$	−0.766474	+	5.57062i	−0.0340739	+	0.247644i
$507$			14.7503i			0.655082i
$508$	−16.7462	−	4.69723i	−0.742995	−	0.208406i
$509$		−	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
$512$	−7.55007	−	21.3306i	−0.333669	−	0.942690i
$513$	6.95864			0.307231
$514$	−7.04754	−	0.969687i	−0.310854	−	0.0427710i
$515$		0			0
$516$	7.87391	+	2.20859i	0.346630	+	0.0972278i
$517$			13.7806i			0.606069i
$518$	−0.0413600	+	0.300599i	−0.00181726	+	0.0132075i
$519$	−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	$0.397669\pi$
$522$	0.870381	−	6.32580i	0.0380955	−	0.276873i
$523$		−	28.2207i		−	1.23401i	−0.786961	−	0.617003i	$-0.788346\pi$
$523$		−	28.2207i		−	1.23401i	0.786961	−	0.617003i	$-0.211654\pi$
$524$	−5.82902	+	20.7812i	−0.254642	+	0.907832i
$525$		0			0
$526$	3.79093	+	0.521603i	0.165292	+	0.0227430i
$527$	−2.12280			−0.0924706
$528$	8.25592	+	5.02699i	0.359293	+	0.218772i
$529$	−20.2926			−0.882287
$530$		0			0
$531$			12.6963i			0.550971i
$532$	0.301769	−	1.07585i	0.0130834	−	0.0466439i
$533$			42.7708i			1.85261i
$534$	−2.29728	+	16.6963i	−0.0994129	+	0.722519i
$535$		0			0
$536$	8.21130	−	18.8822i	0.354674	−	0.815586i
$537$	9.40544			0.405875
$538$	−4.31258	+	31.3432i	−0.185929	+	1.35130i
$539$		−	16.8999i		−	0.727928i
$540$		0			0
$541$			13.4695i			0.579100i	0.957163	+	0.289550i	$0.0935056\pi$
$541$			13.4695i			0.579100i	−0.957163	+	0.289550i	$0.906494\pi$
$542$	1.21852	+	0.167659i	0.0523399	+	0.00720156i
$543$	6.43487			0.276147
$544$	1.12234	+	0.914421i	0.0481198	+	0.0392055i
$545$		0			0
$546$	0.592540	+	0.0815289i	0.0253584	+	0.00348912i
$547$		−	4.42773i		−	0.189316i	−0.995510	−	0.0946581i	$-0.969824\pi$
$547$		−	4.42773i		−	0.189316i	0.995510	−	0.0946581i	$-0.0301758\pi$
$548$	22.2265	+	6.23441i	0.949469	+	0.266321i
$549$			11.9403i			0.509598i
$550$		0			0
$551$	−31.4193			−1.33851
$552$	1.85596	−	4.26785i	0.0789950	−	0.181652i
$553$	0.442008			0.0187961
$554$	−5.52731	+	40.1717i	−0.234833	+	1.70673i
$555$		0			0
$556$	0.115892	−	0.413170i	0.00491492	−	0.0175223i
$557$			40.2017i			1.70340i	0.524030	+	0.851700i	$0.324428\pi$
$557$			40.2017i			1.70340i	−0.524030	+	0.851700i	$0.675572\pi$
$558$	11.6212	+	1.59899i	0.491964	+	0.0676905i
$559$	21.5397			0.911033
$560$		0			0
$561$	−0.618423			−0.0261099
$562$	−21.2154	−	2.91907i	−0.894917	−	0.123134i
$563$		−	13.1128i		−	0.552637i	−0.961066	−	0.276319i	$-0.910885\pi$
$563$		−	13.1128i		−	0.552637i	0.961066	−	0.276319i	$-0.0891145\pi$
$564$	3.08029	−	10.9816i	0.129703	−	0.462410i
$565$		0			0
$566$	1.20138	−	8.73146i	0.0504978	−	0.367011i
$567$	0.0802864			0.00337171
$568$	29.4346	+	12.8002i	1.23505	+	0.537086i
$569$	−11.0257			−0.462222			−0.231111	−	0.972927i	$-0.574236\pi$
$569$	−11.0257			−0.462222			−0.231111	+	0.972927i	$0.574236\pi$
$570$		0			0
$571$		−	45.6960i		−	1.91232i	−0.292847	−	0.956159i	$-0.594603\pi$
$571$		−	45.6960i		−	1.91232i	0.292847	−	0.956159i	$-0.405397\pi$
$572$	24.5134	+	6.87587i	1.02496	+	0.287495i
$573$			5.56270i			0.232385i
$574$	0.913268	+	0.125659i	0.0381191	+	0.00524489i
$575$		0			0
$576$	−5.45542	−	5.85136i	−0.227309	−	0.243807i
$577$	17.2685			0.718899			0.359449	−	0.933165i	$-0.382965\pi$
$577$	17.2685			0.718899			0.359449	+	0.933165i	$0.382965\pi$
$578$	23.7255	+	3.26444i	0.986850	+	0.135783i
$579$			18.4227i			0.765620i
$580$		0			0
$581$			0.739286i			0.0306707i
$582$	−1.63957	+	11.9162i	−0.0679625	+	0.493941i
$583$	27.9411			1.15720
$584$	31.3273	+	13.6233i	1.29633	+	0.563737i
$585$		0			0
$586$	4.14557	−	30.1294i	0.171252	−	1.24463i
$587$			34.7155i			1.43286i	0.697657	+	0.716432i	$0.254226\pi$
$587$			34.7155i			1.43286i	−0.697657	+	0.716432i	$0.745774\pi$
$588$	−3.77752	+	13.4674i	−0.155782	+	0.555384i
$589$		−	57.7208i		−	2.37835i
$590$		0			0
$591$	−18.0239			−0.741403
$592$	5.55938	−	9.13026i	0.228489	−	0.375251i
$593$	9.34022			0.383557			0.191778	−	0.981438i	$-0.438575\pi$
$593$	9.34022			0.383557			0.191778	+	0.981438i	$0.438575\pi$
$594$	3.38554	+	0.465824i	0.138910	+	0.0191130i
$595$		0			0
$596$	−12.4490	+	44.3822i	−0.509930	+	1.81797i
$597$		−	20.1214i		−	0.823513i
$598$	1.67088	−	12.1437i	0.0683274	−	0.496594i
$599$	−13.9110			−0.568389			−0.284195	−	0.958767i	$-0.591726\pi$
$599$	−13.9110			−0.568389			−0.284195	+	0.958767i	$0.591726\pi$
$600$		0			0
$601$	11.7330			0.478600			0.239300	−	0.970946i	$-0.423082\pi$
$601$	11.7330			0.478600			0.239300	+	0.970946i	$0.423082\pi$
$602$	0.0632826	−	0.459929i	0.00257921	−	0.0187453i
$603$		−	7.27979i		−	0.296456i
$604$	18.2665	+	5.12365i	0.743253	+	0.208478i
$605$		0			0
$606$	10.5954	+	1.45785i	0.430410	+	0.0592211i
$607$	10.8158			0.438998			0.219499	−	0.975613i	$-0.429558\pi$
$607$	10.8158			0.438998			0.219499	+	0.975613i	$0.429558\pi$
$608$	−24.8639	+	30.5174i	−1.00837	+	1.23764i
$609$	−0.362505			−0.0146895
$610$		0			0
$611$		−	30.0411i		−	1.21533i
$612$	0.492816	+	0.138232i	0.0199209	+	0.00558771i
$613$			17.9632i			0.725528i	0.931881	+	0.362764i	$0.118167\pi$
$613$			17.9632i			0.725528i	−0.931881	+	0.362764i	$0.881833\pi$
$614$	−0.689546	+	5.01152i	−0.0278278	+	0.202248i
$615$		0			0
$616$	0.218837	−	0.503223i	0.00881718	−	0.0202754i
$617$	−12.3576			−0.497500			−0.248750	−	0.968568i	$-0.580020\pi$
$617$	−12.3576			−0.497500			−0.248750	+	0.968568i	$0.580020\pi$
$618$	0.344177	−	2.50143i	0.0138448	−	0.100622i
$619$		−	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
$622$	3.49498	+	0.480883i	0.140136	+	0.0192816i
$623$	0.956795			0.0383332
$624$	−17.9976	−	10.9586i	−0.720479	−	0.438697i
$625$		0			0
$626$	−13.4112	−	1.84527i	−0.536018	−	0.0737519i
$627$		−	16.8155i		−	0.671546i
$628$	−3.42674	+	12.2168i	−0.136742	+	0.487502i
$629$			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	$0.616417\pi$
$632$	−14.2798	−	6.20985i	−0.568019	−	0.247015i
$633$	3.25592			0.129411
$634$	0.610502	−	4.43704i	0.0242461	−	0.176217i
$635$		0			0
$636$	−22.2661	−	6.24551i	−0.882907	−	0.247651i
$637$			36.8410i			1.45969i
$638$	−15.2862	−	2.10327i	−0.605188	−	0.0832691i
$639$	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	$0.318272\pi$
$642$	−14.6693	−	2.01838i	−0.578950	−	0.0796591i
$643$		−	2.27518i		−	0.0897245i	−0.998993	−	0.0448623i	$-0.985715\pi$
$643$		−	2.27518i		−	0.0897245i	0.998993	−	0.0448623i	$-0.0142849\pi$
$644$	−0.254391	−	0.0713553i	−0.0100244	−	0.00281179i
$645$		0			0
$646$	0.343290	−	2.49498i	0.0135066	−	0.0981638i
$647$	−12.4769			−0.490516			−0.245258	−	0.969458i	$-0.578873\pi$
$647$	−12.4769			−0.490516			−0.245258	+	0.969458i	$0.578873\pi$
$648$	−2.59378	−	1.12796i	−0.101893	−	0.0443104i
$649$	30.6804			1.20431
$650$		0			0
$651$		−	0.665963i		−	0.0261011i
$652$	−6.70320	+	23.8978i	−0.262518	+	0.935909i
$653$		−	29.3055i		−	1.14681i	−0.819271	−	0.573406i	$-0.805622\pi$
$653$		−	29.3055i		−	1.14681i	0.819271	−	0.573406i	$-0.194378\pi$
$654$	−5.10387	−	0.702253i	−0.199577	−	0.0274603i
$655$		0			0
$656$	−27.7392	−	16.8903i	−1.08303	−	0.659455i
$657$	12.0779			0.471202
$658$	−0.641455	−	0.0882593i	−0.0250065	−	0.00344070i
$659$		−	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	$-0.898422\pi$
$661$		−	16.1318i		−	0.627456i	0.949513	−	0.313728i	$-0.101578\pi$
$662$	3.18296	−	23.1333i	0.123709	−	0.899102i
$663$	1.34814			0.0523573
$664$	10.3864	−	23.8838i	0.403069	−	0.926873i
$665$		0			0
$666$	0.515157	−	3.74408i	0.0199619	−	0.145080i
$667$			7.42931i			0.287664i
$668$	44.8018	+	12.5667i	1.73343	+	0.486219i
$669$		−	26.9911i		−	1.04354i
$670$		0			0
$671$	28.8535			1.11388
$672$	−0.286871	+	0.352099i	−0.0110663	+	0.0135825i
$673$	34.1385			1.31594			0.657971	−	0.753043i	$-0.271415\pi$
$673$	34.1385			1.31594			0.657971	+	0.753043i	$0.271415\pi$
$674$	16.5782	+	2.28103i	0.638567	+	0.0878619i
$675$		0			0
$676$	−28.4043	−	7.96725i	−1.09247	−	0.306433i
$677$		−	12.1940i		−	0.468654i	−0.972158	−	0.234327i	$-0.924711\pi$
$677$		−	12.1940i		−	0.468654i	0.972158	−	0.234327i	$-0.0752886\pi$
$678$	−1.70272	+	12.3751i	−0.0653926	+	0.475264i
$679$	0.682867			0.0262060
$680$		0			0
$681$	−19.8219			−0.759578
$682$	3.86393	−	28.0825i	0.147958	−	1.07533i
$683$		−	21.8567i		−	0.836322i	−0.908373	−	0.418161i	$-0.862675\pi$
$683$		−	21.8567i		−	0.836322i	0.908373	−	0.418161i	$-0.137325\pi$
$684$	−3.75866	+	13.4001i	−0.143716	+	0.512366i
$685$		0			0
$686$	1.57403	+	0.216574i	0.0600966	+	0.00826883i
$687$	21.6797			0.827134
$688$	−8.50608	+	13.9697i	−0.324291	+	0.532589i
$689$	−60.9106			−2.32051
$690$		0			0
$691$		−	6.17780i		−	0.235015i	−0.993072	−	0.117507i	$-0.962510\pi$
$691$		−	6.17780i		−	0.235015i	0.993072	−	0.117507i	$-0.0374903\pi$
$692$	4.66628	−	16.6359i	0.177385	−	0.632402i
$693$		−	0.194011i		−	0.00736988i
$694$	−4.62091	+	33.5841i	−0.175407	+	1.27483i
$695$		0			0
$696$	11.7113	+	5.09291i	0.443917	+	0.193046i
$697$	2.07785			0.0787043
$698$	−1.71867	+	12.4910i	−0.0650525	+	0.472792i
$699$		−	17.2733i		−	0.653338i
$700$		0			0
$701$		−	33.9746i		−	1.28320i	−0.767038	−	0.641601i	$-0.778270\pi$
$701$		−	33.9746i		−	1.28320i	0.767038	−	0.641601i	$-0.221730\pi$
$702$	−7.38033	−	1.01548i	−0.278553	−	0.0383267i
$703$	−18.5963			−0.701374
$704$	−14.1398	+	13.1830i	−0.532912	+	0.496852i
$705$		0			0
$706$	10.3059	+	1.41802i	0.387869	+	0.0533678i
$707$		−	0.607181i		−	0.0228354i
$708$	−24.4490	−	6.85781i	−0.918849	−	0.257732i
$709$			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
$712$	−30.9108	−	13.4422i	−1.15843	−	0.503768i
$713$	−13.6485			−0.511139
$714$	0.00396076	−	0.0287862i	0.000148228	−	0.00107730i
$715$		0			0
$716$	−5.08029	+	18.1119i	−0.189859	+	0.676873i
$717$			16.3718i			0.611416i
$718$	−35.3216	−	4.85997i	−1.31819	−	0.181373i
$719$	−17.8427			−0.665422			−0.332711	−	0.943029i	$-0.607963\pi$
$719$	−17.8427			−0.665422			−0.332711	+	0.943029i	$0.607963\pi$
$720$		0			0
$721$	−0.143347			−0.00533851
$722$	41.2216	+	5.67177i	1.53411	+	0.211081i
$723$			6.82654i			0.253882i
$724$	−3.47575	+	12.3915i	−0.129175	+	0.460527i
$725$		0			0
$726$	−0.994797	+	7.23003i	−0.0369204	+	0.268332i
$727$	23.9148			0.886953			0.443476	−	0.896286i	$-0.353745\pi$
$727$	23.9148			0.886953			0.443476	+	0.896286i	$0.353745\pi$
$728$	−0.477055	+	1.09701i	−0.0176808	+	0.0406577i
$729$	−1.00000			−0.0370370
$730$		0			0
$731$		−	1.04642i		−	0.0387034i
$732$	−22.9931	−	6.44945i	−0.849850	−	0.238379i
$733$		−	15.6789i		−	0.579112i	−0.957161	−	0.289556i	$-0.906492\pi$
$733$		−	15.6789i		−	0.579112i	0.957161	−	0.289556i	$-0.0935076\pi$
$734$	−8.21797	−	1.13073i	−0.303331	−	0.0417360i
$735$		0			0
$736$	7.21603	+	5.87924i	0.265987	+	0.216712i
$737$	−17.5915			−0.647992
$738$	−11.3751	−	1.56513i	−0.418724	−	0.0576132i
$739$		−	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
$742$	−0.178952	+	1.30060i	−0.00656955	+	0.0477465i
$743$	−9.78057			−0.358814			−0.179407	−	0.983775i	$-0.557418\pi$
$743$	−9.78057			−0.358814			−0.179407	+	0.983775i	$0.557418\pi$
$744$	−9.35624	+	21.5150i	−0.343017	+	0.788779i
$745$		0			0
$746$	5.30235	−	38.5367i	0.194133	−	1.41093i
$747$		−	9.20811i		−	0.336907i
$748$	0.334037	−	1.19089i	0.0122136	−	0.0435431i
$749$			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	$0.546945\pi$
$752$	19.4833	+	11.8633i	0.710483	+	0.432610i
$753$	−2.96969			−0.108221
$754$	33.3234	+	4.58504i	1.21357	+	0.166977i
$755$		0			0
$756$	−0.0433661	+	0.154606i	−0.00157721	+	0.00562296i
$757$		−	28.4889i		−	1.03545i	−0.855549	−	0.517723i	$-0.826780\pi$
$757$		−	28.4889i		−	1.03545i	0.855549	−	0.517723i	$-0.173220\pi$
$758$	2.26597	−	16.4687i	0.0823037	−	0.598171i
$759$	−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	$0.627420\pi$
$762$	1.67637	−	12.1836i	0.0607285	−	0.441365i
$763$			0.292482i			0.0105886i
$764$	−10.7120	−	3.00465i	−0.387546	−	0.108705i
$765$		0			0
$766$	48.1017	+	6.61842i	1.73799	+	0.239133i
$767$	−66.8821			−2.41497
$768$	14.2146	−	7.34482i	0.512924	−	0.265033i
$769$	23.5596			0.849580			0.424790	−	0.905292i	$-0.360348\pi$
$769$	23.5596			0.849580			0.424790	+	0.905292i	$0.360348\pi$
$770$		0			0
$771$		−	5.03031i		−	0.181162i
$772$	−35.4762	−	9.95088i	−1.27682	−	0.358140i
$773$			31.1655i			1.12094i	0.828173	+	0.560472i	$0.189380\pi$
$773$			31.1655i			1.12094i	−0.828173	+	0.560472i	$0.810620\pi$
$774$	−0.788212	+	5.72861i	−0.0283317	+	0.205910i
$775$		0			0
$776$	−22.0611	−	9.59373i	−0.791949	−	0.344395i
$777$	−0.214558			−0.00769722
$778$	0.558095	−	4.05615i	0.0200087	−	0.145420i
$779$			56.4987i			2.02428i
$780$		0			0
$781$		−	27.4227i		−	0.981260i
$782$	−0.589955	−	0.0811733i	−0.0210968	−	0.00290275i
$783$	4.51516			0.161359
$784$	−23.8934	−	14.5486i	−0.853336	−	0.519593i
$785$		0			0
$786$	−15.1192	−	2.08029i	−0.539284	−	0.0742014i
$787$			5.07812i			0.181015i	0.995896	+	0.0905077i	$0.0288490\pi$
$787$			5.07812i			0.181015i	−0.995896	+	0.0905077i	$0.971151\pi$
$788$	9.73547	−	34.7082i	0.346812	−	1.23643i
$789$			2.70585i			0.0963307i
$790$		0			0
$791$	0.709168			0.0252151
$792$	−2.72570	+	6.26785i	−0.0968536	+	0.222718i
$793$	−62.8995			−2.23363
$794$	4.41632	−	32.0972i	0.156729	−	1.13909i
$795$		0			0
$796$	38.7473	+	10.8684i	1.37336	+	0.385221i
$797$			1.43418i			0.0508012i	0.999677	+	0.0254006i	$0.00808613\pi$
$797$			1.43418i			0.0508012i	−0.999677	+	0.0254006i	$0.991914\pi$
$798$	0.782724	+	0.107697i	0.0277081	+	0.00381242i
$799$	−1.45943			−0.0516309
$800$		0			0
$801$	−11.9173			−0.421076
$802$	17.4198	+	2.39683i	0.615115	+	0.0846350i
$803$		−	29.1860i		−	1.02995i
$804$	14.0185	+	3.93213i	0.494396	+	0.138675i
$805$		0			0
$806$	−8.42322	+	61.2187i	−0.296695	+	2.15634i
$807$	−22.3718			−0.787525
$808$	−8.53041	+	19.6160i	−0.300099	+	0.690088i
$809$	23.7153			0.833787			0.416894	−	0.908955i	$-0.363119\pi$
$809$	23.7153			0.833787			0.416894	+	0.908955i	$0.363119\pi$
$810$		0			0
$811$			47.8394i			1.67987i	0.542689	+	0.839933i	$0.317406\pi$
$811$			47.8394i			1.67987i	−0.542689	+	0.839933i	$0.682594\pi$
$812$	0.195805	−	0.698070i	0.00687140	−	0.0244974i
$813$			0.869741i			0.0305031i
$814$	−9.04754	−	1.24487i	−0.317116	−	0.0436327i
$815$		0			0
$816$	−0.532383	+	0.874341i	−0.0186371	+	0.0306081i
$817$	28.4532			0.995451
$818$	44.9566	+	6.18568i	1.57187	+	0.216277i
$819$			0.422937i			0.0147786i
$820$		0			0
$821$			51.9216i			1.81208i	0.423195	+	0.906038i	$0.360908\pi$
$821$			51.9216i			1.81208i	−0.423195	+	0.906038i	$0.639092\pi$
$822$	−2.22496	+	16.1707i	−0.0776046	+	0.564018i
$823$	−27.8542			−0.970937			−0.485469	−	0.874254i	$-0.661351\pi$
$823$	−27.8542			−0.970937			−0.485469	+	0.874254i	$0.661351\pi$
$824$	4.63105	+	2.01391i	0.161330	+	0.0701577i
$825$		0			0
$826$	−0.196496	+	1.42811i	−0.00683698	+	0.0496902i
$827$		−	43.9365i		−	1.52782i	−0.645321	−	0.763912i	$-0.723276\pi$
$827$		−	43.9365i		−	1.52782i	0.645321	−	0.763912i	$-0.276724\pi$
$828$	3.16855	+	0.888760i	0.110115	+	0.0308866i
$829$		−	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
$832$	30.8241	−	28.7383i	1.06863	−	0.996322i
$833$	1.78978			0.0620121
$834$	0.300599	+	0.0413600i	0.0104089	+	0.00143218i
$835$		0			0
$836$	32.3813	+	9.08277i	1.11993	+	0.314134i
$837$			8.29484i			0.286712i
$838$	3.11060	−	22.6074i	0.107454	−	0.780959i
$839$	−25.4733			−0.879437			−0.439719	−	0.898136i	$-0.644922\pi$
$839$	−25.4733			−0.879437			−0.439719	+	0.898136i	$0.644922\pi$
$840$		0			0
$841$	8.61336			0.297012
$842$	5.54547	−	40.3037i	0.191110	−	1.38896i
$843$		−	15.1429i		−	0.521549i
$844$	−1.75866	+	6.26986i	−0.0605356	+	0.215817i
$845$		0			0
$846$	7.98959	+	1.09931i	0.274688	+	0.0377949i
$847$	0.414324			0.0142363
$848$	24.0537	−	39.5038i	0.826008	−	1.35657i
$849$	6.23225			0.213890
$850$		0			0
$851$			4.39722i			0.150735i
$852$	−6.12962	+	21.8529i	−0.209997	+	0.748668i
$853$		−	12.5366i		−	0.429245i	−0.976697	−	0.214622i	$-0.931148\pi$
$853$		−	12.5366i		−	0.429245i	0.976697	−	0.214622i	$-0.0688521\pi$
$854$	−0.184796	+	1.34307i	−0.00632358	+	0.0459588i
$855$		0			0
$856$	11.8103	−	27.1581i	0.403667	−	0.928246i
$857$	−2.61409			−0.0892956			−0.0446478	−	0.999003i	$-0.514217\pi$
$857$	−2.61409			−0.0892956			−0.0446478	+	0.999003i	$0.514217\pi$
$858$	−2.45389	+	17.8345i	−0.0837744	+	0.608860i
$859$		−	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
$862$	−34.6467	−	4.76711i	−1.18007	−	0.162369i
$863$	22.3335			0.760241			0.380121	−	0.924937i	$-0.375882\pi$
$863$	22.3335			0.760241			0.380121	+	0.924937i	$0.375882\pi$
$864$	3.57310	−	4.38554i	0.121559	−	0.149199i
$865$		0			0
$866$	6.28798	+	0.865177i	0.213674	+	0.0293999i
$867$			16.9345i			0.575126i
$868$	1.28243	+	0.359715i	0.0435286	+	0.0122095i
$869$			13.3037i			0.451298i
$870$		0			0
$871$	38.3488			1.29940
$872$	4.10913	−	9.44910i	0.139153	−	0.319987i
$873$	−8.50539			−0.287864
$874$	2.20717	−	16.0414i	0.0746588	−	0.542609i
$875$		0			0
$876$	−6.52377	+	23.2581i	−0.220418	+	0.785818i
$877$		−	37.4408i		−	1.26429i	−0.774852	−	0.632143i	$-0.782176\pi$
$877$		−	37.4408i		−	1.26429i	0.774852	−	0.632143i	$-0.217824\pi$
$878$	−8.35117	−	1.14906i	−0.281838	−	0.0387788i
$879$	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	$0.146391\pi$
$882$	−9.79807	−	1.34814i	−0.329918	−	0.0453942i
$883$			36.0907i			1.21455i	0.794493	+	0.607274i	$0.207737\pi$
$883$			36.0907i			1.21455i	−0.794493	+	0.607274i	$0.792263\pi$
$884$	−0.728188	+	2.59608i	−0.0244916	+	0.0873157i
$885$		0			0
$886$	−2.75513	+	20.0239i	−0.0925604	+	0.672715i
$887$	43.3018			1.45393			0.726966	−	0.686673i	$-0.240930\pi$
$887$	43.3018			1.45393			0.726966	+	0.686673i	$0.240930\pi$
$888$	6.93165	+	3.01437i	0.232611	+	0.101156i
$889$	−0.698192			−0.0234166
$890$		0			0
$891$			2.41649i			0.0809555i
$892$	51.9763	+	14.5791i	1.74029	+	0.488143i
$893$		−	39.6832i		−	1.32795i
$894$	−32.2899	−	4.44284i	−1.07994	−	0.148591i
$895$		0			0
$896$	−0.523078	−	0.742606i	−0.0174748	−	0.0248087i
$897$	8.66781			0.289410
$898$	−34.3990	−	4.73304i	−1.14791	−	0.157943i
$899$		−	37.4525i		−	1.24911i
$900$		0			0
$901$			2.95910i			0.0985820i
$902$	−3.78212	+	27.4879i	−0.125931	+	0.915247i
$903$	0.328283			0.0109246
$904$	−22.9108	−	9.96324i	−0.762003	−	0.331372i
$905$		0			0
$906$	−1.82855	+	13.2896i	−0.0607496	+	0.441519i
$907$		−	8.75026i		−	0.290548i	−0.989391	−	0.145274i	$-0.953594\pi$
$907$		−	8.75026i		−	0.290548i	0.989391	−	0.145274i	$-0.0464063\pi$
$908$	10.7067	−	38.1707i	0.355314	−	1.26674i
$909$			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	$0.573113\pi$
$912$	−23.7741	−	14.4760i	−0.787240	−	0.479347i
$913$	−22.2513			−0.736411
$914$	−40.5045	−	5.57310i	−1.33977	−	0.184342i
$915$		0			0
$916$	−11.7102	+	41.7483i	−0.386915	+	1.37940i
$917$			0.866420i			0.0286117i
$918$	−0.0493330	+	0.358545i	−0.00162823	+	0.0118337i
$919$	−0.989347			−0.0326355			−0.0163178	−	0.999867i	$-0.505194\pi$
$919$	−0.989347			−0.0326355			−0.0163178	+	0.999867i	$0.505194\pi$
$920$		0			0
$921$	−3.57706			−0.117868
$922$	−0.839427	+	6.10083i	−0.0276451	+	0.200920i
$923$			59.7803i			1.96769i
$924$	0.373604	+	0.104794i	0.0122907	+	0.00344746i
$925$		0			0
$926$	−15.5936	−	2.14557i	−0.512439	−	0.0705076i
$927$	1.78544			0.0586416
$928$	−16.1331	+	19.8014i	−0.529596	+	0.650012i
$929$	−8.49434			−0.278690			−0.139345	−	0.990244i	$-0.544500\pi$
$929$	−8.49434			−0.278690			−0.139345	+	0.990244i	$0.544500\pi$
$930$		0			0
$931$			48.6656i			1.59495i
$932$	33.2629	+	9.33008i	1.08956	+	0.305617i
$933$			2.49461i			0.0816699i
$934$	3.68683	−	26.7953i	0.120637	−	0.876770i
$935$		0			0
$936$	5.94192	−	13.6637i	0.194218	−	0.446611i
$937$	−18.6912			−0.610615			−0.305308	−	0.952254i	$-0.598759\pi$
$937$	−18.6912			−0.610615			−0.305308	+	0.952254i	$0.598759\pi$
$938$	0.112667	−	0.818847i	0.00367871	−	0.0267363i
$939$		−	9.57246i		−	0.312386i
$940$		0			0
$941$			3.03170i			0.0988305i	0.998778	+	0.0494152i	$0.0157358\pi$
$941$			3.03170i			0.0988305i	−0.998778	+	0.0494152i	$0.984264\pi$
$942$	−8.88821	−	1.22295i	−0.289594	−	0.0398458i
$943$	13.3595			0.435045
$944$	26.4119	−	43.3767i	0.859634	−	1.41179i
$945$		0			0
$946$	13.8431	+	1.90471i	0.450079	+	0.0619273i
$947$			16.8327i			0.546990i	0.961873	+	0.273495i	$0.0881797\pi$
$947$			16.8327i			0.546990i	−0.961873	+	0.273495i	$0.911820\pi$
$948$	2.97370	−	10.6016i	0.0965812	−	0.344325i
$949$			63.6243i			2.06533i
$950$		0			0
$951$	3.16702			0.102698
$952$	0.0532937	+	0.0231759i	0.00172726	+	0.000751134i
$953$	−1.73948			−0.0563473			−0.0281737	−	0.999603i	$-0.508969\pi$
$953$	−1.73948			−0.0563473			−0.0281737	+	0.999603i	$0.508969\pi$
$954$	2.22893	−	16.1995i	0.0721641	−	0.524478i
$955$		0			0
$956$	−31.5269	−	8.84312i	−1.01965	−	0.286007i
$957$		−	10.9108i		−	0.352697i
$958$	35.9162	+	4.94179i	1.16040	+	0.159662i
$959$	0.926677			0.0299240
$960$		0			0
$961$	37.8044			1.21950
$962$	19.7233	+	2.71377i	0.635904	+	0.0874954i
$963$		−	10.4705i		−	0.337406i
$964$	−13.1457	−	3.68731i	−0.423395	−	0.118760i
$965$		0			0
$966$	0.0254656	−	0.185080i	0.000819342	−	0.00595486i
$967$	17.3399			0.557615			0.278808	−	0.960347i	$-0.410061\pi$
$967$	17.3399			0.557615			0.278808	+	0.960347i	$0.410061\pi$
$968$	−13.3854	−	5.82091i	−0.430223	−	0.187091i
$969$	1.78084			0.0572089
$970$		0			0
$971$			45.4054i			1.45713i	0.684977	+	0.728565i	$0.259812\pi$
$971$			45.4054i			1.45713i	−0.684977	+	0.728565i	$0.740188\pi$
$972$	0.540143	−	1.92568i	0.0173251	−	0.0617662i
$973$		−	0.0172261i		−	0.000552243i
$974$	17.9938	+	2.47581i	0.576560	+	0.0793302i
$975$		0			0
$976$	24.8392	−	40.7938i	0.795082	−	1.30578i
$977$	−43.4336			−1.38957			−0.694783	−	0.719220i	$-0.744499\pi$
$977$	−43.4336			−1.38957			−0.694783	+	0.719220i	$0.744499\pi$
$978$	−17.3866	−	2.39227i	−0.555964	−	0.0764963i
$979$			28.7980i			0.920388i
$980$		0			0
$981$		−	3.64298i		−	0.116311i
$982$	−3.27489	+	23.8014i	−0.104506	+	0.759533i
$983$	47.4465			1.51331			0.756655	−	0.653815i	$-0.226832\pi$
$983$	47.4465			1.51331			0.756655	+	0.653815i	$0.226832\pi$
$984$	9.15814	−	21.0595i	0.291951	−	0.671351i
$985$		0			0
$986$	0.222746	−	1.61889i	0.00709368	−	0.0515558i
$987$		−	0.457851i		−	0.0145735i
$988$	−70.5898	−	19.8001i	−2.24576	−	0.629924i
$989$		−	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	$0.651477\pi$
$992$	−36.3773	−	29.6383i	−1.15498	−	0.941018i
$993$	16.5118			0.523987
$994$	1.27646	+	0.175632i	0.0404870	+	0.00557070i
$995$		0			0
$996$	17.7319	+	4.97370i	0.561856	+	0.157598i
$997$		−	33.1449i		−	1.04971i	−0.851192	−	0.524855i	$-0.824119\pi$
$997$		−	33.1449i		−	1.04971i	0.851192	−	0.524855i	$-0.175881\pi$
$998$	2.70881	−	19.6872i	0.0857460	−	0.623189i
$999$	2.67241			0.0845513

Twists

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

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

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.k (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.40101 - 0.192769i) q^{2} -1.00000i q^{3} +(1.92568 + 0.540143i) q^{4} +(-0.192769 + 1.40101i) q^{6} +0.0802864 q^{7} +(-2.59378 - 1.12796i) q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+(-1.40101 - 0.192769i) q^{2} -1.00000i q^{3} +(1.92568 + 0.540143i) q^{4} +(-0.192769 + 1.40101i) q^{6} +0.0802864 q^{7} +(-2.59378 - 1.12796i) q^{8} -1.00000 q^{9} +2.41649i q^{11} +(0.540143 - 1.92568i) q^{12} -5.26785i q^{13} +(-0.112482 - 0.0154767i) q^{14} +(3.41649 + 2.08029i) q^{16} -0.255918 q^{17} +(1.40101 + 0.192769i) q^{18} -6.95864i q^{19} -0.0802864i q^{21} +(0.465824 - 3.38554i) q^{22} -1.64542 q^{23} +(-1.12796 + 2.59378i) q^{24} +(-1.01548 + 7.38033i) q^{26} +1.00000i q^{27} +(0.154606 + 0.0433661i) q^{28} -4.51516i q^{29} +8.29484 q^{31} +(-4.38554 - 3.57310i) q^{32} +2.41649 q^{33} +(0.358545 + 0.0493330i) q^{34} +(-1.92568 - 0.540143i) q^{36} -2.67241i q^{37} +(-1.34141 + 9.74915i) q^{38} -5.26785 q^{39} -8.11921 q^{41} +(-0.0154767 + 0.112482i) q^{42} +4.08890i q^{43} +(-1.30525 + 4.65339i) q^{44} +(2.30525 + 0.317185i) q^{46} +5.70272 q^{47} +(2.08029 - 3.41649i) q^{48} -6.99355 q^{49} +0.255918i q^{51} +(2.84539 - 10.1442i) q^{52} -11.5627i q^{53} +(0.192769 - 1.40101i) q^{54} +(-0.208245 - 0.0905597i) q^{56} -6.95864 q^{57} +(-0.870381 + 6.32580i) q^{58} -12.6963i q^{59} -11.9403i q^{61} +(-11.6212 - 1.59899i) q^{62} -0.0802864 q^{63} +(5.45542 + 5.85136i) q^{64} +(-3.38554 - 0.465824i) q^{66} +7.27979i q^{67} +(-0.492816 - 0.138232i) q^{68} +1.64542i q^{69} -11.3481 q^{71} +(2.59378 + 1.12796i) q^{72} -12.0779 q^{73} +(-0.515157 + 3.74408i) q^{74} +(3.75866 - 13.4001i) q^{76} +0.194011i q^{77} +(7.38033 + 1.01548i) q^{78} +5.50539 q^{79} +1.00000 q^{81} +(11.3751 + 1.56513i) q^{82} +9.20811i q^{83} +(0.0433661 - 0.154606i) q^{84} +(0.788212 - 5.72861i) q^{86} -4.51516 q^{87} +(2.72570 - 6.26785i) q^{88} +11.9173 q^{89} -0.422937i q^{91} +(-3.16855 - 0.888760i) q^{92} -8.29484i q^{93} +(-7.98959 - 1.09931i) q^{94} +(-3.57310 + 4.38554i) q^{96} +8.50539 q^{97} +(9.79807 + 1.34814i) q^{98} -2.41649i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} + 4 q^{4} + 2 q^{6} - 8 q^{7} - 4 q^{8} - 8 q^{9}+O(q^{10}) \) 8 * q + 2 * q^2 + 4 * q^4 + 2 * q^6 - 8 * q^7 - 4 * q^8 - 8 * q^9	\( 8 q + 2 q^{2} + 4 q^{4} + 2 q^{6} - 8 q^{7} - 4 q^{8} - 8 q^{9} - 6 q^{14} + 8 q^{16} - 2 q^{18} - 12 q^{22} - 8 q^{23} - 8 q^{24} - 2 q^{26} + 4 q^{28} + 8 q^{31} - 28 q^{32} + 12 q^{34} - 4 q^{36} - 30 q^{38} + 6 q^{42} - 12 q^{44} + 20 q^{46} + 8 q^{48} + 20 q^{52} - 2 q^{54} + 8 q^{56} - 8 q^{57} - 12 q^{58} - 30 q^{62} + 8 q^{63} - 32 q^{64} - 20 q^{66} + 28 q^{68} - 40 q^{71} + 4 q^{72} + 16 q^{73} + 8 q^{74} - 20 q^{76} + 22 q^{78} - 16 q^{79} + 8 q^{81} + 24 q^{82} + 24 q^{84} - 18 q^{86} - 24 q^{87} + 8 q^{88} + 36 q^{92} - 4 q^{94} + 12 q^{96} + 8 q^{97} + 48 q^{98}+O(q^{100}) \) 8 * q + 2 * q^2 + 4 * q^4 + 2 * q^6 - 8 * q^7 - 4 * q^8 - 8 * q^9 - 6 * q^14 + 8 * q^16 - 2 * q^18 - 12 * q^22 - 8 * q^23 - 8 * q^24 - 2 * q^26 + 4 * q^28 + 8 * q^31 - 28 * q^32 + 12 * q^34 - 4 * q^36 - 30 * q^38 + 6 * q^42 - 12 * q^44 + 20 * q^46 + 8 * q^48 + 20 * q^52 - 2 * q^54 + 8 * q^56 - 8 * q^57 - 12 * q^58 - 30 * q^62 + 8 * q^63 - 32 * q^64 - 20 * q^66 + 28 * q^68 - 40 * q^71 + 4 * q^72 + 16 * q^73 + 8 * q^74 - 20 * q^76 + 22 * q^78 - 16 * q^79 + 8 * q^81 + 24 * q^82 + 24 * q^84 - 18 * q^86 - 24 * q^87 + 8 * q^88 + 36 * q^92 - 4 * q^94 + 12 * q^96 + 8 * q^97 + 48 * q^98

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