LMFDB - Embedded newform 441.2.g.g.79.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(67,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 4]))

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

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

chi := DirichletCharacter("441.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.g (of order $3$, degree $2$, 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:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 7x^{10} + 37x^{8} - 78x^{6} + 123x^{4} - 36x^{2} + 9 $ x^12 - 7x^10 + 37x^8 - 78x^6 + 123x^4 - 36*x^2 + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			79.5
Root			$0.474636 - 0.274031i$ of defining polynomial
Character	$\chi$	$=$	441.79
Dual form			441.2.g.g.67.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.849814 + 1.47192i) q^{2} +(-1.58016 - 0.709292i) q^{3} +(-0.444368 + 0.769668i) q^{4} -0.949271 q^{5} +(-0.298820 - 2.92864i) q^{6} +1.88874 q^{8} +(1.99381 + 2.24159i) q^{9} +O(q^{10})$	\(q+(0.849814 + 1.47192i) q^{2} +(-1.58016 - 0.709292i) q^{3} +(-0.444368 + 0.769668i) q^{4} -0.949271 q^{5} +(-0.298820 - 2.92864i) q^{6} +1.88874 q^{8} +(1.99381 + 2.24159i) q^{9} +(-0.806704 - 1.39725i) q^{10} -0.588364 q^{11} +(1.24809 - 0.901012i) q^{12} +(2.50987 + 4.34722i) q^{13} +(1.50000 + 0.673310i) q^{15} +(2.49381 + 4.31941i) q^{16} +(3.79121 + 6.56657i) q^{17} +(-1.60507 + 4.83967i) q^{18} +(2.23061 - 3.86353i) q^{19} +(0.421826 - 0.730623i) q^{20} +(-0.500000 - 0.866025i) q^{22} +2.47710 q^{23} +(-2.98450 - 1.33966i) q^{24} -4.09888 q^{25} +(-4.26584 + 7.38866i) q^{26} +(-1.56060 - 4.95626i) q^{27} +(-2.73855 + 4.74331i) q^{29} +(0.283662 + 2.78007i) q^{30} +(3.03731 - 5.26078i) q^{31} +(-2.34981 + 4.07000i) q^{32} +(0.929709 + 0.417322i) q^{33} +(-6.44364 + 11.1607i) q^{34} +(-2.61126 + 0.538481i) q^{36} +(3.49381 - 6.05146i) q^{37} +7.58242 q^{38} +(-0.882546 - 8.64953i) q^{39} -1.79292 q^{40} +(0.527445 + 0.913562i) q^{41} +(-3.49381 + 6.05146i) q^{43} +(0.261450 - 0.452845i) q^{44} +(-1.89267 - 2.12788i) q^{45} +(2.10507 + 3.64610i) q^{46} +(3.73840 + 6.47510i) q^{47} +(-0.876899 - 8.59419i) q^{48} +(-3.48329 - 6.03323i) q^{50} +(-1.33310 - 13.0653i) q^{51} -4.46122 q^{52} +(-3.46108 - 5.99476i) q^{53} +(5.96901 - 6.50898i) q^{54} +0.558517 q^{55} +(-6.26509 + 4.52284i) q^{57} -9.30903 q^{58} +(-5.21512 + 9.03284i) q^{59} +(-1.18478 + 0.855304i) q^{60} +(-5.82644 - 10.0917i) q^{61} +10.3246 q^{62} +1.98762 q^{64} +(-2.38255 - 4.12669i) q^{65} +(0.175815 + 1.72310i) q^{66} +(5.93199 - 10.2745i) q^{67} -6.73877 q^{68} +(-3.91421 - 1.75699i) q^{69} +4.30037 q^{71} +(3.76578 + 4.23377i) q^{72} +(-2.23061 - 3.86353i) q^{73} +11.8764 q^{74} +(6.47689 + 2.90731i) q^{75} +(1.98242 + 3.43366i) q^{76} +(11.9814 - 8.64953i) q^{78} +(0.666896 + 1.15510i) q^{79} +(-2.36730 - 4.10029i) q^{80} +(-1.04944 + 8.93861i) q^{81} +(-0.896461 + 1.55272i) q^{82} +(2.84194 - 4.92238i) q^{83} +(-3.59888 - 6.23345i) q^{85} -11.8764 q^{86} +(7.69174 - 5.55275i) q^{87} -1.11126 q^{88} +(-0.421826 + 0.730623i) q^{89} +(1.52365 - 4.59415i) q^{90} +(-1.10074 + 1.90654i) q^{92} +(-8.53087 + 6.15854i) q^{93} +(-6.35389 + 11.0053i) q^{94} +(-2.11745 + 3.66754i) q^{95} +(6.59990 - 4.76454i) q^{96} +(1.70317 - 2.94997i) q^{97} +(-1.17309 - 1.31887i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 2 q^{2} - 6 q^{4} + 24 q^{8} - 12 q^{9}+O(q^{10}) $ 12 * q - 2 * q^2 - 6 * q^4 + 24 * q^8 - 12 * q^9	$ 12 q - 2 q^{2} - 6 q^{4} + 24 q^{8} - 12 q^{9} + 16 q^{11} + 18 q^{15} - 6 q^{16} + 18 q^{18} - 6 q^{22} + 8 q^{23} + 24 q^{25} - 22 q^{29} + 42 q^{30} - 16 q^{32} - 30 q^{36} + 6 q^{37} + 24 q^{39} - 6 q^{43} + 14 q^{44} - 12 q^{46} - 56 q^{50} - 18 q^{51} - 28 q^{53} - 6 q^{57} + 36 q^{58} - 126 q^{60} - 48 q^{64} + 6 q^{65} + 76 q^{71} - 30 q^{72} + 72 q^{74} + 36 q^{78} + 6 q^{79} + 24 q^{81} + 30 q^{85} - 72 q^{86} - 12 q^{88} - 62 q^{92} + 42 q^{93} - 60 q^{95} - 48 q^{99}+O(q^{100}) $ 12 * q - 2 * q^2 - 6 * q^4 + 24 * q^8 - 12 * q^9 + 16 * q^11 + 18 * q^15 - 6 * q^16 + 18 * q^18 - 6 * q^22 + 8 * q^23 + 24 * q^25 - 22 * q^29 + 42 * q^30 - 16 * q^32 - 30 * q^36 + 6 * q^37 + 24 * q^39 - 6 * q^43 + 14 * q^44 - 12 * q^46 - 56 * q^50 - 18 * q^51 - 28 * q^53 - 6 * q^57 + 36 * q^58 - 126 * q^60 - 48 * q^64 + 6 * q^65 + 76 * q^71 - 30 * q^72 + 72 * q^74 + 36 * q^78 + 6 * q^79 + 24 * q^81 + 30 * q^85 - 72 * q^86 - 12 * q^88 - 62 * q^92 + 42 * q^93 - 60 * q^95 - 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	0.849814	+	1.47192i	0.600909	+	1.04081i	0.992684	+	0.120744i	$0.0385280\pi$
$2$	0.849814	+	1.47192i	0.600909	+	1.04081i	−0.391774	+	0.920061i	$0.628139\pi$
$3$	−1.58016	−	0.709292i	−0.912306	−	0.409510i
$3$	−1.58016	−	0.709292i	−0.912306	−	0.409510i
$4$	−0.444368	+	0.769668i	−0.222184	+	0.384834i
$5$	−0.949271			−0.424527			−0.212263	−	0.977212i	$-0.568084\pi$
$5$	−0.949271			−0.424527			−0.212263	+	0.977212i	$0.568084\pi$
$6$	−0.298820	−	2.92864i	−0.121993	−	1.19561i
$7$		0			0
$7$		0			0
$8$	1.88874			0.667769
$9$	1.99381	+	2.24159i	0.664603	+	0.747196i
$10$	−0.806704	−	1.39725i	−0.255102	−	0.441850i
$11$	−0.588364			−0.177398			−0.0886992	−	0.996058i	$-0.528271\pi$
$11$	−0.588364			−0.177398			−0.0886992	+	0.996058i	$0.528271\pi$
$12$	1.24809	−	0.901012i	0.360293	−	0.260100i
$13$	2.50987	+	4.34722i	0.696112	+	1.20570i	0.969804	+	0.243885i	$0.0784218\pi$
$13$	2.50987	+	4.34722i	0.696112	+	1.20570i	−0.273692	+	0.961817i	$0.588245\pi$
$14$		0			0
$15$	1.50000	+	0.673310i	0.387298	+	0.173848i
$16$	2.49381	+	4.31941i	0.623453	+	1.07985i
$17$	3.79121	+	6.56657i	0.919503	+	1.59263i	0.800171	+	0.599772i	$0.204742\pi$
$17$	3.79121	+	6.56657i	0.919503	+	1.59263i	0.119332	+	0.992854i	$0.461925\pi$
$18$	−1.60507	+	4.83967i	−0.378320	+	1.14072i
$19$	2.23061	−	3.86353i	0.511737	−	0.886355i	−0.488170	−	0.872748i	$-0.662336\pi$
$19$	2.23061	−	3.86353i	0.511737	−	0.886355i	0.999907	−	0.0136063i	$-0.00433116\pi$
$20$	0.421826	−	0.730623i	0.0943231	−	0.163372i
$21$		0			0
$22$	−0.500000	−	0.866025i	−0.106600	−	0.184637i
$23$	2.47710			0.516511			0.258256	−	0.966077i	$-0.416852\pi$
$23$	2.47710			0.516511			0.258256	+	0.966077i	$0.416852\pi$
$24$	−2.98450	−	1.33966i	−0.609209	−	0.273458i
$25$	−4.09888			−0.819777
$26$	−4.26584	+	7.38866i	−0.836601	+	1.44904i
$27$	−1.56060	−	4.95626i	−0.300337	−	0.953833i
$28$		0			0
$29$	−2.73855	+	4.74331i	−0.508536	+	0.880810i	0.491415	+	0.870925i	$0.336480\pi$
$29$	−2.73855	+	4.74331i	−0.508536	+	0.880810i	−0.999951	+	0.00988468i	$0.996854\pi$
$30$	0.283662	+	2.78007i	0.0517893	+	0.507569i
$31$	3.03731	−	5.26078i	0.545518	−	0.944865i	−0.453056	−	0.891482i	$-0.649666\pi$
$31$	3.03731	−	5.26078i	0.545518	−	0.944865i	0.998574	−	0.0533826i	$-0.0170003\pi$
$32$	−2.34981	+	4.07000i	−0.415392	+	0.719481i
$33$	0.929709	+	0.417322i	0.161842	+	0.0726464i
$34$	−6.44364	+	11.1607i	−1.10508	+	1.91405i
$35$		0			0
$36$	−2.61126	+	0.538481i	−0.435211	+	0.0897469i
$37$	3.49381	−	6.05146i	0.574379	−	0.994853i	−0.421730	−	0.906721i	$-0.638577\pi$
$37$	3.49381	−	6.05146i	0.574379	−	0.994853i	0.996109	−	0.0881319i	$-0.0280897\pi$
$38$	7.58242			1.23003
$39$	−0.882546	−	8.64953i	−0.141320	−	1.38503i
$40$	−1.79292			−0.283486
$41$	0.527445	+	0.913562i	0.0823731	+	0.142674i	0.904269	−	0.426964i	$-0.140417\pi$
$41$	0.527445	+	0.913562i	0.0823731	+	0.142674i	−0.821896	+	0.569638i	$0.807083\pi$
$42$		0			0
$43$	−3.49381	+	6.05146i	−0.532801	+	0.922838i	0.466465	+	0.884540i	$0.345527\pi$
$43$	−3.49381	+	6.05146i	−0.532801	+	0.922838i	−0.999266	+	0.0382990i	$0.987806\pi$
$44$	0.261450	−	0.452845i	0.0394151	−	0.0682689i
$45$	−1.89267	−	2.12788i	−0.282142	−	0.317205i
$46$	2.10507	+	3.64610i	0.310376	+	0.537587i
$47$	3.73840	+	6.47510i	0.545301	+	0.944490i	0.998588	+	0.0531249i	$0.0169181\pi$
$47$	3.73840	+	6.47510i	0.545301	+	0.944490i	−0.453286	+	0.891365i	$0.649749\pi$
$48$	−0.876899	−	8.59419i	−0.126569	−	1.24046i
$49$		0			0
$50$	−3.48329	−	6.03323i	−0.492612	−	0.853228i
$51$	−1.33310	−	13.0653i	−0.186672	−	1.82951i
$52$	−4.46122			−0.618660
$53$	−3.46108	−	5.99476i	−0.475416	−	0.823444i	0.524188	−	0.851603i	$-0.324369\pi$
$53$	−3.46108	−	5.99476i	−0.475416	−	0.823444i	−0.999603	+	0.0281586i	$0.991036\pi$
$54$	5.96901	−	6.50898i	0.812279	−	0.885760i
$55$	0.558517			0.0753104
$56$		0			0
$57$	−6.26509	+	4.52284i	−0.829832	+	0.599065i
$58$	−9.30903			−1.22234
$59$	−5.21512	+	9.03284i	−0.678950	+	1.17598i	0.296347	+	0.955080i	$0.404231\pi$
$59$	−5.21512	+	9.03284i	−0.678950	+	1.17598i	−0.975297	+	0.220896i	$0.929102\pi$
$60$	−1.18478	+	0.855304i	−0.152954	+	0.110419i
$61$	−5.82644	−	10.0917i	−0.745999	−	1.29211i	−0.949726	−	0.313081i	$-0.898639\pi$
$61$	−5.82644	−	10.0917i	−0.745999	−	1.29211i	0.203727	−	0.979028i	$-0.434695\pi$
$62$	10.3246			1.31123
$63$		0			0
$64$	1.98762			0.248453
$65$	−2.38255	−	4.12669i	−0.295518	−	0.511853i
$66$	0.175815	+	1.72310i	0.0216413	+	0.212099i
$67$	5.93199	−	10.2745i	0.724708	−	1.25523i	−0.234387	−	0.972143i	$-0.575308\pi$
$67$	5.93199	−	10.2745i	0.724708	−	1.25523i	0.959094	−	0.283087i	$-0.0913585\pi$
$68$	−6.73877			−0.817195
$69$	−3.91421	−	1.75699i	−0.471216	−	0.211516i
$70$		0			0
$71$	4.30037			0.510360			0.255180	−	0.966894i	$-0.417865\pi$
$71$	4.30037			0.510360			0.255180	+	0.966894i	$0.417865\pi$
$72$	3.76578	+	4.23377i	0.443802	+	0.498955i
$73$	−2.23061	−	3.86353i	−0.261073	−	0.452192i	0.705454	−	0.708756i	$-0.250743\pi$
$73$	−2.23061	−	3.86353i	−0.261073	−	0.452192i	−0.966527	+	0.256563i	$0.917410\pi$
$74$	11.8764			1.38060
$75$	6.47689	+	2.90731i	0.747887	+	0.335707i
$76$	1.98242	+	3.43366i	0.227400	+	0.393868i
$77$		0			0
$78$	11.9814	−	8.64953i	1.35663	−	0.979367i
$79$	0.666896	+	1.15510i	0.0750317	+	0.129959i	0.901100	−	0.433611i	$-0.142761\pi$
$79$	0.666896	+	1.15510i	0.0750317	+	0.129959i	−0.826068	+	0.563570i	$0.809428\pi$
$80$	−2.36730	−	4.10029i	−0.264672	−	0.458426i
$81$	−1.04944	+	8.93861i	−0.116605	+	0.993178i
$82$	−0.896461	+	1.55272i	−0.0989976	+	0.171469i
$83$	2.84194	−	4.92238i	0.311943	−	0.540301i	−0.666840	−	0.745201i	$-0.732353\pi$
$83$	2.84194	−	4.92238i	0.311943	−	0.540301i	0.978783	+	0.204900i	$0.0656868\pi$
$84$		0			0
$85$	−3.59888	−	6.23345i	−0.390354	−	0.676113i
$86$	−11.8764			−1.28066
$87$	7.69174	−	5.55275i	0.824641	−	0.595318i
$88$	−1.11126			−0.118461
$89$	−0.421826	+	0.730623i	−0.0447134	+	0.0774459i	−0.887516	−	0.460777i	$-0.847571\pi$
$89$	−0.421826	+	0.730623i	−0.0447134	+	0.0774459i	0.842803	+	0.538223i	$0.180904\pi$
$90$	1.52365	−	4.59415i	0.160607	−	0.484266i
$91$		0			0
$92$	−1.10074	+	1.90654i	−0.114760	+	0.198771i
$93$	−8.53087	+	6.15854i	−0.884610	+	0.638610i
$94$	−6.35389	+	11.0053i	−0.655353	+	1.13511i
$95$	−2.11745	+	3.66754i	−0.217246	+	0.376281i
$96$	6.59990	−	4.76454i	0.673599	−	0.486279i
$97$	1.70317	−	2.94997i	0.172930	−	0.299524i	−0.766513	−	0.642229i	$-0.778010\pi$
$97$	1.70317	−	2.94997i	0.172930	−	0.299524i	0.939443	+	0.342705i	$0.111343\pi$
$98$		0			0
$99$	−1.17309	−	1.31887i	−0.117900	−	0.132551i
$100$	1.82141	−	3.15478i	0.182141	−	0.315478i
$101$	−9.58658			−0.953900			−0.476950	−	0.878930i	$-0.658258\pi$
$101$	−9.58658			−0.953900			−0.476950	+	0.878930i	$0.658258\pi$
$102$	18.0982	−	13.0653i	1.79199	−	1.29366i
$103$	−11.6529			−1.14819			−0.574096	−	0.818788i	$-0.694647\pi$
$103$	−11.6529			−1.14819			−0.574096	+	0.818788i	$0.694647\pi$
$104$	4.74048	+	8.21075i	0.464842	+	0.805130i
$105$		0			0
$106$	5.88255	−	10.1889i	0.571363	−	0.989630i
$107$	1.89926	−	3.28961i	0.183608	−	0.318018i	−0.759499	−	0.650509i	$-0.774556\pi$
$107$	1.89926	−	3.28961i	0.183608	−	0.318018i	0.943107	+	0.332491i	$0.107889\pi$
$108$	4.50816	+	1.00126i	0.433797	+	0.0963465i
$109$	6.43199	+	11.1405i	0.616073	+	1.06707i	0.990195	+	0.139690i	$0.0446106\pi$
$109$	6.43199	+	11.1405i	0.616073	+	1.06707i	−0.374123	+	0.927379i	$0.622056\pi$
$110$	0.474636	+	0.822093i	0.0452547	+	0.0783835i
$111$	−9.81303	+	7.08414i	−0.931411	+	0.672397i
$112$		0			0
$113$	−4.51052	−	7.81245i	−0.424314	−	0.734934i	0.572042	−	0.820224i	$-0.306151\pi$
$113$	−4.51052	−	7.81245i	−0.424314	−	0.734934i	−0.996356	+	0.0852908i	$0.972818\pi$
$114$	−11.9814	−	5.37815i	−1.12216	−	0.503710i
$115$	−2.35144			−0.219273
$116$	−2.43385	−	4.21555i	−0.225977	−	0.391404i
$117$	−4.74048	+	14.2936i	−0.438257	+	1.32145i
$118$	−17.7275			−1.63195
$119$		0			0
$120$	2.83310	+	1.27171i	0.258626	+	0.116090i
$121$	−10.6538			−0.968530
$122$	9.90278	−	17.1521i	0.896556	−	1.55288i
$123$	−0.185466	−	1.81769i	−0.0167229	−	0.163895i
$124$	2.69937	+	4.67545i	0.242411	+	0.419867i
$125$	8.63731			0.772544
$126$		0			0
$127$	6.43268			0.570808			0.285404	−	0.958407i	$-0.407872\pi$
$127$	6.43268			0.570808			0.285404	+	0.958407i	$0.407872\pi$
$128$	6.38874	+	11.0656i	0.564690	+	0.978071i
$129$	9.81303	−	7.08414i	0.863989	−	0.623724i
$130$	4.04944	−	7.01384i	0.355160	−	0.615154i
$131$	6.63315			0.579541			0.289770	−	0.957096i	$-0.406421\pi$
$131$	6.63315			0.579541			0.289770	+	0.957096i	$0.406421\pi$
$132$	−0.734332	+	0.530123i	−0.0639154	+	0.0461413i
$133$		0			0
$134$	20.1643			1.74193
$135$	1.48143	+	4.70484i	0.127501	+	0.404928i
$136$	7.16059	+	12.4025i	0.614016	+	1.06351i
$137$	14.0334			1.19896			0.599478	−	0.800391i	$-0.295375\pi$
$137$	14.0334			1.19896			0.599478	+	0.800391i	$0.295375\pi$
$138$	−0.740208	−	7.25453i	−0.0630107	−	0.617546i
$139$	−4.40254	−	7.62541i	−0.373418	−	0.646779i	0.616671	−	0.787221i	$-0.288481\pi$
$139$	−4.40254	−	7.62541i	−0.373418	−	0.646779i	−0.990089	+	0.140442i	$0.955148\pi$
$140$		0			0
$141$	−1.31453	−	12.8833i	−0.110704	−	1.08497i
$142$	3.65452	+	6.32981i	0.306680	+	0.531186i
$143$	−1.47672	−	2.55775i	−0.123489	−	0.213890i
$144$	−4.71015	+	14.2022i	−0.392512	+	1.18351i
$145$	2.59963	−	4.50268i	0.215887	−	0.373928i
$146$	3.79121	−	6.56657i	0.313763	−	0.543453i
$147$		0			0
$148$	3.10507	+	5.37815i	0.255236	+	0.442081i
$149$	−4.36584			−0.357663			−0.178832	−	0.983880i	$-0.557232\pi$
$149$	−4.36584			−0.357663			−0.178832	+	0.983880i	$0.557232\pi$
$150$	1.22483	+	12.0041i	0.100007	+	0.980134i
$151$	−12.6538			−1.02975			−0.514877	−	0.857264i	$-0.672162\pi$
$151$	−12.6538			−1.02975			−0.514877	+	0.857264i	$0.672162\pi$
$152$	4.21303	−	7.29719i	0.341722	−	0.591880i
$153$	−7.16059	+	21.5908i	−0.578899	+	1.74551i
$154$		0			0
$155$	−2.88323	+	4.99391i	−0.231587	+	0.401120i
$156$	7.04944	+	3.16431i	0.564407	+	0.253347i
$157$	−5.63694	+	9.76347i	−0.449877	+	0.779210i	−0.998378	−	0.0569405i	$-0.981865\pi$
$157$	−5.63694	+	9.76347i	−0.449877	+	0.779210i	0.548501	+	0.836150i	$0.315199\pi$
$158$	−1.13348	+	1.96324i	−0.0901745	+	0.156187i
$159$	1.21702	+	11.9276i	0.0965160	+	0.945920i
$160$	2.23061	−	3.86353i	0.176345	−	0.305439i
$161$		0			0
$162$	−14.0488	+	6.05146i	−1.10377	+	0.475447i
$163$	0.833104	−	1.44298i	0.0652537	−	0.113023i	−0.831553	−	0.555446i	$-0.812548\pi$
$163$	0.833104	−	1.44298i	0.0652537	−	0.113023i	0.896807	+	0.442423i	$0.145881\pi$
$164$	−0.937519			−0.0732080
$165$	−0.882546	−	0.396151i	−0.0687061	−	0.0308404i
$166$	9.66047			0.749798
$167$	−1.95135	−	3.37984i	−0.151000	−	0.261540i	0.780595	−	0.625037i	$-0.214916\pi$
$167$	−1.95135	−	3.37984i	−0.151000	−	0.261540i	−0.931595	+	0.363497i	$0.881583\pi$
$168$		0			0
$169$	−6.09888	+	10.5636i	−0.469145	+	0.812583i
$170$	6.11677	−	10.5945i	0.469134	−	0.812565i
$171$	13.1079	−	2.70303i	1.00238	−	0.206706i
$172$	−3.10507	−	5.37815i	−0.236760	−	0.410080i
$173$	−8.05705	−	13.9552i	−0.612566	−	1.06100i	−0.990806	−	0.135288i	$-0.956804\pi$
$173$	−8.05705	−	13.9552i	−0.612566	−	1.06100i	0.378240	−	0.925708i	$-0.376529\pi$
$174$	14.7098	+	6.60282i	1.11514	+	0.500559i
$175$		0			0
$176$	−1.46727	−	2.54138i	−0.110599	−	0.191564i
$177$	14.6476	−	10.5743i	1.10098	−	0.794813i
$178$	−1.43389			−0.107475
$179$	−7.14400	−	12.3738i	−0.533967	−	0.924859i	−0.999213	−	0.0396767i	$-0.987367\pi$
$179$	−7.14400	−	12.3738i	−0.533967	−	0.924859i	0.465245	−	0.885182i	$-0.345966\pi$
$180$	2.47880	−	0.511165i	0.184759	−	0.0381000i
$181$	12.8873			0.957905			0.478952	−	0.877841i	$-0.341017\pi$
$181$	12.8873			0.957905			0.478952	+	0.877841i	$0.341017\pi$
$182$		0			0
$183$	2.04875	+	20.0791i	0.151448	+	1.48429i
$184$	4.67859			0.344910
$185$	−3.31657	+	5.74447i	−0.243839	+	0.422342i
$186$	−16.3145	−	7.32316i	−1.19624	−	0.536960i
$187$	−2.23061	−	3.86353i	−0.163118	−	0.282529i
$188$	−6.64490			−0.484629
$189$		0			0
$190$	−7.19777			−0.522181
$191$	1.08217	+	1.87438i	0.0783034	+	0.135625i	0.902518	−	0.430652i	$-0.141716\pi$
$191$	1.08217	+	1.87438i	0.0783034	+	0.135625i	−0.824215	+	0.566277i	$0.808383\pi$
$192$	−3.14076	−	1.40980i	−0.226665	−	0.101744i
$193$	−5.21565	+	9.03377i	−0.375431	+	0.650265i	−0.990391	−	0.138293i	$-0.955839\pi$
$193$	−5.21565	+	9.03377i	−0.375431	+	0.650265i	0.614961	+	0.788558i	$0.289172\pi$
$194$	5.78949			0.415661
$195$	0.837775	+	8.21075i	0.0599943	+	0.587984i
$196$		0			0
$197$	−18.7848			−1.33836			−0.669179	−	0.743101i	$-0.733354\pi$
$197$	−18.7848			−1.33836			−0.669179	+	0.743101i	$0.733354\pi$
$198$	0.944368	−	2.84748i	0.0671133	−	0.202362i
$199$	−4.21303	−	7.29719i	−0.298654	−	0.517284i	0.677174	−	0.735823i	$-0.263204\pi$
$199$	−4.21303	−	7.29719i	−0.298654	−	0.517284i	−0.975828	+	0.218539i	$0.929871\pi$
$200$	−7.74171			−0.547422
$201$	−16.6611	+	12.0278i	−1.17518	+	0.848379i
$202$	−8.14681	−	14.1107i	−0.573208	−	0.992825i
$203$		0			0
$204$	10.6483	+	4.77975i	0.745532	+	0.334650i
$205$	−0.500689	−	0.867218i	−0.0349696	−	0.0605692i
$206$	−9.90278	−	17.1521i	−0.689960	−	1.19505i
$207$	4.93887	+	5.55264i	0.343275	+	0.385935i
$208$	−12.5183	+	21.6823i	−0.867986	+	1.50340i
$209$	−1.31241	+	2.27316i	−0.0907814	+	0.157238i
$210$		0			0
$211$	−5.61126	−	9.71899i	−0.386295	−	0.669083i	0.605653	−	0.795729i	$-0.292912\pi$
$211$	−5.61126	−	9.71899i	−0.386295	−	0.669083i	−0.991948	+	0.126646i	$0.959579\pi$
$212$	6.15197			0.422519
$213$	−6.79527	−	3.05022i	−0.465605	−	0.208998i
$214$	6.45606			0.441327
$215$	3.31657	−	5.74447i	0.226188	−	0.391770i
$216$	−2.94756	−	9.36107i	−0.200556	−	0.636940i
$217$		0			0
$218$	−10.9320	+	18.9348i	−0.740408	+	1.28242i
$219$	0.784350	+	7.68715i	0.0530015	+	0.519449i
$220$	−0.248187	+	0.429872i	−0.0167328	+	0.0289820i
$221$	−19.0309	+	32.9624i	−1.28016	+	2.21729i
$222$	−18.7665	−	8.42380i	−1.25953	−	0.565369i
$223$	10.3774	−	17.9742i	0.694923	−	1.20364i	−0.275283	−	0.961363i	$-0.588772\pi$
$223$	10.3774	−	17.9742i	0.694923	−	1.20364i	0.970206	−	0.242279i	$-0.0778951\pi$
$224$		0			0
$225$	−8.17240	−	9.18801i	−0.544826	−	0.612534i
$226$	7.66621	−	13.2783i	0.509949	−	0.883257i
$227$	−10.4302			−0.692279			−0.346139	−	0.938183i	$-0.612508\pi$
$227$	−10.4302			−0.692279			−0.346139	+	0.938183i	$0.612508\pi$
$228$	−0.697080	−	6.83185i	−0.0461653	−	0.452450i
$229$	15.0592			0.995141			0.497570	−	0.867424i	$-0.334226\pi$
$229$	15.0592			0.995141			0.497570	+	0.867424i	$0.334226\pi$
$230$	−1.99829	−	3.46113i	−0.131763	−	0.228220i
$231$		0			0
$232$	−5.17240	+	8.95886i	−0.339585	+	0.588178i
$233$	−2.19344	+	3.79915i	−0.143697	+	0.248890i	−0.928886	−	0.370366i	$-0.879232\pi$
$233$	−2.19344	+	3.79915i	−0.143697	+	0.248890i	0.785189	+	0.619256i	$0.212566\pi$
$234$	−25.0676	+	5.16931i	−1.63872	+	0.337929i
$235$	−3.54875	−	6.14662i	−0.231495	−	0.400961i
$236$	−4.63486	−	8.02781i	−0.301704	−	0.522566i
$237$	−0.234501	−	2.29826i	−0.0152325	−	0.149288i
$238$		0			0
$239$	4.77561	+	8.27160i	0.308909	+	0.535046i	0.978124	−	0.208023i	$-0.0667029\pi$
$239$	4.77561	+	8.27160i	0.308909	+	0.535046i	−0.669215	+	0.743069i	$0.733370\pi$
$240$	0.832415	+	8.15822i	0.0537322	+	0.526611i
$241$	10.5358			0.678674			0.339337	−	0.940665i	$-0.389797\pi$
$241$	10.5358			0.678674			0.339337	+	0.940665i	$0.389797\pi$
$242$	−9.05377	−	15.6816i	−0.581999	−	1.00805i
$243$	7.99837	−	13.3801i	0.513095	−	0.858332i
$244$	10.3563			0.662996
$245$		0			0
$246$	2.51788	−	1.81769i	0.160534	−	0.115892i
$247$	22.3942			1.42491
$248$	5.73668	−	9.93623i	0.364280	−	0.630951i
$249$	−7.98212	+	5.76238i	−0.505846	+	0.365176i
$250$	7.34011	+	12.7134i	0.464229	+	0.804068i
$251$	−24.4346			−1.54230			−0.771148	−	0.636656i	$-0.780317\pi$
$251$	−24.4346			−1.54230			−0.771148	+	0.636656i	$0.780317\pi$
$252$		0			0
$253$	−1.45744			−0.0916282
$254$	5.46658	+	9.46839i	0.343004	+	0.594100i
$255$	1.26548	+	12.4025i	0.0792472	+	0.776675i
$256$	−8.87085	+	15.3648i	−0.554428	+	0.960298i
$257$	4.00832			0.250032			0.125016	−	0.992155i	$-0.460102\pi$
$257$	4.00832			0.250032			0.125016	+	0.992155i	$0.460102\pi$
$258$	18.7665	+	8.42380i	1.16835	+	0.524443i
$259$		0			0
$260$	4.23491			0.262638
$261$	−16.0927	+	3.31855i	−0.996113	+	0.205413i
$262$	5.63694	+	9.76347i	0.348251	+	0.603189i
$263$	17.6872			1.09064			0.545321	−	0.838227i	$-0.316408\pi$
$263$	17.6872			1.09064			0.545321	+	0.838227i	$0.316408\pi$
$264$	1.75597	+	0.788211i	0.108073	+	0.0485110i
$265$	3.28550	+	5.69066i	0.201827	+	0.349574i
$266$		0			0
$267$	1.18478	−	0.855304i	0.0725072	−	0.0523438i
$268$	5.27197	+	9.13132i	0.322037	+	0.557784i
$269$	7.11366	+	12.3212i	0.433727	+	0.751238i	0.997191	−	0.0749032i	$-0.0238648\pi$
$269$	7.11366	+	12.3212i	0.433727	+	0.751238i	−0.563463	+	0.826141i	$0.690531\pi$
$270$	−5.66621	+	6.17878i	−0.344834	+	0.376029i
$271$	2.69937	−	4.67545i	0.163975	−	0.284013i	−0.772316	−	0.635239i	$-0.780902\pi$
$271$	2.69937	−	4.67545i	0.163975	−	0.284013i	0.936291	+	0.351226i	$0.114235\pi$
$272$	−18.9091	+	32.7515i	−1.14653	+	1.98585i
$273$		0			0
$274$	11.9258	+	20.6561i	0.720464	+	1.24788i
$275$	2.41164			0.145427
$276$	3.09165	−	2.23190i	0.186095	−	0.134344i
$277$	7.66621			0.460618			0.230309	−	0.973118i	$-0.426026\pi$
$277$	7.66621			0.460618			0.230309	+	0.973118i	$0.426026\pi$
$278$	7.48267	−	12.9604i	0.448781	−	0.777311i
$279$	17.8483	−	3.68059i	1.06855	−	0.220351i
$280$		0			0
$281$	11.3312	−	19.6263i	0.675965	−	1.17081i	−0.300220	−	0.953870i	$-0.597060\pi$
$281$	11.3312	−	19.6263i	0.675965	−	1.17081i	0.976186	−	0.216936i	$-0.0696065\pi$
$282$	17.8461	−	12.8833i	1.06272	−	0.767189i
$283$	15.9246	−	27.5822i	0.946619	−	1.63959i	0.194144	−	0.980973i	$-0.437807\pi$
$283$	15.9246	−	27.5822i	0.946619	−	1.63959i	0.752476	−	0.658620i	$-0.228859\pi$
$284$	−1.91095	+	3.30986i	−0.113394	+	0.196404i
$285$	5.94727	−	4.29340i	0.352286	−	0.254319i
$286$	2.50987	−	4.34722i	0.148412	−	0.257057i
$287$		0			0
$288$	−13.8083	+	2.84748i	−0.813664	+	0.167790i
$289$	−20.2465	+	35.0680i	−1.19097	+	2.06282i
$290$	8.83680			0.518915
$291$	−4.78366	+	3.45338i	−0.280423	+	0.202441i
$292$	3.96485			0.232025
$293$	−13.7468	−	23.8102i	−0.803097	−	1.39100i	−0.917568	−	0.397578i	$-0.869851\pi$
$293$	−13.7468	−	23.8102i	−0.803097	−	1.39100i	0.114472	−	0.993427i	$-0.463483\pi$
$294$		0			0
$295$	4.95056	−	8.57462i	0.288233	−	0.499234i
$296$	6.59888	−	11.4296i	0.383552	−	0.664332i
$297$	0.918200	+	2.91609i	0.0532793	+	0.169208i
$298$	−3.71015	−	6.42617i	−0.214923	−	0.372258i
$299$	6.21720	+	10.7685i	0.359550	+	0.622758i
$300$	−5.11578	+	3.69314i	−0.295360	+	0.213224i
$301$		0			0
$302$	−10.7534	−	18.6254i	−0.618789	−	1.07177i
$303$	15.1483	+	6.79968i	0.870249	+	0.390632i
$304$	22.2509			1.27618
$305$	5.53087	+	9.57975i	0.316697	+	0.548535i
$306$	−37.8652	+	7.80835i	−2.16461	+	0.446374i
$307$	14.8176			0.845683			0.422841	−	0.906204i	$-0.361033\pi$
$307$	14.8176			0.845683			0.422841	+	0.906204i	$0.361033\pi$
$308$		0			0
$309$	18.4134	+	8.26530i	1.04750	+	0.470196i
$310$	−9.80085			−0.556651
$311$	−14.5318	+	25.1698i	−0.824021	+	1.42725i	0.0786442	+	0.996903i	$0.474941\pi$
$311$	−14.5318	+	25.1698i	−0.824021	+	1.42725i	−0.902665	+	0.430343i	$0.858392\pi$
$312$	−1.66690	−	16.3367i	−0.0943694	−	0.924883i
$313$	12.2390	+	21.1986i	0.691790	+	1.19822i	0.971251	+	0.238058i	$0.0765110\pi$
$313$	12.2390	+	21.1986i	0.691790	+	1.19822i	−0.279461	+	0.960157i	$0.590156\pi$
$314$	−19.1614			−1.08134
$315$		0			0
$316$	−1.18539			−0.0666834
$317$	3.69344	+	6.39722i	0.207444	+	0.359304i	0.950909	−	0.309472i	$-0.100152\pi$
$317$	3.69344	+	6.39722i	0.207444	+	0.359304i	−0.743465	+	0.668775i	$0.766819\pi$
$318$	−16.5222	+	11.9276i	−0.926521	+	0.668867i
$319$	1.61126	−	2.79079i	0.0902135	−	0.156254i
$320$	−1.88679			−0.105475
$321$	−5.33442	+	3.85098i	−0.297738	+	0.214941i
$322$		0			0
$323$	33.8268			1.88218
$324$	−6.41342	−	4.77975i	−0.356301	−	0.265542i
$325$	−10.2877	−	17.8188i	−0.570657	−	0.988407i
$326$	2.83193			0.156846
$327$	−2.26168	−	22.1660i	−0.125071	−	1.22578i
$328$	0.996205	+	1.72548i	0.0550062	+	0.0952736i
$329$		0			0
$330$	−0.166896	−	1.63569i	−0.00918734	−	0.0900419i
$331$	−10.0309	−	17.3740i	−0.551347	−	0.954960i	−0.998178	−	0.0603420i	$-0.980781\pi$
$331$	−10.0309	−	17.3740i	−0.551347	−	0.954960i	0.446831	−	0.894618i	$-0.352552\pi$
$332$	2.52573	+	4.37470i	0.138618	+	0.240093i
$333$	20.5309	−	4.23377i	1.12508	−	0.232009i
$334$	3.31657	−	5.74447i	0.181475	−	0.314324i
$335$	−5.63106	+	9.75329i	−0.307658	+	0.532879i
$336$		0			0
$337$	−3.20327	−	5.54823i	−0.174493	−	0.302231i	0.765493	−	0.643445i	$-0.222495\pi$
$337$	−3.20327	−	5.54823i	−0.174493	−	0.302231i	−0.939986	+	0.341214i	$0.889162\pi$
$338$	−20.7317			−1.12765
$339$	1.58604	+	15.5442i	0.0861416	+	0.844245i
$340$	6.39692			0.346921
$341$	−1.78705	+	3.09526i	−0.0967740	+	0.167617i
$342$	15.1179	+	16.9967i	0.817482	+	0.919074i
$343$		0			0
$344$	−6.59888	+	11.4296i	−0.355788	+	0.616243i
$345$	3.71565	+	1.66786i	0.200044	+	0.0897944i
$346$	13.6940	−	23.7187i	0.736194	−	1.27512i
$347$	14.5963	−	25.2816i	0.783572	−	1.35719i	−0.146276	−	0.989244i	$-0.546729\pi$
$347$	14.5963	−	25.2816i	0.783572	−	1.35719i	0.929848	−	0.367943i	$-0.119938\pi$
$348$	0.855815	+	8.38755i	0.0458765	+	0.449620i
$349$	2.17192	−	3.76188i	0.116260	−	0.201369i	−0.802022	−	0.597294i	$-0.796243\pi$
$349$	2.17192	−	3.76188i	0.116260	−	0.201369i	0.918283	+	0.395925i	$0.129576\pi$
$350$		0			0
$351$	17.6291	−	19.2238i	0.940970	−	1.02609i
$352$	1.38255	−	2.39464i	0.0736899	−	0.127635i
$353$	25.7007			1.36791			0.683955	−	0.729525i	$-0.260259\pi$
$353$	25.7007			1.36791			0.683955	+	0.729525i	$0.260259\pi$
$354$	28.0123	+	12.5740i	1.48884	+	0.668300i
$355$	−4.08222			−0.216662
$356$	−0.374892	−	0.649331i	−0.0198692	−	0.0344145i
$357$		0			0
$358$	12.1421	−	21.0308i	0.641732	−	1.11151i
$359$	−10.3436	+	17.9157i	−0.545916	+	0.945554i	0.452633	+	0.891697i	$0.350485\pi$
$359$	−10.3436	+	17.9157i	−0.545916	+	0.945554i	−0.998549	+	0.0538567i	$0.982849\pi$
$360$	−3.57475	−	4.01899i	−0.188406	−	0.211820i
$361$	−0.451246	−	0.781582i	−0.0237498	−	0.0411359i
$362$	10.9518	+	18.9691i	0.575614	+	0.996992i
$363$	16.8348	+	7.55667i	0.883595	+	0.396622i
$364$		0			0
$365$	2.11745	+	3.66754i	0.110833	+	0.191968i
$366$	−27.8138	+	20.0791i	−1.45385	+	1.04955i
$367$	−2.84781			−0.148655			−0.0743273	−	0.997234i	$-0.523681\pi$
$367$	−2.84781			−0.148655			−0.0743273	+	0.997234i	$0.523681\pi$
$368$	6.17742	+	10.6996i	0.322020	+	0.557755i
$369$	−0.996205	+	3.00379i	−0.0518604	+	0.156371i
$370$	−11.2739			−0.586101
$371$		0			0
$372$	−0.949180	−	9.30259i	−0.0492127	−	0.482317i
$373$	21.4327			1.10974			0.554871	−	0.831936i	$-0.312768\pi$
$373$	21.4327			1.10974			0.554871	+	0.831936i	$0.312768\pi$
$374$	3.79121	−	6.56657i	0.196039	−	0.339549i
$375$	−13.6483	−	6.12637i	−0.704797	−	0.316364i
$376$	7.06085	+	12.2297i	0.364135	+	0.630701i
$377$	−27.4936			−1.41599
$378$		0			0
$379$	27.0494			1.38943			0.694716	−	0.719284i	$-0.255530\pi$
$379$	27.0494			1.38943			0.694716	+	0.719284i	$0.255530\pi$
$380$	−1.88186	−	3.25947i	−0.0965372	−	0.167207i
$381$	−10.1647	−	4.56265i	−0.520751	−	0.233751i
$382$	−1.83929	+	3.18575i	−0.0941064	+	0.162997i
$383$	−14.4268			−0.737175			−0.368588	−	0.929593i	$-0.620159\pi$
$383$	−14.4268			−0.737175			−0.368588	+	0.929593i	$0.620159\pi$
$384$	−2.24647	−	22.0169i	−0.114640	−	1.12355i
$385$		0			0
$386$	−17.7293			−0.902399
$387$	−20.5309	+	4.23377i	−1.04364	+	0.215215i
$388$	1.51366	+	2.62174i	0.0768446	+	0.133099i
$389$	−6.10755			−0.309665			−0.154832	−	0.987941i	$-0.549484\pi$
$389$	−6.10755			−0.309665			−0.154832	+	0.987941i	$0.549484\pi$
$390$	−11.3736	+	8.21075i	−0.575926	+	0.415768i
$391$	9.39120	+	16.2660i	0.474933	+	0.822609i
$392$		0			0
$393$	−10.4814	−	4.70484i	−0.528718	−	0.237328i
$394$	−15.9635	−	27.6497i	−0.804232	−	1.39297i
$395$	−0.633065	−	1.09650i	−0.0318530	−	0.0551710i
$396$	1.53637	−	0.316823i	0.0772057	−	0.0159210i
$397$	6.44364	−	11.1607i	0.323397	−	0.560140i	−0.657789	−	0.753202i	$-0.728508\pi$
$397$	6.44364	−	11.1607i	0.323397	−	0.560140i	0.981187	+	0.193061i	$0.0618417\pi$
$398$	7.16059	−	12.4025i	0.358928	−	0.621682i
$399$		0			0
$400$	−10.2218	−	17.7047i	−0.511092	−	0.885237i
$401$	8.39060			0.419006			0.209503	−	0.977808i	$-0.432815\pi$
$401$	8.39060			0.419006			0.209503	+	0.977808i	$0.432815\pi$
$402$	−31.8629	−	14.3024i	−1.58918	−	0.713339i
$403$	30.4930			1.51897
$404$	4.25997	−	7.37848i	0.211941	−	0.367093i
$405$	0.996205	−	8.48516i	0.0495018	−	0.421631i
$406$		0			0
$407$	−2.05563	+	3.56046i	−0.101894	+	0.176485i
$408$	−2.51788	−	24.6769i	−0.124654	−	1.22169i
$409$	−3.40633	+	5.89994i	−0.168432	+	0.291733i	−0.937869	−	0.346990i	$-0.887204\pi$
$409$	−3.40633	+	5.89994i	−0.168432	+	0.291733i	0.769437	+	0.638723i	$0.220537\pi$
$410$	0.850985	−	1.47395i	0.0420271	−	0.0727931i
$411$	−22.1750	−	9.95379i	−1.09381	−	0.490984i
$412$	5.17817	−	8.96885i	0.255110	−	0.441864i
$413$		0			0
$414$	−3.97593	+	11.9883i	−0.195406	+	0.589194i
$415$	−2.69777	+	4.67267i	−0.132428	+	0.229372i
$416$	−23.5909			−1.15664
$417$	1.54806	+	15.1721i	0.0758091	+	0.742979i
$418$	−4.46122			−0.218205
$419$	5.16231	+	8.94137i	0.252195	+	0.436815i	0.964130	−	0.265431i	$-0.0855142\pi$
$419$	5.16231	+	8.94137i	0.252195	+	0.436815i	−0.711935	+	0.702246i	$0.752181\pi$
$420$		0			0
$421$	−1.56801	+	2.71588i	−0.0764202	+	0.132364i	−0.901703	−	0.432356i	$-0.857682\pi$
$421$	−1.56801	+	2.71588i	−0.0764202	+	0.132364i	0.825283	+	0.564720i	$0.191016\pi$
$422$	9.53706	−	16.5187i	0.464257	−	0.804117i
$423$	−7.06085	+	21.2901i	−0.343310	+	1.03516i
$424$	−6.53706	−	11.3225i	−0.317468	−	0.549870i
$425$	−15.5397	−	26.9156i	−0.753787	−	1.30560i
$426$	−1.28504	−	12.5942i	−0.0622603	−	0.610192i
$427$		0			0
$428$	1.68794	+	2.92359i	0.0815895	+	0.141317i
$429$	0.519258	+	5.08907i	0.0250700	+	0.245703i
$430$	11.2739			0.543675
$431$	−15.9363	−	27.6025i	−0.767625	−	1.32957i	−0.938847	−	0.344334i	$-0.888105\pi$
$431$	−15.9363	−	27.6025i	−0.767625	−	1.32957i	0.171222	−	0.985233i	$-0.445229\pi$
$432$	17.5163	−	19.1008i	0.842752	−	0.918989i
$433$	7.48855			0.359877			0.179938	−	0.983678i	$-0.442410\pi$
$433$	7.48855			0.359877			0.179938	+	0.983678i	$0.442410\pi$
$434$		0			0
$435$	−7.30154	+	5.27107i	−0.350082	+	0.252728i
$436$	−11.4327			−0.547526
$437$	5.52544	−	9.57035i	0.264318	−	0.457812i
$438$	−10.6483	+	7.68715i	−0.508797	+	0.367306i
$439$	−1.14465	−	1.98259i	−0.0546311	−	0.0946238i	0.837417	−	0.546565i	$-0.184065\pi$
$439$	−1.14465	−	1.98259i	−0.0546311	−	0.0946238i	−0.892048	+	0.451941i	$0.850732\pi$
$440$	1.05489			0.0502900
$441$		0			0
$442$	−64.6908			−3.07703
$443$	−18.6749	−	32.3458i	−0.887270	−	1.53680i	−0.843090	−	0.537773i	$-0.819266\pi$
$443$	−18.6749	−	32.3458i	−0.887270	−	1.53680i	−0.0441800	−	0.999024i	$-0.514067\pi$
$444$	−1.09184	−	10.7007i	−0.0518163	−	0.507834i
$445$	0.400427	−	0.693560i	0.0189821	−	0.0328779i
$446$	35.2755			1.67034
$447$	6.89872	+	3.09665i	0.326298	+	0.146467i
$448$		0			0
$449$	−6.20286			−0.292731			−0.146366	−	0.989231i	$-0.546758\pi$
$449$	−6.20286			−0.292731			−0.146366	+	0.989231i	$0.546758\pi$
$450$	6.57901	−	19.8372i	0.310138	−	0.935136i
$451$	−0.310330	−	0.537507i	−0.0146129	−	0.0253102i
$452$	8.01732			0.377103
$453$	19.9951	+	8.97526i	0.939450	+	0.421694i
$454$	−8.86376	−	15.3525i	−0.415997	−	0.720527i
$455$		0			0
$456$	−11.8331	+	8.54245i	−0.554136	+	0.400037i
$457$	−10.0858	−	17.4691i	−0.471795	−	0.817172i	0.527685	−	0.849440i	$-0.323060\pi$
$457$	−10.0858	−	17.4691i	−0.471795	−	0.817172i	−0.999479	+	0.0322682i	$0.989727\pi$
$458$	12.7975	+	22.1660i	0.597989	+	1.03575i
$459$	26.6291	−	29.0380i	1.24294	−	1.35538i
$460$	1.04490	−	1.80983i	0.0487189	−	0.0843836i
$461$	11.2680	−	19.5168i	0.524803	−	0.908986i	−0.474780	−	0.880105i	$-0.657472\pi$
$461$	11.2680	−	19.5168i	0.524803	−	0.908986i	0.999583	−	0.0288813i	$-0.00919447\pi$
$462$		0			0
$463$	13.8145	+	23.9275i	0.642016	+	1.11200i	0.984982	+	0.172656i	$0.0552350\pi$
$463$	13.8145	+	23.9275i	0.642016	+	1.11200i	−0.342966	+	0.939348i	$0.611432\pi$
$464$	−27.3177			−1.26819
$465$	8.09811	−	5.84612i	0.375541	−	0.271107i
$466$	−7.45606			−0.345395
$467$	−10.0612	+	17.4265i	−0.465577	+	0.806404i	−0.999227	−	0.0393016i	$-0.987487\pi$
$467$	−10.0612	+	17.4265i	−0.465577	+	0.806404i	0.533650	+	0.845705i	$0.320820\pi$
$468$	−8.89483	−	10.0002i	−0.411164	−	0.462261i
$469$		0			0
$470$	6.03156	−	10.4470i	0.278215	−	0.481883i
$471$	15.8324	−	11.4296i	0.729519	−	0.526648i
$472$	−9.84997	+	17.0607i	−0.453382	+	0.785280i
$473$	2.05563	−	3.56046i	0.0945181	−	0.163710i
$474$	3.18358	−	2.29826i	0.146227	−	0.105563i
$475$	−9.14301	+	15.8362i	−0.419510	+	0.726613i
$476$		0			0
$477$	6.53706	−	19.7107i	0.299312	−	0.902493i
$478$	−8.11677	+	14.0586i	−0.371252	+	0.643028i
$479$	−9.58658			−0.438022			−0.219011	−	0.975722i	$-0.570283\pi$
$479$	−9.58658			−0.438022			−0.219011	+	0.975722i	$0.570283\pi$
$480$	−6.26509	+	4.52284i	−0.285961	+	0.206439i
$481$	35.0760			1.59933
$482$	8.95351	+	15.5079i	0.407821	+	0.706367i
$483$		0			0
$484$	4.73422	−	8.19991i	0.215192	−	0.372723i
$485$	−1.61677	+	2.80032i	−0.0734135	+	0.127156i
$486$	26.4915	+	0.402398i	1.20168	+	0.0182531i
$487$	−6.53706	−	11.3225i	−0.296223	−	0.513073i	0.679046	−	0.734096i	$-0.262394\pi$
$487$	−6.53706	−	11.3225i	−0.296223	−	0.513073i	−0.975269	+	0.221023i	$0.929060\pi$
$488$	−11.0046	−	19.0605i	−0.498155	−	0.862830i
$489$	−2.33993	+	1.68922i	−0.105815	+	0.0763893i
$490$		0			0
$491$	−7.67054	−	13.2858i	−0.346167	−	0.599578i	0.639398	−	0.768876i	$-0.279183\pi$
$491$	−7.67054	−	13.2858i	−0.346167	−	0.599578i	−0.985565	+	0.169298i	$0.945850\pi$
$492$	1.48143	+	0.664975i	0.0667880	+	0.0299794i
$493$	−41.5297			−1.87040
$494$	19.0309	+	32.9624i	0.856239	+	1.48305i
$495$	1.11358	+	1.25197i	0.0500515	+	0.0562717i
$496$	30.2979			1.36042
$497$		0			0
$498$	−15.2651	−	6.85210i	−0.684045	−	0.307050i
$499$	4.86535			0.217803			0.108902	−	0.994053i	$-0.465267\pi$
$499$	4.86535			0.217803			0.108902	+	0.994053i	$0.465267\pi$
$500$	−3.83814	+	6.64786i	−0.171647	+	0.297301i
$501$	0.686155	+	6.72477i	0.0306551	+	0.300440i
$502$	−20.7648	−	35.9657i	−0.926780	−	1.60523i
$503$	16.0085			0.713783			0.356892	−	0.934146i	$-0.383837\pi$
$503$	16.0085			0.713783			0.356892	+	0.934146i	$0.383837\pi$
$504$		0			0
$505$	9.10026			0.404956
$506$	−1.23855	−	2.14523i	−0.0550603	−	0.0953672i
$507$	17.1299	−	12.3663i	0.760764	−	0.549205i
$508$	−2.85848	+	4.95102i	−0.126824	+	0.219666i
$509$	−31.1851			−1.38225			−0.691127	−	0.722733i	$-0.742885\pi$
$509$	−31.1851			−1.38225			−0.691127	+	0.722733i	$0.742885\pi$
$510$	−17.1801	+	12.4025i	−0.760747	+	0.549192i
$511$		0			0
$512$	−4.59937			−0.203265
$513$	−22.6298	−	5.02607i	−0.999128	−	0.221907i
$514$	3.40633	+	5.89994i	0.150247	+	0.260235i
$515$	11.0617			0.487439
$516$	1.09184	+	10.7007i	0.0480655	+	0.471074i
$517$	−2.19954	−	3.80971i	−0.0967356	−	0.167551i
$518$		0			0
$519$	2.83310	+	27.7663i	0.124359	+	1.21880i
$520$	−4.50000	−	7.79423i	−0.197338	−	0.341800i
$521$	−10.4830	−	18.1572i	−0.459270	−	0.795480i	0.539652	−	0.841888i	$-0.318556\pi$
$521$	−10.4830	−	18.1572i	−0.459270	−	0.795480i	−0.998923	+	0.0464085i	$0.985222\pi$
$522$	−18.5604	−	20.8670i	−0.812369	−	0.913325i
$523$	−21.7821	+	37.7277i	−0.952465	+	1.64972i	−0.212401	+	0.977183i	$0.568128\pi$
$523$	−21.7821	+	37.7277i	−0.952465	+	1.64972i	−0.740064	+	0.672536i	$0.765205\pi$
$524$	−2.94756	+	5.10532i	−0.128765	+	0.223027i
$525$		0			0
$526$	15.0309	+	26.0342i	0.655377	+	1.13515i
$527$	46.0604			2.00642
$528$	0.515936	+	5.05651i	0.0224532	+	0.220056i
$529$	−16.8640			−0.733216
$530$	−5.58413	+	9.67200i	−0.242559	+	0.420125i
$531$	−30.6459	+	6.31963i	−1.32992	+	0.274249i
$532$		0			0
$533$	−2.64764	+	4.58584i	−0.114682	+	0.198635i
$534$	2.26578	+	1.01705i	0.0980499	+	0.0440120i
$535$	−1.80291	+	3.12273i	−0.0779466	+	0.135007i
$536$	11.2040	−	19.4058i	0.483937	−	0.838204i
$537$	2.51205	+	24.6197i	0.108403	+	1.06242i
$538$	−12.0906	+	20.9415i	−0.521262	+	0.902852i
$539$		0			0
$540$	−4.27946	−	0.950469i	−0.184159	−	0.0409017i
$541$	−4.93268	+	8.54365i	−0.212072	+	0.367320i	−0.952363	−	0.304967i	$-0.901355\pi$
$541$	−4.93268	+	8.54365i	−0.212072	+	0.367320i	0.740291	+	0.672287i	$0.234688\pi$
$542$	9.17585			0.394137
$543$	−20.3640	−	9.14085i	−0.873902	−	0.392271i
$544$	−35.6345			−1.52782
$545$	−6.10570	−	10.5754i	−0.261539	−	0.453000i
$546$		0			0
$547$	−0.284350	+	0.492509i	−0.0121579	+	0.0210582i	−0.872040	−	0.489434i	$-0.837203\pi$
$547$	−0.284350	+	0.492509i	−0.0121579	+	0.0210582i	0.859882	+	0.510492i	$0.170537\pi$
$548$	−6.23600	+	10.8011i	−0.266389	+	0.461399i
$549$	11.0046	−	33.1814i	0.469665	−	1.41615i
$550$	2.04944	+	3.54974i	0.0873885	+	0.151361i
$551$	12.2173	+	21.1609i	0.520473	+	0.901487i
$552$	−7.39292	−	3.31848i	−0.314663	−	0.141244i
$553$		0			0
$554$	6.51485	+	11.2841i	0.276789	+	0.479413i
$555$	9.31522	−	6.72477i	0.395409	−	0.285450i
$556$	7.82538			0.331870
$557$	1.29349	+	2.24040i	0.0548071	+	0.0949286i	0.892127	−	0.451784i	$-0.149212\pi$
$557$	1.29349	+	2.24040i	0.0548071	+	0.0949286i	−0.837320	+	0.546713i	$0.815879\pi$
$558$	20.5853	+	23.1435i	0.871446	+	0.979744i
$559$	−35.0760			−1.48356
$560$		0			0
$561$	0.784350	+	7.68715i	0.0331153	+	0.324552i
$562$	38.5178			1.62478
$563$	16.6416	−	28.8240i	0.701358	−	1.21479i	−0.266632	−	0.963798i	$-0.585911\pi$
$563$	16.6416	−	28.8240i	0.701358	−	1.21479i	0.967990	−	0.250989i	$-0.0807558\pi$
$564$	10.5000	+	4.71317i	0.442130	+	0.198460i
$565$	4.28171	+	7.41613i	0.180133	+	0.311999i
$566$	54.1318			2.27533
$567$		0			0
$568$	8.12227			0.340803
$569$	2.67673	+	4.63623i	0.112214	+	0.194361i	0.916663	−	0.399662i	$-0.130872\pi$
$569$	2.67673	+	4.63623i	0.112214	+	0.194361i	−0.804448	+	0.594022i	$0.797539\pi$
$570$	11.3736	+	5.10532i	0.476389	+	0.213838i
$571$	−2.45056	+	4.24449i	−0.102553	+	0.177626i	−0.912736	−	0.408551i	$-0.866034\pi$
$571$	−2.45056	+	4.24449i	−0.102553	+	0.177626i	0.810183	+	0.586177i	$0.199368\pi$
$572$	2.62482			0.109749
$573$	−0.380525	−	3.72940i	−0.0158967	−	0.155798i
$574$		0			0
$575$	−10.1533			−0.423424
$576$	3.96294	+	4.45543i	0.165122	+	0.185643i
$577$	18.0378	+	31.2425i	0.750925	+	1.30064i	0.947375	+	0.320127i	$0.103725\pi$
$577$	18.0378	+	31.2425i	0.750925	+	1.30064i	−0.196450	+	0.980514i	$0.562941\pi$
$578$	−68.8231			−2.86266
$579$	14.6491	−	10.5754i	0.608797	−	0.439498i
$580$	2.31038	+	4.00170i	0.0959333	+	0.166161i
$581$		0			0
$582$	−9.14833	−	4.10644i	−0.379210	−	0.170217i
$583$	2.03637	+	3.52710i	0.0843380	+	0.146078i
$584$	−4.21303	−	7.29719i	−0.174337	−	0.301960i
$585$	4.50000	−	13.5685i	0.186052	−	0.560990i
$586$	23.3645	−	40.4684i	0.965177	−	1.67174i
$587$	−0.527445	+	0.913562i	−0.0217700	+	0.0377068i	−0.876705	−	0.481028i	$-0.840263\pi$
$587$	−0.527445	+	0.913562i	−0.0217700	+	0.0377068i	0.854935	+	0.518735i	$0.173597\pi$
$588$		0			0
$589$	−13.5501	−	23.4695i	−0.558323	−	0.967045i
$590$	16.8282			0.692807
$591$	29.6829	+	13.3239i	1.22099	+	0.548071i
$592$	34.8516			1.43239
$593$	7.53548	−	13.0518i	0.309445	−	0.535975i	−0.668796	−	0.743446i	$-0.733190\pi$
$593$	7.53548	−	13.0518i	0.309445	−	0.535975i	0.978241	+	0.207471i	$0.0665233\pi$
$594$	−3.51195	+	3.82965i	−0.144097	+	0.157132i
$595$		0			0
$596$	1.94004	−	3.36024i	0.0794670	−	0.137641i
$597$	1.48143	+	14.5190i	0.0606309	+	0.594223i
$598$	−10.5669	+	18.3024i	−0.432114	+	0.748443i
$599$	−21.0283	+	36.4221i	−0.859194	+	1.48817i	0.0135047	+	0.999909i	$0.495701\pi$
$599$	−21.0283	+	36.4221i	−0.859194	+	1.48817i	−0.872699	+	0.488259i	$0.837632\pi$
$600$	12.2331	+	5.49113i	0.499416	+	0.224175i
$601$	−9.44989	+	16.3677i	−0.385469	+	0.667652i	−0.991834	−	0.127534i	$-0.959294\pi$
$601$	−9.44989	+	16.3677i	−0.385469	+	0.667652i	0.606365	+	0.795186i	$0.292627\pi$
$602$		0			0
$603$	34.8585	−	7.18833i	1.41955	−	0.292732i
$604$	5.62296	−	9.73924i	0.228795	−	0.396284i
$605$	10.1134			0.411167
$606$	2.86467	+	28.0756i	0.116369	+	1.14049i
$607$	−29.4425			−1.19504			−0.597518	−	0.801856i	$-0.703846\pi$
$607$	−29.4425			−1.19504			−0.597518	+	0.801856i	$0.703846\pi$
$608$	10.4830	+	18.1572i	0.425143	+	0.736370i
$609$		0			0
$610$	−9.40043	+	16.2820i	−0.380612	+	0.659240i
$611$	−18.7658	+	32.5033i	−0.759182	+	1.31494i
$612$	−13.4358	−	15.1055i	−0.543111	−	0.610605i
$613$	5.83379	+	10.1044i	0.235625	+	0.408114i	0.959454	−	0.281865i	$-0.0909531\pi$
$613$	5.83379	+	10.1044i	0.235625	+	0.408114i	−0.723829	+	0.689979i	$0.757620\pi$
$614$	12.5922	+	21.8103i	0.508179	+	0.880191i
$615$	0.176057	+	1.72548i	0.00709932	+	0.0695780i
$616$		0			0
$617$	16.4054	+	28.4151i	0.660458	+	1.14395i	0.980495	+	0.196542i	$0.0629713\pi$
$617$	16.4054	+	28.4151i	0.660458	+	1.14395i	−0.320037	+	0.947405i	$0.603695\pi$
$618$	3.48212	+	34.1271i	0.140071	+	1.37279i
$619$	−24.1612			−0.971119			−0.485560	−	0.874204i	$-0.661384\pi$
$619$	−24.1612			−0.971119			−0.485560	+	0.874204i	$0.661384\pi$
$620$	−2.56243	−	4.43827i	−0.102910	−	0.178245i
$621$	−3.86576	−	12.2772i	−0.155127	−	0.492665i
$622$	−49.3972			−1.98065
$623$		0			0
$624$	35.1599	−	25.3824i	1.40752	−	1.01611i
$625$	12.2953			0.491811
$626$	−20.8018	+	36.0297i	−0.831406	+	1.44004i
$627$	3.68615	−	2.66108i	0.147211	−	0.106273i
$628$	−5.00975	−	8.67714i	−0.199911	−	0.346256i
$629$	52.9830			2.11257
$630$		0			0
$631$	−11.1003			−0.441894			−0.220947	−	0.975286i	$-0.570915\pi$
$631$	−11.1003			−0.441894			−0.220947	+	0.975286i	$0.570915\pi$
$632$	1.25959	+	2.18168i	0.0501038	+	0.0867824i
$633$	1.97309	+	19.3376i	0.0784233	+	0.768600i
$634$	−6.27747	+	10.8729i	−0.249310	+	0.431818i
$635$	−6.10635			−0.242323
$636$	−9.72109	−	4.36354i	−0.385466	−	0.173026i
$637$		0			0
$638$	5.47710			0.216840
$639$	8.57413	+	9.63967i	0.339187	+	0.381339i
$640$	−6.06464	−	10.5043i	−0.239726	−	0.415218i
$641$	7.30037			0.288347			0.144174	−	0.989552i	$-0.453948\pi$
$641$	7.30037			0.288347			0.144174	+	0.989552i	$0.453948\pi$
$642$	−10.2016	−	4.57923i	−0.402625	−	0.180728i
$643$	−10.6256	−	18.4041i	−0.419033	−	0.725787i	0.576809	−	0.816879i	$-0.304298\pi$
$643$	−10.6256	−	18.4041i	−0.419033	−	0.725787i	−0.995842	+	0.0910922i	$0.970964\pi$
$644$		0			0
$645$	−9.31522	+	6.72477i	−0.366787	+	0.264787i
$646$	28.7465	+	49.7904i	1.13102	+	1.95898i
$647$	−8.47300	−	14.6757i	−0.333108	−	0.576960i	0.650011	−	0.759924i	$-0.274764\pi$
$647$	−8.47300	−	14.6757i	−0.333108	−	0.576960i	−0.983120	+	0.182964i	$0.941431\pi$
$648$	−1.98212	+	16.8827i	−0.0778650	+	0.663214i
$649$	3.06839	−	5.31460i	0.120445	−	0.208616i
$650$	17.4852	−	30.2853i	0.685826	−	1.18789i
$651$		0			0
$652$	0.740409	+	1.28243i	0.0289967	+	0.0502237i
$653$	−3.73305			−0.146085			−0.0730427	−	0.997329i	$-0.523271\pi$
$653$	−3.73305			−0.146085			−0.0730427	+	0.997329i	$0.523271\pi$
$654$	30.7046	−	22.1660i	1.20064	−	0.866758i
$655$	−6.29665			−0.246031
$656$	−2.63070	+	4.55650i	−0.102711	+	0.177902i
$657$	4.21303	−	12.7033i	0.164366	−	0.495601i
$658$		0			0
$659$	11.7992	−	20.4368i	0.459632	−	0.796105i	−0.539310	−	0.842107i	$-0.681315\pi$
$659$	11.7992	−	20.4368i	0.459632	−	0.796105i	0.998941	+	0.0460022i	$0.0146481\pi$
$660$	0.697080	−	0.503230i	0.0271338	−	0.0195882i
$661$	−17.2588	+	29.8930i	−0.671288	+	1.16270i	0.306252	+	0.951951i	$0.400925\pi$
$661$	−17.2588	+	29.8930i	−0.671288	+	1.16270i	−0.977539	+	0.210754i	$0.932408\pi$
$662$	17.0488	−	29.5293i	0.662619	−	1.14769i
$663$	53.4518	−	38.5875i	2.07590	−	1.49861i
$664$	5.36767	−	9.29708i	0.208306	−	0.360796i
$665$		0			0
$666$	23.6792	+	26.6219i	0.917550	+	1.03158i
$667$	−6.78366	+	11.7496i	−0.262664	+	0.454948i
$668$	3.46847			0.134199
$669$	−29.1469	+	21.0415i	−1.12689	+	0.813512i
$670$	−19.1414			−0.739498
$671$	3.42807	+	5.93759i	0.132339	+	0.229218i
$672$		0			0
$673$	12.2287	−	21.1808i	0.471382	−	0.816458i	−0.528082	−	0.849194i	$-0.677088\pi$
$673$	12.2287	−	21.1808i	0.471382	−	0.816458i	0.999464	+	0.0327353i	$0.0104218\pi$
$674$	5.44437	−	9.42992i	0.209709	−	0.363227i
$675$	6.39671	+	20.3151i	0.246210	+	0.781930i
$676$	−5.42030	−	9.38823i	−0.208473	−	0.361086i
$677$	4.16022	+	7.20572i	0.159890	+	0.276938i	0.934829	−	0.355098i	$-0.115553\pi$
$677$	4.16022	+	7.20572i	0.159890	+	0.276938i	−0.774939	+	0.632037i	$0.782219\pi$
$678$	−21.5320	+	15.5442i	−0.826931	+	0.596971i
$679$		0			0
$680$	−6.79734	−	11.7733i	−0.260666	−	0.451487i
$681$	16.4814	+	7.39808i	0.631570	+	0.283495i
$682$	−6.07463			−0.232610
$683$	21.2312	+	36.7735i	0.812389	+	1.40710i	0.911188	+	0.411991i	$0.135167\pi$
$683$	21.2312	+	36.7735i	0.812389	+	1.40710i	−0.0987988	+	0.995107i	$0.531500\pi$
$684$	−3.74427	+	11.2898i	−0.143166	+	0.431678i
$685$	−13.3215			−0.508989
$686$		0			0
$687$	−23.7960	−	10.6814i	−0.907873	−	0.407520i
$688$	−34.8516			−1.32870
$689$	17.3737	−	30.0921i	0.661885	−	1.14642i
$690$	0.702658	+	6.88651i	0.0267497	+	0.262165i
$691$	−17.6964	−	30.6511i	−0.673204	−	1.16602i	−0.976990	−	0.213284i	$-0.931584\pi$
$691$	−17.6964	−	30.6511i	−0.673204	−	1.16602i	0.303786	−	0.952740i	$-0.401749\pi$
$692$	14.3212			0.544410
$693$		0			0
$694$	49.6167			1.88342
$695$	4.17920	+	7.23859i	0.158526	+	0.274575i
$696$	14.5277	−	10.4877i	0.550669	−	0.397535i
$697$	−3.99931	+	6.92701i	−0.151485	+	0.262379i
$698$	7.38293			0.279448
$699$	6.16069	−	4.44747i	0.233019	−	0.168219i
$700$		0			0
$701$	−7.00372			−0.264527			−0.132263	−	0.991215i	$-0.542224\pi$
$701$	−7.00372			−0.264527			−0.132263	+	0.991215i	$0.542224\pi$
$702$	43.2774	+	9.61192i	1.63340	+	0.362778i
$703$	−15.5867	−	26.9969i	−0.587862	−	1.01821i
$704$	−1.16944			−0.0440751
$705$	1.24785	+	12.2297i	0.0469967	+	0.460599i
$706$	21.8408	+	37.8294i	0.821989	+	1.42373i
$707$		0			0
$708$	1.62976	+	15.9727i	0.0612500	+	0.600291i
$709$	1.11126	+	1.92477i	0.0417344	+	0.0722861i	0.886138	−	0.463421i	$-0.153378\pi$
$709$	1.11126	+	1.92477i	0.0417344	+	0.0722861i	−0.844404	+	0.535707i	$0.820045\pi$
$710$	−3.46913	−	6.00870i	−0.130194	−	0.225503i
$711$	−1.25959	+	3.79795i	−0.0472383	+	0.142434i
$712$	−0.796717	+	1.37995i	−0.0298582	+	0.0517160i
$713$	7.52373	−	13.0315i	0.281766	−	0.488033i
$714$		0			0
$715$	1.40180	+	2.42800i	0.0524245	+	0.0908019i
$716$	12.6983			0.474556
$717$	−1.67925	−	16.4578i	−0.0627127	−	0.614626i
$718$	−35.1606			−1.31218
$719$	−13.0088	+	22.5319i	−0.485145	+	0.840296i	−0.999854	−	0.0170686i	$-0.994567\pi$
$719$	−13.0088	+	22.5319i	−0.485145	+	0.840296i	0.514709	+	0.857365i	$0.327900\pi$
$720$	4.47121	−	13.4817i	0.166632	−	0.502434i
$721$		0			0
$722$	0.766951	−	1.32840i	0.0285430	−	0.0494379i
$723$	−16.6483	−	7.47299i	−0.619158	−	0.277924i
$724$	−5.72670	+	9.91893i	−0.212831	+	0.368634i
$725$	11.2250	−	19.4423i	0.416886	−	0.722068i
$726$	3.18358	+	31.2012i	0.118154	+	1.15798i
$727$	0.685875	−	1.18797i	0.0254377	−	0.0440594i	−0.853026	−	0.521868i	$-0.825235\pi$
$727$	0.685875	−	1.18797i	0.0254377	−	0.0440594i	0.878464	+	0.477809i	$0.158569\pi$
$728$		0			0
$729$	−22.1291	+	15.4695i	−0.819595	+	0.572943i
$730$	−3.59888	+	6.23345i	−0.133201	+	0.230710i
$731$	−52.9830			−1.95965
$732$	−16.3647	−	7.34566i	−0.604855	−	0.271504i
$733$	−0.800174			−0.0295551			−0.0147776	−	0.999891i	$-0.504704\pi$
$733$	−0.800174			−0.0295551			−0.0147776	+	0.999891i	$0.504704\pi$
$734$	−2.42011	−	4.19176i	−0.0893280	−	0.154721i
$735$		0			0
$736$	−5.82072	+	10.0818i	−0.214555	+	0.371620i
$737$	−3.49017	+	6.04515i	−0.128562	+	0.222676i
$738$	−5.26792	+	1.08632i	−0.193915	+	0.0399881i
$739$	−2.68547	−	4.65136i	−0.0987865	−	0.171103i	0.812396	−	0.583106i	$-0.198163\pi$
$739$	−2.68547	−	4.65136i	−0.0987865	−	0.171103i	−0.911183	+	0.412003i	$0.864829\pi$
$740$	−2.94756	−	5.10532i	−0.108354	−	0.187675i
$741$	−35.3864	−	15.8840i	−1.29995	−	0.583513i
$742$		0			0
$743$	6.63162	+	11.4863i	0.243290	+	0.421391i	0.961650	−	0.274281i	$-0.0884399\pi$
$743$	6.63162	+	11.4863i	0.243290	+	0.421391i	−0.718359	+	0.695672i	$0.755107\pi$
$744$	−16.1126	+	11.6318i	−0.590715	+	0.426444i
$745$	4.14436			0.151838
$746$	18.2138	+	31.5472i	0.666854	+	1.15503i
$747$	16.7002	−	3.44384i	0.611030	−	0.126003i
$748$	3.96485			0.144969
$749$		0			0
$750$	−2.58100	−	25.2955i	−0.0942449	−	0.923662i
$751$	5.55632			0.202753			0.101377	−	0.994848i	$-0.467675\pi$
$751$	5.55632			0.202753			0.101377	+	0.994848i	$0.467675\pi$
$752$	−18.6457	+	32.2953i	−0.679939	+	1.17769i
$753$	38.6105	+	17.3312i	1.40704	+	0.631585i
$754$	−23.3645	−	40.4684i	−0.850883	−	1.47377i
$755$	12.0119			0.437158
$756$		0			0
$757$	−13.3942			−0.486819			−0.243410	−	0.969924i	$-0.578266\pi$
$757$	−13.3942			−0.486819			−0.243410	+	0.969924i	$0.578266\pi$
$758$	22.9869	+	39.8145i	0.834923	+	1.44613i
$759$	2.30298	+	1.03375i	0.0835930	+	0.0375227i
$760$	−3.99931	+	6.92701i	−0.145070	+	0.251269i
$761$	−12.8438			−0.465588			−0.232794	−	0.972526i	$-0.574787\pi$
$761$	−12.8438			−0.465588			−0.232794	+	0.972526i	$0.574787\pi$
$762$	−1.92221	−	18.8390i	−0.0696345	−	0.682464i
$763$		0			0
$764$	−1.92353			−0.0695910
$765$	6.79734	−	20.4955i	0.245758	−	0.741018i
$766$	−12.2601	−	21.2351i	−0.442975	−	0.767256i
$767$	−52.3570			−1.89050
$768$	24.9155	−	17.9868i	0.899060	−	0.649042i
$769$	−1.48259	−	2.56793i	−0.0534636	−	0.0926018i	0.838055	−	0.545586i	$-0.183693\pi$
$769$	−1.48259	−	2.56793i	−0.0534636	−	0.0926018i	−0.891519	+	0.452984i	$0.850359\pi$
$770$		0			0
$771$	−6.33379	−	2.84307i	−0.228106	−	0.102391i
$772$	−4.63533	−	8.02864i	−0.166829	−	0.288957i
$773$	9.63939	+	16.6959i	0.346705	+	0.600510i	0.985662	−	0.168732i	$-0.0539673\pi$
$773$	9.63939	+	16.6959i	0.346705	+	0.600510i	−0.638957	+	0.769242i	$0.720634\pi$
$774$	−23.6792	−	26.6219i	−0.851131	−	0.956905i
$775$	−12.4496	+	21.5633i	−0.447203	+	0.774578i
$776$	3.21683	−	5.57171i	0.115477	−	0.200013i
$777$		0			0
$778$	−5.19028	−	8.98983i	−0.186080	−	0.322301i
$779$	4.70610			0.168614
$780$	−6.69183	−	3.00379i	−0.239606	−	0.107553i
$781$	−2.53018			−0.0905371
$782$	−15.9616	+	27.6462i	−0.570784	+	0.988627i
$783$	27.7829	+	6.17058i	0.992878	+	0.220518i
$784$		0			0
$785$	5.35098	−	9.26818i	0.190985	−	0.330795i
$786$	−1.98212	−	19.4261i	−0.0706998	−	0.692905i
$787$	−6.82265	+	11.8172i	−0.243201	+	0.421237i	−0.961624	−	0.274370i	$-0.911531\pi$
$787$	−6.82265	+	11.8172i	−0.243201	+	0.421237i	0.718423	+	0.695606i	$0.244864\pi$
$788$	8.34734	−	14.4580i	0.297362	−	0.515046i
$789$	−27.9487	−	12.5454i	−0.994999	−	0.446629i
$790$	1.07598	−	1.86364i	0.0382815	−	0.0663055i
$791$		0			0
$792$	−2.21565	−	2.49100i	−0.0787297	−	0.0885137i
$793$	29.2472	−	50.6577i	1.03860	−	1.79891i
$794$	21.9036			0.777330
$795$	−1.15528	−	11.3225i	−0.0409736	−	0.401569i
$796$	7.48855			0.265425
$797$	11.4792	+	19.8826i	0.406616	+	0.704279i	0.994508	−	0.104660i	$-0.0333755\pi$
$797$	11.4792	+	19.8826i	0.406616	+	0.704279i	−0.587892	+	0.808939i	$0.700042\pi$
$798$		0			0
$799$	−28.3461	+	49.0969i	−1.00281	+	1.73692i
$800$	9.63162	−	16.6824i	0.340529	−	0.589814i
$801$	−2.47880	+	0.511165i	−0.0875840	+	0.0180611i
$802$	7.13045	+	12.3503i	0.251785	+	0.436104i
$803$	1.31241	+	2.27316i	0.0463140	+	0.0802182i
$804$	−1.85378	−	18.1683i	−0.0653779	−	0.640747i
$805$		0			0
$806$	25.9134	+	44.8834i	0.912761	+	1.58095i
$807$	−2.50138	−	24.5151i	−0.0880527	−	0.862974i
$808$	−18.1065			−0.636985
$809$	−19.7291	−	34.1718i	−0.693639	−	1.20142i	−0.970637	−	0.240548i	$-0.922673\pi$
$809$	−19.7291	−	34.1718i	−0.693639	−	1.20142i	0.276998	−	0.960870i	$-0.410660\pi$
$810$	13.3361	−	5.74447i	0.468582	−	0.201840i
$811$	−0.496374			−0.0174300			−0.00871502	−	0.999962i	$-0.502774\pi$
$811$	−0.496374			−0.0174300			−0.00871502	+	0.999962i	$0.502774\pi$
$812$		0			0
$813$	−7.58169	+	5.47331i	−0.265902	+	0.191957i
$814$	−6.98762			−0.244916
$815$	−0.790841	+	1.36978i	−0.0277020	+	0.0479812i
$816$	53.1098	−	38.3406i	1.85922	−	1.34219i
$817$	15.5867	+	26.9969i	0.545308	+	0.944501i
$818$	−11.5790			−0.404850
$819$		0			0
$820$	0.889960			0.0310788
$821$	−23.5519	−	40.7931i	−0.821967	−	1.42369i	−0.904215	−	0.427077i	$-0.859543\pi$
$821$	−23.5519	−	40.7931i	−0.821967	−	1.42369i	0.0822476	−	0.996612i	$-0.473790\pi$
$822$	−4.19347	−	41.0988i	−0.146264	−	1.43349i
$823$	1.09888	−	1.90332i	0.0383047	−	0.0663457i	−0.846237	−	0.532806i	$-0.821138\pi$
$823$	1.09888	−	1.90332i	0.0383047	−	0.0663457i	0.884542	+	0.466460i	$0.154471\pi$
$824$	−22.0092			−0.766727
$825$	−3.81077	−	1.71055i	−0.132674	−	0.0595538i
$826$		0			0
$827$	−55.3360			−1.92422			−0.962110	−	0.272661i	$-0.912096\pi$
$827$	−55.3360			−1.92422			−0.962110	+	0.272661i	$0.912096\pi$
$828$	−6.46836	+	1.33387i	−0.224791	+	0.0463553i
$829$	10.1603	+	17.5982i	0.352882	+	0.611209i	0.986753	−	0.162229i	$-0.0518684\pi$
$829$	10.1603	+	17.5982i	0.352882	+	0.611209i	−0.633871	+	0.773439i	$0.718535\pi$
$830$	−9.17041			−0.318310
$831$	−12.1138	−	5.43758i	−0.420224	−	0.188628i
$832$	4.98867	+	8.64062i	0.172951	+	0.299560i
$833$		0			0
$834$	−21.0165	+	15.1721i	−0.727742	+	0.525365i
$835$	1.85236	+	3.20839i	0.0641036	+	0.111031i
$836$	−1.16639	−	2.02024i	−0.0403403	−	0.0698715i
$837$	−30.8138	−	6.84376i	−1.06508	−	0.236555i
$838$	−8.77400	+	15.1970i	−0.303093	+	0.524972i
$839$	−12.2760	+	21.2626i	−0.423813	+	0.734066i	−0.996309	−	0.0858417i	$-0.972642\pi$
$839$	−12.2760	+	21.2626i	−0.423813	+	0.734066i	0.572496	+	0.819908i	$0.305975\pi$
$840$		0			0
$841$	−0.499311	−	0.864833i	−0.0172176	−	0.0298218i
$842$	−5.33007			−0.183686
$843$	−31.8259	+	22.9755i	−1.09614	+	0.791319i
$844$	9.97386			0.343315
$845$	5.78949	−	10.0277i	0.199165	−	0.344963i
$846$	−37.3377	+	7.69959i	−1.28370	+	0.264717i
$847$		0			0
$848$	17.2625	−	29.8996i	0.592798	−	1.02676i
$849$	−44.7273	+	32.2891i	−1.53504	+	1.10816i
$850$	26.4118	−	45.7465i	0.905916	−	1.56909i
$851$	8.65452	−	14.9901i	0.296673	−	0.513853i
$852$	5.36726	−	3.87468i	0.183879	−	0.132745i
$853$	−26.7708	+	46.3684i	−0.916614	+	1.58762i	−0.112093	+	0.993698i	$0.535756\pi$
$853$	−26.7708	+	46.3684i	−0.916614	+	1.58762i	−0.804521	+	0.593925i	$0.797578\pi$
$854$		0			0
$855$	−12.4429	+	2.56591i	−0.425539	+	0.0877524i
$856$	3.58719	−	6.21320i	0.122608	−	0.212363i
$857$	54.1553			1.84991			0.924955	−	0.380076i	$-0.124102\pi$
$857$	54.1553			1.84991			0.924955	+	0.380076i	$0.124102\pi$
$858$	−7.04944	+	5.08907i	−0.240664	+	0.173738i
$859$	−1.79292			−0.0611737			−0.0305869	−	0.999532i	$-0.509738\pi$
$859$	−1.79292			−0.0611737			−0.0305869	+	0.999532i	$0.509738\pi$
$860$	2.94756	+	5.10532i	0.100511	+	0.174090i
$861$		0			0
$862$	27.0858	−	46.9140i	0.922547	−	1.59790i
$863$	16.2854	−	28.2072i	0.554363	−	0.960185i	−0.443590	−	0.896230i	$-0.646295\pi$
$863$	16.2854	−	28.2072i	0.554363	−	0.960185i	0.997953	−	0.0639549i	$-0.0203714\pi$
$864$	23.8391	+	5.29467i	0.811022	+	0.180128i
$865$	7.64833	+	13.2473i	0.260051	+	0.450421i
$866$	6.36387	+	11.0226i	0.216253	+	0.374562i
$867$	56.8662	−	41.0524i	1.93128	−	1.39421i
$868$		0			0
$869$	−0.392378	−	0.679618i	−0.0133105	−	0.0230545i
$870$	−13.9635	−	6.26787i	−0.473409	−	0.212501i
$871$	59.5541			2.01791
$872$	12.1483	+	21.0415i	0.411394	+	0.712556i
$873$	10.0084	−	2.06388i	0.338733	−	0.0698518i
$874$	18.7824			0.635324
$875$		0			0
$876$	−6.26509	−	2.81223i	−0.211678	−	0.0950166i
$877$	−36.7293			−1.24026			−0.620131	−	0.784499i	$-0.712920\pi$
$877$	−36.7293			−1.24026			−0.620131	+	0.784499i	$0.712920\pi$
$878$	1.94548	−	3.36966i	0.0656566	−	0.113721i
$879$	4.83379	+	47.3744i	0.163040	+	1.59790i
$880$	1.39284	+	2.41246i	0.0469525	+	0.0813241i
$881$	−25.3721			−0.854807			−0.427403	−	0.904061i	$-0.640572\pi$
$881$	−25.3721			−0.854807			−0.427403	+	0.904061i	$0.640572\pi$
$882$		0			0
$883$	−16.9381			−0.570012			−0.285006	−	0.958526i	$-0.591996\pi$
$883$	−16.9381			−0.570012			−0.285006	+	0.958526i	$0.591996\pi$
$884$	−16.9134	−	29.2949i	−0.568860	−	0.985294i
$885$	−13.9046	+	10.0379i	−0.467397	+	0.337420i
$886$	31.7403	−	54.9759i	1.06634	−	1.84695i
$887$	48.0137			1.61214			0.806071	−	0.591819i	$-0.201590\pi$
$887$	48.0137			1.61214			0.806071	+	0.591819i	$0.201590\pi$
$888$	−18.5342	+	13.3801i	−0.621968	+	0.449006i
$889$		0			0
$890$	1.36115			0.0456260
$891$	0.617454	−	5.25915i	0.0206855	−	0.176188i
$892$	9.22279	+	15.9743i	0.308802	+	0.534860i
$893$	33.3556			1.11620
$894$	1.30460	+	12.7859i	0.0436324	+	0.427626i
$895$	6.78159	+	11.7461i	0.226684	+	0.392627i
$896$		0			0
$897$	−2.18615	−	21.4258i	−0.0729936	−	0.715385i
$898$	−5.27128	−	9.13013i	−0.175905	−	0.304676i
$899$	16.6357	+	28.8138i	0.554831	+	0.960995i
$900$	10.7033	−	2.20717i	0.356776	−	0.0735724i
$901$	26.2433	−	45.4548i	0.874292	−	1.51432i
$902$	0.527445	−	0.913562i	0.0175620	−	0.0304183i
$903$		0			0
$904$	−8.51918	−	14.7557i	−0.283344	−	0.490766i
$905$	−12.2335			−0.406656
$906$	3.78122	+	37.0585i	0.125623	+	1.23119i
$907$	−24.7775			−0.822722			−0.411361	−	0.911472i	$-0.634947\pi$
$907$	−24.7775			−0.822722			−0.411361	+	0.911472i	$0.634947\pi$
$908$	4.63486	−	8.02781i	0.153813	−	0.266412i
$909$	−19.1138	−	21.4892i	−0.633965	−	0.712751i
$910$		0			0
$911$	−15.7916	+	27.3519i	−0.523200	+	0.906209i	0.476435	+	0.879210i	$0.341929\pi$
$911$	−15.7916	+	27.3519i	−0.523200	+	0.906209i	−0.999635	+	0.0269997i	$0.991405\pi$
$912$	−35.1599	−	15.7824i	−1.16426	−	0.522606i
$913$	−1.67209	+	2.89615i	−0.0553382	+	0.0958486i
$914$	17.1421	−	29.6911i	0.567011	−	0.982093i
$915$	−1.94482	−	19.0605i	−0.0642938	−	0.630122i
$916$	−6.69183	+	11.5906i	−0.221104	+	0.382964i
$917$		0			0
$918$	65.3714	+	14.5190i	2.15758	+	0.479198i
$919$	−0.796041	+	1.37878i	−0.0262590	+	0.0454819i	−0.878856	−	0.477087i	$-0.841693\pi$
$919$	−0.796041	+	1.37878i	−0.0262590	+	0.0454819i	0.852597	+	0.522569i	$0.175026\pi$
$920$	−4.44125			−0.146424
$921$	−23.4141	−	10.5100i	−0.771521	−	0.346315i
$922$	38.3028			1.26144
$923$	10.7934	+	18.6947i	0.355268	+	0.615342i
$924$		0			0
$925$	−14.3207	+	24.8042i	−0.470863	+	0.815558i
$926$	−23.4796	+	40.6678i	−0.771587	+	1.33643i
$927$	−23.2336	−	26.1210i	−0.763093	−	0.857925i
$928$	−12.8702	−	22.2918i	−0.422484	−	0.731764i
$929$	−13.5356	−	23.4443i	−0.444087	−	0.769182i	0.553901	−	0.832583i	$-0.313139\pi$
$929$	−13.5356	−	23.4443i	−0.444087	−	0.769182i	−0.997988	+	0.0634007i	$0.979805\pi$
$930$	15.4869	+	6.95167i	0.507836	+	0.227954i
$931$		0			0
$932$	−1.94939	−	3.37644i	−0.0638543	−	0.110599i
$933$	40.8152	−	29.4650i	1.33623	−	0.964640i
$934$	−34.2006			−1.11908
$935$	2.11745	+	3.66754i	0.0692482	+	0.119941i
$936$	−8.95351	+	26.9969i	−0.292655	+	0.882421i
$937$	32.6624			1.06704			0.533518	−	0.845789i	$-0.320870\pi$
$937$	32.6624			1.06704			0.533518	+	0.845789i	$0.320870\pi$
$938$		0			0
$939$	−4.30361	−	42.1782i	−0.140443	−	1.37643i
$940$	6.30781			0.205738
$941$	−2.36143	+	4.09011i	−0.0769803	+	0.133334i	−0.901946	−	0.431849i	$-0.857861\pi$
$941$	−2.36143	+	4.09011i	−0.0769803	+	0.133334i	0.824965	+	0.565183i	$0.191195\pi$
$942$	30.2781	+	13.5910i	0.986513	+	0.442820i
$943$	1.30654	+	2.26299i	0.0425466	+	0.0736929i
$944$	−52.0220			−1.69317
$945$		0			0
$946$	6.98762			0.227187
$947$	−28.3905	−	49.1738i	−0.922568	−	1.59793i	−0.795427	−	0.606050i	$-0.792753\pi$
$947$	−28.3905	−	49.1738i	−0.922568	−	1.59793i	−0.127141	−	0.991885i	$-0.540580\pi$
$948$	1.87310	+	0.840787i	0.0608356	+	0.0273075i
$949$	11.1971	−	19.3939i	0.363473	−	0.629553i
$950$	−31.0795			−1.00835
$951$	−1.29872	−	12.7284i	−0.0421140	−	0.412745i
$952$		0			0
$953$	−47.1693			−1.52796			−0.763982	−	0.645238i	$-0.776758\pi$
$953$	−47.1693			−1.52796			−0.763982	+	0.645238i	$0.776758\pi$
$954$	34.5679	−	7.12842i	1.11918	−	0.230791i
$955$	−1.02728	−	1.77930i	−0.0332419	−	0.0575766i
$956$	−8.48852			−0.274538
$957$	−4.52554	+	3.26704i	−0.146290	+	0.105608i
$958$	−8.14681	−	14.1107i	−0.263211	−	0.455896i
$959$		0			0
$960$	2.98143	+	1.33829i	0.0962253	+	0.0431930i
$961$	−2.95056	−	5.11052i	−0.0951793	−	0.164855i
$962$	29.8081	+	51.6291i	0.961052	+	1.66459i
$963$	11.1607	−	2.30150i	0.359649	−	0.0741649i
$964$	−4.68179	+	8.10910i	−0.150790	+	0.261177i
$965$	4.95107	−	8.57550i	0.159380	−	0.276055i
$966$		0			0
$967$	−23.6985	−	41.0469i	−0.762091	−	1.31998i	−0.941771	−	0.336255i	$-0.890840\pi$
$967$	−23.6985	−	41.0469i	−0.762091	−	1.31998i	0.179680	−	0.983725i	$-0.442494\pi$
$968$	−20.1223			−0.646754
$969$	−53.4518	−	23.9931i	−1.71712	−	0.770769i
$970$	−5.49580			−0.176459
$971$	−11.3736	+	19.6997i	−0.364997	+	0.632193i	−0.988776	−	0.149408i	$-0.952263\pi$
$971$	−11.3736	+	19.6997i	−0.364997	+	0.632193i	0.623779	+	0.781601i	$0.285597\pi$
$972$	6.74399	+	12.1018i	0.216314	+	0.388164i
$973$		0			0
$974$	11.1106	−	19.2441i	0.356006	−	0.616620i
$975$	3.61745	+	35.4534i	0.115851	+	1.13542i
$976$	29.0601	−	50.3335i	0.930190	−	1.61114i
$977$	−17.8425	+	30.9040i	−0.570831	+	0.988708i	0.425650	+	0.904888i	$0.360045\pi$
$977$	−17.8425	+	30.9040i	−0.570831	+	0.988708i	−0.996481	+	0.0838200i	$0.973288\pi$
$978$	−4.47491	−	2.00867i	−0.143092	−	0.0642301i
$979$	0.248187	−	0.429872i	0.00793209	−	0.0137388i
$980$		0			0
$981$	−12.1483	+	36.6300i	−0.387866	+	1.16951i
$982$	13.0371	−	22.5809i	0.416029	−	0.720584i
$983$	24.0134			0.765908			0.382954	−	0.923767i	$-0.374907\pi$
$983$	24.0134			0.765908			0.382954	+	0.923767i	$0.374907\pi$
$984$	−0.350296	−	3.43313i	−0.0111670	−	0.109444i
$985$	17.8318			0.568169
$986$	−35.2925	−	61.1284i	−1.12394	−	1.94672i
$987$		0			0
$988$	−9.95125	+	17.2361i	−0.316591	+	0.548352i
$989$	−8.65452	+	14.9901i	−0.275198	+	0.476656i
$990$	−0.896461	+	2.70303i	−0.0284914	+	0.0859081i
$991$	22.2095	+	38.4679i	0.705507	+	1.22197i	0.966508	+	0.256635i	$0.0826139\pi$
$991$	22.2095	+	38.4679i	0.705507	+	1.22197i	−0.261002	+	0.965338i	$0.584053\pi$
$992$	14.2742	+	24.7237i	0.453208	+	0.784979i
$993$	3.52716	+	34.5685i	0.111931	+	1.09700i
$994$		0			0
$995$	3.99931	+	6.92701i	0.126787	+	0.219601i
$996$	−0.888124	−	8.70420i	−0.0281413	−	0.275803i
$997$	9.04673			0.286513			0.143256	−	0.989686i	$-0.454243\pi$
$997$	9.04673			0.286513			0.143256	+	0.989686i	$0.454243\pi$
$998$	4.13465	+	7.16142i	0.130880	+	0.226691i
$999$	−35.4450	−	7.87235i	−1.12143	−	0.249070i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.g.g.79.5		12
3.2	odd	2		1323.2.g.g.667.2		12
7.2	even	3		441.2.f.g.295.6	yes	12
7.3	odd	6		441.2.h.g.214.1		12
7.4	even	3		441.2.h.g.214.2		12
7.5	odd	6		441.2.f.g.295.5	yes	12
7.6	odd	2	inner	441.2.g.g.79.6		12
9.4	even	3		441.2.h.g.373.2		12
9.5	odd	6		1323.2.h.g.226.5		12
21.2	odd	6		1323.2.f.g.883.1		12
21.5	even	6		1323.2.f.g.883.2		12
21.11	odd	6		1323.2.h.g.802.5		12
21.17	even	6		1323.2.h.g.802.6		12
21.20	even	2		1323.2.g.g.667.1		12
63.2	odd	6		3969.2.a.bd.1.6		6
63.4	even	3	inner	441.2.g.g.67.5		12
63.5	even	6		1323.2.f.g.442.2		12
63.13	odd	6		441.2.h.g.373.1		12
63.16	even	3		3969.2.a.be.1.1		6
63.23	odd	6		1323.2.f.g.442.1		12
63.31	odd	6	inner	441.2.g.g.67.6		12
63.32	odd	6		1323.2.g.g.361.2		12
63.40	odd	6		441.2.f.g.148.5	✓	12
63.41	even	6		1323.2.h.g.226.6		12
63.47	even	6		3969.2.a.bd.1.5		6
63.58	even	3		441.2.f.g.148.6	yes	12
63.59	even	6		1323.2.g.g.361.1		12
63.61	odd	6		3969.2.a.be.1.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.f.g.148.5	✓	12	63.40	odd	6
441.2.f.g.148.6	yes	12	63.58	even	3
441.2.f.g.295.5	yes	12	7.5	odd	6
441.2.f.g.295.6	yes	12	7.2	even	3
441.2.g.g.67.5		12	63.4	even	3	inner
441.2.g.g.67.6		12	63.31	odd	6	inner
441.2.g.g.79.5		12	1.1	even	1	trivial
441.2.g.g.79.6		12	7.6	odd	2	inner
441.2.h.g.214.1		12	7.3	odd	6
441.2.h.g.214.2		12	7.4	even	3
441.2.h.g.373.1		12	63.13	odd	6
441.2.h.g.373.2		12	9.4	even	3
1323.2.f.g.442.1		12	63.23	odd	6
1323.2.f.g.442.2		12	63.5	even	6
1323.2.f.g.883.1		12	21.2	odd	6
1323.2.f.g.883.2		12	21.5	even	6
1323.2.g.g.361.1		12	63.59	even	6
1323.2.g.g.361.2		12	63.32	odd	6
1323.2.g.g.667.1		12	21.20	even	2
1323.2.g.g.667.2		12	3.2	odd	2
1323.2.h.g.226.5		12	9.5	odd	6
1323.2.h.g.226.6		12	63.41	even	6
1323.2.h.g.802.5		12	21.11	odd	6
1323.2.h.g.802.6		12	21.17	even	6
3969.2.a.bd.1.5		6	63.47	even	6
3969.2.a.bd.1.6		6	63.2	odd	6
3969.2.a.be.1.1		6	63.16	even	3
3969.2.a.be.1.2		6	63.61	odd	6

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:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.g (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.849814 + 1.47192i) q^{2} +(-1.58016 - 0.709292i) q^{3} +(-0.444368 + 0.769668i) q^{4} -0.949271 q^{5} +(-0.298820 - 2.92864i) q^{6} +1.88874 q^{8} +(1.99381 + 2.24159i) q^{9} +O(q^{10})\)	\(q+(0.849814 + 1.47192i) q^{2} +(-1.58016 - 0.709292i) q^{3} +(-0.444368 + 0.769668i) q^{4} -0.949271 q^{5} +(-0.298820 - 2.92864i) q^{6} +1.88874 q^{8} +(1.99381 + 2.24159i) q^{9} +(-0.806704 - 1.39725i) q^{10} -0.588364 q^{11} +(1.24809 - 0.901012i) q^{12} +(2.50987 + 4.34722i) q^{13} +(1.50000 + 0.673310i) q^{15} +(2.49381 + 4.31941i) q^{16} +(3.79121 + 6.56657i) q^{17} +(-1.60507 + 4.83967i) q^{18} +(2.23061 - 3.86353i) q^{19} +(0.421826 - 0.730623i) q^{20} +(-0.500000 - 0.866025i) q^{22} +2.47710 q^{23} +(-2.98450 - 1.33966i) q^{24} -4.09888 q^{25} +(-4.26584 + 7.38866i) q^{26} +(-1.56060 - 4.95626i) q^{27} +(-2.73855 + 4.74331i) q^{29} +(0.283662 + 2.78007i) q^{30} +(3.03731 - 5.26078i) q^{31} +(-2.34981 + 4.07000i) q^{32} +(0.929709 + 0.417322i) q^{33} +(-6.44364 + 11.1607i) q^{34} +(-2.61126 + 0.538481i) q^{36} +(3.49381 - 6.05146i) q^{37} +7.58242 q^{38} +(-0.882546 - 8.64953i) q^{39} -1.79292 q^{40} +(0.527445 + 0.913562i) q^{41} +(-3.49381 + 6.05146i) q^{43} +(0.261450 - 0.452845i) q^{44} +(-1.89267 - 2.12788i) q^{45} +(2.10507 + 3.64610i) q^{46} +(3.73840 + 6.47510i) q^{47} +(-0.876899 - 8.59419i) q^{48} +(-3.48329 - 6.03323i) q^{50} +(-1.33310 - 13.0653i) q^{51} -4.46122 q^{52} +(-3.46108 - 5.99476i) q^{53} +(5.96901 - 6.50898i) q^{54} +0.558517 q^{55} +(-6.26509 + 4.52284i) q^{57} -9.30903 q^{58} +(-5.21512 + 9.03284i) q^{59} +(-1.18478 + 0.855304i) q^{60} +(-5.82644 - 10.0917i) q^{61} +10.3246 q^{62} +1.98762 q^{64} +(-2.38255 - 4.12669i) q^{65} +(0.175815 + 1.72310i) q^{66} +(5.93199 - 10.2745i) q^{67} -6.73877 q^{68} +(-3.91421 - 1.75699i) q^{69} +4.30037 q^{71} +(3.76578 + 4.23377i) q^{72} +(-2.23061 - 3.86353i) q^{73} +11.8764 q^{74} +(6.47689 + 2.90731i) q^{75} +(1.98242 + 3.43366i) q^{76} +(11.9814 - 8.64953i) q^{78} +(0.666896 + 1.15510i) q^{79} +(-2.36730 - 4.10029i) q^{80} +(-1.04944 + 8.93861i) q^{81} +(-0.896461 + 1.55272i) q^{82} +(2.84194 - 4.92238i) q^{83} +(-3.59888 - 6.23345i) q^{85} -11.8764 q^{86} +(7.69174 - 5.55275i) q^{87} -1.11126 q^{88} +(-0.421826 + 0.730623i) q^{89} +(1.52365 - 4.59415i) q^{90} +(-1.10074 + 1.90654i) q^{92} +(-8.53087 + 6.15854i) q^{93} +(-6.35389 + 11.0053i) q^{94} +(-2.11745 + 3.66754i) q^{95} +(6.59990 - 4.76454i) q^{96} +(1.70317 - 2.94997i) q^{97} +(-1.17309 - 1.31887i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{2} - 6 q^{4} + 24 q^{8} - 12 q^{9}+O(q^{10}) \) 12 * q - 2 * q^2 - 6 * q^4 + 24 * q^8 - 12 * q^9	\( 12 q - 2 q^{2} - 6 q^{4} + 24 q^{8} - 12 q^{9} + 16 q^{11} + 18 q^{15} - 6 q^{16} + 18 q^{18} - 6 q^{22} + 8 q^{23} + 24 q^{25} - 22 q^{29} + 42 q^{30} - 16 q^{32} - 30 q^{36} + 6 q^{37} + 24 q^{39} - 6 q^{43} + 14 q^{44} - 12 q^{46} - 56 q^{50} - 18 q^{51} - 28 q^{53} - 6 q^{57} + 36 q^{58} - 126 q^{60} - 48 q^{64} + 6 q^{65} + 76 q^{71} - 30 q^{72} + 72 q^{74} + 36 q^{78} + 6 q^{79} + 24 q^{81} + 30 q^{85} - 72 q^{86} - 12 q^{88} - 62 q^{92} + 42 q^{93} - 60 q^{95} - 48 q^{99}+O(q^{100}) \) 12 * q - 2 * q^2 - 6 * q^4 + 24 * q^8 - 12 * q^9 + 16 * q^11 + 18 * q^15 - 6 * q^16 + 18 * q^18 - 6 * q^22 + 8 * q^23 + 24 * q^25 - 22 * q^29 + 42 * q^30 - 16 * q^32 - 30 * q^36 + 6 * q^37 + 24 * q^39 - 6 * q^43 + 14 * q^44 - 12 * q^46 - 56 * q^50 - 18 * q^51 - 28 * q^53 - 6 * q^57 + 36 * q^58 - 126 * q^60 - 48 * q^64 + 6 * q^65 + 76 * q^71 - 30 * q^72 + 72 * q^74 + 36 * q^78 + 6 * q^79 + 24 * q^81 + 30 * q^85 - 72 * q^86 - 12 * q^88 - 62 * q^92 + 42 * q^93 - 60 * q^95 - 48 * q^99

Introduction

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