LMFDB - Embedded newform 1089.2.e.k.364.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1089,2,Mod(364,1089)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1089, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("1089.364");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1089 = 3^{2} \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1089.e (of order $3$, degree $2$, 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:	$8.69570878012$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 3x^{14} + 5x^{12} + 15x^{10} + 45x^{8} + 60x^{6} + 80x^{4} + 192x^{2} + 256 $ x^16 + 3x^14 + 5x^12 + 15x^10 + 45x^8 + 60x^6 + 80x^4 + 192*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			364.4
Root			$1.15347 + 0.818235i$ of defining polynomial
Character	$\chi$	$=$	1089.364
Dual form			1089.2.e.k.727.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.131877 - 0.228418i) q^{2} +(-0.532651 - 1.64811i) q^{3} +(0.965217 - 1.67180i) q^{4} +(1.69363 - 2.93346i) q^{5} +(-0.306215 + 0.339016i) q^{6} +(1.65673 + 2.86954i) q^{7} -1.03667 q^{8} +(-2.43257 + 1.75574i) q^{9} +O(q^{10})$	\(q+(-0.131877 - 0.228418i) q^{2} +(-0.532651 - 1.64811i) q^{3} +(0.965217 - 1.67180i) q^{4} +(1.69363 - 2.93346i) q^{5} +(-0.306215 + 0.339016i) q^{6} +(1.65673 + 2.86954i) q^{7} -1.03667 q^{8} +(-2.43257 + 1.75574i) q^{9} -0.893408 q^{10} +(-3.26945 - 0.700300i) q^{12} +(0.494645 - 0.856751i) q^{13} +(0.436969 - 0.756853i) q^{14} +(-5.73680 - 1.22879i) q^{15} +(-1.79372 - 3.10681i) q^{16} +2.21106 q^{17} +(0.721843 + 0.324100i) q^{18} -8.07798 q^{19} +(-3.26945 - 5.66285i) q^{20} +(3.84687 - 4.25894i) q^{21} +(2.46735 - 4.27357i) q^{23} +(0.552183 + 1.70855i) q^{24} +(-3.23680 - 5.60630i) q^{25} -0.260930 q^{26} +(4.18937 + 3.07395i) q^{27} +6.39640 q^{28} +(-5.00403 - 8.66723i) q^{29} +(0.475875 + 1.47244i) q^{30} +(-0.160984 + 0.278832i) q^{31} +(-1.50977 + 2.61500i) q^{32} +(-0.291588 - 0.505045i) q^{34} +11.2236 q^{35} +(0.587301 + 5.76144i) q^{36} -1.35180 q^{37} +(1.06530 + 1.84516i) q^{38} +(-1.67550 - 0.358883i) q^{39} +(-1.75574 + 3.04103i) q^{40} +(0.518335 - 0.897782i) q^{41} +(-1.48013 - 0.317037i) q^{42} +(-3.45180 - 5.97869i) q^{43} +(1.03052 + 10.1094i) q^{45} -1.30155 q^{46} +(3.59355 + 6.22421i) q^{47} +(-4.16496 + 4.61111i) q^{48} +(-1.98949 + 3.44589i) q^{49} +(-0.853720 + 1.47869i) q^{50} +(-1.17772 - 3.64407i) q^{51} +(-0.954880 - 1.65390i) q^{52} +2.44831 q^{53} +(0.149663 - 1.36231i) q^{54} +(-1.71748 - 2.97476i) q^{56} +(4.30274 + 13.3134i) q^{57} +(-1.31984 + 2.28602i) q^{58} +(-1.85249 + 3.20860i) q^{59} +(-7.59156 + 8.40475i) q^{60} +(2.90429 + 5.03038i) q^{61} +0.0849205 q^{62} +(-9.06826 - 4.07155i) q^{63} -6.37846 q^{64} +(-1.67550 - 2.90205i) q^{65} +(-2.93257 + 5.07935i) q^{67} +(2.13415 - 3.69645i) q^{68} +(-8.35758 - 1.79015i) q^{69} +(-1.48013 - 2.56367i) q^{70} +11.6695 q^{71} +(2.52177 - 1.82012i) q^{72} +11.1105 q^{73} +(0.178272 + 0.308776i) q^{74} +(-7.51574 + 8.32082i) q^{75} +(-7.79700 + 13.5048i) q^{76} +(0.138985 + 0.430043i) q^{78} +(-1.07815 - 1.86740i) q^{79} -12.1516 q^{80} +(2.83475 - 8.54191i) q^{81} -0.273426 q^{82} +(4.49431 + 7.78437i) q^{83} +(-3.40705 - 10.5420i) q^{84} +(3.74472 - 6.48605i) q^{85} +(-0.910427 + 1.57691i) q^{86} +(-11.6192 + 12.8638i) q^{87} +13.8921 q^{89} +(2.17327 - 1.56859i) q^{90} +3.27797 q^{91} +(-4.76305 - 8.24985i) q^{92} +(0.545296 + 0.116800i) q^{93} +(0.947815 - 1.64166i) q^{94} +(-13.6811 + 23.6964i) q^{95} +(5.11400 + 1.09539i) q^{96} +(-6.88073 - 11.9178i) q^{97} +1.04947 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{3} - 16 q^{4} + 4 q^{5} - 14 q^{9}+O(q^{10}) $ 16 * q - 2 * q^3 - 16 * q^4 + 4 * q^5 - 14 * q^9	$ 16 q - 2 q^{3} - 16 q^{4} + 4 q^{5} - 14 q^{9} - 6 q^{12} + 4 q^{14} - 52 q^{15} - 24 q^{16} - 6 q^{20} + 46 q^{23} - 12 q^{25} - 60 q^{26} - 32 q^{27} + 14 q^{31} + 38 q^{34} + 54 q^{36} - 12 q^{37} + 4 q^{38} - 4 q^{42} - 28 q^{45} + 16 q^{47} + 20 q^{48} - 42 q^{49} - 96 q^{53} + 46 q^{56} + 50 q^{58} + 48 q^{59} + 12 q^{60} - 12 q^{64} - 22 q^{67} - 10 q^{69} - 4 q^{70} + 68 q^{71} - 10 q^{75} - 72 q^{78} - 148 q^{80} - 14 q^{81} + 112 q^{82} + 14 q^{86} - 16 q^{89} - 96 q^{91} + 84 q^{92} + 30 q^{93} - 4 q^{97}+O(q^{100}) $ 16 * q - 2 * q^3 - 16 * q^4 + 4 * q^5 - 14 * q^9 - 6 * q^12 + 4 * q^14 - 52 * q^15 - 24 * q^16 - 6 * q^20 + 46 * q^23 - 12 * q^25 - 60 * q^26 - 32 * q^27 + 14 * q^31 + 38 * q^34 + 54 * q^36 - 12 * q^37 + 4 * q^38 - 4 * q^42 - 28 * q^45 + 16 * q^47 + 20 * q^48 - 42 * q^49 - 96 * q^53 + 46 * q^56 + 50 * q^58 + 48 * q^59 + 12 * q^60 - 12 * q^64 - 22 * q^67 - 10 * q^69 - 4 * q^70 + 68 * q^71 - 10 * q^75 - 72 * q^78 - 148 * q^80 - 14 * q^81 + 112 * q^82 + 14 * q^86 - 16 * q^89 - 96 * q^91 + 84 * q^92 + 30 * q^93 - 4 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1089\mathbb{Z}\right)^\times$.

$n$	$244$	$848$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.131877	−	0.228418i	−0.0932513	−	0.161516i	0.815626	−	0.578579i	$-0.196393\pi$
$2$	−0.131877	−	0.228418i	−0.0932513	−	0.161516i	−0.908877	+	0.417063i	$0.863059\pi$
$3$	−0.532651	−	1.64811i	−0.307526	−	0.951540i
$3$	−0.532651	−	1.64811i	−0.307526	−	0.951540i
$4$	0.965217	−	1.67180i	0.482608	−	0.835902i
$5$	1.69363	−	2.93346i	0.757417	−	1.31188i	−0.186747	−	0.982408i	$-0.559795\pi$
$5$	1.69363	−	2.93346i	0.757417	−	1.31188i	0.944164	−	0.329476i	$-0.106872\pi$
$6$	−0.306215	+	0.339016i	−0.125012	+	0.138403i
$7$	1.65673	+	2.86954i	0.626184	+	1.08458i	0.988311	+	0.152453i	$0.0487174\pi$
$7$	1.65673	+	2.86954i	0.626184	+	1.08458i	−0.362127	+	0.932129i	$0.617949\pi$
$8$	−1.03667			−0.366518
$9$	−2.43257	+	1.75574i	−0.810855	+	0.585247i
$10$	−0.893408			−0.282520
$11$		0			0
$11$		0			0
$12$	−3.26945	−	0.700300i	−0.943809	−	0.202159i
$13$	0.494645	−	0.856751i	0.137190	−	0.237620i	−0.789242	−	0.614082i	$-0.789526\pi$
$13$	0.494645	−	0.856751i	0.137190	−	0.237620i	0.926432	+	0.376462i	$0.122860\pi$
$14$	0.436969	−	0.756853i	0.116785	−	0.202277i
$15$	−5.73680	−	1.22879i	−1.48124	−	0.317273i
$16$	−1.79372	−	3.10681i	−0.448430	−	0.776704i
$17$	2.21106			0.536260			0.268130	−	0.963383i	$-0.413594\pi$
$17$	2.21106			0.536260			0.268130	+	0.963383i	$0.413594\pi$
$18$	0.721843	+	0.324100i	0.170140	+	0.0763911i
$19$	−8.07798			−1.85322			−0.926608	−	0.376029i	$-0.877289\pi$
$19$	−8.07798			−1.85322			−0.926608	+	0.376029i	$0.877289\pi$
$20$	−3.26945	−	5.66285i	−0.731071	−	1.26625i
$21$	3.84687	−	4.25894i	0.839455	−	0.929376i
$22$		0			0
$23$	2.46735	−	4.27357i	0.514478	−	0.891102i	−0.485381	−	0.874303i	$-0.661319\pi$
$23$	2.46735	−	4.27357i	0.514478	−	0.891102i	0.999859	−	0.0167990i	$-0.00534754\pi$
$24$	0.552183	+	1.70855i	0.112714	+	0.348757i
$25$	−3.23680	−	5.60630i	−0.647360	−	1.12126i
$26$	−0.260930			−0.0511726
$27$	4.18937	+	3.07395i	0.806245	+	0.591582i
$28$	6.39640			1.20881
$29$	−5.00403	−	8.66723i	−0.929225	−	1.60946i	−0.784622	−	0.619975i	$-0.787143\pi$
$29$	−5.00403	−	8.66723i	−0.929225	−	1.60946i	−0.144603	−	0.989490i	$-0.546191\pi$
$30$	0.475875	+	1.47244i	0.0868824	+	0.268829i
$31$	−0.160984	+	0.278832i	−0.0289136	+	0.0500798i	−0.880120	−	0.474751i	$-0.842538\pi$
$31$	−0.160984	+	0.278832i	−0.0289136	+	0.0500798i	0.851207	+	0.524831i	$0.175871\pi$
$32$	−1.50977	+	2.61500i	−0.266892	+	0.462271i
$33$		0			0
$34$	−0.291588	−	0.505045i	−0.0500069	−	0.0866146i
$35$	11.2236			1.89713
$36$	0.587301	+	5.76144i	0.0978836	+	0.960241i
$37$	−1.35180			−0.222235			−0.111117	−	0.993807i	$-0.535443\pi$
$37$	−1.35180			−0.222235			−0.111117	+	0.993807i	$0.535443\pi$
$38$	1.06530	+	1.84516i	0.172815	+	0.299324i
$39$	−1.67550	−	0.358883i	−0.268294	−	0.0574673i
$40$	−1.75574	+	3.04103i	−0.277607	+	0.480829i
$41$	0.518335	−	0.897782i	0.0809503	−	0.140210i	−0.822708	−	0.568464i	$-0.807538\pi$
$41$	0.518335	−	0.897782i	0.0809503	−	0.140210i	0.903658	+	0.428254i	$0.140871\pi$
$42$	−1.48013	−	0.317037i	−0.228389	−	0.0489199i
$43$	−3.45180	−	5.97869i	−0.526394	−	0.911741i	−0.999527	−	0.0307503i	$-0.990210\pi$
$43$	−3.45180	−	5.97869i	−0.526394	−	0.911741i	0.473133	−	0.880991i	$-0.343123\pi$
$44$		0			0
$45$	1.03052	+	10.1094i	0.153621	+	1.50702i
$46$	−1.30155			−0.191903
$47$	3.59355	+	6.22421i	0.524173	+	0.907894i	0.999604	+	0.0281413i	$0.00895884\pi$
$47$	3.59355	+	6.22421i	0.524173	+	0.907894i	−0.475431	+	0.879753i	$0.657708\pi$
$48$	−4.16496	+	4.61111i	−0.601160	+	0.665556i
$49$	−1.98949	+	3.44589i	−0.284212	+	0.492270i
$50$	−0.853720	+	1.47869i	−0.120734	+	0.209118i
$51$	−1.17772	−	3.64407i	−0.164914	−	0.510273i
$52$	−0.954880	−	1.65390i	−0.132418	−	0.229355i
$53$	2.44831			0.336301			0.168150	−	0.985761i	$-0.446221\pi$
$53$	2.44831			0.336301			0.168150	+	0.985761i	$0.446221\pi$
$54$	0.149663	−	1.36231i	0.0203666	−	0.185387i
$55$		0			0
$56$	−1.71748	−	2.97476i	−0.229508	−	0.397519i
$57$	4.30274	+	13.3134i	0.569912	+	1.76341i
$58$	−1.31984	+	2.28602i	−0.173303	+	0.300169i
$59$	−1.85249	+	3.20860i	−0.241173	+	0.417724i	−0.961049	−	0.276379i	$-0.910866\pi$
$59$	−1.85249	+	3.20860i	−0.241173	+	0.417724i	0.719876	+	0.694103i	$0.244199\pi$
$60$	−7.59156	+	8.40475i	−0.980066	+	1.08505i
$61$	2.90429	+	5.03038i	0.371856	+	0.644074i	0.989851	−	0.142108i	$-0.0453881\pi$
$61$	2.90429	+	5.03038i	0.371856	+	0.644074i	−0.617995	+	0.786182i	$0.712055\pi$
$62$	0.0849205			0.0107849
$63$	−9.06826	−	4.07155i	−1.14249	−	0.512967i
$64$	−6.37846			−0.797308
$65$	−1.67550	−	2.90205i	−0.207820	−	0.359955i
$66$		0			0
$67$	−2.93257	+	5.07935i	−0.358270	+	0.620542i	−0.987672	−	0.156538i	$-0.949967\pi$
$67$	−2.93257	+	5.07935i	−0.358270	+	0.620542i	0.629402	+	0.777080i	$0.283300\pi$
$68$	2.13415	−	3.69645i	0.258804	−	0.448261i
$69$	−8.35758	−	1.79015i	−1.00613	−	0.215509i
$70$	−1.48013	−	2.56367i	−0.176910	−	0.306417i
$71$	11.6695			1.38492			0.692458	−	0.721459i	$-0.256528\pi$
$71$	11.6695			1.38492			0.692458	+	0.721459i	$0.256528\pi$
$72$	2.52177	−	1.82012i	0.297193	−	0.214504i
$73$	11.1105			1.30038			0.650190	−	0.759771i	$-0.274689\pi$
$73$	11.1105			1.30038			0.650190	+	0.759771i	$0.274689\pi$
$74$	0.178272	+	0.308776i	0.0207237	+	0.0358944i
$75$	−7.51574	+	8.32082i	−0.867843	+	0.960805i
$76$	−7.79700	+	13.5048i	−0.894377	+	1.54911i
$77$		0			0
$78$	0.138985	+	0.430043i	0.0157369	+	0.0486927i
$79$	−1.07815	−	1.86740i	−0.121301	−	0.210099i	0.798980	−	0.601358i	$-0.205373\pi$
$79$	−1.07815	−	1.86740i	−0.121301	−	0.210099i	−0.920281	+	0.391258i	$0.872040\pi$
$80$	−12.1516			−1.35859
$81$	2.83475	−	8.54191i	0.314972	−	0.949101i
$82$	−0.273426			−0.0301949
$83$	4.49431	+	7.78437i	0.493314	+	0.854445i	0.999970	−	0.00770304i	$-0.00245198\pi$
$83$	4.49431	+	7.78437i	0.493314	+	0.854445i	−0.506656	+	0.862148i	$0.669119\pi$
$84$	−3.40705	−	10.5420i	−0.371740	−	1.15023i
$85$	3.74472	−	6.48605i	0.406172	−	0.703511i
$86$	−0.910427	+	1.57691i	−0.0981739	+	0.170042i
$87$	−11.6192	+	12.8638i	−1.24571	+	1.37915i
$88$		0			0
$89$	13.8921			1.47256			0.736278	−	0.676679i	$-0.236581\pi$
$89$	13.8921			1.47256			0.736278	+	0.676679i	$0.236581\pi$
$90$	2.17327	−	1.56859i	0.229083	−	0.165344i
$91$	3.27797			0.343625
$92$	−4.76305	−	8.24985i	−0.496583	−	0.860106i
$93$	0.545296	+	0.116800i	0.0565445	+	0.0121116i
$94$	0.947815	−	1.64166i	0.0977597	−	0.169325i
$95$	−13.6811	+	23.6964i	−1.40366	+	2.43120i
$96$	5.11400	+	1.09539i	0.521946	+	0.111798i
$97$	−6.88073	−	11.9178i	−0.698633	−	1.21007i	−0.968941	−	0.247293i	$-0.920459\pi$
$97$	−6.88073	−	11.9178i	−0.698633	−	1.21007i	0.270308	−	0.962774i	$-0.412874\pi$
$98$	1.04947			0.106013
$99$		0			0
$100$	−12.4968			−1.24968
$101$	−0.518335	−	0.897782i	−0.0515763	−	0.0893327i	0.839085	−	0.544001i	$-0.183091\pi$
$101$	−0.518335	−	0.897782i	−0.0515763	−	0.0893327i	−0.890661	+	0.454668i	$0.849758\pi$
$102$	−0.677058	+	0.749584i	−0.0670388	+	0.0742198i
$103$	−3.30210	+	5.71941i	−0.325366	+	0.563550i	−0.981586	−	0.191019i	$-0.938821\pi$
$103$	−3.30210	+	5.71941i	−0.325366	+	0.563550i	0.656221	+	0.754569i	$0.272154\pi$
$104$	−0.512784	+	0.888168i	−0.0502826	+	0.0870920i
$105$	−5.97824	−	18.4977i	−0.583417	−	1.80519i
$106$	−0.322876	−	0.559238i	−0.0313605	−	0.0543180i
$107$	−2.88183			−0.278597			−0.139298	−	0.990250i	$-0.544485\pi$
$107$	−2.88183			−0.278597			−0.139298	+	0.990250i	$0.544485\pi$
$108$	9.18270	−	4.03678i	0.883605	−	0.388439i
$109$	11.0349			1.05695			0.528475	−	0.848949i	$-0.322764\pi$
$109$	11.0349			1.05695			0.528475	+	0.848949i	$0.322764\pi$
$110$		0			0
$111$	0.720038	+	2.22792i	0.0683430	+	0.211465i
$112$	5.94341	−	10.2943i	0.561599	−	0.972719i
$113$	5.02398	−	8.70179i	0.472617	−	0.818596i	−0.526892	−	0.849932i	$-0.676643\pi$
$113$	5.02398	−	8.70179i	0.472617	−	0.818596i	0.999509	+	0.0313361i	$0.00997623\pi$
$114$	2.47360	−	2.73857i	0.231674	−	0.256490i
$115$	−8.35758	−	14.4757i	−0.779348	−	1.34987i
$116$	−19.3199			−1.79381
$117$	0.300975	+	2.95257i	0.0278251	+	0.272965i
$118$	0.977204			0.0899589
$119$	3.66312	+	6.34470i	0.335797	+	0.581618i
$120$	5.94717	+	1.27385i	0.542900	+	0.116286i
$121$		0			0
$122$	0.766020	−	1.32679i	0.0693522	−	0.120122i
$123$	−1.75574	−	0.376071i	−0.158310	−	0.0339092i
$124$	0.310769	+	0.538267i	0.0279079	+	0.0483378i
$125$	−4.99147			−0.446451
$126$	0.265881	+	2.60830i	0.0236865	+	0.232366i
$127$	9.91688			0.879980			0.439990	−	0.898003i	$-0.354982\pi$
$127$	9.91688			0.879980			0.439990	+	0.898003i	$0.354982\pi$
$128$	3.86072	+	6.68696i	0.341242	+	0.591049i
$129$	−8.01496	+	8.87351i	−0.705678	+	0.781269i
$130$	−0.441920	+	0.765428i	−0.0387590	+	0.0671325i
$131$	5.84580	−	10.1252i	0.510750	−	0.884645i	−0.489172	−	0.872187i	$-0.662701\pi$
$131$	5.84580	−	10.1252i	0.510750	−	0.884645i	0.999922	−	0.0124580i	$-0.00396560\pi$
$132$		0			0
$133$	−13.3830	−	23.1800i	−1.16045	−	2.00996i
$134$	1.54696			0.133637
$135$	16.1126	−	7.08321i	1.38675	−	0.609625i
$136$	−2.29214			−0.196549
$137$	−2.55039	−	4.41740i	−0.217894	−	0.377404i	0.736270	−	0.676688i	$-0.236585\pi$
$137$	−2.55039	−	4.41740i	−0.217894	−	0.377404i	−0.954164	+	0.299284i	$0.903252\pi$
$138$	0.693272	+	2.14510i	0.0590152	+	0.182603i
$139$	3.84195	−	6.65445i	0.325870	−	0.564423i	−0.655818	−	0.754919i	$-0.727676\pi$
$139$	3.84195	−	6.65445i	0.325870	−	0.564423i	0.981688	+	0.190496i	$0.0610096\pi$
$140$	10.8332	−	18.7636i	0.915570	−	1.58581i
$141$	8.34411	−	9.23792i	0.702701	−	0.777973i
$142$	−1.53894	−	2.66553i	−0.129145	−	0.223686i
$143$		0			0
$144$	9.81810	+	4.40822i	0.818175	+	0.367352i
$145$	−33.9000			−2.81524
$146$	−1.46522	−	2.53783i	−0.121262	−	0.210032i
$147$	6.73893	+	1.44345i	0.555818	+	0.119053i
$148$	−1.30478	+	2.25995i	−0.107252	+	0.185766i
$149$	−3.36688	+	5.83160i	−0.275825	+	0.477743i	−0.970343	−	0.241732i	$-0.922284\pi$
$149$	−3.36688	+	5.83160i	−0.275825	+	0.477743i	0.694518	+	0.719476i	$0.255618\pi$
$150$	2.89178	+	0.619405i	0.236113	+	0.0505742i
$151$	5.30926	+	9.19591i	0.432061	+	0.748352i	0.997051	−	0.0767460i	$-0.0244530\pi$
$151$	5.30926	+	9.19591i	0.432061	+	0.748352i	−0.564989	+	0.825098i	$0.691120\pi$
$152$	8.37420			0.679237
$153$	−5.37854	+	3.88204i	−0.434829	+	0.313844i
$154$		0			0
$155$	0.545296	+	0.944480i	0.0437992	+	0.0758625i
$156$	−2.21720	+	2.45470i	−0.177518	+	0.196534i
$157$	−0.553676	+	0.958995i	−0.0441882	+	0.0765362i	−0.887274	−	0.461244i	$-0.847403\pi$
$157$	−0.553676	+	0.958995i	−0.0441882	+	0.0765362i	0.843085	+	0.537780i	$0.180737\pi$
$158$	−0.284366	+	0.492536i	−0.0226229	+	0.0391841i
$159$	−1.30409	−	4.03509i	−0.103421	−	0.320004i
$160$	5.11400	+	8.85772i	0.404298	+	0.700264i
$161$	16.3509			1.28863
$162$	−2.32497	+	0.478975i	−0.182667	+	0.0376318i
$163$	−3.04659			−0.238628			−0.119314	−	0.992857i	$-0.538069\pi$
$163$	−3.04659			−0.238628			−0.119314	+	0.992857i	$0.538069\pi$
$164$	−1.00061	−	1.73311i	−0.0781346	−	0.135333i
$165$		0			0
$166$	1.18539	−	2.05316i	0.0920044	−	0.159356i
$167$	9.31595	−	16.1357i	0.720890	−	1.24862i	−0.239754	−	0.970834i	$-0.577067\pi$
$167$	9.31595	−	16.1357i	0.720890	−	1.24862i	0.960644	−	0.277784i	$-0.0895999\pi$
$168$	−3.98793	+	4.41511i	−0.307676	+	0.340633i
$169$	6.01065	+	10.4108i	0.462358	+	0.800827i
$170$	−1.97538			−0.151504
$171$	19.6502	−	14.1828i	1.50269	−	1.08459i
$172$	−13.3269			−1.01617
$173$	6.22421	+	10.7806i	0.473218	+	0.819638i	0.999530	−	0.0306539i	$-0.00975897\pi$
$173$	6.22421	+	10.7806i	0.473218	+	0.819638i	−0.526312	+	0.850291i	$0.676426\pi$
$174$	4.47064	+	0.957589i	0.338918	+	0.0725946i
$175$	10.7250	−	18.5762i	0.810732	−	1.40423i
$176$		0			0
$177$	6.27487	+	1.34405i	0.471648	+	0.101025i
$178$	−1.83205	−	3.17320i	−0.137318	−	0.237842i
$179$	−0.335039			−0.0250420			−0.0125210	−	0.999922i	$-0.503986\pi$
$179$	−0.335039			−0.0250420			−0.0125210	+	0.999922i	$0.503986\pi$
$180$	17.8957	+	8.03496i	1.33386	+	0.598890i
$181$	−8.90941			−0.662231			−0.331116	−	0.943590i	$-0.607425\pi$
$181$	−8.90941			−0.662231			−0.331116	+	0.943590i	$0.607425\pi$
$182$	−0.432290	−	0.748748i	−0.0320434	−	0.0555009i
$183$	6.74367	−	7.46604i	0.498506	−	0.551906i
$184$	−2.55783	+	4.43029i	−0.188565	+	0.326605i
$185$	−2.28946	+	3.96545i	−0.168324	+	0.291546i
$186$	−0.0452330	−	0.139959i	−0.00331664	−	0.0102623i
$187$		0			0
$188$	13.8742			1.01188
$189$	−1.88017	+	17.1142i	−0.136762	+	1.24488i
$190$	7.21693			0.523571
$191$	13.7156	+	23.7562i	0.992428	+	1.71894i	0.602587	+	0.798053i	$0.294137\pi$
$191$	13.7156	+	23.7562i	0.992428	+	1.71894i	0.389841	+	0.920882i	$0.372530\pi$
$192$	3.39749	+	10.5124i	0.245193	+	0.758670i
$193$	−9.83428	+	17.0335i	−0.707887	+	1.22610i	0.257752	+	0.966211i	$0.417018\pi$
$193$	−9.83428	+	17.0335i	−0.707887	+	1.22610i	−0.965639	+	0.259885i	$0.916315\pi$
$194$	−1.81483	+	3.14337i	−0.130297	+	0.225681i
$195$	−3.89045	+	4.30719i	−0.278601	+	0.308444i
$196$	3.84057	+	6.65207i	0.274327	+	0.475148i
$197$	14.4885			1.03226			0.516132	−	0.856509i	$-0.327371\pi$
$197$	14.4885			1.03226			0.516132	+	0.856509i	$0.327371\pi$
$198$		0			0
$199$	−6.18710			−0.438592			−0.219296	−	0.975658i	$-0.570376\pi$
$199$	−6.18710			−0.438592			−0.219296	+	0.975658i	$0.570376\pi$
$200$	3.35549	+	5.81188i	0.237269	+	0.410962i
$201$	9.93339	+	2.12768i	0.700647	+	0.150075i
$202$	−0.136713	+	0.236794i	−0.00961911	+	0.0166608i
$203$	16.5806	−	28.7185i	1.16373	−	2.01564i
$204$	−7.22894	−	1.54840i	−0.506127	−	0.108410i
$205$	−1.75574	−	3.04103i	−0.122626	−	0.212395i
$206$	1.74189			0.121363
$207$	1.50130	+	14.7278i	0.104347	+	1.02365i
$208$	−3.54902			−0.246080
$209$		0			0
$210$	−3.43682	+	3.80497i	−0.237163	+	0.262568i
$211$	−9.37563	+	16.2391i	−0.645445	+	1.11794i	0.338753	+	0.940875i	$0.389995\pi$
$211$	−9.37563	+	16.2391i	−0.645445	+	1.11794i	−0.984199	+	0.177069i	$0.943339\pi$
$212$	2.36315	−	4.09309i	0.162302	−	0.281115i
$213$	−6.21577	−	19.2327i	−0.425898	−	1.31780i
$214$	0.380048	+	0.658262i	0.0259795	+	0.0449978i
$215$	−23.3843			−1.59480
$216$	−4.34299	−	3.18667i	−0.295503	−	0.216826i
$217$	−1.06683			−0.0724208
$218$	−1.45525	−	2.52057i	−0.0985621	−	0.170715i
$219$	−5.91800	−	18.3113i	−0.399901	−	1.23736i
$220$		0			0
$221$	1.09369	−	1.89432i	0.0735695	−	0.127426i
$222$	0.413941	−	0.458282i	0.0277819	−	0.0307579i
$223$	7.67673	+	13.2965i	0.514072	+	0.890398i	0.999867	+	0.0163254i	$0.00519677\pi$
$223$	7.67673	+	13.2965i	0.514072	+	0.890398i	−0.485795	+	0.874073i	$0.661470\pi$
$224$	−10.0051			−0.668495
$225$	17.7169	+	7.95471i	1.18113	+	0.530314i
$226$	−2.65020			−0.176288
$227$	−9.12382	−	15.8029i	−0.605569	−	1.04888i	−0.991961	−	0.126542i	$-0.959612\pi$
$227$	−9.12382	−	15.8029i	−0.605569	−	1.04888i	0.386392	−	0.922335i	$-0.373721\pi$
$228$	26.4105	+	5.65701i	1.74908	+	0.374644i
$229$	2.39565	−	4.14939i	0.158309	−	0.274199i	−0.775950	−	0.630794i	$-0.782729\pi$
$229$	2.39565	−	4.14939i	0.158309	−	0.274199i	0.934259	+	0.356595i	$0.116062\pi$
$230$	−2.20435	+	3.81804i	−0.145350	+	0.251754i
$231$		0			0
$232$	5.18753	+	8.98506i	0.340578	+	0.589898i
$233$	−19.3958			−1.27066			−0.635331	−	0.772240i	$-0.719136\pi$
$233$	−19.3958			−1.27066			−0.635331	+	0.772240i	$0.719136\pi$
$234$	0.634729	−	0.458125i	0.0414936	−	0.0299486i
$235$	24.3446			1.58807
$236$	3.57610	+	6.19399i	0.232784	+	0.403194i
$237$	−2.50342	+	2.77158i	−0.162615	+	0.180034i
$238$	0.966164	−	1.67344i	0.0626271	−	0.108473i
$239$	−4.55732	+	7.89352i	−0.294789	+	0.510589i	−0.974936	−	0.222487i	$-0.928583\pi$
$239$	−4.55732	+	7.89352i	−0.294789	+	0.510589i	0.680147	+	0.733076i	$0.261916\pi$
$240$	6.47258	+	20.0273i	0.417803	+	1.29276i
$241$	6.29429	+	10.9020i	0.405451	+	0.702262i	0.994374	−	0.105927i	$-0.0337811\pi$
$241$	6.29429	+	10.9020i	0.405451	+	0.702262i	−0.588923	+	0.808189i	$0.700448\pi$
$242$		0			0
$243$	−15.5880	−	0.122141i	−0.999969	−	0.00783533i
$244$	11.2131			0.717844
$245$	6.73893	+	11.6722i	0.430534	+	0.745708i
$246$	0.145641	+	0.450638i	0.00928572	+	0.0287316i
$247$	−3.99574	+	6.92082i	−0.254243	+	0.440361i
$248$	0.166887	−	0.289057i	0.0105973	−	0.0183551i
$249$	10.4356	−	11.5535i	0.661331	−	0.732172i
$250$	0.658262	+	1.14014i	0.0416321	+	0.0721090i
$251$	16.5048			1.04177			0.520887	−	0.853626i	$-0.325601\pi$
$251$	16.5048			1.04177			0.520887	+	0.853626i	$0.325601\pi$
$252$	−15.5597	+	11.2304i	−0.980167	+	0.707450i
$253$		0			0
$254$	−1.30781	−	2.26519i	−0.0820593	−	0.142131i
$255$	−12.6844	−	2.71693i	−0.794327	−	0.170141i
$256$	−5.36018	+	9.28411i	−0.335011	+	0.580257i
$257$	9.50412	−	16.4616i	0.592850	−	1.02685i	−0.400996	−	0.916080i	$-0.631336\pi$
$257$	9.50412	−	16.4616i	0.592850	−	1.02685i	0.993846	−	0.110767i	$-0.0353308\pi$
$258$	3.08386	+	0.660548i	0.191993	+	0.0411239i
$259$	−2.23956	−	3.87904i	−0.139160	−	0.241032i
$260$	−6.46887			−0.401182
$261$	27.3900	+	12.2978i	1.69540	+	0.761217i
$262$	−3.08371			−0.190513
$263$	3.12035	+	5.40460i	0.192409	+	0.333262i	0.946048	−	0.324027i	$-0.105037\pi$
$263$	3.12035	+	5.40460i	0.192409	+	0.333262i	−0.753639	+	0.657288i	$0.771703\pi$
$264$		0			0
$265$	4.14654	−	7.18202i	0.254720	−	0.441188i
$266$	−3.52983	+	6.11384i	−0.216428	+	0.374864i
$267$	−7.39963	−	22.8957i	−0.452850	−	1.40120i
$268$	5.66112	+	9.80535i	0.345808	+	0.598957i
$269$	−14.1008			−0.859739			−0.429870	−	0.902891i	$-0.641440\pi$
$269$	−14.1008			−0.859739			−0.429870	+	0.902891i	$0.641440\pi$
$270$	−3.74282	−	2.74629i	−0.227781	−	0.167134i
$271$	19.6393			1.19300			0.596500	−	0.802613i	$-0.296558\pi$
$271$	19.6393			1.19300			0.596500	+	0.802613i	$0.296558\pi$
$272$	−3.96602	−	6.86934i	−0.240475	−	0.416515i
$273$	−1.74601	−	5.40247i	−0.105674	−	0.326972i
$274$	−0.672676	+	1.16511i	−0.0406378	+	0.0703868i
$275$		0			0
$276$	−11.0597	+	12.2444i	−0.665713	+	0.737023i
$277$	−10.7526	−	18.6241i	−0.646061	−	1.11901i	−0.984055	−	0.177863i	$-0.943082\pi$
$277$	−10.7526	−	18.6241i	−0.646061	−	1.11901i	0.337994	−	0.941148i	$-0.390252\pi$
$278$	−2.02666			−0.121551
$279$	−0.0979532	−	0.960924i	−0.00586430	−	0.0575290i
$280$	−11.6351			−0.695332
$281$	−8.50278	−	14.7273i	−0.507233	−	0.878554i	−0.999965	−	0.00837273i	$-0.997335\pi$
$281$	−8.50278	−	14.7273i	−0.507233	−	0.878554i	0.492731	−	0.870181i	$-0.335998\pi$
$282$	−3.21051	−	0.687674i	−0.191183	−	0.0409504i
$283$	−0.886584	+	1.53561i	−0.0527020	+	0.0912825i	−0.891173	−	0.453664i	$-0.850117\pi$
$283$	−0.886584	+	1.53561i	−0.0527020	+	0.0912825i	0.838471	+	0.544946i	$0.183450\pi$
$284$	11.2636	−	19.5091i	0.668372	−	1.15765i
$285$	46.3417	+	9.92617i	2.74505	+	0.587976i
$286$		0			0
$287$	3.43496			0.202759
$288$	−0.918644	−	9.01193i	−0.0541316	−	0.531033i
$289$	−12.1112			−0.712425
$290$	4.47064	+	7.74337i	0.262525	+	0.454707i
$291$	−15.9768	+	17.6883i	−0.936579	+	1.03690i
$292$	10.7240	−	18.5745i	0.627574	−	1.08699i
$293$	4.28496	−	7.42177i	0.250330	−	0.433584i	−0.713287	−	0.700872i	$-0.752794\pi$
$293$	4.28496	−	7.42177i	0.250330	−	0.433584i	0.963617	+	0.267288i	$0.0861276\pi$
$294$	−0.559003	−	1.72965i	−0.0326017	−	0.100875i
$295$	6.27487	+	10.8684i	0.365337	+	0.632783i
$296$	1.40137			0.0814530
$297$		0			0
$298$	1.77606			0.102884
$299$	−2.44093	−	4.22781i	−0.141162	−	0.244500i
$300$	6.65646	+	20.5962i	0.384311	+	1.18912i
$301$	11.4374	−	19.8101i	0.659239	−	1.14184i
$302$	1.40034	−	2.42546i	0.0805806	−	0.139570i
$303$	−1.20356	+	1.33248i	−0.0691425	+	0.0765490i
$304$	14.4896	+	25.0968i	0.831038	+	1.43940i
$305$	19.6752			1.12660
$306$	1.59604	+	0.716603i	0.0912393	+	0.0409655i
$307$	−19.9453			−1.13834			−0.569168	−	0.822221i	$-0.692735\pi$
$307$	−19.9453			−1.13834			−0.569168	+	0.822221i	$0.692735\pi$
$308$		0			0
$309$	11.1851	+	2.39579i	0.636298	+	0.136292i
$310$	0.143824	−	0.249111i	0.00816867	−	0.0141486i
$311$	4.30409	−	7.45491i	0.244063	−	0.422729i	−0.717805	−	0.696244i	$-0.754853\pi$
$311$	4.30409	−	7.45491i	0.244063	−	0.422729i	0.961868	+	0.273515i	$0.0881864\pi$
$312$	1.73694	+	0.372043i	0.0983347	+	0.0210628i
$313$	−1.65376	−	2.86440i	−0.0934761	−	0.161905i	0.815495	−	0.578763i	$-0.196465\pi$
$313$	−1.65376	−	2.86440i	−0.0934761	−	0.161905i	−0.908972	+	0.416858i	$0.863131\pi$
$314$	0.292069			0.0164824
$315$	−27.3021	+	19.7057i	−1.53830	+	1.11029i
$316$	−4.16258			−0.234163
$317$	−1.66030	−	2.87572i	−0.0932516	−	0.161516i	0.815626	−	0.578580i	$-0.196393\pi$
$317$	−1.66030	−	2.87572i	−0.0932516	−	0.161516i	−0.908878	+	0.417063i	$0.863059\pi$
$318$	−0.749708	+	0.830016i	−0.0420415	+	0.0465450i
$319$		0			0
$320$	−10.8028	+	18.7110i	−0.603894	+	1.04598i
$321$	1.53501	+	4.74958i	0.0856758	+	0.265096i
$322$	−2.15631	−	3.73484i	−0.120167	−	0.208135i
$323$	−17.8609			−0.993805
$324$	−11.5442	−	12.9839i	−0.641347	−	0.721330i
$325$	−6.40427			−0.355245
$326$	0.401776	+	0.695897i	0.0222523	+	0.0385422i
$327$	−5.87775	−	18.1868i	−0.325040	−	1.00573i
$328$	−0.537342	+	0.930704i	−0.0296698	+	0.0513895i
$329$	−11.9071	+	20.6236i	−0.656457	+	1.13702i
$330$		0			0
$331$	8.17774	+	14.1643i	0.449489	+	0.778539i	0.998353	−	0.0573735i	$-0.0182726\pi$
$331$	8.17774	+	14.1643i	0.449489	+	0.778539i	−0.548863	+	0.835912i	$0.684939\pi$
$332$	17.3519			0.952310
$333$	3.28834	−	2.37341i	0.180200	−	0.130062i
$334$	−4.91425			−0.268896
$335$	9.93339	+	17.2051i	0.542719	+	0.940017i
$336$	−20.1319	−	4.31216i	−1.09829	−	0.235248i
$337$	−5.79473	+	10.0368i	−0.315659	+	0.546738i	−0.979577	−	0.201068i	$-0.935559\pi$
$337$	−5.79473	+	10.0368i	−0.315659	+	0.546738i	0.663918	+	0.747805i	$0.268892\pi$
$338$	1.58534	−	2.74588i	0.0862310	−	0.149356i
$339$	−17.0176	−	3.64508i	−0.924268	−	0.197974i
$340$	−7.22894	−	12.5209i	−0.392044	−	0.679040i
$341$		0			0
$342$	−5.83103	−	2.61807i	−0.315306	−	0.141569i
$343$	10.0100			0.540491
$344$	3.57837	+	6.19793i	0.192933	+	0.334170i
$345$	−19.4060	+	21.4848i	−1.04479	+	1.15670i
$346$	1.64166	−	2.84345i	0.0882564	−	0.152865i
$347$	13.8083	−	23.9168i	0.741271	−	1.28392i	−0.210646	−	0.977562i	$-0.567557\pi$
$347$	13.8083	−	23.9168i	0.741271	−	1.28392i	0.951917	−	0.306357i	$-0.0991100\pi$
$348$	10.2908	+	31.8414i	0.551643	+	1.70688i
$349$	−11.3573	−	19.6715i	−0.607945	−	1.05299i	−0.991579	−	0.129506i	$-0.958661\pi$
$349$	−11.3573	−	19.6715i	−0.607945	−	1.05299i	0.383634	−	0.923485i	$-0.374672\pi$
$350$	−5.65753			−0.302408
$351$	4.70586	−	2.06873i	0.251180	−	0.110421i
$352$		0			0
$353$	−12.7261	−	22.0423i	−0.677344	−	1.17319i	−0.975778	−	0.218764i	$-0.929798\pi$
$353$	−12.7261	−	22.0423i	−0.677344	−	1.17319i	0.298434	−	0.954430i	$-0.403536\pi$
$354$	−0.520509	−	1.61054i	−0.0276647	−	0.0855994i
$355$	19.7639	−	34.2320i	1.04896	−	1.81685i
$356$	13.4089	−	23.2248i	0.710668	−	1.23091i
$357$	8.50564	−	9.41675i	0.450166	−	0.498387i
$358$	0.0441841	+	0.0765291i	0.00233520	+	0.00404469i
$359$	−2.44711			−0.129153			−0.0645767	−	0.997913i	$-0.520570\pi$
$359$	−2.44711			−0.129153			−0.0645767	+	0.997913i	$0.520570\pi$
$360$	−1.06831	−	10.4801i	−0.0563048	−	0.552352i
$361$	46.2538			2.43441
$362$	1.17495	+	2.03507i	0.0617539	+	0.106961i
$363$		0			0
$364$	3.16395	−	5.48012i	0.165836	−	0.287237i
$365$	18.8171	−	32.5921i	0.984930	−	1.70595i
$366$	−2.59472	−	0.555775i	−0.135628	−	0.0290508i
$367$	−10.1028	−	17.4985i	−0.527360	−	0.913414i	−0.999492	−	0.0318857i	$-0.989849\pi$
$367$	−10.1028	−	17.4985i	−0.527360	−	0.913414i	0.472132	−	0.881528i	$-0.343485\pi$
$368$	−17.7029			−0.922829
$369$	0.315389	+	3.09398i	0.0164185	+	0.161066i
$370$	1.20771			0.0627858
$371$	4.05618	+	7.02550i	0.210586	+	0.364746i
$372$	0.721595	−	0.798891i	0.0374129	−	0.0414206i
$373$	−0.577034	+	0.999453i	−0.0298777	+	0.0517497i	−0.880578	−	0.473902i	$-0.842845\pi$
$373$	−0.577034	+	0.999453i	−0.0298777	+	0.0517497i	0.850700	+	0.525652i	$0.176178\pi$
$374$		0			0
$375$	2.65871	+	8.22652i	0.137295	+	0.424816i
$376$	−3.72532	−	6.45245i	−0.192119	−	0.332760i
$377$	−9.90088			−0.509921
$378$	4.15716	−	1.82752i	0.213821	−	0.0939973i
$379$	5.49657			0.282340			0.141170	−	0.989985i	$-0.454914\pi$
$379$	5.49657			0.282340			0.141170	+	0.989985i	$0.454914\pi$
$380$	26.4105	+	45.7444i	1.35483	+	2.34664i
$381$	−5.28223	−	16.3442i	−0.270617	−	0.837336i
$382$	3.61756	−	6.26580i	0.185090	−	0.320586i
$383$	2.51705	−	4.35966i	0.128615	−	0.222768i	−0.794525	−	0.607231i	$-0.792280\pi$
$383$	2.51705	−	4.35966i	0.128615	−	0.222768i	0.923140	+	0.384463i	$0.125613\pi$
$384$	8.96446	−	9.92472i	0.457466	−	0.506469i
$385$		0			0
$386$	5.18767			0.264046
$387$	18.8937	+	8.48309i	0.960423	+	0.431220i
$388$	−26.5656			−1.34866
$389$	10.4399	+	18.0825i	0.529325	+	0.916818i	0.999415	+	0.0341997i	$0.0108882\pi$
$389$	10.4399	+	18.0825i	0.529325	+	0.916818i	−0.470090	+	0.882619i	$0.655778\pi$
$390$	1.49690	+	0.320629i	0.0757986	+	0.0162357i
$391$	5.45545	−	9.44911i	0.275894	−	0.477862i
$392$	2.06244	−	3.57225i	0.104169	−	0.180426i
$393$	−19.8013	−	4.24134i	−0.998844	−	0.213947i
$394$	−1.91071	−	3.30944i	−0.0962600	−	0.166727i
$395$	−7.30394			−0.367501
$396$		0			0
$397$	2.56243			0.128605			0.0643023	−	0.997930i	$-0.479518\pi$
$397$	2.56243			0.128605			0.0643023	+	0.997930i	$0.479518\pi$
$398$	0.815938	+	1.41325i	0.0408993	+	0.0708396i
$399$	−31.0749	+	34.4036i	−1.55569	+	1.72233i
$400$	−11.6118	+	20.1123i	−0.580591	+	1.00561i
$401$	−8.27852	+	14.3388i	−0.413409	+	0.716046i	−0.995260	−	0.0972496i	$-0.968995\pi$
$401$	−8.27852	+	14.3388i	−0.413409	+	0.716046i	0.581851	+	0.813296i	$0.302329\pi$
$402$	−0.823987	−	2.54956i	−0.0410968	−	0.127161i
$403$	0.159260	+	0.275846i	0.00793330	+	0.0137409i
$404$	−2.00122			−0.0995645
$405$	−20.2563	−	22.7825i	−1.00654	−	1.13207i
$406$	−8.74643			−0.434078
$407$		0			0
$408$	1.22091	+	3.77770i	0.0604440	+	0.187024i
$409$	3.34822	−	5.79929i	0.165559	−	0.286756i	−0.771295	−	0.636478i	$-0.780391\pi$
$409$	3.34822	−	5.79929i	0.165559	−	0.286756i	0.936854	+	0.349722i	$0.113724\pi$
$410$	−0.463085	+	0.802086i	−0.0228701	+	0.0396122i
$411$	−5.92191	+	6.55626i	−0.292106	+	0.323396i
$412$	6.37449	+	11.0409i	0.314048	+	0.543948i
$413$	−12.2763			−0.604075
$414$	3.16610	−	2.28518i	0.155606	−	0.112311i
$415$	30.4469			1.49458
$416$	1.49360	+	2.58700i	0.0732299	+	0.126838i
$417$	−13.0137	−	2.78747i	−0.637284	−	0.136503i
$418$		0			0
$419$	11.5512	−	20.0073i	0.564314	−	0.977420i	−0.432800	−	0.901490i	$-0.642474\pi$
$419$	11.5512	−	20.0073i	0.564314	−	0.977420i	0.997113	−	0.0759297i	$-0.0241925\pi$
$420$	−36.6949	−	7.85986i	−1.79053	−	0.383522i
$421$	5.87958	+	10.1837i	0.286553	+	0.496324i	0.972985	−	0.230870i	$-0.0741572\pi$
$421$	5.87958	+	10.1837i	0.286553	+	0.496324i	−0.686432	+	0.727194i	$0.740824\pi$
$422$	4.94573			0.240754
$423$	−19.6696	−	8.83146i	−0.956371	−	0.429400i
$424$	−2.53809			−0.123260
$425$	−7.15674	−	12.3958i	−0.347153	−	0.601287i
$426$	−3.57338	+	3.95615i	−0.173131	+	0.191676i
$427$	−9.62323	+	16.6679i	−0.465701	+	0.806618i
$428$	−2.78159	+	4.81785i	−0.134453	+	0.232880i
$429$		0			0
$430$	3.08386	+	5.34141i	0.148717	+	0.257586i
$431$	−30.1925			−1.45432			−0.727160	−	0.686468i	$-0.759160\pi$
$431$	−30.1925			−1.45432			−0.727160	+	0.686468i	$0.759160\pi$
$432$	2.03564	−	18.5294i	0.0979396	−	0.891496i
$433$	−4.30491			−0.206881			−0.103440	−	0.994636i	$-0.532985\pi$
$433$	−4.30491			−0.206881			−0.103440	+	0.994636i	$0.532985\pi$
$434$	0.140690	+	0.243682i	0.00675334	+	0.0116971i
$435$	18.0569	+	55.8711i	0.865760	+	2.67881i
$436$	10.6511	−	18.4482i	0.510093	−	0.883507i
$437$	−19.9312	+	34.5218i	−0.953438	+	1.65140i
$438$	−3.40219	+	3.76662i	−0.162563	+	0.179976i
$439$	14.6366	+	25.3513i	0.698566	+	1.20995i	0.968964	+	0.247204i	$0.0795117\pi$
$439$	14.6366	+	25.3513i	0.698566	+	1.20995i	−0.270397	+	0.962749i	$0.587155\pi$
$440$		0			0
$441$	−1.21053	−	11.8754i	−0.0576445	−	0.565495i
$442$	−0.576931			−0.0274418
$443$	10.7892	+	18.6874i	0.512609	+	0.887865i	0.999893	+	0.0146212i	$0.00465423\pi$
$443$	10.7892	+	18.6874i	0.512609	+	0.887865i	−0.487284	+	0.873243i	$0.662012\pi$
$444$	4.41964	+	0.946665i	0.209747	+	0.0449267i
$445$	23.5281	−	40.7519i	1.11534	−	1.93182i
$446$	2.02477	−	3.50701i	0.0958757	−	0.166062i
$447$	11.4045	+	2.44279i	0.539415	+	0.115540i
$448$	−10.5674	−	18.3032i	−0.499261	−	0.864746i
$449$	−37.3023			−1.76040			−0.880202	−	0.474599i	$-0.842593\pi$
$449$	−37.3023			−1.76040			−0.880202	+	0.474599i	$0.842593\pi$
$450$	−0.519460	−	5.09592i	−0.0244876	−	0.240224i
$451$		0			0
$452$	−9.69847	−	16.7982i	−0.456177	−	0.790122i
$453$	12.3279	−	13.6485i	0.579217	−	0.641261i
$454$	−2.40645	+	4.16809i	−0.112940	+	0.195618i
$455$	5.55168	−	9.61580i	0.260267	−	0.450796i
$456$	−4.46053	−	13.8016i	−0.208883	−	0.646321i
$457$	−0.375073	−	0.649646i	−0.0175452	−	0.0303891i	0.857120	−	0.515118i	$-0.172252\pi$
$457$	−0.375073	−	0.649646i	−0.0175452	−	0.0303891i	−0.874665	+	0.484728i	$0.838918\pi$
$458$	−1.26373			−0.0590501
$459$	9.26293	+	6.79668i	0.432357	+	0.317242i
$460$	−32.2675			−1.50448
$461$	−11.7253	−	20.3088i	−0.546100	−	0.945874i	−0.998537	−	0.0540769i	$-0.982778\pi$
$461$	−11.7253	−	20.3088i	−0.546100	−	0.945874i	0.452436	−	0.891797i	$-0.350555\pi$
$462$		0			0
$463$	−3.74320	+	6.48340i	−0.173961	+	0.301309i	−0.939801	−	0.341722i	$-0.888990\pi$
$463$	−3.74320	+	6.48340i	−0.173961	+	0.301309i	0.765840	+	0.643031i	$0.222323\pi$
$464$	−17.9517	+	31.0932i	−0.833385	+	1.44346i
$465$	1.26616	−	1.40179i	0.0587167	−	0.0650064i
$466$	2.55787	+	4.43036i	0.118491	+	0.205232i
$467$	27.3935			1.26762			0.633809	−	0.773489i	$-0.281490\pi$
$467$	27.3935			1.26762			0.633809	+	0.773489i	$0.281490\pi$
$468$	5.22663	+	2.34670i	0.241601	+	0.108476i
$469$	−19.4338			−0.897371
$470$	−3.21051	−	5.56076i	−0.148090	−	0.256499i
$471$	1.87545	+	0.401712i	0.0864162	+	0.0185099i
$472$	1.92042	−	3.32626i	0.0883944	−	0.153104i
$473$		0			0
$474$	0.963224	+	0.206318i	0.0442423	+	0.00947649i
$475$	26.1468	+	45.2876i	1.19970	+	2.07794i
$476$	14.1428			0.648234
$477$	−5.95567	+	4.29859i	−0.272691	+	0.196819i
$478$	2.40403			0.109958
$479$	12.6295	+	21.8749i	0.577055	+	0.999489i	0.995815	+	0.0913916i	$0.0291315\pi$
$479$	12.6295	+	21.8749i	0.577055	+	0.999489i	−0.418760	+	0.908097i	$0.637535\pi$
$480$	11.8746	−	13.1465i	0.541997	−	0.600055i
$481$	−0.668662	+	1.15816i	−0.0304884	+	0.0528074i
$482$	1.66015	−	2.87546i	0.0756177	−	0.130974i
$483$	−8.70932	−	26.9482i	−0.396288	−	1.22618i
$484$		0			0
$485$	−46.6138			−2.11662
$486$	2.02780	+	3.57669i	0.0919829	+	0.162242i
$487$	17.5661			0.795997			0.397998	−	0.917386i	$-0.369705\pi$
$487$	17.5661			0.795997			0.397998	+	0.917386i	$0.369705\pi$
$488$	−3.01079	−	5.21484i	−0.136292	−	0.236065i
$489$	1.62277	+	5.02114i	0.0733842	+	0.227064i
$490$	1.77742	−	3.07859i	0.0802958	−	0.139076i
$491$	−11.3476	+	19.6546i	−0.512110	+	0.887001i	0.487791	+	0.872960i	$0.337803\pi$
$491$	−11.3476	+	19.6546i	−0.512110	+	0.887001i	−0.999901	+	0.0140407i	$0.995531\pi$
$492$	−2.32339	+	2.57226i	−0.104746	+	0.115967i
$493$	−11.0642	−	19.1637i	−0.498306	−	0.863091i
$494$	2.10779			0.0948338
$495$		0			0
$496$	1.15504			0.0518628
$497$	19.3332	+	33.4860i	0.867212	+	1.50205i
$498$	−4.01525	−	0.860046i	−0.179928	−	0.0385396i
$499$	3.91325	−	6.77794i	0.175181	−	0.303422i	−0.765043	−	0.643979i	$-0.777282\pi$
$499$	3.91325	−	6.77794i	0.175181	−	0.303422i	0.940224	+	0.340557i	$0.110616\pi$
$500$	−4.81785	+	8.34476i	−0.215461	+	0.373189i
$501$	−31.5556	−	6.75906i	−1.40980	−	0.301972i
$502$	−2.17661	−	3.77000i	−0.0971468	−	0.168263i
$503$	−35.5630			−1.58568			−0.792838	−	0.609432i	$-0.791398\pi$
$503$	−35.5630			−1.58568			−0.792838	+	0.609432i	$0.791398\pi$
$504$	9.40079	+	4.22085i	0.418744	+	0.188012i
$505$	−3.51148			−0.156259
$506$		0			0
$507$	13.9565	−	15.4515i	0.619832	−	0.686227i
$508$	9.57193	−	16.5791i	0.424686	−	0.735578i
$509$	3.62565	−	6.27982i	0.160704	−	0.278348i	−0.774417	−	0.632675i	$-0.781957\pi$
$509$	3.62565	−	6.27982i	0.160704	−	0.278348i	0.935121	+	0.354327i	$0.115290\pi$
$510$	1.05219	+	3.25565i	0.0465916	+	0.144162i
$511$	18.4070	+	31.8818i	0.814277	+	1.41037i
$512$	18.2704			0.807446
$513$	−33.8417	−	24.8313i	−1.49415	−	1.09633i
$514$	−5.01351			−0.221136
$515$	11.1851	+	19.3732i	0.492875	+	0.853684i
$516$	7.09860	+	21.9643i	0.312499	+	0.966925i
$517$		0			0
$518$	−0.590695	+	1.02311i	−0.0259537	+	0.0449530i
$519$	14.4524	−	16.0005i	0.634391	−	0.702346i
$520$	1.73694	+	3.00846i	0.0761698	+	0.131930i
$521$	−28.9318			−1.26753			−0.633763	−	0.773528i	$-0.718490\pi$
$521$	−28.9318			−1.26753			−0.633763	+	0.773528i	$0.718490\pi$
$522$	−0.803075	−	7.87819i	−0.0351496	−	0.344819i
$523$	−5.47332			−0.239332			−0.119666	−	0.992814i	$-0.538182\pi$
$523$	−5.47332			−0.239332			−0.119666	+	0.992814i	$0.538182\pi$
$524$	−11.2849	−	19.5461i	−0.492985	−	0.853874i
$525$	−36.3284	−	7.78136i	−1.58550	−	0.339607i
$526$	0.823005	−	1.42549i	0.0358847	−	0.0621542i
$527$	−0.355944	+	0.616514i	−0.0155052	+	0.0268558i
$528$		0			0
$529$	−0.675622	−	1.17021i	−0.0293749	−	0.0508787i
$530$	−2.18734			−0.0950119
$531$	−1.12717	−	11.0576i	−0.0489152	−	0.479860i
$532$	−51.6700			−2.24018
$533$	−0.512784	−	0.888168i	−0.0222111	−	0.0384708i
$534$	−4.25396	+	4.70964i	−0.184087	+	0.203806i
$535$	−4.88076	+	8.45373i	−0.211014	+	0.365487i
$536$	3.04010	−	5.26561i	0.131312	−	0.227440i
$537$	0.178459	+	0.552183i	0.00770108	+	0.0238285i
$538$	1.85957	+	3.22087i	0.0801718	+	0.138862i
$539$		0			0
$540$	3.71040	−	33.7739i	0.159670	−	1.45340i
$541$	35.4595			1.52452			0.762261	−	0.647270i	$-0.224089\pi$
$541$	35.4595			1.52452			0.762261	+	0.647270i	$0.224089\pi$
$542$	−2.58997	−	4.48596i	−0.111249	−	0.192689i
$543$	4.74561	+	14.6837i	0.203653	+	0.630139i
$544$	−3.33819	+	5.78192i	−0.143124	+	0.247898i
$545$	18.6891	−	32.3704i	0.800552	−	1.38660i
$546$	−1.00376	+	1.11128i	−0.0429571	+	0.0475586i
$547$	5.76464	+	9.98465i	0.246478	+	0.426913i	0.962546	−	0.271118i	$-0.0873933\pi$
$547$	5.76464	+	9.98465i	0.246478	+	0.426913i	−0.716068	+	0.698031i	$0.754060\pi$
$548$	−9.84670			−0.420630
$549$	−15.8969	−	7.13755i	−0.678464	−	0.304623i
$550$		0			0
$551$	40.4224	+	70.0137i	1.72205	+	2.98268i
$552$	8.66405	+	1.85580i	0.368766	+	0.0789879i
$553$	3.57239	−	6.18755i	0.151913	−	0.263122i
$554$	−2.83605	+	4.91218i	−0.120492	+	0.208699i
$555$	7.75501	+	1.66108i	0.329182	+	0.0705091i
$556$	−7.41662	−	12.8460i	−0.314535	−	0.544790i
$557$	38.8123			1.64453			0.822265	−	0.569105i	$-0.192710\pi$
$557$	38.8123			1.64453			0.822265	+	0.569105i	$0.192710\pi$
$558$	−0.206575	+	0.149098i	−0.00874500	+	0.00631183i
$559$	−6.82966			−0.288864
$560$	−20.1319	−	34.8695i	−0.850729	−	1.47351i
$561$		0			0
$562$	−2.24265	+	3.88438i	−0.0946004	+	0.163853i
$563$	−5.01931	+	8.69370i	−0.211539	+	0.366396i	−0.952196	−	0.305487i	$-0.901181\pi$
$563$	−5.01931	+	8.69370i	−0.211539	+	0.366396i	0.740658	+	0.671883i	$0.234514\pi$
$564$	−7.39012	−	22.8663i	−0.311180	−	0.962845i
$565$	−17.0176	−	29.4753i	−0.715935	−	1.24004i
$566$	0.467681			0.0196581
$567$	29.2077	−	6.01719i	1.22661	−	0.252698i
$568$	−12.0974			−0.507597
$569$	−0.251245	−	0.435170i	−0.0105327	−	0.0182433i	0.860711	−	0.509094i	$-0.170019\pi$
$569$	−0.251245	−	0.435170i	−0.0105327	−	0.0182433i	−0.871244	+	0.490851i	$0.836686\pi$
$570$	−3.84411	−	11.8943i	−0.161012	−	0.498199i
$571$	6.97209	−	12.0760i	0.291773	−	0.505366i	−0.682456	−	0.730927i	$-0.739088\pi$
$571$	6.97209	−	12.0760i	0.291773	−	0.505366i	0.974229	+	0.225561i	$0.0724215\pi$
$572$		0			0
$573$	31.8472	−	35.2587i	1.33044	−	1.47295i
$574$	−0.452993	−	0.784607i	−0.0189076	−	0.0327489i
$575$	−31.9452			−1.33221
$576$	15.5160	−	11.1989i	0.646501	−	0.466622i
$577$	7.55169			0.314381			0.157191	−	0.987568i	$-0.449756\pi$
$577$	7.55169			0.314381			0.157191	+	0.987568i	$0.449756\pi$
$578$	1.59720	+	2.76643i	0.0664346	+	0.115068i
$579$	33.3114	+	7.13513i	1.38437	+	0.296526i
$580$	−32.7208	+	56.6742i	−1.35866	+	2.35327i
$581$	−14.8917	+	25.7931i	−0.617811	+	1.07008i
$582$	6.14730	+	1.31672i	0.254814	+	0.0545799i
$583$		0			0
$584$	−11.5179			−0.476613
$585$	9.17100	+	4.11768i	0.379174	+	0.170245i
$586$	−2.26035			−0.0933744
$587$	2.49119	+	4.31487i	0.102823	+	0.178094i	0.912846	−	0.408303i	$-0.133879\pi$
$587$	2.49119	+	4.31487i	0.102823	+	0.178094i	−0.810024	+	0.586397i	$0.800546\pi$
$588$	8.91769	−	9.87294i	0.367759	−	0.407153i
$589$	1.30042	−	2.25240i	0.0535831	−	0.0928086i
$590$	1.65503	−	2.86659i	0.0681364	−	0.118016i
$591$	−7.71732	−	23.8787i	−0.317448	−	0.982240i
$592$	2.42475	+	4.19979i	0.0996567	+	0.172610i
$593$	17.8923			0.734749			0.367374	−	0.930073i	$-0.380257\pi$
$593$	17.8923			0.734749			0.367374	+	0.930073i	$0.380257\pi$
$594$		0			0
$595$	24.8159			1.01735
$596$	6.49953	+	11.2575i	0.266231	+	0.461126i
$597$	3.29556	+	10.1971i	0.134878	+	0.417337i
$598$	−0.643805	+	1.11510i	−0.0263272	+	0.0456000i
$599$	−4.55904	+	7.89650i	−0.186278	+	0.322642i	−0.944006	−	0.329928i	$-0.892976\pi$
$599$	−4.55904	+	7.89650i	−0.186278	+	0.322642i	0.757729	+	0.652570i	$0.226309\pi$
$600$	7.79134	−	8.62594i	0.318080	−	0.352153i
$601$	−16.6269	−	28.7987i	−0.678226	−	1.17472i	−0.975515	−	0.219934i	$-0.929416\pi$
$601$	−16.6269	−	28.7987i	−0.678226	−	1.17472i	0.297289	−	0.954788i	$-0.403918\pi$
$602$	−6.03332			−0.245900
$603$	−1.78437	−	17.5047i	−0.0726650	−	0.712846i
$604$	20.4983			0.834066
$605$		0			0
$606$	0.463085	+	0.0991904i	0.0188115	+	0.00402933i
$607$	−23.8878	+	41.3749i	−0.969576	+	1.67935i	−0.272792	+	0.962073i	$0.587947\pi$
$607$	−23.8878	+	41.3749i	−0.969576	+	1.67935i	−0.696784	+	0.717281i	$0.745386\pi$
$608$	12.1959	−	21.1239i	0.494609	−	0.856688i
$609$	−56.1630	−	12.0298i	−2.27584	−	0.487474i
$610$	−2.59472	−	4.49418i	−0.105057	−	0.181964i
$611$	7.11013			0.287645
$612$	1.29856	+	12.7389i	0.0524910	+	0.514939i
$613$	7.96403			0.321664			0.160832	−	0.986982i	$-0.448582\pi$
$613$	7.96403			0.321664			0.160832	+	0.986982i	$0.448582\pi$
$614$	2.63033	+	4.55586i	0.106151	+	0.183859i
$615$	−4.07677	+	4.51347i	−0.164391	+	0.182001i
$616$		0			0
$617$	−21.3059	+	36.9029i	−0.857743	+	1.48565i	0.0163345	+	0.999867i	$0.494800\pi$
$617$	−21.3059	+	36.9029i	−0.857743	+	1.48565i	−0.874077	+	0.485787i	$0.838533\pi$
$618$	−0.927819	−	2.87083i	−0.0373223	−	0.115482i
$619$	−13.3424	−	23.1097i	−0.536275	−	0.928856i	−0.999100	−	0.0424064i	$-0.986498\pi$
$619$	−13.3424	−	23.1097i	−0.536275	−	0.928856i	0.462825	−	0.886450i	$-0.346836\pi$
$620$	2.10531			0.0845515
$621$	23.4734	−	10.3191i	0.941955	−	0.414090i
$622$	−2.27045			−0.0910367
$623$	23.0154	+	39.8638i	0.922091	+	1.59711i
$624$	1.89039	+	5.84920i	0.0756762	+	0.234155i
$625$	7.73026	−	13.3892i	0.309211	−	0.535568i
$626$	−0.436187	+	0.755498i	−0.0174335	+	0.0301958i
$627$		0			0
$628$	1.06884	+	1.85128i	0.0426512	+	0.0738740i
$629$	−2.98891			−0.119175
$630$	8.10165	+	3.63756i	0.322778	+	0.144924i
$631$	28.6714			1.14139			0.570696	−	0.821162i	$-0.306674\pi$
$631$	28.6714			1.14139			0.570696	+	0.821162i	$0.306674\pi$
$632$	1.11768	+	1.93588i	0.0444590	+	0.0770052i
$633$	31.7578	+	6.80236i	1.26226	+	0.270370i
$634$	−0.437911	+	0.758484i	−0.0173917	+	0.0301233i
$635$	16.7956	−	29.0908i	0.666512	−	1.15443i
$636$	−8.00462	−	1.71455i	−0.317404	−	0.0679863i
$637$	1.96818	+	3.40899i	0.0779822	+	0.135069i
$638$		0			0
$639$	−28.3868	+	20.4886i	−1.12297	+	0.810517i
$640$	26.1546			1.03385
$641$	−8.39510	−	14.5407i	−0.331587	−	0.574325i	0.651237	−	0.758875i	$-0.274251\pi$
$641$	−8.39510	−	14.5407i	−0.331587	−	0.574325i	−0.982823	+	0.184550i	$0.940917\pi$
$642$	0.882458	−	0.976986i	0.0348278	−	0.0385586i
$643$	−7.02384	+	12.1657i	−0.276993	+	0.479767i	−0.970636	−	0.240553i	$-0.922671\pi$
$643$	−7.02384	+	12.1657i	−0.276993	+	0.479767i	0.693643	+	0.720319i	$0.256005\pi$
$644$	15.7822	−	27.3355i	0.621904	−	1.07717i
$645$	12.4557	+	38.5401i	0.490442	+	1.51751i
$646$	2.35544	+	4.07975i	0.0926737	+	0.160515i
$647$	−26.8382			−1.05512			−0.527559	−	0.849519i	$-0.676893\pi$
$647$	−26.8382			−1.05512			−0.527559	+	0.849519i	$0.676893\pi$
$648$	−2.93870	+	8.85514i	−0.115443	+	0.347863i
$649$		0			0
$650$	0.844578	+	1.46285i	0.0331271	+	0.0573778i
$651$	0.568246	+	1.75825i	0.0222713	+	0.0689113i
$652$	−2.94062	+	5.09331i	−0.115164	+	0.199469i
$653$	−8.92728	+	15.4625i	−0.349352	+	0.605095i	−0.986134	−	0.165949i	$-0.946931\pi$
$653$	−8.92728	+	15.4625i	−0.349352	+	0.605095i	0.636783	+	0.771043i	$0.280265\pi$
$654$	−3.37905	+	3.74101i	−0.132131	+	0.146285i
$655$	−19.8013	−	34.2969i	−0.773701	−	1.34009i
$656$	−3.71899			−0.145202
$657$	−27.0269	+	19.5071i	−1.05442	+	0.761043i
$658$	6.28108			0.244862
$659$	−6.91632	−	11.9794i	−0.269422	−	0.466652i	0.699291	−	0.714837i	$-0.253499\pi$
$659$	−6.91632	−	11.9794i	−0.269422	−	0.466652i	−0.968713	+	0.248185i	$0.920166\pi$
$660$		0			0
$661$	4.54659	−	7.87493i	0.176842	−	0.306299i	−0.763955	−	0.645269i	$-0.776745\pi$
$661$	4.54659	−	7.87493i	0.176842	−	0.306299i	0.940797	+	0.338970i	$0.110079\pi$
$662$	2.15692	−	3.73589i	0.0838310	−	0.145200i
$663$	−3.70462	−	0.793511i	−0.143875	−	0.0308174i
$664$	−4.65911	−	8.06982i	−0.180809	−	0.313170i
$665$	−90.6637			−3.51579
$666$	−0.975788	−	0.438118i	−0.0378110	−	0.0169767i
$667$	−49.3867			−1.91226
$668$	−17.9838	−	31.1489i	−0.695815	−	1.20519i
$669$	17.8251	−	19.7345i	0.689159	−	0.762980i
$670$	2.61998	−	4.53793i	0.101219	−	0.175316i
$671$		0			0
$672$	5.32924	+	16.4896i	0.205580	+	0.636100i
$673$	−8.54813	−	14.8058i	−0.329506	−	0.570722i	0.652908	−	0.757437i	$-0.273549\pi$
$673$	−8.54813	−	14.8058i	−0.329506	−	0.570722i	−0.982414	+	0.186716i	$0.940216\pi$
$674$	3.05677			0.117743
$675$	3.67334	−	33.4366i	0.141387	−	1.28698i
$676$	23.2063			0.892551
$677$	−14.1120	−	24.4427i	−0.542367	−	0.939407i	−0.998768	−	0.0496329i	$-0.984195\pi$
$677$	−14.1120	−	24.4427i	−0.542367	−	0.939407i	0.456400	−	0.889775i	$-0.349138\pi$
$678$	1.41163	+	4.36783i	0.0542133	+	0.167745i
$679$	22.7990	−	39.4890i	0.874945	−	1.51545i
$680$	−3.88204	+	6.72389i	−0.148869	+	0.257849i
$681$	−21.1852	+	23.4546i	−0.811820	+	0.898781i
$682$		0			0
$683$	−6.54055			−0.250267			−0.125134	−	0.992140i	$-0.539936\pi$
$683$	−6.54055			−0.250267			−0.125134	+	0.992140i	$0.539936\pi$
$684$	−4.74421	−	46.5408i	−0.181399	−	1.77953i
$685$	−17.2777			−0.660147
$686$	−1.32010	−	2.28647i	−0.0504015	−	0.0872979i
$687$	−8.11471	−	1.73813i	−0.309596	−	0.0663138i
$688$	−12.3831	+	21.4482i	−0.472102	+	0.817704i
$689$	1.21104	−	2.09759i	0.0461371	−	0.0799118i
$690$	7.46673	+	1.59934i	0.284253	+	0.0608857i
$691$	1.33559	+	2.31330i	0.0508081	+	0.0880022i	0.890311	−	0.455353i	$-0.150487\pi$
$691$	1.33559	+	2.31330i	0.0508081	+	0.0880022i	−0.839503	+	0.543355i	$0.817154\pi$
$692$	24.0308			0.913516
$693$		0			0
$694$	−7.28403			−0.276498
$695$	−13.0137	−	22.5404i	−0.493638	−	0.855007i
$696$	12.0453	−	13.3355i	0.456575	−	0.505482i
$697$	1.14607	−	1.98505i	0.0434104	−	0.0751890i
$698$	−2.99555	+	5.18845i	−0.113383	+	0.196386i
$699$	10.3312	+	31.9665i	0.390762	+	1.20909i
$700$	−20.7039	−	35.8601i	−0.782533	−	1.35539i
$701$	−12.0216			−0.454048			−0.227024	−	0.973889i	$-0.572900\pi$
$701$	−12.0216			−0.454048			−0.227024	+	0.973889i	$0.572900\pi$
$702$	−1.09313	−	0.802086i	−0.0412576	−	0.0302728i
$703$	10.9198			0.411849
$704$		0			0
$705$	−12.9672	−	40.1228i	−0.488373	−	1.51111i
$706$	−3.35658	+	5.81376i	−0.126326	+	0.218804i
$707$	1.71748	−	2.97476i	0.0645924	−	0.111877i
$708$	8.30359	−	9.19306i	0.312068	−	0.345496i
$709$	16.5509	+	28.6670i	0.621583	+	1.07661i	0.989191	+	0.146633i	$0.0468435\pi$
$709$	16.5509	+	28.6670i	0.621583	+	1.07661i	−0.367608	+	0.929981i	$0.619823\pi$
$710$	−10.4256			−0.391267
$711$	5.90133	+	2.64964i	0.221317	+	0.0993691i
$712$	−14.4015			−0.539719
$713$	0.794407	+	1.37595i	0.0297508	+	0.0515298i
$714$	−3.27266	−	0.700987i	−0.122476	−	0.0262338i
$715$		0			0
$716$	−0.323386	+	0.560120i	−0.0120855	+	0.0209327i
$717$	15.4369	+	3.30650i	0.576501	+	0.123484i
$718$	0.322718	+	0.558964i	0.0120437	+	0.0208603i
$719$	−8.11421			−0.302609			−0.151305	−	0.988487i	$-0.548347\pi$
$719$	−8.11421			−0.302609			−0.151305	+	0.988487i	$0.548347\pi$
$720$	29.5596	−	21.3351i	1.10162	−	0.795112i
$721$	−21.8827			−0.814955
$722$	−6.09982	−	10.5652i	−0.227012	−	0.393196i
$723$	14.6151	−	16.1807i	0.543543	−	0.601767i
$724$	−8.59951	+	14.8948i	−0.319598	+	0.553560i
$725$	−32.3941	+	56.1082i	−1.20309	+	2.08381i
$726$		0			0
$727$	14.0124	+	24.2701i	0.519690	+	0.900129i	0.999738	+	0.0228868i	$0.00728572\pi$
$727$	14.0124	+	24.2701i	0.519690	+	0.900129i	−0.480049	+	0.877242i	$0.659381\pi$
$728$	−3.39817			−0.125945
$729$	8.10165	+	25.7558i	0.300061	+	0.953920i
$730$	−9.92617			−0.367384
$731$	−7.63212	−	13.2192i	−0.282284	−	0.488930i
$732$	−5.97266	−	18.4804i	−0.220756	−	0.683057i
$733$	−4.77918	+	8.27779i	−0.176523	+	0.305747i	−0.940687	−	0.339275i	$-0.889818\pi$
$733$	−4.77918	+	8.27779i	−0.176523	+	0.305747i	0.764164	+	0.645022i	$0.223152\pi$
$734$	−2.66465	+	4.61531i	−0.0983540	+	0.170354i
$735$	15.6476	−	17.3237i	0.577170	−	0.638995i
$736$	7.45027	+	12.9042i	0.274621	+	0.475657i
$737$		0			0
$738$	0.665128	−	0.480066i	0.0244837	−	0.0176715i
$739$	16.3343			0.600867			0.300434	−	0.953803i	$-0.402869\pi$
$739$	16.3343			0.600867			0.300434	+	0.953803i	$0.402869\pi$
$740$	4.41964	+	7.65505i	0.162469	+	0.281405i
$741$	13.5346	+	2.89905i	0.497207	+	0.106499i
$742$	1.06984	−	1.85301i	0.0392749	−	0.0680261i
$743$	−7.83257	+	13.5664i	−0.287349	+	0.497704i	−0.973176	−	0.230061i	$-0.926107\pi$
$743$	−7.83257	+	13.5664i	−0.287349	+	0.497704i	0.685827	+	0.727765i	$0.259441\pi$
$744$	−0.565292	−	0.121083i	−0.0207246	−	0.00443911i
$745$	11.4045	+	19.7532i	0.417829	+	0.723701i
$746$	0.304391			0.0111445
$747$	−24.6000	−	11.0451i	−0.900068	−	0.404121i
$748$		0			0
$749$	−4.77440	−	8.26950i	−0.174453	−	0.302161i
$750$	1.52846	−	1.69219i	0.0558116	−	0.0617900i
$751$	−19.4743	+	33.7304i	−0.710626	+	1.23084i	0.253996	+	0.967205i	$0.418255\pi$
$751$	−19.4743	+	33.7304i	−0.710626	+	1.23084i	−0.964622	+	0.263636i	$0.915078\pi$
$752$	12.8916	−	22.3290i	0.470110	−	0.814254i
$753$	−8.79130	−	27.2018i	−0.320373	−	0.991289i
$754$	1.30570	+	2.26154i	0.0475508	+	0.0823605i
$755$	35.9678			1.30900
$756$	26.7969	+	19.6622i	0.974594	+	0.715108i
$757$	−20.5459			−0.746754			−0.373377	−	0.927680i	$-0.621800\pi$
$757$	−20.5459			−0.746754			−0.373377	+	0.927680i	$0.621800\pi$
$758$	−0.724873	−	1.25552i	−0.0263286	−	0.0456024i
$759$		0			0
$760$	14.1828	−	24.5654i	0.514465	−	0.891080i
$761$	−12.9329	+	22.4005i	−0.468819	+	0.812018i	−0.999365	−	0.0356381i	$-0.988654\pi$
$761$	−12.9329	+	22.4005i	−0.468819	+	0.812018i	0.530546	+	0.847656i	$0.321987\pi$
$762$	−3.03669	+	3.36198i	−0.110008	+	0.121792i
$763$	18.2818	+	31.6650i	0.661846	+	1.14635i
$764$	52.9542			1.91582
$765$	2.27854	+	22.3525i	0.0823806	+	0.808156i
$766$	−1.32777			−0.0479741
$767$	1.83265	+	3.17424i	0.0661731	+	0.114615i
$768$	18.1564	+	3.88901i	0.655162	+	0.140332i
$769$	−16.7050	+	28.9339i	−0.602398	+	1.04338i	0.390059	+	0.920790i	$0.372455\pi$
$769$	−16.7050	+	28.9339i	−0.602398	+	1.04338i	−0.992457	+	0.122594i	$0.960879\pi$
$770$		0			0
$771$	−32.1930	−	6.89558i	−1.15940	−	0.248338i
$772$	18.9844	+	32.8820i	0.683265	+	1.18345i
$773$	−54.9006			−1.97464			−0.987318	−	0.158753i	$-0.949253\pi$
$773$	−54.9006			−1.97464			−0.987318	+	0.158753i	$0.949253\pi$
$774$	−0.553964	−	5.43440i	−0.0199118	−	0.195336i
$775$	2.08429			0.0748699
$776$	7.13305	+	12.3548i	0.256062	+	0.443512i
$777$	−5.20019	+	5.75723i	−0.186556	+	0.206540i
$778$	2.75358	−	4.76934i	0.0987206	−	0.170989i
$779$	−4.18710	+	7.25227i	−0.150018	+	0.259839i
$780$	3.44565	+	10.6614i	0.123374	+	0.381741i
$781$		0			0
$782$	−2.87780			−0.102910
$783$	5.67892	−	51.6924i	0.202948	−	1.84734i
$784$	14.2743			0.509798
$785$	1.87545	+	3.24838i	0.0669377	+	0.115940i
$786$	1.64254	+	5.08232i	0.0585876	+	0.181280i
$787$	−22.7205	+	39.3530i	−0.809897	+	1.40278i	0.103037	+	0.994678i	$0.467144\pi$
$787$	−22.7205	+	39.3530i	−0.809897	+	1.40278i	−0.912935	+	0.408106i	$0.866189\pi$
$788$	13.9846	−	24.2220i	0.498179	−	0.862872i
$789$	7.24534	−	8.02145i	0.257941	−	0.285571i
$790$	0.963224	+	1.66835i	0.0342700	+	0.0593573i
$791$	33.2935			1.18378
$792$		0			0
$793$	5.74638			0.204060
$794$	−0.337926	−	0.585305i	−0.0119926	−	0.0207717i
$795$	−14.0454	−	3.00846i	−0.498141	−	0.106699i
$796$	−5.97189	+	10.3436i	−0.211668	+	0.366620i
$797$	5.71295	−	9.89513i	0.202363	−	0.350503i	−0.746926	−	0.664907i	$-0.768471\pi$
$797$	5.71295	−	9.89513i	0.202363	−	0.350503i	0.949289	+	0.314404i	$0.101805\pi$
$798$	11.9565	+	2.56102i	0.423255	+	0.0906591i
$799$	7.94554	+	13.7621i	0.281093	+	0.486867i
$800$	19.5473			0.691102
$801$	−33.7934	+	24.3909i	−1.19403	+	0.861809i
$802$	4.36699			0.154204
$803$		0			0
$804$	13.1449	−	14.5530i	0.463586	−	0.513245i
$805$	27.6924	−	47.9647i	0.976030	−	1.69053i
$806$	0.0420055	−	0.0727557i	0.00147958	−	0.00256271i
$807$	7.51079	+	23.2397i	0.264392	+	0.818076i
$808$	0.537342	+	0.930704i	0.0189036	+	0.0327421i
$809$	44.3944			1.56083			0.780413	−	0.625265i	$-0.215009\pi$
$809$	44.3944			1.56083			0.780413	+	0.625265i	$0.215009\pi$
$810$	−2.53259	+	7.63141i	−0.0889861	+	0.268140i
$811$	−13.9125			−0.488534			−0.244267	−	0.969708i	$-0.578547\pi$
$811$	−13.9125			−0.488534			−0.244267	+	0.969708i	$0.578547\pi$
$812$	−32.0078	−	55.4391i	−1.12325	−	1.94553i
$813$	−10.4609	−	32.3677i	−0.366879	−	1.13519i
$814$		0			0
$815$	−5.15982	+	8.93706i	−0.180740	+	0.313052i
$816$	−9.20896	+	10.1954i	−0.322378	+	0.356911i
$817$	27.8835	+	48.2957i	0.975522	+	1.68965i
$818$	−1.76622			−0.0617544
$819$	−7.97388	+	5.75526i	−0.278630	+	0.201105i
$820$	−6.77868			−0.236722
$821$	−13.2716	−	22.9871i	−0.463183	−	0.802257i	0.535934	−	0.844260i	$-0.319959\pi$
$821$	−13.2716	−	22.9871i	−0.463183	−	0.802257i	−0.999117	+	0.0420031i	$0.986626\pi$
$822$	2.27854	+	0.488051i	0.0794730	+	0.0170227i
$823$	8.77551	−	15.1996i	0.305895	−	0.529826i	−0.671565	−	0.740946i	$-0.734378\pi$
$823$	8.77551	−	15.1996i	0.305895	−	0.529826i	0.977460	+	0.211120i	$0.0677110\pi$
$824$	3.42319	−	5.92914i	0.119252	−	0.206551i
$825$		0			0
$826$	1.61896	+	2.80412i	0.0563308	+	0.0975678i
$827$	−26.1786			−0.910318			−0.455159	−	0.890410i	$-0.650418\pi$
$827$	−26.1786			−0.910318			−0.455159	+	0.890410i	$0.650418\pi$
$828$	26.0710	+	11.7056i	0.906031	+	0.406798i
$829$	−5.92561			−0.205805			−0.102903	−	0.994691i	$-0.532813\pi$
$829$	−5.92561			−0.205805			−0.102903	+	0.994691i	$0.532813\pi$
$830$	−4.01525	−	6.95461i	−0.139371	−	0.241398i
$831$	−24.9672	+	27.6417i	−0.866103	+	0.958878i
$832$	−3.15508	+	5.46475i	−0.109383	+	0.189456i
$833$	−4.39887	+	7.61906i	−0.152412	+	0.263985i
$834$	1.07950	+	3.34017i	0.0373802	+	0.115661i
$835$	−31.5556	−	54.6560i	−1.09203	−	1.89145i
$836$		0			0
$837$	−1.53154	+	0.673275i	−0.0529377	+	0.0232718i
$838$	−6.09337			−0.210492
$839$	13.6219	+	23.5938i	0.470280	+	0.814549i	0.999422	−	0.0339843i	$-0.0108196\pi$
$839$	13.6219	+	23.5938i	0.470280	+	0.814549i	−0.529142	+	0.848533i	$0.677486\pi$
$840$	6.19746	+	19.1760i	0.213833	+	0.661636i
$841$	−35.5806	+	61.6274i	−1.22692	+	2.12508i
$842$	1.55077	−	2.68600i	0.0534429	−	0.0925658i
$843$	−19.7432	+	21.8580i	−0.679991	+	0.752831i
$844$	18.0990	+	31.3484i	0.622994	+	1.07906i
$845$	40.7194			1.40079
$846$	0.576713	+	5.65757i	0.0198278	+	0.194511i
$847$		0			0
$848$	−4.39158	−	7.60644i	−0.150807	−	0.261206i
$849$	3.00310	+	0.643249i	0.103066	+	0.0220762i
$850$	−1.88762	+	3.26946i	−0.0647450	+	0.112142i
$851$	−3.33536	+	5.77702i	−0.114335	+	0.198034i
$852$	−38.1529	−	8.17215i	−1.30710	−	0.279973i
$853$	21.0232	+	36.4132i	0.719820	+	1.24677i	0.961071	+	0.276303i	$0.0891092\pi$
$853$	21.0232	+	36.4132i	0.719820	+	1.24677i	−0.241250	+	0.970463i	$0.577557\pi$
$854$	5.07634			0.173709
$855$	−8.32451	−	81.6637i	−0.284692	−	2.79284i
$856$	2.98750			0.102111
$857$	3.83960	+	6.65038i	0.131158	+	0.227173i	0.924123	−	0.382094i	$-0.124797\pi$
$857$	3.83960	+	6.65038i	0.131158	+	0.227173i	−0.792965	+	0.609267i	$0.791464\pi$
$858$		0			0
$859$	−22.3735	+	38.7520i	−0.763374	+	1.32220i	0.177728	+	0.984080i	$0.443125\pi$
$859$	−22.3735	+	38.7520i	−0.763374	+	1.32220i	−0.941102	+	0.338123i	$0.890208\pi$
$860$	−22.5710	+	39.0940i	−0.769663	+	1.33310i
$861$	−1.82963	−	5.66120i	−0.0623538	−	0.192933i
$862$	3.98170	+	6.89651i	0.135617	+	0.234896i
$863$	−45.9577			−1.56442			−0.782208	−	0.623017i	$-0.785907\pi$
$863$	−45.9577			−1.56442			−0.782208	+	0.623017i	$0.785907\pi$
$864$	−14.3634	+	6.31425i	−0.488652	+	0.214815i
$865$	42.1662			1.43369
$866$	0.567720	+	0.983320i	0.0192919	+	0.0334146i
$867$	6.45106	+	19.9607i	0.219089	+	0.677901i
$868$	−1.02972	+	1.78352i	−0.0349509	+	0.0605367i
$869$		0			0
$870$	10.3807	−	11.4926i	0.351938	−	0.389637i
$871$	2.90116	+	5.02496i	0.0983021	+	0.170264i
$872$	−11.4395			−0.387392
$873$	37.6624	+	16.9100i	1.27468	+	0.572317i
$874$	10.5139			0.355638
$875$	−8.26950	−	14.3232i	−0.279560	−	0.484213i
$876$	−36.3251	−	7.78065i	−1.22731	−	0.262884i
$877$	13.1948	−	22.8540i	0.445555	−	0.771724i	−0.552535	−	0.833489i	$-0.686340\pi$
$877$	13.1948	−	22.8540i	0.445555	−	0.771724i	0.998091	+	0.0617650i	$0.0196729\pi$
$878$	3.86047	−	6.68653i	0.130284	−	0.225659i
$879$	−14.5143	−	3.10889i	−0.489556	−	0.104860i
$880$		0			0
$881$	−30.6027			−1.03103			−0.515515	−	0.856880i	$-0.672399\pi$
$881$	−30.6027			−1.03103			−0.515515	+	0.856880i	$0.672399\pi$
$882$	−2.55291	+	1.84260i	−0.0859610	+	0.0620436i
$883$	26.7450			0.900040			0.450020	−	0.893018i	$-0.351417\pi$
$883$	26.7450			0.900040			0.450020	+	0.893018i	$0.351417\pi$
$884$	−2.11129	−	3.65687i	−0.0710105	−	0.122994i
$885$	14.5701	−	16.1308i	0.489767	−	0.542230i
$886$	2.84569	−	4.92888i	0.0956029	−	0.165589i
$887$	3.13360	−	5.42755i	0.105216	−	0.182239i	−0.808610	−	0.588344i	$-0.799780\pi$
$887$	3.13360	−	5.42755i	0.105216	−	0.182239i	0.913826	+	0.406105i	$0.133113\pi$
$888$	−0.746441	−	2.30962i	−0.0250489	−	0.0775058i
$889$	16.4296	+	28.4568i	0.551030	+	0.954411i
$890$	−12.4113			−0.416027
$891$		0			0
$892$	29.6388			0.992381
$893$	−29.0286	−	50.2790i	−0.971406	−	1.68252i
$894$	−0.946019	−	2.92715i	−0.0316396	−	0.0978985i
$895$	−0.567434	+	0.982825i	−0.0189672	+	0.0328522i
$896$	−12.7923	+	22.1569i	−0.427361	+	0.740211i
$897$	−5.66775	+	6.27487i	−0.189241	+	0.209512i
$898$	4.91933	+	8.52052i	0.164160	+	0.284334i
$899$	3.22227			0.107469
$900$	30.3994	−	21.9412i	1.01331	−	0.731374i
$901$	5.41335			0.180345
$902$		0			0
$903$	−38.7415	−	8.29823i	−1.28923	−	0.276148i
$904$	−5.20821	+	9.02089i	−0.173223	+	0.300030i
$905$	−15.0893	+	26.1354i	−0.501585	+	0.868770i
$906$	−4.74333	−	1.01600i	−0.157587	−	0.0337543i
$907$	−13.7952	−	23.8940i	−0.458063	−	0.793389i	0.540795	−	0.841154i	$-0.318123\pi$
$907$	−13.7952	−	23.8940i	−0.458063	−	0.793389i	−0.998859	+	0.0477655i	$0.984790\pi$
$908$	−35.2259			−1.16901
$909$	2.83716	+	1.27385i	0.0941025	+	0.0422510i
$910$	−2.92856			−0.0970809
$911$	22.8190	+	39.5237i	0.756027	+	1.30948i	0.944862	+	0.327469i	$0.106196\pi$
$911$	22.8190	+	39.5237i	0.756027	+	1.30948i	−0.188835	+	0.982009i	$0.560471\pi$
$912$	33.6445	−	37.2484i	1.11408	−	1.23342i
$913$		0			0
$914$	−0.0989272	+	0.171347i	−0.00327222	+	0.00566765i
$915$	−10.4800	−	32.4270i	−0.346459	−	1.07201i
$916$	−4.62464	−	8.01012i	−0.152803	−	0.264662i
$917$	38.7396			1.27929
$918$	0.330914	−	3.01215i	0.0109218	−	0.0994158i
$919$	−7.54464			−0.248875			−0.124437	−	0.992227i	$-0.539713\pi$
$919$	−7.54464			−0.248875			−0.124437	+	0.992227i	$0.539713\pi$
$920$	8.66405	+	15.0066i	0.285645	+	0.494752i
$921$	10.6239	+	32.8721i	0.350068	+	1.08317i
$922$	−3.09259	+	5.35653i	−0.101849	+	0.176408i
$923$	5.77227	−	9.99786i	0.189996	−	0.329084i
$924$		0			0
$925$	4.37550	+	7.57860i	0.143866	+	0.249183i
$926$	1.97457			0.0648884
$927$	−2.00922	−	19.7105i	−0.0659913	−	0.647377i
$928$	30.2198			0.992012
$929$	26.1518	+	45.2962i	0.858012	+	1.48612i	0.873823	+	0.486245i	$0.161634\pi$
$929$	26.1518	+	45.2962i	0.858012	+	1.48612i	−0.0158109	+	0.999875i	$0.505033\pi$
$930$	−0.487172	−	0.104350i	−0.0159750	−	0.00342176i
$931$	16.0710	−	27.8359i	0.526707	−	0.912283i
$932$	−18.7212	+	32.4260i	−0.613232	+	1.06215i
$933$	−14.5791	−	3.12278i	−0.477299	−	0.102235i
$934$	−3.61258	−	6.25717i	−0.118207	−	0.204741i
$935$		0			0
$936$	−0.312012	−	3.06084i	−0.0101984	−	0.100047i
$937$	−15.4393			−0.504380			−0.252190	−	0.967678i	$-0.581151\pi$
$937$	−15.4393			−0.504380			−0.252190	+	0.967678i	$0.581151\pi$
$938$	2.56288	+	4.43904i	0.0836811	+	0.144940i
$939$	−3.83998	+	4.25131i	−0.125313	+	0.138736i
$940$	23.4979	−	40.6995i	0.766416	−	1.32747i
$941$	23.0768	−	39.9701i	0.752281	−	1.30299i	−0.194433	−	0.980916i	$-0.562287\pi$
$941$	23.0768	−	39.9701i	0.752281	−	1.30299i	0.946715	−	0.322074i	$-0.104380\pi$
$942$	−0.155571	−	0.481364i	−0.00506878	−	0.0156837i
$943$	−2.55783	−	4.43029i	−0.0832943	−	0.144270i
$944$	13.2914			0.432597
$945$	47.0197	+	34.5007i	1.52955	+	1.12231i
$946$		0			0
$947$	−14.3556	−	24.8647i	−0.466495	−	0.807993i	0.532772	−	0.846259i	$-0.321150\pi$
$947$	−14.3556	−	24.8647i	−0.466495	−	0.807993i	−0.999268	+	0.0382651i	$0.987817\pi$
$948$	2.21720	+	6.86040i	0.0720113	+	0.222816i
$949$	5.49574	−	9.51889i	0.178399	−	0.308996i
$950$	6.89634	−	11.9448i	0.223747	−	0.387541i
$951$	−3.85516	+	4.26812i	−0.125012	+	0.138403i
$952$	−3.79744	−	6.57736i	−0.123076	−	0.213174i
$953$	−13.2847			−0.430333			−0.215167	−	0.976577i	$-0.569029\pi$
$953$	−13.2847			−0.430333			−0.215167	+	0.976577i	$0.569029\pi$
$954$	1.76729	+	0.793496i	0.0572183	+	0.0256904i
$955$	92.9170			3.00673
$956$	8.79761	+	15.2379i	0.284535	+	0.492829i
$957$		0			0
$958$	3.33108	−	5.76960i	0.107622	−	0.186407i
$959$	8.45059	−	14.6368i	0.272884	−	0.472648i
$960$	36.5920	+	7.83781i	1.18100	+	0.252964i
$961$	15.4482	+	26.7570i	0.498328	+	0.863129i
$962$	0.352725			0.0113723
$963$	7.01023	−	5.05974i	0.225902	−	0.163048i
$964$	24.3014			0.782696
$965$	33.3114	+	57.6970i	1.07233	+	1.85733i
$966$	−5.00689	+	5.54322i	−0.161094	+	0.178350i
$967$	5.70513	−	9.88158i	0.183465	−	0.317770i	−0.759593	−	0.650398i	$-0.774602\pi$
$967$	5.70513	−	9.88158i	0.183465	−	0.317770i	0.943058	+	0.332628i	$0.107935\pi$
$968$		0			0
$969$	9.51361	+	29.4368i	0.305621	+	0.945645i
$970$	6.14730	+	10.6474i	0.197378	+	0.341869i
$971$	38.3441			1.23052			0.615260	−	0.788324i	$-0.289051\pi$
$971$	38.3441			1.23052			0.615260	+	0.788324i	$0.289051\pi$
$972$	−15.2500	+	25.9422i	−0.489143	+	0.832095i
$973$	25.4602			0.816217
$974$	−2.31657	−	4.01242i	−0.0742278	−	0.128566i
$975$	3.41124	+	10.5550i	0.109247	+	0.338030i
$976$	10.4190	−	18.0462i	0.333503	−	0.577644i
$977$	3.27487	−	5.67224i	0.104772	−	0.181471i	−0.808873	−	0.587984i	$-0.799922\pi$
$977$	3.27487	−	5.67224i	0.104772	−	0.181471i	0.913645	+	0.406513i	$0.133255\pi$
$978$	0.932912	−	1.03284i	0.0298312	−	0.0330267i
$979$		0			0
$980$	26.0181			0.831118
$981$	−26.8431	+	19.3744i	−0.857034	+	0.618577i
$982$	5.98597			0.191020
$983$	−9.01162	−	15.6086i	−0.287426	−	0.497836i	0.685769	−	0.727820i	$-0.259466\pi$
$983$	−9.01162	−	15.6086i	−0.287426	−	0.497836i	−0.973195	+	0.229983i	$0.926133\pi$
$984$	1.82012	+	0.389861i	0.0580234	+	0.0124283i
$985$	24.5382	−	42.5015i	0.781854	−	1.35421i
$986$	−2.91823	+	5.05452i	−0.0929354	+	0.160969i
$987$	40.3324	+	8.63900i	1.28380	+	0.274983i
$988$	7.71350	+	13.3602i	0.245399	+	0.425044i
$989$	−34.0671			−1.08327
$990$		0			0
$991$	52.5579			1.66956			0.834778	−	0.550586i	$-0.185596\pi$
$991$	52.5579			1.66956			0.834778	+	0.550586i	$0.185596\pi$
$992$	−0.486098	−	0.841946i	−0.0154336	−	0.0267318i
$993$	18.9885	−	21.0225i	0.602581	−	0.667128i
$994$	5.09921	−	8.83210i	0.161737	−	0.280137i
$995$	−10.4787	+	18.1496i	−0.332197	+	0.575382i
$996$	−9.24252	−	28.5980i	−0.292860	−	0.906161i
$997$	−9.29780	−	16.1043i	−0.294464	−	0.510027i	0.680396	−	0.732845i	$-0.261808\pi$
$997$	−9.29780	−	16.1043i	−0.294464	−	0.510027i	−0.974860	+	0.222818i	$0.928475\pi$
$998$	−2.06427			−0.0653434
$999$	−5.66319	−	4.15537i	−0.179175	−	0.131470i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1089.2.e.k.364.4	✓	16
9.4	even	3		9801.2.a.bz.1.5		8
9.5	odd	6		9801.2.a.ca.1.4		8
9.7	even	3	inner	1089.2.e.k.727.4	yes	16
11.10	odd	2	inner	1089.2.e.k.364.5	yes	16
99.32	even	6		9801.2.a.ca.1.5		8
99.43	odd	6	inner	1089.2.e.k.727.5	yes	16
99.76	odd	6		9801.2.a.bz.1.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1089.2.e.k.364.4	✓	16	1.1	even	1	trivial
1089.2.e.k.364.5	yes	16	11.10	odd	2	inner
1089.2.e.k.727.4	yes	16	9.7	even	3	inner
1089.2.e.k.727.5	yes	16	99.43	odd	6	inner
9801.2.a.bz.1.4		8	99.76	odd	6
9801.2.a.bz.1.5		8	9.4	even	3
9801.2.a.ca.1.4		8	9.5	odd	6
9801.2.a.ca.1.5		8	99.32	even	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:	\( N \)	\(=\)	\( 1089 = 3^{2} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1089.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.131877 - 0.228418i) q^{2} +(-0.532651 - 1.64811i) q^{3} +(0.965217 - 1.67180i) q^{4} +(1.69363 - 2.93346i) q^{5} +(-0.306215 + 0.339016i) q^{6} +(1.65673 + 2.86954i) q^{7} -1.03667 q^{8} +(-2.43257 + 1.75574i) q^{9} +O(q^{10})\)	\(q+(-0.131877 - 0.228418i) q^{2} +(-0.532651 - 1.64811i) q^{3} +(0.965217 - 1.67180i) q^{4} +(1.69363 - 2.93346i) q^{5} +(-0.306215 + 0.339016i) q^{6} +(1.65673 + 2.86954i) q^{7} -1.03667 q^{8} +(-2.43257 + 1.75574i) q^{9} -0.893408 q^{10} +(-3.26945 - 0.700300i) q^{12} +(0.494645 - 0.856751i) q^{13} +(0.436969 - 0.756853i) q^{14} +(-5.73680 - 1.22879i) q^{15} +(-1.79372 - 3.10681i) q^{16} +2.21106 q^{17} +(0.721843 + 0.324100i) q^{18} -8.07798 q^{19} +(-3.26945 - 5.66285i) q^{20} +(3.84687 - 4.25894i) q^{21} +(2.46735 - 4.27357i) q^{23} +(0.552183 + 1.70855i) q^{24} +(-3.23680 - 5.60630i) q^{25} -0.260930 q^{26} +(4.18937 + 3.07395i) q^{27} +6.39640 q^{28} +(-5.00403 - 8.66723i) q^{29} +(0.475875 + 1.47244i) q^{30} +(-0.160984 + 0.278832i) q^{31} +(-1.50977 + 2.61500i) q^{32} +(-0.291588 - 0.505045i) q^{34} +11.2236 q^{35} +(0.587301 + 5.76144i) q^{36} -1.35180 q^{37} +(1.06530 + 1.84516i) q^{38} +(-1.67550 - 0.358883i) q^{39} +(-1.75574 + 3.04103i) q^{40} +(0.518335 - 0.897782i) q^{41} +(-1.48013 - 0.317037i) q^{42} +(-3.45180 - 5.97869i) q^{43} +(1.03052 + 10.1094i) q^{45} -1.30155 q^{46} +(3.59355 + 6.22421i) q^{47} +(-4.16496 + 4.61111i) q^{48} +(-1.98949 + 3.44589i) q^{49} +(-0.853720 + 1.47869i) q^{50} +(-1.17772 - 3.64407i) q^{51} +(-0.954880 - 1.65390i) q^{52} +2.44831 q^{53} +(0.149663 - 1.36231i) q^{54} +(-1.71748 - 2.97476i) q^{56} +(4.30274 + 13.3134i) q^{57} +(-1.31984 + 2.28602i) q^{58} +(-1.85249 + 3.20860i) q^{59} +(-7.59156 + 8.40475i) q^{60} +(2.90429 + 5.03038i) q^{61} +0.0849205 q^{62} +(-9.06826 - 4.07155i) q^{63} -6.37846 q^{64} +(-1.67550 - 2.90205i) q^{65} +(-2.93257 + 5.07935i) q^{67} +(2.13415 - 3.69645i) q^{68} +(-8.35758 - 1.79015i) q^{69} +(-1.48013 - 2.56367i) q^{70} +11.6695 q^{71} +(2.52177 - 1.82012i) q^{72} +11.1105 q^{73} +(0.178272 + 0.308776i) q^{74} +(-7.51574 + 8.32082i) q^{75} +(-7.79700 + 13.5048i) q^{76} +(0.138985 + 0.430043i) q^{78} +(-1.07815 - 1.86740i) q^{79} -12.1516 q^{80} +(2.83475 - 8.54191i) q^{81} -0.273426 q^{82} +(4.49431 + 7.78437i) q^{83} +(-3.40705 - 10.5420i) q^{84} +(3.74472 - 6.48605i) q^{85} +(-0.910427 + 1.57691i) q^{86} +(-11.6192 + 12.8638i) q^{87} +13.8921 q^{89} +(2.17327 - 1.56859i) q^{90} +3.27797 q^{91} +(-4.76305 - 8.24985i) q^{92} +(0.545296 + 0.116800i) q^{93} +(0.947815 - 1.64166i) q^{94} +(-13.6811 + 23.6964i) q^{95} +(5.11400 + 1.09539i) q^{96} +(-6.88073 - 11.9178i) q^{97} +1.04947 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{3} - 16 q^{4} + 4 q^{5} - 14 q^{9}+O(q^{10}) \) 16 * q - 2 * q^3 - 16 * q^4 + 4 * q^5 - 14 * q^9	\( 16 q - 2 q^{3} - 16 q^{4} + 4 q^{5} - 14 q^{9} - 6 q^{12} + 4 q^{14} - 52 q^{15} - 24 q^{16} - 6 q^{20} + 46 q^{23} - 12 q^{25} - 60 q^{26} - 32 q^{27} + 14 q^{31} + 38 q^{34} + 54 q^{36} - 12 q^{37} + 4 q^{38} - 4 q^{42} - 28 q^{45} + 16 q^{47} + 20 q^{48} - 42 q^{49} - 96 q^{53} + 46 q^{56} + 50 q^{58} + 48 q^{59} + 12 q^{60} - 12 q^{64} - 22 q^{67} - 10 q^{69} - 4 q^{70} + 68 q^{71} - 10 q^{75} - 72 q^{78} - 148 q^{80} - 14 q^{81} + 112 q^{82} + 14 q^{86} - 16 q^{89} - 96 q^{91} + 84 q^{92} + 30 q^{93} - 4 q^{97}+O(q^{100}) \) 16 * q - 2 * q^3 - 16 * q^4 + 4 * q^5 - 14 * q^9 - 6 * q^12 + 4 * q^14 - 52 * q^15 - 24 * q^16 - 6 * q^20 + 46 * q^23 - 12 * q^25 - 60 * q^26 - 32 * q^27 + 14 * q^31 + 38 * q^34 + 54 * q^36 - 12 * q^37 + 4 * q^38 - 4 * q^42 - 28 * q^45 + 16 * q^47 + 20 * q^48 - 42 * q^49 - 96 * q^53 + 46 * q^56 + 50 * q^58 + 48 * q^59 + 12 * q^60 - 12 * q^64 - 22 * q^67 - 10 * q^69 - 4 * q^70 + 68 * q^71 - 10 * q^75 - 72 * q^78 - 148 * q^80 - 14 * q^81 + 112 * q^82 + 14 * q^86 - 16 * q^89 - 96 * q^91 + 84 * q^92 + 30 * q^93 - 4 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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